LMFDB - Embedded newform 287.2.c.a.204.5

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			204.5
Root			$-1.45275i$ of defining polynomial
Character	$\chi$	$=$	287.204
Dual form			287.2.c.a.204.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.889527 q^{2} -2.45275i q^{3} -1.20874 q^{4} +0.645522 q^{5} -2.18179i q^{6} -1.00000i q^{7} -2.85426 q^{8} -3.01597 q^{9} +O(q^{10})$	\(q+0.889527 q^{2} -2.45275i q^{3} -1.20874 q^{4} +0.645522 q^{5} -2.18179i q^{6} -1.00000i q^{7} -2.85426 q^{8} -3.01597 q^{9} +0.574209 q^{10} -3.84327i q^{11} +2.96474i q^{12} -2.91648i q^{13} -0.889527i q^{14} -1.58330i q^{15} -0.121463 q^{16} +3.75599i q^{17} -2.68278 q^{18} +3.44176i q^{19} -0.780269 q^{20} -2.45275 q^{21} -3.41870i q^{22} +3.35824 q^{23} +7.00078i q^{24} -4.58330 q^{25} -2.59429i q^{26} +0.0391601i q^{27} +1.20874i q^{28} -5.39429i q^{29} -1.40839i q^{30} +6.35648 q^{31} +5.60048 q^{32} -9.42657 q^{33} +3.34106i q^{34} -0.645522i q^{35} +3.64552 q^{36} +5.14531 q^{37} +3.06154i q^{38} -7.15339 q^{39} -1.84249 q^{40} +(5.62233 + 3.06422i) q^{41} -2.18179 q^{42} +10.5370 q^{43} +4.64552i q^{44} -1.94687 q^{45} +2.98725 q^{46} +6.65972i q^{47} +0.297917i q^{48} -1.00000 q^{49} -4.07697 q^{50} +9.21250 q^{51} +3.52527i q^{52} +2.47849i q^{53} +0.0348340i q^{54} -2.48092i q^{55} +2.85426i q^{56} +8.44176 q^{57} -4.79837i q^{58} +6.30256 q^{59} +1.91380i q^{60} -11.1343 q^{61} +5.65426 q^{62} +3.01597i q^{63} +5.22471 q^{64} -1.88265i q^{65} -8.38520 q^{66} -3.57300i q^{67} -4.54002i q^{68} -8.23691i q^{69} -0.574209i q^{70} -8.70265i q^{71} +8.60836 q^{72} -6.04224 q^{73} +4.57689 q^{74} +11.2417i q^{75} -4.16019i q^{76} -3.84327 q^{77} -6.36314 q^{78} +6.53949i q^{79} -0.0784069 q^{80} -8.95185 q^{81} +(5.00121 + 2.72571i) q^{82} -13.3872 q^{83} +2.96474 q^{84} +2.42458i q^{85} +9.37299 q^{86} -13.2308 q^{87} +10.9697i q^{88} -1.08030i q^{89} -1.73180 q^{90} -2.91648 q^{91} -4.05924 q^{92} -15.5908i q^{93} +5.92401i q^{94} +2.22173i q^{95} -13.7366i q^{96} +13.8403i q^{97} -0.889527 q^{98} +11.5912i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.889527			0.628991			0.314495	−	0.949259i	$-0.398165\pi$
$2$	0.889527			0.628991			0.314495	+	0.949259i	$0.398165\pi$
$3$		−	2.45275i		−	1.41609i	−0.706165	−	0.708047i	$-0.749576\pi$
$3$		−	2.45275i		−	1.41609i	0.706165	−	0.708047i	$-0.250424\pi$
$4$	−1.20874			−0.604371
$5$	0.645522			0.288686			0.144343	−	0.989528i	$-0.453893\pi$
$5$	0.645522			0.288686			0.144343	+	0.989528i	$0.453893\pi$
$6$		−	2.18179i		−	0.890710i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.85426			−1.00913
$9$	−3.01597			−1.00532
$10$	0.574209			0.181581
$11$		−	3.84327i		−	1.15879i	−0.815047	−	0.579395i	$-0.803289\pi$
$11$		−	3.84327i		−	1.15879i	0.815047	−	0.579395i	$-0.196711\pi$
$12$			2.96474i			0.855845i
$13$		−	2.91648i		−	0.808887i	−0.914563	−	0.404443i	$-0.867465\pi$
$13$		−	2.91648i		−	0.808887i	0.914563	−	0.404443i	$-0.132535\pi$
$14$		−	0.889527i		−	0.237736i
$15$		−	1.58330i		−	0.408807i
$16$	−0.121463			−0.0303657
$17$			3.75599i			0.910962i	0.890245	+	0.455481i	$0.150533\pi$
$17$			3.75599i			0.910962i	−0.890245	+	0.455481i	$0.849467\pi$
$18$	−2.68278			−0.632338
$19$			3.44176i			0.789593i	0.918769	+	0.394797i	$0.129185\pi$
$19$			3.44176i			0.789593i	−0.918769	+	0.394797i	$0.870815\pi$
$20$	−0.780269			−0.174473
$21$	−2.45275			−0.535233
$22$		−	3.41870i		−	0.728869i
$23$	3.35824			0.700241			0.350121	−	0.936705i	$-0.386141\pi$
$23$	3.35824			0.700241			0.350121	+	0.936705i	$0.386141\pi$
$24$			7.00078i			1.42903i
$25$	−4.58330			−0.916660
$26$		−	2.59429i		−	0.508782i
$27$			0.0391601i			0.00753637i
$28$			1.20874i			0.228431i
$29$		−	5.39429i		−	1.00169i	−0.865536	−	0.500847i	$-0.833022\pi$
$29$		−	5.39429i		−	1.00169i	0.865536	−	0.500847i	$-0.166978\pi$
$30$		−	1.40839i		−	0.257136i
$31$	6.35648			1.14166			0.570828	−	0.821069i	$-0.306622\pi$
$31$	6.35648			1.14166			0.570828	+	0.821069i	$0.306622\pi$
$32$	5.60048			0.990035
$33$	−9.42657			−1.64096
$34$			3.34106i			0.572987i
$35$		−	0.645522i		−	0.109113i
$36$	3.64552			0.607587
$37$	5.14531			0.845883			0.422942	−	0.906157i	$-0.360998\pi$
$37$	5.14531			0.845883			0.422942	+	0.906157i	$0.360998\pi$
$38$			3.06154i			0.496647i
$39$	−7.15339			−1.14546
$40$	−1.84249			−0.291323
$41$	5.62233	+	3.06422i	0.878060	+	0.478550i
$41$	5.62233	+	3.06422i	0.878060	+	0.478550i
$42$	−2.18179			−0.336657
$43$	10.5370			1.60688			0.803442	−	0.595383i	$-0.203000\pi$
$43$	10.5370			1.60688			0.803442	+	0.595383i	$0.203000\pi$
$44$			4.64552i			0.700339i
$45$	−1.94687			−0.290223
$46$	2.98725			0.440445
$47$			6.65972i			0.971421i	0.874120	+	0.485710i	$0.161439\pi$
$47$			6.65972i			0.971421i	−0.874120	+	0.485710i	$0.838561\pi$
$48$			0.297917i			0.0430007i
$49$	−1.00000			−0.142857
$50$	−4.07697			−0.576571
$51$	9.21250			1.29001
$52$			3.52527i			0.488867i
$53$			2.47849i			0.340447i	0.985406	+	0.170223i	$0.0544489\pi$
$53$			2.47849i			0.340447i	−0.985406	+	0.170223i	$0.945551\pi$
$54$			0.0348340i			0.00474031i
$55$		−	2.48092i		−	0.334527i
$56$			2.85426i			0.381417i
$57$	8.44176			1.11814
$58$		−	4.79837i		−	0.630056i
$59$	6.30256			0.820524			0.410262	−	0.911968i	$-0.365437\pi$
$59$	6.30256			0.820524			0.410262	+	0.911968i	$0.365437\pi$
$60$			1.91380i			0.247071i
$61$	−11.1343			−1.42560			−0.712802	−	0.701366i	$-0.752574\pi$
$61$	−11.1343			−1.42560			−0.712802	+	0.701366i	$0.752574\pi$
$62$	5.65426			0.718092
$63$			3.01597i			0.379976i
$64$	5.22471			0.653088
$65$		−	1.88265i		−	0.233514i
$66$	−8.38520			−1.03215
$67$		−	3.57300i		−	0.436511i	−0.975892	−	0.218255i	$-0.929963\pi$
$67$		−	3.57300i		−	0.436511i	0.975892	−	0.218255i	$-0.0700366\pi$
$68$		−	4.54002i		−	0.550559i
$69$		−	8.23691i		−	0.991608i
$70$		−	0.574209i		−	0.0686311i
$71$		−	8.70265i		−	1.03281i	−0.856343	−	0.516407i	$-0.827269\pi$
$71$		−	8.70265i		−	1.03281i	0.856343	−	0.516407i	$-0.172731\pi$
$72$	8.60836			1.01450
$73$	−6.04224			−0.707190			−0.353595	−	0.935399i	$-0.615041\pi$
$73$	−6.04224			−0.707190			−0.353595	+	0.935399i	$0.615041\pi$
$74$	4.57689			0.532053
$75$			11.2417i			1.29808i
$76$		−	4.16019i		−	0.477207i
$77$	−3.84327			−0.437982
$78$	−6.36314			−0.720484
$79$			6.53949i			0.735751i	0.929875	+	0.367875i	$0.119915\pi$
$79$			6.53949i			0.735751i	−0.929875	+	0.367875i	$0.880085\pi$
$80$	−0.0784069			−0.00876615
$81$	−8.95185			−0.994650
$82$	5.00121	+	2.72571i	0.552292	+	0.301004i
$83$	−13.3872			−1.46944			−0.734718	−	0.678373i	$-0.762685\pi$
$83$	−13.3872			−1.46944			−0.734718	+	0.678373i	$0.762685\pi$
$84$	2.96474			0.323479
$85$			2.42458i			0.262982i
$86$	9.37299			1.01072
$87$	−13.2308			−1.41849
$88$			10.9697i			1.16938i
$89$		−	1.08030i		−	0.114512i	−0.998360	−	0.0572560i	$-0.981765\pi$
$89$		−	1.08030i		−	0.114512i	0.998360	−	0.0572560i	$-0.0182351\pi$
$90$	−1.73180			−0.182547
$91$	−2.91648			−0.305731
$92$	−4.05924			−0.423205
$93$		−	15.5908i		−	1.61669i
$94$			5.92401i			0.611015i
$95$			2.22173i			0.227945i
$96$		−	13.7366i		−	1.40198i
$97$			13.8403i			1.40527i	0.711551	+	0.702635i	$0.247993\pi$
$97$			13.8403i			1.40527i	−0.711551	+	0.702635i	$0.752007\pi$
$98$	−0.889527			−0.0898558
$99$			11.5912i			1.16496i
$100$	5.54002			0.554002
$101$		−	2.45596i		−	0.244377i	−0.992507	−	0.122189i	$-0.961009\pi$
$101$		−	2.45596i		−	0.244377i	0.992507	−	0.122189i	$-0.0389912\pi$
$102$	8.19477			0.811403
$103$	2.14720			0.211570			0.105785	−	0.994389i	$-0.466264\pi$
$103$	2.14720			0.211570			0.105785	+	0.994389i	$0.466264\pi$
$104$			8.32441i			0.816276i
$105$	−1.58330			−0.154514
$106$			2.20468i			0.214138i
$107$	−7.70173			−0.744554			−0.372277	−	0.928122i	$-0.621423\pi$
$107$	−7.70173			−0.744554			−0.372277	+	0.928122i	$0.621423\pi$
$108$		−	0.0473345i		−	0.00455476i
$109$			8.54592i			0.818551i	0.912411	+	0.409275i	$0.134218\pi$
$109$			8.54592i			0.818551i	−0.912411	+	0.409275i	$0.865782\pi$
$110$		−	2.20684i		−	0.210414i
$111$		−	12.6201i		−	1.19785i
$112$			0.121463i			0.0114772i
$113$	−9.09439			−0.855528			−0.427764	−	0.903890i	$-0.640699\pi$
$113$	−9.09439			−0.855528			−0.427764	+	0.903890i	$0.640699\pi$
$114$	7.50917			0.703299
$115$	2.16782			0.202150
$116$			6.52030i			0.605394i
$117$			8.79601i			0.813192i
$118$	5.60630			0.516102
$119$	3.75599			0.344311
$120$			4.51916i			0.412541i
$121$	−3.77075			−0.342795
$122$	−9.90428			−0.896691
$123$	7.51575	−	13.7901i	0.677672	−	1.24342i
$124$	−7.68333			−0.689984
$125$	−6.18623			−0.553313
$126$			2.68278i			0.239001i
$127$	1.11545			0.0989800			0.0494900	−	0.998775i	$-0.484240\pi$
$127$	1.11545			0.0989800			0.0494900	+	0.998775i	$0.484240\pi$
$128$	−6.55344			−0.579248
$129$		−	25.8447i		−	2.27550i
$130$		−	1.67467i		−	0.146878i
$131$	9.15951			0.800270			0.400135	−	0.916456i	$-0.368963\pi$
$131$	9.15951			0.800270			0.400135	+	0.916456i	$0.368963\pi$
$132$	11.3943			0.991745
$133$	3.44176			0.298438
$134$		−	3.17828i		−	0.274561i
$135$			0.0252787i			0.00217565i
$136$		−	10.7206i		−	0.919284i
$137$		−	12.1087i		−	1.03452i	−0.855830	−	0.517258i	$-0.826953\pi$
$137$		−	12.1087i		−	1.03452i	0.855830	−	0.517258i	$-0.173047\pi$
$138$		−	7.32696i		−	0.623712i
$139$	23.1662			1.96494			0.982468	−	0.186433i	$-0.0596926\pi$
$139$	23.1662			1.96494			0.982468	+	0.186433i	$0.0596926\pi$
$140$			0.780269i			0.0659447i
$141$	16.3346			1.37562
$142$		−	7.74124i		−	0.649631i
$143$	−11.2088			−0.937330
$144$	0.366328			0.0305273
$145$		−	3.48213i		−	0.289175i
$146$	−5.37474			−0.444816
$147$			2.45275i			0.202299i
$148$	−6.21934			−0.511227
$149$		−	19.4195i		−	1.59091i	−0.606015	−	0.795453i	$-0.707233\pi$
$149$		−	19.4195i		−	1.59091i	0.606015	−	0.795453i	$-0.292767\pi$
$150$			9.99978i			0.816479i
$151$			20.2144i			1.64502i	0.568749	+	0.822511i	$0.307427\pi$
$151$			20.2144i			1.64502i	−0.568749	+	0.822511i	$0.692573\pi$
$152$		−	9.82368i		−	0.796806i
$153$		−	11.3280i		−	0.915811i
$154$	−3.41870			−0.275486
$155$	4.10324			0.329581
$156$	8.64660			0.692282
$157$			9.86633i			0.787419i	0.919235	+	0.393710i	$0.128808\pi$
$157$			9.86633i			0.787419i	−0.919235	+	0.393710i	$0.871192\pi$
$158$			5.81706i			0.462780i
$159$	6.07910			0.482104
$160$	3.61523			0.285809
$161$		−	3.35824i		−	0.264666i
$162$	−7.96291			−0.625626
$163$	−3.17416			−0.248619			−0.124310	−	0.992243i	$-0.539672\pi$
$163$	−3.17416			−0.248619			−0.124310	+	0.992243i	$0.539672\pi$
$164$	−6.79594	−	3.70385i	−0.530674	−	0.289222i
$165$	−6.08506			−0.473721
$166$	−11.9083			−0.924261
$167$			15.2755i			1.18205i	0.806652	+	0.591027i	$0.201277\pi$
$167$			15.2755i			1.18205i	−0.806652	+	0.591027i	$0.798723\pi$
$168$	7.00078			0.540122
$169$	4.49413			0.345702
$170$			2.15673i			0.165413i
$171$		−	10.3802i		−	0.793795i
$172$	−12.7366			−0.971154
$173$	−12.0717			−0.917798			−0.458899	−	0.888489i	$-0.651756\pi$
$173$	−12.0717			−0.917798			−0.458899	+	0.888489i	$0.651756\pi$
$174$	−11.7692			−0.892219
$175$			4.58330i			0.346465i
$176$			0.466815i			0.0351875i
$177$		−	15.4586i		−	1.16194i
$178$		−	0.960961i		−	0.0720270i
$179$		−	22.8279i		−	1.70624i	−0.521719	−	0.853118i	$-0.674709\pi$
$179$		−	22.8279i		−	1.70624i	0.521719	−	0.853118i	$-0.325291\pi$
$180$	2.35326			0.175402
$181$			12.9774i			0.964599i	0.876006	+	0.482300i	$0.160198\pi$
$181$			12.9774i			0.964599i	−0.876006	+	0.482300i	$0.839802\pi$
$182$	−2.59429			−0.192302
$183$			27.3097i			2.01879i
$184$	−9.58530			−0.706638
$185$	3.32141			0.244195
$186$		−	13.8685i		−	1.01689i
$187$	14.4353			1.05561
$188$		−	8.04988i		−	0.587098i
$189$	0.0391601			0.00284848
$190$			1.97629i			0.143375i
$191$		−	4.12201i		−	0.298258i	−0.988818	−	0.149129i	$-0.952353\pi$
$191$		−	4.12201i		−	0.298258i	0.988818	−	0.149129i	$-0.0476470\pi$
$192$		−	12.8149i		−	0.924834i
$193$			12.5219i			0.901344i	0.892690	+	0.450672i	$0.148816\pi$
$193$			12.5219i			0.901344i	−0.892690	+	0.450672i	$0.851184\pi$
$194$			12.3113i			0.883901i
$195$	−4.61767			−0.330678
$196$	1.20874			0.0863386
$197$	−7.78119			−0.554387			−0.277193	−	0.960814i	$-0.589404\pi$
$197$	−7.78119			−0.554387			−0.277193	+	0.960814i	$0.589404\pi$
$198$			10.3107i			0.732747i
$199$			6.42847i			0.455702i	0.973696	+	0.227851i	$0.0731700\pi$
$199$			6.42847i			0.455702i	−0.973696	+	0.227851i	$0.926830\pi$
$200$	13.0819			0.925033
$201$	−8.76365			−0.618140
$202$		−	2.18464i		−	0.153711i
$203$	−5.39429			−0.378605
$204$	−11.1355			−0.779643
$205$	3.62934	+	1.97802i	0.253484	+	0.138151i
$206$	1.91000			0.133076
$207$	−10.1283			−0.703968
$208$			0.354244i			0.0245624i
$209$	13.2276			0.914973
$210$	−1.40839			−0.0971881
$211$		−	23.8093i		−	1.63910i	−0.573006	−	0.819551i	$-0.694223\pi$
$211$		−	23.8093i		−	1.63910i	0.573006	−	0.819551i	$-0.305777\pi$
$212$		−	2.99585i		−	0.205756i
$213$	−21.3454			−1.46256
$214$	−6.85090			−0.468318
$215$	6.80189			0.463885
$216$		−	0.111773i		−	0.00760521i
$217$		−	6.35648i		−	0.431506i
$218$			7.60183i			0.514861i
$219$			14.8201i			1.00145i
$220$			2.99879i			0.202178i
$221$	10.9543			0.736866
$222$		−	11.2260i		−	0.753437i
$223$	−0.0390260			−0.00261338			−0.00130669	−	0.999999i	$-0.500416\pi$
$223$	−0.0390260			−0.00261338			−0.00130669	+	0.999999i	$0.500416\pi$
$224$		−	5.60048i		−	0.374198i
$225$	13.8231			0.921539
$226$	−8.08971			−0.538119
$227$			0.138275i			0.00917760i	0.999989	+	0.00458880i	$0.00146067\pi$
$227$			0.138275i			0.00917760i	−0.999989	+	0.00458880i	$0.998539\pi$
$228$	−10.2039			−0.675770
$229$			15.1728i			1.00265i	0.865260	+	0.501323i	$0.167153\pi$
$229$			15.1728i			1.00265i	−0.865260	+	0.501323i	$0.832847\pi$
$230$	1.92833			0.127150
$231$			9.42657i			0.620223i
$232$			15.3967i			1.01084i
$233$		−	13.9493i		−	0.913849i	−0.889505	−	0.456925i	$-0.848951\pi$
$233$		−	13.9493i		−	0.913849i	0.889505	−	0.456925i	$-0.151049\pi$
$234$			7.82429i			0.511490i
$235$			4.29900i			0.280436i
$236$	−7.61817			−0.495901
$237$	16.0397			1.04189
$238$	3.34106			0.216569
$239$			10.1689i			0.657773i	0.944370	+	0.328886i	$0.106673\pi$
$239$			10.1689i			0.657773i	−0.944370	+	0.328886i	$0.893327\pi$
$240$			0.192312i			0.0124137i
$241$	18.8926			1.21698			0.608490	−	0.793562i	$-0.291776\pi$
$241$	18.8926			1.21698			0.608490	+	0.793562i	$0.291776\pi$
$242$	−3.35418			−0.215615
$243$			22.0741i			1.41605i
$244$	13.4585			0.861593
$245$	−0.645522			−0.0412409
$246$	6.68547	−	12.2667i	0.426250	−	0.782097i
$247$	10.0378			0.638692
$248$	−18.1431			−1.15209
$249$			32.8354i			2.08086i
$250$	−5.50282			−0.348029
$251$	−0.256759			−0.0162065			−0.00810325	−	0.999967i	$-0.502579\pi$
$251$	−0.256759			−0.0162065			−0.00810325	+	0.999967i	$0.502579\pi$
$252$		−	3.64552i		−	0.229646i
$253$		−	12.9066i		−	0.811433i
$254$	0.992222			0.0622575
$255$	5.94687			0.372408
$256$	−16.2789			−1.01743
$257$		−	3.75296i		−	0.234103i	−0.993126	−	0.117052i	$-0.962656\pi$
$257$		−	3.75296i		−	0.234103i	0.993126	−	0.117052i	$-0.0373443\pi$
$258$		−	22.9896i		−	1.43127i
$259$		−	5.14531i		−	0.319714i
$260$			2.27564i			0.141129i
$261$			16.2690i			1.00703i
$262$	8.14763			0.503362
$263$		−	12.4356i		−	0.766811i	−0.923580	−	0.383405i	$-0.874751\pi$
$263$		−	12.4356i		−	0.766811i	0.923580	−	0.383405i	$-0.125249\pi$
$264$	26.9059			1.65595
$265$			1.59992i			0.0982822i
$266$	3.06154			0.187715
$267$	−2.64971			−0.162160
$268$			4.31883i			0.263814i
$269$	18.8382			1.14858			0.574292	−	0.818651i	$-0.305277\pi$
$269$	18.8382			1.14858			0.574292	+	0.818651i	$0.305277\pi$
$270$			0.0224861i			0.00136846i
$271$	−28.1232			−1.70836			−0.854182	−	0.519974i	$-0.825942\pi$
$271$	−28.1232			−1.70836			−0.854182	+	0.519974i	$0.825942\pi$
$272$		−	0.456213i		−	0.0276620i
$273$			7.15339i			0.432943i
$274$		−	10.7710i		−	0.650701i
$275$			17.6149i			1.06222i
$276$			9.95629i			0.599298i
$277$	10.7064			0.643286			0.321643	−	0.946861i	$-0.395765\pi$
$277$	10.7064			0.643286			0.321643	+	0.946861i	$0.395765\pi$
$278$	20.6070			1.23593
$279$	−19.1709			−1.14773
$280$			1.84249i			0.110110i
$281$		−	2.23098i		−	0.133089i	−0.997783	−	0.0665447i	$-0.978803\pi$
$281$		−	2.23098i		−	0.133089i	0.997783	−	0.0665447i	$-0.0211975\pi$
$282$	14.5301			0.865254
$283$	19.7225			1.17238			0.586190	−	0.810174i	$-0.300627\pi$
$283$	19.7225			1.17238			0.586190	+	0.810174i	$0.300627\pi$
$284$			10.5192i			0.624202i
$285$	5.44934			0.322791
$286$	−9.97057			−0.589572
$287$	3.06422	−	5.62233i	0.180875	−	0.331876i
$288$	−16.8909			−0.995304
$289$	2.89251			0.170147
$290$		−	3.09745i		−	0.181889i
$291$	33.9467			1.98999
$292$	7.30350			0.427405
$293$		−	5.28426i		−	0.308710i	−0.988015	−	0.154355i	$-0.950670\pi$
$293$		−	5.28426i		−	0.308710i	0.988015	−	0.154355i	$-0.0493300\pi$
$294$			2.18179i			0.127244i
$295$	4.06844			0.236874
$296$	−14.6861			−0.853610
$297$	0.150503			0.00873308
$298$		−	17.2742i		−	1.00067i
$299$		−	9.79425i		−	0.566416i
$300$		−	13.5883i		−	0.784520i
$301$		−	10.5370i		−	0.607345i
$302$			17.9812i			1.03470i
$303$	−6.02384			−0.346061
$304$		−	0.418045i		−	0.0239765i
$305$	−7.18744			−0.411552
$306$		−	10.0765i		−	0.576036i
$307$	−14.7602			−0.842407			−0.421204	−	0.906966i	$-0.638392\pi$
$307$	−14.7602			−0.842407			−0.421204	+	0.906966i	$0.638392\pi$
$308$	4.64552			0.264703
$309$		−	5.26655i		−	0.299603i
$310$	3.64995			0.207303
$311$			25.7770i			1.46168i	0.682548	+	0.730841i	$0.260872\pi$
$311$			25.7770i			1.46168i	−0.682548	+	0.730841i	$0.739128\pi$
$312$	20.4177			1.15592
$313$		−	4.07102i		−	0.230107i	−0.993359	−	0.115054i	$-0.963296\pi$
$313$		−	4.07102i		−	0.230107i	0.993359	−	0.115054i	$-0.0367040\pi$
$314$			8.77637i			0.495279i
$315$			1.94687i			0.109694i
$316$		−	7.90456i		−	0.444666i
$317$			26.3149i			1.47799i	0.673711	+	0.738995i	$0.264699\pi$
$317$			26.3149i			1.47799i	−0.673711	+	0.738995i	$0.735301\pi$
$318$	5.40753			0.303239
$319$	−20.7317			−1.16075
$320$	3.37266			0.188538
$321$			18.8904i			1.05436i
$322$		−	2.98725i		−	0.166473i
$323$	−12.9272			−0.719290
$324$	10.8205			0.601137
$325$			13.3671i			0.741475i
$326$	−2.82350			−0.156379
$327$	20.9610			1.15914
$328$	−16.0476	−	8.74608i	−0.886081	−	0.482922i
$329$	6.65972			0.367162
$330$	−5.41283			−0.297966
$331$			33.3838i			1.83494i	0.397808	+	0.917468i	$0.369771\pi$
$331$			33.3838i			1.83494i	−0.397808	+	0.917468i	$0.630229\pi$
$332$	16.1817			0.888083
$333$	−15.5181			−0.850385
$334$			13.5880i			0.743501i
$335$		−	2.30645i		−	0.126015i
$336$	0.297917			0.0162527
$337$	−23.0974			−1.25820			−0.629098	−	0.777326i	$-0.716576\pi$
$337$	−23.0974			−1.25820			−0.629098	+	0.777326i	$0.716576\pi$
$338$	3.99765			0.217443
$339$			22.3062i			1.21151i
$340$		−	2.93069i		−	0.158939i
$341$		−	24.4297i		−	1.32294i
$342$		−	9.23349i		−	0.499290i
$343$			1.00000i			0.0539949i
$344$	−30.0755			−1.62156
$345$		−	5.31711i		−	0.286263i
$346$	−10.7381			−0.577286
$347$			17.2216i			0.924505i	0.886748	+	0.462252i	$0.152959\pi$
$347$			17.2216i			0.924505i	−0.886748	+	0.462252i	$0.847041\pi$
$348$	15.9926			0.857295
$349$	24.2807			1.29971			0.649857	−	0.760057i	$-0.274829\pi$
$349$	24.2807			1.29971			0.649857	+	0.760057i	$0.274829\pi$
$350$			4.07697i			0.217923i
$351$	0.114210			0.00609607
$352$		−	21.5242i		−	1.14724i
$353$	27.7546			1.47723			0.738615	−	0.674127i	$-0.235480\pi$
$353$	27.7546			1.47723			0.738615	+	0.674127i	$0.235480\pi$
$354$		−	13.7508i		−	0.730849i
$355$		−	5.61775i		−	0.298159i
$356$			1.30581i			0.0692077i
$357$		−	9.21250i		−	0.487577i
$358$		−	20.3060i		−	1.07321i
$359$	−19.6216			−1.03559			−0.517793	−	0.855506i	$-0.673246\pi$
$359$	−19.6216			−1.03559			−0.517793	+	0.855506i	$0.673246\pi$
$360$	5.55688			0.292874
$361$	7.15431			0.376543
$362$			11.5437i			0.606724i
$363$			9.24868i			0.485430i
$364$	3.52527			0.184775
$365$	−3.90040			−0.204156
$366$			24.2927i			1.26980i
$367$	−3.61014			−0.188448			−0.0942238	−	0.995551i	$-0.530037\pi$
$367$	−3.61014			−0.188448			−0.0942238	+	0.995551i	$0.530037\pi$
$368$	−0.407901			−0.0212633
$369$	−16.9567	−	9.24158i	−0.882733	−	0.481097i
$370$	2.95448			0.153596
$371$	2.47849			0.128677
$372$			18.8453i			0.977082i
$373$	−12.0593			−0.624407			−0.312204	−	0.950015i	$-0.601067\pi$
$373$	−12.0593			−0.624407			−0.312204	+	0.950015i	$0.601067\pi$
$374$	12.8406			0.663972
$375$			15.1733i			0.783544i
$376$		−	19.0086i		−	0.980294i
$377$	−15.7324			−0.810257
$378$	0.0348340			0.00179167
$379$	34.5175			1.77304			0.886522	−	0.462687i	$-0.153114\pi$
$379$	34.5175			1.77304			0.886522	+	0.462687i	$0.153114\pi$
$380$		−	2.68550i		−	0.137763i
$381$		−	2.73591i		−	0.140165i
$382$		−	3.66664i		−	0.187602i
$383$		−	21.2590i		−	1.08628i	−0.839641	−	0.543142i	$-0.817235\pi$
$383$		−	21.2590i		−	1.08628i	0.839641	−	0.543142i	$-0.182765\pi$
$384$			16.0739i			0.820270i
$385$	−2.48092			−0.126439
$386$			11.1385i			0.566937i
$387$	−31.7794			−1.61544
$388$		−	16.7293i		−	0.849303i
$389$	−14.8091			−0.750851			−0.375425	−	0.926853i	$-0.622503\pi$
$389$	−14.8091			−0.750851			−0.375425	+	0.926853i	$0.622503\pi$
$390$	−4.10755			−0.207994
$391$			12.6135i			0.637894i
$392$	2.85426			0.144162
$393$		−	22.4660i		−	1.13326i
$394$	−6.92158			−0.348704
$395$			4.22139i			0.212401i
$396$		−	14.0107i		−	0.704066i
$397$			19.0348i			0.955329i	0.878542	+	0.477665i	$0.158517\pi$
$397$			19.0348i			0.955329i	−0.878542	+	0.477665i	$0.841483\pi$
$398$			5.71830i			0.286633i
$399$		−	8.44176i		−	0.422616i
$400$	0.556700			0.0278350
$401$	−37.6448			−1.87989			−0.939947	−	0.341321i	$-0.889126\pi$
$401$	−37.6448			−1.87989			−0.939947	+	0.341321i	$0.889126\pi$
$402$	−7.79551			−0.388805
$403$		−	18.5386i		−	0.923471i
$404$			2.96862i			0.147694i
$405$	−5.77861			−0.287142
$406$	−4.79837			−0.238139
$407$		−	19.7748i		−	0.980201i
$408$	−26.2949			−1.30179
$409$	5.97595			0.295492			0.147746	−	0.989025i	$-0.452798\pi$
$409$	5.97595			0.295492			0.147746	+	0.989025i	$0.452798\pi$
$410$	3.22839	+	1.75950i	0.159439	+	0.0868956i
$411$	−29.6996			−1.46497
$412$	−2.59541			−0.127867
$413$		−	6.30256i		−	0.310129i
$414$	−9.00943			−0.442789
$415$	−8.64173			−0.424206
$416$		−	16.3337i		−	0.800826i
$417$		−	56.8209i		−	2.78253i
$418$	11.7663			0.575510
$419$	−7.95709			−0.388729			−0.194365	−	0.980929i	$-0.562265\pi$
$419$	−7.95709			−0.388729			−0.194365	+	0.980929i	$0.562265\pi$
$420$	1.91380			0.0933840
$421$		−	12.4641i		−	0.607462i	−0.952758	−	0.303731i	$-0.901768\pi$
$421$		−	12.4641i		−	0.607462i	0.952758	−	0.303731i	$-0.0982324\pi$
$422$		−	21.1791i		−	1.03098i
$423$		−	20.0855i		−	0.976590i
$424$		−	7.07426i		−	0.343556i
$425$		−	17.2149i		−	0.835043i
$426$	−18.9873			−0.919938
$427$			11.1343i			0.538827i
$428$	9.30939			0.449987
$429$			27.4924i			1.32735i
$430$	6.05047			0.291780
$431$	34.7284			1.67281			0.836403	−	0.548115i	$-0.184654\pi$
$431$	34.7284			1.67281			0.836403	+	0.548115i	$0.184654\pi$
$432$		−	0.00475650i		−	0.000228847i
$433$	0.996713			0.0478989			0.0239495	−	0.999713i	$-0.492376\pi$
$433$	0.996713			0.0478989			0.0239495	+	0.999713i	$0.492376\pi$
$434$		−	5.65426i		−	0.271413i
$435$	−8.54078			−0.409499
$436$		−	10.3298i		−	0.494708i
$437$			11.5582i			0.552906i
$438$			13.1829i			0.629902i
$439$			16.1744i			0.771964i	0.922506	+	0.385982i	$0.126137\pi$
$439$			16.1744i			0.771964i	−0.922506	+	0.385982i	$0.873863\pi$
$440$			7.08119i			0.337582i
$441$	3.01597			0.143617
$442$	9.74415			0.463482
$443$	11.6540			0.553699			0.276849	−	0.960913i	$-0.410710\pi$
$443$	11.6540			0.553699			0.276849	+	0.960913i	$0.410710\pi$
$444$			15.2545i			0.723945i
$445$		−	0.697360i		−	0.0330581i
$446$	−0.0347147			−0.00164379
$447$	−47.6311			−2.25287
$448$		−	5.22471i		−	0.246844i
$449$	22.6529			1.06905			0.534527	−	0.845151i	$-0.320490\pi$
$449$	22.6529			1.06905			0.534527	+	0.845151i	$0.320490\pi$
$450$	12.2960			0.579639
$451$	11.7766	−	21.6081i	0.554540	−	1.01749i
$452$	10.9928			0.517056
$453$	49.5807			2.32951
$454$			0.122999i			0.00577263i
$455$	−1.88265			−0.0882602
$456$	−24.0950			−1.12835
$457$		−	18.9997i		−	0.888766i	−0.895837	−	0.444383i	$-0.853423\pi$
$457$		−	18.9997i		−	0.888766i	0.895837	−	0.444383i	$-0.146577\pi$
$458$			13.4966i			0.630655i
$459$	−0.147085			−0.00686535
$460$	−2.62033			−0.122174
$461$	−33.6054			−1.56516			−0.782581	−	0.622549i	$-0.786097\pi$
$461$	−33.6054			−1.56516			−0.782581	+	0.622549i	$0.786097\pi$
$462$			8.38520i			0.390115i
$463$		−	7.83834i		−	0.364278i	−0.983273	−	0.182139i	$-0.941698\pi$
$463$		−	7.83834i		−	0.364278i	0.983273	−	0.182139i	$-0.0583022\pi$
$464$			0.655205i			0.0304171i
$465$		−	10.0642i		−	0.466717i
$466$		−	12.4083i		−	0.574803i
$467$	−13.5150			−0.625400			−0.312700	−	0.949852i	$-0.601233\pi$
$467$	−13.5150			−0.625400			−0.312700	+	0.949852i	$0.601233\pi$
$468$		−	10.6321i		−	0.491469i
$469$	−3.57300			−0.164986
$470$			3.82408i			0.176391i
$471$	24.1996			1.11506
$472$	−17.9892			−0.828019
$473$		−	40.4967i		−	1.86204i
$474$	14.2678			0.655340
$475$		−	15.7746i		−	0.723789i
$476$	−4.54002			−0.208092
$477$		−	7.47504i		−	0.342258i
$478$			9.04553i			0.413733i
$479$		−	38.0621i		−	1.73910i	−0.493843	−	0.869551i	$-0.664408\pi$
$479$		−	38.0621i		−	1.73910i	0.493843	−	0.869551i	$-0.335592\pi$
$480$		−	8.86725i		−	0.404733i
$481$		−	15.0062i		−	0.684224i
$482$	16.8055			0.765469
$483$	−8.23691			−0.374792
$484$	4.55786			0.207175
$485$			8.93421i			0.405682i
$486$			19.6355i			0.890685i
$487$	−24.5908			−1.11432			−0.557158	−	0.830407i	$-0.688108\pi$
$487$	−24.5908			−1.11432			−0.557158	+	0.830407i	$0.688108\pi$
$488$	31.7803			1.43863
$489$			7.78541i			0.352068i
$490$	−0.574209			−0.0259401
$491$	39.9182			1.80148			0.900741	−	0.434356i	$-0.143024\pi$
$491$	39.9182			1.80148			0.900741	+	0.434356i	$0.143024\pi$
$492$	−9.08460	+	16.6687i	−0.409565	+	0.751484i
$493$	20.2609			0.912506
$494$	8.92892			0.401731
$495$			7.48236i			0.336307i
$496$	−0.772075			−0.0346672
$497$	−8.70265			−0.390367
$498$			29.2080i			1.30884i
$499$		−	16.6258i		−	0.744272i	−0.928178	−	0.372136i	$-0.878625\pi$
$499$		−	16.6258i		−	0.744272i	0.928178	−	0.372136i	$-0.121375\pi$
$500$	7.47755			0.334406
$501$	37.4669			1.67390
$502$	−0.228394			−0.0101937
$503$			0.346135i			0.0154334i	0.999970	+	0.00771671i	$0.00245633\pi$
$503$			0.346135i			0.0154334i	−0.999970	+	0.00771671i	$0.997544\pi$
$504$		−	8.60836i		−	0.383447i
$505$		−	1.58537i		−	0.0705483i
$506$		−	11.4808i		−	0.510384i
$507$		−	11.0230i		−	0.489546i
$508$	−1.34829			−0.0598206
$509$			27.3746i			1.21336i	0.794948	+	0.606678i	$0.207498\pi$
$509$			27.3746i			1.21336i	−0.794948	+	0.606678i	$0.792502\pi$
$510$	5.28991			0.234241
$511$			6.04224i			0.267293i
$512$	−1.37362			−0.0607061
$513$	−0.134780			−0.00595067
$514$		−	3.33836i		−	0.147249i
$515$	1.38607			0.0610774
$516$			31.2396i			1.37524i
$517$	25.5951			1.12567
$518$		−	4.57689i		−	0.201097i
$519$			29.6089i			1.29969i
$520$			5.37359i			0.235647i
$521$		−	5.42942i		−	0.237867i	−0.992902	−	0.118934i	$-0.962052\pi$
$521$		−	5.42942i		−	0.237867i	0.992902	−	0.118934i	$-0.0379476\pi$
$522$			14.4717i			0.633410i
$523$	−10.7992			−0.472214			−0.236107	−	0.971727i	$-0.575872\pi$
$523$	−10.7992			−0.472214			−0.236107	+	0.971727i	$0.575872\pi$
$524$	−11.0715			−0.483660
$525$	11.2417			0.490627
$526$		−	11.0618i		−	0.482317i
$527$			23.8749i			1.04001i
$528$	1.14498			0.0498288
$529$	−11.7222			−0.509662
$530$			1.42317i			0.0618186i
$531$	−19.0083			−0.824891
$532$	−4.16019			−0.180367
$533$	8.93674	−	16.3974i	0.387093	−	0.710251i
$534$	−2.35699			−0.101997
$535$	−4.97163			−0.214942
$536$			10.1983i			0.440498i
$537$	−55.9910			−2.41619
$538$	16.7571			0.722449
$539$			3.84327i			0.165541i
$540$		−	0.0305554i		−	0.00131490i
$541$	−42.5735			−1.83038			−0.915189	−	0.403026i	$-0.867959\pi$
$541$	−42.5735			−1.83038			−0.915189	+	0.403026i	$0.867959\pi$
$542$	−25.0164			−1.07455
$543$	31.8302			1.36596
$544$			21.0354i			0.901884i
$545$			5.51658i			0.236304i
$546$			6.36314i			0.272317i
$547$			21.2514i			0.908646i	0.890837	+	0.454323i	$0.150119\pi$
$547$			21.2514i			0.908646i	−0.890837	+	0.454323i	$0.849881\pi$
$548$			14.6363i			0.625231i
$549$	33.5807			1.43319
$550$			15.6689i			0.668125i
$551$	18.5658			0.790931
$552$			23.5103i			1.00067i
$553$	6.53949			0.278088
$554$	9.52364			0.404621
$555$		−	8.14657i		−	0.345803i
$556$	−28.0020			−1.18755
$557$			45.6364i			1.93367i	0.255394	+	0.966837i	$0.417795\pi$
$557$			45.6364i			1.93367i	−0.255394	+	0.966837i	$0.582205\pi$
$558$	−17.0531			−0.721913
$559$		−	30.7311i		−	1.29979i
$560$			0.0784069i			0.00331329i
$561$		−	35.4062i		−	1.49485i
$562$		−	1.98452i		−	0.0837120i
$563$		−	18.5553i		−	0.782014i	−0.920388	−	0.391007i	$-0.872127\pi$
$563$		−	18.5553i		−	0.782014i	0.920388	−	0.391007i	$-0.127873\pi$
$564$	−19.7443			−0.831386
$565$	−5.87062			−0.246979
$566$	17.5437			0.737416
$567$			8.95185i			0.375942i
$568$			24.8396i			1.04225i
$569$	−41.2306			−1.72848			−0.864239	−	0.503082i	$-0.832199\pi$
$569$	−41.2306			−1.72848			−0.864239	+	0.503082i	$0.832199\pi$
$570$	4.84734			0.203033
$571$			39.2844i			1.64400i	0.569487	+	0.822000i	$0.307142\pi$
$571$			39.2844i			1.64400i	−0.569487	+	0.822000i	$0.692858\pi$
$572$	13.5486			0.566495
$573$	−10.1103			−0.422362
$574$	2.72571	−	5.00121i	0.113769	−	0.208747i
$575$	−15.3918			−0.641883
$576$	−15.7575			−0.656564
$577$		−	45.4309i		−	1.89131i	−0.325168	−	0.945656i	$-0.605421\pi$
$577$		−	45.4309i		−	1.89131i	0.325168	−	0.945656i	$-0.394579\pi$
$578$	2.57296			0.107021
$579$	30.7130			1.27639
$580$			4.20899i			0.174769i
$581$			13.3872i			0.555394i
$582$	30.1966			1.25169
$583$	9.52551			0.394506
$584$	17.2461			0.713650
$585$			5.67802i			0.234757i
$586$		−	4.70050i		−	0.194176i
$587$		−	2.87888i		−	0.118824i	−0.998234	−	0.0594120i	$-0.981077\pi$
$587$		−	2.87888i		−	0.118824i	0.998234	−	0.0594120i	$-0.0189226\pi$
$588$		−	2.96474i		−	0.122264i
$589$			21.8774i			0.901444i
$590$	3.61899			0.148992
$591$			19.0853i			0.785063i
$592$	−0.624963			−0.0256858
$593$			7.89822i			0.324341i	0.986763	+	0.162171i	$0.0518495\pi$
$593$			7.89822i			0.324341i	−0.986763	+	0.162171i	$0.948151\pi$
$594$	0.133877			0.00549302
$595$	2.42458			0.0993979
$596$			23.4731i			0.961497i
$597$	15.7674			0.645317
$598$		−	8.71225i		−	0.356271i
$599$	31.3373			1.28041			0.640204	−	0.768205i	$-0.278850\pi$
$599$	31.3373			1.28041			0.640204	+	0.768205i	$0.278850\pi$
$600$		−	32.0867i		−	1.30993i
$601$			36.4610i			1.48727i	0.668583	+	0.743637i	$0.266901\pi$
$601$			36.4610i			1.48727i	−0.668583	+	0.743637i	$0.733099\pi$
$602$		−	9.37299i		−	0.382015i
$603$			10.7760i			0.438834i
$604$		−	24.4339i		−	0.994203i
$605$	−2.43410			−0.0989602
$606$	−5.35837			−0.217669
$607$	−29.0596			−1.17949			−0.589745	−	0.807589i	$-0.700772\pi$
$607$	−29.0596			−1.17949			−0.589745	+	0.807589i	$0.700772\pi$
$608$			19.2755i			0.781724i
$609$			13.2308i			0.536140i
$610$	−6.39343			−0.258862
$611$	19.4230			0.785769
$612$			13.6926i			0.553489i
$613$	−5.82721			−0.235359			−0.117679	−	0.993052i	$-0.537545\pi$
$613$	−5.82721			−0.235359			−0.117679	+	0.993052i	$0.537545\pi$
$614$	−13.1296			−0.529867
$615$	4.85158	−	8.90184i	0.195635	−	0.358957i
$616$	10.9697			0.441982
$617$	13.6244			0.548499			0.274249	−	0.961659i	$-0.411571\pi$
$617$	13.6244			0.548499			0.274249	+	0.961659i	$0.411571\pi$
$618$		−	4.68474i		−	0.188448i
$619$	−23.7891			−0.956164			−0.478082	−	0.878315i	$-0.658668\pi$
$619$	−23.7891			−0.956164			−0.478082	+	0.878315i	$0.658668\pi$
$620$	−4.95976			−0.199189
$621$			0.131509i			0.00527728i
$622$			22.9294i			0.919384i
$623$	−1.08030			−0.0432815
$624$	0.868871			0.0347827
$625$	18.9232			0.756926
$626$		−	3.62128i		−	0.144735i
$627$		−	32.4440i		−	1.29569i
$628$		−	11.9258i		−	0.475893i
$629$			19.3257i			0.770568i
$630$			1.73180i			0.0689964i
$631$	−16.0309			−0.638180			−0.319090	−	0.947724i	$-0.603377\pi$
$631$	−16.0309			−0.638180			−0.319090	+	0.947724i	$0.603377\pi$
$632$		−	18.6654i		−	0.742471i
$633$	−58.3983			−2.32112
$634$			23.4078i			0.929642i
$635$	0.720046			0.0285742
$636$	−7.34806			−0.291370
$637$			2.91648i			0.115555i
$638$	−18.4414			−0.730103
$639$			26.2469i			1.03831i
$640$	−4.23039			−0.167221
$641$			42.7206i			1.68736i	0.536846	+	0.843680i	$0.319616\pi$
$641$			42.7206i			1.68736i	−0.536846	+	0.843680i	$0.680384\pi$
$642$			16.8035i			0.663182i
$643$		−	44.1165i		−	1.73979i	−0.493241	−	0.869893i	$-0.664188\pi$
$643$		−	44.1165i		−	1.73979i	0.493241	−	0.869893i	$-0.335812\pi$
$644$			4.05924i			0.159957i
$645$		−	16.6833i		−	0.656905i
$646$	−11.4991			−0.452427
$647$	−15.4908			−0.609004			−0.304502	−	0.952512i	$-0.598490\pi$
$647$	−15.4908			−0.609004			−0.304502	+	0.952512i	$0.598490\pi$
$648$	25.5509			1.00374
$649$		−	24.2225i		−	0.950815i
$650$			11.8904i			0.466381i
$651$	−15.5908			−0.611053
$652$	3.83674			0.150258
$653$		−	8.30014i		−	0.324809i	−0.986724	−	0.162405i	$-0.948075\pi$
$653$		−	8.30014i		−	0.324809i	0.986724	−	0.162405i	$-0.0519250\pi$
$654$	18.6454			0.729091
$655$	5.91266			0.231027
$656$	−0.682903	−	0.372188i	−0.0266629	−	0.0145315i
$657$	18.2232			0.710954
$658$	5.92401			0.230942
$659$			2.29426i			0.0893716i	0.999001	+	0.0446858i	$0.0142287\pi$
$659$			2.29426i			0.0893716i	−0.999001	+	0.0446858i	$0.985771\pi$
$660$	7.35526			0.286303
$661$	34.6650			1.34831			0.674156	−	0.738589i	$-0.264508\pi$
$661$	34.6650			1.34831			0.674156	+	0.738589i	$0.264508\pi$
$662$			29.6958i			1.15416i
$663$		−	26.8681i		−	1.04347i
$664$	38.2106			1.48286
$665$	2.22173			0.0861550
$666$	−13.8037			−0.534884
$667$		−	18.1153i		−	0.701428i
$668$		−	18.4641i		−	0.714399i
$669$			0.0957209i			0.00370078i
$670$		−	2.05165i		−	0.0792620i
$671$			42.7922i			1.65198i
$672$	−13.7366			−0.529899
$673$			1.90177i			0.0733080i	0.999328	+	0.0366540i	$0.0116699\pi$
$673$			1.90177i			0.0733080i	−0.999328	+	0.0366540i	$0.988330\pi$
$674$	−20.5458			−0.791394
$675$		−	0.179483i		−	0.00690829i
$676$	−5.43223			−0.208932
$677$	−6.53953			−0.251335			−0.125667	−	0.992072i	$-0.540107\pi$
$677$	−6.53953			−0.251335			−0.125667	+	0.992072i	$0.540107\pi$
$678$			19.8420i			0.762027i
$679$	13.8403			0.531142
$680$		−	6.92038i		−	0.265384i
$681$	0.339152			0.0129963
$682$		−	21.7309i		−	0.832118i
$683$		−	47.0502i		−	1.80033i	−0.435554	−	0.900163i	$-0.643447\pi$
$683$		−	47.0502i		−	1.80033i	0.435554	−	0.900163i	$-0.356553\pi$
$684$			12.5470i			0.479746i
$685$		−	7.81643i		−	0.298650i
$686$			0.889527i			0.0339623i
$687$	37.2150			1.41984
$688$	−1.27986			−0.0487942
$689$	7.22847			0.275383
$690$		−	4.72971i		−	0.180057i
$691$		−	44.3053i		−	1.68545i	−0.538341	−	0.842727i	$-0.680949\pi$
$691$		−	44.3053i		−	1.68545i	0.538341	−	0.842727i	$-0.319051\pi$
$692$	14.5916			0.554690
$693$	11.5912			0.440313
$694$			15.3191i			0.581505i
$695$	14.9543			0.567250
$696$	37.7642			1.43145
$697$	−11.5092	+	21.1174i	−0.435942	+	0.799880i
$698$	21.5983			0.817508
$699$	−34.2141			−1.29410
$700$		−	5.54002i		−	0.209393i
$701$	−35.7420			−1.34996			−0.674979	−	0.737837i	$-0.735847\pi$
$701$	−35.7420			−1.34996			−0.674979	+	0.737837i	$0.735847\pi$
$702$	0.101593			0.00383437
$703$			17.7089i			0.667904i
$704$		−	20.0800i		−	0.756793i
$705$	10.5444			0.397123
$706$	24.6885			0.929165
$707$	−2.45596			−0.0923658
$708$			18.6854i			0.702242i
$709$			42.0002i			1.57735i	0.614810	+	0.788675i	$0.289233\pi$
$709$			42.0002i			1.57735i	−0.614810	+	0.788675i	$0.710767\pi$
$710$		−	4.99714i		−	0.187539i
$711$		−	19.7229i		−	0.739666i
$712$			3.08347i			0.115558i
$713$	21.3466			0.799435
$714$		−	8.19477i		−	0.306682i
$715$	−7.23555			−0.270594
$716$			27.5930i			1.03120i
$717$	24.9418			0.931468
$718$	−17.4539			−0.651374
$719$		−	36.2543i		−	1.35206i	−0.736876	−	0.676028i	$-0.763700\pi$
$719$		−	36.2543i		−	1.35206i	0.736876	−	0.676028i	$-0.236300\pi$
$720$	0.236472			0.00881281
$721$		−	2.14720i		−	0.0799661i
$722$	6.36396			0.236842
$723$		−	46.3388i		−	1.72336i
$724$		−	15.6863i		−	0.582975i
$725$			24.7236i			0.918213i
$726$			8.22696i			0.305331i
$727$		−	42.9640i		−	1.59345i	−0.604344	−	0.796724i	$-0.706565\pi$
$727$		−	42.9640i		−	1.59345i	0.604344	−	0.796724i	$-0.293435\pi$
$728$	8.32441			0.308523
$729$	27.2866			1.01062
$730$	−3.46951			−0.128412
$731$			39.5771i			1.46381i
$732$		−	33.0103i		−	1.22010i
$733$	2.87990			0.106371			0.0531857	−	0.998585i	$-0.483062\pi$
$733$	2.87990			0.106371			0.0531857	+	0.998585i	$0.483062\pi$
$734$	−3.21132			−0.118532
$735$			1.58330i			0.0584010i
$736$	18.8078			0.693263
$737$	−13.7320			−0.505825
$738$	−15.0835	−	8.22064i	−0.555231	−	0.302606i
$739$	28.6479			1.05383			0.526914	−	0.849918i	$-0.323349\pi$
$739$	28.6479			1.05383			0.526914	+	0.849918i	$0.323349\pi$
$740$	−4.01472			−0.147584
$741$		−	24.6202i		−	0.904447i
$742$	2.20468			0.0809365
$743$	−8.37331			−0.307187			−0.153594	−	0.988134i	$-0.549085\pi$
$743$	−8.37331			−0.307187			−0.153594	+	0.988134i	$0.549085\pi$
$744$			44.5003i			1.63146i
$745$		−	12.5357i		−	0.459272i
$746$	−10.7271			−0.392746
$747$	40.3753			1.47726
$748$	−17.4486			−0.637982
$749$			7.70173i			0.281415i
$750$			13.4970i			0.492842i
$751$		−	18.7984i		−	0.685965i	−0.939342	−	0.342982i	$-0.888563\pi$
$751$		−	18.7984i		−	0.685965i	0.939342	−	0.342982i	$-0.111437\pi$
$752$		−	0.808908i		−	0.0294979i
$753$			0.629766i			0.0229499i
$754$	−13.9944			−0.509644
$755$			13.0488i			0.474895i
$756$	−0.0473345			−0.00172154
$757$		−	35.4181i		−	1.28729i	−0.765323	−	0.643647i	$-0.777421\pi$
$757$		−	35.4181i		−	1.28729i	0.765323	−	0.643647i	$-0.222579\pi$
$758$	30.7042			1.11523
$759$	−31.6567			−1.14907
$760$		−	6.34140i		−	0.230027i
$761$	−29.9316			−1.08502			−0.542510	−	0.840049i	$-0.682526\pi$
$761$	−29.9316			−1.08502			−0.542510	+	0.840049i	$0.682526\pi$
$762$		−	2.43367i		−	0.0881625i
$763$	8.54592			0.309383
$764$			4.98245i			0.180259i
$765$		−	7.31244i		−	0.264382i
$766$		−	18.9105i		−	0.683262i
$767$		−	18.3813i		−	0.663711i
$768$			39.9280i			1.44078i
$769$	−12.3539			−0.445491			−0.222746	−	0.974877i	$-0.571502\pi$
$769$	−12.3539			−0.445491			−0.222746	+	0.974877i	$0.571502\pi$
$770$	−2.20684			−0.0795291
$771$	−9.20506			−0.331512
$772$		−	15.1357i		−	0.544746i
$773$			34.0743i			1.22557i	0.790251	+	0.612784i	$0.209950\pi$
$773$			34.0743i			1.22557i	−0.790251	+	0.612784i	$0.790050\pi$
$774$	−28.2686			−1.01609
$775$	−29.1336			−1.04651
$776$		−	39.5038i		−	1.41811i
$777$	−12.6201			−0.452745
$778$	−13.1731			−0.472278
$779$	−10.5463	+	19.3507i	−0.377860	+	0.693310i
$780$	5.58157			0.199852
$781$	−33.4466			−1.19681
$782$			11.2201i			0.401229i
$783$	0.211241			0.00754914
$784$	0.121463			0.00433796
$785$			6.36893i			0.227317i
$786$		−	19.9841i		−	0.712809i
$787$	−3.86537			−0.137785			−0.0688927	−	0.997624i	$-0.521947\pi$
$787$	−3.86537			−0.137785			−0.0688927	+	0.997624i	$0.521947\pi$
$788$	9.40544			0.335055
$789$	−30.5013			−1.08588
$790$			3.75504i			0.133598i
$791$			9.09439i			0.323359i
$792$		−	33.0843i		−	1.17560i
$793$			32.4730i			1.15315i
$794$			16.9320i			0.600893i
$795$	3.92419			0.139177
$796$		−	7.77036i		−	0.275413i
$797$	6.47548			0.229373			0.114687	−	0.993402i	$-0.463414\pi$
$797$	6.47548			0.229373			0.114687	+	0.993402i	$0.463414\pi$
$798$		−	7.50917i		−	0.265822i
$799$	−25.0139			−0.884928
$800$	−25.6687			−0.907525
$801$			3.25816i			0.115122i
$802$	−33.4861			−1.18244
$803$			23.2220i			0.819485i
$804$	10.5930			0.373586
$805$		−	2.16782i		−	0.0764055i
$806$		−	16.4906i		−	0.580855i
$807$		−	46.2053i		−	1.62650i
$808$			7.00995i			0.246609i
$809$			9.84578i			0.346159i	0.984908	+	0.173080i	$0.0553718\pi$
$809$			9.84578i			0.346159i	−0.984908	+	0.173080i	$0.944628\pi$
$810$	−5.14023			−0.180609
$811$	−26.5573			−0.932554			−0.466277	−	0.884639i	$-0.654405\pi$
$811$	−26.5573			−0.932554			−0.466277	+	0.884639i	$0.654405\pi$
$812$	6.52030			0.228818
$813$			68.9791i			2.41920i
$814$		−	17.5902i		−	0.616538i
$815$	−2.04899			−0.0717730
$816$	−1.11898			−0.0391720
$817$			36.2660i			1.26878i
$818$	5.31577			0.185861
$819$	8.79601			0.307358
$820$	−4.38693	−	2.39091i	−0.153198	−	0.0834943i
$821$	26.3942			0.921163			0.460582	−	0.887617i	$-0.347641\pi$
$821$	26.3942			0.921163			0.460582	+	0.887617i	$0.347641\pi$
$822$	−26.4186			−0.921453
$823$			31.8394i			1.10985i	0.831899	+	0.554927i	$0.187254\pi$
$823$			31.8394i			1.10985i	−0.831899	+	0.554927i	$0.812746\pi$
$824$	−6.12869			−0.213503
$825$	43.2048			1.50420
$826$		−	5.60630i		−	0.195068i
$827$		−	14.8956i		−	0.517972i	−0.965881	−	0.258986i	$-0.916612\pi$
$827$		−	14.8956i		−	0.517972i	0.965881	−	0.258986i	$-0.0833883\pi$
$828$	12.2425			0.425458
$829$	18.3559			0.637528			0.318764	−	0.947834i	$-0.396732\pi$
$829$	18.3559			0.637528			0.318764	+	0.947834i	$0.396732\pi$
$830$	−7.68705			−0.266821
$831$		−	26.2601i		−	0.910953i
$832$		−	15.2378i		−	0.528275i
$833$		−	3.75599i		−	0.130137i
$834$		−	50.5438i		−	1.75019i
$835$			9.86067i			0.341243i
$836$	−15.9888			−0.552983
$837$			0.248920i			0.00860395i
$838$	−7.07805			−0.244507
$839$		−	23.0672i		−	0.796368i	−0.917306	−	0.398184i	$-0.869641\pi$
$839$		−	23.0672i		−	0.796368i	0.917306	−	0.398184i	$-0.130359\pi$
$840$	4.51916			0.155926
$841$	−0.0983418			−0.00339110
$842$		−	11.0871i		−	0.382088i
$843$	−5.47204			−0.188467
$844$			28.7793i			0.990625i
$845$	2.90106			0.0997994
$846$		−	17.8666i		−	0.614266i
$847$			3.77075i			0.129564i
$848$		−	0.301044i		−	0.0103379i
$849$		−	48.3742i		−	1.66020i
$850$		−	15.3131i		−	0.525234i
$851$	17.2792			0.592322
$852$	25.8010			0.883929
$853$	−15.3915			−0.526996			−0.263498	−	0.964660i	$-0.584876\pi$
$853$	−15.3915			−0.526996			−0.263498	+	0.964660i	$0.584876\pi$
$854$			9.90428i			0.338917i
$855$		−	6.70066i		−	0.229158i
$856$	21.9828			0.751355
$857$	−41.0695			−1.40291			−0.701454	−	0.712715i	$-0.747465\pi$
$857$	−41.0695			−1.40291			−0.701454	+	0.712715i	$0.747465\pi$
$858$			24.4553i			0.834890i
$859$	43.0405			1.46852			0.734262	−	0.678867i	$-0.237529\pi$
$859$	43.0405			1.46852			0.734262	+	0.678867i	$0.237529\pi$
$860$	−8.22173			−0.280359
$861$	−13.7901	−	7.51575i	−0.469967	−	0.256136i
$862$	30.8918			1.05218
$863$	55.2711			1.88145			0.940725	−	0.339170i	$-0.110146\pi$
$863$	55.2711			1.88145			0.940725	+	0.339170i	$0.110146\pi$
$864$			0.219316i			0.00746127i
$865$	−7.79257			−0.264955
$866$	0.886603			0.0301280
$867$		−	7.09458i		−	0.240945i
$868$			7.68333i			0.260789i
$869$	25.1331			0.852581
$870$	−7.59726			−0.257571
$871$	−10.4206			−0.353088
$872$		−	24.3923i		−	0.826027i
$873$		−	41.7419i		−	1.41275i
$874$			10.2814i			0.347773i
$875$			6.18623i			0.209133i
$876$		−	17.9136i		−	0.605246i
$877$	−36.5325			−1.23361			−0.616807	−	0.787115i	$-0.711574\pi$
$877$	−36.5325			−1.23361			−0.616807	+	0.787115i	$0.711574\pi$
$878$			14.3876i			0.485558i
$879$	−12.9610			−0.437162
$880$			0.301339i			0.0101581i
$881$	−52.3225			−1.76279			−0.881396	−	0.472379i	$-0.843395\pi$
$881$	−52.3225			−1.76279			−0.881396	+	0.472379i	$0.843395\pi$
$882$	2.68278			0.0903340
$883$			5.10109i			0.171665i	0.996310	+	0.0858327i	$0.0273551\pi$
$883$			5.10109i			0.171665i	−0.996310	+	0.0858327i	$0.972645\pi$
$884$	−13.2409			−0.445340
$885$		−	9.97886i		−	0.335436i
$886$	10.3666			0.348271
$887$			33.2560i			1.11663i	0.829630	+	0.558314i	$0.188551\pi$
$887$			33.2560i			1.11663i	−0.829630	+	0.558314i	$0.811449\pi$
$888$			36.0212i			1.20879i
$889$		−	1.11545i		−	0.0374109i
$890$		−	0.620321i		−	0.0207932i
$891$			34.4044i			1.15259i
$892$	0.0471723			0.00157945
$893$	−22.9211			−0.767027
$894$	−42.3691			−1.41704
$895$		−	14.7359i		−	0.492566i
$896$			6.55344i			0.218935i
$897$	−24.0228			−0.802098
$898$	20.1503			0.672425
$899$		−	34.2887i		−	1.14359i
$900$	−16.7085			−0.556951
$901$	−9.30919			−0.310134
$902$	10.4756	−	19.2210i	0.348800	−	0.639990i
$903$	−25.8447			−0.860058
$904$	25.9578			0.863343
$905$			8.37717i			0.278466i
$906$	44.1034			1.46524
$907$	−26.9243			−0.894006			−0.447003	−	0.894532i	$-0.647509\pi$
$907$	−26.9243			−0.894006			−0.447003	+	0.894532i	$0.647509\pi$
$908$		−	0.167138i		−	0.00554667i
$909$			7.40709i			0.245678i
$910$	−1.67467			−0.0555148
$911$	14.9485			0.495265			0.247633	−	0.968854i	$-0.420347\pi$
$911$	14.9485			0.495265			0.247633	+	0.968854i	$0.420347\pi$
$912$	−1.02536			−0.0339530
$913$			51.4506i			1.70277i
$914$		−	16.9007i		−	0.559026i
$915$			17.6290i			0.582796i
$916$		−	18.3400i		−	0.605970i
$917$		−	9.15951i		−	0.302474i
$918$	−0.130836			−0.00431824
$919$		−	4.48515i		−	0.147951i	−0.997260	−	0.0739757i	$-0.976431\pi$
$919$		−	4.48515i		−	0.147951i	0.997260	−	0.0739757i	$-0.0235687\pi$
$920$	−6.18752			−0.203997
$921$			36.2030i			1.19293i
$922$	−29.8930			−0.984472
$923$	−25.3811			−0.835430
$924$		−	11.3943i		−	0.374845i
$925$	−23.5825			−0.775388
$926$		−	6.97242i		−	0.229128i
$927$	−6.47590			−0.212696
$928$		−	30.2106i		−	0.991712i
$929$		−	4.23482i		−	0.138940i	−0.997584	−	0.0694700i	$-0.977869\pi$
$929$		−	4.23482i		−	0.138940i	0.997584	−	0.0694700i	$-0.0221308\pi$
$930$		−	8.95240i		−	0.293561i
$931$		−	3.44176i		−	0.112799i
$932$			16.8611i			0.552303i
$933$	63.2245			2.06988
$934$	−12.0220			−0.393371
$935$	9.31831			0.304741
$936$		−	25.1061i		−	0.820620i
$937$			43.1984i			1.41123i	0.708595	+	0.705616i	$0.249330\pi$
$937$			43.1984i			1.41123i	−0.708595	+	0.705616i	$0.750670\pi$
$938$	−3.17828			−0.103774
$939$	−9.98517			−0.325854
$940$		−	5.19637i		−	0.169487i
$941$	26.6450			0.868603			0.434301	−	0.900768i	$-0.356995\pi$
$941$	26.6450			0.868603			0.434301	+	0.900768i	$0.356995\pi$
$942$	21.5262			0.701362
$943$	18.8811	+	10.2904i	0.614854	+	0.335101i
$944$	−0.765527			−0.0249158
$945$	0.0252787			0.000822317
$946$		−	36.0230i		−	1.17121i
$947$	−0.964984			−0.0313578			−0.0156789	−	0.999877i	$-0.504991\pi$
$947$	−0.964984			−0.0313578			−0.0156789	+	0.999877i	$0.504991\pi$
$948$	−19.3879			−0.629689
$949$			17.6221i			0.572037i
$950$		−	14.0319i		−	0.455256i
$951$	64.5437			2.09297
$952$	−10.7206			−0.347457
$953$	−42.0964			−1.36363			−0.681817	−	0.731522i	$-0.738810\pi$
$953$	−42.0964			−1.36363			−0.681817	+	0.731522i	$0.738810\pi$
$954$		−	6.64925i		−	0.215277i
$955$		−	2.66085i		−	0.0861031i
$956$		−	12.2916i		−	0.397538i
$957$			50.8497i			1.64374i
$958$		−	33.8573i		−	1.09388i
$959$	−12.1087			−0.391010
$960$		−	8.27229i		−	0.266987i
$961$	9.40479			0.303380
$962$		−	13.3484i		−	0.430371i
$963$	23.2281			0.748517
$964$	−22.8363			−0.735507
$965$			8.08314i			0.260205i
$966$	−7.32696			−0.235741
$967$			44.7535i			1.43918i	0.694401	+	0.719588i	$0.255669\pi$
$967$			44.7535i			1.43918i	−0.694401	+	0.719588i	$0.744331\pi$
$968$	10.7627			0.345926
$969$			31.7072i			1.01858i
$970$			7.94723i			0.255170i
$971$			13.4547i			0.431780i	0.976418	+	0.215890i	$0.0692653\pi$
$971$			13.4547i			0.431780i	−0.976418	+	0.215890i	$0.930735\pi$
$972$		−	26.6819i		−	0.855821i
$973$		−	23.1662i		−	0.742676i
$974$	−21.8742			−0.700894
$975$	32.7862			1.05000
$976$	1.35240			0.0432894
$977$		−	31.1565i		−	0.996783i	−0.866952	−	0.498392i	$-0.833924\pi$
$977$		−	31.1565i		−	0.996783i	0.866952	−	0.498392i	$-0.166076\pi$
$978$			6.92534i			0.221448i
$979$	−4.15191			−0.132695
$980$	0.780269			0.0249248
$981$		−	25.7742i		−	0.822907i
$982$	35.5083			1.13312
$983$	−48.0127			−1.53137			−0.765684	−	0.643217i	$-0.777599\pi$
$983$	−48.0127			−1.53137			−0.765684	+	0.643217i	$0.777599\pi$
$984$	−21.4519	+	39.3607i	−0.683863	+	1.25477i
$985$	−5.02293			−0.160044
$986$	18.0226			0.573958
$987$		−	16.3346i		−	0.519937i
$988$	−12.1331			−0.386006
$989$	35.3859			1.12521
$990$			6.65576i			0.211534i
$991$		−	52.9823i		−	1.68304i	−0.540227	−	0.841520i	$-0.681661\pi$
$991$		−	52.9823i		−	1.68304i	0.540227	−	0.841520i	$-0.318339\pi$
$992$	35.5993			1.13028
$993$	81.8819			2.59844
$994$	−7.74124			−0.245537
$995$			4.14972i			0.131555i
$996$		−	39.6895i		−	1.25761i
$997$			43.5980i			1.38076i	0.723445	+	0.690382i	$0.242558\pi$
$997$			43.5980i			1.38076i	−0.723445	+	0.690382i	$0.757442\pi$
$998$		−	14.7891i		−	0.468140i
$999$			0.201491i			0.00637489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.c.a.204.5	✓	10
41.40	even	2	inner	287.2.c.a.204.6	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.c.a.204.5	✓	10	1.1	even	1	trivial
287.2.c.a.204.6	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)

\(f(q)\)	\(=\)	\(q+0.889527 q^{2} -2.45275i q^{3} -1.20874 q^{4} +0.645522 q^{5} -2.18179i q^{6} -1.00000i q^{7} -2.85426 q^{8} -3.01597 q^{9} +O(q^{10})\)	\(q+0.889527 q^{2} -2.45275i q^{3} -1.20874 q^{4} +0.645522 q^{5} -2.18179i q^{6} -1.00000i q^{7} -2.85426 q^{8} -3.01597 q^{9} +0.574209 q^{10} -3.84327i q^{11} +2.96474i q^{12} -2.91648i q^{13} -0.889527i q^{14} -1.58330i q^{15} -0.121463 q^{16} +3.75599i q^{17} -2.68278 q^{18} +3.44176i q^{19} -0.780269 q^{20} -2.45275 q^{21} -3.41870i q^{22} +3.35824 q^{23} +7.00078i q^{24} -4.58330 q^{25} -2.59429i q^{26} +0.0391601i q^{27} +1.20874i q^{28} -5.39429i q^{29} -1.40839i q^{30} +6.35648 q^{31} +5.60048 q^{32} -9.42657 q^{33} +3.34106i q^{34} -0.645522i q^{35} +3.64552 q^{36} +5.14531 q^{37} +3.06154i q^{38} -7.15339 q^{39} -1.84249 q^{40} +(5.62233 + 3.06422i) q^{41} -2.18179 q^{42} +10.5370 q^{43} +4.64552i q^{44} -1.94687 q^{45} +2.98725 q^{46} +6.65972i q^{47} +0.297917i q^{48} -1.00000 q^{49} -4.07697 q^{50} +9.21250 q^{51} +3.52527i q^{52} +2.47849i q^{53} +0.0348340i q^{54} -2.48092i q^{55} +2.85426i q^{56} +8.44176 q^{57} -4.79837i q^{58} +6.30256 q^{59} +1.91380i q^{60} -11.1343 q^{61} +5.65426 q^{62} +3.01597i q^{63} +5.22471 q^{64} -1.88265i q^{65} -8.38520 q^{66} -3.57300i q^{67} -4.54002i q^{68} -8.23691i q^{69} -0.574209i q^{70} -8.70265i q^{71} +8.60836 q^{72} -6.04224 q^{73} +4.57689 q^{74} +11.2417i q^{75} -4.16019i q^{76} -3.84327 q^{77} -6.36314 q^{78} +6.53949i q^{79} -0.0784069 q^{80} -8.95185 q^{81} +(5.00121 + 2.72571i) q^{82} -13.3872 q^{83} +2.96474 q^{84} +2.42458i q^{85} +9.37299 q^{86} -13.2308 q^{87} +10.9697i q^{88} -1.08030i q^{89} -1.73180 q^{90} -2.91648 q^{91} -4.05924 q^{92} -15.5908i q^{93} +5.92401i q^{94} +2.22173i q^{95} -13.7366i q^{96} +13.8403i q^{97} -0.889527 q^{98} +11.5912i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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