LMFDB - Embedded newform 287.3.d.d.286.13

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			286.13
Character	$\chi$	$=$	287.286
Dual form			287.3.d.d.286.14

$q$-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	$-0.631854\pi$
$3$	−2.41493			−0.804975			−0.402488	+	0.915425i	$0.631854\pi$
$4$	−3.73212			−0.933031
$5$		−	2.97759i		−	0.595518i	−0.954641	−	0.297759i	$-0.903761\pi$
$5$		−	2.97759i		−	0.595518i	0.954641	−	0.297759i	$-0.0962392\pi$
$6$	−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	$-0.311687\pi$
$13$	14.5000			1.11538			0.557692	+	0.830048i	$0.311687\pi$
$14$	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	$-0.362165\pi$
$17$	14.2669			0.839232			0.419616	+	0.907702i	$0.362165\pi$
$18$	−1.63972			−0.0910956
$19$	7.77425			0.409171			0.204586	−	0.978849i	$-0.434415\pi$
$19$	7.77425			0.409171			0.204586	+	0.978849i	$0.434415\pi$
$20$			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	$-0.719183\pi$
$31$		−	47.8731i		−	1.54429i	0.635444	−	0.772147i	$-0.280817\pi$
$32$	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	$-0.506253\pi$
$47$	−1.84650			−0.0392873			−0.0196437	+	0.999807i	$0.506253\pi$
$48$	−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	$-0.836582\pi$
$59$		−	57.9540i		−	0.982271i	0.871083	−	0.491135i	$-0.163418\pi$
$60$		−	26.8364i		−	0.447274i
$61$			36.3183i			0.595383i	0.954662	+	0.297691i	$0.0962166\pi$
$61$			36.3183i			0.595383i	−0.954662	+	0.297691i	$0.903783\pi$
$62$		−	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	$-0.810010\pi$
$73$		−	82.0605i		−	1.12412i	0.827098	−	0.562058i	$-0.189990\pi$
$74$	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	$0.236175\pi$
$83$			112.173i			1.35148i	−0.737141	+	0.675739i	$0.763825\pi$
$84$	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	$-0.312411\pi$
$89$	98.9327			1.11160			0.555802	+	0.831315i	$0.312411\pi$
$90$			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	$-0.368078\pi$
$97$	78.1202			0.805363			0.402682	+	0.915340i	$0.368078\pi$
$98$	−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	$-0.648730\pi$
$101$	−90.9875			−0.900866			−0.450433	+	0.892810i	$0.648730\pi$
$102$	−17.8320			−0.174824
$103$		−	28.3827i		−	0.275560i	−0.990463	−	0.137780i	$-0.956003\pi$
$103$		−	28.3827i		−	0.275560i	0.990463	−	0.137780i	$-0.0439967\pi$
$104$	−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	$0.0833185\pi$
$131$			67.7988i			0.517548i	−0.965938	+	0.258774i	$0.916682\pi$
$132$		−	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	$-0.788126\pi$
$139$		−	171.678i		−	1.23510i	0.786533	−	0.617548i	$-0.211874\pi$
$140$	−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	$-0.213662\pi$
$157$	245.878			1.56610			0.783051	+	0.621958i	$0.213662\pi$
$158$		−	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	$-0.429568\pi$
$167$	73.3023			0.438936			0.219468	+	0.975620i	$0.429568\pi$
$168$	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	$0.0948294\pi$
$173$			101.561i			0.587056i	−0.955950	+	0.293528i	$0.905171\pi$
$174$		−	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	$-0.295937\pi$
$181$	216.499			1.19613			0.598064	+	0.801448i	$0.295937\pi$
$182$	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	$-0.407048\pi$
$199$	114.578			0.575768			0.287884	+	0.957665i	$0.407048\pi$
$200$	−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	$-0.625925\pi$
$223$		−	411.553i		−	1.84553i	0.385365	−	0.922764i	$-0.374075\pi$
$224$	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	$-0.842941\pi$
$227$	−399.847			−1.76144			−0.880720	+	0.473638i	$0.842941\pi$
$228$	70.0678			0.307315
$229$	322.155			1.40679			0.703395	−	0.710799i	$-0.251667\pi$
$229$	322.155			1.40679			0.703395	+	0.710799i	$0.251667\pi$
$230$			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	$-0.811742\pi$
$241$		−	268.738i		−	1.11510i	0.830145	−	0.557548i	$-0.188258\pi$
$242$	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	$0.215334\pi$
$251$			314.282i			1.25212i	−0.779775	+	0.626060i	$0.784666\pi$
$252$	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	$-0.486301\pi$
$257$	22.1148			0.0860498			0.0430249	+	0.999074i	$0.486301\pi$
$258$	−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	$-0.654709\pi$
$269$		−	475.696i		−	1.76839i	0.467122	−	0.884193i	$-0.345291\pi$
$270$		−	45.2855i		−	0.167724i
$271$			338.974i			1.25083i	0.780293	+	0.625414i	$0.215070\pi$
$271$			338.974i			1.25083i	−0.780293	+	0.625414i	$0.784930\pi$
$272$	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	$-0.921687\pi$
$283$		−	137.851i		−	0.487105i	0.969888	−	0.243552i	$-0.0783128\pi$
$284$		−	238.959i		−	0.841405i
$285$			55.9020i			0.196148i
$286$		−	32.0460i		−	0.112049i
$287$	−285.101	+	32.9651i	−0.993382	+	0.114861i
$288$	−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	$-0.746463\pi$
$293$	−409.735			−1.39841			−0.699206	+	0.714920i	$0.746463\pi$
$294$	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	$-0.998265\pi$
$307$		−	3.34764i		−	0.0109044i	0.999985	−	0.00545218i	$-0.00173549\pi$
$308$	−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	$-0.712006\pi$
$311$	−384.318			−1.23575			−0.617875	+	0.786277i	$0.712006\pi$
$312$	140.132			0.449140
$313$	−198.958			−0.635647			−0.317824	−	0.948150i	$-0.602952\pi$
$313$	−198.958			−0.635647			−0.317824	+	0.948150i	$0.602952\pi$
$314$	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	$-0.992849\pi$
$349$		−	15.6785i		−	0.0449242i	0.999748	−	0.0224621i	$-0.00715051\pi$
$350$	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	$0.00614808\pi$
$353$			13.6354i			0.0386271i	−0.999813	+	0.0193136i	$0.993852\pi$
$354$			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	$0.231806\pi$
$367$			488.518i			1.33111i	−0.746348	+	0.665556i	$0.768194\pi$
$368$	−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	$-0.891172\pi$
$383$	−721.665			−1.88424			−0.942122	+	0.335271i	$0.891172\pi$
$384$	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	$-0.545428\pi$
$397$	−112.933			−0.284466			−0.142233	+	0.989833i	$0.545428\pi$
$398$	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	$0.124063\pi$
$409$			310.808i			0.759922i	−0.925002	+	0.379961i	$0.875937\pi$
$410$	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	$0.113174\pi$
$419$			291.710i			0.696205i	−0.937456	+	0.348103i	$0.886826\pi$
$420$	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	$-0.995774\pi$
$433$		−	11.4981i		−	0.0265546i	0.999912	−	0.0132773i	$-0.00422642\pi$
$434$	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	$-0.683490\pi$
$439$	−478.556			−1.09010			−0.545052	+	0.838402i	$0.683490\pi$
$440$	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	$-0.940002\pi$
$461$		−	172.759i		−	0.374748i	0.982289	−	0.187374i	$-0.0599976\pi$
$462$	−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	$-0.830676\pi$
$467$		−	473.736i		−	1.01442i	0.861821	−	0.507212i	$-0.169324\pi$
$468$	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	$-0.240266\pi$
$479$	697.803			1.45679			0.728396	+	0.685157i	$0.240266\pi$
$480$			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	$-0.457463\pi$
$503$	134.035			0.266472			0.133236	+	0.991084i	$0.457463\pi$
$504$	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	$-0.599582\pi$
$509$	−313.307			−0.615535			−0.307767	+	0.951462i	$0.599582\pi$
$510$			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	$-0.311013\pi$
$521$	582.945			1.11890			0.559448	+	0.828865i	$0.311013\pi$
$522$		−	77.7054i		−	0.148861i
$523$		−	273.006i		−	0.522001i	−0.965339	−	0.261000i	$-0.915948\pi$
$523$		−	273.006i		−	0.522001i	0.965339	−	0.261000i	$-0.0840524\pi$
$524$		−	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	$-0.718827\pi$
$563$	−714.538			−1.26916			−0.634581	+	0.772857i	$0.718827\pi$
$564$	−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
$574$	−147.559	+	17.0616i	−0.257071	+	0.0297241i
$575$	−92.3150			−0.160548
$576$	125.774			0.218358
$577$	292.273			0.506539			0.253269	−	0.967396i	$-0.418494\pi$
$577$	292.273			0.506539			0.253269	+	0.967396i	$0.418494\pi$
$578$	−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	$-0.546351\pi$
$587$	−170.351			−0.290206			−0.145103	+	0.989417i	$0.546351\pi$
$588$	−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	$-0.474501\pi$
$593$	94.9074			0.160046			0.0800231	+	0.996793i	$0.474501\pi$
$594$		−	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	$-0.323971\pi$
$601$	631.354			1.05051			0.525253	+	0.850946i	$0.323971\pi$
$602$	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	$-0.784481\pi$
$607$		−	760.587i		−	1.25303i	0.779411	−	0.626513i	$-0.215519\pi$
$608$	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	$0.163947\pi$
$619$			609.816i			0.985163i	−0.870266	+	0.492582i	$0.836053\pi$
$620$	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	$-0.765614\pi$
$643$	−952.833			−1.48186			−0.740928	+	0.671585i	$0.765614\pi$
$644$	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	$0.191738\pi$
$647$			733.168i			1.13318i	−0.824000	+	0.566590i	$0.808262\pi$
$648$	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	$0.136300\pi$
$661$			548.940i			0.830469i	−0.909714	+	0.415234i	$0.863700\pi$
$662$		−	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	$-0.684971\pi$
$677$		−	1131.75i		−	1.67172i	0.548945	−	0.835858i	$-0.315029\pi$
$678$	−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	$-0.483446\pi$
$691$	71.8416			0.103968			0.0519838	+	0.998648i	$0.483446\pi$
$692$		−	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	$-0.353681\pi$
$719$	637.980			0.887315			0.443658	+	0.896196i	$0.353681\pi$
$720$			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	$-0.732942\pi$
$727$	−971.587			−1.33643			−0.668216	+	0.743967i	$0.732942\pi$
$728$	−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	$0.0689256\pi$
$733$			314.967i			0.429696i	−0.976648	+	0.214848i	$0.931074\pi$
$734$			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	$-0.769974\pi$
$761$		−	1006.61i		−	1.32275i	0.750056	−	0.661374i	$-0.230026\pi$
$762$	−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	$-0.814534\pi$
$769$		−	846.277i		−	1.10049i	0.835003	−	0.550245i	$-0.185466\pi$
$770$	−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	$-0.702426\pi$
$773$	−918.223			−1.18787			−0.593935	+	0.804513i	$0.702426\pi$
$774$	−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	$0.0516394\pi$
$787$			254.231i			0.323039i	−0.986870	+	0.161519i	$0.948361\pi$
$788$	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	$0.338987\pi$
$797$			1394.38i			1.74954i	−0.484539	+	0.874769i	$0.661013\pi$
$798$	−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	$-0.921952\pi$
$811$		−	393.731i		−	0.485488i	0.970090	−	0.242744i	$-0.0780476\pi$
$812$	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	$-0.858381\pi$
$829$		−	713.565i		−	0.860754i	0.902649	−	0.430377i	$-0.141619\pi$
$830$	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	$-0.363875\pi$
$839$	695.924			0.829469			0.414734	+	0.909943i	$0.363875\pi$
$840$	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	$0.0303260\pi$
$853$			162.288i			0.190255i	−0.995465	+	0.0951277i	$0.969674\pi$
$854$	−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	$-0.962107\pi$
$857$		−	203.560i		−	0.237526i	0.992923	−	0.118763i	$-0.0378928\pi$
$858$			77.3887i			0.0901966i
$859$			112.370i			0.130814i	0.997859	+	0.0654072i	$0.0208346\pi$
$859$			112.370i			0.130814i	−0.997859	+	0.0654072i	$0.979165\pi$
$860$			80.5510i			0.0936639i
$861$	688.497	−	79.6083i	0.799648	−	0.0924603i
$862$	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	$-0.955841\pi$
$881$		−	243.660i		−	0.276572i	0.990392	−	0.138286i	$-0.0441593\pi$
$882$	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	$-0.662677\pi$
$887$	−867.676			−0.978214			−0.489107	+	0.872224i	$0.662677\pi$
$888$	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	$-0.230266\pi$
$929$	1392.68			1.49911			0.749557	+	0.661939i	$0.230266\pi$
$930$	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	$-0.311988\pi$
$937$	1043.64			1.11381			0.556907	+	0.830575i	$0.311988\pi$
$938$	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	$-0.861880\pi$
$941$		−	791.247i		−	0.840858i	0.907326	−	0.420429i	$-0.138120\pi$
$942$	−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	$-0.570892\pi$
$971$	−428.945			−0.441756			−0.220878	+	0.975301i	$0.570892\pi$
$972$	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	$-0.668377\pi$
$983$		−	1697.30i		−	1.72665i	0.504646	−	0.863326i	$-0.331623\pi$
$984$	−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	$-0.591511\pi$
$997$	−565.393			−0.567094			−0.283547	+	0.958958i	$0.591511\pi$
$998$			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.286.13	✓	32
7.6	odd	2	inner	287.3.d.d.286.16	yes	32
41.40	even	2	inner	287.3.d.d.286.15	yes	32
287.286	odd	2	inner	287.3.d.d.286.14	yes	32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.d (of order \(2\), degree \(1\), minimal)

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