LMFDB - Embedded newform 287.2.c.a.204.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(204,287)]

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([0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("287.204");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.c (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 60x^{6} + 118x^{4} + 96x^{2} + 25 $ x^10 + 13x^8 + 60x^6 + 118x^4 + 96x^2 + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			204.1
Root			$-2.19548i$ of defining polynomial
Character	$\chi$	$=$	287.204
Dual form			287.2.c.a.204.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82015 q^{2} -1.19548i q^{3} +1.31294 q^{4} -0.937607 q^{5} +2.17596i q^{6} +1.00000i q^{7} +1.25055 q^{8} +1.57082 q^{9} +O(q^{10})$	\(q-1.82015 q^{2} -1.19548i q^{3} +1.31294 q^{4} -0.937607 q^{5} +2.17596i q^{6} +1.00000i q^{7} +1.25055 q^{8} +1.57082 q^{9} +1.70658 q^{10} -2.33247i q^{11} -1.56960i q^{12} -2.30905i q^{13} -1.82015i q^{14} +1.12089i q^{15} -4.90207 q^{16} -4.88254i q^{17} -2.85912 q^{18} +2.27740i q^{19} -1.23102 q^{20} +1.19548 q^{21} +4.24544i q^{22} -7.58645 q^{23} -1.49501i q^{24} -4.12089 q^{25} +4.20281i q^{26} -5.46434i q^{27} +1.31294i q^{28} -9.66104i q^{29} -2.04019i q^{30} +8.30394 q^{31} +6.42140 q^{32} -2.78843 q^{33} +8.88695i q^{34} -0.937607i q^{35} +2.06239 q^{36} -2.12576 q^{37} -4.14521i q^{38} -2.76043 q^{39} -1.17252 q^{40} +(-5.97276 - 2.30783i) q^{41} -2.17596 q^{42} +6.60858 q^{43} -3.06239i q^{44} -1.47281 q^{45} +13.8085 q^{46} -13.3820i q^{47} +5.86034i q^{48} -1.00000 q^{49} +7.50064 q^{50} -5.83700 q^{51} -3.03165i q^{52} +9.55570i q^{53} +9.94591i q^{54} +2.18694i q^{55} +1.25055i q^{56} +2.72260 q^{57} +17.5845i q^{58} +13.2817 q^{59} +1.47167i q^{60} -1.79232 q^{61} -15.1144 q^{62} +1.57082i q^{63} -1.88376 q^{64} +2.16498i q^{65} +5.07535 q^{66} -1.16474i q^{67} -6.41049i q^{68} +9.06948i q^{69} +1.70658i q^{70} +8.32224i q^{71} +1.96438 q^{72} -1.14399 q^{73} +3.86920 q^{74} +4.92646i q^{75} +2.99010i q^{76} +2.33247 q^{77} +5.02439 q^{78} +12.4855i q^{79} +4.59621 q^{80} -1.82007 q^{81} +(10.8713 + 4.20059i) q^{82} -0.290980 q^{83} +1.56960 q^{84} +4.57790i q^{85} -12.0286 q^{86} -11.5496 q^{87} -2.91686i q^{88} +0.0713974i q^{89} +2.68073 q^{90} +2.30905 q^{91} -9.96057 q^{92} -9.92722i q^{93} +24.3572i q^{94} -2.13531i q^{95} -7.67667i q^{96} -14.6866i q^{97} +1.82015 q^{98} -3.66388i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9	$ 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9} + 8 q^{10} - 16 q^{16} + 20 q^{18} - 22 q^{20} - 12 q^{21} - 4 q^{23} - 4 q^{25} + 14 q^{31} + 18 q^{32} - 2 q^{33} + 20 q^{36} - 22 q^{37} - 46 q^{39} - 58 q^{40} - 4 q^{41} - 8 q^{42} + 18 q^{43} + 50 q^{45} + 8 q^{46} - 10 q^{49} - 22 q^{50} + 14 q^{51} + 62 q^{57} + 34 q^{59} - 28 q^{61} - 44 q^{62} + 8 q^{64} - 36 q^{66} - 20 q^{72} + 12 q^{74} + 12 q^{77} + 78 q^{78} - 4 q^{80} + 10 q^{81} + 74 q^{82} - 20 q^{83} - 6 q^{84} + 12 q^{86} - 8 q^{87} - 54 q^{90} - 14 q^{91} - 30 q^{92} - 4 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9 + 8 * q^10 - 16 * q^16 + 20 * q^18 - 22 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^25 + 14 * q^31 + 18 * q^32 - 2 * q^33 + 20 * q^36 - 22 * q^37 - 46 * q^39 - 58 * q^40 - 4 * q^41 - 8 * q^42 + 18 * q^43 + 50 * q^45 + 8 * q^46 - 10 * q^49 - 22 * q^50 + 14 * q^51 + 62 * q^57 + 34 * q^59 - 28 * q^61 - 44 * q^62 + 8 * q^64 - 36 * q^66 - 20 * q^72 + 12 * q^74 + 12 * q^77 + 78 * q^78 - 4 * q^80 + 10 * q^81 + 74 * q^82 - 20 * q^83 - 6 * q^84 + 12 * q^86 - 8 * q^87 - 54 * q^90 - 14 * q^91 - 30 * q^92 - 4 * 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 $

$2$	−1.82015			−1.28704			−0.643520	−	0.765429i	$-0.722527\pi$
$2$	−1.82015			−1.28704			−0.643520	+	0.765429i	$0.722527\pi$
$3$		−	1.19548i		−	0.690213i	−0.938564	−	0.345106i	$-0.887843\pi$
$3$		−	1.19548i		−	0.690213i	0.938564	−	0.345106i	$-0.112157\pi$
$4$	1.31294			0.656471
$5$	−0.937607			−0.419310			−0.209655	−	0.977775i	$-0.567234\pi$
$5$	−0.937607			−0.419310			−0.209655	+	0.977775i	$0.567234\pi$
$6$			2.17596i			0.888331i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.25055			0.442136
$9$	1.57082			0.523606
$10$	1.70658			0.539669
$11$		−	2.33247i		−	0.703265i	−0.936138	−	0.351633i	$-0.885627\pi$
$11$		−	2.33247i		−	0.703265i	0.936138	−	0.351633i	$-0.114373\pi$
$12$		−	1.56960i		−	0.453105i
$13$		−	2.30905i		−	0.640415i	−0.947347	−	0.320207i	$-0.896247\pi$
$13$		−	2.30905i		−	0.640415i	0.947347	−	0.320207i	$-0.103753\pi$
$14$		−	1.82015i		−	0.486455i
$15$			1.12089i			0.289413i
$16$	−4.90207			−1.22552
$17$		−	4.88254i		−	1.18419i	−0.805868	−	0.592095i	$-0.798301\pi$
$17$		−	4.88254i		−	1.18419i	0.805868	−	0.592095i	$-0.201699\pi$
$18$	−2.85912			−0.673902
$19$			2.27740i			0.522472i	0.965275	+	0.261236i	$0.0841301\pi$
$19$			2.27740i			0.522472i	−0.965275	+	0.261236i	$0.915870\pi$
$20$	−1.23102			−0.275265
$21$	1.19548			0.260876
$22$			4.24544i			0.905130i
$23$	−7.58645			−1.58188			−0.790942	−	0.611891i	$-0.790409\pi$
$23$	−7.58645			−1.58188			−0.790942	+	0.611891i	$0.790409\pi$
$24$		−	1.49501i		−	0.305168i
$25$	−4.12089			−0.824179
$26$			4.20281i			0.824239i
$27$		−	5.46434i		−	1.05161i
$28$			1.31294i			0.248123i
$29$		−	9.66104i		−	1.79401i	−0.442020	−	0.897005i	$-0.645738\pi$
$29$		−	9.66104i		−	1.79401i	0.442020	−	0.897005i	$-0.354262\pi$
$30$		−	2.04019i		−	0.372487i
$31$	8.30394			1.49143			0.745716	−	0.666264i	$-0.232108\pi$
$31$	8.30394			1.49143			0.745716	+	0.666264i	$0.232108\pi$
$32$	6.42140			1.13515
$33$	−2.78843			−0.485403
$34$			8.88695i			1.52410i
$35$		−	0.937607i		−	0.158484i
$36$	2.06239			0.343732
$37$	−2.12576			−0.349473			−0.174737	−	0.984615i	$-0.555907\pi$
$37$	−2.12576			−0.349473			−0.174737	+	0.984615i	$0.555907\pi$
$38$		−	4.14521i		−	0.672442i
$39$	−2.76043			−0.442023
$40$	−1.17252			−0.185392
$41$	−5.97276	−	2.30783i	−0.932789	−	0.360423i
$41$	−5.97276	−	2.30783i	−0.932789	−	0.360423i
$42$	−2.17596			−0.335758
$43$	6.60858			1.00780			0.503899	−	0.863762i	$-0.331898\pi$
$43$	6.60858			1.00780			0.503899	+	0.863762i	$0.331898\pi$
$44$		−	3.06239i		−	0.461673i
$45$	−1.47281			−0.219554
$46$	13.8085			2.03595
$47$		−	13.3820i		−	1.95196i	−0.217860	−	0.975980i	$-0.569908\pi$
$47$		−	13.3820i		−	1.95196i	0.217860	−	0.975980i	$-0.430092\pi$
$48$			5.86034i			0.845868i
$49$	−1.00000			−0.142857
$50$	7.50064			1.06075
$51$	−5.83700			−0.817343
$52$		−	3.03165i		−	0.420414i
$53$			9.55570i			1.31258i	0.754510	+	0.656288i	$0.227875\pi$
$53$			9.55570i			1.31258i	−0.754510	+	0.656288i	$0.772125\pi$
$54$			9.94591i			1.35347i
$55$			2.18694i			0.294887i
$56$			1.25055i			0.167112i
$57$	2.72260			0.360617
$58$			17.5845i			2.30896i
$59$	13.2817			1.72913			0.864567	−	0.502517i	$-0.167592\pi$
$59$	13.2817			1.72913			0.864567	+	0.502517i	$0.167592\pi$
$60$			1.47167i			0.189992i
$61$	−1.79232			−0.229483			−0.114741	−	0.993395i	$-0.536604\pi$
$61$	−1.79232			−0.229483			−0.114741	+	0.993395i	$0.536604\pi$
$62$	−15.1144			−1.91953
$63$			1.57082i			0.197905i
$64$	−1.88376			−0.235470
$65$			2.16498i			0.268533i
$66$	5.07535			0.624733
$67$		−	1.16474i		−	0.142295i	−0.997466	−	0.0711476i	$-0.977334\pi$
$67$		−	1.16474i		−	0.142295i	0.997466	−	0.0711476i	$-0.0226661\pi$
$68$		−	6.41049i		−	0.777386i
$69$			9.06948i			1.09184i
$70$			1.70658i			0.203976i
$71$			8.32224i			0.987669i	0.869556	+	0.493834i	$0.164405\pi$
$71$			8.32224i			0.987669i	−0.869556	+	0.493834i	$0.835595\pi$
$72$	1.96438			0.231505
$73$	−1.14399			−0.133894			−0.0669471	−	0.997757i	$-0.521326\pi$
$73$	−1.14399			−0.133894			−0.0669471	+	0.997757i	$0.521326\pi$
$74$	3.86920			0.449786
$75$			4.92646i			0.568859i
$76$			2.99010i			0.342988i
$77$	2.33247			0.265809
$78$	5.02439			0.568901
$79$			12.4855i			1.40473i	0.711816	+	0.702366i	$0.247873\pi$
$79$			12.4855i			1.40473i	−0.711816	+	0.702366i	$0.752127\pi$
$80$	4.59621			0.513872
$81$	−1.82007			−0.202230
$82$	10.8713	+	4.20059i	1.20054	+	0.463878i
$83$	−0.290980			−0.0319392			−0.0159696	−	0.999872i	$-0.505083\pi$
$83$	−0.290980			−0.0319392			−0.0159696	+	0.999872i	$0.505083\pi$
$84$	1.56960			0.171257
$85$			4.57790i			0.496543i
$86$	−12.0286			−1.29708
$87$	−11.5496			−1.23825
$88$		−	2.91686i		−	0.310939i
$89$			0.0713974i			0.00756810i	0.999993	+	0.00378405i	$0.00120450\pi$
$89$			0.0713974i			0.00756810i	−0.999993	+	0.00378405i	$0.998795\pi$
$90$	2.68073			0.282574
$91$	2.30905			0.242054
$92$	−9.96057			−1.03846
$93$		−	9.92722i		−	1.02940i
$94$			24.3572i			2.51225i
$95$		−	2.13531i		−	0.219078i
$96$		−	7.67667i		−	0.783497i
$97$		−	14.6866i		−	1.49120i	−0.666395	−	0.745599i	$-0.732163\pi$
$97$		−	14.6866i		−	1.49120i	0.666395	−	0.745599i	$-0.267837\pi$
$98$	1.82015			0.183863
$99$		−	3.66388i		−	0.368234i
$100$	−5.41049			−0.541049
$101$			5.04217i			0.501714i	0.968024	+	0.250857i	$0.0807125\pi$
$101$			5.04217i			0.501714i	−0.968024	+	0.250857i	$0.919288\pi$
$102$	10.6242			1.05195
$103$	−1.45815			−0.143676			−0.0718380	−	0.997416i	$-0.522886\pi$
$103$	−1.45815			−0.143676			−0.0718380	+	0.997416i	$0.522886\pi$
$104$		−	2.88758i		−	0.283150i
$105$	−1.12089			−0.109388
$106$		−	17.3928i		−	1.68934i
$107$	3.73076			0.360666			0.180333	−	0.983606i	$-0.442282\pi$
$107$	3.73076			0.360666			0.180333	+	0.983606i	$0.442282\pi$
$108$		−	7.17436i		−	0.690353i
$109$		−	1.98978i		−	0.190586i	−0.995449	−	0.0952931i	$-0.969621\pi$
$109$		−	1.98978i		−	0.190586i	0.995449	−	0.0952931i	$-0.0303788\pi$
$110$		−	3.98055i		−	0.379531i
$111$			2.54131i			0.241211i
$112$		−	4.90207i		−	0.463202i
$113$	−12.0566			−1.13419			−0.567094	−	0.823653i	$-0.691932\pi$
$113$	−12.0566			−1.13419			−0.567094	+	0.823653i	$0.691932\pi$
$114$	−4.95553			−0.464128
$115$	7.11311			0.663301
$116$		−	12.6844i		−	1.17772i
$117$		−	3.62710i		−	0.335325i
$118$	−24.1747			−2.22547
$119$	4.88254			0.447582
$120$			1.40173i			0.127960i
$121$	5.55960			0.505418
$122$	3.26229			0.295354
$123$	−2.75897	+	7.14034i	−0.248768	+	0.643823i
$124$	10.9026			0.979081
$125$	8.55181			0.764897
$126$		−	2.85912i		−	0.254711i
$127$	−2.83259			−0.251352			−0.125676	−	0.992071i	$-0.540110\pi$
$127$	−2.83259			−0.251352			−0.125676	+	0.992071i	$0.540110\pi$
$128$	−9.41407			−0.832094
$129$		−	7.90044i		−	0.695595i
$130$		−	3.94059i		−	0.345612i
$131$	10.1938			0.890637			0.445319	−	0.895372i	$-0.353090\pi$
$131$	10.1938			0.890637			0.445319	+	0.895372i	$0.353090\pi$
$132$	−3.66104			−0.318653
$133$	−2.27740			−0.197476
$134$			2.11999i			0.183140i
$135$			5.12340i			0.440952i
$136$		−	6.10586i		−	0.523573i
$137$		−	18.9855i		−	1.62204i	−0.585019	−	0.811019i	$-0.698913\pi$
$137$		−	18.9855i		−	1.62204i	0.585019	−	0.811019i	$-0.301087\pi$
$138$		−	16.5078i		−	1.40524i
$139$	4.65068			0.394466			0.197233	−	0.980357i	$-0.436804\pi$
$139$	4.65068			0.394466			0.197233	+	0.980357i	$0.436804\pi$
$140$		−	1.23102i		−	0.104040i
$141$	−15.9979			−1.34727
$142$		−	15.1477i		−	1.27117i
$143$	−5.38578			−0.450382
$144$	−7.70026			−0.641688
$145$			9.05826i			0.752247i
$146$	2.08224			0.172327
$147$			1.19548i			0.0986018i
$148$	−2.79100			−0.229419
$149$			14.7404i			1.20758i	0.797142	+	0.603792i	$0.206344\pi$
$149$			14.7404i			1.20758i	−0.797142	+	0.603792i	$0.793656\pi$
$150$		−	8.96689i		−	0.732144i
$151$			11.0287i			0.897500i	0.893657	+	0.448750i	$0.148131\pi$
$151$			11.0287i			0.897500i	−0.893657	+	0.448750i	$0.851869\pi$
$152$			2.84800i			0.231003i
$153$		−	7.66959i		−	0.620049i
$154$	−4.24544			−0.342107
$155$	−7.78583			−0.625373
$156$	−3.62428			−0.290175
$157$			2.85531i			0.227878i	0.993488	+	0.113939i	$0.0363469\pi$
$157$			2.85531i			0.227878i	−0.993488	+	0.113939i	$0.963653\pi$
$158$		−	22.7255i		−	1.80794i
$159$	11.4237			0.905957
$160$	−6.02074			−0.475982
$161$		−	7.58645i		−	0.597896i
$162$	3.31280			0.260278
$163$	2.94705			0.230831			0.115416	−	0.993317i	$-0.463180\pi$
$163$	2.94705			0.230831			0.115416	+	0.993317i	$0.463180\pi$
$164$	−7.84189	−	3.03005i	−0.612349	−	0.236607i
$165$	2.61445			0.203534
$166$	0.529626			0.0411070
$167$			6.40049i			0.495285i	0.968852	+	0.247642i	$0.0796558\pi$
$167$			6.40049i			0.495285i	−0.968852	+	0.247642i	$0.920344\pi$
$168$	1.49501			0.115343
$169$	7.66829			0.589869
$170$		−	8.33247i		−	0.639071i
$171$			3.57739i			0.273570i
$172$	8.67667			0.661590
$173$	13.7403			1.04465			0.522327	−	0.852745i	$-0.325064\pi$
$173$	13.7403			1.04465			0.522327	+	0.852745i	$0.325064\pi$
$174$	21.0220			1.59368
$175$		−	4.12089i		−	0.311510i
$176$			11.4339i			0.861863i
$177$		−	15.8781i		−	1.19347i
$178$		−	0.129954i		−	0.00974045i
$179$			14.7003i			1.09875i	0.835576	+	0.549374i	$0.185134\pi$
$179$			14.7003i			1.09875i	−0.835576	+	0.549374i	$0.814866\pi$
$180$	−1.93371			−0.144131
$181$			15.7969i			1.17417i	0.809525	+	0.587086i	$0.199725\pi$
$181$			15.7969i			1.17417i	−0.809525	+	0.587086i	$0.800275\pi$
$182$	−4.20281			−0.311533
$183$			2.14269i			0.158392i
$184$	−9.48722			−0.699407
$185$	1.99313			0.146538
$186$			18.0690i			1.32488i
$187$	−11.3884			−0.832800
$188$		−	17.5697i		−	1.28140i
$189$	5.46434			0.397472
$190$			3.88658i			0.281962i
$191$		−	9.85964i		−	0.713419i	−0.934215	−	0.356709i	$-0.883899\pi$
$191$		−	9.85964i		−	0.713419i	0.934215	−	0.356709i	$-0.116101\pi$
$192$			2.25200i			0.162524i
$193$		−	7.67440i		−	0.552416i	−0.961098	−	0.276208i	$-0.910922\pi$
$193$		−	7.67440i		−	0.552416i	0.961098	−	0.276208i	$-0.0890778\pi$
$194$			26.7318i			1.91923i
$195$	2.58820			0.185345
$196$	−1.31294			−0.0937815
$197$	−19.2840			−1.37393			−0.686965	−	0.726690i	$-0.741058\pi$
$197$	−19.2840			−1.37393			−0.686965	+	0.726690i	$0.741058\pi$
$198$			6.66881i			0.473932i
$199$		−	3.45604i		−	0.244992i	−0.992469	−	0.122496i	$-0.960910\pi$
$199$		−	3.45604i		−	0.244992i	0.992469	−	0.122496i	$-0.0390898\pi$
$200$	−5.15338			−0.364399
$201$	−1.39242			−0.0982140
$202$		−	9.17750i		−	0.645726i
$203$	9.66104			0.678072
$204$	−7.66364			−0.536562
$205$	5.60010	+	2.16384i	0.391128	+	0.151129i
$206$	2.65406			0.184917
$207$	−11.9169			−0.828285
$208$			11.3191i			0.784839i
$209$	5.31197			0.367436
$210$	2.04019			0.140787
$211$		−	8.02957i		−	0.552778i	−0.961046	−	0.276389i	$-0.910862\pi$
$211$		−	8.02957i		−	0.552778i	0.961046	−	0.276389i	$-0.0891378\pi$
$212$			12.5461i			0.861668i
$213$	9.94911			0.681702
$214$	−6.79054			−0.464192
$215$	−6.19624			−0.422580
$216$		−	6.83342i		−	0.464955i
$217$			8.30394i			0.563708i
$218$			3.62169i			0.245292i
$219$			1.36763i			0.0924155i
$220$			2.87132i			0.193584i
$221$	−11.2740			−0.758373
$222$		−	4.62557i		−	0.310448i
$223$	11.0937			0.742886			0.371443	−	0.928456i	$-0.378863\pi$
$223$	11.0937			0.742886			0.371443	+	0.928456i	$0.378863\pi$
$224$			6.42140i			0.429048i
$225$	−6.47318			−0.431545
$226$	21.9448			1.45974
$227$			23.6121i			1.56719i	0.621270	+	0.783597i	$0.286617\pi$
$227$			23.6121i			1.56719i	−0.621270	+	0.783597i	$0.713383\pi$
$228$	3.57461			0.236734
$229$		−	13.4604i		−	0.889486i	−0.895658	−	0.444743i	$-0.853295\pi$
$229$		−	13.4604i		−	0.889486i	0.895658	−	0.444743i	$-0.146705\pi$
$230$	−12.9469			−0.853694
$231$		−	2.78843i		−	0.183465i
$232$		−	12.0816i		−	0.793196i
$233$			25.2155i			1.65192i	0.563729	+	0.825960i	$0.309366\pi$
$233$			25.2155i			1.65192i	−0.563729	+	0.825960i	$0.690634\pi$
$234$			6.60186i			0.431577i
$235$			12.5470i			0.818477i
$236$	17.4381			1.13513
$237$	14.9262			0.969564
$238$	−8.88695			−0.576056
$239$			22.4103i			1.44960i	0.688958	+	0.724801i	$0.258068\pi$
$239$			22.4103i			1.44960i	−0.688958	+	0.724801i	$0.741932\pi$
$240$		−	5.49470i		−	0.354681i
$241$	−28.6129			−1.84312			−0.921559	−	0.388237i	$-0.873084\pi$
$241$	−28.6129			−1.84312			−0.921559	+	0.388237i	$0.873084\pi$
$242$	−10.1193			−0.650493
$243$		−	14.2172i		−	0.912031i
$244$	−2.35321			−0.150649
$245$	0.937607			0.0599015
$246$	5.02174	−	12.9965i	0.320175	−	0.828626i
$247$	5.25863			0.334599
$248$	10.3845			0.659415
$249$			0.347861i			0.0220448i
$250$	−15.5656			−0.984453
$251$	11.6910			0.737930			0.368965	−	0.929443i	$-0.379712\pi$
$251$	11.6910			0.737930			0.368965	+	0.929443i	$0.379712\pi$
$252$			2.06239i			0.129919i
$253$			17.6951i			1.11248i
$254$	5.15573			0.323499
$255$	5.47281			0.342721
$256$	20.9025			1.30641
$257$		−	10.8712i		−	0.678126i	−0.940764	−	0.339063i	$-0.889890\pi$
$257$		−	10.8712i		−	0.678126i	0.940764	−	0.339063i	$-0.110110\pi$
$258$			14.3800i			0.895259i
$259$		−	2.12576i		−	0.132088i
$260$			2.84249i			0.176284i
$261$		−	15.1757i		−	0.939355i
$262$	−18.5542			−1.14629
$263$			19.7276i			1.21646i	0.793762	+	0.608229i	$0.208120\pi$
$263$			19.7276i			1.21646i	−0.793762	+	0.608229i	$0.791880\pi$
$264$	−3.48706			−0.214614
$265$		−	8.95949i		−	0.550377i
$266$	4.14521			0.254159
$267$	0.0853544			0.00522360
$268$		−	1.52923i		−	0.0934127i
$269$	14.9859			0.913706			0.456853	−	0.889542i	$-0.348977\pi$
$269$	14.9859			0.913706			0.456853	+	0.889542i	$0.348977\pi$
$270$		−	9.32535i		−	0.567523i
$271$	14.4607			0.878427			0.439213	−	0.898383i	$-0.355257\pi$
$271$	14.4607			0.878427			0.439213	+	0.898383i	$0.355257\pi$
$272$			23.9346i			1.45125i
$273$		−	2.76043i		−	0.167069i
$274$			34.5564i			2.08763i
$275$			9.61185i			0.579616i
$276$			11.9077i			0.716759i
$277$	−2.20181			−0.132294			−0.0661471	−	0.997810i	$-0.521071\pi$
$277$	−2.20181			−0.132294			−0.0661471	+	0.997810i	$0.521071\pi$
$278$	−8.46493			−0.507693
$279$	13.0440			0.780923
$280$		−	1.17252i		−	0.0700716i
$281$		−	21.1901i		−	1.26409i	−0.774930	−	0.632047i	$-0.782215\pi$
$281$		−	21.1901i		−	1.26409i	0.774930	−	0.632047i	$-0.217785\pi$
$282$	29.1186			1.73399
$283$	−1.07391			−0.0638373			−0.0319187	−	0.999490i	$-0.510162\pi$
$283$	−1.07391			−0.0638373			−0.0319187	+	0.999490i	$0.510162\pi$
$284$			10.9266i			0.648376i
$285$	−2.55273			−0.151210
$286$	9.80292			0.579659
$287$	2.30783	−	5.97276i	0.136227	−	0.352561i
$288$	10.0868			0.594373
$289$	−6.83922			−0.402307
$290$		−	16.4874i		−	0.968172i
$291$	−17.5576			−1.02924
$292$	−1.50200			−0.0878977
$293$		−	27.9416i		−	1.63237i	−0.577793	−	0.816183i	$-0.696086\pi$
$293$		−	27.9416i		−	1.63237i	0.577793	−	0.816183i	$-0.303914\pi$
$294$		−	2.17596i		−	0.126904i
$295$	−12.4530			−0.725044
$296$	−2.65837			−0.154515
$297$	−12.7454			−0.739563
$298$		−	26.8298i		−	1.55421i
$299$			17.5175i			1.01306i
$300$			6.46816i			0.373439i
$301$			6.60858i			0.380912i
$302$		−	20.0738i		−	1.15512i
$303$	6.02783			0.346290
$304$		−	11.1640i		−	0.640298i
$305$	1.68049			0.0962246
$306$			13.9598i			0.798028i
$307$	31.9612			1.82412			0.912062	−	0.410053i	$-0.134490\pi$
$307$	31.9612			1.82412			0.912062	+	0.410053i	$0.134490\pi$
$308$	3.06239			0.174496
$309$			1.74320i			0.0991671i
$310$	14.1714			0.804879
$311$		−	12.3577i		−	0.700741i	−0.936611	−	0.350371i	$-0.886056\pi$
$311$		−	12.3577i		−	0.700741i	0.936611	−	0.350371i	$-0.113944\pi$
$312$	−3.45205			−0.195434
$313$			6.53750i			0.369521i	0.982784	+	0.184761i	$0.0591510\pi$
$313$			6.53750i			0.369521i	−0.982784	+	0.184761i	$0.940849\pi$
$314$		−	5.19708i		−	0.293288i
$315$		−	1.47281i		−	0.0829835i
$316$			16.3928i			0.922165i
$317$		−	3.46129i		−	0.194406i	−0.995265	−	0.0972028i	$-0.969010\pi$
$317$		−	3.46129i		−	0.194406i	0.995265	−	0.0972028i	$-0.0309895\pi$
$318$	−20.7928			−1.16600
$319$	−22.5341			−1.26167
$320$	1.76623			0.0987351
$321$		−	4.46007i		−	0.248937i
$322$			13.8085i			0.769516i
$323$	11.1195			0.618706
$324$	−2.38965			−0.132758
$325$			9.51534i			0.527816i
$326$	−5.36407			−0.297089
$327$	−2.37875			−0.131545
$328$	−7.46923	−	2.88605i	−0.412419	−	0.159356i
$329$	13.3820			0.737772
$330$	−4.75868			−0.261957
$331$		−	30.5469i		−	1.67901i	−0.543354	−	0.839504i	$-0.682846\pi$
$331$		−	30.5469i		−	1.67901i	0.543354	−	0.839504i	$-0.317154\pi$
$332$	−0.382039			−0.0209671
$333$	−3.33919			−0.182986
$334$		−	11.6498i		−	0.637451i
$335$			1.09207i			0.0596659i
$336$	−5.86034			−0.319708
$337$	4.88571			0.266142			0.133071	−	0.991107i	$-0.457516\pi$
$337$	4.88571			0.266142			0.133071	+	0.991107i	$0.457516\pi$
$338$	−13.9574			−0.759184
$339$			14.4134i			0.782831i
$340$			6.01052i			0.325966i
$341$		−	19.3687i		−	1.04887i
$342$		−	6.51138i		−	0.352095i
$343$		−	1.00000i		−	0.0539949i
$344$	8.26434			0.445584
$345$		−	8.50360i		−	0.457819i
$346$	−25.0094			−1.34451
$347$			26.2594i			1.40968i	0.709366	+	0.704840i	$0.248981\pi$
$347$			26.2594i			1.40968i	−0.709366	+	0.704840i	$0.751019\pi$
$348$	−15.1640			−0.812874
$349$	−13.5693			−0.726348			−0.363174	−	0.931721i	$-0.618307\pi$
$349$	−13.5693			−0.726348			−0.363174	+	0.931721i	$0.618307\pi$
$350$			7.50064i			0.400926i
$351$	−12.6174			−0.673468
$352$		−	14.9777i		−	0.798314i
$353$	6.45322			0.343470			0.171735	−	0.985143i	$-0.445063\pi$
$353$	6.45322			0.343470			0.171735	+	0.985143i	$0.445063\pi$
$354$			28.9005i			1.53604i
$355$		−	7.80299i		−	0.414140i
$356$			0.0937406i			0.00496824i
$357$		−	5.83700i		−	0.308927i
$358$		−	26.7567i		−	1.41413i
$359$	−25.7558			−1.35934			−0.679671	−	0.733518i	$-0.737877\pi$
$359$	−25.7558			−1.35934			−0.679671	+	0.733518i	$0.737877\pi$
$360$	−1.84182			−0.0970725
$361$	13.8134			0.727023
$362$		−	28.7526i		−	1.51121i
$363$		−	6.64641i		−	0.348846i
$364$	3.03165			0.158901
$365$	1.07262			0.0561433
$366$		−	3.90001i		−	0.203857i
$367$	−30.7700			−1.60618			−0.803091	−	0.595857i	$-0.796813\pi$
$367$	−30.7700			−1.60618			−0.803091	+	0.595857i	$0.796813\pi$
$368$	37.1893			1.93863
$369$	−9.38213	−	3.62518i	−0.488414	−	0.188719i
$370$	−3.62779			−0.188600
$371$	−9.55570			−0.496107
$372$		−	13.0339i		−	0.675774i
$373$	34.9502			1.80966			0.904828	−	0.425778i	$-0.140000\pi$
$373$	34.9502			1.80966			0.904828	+	0.425778i	$0.140000\pi$
$374$	20.7285			1.07185
$375$		−	10.2236i		−	0.527942i
$376$		−	16.7348i		−	0.863031i
$377$	−22.3078			−1.14891
$378$	−9.94591			−0.511562
$379$	−8.50864			−0.437059			−0.218530	−	0.975830i	$-0.570126\pi$
$379$	−8.50864			−0.437059			−0.218530	+	0.975830i	$0.570126\pi$
$380$		−	2.80353i		−	0.143818i
$381$			3.38631i			0.173486i
$382$			17.9460i			0.918198i
$383$			22.9320i			1.17177i	0.810393	+	0.585886i	$0.199253\pi$
$383$			22.9320i			1.17177i	−0.810393	+	0.585886i	$0.800747\pi$
$384$			11.2544i			0.574322i
$385$	−2.18694			−0.111457
$386$			13.9686i			0.710981i
$387$	10.3809			0.527689
$388$		−	19.2827i		−	0.978928i
$389$	3.44954			0.174899			0.0874494	−	0.996169i	$-0.472128\pi$
$389$	3.44954			0.174899			0.0874494	+	0.996169i	$0.472128\pi$
$390$	−4.71091			−0.238546
$391$			37.0412i			1.87325i
$392$	−1.25055			−0.0631622
$393$		−	12.1865i		−	0.614729i
$394$	35.0998			1.76830
$395$		−	11.7065i		−	0.589019i
$396$		−	4.81046i		−	0.241735i
$397$			10.8052i			0.542297i	0.962538	+	0.271148i	$0.0874034\pi$
$397$			10.8052i			0.542297i	−0.962538	+	0.271148i	$0.912597\pi$
$398$			6.29050i			0.315314i
$399$			2.72260i			0.136300i
$400$	20.2009			1.01004
$401$	−3.79370			−0.189448			−0.0947242	−	0.995504i	$-0.530197\pi$
$401$	−3.79370			−0.189448			−0.0947242	+	0.995504i	$0.530197\pi$
$402$	2.53442			0.126405
$403$		−	19.1742i		−	0.955135i
$404$			6.62007i			0.329361i
$405$	1.70651			0.0847973
$406$	−17.5845			−0.872706
$407$			4.95827i			0.245772i
$408$	−7.29945			−0.361377
$409$	7.68463			0.379980			0.189990	−	0.981786i	$-0.439154\pi$
$409$	7.68463			0.379980			0.189990	+	0.981786i	$0.439154\pi$
$410$	−10.1930	−	3.93851i	−0.503398	−	0.194509i
$411$	−22.6968			−1.11955
$412$	−1.91447			−0.0943192
$413$			13.2817i			0.653552i
$414$	21.6906			1.06603
$415$	0.272825			0.0133924
$416$		−	14.8273i		−	0.726969i
$417$		−	5.55981i		−	0.272265i
$418$	−9.66857			−0.472905
$419$	−27.2833			−1.33288			−0.666439	−	0.745560i	$-0.732182\pi$
$419$	−27.2833			−1.33288			−0.666439	+	0.745560i	$0.732182\pi$
$420$	−1.47167			−0.0718100
$421$			20.8419i			1.01577i	0.861425	+	0.507885i	$0.169573\pi$
$421$			20.8419i			1.01577i	−0.861425	+	0.507885i	$0.830427\pi$
$422$			14.6150i			0.711447i
$423$		−	21.0206i		−	1.02206i
$424$			11.9499i			0.580337i
$425$			20.1204i			0.975985i
$426$	−18.1089			−0.877377
$427$		−	1.79232i		−	0.0867364i
$428$	4.89827			0.236767
$429$			6.43861i			0.310859i
$430$	11.2781			0.543878
$431$	6.10275			0.293959			0.146980	−	0.989140i	$-0.453045\pi$
$431$	6.10275			0.293959			0.146980	+	0.989140i	$0.453045\pi$
$432$			26.7866i			1.28877i
$433$	0.977143			0.0469585			0.0234793	−	0.999724i	$-0.492526\pi$
$433$	0.977143			0.0469585			0.0234793	+	0.999724i	$0.492526\pi$
$434$		−	15.1144i		−	0.725515i
$435$	10.8290			0.519211
$436$		−	2.61246i		−	0.125114i
$437$		−	17.2774i		−	0.826490i
$438$		−	2.48928i		−	0.118942i
$439$			2.76440i			0.131938i	0.997822	+	0.0659689i	$0.0210138\pi$
$439$			2.76440i			0.131938i	−0.997822	+	0.0659689i	$0.978986\pi$
$440$			2.73487i			0.130380i
$441$	−1.57082			−0.0748009
$442$	20.5204			0.976056
$443$	6.61647			0.314358			0.157179	−	0.987570i	$-0.449760\pi$
$443$	6.61647			0.314358			0.157179	+	0.987570i	$0.449760\pi$
$444$			3.33660i			0.158348i
$445$		−	0.0669426i		−	0.00317339i
$446$	−20.1921			−0.956124
$447$	17.6220			0.833490
$448$		−	1.88376i		−	0.0889993i
$449$	32.3671			1.52750			0.763749	−	0.645514i	$-0.223357\pi$
$449$	32.3671			1.52750			0.763749	+	0.645514i	$0.223357\pi$
$450$	11.7821			0.555416
$451$	−5.38294	+	13.9313i	−0.253473	+	0.655998i
$452$	−15.8296			−0.744561
$453$	13.1846			0.619466
$454$		−	42.9776i		−	2.01704i
$455$	−2.16498			−0.101496
$456$	3.40474			0.159442
$457$		−	7.90120i		−	0.369603i	−0.982776	−	0.184801i	$-0.940836\pi$
$457$		−	7.90120i		−	0.369603i	0.982776	−	0.184801i	$-0.0591642\pi$
$458$			24.4999i			1.14480i
$459$	−26.6799			−1.24531
$460$	9.33910			0.435438
$461$	18.9274			0.881535			0.440767	−	0.897621i	$-0.354706\pi$
$461$	18.9274			0.881535			0.440767	+	0.897621i	$0.354706\pi$
$462$			5.07535i			0.236127i
$463$		−	17.7538i		−	0.825089i	−0.910937	−	0.412545i	$-0.864640\pi$
$463$		−	17.7538i		−	0.825089i	0.910937	−	0.412545i	$-0.135360\pi$
$464$			47.3591i			2.19859i
$465$			9.30783i			0.431640i
$466$		−	45.8959i		−	2.12609i
$467$	15.1772			0.702317			0.351159	−	0.936316i	$-0.385788\pi$
$467$	15.1772			0.702317			0.351159	+	0.936316i	$0.385788\pi$
$468$		−	4.76217i		−	0.220131i
$469$	1.16474			0.0537825
$470$		−	22.8374i		−	1.05341i
$471$	3.41347			0.157285
$472$	16.6095			0.764512
$473$		−	15.4143i		−	0.708750i
$474$	−27.1680			−1.24787
$475$		−	9.38493i		−	0.430610i
$476$	6.41049			0.293824
$477$			15.0103i			0.687273i
$478$		−	40.7901i		−	1.86570i
$479$		−	1.86529i		−	0.0852273i	−0.999092	−	0.0426137i	$-0.986432\pi$
$479$		−	1.86529i		−	0.0852273i	0.999092	−	0.0426137i	$-0.0135685\pi$
$480$			7.19770i			0.328529i
$481$			4.90849i			0.223808i
$482$	52.0797			2.37217
$483$	−9.06948			−0.412676
$484$	7.29943			0.331792
$485$			13.7703i			0.625275i
$486$			25.8773i			1.17382i
$487$	8.56289			0.388021			0.194011	−	0.980999i	$-0.437850\pi$
$487$	8.56289			0.388021			0.194011	+	0.980999i	$0.437850\pi$
$488$	−2.24138			−0.101463
$489$		−	3.52315i		−	0.159323i
$490$	−1.70658			−0.0770956
$491$	−5.69438			−0.256984			−0.128492	−	0.991711i	$-0.541014\pi$
$491$	−5.69438			−0.256984			−0.128492	+	0.991711i	$0.541014\pi$
$492$	−3.62237	+	9.37485i	−0.163309	+	0.422651i
$493$	−47.1704			−2.12445
$494$	−9.57150			−0.430642
$495$			3.43528i			0.154404i
$496$	−40.7065			−1.82777
$497$	−8.32224			−0.373304
$498$		−	0.633160i		−	0.0283726i
$499$		−	14.5387i		−	0.650844i	−0.945569	−	0.325422i	$-0.894494\pi$
$499$		−	14.5387i		−	0.650844i	0.945569	−	0.325422i	$-0.105506\pi$
$500$	11.2280			0.502133
$501$	7.65168			0.341852
$502$	−21.2794			−0.949745
$503$			21.8410i			0.973841i	0.873446	+	0.486920i	$0.161880\pi$
$503$			21.8410i			0.973841i	−0.873446	+	0.486920i	$0.838120\pi$
$504$			1.96438i			0.0875007i
$505$		−	4.72757i		−	0.210374i
$506$		−	32.2078i		−	1.43181i
$507$		−	9.16732i		−	0.407135i
$508$	−3.71902			−0.165005
$509$			5.03857i			0.223331i	0.993746	+	0.111665i	$0.0356185\pi$
$509$			5.03857i			0.223331i	−0.993746	+	0.111665i	$0.964382\pi$
$510$	−9.96133			−0.441095
$511$		−	1.14399i		−	0.0506073i
$512$	−19.2176			−0.849305
$513$	12.4445			0.549438
$514$			19.7872i			0.872775i
$515$	1.36717			0.0602449
$516$		−	10.3728i		−	0.456638i
$517$	−31.2130			−1.37275
$518$			3.86920i			0.170003i
$519$		−	16.4263i		−	0.721034i
$520$			2.70741i			0.118728i
$521$		−	24.7886i		−	1.08601i	−0.839729	−	0.543005i	$-0.817286\pi$
$521$		−	24.7886i		−	1.08601i	0.839729	−	0.543005i	$-0.182714\pi$
$522$			27.6221i			1.20899i
$523$	−18.0795			−0.790563			−0.395282	−	0.918560i	$-0.629353\pi$
$523$	−18.0795			−0.790563			−0.395282	+	0.918560i	$0.629353\pi$
$524$	13.3839			0.584677
$525$	−4.92646			−0.215008
$526$		−	35.9072i		−	1.56563i
$527$		−	40.5443i		−	1.76614i
$528$	13.6691			0.594869
$529$	34.5542			1.50236
$530$			16.3076i			0.708357i
$531$	20.8632			0.905386
$532$	−2.99010			−0.129637
$533$	−5.32889	+	13.7914i	−0.230820	+	0.597372i
$534$	−0.155358			−0.00672298
$535$	−3.49799			−0.151231
$536$		−	1.45656i		−	0.0629138i
$537$	17.5739			0.758370
$538$	−27.2765			−1.17598
$539$			2.33247i			0.100466i
$540$			6.72673i			0.289472i
$541$	8.42139			0.362064			0.181032	−	0.983477i	$-0.442056\pi$
$541$	8.42139			0.362064			0.181032	+	0.983477i	$0.442056\pi$
$542$	−26.3207			−1.13057
$543$	18.8849			0.810429
$544$		−	31.3527i		−	1.34424i
$545$			1.86563i			0.0799148i
$546$			5.02439i			0.215024i
$547$		−	28.1209i		−	1.20236i	−0.799113	−	0.601181i	$-0.794697\pi$
$547$		−	28.1209i		−	1.20236i	0.799113	−	0.601181i	$-0.205303\pi$
$548$		−	24.9268i		−	1.06482i
$549$	−2.81541			−0.120159
$550$		−	17.4950i		−	0.745989i
$551$	22.0021			0.937320
$552$			11.3418i			0.482740i
$553$	−12.4855			−0.530939
$554$	4.00763			0.170268
$555$		−	2.38275i		−	0.101142i
$556$	6.10607			0.258955
$557$		−	17.3905i		−	0.736858i	−0.929656	−	0.368429i	$-0.879896\pi$
$557$		−	17.3905i		−	0.736858i	0.929656	−	0.368429i	$-0.120104\pi$
$558$	−23.7420			−1.00508
$559$		−	15.2595i		−	0.645409i
$560$			4.59621i			0.194225i
$561$			13.6146i			0.574809i
$562$			38.5691i			1.62694i
$563$			25.0817i			1.05707i	0.848913	+	0.528533i	$0.177258\pi$
$563$			25.0817i			1.05707i	−0.848913	+	0.528533i	$0.822742\pi$
$564$	−21.0043			−0.884442
$565$	11.3043			0.475577
$566$	1.95468			0.0821612
$567$		−	1.82007i		−	0.0764359i
$568$			10.4074i			0.436684i
$569$	−29.2064			−1.22440			−0.612198	−	0.790704i	$-0.709715\pi$
$569$	−29.2064			−1.22440			−0.612198	+	0.790704i	$0.709715\pi$
$570$	4.64634			0.194614
$571$		−	14.9807i		−	0.626923i	−0.949601	−	0.313462i	$-0.898511\pi$
$571$		−	14.9807i		−	0.626923i	0.949601	−	0.313462i	$-0.101489\pi$
$572$	−7.07122			−0.295662
$573$	−11.7870			−0.492411
$574$	−4.20059	+	10.8713i	−0.175329	+	0.453760i
$575$	31.2630			1.30376
$576$	−2.95905			−0.123294
$577$			12.0906i			0.503339i	0.967813	+	0.251669i	$0.0809795\pi$
$577$			12.0906i			0.503339i	−0.967813	+	0.251669i	$0.919020\pi$
$578$	12.4484			0.517785
$579$	−9.17463			−0.381284
$580$			11.8930i			0.493828i
$581$		−	0.290980i		−	0.0120719i
$582$	31.9574			1.32468
$583$	22.2884			0.923090
$584$	−1.43062			−0.0591994
$585$			3.40079i			0.140605i
$586$			50.8579i			2.10092i
$587$			3.46543i			0.143033i	0.997439	+	0.0715167i	$0.0227839\pi$
$587$			3.46543i			0.143033i	−0.997439	+	0.0715167i	$0.977216\pi$
$588$			1.56960i			0.0647292i
$589$			18.9114i			0.779231i
$590$	22.6664			0.933161
$591$			23.0537i			0.948304i
$592$	10.4206			0.428285
$593$		−	12.0771i		−	0.495948i	−0.968767	−	0.247974i	$-0.920235\pi$
$593$		−	12.0771i		−	0.495948i	0.968767	−	0.247974i	$-0.0797648\pi$
$594$	23.1985			0.951846
$595$	−4.57790			−0.187676
$596$			19.3533i			0.792744i
$597$	−4.13163			−0.169097
$598$		−	31.8844i		−	1.30385i
$599$	−28.9094			−1.18120			−0.590602	−	0.806963i	$-0.701110\pi$
$599$	−28.9094			−1.18120			−0.590602	+	0.806963i	$0.701110\pi$
$600$			6.16078i			0.251513i
$601$		−	20.6898i		−	0.843955i	−0.906606	−	0.421978i	$-0.861336\pi$
$601$		−	20.6898i		−	0.843955i	0.906606	−	0.421978i	$-0.138664\pi$
$602$		−	12.0286i		−	0.490249i
$603$		−	1.82959i		−	0.0745067i
$604$			14.4800i			0.589183i
$605$	−5.21272			−0.211927
$606$	−10.9715			−0.445689
$607$	−7.53009			−0.305637			−0.152818	−	0.988254i	$-0.548835\pi$
$607$	−7.53009			−0.305637			−0.152818	+	0.988254i	$0.548835\pi$
$608$			14.6241i			0.593086i
$609$		−	11.5496i		−	0.468014i
$610$	−3.05874			−0.123845
$611$	−30.8996			−1.25006
$612$		−	10.0697i		−	0.407044i
$613$	26.9328			1.08780			0.543902	−	0.839149i	$-0.316946\pi$
$613$	26.9328			1.08780			0.543902	+	0.839149i	$0.316946\pi$
$614$	−58.1742			−2.34772
$615$	2.58683	−	6.69483i	0.104311	−	0.269962i
$616$	2.91686			0.117524
$617$	−30.6580			−1.23424			−0.617122	−	0.786868i	$-0.711701\pi$
$617$	−30.6580			−1.23424			−0.617122	+	0.786868i	$0.711701\pi$
$618$		−	3.17288i		−	0.127632i
$619$	35.6330			1.43221			0.716105	−	0.697993i	$-0.245923\pi$
$619$	35.6330			1.43221			0.716105	+	0.697993i	$0.245923\pi$
$620$	−10.2223			−0.410539
$621$			41.4549i			1.66353i
$622$			22.4929i			0.901882i
$623$	−0.0713974			−0.00286047
$624$	13.5318			0.541706
$625$	12.5862			0.503449
$626$		−	11.8992i		−	0.475588i
$627$		−	6.35037i		−	0.253609i
$628$			3.74885i			0.149595i
$629$			10.3791i			0.413843i
$630$			2.68073i			0.106803i
$631$	8.52903			0.339535			0.169768	−	0.985484i	$-0.445698\pi$
$631$	8.52903			0.339535			0.169768	+	0.985484i	$0.445698\pi$
$632$			15.6138i			0.621082i
$633$	−9.59922			−0.381535
$634$			6.30007i			0.250208i
$635$	2.65585			0.105394
$636$	14.9986			0.594735
$637$			2.30905i			0.0914878i
$638$	41.0153			1.62381
$639$			13.0727i			0.517149i
$640$	8.82669			0.348906
$641$		−	6.03487i		−	0.238363i	−0.992872	−	0.119181i	$-0.961973\pi$
$641$		−	6.03487i		−	0.238363i	0.992872	−	0.119181i	$-0.0380270\pi$
$642$			8.11798i			0.320391i
$643$			21.8451i			0.861485i	0.902475	+	0.430743i	$0.141748\pi$
$643$			21.8451i			0.861485i	−0.902475	+	0.430743i	$0.858252\pi$
$644$		−	9.96057i		−	0.392501i
$645$			7.40751i			0.291670i
$646$	−20.2392			−0.796299
$647$	41.5133			1.63206			0.816028	−	0.578013i	$-0.196172\pi$
$647$	41.5133			1.63206			0.816028	+	0.578013i	$0.196172\pi$
$648$	−2.27609			−0.0894132
$649$		−	30.9792i		−	1.21604i
$650$		−	17.3193i		−	0.679320i
$651$	9.92722			0.389079
$652$	3.86931			0.151534
$653$			3.53910i			0.138496i	0.997599	+	0.0692478i	$0.0220599\pi$
$653$			3.53910i			0.138496i	−0.997599	+	0.0692478i	$0.977940\pi$
$654$	4.32967			0.169304
$655$	−9.55778			−0.373453
$656$	29.2789	+	11.3131i	1.14315	+	0.441704i
$657$	−1.79701			−0.0701079
$658$	−24.3572			−0.949541
$659$		−	39.8348i		−	1.55175i	−0.630890	−	0.775873i	$-0.717310\pi$
$659$		−	39.8348i		−	1.55175i	0.630890	−	0.775873i	$-0.282690\pi$
$660$	3.43262			0.133614
$661$	−39.3973			−1.53238			−0.766188	−	0.642616i	$-0.777849\pi$
$661$	−39.3973			−1.53238			−0.766188	+	0.642616i	$0.777849\pi$
$662$			55.5998i			2.16095i
$663$			13.4779i			0.523439i
$664$	−0.363884			−0.0141214
$665$	2.13531			0.0828037
$666$	6.07782			0.235511
$667$			73.2930i			2.83792i
$668$			8.40347i			0.325140i
$669$		−	13.2623i		−	0.512750i
$670$		−	1.98772i		−	0.0767924i
$671$			4.18053i			0.161387i
$672$	7.67667			0.296134
$673$			18.9410i			0.730121i	0.930984	+	0.365061i	$0.118952\pi$
$673$			18.9410i			0.730121i	−0.930984	+	0.365061i	$0.881048\pi$
$674$	−8.89272			−0.342535
$675$			22.5180i			0.866717i
$676$	10.0680			0.387232
$677$	−37.1240			−1.42679			−0.713396	−	0.700761i	$-0.752844\pi$
$677$	−37.1240			−1.42679			−0.713396	+	0.700761i	$0.752844\pi$
$678$		−	26.2346i		−	1.00753i
$679$	14.6866			0.563620
$680$			5.72489i			0.219540i
$681$	28.2279			1.08170
$682$			35.2538i			1.34994i
$683$		−	40.4726i		−	1.54864i	−0.632793	−	0.774321i	$-0.718092\pi$
$683$		−	40.4726i		−	1.54864i	0.632793	−	0.774321i	$-0.281908\pi$
$684$			4.69690i			0.179590i
$685$			17.8009i			0.680138i
$686$			1.82015i			0.0694936i
$687$	−16.0917			−0.613935
$688$	−32.3957			−1.23507
$689$	22.0646			0.840594
$690$			15.4778i			0.589231i
$691$		−	25.7152i		−	0.978254i	−0.872213	−	0.489127i	$-0.837315\pi$
$691$		−	25.7152i		−	0.978254i	0.872213	−	0.489127i	$-0.162685\pi$
$692$	18.0402			0.685785
$693$	3.66388			0.139179
$694$		−	47.7961i		−	1.81431i
$695$	−4.36051			−0.165404
$696$	−14.4434			−0.547474
$697$	−11.2681	+	29.1623i	−0.426809	+	1.10460i
$698$	24.6981			0.934839
$699$	30.1447			1.14018
$700$		−	5.41049i		−	0.204497i
$701$	4.87633			0.184176			0.0920881	−	0.995751i	$-0.470646\pi$
$701$	4.87633			0.184176			0.0920881	+	0.995751i	$0.470646\pi$
$702$	22.9656			0.866780
$703$		−	4.84122i		−	0.182590i
$704$			4.39381i			0.165598i
$705$	14.9998			0.564924
$706$	−11.7458			−0.442060
$707$	−5.04217			−0.189630
$708$		−	20.8470i		−	0.783479i
$709$		−	35.3974i		−	1.32938i	−0.747120	−	0.664689i	$-0.768564\pi$
$709$		−	35.3974i		−	1.32938i	0.747120	−	0.664689i	$-0.231436\pi$
$710$			14.2026i			0.533014i
$711$			19.6125i			0.735526i
$712$			0.0892858i			0.00334613i
$713$	−62.9974			−2.35927
$714$			10.6242i			0.397601i
$715$	5.04974			0.188850
$716$			19.3006i			0.721296i
$717$	26.7912			1.00053
$718$	46.8795			1.74953
$719$		−	27.1522i		−	1.01261i	−0.862356	−	0.506303i	$-0.831012\pi$
$719$		−	27.1522i		−	1.01261i	0.862356	−	0.506303i	$-0.168988\pi$
$720$	7.21981			0.269067
$721$		−	1.45815i		−	0.0543045i
$722$	−25.1425			−0.935707
$723$			34.2063i			1.27214i
$724$			20.7404i			0.770810i
$725$			39.8121i			1.47859i
$726$			12.0975i			0.448979i
$727$		−	49.6187i		−	1.84026i	−0.391617	−	0.920128i	$-0.628084\pi$
$727$		−	49.6187i		−	1.84026i	0.391617	−	0.920128i	$-0.371916\pi$
$728$	2.88758			0.107021
$729$	−22.4566			−0.831726
$730$	−1.95232			−0.0722586
$731$		−	32.2666i		−	1.19343i
$732$			2.81323i			0.103980i
$733$	32.7509			1.20968			0.604840	−	0.796347i	$-0.293237\pi$
$733$	32.7509			1.20968			0.604840	+	0.796347i	$0.293237\pi$
$734$	56.0060			2.06722
$735$		−	1.12089i		−	0.0413448i
$736$	−48.7156			−1.79568
$737$	−2.71671			−0.100071
$738$	17.0769	+	6.59837i	0.628608	+	0.242889i
$739$	−1.67619			−0.0616596			−0.0308298	−	0.999525i	$-0.509815\pi$
$739$	−1.67619			−0.0616596			−0.0308298	+	0.999525i	$0.509815\pi$
$740$	2.61686			0.0961977
$741$		−	6.28661i		−	0.230944i
$742$	17.3928			0.638510
$743$	15.2968			0.561184			0.280592	−	0.959827i	$-0.409469\pi$
$743$	15.2968			0.561184			0.280592	+	0.959827i	$0.409469\pi$
$744$		−	12.4145i		−	0.455137i
$745$		−	13.8207i		−	0.506353i
$746$	−63.6146			−2.32910
$747$	−0.457076			−0.0167235
$748$	−14.9523			−0.546709
$749$			3.73076i			0.136319i
$750$			18.6084i			0.679482i
$751$		−	9.10267i		−	0.332161i	−0.986112	−	0.166081i	$-0.946889\pi$
$751$		−	9.10267i		−	0.332161i	0.986112	−	0.166081i	$-0.0531112\pi$
$752$			65.5993i			2.39216i
$753$		−	13.9764i		−	0.509329i
$754$	40.6035			1.47869
$755$		−	10.3406i		−	0.376331i
$756$	7.17436			0.260929
$757$			35.1479i			1.27747i	0.769426	+	0.638736i	$0.220542\pi$
$757$			35.1479i			1.27747i	−0.769426	+	0.638736i	$0.779458\pi$
$758$	15.4870			0.562513
$759$	21.1543			0.767851
$760$		−	2.67031i		−	0.0968622i
$761$	−5.76585			−0.209012			−0.104506	−	0.994524i	$-0.533326\pi$
$761$	−5.76585			−0.209012			−0.104506	+	0.994524i	$0.533326\pi$
$762$		−	6.16359i		−	0.223283i
$763$	1.98978			0.0720348
$764$		−	12.9451i		−	0.468339i
$765$			7.19106i			0.259993i
$766$		−	41.7397i		−	1.50812i
$767$		−	30.6682i		−	1.10736i
$768$		−	24.9886i		−	0.901699i
$769$	34.6186			1.24838			0.624190	−	0.781272i	$-0.285429\pi$
$769$	34.6186			1.24838			0.624190	+	0.781272i	$0.285429\pi$
$770$	3.98055			0.143449
$771$	−12.9963			−0.468051
$772$		−	10.0760i		−	0.362645i
$773$		−	2.08795i		−	0.0750983i	−0.999295	−	0.0375491i	$-0.988045\pi$
$773$		−	2.08795i		−	0.0750983i	0.999295	−	0.0375491i	$-0.0119551\pi$
$774$	−18.8947			−0.679157
$775$	−34.2196			−1.22921
$776$		−	18.3663i		−	0.659312i
$777$	−2.54131			−0.0911691
$778$	−6.27868			−0.225102
$779$	5.25586	−	13.6024i	0.188311	−	0.487356i
$780$	3.39815			0.121673
$781$	19.4114			0.694593
$782$		−	67.4204i		−	2.41095i
$783$	−52.7912			−1.88660
$784$	4.90207			0.175074
$785$		−	2.67715i		−	0.0955518i
$786$			22.1813i			0.791181i
$787$	−10.7537			−0.383328			−0.191664	−	0.981461i	$-0.561388\pi$
$787$	−10.7537			−0.383328			−0.191664	+	0.981461i	$0.561388\pi$
$788$	−25.3188			−0.901945
$789$	23.5841			0.839615
$790$			21.3076i			0.758090i
$791$		−	12.0566i		−	0.428683i
$792$		−	4.58186i		−	0.162809i
$793$			4.13855i			0.146964i
$794$		−	19.6670i		−	0.697957i
$795$	−10.7109			−0.379877
$796$		−	4.53757i		−	0.160830i
$797$	−18.3959			−0.651617			−0.325808	−	0.945436i	$-0.605636\pi$
$797$	−18.3959			−0.651617			−0.325808	+	0.945436i	$0.605636\pi$
$798$		−	4.95553i		−	0.175424i
$799$	−65.3380			−2.31149
$800$	−26.4619			−0.935569
$801$			0.112152i			0.00396271i
$802$	6.90510			0.243827
$803$			2.66833i			0.0941632i
$804$	−1.82817			−0.0644746
$805$			7.11311i			0.250704i
$806$			34.8999i			1.22930i
$807$		−	17.9154i		−	0.630651i
$808$			6.30547i			0.221826i
$809$			25.2770i			0.888693i	0.895855	+	0.444346i	$0.146564\pi$
$809$			25.2770i			0.888693i	−0.895855	+	0.444346i	$0.853436\pi$
$810$	−3.10611			−0.109137
$811$	13.2480			0.465201			0.232600	−	0.972572i	$-0.425277\pi$
$811$	13.2480			0.465201			0.232600	+	0.972572i	$0.425277\pi$
$812$	12.6844			0.445135
$813$		−	17.2876i		−	0.606301i
$814$		−	9.02479i		−	0.316319i
$815$	−2.76318			−0.0967899
$816$	28.6134			1.00167
$817$			15.0504i			0.526546i
$818$	−13.9872			−0.489050
$819$	3.62710			0.126741
$820$	7.35261	+	2.84099i	0.256764	+	0.0992118i
$821$	19.2282			0.671068			0.335534	−	0.942028i	$-0.391083\pi$
$821$	19.2282			0.671068			0.335534	+	0.942028i	$0.391083\pi$
$822$	41.3116			1.44091
$823$			31.2772i			1.09026i	0.838353	+	0.545128i	$0.183519\pi$
$823$			31.2772i			1.09026i	−0.838353	+	0.545128i	$0.816481\pi$
$824$	−1.82349			−0.0635243
$825$	11.4908			0.400059
$826$		−	24.1747i		−	0.841147i
$827$			5.38962i			0.187415i	0.995600	+	0.0937077i	$0.0298719\pi$
$827$			5.38962i			0.187415i	−0.995600	+	0.0937077i	$0.970128\pi$
$828$	−15.6462			−0.543745
$829$	−34.4671			−1.19709			−0.598546	−	0.801088i	$-0.704255\pi$
$829$	−34.4671			−1.19709			−0.598546	+	0.801088i	$0.704255\pi$
$830$	−0.496581			−0.0172366
$831$			2.63223i			0.0913111i
$832$			4.34969i			0.150799i
$833$			4.88254i			0.169170i
$834$			10.1197i			0.350416i
$835$		−	6.00114i		−	0.207678i
$836$	6.97430			0.241211
$837$		−	45.3755i		−	1.56841i
$838$	49.6597			1.71547
$839$		−	19.1836i		−	0.662293i	−0.943579	−	0.331146i	$-0.892565\pi$
$839$		−	19.1836i		−	0.662293i	0.943579	−	0.331146i	$-0.107435\pi$
$840$	−1.40173			−0.0483643
$841$	−64.3357			−2.21847
$842$		−	37.9353i		−	1.30734i
$843$	−25.3324			−0.872494
$844$		−	10.5424i		−	0.362883i
$845$	−7.18984			−0.247338
$846$			38.2607i			1.31543i
$847$			5.55960i			0.191030i
$848$		−	46.8427i		−	1.60859i
$849$			1.28384i			0.0440613i
$850$		−	36.6222i		−	1.25613i
$851$	16.1270			0.552826
$852$	13.0626			0.447517
$853$	3.83248			0.131222			0.0656108	−	0.997845i	$-0.479100\pi$
$853$	3.83248			0.131222			0.0656108	+	0.997845i	$0.479100\pi$
$854$			3.26229i			0.111633i
$855$		−	3.35418i		−	0.114711i
$856$	4.66550			0.159464
$857$	−31.3869			−1.07216			−0.536078	−	0.844168i	$-0.680095\pi$
$857$	−31.3869			−1.07216			−0.536078	+	0.844168i	$0.680095\pi$
$858$		−	11.7192i		−	0.400088i
$859$	−9.51209			−0.324548			−0.162274	−	0.986746i	$-0.551883\pi$
$859$	−9.51209			−0.324548			−0.162274	+	0.986746i	$0.551883\pi$
$860$	−8.13531			−0.277412
$861$	−7.14034	−	2.75897i	−0.243342	−	0.0940256i
$862$	−11.1079			−0.378337
$863$	−51.2795			−1.74558			−0.872788	−	0.488099i	$-0.837690\pi$
$863$	−51.2795			−1.74558			−0.872788	+	0.488099i	$0.837690\pi$
$864$		−	35.0887i		−	1.19374i
$865$	−12.8830			−0.438035
$866$	−1.77855			−0.0604375
$867$			8.17617i			0.277677i
$868$			10.9026i			0.370058i
$869$	29.1221			0.987899
$870$	−19.7104			−0.668245
$871$	−2.68943			−0.0911280
$872$		−	2.48831i		−	0.0842649i
$873$		−	23.0700i		−	0.780801i
$874$			31.4474i			1.06373i
$875$			8.55181i			0.289104i
$876$			1.79561i			0.0606681i
$877$	15.9177			0.537502			0.268751	−	0.963210i	$-0.413389\pi$
$877$	15.9177			0.537502			0.268751	+	0.963210i	$0.413389\pi$
$878$		−	5.03163i		−	0.169809i
$879$	−33.4038			−1.12668
$880$		−	10.7205i		−	0.361388i
$881$	−28.6068			−0.963789			−0.481894	−	0.876229i	$-0.660051\pi$
$881$	−28.6068			−0.963789			−0.481894	+	0.876229i	$0.660051\pi$
$882$	2.85912			0.0962717
$883$			31.3458i			1.05487i	0.849595	+	0.527435i	$0.176846\pi$
$883$			31.3458i			1.05487i	−0.849595	+	0.527435i	$0.823154\pi$
$884$	−14.8021			−0.497850
$885$			14.8874i			0.500435i
$886$	−12.0430			−0.404591
$887$		−	29.7275i		−	0.998152i	−0.866558	−	0.499076i	$-0.833673\pi$
$887$		−	29.7275i		−	0.998152i	0.866558	−	0.499076i	$-0.166327\pi$
$888$			3.17804i			0.106648i
$889$		−	2.83259i		−	0.0950020i
$890$			0.121846i			0.00408427i
$891$			4.24526i			0.142222i
$892$	14.5653			0.487683
$893$	30.4761			1.01984
$894$	−32.0746			−1.07274
$895$		−	13.7831i		−	0.460717i
$896$		−	9.41407i		−	0.314502i
$897$	20.9419			0.699229
$898$	−58.9129			−1.96595
$899$		−	80.2247i		−	2.67564i
$900$	−8.49890			−0.283297
$901$	46.6561			1.55434
$902$	9.79775	−	25.3570i	0.326229	−	0.844296i
$903$	7.90044			0.262910
$904$	−15.0773			−0.501465
$905$		−	14.8112i		−	0.492343i
$906$	−23.9979			−0.797277
$907$	14.0237			0.465648			0.232824	−	0.972519i	$-0.425203\pi$
$907$	14.0237			0.465648			0.232824	+	0.972519i	$0.425203\pi$
$908$			31.0014i			1.02882i
$909$			7.92033i			0.262701i
$910$	3.94059			0.130629
$911$	35.5457			1.17768			0.588841	−	0.808249i	$-0.299584\pi$
$911$	35.5457			1.17768			0.588841	+	0.808249i	$0.299584\pi$
$912$	−13.3464			−0.441942
$913$			0.678701i			0.0224617i
$914$			14.3814i			0.475693i
$915$		−	2.00900i		−	0.0664155i
$916$		−	17.6727i		−	0.583922i
$917$			10.1938i			0.336629i
$918$	48.5613			1.60276
$919$		−	23.0349i		−	0.759851i	−0.925017	−	0.379925i	$-0.875950\pi$
$919$		−	23.0349i		−	0.759851i	0.925017	−	0.379925i	$-0.124050\pi$
$920$	8.89529			0.293269
$921$		−	38.2091i		−	1.25903i
$922$	−34.4506			−1.13457
$923$	19.2165			0.632518
$924$		−	3.66104i		−	0.120439i
$925$	8.76004			0.288028
$926$			32.3146i			1.06192i
$927$	−2.29049			−0.0752297
$928$		−	62.0374i		−	2.03648i
$929$		−	35.7781i		−	1.17384i	−0.809645	−	0.586920i	$-0.800340\pi$
$929$		−	35.7781i		−	1.17384i	0.809645	−	0.586920i	$-0.199660\pi$
$930$		−	16.9416i		−	0.555538i
$931$		−	2.27740i		−	0.0746389i
$932$			33.1064i			1.08444i
$933$	−14.7734			−0.483661
$934$	−27.6248			−0.903910
$935$	10.6778			0.349202
$936$		−	4.53586i		−	0.148259i
$937$			7.38107i			0.241129i	0.992705	+	0.120565i	$0.0384705\pi$
$937$			7.38107i			0.241129i	−0.992705	+	0.120565i	$0.961530\pi$
$938$	−2.11999			−0.0692203
$939$	7.81547			0.255048
$940$			16.4735i			0.537306i
$941$	−16.7224			−0.545134			−0.272567	−	0.962137i	$-0.587873\pi$
$941$	−16.7224			−0.545134			−0.272567	+	0.962137i	$0.587873\pi$
$942$	−6.21303			−0.202431
$943$	45.3121	+	17.5082i	1.47556	+	0.570147i
$944$	−65.1080			−2.11908
$945$	−5.12340			−0.166664
$946$			28.0563i			0.912189i
$947$	37.6950			1.22492			0.612461	−	0.790501i	$-0.290180\pi$
$947$	37.6950			1.22492			0.612461	+	0.790501i	$0.290180\pi$
$948$	19.5973			0.636490
$949$			2.64154i			0.0857479i
$950$			17.0820i			0.554212i
$951$	−4.13792			−0.134181
$952$	6.10586			0.197892
$953$	−37.7872			−1.22405			−0.612025	−	0.790839i	$-0.709645\pi$
$953$	−37.7872			−1.22405			−0.612025	+	0.790839i	$0.709645\pi$
$954$		−	27.3209i		−	0.884548i
$955$			9.24447i			0.299144i
$956$			29.4234i			0.951622i
$957$			26.9391i			0.870818i
$958$			3.39511i			0.109691i
$959$	18.9855			0.613073
$960$		−	2.11149i		−	0.0681482i
$961$	37.9554			1.22437
$962$		−	8.93418i		−	0.288049i
$963$	5.86035			0.188847
$964$	−37.5671			−1.20995
$965$			7.19557i			0.231634i
$966$	16.5078			0.531130
$967$			23.1053i			0.743016i	0.928430	+	0.371508i	$0.121159\pi$
$967$			23.1053i			0.743016i	−0.928430	+	0.371508i	$0.878841\pi$
$968$	6.95255			0.223463
$969$		−	13.2932i		−	0.427039i
$970$		−	25.0639i		−	0.804754i
$971$			32.4612i			1.04173i	0.853639	+	0.520865i	$0.174391\pi$
$971$			32.4612i			1.04173i	−0.853639	+	0.520865i	$0.825609\pi$
$972$		−	18.6663i		−	0.598722i
$973$			4.65068i			0.149094i
$974$	−15.5857			−0.499399
$975$	11.3754			0.364306
$976$	8.78607			0.281235
$977$		−	30.2559i		−	0.967973i	−0.875075	−	0.483987i	$-0.839188\pi$
$977$		−	30.2559i		−	0.967973i	0.875075	−	0.483987i	$-0.160812\pi$
$978$			6.41266i			0.205054i
$979$	0.166532			0.00532239
$980$	1.23102			0.0393236
$981$		−	3.12558i		−	0.0997921i
$982$	10.3646			0.330748
$983$	4.91654			0.156813			0.0784066	−	0.996921i	$-0.475017\pi$
$983$	4.91654			0.156813			0.0784066	+	0.996921i	$0.475017\pi$
$984$	−3.45023	+	8.92934i	−0.109989	+	0.284657i
$985$	18.0808			0.576103
$986$	85.8572			2.73425
$987$		−	15.9979i		−	0.509219i
$988$	6.90428			0.219654
$989$	−50.1356			−1.59422
$990$		−	6.25272i		−	0.198725i
$991$		−	16.9220i		−	0.537545i	−0.963204	−	0.268773i	$-0.913382\pi$
$991$		−	16.9220i		−	0.537545i	0.963204	−	0.268773i	$-0.0866180\pi$
$992$	53.3229			1.69300
$993$	−36.5183			−1.15887
$994$	15.1477			0.480457
$995$			3.24040i			0.102728i
$996$			0.456722i			0.0144718i
$997$			59.9506i			1.89865i	0.314289	+	0.949327i	$0.398234\pi$
$997$			59.9506i			1.89865i	−0.314289	+	0.949327i	$0.601766\pi$
$998$			26.4627i			0.837662i
$999$			11.6159i			0.367510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.c.a.204.1	✓	10
41.40	even	2	inner	287.2.c.a.204.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.c.a.204.1	✓	10	1.1	even	1	trivial
287.2.c.a.204.2	yes	10	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.82015 q^{2} -1.19548i q^{3} +1.31294 q^{4} -0.937607 q^{5} +2.17596i q^{6} +1.00000i q^{7} +1.25055 q^{8} +1.57082 q^{9} +O(q^{10})\)	\(q-1.82015 q^{2} -1.19548i q^{3} +1.31294 q^{4} -0.937607 q^{5} +2.17596i q^{6} +1.00000i q^{7} +1.25055 q^{8} +1.57082 q^{9} +1.70658 q^{10} -2.33247i q^{11} -1.56960i q^{12} -2.30905i q^{13} -1.82015i q^{14} +1.12089i q^{15} -4.90207 q^{16} -4.88254i q^{17} -2.85912 q^{18} +2.27740i q^{19} -1.23102 q^{20} +1.19548 q^{21} +4.24544i q^{22} -7.58645 q^{23} -1.49501i q^{24} -4.12089 q^{25} +4.20281i q^{26} -5.46434i q^{27} +1.31294i q^{28} -9.66104i q^{29} -2.04019i q^{30} +8.30394 q^{31} +6.42140 q^{32} -2.78843 q^{33} +8.88695i q^{34} -0.937607i q^{35} +2.06239 q^{36} -2.12576 q^{37} -4.14521i q^{38} -2.76043 q^{39} -1.17252 q^{40} +(-5.97276 - 2.30783i) q^{41} -2.17596 q^{42} +6.60858 q^{43} -3.06239i q^{44} -1.47281 q^{45} +13.8085 q^{46} -13.3820i q^{47} +5.86034i q^{48} -1.00000 q^{49} +7.50064 q^{50} -5.83700 q^{51} -3.03165i q^{52} +9.55570i q^{53} +9.94591i q^{54} +2.18694i q^{55} +1.25055i q^{56} +2.72260 q^{57} +17.5845i q^{58} +13.2817 q^{59} +1.47167i q^{60} -1.79232 q^{61} -15.1144 q^{62} +1.57082i q^{63} -1.88376 q^{64} +2.16498i q^{65} +5.07535 q^{66} -1.16474i q^{67} -6.41049i q^{68} +9.06948i q^{69} +1.70658i q^{70} +8.32224i q^{71} +1.96438 q^{72} -1.14399 q^{73} +3.86920 q^{74} +4.92646i q^{75} +2.99010i q^{76} +2.33247 q^{77} +5.02439 q^{78} +12.4855i q^{79} +4.59621 q^{80} -1.82007 q^{81} +(10.8713 + 4.20059i) q^{82} -0.290980 q^{83} +1.56960 q^{84} +4.57790i q^{85} -12.0286 q^{86} -11.5496 q^{87} -2.91686i q^{88} +0.0713974i q^{89} +2.68073 q^{90} +2.30905 q^{91} -9.96057 q^{92} -9.92722i q^{93} +24.3572i q^{94} -2.13531i q^{95} -7.67667i q^{96} -14.6866i q^{97} +1.82015 q^{98} -3.66388i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9	\( 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9} + 8 q^{10} - 16 q^{16} + 20 q^{18} - 22 q^{20} - 12 q^{21} - 4 q^{23} - 4 q^{25} + 14 q^{31} + 18 q^{32} - 2 q^{33} + 20 q^{36} - 22 q^{37} - 46 q^{39} - 58 q^{40} - 4 q^{41} - 8 q^{42} + 18 q^{43} + 50 q^{45} + 8 q^{46} - 10 q^{49} - 22 q^{50} + 14 q^{51} + 62 q^{57} + 34 q^{59} - 28 q^{61} - 44 q^{62} + 8 q^{64} - 36 q^{66} - 20 q^{72} + 12 q^{74} + 12 q^{77} + 78 q^{78} - 4 q^{80} + 10 q^{81} + 74 q^{82} - 20 q^{83} - 6 q^{84} + 12 q^{86} - 8 q^{87} - 54 q^{90} - 14 q^{91} - 30 q^{92} - 4 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9 + 8 * q^10 - 16 * q^16 + 20 * q^18 - 22 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^25 + 14 * q^31 + 18 * q^32 - 2 * q^33 + 20 * q^36 - 22 * q^37 - 46 * q^39 - 58 * q^40 - 4 * q^41 - 8 * q^42 + 18 * q^43 + 50 * q^45 + 8 * q^46 - 10 * q^49 - 22 * q^50 + 14 * q^51 + 62 * q^57 + 34 * q^59 - 28 * q^61 - 44 * q^62 + 8 * q^64 - 36 * q^66 - 20 * q^72 + 12 * q^74 + 12 * q^77 + 78 * q^78 - 4 * q^80 + 10 * q^81 + 74 * q^82 - 20 * q^83 - 6 * q^84 + 12 * q^86 - 8 * q^87 - 54 * q^90 - 14 * q^91 - 30 * q^92 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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