LMFDB - Embedded newform 92.3.f.a.5.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [92,3,Mod(5,92)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("92.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(92, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	92.f (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.50681843211$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	92.5
Dual form			92.3.f.a.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.05837 + 2.37548i) q^{3} +(5.87759 + 0.845069i) q^{5} +(-11.1861 + 5.10852i) q^{7} +(-0.125205 - 0.870819i) q^{9} +(3.20967 + 10.9311i) q^{11} +(-3.12123 + 6.83453i) q^{13} +(-14.1057 + 12.2226i) q^{15} +(4.18019 + 6.50451i) q^{17} +(16.9234 - 26.3334i) q^{19} +(10.8899 - 37.0876i) q^{21} +(11.2408 - 20.0660i) q^{23} +(9.84455 + 2.89062i) q^{25} +(-21.4718 - 13.7991i) q^{27} +(5.54128 - 3.56117i) q^{29} +(32.9159 + 37.9870i) q^{31} +(-32.5733 - 14.8757i) q^{33} +(-70.0644 + 20.5728i) q^{35} +(26.3757 - 3.79226i) q^{37} +(-9.81067 - 21.4824i) q^{39} +(5.64863 - 39.2871i) q^{41} +(37.0006 + 32.0612i) q^{43} -5.22412i q^{45} +7.37372 q^{47} +(66.9438 - 77.2573i) q^{49} +(-24.0557 - 3.45869i) q^{51} +(-70.7218 + 32.2976i) q^{53} +(9.62754 + 66.9610i) q^{55} +(27.7198 + 94.4050i) q^{57} +(-1.87466 + 4.10493i) q^{59} +(-29.6733 + 25.7121i) q^{61} +(5.84915 + 9.10146i) q^{63} +(-24.1209 + 37.5329i) q^{65} +(10.8850 - 37.0708i) q^{67} +(24.5286 + 68.0055i) q^{69} +(34.6570 + 10.1762i) q^{71} +(-10.2280 - 6.57315i) q^{73} +(-27.1303 + 17.4356i) q^{75} +(-91.7456 - 105.880i) q^{77} +(-10.5682 - 4.82632i) q^{79} +(84.5735 - 24.8330i) q^{81} +(-146.472 + 21.0595i) q^{83} +(19.0727 + 41.7634i) q^{85} +(-2.94650 + 20.4934i) q^{87} +(88.3431 + 76.5498i) q^{89} -92.3967i q^{91} -157.990 q^{93} +(121.723 - 140.475i) q^{95} +(95.6287 + 13.7493i) q^{97} +(9.11717 - 4.16367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{3} - 6 q^{9} - 2 q^{13} + 77 q^{15} + 55 q^{17} + 33 q^{19} + 33 q^{21} - 50 q^{23} - 54 q^{25} - 191 q^{27} + q^{29} - 53 q^{31} - 121 q^{33} - 156 q^{35} - 352 q^{37} - 306 q^{39} + 6 q^{41}+ \cdots + 1353 q^{99}+O(q^{100}) $ 40 * q - 2 * q^3 - 6 * q^9 - 2 * q^13 + 77 * q^15 + 55 * q^17 + 33 * q^19 + 33 * q^21 - 50 * q^23 - 54 * q^25 - 191 * q^27 + q^29 - 53 * q^31 - 121 * q^33 - 156 * q^35 - 352 * q^37 - 306 * q^39 + 6 * q^41 - 88 * q^43 - 58 * q^47 + 292 * q^49 + 264 * q^51 + 176 * q^53 + 518 * q^55 + 891 * q^57 + 696 * q^59 + 308 * q^61 + 275 * q^63 + 231 * q^65 + 22 * q^67 - 233 * q^69 - 215 * q^71 - 400 * q^73 - 557 * q^75 - 239 * q^77 - 748 * q^79 - 684 * q^81 - 671 * q^83 - 794 * q^85 + 62 * q^87 - 44 * q^89 - 346 * q^93 + 561 * q^95 + 693 * q^97 + 1353 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.05837	+	2.37548i	−0.686122	+	0.791827i	−0.986808	−	0.161896i	$-0.948239\pi$
$3$	−2.05837	+	2.37548i	−0.686122	+	0.791827i	0.300686	+	0.953723i	$0.402784\pi$
$4$		0			0
$5$	5.87759	+	0.845069i	1.17552	+	0.169014i	0.702267	−	0.711914i	$-0.252171\pi$
$5$	5.87759	+	0.845069i	1.17552	+	0.169014i	0.473251	+	0.880928i	$0.343081\pi$
$6$		0			0
$7$	−11.1861	+	5.10852i	−1.59802	+	0.729789i	−0.997556	−	0.0698665i	$-0.977743\pi$
$7$	−11.1861	+	5.10852i	−1.59802	+	0.729789i	−0.600459	+	0.799656i	$0.705015\pi$
$8$		0			0
$9$	−0.125205	−	0.870819i	−0.0139117	−	0.0967577i
$10$		0			0
$11$	3.20967	+	10.9311i	0.291788	+	0.993739i	0.966715	+	0.255854i	$0.0823568\pi$
$11$	3.20967	+	10.9311i	0.291788	+	0.993739i	−0.674927	+	0.737884i	$0.735825\pi$
$12$		0			0
$13$	−3.12123	+	6.83453i	−0.240094	+	0.525733i	−0.990869	−	0.134825i	$-0.956953\pi$
$13$	−3.12123	+	6.83453i	−0.240094	+	0.525733i	0.750775	+	0.660558i	$0.229680\pi$
$14$		0			0
$15$	−14.1057	+	12.2226i	−0.940378	+	0.814842i
$16$		0			0
$17$	4.18019	+	6.50451i	0.245894	+	0.382618i	0.942159	−	0.335166i	$-0.108793\pi$
$17$	4.18019	+	6.50451i	0.245894	+	0.382618i	−0.696265	+	0.717785i	$0.745156\pi$
$18$		0			0
$19$	16.9234	−	26.3334i	0.890708	−	1.38597i	−0.0315956	−	0.999501i	$-0.510059\pi$
$19$	16.9234	−	26.3334i	0.890708	−	1.38597i	0.922303	−	0.386467i	$-0.126305\pi$
$20$		0			0
$21$	10.8899	−	37.0876i	0.518567	−	1.76608i
$22$		0			0
$23$	11.2408	−	20.0660i	0.488732	−	0.872434i
$23$	11.2408	−	20.0660i	0.488732	−	0.872434i
$24$		0			0
$25$	9.84455	+	2.89062i	0.393782	+	0.115625i
$26$		0			0
$27$	−21.4718	−	13.7991i	−0.795252	−	0.511077i
$28$		0			0
$29$	5.54128	−	3.56117i	0.191079	−	0.122799i	−0.441604	−	0.897210i	$-0.645590\pi$
$29$	5.54128	−	3.56117i	0.191079	−	0.122799i	0.632682	+	0.774411i	$0.281954\pi$
$30$		0			0
$31$	32.9159	+	37.9870i	1.06180	+	1.22539i	0.973354	+	0.229306i	$0.0736455\pi$
$31$	32.9159	+	37.9870i	1.06180	+	1.22539i	0.0884488	+	0.996081i	$0.471809\pi$
$32$		0			0
$33$	−32.5733	−	14.8757i	−0.987071	−	0.450780i
$34$		0			0
$35$	−70.0644	+	20.5728i	−2.00184	+	0.587793i
$36$		0			0
$37$	26.3757	−	3.79226i	0.712857	−	0.102493i	0.223661	−	0.974667i	$-0.428199\pi$
$37$	26.3757	−	3.79226i	0.712857	−	0.102493i	0.489196	+	0.872174i	$0.337290\pi$
$38$		0			0
$39$	−9.81067	−	21.4824i	−0.251556	−	0.550830i
$40$		0			0
$41$	5.64863	−	39.2871i	0.137772	−	0.958222i	−0.797254	−	0.603643i	$-0.793715\pi$
$41$	5.64863	−	39.2871i	0.137772	−	0.958222i	0.935026	−	0.354579i	$-0.115376\pi$
$42$		0			0
$43$	37.0006	+	32.0612i	0.860480	+	0.745610i	0.968625	−	0.248525i	$-0.0799459\pi$
$43$	37.0006	+	32.0612i	0.860480	+	0.745610i	−0.108146	+	0.994135i	$0.534491\pi$
$44$		0			0
$45$		−	5.22412i		−	0.116092i
$46$		0			0
$47$	7.37372			0.156888			0.0784438	−	0.996919i	$-0.475005\pi$
$47$	7.37372			0.156888			0.0784438	+	0.996919i	$0.475005\pi$
$48$		0			0
$49$	66.9438	−	77.2573i	1.36620	−	1.57668i
$50$		0			0
$51$	−24.0557	−	3.45869i	−0.471680	−	0.0678174i
$52$		0			0
$53$	−70.7218	+	32.2976i	−1.33437	+	0.609388i	−0.949554	−	0.313604i	$-0.898464\pi$
$53$	−70.7218	+	32.2976i	−1.33437	+	0.609388i	−0.384819	+	0.922992i	$0.625736\pi$
$54$		0			0
$55$	9.62754	+	66.9610i	0.175046	+	1.21747i
$56$		0			0
$57$	27.7198	+	94.4050i	0.486313	+	1.65623i
$58$		0			0
$59$	−1.87466	+	4.10493i	−0.0317739	+	0.0695751i	−0.924854	−	0.380324i	$-0.875813\pi$
$59$	−1.87466	+	4.10493i	−0.0317739	+	0.0695751i	0.893080	+	0.449899i	$0.148540\pi$
$60$		0			0
$61$	−29.6733	+	25.7121i	−0.486447	+	0.421509i	−0.863244	−	0.504787i	$-0.831571\pi$
$61$	−29.6733	+	25.7121i	−0.486447	+	0.421509i	0.376797	+	0.926296i	$0.377026\pi$
$62$		0			0
$63$	5.84915	+	9.10146i	0.0928437	+	0.144468i
$64$		0			0
$65$	−24.1209	+	37.5329i	−0.371091	+	0.577429i
$66$		0			0
$67$	10.8850	−	37.0708i	0.162462	−	0.553295i	−0.837514	−	0.546415i	$-0.815992\pi$
$67$	10.8850	−	37.0708i	0.162462	−	0.553295i	0.999976	−	0.00687954i	$-0.00218984\pi$
$68$		0			0
$69$	24.5286	+	68.0055i	0.355487	+	0.985587i
$70$		0			0
$71$	34.6570	+	10.1762i	0.488126	+	0.143327i	0.516529	−	0.856270i	$-0.327224\pi$
$71$	34.6570	+	10.1762i	0.488126	+	0.143327i	−0.0284027	+	0.999597i	$0.509042\pi$
$72$		0			0
$73$	−10.2280	−	6.57315i	−0.140110	−	0.0900432i	0.468708	−	0.883353i	$-0.344720\pi$
$73$	−10.2280	−	6.57315i	−0.140110	−	0.0900432i	−0.608818	+	0.793310i	$0.708356\pi$
$74$		0			0
$75$	−27.1303	+	17.4356i	−0.361737	+	0.232474i
$76$		0			0
$77$	−91.7456	−	105.880i	−1.19150	−	1.37507i
$78$		0			0
$79$	−10.5682	−	4.82632i	−0.133774	−	0.0610926i	0.347403	−	0.937716i	$-0.387063\pi$
$79$	−10.5682	−	4.82632i	−0.133774	−	0.0610926i	−0.481177	+	0.876623i	$0.659791\pi$
$80$		0			0
$81$	84.5735	−	24.8330i	1.04412	−	0.306581i
$82$		0			0
$83$	−146.472	+	21.0595i	−1.76472	+	0.253728i	−0.946850	−	0.321676i	$-0.895754\pi$
$83$	−146.472	+	21.0595i	−1.76472	+	0.253728i	−0.817869	+	0.575404i	$0.804845\pi$
$84$		0			0
$85$	19.0727	+	41.7634i	0.224385	+	0.491334i
$86$		0			0
$87$	−2.94650	+	20.4934i	−0.0338679	+	0.235556i
$88$		0			0
$89$	88.3431	+	76.5498i	0.992620	+	0.860110i	0.990167	−	0.139887i	$-0.0446740\pi$
$89$	88.3431	+	76.5498i	0.992620	+	0.860110i	0.00245209	+	0.999997i	$0.499219\pi$
$90$		0			0
$91$		−	92.3967i		−	1.01535i
$92$		0			0
$93$	−157.990			−1.69882
$94$		0			0
$95$	121.723	−	140.475i	1.28129	−	1.47869i
$96$		0			0
$97$	95.6287	+	13.7493i	0.985863	+	0.141746i	0.616344	−	0.787477i	$-0.288613\pi$
$97$	95.6287	+	13.7493i	0.985863	+	0.141746i	0.369520	+	0.929223i	$0.379522\pi$
$98$		0			0
$99$	9.11717	−	4.16367i	0.0920926	−	0.0420573i
$100$		0			0
$101$	20.7542	+	144.349i	0.205487	+	1.42919i	0.787650	+	0.616122i	$0.211297\pi$
$101$	20.7542	+	144.349i	0.205487	+	1.42919i	−0.582163	+	0.813072i	$0.697794\pi$
$102$		0			0
$103$	2.52321	+	8.59327i	0.0244972	+	0.0834298i	0.970834	−	0.239751i	$-0.0770659\pi$
$103$	2.52321	+	8.59327i	0.0244972	+	0.0834298i	−0.946337	+	0.323181i	$0.895248\pi$
$104$		0			0
$105$	95.3479	−	208.783i	0.908075	−	1.98841i
$106$		0			0
$107$	141.230	−	122.376i	1.31991	−	1.14370i	0.340848	−	0.940118i	$-0.389286\pi$
$107$	141.230	−	122.376i	1.31991	−	1.14370i	0.979057	−	0.203586i	$-0.0652597\pi$
$108$		0			0
$109$	−111.156	−	172.961i	−1.01978	−	1.58680i	−0.789570	−	0.613660i	$-0.789696\pi$
$109$	−111.156	−	172.961i	−1.01978	−	1.58680i	−0.230206	−	0.973142i	$-0.573940\pi$
$110$		0			0
$111$	−45.2824	+	70.4608i	−0.407950	+	0.634782i
$112$		0			0
$113$	−16.6504	+	56.7061i	−0.147349	+	0.501824i	−0.999779	−	0.0210169i	$-0.993310\pi$
$113$	−16.6504	+	56.7061i	−0.147349	+	0.501824i	0.852430	+	0.522841i	$0.175128\pi$
$114$		0			0
$115$	83.0262	−	108.440i	0.721967	−	0.942958i
$116$		0			0
$117$	6.34243	+	1.86231i	0.0542088	+	0.0159171i
$118$		0			0
$119$	−79.9885	−	51.4055i	−0.672173	−	0.431979i
$120$		0			0
$121$	−7.39587	+	4.75304i	−0.0611229	+	0.0392813i
$122$		0			0
$123$	81.6988	+	94.2855i	0.664218	+	0.766548i
$124$		0			0
$125$	−79.6161	−	36.3594i	−0.636928	−	0.290875i
$126$		0			0
$127$	55.4306	−	16.2759i	0.436461	−	0.128157i	−0.0561180	−	0.998424i	$-0.517872\pi$
$127$	55.4306	−	16.2759i	0.436461	−	0.128157i	0.492579	+	0.870268i	$0.336054\pi$
$128$		0			0
$129$	−152.322	+	21.9005i	−1.18079	+	0.169772i
$130$		0			0
$131$	−16.9139	−	37.0362i	−0.129114	−	0.282719i	0.834024	−	0.551728i	$-0.186031\pi$
$131$	−16.9139	−	37.0362i	−0.129114	−	0.282719i	−0.963138	+	0.269009i	$0.913304\pi$
$132$		0			0
$133$	−54.7827	+	381.022i	−0.411900	+	2.86483i
$134$		0			0
$135$	−114.541	−	99.2505i	−0.848453	−	0.735189i
$136$		0			0
$137$		−	132.675i		−	0.968427i	−0.874950	−	0.484214i	$-0.839106\pi$
$137$		−	132.675i		−	0.968427i	0.874950	−	0.484214i	$-0.160894\pi$
$138$		0			0
$139$	133.153			0.957937			0.478969	−	0.877832i	$-0.341011\pi$
$139$	133.153			0.957937			0.478969	+	0.877832i	$0.341011\pi$
$140$		0			0
$141$	−15.1778	+	17.5161i	−0.107644	+	0.124228i
$142$		0			0
$143$	−84.7272	−	12.1819i	−0.592498	−	0.0851884i
$144$		0			0
$145$	35.5788	−	16.2483i	0.245371	−	0.112057i
$146$		0			0
$147$	45.7283	+	318.047i	0.311077	+	2.16359i
$148$		0			0
$149$	−47.1861	−	160.701i	−0.316685	−	1.07853i	−0.951954	−	0.306240i	$-0.900929\pi$
$149$	−47.1861	−	160.701i	−0.316685	−	1.07853i	0.635269	−	0.772291i	$-0.280889\pi$
$150$		0			0
$151$	2.78127	−	6.09014i	0.0184190	−	0.0403321i	−0.900199	−	0.435479i	$-0.856579\pi$
$151$	2.78127	−	6.09014i	0.0184190	−	0.0403321i	0.918618	+	0.395147i	$0.129306\pi$
$152$		0			0
$153$	5.14087	−	4.45459i	0.0336005	−	0.0291150i
$154$		0			0
$155$	161.364	+	251.088i	1.04106	+	1.61992i
$156$		0			0
$157$	−84.9397	+	132.169i	−0.541017	+	0.841840i	−0.998886	−	0.0471801i	$-0.984977\pi$
$157$	−84.9397	+	132.169i	−0.541017	+	0.841840i	0.457869	+	0.889020i	$0.348613\pi$
$158$		0			0
$159$	68.8491	−	234.478i	0.433013	−	1.47471i
$160$		0			0
$161$	−23.2337	+	281.884i	−0.144309	+	1.75083i
$162$		0			0
$163$	148.179	+	43.5093i	0.909074	+	0.266928i	0.702651	−	0.711535i	$-0.251999\pi$
$163$	148.179	+	43.5093i	0.909074	+	0.266928i	0.206423	+	0.978463i	$0.433818\pi$
$164$		0			0
$165$	−178.882	−	114.960i	−1.08413	−	0.696729i
$166$		0			0
$167$	−57.6530	+	37.0513i	−0.345227	+	0.221864i	−0.701751	−	0.712422i	$-0.747598\pi$
$167$	−57.6530	+	37.0513i	−0.345227	+	0.221864i	0.356524	+	0.934286i	$0.383962\pi$
$168$		0			0
$169$	73.7027	+	85.0574i	0.436111	+	0.503298i
$170$		0			0
$171$	−25.0505	−	11.4402i	−0.146494	−	0.0669017i
$172$		0			0
$173$	88.9709	−	26.1242i	0.514283	−	0.151007i	−0.0142854	−	0.999898i	$-0.504547\pi$
$173$	88.9709	−	26.1242i	0.514283	−	0.151007i	0.528568	+	0.848891i	$0.322729\pi$
$174$		0			0
$175$	−124.889	+	17.9563i	−0.713651	+	0.102608i
$176$		0			0
$177$	−5.89245	−	12.9027i	−0.0332907	−	0.0728964i
$178$		0			0
$179$	14.3907	−	100.089i	0.0803948	−	0.559158i	−0.909319	−	0.416099i	$-0.863397\pi$
$179$	14.3907	−	100.089i	0.0803948	−	0.559158i	0.989714	−	0.143059i	$-0.0456939\pi$
$180$		0			0
$181$	−32.3537	−	28.0347i	−0.178750	−	0.154888i	0.560890	−	0.827890i	$-0.310459\pi$
$181$	−32.3537	−	28.0347i	−0.178750	−	0.154888i	−0.739640	+	0.673002i	$0.765004\pi$
$182$		0			0
$183$		−	123.413i		−	0.674389i
$184$		0			0
$185$	158.230			0.855299
$186$		0			0
$187$	−57.6846	+	66.5716i	−0.308474	+	0.355998i
$188$		0			0
$189$	310.679	+	44.6689i	1.64380	+	0.236343i
$190$		0			0
$191$	−320.420	+	146.331i	−1.67759	+	0.766130i	−0.678076	+	0.734991i	$0.737186\pi$
$191$	−320.420	+	146.331i	−1.67759	+	0.766130i	−0.999515	+	0.0311389i	$0.990087\pi$
$192$		0			0
$193$	−13.1272	−	91.3019i	−0.0680168	−	0.473067i	−0.995153	−	0.0983418i	$-0.968646\pi$
$193$	−13.1272	−	91.3019i	−0.0680168	−	0.473067i	0.927136	−	0.374725i	$-0.122263\pi$
$194$		0			0
$195$	−39.5090	−	134.555i	−0.202610	−	0.690027i
$196$		0			0
$197$	−70.4645	+	154.296i	−0.357688	+	0.783227i	0.642173	+	0.766559i	$0.278033\pi$
$197$	−70.4645	+	154.296i	−0.357688	+	0.783227i	−0.999861	+	0.0166673i	$0.994694\pi$
$198$		0			0
$199$	−12.6596	+	10.9696i	−0.0636161	+	0.0551236i	−0.686089	−	0.727518i	$-0.740674\pi$
$199$	−12.6596	+	10.9696i	−0.0636161	+	0.0551236i	0.622472	+	0.782642i	$0.286128\pi$
$200$		0			0
$201$	65.6556	+	102.162i	0.326645	+	0.508270i
$202$		0			0
$203$	−43.7931	+	68.1433i	−0.215729	+	0.335681i
$204$		0			0
$205$	66.4007	−	226.140i	0.323906	−	1.10312i
$206$		0			0
$207$	−18.8812	−	7.27638i	−0.0912137	−	0.0351516i
$208$		0			0
$209$	342.172	+	100.471i	1.63719	+	0.480722i
$210$		0			0
$211$	−279.840	−	179.842i	−1.32626	−	0.852333i	−0.330450	−	0.943823i	$-0.607201\pi$
$211$	−279.840	−	179.842i	−1.32626	−	0.852333i	−0.995806	+	0.0914904i	$0.970837\pi$
$212$		0			0
$213$	−95.5100	+	61.3806i	−0.448404	+	0.288172i
$214$		0			0
$215$	190.380	+	219.711i	0.885490	+	1.02191i
$216$		0			0
$217$	−562.258	−	256.775i	−2.59105	−	1.18329i
$218$		0			0
$219$	36.6674	−	10.7665i	0.167431	−	0.0491622i
$220$		0			0
$221$	−57.5026	+	8.26763i	−0.260193	+	0.0374101i
$222$		0			0
$223$	124.690	+	273.034i	0.559150	+	1.22437i	0.952376	+	0.304926i	$0.0986318\pi$
$223$	124.690	+	273.034i	0.559150	+	1.22437i	−0.393226	+	0.919442i	$0.628641\pi$
$224$		0			0
$225$	1.28462	−	8.93474i	0.00570943	−	0.0397100i
$226$		0			0
$227$	−262.115	−	227.124i	−1.15469	−	1.00054i	−0.999921	−	0.0125936i	$-0.995991\pi$
$227$	−262.115	−	227.124i	−1.15469	−	1.00054i	−0.154769	−	0.987951i	$-0.549463\pi$
$228$		0			0
$229$		−	241.786i		−	1.05583i	−0.849296	−	0.527917i	$-0.822973\pi$
$229$		−	241.786i		−	1.05583i	0.849296	−	0.527917i	$-0.177027\pi$
$230$		0			0
$231$	440.362			1.90633
$232$		0			0
$233$	104.001	−	120.023i	0.446355	−	0.515121i	−0.487330	−	0.873218i	$-0.662029\pi$
$233$	104.001	−	120.023i	0.446355	−	0.515121i	0.933684	+	0.358097i	$0.116574\pi$
$234$		0			0
$235$	43.3397	+	6.23130i	0.184424	+	0.0265162i
$236$		0			0
$237$	33.2179	−	15.1701i	0.140160	−	0.0640090i
$238$		0			0
$239$	−61.9976	−	431.203i	−0.259404	−	1.80420i	−0.537091	−	0.843525i	$-0.680477\pi$
$239$	−61.9976	−	431.203i	−0.259404	−	1.80420i	0.277686	−	0.960672i	$-0.410432\pi$
$240$		0			0
$241$	−61.2600	−	208.632i	−0.254191	−	0.865694i	−0.983407	−	0.181411i	$-0.941933\pi$
$241$	−61.2600	−	208.632i	−0.254191	−	0.865694i	0.729217	−	0.684283i	$-0.239885\pi$
$242$		0			0
$243$	−19.6669	+	43.0645i	−0.0809338	+	0.177220i
$244$		0			0
$245$	458.756	−	397.514i	1.87247	−	1.62251i
$246$		0			0
$247$	127.155	+	197.856i	0.514796	+	0.801038i
$248$		0			0
$249$	251.466	−	391.289i	1.00990	−	1.57144i
$250$		0			0
$251$	32.6756	−	111.283i	0.130182	−	0.443358i	−0.868443	−	0.495789i	$-0.834879\pi$
$251$	32.6756	−	111.283i	0.130182	−	0.443358i	0.998625	+	0.0524310i	$0.0166970\pi$
$252$		0			0
$253$	255.423	+	58.4699i	1.00958	+	0.231106i
$254$		0			0
$255$	−138.467	−	40.6575i	−0.543006	−	0.159441i
$256$		0			0
$257$	367.866	+	236.413i	1.43138	+	0.919895i	0.999842	+	0.0178025i	$0.00566701\pi$
$257$	367.866	+	236.413i	1.43138	+	0.919895i	0.431543	+	0.902092i	$0.357969\pi$
$258$		0			0
$259$	−275.669	+	177.162i	−1.06436	+	0.684021i
$260$		0			0
$261$	−3.79493	−	4.37958i	−0.0145399	−	0.0167800i
$262$		0			0
$263$	−278.498	−	127.186i	−1.05893	−	0.483596i	−0.191672	−	0.981459i	$-0.561391\pi$
$263$	−278.498	−	127.186i	−1.05893	−	0.483596i	−0.867256	+	0.497863i	$0.834118\pi$
$264$		0			0
$265$	−442.967	+	130.067i	−1.67157	+	0.490818i
$266$		0			0
$267$	−363.685	+	52.2900i	−1.36212	+	0.195843i
$268$		0			0
$269$	28.9363	+	63.3616i	0.107570	+	0.235545i	0.955760	−	0.294146i	$-0.0950352\pi$
$269$	28.9363	+	63.3616i	0.107570	+	0.235545i	−0.848191	+	0.529691i	$0.822308\pi$
$270$		0			0
$271$	−49.4641	+	344.030i	−0.182524	+	1.26948i	0.668243	+	0.743943i	$0.267047\pi$
$271$	−49.4641	+	344.030i	−0.182524	+	1.26948i	−0.850768	+	0.525542i	$0.823863\pi$
$272$		0			0
$273$	219.486	+	190.186i	0.803980	+	0.696652i
$274$		0			0
$275$			116.890i			0.425054i
$276$		0			0
$277$	−200.629			−0.724292			−0.362146	−	0.932121i	$-0.617956\pi$
$277$	−200.629			−0.724292			−0.362146	+	0.932121i	$0.617956\pi$
$278$		0			0
$279$	28.9585	−	33.4199i	0.103794	−	0.119785i
$280$		0			0
$281$	−132.513	−	19.0525i	−0.471576	−	0.0678024i	−0.0975700	−	0.995229i	$-0.531107\pi$
$281$	−132.513	−	19.0525i	−0.471576	−	0.0678024i	−0.374006	+	0.927426i	$0.622016\pi$
$282$		0			0
$283$	270.374	−	123.475i	0.955384	−	0.436309i	0.124169	−	0.992261i	$-0.460373\pi$
$283$	270.374	−	123.475i	0.955384	−	0.436309i	0.831214	+	0.555952i	$0.187646\pi$
$284$		0			0
$285$	83.1468	+	578.299i	0.291743	+	2.02912i
$286$		0			0
$287$	137.513	+	468.326i	0.479139	+	1.63180i
$288$		0			0
$289$	95.2203	−	208.503i	0.329482	−	0.721465i
$290$		0			0
$291$	−229.500	+	198.863i	−0.788660	+	0.683378i
$292$		0			0
$293$	0.643565	+	1.00141i	0.00219647	+	0.00341777i	0.842350	−	0.538931i	$-0.181172\pi$
$293$	0.643565	+	1.00141i	0.00219647	+	0.00341777i	−0.840154	+	0.542349i	$0.817535\pi$
$294$		0			0
$295$	−14.4874	+	22.5429i	−0.0491099	+	0.0764165i
$296$		0			0
$297$	81.9222	−	279.002i	0.275832	−	0.939399i
$298$		0			0
$299$	102.056	+	139.456i	0.341326	+	0.466409i
$300$		0			0
$301$	−577.678	−	169.622i	−1.91920	−	0.563527i
$302$		0			0
$303$	−385.617	−	247.821i	−1.27266	−	0.817891i
$304$		0			0
$305$	−196.136	+	126.049i	−0.643068	+	0.413275i
$306$		0			0
$307$	50.5249	+	58.3088i	0.164576	+	0.189931i	0.832047	−	0.554705i	$-0.187169\pi$
$307$	50.5249	+	58.3088i	0.164576	+	0.189931i	−0.667471	+	0.744636i	$0.732623\pi$
$308$		0			0
$309$	−25.6068	−	11.6942i	−0.0828700	−	0.0378455i
$310$		0			0
$311$	254.557	−	74.7445i	0.818510	−	0.240336i	0.154436	−	0.988003i	$-0.450644\pi$
$311$	254.557	−	74.7445i	0.818510	−	0.240336i	0.664074	+	0.747667i	$0.268826\pi$
$312$		0			0
$313$	−23.4081	+	3.36558i	−0.0747863	+	0.0107526i	−0.179606	−	0.983739i	$-0.557482\pi$
$313$	−23.4081	+	3.36558i	−0.0747863	+	0.0107526i	0.104820	+	0.994491i	$0.466573\pi$
$314$		0			0
$315$	26.6875	+	58.4376i	0.0847224	+	0.185516i
$316$		0			0
$317$	47.9875	−	333.760i	0.151380	−	1.05287i	−0.762529	−	0.646953i	$-0.776043\pi$
$317$	47.9875	−	333.760i	0.151380	−	1.05287i	0.913910	−	0.405918i	$-0.133048\pi$
$318$		0			0
$319$	56.7132	+	49.1423i	0.177784	+	0.154051i
$320$		0			0
$321$			587.384i			1.82986i
$322$		0			0
$323$	242.029			0.749316
$324$		0			0
$325$	−50.4831	+	58.2606i	−0.155333	+	0.179263i
$326$		0			0
$327$	639.665	+	91.9700i	1.95616	+	0.281254i
$328$		0			0
$329$	−82.4832	+	37.6688i	−0.250709	+	0.114495i
$330$		0			0
$331$	−23.7383	−	165.103i	−0.0717169	−	0.498802i	−0.993744	−	0.111678i	$-0.964378\pi$
$331$	−23.7383	−	165.103i	−0.0717169	−	0.498802i	0.922028	−	0.387124i	$-0.126532\pi$
$332$		0			0
$333$	−6.60474	−	22.4937i	−0.0198340	−	0.0675485i
$334$		0			0
$335$	95.3046	−	208.688i	0.284491	−	0.622949i
$336$		0			0
$337$	−23.9240	+	20.7303i	−0.0709912	+	0.0615142i	−0.689634	−	0.724158i	$-0.742228\pi$
$337$	−23.9240	+	20.7303i	−0.0709912	+	0.0615142i	0.618642	+	0.785673i	$0.287683\pi$
$338$		0			0
$339$	−100.432	−	156.275i	−0.296258	−	0.460987i
$340$		0			0
$341$	−309.591	+	481.733i	−0.907892	+	1.41271i
$342$		0			0
$343$	−184.406	+	628.028i	−0.537626	+	1.83098i
$344$		0			0
$345$	86.6994	+	420.437i	0.251303	+	1.21866i
$346$		0			0
$347$	−325.038	−	95.4399i	−0.936710	−	0.275043i	−0.222467	−	0.974940i	$-0.571411\pi$
$347$	−325.038	−	95.4399i	−0.936710	−	0.275043i	−0.714243	+	0.699897i	$0.753229\pi$
$348$		0			0
$349$	168.198	+	108.095i	0.481944	+	0.309726i	0.758958	−	0.651139i	$-0.225709\pi$
$349$	168.198	+	108.095i	0.481944	+	0.309726i	−0.277014	+	0.960866i	$0.589345\pi$
$350$		0			0
$351$	161.329	−	103.680i	0.459626	−	0.295384i
$352$		0			0
$353$	−4.68012	−	5.40114i	−0.0132581	−	0.0153007i	0.749082	−	0.662478i	$-0.230495\pi$
$353$	−4.68012	−	5.40114i	−0.0132581	−	0.0153007i	−0.762340	+	0.647177i	$0.775950\pi$
$354$		0			0
$355$	195.100	+	89.0990i	0.549576	+	0.250983i
$356$		0			0
$357$	286.758	−	84.1999i	0.803245	−	0.235854i
$358$		0			0
$359$	−172.261	+	24.7674i	−0.479836	+	0.0689901i	−0.377989	−	0.925810i	$-0.623384\pi$
$359$	−172.261	+	24.7674i	−0.479836	+	0.0689901i	−0.101847	+	0.994800i	$0.532475\pi$
$360$		0			0
$361$	−257.080	−	562.926i	−0.712132	−	1.55935i
$362$		0			0
$363$	3.93266	−	27.3522i	0.0108338	−	0.0753505i
$364$		0			0
$365$	−54.5613	−	47.2776i	−0.149483	−	0.129528i
$366$		0			0
$367$		−	618.663i		−	1.68573i	−0.538124	−	0.842866i	$-0.680867\pi$
$367$		−	618.663i		−	1.68573i	0.538124	−	0.842866i	$-0.319133\pi$
$368$		0			0
$369$	−34.9192			−0.0946320
$370$		0			0
$371$	626.109	−	722.568i	1.68762	−	1.94762i
$372$		0			0
$373$	6.64357	+	0.955200i	0.0178112	+	0.00256086i	0.151215	−	0.988501i	$-0.451682\pi$
$373$	6.64357	+	0.955200i	0.0178112	+	0.00256086i	−0.133403	+	0.991062i	$0.542591\pi$
$374$		0			0
$375$	250.250	−	114.285i	0.667333	−	0.304761i
$376$		0			0
$377$	7.04331	+	48.9873i	0.0186825	+	0.129940i
$378$		0			0
$379$	93.2086	+	317.439i	0.245933	+	0.837571i	0.986243	+	0.165305i	$0.0528608\pi$
$379$	93.2086	+	317.439i	0.245933	+	0.837571i	−0.740310	+	0.672266i	$0.765321\pi$
$380$		0			0
$381$	−75.4334	+	165.176i	−0.197988	+	0.433533i
$382$		0			0
$383$	−289.286	+	250.668i	−0.755317	+	0.654486i	−0.944893	−	0.327380i	$-0.893834\pi$
$383$	−289.286	+	250.668i	−0.755317	+	0.654486i	0.189576	+	0.981866i	$0.439289\pi$
$384$		0			0
$385$	−449.767	−	699.851i	−1.16823	−	1.81779i
$386$		0			0
$387$	23.2869	−	36.2351i	0.0601728	−	0.0936307i
$388$		0			0
$389$	40.1802	−	136.841i	0.103291	−	0.351777i	−0.891588	−	0.452847i	$-0.850408\pi$
$389$	40.1802	−	136.841i	0.103291	−	0.351777i	0.994879	+	0.101070i	$0.0322267\pi$
$390$		0			0
$391$	177.508	−	10.7635i	0.453985	−	0.0275282i
$392$		0			0
$393$	122.794	+	36.0555i	0.312452	+	0.0917443i
$394$		0			0
$395$	−58.0367	−	37.2979i	−0.146928	−	0.0944251i
$396$		0			0
$397$	293.987	−	188.934i	0.740523	−	0.475905i	−0.115198	−	0.993343i	$-0.536750\pi$
$397$	293.987	−	188.934i	0.740523	−	0.475905i	0.855721	+	0.517438i	$0.173114\pi$
$398$		0			0
$399$	−792.347	−	914.418i	−1.98583	−	2.29177i
$400$		0			0
$401$	195.948	+	89.4864i	0.488648	+	0.223158i	0.644474	−	0.764626i	$-0.277077\pi$
$401$	195.948	+	89.4864i	0.488648	+	0.223158i	−0.155826	+	0.987785i	$0.549804\pi$
$402$		0			0
$403$	−362.361	+	106.399i	−0.899159	+	0.264017i
$404$		0			0
$405$	518.074	−	74.4878i	1.27919	−	0.183920i
$406$		0			0
$407$	126.111	+	276.144i	0.309855	+	0.678487i
$408$		0			0
$409$	−66.2202	+	460.572i	−0.161908	+	1.12609i	0.733126	+	0.680093i	$0.238061\pi$
$409$	−66.2202	+	460.572i	−0.161908	+	1.12609i	−0.895033	+	0.445999i	$0.852848\pi$
$410$		0			0
$411$	315.166	+	273.093i	0.766826	+	0.664459i
$412$		0			0
$413$		−	55.4950i		−	0.134370i
$414$		0			0
$415$	−878.697			−2.11734
$416$		0			0
$417$	−274.078	+	316.303i	−0.657262	+	0.758520i
$418$		0			0
$419$	−490.436	−	70.5140i	−1.17049	−	0.168291i	−0.470472	−	0.882415i	$-0.655916\pi$
$419$	−490.436	−	70.5140i	−1.17049	−	0.168291i	−0.700020	+	0.714124i	$0.746825\pi$
$420$		0			0
$421$	−8.41092	+	3.84114i	−0.0199784	+	0.00912384i	−0.425379	−	0.905015i	$-0.639859\pi$
$421$	−8.41092	+	3.84114i	−0.0199784	+	0.00912384i	0.405401	+	0.914139i	$0.367132\pi$
$422$		0			0
$423$	−0.923225	−	6.42117i	−0.00218257	−	0.0151801i
$424$		0			0
$425$	22.3501	+	76.1173i	0.0525884	+	0.179100i
$426$		0			0
$427$	200.578	−	439.205i	0.469738	−	1.02858i
$428$		0			0
$429$	203.338	−	176.193i	0.473980	−	0.410706i
$430$		0			0
$431$	207.682	+	323.160i	0.481862	+	0.749792i	0.994032	−	0.109093i	$-0.0347945\pi$
$431$	207.682	+	323.160i	0.481862	+	0.749792i	−0.512170	+	0.858884i	$0.671158\pi$
$432$		0			0
$433$	292.183	−	454.646i	0.674788	−	1.04999i	−0.319939	−	0.947438i	$-0.603662\pi$
$433$	292.183	−	454.646i	0.674788	−	1.04999i	0.994728	−	0.102553i	$-0.0327012\pi$
$434$		0			0
$435$	−34.6367	+	117.962i	−0.0796245	+	0.271176i
$436$		0			0
$437$	−338.171	−	635.595i	−0.773848	−	1.45445i
$438$		0			0
$439$	672.006	+	197.319i	1.53077	+	0.449473i	0.935285	−	0.353896i	$-0.115143\pi$
$439$	672.006	+	197.319i	1.53077	+	0.449473i	0.595481	+	0.803370i	$0.296962\pi$
$440$		0			0
$441$	−75.6588	−	48.6229i	−0.171562	−	0.110256i
$442$		0			0
$443$	112.803	−	72.4941i	0.254634	−	0.163644i	−0.407096	−	0.913385i	$-0.633459\pi$
$443$	112.803	−	72.4941i	0.254634	−	0.163644i	0.661731	+	0.749742i	$0.269822\pi$
$444$		0			0
$445$	454.555	+	524.584i	1.02147	+	1.17884i
$446$		0			0
$447$	478.869	+	218.692i	1.07129	+	0.489244i
$448$		0			0
$449$	107.362	−	31.5244i	0.239114	−	0.0702102i	−0.159980	−	0.987120i	$-0.551143\pi$
$449$	107.362	−	31.5244i	0.239114	−	0.0702102i	0.399094	+	0.916910i	$0.369325\pi$
$450$		0			0
$451$	447.583	−	64.3527i	0.992423	−	0.142689i
$452$		0			0
$453$	8.74213	+	19.1426i	0.0192983	+	0.0422574i
$454$		0			0
$455$	78.0816	−	543.069i	0.171608	−	1.19356i
$456$		0			0
$457$	107.011	+	92.7256i	0.234160	+	0.202901i	0.764035	−	0.645175i	$-0.223216\pi$
$457$	107.011	+	92.7256i	0.234160	+	0.202901i	−0.529875	+	0.848076i	$0.677761\pi$
$458$		0			0
$459$		−	197.346i		−	0.429949i
$460$		0			0
$461$	−110.581			−0.239872			−0.119936	−	0.992782i	$-0.538269\pi$
$461$	−110.581			−0.239872			−0.119936	+	0.992782i	$0.538269\pi$
$462$		0			0
$463$	51.8422	−	59.8291i	0.111970	−	0.129220i	−0.696998	−	0.717073i	$-0.745481\pi$
$463$	51.8422	−	59.8291i	0.111970	−	0.129220i	0.808968	+	0.587853i	$0.200027\pi$
$464$		0			0
$465$	−928.601	−	133.513i	−1.99699	−	0.287124i
$466$		0			0
$467$	−273.684	+	124.987i	−0.586047	+	0.267639i	−0.686294	−	0.727324i	$-0.740764\pi$
$467$	−273.684	+	124.987i	−0.586047	+	0.267639i	0.100248	+	0.994963i	$0.468037\pi$
$468$		0			0
$469$	67.6166	+	470.284i	0.144172	+	1.00274i
$470$		0			0
$471$	−139.127	−	473.824i	−0.295387	−	1.00600i
$472$		0			0
$473$	−231.706	+	507.364i	−0.489864	+	1.07265i
$474$		0			0
$475$	242.724	−	210.321i	0.510997	−	0.442781i
$476$		0			0
$477$	36.9800	+	57.5420i	0.0775263	+	0.120633i
$478$		0			0
$479$	−273.544	+	425.643i	−0.571074	+	0.888608i	−0.999891	−	0.0147831i	$-0.995294\pi$
$479$	−273.544	+	425.643i	−0.571074	+	0.888608i	0.428817	+	0.903391i	$0.358931\pi$
$480$		0			0
$481$	−56.4063	+	192.102i	−0.117269	+	0.399381i
$482$		0			0
$483$	−621.787	−	635.412i	−1.28734	−	1.31555i
$484$		0			0
$485$	550.447	+	161.626i	1.13494	+	0.333249i
$486$		0			0
$487$	591.509	+	380.140i	1.21460	+	0.780574i	0.981422	−	0.191860i	$-0.0614520\pi$
$487$	591.509	+	380.140i	1.21460	+	0.780574i	0.233175	+	0.972435i	$0.425088\pi$
$488$		0			0
$489$	−408.362	+	262.438i	−0.835097	+	0.536684i
$490$		0			0
$491$	116.837	+	134.837i	0.237957	+	0.274617i	0.862150	−	0.506653i	$-0.169118\pi$
$491$	116.837	+	134.837i	0.237957	+	0.274617i	−0.624193	+	0.781270i	$0.714572\pi$
$492$		0			0
$493$	46.3273	+	21.1570i	0.0939701	+	0.0429147i
$494$		0			0
$495$	57.1055	−	16.7677i	0.115365	−	0.0338741i
$496$		0			0
$497$	−439.662	+	63.2138i	−0.884631	+	0.127191i
$498$		0			0
$499$	184.156	+	403.246i	0.369051	+	0.808109i	0.999492	+	0.0318717i	$0.0101468\pi$
$499$	184.156	+	403.246i	0.369051	+	0.808109i	−0.630441	+	0.776237i	$0.717126\pi$
$500$		0			0
$501$	30.6562	−	213.219i	0.0611900	−	0.425586i
$502$		0			0
$503$	−77.2184	−	66.9101i	−0.153516	−	0.133022i	0.574717	−	0.818353i	$-0.305112\pi$
$503$	−77.2184	−	66.9101i	−0.153516	−	0.133022i	−0.728232	+	0.685330i	$0.759658\pi$
$504$		0			0
$505$			865.960i			1.71477i
$506$		0			0
$507$	−353.759			−0.697750
$508$		0			0
$509$	−453.232	+	523.058i	−0.890436	+	1.02762i	0.109000	+	0.994042i	$0.465235\pi$
$509$	−453.232	+	523.058i	−0.890436	+	1.02762i	−0.999436	+	0.0335763i	$0.989310\pi$
$510$		0			0
$511$	147.991	+	21.2779i	0.289610	+	0.0416397i
$512$		0			0
$513$	−726.754	+	331.897i	−1.41667	+	0.646973i
$514$		0			0
$515$	7.56848	+	52.6400i	0.0146961	+	0.102214i
$516$		0			0
$517$	23.6672	+	80.6030i	0.0457779	+	0.155905i
$518$		0			0
$519$	−121.077	+	265.122i	−0.233289	+	0.510832i
$520$		0			0
$521$	−483.431	+	418.895i	−0.927890	+	0.804022i	−0.980888	−	0.194573i	$-0.937668\pi$
$521$	−483.431	+	418.895i	−0.927890	+	0.804022i	0.0529976	+	0.998595i	$0.483122\pi$
$522$		0			0
$523$	167.135	+	260.066i	0.319569	+	0.497259i	0.963458	−	0.267860i	$-0.0863165\pi$
$523$	167.135	+	260.066i	0.319569	+	0.497259i	−0.643889	+	0.765119i	$0.722680\pi$
$524$		0			0
$525$	214.412	−	333.632i	0.408404	−	0.635490i
$526$		0			0
$527$	−109.492	+	372.895i	−0.207764	+	0.707580i
$528$		0			0
$529$	−276.287	−	451.117i	−0.522282	−	0.852773i
$530$		0			0
$531$	3.80937	+	1.11853i	0.00717395	+	0.00210646i
$532$		0			0
$533$	250.878	+	161.230i	0.470691	+	0.302495i
$534$		0			0
$535$	933.507	−	599.929i	1.74487	−	1.12136i
$536$		0			0
$537$	208.139	+	240.205i	0.387595	+	0.447309i
$538$		0			0
$539$	1059.38	+	483.801i	1.96545	+	0.897590i
$540$		0			0
$541$	−226.716	+	66.5699i	−0.419069	+	0.123050i	−0.484467	−	0.874809i	$-0.660986\pi$
$541$	−226.716	+	66.5699i	−0.419069	+	0.123050i	0.0653980	+	0.997859i	$0.479168\pi$
$542$		0			0
$543$	133.192	−	19.1501i	0.245288	−	0.0352671i
$544$		0			0
$545$	−507.162	−	1110.53i	−0.930572	−	2.03767i
$546$		0			0
$547$	54.0700	−	376.065i	0.0988482	−	0.687505i	−0.878790	−	0.477209i	$-0.841648\pi$
$547$	54.0700	−	376.065i	0.0988482	−	0.687505i	0.977638	−	0.210295i	$-0.0674425\pi$
$548$		0			0
$549$	26.1058	+	22.6208i	0.0475515	+	0.0412036i
$550$		0			0
$551$		−	206.188i		−	0.374207i
$552$		0			0
$553$	142.872			0.258358
$554$		0			0
$555$	−325.696	+	375.873i	−0.586839	+	0.677248i
$556$		0			0
$557$	−367.253	−	52.8030i	−0.659341	−	0.0947989i	−0.195481	−	0.980708i	$-0.562627\pi$
$557$	−367.253	−	52.8030i	−0.659341	−	0.0947989i	−0.463860	+	0.885909i	$0.653536\pi$
$558$		0			0
$559$	−334.611	+	152.812i	−0.598588	+	0.273366i
$560$		0			0
$561$	−39.4035	−	274.057i	−0.0702379	−	0.488515i
$562$		0			0
$563$	30.0924	+	102.485i	0.0534501	+	0.182034i	0.981891	−	0.189445i	$-0.0606688\pi$
$563$	30.0924	+	102.485i	0.0534501	+	0.182034i	−0.928441	+	0.371479i	$0.878851\pi$
$564$		0			0
$565$	−145.785	+	319.224i	−0.258026	+	0.564999i
$566$		0			0
$567$	−819.188	+	709.831i	−1.44478	+	1.25191i
$568$		0			0
$569$	−271.953	−	423.167i	−0.477949	−	0.743704i	0.515634	−	0.856809i	$-0.327557\pi$
$569$	−271.953	−	423.167i	−0.477949	−	0.743704i	−0.993583	+	0.113105i	$0.963920\pi$
$570$		0			0
$571$	−365.306	+	568.427i	−0.639765	+	0.995494i	0.358317	+	0.933600i	$0.383351\pi$
$571$	−365.306	+	568.427i	−0.639765	+	0.995494i	−0.998083	+	0.0618944i	$0.980286\pi$
$572$		0			0
$573$	311.935	−	1062.35i	0.544390	−	1.85402i
$574$		0			0
$575$	168.664	−	165.048i	0.293329	−	0.287039i
$576$		0			0
$577$	971.300	+	285.199i	1.68336	+	0.494280i	0.976940	−	0.213512i	$-0.0684904\pi$
$577$	971.300	+	285.199i	1.68336	+	0.494280i	0.706421	+	0.707792i	$0.250309\pi$
$578$		0			0
$579$	243.907	+	156.749i	0.421255	+	0.270724i
$580$		0			0
$581$	1530.87	−	983.827i	2.63488	−	1.69333i
$582$		0			0
$583$	−580.042	−	669.404i	−0.994926	−	1.14821i
$584$		0			0
$585$	35.7044	+	16.3057i	0.0610332	+	0.0278729i
$586$		0			0
$587$	−195.167	+	57.3061i	−0.332481	+	0.0976253i	−0.443712	−	0.896169i	$-0.646339\pi$
$587$	−195.167	+	57.3061i	−0.332481	+	0.0976253i	0.111231	+	0.993795i	$0.464521\pi$
$588$		0			0
$589$	1557.38	−	223.917i	2.64410	−	0.380165i
$590$		0			0
$591$	−221.485	−	484.984i	−0.374763	−	0.820615i
$592$		0			0
$593$	−38.4840	+	267.662i	−0.0648972	+	0.451370i	0.931301	+	0.364251i	$0.118675\pi$
$593$	−38.4840	+	267.662i	−0.0648972	+	0.451370i	−0.996198	+	0.0871187i	$0.972234\pi$
$594$		0			0
$595$	−426.698	−	369.736i	−0.717140	−	0.621405i
$596$		0			0
$597$		−	52.6521i		−	0.0881944i
$598$		0			0
$599$	360.150			0.601252			0.300626	−	0.953742i	$-0.402804\pi$
$599$	360.150			0.601252			0.300626	+	0.953742i	$0.402804\pi$
$600$		0			0
$601$	−58.4554	+	67.4612i	−0.0972636	+	0.112248i	−0.802295	−	0.596928i	$-0.796388\pi$
$601$	−58.4554	+	67.4612i	−0.0972636	+	0.112248i	0.705031	+	0.709177i	$0.250933\pi$
$602$		0			0
$603$	−33.6448	−	4.83739i	−0.0557956	−	0.00802220i
$604$		0			0
$605$	−47.4865	+	21.6864i	−0.0784901	+	0.0358452i
$606$		0			0
$607$	−147.615	−	1026.69i	−0.243189	−	1.69141i	−0.635915	−	0.771759i	$-0.719377\pi$
$607$	−147.615	−	1026.69i	−0.243189	−	1.69141i	0.392727	−	0.919655i	$-0.371532\pi$
$608$		0			0
$609$	−71.7310	−	244.293i	−0.117785	−	0.401139i
$610$		0			0
$611$	−23.0150	+	50.3959i	−0.0376678	+	0.0824810i
$612$		0			0
$613$	223.396	−	193.573i	0.364430	−	0.315780i	−0.453327	−	0.891344i	$-0.649763\pi$
$613$	223.396	−	193.573i	0.364430	−	0.315780i	0.817757	+	0.575564i	$0.195217\pi$
$614$		0			0
$615$	400.514	+	623.212i	0.651242	+	1.01335i
$616$		0			0
$617$	636.911	−	991.053i	1.03227	−	1.60624i	0.265731	−	0.964047i	$-0.414387\pi$
$617$	636.911	−	991.053i	1.03227	−	1.60624i	0.766540	−	0.642197i	$-0.221977\pi$
$618$		0			0
$619$	−30.6669	+	104.442i	−0.0495427	+	0.168727i	−0.980548	−	0.196278i	$-0.937115\pi$
$619$	−30.6669	+	104.442i	−0.0495427	+	0.168727i	0.931006	+	0.365005i	$0.118933\pi$
$620$		0			0
$621$	−518.253	+	275.739i	−0.834547	+	0.444025i
$622$		0			0
$623$	−1379.27	−	404.991i	−2.21392	−	0.650066i
$624$		0			0
$625$	−653.009	−	419.663i	−1.04481	−	0.671461i
$626$		0			0
$627$	−942.982	+	606.018i	−1.50396	+	0.966535i
$628$		0			0
$629$	134.922	+	155.709i	0.214503	+	0.247550i
$630$		0			0
$631$	328.847	+	150.179i	0.521152	+	0.238002i	0.658582	−	0.752509i	$-0.271157\pi$
$631$	328.847	+	150.179i	0.521152	+	0.238002i	−0.137429	+	0.990512i	$0.543884\pi$
$632$		0			0
$633$	1003.22	−	294.573i	1.58487	−	0.465361i
$634$		0			0
$635$	339.552	−	48.8203i	0.534728	−	0.0768823i
$636$		0			0
$637$	319.070	+	698.667i	0.500896	+	1.09681i
$638$		0			0
$639$	4.52241	−	31.4540i	0.00707732	−	0.0492239i
$640$		0			0
$641$	21.8212	+	18.9082i	0.0340424	+	0.0294979i	0.671716	−	0.740809i	$-0.265558\pi$
$641$	21.8212	+	18.9082i	0.0340424	+	0.0294979i	−0.637673	+	0.770307i	$0.720103\pi$
$642$		0			0
$643$			887.952i			1.38095i	0.723355	+	0.690476i	$0.242599\pi$
$643$			887.952i			1.38095i	−0.723355	+	0.690476i	$0.757401\pi$
$644$		0			0
$645$	−913.791			−1.41673
$646$		0			0
$647$	−514.676	+	593.967i	−0.795480	+	0.918033i	−0.998124	−	0.0612193i	$-0.980501\pi$
$647$	−514.676	+	593.967i	−0.795480	+	0.918033i	0.202644	+	0.979252i	$0.435047\pi$
$648$		0			0
$649$	−50.8886	−	7.31667i	−0.0784108	−	0.0112738i
$650$		0			0
$651$	1767.30	−	807.097i	2.71474	−	1.23978i
$652$		0			0
$653$	−135.917	−	945.325i	−0.208143	−	1.44766i	−0.779211	−	0.626762i	$-0.784380\pi$
$653$	−135.917	−	945.325i	−0.208143	−	1.44766i	0.571068	−	0.820903i	$-0.306529\pi$
$654$		0			0
$655$	−68.1146	−	231.977i	−0.103992	−	0.354163i
$656$		0			0
$657$	−4.44343	+	9.72975i	−0.00676321	+	0.0148094i
$658$		0			0
$659$	−303.974	+	263.395i	−0.461266	+	0.399689i	−0.854255	−	0.519854i	$-0.825986\pi$
$659$	−303.974	+	263.395i	−0.461266	+	0.399689i	0.392989	+	0.919543i	$0.371441\pi$
$660$		0			0
$661$	−130.028	−	202.327i	−0.196714	−	0.306093i	0.728858	−	0.684665i	$-0.240052\pi$
$661$	−130.028	−	202.327i	−0.196714	−	0.306093i	−0.925572	+	0.378572i	$0.876415\pi$
$662$		0			0
$663$	98.7218	−	153.614i	0.148902	−	0.231695i
$664$		0			0
$665$	−643.980	+	2193.19i	−0.968391	+	3.29804i
$666$		0			0
$667$	−9.16959	−	151.222i	−0.0137475	−	0.226719i
$668$		0			0
$669$	−905.246	−	265.804i	−1.35313	−	0.397316i
$670$		0			0
$671$	−376.303	−	241.835i	−0.560809	−	0.360410i
$672$		0			0
$673$	6.58105	−	4.22939i	0.00977868	−	0.00628438i	−0.535742	−	0.844382i	$-0.679968\pi$
$673$	6.58105	−	4.22939i	0.00977868	−	0.00628438i	0.545521	+	0.838097i	$0.316332\pi$
$674$		0			0
$675$	−171.492	−	197.913i	−0.254063	−	0.293204i
$676$		0			0
$677$	−232.541	−	106.198i	−0.343487	−	0.156865i	0.236200	−	0.971704i	$-0.424098\pi$
$677$	−232.541	−	106.198i	−0.343487	−	0.156865i	−0.579687	+	0.814839i	$0.696825\pi$
$678$		0			0
$679$	−1139.95	+	334.720i	−1.67887	+	0.492960i
$680$		0			0
$681$	1079.05	−	155.145i	1.58452	−	0.227819i
$682$		0			0
$683$	−78.4858	−	171.860i	−0.114913	−	0.251625i	0.843433	−	0.537235i	$-0.180531\pi$
$683$	−78.4858	−	171.860i	−0.114913	−	0.251625i	−0.958346	+	0.285610i	$0.907804\pi$
$684$		0			0
$685$	112.119	−	779.806i	0.163678	−	1.13840i
$686$		0			0
$687$	574.358	+	497.684i	0.836038	+	0.724431i
$688$		0			0
$689$		−	584.158i		−	0.847835i
$690$		0			0
$691$	599.732			0.867919			0.433960	−	0.900932i	$-0.357116\pi$
$691$	599.732			0.867919			0.433960	+	0.900932i	$0.357116\pi$
$692$		0			0
$693$	−80.7154	+	93.1505i	−0.116472	+	0.134416i
$694$		0			0
$695$	782.620	+	112.524i	1.12607	+	0.161905i
$696$		0			0
$697$	279.156	−	127.486i	0.400511	−	0.182907i
$698$		0			0
$699$	71.0413	+	494.103i	0.101633	+	0.706871i
$700$		0			0
$701$	209.376	+	713.068i	0.298681	+	1.01722i	0.962941	+	0.269713i	$0.0869289\pi$
$701$	209.376	+	713.068i	0.298681	+	1.01722i	−0.664259	+	0.747502i	$0.731253\pi$
$702$		0			0
$703$	346.505	−	758.740i	0.492895	−	1.07929i
$704$		0			0
$705$	−104.011	+	90.1262i	−0.147534	+	0.127839i
$706$		0			0
$707$	−969.567	−	1508.68i	−1.37138	−	2.13391i
$708$		0			0
$709$	55.9500	−	87.0600i	0.0789140	−	0.122793i	−0.799553	−	0.600595i	$-0.794930\pi$
$709$	55.9500	−	87.0600i	0.0789140	−	0.122793i	0.878467	+	0.477803i	$0.158567\pi$
$710$		0			0
$711$	−2.87966	+	9.80723i	−0.00405016	+	0.0137936i
$712$		0			0
$713$	1132.25	−	233.484i	1.58801	−	0.327467i
$714$		0			0
$715$	−487.697	−	143.201i	−0.682094	−	0.200281i
$716$		0			0
$717$	1151.93	+	740.299i	1.60659	+	1.03250i
$718$		0			0
$719$	−896.429	+	576.100i	−1.24677	+	0.801251i	−0.986417	−	0.164262i	$-0.947476\pi$
$719$	−896.429	+	576.100i	−1.24677	+	0.801251i	−0.260355	+	0.965513i	$0.583839\pi$
$720$		0			0
$721$	−72.1238	−	83.2353i	−0.100033	−	0.115444i
$722$		0			0
$723$	621.697	+	283.920i	0.859886	+	0.392697i
$724$		0			0
$725$	64.8454	−	19.0403i	0.0894419	−	0.0262625i
$726$		0			0
$727$	−666.062	+	95.7652i	−0.916178	+	0.131727i	−0.584246	−	0.811577i	$-0.698610\pi$
$727$	−666.062	+	95.7652i	−0.916178	+	0.131727i	−0.331932	+	0.943303i	$0.607701\pi$
$728$		0			0
$729$	267.730	+	586.246i	0.367256	+	0.804179i
$730$		0			0
$731$	−53.8727	+	374.693i	−0.0736973	+	0.512576i
$732$		0			0
$733$	−16.7913	−	14.5497i	−0.0229076	−	0.0198496i	0.643332	−	0.765588i	$-0.277552\pi$
$733$	−16.7913	−	14.5497i	−0.0229076	−	0.0198496i	−0.666239	+	0.745738i	$0.732097\pi$
$734$		0			0
$735$			1907.99i			2.59591i
$736$		0			0
$737$	440.162			0.597235
$738$		0			0
$739$	−37.8995	+	43.7383i	−0.0512848	+	0.0591858i	−0.780812	−	0.624766i	$-0.785195\pi$
$739$	−37.8995	+	43.7383i	−0.0512848	+	0.0591858i	0.729528	+	0.683951i	$0.239740\pi$
$740$		0			0
$741$	−731.734	−	105.207i	−0.987495	−	0.141980i
$742$		0			0
$743$	701.647	−	320.431i	0.944343	−	0.431267i	0.117106	−	0.993119i	$-0.462638\pi$
$743$	701.647	−	320.431i	0.944343	−	0.431267i	0.827237	+	0.561852i	$0.189911\pi$
$744$		0			0
$745$	−141.537	−	984.410i	−0.189982	−	1.32136i
$746$		0			0
$747$	36.6779	+	124.914i	0.0491003	+	0.167220i
$748$		0			0
$749$	−954.650	+	2090.39i	−1.27457	+	2.79091i
$750$		0			0
$751$	128.748	−	111.561i	0.171435	−	0.148550i	−0.564917	−	0.825148i	$-0.691092\pi$
$751$	128.748	−	111.561i	0.171435	−	0.148550i	0.736353	+	0.676598i	$0.236546\pi$
$752$		0			0
$753$	197.092	+	306.681i	0.261743	+	0.407279i
$754$		0			0
$755$	21.4938	−	33.4450i	0.0284686	−	0.0442980i
$756$		0			0
$757$	−128.192	+	436.583i	−0.169342	+	0.576727i	0.830464	+	0.557072i	$0.188075\pi$
$757$	−128.192	+	436.583i	−0.169342	+	0.576727i	−0.999807	+	0.0196556i	$0.993743\pi$
$758$		0			0
$759$	−664.648	+	486.400i	−0.875689	+	0.640843i
$760$		0			0
$761$	−1166.46	−	342.504i	−1.53280	−	0.450071i	−0.596894	−	0.802320i	$-0.703599\pi$
$761$	−1166.46	−	342.504i	−1.53280	−	0.450071i	−0.935906	+	0.352249i	$0.885417\pi$
$762$		0			0
$763$	2126.98	+	1366.92i	2.78765	+	1.79151i
$764$		0			0
$765$	33.9803	−	21.8378i	0.0444187	−	0.0285462i
$766$		0			0
$767$	−22.2041	−	25.6248i	−0.0289492	−	0.0334092i
$768$		0			0
$769$	−74.8887	−	34.2005i	−0.0973846	−	0.0444740i	0.366127	−	0.930565i	$-0.380684\pi$
$769$	−74.8887	−	34.2005i	−0.0973846	−	0.0444740i	−0.463512	+	0.886091i	$0.653411\pi$
$770$		0			0
$771$	−1318.80	+	387.234i	−1.71050	+	0.502249i
$772$		0			0
$773$	−858.101	+	123.376i	−1.11009	+	0.159607i	−0.672880	−	0.739751i	$-0.734943\pi$
$773$	−858.101	+	123.376i	−1.11009	+	0.159607i	−0.437212	+	0.899359i	$0.644034\pi$
$774$		0			0
$775$	214.236	+	469.112i	0.276434	+	0.605306i
$776$		0			0
$777$	146.583	−	1019.51i	0.188653	−	1.31211i
$778$		0			0
$779$	−938.969	−	813.621i	−1.20535	−	1.04444i
$780$		0			0
$781$			411.502i			0.526891i
$782$		0			0
$783$	−168.122			−0.214715
$784$		0			0
$785$	−610.932	+	705.054i	−0.778258	+	0.898157i
$786$		0			0
$787$	−241.523	−	34.7258i	−0.306891	−	0.0441243i	−0.0128512	−	0.999917i	$-0.504091\pi$
$787$	−241.523	−	34.7258i	−0.306891	−	0.0441243i	−0.294040	+	0.955793i	$0.595000\pi$
$788$		0			0
$789$	875.378	−	399.772i	1.10948	−	0.506682i
$790$		0			0
$791$	−103.431	−	719.380i	−0.130760	−	0.909456i
$792$		0			0
$793$	−83.1128	−	283.056i	−0.104808	−	0.356943i
$794$		0			0
$795$	602.817	−	1319.98i	0.758260	−	1.66036i
$796$		0			0
$797$	962.972	−	834.420i	1.20825	−	1.04695i	0.210657	−	0.977560i	$-0.432440\pi$
$797$	962.972	−	834.420i	1.20825	−	1.04695i	0.997590	−	0.0693912i	$-0.0221057\pi$
$798$		0			0
$799$	30.8236	+	47.9624i	0.0385777	+	0.0600281i
$800$		0			0
$801$	55.6000	−	86.5153i	0.0694132	−	0.108009i
$802$		0			0
$803$	39.0234	−	132.901i	0.0485970	−	0.165506i
$804$		0			0
$805$	−374.770	+	1637.16i	−0.465553	+	2.03375i
$806$		0			0
$807$	−210.076	−	61.6838i	−0.260317	−	0.0764359i
$808$		0			0
$809$	182.502	+	117.287i	0.225589	+	0.144977i	0.648554	−	0.761169i	$-0.275374\pi$
$809$	182.502	+	117.287i	0.225589	+	0.144977i	−0.422965	+	0.906146i	$0.639011\pi$
$810$		0			0
$811$	−841.926	+	541.073i	−1.03813	+	0.667167i	−0.944524	−	0.328442i	$-0.893477\pi$
$811$	−841.926	+	541.073i	−1.03813	+	0.667167i	−0.0936084	+	0.995609i	$0.529840\pi$
$812$		0			0
$813$	−715.422	−	825.641i	−0.879978	−	1.01555i
$814$		0			0
$815$	834.167	+	380.951i	1.02352	+	0.467425i
$816$		0			0
$817$	1470.46	−	431.766i	1.79983	−	0.528477i
$818$		0			0
$819$	−80.4608	+	11.5685i	−0.0982427	+	0.0141252i
$820$		0			0
$821$	−272.627	−	596.970i	−0.332067	−	0.727126i	0.667784	−	0.744355i	$-0.267243\pi$
$821$	−272.627	−	596.970i	−0.332067	−	0.727126i	−0.999852	+	0.0172290i	$0.994516\pi$
$822$		0			0
$823$	69.3610	−	482.417i	0.0842783	−	0.586168i	−0.903296	−	0.429017i	$-0.858860\pi$
$823$	69.3610	−	482.417i	0.0842783	−	0.586168i	0.987575	−	0.157151i	$-0.0502310\pi$
$824$		0			0
$825$	−277.670	−	240.602i	−0.336569	−	0.291639i
$826$		0			0
$827$			141.931i			0.171622i	0.996311	+	0.0858109i	$0.0273481\pi$
$827$			141.931i			0.171622i	−0.996311	+	0.0858109i	$0.972652\pi$
$828$		0			0
$829$	−111.316			−0.134277			−0.0671387	−	0.997744i	$-0.521387\pi$
$829$	−111.316			−0.134277			−0.0671387	+	0.997744i	$0.521387\pi$
$830$		0			0
$831$	412.967	−	476.590i	0.496952	−	0.573514i
$832$		0			0
$833$	782.359	+	112.486i	0.939206	+	0.135037i
$834$		0			0
$835$	−370.171	+	169.052i	−0.443319	+	0.202457i
$836$		0			0
$837$	−182.578	−	1269.86i	−0.218134	−	1.51715i
$838$		0			0
$839$	130.031	+	442.844i	0.154983	+	0.527823i	0.999976	−	0.00695430i	$-0.00221364\pi$
$839$	130.031	+	442.844i	0.154983	+	0.527823i	−0.844993	+	0.534777i	$0.820395\pi$
$840$		0			0
$841$	−331.340	+	725.534i	−0.393984	+	0.862704i
$842$		0			0
$843$	318.019	−	275.565i	0.377246	−	0.326886i
$844$		0			0
$845$	361.314	+	562.216i	0.427591	+	0.665345i
$846$		0			0
$847$	58.4500	−	90.9500i	0.0690083	−	0.107379i
$848$		0			0
$849$	−263.214	+	896.425i	−0.310028	+	1.05586i
$850$		0			0
$851$	220.390	−	571.883i	0.258978	−	0.672012i
$852$		0			0
$853$	−1280.14	−	375.884i	−1.50075	−	0.440661i	−0.574798	−	0.818295i	$-0.694919\pi$
$853$	−1280.14	−	375.884i	−1.50075	−	0.440661i	−0.925955	+	0.377635i	$0.876738\pi$
$854$		0			0
$855$	−137.569	−	88.4101i	−0.160899	−	0.103404i
$856$		0			0
$857$	−22.6048	+	14.5272i	−0.0263766	+	0.0169512i	−0.553763	−	0.832675i	$-0.686809\pi$
$857$	−22.6048	+	14.5272i	−0.0263766	+	0.0169512i	0.527386	+	0.849626i	$0.323172\pi$
$858$		0			0
$859$	−129.946	−	149.965i	−0.151276	−	0.174581i	0.675054	−	0.737769i	$-0.264120\pi$
$859$	−129.946	−	149.965i	−0.151276	−	0.174581i	−0.826329	+	0.563187i	$0.809575\pi$
$860$		0			0
$861$	−1395.55	−	637.327i	−1.62085	−	0.740217i
$862$		0			0
$863$	1149.11	−	337.408i	1.33152	−	0.390971i	0.462886	−	0.886418i	$-0.346814\pi$
$863$	1149.11	−	337.408i	1.33152	−	0.390971i	0.868638	+	0.495447i	$0.164996\pi$
$864$		0			0
$865$	545.011	−	78.3607i	0.630070	−	0.0905904i
$866$		0			0
$867$	299.298	+	655.370i	0.345211	+	0.755906i
$868$		0			0
$869$	18.8368	−	131.013i	0.0216764	−	0.150763i
$870$		0			0
$871$	219.387	+	190.100i	0.251879	+	0.218255i
$872$		0			0
$873$		−	84.9968i		−	0.0973617i
$874$		0			0
$875$	1076.34			1.23010
$876$		0			0
$877$	−435.404	+	502.483i	−0.496470	+	0.572957i	−0.947583	−	0.319510i	$-0.896482\pi$
$877$	−435.404	+	502.483i	−0.496470	+	0.572957i	0.451113	+	0.892467i	$0.351027\pi$
$878$		0			0
$879$	−3.70352	−	0.532485i	−0.00421333	−	0.000605785i
$880$		0			0
$881$	704.486	−	321.728i	0.799643	−	0.365185i	0.0266868	−	0.999644i	$-0.491504\pi$
$881$	704.486	−	321.728i	0.799643	−	0.365185i	0.772957	+	0.634459i	$0.218777\pi$
$882$		0			0
$883$	−113.136	−	786.875i	−0.128126	−	0.891139i	−0.947927	−	0.318489i	$-0.896825\pi$
$883$	−113.136	−	786.875i	−0.128126	−	0.891139i	0.819800	−	0.572650i	$-0.194084\pi$
$884$		0			0
$885$	−23.7297	−	80.8161i	−0.0268133	−	0.0913176i
$886$		0			0
$887$	465.014	−	1018.24i	0.524254	−	1.14796i	−0.443549	−	0.896250i	$-0.646281\pi$
$887$	465.014	−	1018.24i	0.524254	−	1.14796i	0.967804	−	0.251707i	$-0.0809918\pi$
$888$		0			0
$889$	−536.907	+	465.232i	−0.603945	+	0.523321i
$890$		0			0
$891$	542.906	+	844.778i	0.609322	+	0.948123i
$892$		0			0
$893$	124.789	−	194.175i	0.139741	−	0.217441i
$894$		0			0
$895$	169.165	−	576.122i	0.189011	−	0.643712i
$896$		0			0
$897$	−541.345	−	44.6193i	−0.603506	−	0.0497428i
$898$		0			0
$899$	317.674	+	93.2776i	0.353364	+	0.103757i
$900$		0			0
$901$	−505.711	−	325.000i	−0.561277	−	0.360711i
$902$		0			0
$903$	1592.01	−	1023.12i	1.76302	−	1.13302i
$904$		0			0
$905$	−166.471	−	192.117i	−0.183945	−	0.212284i
$906$		0			0
$907$	−227.401	−	103.851i	−0.250718	−	0.114499i	0.286092	−	0.958202i	$-0.407644\pi$
$907$	−227.401	−	103.851i	−0.250718	−	0.114499i	−0.536810	+	0.843703i	$0.680371\pi$
$908$		0			0
$909$	123.103	−	36.1463i	0.135427	−	0.0397649i
$910$		0			0
$911$	1460.62	−	210.005i	1.60331	−	0.230522i	0.718179	−	0.695858i	$-0.244976\pi$
$911$	1460.62	−	210.005i	1.60331	−	0.230522i	0.885134	+	0.465337i	$0.154067\pi$
$912$		0			0
$913$	−700.329	−	1533.51i	−0.767064	−	1.67964i
$914$		0			0
$915$	104.293	−	725.371i	0.113981	−	0.792755i
$916$		0			0
$917$	378.401	+	327.886i	0.412651	+	0.357564i
$918$		0			0
$919$		−	219.965i		−	0.239353i	−0.992813	−	0.119676i	$-0.961814\pi$
$919$		−	219.965i		−	0.239353i	0.992813	−	0.119676i	$-0.0381857\pi$
$920$		0			0
$921$	−242.510			−0.263312
$922$		0			0
$923$	−177.722	+	205.102i	−0.192548	+	0.222212i
$924$		0			0
$925$	270.619	+	38.9091i	0.292561	+	0.0420639i
$926$		0			0
$927$	7.16726	−	3.27318i	0.00773167	−	0.00353094i
$928$		0			0
$929$	53.4767	+	371.939i	0.0575637	+	0.400365i	0.998149	+	0.0608083i	$0.0193678\pi$
$929$	53.4767	+	371.939i	0.0575637	+	0.400365i	−0.940586	+	0.339556i	$0.889723\pi$
$930$		0			0
$931$	−901.526	−	3070.32i	−0.968342	−	3.29787i
$932$		0			0
$933$	−346.416	+	758.546i	−0.371293	+	0.813018i
$934$		0			0
$935$	−395.304	+	342.533i	−0.422785	+	0.366345i
$936$		0			0
$937$	−48.7706	−	75.8885i	−0.0520497	−	0.0809909i	0.814253	−	0.580510i	$-0.197147\pi$
$937$	−48.7706	−	75.8885i	−0.0520497	−	0.0809909i	−0.866303	+	0.499519i	$0.833510\pi$
$938$		0			0
$939$	40.1876	−	62.5331i	0.0427983	−	0.0665954i
$940$		0			0
$941$	−276.462	+	941.543i	−0.293796	+	1.00058i	0.671844	+	0.740693i	$0.265503\pi$
$941$	−276.462	+	941.543i	−0.293796	+	1.00058i	−0.965640	+	0.259885i	$0.916315\pi$
$942$		0			0
$943$	−724.839	−	554.966i	−0.768652	−	0.588511i
$944$		0			0
$945$	1788.29	+	525.090i	1.89237	+	0.555651i
$946$		0			0
$947$	−1393.95	−	895.839i	−1.47197	−	0.945976i	−0.997852	−	0.0655138i	$-0.979131\pi$
$947$	−1393.95	−	895.839i	−1.47197	−	0.945976i	−0.474116	−	0.880462i	$-0.657232\pi$
$948$		0			0
$949$	76.8484	−	49.3875i	0.0809783	−	0.0520416i
$950$		0			0
$951$	694.065	+	800.994i	0.729827	+	0.842265i
$952$		0			0
$953$	370.652	+	169.271i	0.388932	+	0.177619i	0.600277	−	0.799792i	$-0.295057\pi$
$953$	370.652	+	169.271i	0.388932	+	0.177619i	−0.211345	+	0.977412i	$0.567784\pi$
$954$		0			0
$955$	−2006.96	+	589.295i	−2.10152	+	0.617063i
$956$		0			0
$957$	−233.473	+	33.5684i	−0.243963	+	0.0350767i
$958$		0			0
$959$	677.771	+	1484.11i	0.706748	+	1.54756i
$960$		0			0
$961$	−222.789	+	1549.53i	−0.231831	+	1.61242i
$962$		0			0
$963$	−124.250	−	107.664i	−0.129024	−	0.111800i
$964$		0			0
$965$		−	547.728i		−	0.567594i
$966$		0			0
$967$	−131.126			−0.135601			−0.0678003	−	0.997699i	$-0.521598\pi$
$967$	−131.126			−0.135601			−0.0678003	+	0.997699i	$0.521598\pi$
$968$		0			0
$969$	−498.184	+	574.935i	−0.514122	+	0.593328i
$970$		0			0
$971$	−1096.45	−	157.645i	−1.12919	−	0.162353i	−0.447704	−	0.894182i	$-0.647758\pi$
$971$	−1096.45	−	157.645i	−1.12919	−	0.162353i	−0.681489	+	0.731828i	$0.738667\pi$
$972$		0			0
$973$	−1489.47	+	680.217i	−1.53080	+	0.699092i
$974$		0			0
$975$	−34.4843	−	239.843i	−0.0353685	−	0.245993i
$976$		0			0
$977$	232.138	+	790.589i	0.237603	+	0.809201i	0.988816	+	0.149141i	$0.0476509\pi$
$977$	232.138	+	790.589i	0.237603	+	0.809201i	−0.751213	+	0.660060i	$0.770531\pi$
$978$		0			0
$979$	−553.223	+	1211.39i	−0.565090	+	1.23737i
$980$		0			0
$981$	−136.701	+	118.452i	−0.139348	+	0.120746i
$982$		0			0
$983$	598.670	+	931.548i	0.609023	+	0.947659i	0.999633	+	0.0271021i	$0.00862791\pi$
$983$	598.670	+	931.548i	0.609023	+	0.947659i	−0.390610	+	0.920556i	$0.627736\pi$
$984$		0			0
$985$	−544.551	+	847.339i	−0.552844	+	0.860242i
$986$		0			0
$987$	80.2990	−	273.473i	0.0813567	−	0.277075i
$988$		0			0
$989$	1059.26	−	382.059i	1.07104	−	0.386308i
$990$		0			0
$991$	618.787	+	181.692i	0.624407	+	0.183342i	0.578605	−	0.815608i	$-0.303597\pi$
$991$	618.787	+	181.692i	0.624407	+	0.183342i	0.0458020	+	0.998951i	$0.485416\pi$
$992$		0			0
$993$	441.062	+	283.453i	0.444171	+	0.285451i
$994$		0			0
$995$	−83.6780	+	53.7766i	−0.0840985	+	0.0540468i
$996$		0			0
$997$	543.712	+	627.477i	0.545348	+	0.629365i	0.959793	−	0.280709i	$-0.0905696\pi$
$997$	543.712	+	627.477i	0.545348	+	0.629365i	−0.414445	+	0.910074i	$0.636024\pi$
$998$		0			0
$999$	−618.664	−	282.534i	−0.619283	−	0.282817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.3.f.a.5.1	✓	40
4.3	odd	2		368.3.p.c.97.4		40
23.3	even	11		2116.3.d.c.1057.31		40
23.14	odd	22	inner	92.3.f.a.37.1	yes	40
23.20	odd	22		2116.3.d.c.1057.32		40
92.83	even	22		368.3.p.c.129.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.3.f.a.5.1	✓	40	1.1	even	1	trivial
92.3.f.a.37.1	yes	40	23.14	odd	22	inner
368.3.p.c.97.4		40	4.3	odd	2
368.3.p.c.129.4		40	92.83	even	22
2116.3.d.c.1057.31		40	23.3	even	11
2116.3.d.c.1057.32		40	23.20	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	92.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.05837 + 2.37548i) q^{3} +(5.87759 + 0.845069i) q^{5} +(-11.1861 + 5.10852i) q^{7} +(-0.125205 - 0.870819i) q^{9} +(3.20967 + 10.9311i) q^{11} +(-3.12123 + 6.83453i) q^{13} +(-14.1057 + 12.2226i) q^{15} +(4.18019 + 6.50451i) q^{17} +(16.9234 - 26.3334i) q^{19} +(10.8899 - 37.0876i) q^{21} +(11.2408 - 20.0660i) q^{23} +(9.84455 + 2.89062i) q^{25} +(-21.4718 - 13.7991i) q^{27} +(5.54128 - 3.56117i) q^{29} +(32.9159 + 37.9870i) q^{31} +(-32.5733 - 14.8757i) q^{33} +(-70.0644 + 20.5728i) q^{35} +(26.3757 - 3.79226i) q^{37} +(-9.81067 - 21.4824i) q^{39} +(5.64863 - 39.2871i) q^{41} +(37.0006 + 32.0612i) q^{43} -5.22412i q^{45} +7.37372 q^{47} +(66.9438 - 77.2573i) q^{49} +(-24.0557 - 3.45869i) q^{51} +(-70.7218 + 32.2976i) q^{53} +(9.62754 + 66.9610i) q^{55} +(27.7198 + 94.4050i) q^{57} +(-1.87466 + 4.10493i) q^{59} +(-29.6733 + 25.7121i) q^{61} +(5.84915 + 9.10146i) q^{63} +(-24.1209 + 37.5329i) q^{65} +(10.8850 - 37.0708i) q^{67} +(24.5286 + 68.0055i) q^{69} +(34.6570 + 10.1762i) q^{71} +(-10.2280 - 6.57315i) q^{73} +(-27.1303 + 17.4356i) q^{75} +(-91.7456 - 105.880i) q^{77} +(-10.5682 - 4.82632i) q^{79} +(84.5735 - 24.8330i) q^{81} +(-146.472 + 21.0595i) q^{83} +(19.0727 + 41.7634i) q^{85} +(-2.94650 + 20.4934i) q^{87} +(88.3431 + 76.5498i) q^{89} -92.3967i q^{91} -157.990 q^{93} +(121.723 - 140.475i) q^{95} +(95.6287 + 13.7493i) q^{97} +(9.11717 - 4.16367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{3} - 6 q^{9} - 2 q^{13} + 77 q^{15} + 55 q^{17} + 33 q^{19} + 33 q^{21} - 50 q^{23} - 54 q^{25} - 191 q^{27} + q^{29} - 53 q^{31} - 121 q^{33} - 156 q^{35} - 352 q^{37} - 306 q^{39} + 6 q^{41}+ \cdots + 1353 q^{99}+O(q^{100}) \) 40 * q - 2 * q^3 - 6 * q^9 - 2 * q^13 + 77 * q^15 + 55 * q^17 + 33 * q^19 + 33 * q^21 - 50 * q^23 - 54 * q^25 - 191 * q^27 + q^29 - 53 * q^31 - 121 * q^33 - 156 * q^35 - 352 * q^37 - 306 * q^39 + 6 * q^41 - 88 * q^43 - 58 * q^47 + 292 * q^49 + 264 * q^51 + 176 * q^53 + 518 * q^55 + 891 * q^57 + 696 * q^59 + 308 * q^61 + 275 * q^63 + 231 * q^65 + 22 * q^67 - 233 * q^69 - 215 * q^71 - 400 * q^73 - 557 * q^75 - 239 * q^77 - 748 * q^79 - 684 * q^81 - 671 * q^83 - 794 * q^85 + 62 * q^87 - 44 * q^89 - 346 * q^93 + 561 * q^95 + 693 * q^97 + 1353 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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