LMFDB - Embedded newform 92.5.c.a.47.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,5,Mod(47,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("92.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.c (of order $2$, degree $1$, 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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.13
Character	$\chi$	$=$	92.47
Dual form			92.5.c.a.47.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.57175 - 3.06367i) q^{2} -5.48369i q^{3} +(-2.77216 + 15.7580i) q^{4} -44.5238 q^{5} +(-16.8002 + 14.1027i) q^{6} +30.2349i q^{7} +(55.4067 - 32.0328i) q^{8} +50.9292 q^{9} +(114.504 + 136.406i) q^{10} -22.6187i q^{11} +(86.4121 + 15.2016i) q^{12} +30.9952 q^{13} +(92.6298 - 77.7568i) q^{14} +244.154i q^{15} +(-240.630 - 87.3674i) q^{16} +139.235 q^{17} +(-130.977 - 156.030i) q^{18} +262.192i q^{19} +(123.427 - 701.606i) q^{20} +165.799 q^{21} +(-69.2963 + 58.1698i) q^{22} -110.304i q^{23} +(-175.658 - 303.833i) q^{24} +1357.36 q^{25} +(-79.7119 - 94.9589i) q^{26} -723.458i q^{27} +(-476.442 - 83.8160i) q^{28} +1586.56 q^{29} +(748.009 - 627.905i) q^{30} +1375.02i q^{31} +(351.177 + 961.900i) q^{32} -124.034 q^{33} +(-358.078 - 426.570i) q^{34} -1346.17i q^{35} +(-141.184 + 802.543i) q^{36} -1136.05 q^{37} +(803.269 - 674.292i) q^{38} -169.968i q^{39} +(-2466.91 + 1426.22i) q^{40} +279.608 q^{41} +(-426.394 - 507.953i) q^{42} +1948.26i q^{43} +(356.426 + 62.7027i) q^{44} -2267.56 q^{45} +(-337.936 + 283.675i) q^{46} +3539.82i q^{47} +(-479.096 + 1319.54i) q^{48} +1486.85 q^{49} +(-3490.81 - 4158.52i) q^{50} -763.520i q^{51} +(-85.9234 + 488.422i) q^{52} -1622.94 q^{53} +(-2216.44 + 1860.56i) q^{54} +1007.07i q^{55} +(968.508 + 1675.22i) q^{56} +1437.78 q^{57} +(-4080.23 - 4860.69i) q^{58} -2511.03i q^{59} +(-3847.39 - 676.834i) q^{60} +2934.00 q^{61} +(4212.60 - 3536.21i) q^{62} +1539.84i q^{63} +(2043.80 - 3549.66i) q^{64} -1380.02 q^{65} +(318.985 + 379.999i) q^{66} +3785.29i q^{67} +(-385.981 + 2194.06i) q^{68} -604.873 q^{69} +(-4124.23 + 3462.02i) q^{70} +5279.33i q^{71} +(2821.82 - 1631.40i) q^{72} -677.672 q^{73} +(2921.65 + 3480.50i) q^{74} -7443.36i q^{75} +(-4131.62 - 726.836i) q^{76} +683.875 q^{77} +(-520.725 + 437.115i) q^{78} +10397.5i q^{79} +(10713.8 + 3889.93i) q^{80} +158.041 q^{81} +(-719.083 - 856.626i) q^{82} -13523.6i q^{83} +(-459.621 + 2612.66i) q^{84} -6199.26 q^{85} +(5968.83 - 5010.45i) q^{86} -8700.18i q^{87} +(-724.540 - 1253.23i) q^{88} -6551.94 q^{89} +(5831.60 + 6947.05i) q^{90} +937.136i q^{91} +(1738.17 + 305.780i) q^{92} +7540.17 q^{93} +(10844.8 - 9103.54i) q^{94} -11673.8i q^{95} +(5274.76 - 1925.75i) q^{96} +7011.29 q^{97} +(-3823.81 - 4555.22i) q^{98} -1151.95i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) $ 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

Character values

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

$n$	$5$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.57175	−	3.06367i	−0.642939	−	0.765918i
$2$	−2.57175	−	3.06367i	−0.642939	−	0.765918i
$3$		−	5.48369i		−	0.609299i	−0.952465	−	0.304649i	$-0.901461\pi$
$3$		−	5.48369i		−	0.609299i	0.952465	−	0.304649i	$-0.0985393\pi$
$4$	−2.77216	+	15.7580i	−0.173260	+	0.984876i
$5$	−44.5238			−1.78095			−0.890475	−	0.455032i	$-0.849628\pi$
$5$	−44.5238			−1.78095			−0.890475	+	0.455032i	$0.849628\pi$
$6$	−16.8002	+	14.1027i	−0.466673	+	0.391742i
$7$			30.2349i			0.617039i	0.951218	+	0.308520i	$0.0998335\pi$
$7$			30.2349i			0.617039i	−0.951218	+	0.308520i	$0.900166\pi$
$8$	55.4067	−	32.0328i	0.865730	−	0.500512i
$9$	50.9292			0.628755
$10$	114.504	+	136.406i	1.14504	+	1.36406i
$11$		−	22.6187i		−	0.186932i	−0.995622	−	0.0934658i	$-0.970205\pi$
$11$		−	22.6187i		−	0.186932i	0.995622	−	0.0934658i	$-0.0297946\pi$
$12$	86.4121	+	15.2016i	0.600084	+	0.105567i
$13$	30.9952			0.183403			0.0917016	−	0.995787i	$-0.470769\pi$
$13$	30.9952			0.183403			0.0917016	+	0.995787i	$0.470769\pi$
$14$	92.6298	−	77.7568i	0.472601	−	0.396718i
$15$			244.154i			1.08513i
$16$	−240.630	−	87.3674i	−0.939962	−	0.341279i
$17$	139.235			0.481781			0.240891	−	0.970552i	$-0.422560\pi$
$17$	139.235			0.481781			0.240891	+	0.970552i	$0.422560\pi$
$18$	−130.977	−	156.030i	−0.404251	−	0.481575i
$19$			262.192i			0.726293i	0.931732	+	0.363146i	$0.118297\pi$
$19$			262.192i			0.726293i	−0.931732	+	0.363146i	$0.881703\pi$
$20$	123.427	−	701.606i	0.308567	−	1.75402i
$21$	165.799			0.375961
$22$	−69.2963	+	58.1698i	−0.143174	+	0.120186i
$23$		−	110.304i		−	0.208514i
$23$		−	110.304i		−	0.208514i
$24$	−175.658	−	303.833i	−0.304961	−	0.527488i
$25$	1357.36			2.17178
$26$	−79.7119	−	94.9589i	−0.117917	−	0.140472i
$27$		−	723.458i		−	0.992398i
$28$	−476.442	−	83.8160i	−0.607707	−	0.106908i
$29$	1586.56			1.88651			0.943256	−	0.332067i	$-0.107746\pi$
$29$	1586.56			1.88651			0.943256	+	0.332067i	$0.107746\pi$
$30$	748.009	−	627.905i	0.831121	−	0.697672i
$31$			1375.02i			1.43082i	0.698705	+	0.715409i	$0.253760\pi$
$31$			1375.02i			1.43082i	−0.698705	+	0.715409i	$0.746240\pi$
$32$	351.177	+	961.900i	0.342946	+	0.939355i
$33$	−124.034			−0.113897
$34$	−358.078	−	426.570i	−0.309756	−	0.369005i
$35$		−	1346.17i		−	1.09892i
$36$	−141.184	+	802.543i	−0.108938	+	0.619246i
$37$	−1136.05			−0.829842			−0.414921	−	0.909857i	$-0.636191\pi$
$37$	−1136.05			−0.829842			−0.414921	+	0.909857i	$0.636191\pi$
$38$	803.269	−	674.292i	0.556280	−	0.466962i
$39$		−	169.968i		−	0.111747i
$40$	−2466.91	+	1426.22i	−1.54182	+	0.891387i
$41$	279.608			0.166334			0.0831671	−	0.996536i	$-0.473496\pi$
$41$	279.608			0.166334			0.0831671	+	0.996536i	$0.473496\pi$
$42$	−426.394	−	507.953i	−0.241720	−	0.287955i
$43$			1948.26i			1.05368i	0.849963	+	0.526842i	$0.176624\pi$
$43$			1948.26i			1.05368i	−0.849963	+	0.526842i	$0.823376\pi$
$44$	356.426	+	62.7027i	0.184104	+	0.0323877i
$45$	−2267.56			−1.11978
$46$	−337.936	+	283.675i	−0.159705	+	0.134062i
$47$			3539.82i			1.60245i	0.598362	+	0.801226i	$0.295819\pi$
$47$			3539.82i			1.60245i	−0.598362	+	0.801226i	$0.704181\pi$
$48$	−479.096	+	1319.54i	−0.207941	+	0.572718i
$49$	1486.85			0.619263
$50$	−3490.81	−	4158.52i	−1.39632	−	1.66341i
$51$		−	763.520i		−	0.293549i
$52$	−85.9234	+	488.422i	−0.0317764	+	0.180629i
$53$	−1622.94			−0.577764			−0.288882	−	0.957365i	$-0.593284\pi$
$53$	−1622.94			−0.577764			−0.288882	+	0.957365i	$0.593284\pi$
$54$	−2216.44	+	1860.56i	−0.760096	+	0.638051i
$55$			1007.07i			0.332916i
$56$	968.508	+	1675.22i	0.308836	+	0.534189i
$57$	1437.78			0.442529
$58$	−4080.23	−	4860.69i	−1.21291	−	1.44491i
$59$		−	2511.03i		−	0.721352i	−0.932691	−	0.360676i	$-0.882546\pi$
$59$		−	2511.03i		−	0.721352i	0.932691	−	0.360676i	$-0.117454\pi$
$60$	−3847.39	−	676.834i	−1.06872	−	0.188010i
$61$	2934.00			0.788499			0.394249	−	0.919004i	$-0.371005\pi$
$61$	2934.00			0.788499			0.394249	+	0.919004i	$0.371005\pi$
$62$	4212.60	−	3536.21i	1.09589	−	0.919929i
$63$			1539.84i			0.387966i
$64$	2043.80	−	3549.66i	0.498975	−	0.866616i
$65$	−1380.02			−0.326632
$66$	318.985	+	379.999i	0.0732289	+	0.0872359i
$67$			3785.29i			0.843237i	0.906773	+	0.421618i	$0.138538\pi$
$67$			3785.29i			0.843237i	−0.906773	+	0.421618i	$0.861462\pi$
$68$	−385.981	+	2194.06i	−0.0834734	+	0.474495i
$69$	−604.873			−0.127048
$70$	−4124.23	+	3462.02i	−0.841679	+	0.706535i
$71$			5279.33i			1.04728i	0.851940	+	0.523639i	$0.175426\pi$
$71$			5279.33i			1.04728i	−0.851940	+	0.523639i	$0.824574\pi$
$72$	2821.82	−	1631.40i	0.544332	−	0.314700i
$73$	−677.672			−0.127167			−0.0635834	−	0.997977i	$-0.520253\pi$
$73$	−677.672			−0.127167			−0.0635834	+	0.997977i	$0.520253\pi$
$74$	2921.65	+	3480.50i	0.533538	+	0.635591i
$75$		−	7443.36i		−	1.32326i
$76$	−4131.62	−	726.836i	−0.715308	−	0.125837i
$77$	683.875			0.115344
$78$	−520.725	+	437.115i	−0.0855893	+	0.0718467i
$79$			10397.5i			1.66600i	0.553275	+	0.832999i	$0.313378\pi$
$79$			10397.5i			1.66600i	−0.553275	+	0.832999i	$0.686622\pi$
$80$	10713.8	+	3889.93i	1.67403	+	0.607801i
$81$	158.041			0.0240880
$82$	−719.083	−	856.626i	−0.106943	−	0.127398i
$83$		−	13523.6i		−	1.96307i	−0.191289	−	0.981534i	$-0.561267\pi$
$83$		−	13523.6i		−	1.96307i	0.191289	−	0.981534i	$-0.438733\pi$
$84$	−459.621	+	2612.66i	−0.0651390	+	0.370275i
$85$	−6199.26			−0.858029
$86$	5968.83	−	5010.45i	0.807035	−	0.677454i
$87$		−	8700.18i		−	1.14945i
$88$	−724.540	−	1253.23i	−0.0935615	−	0.161832i
$89$	−6551.94			−0.827160			−0.413580	−	0.910468i	$-0.635722\pi$
$89$	−6551.94			−0.827160			−0.413580	+	0.910468i	$0.635722\pi$
$90$	5831.60	+	6947.05i	0.719951	+	0.857660i
$91$			937.136i			0.113167i
$92$	1738.17	+	305.780i	0.205361	+	0.0361272i
$93$	7540.17			0.871796
$94$	10844.8	−	9103.54i	1.22735	−	1.03028i
$95$		−	11673.8i		−	1.29349i
$96$	5274.76	−	1925.75i	0.572348	−	0.208957i
$97$	7011.29			0.745168			0.372584	−	0.927998i	$-0.378472\pi$
$97$	7011.29			0.745168			0.372584	+	0.927998i	$0.378472\pi$
$98$	−3823.81	−	4555.22i	−0.398148	−	0.474304i
$99$		−	1151.95i		−	0.117534i
$100$	−3762.83	+	21389.4i	−0.376283	+	2.13894i
$101$	−1117.76			−0.109573			−0.0547865	−	0.998498i	$-0.517448\pi$
$101$	−1117.76			−0.109573			−0.0547865	+	0.998498i	$0.517448\pi$
$102$	−2339.18	+	1963.59i	−0.224834	+	0.188734i
$103$		−	7418.69i		−	0.699283i	−0.936884	−	0.349642i	$-0.886303\pi$
$103$		−	7418.69i		−	0.699283i	0.936884	−	0.349642i	$-0.113697\pi$
$104$	1717.34	−	992.861i	0.158778	−	0.0917956i
$105$	−7381.99			−0.669568
$106$	4173.80	+	4972.15i	0.371467	+	0.442520i
$107$		−	3121.54i		−	0.272647i	−0.990664	−	0.136324i	$-0.956471\pi$
$107$		−	3121.54i		−	0.272647i	0.990664	−	0.136324i	$-0.0435287\pi$
$108$	11400.3	+	2005.54i	0.977390	+	0.171943i
$109$	−9546.71			−0.803527			−0.401764	−	0.915743i	$-0.631603\pi$
$109$	−9546.71			−0.803527			−0.401764	+	0.915743i	$0.631603\pi$
$110$	3085.33	−	2589.94i	0.254986	−	0.214044i
$111$			6229.77i			0.505622i
$112$	2641.55	−	7275.44i	0.210582	−	0.579993i
$113$	13939.7			1.09168			0.545842	−	0.837888i	$-0.316210\pi$
$113$	13939.7			1.09168			0.545842	+	0.837888i	$0.316210\pi$
$114$	−3697.61	−	4404.88i	−0.284519	−	0.338941i
$115$			4911.15i			0.371354i
$116$	−4398.18	+	25001.0i	−0.326857	+	1.85798i
$117$	1578.56			0.115316
$118$	−7692.96	+	6457.75i	−0.552496	+	0.463785i
$119$			4209.75i			0.297278i
$120$	7820.94	+	13527.8i	0.543121	+	0.939430i
$121$	14129.4			0.965057
$122$	−7545.54	−	8988.82i	−0.506956	−	0.603925i
$123$		−	1533.28i		−	0.101347i
$124$	−21667.5	−	3811.76i	−1.40918	−	0.247903i
$125$	−32607.6			−2.08689
$126$	4717.56	−	3960.09i	0.297150	−	0.249439i
$127$		−	16742.2i		−	1.03802i	−0.854769	−	0.519008i	$-0.826301\pi$
$127$		−	16742.2i		−	1.03802i	0.854769	−	0.519008i	$-0.173699\pi$
$128$	−16131.1	+	2867.32i	−0.984567	+	0.175007i
$129$	10683.7			0.642008
$130$	3549.07	+	4227.93i	0.210004	+	0.250173i
$131$			12176.5i			0.709547i	0.934952	+	0.354774i	$0.115442\pi$
$131$			12176.5i			0.709547i	−0.934952	+	0.354774i	$0.884558\pi$
$132$	343.842	−	1954.53i	0.0197338	−	0.112175i
$133$	−7927.34			−0.448151
$134$	11596.9	−	9734.84i	0.645850	−	0.542150i
$135$			32211.1i			1.76741i
$136$	7714.54	−	4460.08i	0.417092	−	0.241137i
$137$	2440.37			0.130021			0.0650107	−	0.997885i	$-0.479292\pi$
$137$	2440.37			0.130021			0.0650107	+	0.997885i	$0.479292\pi$
$138$	1555.59	+	1853.13i	0.0816838	+	0.0973080i
$139$			10164.2i			0.526072i	0.964786	+	0.263036i	$0.0847238\pi$
$139$			10164.2i			0.526072i	−0.964786	+	0.263036i	$0.915276\pi$
$140$	21213.0	+	3731.80i	1.08230	+	0.190398i
$141$	19411.3			0.976372
$142$	16174.1	−	13577.1i	0.802128	−	0.673335i
$143$		−	701.071i		−	0.0342839i
$144$	−12255.1	−	4449.55i	−0.591006	−	0.214581i
$145$	−70639.4			−3.35978
$146$	1742.81	+	2076.16i	0.0817604	+	0.0973993i
$147$		−	8153.42i		−	0.377316i
$148$	3149.32	−	17902.0i	0.143778	−	0.817292i
$149$	21021.7			0.946879			0.473440	−	0.880826i	$-0.343012\pi$
$149$	21021.7			0.946879			0.473440	+	0.880826i	$0.343012\pi$
$150$	−22804.0	+	19142.5i	−1.01351	+	0.850778i
$151$		−	28768.0i		−	1.26170i	−0.775904	−	0.630851i	$-0.782706\pi$
$151$		−	28768.0i		−	1.26170i	0.775904	−	0.630851i	$-0.217294\pi$
$152$	8398.72	+	14527.2i	0.363518	+	0.628773i
$153$	7091.11			0.302922
$154$	−1758.76	−	2095.17i	−0.0741592	−	0.0883441i
$155$		−	61220.9i		−	2.54822i
$156$	2678.36	+	471.177i	0.110057	+	0.0193613i
$157$	−17198.0			−0.697715			−0.348858	−	0.937176i	$-0.613430\pi$
$157$	−17198.0			−0.697715			−0.348858	+	0.937176i	$0.613430\pi$
$158$	31854.5	−	26739.8i	1.27602	−	1.07113i
$159$			8899.69i			0.352031i
$160$	−15635.7	−	42827.4i	−0.610770	−	1.67294i
$161$	3335.04			0.128662
$162$	−406.443	−	484.186i	−0.0154871	−	0.0184494i
$163$			16825.0i			0.633258i	0.948550	+	0.316629i	$0.102551\pi$
$163$			16825.0i			0.633258i	−0.948550	+	0.316629i	$0.897449\pi$
$164$	−775.117	+	4406.06i	−0.0288190	+	0.163819i
$165$	5522.46			0.202845
$166$	−41431.8	+	34779.3i	−1.50355	+	1.26213i
$167$		−	22936.3i		−	0.822413i	−0.911542	−	0.411207i	$-0.865107\pi$
$167$		−	22936.3i		−	0.822413i	0.911542	−	0.411207i	$-0.134893\pi$
$168$	9186.37	−	5311.00i	0.325481	−	0.188173i
$169$	−27600.3			−0.966363
$170$	15943.0	+	18992.5i	0.551660	+	0.657179i
$171$			13353.2i			0.456660i
$172$	−30700.7	−	5400.89i	−1.03775	−	0.182561i
$173$	−26139.9			−0.873398			−0.436699	−	0.899608i	$-0.643853\pi$
$173$	−26139.9			−0.873398			−0.436699	+	0.899608i	$0.643853\pi$
$174$	−26654.5	+	22374.7i	−0.880383	+	0.739025i
$175$			41039.8i			1.34008i
$176$	−1976.14	+	5442.75i	−0.0637958	+	0.175709i
$177$	−13769.7			−0.439519
$178$	16850.0	+	20073.0i	0.531813	+	0.633537i
$179$			41969.6i			1.30987i	0.755685	+	0.654935i	$0.227304\pi$
$179$			41969.6i			1.30987i	−0.755685	+	0.654935i	$0.772696\pi$
$180$	6286.03	−	35732.2i	0.194013	−	1.10285i
$181$	6103.48			0.186303			0.0931516	−	0.995652i	$-0.470306\pi$
$181$	6103.48			0.186303			0.0931516	+	0.995652i	$0.470306\pi$
$182$	2871.08	−	2410.08i	0.0866766	−	0.0727594i
$183$		−	16089.2i		−	0.480431i
$184$	−3533.35	−	6111.59i	−0.104364	−	0.180517i
$185$	50581.4			1.47791
$186$	−19391.5	−	23100.6i	−0.560511	−	0.667724i
$187$		−	3149.31i		−	0.0900602i
$188$	−55780.5	−	9812.93i	−1.57822	−	0.277641i
$189$	21873.7			0.612349
$190$	−35764.5	+	30022.0i	−0.990707	+	0.831635i
$191$			59907.4i			1.64215i	0.570818	+	0.821076i	$0.306626\pi$
$191$			59907.4i			1.64215i	−0.570818	+	0.821076i	$0.693374\pi$
$192$	−19465.2	−	11207.6i	−0.528028	−	0.304025i
$193$	68234.5			1.83185			0.915923	−	0.401353i	$-0.131460\pi$
$193$	68234.5			1.83185			0.915923	+	0.401353i	$0.131460\pi$
$194$	−18031.3	−	21480.3i	−0.479097	−	0.570738i
$195$			7567.60i			0.199016i
$196$	−4121.78	+	23429.8i	−0.107293	+	0.609897i
$197$	74100.3			1.90936			0.954680	−	0.297634i	$-0.0961976\pi$
$197$	74100.3			1.90936			0.954680	+	0.297634i	$0.0961976\pi$
$198$	−3529.20	+	2962.54i	−0.0900215	+	0.0755673i
$199$			22922.2i			0.578830i	0.957204	+	0.289415i	$0.0934607\pi$
$199$			22922.2i			0.578830i	−0.957204	+	0.289415i	$0.906539\pi$
$200$	75207.1	−	43480.2i	1.88018	−	1.08700i
$201$	20757.4			0.513783
$202$	2874.59	+	3424.43i	0.0704488	+	0.0839240i
$203$			47969.4i			1.16405i
$204$	12031.6	+	2116.60i	0.289109	+	0.0508602i
$205$	−12449.2			−0.296233
$206$	−22728.4	+	19079.1i	−0.535593	+	0.449596i
$207$		−	5617.70i		−	0.131104i
$208$	−7458.37	−	2707.97i	−0.172392	−	0.0625917i
$209$	5930.44			0.135767
$210$	18984.7	+	22616.0i	0.430491	+	0.512834i
$211$		−	15098.1i		−	0.339123i	−0.985520	−	0.169562i	$-0.945765\pi$
$211$		−	15098.1i		−	0.339123i	0.985520	−	0.169562i	$-0.0542351\pi$
$212$	4499.04	−	25574.3i	0.100103	−	0.569026i
$213$	28950.2			0.638105
$214$	−9563.37	+	8027.83i	−0.208825	+	0.175295i
$215$		−	86743.9i		−	1.87656i
$216$	−23174.4	−	40084.4i	−0.496707	−	0.859149i
$217$	−41573.5			−0.882871
$218$	24551.8	+	29248.0i	0.516619	+	0.615436i
$219$			3716.14i			0.0774826i
$220$	−15869.4	−	2791.76i	−0.327881	−	0.0576809i
$221$	4315.60			0.0883603
$222$	19086.0	−	16021.4i	0.387265	−	0.325084i
$223$			60056.0i			1.20767i	0.797111	+	0.603833i	$0.206361\pi$
$223$			60056.0i			1.20767i	−0.797111	+	0.603833i	$0.793639\pi$
$224$	−29083.0	+	10617.8i	−0.579619	+	0.211611i
$225$	69129.4			1.36552
$226$	−35849.5	−	42706.7i	−0.701886	−	0.836140i
$227$			59414.8i			1.15304i	0.817084	+	0.576518i	$0.195589\pi$
$227$			59414.8i			1.15304i	−0.817084	+	0.576518i	$0.804411\pi$
$228$	−3985.74	+	22656.5i	−0.0766725	+	0.435836i
$229$	−69073.8			−1.31717			−0.658586	−	0.752505i	$-0.728845\pi$
$229$	−69073.8			−1.31717			−0.658586	+	0.752505i	$0.728845\pi$
$230$	15046.2	−	12630.3i	0.284426	−	0.238758i
$231$		−	3750.16i		−	0.0702790i
$232$	87905.8	−	50821.8i	1.63321	−	0.944222i
$233$	1533.44			0.0282458			0.0141229	−	0.999900i	$-0.495504\pi$
$233$	1533.44			0.0282458			0.0141229	+	0.999900i	$0.495504\pi$
$234$	−4059.66	−	4836.18i	−0.0741409	−	0.0883224i
$235$		−	157606.i		−	2.85389i
$236$	39568.8	+	6960.96i	0.710443	+	0.124981i
$237$	57016.6			1.01509
$238$	12897.3	−	10826.5i	0.227690	−	0.191131i
$239$			50659.3i			0.886877i	0.896305	+	0.443439i	$0.146242\pi$
$239$			50659.3i			0.886877i	−0.896305	+	0.443439i	$0.853758\pi$
$240$	21331.1	−	58750.9i	0.370332	−	1.01998i
$241$	58870.1			1.01359			0.506793	−	0.862068i	$-0.330831\pi$
$241$	58870.1			1.01359			0.506793	+	0.862068i	$0.330831\pi$
$242$	−36337.3	−	43287.8i	−0.620472	−	0.739154i
$243$		−	59466.8i		−	1.00708i
$244$	−8133.52	+	46234.1i	−0.136615	+	0.776573i
$245$	−66200.1			−1.10288
$246$	−4697.47	+	3943.22i	−0.0776236	+	0.0651600i
$247$			8126.67i			0.133204i
$248$	44045.6	+	76185.1i	0.716142	+	1.23870i
$249$	−74159.1			−1.19609
$250$	83858.8	+	99899.0i	1.34174	+	1.59838i
$251$		−	60851.2i		−	0.965876i	−0.875654	−	0.482938i	$-0.839570\pi$
$251$		−	60851.2i		−	0.965876i	0.875654	−	0.482938i	$-0.160430\pi$
$252$	−24264.8	−	4268.68i	−0.382099	−	0.0672190i
$253$	−2494.94			−0.0389779
$254$	−51292.5	+	43056.7i	−0.795035	+	0.667381i
$255$			33994.8i			0.522796i
$256$	50269.9	+	42046.5i	0.767057	+	0.641579i
$257$	−77955.9			−1.18027			−0.590137	−	0.807303i	$-0.700926\pi$
$257$	−77955.9			−1.18027			−0.590137	+	0.807303i	$0.700926\pi$
$258$	−27475.7	−	32731.2i	−0.412772	−	0.491725i
$259$		−	34348.5i		−	0.512045i
$260$	3825.63	−	21746.4i	0.0565922	−	0.321692i
$261$	80802.0			1.18615
$262$	37304.9	−	31315.1i	0.543455	−	0.456195i
$263$		−	62647.1i		−	0.905711i	−0.891584	−	0.452856i	$-0.850405\pi$
$263$		−	62647.1i		−	0.905711i	0.891584	−	0.452856i	$-0.149595\pi$
$264$	−6872.31	+	3973.15i	−0.0986042	+	0.0570069i
$265$	72259.3			1.02897
$266$	20387.2	+	24286.8i	0.288133	+	0.343247i
$267$			35928.8i			0.503988i
$268$	−59648.7	−	10493.4i	−0.830484	−	0.146099i
$269$	−94328.6			−1.30358			−0.651791	−	0.758398i	$-0.725982\pi$
$269$	−94328.6			−1.30358			−0.651791	+	0.758398i	$0.725982\pi$
$270$	98684.2	−	82839.0i	1.35369	−	1.13634i
$271$			136475.i			1.85829i	0.369711	+	0.929147i	$0.379457\pi$
$271$			136475.i			1.85829i	−0.369711	+	0.929147i	$0.620543\pi$
$272$	−33504.1	−	12164.6i	−0.452856	−	0.164422i
$273$	5138.96			0.0689525
$274$	−6276.04	−	7476.50i	−0.0835958	−	0.0995858i
$275$		−	30701.8i		−	0.405975i
$276$	1676.80	−	9531.61i	0.0220122	−	0.125126i
$277$	133086.			1.73450			0.867249	−	0.497875i	$-0.165886\pi$
$277$	133086.			1.73450			0.867249	+	0.497875i	$0.165886\pi$
$278$	31139.9	−	26139.9i	0.402928	−	0.338232i
$279$			70028.5i			0.899635i
$280$	−43121.6	−	74586.9i	−0.550021	−	0.951364i
$281$	−60208.4			−0.762507			−0.381254	−	0.924470i	$-0.624508\pi$
$281$	−60208.4			−0.762507			−0.381254	+	0.924470i	$0.624508\pi$
$282$	−49921.0	−	59469.7i	−0.627747	−	0.747821i
$283$		−	62011.7i		−	0.774285i	−0.922020	−	0.387142i	$-0.873462\pi$
$283$		−	62011.7i		−	0.774285i	0.922020	−	0.387142i	$-0.126538\pi$
$284$	−83191.7	−	14635.1i	−1.03144	−	0.181451i
$285$	−64015.2			−0.788122
$286$	−2147.85	+	1802.98i	−0.0262586	+	0.0220424i
$287$			8453.92i			0.102635i
$288$	17885.1	+	48988.7i	0.215629	+	0.590624i
$289$	−64134.7			−0.767887
$290$	181667.	+	216416.i	2.16013	+	2.57332i
$291$		−	38447.7i		−	0.454030i
$292$	1878.61	−	10678.8i	0.0220329	−	0.125244i
$293$	−104530.			−1.21760			−0.608799	−	0.793324i	$-0.708348\pi$
$293$	−104530.			−1.21760			−0.608799	+	0.793324i	$0.708348\pi$
$294$	−24979.4	+	20968.6i	−0.288993	+	0.242591i
$295$			111800.i			1.28469i
$296$	−62945.0	+	36391.0i	−0.718419	+	0.415346i
$297$	−16363.7			−0.185511
$298$	−54062.6	−	64403.5i	−0.608785	−	0.725232i
$299$		−	3418.89i		−	0.0382422i
$300$	117293.	+	20634.2i	1.30325	+	0.229269i
$301$	−58905.5			−0.650164
$302$	−88135.8	+	73984.4i	−0.966359	+	0.811196i
$303$			6129.42i			0.0667627i
$304$	22907.0	−	63091.2i	0.247868	−	0.682687i
$305$	−130633.			−1.40428
$306$	−18236.6	−	21724.8i	−0.194761	−	0.232014i
$307$			53532.5i			0.567991i	0.958826	+	0.283995i	$0.0916600\pi$
$307$			53532.5i			0.567991i	−0.958826	+	0.283995i	$0.908340\pi$
$308$	−1895.81	+	10776.5i	−0.0199845	+	0.113600i
$309$	−40681.8			−0.426072
$310$	−187561.	+	157445.i	−1.95172	+	1.63835i
$311$		−	62979.4i		−	0.651145i	−0.945517	−	0.325573i	$-0.894443\pi$
$311$		−	62979.4i		−	0.651145i	0.945517	−	0.325573i	$-0.105557\pi$
$312$	−5444.54	−	9417.35i	−0.0559309	−	0.0967430i
$313$	−13166.2			−0.134391			−0.0671956	−	0.997740i	$-0.521405\pi$
$313$	−13166.2			−0.134391			−0.0671956	+	0.997740i	$0.521405\pi$
$314$	44229.0	+	52688.9i	0.448588	+	0.534392i
$315$		−	68559.4i		−	0.690949i
$316$	−163844.	−	28823.5i	−1.64080	−	0.288650i
$317$	85277.8			0.848628			0.424314	−	0.905515i	$-0.360515\pi$
$317$	85277.8			0.848628			0.424314	+	0.905515i	$0.360515\pi$
$318$	27265.7	−	22887.8i	0.269627	−	0.226334i
$319$		−	35885.9i		−	0.352649i
$320$	−90997.8	+	158044.i	−0.888650	+	1.54340i
$321$	−17117.5			−0.166124
$322$	−8576.89	−	10217.5i	−0.0827215	−	0.0985442i
$323$			36506.2i			0.349914i
$324$	−438.115	+	2490.41i	−0.00417348	+	0.0237237i
$325$	42071.7			0.398312
$326$	51546.3	−	43269.8i	0.485023	−	0.407146i
$327$			52351.2i			0.489588i
$328$	15492.1	−	8956.61i	0.144000	−	0.0832523i
$329$	−107026.			−0.988775
$330$	−14202.4	−	16919.0i	−0.130417	−	0.155363i
$331$		−	93810.9i		−	0.856244i	−0.903721	−	0.428122i	$-0.859175\pi$
$331$		−	93810.9i		−	0.856244i	0.903721	−	0.428122i	$-0.140825\pi$
$332$	213105.	+	37489.5i	1.93338	+	0.340121i
$333$	−57858.3			−0.521768
$334$	−70269.2	+	58986.5i	−0.629901	+	0.528761i
$335$		−	168535.i		−	1.50176i
$336$	−39896.2	−	14485.4i	−0.353389	−	0.128308i
$337$	−54093.7			−0.476307			−0.238153	−	0.971228i	$-0.576542\pi$
$337$	−54093.7			−0.476307			−0.238153	+	0.971228i	$0.576542\pi$
$338$	70981.2	+	84558.2i	0.621312	+	0.740155i
$339$		−	76441.1i		−	0.665162i
$340$	17185.3	−	97688.0i	0.148662	−	0.845052i
$341$	31101.1			0.267465
$342$	40909.8	−	34341.1i	0.349764	−	0.293604i
$343$			117549.i			0.999148i
$344$	62408.2	+	107947.i	0.527381	+	0.912205i
$345$	26931.2			0.226265
$346$	67225.5	+	80084.1i	0.561541	+	0.668951i
$347$		−	154867.i		−	1.28617i	−0.765794	−	0.643086i	$-0.777654\pi$
$347$		−	154867.i		−	1.28617i	0.765794	−	0.643086i	$-0.222346\pi$
$348$	137098.	+	24118.3i	1.13206	+	0.199153i
$349$	159957.			1.31327			0.656634	−	0.754209i	$-0.271980\pi$
$349$	159957.			1.31327			0.656634	+	0.754209i	$0.271980\pi$
$350$	125732.	−	105544.i	1.02639	−	0.861586i
$351$		−	22423.7i		−	0.182009i
$352$	21756.9	−	7943.17i	0.175595	−	0.0641075i
$353$	−115356.			−0.925745			−0.462872	−	0.886425i	$-0.653181\pi$
$353$	−115356.			−0.925745			−0.462872	+	0.886425i	$0.653181\pi$
$354$	35412.3	+	42185.8i	0.282584	+	0.336635i
$355$		−	235055.i		−	1.86515i
$356$	18163.0	−	103246.i	0.143314	−	0.814651i
$357$	23085.0			0.181131
$358$	128581.	−	107935.i	1.00325	−	0.842166i
$359$			123700.i			0.959798i	0.877324	+	0.479899i	$0.159327\pi$
$359$			123700.i			0.959798i	−0.877324	+	0.479899i	$0.840673\pi$
$360$	−125638.	+	72636.2i	−0.969428	+	0.560464i
$361$	61576.6			0.472499
$362$	−15696.7	−	18699.1i	−0.119782	−	0.142693i
$363$		−	77481.2i		−	0.588008i
$364$	−14767.4	−	2597.89i	−0.111455	−	0.0196073i
$365$	30172.5			0.226478
$366$	−49291.9	+	41377.4i	−0.367971	+	0.308888i
$367$			47343.6i			0.351503i	0.984435	+	0.175752i	$0.0562355\pi$
$367$			47343.6i			0.351503i	−0.984435	+	0.175752i	$0.943764\pi$
$368$	−9636.99	+	26542.5i	−0.0711616	+	0.195996i
$369$	14240.2			0.104583
$370$	−130083.	−	154965.i	−0.950204	−	1.13196i
$371$		−	49069.4i		−	0.356503i
$372$	−20902.5	+	118818.i	−0.151047	+	0.858611i
$373$	116789.			0.839427			0.419714	−	0.907657i	$-0.362130\pi$
$373$	116789.			0.839427			0.419714	+	0.907657i	$0.362130\pi$
$374$	−9648.46	+	8099.26i	−0.0689787	+	0.0579032i
$375$			178810.i			1.27154i
$376$	113390.	+	196130.i	0.802047	+	1.38729i
$377$	49175.5			0.345992
$378$	−56253.8	−	67013.8i	−0.393703	−	0.469009i
$379$			21564.2i			0.150126i	0.997179	+	0.0750630i	$0.0239158\pi$
$379$			21564.2i			0.150126i	−0.997179	+	0.0750630i	$0.976084\pi$
$380$	183955.	+	32361.5i	1.27393	+	0.224110i
$381$	−91808.8			−0.632462
$382$	183536.	−	154067.i	1.25775	−	1.05580i
$383$			144457.i			0.984784i	0.870374	+	0.492392i	$0.163877\pi$
$383$			144457.i			0.984784i	−0.870374	+	0.492392i	$0.836123\pi$
$384$	15723.5	+	88458.2i	0.106632	+	0.599896i
$385$	−30448.7			−0.205422
$386$	−175482.	−	209048.i	−1.17776	−	1.40304i
$387$			99223.3i			0.662509i
$388$	−19436.4	+	110484.i	−0.129108	+	0.733898i
$389$	−70461.2			−0.465641			−0.232820	−	0.972520i	$-0.574795\pi$
$389$	−70461.2			−0.465641			−0.232820	+	0.972520i	$0.574795\pi$
$390$	23184.6	−	19462.0i	0.152430	−	0.127955i
$391$		−	15358.2i		−	0.100458i
$392$	82381.4	−	47627.9i	0.536114	−	0.309949i
$393$	66772.3			0.432326
$394$	−190568.	−	227019.i	−1.22760	−	1.46241i
$395$		−	462935.i		−	2.96706i
$396$	18152.5	+	3193.39i	0.115757	+	0.0203640i
$397$	−148304.			−0.940960			−0.470480	−	0.882411i	$-0.655919\pi$
$397$	−148304.			−0.940960			−0.470480	+	0.882411i	$0.655919\pi$
$398$	70226.2	−	58950.3i	0.443336	−	0.372152i
$399$			43471.1i			0.273058i
$400$	−326623.	−	118589.i	−2.04139	−	0.741184i
$401$	254274.			1.58130			0.790648	−	0.612272i	$-0.209744\pi$
$401$	254274.			1.58130			0.790648	+	0.612272i	$0.209744\pi$
$402$	−53382.8	−	63593.7i	−0.330331	−	0.393516i
$403$			42618.9i			0.262417i
$404$	3098.59	−	17613.6i	0.0189846	−	0.107916i
$405$	−7036.58			−0.0428994
$406$	146962.	−	123365.i	0.891568	−	0.748414i
$407$			25696.1i			0.155124i
$408$	−24457.7	−	42304.1i	−0.146925	−	0.254134i
$409$	95983.2			0.573784			0.286892	−	0.957963i	$-0.407378\pi$
$409$	95983.2			0.573784			0.286892	+	0.957963i	$0.407378\pi$
$410$	32016.3	+	38140.2i	0.190460	+	0.226890i
$411$		−	13382.2i		−	0.0792219i
$412$	116904.	+	20565.8i	0.688707	+	0.121158i
$413$	75920.7			0.445103
$414$	−17210.8	+	14447.3i	−0.100415	+	0.0842921i
$415$			602120.i			3.49613i
$416$	10884.8	+	29814.2i	0.0628975	+	0.172281i
$417$	55737.5			0.320535
$418$	−15251.6	−	18168.9i	−0.0872899	−	0.103986i
$419$			285148.i			1.62421i	0.583510	+	0.812106i	$0.301679\pi$
$419$			285148.i			1.62421i	−0.583510	+	0.812106i	$0.698321\pi$
$420$	20464.0	−	116325.i	0.116009	−	0.659442i
$421$	267715.			1.51046			0.755229	−	0.655460i	$-0.227525\pi$
$421$	267715.			1.51046			0.755229	+	0.655460i	$0.227525\pi$
$422$	−46255.6	+	38828.6i	−0.259740	+	0.218035i
$423$			180280.i			1.00755i
$424$	−89921.7	+	51987.3i	−0.500187	+	0.289178i
$425$	188992.			1.04632
$426$	−74452.8	−	88693.8i	−0.410262	−	0.488736i
$427$			88709.3i			0.486534i
$428$	49189.3	+	8653.40i	0.268524	+	0.0472388i
$429$	−3844.45			−0.0208891
$430$	−265755.	+	223084.i	−1.43729	+	1.20651i
$431$		−	270794.i		−	1.45776i	−0.684644	−	0.728878i	$-0.740042\pi$
$431$		−	270794.i		−	1.45776i	0.684644	−	0.728878i	$-0.259958\pi$
$432$	−63206.7	+	174086.i	−0.338685	+	0.932817i
$433$	78598.9			0.419219			0.209609	−	0.977785i	$-0.432781\pi$
$433$	78598.9			0.419219			0.209609	+	0.977785i	$0.432781\pi$
$434$	106917.	+	127368.i	0.567632	+	0.676207i
$435$			387365.i			2.04711i
$436$	26465.0	−	150437.i	0.139219	−	0.791375i
$437$	28920.8			0.151442
$438$	11385.0	−	9557.00i	0.0593453	−	0.0498165i
$439$		−	86920.9i		−	0.451019i	−0.974241	−	0.225510i	$-0.927595\pi$
$439$		−	86920.9i		−	0.451019i	0.974241	−	0.225510i	$-0.0724047\pi$
$440$	32259.3	+	55798.4i	0.166628	+	0.288215i
$441$	75724.0			0.389365
$442$	−11098.7	−	13221.6i	−0.0568102	−	0.0676767i
$443$		−	128470.i		−	0.654628i	−0.944916	−	0.327314i	$-0.893857\pi$
$443$		−	128470.i		−	0.654628i	0.944916	−	0.327314i	$-0.106143\pi$
$444$	−98168.8	−	17269.9i	−0.497975	−	0.0876040i
$445$	291717.			1.47313
$446$	183992.	−	154449.i	0.924973	−	0.776455i
$447$		−	115276.i		−	0.576932i
$448$	107324.	+	61794.2i	0.534736	+	0.307887i
$449$	−288030.			−1.42872			−0.714358	−	0.699781i	$-0.753281\pi$
$449$	−288030.			−1.42872			−0.714358	+	0.699781i	$0.753281\pi$
$450$	−177784.	−	211790.i	−0.877945	−	1.04588i
$451$		−	6324.37i		−	0.0310931i
$452$	−38643.1	+	219662.i	−0.189145	+	1.07517i
$453$	−157755.			−0.768753
$454$	182027.	−	152800.i	0.883131	−	0.741332i
$455$		−	41724.8i		−	0.201545i
$456$	79662.5	−	46056.0i	0.383111	−	0.221491i
$457$	150727.			0.721704			0.360852	−	0.932623i	$-0.382486\pi$
$457$	150727.			0.721704			0.360852	+	0.932623i	$0.382486\pi$
$458$	177641.	+	211619.i	0.846861	+	1.00885i
$459$		−	100731.i		−	0.478119i
$460$	−77390.0	−	13614.5i	−0.365737	−	0.0643407i
$461$	−251105.			−1.18155			−0.590777	−	0.806835i	$-0.701179\pi$
$461$	−251105.			−1.18155			−0.590777	+	0.806835i	$0.701179\pi$
$462$	−11489.3	+	9644.49i	−0.0538279	+	0.0451851i
$463$		−	316650.i		−	1.47713i	−0.674184	−	0.738563i	$-0.735505\pi$
$463$		−	316650.i		−	1.47713i	0.674184	−	0.738563i	$-0.264495\pi$
$464$	−381773.	−	138613.i	−1.77325	−	0.643827i
$465$	−335716.			−1.55263
$466$	−3943.62	−	4697.95i	−0.0181603	−	0.0216340i
$467$			69521.5i			0.318776i	0.987216	+	0.159388i	$0.0509520\pi$
$467$			69521.5i			0.318776i	−0.987216	+	0.159388i	$0.949048\pi$
$468$	−4376.01	+	24874.9i	−0.0199796	+	0.113572i
$469$	−114448.			−0.520310
$470$	−482853.	+	405324.i	−2.18584	+	1.83487i
$471$			94308.4i			0.425117i
$472$	−80435.2	−	139128.i	−0.361046	−	0.624496i
$473$	44067.2			0.196967
$474$	−146633.	−	174680.i	−0.652641	−	0.777476i
$475$			355890.i			1.57735i
$476$	−66337.4	−	11670.1i	−0.292782	−	0.0515063i
$477$	−82654.9			−0.363272
$478$	155204.	−	130283.i	0.679275	−	0.570208i
$479$		−	268700.i		−	1.17111i	−0.810634	−	0.585553i	$-0.800878\pi$
$479$		−	268700.i		−	1.17111i	0.810634	−	0.585553i	$-0.199122\pi$
$480$	−234852.	+	85741.4i	−1.01932	+	0.372142i
$481$	−35212.2			−0.152196
$482$	−151399.	−	180359.i	−0.651673	−	0.776323i
$483$		−	18288.3i		−	0.0783933i
$484$	−39168.9	+	222651.i	−0.167206	+	0.950461i
$485$	−312169.			−1.32711
$486$	−182187.	+	152934.i	−0.771337	+	0.647488i
$487$		−	248749.i		−	1.04883i	−0.851464	−	0.524413i	$-0.824285\pi$
$487$		−	248749.i		−	1.04883i	0.851464	−	0.524413i	$-0.175715\pi$
$488$	162563.	−	93984.3i	0.682627	−	0.394653i
$489$	92263.2			0.385843
$490$	170250.	+	202815.i	0.709082	+	0.844712i
$491$			36717.3i			0.152303i	0.997096	+	0.0761513i	$0.0242632\pi$
$491$			36717.3i			0.152303i	−0.997096	+	0.0761513i	$0.975737\pi$
$492$	24161.5	+	4250.50i	0.0998145	+	0.0175594i
$493$	220904.			0.908886
$494$	24897.4	−	20899.8i	0.102024	−	0.0856423i
$495$			51289.2i			0.209322i
$496$	120132.	−	330871.i	0.488308	−	1.34492i
$497$	−159620.			−0.646211
$498$	190719.	+	227199.i	0.769015	+	0.916110i
$499$			17548.7i			0.0704764i	0.999379	+	0.0352382i	$0.0112190\pi$
$499$			17548.7i			0.0704764i	−0.999379	+	0.0352382i	$0.988781\pi$
$500$	90393.4	−	513831.i	0.361574	−	2.05533i
$501$	−125775.			−0.501095
$502$	−186428.	+	156494.i	−0.739782	+	0.620999i
$503$		−	416903.i		−	1.64778i	−0.566750	−	0.823890i	$-0.691800\pi$
$503$		−	416903.i		−	1.64778i	0.566750	−	0.823890i	$-0.308200\pi$
$504$	49325.3	+	85317.4i	0.194182	+	0.335874i
$505$	49766.6			0.195144
$506$	6416.37	+	7643.67i	0.0250604	+	0.0298539i
$507$			151351.i			0.588804i
$508$	263823.	+	46411.9i	1.02232	+	0.179846i
$509$	−55565.6			−0.214472			−0.107236	−	0.994234i	$-0.534200\pi$
$509$	−55565.6			−0.214472			−0.107236	+	0.994234i	$0.534200\pi$
$510$	104149.	−	87426.3i	0.400418	−	0.336126i
$511$		−	20489.3i		−	0.0784669i
$512$	−465.131	−	262144.i	−0.00177433	−	0.999998i
$513$	189685.			0.720772
$514$	200483.	+	238831.i	0.758843	+	0.903992i
$515$			330308.i			1.24539i
$516$	−29616.8	+	168353.i	−0.111234	+	0.632298i
$517$	80066.1			0.299549
$518$	−105232.	+	88335.9i	−0.392184	+	0.329214i
$519$			143343.i			0.532160i
$520$	−76462.4	+	44205.9i	−0.282775	+	0.163483i
$521$	273621.			1.00803			0.504016	−	0.863694i	$-0.331855\pi$
$521$	273621.			1.00803			0.504016	+	0.863694i	$0.331855\pi$
$522$	−207803.	−	247551.i	−0.762624	−	0.908496i
$523$			54651.2i			0.199800i	0.994997	+	0.0999002i	$0.0318523\pi$
$523$			54651.2i			0.199800i	−0.994997	+	0.0999002i	$0.968148\pi$
$524$	−191878.	−	33755.3i	−0.698816	−	0.122936i
$525$	225049.			0.816506
$526$	−191930.	+	161113.i	−0.693700	+	0.582317i
$527$			191450.i			0.689342i
$528$	29846.3	+	10836.5i	0.107059	+	0.0388707i
$529$	−12167.0			−0.0434783
$530$	−185833.	−	221379.i	−0.661564	−	0.788106i
$531$		−	127885.i		−	0.453554i
$532$	21975.8	−	124919.i	0.0776466	−	0.441373i
$533$	8666.49			0.0305062
$534$	110074.	−	92400.0i	0.386013	−	0.324033i
$535$			138983.i			0.485571i
$536$	121253.	+	209730.i	0.422050	+	0.730015i
$537$	230148.			0.798103
$538$	242590.	+	288992.i	0.838124	+	0.998437i
$539$		−	33630.6i		−	0.115760i
$540$	−507583.	−	89294.2i	−1.74068	−	0.306222i
$541$	176569.			0.603282			0.301641	−	0.953422i	$-0.402466\pi$
$541$	176569.			0.603282			0.301641	+	0.953422i	$0.402466\pi$
$542$	418114.	−	350980.i	1.42330	−	1.19477i
$543$		−	33469.6i		−	0.113514i
$544$	48896.1	+	133930.i	0.165225	+	0.452564i
$545$	425055.			1.43104
$546$	−13216.1	−	15744.1i	−0.0443322	−	0.0528119i
$547$		−	327129.i		−	1.09331i	−0.837357	−	0.546656i	$-0.815900\pi$
$547$		−	327129.i		−	1.09331i	0.837357	−	0.546656i	$-0.184100\pi$
$548$	−6765.10	+	38455.4i	−0.0225275	+	0.128055i
$549$	149426.			0.495772
$550$	−94060.4	+	78957.6i	−0.310943	+	0.261017i
$551$			415982.i			1.37016i
$552$	−33514.0	+	19375.8i	−0.109989	+	0.0635888i
$553$	−314367.			−1.02799
$554$	−342265.	−	407732.i	−1.11518	−	1.32848i
$555$		−	277373.i		−	0.900487i
$556$	−160168.	−	28176.9i	−0.518116	−	0.0911472i
$557$	−593961.			−1.91447			−0.957233	−	0.289320i	$-0.906571\pi$
$557$	−593961.			−1.91447			−0.957233	+	0.289320i	$0.906571\pi$
$558$	214544.	−	180096.i	0.689046	−	0.578410i
$559$			60386.6i			0.193249i
$560$	−117612.	+	323930.i	−0.375037	+	1.03294i
$561$	−17269.9			−0.0548735
$562$	154841.	+	184459.i	0.490246	+	0.584018i
$563$		−	192698.i		−	0.607940i	−0.952682	−	0.303970i	$-0.901688\pi$
$563$		−	192698.i		−	0.607940i	0.952682	−	0.303970i	$-0.0983123\pi$
$564$	−53811.0	+	305883.i	−0.169166	+	0.961605i
$565$	−620649.			−1.94424
$566$	−189983.	+	159479.i	−0.593038	+	0.497817i
$567$			4778.36i			0.0148632i
$568$	169111.	+	292510.i	0.524175	+	0.906659i
$569$	−495420.			−1.53020			−0.765101	−	0.643910i	$-0.777311\pi$
$569$	−495420.			−1.53020			−0.765101	+	0.643910i	$0.777311\pi$
$570$	164631.	+	196122.i	0.506714	+	0.603637i
$571$			498704.i			1.52958i	0.644282	+	0.764788i	$0.277156\pi$
$571$			498704.i			1.52958i	−0.644282	+	0.764788i	$0.722844\pi$
$572$	11047.5	+	1943.48i	0.0337654	+	0.00594002i
$573$	328513.			1.00056
$574$	25900.0	−	21741.4i	0.0786097	−	0.0659878i
$575$		−	149723.i		−	0.452848i
$576$	104089.	−	180781.i	0.313733	−	0.544889i
$577$	−319578.			−0.959898			−0.479949	−	0.877296i	$-0.659345\pi$
$577$	−319578.			−0.959898			−0.479949	+	0.877296i	$0.659345\pi$
$578$	164939.	+	196488.i	0.493704	+	0.588138i
$579$		−	374176.i		−	1.11614i
$580$	195824.	−	1.11314e6i	0.582115	−	3.30897i
$581$	408884.			1.21129
$582$	−117791.	+	98878.1i	−0.347750	+	0.291913i
$583$			36708.8i			0.108002i
$584$	−37547.5	+	21707.7i	−0.110092	+	0.0636485i
$585$	−70283.3			−0.205372
$586$	268824.	+	320244.i	0.782841	+	0.932580i
$587$			53996.2i			0.156706i	0.996926	+	0.0783532i	$0.0249662\pi$
$587$			53996.2i			0.156706i	−0.996926	+	0.0783532i	$0.975034\pi$
$588$	128482.	+	22602.6i	0.371610	+	0.0653737i
$589$	−360518.			−1.03919
$590$	342519.	−	287523.i	0.983969	−	0.825978i
$591$		−	406343.i		−	1.16337i
$592$	273369.	+	99254.1i	0.780020	+	0.283208i
$593$	−377167.			−1.07257			−0.536283	−	0.844038i	$-0.680172\pi$
$593$	−377167.			−1.07257			−0.536283	+	0.844038i	$0.680172\pi$
$594$	42083.4	+	50133.0i	0.119272	+	0.142086i
$595$		−	187434.i		−	0.529437i
$596$	−58275.4	+	331260.i	−0.164056	+	0.932559i
$597$	125698.			0.352680
$598$	−10474.4	+	8792.55i	−0.0292904	+	0.0245874i
$599$		−	6321.51i		−	0.0176184i	−0.999961	−	0.00880922i	$-0.997196\pi$
$599$		−	6321.51i		−	0.0176184i	0.999961	−	0.00880922i	$-0.00280410\pi$
$600$	−238432.	−	412412.i	−0.662310	−	1.14559i
$601$	58908.9			0.163092			0.0815459	−	0.996670i	$-0.474014\pi$
$601$	58908.9			0.163092			0.0815459	+	0.996670i	$0.474014\pi$
$602$	151490.	+	180467.i	0.418015	+	0.497972i
$603$			192782.i			0.530189i
$604$	453327.	+	79749.6i	1.24262	+	0.218602i
$605$	−629094.			−1.71872
$606$	18778.5	−	15763.4i	0.0511348	−	0.0429243i
$607$		−	358907.i		−	0.974104i	−0.873373	−	0.487052i	$-0.838072\pi$
$607$		−	358907.i		−	0.974104i	0.873373	−	0.487052i	$-0.161928\pi$
$608$	−252202.	+	92075.7i	−0.682247	+	0.249079i
$609$	263049.			0.709255
$610$	335956.	+	400216.i	0.902864	+	1.07556i
$611$			109717.i			0.293895i
$612$	−19657.7	+	111742.i	−0.0524843	+	0.298341i
$613$	295756.			0.787068			0.393534	−	0.919310i	$-0.371252\pi$
$613$	295756.			0.787068			0.393534	+	0.919310i	$0.371252\pi$
$614$	164006.	−	137673.i	0.435034	−	0.365183i
$615$			68267.5i			0.180494i
$616$	37891.3	−	21906.4i	0.0998568	−	0.0577311i
$617$	9107.73			0.0239243			0.0119622	−	0.999928i	$-0.496192\pi$
$617$	9107.73			0.0239243			0.0119622	+	0.999928i	$0.496192\pi$
$618$	104624.	+	124636.i	0.273938	+	0.326336i
$619$		−	366446.i		−	0.956375i	−0.878258	−	0.478187i	$-0.841294\pi$
$619$		−	366446.i		−	0.956375i	0.878258	−	0.478187i	$-0.158706\pi$
$620$	964720.	+	169714.i	2.50968	+	0.441504i
$621$	−79800.4			−0.206929
$622$	−192948.	+	161968.i	−0.498724	+	0.418646i
$623$		−	198097.i		−	0.510390i
$624$	−14849.6	+	40899.4i	−0.0381370	+	0.105038i
$625$	603460.			1.54486
$626$	33860.2	+	40336.8i	0.0864053	+	0.102933i
$627$		−	32520.7i		−	0.0827227i
$628$	47675.5	−	271006.i	0.120886	−	0.687163i
$629$	−158178.			−0.399803
$630$	−210043.	+	176318.i	−0.529210	+	0.444238i
$631$		−	426323.i		−	1.07073i	−0.844621	−	0.535365i	$-0.820174\pi$
$631$		−	426323.i		−	1.07073i	0.844621	−	0.535365i	$-0.179826\pi$
$632$	333060.	+	576091.i	0.833852	+	1.44230i
$633$	−82793.3			−0.206627
$634$	−219313.	−	261263.i	−0.545616	−	0.649979i
$635$			745424.i			1.84865i
$636$	−140242.	−	24671.4i	−0.346707	−	0.0609928i
$637$	46085.1			0.113575
$638$	−109943.	+	92289.7i	−0.270100	+	0.226731i
$639$			268872.i			0.658481i
$640$	718219.	−	127664.i	1.75346	−	0.311679i
$641$	115069.			0.280055			0.140027	−	0.990148i	$-0.455281\pi$
$641$	115069.			0.280055			0.140027	+	0.990148i	$0.455281\pi$
$642$	44022.1	+	52442.5i	0.106807	+	0.127237i
$643$		−	399150.i		−	0.965417i	−0.875781	−	0.482708i	$-0.839653\pi$
$643$		−	399150.i		−	0.965417i	0.875781	−	0.482708i	$-0.160347\pi$
$644$	−9245.25	+	52553.6i	−0.0222919	+	0.126716i
$645$	−475676.			−1.14338
$646$	111843.	−	93885.0i	0.268005	−	0.224973i
$647$			388586.i			0.928279i	0.885762	+	0.464139i	$0.153636\pi$
$647$			388586.i			0.928279i	−0.885762	+	0.464139i	$0.846364\pi$
$648$	8756.53	−	5062.49i	0.0208537	−	0.0120563i
$649$	−56796.2			−0.134844
$650$	−108198.	−	128894.i	−0.256090	−	0.305074i
$651$			227976.i			0.537932i
$652$	−265129.	−	46641.6i	−0.623680	−	0.109718i
$653$	−33091.6			−0.0776053			−0.0388027	−	0.999247i	$-0.512354\pi$
$653$	−33091.6			−0.0776053			−0.0388027	+	0.999247i	$0.512354\pi$
$654$	160387.	−	134634.i	0.374984	−	0.314775i
$655$		−	542145.i		−	1.26367i
$656$	−67282.1	−	24428.6i	−0.156348	−	0.0567664i
$657$	−34513.3			−0.0799567
$658$	275245.	+	327893.i	0.635722	+	0.757321i
$659$			237713.i			0.547372i	0.961819	+	0.273686i	$0.0882429\pi$
$659$			237713.i			0.547372i	−0.961819	+	0.273686i	$0.911757\pi$
$660$	−15309.1	+	87023.0i	−0.0351449	+	0.199777i
$661$	530619.			1.21445			0.607225	−	0.794530i	$-0.292283\pi$
$661$	530619.			1.21445			0.607225	+	0.794530i	$0.292283\pi$
$662$	−287406.	+	241259.i	−0.655812	+	0.550512i
$663$		−	23665.4i		−	0.0538378i
$664$	−433198.	−	749296.i	−0.982539	−	1.69949i
$665$	352955.			0.798134
$666$	148797.	+	177259.i	0.335464	+	0.399631i
$667$		−	175004.i		−	0.393365i
$668$	361430.	+	63583.0i	0.809975	+	0.142491i
$669$	329329.			0.735830
$670$	−516337.	+	433432.i	−1.15023	+	0.965541i
$671$		−	66363.4i		−	0.147395i
$672$	58224.7	+	159482.i	0.128934	+	0.353161i
$673$	−175499.			−0.387476			−0.193738	−	0.981053i	$-0.562061\pi$
$673$	−175499.			−0.387476			−0.193738	+	0.981053i	$0.562061\pi$
$674$	139116.	+	165725.i	0.306236	+	0.364812i
$675$		−	981997.i		−	2.15527i
$676$	76512.4	−	434926.i	0.167432	−	0.951748i
$677$	112908.			0.246348			0.123174	−	0.992385i	$-0.460693\pi$
$677$	112908.			0.246348			0.123174	+	0.992385i	$0.460693\pi$
$678$	−234190.	+	196588.i	−0.509459	+	0.427658i
$679$			211986.i			0.459798i
$680$	−343480.	+	198579.i	−0.742821	+	0.429454i
$681$	325812.			0.702544
$682$	−79984.5	−	95283.6i	−0.171964	−	0.204856i
$683$		−	136478.i		−	0.292564i	−0.989243	−	0.146282i	$-0.953269\pi$
$683$		−	136478.i		−	0.292564i	0.989243	−	0.146282i	$-0.0467307\pi$
$684$	−210420.	−	37017.2i	−0.449754	−	0.0791209i
$685$	−108655.			−0.231562
$686$	360131.	−	302307.i	0.765265	−	0.642391i
$687$			378779.i			0.802551i
$688$	170214.	−	468810.i	0.359600	−	0.990422i
$689$	−50303.2			−0.105964
$690$	−69260.5	−	82508.4i	−0.145475	−	0.173301i
$691$			585637.i			1.22651i	0.789883	+	0.613257i	$0.210141\pi$
$691$			585637.i			1.22651i	−0.789883	+	0.613257i	$0.789859\pi$
$692$	72464.0	−	411914.i	0.151325	−	0.860189i
$693$	34829.2			0.0725232
$694$	−474461.	+	398279.i	−0.985102	+	0.826930i
$695$		−	452550.i		−	0.936908i
$696$	−278691.	−	482048.i	−0.575313	−	0.995112i
$697$	38931.1			0.0801367
$698$	−411371.	−	490057.i	−0.844351	−	1.00586i
$699$		−	8408.89i		−	0.0172101i
$700$	−646706.	−	113769.i	−1.31981	−	0.232181i
$701$	−119216.			−0.242605			−0.121303	−	0.992616i	$-0.538707\pi$
$701$	−119216.			−0.242605			−0.121303	+	0.992616i	$0.538707\pi$
$702$	−68698.8	+	57668.3i	−0.139404	+	0.117021i
$703$		−	297864.i		−	0.602708i
$704$	−80288.8	−	46228.2i	−0.161998	−	0.0932742i
$705$	−864262.			−1.73887
$706$	296668.	+	353413.i	0.595197	+	0.709044i
$707$		−	33795.2i		−	0.0676109i
$708$	38171.8	−	216983.i	0.0761510	−	0.432872i
$709$	−863137.			−1.71707			−0.858533	−	0.512758i	$-0.828624\pi$
$709$	−863137.			−1.71707			−0.858533	+	0.512758i	$0.828624\pi$
$710$	−720132.	+	604505.i	−1.42855	+	1.19918i
$711$			529535.i			1.04750i
$712$	−363021.	+	209877.i	−0.716097	+	0.414004i
$713$	151670.			0.298346
$714$	−59368.9	−	70724.8i	−0.116456	−	0.138731i
$715$			31214.3i			0.0610578i
$716$	−661357.	−	116346.i	−1.29006	−	0.226948i
$717$	277800.			0.540373
$718$	378975.	−	318125.i	0.735127	−	0.617091i
$719$		−	608990.i		−	1.17802i	−0.808126	−	0.589009i	$-0.799518\pi$
$719$		−	608990.i		−	1.17802i	0.808126	−	0.589009i	$-0.200482\pi$
$720$	545643.	+	198111.i	1.05255	+	0.382158i
$721$	224304.			0.431485
$722$	−158360.	−	188650.i	−0.303788	−	0.361896i
$723$		−	322825.i		−	0.617577i
$724$	−16919.8	+	96178.8i	−0.0322789	+	0.183486i
$725$	2.15353e6			4.09709
$726$	−237377.	+	199263.i	−0.450366	+	0.378053i
$727$			877940.i			1.66110i	0.556944	+	0.830550i	$0.311974\pi$
$727$			877940.i			1.66110i	−0.556944	+	0.830550i	$0.688026\pi$
$728$	30019.1	+	51923.6i	0.0566414	+	0.0979720i
$729$	−313296.			−0.589522
$730$	−77596.2	−	92438.6i	−0.145611	−	0.173463i
$731$			271266.i			0.507645i
$732$	253533.	+	44601.7i	0.473165	+	0.0832394i
$733$	−359507.			−0.669112			−0.334556	−	0.942376i	$-0.608586\pi$
$733$	−359507.			−0.669112			−0.334556	+	0.942376i	$0.608586\pi$
$734$	145045.	−	121756.i	0.269222	−	0.225995i
$735$			363021.i			0.671981i
$736$	106101.	−	38736.3i	0.195869	−	0.0715092i
$737$	85618.4			0.157628
$738$	−36622.3	−	43627.3i	−0.0672407	−	0.0801023i
$739$		−	323164.i		−	0.591745i	−0.955227	−	0.295873i	$-0.904390\pi$
$739$		−	323164.i		−	0.591745i	0.955227	−	0.295873i	$-0.0956104\pi$
$740$	−140220.	+	797062.i	−0.256062	+	1.45556i
$741$	44564.1			0.0811613
$742$	−150333.	+	126195.i	−0.273052	+	0.229210i
$743$			565953.i			1.02519i	0.858632	+	0.512593i	$0.171315\pi$
$743$			565953.i			1.02519i	−0.858632	+	0.512593i	$0.828685\pi$
$744$	417776.	−	241532.i	0.754740	−	0.436345i
$745$	−935964.			−1.68634
$746$	−300352.	−	357802.i	−0.539700	−	0.642932i
$747$		−	688744.i		−	1.23429i
$748$	49626.9	+	8730.39i	0.0886981	+	0.0156038i
$749$	94379.5			0.168234
$750$	547815.	−	459855.i	0.973893	−	0.817521i
$751$		−	204183.i		−	0.362025i	−0.983481	−	0.181013i	$-0.942062\pi$
$751$		−	204183.i		−	0.362025i	0.983481	−	0.181013i	$-0.0579375\pi$
$752$	309265.	−	851787.i	0.546883	−	1.50624i
$753$	−333689.			−0.588507
$754$	−126467.	−	150658.i	−0.222452	−	0.265002i
$755$			1.28086e6i			2.24703i
$756$	−60637.4	+	344686.i	−0.106095	+	0.603088i
$757$	177058.			0.308976			0.154488	−	0.987995i	$-0.450627\pi$
$757$	177058.			0.308976			0.154488	+	0.987995i	$0.450627\pi$
$758$	66065.8	−	55458.0i	0.114984	−	0.0965218i
$759$			13681.5i			0.0237492i
$760$	−373943.	−	646804.i	−0.647408	−	1.11981i
$761$	−828023.			−1.42979			−0.714896	−	0.699231i	$-0.753526\pi$
$761$	−828023.			−1.42979			−0.714896	+	0.699231i	$0.753526\pi$
$762$	236110.	+	281272.i	0.406634	+	0.484414i
$763$		−	288644.i		−	0.495808i
$764$	−944021.	−	166073.i	−1.61732	−	0.284519i
$765$	−315723.			−0.539490
$766$	442569.	−	371508.i	0.754263	−	0.633156i
$767$		−	77829.7i		−	0.132298i
$768$	230570.	−	275664.i	0.390913	−	0.467367i
$769$	605732.			1.02430			0.512151	−	0.858896i	$-0.328849\pi$
$769$	605732.			1.02430			0.512151	+	0.858896i	$0.328849\pi$
$770$	78306.5	+	93284.8i	0.132074	+	0.157336i
$771$			427486.i			0.719139i
$772$	−189157.	+	1.07524e6i	−0.317385	+	1.80414i
$773$	−911702.			−1.52579			−0.762893	−	0.646525i	$-0.776222\pi$
$773$	−911702.			−1.52579			−0.762893	+	0.646525i	$0.776222\pi$
$774$	303987.	−	255178.i	0.507427	−	0.425952i
$775$			1.86640e6i			3.10743i
$776$	388472.	−	224591.i	0.645114	−	0.372966i
$777$	−188356.			−0.311988
$778$	181209.	+	215870.i	0.299379	+	0.356643i
$779$			73310.8i			0.120807i
$780$	−119250.	−	20978.6i	−0.196007	−	0.0344816i
$781$	119412.			0.195769
$782$	−47052.4	+	39497.5i	−0.0769428	+	0.0645886i
$783$		−	1.14781e6i		−	1.87217i
$784$	−357781.	−	129902.i	−0.582083	−	0.211341i
$785$	765718.			1.24260
$786$	−171722.	−	204568.i	−0.277959	−	0.331126i
$787$		−	131294.i		−	0.211980i	−0.994367	−	0.105990i	$-0.966199\pi$
$787$		−	131294.i		−	0.211980i	0.994367	−	0.105990i	$-0.0338012\pi$
$788$	−205418.	+	1.16767e6i	−0.330815	+	1.88048i
$789$	−343537.			−0.551849
$790$	−1.41828e6	+	1.19056e6i	−2.27252	+	1.90764i
$791$			421466.i			0.673612i
$792$	−36900.2	−	63825.9i	−0.0588273	−	0.101753i
$793$	90939.9			0.144613
$794$	381401.	+	454354.i	0.604979	+	0.720698i
$795$		−	396248.i		−	0.626950i
$796$	−361209.	−	63544.0i	−0.570075	−	0.100288i
$797$	270247.			0.425446			0.212723	−	0.977113i	$-0.431767\pi$
$797$	270247.			0.425446			0.212723	+	0.977113i	$0.431767\pi$
$798$	133181.	−	111797.i	0.209140	−	0.175559i
$799$			492866.i			0.772031i
$800$	476675.	+	1.30565e6i	0.744805	+	2.04008i
$801$	−333685.			−0.520081
$802$	−653930.	−	779011.i	−1.01668	−	1.21114i
$803$			15328.1i			0.0237715i
$804$	−57542.7	+	327095.i	−0.0890180	+	0.506013i
$805$	−148488.			−0.229140
$806$	130570.	−	109605.i	0.200990	−	0.168718i
$807$			517268.i			0.794271i
$808$	−61931.1	+	35804.8i	−0.0948607	+	0.0548427i
$809$	−174780.			−0.267051			−0.133526	−	0.991045i	$-0.542630\pi$
$809$	−174780.			−0.267051			−0.133526	+	0.991045i	$0.542630\pi$
$810$	18096.4	+	21557.8i	0.0275817	+	0.0328574i
$811$			1.14514e6i			1.74107i	0.492106	+	0.870535i	$0.336227\pi$
$811$			1.14514e6i			1.74107i	−0.492106	+	0.870535i	$0.663773\pi$
$812$	−755903.	−	132979.i	−1.14645	−	0.201683i
$813$	748386.			1.13226
$814$	78724.4	−	66084.0i	0.118812	−	0.0997350i
$815$		−	749113.i		−	1.12780i
$816$	−66706.8	+	183726.i	−0.100182	+	0.275925i
$817$	−510818.			−0.765282
$818$	−246845.	−	294061.i	−0.368908	−	0.439472i
$819$			47727.5i			0.0711543i
$820$	34511.1	−	196175.i	0.0513253	−	0.291753i
$821$	176992.			0.262583			0.131291	−	0.991344i	$-0.458088\pi$
$821$	176992.			0.262583			0.131291	+	0.991344i	$0.458088\pi$
$822$	−40998.8	+	34415.9i	−0.0606775	+	0.0509348i
$823$		−	979151.i		−	1.44561i	−0.691054	−	0.722803i	$-0.742853\pi$
$823$		−	979151.i		−	1.44561i	0.691054	−	0.722803i	$-0.257147\pi$
$824$	−237641.	−	411045.i	−0.350000	−	0.605390i
$825$	−168359.			−0.247360
$826$	−195249.	−	232596.i	−0.286174	−	0.340912i
$827$			718923.i			1.05117i	0.850742	+	0.525583i	$0.176153\pi$
$827$			718923.i			1.05117i	−0.850742	+	0.525583i	$0.823847\pi$
$828$	88523.8	+	15573.1i	0.129122	+	0.0227151i
$829$	230095.			0.334809			0.167405	−	0.985888i	$-0.446461\pi$
$829$	230095.			0.334809			0.167405	+	0.985888i	$0.446461\pi$
$830$	1.84470e6	−	1.54851e6i	2.67774	−	2.24779i
$831$		−	729804.i		−	1.05683i
$832$	63348.0	−	110022.i	0.0915137	−	0.158940i
$833$	207021.			0.298349
$834$	−143343.	−	170761.i	−0.206084	−	0.245504i
$835$			1.02121e6i			1.46468i
$836$	−16440.1	+	93452.0i	−0.0235230	+	0.133714i
$837$	994768.			1.41994
$838$	873600.	−	733331.i	1.24401	−	1.04427i
$839$		−	951712.i		−	1.35202i	−0.736894	−	0.676008i	$-0.763708\pi$
$839$		−	951712.i		−	1.35202i	0.736894	−	0.676008i	$-0.236292\pi$
$840$	−409011.	+	236466.i	−0.579665	+	0.335127i
$841$	1.80988e6			2.55893
$842$	−688498.	−	820191.i	−0.971132	−	1.15689i
$843$			330164.i			0.464595i
$844$	237916.	+	41854.3i	0.333994	+	0.0587564i
$845$	1.22887e6			1.72104
$846$	552318.	−	463636.i	0.771700	−	0.647793i
$847$			427201.i			0.595478i
$848$	390528.	+	141792.i	0.543076	+	0.197179i
$849$	−340053.			−0.471771
$850$	−486042.	−	579010.i	−0.672723	−	0.801399i
$851$			125311.i			0.173034i
$852$	−80254.5	+	456198.i	−0.110558	+	0.628454i
$853$	−759394.			−1.04368			−0.521842	−	0.853042i	$-0.674755\pi$
$853$	−759394.			−1.04368			−0.521842	+	0.853042i	$0.674755\pi$
$854$	271776.	−	228139.i	0.372645	−	0.312812i
$855$		−	594534.i		−	0.813289i
$856$	−99991.6	−	172954.i	−0.136463	−	0.236039i
$857$	448123.			0.610148			0.305074	−	0.952329i	$-0.401319\pi$
$857$	448123.			0.610148			0.305074	+	0.952329i	$0.401319\pi$
$858$	9886.99	+	11778.1i	0.0134304	+	0.0159993i
$859$		−	510433.i		−	0.691756i	−0.938280	−	0.345878i	$-0.887581\pi$
$859$		−	510433.i		−	0.691756i	0.938280	−	0.345878i	$-0.112419\pi$
$860$	1.36691e6	+	240468.i	1.84818	+	0.325132i
$861$	46358.7			0.0625352
$862$	−829624.	+	696416.i	−1.11652	+	0.937247i
$863$		−	953964.i		−	1.28089i	−0.768006	−	0.640443i	$-0.778751\pi$
$863$		−	953964.i		−	1.28089i	0.768006	−	0.640443i	$-0.221249\pi$
$864$	695894.	−	254062.i	0.932214	−	0.340339i
$865$	1.16385e6			1.55548
$866$	−202137.	−	240801.i	−0.269532	−	0.321087i
$867$			351695.i			0.467872i
$868$	115248.	−	655116.i	0.152966	−	0.869519i
$869$	235178.			0.311428
$870$	1.18676e6	−	996207.i	1.56792	−	1.31617i
$871$			117326.i			0.154652i
$872$	−528952.	+	305808.i	−0.695637	+	0.402175i
$873$	357079.			0.468528
$874$	−74377.2	−	88603.9i	−0.0973682	−	0.115992i
$875$		−	985888.i		−	1.28769i
$876$	−58559.0	−	10301.7i	−0.0763107	−	0.0134246i
$877$	417003.			0.542176			0.271088	−	0.962555i	$-0.412617\pi$
$877$	417003.			0.542176			0.271088	+	0.962555i	$0.412617\pi$
$878$	−266297.	+	223539.i	−0.345444	+	0.289978i
$879$			573208.i			0.741881i
$880$	87985.1	−	242332.i	0.113617	−	0.312928i
$881$	−351359.			−0.452689			−0.226344	−	0.974047i	$-0.572677\pi$
$881$	−351359.			−0.452689			−0.226344	+	0.974047i	$0.572677\pi$
$882$	−194744.	−	231993.i	−0.250338	−	0.298221i
$883$		−	641008.i		−	0.822133i	−0.911605	−	0.411066i	$-0.865156\pi$
$883$		−	641008.i		−	0.822133i	0.911605	−	0.411066i	$-0.134844\pi$
$884$	−11963.5	+	68005.4i	−0.0153093	+	0.0870239i
$885$	613078.			0.782761
$886$	−393590.	+	330393.i	−0.501391	+	0.420885i
$887$		−	232704.i		−	0.295772i	−0.989004	−	0.147886i	$-0.952753\pi$
$887$		−	232704.i		−	0.295772i	0.989004	−	0.147886i	$-0.0472468\pi$
$888$	199557.	+	345171.i	0.253070	+	0.437732i
$889$	506198.			0.640496
$890$	−750224.	−	893724.i	−0.947133	−	1.12830i
$891$		−	3574.69i		−	0.00450280i
$892$	−946364.	−	166485.i	−1.18940	−	0.209240i
$893$	−928110.			−1.16385
$894$	−353169.	+	296462.i	−0.441883	+	0.370932i
$895$		−	1.86864e6i		−	2.33281i
$896$	−86693.1	−	487724.i	−0.107986	−	0.607516i
$897$	−18748.1			−0.0233009
$898$	740744.	+	882431.i	0.918576	+	1.09428i
$899$			2.18154e6i			2.69926i
$900$	−191638.	+	1.08934e6i	−0.236590	+	1.34487i
$901$	−225970.			−0.278356
$902$	−19375.8	+	16264.7i	−0.0238148	+	0.0199910i
$903$			323019.i			0.396144i
$904$	772354.	−	446528.i	0.945103	−	0.546401i
$905$	−271750.			−0.331797
$906$	405707.	+	483309.i	0.494261	+	0.588802i
$907$			1.62607e6i			1.97663i	0.152429	+	0.988314i	$0.451290\pi$
$907$			1.62607e6i			1.97663i	−0.152429	+	0.988314i	$0.548710\pi$
$908$	−936260.	−	164707.i	−1.13560	−	0.199775i
$909$	−56926.3			−0.0688946
$910$	−127831.	+	107306.i	−0.154367	+	0.129581i
$911$		−	1.08097e6i		−	1.30250i	−0.758865	−	0.651248i	$-0.774246\pi$
$911$		−	1.08097e6i		−	1.30250i	0.758865	−	0.651248i	$-0.225754\pi$
$912$	−345973.	−	125615.i	−0.415961	−	0.151026i
$913$	−305886.			−0.366959
$914$	−387633.	−	461779.i	−0.464012	−	0.552766i
$915$			716350.i			0.855624i
$916$	191484.	−	1.08847e6i	0.228213	−	1.29725i
$917$	−368157.			−0.437818
$918$	−308605.	+	259054.i	−0.366200	+	0.307401i
$919$		−	1.17701e6i		−	1.39363i	−0.717249	−	0.696817i	$-0.754599\pi$
$919$		−	1.17701e6i		−	1.39363i	0.717249	−	0.696817i	$-0.245401\pi$
$920$	157318.	+	272111.i	0.185867	+	0.321492i
$921$	293556.			0.346076
$922$	645780.	+	769303.i	0.759666	+	0.904973i
$923$			163634.i			0.192074i
$924$	59095.1	+	10396.0i	0.0692161	+	0.0121765i
$925$	−1.54204e6			−1.80224
$926$	−970112.	+	814346.i	−1.13136	+	0.949702i
$927$		−	377828.i		−	0.439678i
$928$	557162.	+	1.52611e6i	0.646972	+	1.77210i
$929$	809977.			0.938516			0.469258	−	0.883061i	$-0.344522\pi$
$929$	809977.			0.938516			0.469258	+	0.883061i	$0.344522\pi$
$930$	863380.	+	1.02852e6i	0.998243	+	1.18918i
$931$			389840.i			0.449766i
$932$	−4250.93	+	24163.9i	−0.00489387	+	0.0278186i
$933$	−345360.			−0.396742
$934$	212991.	−	178792.i	0.244156	−	0.204953i
$935$			140219.i			0.160393i
$936$	87462.6	−	50565.6i	0.0998322	−	0.0577169i
$937$	−1.27074e6			−1.44737			−0.723684	−	0.690131i	$-0.757553\pi$
$937$	−1.27074e6			−1.44737			−0.723684	+	0.690131i	$0.757553\pi$
$938$	294332.	+	350631.i	0.334528	+	0.398515i
$939$			72199.2i			0.0818844i
$940$	2.48356e6	+	436908.i	2.81073	+	0.494464i
$941$	1.56957e6			1.77256			0.886282	−	0.463145i	$-0.153279\pi$
$941$	1.56957e6			1.77256			0.886282	+	0.463145i	$0.153279\pi$
$942$	288930.	−	242538.i	0.325605	−	0.273324i
$943$		−	30841.9i		−	0.0346831i
$944$	−219382.	+	604229.i	−0.246182	+	0.678044i
$945$	−973899.			−1.09056
$946$	−113330.	−	135007.i	−0.126637	−	0.150860i
$947$			10114.4i			0.0112782i	0.999984	+	0.00563908i	$0.00179498\pi$
$947$			10114.4i			0.0112782i	−0.999984	+	0.00563908i	$0.998205\pi$
$948$	−158059.	+	898469.i	−0.175874	+	0.999738i
$949$	−21004.5			−0.0233228
$950$	1.09033e6	−	915261.i	1.20812	−	1.01414i
$951$		−	467637.i		−	0.517068i
$952$	134850.	+	233248.i	0.148791	+	0.257362i
$953$	401713.			0.442313			0.221157	−	0.975238i	$-0.429017\pi$
$953$	401713.			0.442313			0.221157	+	0.975238i	$0.429017\pi$
$954$	212568.	+	253228.i	0.233562	+	0.278237i
$955$		−	2.66730e6i		−	2.92459i
$956$	−798291.	−	140436.i	−0.873464	−	0.153660i
$957$	−196787.			−0.214868
$958$	−823207.	+	691029.i	−0.896970	+	0.752949i
$959$			73784.5i			0.0802283i
$960$	866665.	+	499003.i	0.940392	+	0.541453i
$961$	−967151.			−1.04724
$962$	90557.0	+	107878.i	0.0978525	+	0.116569i
$963$		−	158977.i		−	0.171428i
$964$	−163197.	+	927676.i	−0.175614	+	0.998256i
$965$	−3.03805e6			−3.26243
$966$	−56029.3	+	47033.0i	−0.0600428	+	0.0504021i
$967$			95844.6i			0.102498i	0.998686	+	0.0512489i	$0.0163202\pi$
$967$			95844.6i			0.102498i	−0.998686	+	0.0512489i	$0.983680\pi$
$968$	782863.	−	452604.i	0.835478	−	0.483023i
$969$	200189.			0.213202
$970$	802822.	+	956383.i	0.853249	+	1.01645i
$971$			1.25558e6i			1.33170i	0.746084	+	0.665852i	$0.231932\pi$
$971$			1.25558e6i			1.33170i	−0.746084	+	0.665852i	$0.768068\pi$
$972$	937079.	+	164851.i	0.991844	+	0.174486i
$973$	−307315.			−0.324607
$974$	−762086.	+	639722.i	−0.803315	+	0.674331i
$975$		−	230708.i		−	0.242691i
$976$	−706010.	−	256336.i	−0.741159	−	0.269098i
$977$	1.68818e6			1.76860			0.884299	−	0.466920i	$-0.154637\pi$
$977$	1.68818e6			1.76860			0.884299	+	0.466920i	$0.154637\pi$
$978$	−237278.	−	282664.i	−0.248073	−	0.295524i
$979$			148196.i			0.154622i
$980$	183517.	−	1.04318e6i	0.191084	−	1.08620i
$981$	−486206.			−0.505222
$982$	112490.	−	94427.8i	0.116651	−	0.0979213i
$983$		−	174844.i		−	0.180944i	−0.995899	−	0.0904718i	$-0.971163\pi$
$983$		−	174844.i		−	0.180944i	0.995899	−	0.0904718i	$-0.0288375\pi$
$984$	−49115.3	−	84954.1i	−0.0507255	−	0.0877393i
$985$	−3.29923e6			−3.40047
$986$	−568110.	−	676777.i	−0.584358	−	0.696132i
$987$			586898.i			0.602460i
$988$	−128060.	−	22528.4i	−0.131190	−	0.0230790i
$989$	214901.			0.219708
$990$	157133.	−	131903.i	0.160324	−	0.134582i
$991$			1.04063e6i			1.05962i	0.848118	+	0.529808i	$0.177736\pi$
$991$			1.04063e6i			1.05962i	−0.848118	+	0.529808i	$0.822264\pi$
$992$	−1.32263e6	+	482874.i	−1.34405	+	0.490694i
$993$	−514430.			−0.521708
$994$	410503.	+	489023.i	0.415474	+	0.494945i
$995$		−	1.02058e6i		−	1.03087i
$996$	205581.	−	1.16860e6i	0.207235	−	1.17801i
$997$	1.22050e6			1.22786			0.613930	−	0.789361i	$-0.289588\pi$
$997$	1.22050e6			1.22786			0.613930	+	0.789361i	$0.289588\pi$
$998$	53763.4	−	45130.9i	0.0539791	−	0.0453120i
$999$			821888.i			0.823534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.c.a.47.13	✓	44
4.3	odd	2	inner	92.5.c.a.47.14	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.c.a.47.13	✓	44	1.1	even	1	trivial
92.5.c.a.47.14	yes	44	4.3	odd	2	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.57175 - 3.06367i) q^{2} -5.48369i q^{3} +(-2.77216 + 15.7580i) q^{4} -44.5238 q^{5} +(-16.8002 + 14.1027i) q^{6} +30.2349i q^{7} +(55.4067 - 32.0328i) q^{8} +50.9292 q^{9} +(114.504 + 136.406i) q^{10} -22.6187i q^{11} +(86.4121 + 15.2016i) q^{12} +30.9952 q^{13} +(92.6298 - 77.7568i) q^{14} +244.154i q^{15} +(-240.630 - 87.3674i) q^{16} +139.235 q^{17} +(-130.977 - 156.030i) q^{18} +262.192i q^{19} +(123.427 - 701.606i) q^{20} +165.799 q^{21} +(-69.2963 + 58.1698i) q^{22} -110.304i q^{23} +(-175.658 - 303.833i) q^{24} +1357.36 q^{25} +(-79.7119 - 94.9589i) q^{26} -723.458i q^{27} +(-476.442 - 83.8160i) q^{28} +1586.56 q^{29} +(748.009 - 627.905i) q^{30} +1375.02i q^{31} +(351.177 + 961.900i) q^{32} -124.034 q^{33} +(-358.078 - 426.570i) q^{34} -1346.17i q^{35} +(-141.184 + 802.543i) q^{36} -1136.05 q^{37} +(803.269 - 674.292i) q^{38} -169.968i q^{39} +(-2466.91 + 1426.22i) q^{40} +279.608 q^{41} +(-426.394 - 507.953i) q^{42} +1948.26i q^{43} +(356.426 + 62.7027i) q^{44} -2267.56 q^{45} +(-337.936 + 283.675i) q^{46} +3539.82i q^{47} +(-479.096 + 1319.54i) q^{48} +1486.85 q^{49} +(-3490.81 - 4158.52i) q^{50} -763.520i q^{51} +(-85.9234 + 488.422i) q^{52} -1622.94 q^{53} +(-2216.44 + 1860.56i) q^{54} +1007.07i q^{55} +(968.508 + 1675.22i) q^{56} +1437.78 q^{57} +(-4080.23 - 4860.69i) q^{58} -2511.03i q^{59} +(-3847.39 - 676.834i) q^{60} +2934.00 q^{61} +(4212.60 - 3536.21i) q^{62} +1539.84i q^{63} +(2043.80 - 3549.66i) q^{64} -1380.02 q^{65} +(318.985 + 379.999i) q^{66} +3785.29i q^{67} +(-385.981 + 2194.06i) q^{68} -604.873 q^{69} +(-4124.23 + 3462.02i) q^{70} +5279.33i q^{71} +(2821.82 - 1631.40i) q^{72} -677.672 q^{73} +(2921.65 + 3480.50i) q^{74} -7443.36i q^{75} +(-4131.62 - 726.836i) q^{76} +683.875 q^{77} +(-520.725 + 437.115i) q^{78} +10397.5i q^{79} +(10713.8 + 3889.93i) q^{80} +158.041 q^{81} +(-719.083 - 856.626i) q^{82} -13523.6i q^{83} +(-459.621 + 2612.66i) q^{84} -6199.26 q^{85} +(5968.83 - 5010.45i) q^{86} -8700.18i q^{87} +(-724.540 - 1253.23i) q^{88} -6551.94 q^{89} +(5831.60 + 6947.05i) q^{90} +937.136i q^{91} +(1738.17 + 305.780i) q^{92} +7540.17 q^{93} +(10844.8 - 9103.54i) q^{94} -11673.8i q^{95} +(5274.76 - 1925.75i) q^{96} +7011.29 q^{97} +(-3823.81 - 4555.22i) q^{98} -1151.95i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) \) 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more