LMFDB - Embedded newform 92.3.f.a.21.4

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			21.4
Character	$\chi$	$=$	92.21
Dual form			92.3.f.a.57.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.652910 + 4.54109i) q^{3} +(-1.15784 + 3.94325i) q^{5} +(-4.50708 - 3.90541i) q^{7} +(-11.5598 + 3.39426i) q^{9} +(-2.23489 - 3.47756i) q^{11} +(14.6306 + 16.8846i) q^{13} +(-18.6626 - 2.68328i) q^{15} +(9.68346 + 4.42229i) q^{17} +(20.2597 - 9.25228i) q^{19} +(14.7921 - 23.0169i) q^{21} +(-14.0368 + 18.2200i) q^{23} +(6.82268 + 4.38467i) q^{25} +(-5.80859 - 12.7190i) q^{27} +(2.96443 - 6.49120i) q^{29} +(5.77656 - 40.1769i) q^{31} +(14.3327 - 12.4194i) q^{33} +(20.6185 - 13.2507i) q^{35} +(-18.4913 - 62.9755i) q^{37} +(-67.1219 + 77.4628i) q^{39} +(43.3495 + 12.7286i) q^{41} +(-14.0003 + 2.01294i) q^{43} -49.5131i q^{45} -42.3125 q^{47} +(-1.91186 - 13.2973i) q^{49} +(-13.7596 + 46.8608i) q^{51} +(69.2461 + 60.0021i) q^{53} +(16.3005 - 4.78627i) q^{55} +(55.2432 + 85.9601i) q^{57} +(46.8794 + 54.1017i) q^{59} +(-74.4782 - 10.7083i) q^{61} +(65.3567 + 29.8474i) q^{63} +(-83.5201 + 38.1423i) q^{65} +(29.2979 - 45.5884i) q^{67} +(-91.9035 - 51.8461i) q^{69} +(-102.888 - 66.1223i) q^{71} +(26.3453 + 57.6881i) q^{73} +(-15.4566 + 33.8452i) q^{75} +(-3.50845 + 24.4018i) q^{77} +(26.5494 - 23.0052i) q^{79} +(-37.2514 + 23.9400i) q^{81} +(-34.8453 - 118.672i) q^{83} +(-28.6501 + 33.0640i) q^{85} +(31.4126 + 9.22358i) q^{87} +(-42.7385 + 6.14487i) q^{89} -133.238i q^{91} +186.218 q^{93} +(13.0266 + 90.6018i) q^{95} +(25.2240 - 85.9050i) q^{97} +(37.6385 + 32.6140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$1$

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
$3$	0.652910	+	4.54109i	0.217637	+	1.51370i	0.746727	+	0.665131i	$0.231624\pi$
$3$	0.652910	+	4.54109i	0.217637	+	1.51370i	−0.529090	+	0.848566i	$0.677467\pi$
$4$		0			0
$5$	−1.15784	+	3.94325i	−0.231569	+	0.788651i	0.758935	+	0.651166i	$0.225720\pi$
$5$	−1.15784	+	3.94325i	−0.231569	+	0.788651i	−0.990504	+	0.137485i	$0.956098\pi$
$6$		0			0
$7$	−4.50708	−	3.90541i	−0.643868	−	0.557915i	0.270540	−	0.962709i	$-0.412798\pi$
$7$	−4.50708	−	3.90541i	−0.643868	−	0.557915i	−0.914408	+	0.404794i	$0.867343\pi$
$8$		0			0
$9$	−11.5598	+	3.39426i	−1.28442	+	0.377140i
$10$		0			0
$11$	−2.23489	−	3.47756i	−0.203172	−	0.316142i	0.724684	−	0.689082i	$-0.241986\pi$
$11$	−2.23489	−	3.47756i	−0.203172	−	0.316142i	−0.927855	+	0.372940i	$0.878350\pi$
$12$		0			0
$13$	14.6306	+	16.8846i	1.12543	+	1.29881i	0.949274	+	0.314451i	$0.101820\pi$
$13$	14.6306	+	16.8846i	1.12543	+	1.29881i	0.176154	+	0.984363i	$0.443634\pi$
$14$		0			0
$15$	−18.6626	−	2.68328i	−1.24418	−	0.178886i
$16$		0			0
$17$	9.68346	+	4.42229i	0.569615	+	0.260135i	0.679335	−	0.733828i	$-0.262268\pi$
$17$	9.68346	+	4.42229i	0.569615	+	0.260135i	−0.109720	+	0.993963i	$0.534995\pi$
$18$		0			0
$19$	20.2597	−	9.25228i	1.06630	−	0.486962i	0.196569	−	0.980490i	$-0.437020\pi$
$19$	20.2597	−	9.25228i	1.06630	−	0.486962i	0.869730	+	0.493528i	$0.164293\pi$
$20$		0			0
$21$	14.7921	−	23.0169i	0.704385	−	1.09604i
$22$		0			0
$23$	−14.0368	+	18.2200i	−0.610294	+	0.792175i
$23$	−14.0368	+	18.2200i	−0.610294	+	0.792175i
$24$		0			0
$25$	6.82268	+	4.38467i	0.272907	+	0.175387i
$26$		0			0
$27$	−5.80859	−	12.7190i	−0.215133	−	0.471076i
$28$		0			0
$29$	2.96443	−	6.49120i	0.102222	−	0.223835i	−0.851610	−	0.524176i	$-0.824373\pi$
$29$	2.96443	−	6.49120i	0.102222	−	0.223835i	0.953832	+	0.300342i	$0.0971007\pi$
$30$		0			0
$31$	5.77656	−	40.1769i	0.186341	−	1.29603i	−0.655044	−	0.755591i	$-0.727350\pi$
$31$	5.77656	−	40.1769i	0.186341	−	1.29603i	0.841384	−	0.540437i	$-0.181741\pi$
$32$		0			0
$33$	14.3327	−	12.4194i	0.434325	−	0.376345i
$34$		0			0
$35$	20.6185	−	13.2507i	0.589100	−	0.378592i
$36$		0			0
$37$	−18.4913	−	62.9755i	−0.499765	−	1.70204i	−0.693042	−	0.720898i	$-0.743730\pi$
$37$	−18.4913	−	62.9755i	−0.499765	−	1.70204i	0.193277	−	0.981144i	$-0.438088\pi$
$38$		0			0
$39$	−67.1219	+	77.4628i	−1.72107	+	1.98623i
$40$		0			0
$41$	43.3495	+	12.7286i	1.05731	+	0.310453i	0.763765	−	0.645494i	$-0.223348\pi$
$41$	43.3495	+	12.7286i	1.05731	+	0.310453i	0.293540	+	0.955947i	$0.405167\pi$
$42$		0			0
$43$	−14.0003	+	2.01294i	−0.325588	+	0.0468125i	−0.303171	−	0.952936i	$-0.598045\pi$
$43$	−14.0003	+	2.01294i	−0.325588	+	0.0468125i	−0.0224171	+	0.999749i	$0.507136\pi$
$44$		0			0
$45$		−	49.5131i		−	1.10029i
$46$		0			0
$47$	−42.3125			−0.900266			−0.450133	−	0.892961i	$-0.648623\pi$
$47$	−42.3125			−0.900266			−0.450133	+	0.892961i	$0.648623\pi$
$48$		0			0
$49$	−1.91186	−	13.2973i	−0.0390177	−	0.271374i
$50$		0			0
$51$	−13.7596	+	46.8608i	−0.269796	+	0.918839i
$52$		0			0
$53$	69.2461	+	60.0021i	1.30653	+	1.13211i	0.982540	+	0.186054i	$0.0595698\pi$
$53$	69.2461	+	60.0021i	1.30653	+	1.13211i	0.323990	+	0.946061i	$0.394976\pi$
$54$		0			0
$55$	16.3005	−	4.78627i	0.296374	−	0.0870231i
$56$		0			0
$57$	55.2432	+	85.9601i	0.969179	+	1.50807i
$58$		0			0
$59$	46.8794	+	54.1017i	0.794566	+	0.916978i	0.998070	−	0.0620958i	$-0.0197784\pi$
$59$	46.8794	+	54.1017i	0.794566	+	0.916978i	−0.203504	+	0.979074i	$0.565233\pi$
$60$		0			0
$61$	−74.4782	−	10.7083i	−1.22095	−	0.175547i	−0.498453	−	0.866917i	$-0.666098\pi$
$61$	−74.4782	−	10.7083i	−1.22095	−	0.175547i	−0.722501	+	0.691370i	$0.757007\pi$
$62$		0			0
$63$	65.3567	+	29.8474i	1.03741	+	0.473769i
$64$		0			0
$65$	−83.5201	+	38.1423i	−1.28492	+	0.586805i
$66$		0			0
$67$	29.2979	−	45.5884i	0.437282	−	0.680424i	−0.550750	−	0.834670i	$-0.685658\pi$
$67$	29.2979	−	45.5884i	0.437282	−	0.680424i	0.988033	+	0.154246i	$0.0492947\pi$
$68$		0			0
$69$	−91.9035	−	51.8461i	−1.33194	−	0.751393i
$70$		0			0
$71$	−102.888	−	66.1223i	−1.44913	−	0.931300i	−0.999270	−	0.0382010i	$-0.987837\pi$
$71$	−102.888	−	66.1223i	−1.44913	−	0.931300i	−0.449861	−	0.893099i	$-0.648526\pi$
$72$		0			0
$73$	26.3453	+	57.6881i	0.360894	+	0.790248i	0.999781	+	0.0209467i	$0.00666803\pi$
$73$	26.3453	+	57.6881i	0.360894	+	0.790248i	−0.638887	+	0.769301i	$0.720605\pi$
$74$		0			0
$75$	−15.4566	+	33.8452i	−0.206088	+	0.451270i
$76$		0			0
$77$	−3.50845	+	24.4018i	−0.0455642	+	0.316906i
$78$		0			0
$79$	26.5494	−	23.0052i	0.336068	−	0.291204i	−0.470435	−	0.882435i	$-0.655903\pi$
$79$	26.5494	−	23.0052i	0.336068	−	0.291204i	0.806503	+	0.591230i	$0.201358\pi$
$80$		0			0
$81$	−37.2514	+	23.9400i	−0.459894	+	0.295556i
$82$		0			0
$83$	−34.8453	−	118.672i	−0.419823	−	1.42979i	−0.849876	−	0.526983i	$-0.823323\pi$
$83$	−34.8453	−	118.672i	−0.419823	−	1.42979i	0.430052	−	0.902804i	$-0.358495\pi$
$84$		0			0
$85$	−28.6501	+	33.0640i	−0.337060	+	0.388988i
$86$		0			0
$87$	31.4126	+	9.22358i	0.361065	+	0.106018i
$88$		0			0
$89$	−42.7385	+	6.14487i	−0.480208	+	0.0690435i	−0.378168	−	0.925737i	$-0.623446\pi$
$89$	−42.7385	+	6.14487i	−0.480208	+	0.0690435i	−0.102040	+	0.994780i	$0.532537\pi$
$90$		0			0
$91$		−	133.238i		−	1.46416i
$92$		0			0
$93$	186.218			2.00235
$94$		0			0
$95$	13.0266	+	90.6018i	0.137122	+	0.953703i
$96$		0			0
$97$	25.2240	−	85.9050i	0.260041	−	0.885619i	−0.721182	−	0.692745i	$-0.756401\pi$
$97$	25.2240	−	85.9050i	0.260041	−	0.885619i	0.981224	−	0.192874i	$-0.0617807\pi$
$98$		0			0
$99$	37.6385	+	32.6140i	0.380187	+	0.329434i
$100$		0			0
$101$	−35.2693	+	10.3560i	−0.349201	+	0.102535i	−0.451629	−	0.892206i	$-0.649157\pi$
$101$	−35.2693	+	10.3560i	−0.349201	+	0.102535i	0.102428	+	0.994740i	$0.467339\pi$
$102$		0			0
$103$	9.11413	+	14.1819i	0.0884867	+	0.137688i	0.882675	−	0.469983i	$-0.155740\pi$
$103$	9.11413	+	14.1819i	0.0884867	+	0.137688i	−0.794189	+	0.607671i	$0.792104\pi$
$104$		0			0
$105$	73.6347	+	84.9790i	0.701283	+	0.809323i
$106$		0			0
$107$	78.7091	+	11.3167i	0.735599	+	0.105763i	0.499924	−	0.866069i	$-0.333361\pi$
$107$	78.7091	+	11.3167i	0.735599	+	0.105763i	0.235674	+	0.971832i	$0.424270\pi$
$108$		0			0
$109$	−36.0128	−	16.4465i	−0.330393	−	0.150885i	0.243311	−	0.969948i	$-0.421767\pi$
$109$	−36.0128	−	16.4465i	−0.330393	−	0.150885i	−0.573704	+	0.819063i	$0.694494\pi$
$110$		0			0
$111$	273.905	−	125.088i	2.46761	−	1.12692i
$112$		0			0
$113$	52.0211	−	80.9465i	0.460364	−	0.716340i	−0.531016	−	0.847362i	$-0.678189\pi$
$113$	52.0211	−	80.9465i	0.460364	−	0.716340i	0.991379	+	0.131022i	$0.0418258\pi$
$114$		0			0
$115$	−55.5938	−	76.4465i	−0.483425	−	0.664752i
$116$		0			0
$117$	−226.437	−	145.522i	−1.93536	−	1.24378i
$118$		0			0
$119$	−26.3733	−	57.7494i	−0.221624	−	0.485289i
$120$		0			0
$121$	43.1665	−	94.5216i	0.356748	−	0.781170i
$122$		0			0
$123$	−29.4982	+	205.165i	−0.239823	+	1.66801i
$124$		0			0
$125$	−102.838	+	89.1093i	−0.822701	+	0.712874i
$126$		0			0
$127$	25.8646	−	16.6222i	0.203658	−	0.130883i	−0.434836	−	0.900510i	$-0.643194\pi$
$127$	25.8646	−	16.6222i	0.203658	−	0.130883i	0.638495	+	0.769626i	$0.279557\pi$
$128$		0			0
$129$	−18.2819	−	62.2623i	−0.141720	−	0.482653i
$130$		0			0
$131$	−98.9165	+	114.156i	−0.755088	+	0.871418i	−0.995051	−	0.0993640i	$-0.968319\pi$
$131$	−98.9165	+	114.156i	−0.755088	+	0.871418i	0.239963	+	0.970782i	$0.422865\pi$
$132$		0			0
$133$	−127.446	−	37.4215i	−0.958240	−	0.281365i
$134$		0			0
$135$	56.8799	−	8.17809i	0.421332	−	0.0605785i
$136$		0			0
$137$			202.579i			1.47868i	0.673331	+	0.739341i	$0.264863\pi$
$137$			202.579i			1.47868i	−0.673331	+	0.739341i	$0.735137\pi$
$138$		0			0
$139$	−46.0946			−0.331616			−0.165808	−	0.986158i	$-0.553023\pi$
$139$	−46.0946			−0.331616			−0.165808	+	0.986158i	$0.553023\pi$
$140$		0			0
$141$	−27.6263	−	192.145i	−0.195931	−	1.36273i
$142$		0			0
$143$	26.0194	−	88.6138i	0.181954	−	0.619677i
$144$		0			0
$145$	22.1641	+	19.2053i	0.152856	+	0.132450i
$146$		0			0
$147$	59.1360	−	17.3639i	0.402286	−	0.118122i
$148$		0			0
$149$	−58.3434	−	90.7841i	−0.391567	−	0.609289i	0.588372	−	0.808591i	$-0.299769\pi$
$149$	−58.3434	−	90.7841i	−0.391567	−	0.609289i	−0.979938	+	0.199301i	$0.936133\pi$
$150$		0			0
$151$	73.8459	+	85.2227i	0.489046	+	0.564389i	0.945610	−	0.325301i	$-0.105466\pi$
$151$	73.8459	+	85.2227i	0.489046	+	0.564389i	−0.456565	+	0.889690i	$0.650920\pi$
$152$		0			0
$153$	−126.949	−	18.2525i	−0.829732	−	0.119297i
$154$		0			0
$155$	151.739	+	69.2970i	0.978963	+	0.447077i
$156$		0			0
$157$	34.2215	−	15.6284i	0.217971	−	0.0995441i	−0.303437	−	0.952852i	$-0.598134\pi$
$157$	34.2215	−	15.6284i	0.217971	−	0.0995441i	0.521408	+	0.853307i	$0.325407\pi$
$158$		0			0
$159$	−227.263	+	353.629i	−1.42933	+	2.22408i
$160$		0			0
$161$	134.421	−	27.2999i	0.834915	−	0.169564i
$162$		0			0
$163$	224.042	+	143.983i	1.37449	+	0.883331i	0.999053	−	0.0435174i	$-0.0138564\pi$
$163$	224.042	+	143.983i	1.37449	+	0.883331i	0.375437	+	0.926848i	$0.377493\pi$
$164$		0			0
$165$	32.3777	+	70.8972i	0.196228	+	0.429680i
$166$		0			0
$167$	−7.86457	+	17.2210i	−0.0470932	+	0.103120i	−0.931716	−	0.363187i	$-0.881689\pi$
$167$	−7.86457	+	17.2210i	−0.0470932	+	0.103120i	0.884623	+	0.466307i	$0.154416\pi$
$168$		0			0
$169$	−46.9841	+	326.782i	−0.278013	+	1.93362i
$170$		0			0
$171$	−202.793	+	175.721i	−1.18592	+	1.02761i
$172$		0			0
$173$	219.370	−	140.981i	1.26804	−	0.814917i	0.278672	−	0.960386i	$-0.410106\pi$
$173$	219.370	−	140.981i	1.26804	−	0.814917i	0.989363	+	0.145470i	$0.0464693\pi$
$174$		0			0
$175$	−13.6264	−	46.4074i	−0.0778654	−	0.265185i
$176$		0			0
$177$	−215.073	+	248.207i	−1.21510	+	1.40230i
$178$		0			0
$179$	−280.793	−	82.4483i	−1.56868	−	0.460605i	−0.622061	−	0.782969i	$-0.713704\pi$
$179$	−280.793	−	82.4483i	−1.56868	−	0.460605i	−0.946616	+	0.322364i	$0.895523\pi$
$180$		0			0
$181$	136.599	−	19.6399i	0.754689	−	0.108508i	0.245777	−	0.969326i	$-0.420957\pi$
$181$	136.599	−	19.6399i	0.754689	−	0.108508i	0.508912	+	0.860818i	$0.330048\pi$
$182$		0			0
$183$		−	345.204i		−	1.88636i
$184$		0			0
$185$	269.739			1.45805
$186$		0			0
$187$	−6.26271	−	43.5581i	−0.0334904	−	0.232931i
$188$		0			0
$189$	−23.4932	+	80.0106i	−0.124303	+	0.423337i
$190$		0			0
$191$	145.689	+	126.240i	0.762771	+	0.660945i	0.946744	−	0.321986i	$-0.104351\pi$
$191$	145.689	+	126.240i	0.762771	+	0.660945i	−0.183973	+	0.982931i	$0.558896\pi$
$192$		0			0
$193$	−157.034	+	46.1093i	−0.813646	+	0.238908i	−0.661978	−	0.749523i	$-0.730283\pi$
$193$	−157.034	+	46.1093i	−0.813646	+	0.238908i	−0.151668	+	0.988431i	$0.548465\pi$
$194$		0			0
$195$	−227.739	−	354.369i	−1.16789	−	1.81728i
$196$		0			0
$197$	−143.126	−	165.176i	−0.726529	−	0.838459i	0.265547	−	0.964098i	$-0.414447\pi$
$197$	−143.126	−	165.176i	−0.726529	−	0.838459i	−0.992076	+	0.125639i	$0.959902\pi$
$198$		0			0
$199$	22.0140	+	3.16514i	0.110623	+	0.0159052i	0.197404	−	0.980322i	$-0.436749\pi$
$199$	22.0140	+	3.16514i	0.110623	+	0.0159052i	−0.0867808	+	0.996227i	$0.527658\pi$
$200$		0			0
$201$	226.150	+	103.279i	1.12512	+	0.513827i
$202$		0			0
$203$	−38.7117	+	17.6790i	−0.190698	+	0.0870889i
$204$		0			0
$205$	−100.384	+	156.200i	−0.489678	+	0.761954i
$206$		0			0
$207$	100.418	−	258.264i	0.485112	−	1.24765i
$208$		0			0
$209$	−77.4535	−	49.7763i	−0.370591	−	0.238164i
$210$		0			0
$211$	13.2244	+	28.9574i	0.0626750	+	0.137239i	0.938378	−	0.345612i	$-0.112329\pi$
$211$	13.2244	+	28.9574i	0.0626750	+	0.137239i	−0.875703	+	0.482851i	$0.839601\pi$
$212$		0			0
$213$	233.090	−	510.397i	1.09432	−	2.39623i
$214$		0			0
$215$	8.27262	−	57.5373i	0.0384773	−	0.267616i
$216$		0			0
$217$	−182.942	+	158.521i	−0.843053	+	0.730509i
$218$		0			0
$219$	−244.766	+	157.301i	−1.11765	+	0.718271i
$220$		0			0
$221$	67.0060	+	228.202i	0.303195	+	1.03259i
$222$		0			0
$223$	104.179	−	120.229i	0.467169	−	0.539142i	−0.472453	−	0.881356i	$-0.656631\pi$
$223$	104.179	−	120.229i	0.467169	−	0.539142i	0.939622	+	0.342214i	$0.111177\pi$
$224$		0			0
$225$	−93.7514	−	27.5279i	−0.416673	−	0.122346i
$226$		0			0
$227$	349.537	−	50.2558i	1.53981	−	0.221391i	0.680462	−	0.732783i	$-0.261779\pi$
$227$	349.537	−	50.2558i	1.53981	−	0.221391i	0.859347	+	0.511392i	$0.170870\pi$
$228$		0			0
$229$			23.9320i			0.104507i	0.998634	+	0.0522534i	$0.0166403\pi$
$229$			23.9320i			0.104507i	−0.998634	+	0.0522534i	$0.983360\pi$
$230$		0			0
$231$	−113.101			−0.489616
$232$		0			0
$233$	−46.7553	−	325.190i	−0.200666	−	1.39567i	−0.802313	−	0.596903i	$-0.796398\pi$
$233$	−46.7553	−	325.190i	−0.200666	−	1.39567i	0.601647	−	0.798762i	$-0.294511\pi$
$234$		0			0
$235$	48.9913	−	166.849i	0.208474	−	0.709996i
$236$		0			0
$237$	121.803	+	105.543i	0.513936	+	0.445328i
$238$		0			0
$239$	−32.6548	+	9.58830i	−0.136631	+	0.0401184i	−0.349333	−	0.936999i	$-0.613592\pi$
$239$	−32.6548	+	9.58830i	−0.136631	+	0.0401184i	0.212702	+	0.977117i	$0.431774\pi$
$240$		0			0
$241$	54.1794	+	84.3048i	0.224811	+	0.349813i	0.935276	−	0.353920i	$-0.115152\pi$
$241$	54.1794	+	84.3048i	0.224811	+	0.349813i	−0.710465	+	0.703733i	$0.751515\pi$
$242$		0			0
$243$	−215.446	−	248.638i	−0.886608	−	1.02320i
$244$		0			0
$245$	54.6483	+	7.85724i	0.223054	+	0.0320704i
$246$		0			0
$247$	452.631	+	206.710i	1.83252	+	0.836882i
$248$		0			0
$249$	516.151	−	235.718i	2.07290	−	0.946660i
$250$		0			0
$251$	128.053	−	199.254i	0.510171	−	0.793842i	−0.486643	−	0.873601i	$-0.661779\pi$
$251$	128.053	−	199.254i	0.510171	−	0.793842i	0.996814	+	0.0797589i	$0.0254150\pi$
$252$		0			0
$253$	94.7318	+	8.09386i	0.374434	+	0.0319915i
$254$		0			0
$255$	−168.853	−	108.515i	−0.662167	−	0.425549i
$256$		0			0
$257$	21.6669	+	47.4439i	0.0843071	+	0.184607i	0.947090	−	0.320967i	$-0.104008\pi$
$257$	21.6669	+	47.4439i	0.0843071	+	0.184607i	−0.862783	+	0.505574i	$0.831281\pi$
$258$		0			0
$259$	−162.603	+	356.052i	−0.627812	+	1.37472i
$260$		0			0
$261$	−12.2354	+	85.0988i	−0.0468788	+	0.326049i
$262$		0			0
$263$	−345.839	+	299.672i	−1.31498	+	1.13944i	−0.334590	+	0.942364i	$0.608598\pi$
$263$	−345.839	+	299.672i	−1.31498	+	1.13944i	−0.980389	+	0.197072i	$0.936857\pi$
$264$		0			0
$265$	−316.780	+	203.582i	−1.19539	+	0.768233i
$266$		0			0
$267$	−55.8089	−	190.068i	−0.209022	−	0.711863i
$268$		0			0
$269$	90.3607	−	104.282i	0.335913	−	0.387665i	−0.562513	−	0.826788i	$-0.690165\pi$
$269$	90.3607	−	104.282i	0.335913	−	0.387665i	0.898427	+	0.439124i	$0.144711\pi$
$270$		0			0
$271$	−251.816	−	73.9397i	−0.929209	−	0.272840i	−0.218103	−	0.975926i	$-0.569987\pi$
$271$	−251.816	−	73.9397i	−0.929209	−	0.272840i	−0.711106	+	0.703085i	$0.751805\pi$
$272$		0			0
$273$	605.048	−	86.9927i	2.21629	−	0.318655i
$274$		0			0
$275$		−	33.5255i		−	0.121911i
$276$		0			0
$277$	226.528			0.817789			0.408895	−	0.912582i	$-0.365914\pi$
$277$	226.528			0.817789			0.408895	+	0.912582i	$0.365914\pi$
$278$		0			0
$279$	69.5948	+	484.043i	0.249444	+	1.73492i
$280$		0			0
$281$	15.7801	−	53.7421i	0.0561570	−	0.191253i	−0.926637	−	0.375956i	$-0.877314\pi$
$281$	15.7801	−	53.7421i	0.0561570	−	0.191253i	0.982794	+	0.184703i	$0.0591324\pi$
$282$		0			0
$283$	49.7570	+	43.1147i	0.175820	+	0.152349i	0.738325	−	0.674445i	$-0.235617\pi$
$283$	49.7570	+	43.1147i	0.175820	+	0.152349i	−0.562505	+	0.826794i	$0.690162\pi$
$284$		0			0
$285$	−402.926	+	118.310i	−1.41377	+	0.415122i
$286$		0			0
$287$	−145.669	−	226.666i	−0.507559	−	0.789777i
$288$		0			0
$289$	−115.042	−	132.766i	−0.398069	−	0.459396i
$290$		0			0
$291$	406.571	+	58.4562i	1.39715	+	0.200880i
$292$		0			0
$293$	−386.498	−	176.508i	−1.31911	−	0.602416i	−0.373470	−	0.927642i	$-0.621832\pi$
$293$	−386.498	−	176.508i	−1.31911	−	0.602416i	−0.945636	+	0.325226i	$0.894560\pi$
$294$		0			0
$295$	−267.616	+	122.216i	−0.907173	+	0.414292i
$296$		0			0
$297$	−31.2496	+	48.6254i	−0.105218	+	0.163722i
$298$		0			0
$299$	−513.003	+	29.5647i	−1.71573	+	0.0988785i
$300$		0			0
$301$	70.9617	+	45.6043i	0.235753	+	0.151509i
$302$		0			0
$303$	−70.0552	−	153.399i	−0.231205	−	0.506269i
$304$		0			0
$305$	128.460	−	281.288i	0.421180	−	0.922255i
$306$		0			0
$307$	−55.6170	+	386.824i	−0.181163	+	1.26001i	0.672856	+	0.739773i	$0.265067\pi$
$307$	−55.6170	+	386.824i	−0.181163	+	1.26001i	−0.854019	+	0.520241i	$0.825842\pi$
$308$		0			0
$309$	−58.4504	+	50.6476i	−0.189160	+	0.163908i
$310$		0			0
$311$	−358.452	+	230.363i	−1.15258	+	0.740718i	−0.970151	−	0.242501i	$-0.922032\pi$
$311$	−358.452	+	230.363i	−1.15258	+	0.740718i	−0.182429	+	0.983219i	$0.558396\pi$
$312$		0			0
$313$	−97.7992	−	333.073i	−0.312457	−	1.06413i	−0.954685	−	0.297618i	$-0.903808\pi$
$313$	−97.7992	−	333.073i	−0.312457	−	1.06413i	0.642227	−	0.766514i	$-0.278010\pi$
$314$		0			0
$315$	−193.369	+	223.160i	−0.613870	+	0.708443i
$316$		0			0
$317$	8.13498	+	2.38865i	0.0256624	+	0.00753516i	0.294539	−	0.955640i	$-0.404834\pi$
$317$	8.13498	+	2.38865i	0.0256624	+	0.00753516i	−0.268876	+	0.963175i	$0.586652\pi$
$318$		0			0
$319$	−29.1987	+	4.19814i	−0.0915320	+	0.0131603i
$320$		0			0
$321$			364.814i			1.13649i
$322$		0			0
$323$	237.100			0.734056
$324$		0			0
$325$	25.7864	+	179.348i	0.0793428	+	0.551841i
$326$		0			0
$327$	51.1719	−	174.276i	0.156489	−	0.532953i
$328$		0			0
$329$	190.706	+	165.248i	0.579653	+	0.502272i
$330$		0			0
$331$	274.611	−	80.6330i	0.829640	−	0.243604i	0.160778	−	0.986991i	$-0.448600\pi$
$331$	274.611	−	80.6330i	0.829640	−	0.243604i	0.668862	+	0.743386i	$0.266782\pi$
$332$		0			0
$333$	427.510	+	665.219i	1.28381	+	1.99765i
$334$		0			0
$335$	145.844	+	168.313i	0.435356	+	0.502428i
$336$		0			0
$337$	−615.867	−	88.5483i	−1.82750	−	0.262755i	−0.859036	−	0.511915i	$-0.828936\pi$
$337$	−615.867	−	88.5483i	−1.82750	−	0.262755i	−0.968462	+	0.249160i	$0.919845\pi$
$338$		0			0
$339$	401.550	+	183.382i	1.18451	+	0.540950i
$340$		0			0
$341$	−152.627	+	69.7026i	−0.447588	+	0.204406i
$342$		0			0
$343$	−201.302	+	313.232i	−0.586886	+	0.913212i
$344$		0			0
$345$	310.852	−	302.369i	0.901022	−	0.876433i
$346$		0			0
$347$	288.389	+	185.336i	0.831092	+	0.534110i	0.885625	−	0.464402i	$-0.153731\pi$
$347$	288.389	+	185.336i	0.831092	+	0.534110i	−0.0545329	+	0.998512i	$0.517367\pi$
$348$		0			0
$349$	−63.2248	−	138.443i	−0.181160	−	0.396685i	0.797165	−	0.603762i	$-0.206332\pi$
$349$	−63.2248	−	138.443i	−0.181160	−	0.396685i	−0.978325	+	0.207077i	$0.933605\pi$
$350$		0			0
$351$	129.773	−	284.162i	0.369723	−	0.809580i
$352$		0			0
$353$	5.61754	−	39.0708i	0.0159137	−	0.110682i	−0.980316	−	0.197433i	$-0.936739\pi$
$353$	5.61754	−	39.0708i	0.0159137	−	0.110682i	0.996230	+	0.0867511i	$0.0276485\pi$
$354$		0			0
$355$	379.866	−	329.155i	1.07004	−	0.927198i
$356$		0			0
$357$	245.026	−	157.469i	0.686347	−	0.441089i
$358$		0			0
$359$	13.8682	+	47.2307i	0.0386300	+	0.131562i	0.976550	−	0.215289i	$-0.0690693\pi$
$359$	13.8682	+	47.2307i	0.0386300	+	0.131562i	−0.937920	+	0.346851i	$0.887251\pi$
$360$		0			0
$361$	88.4450	−	102.071i	0.245000	−	0.282745i
$362$		0			0
$363$	457.415	+	134.309i	1.26010	+	0.369998i
$364$		0			0
$365$	−257.982	+	37.0923i	−0.706801	+	0.101623i
$366$		0			0
$367$			148.649i			0.405039i	0.979278	+	0.202519i	$0.0649129\pi$
$367$			148.649i			0.405039i	−0.979278	+	0.202519i	$0.935087\pi$
$368$		0			0
$369$	−544.315			−1.47511
$370$		0			0
$371$	−77.7651	−	540.868i	−0.209609	−	1.45786i
$372$		0			0
$373$	−130.556	+	444.634i	−0.350017	+	1.19205i	0.576911	+	0.816807i	$0.304258\pi$
$373$	−130.556	+	444.634i	−0.350017	+	1.19205i	−0.926927	+	0.375241i	$0.877560\pi$
$374$		0			0
$375$	−471.797	−	408.814i	−1.25813	−	1.09017i
$376$		0			0
$377$	152.972	−	44.9168i	0.405762	−	0.119143i
$378$		0			0
$379$	−201.015	−	312.785i	−0.530382	−	0.825290i	0.467907	−	0.883778i	$-0.345008\pi$
$379$	−201.015	−	312.785i	−0.530382	−	0.825290i	−0.998288	+	0.0584882i	$0.981372\pi$
$380$		0			0
$381$	92.3701	+	106.601i	0.242441	+	0.279792i
$382$		0			0
$383$	−227.561	−	32.7184i	−0.594155	−	0.0854266i	−0.161324	−	0.986902i	$-0.551576\pi$
$383$	−227.561	−	32.7184i	−0.594155	−	0.0854266i	−0.432831	+	0.901475i	$0.642485\pi$
$384$		0			0
$385$	−92.1602	−	42.0881i	−0.239377	−	0.109320i
$386$		0			0
$387$	155.008	−	70.7896i	0.400537	−	0.182919i
$388$		0			0
$389$	152.821	−	237.794i	0.392856	−	0.611296i	−0.587336	−	0.809343i	$-0.699823\pi$
$389$	152.821	−	237.794i	0.392856	−	0.611296i	0.980193	+	0.198047i	$0.0634597\pi$
$390$		0			0
$391$	−216.499	+	114.358i	−0.553705	+	0.292477i
$392$		0			0
$393$	−582.975	−	374.655i	−1.48340	−	0.953322i
$394$		0			0
$395$	59.9752	+	131.327i	0.151836	+	0.332474i
$396$		0			0
$397$	−95.3365	+	208.758i	−0.240142	+	0.525839i	−0.990878	−	0.134765i	$-0.956972\pi$
$397$	−95.3365	+	208.758i	−0.240142	+	0.525839i	0.750735	+	0.660603i	$0.229699\pi$
$398$		0			0
$399$	86.7236	−	603.176i	0.217352	−	1.51172i
$400$		0			0
$401$	255.812	−	221.662i	0.637934	−	0.552773i	−0.274710	−	0.961527i	$-0.588582\pi$
$401$	255.812	−	221.662i	0.637934	−	0.552773i	0.912645	+	0.408754i	$0.134036\pi$
$402$		0			0
$403$	762.884	−	490.276i	1.89301	−	1.21656i
$404$		0			0
$405$	−51.2703	−	174.611i	−0.126593	−	0.431137i
$406$		0			0
$407$	−177.675	+	205.048i	−0.436548	+	0.503803i
$408$		0			0
$409$	−181.420	−	53.2698i	−0.443570	−	0.130244i	0.0523178	−	0.998630i	$-0.483339\pi$
$409$	−181.420	−	53.2698i	−0.443570	−	0.130244i	−0.495888	+	0.868387i	$0.665157\pi$
$410$		0			0
$411$	−919.931	+	132.266i	−2.23828	+	0.321815i
$412$		0			0
$413$		−	426.924i		−	1.03371i
$414$		0			0
$415$	508.301			1.22482
$416$		0			0
$417$	−30.0956	−	209.320i	−0.0721718	−	0.501966i
$418$		0			0
$419$	26.0736	−	88.7987i	0.0622283	−	0.211930i	−0.922510	−	0.385974i	$-0.873865\pi$
$419$	26.0736	−	88.7987i	0.0622283	−	0.211930i	0.984738	+	0.174044i	$0.0556836\pi$
$420$		0			0
$421$	212.022	+	183.718i	0.503616	+	0.436386i	0.869250	−	0.494373i	$-0.164602\pi$
$421$	212.022	+	183.718i	0.503616	+	0.436386i	−0.365634	+	0.930759i	$0.619148\pi$
$422$		0			0
$423$	489.123	−	143.619i	1.15632	−	0.339526i
$424$		0			0
$425$	46.6769	+	72.6307i	0.109828	+	0.170896i
$426$		0			0
$427$	293.859	+	339.131i	0.688193	+	0.794218i
$428$		0			0
$429$	419.391	+	60.2994i	0.977602	+	0.140558i
$430$		0			0
$431$	176.562	+	80.6333i	0.409657	+	0.187084i	0.609575	−	0.792729i	$-0.291340\pi$
$431$	176.562	+	80.6333i	0.409657	+	0.187084i	−0.199918	+	0.979813i	$0.564067\pi$
$432$		0			0
$433$	−249.896	+	114.124i	−0.577128	+	0.263566i	−0.682522	−	0.730865i	$-0.739117\pi$
$433$	−249.896	+	114.124i	−0.577128	+	0.263566i	0.105394	+	0.994431i	$0.466390\pi$
$434$		0			0
$435$	−72.7419	+	113.189i	−0.167223	+	0.260204i
$436$		0			0
$437$	−115.803	+	499.004i	−0.264996	+	1.14189i
$438$		0			0
$439$	44.4677	+	28.5776i	0.101293	+	0.0650971i	0.590307	−	0.807179i	$-0.299007\pi$
$439$	44.4677	+	28.5776i	0.101293	+	0.0650971i	−0.489014	+	0.872276i	$0.662643\pi$
$440$		0			0
$441$	67.2352	+	147.225i	0.152461	+	0.333843i
$442$		0			0
$443$	39.4183	−	86.3140i	0.0889803	−	0.194840i	−0.859910	−	0.510446i	$-0.829480\pi$
$443$	39.4183	−	86.3140i	0.0889803	−	0.194840i	0.948890	+	0.315606i	$0.102208\pi$
$444$		0			0
$445$	25.2538	−	175.644i	0.0567500	−	0.394705i
$446$		0			0
$447$	374.166	−	324.217i	0.837060	−	0.725317i
$448$		0			0
$449$	267.976	−	172.218i	0.596829	−	0.383559i	−0.207068	−	0.978326i	$-0.566392\pi$
$449$	267.976	−	172.218i	0.596829	−	0.383559i	0.803898	+	0.594768i	$0.202756\pi$
$450$		0			0
$451$	−52.6171	−	179.197i	−0.116668	−	0.397333i
$452$		0			0
$453$	−338.789	+	390.984i	−0.747879	+	0.863099i
$454$		0			0
$455$	525.393	+	154.269i	1.15471	+	0.339053i
$456$		0			0
$457$	−590.258	+	84.8663i	−1.29159	+	0.185703i	−0.753649	−	0.657277i	$-0.771708\pi$
$457$	−590.258	+	84.8663i	−1.29159	+	0.185703i	−0.537945	+	0.842980i	$0.680799\pi$
$458$		0			0
$459$		−	148.852i		−	0.324295i
$460$		0			0
$461$	155.035			0.336301			0.168151	−	0.985761i	$-0.446220\pi$
$461$	155.035			0.336301			0.168151	+	0.985761i	$0.446220\pi$
$462$		0			0
$463$	46.9176	+	326.319i	0.101334	+	0.704793i	0.975634	+	0.219406i	$0.0704121\pi$
$463$	46.9176	+	326.319i	0.101334	+	0.704793i	−0.874300	+	0.485387i	$0.838679\pi$
$464$		0			0
$465$	−215.612	+	734.307i	−0.463681	+	1.57915i
$466$		0			0
$467$	−97.7755	−	84.7229i	−0.209369	−	0.181420i	0.543863	−	0.839174i	$-0.316961\pi$
$467$	−97.7755	−	84.7229i	−0.209369	−	0.181420i	−0.753233	+	0.657754i	$0.771506\pi$
$468$		0			0
$469$	−310.089	+	91.0504i	−0.661171	+	0.194137i
$470$		0			0
$471$	93.3137	+	145.199i	0.198118	+	0.308278i
$472$		0			0
$473$	38.2892	+	44.1881i	0.0809497	+	0.0934209i
$474$		0			0
$475$	178.794	+	25.7066i	0.376408	+	0.0541192i
$476$		0			0
$477$	−1004.13	−	458.571i	−2.10510	−	0.961365i
$478$		0			0
$479$	40.0901	−	18.3085i	0.0836954	−	0.0382224i	−0.373127	−	0.927780i	$-0.621715\pi$
$479$	40.0901	−	18.3085i	0.0836954	−	0.0382224i	0.456823	+	0.889558i	$0.348987\pi$
$480$		0			0
$481$	792.777	−	1233.59i	1.64819	−	2.56463i
$482$		0			0
$483$	211.736	+	592.595i	0.438377	+	1.22691i
$484$		0			0
$485$	309.540	+	198.929i	0.638227	+	0.410163i
$486$		0			0
$487$	−129.184	−	282.872i	−0.265264	−	0.580847i	0.729392	−	0.684096i	$-0.239803\pi$
$487$	−129.184	−	282.872i	−0.265264	−	0.580847i	−0.994655	+	0.103249i	$0.967076\pi$
$488$		0			0
$489$	−507.560	+	1111.40i	−1.03796	+	2.27281i
$490$		0			0
$491$	−85.1490	+	592.224i	−0.173420	+	1.20616i	0.698173	+	0.715929i	$0.253997\pi$
$491$	−85.1490	+	592.224i	−0.173420	+	1.20616i	−0.871593	+	0.490231i	$0.836912\pi$
$492$		0			0
$493$	57.4119	−	49.7477i	0.116454	−	0.100908i
$494$		0			0
$495$	−172.185	+	110.656i	−0.347848	+	0.223548i
$496$		0			0
$497$	205.491	+	699.839i	0.413463	+	1.40813i
$498$		0			0
$499$	352.186	−	406.445i	0.705784	−	0.814518i	−0.283738	−	0.958902i	$-0.591574\pi$
$499$	352.186	−	406.445i	0.705784	−	0.814518i	0.989522	+	0.144384i	$0.0461199\pi$
$500$		0			0
$501$	−83.3370	−	24.4700i	−0.166341	−	0.0488422i
$502$		0			0
$503$	−702.832	+	101.052i	−1.39728	+	0.200898i	−0.799454	−	0.600728i	$-0.794878\pi$
$503$	−702.832	+	101.052i	−1.39728	+	0.200898i	−0.597826	+	0.801626i	$0.703969\pi$
$504$		0			0
$505$		−	151.066i		−	0.299141i
$506$		0			0
$507$	−1514.62			−2.98742
$508$		0			0
$509$	43.4268	+	302.040i	0.0853178	+	0.593398i	0.986966	+	0.160928i	$0.0514488\pi$
$509$	43.4268	+	302.040i	0.0853178	+	0.593398i	−0.901648	+	0.432470i	$0.857642\pi$
$510$		0			0
$511$	106.555	−	362.894i	0.208523	−	0.710164i
$512$		0			0
$513$	−235.360	−	203.941i	−0.458792	−	0.397546i
$514$		0			0
$515$	−66.4754	+	19.5190i	−0.129079	+	0.0379009i
$516$		0			0
$517$	94.5638	+	147.144i	0.182909	+	0.284611i
$518$		0			0
$519$	783.434	+	904.132i	1.50951	+	1.74206i
$520$		0			0
$521$	−937.654	−	134.814i	−1.79972	−	0.258761i	−0.840579	−	0.541688i	$-0.817785\pi$
$521$	−937.654	−	134.814i	−1.79972	−	0.258761i	−0.959141	+	0.282928i	$0.908694\pi$
$522$		0			0
$523$	−409.411	−	186.972i	−0.782812	−	0.357498i	−0.0164149	−	0.999865i	$-0.505225\pi$
$523$	−409.411	−	186.972i	−0.782812	−	0.357498i	−0.766397	+	0.642367i	$0.777953\pi$
$524$		0			0
$525$	201.843	−	92.1788i	0.384464	−	0.175579i
$526$		0			0
$527$	233.611	−	363.505i	0.443284	−	0.689764i
$528$		0			0
$529$	−134.939	−	511.500i	−0.255083	−	0.966919i
$530$		0			0
$531$	−725.550	−	466.283i	−1.36638	−	0.878122i
$532$		0			0
$533$	419.312	+	918.164i	0.786701	+	1.72263i
$534$		0			0
$535$	−135.757	+	297.267i	−0.253752	+	0.555639i
$536$		0			0
$537$	191.072	−	1328.94i	0.355815	−	2.47475i
$538$		0			0
$539$	−41.9694	+	36.3666i	−0.0778652	+	0.0674706i
$540$		0			0
$541$	68.7661	−	44.1933i	0.127109	−	0.0816882i	−0.475541	−	0.879693i	$-0.657748\pi$
$541$	68.7661	−	44.1933i	0.127109	−	0.0816882i	0.602650	+	0.798005i	$0.294111\pi$
$542$		0			0
$543$	178.373	+	607.484i	0.328496	+	1.11876i
$544$		0			0
$545$	106.550	−	122.965i	0.195505	−	0.225624i
$546$		0			0
$547$	516.577	+	151.681i	0.944381	+	0.277295i	0.717446	−	0.696614i	$-0.245311\pi$
$547$	516.577	+	151.681i	0.944381	+	0.277295i	0.226936	+	0.973910i	$0.427129\pi$
$548$		0			0
$549$	897.298	−	129.012i	1.63442	−	0.234994i
$550$		0			0
$551$		−	158.937i		−	0.288453i
$552$		0			0
$553$	−209.505			−0.378851
$554$		0			0
$555$	176.115	+	1224.91i	0.317325	+	2.20704i
$556$		0			0
$557$	253.770	−	864.261i	0.455601	−	1.55164i	−0.336764	−	0.941589i	$-0.609332\pi$
$557$	253.770	−	864.261i	0.455601	−	1.55164i	0.792365	−	0.610047i	$-0.208849\pi$
$558$		0			0
$559$	−238.820	−	206.938i	−0.427226	−	0.370194i
$560$		0			0
$561$	193.712	−	56.8791i	0.345298	−	0.101389i
$562$		0			0
$563$	436.398	+	679.048i	0.775129	+	1.20612i	0.974100	+	0.226119i	$0.0726037\pi$
$563$	436.398	+	679.048i	0.775129	+	1.20612i	−0.198971	+	0.980005i	$0.563760\pi$
$564$		0			0
$565$	258.960	+	298.856i	0.458337	+	0.528949i
$566$		0			0
$567$	261.390	+	37.5823i	0.461006	+	0.0662827i
$568$		0			0
$569$	−735.254	−	335.779i	−1.29219	−	0.590122i	−0.353675	−	0.935368i	$-0.615068\pi$
$569$	−735.254	−	335.779i	−1.29219	−	0.590122i	−0.938512	+	0.345246i	$0.887795\pi$
$570$		0			0
$571$	−690.428	+	315.308i	−1.20916	+	0.552203i	−0.914961	−	0.403543i	$-0.867779\pi$
$571$	−690.428	+	315.308i	−1.20916	+	0.552203i	−0.294195	+	0.955746i	$0.595051\pi$
$572$		0			0
$573$	−478.147	+	744.012i	−0.834463	+	1.29845i
$574$		0			0
$575$	−175.657	+	62.7629i	−0.305491	+	0.109153i
$576$		0			0
$577$	797.093	+	512.261i	1.38144	+	0.887800i	0.999340	−	0.0363194i	$-0.0115634\pi$
$577$	797.093	+	512.261i	1.38144	+	0.887800i	0.382104	+	0.924119i	$0.375200\pi$
$578$		0			0
$579$	−311.915	−	682.999i	−0.538714	−	1.17962i
$580$		0			0
$581$	−306.413	+	670.951i	−0.527389	+	1.15482i
$582$		0			0
$583$	53.9032	−	374.905i	0.0924583	−	0.643062i
$584$		0			0
$585$	836.008	−	724.405i	1.42907	−	1.23830i
$586$		0			0
$587$	−14.6822	+	9.43567i	−0.0250123	+	0.0160744i	−0.553087	−	0.833123i	$-0.686550\pi$
$587$	−14.6822	+	9.43567i	−0.0250123	+	0.0160744i	0.528075	+	0.849198i	$0.322914\pi$
$588$		0			0
$589$	−254.697	−	867.417i	−0.432422	−	1.47269i
$590$		0			0
$591$	656.633	−	757.794i	1.11105	−	1.28222i
$592$		0			0
$593$	349.853	+	102.726i	0.589972	+	0.173231i	0.563074	−	0.826407i	$-0.309619\pi$
$593$	349.853	+	102.726i	0.589972	+	0.173231i	0.0268985	+	0.999638i	$0.491437\pi$
$594$		0			0
$595$	258.257	−	37.1317i	0.434045	−	0.0624063i
$596$		0			0
$597$			102.034i			0.170912i
$598$		0			0
$599$	353.210			0.589666			0.294833	−	0.955549i	$-0.404736\pi$
$599$	353.210			0.589666			0.294833	+	0.955549i	$0.404736\pi$
$600$		0			0
$601$	−86.5051	−	601.656i	−0.143935	−	1.00109i	−0.925900	−	0.377769i	$-0.876691\pi$
$601$	−86.5051	−	601.656i	−0.143935	−	1.00109i	0.781965	−	0.623323i	$-0.214218\pi$
$602$		0			0
$603$	−183.938	+	626.436i	−0.305039	+	1.03887i
$604$		0			0
$605$	322.742	+	279.658i	0.533459	+	0.462244i
$606$		0			0
$607$	76.1375	−	22.3560i	0.125432	−	0.0368303i	−0.218414	−	0.975856i	$-0.570088\pi$
$607$	76.1375	−	22.3560i	0.125432	−	0.0368303i	0.343846	+	0.939026i	$0.388270\pi$
$608$		0			0
$609$	−105.557	−	164.250i	−0.173329	−	0.269705i
$610$		0			0
$611$	−619.056	−	714.429i	−1.01318	−	1.16928i
$612$		0			0
$613$	904.918	+	130.108i	1.47621	+	0.212247i	0.832929	−	0.553381i	$-0.186662\pi$
$613$	904.918	+	130.108i	1.47621	+	0.212247i	0.643284	+	0.765628i	$0.277572\pi$
$614$		0			0
$615$	−774.862	−	353.868i	−1.25994	−	0.575395i
$616$		0			0
$617$	−348.068	+	158.957i	−0.564130	+	0.257630i	−0.677003	−	0.735980i	$-0.736722\pi$
$617$	−348.068	+	158.957i	−0.564130	+	0.257630i	0.112873	+	0.993609i	$0.463995\pi$
$618$		0			0
$619$	53.5130	−	83.2678i	0.0864507	−	0.134520i	−0.795335	−	0.606170i	$-0.792705\pi$
$619$	53.5130	−	83.2678i	0.0864507	−	0.134520i	0.881786	+	0.471650i	$0.156341\pi$
$620$		0			0
$621$	313.275	+	72.7014i	0.504469	+	0.117072i
$622$		0			0
$623$	216.624	+	139.216i	0.347711	+	0.223461i
$624$		0			0
$625$	−148.084	−	324.258i	−0.236934	−	0.518813i
$626$		0			0
$627$	175.469	−	384.223i	0.279854	−	0.612795i
$628$		0			0
$629$	99.4363	−	691.595i	0.158086	−	1.09951i
$630$		0			0
$631$	−78.1637	+	67.7292i	−0.123873	+	0.107336i	−0.714594	−	0.699539i	$-0.753389\pi$
$631$	−78.1637	+	67.7292i	−0.123873	+	0.107336i	0.590722	+	0.806876i	$0.298843\pi$
$632$		0			0
$633$	−122.864	+	78.9599i	−0.194098	+	0.124739i
$634$		0			0
$635$	35.5983	+	121.237i	0.0560603	+	0.190924i
$636$		0			0
$637$	196.548	−	226.828i	0.308552	−	0.356088i
$638$		0			0
$639$	1413.80	+	415.129i	2.21252	+	0.649655i
$640$		0			0
$641$	−510.875	+	73.4527i	−0.796997	+	0.114591i	−0.528770	−	0.848765i	$-0.677347\pi$
$641$	−510.875	+	73.4527i	−0.796997	+	0.114591i	−0.268227	+	0.963356i	$0.586438\pi$
$642$		0			0
$643$		−	498.014i		−	0.774516i	−0.921971	−	0.387258i	$-0.873422\pi$
$643$		−	498.014i		−	0.774516i	0.921971	−	0.387258i	$-0.126578\pi$
$644$		0			0
$645$	266.684			0.413463
$646$		0			0
$647$	−111.460	−	775.222i	−0.172272	−	1.19818i	−0.874069	−	0.485802i	$-0.838528\pi$
$647$	−111.460	−	775.222i	−0.172272	−	1.19818i	0.701797	−	0.712377i	$-0.252382\pi$
$648$		0			0
$649$	83.3715	−	283.937i	0.128461	−	0.437500i
$650$		0			0
$651$	−839.301	−	727.258i	−1.28925	−	1.11714i
$652$		0			0
$653$	−902.763	+	265.075i	−1.38249	+	0.405934i	−0.886634	−	0.462473i	$-0.846962\pi$
$653$	−902.763	+	265.075i	−1.38249	+	0.405934i	−0.495852	+	0.868407i	$0.665144\pi$
$654$		0			0
$655$	−335.615	−	522.228i	−0.512390	−	0.797294i
$656$		0			0
$657$	−500.353	−	577.438i	−0.761573	−	0.878902i
$658$		0			0
$659$	−540.683	−	77.7384i	−0.820459	−	0.117964i	−0.280713	−	0.959792i	$-0.590571\pi$
$659$	−540.683	−	77.7384i	−0.820459	−	0.117964i	−0.539747	+	0.841828i	$0.681480\pi$
$660$		0			0
$661$	568.988	+	259.848i	0.860799	+	0.393114i	0.796371	−	0.604809i	$-0.206750\pi$
$661$	568.988	+	259.848i	0.860799	+	0.393114i	0.0644283	+	0.997922i	$0.479478\pi$
$662$		0			0
$663$	−992.535	+	453.276i	−1.49704	+	0.683674i
$664$		0			0
$665$	295.125	−	459.223i	0.443797	−	0.690561i
$666$		0			0
$667$	76.6589	+	145.127i	0.114931	+	0.217582i
$668$		0			0
$669$	613.989	+	394.586i	0.917771	+	0.589815i
$670$		0			0
$671$	129.212	+	282.934i	0.192566	+	0.421660i
$672$		0			0
$673$	−311.460	+	682.003i	−0.462794	+	1.01338i	0.524048	+	0.851689i	$0.324421\pi$
$673$	−311.460	+	682.003i	−0.462794	+	1.01338i	−0.986842	+	0.161688i	$0.948306\pi$
$674$		0			0
$675$	16.1387	−	112.247i	0.0239091	−	0.166292i
$676$		0			0
$677$	381.369	−	330.458i	0.563322	−	0.488121i	−0.326021	−	0.945363i	$-0.605708\pi$
$677$	381.369	−	330.458i	0.563322	−	0.488121i	0.889343	+	0.457241i	$0.151162\pi$
$678$		0			0
$679$	−449.180	+	288.671i	−0.661532	+	0.425141i
$680$		0			0
$681$	456.432	+	1554.47i	0.670238	+	2.28262i
$682$		0			0
$683$	118.673	−	136.956i	0.173753	−	0.200522i	−0.662193	−	0.749333i	$-0.730374\pi$
$683$	118.673	−	136.956i	0.173753	−	0.200522i	0.835946	+	0.548812i	$0.184920\pi$
$684$		0			0
$685$	−798.822	−	234.555i	−1.16616	−	0.342417i
$686$		0			0
$687$	−108.678	+	15.6255i	−0.158192	+	0.0227445i
$688$		0			0
$689$			2047.05i			2.97105i
$690$		0			0
$691$	−1097.50			−1.58828			−0.794141	−	0.607733i	$-0.792079\pi$
$691$	−1097.50			−1.58828			−0.794141	+	0.607733i	$0.792079\pi$
$692$		0			0
$693$	−42.2690	−	293.987i	−0.0609943	−	0.424224i
$694$		0			0
$695$	53.3704	−	181.763i	0.0767919	−	0.261529i
$696$		0			0
$697$	363.484	+	314.961i	0.521498	+	0.451880i
$698$		0			0
$699$	1446.19	−	424.640i	2.06894	−	0.607496i
$700$		0			0
$701$	−41.4868	−	64.5547i	−0.0591823	−	0.0920895i	0.810401	−	0.585875i	$-0.199249\pi$
$701$	−41.4868	−	64.5547i	−0.0591823	−	0.0920895i	−0.869584	+	0.493786i	$0.835613\pi$
$702$		0			0
$703$	−957.295	−	1104.78i	−1.36173	−	1.57152i
$704$		0			0
$705$	789.663	+	113.536i	1.12009	+	0.161045i
$706$		0			0
$707$	199.406	+	91.0656i	0.282045	+	0.128806i
$708$		0			0
$709$	476.205	−	217.475i	0.671657	−	0.306735i	−0.0502389	−	0.998737i	$-0.515998\pi$
$709$	476.205	−	217.475i	0.671657	−	0.306735i	0.721896	+	0.692002i	$0.243271\pi$
$710$		0			0
$711$	−228.819	+	356.050i	−0.321827	+	0.500773i
$712$		0			0
$713$	650.940	+	669.202i	0.912959	+	0.938572i
$714$		0			0
$715$	319.300	+	205.202i	0.446574	+	0.286996i
$716$		0			0
$717$	−64.8620	−	142.028i	−0.0904630	−	0.198086i
$718$		0			0
$719$	445.125	−	974.687i	0.619088	−	1.35561i	−0.297092	−	0.954849i	$-0.596017\pi$
$719$	445.125	−	974.687i	0.619088	−	1.35561i	0.916181	−	0.400766i	$-0.131256\pi$
$720$		0			0
$721$	14.3078	−	99.5132i	0.0198444	−	0.138021i
$722$		0			0
$723$	−347.462	+	301.077i	−0.480583	+	0.416428i
$724$		0			0
$725$	48.6872	−	31.2893i	0.0671547	−	0.0431577i
$726$		0			0
$727$	209.327	+	712.904i	0.287933	+	0.980610i	0.968726	+	0.248134i	$0.0798173\pi$
$727$	209.327	+	712.904i	0.287933	+	0.980610i	−0.680793	+	0.732476i	$0.738364\pi$
$728$		0			0
$729$	727.439	−	839.509i	0.997859	−	1.15159i
$730$		0			0
$731$	−144.473	−	42.4211i	−0.197637	−	0.0580316i
$732$		0			0
$733$	−1149.32	+	165.247i	−1.56797	+	0.225439i	−0.870861	−	0.491530i	$-0.836438\pi$
$733$	−1149.32	+	165.247i	−1.56797	+	0.225439i	−0.697105	+	0.716969i	$0.745529\pi$
$734$		0			0
$735$			253.293i			0.344616i
$736$		0			0
$737$	−224.014			−0.303954
$738$		0			0
$739$	61.9143	+	430.624i	0.0837812	+	0.582711i	0.987860	+	0.155346i	$0.0496492\pi$
$739$	61.9143	+	430.624i	0.0837812	+	0.582711i	−0.904079	+	0.427366i	$0.859442\pi$
$740$		0			0
$741$	−643.160	+	2190.40i	−0.867963	+	2.95601i
$742$		0			0
$743$	−342.586	−	296.852i	−0.461084	−	0.399532i	0.393105	−	0.919493i	$-0.371401\pi$
$743$	−342.586	−	296.852i	−0.461084	−	0.399532i	−0.854190	+	0.519962i	$0.825946\pi$
$744$		0			0
$745$	425.538	−	124.949i	0.571191	−	0.167717i
$746$		0			0
$747$	805.609	+	1253.55i	1.07846	+	1.67811i
$748$		0			0
$749$	−310.552	−	358.396i	−0.414622	−	0.478499i
$750$		0			0
$751$	32.9586	+	4.73874i	0.0438863	+	0.00630990i	0.164223	−	0.986423i	$-0.447488\pi$
$751$	32.9586	+	4.73874i	0.0438863	+	0.00630990i	−0.120337	+	0.992733i	$0.538397\pi$
$752$		0			0
$753$	988.439	+	451.405i	1.31267	+	0.599476i
$754$		0			0
$755$	−421.557	+	192.519i	−0.558354	+	0.254992i
$756$		0			0
$757$	−751.204	+	1168.90i	−0.992343	+	1.54412i	−0.162055	+	0.986782i	$0.551812\pi$
$757$	−751.204	+	1168.90i	−0.992343	+	1.54412i	−0.830288	+	0.557334i	$0.811824\pi$
$758$		0			0
$759$	25.0964	+	435.470i	0.0330651	+	0.573742i
$760$		0			0
$761$	334.245	+	214.806i	0.439218	+	0.282268i	0.741503	−	0.670949i	$-0.234113\pi$
$761$	334.245	+	214.806i	0.439218	+	0.282268i	−0.302285	+	0.953217i	$0.597750\pi$
$762$		0			0
$763$	98.0824	+	214.770i	0.128548	+	0.281482i
$764$		0			0
$765$	218.961	−	479.458i	0.286224	−	0.626743i
$766$		0			0
$767$	−227.612	+	1583.08i	−0.296756	+	2.06399i
$768$		0			0
$769$	435.262	−	377.157i	0.566010	−	0.490451i	−0.324207	−	0.945986i	$-0.605098\pi$
$769$	435.262	−	377.157i	0.566010	−	0.490451i	0.890218	+	0.455535i	$0.150552\pi$
$770$		0			0
$771$	−201.301	+	129.368i	−0.261090	+	0.167793i
$772$		0			0
$773$	−390.863	−	1331.16i	−0.505645	−	1.72207i	−0.676199	−	0.736719i	$-0.736374\pi$
$773$	−390.863	−	1331.16i	−0.505645	−	1.72207i	0.170555	−	0.985348i	$-0.445444\pi$
$774$		0			0
$775$	215.574	−	248.786i	0.278160	−	0.321014i
$776$		0			0
$777$	−1723.03	−	505.927i	−2.21754	−	0.651128i
$778$		0			0
$779$	996.016	−	143.205i	1.27858	−	0.183832i
$780$		0			0
$781$			505.576i			0.647344i
$782$		0			0
$783$	−99.7810			−0.127434
$784$		0			0
$785$	22.0037	+	153.039i	0.0280302	+	0.194955i
$786$		0			0
$787$	10.9848	−	37.4108i	0.0139578	−	0.0475360i	−0.952220	−	0.305414i	$-0.901205\pi$
$787$	10.9848	−	37.4108i	0.0139578	−	0.0475360i	0.966177	+	0.257878i	$0.0830233\pi$
$788$		0			0
$789$	−1586.64	−	1374.83i	−2.01095	−	1.74250i
$790$		0			0
$791$	−550.592	+	161.668i	−0.696071	+	0.204385i
$792$		0			0
$793$	−908.852	−	1414.20i	−1.14609	−	1.78336i
$794$		0			0
$795$	−1131.31	−	1305.60i	−1.42303	−	1.64227i
$796$		0			0
$797$	341.975	+	49.1686i	0.429078	+	0.0616921i	0.353471	−	0.935446i	$-0.385001\pi$
$797$	341.975	+	49.1686i	0.429078	+	0.0616921i	0.0756074	+	0.997138i	$0.475910\pi$
$798$		0			0
$799$	−409.731	−	187.118i	−0.512805	−	0.234190i
$800$		0			0
$801$	473.191	−	216.099i	0.590750	−	0.269786i
$802$		0			0
$803$	141.735	−	220.544i	0.176507	−	0.274650i
$804$		0			0
$805$	−47.9886	+	561.667i	−0.0596132	+	0.697723i
$806$		0			0
$807$	532.551	+	342.249i	0.659914	+	0.424101i
$808$		0			0
$809$	−239.809	−	525.109i	−0.296427	−	0.649084i	0.701553	−	0.712617i	$-0.252490\pi$
$809$	−239.809	−	525.109i	−0.296427	−	0.649084i	−0.997980	+	0.0635331i	$0.979763\pi$
$810$		0			0
$811$	328.090	−	718.417i	0.404550	−	0.885841i	−0.592239	−	0.805763i	$-0.701756\pi$
$811$	328.090	−	718.417i	0.404550	−	0.885841i	0.996789	−	0.0800783i	$-0.0255170\pi$
$812$		0			0
$813$	171.354	−	1191.79i	0.210768	−	1.46592i
$814$		0			0
$815$	−827.167	+	716.744i	−1.01493	+	0.879440i
$816$		0			0
$817$	−265.017	+	170.316i	−0.324378	+	0.208465i
$818$		0			0
$819$	452.245	+	1540.21i	0.552192	+	1.88059i
$820$		0			0
$821$	981.965	−	1133.25i	1.19606	−	1.38033i	0.290082	−	0.957002i	$-0.406318\pi$
$821$	981.965	−	1133.25i	1.19606	−	1.38033i	0.905978	−	0.423325i	$-0.139137\pi$
$822$		0			0
$823$	−608.029	−	178.534i	−0.738796	−	0.216930i	−0.109382	−	0.994000i	$-0.534887\pi$
$823$	−608.029	−	178.534i	−0.738796	−	0.216930i	−0.629415	+	0.777070i	$0.716705\pi$
$824$		0			0
$825$	152.242	−	21.8892i	0.184536	−	0.0265323i
$826$		0			0
$827$			441.652i			0.534041i	0.963691	+	0.267020i	$0.0860391\pi$
$827$			441.652i			0.534041i	−0.963691	+	0.267020i	$0.913961\pi$
$828$		0			0
$829$	1234.02			1.48856			0.744282	−	0.667866i	$-0.232792\pi$
$829$	1234.02			1.48856			0.744282	+	0.667866i	$0.232792\pi$
$830$		0			0
$831$	147.902	+	1028.68i	0.177981	+	1.23788i
$832$		0			0
$833$	40.2911	−	137.219i	0.0483686	−	0.164728i
$834$		0			0
$835$	−58.8009	−	50.9512i	−0.0704202	−	0.0610194i
$836$		0			0
$837$	−544.565	+	159.899i	−0.650615	+	0.191038i
$838$		0			0
$839$	−197.829	−	307.828i	−0.235792	−	0.366899i	0.703112	−	0.711079i	$-0.251793\pi$
$839$	−197.829	−	307.828i	−0.235792	−	0.366899i	−0.938904	+	0.344180i	$0.888157\pi$
$840$		0			0
$841$	517.390	+	597.100i	0.615208	+	0.709988i
$842$		0			0
$843$	254.351	+	36.5701i	0.301721	+	0.0433809i
$844$		0			0
$845$	−1234.18	−	563.633i	−1.46057	−	0.667021i
$846$		0			0
$847$	−563.700	+	257.433i	−0.665525	+	0.303935i
$848$		0			0
$849$	−163.301	+	254.101i	−0.192345	+	0.299294i
$850$		0			0
$851$	1406.97	+	547.061i	1.65332	+	0.642844i
$852$		0			0
$853$	946.360	+	608.189i	1.10945	+	0.713000i	0.961173	−	0.275946i	$-0.0889912\pi$
$853$	946.360	+	608.189i	1.10945	+	0.713000i	0.148276	+	0.988946i	$0.452628\pi$
$854$		0			0
$855$	−458.110	−	1003.12i	−0.535801	−	1.17324i
$856$		0			0
$857$	309.596	−	677.921i	0.361256	−	0.791039i	−0.638515	−	0.769610i	$-0.720451\pi$
$857$	309.596	−	677.921i	0.361256	−	0.791039i	0.999770	−	0.0214297i	$-0.00682182\pi$
$858$		0			0
$859$	46.1609	−	321.056i	0.0537380	−	0.373756i	−0.945151	−	0.326633i	$-0.894086\pi$
$859$	46.1609	−	321.056i	0.0537380	−	0.373756i	0.998889	−	0.0471225i	$-0.0150051\pi$
$860$		0			0
$861$	934.202	−	809.491i	1.08502	−	0.940175i
$862$		0			0
$863$	121.418	−	78.0307i	0.140693	−	0.0904180i	−0.468401	−	0.883516i	$-0.655170\pi$
$863$	121.418	−	78.0307i	0.140693	−	0.0904180i	0.609094	+	0.793098i	$0.291533\pi$
$864$		0			0
$865$	301.926	+	1028.27i	0.349047	+	1.18875i
$866$		0			0
$867$	527.788	−	609.100i	0.608752	−	0.702538i
$868$		0			0
$869$	−139.337	−	40.9129i	−0.160341	−	0.0470805i
$870$		0			0
$871$	1198.39	−	172.302i	1.37587	−	0.197821i
$872$		0			0
$873$			1078.66i			1.23558i
$874$		0			0
$875$	811.505			0.927434
$876$		0			0
$877$	108.228	+	752.744i	0.123407	+	0.858317i	0.953651	+	0.300916i	$0.0972924\pi$
$877$	108.228	+	752.744i	0.123407	+	0.858317i	−0.830243	+	0.557401i	$0.811799\pi$
$878$		0			0
$879$	549.189	−	1870.37i	0.624789	−	2.12784i
$880$		0			0
$881$	185.788	+	160.986i	0.210883	+	0.182731i	0.753897	−	0.656992i	$-0.228172\pi$
$881$	185.788	+	160.986i	0.210883	+	0.182731i	−0.543014	+	0.839723i	$0.682717\pi$
$882$		0			0
$883$	855.787	−	251.282i	0.969182	−	0.284577i	0.241430	−	0.970418i	$-0.422384\pi$
$883$	855.787	−	251.282i	0.969182	−	0.284577i	0.727752	+	0.685841i	$0.240565\pi$
$884$		0			0
$885$	−729.723	−	1135.47i	−0.824546	−	1.28302i
$886$		0			0
$887$	670.197	+	773.448i	0.755577	+	0.871982i	0.995096	−	0.0989093i	$-0.0315354\pi$
$887$	670.197	+	773.448i	0.755577	+	0.871982i	−0.239520	+	0.970892i	$0.576990\pi$
$888$		0			0
$889$	−181.490	−	26.0944i	−0.204151	−	0.0293525i
$890$		0			0
$891$	166.506	+	76.0405i	0.186875	+	0.0853429i
$892$		0			0
$893$	−857.238	+	391.487i	−0.959953	+	0.438396i
$894$		0			0
$895$	650.229	−	1011.78i	0.726513	−	1.13048i
$896$		0			0
$897$	−469.201	−	2310.29i	−0.523078	−	2.57557i
$898$		0			0
$899$	−243.672	−	156.598i	−0.271048	−	0.174192i
$900$		0			0
$901$	405.195	+	887.253i	0.449717	+	0.984743i
$902$		0			0
$903$	−160.762	+	352.019i	−0.178031	+	0.389833i
$904$		0			0
$905$	−80.7148	+	561.384i	−0.0891876	+	0.620313i
$906$		0			0
$907$	−853.773	+	739.799i	−0.941315	+	0.815654i	−0.983024	−	0.183475i	$-0.941265\pi$
$907$	−853.773	+	739.799i	−0.941315	+	0.815654i	0.0417089	+	0.999130i	$0.486720\pi$
$908$		0			0
$909$	372.554	−	239.426i	0.409850	−	0.263395i
$910$		0			0
$911$	13.9867	+	47.6344i	0.0153532	+	0.0522881i	0.966813	−	0.255484i	$-0.0822348\pi$
$911$	13.9867	+	47.6344i	0.0153532	+	0.0522881i	−0.951460	+	0.307772i	$0.900417\pi$
$912$		0			0
$913$	−334.814	+	386.396i	−0.366719	+	0.423216i
$914$		0			0
$915$	1361.23	+	399.692i	1.48768	+	0.436822i
$916$		0			0
$917$	891.649	−	128.200i	0.972355	−	0.139803i
$918$		0			0
$919$			1349.99i			1.46897i	0.678624	+	0.734486i	$0.262577\pi$
$919$			1349.99i			1.46897i	−0.678624	+	0.734486i	$0.737423\pi$
$920$		0			0
$921$	−1792.92			−1.94671
$922$		0			0
$923$	−388.867	−	2704.63i	−0.421308	−	2.93026i
$924$		0			0
$925$	149.967	−	510.741i	0.162126	−	0.552152i
$926$		0			0
$927$	−153.494	−	133.003i	−0.165582	−	0.143477i
$928$		0			0
$929$	−692.545	+	203.350i	−0.745474	+	0.218891i	−0.632342	−	0.774689i	$-0.717906\pi$
$929$	−692.545	+	203.350i	−0.745474	+	0.218891i	−0.113132	+	0.993580i	$0.536088\pi$
$930$		0			0
$931$	−161.764	−	251.710i	−0.173753	−	0.270365i
$932$		0			0
$933$	−1280.14	−	1477.36i	−1.37207	−	1.58345i
$934$		0			0
$935$	179.012	+	25.7380i	0.191457	+	0.0275273i
$936$		0			0
$937$	342.448	+	156.391i	0.365473	+	0.166906i	0.589683	−	0.807635i	$-0.299253\pi$
$937$	342.448	+	156.391i	0.365473	+	0.166906i	−0.224210	+	0.974541i	$0.571980\pi$
$938$		0			0
$939$	1448.66	−	661.582i	1.54277	−	0.704560i
$940$		0			0
$941$	−726.514	+	1130.48i	−0.772066	+	1.20136i	0.202943	+	0.979191i	$0.434949\pi$
$941$	−726.514	+	1130.48i	−0.772066	+	1.20136i	−0.975009	+	0.222167i	$0.928687\pi$
$942$		0			0
$943$	−840.402	+	611.162i	−0.891200	+	0.648104i
$944$		0			0
$945$	−288.301	−	185.280i	−0.305080	−	0.196063i
$946$		0			0
$947$	−448.917	−	982.990i	−0.474041	−	1.03800i	−0.984059	−	0.177841i	$-0.943089\pi$
$947$	−448.917	−	982.990i	−0.474041	−	1.03800i	0.510018	−	0.860164i	$-0.329639\pi$
$948$		0			0
$949$	−588.592	+	1288.84i	−0.620224	+	1.35810i
$950$		0			0
$951$	−5.53564	+	38.5013i	−0.00582087	+	0.0404850i
$952$		0			0
$953$	−183.747	+	159.218i	−0.192809	+	0.167070i	−0.745915	−	0.666041i	$-0.767988\pi$
$953$	−183.747	+	159.218i	−0.192809	+	0.167070i	0.553107	+	0.833111i	$0.313442\pi$
$954$		0			0
$955$	−666.484	+	428.323i	−0.697889	+	0.448506i
$956$		0			0
$957$	−38.1283	−	129.853i	−0.0398414	−	0.135687i
$958$		0			0
$959$	791.155	−	913.041i	0.824979	−	0.952076i
$960$		0			0
$961$	−658.740	−	193.423i	−0.685473	−	0.201273i
$962$		0			0
$963$	−948.270	+	136.341i	−0.984705	+	0.141579i
$964$		0			0
$965$		−	672.611i		−	0.697007i
$966$		0			0
$967$	−117.933			−0.121957			−0.0609786	−	0.998139i	$-0.519422\pi$
$967$	−117.933			−0.121957			−0.0609786	+	0.998139i	$0.519422\pi$
$968$		0			0
$969$	154.805	+	1076.69i	0.159757	+	1.11114i
$970$		0			0
$971$	74.0080	−	252.048i	0.0762183	−	0.259576i	−0.912565	−	0.408931i	$-0.865902\pi$
$971$	74.0080	−	252.048i	0.0762183	−	0.259576i	0.988784	+	0.149355i	$0.0477198\pi$
$972$		0			0
$973$	207.752	+	180.018i	0.213517	+	0.185013i
$974$		0			0
$975$	−797.601	+	234.197i	−0.818052	+	0.240202i
$976$		0			0
$977$	655.907	+	1020.61i	0.671348	+	1.04464i	0.995136	+	0.0985080i	$0.0314070\pi$
$977$	655.907	+	1020.61i	0.671348	+	1.04464i	−0.323789	+	0.946129i	$0.604957\pi$
$978$		0			0
$979$	116.885	+	134.893i	0.119392	+	0.137786i
$980$		0			0
$981$	472.124	+	67.8811i	0.481268	+	0.0691959i
$982$		0			0
$983$	−364.849	−	166.621i	−0.371159	−	0.169503i	0.221098	−	0.975251i	$-0.429036\pi$
$983$	−364.849	−	166.621i	−0.371159	−	0.169503i	−0.592257	+	0.805749i	$0.701763\pi$
$984$		0			0
$985$	817.050	−	373.134i	0.829493	−	0.378817i
$986$		0			0
$987$	−625.890	+	973.904i	−0.634134	+	0.986732i
$988$		0			0
$989$	159.843	−	283.341i	0.161621	−	0.286492i
$990$		0			0
$991$	249.059	+	160.060i	0.251320	+	0.161514i	0.660236	−	0.751059i	$-0.270456\pi$
$991$	249.059	+	160.060i	0.251320	+	0.161514i	−0.408915	+	0.912572i	$0.634093\pi$
$992$		0			0
$993$	545.458	+	1194.39i	0.549303	+	1.20281i
$994$		0			0
$995$	−37.9698	+	83.1422i	−0.0381606	+	0.0835600i
$996$		0			0
$997$	150.061	−	1043.70i	0.150512	−	1.04684i	−0.764851	−	0.644207i	$-0.777187\pi$
$997$	150.061	−	1043.70i	0.150512	−	1.04684i	0.915363	−	0.402629i	$-0.131904\pi$
$998$		0			0
$999$	−693.580	+	600.991i	−0.694275	+	0.601592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.3.f.a.21.4	✓	40
4.3	odd	2		368.3.p.c.113.1		40
23.9	even	11		2116.3.d.c.1057.5		40
23.11	odd	22	inner	92.3.f.a.57.4	yes	40
23.14	odd	22		2116.3.d.c.1057.6		40
92.11	even	22		368.3.p.c.241.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.3.f.a.21.4	✓	40	1.1	even	1	trivial
92.3.f.a.57.4	yes	40	23.11	odd	22	inner
368.3.p.c.113.1		40	4.3	odd	2
368.3.p.c.241.1		40	92.11	even	22
2116.3.d.c.1057.5		40	23.9	even	11
2116.3.d.c.1057.6		40	23.14	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)

\(f(q)\)	\(=\)	\(q+(0.652910 + 4.54109i) q^{3} +(-1.15784 + 3.94325i) q^{5} +(-4.50708 - 3.90541i) q^{7} +(-11.5598 + 3.39426i) q^{9} +(-2.23489 - 3.47756i) q^{11} +(14.6306 + 16.8846i) q^{13} +(-18.6626 - 2.68328i) q^{15} +(9.68346 + 4.42229i) q^{17} +(20.2597 - 9.25228i) q^{19} +(14.7921 - 23.0169i) q^{21} +(-14.0368 + 18.2200i) q^{23} +(6.82268 + 4.38467i) q^{25} +(-5.80859 - 12.7190i) q^{27} +(2.96443 - 6.49120i) q^{29} +(5.77656 - 40.1769i) q^{31} +(14.3327 - 12.4194i) q^{33} +(20.6185 - 13.2507i) q^{35} +(-18.4913 - 62.9755i) q^{37} +(-67.1219 + 77.4628i) q^{39} +(43.3495 + 12.7286i) q^{41} +(-14.0003 + 2.01294i) q^{43} -49.5131i q^{45} -42.3125 q^{47} +(-1.91186 - 13.2973i) q^{49} +(-13.7596 + 46.8608i) q^{51} +(69.2461 + 60.0021i) q^{53} +(16.3005 - 4.78627i) q^{55} +(55.2432 + 85.9601i) q^{57} +(46.8794 + 54.1017i) q^{59} +(-74.4782 - 10.7083i) q^{61} +(65.3567 + 29.8474i) q^{63} +(-83.5201 + 38.1423i) q^{65} +(29.2979 - 45.5884i) q^{67} +(-91.9035 - 51.8461i) q^{69} +(-102.888 - 66.1223i) q^{71} +(26.3453 + 57.6881i) q^{73} +(-15.4566 + 33.8452i) q^{75} +(-3.50845 + 24.4018i) q^{77} +(26.5494 - 23.0052i) q^{79} +(-37.2514 + 23.9400i) q^{81} +(-34.8453 - 118.672i) q^{83} +(-28.6501 + 33.0640i) q^{85} +(31.4126 + 9.22358i) q^{87} +(-42.7385 + 6.14487i) q^{89} -133.238i q^{91} +186.218 q^{93} +(13.0266 + 90.6018i) q^{95} +(25.2240 - 85.9050i) q^{97} +(37.6385 + 32.6140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{3} - 6 q^{9} - 2 q^{13} + 77 q^{15} + 55 q^{17} + 33 q^{19} + 33 q^{21} - 50 q^{23} - 54 q^{25} - 191 q^{27} + q^{29} - 53 q^{31} - 121 q^{33} - 156 q^{35} - 352 q^{37} - 306 q^{39} + 6 q^{41}+ \cdots + 1353 q^{99}+O(q^{100}) \) 40 * q - 2 * q^3 - 6 * q^9 - 2 * q^13 + 77 * q^15 + 55 * q^17 + 33 * q^19 + 33 * q^21 - 50 * q^23 - 54 * q^25 - 191 * q^27 + q^29 - 53 * q^31 - 121 * q^33 - 156 * q^35 - 352 * q^37 - 306 * q^39 + 6 * q^41 - 88 * q^43 - 58 * q^47 + 292 * q^49 + 264 * q^51 + 176 * q^53 + 518 * q^55 + 891 * q^57 + 696 * q^59 + 308 * q^61 + 275 * q^63 + 231 * q^65 + 22 * q^67 - 233 * q^69 - 215 * q^71 - 400 * q^73 - 557 * q^75 - 239 * q^77 - 748 * q^79 - 684 * q^81 - 671 * q^83 - 794 * q^85 + 62 * q^87 - 44 * q^89 - 346 * q^93 + 561 * q^95 + 693 * q^97 + 1353 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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