LMFDB - Embedded newform 287.3.b.a.83.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(83,287)]

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, 0]))

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

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

chi := DirichletCharacter("287.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.b (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:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			83.12
Character	$\chi$	$=$	287.83
Dual form			287.3.b.a.83.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44013 q^{2} +4.97182i q^{3} +1.95424 q^{4} +3.83331i q^{5} -12.1319i q^{6} +(-6.90407 + 1.15493i) q^{7} +4.99192 q^{8} -15.7190 q^{9} +O(q^{10})$	\(q-2.44013 q^{2} +4.97182i q^{3} +1.95424 q^{4} +3.83331i q^{5} -12.1319i q^{6} +(-6.90407 + 1.15493i) q^{7} +4.99192 q^{8} -15.7190 q^{9} -9.35378i q^{10} -8.46862 q^{11} +9.71615i q^{12} -9.27142i q^{13} +(16.8468 - 2.81818i) q^{14} -19.0585 q^{15} -19.9979 q^{16} +1.99229i q^{17} +38.3565 q^{18} +24.3633i q^{19} +7.49122i q^{20} +(-5.74211 - 34.3258i) q^{21} +20.6645 q^{22} -22.4925 q^{23} +24.8189i q^{24} +10.3057 q^{25} +22.6235i q^{26} -33.4059i q^{27} +(-13.4922 + 2.25701i) q^{28} +56.5997 q^{29} +46.5054 q^{30} -20.4692i q^{31} +28.8298 q^{32} -42.1045i q^{33} -4.86145i q^{34} +(-4.42721 - 26.4654i) q^{35} -30.7188 q^{36} -5.78701 q^{37} -59.4498i q^{38} +46.0959 q^{39} +19.1356i q^{40} +6.40312i q^{41} +(14.0115 + 83.7595i) q^{42} -63.2121 q^{43} -16.5497 q^{44} -60.2560i q^{45} +54.8846 q^{46} -62.1216i q^{47} -99.4261i q^{48} +(46.3323 - 15.9474i) q^{49} -25.1473 q^{50} -9.90531 q^{51} -18.1186i q^{52} -4.33948 q^{53} +81.5147i q^{54} -32.4629i q^{55} +(-34.4645 + 5.76532i) q^{56} -121.130 q^{57} -138.111 q^{58} -53.7227i q^{59} -37.2450 q^{60} +74.6441i q^{61} +49.9476i q^{62} +(108.525 - 18.1544i) q^{63} +9.64300 q^{64} +35.5402 q^{65} +102.740i q^{66} +13.6686 q^{67} +3.89341i q^{68} -111.829i q^{69} +(10.8030 + 64.5791i) q^{70} -21.0182 q^{71} -78.4681 q^{72} +82.5094i q^{73} +14.1211 q^{74} +51.2383i q^{75} +47.6119i q^{76} +(58.4679 - 9.78067i) q^{77} -112.480 q^{78} +15.4332 q^{79} -76.6582i q^{80} +24.6168 q^{81} -15.6245i q^{82} -138.469i q^{83} +(-11.2215 - 67.0809i) q^{84} -7.63706 q^{85} +154.246 q^{86} +281.404i q^{87} -42.2747 q^{88} -11.0966i q^{89} +147.032i q^{90} +(10.7078 + 64.0105i) q^{91} -43.9558 q^{92} +101.769 q^{93} +151.585i q^{94} -93.3923 q^{95} +143.337i q^{96} +111.867i q^{97} +(-113.057 + 38.9138i) q^{98} +133.119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) $ 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9	$ 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9} + 24 q^{11} - 14 q^{14} + 44 q^{15} + 194 q^{16} + 70 q^{18} - 16 q^{21} - 48 q^{22} - 80 q^{23} - 304 q^{25} + 64 q^{28} - 12 q^{29} + 64 q^{30} - 166 q^{32} + 30 q^{35} - 70 q^{36} + 36 q^{37} - 68 q^{39} + 164 q^{42} - 172 q^{43} + 72 q^{44} + 68 q^{46} - 172 q^{49} - 234 q^{50} + 156 q^{51} + 64 q^{53} - 234 q^{56} + 140 q^{57} - 556 q^{58} + 152 q^{60} - 130 q^{63} + 334 q^{64} - 76 q^{65} + 160 q^{67} + 202 q^{70} - 408 q^{71} - 40 q^{72} + 398 q^{74} - 248 q^{77} + 390 q^{78} + 264 q^{79} - 116 q^{81} - 418 q^{84} + 232 q^{85} + 368 q^{86} - 220 q^{88} + 32 q^{91} - 74 q^{92} + 240 q^{93} - 44 q^{95} + 838 q^{98} - 24 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9 + 24 * q^11 - 14 * q^14 + 44 * q^15 + 194 * q^16 + 70 * q^18 - 16 * q^21 - 48 * q^22 - 80 * q^23 - 304 * q^25 + 64 * q^28 - 12 * q^29 + 64 * q^30 - 166 * q^32 + 30 * q^35 - 70 * q^36 + 36 * q^37 - 68 * q^39 + 164 * q^42 - 172 * q^43 + 72 * q^44 + 68 * q^46 - 172 * q^49 - 234 * q^50 + 156 * q^51 + 64 * q^53 - 234 * q^56 + 140 * q^57 - 556 * q^58 + 152 * q^60 - 130 * q^63 + 334 * q^64 - 76 * q^65 + 160 * q^67 + 202 * q^70 - 408 * q^71 - 40 * q^72 + 398 * q^74 - 248 * q^77 + 390 * q^78 + 264 * q^79 - 116 * q^81 - 418 * q^84 + 232 * q^85 + 368 * q^86 - 220 * q^88 + 32 * q^91 - 74 * q^92 + 240 * q^93 - 44 * q^95 + 838 * q^98 - 24 * q^99

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 $

$2$	−2.44013			−1.22007			−0.610033	−	0.792376i	$-0.708844\pi$
$2$	−2.44013			−1.22007			−0.610033	+	0.792376i	$0.708844\pi$
$3$			4.97182i			1.65727i	0.559786	+	0.828637i	$0.310883\pi$
$3$			4.97182i			1.65727i	−0.559786	+	0.828637i	$0.689117\pi$
$4$	1.95424			0.488561
$5$			3.83331i			0.766662i	0.923611	+	0.383331i	$0.125223\pi$
$5$			3.83331i			0.766662i	−0.923611	+	0.383331i	$0.874777\pi$
$6$		−	12.1319i		−	2.02198i
$7$	−6.90407	+	1.15493i	−0.986295	+	0.164990i
$7$	−6.90407	+	1.15493i	−0.986295	+	0.164990i
$8$	4.99192			0.623990
$9$	−15.7190			−1.74656
$10$		−	9.35378i		−	0.935378i
$11$	−8.46862			−0.769874			−0.384937	−	0.922943i	$-0.625777\pi$
$11$	−8.46862			−0.769874			−0.384937	+	0.922943i	$0.625777\pi$
$12$			9.71615i			0.809679i
$13$		−	9.27142i		−	0.713186i	−0.934260	−	0.356593i	$-0.883938\pi$
$13$		−	9.27142i		−	0.713186i	0.934260	−	0.356593i	$-0.116062\pi$
$14$	16.8468	−	2.81818i	1.20335	−	0.201299i
$15$	−19.0585			−1.27057
$16$	−19.9979			−1.24987
$17$			1.99229i			0.117193i	0.998282	+	0.0585967i	$0.0186626\pi$
$17$			1.99229i			0.117193i	−0.998282	+	0.0585967i	$0.981337\pi$
$18$	38.3565			2.13092
$19$			24.3633i			1.28228i	0.767423	+	0.641141i	$0.221539\pi$
$19$			24.3633i			1.28228i	−0.767423	+	0.641141i	$0.778461\pi$
$20$			7.49122i			0.374561i
$21$	−5.74211	−	34.3258i	−0.273434	−	1.63456i
$22$	20.6645			0.939298
$23$	−22.4925			−0.977934			−0.488967	−	0.872302i	$-0.662626\pi$
$23$	−22.4925			−0.977934			−0.488967	+	0.872302i	$0.662626\pi$
$24$			24.8189i			1.03412i
$25$	10.3057			0.412229
$26$			22.6235i			0.870134i
$27$		−	33.4059i		−	1.23725i
$28$	−13.4922	+	2.25701i	−0.481865	+	0.0806077i
$29$	56.5997			1.95171			0.975856	−	0.218414i	$-0.0700883\pi$
$29$	56.5997			1.95171			0.975856	+	0.218414i	$0.0700883\pi$
$30$	46.5054			1.55018
$31$		−	20.4692i		−	0.660297i	−0.943929	−	0.330149i	$-0.892901\pi$
$31$		−	20.4692i		−	0.660297i	0.943929	−	0.330149i	$-0.107099\pi$
$32$	28.8298			0.900933
$33$		−	42.1045i		−	1.27589i
$34$		−	4.86145i		−	0.142984i
$35$	−4.42721	−	26.4654i	−0.126492	−	0.756155i
$36$	−30.7188			−0.853300
$37$	−5.78701			−0.156406			−0.0782028	−	0.996937i	$-0.524918\pi$
$37$	−5.78701			−0.156406			−0.0782028	+	0.996937i	$0.524918\pi$
$38$		−	59.4498i		−	1.56447i
$39$	46.0959			1.18195
$40$			19.1356i			0.478389i
$41$			6.40312i			0.156174i
$41$			6.40312i			0.156174i
$42$	14.0115	+	83.7595i	0.333607	+	1.99427i
$43$	−63.2121			−1.47005			−0.735025	−	0.678040i	$-0.762829\pi$
$43$	−63.2121			−1.47005			−0.735025	+	0.678040i	$0.762829\pi$
$44$	−16.5497			−0.376130
$45$		−	60.2560i		−	1.33902i
$46$	54.8846			1.19314
$47$		−	62.1216i		−	1.32174i	−0.750502	−	0.660868i	$-0.770188\pi$
$47$		−	62.1216i		−	1.32174i	0.750502	−	0.660868i	$-0.229812\pi$
$48$		−	99.4261i		−	2.07138i
$49$	46.3323	−	15.9474i	0.945557	−	0.325458i
$50$	−25.1473			−0.502947
$51$	−9.90531			−0.194222
$52$		−	18.1186i		−	0.348435i
$53$	−4.33948			−0.0818770			−0.0409385	−	0.999162i	$-0.513035\pi$
$53$	−4.33948			−0.0818770			−0.0409385	+	0.999162i	$0.513035\pi$
$54$			81.5147i			1.50953i
$55$		−	32.4629i		−	0.590234i
$56$	−34.4645	+	5.76532i	−0.615438	+	0.102952i
$57$	−121.130			−2.12509
$58$	−138.111			−2.38122
$59$		−	53.7227i		−	0.910554i	−0.890350	−	0.455277i	$-0.849540\pi$
$59$		−	53.7227i		−	0.910554i	0.890350	−	0.455277i	$-0.150460\pi$
$60$	−37.2450			−0.620750
$61$			74.6441i			1.22367i	0.790984	+	0.611837i	$0.209569\pi$
$61$			74.6441i			1.22367i	−0.790984	+	0.611837i	$0.790431\pi$
$62$			49.9476i			0.805606i
$63$	108.525	−	18.1544i	1.72262	−	0.288165i
$64$	9.64300			0.150672
$65$	35.5402			0.546773
$66$			102.740i			1.55667i
$67$	13.6686			0.204009			0.102004	−	0.994784i	$-0.467474\pi$
$67$	13.6686			0.204009			0.102004	+	0.994784i	$0.467474\pi$
$68$			3.89341i			0.0572561i
$69$		−	111.829i		−	1.62071i
$70$	10.8030	+	64.5791i	0.154328	+	0.922559i
$71$	−21.0182			−0.296032			−0.148016	−	0.988985i	$-0.547289\pi$
$71$	−21.0182			−0.296032			−0.148016	+	0.988985i	$0.547289\pi$
$72$	−78.4681			−1.08984
$73$			82.5094i			1.13027i	0.825000	+	0.565133i	$0.191175\pi$
$73$			82.5094i			1.13027i	−0.825000	+	0.565133i	$0.808825\pi$
$74$	14.1211			0.190825
$75$			51.2383i			0.683177i
$76$			47.6119i			0.626472i
$77$	58.4679	−	9.78067i	0.759324	−	0.127022i
$78$	−112.480			−1.44205
$79$	15.4332			0.195357			0.0976787	−	0.995218i	$-0.468858\pi$
$79$	15.4332			0.195357			0.0976787	+	0.995218i	$0.468858\pi$
$80$		−	76.6582i		−	0.958227i
$81$	24.6168			0.303911
$82$		−	15.6245i		−	0.190542i
$83$		−	138.469i		−	1.66830i	−0.551541	−	0.834148i	$-0.685960\pi$
$83$		−	138.469i		−	1.66830i	0.551541	−	0.834148i	$-0.314040\pi$
$84$	−11.2215	−	67.0809i	−0.133589	−	0.798583i
$85$	−7.63706			−0.0898478
$86$	154.246			1.79356
$87$			281.404i			3.23452i
$88$	−42.2747			−0.480394
$89$		−	11.0966i		−	0.124681i	−0.998055	−	0.0623406i	$-0.980143\pi$
$89$		−	11.0966i		−	0.124681i	0.998055	−	0.0623406i	$-0.0198565\pi$
$90$			147.032i			1.63369i
$91$	10.7078	+	64.0105i	0.117669	+	0.703412i
$92$	−43.9558			−0.477780
$93$	101.769			1.09429
$94$			151.585i			1.61260i
$95$	−93.3923			−0.983077
$96$			143.337i			1.49309i
$97$			111.867i			1.15327i	0.817002	+	0.576634i	$0.195634\pi$
$97$			111.867i			1.15327i	−0.817002	+	0.576634i	$0.804366\pi$
$98$	−113.057	+	38.9138i	−1.15364	+	0.397080i
$99$	133.119			1.34463
$100$	20.1399			0.201399
$101$		−	91.6530i		−	0.907456i	−0.891140	−	0.453728i	$-0.850094\pi$
$101$		−	91.6530i		−	0.907456i	0.891140	−	0.453728i	$-0.149906\pi$
$102$	24.1703			0.236963
$103$			147.844i			1.43538i	0.696363	+	0.717690i	$0.254801\pi$
$103$			147.844i			1.43538i	−0.696363	+	0.717690i	$0.745199\pi$
$104$		−	46.2822i		−	0.445021i
$105$	131.581	−	22.0113i	1.25316	−	0.209631i
$106$	10.5889			0.0998953
$107$	−147.881			−1.38206			−0.691031	−	0.722826i	$-0.742843\pi$
$107$	−147.881			−1.38206			−0.691031	+	0.722826i	$0.742843\pi$
$108$		−	65.2832i		−	0.604474i
$109$	−138.665			−1.27216			−0.636079	−	0.771624i	$-0.719445\pi$
$109$	−138.665			−1.27216			−0.636079	+	0.771624i	$0.719445\pi$
$110$			79.2136i			0.720124i
$111$		−	28.7720i		−	0.259207i
$112$	138.067	−	23.0962i	1.23274	−	0.206216i
$113$	−32.3708			−0.286467			−0.143233	−	0.989689i	$-0.545750\pi$
$113$	−32.3708			−0.286467			−0.143233	+	0.989689i	$0.545750\pi$
$114$	295.574			2.59275
$115$		−	86.2207i		−	0.749745i
$116$	110.609			0.953530
$117$			145.738i			1.24562i
$118$			131.090i			1.11094i
$119$	−2.30095	−	13.7549i	−0.0193358	−	0.115587i
$120$	−95.1387			−0.792823
$121$	−49.2825			−0.407293
$122$		−	182.141i		−	1.49296i
$123$	−31.8352			−0.258823
$124$		−	40.0018i		−	0.322595i
$125$			135.338i			1.08270i
$126$	−264.816	+	44.2991i	−2.10171	+	0.351580i
$127$	−57.0852			−0.449490			−0.224745	−	0.974418i	$-0.572155\pi$
$127$	−57.0852			−0.449490			−0.224745	+	0.974418i	$0.572155\pi$
$128$	−138.850			−1.08476
$129$		−	314.280i		−	2.43628i
$130$	−86.7228			−0.667099
$131$		−	134.584i		−	1.02736i	−0.857981	−	0.513681i	$-0.828282\pi$
$131$		−	134.584i		−	1.02736i	0.857981	−	0.513681i	$-0.171718\pi$
$132$		−	82.2824i		−	0.623351i
$133$	−28.1380	−	168.206i	−0.211564	−	1.26471i
$134$	−33.3531			−0.248904
$135$	128.055			0.948556
$136$			9.94534i			0.0731275i
$137$	−109.644			−0.800321			−0.400160	−	0.916445i	$-0.631046\pi$
$137$	−109.644			−0.800321			−0.400160	+	0.916445i	$0.631046\pi$
$138$			272.877i			1.97737i
$139$		−	80.3222i		−	0.577858i	−0.957351	−	0.288929i	$-0.906701\pi$
$139$		−	80.3222i		−	0.577858i	0.957351	−	0.288929i	$-0.0932991\pi$
$140$	−8.65184	−	51.7199i	−0.0617988	−	0.369428i
$141$	308.858			2.19048
$142$	51.2873			0.361178
$143$			78.5161i			0.549064i
$144$	314.348			2.18297
$145$			216.964i			1.49630i
$146$		−	201.334i		−	1.37900i
$147$	79.2879	+	230.356i	0.539373	+	1.56705i
$148$	−11.3092			−0.0764136
$149$	18.1575			0.121863			0.0609313	−	0.998142i	$-0.480593\pi$
$149$	18.1575			0.121863			0.0609313	+	0.998142i	$0.480593\pi$
$150$		−	125.028i		−	0.833521i
$151$	−173.035			−1.14593			−0.572963	−	0.819581i	$-0.694206\pi$
$151$	−173.035			−1.14593			−0.572963	+	0.819581i	$0.694206\pi$
$152$			121.620i			0.800131i
$153$		−	31.3169i		−	0.204685i
$154$	−142.669	+	23.8661i	−0.926425	+	0.154975i
$155$	78.4649			0.506225
$156$	90.0825			0.577452
$157$		−	288.870i		−	1.83994i	−0.391994	−	0.919968i	$-0.628215\pi$
$157$		−	288.870i		−	1.83994i	0.391994	−	0.919968i	$-0.371785\pi$
$158$	−37.6591			−0.238349
$159$		−	21.5751i		−	0.135693i
$160$			110.514i			0.690711i
$161$	155.290	−	25.9773i	0.964532	−	0.161349i
$162$	−60.0682			−0.370792
$163$	−140.066			−0.859301			−0.429651	−	0.902995i	$-0.641363\pi$
$163$	−140.066			−0.859301			−0.429651	+	0.902995i	$0.641363\pi$
$164$			12.5133i			0.0763003i
$165$	161.400			0.978179
$166$			337.881i			2.03543i
$167$			56.0903i			0.335870i	0.985798	+	0.167935i	$0.0537099\pi$
$167$			56.0903i			0.335870i	−0.985798	+	0.167935i	$0.946290\pi$
$168$	−28.6642	−	171.352i	−0.170620	−	1.01995i
$169$	83.0408			0.491366
$170$	18.6354			0.109620
$171$		−	382.968i		−	2.23958i
$172$	−123.532			−0.718208
$173$		−	200.251i		−	1.15752i	−0.815497	−	0.578761i	$-0.803536\pi$
$173$		−	200.251i		−	1.15752i	0.815497	−	0.578761i	$-0.196464\pi$
$174$		−	686.662i		−	3.94633i
$175$	−71.1514	+	11.9024i	−0.406580	+	0.0680137i
$176$	169.355			0.962242
$177$	267.100			1.50904
$178$			27.0772i			0.152119i
$179$	−304.473			−1.70097			−0.850484	−	0.526001i	$-0.823691\pi$
$179$	−304.473			−1.70097			−0.850484	+	0.526001i	$0.823691\pi$
$180$		−	117.755i		−	0.654193i
$181$		−	116.912i		−	0.645923i	−0.946412	−	0.322962i	$-0.895322\pi$
$181$		−	116.912i		−	0.645923i	0.946412	−	0.322962i	$-0.104678\pi$
$182$	−26.1286	−	156.194i	−0.143563	−	0.858209i
$183$	−371.117			−2.02796
$184$	−112.281			−0.610221
$185$		−	22.1834i		−	0.119910i
$186$	−248.331			−1.33511
$187$		−	16.8719i		−	0.0902242i
$188$		−	121.401i		−	0.645748i
$189$	38.5815	+	230.636i	0.204135	+	1.22030i
$190$	227.889			1.19942
$191$	173.646			0.909144			0.454572	−	0.890710i	$-0.349792\pi$
$191$	173.646			0.909144			0.454572	+	0.890710i	$0.349792\pi$
$192$			47.9433i			0.249705i
$193$	−315.318			−1.63377			−0.816886	−	0.576799i	$-0.804302\pi$
$193$	−315.318			−1.63377			−0.816886	+	0.576799i	$0.804302\pi$
$194$		−	272.970i		−	1.40706i
$195$			176.700i			0.906153i
$196$	90.5445	−	31.1652i	0.461962	−	0.159006i
$197$	121.390			0.616195			0.308097	−	0.951355i	$-0.400308\pi$
$197$	121.390			0.616195			0.308097	+	0.951355i	$0.400308\pi$
$198$	−324.827			−1.64054
$199$			278.090i			1.39744i	0.715396	+	0.698719i	$0.246246\pi$
$199$			278.090i			1.39744i	−0.715396	+	0.698719i	$0.753754\pi$
$200$	51.4453			0.257227
$201$			67.9578i			0.338099i
$202$			223.645i			1.10716i
$203$	−390.768	+	65.3687i	−1.92496	+	0.322013i
$204$	−19.3574			−0.0948891
$205$	−24.5452			−0.119733
$206$		−	360.759i		−	1.75126i
$207$	353.560			1.70802
$208$			185.409i			0.891389i
$209$		−	206.324i		−	0.987196i
$210$	−321.076	+	53.7105i	−1.52893	+	0.255764i
$211$	66.0953			0.313248			0.156624	−	0.987658i	$-0.449939\pi$
$211$	66.0953			0.313248			0.156624	+	0.987658i	$0.449939\pi$
$212$	−8.48039			−0.0400019
$213$		−	104.499i		−	0.490606i
$214$	360.848			1.68621
$215$		−	242.312i		−	1.12703i
$216$		−	166.759i		−	0.772034i
$217$	23.6405	+	141.321i	0.108943	+	0.651248i
$218$	338.361			1.55212
$219$	−410.222			−1.87316
$220$		−	63.4403i		−	0.288365i
$221$	18.4713			0.0835807
$222$			70.2074i			0.316250i
$223$		−	223.904i		−	1.00405i	−0.864852	−	0.502026i	$-0.832588\pi$
$223$		−	223.904i		−	1.00405i	0.864852	−	0.502026i	$-0.167412\pi$
$224$	−199.043	+	33.2965i	−0.888586	+	0.148645i
$225$	−161.996			−0.719983
$226$	78.9889			0.349509
$227$			271.467i			1.19589i	0.801537	+	0.597945i	$0.204016\pi$
$227$			271.467i			1.19589i	−0.801537	+	0.597945i	$0.795984\pi$
$228$	−236.718			−1.03824
$229$		−	127.958i		−	0.558767i	−0.960180	−	0.279383i	$-0.909870\pi$
$229$		−	127.958i		−	0.558767i	0.960180	−	0.279383i	$-0.0901300\pi$
$230$			210.390i			0.914738i
$231$	48.6278	+	290.692i	0.210510	+	1.25841i
$232$	282.541			1.21785
$233$	121.853			0.522973			0.261486	−	0.965207i	$-0.415787\pi$
$233$	121.853			0.522973			0.261486	+	0.965207i	$0.415787\pi$
$234$		−	355.619i		−	1.51974i
$235$	238.131			1.01332
$236$		−	104.987i		−	0.444861i
$237$			76.7313i			0.323761i
$238$	5.61463	+	33.5637i	0.0235909	+	0.141024i
$239$	−16.1630			−0.0676275			−0.0338137	−	0.999428i	$-0.510765\pi$
$239$	−16.1630			−0.0676275			−0.0338137	+	0.999428i	$0.510765\pi$
$240$	381.131			1.58805
$241$		−	30.1028i		−	0.124908i	−0.998048	−	0.0624539i	$-0.980107\pi$
$241$		−	30.1028i		−	0.124908i	0.998048	−	0.0624539i	$-0.0198926\pi$
$242$	120.256			0.496925
$243$		−	178.262i		−	0.733590i
$244$			145.873i			0.597839i
$245$	61.1315	+	177.606i	0.249516	+	0.724922i
$246$	77.6821			0.315781
$247$	225.883			0.914505
$248$		−	102.181i		−	0.412019i
$249$	688.441			2.76482
$250$		−	330.242i		−	1.32097i
$251$			294.126i			1.17182i	0.810377	+	0.585909i	$0.199262\pi$
$251$			294.126i			1.17182i	−0.810377	+	0.585909i	$0.800738\pi$
$252$	212.085	−	35.4781i	0.841606	−	0.140786i
$253$	190.480			0.752887
$254$	139.295			0.548407
$255$		−	37.9701i		−	0.148902i
$256$	300.239			1.17281
$257$			405.263i			1.57690i	0.615099	+	0.788450i	$0.289116\pi$
$257$			405.263i			1.57690i	−0.615099	+	0.788450i	$0.710884\pi$
$258$			766.883i			2.97242i
$259$	39.9539	−	6.68359i	0.154262	−	0.0258054i
$260$	69.4542			0.267132
$261$	−889.692			−3.40878
$262$			328.404i			1.25345i
$263$	191.524			0.728229			0.364115	−	0.931354i	$-0.381372\pi$
$263$	191.524			0.728229			0.364115	+	0.931354i	$0.381372\pi$
$264$		−	210.182i		−	0.796145i
$265$		−	16.6346i		−	0.0627720i
$266$	68.6604	+	410.445i	0.258122	+	1.54303i
$267$	55.1705			0.206631
$268$	26.7117			0.0996706
$269$			302.274i			1.12369i	0.827241	+	0.561847i	$0.189909\pi$
$269$			302.274i			1.12369i	−0.827241	+	0.561847i	$0.810091\pi$
$270$	−312.471			−1.15730
$271$			75.7443i			0.279499i	0.990187	+	0.139750i	$0.0446298\pi$
$271$			75.7443i			0.279499i	−0.990187	+	0.139750i	$0.955370\pi$
$272$		−	39.8416i		−	0.146476i
$273$	−318.249	+	53.2375i	−1.16575	+	0.195009i
$274$	267.546			0.976444
$275$	−87.2753			−0.317365
$276$		−	218.540i		−	0.791813i
$277$	−330.683			−1.19380			−0.596901	−	0.802315i	$-0.703601\pi$
$277$	−330.683			−1.19380			−0.596901	+	0.802315i	$0.703601\pi$
$278$			195.997i			0.705024i
$279$			321.756i			1.15325i
$280$	−22.1003	−	132.113i	−0.0789295	−	0.471833i
$281$	437.606			1.55732			0.778658	−	0.627448i	$-0.215901\pi$
$281$	437.606			1.55732			0.778658	+	0.627448i	$0.215901\pi$
$282$	−753.653			−2.67253
$283$			328.197i			1.15971i	0.814721	+	0.579853i	$0.196890\pi$
$283$			328.197i			1.15971i	−0.814721	+	0.579853i	$0.803110\pi$
$284$	−41.0747			−0.144629
$285$		−	464.330i		−	1.62923i
$286$		−	191.590i		−	0.669894i
$287$	−7.39516	−	44.2076i	−0.0257671	−	0.154033i
$288$	−453.177			−1.57353
$289$	285.031			0.986266
$290$		−	529.421i		−	1.82559i
$291$	−556.183			−1.91128
$292$			161.243i			0.552203i
$293$		−	55.5669i		−	0.189648i	−0.995494	−	0.0948241i	$-0.969771\pi$
$293$		−	55.5669i		−	0.189648i	0.995494	−	0.0948241i	$-0.0302289\pi$
$294$	−193.473	−	562.099i	−0.658071	−	1.91190i
$295$	205.936			0.698088
$296$	−28.8883			−0.0975955
$297$			282.902i			0.952531i
$298$	−44.3067			−0.148680
$299$			208.537i			0.697449i
$300$			100.132i			0.333773i
$301$	436.421	−	73.0056i	1.44990	−	0.242544i
$302$	422.228			1.39811
$303$	455.683			1.50390
$304$		−	487.216i		−	1.60268i
$305$	−286.134			−0.938145
$306$			76.4172i			0.249730i
$307$			135.678i			0.441948i	0.975280	+	0.220974i	$0.0709235\pi$
$307$			135.678i			0.441948i	−0.975280	+	0.220974i	$0.929076\pi$
$308$	114.260	−	19.1138i	0.370976	−	0.0620578i
$309$	−735.055			−2.37882
$310$	−191.465			−0.617628
$311$			125.987i			0.405102i	0.979272	+	0.202551i	$0.0649232\pi$
$311$			125.987i			0.405102i	−0.979272	+	0.202551i	$0.935077\pi$
$312$	230.107			0.737522
$313$		−	402.228i		−	1.28507i	−0.766255	−	0.642536i	$-0.777882\pi$
$313$		−	402.228i		−	1.28507i	0.766255	−	0.642536i	$-0.222118\pi$
$314$			704.881i			2.24484i
$315$	69.5915	+	416.011i	0.220925	+	1.32067i
$316$	30.1603			0.0954439
$317$	−462.669			−1.45952			−0.729762	−	0.683701i	$-0.760369\pi$
$317$	−462.669			−1.45952			−0.729762	+	0.683701i	$0.760369\pi$
$318$			52.6462i			0.165554i
$319$	−479.321			−1.50257
$320$			36.9646i			0.115514i
$321$		−	735.236i		−	2.29046i
$322$	−378.927	+	63.3879i	−1.17679	+	0.196857i
$323$	−48.5388			−0.150275
$324$	48.1072			0.148479
$325$		−	95.5487i		−	0.293996i
$326$	341.780			1.04840
$327$		−	689.419i		−	2.10831i
$328$			31.9639i			0.0974508i
$329$	71.7461	+	428.892i	0.218073	+	1.30362i
$330$	−393.836			−1.19344
$331$	−48.7701			−0.147342			−0.0736709	−	0.997283i	$-0.523471\pi$
$331$	−48.7701			−0.147342			−0.0736709	+	0.997283i	$0.523471\pi$
$332$		−	270.601i		−	0.815063i
$333$	90.9662			0.273172
$334$		−	136.868i		−	0.409784i
$335$			52.3959i			0.156406i
$336$	114.830	+	686.444i	0.341757	+	2.04299i
$337$	−556.064			−1.65004			−0.825020	−	0.565103i	$-0.808836\pi$
$337$	−556.064			−1.65004			−0.825020	+	0.565103i	$0.808836\pi$
$338$	−202.630			−0.599498
$339$		−	160.942i		−	0.474755i
$340$	−14.9247			−0.0438961
$341$			173.346i			0.508346i
$342$			934.493i			2.73244i
$343$	−301.463	+	163.613i	−0.878901	+	0.477005i
$344$	−315.550			−0.917296
$345$	428.674			1.24253
$346$			488.640i			1.41225i
$347$	−290.822			−0.838105			−0.419052	−	0.907962i	$-0.637638\pi$
$347$	−290.822			−0.838105			−0.419052	+	0.907962i	$0.637638\pi$
$348$			549.931i			1.58026i
$349$		−	75.2343i		−	0.215571i	−0.994174	−	0.107786i	$-0.965624\pi$
$349$		−	75.2343i		−	0.215571i	0.994174	−	0.107786i	$-0.0343760\pi$
$350$	173.619	−	29.0434i	0.496054	−	0.0829812i
$351$	−309.720			−0.882393
$352$	−244.149			−0.693605
$353$		−	214.961i		−	0.608956i	−0.952519	−	0.304478i	$-0.901518\pi$
$353$		−	214.961i		−	0.608956i	0.952519	−	0.304478i	$-0.0984820\pi$
$354$	−651.759			−1.84113
$355$		−	80.5695i		−	0.226956i
$356$		−	21.6855i		−	0.0609143i
$357$	68.3869	−	11.4399i	0.191560	−	0.0320447i
$358$	742.955			2.07529
$359$	−86.3984			−0.240664			−0.120332	−	0.992734i	$-0.538396\pi$
$359$	−86.3984			−0.240664			−0.120332	+	0.992734i	$0.538396\pi$
$360$		−	300.793i		−	0.835536i
$361$	−232.573			−0.644246
$362$			285.281i			0.788069i
$363$		−	245.024i		−	0.674997i
$364$	20.9257	+	125.092i	0.0574883	+	0.343659i
$365$	−316.284			−0.866532
$366$	905.575			2.47425
$367$			526.143i			1.43363i	0.697262	+	0.716817i	$0.254402\pi$
$367$			526.143i			1.43363i	−0.697262	+	0.716817i	$0.745598\pi$
$368$	449.803			1.22229
$369$		−	100.651i		−	0.272767i
$370$			54.1304i			0.146298i
$371$	29.9601	−	5.01180i	0.0807549	−	0.0135089i
$372$	198.882			0.534629
$373$	376.321			1.00890			0.504451	−	0.863440i	$-0.331695\pi$
$373$	376.321			1.00890			0.504451	+	0.863440i	$0.331695\pi$
$374$			41.1697i			0.110079i
$375$	−672.876			−1.79434
$376$		−	310.106i		−	0.824750i
$377$		−	524.759i		−	1.39193i
$378$	−94.1439	−	562.783i	−0.249058	−	1.48884i
$379$	306.860			0.809657			0.404828	−	0.914393i	$-0.367331\pi$
$379$	306.860			0.809657			0.404828	+	0.914393i	$0.367331\pi$
$380$	−182.511			−0.480293
$381$		−	283.818i		−	0.744928i
$382$	−423.720			−1.10922
$383$		−	371.209i		−	0.969213i	−0.874732	−	0.484606i	$-0.838963\pi$
$383$		−	371.209i		−	0.969213i	0.874732	−	0.484606i	$-0.161037\pi$
$384$		−	690.336i		−	1.79775i
$385$	37.4923	+	224.126i	0.0973827	+	0.582145i
$386$	769.418			1.99331
$387$	993.634			2.56753
$388$			218.615i			0.563442i
$389$	656.450			1.68753			0.843766	−	0.536711i	$-0.180334\pi$
$389$	656.450			1.68753			0.843766	+	0.536711i	$0.180334\pi$
$390$		−	431.171i		−	1.10557i
$391$		−	44.8115i		−	0.114607i
$392$	231.287	−	79.6083i	0.590018	−	0.203082i
$393$	669.130			1.70262
$394$	−296.208			−0.751798
$395$			59.1604i			0.149773i
$396$	260.146			0.656934
$397$			666.464i			1.67875i	0.543552	+	0.839376i	$0.317079\pi$
$397$			666.464i			1.67875i	−0.543552	+	0.839376i	$0.682921\pi$
$398$		−	678.577i		−	1.70497i
$399$	836.292	−	139.897i	2.09597	−	0.350619i
$400$	−206.093			−0.515232
$401$	−83.9875			−0.209445			−0.104723	−	0.994501i	$-0.533395\pi$
$401$	−83.9875			−0.209445			−0.104723	+	0.994501i	$0.533395\pi$
$402$		−	165.826i		−	0.412502i
$403$	−189.779			−0.470915
$404$		−	179.112i		−	0.443347i
$405$			94.3638i			0.232997i
$406$	953.525	−	159.508i	2.34858	−	0.392877i
$407$	49.0080			0.120413
$408$	−49.4465			−0.121192
$409$			238.056i			0.582044i	0.956716	+	0.291022i	$0.0939952\pi$
$409$			238.056i			0.582044i	−0.956716	+	0.291022i	$0.906005\pi$
$410$	59.8934			0.146082
$411$		−	545.130i		−	1.32635i
$412$			288.923i			0.701270i
$413$	62.0460	+	370.905i	0.150232	+	0.898076i
$414$	−862.733			−2.08390
$415$	530.793			1.27902
$416$		−	267.294i		−	0.642533i
$417$	399.348			0.957669
$418$			503.458i			1.20444i
$419$		−	225.067i		−	0.537152i	−0.963258	−	0.268576i	$-0.913447\pi$
$419$		−	225.067i		−	0.537152i	0.963258	−	0.268576i	$-0.0865531\pi$
$420$	257.142	−	43.0154i	0.612243	−	0.102418i
$421$	−350.787			−0.833224			−0.416612	−	0.909084i	$-0.636783\pi$
$421$	−350.787			−0.833224			−0.416612	+	0.909084i	$0.636783\pi$
$422$	−161.281			−0.382183
$423$			976.492i			2.30849i
$424$	−21.6623			−0.0510904
$425$			20.5320i			0.0483105i
$426$			254.991i			0.598571i
$427$	−86.2088	−	515.348i	−0.201894	−	1.20690i
$428$	−288.994			−0.675221
$429$	−390.368			−0.909950
$430$			591.272i			1.37505i
$431$	219.772			0.509912			0.254956	−	0.966953i	$-0.417939\pi$
$431$	219.772			0.509912			0.254956	+	0.966953i	$0.417939\pi$
$432$			668.048i			1.54641i
$433$			441.969i			1.02071i	0.859963	+	0.510356i	$0.170487\pi$
$433$			441.969i			1.02071i	−0.859963	+	0.510356i	$0.829513\pi$
$434$	−57.6860	−	344.841i	−0.132917	−	0.794566i
$435$	−1078.71			−2.47979
$436$	−270.985			−0.621526
$437$		−	547.992i		−	1.25399i
$438$	1001.00			2.28538
$439$		−	375.505i		−	0.855365i	−0.903929	−	0.427682i	$-0.859330\pi$
$439$		−	375.505i		−	0.855365i	0.903929	−	0.427682i	$-0.140670\pi$
$440$		−	162.052i		−	0.368300i
$441$	−728.299	+	250.678i	−1.65147	+	0.568432i
$442$	−45.0725			−0.101974
$443$	774.902			1.74922			0.874608	−	0.484831i	$-0.161119\pi$
$443$	774.902			1.74922			0.874608	+	0.484831i	$0.161119\pi$
$444$		−	56.2274i		−	0.126638i
$445$	42.5368			0.0955884
$446$			546.354i			1.22501i
$447$			90.2760i			0.201960i
$448$	−66.5759	+	11.1370i	−0.148607	+	0.0248594i
$449$	204.717			0.455940			0.227970	−	0.973668i	$-0.426791\pi$
$449$	204.717			0.455940			0.227970	+	0.973668i	$0.426791\pi$
$450$	395.292			0.878426
$451$		−	54.2256i		−	0.120234i
$452$	−63.2603			−0.139956
$453$		−	860.299i		−	1.89912i
$454$		−	662.415i		−	1.45906i
$455$	−245.372	+	41.0465i	−0.539279	+	0.0902121i
$456$	−604.673			−1.32604
$457$	−510.934			−1.11802			−0.559008	−	0.829162i	$-0.688818\pi$
$457$	−510.934			−1.11802			−0.559008	+	0.829162i	$0.688818\pi$
$458$			312.233i			0.681732i
$459$	66.5541			0.144998
$460$		−	168.496i		−	0.366296i
$461$			250.302i			0.542955i	0.962445	+	0.271478i	$0.0875123\pi$
$461$			250.302i			0.542955i	−0.962445	+	0.271478i	$0.912488\pi$
$462$	−118.658	−	709.327i	−0.256836	−	1.53534i
$463$	−632.010			−1.36503			−0.682516	−	0.730870i	$-0.739114\pi$
$463$	−632.010			−1.36503			−0.682516	+	0.730870i	$0.739114\pi$
$464$	−1131.87			−2.43939
$465$			390.114i			0.838954i
$466$	−297.336			−0.638061
$467$			785.192i			1.68135i	0.541538	+	0.840677i	$0.317842\pi$
$467$			785.192i			1.68135i	−0.541538	+	0.840677i	$0.682158\pi$
$468$			284.807i			0.608562i
$469$	−94.3688	+	15.7863i	−0.201213	+	0.0336594i
$470$	−581.072			−1.23632
$471$	1436.21			3.04928
$472$		−	268.179i		−	0.568177i
$473$	535.319			1.13175
$474$		−	187.234i		−	0.395009i
$475$			251.082i			0.528594i
$476$	−4.49662	−	26.8804i	−0.00944669	−	0.0564714i
$477$	68.2124			0.143003
$478$	39.4398			0.0825100
$479$			211.815i			0.442202i	0.975251	+	0.221101i	$0.0709650\pi$
$479$			211.815i			0.442202i	−0.975251	+	0.221101i	$0.929035\pi$
$480$	−549.455			−1.14470
$481$			53.6538i			0.111546i
$482$			73.4548i			0.152396i
$483$	129.154	+	772.073i	0.267400	+	1.59849i
$484$	−96.3099			−0.198987
$485$	−428.821			−0.884168
$486$			434.984i			0.895029i
$487$	509.269			1.04573			0.522863	−	0.852416i	$-0.324864\pi$
$487$	509.269			1.04573			0.522863	+	0.852416i	$0.324864\pi$
$488$			372.617i			0.763560i
$489$		−	696.384i		−	1.42410i
$490$	−149.169	−	433.382i	−0.304426	−	0.884453i
$491$	−128.327			−0.261359			−0.130679	−	0.991425i	$-0.541716\pi$
$491$	−128.327			−0.261359			−0.130679	+	0.991425i	$0.541716\pi$
$492$	−62.2137			−0.126451
$493$			112.763i			0.228728i
$494$	−551.184			−1.11576
$495$			510.285i			1.03088i
$496$			409.341i			0.825285i
$497$	145.111	−	24.2746i	0.291975	−	0.0488423i
$498$	−1679.89			−3.37327
$499$	236.891			0.474732			0.237366	−	0.971420i	$-0.423716\pi$
$499$	236.891			0.474732			0.237366	+	0.971420i	$0.423716\pi$
$500$			264.483i			0.528966i
$501$	−278.871			−0.556629
$502$		−	717.707i		−	1.42969i
$503$			740.385i			1.47194i	0.677015	+	0.735969i	$0.263273\pi$
$503$			740.385i			1.47194i	−0.677015	+	0.735969i	$0.736727\pi$
$504$	541.749	−	90.6253i	1.07490	−	0.179812i
$505$	351.335			0.695712
$506$	−464.797			−0.918571
$507$			412.864i			0.814328i
$508$	−111.558			−0.219603
$509$		−	431.033i		−	0.846824i	−0.905937	−	0.423412i	$-0.860832\pi$
$509$		−	431.033i		−	0.846824i	0.905937	−	0.423412i	$-0.139168\pi$
$510$			92.6521i			0.181671i
$511$	−95.2926	−	569.650i	−0.186483	−	1.11478i
$512$	−177.225			−0.346143
$513$	813.879			1.58651
$514$		−	988.896i		−	1.92392i
$515$	−566.733			−1.10045
$516$		−	614.178i		−	1.19027i
$517$			526.084i			1.01757i
$518$	−97.4927	+	16.3088i	−0.188210	+	0.0314843i
$519$	995.615			1.91833
$520$	177.414			0.341181
$521$		−	593.563i		−	1.13928i	−0.821896	−	0.569638i	$-0.807083\pi$
$521$		−	593.563i		−	1.13928i	0.821896	−	0.569638i	$-0.192917\pi$
$522$	2170.97			4.15894
$523$		−	145.052i		−	0.277346i	−0.990338	−	0.138673i	$-0.955716\pi$
$523$		−	145.052i		−	0.277346i	0.990338	−	0.138673i	$-0.0442837\pi$
$524$		−	263.010i		−	0.501928i
$525$	−59.1766	−	353.752i	−0.112717	−	0.673814i
$526$	−467.345			−0.888488
$527$	40.7806			0.0773825
$528$			842.002i			1.59470i
$529$	−23.0882			−0.0436449
$530$			40.5906i			0.0765859i
$531$			844.469i			1.59034i
$532$	−54.9884	−	328.716i	−0.103362	−	0.617887i
$533$	59.3660			0.111381
$534$	−134.623			−0.252103
$535$		−	566.872i		−	1.05957i
$536$	68.2325			0.127299
$537$		−	1513.79i		−	2.81897i
$538$		−	737.588i		−	1.37098i
$539$	−392.370	+	135.053i	−0.727960	+	0.250562i
$540$	250.251			0.463427
$541$	−669.919			−1.23830			−0.619149	−	0.785274i	$-0.712522\pi$
$541$	−669.919			−1.23830			−0.619149	+	0.785274i	$0.712522\pi$
$542$		−	184.826i		−	0.341008i
$543$	581.266			1.07047
$544$			57.4374i			0.105583i
$545$		−	531.547i		−	0.975315i
$546$	776.569	−	129.907i	1.42229	−	0.237924i
$547$	−50.3870			−0.0921152			−0.0460576	−	0.998939i	$-0.514666\pi$
$547$	−50.3870			−0.0921152			−0.0460576	+	0.998939i	$0.514666\pi$
$548$	−214.271			−0.391005
$549$		−	1173.33i		−	2.13722i
$550$	212.963			0.387206
$551$			1378.96i			2.50264i
$552$		−	558.240i		−	1.01130i
$553$	−106.552	+	17.8243i	−0.192680	+	0.0322320i
$554$	806.910			1.45652
$555$	110.292			0.198724
$556$		−	156.969i		−	0.282318i
$557$	142.761			0.256303			0.128152	−	0.991755i	$-0.459096\pi$
$557$	142.761			0.256303			0.128152	+	0.991755i	$0.459096\pi$
$558$		−	785.128i		−	1.40704i
$559$			586.066i			1.04842i
$560$	88.5349	+	529.253i	0.158098	+	0.945095i
$561$	83.8843			0.149526
$562$	−1067.82			−1.90003
$563$		−	401.378i		−	0.712927i	−0.934309	−	0.356464i	$-0.883982\pi$
$563$		−	401.378i		−	0.712927i	0.934309	−	0.356464i	$-0.116018\pi$
$564$	603.583			1.07018
$565$		−	124.087i		−	0.219623i
$566$		−	800.843i		−	1.41492i
$567$	−169.956	+	28.4307i	−0.299746	+	0.0501423i
$568$	−104.921			−0.184721
$569$	−569.373			−1.00065			−0.500327	−	0.865836i	$-0.666787\pi$
$569$	−569.373			−1.00065			−0.500327	+	0.865836i	$0.666787\pi$
$570$			1133.03i			1.98777i
$571$	522.826			0.915632			0.457816	−	0.889047i	$-0.348632\pi$
$571$	522.826			0.915632			0.457816	+	0.889047i	$0.348632\pi$
$572$			153.440i			0.268251i
$573$			863.340i			1.50670i
$574$	18.0452	+	107.872i	0.0314376	+	0.187931i
$575$	−231.801			−0.403133
$576$	−151.579			−0.263157
$577$		−	927.796i		−	1.60796i	−0.594653	−	0.803982i	$-0.702711\pi$
$577$		−	927.796i		−	1.60796i	0.594653	−	0.803982i	$-0.297289\pi$
$578$	−695.513			−1.20331
$579$		−	1567.71i		−	2.70761i
$580$			424.000i			0.731035i
$581$	159.922	+	955.996i	0.275252	+	1.64543i
$582$	1357.16			2.33189
$583$	36.7494			0.0630350
$584$			411.880i			0.705274i
$585$	−558.658			−0.954971
$586$			135.591i			0.231383i
$587$		−	87.3727i		−	0.148846i	−0.997227	−	0.0744231i	$-0.976288\pi$
$587$		−	87.3727i		−	0.148846i	0.997227	−	0.0744231i	$-0.0237115\pi$
$588$	154.948	+	450.171i	0.263516	+	0.765597i
$589$	498.699			0.846687
$590$	−502.511			−0.851713
$591$			603.532i			1.02120i
$592$	115.728			0.195487
$593$		−	1003.89i		−	1.69290i	−0.532472	−	0.846448i	$-0.678737\pi$
$593$		−	1003.89i		−	1.69290i	0.532472	−	0.846448i	$-0.321263\pi$
$594$		−	690.317i		−	1.16215i
$595$	52.7268	−	8.82027i	0.0886164	−	0.0148240i
$596$	35.4842			0.0595372
$597$	−1382.62			−2.31594
$598$		−	508.858i		−	0.850934i
$599$	784.057			1.30894			0.654472	−	0.756087i	$-0.272891\pi$
$599$	784.057			1.30894			0.654472	+	0.756087i	$0.272891\pi$
$600$			255.777i			0.426295i
$601$			879.714i			1.46375i	0.681439	+	0.731875i	$0.261355\pi$
$601$			879.714i			1.46375i	−0.681439	+	0.731875i	$0.738645\pi$
$602$	−1064.92	+	178.143i	−1.76898	+	0.295919i
$603$	−214.857			−0.356313
$604$	−338.152			−0.559855
$605$		−	188.915i		−	0.312256i
$606$	−1111.93			−1.83486
$607$			662.906i			1.09210i	0.837752	+	0.546051i	$0.183870\pi$
$607$			662.906i			1.09210i	−0.837752	+	0.546051i	$0.816130\pi$
$608$			702.392i			1.15525i
$609$	−325.002	−	1942.83i	−0.533664	−	3.19020i
$610$	698.205			1.14460
$611$	−575.955			−0.942644
$612$		−	61.2007i		−	0.100001i
$613$	−819.459			−1.33680			−0.668401	−	0.743802i	$-0.733021\pi$
$613$	−819.459			−1.33680			−0.668401	+	0.743802i	$0.733021\pi$
$614$		−	331.072i		−	0.539205i
$615$		−	122.034i		−	0.198430i
$616$	291.867	−	48.8243i	0.473810	−	0.0792602i
$617$	−742.529			−1.20345			−0.601725	−	0.798703i	$-0.705520\pi$
$617$	−742.529			−1.20345			−0.601725	+	0.798703i	$0.705520\pi$
$618$	1793.63			2.90232
$619$			1195.27i			1.93097i	0.260467	+	0.965483i	$0.416123\pi$
$619$			1195.27i			1.93097i	−0.260467	+	0.965483i	$0.583877\pi$
$620$	153.339			0.247322
$621$			751.381i			1.20995i
$622$		−	307.424i		−	0.494252i
$623$	12.8158	+	76.6118i	0.0205712	+	0.122972i
$624$	−921.821			−1.47728
$625$	−261.149			−0.417838
$626$			981.488i			1.56787i
$627$	1025.81			1.63605
$628$		−	564.522i		−	0.898920i
$629$		−	11.5294i		−	0.0183297i
$630$	−169.812	−	1015.12i	−0.269543	−	1.61130i
$631$	383.855			0.608329			0.304164	−	0.952620i	$-0.401623\pi$
$631$	383.855			0.608329			0.304164	+	0.952620i	$0.401623\pi$
$632$	77.0414			0.121901
$633$			328.614i			0.519138i
$634$	1128.97			1.78072
$635$		−	218.825i		−	0.344607i
$636$		−	42.1630i		−	0.0662941i
$637$	−147.855	−	429.566i	−0.232112	−	0.674358i
$638$	1169.61			1.83324
$639$	330.387			0.517037
$640$		−	532.254i		−	0.831646i
$641$	−1166.29			−1.81949			−0.909745	−	0.415168i	$-0.863723\pi$
$641$	−1166.29			−1.81949			−0.909745	+	0.415168i	$0.863723\pi$
$642$			1794.07i			2.79451i
$643$		−	739.745i		−	1.15046i	−0.817992	−	0.575229i	$-0.804913\pi$
$643$		−	739.745i		−	1.15046i	0.817992	−	0.575229i	$-0.195087\pi$
$644$	303.474	−	50.7659i	0.471232	−	0.0788290i
$645$	1204.73			1.86780
$646$	118.441			0.183345
$647$			387.812i			0.599400i	0.954034	+	0.299700i	$0.0968865\pi$
$647$			387.812i			0.599400i	−0.954034	+	0.299700i	$0.903113\pi$
$648$	122.885			0.189637
$649$			454.957i			0.701013i
$650$			233.151i			0.358695i
$651$	−702.622	+	117.537i	−1.07930	+	0.180548i
$652$	−273.723			−0.419821
$653$	300.399			0.460029			0.230015	−	0.973187i	$-0.426123\pi$
$653$	300.399			0.460029			0.230015	+	0.973187i	$0.426123\pi$
$654$			1682.27i			2.57228i
$655$	515.904			0.787639
$656$		−	128.049i		−	0.195197i
$657$		−	1296.97i		−	1.97408i
$658$	−175.070	−	1046.55i	−0.266064	−	1.59050i
$659$	−579.322			−0.879093			−0.439546	−	0.898220i	$-0.644861\pi$
$659$	−579.322			−0.879093			−0.439546	+	0.898220i	$0.644861\pi$
$660$	315.414			0.477900
$661$			1259.79i			1.90588i	0.303163	+	0.952939i	$0.401957\pi$
$661$			1259.79i			1.90588i	−0.303163	+	0.952939i	$0.598043\pi$
$662$	119.006			0.179767
$663$			91.8362i			0.138516i
$664$		−	691.224i		−	1.04100i
$665$	644.787	−	107.862i	0.969604	−	0.162198i
$666$	−221.969			−0.333287
$667$	−1273.07			−1.90865
$668$			109.614i			0.164093i
$669$	1113.21			1.66399
$670$		−	127.853i		−	0.190825i
$671$		−	632.133i		−	0.942075i
$672$	−165.544	−	989.608i	−0.246346	−	1.47263i
$673$	288.739			0.429033			0.214516	−	0.976720i	$-0.431182\pi$
$673$	288.739			0.429033			0.214516	+	0.976720i	$0.431182\pi$
$674$	1356.87			2.01316
$675$		−	344.272i		−	0.510032i
$676$	162.282			0.240062
$677$			865.508i			1.27845i	0.769021	+	0.639223i	$0.220744\pi$
$677$			865.508i			1.27845i	−0.769021	+	0.639223i	$0.779256\pi$
$678$			392.719i			0.579232i
$679$	−129.199	−	772.338i	−0.190278	−	1.13746i
$680$	−38.1236			−0.0560641
$681$	−1349.69			−1.98192
$682$		−	422.987i		−	0.620216i
$683$	−766.924			−1.12287			−0.561437	−	0.827519i	$-0.689751\pi$
$683$	−766.924			−1.12287			−0.561437	+	0.827519i	$0.689751\pi$
$684$		−	748.413i		−	1.09417i
$685$		−	420.299i		−	0.613576i
$686$	735.609	−	399.237i	1.07232	−	0.581978i
$687$	636.182			0.926030
$688$	1264.11			1.83737
$689$			40.2331i			0.0583935i
$690$	−1046.02			−1.51597
$691$		−	1092.86i		−	1.58156i	−0.612099	−	0.790781i	$-0.709675\pi$
$691$		−	1092.86i		−	1.58156i	0.612099	−	0.790781i	$-0.290325\pi$
$692$		−	391.340i		−	0.565520i
$693$	−919.059	+	153.743i	−1.32620	+	0.221851i
$694$	709.645			1.02254
$695$	307.900			0.443022
$696$			1404.74i			2.01831i
$697$	−12.7569			−0.0183025
$698$			183.582i			0.263011i
$699$			605.830i			0.866709i
$700$	−139.047	+	23.2602i	−0.198639	+	0.0332288i
$701$	−900.508			−1.28460			−0.642302	−	0.766452i	$-0.722021\pi$
$701$	−900.508			−1.28460			−0.642302	+	0.766452i	$0.722021\pi$
$702$	755.757			1.07658
$703$		−	140.991i		−	0.200556i
$704$	−81.6629			−0.115998
$705$			1183.95i			1.67936i
$706$			524.534i			0.742966i
$707$	105.853	+	632.779i	0.149721	+	0.895019i
$708$	521.978			0.737257
$709$	212.814			0.300161			0.150080	−	0.988674i	$-0.452047\pi$
$709$	212.814			0.300161			0.150080	+	0.988674i	$0.452047\pi$
$710$			196.600i			0.276902i
$711$	−242.595			−0.341203
$712$		−	55.3935i		−	0.0777998i
$713$			460.404i			0.645727i
$714$	−166.873	+	27.9150i	−0.233716	+	0.0390966i
$715$	−300.977			−0.420946
$716$	−595.014			−0.831026
$717$		−	80.3594i		−	0.112077i
$718$	210.823			0.293626
$719$			449.020i			0.624506i	0.949999	+	0.312253i	$0.101084\pi$
$719$			449.020i			0.624506i	−0.949999	+	0.312253i	$0.898916\pi$
$720$			1204.99i			1.67360i
$721$	−170.750	−	1020.73i	−0.236824	−	1.41571i
$722$	567.508			0.786022
$723$	149.666			0.207007
$724$		−	228.475i		−	0.315573i
$725$	583.301			0.804553
$726$			597.890i			0.823541i
$727$			508.187i			0.699019i	0.936933	+	0.349509i	$0.113652\pi$
$727$			508.187i			0.699019i	−0.936933	+	0.349509i	$0.886348\pi$
$728$	53.4527	+	319.535i	0.0734240	+	0.438922i
$729$	1107.84			1.51967
$730$	771.775			1.05723
$731$		−	125.937i		−	0.172280i
$732$	−725.253			−0.990783
$733$			213.294i			0.290987i	0.989359	+	0.145494i	$0.0464770\pi$
$733$			213.294i			0.290987i	−0.989359	+	0.145494i	$0.953523\pi$
$734$		−	1283.86i		−	1.74913i
$735$	−883.026	+	303.935i	−1.20140	+	0.413517i
$736$	−648.455			−0.881053
$737$	−115.754			−0.157061
$738$			245.602i			0.332793i
$739$	−810.600			−1.09689			−0.548444	−	0.836188i	$-0.684779\pi$
$739$	−810.600			−1.09689			−0.548444	+	0.836188i	$0.684779\pi$
$740$		−	43.3517i		−	0.0585834i
$741$			1123.05i			1.51559i
$742$	−73.1065	+	12.2294i	−0.0985263	+	0.0164817i
$743$	−728.164			−0.980033			−0.490016	−	0.871713i	$-0.663009\pi$
$743$	−728.164			−0.980033			−0.490016	+	0.871713i	$0.663009\pi$
$744$	508.024			0.682828
$745$			69.6034i			0.0934274i
$746$	−918.272			−1.23093
$747$			2176.59i			2.91378i
$748$		−	32.9718i		−	0.0440800i
$749$	1020.98	−	170.792i	1.36312	−	0.228026i
$750$	1641.91			2.18921
$751$	1370.62			1.82506			0.912531	−	0.409008i	$-0.134125\pi$
$751$	1370.62			1.82506			0.912531	+	0.409008i	$0.134125\pi$
$752$			1242.30i			1.65200i
$753$	−1462.34			−1.94202
$754$			1280.48i			1.69825i
$755$		−	663.297i		−	0.878539i
$756$	75.3975	+	450.719i	0.0997322	+	0.596190i
$757$	413.568			0.546325			0.273162	−	0.961968i	$-0.411930\pi$
$757$	413.568			0.546325			0.273162	+	0.961968i	$0.411930\pi$
$758$	−748.779			−0.987835
$759$			947.035i			1.24774i
$760$	−466.207			−0.613430
$761$		−	1059.96i		−	1.39285i	−0.717631	−	0.696424i	$-0.754773\pi$
$761$		−	1059.96i		−	1.39285i	0.717631	−	0.696424i	$-0.245227\pi$
$762$			692.552i			0.908861i
$763$	957.353	−	160.149i	1.25472	−	0.209893i
$764$	339.347			0.444172
$765$	120.047			0.156924
$766$			905.798i			1.18250i
$767$	−498.086			−0.649395
$768$			1492.74i			1.94367i
$769$			677.987i			0.881647i	0.897594	+	0.440824i	$0.145314\pi$
$769$			677.987i			0.881647i	−0.897594	+	0.440824i	$0.854686\pi$
$770$	−91.4862	−	546.896i	−0.118813	−	0.710255i
$771$	−2014.90			−2.61336
$772$	−616.208			−0.798197
$773$			88.7708i			0.114839i	0.998350	+	0.0574197i	$0.0182873\pi$
$773$			88.7708i			0.114839i	−0.998350	+	0.0574197i	$0.981713\pi$
$774$	−2424.60			−3.13255
$775$		−	210.950i		−	0.272194i
$776$			558.431i			0.719628i
$777$	33.2296	+	198.644i	0.0427666	+	0.255655i
$778$	−1601.82			−2.05890
$779$	−156.002			−0.200259
$780$			345.314i			0.442711i
$781$	177.996			0.227907
$782$			109.346i			0.139829i
$783$		−	1890.76i		−	2.41477i
$784$	−926.548	+	318.915i	−1.18182	+	0.406780i
$785$	1107.33			1.41061
$786$	−1632.77			−2.07731
$787$		−	1104.27i		−	1.40314i	−0.712599	−	0.701572i	$-0.752482\pi$
$787$		−	1104.27i		−	1.40314i	0.712599	−	0.701572i	$-0.247518\pi$
$788$	237.226			0.301048
$789$			952.225i			1.20688i
$790$		−	144.359i		−	0.182733i
$791$	223.490	−	37.3860i	0.282541	−	0.0472642i
$792$	664.517			0.839036
$793$	692.057			0.872707
$794$		−	1626.26i		−	2.04819i
$795$	82.7042			0.104030
$796$			543.456i			0.682733i
$797$			408.281i			0.512273i	0.966641	+	0.256136i	$0.0824496\pi$
$797$			408.281i			0.512273i	−0.966641	+	0.256136i	$0.917550\pi$
$798$	−2040.66	+	341.367i	−2.55722	+	0.427779i
$799$	123.764			0.154899
$800$	297.113			0.371391
$801$			174.428i			0.217763i
$802$	204.941			0.255537
$803$		−	698.740i		−	0.870162i
$804$			132.806i			0.165182i
$805$	99.5789	+	595.273i	0.123701	+	0.739470i
$806$	463.085			0.574547
$807$	−1502.85			−1.86227
$808$		−	457.524i		−	0.566243i
$809$	140.712			0.173934			0.0869669	−	0.996211i	$-0.472283\pi$
$809$	140.712			0.173934			0.0869669	+	0.996211i	$0.472283\pi$
$810$		−	230.260i		−	0.284272i
$811$			665.442i			0.820520i	0.911969	+	0.410260i	$0.134562\pi$
$811$			665.442i			0.820520i	−0.911969	+	0.410260i	$0.865438\pi$
$812$	−763.655	+	127.746i	−0.940462	+	0.157323i
$813$	−376.587			−0.463207
$814$	−119.586			−0.146911
$815$		−	536.917i		−	0.658794i
$816$	198.085			0.242752
$817$		−	1540.06i		−	1.88502i
$818$		−	580.888i		−	0.710131i
$819$	−168.317	−	1006.18i	−0.205515	−	1.22855i
$820$	−47.9672			−0.0584966
$821$	−30.8103			−0.0375278			−0.0187639	−	0.999824i	$-0.505973\pi$
$821$	−30.8103			−0.0375278			−0.0187639	+	0.999824i	$0.505973\pi$
$822$			1330.19i			1.61824i
$823$	100.490			0.122102			0.0610512	−	0.998135i	$-0.480555\pi$
$823$	100.490			0.122102			0.0610512	+	0.998135i	$0.480555\pi$
$824$			738.026i			0.895663i
$825$		−	433.917i		−	0.525960i
$826$	−151.400	−	905.057i	−0.183293	−	1.09571i
$827$	659.624			0.797610			0.398805	−	0.917036i	$-0.369425\pi$
$827$	659.624			0.797610			0.398805	+	0.917036i	$0.369425\pi$
$828$	690.942			0.834471
$829$			331.134i			0.399438i	0.979853	+	0.199719i	$0.0640029\pi$
$829$			331.134i			0.399438i	−0.979853	+	0.199719i	$0.935997\pi$
$830$	−1295.20			−1.56049
$831$		−	1644.10i		−	1.97846i
$832$		−	89.4043i		−	0.107457i
$833$	31.7719	+	92.3072i	0.0381415	+	0.110813i
$834$	−974.461			−1.16842
$835$	−215.012			−0.257499
$836$		−	403.207i		−	0.482305i
$837$	−683.792			−0.816956
$838$			549.193i			0.655361i
$839$		−	1138.98i		−	1.35754i	−0.734351	−	0.678770i	$-0.762513\pi$
$839$		−	1138.98i		−	1.35754i	0.734351	−	0.678770i	$-0.237487\pi$
$840$	656.844	−	109.879i	0.781957	−	0.130808i
$841$	2362.52			2.80918
$842$	855.967			1.01659
$843$			2175.70i			2.58090i
$844$	129.166			0.153041
$845$			318.321i			0.376711i
$846$		−	2382.77i		−	2.81651i
$847$	340.250	−	56.9179i	0.401711	−	0.0671994i
$848$	86.7805			0.102336
$849$	−1631.74			−1.92195
$850$		−	50.1007i		−	0.0589420i
$851$	130.164			0.152954
$852$		−	204.216i		−	0.239691i
$853$			295.096i			0.345951i	0.984926	+	0.172976i	$0.0553382\pi$
$853$			295.096i			0.345951i	−0.984926	+	0.172976i	$0.944662\pi$
$854$	210.361	+	1257.52i	0.246324	+	1.47250i
$855$	1468.04			1.71700
$856$	−738.208			−0.862392
$857$		−	412.027i		−	0.480778i	−0.970677	−	0.240389i	$-0.922725\pi$
$857$		−	412.027i		−	0.480778i	0.970677	−	0.240389i	$-0.0772751\pi$
$858$	952.550			1.11020
$859$		−	947.029i		−	1.10248i	−0.834347	−	0.551239i	$-0.814155\pi$
$859$		−	947.029i		−	1.10248i	0.834347	−	0.551239i	$-0.185845\pi$
$860$		−	473.536i		−	0.550623i
$861$	219.792	−	36.7675i	0.255276	−	0.0427032i
$862$	−536.273			−0.622126
$863$	918.071			1.06381			0.531907	−	0.846803i	$-0.321476\pi$
$863$	918.071			1.06381			0.531907	+	0.846803i	$0.321476\pi$
$864$		−	963.086i		−	1.11468i
$865$	767.626			0.887429
$866$		−	1078.46i		−	1.24534i
$867$			1417.12i			1.63451i
$868$	46.1993	+	276.175i	0.0532250	+	0.318174i
$869$	−130.698			−0.150401
$870$	2632.19			3.02550
$871$		−	126.727i		−	0.145496i
$872$	−692.205			−0.793813
$873$		−	1758.44i		−	2.01425i
$874$			1337.17i			1.52995i
$875$	−156.306	−	934.381i	−0.178635	−	1.06786i
$876$	−801.673			−0.915152
$877$	−1000.81			−1.14117			−0.570585	−	0.821238i	$-0.693284\pi$
$877$	−1000.81			−1.14117			−0.570585	+	0.821238i	$0.693284\pi$
$878$			916.282i			1.04360i
$879$	276.269			0.314299
$880$			649.189i			0.737715i
$881$		−	546.821i		−	0.620682i	−0.950625	−	0.310341i	$-0.899557\pi$
$881$		−	546.821i		−	0.620682i	0.950625	−	0.310341i	$-0.100443\pi$
$882$	1777.14	−	611.688i	2.01490	−	0.693524i
$883$	−288.367			−0.326576			−0.163288	−	0.986578i	$-0.552210\pi$
$883$	−288.367			−0.326576			−0.163288	+	0.986578i	$0.552210\pi$
$884$	36.0975			0.0408342
$885$			1023.88i			1.15692i
$886$	−1890.86			−2.13416
$887$			1516.47i			1.70966i	0.518907	+	0.854831i	$0.326339\pi$
$887$			1516.47i			1.70966i	−0.518907	+	0.854831i	$0.673661\pi$
$888$		−	143.627i		−	0.161743i
$889$	394.120	−	65.9294i	0.443330	−	0.0741613i
$890$	−103.795			−0.116624
$891$	−208.470			−0.233973
$892$		−	437.562i		−	0.490540i
$893$	1513.49			1.69484
$894$		−	220.285i		−	0.246404i
$895$		−	1167.14i		−	1.30407i
$896$	958.627	−	160.362i	1.06990	−	0.178975i
$897$	−1036.81			−1.15586
$898$	−499.537			−0.556277
$899$		−	1158.55i		−	1.28871i
$900$	−316.580			−0.351755
$901$		−	8.64549i		−	0.00959544i
$902$			132.318i			0.146694i
$903$	362.971	+	2169.81i	0.401961	+	2.40289i
$904$	−161.592			−0.178752
$905$	448.160			0.495205
$906$			2099.24i			2.31705i
$907$	−458.880			−0.505932			−0.252966	−	0.967475i	$-0.581406\pi$
$907$	−458.880			−0.505932			−0.252966	+	0.967475i	$0.581406\pi$
$908$			530.512i			0.584264i
$909$			1440.70i			1.58493i
$910$	598.740	−	100.159i	0.657956	−	0.110065i
$911$	1470.54			1.61420			0.807100	−	0.590415i	$-0.201036\pi$
$911$	1470.54			1.61420			0.807100	+	0.590415i	$0.201036\pi$
$912$	2422.35			2.65609
$913$			1172.64i			1.28438i
$914$	1246.75			1.36405
$915$		−	1422.61i		−	1.55476i
$916$		−	250.060i		−	0.272991i
$917$	155.436	+	929.180i	0.169505	+	1.01328i
$918$	−162.401			−0.176907
$919$	−182.597			−0.198691			−0.0993453	−	0.995053i	$-0.531675\pi$
$919$	−182.597			−0.198691			−0.0993453	+	0.995053i	$0.531675\pi$
$920$		−	430.407i		−	0.467833i
$921$	−674.567			−0.732429
$922$		−	610.771i		−	0.662441i
$923$			194.869i			0.211126i
$924$	95.0304	+	568.083i	0.102847	+	0.614808i
$925$	−59.6393			−0.0644749
$926$	1542.19			1.66543
$927$		−	2323.97i		−	2.50698i
$928$	1631.76			1.75836
$929$		−	311.412i		−	0.335212i	−0.985854	−	0.167606i	$-0.946396\pi$
$929$		−	311.412i		−	0.335212i	0.985854	−	0.167606i	$-0.0536036\pi$
$930$		−	951.928i		−	1.02358i
$931$	388.533	+	1128.81i	0.417329	+	1.21247i
$932$	238.130			0.255504
$933$	−626.384			−0.671366
$934$		−	1915.97i		−	2.05136i
$935$	64.6754			0.0691715
$936$			727.511i			0.777255i
$937$			970.690i			1.03596i	0.855394	+	0.517978i	$0.173315\pi$
$937$			970.690i			1.03596i	−0.855394	+	0.517978i	$0.826685\pi$
$938$	230.272	−	38.5206i	0.245493	−	0.0410667i
$939$	1999.81			2.12972
$940$	465.366			0.495071
$941$			291.860i			0.310159i	0.987902	+	0.155079i	$0.0495634\pi$
$941$			291.860i			0.310159i	−0.987902	+	0.155079i	$0.950437\pi$
$942$	−3504.54			−3.72032
$943$		−	144.022i		−	0.152728i
$944$			1074.34i			1.13807i
$945$	−884.101	+	147.895i	−0.935557	+	0.156502i
$946$	−1306.25			−1.38081
$947$	−1701.82			−1.79706			−0.898532	−	0.438907i	$-0.855366\pi$
$947$	−1701.82			−1.79706			−0.898532	+	0.438907i	$0.855366\pi$
$948$			149.952i			0.158177i
$949$	764.979			0.806089
$950$		−	612.673i		−	0.644919i
$951$		−	2300.31i		−	2.41883i
$952$	−11.4862	−	68.6633i	−0.0120653	−	0.0721253i
$953$	−588.366			−0.617383			−0.308691	−	0.951162i	$-0.599891\pi$
$953$	−588.366			−0.617383			−0.308691	+	0.951162i	$0.599891\pi$
$954$	−166.447			−0.174473
$955$			665.641i			0.697006i
$956$	−31.5864			−0.0330401
$957$		−	2383.10i		−	2.49018i
$958$		−	516.856i		−	0.539515i
$959$	756.989	−	126.631i	0.789352	−	0.132045i
$960$	−183.782			−0.191439
$961$	542.011			0.564007
$962$		−	130.922i		−	0.136094i
$963$	2324.54			2.41385
$964$		−	58.8281i		−	0.0610250i
$965$		−	1208.71i		−	1.25255i
$966$	−315.154	−	1883.96i	−0.326246	−	1.95027i
$967$	−1195.93			−1.23674			−0.618372	−	0.785886i	$-0.712207\pi$
$967$	−1195.93			−1.23674			−0.618372	+	0.785886i	$0.712207\pi$
$968$	−246.014			−0.254147
$969$		−	241.326i		−	0.249047i
$970$	1046.38			1.07874
$971$		−	461.355i		−	0.475133i	−0.971371	−	0.237567i	$-0.923650\pi$
$971$		−	461.355i		−	0.475133i	0.971371	−	0.237567i	$-0.0763498\pi$
$972$		−	348.368i		−	0.358403i
$973$	92.7666	+	554.550i	0.0953408	+	0.569938i
$974$	−1242.68			−1.27586
$975$	475.051			0.487232
$976$		−	1492.73i		−	1.52943i
$977$	1341.19			1.37276			0.686381	−	0.727242i	$-0.259198\pi$
$977$	1341.19			1.37276			0.686381	+	0.727242i	$0.259198\pi$
$978$			1699.27i			1.73749i
$979$			93.9731i			0.0959889i
$980$	119.466	+	347.085i	0.121904	+	0.354169i
$981$	2179.68			2.22190
$982$	313.135			0.318875
$983$		−	159.110i		−	0.161861i	−0.996720	−	0.0809307i	$-0.974211\pi$
$983$		−	159.110i		−	0.161861i	0.996720	−	0.0809307i	$-0.0257892\pi$
$984$	−158.919			−0.161503
$985$			465.327i			0.472413i
$986$		−	275.156i		−	0.279063i
$987$	−2132.37	+	356.709i	−2.16046	+	0.361407i
$988$	441.430			0.446791
$989$	1421.80			1.43761
$990$		−	1245.16i		−	1.25774i
$991$	−404.558			−0.408232			−0.204116	−	0.978947i	$-0.565432\pi$
$991$	−404.558			−0.408232			−0.204116	+	0.978947i	$0.565432\pi$
$992$		−	590.124i		−	0.594884i
$993$		−	242.477i		−	0.244186i
$994$	−354.091	+	59.2333i	−0.356228	+	0.0595908i
$995$	−1066.01			−1.07136
$996$	1345.38			1.35078
$997$		−	1186.56i		−	1.19013i	−0.803678	−	0.595065i	$-0.797126\pi$
$997$		−	1186.56i		−	1.19013i	0.803678	−	0.595065i	$-0.202874\pi$
$998$	−578.046			−0.579204
$999$			193.320i			0.193514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.b.a.83.12	yes	52
7.6	odd	2	inner	287.3.b.a.83.11	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.b.a.83.11	✓	52	7.6	odd	2	inner
287.3.b.a.83.12	yes	52	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.44013 q^{2} +4.97182i q^{3} +1.95424 q^{4} +3.83331i q^{5} -12.1319i q^{6} +(-6.90407 + 1.15493i) q^{7} +4.99192 q^{8} -15.7190 q^{9} +O(q^{10})\)	\(q-2.44013 q^{2} +4.97182i q^{3} +1.95424 q^{4} +3.83331i q^{5} -12.1319i q^{6} +(-6.90407 + 1.15493i) q^{7} +4.99192 q^{8} -15.7190 q^{9} -9.35378i q^{10} -8.46862 q^{11} +9.71615i q^{12} -9.27142i q^{13} +(16.8468 - 2.81818i) q^{14} -19.0585 q^{15} -19.9979 q^{16} +1.99229i q^{17} +38.3565 q^{18} +24.3633i q^{19} +7.49122i q^{20} +(-5.74211 - 34.3258i) q^{21} +20.6645 q^{22} -22.4925 q^{23} +24.8189i q^{24} +10.3057 q^{25} +22.6235i q^{26} -33.4059i q^{27} +(-13.4922 + 2.25701i) q^{28} +56.5997 q^{29} +46.5054 q^{30} -20.4692i q^{31} +28.8298 q^{32} -42.1045i q^{33} -4.86145i q^{34} +(-4.42721 - 26.4654i) q^{35} -30.7188 q^{36} -5.78701 q^{37} -59.4498i q^{38} +46.0959 q^{39} +19.1356i q^{40} +6.40312i q^{41} +(14.0115 + 83.7595i) q^{42} -63.2121 q^{43} -16.5497 q^{44} -60.2560i q^{45} +54.8846 q^{46} -62.1216i q^{47} -99.4261i q^{48} +(46.3323 - 15.9474i) q^{49} -25.1473 q^{50} -9.90531 q^{51} -18.1186i q^{52} -4.33948 q^{53} +81.5147i q^{54} -32.4629i q^{55} +(-34.4645 + 5.76532i) q^{56} -121.130 q^{57} -138.111 q^{58} -53.7227i q^{59} -37.2450 q^{60} +74.6441i q^{61} +49.9476i q^{62} +(108.525 - 18.1544i) q^{63} +9.64300 q^{64} +35.5402 q^{65} +102.740i q^{66} +13.6686 q^{67} +3.89341i q^{68} -111.829i q^{69} +(10.8030 + 64.5791i) q^{70} -21.0182 q^{71} -78.4681 q^{72} +82.5094i q^{73} +14.1211 q^{74} +51.2383i q^{75} +47.6119i q^{76} +(58.4679 - 9.78067i) q^{77} -112.480 q^{78} +15.4332 q^{79} -76.6582i q^{80} +24.6168 q^{81} -15.6245i q^{82} -138.469i q^{83} +(-11.2215 - 67.0809i) q^{84} -7.63706 q^{85} +154.246 q^{86} +281.404i q^{87} -42.2747 q^{88} -11.0966i q^{89} +147.032i q^{90} +(10.7078 + 64.0105i) q^{91} -43.9558 q^{92} +101.769 q^{93} +151.585i q^{94} -93.3923 q^{95} +143.337i q^{96} +111.867i q^{97} +(-113.057 + 38.9138i) q^{98} +133.119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) \) 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9} + 24 q^{11} - 14 q^{14} + 44 q^{15} + 194 q^{16} + 70 q^{18} - 16 q^{21} - 48 q^{22} - 80 q^{23} - 304 q^{25} + 64 q^{28} - 12 q^{29} + 64 q^{30} - 166 q^{32} + 30 q^{35} - 70 q^{36} + 36 q^{37} - 68 q^{39} + 164 q^{42} - 172 q^{43} + 72 q^{44} + 68 q^{46} - 172 q^{49} - 234 q^{50} + 156 q^{51} + 64 q^{53} - 234 q^{56} + 140 q^{57} - 556 q^{58} + 152 q^{60} - 130 q^{63} + 334 q^{64} - 76 q^{65} + 160 q^{67} + 202 q^{70} - 408 q^{71} - 40 q^{72} + 398 q^{74} - 248 q^{77} + 390 q^{78} + 264 q^{79} - 116 q^{81} - 418 q^{84} + 232 q^{85} + 368 q^{86} - 220 q^{88} + 32 q^{91} - 74 q^{92} + 240 q^{93} - 44 q^{95} + 838 q^{98} - 24 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9 + 24 * q^11 - 14 * q^14 + 44 * q^15 + 194 * q^16 + 70 * q^18 - 16 * q^21 - 48 * q^22 - 80 * q^23 - 304 * q^25 + 64 * q^28 - 12 * q^29 + 64 * q^30 - 166 * q^32 + 30 * q^35 - 70 * q^36 + 36 * q^37 - 68 * q^39 + 164 * q^42 - 172 * q^43 + 72 * q^44 + 68 * q^46 - 172 * q^49 - 234 * q^50 + 156 * q^51 + 64 * q^53 - 234 * q^56 + 140 * q^57 - 556 * q^58 + 152 * q^60 - 130 * q^63 + 334 * q^64 - 76 * q^65 + 160 * q^67 + 202 * q^70 - 408 * q^71 - 40 * q^72 + 398 * q^74 - 248 * q^77 + 390 * q^78 + 264 * q^79 - 116 * q^81 - 418 * q^84 + 232 * q^85 + 368 * q^86 - 220 * q^88 + 32 * q^91 - 74 * q^92 + 240 * q^93 - 44 * q^95 + 838 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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