LMFDB - Embedded newform 99.5.k.c.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,5,Mod(19,99)]

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, 3]))

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

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, 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:	$10.2336263453$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	99.19
Dual form			99.5.k.c.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01888 - 1.40237i) q^{2} +(4.01574 - 12.3592i) q^{4} +(32.0081 + 23.2552i) q^{5} +(27.3116 + 8.87408i) q^{7} +(-47.8012 + 15.5316i) q^{8} +O(q^{10})$	\(q+(-1.01888 - 1.40237i) q^{2} +(4.01574 - 12.3592i) q^{4} +(32.0081 + 23.2552i) q^{5} +(27.3116 + 8.87408i) q^{7} +(-47.8012 + 15.5316i) q^{8} -68.5817i q^{10} +(-30.6027 + 117.066i) q^{11} +(94.6157 + 130.227i) q^{13} +(-15.3826 - 47.3428i) q^{14} +(-97.7287 - 71.0040i) q^{16} +(141.875 - 195.274i) q^{17} +(439.357 - 142.756i) q^{19} +(415.952 - 302.207i) q^{20} +(195.351 - 76.3605i) q^{22} +241.540 q^{23} +(290.575 + 894.298i) q^{25} +(86.2250 - 265.373i) q^{26} +(219.353 - 301.913i) q^{28} +(-553.272 - 179.769i) q^{29} +(580.162 - 421.513i) q^{31} +1013.58i q^{32} -418.402 q^{34} +(667.823 + 919.179i) q^{35} +(757.807 - 2332.29i) q^{37} +(-647.851 - 470.691i) q^{38} +(-1891.21 - 614.493i) q^{40} +(-529.997 + 172.207i) q^{41} +3168.88i q^{43} +(1323.95 + 848.332i) q^{44} +(-246.102 - 338.730i) q^{46} +(-777.518 - 2392.95i) q^{47} +(-1275.28 - 926.542i) q^{49} +(958.079 - 1318.68i) q^{50} +(1989.46 - 646.413i) q^{52} +(-2716.68 + 1973.78i) q^{53} +(-3701.93 + 3035.39i) q^{55} -1443.36 q^{56} +(311.617 + 959.059i) q^{58} +(850.781 - 2618.44i) q^{59} +(-3694.91 + 5085.60i) q^{61} +(-1182.24 - 384.132i) q^{62} +(-142.245 + 103.347i) q^{64} +6368.63i q^{65} +309.930 q^{67} +(-1843.70 - 2537.63i) q^{68} +(608.599 - 1873.08i) q^{70} +(4765.74 + 3462.51i) q^{71} +(-2840.74 - 923.012i) q^{73} +(-4042.86 + 1313.61i) q^{74} -6003.36i q^{76} +(-1874.66 + 2925.69i) q^{77} +(-2715.61 - 3737.72i) q^{79} +(-1476.89 - 4545.40i) q^{80} +(781.504 + 567.796i) q^{82} +(4057.27 - 5584.35i) q^{83} +(9082.28 - 2951.01i) q^{85} +(4443.95 - 3228.72i) q^{86} +(-355.374 - 6071.21i) q^{88} -6528.45 q^{89} +(1428.46 + 4396.34i) q^{91} +(969.964 - 2985.24i) q^{92} +(-2563.62 + 3528.52i) q^{94} +(17382.8 + 5648.00i) q^{95} +(5078.93 - 3690.06i) q^{97} +2732.45i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8}+O(q^{10}) $ 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8	$ 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8} + 246 q^{11} - 510 q^{13} + 1290 q^{14} - 232 q^{16} - 2490 q^{17} + 582 q^{20} - 510 q^{22} + 2196 q^{23} - 370 q^{25} + 5226 q^{26} + 4310 q^{28} - 960 q^{29} + 1658 q^{31} - 2320 q^{34} - 1920 q^{35} + 1374 q^{37} - 12054 q^{38} + 11070 q^{40} - 9360 q^{41} + 4350 q^{44} - 12950 q^{46} + 3450 q^{47} - 11838 q^{49} + 11550 q^{50} - 19250 q^{52} + 2790 q^{53} + 12356 q^{55} + 5604 q^{56} + 9486 q^{58} - 2682 q^{59} - 17190 q^{61} + 39360 q^{62} + 16248 q^{64} + 2796 q^{67} - 68160 q^{68} + 18188 q^{70} - 132 q^{71} - 21790 q^{73} + 2130 q^{74} - 4542 q^{77} + 12270 q^{79} - 32346 q^{80} + 29442 q^{82} - 35430 q^{83} - 11990 q^{85} + 49416 q^{86} + 1176 q^{88} + 38748 q^{89} - 51858 q^{91} + 25590 q^{92} - 34510 q^{94} + 71670 q^{95} + 30306 q^{97}+O(q^{100}) $ 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8 + 246 * q^11 - 510 * q^13 + 1290 * q^14 - 232 * q^16 - 2490 * q^17 + 582 * q^20 - 510 * q^22 + 2196 * q^23 - 370 * q^25 + 5226 * q^26 + 4310 * q^28 - 960 * q^29 + 1658 * q^31 - 2320 * q^34 - 1920 * q^35 + 1374 * q^37 - 12054 * q^38 + 11070 * q^40 - 9360 * q^41 + 4350 * q^44 - 12950 * q^46 + 3450 * q^47 - 11838 * q^49 + 11550 * q^50 - 19250 * q^52 + 2790 * q^53 + 12356 * q^55 + 5604 * q^56 + 9486 * q^58 - 2682 * q^59 - 17190 * q^61 + 39360 * q^62 + 16248 * q^64 + 2796 * q^67 - 68160 * q^68 + 18188 * q^70 - 132 * q^71 - 21790 * q^73 + 2130 * q^74 - 4542 * q^77 + 12270 * q^79 - 32346 * q^80 + 29442 * q^82 - 35430 * q^83 - 11990 * q^85 + 49416 * q^86 + 1176 * q^88 + 38748 * q^89 - 51858 * q^91 + 25590 * q^92 - 34510 * q^94 + 71670 * q^95 + 30306 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−1.01888	−	1.40237i	−0.254721	−	0.350594i	0.662437	−	0.749118i	$-0.269522\pi$
$2$	−1.01888	−	1.40237i	−0.254721	−	0.350594i	−0.917158	+	0.398524i	$0.869522\pi$
$3$		0			0
$3$		0			0
$4$	4.01574	−	12.3592i	0.250984	−	0.772449i
$5$	32.0081	+	23.2552i	1.28032	+	0.930209i	0.999563	−	0.0295695i	$-0.00941363\pi$
$5$	32.0081	+	23.2552i	1.28032	+	0.930209i	0.280760	+	0.959778i	$0.409414\pi$
$6$		0			0
$7$	27.3116	+	8.87408i	0.557380	+	0.181104i	0.574142	−	0.818756i	$-0.305336\pi$
$7$	27.3116	+	8.87408i	0.557380	+	0.181104i	−0.0167621	+	0.999860i	$0.505336\pi$
$8$	−47.8012	+	15.5316i	−0.746894	+	0.242681i
$9$		0			0
$10$		−	68.5817i		−	0.685817i
$11$	−30.6027	+	117.066i	−0.252915	+	0.967489i
$11$	−30.6027	+	117.066i	−0.252915	+	0.967489i
$12$		0			0
$13$	94.6157	+	130.227i	0.559856	+	0.770576i	0.991308	−	0.131560i	$-0.0419986\pi$
$13$	94.6157	+	130.227i	0.559856	+	0.770576i	−0.431452	+	0.902136i	$0.641999\pi$
$14$	−15.3826	−	47.3428i	−0.0784826	−	0.241545i
$15$		0			0
$16$	−97.7287	−	71.0040i	−0.381753	−	0.277359i
$17$	141.875	−	195.274i	0.490917	−	0.675689i	−0.489640	−	0.871925i	$-0.662872\pi$
$17$	141.875	−	195.274i	0.490917	−	0.675689i	0.980557	+	0.196236i	$0.0628718\pi$
$18$		0			0
$19$	439.357	−	142.756i	1.21705	−	0.395445i	0.371046	−	0.928615i	$-0.378999\pi$
$19$	439.357	−	142.756i	1.21705	−	0.395445i	0.846008	+	0.533170i	$0.178999\pi$
$20$	415.952	−	302.207i	1.03988	−	0.755517i
$21$		0			0
$22$	195.351	−	76.3605i	0.403618	−	0.157770i
$23$	241.540			0.456598			0.228299	−	0.973591i	$-0.426684\pi$
$23$	241.540			0.456598			0.228299	+	0.973591i	$0.426684\pi$
$24$		0			0
$25$	290.575	+	894.298i	0.464920	+	1.43088i
$26$	86.2250	−	265.373i	0.127552	−	0.392564i
$27$		0			0
$28$	219.353	−	301.913i	0.279787	−	0.385093i
$29$	−553.272	−	179.769i	−0.657874	−	0.213756i	−0.0389915	−	0.999240i	$-0.512415\pi$
$29$	−553.272	−	179.769i	−0.657874	−	0.213756i	−0.618883	+	0.785483i	$0.712415\pi$
$30$		0			0
$31$	580.162	−	421.513i	0.603707	−	0.438619i	−0.243486	−	0.969904i	$-0.578291\pi$
$31$	580.162	−	421.513i	0.603707	−	0.438619i	0.847193	+	0.531286i	$0.178291\pi$
$32$			1013.58i			0.989820i
$33$		0			0
$34$	−418.402			−0.361939
$35$	667.823	+	919.179i	0.545162	+	0.750351i
$36$		0			0
$37$	757.807	−	2332.29i	0.553548	−	1.70365i	−0.146200	−	0.989255i	$-0.546704\pi$
$37$	757.807	−	2332.29i	0.553548	−	1.70365i	0.699748	−	0.714390i	$-0.253296\pi$
$38$	−647.851	−	470.691i	−0.448650	−	0.325963i
$39$		0			0
$40$	−1891.21	−	614.493i	−1.18201	−	0.384058i
$41$	−529.997	+	172.207i	−0.315287	+	0.102443i	−0.462386	−	0.886679i	$-0.653006\pi$
$41$	−529.997	+	172.207i	−0.315287	+	0.102443i	0.147099	+	0.989122i	$0.453006\pi$
$42$		0			0
$43$			3168.88i			1.71383i	0.515456	+	0.856916i	$0.327623\pi$
$43$			3168.88i			1.71383i	−0.515456	+	0.856916i	$0.672377\pi$
$44$	1323.95	+	848.332i	0.683858	+	0.438188i
$45$		0			0
$46$	−246.102	−	338.730i	−0.116305	−	0.160080i
$47$	−777.518	−	2392.95i	−0.351977	−	1.08327i	−0.957741	−	0.287630i	$-0.907133\pi$
$47$	−777.518	−	2392.95i	−0.351977	−	1.08327i	0.605764	−	0.795644i	$-0.292867\pi$
$48$		0			0
$49$	−1275.28	−	926.542i	−0.531143	−	0.385898i
$50$	958.079	−	1318.68i	0.383231	−	0.527473i
$51$		0			0
$52$	1989.46	−	646.413i	0.735746	−	0.239058i
$53$	−2716.68	+	1973.78i	−0.967135	+	0.702665i	−0.954797	−	0.297259i	$-0.903927\pi$
$53$	−2716.68	+	1973.78i	−0.967135	+	0.702665i	−0.0123381	+	0.999924i	$0.503927\pi$
$54$		0			0
$55$	−3701.93	+	3035.39i	−1.22378	+	1.00343i
$56$	−1443.36			−0.460254
$57$		0			0
$58$	311.617	+	959.059i	0.0926329	+	0.285095i
$59$	850.781	−	2618.44i	0.244407	−	0.752208i	−0.751326	−	0.659931i	$-0.770586\pi$
$59$	850.781	−	2618.44i	0.244407	−	0.752208i	0.995733	−	0.0922768i	$-0.0294145\pi$
$60$		0			0
$61$	−3694.91	+	5085.60i	−0.992987	+	1.36673i	−0.0634568	+	0.997985i	$0.520213\pi$
$61$	−3694.91	+	5085.60i	−0.992987	+	1.36673i	−0.929530	+	0.368745i	$0.879787\pi$
$62$	−1182.24	−	384.132i	−0.307554	−	0.0999303i
$63$		0			0
$64$	−142.245	+	103.347i	−0.0347278	+	0.0252313i
$65$			6368.63i			1.50737i
$66$		0			0
$67$	309.930			0.0690421			0.0345210	−	0.999404i	$-0.489009\pi$
$67$	309.930			0.0690421			0.0345210	+	0.999404i	$0.489009\pi$
$68$	−1843.70	−	2537.63i	−0.398723	−	0.548795i
$69$		0			0
$70$	608.599	−	1873.08i	0.124204	−	0.382260i
$71$	4765.74	+	3462.51i	0.945396	+	0.686871i	0.949714	−	0.313120i	$-0.101374\pi$
$71$	4765.74	+	3462.51i	0.945396	+	0.686871i	−0.00431730	+	0.999991i	$0.501374\pi$
$72$		0			0
$73$	−2840.74	−	923.012i	−0.533072	−	0.173206i	0.0300977	−	0.999547i	$-0.490418\pi$
$73$	−2840.74	−	923.012i	−0.533072	−	0.173206i	−0.563169	+	0.826341i	$0.690418\pi$
$74$	−4042.86	+	1313.61i	−0.738287	+	0.239884i
$75$		0			0
$76$		−	6003.36i		−	1.03936i
$77$	−1874.66	+	2925.69i	−0.316185	+	0.493455i
$78$		0			0
$79$	−2715.61	−	3737.72i	−0.435124	−	0.598897i	0.533995	−	0.845487i	$-0.320690\pi$
$79$	−2715.61	−	3737.72i	−0.435124	−	0.598897i	−0.969120	+	0.246590i	$0.920690\pi$
$80$	−1476.89	−	4545.40i	−0.230764	−	0.710219i
$81$		0			0
$82$	781.504	+	567.796i	0.116226	+	0.0844432i
$83$	4057.27	−	5584.35i	0.588949	−	0.810618i	−0.405692	−	0.914010i	$-0.632969\pi$
$83$	4057.27	−	5584.35i	0.588949	−	0.810618i	0.994641	+	0.103391i	$0.0329694\pi$
$84$		0			0
$85$	9082.28	−	2951.01i	1.25706	−	0.408445i
$86$	4443.95	−	3228.72i	0.600859	−	0.436549i
$87$		0			0
$88$	−355.374	−	6071.21i	−0.0458902	−	0.783989i
$89$	−6528.45			−0.824196			−0.412098	−	0.911140i	$-0.635204\pi$
$89$	−6528.45			−0.824196			−0.412098	+	0.911140i	$0.635204\pi$
$90$		0			0
$91$	1428.46	+	4396.34i	0.172498	+	0.530895i
$92$	969.964	−	2985.24i	0.114599	−	0.352699i
$93$		0			0
$94$	−2563.62	+	3528.52i	−0.290133	+	0.399334i
$95$	17382.8	+	5648.00i	1.92607	+	0.625817i
$96$		0			0
$97$	5078.93	−	3690.06i	0.539795	−	0.392184i	−0.284214	−	0.958761i	$-0.591733\pi$
$97$	5078.93	−	3690.06i	0.539795	−	0.392184i	0.824009	+	0.566577i	$0.191733\pi$
$98$			2732.45i			0.284512i
$99$		0			0
$100$	12219.7			1.22197
$101$	1494.35	+	2056.80i	0.146491	+	0.201627i	0.875956	−	0.482390i	$-0.160231\pi$
$101$	1494.35	+	2056.80i	0.146491	+	0.201627i	−0.729466	+	0.684017i	$0.760231\pi$
$102$		0			0
$103$	−2845.46	+	8757.43i	−0.268212	+	0.825472i	0.722724	+	0.691137i	$0.242890\pi$
$103$	−2845.46	+	8757.43i	−0.268212	+	0.825472i	−0.990936	+	0.134335i	$0.957110\pi$
$104$	−6545.38	−	4755.50i	−0.605157	−	0.439672i
$105$		0			0
$106$	5535.97	+	1798.75i	0.492699	+	0.160088i
$107$	−10456.8	+	3397.62i	−0.913336	+	0.296761i	−0.727730	−	0.685863i	$-0.759425\pi$
$107$	−10456.8	+	3397.62i	−0.913336	+	0.296761i	−0.185606	+	0.982624i	$0.559425\pi$
$108$		0			0
$109$			15439.8i			1.29953i	0.760133	+	0.649767i	$0.225134\pi$
$109$			15439.8i			1.29953i	−0.760133	+	0.649767i	$0.774866\pi$
$110$	8028.59	+	2098.78i	0.663520	+	0.173453i
$111$		0			0
$112$	−2039.03	−	2806.49i	−0.162550	−	0.223731i
$113$	−4499.91	−	13849.3i	−0.352409	−	1.08460i	−0.957496	−	0.288445i	$-0.906862\pi$
$113$	−4499.91	−	13849.3i	−0.352409	−	1.08460i	0.605087	−	0.796159i	$-0.293138\pi$
$114$		0			0
$115$	7731.24	+	5617.07i	0.584593	+	0.424731i
$116$	−4443.60	+	6116.09i	−0.330232	+	0.454525i
$117$		0			0
$118$	−4538.87	+	1474.77i	−0.325975	+	0.105916i
$119$	5607.71	−	4074.24i	0.395997	−	0.287709i
$120$		0			0
$121$	−12768.0	−	7165.07i	−0.872068	−	0.489384i
$122$	10896.6			0.732102
$123$		0			0
$124$	−2879.77	−	8863.02i	−0.187290	−	0.576419i
$125$	−3855.11	+	11864.8i	−0.246727	+	0.759348i
$126$		0			0
$127$	8726.57	−	12011.1i	0.541049	−	0.744690i	−0.447715	−	0.894176i	$-0.647762\pi$
$127$	8726.57	−	12011.1i	0.541049	−	0.744690i	0.988764	+	0.149487i	$0.0477621\pi$
$128$	15713.4	+	5105.58i	0.959067	+	0.311620i
$129$		0			0
$130$	8931.21	−	6488.90i	0.528474	−	0.383959i
$131$		−	7298.07i		−	0.425271i	−0.977132	−	0.212635i	$-0.931795\pi$
$131$		−	7298.07i		−	0.425271i	0.977132	−	0.212635i	$-0.0682047\pi$
$132$		0			0
$133$	13266.4			0.749978
$134$	−315.783	−	434.638i	−0.0175865	−	0.0242057i
$135$		0			0
$136$	−3748.89	+	11537.9i	−0.202686	+	0.623804i
$137$	−18402.8	−	13370.4i	−0.980491	−	0.712369i	−0.0226729	−	0.999743i	$-0.507218\pi$
$137$	−18402.8	−	13370.4i	−0.980491	−	0.712369i	−0.957818	+	0.287374i	$0.907218\pi$
$138$		0			0
$139$	17635.6	+	5730.14i	0.912767	+	0.296576i	0.727496	−	0.686112i	$-0.240684\pi$
$139$	17635.6	+	5730.14i	0.912767	+	0.296576i	0.185271	+	0.982688i	$0.440684\pi$
$140$	14042.1	−	4562.56i	0.716435	−	0.232784i
$141$		0			0
$142$		−	10211.3i		−	0.506410i
$143$	−18140.7	+	7090.99i	−0.887119	+	0.346764i
$144$		0			0
$145$	−13528.6	−	18620.5i	−0.643453	−	0.885638i
$146$	1599.98	+	4924.22i	0.0750599	+	0.231011i
$147$		0			0
$148$	−25782.1	−	18731.8i	−1.17705	−	0.855175i
$149$	−12520.6	+	17233.2i	−0.563967	+	0.776234i	−0.991824	−	0.127612i	$-0.959269\pi$
$149$	−12520.6	+	17233.2i	−0.563967	+	0.776234i	0.427857	+	0.903846i	$0.359269\pi$
$150$		0			0
$151$	−23518.9	+	7641.75i	−1.03149	+	0.335150i	−0.775377	−	0.631498i	$-0.782440\pi$
$151$	−23518.9	+	7641.75i	−1.03149	+	0.335150i	−0.256108	+	0.966648i	$0.582440\pi$
$152$	−18784.6	+	13647.8i	−0.813044	+	0.590711i
$153$		0			0
$154$	6012.98	−	351.965i	0.253541	−	0.0148408i
$155$	28372.2			1.18095
$156$		0			0
$157$	1089.79	+	3354.04i	0.0442125	+	0.136072i	0.970726	−	0.240189i	$-0.0772095\pi$
$157$	1089.79	+	3354.04i	0.0442125	+	0.136072i	−0.926514	+	0.376261i	$0.877209\pi$
$158$	−2474.79	+	7616.61i	−0.0991342	+	0.305104i
$159$		0			0
$160$	−23570.9	+	32442.6i	−0.920739	+	1.26729i
$161$	6596.85	+	2143.45i	0.254498	+	0.0826916i
$162$		0			0
$163$	−17060.0	+	12394.8i	−0.642102	+	0.466514i	−0.860572	−	0.509329i	$-0.829894\pi$
$163$	−17060.0	+	12394.8i	−0.642102	+	0.466514i	0.218470	+	0.975844i	$0.429894\pi$
$164$			7241.87i			0.269255i
$165$		0			0
$166$	−11965.2			−0.434215
$167$	−23248.4	−	31998.7i	−0.833606	−	1.14736i	−0.987241	−	0.159232i	$-0.949098\pi$
$167$	−23248.4	−	31998.7i	−0.833606	−	1.14736i	0.153635	−	0.988128i	$-0.450902\pi$
$168$		0			0
$169$	818.809	−	2520.04i	0.0286688	−	0.0882335i
$170$	−13392.2	−	9730.02i	−0.463399	−	0.336679i
$171$		0			0
$172$	39164.7	+	12725.4i	1.32385	+	0.430144i
$173$	−21543.6	+	6999.95i	−0.719825	+	0.233885i	−0.645947	−	0.763382i	$-0.723537\pi$
$173$	−21543.6	+	6999.95i	−0.719825	+	0.233885i	−0.0738777	+	0.997267i	$0.523537\pi$
$174$		0			0
$175$			27003.3i			0.881741i
$176$	11302.9	−	9267.80i	0.364893	−	0.299193i
$177$		0			0
$178$	6651.74	+	9155.34i	0.209940	+	0.288958i
$179$	991.677	+	3052.07i	0.0309503	+	0.0952551i	0.965338	−	0.261002i	$-0.0840528\pi$
$179$	991.677	+	3052.07i	0.0309503	+	0.0952551i	−0.934388	+	0.356257i	$0.884053\pi$
$180$		0			0
$181$	−32427.1	−	23559.7i	−0.989809	−	0.719138i	−0.0299297	−	0.999552i	$-0.509528\pi$
$181$	−32427.1	−	23559.7i	−0.989809	−	0.719138i	−0.959879	+	0.280414i	$0.909528\pi$
$182$	4709.89	−	6482.60i	0.142190	−	0.195707i
$183$		0			0
$184$	−11545.9	+	3751.50i	−0.341030	+	0.110807i
$185$	78493.8	−	57029.1i	2.29347	−	1.66630i
$186$		0			0
$187$	18518.2	+	22584.7i	0.529561	+	0.645848i
$188$	−32697.3			−0.925115
$189$		0			0
$190$	−9790.42	−	30131.8i	−0.271203	−	0.834676i
$191$	2173.33	−	6688.81i	0.0595742	−	0.183350i	−0.916841	−	0.399253i	$-0.869269\pi$
$191$	2173.33	−	6688.81i	0.0595742	−	0.183350i	0.976415	+	0.215903i	$0.0692694\pi$
$192$		0			0
$193$	25522.4	−	35128.6i	0.685183	−	0.943074i	−0.314798	−	0.949159i	$-0.601937\pi$
$193$	25522.4	−	35128.6i	0.685183	−	0.943074i	0.999981	+	0.00608469i	$0.00193683\pi$
$194$	−10349.7	−	3362.82i	−0.274994	−	0.0893511i
$195$		0			0
$196$	−16572.5	+	12040.6i	−0.431395	+	0.313427i
$197$			41922.3i			1.08022i	0.841594	+	0.540111i	$0.181618\pi$
$197$			41922.3i			1.08022i	−0.841594	+	0.540111i	$0.818382\pi$
$198$		0			0
$199$	−23640.6			−0.596970			−0.298485	−	0.954414i	$-0.596481\pi$
$199$	−23640.6			−0.596970			−0.298485	+	0.954414i	$0.596481\pi$
$200$	−27779.7	−	38235.5i	−0.694492	−	0.955887i
$201$		0			0
$202$	1361.83	−	4191.28i	0.0333749	−	0.102717i
$203$	−13515.5	−	9819.57i	−0.327974	−	0.238287i
$204$		0			0
$205$	−20968.9	−	6813.20i	−0.498962	−	0.162123i
$206$	15180.4	−	4932.41i	0.357725	−	0.116232i
$207$		0			0
$208$		−	19445.0i		−	0.449451i
$209$	3266.36	+	55802.5i	0.0747775	+	1.27750i
$210$		0			0
$211$	4977.33	+	6850.71i	0.111797	+	0.153876i	0.861249	−	0.508183i	$-0.169683\pi$
$211$	4977.33	+	6850.71i	0.111797	+	0.153876i	−0.749452	+	0.662059i	$0.769683\pi$
$212$	13484.9	+	41502.2i	0.300037	+	0.923420i
$213$		0			0
$214$	15419.0	+	11202.5i	0.336688	+	0.244619i
$215$	−73692.9	+	101430.i	−1.59422	+	2.19426i
$216$		0			0
$217$	19585.7	−	6363.78i	0.415929	−	0.135144i
$218$	21652.3	−	15731.3i	0.455609	−	0.331019i
$219$		0			0
$220$	22648.9	+	57942.2i	0.467953	+	1.19715i
$221$	38853.6			0.795512
$222$		0			0
$223$	−15927.2	−	49019.0i	−0.320281	−	0.985723i	−0.973526	−	0.228577i	$-0.926593\pi$
$223$	−15927.2	−	49019.0i	−0.320281	−	0.985723i	0.653245	−	0.757147i	$-0.273407\pi$
$224$	−8994.55	+	27682.4i	−0.179260	+	0.551706i
$225$		0			0
$226$	−14837.0	+	20421.4i	−0.290489	+	0.399824i
$227$	16559.9	+	5380.65i	0.321371	+	0.104420i	0.465260	−	0.885174i	$-0.345961\pi$
$227$	16559.9	+	5380.65i	0.321371	+	0.104420i	−0.143889	+	0.989594i	$0.545961\pi$
$228$		0			0
$229$	56030.1	−	40708.3i	1.06844	−	0.776268i	0.0928100	−	0.995684i	$-0.470415\pi$
$229$	56030.1	−	40708.3i	1.06844	−	0.776268i	0.975631	+	0.219416i	$0.0704151\pi$
$230$		−	16565.2i		−	0.313142i
$231$		0			0
$232$	29239.2			0.543237
$233$	−18729.9	−	25779.5i	−0.345004	−	0.474857i	0.600891	−	0.799331i	$-0.294813\pi$
$233$	−18729.9	−	25779.5i	−0.345004	−	0.474857i	−0.945894	+	0.324474i	$0.894813\pi$
$234$		0			0
$235$	30761.8	−	94675.1i	0.557027	−	1.71435i
$236$	−28945.2	−	21029.9i	−0.519700	−	0.377584i
$237$		0			0
$238$	−11427.2	−	3712.93i	−0.201738	−	0.0655485i
$239$	105483.	−	34273.5i	1.84666	−	0.600016i	0.849258	−	0.527978i	$-0.177050\pi$
$239$	105483.	−	34273.5i	1.84666	−	0.600016i	0.997402	−	0.0720382i	$-0.0229504\pi$
$240$		0			0
$241$			54085.5i			0.931207i	0.884993	+	0.465604i	$0.154163\pi$
$241$			54085.5i			0.931207i	−0.884993	+	0.465604i	$0.845837\pi$
$242$	2960.95	+	25205.8i	0.0505593	+	0.430398i
$243$		0			0
$244$	48016.1	+	66088.5i	0.806506	+	1.11006i
$245$	−19272.2	−	59313.6i	−0.321069	−	0.988148i
$246$		0			0
$247$	60160.7	+	43709.3i	0.986096	+	0.716440i
$248$	−21185.7	+	29159.6i	−0.344461	+	0.474110i
$249$		0			0
$250$	20566.8	−	6682.56i	0.329069	−	0.106921i
$251$	70707.4	−	51371.9i	1.12232	−	0.815414i	0.137762	−	0.990465i	$-0.456009\pi$
$251$	70707.4	−	51371.9i	1.12232	−	0.815414i	0.984559	+	0.175051i	$0.0560090\pi$
$252$		0			0
$253$	−7391.78	+	28276.2i	−0.115480	+	0.441753i
$254$	−25735.4			−0.398900
$255$		0			0
$256$	−7980.84	−	24562.5i	−0.121778	−	0.374794i
$257$	27175.6	−	83637.7i	0.411445	−	1.26630i	−0.503947	−	0.863735i	$-0.668119\pi$
$257$	27175.6	−	83637.7i	0.411445	−	1.26630i	0.915392	−	0.402564i	$-0.131881\pi$
$258$		0			0
$259$	41393.9	−	56973.8i	0.617073	−	0.849328i
$260$	78711.1	+	25574.8i	1.16437	+	0.378325i
$261$		0			0
$262$	−10234.6	+	7435.89i	−0.149097	+	0.108325i
$263$			19661.7i			0.284255i	0.989848	+	0.142128i	$0.0453943\pi$
$263$			19661.7i			0.284255i	−0.989848	+	0.142128i	$0.954606\pi$
$264$		0			0
$265$	−132857.			−1.89187
$266$	−13516.9	−	18604.4i	−0.191035	−	0.262937i
$267$		0			0
$268$	1244.60	−	3830.48i	0.0173285	−	0.0533315i
$269$	3199.10	+	2324.28i	0.0442103	+	0.0321207i	0.609671	−	0.792655i	$-0.291302\pi$
$269$	3199.10	+	2324.28i	0.0442103	+	0.0321207i	−0.565461	+	0.824775i	$0.691302\pi$
$270$		0			0
$271$	85005.7	+	27620.0i	1.15747	+	0.376085i	0.823952	−	0.566659i	$-0.191764\pi$
$271$	85005.7	+	27620.0i	1.15747	+	0.376085i	0.333517	+	0.942744i	$0.391764\pi$
$272$	−27730.5	+	9010.18i	−0.374817	+	0.121786i
$273$		0			0
$274$			39430.6i			0.525209i
$275$	−113584.	+	6648.58i	−1.50194	+	0.0879151i
$276$		0			0
$277$	−65233.9	−	89786.7i	−0.850185	−	1.17018i	−0.983822	−	0.179149i	$-0.942666\pi$
$277$	−65233.9	−	89786.7i	−0.850185	−	1.17018i	0.133637	−	0.991030i	$-0.457334\pi$
$278$	−9932.80	−	30570.0i	−0.128523	−	0.395554i
$279$		0			0
$280$	−46199.0	−	33565.6i	−0.589274	−	0.428132i
$281$	58562.1	−	80603.8i	0.741658	−	1.02080i	−0.256864	−	0.966448i	$-0.582689\pi$
$281$	58562.1	−	80603.8i	0.741658	−	1.02080i	0.998522	−	0.0543570i	$-0.0173109\pi$
$282$		0			0
$283$	−32503.2	+	10560.9i	−0.405839	+	0.131865i	−0.504821	−	0.863224i	$-0.668441\pi$
$283$	−32503.2	+	10560.9i	−0.405839	+	0.131865i	0.0989820	+	0.995089i	$0.468441\pi$
$284$	61931.9	−	44996.1i	0.767852	−	0.557877i
$285$		0			0
$286$	28427.5	+	18215.2i	0.347541	+	0.222690i
$287$	−16003.3			−0.194287
$288$		0			0
$289$	7805.93	+	24024.2i	0.0934607	+	0.287642i
$290$	−12328.9	+	37944.3i	−0.146598	+	0.451181i
$291$		0			0
$292$	−22815.4	+	31402.7i	−0.267585	+	0.368299i
$293$	−45950.6	−	14930.2i	−0.535249	−	0.173913i	0.0289057	−	0.999582i	$-0.490798\pi$
$293$	−45950.6	−	14930.2i	−0.535249	−	0.173913i	−0.564154	+	0.825669i	$0.690798\pi$
$294$		0			0
$295$	88124.1	−	64025.9i	1.01263	−	0.735719i
$296$			123256.i			1.40678i
$297$		0			0
$298$	36924.5			0.415797
$299$	22853.5	+	31455.1i	0.255629	+	0.351843i
$300$		0			0
$301$	−28120.9	+	86547.1i	−0.310381	+	0.955255i
$302$	34679.6	+	25196.2i	0.380243	+	0.276262i
$303$		0			0
$304$	−53074.0	−	17244.8i	−0.574294	−	0.186599i
$305$	−236534.	+	76854.4i	−2.54269	+	0.826169i
$306$		0			0
$307$			47042.3i			0.499128i	0.968358	+	0.249564i	$0.0802872\pi$
$307$			47042.3i			0.499128i	−0.968358	+	0.249564i	$0.919713\pi$
$308$	28631.0	+	34918.1i	0.301811	+	0.368086i
$309$		0			0
$310$	−28908.0	−	39788.5i	−0.300812	−	0.414032i
$311$	41966.1	+	129158.i	0.433888	+	1.33537i	0.894221	+	0.447625i	$0.147730\pi$
$311$	41966.1	+	129158.i	0.433888	+	1.33537i	−0.460333	+	0.887746i	$0.652270\pi$
$312$		0			0
$313$	−94424.7	−	68603.5i	−0.963822	−	0.700258i	−0.00978680	−	0.999952i	$-0.503115\pi$
$313$	−94424.7	−	68603.5i	−0.963822	−	0.700258i	−0.954035	+	0.299694i	$0.903115\pi$
$314$	3593.25	−	4945.68i	0.0364442	−	0.0501611i
$315$		0			0
$316$	−57100.4	+	18553.0i	−0.571827	+	0.185798i
$317$	−31402.4	+	22815.2i	−0.312496	+	0.227042i	−0.732967	−	0.680264i	$-0.761865\pi$
$317$	−31402.4	+	22815.2i	−0.312496	+	0.227042i	0.420471	+	0.907306i	$0.361865\pi$
$318$		0			0
$319$	37976.5	−	59268.0i	0.373193	−	0.582424i
$320$	−6956.36			−0.0679332
$321$		0			0
$322$	−3715.52	−	11435.2i	−0.0358350	−	0.110289i
$323$	34457.2	−	106048.i	0.330275	−	1.01648i
$324$		0			0
$325$	−88969.1	+	122455.i	−0.842311	+	1.15934i
$326$	34764.4	+	11295.6i	0.327114	+	0.106286i
$327$		0			0
$328$	22659.9	−	16463.4i	0.210625	−	0.153028i
$329$		−	72255.2i		−	0.667540i
$330$		0			0
$331$	48824.2			0.445635			0.222818	−	0.974860i	$-0.428475\pi$
$331$	48824.2			0.445635			0.222818	+	0.974860i	$0.428475\pi$
$332$	−52725.1	−	72569.9i	−0.478345	−	0.658385i
$333$		0			0
$334$	−21186.7	+	65206.0i	−0.189920	+	0.584514i
$335$	9920.26	+	7207.49i	0.0883961	+	0.0642236i
$336$		0			0
$337$	25500.8	+	8285.71i	0.224540	+	0.0729575i	0.419126	−	0.907928i	$-0.362336\pi$
$337$	25500.8	+	8285.71i	0.224540	+	0.0729575i	−0.194586	+	0.980885i	$0.562336\pi$
$338$	−4368.31	+	1419.35i	−0.0382366	+	0.0124238i
$339$		0			0
$340$		−	124100.i		−	1.07353i
$341$	31590.3	+	80816.8i	0.271672	+	0.695013i
$342$		0			0
$343$	−67135.3	−	92403.8i	−0.570641	−	0.785419i
$344$	−49217.6	−	151476.i	−0.415914	−	1.28005i
$345$		0			0
$346$	31767.0	+	23080.1i	0.265353	+	0.192791i
$347$	−71582.6	+	98524.9i	−0.594495	+	0.818252i	−0.995190	−	0.0979590i	$-0.968769\pi$
$347$	−71582.6	+	98524.9i	−0.594495	+	0.818252i	0.400695	+	0.916211i	$0.368769\pi$
$348$		0			0
$349$	−138907.	+	45133.6i	−1.14044	+	0.370552i	−0.817535	−	0.575879i	$-0.804660\pi$
$349$	−138907.	+	45133.6i	−1.14044	+	0.370552i	−0.322906	+	0.946431i	$0.604660\pi$
$350$	37868.8	−	27513.3i	0.309133	−	0.224598i
$351$		0			0
$352$	−118655.	−	31018.1i	−0.957640	−	0.250340i
$353$	36019.5			0.289061			0.144530	−	0.989500i	$-0.453833\pi$
$353$	36019.5			0.289061			0.144530	+	0.989500i	$0.453833\pi$
$354$		0			0
$355$	72020.6	+	221657.i	0.571479	+	1.75883i
$356$	−26216.6	+	80686.4i	−0.206860	+	0.636649i
$357$		0			0
$358$	3269.74	−	4500.41i	0.0255121	−	0.0351145i
$359$	95618.4	+	31068.3i	0.741913	+	0.241062i	0.655498	−	0.755197i	$-0.272459\pi$
$359$	95618.4	+	31068.3i	0.741913	+	0.241062i	0.0864149	+	0.996259i	$0.472459\pi$
$360$		0			0
$361$	67223.2	−	48840.5i	0.515828	−	0.374771i
$362$			69479.6i			0.530200i
$363$		0			0
$364$	60071.6			0.453384
$365$	−69461.7	−	95605.8i	−0.521386	−	0.717627i
$366$		0			0
$367$	−40182.8	+	123670.i	−0.298338	+	0.918189i	0.683742	+	0.729724i	$0.260351\pi$
$367$	−40182.8	+	123670.i	−0.298338	+	0.918189i	−0.982080	+	0.188465i	$0.939649\pi$
$368$	−23605.4	−	17150.3i	−0.174307	−	0.126642i
$369$		0			0
$370$	−159952.	−	51971.7i	−1.16839	−	0.379632i
$371$	−91712.5	+	29799.2i	−0.666317	+	0.216499i
$372$		0			0
$373$		−	149908.i		−	1.07747i	−0.842474	−	0.538737i	$-0.818902\pi$
$373$		−	149908.i		−	1.07747i	0.842474	−	0.538737i	$-0.181098\pi$
$374$	12804.2	−	48980.7i	0.0915397	−	0.350172i
$375$		0			0
$376$	74332.6	+	102310.i	0.525780	+	0.723674i
$377$	−28937.4	−	89060.2i	−0.203600	−	0.626615i
$378$		0			0
$379$	179055.	+	130091.i	1.24655	+	0.905670i	0.998016	−	0.0629540i	$-0.0200521\pi$
$379$	179055.	+	130091.i	1.24655	+	0.905670i	0.248531	+	0.968624i	$0.420052\pi$
$380$	139609.	−	192156.i	0.966825	−	1.33072i
$381$		0			0
$382$	−11594.6	+	3767.31i	−0.0794563	+	0.0258169i
$383$	17981.5	−	13064.3i	0.122583	−	0.0890614i	−0.524805	−	0.851223i	$-0.675862\pi$
$383$	17981.5	−	13064.3i	0.122583	−	0.0890614i	0.647387	+	0.762161i	$0.275862\pi$
$384$		0			0
$385$	−128042.	+	50050.1i	−0.863835	+	0.337663i
$386$	−75267.8			−0.505166
$387$		0			0
$388$	−25210.5	−	77589.8i	−0.167462	−	0.515396i
$389$	−53692.0	+	165247.i	−0.354822	+	1.09203i	0.601291	+	0.799030i	$0.294653\pi$
$389$	−53692.0	+	165247.i	−0.354822	+	1.09203i	−0.956113	+	0.292999i	$0.905347\pi$
$390$		0			0
$391$	34268.5	−	47166.6i	0.224152	−	0.308518i
$392$	75350.4	+	24482.8i	0.490358	+	0.159327i
$393$		0			0
$394$	58790.8	−	42714.0i	0.378719	−	0.275155i
$395$		−	182789.i		−	1.17154i
$396$		0			0
$397$	61730.8			0.391671			0.195835	−	0.980637i	$-0.437258\pi$
$397$	61730.8			0.391671			0.195835	+	0.980637i	$0.437258\pi$
$398$	24087.1	+	33153.0i	0.152061	+	0.209294i
$399$		0			0
$400$	35101.3	−	108031.i	0.219383	−	0.675191i
$401$	−111862.	−	81272.2i	−0.695652	−	0.505421i	0.182861	−	0.983139i	$-0.441464\pi$
$401$	−111862.	−	81272.2i	−0.695652	−	0.505421i	−0.878513	+	0.477718i	$0.841464\pi$
$402$		0			0
$403$	109785.	+	35671.3i	0.675978	+	0.219639i
$404$	31421.3	−	10209.4i	0.192514	−	0.0625515i
$405$		0			0
$406$			28958.8i			0.175682i
$407$	249841.	+	160088.i	1.50826	+	0.966428i
$408$		0			0
$409$	−132243.	−	182018.i	−0.790547	−	1.08809i	−0.994040	−	0.109018i	$-0.965229\pi$
$409$	−132243.	−	182018.i	−0.790547	−	1.08809i	0.203493	−	0.979076i	$-0.434771\pi$
$410$	11810.2	+	36348.1i	0.0702571	+	0.216229i
$411$		0			0
$412$	96808.1	+	70335.2i	0.570318	+	0.414361i
$413$	46472.4	−	63963.8i	0.272455	−	0.375002i
$414$		0			0
$415$	259731.	−	84391.6i	1.50809	−	0.490008i
$416$	−131995.	+	95900.2i	−0.762732	+	0.554157i
$417$		0			0
$418$	74927.9	−	61436.9i	0.428836	−	0.351623i
$419$	86800.6			0.494418			0.247209	−	0.968962i	$-0.420487\pi$
$419$	86800.6			0.494418			0.247209	+	0.968962i	$0.420487\pi$
$420$		0			0
$421$	51322.7	+	157955.i	0.289565	+	0.891189i	0.984993	+	0.172593i	$0.0552146\pi$
$421$	51322.7	+	157955.i	0.289565	+	0.891189i	−0.695428	+	0.718595i	$0.744785\pi$
$422$	4535.93	−	13960.2i	0.0254707	−	0.0783909i
$423$		0			0
$424$	99204.8	−	136544.i	0.551824	−	0.759521i
$425$	215859.	+	70136.7i	1.19507	+	0.388300i
$426$		0			0
$427$	−146044.	+	106107.i	−0.800991	+	0.581954i
$428$			142881.i			0.779988i
$429$		0			0
$430$	217327.			1.17537
$431$	104301.	+	143558.i	0.561480	+	0.772811i	0.991514	−	0.130002i	$-0.0414983\pi$
$431$	104301.	+	143558.i	0.561480	+	0.772811i	−0.430034	+	0.902813i	$0.641498\pi$
$432$		0			0
$433$	8804.75	−	27098.2i	0.0469614	−	0.144532i	−0.924826	−	0.380390i	$-0.875790\pi$
$433$	8804.75	−	27098.2i	0.0469614	−	0.144532i	0.971788	+	0.235857i	$0.0757898\pi$
$434$	−28880.0	−	20982.5i	−0.153327	−	0.111398i
$435$		0			0
$436$	190823.	+	62002.2i	1.00382	+	0.326162i
$437$	106122.	−	34481.2i	0.555705	−	0.180559i
$438$		0			0
$439$		−	208514.i		−	1.08195i	−0.841039	−	0.540974i	$-0.818056\pi$
$439$		−	208514.i		−	1.08195i	0.841039	−	0.540974i	$-0.181944\pi$
$440$	129813.	−	202592.i	0.670519	−	1.04645i
$441$		0			0
$442$	−39587.4	−	54487.3i	−0.202634	−	0.278902i
$443$	−65857.3	−	202688.i	−0.335580	−	1.03281i	−0.966436	−	0.256909i	$-0.917296\pi$
$443$	−65857.3	−	202688.i	−0.335580	−	1.03281i	0.630855	−	0.775900i	$-0.282704\pi$
$444$		0			0
$445$	−208963.	−	151821.i	−1.05524	−	0.766674i
$446$	−52515.0	+	72280.7i	−0.264006	+	0.363373i
$447$		0			0
$448$	−4802.06	+	1560.28i	−0.0239261	+	0.00777405i
$449$	−50468.3	+	36667.4i	−0.250338	+	0.181881i	−0.705876	−	0.708335i	$-0.749447\pi$
$449$	−50468.3	+	36667.4i	−0.250338	+	0.181881i	0.455539	+	0.890216i	$0.349447\pi$
$450$		0			0
$451$	−3940.22	−	67314.7i	−0.0193717	−	0.330946i
$452$	−189237.			−0.926251
$453$		0			0
$454$	−9326.98	−	28705.5i	−0.0452511	−	0.139269i
$455$	−56515.7	+	173938.i	−0.272990	+	0.840177i
$456$		0			0
$457$	−200452.	+	275899.i	−0.959796	+	1.32105i	−0.0127595	+	0.999919i	$0.504062\pi$
$457$	−200452.	+	275899.i	−0.959796	+	1.32105i	−0.947036	+	0.321127i	$0.895938\pi$
$458$	−114177.	−	37098.2i	−0.544309	−	0.176857i
$459$		0			0
$460$	100469.	−	72995.1i	0.474807	−	0.344967i
$461$			66165.6i			0.311337i	0.987809	+	0.155668i	$0.0497532\pi$
$461$			66165.6i			0.311337i	−0.987809	+	0.155668i	$0.950247\pi$
$462$		0			0
$463$	−255213.			−1.19053			−0.595265	−	0.803529i	$-0.702953\pi$
$463$	−255213.			−1.19053			−0.595265	+	0.803529i	$0.702953\pi$
$464$	41306.2	+	56853.2i	0.191858	+	0.264070i
$465$		0			0
$466$	−17068.9	+	52532.7i	−0.0786020	+	0.241912i
$467$	98066.8	+	71249.7i	0.449664	+	0.326700i	0.789463	−	0.613798i	$-0.210359\pi$
$467$	98066.8	+	71249.7i	0.449664	+	0.326700i	−0.339799	+	0.940498i	$0.610359\pi$
$468$		0			0
$469$	8464.69	+	2750.34i	0.0384827	+	0.0125038i
$470$	−164113.	+	53323.5i	−0.742928	+	0.241392i
$471$		0			0
$472$			138378.i			0.621132i
$473$	−370968.	−	96976.1i	−1.65811	−	0.433453i
$474$		0			0
$475$	255332.	+	351435.i	1.13167	+	1.55761i
$476$	−27835.2	−	85667.9i	−0.122851	−	0.378098i
$477$		0			0
$478$	−155539.	−	113006.i	−0.680745	−	0.494590i
$479$	−34782.6	+	47874.1i	−0.151597	+	0.208655i	−0.878060	−	0.478550i	$-0.841163\pi$
$479$	−34782.6	+	47874.1i	−0.151597	+	0.208655i	0.726463	+	0.687205i	$0.241163\pi$
$480$		0			0
$481$	375428.	−	121984.i	1.62269	−	0.527245i
$482$	75848.1	−	55106.8i	0.326475	−	0.237198i
$483$		0			0
$484$	−139827.	+	129028.i	−0.596900	+	0.550801i
$485$	248380.			1.05592
$486$		0			0
$487$	33501.8	+	103108.i	0.141257	+	0.434744i	0.996511	−	0.0834653i	$-0.0265988\pi$
$487$	33501.8	+	103108.i	0.141257	+	0.434744i	−0.855254	+	0.518209i	$0.826599\pi$
$488$	97633.7	−	300486.i	0.409978	−	1.26178i
$489$		0			0
$490$	−63543.8	+	87460.5i	−0.264655	+	0.364267i
$491$	−419208.	−	136209.i	−1.73887	−	0.564993i	−0.744185	−	0.667973i	$-0.767162\pi$
$491$	−419208.	−	136209.i	−1.73887	−	0.564993i	−0.994683	+	0.102981i	$0.967162\pi$
$492$		0			0
$493$	−113600.	+	82535.0i	−0.467394	+	0.339582i
$494$		−	128903.i		−	0.528211i
$495$		0			0
$496$	−86627.6			−0.352122
$497$	99433.5	+	136858.i	0.402550	+	0.554062i
$498$		0			0
$499$	−25259.2	+	77739.8i	−0.101442	+	0.312207i	−0.988879	−	0.148723i	$-0.952484\pi$
$499$	−25259.2	+	77739.8i	−0.101442	+	0.312207i	0.887437	+	0.460929i	$0.152484\pi$
$500$	131158.	+	95292.1i	0.524633	+	0.381168i
$501$		0			0
$502$	−144085.	−	46816.2i	−0.571758	−	0.185775i
$503$	429446.	−	139535.i	1.69735	−	0.551504i	0.709205	−	0.705002i	$-0.249054\pi$
$503$	429446.	−	139535.i	1.69735	−	0.551504i	0.988149	+	0.153498i	$0.0490540\pi$
$504$		0			0
$505$			100586.i			0.394415i
$506$	47185.2	−	18444.1i	0.184291	−	0.0720373i
$507$		0			0
$508$	−113404.	−	156087.i	−0.439440	−	0.604838i
$509$	119556.	+	367954.i	0.461460	+	1.42023i	0.863380	+	0.504554i	$0.168343\pi$
$509$	119556.	+	367954.i	0.461460	+	1.42023i	−0.401920	+	0.915675i	$0.631657\pi$
$510$		0			0
$511$	−69394.3	−	50417.9i	−0.265755	−	0.193082i
$512$	129068.	−	177647.i	0.492355	−	0.677669i
$513$		0			0
$514$	−144980.	+	47106.9i	−0.548760	+	0.178303i
$515$	−294734.	+	214137.i	−1.11126	+	0.807377i
$516$		0			0
$517$	303928.	−	17790.2i	1.13708	−	0.0665579i
$518$	−122074.			−0.454950
$519$		0			0
$520$	−98914.8	−	304428.i	−0.365809	−	1.12584i
$521$	49678.5	−	152895.i	0.183018	−	0.563270i	−0.816891	−	0.576792i	$-0.804304\pi$
$521$	49678.5	−	152895.i	0.183018	−	0.563270i	0.999909	+	0.0135219i	$0.00430429\pi$
$522$		0			0
$523$	−15895.2	+	21877.8i	−0.0581115	+	0.0799836i	−0.837084	−	0.547075i	$-0.815741\pi$
$523$	−15895.2	+	21877.8i	−0.0581115	+	0.0799836i	0.778972	+	0.627058i	$0.215741\pi$
$524$	−90198.3	−	29307.2i	−0.328500	−	0.106736i
$525$		0			0
$526$	27573.0	−	20033.0i	0.0996581	−	0.0724058i
$527$		−	173093.i		−	0.623243i
$528$		0			0
$529$	−221499.			−0.791518
$530$	135365.	+	186315.i	0.481899	+	0.663277i
$531$		0			0
$532$	53274.3	−	163961.i	0.188232	−	0.579320i
$533$	−72572.0	−	52726.7i	−0.255455	−	0.185599i
$534$		0			0
$535$	−413714.	−	134424.i	−1.44541	−	0.469644i
$536$	−14815.0	+	4813.70i	−0.0515671	+	0.0167552i
$537$		0			0
$538$		−	6854.51i		−	0.0236817i
$539$	147493.	−	120937.i	0.507686	−	0.416276i
$540$		0			0
$541$	172728.	+	237739.i	0.590157	+	0.812282i	0.994763	−	0.102210i	$-0.0325912\pi$
$541$	172728.	+	237739.i	0.590157	+	0.812282i	−0.404606	+	0.914491i	$0.632591\pi$
$542$	−47877.4	−	147352.i	−0.162979	−	0.501598i
$543$		0			0
$544$	197925.	+	143801.i	0.668811	+	0.485919i
$545$	−359055.	+	494197.i	−1.20884	+	1.66382i
$546$		0			0
$547$	81755.0	−	26563.8i	0.273237	−	0.0887801i	−0.169194	−	0.985583i	$-0.554116\pi$
$547$	81755.0	−	26563.8i	0.273237	−	0.0887801i	0.442431	+	0.896803i	$0.354116\pi$
$548$	−239149.	+	173752.i	−0.796356	+	0.578587i
$549$		0			0
$550$	125053.	+	152514.i	0.413399	+	0.504178i
$551$	−268747.			−0.885198
$552$		0			0
$553$	−40998.9	−	126182.i	−0.134067	−	0.412616i
$554$	−59448.8	+	182965.i	−0.193697	+	0.596139i
$555$		0			0
$556$	141640.	−	194951.i	0.458180	−	0.630630i
$557$	−86069.8	−	27965.8i	−0.277422	−	0.0901397i	0.167002	−	0.985957i	$-0.446591\pi$
$557$	−86069.8	−	27965.8i	−0.277422	−	0.0901397i	−0.444423	+	0.895817i	$0.646591\pi$
$558$		0			0
$559$	−412674.	+	299825.i	−1.32064	+	0.959499i
$560$		−	137248.i		−	0.437654i
$561$		0			0
$562$	−172705.			−0.546804
$563$	−45940.1	−	63231.1i	−0.144935	−	0.199487i	0.730377	−	0.683044i	$-0.239344\pi$
$563$	−45940.1	−	63231.1i	−0.144935	−	0.199487i	−0.875313	+	0.483558i	$0.839344\pi$
$564$		0			0
$565$	178035.	−	547936.i	0.557711	−	1.71646i
$566$	47927.4	+	34821.3i	0.149607	+	0.108696i
$567$		0			0
$568$	−281587.	−	91493.0i	−0.872801	−	0.283590i
$569$	41195.0	−	13385.1i	0.127239	−	0.0413425i	−0.244705	−	0.969597i	$-0.578691\pi$
$569$	41195.0	−	13385.1i	0.127239	−	0.0413425i	0.371944	+	0.928255i	$0.378691\pi$
$570$		0			0
$571$			429216.i			1.31645i	0.752823	+	0.658223i	$0.228692\pi$
$571$			429216.i			1.31645i	−0.752823	+	0.658223i	$0.771308\pi$
$572$	14790.4	+	252680.i	0.0452052	+	0.772287i
$573$		0			0
$574$	16305.5	+	22442.6i	0.0494891	+	0.0681159i
$575$	70185.6	+	216009.i	0.212282	+	0.653336i
$576$		0			0
$577$	−163903.	−	119082.i	−0.492305	−	0.357681i	0.313765	−	0.949501i	$-0.398410\pi$
$577$	−163903.	−	119082.i	−0.492305	−	0.357681i	−0.806070	+	0.591820i	$0.798410\pi$
$578$	25737.6	−	35424.7i	0.0770392	−	0.106035i
$579$		0			0
$580$	−284462.	+	92427.3i	−0.845607	+	0.274754i
$581$	160366.	−	116513.i	0.475074	−	0.345161i
$582$		0			0
$583$	−147926.	−	378435.i	−0.435217	−	1.11341i
$584$	150127.			0.440182
$585$		0			0
$586$	25880.5	+	79652.1i	0.0753664	+	0.231954i
$587$	27605.0	−	84959.5i	0.0801146	−	0.246567i	−0.902975	−	0.429693i	$-0.858622\pi$
$587$	27605.0	−	84959.5i	0.0801146	−	0.246567i	0.983089	+	0.183126i	$0.0586216\pi$
$588$		0			0
$589$	194725.	−	268016.i	0.561295	−	0.772556i
$590$	−179577.	−	58348.0i	−0.515877	−	0.167618i
$591$		0			0
$592$	−239661.	+	174124.i	−0.683840	+	0.496839i
$593$		−	274181.i		−	0.779702i	−0.920878	−	0.389851i	$-0.872527\pi$
$593$		−	274181.i		−	0.779702i	0.920878	−	0.389851i	$-0.127473\pi$
$594$		0			0
$595$	274239.			0.774632
$596$	162708.	+	223949.i	0.458055	+	0.630458i
$597$		0			0
$598$	20826.8	−	64098.3i	0.0582399	−	0.179244i
$599$	−138133.	−	100359.i	−0.384984	−	0.279708i	0.378413	−	0.925637i	$-0.376470\pi$
$599$	−138133.	−	100359.i	−0.384984	−	0.279708i	−0.763397	+	0.645929i	$0.776470\pi$
$600$		0			0
$601$	404972.	+	131583.i	1.12118	+	0.364294i	0.810219	−	0.586127i	$-0.199348\pi$
$601$	404972.	+	131583.i	1.12118	+	0.364294i	0.310964	+	0.950422i	$0.399348\pi$
$602$	150023.	−	48745.5i	0.413967	−	0.134506i
$603$		0			0
$604$			321362.i			0.880887i
$605$	−242052.	−	526262.i	−0.661299	−	1.43777i
$606$		0			0
$607$	63832.4	+	87857.8i	0.173246	+	0.238453i	0.886807	−	0.462141i	$-0.152919\pi$
$607$	63832.4	+	87857.8i	0.173246	+	0.238453i	−0.713560	+	0.700594i	$0.752919\pi$
$608$	144694.	+	445321.i	0.391419	+	1.20467i
$609$		0			0
$610$	348779.	+	253403.i	0.937326	+	0.681007i
$611$	238063.	−	327665.i	0.637689	−	0.877703i
$612$		0			0
$613$	−120885.	+	39277.8i	−0.321699	+	0.104526i	−0.465415	−	0.885093i	$-0.654095\pi$
$613$	−120885.	+	39277.8i	−0.321699	+	0.104526i	0.143716	+	0.989619i	$0.454095\pi$
$614$	65970.9	−	47930.7i	0.174991	−	0.127138i
$615$		0			0
$616$	44170.6	−	168968.i	0.116405	−	0.445291i
$617$	132931.			0.349186			0.174593	−	0.984641i	$-0.444139\pi$
$617$	132931.			0.349186			0.174593	+	0.984641i	$0.444139\pi$
$618$		0			0
$619$	−49866.9	−	153475.i	−0.130146	−	0.400548i	0.864657	−	0.502362i	$-0.167536\pi$
$619$	−49866.9	−	153475.i	−0.130146	−	0.400548i	−0.994804	+	0.101813i	$0.967536\pi$
$620$	113936.	−	350658.i	0.296399	−	0.912221i
$621$		0			0
$622$	138370.	−	190450.i	0.357652	−	0.492266i
$623$	−178303.	−	57934.0i	−0.459390	−	0.149265i
$624$		0			0
$625$	76146.4	−	55323.6i	0.194935	−	0.141628i
$626$			202318.i			0.516280i
$627$		0			0
$628$	45829.6			0.116205
$629$	−347922.	−	478874.i	−0.879388	−	1.21037i
$630$		0			0
$631$	−69740.9	+	214640.i	−0.175158	+	0.539080i	−0.999641	−	0.0268070i	$-0.991466\pi$
$631$	−69740.9	+	214640.i	−0.175158	+	0.539080i	0.824483	+	0.565887i	$0.191466\pi$
$632$	187862.	+	136490.i	0.470333	+	0.341717i
$633$		0			0
$634$	63990.9	+	20791.9i	0.159199	+	0.0517268i
$635$	558641.	−	181514.i	1.38543	−	0.450155i
$636$		0			0
$637$		−	253741.i		−	0.625334i
$638$	−121810.	+	7130.04i	−0.299254	+	0.0175166i
$639$		0			0
$640$	384223.	+	528837.i	0.938044	+	1.29111i
$641$	240298.	+	739563.i	0.584837	+	1.79994i	0.599923	+	0.800058i	$0.295198\pi$
$641$	240298.	+	739563.i	0.584837	+	1.79994i	−0.0150860	+	0.999886i	$0.504802\pi$
$642$		0			0
$643$	66190.5	+	48090.2i	0.160094	+	0.116315i	0.664948	−	0.746890i	$-0.268454\pi$
$643$	66190.5	+	48090.2i	0.160094	+	0.116315i	−0.504854	+	0.863205i	$0.668454\pi$
$644$	52982.6	−	72924.2i	0.127750	−	0.175833i
$645$		0			0
$646$	−183828.	+	59729.2i	−0.440500	+	0.143127i
$647$	−290193.	+	210838.i	−0.693232	+	0.503662i	−0.877721	−	0.479172i	$-0.840937\pi$
$647$	−290193.	+	210838.i	−0.693232	+	0.503662i	0.184489	+	0.982835i	$0.440937\pi$
$648$		0			0
$649$	280494.	+	179729.i	0.665938	+	0.426705i
$650$	262378.			0.621012
$651$		0			0
$652$	84681.3	+	260622.i	0.199201	+	0.613079i
$653$	−18125.2	+	55783.5i	−0.0425065	+	0.130822i	−0.970058	−	0.242874i	$-0.921910\pi$
$653$	−18125.2	+	55783.5i	−0.0425065	+	0.130822i	0.927551	+	0.373696i	$0.121910\pi$
$654$		0			0
$655$	169718.	−	233597.i	0.395591	−	0.544484i
$656$	64023.3	+	20802.4i	0.148775	+	0.0483400i
$657$		0			0
$658$	−101329.	+	73619.7i	−0.234035	+	0.170036i
$659$			203272.i			0.468066i	0.972229	+	0.234033i	$0.0751924\pi$
$659$			203272.i			0.468066i	−0.972229	+	0.234033i	$0.924808\pi$
$660$		0			0
$661$	354885.			0.812241			0.406120	−	0.913820i	$-0.366881\pi$
$661$	354885.			0.812241			0.406120	+	0.913820i	$0.366881\pi$
$662$	−49746.3	−	68469.9i	−0.113513	−	0.156237i
$663$		0			0
$664$	−107209.	+	329954.i	−0.243161	+	0.748373i
$665$	424630.	+	308512.i	0.960214	+	0.697636i
$666$		0			0
$667$	−133638.	−	43421.5i	−0.300384	−	0.0976007i
$668$	−488838.	+	158833.i	−1.09550	+	0.355949i
$669$		0			0
$670$		−	21255.5i		−	0.0473502i
$671$	−482278.	−	588181.i	−1.07115	−	1.30637i
$672$		0			0
$673$	−38666.6	−	53220.0i	−0.0853701	−	0.117502i	0.764196	−	0.644984i	$-0.223136\pi$
$673$	−38666.6	−	53220.0i	−0.0853701	−	0.117502i	−0.849566	+	0.527482i	$0.823136\pi$
$674$	−14362.7	−	44203.9i	−0.0316167	−	0.0973062i
$675$		0			0
$676$	−27857.5	−	20239.6i	−0.0609605	−	0.0442904i
$677$	166023.	−	228511.i	0.362236	−	0.498575i	−0.588534	−	0.808472i	$-0.700295\pi$
$677$	166023.	−	228511.i	0.362236	−	0.498575i	0.950770	+	0.309897i	$0.100295\pi$
$678$		0			0
$679$	171460.	−	55710.6i	0.371897	−	0.120837i
$680$	−388310.	+	282124.i	−0.839772	+	0.610130i
$681$		0			0
$682$	81148.5	−	126644.i	0.174466	−	0.272281i
$683$	295282.			0.632987			0.316494	−	0.948595i	$-0.397494\pi$
$683$	295282.			0.632987			0.316494	+	0.948595i	$0.397494\pi$
$684$		0			0
$685$	−278107.	−	855924.i	−0.592693	−	1.82412i
$686$	−61181.6	+	188298.i	−0.130009	+	0.400126i
$687$		0			0
$688$	225003.	−	309690.i	0.475348	−	0.654260i
$689$	−514081.	−	167035.i	−1.08291	−	0.351860i
$690$		0			0
$691$	−122496.	+	88998.6i	−0.256547	+	0.186392i	−0.708623	−	0.705587i	$-0.750683\pi$
$691$	−122496.	+	88998.6i	−0.256547	+	0.186392i	0.452077	+	0.891979i	$0.350683\pi$
$692$			294372.i			0.614730i
$693$		0			0
$694$	211103.			0.438305
$695$	431225.	+	593530.i	0.892758	+	1.22878i
$696$		0			0
$697$	−41565.9	+	127927.i	−0.0855601	+	0.263327i
$698$	204824.	+	148814.i	0.420408	+	0.305444i
$699$		0			0
$700$	333739.	+	108438.i	0.681100	+	0.221303i
$701$	63426.4	−	20608.5i	0.129073	−	0.0419382i	−0.243768	−	0.969833i	$-0.578384\pi$
$701$	63426.4	−	20608.5i	0.129073	−	0.0419382i	0.372841	+	0.927895i	$0.378384\pi$
$702$		0			0
$703$		−	1.13289e6i		−	2.29233i
$704$	−7745.37	−	19814.8i	−0.0156278	−	0.0399802i
$705$		0			0
$706$	−36699.8	−	50512.9i	−0.0736298	−	0.101343i
$707$	22561.0	+	69435.5i	0.0451356	+	0.138913i
$708$		0			0
$709$	−3566.05	−	2590.88i	−0.00709406	−	0.00515413i	0.584233	−	0.811586i	$-0.301396\pi$
$709$	−3566.05	−	2590.88i	−0.00709406	−	0.00515413i	−0.591327	+	0.806432i	$0.701396\pi$
$710$	237465.	−	326843.i	0.471067	−	0.648368i
$711$		0			0
$712$	312068.	−	101397.i	0.615587	−	0.200016i
$713$	140133.	−	101812.i	0.275651	−	0.200272i
$714$		0			0
$715$	−745551.	−	194897.i	−1.45836	−	0.381236i
$716$	41703.4			0.0813477
$717$		0			0
$718$	−53854.8	−	165748.i	−0.104466	−	0.321513i
$719$	−69071.6	+	212581.i	−0.133611	+	0.411212i	−0.995371	−	0.0961033i	$-0.969362\pi$
$719$	−69071.6	+	212581.i	−0.133611	+	0.411212i	0.861760	+	0.507315i	$0.169362\pi$
$720$		0			0
$721$	−155428.	+	213929.i	−0.298992	+	0.411527i
$722$	−136985.	−	44509.2i	−0.262784	−	0.0853838i
$723$		0			0
$724$	−421398.	+	306163.i	−0.803924	+	0.584085i
$725$		−	547027.i		−	1.04072i
$726$		0			0
$727$	774400.			1.46520			0.732599	−	0.680660i	$-0.238307\pi$
$727$	774400.			1.46520			0.732599	+	0.680660i	$0.238307\pi$
$728$	−136564.	−	187964.i	−0.257676	−	0.354661i
$729$		0			0
$730$	−63301.7	+	194823.i	−0.118787	+	0.365590i
$731$	618799.	+	449584.i	1.15802	+	0.841349i
$732$		0			0
$733$	350012.	+	113726.i	0.651441	+	0.211666i	0.616049	−	0.787708i	$-0.288732\pi$
$733$	350012.	+	113726.i	0.651441	+	0.211666i	0.0353914	+	0.999374i	$0.488732\pi$
$734$	214373.	−	69654.1i	0.397904	−	0.129287i
$735$		0			0
$736$			244819.i			0.451950i
$737$	−9484.69	+	36282.3i	−0.0174618	+	0.0667974i
$738$		0			0
$739$	−305723.	−	420791.i	−0.559808	−	0.770509i	0.431494	−	0.902116i	$-0.357986\pi$
$739$	−305723.	−	420791.i	−0.559808	−	0.770509i	−0.991302	+	0.131606i	$0.957986\pi$
$740$	−389622.	−	1.19913e6i	−0.711509	−	2.18980i
$741$		0			0
$742$	135234.	+	98253.3i	0.245628	+	0.178459i
$743$	450699.	−	620334.i	0.816412	−	1.12369i	−0.173891	−	0.984765i	$-0.555634\pi$
$743$	450699.	−	620334.i	0.816412	−	1.12369i	0.990302	−	0.138929i	$-0.0443661\pi$
$744$		0			0
$745$	−801523.	+	260430.i	−1.44412	+	0.469223i
$746$	−210227.	+	152739.i	−0.377755	+	0.274455i
$747$		0			0
$748$	353493.	−	138176.i	0.631796	−	0.246962i
$749$	−315742.			−0.562819
$750$		0			0
$751$	162962.	+	501545.i	0.288939	+	0.889263i	0.985190	+	0.171465i	$0.0548500\pi$
$751$	162962.	+	501545.i	0.288939	+	0.889263i	−0.696251	+	0.717798i	$0.745150\pi$
$752$	−93923.6	+	289067.i	−0.166088	+	0.511167i
$753$		0			0
$754$	−95411.8	+	131323.i	−0.167826	+	0.230993i
$755$	−930505.	−	302339.i	−1.63239	−	0.530397i
$756$		0			0
$757$	371072.	−	269599.i	0.647539	−	0.470465i	−0.214893	−	0.976638i	$-0.568940\pi$
$757$	371072.	−	269599.i	0.647539	−	0.470465i	0.862432	+	0.506173i	$0.168940\pi$
$758$		−	383651.i		−	0.667725i
$759$		0			0
$760$	−918640.			−1.59044
$761$	358387.	+	493277.i	0.618846	+	0.851769i	0.997268	−	0.0738645i	$-0.0235332\pi$
$761$	358387.	+	493277.i	0.618846	+	0.851769i	−0.378422	+	0.925633i	$0.623533\pi$
$762$		0			0
$763$	−137014.	+	421685.i	−0.235350	+	0.724334i
$764$	−73940.7	−	53721.1i	−0.126677	−	0.0920361i
$765$		0			0
$766$	−36642.2	−	11905.8i	−0.0624487	−	0.0202908i
$767$	421489.	−	136950.i	0.716466	−	0.232794i
$768$		0			0
$769$			652888.i			1.10404i	0.833830	+	0.552022i	$0.186143\pi$
$769$			652888.i			1.10404i	−0.833830	+	0.552022i	$0.813857\pi$
$770$	200649.	+	128567.i	0.338419	+	0.216845i
$771$		0			0
$772$	−331669.	−	456503.i	−0.556507	−	0.765966i
$773$	181494.	+	558580.i	0.303740	+	0.934817i	0.980144	+	0.198286i	$0.0635375\pi$
$773$	181494.	+	558580.i	0.303740	+	0.934817i	−0.676404	+	0.736531i	$0.736463\pi$
$774$		0			0
$775$	545539.	+	396357.i	0.908285	+	0.659908i
$776$	−185467.	+	255273.i	−0.307994	+	0.423918i
$777$		0			0
$778$	286444.	−	93071.3i	0.473239	−	0.153765i
$779$	−208274.	+	151320.i	−0.343211	+	0.249357i
$780$		0			0
$781$	−551188.	+	451945.i	−0.903644	+	0.740940i
$782$	−101061.			−0.165261
$783$		0			0
$784$	58842.7	+	181099.i	0.0957328	+	0.294635i
$785$	−43116.8	+	132700.i	−0.0699692	+	0.215343i
$786$		0			0
$787$	129663.	−	178466.i	0.209347	−	0.288142i	−0.691412	−	0.722461i	$-0.743011\pi$
$787$	129663.	−	178466.i	0.209347	−	0.288142i	0.900759	+	0.434319i	$0.143011\pi$
$788$	518126.	+	168349.i	0.834416	+	0.271118i
$789$		0			0
$790$	−256339.	+	186241.i	−0.410734	+	0.298416i
$791$		−	418180.i		−	0.668359i
$792$		0			0
$793$	−1.01188e6			−1.60910
$794$	−62896.6	−	86569.8i	−0.0997668	−	0.137317i
$795$		0			0
$796$	−94934.6	+	292179.i	−0.149830	+	0.461129i
$797$	−340909.	−	247685.i	−0.536688	−	0.389926i	0.286166	−	0.958180i	$-0.407619\pi$
$797$	−340909.	−	247685.i	−0.536688	−	0.389926i	−0.822853	+	0.568254i	$0.807619\pi$
$798$		0			0
$799$	−577592.	−	187671.i	−0.904748	−	0.293971i
$800$	−906439.	+	294520.i	−1.41631	+	0.460188i
$801$		0			0
$802$			239679.i			0.372633i
$803$	194988.	−	304308.i	0.302396	−	0.471935i
$804$		0			0
$805$	161306.	+	222019.i	0.248920	+	0.342609i
$806$	−61833.7	−	190304.i	−0.0951820	−	0.292940i
$807$		0			0
$808$	−103377.	−	75107.9i	−0.158344	−	0.115044i
$809$	−723976.	+	996468.i	−1.10618	+	1.52253i	−0.279261	+	0.960215i	$0.590089\pi$
$809$	−723976.	+	996468.i	−1.10618	+	1.52253i	−0.826923	+	0.562316i	$0.809911\pi$
$810$		0			0
$811$	−140894.	+	45779.2i	−0.214215	+	0.0696028i	−0.414159	−	0.910205i	$-0.635924\pi$
$811$	−140894.	+	45779.2i	−0.214215	+	0.0696028i	0.199943	+	0.979807i	$0.435924\pi$
$812$	−175637.	+	127607.i	−0.266381	+	0.193537i
$813$		0			0
$814$	−30056.3	−	513482.i	−0.0453614	−	0.774955i
$815$	−834302.			−1.25605
$816$		0			0
$817$	452375.	+	1.39227e6i	0.677726	+	2.08583i
$818$	−120516.	+	370910.i	−0.180110	+	0.554321i
$819$		0			0
$820$	−168411.	+	231798.i	−0.250463	+	0.344733i
$821$	605342.	+	196687.i	0.898078	+	0.291803i	0.721444	−	0.692473i	$-0.243479\pi$
$821$	605342.	+	196687.i	0.898078	+	0.291803i	0.176635	+	0.984276i	$0.443479\pi$
$822$		0			0
$823$	−3262.96	+	2370.68i	−0.00481740	+	0.00350005i	−0.590191	−	0.807263i	$-0.700948\pi$
$823$	−3262.96	+	2370.68i	−0.00481740	+	0.00350005i	0.585374	+	0.810763i	$0.300948\pi$
$824$		−	462811.i		−	0.681630i
$825$		0			0
$826$	−137051.			−0.200874
$827$	−96571.7	−	132920.i	−0.141201	−	0.194347i	0.732559	−	0.680703i	$-0.238326\pi$
$827$	−96571.7	−	132920.i	−0.141201	−	0.194347i	−0.873761	+	0.486356i	$0.838326\pi$
$828$		0			0
$829$	301205.	−	927012.i	0.438281	−	1.34889i	−0.451406	−	0.892319i	$-0.649077\pi$
$829$	301205.	−	927012.i	0.438281	−	1.34889i	0.889687	−	0.456571i	$-0.150923\pi$
$830$	−382984.	−	278254.i	−0.555936	−	0.403911i
$831$		0			0
$832$	−26917.3	−	8745.95i	−0.0388852	−	0.0126346i
$833$	−361859.	+	117575.i	−0.521494	+	0.169444i
$834$		0			0
$835$		−	1.56486e6i		−	2.24442i
$836$	702790.	+	183719.i	1.00557	+	0.262870i
$837$		0			0
$838$	−88439.8	−	121727.i	−0.125939	−	0.173340i
$839$	167627.	+	515903.i	0.238133	+	0.732898i	0.996690	+	0.0812920i	$0.0259046\pi$
$839$	167627.	+	515903.i	0.238133	+	0.732898i	−0.758557	+	0.651606i	$0.774095\pi$
$840$		0			0
$841$	−298409.	−	216807.i	−0.421910	−	0.306536i
$842$	169220.	−	232912.i	0.238687	−	0.328524i
$843$		0			0
$844$	104657.	−	34005.1i	0.146921	−	0.0477374i
$845$	84812.5	−	61619.9i	0.118781	−	0.0862993i
$846$		0			0
$847$	−285130.	−	308993.i	−0.397444	−	0.430708i
$848$	405644.			0.564097
$849$		0			0
$850$	−121577.	−	374176.i	−0.168273	−	0.517890i
$851$	183041.	−	563342.i	0.252749	−	0.777881i
$852$		0			0
$853$	−115572.	+	159072.i	−0.158838	+	0.218622i	−0.881017	−	0.473084i	$-0.843141\pi$
$853$	−115572.	+	159072.i	−0.158838	+	0.218622i	0.722179	+	0.691706i	$0.243141\pi$
$854$	297604.	+	96697.3i	0.408059	+	0.132586i
$855$		0			0
$856$	447077.	−	324820.i	0.610147	−	0.443298i
$857$			609696.i			0.830141i	0.909789	+	0.415070i	$0.136243\pi$
$857$			609696.i			0.830141i	−0.909789	+	0.415070i	$0.863757\pi$
$858$		0			0
$859$	364464.			0.493933			0.246967	−	0.969024i	$-0.420566\pi$
$859$	364464.			0.493933			0.246967	+	0.969024i	$0.420566\pi$
$860$	957655.	+	1.31810e6i	1.29483	+	1.78218i
$861$		0			0
$862$	95051.5	−	292538.i	0.127922	−	0.393703i
$863$	−461500.	−	335299.i	−0.619655	−	0.450206i	0.233146	−	0.972442i	$-0.425098\pi$
$863$	−461500.	−	335299.i	−0.619655	−	0.450206i	−0.852801	+	0.522236i	$0.825098\pi$
$864$		0			0
$865$	−852356.	−	276947.i	−1.13917	−	0.370139i
$866$	−46972.9	+	15262.4i	−0.0626342	+	0.0203511i
$867$		0			0
$868$		−	267619.i		−	0.355203i
$869$	520665.	−	203522.i	0.689476	−	0.269508i
$870$		0			0
$871$	29324.2	+	40361.3i	0.0386536	+	0.0532022i
$872$	−239804.	−	738040.i	−0.315372	−	0.970615i
$873$		0			0
$874$	−156482.	−	113691.i	−0.204853	−	0.148834i
$875$	−210579.	+	289836.i	−0.275041	+	0.378562i
$876$		0			0
$877$	1.06203e6	−	345074.i	1.38082	−	0.448656i	0.477882	−	0.878424i	$-0.341405\pi$
$877$	1.06203e6	−	345074.i	1.38082	−	0.448656i	0.902939	+	0.429768i	$0.141405\pi$
$878$	−292415.	+	212452.i	−0.379324	+	0.275595i
$879$		0			0
$880$	577309.	−	33792.4i	0.745492	−	0.0436368i
$881$	134195.			0.172896			0.0864480	−	0.996256i	$-0.472448\pi$
$881$	134195.			0.172896			0.0864480	+	0.996256i	$0.472448\pi$
$882$		0			0
$883$	435707.	+	1.34097e6i	0.558821	+	1.71988i	0.685632	+	0.727948i	$0.259526\pi$
$883$	435707.	+	1.34097e6i	0.558821	+	1.71988i	−0.126811	+	0.991927i	$0.540474\pi$
$884$	156026.	−	480199.i	0.199661	−	0.614493i
$885$		0			0
$886$	−217143.	+	298872.i	−0.276617	+	0.380731i
$887$	367764.	+	119494.i	0.467436	+	0.151879i	0.533259	−	0.845952i	$-0.320967\pi$
$887$	367764.	+	119494.i	0.467436	+	0.151879i	−0.0658229	+	0.997831i	$0.520967\pi$
$888$		0			0
$889$	344924.	−	250602.i	0.436436	−	0.317089i
$890$			447732.i			0.565247i
$891$		0			0
$892$	−669795.			−0.841806
$893$	−683215.	−	940365.i	−0.856751	−	1.17922i
$894$		0			0
$895$	−39234.9	+	120752.i	−0.0489808	+	0.150747i
$896$	383850.	+	278883.i	0.478129	+	0.347381i
$897$		0			0
$898$	102843.	+	33415.6i	0.127533	+	0.0414378i
$899$	−396763.	+	128916.i	−0.490921	+	0.159510i
$900$		0			0
$901$			810528.i			0.998432i
$902$	−90385.8	+	74111.6i	−0.111093	+	0.0910905i
$903$		0			0
$904$	430203.	+	592124.i	0.526425	+	0.724562i
$905$	−490044.	−	1.50820e6i	−0.598326	−	1.84146i
$906$		0			0
$907$	187545.	+	136259.i	0.227977	+	0.165635i	0.695910	−	0.718129i	$-0.255001\pi$
$907$	187545.	+	136259.i	0.227977	+	0.165635i	−0.467933	+	0.883764i	$0.655001\pi$
$908$	133001.	−	183060.i	0.161318	−	0.222035i
$909$		0			0
$910$	301509.	−	97966.1i	0.364097	−	0.118302i
$911$	64995.6	−	47222.0i	0.0783154	−	0.0568994i	−0.547939	−	0.836519i	$-0.684587\pi$
$911$	64995.6	−	47222.0i	0.0783154	−	0.0568994i	0.626254	+	0.779619i	$0.284587\pi$
$912$		0			0
$913$	529575.	+	645865.i	0.635310	+	0.774818i
$914$	591152.			0.707630
$915$		0			0
$916$	−278119.	−	855961.i	−0.331466	−	1.02015i
$917$	64763.7	−	199322.i	0.0770181	−	0.237037i
$918$		0			0
$919$	−438830.	+	603998.i	−0.519596	+	0.715162i	−0.985501	−	0.169673i	$-0.945729\pi$
$919$	−438830.	+	603998.i	−0.519596	+	0.715162i	0.465905	+	0.884835i	$0.345729\pi$
$920$	−456805.	−	148425.i	−0.539703	−	0.175360i
$921$		0			0
$922$	92789.0	−	67415.2i	0.109153	−	0.0793041i
$923$			948238.i			1.11305i
$924$		0			0
$925$	2.30596e6			2.69506
$926$	260032.	+	357904.i	0.303253	+	0.417392i
$927$		0			0
$928$	182210.	−	560784.i	0.211580	−	0.651178i
$929$	620024.	+	450474.i	0.718418	+	0.521961i	0.885878	−	0.463917i	$-0.153557\pi$
$929$	620024.	+	450474.i	0.718418	+	0.521961i	−0.167460	+	0.985879i	$0.553557\pi$
$930$		0			0
$931$	−692570.	−	225030.i	−0.799032	−	0.259621i
$932$	−393828.	+	127963.i	−0.453393	+	0.147316i
$933$		0			0
$934$		−	210122.i		−	0.240867i
$935$	67521.4	+	1.15354e6i	0.0772357	+	1.31950i
$936$		0			0
$937$	583554.	+	803193.i	0.664664	+	0.914831i	0.999625	−	0.0274011i	$-0.00872312\pi$
$937$	583554.	+	803193.i	0.664664	+	0.914831i	−0.334961	+	0.942232i	$0.608723\pi$
$938$	−4767.53	−	14672.9i	−0.00541861	−	0.0166768i
$939$		0			0
$940$	−1.04658e6	−	760382.i	−1.18445	−	0.860550i
$941$	971018.	−	1.33649e6i	1.09660	−	1.50934i	0.256782	−	0.966469i	$-0.417338\pi$
$941$	971018.	−	1.33649e6i	1.09660	−	1.50934i	0.839817	−	0.542870i	$-0.182662\pi$
$942$		0			0
$943$	−128016.	+	41594.8i	−0.143959	+	0.0467752i
$944$	−269065.	+	195487.i	−0.301935	+	0.219369i
$945$		0			0
$946$	241977.	+	619044.i	0.270391	+	0.691734i
$947$	−1.33055e6			−1.48365			−0.741827	−	0.670592i	$-0.766040\pi$
$947$	−1.33055e6			−1.48365			−0.741827	+	0.670592i	$0.766040\pi$
$948$		0			0
$949$	−148577.	−	457273.i	−0.164975	−	0.507742i
$950$	232689.	−	716143.i	0.257827	−	0.793510i
$951$		0			0
$952$	−204776.	+	281850.i	−0.225946	+	0.310989i
$953$	952556.	+	309504.i	1.04883	+	0.340785i	0.782209	−	0.623016i	$-0.214093\pi$
$953$	952556.	+	309504.i	1.04883	+	0.340785i	0.266620	+	0.963802i	$0.414093\pi$
$954$		0			0
$955$	225114.	−	163555.i	0.246828	−	0.179331i
$956$		−	1.44132e6i		−	1.57705i
$957$		0			0
$958$	102577.			0.111768
$959$	−383961.	−	528477.i	−0.417493	−	0.574630i
$960$		0			0
$961$	−126468.	+	389229.i	−0.136941	+	0.421462i
$962$	−553585.	−	402203.i	−0.598184	−	0.434606i
$963$		0			0
$964$	668452.	+	217193.i	0.719311	+	0.233718i
$965$	1.63384e6	−	530868.i	1.75451	−	0.570075i
$966$		0			0
$967$		−	154811.i		−	0.165558i	−0.996568	−	0.0827788i	$-0.973621\pi$
$967$		−	154811.i		−	0.165558i	0.996568	−	0.0827788i	$-0.0263795\pi$
$968$	721609.	+	144193.i	0.770107	+	0.153884i
$969$		0			0
$970$	−253070.	−	348322.i	−0.268966	−	0.370200i
$971$	448502.	+	1.38035e6i	0.475692	+	1.46403i	0.845023	+	0.534730i	$0.179587\pi$
$971$	448502.	+	1.38035e6i	0.475692	+	1.46403i	−0.369331	+	0.929298i	$0.620413\pi$
$972$		0			0
$973$	430806.	+	312999.i	0.455047	+	0.330611i
$974$	110461.	−	152037.i	0.116437	−	0.160262i
$975$		0			0
$976$	722196.	−	234656.i	0.758151	−	0.246338i
$977$	1.24358e6	−	903512.i	1.30282	−	0.946553i	0.302840	−	0.953042i	$-0.402065\pi$
$977$	1.24358e6	−	903512.i	1.30282	−	0.946553i	0.999979	+	0.00648852i	$0.00206538\pi$
$978$		0			0
$979$	199788.	−	764261.i	0.208451	−	0.797400i
$980$	−810460.			−0.843878
$981$		0			0
$982$	236109.	+	726668.i	0.244844	+	0.753552i
$983$	−37134.0	+	114287.i	−0.0384295	+	0.118274i	−0.968431	−	0.249282i	$-0.919805\pi$
$983$	−37134.0	+	114287.i	−0.0384295	+	0.118274i	0.930001	+	0.367556i	$0.119805\pi$
$984$		0			0
$985$	−974912.	+	1.34185e6i	−1.00483	+	1.38303i
$986$	231490.	+	75215.7i	0.238111	+	0.0773668i
$987$		0			0
$988$	781802.	−	568012.i	0.800908	−	0.581894i
$989$			765411.i			0.782532i
$990$		0			0
$991$	−1.11523e6			−1.13558			−0.567791	−	0.823173i	$-0.692202\pi$
$991$	−1.11523e6			−1.13558			−0.567791	+	0.823173i	$0.692202\pi$
$992$	427235.	+	588039.i	0.434154	+	0.597561i
$993$		0			0
$994$	90615.5	−	278886.i	0.0917128	−	0.282263i
$995$	−756690.	−	549768.i	−0.764314	−	0.555307i
$996$		0			0
$997$	−709598.	−	230562.i	−0.713875	−	0.231952i	−0.0705091	−	0.997511i	$-0.522462\pi$
$997$	−709598.	−	230562.i	−0.713875	−	0.231952i	−0.643365	+	0.765559i	$0.722462\pi$
$998$	134756.	−	43785.0i	0.135297	−	0.0439607i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.5.k.c.19.3		32
3.2	odd	2		33.5.g.a.19.6	yes	32
11.7	odd	10	inner	99.5.k.c.73.3		32
33.2	even	10		363.5.c.e.241.21		32
33.20	odd	10		363.5.c.e.241.12		32
33.29	even	10		33.5.g.a.7.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.g.a.7.6	✓	32	33.29	even	10
33.5.g.a.19.6	yes	32	3.2	odd	2
99.5.k.c.19.3		32	1.1	even	1	trivial
99.5.k.c.73.3		32	11.7	odd	10	inner
363.5.c.e.241.12		32	33.20	odd	10
363.5.c.e.241.21		32	33.2	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01888 - 1.40237i) q^{2} +(4.01574 - 12.3592i) q^{4} +(32.0081 + 23.2552i) q^{5} +(27.3116 + 8.87408i) q^{7} +(-47.8012 + 15.5316i) q^{8} +O(q^{10})\)	\(q+(-1.01888 - 1.40237i) q^{2} +(4.01574 - 12.3592i) q^{4} +(32.0081 + 23.2552i) q^{5} +(27.3116 + 8.87408i) q^{7} +(-47.8012 + 15.5316i) q^{8} -68.5817i q^{10} +(-30.6027 + 117.066i) q^{11} +(94.6157 + 130.227i) q^{13} +(-15.3826 - 47.3428i) q^{14} +(-97.7287 - 71.0040i) q^{16} +(141.875 - 195.274i) q^{17} +(439.357 - 142.756i) q^{19} +(415.952 - 302.207i) q^{20} +(195.351 - 76.3605i) q^{22} +241.540 q^{23} +(290.575 + 894.298i) q^{25} +(86.2250 - 265.373i) q^{26} +(219.353 - 301.913i) q^{28} +(-553.272 - 179.769i) q^{29} +(580.162 - 421.513i) q^{31} +1013.58i q^{32} -418.402 q^{34} +(667.823 + 919.179i) q^{35} +(757.807 - 2332.29i) q^{37} +(-647.851 - 470.691i) q^{38} +(-1891.21 - 614.493i) q^{40} +(-529.997 + 172.207i) q^{41} +3168.88i q^{43} +(1323.95 + 848.332i) q^{44} +(-246.102 - 338.730i) q^{46} +(-777.518 - 2392.95i) q^{47} +(-1275.28 - 926.542i) q^{49} +(958.079 - 1318.68i) q^{50} +(1989.46 - 646.413i) q^{52} +(-2716.68 + 1973.78i) q^{53} +(-3701.93 + 3035.39i) q^{55} -1443.36 q^{56} +(311.617 + 959.059i) q^{58} +(850.781 - 2618.44i) q^{59} +(-3694.91 + 5085.60i) q^{61} +(-1182.24 - 384.132i) q^{62} +(-142.245 + 103.347i) q^{64} +6368.63i q^{65} +309.930 q^{67} +(-1843.70 - 2537.63i) q^{68} +(608.599 - 1873.08i) q^{70} +(4765.74 + 3462.51i) q^{71} +(-2840.74 - 923.012i) q^{73} +(-4042.86 + 1313.61i) q^{74} -6003.36i q^{76} +(-1874.66 + 2925.69i) q^{77} +(-2715.61 - 3737.72i) q^{79} +(-1476.89 - 4545.40i) q^{80} +(781.504 + 567.796i) q^{82} +(4057.27 - 5584.35i) q^{83} +(9082.28 - 2951.01i) q^{85} +(4443.95 - 3228.72i) q^{86} +(-355.374 - 6071.21i) q^{88} -6528.45 q^{89} +(1428.46 + 4396.34i) q^{91} +(969.964 - 2985.24i) q^{92} +(-2563.62 + 3528.52i) q^{94} +(17382.8 + 5648.00i) q^{95} +(5078.93 - 3690.06i) q^{97} +2732.45i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8}+O(q^{10}) \) 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8	\( 32 q + 76 q^{4} - 36 q^{5} + 150 q^{7} - 480 q^{8} + 246 q^{11} - 510 q^{13} + 1290 q^{14} - 232 q^{16} - 2490 q^{17} + 582 q^{20} - 510 q^{22} + 2196 q^{23} - 370 q^{25} + 5226 q^{26} + 4310 q^{28} - 960 q^{29} + 1658 q^{31} - 2320 q^{34} - 1920 q^{35} + 1374 q^{37} - 12054 q^{38} + 11070 q^{40} - 9360 q^{41} + 4350 q^{44} - 12950 q^{46} + 3450 q^{47} - 11838 q^{49} + 11550 q^{50} - 19250 q^{52} + 2790 q^{53} + 12356 q^{55} + 5604 q^{56} + 9486 q^{58} - 2682 q^{59} - 17190 q^{61} + 39360 q^{62} + 16248 q^{64} + 2796 q^{67} - 68160 q^{68} + 18188 q^{70} - 132 q^{71} - 21790 q^{73} + 2130 q^{74} - 4542 q^{77} + 12270 q^{79} - 32346 q^{80} + 29442 q^{82} - 35430 q^{83} - 11990 q^{85} + 49416 q^{86} + 1176 q^{88} + 38748 q^{89} - 51858 q^{91} + 25590 q^{92} - 34510 q^{94} + 71670 q^{95} + 30306 q^{97}+O(q^{100}) \) 32 * q + 76 * q^4 - 36 * q^5 + 150 * q^7 - 480 * q^8 + 246 * q^11 - 510 * q^13 + 1290 * q^14 - 232 * q^16 - 2490 * q^17 + 582 * q^20 - 510 * q^22 + 2196 * q^23 - 370 * q^25 + 5226 * q^26 + 4310 * q^28 - 960 * q^29 + 1658 * q^31 - 2320 * q^34 - 1920 * q^35 + 1374 * q^37 - 12054 * q^38 + 11070 * q^40 - 9360 * q^41 + 4350 * q^44 - 12950 * q^46 + 3450 * q^47 - 11838 * q^49 + 11550 * q^50 - 19250 * q^52 + 2790 * q^53 + 12356 * q^55 + 5604 * q^56 + 9486 * q^58 - 2682 * q^59 - 17190 * q^61 + 39360 * q^62 + 16248 * q^64 + 2796 * q^67 - 68160 * q^68 + 18188 * q^70 - 132 * q^71 - 21790 * q^73 + 2130 * q^74 - 4542 * q^77 + 12270 * q^79 - 32346 * q^80 + 29442 * q^82 - 35430 * q^83 - 11990 * q^85 + 49416 * q^86 + 1176 * q^88 + 38748 * q^89 - 51858 * q^91 + 25590 * q^92 - 34510 * q^94 + 71670 * q^95 + 30306 * q^97

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