LMFDB - Embedded newform 287.3.d.d.286.16

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			286.16
Character	$\chi$	$=$	287.286
Dual form			287.3.d.d.286.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.517567 q^{2} +2.41493 q^{3} -3.73212 q^{4} +2.97759i q^{5} +1.24989 q^{6} +(-2.38045 + 6.58281i) q^{7} -4.00189 q^{8} -3.16813 q^{9} +O(q^{10})$	\(q+0.517567 q^{2} +2.41493 q^{3} -3.73212 q^{4} +2.97759i q^{5} +1.24989 q^{6} +(-2.38045 + 6.58281i) q^{7} -4.00189 q^{8} -3.16813 q^{9} +1.54110i q^{10} -4.27011i q^{11} -9.01280 q^{12} -14.5000 q^{13} +(-1.23204 + 3.40705i) q^{14} +7.19066i q^{15} +12.8573 q^{16} -14.2669 q^{17} -1.63972 q^{18} -7.77425 q^{19} -11.1127i q^{20} +(-5.74862 + 15.8970i) q^{21} -2.21007i q^{22} -5.72179 q^{23} -9.66427 q^{24} +16.1339 q^{25} -7.50471 q^{26} -29.3851 q^{27} +(8.88415 - 24.5679i) q^{28} +47.3894i q^{29} +3.72165i q^{30} +47.8731i q^{31} +22.6621 q^{32} -10.3120i q^{33} -7.38410 q^{34} +(-19.6009 - 7.08802i) q^{35} +11.8239 q^{36} +46.7632 q^{37} -4.02370 q^{38} -35.0164 q^{39} -11.9160i q^{40} +(9.42175 - 39.9028i) q^{41} +(-2.97530 + 8.22776i) q^{42} +7.24853 q^{43} +15.9366i q^{44} -9.43340i q^{45} -2.96141 q^{46} +1.84650 q^{47} +31.0493 q^{48} +(-37.6669 - 31.3402i) q^{49} +8.35040 q^{50} -34.4536 q^{51} +54.1158 q^{52} -2.40642i q^{53} -15.2088 q^{54} +12.7147 q^{55} +(9.52632 - 26.3437i) q^{56} -18.7742 q^{57} +24.5272i q^{58} +57.9540i q^{59} -26.8364i q^{60} -36.3183i q^{61} +24.7775i q^{62} +(7.54160 - 20.8552i) q^{63} -39.6999 q^{64} -43.1750i q^{65} -5.33716i q^{66} -10.0902i q^{67} +53.2460 q^{68} -13.8177 q^{69} +(-10.1448 - 3.66852i) q^{70} +64.0276i q^{71} +12.6785 q^{72} +82.0605i q^{73} +24.2031 q^{74} +38.9623 q^{75} +29.0145 q^{76} +(28.1094 + 10.1648i) q^{77} -18.1233 q^{78} -60.4435i q^{79} +38.2836i q^{80} -42.4497 q^{81} +(4.87638 - 20.6523i) q^{82} -112.173i q^{83} +(21.4546 - 59.3296i) q^{84} -42.4811i q^{85} +3.75160 q^{86} +114.442i q^{87} +17.0885i q^{88} -98.9327 q^{89} -4.88242i q^{90} +(34.5166 - 95.4507i) q^{91} +21.3544 q^{92} +115.610i q^{93} +0.955689 q^{94} -23.1486i q^{95} +54.7272 q^{96} -78.1202 q^{97} +(-19.4951 - 16.2206i) q^{98} +13.5283i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.517567			0.258783			0.129392	−	0.991594i	$-0.458698\pi$
$2$	0.517567			0.258783			0.129392	+	0.991594i	$0.458698\pi$
$3$	2.41493			0.804975			0.402488	−	0.915425i	$-0.368146\pi$
$3$	2.41493			0.804975			0.402488	+	0.915425i	$0.368146\pi$
$4$	−3.73212			−0.933031
$5$			2.97759i			0.595518i	0.954641	+	0.297759i	$0.0962392\pi$
$5$			2.97759i			0.595518i	−0.954641	+	0.297759i	$0.903761\pi$
$6$	1.24989			0.208314
$7$	−2.38045	+	6.58281i	−0.340065	+	0.940402i
$7$	−2.38045	+	6.58281i	−0.340065	+	0.940402i
$8$	−4.00189			−0.500236
$9$	−3.16813			−0.352015
$10$			1.54110i			0.154110i
$11$		−	4.27011i		−	0.388192i	−0.980983	−	0.194096i	$-0.937823\pi$
$11$		−	4.27011i		−	0.388192i	0.980983	−	0.194096i	$-0.0621774\pi$
$12$	−9.01280			−0.751067
$13$	−14.5000			−1.11538			−0.557692	−	0.830048i	$-0.688313\pi$
$13$	−14.5000			−1.11538			−0.557692	+	0.830048i	$0.688313\pi$
$14$	−1.23204	+	3.40705i	−0.0880032	+	0.243360i
$15$			7.19066i			0.479378i
$16$	12.8573			0.803578
$17$	−14.2669			−0.839232			−0.419616	−	0.907702i	$-0.637835\pi$
$17$	−14.2669			−0.839232			−0.419616	+	0.907702i	$0.637835\pi$
$18$	−1.63972			−0.0910956
$19$	−7.77425			−0.409171			−0.204586	−	0.978849i	$-0.565585\pi$
$19$	−7.77425			−0.409171			−0.204586	+	0.978849i	$0.565585\pi$
$20$		−	11.1127i		−	0.555637i
$21$	−5.74862	+	15.8970i	−0.273744	+	0.757000i
$22$		−	2.21007i		−	0.100458i
$23$	−5.72179			−0.248773			−0.124387	−	0.992234i	$-0.539696\pi$
$23$	−5.72179			−0.248773			−0.124387	+	0.992234i	$0.539696\pi$
$24$	−9.66427			−0.402678
$25$	16.1339			0.645358
$26$	−7.50471			−0.288643
$27$	−29.3851			−1.08834
$28$	8.88415	−	24.5679i	0.317291	−	0.877424i
$29$			47.3894i			1.63412i	0.576553	+	0.817059i	$0.304397\pi$
$29$			47.3894i			1.63412i	−0.576553	+	0.817059i	$0.695603\pi$
$30$			3.72165i			0.124055i
$31$			47.8731i			1.54429i	0.635444	+	0.772147i	$0.280817\pi$
$31$			47.8731i			1.54429i	−0.635444	+	0.772147i	$0.719183\pi$
$32$	22.6621			0.708189
$33$		−	10.3120i		−	0.312485i
$34$	−7.38410			−0.217179
$35$	−19.6009	−	7.08802i	−0.560027	−	0.202515i
$36$	11.8239			0.328441
$37$	46.7632			1.26387			0.631935	−	0.775021i	$-0.282261\pi$
$37$	46.7632			1.26387			0.631935	+	0.775021i	$0.282261\pi$
$38$	−4.02370			−0.105887
$39$	−35.0164			−0.897856
$40$		−	11.9160i		−	0.297900i
$41$	9.42175	−	39.9028i	0.229799	−	0.973238i
$41$	9.42175	−	39.9028i	0.229799	−	0.973238i
$42$	−2.97530	+	8.22776i	−0.0708404	+	0.195899i
$43$	7.24853			0.168570			0.0842852	−	0.996442i	$-0.473139\pi$
$43$	7.24853			0.168570			0.0842852	+	0.996442i	$0.473139\pi$
$44$			15.9366i			0.362195i
$45$		−	9.43340i		−	0.209631i
$46$	−2.96141			−0.0643784
$47$	1.84650			0.0392873			0.0196437	−	0.999807i	$-0.493747\pi$
$47$	1.84650			0.0392873			0.0196437	+	0.999807i	$0.493747\pi$
$48$	31.0493			0.646861
$49$	−37.6669	−	31.3402i	−0.768712	−	0.639595i
$50$	8.35040			0.167008
$51$	−34.4536			−0.675561
$52$	54.1158			1.04069
$53$		−	2.40642i		−	0.0454041i	−0.999742	−	0.0227020i	$-0.992773\pi$
$53$		−	2.40642i		−	0.0454041i	0.999742	−	0.0227020i	$-0.00722690\pi$
$54$	−15.2088			−0.281644
$55$	12.7147			0.231176
$56$	9.52632	−	26.3437i	0.170113	−	0.470423i
$57$	−18.7742			−0.329373
$58$			24.5272i			0.422883i
$59$			57.9540i			0.982271i	0.871083	+	0.491135i	$0.163418\pi$
$59$			57.9540i			0.982271i	−0.871083	+	0.491135i	$0.836582\pi$
$60$		−	26.8364i		−	0.447274i
$61$		−	36.3183i		−	0.595383i	−0.954662	−	0.297691i	$-0.903783\pi$
$61$		−	36.3183i		−	0.595383i	0.954662	−	0.297691i	$-0.0962166\pi$
$62$			24.7775i			0.399637i
$63$	7.54160	−	20.8552i	0.119708	−	0.331035i
$64$	−39.6999			−0.620311
$65$		−	43.1750i		−	0.664231i
$66$		−	5.33716i		−	0.0808660i
$67$		−	10.0902i		−	0.150600i	−0.997161	−	0.0752998i	$-0.976009\pi$
$67$		−	10.0902i		−	0.150600i	0.997161	−	0.0752998i	$-0.0239914\pi$
$68$	53.2460			0.783030
$69$	−13.8177			−0.200256
$70$	−10.1448	−	3.66852i	−0.144926	−	0.0524075i
$71$			64.0276i			0.901797i	0.892575	+	0.450899i	$0.148896\pi$
$71$			64.0276i			0.901797i	−0.892575	+	0.450899i	$0.851104\pi$
$72$	12.6785			0.176091
$73$			82.0605i			1.12412i	0.827098	+	0.562058i	$0.189990\pi$
$73$			82.0605i			1.12412i	−0.827098	+	0.562058i	$0.810010\pi$
$74$	24.2031			0.327069
$75$	38.9623			0.519497
$76$	29.0145			0.381770
$77$	28.1094	+	10.1648i	0.365057	+	0.132011i
$78$	−18.1233			−0.232350
$79$		−	60.4435i		−	0.765108i	−0.923933	−	0.382554i	$-0.875045\pi$
$79$		−	60.4435i		−	0.765108i	0.923933	−	0.382554i	$-0.124955\pi$
$80$			38.2836i			0.478546i
$81$	−42.4497			−0.524071
$82$	4.87638	−	20.6523i	0.0594681	−	0.251858i
$83$		−	112.173i		−	1.35148i	−0.737141	−	0.675739i	$-0.763825\pi$
$83$		−	112.173i		−	1.35148i	0.737141	−	0.675739i	$-0.236175\pi$
$84$	21.4546	−	59.3296i	0.255412	−	0.706305i
$85$		−	42.4811i		−	0.499778i
$86$	3.75160			0.0436232
$87$			114.442i			1.31543i
$88$			17.0885i			0.194188i
$89$	−98.9327			−1.11160			−0.555802	−	0.831315i	$-0.687589\pi$
$89$	−98.9327			−1.11160			−0.555802	+	0.831315i	$0.687589\pi$
$90$		−	4.88242i		−	0.0542491i
$91$	34.5166	−	95.4507i	0.379303	−	1.04891i
$92$	21.3544			0.232113
$93$			115.610i			1.24312i
$94$	0.955689			0.0101669
$95$		−	23.1486i		−	0.243669i
$96$	54.7272			0.570075
$97$	−78.1202			−0.805363			−0.402682	−	0.915340i	$-0.631922\pi$
$97$	−78.1202			−0.805363			−0.402682	+	0.915340i	$0.631922\pi$
$98$	−19.4951	−	16.2206i	−0.198930	−	0.165517i
$99$			13.5283i			0.136649i
$100$	−60.2139			−0.602139
$101$	90.9875			0.900866			0.450433	−	0.892810i	$-0.351270\pi$
$101$	90.9875			0.900866			0.450433	+	0.892810i	$0.351270\pi$
$102$	−17.8320			−0.174824
$103$			28.3827i			0.275560i	0.990463	+	0.137780i	$0.0439967\pi$
$103$			28.3827i			0.275560i	−0.990463	+	0.137780i	$0.956003\pi$
$104$	58.0274			0.557956
$105$	−47.3348	−	17.1170i	−0.450808	−	0.163019i
$106$		−	1.24548i		−	0.0117498i
$107$	−8.25184			−0.0771200			−0.0385600	−	0.999256i	$-0.512277\pi$
$107$	−8.25184			−0.0771200			−0.0385600	+	0.999256i	$0.512277\pi$
$108$	109.669			1.01545
$109$		−	6.54302i		−	0.0600277i	−0.999549	−	0.0300139i	$-0.990445\pi$
$109$		−	6.54302i		−	0.0600277i	0.999549	−	0.0300139i	$-0.00955515\pi$
$110$	6.58068			0.0598244
$111$	112.930			1.01738
$112$	−30.6061	+	84.6369i	−0.273269	+	0.755687i
$113$	126.884			1.12287			0.561435	−	0.827521i	$-0.310249\pi$
$113$	126.884			1.12287			0.561435	+	0.827521i	$0.310249\pi$
$114$	−9.71693			−0.0852362
$115$		−	17.0371i		−	0.148149i
$116$		−	176.863i		−	1.52468i
$117$	45.9379			0.392632
$118$			29.9951i			0.254195i
$119$	33.9618	−	93.9166i	0.285393	−	0.789215i
$120$		−	28.7763i		−	0.239802i
$121$	102.766			0.849307
$122$		−	18.7972i		−	0.154075i
$123$	22.7528	−	96.3622i	0.184982	−	0.783433i
$124$		−	178.668i		−	1.44087i
$125$			122.480i			0.979841i
$126$	3.90328	−	10.7940i	0.0309784	−	0.0856665i
$127$	165.474			1.30295			0.651473	−	0.758672i	$-0.274151\pi$
$127$	165.474			1.30295			0.651473	+	0.758672i	$0.274151\pi$
$128$	−111.196			−0.868715
$129$	17.5047			0.135695
$130$		−	22.3460i		−	0.171892i
$131$		−	67.7988i		−	0.517548i	−0.965938	−	0.258774i	$-0.916682\pi$
$131$		−	67.7988i		−	0.517548i	0.965938	−	0.258774i	$-0.0833185\pi$
$132$			38.4857i			0.291558i
$133$	18.5063	−	51.1765i	0.139145	−	0.384785i
$134$		−	5.22234i		−	0.0389727i
$135$		−	87.4969i		−	0.648125i
$136$	57.0948			0.419814
$137$			75.2868i			0.549538i	0.961510	+	0.274769i	$0.0886015\pi$
$137$			75.2868i			0.549538i	−0.961510	+	0.274769i	$0.911399\pi$
$138$	−7.15158			−0.0518230
$139$			171.678i			1.23510i	0.786533	+	0.617548i	$0.211874\pi$
$139$			171.678i			1.23510i	−0.786533	+	0.617548i	$0.788126\pi$
$140$	73.1531	+	26.4534i	0.522522	+	0.188953i
$141$	4.45917			0.0316253
$142$			33.1386i			0.233370i
$143$			61.9166i			0.432983i
$144$	−40.7335			−0.282871
$145$	−141.106			−0.973148
$146$			42.4718i			0.290903i
$147$	−90.9627	−	75.6842i	−0.618794	−	0.514859i
$148$	−174.526			−1.17923
$149$			14.1269i			0.0948117i	0.998876	+	0.0474058i	$0.0150954\pi$
$149$			14.1269i			0.0948117i	−0.998876	+	0.0474058i	$0.984905\pi$
$150$	20.1656			0.134437
$151$			178.946i			1.18507i	0.805544	+	0.592536i	$0.201873\pi$
$151$			178.946i			1.18507i	−0.805544	+	0.592536i	$0.798127\pi$
$152$	31.1117			0.204682
$153$	45.1996			0.295422
$154$	14.5485	+	5.26097i	0.0944706	+	0.0341621i
$155$	−142.546			−0.919655
$156$	130.686			0.837728
$157$	−245.878			−1.56610			−0.783051	−	0.621958i	$-0.786338\pi$
$157$	−245.878			−1.56610			−0.783051	+	0.621958i	$0.786338\pi$
$158$		−	31.2836i		−	0.197997i
$159$		−	5.81132i		−	0.0365492i
$160$			67.4783i			0.421740i
$161$	13.6205	−	37.6655i	0.0845991	−	0.233947i
$162$	−21.9706			−0.135621
$163$	−284.935			−1.74807			−0.874033	−	0.485867i	$-0.838504\pi$
$163$	−284.935			−1.74807			−0.874033	+	0.485867i	$0.838504\pi$
$164$	−35.1631	+	148.922i	−0.214409	+	0.908062i
$165$	30.7050			0.186091
$166$		−	58.0568i		−	0.349740i
$167$	−73.3023			−0.438936			−0.219468	−	0.975620i	$-0.570432\pi$
$167$	−73.3023			−0.438936			−0.219468	+	0.975620i	$0.570432\pi$
$168$	23.0054	−	63.6181i	0.136937	−	0.378679i
$169$	41.2497			0.244081
$170$		−	21.9868i		−	0.129334i
$171$	24.6299			0.144034
$172$	−27.0524			−0.157281
$173$		−	101.561i		−	0.587056i	−0.955950	−	0.293528i	$-0.905171\pi$
$173$		−	101.561i		−	0.587056i	0.955950	−	0.293528i	$-0.0948294\pi$
$174$			59.2314i			0.340410i
$175$	−38.4061	+	106.207i	−0.219464	+	0.606896i
$176$		−	54.9019i		−	0.311943i
$177$			139.955i			0.790704i
$178$	−51.2043			−0.287664
$179$			256.549i			1.43323i	0.697468	+	0.716616i	$0.254310\pi$
$179$			256.549i			1.43323i	−0.697468	+	0.716616i	$0.745690\pi$
$180$			35.2066i			0.195592i
$181$	−216.499			−1.19613			−0.598064	−	0.801448i	$-0.704063\pi$
$181$	−216.499			−1.19613			−0.598064	+	0.801448i	$0.704063\pi$
$182$	17.8646	−	49.4021i	0.0981573	−	0.271440i
$183$		−	87.7061i		−	0.479268i
$184$	22.8980			0.124445
$185$			139.242i			0.752658i
$186$			59.8359i			0.321698i
$187$			60.9215i			0.325783i
$188$	−6.89138			−0.0366563
$189$	69.9500	−	193.437i	0.370106	−	1.02348i
$190$		−	11.9809i		−	0.0630575i
$191$		−	264.226i		−	1.38338i	−0.722193	−	0.691691i	$-0.756866\pi$
$191$		−	264.226i		−	1.38338i	0.722193	−	0.691691i	$-0.243134\pi$
$192$	−95.8723			−0.499335
$193$			282.996i			1.46630i	0.680066	+	0.733151i	$0.261951\pi$
$193$			282.996i			1.46630i	−0.680066	+	0.733151i	$0.738049\pi$
$194$	−40.4324			−0.208415
$195$		−	104.265i		−	0.534690i
$196$	140.577	+	116.965i	0.717232	+	0.596762i
$197$	−19.4800			−0.0988834			−0.0494417	−	0.998777i	$-0.515744\pi$
$197$	−19.4800			−0.0988834			−0.0494417	+	0.998777i	$0.515744\pi$
$198$			7.00179i			0.0353626i
$199$	−114.578			−0.575768			−0.287884	−	0.957665i	$-0.592952\pi$
$199$	−114.578			−0.575768			−0.287884	+	0.957665i	$0.592952\pi$
$200$	−64.5663			−0.322832
$201$		−	24.3670i		−	0.121229i
$202$	47.0921			0.233129
$203$	−311.956	−	112.808i	−1.53673	−	0.555707i
$204$	128.585			0.630319
$205$	118.814	+	28.0541i	0.579581	+	0.136849i
$206$			14.6900i			0.0713105i
$207$	18.1274			0.0875719
$208$	−186.430			−0.896298
$209$			33.1970i			0.158837i
$210$	−24.4989	−	8.85922i	−0.116662	−	0.0421867i
$211$			83.3070i			0.394820i	0.980321	+	0.197410i	$0.0632530\pi$
$211$			83.3070i			0.394820i	−0.980321	+	0.197410i	$0.936747\pi$
$212$			8.98104i			0.0423634i
$213$			154.622i			0.725925i
$214$	−4.27088			−0.0199574
$215$			21.5831i			0.100387i
$216$	117.596			0.544427
$217$	−315.140	−	113.960i	−1.45226	−	0.525160i
$218$		−	3.38645i		−	0.0155342i
$219$			198.170i			0.904886i
$220$	−47.4527			−0.215694
$221$	206.871			0.936066
$222$	58.4487			0.263282
$223$			411.553i			1.84553i	0.385365	+	0.922764i	$0.374075\pi$
$223$			411.553i			1.84553i	−0.385365	+	0.922764i	$0.625925\pi$
$224$	−53.9460	+	149.180i	−0.240830	+	0.665982i
$225$	−51.1145			−0.227176
$226$	65.6711			0.290580
$227$	399.847			1.76144			0.880720	−	0.473638i	$-0.157059\pi$
$227$	399.847			1.76144			0.880720	+	0.473638i	$0.157059\pi$
$228$	70.0678			0.307315
$229$	−322.155			−1.40679			−0.703395	−	0.710799i	$-0.748333\pi$
$229$	−322.155			−1.40679			−0.703395	+	0.710799i	$0.748333\pi$
$230$		−	8.81786i		−	0.0383385i
$231$	67.8821	+	24.5473i	0.293862	+	0.106265i
$232$		−	189.647i		−	0.817446i
$233$		−	150.194i		−	0.644608i	−0.946636	−	0.322304i	$-0.895543\pi$
$233$		−	150.194i		−	0.644608i	0.946636	−	0.322304i	$-0.104457\pi$
$234$	23.7759			0.101607
$235$			5.49813i			0.0233963i
$236$		−	216.291i		−	0.916489i
$237$		−	145.967i		−	0.615893i
$238$	17.5775	−	48.6081i	0.0738551	−	0.204236i
$239$		−	354.480i		−	1.48318i	−0.670854	−	0.741589i	$-0.734072\pi$
$239$		−	354.480i		−	1.48318i	0.670854	−	0.741589i	$-0.265928\pi$
$240$			92.4522i			0.385217i
$241$			268.738i			1.11510i	0.830145	+	0.557548i	$0.188258\pi$
$241$			268.738i			1.11510i	−0.830145	+	0.557548i	$0.811742\pi$
$242$	53.1883			0.219787
$243$	161.953			0.666474
$244$			135.545i			0.555511i
$245$	93.3182	−	112.157i	0.380891	−	0.457782i
$246$	11.7761	−	49.8739i	0.0478704	−	0.202739i
$247$	112.727			0.456383
$248$		−	191.583i		−	0.772512i
$249$		−	270.889i		−	1.08791i
$250$			63.3916i			0.253567i
$251$		−	314.282i		−	1.25212i	−0.779775	−	0.626060i	$-0.784666\pi$
$251$		−	314.282i		−	1.25212i	0.779775	−	0.626060i	$-0.215334\pi$
$252$	−28.1462	+	77.8343i	−0.111691	+	0.308866i
$253$			24.4327i			0.0965719i
$254$	85.6439			0.337181
$255$		−	102.589i		−	0.402309i
$256$	101.248			0.395502
$257$	−22.1148			−0.0860498			−0.0430249	−	0.999074i	$-0.513699\pi$
$257$	−22.1148			−0.0860498			−0.0430249	+	0.999074i	$0.513699\pi$
$258$	9.05983			0.0351156
$259$	−111.318	+	307.834i	−0.429798	+	1.18855i
$260$			161.135i			0.619749i
$261$		−	150.136i		−	0.575234i
$262$		−	35.0904i		−	0.133933i
$263$			128.337i			0.487973i	0.969779	+	0.243986i	$0.0784553\pi$
$263$			128.337i			0.487973i	−0.969779	+	0.243986i	$0.921545\pi$
$264$			41.2675i			0.156316i
$265$	7.16532			0.0270390
$266$	9.57823	−	26.4872i	0.0360084	−	0.0995761i
$267$	−238.915			−0.894813
$268$			37.6578i			0.140514i
$269$			475.696i			1.76839i	0.467122	+	0.884193i	$0.345291\pi$
$269$			475.696i			1.76839i	−0.467122	+	0.884193i	$0.654709\pi$
$270$		−	45.2855i		−	0.167724i
$271$		−	338.974i		−	1.25083i	−0.780293	−	0.625414i	$-0.784930\pi$
$271$		−	338.974i		−	1.25083i	0.780293	−	0.625414i	$-0.215070\pi$
$272$	−183.434			−0.674389
$273$	83.3550	−	230.506i	0.305329	−	0.844346i
$274$			38.9659i			0.142211i
$275$		−	68.8938i		−	0.250523i
$276$	51.5693			0.186845
$277$	−202.117			−0.729664			−0.364832	−	0.931073i	$-0.618874\pi$
$277$	−202.117			−0.729664			−0.364832	+	0.931073i	$0.618874\pi$
$278$			88.8550i			0.319622i
$279$		−	151.668i		−	0.543614i
$280$	78.4408	+	28.3655i	0.280146	+	0.101305i
$281$		−	43.2050i		−	0.153755i	−0.997041	−	0.0768773i	$-0.975505\pi$
$281$		−	43.2050i		−	0.153755i	0.997041	−	0.0768773i	$-0.0244950\pi$
$282$	2.30792			0.00818411
$283$			137.851i			0.487105i	0.969888	+	0.243552i	$0.0783128\pi$
$283$			137.851i			0.487105i	−0.969888	+	0.243552i	$0.921687\pi$
$284$		−	238.959i		−	0.841405i
$285$		−	55.9020i		−	0.196148i
$286$			32.0460i			0.112049i
$287$	240.244	+	157.008i	0.837089	+	0.547067i
$288$	−71.7964			−0.249293
$289$	−85.4543			−0.295690
$290$	−73.0320			−0.251834
$291$	−188.655			−0.648297
$292$		−	306.260i		−	1.04884i
$293$	409.735			1.39841			0.699206	−	0.714920i	$-0.253537\pi$
$293$	409.735			1.39841			0.699206	+	0.714920i	$0.253537\pi$
$294$	−47.0793	−	39.1716i	−0.160134	−	0.133237i
$295$	−172.563			−0.584960
$296$	−187.141			−0.632234
$297$			125.478i			0.422485i
$298$			7.31164i			0.0245357i
$299$	82.9658			0.277478
$300$	−145.412			−0.484707
$301$	−17.2548	+	47.7157i	−0.0573249	+	0.158524i
$302$			92.6164i			0.306677i
$303$	219.728			0.725175
$304$	−99.9555			−0.328801
$305$	108.141			0.354561
$306$	23.3938			0.0764503
$307$			3.34764i			0.0109044i	0.999985	+	0.00545218i	$0.00173549\pi$
$307$			3.34764i			0.0109044i	−0.999985	+	0.00545218i	$0.998265\pi$
$308$	−104.908	−	37.9364i	−0.340609	−	0.123170i
$309$			68.5422i			0.221819i
$310$	−73.7773			−0.237991
$311$	384.318			1.23575			0.617875	−	0.786277i	$-0.287994\pi$
$311$	384.318			1.23575			0.617875	+	0.786277i	$0.287994\pi$
$312$	140.132			0.449140
$313$	198.958			0.635647			0.317824	−	0.948150i	$-0.397048\pi$
$313$	198.958			0.635647			0.317824	+	0.948150i	$0.397048\pi$
$314$	−127.258			−0.405281
$315$	62.0983	+	22.4558i	0.197138	+	0.0712882i
$316$			225.583i			0.713870i
$317$			433.486i			1.36746i	0.729733	+	0.683732i	$0.239644\pi$
$317$			433.486i			1.36746i	−0.729733	+	0.683732i	$0.760356\pi$
$318$		−	3.00774i		−	0.00945832i
$319$	202.358			0.634352
$320$		−	118.210i		−	0.369406i
$321$	−19.9276			−0.0620797
$322$	7.04949	−	19.4944i	0.0218928	−	0.0605416i
$323$	110.915			0.343390
$324$	158.428			0.488974
$325$	−233.942			−0.719822
$326$	−147.473			−0.452370
$327$		−	15.8009i		−	0.0483209i
$328$	−37.7048	+	159.687i	−0.114954	+	0.486849i
$329$	−4.39552	+	12.1552i	−0.0133602	+	0.0369459i
$330$	15.8919			0.0481572
$331$		−	611.138i		−	1.84634i	−0.384393	−	0.923169i	$-0.625589\pi$
$331$		−	611.138i		−	1.84634i	0.384393	−	0.923169i	$-0.374411\pi$
$332$			418.642i			1.26097i
$333$	−148.152			−0.444901
$334$	−37.9388			−0.113589
$335$	30.0444			0.0896848
$336$	−73.9115	+	204.392i	−0.219975	+	0.608309i
$337$	−11.7367			−0.0348270			−0.0174135	−	0.999848i	$-0.505543\pi$
$337$	−11.7367			−0.0348270			−0.0174135	+	0.999848i	$0.505543\pi$
$338$	21.3495			0.0631641
$339$	306.416			0.903883
$340$			158.545i			0.466308i
$341$	204.424			0.599483
$342$	12.7476			0.0372737
$343$	295.971	−	173.350i	0.862889	−	0.505394i
$344$	−29.0078			−0.0843250
$345$		−	41.1434i		−	0.119256i
$346$		−	52.5644i		−	0.151920i
$347$		−	246.644i		−	0.710790i	−0.934716	−	0.355395i	$-0.884346\pi$
$347$		−	246.644i		−	0.710790i	0.934716	−	0.355395i	$-0.115654\pi$
$348$		−	427.112i		−	1.22733i
$349$			15.6785i			0.0449242i	0.999748	+	0.0224621i	$0.00715051\pi$
$349$			15.6785i			0.0449242i	−0.999748	+	0.0224621i	$0.992849\pi$
$350$	−19.8777	+	54.9691i	−0.0567935	+	0.157055i
$351$	426.084			1.21392
$352$		−	96.7696i		−	0.274914i
$353$		−	13.6354i		−	0.0386271i	−0.999813	−	0.0193136i	$-0.993852\pi$
$353$		−	13.6354i		−	0.0386271i	0.999813	−	0.0193136i	$-0.00614808\pi$
$354$			72.4358i			0.204621i
$355$	−190.648			−0.537037
$356$	369.229			1.03716
$357$	82.0153	−	226.802i	0.229735	−	0.635299i
$358$			132.781i			0.370897i
$359$	−196.941			−0.548582			−0.274291	−	0.961647i	$-0.588443\pi$
$359$	−196.941			−0.548582			−0.274291	+	0.961647i	$0.588443\pi$
$360$			37.7515i			0.104865i
$361$	−300.561			−0.832579
$362$	−112.053			−0.309538
$363$	248.173			0.683671
$364$	−128.820	+	356.234i	−0.353901	+	0.978665i
$365$	−244.343			−0.669432
$366$		−	45.3938i		−	0.124027i
$367$		−	488.518i		−	1.33111i	−0.746348	−	0.665556i	$-0.768194\pi$
$367$		−	488.518i		−	1.33111i	0.746348	−	0.665556i	$-0.231806\pi$
$368$	−73.5665			−0.199909
$369$	−29.8493	+	126.417i	−0.0808925	+	0.342594i
$370$			72.0669i			0.194775i
$371$	15.8410	+	5.72836i	0.0426981	+	0.0154403i
$372$		−	431.471i		−	1.15987i
$373$	69.9214			0.187457			0.0937284	−	0.995598i	$-0.470121\pi$
$373$	69.9214			0.187457			0.0937284	+	0.995598i	$0.470121\pi$
$374$			31.5309i			0.0843073i
$375$			295.780i			0.788748i
$376$	−7.38951			−0.0196529
$377$		−	687.146i		−	1.82267i
$378$	36.2038	−	100.117i	0.0957772	−	0.264859i
$379$	17.5415			0.0462837			0.0231418	−	0.999732i	$-0.492633\pi$
$379$	17.5415			0.0462837			0.0231418	+	0.999732i	$0.492633\pi$
$380$			86.3933i			0.227351i
$381$	399.608			1.04884
$382$		−	136.755i		−	0.357996i
$383$	721.665			1.88424			0.942122	−	0.335271i	$-0.108828\pi$
$383$	721.665			1.88424			0.942122	+	0.335271i	$0.108828\pi$
$384$	−268.529			−0.699294
$385$	−30.2667	+	83.6982i	−0.0786147	+	0.217398i
$386$			146.470i			0.379455i
$387$	−22.9643			−0.0593393
$388$	291.554			0.751429
$389$	−101.852			−0.261829			−0.130915	−	0.991394i	$-0.541791\pi$
$389$	−101.852			−0.261829			−0.130915	+	0.991394i	$0.541791\pi$
$390$		−	53.9639i		−	0.138369i
$391$	81.6324			0.208779
$392$	150.739	+	125.420i	0.384538	+	0.319949i
$393$		−	163.729i		−	0.416613i
$394$	−10.0822			−0.0255894
$395$	179.976			0.455636
$396$		−	50.4893i		−	0.127498i
$397$	112.933			0.284466			0.142233	−	0.989833i	$-0.454572\pi$
$397$	112.933			0.284466			0.142233	+	0.989833i	$0.454572\pi$
$398$	−59.3017			−0.148999
$399$	44.6912	−	123.587i	0.112008	−	0.309743i
$400$	207.438			0.518596
$401$	−390.202			−0.973072			−0.486536	−	0.873661i	$-0.661740\pi$
$401$	−390.202			−0.973072			−0.486536	+	0.873661i	$0.661740\pi$
$402$		−	12.6116i		−	0.0313720i
$403$		−	694.159i		−	1.72248i
$404$	−339.577			−0.840536
$405$		−	126.398i		−	0.312094i
$406$	−161.458	−	58.3859i	−0.397680	−	0.143808i
$407$		−	199.684i		−	0.490625i
$408$	137.880			0.337940
$409$		−	310.808i		−	0.759922i	−0.925002	−	0.379961i	$-0.875937\pi$
$409$		−	310.808i		−	0.759922i	0.925002	−	0.379961i	$-0.124063\pi$
$410$	61.4943	+	14.5199i	0.149986	+	0.0354143i
$411$			181.812i			0.442365i
$412$		−	105.928i		−	0.257106i
$413$	−381.500	−	137.957i	−0.923729	−	0.334036i
$414$	9.38213			0.0226621
$415$	334.004			0.804830
$416$	−328.600			−0.789903
$417$			414.590i			0.994221i
$418$			17.1816i			0.0411044i
$419$		−	291.710i		−	0.696205i	−0.937456	−	0.348103i	$-0.886826\pi$
$419$		−	291.710i		−	0.696205i	0.937456	−	0.348103i	$-0.113174\pi$
$420$	176.659	+	63.8829i	0.420617	+	0.152102i
$421$			465.187i			1.10496i	0.833527	+	0.552479i	$0.186318\pi$
$421$			465.187i			1.10496i	−0.833527	+	0.552479i	$0.813682\pi$
$422$			43.1169i			0.102173i
$423$	−5.84997			−0.0138297
$424$			9.63021i			0.0227128i
$425$	−230.182			−0.541605
$426$			80.0272i			0.187857i
$427$	239.077	+	86.4542i	0.559899	+	0.202469i
$428$	30.7969			0.0719554
$429$			149.524i			0.348541i
$430$			11.1707i			0.0259784i
$431$	787.103			1.82623			0.913113	−	0.407707i	$-0.133671\pi$
$431$	787.103			1.82623			0.913113	+	0.407707i	$0.133671\pi$
$432$	−377.812			−0.874565
$433$			11.4981i			0.0265546i	0.999912	+	0.0132773i	$0.00422642\pi$
$433$			11.4981i			0.0265546i	−0.999912	+	0.0132773i	$0.995774\pi$
$434$	−163.106	−	58.9818i	−0.375820	−	0.135903i
$435$	−340.762			−0.783360
$436$			24.4194i			0.0560078i
$437$	44.4826			0.101791
$438$			102.566i			0.234169i
$439$	478.556			1.09010			0.545052	−	0.838402i	$-0.316510\pi$
$439$	478.556			1.09010			0.545052	+	0.838402i	$0.316510\pi$
$440$	−50.8827			−0.115642
$441$	119.334	+	99.2898i	0.270598	+	0.225147i
$442$	107.069			0.242238
$443$	86.6834			0.195673			0.0978367	−	0.995202i	$-0.468808\pi$
$443$	86.6834			0.195673			0.0978367	+	0.995202i	$0.468808\pi$
$444$	−421.468			−0.949252
$445$		−	294.581i		−	0.661980i
$446$			213.006i			0.477592i
$447$			34.1155i			0.0763211i
$448$	94.5038	−	261.337i	0.210946	−	0.583341i
$449$	370.557			0.825294			0.412647	−	0.910891i	$-0.364604\pi$
$449$	370.557			0.825294			0.412647	+	0.910891i	$0.364604\pi$
$450$	−26.4552			−0.0587893
$451$	−170.389	−	40.2319i	−0.377804	−	0.0892061i
$452$	−473.548			−1.04767
$453$			432.141i			0.953953i
$454$	206.947			0.455831
$455$	284.213	+	102.776i	0.624645	+	0.225882i
$456$	75.1325			0.164764
$457$			377.799i			0.826694i	0.910574	+	0.413347i	$0.135640\pi$
$457$			377.799i			0.826694i	−0.910574	+	0.413347i	$0.864360\pi$
$458$	−166.737			−0.364054
$459$	419.236			0.913368
$460$			63.5847i			0.138228i
$461$			172.759i			0.374748i	0.982289	+	0.187374i	$0.0599976\pi$
$461$			172.759i			0.374748i	−0.982289	+	0.187374i	$0.940002\pi$
$462$	35.1335	+	12.7049i	0.0760465	+	0.0274997i
$463$			600.443i			1.29685i	0.761277	+	0.648427i	$0.224573\pi$
$463$			600.443i			1.29685i	−0.761277	+	0.648427i	$0.775427\pi$
$464$			609.298i			1.31314i
$465$	−344.239			−0.740299
$466$		−	77.7352i		−	0.166814i
$467$			473.736i			1.01442i	0.861821	+	0.507212i	$0.169324\pi$
$467$			473.736i			1.01442i	−0.861821	+	0.507212i	$0.830676\pi$
$468$	−171.446			−0.366337
$469$	66.4217	+	24.0192i	0.141624	+	0.0512136i
$470$			2.84565i			0.00605458i
$471$	−593.777			−1.26067
$472$		−	231.926i		−	0.491368i
$473$		−	30.9520i		−	0.0654377i
$474$		−	75.5475i		−	0.159383i
$475$	−125.429			−0.264062
$476$	−126.750	+	350.509i	−0.266281	+	0.736363i
$477$			7.62384i			0.0159829i
$478$		−	183.467i		−	0.383822i
$479$	−697.803			−1.45679			−0.728396	−	0.685157i	$-0.759734\pi$
$479$	−697.803			−1.45679			−0.728396	+	0.685157i	$0.759734\pi$
$480$			162.955i			0.339490i
$481$	−678.066			−1.40970
$482$			139.090i			0.288568i
$483$	32.8924	−	90.9593i	0.0681002	−	0.188322i
$484$	−383.536			−0.792430
$485$		−	232.610i		−	0.479608i
$486$	83.8216			0.172473
$487$	238.968			0.490695			0.245347	−	0.969435i	$-0.421098\pi$
$487$	238.968			0.490695			0.245347	+	0.969435i	$0.421098\pi$
$488$			145.342i			0.297832i
$489$	−688.096			−1.40715
$490$	48.2984	−	58.0485i	0.0985682	−	0.118466i
$491$	384.865			0.783839			0.391920	−	0.919999i	$-0.371811\pi$
$491$	384.865			0.783839			0.391920	+	0.919999i	$0.371811\pi$
$492$	−84.9164	+	359.636i	−0.172594	+	0.730967i
$493$		−	676.103i		−	1.37140i
$494$	58.3435			0.118104
$495$	−40.2817			−0.0813772
$496$			615.516i			1.24096i
$497$	−421.482	−	152.415i	−0.848052	−	0.306670i
$498$		−	140.203i		−	0.281532i
$499$			398.574i			0.798745i	0.916789	+	0.399373i	$0.130772\pi$
$499$			398.574i			0.798745i	−0.916789	+	0.399373i	$0.869228\pi$
$500$		−	457.111i		−	0.914222i
$501$	−177.020			−0.353333
$502$		−	162.662i		−	0.324028i
$503$	−134.035			−0.266472			−0.133236	−	0.991084i	$-0.542537\pi$
$503$	−134.035			−0.266472			−0.133236	+	0.991084i	$0.542537\pi$
$504$	−30.1806	+	83.4603i	−0.0598822	+	0.165596i
$505$			270.924i			0.536482i
$506$			12.6455i			0.0249912i
$507$	99.6149			0.196479
$508$	−617.570			−1.21569
$509$	313.307			0.615535			0.307767	−	0.951462i	$-0.400418\pi$
$509$	313.307			0.615535			0.307767	+	0.951462i	$0.400418\pi$
$510$		−	53.0966i		−	0.104111i
$511$	−540.189	−	195.341i	−1.05712	−	0.382272i
$512$	497.185			0.971064
$513$	228.448			0.445317
$514$	−11.4459			−0.0222683
$515$	−84.5121			−0.164101
$516$	−65.3295			−0.126608
$517$		−	7.88478i		−	0.0152510i
$518$	−57.6144	+	159.324i	−0.111225	+	0.307576i
$519$		−	245.262i		−	0.472566i
$520$			172.782i			0.332273i
$521$	−582.945			−1.11890			−0.559448	−	0.828865i	$-0.688987\pi$
$521$	−582.945			−1.11890			−0.559448	+	0.828865i	$0.688987\pi$
$522$		−	77.7054i		−	0.148861i
$523$			273.006i			0.522001i	0.965339	+	0.261000i	$0.0840524\pi$
$523$			273.006i			0.522001i	−0.965339	+	0.261000i	$0.915948\pi$
$524$			253.034i			0.482888i
$525$	−92.7480	+	256.482i	−0.176663	+	0.488536i
$526$			66.4229i			0.126279i
$527$		−	683.003i		−	1.29602i
$528$		−	132.584i		−	0.251106i
$529$	−496.261			−0.938112
$530$	3.70853			0.00699723
$531$		−	183.606i		−	0.345774i
$532$	−69.0677	+	190.997i	−0.129826	+	0.359017i
$533$	−136.615	+	578.590i	−0.256314	+	1.08553i
$534$	−123.655			−0.231563
$535$		−	24.5706i		−	0.0459264i
$536$			40.3798i			0.0753354i
$537$			619.546i			1.15372i
$538$			246.204i			0.457629i
$539$	−133.826	+	160.842i	−0.248286	+	0.298408i
$540$			326.549i			0.604721i
$541$	−477.767			−0.883119			−0.441559	−	0.897232i	$-0.645575\pi$
$541$	−477.767			−0.883119			−0.441559	+	0.897232i	$0.645575\pi$
$542$		−	175.442i		−	0.323693i
$543$	−522.830			−0.962854
$544$	−323.318			−0.594335
$545$	19.4825			0.0357476
$546$	43.1418	−	119.302i	0.0790142	−	0.218503i
$547$			406.836i			0.743759i	0.928281	+	0.371880i	$0.121287\pi$
$547$			406.836i			0.743759i	−0.928281	+	0.371880i	$0.878713\pi$
$548$		−	280.980i		−	0.512736i
$549$			115.061i			0.209583i
$550$		−	35.6572i		−	0.0648312i
$551$		−	368.418i		−	0.668634i
$552$	55.2969			0.100176
$553$	397.888	+	143.883i	0.719509	+	0.260186i
$554$	−104.609			−0.188825
$555$			336.259i			0.605871i
$556$		−	640.725i		−	1.15238i
$557$		−	632.252i		−	1.13510i	−0.823338	−	0.567551i	$-0.807891\pi$
$557$		−	632.252i		−	1.13510i	0.823338	−	0.567551i	$-0.192109\pi$
$558$		−	78.4985i		−	0.140678i
$559$	−105.104			−0.188021
$560$	−252.014	−	91.1325i	−0.450025	−	0.162737i
$561$			147.121i			0.262248i
$562$		−	22.3615i		−	0.0397891i
$563$	714.538			1.26916			0.634581	−	0.772857i	$-0.281173\pi$
$563$	714.538			1.26916			0.634581	+	0.772857i	$0.281173\pi$
$564$	−16.6422			−0.0295074
$565$			377.810i			0.668690i
$566$			71.3469i			0.126055i
$567$	101.050	−	279.439i	0.178218	−	0.492837i
$568$		−	256.232i		−	0.451112i
$569$	801.924			1.40936			0.704678	−	0.709527i	$-0.251091\pi$
$569$	801.924			1.40936			0.704678	+	0.709527i	$0.251091\pi$
$570$		−	28.9330i		−	0.0507597i
$571$		−	440.397i		−	0.771273i	−0.922651	−	0.385637i	$-0.873982\pi$
$571$		−	440.397i		−	0.771273i	0.922651	−	0.385637i	$-0.126018\pi$
$572$		−	231.081i		−	0.403987i
$573$		−	638.086i		−	1.11359i
$574$	124.343	+	81.2623i	0.216625	+	0.141572i
$575$	−92.3150			−0.160548
$576$	125.774			0.218358
$577$	−292.273			−0.506539			−0.253269	−	0.967396i	$-0.581506\pi$
$577$	−292.273			−0.506539			−0.253269	+	0.967396i	$0.581506\pi$
$578$	−44.2283			−0.0765196
$579$			683.415i			1.18034i
$580$	526.627			0.907977
$581$	738.412	+	267.022i	1.27093	+	0.459590i
$582$	−97.6413			−0.167769
$583$	−10.2757			−0.0176255
$584$		−	328.397i		−	0.562324i
$585$			136.784i			0.233819i
$586$	212.065			0.361886
$587$	170.351			0.290206			0.145103	−	0.989417i	$-0.453649\pi$
$587$	170.351			0.290206			0.145103	+	0.989417i	$0.453649\pi$
$588$	339.484	+	282.463i	0.577354	+	0.480379i
$589$		−	372.178i		−	0.631880i
$590$	−89.3130			−0.151378
$591$	−47.0428			−0.0795987
$592$	601.247			1.01562
$593$	−94.9074			−0.160046			−0.0800231	−	0.996793i	$-0.525499\pi$
$593$	−94.9074			−0.160046			−0.0800231	+	0.996793i	$0.525499\pi$
$594$			64.9432i			0.109332i
$595$	279.645	+	101.124i	0.469992	+	0.169957i
$596$		−	52.7235i		−	0.0884623i
$597$	−276.697			−0.463479
$598$	42.9404			0.0718066
$599$	−179.381			−0.299468			−0.149734	−	0.988726i	$-0.547842\pi$
$599$	−179.381			−0.299468			−0.149734	+	0.988726i	$0.547842\pi$
$600$	−155.923			−0.259871
$601$	−631.354			−1.05051			−0.525253	−	0.850946i	$-0.676029\pi$
$601$	−631.354			−1.05051			−0.525253	+	0.850946i	$0.676029\pi$
$602$	−8.93051	+	24.6961i	−0.0148347	+	0.0410234i
$603$			31.9670i			0.0530133i
$604$		−	667.848i		−	1.10571i
$605$			305.996i			0.505778i
$606$	113.724			0.187663
$607$			760.587i			1.25303i	0.779411	+	0.626513i	$0.215519\pi$
$607$			760.587i			1.25303i	−0.779411	+	0.626513i	$0.784481\pi$
$608$	−176.181			−0.289771
$609$	−753.350	−	272.424i	−1.23703	−	0.447330i
$610$	55.9703			0.0917546
$611$	−26.7743			−0.0438204
$612$	−168.690			−0.275638
$613$	605.381			0.987571			0.493785	−	0.869584i	$-0.335613\pi$
$613$	605.381			0.987571			0.493785	+	0.869584i	$0.335613\pi$
$614$			1.73263i			0.00282187i
$615$	286.927	+	67.7486i	0.466548	+	0.110160i
$616$	−112.491	−	40.6785i	−0.182615	−	0.0660365i
$617$	−644.367			−1.04435			−0.522177	−	0.852837i	$-0.674880\pi$
$617$	−644.367			−1.04435			−0.522177	+	0.852837i	$0.674880\pi$
$618$			35.4751i			0.0574032i
$619$		−	609.816i		−	0.985163i	−0.870266	−	0.492582i	$-0.836053\pi$
$619$		−	609.816i		−	0.985163i	0.870266	−	0.492582i	$-0.163947\pi$
$620$	532.001			0.858067
$621$	168.135			0.270750
$622$	198.910			0.319791
$623$	235.505	−	651.255i	0.378017	−	1.04535i
$624$	−450.215			−0.721498
$625$	38.6531			0.0618449
$626$	102.974			0.164495
$627$			80.1682i			0.127860i
$628$	917.647			1.46122
$629$	−667.168			−1.06068
$630$	32.1400	+	11.6224i	0.0510159	+	0.0184482i
$631$	636.847			1.00927			0.504633	−	0.863334i	$-0.331628\pi$
$631$	636.847			1.00927			0.504633	+	0.863334i	$0.331628\pi$
$632$			241.888i			0.382735i
$633$			201.180i			0.317820i
$634$			224.358i			0.353877i
$635$			492.714i			0.775928i
$636$			21.6886i			0.0341015i
$637$	546.169	+	454.432i	0.857409	+	0.713394i
$638$	104.734			0.164160
$639$		−	202.848i		−	0.317446i
$640$		−	331.095i		−	0.517336i
$641$			982.593i			1.53291i	0.642300	+	0.766453i	$0.277980\pi$
$641$			982.593i			1.53291i	−0.642300	+	0.766453i	$0.722020\pi$
$642$	−10.3139			−0.0160652
$643$	952.833			1.48186			0.740928	−	0.671585i	$-0.234386\pi$
$643$	952.833			1.48186			0.740928	+	0.671585i	$0.234386\pi$
$644$	−50.8332	+	140.572i	−0.0789336	+	0.218280i
$645$			52.1217i			0.0808088i
$646$	57.4058			0.0888635
$647$		−	733.168i		−	1.13318i	−0.824000	−	0.566590i	$-0.808262\pi$
$647$		−	733.168i		−	1.13318i	0.824000	−	0.566590i	$-0.191738\pi$
$648$	169.879			0.262159
$649$	247.470			0.381310
$650$	−121.081			−0.186278
$651$	−761.039	−	275.204i	−1.16903	−	0.422741i
$652$	1063.41			1.63100
$653$		−	609.323i		−	0.933113i	−0.884491	−	0.466557i	$-0.845494\pi$
$653$		−	609.323i		−	0.933113i	0.884491	−	0.466557i	$-0.154506\pi$
$654$		−	8.17803i		−	0.0125046i
$655$	201.877			0.308209
$656$	121.138	−	513.040i	0.184661	−	0.782073i
$657$		−	259.978i		−	0.395705i
$658$	−2.27497	+	6.29112i	−0.00345741	+	0.00956098i
$659$		−	612.134i		−	0.928882i	−0.885604	−	0.464441i	$-0.846255\pi$
$659$		−	612.134i		−	0.928882i	0.885604	−	0.464441i	$-0.153745\pi$
$660$	−114.595			−0.173628
$661$		−	548.940i		−	0.830469i	−0.909714	−	0.415234i	$-0.863700\pi$
$661$		−	548.940i		−	0.830469i	0.909714	−	0.415234i	$-0.136300\pi$
$662$		−	316.305i		−	0.477802i
$663$	499.577			0.753510
$664$			448.903i			0.676058i
$665$	152.383	+	55.1041i	0.229147	+	0.0828633i
$666$	−76.6786			−0.115133
$667$		−	271.152i		−	0.406525i
$668$	273.573			0.409541
$669$			993.870i			1.48560i
$670$	15.5500			0.0232089
$671$	−155.083			−0.231123
$672$	−130.276	+	360.259i	−0.193862	+	0.536099i
$673$		−	899.044i		−	1.33588i	−0.744217	−	0.667938i	$-0.767177\pi$
$673$		−	899.044i		−	1.33588i	0.744217	−	0.667938i	$-0.232823\pi$
$674$	−6.07452			−0.00901265
$675$	−474.098			−0.702368
$676$	−153.949			−0.227735
$677$			1131.75i			1.67172i	0.548945	+	0.835858i	$0.315029\pi$
$677$			1131.75i			1.67172i	−0.548945	+	0.835858i	$0.684971\pi$
$678$	158.591			0.233910
$679$	185.962	−	514.251i	0.273876	−	0.757365i
$680$			170.005i			0.250007i
$681$	965.600			1.41792
$682$	105.803			0.155136
$683$		−	773.630i		−	1.13269i	−0.824167	−	0.566347i	$-0.808356\pi$
$683$		−	773.630i		−	1.13269i	0.824167	−	0.566347i	$-0.191644\pi$
$684$	−91.9217			−0.134388
$685$	−224.173			−0.327260
$686$	153.185	−	89.7203i	0.223301	−	0.130788i
$687$	−777.980			−1.13243
$688$	93.1961			0.135459
$689$			34.8930i			0.0506430i
$690$		−	21.2945i		−	0.0308616i
$691$	−71.8416			−0.103968			−0.0519838	−	0.998648i	$-0.516554\pi$
$691$	−71.8416			−0.103968			−0.0519838	+	0.998648i	$0.516554\pi$
$692$			379.037i			0.547741i
$693$	−89.0542	−	32.2035i	−0.128505	−	0.0464697i
$694$		−	127.655i		−	0.183941i
$695$	−511.188			−0.735522
$696$		−	457.984i		−	0.658024i
$697$	−134.420	+	569.291i	−0.192854	+	0.816773i
$698$			8.11470i			0.0116256i
$699$		−	362.706i		−	0.518893i
$700$	143.336	−	396.377i	0.204766	−	0.566253i
$701$	−1032.47			−1.47285			−0.736426	−	0.676518i	$-0.763488\pi$
$701$	−1032.47			−1.47285			−0.736426	+	0.676518i	$0.763488\pi$
$702$	220.527			0.314141
$703$	−363.549			−0.517140
$704$			169.523i			0.240800i
$705$			13.2776i			0.0188335i
$706$		−	7.05722i		−	0.00999606i
$707$	−216.592	+	598.954i	−0.306353	+	0.847176i
$708$		−	522.328i		−	0.737751i
$709$			1105.28i			1.55893i	0.626445	+	0.779466i	$0.284509\pi$
$709$			1105.28i			1.55893i	−0.626445	+	0.779466i	$0.715491\pi$
$710$	−98.6731			−0.138976
$711$			191.493i			0.269329i
$712$	395.918			0.556064
$713$		−	273.920i		−	0.384179i
$714$	42.4484	−	117.385i	0.0594515	−	0.164405i
$715$	−184.362			−0.257849
$716$		−	957.471i		−	1.33725i
$717$		−	856.042i		−	1.19392i
$718$	−101.930			−0.141964
$719$	−637.980			−0.887315			−0.443658	−	0.896196i	$-0.646319\pi$
$719$	−637.980			−0.887315			−0.443658	+	0.896196i	$0.646319\pi$
$720$		−	121.288i		−	0.168455i
$721$	−186.838	−	67.5638i	−0.259137	−	0.0937084i
$722$	−155.560			−0.215458
$723$			648.983i			0.897625i
$724$	808.002			1.11602
$725$			764.579i			1.05459i
$726$	128.446			0.176923
$727$	971.587			1.33643			0.668216	−	0.743967i	$-0.267058\pi$
$727$	971.587			1.33643			0.668216	+	0.743967i	$0.267058\pi$
$728$	−138.132	+	381.983i	−0.189741	+	0.524703i
$729$	773.153			1.06057
$730$	−126.464			−0.173238
$731$	−103.414			−0.141470
$732$			327.330i			0.447172i
$733$		−	314.967i		−	0.429696i	−0.976648	−	0.214848i	$-0.931074\pi$
$733$		−	314.967i		−	0.429696i	0.976648	−	0.214848i	$-0.0689256\pi$
$734$		−	252.841i		−	0.344470i
$735$	225.357	−	270.850i	0.306608	−	0.368503i
$736$	−129.667			−0.176179
$737$	−43.0862			−0.0584616
$738$	−15.4490	+	65.4294i	−0.0209336	+	0.0886577i
$739$	−567.418			−0.767819			−0.383910	−	0.923371i	$-0.625423\pi$
$739$	−567.418			−0.767819			−0.383910	+	0.923371i	$0.625423\pi$
$740$		−	519.668i		−	0.702254i
$741$	272.226			0.367377
$742$	8.19877	+	2.96481i	0.0110496	+	0.00399570i
$743$	245.087			0.329862			0.164931	−	0.986305i	$-0.447260\pi$
$743$	245.087			0.329862			0.164931	+	0.986305i	$0.447260\pi$
$744$		−	462.659i		−	0.621853i
$745$	−42.0643			−0.0564621
$746$	36.1890			0.0485107
$747$			355.378i			0.475740i
$748$		−	227.367i		−	0.303966i
$749$	19.6431	−	54.3203i	0.0262258	−	0.0725238i
$750$			153.086i			0.204115i
$751$		−	293.629i		−	0.390984i	−0.980705	−	0.195492i	$-0.937370\pi$
$751$		−	293.629i		−	0.390984i	0.980705	−	0.195492i	$-0.0626304\pi$
$752$	23.7410			0.0315704
$753$		−	758.968i		−	1.00793i
$754$		−	355.644i		−	0.471677i
$755$	−532.828			−0.705732
$756$	−261.062	+	721.931i	−0.345320	+	0.954935i
$757$		−	1142.74i		−	1.50957i	−0.655975	−	0.754783i	$-0.727742\pi$
$757$		−	1142.74i		−	1.50957i	0.655975	−	0.754783i	$-0.272258\pi$
$758$	9.07890			0.0119774
$759$			59.0031i			0.0777380i
$760$			92.6380i			0.121892i
$761$			1006.61i			1.32275i	0.750056	+	0.661374i	$0.230026\pi$
$761$			1006.61i			1.32275i	−0.750056	+	0.661374i	$0.769974\pi$
$762$	206.824			0.271422
$763$	43.0715	+	15.5754i	0.0564502	+	0.0204133i
$764$			986.125i			1.29074i
$765$			134.586i			0.175929i
$766$	373.510			0.487611
$767$		−	840.332i		−	1.09561i
$768$	244.507			0.318369
$769$			846.277i			1.10049i	0.835003	+	0.550245i	$0.185466\pi$
$769$			846.277i			1.10049i	−0.835003	+	0.550245i	$0.814534\pi$
$770$	−15.6650	+	43.3194i	−0.0203442	+	0.0562590i
$771$	−53.4056			−0.0692680
$772$		−	1056.18i		−	1.36811i
$773$	918.223			1.18787			0.593935	−	0.804513i	$-0.297574\pi$
$773$	918.223			1.18787			0.593935	+	0.804513i	$0.297574\pi$
$774$	−11.8856			−0.0153560
$775$			772.382i			0.996622i
$776$	312.629			0.402872
$777$	−268.824	+	743.395i	−0.345977	+	0.956751i
$778$	−52.7150			−0.0677571
$779$	−73.2471	+	310.214i	−0.0940270	+	0.398221i
$780$			389.128i			0.498882i
$781$	273.405			0.350071
$782$	42.2502			0.0540284
$783$		−	1392.55i		−	1.77847i
$784$	−484.292	−	402.949i	−0.617720	−	0.513965i
$785$		−	732.124i		−	0.932642i
$786$		−	84.7407i		−	0.107813i
$787$		−	254.231i		−	0.323039i	−0.986870	−	0.161519i	$-0.948361\pi$
$787$		−	254.231i		−	0.323039i	0.986870	−	0.161519i	$-0.0516394\pi$
$788$	72.7019			0.0922613
$789$			309.924i			0.392806i
$790$	93.1497			0.117911
$791$	−302.042	+	835.256i	−0.381849	+	1.05595i
$792$		−	54.1387i		−	0.0683570i
$793$			526.616i			0.664080i
$794$	58.4504			0.0736151
$795$	17.3037			0.0217657
$796$	427.619			0.537209
$797$		−	1394.38i		−	1.74954i	−0.484539	−	0.874769i	$-0.661013\pi$
$797$		−	1394.38i		−	1.74954i	0.484539	−	0.874769i	$-0.338987\pi$
$798$	23.1307	−	63.9647i	0.0289858	−	0.0801563i
$799$	−26.3440			−0.0329712
$800$	365.628			0.457036
$801$	313.432			0.391301
$802$	−201.956			−0.251815
$803$	350.408			0.436373
$804$			90.9407i			0.113110i
$805$	112.152	+	40.5561i	0.139320	+	0.0503803i
$806$		−	359.274i		−	0.445749i
$807$			1148.77i			1.42351i
$808$	−364.122			−0.450646
$809$			645.854i			0.798336i	0.916878	+	0.399168i	$0.130701\pi$
$809$			645.854i			0.798336i	−0.916878	+	0.399168i	$0.869299\pi$
$810$		−	65.4194i		−	0.0807647i
$811$			393.731i			0.485488i	0.970090	+	0.242744i	$0.0780476\pi$
$811$			393.731i			0.485488i	−0.970090	+	0.242744i	$0.921952\pi$
$812$	1164.26	+	421.015i	1.43382	+	0.518491i
$813$		−	818.597i		−	1.00688i
$814$		−	103.350i		−	0.126966i
$815$		−	848.419i		−	1.04100i
$816$	−442.979			−0.542866
$817$	−56.3519			−0.0689742
$818$		−	160.864i		−	0.196655i
$819$	−109.353	+	302.401i	−0.133520	+	0.369231i
$820$	−443.429	−	104.701i	−0.540767	−	0.127685i
$821$	627.719			0.764578			0.382289	−	0.924043i	$-0.375136\pi$
$821$	627.719			0.764578			0.382289	+	0.924043i	$0.375136\pi$
$822$			94.0998i			0.114477i
$823$		−	262.723i		−	0.319226i	−0.987180	−	0.159613i	$-0.948975\pi$
$823$		−	262.723i		−	0.319226i	0.987180	−	0.159613i	$-0.0510246\pi$
$824$		−	113.585i		−	0.137845i
$825$		−	166.373i		−	0.201665i
$826$	−197.452	−	71.4019i	−0.239046	−	0.0864429i
$827$			1404.52i			1.69833i	0.528125	+	0.849166i	$0.322895\pi$
$827$			1404.52i			1.69833i	−0.528125	+	0.849166i	$0.677105\pi$
$828$	−67.6536			−0.0817073
$829$			713.565i			0.860754i	0.902649	+	0.430377i	$0.141619\pi$
$829$			713.565i			0.860754i	−0.902649	+	0.430377i	$0.858381\pi$
$830$	172.870			0.208277
$831$	−488.097			−0.587361
$832$	575.648			0.691884
$833$	537.391	+	447.129i	0.645127	+	0.536769i
$834$			214.578i			0.257288i
$835$		−	218.264i		−	0.261394i
$836$		−	123.895i		−	0.148200i
$837$		−	1406.76i		−	1.68071i
$838$		−	150.979i		−	0.180166i
$839$	−695.924			−0.829469			−0.414734	−	0.909943i	$-0.636125\pi$
$839$	−695.924			−0.829469			−0.414734	+	0.909943i	$0.636125\pi$
$840$	189.429	+	68.5006i	0.225510	+	0.0815483i
$841$	−1404.76			−1.67034
$842$			240.765i			0.285945i
$843$		−	104.337i		−	0.123769i
$844$		−	310.912i		−	0.368379i
$845$			122.825i			0.145355i
$846$	−3.02775			−0.00357890
$847$	−244.630	+	676.490i	−0.288819	+	0.798690i
$848$		−	30.9399i		−	0.0364857i
$849$			332.899i			0.392107i
$850$	−119.135			−0.140158
$851$	−267.569			−0.314417
$852$		−	577.068i		−	0.677310i
$853$		−	162.288i		−	0.190255i	−0.995465	−	0.0951277i	$-0.969674\pi$
$853$		−	162.288i		−	0.190255i	0.995465	−	0.0951277i	$-0.0303260\pi$
$854$	123.738	+	44.7458i	0.144893	+	0.0523956i
$855$			73.3377i			0.0857751i
$856$	33.0230			0.0385782
$857$			203.560i			0.237526i	0.992923	+	0.118763i	$0.0378928\pi$
$857$			203.560i			0.237526i	−0.992923	+	0.118763i	$0.962107\pi$
$858$			77.3887i			0.0901966i
$859$		−	112.370i		−	0.130814i	−0.997859	−	0.0654072i	$-0.979165\pi$
$859$		−	112.370i		−	0.130814i	0.997859	−	0.0654072i	$-0.0208346\pi$
$860$		−	80.5510i		−	0.0936639i
$861$	580.173	+	379.163i	0.673836	+	0.440376i
$862$	407.379			0.472597
$863$	−378.691			−0.438807			−0.219404	−	0.975634i	$-0.570411\pi$
$863$	−378.691			−0.438807			−0.219404	+	0.975634i	$0.570411\pi$
$864$	−665.928			−0.770750
$865$	302.406			0.349603
$866$			5.95106i			0.00687189i
$867$	−206.366			−0.238023
$868$	1176.14	+	425.312i	1.35500	+	0.489991i
$869$	−258.101			−0.297009
$870$	−176.367			−0.202721
$871$			146.307i			0.167976i
$872$			26.1845i			0.0300281i
$873$	247.495			0.283500
$874$	23.0227			0.0263418
$875$	−806.264	−	291.558i	−0.921444	−	0.333209i
$876$		−	739.595i		−	0.844287i
$877$	−103.465			−0.117976			−0.0589880	−	0.998259i	$-0.518787\pi$
$877$	−103.465			−0.117976			−0.0589880	+	0.998259i	$0.518787\pi$
$878$	247.684			0.282101
$879$	989.479			1.12569
$880$	163.476			0.185768
$881$			243.660i			0.276572i	0.990392	+	0.138286i	$0.0441593\pi$
$881$			243.660i			0.276572i	−0.990392	+	0.138286i	$0.955841\pi$
$882$	61.7631	+	51.3891i	0.0700262	+	0.0582643i
$883$			684.924i			0.775678i	0.921727	+	0.387839i	$0.126778\pi$
$883$			684.924i			0.775678i	−0.921727	+	0.387839i	$0.873222\pi$
$884$	−772.067			−0.873378
$885$	−416.728			−0.470879
$886$	44.8644			0.0506371
$887$	867.676			0.978214			0.489107	−	0.872224i	$-0.337323\pi$
$887$	867.676			0.978214			0.489107	+	0.872224i	$0.337323\pi$
$888$	−451.933			−0.508933
$889$	−393.904	+	1089.29i	−0.443086	+	1.22529i
$890$		−	152.465i		−	0.171309i
$891$			181.265i			0.203440i
$892$		−	1535.97i		−	1.72194i
$893$	−14.3552			−0.0160752
$894$			17.6571i			0.0197506i
$895$	−763.897			−0.853516
$896$	264.696	−	731.980i	0.295420	−	0.816942i
$897$	200.356			0.223363
$898$	191.788			0.213572
$899$	−2268.68			−2.52356
$900$	190.766			0.211962
$901$			34.3322i			0.0381045i
$902$	−88.1879	−	20.8227i	−0.0977693	−	0.0230851i
$903$	−41.6690	+	115.230i	−0.0461451	+	0.127608i
$904$	−507.777			−0.561700
$905$		−	644.646i		−	0.712316i
$906$			223.662i			0.246867i
$907$	−416.475			−0.459179			−0.229589	−	0.973288i	$-0.573738\pi$
$907$	−416.475			−0.459179			−0.229589	+	0.973288i	$0.573738\pi$
$908$	−1492.28			−1.64348
$909$	−288.260			−0.317118
$910$	147.099	+	53.1936i	0.161648	+	0.0584545i
$911$	777.073			0.852988			0.426494	−	0.904490i	$-0.359748\pi$
$911$	777.073			0.852988			0.426494	+	0.904490i	$0.359748\pi$
$912$	−241.385			−0.264677
$913$	−478.990			−0.524633
$914$			195.536i			0.213935i
$915$	261.153			0.285413
$916$	1202.32			1.31258
$917$	446.307	+	161.392i	0.486703	+	0.176000i
$918$	216.983			0.236365
$919$		−	1115.63i		−	1.21396i	−0.794715	−	0.606982i	$-0.792380\pi$
$919$		−	1115.63i		−	1.21396i	0.794715	−	0.606982i	$-0.207620\pi$
$920$			68.1808i			0.0741096i
$921$			8.08429i			0.00877773i
$922$			89.4143i			0.0969786i
$923$		−	928.400i		−	1.00585i
$924$	−253.344	−	91.6135i	−0.274182	−	0.0991488i
$925$	754.476			0.815649
$926$			310.769i			0.335604i
$927$		−	89.9202i		−	0.0970013i
$928$			1073.94i			1.15727i
$929$	−1392.68			−1.49911			−0.749557	−	0.661939i	$-0.769734\pi$
$929$	−1392.68			−1.49911			−0.749557	+	0.661939i	$0.769734\pi$
$930$	−178.167			−0.191577
$931$	292.832	+	243.646i	0.314535	+	0.261704i
$932$			560.541i			0.601439i
$933$	928.100			0.994748
$934$			245.190i			0.262516i
$935$	−181.399			−0.194010
$936$	−183.838			−0.196409
$937$	−1043.64			−1.11381			−0.556907	−	0.830575i	$-0.688012\pi$
$937$	−1043.64			−1.11381			−0.556907	+	0.830575i	$0.688012\pi$
$938$	34.3777	+	12.4315i	0.0366500	+	0.0132532i
$939$	480.468			0.511680
$940$		−	20.5197i		−	0.0218295i
$941$			791.247i			0.840858i	0.907326	+	0.420429i	$0.138120\pi$
$941$			791.247i			0.840858i	−0.907326	+	0.420429i	$0.861880\pi$
$942$	−307.319			−0.326241
$943$	−53.9092	+	228.315i	−0.0571678	+	0.242116i
$944$			745.129i			0.789331i
$945$	575.976	+	208.282i	0.609498	+	0.220405i
$946$		−	16.0197i		−	0.0169342i
$947$	1183.63			1.24988			0.624939	−	0.780674i	$-0.285124\pi$
$947$	1183.63			1.24988			0.624939	+	0.780674i	$0.285124\pi$
$948$			544.766i			0.574647i
$949$		−	1189.88i		−	1.25382i
$950$	−64.9181			−0.0683349
$951$			1046.84i			1.10078i
$952$	−135.911	+	375.844i	−0.142764	+	0.394794i
$953$	1775.29			1.86284			0.931420	−	0.363945i	$-0.118571\pi$
$953$	1775.29			1.86284			0.931420	+	0.363945i	$0.118571\pi$
$954$			3.94585i			0.00413611i
$955$	786.757			0.823830
$956$			1322.96i			1.38385i
$957$	488.681			0.510638
$958$	−361.160			−0.376993
$959$	−495.599	−	179.217i	−0.516787	−	0.186879i
$960$		−	285.468i		−	0.297363i
$961$	−1330.83			−1.38484
$962$	−350.945			−0.364807
$963$	26.1429			0.0271474
$964$		−	1002.96i		−	1.04042i
$965$	−842.648			−0.873210
$966$	17.0240	−	47.0775i	0.0176232	−	0.0487345i
$967$		−	1193.17i		−	1.23389i	−0.787006	−	0.616945i	$-0.788370\pi$
$967$		−	1193.17i		−	1.23389i	0.787006	−	0.616945i	$-0.211630\pi$
$968$	−411.259			−0.424854
$969$	267.851			0.276420
$970$		−	120.391i		−	0.124115i
$971$	428.945			0.441756			0.220878	−	0.975301i	$-0.429108\pi$
$971$	428.945			0.441756			0.220878	+	0.975301i	$0.429108\pi$
$972$	−604.430			−0.621841
$973$	−1130.13	−	408.672i	−1.16149	−	0.420013i
$974$	123.682			0.126984
$975$	−564.953			−0.579439
$976$		−	466.954i		−	0.478437i
$977$			376.472i			0.385334i	0.981264	+	0.192667i	$0.0617138\pi$
$977$			376.472i			0.385334i	−0.981264	+	0.192667i	$0.938286\pi$
$978$	−356.136			−0.364147
$979$			422.454i			0.431516i
$980$	−348.275	+	418.582i	−0.355383	+	0.427125i
$981$			20.7292i			0.0211306i
$982$	199.193			0.202845
$983$			1697.30i			1.72665i	0.504646	+	0.863326i	$0.331623\pi$
$983$			1697.30i			1.72665i	−0.504646	+	0.863326i	$0.668377\pi$
$984$	−91.0543	+	385.631i	−0.0925349	+	0.391902i
$985$		−	58.0036i		−	0.0588869i
$986$		−	349.928i		−	0.354897i
$987$	−10.6148	+	29.3539i	−0.0107547	+	0.0297405i
$988$	−420.710			−0.425820
$989$	−41.4745			−0.0419358
$990$	−20.8485			−0.0210591
$991$			1788.72i			1.80497i	0.430724	+	0.902484i	$0.358258\pi$
$991$			1788.72i			1.80497i	−0.430724	+	0.902484i	$0.641742\pi$
$992$			1084.90i			1.09365i
$993$		−	1475.85i		−	1.48626i
$994$	−218.145	−	78.8849i	−0.219462	−	0.0793610i
$995$		−	341.166i		−	0.342880i
$996$			1010.99i			1.01505i
$997$	565.393			0.567094			0.283547	−	0.958958i	$-0.408489\pi$
$997$	565.393			0.567094			0.283547	+	0.958958i	$0.408489\pi$
$998$			206.289i			0.206702i
$999$	−1374.14			−1.37552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.d.286.16	yes	32
7.6	odd	2	inner	287.3.d.d.286.13	✓	32
41.40	even	2	inner	287.3.d.d.286.14	yes	32
287.286	odd	2	inner	287.3.d.d.286.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.d.286.13	✓	32	7.6	odd	2	inner
287.3.d.d.286.14	yes	32	41.40	even	2	inner
287.3.d.d.286.15	yes	32	287.286	odd	2	inner
287.3.d.d.286.16	yes	32	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+0.517567 q^{2} +2.41493 q^{3} -3.73212 q^{4} +2.97759i q^{5} +1.24989 q^{6} +(-2.38045 + 6.58281i) q^{7} -4.00189 q^{8} -3.16813 q^{9} +O(q^{10})\)	\(q+0.517567 q^{2} +2.41493 q^{3} -3.73212 q^{4} +2.97759i q^{5} +1.24989 q^{6} +(-2.38045 + 6.58281i) q^{7} -4.00189 q^{8} -3.16813 q^{9} +1.54110i q^{10} -4.27011i q^{11} -9.01280 q^{12} -14.5000 q^{13} +(-1.23204 + 3.40705i) q^{14} +7.19066i q^{15} +12.8573 q^{16} -14.2669 q^{17} -1.63972 q^{18} -7.77425 q^{19} -11.1127i q^{20} +(-5.74862 + 15.8970i) q^{21} -2.21007i q^{22} -5.72179 q^{23} -9.66427 q^{24} +16.1339 q^{25} -7.50471 q^{26} -29.3851 q^{27} +(8.88415 - 24.5679i) q^{28} +47.3894i q^{29} +3.72165i q^{30} +47.8731i q^{31} +22.6621 q^{32} -10.3120i q^{33} -7.38410 q^{34} +(-19.6009 - 7.08802i) q^{35} +11.8239 q^{36} +46.7632 q^{37} -4.02370 q^{38} -35.0164 q^{39} -11.9160i q^{40} +(9.42175 - 39.9028i) q^{41} +(-2.97530 + 8.22776i) q^{42} +7.24853 q^{43} +15.9366i q^{44} -9.43340i q^{45} -2.96141 q^{46} +1.84650 q^{47} +31.0493 q^{48} +(-37.6669 - 31.3402i) q^{49} +8.35040 q^{50} -34.4536 q^{51} +54.1158 q^{52} -2.40642i q^{53} -15.2088 q^{54} +12.7147 q^{55} +(9.52632 - 26.3437i) q^{56} -18.7742 q^{57} +24.5272i q^{58} +57.9540i q^{59} -26.8364i q^{60} -36.3183i q^{61} +24.7775i q^{62} +(7.54160 - 20.8552i) q^{63} -39.6999 q^{64} -43.1750i q^{65} -5.33716i q^{66} -10.0902i q^{67} +53.2460 q^{68} -13.8177 q^{69} +(-10.1448 - 3.66852i) q^{70} +64.0276i q^{71} +12.6785 q^{72} +82.0605i q^{73} +24.2031 q^{74} +38.9623 q^{75} +29.0145 q^{76} +(28.1094 + 10.1648i) q^{77} -18.1233 q^{78} -60.4435i q^{79} +38.2836i q^{80} -42.4497 q^{81} +(4.87638 - 20.6523i) q^{82} -112.173i q^{83} +(21.4546 - 59.3296i) q^{84} -42.4811i q^{85} +3.75160 q^{86} +114.442i q^{87} +17.0885i q^{88} -98.9327 q^{89} -4.88242i q^{90} +(34.5166 - 95.4507i) q^{91} +21.3544 q^{92} +115.610i q^{93} +0.955689 q^{94} -23.1486i q^{95} +54.7272 q^{96} -78.1202 q^{97} +(-19.4951 - 16.2206i) q^{98} +13.5283i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9}+O(q^{10}) \) 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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