LMFDB - Embedded newform 92.3.f.a.57.1

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			57.1
Character	$\chi$	$=$	92.57
Dual form			92.3.f.a.21.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.591227 + 4.11207i) q^{3} +(0.143195 + 0.487679i) q^{5} +(-4.01704 + 3.48078i) q^{7} +(-7.92417 - 2.32675i) q^{9} +(-6.52142 + 10.1475i) q^{11} +(-0.185481 + 0.214056i) q^{13} +(-2.09003 + 0.300501i) q^{15} +(8.31682 - 3.79816i) q^{17} +(19.0197 + 8.68598i) q^{19} +(-11.9383 - 18.5763i) q^{21} +(22.9996 - 0.143656i) q^{23} +(20.8140 - 13.3764i) q^{25} +(-1.27932 + 2.80132i) q^{27} +(5.03736 + 11.0303i) q^{29} +(-4.95757 - 34.4806i) q^{31} +(-37.8717 - 32.8160i) q^{33} +(-2.27273 - 1.46059i) q^{35} +(6.10065 - 20.7769i) q^{37} +(-0.770554 - 0.889267i) q^{39} +(-66.2338 + 19.4480i) q^{41} +(74.8120 + 10.7563i) q^{43} -4.19763i q^{45} +14.5226 q^{47} +(-2.95269 + 20.5364i) q^{49} +(10.7012 + 36.4450i) q^{51} +(31.0669 - 26.9196i) q^{53} +(-5.88257 - 1.72728i) q^{55} +(-46.9623 + 73.0748i) q^{57} +(-68.4839 + 79.0346i) q^{59} +(55.9818 - 8.04896i) q^{61} +(39.9306 - 18.2357i) q^{63} +(-0.130951 - 0.0598032i) q^{65} +(-37.2684 - 57.9908i) q^{67} +(-13.0072 + 94.6608i) q^{69} +(-72.3535 + 46.4987i) q^{71} +(13.6043 - 29.7893i) q^{73} +(42.6988 + 93.4972i) q^{75} +(-9.12454 - 63.4626i) q^{77} +(-104.028 - 90.1406i) q^{79} +(-73.2918 - 47.1018i) q^{81} +(6.06438 - 20.6534i) q^{83} +(3.04321 + 3.51206i) q^{85} +(-48.3355 + 14.1926i) q^{87} +(83.0960 + 11.9474i) q^{89} -1.50549i q^{91} +144.718 q^{93} +(-1.51244 + 10.5193i) q^{95} +(8.18745 + 27.8839i) q^{97} +(75.2875 - 65.2370i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.591227	+	4.11207i	−0.197076	+	1.37069i	0.615638	+	0.788029i	$0.288898\pi$
$3$	−0.591227	+	4.11207i	−0.197076	+	1.37069i	−0.812714	+	0.582663i	$0.802011\pi$
$4$		0			0
$5$	0.143195	+	0.487679i	0.0286391	+	0.0975358i	0.972572	−	0.232601i	$-0.0747235\pi$
$5$	0.143195	+	0.487679i	0.0286391	+	0.0975358i	−0.943933	+	0.330136i	$0.892905\pi$
$6$		0			0
$7$	−4.01704	+	3.48078i	−0.573862	+	0.497255i	−0.892759	−	0.450535i	$-0.851233\pi$
$7$	−4.01704	+	3.48078i	−0.573862	+	0.497255i	0.318896	+	0.947790i	$0.396688\pi$
$8$		0			0
$9$	−7.92417	−	2.32675i	−0.880463	−	0.258527i
$10$		0			0
$11$	−6.52142	+	10.1475i	−0.592856	+	0.922502i	0.407102	+	0.913383i	$0.366539\pi$
$11$	−6.52142	+	10.1475i	−0.592856	+	0.922502i	−0.999958	+	0.00911941i	$0.997097\pi$
$12$		0			0
$13$	−0.185481	+	0.214056i	−0.0142678	+	0.0164659i	−0.762839	−	0.646589i	$-0.776195\pi$
$13$	−0.185481	+	0.214056i	−0.0142678	+	0.0164659i	0.748571	+	0.663055i	$0.230740\pi$
$14$		0			0
$15$	−2.09003	+	0.300501i	−0.139336	+	0.0200334i
$16$		0			0
$17$	8.31682	−	3.79816i	0.489225	−	0.223421i	−0.155501	−	0.987836i	$-0.549699\pi$
$17$	8.31682	−	3.79816i	0.489225	−	0.223421i	0.644725	+	0.764414i	$0.276972\pi$
$18$		0			0
$19$	19.0197	+	8.68598i	1.00103	+	0.457157i	0.847391	−	0.530969i	$-0.178172\pi$
$19$	19.0197	+	8.68598i	1.00103	+	0.457157i	0.153643	+	0.988126i	$0.450899\pi$
$20$		0			0
$21$	−11.9383	−	18.5763i	−0.568488	−	0.884585i
$22$		0			0
$23$	22.9996	−	0.143656i	0.999980	−	0.00624591i
$23$	22.9996	−	0.143656i	0.999980	−	0.00624591i
$24$		0			0
$25$	20.8140	−	13.3764i	0.832561	−	0.535054i
$26$		0			0
$27$	−1.27932	+	2.80132i	−0.0473822	+	0.103753i
$28$		0			0
$29$	5.03736	+	11.0303i	0.173702	+	0.380354i	0.976381	−	0.216058i	$-0.0693199\pi$
$29$	5.03736	+	11.0303i	0.173702	+	0.380354i	−0.802679	+	0.596412i	$0.796593\pi$
$30$		0			0
$31$	−4.95757	−	34.4806i	−0.159922	−	1.11228i	−0.898774	−	0.438412i	$-0.855541\pi$
$31$	−4.95757	−	34.4806i	−0.159922	−	1.11228i	0.738853	−	0.673867i	$-0.235368\pi$
$32$		0			0
$33$	−37.8717	−	32.8160i	−1.14763	−	0.994425i
$34$		0			0
$35$	−2.27273	−	1.46059i	−0.0649350	−	0.0417312i
$36$		0			0
$37$	6.10065	−	20.7769i	0.164883	−	0.561538i	−0.835053	−	0.550170i	$-0.814563\pi$
$37$	6.10065	−	20.7769i	0.164883	−	0.561538i	0.999935	−	0.0113686i	$-0.00361882\pi$
$38$		0			0
$39$	−0.770554	−	0.889267i	−0.0197578	−	0.0228017i
$40$		0			0
$41$	−66.2338	+	19.4480i	−1.61546	+	0.474341i	−0.959793	−	0.280710i	$-0.909430\pi$
$41$	−66.2338	+	19.4480i	−1.61546	+	0.474341i	−0.655666	+	0.755051i	$0.727612\pi$
$42$		0			0
$43$	74.8120	+	10.7563i	1.73981	+	0.250147i	0.937804	−	0.347164i	$-0.112855\pi$
$43$	74.8120	+	10.7563i	1.73981	+	0.250147i	0.802009	+	0.597312i	$0.203765\pi$
$44$		0			0
$45$		−	4.19763i		−	0.0932806i
$46$		0			0
$47$	14.5226			0.308991			0.154496	−	0.987993i	$-0.450625\pi$
$47$	14.5226			0.308991			0.154496	+	0.987993i	$0.450625\pi$
$48$		0			0
$49$	−2.95269	+	20.5364i	−0.0602589	+	0.419110i
$50$		0			0
$51$	10.7012	+	36.4450i	0.209828	+	0.714607i
$52$		0			0
$53$	31.0669	−	26.9196i	0.586168	−	0.507917i	−0.310528	−	0.950564i	$-0.600506\pi$
$53$	31.0669	−	26.9196i	0.586168	−	0.507917i	0.896696	+	0.442647i	$0.145961\pi$
$54$		0			0
$55$	−5.88257	−	1.72728i	−0.106956	−	0.0314051i
$56$		0			0
$57$	−46.9623	+	73.0748i	−0.823901	+	1.28201i
$58$		0			0
$59$	−68.4839	+	79.0346i	−1.16074	+	1.33957i	−0.230307	+	0.973118i	$0.573973\pi$
$59$	−68.4839	+	79.0346i	−1.16074	+	1.33957i	−0.930437	+	0.366452i	$0.880572\pi$
$60$		0			0
$61$	55.9818	−	8.04896i	0.917734	−	0.131950i	0.332769	−	0.943009i	$-0.392017\pi$
$61$	55.9818	−	8.04896i	0.917734	−	0.131950i	0.584965	+	0.811058i	$0.301108\pi$
$62$		0			0
$63$	39.9306	−	18.2357i	0.633818	−	0.289455i
$64$		0			0
$65$	−0.130951	−	0.0598032i	−0.00201463	−	0.000920049i
$66$		0			0
$67$	−37.2684	−	57.9908i	−0.556245	−	0.865534i	0.443279	−	0.896384i	$-0.353815\pi$
$67$	−37.2684	−	57.9908i	−0.556245	−	0.865534i	−0.999524	+	0.0308494i	$0.990179\pi$
$68$		0			0
$69$	−13.0072	+	94.6608i	−0.188511	+	1.37190i
$70$		0			0
$71$	−72.3535	+	46.4987i	−1.01906	+	0.654912i	−0.939723	−	0.341936i	$-0.888917\pi$
$71$	−72.3535	+	46.4987i	−1.01906	+	0.654912i	−0.0793394	+	0.996848i	$0.525281\pi$
$72$		0			0
$73$	13.6043	−	29.7893i	0.186361	−	0.408073i	−0.793273	−	0.608866i	$-0.791625\pi$
$73$	13.6043	−	29.7893i	0.186361	−	0.408073i	0.979634	+	0.200793i	$0.0643519\pi$
$74$		0			0
$75$	42.6988	+	93.4972i	0.569317	+	1.24663i
$76$		0			0
$77$	−9.12454	−	63.4626i	−0.118501	−	0.824190i
$78$		0			0
$79$	−104.028	−	90.1406i	−1.31681	−	1.14102i	−0.979901	−	0.199483i	$-0.936074\pi$
$79$	−104.028	−	90.1406i	−1.31681	−	1.14102i	−0.336907	−	0.941538i	$-0.609381\pi$
$80$		0			0
$81$	−73.2918	−	47.1018i	−0.904837	−	0.581504i
$82$		0			0
$83$	6.06438	−	20.6534i	0.0730649	−	0.248836i	−0.914860	−	0.403772i	$-0.867699\pi$
$83$	6.06438	−	20.6534i	0.0730649	−	0.248836i	0.987925	+	0.154936i	$0.0495171\pi$
$84$		0			0
$85$	3.04321	+	3.51206i	0.0358025	+	0.0413183i
$86$		0			0
$87$	−48.3355	+	14.1926i	−0.555581	+	0.163133i
$88$		0			0
$89$	83.0960	+	11.9474i	0.933663	+	0.134240i	0.592324	−	0.805700i	$-0.298210\pi$
$89$	83.0960	+	11.9474i	0.933663	+	0.134240i	0.341339	+	0.939940i	$0.389120\pi$
$90$		0			0
$91$		−	1.50549i		−	0.0165438i
$92$		0			0
$93$	144.718			1.55611
$94$		0			0
$95$	−1.51244	+	10.5193i	−0.0159205	+	0.110729i
$96$		0			0
$97$	8.18745	+	27.8839i	0.0844067	+	0.287463i	0.990870	−	0.134822i	$-0.0430463\pi$
$97$	8.18745	+	27.8839i	0.0844067	+	0.287463i	−0.906463	+	0.422285i	$0.861228\pi$
$98$		0			0
$99$	75.2875	−	65.2370i	0.760480	−	0.658959i
$100$		0			0
$101$	3.90433	+	1.14642i	0.0386567	+	0.0113506i	0.301004	−	0.953623i	$-0.402678\pi$
$101$	3.90433	+	1.14642i	0.0386567	+	0.0113506i	−0.262347	+	0.964974i	$0.584497\pi$
$102$		0			0
$103$	51.0998	−	79.5129i	0.496115	−	0.771970i	−0.499420	−	0.866360i	$-0.666454\pi$
$103$	51.0998	−	79.5129i	0.496115	−	0.771970i	0.995535	+	0.0943899i	$0.0300900\pi$
$104$		0			0
$105$	7.34976	−	8.48207i	0.0699977	−	0.0807817i
$106$		0			0
$107$	−41.1603	+	5.91796i	−0.384676	+	0.0553080i	−0.331940	−	0.943301i	$-0.607703\pi$
$107$	−41.1603	+	5.91796i	−0.384676	+	0.0553080i	−0.0527356	+	0.998609i	$0.516794\pi$
$108$		0			0
$109$	162.686	−	74.2964i	1.49254	−	0.681618i	0.508742	−	0.860919i	$-0.330111\pi$
$109$	162.686	−	74.2964i	1.49254	−	0.681618i	0.983794	+	0.179301i	$0.0573836\pi$
$110$		0			0
$111$	81.8294	+	37.3702i	0.737201	+	0.336669i
$112$		0			0
$113$	−48.4135	−	75.3329i	−0.428438	−	0.666663i	0.558178	−	0.829721i	$-0.311500\pi$
$113$	−48.4135	−	75.3329i	−0.428438	−	0.666663i	−0.986616	+	0.163058i	$0.947864\pi$
$114$		0			0
$115$	3.36349	+	11.1958i	0.0292477	+	0.0973550i
$116$		0			0
$117$	1.96784	−	1.26465i	0.0168191	−	0.0108090i
$118$		0			0
$119$	−20.1884	+	44.2064i	−0.169650	+	0.371482i
$120$		0			0
$121$	−10.1781	−	22.2869i	−0.0841166	−	0.184190i
$122$		0			0
$123$	−40.8124	−	283.856i	−0.331808	−	2.30778i
$124$		0			0
$125$	19.1069	+	16.5562i	0.152855	+	0.132450i
$126$		0			0
$127$	0.764352	+	0.491219i	0.00601852	+	0.00386787i	0.543647	−	0.839314i	$-0.317043\pi$
$127$	0.764352	+	0.491219i	0.00601852	+	0.00386787i	−0.537628	+	0.843182i	$0.680680\pi$
$128$		0			0
$129$	−88.4617	+	301.273i	−0.685750	+	2.33545i
$130$		0			0
$131$	−126.261	−	145.713i	−0.963822	−	1.11231i	−0.993623	−	0.112755i	$-0.964033\pi$
$131$	−126.261	−	145.713i	−0.963822	−	1.11231i	0.0298005	−	0.999556i	$-0.490513\pi$
$132$		0			0
$133$	−106.637	+	31.3114i	−0.801779	+	0.235424i
$134$		0			0
$135$	−1.54934	−	0.222761i	−0.0114766	−	0.00165008i
$136$		0			0
$137$			34.0085i			0.248237i	0.992267	+	0.124119i	$0.0396103\pi$
$137$			34.0085i			0.248237i	−0.992267	+	0.124119i	$0.960390\pi$
$138$		0			0
$139$	3.78150			0.0272050			0.0136025	−	0.999907i	$-0.495670\pi$
$139$	3.78150			0.0272050			0.0136025	+	0.999907i	$0.495670\pi$
$140$		0			0
$141$	−8.58614	+	59.7179i	−0.0608946	+	0.423531i
$142$		0			0
$143$	−0.962543	−	3.27812i	−0.00673107	−	0.0229239i
$144$		0			0
$145$	−4.65790	+	4.03610i	−0.0321235	+	0.0278351i
$146$		0			0
$147$	−82.7014	−	24.2833i	−0.562595	−	0.165193i
$148$		0			0
$149$	−46.0470	+	71.6505i	−0.309040	+	0.480876i	−0.960682	−	0.277651i	$-0.910444\pi$
$149$	−46.0470	+	71.6505i	−0.309040	+	0.480876i	0.651642	+	0.758527i	$0.274081\pi$
$150$		0			0
$151$	126.433	−	145.912i	0.837307	−	0.966304i	−0.162484	−	0.986711i	$-0.551951\pi$
$151$	126.433	−	145.912i	0.837307	−	0.966304i	0.999792	+	0.0204068i	$0.00649615\pi$
$152$		0			0
$153$	−74.7412	+	10.7462i	−0.488505	+	0.0702364i
$154$		0			0
$155$	16.1056	−	7.35517i	0.103907	−	0.0474527i
$156$		0			0
$157$	237.262	+	108.354i	1.51123	+	0.690153i	0.986895	−	0.161362i	$-0.0515886\pi$
$157$	237.262	+	108.354i	1.51123	+	0.690153i	0.524330	+	0.851515i	$0.324316\pi$
$158$		0			0
$159$	92.3278	+	143.665i	0.580678	+	0.903553i
$160$		0			0
$161$	−91.8900	+	80.6335i	−0.570745	+	0.500829i
$162$		0			0
$163$	−152.263	+	97.8536i	−0.934130	+	0.600329i	−0.916725	−	0.399520i	$-0.869177\pi$
$163$	−152.263	+	97.8536i	−0.934130	+	0.600329i	−0.0174050	+	0.999849i	$0.505540\pi$
$164$		0			0
$165$	10.5806	−	23.1683i	0.0641250	−	0.140414i
$166$		0			0
$167$	116.311	+	254.686i	0.696475	+	1.52507i	0.844194	+	0.536039i	$0.180080\pi$
$167$	116.311	+	254.686i	0.696475	+	1.52507i	−0.147718	+	0.989029i	$0.547193\pi$
$168$		0			0
$169$	24.0398	+	167.200i	0.142247	+	0.989352i
$170$		0			0
$171$	−130.505	−	113.083i	−0.763186	−	0.661305i
$172$		0			0
$173$	117.055	+	75.2267i	0.676619	+	0.434836i	0.833306	−	0.552812i	$-0.186445\pi$
$173$	117.055	+	75.2267i	0.676619	+	0.434836i	−0.156687	+	0.987648i	$0.550082\pi$
$174$		0			0
$175$	−37.0505	+	126.182i	−0.211717	+	0.721042i
$176$		0			0
$177$	−284.507	−	328.338i	−1.60738	−	1.85502i
$178$		0			0
$179$	199.070	−	58.4522i	1.11212	−	0.326548i	0.326464	−	0.945210i	$-0.394143\pi$
$179$	199.070	−	58.4522i	1.11212	−	0.326548i	0.785658	+	0.618661i	$0.212325\pi$
$180$		0			0
$181$	−69.8790	−	10.0471i	−0.386072	−	0.0555088i	−0.0534537	−	0.998570i	$-0.517023\pi$
$181$	−69.8790	−	10.0471i	−0.386072	−	0.0555088i	−0.332618	+	0.943062i	$0.607932\pi$
$182$		0			0
$183$			234.960i			1.28393i
$184$		0			0
$185$	11.0061			0.0594922
$186$		0			0
$187$	−15.6955	+	109.164i	−0.0839331	+	0.583767i
$188$		0			0
$189$	−4.61171	−	15.7060i	−0.0244006	−	0.0831007i
$190$		0			0
$191$	123.958	−	107.410i	0.648994	−	0.562357i	−0.266926	−	0.963717i	$-0.586008\pi$
$191$	123.958	−	107.410i	0.648994	−	0.562357i	0.915920	+	0.401360i	$0.131463\pi$
$192$		0			0
$193$	−91.2762	−	26.8011i	−0.472933	−	0.138866i	0.0365759	−	0.999331i	$-0.488355\pi$
$193$	−91.2762	−	26.8011i	−0.472933	−	0.138866i	−0.509509	+	0.860465i	$0.670173\pi$
$194$		0			0
$195$	0.323337	−	0.503122i	0.00165814	−	0.00258011i
$196$		0			0
$197$	233.300	−	269.243i	1.18426	−	1.36671i	0.269362	−	0.963039i	$-0.413187\pi$
$197$	233.300	−	269.243i	1.18426	−	1.36671i	0.914902	−	0.403675i	$-0.132267\pi$
$198$		0			0
$199$	−281.059	+	40.4102i	−1.41236	+	0.203067i	−0.805901	−	0.592050i	$-0.798319\pi$
$199$	−281.059	+	40.4102i	−1.41236	+	0.203067i	−0.606457	+	0.795116i	$0.707410\pi$
$200$		0			0
$201$	260.497	−	118.965i	1.29600	−	0.591865i
$202$		0			0
$203$	−58.6292	−	26.7751i	−0.288814	−	0.131897i
$204$		0			0
$205$	−18.9688	−	29.5160i	−0.0925305	−	0.143980i
$206$		0			0
$207$	−182.587	−	52.3757i	−0.882061	−	0.253023i
$208$		0			0
$209$	−212.176	+	136.357i	−1.01520	+	0.652428i
$210$		0			0
$211$	31.5788	−	69.1478i	0.149662	−	0.327715i	−0.819921	−	0.572477i	$-0.805983\pi$
$211$	31.5788	−	69.1478i	0.149662	−	0.327715i	0.969583	+	0.244762i	$0.0787099\pi$
$212$		0			0
$213$	−148.429	−	325.014i	−0.696850	−	1.52589i
$214$		0			0
$215$	5.46709	+	38.0245i	0.0254283	+	0.176858i
$216$		0			0
$217$	139.934	+	121.254i	0.644859	+	0.558773i
$218$		0			0
$219$	114.453	+	73.5543i	0.522615	+	0.335864i
$220$		0			0
$221$	−0.729590	+	2.48475i	−0.00330131	+	0.0112432i
$222$		0			0
$223$	−171.555	−	197.985i	−0.769305	−	0.887825i	0.226984	−	0.973899i	$-0.427114\pi$
$223$	−171.555	−	197.985i	−0.769305	−	0.887825i	−0.996289	+	0.0860733i	$0.972568\pi$
$224$		0			0
$225$	−196.057	+	57.5676i	−0.871365	+	0.255856i
$226$		0			0
$227$	90.9603	+	13.0781i	0.400706	+	0.0576128i	0.339722	−	0.940526i	$-0.389667\pi$
$227$	90.9603	+	13.0781i	0.400706	+	0.0576128i	0.0609841	+	0.998139i	$0.480576\pi$
$228$		0			0
$229$			260.193i			1.13621i	0.822954	+	0.568107i	$0.192324\pi$
$229$			260.193i			1.13621i	−0.822954	+	0.568107i	$0.807676\pi$
$230$		0			0
$231$	266.358			1.15306
$232$		0			0
$233$	55.5470	−	386.338i	0.238399	−	1.65810i	−0.421559	−	0.906801i	$-0.638517\pi$
$233$	55.5470	−	386.338i	0.238399	−	1.65810i	0.659958	−	0.751302i	$-0.270574\pi$
$234$		0			0
$235$	2.07957	+	7.08236i	0.00884922	+	0.0301377i
$236$		0			0
$237$	432.169	−	374.477i	1.82350	−	1.58007i
$238$		0			0
$239$	92.8639	+	27.2673i	0.388552	+	0.114089i	0.470173	−	0.882574i	$-0.344192\pi$
$239$	92.8639	+	27.2673i	0.388552	+	0.114089i	−0.0816212	+	0.996663i	$0.526010\pi$
$240$		0			0
$241$	83.5909	−	130.070i	0.346850	−	0.539709i	−0.623372	−	0.781925i	$-0.714238\pi$
$241$	83.5909	−	130.070i	0.346850	−	0.539709i	0.970222	+	0.242216i	$0.0778742\pi$
$242$		0			0
$243$	218.868	−	252.587i	0.900690	−	1.03945i
$244$		0			0
$245$	−10.4380	+	1.50075i	−0.0426040	+	0.00612553i
$246$		0			0
$247$	−5.38707	+	2.46019i	−0.0218100	+	0.00996029i
$248$		0			0
$249$	81.3429	+	37.1480i	0.326678	+	0.149189i
$250$		0			0
$251$	252.052	+	392.201i	1.00419	+	1.56255i	0.814050	+	0.580795i	$0.197258\pi$
$251$	252.052	+	392.201i	1.00419	+	1.56255i	0.190142	+	0.981757i	$0.439105\pi$
$252$		0			0
$253$	−148.532	+	234.325i	−0.587083	+	0.926187i
$254$		0			0
$255$	−16.2411	+	10.4375i	−0.0636905	+	0.0409314i
$256$		0			0
$257$	36.2115	−	79.2922i	0.140901	−	0.308530i	−0.826005	−	0.563662i	$-0.809392\pi$
$257$	36.2115	−	79.2922i	0.140901	−	0.308530i	0.966906	+	0.255133i	$0.0821191\pi$
$258$		0			0
$259$	47.8134	+	104.697i	0.184608	+	0.404234i
$260$		0			0
$261$	−14.2522	−	99.1263i	−0.0546062	−	0.379794i
$262$		0			0
$263$	−282.310	−	244.623i	−1.07342	−	0.930126i	−0.0756704	−	0.997133i	$-0.524110\pi$
$263$	−282.310	−	244.623i	−1.07342	−	0.930126i	−0.997753	+	0.0670066i	$0.978655\pi$
$264$		0			0
$265$	17.5768	+	11.2959i	0.0663274	+	0.0426260i
$266$		0			0
$267$	−98.2572	+	334.633i	−0.368005	+	1.25331i
$268$		0			0
$269$	−155.218	−	179.131i	−0.577017	−	0.665913i	0.389944	−	0.920839i	$-0.372494\pi$
$269$	−155.218	−	179.131i	−0.577017	−	0.665913i	−0.966961	+	0.254926i	$0.917949\pi$
$270$		0			0
$271$	332.647	−	97.6739i	1.22748	−	0.360420i	0.397181	−	0.917740i	$-0.369989\pi$
$271$	332.647	−	97.6739i	1.22748	−	0.360420i	0.830298	+	0.557320i	$0.188170\pi$
$272$		0			0
$273$	6.19069	+	0.890086i	0.0226765	+	0.00326039i
$274$		0			0
$275$			298.443i			1.08525i
$276$		0			0
$277$	−400.755			−1.44677			−0.723385	−	0.690445i	$-0.757415\pi$
$277$	−400.755			−1.44677			−0.723385	+	0.690445i	$0.757415\pi$
$278$		0			0
$279$	−40.9431	+	284.765i	−0.146749	+	1.02066i
$280$		0			0
$281$	−74.4668	−	253.611i	−0.265007	−	0.902529i	−0.979254	−	0.202636i	$-0.935049\pi$
$281$	−74.4668	−	253.611i	−0.265007	−	0.902529i	0.714248	−	0.699893i	$-0.246769\pi$
$282$		0			0
$283$	−112.371	+	97.3702i	−0.397071	+	0.344064i	−0.830396	−	0.557174i	$-0.811886\pi$
$283$	−112.371	+	97.3702i	−0.397071	+	0.344064i	0.433325	+	0.901238i	$0.357340\pi$
$284$		0			0
$285$	−42.3618	−	12.4386i	−0.148638	−	0.0436441i
$286$		0			0
$287$	198.369	−	308.669i	0.691182	−	1.07550i
$288$		0			0
$289$	−134.511	+	155.234i	−0.465437	+	0.537143i
$290$		0			0
$291$	−119.501	+	17.1817i	−0.410657	+	0.0590436i
$292$		0			0
$293$	−176.752	+	80.7199i	−0.603249	+	0.275494i	−0.693537	−	0.720421i	$-0.743949\pi$
$293$	−176.752	+	80.7199i	−0.603249	+	0.275494i	0.0902880	+	0.995916i	$0.471221\pi$
$294$		0			0
$295$	−48.3501	−	22.0808i	−0.163899	−	0.0748500i
$296$		0			0
$297$	−20.0835	−	31.2505i	−0.0676211	−	0.105220i
$298$		0			0
$299$	−4.23523	+	4.94984i	−0.0141646	+	0.0165547i
$300$		0			0
$301$	−337.963	+	217.196i	−1.12280	+	0.721580i
$302$		0			0
$303$	−7.02249	+	15.3771i	−0.0231765	+	0.0507495i
$304$		0			0
$305$	11.9416	+	26.1485i	0.0391529	+	0.0857329i
$306$		0			0
$307$	−36.3487	−	252.811i	−0.118400	−	0.823487i	−0.959318	−	0.282326i	$-0.908894\pi$
$307$	−36.3487	−	252.811i	−0.118400	−	0.823487i	0.840919	−	0.541161i	$-0.182015\pi$
$308$		0			0
$309$	296.751	+	257.137i	0.960360	+	0.832157i
$310$		0			0
$311$	−185.020	−	118.905i	−0.594919	−	0.382331i	0.208256	−	0.978074i	$-0.433221\pi$
$311$	−185.020	−	118.905i	−0.594919	−	0.382331i	−0.803175	+	0.595743i	$0.796858\pi$
$312$		0			0
$313$	−144.555	+	492.309i	−0.461837	+	1.57287i	0.318759	+	0.947836i	$0.396734\pi$
$313$	−144.555	+	492.309i	−0.461837	+	1.57287i	−0.780596	+	0.625036i	$0.785084\pi$
$314$		0			0
$315$	14.6110	+	16.8620i	0.0463842	+	0.0535302i
$316$		0			0
$317$	−163.485	+	48.0035i	−0.515726	+	0.151431i	−0.529231	−	0.848478i	$-0.677519\pi$
$317$	−163.485	+	48.0035i	−0.515726	+	0.151431i	0.0135048	+	0.999909i	$0.495701\pi$
$318$		0			0
$319$	−144.781	−	20.8163i	−0.453858	−	0.0652549i
$320$		0			0
$321$		−	172.753i		−	0.538171i
$322$		0			0
$323$	191.174			0.591869
$324$		0			0
$325$	−0.997308	+	6.93643i	−0.00306864	+	0.0213429i
$326$		0			0
$327$	209.328	+	712.905i	0.640146	+	2.18014i
$328$		0			0
$329$	−58.3378	+	50.5500i	−0.177318	+	0.153647i
$330$		0			0
$331$	13.0725	+	3.83843i	0.0394939	+	0.0115965i	0.301420	−	0.953492i	$-0.402539\pi$
$331$	13.0725	+	3.83843i	0.0394939	+	0.0115965i	−0.261926	+	0.965088i	$0.584358\pi$
$332$		0			0
$333$	−96.6852	+	150.445i	−0.290346	+	0.451787i
$334$		0			0
$335$	22.9442	−	26.4790i	0.0684902	−	0.0790419i
$336$		0			0
$337$	361.214	−	51.9347i	1.07185	−	0.154109i	0.416275	−	0.909239i	$-0.363335\pi$
$337$	361.214	−	51.9347i	1.07185	−	0.154109i	0.655575	+	0.755130i	$0.272426\pi$
$338$		0			0
$339$	338.398	−	154.541i	0.998223	−	0.455873i
$340$		0			0
$341$	382.223	+	174.556i	1.12089	+	0.511893i
$342$		0			0
$343$	−200.431	−	311.877i	−0.584348	−	0.909264i
$344$		0			0
$345$	−48.0266	+	7.21164i	−0.139208	+	0.0209033i
$346$		0			0
$347$	−124.998	+	80.3311i	−0.360224	+	0.231502i	−0.708216	−	0.705996i	$-0.750500\pi$
$347$	−124.998	+	80.3311i	−0.360224	+	0.231502i	0.347993	+	0.937497i	$0.386863\pi$
$348$		0			0
$349$	−68.9481	+	150.975i	−0.197559	+	0.432594i	−0.982321	−	0.187203i	$-0.940058\pi$
$349$	−68.9481	+	150.975i	−0.197559	+	0.432594i	0.784762	+	0.619797i	$0.212785\pi$
$350$		0			0
$351$	−0.362351	−	0.793437i	−0.00103234	−	0.00226050i
$352$		0			0
$353$	23.0494	+	160.312i	0.0652957	+	0.454141i	0.996072	+	0.0885513i	$0.0282237\pi$
$353$	23.0494	+	160.312i	0.0652957	+	0.454141i	−0.930776	+	0.365590i	$0.880867\pi$
$354$		0			0
$355$	−33.0371	−	28.6268i	−0.0930624	−	0.0806390i
$356$		0			0
$357$	−169.844	−	109.152i	−0.475754	−	0.305748i
$358$		0			0
$359$	122.042	−	415.637i	0.339950	−	1.15776i	−0.595220	−	0.803563i	$-0.702935\pi$
$359$	122.042	−	415.637i	0.339950	−	1.15776i	0.935170	−	0.354200i	$-0.115247\pi$
$360$		0			0
$361$	49.8962	+	57.5833i	0.138217	+	0.159510i
$362$		0			0
$363$	97.6631	−	28.6765i	0.269044	−	0.0789986i
$364$		0			0
$365$	16.4757	+	2.36885i	0.0451389	+	0.00649000i
$366$		0			0
$367$		−	293.723i		−	0.800334i	−0.916442	−	0.400167i	$-0.868952\pi$
$367$		−	293.723i		−	0.800334i	0.916442	−	0.400167i	$-0.131048\pi$
$368$		0			0
$369$	570.098			1.54498
$370$		0			0
$371$	−31.0955	+	216.274i	−0.0838154	+	0.582949i
$372$		0			0
$373$	−104.067	−	354.420i	−0.279000	−	0.950187i	−0.973114	−	0.230322i	$-0.926022\pi$
$373$	−104.067	−	354.420i	−0.279000	−	0.950187i	0.694114	−	0.719865i	$-0.255796\pi$
$374$		0			0
$375$	−79.3770	+	68.7805i	−0.211672	+	0.183415i
$376$		0			0
$377$	−3.29543	−	0.967626i	−0.00874120	−	0.00256665i
$378$		0			0
$379$	−126.682	+	197.122i	−0.334255	+	0.520110i	−0.967177	−	0.254105i	$-0.918219\pi$
$379$	−126.682	+	197.122i	−0.334255	+	0.520110i	0.632922	+	0.774216i	$0.281855\pi$
$380$		0			0
$381$	−2.47184	+	2.85265i	−0.00648776	+	0.00748727i
$382$		0			0
$383$	−198.243	+	28.5031i	−0.517607	+	0.0744206i	−0.396168	−	0.918178i	$-0.629660\pi$
$383$	−198.243	+	28.5031i	−0.517607	+	0.0744206i	−0.121439	+	0.992599i	$0.538751\pi$
$384$		0			0
$385$	29.6428	−	13.5374i	0.0769942	−	0.0351621i
$386$		0			0
$387$	−567.795	−	259.303i	−1.46717	−	0.670035i
$388$		0			0
$389$	−193.489	−	301.075i	−0.497401	−	0.773971i	0.498260	−	0.867028i	$-0.333973\pi$
$389$	−193.489	−	301.075i	−0.497401	−	0.773971i	−0.995661	+	0.0930564i	$0.970336\pi$
$390$		0			0
$391$	190.737	−	88.5508i	0.487820	−	0.226473i
$392$		0			0
$393$	673.830	−	433.044i	1.71458	−	1.10189i
$394$		0			0
$395$	29.0634	−	63.6399i	0.0735782	−	0.161114i
$396$		0			0
$397$	48.0793	+	105.279i	0.121107	+	0.265186i	0.960470	−	0.278385i	$-0.0897991\pi$
$397$	48.0793	+	105.279i	0.121107	+	0.265186i	−0.839363	+	0.543571i	$0.817072\pi$
$398$		0			0
$399$	−65.7081	−	457.010i	−0.164682	−	1.14539i
$400$		0			0
$401$	−135.822	−	117.690i	−0.338708	−	0.293492i	0.468853	−	0.883276i	$-0.344667\pi$
$401$	−135.822	−	117.690i	−0.338708	−	0.293492i	−0.807561	+	0.589784i	$0.799213\pi$
$402$		0			0
$403$	8.30033	+	5.33430i	0.0205964	+	0.0132365i
$404$		0			0
$405$	12.4755	−	42.4876i	0.0308037	−	0.104908i
$406$		0			0
$407$	171.049	+	197.401i	0.420269	+	0.485016i
$408$		0			0
$409$	−363.170	+	106.636i	−0.887947	+	0.260725i	−0.693731	−	0.720234i	$-0.744034\pi$
$409$	−363.170	+	106.636i	−0.887947	+	0.260725i	−0.194216	+	0.980959i	$0.562216\pi$
$410$		0			0
$411$	−139.845	−	20.1067i	−0.340257	−	0.0489215i
$412$		0			0
$413$		−	555.863i		−	1.34591i
$414$		0			0
$415$	10.9406			0.0263629
$416$		0			0
$417$	−2.23573	+	15.5498i	−0.00536145	+	0.0372897i
$418$		0			0
$419$	−82.6386	−	281.441i	−0.197228	−	0.671697i	−0.997409	−	0.0719387i	$-0.977081\pi$
$419$	−82.6386	−	281.441i	−0.197228	−	0.671697i	0.800181	−	0.599759i	$-0.204737\pi$
$420$		0			0
$421$	−109.598	+	94.9676i	−0.260329	+	0.225576i	−0.775239	−	0.631668i	$-0.782371\pi$
$421$	−109.598	+	94.9676i	−0.260329	+	0.225576i	0.514910	+	0.857244i	$0.327825\pi$
$422$		0			0
$423$	−115.079	−	33.7904i	−0.272055	−	0.0798826i
$424$		0			0
$425$	122.301	−	190.304i	0.287767	−	0.447774i
$426$		0			0
$427$	−196.864	+	227.193i	−0.461040	+	0.532069i
$428$		0			0
$429$	14.0490	−	2.01993i	0.0327481	−	0.00470847i
$430$		0			0
$431$	−30.0663	+	13.7308i	−0.0697593	+	0.0318580i	−0.449989	−	0.893034i	$-0.648572\pi$
$431$	−30.0663	+	13.7308i	−0.0697593	+	0.0318580i	0.380230	+	0.924892i	$0.375845\pi$
$432$		0			0
$433$	497.978	+	227.419i	1.15006	+	0.525217i	0.896912	−	0.442209i	$-0.145805\pi$
$433$	497.978	+	227.419i	1.15006	+	0.525217i	0.253153	+	0.967426i	$0.418532\pi$
$434$		0			0
$435$	−13.8428	−	21.5399i	−0.0318226	−	0.0495170i
$436$		0			0
$437$	438.691	+	197.041i	1.00387	+	0.450896i
$438$		0			0
$439$	51.8019	−	33.2911i	0.118000	−	0.0758339i	−0.480310	−	0.877099i	$-0.659476\pi$
$439$	51.8019	−	33.2911i	0.118000	−	0.0758339i	0.598309	+	0.801265i	$0.295839\pi$
$440$		0			0
$441$	71.1805	−	155.864i	0.161407	−	0.353432i
$442$		0			0
$443$	321.694	+	704.412i	0.726172	+	1.59010i	0.805047	+	0.593211i	$0.202140\pi$
$443$	321.694	+	704.412i	0.726172	+	1.59010i	−0.0788751	+	0.996885i	$0.525133\pi$
$444$		0			0
$445$	6.07247	+	42.2350i	0.0136460	+	0.0949101i
$446$		0			0
$447$	−267.408	−	231.710i	−0.598228	−	0.518368i
$448$		0			0
$449$	445.424	+	286.257i	0.992036	+	0.637543i	0.932684	−	0.360694i	$-0.117460\pi$
$449$	445.424	+	286.257i	0.992036	+	0.637543i	0.0593522	+	0.998237i	$0.481096\pi$
$450$		0			0
$451$	234.589	−	798.937i	0.520153	−	1.77148i
$452$		0			0
$453$	525.250	+	606.171i	1.15949	+	1.33813i
$454$		0			0
$455$	0.734196	−	0.215579i	0.00161362	−	0.000473801i
$456$		0			0
$457$	516.622	+	74.2791i	1.13046	+	0.162536i	0.682061	−	0.731295i	$-0.261084\pi$
$457$	516.622	+	74.2791i	1.13046	+	0.162536i	0.448403	+	0.893831i	$0.351993\pi$
$458$		0			0
$459$			28.1571i			0.0613445i
$460$		0			0
$461$	−527.521			−1.14430			−0.572149	−	0.820150i	$-0.693890\pi$
$461$	−527.521			−1.14430			−0.572149	+	0.820150i	$0.693890\pi$
$462$		0			0
$463$	123.518	−	859.085i	0.266777	−	1.85548i	−0.211647	−	0.977346i	$-0.567883\pi$
$463$	123.518	−	859.085i	0.266777	−	1.85548i	0.478424	−	0.878129i	$-0.341208\pi$
$464$		0			0
$465$	20.7230	+	70.5759i	0.0445655	+	0.151776i
$466$		0			0
$467$	−311.132	+	269.598i	−0.666236	+	0.577297i	−0.920932	−	0.389724i	$-0.872570\pi$
$467$	−311.132	+	269.598i	−0.666236	+	0.577297i	0.254695	+	0.967021i	$0.418025\pi$
$468$		0			0
$469$	351.562	+	103.228i	0.749599	+	0.220102i
$470$		0			0
$471$	−585.836	+	911.578i	−1.24381	+	1.93541i
$472$		0			0
$473$	−597.030	+	689.010i	−1.26222	+	1.45668i
$474$		0			0
$475$	512.062	−	73.6234i	1.07803	−	0.154997i
$476$		0			0
$477$	−308.814	+	141.031i	−0.647409	+	0.295662i
$478$		0			0
$479$	−201.772	−	92.1460i	−0.421235	−	0.192372i	0.193509	−	0.981099i	$-0.438013\pi$
$479$	−201.772	−	92.1460i	−0.421235	−	0.192372i	−0.614744	+	0.788727i	$0.710741\pi$
$480$		0			0
$481$	3.31588	+	5.15960i	0.00689371	+	0.0107268i
$482$		0			0
$483$	−277.243	−	425.531i	−0.574002	−	0.881017i
$484$		0			0
$485$	−12.4260	+	7.98569i	−0.0256206	+	0.0164653i
$486$		0			0
$487$	−235.358	+	515.362i	−0.483281	+	1.05824i	0.498267	+	0.867024i	$0.333970\pi$
$487$	−235.358	+	515.362i	−0.483281	+	1.05824i	−0.981548	+	0.191214i	$0.938757\pi$
$488$		0			0
$489$	−312.359	−	683.971i	−0.638771	−	1.39871i
$490$		0			0
$491$	6.31765	+	43.9402i	0.0128669	+	0.0894913i	0.995243	−	0.0974237i	$-0.0310602\pi$
$491$	6.31765	+	43.9402i	0.0128669	+	0.0894913i	−0.982376	+	0.186915i	$0.940151\pi$
$492$		0			0
$493$	83.7895	+	72.6040i	0.169958	+	0.147270i
$494$		0			0
$495$	42.5955	+	27.3745i	0.0860516	+	0.0553020i
$496$		0			0
$497$	128.794	−	438.634i	0.259144	−	0.882563i
$498$		0			0
$499$	41.0545	+	47.3795i	0.0822736	+	0.0949488i	0.795394	−	0.606093i	$-0.207264\pi$
$499$	41.0545	+	47.3795i	0.0822736	+	0.0949488i	−0.713120	+	0.701042i	$0.752719\pi$
$500$		0			0
$501$	−1116.06	+	327.703i	−2.22766	+	0.654099i
$502$		0			0
$503$	690.036	+	99.2121i	1.37184	+	0.197241i	0.788524	−	0.615004i	$-0.210846\pi$
$503$	690.036	+	99.2121i	1.37184	+	0.197241i	0.583316	+	0.812245i	$0.301755\pi$
$504$		0			0
$505$			2.06822i			0.00409549i
$506$		0			0
$507$	−701.753			−1.38413
$508$		0			0
$509$	−133.208	+	926.481i	−0.261705	+	1.82020i	0.258333	+	0.966056i	$0.416827\pi$
$509$	−133.208	+	926.481i	−0.261705	+	1.82020i	−0.520038	+	0.854143i	$0.674082\pi$
$510$		0			0
$511$	49.0411	+	167.019i	0.0959708	+	0.326847i
$512$		0			0
$513$	−48.6644	+	42.1680i	−0.0948624	+	0.0821987i
$514$		0			0
$515$	46.0940	+	13.5344i	0.0895030	+	0.0262804i
$516$		0			0
$517$	−94.7078	+	147.368i	−0.183187	+	0.285045i
$518$		0			0
$519$	−378.544	+	436.863i	−0.729372	+	0.841740i
$520$		0			0
$521$	36.6368	−	5.26757i	0.0703201	−	0.0101105i	−0.107065	−	0.994252i	$-0.534145\pi$
$521$	36.6368	−	5.26757i	0.0703201	−	0.0101105i	0.177385	+	0.984142i	$0.443236\pi$
$522$		0			0
$523$	−134.443	+	61.3982i	−0.257062	+	0.117396i	−0.539778	−	0.841807i	$-0.681492\pi$
$523$	−134.443	+	61.3982i	−0.257062	+	0.117396i	0.282716	+	0.959204i	$0.408765\pi$
$524$		0			0
$525$	−496.966	−	226.957i	−0.946602	−	0.432299i
$526$		0			0
$527$	−172.194	−	267.940i	−0.326744	−	0.508424i
$528$		0			0
$529$	528.959	−	6.60805i	0.999922	−	0.0124916i
$530$		0			0
$531$	726.571	−	466.939i	1.36831	−	0.879358i
$532$		0			0
$533$	8.12213	−	17.7850i	0.0152385	−	0.0333677i
$534$		0			0
$535$	−8.78003	−	19.2256i	−0.0164113	−	0.0359357i
$536$		0			0
$537$	122.664	+	853.148i	0.228425	+	1.58873i
$538$		0			0
$539$	−189.138	−	163.889i	−0.350905	−	0.304061i
$540$		0			0
$541$	−803.307	−	516.254i	−1.48486	−	0.954259i	−0.996672	−	0.0815192i	$-0.974023\pi$
$541$	−803.307	−	516.254i	−1.48486	−	0.954259i	−0.488185	−	0.872740i	$-0.662341\pi$
$542$		0			0
$543$	82.6287	−	281.408i	0.152171	−	0.518246i
$544$		0			0
$545$	59.5287	+	68.6998i	0.109227	+	0.126055i
$546$		0			0
$547$	569.680	−	167.273i	1.04146	−	0.305801i	0.284099	−	0.958795i	$-0.408306\pi$
$547$	569.680	−	167.273i	1.04146	−	0.305801i	0.757363	+	0.652994i	$0.226487\pi$
$548$		0			0
$549$	−462.337	−	66.4740i	−0.842143	−	0.121082i
$550$		0			0
$551$			253.546i			0.460157i
$552$		0			0
$553$	731.644			1.32304
$554$		0			0
$555$	−6.50707	+	45.2577i	−0.0117245	+	0.0815454i
$556$		0			0
$557$	57.9781	+	197.455i	0.104090	+	0.354498i	0.995024	−	0.0996348i	$-0.0317675\pi$
$557$	57.9781	+	197.455i	0.104090	+	0.354498i	−0.890934	+	0.454132i	$0.849949\pi$
$558$		0			0
$559$	−16.1786	+	14.0189i	−0.0289421	+	0.0250785i
$560$		0			0
$561$	−439.613	−	129.082i	−0.783624	−	0.230093i
$562$		0			0
$563$	119.290	−	185.619i	0.211883	−	0.329696i	−0.719003	−	0.695007i	$-0.755401\pi$
$563$	119.290	−	185.619i	0.211883	−	0.329696i	0.930885	+	0.365311i	$0.119037\pi$
$564$		0			0
$565$	29.8057	−	34.3976i	0.0527534	−	0.0608807i
$566$		0			0
$567$	458.367	−	65.9032i	0.808407	−	0.116231i
$568$		0			0
$569$	−702.599	+	320.866i	−1.23480	+	0.563913i	−0.922472	−	0.386063i	$-0.873835\pi$
$569$	−702.599	+	320.866i	−1.23480	+	0.563913i	−0.312324	+	0.949976i	$0.601107\pi$
$570$		0			0
$571$	−35.0993	−	16.0293i	−0.0614699	−	0.0280724i	0.384443	−	0.923149i	$-0.374394\pi$
$571$	−35.0993	−	16.0293i	−0.0614699	−	0.0280724i	−0.445913	+	0.895076i	$0.647121\pi$
$572$		0			0
$573$	368.391	+	573.228i	0.642916	+	1.00040i
$574$		0			0
$575$	476.791	−	310.640i	0.829202	−	0.540244i
$576$		0			0
$577$	437.101	−	280.908i	0.757541	−	0.486842i	−0.103970	−	0.994580i	$-0.533155\pi$
$577$	437.101	−	280.908i	0.757541	−	0.486842i	0.861511	+	0.507738i	$0.169518\pi$
$578$		0			0
$579$	164.173	−	359.489i	0.283546	−	0.620879i
$580$		0			0
$581$	47.5291	+	104.074i	0.0818057	+	0.179130i
$582$		0			0
$583$	70.5672	+	490.806i	0.121042	+	0.841862i
$584$		0			0
$585$	0.898529	+	0.778580i	0.00153595	+	0.00133091i
$586$		0			0
$587$	−164.166	−	105.503i	−0.279670	−	0.179733i	0.393285	−	0.919417i	$-0.371339\pi$
$587$	−164.166	−	105.503i	−0.279670	−	0.179733i	−0.672955	+	0.739684i	$0.734975\pi$
$588$		0			0
$589$	205.207	−	698.871i	0.348399	−	1.18654i
$590$		0			0
$591$	969.213	+	1118.53i	1.63995	+	1.89261i
$592$		0			0
$593$	727.164	−	213.514i	1.22625	−	0.360058i	0.396414	−	0.918072i	$-0.370255\pi$
$593$	727.164	−	213.514i	1.22625	−	0.360058i	0.829832	+	0.558014i	$0.188436\pi$
$594$		0			0
$595$	−24.4494	−	3.51529i	−0.0410914	−	0.00590806i
$596$		0			0
$597$		−	1179.63i		−	1.97593i
$598$		0			0
$599$	−734.619			−1.22641			−0.613204	−	0.789924i	$-0.710120\pi$
$599$	−734.619			−1.22641			−0.613204	+	0.789924i	$0.710120\pi$
$600$		0			0
$601$	63.8759	−	444.267i	0.106283	−	0.739212i	−0.865084	−	0.501627i	$-0.832735\pi$
$601$	63.8759	−	444.267i	0.106283	−	0.739212i	0.971367	−	0.237585i	$-0.0763559\pi$
$602$		0			0
$603$	160.391	+	546.243i	0.265989	+	0.905875i
$604$		0			0
$605$	9.41141	−	8.15503i	0.0155561	−	0.0134794i
$606$		0			0
$607$	310.839	+	91.2704i	0.512090	+	0.150363i	0.527561	−	0.849517i	$-0.323107\pi$
$607$	310.839	+	91.2704i	0.512090	+	0.150363i	−0.0154711	+	0.999880i	$0.504925\pi$
$608$		0			0
$609$	144.764	−	225.257i	0.237708	−	0.369881i
$610$		0			0
$611$	−2.69366	+	3.10865i	−0.00440861	+	0.00508781i
$612$		0			0
$613$	103.646	−	14.9020i	0.169080	−	0.0243100i	−0.0572549	−	0.998360i	$-0.518235\pi$
$613$	103.646	−	14.9020i	0.169080	−	0.0243100i	0.226335	+	0.974050i	$0.427326\pi$
$614$		0			0
$615$	132.587	−	60.5503i	0.215588	−	0.0984558i
$616$		0			0
$617$	−558.932	−	255.256i	−0.905886	−	0.413704i	−0.0926907	−	0.995695i	$-0.529547\pi$
$617$	−558.932	−	255.256i	−0.905886	−	0.413704i	−0.813196	+	0.581991i	$0.802274\pi$
$618$		0			0
$619$	−585.673	−	911.325i	−0.946160	−	1.47225i	−0.880296	−	0.474425i	$-0.842656\pi$
$619$	−585.673	−	911.325i	−0.946160	−	1.47225i	−0.0658646	−	0.997829i	$-0.520981\pi$
$620$		0			0
$621$	−29.0213	+	64.6128i	−0.0467332	+	0.104046i
$622$		0			0
$623$	−375.386	+	241.246i	−0.602546	+	0.387233i
$624$		0			0
$625$	251.613	−	550.956i	0.402581	−	0.881530i
$626$		0			0
$627$	−435.267	−	953.103i	−0.694206	−	1.52010i
$628$		0			0
$629$	−28.1761	−	195.969i	−0.0447951	−	0.311557i
$630$		0			0
$631$	579.678	+	502.294i	0.918665	+	0.796028i	0.979359	−	0.202128i	$-0.0647858\pi$
$631$	579.678	+	502.294i	0.918665	+	0.796028i	−0.0606936	+	0.998156i	$0.519331\pi$
$632$		0			0
$633$	265.671	+	170.736i	0.419701	+	0.269726i
$634$		0			0
$635$	−0.130106	+	0.443099i	−0.000204891	+	0.000697793i
$636$		0			0
$637$	−3.84828	−	4.44115i	−0.00604125	−	0.00697197i
$638$		0			0
$639$	681.532	−	200.116i	1.06656	−	0.313170i
$640$		0			0
$641$	90.7553	+	13.0486i	0.141584	+	0.0203567i	0.212742	−	0.977108i	$-0.431761\pi$
$641$	90.7553	+	13.0486i	0.141584	+	0.0203567i	−0.0711584	+	0.997465i	$0.522670\pi$
$642$		0			0
$643$			596.760i			0.928088i	0.885812	+	0.464044i	$0.153602\pi$
$643$			596.760i			0.928088i	−0.885812	+	0.464044i	$0.846398\pi$
$644$		0			0
$645$	−159.592			−0.247429
$646$		0			0
$647$	69.3892	−	482.613i	0.107248	−	0.745924i	−0.863244	−	0.504787i	$-0.831571\pi$
$647$	69.3892	−	482.613i	0.107248	−	0.745924i	0.970491	−	0.241136i	$-0.0775200\pi$
$648$		0			0
$649$	−355.394	−	1210.36i	−0.547602	−	1.86496i
$650$		0			0
$651$	−581.338	+	503.732i	−0.892992	+	0.773782i
$652$		0			0
$653$	−982.088	−	288.367i	−1.50396	−	0.441603i	−0.576996	−	0.816747i	$-0.695775\pi$
$653$	−982.088	−	288.367i	−1.50396	−	0.441603i	−0.926967	+	0.375143i	$0.877594\pi$
$654$		0			0
$655$	52.9810	−	82.4401i	0.0808871	−	0.125863i
$656$		0			0
$657$	−177.115	+	204.402i	−0.269582	+	0.311114i
$658$		0			0
$659$	−261.334	+	37.5742i	−0.396562	+	0.0570170i	−0.337711	−	0.941250i	$-0.609653\pi$
$659$	−261.334	+	37.5742i	−0.396562	+	0.0570170i	−0.0588508	+	0.998267i	$0.518744\pi$
$660$		0			0
$661$	−359.139	+	164.013i	−0.543327	+	0.248129i	−0.668120	−	0.744054i	$-0.732901\pi$
$661$	−359.139	+	164.013i	−0.543327	+	0.248129i	0.124793	+	0.992183i	$0.460173\pi$
$662$		0			0
$663$	−9.78614	−	4.46918i	−0.0147604	−	0.00674084i
$664$		0			0
$665$	−30.5398	−	47.5208i	−0.0459245	−	0.0714599i
$666$		0			0
$667$	117.441	+	252.968i	0.176074	+	0.379262i
$668$		0			0
$669$	915.557	−	588.393i	1.36855	−	0.879511i
$670$		0			0
$671$	−283.403	+	620.567i	−0.422360	+	0.924839i
$672$		0			0
$673$	−174.974	−	383.140i	−0.259991	−	0.569301i	0.733951	−	0.679202i	$-0.237674\pi$
$673$	−174.974	−	383.140i	−0.259991	−	0.569301i	−0.993943	+	0.109901i	$0.964947\pi$
$674$		0			0
$675$	10.8437	+	75.4193i	0.0160647	+	0.111732i
$676$		0			0
$677$	755.275	+	654.450i	1.11562	+	0.966691i	0.999647	−	0.0265617i	$-0.00845586\pi$
$677$	755.275	+	654.450i	1.11562	+	0.966691i	0.115973	+	0.993252i	$0.463001\pi$
$678$		0			0
$679$	−129.947	−	83.5119i	−0.191380	−	0.122993i
$680$		0			0
$681$	−107.556	+	366.303i	−0.157939	+	0.537890i
$682$		0			0
$683$	354.454	+	409.062i	0.518966	+	0.598919i	0.953372	−	0.301798i	$-0.0975869\pi$
$683$	354.454	+	409.062i	0.518966	+	0.598919i	−0.434405	+	0.900717i	$0.643041\pi$
$684$		0			0
$685$	−16.5852	+	4.86986i	−0.0242120	+	0.00710929i
$686$		0			0
$687$	−1069.93	−	153.833i	−1.55740	−	0.223920i
$688$		0			0
$689$			11.6431i			0.0168986i
$690$		0			0
$691$	−819.906			−1.18655			−0.593275	−	0.805000i	$-0.702165\pi$
$691$	−819.906			−1.18655			−0.593275	+	0.805000i	$0.702165\pi$
$692$		0			0
$693$	−75.3569	+	524.119i	−0.108740	+	0.756304i
$694$		0			0
$695$	0.541494	+	1.84416i	0.000779128	+	0.00265346i
$696$		0			0
$697$	−476.988	+	413.312i	−0.684344	+	0.592988i
$698$		0			0
$699$	1555.81	+	456.827i	2.22576	+	0.653543i
$700$		0			0
$701$	602.226	−	937.082i	0.859096	−	1.33678i	−0.0812972	−	0.996690i	$-0.525906\pi$
$701$	602.226	−	937.082i	0.859096	−	1.33678i	0.940393	−	0.340089i	$-0.110457\pi$
$702$		0			0
$703$	296.500	−	342.180i	0.421764	−	0.486742i
$704$		0			0
$705$	−30.3527	+	4.36406i	−0.0430534	+	0.00619015i
$706$		0			0
$707$	−19.6743	+	8.98494i	−0.0278278	+	0.0127085i
$708$		0			0
$709$	−444.911	−	203.184i	−0.627518	−	0.286578i	0.0761612	−	0.997096i	$-0.475734\pi$
$709$	−444.911	−	203.184i	−0.627518	−	0.286578i	−0.703680	+	0.710517i	$0.748461\pi$
$710$		0			0
$711$	614.600	+	956.336i	0.864416	+	1.34506i
$712$		0			0
$713$	−118.975	−	792.327i	−0.166866	−	1.11126i
$714$		0			0
$715$	1.46084	−	0.938824i	0.00204313	−	0.00131304i
$716$		0			0
$717$	−167.029	+	365.742i	−0.232955	+	0.510100i
$718$		0			0
$719$	59.9432	+	131.257i	0.0833703	+	0.182556i	0.946726	−	0.322041i	$-0.104369\pi$
$719$	59.9432	+	131.257i	0.0833703	+	0.182556i	−0.863356	+	0.504596i	$0.831641\pi$
$720$		0			0
$721$	71.4972	+	497.274i	0.0991639	+	0.689700i
$722$		0			0
$723$	485.436	+	420.633i	0.671419	+	0.581788i
$724$		0			0
$725$	252.392	+	162.203i	0.348127	+	0.223728i
$726$		0			0
$727$	−67.1964	+	228.850i	−0.0924298	+	0.314787i	−0.992711	−	0.120523i	$-0.961543\pi$
$727$	−67.1964	+	228.850i	−0.0924298	+	0.314787i	0.900281	+	0.435310i	$0.143361\pi$
$728$		0			0
$729$	395.779	+	456.753i	0.542907	+	0.626548i
$730$		0			0
$731$	663.052	−	194.690i	0.907048	−	0.266333i
$732$		0			0
$733$	−335.867	−	48.2904i	−0.458209	−	0.0658806i	−0.0906545	−	0.995882i	$-0.528896\pi$
$733$	−335.867	−	48.2904i	−0.458209	−	0.0658806i	−0.367555	+	0.930002i	$0.619805\pi$
$734$		0			0
$735$		−	43.8090i		−	0.0596041i
$736$		0			0
$737$	831.506			1.12823
$738$		0			0
$739$	15.0572	−	104.725i	0.0203750	−	0.141712i	−0.977095	−	0.212806i	$-0.931740\pi$
$739$	15.0572	−	104.725i	0.0203750	−	0.141712i	0.997470	+	0.0710940i	$0.0226490\pi$
$740$		0			0
$741$	−6.93151	−	23.6066i	−0.00935427	−	0.0318577i
$742$		0			0
$743$	−1113.16	+	964.554i	−1.49819	+	1.29819i	−0.662383	+	0.749165i	$0.730455\pi$
$743$	−1113.16	+	964.554i	−1.49819	+	1.29819i	−0.835807	+	0.549024i	$0.815000\pi$
$744$		0			0
$745$	−41.5362	−	12.1961i	−0.0557532	−	0.0163706i
$746$		0			0
$747$	−96.1104	+	149.551i	−0.128662	+	0.200202i
$748$		0			0
$749$	144.743	−	167.043i	0.193249	−	0.223021i
$750$		0			0
$751$	401.385	−	57.7104i	0.534467	−	0.0768447i	0.130203	−	0.991487i	$-0.458437\pi$
$751$	401.385	−	57.7104i	0.534467	−	0.0768447i	0.404263	+	0.914643i	$0.367528\pi$
$752$		0			0
$753$	−1761.78	+	804.577i	−2.33968	+	1.06850i
$754$		0			0
$755$	89.2629	+	40.7650i	0.118229	+	0.0539934i
$756$		0			0
$757$	641.109	+	997.585i	0.846907	+	1.31781i	0.946473	+	0.322783i	$0.104618\pi$
$757$	641.109	+	997.585i	0.846907	+	1.31781i	−0.0995658	+	0.995031i	$0.531745\pi$
$758$		0			0
$759$	−875.747	−	749.314i	−1.15382	−	0.987238i
$760$		0			0
$761$	−1136.26	+	730.227i	−1.49311	+	0.959562i	−0.497350	+	0.867550i	$0.665694\pi$
$761$	−1136.26	+	730.227i	−1.49311	+	0.959562i	−0.995758	+	0.0920124i	$0.970670\pi$
$762$		0			0
$763$	−394.908	+	864.727i	−0.517572	+	1.13333i
$764$		0			0
$765$	−15.9433	−	34.9109i	−0.0208409	−	0.0456352i
$766$		0			0
$767$	−4.21541	−	29.3188i	−0.00549597	−	0.0382253i
$768$		0			0
$769$	488.853	+	423.594i	0.635700	+	0.550837i	0.911977	−	0.410241i	$-0.134555\pi$
$769$	488.853	+	423.594i	0.635700	+	0.550837i	−0.276277	+	0.961078i	$0.589101\pi$
$770$		0			0
$771$	304.646	+	195.784i	0.395131	+	0.253935i
$772$		0			0
$773$	138.664	−	472.246i	0.179384	−	0.610926i	−0.819879	−	0.572537i	$-0.805959\pi$
$773$	138.664	−	472.246i	0.179384	−	0.610926i	0.999263	−	0.0383891i	$-0.0122226\pi$
$774$		0			0
$775$	−564.412	−	651.366i	−0.728274	−	0.840473i
$776$		0			0
$777$	−458.789	+	134.713i	−0.590462	+	0.173375i
$778$		0			0
$779$	−1428.67	−	205.412i	−1.83398	−	0.263686i
$780$		0			0
$781$		−	1037.45i		−	1.32836i
$782$		0			0
$783$	−37.3437			−0.0476931
$784$		0			0
$785$	−18.8671	+	131.224i	−0.0240345	+	0.167164i
$786$		0			0
$787$	−65.0689	−	221.604i	−0.0826797	−	0.281581i	0.907768	−	0.419474i	$-0.137785\pi$
$787$	−65.0689	−	221.604i	−0.0826797	−	0.281581i	−0.990447	+	0.137893i	$0.955967\pi$
$788$		0			0
$789$	1172.82	−	1016.25i	1.48646	−	1.28803i
$790$		0			0
$791$	456.696	+	134.098i	0.577366	+	0.169530i
$792$		0			0
$793$	−8.66061	+	13.4762i	−0.0109213	+	0.0169939i
$794$		0			0
$795$	−56.8414	+	65.5985i	−0.0714986	+	0.0825138i
$796$		0			0
$797$	−1384.05	+	198.996i	−1.73657	+	0.249681i	−0.936610	−	0.350373i	$-0.886055\pi$
$797$	−1384.05	+	198.996i	−1.73657	+	0.249681i	−0.799960	+	0.600054i	$0.795146\pi$
$798$		0			0
$799$	120.782	−	55.1592i	0.151166	−	0.0690352i
$800$		0			0
$801$	−630.668	−	288.016i	−0.787351	−	0.359571i
$802$		0			0
$803$	213.568	+	332.319i	0.265963	+	0.413847i
$804$		0			0
$805$	−52.4815	−	33.2665i	−0.0651944	−	0.0413248i
$806$		0			0
$807$	828.367	−	532.359i	1.02648	−	0.659677i
$808$		0			0
$809$	507.632	−	1111.56i	0.627481	−	1.37399i	−0.282469	−	0.959276i	$-0.591154\pi$
$809$	507.632	−	1111.56i	0.627481	−	1.37399i	0.909951	−	0.414716i	$-0.136119\pi$
$810$		0			0
$811$	−172.707	−	378.175i	−0.212955	−	0.466307i	0.772766	−	0.634691i	$-0.218872\pi$
$811$	−172.707	−	378.175i	−0.212955	−	0.466307i	−0.985721	+	0.168384i	$0.946145\pi$
$812$		0			0
$813$	204.973	+	1425.62i	0.252119	+	1.75352i
$814$		0			0
$815$	−69.5245	−	60.2433i	−0.0853061	−	0.0739182i
$816$		0			0
$817$	1329.47	+	854.398i	1.62726	+	1.04577i
$818$		0			0
$819$	−3.50289	+	11.9298i	−0.00427704	+	0.0145662i
$820$		0			0
$821$	254.015	+	293.148i	0.309397	+	0.357063i	0.889058	−	0.457795i	$-0.151361\pi$
$821$	254.015	+	293.148i	0.309397	+	0.357063i	−0.579661	+	0.814858i	$0.696815\pi$
$822$		0			0
$823$	33.2587	−	9.76563i	0.0404115	−	0.0118659i	−0.261464	−	0.965213i	$-0.584205\pi$
$823$	33.2587	−	9.76563i	0.0404115	−	0.0118659i	0.301876	+	0.953347i	$0.402387\pi$
$824$		0			0
$825$	−1227.22	−	176.448i	−1.48754	−	0.213876i
$826$		0			0
$827$		−	203.231i		−	0.245744i	−0.992423	−	0.122872i	$-0.960789\pi$
$827$		−	203.231i		−	0.245744i	0.992423	−	0.122872i	$-0.0392105\pi$
$828$		0			0
$829$	−1341.34			−1.61802			−0.809011	−	0.587794i	$-0.799997\pi$
$829$	−1341.34			−1.61802			−0.809011	+	0.587794i	$0.799997\pi$
$830$		0			0
$831$	236.937	−	1647.94i	0.285123	−	1.98308i
$832$		0			0
$833$	53.4436	+	182.012i	0.0641580	+	0.218502i
$834$		0			0
$835$	−107.550	+	93.1925i	−0.128802	+	0.111608i
$836$		0			0
$837$	102.934	+	30.2240i	0.122979	+	0.0361099i
$838$		0			0
$839$	362.076	−	563.401i	0.431556	−	0.671515i	−0.555568	−	0.831471i	$-0.687499\pi$
$839$	362.076	−	563.401i	0.431556	−	0.671515i	0.987124	+	0.159957i	$0.0511355\pi$
$840$		0			0
$841$	454.446	−	524.459i	0.540364	−	0.623613i
$842$		0			0
$843$	1086.89	−	156.272i	1.28932	−	0.185376i
$844$		0			0
$845$	−78.0977	+	35.6660i	−0.0924233	+	0.0422083i
$846$		0			0
$847$	118.462	+	54.0997i	0.139860	+	0.0638721i
$848$		0			0
$849$	−333.957	−	519.647i	−0.393353	−	0.612069i
$850$		0			0
$851$	137.328	−	478.736i	0.161372	−	0.562557i
$852$		0			0
$853$	−793.676	+	510.064i	−0.930452	+	0.597965i	−0.915672	−	0.401925i	$-0.868341\pi$
$853$	−793.676	+	510.064i	−0.930452	+	0.597965i	−0.0147798	+	0.999891i	$0.504705\pi$
$854$		0			0
$855$	36.4605	−	79.8374i	0.0426439	−	0.0933771i
$856$		0			0
$857$	480.945	+	1053.12i	0.561197	+	1.22885i	0.951354	+	0.308101i	$0.0996934\pi$
$857$	480.945	+	1053.12i	0.561197	+	1.22885i	−0.390157	+	0.920748i	$0.627579\pi$
$858$		0			0
$859$	163.143	+	1134.69i	0.189922	+	1.32094i	0.832204	+	0.554470i	$0.187079\pi$
$859$	163.143	+	1134.69i	0.189922	+	1.32094i	−0.642281	+	0.766469i	$0.722012\pi$
$860$		0			0
$861$	1151.99	+	998.203i	1.33796	+	1.15935i
$862$		0			0
$863$	−407.422	−	261.834i	−0.472100	−	0.303400i	0.282872	−	0.959158i	$-0.408713\pi$
$863$	−407.422	−	261.834i	−0.472100	−	0.303400i	−0.754972	+	0.655758i	$0.772349\pi$
$864$		0			0
$865$	−19.9247	+	67.8574i	−0.0230344	+	0.0784478i
$866$		0			0
$867$	−558.808	−	644.899i	−0.644531	−	0.743828i
$868$		0			0
$869$	1593.11	−	467.780i	1.83327	−	0.538297i
$870$		0			0
$871$	19.3259	+	2.77864i	0.0221881	+	0.00319017i
$872$		0			0
$873$		−	240.007i		−	0.274922i
$874$		0			0
$875$	−134.382			−0.153579
$876$		0			0
$877$	0.837900	−	5.82772i	0.000955416	−	0.00664507i	−0.989338	−	0.145637i	$-0.953477\pi$
$877$	0.837900	−	5.82772i	0.000955416	−	0.00664507i	0.990294	+	0.138992i	$0.0443861\pi$
$878$		0			0
$879$	−227.426	−	774.541i	−0.258732	−	0.881161i
$880$		0			0
$881$	−114.530	+	99.2405i	−0.130000	+	0.112645i	−0.717434	−	0.696627i	$-0.754683\pi$
$881$	−114.530	+	99.2405i	−0.130000	+	0.112645i	0.587434	+	0.809272i	$0.300138\pi$
$882$		0			0
$883$	916.663	+	269.157i	1.03812	+	0.304821i	0.756010	−	0.654560i	$-0.227146\pi$
$883$	916.663	+	269.157i	1.03812	+	0.304821i	0.282114	+	0.959381i	$0.408964\pi$
$884$		0			0
$885$	119.384	−	185.764i	0.134897	−	0.209903i
$886$		0			0
$887$	907.506	−	1047.32i	1.02312	−	1.18074i	0.0397333	−	0.999210i	$-0.487349\pi$
$887$	907.506	−	1047.32i	1.02312	−	1.18074i	0.983385	−	0.181531i	$-0.0581054\pi$
$888$		0			0
$889$	−4.78026	+	0.687297i	−0.00537712	+	0.000773113i
$890$		0			0
$891$	955.933	−	436.560i	1.07288	−	0.489966i
$892$		0			0
$893$	276.215	+	126.143i	0.309311	+	0.141257i
$894$		0			0
$895$	57.0118	+	88.7121i	0.0637003	+	0.0991196i
$896$		0			0
$897$	−17.8501	−	20.3420i	−0.0198998	−	0.0226779i
$898$		0			0
$899$	355.358	−	228.375i	0.395281	−	0.254032i
$900$		0			0
$901$	156.133	−	341.883i	0.173288	−	0.379448i
$902$		0			0
$903$	−693.312	−	1518.14i	−0.767787	−	1.68122i
$904$		0			0
$905$	−5.10661	−	35.5172i	−0.00564266	−	0.0392455i
$906$		0			0
$907$	11.9801	+	10.3808i	0.0132084	+	0.0114452i	0.661440	−	0.749998i	$-0.269946\pi$
$907$	11.9801	+	10.3808i	0.0132084	+	0.0114452i	−0.648232	+	0.761443i	$0.724491\pi$
$908$		0			0
$909$	−28.2712	−	18.1688i	−0.0311014	−	0.0199876i
$910$		0			0
$911$	113.499	−	386.543i	0.124587	−	0.424306i	−0.873451	−	0.486912i	$-0.838123\pi$
$911$	113.499	−	386.543i	0.124587	−	0.424306i	0.998038	+	0.0626065i	$0.0199413\pi$
$912$		0			0
$913$	170.032	+	196.228i	0.186235	+	0.214926i
$914$		0			0
$915$	−114.585	+	33.6452i	−0.125229	+	0.0367707i
$916$		0			0
$917$	1014.39	+	145.847i	1.10620	+	0.159048i
$918$		0			0
$919$			1163.05i			1.26557i	0.774329	+	0.632783i	$0.218087\pi$
$919$			1163.05i			1.26557i	−0.774329	+	0.632783i	$0.781913\pi$
$920$		0			0
$921$	1061.07			1.15208
$922$		0			0
$923$	3.46683	−	24.1123i	0.00375605	−	0.0261239i
$924$		0			0
$925$	−150.940	−	514.056i	−0.163179	−	0.555736i
$926$		0			0
$927$	−589.930	+	511.177i	−0.636386	+	0.551432i
$928$		0			0
$929$	−1132.41	−	332.505i	−1.21895	−	0.357917i	−0.391882	−	0.920015i	$-0.628176\pi$
$929$	−1132.41	−	332.505i	−1.21895	−	0.357917i	−0.827070	+	0.562099i	$0.809994\pi$
$930$		0			0
$931$	−234.538	+	364.948i	−0.251920	+	0.391996i
$932$		0			0
$933$	598.335	−	690.516i	0.641302	−	0.740102i
$934$		0			0
$935$	−55.4847	+	7.97750i	−0.0593420	+	0.00853209i
$936$		0			0
$937$	−830.817	+	379.421i	−0.886677	+	0.404932i	−0.806074	−	0.591814i	$-0.798412\pi$
$937$	−830.817	+	379.421i	−0.886677	+	0.404932i	−0.0806029	+	0.996746i	$0.525685\pi$
$938$		0			0
$939$	−1938.95	−	885.487i	−2.06490	−	0.943010i
$940$		0			0
$941$	842.159	+	1310.42i	0.894962	+	1.39259i	0.919585	+	0.392891i	$0.128525\pi$
$941$	842.159	+	1310.42i	0.894962	+	1.39259i	−0.0246234	+	0.999697i	$0.507839\pi$
$942$		0			0
$943$	−1520.55	+	456.810i	−1.61246	+	0.484422i
$944$		0			0
$945$	6.99912	−	4.49806i	0.00740648	−	0.00475986i
$946$		0			0
$947$	−204.993	+	448.873i	−0.216466	+	0.473994i	−0.986449	−	0.164070i	$-0.947538\pi$
$947$	−204.993	+	448.873i	−0.216466	+	0.473994i	0.769983	+	0.638065i	$0.220265\pi$
$948$		0			0
$949$	3.85325	+	8.43745i	0.00406033	+	0.00889088i
$950$		0			0
$951$	−100.737	−	700.644i	−0.105928	−	0.736744i
$952$		0			0
$953$	−298.040	−	258.253i	−0.312738	−	0.270989i	0.484321	−	0.874890i	$-0.339067\pi$
$953$	−298.040	−	258.253i	−0.312738	−	0.270989i	−0.797059	+	0.603901i	$0.793612\pi$
$954$		0			0
$955$	70.1318	+	45.0710i	0.0734365	+	0.0471948i
$956$		0			0
$957$	171.196	−	583.041i	0.178889	−	0.609239i
$958$		0			0
$959$	−118.376	−	136.613i	−0.123437	−	0.142454i
$960$		0			0
$961$	−242.264	+	71.1353i	−0.252096	+	0.0740221i
$962$		0			0
$963$	339.931	+	48.8746i	0.352991	+	0.0507525i
$964$		0			0
$965$		−	48.3513i		−	0.0501049i
$966$		0			0
$967$	−951.697			−0.984175			−0.492087	−	0.870546i	$-0.663766\pi$
$967$	−951.697			−0.984175			−0.492087	+	0.870546i	$0.663766\pi$
$968$		0			0
$969$	−113.027	+	786.121i	−0.116643	+	0.811270i
$970$		0			0
$971$	44.2245	+	150.615i	0.0455453	+	0.155113i	0.979126	−	0.203254i	$-0.0651518\pi$
$971$	44.2245	+	150.615i	0.0455453	+	0.155113i	−0.933581	+	0.358367i	$0.883334\pi$
$972$		0			0
$973$	−15.1904	+	13.1626i	−0.0156120	+	0.0135278i
$974$		0			0
$975$	−27.9335	−	8.20201i	−0.0286497	−	0.00841231i
$976$		0			0
$977$	847.836	−	1319.26i	0.867795	−	1.35032i	−0.0679684	−	0.997687i	$-0.521652\pi$
$977$	847.836	−	1319.26i	0.867795	−	1.35032i	0.935764	−	0.352628i	$-0.114712\pi$
$978$		0			0
$979$	−663.140	+	765.305i	−0.677365	+	0.781721i
$980$		0			0
$981$	−1462.02	+	210.207i	−1.49034	+	0.214278i
$982$		0			0
$983$	−1482.06	+	676.836i	−1.50769	+	0.688541i	−0.986328	−	0.164792i	$-0.947305\pi$
$983$	−1482.06	+	676.836i	−1.50769	+	0.688541i	−0.521366	+	0.853333i	$0.674577\pi$
$984$		0			0
$985$	164.711	+	75.2212i	0.167220	+	0.0763667i
$986$		0			0
$987$	−173.374	−	269.776i	−0.175658	−	0.273329i
$988$		0			0
$989$	1722.19	+	236.644i	1.74134	+	0.239276i
$990$		0			0
$991$	303.039	−	194.751i	0.305791	−	0.196520i	−0.378741	−	0.925503i	$-0.623643\pi$
$991$	303.039	−	194.751i	0.305791	−	0.196520i	0.684532	+	0.728983i	$0.260006\pi$
$992$		0			0
$993$	−23.5127	+	51.4857i	−0.0236785	+	0.0518486i
$994$		0			0
$995$	−59.9536	−	131.280i	−0.0602549	−	0.131940i
$996$		0			0
$997$	23.1928	+	161.310i	0.0232626	+	0.161795i	0.998141	−	0.0609412i	$-0.0194102\pi$
$997$	23.1928	+	161.310i	0.0232626	+	0.161795i	−0.974879	+	0.222736i	$0.928501\pi$
$998$		0			0
$999$	50.3981	+	43.6702i	0.0504485	+	0.0437139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.3.f.a.57.1	yes	40
4.3	odd	2		368.3.p.c.241.4		40
23.5	odd	22		2116.3.d.c.1057.34		40
23.18	even	11		2116.3.d.c.1057.33		40
23.21	odd	22	inner	92.3.f.a.21.1	✓	40
92.67	even	22		368.3.p.c.113.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.3.f.a.21.1	✓	40	23.21	odd	22	inner
92.3.f.a.57.1	yes	40	1.1	even	1	trivial
368.3.p.c.113.4		40	92.67	even	22
368.3.p.c.241.4		40	4.3	odd	2
2116.3.d.c.1057.33		40	23.18	even	11
2116.3.d.c.1057.34		40	23.5	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)

\(f(q)\)	\(=\)	\(q+(-0.591227 + 4.11207i) q^{3} +(0.143195 + 0.487679i) q^{5} +(-4.01704 + 3.48078i) q^{7} +(-7.92417 - 2.32675i) q^{9} +(-6.52142 + 10.1475i) q^{11} +(-0.185481 + 0.214056i) q^{13} +(-2.09003 + 0.300501i) q^{15} +(8.31682 - 3.79816i) q^{17} +(19.0197 + 8.68598i) q^{19} +(-11.9383 - 18.5763i) q^{21} +(22.9996 - 0.143656i) q^{23} +(20.8140 - 13.3764i) q^{25} +(-1.27932 + 2.80132i) q^{27} +(5.03736 + 11.0303i) q^{29} +(-4.95757 - 34.4806i) q^{31} +(-37.8717 - 32.8160i) q^{33} +(-2.27273 - 1.46059i) q^{35} +(6.10065 - 20.7769i) q^{37} +(-0.770554 - 0.889267i) q^{39} +(-66.2338 + 19.4480i) q^{41} +(74.8120 + 10.7563i) q^{43} -4.19763i q^{45} +14.5226 q^{47} +(-2.95269 + 20.5364i) q^{49} +(10.7012 + 36.4450i) q^{51} +(31.0669 - 26.9196i) q^{53} +(-5.88257 - 1.72728i) q^{55} +(-46.9623 + 73.0748i) q^{57} +(-68.4839 + 79.0346i) q^{59} +(55.9818 - 8.04896i) q^{61} +(39.9306 - 18.2357i) q^{63} +(-0.130951 - 0.0598032i) q^{65} +(-37.2684 - 57.9908i) q^{67} +(-13.0072 + 94.6608i) q^{69} +(-72.3535 + 46.4987i) q^{71} +(13.6043 - 29.7893i) q^{73} +(42.6988 + 93.4972i) q^{75} +(-9.12454 - 63.4626i) q^{77} +(-104.028 - 90.1406i) q^{79} +(-73.2918 - 47.1018i) q^{81} +(6.06438 - 20.6534i) q^{83} +(3.04321 + 3.51206i) q^{85} +(-48.3355 + 14.1926i) q^{87} +(83.0960 + 11.9474i) q^{89} -1.50549i q^{91} +144.718 q^{93} +(-1.51244 + 10.5193i) q^{95} +(8.18745 + 27.8839i) q^{97} +(75.2875 - 65.2370i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{3} - 6 q^{9} - 2 q^{13} + 77 q^{15} + 55 q^{17} + 33 q^{19} + 33 q^{21} - 50 q^{23} - 54 q^{25} - 191 q^{27} + q^{29} - 53 q^{31} - 121 q^{33} - 156 q^{35} - 352 q^{37} - 306 q^{39} + 6 q^{41}+ \cdots + 1353 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more