LMFDB - Embedded newform 483.3.g.a.139.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(139,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("483.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.15
Character	$\chi$	$=$	483.139
Dual form			483.3.g.a.139.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20043 q^{2} -1.73205i q^{3} +0.841896 q^{4} +0.777779i q^{5} +3.81126i q^{6} +(2.99585 - 6.32652i) q^{7} +6.94919 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-2.20043 q^{2} -1.73205i q^{3} +0.841896 q^{4} +0.777779i q^{5} +3.81126i q^{6} +(2.99585 - 6.32652i) q^{7} +6.94919 q^{8} -3.00000 q^{9} -1.71145i q^{10} +7.82318 q^{11} -1.45821i q^{12} +22.1848i q^{13} +(-6.59217 + 13.9211i) q^{14} +1.34715 q^{15} -18.6588 q^{16} -7.29445i q^{17} +6.60129 q^{18} +3.16319i q^{19} +0.654808i q^{20} +(-10.9579 - 5.18897i) q^{21} -17.2144 q^{22} -4.79583 q^{23} -12.0364i q^{24} +24.3951 q^{25} -48.8162i q^{26} +5.19615i q^{27} +(2.52220 - 5.32627i) q^{28} -14.1115 q^{29} -2.96431 q^{30} +55.2840i q^{31} +13.2606 q^{32} -13.5501i q^{33} +16.0509i q^{34} +(4.92063 + 2.33011i) q^{35} -2.52569 q^{36} +46.0629 q^{37} -6.96039i q^{38} +38.4253 q^{39} +5.40493i q^{40} -3.39130i q^{41} +(24.1120 + 11.4180i) q^{42} +44.9751 q^{43} +6.58630 q^{44} -2.33334i q^{45} +10.5529 q^{46} -63.9679i q^{47} +32.3180i q^{48} +(-31.0497 - 37.9067i) q^{49} -53.6796 q^{50} -12.6344 q^{51} +18.6773i q^{52} +18.5805 q^{53} -11.4338i q^{54} +6.08470i q^{55} +(20.8188 - 43.9642i) q^{56} +5.47881 q^{57} +31.0514 q^{58} -31.2375i q^{59} +1.13416 q^{60} -1.63945i q^{61} -121.649i q^{62} +(-8.98756 + 18.9796i) q^{63} +45.4561 q^{64} -17.2549 q^{65} +29.8162i q^{66} +53.5848 q^{67} -6.14117i q^{68} +8.30662i q^{69} +(-10.8275 - 5.12725i) q^{70} +126.088 q^{71} -20.8476 q^{72} -63.7410i q^{73} -101.358 q^{74} -42.2535i q^{75} +2.66308i q^{76} +(23.4371 - 49.4935i) q^{77} -84.5522 q^{78} +111.159 q^{79} -14.5124i q^{80} +9.00000 q^{81} +7.46232i q^{82} +102.957i q^{83} +(-9.22537 - 4.36857i) q^{84} +5.67347 q^{85} -98.9646 q^{86} +24.4419i q^{87} +54.3648 q^{88} -116.506i q^{89} +5.13434i q^{90} +(140.353 + 66.4625i) q^{91} -4.03759 q^{92} +95.7548 q^{93} +140.757i q^{94} -2.46026 q^{95} -22.9681i q^{96} -19.9527i q^{97} +(68.3228 + 83.4110i) q^{98} -23.4695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.20043			−1.10022			−0.550108	−	0.835094i	$-0.685413\pi$
$2$	−2.20043			−1.10022			−0.550108	+	0.835094i	$0.685413\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	0.841896			0.210474
$5$			0.777779i			0.155556i	0.996971	+	0.0777779i	$0.0247825\pi$
$5$			0.777779i			0.155556i	−0.996971	+	0.0777779i	$0.975218\pi$
$6$			3.81126i			0.635210i
$7$	2.99585	−	6.32652i	0.427979	−	0.903789i
$7$	2.99585	−	6.32652i	0.427979	−	0.903789i
$8$	6.94919			0.868649
$9$	−3.00000			−0.333333
$10$		−	1.71145i		−	0.171145i
$11$	7.82318			0.711198			0.355599	−	0.934639i	$-0.384277\pi$
$11$	7.82318			0.711198			0.355599	+	0.934639i	$0.384277\pi$
$12$		−	1.45821i		−	0.121517i
$13$			22.1848i			1.70653i	0.521480	+	0.853263i	$0.325380\pi$
$13$			22.1848i			1.70653i	−0.521480	+	0.853263i	$0.674620\pi$
$14$	−6.59217	+	13.9211i	−0.470869	+	0.994362i
$15$	1.34715			0.0898101
$16$	−18.6588			−1.16617
$17$		−	7.29445i		−	0.429085i	−0.976715	−	0.214543i	$-0.931174\pi$
$17$		−	7.29445i		−	0.429085i	0.976715	−	0.214543i	$-0.0688261\pi$
$18$	6.60129			0.366738
$19$			3.16319i			0.166484i	0.996529	+	0.0832419i	$0.0265274\pi$
$19$			3.16319i			0.166484i	−0.996529	+	0.0832419i	$0.973473\pi$
$20$			0.654808i			0.0327404i
$21$	−10.9579	−	5.18897i	−0.521803	−	0.247094i
$22$	−17.2144			−0.782471
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$		−	12.0364i		−	0.501515i
$25$	24.3951			0.975802
$26$		−	48.8162i		−	1.87755i
$27$			5.19615i			0.192450i
$28$	2.52220	−	5.32627i	0.0900784	−	0.190224i
$29$	−14.1115			−0.486604			−0.243302	−	0.969951i	$-0.578231\pi$
$29$	−14.1115			−0.486604			−0.243302	+	0.969951i	$0.578231\pi$
$30$	−2.96431			−0.0988105
$31$			55.2840i			1.78336i	0.452670	+	0.891678i	$0.350472\pi$
$31$			55.2840i			1.78336i	−0.452670	+	0.891678i	$0.649528\pi$
$32$	13.2606			0.414395
$33$		−	13.5501i		−	0.410610i
$34$			16.0509i			0.472086i
$35$	4.92063	+	2.33011i	0.140589	+	0.0665746i
$36$	−2.52569			−0.0701580
$37$	46.0629			1.24494			0.622471	−	0.782643i	$-0.286129\pi$
$37$	46.0629			1.24494			0.622471	+	0.782643i	$0.286129\pi$
$38$		−	6.96039i		−	0.183168i
$39$	38.4253			0.985264
$40$			5.40493i			0.135123i
$41$		−	3.39130i		−	0.0827146i	−0.999144	−	0.0413573i	$-0.986832\pi$
$41$		−	3.39130i		−	0.0827146i	0.999144	−	0.0413573i	$-0.0131682\pi$
$42$	24.1120	+	11.4180i	0.574095	+	0.271856i
$43$	44.9751			1.04593			0.522966	−	0.852353i	$-0.324825\pi$
$43$	44.9751			1.04593			0.522966	+	0.852353i	$0.324825\pi$
$44$	6.58630			0.149689
$45$		−	2.33334i		−	0.0518519i
$46$	10.5529			0.229411
$47$		−	63.9679i		−	1.36102i	−0.732740	−	0.680509i	$-0.761759\pi$
$47$		−	63.9679i		−	1.36102i	0.732740	−	0.680509i	$-0.238241\pi$
$48$			32.3180i			0.673291i
$49$	−31.0497	−	37.9067i	−0.633668	−	0.773605i
$50$	−53.6796			−1.07359
$51$	−12.6344			−0.247733
$52$			18.6773i			0.359179i
$53$	18.5805			0.350575			0.175288	−	0.984517i	$-0.443914\pi$
$53$	18.5805			0.350575			0.175288	+	0.984517i	$0.443914\pi$
$54$		−	11.4338i		−	0.211737i
$55$			6.08470i			0.110631i
$56$	20.8188	−	43.9642i	0.371763	−	0.785075i
$57$	5.47881			0.0961195
$58$	31.0514			0.535369
$59$		−	31.2375i		−	0.529449i	−0.964324	−	0.264724i	$-0.914719\pi$
$59$		−	31.2375i		−	0.529449i	0.964324	−	0.264724i	$-0.0852810\pi$
$60$	1.13416			0.0189027
$61$		−	1.63945i		−	0.0268762i	−0.999910	−	0.0134381i	$-0.995722\pi$
$61$		−	1.63945i		−	0.0268762i	0.999910	−	0.0134381i	$-0.00427762\pi$
$62$		−	121.649i		−	1.96208i
$63$	−8.98756	+	18.9796i	−0.142660	+	0.301263i
$64$	45.4561			0.710251
$65$	−17.2549			−0.265460
$66$			29.8162i			0.451760i
$67$	53.5848			0.799774			0.399887	−	0.916564i	$-0.369049\pi$
$67$	53.5848			0.799774			0.399887	+	0.916564i	$0.369049\pi$
$68$		−	6.14117i		−	0.0903113i
$69$			8.30662i			0.120386i
$70$	−10.8275	−	5.12725i	−0.154679	−	0.0732464i
$71$	126.088			1.77589			0.887946	−	0.459947i	$-0.152132\pi$
$71$	126.088			1.77589			0.887946	+	0.459947i	$0.152132\pi$
$72$	−20.8476			−0.289550
$73$		−	63.7410i		−	0.873165i	−0.899664	−	0.436582i	$-0.856189\pi$
$73$		−	63.7410i		−	0.873165i	0.899664	−	0.436582i	$-0.143811\pi$
$74$	−101.358			−1.36970
$75$		−	42.2535i		−	0.563380i
$76$			2.66308i			0.0350405i
$77$	23.4371	−	49.4935i	0.304378	−	0.642773i
$78$	−84.5522			−1.08400
$79$	111.159			1.40707			0.703537	−	0.710659i	$-0.251603\pi$
$79$	111.159			1.40707			0.703537	+	0.710659i	$0.251603\pi$
$80$		−	14.5124i		−	0.181405i
$81$	9.00000			0.111111
$82$			7.46232i			0.0910039i
$83$			102.957i			1.24045i	0.784425	+	0.620224i	$0.212958\pi$
$83$			102.957i			1.24045i	−0.784425	+	0.620224i	$0.787042\pi$
$84$	−9.22537	−	4.36857i	−0.109826	−	0.0520068i
$85$	5.67347			0.0667467
$86$	−98.9646			−1.15075
$87$			24.4419i			0.280941i
$88$	54.3648			0.617781
$89$		−	116.506i		−	1.30905i	−0.756039	−	0.654526i	$-0.772868\pi$
$89$		−	116.506i		−	1.30905i	0.756039	−	0.654526i	$-0.227132\pi$
$90$			5.13434i			0.0570483i
$91$	140.353	+	66.4625i	1.54234	+	0.730358i
$92$	−4.03759			−0.0438868
$93$	95.7548			1.02962
$94$			140.757i			1.49741i
$95$	−2.46026			−0.0258975
$96$		−	22.9681i		−	0.239251i
$97$		−	19.9527i		−	0.205698i	−0.994697	−	0.102849i	$-0.967204\pi$
$97$		−	19.9527i		−	0.205698i	0.994697	−	0.102849i	$-0.0327959\pi$
$98$	68.3228	+	83.4110i	0.697171	+	0.851132i
$99$	−23.4695			−0.237066
$100$	20.5381			0.205381
$101$		−	83.2425i		−	0.824183i	−0.911142	−	0.412092i	$-0.864798\pi$
$101$		−	83.2425i		−	0.824183i	0.911142	−	0.412092i	$-0.135202\pi$
$102$	27.8010			0.272559
$103$			91.2405i			0.885830i	0.896564	+	0.442915i	$0.146056\pi$
$103$			91.2405i			0.885830i	−0.896564	+	0.442915i	$0.853944\pi$
$104$			154.167i			1.48237i
$105$	4.03587	−	8.52279i	0.0384369	−	0.0811694i
$106$	−40.8851			−0.385708
$107$	68.2742			0.638076			0.319038	−	0.947742i	$-0.396640\pi$
$107$	68.2742			0.638076			0.319038	+	0.947742i	$0.396640\pi$
$108$			4.37462i			0.0405057i
$109$	−117.841			−1.08111			−0.540555	−	0.841309i	$-0.681786\pi$
$109$	−117.841			−1.08111			−0.540555	+	0.841309i	$0.681786\pi$
$110$		−	13.3890i		−	0.121718i
$111$		−	79.7832i		−	0.718768i
$112$	−55.8990	+	118.045i	−0.499098	+	1.05398i
$113$	−45.2602			−0.400533			−0.200266	−	0.979741i	$-0.564181\pi$
$113$	−45.2602			−0.400533			−0.200266	+	0.979741i	$0.564181\pi$
$114$	−12.0557			−0.105752
$115$		−	3.73010i		−	0.0324356i
$116$	−11.8804			−0.102417
$117$		−	66.5545i		−	0.568842i
$118$			68.7359i			0.582508i
$119$	−46.1485	−	21.8531i	−0.387802	−	0.183640i
$120$	9.36162			0.0780135
$121$	−59.7979			−0.494197
$122$			3.60750i			0.0295697i
$123$	−5.87390			−0.0477553
$124$			46.5434i			0.375350i
$125$			38.4184i			0.307347i
$126$	19.7765	−	41.7632i	0.156956	−	0.331454i
$127$	−82.3781			−0.648646			−0.324323	−	0.945946i	$-0.605137\pi$
$127$	−82.3781			−0.648646			−0.324323	+	0.945946i	$0.605137\pi$
$128$	−153.065			−1.19582
$129$		−	77.8991i		−	0.603869i
$130$	37.9682			0.292063
$131$		−	227.554i		−	1.73705i	−0.495643	−	0.868527i	$-0.665067\pi$
$131$		−	227.554i		−	1.73705i	0.495643	−	0.868527i	$-0.334933\pi$
$132$		−	11.4078i		−	0.0864228i
$133$	20.0120	+	9.47646i	0.150466	+	0.0712516i
$134$	−117.910			−0.879923
$135$	−4.04146			−0.0299367
$136$		−	50.6905i		−	0.372724i
$137$	85.4533			0.623747			0.311874	−	0.950124i	$-0.399043\pi$
$137$	85.4533			0.623747			0.311874	+	0.950124i	$0.399043\pi$
$138$		−	18.2782i		−	0.132450i
$139$			128.759i			0.926321i	0.886274	+	0.463161i	$0.153285\pi$
$139$			128.759i			0.926321i	−0.886274	+	0.463161i	$0.846715\pi$
$140$	4.14266	+	1.96171i	0.0295904	+	0.0140122i
$141$	−110.796			−0.785784
$142$	−277.449			−1.95386
$143$			173.556i			1.21368i
$144$	55.9764			0.388725
$145$		−	10.9756i		−	0.0756940i
$146$			140.258i			0.960669i
$147$	−65.6563	+	53.7797i	−0.446641	+	0.365848i
$148$	38.7801			0.262028
$149$	258.729			1.73644			0.868219	−	0.496181i	$-0.165265\pi$
$149$	258.729			1.73644			0.868219	+	0.496181i	$0.165265\pi$
$150$			92.9759i			0.619839i
$151$	60.1046			0.398044			0.199022	−	0.979995i	$-0.436224\pi$
$151$	60.1046			0.398044			0.199022	+	0.979995i	$0.436224\pi$
$152$			21.9816i			0.144616i
$153$			21.8834i			0.143028i
$154$	−51.5717	+	108.907i	−0.334881	+	0.707189i
$155$	−42.9987			−0.277411
$156$	32.3501			0.207372
$157$			186.297i			1.18661i	0.804979	+	0.593303i	$0.202176\pi$
$157$			186.297i			1.18661i	−0.804979	+	0.593303i	$0.797824\pi$
$158$	−244.597			−1.54808
$159$		−	32.1823i		−	0.202405i
$160$			10.3138i			0.0644614i
$161$	−14.3676	+	30.3409i	−0.0892398	+	0.188453i
$162$	−19.8039			−0.122246
$163$	−143.746			−0.881878			−0.440939	−	0.897537i	$-0.645355\pi$
$163$	−143.746			−0.881878			−0.440939	+	0.897537i	$0.645355\pi$
$164$		−	2.85512i		−	0.0174093i
$165$	10.5390			0.0638728
$166$		−	226.550i		−	1.36476i
$167$		−	25.5151i		−	0.152785i	−0.997078	−	0.0763924i	$-0.975660\pi$
$167$		−	25.5151i		−	0.152785i	0.997078	−	0.0763924i	$-0.0243402\pi$
$168$	−76.1482	−	36.0591i	−0.453263	−	0.214638i
$169$	−323.167			−1.91223
$170$	−12.4841			−0.0734357
$171$		−	9.48958i		−	0.0554946i
$172$	37.8643			0.220141
$173$		−	18.6160i		−	0.107607i	−0.998552	−	0.0538035i	$-0.982866\pi$
$173$		−	18.6160i		−	0.107607i	0.998552	−	0.0538035i	$-0.0171345\pi$
$174$		−	53.7826i		−	0.309095i
$175$	73.0840	−	154.336i	0.417623	−	0.881919i
$176$	−145.971			−0.829381
$177$	−54.1049			−0.305677
$178$			256.363i			1.44024i
$179$	−338.460			−1.89084			−0.945418	−	0.325861i	$-0.894346\pi$
$179$	−338.460			−1.89084			−0.945418	+	0.325861i	$0.894346\pi$
$180$		−	1.96443i		−	0.0109135i
$181$			222.261i			1.22796i	0.789321	+	0.613981i	$0.210433\pi$
$181$			222.261i			1.22796i	−0.789321	+	0.613981i	$0.789567\pi$
$182$	−308.837	−	146.246i	−1.69691	−	0.803551i
$183$	−2.83961			−0.0155170
$184$	−33.3271			−0.181126
$185$			35.8267i			0.193658i
$186$	−210.702			−1.13281
$187$		−	57.0658i		−	0.305165i
$188$		−	53.8543i		−	0.286459i
$189$	32.8736	+	15.5669i	0.173934	+	0.0823646i
$190$	5.41364			0.0284928
$191$	−192.950			−1.01021			−0.505105	−	0.863058i	$-0.668546\pi$
$191$	−192.950			−1.01021			−0.505105	+	0.863058i	$0.668546\pi$
$192$		−	78.7323i		−	0.410064i
$193$	42.4054			0.219717			0.109859	−	0.993947i	$-0.464960\pi$
$193$	42.4054			0.219717			0.109859	+	0.993947i	$0.464960\pi$
$194$			43.9046i			0.226312i
$195$			29.8864i			0.153263i
$196$	−26.1406	−	31.9134i	−0.133371	−	0.162824i
$197$	347.028			1.76156			0.880782	−	0.473522i	$-0.157018\pi$
$197$	347.028			1.76156			0.880782	+	0.473522i	$0.157018\pi$
$198$	51.6431			0.260824
$199$		−	14.6280i		−	0.0735077i	−0.999324	−	0.0367539i	$-0.988298\pi$
$199$		−	14.6280i		−	0.0735077i	0.999324	−	0.0367539i	$-0.0117018\pi$
$200$	169.526			0.847630
$201$		−	92.8117i		−	0.461750i
$202$			183.169i			0.906779i
$203$	−42.2760	+	89.2768i	−0.208256	+	0.439787i
$204$	−10.6368			−0.0521412
$205$	2.63768			0.0128667
$206$		−	200.768i		−	0.974604i
$207$	14.3875			0.0695048
$208$		−	413.942i		−	1.99011i
$209$			24.7462i			0.118403i
$210$	−8.88065	+	18.7538i	−0.0422888	+	0.0893038i
$211$	254.736			1.20728			0.603639	−	0.797258i	$-0.293717\pi$
$211$	254.736			1.20728			0.603639	+	0.797258i	$0.293717\pi$
$212$	15.6428			0.0737869
$213$		−	218.391i		−	1.02531i
$214$	−150.233			−0.702022
$215$			34.9807i			0.162701i
$216$			36.1091i			0.167172i
$217$	349.756	+	165.623i	1.61178	+	0.763239i
$218$	259.301			1.18945
$219$	−110.403			−0.504122
$220$			5.12268i			0.0232849i
$221$	161.826			0.732246
$222$			175.557i			0.790799i
$223$			51.1298i			0.229282i	0.993407	+	0.114641i	$0.0365717\pi$
$223$			51.1298i			0.229282i	−0.993407	+	0.114641i	$0.963428\pi$
$224$	39.7269	−	83.8936i	0.177352	−	0.374525i
$225$	−73.1852			−0.325267
$226$	99.5920			0.440673
$227$			402.737i			1.77417i	0.461604	+	0.887086i	$0.347274\pi$
$227$			402.737i			1.77417i	−0.461604	+	0.887086i	$0.652726\pi$
$228$	4.61259			0.0202306
$229$		−	50.8948i		−	0.222248i	−0.993807	−	0.111124i	$-0.964555\pi$
$229$		−	50.8948i		−	0.222248i	0.993807	−	0.111124i	$-0.0354451\pi$
$230$			8.20782i			0.0356862i
$231$	−85.7253	−	40.5942i	−0.371105	−	0.175733i
$232$	−98.0636			−0.422688
$233$	−187.135			−0.803156			−0.401578	−	0.915825i	$-0.631538\pi$
$233$	−187.135			−0.803156			−0.401578	+	0.915825i	$0.631538\pi$
$234$			146.449i			0.625849i
$235$	49.7528			0.211714
$236$		−	26.2987i		−	0.111435i
$237$		−	192.533i		−	0.812374i
$238$	101.547	+	48.0862i	0.426666	+	0.202043i
$239$	304.750			1.27511			0.637553	−	0.770407i	$-0.279947\pi$
$239$	304.750			1.27511			0.637553	+	0.770407i	$0.279947\pi$
$240$	−25.1362			−0.104734
$241$		−	220.739i		−	0.915931i	−0.888970	−	0.457965i	$-0.848578\pi$
$241$		−	220.739i		−	0.915931i	0.888970	−	0.457965i	$-0.151422\pi$
$242$	131.581			0.543723
$243$		−	15.5885i		−	0.0641500i
$244$		−	1.38025i		−	0.00565675i
$245$	29.4830	−	24.1498i	0.120339	−	0.0985707i
$246$	12.9251			0.0525411
$247$	−70.1749			−0.284109
$248$			384.179i			1.54911i
$249$	178.327			0.716173
$250$		−	84.5371i		−	0.338148i
$251$			172.067i			0.685527i	0.939422	+	0.342763i	$0.111363\pi$
$251$			172.067i			0.685527i	−0.939422	+	0.342763i	$0.888637\pi$
$252$	−7.56659	+	15.9788i	−0.0300261	+	0.0634080i
$253$	−37.5187			−0.148295
$254$	181.267			0.713651
$255$		−	9.82673i		−	0.0385362i
$256$	154.986			0.605413
$257$		−	63.1720i		−	0.245806i	−0.992419	−	0.122903i	$-0.960780\pi$
$257$		−	63.1720i		−	0.245806i	0.992419	−	0.122903i	$-0.0392203\pi$
$258$			171.412i			0.664386i
$259$	137.998	−	291.418i	0.532809	−	1.12516i
$260$	−14.5268			−0.0558724
$261$	42.3345			0.162201
$262$			500.717i			1.91113i
$263$	−380.351			−1.44620			−0.723101	−	0.690742i	$-0.757284\pi$
$263$	−380.351			−1.44620			−0.723101	+	0.690742i	$0.757284\pi$
$264$		−	94.1625i		−	0.356676i
$265$			14.4515i			0.0545340i
$266$	−44.0350	−	20.8523i	−0.165545	−	0.0783921i
$267$	−201.794			−0.755782
$268$	45.1128			0.168332
$269$			94.0757i			0.349724i	0.984593	+	0.174862i	$0.0559479\pi$
$269$			94.0757i			0.349724i	−0.984593	+	0.174862i	$0.944052\pi$
$270$	8.89294			0.0329368
$271$		−	207.446i		−	0.765485i	−0.923855	−	0.382742i	$-0.874980\pi$
$271$		−	207.446i		−	0.765485i	0.923855	−	0.382742i	$-0.125020\pi$
$272$			136.106i			0.500388i
$273$	115.117	−	243.098i	0.421672	−	0.890470i
$274$	−188.034			−0.686256
$275$	190.847			0.693989
$276$			6.99331i			0.0253381i
$277$	98.5533			0.355788			0.177894	−	0.984050i	$-0.443072\pi$
$277$	98.5533			0.355788			0.177894	+	0.984050i	$0.443072\pi$
$278$		−	283.324i		−	1.01915i
$279$		−	165.852i		−	0.594452i
$280$	34.1944	+	16.1924i	0.122123	+	0.0578299i
$281$	273.991			0.975058			0.487529	−	0.873107i	$-0.337898\pi$
$281$	273.991			0.975058			0.487529	+	0.873107i	$0.337898\pi$
$282$	243.798			0.864532
$283$		−	289.743i		−	1.02383i	−0.859037	−	0.511913i	$-0.828937\pi$
$283$		−	289.743i		−	1.02383i	0.859037	−	0.511913i	$-0.171063\pi$
$284$	106.153			0.373779
$285$			4.26130i			0.0149519i
$286$		−	381.898i		−	1.33531i
$287$	−21.4551	−	10.1598i	−0.0747565	−	0.0354001i
$288$	−39.7819			−0.138132
$289$	235.791			0.815886
$290$			24.1511i			0.0832797i
$291$	−34.5591			−0.118760
$292$		−	53.6633i		−	0.183778i
$293$			105.128i			0.358798i	0.983776	+	0.179399i	$0.0574153\pi$
$293$			105.128i			0.358798i	−0.983776	+	0.179399i	$0.942585\pi$
$294$	144.472	−	118.339i	0.491402	−	0.402512i
$295$	24.2958			0.0823588
$296$	320.100			1.08142
$297$			40.6504i			0.136870i
$298$	−569.316			−1.91046
$299$		−	106.395i		−	0.355835i
$300$		−	35.5730i		−	0.118577i
$301$	134.739	−	284.536i	0.447637	−	0.945302i
$302$	−132.256			−0.437934
$303$	−144.180			−0.475842
$304$		−	59.0214i		−	0.194149i
$305$	1.27513			0.00418075
$306$		−	48.1528i		−	0.157362i
$307$			485.003i			1.57981i	0.613227	+	0.789907i	$0.289871\pi$
$307$			485.003i			1.57981i	−0.613227	+	0.789907i	$0.710129\pi$
$308$	19.7316	−	41.6684i	0.0640636	−	0.135287i
$309$	158.033			0.511434
$310$	94.6158			0.305212
$311$			86.6326i			0.278561i	0.990253	+	0.139281i	$0.0444790\pi$
$311$			86.6326i			0.278561i	−0.990253	+	0.139281i	$0.955521\pi$
$312$	267.025			0.855848
$313$		−	561.399i		−	1.79361i	−0.442428	−	0.896804i	$-0.645883\pi$
$313$		−	561.399i		−	1.79361i	0.442428	−	0.896804i	$-0.354117\pi$
$314$		−	409.934i		−	1.30552i
$315$	−14.7619	−	6.99033i	−0.0468632	−	0.0221915i
$316$	93.5841			0.296152
$317$	13.4473			0.0424205			0.0212102	−	0.999775i	$-0.493248\pi$
$317$	13.4473			0.0424205			0.0212102	+	0.999775i	$0.493248\pi$
$318$			70.8150i			0.222689i
$319$	−110.397			−0.346072
$320$			35.3548i			0.110484i
$321$		−	118.254i		−	0.368394i
$322$	31.6149	−	66.7631i	0.0981830	−	0.207339i
$323$	23.0737			0.0714358
$324$	7.57706			0.0233860
$325$			541.201i			1.66523i
$326$	316.303			0.970256
$327$			204.107i			0.624179i
$328$		−	23.5668i		−	0.0718499i
$329$	−404.694	−	191.638i	−1.23007	−	0.582487i
$330$	−23.1904			−0.0702738
$331$	211.917			0.640231			0.320116	−	0.947378i	$-0.396278\pi$
$331$	211.917			0.640231			0.320116	+	0.947378i	$0.396278\pi$
$332$			86.6792i			0.261082i
$333$	−138.189			−0.414981
$334$			56.1442i			0.168096i
$335$			41.6771i			0.124409i
$336$	204.460	+	96.8199i	0.608513	+	0.288155i
$337$	−94.6588			−0.280887			−0.140443	−	0.990089i	$-0.544853\pi$
$337$	−94.6588			−0.280887			−0.140443	+	0.990089i	$0.544853\pi$
$338$	711.108			2.10387
$339$			78.3930i			0.231248i
$340$	4.77647			0.0140484
$341$			432.497i			1.26832i
$342$			20.8812i			0.0610560i
$343$	−332.838	+	82.8739i	−0.970372	+	0.241615i
$344$	312.540			0.908548
$345$	−6.46071			−0.0187267
$346$			40.9632i			0.118391i
$347$	182.354			0.525517			0.262758	−	0.964862i	$-0.415368\pi$
$347$	182.354			0.525517			0.262758	+	0.964862i	$0.415368\pi$
$348$			20.5775i			0.0591307i
$349$		−	378.416i		−	1.08429i	−0.840286	−	0.542144i	$-0.817613\pi$
$349$		−	378.416i		−	1.08429i	0.840286	−	0.542144i	$-0.182387\pi$
$350$	−160.816	+	339.605i	−0.459475	+	0.970301i
$351$	−115.276			−0.328421
$352$	103.740			0.294717
$353$			192.974i			0.546668i	0.961919	+	0.273334i	$0.0881264\pi$
$353$			192.974i			0.546668i	−0.961919	+	0.273334i	$0.911874\pi$
$354$	119.054			0.336311
$355$			98.0688i			0.276250i
$356$		−	98.0856i		−	0.275521i
$357$	−37.8507	+	79.9315i	−0.106024	+	0.223898i
$358$	744.757			2.08033
$359$	84.6179			0.235705			0.117852	−	0.993031i	$-0.462399\pi$
$359$	84.6179			0.235705			0.117852	+	0.993031i	$0.462399\pi$
$360$		−	16.2148i		−	0.0450411i
$361$	350.994			0.972283
$362$		−	489.070i		−	1.35102i
$363$			103.573i			0.285325i
$364$	118.162	+	55.9545i	0.324622	+	0.153721i
$365$	49.5764			0.135826
$366$	6.24837			0.0170720
$367$		−	282.252i		−	0.769078i	−0.923109	−	0.384539i	$-0.874360\pi$
$367$		−	282.252i		−	0.769078i	0.923109	−	0.384539i	$-0.125640\pi$
$368$	89.4844			0.243164
$369$			10.1739i			0.0275715i
$370$		−	78.8342i		−	0.213065i
$371$	55.6644	−	117.550i	0.150039	−	0.316846i
$372$	80.6155			0.216708
$373$	−578.614			−1.55125			−0.775623	−	0.631197i	$-0.782564\pi$
$373$	−578.614			−1.55125			−0.775623	+	0.631197i	$0.782564\pi$
$374$			125.569i			0.335747i
$375$	66.5427			0.177447
$376$		−	444.525i		−	1.18225i
$377$		−	313.062i		−	0.830403i
$378$	−72.3360	−	34.2539i	−0.191365	−	0.0906188i
$379$	629.039			1.65973			0.829867	−	0.557962i	$-0.188416\pi$
$379$	629.039			1.65973			0.829867	+	0.557962i	$0.188416\pi$
$380$	−2.07128			−0.00545075
$381$			142.683i			0.374496i
$382$	424.574			1.11145
$383$			132.130i			0.344986i	0.985011	+	0.172493i	$0.0551823\pi$
$383$			132.130i			0.344986i	−0.985011	+	0.172493i	$0.944818\pi$
$384$			265.117i			0.690409i
$385$	38.4950	+	18.2289i	0.0999870	+	0.0473477i
$386$	−93.3102			−0.241736
$387$	−134.925			−0.348644
$388$		−	16.7981i		−	0.0432941i
$389$	−273.365			−0.702737			−0.351368	−	0.936237i	$-0.614284\pi$
$389$	−273.365			−0.702737			−0.351368	+	0.936237i	$0.614284\pi$
$390$		−	65.7629i		−	0.168623i
$391$			34.9830i			0.0894705i
$392$	−215.770	−	263.421i	−0.550435	−	0.671991i
$393$	−394.135			−1.00289
$394$	−763.611			−1.93810
$395$			86.4570i			0.218878i
$396$	−19.7589			−0.0498962
$397$		−	160.627i		−	0.404601i	−0.979323	−	0.202300i	$-0.935158\pi$
$397$		−	160.627i		−	0.404601i	0.979323	−	0.202300i	$-0.0648418\pi$
$398$			32.1880i			0.0808743i
$399$	16.4137	−	34.6618i	0.0411371	−	0.0868717i
$400$	−455.182			−1.13796
$401$	430.423			1.07337			0.536686	−	0.843782i	$-0.319676\pi$
$401$	430.423			1.07337			0.536686	+	0.843782i	$0.319676\pi$
$402$			204.226i			0.508024i
$403$	−1226.47			−3.04334
$404$		−	70.0815i		−	0.173469i
$405$			7.00001i			0.0172840i
$406$	93.0255	−	196.447i	0.229127	−	0.483861i
$407$	360.358			0.885401
$408$	−87.7986			−0.215193
$409$			221.197i			0.540824i	0.962745	+	0.270412i	$0.0871599\pi$
$409$			221.197i			0.540824i	−0.962745	+	0.270412i	$0.912840\pi$
$410$	−5.80403			−0.0141562
$411$		−	148.010i		−	0.360121i
$412$			76.8150i			0.186444i
$413$	−197.625	−	93.5829i	−0.478510	−	0.226593i
$414$	−31.6587			−0.0764703
$415$	−80.0779			−0.192959
$416$			294.185i			0.707175i
$417$	223.017			0.534812
$418$		−	54.4523i		−	0.130269i
$419$		−	70.9100i		−	0.169236i	−0.996413	−	0.0846181i	$-0.973033\pi$
$419$		−	70.9100i		−	0.169236i	0.996413	−	0.0846181i	$-0.0269670\pi$
$420$	3.39778	−	7.17530i	0.00808996	−	0.0170840i
$421$	570.023			1.35397			0.676987	−	0.735995i	$-0.263285\pi$
$421$	570.023			1.35397			0.676987	+	0.735995i	$0.263285\pi$
$422$	−560.528			−1.32827
$423$			191.904i			0.453673i
$424$	129.119			0.304527
$425$		−	177.949i		−	0.418702i
$426$			480.555i			1.12806i
$427$	−10.3720	−	4.91155i	−0.0242904	−	0.0115025i
$428$	57.4797			0.134298
$429$	300.608			0.700718
$430$		−	76.9725i		−	0.179006i
$431$	−689.862			−1.60061			−0.800304	−	0.599594i	$-0.795329\pi$
$431$	−689.862			−1.60061			−0.800304	+	0.599594i	$0.795329\pi$
$432$		−	96.9539i		−	0.224430i
$433$			263.889i			0.609443i	0.952442	+	0.304721i	$0.0985634\pi$
$433$			263.889i			0.609443i	−0.952442	+	0.304721i	$0.901437\pi$
$434$	−769.613	−	364.442i	−1.77330	−	0.839727i
$435$	−19.0104			−0.0437020
$436$	−99.2099			−0.227546
$437$		−	15.1701i		−	0.0347143i
$438$	242.933			0.554643
$439$			851.790i			1.94030i	0.242513	+	0.970148i	$0.422028\pi$
$439$			851.790i			1.94030i	−0.242513	+	0.970148i	$0.577972\pi$
$440$			42.2838i			0.0960994i
$441$	93.1492	+	113.720i	0.211223	+	0.257868i
$442$	−356.088			−0.805628
$443$	−663.850			−1.49853			−0.749267	−	0.662268i	$-0.769594\pi$
$443$	−663.850			−1.49853			−0.749267	+	0.662268i	$0.769594\pi$
$444$		−	67.1692i		−	0.151282i
$445$	90.6156			0.203631
$446$		−	112.508i		−	0.252259i
$447$		−	448.132i		−	1.00253i
$448$	136.180	−	287.579i	0.303973	−	0.641917i
$449$	−80.1188			−0.178438			−0.0892191	−	0.996012i	$-0.528437\pi$
$449$	−80.1188			−0.178438			−0.0892191	+	0.996012i	$0.528437\pi$
$450$	161.039			0.357864
$451$		−	26.5307i		−	0.0588265i
$452$	−38.1044			−0.0843017
$453$		−	104.104i		−	0.229811i
$454$		−	886.195i		−	1.95197i
$455$	−51.6931	+	109.163i	−0.113611	+	0.239920i
$456$	38.0733			0.0834941
$457$	−571.065			−1.24960			−0.624798	−	0.780786i	$-0.714819\pi$
$457$	−571.065			−1.24960			−0.624798	+	0.780786i	$0.714819\pi$
$458$			111.991i			0.244521i
$459$	37.9031			0.0825775
$460$		−	3.14035i		−	0.00682685i
$461$			222.271i			0.482150i	0.970507	+	0.241075i	$0.0774999\pi$
$461$			222.271i			0.482150i	−0.970507	+	0.241075i	$0.922500\pi$
$462$	188.633	+	89.3248i	0.408296	+	0.193344i
$463$	−737.547			−1.59297			−0.796487	−	0.604656i	$-0.793311\pi$
$463$	−737.547			−1.59297			−0.796487	+	0.604656i	$0.793311\pi$
$464$	263.304			0.567465
$465$			74.4760i			0.160163i
$466$	411.779			0.883645
$467$			664.188i			1.42224i	0.703069	+	0.711122i	$0.251813\pi$
$467$			664.188i			1.42224i	−0.703069	+	0.711122i	$0.748187\pi$
$468$		−	56.0320i		−	0.119726i
$469$	160.532	−	339.006i	0.342286	−	0.722827i
$470$	−109.478			−0.232931
$471$	322.676			0.685087
$472$		−	217.075i		−	0.459905i
$473$	351.848			0.743865
$474$			423.655i			0.893787i
$475$			77.1663i			0.162455i
$476$	−38.8522	−	18.3980i	−0.0816223	−	0.0386513i
$477$	−55.7414			−0.116858
$478$	−670.582			−1.40289
$479$		−	655.036i		−	1.36751i	−0.729713	−	0.683754i	$-0.760346\pi$
$479$		−	655.036i		−	1.36751i	0.729713	−	0.683754i	$-0.239654\pi$
$480$	17.8641			0.0372168
$481$			1021.90i			2.12453i
$482$			485.722i			1.00772i
$483$	52.5520	+	24.8854i	0.108803	+	0.0515226i
$484$	−50.3436			−0.104016
$485$	15.5188			0.0319975
$486$			34.3013i			0.0705789i
$487$	314.145			0.645062			0.322531	−	0.946559i	$-0.395466\pi$
$487$	314.145			0.645062			0.322531	+	0.946559i	$0.395466\pi$
$488$		−	11.3929i		−	0.0233460i
$489$			248.976i			0.509153i
$490$	−64.8753	+	53.1400i	−0.132399	+	0.108449i
$491$	−383.420			−0.780896			−0.390448	−	0.920625i	$-0.627680\pi$
$491$	−383.420			−0.780896			−0.390448	+	0.920625i	$0.627680\pi$
$492$	−4.94521			−0.0100512
$493$			102.936i			0.208795i
$494$	154.415			0.312581
$495$		−	18.2541i		−	0.0368770i
$496$		−	1031.53i		−	2.07970i
$497$	377.742	−	797.701i	0.760045	−	1.60503i
$498$	−392.396			−0.787944
$499$	66.5242			0.133315			0.0666575	−	0.997776i	$-0.478767\pi$
$499$	66.5242			0.133315			0.0666575	+	0.997776i	$0.478767\pi$
$500$			32.3443i			0.0646886i
$501$	−44.1934			−0.0882104
$502$		−	378.622i		−	0.754227i
$503$			30.4447i			0.0605262i	0.999542	+	0.0302631i	$0.00963452\pi$
$503$			30.4447i			0.0605262i	−0.999542	+	0.0302631i	$0.990365\pi$
$504$	−62.4563	+	131.893i	−0.123921	+	0.261692i
$505$	64.7442			0.128206
$506$	82.5572			0.163157
$507$			559.742i			1.10403i
$508$	−69.3538			−0.136523
$509$			638.832i			1.25507i	0.778587	+	0.627537i	$0.215937\pi$
$509$			638.832i			1.25507i	−0.778587	+	0.627537i	$0.784063\pi$
$510$			21.6230i			0.0423981i
$511$	−403.259	−	190.959i	−0.789156	−	0.373696i
$512$	271.227			0.529740
$513$	−16.4364			−0.0320398
$514$			139.006i			0.270439i
$515$	−70.9649			−0.137796
$516$		−	65.5830i		−	0.127099i
$517$		−	500.432i		−	0.967954i
$518$	−303.654	+	641.244i	−0.586205	+	1.23792i
$519$	−32.2439			−0.0621269
$520$	−119.908			−0.230591
$521$		−	586.434i		−	1.12559i	−0.826595	−	0.562797i	$-0.809725\pi$
$521$		−	586.434i		−	1.12559i	0.826595	−	0.562797i	$-0.190275\pi$
$522$	−93.1542			−0.178456
$523$			926.562i			1.77163i	0.464040	+	0.885814i	$0.346400\pi$
$523$			926.562i			1.77163i	−0.464040	+	0.885814i	$0.653600\pi$
$524$		−	191.577i		−	0.365604i
$525$	−267.318	−	126.585i	−0.509176	−	0.241115i
$526$	836.936			1.59113
$527$	403.267			0.765212
$528$			252.829i			0.478844i
$529$	23.0000			0.0434783
$530$		−	31.7995i		−	0.0599991i
$531$			93.7124i			0.176483i
$532$	16.8480	+	7.97819i	0.0316692	+	0.0149966i
$533$	75.2354			0.141155
$534$	444.033			0.831523
$535$			53.1022i			0.0992564i
$536$	372.371			0.694723
$537$			586.229i			1.09167i
$538$		−	207.007i		−	0.384772i
$539$	−242.908	−	296.551i	−0.450663	−	0.550187i
$540$	−3.40248			−0.00630090
$541$	−579.609			−1.07137			−0.535683	−	0.844419i	$-0.679946\pi$
$541$	−579.609			−1.07137			−0.535683	+	0.844419i	$0.679946\pi$
$542$			456.471i			0.842198i
$543$	384.967			0.708964
$544$		−	96.7290i		−	0.177811i
$545$		−	91.6542i		−	0.168173i
$546$	−253.306	+	534.921i	−0.463930	+	0.979709i
$547$	−483.605			−0.884104			−0.442052	−	0.896990i	$-0.645749\pi$
$547$	−483.605			−0.884104			−0.442052	+	0.896990i	$0.645749\pi$
$548$	71.9428			0.131282
$549$			4.91835i			0.00895875i
$550$	−419.946			−0.763537
$551$		−	44.6374i		−	0.0810117i
$552$			57.7243i			0.104573i
$553$	333.016	−	703.249i	0.602198	−	1.27170i
$554$	−216.860			−0.391443
$555$	62.0537			0.111808
$556$			108.401i			0.194966i
$557$	−1044.94			−1.87602			−0.938008	−	0.346614i	$-0.887331\pi$
$557$	−1044.94			−1.87602			−0.938008	+	0.346614i	$0.887331\pi$
$558$			364.946i			0.654025i
$559$			997.766i			1.78491i
$560$	−91.8131	−	43.4771i	−0.163952	−	0.0776376i
$561$	−98.8409			−0.176187
$562$	−602.899			−1.07277
$563$		−	681.206i		−	1.20996i	−0.796242	−	0.604979i	$-0.793182\pi$
$563$		−	681.206i		−	1.20996i	0.796242	−	0.604979i	$-0.206818\pi$
$564$	−93.2783			−0.165387
$565$		−	35.2024i		−	0.0623052i
$566$			637.559i			1.12643i
$567$	26.9627	−	56.9387i	0.0475532	−	0.100421i
$568$	876.212			1.54263
$569$	453.781			0.797506			0.398753	−	0.917058i	$-0.369443\pi$
$569$	453.781			0.797506			0.398753	+	0.917058i	$0.369443\pi$
$570$		−	9.37670i		−	0.0164503i
$571$	277.828			0.486563			0.243282	−	0.969956i	$-0.421776\pi$
$571$	277.828			0.486563			0.243282	+	0.969956i	$0.421776\pi$
$572$			146.116i			0.255448i
$573$			334.200i			0.583245i
$574$	47.2105	+	22.3560i	0.0822483	+	0.0389478i
$575$	−116.995			−0.203469
$576$	−136.368			−0.236750
$577$			672.522i			1.16555i	0.812634	+	0.582775i	$0.198033\pi$
$577$			672.522i			1.16555i	−0.812634	+	0.582775i	$0.801967\pi$
$578$	−518.842			−0.897650
$579$		−	73.4483i		−	0.126854i
$580$		−	9.24034i		−	0.0159316i
$581$	651.361	+	308.445i	1.12110	+	0.530886i
$582$	76.0450			0.130662
$583$	145.358			0.249328
$584$		−	442.948i		−	0.758473i
$585$	51.7647			0.0884867
$586$		−	231.326i		−	0.394755i
$587$		−	207.592i		−	0.353648i	−0.984242	−	0.176824i	$-0.943418\pi$
$587$		−	207.592i		−	0.353648i	0.984242	−	0.176824i	$-0.0565824\pi$
$588$	−55.2757	+	45.2769i	−0.0940063	+	0.0770015i
$589$	−174.874			−0.296900
$590$	−53.4613			−0.0906124
$591$		−	601.070i		−	1.01704i
$592$	−859.478			−1.45182
$593$			661.484i			1.11549i	0.830013	+	0.557743i	$0.188333\pi$
$593$			661.484i			1.11549i	−0.830013	+	0.557743i	$0.811667\pi$
$594$		−	89.4485i		−	0.150587i
$595$	16.9969	−	35.8933i	0.0285662	−	0.0603249i
$596$	217.823			0.365475
$597$	−25.3365			−0.0424397
$598$			234.114i			0.391496i
$599$	−289.111			−0.482655			−0.241328	−	0.970444i	$-0.577583\pi$
$599$	−289.111			−0.482655			−0.241328	+	0.970444i	$0.577583\pi$
$600$		−	293.627i		−	0.489379i
$601$		−	433.438i		−	0.721194i	−0.932722	−	0.360597i	$-0.882573\pi$
$601$		−	433.438i		−	0.721194i	0.932722	−	0.360597i	$-0.117427\pi$
$602$	−296.483	+	626.101i	−0.492497	+	1.04004i
$603$	−160.755			−0.266591
$604$	50.6018			0.0837778
$605$		−	46.5095i		−	0.0768752i
$606$	317.259			0.523529
$607$			1023.64i			1.68640i	0.537602	+	0.843199i	$0.319330\pi$
$607$			1023.64i			1.68640i	−0.537602	+	0.843199i	$0.680670\pi$
$608$			41.9459i			0.0689900i
$609$	154.632	+	73.2242i	0.253911	+	0.120237i
$610$	−2.80583			−0.00459973
$611$	1419.12			2.32261
$612$			18.4235i			0.0301038i
$613$	757.177			1.23520			0.617599	−	0.786493i	$-0.288105\pi$
$613$	757.177			1.23520			0.617599	+	0.786493i	$0.288105\pi$
$614$		−	1067.22i		−	1.73814i
$615$		−	4.56859i		−	0.00742861i
$616$	162.869	−	343.940i	0.264398	−	0.558344i
$617$	−521.225			−0.844774			−0.422387	−	0.906416i	$-0.638808\pi$
$617$	−521.225			−0.844774			−0.422387	+	0.906416i	$0.638808\pi$
$618$	−347.741			−0.562688
$619$			35.0723i			0.0566597i	0.999599	+	0.0283298i	$0.00901888\pi$
$619$			35.0723i			0.0566597i	−0.999599	+	0.0283298i	$0.990981\pi$
$620$	−36.2005			−0.0583878
$621$		−	24.9199i		−	0.0401286i
$622$		−	190.629i		−	0.306477i
$623$	−737.076	−	349.034i	−1.18311	−	0.560247i
$624$	−716.969			−1.14899
$625$	579.995			0.927993
$626$			1235.32i			1.97336i
$627$	42.8617			0.0683600
$628$			156.843i			0.249750i
$629$		−	336.003i		−	0.534186i
$630$	32.4825	+	15.3817i	0.0515596	+	0.0244155i
$631$	−65.9432			−0.104506			−0.0522530	−	0.998634i	$-0.516640\pi$
$631$	−65.9432			−0.104506			−0.0522530	+	0.998634i	$0.516640\pi$
$632$	772.464			1.22225
$633$		−	441.215i		−	0.697022i
$634$	−29.5898			−0.0466717
$635$		−	64.0719i		−	0.100901i
$636$		−	27.0942i		−	0.0426009i
$637$	840.953	−	688.833i	1.32018	−	1.08137i
$638$	242.921			0.380754
$639$	−378.265			−0.591964
$640$		−	119.051i		−	0.186017i
$641$	−983.246			−1.53393			−0.766963	−	0.641692i	$-0.778233\pi$
$641$	−983.246			−1.53393			−0.766963	+	0.641692i	$0.778233\pi$
$642$			260.211i			0.405312i
$643$		−	238.129i		−	0.370341i	−0.982706	−	0.185171i	$-0.940716\pi$
$643$		−	238.129i		−	0.370341i	0.982706	−	0.185171i	$-0.0592837\pi$
$644$	−12.0960	+	25.5439i	−0.0187827	+	0.0396644i
$645$	60.5883			0.0939353
$646$	−50.7722			−0.0785947
$647$			459.062i			0.709524i	0.934957	+	0.354762i	$0.115438\pi$
$647$			459.062i			0.709524i	−0.934957	+	0.354762i	$0.884562\pi$
$648$	62.5427			0.0965165
$649$		−	244.376i		−	0.376543i
$650$		−	1190.87i		−	1.83211i
$651$	286.867	−	605.795i	0.440656	−	0.930560i
$652$	−121.019			−0.185612
$653$	−228.323			−0.349652			−0.174826	−	0.984599i	$-0.555936\pi$
$653$	−228.323			−0.349652			−0.174826	+	0.984599i	$0.555936\pi$
$654$		−	449.123i		−	0.686732i
$655$	176.987			0.270209
$656$			63.2775i			0.0964597i
$657$			191.223i			0.291055i
$658$	890.501	+	421.687i	1.35334	+	0.640861i
$659$	−340.682			−0.516968			−0.258484	−	0.966016i	$-0.583223\pi$
$659$	−340.682			−0.516968			−0.258484	+	0.966016i	$0.583223\pi$
$660$	8.87275			0.0134436
$661$		−	311.781i		−	0.471680i	−0.971792	−	0.235840i	$-0.924216\pi$
$661$		−	311.781i		−	0.471680i	0.971792	−	0.235840i	$-0.0757842\pi$
$662$	−466.308			−0.704393
$663$		−	280.291i		−	0.422762i
$664$			715.469i			1.07751i
$665$	−7.37059	+	15.5649i	−0.0110836	+	0.0234059i
$666$	304.074			0.456568
$667$	67.6764			0.101464
$668$		−	21.4810i		−	0.0321572i
$669$	88.5595			0.132376
$670$		−	91.7077i		−	0.136877i
$671$		−	12.8257i		−	0.0191143i
$672$	−145.308	−	68.8090i	−0.216232	−	0.102394i
$673$	−697.932			−1.03705			−0.518523	−	0.855064i	$-0.673518\pi$
$673$	−697.932			−1.03705			−0.518523	+	0.855064i	$0.673518\pi$
$674$	208.290			0.309036
$675$			126.760i			0.187793i
$676$	−272.073			−0.402475
$677$		−	308.158i		−	0.455182i	−0.973757	−	0.227591i	$-0.926915\pi$
$677$		−	308.158i		−	0.455182i	0.973757	−	0.227591i	$-0.0730850\pi$
$678$		−	172.498i		−	0.254422i
$679$	−126.231	−	59.7755i	−0.185908	−	0.0880345i
$680$	39.4260			0.0579794
$681$	697.561			1.02432
$682$		−	951.680i		−	1.39542i
$683$	177.008			0.259162			0.129581	−	0.991569i	$-0.458637\pi$
$683$	177.008			0.259162			0.129581	+	0.991569i	$0.458637\pi$
$684$		−	7.98923i		−	0.0116802i
$685$			66.4638i			0.0970274i
$686$	732.386	−	182.358i	1.06762	−	0.265829i
$687$	−88.1524			−0.128315
$688$	−839.181			−1.21974
$689$			412.205i			0.598266i
$690$	14.2164			0.0206034
$691$		−	839.057i		−	1.21426i	−0.794601	−	0.607132i	$-0.792320\pi$
$691$		−	839.057i		−	1.21426i	0.794601	−	0.607132i	$-0.207680\pi$
$692$		−	15.6727i		−	0.0226485i
$693$	−70.3113	+	148.481i	−0.101459	+	0.214258i
$694$	−401.258			−0.578182
$695$	−100.146			−0.144095
$696$			169.851i			0.244039i
$697$	−24.7377			−0.0354916
$698$			832.679i			1.19295i
$699$			324.128i			0.463703i
$700$	61.5291	−	129.935i	0.0878987	−	0.185621i
$701$	1087.91			1.55194			0.775970	−	0.630769i	$-0.217261\pi$
$701$	1087.91			1.55194			0.775970	+	0.630769i	$0.217261\pi$
$702$	253.657			0.361334
$703$			145.706i			0.207263i
$704$	355.611			0.505130
$705$		−	86.1744i		−	0.122233i
$706$		−	424.625i		−	0.601452i
$707$	−526.635	−	249.382i	−0.744887	−	0.352733i
$708$	−45.5507			−0.0643371
$709$	−423.671			−0.597561			−0.298780	−	0.954322i	$-0.596580\pi$
$709$	−423.671			−0.597561			−0.298780	+	0.954322i	$0.596580\pi$
$710$		−	215.794i		−	0.303935i
$711$	−333.476			−0.469025
$712$		−	809.620i		−	1.13711i
$713$		−	265.133i		−	0.371855i
$714$	83.2878	−	175.884i	0.116650	−	0.246336i
$715$	−134.988			−0.188795
$716$	−284.948			−0.397972
$717$		−	527.843i		−	0.736183i
$718$	−186.196			−0.259326
$719$		−	265.334i		−	0.369032i	−0.982830	−	0.184516i	$-0.940928\pi$
$719$		−	265.334i		−	0.369032i	0.982830	−	0.184516i	$-0.0590717\pi$
$720$			43.5372i			0.0604684i
$721$	577.235	+	273.343i	0.800603	+	0.379117i
$722$	−772.338			−1.06972
$723$	−382.332			−0.528813
$724$			187.121i			0.258454i
$725$	−344.251			−0.474829
$726$		−	227.905i		−	0.313919i
$727$			275.068i			0.378361i	0.981942	+	0.189180i	$0.0605831\pi$
$727$			275.068i			0.378361i	−0.981942	+	0.189180i	$0.939417\pi$
$728$	975.339	+	461.861i	1.33975	+	0.634424i
$729$	−27.0000			−0.0370370
$730$	−109.089			−0.149438
$731$		−	328.069i		−	0.448794i
$732$	−2.39066			−0.00326593
$733$			93.2472i			0.127213i	0.997975	+	0.0636066i	$0.0202603\pi$
$733$			93.2472i			0.127213i	−0.997975	+	0.0636066i	$0.979740\pi$
$734$			621.075i			0.846151i
$735$	−41.8287	−	51.0660i	−0.0569098	−	0.0694776i
$736$	−63.5957			−0.0864072
$737$	419.204			0.568798
$738$		−	22.3870i		−	0.0303346i
$739$	−660.766			−0.894135			−0.447068	−	0.894500i	$-0.647532\pi$
$739$	−660.766			−0.894135			−0.447068	+	0.894500i	$0.647532\pi$
$740$			30.1624i			0.0407599i
$741$			121.547i			0.164030i
$742$	−122.486	+	258.660i	−0.165075	+	0.348599i
$743$	−494.691			−0.665802			−0.332901	−	0.942962i	$-0.608028\pi$
$743$	−494.691			−0.665802			−0.332901	+	0.942962i	$0.608028\pi$
$744$	665.418			0.894379
$745$			201.234i			0.270113i
$746$	1273.20			1.70670
$747$		−	308.871i		−	0.413483i
$748$		−	48.0435i		−	0.0642292i
$749$	204.539	−	431.938i	0.273083	−	0.576686i
$750$	−146.423			−0.195230
$751$	−947.602			−1.26179			−0.630894	−	0.775869i	$-0.717312\pi$
$751$	−947.602			−1.26179			−0.630894	+	0.775869i	$0.717312\pi$
$752$			1193.56i			1.58718i
$753$	298.029			0.395789
$754$			688.871i			0.913622i
$755$			46.7480i			0.0619179i
$756$	27.6761	+	13.1057i	0.0366086	+	0.0173356i
$757$	134.619			0.177832			0.0889162	−	0.996039i	$-0.471660\pi$
$757$	134.619			0.177832			0.0889162	+	0.996039i	$0.471660\pi$
$758$	−1384.16			−1.82606
$759$			64.9842i			0.0856182i
$760$	−17.0968			−0.0224958
$761$			530.540i			0.697162i	0.937279	+	0.348581i	$0.113336\pi$
$761$			530.540i			0.697162i	−0.937279	+	0.348581i	$0.886664\pi$
$762$		−	313.964i		−	0.412026i
$763$	−353.034	+	745.524i	−0.462693	+	0.977095i
$764$	−162.444			−0.212623
$765$	−17.0204			−0.0222489
$766$		−	290.742i		−	0.379559i
$767$	692.999			0.903518
$768$		−	268.443i		−	0.349535i
$769$			1425.02i			1.85308i	0.376195	+	0.926540i	$0.377232\pi$
$769$			1425.02i			1.85308i	−0.376195	+	0.926540i	$0.622768\pi$
$770$	−84.7056	−	40.1114i	−0.110007	−	0.0520927i
$771$	−109.417			−0.141916
$772$	35.7009			0.0462447
$773$		−	163.758i		−	0.211847i	−0.994374	−	0.105924i	$-0.966220\pi$
$773$		−	163.758i		−	0.211847i	0.994374	−	0.105924i	$-0.0337799\pi$
$774$	296.894			0.383584
$775$			1348.66i			1.74020i
$776$		−	138.655i		−	0.178680i
$777$	−504.750	−	239.019i	−0.649614	−	0.307618i
$778$	601.520			0.773162
$779$	10.7273			0.0137706
$780$			25.1612i			0.0322579i
$781$	986.412			1.26301
$782$		−	76.9776i		−	0.0984368i
$783$		−	73.3256i		−	0.0936470i
$784$	579.350	+	707.293i	0.738967	+	0.902159i
$785$	−144.898			−0.184583
$786$	867.267			1.10339
$787$		−	1242.14i		−	1.57832i	−0.614189	−	0.789159i	$-0.710517\pi$
$787$		−	1242.14i		−	1.57832i	0.614189	−	0.789159i	$-0.289483\pi$
$788$	292.161			0.370763
$789$			658.787i			0.834965i
$790$		−	190.243i		−	0.240813i
$791$	−135.593	+	286.340i	−0.171420	+	0.361997i
$792$	−163.094			−0.205927
$793$	36.3710			0.0458650
$794$			353.448i			0.445148i
$795$	25.0307			0.0314852
$796$		−	12.3153i		−	0.0154715i
$797$		−	434.047i		−	0.544601i	−0.962212	−	0.272300i	$-0.912216\pi$
$797$		−	434.047i		−	0.544601i	0.962212	−	0.272300i	$-0.0877845\pi$
$798$	−36.1172	+	76.2709i	−0.0452597	+	0.0955776i
$799$	−466.610			−0.583993
$800$	323.494			0.404367
$801$			349.517i			0.436351i
$802$	−947.115			−1.18094
$803$		−	498.657i		−	0.620993i
$804$		−	78.1377i		−	0.0971863i
$805$	−23.5985	−	11.1748i	−0.0293149	−	0.0138818i
$806$	2698.76			3.34834
$807$	162.944			0.201913
$808$		−	578.468i		−	0.715926i
$809$	−618.510			−0.764536			−0.382268	−	0.924052i	$-0.624857\pi$
$809$	−618.510			−0.764536			−0.382268	+	0.924052i	$0.624857\pi$
$810$		−	15.4030i		−	0.0190161i
$811$		−	366.676i		−	0.452128i	−0.974112	−	0.226064i	$-0.927414\pi$
$811$		−	366.676i		−	0.452128i	0.974112	−	0.226064i	$-0.0725858\pi$
$812$	−35.5920	+	75.1617i	−0.0438325	+	0.0925637i
$813$	−359.308			−0.441953
$814$	−792.943			−0.974132
$815$		−	111.803i		−	0.137181i
$816$	235.742			0.288899
$817$			142.265i			0.174131i
$818$		−	486.728i		−	0.595022i
$819$	−421.059	−	199.388i	−0.514113	−	0.243453i
$820$	2.22065			0.00270811
$821$	860.107			1.04763			0.523817	−	0.851831i	$-0.324508\pi$
$821$	860.107			1.04763			0.523817	+	0.851831i	$0.324508\pi$
$822$			325.685i			0.396210i
$823$	725.939			0.882065			0.441032	−	0.897491i	$-0.354612\pi$
$823$	725.939			0.882065			0.441032	+	0.897491i	$0.354612\pi$
$824$			634.048i			0.769475i
$825$		−	330.557i		−	0.400675i
$826$	434.859	+	205.923i	0.526464	+	0.249301i
$827$	−1376.26			−1.66415			−0.832077	−	0.554660i	$-0.812849\pi$
$827$	−1376.26			−1.66415			−0.832077	+	0.554660i	$0.812849\pi$
$828$	12.1128			0.0146289
$829$		−	687.794i		−	0.829668i	−0.909897	−	0.414834i	$-0.863840\pi$
$829$		−	687.794i		−	0.829668i	0.909897	−	0.414834i	$-0.136160\pi$
$830$	176.206			0.212296
$831$		−	170.699i		−	0.205414i
$832$			1008.44i			1.21206i
$833$	−276.508	+	226.491i	−0.331943	+	0.271898i
$834$	−490.732			−0.588408
$835$	19.8451			0.0237666
$836$			20.8337i			0.0249207i
$837$	−287.264			−0.343207
$838$			156.032i			0.186196i
$839$		−	73.8970i		−	0.0880774i	−0.999030	−	0.0440387i	$-0.985978\pi$
$839$		−	73.8970i		−	0.0880774i	0.999030	−	0.0440387i	$-0.0140225\pi$
$840$	28.0460	−	59.2265i	0.0333881	−	0.0705077i
$841$	−641.865			−0.763217
$842$	−1254.30			−1.48966
$843$		−	474.567i		−	0.562950i
$844$	214.461			0.254100
$845$		−	251.353i		−	0.297459i
$846$		−	422.270i		−	0.499138i
$847$	−179.146	+	378.312i	−0.211506	+	0.446650i
$848$	−346.689			−0.408832
$849$	−501.849			−0.591106
$850$			391.563i			0.460663i
$851$	−220.910			−0.259588
$852$		−	183.863i		−	0.215801i
$853$		−	1423.23i		−	1.66850i	−0.551384	−	0.834252i	$-0.685900\pi$
$853$		−	1423.23i		−	1.66850i	0.551384	−	0.834252i	$-0.314100\pi$
$854$	22.8229	+	10.8075i	0.0267247	+	0.0126552i
$855$	7.38079			0.00863250
$856$	474.450			0.554264
$857$			1474.74i			1.72082i	0.509606	+	0.860408i	$0.329791\pi$
$857$			1474.74i			1.72082i	−0.509606	+	0.860408i	$0.670209\pi$
$858$	−661.467			−0.770940
$859$		−	934.346i		−	1.08771i	−0.839178	−	0.543857i	$-0.816964\pi$
$859$		−	934.346i		−	1.08771i	0.839178	−	0.543857i	$-0.183036\pi$
$860$			29.4501i			0.0342443i
$861$	−17.5973	+	37.1614i	−0.0204383	+	0.0431607i
$862$	1517.99			1.76101
$863$	−987.187			−1.14390			−0.571951	−	0.820288i	$-0.693813\pi$
$863$	−987.187			−1.14390			−0.571951	+	0.820288i	$0.693813\pi$
$864$			68.9042i			0.0797503i
$865$	14.4791			0.0167389
$866$		−	580.669i		−	0.670518i
$867$		−	408.402i		−	0.471052i
$868$	294.458	+	139.437i	0.339237	+	0.160642i
$869$	869.616			1.00071
$870$	41.8310			0.0480816
$871$			1188.77i			1.36484i
$872$	−818.900			−0.939105
$873$			59.8582i			0.0685661i
$874$			33.3808i			0.0381932i
$875$	243.055	+	115.096i	0.277777	+	0.131538i
$876$	−92.9475			−0.106104
$877$	1025.07			1.16884			0.584418	−	0.811453i	$-0.301323\pi$
$877$	1025.07			1.16884			0.584418	+	0.811453i	$0.301323\pi$
$878$		−	1874.31i		−	2.13474i
$879$	182.087			0.207152
$880$		−	113.533i		−	0.129015i
$881$		−	1512.46i		−	1.71675i	−0.513024	−	0.858374i	$-0.671475\pi$
$881$		−	1512.46i		−	1.71675i	0.513024	−	0.858374i	$-0.328525\pi$
$882$	−204.968	−	250.233i	−0.232390	−	0.283711i
$883$	637.637			0.722126			0.361063	−	0.932541i	$-0.382414\pi$
$883$	637.637			0.722126			0.361063	+	0.932541i	$0.382414\pi$
$884$	136.241			0.154119
$885$		−	42.0816i		−	0.0475499i
$886$	1460.76			1.64871
$887$			174.108i			0.196288i	0.995172	+	0.0981442i	$0.0312907\pi$
$887$			174.108i			0.196288i	−0.995172	+	0.0981442i	$0.968709\pi$
$888$		−	554.429i		−	0.624357i
$889$	−246.793	+	521.167i	−0.277607	+	0.586239i
$890$	−199.393			−0.224038
$891$	70.4086			0.0790220
$892$			43.0460i			0.0482578i
$893$	202.343			0.226587
$894$			986.084i			1.10300i
$895$		−	263.247i		−	0.294130i
$896$	−458.562	+	968.372i	−0.511788	+	1.08077i
$897$	−184.281			−0.205442
$898$	176.296			0.196320
$899$		−	780.142i		−	0.867788i
$900$	−61.6143			−0.0684603
$901$		−	135.534i		−	0.150427i
$902$			58.3791i			0.0647218i
$903$	−492.831	−	233.374i	−0.545770	−	0.258443i
$904$	−314.522			−0.347922
$905$	−172.870			−0.191016
$906$			229.074i			0.252841i
$907$	559.950			0.617365			0.308682	−	0.951165i	$-0.400112\pi$
$907$	559.950			0.617365			0.308682	+	0.951165i	$0.400112\pi$
$908$			339.063i			0.373417i
$909$			249.728i			0.274728i
$910$	113.747	−	240.207i	0.124997	−	0.263963i
$911$	1207.46			1.32542			0.662709	−	0.748877i	$-0.269407\pi$
$911$	1207.46			1.32542			0.662709	+	0.748877i	$0.269407\pi$
$912$	−102.228			−0.112092
$913$			805.452i			0.882204i
$914$	1256.59			1.37482
$915$		−	2.20859i		−	0.00241376i
$916$		−	42.8481i		−	0.0467775i
$917$	−1439.62	−	681.718i	−1.56993	−	0.743422i
$918$	−83.4031			−0.0908530
$919$	8.53505			0.00928732			0.00464366	−	0.999989i	$-0.498522\pi$
$919$	8.53505			0.00928732			0.00464366	+	0.999989i	$0.498522\pi$
$920$		−	25.9211i		−	0.0281752i
$921$	840.050			0.912106
$922$		−	489.092i		−	0.530469i
$923$			2797.25i			3.03061i
$924$	−72.1717	−	34.1761i	−0.0781079	−	0.0369871i
$925$	1123.71			1.21482
$926$	1622.92			1.75261
$927$		−	273.722i		−	0.295277i
$928$	−187.127			−0.201646
$929$			392.618i			0.422625i	0.977419	+	0.211312i	$0.0677737\pi$
$929$			392.618i			0.422625i	−0.977419	+	0.211312i	$0.932226\pi$
$930$		−	163.879i		−	0.176214i
$931$	119.906	−	98.2162i	0.128793	−	0.105495i
$932$	−157.549			−0.169043
$933$	150.052			0.160827
$934$		−	1461.50i		−	1.56477i
$935$	44.3846			0.0474701
$936$		−	462.500i		−	0.494124i
$937$		−	355.556i		−	0.379462i	−0.981836	−	0.189731i	$-0.939238\pi$
$937$		−	355.556i		−	0.379462i	0.981836	−	0.189731i	$-0.0607616\pi$
$938$	−353.240	+	745.958i	−0.376589	+	0.795265i
$939$	−972.372			−1.03554
$940$	41.8867			0.0445603
$941$		−	1204.31i		−	1.27982i	−0.768451	−	0.639909i	$-0.778972\pi$
$941$		−	1204.31i		−	1.27982i	0.768451	−	0.639909i	$-0.221028\pi$
$942$	−710.026			−0.753743
$943$			16.2641i			0.0172472i
$944$			582.854i			0.617430i
$945$	−12.1076	+	25.5684i	−0.0128123	+	0.0270565i
$946$	−774.218			−0.818412
$947$	823.952			0.870065			0.435033	−	0.900415i	$-0.356737\pi$
$947$	823.952			0.870065			0.435033	+	0.900415i	$0.356737\pi$
$948$		−	162.092i		−	0.170984i
$949$	1414.08			1.49008
$950$		−	169.799i		−	0.178736i
$951$		−	23.2914i		−	0.0244915i
$952$	−320.695	−	151.861i	−0.336864	−	0.159518i
$953$	694.447			0.728696			0.364348	−	0.931263i	$-0.381292\pi$
$953$	694.447			0.728696			0.364348	+	0.931263i	$0.381292\pi$
$954$	122.655			0.128569
$955$		−	150.073i		−	0.157144i
$956$	256.568			0.268377
$957$			191.213i			0.199805i
$958$			1441.36i			1.50455i
$959$	256.006	−	540.622i	0.266951	−	0.563736i
$960$	61.2363			0.0637878
$961$	−2095.33			−2.18036
$962$		−	2248.61i		−	2.33744i
$963$	−204.823			−0.212692
$964$		−	185.839i		−	0.192780i
$965$			32.9820i			0.0341783i
$966$	−115.637	−	54.7587i	−0.119707	−	0.0566860i
$967$	626.335			0.647709			0.323855	−	0.946107i	$-0.395021\pi$
$967$	626.335			0.647709			0.323855	+	0.946107i	$0.395021\pi$
$968$	−415.547			−0.429284
$969$		−	39.9649i		−	0.0412435i
$970$	−34.1481			−0.0352042
$971$			934.916i			0.962839i	0.876490	+	0.481419i	$0.159879\pi$
$971$			934.916i			0.962839i	−0.876490	+	0.481419i	$0.840121\pi$
$972$		−	13.1239i		−	0.0135019i
$973$	814.594	+	385.742i	0.837199	+	0.396446i
$974$	−691.254			−0.709707
$975$	937.387			0.961423
$976$			30.5902i			0.0313424i
$977$	1127.49			1.15403			0.577017	−	0.816732i	$-0.304217\pi$
$977$	1127.49			1.15403			0.577017	+	0.816732i	$0.304217\pi$
$978$		−	547.854i		−	0.560178i
$979$		−	911.445i		−	0.930996i
$980$	24.8216	−	20.3316i	0.0253282	−	0.0207466i
$981$	353.523			0.360370
$982$	843.689			0.859154
$983$			1214.98i			1.23600i	0.786179	+	0.617998i	$0.212056\pi$
$983$			1214.98i			1.23600i	−0.786179	+	0.617998i	$0.787944\pi$
$984$	−40.8189			−0.0414826
$985$			269.911i			0.274021i
$986$		−	226.503i		−	0.229719i
$987$	−331.927	+	700.950i	−0.336299	+	0.710183i
$988$	−59.0800			−0.0597975
$989$	−215.693			−0.218092
$990$			40.1669i			0.0405726i
$991$	514.290			0.518960			0.259480	−	0.965748i	$-0.416449\pi$
$991$	514.290			0.518960			0.259480	+	0.965748i	$0.416449\pi$
$992$			733.101i			0.739013i
$993$		−	367.050i		−	0.369638i
$994$	−831.196	+	1755.29i	−0.836213	+	1.76588i
$995$	11.3774			0.0114345
$996$	150.133			0.150736
$997$		−	1296.62i		−	1.30052i	−0.759713	−	0.650259i	$-0.774660\pi$
$997$		−	1296.62i		−	1.30052i	0.759713	−	0.650259i	$-0.225340\pi$
$998$	−146.382			−0.146675
$999$			239.350i			0.239589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.g.a.139.15	✓	60
7.6	odd	2	inner	483.3.g.a.139.16	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.g.a.139.15	✓	60	1.1	even	1	trivial
483.3.g.a.139.16	yes	60	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.20043 q^{2} -1.73205i q^{3} +0.841896 q^{4} +0.777779i q^{5} +3.81126i q^{6} +(2.99585 - 6.32652i) q^{7} +6.94919 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-2.20043 q^{2} -1.73205i q^{3} +0.841896 q^{4} +0.777779i q^{5} +3.81126i q^{6} +(2.99585 - 6.32652i) q^{7} +6.94919 q^{8} -3.00000 q^{9} -1.71145i q^{10} +7.82318 q^{11} -1.45821i q^{12} +22.1848i q^{13} +(-6.59217 + 13.9211i) q^{14} +1.34715 q^{15} -18.6588 q^{16} -7.29445i q^{17} +6.60129 q^{18} +3.16319i q^{19} +0.654808i q^{20} +(-10.9579 - 5.18897i) q^{21} -17.2144 q^{22} -4.79583 q^{23} -12.0364i q^{24} +24.3951 q^{25} -48.8162i q^{26} +5.19615i q^{27} +(2.52220 - 5.32627i) q^{28} -14.1115 q^{29} -2.96431 q^{30} +55.2840i q^{31} +13.2606 q^{32} -13.5501i q^{33} +16.0509i q^{34} +(4.92063 + 2.33011i) q^{35} -2.52569 q^{36} +46.0629 q^{37} -6.96039i q^{38} +38.4253 q^{39} +5.40493i q^{40} -3.39130i q^{41} +(24.1120 + 11.4180i) q^{42} +44.9751 q^{43} +6.58630 q^{44} -2.33334i q^{45} +10.5529 q^{46} -63.9679i q^{47} +32.3180i q^{48} +(-31.0497 - 37.9067i) q^{49} -53.6796 q^{50} -12.6344 q^{51} +18.6773i q^{52} +18.5805 q^{53} -11.4338i q^{54} +6.08470i q^{55} +(20.8188 - 43.9642i) q^{56} +5.47881 q^{57} +31.0514 q^{58} -31.2375i q^{59} +1.13416 q^{60} -1.63945i q^{61} -121.649i q^{62} +(-8.98756 + 18.9796i) q^{63} +45.4561 q^{64} -17.2549 q^{65} +29.8162i q^{66} +53.5848 q^{67} -6.14117i q^{68} +8.30662i q^{69} +(-10.8275 - 5.12725i) q^{70} +126.088 q^{71} -20.8476 q^{72} -63.7410i q^{73} -101.358 q^{74} -42.2535i q^{75} +2.66308i q^{76} +(23.4371 - 49.4935i) q^{77} -84.5522 q^{78} +111.159 q^{79} -14.5124i q^{80} +9.00000 q^{81} +7.46232i q^{82} +102.957i q^{83} +(-9.22537 - 4.36857i) q^{84} +5.67347 q^{85} -98.9646 q^{86} +24.4419i q^{87} +54.3648 q^{88} -116.506i q^{89} +5.13434i q^{90} +(140.353 + 66.4625i) q^{91} -4.03759 q^{92} +95.7548 q^{93} +140.757i q^{94} -2.46026 q^{95} -22.9681i q^{96} -19.9527i q^{97} +(68.3228 + 83.4110i) q^{98} -23.4695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Introduction

L-functions

Modular forms

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