LMFDB - Embedded newform 287.3.d.d.286.3

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			286.3
Character	$\chi$	$=$	287.286
Dual form			287.3.d.d.286.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.60835 q^{2} +0.377109 q^{3} +9.02020 q^{4} -7.18702i q^{5} -1.36074 q^{6} +(2.11657 + 6.67234i) q^{7} -18.1146 q^{8} -8.85779 q^{9} +O(q^{10})$	\(q-3.60835 q^{2} +0.377109 q^{3} +9.02020 q^{4} -7.18702i q^{5} -1.36074 q^{6} +(2.11657 + 6.67234i) q^{7} -18.1146 q^{8} -8.85779 q^{9} +25.9333i q^{10} +13.5626i q^{11} +3.40160 q^{12} +11.7379 q^{13} +(-7.63734 - 24.0761i) q^{14} -2.71029i q^{15} +29.2832 q^{16} -31.2229 q^{17} +31.9620 q^{18} +15.4496 q^{19} -64.8283i q^{20} +(0.798180 + 2.51620i) q^{21} -48.9386i q^{22} +12.7820 q^{23} -6.83120 q^{24} -26.6532 q^{25} -42.3544 q^{26} -6.73434 q^{27} +(19.0919 + 60.1858i) q^{28} +8.50181i q^{29} +9.77969i q^{30} +39.3288i q^{31} -33.2055 q^{32} +5.11458i q^{33} +112.663 q^{34} +(47.9542 - 15.2119i) q^{35} -79.8990 q^{36} -5.11022 q^{37} -55.7475 q^{38} +4.42646 q^{39} +130.190i q^{40} +(30.1346 + 27.8012i) q^{41} +(-2.88011 - 9.07934i) q^{42} +21.8570 q^{43} +122.337i q^{44} +63.6611i q^{45} -46.1218 q^{46} +34.3832 q^{47} +11.0430 q^{48} +(-40.0402 + 28.2450i) q^{49} +96.1742 q^{50} -11.7745 q^{51} +105.878 q^{52} +41.0702i q^{53} +24.2999 q^{54} +97.4745 q^{55} +(-38.3410 - 120.867i) q^{56} +5.82619 q^{57} -30.6775i q^{58} +27.2473i q^{59} -24.4474i q^{60} +77.6635i q^{61} -141.912i q^{62} +(-18.7482 - 59.1022i) q^{63} +2.68436 q^{64} -84.3603i q^{65} -18.4552i q^{66} +87.5529i q^{67} -281.637 q^{68} +4.82020 q^{69} +(-173.036 + 54.8897i) q^{70} +60.1512i q^{71} +160.456 q^{72} -89.0139i q^{73} +18.4395 q^{74} -10.0512 q^{75} +139.358 q^{76} +(-90.4941 + 28.7062i) q^{77} -15.9722 q^{78} -56.8520i q^{79} -210.459i q^{80} +77.1805 q^{81} +(-108.736 - 100.317i) q^{82} -52.4907i q^{83} +(7.19974 + 22.6966i) q^{84} +224.400i q^{85} -78.8679 q^{86} +3.20611i q^{87} -245.681i q^{88} +78.5211 q^{89} -229.712i q^{90} +(24.8441 + 78.3191i) q^{91} +115.296 q^{92} +14.8313i q^{93} -124.067 q^{94} -111.036i q^{95} -12.5221 q^{96} -71.6567 q^{97} +(144.479 - 101.918i) q^{98} -120.134i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.479981\pi$
$3$	0.377109			0.125703			0.0628516	+	0.998023i	$0.479981\pi$
$4$	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	$0.211442\pi$
$11$			13.5626i			1.23296i	−0.787370	+	0.616481i	$0.788558\pi$
$12$	3.40160			0.283467
$13$	11.7379			0.902913			0.451457	−	0.892293i	$-0.350905\pi$
$13$	11.7379			0.902913			0.451457	+	0.892293i	$0.350905\pi$
$14$	−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	$-0.870455\pi$
$17$	−31.2229			−1.83664			−0.918322	+	0.395835i	$0.870455\pi$
$18$	31.9620			1.77567
$19$	15.4496			0.813136			0.406568	−	0.913620i	$-0.366725\pi$
$19$	15.4496			0.813136			0.406568	+	0.913620i	$0.366725\pi$
$20$		−	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	$0.0468275\pi$
$29$			8.50181i			0.293166i	−0.989198	+	0.146583i	$0.953172\pi$
$30$			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	$-0.380803\pi$
$47$	34.3832			0.731558			0.365779	+	0.930702i	$0.380803\pi$
$48$	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	$0.126646\pi$
$53$			41.0702i			0.774910i	−0.921889	+	0.387455i	$0.873354\pi$
$54$	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	$0.226649\pi$
$67$			87.5529i			1.30676i	−0.757030	+	0.653380i	$0.773351\pi$
$68$	−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	$0.139234\pi$
$71$			60.1512i			0.847201i	−0.905849	+	0.423600i	$0.860766\pi$
$72$	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	$-0.882837\pi$
$79$		−	56.8520i		−	0.719646i	0.933021	−	0.359823i	$-0.117163\pi$
$80$		−	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	$-0.354578\pi$
$89$	78.5211			0.882260			0.441130	+	0.897443i	$0.354578\pi$
$90$		−	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	$-0.620425\pi$
$97$	−71.6567			−0.738729			−0.369365	+	0.929285i	$0.620425\pi$
$98$	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	$-0.320498\pi$
$101$	107.970			1.06901			0.534504	+	0.845166i	$0.320498\pi$
$102$	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	$-0.978892\pi$
$109$		−	14.4456i		−	0.132529i	0.997802	−	0.0662643i	$-0.0211081\pi$
$110$	−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	$-0.632231\pi$
$137$		−	250.696i		−	1.82990i	0.403569	−	0.914949i	$-0.367769\pi$
$138$	−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	$0.358258\pi$
$149$			268.940i			1.80497i	−0.430726	+	0.902483i	$0.641742\pi$
$150$	36.2682			0.241788
$151$			118.119i			0.782243i	0.920339	+	0.391122i	$0.127913\pi$
$151$			118.119i			0.782243i	−0.920339	+	0.391122i	$0.872087\pi$
$152$	−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	$-0.390404\pi$
$157$	105.988			0.675085			0.337543	+	0.941310i	$0.390404\pi$
$158$			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	$-0.914671\pi$
$167$	−322.071			−1.92857			−0.964284	+	0.264871i	$0.914671\pi$
$168$	−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	$0.177012\pi$
$179$			188.980i			1.05576i	−0.849320	+	0.527878i	$0.822988\pi$
$180$			574.236i			3.19020i
$181$	24.4170			0.134901			0.0674503	−	0.997723i	$-0.478514\pi$
$181$	24.4170			0.134901			0.0674503	+	0.997723i	$0.478514\pi$
$182$	−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	$0.188745\pi$
$191$			213.468i			1.11763i	−0.829291	+	0.558817i	$0.811255\pi$
$192$	1.01230			0.00527238
$193$		−	258.434i		−	1.33904i	−0.742796	−	0.669518i	$-0.766501\pi$
$193$		−	258.434i		−	1.33904i	0.742796	−	0.669518i	$-0.233499\pi$
$194$	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	$-0.727584\pi$
$199$	−260.928			−1.31120			−0.655598	+	0.755110i	$0.727584\pi$
$200$	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	$-0.767101\pi$
$211$		−	281.945i		−	1.33623i	0.744056	−	0.668117i	$-0.232899\pi$
$212$			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	$-0.727807\pi$
$227$	−297.883			−1.31226			−0.656129	+	0.754649i	$0.727807\pi$
$228$	52.5534			0.230497
$229$	72.1152			0.314914			0.157457	−	0.987526i	$-0.449670\pi$
$229$	72.1152			0.314914			0.157457	+	0.987526i	$0.449670\pi$
$230$			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	$0.124907\pi$
$233$			178.205i			0.764828i	−0.923991	+	0.382414i	$0.875093\pi$
$234$	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	$0.112792\pi$
$239$			165.856i			0.693958i	−0.937873	+	0.346979i	$0.887208\pi$
$240$		−	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	$-0.543277\pi$
$257$	−69.6675			−0.271080			−0.135540	+	0.990772i	$0.543277\pi$
$258$	−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	$-0.937571\pi$
$263$		−	102.503i		−	0.389745i	0.980829	−	0.194873i	$-0.0624293\pi$
$264$		−	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	$-0.874237\pi$
$281$		−	216.312i		−	0.769794i	0.922960	−	0.384897i	$-0.125763\pi$
$282$	−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
$287$	−121.717	+	259.911i	−0.424102	+	0.905614i
$288$	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	$-0.385244\pi$
$293$	206.716			0.705515			0.352758	+	0.935715i	$0.385244\pi$
$294$	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	$-0.339954\pi$
$311$	299.729			0.963760			0.481880	+	0.876237i	$0.339954\pi$
$312$	−80.1838			−0.256999
$313$	253.628			0.810312			0.405156	−	0.914247i	$-0.367217\pi$
$313$	253.628			0.810312			0.405156	+	0.914247i	$0.367217\pi$
$314$	−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	$-0.966431\pi$
$317$		−	66.7388i		−	0.210533i	0.994444	−	0.105266i	$-0.0335695\pi$
$318$		−	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	$0.153234\pi$
$331$			306.519i			0.926040i	−0.886348	+	0.463020i	$0.846766\pi$
$332$		−	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	$0.160955\pi$
$347$			336.160i			0.968762i	−0.874857	+	0.484381i	$0.839045\pi$
$348$			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	$-0.116947\pi$
$383$	714.880			1.86653			0.933264	+	0.359190i	$0.116947\pi$
$384$	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	$-0.168254\pi$
$397$	685.635			1.72704			0.863520	+	0.504314i	$0.168254\pi$
$398$	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	$-0.847499\pi$
$421$		−	388.142i		−	0.921953i	0.887412	−	0.460977i	$-0.152501\pi$
$422$			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	$-0.452951\pi$
$439$	129.304			0.294543			0.147272	+	0.989096i	$0.452951\pi$
$440$	−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	$0.163536\pi$
$457$			449.194i			0.982919i	−0.870900	+	0.491460i	$0.836464\pi$
$458$	−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	$0.294085\pi$
$463$			738.907i			1.59591i	−0.602716	+	0.797955i	$0.705915\pi$
$464$			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	$-0.544759\pi$
$479$	−134.266			−0.280306			−0.140153	+	0.990130i	$0.544759\pi$
$480$			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	$-0.717552\pi$
$499$		−	773.841i		−	1.55078i	0.631480	−	0.775392i	$-0.282448\pi$
$500$			107.177i			0.214353i
$501$	−121.456			−0.242427
$502$			573.436i			1.14230i
$503$	−149.544			−0.297304			−0.148652	−	0.988890i	$-0.547493\pi$
$503$	−149.544			−0.297304			−0.148652	+	0.988890i	$0.547493\pi$
$504$	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	$-0.586597\pi$
$509$	−273.545			−0.537416			−0.268708	+	0.963222i	$0.586597\pi$
$510$		−	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	$-0.381013\pi$
$521$	380.502			0.730329			0.365165	+	0.930943i	$0.381013\pi$
$522$			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	$0.0228474\pi$
$547$			78.4570i			0.143431i	−0.997425	+	0.0717157i	$0.977153\pi$
$548$		−	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	$0.0556392\pi$
$557$			193.732i			0.347814i	−0.984762	+	0.173907i	$0.944361\pi$
$558$			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	$-0.322948\pi$
$563$	594.511			1.05597			0.527985	+	0.849253i	$0.322948\pi$
$564$	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	$0.0715365\pi$
$571$			254.496i			0.445703i	−0.974852	+	0.222851i	$0.928464\pi$
$572$			1435.98i			2.51045i
$573$			80.5009i			0.140490i
$574$	439.199	−	937.851i	0.765155	−	1.63389i
$575$	−340.681			−0.592488
$576$	−23.7775			−0.0412804
$577$	17.6727			0.0306285			0.0153143	−	0.999883i	$-0.495125\pi$
$577$	17.6727			0.0306285			0.0153143	+	0.999883i	$0.495125\pi$
$578$	−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	$-0.373411\pi$
$587$	454.679			0.774581			0.387291	+	0.921958i	$0.373411\pi$
$588$	−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	$-0.376882\pi$
$593$	447.375			0.754427			0.377214	+	0.926126i	$0.376882\pi$
$594$			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	$-0.296925\pi$
$601$	715.878			1.19115			0.595573	+	0.803301i	$0.296925\pi$
$602$	−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	$0.103185\pi$
$641$			408.341i			0.637038i	−0.947917	+	0.318519i	$0.896815\pi$
$642$	−120.833			−0.188214
$643$	−426.772			−0.663720			−0.331860	−	0.943329i	$-0.607676\pi$
$643$	−426.772			−0.663720			−0.331860	+	0.943329i	$0.607676\pi$
$644$	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	$0.323378\pi$
$653$			1110.06i			1.69993i	−0.526837	+	0.849966i	$0.676622\pi$
$654$			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	$-0.836342\pi$
$659$		−	648.182i		−	0.983584i	0.870713	−	0.491792i	$-0.163658\pi$
$660$	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	$0.147387\pi$
$673$			601.208i			0.893325i	−0.894703	+	0.446662i	$0.852613\pi$
$674$	−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	$-0.897256\pi$
$683$		−	433.302i		−	0.634410i	0.948357	−	0.317205i	$-0.102744\pi$
$684$	−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	$-0.646794\pi$
$691$	−614.980			−0.889985			−0.444993	+	0.895534i	$0.646794\pi$
$692$		−	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	$0.00210524\pi$
$709$			9.37833i			0.0132275i	−0.999978	+	0.00661377i	$0.997895\pi$
$710$	−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	$-0.422883\pi$
$719$	344.988			0.479817			0.239908	+	0.970796i	$0.422883\pi$
$720$			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	$-0.393191\pi$
$727$	478.785			0.658576			0.329288	+	0.944230i	$0.393191\pi$
$728$	−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	$-0.847888\pi$
$751$		−	690.760i		−	0.919787i	0.887974	−	0.459894i	$-0.152112\pi$
$752$	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	$0.143081\pi$
$757$			657.859i			0.869035i	−0.900663	+	0.434517i	$0.856919\pi$
$758$	−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	$-0.693128\pi$
$773$	−881.505			−1.14037			−0.570185	+	0.821517i	$0.693128\pi$
$774$	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	$0.197064\pi$
$809$			938.921i			1.16059i	−0.814405	+	0.580297i	$0.802936\pi$
$810$			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	$-0.967571\pi$
$823$		−	167.401i		−	0.203403i	0.994815	−	0.101702i	$-0.0324287\pi$
$824$		−	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	$-0.903983\pi$
$827$		−	491.390i		−	0.594184i	0.954849	−	0.297092i	$-0.0960168\pi$
$828$	−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	$-0.524576\pi$
$839$	−129.428			−0.154264			−0.0771322	+	0.997021i	$0.524576\pi$
$840$	−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
$861$	−45.9007	+	98.0150i	−0.0533110	+	0.113839i
$862$	−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	$0.0483334\pi$
$883$			267.127i			0.302522i	−0.988494	+	0.151261i	$0.951667\pi$
$884$	−3305.82			−3.73962
$885$	73.8482			0.0834442
$886$	−1597.90			−1.80349
$887$	−1279.75			−1.44279			−0.721395	−	0.692524i	$-0.756499\pi$
$887$	−1279.75			−1.44279			−0.721395	+	0.692524i	$0.756499\pi$
$888$	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	$-0.951835\pi$
$919$		−	277.056i		−	0.301476i	0.988574	−	0.150738i	$-0.0481649\pi$
$920$			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	$-0.211296\pi$
$929$	1463.46			1.57530			0.787652	+	0.616120i	$0.211296\pi$
$930$	−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	$-0.316671\pi$
$937$	1020.63			1.08926			0.544628	+	0.838678i	$0.316671\pi$
$938$	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	$0.196950\pi$
$967$			1121.73i			1.16001i	−0.814611	+	0.580007i	$0.803050\pi$
$968$	1140.20			1.17789
$969$	−181.911			−0.187730
$970$		−	1858.29i		−	1.91577i
$971$	1577.83			1.62495			0.812476	−	0.582995i	$-0.198119\pi$
$971$	1577.83			1.62495			0.812476	+	0.582995i	$0.198119\pi$
$972$	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	$-0.758946\pi$
$977$		−	1342.31i		−	1.37391i	0.726698	−	0.686957i	$-0.241054\pi$
$978$	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	$-0.823106\pi$
$991$		−	1045.63i		−	1.05512i	0.849517	−	0.527562i	$-0.176894\pi$
$992$		−	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	$-0.317515\pi$
$997$	1081.55			1.08481			0.542403	+	0.840119i	$0.317515\pi$
$998$			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.286.3	yes	32
7.6	odd	2	inner	287.3.d.d.286.2	yes	32
41.40	even	2	inner	287.3.d.d.286.1	✓	32
287.286	odd	2	inner	287.3.d.d.286.4	yes	32

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

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Database

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