LMFDB - Embedded newform 287.3.d.d.286.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(286,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("287.286");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.d (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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			286.1
Character	$\chi$	$=$	287.286
Dual form			287.3.d.d.286.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.60835 q^{2} -0.377109 q^{3} +9.02020 q^{4} -7.18702i q^{5} +1.36074 q^{6} +(-2.11657 - 6.67234i) q^{7} -18.1146 q^{8} -8.85779 q^{9} +O(q^{10})$	\(q-3.60835 q^{2} -0.377109 q^{3} +9.02020 q^{4} -7.18702i q^{5} +1.36074 q^{6} +(-2.11657 - 6.67234i) q^{7} -18.1146 q^{8} -8.85779 q^{9} +25.9333i q^{10} -13.5626i q^{11} -3.40160 q^{12} -11.7379 q^{13} +(7.63734 + 24.0761i) q^{14} +2.71029i q^{15} +29.2832 q^{16} +31.2229 q^{17} +31.9620 q^{18} -15.4496 q^{19} -64.8283i q^{20} +(0.798180 + 2.51620i) q^{21} +48.9386i q^{22} +12.7820 q^{23} +6.83120 q^{24} -26.6532 q^{25} +42.3544 q^{26} +6.73434 q^{27} +(-19.0919 - 60.1858i) q^{28} -8.50181i q^{29} -9.77969i q^{30} +39.3288i q^{31} -33.2055 q^{32} +5.11458i q^{33} -112.663 q^{34} +(-47.9542 + 15.2119i) q^{35} -79.8990 q^{36} -5.11022 q^{37} +55.7475 q^{38} +4.42646 q^{39} +130.190i q^{40} +(-30.1346 + 27.8012i) q^{41} +(-2.88011 - 9.07934i) q^{42} +21.8570 q^{43} -122.337i q^{44} +63.6611i q^{45} -46.1218 q^{46} -34.3832 q^{47} -11.0430 q^{48} +(-40.0402 + 28.2450i) q^{49} +96.1742 q^{50} -11.7745 q^{51} -105.878 q^{52} -41.0702i q^{53} -24.2999 q^{54} -97.4745 q^{55} +(38.3410 + 120.867i) q^{56} +5.82619 q^{57} +30.6775i q^{58} +27.2473i q^{59} +24.4474i q^{60} +77.6635i q^{61} -141.912i q^{62} +(18.7482 + 59.1022i) q^{63} +2.68436 q^{64} +84.3603i q^{65} -18.4552i q^{66} -87.5529i q^{67} +281.637 q^{68} -4.82020 q^{69} +(173.036 - 54.8897i) q^{70} -60.1512i q^{71} +160.456 q^{72} -89.0139i q^{73} +18.4395 q^{74} +10.0512 q^{75} -139.358 q^{76} +(-90.4941 + 28.7062i) q^{77} -15.9722 q^{78} +56.8520i q^{79} -210.459i q^{80} +77.1805 q^{81} +(108.736 - 100.317i) q^{82} -52.4907i q^{83} +(7.19974 + 22.6966i) q^{84} -224.400i q^{85} -78.8679 q^{86} +3.20611i q^{87} +245.681i q^{88} -78.5211 q^{89} -229.712i q^{90} +(24.8441 + 78.3191i) q^{91} +115.296 q^{92} -14.8313i q^{93} +124.067 q^{94} +111.036i q^{95} +12.5221 q^{96} +71.6567 q^{97} +(144.479 - 101.918i) q^{98} +120.134i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9	$ 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9} - 92 q^{16} - 48 q^{18} - 72 q^{21} + 140 q^{23} - 500 q^{25} + 92 q^{32} - 284 q^{36} + 312 q^{37} + 140 q^{39} + 8 q^{42} - 120 q^{43} - 344 q^{46} - 552 q^{49} + 416 q^{50} - 364 q^{51} - 316 q^{57} - 320 q^{64} + 972 q^{72} + 680 q^{74} + 428 q^{77} + 1144 q^{78} - 240 q^{81} + 640 q^{84} + 260 q^{86} - 160 q^{91} + 676 q^{92} + 532 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9 - 92 * q^16 - 48 * q^18 - 72 * q^21 + 140 * q^23 - 500 * q^25 + 92 * q^32 - 284 * q^36 + 312 * q^37 + 140 * q^39 + 8 * q^42 - 120 * q^43 - 344 * q^46 - 552 * q^49 + 416 * q^50 - 364 * q^51 - 316 * q^57 - 320 * q^64 + 972 * q^72 + 680 * q^74 + 428 * q^77 + 1144 * q^78 - 240 * q^81 + 640 * q^84 + 260 * q^86 - 160 * q^91 + 676 * q^92 + 532 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−3.60835			−1.80418			−0.902088	−	0.431552i	$-0.857966\pi$
$2$	−3.60835			−1.80418			−0.902088	+	0.431552i	$0.857966\pi$
$3$	−0.377109			−0.125703			−0.0628516	−	0.998023i	$-0.520019\pi$
$3$	−0.377109			−0.125703			−0.0628516	+	0.998023i	$0.520019\pi$
$4$	9.02020			2.25505
$5$		−	7.18702i		−	1.43740i	−0.695318	−	0.718702i	$-0.744737\pi$
$5$		−	7.18702i		−	1.43740i	0.695318	−	0.718702i	$-0.255263\pi$
$6$	1.36074			0.226791
$7$	−2.11657	−	6.67234i	−0.302368	−	0.953191i
$7$	−2.11657	−	6.67234i	−0.302368	−	0.953191i
$8$	−18.1146			−2.26433
$9$	−8.85779			−0.984199
$10$			25.9333i			2.59333i
$11$		−	13.5626i		−	1.23296i	−0.787370	−	0.616481i	$-0.788558\pi$
$11$		−	13.5626i		−	1.23296i	0.787370	−	0.616481i	$-0.211442\pi$
$12$	−3.40160			−0.283467
$13$	−11.7379			−0.902913			−0.451457	−	0.892293i	$-0.649095\pi$
$13$	−11.7379			−0.902913			−0.451457	+	0.892293i	$0.649095\pi$
$14$	7.63734	+	24.0761i	0.545524	+	1.71972i
$15$			2.71029i			0.180686i
$16$	29.2832			1.83020
$17$	31.2229			1.83664			0.918322	−	0.395835i	$-0.129545\pi$
$17$	31.2229			1.83664			0.918322	+	0.395835i	$0.129545\pi$
$18$	31.9620			1.77567
$19$	−15.4496			−0.813136			−0.406568	−	0.913620i	$-0.633275\pi$
$19$	−15.4496			−0.813136			−0.406568	+	0.913620i	$0.633275\pi$
$20$		−	64.8283i		−	3.24142i
$21$	0.798180	+	2.51620i	0.0380086	+	0.119819i
$22$			48.9386i			2.22448i
$23$	12.7820			0.555738			0.277869	−	0.960619i	$-0.410372\pi$
$23$	12.7820			0.555738			0.277869	+	0.960619i	$0.410372\pi$
$24$	6.83120			0.284634
$25$	−26.6532			−1.06613
$26$	42.3544			1.62901
$27$	6.73434			0.249420
$28$	−19.0919	−	60.1858i	−0.681854	−	2.14949i
$29$		−	8.50181i		−	0.293166i	−0.989198	−	0.146583i	$-0.953172\pi$
$29$		−	8.50181i		−	0.293166i	0.989198	−	0.146583i	$-0.0468275\pi$
$30$		−	9.77969i		−	0.325990i
$31$			39.3288i			1.26867i	0.773058	+	0.634336i	$0.218726\pi$
$31$			39.3288i			1.26867i	−0.773058	+	0.634336i	$0.781274\pi$
$32$	−33.2055			−1.03767
$33$			5.11458i			0.154987i
$34$	−112.663			−3.31363
$35$	−47.9542	+	15.2119i	−1.37012	+	0.434624i
$36$	−79.8990			−2.21942
$37$	−5.11022			−0.138114			−0.0690570	−	0.997613i	$-0.521999\pi$
$37$	−5.11022			−0.138114			−0.0690570	+	0.997613i	$0.521999\pi$
$38$	55.7475			1.46704
$39$	4.42646			0.113499
$40$			130.190i			3.25476i
$41$	−30.1346	+	27.8012i	−0.734989	+	0.678079i
$41$	−30.1346	+	27.8012i	−0.734989	+	0.678079i
$42$	−2.88011	−	9.07934i	−0.0685741	−	0.216175i
$43$	21.8570			0.508303			0.254152	−	0.967164i	$-0.418204\pi$
$43$	21.8570			0.508303			0.254152	+	0.967164i	$0.418204\pi$
$44$		−	122.337i		−	2.78039i
$45$			63.6611i			1.41469i
$46$	−46.1218			−1.00265
$47$	−34.3832			−0.731558			−0.365779	−	0.930702i	$-0.619197\pi$
$47$	−34.3832			−0.731558			−0.365779	+	0.930702i	$0.619197\pi$
$48$	−11.0430			−0.230062
$49$	−40.0402	+	28.2450i	−0.817148	+	0.576428i
$50$	96.1742			1.92348
$51$	−11.7745			−0.230872
$52$	−105.878			−2.03611
$53$		−	41.0702i		−	0.774910i	−0.921889	−	0.387455i	$-0.873354\pi$
$53$		−	41.0702i		−	0.774910i	0.921889	−	0.387455i	$-0.126646\pi$
$54$	−24.2999			−0.449998
$55$	−97.4745			−1.77226
$56$	38.3410	+	120.867i	0.684660	+	2.15834i
$57$	5.82619			0.102214
$58$			30.6775i			0.528923i
$59$			27.2473i			0.461819i	0.972975	+	0.230909i	$0.0741701\pi$
$59$			27.2473i			0.461819i	−0.972975	+	0.230909i	$0.925830\pi$
$60$			24.4474i			0.407456i
$61$			77.6635i			1.27317i	0.771205	+	0.636586i	$0.219654\pi$
$61$			77.6635i			1.27317i	−0.771205	+	0.636586i	$0.780346\pi$
$62$		−	141.912i		−	2.28891i
$63$	18.7482	+	59.1022i	0.297590	+	0.938130i
$64$	2.68436			0.0419431
$65$			84.3603i			1.29785i
$66$		−	18.4552i		−	0.279624i
$67$		−	87.5529i		−	1.30676i	−0.757030	−	0.653380i	$-0.773351\pi$
$67$		−	87.5529i		−	1.30676i	0.757030	−	0.653380i	$-0.226649\pi$
$68$	281.637			4.14172
$69$	−4.82020			−0.0698580
$70$	173.036	−	54.8897i	2.47194	−	0.784139i
$71$		−	60.1512i		−	0.847201i	−0.905849	−	0.423600i	$-0.860766\pi$
$71$		−	60.1512i		−	0.847201i	0.905849	−	0.423600i	$-0.139234\pi$
$72$	160.456			2.22855
$73$		−	89.0139i		−	1.21937i	−0.792645	−	0.609684i	$-0.791296\pi$
$73$		−	89.0139i		−	1.21937i	0.792645	−	0.609684i	$-0.208704\pi$
$74$	18.4395			0.249182
$75$	10.0512			0.134016
$76$	−139.358			−1.83366
$77$	−90.4941	+	28.7062i	−1.17525	+	0.372808i
$78$	−15.9722			−0.204772
$79$			56.8520i			0.719646i	0.933021	+	0.359823i	$0.117163\pi$
$79$			56.8520i			0.719646i	−0.933021	+	0.359823i	$0.882837\pi$
$80$		−	210.459i		−	2.63074i
$81$	77.1805			0.952846
$82$	108.736	−	100.317i	1.32605	−	1.22337i
$83$		−	52.4907i		−	0.632418i	−0.948690	−	0.316209i	$-0.897590\pi$
$83$		−	52.4907i		−	0.632418i	0.948690	−	0.316209i	$-0.102410\pi$
$84$	7.19974	+	22.6966i	0.0857112	+	0.270198i
$85$		−	224.400i		−	2.64000i
$86$	−78.8679			−0.917068
$87$			3.20611i			0.0368519i
$88$			245.681i			2.79183i
$89$	−78.5211			−0.882260			−0.441130	−	0.897443i	$-0.645422\pi$
$89$	−78.5211			−0.882260			−0.441130	+	0.897443i	$0.645422\pi$
$90$		−	229.712i		−	2.55235i
$91$	24.8441	+	78.3191i	0.273012	+	0.860649i
$92$	115.296			1.25322
$93$		−	14.8313i		−	0.159476i
$94$	124.067			1.31986
$95$			111.036i			1.16880i
$96$	12.5221			0.130439
$97$	71.6567			0.738729			0.369365	−	0.929285i	$-0.379575\pi$
$97$	71.6567			0.738729			0.369365	+	0.929285i	$0.379575\pi$
$98$	144.479	−	101.918i	1.47428	−	1.03998i
$99$			120.134i			1.21348i
$100$	−240.418			−2.40418
$101$	−107.970			−1.06901			−0.534504	−	0.845166i	$-0.679502\pi$
$101$	−107.970			−1.06901			−0.534504	+	0.845166i	$0.679502\pi$
$102$	42.4864			0.416533
$103$			114.241i			1.10914i	0.832137	+	0.554569i	$0.187117\pi$
$103$			114.241i			1.10914i	−0.832137	+	0.554569i	$0.812883\pi$
$104$	212.627			2.04449
$105$	18.0840	−	5.73653i	0.172229	−	0.0546337i
$106$			148.196i			1.39807i
$107$	88.7996			0.829903			0.414951	−	0.909844i	$-0.363799\pi$
$107$	88.7996			0.829903			0.414951	+	0.909844i	$0.363799\pi$
$108$	60.7451			0.562455
$109$			14.4456i			0.132529i	0.997802	+	0.0662643i	$0.0211081\pi$
$109$			14.4456i			0.132529i	−0.997802	+	0.0662643i	$0.978892\pi$
$110$	351.722			3.19748
$111$	1.92711			0.0173614
$112$	−61.9801	−	195.388i	−0.553393	−	1.74453i
$113$	−175.282			−1.55116			−0.775582	−	0.631247i	$-0.782544\pi$
$113$	−175.282			−1.55116			−0.775582	+	0.631247i	$0.782544\pi$
$114$	−21.0229			−0.184412
$115$		−	91.8642i		−	0.798819i
$116$		−	76.6880i		−	0.661104i
$117$	103.972			0.888646
$118$		−	98.3178i		−	0.833202i
$119$	−66.0857	−	208.330i	−0.555342	−	1.75067i
$120$		−	49.0960i		−	0.409133i
$121$	−62.9436			−0.520195
$122$		−	280.237i		−	2.29703i
$123$	11.3640	−	10.4841i	0.0923905	−	0.0852367i
$124$			354.754i			2.86092i
$125$			11.8818i			0.0950547i
$126$	−67.6500	−	213.261i	−0.536904	−	1.69255i
$127$	111.863			0.880811			0.440406	−	0.897799i	$-0.354835\pi$
$127$	111.863			0.880811			0.440406	+	0.897799i	$0.354835\pi$
$128$	123.136			0.962000
$129$	−8.24250			−0.0638953
$130$		−	304.402i		−	2.34155i
$131$			171.185i			1.30676i	0.757032	+	0.653378i	$0.226649\pi$
$131$			171.185i			1.30676i	−0.757032	+	0.653378i	$0.773351\pi$
$132$			46.1345i			0.349504i
$133$	32.7002	+	103.085i	0.245866	+	0.775074i
$134$			315.922i			2.35762i
$135$		−	48.3998i		−	0.358517i
$136$	−565.593			−4.15877
$137$			250.696i			1.82990i	0.403569	+	0.914949i	$0.367769\pi$
$137$			250.696i			1.82990i	−0.403569	+	0.914949i	$0.632231\pi$
$138$	17.3930			0.126036
$139$		−	42.0475i		−	0.302500i	−0.988496	−	0.151250i	$-0.951670\pi$
$139$		−	42.0475i		−	0.302500i	0.988496	−	0.151250i	$-0.0483299\pi$
$140$	−432.557	+	137.214i	−3.08969	+	0.980100i
$141$	12.9662			0.0919592
$142$			217.047i			1.52850i
$143$			159.196i			1.11326i
$144$	−259.384			−1.80128
$145$	−61.1027			−0.421398
$146$			321.193i			2.19995i
$147$	15.0996	−	10.6515i	0.102718	−	0.0724589i
$148$	−46.0952			−0.311454
$149$		−	268.940i		−	1.80497i	−0.430726	−	0.902483i	$-0.641742\pi$
$149$		−	268.940i		−	1.80497i	0.430726	−	0.902483i	$-0.358258\pi$
$150$	−36.2682			−0.241788
$151$		−	118.119i		−	0.782243i	−0.920339	−	0.391122i	$-0.872087\pi$
$151$		−	118.119i		−	0.782243i	0.920339	−	0.391122i	$-0.127913\pi$
$152$	279.864			1.84121
$153$	−276.566			−1.80762
$154$	326.535	−	103.582i	2.12036	−	0.672611i
$155$	282.657			1.82359
$156$	39.9276			0.255946
$157$	−105.988			−0.675085			−0.337543	−	0.941310i	$-0.609596\pi$
$157$	−105.988			−0.675085			−0.337543	+	0.941310i	$0.609596\pi$
$158$		−	205.142i		−	1.29837i
$159$			15.4880i			0.0974086i
$160$			238.649i			1.49155i
$161$	−27.0540	−	85.2856i	−0.168037	−	0.529724i
$162$	−278.494			−1.71910
$163$	−313.122			−1.92100			−0.960498	−	0.278286i	$-0.910234\pi$
$163$	−313.122			−1.92100			−0.960498	+	0.278286i	$0.910234\pi$
$164$	−271.820	+	250.773i	−1.65744	+	1.52910i
$165$	36.7586			0.222779
$166$			189.405i			1.14099i
$167$	322.071			1.92857			0.964284	−	0.264871i	$-0.0853292\pi$
$167$	322.071			1.92857			0.964284	+	0.264871i	$0.0853292\pi$
$168$	−14.4587	−	45.5801i	−0.0860640	−	0.271310i
$169$	−31.2223			−0.184747
$170$			809.714i			4.76302i
$171$	136.849			0.800288
$172$	197.155			1.14625
$173$		−	263.813i		−	1.52493i	−0.647028	−	0.762466i	$-0.723988\pi$
$173$		−	263.813i		−	1.52493i	0.647028	−	0.762466i	$-0.276012\pi$
$174$		−	11.5688i		−	0.0664873i
$175$	56.4135	+	177.839i	0.322363	+	1.01623i
$176$		−	397.156i		−	2.25657i
$177$		−	10.2752i		−	0.0580521i
$178$	283.332			1.59175
$179$		−	188.980i		−	1.05576i	−0.849320	−	0.527878i	$-0.822988\pi$
$179$		−	188.980i		−	1.05576i	0.849320	−	0.527878i	$-0.177012\pi$
$180$			574.236i			3.19020i
$181$	−24.4170			−0.134901			−0.0674503	−	0.997723i	$-0.521486\pi$
$181$	−24.4170			−0.134901			−0.0674503	+	0.997723i	$0.521486\pi$
$182$	−89.6462	−	282.603i	−0.492561	−	1.55276i
$183$		−	29.2877i		−	0.160042i
$184$	−231.541			−1.25837
$185$			36.7272i			0.198526i
$186$			53.5164i			0.287723i
$187$		−	423.464i		−	2.26451i
$188$	−310.144			−1.64970
$189$	−14.2537	−	44.9338i	−0.0754165	−	0.237745i
$190$		−	400.659i		−	2.10873i
$191$		−	213.468i		−	1.11763i	−0.829291	−	0.558817i	$-0.811255\pi$
$191$		−	213.468i		−	1.11763i	0.829291	−	0.558817i	$-0.188745\pi$
$192$	−1.01230			−0.00527238
$193$			258.434i			1.33904i	0.742796	+	0.669518i	$0.233499\pi$
$193$			258.434i			1.33904i	−0.742796	+	0.669518i	$0.766501\pi$
$194$	−258.563			−1.33280
$195$		−	31.8131i		−	0.163144i
$196$	−361.171	+	254.776i	−1.84271	+	1.29988i
$197$	−130.427			−0.662068			−0.331034	−	0.943619i	$-0.607397\pi$
$197$	−130.427			−0.662068			−0.331034	+	0.943619i	$0.607397\pi$
$198$		−	433.487i		−	2.18933i
$199$	260.928			1.31120			0.655598	−	0.755110i	$-0.272416\pi$
$199$	260.928			1.31120			0.655598	+	0.755110i	$0.272416\pi$
$200$	482.814			2.41407
$201$			33.0170i			0.164264i
$202$	389.593			1.92868
$203$	−56.7270	+	17.9947i	−0.279443	+	0.0886439i
$204$	−106.208			−0.520628
$205$	199.808	+	216.578i	0.974673	+	1.05648i
$206$		−	412.223i		−	2.00108i
$207$	−113.220			−0.546956
$208$	−343.723			−1.65251
$209$			209.536i			1.00257i
$210$	−65.2534	+	20.6994i	−0.310730	+	0.0985687i
$211$			281.945i			1.33623i	0.744056	+	0.668117i	$0.232899\pi$
$211$			281.945i			1.33623i	−0.744056	+	0.668117i	$0.767101\pi$
$212$		−	370.461i		−	1.74746i
$213$			22.6836i			0.106496i
$214$	−320.420			−1.49729
$215$		−	157.087i		−	0.730637i
$216$	−121.990			−0.564769
$217$	262.415	−	83.2423i	1.20929	−	0.383605i
$218$		−	52.1249i		−	0.239105i
$219$			33.5680i			0.153278i
$220$	−879.240			−3.99654
$221$	−366.491			−1.65833
$222$	−6.95369			−0.0313229
$223$		−	161.668i		−	0.724969i	−0.931990	−	0.362484i	$-0.881929\pi$
$223$		−	161.668i		−	0.724969i	0.931990	−	0.362484i	$-0.118071\pi$
$224$	70.2819	+	221.559i	0.313759	+	0.989101i
$225$	236.089			1.04928
$226$	632.478			2.79857
$227$	297.883			1.31226			0.656129	−	0.754649i	$-0.272193\pi$
$227$	297.883			1.31226			0.656129	+	0.754649i	$0.272193\pi$
$228$	52.5534			0.230497
$229$	−72.1152			−0.314914			−0.157457	−	0.987526i	$-0.550330\pi$
$229$	−72.1152			−0.314914			−0.157457	+	0.987526i	$0.550330\pi$
$230$			331.478i			1.44121i
$231$	34.1262	−	10.8254i	0.147732	−	0.0468631i
$232$			154.007i			0.663825i
$233$		−	178.205i		−	0.764828i	−0.923991	−	0.382414i	$-0.875093\pi$
$233$		−	178.205i		−	0.764828i	0.923991	−	0.382414i	$-0.124907\pi$
$234$	−375.166			−1.60327
$235$			247.113i			1.05154i
$236$			245.776i			1.04142i
$237$		−	21.4394i		−	0.0904618i
$238$	238.460	+	751.728i	1.00193	+	3.15852i
$239$		−	165.856i		−	0.693958i	−0.937873	−	0.346979i	$-0.887208\pi$
$239$		−	165.856i		−	0.693958i	0.937873	−	0.346979i	$-0.112792\pi$
$240$			79.3661i			0.330692i
$241$		−	83.3667i		−	0.345920i	−0.984929	−	0.172960i	$-0.944667\pi$
$241$		−	83.3667i		−	0.345920i	0.984929	−	0.172960i	$-0.0553331\pi$
$242$	227.123			0.938523
$243$	−89.7146			−0.369196
$244$			700.541i			2.87107i
$245$	202.997	+	287.770i	0.828560	+	1.17457i
$246$	−41.0054	+	37.8303i	−0.166689	+	0.153782i
$247$	181.345			0.734192
$248$		−	712.428i		−	2.87269i
$249$			19.7947i			0.0794969i
$250$		−	42.8738i		−	0.171495i
$251$		−	158.919i		−	0.633143i	−0.948569	−	0.316572i	$-0.897468\pi$
$251$		−	158.919i		−	0.633143i	0.948569	−	0.316572i	$-0.102532\pi$
$252$	169.112	+	533.113i	0.671080	+	2.11553i
$253$		−	173.356i		−	0.685203i
$254$	−403.641			−1.58914
$255$			84.6233i			0.331856i
$256$	−455.055			−1.77756
$257$	69.6675			0.271080			0.135540	−	0.990772i	$-0.456723\pi$
$257$	69.6675			0.271080			0.135540	+	0.990772i	$0.456723\pi$
$258$	29.7418			0.115278
$259$	10.8161	+	34.0971i	0.0417612	+	0.131649i
$260$			760.947i			2.92672i
$261$			75.3073i			0.288534i
$262$		−	617.696i		−	2.35762i
$263$			102.503i			0.389745i	0.980829	+	0.194873i	$0.0624293\pi$
$263$			102.503i			0.389745i	−0.980829	+	0.194873i	$0.937571\pi$
$264$		−	92.6488i		−	0.350942i
$265$	−295.172			−1.11386
$266$	−117.994	−	371.967i	−0.443586	−	1.39837i
$267$	29.6111			0.110903
$268$		−	789.744i		−	2.94681i
$269$			77.6370i			0.288614i	0.989533	+	0.144307i	$0.0460952\pi$
$269$			77.6370i			0.288614i	−0.989533	+	0.144307i	$0.953905\pi$
$270$			174.644i			0.646828i
$271$		−	435.523i		−	1.60709i	−0.595241	−	0.803547i	$-0.702943\pi$
$271$		−	435.523i		−	1.60709i	0.595241	−	0.803547i	$-0.297057\pi$
$272$	914.308			3.36143
$273$	−9.36894	−	29.5349i	−0.0343184	−	0.108186i
$274$		−	904.599i		−	3.30146i
$275$			361.487i			1.31450i
$276$	−43.4792			−0.157533
$277$	−244.822			−0.883836			−0.441918	−	0.897056i	$-0.645702\pi$
$277$	−244.822			−0.883836			−0.441918	+	0.897056i	$0.645702\pi$
$278$			151.722i			0.545763i
$279$		−	348.366i		−	1.24863i
$280$	868.674	−	275.557i	3.10241	−	0.984133i
$281$			216.312i			0.769794i	0.922960	+	0.384897i	$0.125763\pi$
$281$			216.312i			0.769794i	−0.922960	+	0.384897i	$0.874237\pi$
$282$	−46.7868			−0.165910
$283$			422.274i			1.49214i	0.665870	+	0.746068i	$0.268061\pi$
$283$			422.274i			1.49214i	−0.665870	+	0.746068i	$0.731939\pi$
$284$		−	542.576i		−	1.91048i
$285$		−	41.8729i		−	0.146922i
$286$		−	574.435i		−	2.00851i
$287$	249.281	+	142.225i	0.868576	+	0.495556i
$288$	294.127			1.02128
$289$	685.872			2.37326
$290$	220.480			0.760276
$291$	−27.0224			−0.0928606
$292$		−	802.923i		−	2.74974i
$293$	−206.716			−0.705515			−0.352758	−	0.935715i	$-0.614756\pi$
$293$	−206.716			−0.705515			−0.352758	+	0.935715i	$0.614756\pi$
$294$	−54.4845	+	38.4342i	−0.185321	+	0.130729i
$295$	195.827			0.663820
$296$	92.5698			0.312736
$297$		−	91.3350i		−	0.307525i
$298$			970.429i			3.25647i
$299$	−150.033			−0.501783
$300$	90.6637			0.302212
$301$	−46.2620	−	145.838i	−0.153694	−	0.484510i
$302$			426.214i			1.41130i
$303$	40.7164			0.134378
$304$	−452.413			−1.48820
$305$	558.169			1.83006
$306$	997.948			3.26127
$307$		−	168.801i		−	0.549839i	−0.961467	−	0.274920i	$-0.911349\pi$
$307$		−	168.801i		−	0.549839i	0.961467	−	0.274920i	$-0.0886512\pi$
$308$	−816.275	+	258.936i	−2.65024	+	0.840700i
$309$		−	43.0815i		−	0.139422i
$310$	−1019.93			−3.29008
$311$	−299.729			−0.963760			−0.481880	−	0.876237i	$-0.660046\pi$
$311$	−299.729			−0.963760			−0.481880	+	0.876237i	$0.660046\pi$
$312$	−80.1838			−0.256999
$313$	−253.628			−0.810312			−0.405156	−	0.914247i	$-0.632783\pi$
$313$	−253.628			−0.810312			−0.405156	+	0.914247i	$0.632783\pi$
$314$	382.443			1.21797
$315$	424.768	−	134.743i	1.34847	−	0.427757i
$316$			512.817i			1.62284i
$317$			66.7388i			0.210533i	0.994444	+	0.105266i	$0.0335695\pi$
$317$			66.7388i			0.210533i	−0.994444	+	0.105266i	$0.966431\pi$
$318$		−	55.8860i		−	0.175742i
$319$	−115.307			−0.361462
$320$		−	19.2926i		−	0.0602892i
$321$	−33.4872			−0.104321
$322$	97.6202	+	307.740i	0.303168	+	0.955716i
$323$	−482.382			−1.49344
$324$	696.184			2.14871
$325$	312.852			0.962623
$326$	1129.86			3.46582
$327$		−	5.44758i		−	0.0166593i
$328$	545.877	−	503.610i	1.66426	−	1.53539i
$329$	72.7746	+	229.417i	0.221200	+	0.697315i
$330$	−132.638			−0.401933
$331$		−	306.519i		−	0.926040i	−0.886348	−	0.463020i	$-0.846766\pi$
$331$		−	306.519i		−	0.926040i	0.886348	−	0.463020i	$-0.153234\pi$
$332$		−	473.476i		−	1.42613i
$333$	45.2652			0.135932
$334$	−1162.14			−3.47948
$335$	−629.244			−1.87834
$336$	23.3733	+	73.6825i	0.0695633	+	0.219293i
$337$	255.287			0.757529			0.378764	−	0.925493i	$-0.376349\pi$
$337$	255.287			0.757529			0.378764	+	0.925493i	$0.376349\pi$
$338$	112.661			0.333317
$339$	66.1003			0.194986
$340$		−	2024.13i		−	5.95333i
$341$	533.400			1.56422
$342$	−493.800			−1.44386
$343$	273.208	+	207.379i	0.796526	+	0.604605i
$344$	−395.933			−1.15097
$345$			34.6429i			0.100414i
$346$			951.931i			2.75125i
$347$		−	336.160i		−	0.968762i	−0.874857	−	0.484381i	$-0.839045\pi$
$347$		−	336.160i		−	0.968762i	0.874857	−	0.484381i	$-0.160955\pi$
$348$			28.9198i			0.0831028i
$349$			6.76839i			0.0193937i	0.999953	+	0.00969683i	$0.00308665\pi$
$349$			6.76839i			0.0193937i	−0.999953	+	0.00969683i	$0.996913\pi$
$350$	−203.560	−	641.707i	−0.581600	−	1.83345i
$351$	−79.0468			−0.225205
$352$			450.353i			1.27941i
$353$			689.135i			1.95222i	0.217271	+	0.976111i	$0.430284\pi$
$353$			689.135i			1.95222i	−0.217271	+	0.976111i	$0.569716\pi$
$354$			37.0766i			0.104736i
$355$	−432.308			−1.21777
$356$	−708.276			−1.98954
$357$	24.9215	+	78.5632i	0.0698082	+	0.220065i
$358$			681.908i			1.90477i
$359$	−346.642			−0.965577			−0.482788	−	0.875737i	$-0.660376\pi$
$359$	−346.642			−0.965577			−0.482788	+	0.875737i	$0.660376\pi$
$360$		−	1153.20i		−	3.20333i
$361$	−122.310			−0.338810
$362$	88.1051			0.243384
$363$	23.7366			0.0653901
$364$	224.099	+	706.454i	0.615655	+	1.94081i
$365$	−639.744			−1.75272
$366$			105.680i			0.288744i
$367$		−	492.498i		−	1.34196i	−0.741477	−	0.670978i	$-0.765874\pi$
$367$		−	492.498i		−	1.34196i	0.741477	−	0.670978i	$-0.234126\pi$
$368$	374.297			1.01711
$369$	266.926	−	246.257i	0.723375	−	0.667364i
$370$		−	132.525i		−	0.358175i
$371$	−274.034	+	86.9281i	−0.738637	+	0.234308i
$372$		−	133.781i		−	0.359626i
$373$	−76.6413			−0.205473			−0.102736	−	0.994709i	$-0.532760\pi$
$373$	−76.6413			−0.205473			−0.102736	+	0.994709i	$0.532760\pi$
$374$			1528.01i			4.08558i
$375$		−	4.48075i		−	0.0119487i
$376$	622.840			1.65649
$377$			99.7932i			0.264703i
$378$	51.4325	+	162.137i	0.136065	+	0.428934i
$379$	114.003			0.300799			0.150399	−	0.988625i	$-0.451944\pi$
$379$	114.003			0.300799			0.150399	+	0.988625i	$0.451944\pi$
$380$			1001.57i			2.63571i
$381$	−42.1846			−0.110721
$382$			770.268i			2.01641i
$383$	−714.880			−1.86653			−0.933264	−	0.359190i	$-0.883053\pi$
$383$	−714.880			−1.86653			−0.933264	+	0.359190i	$0.883053\pi$
$384$	−46.4357			−0.120926
$385$	206.312	+	650.383i	0.535875	+	1.68931i
$386$		−	932.521i		−	2.41586i
$387$	−193.605			−0.500271
$388$	646.358			1.66587
$389$	−412.535			−1.06050			−0.530251	−	0.847841i	$-0.677902\pi$
$389$	−412.535			−1.06050			−0.530251	+	0.847841i	$0.677902\pi$
$390$			114.793i			0.294340i
$391$	399.091			1.02069
$392$	725.315	−	511.648i	1.85029	−	1.30522i
$393$		−	64.5555i		−	0.164263i
$394$	470.628			1.19449
$395$	408.597			1.03442
$396$			1083.64i			2.73646i
$397$	−685.635			−1.72704			−0.863520	−	0.504314i	$-0.831746\pi$
$397$	−685.635			−1.72704			−0.863520	+	0.504314i	$0.831746\pi$
$398$	−941.520			−2.36563
$399$	−12.3316	−	38.8743i	−0.0309061	−	0.0974293i
$400$	−780.492			−1.95123
$401$	−506.192			−1.26233			−0.631163	−	0.775651i	$-0.717422\pi$
$401$	−506.192			−1.26233			−0.631163	+	0.775651i	$0.717422\pi$
$402$		−	119.137i		−	0.296361i
$403$		−	461.637i		−	1.14550i
$404$	−973.909			−2.41067
$405$		−	554.698i		−	1.36962i
$406$	204.691	−	64.9312i	0.504165	−	0.159929i
$407$			69.3077i			0.170289i
$408$	213.290			0.522770
$409$			91.2293i			0.223055i	0.993761	+	0.111527i	$0.0355742\pi$
$409$			91.2293i			0.223055i	−0.993761	+	0.111527i	$0.964426\pi$
$410$	−720.977	−	781.488i	−1.75848	−	1.90607i
$411$		−	94.5399i		−	0.230024i
$412$			1030.48i			2.50116i
$413$	181.803	−	57.6709i	0.440202	−	0.139639i
$414$	408.537			0.986805
$415$	−377.251			−0.909040
$416$	389.762			0.936928
$417$			15.8565i			0.0380252i
$418$		−	756.081i		−	1.80881i
$419$		−	78.2604i		−	0.186779i	−0.995630	−	0.0933895i	$-0.970230\pi$
$419$		−	78.2604i		−	0.186779i	0.995630	−	0.0933895i	$-0.0297702\pi$
$420$	163.121	−	51.7447i	0.388384	−	0.123202i
$421$			388.142i			0.921953i	0.887412	+	0.460977i	$0.152501\pi$
$421$			388.142i			0.921953i	−0.887412	+	0.460977i	$0.847499\pi$
$422$		−	1017.36i		−	2.41080i
$423$	304.559			0.719999
$424$			743.972i			1.75465i
$425$	−832.192			−1.95810
$426$		−	81.8504i		−	0.192137i
$427$	518.198	−	164.381i	1.21358	−	0.384966i
$428$	800.990			1.87147
$429$		−	60.0343i		−	0.139940i
$430$			566.825i			1.31820i
$431$	438.159			1.01661			0.508305	−	0.861177i	$-0.330272\pi$
$431$	438.159			1.01661			0.508305	+	0.861177i	$0.330272\pi$
$432$	197.203			0.456489
$433$			561.509i			1.29679i	0.761305	+	0.648394i	$0.224559\pi$
$433$			561.509i			1.29679i	−0.761305	+	0.648394i	$0.775441\pi$
$434$	−946.887	+	300.368i	−2.18177	+	0.692091i
$435$	23.0424			0.0529710
$436$			130.302i			0.298859i
$437$	−197.476			−0.451890
$438$		−	121.125i		−	0.276541i
$439$	−129.304			−0.294543			−0.147272	−	0.989096i	$-0.547049\pi$
$439$	−129.304			−0.294543			−0.147272	+	0.989096i	$0.547049\pi$
$440$	1765.72			4.01299
$441$	354.668	−	250.188i	0.804236	−	0.567320i
$442$	1322.43			2.99192
$443$	442.832			0.999622			0.499811	−	0.866135i	$-0.333403\pi$
$443$	442.832			0.999622			0.499811	+	0.866135i	$0.333403\pi$
$444$	17.3829			0.0391507
$445$			564.333i			1.26816i
$446$			583.355i			1.30797i
$447$			101.420i			0.226890i
$448$	−5.68165	−	17.9110i	−0.0126822	−	0.0399798i
$449$	−405.727			−0.903625			−0.451812	−	0.892113i	$-0.649222\pi$
$449$	−405.727			−0.903625			−0.451812	+	0.892113i	$0.649222\pi$
$450$	−851.891			−1.89309
$451$	377.056	+	408.702i	0.836045	+	0.906214i
$452$	−1581.07			−3.49795
$453$			44.5437i			0.0983304i
$454$	−1074.86			−2.36754
$455$	562.881	−	178.555i	1.23710	−	0.392428i
$456$	−105.539			−0.231446
$457$		−	449.194i		−	0.982919i	−0.870900	−	0.491460i	$-0.836464\pi$
$457$		−	449.194i		−	0.982919i	0.870900	−	0.491460i	$-0.163536\pi$
$458$	260.217			0.568160
$459$	210.266			0.458096
$460$		−	828.634i		−	1.80138i
$461$		−	564.490i		−	1.22449i	−0.790668	−	0.612245i	$-0.790267\pi$
$461$		−	564.490i		−	1.22449i	0.790668	−	0.612245i	$-0.209733\pi$
$462$	−123.139	+	39.0618i	−0.266535	+	0.0845493i
$463$		−	738.907i		−	1.59591i	−0.602716	−	0.797955i	$-0.705915\pi$
$463$		−	738.907i		−	1.59591i	0.602716	−	0.797955i	$-0.294085\pi$
$464$		−	248.960i		−	0.536552i
$465$	−106.593			−0.229231
$466$			643.026i			1.37988i
$467$		−	244.218i		−	0.522951i	−0.965210	−	0.261475i	$-0.915791\pi$
$467$		−	244.218i		−	0.522951i	0.965210	−	0.261475i	$-0.0842090\pi$
$468$	937.845			2.00394
$469$	−584.182	+	185.312i	−1.24559	+	0.395122i
$470$		−	891.670i		−	1.89717i
$471$	39.9692			0.0848604
$472$		−	493.575i		−	1.04571i
$473$		−	296.438i		−	0.626719i
$474$			77.3610i			0.163209i
$475$	411.782			0.866908
$476$	−596.106	−	1879.18i	−1.25232	−	3.94786i
$477$			363.791i			0.762665i
$478$			598.466i			1.25202i
$479$	134.266			0.280306			0.140153	−	0.990130i	$-0.455241\pi$
$479$	134.266			0.280306			0.140153	+	0.990130i	$0.455241\pi$
$480$		−	89.9967i		−	0.187493i
$481$	59.9831			0.124705
$482$			300.816i			0.624100i
$483$	10.2023	+	32.1620i	0.0211228	+	0.0665880i
$484$	−567.764			−1.17307
$485$		−	514.998i		−	1.06185i
$486$	323.722			0.666094
$487$	548.952			1.12721			0.563606	−	0.826044i	$-0.309414\pi$
$487$	548.952			1.12721			0.563606	+	0.826044i	$0.309414\pi$
$488$		−	1406.85i		−	2.88288i
$489$	118.081			0.241475
$490$	−732.486	−	1038.37i	−1.49487	−	2.11913i
$491$	364.130			0.741609			0.370804	−	0.928711i	$-0.379082\pi$
$491$	364.130			0.741609			0.370804	+	0.928711i	$0.379082\pi$
$492$	102.506	−	94.5688i	0.208345	−	0.192213i
$493$		−	265.452i		−	0.538441i
$494$	−654.358			−1.32461
$495$	863.409			1.74426
$496$			1151.67i			2.32192i
$497$	−401.350	+	127.315i	−0.807544	+	0.256166i
$498$		−	71.4263i		−	0.143426i
$499$			773.841i			1.55078i	0.631480	+	0.775392i	$0.282448\pi$
$499$			773.841i			1.55078i	−0.631480	+	0.775392i	$0.717552\pi$
$500$			107.177i			0.214353i
$501$	−121.456			−0.242427
$502$			573.436i			1.14230i
$503$	149.544			0.297304			0.148652	−	0.988890i	$-0.452507\pi$
$503$	149.544			0.297304			0.148652	+	0.988890i	$0.452507\pi$
$504$	−339.616	−	1070.61i	−0.673842	−	2.12424i
$505$			775.981i			1.53660i
$506$			625.531i			1.23623i
$507$	11.7742			0.0232233
$508$	1009.03			1.98627
$509$	273.545			0.537416			0.268708	−	0.963222i	$-0.413403\pi$
$509$	273.545			0.537416			0.268708	+	0.963222i	$0.413403\pi$
$510$		−	305.351i		−	0.598727i
$511$	−593.931	+	188.404i	−1.16229	+	0.368697i
$512$	1149.46			2.24503
$513$	−104.043			−0.202812
$514$	−251.385			−0.489075
$515$	821.054			1.59428
$516$	−74.3490			−0.144087
$517$			466.325i			0.901983i
$518$	−39.0285	−	123.034i	−0.0753445	−	0.237518i
$519$			99.4865i			0.191689i
$520$		−	1528.16i		−	2.93876i
$521$	−380.502			−0.730329			−0.365165	−	0.930943i	$-0.618987\pi$
$521$	−380.502			−0.730329			−0.365165	+	0.930943i	$0.618987\pi$
$522$		−	271.735i		−	0.520565i
$523$		−	583.231i		−	1.11516i	−0.830122	−	0.557582i	$-0.811729\pi$
$523$		−	583.231i		−	1.11516i	0.830122	−	0.557582i	$-0.188271\pi$
$524$			1544.12i			2.94680i
$525$	−21.2741	−	67.0649i	−0.0405221	−	0.127743i
$526$		−	369.867i		−	0.703169i
$527$			1227.96i			2.33010i
$528$			149.771i			0.283658i
$529$	−365.621			−0.691156
$530$	1065.09			2.00960
$531$		−	241.351i		−	0.454521i
$532$	294.962	+	929.846i	0.554440	+	1.74783i
$533$	353.716	−	326.327i	0.663632	−	0.612247i
$534$	−106.847			−0.200088
$535$		−	638.204i		−	1.19291i
$536$			1585.99i			2.95894i
$537$			71.2663i			0.132712i
$538$		−	280.142i		−	0.520710i
$539$	383.075	+	543.049i	0.710714	+	1.00751i
$540$		−	436.576i		−	0.808474i
$541$	68.0799			0.125841			0.0629204	−	0.998019i	$-0.479959\pi$
$541$	68.0799			0.125841			0.0629204	+	0.998019i	$0.479959\pi$
$542$			1571.52i			2.89948i
$543$	9.20788			0.0169574
$544$	−1036.77			−1.90583
$545$	103.821			0.190497
$546$	33.8064	+	106.572i	0.0619165	+	0.195187i
$547$		−	78.4570i		−	0.143431i	−0.997425	−	0.0717157i	$-0.977153\pi$
$547$		−	78.4570i		−	0.143431i	0.997425	−	0.0717157i	$-0.0228474\pi$
$548$			2261.33i			4.12651i
$549$		−	687.927i		−	1.25306i
$550$		−	1304.37i		−	2.37158i
$551$			131.349i			0.238384i
$552$	87.3162			0.158182
$553$	379.336	−	120.332i	0.685961	−	0.217598i
$554$	883.406			1.59459
$555$		−	13.8502i		−	0.0249553i
$556$		−	379.277i		−	0.682153i
$557$		−	193.732i		−	0.347814i	−0.984762	−	0.173907i	$-0.944361\pi$
$557$		−	193.732i		−	0.347814i	0.984762	−	0.173907i	$-0.0556392\pi$
$558$			1257.03i			2.25274i
$559$	−256.555			−0.458954
$560$	−1404.25	+	445.452i	−2.50760	+	0.795450i
$561$			159.692i			0.284656i
$562$		−	780.530i		−	1.38884i
$563$	−594.511			−1.05597			−0.527985	−	0.849253i	$-0.677052\pi$
$563$	−594.511			−1.05597			−0.527985	+	0.849253i	$0.677052\pi$
$564$	116.958			0.207373
$565$			1259.75i			2.22965i
$566$		−	1523.71i		−	2.69207i
$567$	−163.358	−	514.975i	−0.288110	−	0.908244i
$568$			1089.62i			1.91834i
$569$	716.336			1.25894			0.629469	−	0.777025i	$-0.283272\pi$
$569$	716.336			1.25894			0.629469	+	0.777025i	$0.283272\pi$
$570$			151.092i			0.265074i
$571$		−	254.496i		−	0.445703i	−0.974852	−	0.222851i	$-0.928464\pi$
$571$		−	254.496i		−	0.445703i	0.974852	−	0.222851i	$-0.0715365\pi$
$572$			1435.98i			2.51045i
$573$			80.5009i			0.140490i
$574$	−899.494	−	513.196i	−1.56706	−	0.894070i
$575$	−340.681			−0.592488
$576$	−23.7775			−0.0412804
$577$	−17.6727			−0.0306285			−0.0153143	−	0.999883i	$-0.504875\pi$
$577$	−17.6727			−0.0306285			−0.0153143	+	0.999883i	$0.504875\pi$
$578$	−2474.87			−4.28178
$579$		−	97.4579i		−	0.168321i
$580$	−551.158			−0.950273
$581$	−350.236	+	111.100i	−0.602815	+	0.191223i
$582$	97.5064			0.167537
$583$	−557.018			−0.955434
$584$			1612.45i			2.76105i
$585$		−	747.246i		−	1.27734i
$586$	745.904			1.27287
$587$	−454.679			−0.774581			−0.387291	−	0.921958i	$-0.626589\pi$
$587$	−454.679			−0.774581			−0.387291	+	0.921958i	$0.626589\pi$
$588$	136.201	−	96.0782i	0.231634	−	0.163398i
$589$		−	607.614i		−	1.03160i
$590$	−706.612			−1.19765
$591$	49.1854			0.0832240
$592$	−149.644			−0.252776
$593$	−447.375			−0.754427			−0.377214	−	0.926126i	$-0.623118\pi$
$593$	−447.375			−0.754427			−0.377214	+	0.926126i	$0.623118\pi$
$594$			329.569i			0.554830i
$595$	−1497.27	+	474.959i	−2.51642	+	0.798250i
$596$		−	2425.89i		−	4.07029i
$597$	−98.3985			−0.164822
$598$	541.372			0.905305
$599$	20.1570			0.0336511			0.0168256	−	0.999858i	$-0.494644\pi$
$599$	20.1570			0.0336511			0.0168256	+	0.999858i	$0.494644\pi$
$600$	−182.074			−0.303456
$601$	−715.878			−1.19115			−0.595573	−	0.803301i	$-0.703075\pi$
$601$	−715.878			−1.19115			−0.595573	+	0.803301i	$0.703075\pi$
$602$	166.930	+	526.233i	0.277292	+	0.874142i
$603$			775.525i			1.28611i
$604$		−	1065.45i		−	1.76400i
$605$			452.377i			0.747730i
$606$	−146.919			−0.242441
$607$			320.680i			0.528303i	0.964481	+	0.264152i	$0.0850920\pi$
$607$			320.680i			0.528303i	−0.964481	+	0.264152i	$0.914908\pi$
$608$	513.012			0.843769
$609$	21.3923	−	6.78598i	0.0351269	−	0.0111428i
$610$	−2014.07			−3.30176
$611$	403.586			0.660534
$612$	−2494.68			−4.07628
$613$	456.811			0.745205			0.372603	−	0.927991i	$-0.378465\pi$
$613$	456.811			0.745205			0.372603	+	0.927991i	$0.378465\pi$
$614$			609.092i			0.992007i
$615$	−75.3495	−	81.6735i	−0.122519	−	0.132802i
$616$	1639.27	−	520.003i	2.66115	−	0.844160i
$617$	−125.871			−0.204005			−0.102002	−	0.994784i	$-0.532525\pi$
$617$	−125.871			−0.204005			−0.102002	+	0.994784i	$0.532525\pi$
$618$			155.453i			0.251542i
$619$		−	184.074i		−	0.297374i	−0.988884	−	0.148687i	$-0.952495\pi$
$619$		−	184.074i		−	0.297374i	0.988884	−	0.148687i	$-0.0475046\pi$
$620$	2549.62			4.11229
$621$	86.0781			0.138612
$622$	1081.53			1.73879
$623$	166.196	+	523.920i	0.266767	+	0.840962i
$624$	129.621			0.207726
$625$	−580.936			−0.929497
$626$	915.178			1.46195
$627$		−	79.0181i		−	0.126026i
$628$	−956.037			−1.52235
$629$	−159.556			−0.253666
$630$	−1532.71	+	486.201i	−2.43288	+	0.771748i
$631$	−187.852			−0.297706			−0.148853	−	0.988859i	$-0.547558\pi$
$631$	−187.852			−0.297706			−0.148853	+	0.988859i	$0.547558\pi$
$632$		−	1029.85i		−	1.62952i
$633$		−	106.324i		−	0.167969i
$634$		−	240.817i		−	0.379838i
$635$		−	803.962i		−	1.26608i
$636$			139.705i			0.219661i
$637$	469.987	−	331.536i	0.737814	−	0.520465i
$638$	416.066			0.652142
$639$			532.807i			0.833814i
$640$		−	884.981i		−	1.38278i
$641$		−	408.341i		−	0.637038i	−0.947917	−	0.318519i	$-0.896815\pi$
$641$		−	408.341i		−	0.637038i	0.947917	−	0.318519i	$-0.103185\pi$
$642$	120.833			0.188214
$643$	426.772			0.663720			0.331860	−	0.943329i	$-0.392324\pi$
$643$	426.772			0.663720			0.331860	+	0.943329i	$0.392324\pi$
$644$	−244.032	−	769.293i	−0.378932	−	1.19455i
$645$			59.2390i			0.0918434i
$646$	1740.60			2.69443
$647$		−	686.319i		−	1.06077i	−0.847757	−	0.530385i	$-0.822047\pi$
$647$		−	686.319i		−	1.06077i	0.847757	−	0.530385i	$-0.177953\pi$
$648$	−1398.10			−2.15756
$649$	369.544			0.569405
$650$	−1128.88			−1.73674
$651$	−98.9593	+	31.3915i	−0.152011	+	0.0482204i
$652$	−2824.43			−4.33194
$653$		−	1110.06i		−	1.69993i	−0.526837	−	0.849966i	$-0.676622\pi$
$653$		−	1110.06i		−	1.69993i	0.526837	−	0.849966i	$-0.323378\pi$
$654$			19.6568i			0.0300562i
$655$	1230.31			1.87834
$656$	−882.436	+	814.109i	−1.34518	+	1.24102i
$657$			788.466i			1.20010i
$658$	−262.596	−	827.816i	−0.399083	−	1.25808i
$659$			648.182i			0.983584i	0.870713	+	0.491792i	$0.163658\pi$
$659$			648.182i			0.983584i	−0.870713	+	0.491792i	$0.836342\pi$
$660$	331.570			0.502378
$661$		−	546.969i		−	0.827487i	−0.910394	−	0.413743i	$-0.864221\pi$
$661$		−	546.969i		−	0.827487i	0.910394	−	0.413743i	$-0.135779\pi$
$662$			1106.03i			1.67074i
$663$	138.207			0.208457
$664$			950.850i			1.43200i
$665$	740.873	−	235.017i	1.11409	−	0.353409i
$666$	−163.333			−0.245244
$667$		−	108.670i		−	0.162923i
$668$	2905.14			4.34902
$669$			60.9665i			0.0911308i
$670$	2270.53			3.38886
$671$	1053.32			1.56977
$672$	−26.5040	−	83.5518i	−0.0394404	−	0.124333i
$673$		−	601.208i		−	0.893325i	−0.894703	−	0.446662i	$-0.852613\pi$
$673$		−	601.208i		−	0.893325i	0.894703	−	0.446662i	$-0.147387\pi$
$674$	−921.166			−1.36671
$675$	−179.492			−0.265914
$676$	−281.631			−0.416615
$677$		−	1300.46i		−	1.92091i	−0.278428	−	0.960457i	$-0.589813\pi$
$677$		−	1300.46i		−	1.92091i	0.278428	−	0.960457i	$-0.410187\pi$
$678$	−238.513			−0.351789
$679$	−151.667	−	478.118i	−0.223368	−	0.704150i
$680$			4064.92i			5.97783i
$681$	−112.334			−0.164955
$682$	−1924.70			−2.82213
$683$			433.302i			0.634410i	0.948357	+	0.317205i	$0.102744\pi$
$683$			433.302i			0.634410i	−0.948357	+	0.317205i	$0.897256\pi$
$684$	1234.41			1.80469
$685$	1801.76			2.63030
$686$	−985.832	−	748.298i	−1.43707	−	1.09081i
$687$	27.1953			0.0395856
$688$	640.044			0.930297
$689$			482.077i			0.699676i
$690$		−	125.004i		−	0.181165i
$691$	614.980			0.889985			0.444993	−	0.895534i	$-0.353206\pi$
$691$	614.980			0.889985			0.444993	+	0.895534i	$0.353206\pi$
$692$		−	2379.65i		−	3.43880i
$693$	801.578	−	254.273i	1.15668	−	0.366917i
$694$			1212.98i			1.74782i
$695$	−302.196			−0.434815
$696$		−	58.0776i		−	0.0834449i
$697$	−940.890	+	868.036i	−1.34991	+	1.24539i
$698$		−	24.4227i		−	0.0349896i
$699$			67.2028i			0.0961413i
$700$	508.861	+	1604.15i	0.726945	+	2.29164i
$701$	444.298			0.633806			0.316903	−	0.948458i	$-0.397357\pi$
$701$	444.298			0.633806			0.316903	+	0.948458i	$0.397357\pi$
$702$	285.229			0.406309
$703$	78.9507			0.112305
$704$		−	36.4069i		−	0.0517143i
$705$		−	93.1886i		−	0.132182i
$706$		−	2486.64i		−	3.52215i
$707$	228.526	+	720.411i	0.323233	+	1.01897i
$708$		−	92.6845i		−	0.130910i
$709$		−	9.37833i		−	0.0132275i	−0.999978	−	0.00661377i	$-0.997895\pi$
$709$		−	9.37833i		−	0.0132275i	0.999978	−	0.00661377i	$-0.00210524\pi$
$710$	1559.92			2.19707
$711$		−	503.583i		−	0.708275i
$712$	1422.38			1.99773
$713$			502.700i			0.705049i
$714$	−89.9256	−	283.484i	−0.125946	−	0.397036i
$715$	1144.14			1.60020
$716$		−	1704.64i		−	2.38078i
$717$			62.5458i			0.0872327i
$718$	1250.81			1.74207
$719$	−344.988			−0.479817			−0.239908	−	0.970796i	$-0.577117\pi$
$719$	−344.988			−0.479817			−0.239908	+	0.970796i	$0.577117\pi$
$720$			1864.20i			2.58917i
$721$	762.257	−	241.800i	1.05722	−	0.335368i
$722$	441.338			0.611272
$723$			31.4384i			0.0434832i
$724$	−220.246			−0.304208
$725$			226.601i			0.312553i
$726$	−85.6501			−0.117975
$727$	−478.785			−0.658576			−0.329288	−	0.944230i	$-0.606809\pi$
$727$	−478.785			−0.658576			−0.329288	+	0.944230i	$0.606809\pi$
$728$	−450.042	−	1418.72i	−0.618189	−	1.94879i
$729$	−660.792			−0.906437
$730$	2308.42			3.16222
$731$	682.441			0.933572
$732$		−	264.181i		−	0.360902i
$733$		−	559.854i		−	0.763784i	−0.924207	−	0.381892i	$-0.875273\pi$
$733$		−	559.854i		−	0.763784i	0.924207	−	0.381892i	$-0.124727\pi$
$734$			1777.11i			2.42112i
$735$	−76.5522	−	108.521i	−0.104153	−	0.147647i
$736$	−424.432			−0.576674
$737$	−1187.44			−1.61118
$738$	−963.161	+	888.583i	−1.30510	+	1.20404i
$739$	−94.8444			−0.128342			−0.0641708	−	0.997939i	$-0.520440\pi$
$739$	−94.8444			−0.128342			−0.0641708	+	0.997939i	$0.520440\pi$
$740$			331.287i			0.447685i
$741$	−68.3870			−0.0922902
$742$	988.812	−	313.667i	1.33263	−	0.422732i
$743$	−625.642			−0.842049			−0.421024	−	0.907049i	$-0.638329\pi$
$743$	−625.642			−0.842049			−0.421024	+	0.907049i	$0.638329\pi$
$744$			268.663i			0.361106i
$745$	−1932.88			−2.59446
$746$	276.549			0.370709
$747$			464.951i			0.622425i
$748$		−	3819.73i		−	5.10659i
$749$	−187.951	−	592.501i	−0.250936	−	0.791056i
$750$			16.1681i			0.0215575i
$751$			690.760i			0.919787i	0.887974	+	0.459894i	$0.152112\pi$
$751$			690.760i			0.919787i	−0.887974	+	0.459894i	$0.847888\pi$
$752$	−1006.85			−1.33890
$753$			59.9299i			0.0795881i
$754$		−	360.089i		−	0.477572i
$755$	−848.921			−1.12440
$756$	−128.571	−	405.312i	−0.170068	−	0.536127i
$757$		−	657.859i		−	0.869035i	−0.900663	−	0.434517i	$-0.856919\pi$
$757$		−	657.859i		−	0.869035i	0.900663	−	0.434517i	$-0.143081\pi$
$758$	−411.362			−0.542694
$759$			65.3743i			0.0861322i
$760$		−	2011.39i		−	2.64656i
$761$			953.926i			1.25352i	0.779214	+	0.626758i	$0.215619\pi$
$761$			953.926i			1.25352i	−0.779214	+	0.626758i	$0.784381\pi$
$762$	152.217			0.199760
$763$	96.3861	−	30.5752i	0.126325	−	0.0400724i
$764$		−	1925.53i		−	2.52032i
$765$			1987.69i			2.59828i
$766$	2579.54			3.36755
$767$		−	319.825i		−	0.416982i
$768$	171.606			0.223445
$769$			619.028i			0.804978i	0.915425	+	0.402489i	$0.131855\pi$
$769$			619.028i			0.804978i	−0.915425	+	0.402489i	$0.868145\pi$
$770$	−744.446	−	2346.81i	−0.966813	−	3.04781i
$771$	−26.2723			−0.0340756
$772$			2331.13i			3.01959i
$773$	881.505			1.14037			0.570185	−	0.821517i	$-0.306872\pi$
$773$	881.505			1.14037			0.570185	+	0.821517i	$0.306872\pi$
$774$	698.595			0.902578
$775$		−	1048.24i		−	1.35257i
$776$	−1298.04			−1.67273
$777$	−4.07887	−	12.8583i	−0.00524951	−	0.0165487i
$778$	1488.57			1.91333
$779$	465.566	−	429.518i	0.597646	−	0.551370i
$780$		−	286.960i		−	0.367898i
$781$	−815.806			−1.04457
$782$	−1440.06			−1.84151
$783$		−	57.2541i		−	0.0731215i
$784$	−1172.51	+	827.104i	−1.49554	+	1.05498i
$785$			761.741i			0.970370i
$786$			232.939i			0.296360i
$787$		−	361.400i		−	0.459212i	−0.973284	−	0.229606i	$-0.926256\pi$
$787$		−	361.400i		−	0.459212i	0.973284	−	0.229606i	$-0.0737438\pi$
$788$	−1176.48			−1.49300
$789$		−	38.6548i		−	0.0489922i
$790$	−1474.36			−1.86628
$791$	370.996	+	1169.54i	0.469022	+	1.47856i
$792$		−	2176.19i		−	2.74772i
$793$		−	911.605i		−	1.14956i
$794$	2474.01			3.11589
$795$	111.312			0.140015
$796$	2353.62			2.95681
$797$		−	248.629i		−	0.311956i	−0.987761	−	0.155978i	$-0.950147\pi$
$797$		−	248.629i		−	0.311956i	0.987761	−	0.155978i	$-0.0498528\pi$
$798$	44.4966	+	140.272i	0.0557601	+	0.175780i
$799$	−1073.55			−1.34361
$800$	885.035			1.10629
$801$	695.523			0.868319
$802$	1826.52			2.27746
$803$	−1207.26			−1.50343
$804$			297.820i			0.370423i
$805$	−612.949	+	194.437i	−0.761428	+	0.241537i
$806$			1665.75i			2.06668i
$807$		−	29.2777i		−	0.0362796i
$808$	1955.83			2.42059
$809$		−	938.921i		−	1.16059i	−0.814405	−	0.580297i	$-0.802936\pi$
$809$		−	938.921i		−	1.16059i	0.814405	−	0.580297i	$-0.197064\pi$
$810$			2001.54i			2.47104i
$811$		−	451.895i		−	0.557207i	−0.960406	−	0.278604i	$-0.910128\pi$
$811$		−	451.895i		−	0.557207i	0.960406	−	0.278604i	$-0.0898715\pi$
$812$	−511.689	+	162.316i	−0.630159	+	0.199896i
$813$			164.240i			0.202017i
$814$		−	250.087i		−	0.307232i
$815$			2250.42i			2.76125i
$816$	−344.794			−0.422542
$817$	−337.682			−0.413320
$818$		−	329.187i		−	0.402430i
$819$	−220.064	−	693.734i	−0.268698	−	0.847050i
$820$	1802.31	+	1953.57i	2.19794	+	2.38241i
$821$	742.625			0.904537			0.452268	−	0.891882i	$-0.350615\pi$
$821$	742.625			0.904537			0.452268	+	0.891882i	$0.350615\pi$
$822$			341.133i			0.415004i
$823$			167.401i			0.203403i	0.994815	+	0.101702i	$0.0324287\pi$
$823$			167.401i			0.203403i	−0.994815	+	0.101702i	$0.967571\pi$
$824$		−	2069.44i		−	2.51146i
$825$		−	136.320i		−	0.165236i
$826$	−656.010	+	208.097i	−0.794201	+	0.251933i
$827$			491.390i			0.594184i	0.954849	+	0.297092i	$0.0960168\pi$
$827$			491.390i			0.594184i	−0.954849	+	0.297092i	$0.903983\pi$
$828$	−1021.27			−1.23341
$829$			766.117i			0.924146i	0.886842	+	0.462073i	$0.152894\pi$
$829$			766.117i			0.924146i	−0.886842	+	0.462073i	$0.847106\pi$
$830$	1361.26			1.64007
$831$	92.3249			0.111101
$832$	−31.5087			−0.0378710
$833$	−1250.17	+	881.892i	−1.50081	+	1.05869i
$834$		−	57.2159i		−	0.0686042i
$835$		−	2314.73i		−	2.77213i
$836$			1890.06i			2.26084i
$837$			264.854i			0.316432i
$838$			282.391i			0.336982i
$839$	129.428			0.154264			0.0771322	−	0.997021i	$-0.475424\pi$
$839$	129.428			0.154264			0.0771322	+	0.997021i	$0.475424\pi$
$840$	−327.585	+	103.915i	−0.389982	+	0.123709i
$841$	768.719			0.914054
$842$		−	1400.55i		−	1.66337i
$843$		−	81.5733i		−	0.0967655i
$844$			2543.20i			3.01327i
$845$			224.395i			0.265557i
$846$	−1098.96			−1.29900
$847$	133.225	+	419.981i	0.157290	+	0.495845i
$848$		−	1202.67i		−	1.41824i
$849$		−	159.244i		−	0.187566i
$850$	3002.84			3.53276
$851$	−65.3186			−0.0767551
$852$			204.611i			0.240153i
$853$		−	223.261i		−	0.261736i	−0.991400	−	0.130868i	$-0.958224\pi$
$853$		−	223.261i		−	0.261736i	0.991400	−	0.130868i	$-0.0417764\pi$
$854$	−1869.84	+	593.143i	−2.18951	+	0.694547i
$855$		−	983.538i		−	1.15034i
$856$	−1608.57			−1.87917
$857$		−	541.478i		−	0.631830i	−0.948788	−	0.315915i	$-0.897689\pi$
$857$		−	541.478i		−	0.631830i	0.948788	−	0.315915i	$-0.102311\pi$
$858$			216.625i			0.252476i
$859$			1009.03i			1.17466i	0.809347	+	0.587331i	$0.199821\pi$
$859$			1009.03i			1.17466i	−0.809347	+	0.587331i	$0.800179\pi$
$860$		−	1416.96i		−	1.64762i
$861$	−94.0063	−	53.6343i	−0.109183	−	0.0622930i
$862$	−1581.03			−1.83414
$863$	537.333			0.622634			0.311317	−	0.950306i	$-0.399230\pi$
$863$	537.333			0.622634			0.311317	+	0.950306i	$0.399230\pi$
$864$	−223.617			−0.258816
$865$	−1896.03			−2.19194
$866$		−	2026.12i		−	2.33963i
$867$	−258.649			−0.298326
$868$	2367.04	−	750.863i	2.72700	−	0.865049i
$869$	771.060			0.887296
$870$	−83.1451			−0.0955691
$871$			1027.68i			1.17989i
$872$		−	261.677i		−	0.300089i
$873$	−634.720			−0.727056
$874$	712.563			0.815290
$875$	79.2797	−	25.1488i	0.0906053	−	0.0287415i
$876$			302.790i			0.345650i
$877$	300.027			0.342106			0.171053	−	0.985262i	$-0.445283\pi$
$877$	300.027			0.342106			0.171053	+	0.985262i	$0.445283\pi$
$878$	466.576			0.531407
$879$	77.9545			0.0886855
$880$	−2854.37			−3.24360
$881$		−	185.198i		−	0.210213i	−0.994461	−	0.105107i	$-0.966482\pi$
$881$		−	185.198i		−	0.210213i	0.994461	−	0.105107i	$-0.0335184\pi$
$882$	−1279.77	+	902.767i	−1.45098	+	1.02355i
$883$		−	267.127i		−	0.302522i	−0.988494	−	0.151261i	$-0.951667\pi$
$883$		−	267.127i		−	0.302522i	0.988494	−	0.151261i	$-0.0483334\pi$
$884$	−3305.82			−3.73962
$885$	−73.8482			−0.0834442
$886$	−1597.90			−1.80349
$887$	1279.75			1.44279			0.721395	−	0.692524i	$-0.243501\pi$
$887$	1279.75			1.44279			0.721395	+	0.692524i	$0.243501\pi$
$888$	−34.9089			−0.0393119
$889$	−236.766	−	746.388i	−0.266329	−	0.839582i
$890$		−	2036.31i		−	2.28799i
$891$		−	1046.77i		−	1.17482i
$892$		−	1458.28i		−	1.63484i
$893$	531.207			0.594856
$894$		−	365.958i		−	0.409349i
$895$	−1358.21			−1.51755
$896$	−260.626	−	821.605i	−0.290878	−	0.916970i
$897$	56.5789			0.0630757
$898$	1464.01			1.63030
$899$	334.366			0.371931
$900$	2129.57			2.36619
$901$		−	1282.33i		−	1.42323i
$902$	−1360.55	−	1474.74i	−1.50837	−	1.63497i
$903$	17.4458	+	54.9967i	0.0193199	+	0.0609045i
$904$	3175.16			3.51235
$905$			175.485i			0.193907i
$906$		−	160.729i		−	0.177405i
$907$	783.391			0.863717			0.431858	−	0.901941i	$-0.357858\pi$
$907$	783.391			0.863717			0.431858	+	0.901941i	$0.357858\pi$
$908$	2686.96			2.95921
$909$	956.374			1.05212
$910$	−2031.07	+	644.289i	−2.23195	+	0.708009i
$911$	−113.566			−0.124661			−0.0623304	−	0.998056i	$-0.519853\pi$
$911$	−113.566			−0.124661			−0.0623304	+	0.998056i	$0.519853\pi$
$912$	170.609			0.187072
$913$	−711.909			−0.779747
$914$			1620.85i			1.77336i
$915$	−210.491			−0.230045
$916$	−650.494			−0.710146
$917$	1142.20	−	362.326i	1.24559	−	0.395121i
$918$	−758.713			−0.826485
$919$			277.056i			0.301476i	0.988574	+	0.150738i	$0.0481649\pi$
$919$			277.056i			0.301476i	−0.988574	+	0.150738i	$0.951835\pi$
$920$			1664.09i			1.80879i
$921$			63.6563i			0.0691165i
$922$			2036.88i			2.20920i
$923$			706.048i			0.764949i
$924$	307.825	−	97.6471i	0.333144	−	0.105679i
$925$	136.204			0.147247
$926$			2666.24i			2.87930i
$927$		−	1011.93i		−	1.09161i
$928$			282.307i			0.304210i
$929$	−1463.46			−1.57530			−0.787652	−	0.616120i	$-0.788704\pi$
$929$	−1463.46			−1.57530			−0.787652	+	0.616120i	$0.788704\pi$
$930$	384.624			0.413574
$931$	618.605	−	436.374i	0.664452	−	0.468715i
$932$		−	1607.44i		−	1.72473i
$933$	113.031			0.121148
$934$			881.224i			0.943495i
$935$	−3043.44			−3.25502
$936$	−1883.41			−2.01219
$937$	−1020.63			−1.08926			−0.544628	−	0.838678i	$-0.683329\pi$
$937$	−1020.63			−1.08926			−0.544628	+	0.838678i	$0.683329\pi$
$938$	2107.94	−	668.671i	2.24727	−	0.712869i
$939$	95.6454			0.101859
$940$			2229.01i			2.37129i
$941$		−	36.1275i		−	0.0383927i	−0.999816	−	0.0191963i	$-0.993889\pi$
$941$		−	36.1275i		−	0.0383927i	0.999816	−	0.0191963i	$-0.00611076\pi$
$942$	−144.223			−0.153103
$943$	−385.179	+	355.354i	−0.408461	+	0.376834i
$944$			797.888i			0.845221i
$945$	−322.940	+	102.442i	−0.341736	+	0.108404i
$946$			1069.65i			1.13071i
$947$	795.569			0.840094			0.420047	−	0.907502i	$-0.362014\pi$
$947$	795.569			0.840094			0.420047	+	0.907502i	$0.362014\pi$
$948$		−	193.388i		−	0.203996i
$949$			1044.83i			1.10098i
$950$	−1485.85			−1.56406
$951$		−	25.1678i		−	0.0264646i
$952$	1197.12	+	3773.83i	1.25748	+	3.96410i
$953$	−1728.29			−1.81353			−0.906765	−	0.421636i	$-0.861456\pi$
$953$	−1728.29			−1.81353			−0.906765	+	0.421636i	$0.861456\pi$
$954$		−	1312.69i		−	1.37598i
$955$	−1534.20			−1.60649
$956$		−	1496.05i		−	1.56491i
$957$	43.4832			0.0454370
$958$	−484.481			−0.505721
$959$	1672.73	−	530.617i	1.74424	−	0.553302i
$960$			7.27540i			0.00757855i
$961$	−585.756			−0.609528
$962$	−216.440			−0.224990
$963$	−786.568			−0.816789
$964$		−	751.984i		−	0.780066i
$965$	1857.37			1.92474
$966$	−36.8135	−	116.052i	−0.0381092	−	0.120136i
$967$		−	1121.73i		−	1.16001i	−0.814611	−	0.580007i	$-0.803050\pi$
$967$		−	1121.73i		−	1.16001i	0.814611	−	0.580007i	$-0.196950\pi$
$968$	1140.20			1.17789
$969$	181.911			0.187730
$970$			1858.29i			1.91577i
$971$	−1577.83			−1.62495			−0.812476	−	0.582995i	$-0.801881\pi$
$971$	−1577.83			−1.62495			−0.812476	+	0.582995i	$0.801881\pi$
$972$	−809.243			−0.832555
$973$	−280.555	+	88.9966i	−0.288340	+	0.0914662i
$974$	−1980.81			−2.03369
$975$	−117.980			−0.121005
$976$			2274.24i			2.33016i
$977$			1342.31i			1.37391i	0.726698	+	0.686957i	$0.241054\pi$
$977$			1342.31i			1.37391i	−0.726698	+	0.686957i	$0.758946\pi$
$978$	−426.079			−0.435664
$979$			1064.95i			1.08779i
$980$	1831.08	+	2595.74i	1.86845	+	2.64872i
$981$		−	127.956i		−	0.130435i
$982$	−1313.91			−1.33799
$983$			1191.34i			1.21195i	0.795485	+	0.605974i	$0.207216\pi$
$983$			1191.34i			1.21195i	−0.795485	+	0.605974i	$0.792784\pi$
$984$	−205.855	+	189.916i	−0.209203	+	0.193004i
$985$			937.384i			0.951659i
$986$			957.843i			0.971443i
$987$	−27.4440	−	86.5152i	−0.0278055	−	0.0876547i
$988$	1635.77			1.65564
$989$	279.376			0.282483
$990$	−3115.48			−3.14695
$991$			1045.63i			1.05512i	0.849517	+	0.527562i	$0.176894\pi$
$991$			1045.63i			1.05512i	−0.849517	+	0.527562i	$0.823106\pi$
$992$		−	1305.93i		−	1.31647i
$993$			115.591i			0.116406i
$994$	1448.21	−	459.396i	1.45695	−	0.462169i
$995$		−	1875.30i		−	1.88472i
$996$			178.552i			0.179270i
$997$	−1081.55			−1.08481			−0.542403	−	0.840119i	$-0.682485\pi$
$997$	−1081.55			−1.08481			−0.542403	+	0.840119i	$0.682485\pi$
$998$		−	2792.29i		−	2.79789i
$999$	−34.4139			−0.0344484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.d.286.1	✓	32
7.6	odd	2	inner	287.3.d.d.286.4	yes	32
41.40	even	2	inner	287.3.d.d.286.3	yes	32
287.286	odd	2	inner	287.3.d.d.286.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.d.286.1	✓	32	1.1	even	1	trivial
287.3.d.d.286.2	yes	32	287.286	odd	2	inner
287.3.d.d.286.3	yes	32	41.40	even	2	inner
287.3.d.d.286.4	yes	32	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.60835 q^{2} -0.377109 q^{3} +9.02020 q^{4} -7.18702i q^{5} +1.36074 q^{6} +(-2.11657 - 6.67234i) q^{7} -18.1146 q^{8} -8.85779 q^{9} +O(q^{10})\)	\(q-3.60835 q^{2} -0.377109 q^{3} +9.02020 q^{4} -7.18702i q^{5} +1.36074 q^{6} +(-2.11657 - 6.67234i) q^{7} -18.1146 q^{8} -8.85779 q^{9} +25.9333i q^{10} -13.5626i q^{11} -3.40160 q^{12} -11.7379 q^{13} +(7.63734 + 24.0761i) q^{14} +2.71029i q^{15} +29.2832 q^{16} +31.2229 q^{17} +31.9620 q^{18} -15.4496 q^{19} -64.8283i q^{20} +(0.798180 + 2.51620i) q^{21} +48.9386i q^{22} +12.7820 q^{23} +6.83120 q^{24} -26.6532 q^{25} +42.3544 q^{26} +6.73434 q^{27} +(-19.0919 - 60.1858i) q^{28} -8.50181i q^{29} -9.77969i q^{30} +39.3288i q^{31} -33.2055 q^{32} +5.11458i q^{33} -112.663 q^{34} +(-47.9542 + 15.2119i) q^{35} -79.8990 q^{36} -5.11022 q^{37} +55.7475 q^{38} +4.42646 q^{39} +130.190i q^{40} +(-30.1346 + 27.8012i) q^{41} +(-2.88011 - 9.07934i) q^{42} +21.8570 q^{43} -122.337i q^{44} +63.6611i q^{45} -46.1218 q^{46} -34.3832 q^{47} -11.0430 q^{48} +(-40.0402 + 28.2450i) q^{49} +96.1742 q^{50} -11.7745 q^{51} -105.878 q^{52} -41.0702i q^{53} -24.2999 q^{54} -97.4745 q^{55} +(38.3410 + 120.867i) q^{56} +5.82619 q^{57} +30.6775i q^{58} +27.2473i q^{59} +24.4474i q^{60} +77.6635i q^{61} -141.912i q^{62} +(18.7482 + 59.1022i) q^{63} +2.68436 q^{64} +84.3603i q^{65} -18.4552i q^{66} -87.5529i q^{67} +281.637 q^{68} -4.82020 q^{69} +(173.036 - 54.8897i) q^{70} -60.1512i q^{71} +160.456 q^{72} -89.0139i q^{73} +18.4395 q^{74} +10.0512 q^{75} -139.358 q^{76} +(-90.4941 + 28.7062i) q^{77} -15.9722 q^{78} +56.8520i q^{79} -210.459i q^{80} +77.1805 q^{81} +(108.736 - 100.317i) q^{82} -52.4907i q^{83} +(7.19974 + 22.6966i) q^{84} -224.400i q^{85} -78.8679 q^{86} +3.20611i q^{87} +245.681i q^{88} -78.5211 q^{89} -229.712i q^{90} +(24.8441 + 78.3191i) q^{91} +115.296 q^{92} -14.8313i q^{93} +124.067 q^{94} +111.036i q^{95} +12.5221 q^{96} +71.6567 q^{97} +(144.479 - 101.918i) q^{98} +120.134i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9	\( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9} - 92 q^{16} - 48 q^{18} - 72 q^{21} + 140 q^{23} - 500 q^{25} + 92 q^{32} - 284 q^{36} + 312 q^{37} + 140 q^{39} + 8 q^{42} - 120 q^{43} - 344 q^{46} - 552 q^{49} + 416 q^{50} - 364 q^{51} - 316 q^{57} - 320 q^{64} + 972 q^{72} + 680 q^{74} + 428 q^{77} + 1144 q^{78} - 240 q^{81} + 640 q^{84} + 260 q^{86} - 160 q^{91} + 676 q^{92} + 532 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9 - 92 * q^16 - 48 * q^18 - 72 * q^21 + 140 * q^23 - 500 * q^25 + 92 * q^32 - 284 * q^36 + 312 * q^37 + 140 * q^39 + 8 * q^42 - 120 * q^43 - 344 * q^46 - 552 * q^49 + 416 * q^50 - 364 * q^51 - 316 * q^57 - 320 * q^64 + 972 * q^72 + 680 * q^74 + 428 * q^77 + 1144 * q^78 - 240 * q^81 + 640 * q^84 + 260 * q^86 - 160 * q^91 + 676 * q^92 + 532 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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