LMFDB - Embedded newform 99.4.f.e.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,4,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$99 = 3^{2} \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	99.f (of order $5$ , degree $4$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.84118909057$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Character	$\chi$	$=$	99.91
Dual form			99.4.f.e.37.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.91330 + 2.11664i) q^{2} +(1.53504 - 4.72436i) q^{4} +(12.8877 + 9.36349i) q^{5} +(9.79985 - 30.1608i) q^{7} +(-3.37453 - 10.3857i) q^{8} -57.3650 q^{10} +(24.0631 + 27.4220i) q^{11} +(33.3572 - 24.2354i) q^{13} +(35.2896 + 108.610i) q^{14} +(63.9641 + 46.4726i) q^{16} +(-17.3758 - 12.6243i) q^{17} +(41.7935 + 128.627i) q^{19} +(64.0197 - 46.5130i) q^{20} +(-128.146 - 28.9555i) q^{22} +4.92310 q^{23} +(39.7917 + 122.466i) q^{25} +(-45.8820 + 141.210i) q^{26} +(-127.447 - 92.5960i) q^{28} +(-18.3820 + 56.5738i) q^{29} +(-32.5863 + 23.6753i) q^{31} -197.351 q^{32} +77.3419 q^{34} +(408.708 - 296.944i) q^{35} +(56.9507 - 175.276i) q^{37} +(-394.014 - 286.268i) q^{38} +(53.7566 - 165.446i) q^{40} +(-113.980 - 350.795i) q^{41} +407.910 q^{43} +(166.489 - 71.5892i) q^{44} +(-14.3425 + 10.4204i) q^{46} +(161.944 + 498.412i) q^{47} +(-536.146 - 389.533i) q^{49} +(-375.142 - 272.557i) q^{50} +(-63.2924 - 194.794i) q^{52} +(-345.667 + 251.142i) q^{53} +(53.3541 + 578.722i) q^{55} -346.312 q^{56} +(-66.1941 - 203.725i) q^{58} +(134.309 - 413.361i) q^{59} +(114.856 + 83.4480i) q^{61} +(44.8217 - 137.947i) q^{62} +(63.2300 - 45.9393i) q^{64} +656.827 q^{65} -5.94006 q^{67} +(-86.3140 + 62.7108i) q^{68} +(-562.168 + 1730.18i) q^{70} +(107.505 + 78.1072i) q^{71} +(129.897 - 399.783i) q^{73} +(205.082 + 631.177i) q^{74} +671.836 q^{76} +(1062.88 - 457.033i) q^{77} +(-296.522 + 215.436i) q^{79} +(389.206 + 1197.85i) q^{80} +(1074.56 + 780.717i) q^{82} +(-625.879 - 454.728i) q^{83} +(-105.728 - 325.396i) q^{85} +(-1188.36 + 863.398i) q^{86} +(203.595 - 342.450i) q^{88} +14.6027 q^{89} +(-404.065 - 1243.58i) q^{91} +(7.55714 - 23.2585i) q^{92} +(-1526.75 - 1109.25i) q^{94} +(-665.775 + 2049.05i) q^{95} +(-966.650 + 702.312i) q^{97} +2386.45 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q - 4 q^{4} - 28 q^{7} + 208 q^{10} + 20 q^{13} - 224 q^{16} - 40 q^{19} - 586 q^{22} + 362 q^{25} - 150 q^{28} + 670 q^{31} - 2520 q^{34} - 516 q^{37} + 2002 q^{40} + 4008 q^{43} + 2174 q^{46} + 342 q^{49}+ \cdots - 1224 q^{97}+O(q^{100})$ 24 * q - 4 * q^4 - 28 * q^7 + 208 * q^10 + 20 * q^13 - 224 * q^16 - 40 * q^19 - 586 * q^22 + 362 * q^25 - 150 * q^28 + 670 * q^31 - 2520 * q^34 - 516 * q^37 + 2002 * q^40 + 4008 * q^43 + 2174 * q^46 + 342 * q^49 - 1894 * q^52 - 3300 * q^55 + 22 * q^58 - 2952 * q^61 - 3992 * q^64 - 1936 * q^67 - 1024 * q^70 + 2194 * q^73 + 15336 * q^76 + 1524 * q^79 + 2898 * q^82 - 7428 * q^85 - 3936 * q^88 - 6460 * q^91 - 16982 * q^94 - 1224 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$ .

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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

)

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

$2$	−2.91330	+	2.11664i	−1.03001	+	0.748345i	−0.968310	−	0.249750i	$-0.919651\pi$
$2$	−2.91330	+	2.11664i	−1.03001	+	0.748345i	−0.0616976	+	0.998095i	$0.519651\pi$
$3$		0			0
$3$		0			0
$4$	1.53504	−	4.72436i	0.191880	−	0.590545i
$5$	12.8877	+	9.36349i	1.15271	+	0.837496i	0.988839	−	0.148985i	$-0.0476007\pi$
$5$	12.8877	+	9.36349i	1.15271	+	0.837496i	0.163875	+	0.986481i	$0.447601\pi$
$6$		0			0
$7$	9.79985	−	30.1608i	0.529142	−	1.62853i	−0.226835	−	0.973933i	$-0.572838\pi$
$7$	9.79985	−	30.1608i	0.529142	−	1.62853i	0.755977	−	0.654598i	$-0.227162\pi$
$8$	−3.37453	−	10.3857i	−0.149134	−	0.458989i
$9$		0			0
$10$	−57.3650			−1.81404
$11$	24.0631	+	27.4220i	0.659574	+	0.751640i
$11$	24.0631	+	27.4220i	0.659574	+	0.751640i
$12$		0			0
$13$	33.3572	−	24.2354i	0.711664	−	0.517054i	−0.172046	−	0.985089i	$-0.555038\pi$
$13$	33.3572	−	24.2354i	0.711664	−	0.517054i	0.883710	+	0.468035i	$0.155038\pi$
$14$	35.2896	+	108.610i	0.673682	+	2.07338i
$15$		0			0
$16$	63.9641	+	46.4726i	0.999439	+	0.726135i
$17$	−17.3758	−	12.6243i	−0.247897	−	0.180108i	0.456897	−	0.889519i	$-0.348961\pi$
$17$	−17.3758	−	12.6243i	−0.247897	−	0.180108i	−0.704794	+	0.709412i	$0.748961\pi$
$18$		0			0
$19$	41.7935	+	128.627i	0.504636	+	1.55311i	0.801381	+	0.598154i	$0.204099\pi$
$19$	41.7935	+	128.627i	0.504636	+	1.55311i	−0.296745	+	0.954957i	$0.595901\pi$
$20$	64.0197	−	46.5130i	0.715762	−	0.520031i
$21$		0			0
$22$	−128.146	−	28.9555i	−1.24185	−	0.280606i
$23$	4.92310			0.0446320			0.0223160	−	0.999751i	$-0.492896\pi$
$23$	4.92310			0.0446320			0.0223160	+	0.999751i	$0.492896\pi$
$24$		0			0
$25$	39.7917	+	122.466i	0.318334	+	0.979730i
$26$	−45.8820	+	141.210i	−0.346085	+	1.06514i
$27$		0			0
$28$	−127.447	−	92.5960i	−0.860190	−	0.624964i
$29$	−18.3820	+	56.5738i	−0.117705	+	0.362258i	−0.992502	−	0.122232i	$-0.960995\pi$
$29$	−18.3820	+	56.5738i	−0.117705	+	0.362258i	0.874797	+	0.484490i	$0.160995\pi$
$30$		0			0
$31$	−32.5863	+	23.6753i	−0.188796	+	0.137168i	−0.678168	−	0.734907i	$-0.737226\pi$
$31$	−32.5863	+	23.6753i	−0.188796	+	0.137168i	0.489372	+	0.872075i	$0.337226\pi$
$32$	−197.351			−1.09022
$33$		0			0
$34$	77.3419			0.390118
$35$	408.708	−	296.944i	1.97384	−	1.43408i
$36$		0			0
$37$	56.9507	−	175.276i	0.253044	−	0.778791i	−0.741164	−	0.671324i	$-0.765726\pi$
$37$	56.9507	−	175.276i	0.253044	−	0.778791i	0.994209	−	0.107467i	$-0.0342739\pi$
$38$	−394.014	−	286.268i	−1.68204	−	1.22207i
$39$		0			0
$40$	53.7566	−	165.446i	0.212492	−	0.653982i
$41$	−113.980	−	350.795i	−0.434164	−	1.33622i	−0.893941	−	0.448184i	$-0.852071\pi$
$41$	−113.980	−	350.795i	−0.434164	−	1.33622i	0.459778	−	0.888034i	$-0.347929\pi$
$42$		0			0
$43$	407.910			1.44664			0.723322	−	0.690511i	$-0.242614\pi$
$43$	407.910			1.44664			0.723322	+	0.690511i	$0.242614\pi$
$44$	166.489	−	71.5892i	0.570436	−	0.245284i
$45$		0			0
$46$	−14.3425	+	10.4204i	−0.0459713	+	0.0334001i
$47$	161.944	+	498.412i	0.502594	+	1.54683i	0.804778	+	0.593576i	$0.202284\pi$
$47$	161.944	+	498.412i	0.502594	+	1.54683i	−0.302184	+	0.953250i	$0.597716\pi$
$48$		0			0
$49$	−536.146	−	389.533i	−1.56311	−	1.13566i
$50$	−375.142	−	272.557i	−1.06106	−	0.770906i
$51$		0			0
$52$	−63.2924	−	194.794i	−0.168790	−	0.519482i
$53$	−345.667	+	251.142i	−0.895868	+	0.650886i	−0.937401	−	0.348251i	$-0.886776\pi$
$53$	−345.667	+	251.142i	−0.895868	+	0.650886i	0.0415337	+	0.999137i	$0.486776\pi$
$54$		0			0
$55$	53.3541	+	578.722i	0.130805	+	1.41882i
$56$	−346.312			−0.826391
$57$		0			0
$58$	−66.1941	−	203.725i	−0.149857	−	0.461213i
$59$	134.309	−	413.361i	0.296365	−	0.912118i	−0.686394	−	0.727229i	$-0.740808\pi$
$59$	134.309	−	413.361i	0.296365	−	0.912118i	0.982760	−	0.184888i	$-0.0591924\pi$
$60$		0			0
$61$	114.856	+	83.4480i	0.241079	+	0.175154i	0.701764	−	0.712410i	$-0.252396\pi$
$61$	114.856	+	83.4480i	0.241079	+	0.175154i	−0.460685	+	0.887564i	$0.652396\pi$
$62$	44.8217	−	137.947i	0.0918122	−	0.282569i
$63$		0			0
$64$	63.2300	−	45.9393i	0.123496	−	0.0897252i
$65$	656.827			1.25338
$66$		0			0
$67$	−5.94006			−0.0108312			−0.00541562	−	0.999985i	$-0.501724\pi$
$67$	−5.94006			−0.0108312			−0.00541562	+	0.999985i	$0.501724\pi$
$68$	−86.3140	+	62.7108i	−0.153928	+	0.111835i
$69$		0			0
$70$	−562.168	+	1730.18i	−0.959885	+	2.95422i
$71$	107.505	+	78.1072i	0.179698	+	0.130558i	0.673998	−	0.738733i	$-0.264576\pi$
$71$	107.505	+	78.1072i	0.179698	+	0.130558i	−0.494300	+	0.869291i	$0.664576\pi$
$72$		0			0
$73$	129.897	−	399.783i	0.208265	−	0.640974i	−0.791299	−	0.611430i	$-0.790595\pi$
$73$	129.897	−	399.783i	0.208265	−	0.640974i	0.999563	−	0.0295437i	$-0.00940542\pi$
$74$	205.082	+	631.177i	0.322166	+	0.991525i
$75$		0			0
$76$	671.836			1.01401
$77$	1062.88	−	457.033i	1.57308	−	0.676413i
$78$		0			0
$79$	−296.522	+	215.436i	−0.422295	+	0.306815i	−0.778561	−	0.627569i	$-0.784050\pi$
$79$	−296.522	+	215.436i	−0.422295	+	0.306815i	0.356266	+	0.934385i	$0.384050\pi$
$80$	389.206	+	1197.85i	0.543932	+	1.67405i
$81$		0			0
$82$	1074.56	+	780.717i	1.44714	+	1.05141i
$83$	−625.879	−	454.728i	−0.827701	−	0.601360i	0.0912072	−	0.995832i	$-0.470927\pi$
$83$	−625.879	−	454.728i	−0.827701	−	0.601360i	−0.918908	+	0.394472i	$0.870927\pi$
$84$		0			0
$85$	−105.728	−	325.396i	−0.134915	−	0.415225i
$86$	−1188.36	+	863.398i	−1.49005	+	1.08259i
$87$		0			0
$88$	203.595	−	342.450i	0.246629	−	0.414832i
$89$	14.6027			0.0173919			0.00869595	−	0.999962i	$-0.497232\pi$
$89$	14.6027			0.0173919			0.00869595	+	0.999962i	$0.497232\pi$
$90$		0			0
$91$	−404.065	−	1243.58i	−0.465467	−	1.43256i
$92$	7.55714	−	23.2585i	0.00856398	−	0.0263572i
$93$		0			0
$94$	−1526.75	−	1109.25i	−1.67523	−	1.21713i
$95$	−665.775	+	2049.05i	−0.719022	+	2.21292i
$96$		0			0
$97$	−966.650	+	702.312i	−1.01184	+	0.735144i	−0.964594	−	0.263739i	$-0.915044\pi$
$97$	−966.650	+	702.312i	−1.01184	+	0.735144i	−0.0472452	+	0.998883i	$0.515044\pi$
$98$	2386.45			2.45988
$99$		0			0
$100$	639.656			0.639656
$101$	1151.21	−	836.401i	1.13415	−	0.824010i	0.147859	−	0.989008i	$-0.452762\pi$
$101$	1151.21	−	836.401i	1.13415	−	0.824010i	0.986294	+	0.164998i	$0.0527619\pi$
$102$		0			0
$103$	18.8817	−	58.1118i	0.0180628	−	0.0555916i	−0.941619	−	0.336681i	$-0.890696\pi$
$103$	18.8817	−	58.1118i	0.0180628	−	0.0555916i	0.959682	+	0.281089i	$0.0906957\pi$
$104$	−364.268	−	264.656i	−0.343455	−	0.249535i
$105$		0			0
$106$	475.456	−	1463.30i	0.435664	−	1.34084i
$107$	275.331	+	847.380i	0.248759	+	0.765601i	0.994995	+	0.0999205i	$0.0318588\pi$
$107$	275.331	+	847.380i	0.248759	+	0.765601i	−0.746236	+	0.665681i	$0.768141\pi$
$108$		0			0
$109$	−363.454			−0.319382			−0.159691	−	0.987167i	$-0.551050\pi$
$109$	−363.454			−0.319382			−0.159691	+	0.987167i	$0.551050\pi$
$110$	−1380.38	−	1573.06i	−1.19649	−	1.36350i
$111$		0			0
$112$	2028.49	−	1473.79i	1.71138	−	1.24339i
$113$	−316.920	−	975.378i	−0.263834	−	0.811999i	−0.991960	−	0.126555i	$-0.959608\pi$
$113$	−316.920	−	975.378i	−0.263834	−	0.811999i	0.728125	−	0.685444i	$-0.240392\pi$
$114$		0			0
$115$	63.4476	+	46.0973i	0.0514480	+	0.0373791i
$116$	239.058	+	173.686i	0.191345	+	0.139020i
$117$		0			0
$118$	483.652	+	1488.53i	0.377320	+	1.16127i
$119$	−551.038	+	400.353i	−0.424484	+	0.308406i
$120$		0			0
$121$	−172.930	+	1319.72i	−0.129925	+	0.991524i
$122$	−511.240			−0.379389
$123$		0			0
$124$	61.8296	+	190.292i	0.0447779	+	0.137812i
$125$	−18.5518	+	57.0965i	−0.0132746	+	0.0408549i
$126$		0			0
$127$	−1933.50	−	1404.77i	−1.35095	−	0.981522i	−0.998964	−	0.0455164i	$-0.985507\pi$
$127$	−1933.50	−	1404.77i	−1.35095	−	0.981522i	−0.351985	−	0.936005i	$-0.614493\pi$
$128$	400.907	−	1233.86i	0.276840	−	0.852025i
$129$		0			0
$130$	−1913.54	+	1390.27i	−1.29099	+	0.937957i
$131$	−878.775			−0.586099			−0.293050	−	0.956097i	$-0.594670\pi$
$131$	−878.775			−0.586099			−0.293050	+	0.956097i	$0.594670\pi$
$132$		0			0
$133$	4289.07			2.79631
$134$	17.3052	−	12.5729i	0.0111563	−	0.00810550i
$135$		0			0
$136$	−72.4770	+	223.061i	−0.0456974	+	0.140642i
$137$	−796.789	−	578.901i	−0.496893	−	0.361014i	0.310936	−	0.950431i	$-0.399357\pi$
$137$	−796.789	−	578.901i	−0.496893	−	0.361014i	−0.807829	+	0.589417i	$0.799357\pi$
$138$		0			0
$139$	−563.156	+	1733.21i	−0.343642	+	1.05762i	0.618665	+	0.785655i	$0.287674\pi$
$139$	−563.156	+	1733.21i	−0.343642	+	1.05762i	−0.962307	+	0.271966i	$0.912326\pi$
$140$	−775.488	−	2386.71i	−0.468148	−	1.44081i
$141$		0			0
$142$	−478.520			−0.282792
$143$	1467.26	+	331.540i	0.858033	+	0.193880i
$144$		0			0
$145$	−766.630	+	556.989i	−0.439070	+	0.319003i
$146$	467.766	+	1439.64i	0.265155	+	0.816062i
$147$		0			0
$148$	−740.647	−	538.112i	−0.411357	−	0.298868i
$149$	−2752.37	−	1999.71i	−1.51331	−	1.09948i	−0.964683	−	0.263415i	$-0.915151\pi$
$149$	−2752.37	−	1999.71i	−1.51331	−	1.09948i	−0.548626	−	0.836068i	$-0.684849\pi$
$150$		0			0
$151$	−327.363	−	1007.52i	−0.176427	−	0.542986i	0.823269	−	0.567651i	$-0.192148\pi$
$151$	−327.363	−	1007.52i	−0.176427	−	0.542986i	−0.999696	+	0.0246657i	$0.992148\pi$
$152$	1194.85	−	868.112i	0.637601	−	0.463245i
$153$		0			0
$154$	−2129.13	+	3581.22i	−1.11409	+	1.87391i
$155$	−641.648			−0.332506
$156$		0			0
$157$	468.656	+	1442.37i	0.238234	+	0.733210i	0.996676	+	0.0814689i	$0.0259611\pi$
$157$	468.656	+	1442.37i	0.238234	+	0.733210i	−0.758442	+	0.651741i	$0.774039\pi$
$158$	407.858	−	1255.26i	0.205364	−	0.632044i
$159$		0			0
$160$	−2543.41	−	1847.89i	−1.25671	−	0.913055i
$161$	48.2456	−	148.485i	0.0236167	−	0.0726846i
$162$		0			0
$163$	1938.29	−	1408.25i	0.931404	−	0.676705i	−0.0149320	−	0.999889i	$-0.504753\pi$
$163$	1938.29	−	1408.25i	0.931404	−	0.676705i	0.946336	+	0.323184i	$0.104753\pi$
$164$	−1832.24			−0.872404
$165$		0			0
$166$	2785.87			1.30256
$167$	−2131.85	+	1548.88i	−0.987829	+	0.717700i	−0.959445	−	0.281897i	$-0.909036\pi$
$167$	−2131.85	+	1548.88i	−0.987829	+	0.717700i	−0.0283843	+	0.999597i	$0.509036\pi$
$168$		0			0
$169$	−153.563	+	472.618i	−0.0698966	+	0.215120i
$170$	996.762	+	724.190i	0.449695	+	0.326723i
$171$		0			0
$172$	626.157	−	1927.11i	0.277582	−	0.854308i
$173$	134.045	+	412.547i	0.0589089	+	0.181303i	0.976181	−	0.216959i	$-0.0696137\pi$
$173$	134.045	+	412.547i	0.0589089	+	0.181303i	−0.917272	+	0.398261i	$0.869614\pi$
$174$		0			0
$175$	4083.64			1.76396
$176$	264.806	+	2872.30i	0.113412	+	1.23016i
$177$		0			0
$178$	−42.5420	+	30.9085i	−0.0179138	+	0.0130151i
$179$	−500.750	−	1541.15i	−0.209094	−	0.643525i	−0.999520	−	0.0309682i	$-0.990141\pi$
$179$	−500.750	−	1541.15i	−0.209094	−	0.643525i	0.790426	−	0.612557i	$-0.209859\pi$
$180$		0			0
$181$	1435.82	+	1043.19i	0.589635	+	0.428395i	0.842185	−	0.539189i	$-0.181269\pi$
$181$	1435.82	+	1043.19i	0.589635	+	0.428395i	−0.252550	+	0.967584i	$0.581269\pi$
$182$	3809.38	+	2767.68i	1.55148	+	1.12722i
$183$		0			0
$184$	−16.6131	−	51.1299i	−0.00665617	−	0.0204856i
$185$	2375.16	−	1725.66i	0.943922	−	0.685799i
$186$		0			0
$187$	−71.9343	−	780.258i	−0.0281302	−	0.305124i
$188$	2603.27			1.00991
$189$		0			0
$190$	−2397.48	−	7378.70i	−0.915430	−	2.81740i
$191$	−614.138	+	1890.12i	−0.232657	+	0.716045i	0.764766	+	0.644308i	$0.222854\pi$
$191$	−614.138	+	1890.12i	−0.232657	+	0.716045i	−0.997424	+	0.0717373i	$0.977146\pi$
$192$		0			0
$193$	−1774.07	−	1288.93i	−0.661658	−	0.480723i	0.205564	−	0.978644i	$-0.434097\pi$
$193$	−1774.07	−	1288.93i	−0.661658	−	0.480723i	−0.867223	+	0.497921i	$0.834097\pi$
$194$	1329.60	−	4092.09i	0.492061	−	1.51441i
$195$		0			0
$196$	−2663.30	+	1935.00i	−0.970589	+	0.705174i
$197$	−4825.72			−1.74527			−0.872636	−	0.488372i	$-0.837591\pi$
$197$	−4825.72			−1.74527			−0.872636	+	0.488372i	$0.837591\pi$
$198$		0			0
$199$	−3488.25			−1.24259			−0.621296	−	0.783576i	$-0.713393\pi$
$199$	−3488.25			−1.24259			−0.621296	+	0.783576i	$0.713393\pi$
$200$	1137.62	−	826.531i	0.402210	−	0.292223i
$201$		0			0
$202$	−1583.46	+	4873.38i	−0.551543	+	1.69747i
$203$	1526.17	+	1108.83i	0.527667	+	0.383372i
$204$		0			0
$205$	1815.72	−	5588.20i	0.618611	−	1.90389i
$206$	67.9937	+	209.263i	0.0229968	+	0.0707769i
$207$		0			0
$208$	3259.95			1.08672
$209$	−2521.53	+	4241.23i	−0.834535	+	1.40370i
$210$		0			0
$211$	1233.99	−	896.546i	0.402613	−	0.292516i	−0.367991	−	0.929829i	$-0.619954\pi$
$211$	1233.99	−	896.546i	0.402613	−	0.292516i	0.770605	+	0.637314i	$0.219954\pi$
$212$	655.872	+	2018.57i	0.212479	+	0.653942i
$213$		0			0
$214$	−2595.72	−	1885.90i	−0.829157	−	0.602418i
$215$	5257.04	+	3819.46i	1.66757	+	1.21156i
$216$		0			0
$217$	394.727	+	1214.84i	0.123483	+	0.380042i
$218$	1058.85	−	769.301i	0.328966	−	0.239008i
$219$		0			0
$220$	2815.99	+	636.296i	0.862974	+	0.194996i
$221$	−885.562			−0.269545
$222$		0			0
$223$	851.393	+	2620.32i	0.255666	+	0.786859i	0.993698	+	0.112093i	$0.0357554\pi$
$223$	851.393	+	2620.32i	0.255666	+	0.786859i	−0.738032	+	0.674766i	$0.764245\pi$
$224$	−1934.01	+	5952.27i	−0.576881	+	1.77546i
$225$		0			0
$226$	2987.81	+	2170.77i	0.879406	+	0.638926i
$227$	−1455.95	+	4480.94i	−0.425703	+	1.31018i	0.476616	+	0.879111i	$0.341863\pi$
$227$	−1455.95	+	4480.94i	−0.425703	+	1.31018i	−0.902319	+	0.431068i	$0.858137\pi$
$228$		0			0
$229$	−3289.67	+	2390.09i	−0.949292	+	0.689701i	−0.950639	−	0.310298i	$-0.899571\pi$
$229$	−3289.67	+	2390.09i	−0.949292	+	0.689701i	0.00134745	+	0.999999i	$0.499571\pi$
$230$	−282.413			−0.0809643
$231$		0			0
$232$	649.591			0.183826
$233$	2252.38	−	1636.45i	0.633296	−	0.460117i	−0.224244	−	0.974533i	$-0.571991\pi$
$233$	2252.38	−	1636.45i	0.633296	−	0.460117i	0.857541	+	0.514416i	$0.171991\pi$
$234$		0			0
$235$	−2579.78	+	7939.75i	−0.716113	+	2.20397i
$236$	−1746.69	−	1269.05i	−0.481780	−	0.350034i
$237$		0			0
$238$	757.939	−	2332.70i	0.206428	−	0.635320i
$239$	480.477	+	1478.76i	0.130040	+	0.400221i	0.994786	−	0.101989i	$-0.0325206\pi$
$239$	480.477	+	1478.76i	0.130040	+	0.400221i	−0.864746	+	0.502210i	$0.832521\pi$
$240$		0			0
$241$	−924.309			−0.247054			−0.123527	−	0.992341i	$-0.539421\pi$
$241$	−924.309			−0.247054			−0.123527	+	0.992341i	$0.539421\pi$
$242$	−2289.57	−	4210.77i	−0.608178	−	1.11851i
$243$		0			0
$244$	570.547	−	414.527i	0.149695	−	0.108760i
$245$	−3262.32	−	10040.4i	−0.850702	−	2.61819i
$246$		0			0
$247$	4511.45	+	3277.76i	1.16217	+	0.844368i
$248$	355.849	+	258.540i	0.0911147	+	0.0661987i
$249$		0			0
$250$	−66.8057	−	205.607i	−0.0169006	−	0.0520148i
$251$	2759.50	−	2004.90i	0.693937	−	0.504175i	−0.184015	−	0.982923i	$-0.558909\pi$
$251$	2759.50	−	2004.90i	0.693937	−	0.504175i	0.877952	+	0.478748i	$0.158909\pi$
$252$		0			0
$253$	118.465	+	135.001i	0.0294381	+	0.0335472i
$254$	8606.27			2.12600
$255$		0			0
$256$	1636.90	+	5037.85i	0.399633	+	1.22994i
$257$	1806.34	−	5559.33i	0.438429	−	1.34935i	−0.451103	−	0.892472i	$-0.648969\pi$
$257$	1806.34	−	5559.33i	0.438429	−	1.34935i	0.889532	−	0.456873i	$-0.151031\pi$
$258$		0			0
$259$	−4728.37	−	3435.36i	−1.13439	−	0.824181i
$260$	1008.25	−	3103.09i	0.240497	−	0.740175i
$261$		0			0
$262$	2560.14	−	1860.05i	0.603687	−	0.438604i
$263$	−426.069			−0.0998955			−0.0499477	−	0.998752i	$-0.515905\pi$
$263$	−426.069			−0.0998955			−0.0499477	+	0.998752i	$0.515905\pi$
$264$		0			0
$265$	−6806.42			−1.57779
$266$	−12495.4	+	9078.41i	−2.88022	+	2.09261i
$267$		0			0
$268$	−9.11821	+	28.0630i	−0.00207830	+	0.00639634i
$269$	5310.12	+	3858.03i	1.20358	+	0.874454i	0.994632	−	0.103472i	$-0.0329953\pi$
$269$	5310.12	+	3858.03i	1.20358	+	0.874454i	0.208950	+	0.977926i	$0.432995\pi$
$270$		0			0
$271$	920.948	−	2834.39i	0.206434	−	0.635338i	−0.793217	−	0.608938i	$-0.791596\pi$
$271$	920.948	−	2834.39i	0.206434	−	0.635338i	0.999651	−	0.0264000i	$-0.00840436\pi$
$272$	−524.745	−	1615.00i	−0.116975	−	0.360013i
$273$		0			0
$274$	3546.61			0.781966
$275$	−2400.75	+	4038.09i	−0.526440	+	0.885476i
$276$		0			0
$277$	−349.406	+	253.858i	−0.0757898	+	0.0550645i	−0.625035	−	0.780597i	$-0.714915\pi$
$277$	−349.406	+	253.858i	−0.0757898	+	0.0550645i	0.549245	+	0.835661i	$0.314915\pi$
$278$	−2027.95	−	6241.37i	−0.437511	−	1.34652i
$279$		0			0
$280$	−4463.18	−	3242.69i	−0.952592	−	0.692099i
$281$	−2290.41	−	1664.08i	−0.486243	−	0.353276i	0.317494	−	0.948260i	$-0.397159\pi$
$281$	−2290.41	−	1664.08i	−0.486243	−	0.353276i	−0.803738	+	0.594984i	$0.797159\pi$
$282$		0			0
$283$	−636.174	−	1957.94i	−0.133628	−	0.411264i	0.861746	−	0.507339i	$-0.169371\pi$
$283$	−636.174	−	1957.94i	−0.133628	−	0.411264i	−0.995374	+	0.0960756i	$0.969371\pi$
$284$	534.031	−	387.996i	0.111581	−	0.0810681i
$285$		0			0
$286$	−4976.33	+	2139.79i	−1.02887	+	0.442407i
$287$	−11697.2			−2.40581
$288$		0			0
$289$	−1375.65	−	4233.83i	−0.280003	−	0.861760i
$290$	1054.48	−	3245.36i	0.213521	−	0.657151i
$291$		0			0
$292$	−1689.32	−	1227.36i	−0.338562	−	0.245980i
$293$	2360.41	−	7264.61i	0.470638	−	1.44847i	−0.381114	−	0.924528i	$-0.624460\pi$
$293$	2360.41	−	7264.61i	0.470638	−	1.44847i	0.851752	−	0.523946i	$-0.175540\pi$
$294$		0			0
$295$	5601.44	−	4069.68i	1.10552	−	0.803207i
$296$	−2012.55			−0.395194
$297$		0			0
$298$	12251.2			2.38151
$299$	164.221	−	119.313i	0.0317630	−	0.0230772i
$300$		0			0
$301$	3997.45	−	12302.9i	0.765480	−	2.35590i
$302$	3086.26	+	2242.30i	0.588061	+	0.427252i
$303$		0			0
$304$	−3304.36	+	10169.8i	−0.623415	+	1.91867i
$305$	698.873	+	2150.91i	0.131204	+	0.403806i
$306$		0			0
$307$	−4284.72			−0.796553			−0.398277	−	0.917265i	$-0.630392\pi$
$307$	−4284.72			−0.796553			−0.398277	+	0.917265i	$0.630392\pi$
$308$	−527.622	−	5723.01i	−0.0976105	−	1.05876i
$309$		0			0
$310$	1869.31	−	1358.14i	0.342483	−	0.248829i
$311$	229.842	+	707.382i	0.0419073	+	0.128977i	0.969821	−	0.243817i	$-0.0783997\pi$
$311$	229.842	+	707.382i	0.0419073	+	0.128977i	−0.927914	+	0.372794i	$0.878400\pi$
$312$		0			0
$313$	−956.411	−	694.873i	−0.172714	−	0.125484i	0.498070	−	0.867137i	$-0.334042\pi$
$313$	−956.411	−	694.873i	−0.172714	−	0.125484i	−0.670784	+	0.741653i	$0.734042\pi$
$314$	−4418.32	−	3210.10i	−0.794077	−	0.576931i
$315$		0			0
$316$	562.624	+	1731.58i	0.100158	+	0.308256i
$317$	826.987	−	600.841i	0.146524	−	0.106456i	−0.512108	−	0.858921i	$-0.671135\pi$
$317$	826.987	−	600.841i	0.146524	−	0.106456i	0.658632	+	0.752465i	$0.271135\pi$
$318$		0			0
$319$	−1993.69	+	857.275i	−0.349923	+	0.150465i
$320$	1245.04			0.217500
$321$		0			0
$322$	173.734	+	534.699i	0.0300678	+	0.0925392i
$323$	897.627	−	2762.61i	0.154629	−	0.475900i
$324$		0			0
$325$	4295.36	+	3120.76i	0.733120	+	0.532643i
$326$	−2666.07	+	8205.33i	−0.452945	+	1.39402i
$327$		0			0
$328$	−3258.63	+	2367.53i	−0.548560	+	0.398552i
$329$	16619.5			2.78500
$330$		0			0
$331$	4137.81			0.687113			0.343557	−	0.939132i	$-0.388368\pi$
$331$	4137.81			0.687113			0.343557	+	0.939132i	$0.388368\pi$
$332$	−3109.05	+	2258.85i	−0.513949	+	0.373406i
$333$		0			0
$334$	2932.30	−	9024.71i	0.480385	−	1.47847i
$335$	−76.5539	−	55.6196i	−0.0124853	−	0.00907112i
$336$		0			0
$337$	625.388	−	1924.75i	0.101089	−	0.311121i	−0.887703	−	0.460416i	$-0.847700\pi$
$337$	625.388	−	1924.75i	0.101089	−	0.311121i	0.988793	+	0.149295i	$0.0477004\pi$
$338$	−552.986	−	1701.91i	−0.0889895	−	0.273882i
$339$		0			0
$340$	−1699.58			−0.271097
$341$	−1433.35	−	323.878i	−0.227626	−	0.0514339i
$342$		0			0
$343$	−8202.65	+	5959.57i	−1.29126	+	0.938153i
$344$	−1376.50	−	4236.44i	−0.215744	−	0.663993i
$345$		0			0
$346$	−1263.73	−	918.151i	−0.196354	−	0.142659i
$347$	5915.26	+	4297.69i	0.915123	+	0.664876i	0.942305	−	0.334755i	$-0.108653\pi$
$347$	5915.26	+	4297.69i	0.915123	+	0.664876i	−0.0271821	+	0.999630i	$0.508653\pi$
$348$		0			0
$349$	3157.81	+	9718.73i	0.484337	+	1.49064i	0.832939	+	0.553364i	$0.186656\pi$
$349$	3157.81	+	9718.73i	0.484337	+	1.49064i	−0.348603	+	0.937271i	$0.613344\pi$
$350$	−11896.9	+	8643.58i	−1.81690	+	1.32005i
$351$		0			0
$352$	−4748.88	−	5411.75i	−0.719081	−	0.819453i
$353$	4008.76			0.604433			0.302216	−	0.953239i	$-0.402274\pi$
$353$	4008.76			0.604433			0.302216	+	0.953239i	$0.402274\pi$
$354$		0			0
$355$	654.144	+	2013.25i	0.0977982	+	0.300992i
$356$	22.4156	−	68.9882i	0.00333715	−	0.0102707i
$357$		0			0
$358$	4720.90	+	3429.93i	0.696947	+	0.506362i
$359$	−246.704	+	759.277i	−0.0362689	+	0.111624i	−0.967552	−	0.252672i	$-0.918691\pi$
$359$	−246.704	+	759.277i	−0.0362689	+	0.111624i	0.931283	+	0.364297i	$0.118691\pi$
$360$		0			0
$361$	−9249.20	+	6719.94i	−1.34848	+	0.979726i
$362$	−6391.04			−0.927916
$363$		0			0
$364$	−6495.40			−0.935306
$365$	5417.45	−	3936.01i	0.776883	−	0.564438i
$366$		0			0
$367$	773.794	−	2381.49i	0.110059	−	0.338727i	−0.880825	−	0.473441i	$-0.843012\pi$
$367$	773.794	−	2381.49i	0.110059	−	0.338727i	0.990885	+	0.134714i	$0.0430116\pi$
$368$	314.901	+	228.789i	0.0446070	+	0.0324089i
$369$		0			0
$370$	−3266.98	+	10054.7i	−0.459033	+	1.41276i
$371$	4187.16	+	12886.7i	0.585947	+	1.80336i
$372$		0			0
$373$	−9807.89			−1.36148			−0.680742	−	0.732524i	$-0.738342\pi$
$373$	−9807.89			−1.36148			−0.680742	+	0.732524i	$0.738342\pi$
$374$	1861.09	+	2120.87i	0.257312	+	0.293229i
$375$		0			0
$376$	4629.88	−	3363.81i	0.635021	−	0.461370i
$377$	757.921	+	2332.64i	0.103541	+	0.318666i
$378$		0			0
$379$	8814.70	+	6404.25i	1.19467	+	0.867980i	0.993750	−	0.111628i	$-0.0356063\pi$
$379$	8814.70	+	6404.25i	1.19467	+	0.867980i	0.200922	+	0.979607i	$0.435606\pi$
$380$	8658.44	+	6290.73i	1.16886	+	0.849230i
$381$		0			0
$382$	−2211.54	−	6806.41i	−0.296210	−	0.911640i
$383$	7842.42	−	5697.85i	1.04629	−	0.760173i	0.0747857	−	0.997200i	$-0.476173\pi$
$383$	7842.42	−	5697.85i	1.04629	−	0.760173i	0.971503	+	0.237026i	$0.0761727\pi$
$384$		0			0
$385$	17977.6	+	4062.18i	2.37980	+	0.537735i
$386$	7896.60			1.04126
$387$		0			0
$388$	1834.13	+	5644.88i	0.239984	+	0.738596i
$389$	−3797.38	+	11687.1i	−0.494948	+	1.52329i	0.322089	+	0.946709i	$0.395615\pi$
$389$	−3797.38	+	11687.1i	−0.494948	+	1.52329i	−0.817037	+	0.576585i	$0.804385\pi$
$390$		0			0
$391$	−85.5427	−	62.1504i	−0.0110641	−	0.00803857i
$392$	−2236.34	+	6882.75i	−0.288144	+	0.886815i
$393$		0			0
$394$	14058.8	−	10214.3i	1.79764	−	1.30606i
$395$	−5838.72			−0.743742
$396$		0			0
$397$	−2988.47			−0.377801			−0.188901	−	0.981996i	$-0.560492\pi$
$397$	−2988.47			−0.377801			−0.188901	+	0.981996i	$0.560492\pi$
$398$	10162.3	−	7383.37i	1.27988	−	0.929887i
$399$		0			0
$400$	−3146.09	+	9682.67i	−0.393261	+	1.21033i
$401$	−10944.2	−	7951.41i	−1.36291	−	0.990210i	−0.998254	−	0.0590672i	$-0.981187\pi$
$401$	−10944.2	−	7951.41i	−1.36291	−	0.990210i	−0.364654	−	0.931143i	$-0.618813\pi$
$402$		0			0
$403$	−513.207	+	1579.49i	−0.0634358	+	0.195235i
$404$	−2184.31	−	6722.63i	−0.268994	−	0.827879i
$405$		0			0
$406$	−6793.19			−0.830396
$407$	6176.84	−	2656.00i	0.752271	−	0.323472i
$408$		0			0
$409$	3260.87	−	2369.16i	0.394229	−	0.286424i	−0.372957	−	0.927848i	$-0.621656\pi$
$409$	3260.87	−	2369.16i	0.394229	−	0.286424i	0.767186	+	0.641425i	$0.221656\pi$
$410$	6538.47	+	20123.3i	0.787590	+	2.42395i
$411$		0			0
$412$	−245.557	−	178.408i	−0.0293634	−	0.0213338i
$413$	−11151.1	−	8101.74i	−1.32859	−	0.965280i
$414$		0			0
$415$	−3808.33	−	11720.8i	−0.450466	−	1.38639i
$416$	−6583.08	+	4782.89i	−0.775870	+	0.563702i
$417$		0			0
$418$	−1631.18	−	17693.2i	−0.190870	−	2.07034i
$419$	−8327.13			−0.970900			−0.485450	−	0.874264i	$-0.661344\pi$
$419$	−8327.13			−0.970900			−0.485450	+	0.874264i	$0.661344\pi$
$420$		0			0
$421$	196.275	+	604.071i	0.0227217	+	0.0699303i	0.961774	−	0.273843i	$-0.0882949\pi$
$421$	196.275	+	604.071i	0.0227217	+	0.0699303i	−0.939053	+	0.343773i	$0.888295\pi$
$422$	−1697.32	+	5223.82i	−0.195792	+	0.602587i
$423$		0			0
$424$	3774.75	+	2742.52i	0.432354	+	0.314124i
$425$	854.633	−	2630.29i	0.0975430	−	0.300206i
$426$		0			0
$427$	3642.43	−	2646.38i	0.412810	−	0.299924i
$428$	4425.97			0.499854
$429$		0			0
$430$	−23399.7			−2.62427
$431$	7838.74	−	5695.18i	0.876053	−	0.636490i	−0.0561511	−	0.998422i	$-0.517883\pi$
$431$	7838.74	−	5695.18i	0.876053	−	0.636490i	0.932204	+	0.361932i	$0.117883\pi$
$432$		0			0
$433$	1206.52	−	3713.27i	0.133906	−	0.412121i	−0.861512	−	0.507737i	$-0.830482\pi$
$433$	1206.52	−	3713.27i	0.133906	−	0.412121i	0.995418	+	0.0956160i	$0.0304821\pi$
$434$	−3721.35	−	2703.72i	−0.411591	−	0.299038i
$435$		0			0
$436$	−557.916	+	1717.09i	−0.0612829	+	0.188609i
$437$	205.753	+	633.244i	0.0225229	+	0.0693184i
$438$		0			0
$439$	1221.08			0.132754			0.0663771	−	0.997795i	$-0.478856\pi$
$439$	1221.08			0.132754			0.0663771	+	0.997795i	$0.478856\pi$
$440$	5830.41	−	2507.04i	0.631713	−	0.271632i
$441$		0			0
$442$	2579.91	−	1874.42i	0.277633	−	0.201712i
$443$	4715.93	+	14514.2i	0.505781	+	1.55663i	0.799454	+	0.600727i	$0.205122\pi$
$443$	4715.93	+	14514.2i	0.505781	+	1.55663i	−0.293674	+	0.955906i	$0.594878\pi$
$444$		0			0
$445$	188.195	+	136.732i	0.0200479	+	0.0145656i
$446$	−8026.63	−	5831.69i	−0.852179	−	0.619145i
$447$		0			0
$448$	−765.923	−	2357.27i	−0.0807733	−	0.248595i
$449$	−648.769	+	471.359i	−0.0681900	+	0.0495430i	−0.621358	−	0.783527i	$-0.713419\pi$
$449$	−648.769	+	471.359i	−0.0681900	+	0.0495430i	0.553168	+	0.833070i	$0.313419\pi$
$450$		0			0
$451$	6876.77	−	11566.8i	0.717992	−	1.20767i
$452$	−5094.52			−0.530146
$453$		0			0
$454$	−5242.92	−	16136.1i	−0.541988	−	1.66807i
$455$	6436.81	−	19810.5i	0.663213	−	2.04116i
$456$		0			0
$457$	10018.2	+	7278.66i	1.02545	+	0.745036i	0.967394	−	0.253277i	$-0.0815084\pi$
$457$	10018.2	+	7278.66i	1.02545	+	0.745036i	0.0580605	+	0.998313i	$0.481508\pi$
$458$	4524.86	−	13926.1i	0.461644	−	1.42079i
$459$		0			0
$460$	315.175	−	228.988i	0.0319459	−	0.0232100i
$461$	4583.73			0.463092			0.231546	−	0.972824i	$-0.425622\pi$
$461$	4583.73			0.463092			0.231546	+	0.972824i	$0.425622\pi$
$462$		0			0
$463$	−144.386			−0.0144928			−0.00724642	−	0.999974i	$-0.502307\pi$
$463$	−144.386			−0.0144928			−0.00724642	+	0.999974i	$0.502307\pi$
$464$	−3804.92	+	2764.44i	−0.380687	+	0.276586i
$465$		0			0
$466$	−3098.09	+	9534.93i	−0.307974	+	0.947848i
$467$	−2786.89	−	2024.79i	−0.276149	−	0.200634i	0.441087	−	0.897464i	$-0.354593\pi$
$467$	−2786.89	−	2024.79i	−0.276149	−	0.200634i	−0.717236	+	0.696830i	$0.754593\pi$
$468$		0			0
$469$	−58.2116	+	179.157i	−0.00573126	+	0.0176390i
$470$	−9289.90	−	28591.4i	−0.911726	−	2.80600i
$471$		0			0
$472$	−4746.28			−0.462850
$473$	9815.60	+	11185.7i	0.954168	+	1.08736i
$474$		0			0
$475$	−14089.5	+	10236.6i	−1.36099	+	0.988814i
$476$	1045.55	+	3217.86i	0.100678	+	0.309854i
$477$		0			0
$478$	−4529.77	−	3291.07i	−0.433445	−	0.314916i
$479$	−10819.0	−	7860.44i	−1.03201	−	0.749796i	−0.0632970	−	0.997995i	$-0.520162\pi$
$479$	−10819.0	−	7860.44i	−1.03201	−	0.749796i	−0.968709	+	0.248198i	$0.920162\pi$
$480$		0			0
$481$	−2348.18	−	7226.96i	−0.222594	−	0.685075i
$482$	2692.79	−	1956.43i	0.254468	−	0.184881i
$483$		0			0
$484$	5969.37	+	2842.80i	0.560610	+	0.266980i
$485$	−19034.0			−1.78204
$486$		0			0
$487$	5561.96	+	17117.9i	0.517528	+	1.59279i	0.778634	+	0.627478i	$0.215913\pi$
$487$	5561.96	+	17117.9i	0.517528	+	1.59279i	−0.261106	+	0.965310i	$0.584087\pi$
$488$	479.082	−	1474.46i	0.0444406	−	0.136774i
$489$		0			0
$490$	30756.0	+	22345.5i	2.83554	+	2.06014i
$491$	−4112.56	+	12657.2i	−0.377998	+	1.16336i	0.563435	+	0.826160i	$0.309479\pi$
$491$	−4112.56	+	12657.2i	−0.377998	+	1.16336i	−0.941434	+	0.337199i	$0.890521\pi$
$492$		0			0
$493$	1033.60	−	750.957i	0.0944242	−	0.0686032i
$494$	−20081.1			−1.82893
$495$		0			0
$496$	−3184.61			−0.288293
$497$	3409.31	−	2477.01i	0.307703	−	0.223560i
$498$		0			0
$499$	6285.77	−	19345.6i	0.563907	−	1.73553i	−0.107270	−	0.994230i	$-0.534211\pi$
$499$	6285.77	−	19345.6i	0.563907	−	1.73553i	0.671177	−	0.741297i	$-0.265789\pi$
$500$	241.267	+	175.291i	0.0215796	+	0.0156785i
$501$		0			0
$502$	−3795.63	+	11681.7i	−0.337464	+	1.03861i
$503$	634.369	+	1952.39i	0.0562328	+	0.173067i	0.975228	−	0.221202i	$-0.0709980\pi$
$503$	634.369	+	1952.39i	0.0562328	+	0.173067i	−0.918995	+	0.394269i	$0.870998\pi$
$504$		0			0
$505$	22668.1			1.99746
$506$	−630.873	−	142.551i	−0.0554263	−	0.0125240i
$507$		0			0
$508$	−9604.64	+	6978.18i	−0.838853	+	0.609462i
$509$	2449.99	+	7540.30i	0.213348	+	0.656617i	0.999267	+	0.0382874i	$0.0121902\pi$
$509$	2449.99	+	7540.30i	0.213348	+	0.656617i	−0.785919	+	0.618329i	$0.787810\pi$
$510$		0			0
$511$	−10784.8	−	7835.63i	−0.933644	−	0.678332i
$512$	−7035.37	−	5111.49i	−0.607270	−	0.441207i
$513$		0			0
$514$	6504.69	+	20019.4i	0.558190	+	1.71793i
$515$	787.472	−	572.132i	0.0673789	−	0.0489537i
$516$		0			0
$517$	−9770.55	+	16434.2i	−0.831158	+	1.39802i
$518$	21046.6			1.78520
$519$		0			0
$520$	−2216.48	−	6821.63i	−0.186921	−	0.575285i
$521$	−5281.43	+	16254.6i	−0.444114	+	1.36684i	0.439338	+	0.898322i	$0.355213\pi$
$521$	−5281.43	+	16254.6i	−0.444114	+	1.36684i	−0.883452	+	0.468522i	$0.844787\pi$
$522$		0			0
$523$	−8762.59	−	6366.40i	−0.732622	−	0.532281i	0.157770	−	0.987476i	$-0.449570\pi$
$523$	−8762.59	−	6366.40i	−0.732622	−	0.532281i	−0.890392	+	0.455195i	$0.849570\pi$
$524$	−1348.95	+	4151.65i	−0.112461	+	0.346118i
$525$		0			0
$526$	1241.27	−	901.833i	0.102893	−	0.0747562i
$527$	865.097			0.0715070
$528$		0			0
$529$	−12142.8			−0.998008
$530$	19829.2	−	14406.7i	1.62514	−	1.18073i
$531$		0			0
$532$	6583.89	−	20263.1i	0.536556	−	1.65135i
$533$	−12303.7	−	8939.18i	−0.999875	−	0.726452i
$534$		0			0
$535$	−4386.05	+	13498.9i	−0.354440	+	1.09085i
$536$	20.0449	+	61.6918i	0.00161531	+	0.00497142i
$537$		0			0
$538$	−23636.0			−1.89409
$539$	−2219.60	−	24075.6i	−0.177374	−	1.92395i
$540$		0			0
$541$	−16843.7	+	12237.7i	−1.33857	+	0.972528i	−0.339075	+	0.940759i	$0.610114\pi$
$541$	−16843.7	+	12237.7i	−1.33857	+	0.972528i	−0.999495	+	0.0317692i	$0.989886\pi$
$542$	3316.37	+	10206.7i	0.262823	+	0.808887i
$543$		0			0
$544$	3429.13	+	2491.41i	0.270262	+	0.196357i
$545$	−4684.10	−	3403.20i	−0.368156	−	0.267481i
$546$		0			0
$547$	−1331.66	−	4098.41i	−0.104090	−	0.320357i	0.885425	−	0.464781i	$-0.153867\pi$
$547$	−1331.66	−	4098.41i	−0.104090	−	0.320357i	−0.989516	+	0.144424i	$0.953867\pi$
$548$	−3958.04	+	2875.68i	−0.308538	+	0.224166i
$549$		0			0
$550$	−1553.06	−	16845.7i	−0.120405	−	1.30601i
$551$	−8045.18			−0.622026
$552$		0			0
$553$	3591.85	+	11054.6i	0.276204	+	0.850070i
$554$	480.599	−	1479.13i	0.0368569	−	0.113434i
$555$		0			0
$556$	7323.87	+	5321.10i	0.558635	+	0.405872i
$557$	578.432	−	1780.23i	0.0440017	−	0.135423i	−0.926642	−	0.375945i	$-0.877318\pi$
$557$	578.432	−	1780.23i	0.0440017	−	0.135423i	0.970644	+	0.240521i	$0.0773183\pi$
$558$		0			0
$559$	13606.7	−	9885.88i	1.02952	−	0.747993i
$560$	39942.4			3.01406
$561$		0			0
$562$	10194.9			0.765207
$563$	868.778	−	631.205i	0.0650349	−	0.0472506i	−0.554793	−	0.831989i	$-0.687202\pi$
$563$	868.778	−	631.205i	0.0650349	−	0.0472506i	0.619828	+	0.784738i	$0.287202\pi$
$564$		0			0
$565$	5048.57	−	15537.9i	0.375920	−	1.15696i
$566$	5997.63	+	4357.53i	0.445405	+	0.323605i
$567$		0			0
$568$	448.420	−	1380.10i	0.0331255	−	0.101950i
$569$	4279.16	+	13169.9i	0.315275	+	0.970317i	0.975641	+	0.219373i	$0.0704012\pi$
$569$	4279.16	+	13169.9i	0.315275	+	0.970317i	−0.660366	+	0.750944i	$0.729599\pi$
$570$		0			0
$571$	−781.386			−0.0572680			−0.0286340	−	0.999590i	$-0.509116\pi$
$571$	−781.386			−0.0572680			−0.0286340	+	0.999590i	$0.509116\pi$
$572$	3818.62	−	6422.95i	0.279134	−	0.469506i
$573$		0			0
$574$	34077.6	−	24758.8i	2.47800	−	1.80037i
$575$	195.898	+	602.913i	0.0142079	+	0.0437273i
$576$		0			0
$577$	−7086.19	−	5148.42i	−0.511268	−	0.371458i	0.302036	−	0.953296i	$-0.402334\pi$
$577$	−7086.19	−	5148.42i	−0.511268	−	0.371458i	−0.813305	+	0.581838i	$0.802334\pi$
$578$	12969.2	+	9422.66i	0.933299	+	0.678081i
$579$		0			0
$580$	1454.61	+	4476.84i	0.104137	+	0.320501i
$581$	−19848.5	+	14420.8i	−1.41730	+	1.02973i
$582$		0			0
$583$	−15204.6	−	3435.61i	−1.08012	−	0.244062i
$584$	−4590.38			−0.325259
$585$		0			0
$586$	8499.94	+	26160.1i	0.599197	+	1.84414i
$587$	−297.166	+	914.581i	−0.0208949	+	0.0643080i	−0.960960	−	0.276686i	$-0.910764\pi$
$587$	−297.166	+	914.581i	−0.0208949	+	0.0643080i	0.940065	+	0.340994i	$0.110764\pi$
$588$		0			0
$589$	−4407.19	−	3202.01i	−0.308311	−	0.224001i
$590$	−7704.63	+	23712.4i	−0.537618	+	1.65462i
$591$		0			0
$592$	11788.4	−	8564.74i	0.818409	−	0.594609i
$593$	−1880.24			−0.130206			−0.0651030	−	0.997879i	$-0.520738\pi$
$593$	−1880.24			−0.130206			−0.0651030	+	0.997879i	$0.520738\pi$
$594$		0			0
$595$	−10850.3			−0.747597
$596$	−13672.4	+	9933.55i	−0.939668	+	0.682708i
$597$		0			0
$598$	−225.882	+	695.192i	−0.0154465	+	0.0475393i
$599$	−4095.79	−	2975.76i	−0.279381	−	0.202982i	0.439266	−	0.898357i	$-0.355238\pi$
$599$	−4095.79	−	2975.76i	−0.279381	−	0.202982i	−0.718647	+	0.695375i	$0.755238\pi$
$600$		0			0
$601$	4384.18	−	13493.1i	0.297561	−	0.915800i	−0.684788	−	0.728743i	$-0.740105\pi$
$601$	4384.18	−	13493.1i	0.297561	−	0.915800i	0.982349	−	0.187057i	$-0.0598950\pi$
$602$	14395.0	+	44303.2i	0.974578	+	2.99944i
$603$		0			0
$604$	−5262.40			−0.354510
$605$	−14585.8	+	15389.0i	−0.980163	+	1.03413i
$606$		0			0
$607$	−6852.98	+	4978.98i	−0.458244	+	0.332934i	−0.792842	−	0.609427i	$-0.791399\pi$
$607$	−6852.98	+	4978.98i	−0.458244	+	0.332934i	0.334598	+	0.942361i	$0.391399\pi$
$608$	−8247.98	−	25384.7i	−0.550164	−	1.69323i
$609$		0			0
$610$	−6588.73	−	4786.99i	−0.437327	−	0.317737i
$611$	17481.2	+	12700.8i	1.15747	+	0.840951i
$612$		0			0
$613$	−3603.15	−	11089.3i	−0.237406	−	0.730660i	−0.996793	−	0.0800209i	$-0.974501\pi$
$613$	−3603.15	−	11089.3i	−0.237406	−	0.730660i	0.759388	−	0.650639i	$-0.225499\pi$
$614$	12482.7	−	9069.20i	0.820456	−	0.596096i
$615$		0			0
$616$	−8333.36	−	9496.56i	−0.545066	−	0.621148i
$617$	29514.0			1.92575			0.962877	−	0.269941i	$-0.0870041\pi$
$617$	29514.0			1.92575			0.962877	+	0.269941i	$0.0870041\pi$
$618$		0			0
$619$	4614.68	+	14202.5i	0.299644	+	0.922210i	0.981622	+	0.190837i	$0.0611202\pi$
$619$	4614.68	+	14202.5i	0.299644	+	0.922210i	−0.681978	+	0.731373i	$0.738880\pi$
$620$	−984.953	+	3031.37i	−0.0638011	+	0.196360i
$621$		0			0
$622$	−2166.87	−	1574.33i	−0.139684	−	0.101487i
$623$	143.104	−	440.428i	0.00920278	−	0.0283233i
$624$		0			0
$625$	12248.3	−	8898.90i	0.783891	−	0.569530i
$626$	4257.11			0.271802
$627$		0			0
$628$	7533.70			0.478706
$629$	−3202.30	+	2326.60i	−0.202995	+	0.147485i
$630$		0			0
$631$	1756.75	−	5406.71i	0.110832	−	0.341106i	−0.880223	−	0.474561i	$-0.842607\pi$
$631$	1756.75	−	5406.71i	0.110832	−	0.341106i	0.991055	+	0.133455i	$0.0426070\pi$
$632$	3238.08	+	2352.60i	0.203803	+	0.148072i
$633$		0			0
$634$	−1137.50	+	3500.87i	−0.0712554	+	0.219301i
$635$	−11764.9	−	36208.6i	−0.735237	−	2.26283i
$636$		0			0
$637$	−27324.8			−1.69961
$638$	3993.69	−	6717.43i	0.247824	−	0.416843i
$639$		0			0
$640$	16720.1	−	12147.8i	1.03268	−	0.750289i
$641$	−2830.60	−	8711.70i	−0.174418	−	0.536804i	0.825188	−	0.564858i	$-0.191069\pi$
$641$	−2830.60	−	8711.70i	−0.174418	−	0.536804i	−0.999606	+	0.0280537i	$0.991069\pi$
$642$		0			0
$643$	24254.2	+	17621.7i	1.48755	+	1.08077i	0.975026	+	0.222092i	$0.0712885\pi$
$643$	24254.2	+	17621.7i	1.48755	+	1.08077i	0.512521	+	0.858674i	$0.328712\pi$
$644$	−627.436	−	455.859i	−0.0383920	−	0.0278934i
$645$		0			0
$646$	3232.39	+	9948.27i	0.196868	+	0.605897i
$647$	−10601.1	+	7702.18i	−0.644163	+	0.468012i	−0.861278	−	0.508134i	$-0.830335\pi$
$647$	−10601.1	+	7702.18i	−0.644163	+	0.468012i	0.217115	+	0.976146i	$0.430335\pi$
$648$		0			0
$649$	14567.1	−	6263.74i	0.881059	−	0.378849i
$650$	−19119.2			−1.15372
$651$		0			0
$652$	−3677.74	−	11318.9i	−0.220907	−	0.679882i
$653$	3630.18	−	11172.5i	0.217550	−	0.669549i	−0.781413	−	0.624014i	$-0.785501\pi$
$653$	3630.18	−	11172.5i	0.217550	−	0.669549i	0.998963	−	0.0455347i	$-0.0144992\pi$
$654$		0			0
$655$	−11325.4	−	8228.40i	−0.675605	−	0.490855i
$656$	9011.72	−	27735.2i	0.536355	−	1.65073i
$657$		0			0
$658$	−48417.7	+	35177.5i	−2.86857	+	2.08414i
$659$	−1585.28			−0.0937081			−0.0468541	−	0.998902i	$-0.514920\pi$
$659$	−1585.28			−0.0937081			−0.0468541	+	0.998902i	$0.514920\pi$
$660$		0			0
$661$	−9070.54			−0.533741			−0.266871	−	0.963732i	$-0.585990\pi$
$661$	−9070.54			−0.533741			−0.266871	+	0.963732i	$0.585990\pi$
$662$	−12054.7	+	8758.24i	−0.707732	+	0.514198i
$663$		0			0
$664$	−2610.63	+	8034.70i	−0.152579	+	0.469589i
$665$	55276.4	+	40160.7i	3.22335	+	2.34190i
$666$		0			0
$667$	−90.4961	+	278.518i	−0.00525341	+	0.0161683i
$668$	4044.99	+	12449.2i	0.234290	+	0.721070i
$669$		0			0
$670$	340.751			0.0196483
$671$	475.495	+	5157.61i	0.0273566	+	0.296732i
$672$		0			0
$673$	−12739.3	+	9255.63i	−0.729663	+	0.530131i	−0.889457	−	0.457019i	$-0.848917\pi$
$673$	−12739.3	+	9255.63i	−0.729663	+	0.530131i	0.159794	+	0.987150i	$0.448917\pi$
$674$	2252.05	+	6931.09i	0.128703	+	0.396106i
$675$		0			0
$676$	1997.09	+	1450.97i	0.113626	+	0.0825541i
$677$	−14601.0	−	10608.2i	−0.828895	−	0.602228i	0.0903513	−	0.995910i	$-0.471201\pi$
$677$	−14601.0	−	10608.2i	−0.828895	−	0.602228i	−0.919247	+	0.393682i	$0.871201\pi$
$678$		0			0
$679$	11709.3	+	36037.5i	0.661799	+	2.03681i
$680$	−3022.69	+	2196.12i	−0.170463	+	0.123849i
$681$		0			0
$682$	4861.33	−	2090.34i	0.272947	−	0.117365i
$683$	−10422.1			−0.583881			−0.291941	−	0.956436i	$-0.594301\pi$
$683$	−10422.1			−0.583881			−0.291941	+	0.956436i	$0.594301\pi$
$684$		0			0
$685$	−4848.27	−	14921.5i	−0.270428	−	0.832291i
$686$	11282.5	−	34724.1i	0.627943	−	1.93261i
$687$		0			0
$688$	26091.6	+	18956.6i	1.44583	+	1.05046i
$689$	−5443.95	+	16754.8i	−0.301013	+	0.926424i
$690$		0			0
$691$	6497.39	−	4720.63i	0.357703	−	0.259886i	−0.394391	−	0.918943i	$-0.629044\pi$
$691$	6497.39	−	4720.63i	0.357703	−	0.259886i	0.752093	+	0.659057i	$0.229044\pi$
$692$	2154.79			0.118371
$693$		0			0
$694$	−26329.6			−1.44014
$695$	−23486.7	+	17064.1i	−1.28187	+	0.931336i
$696$		0			0
$697$	−2448.03	+	7534.25i	−0.133035	+	0.409441i
$698$	−29770.7	−	21629.7i	−1.61438	−	1.17292i
$699$		0			0
$700$	6268.54	−	19292.6i	0.338469	−	1.04170i
$701$	−1604.92	−	4939.43i	−0.0864720	−	0.266134i	0.898465	−	0.439044i	$-0.144683\pi$
$701$	−1604.92	−	4939.43i	−0.0864720	−	0.266134i	−0.984938	+	0.172911i	$0.944683\pi$
$702$		0			0
$703$	24925.5			1.33724
$704$	2781.26	+	628.448i	0.148896	+	0.0336442i
$705$		0			0
$706$	−11678.7	+	8485.09i	−0.622570	+	0.452324i
$707$	−13944.9	−	42918.0i	−0.741799	−	2.28302i
$708$		0			0
$709$	26122.2	+	18978.9i	1.38370	+	1.00531i	0.996524	+	0.0833054i	$0.0265477\pi$
$709$	26122.2	+	18978.9i	1.38370	+	1.00531i	0.387171	+	0.922008i	$0.373452\pi$
$710$	−6167.04	−	4480.62i	−0.325979	−	0.236837i
$711$		0			0
$712$	−49.2771	−	151.659i	−0.00259373	−	0.00798268i
$713$	−160.426	+	116.556i	−0.00842634	+	0.00612210i
$714$		0			0
$715$	15805.3	+	18011.5i	0.826694	+	0.942087i
$716$	−8049.62			−0.420152
$717$		0			0
$718$	−888.391	−	2734.19i	−0.0461761	−	0.142116i
$719$	2733.18	−	8411.87i	0.141767	−	0.436314i	−0.854814	−	0.518934i	$-0.826329\pi$
$719$	2733.18	−	8411.87i	0.141767	−	0.436314i	0.996581	+	0.0826204i	$0.0263289\pi$
$720$		0			0
$721$	−1567.66	−	1138.97i	−0.0809748	−	0.0588317i
$722$	12722.0	−	39154.4i	0.655769	−	2.01825i
$723$		0			0
$724$	7132.44	−	5182.02i	0.366126	−	0.266006i
$725$	−7659.83			−0.392385
$726$		0			0
$727$	17537.4			0.894670			0.447335	−	0.894367i	$-0.352373\pi$
$727$	17537.4			0.894670			0.447335	+	0.894367i	$0.352373\pi$
$728$	−11552.0	+	8393.02i	−0.588112	+	0.427289i
$729$		0			0
$730$	−7451.56	+	22933.6i	−0.377801	+	1.16275i
$731$	−7087.76	−	5149.56i	−0.358619	−	0.260552i
$732$		0			0
$733$	−272.607	+	838.998i	−0.0137367	+	0.0422771i	−0.957690	−	0.287802i	$-0.907075\pi$
$733$	−272.607	+	838.998i	−0.0137367	+	0.0422771i	0.943953	+	0.330079i	$0.107075\pi$
$734$	2786.46	+	8575.85i	0.140123	+	0.431254i
$735$		0			0
$736$	−971.577			−0.0486587
$737$	−142.936	−	162.888i	−0.00714400	−	0.00814119i
$738$		0			0
$739$	1166.37	−	847.419i	0.0580591	−	0.0421824i	−0.558377	−	0.829587i	$-0.688576\pi$
$739$	1166.37	−	847.419i	0.0580591	−	0.0421824i	0.616436	+	0.787405i	$0.288576\pi$
$740$	−4506.66	−	13870.1i	−0.223876	−	0.689019i
$741$		0			0
$742$	−39475.0	−	28680.3i	−1.95306	−	1.41898i
$743$	25842.7	+	18775.8i	1.27601	+	0.927075i	0.999425	−	0.0339141i	$-0.0107973\pi$
$743$	25842.7	+	18775.8i	1.27601	+	0.927075i	0.276585	+	0.960989i	$0.410797\pi$
$744$		0			0
$745$	−16747.5	−	51543.6i	−0.823600	−	2.53478i
$746$	28573.3	−	20759.7i	1.40234	−	1.01886i
$747$		0			0
$748$	−3796.64	−	857.882i	−0.185587	−	0.0419349i
$749$	28255.9			1.37843
$750$		0			0
$751$	−10165.3	−	31285.5i	−0.493922	−	1.52014i	−0.818630	−	0.574322i	$-0.805266\pi$
$751$	−10165.3	−	31285.5i	−0.493922	−	1.52014i	0.324707	−	0.945815i	$-0.394734\pi$
$752$	−12803.9	+	39406.4i	−0.620892	+	1.91091i
$753$		0			0
$754$	−7145.41	−	5191.44i	−0.345120	−	0.250744i
$755$	5214.93	−	16049.9i	0.251379	−	0.773664i
$756$		0			0
$757$	−1452.12	+	1055.03i	−0.0697204	+	0.0506549i	−0.622100	−	0.782938i	$-0.713720\pi$
$757$	−1452.12	+	1055.03i	−0.0697204	+	0.0506549i	0.552379	+	0.833593i	$0.313720\pi$
$758$	−39235.4			−1.88007
$759$		0			0
$760$	23527.5			1.12294
$761$	−246.368	+	178.996i	−0.0117356	+	0.00852644i	−0.593638	−	0.804732i	$-0.702309\pi$
$761$	−246.368	+	178.996i	−0.0117356	+	0.00852644i	0.581902	+	0.813259i	$0.302309\pi$
$762$		0			0
$763$	−3561.80	+	10962.1i	−0.168998	+	0.520123i
$764$	7986.90	+	5802.82i	0.378215	+	0.274789i
$765$		0			0
$766$	−10787.0	+	33199.1i	−0.508814	+	1.56597i
$767$	−5537.80	−	17043.6i	−0.260702	−	0.802358i
$768$		0			0
$769$	23116.6			1.08402			0.542008	−	0.840374i	$-0.317664\pi$
$769$	23116.6			1.08402			0.542008	+	0.840374i	$0.317664\pi$
$770$	−60972.4	+	26217.7i	−2.85363	+	1.22704i
$771$		0			0
$772$	−8812.65	+	6402.76i	−0.410847	+	0.298498i
$773$	−3367.32	−	10363.6i	−0.156681	−	0.482214i	0.841647	−	0.540029i	$-0.181587\pi$
$773$	−3367.32	−	10363.6i	−0.156681	−	0.482214i	−0.998327	+	0.0578149i	$0.981587\pi$
$774$		0			0
$775$	−4196.10	−	3048.64i	−0.194488	−	0.141304i
$776$	10556.0	+	7669.39i	0.488323	+	0.354787i
$777$		0			0
$778$	−13674.5	−	42085.8i	−0.630148	−	1.93940i
$779$	40358.1	−	29321.9i	1.85620	−	1.34861i
$780$		0			0
$781$	445.063	+	4827.51i	0.0203913	+	0.221181i
$782$	380.762			0.0174118
$783$		0			0
$784$	−16191.5	−	49832.2i	−0.737585	−	2.27005i
$785$	−7465.74	+	22977.2i	−0.339444	+	1.04470i
$786$		0			0
$787$	−15622.8	−	11350.7i	−0.707616	−	0.514113i	0.174788	−	0.984606i	$-0.444076\pi$
$787$	−15622.8	−	11350.7i	−0.707616	−	0.514113i	−0.882404	+	0.470493i	$0.844076\pi$
$788$	−7407.66	+	22798.4i	−0.334882	+	1.03066i
$789$		0			0
$790$	17010.0	−	12358.5i	0.766060	−	0.556575i
$791$	−32524.0			−1.46197
$792$		0			0
$793$	5853.68			0.262132
$794$	8706.32	−	6325.51i	0.389138	−	0.282726i
$795$		0			0
$796$	−5354.60	+	16479.8i	−0.238428	+	0.733806i
$797$	−27357.8	−	19876.6i	−1.21589	−	0.883394i	−0.220136	−	0.975469i	$-0.570650\pi$
$797$	−27357.8	−	19876.6i	−1.21589	−	0.883394i	−0.995752	+	0.0920748i	$0.970650\pi$
$798$		0			0
$799$	3478.17	−	10704.7i	0.154004	−	0.473974i
$800$	−7852.93	−	24168.8i	−0.347054	−	1.06812i
$801$		0			0
$802$	48713.9			2.14482
$803$	14088.6	−	6058.00i	0.619147	−	0.266229i
$804$		0			0
$805$	2012.11	−	1461.88i	0.0880964	−	0.0640057i
$806$	−1848.08	−	5687.80i	−0.0807639	−	0.248566i
$807$		0			0
$808$	−12571.4	−	9133.67i	−0.547353	−	0.397675i
$809$	25666.8	+	18648.0i	1.11545	+	0.810420i	0.983513	−	0.180839i	$-0.0578812\pi$
$809$	25666.8	+	18648.0i	1.11545	+	0.810420i	0.131934	+	0.991258i	$0.457881\pi$
$810$		0			0
$811$	4028.01	+	12397.0i	0.174405	+	0.536764i	0.999606	−	0.0280756i	$-0.00893790\pi$
$811$	4028.01	+	12397.0i	0.174405	+	0.536764i	−0.825200	+	0.564840i	$0.808938\pi$
$812$	7581.24	−	5508.10i	0.327647	−	0.238050i
$813$		0			0
$814$	−12373.2	+	20811.9i	−0.532777	+	0.896137i
$815$	38166.4			1.64038
$816$		0			0
$817$	17048.0	+	52468.3i	0.730029	+	2.24680i
$818$	−4485.24	+	13804.2i	−0.191715	+	0.590038i
$819$		0			0
$820$	−23613.5	−	17156.2i	−1.00563	−	0.730635i
$821$	−589.658	+	1814.78i	−0.0250660	+	0.0771453i	−0.962807	−	0.270190i	$-0.912913\pi$
$821$	−589.658	+	1814.78i	−0.0250660	+	0.0771453i	0.937741	+	0.347335i	$0.112913\pi$
$822$		0			0
$823$	−13773.5	+	10007.0i	−0.583369	+	0.423842i	−0.839937	−	0.542684i	$-0.817408\pi$
$823$	−13773.5	+	10007.0i	−0.583369	+	0.423842i	0.256568	+	0.966526i	$0.417408\pi$
$824$	−667.251			−0.0282097
$825$		0			0
$826$	49634.9			2.09082
$827$	16950.8	−	12315.5i	0.712740	−	0.517836i	−0.171316	−	0.985216i	$-0.554802\pi$
$827$	16950.8	−	12315.5i	0.712740	−	0.517836i	0.884057	+	0.467380i	$0.154802\pi$
$828$		0			0
$829$	1874.06	−	5767.78i	0.0785150	−	0.241644i	−0.904093	−	0.427335i	$-0.859452\pi$
$829$	1874.06	−	5767.78i	0.0785150	−	0.241644i	0.982608	+	0.185691i	$0.0594523\pi$
$830$	35903.5	+	26085.5i	1.50148	+	1.09089i
$831$		0			0
$832$	995.819	−	3064.82i	0.0414950	−	0.127708i
$833$	4398.40	+	13536.9i	0.182948	+	0.563055i
$834$		0			0
$835$	−41977.6			−1.73975
$836$	16166.5	+	18423.1i	0.668815	+	0.762171i
$837$		0			0
$838$	24259.5	−	17625.5i	1.00003	−	0.726568i
$839$	4540.38	+	13973.8i	0.186831	+	0.575007i	0.999975	−	0.00705566i	$-0.00224591\pi$
$839$	4540.38	+	13973.8i	0.186831	+	0.575007i	−0.813144	+	0.582062i	$0.802246\pi$
$840$		0			0
$841$	16868.4	+	12255.6i	0.691640	+	0.502506i
$842$	−1850.41	−	1344.40i	−0.0757355	−	0.0550250i
$843$		0			0
$844$	−2341.39	−	7206.05i	−0.0954903	−	0.293889i
$845$	−6404.43	+	4653.09i	−0.260732	+	0.189433i
$846$		0			0
$847$	38109.1	+	18148.7i	1.54598	+	0.736243i
$848$	−33781.5			−1.36800
$849$		0			0
$850$	3077.57	+	9471.77i	0.124188	+	0.382211i
$851$	280.374	−	862.902i	0.0112939	−	0.0347590i
$852$		0			0
$853$	−965.318	−	701.344i	−0.0387478	−	0.0281519i	0.568243	−	0.822861i	$-0.307623\pi$
$853$	−965.318	−	701.344i	−0.0387478	−	0.0281519i	−0.606991	+	0.794709i	$0.707623\pi$
$854$	−5010.07	+	15419.4i	−0.200751	+	0.617848i
$855$		0			0
$856$	7871.55	−	5719.02i	0.314304	−	0.228355i
$857$	−12579.5			−0.501410			−0.250705	−	0.968064i	$-0.580662\pi$
$857$	−12579.5			−0.501410			−0.250705	+	0.968064i	$0.580662\pi$
$858$		0			0
$859$	−23421.2			−0.930293			−0.465146	−	0.885234i	$-0.653998\pi$
$859$	−23421.2			−0.930293			−0.465146	+	0.885234i	$0.653998\pi$
$860$	26114.3	−	18973.1i	1.03545	−	0.752300i
$861$		0			0
$862$	−10782.0	+	33183.6i	−0.426028	+	1.31118i
$863$	32968.7	+	23953.2i	1.30043	+	0.944816i	0.999960	−	0.00897626i	$-0.00285727\pi$
$863$	32968.7	+	23953.2i	1.30043	+	0.944816i	0.300468	+	0.953792i	$0.402857\pi$
$864$		0			0
$865$	−2135.35	+	6571.93i	−0.0839353	+	0.258326i
$866$	4344.71	+	13371.6i	0.170484	+	0.524696i
$867$		0			0
$868$	6345.29			0.248126
$869$	−13042.9	−	2947.15i	−0.509149	−	0.115046i
$870$		0			0
$871$	−198.144	+	143.960i	−0.00770820	+	0.00560034i
$872$	1226.49	+	3774.74i	0.0476308	+	0.146593i
$873$		0			0
$874$	−1939.77	−	1409.33i	−0.0750729	−	0.0545436i
$875$	1540.27	+	1119.07i	0.0595094	+	0.0432361i
$876$		0			0
$877$	7090.82	+	21823.3i	0.273022	+	0.840274i	0.989736	+	0.142908i	$0.0456452\pi$
$877$	7090.82	+	21823.3i	0.273022	+	0.840274i	−0.716714	+	0.697367i	$0.754355\pi$
$878$	−3557.38	+	2584.59i	−0.136738	+	0.0993459i
$879$		0			0
$880$	−23482.0	+	39496.9i	−0.899520	+	1.51300i
$881$	34636.1			1.32454			0.662269	−	0.749266i	$-0.269594\pi$
$881$	34636.1			1.32454			0.662269	+	0.749266i	$0.269594\pi$
$882$		0			0
$883$	−6556.34	−	20178.3i	−0.249874	−	0.769032i	−0.994797	−	0.101882i	$-0.967514\pi$
$883$	−6556.34	−	20178.3i	−0.249874	−	0.769032i	0.744923	−	0.667151i	$-0.232486\pi$
$884$	−1359.37	+	4183.72i	−0.0517202	+	0.159178i
$885$		0			0
$886$	−44460.2	−	32302.2i	−1.68586	−	1.22485i
$887$	5915.07	−	18204.7i	0.223910	−	0.689126i	−0.774490	−	0.632586i	$-0.781993\pi$
$887$	5915.07	−	18204.7i	0.223910	−	0.689126i	0.998400	−	0.0565393i	$-0.0180066\pi$
$888$		0			0
$889$	−61317.1	+	44549.5i	−2.31328	+	1.68070i
$890$	−837.681			−0.0315496
$891$		0			0
$892$	13686.2			0.513733
$893$	−57341.1	+	41660.7i	−2.14876	+	1.56117i
$894$		0			0
$895$	7977.01	−	24550.7i	0.297924	−	0.916916i
$896$	−33285.5	−	24183.4i	−1.24106	−	0.901685i
$897$		0			0
$898$	892.366	−	2746.42i	0.0331611	−	0.102059i
$899$	−740.405	−	2278.73i	−0.0274682	−	0.0845383i
$900$		0			0
$901$	9176.71			0.339312
$902$	4448.60	+	48253.2i	0.164215	+	1.78121i
$903$		0			0
$904$	−9060.56	+	6582.88i	−0.333351	+	0.242194i
$905$	8736.65	+	26888.7i	0.320902	+	0.987634i
$906$		0			0
$907$	−5452.83	−	3961.71i	−0.199623	−	0.145035i	0.483483	−	0.875354i	$-0.339371\pi$
$907$	−5452.83	−	3961.71i	−0.199623	−	0.145035i	−0.683106	+	0.730319i	$0.739371\pi$
$908$	18934.7	+	13756.8i	0.692036	+	0.502794i
$909$		0			0
$910$	23179.2	+	71338.2i	0.844377	+	2.59872i
$911$	17666.4	−	12835.4i	0.642496	−	0.466801i	−0.218211	−	0.975902i	$-0.570022\pi$
$911$	17666.4	−	12835.4i	0.642496	−	0.466801i	0.860707	+	0.509101i	$0.170022\pi$
$912$		0			0
$913$	−2591.09	−	28105.0i	−0.0939238	−	1.01877i
$914$	−44592.4			−1.61377
$915$		0			0
$916$	6241.87	+	19210.5i	0.225150	+	0.692939i
$917$	−8611.86	+	26504.6i	−0.310130	+	0.954481i
$918$		0			0
$919$	−9296.26	−	6754.13i	−0.333684	−	0.242435i	0.408308	−	0.912844i	$-0.366119\pi$
$919$	−9296.26	−	6754.13i	−0.333684	−	0.242435i	−0.741992	+	0.670409i	$0.766119\pi$
$920$	264.649	−	814.506i	0.00948393	−	0.0291885i
$921$		0			0
$922$	−13353.8	+	9702.09i	−0.476989	+	0.346553i
$923$	5479.04			0.195390
$924$		0			0
$925$	23731.6			0.843557
$926$	420.640	−	305.613i	0.0149277	−	0.0108456i
$927$		0			0
$928$	3627.69	−	11164.9i	0.128324	−	0.394941i
$929$	18320.2	+	13310.4i	0.647003	+	0.470075i	0.862249	−	0.506485i	$-0.169055\pi$
$929$	18320.2	+	13310.4i	0.647003	+	0.470075i	−0.215246	+	0.976560i	$0.569055\pi$
$930$		0			0
$931$	27697.1	−	85242.8i	0.975011	−	3.00077i
$932$	−4273.68	−	13153.0i	−0.150203	−	0.462277i
$933$		0			0
$934$	12404.8			0.434579
$935$	6378.87	−	10729.3i	0.223114	−	0.375279i
$936$		0			0
$937$	17785.9	−	12922.2i	0.620106	−	0.450534i	−0.232852	−	0.972512i	$-0.574806\pi$
$937$	17785.9	−	12922.2i	0.620106	−	0.450534i	0.852959	+	0.521978i	$0.174806\pi$
$938$	−209.622	−	645.151i	−0.00729682	−	0.0224573i
$939$		0			0
$940$	33550.2	+	24375.6i	1.16413	+	0.845794i
$941$	1193.63	+	867.223i	0.0413509	+	0.0300432i	0.608269	−	0.793731i	$-0.291864\pi$
$941$	1193.63	+	867.223i	0.0413509	+	0.0300432i	−0.566918	+	0.823774i	$0.691864\pi$
$942$		0			0
$943$	−561.135	−	1727.00i	−0.0193776	−	0.0596381i
$944$	27800.9	−	20198.5i	0.958520	−	0.696405i
$945$		0			0
$946$	−52271.9	−	11811.3i	−1.79652	−	0.405938i
$947$	44129.0			1.51426			0.757128	−	0.653266i	$-0.226602\pi$
$947$	44129.0			1.51426			0.757128	+	0.653266i	$0.226602\pi$
$948$		0			0
$949$	−5355.90	−	16483.8i	−0.183203	−	0.563842i
$950$	19379.7	−	59644.5i	0.661853	−	2.03697i
$951$		0			0
$952$	6017.45	+	4371.93i	0.204860	+	0.148839i
$953$	14305.9	−	44029.1i	0.486269	−	1.49658i	−0.343867	−	0.939018i	$-0.611737\pi$
$953$	14305.9	−	44029.1i	0.486269	−	1.49658i	0.830135	−	0.557562i	$-0.188263\pi$
$954$		0			0
$955$	−25613.0	+	18608.9i	−0.867872	+	0.630546i
$956$	7723.73			0.261300
$957$		0			0
$958$	48156.6			1.62408
$959$	−25268.6	+	18358.7i	−0.850849	+	0.618178i
$960$		0			0
$961$	−8704.58	+	26789.9i	−0.292188	+	0.899263i
$962$	22137.8	+	16084.1i	0.741946	+	0.539055i
$963$		0			0
$964$	−1418.85	+	4366.77i	−0.0474046	+	0.145897i
$965$	−10794.8	−	33222.9i	−0.360099	−	1.10827i
$966$		0			0
$967$	−41724.4			−1.38755			−0.693777	−	0.720189i	$-0.744055\pi$
$967$	−41724.4			−1.38755			−0.693777	+	0.720189i	$0.744055\pi$
$968$	14289.8	−	2657.42i	0.474474	−	0.0882364i
$969$		0			0
$970$	55451.8	−	40288.1i	1.83552	−	1.33358i
$971$	−1289.25	−	3967.89i	−0.0426095	−	0.131139i	0.927489	−	0.373851i	$-0.121963\pi$
$971$	−1289.25	−	3967.89i	−0.0426095	−	0.131139i	−0.970098	+	0.242712i	$0.921963\pi$
$972$		0			0
$973$	46756.3	+	33970.5i	1.54053	+	1.11926i
$974$	−52436.2	−	38097.1i	−1.72501	−	1.25330i
$975$		0			0
$976$	3468.63	+	10675.3i	0.113758	+	0.350112i
$977$	−16292.7	+	11837.4i	−0.533522	+	0.387627i	−0.821674	−	0.569958i	$-0.806959\pi$
$977$	−16292.7	+	11837.4i	−0.533522	+	0.387627i	0.288151	+	0.957585i	$0.406959\pi$
$978$		0			0
$979$	351.386	+	400.434i	0.0114712	+	0.0130724i
$980$	−52442.2			−1.70939
$981$		0			0
$982$	−14809.5	−	45578.9i	−0.481252	−	1.48114i
$983$	11895.7	−	36611.1i	0.385975	−	1.18791i	−0.549796	−	0.835299i	$-0.685294\pi$
$983$	11895.7	−	36611.1i	0.385975	−	1.18791i	0.935771	−	0.352609i	$-0.114706\pi$
$984$		0			0
$985$	−62192.6	−	45185.6i	−2.01180	−	1.46166i
$986$	−1421.70	+	4375.53i	−0.0459189	+	0.141324i
$987$		0			0
$988$	22410.6	−	16282.2i	0.721635	−	0.524298i
$989$	2008.18			0.0645666
$990$		0			0
$991$	−920.782			−0.0295152			−0.0147576	−	0.999891i	$-0.504698\pi$
$991$	−920.782			−0.0295152			−0.0147576	+	0.999891i	$0.504698\pi$
$992$	6430.94	−	4672.35i	0.205829	−	0.149544i
$993$		0			0
$994$	−4689.42	+	14432.6i	−0.149637	+	0.460536i
$995$	−44955.7	−	32662.2i	−1.43235	−	1.04067i
$996$		0			0
$997$	17300.8	−	53246.3i	0.549569	−	1.69140i	−0.160301	−	0.987068i	$-0.551247\pi$
$997$	17300.8	−	53246.3i	0.549569	−	1.69140i	0.709870	−	0.704332i	$-0.248753\pi$
$998$	22635.3	+	69664.3i	0.717944	+	2.20960i
$999$		0			0

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.e.91.2	yes	24
3.2	odd	2	inner	99.4.f.e.91.5	yes	24
11.2	odd	10		1089.4.a.bl.1.3		12
11.4	even	5	inner	99.4.f.e.37.2	✓	24
11.9	even	5		1089.4.a.bm.1.10		12
33.2	even	10		1089.4.a.bl.1.10		12
33.20	odd	10		1089.4.a.bm.1.3		12
33.26	odd	10	inner	99.4.f.e.37.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.4.f.e.37.2	✓	24	11.4	even	5	inner
99.4.f.e.37.5	yes	24	33.26	odd	10	inner
99.4.f.e.91.2	yes	24	1.1	even	1	trivial
99.4.f.e.91.5	yes	24	3.2	odd	2	inner
1089.4.a.bl.1.3		12	11.2	odd	10
1089.4.a.bl.1.10		12	33.2	even	10
1089.4.a.bm.1.3		12	33.20	odd	10
1089.4.a.bm.1.10		12	11.9	even	5

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	99.4.f.e.91.2

Level	$99$
Weight	$4$
Character	99.91
Analytic conductor	$5.841$
Analytic rank	$0$
Dimension	$24$
Inner twists	$4$