LMFDB - Embedded newform 287.3.d.d.286.6

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			286.6
Character	$\chi$	$=$	287.286
Dual form			287.3.d.d.286.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67431 q^{2} -2.89735 q^{3} +3.15194 q^{4} +3.34396i q^{5} +7.74841 q^{6} +(4.11915 + 5.65974i) q^{7} +2.26798 q^{8} -0.605380 q^{9} +O(q^{10})$	\(q-2.67431 q^{2} -2.89735 q^{3} +3.15194 q^{4} +3.34396i q^{5} +7.74841 q^{6} +(4.11915 + 5.65974i) q^{7} +2.26798 q^{8} -0.605380 q^{9} -8.94280i q^{10} -15.3848i q^{11} -9.13226 q^{12} +7.80554 q^{13} +(-11.0159 - 15.1359i) q^{14} -9.68862i q^{15} -18.6730 q^{16} +8.48488 q^{17} +1.61897 q^{18} +0.826108 q^{19} +10.5400i q^{20} +(-11.9346 - 16.3982i) q^{21} +41.1438i q^{22} -2.74675 q^{23} -6.57113 q^{24} +13.8179 q^{25} -20.8744 q^{26} +27.8301 q^{27} +(12.9833 + 17.8391i) q^{28} +15.8500i q^{29} +25.9104i q^{30} +52.1405i q^{31} +40.8656 q^{32} +44.5751i q^{33} -22.6912 q^{34} +(-18.9260 + 13.7743i) q^{35} -1.90812 q^{36} -39.7168 q^{37} -2.20927 q^{38} -22.6154 q^{39} +7.58404i q^{40} +(38.1158 + 15.1057i) q^{41} +(31.9168 + 43.8539i) q^{42} -71.9168 q^{43} -48.4920i q^{44} -2.02437i q^{45} +7.34566 q^{46} -0.994000 q^{47} +54.1023 q^{48} +(-15.0652 + 46.6266i) q^{49} -36.9534 q^{50} -24.5837 q^{51} +24.6026 q^{52} +10.7924i q^{53} -74.4264 q^{54} +51.4462 q^{55} +(9.34215 + 12.8362i) q^{56} -2.39352 q^{57} -42.3879i q^{58} +24.7187i q^{59} -30.5379i q^{60} +59.3552i q^{61} -139.440i q^{62} +(-2.49365 - 3.42629i) q^{63} -34.5951 q^{64} +26.1014i q^{65} -119.208i q^{66} -3.55600i q^{67} +26.7438 q^{68} +7.95829 q^{69} +(50.6139 - 36.8367i) q^{70} -49.0576i q^{71} -1.37299 q^{72} +106.882i q^{73} +106.215 q^{74} -40.0353 q^{75} +2.60384 q^{76} +(87.0739 - 63.3723i) q^{77} +60.4805 q^{78} +109.832i q^{79} -62.4420i q^{80} -75.1851 q^{81} +(-101.934 - 40.3974i) q^{82} -117.729i q^{83} +(-37.6171 - 51.6862i) q^{84} +28.3731i q^{85} +192.328 q^{86} -45.9231i q^{87} -34.8924i q^{88} -171.753 q^{89} +5.41379i q^{90} +(32.1522 + 44.1773i) q^{91} -8.65759 q^{92} -151.069i q^{93} +2.65826 q^{94} +2.76247i q^{95} -118.402 q^{96} +41.4772 q^{97} +(40.2891 - 124.694i) q^{98} +9.31366i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67431			−1.33716			−0.668578	−	0.743642i	$-0.733097\pi$
$2$	−2.67431			−1.33716			−0.668578	+	0.743642i	$0.733097\pi$
$3$	−2.89735			−0.965782			−0.482891	−	0.875680i	$-0.660413\pi$
$3$	−2.89735			−0.965782			−0.482891	+	0.875680i	$0.660413\pi$
$4$	3.15194			0.787985
$5$			3.34396i			0.668793i	0.942433	+	0.334396i	$0.108532\pi$
$5$			3.34396i			0.668793i	−0.942433	+	0.334396i	$0.891468\pi$
$6$	7.74841			1.29140
$7$	4.11915	+	5.65974i	0.588450	+	0.808534i
$7$	4.11915	+	5.65974i	0.588450	+	0.808534i
$8$	2.26798			0.283498
$9$	−0.605380			−0.0672645
$10$		−	8.94280i		−	0.894280i
$11$		−	15.3848i		−	1.39862i	−0.714819	−	0.699309i	$-0.753491\pi$
$11$		−	15.3848i		−	1.39862i	0.714819	−	0.699309i	$-0.246509\pi$
$12$	−9.13226			−0.761022
$13$	7.80554			0.600426			0.300213	−	0.953872i	$-0.402942\pi$
$13$	7.80554			0.600426			0.300213	+	0.953872i	$0.402942\pi$
$14$	−11.0159	−	15.1359i	−0.786849	−	1.08114i
$15$		−	9.68862i		−	0.645908i
$16$	−18.6730			−1.16706
$17$	8.48488			0.499111			0.249555	−	0.968361i	$-0.419716\pi$
$17$	8.48488			0.499111			0.249555	+	0.968361i	$0.419716\pi$
$18$	1.61897			0.0899430
$19$	0.826108			0.0434793			0.0217397	−	0.999764i	$-0.493080\pi$
$19$	0.826108			0.0434793			0.0217397	+	0.999764i	$0.493080\pi$
$20$			10.5400i			0.526998i
$21$	−11.9346	−	16.3982i	−0.568315	−	0.780868i
$22$			41.1438i			1.87017i
$23$	−2.74675			−0.119424			−0.0597119	−	0.998216i	$-0.519018\pi$
$23$	−2.74675			−0.119424			−0.0597119	+	0.998216i	$0.519018\pi$
$24$	−6.57113			−0.273797
$25$	13.8179			0.552716
$26$	−20.8744			−0.802863
$27$	27.8301			1.03075
$28$	12.9833	+	17.8391i	0.463689	+	0.637112i
$29$			15.8500i			0.546553i	0.961936	+	0.273276i	$0.0881074\pi$
$29$			15.8500i			0.546553i	−0.961936	+	0.273276i	$0.911893\pi$
$30$			25.9104i			0.863680i
$31$			52.1405i			1.68195i	0.541073	+	0.840975i	$0.318018\pi$
$31$			52.1405i			1.68195i	−0.541073	+	0.840975i	$0.681982\pi$
$32$	40.8656			1.27705
$33$			44.5751i			1.35076i
$34$	−22.6912			−0.667389
$35$	−18.9260	+	13.7743i	−0.540741	+	0.393551i
$36$	−1.90812			−0.0530034
$37$	−39.7168			−1.07343			−0.536714	−	0.843764i	$-0.680335\pi$
$37$	−39.7168			−1.07343			−0.536714	+	0.843764i	$0.680335\pi$
$38$	−2.20927			−0.0581386
$39$	−22.6154			−0.579881
$40$			7.58404i			0.189601i
$41$	38.1158	+	15.1057i	0.929655	+	0.368432i
$41$	38.1158	+	15.1057i	0.929655	+	0.368432i
$42$	31.9168	+	43.8539i	0.759925	+	1.04414i
$43$	−71.9168			−1.67248			−0.836242	−	0.548361i	$-0.815252\pi$
$43$	−71.9168			−1.67248			−0.836242	+	0.548361i	$0.815252\pi$
$44$		−	48.4920i		−	1.10209i
$45$		−	2.02437i		−	0.0449860i
$46$	7.34566			0.159688
$47$	−0.994000			−0.0211489			−0.0105745	−	0.999944i	$-0.503366\pi$
$47$	−0.994000			−0.0211489			−0.0105745	+	0.999944i	$0.503366\pi$
$48$	54.1023			1.12713
$49$	−15.0652	+	46.6266i	−0.307453	+	0.951563i
$50$	−36.9534			−0.739068
$51$	−24.5837			−0.482032
$52$	24.6026			0.473127
$53$			10.7924i			0.203630i	0.994803	+	0.101815i	$0.0324650\pi$
$53$			10.7924i			0.203630i	−0.994803	+	0.101815i	$0.967535\pi$
$54$	−74.4264			−1.37827
$55$	51.4462			0.935386
$56$	9.34215	+	12.8362i	0.166824	+	0.229217i
$57$	−2.39352			−0.0419916
$58$		−	42.3879i		−	0.730826i
$59$			24.7187i			0.418961i	0.977813	+	0.209480i	$0.0671772\pi$
$59$			24.7187i			0.418961i	−0.977813	+	0.209480i	$0.932823\pi$
$60$		−	30.5379i		−	0.508966i
$61$			59.3552i			0.973036i	0.873671	+	0.486518i	$0.161733\pi$
$61$			59.3552i			0.973036i	−0.873671	+	0.486518i	$0.838267\pi$
$62$		−	139.440i		−	2.24903i
$63$	−2.49365	−	3.42629i	−0.0395818	−	0.0543856i
$64$	−34.5951			−0.540549
$65$			26.1014i			0.401561i
$66$		−	119.208i		−	1.80618i
$67$		−	3.55600i		−	0.0530747i	−0.999648	−	0.0265373i	$-0.991552\pi$
$67$		−	3.55600i		−	0.0530747i	0.999648	−	0.0265373i	$-0.00844809\pi$
$68$	26.7438			0.393292
$69$	7.95829			0.115337
$70$	50.6139	−	36.8367i	0.723055	−	0.526239i
$71$		−	49.0576i		−	0.690952i	−0.938428	−	0.345476i	$-0.887717\pi$
$71$		−	49.0576i		−	0.690952i	0.938428	−	0.345476i	$-0.112283\pi$
$72$	−1.37299			−0.0190693
$73$			106.882i			1.46414i	0.681232	+	0.732068i	$0.261445\pi$
$73$			106.882i			1.46414i	−0.681232	+	0.732068i	$0.738555\pi$
$74$	106.215			1.43534
$75$	−40.0353			−0.533804
$76$	2.60384			0.0342611
$77$	87.0739	−	63.3723i	1.13083	−	0.823017i
$78$	60.4805			0.775391
$79$			109.832i			1.39028i	0.718874	+	0.695140i	$0.244658\pi$
$79$			109.832i			1.39028i	−0.718874	+	0.695140i	$0.755342\pi$
$80$		−	62.4420i		−	0.780525i
$81$	−75.1851			−0.928211
$82$	−101.934	−	40.3974i	−1.24309	−	0.492651i
$83$		−	117.729i		−	1.41842i	−0.704996	−	0.709211i	$-0.749051\pi$
$83$		−	117.729i		−	1.41842i	0.704996	−	0.709211i	$-0.250949\pi$
$84$	−37.6171	−	51.6862i	−0.447823	−	0.615312i
$85$			28.3731i			0.333802i
$86$	192.328			2.23637
$87$		−	45.9231i		−	0.527851i
$88$		−	34.8924i		−	0.396505i
$89$	−171.753			−1.92981			−0.964905	−	0.262598i	$-0.915421\pi$
$89$	−171.753			−1.92981			−0.964905	+	0.262598i	$0.915421\pi$
$90$			5.41379i			0.0601532i
$91$	32.1522	+	44.1773i	0.353321	+	0.485465i
$92$	−8.65759			−0.0941042
$93$		−	151.069i		−	1.62440i
$94$	2.65826			0.0282794
$95$			2.76247i			0.0290787i
$96$	−118.402			−1.23335
$97$	41.4772			0.427600			0.213800	−	0.976878i	$-0.431416\pi$
$97$	41.4772			0.427600			0.213800	+	0.976878i	$0.431416\pi$
$98$	40.2891	−	124.694i	0.411113	−	1.27239i
$99$			9.31366i			0.0940773i
$100$	43.5532			0.435532
$101$	−40.4210			−0.400208			−0.200104	−	0.979775i	$-0.564128\pi$
$101$	−40.4210			−0.400208			−0.200104	+	0.979775i	$0.564128\pi$
$102$	65.7443			0.644552
$103$		−	105.805i		−	1.02723i	−0.858019	−	0.513617i	$-0.828305\pi$
$103$		−	105.805i		−	1.02723i	0.858019	−	0.513617i	$-0.171695\pi$
$104$	17.7028			0.170219
$105$	54.8350	−	39.9089i	0.522239	−	0.380085i
$106$		−	28.8623i		−	0.272286i
$107$	53.1045			0.496304			0.248152	−	0.968721i	$-0.420177\pi$
$107$	53.1045			0.496304			0.248152	+	0.968721i	$0.420177\pi$
$108$	87.7188			0.812211
$109$			113.233i			1.03883i	0.854522	+	0.519416i	$0.173850\pi$
$109$			113.233i			1.03883i	−0.854522	+	0.519416i	$0.826150\pi$
$110$	−137.583			−1.25076
$111$	115.073			1.03670
$112$	−76.9170	−	105.684i	−0.686759	−	0.943611i
$113$	25.9757			0.229873			0.114937	−	0.993373i	$-0.463333\pi$
$113$	25.9757			0.229873			0.114937	+	0.993373i	$0.463333\pi$
$114$	6.40102			0.0561493
$115$		−	9.18503i		−	0.0798698i
$116$			49.9583i			0.430675i
$117$	−4.72532			−0.0403873
$118$		−	66.1054i		−	0.560215i
$119$	34.9505	+	48.0222i	0.293702	+	0.403548i
$120$		−	21.9736i		−	0.183113i
$121$	−115.692			−0.956134
$122$		−	158.734i		−	1.30110i
$123$	−110.435	−	43.7665i	−0.897844	−	0.355825i
$124$			164.344i			1.32535i
$125$			129.806i			1.03845i
$126$	6.66880	+	9.16297i	0.0529270	+	0.0727220i
$127$	122.410			0.963855			0.481927	−	0.876211i	$-0.339937\pi$
$127$	122.410			0.963855			0.481927	+	0.876211i	$0.339937\pi$
$128$	−70.9442			−0.554252
$129$	208.368			1.61525
$130$		−	69.8034i		−	0.536949i
$131$			48.9887i			0.373959i	0.982364	+	0.186980i	$0.0598699\pi$
$131$			48.9887i			0.373959i	−0.982364	+	0.186980i	$0.940130\pi$
$132$			140.498i			1.06438i
$133$	3.40286	+	4.67555i	0.0255854	+	0.0351545i
$134$			9.50985i			0.0709691i
$135$			93.0629i			0.689355i
$136$	19.2436			0.141497
$137$			51.3949i			0.375145i	0.982251	+	0.187573i	$0.0600620\pi$
$137$			51.3949i			0.375145i	−0.982251	+	0.187573i	$0.939938\pi$
$138$	−21.2829			−0.154224
$139$			121.729i			0.875746i	0.899037	+	0.437873i	$0.144268\pi$
$139$			121.729i			0.875746i	−0.899037	+	0.437873i	$0.855732\pi$
$140$	−59.6534	+	43.4157i	−0.426096	+	0.310112i
$141$	2.87996			0.0204253
$142$			131.195i			0.923911i
$143$		−	120.087i		−	0.839767i
$144$	11.3043			0.0785020
$145$	−53.0019			−0.365531
$146$		−	285.835i		−	1.95778i
$147$	43.6492	−	135.093i	0.296933	−	0.919003i
$148$	−125.185			−0.845844
$149$			147.905i			0.992652i	0.868136	+	0.496326i	$0.165318\pi$
$149$			147.905i			0.992652i	−0.868136	+	0.496326i	$0.834682\pi$
$150$	107.067			0.713778
$151$			198.902i			1.31723i	0.752479	+	0.658616i	$0.228858\pi$
$151$			198.902i			1.31723i	−0.752479	+	0.658616i	$0.771142\pi$
$152$	1.87360			0.0123263
$153$	−5.13658			−0.0335724
$154$	−232.863	+	169.477i	−1.51210	+	1.10050i
$155$	−174.356			−1.12488
$156$	−71.2822			−0.456937
$157$	−153.292			−0.976381			−0.488190	−	0.872737i	$-0.662343\pi$
$157$	−153.292			−0.976381			−0.488190	+	0.872737i	$0.662343\pi$
$158$		−	293.725i		−	1.85902i
$159$		−	31.2694i		−	0.196663i
$160$			136.653i			0.854081i
$161$	−11.3143	−	15.5459i	−0.0702750	−	0.0965582i
$162$	201.068			1.24116
$163$	177.866			1.09120			0.545600	−	0.838046i	$-0.316302\pi$
$163$	177.866			1.09120			0.545600	+	0.838046i	$0.316302\pi$
$164$	120.139	+	47.6123i	0.732553	+	0.290319i
$165$	−149.058			−0.903379
$166$			314.844i			1.89665i
$167$	−123.493			−0.739479			−0.369739	−	0.929136i	$-0.620553\pi$
$167$	−123.493			−0.739479			−0.369739	+	0.929136i	$0.620553\pi$
$168$	−27.0675	−	37.1908i	−0.161116	−	0.221374i
$169$	−108.074			−0.639488
$170$		−	75.8786i		−	0.446345i
$171$	−0.500109			−0.00292461
$172$	−226.677			−1.31789
$173$			335.378i			1.93860i	0.245875	+	0.969301i	$0.420925\pi$
$173$			335.378i			1.93860i	−0.245875	+	0.969301i	$0.579075\pi$
$174$			122.813i			0.705819i
$175$	56.9180	+	78.2057i	0.325246	+	0.446890i
$176$			287.281i			1.63228i
$177$		−	71.6186i		−	0.404625i
$178$	459.321			2.58046
$179$		−	262.625i		−	1.46718i	−0.679593	−	0.733590i	$-0.737843\pi$
$179$		−	262.625i		−	1.46718i	0.679593	−	0.733590i	$-0.262157\pi$
$180$		−	6.38069i		−	0.0354483i
$181$	28.4415			0.157135			0.0785677	−	0.996909i	$-0.474965\pi$
$181$	28.4415			0.157135			0.0785677	+	0.996909i	$0.474965\pi$
$182$	−85.9850	−	118.144i	−0.472445	−	0.649142i
$183$		−	171.973i		−	0.939741i
$184$	−6.22958			−0.0338564
$185$		−	132.812i		−	0.717901i
$186$			404.006i			2.17207i
$187$		−	130.538i		−	0.698066i
$188$	−3.13303			−0.0166650
$189$	114.636	+	157.511i	0.606542	+	0.833392i
$190$		−	7.38771i		−	0.0388827i
$191$		−	220.420i		−	1.15403i	−0.816733	−	0.577016i	$-0.804217\pi$
$191$		−	220.420i		−	1.15403i	0.816733	−	0.577016i	$-0.195783\pi$
$192$	100.234			0.522052
$193$			19.7965i			0.102572i	0.998684	+	0.0512862i	$0.0163321\pi$
$193$			19.7965i			0.102572i	−0.998684	+	0.0512862i	$0.983668\pi$
$194$	−110.923			−0.571767
$195$		−	75.6250i		−	0.387820i
$196$	−47.4846	+	146.964i	−0.242269	+	0.749817i
$197$	249.634			1.26718			0.633589	−	0.773670i	$-0.281581\pi$
$197$	249.634			1.26718			0.633589	+	0.773670i	$0.281581\pi$
$198$		−	24.9076i		−	0.125796i
$199$	207.110			1.04075			0.520376	−	0.853937i	$-0.325792\pi$
$199$	207.110			1.04075			0.520376	+	0.853937i	$0.325792\pi$
$200$	31.3387			0.156694
$201$			10.3030i			0.0512586i
$202$	108.098			0.535140
$203$	−89.7070	+	65.2887i	−0.441906	+	0.321619i
$204$	−77.4862			−0.379834
$205$	−50.5130	+	127.458i	−0.246405	+	0.621746i
$206$			282.956i			1.37357i
$207$	1.66283			0.00803298
$208$	−145.753			−0.700736
$209$		−	12.7095i		−	0.0608110i
$210$	−146.646	+	106.729i	−0.698314	+	0.508232i
$211$		−	342.458i		−	1.62302i	−0.584337	−	0.811511i	$-0.698645\pi$
$211$		−	342.458i		−	1.62302i	0.584337	−	0.811511i	$-0.301355\pi$
$212$			34.0170i			0.160458i
$213$			142.137i			0.667310i
$214$	−142.018			−0.663635
$215$		−	240.487i		−	1.11854i
$216$	63.1182			0.292214
$217$	−295.101	+	214.774i	−1.35991	+	0.989744i
$218$		−	302.819i		−	1.38908i
$219$		−	309.674i		−	1.41404i
$220$	162.155			0.737070
$221$	66.2291			0.299679
$222$	−307.742			−1.38623
$223$			89.7556i			0.402491i	0.979541	+	0.201246i	$0.0644990\pi$
$223$			89.7556i			0.402491i	−0.979541	+	0.201246i	$0.935501\pi$
$224$	168.331	+	231.288i	0.751480	+	1.03254i
$225$	−8.36509			−0.0371782
$226$	−69.4671			−0.307376
$227$	−54.6292			−0.240657			−0.120329	−	0.992734i	$-0.538395\pi$
$227$	−54.6292			−0.240657			−0.120329	+	0.992734i	$0.538395\pi$
$228$	−7.54423			−0.0330887
$229$	245.368			1.07148			0.535739	−	0.844384i	$-0.320033\pi$
$229$	245.368			1.07148			0.535739	+	0.844384i	$0.320033\pi$
$230$			24.5636i			0.106798i
$231$	−252.283	+	183.612i	−1.09214	+	0.794855i
$232$			35.9476i			0.154946i
$233$			237.177i			1.01793i	0.860788	+	0.508963i	$0.169971\pi$
$233$			237.177i			1.01793i	−0.860788	+	0.508963i	$0.830029\pi$
$234$	12.6370			0.0540042
$235$		−	3.32390i		−	0.0141443i
$236$			77.9117i			0.330134i
$237$		−	318.222i		−	1.34271i
$238$	−93.4685	−	128.426i	−0.392725	−	0.539606i
$239$			348.003i			1.45608i	0.685535	+	0.728040i	$0.259568\pi$
$239$			348.003i			1.45608i	−0.685535	+	0.728040i	$0.740432\pi$
$240$			180.916i			0.753817i
$241$			48.8897i			0.202862i	0.994843	+	0.101431i	$0.0323421\pi$
$241$			48.8897i			0.202862i	−0.994843	+	0.101431i	$0.967658\pi$
$242$	309.397			1.27850
$243$	−32.6338			−0.134295
$244$			187.084i			0.766737i
$245$	−155.918	−	50.3775i	−0.636399	−	0.205623i
$246$	295.337	+	117.045i	1.20056	+	0.475794i
$247$	6.44822			0.0261061
$248$			118.254i			0.476829i
$249$			341.102i			1.36989i
$250$		−	347.141i		−	1.38856i
$251$		−	129.340i		−	0.515299i	−0.966238	−	0.257650i	$-0.917052\pi$
$251$		−	129.340i		−	0.515299i	0.966238	−	0.257650i	$-0.0829480\pi$
$252$	−7.85983	−	10.7995i	−0.0311898	−	0.0428550i
$253$			42.2582i			0.167029i
$254$	−327.361			−1.28882
$255$		−	82.2068i		−	0.322380i
$256$	328.107			1.28167
$257$	364.713			1.41912			0.709558	−	0.704647i	$-0.248894\pi$
$257$	364.713			1.41912			0.709558	+	0.704647i	$0.248894\pi$
$258$	−557.240			−2.15985
$259$	−163.600	−	224.787i	−0.631658	−	0.867902i
$260$			82.2701i			0.316424i
$261$		−	9.59530i		−	0.0367636i
$262$		−	131.011i		−	0.500042i
$263$			48.9787i			0.186231i	0.995655	+	0.0931153i	$0.0296825\pi$
$263$			48.9787i			0.186231i	−0.995655	+	0.0931153i	$0.970317\pi$
$264$			101.096i			0.382938i
$265$	−36.0894			−0.136187
$266$	−9.10031	−	12.5039i	−0.0342117	−	0.0470070i
$267$	497.629			1.86378
$268$		−	11.2083i		−	0.0418220i
$269$		−	116.578i		−	0.433374i	−0.976241	−	0.216687i	$-0.930475\pi$
$269$		−	116.578i		−	0.433374i	0.976241	−	0.216687i	$-0.0695252\pi$
$270$		−	248.879i		−	0.921775i
$271$		−	23.3593i		−	0.0861967i	−0.999071	−	0.0430983i	$-0.986277\pi$
$271$		−	23.3593i		−	0.0861967i	0.999071	−	0.0430983i	$-0.0137229\pi$
$272$	−158.439			−0.582495
$273$	−93.1561	−	127.997i	−0.341231	−	0.468853i
$274$		−	137.446i		−	0.501627i
$275$		−	212.586i		−	0.773039i
$276$	25.0840			0.0908842
$277$	199.356			0.719696			0.359848	−	0.933011i	$-0.382829\pi$
$277$	199.356			0.719696			0.359848	+	0.933011i	$0.382829\pi$
$278$		−	325.540i		−	1.17101i
$279$		−	31.5648i		−	0.113136i
$280$	−42.9237	+	31.2398i	−0.153299	+	0.111571i
$281$		−	192.518i		−	0.685119i	−0.939496	−	0.342559i	$-0.888706\pi$
$281$		−	192.518i		−	0.685119i	0.939496	−	0.342559i	$-0.111294\pi$
$282$	−7.70192			−0.0273118
$283$		−	258.377i		−	0.912994i	−0.889725	−	0.456497i	$-0.849104\pi$
$283$		−	258.377i		−	0.912994i	0.889725	−	0.456497i	$-0.150896\pi$
$284$		−	154.627i		−	0.544460i
$285$		−	8.00384i		−	0.0280837i
$286$			321.149i			1.12290i
$287$	71.5104	+	277.948i	0.249165	+	0.968461i
$288$	−24.7392			−0.0859000
$289$	−217.007			−0.750888
$290$	141.744			0.488771
$291$	−120.174			−0.412968
$292$			336.885i			1.15372i
$293$	203.782			0.695503			0.347751	−	0.937587i	$-0.386945\pi$
$293$	203.782			0.695503			0.347751	+	0.937587i	$0.386945\pi$
$294$	−116.731	+	361.282i	−0.397046	+	1.22885i
$295$	−82.6583			−0.280198
$296$	−90.0770			−0.304314
$297$		−	428.161i		−	1.44162i
$298$		−	395.544i		−	1.32733i
$299$	−21.4399			−0.0717052
$300$	−126.189			−0.420629
$301$	−296.236	−	407.030i	−0.984173	−	1.35226i
$302$		−	531.926i		−	1.76134i
$303$	117.114			0.386514
$304$	−15.4259			−0.0507432
$305$	−198.482			−0.650759
$306$	13.7368			0.0448915
$307$		−	395.521i		−	1.28834i	−0.764881	−	0.644171i	$-0.777202\pi$
$307$		−	395.521i		−	1.28834i	0.764881	−	0.644171i	$-0.222798\pi$
$308$	274.452	−	199.746i	0.891077	−	0.648525i
$309$			306.554i			0.992085i
$310$	466.282			1.50413
$311$	−237.771			−0.764537			−0.382269	−	0.924051i	$-0.624857\pi$
$311$	−237.771			−0.764537			−0.382269	+	0.924051i	$0.624857\pi$
$312$	−51.2912			−0.164395
$313$	435.532			1.39148			0.695738	−	0.718295i	$-0.255077\pi$
$313$	435.532			1.39148			0.695738	+	0.718295i	$0.255077\pi$
$314$	409.950			1.30557
$315$	11.4574	−	8.33868i	0.0363727	−	0.0264720i
$316$			346.184i			1.09552i
$317$		−	169.230i		−	0.533849i	−0.963717	−	0.266925i	$-0.913993\pi$
$317$		−	169.230i		−	0.533849i	0.963717	−	0.266925i	$-0.0860075\pi$
$318$			83.6240i			0.262969i
$319$	243.850			0.764419
$320$		−	115.685i		−	0.361515i
$321$	−153.862			−0.479321
$322$	30.2579	+	41.5745i	0.0939686	+	0.129113i
$323$	7.00943			0.0217010
$324$	−236.979			−0.731416
$325$	107.856			0.331865
$326$	−475.668			−1.45910
$327$		−	328.074i		−	1.00329i
$328$	86.4460	+	34.2595i	0.263555	+	0.104450i
$329$	−4.09443	−	5.62578i	−0.0124451	−	0.0170996i
$330$	398.626			1.20796
$331$		−	86.5093i		−	0.261358i	−0.991425	−	0.130679i	$-0.958284\pi$
$331$		−	86.5093i		−	0.261358i	0.991425	−	0.130679i	$-0.0417157\pi$
$332$		−	371.075i		−	1.11769i
$333$	24.0438			0.0722035
$334$	330.258			0.988798
$335$	11.8911			0.0354959
$336$	222.855	+	306.205i	0.663260	+	0.911323i
$337$	−380.320			−1.12855			−0.564273	−	0.825588i	$-0.690844\pi$
$337$	−380.320			−1.12855			−0.564273	+	0.825588i	$0.690844\pi$
$338$	289.022			0.855095
$339$	−75.2606			−0.222008
$340$			89.4304i			0.263031i
$341$	802.171			2.35241
$342$	1.33745			0.00391066
$343$	−325.950	+	106.797i	−0.950292	+	0.311361i
$344$	−163.106			−0.474145
$345$			26.6122i			0.0771369i
$346$		−	896.906i		−	2.59221i
$347$		−	82.6726i		−	0.238250i	−0.992879	−	0.119125i	$-0.961991\pi$
$347$		−	82.6726i		−	0.238250i	0.992879	−	0.119125i	$-0.0380089\pi$
$348$		−	144.747i		−	0.415939i
$349$			315.374i			0.903651i	0.892106	+	0.451826i	$0.149227\pi$
$349$			315.374i			0.903651i	−0.892106	+	0.451826i	$0.850773\pi$
$350$	−152.216	−	209.146i	−0.434904	−	0.597561i
$351$	217.229			0.618886
$352$		−	628.709i		−	1.78611i
$353$			584.610i			1.65612i	0.560640	+	0.828060i	$0.310555\pi$
$353$			584.610i			1.65612i	−0.560640	+	0.828060i	$0.689445\pi$
$354$			191.530i			0.541046i
$355$	164.047			0.462104
$356$	−541.355			−1.52066
$357$	−101.264	−	139.137i	−0.283652	−	0.389739i
$358$			702.341i			1.96185i
$359$	479.495			1.33564			0.667821	−	0.744322i	$-0.267227\pi$
$359$	479.495			1.33564			0.667821	+	0.744322i	$0.267227\pi$
$360$		−	4.59123i		−	0.0127534i
$361$	−360.318			−0.998110
$362$	−76.0614			−0.210114
$363$	335.201			0.923418
$364$	101.342	+	139.244i	0.278411	+	0.382539i
$365$	−357.409			−0.979203
$366$			459.908i			1.25658i
$367$			273.041i			0.743982i	0.928236	+	0.371991i	$0.121325\pi$
$367$			273.041i			0.743982i	−0.928236	+	0.371991i	$0.878675\pi$
$368$	51.2902			0.139375
$369$	−23.0746	−	9.14471i	−0.0625327	−	0.0247824i
$370$			355.180i			0.959945i
$371$	−61.0822	+	44.4556i	−0.164642	+	0.119826i
$372$		−	476.160i		−	1.28000i
$373$	1.89956			0.00509264			0.00254632	−	0.999997i	$-0.499189\pi$
$373$	1.89956			0.00509264			0.00254632	+	0.999997i	$0.499189\pi$
$374$			349.100i			0.933422i
$375$		−	376.092i		−	1.00291i
$376$	−2.25437			−0.00599567
$377$			123.718i			0.328165i
$378$	−306.573	−	421.234i	−0.811041	−	1.11437i
$379$	−418.879			−1.10522			−0.552611	−	0.833439i	$-0.686368\pi$
$379$	−418.879			−1.10522			−0.552611	+	0.833439i	$0.686368\pi$
$380$			8.70715i			0.0229135i
$381$	−354.663			−0.930874
$382$			589.472i			1.54312i
$383$	184.199			0.480936			0.240468	−	0.970657i	$-0.422699\pi$
$383$	184.199			0.480936			0.240468	+	0.970657i	$0.422699\pi$
$384$	205.550			0.535287
$385$	211.915	+	291.172i	0.550428	+	0.756291i
$386$		−	52.9419i		−	0.137155i
$387$	43.5370			0.112499
$388$	130.733			0.336942
$389$	−145.229			−0.373339			−0.186670	−	0.982423i	$-0.559769\pi$
$389$	−145.229			−0.373339			−0.186670	+	0.982423i	$0.559769\pi$
$390$			202.245i			0.518576i
$391$	−23.3059			−0.0596058
$392$	−34.1676	+	105.748i	−0.0871623	+	0.269766i
$393$		−	141.937i		−	0.361163i
$394$	−667.599			−1.69441
$395$	−367.275			−0.929810
$396$			29.3561i			0.0741315i
$397$	−498.076			−1.25460			−0.627300	−	0.778778i	$-0.715840\pi$
$397$	−498.076			−1.25460			−0.627300	+	0.778778i	$0.715840\pi$
$398$	−553.875			−1.39165
$399$	−9.85927	−	13.5467i	−0.0247099	−	0.0339516i
$400$	−258.022			−0.645056
$401$	165.137			0.411812			0.205906	−	0.978572i	$-0.433986\pi$
$401$	165.137			0.411812			0.205906	+	0.978572i	$0.433986\pi$
$402$		−	27.5533i		−	0.0685407i
$403$			406.985i			1.00989i
$404$	−127.404			−0.315358
$405$		−	251.416i		−	0.620781i
$406$	239.904	−	174.602i	0.590898	−	0.430055i
$407$			611.036i			1.50132i
$408$	−55.7552			−0.136655
$409$			643.763i			1.57399i	0.616958	+	0.786996i	$0.288365\pi$
$409$			643.763i			1.57399i	−0.616958	+	0.786996i	$0.711635\pi$
$410$	135.087	−	340.862i	0.329482	−	0.831371i
$411$		−	148.909i		−	0.362309i
$412$		−	333.491i		−	0.809445i
$413$	−139.901	+	101.820i	−0.338744	+	0.246537i
$414$	−4.44692			−0.0107413
$415$	393.682			0.948630
$416$	318.978			0.766774
$417$		−	352.690i		−	0.845780i
$418$			33.9892i			0.0813138i
$419$			755.940i			1.80415i	0.431576	+	0.902077i	$0.357958\pi$
$419$			755.940i			1.80415i	−0.431576	+	0.902077i	$0.642042\pi$
$420$	172.837	−	125.790i	0.411516	−	0.299501i
$421$		−	231.259i		−	0.549308i	−0.961543	−	0.274654i	$-0.911437\pi$
$421$		−	231.259i		−	0.549308i	0.961543	−	0.274654i	$-0.0885633\pi$
$422$			915.839i			2.17023i
$423$	0.601748			0.00142257
$424$			24.4770i			0.0577287i
$425$	117.243			0.275867
$426$		−	380.118i		−	0.892297i
$427$	−335.935	+	244.493i	−0.786732	+	0.572583i
$428$	167.382			0.391080
$429$			347.933i			0.811033i
$430$			643.137i			1.49567i
$431$	−90.1501			−0.209165			−0.104582	−	0.994516i	$-0.533351\pi$
$431$	−90.1501			−0.209165			−0.104582	+	0.994516i	$0.533351\pi$
$432$	−519.673			−1.20295
$433$		−	391.594i		−	0.904373i	−0.891923	−	0.452187i	$-0.850644\pi$
$433$		−	391.594i		−	0.904373i	0.891923	−	0.452187i	$-0.149356\pi$
$434$	789.193	−	574.374i	1.81842	−	1.32344i
$435$	153.565			0.353023
$436$			356.902i			0.818583i
$437$	−2.26911			−0.00519247
$438$			828.164i			1.89079i
$439$	610.875			1.39151			0.695757	−	0.718277i	$-0.255069\pi$
$439$	610.875			1.39151			0.695757	+	0.718277i	$0.255069\pi$
$440$	116.679			0.265180
$441$	9.12018	−	28.2268i	0.0206807	−	0.0640064i
$442$	−177.117			−0.400718
$443$	293.107			0.661640			0.330820	−	0.943694i	$-0.392675\pi$
$443$	293.107			0.661640			0.330820	+	0.943694i	$0.392675\pi$
$444$	362.704			0.816902
$445$		−	574.336i		−	1.29064i
$446$		−	240.034i		−	0.538194i
$447$		−	428.532i		−	0.958686i
$448$	−142.502	−	195.799i	−0.318086	−	0.437052i
$449$	−317.488			−0.707101			−0.353551	−	0.935415i	$-0.615026\pi$
$449$	−317.488			−0.707101			−0.353551	+	0.935415i	$0.615026\pi$
$450$	22.3708			0.0497130
$451$	232.399	−	586.405i	0.515296	−	1.30023i
$452$	81.8738			0.181137
$453$		−	576.288i		−	1.27216i
$454$	146.095			0.321796
$455$	−147.727	+	107.516i	−0.324675	+	0.236298i
$456$	−5.42846			−0.0119045
$457$		−	816.773i		−	1.78725i	−0.448814	−	0.893625i	$-0.648154\pi$
$457$		−	816.773i		−	1.78725i	0.448814	−	0.893625i	$-0.351846\pi$
$458$	−656.191			−1.43273
$459$	236.135			0.514456
$460$		−	28.9507i		−	0.0629362i
$461$			554.338i			1.20247i	0.799073	+	0.601235i	$0.205324\pi$
$461$			554.338i			1.20247i	−0.799073	+	0.601235i	$0.794676\pi$
$462$	674.684	−	491.034i	1.46036	−	1.06285i
$463$			735.278i			1.58807i	0.607870	+	0.794036i	$0.292024\pi$
$463$			735.278i			1.58807i	−0.607870	+	0.794036i	$0.707976\pi$
$464$		−	295.968i		−	0.637863i
$465$	505.169			1.08639
$466$		−	634.285i		−	1.36113i
$467$		−	387.715i		−	0.830225i	−0.909770	−	0.415113i	$-0.863742\pi$
$467$		−	387.715i		−	0.830225i	0.909770	−	0.415113i	$-0.136258\pi$
$468$	−14.8939			−0.0318246
$469$	20.1260	−	14.6477i	0.0429126	−	0.0312318i
$470$			8.88914i			0.0189131i
$471$	444.139			0.942971
$472$			56.0615i			0.118774i
$473$			1106.43i			2.33917i
$474$			851.024i			1.79541i
$475$	11.4151			0.0240317
$476$	110.162	+	151.363i	0.231432	+	0.317989i
$477$		−	6.53351i		−	0.0136971i
$478$		−	930.668i		−	1.94700i
$479$	−930.051			−1.94165			−0.970826	−	0.239785i	$-0.922923\pi$
$479$	−930.051			−1.94165			−0.970826	+	0.239785i	$0.922923\pi$
$480$		−	395.931i		−	0.824857i
$481$	−310.011			−0.644514
$482$		−	130.746i		−	0.271258i
$483$	32.7814	+	45.0418i	0.0678703	+	0.0932542i
$484$	−364.655			−0.753419
$485$			138.698i			0.285975i
$486$	87.2728			0.179574
$487$	290.975			0.597485			0.298743	−	0.954334i	$-0.403433\pi$
$487$	290.975			0.597485			0.298743	+	0.954334i	$0.403433\pi$
$488$			134.616i			0.275853i
$489$	−515.338			−1.05386
$490$	416.972	+	134.725i	0.850964	+	0.274949i
$491$	−410.398			−0.835840			−0.417920	−	0.908484i	$-0.637241\pi$
$491$	−410.398			−0.835840			−0.417920	+	0.908484i	$0.637241\pi$
$492$	−348.084	−	137.949i	−0.707487	−	0.280385i
$493$			134.486i			0.272790i
$494$	−17.2445			−0.0349080
$495$	−31.1445			−0.0629182
$496$		−	973.621i		−	1.96295i
$497$	277.653	−	202.076i	0.558658	−	0.406591i
$498$		−	912.212i		−	1.83175i
$499$			588.240i			1.17884i	0.807828	+	0.589419i	$0.200643\pi$
$499$			588.240i			1.17884i	−0.807828	+	0.589419i	$0.799357\pi$
$500$			409.139i			0.818279i
$501$	357.802			0.714175
$502$			345.896i			0.689035i
$503$	126.971			0.252428			0.126214	−	0.992003i	$-0.459717\pi$
$503$	126.971			0.252428			0.126214	+	0.992003i	$0.459717\pi$
$504$	−5.65555	−	7.77076i	−0.0112213	−	0.0154182i
$505$		−	135.166i		−	0.267656i
$506$		−	113.012i		−	0.223343i
$507$	313.126			0.617607
$508$	385.827			0.759502
$509$	580.463			1.14040			0.570199	−	0.821506i	$-0.306866\pi$
$509$	580.463			1.14040			0.570199	+	0.821506i	$0.306866\pi$
$510$			219.847i			0.431072i
$511$	−604.923	+	440.262i	−1.18380	+	0.861570i
$512$	−593.684			−1.15954
$513$	22.9907			0.0448161
$514$	−975.356			−1.89758
$515$	353.809			0.687007
$516$	656.763			1.27280
$517$			15.2925i			0.0295793i
$518$	437.516	+	601.150i	0.844625	+	1.16052i
$519$		−	971.707i		−	1.87227i
$520$			59.1976i			0.113841i
$521$	−104.630			−0.200825			−0.100412	−	0.994946i	$-0.532016\pi$
$521$	−104.630			−0.200825			−0.100412	+	0.994946i	$0.532016\pi$
$522$			25.6608i			0.0491586i
$523$		−	822.767i		−	1.57317i	−0.617483	−	0.786584i	$-0.711848\pi$
$523$		−	822.767i		−	1.57317i	0.617483	−	0.786584i	$-0.288152\pi$
$524$			154.409i			0.294674i
$525$	−164.911	−	226.589i	−0.314117	−	0.431598i
$526$		−	130.984i		−	0.249019i
$527$			442.406i			0.839480i
$528$		−	832.353i		−	1.57643i
$529$	−521.455			−0.985738
$530$	96.5144			0.182103
$531$		−	14.9642i		−	0.0281812i
$532$	10.7256	+	14.7370i	0.0201609	+	0.0277012i
$533$	297.515	+	117.908i	0.558189	+	0.221216i
$534$	−1330.81			−2.49216
$535$			177.579i			0.331924i
$536$		−	8.06494i		−	0.0150465i
$537$			760.916i			1.41698i
$538$			311.765i			0.579489i
$539$	717.341	+	231.775i	1.33087	+	0.430010i
$540$			293.329i			0.543201i
$541$	135.498			0.250459			0.125230	−	0.992128i	$-0.460033\pi$
$541$	135.498			0.250459			0.125230	+	0.992128i	$0.460033\pi$
$542$			62.4700i			0.115258i
$543$	−82.4049			−0.151759
$544$	346.740			0.637389
$545$	−378.646			−0.694763
$546$	249.128	+	342.304i	0.456279	+	0.626930i
$547$		−	73.5580i		−	0.134475i	−0.997737	−	0.0672376i	$-0.978581\pi$
$547$		−	73.5580i		−	0.134475i	0.997737	−	0.0672376i	$-0.0214186\pi$
$548$			161.994i			0.295609i
$549$		−	35.9324i		−	0.0654507i
$550$			568.521i			1.03367i
$551$			13.0938i			0.0237638i
$552$	18.0492			0.0326979
$553$	−621.621	+	452.415i	−1.12409	+	0.818111i
$554$	−533.139			−0.962346
$555$			384.801i			0.693336i
$556$			383.681i			0.690074i
$557$		−	806.927i		−	1.44870i	−0.689431	−	0.724351i	$-0.742139\pi$
$557$		−	806.927i		−	1.44870i	0.689431	−	0.724351i	$-0.257861\pi$
$558$			84.4141i			0.151280i
$559$	−561.349			−1.00420
$560$	353.405	−	257.208i	0.631080	−	0.459300i
$561$			378.215i			0.674180i
$562$			514.854i			0.916110i
$563$	−310.513			−0.551532			−0.275766	−	0.961225i	$-0.588932\pi$
$563$	−310.513			−0.551532			−0.275766	+	0.961225i	$0.588932\pi$
$564$	9.07746			0.0160948
$565$			86.8618i			0.153738i
$566$			690.981i			1.22082i
$567$	−309.699	−	425.528i	−0.546206	−	0.750490i
$568$		−	111.262i		−	0.195883i
$569$	−1064.91			−1.87155			−0.935777	−	0.352594i	$-0.885300\pi$
$569$	−1064.91			−1.87155			−0.935777	+	0.352594i	$0.885300\pi$
$570$			21.4048i			0.0375522i
$571$		−	571.145i		−	1.00025i	−0.865952	−	0.500127i	$-0.833287\pi$
$571$		−	571.145i		−	1.00025i	0.865952	−	0.500127i	$-0.166713\pi$
$572$		−	378.506i		−	0.661724i
$573$			638.633i			1.11454i
$574$	−191.241	−	743.320i	−0.333173	−	1.29498i
$575$	−37.9543			−0.0660075
$576$	20.9432			0.0363597
$577$	937.964			1.62559			0.812793	−	0.582552i	$-0.197946\pi$
$577$	937.964			1.62559			0.812793	+	0.582552i	$0.197946\pi$
$578$	580.344			1.00405
$579$		−	57.3572i		−	0.0990625i
$580$	−167.059			−0.288032
$581$	666.315	−	484.943i	1.14684	−	0.834670i
$582$	321.382			0.552203
$583$	166.039			0.284801
$584$			242.406i			0.415079i
$585$		−	15.8013i		−	0.0270108i
$586$	−544.977			−0.929996
$587$	186.707			0.318070			0.159035	−	0.987273i	$-0.449162\pi$
$587$	186.707			0.318070			0.159035	+	0.987273i	$0.449162\pi$
$588$	137.579	−	425.806i	0.233979	−	0.724160i
$589$			43.0736i			0.0731301i
$590$	221.054			0.374668
$591$	−723.276			−1.22382
$592$	741.634			1.25276
$593$	−363.034			−0.612199			−0.306099	−	0.952000i	$-0.599024\pi$
$593$	−363.034			−0.612199			−0.306099	+	0.952000i	$0.599024\pi$
$594$			1145.04i			1.92767i
$595$	−160.584	+	116.873i	−0.269890	+	0.196426i
$596$			466.188i			0.782194i
$597$	−600.068			−1.00514
$598$	57.3369			0.0958811
$599$	−720.720			−1.20321			−0.601603	−	0.798795i	$-0.705471\pi$
$599$	−720.720			−1.20321			−0.601603	+	0.798795i	$0.705471\pi$
$600$	−90.7992			−0.151332
$601$	769.330			1.28008			0.640042	−	0.768340i	$-0.278917\pi$
$601$	769.330			1.28008			0.640042	+	0.768340i	$0.278917\pi$
$602$	792.227	+	1088.52i	1.31599	+	1.80818i
$603$			2.15273i			0.00357004i
$604$			626.927i			1.03796i
$605$		−	386.871i		−	0.639456i
$606$	−313.198			−0.516829
$607$			89.4029i			0.147286i	0.997285	+	0.0736432i	$0.0234626\pi$
$607$			89.4029i			0.147286i	−0.997285	+	0.0736432i	$0.976537\pi$
$608$	33.7594			0.0555253
$609$	259.912	−	189.164i	0.426785	−	0.310614i
$610$	530.801			0.870166
$611$	−7.75871			−0.0126984
$612$	−16.1902			−0.0264545
$613$	909.661			1.48395			0.741974	−	0.670428i	$-0.233890\pi$
$613$	909.661			1.48395			0.741974	+	0.670428i	$0.233890\pi$
$614$			1057.75i			1.72271i
$615$	146.354	−	369.290i	0.237973	−	0.600472i
$616$	197.482	−	143.727i	0.320588	−	0.233323i
$617$	164.383			0.266422			0.133211	−	0.991088i	$-0.457471\pi$
$617$	164.383			0.266422			0.133211	+	0.991088i	$0.457471\pi$
$618$		−	819.821i		−	1.32657i
$619$			511.799i			0.826816i	0.910546	+	0.413408i	$0.135662\pi$
$619$			511.799i			0.826816i	−0.910546	+	0.413408i	$0.864338\pi$
$620$	−549.559			−0.886385
$621$	−76.4424			−0.123096
$622$	635.874			1.02230
$623$	−707.477	−	972.078i	−1.13560	−	1.56032i
$624$	422.298			0.676759
$625$	−88.6178			−0.141788
$626$	−1164.75			−1.86062
$627$			36.8238i			0.0587302i
$628$	−483.166			−0.769373
$629$	−336.993			−0.535759
$630$	−30.6406	+	22.3002i	−0.0486359	+	0.0353972i
$631$	738.033			1.16962			0.584812	−	0.811169i	$-0.301168\pi$
$631$	738.033			1.16962			0.584812	+	0.811169i	$0.301168\pi$
$632$			249.097i			0.394141i
$633$			992.219i			1.56749i
$634$			452.574i			0.713839i
$635$			409.333i			0.644619i
$636$		−	98.5591i		−	0.154967i
$637$	−117.592	+	363.946i	−0.184603	+	0.571344i
$638$	−652.130			−1.02215
$639$			29.6985i			0.0464765i
$640$		−	237.235i		−	0.370680i
$641$			255.387i			0.398419i	0.979957	+	0.199209i	$0.0638374\pi$
$641$			255.387i			0.398419i	−0.979957	+	0.199209i	$0.936163\pi$
$642$	411.475			0.640927
$643$	−44.4007			−0.0690524			−0.0345262	−	0.999404i	$-0.510992\pi$
$643$	−44.4007			−0.0690524			−0.0345262	+	0.999404i	$0.510992\pi$
$644$	−35.6619	−	48.9996i	−0.0553756	−	0.0760864i
$645$			696.775i			1.08027i
$646$	−18.7454			−0.0290176
$647$			121.051i			0.187097i	0.995615	+	0.0935483i	$0.0298209\pi$
$647$			121.051i			0.187097i	−0.995615	+	0.0935483i	$0.970179\pi$
$648$	−170.518			−0.263146
$649$	380.292			0.585966
$650$	−288.441			−0.443756
$651$	855.011	−	622.276i	1.31338	−	0.955877i
$652$	560.621			0.859848
$653$		−	815.923i		−	1.24950i	−0.780825	−	0.624749i	$-0.785201\pi$
$653$		−	815.923i		−	1.24950i	0.780825	−	0.624749i	$-0.214799\pi$
$654$			877.373i			1.34155i
$655$	−163.816			−0.250101
$656$	−711.738	−	282.070i	−1.08497	−	0.429984i
$657$		−	64.7042i		−	0.0984843i
$658$	10.9498	+	15.0451i	0.0166410	+	0.0228649i
$659$		−	23.2550i		−	0.0352883i	−0.999844	−	0.0176442i	$-0.994383\pi$
$659$		−	23.2550i		−	0.0352883i	0.999844	−	0.0176442i	$-0.00561661\pi$
$660$	−469.820			−0.711849
$661$		−	600.186i		−	0.907996i	−0.891003	−	0.453998i	$-0.849997\pi$
$661$		−	600.186i		−	0.907996i	0.891003	−	0.453998i	$-0.150003\pi$
$662$			231.353i			0.349476i
$663$	−191.889			−0.289425
$664$		−	267.007i		−	0.402119i
$665$	−15.6349	+	11.3790i	−0.0235111	+	0.0171113i
$666$	−64.3005			−0.0965473
$667$		−	43.5361i		−	0.0652715i
$668$	−389.242			−0.582698
$669$		−	260.053i		−	0.388719i
$670$	−31.8006			−0.0474636
$671$	913.168			1.36091
$672$	−487.715	−	670.123i	−0.725766	−	0.997207i
$673$			125.725i			0.186813i	0.995628	+	0.0934066i	$0.0297757\pi$
$673$			125.725i			0.186813i	−0.995628	+	0.0934066i	$0.970224\pi$
$674$	1017.09			1.50904
$675$	384.554			0.569710
$676$	−340.641			−0.503907
$677$			218.443i			0.322663i	0.986900	+	0.161331i	$0.0515788\pi$
$677$			218.443i			0.322663i	−0.986900	+	0.161331i	$0.948421\pi$
$678$	201.270			0.296859
$679$	170.851	+	234.750i	0.251621	+	0.345729i
$680$			64.3497i			0.0946320i
$681$	158.280			0.232422
$682$	−2145.25			−3.14553
$683$		−	1038.31i		−	1.52022i	−0.649797	−	0.760108i	$-0.725146\pi$
$683$		−	1038.31i		−	1.52022i	0.649797	−	0.760108i	$-0.274854\pi$
$684$	−1.57631			−0.00230455
$685$	−171.863			−0.250894
$686$	871.692	−	285.608i	1.27069	−	0.416338i
$687$	−710.917			−1.03481
$688$	1342.90			1.95190
$689$			84.2406i			0.122265i
$690$		−	71.1694i		−	0.103144i
$691$	752.770			1.08939			0.544696	−	0.838634i	$-0.316645\pi$
$691$	752.770			1.08939			0.544696	+	0.838634i	$0.316645\pi$
$692$			1057.09i			1.52759i
$693$	−52.7128	+	38.3643i	−0.0760647	+	0.0553598i
$694$			221.092i			0.318577i
$695$	−407.056			−0.585692
$696$		−	104.153i		−	0.149645i
$697$	323.408	+	128.170i	0.464001	+	0.183889i
$698$		−	843.409i		−	1.20832i
$699$		−	687.184i		−	0.983096i
$700$	179.402	+	246.500i	0.256289	+	0.352142i
$701$	631.386			0.900693			0.450347	−	0.892854i	$-0.351300\pi$
$701$	631.386			0.900693			0.450347	+	0.892854i	$0.351300\pi$
$702$	−580.938			−0.827547
$703$	−32.8104			−0.0466719
$704$			532.239i			0.756022i
$705$			9.63049i			0.0136603i
$706$		−	1563.43i		−	2.21449i
$707$	−166.500	−	228.772i	−0.235502	−	0.323582i
$708$		−	225.737i		−	0.318838i
$709$			270.461i			0.381468i	0.981642	+	0.190734i	$0.0610868\pi$
$709$			270.461i			0.381468i	−0.981642	+	0.190734i	$0.938913\pi$
$710$	−438.712			−0.617905
$711$		−	66.4902i		−	0.0935165i
$712$	−389.533			−0.547097
$713$		−	143.217i		−	0.200865i
$714$	270.811	+	372.096i	0.379287	+	0.521142i
$715$	401.566			0.561630
$716$		−	827.778i		−	1.15611i
$717$		−	1008.29i		−	1.40626i
$718$	−1282.32			−1.78596
$719$	−1057.01			−1.47011			−0.735055	−	0.678007i	$-0.762844\pi$
$719$	−1057.01			−1.47011			−0.735055	+	0.678007i	$0.762844\pi$
$720$			37.8011i			0.0525016i
$721$	598.829	−	435.827i	0.830554	−	0.604476i
$722$	963.601			1.33463
$723$		−	141.650i		−	0.195920i
$724$	89.6458			0.123820
$725$			219.014i			0.302089i
$726$	−896.431			−1.23475
$727$	−504.265			−0.693624			−0.346812	−	0.937935i	$-0.612736\pi$
$727$	−504.265			−0.693624			−0.346812	+	0.937935i	$0.612736\pi$
$728$	72.9206	+	100.193i	0.100166	+	0.137628i
$729$	771.217			1.05791
$730$	955.823			1.30935
$731$	−610.205			−0.834754
$732$		−	542.047i		−	0.740501i
$733$		−	10.4157i		−	0.0142097i	−0.999975	−	0.00710485i	$-0.997738\pi$
$733$		−	10.4157i		−	0.0142097i	0.999975	−	0.00710485i	$-0.00226156\pi$
$734$		−	730.197i		−	0.994819i
$735$	451.747	+	145.961i	0.614622	+	0.198587i
$736$	−112.248			−0.152510
$737$	−54.7084			−0.0742312
$738$	61.7086	+	24.4558i	0.0836159	+	0.0331379i
$739$	855.658			1.15786			0.578929	−	0.815378i	$-0.303471\pi$
$739$	855.658			1.15786			0.578929	+	0.815378i	$0.303471\pi$
$740$		−	418.614i		−	0.565695i
$741$	−18.6827			−0.0252128
$742$	163.353	−	118.888i	0.220152	−	0.160226i
$743$	−32.4259			−0.0436419			−0.0218209	−	0.999762i	$-0.506946\pi$
$743$	−32.4259			−0.0436419			−0.0218209	+	0.999762i	$0.506946\pi$
$744$		−	342.622i		−	0.460513i
$745$	−494.589			−0.663878
$746$	−5.08000			−0.00680966
$747$			71.2708i			0.0954094i
$748$		−	411.449i		−	0.550065i
$749$	218.745	+	300.557i	0.292050	+	0.401278i
$750$			1005.79i			1.34105i
$751$		−	1167.73i		−	1.55490i	−0.628947	−	0.777448i	$-0.716514\pi$
$751$		−	1167.73i		−	1.55490i	0.628947	−	0.777448i	$-0.283486\pi$
$752$	18.5610			0.0246822
$753$			374.743i			0.497667i
$754$		−	330.861i		−	0.438807i
$755$	−665.121			−0.880955
$756$	361.327	+	496.465i	0.477946	+	0.656700i
$757$		−	757.594i		−	1.00078i	−0.865799	−	0.500392i	$-0.833189\pi$
$757$		−	757.594i		−	1.00078i	0.865799	−	0.500392i	$-0.166811\pi$
$758$	1120.21			1.47785
$759$		−	122.437i		−	0.161313i
$760$			6.26524i			0.00824373i
$761$		−	1155.38i		−	1.51823i	−0.650955	−	0.759117i	$-0.725631\pi$
$761$		−	1155.38i		−	1.51823i	0.650955	−	0.759117i	$-0.274369\pi$
$762$	948.479			1.24472
$763$	−640.867	+	466.422i	−0.839930	+	0.611300i
$764$		−	694.750i		−	0.909359i
$765$		−	17.1765i		−	0.0224530i
$766$	−492.604			−0.643086
$767$			192.943i			0.251555i
$768$	−950.641			−1.23781
$769$		−	425.981i		−	0.553942i	−0.960878	−	0.276971i	$-0.910669\pi$
$769$		−	425.981i		−	0.553942i	0.960878	−	0.276971i	$-0.0893306\pi$
$770$	−566.726	−	778.685i	−0.736008	−	1.01128i
$771$	−1056.70			−1.37056
$772$			62.3972i			0.0808254i
$773$	−170.364			−0.220393			−0.110197	−	0.993910i	$-0.535148\pi$
$773$	−170.364			−0.220393			−0.110197	+	0.993910i	$0.535148\pi$
$774$	−116.431			−0.150428
$775$			720.472i			0.929642i
$776$	94.0694			0.121223
$777$	474.005	+	651.285i	0.610045	+	0.838205i
$778$	388.387			0.499212
$779$	31.4878	+	12.4790i	0.0404208	+	0.0160192i
$780$		−	238.365i		−	0.305596i
$781$	−754.742			−0.966379
$782$	62.3271			0.0797022
$783$			441.108i			0.563357i
$784$	281.313	−	870.660i	0.358818	−	1.11054i
$785$		−	512.602i		−	0.652996i
$786$			379.584i			0.482932i
$787$		−	644.912i		−	0.819456i	−0.912208	−	0.409728i	$-0.865624\pi$
$787$		−	644.912i		−	0.819456i	0.912208	−	0.409728i	$-0.134376\pi$
$788$	786.831			0.998516
$789$		−	141.908i		−	0.179858i
$790$	982.207			1.24330
$791$	106.998	+	147.016i	0.135269	+	0.185860i
$792$			21.1232i			0.0266707i
$793$			463.299i			0.584236i
$794$	1332.01			1.67759
$795$	104.564			0.131527
$796$	652.796			0.820096
$797$		−	22.0824i		−	0.0277069i	−0.999904	−	0.0138535i	$-0.995590\pi$
$797$		−	22.0824i		−	0.0277069i	0.999904	−	0.0138535i	$-0.00440984\pi$
$798$	26.3667	+	36.2281i	0.0330410	+	0.0453986i
$799$	−8.43397			−0.0105557
$800$	564.677			0.705846
$801$	103.976			0.129808
$802$	−441.626			−0.550656
$803$	1644.36			2.04777
$804$			32.4743i			0.0403910i
$805$	51.9848	−	37.8345i	0.0645775	−	0.0469994i
$806$		−	1088.40i		−	1.35038i
$807$			337.766i			0.418545i
$808$	−91.6740			−0.113458
$809$		−	164.851i		−	0.203772i	−0.994796	−	0.101886i	$-0.967512\pi$
$809$		−	164.851i		−	0.203772i	0.994796	−	0.101886i	$-0.0324876\pi$
$810$			672.365i			0.830080i
$811$		−	851.489i		−	1.04992i	−0.851125	−	0.524962i	$-0.824079\pi$
$811$		−	851.489i		−	1.04992i	0.851125	−	0.524962i	$-0.175921\pi$
$812$	−282.751	+	205.786i	−0.348215	+	0.253431i
$813$			67.6800i			0.0832472i
$814$		−	1634.10i		−	2.00749i
$815$			594.776i			0.729786i
$816$	459.051			0.562563
$817$	−59.4110			−0.0727185
$818$		−	1721.62i		−	2.10467i
$819$	−19.4643	−	26.7441i	−0.0237659	−	0.0326545i
$820$	−159.214	+	401.740i	−0.194163	+	0.489926i
$821$	−439.368			−0.535162			−0.267581	−	0.963535i	$-0.586224\pi$
$821$	−439.368			−0.535162			−0.267581	+	0.963535i	$0.586224\pi$
$822$			398.228i			0.484463i
$823$		−	502.881i		−	0.611034i	−0.952187	−	0.305517i	$-0.901171\pi$
$823$		−	502.881i		−	0.611034i	0.952187	−	0.305517i	$-0.0988292\pi$
$824$		−	239.964i		−	0.291218i
$825$			615.935i			0.746588i
$826$	374.139	−	272.298i	0.452953	−	0.329659i
$827$		−	920.174i		−	1.11267i	−0.830960	−	0.556333i	$-0.812208\pi$
$827$		−	920.174i		−	1.11267i	0.830960	−	0.556333i	$-0.187792\pi$
$828$	5.24113			0.00632987
$829$		−	331.557i		−	0.399948i	−0.979801	−	0.199974i	$-0.935914\pi$
$829$		−	331.557i		−	0.399948i	0.979801	−	0.199974i	$-0.0640858\pi$
$830$	−1052.83			−1.26847
$831$	−577.603			−0.695070
$832$	−270.034			−0.324560
$833$	−127.827	+	395.621i	−0.153453	+	0.474935i
$834$			943.203i			1.13094i
$835$		−	412.956i		−	0.494558i
$836$		−	40.0596i		−	0.0479181i
$837$			1451.08i			1.73366i
$838$		−	2021.62i		−	2.41243i
$839$	−1249.10			−1.48879			−0.744397	−	0.667738i	$-0.767263\pi$
$839$	−1249.10			−1.48879			−0.744397	+	0.667738i	$0.767263\pi$
$840$	124.365	−	90.5126i	0.148053	−	0.107753i
$841$	589.776			0.701280
$842$			618.457i			0.734510i
$843$			557.793i			0.661676i
$844$		−	1079.41i		−	1.27892i
$845$		−	361.394i		−	0.427685i
$846$	−1.60926			−0.00190220
$847$	−476.554	−	654.788i	−0.562637	−	0.773067i
$848$		−	201.527i		−	0.237650i
$849$			748.609i			0.881754i
$850$	−313.545			−0.368877
$851$	109.092			0.128193
$852$			448.007i			0.525830i
$853$			318.424i			0.373299i	0.982427	+	0.186650i	$0.0597629\pi$
$853$			318.424i			0.373299i	−0.982427	+	0.186650i	$0.940237\pi$
$854$	898.393	−	653.850i	1.05198	−	0.765632i
$855$		−	1.67235i		−	0.00195596i
$856$	120.440			0.140701
$857$			1484.46i			1.73216i	0.499902	+	0.866082i	$0.333369\pi$
$857$			1484.46i			1.73216i	−0.499902	+	0.866082i	$0.666631\pi$
$858$		−	930.481i		−	1.08448i
$859$			644.561i			0.750362i	0.926952	+	0.375181i	$0.122419\pi$
$859$			644.561i			0.750362i	−0.926952	+	0.375181i	$0.877581\pi$
$860$		−	758.000i		−	0.881396i
$861$	−207.190	−	805.313i	−0.240639	−	0.935323i
$862$	241.089			0.279686
$863$	421.677			0.488618			0.244309	−	0.969697i	$-0.421439\pi$
$863$	421.677			0.488618			0.244309	+	0.969697i	$0.421439\pi$
$864$	1137.29			1.31631
$865$	−1121.49			−1.29652
$866$			1047.24i			1.20929i
$867$	628.744			0.725195
$868$	−930.141	+	676.956i	−1.07159	+	0.779903i
$869$	1689.75			1.94447
$870$	−410.681			−0.472047
$871$		−	27.7565i		−	0.0318674i
$872$			256.809i			0.294506i
$873$	−25.1094			−0.0287623
$874$	6.06831			0.00694314
$875$	−734.666	+	534.689i	−0.839618	+	0.611073i
$876$		−	976.073i		−	1.11424i
$877$	−1393.92			−1.58942			−0.794711	−	0.606988i	$-0.792378\pi$
$877$	−1393.92			−1.58942			−0.794711	+	0.606988i	$0.792378\pi$
$878$	−1633.67			−1.86067
$879$	−590.428			−0.671704
$880$	−960.657			−1.09166
$881$			1208.12i			1.37131i	0.727928	+	0.685654i	$0.240484\pi$
$881$			1208.12i			1.37131i	−0.727928	+	0.685654i	$0.759516\pi$
$882$	−24.3902	+	75.4873i	−0.0276533	+	0.0855865i
$883$			474.857i			0.537777i	0.963171	+	0.268889i	$0.0866563\pi$
$883$			474.857i			0.537777i	−0.963171	+	0.268889i	$0.913344\pi$
$884$	208.750			0.236143
$885$	239.490			0.270610
$886$	−783.858			−0.884716
$887$	1313.75			1.48111			0.740556	−	0.671995i	$-0.234562\pi$
$887$	1313.75			1.48111			0.740556	+	0.671995i	$0.234562\pi$
$888$	260.984			0.293901
$889$	504.223	+	692.806i	0.567180	+	0.779309i
$890$			1535.95i			1.72579i
$891$			1156.71i			1.29821i
$892$			282.904i			0.317157i
$893$	−0.821151			−0.000919542
$894$			1146.03i			1.28191i
$895$	878.209			0.981239
$896$	−292.230	−	401.526i	−0.326149	−	0.448131i
$897$	62.1187			0.0692517
$898$	849.063			0.945504
$899$	−826.428			−0.919275
$900$	−26.3662			−0.0292958
$901$			91.5724i			0.101634i
$902$	−621.506	+	1568.23i	−0.689031	+	1.73861i
$903$	858.298	+	1179.31i	0.950496	+	1.30599i
$904$	58.9124			0.0651685
$905$			95.1073i			0.105091i
$906$			1541.17i			1.70107i
$907$	902.223			0.994733			0.497366	−	0.867541i	$-0.334300\pi$
$907$	902.223			0.994733			0.497366	+	0.867541i	$0.334300\pi$
$908$	−172.188			−0.189634
$909$	24.4701			0.0269198
$910$	395.069	−	287.531i	0.434141	−	0.315968i
$911$	188.927			0.207385			0.103692	−	0.994609i	$-0.466934\pi$
$911$	188.927			0.207385			0.103692	+	0.994609i	$0.466934\pi$
$912$	44.6943			0.0490069
$913$	−1811.24			−1.98383
$914$			2184.31i			2.38983i
$915$	575.070			0.628492
$916$	773.386			0.844308
$917$	−277.263	+	201.792i	−0.302359	+	0.220056i
$918$	−631.499			−0.687908
$919$			936.432i			1.01897i	0.860480	+	0.509484i	$0.170164\pi$
$919$			936.432i			1.01897i	−0.860480	+	0.509484i	$0.829836\pi$
$920$		−	20.8315i		−	0.0226429i
$921$			1145.96i			1.24426i
$922$		−	1482.47i		−	1.60789i
$923$		−	382.921i		−	0.414866i
$924$	−795.182	+	578.732i	−0.860586	+	0.626334i
$925$	−548.803			−0.593301
$926$		−	1966.36i		−	2.12350i
$927$			64.0523i			0.0690964i
$928$			647.721i			0.697975i
$929$	1398.53			1.50541			0.752705	−	0.658357i	$-0.228748\pi$
$929$	1398.53			1.50541			0.752705	+	0.658357i	$0.228748\pi$
$930$	−1350.98			−1.45267
$931$	−12.4455	+	38.5186i	−0.0133679	+	0.0413733i
$932$			747.567i			0.802111i
$933$	688.905			0.738376
$934$			1036.87i			1.11014i
$935$	436.515			0.466861
$936$	−10.7169			−0.0114497
$937$	609.901			0.650908			0.325454	−	0.945558i	$-0.394483\pi$
$937$	609.901			0.650908			0.325454	+	0.945558i	$0.394483\pi$
$938$	−53.8233	+	39.1725i	−0.0573809	+	0.0417617i
$939$	−1261.89			−1.34386
$940$		−	10.4767i		−	0.0111455i
$941$		−	475.722i		−	0.505549i	−0.967525	−	0.252775i	$-0.918657\pi$
$941$		−	475.722i		−	0.505549i	0.967525	−	0.252775i	$-0.0813432\pi$
$942$	−1187.77			−1.26090
$943$	−104.695	−	41.4916i	−0.111023	−	0.0439996i
$944$		−	461.573i		−	0.488954i
$945$	−526.711	+	383.340i	−0.557367	+	0.405651i
$946$		−	2958.93i		−	3.12783i
$947$	−1018.93			−1.07596			−0.537978	−	0.842959i	$-0.680812\pi$
$947$	−1018.93			−1.07596			−0.537978	+	0.842959i	$0.680812\pi$
$948$		−	1003.02i		−	1.05803i
$949$			834.271i			0.879105i
$950$	−30.5275			−0.0321342
$951$			490.319i			0.515582i
$952$	79.2671	+	108.913i	0.0832637	+	0.114405i
$953$	−141.741			−0.148732			−0.0743658	−	0.997231i	$-0.523693\pi$
$953$	−141.741			−0.148732			−0.0743658	+	0.997231i	$0.523693\pi$
$954$			17.4726i			0.0183151i
$955$	737.076			0.771808
$956$			1096.88i			1.14737i
$957$	−706.517			−0.738263
$958$	2487.25			2.59629
$959$	−290.881	+	211.703i	−0.303318	+	0.220754i
$960$			335.179i			0.349145i
$961$	−1757.63			−1.82896
$962$	829.067			0.861816
$963$	−32.1484			−0.0333836
$964$			154.097i			0.159852i
$965$	−66.1986			−0.0685996
$966$	−87.6676	−	120.456i	−0.0907532	−	0.124695i
$967$		−	210.263i		−	0.217439i	−0.994072	−	0.108719i	$-0.965325\pi$
$967$		−	210.263i		−	0.217439i	0.994072	−	0.108719i	$-0.0346750\pi$
$968$	−262.388			−0.271062
$969$	−20.3087			−0.0209585
$970$		−	370.922i		−	0.382394i
$971$	386.037			0.397566			0.198783	−	0.980043i	$-0.436301\pi$
$971$	386.037			0.397566			0.198783	+	0.980043i	$0.436301\pi$
$972$	−102.860			−0.105823
$973$	−688.952	+	501.419i	−0.708070	+	0.515333i
$974$	−778.159			−0.798931
$975$	−312.497			−0.320510
$976$		−	1108.34i		−	1.13560i
$977$		−	991.983i		−	1.01534i	−0.861553	−	0.507668i	$-0.830508\pi$
$977$		−	991.983i		−	1.01534i	0.861553	−	0.507668i	$-0.169492\pi$
$978$	1378.17			1.40918
$979$			2642.39i			2.69907i
$980$	−491.443	−	158.787i	−0.501472	−	0.162027i
$981$		−	68.5488i		−	0.0698764i
$982$	1097.53			1.11765
$983$		−	1043.79i		−	1.06185i	−0.847420	−	0.530923i	$-0.821845\pi$
$983$		−	1043.79i		−	1.06185i	0.847420	−	0.530923i	$-0.178155\pi$
$984$	−250.464	−	99.2616i	−0.254537	−	0.100876i
$985$			834.767i			0.847479i
$986$		−	359.657i		−	0.364763i
$987$	11.8630	+	16.2998i	0.0120192	+	0.0165145i
$988$	20.3244			0.0205712
$989$	197.537			0.199734
$990$	83.2901			0.0841315
$991$			1131.06i			1.14134i	0.821181	+	0.570668i	$0.193316\pi$
$991$			1131.06i			1.14134i	−0.821181	+	0.570668i	$0.806684\pi$
$992$			2130.75i			2.14793i
$993$			250.648i			0.252415i
$994$	−742.531	+	540.413i	−0.747013	+	0.543675i
$995$			692.567i			0.696047i
$996$			1075.13i			1.07945i
$997$	1647.10			1.65205			0.826026	−	0.563632i	$-0.190596\pi$
$997$	1647.10			1.65205			0.826026	+	0.563632i	$0.190596\pi$
$998$		−	1573.14i		−	1.57629i
$999$	−1105.32			−1.10643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.d.286.6	yes	32
7.6	odd	2	inner	287.3.d.d.286.7	yes	32
41.40	even	2	inner	287.3.d.d.286.8	yes	32
287.286	odd	2	inner	287.3.d.d.286.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.d.286.5	✓	32	287.286	odd	2	inner
287.3.d.d.286.6	yes	32	1.1	even	1	trivial
287.3.d.d.286.7	yes	32	7.6	odd	2	inner
287.3.d.d.286.8	yes	32	41.40	even	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)

\(f(q)\)	\(=\)	\(q-2.67431 q^{2} -2.89735 q^{3} +3.15194 q^{4} +3.34396i q^{5} +7.74841 q^{6} +(4.11915 + 5.65974i) q^{7} +2.26798 q^{8} -0.605380 q^{9} +O(q^{10})\)	\(q-2.67431 q^{2} -2.89735 q^{3} +3.15194 q^{4} +3.34396i q^{5} +7.74841 q^{6} +(4.11915 + 5.65974i) q^{7} +2.26798 q^{8} -0.605380 q^{9} -8.94280i q^{10} -15.3848i q^{11} -9.13226 q^{12} +7.80554 q^{13} +(-11.0159 - 15.1359i) q^{14} -9.68862i q^{15} -18.6730 q^{16} +8.48488 q^{17} +1.61897 q^{18} +0.826108 q^{19} +10.5400i q^{20} +(-11.9346 - 16.3982i) q^{21} +41.1438i q^{22} -2.74675 q^{23} -6.57113 q^{24} +13.8179 q^{25} -20.8744 q^{26} +27.8301 q^{27} +(12.9833 + 17.8391i) q^{28} +15.8500i q^{29} +25.9104i q^{30} +52.1405i q^{31} +40.8656 q^{32} +44.5751i q^{33} -22.6912 q^{34} +(-18.9260 + 13.7743i) q^{35} -1.90812 q^{36} -39.7168 q^{37} -2.20927 q^{38} -22.6154 q^{39} +7.58404i q^{40} +(38.1158 + 15.1057i) q^{41} +(31.9168 + 43.8539i) q^{42} -71.9168 q^{43} -48.4920i q^{44} -2.02437i q^{45} +7.34566 q^{46} -0.994000 q^{47} +54.1023 q^{48} +(-15.0652 + 46.6266i) q^{49} -36.9534 q^{50} -24.5837 q^{51} +24.6026 q^{52} +10.7924i q^{53} -74.4264 q^{54} +51.4462 q^{55} +(9.34215 + 12.8362i) q^{56} -2.39352 q^{57} -42.3879i q^{58} +24.7187i q^{59} -30.5379i q^{60} +59.3552i q^{61} -139.440i q^{62} +(-2.49365 - 3.42629i) q^{63} -34.5951 q^{64} +26.1014i q^{65} -119.208i q^{66} -3.55600i q^{67} +26.7438 q^{68} +7.95829 q^{69} +(50.6139 - 36.8367i) q^{70} -49.0576i q^{71} -1.37299 q^{72} +106.882i q^{73} +106.215 q^{74} -40.0353 q^{75} +2.60384 q^{76} +(87.0739 - 63.3723i) q^{77} +60.4805 q^{78} +109.832i q^{79} -62.4420i q^{80} -75.1851 q^{81} +(-101.934 - 40.3974i) q^{82} -117.729i q^{83} +(-37.6171 - 51.6862i) q^{84} +28.3731i q^{85} +192.328 q^{86} -45.9231i q^{87} -34.8924i q^{88} -171.753 q^{89} +5.41379i q^{90} +(32.1522 + 44.1773i) q^{91} -8.65759 q^{92} -151.069i q^{93} +2.65826 q^{94} +2.76247i q^{95} -118.402 q^{96} +41.4772 q^{97} +(40.2891 - 124.694i) q^{98} +9.31366i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9}+O(q^{10}) \) 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

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