LMFDB - Embedded newform 360.6.k.b.181.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [360,6,Mod(181,360)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("360.181"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(360, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	360.k (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$57.7381751327$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{8}\cdot 5^{12} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.17
Root			$-3.90102 - 0.884346i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.6.k.b.181.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.78536 - 3.01667i) q^{2} +(13.7994 - 28.8717i) q^{4} +25.0000i q^{5} -56.4938 q^{7} +(-21.0614 - 179.790i) q^{8} +(75.4168 + 119.634i) q^{10} -261.019i q^{11} -720.631i q^{13} +(-270.343 + 170.423i) q^{14} +(-643.154 - 796.825i) q^{16} +1876.44 q^{17} +1992.33i q^{19} +(721.793 + 344.985i) q^{20} +(-787.408 - 1249.07i) q^{22} -2570.29 q^{23} -625.000 q^{25} +(-2173.91 - 3448.48i) q^{26} +(-779.581 + 1631.07i) q^{28} +1700.16i q^{29} -7734.68 q^{31} +(-5481.48 - 1872.91i) q^{32} +(8979.46 - 5660.61i) q^{34} -1412.35i q^{35} -12228.1i q^{37} +(6010.20 + 9534.02i) q^{38} +(4494.75 - 526.535i) q^{40} -14979.3 q^{41} -18113.9i q^{43} +(-7536.06 - 3601.90i) q^{44} +(-12299.8 + 7753.73i) q^{46} -2141.03 q^{47} -13615.4 q^{49} +(-2990.85 + 1885.42i) q^{50} +(-20805.9 - 9944.27i) q^{52} +1605.71i q^{53} +6525.47 q^{55} +(1189.84 + 10157.0i) q^{56} +(5128.81 + 8135.87i) q^{58} +2680.90i q^{59} -44521.9i q^{61} +(-37013.2 + 23333.0i) q^{62} +(-31880.8 + 7573.26i) q^{64} +18015.8 q^{65} +12486.0i q^{67} +(25893.8 - 54176.2i) q^{68} +(-4260.58 - 6758.59i) q^{70} -8189.38 q^{71} -41082.7 q^{73} +(-36888.2 - 58516.0i) q^{74} +(57522.0 + 27492.9i) q^{76} +14746.0i q^{77} +46325.9 q^{79} +(19920.6 - 16078.8i) q^{80} +(-71681.6 + 45187.8i) q^{82} +61655.4i q^{83} +46911.1i q^{85} +(-54643.7 - 86681.7i) q^{86} +(-46928.5 + 5497.42i) q^{88} -53205.4 q^{89} +40711.2i q^{91} +(-35468.5 + 74208.8i) q^{92} +(-10245.6 + 6458.79i) q^{94} -49808.2 q^{95} -39211.8 q^{97} +(-65154.8 + 41073.3i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32}+ \cdots - 216942 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	4.78536	−	3.01667i	0.845941	−	0.533277i
$2$	4.78536	−	3.01667i	0.845941	−	0.533277i
$3$		0			0
$3$		0			0
$4$	13.7994	−	28.8717i	0.431231	−	0.902242i
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$		0			0
$7$	−56.4938			−0.435769			−0.217884	−	0.975975i	$-0.569916\pi$
$7$	−56.4938			−0.435769			−0.217884	+	0.975975i	$0.569916\pi$
$8$	−21.0614	−	179.790i	−0.116349	−	0.993208i
$9$		0			0
$10$	75.4168	+	119.634i	0.238489	+	0.378316i
$11$		−	261.019i		−	0.650414i	−0.945643	−	0.325207i	$-0.894566\pi$
$11$		−	261.019i		−	0.650414i	0.945643	−	0.325207i	$-0.105434\pi$
$12$		0			0
$13$		−	720.631i		−	1.18265i	−0.806435	−	0.591323i	$-0.798606\pi$
$13$		−	720.631i		−	1.18265i	0.806435	−	0.591323i	$-0.201394\pi$
$14$	−270.343	+	170.423i	−0.368634	+	0.232385i
$15$		0			0
$16$	−643.154	−	796.825i	−0.628080	−	0.778149i
$17$	1876.44			1.57476			0.787378	−	0.616471i	$-0.211438\pi$
$17$	1876.44			1.57476			0.787378	+	0.616471i	$0.211438\pi$
$18$		0			0
$19$			1992.33i			1.26613i	0.774100	+	0.633063i	$0.218203\pi$
$19$			1992.33i			1.26613i	−0.774100	+	0.633063i	$0.781797\pi$
$20$	721.793	+	344.985i	0.403495	+	0.192852i
$21$		0			0
$22$	−787.408	−	1249.07i	−0.346851	−	0.550212i
$23$	−2570.29			−1.01313			−0.506563	−	0.862203i	$-0.669084\pi$
$23$	−2570.29			−1.01313			−0.506563	+	0.862203i	$0.669084\pi$
$24$		0			0
$25$	−625.000			−0.200000
$26$	−2173.91	−	3448.48i	−0.630678	−	1.00045i
$27$		0			0
$28$	−779.581	+	1631.07i	−0.187917	+	0.393169i
$29$			1700.16i			0.375400i	0.982226	+	0.187700i	$0.0601032\pi$
$29$			1700.16i			0.375400i	−0.982226	+	0.187700i	$0.939897\pi$
$30$		0			0
$31$	−7734.68			−1.44557			−0.722783	−	0.691075i	$-0.757137\pi$
$31$	−7734.68			−1.44557			−0.722783	+	0.691075i	$0.757137\pi$
$32$	−5481.48	−	1872.91i	−0.946287	−	0.323327i
$33$		0			0
$34$	8979.46	−	5660.61i	1.33215	−	0.839781i
$35$		−	1412.35i		−	0.194882i
$36$		0			0
$37$		−	12228.1i		−	1.46844i	−0.678913	−	0.734218i	$-0.737549\pi$
$37$		−	12228.1i		−	1.46844i	0.678913	−	0.734218i	$-0.262451\pi$
$38$	6010.20	+	9534.02i	0.675196	+	1.07107i
$39$		0			0
$40$	4494.75	−	526.535i	0.444176	−	0.0520328i
$41$	−14979.3			−1.39166			−0.695830	−	0.718206i	$-0.744963\pi$
$41$	−14979.3			−1.39166			−0.695830	+	0.718206i	$0.744963\pi$
$42$		0			0
$43$		−	18113.9i		−	1.49397i	−0.664842	−	0.746984i	$-0.731501\pi$
$43$		−	18113.9i		−	1.49397i	0.664842	−	0.746984i	$-0.268499\pi$
$44$	−7536.06	−	3601.90i	−0.586831	−	0.280479i
$45$		0			0
$46$	−12299.8	+	7753.73i	−0.857044	+	0.540277i
$47$	−2141.03			−0.141377			−0.0706885	−	0.997498i	$-0.522520\pi$
$47$	−2141.03			−0.141377			−0.0706885	+	0.997498i	$0.522520\pi$
$48$		0			0
$49$	−13615.4			−0.810106
$50$	−2990.85	+	1885.42i	−0.169188	+	0.106655i
$51$		0			0
$52$	−20805.9	−	9944.27i	−1.06703	−	0.509993i
$53$			1605.71i			0.0785192i	0.999229	+	0.0392596i	$0.0124999\pi$
$53$			1605.71i			0.0785192i	−0.999229	+	0.0392596i	$0.987500\pi$
$54$		0			0
$55$	6525.47			0.290874
$56$	1189.84	+	10157.0i	0.0507012	+	0.432809i
$57$		0			0
$58$	5128.81	+	8135.87i	0.200192	+	0.317566i
$59$			2680.90i			0.100265i	0.998743	+	0.0501327i	$0.0159644\pi$
$59$			2680.90i			0.100265i	−0.998743	+	0.0501327i	$0.984036\pi$
$60$		0			0
$61$		−	44521.9i		−	1.53197i	−0.642860	−	0.765984i	$-0.722252\pi$
$61$		−	44521.9i		−	1.53197i	0.642860	−	0.765984i	$-0.277748\pi$
$62$	−37013.2	+	23333.0i	−1.22286	+	0.770887i
$63$		0			0
$64$	−31880.8	+	7573.26i	−0.972926	+	0.231117i
$65$	18015.8			0.528895
$66$		0			0
$67$			12486.0i			0.339809i	0.985461	+	0.169905i	$0.0543460\pi$
$67$			12486.0i			0.339809i	−0.985461	+	0.169905i	$0.945654\pi$
$68$	25893.8	−	54176.2i	0.679083	−	1.42081i
$69$		0			0
$70$	−4260.58	−	6758.59i	−0.103926	−	0.164858i
$71$	−8189.38			−0.192799			−0.0963996	−	0.995343i	$-0.530733\pi$
$71$	−8189.38			−0.192799			−0.0963996	+	0.995343i	$0.530733\pi$
$72$		0			0
$73$	−41082.7			−0.902302			−0.451151	−	0.892448i	$-0.648986\pi$
$73$	−41082.7			−0.902302			−0.451151	+	0.892448i	$0.648986\pi$
$74$	−36888.2	−	58516.0i	−0.783084	−	1.24221i
$75$		0			0
$76$	57522.0	+	27492.9i	1.14235	+	0.545993i
$77$			14746.0i			0.283430i
$78$		0			0
$79$	46325.9			0.835134			0.417567	−	0.908646i	$-0.362883\pi$
$79$	46325.9			0.835134			0.417567	+	0.908646i	$0.362883\pi$
$80$	19920.6	−	16078.8i	0.347999	−	0.280886i
$81$		0			0
$82$	−71681.6	+	45187.8i	−1.17726	+	0.742141i
$83$			61655.4i			0.982372i	0.871055	+	0.491186i	$0.163436\pi$
$83$			61655.4i			0.982372i	−0.871055	+	0.491186i	$0.836564\pi$
$84$		0			0
$85$			46911.1i			0.704252i
$86$	−54643.7	−	86681.7i	−0.796699	−	1.26381i
$87$		0			0
$88$	−46928.5	+	5497.42i	−0.645997	+	0.0756750i
$89$	−53205.4			−0.712001			−0.356000	−	0.934486i	$-0.615860\pi$
$89$	−53205.4			−0.712001			−0.356000	+	0.934486i	$0.615860\pi$
$90$		0			0
$91$			40711.2i			0.515360i
$92$	−35468.5	+	74208.8i	−0.436891	+	0.914084i
$93$		0			0
$94$	−10245.6	+	6458.79i	−0.119597	+	0.0753931i
$95$	−49808.2			−0.566229
$96$		0			0
$97$	−39211.8			−0.423143			−0.211571	−	0.977363i	$-0.567858\pi$
$97$	−39211.8			−0.423143			−0.211571	+	0.977363i	$0.567858\pi$
$98$	−65154.8	+	41073.3i	−0.685301	+	0.432011i
$99$		0			0
$100$	−8624.62	+	18044.8i	−0.0862462	+	0.180448i
$101$		−	41893.0i		−	0.408637i	−0.978904	−	0.204319i	$-0.934502\pi$
$101$		−	41893.0i		−	0.408637i	0.978904	−	0.204319i	$-0.0654979\pi$
$102$		0			0
$103$	−118358.			−1.09927			−0.549635	−	0.835405i	$-0.685233\pi$
$103$	−118358.			−1.09927			−0.549635	+	0.835405i	$0.685233\pi$
$104$	−129562.	+	15177.5i	−1.17461	+	0.137600i
$105$		0			0
$106$	4843.88	+	7683.88i	0.0418725	+	0.0664226i
$107$		−	147978.i		−	1.24951i	−0.780822	−	0.624754i	$-0.785199\pi$
$107$		−	147978.i		−	1.24951i	0.780822	−	0.624754i	$-0.214801\pi$
$108$		0			0
$109$		−	126538.i		−	1.02013i	−0.860135	−	0.510066i	$-0.829621\pi$
$109$		−	126538.i		−	1.02013i	0.860135	−	0.510066i	$-0.170379\pi$
$110$	31226.7	−	19685.2i	0.246062	−	0.155116i
$111$		0			0
$112$	36334.2	+	45015.7i	0.273697	+	0.339093i
$113$	221898.			1.63478			0.817388	−	0.576088i	$-0.195421\pi$
$113$	221898.			1.63478			0.817388	+	0.576088i	$0.195421\pi$
$114$		0			0
$115$		−	64257.4i		−	0.453084i
$116$	49086.5	+	23461.1i	0.338701	+	0.161884i
$117$		0			0
$118$	8087.40	+	12829.1i	0.0534692	+	0.0848185i
$119$	−106007.			−0.686229
$120$		0			0
$121$	92920.2			0.576961
$122$	−134308.	−	213054.i	−0.816963	−	1.29595i
$123$		0			0
$124$	−106734.	+	223313.i	−0.623373	+	1.30425i
$125$		−	15625.0i		−	0.0894427i
$126$		0			0
$127$	237825.			1.30842			0.654212	−	0.756312i	$-0.273001\pi$
$127$	237825.			1.30842			0.654212	+	0.756312i	$0.273001\pi$
$128$	−129715.	+	132415.i	−0.699788	+	0.714351i
$129$		0			0
$130$	86212.0	−	54347.7i	0.447414	−	0.282048i
$131$			151213.i			0.769856i	0.922947	+	0.384928i	$0.125774\pi$
$131$			151213.i			0.769856i	−0.922947	+	0.384928i	$0.874226\pi$
$132$		0			0
$133$		−	112554.i		−	0.551738i
$134$	37666.1	+	59749.9i	0.181213	+	0.287458i
$135$		0			0
$136$	−39520.5	−	337366.i	−0.183221	−	1.56406i
$137$	−163216.			−0.742954			−0.371477	−	0.928442i	$-0.621148\pi$
$137$	−163216.			−0.742954			−0.371477	+	0.928442i	$0.621148\pi$
$138$		0			0
$139$			7490.33i			0.0328824i	0.999865	+	0.0164412i	$0.00523364\pi$
$139$			7490.33i			0.0328824i	−0.999865	+	0.0164412i	$0.994766\pi$
$140$	−40776.9	−	19489.5i	−0.175830	−	0.0840390i
$141$		0			0
$142$	−39189.2	+	24704.7i	−0.163097	+	0.102815i
$143$	−188098.			−0.769209
$144$		0			0
$145$	−42503.9			−0.167884
$146$	−196596.	+	123933.i	−0.763294	+	0.481177i
$147$		0			0
$148$	−353047.	−	168741.i	−1.32488	−	0.633236i
$149$			35543.3i			0.131157i	0.997847	+	0.0655786i	$0.0208893\pi$
$149$			35543.3i			0.131157i	−0.997847	+	0.0655786i	$0.979111\pi$
$150$		0			0
$151$	549802.			1.96229			0.981147	−	0.193263i	$-0.0619070\pi$
$151$	549802.			1.96229			0.981147	+	0.193263i	$0.0619070\pi$
$152$	358201.	−	41961.3i	1.25753	−	0.147312i
$153$		0			0
$154$	44483.7	+	70564.7i	0.151147	+	0.239765i
$155$		−	193367.i		−	0.646477i
$156$		0			0
$157$			252420.i			0.817287i	0.912694	+	0.408643i	$0.133998\pi$
$157$			252420.i			0.817287i	−0.912694	+	0.408643i	$0.866002\pi$
$158$	221686.	−	139750.i	0.706474	−	0.445358i
$159$		0			0
$160$	46822.8	−	137037.i	0.144596	−	0.423192i
$161$	145206.			0.441488
$162$		0			0
$163$			383218.i			1.12974i	0.825182	+	0.564868i	$0.191073\pi$
$163$			383218.i			1.12974i	−0.825182	+	0.564868i	$0.808927\pi$
$164$	−206706.	+	432480.i	−0.600127	+	1.25561i
$165$		0			0
$166$	185994.	+	295043.i	0.523876	+	0.831028i
$167$	−108418.			−0.300821			−0.150411	−	0.988624i	$-0.548060\pi$
$167$	−108418.			−0.300821			−0.150411	+	0.988624i	$0.548060\pi$
$168$		0			0
$169$	−148016.			−0.398650
$170$	141515.	+	224487.i	0.375561	+	0.595755i
$171$		0			0
$172$	−522980.	−	249961.i	−1.34792	−	0.644245i
$173$			305932.i			0.777157i	0.921416	+	0.388579i	$0.127034\pi$
$173$			305932.i			0.777157i	−0.921416	+	0.388579i	$0.872966\pi$
$174$		0			0
$175$	35308.6			0.0871537
$176$	−207986.	+	167875.i	−0.506119	+	0.408512i
$177$		0			0
$178$	−254607.	+	160503.i	−0.602311	+	0.379694i
$179$		−	209868.i		−	0.489568i	−0.969578	−	0.244784i	$-0.921283\pi$
$179$		−	209868.i		−	0.489568i	0.969578	−	0.244784i	$-0.0787170\pi$
$180$		0			0
$181$		−	212990.i		−	0.483239i	−0.970371	−	0.241620i	$-0.922321\pi$
$181$		−	212990.i		−	0.483239i	0.970371	−	0.241620i	$-0.0776786\pi$
$182$	122812.	+	194818.i	0.274830	+	0.435964i
$183$		0			0
$184$	54134.0	+	462113.i	0.117876	+	1.00624i
$185$	305703.			0.656705
$186$		0			0
$187$		−	489787.i		−	1.02424i
$188$	−29545.0	+	61815.3i	−0.0609662	+	0.127556i
$189$		0			0
$190$	−238350.	+	150255.i	−0.478996	+	0.301957i
$191$	177246.			0.351555			0.175777	−	0.984430i	$-0.443756\pi$
$191$	177246.			0.351555			0.175777	+	0.984430i	$0.443756\pi$
$192$		0			0
$193$	758117.			1.46502			0.732509	−	0.680758i	$-0.238349\pi$
$193$	758117.			1.46502			0.732509	+	0.680758i	$0.238349\pi$
$194$	−187643.	+	118289.i	−0.357954	+	0.225652i
$195$		0			0
$196$	−187885.	+	393101.i	−0.349343	+	0.730911i
$197$		−	353509.i		−	0.648985i	−0.945888	−	0.324492i	$-0.894807\pi$
$197$		−	353509.i		−	0.648985i	0.945888	−	0.324492i	$-0.105193\pi$
$198$		0			0
$199$	233027.			0.417132			0.208566	−	0.978008i	$-0.433120\pi$
$199$	233027.			0.417132			0.208566	+	0.978008i	$0.433120\pi$
$200$	13163.4	+	112369.i	0.0232698	+	0.198642i
$201$		0			0
$202$	−126377.	−	200473.i	−0.217917	−	0.345683i
$203$		−	96048.4i		−	0.163587i
$204$		0			0
$205$		−	374484.i		−	0.622369i
$206$	−566385.	+	357047.i	−0.929917	+	0.586215i
$207$		0			0
$208$	−574217.	+	463476.i	−0.920274	+	0.742795i
$209$	520035.			0.823507
$210$		0			0
$211$			401222.i			0.620410i	0.950670	+	0.310205i	$0.100398\pi$
$211$			401222.i			0.620410i	−0.950670	+	0.310205i	$0.899602\pi$
$212$	46359.5	+	22157.8i	0.0708433	+	0.0338599i
$213$		0			0
$214$	−446402.	−	708130.i	−0.666334	−	1.05701i
$215$	452848.			0.668123
$216$		0			0
$217$	436961.			0.629932
$218$	−381725.	−	605533.i	−0.544013	−	0.862971i
$219$		0			0
$220$	90047.5	−	188402.i	0.125434	−	0.262439i
$221$		−	1.35222e6i		−	1.86238i
$222$		0			0
$223$	−475659.			−0.640521			−0.320260	−	0.947330i	$-0.603770\pi$
$223$	−475659.			−0.640521			−0.320260	+	0.947330i	$0.603770\pi$
$224$	309670.	+	105808.i	0.412362	+	0.140896i
$225$		0			0
$226$	1.06186e6	−	669395.i	1.38292	−	0.871789i
$227$		−	28559.0i		−	0.0367856i	−0.999831	−	0.0183928i	$-0.994145\pi$
$227$		−	28559.0i		−	0.0367856i	0.999831	−	0.0183928i	$-0.00585494\pi$
$228$		0			0
$229$		−	969736.i		−	1.22198i	−0.791638	−	0.610991i	$-0.790771\pi$
$229$		−	969736.i		−	1.22198i	0.791638	−	0.610991i	$-0.209229\pi$
$230$	−193843.	−	307495.i	−0.241619	−	0.383282i
$231$		0			0
$232$	305671.	−	35807.7i	0.372850	−	0.0436774i
$233$	16005.7			0.0193146			0.00965728	−	0.999953i	$-0.496926\pi$
$233$	16005.7			0.0193146			0.00965728	+	0.999953i	$0.496926\pi$
$234$		0			0
$235$		−	53525.8i		−	0.0632257i
$236$	77402.3	+	36994.8i	0.0904636	+	0.0432375i
$237$		0			0
$238$	−507284.	+	319790.i	−0.580509	+	0.365950i
$239$	−1.26598e6			−1.43361			−0.716807	−	0.697272i	$-0.754397\pi$
$239$	−1.26598e6			−1.43361			−0.716807	+	0.697272i	$0.754397\pi$
$240$		0			0
$241$	414590.			0.459807			0.229904	−	0.973213i	$-0.426159\pi$
$241$	414590.			0.459807			0.229904	+	0.973213i	$0.426159\pi$
$242$	444657.	−	280310.i	0.488075	−	0.307680i
$243$		0			0
$244$	−1.28543e6	−	614376.i	−1.38220	−	0.660632i
$245$		−	340386.i		−	0.362290i
$246$		0			0
$247$	1.43573e6			1.49738
$248$	162903.	+	1.39062e6i	0.168190	+	1.43575i
$249$		0			0
$250$	−47135.5	−	74771.3i	−0.0476978	−	0.0756632i
$251$			184150.i			0.184496i	0.995736	+	0.0922479i	$0.0294052\pi$
$251$			184150.i			0.184496i	−0.995736	+	0.0922479i	$0.970595\pi$
$252$		0			0
$253$			670895.i			0.658951i
$254$	1.13808e6	−	717440.i	1.10685	−	0.697752i
$255$		0			0
$256$	−221283.	+	1.02496e6i	−0.211032	+	0.977479i
$257$	846268.			0.799236			0.399618	−	0.916682i	$-0.369143\pi$
$257$	846268.			0.799236			0.399618	+	0.916682i	$0.369143\pi$
$258$		0			0
$259$			690813.i			0.639899i
$260$	248607.	−	520147.i	0.228076	−	0.477191i
$261$		0			0
$262$	456159.	+	723607.i	0.410547	+	0.651253i
$263$	1.53385e6			1.36740			0.683698	−	0.729765i	$-0.260371\pi$
$263$	1.53385e6			1.36740			0.683698	+	0.729765i	$0.260371\pi$
$264$		0			0
$265$	−40142.6			−0.0351149
$266$	−339539.	−	538613.i	−0.294229	−	0.466738i
$267$		0			0
$268$	360492.	+	172299.i	0.306590	+	0.146536i
$269$			646714.i			0.544918i	0.962167	+	0.272459i	$0.0878370\pi$
$269$			646714.i			0.544918i	−0.962167	+	0.272459i	$0.912163\pi$
$270$		0			0
$271$	−1.58318e6			−1.30950			−0.654752	−	0.755844i	$-0.727227\pi$
$271$	−1.58318e6			−1.30950			−0.654752	+	0.755844i	$0.727227\pi$
$272$	−1.20684e6	−	1.49520e6i	−0.989072	−	1.22539i
$273$		0			0
$274$	−781049.	+	492369.i	−0.628495	+	0.396200i
$275$			163137.i			0.130083i
$276$		0			0
$277$		−	1.62475e6i		−	1.27229i	−0.771568	−	0.636147i	$-0.780527\pi$
$277$		−	1.62475e6i		−	1.27229i	0.771568	−	0.636147i	$-0.219473\pi$
$278$	22595.9	+	35844.0i	0.0175355	+	0.0278166i
$279$		0			0
$280$	−253926.	+	29746.0i	−0.193558	+	0.0226743i
$281$	1.48375e6			1.12097			0.560487	−	0.828163i	$-0.310614\pi$
$281$	1.48375e6			1.12097			0.560487	+	0.828163i	$0.310614\pi$
$282$		0			0
$283$		−	1.18244e6i		−	0.877634i	−0.898577	−	0.438817i	$-0.855398\pi$
$283$		−	1.18244e6i		−	0.877634i	0.898577	−	0.438817i	$-0.144602\pi$
$284$	−113008.	+	236442.i	−0.0831410	+	0.173951i
$285$		0			0
$286$	−900118.	+	567430.i	−0.650705	+	0.410202i
$287$	846241.			0.606442
$288$		0			0
$289$	2.10118e6			1.47985
$290$	−203397.	+	128220.i	−0.142020	+	0.0895286i
$291$		0			0
$292$	−566916.	+	1.18613e6i	−0.389101	+	0.814094i
$293$		−	887981.i		−	0.604275i	−0.953264	−	0.302137i	$-0.902300\pi$
$293$		−	887981.i		−	0.604275i	0.953264	−	0.302137i	$-0.0977002\pi$
$294$		0			0
$295$	−67022.6			−0.0448400
$296$	−2.19849e6	+	257541.i	−1.45846	+	0.170851i
$297$		0			0
$298$	107223.	+	170088.i	0.0699432	+	0.110951i
$299$			1.85223e6i			1.19817i
$300$		0			0
$301$			1.02332e6i			0.651024i
$302$	2.63100e6	−	1.65857e6i	1.65998	−	1.04645i
$303$		0			0
$304$	1.58754e6	−	1.28137e6i	0.985235	−	0.795228i
$305$	1.11305e6			0.685117
$306$		0			0
$307$		−	1.47690e6i		−	0.894346i	−0.894447	−	0.447173i	$-0.852431\pi$
$307$		−	1.47690e6i		−	0.894346i	0.894447	−	0.447173i	$-0.147569\pi$
$308$	425741.	+	203485.i	0.255722	+	0.122224i
$309$		0			0
$310$	−583324.	−	925331.i	−0.344751	−	0.546881i
$311$	−364521.			−0.213708			−0.106854	−	0.994275i	$-0.534078\pi$
$311$	−364521.			−0.213708			−0.106854	+	0.994275i	$0.534078\pi$
$312$		0			0
$313$	324246.			0.187074			0.0935371	−	0.995616i	$-0.470183\pi$
$313$	324246.			0.187074			0.0935371	+	0.995616i	$0.470183\pi$
$314$	761468.	+	1.20792e6i	0.435840	+	0.691376i
$315$		0			0
$316$	639269.	−	1.33751e6i	0.360136	−	0.753493i
$317$		−	1.55670e6i		−	0.870074i	−0.900413	−	0.435037i	$-0.856735\pi$
$317$		−	1.55670e6i		−	0.870074i	0.900413	−	0.435037i	$-0.143265\pi$
$318$		0			0
$319$	443773.			0.244165
$320$	−189331.	−	797021.i	−0.103359	−	0.435106i
$321$		0			0
$322$	694862.	−	438038.i	0.373473	−	0.235436i
$323$			3.73849e6i			1.99384i
$324$		0			0
$325$			450394.i			0.236529i
$326$	1.15604e6	+	1.83384e6i	0.602462	+	0.955689i
$327$		0			0
$328$	315486.	+	2.69314e6i	0.161918	+	1.38221i
$329$	120955.			0.0616077
$330$		0			0
$331$			558769.i			0.280325i	0.990128	+	0.140163i	$0.0447626\pi$
$331$			558769.i			0.280325i	−0.990128	+	0.140163i	$0.955237\pi$
$332$	1.78010e6	+	850807.i	0.886336	+	0.423629i
$333$		0			0
$334$	−518818.	+	327060.i	−0.254477	+	0.160421i
$335$	−312149.			−0.151967
$336$		0			0
$337$	2.18320e6			1.04717			0.523587	−	0.851972i	$-0.324593\pi$
$337$	2.18320e6			1.04717			0.523587	+	0.851972i	$0.324593\pi$
$338$	−708310.	+	446516.i	−0.337234	+	0.212591i
$339$		0			0
$340$	1.35440e6	+	647344.i	0.635405	+	0.303695i
$341$			2.01890e6i			0.940216i
$342$		0			0
$343$	1.71868e6			0.788787
$344$	−3.25670e6	+	381505.i	−1.48382	+	0.173822i
$345$		0			0
$346$	922895.	+	1.46399e6i	0.414440	+	0.657429i
$347$			2.53924e6i			1.13209i	0.824375	+	0.566043i	$0.191527\pi$
$347$			2.53924e6i			1.13209i	−0.824375	+	0.566043i	$0.808473\pi$
$348$		0			0
$349$		−	2.58452e6i		−	1.13584i	−0.823085	−	0.567918i	$-0.807749\pi$
$349$		−	2.58452e6i		−	1.13584i	0.823085	−	0.567918i	$-0.192251\pi$
$350$	168965.	−	106515.i	0.0737269	−	0.0464771i
$351$		0			0
$352$	−488865.	+	1.43077e6i	−0.210297	+	0.615479i
$353$	−284338.			−0.121450			−0.0607250	−	0.998155i	$-0.519341\pi$
$353$	−284338.			−0.121450			−0.0607250	+	0.998155i	$0.519341\pi$
$354$		0			0
$355$		−	204734.i		−	0.0862224i
$356$	−734202.	+	1.53613e6i	−0.307037	+	0.642397i
$357$		0			0
$358$	−633102.	−	1.00429e6i	−0.261075	−	0.414145i
$359$	1.97109e6			0.807179			0.403590	−	0.914940i	$-0.367762\pi$
$359$	1.97109e6			0.807179			0.403590	+	0.914940i	$0.367762\pi$
$360$		0			0
$361$	−1.49328e6			−0.603077
$362$	−642520.	−	1.01923e6i	−0.257701	−	0.408792i
$363$		0			0
$364$	1.17540e6	+	561790.i	0.464979	+	0.222239i
$365$		−	1.02707e6i		−	0.403522i
$366$		0			0
$367$	1.04179e6			0.403754			0.201877	−	0.979411i	$-0.435296\pi$
$367$	1.04179e6			0.403754			0.201877	+	0.979411i	$0.435296\pi$
$368$	1.65309e6	+	2.04807e6i	0.636324	+	0.788363i
$369$		0			0
$370$	1.46290e6	−	922205.i	0.555533	−	0.350206i
$371$		−	90712.4i		−	0.0342162i
$372$		0			0
$373$			1.58767e6i			0.590866i	0.955363	+	0.295433i	$0.0954639\pi$
$373$			1.58767e6i			0.590866i	−0.955363	+	0.295433i	$0.904536\pi$
$374$	−1.47753e6	−	2.34381e6i	−0.546205	−	0.866449i
$375$		0			0
$376$	45093.2	+	384936.i	0.0164491	+	0.140417i
$377$	1.22519e6			0.443965
$378$		0			0
$379$		−	995922.i		−	0.356145i	−0.984017	−	0.178073i	$-0.943014\pi$
$379$		−	995922.i		−	0.356145i	0.984017	−	0.178073i	$-0.0569862\pi$
$380$	−687323.	+	1.43805e6i	−0.244176	+	0.510875i
$381$		0			0
$382$	848186.	−	534692.i	0.297394	−	0.187476i
$383$	−1.53418e6			−0.534415			−0.267208	−	0.963639i	$-0.586101\pi$
$383$	−1.53418e6			−0.534415			−0.267208	+	0.963639i	$0.586101\pi$
$384$		0			0
$385$	−368649.			−0.126754
$386$	3.62786e6	−	2.28699e6i	1.23932	−	0.781260i
$387$		0			0
$388$	−541099.	+	1.13211e6i	−0.182472	+	0.381777i
$389$		−	4.70941e6i		−	1.57795i	−0.614428	−	0.788973i	$-0.710613\pi$
$389$		−	4.70941e6i		−	1.57795i	0.614428	−	0.788973i	$-0.289387\pi$
$390$		0			0
$391$	−4.82301e6			−1.59542
$392$	286760.	+	2.44792e6i	0.0942549	+	0.804604i
$393$		0			0
$394$	−1.06642e6	−	1.69167e6i	−0.346089	−	0.549002i
$395$			1.15815e6i			0.373483i
$396$		0			0
$397$		−	485420.i		−	0.154576i	−0.997009	−	0.0772879i	$-0.975374\pi$
$397$		−	485420.i		−	0.154576i	0.997009	−	0.0772879i	$-0.0246261\pi$
$398$	1.11512e6	−	702966.i	0.352869	−	0.222447i
$399$		0			0
$400$	401971.	+	498015.i	0.125616	+	0.155630i
$401$	−1.73402e6			−0.538508			−0.269254	−	0.963069i	$-0.586777\pi$
$401$	−1.73402e6			−0.538508			−0.269254	+	0.963069i	$0.586777\pi$
$402$		0			0
$403$			5.57385e6i			1.70959i
$404$	−1.20952e6	−	578098.i	−0.368690	−	0.176217i
$405$		0			0
$406$	−289746.	−	459626.i	−0.0872374	−	0.138385i
$407$	−3.19177e6			−0.955092
$408$		0			0
$409$	−853587.			−0.252313			−0.126156	−	0.992010i	$-0.540264\pi$
$409$	−853587.			−0.252313			−0.126156	+	0.992010i	$0.540264\pi$
$410$	−1.12969e6	−	1.79204e6i	−0.331895	−	0.526488i
$411$		0			0
$412$	−1.63327e6	+	3.41720e6i	−0.474039	+	0.991807i
$413$		−	151454.i		−	0.0436925i
$414$		0			0
$415$	−1.54138e6			−0.439330
$416$	−1.34968e6	+	3.95012e6i	−0.382382	+	1.11912i
$417$		0			0
$418$	2.48856e6	−	1.56878e6i	0.696638	−	0.439157i
$419$		−	3.86903e6i		−	1.07663i	−0.842743	−	0.538316i	$-0.819061\pi$
$419$		−	3.86903e6i		−	1.07663i	0.842743	−	0.538316i	$-0.180939\pi$
$420$		0			0
$421$		−	1.15014e6i		−	0.316260i	−0.987418	−	0.158130i	$-0.949454\pi$
$421$		−	1.15014e6i		−	0.316260i	0.987418	−	0.158130i	$-0.0505464\pi$
$422$	1.21036e6	+	1.91999e6i	0.330851	+	0.524830i
$423$		0			0
$424$	288690.	−	33818.4i	0.0779860	−	0.00913563i
$425$	−1.17278e6			−0.314951
$426$		0			0
$427$			2.51522e6i			0.667583i
$428$	−4.27239e6	−	2.04201e6i	−1.12736	−	0.538826i
$429$		0			0
$430$	2.16704e6	−	1.36609e6i	0.565192	−	0.356295i
$431$	3.09078e6			0.801448			0.400724	−	0.916199i	$-0.368759\pi$
$431$	3.09078e6			0.801448			0.400724	+	0.916199i	$0.368759\pi$
$432$		0			0
$433$	2.47892e6			0.635394			0.317697	−	0.948192i	$-0.397090\pi$
$433$	2.47892e6			0.635394			0.317697	+	0.948192i	$0.397090\pi$
$434$	2.09102e6	−	1.31817e6i	0.532885	−	0.335928i
$435$		0			0
$436$	−3.65338e6	−	1.74615e6i	−0.920405	−	0.439913i
$437$		−	5.12087e6i		−	1.28275i
$438$		0			0
$439$	997159.			0.246947			0.123473	−	0.992348i	$-0.460597\pi$
$439$	997159.			0.246947			0.123473	+	0.992348i	$0.460597\pi$
$440$	−137436.	−	1.17321e6i	−0.0338429	−	0.288899i
$441$		0			0
$442$	−4.07921e6	−	6.47088e6i	−0.993163	−	1.57546i
$443$			2.10966e6i			0.510744i	0.966843	+	0.255372i	$0.0821980\pi$
$443$			2.10966e6i			0.510744i	−0.966843	+	0.255372i	$0.917802\pi$
$444$		0			0
$445$		−	1.33013e6i		−	0.318416i
$446$	−2.27620e6	+	1.43491e6i	−0.541843	+	0.341575i
$447$		0			0
$448$	1.80107e6	−	427842.i	0.423971	−	0.100714i
$449$	−6.24963e6			−1.46298			−0.731490	−	0.681852i	$-0.761175\pi$
$449$	−6.24963e6			−1.46298			−0.731490	+	0.681852i	$0.761175\pi$
$450$		0			0
$451$			3.90989e6i			0.905156i
$452$	3.06206e6	−	6.40659e6i	0.704966	−	1.47496i
$453$		0			0
$454$	−86153.0	−	136665.i	−0.0196169	−	0.0311184i
$455$	−1.01778e6			−0.230476
$456$		0			0
$457$	1.87669e6			0.420340			0.210170	−	0.977665i	$-0.432598\pi$
$457$	1.87669e6			0.420340			0.210170	+	0.977665i	$0.432598\pi$
$458$	−2.92537e6	−	4.64054e6i	−0.651655	−	1.03372i
$459$		0			0
$460$	−1.85522e6	−	886713.i	−0.408791	−	0.195384i
$461$		−	8.54777e6i		−	1.87327i	−0.350307	−	0.936635i	$-0.613923\pi$
$461$		−	8.54777e6i		−	1.87327i	0.350307	−	0.936635i	$-0.386077\pi$
$462$		0			0
$463$	−7.55869e6			−1.63868			−0.819340	−	0.573308i	$-0.805660\pi$
$463$	−7.55869e6			−1.63868			−0.819340	+	0.573308i	$0.805660\pi$
$464$	1.35473e6	−	1.09346e6i	0.292117	−	0.235781i
$465$		0			0
$466$	76593.1	−	48283.9i	0.0163390	−	0.0103000i
$467$			3.29127e6i			0.698346i	0.937058	+	0.349173i	$0.113538\pi$
$467$			3.29127e6i			0.698346i	−0.937058	+	0.349173i	$0.886462\pi$
$468$		0			0
$469$		−	705380.i		−	0.148078i
$470$	−161470.	−	256141.i	−0.0337168	−	0.0534852i
$471$		0			0
$472$	481999.	−	56463.6i	0.0995844	−	0.0116658i
$473$	−4.72807e6			−0.971698
$474$		0			0
$475$		−	1.24521e6i		−	0.253225i
$476$	−1.46284e6	+	3.06062e6i	−0.295923	+	0.619144i
$477$		0			0
$478$	−6.05817e6	+	3.81905e6i	−1.21275	+	0.764513i
$479$	−4.95610e6			−0.986965			−0.493482	−	0.869756i	$-0.664276\pi$
$479$	−4.95610e6			−0.986965			−0.493482	+	0.869756i	$0.664276\pi$
$480$		0			0
$481$	−8.81196e6			−1.73664
$482$	1.98396e6	−	1.25068e6i	0.388970	−	0.245205i
$483$		0			0
$484$	1.28224e6	−	2.68277e6i	0.248804	−	0.520559i
$485$		−	980294.i		−	0.189235i
$486$		0			0
$487$	−7.56942e6			−1.44624			−0.723120	−	0.690723i	$-0.757293\pi$
$487$	−7.56942e6			−1.44624			−0.723120	+	0.690723i	$0.757293\pi$
$488$	−8.00460e6	+	937695.i	−1.52156	+	0.178243i
$489$		0			0
$490$	−1.02683e6	−	1.62887e6i	−0.193201	−	0.306476i
$491$			1.25015e6i			0.234023i	0.993131	+	0.117012i	$0.0373315\pi$
$491$			1.25015e6i			0.234023i	−0.993131	+	0.117012i	$0.962668\pi$
$492$		0			0
$493$			3.19025e6i			0.591163i
$494$	6.87051e6	−	4.33114e6i	1.26669	−	0.798518i
$495$		0			0
$496$	4.97458e6	+	6.16318e6i	0.907930	+	1.12487i
$497$	462649.			0.0840158
$498$		0			0
$499$		−	5.59295e6i		−	1.00552i	−0.864427	−	0.502758i	$-0.832319\pi$
$499$		−	5.59295e6i		−	1.00552i	0.864427	−	0.502758i	$-0.167681\pi$
$500$	−451121.	−	215616.i	−0.0806989	−	0.0385705i
$501$		0			0
$502$	555519.	+	881223.i	0.0983874	+	0.156073i
$503$	−9.76813e6			−1.72144			−0.860719	−	0.509080i	$-0.829986\pi$
$503$	−9.76813e6			−1.72144			−0.860719	+	0.509080i	$0.829986\pi$
$504$		0			0
$505$	1.04733e6			0.182748
$506$	2.02387e6	+	3.21048e6i	0.351404	+	0.557434i
$507$		0			0
$508$	3.28184e6	−	6.86642e6i	0.564233	−	1.18051i
$509$			9.05091e6i			1.54845i	0.632909	+	0.774226i	$0.281861\pi$
$509$			9.05091e6i			1.54845i	−0.632909	+	0.774226i	$0.718139\pi$
$510$		0			0
$511$	2.32092e6			0.393195
$512$	2.03305e6	+	5.57235e6i	0.342747	+	0.939428i
$513$		0			0
$514$	4.04970e6	−	2.55291e6i	0.676106	−	0.426214i
$515$		−	2.95895e6i		−	0.491608i
$516$		0			0
$517$			558850.i			0.0919536i
$518$	2.08396e6	+	3.30579e6i	0.341243	+	0.541316i
$519$		0			0
$520$	−379438.	−	3.23905e6i	−0.0615364	−	0.525303i
$521$	7.68287e6			1.24002			0.620011	−	0.784593i	$-0.287128\pi$
$521$	7.68287e6			1.24002			0.620011	+	0.784593i	$0.287128\pi$
$522$		0			0
$523$			8.45353e6i			1.35140i	0.737177	+	0.675700i	$0.236159\pi$
$523$			8.45353e6i			1.35140i	−0.737177	+	0.675700i	$0.763841\pi$
$524$	4.36577e6	+	2.08664e6i	0.694596	+	0.331986i
$525$		0			0
$526$	7.34004e6	−	4.62713e6i	1.15674	−	0.729201i
$527$	−1.45137e7			−2.27641
$528$		0			0
$529$	170070.			0.0264234
$530$	−192097.	+	121097.i	−0.0297051	+	0.0187260i
$531$		0			0
$532$	−3.24964e6	−	1.55318e6i	−0.497801	−	0.237927i
$533$			1.07946e7i			1.64584i
$534$		0			0
$535$	3.69946e6			0.558797
$536$	2.24485e6	−	262972.i	0.337501	−	0.0395365i
$537$		0			0
$538$	1.95092e6	+	3.09476e6i	0.290592	+	0.460969i
$539$			3.55389e6i			0.526904i
$540$		0			0
$541$			4.67406e6i			0.686596i	0.939227	+	0.343298i	$0.111544\pi$
$541$			4.67406e6i			0.686596i	−0.939227	+	0.343298i	$0.888456\pi$
$542$	−7.57609e6	+	4.77593e6i	−1.10776	+	0.698329i
$543$		0			0
$544$	−1.02857e7	−	3.51441e6i	−1.49017	−	0.509162i
$545$	3.16346e6			0.456217
$546$		0			0
$547$			1.86478e6i			0.266477i	0.991084	+	0.133238i	$0.0425376\pi$
$547$			1.86478e6i			0.266477i	−0.991084	+	0.133238i	$0.957462\pi$
$548$	−2.25228e6	+	4.71233e6i	−0.320385	+	0.670324i
$549$		0			0
$550$	492130.	+	780668.i	0.0693702	+	0.110042i
$551$	−3.38727e6			−0.475304
$552$		0			0
$553$	−2.61713e6			−0.363925
$554$	−4.90134e6	−	7.77503e6i	−0.678486	−	1.07629i
$555$		0			0
$556$	216259.	+	103362.i	0.0296679	+	0.0141799i
$557$		−	9.40472e6i		−	1.28442i	−0.766528	−	0.642211i	$-0.778017\pi$
$557$		−	9.40472e6i		−	1.28442i	0.766528	−	0.642211i	$-0.221983\pi$
$558$		0			0
$559$	−1.30535e7			−1.76683
$560$	−1.12539e6	+	908355.i	−0.151647	+	0.122401i
$561$		0			0
$562$	7.10029e6	−	4.47599e6i	0.948277	−	0.597790i
$563$		−	849619.i		−	0.112967i	−0.998404	−	0.0564837i	$-0.982011\pi$
$563$		−	849619.i		−	0.112967i	0.998404	−	0.0564837i	$-0.0179889\pi$
$564$		0			0
$565$			5.54746e6i			0.731094i
$566$	−3.56703e6	−	5.65841e6i	−0.468022	−	0.742426i
$567$		0			0
$568$	172480.	+	1.47237e6i	0.0224320	+	0.191490i
$569$	5.41948e6			0.701741			0.350870	−	0.936424i	$-0.385886\pi$
$569$	5.41948e6			0.701741			0.350870	+	0.936424i	$0.385886\pi$
$570$		0			0
$571$		−	331372.i		−	0.0425329i	−0.999774	−	0.0212664i	$-0.993230\pi$
$571$		−	331372.i		−	0.0425329i	0.999774	−	0.0212664i	$-0.00676983\pi$
$572$	−2.59564e6	+	5.43072e6i	−0.331707	+	0.694013i
$573$		0			0
$574$	4.04957e6	−	2.55283e6i	0.513014	−	0.323402i
$575$	1.60643e6			0.202625
$576$		0			0
$577$	−1.51001e7			−1.88817			−0.944086	−	0.329701i	$-0.893052\pi$
$577$	−1.51001e7			−1.88817			−0.944086	+	0.329701i	$0.893052\pi$
$578$	1.00549e7	−	6.33857e6i	1.25187	−	0.789173i
$579$		0			0
$580$	−586528.	+	1.22716e6i	−0.0723967	+	0.151472i
$581$		−	3.48315e6i		−	0.428087i
$582$		0			0
$583$	419119.			0.0510700
$584$	865260.	+	7.38626e6i	0.104982	+	0.896174i
$585$		0			0
$586$	−2.67875e6	−	4.24931e6i	−0.322246	−	0.511181i
$587$			1.51509e7i			1.81486i	0.420199	+	0.907432i	$0.361960\pi$
$587$			1.51509e7i			1.81486i	−0.420199	+	0.907432i	$0.638040\pi$
$588$		0			0
$589$		−	1.54100e7i		−	1.83027i
$590$	−320727.	+	202185.i	−0.0379320	+	0.0239122i
$591$		0			0
$592$	−9.74367e6	+	7.86456e6i	−1.14266	+	0.922295i
$593$	1.46568e7			1.71160			0.855800	−	0.517307i	$-0.173066\pi$
$593$	1.46568e7			1.71160			0.855800	+	0.517307i	$0.173066\pi$
$594$		0			0
$595$		−	2.65019e6i		−	0.306891i
$596$	1.02620e6	+	490476.i	0.118336	+	0.0565591i
$597$		0			0
$598$	5.58758e6	+	8.86361e6i	0.638956	+	1.01358i
$599$	5.14552e6			0.585952			0.292976	−	0.956120i	$-0.405354\pi$
$599$	5.14552e6			0.585952			0.292976	+	0.956120i	$0.405354\pi$
$600$		0			0
$601$	9.03954e6			1.02085			0.510423	−	0.859923i	$-0.329489\pi$
$601$	9.03954e6			1.02085			0.510423	+	0.859923i	$0.329489\pi$
$602$	3.08703e6	+	4.89698e6i	0.347176	+	0.550728i
$603$		0			0
$604$	7.58694e6	−	1.58737e7i	0.846202	−	1.77046i
$605$			2.32301e6i			0.258025i
$606$		0			0
$607$	1.25949e7			1.38747			0.693733	−	0.720232i	$-0.255965\pi$
$607$	1.25949e7			1.38747			0.693733	+	0.720232i	$0.255965\pi$
$608$	3.73146e6	−	1.09209e7i	0.409373	−	1.19812i
$609$		0			0
$610$	5.32634e6	−	3.35770e6i	0.579568	−	0.365357i
$611$			1.54290e6i			0.167199i
$612$		0			0
$613$		−	8.66424e6i		−	0.931278i	−0.884975	−	0.465639i	$-0.845825\pi$
$613$		−	8.66424e6i		−	0.931278i	0.884975	−	0.465639i	$-0.154175\pi$
$614$	−4.45533e6	−	7.06751e6i	−0.476934	−	0.756564i
$615$		0			0
$616$	2.65117e6	−	310570.i	0.281505	−	0.0329768i
$617$	−6.86089e6			−0.725551			−0.362775	−	0.931877i	$-0.618171\pi$
$617$	−6.86089e6			−0.725551			−0.362775	+	0.931877i	$0.618171\pi$
$618$		0			0
$619$			3.44552e6i			0.361434i	0.983535	+	0.180717i	$0.0578417\pi$
$619$			3.44552e6i			0.361434i	−0.983535	+	0.180717i	$0.942158\pi$
$620$	−5.58284e6	−	2.66835e6i	−0.583278	−	0.278781i
$621$		0			0
$622$	−1.74436e6	+	1.09964e6i	−0.180785	+	0.113966i
$623$	3.00578e6			0.310268
$624$		0			0
$625$	390625.			0.0400000
$626$	1.55164e6	−	978144.i	0.158254	−	0.0997624i
$627$		0			0
$628$	7.28780e6	+	3.48324e6i	0.737390	+	0.352439i
$629$		−	2.29454e7i		−	2.31243i
$630$		0			0
$631$	−7.79725e6			−0.779593			−0.389797	−	0.920901i	$-0.627455\pi$
$631$	−7.79725e6			−0.779593			−0.389797	+	0.920901i	$0.627455\pi$
$632$	−975689.	−	8.32893e6i	−0.0971670	−	0.829462i
$633$		0			0
$634$	−4.69604e6	−	7.44936e6i	−0.463990	−	0.736031i
$635$			5.94563e6i			0.585145i
$636$		0			0
$637$			9.81171e6i			0.958068i
$638$	2.12361e6	−	1.33872e6i	0.206549	−	0.130208i
$639$		0			0
$640$	−3.31037e6	−	3.24288e6i	−0.319467	−	0.312955i
$641$	−7.82134e6			−0.751859			−0.375929	−	0.926648i	$-0.622676\pi$
$641$	−7.82134e6			−0.751859			−0.375929	+	0.926648i	$0.622676\pi$
$642$		0			0
$643$			1.35325e7i			1.29078i	0.763854	+	0.645389i	$0.223305\pi$
$643$			1.35325e7i			1.29078i	−0.763854	+	0.645389i	$0.776695\pi$
$644$	2.00375e6	−	4.19234e6i	0.190383	−	0.398329i
$645$		0			0
$646$	1.12778e7	+	1.78900e7i	1.06327	+	1.68667i
$647$	1.34237e6			0.126070			0.0630352	−	0.998011i	$-0.479922\pi$
$647$	1.34237e6			0.126070			0.0630352	+	0.998011i	$0.479922\pi$
$648$		0			0
$649$	699766.			0.0652140
$650$	1.35869e6	+	2.15530e6i	0.126136	+	0.200090i
$651$		0			0
$652$	1.10642e7	+	5.28817e6i	1.01929	+	0.487177i
$653$			5.36490e6i			0.492355i	0.969225	+	0.246178i	$0.0791747\pi$
$653$			5.36490e6i			0.492355i	−0.969225	+	0.246178i	$0.920825\pi$
$654$		0			0
$655$	−3.78031e6			−0.344290
$656$	9.63402e6	+	1.19359e7i	0.874074	+	1.08292i
$657$		0			0
$658$	578815.	−	364882.i	0.0521164	−	0.0328540i
$659$		−	8.49067e6i		−	0.761603i	−0.924657	−	0.380801i	$-0.875648\pi$
$659$		−	8.49067e6i		−	0.761603i	0.924657	−	0.380801i	$-0.124352\pi$
$660$		0			0
$661$		−	9.80254e6i		−	0.872640i	−0.899792	−	0.436320i	$-0.856282\pi$
$661$		−	9.80254e6i		−	0.872640i	0.899792	−	0.436320i	$-0.143718\pi$
$662$	1.68562e6	+	2.67391e6i	0.149491	+	0.237139i
$663$		0			0
$664$	1.10850e7	−	1.29855e6i	0.975700	−	0.114298i
$665$	2.81386e6			0.246745
$666$		0			0
$667$		−	4.36990e6i		−	0.380327i
$668$	−1.49610e6	+	3.13020e6i	−0.129723	+	0.271413i
$669$		0			0
$670$	−1.49375e6	+	941652.i	−0.128555	+	0.0810407i
$671$	−1.16211e7			−0.996413
$672$		0			0
$673$	7.99241e6			0.680205			0.340103	−	0.940388i	$-0.389538\pi$
$673$	7.99241e6			0.680205			0.340103	+	0.940388i	$0.389538\pi$
$674$	1.04474e7	−	6.58600e6i	0.885848	−	0.558434i
$675$		0			0
$676$	−2.04253e6	+	4.27348e6i	−0.171910	+	0.359679i
$677$			8.50891e6i			0.713514i	0.934197	+	0.356757i	$0.116118\pi$
$677$			8.50891e6i			0.713514i	−0.934197	+	0.356757i	$0.883882\pi$
$678$		0			0
$679$	2.21522e6			0.184392
$680$	8.43414e6	−	988013.i	0.699469	−	0.0819390i
$681$		0			0
$682$	6.09034e6	+	9.66115e6i	0.501396	+	0.795367i
$683$			1.39302e7i			1.14263i	0.820732	+	0.571314i	$0.193566\pi$
$683$			1.39302e7i			1.14263i	−0.820732	+	0.571314i	$0.806434\pi$
$684$		0			0
$685$		−	4.08040e6i		−	0.332259i
$686$	8.22451e6	−	5.18469e6i	0.667267	−	0.420642i
$687$		0			0
$688$	−1.44336e7	+	1.16500e7i	−1.16253	+	0.938331i
$689$	1.15712e6			0.0928604
$690$		0			0
$691$			1.79579e6i			0.143074i	0.997438	+	0.0715371i	$0.0227904\pi$
$691$			1.79579e6i			0.143074i	−0.997438	+	0.0715371i	$0.977210\pi$
$692$	8.83277e6	+	4.22167e6i	0.701184	+	0.335134i
$693$		0			0
$694$	7.66005e6	+	1.21512e7i	0.603716	+	0.957678i
$695$	−187258.			−0.0147055
$696$		0			0
$697$	−2.81079e7			−2.19152
$698$	−7.79664e6	−	1.23678e7i	−0.605716	−	0.960850i
$699$		0			0
$700$	487238.	−	1.01942e6i	0.0375834	−	0.0786337i
$701$			1.76628e7i			1.35758i	0.734334	+	0.678789i	$0.237495\pi$
$701$			1.76628e7i			1.35758i	−0.734334	+	0.678789i	$0.762505\pi$
$702$		0			0
$703$	2.43624e7			1.85923
$704$	1.97676e6	+	8.32150e6i	0.150322	+	0.632805i
$705$		0			0
$706$	−1.36066e6	+	857753.i	−0.102740	+	0.0647665i
$707$			2.36670e6i			0.178071i
$708$		0			0
$709$		−	1.67397e7i		−	1.25064i	−0.780369	−	0.625319i	$-0.784969\pi$
$709$		−	1.67397e7i		−	1.25064i	0.780369	−	0.625319i	$-0.215031\pi$
$710$	−617617.	−	979729.i	−0.0459804	−	0.0729390i
$711$		0			0
$712$	1.12058e6	+	9.56579e6i	0.0828405	+	0.707165i
$713$	1.98804e7			1.46454
$714$		0			0
$715$		−	4.70246e6i		−	0.344001i
$716$	−6.05924e6	−	2.89605e6i	−0.441709	−	0.211117i
$717$		0			0
$718$	9.43238e6	−	5.94613e6i	0.682826	−	0.430450i
$719$	1.41699e7			1.02222			0.511111	−	0.859515i	$-0.329234\pi$
$719$	1.41699e7			1.02222			0.511111	+	0.859515i	$0.329234\pi$
$720$		0			0
$721$	6.68649e6			0.479027
$722$	−7.14588e6	+	4.50473e6i	−0.510167	+	0.321607i
$723$		0			0
$724$	−6.14938e6	−	2.93913e6i	−0.435999	−	0.208388i
$725$		−	1.06260e6i		−	0.0750800i
$726$		0			0
$727$	3.78412e6			0.265539			0.132770	−	0.991147i	$-0.457613\pi$
$727$	3.78412e6			0.265539			0.132770	+	0.991147i	$0.457613\pi$
$728$	7.31947e6	−	857435.i	0.511860	−	0.0599616i
$729$		0			0
$730$	−3.09833e6	−	4.91489e6i	−0.215189	−	0.341355i
$731$		−	3.39897e7i		−	2.35263i
$732$		0			0
$733$			2.58722e7i			1.77858i	0.457345	+	0.889290i	$0.348801\pi$
$733$			2.58722e7i			1.77858i	−0.457345	+	0.889290i	$0.651199\pi$
$734$	4.98536e6	−	3.14275e6i	0.341552	−	0.215313i
$735$		0			0
$736$	1.40890e7	+	4.81394e6i	0.958708	+	0.327571i
$737$	3.25907e6			0.221017
$738$		0			0
$739$			5.89215e6i			0.396883i	0.980113	+	0.198441i	$0.0635880\pi$
$739$			5.89215e6i			0.396883i	−0.980113	+	0.198441i	$0.936412\pi$
$740$	4.21851e6	−	8.82617e6i	0.283192	−	0.592506i
$741$		0			0
$742$	−273650.	−	434092.i	−0.0182467	−	0.0289449i
$743$	2.47551e7			1.64510			0.822551	−	0.568692i	$-0.192550\pi$
$743$	2.47551e7			1.64510			0.822551	+	0.568692i	$0.192550\pi$
$744$		0			0
$745$	−888583.			−0.0586553
$746$	4.78949e6	+	7.59759e6i	0.315095	+	0.499838i
$747$		0			0
$748$	−1.41410e7	−	6.75876e6i	−0.924115	−	0.441685i
$749$			8.35986e6i			0.544496i
$750$		0			0
$751$	1.98371e6			0.128345			0.0641724	−	0.997939i	$-0.479559\pi$
$751$	1.98371e6			0.128345			0.0641724	+	0.997939i	$0.479559\pi$
$752$	1.37701e6	+	1.70603e6i	0.0887960	+	0.110012i
$753$		0			0
$754$	5.86296e6	−	3.69598e6i	0.375568	−	0.236756i
$755$			1.37451e7i			0.877565i
$756$		0			0
$757$			1.85647e7i			1.17746i	0.808328	+	0.588732i	$0.200373\pi$
$757$			1.85647e7i			1.17746i	−0.808328	+	0.588732i	$0.799627\pi$
$758$	−3.00437e6	−	4.76585e6i	−0.189924	−	0.301278i
$759$		0			0
$760$	1.04903e6	+	8.95502e6i	0.0658801	+	0.562383i
$761$	5.16348e6			0.323207			0.161603	−	0.986856i	$-0.448333\pi$
$761$	5.16348e6			0.323207			0.161603	+	0.986856i	$0.448333\pi$
$762$		0			0
$763$			7.14864e6i			0.444542i
$764$	2.44589e6	−	5.11739e6i	0.151601	−	0.317187i
$765$		0			0
$766$	−7.34160e6	+	4.62811e6i	−0.452083	+	0.284991i
$767$	1.93194e6			0.118578
$768$		0			0
$769$	3.01408e7			1.83797			0.918985	−	0.394293i	$-0.129011\pi$
$769$	3.01408e7			1.83797			0.918985	+	0.394293i	$0.129011\pi$
$770$	−1.76412e6	+	1.11209e6i	−0.107226	+	0.0675949i
$771$		0			0
$772$	1.04615e7	−	2.18881e7i	0.631761	−	1.32180i
$773$			1.51718e7i			0.913246i	0.889660	+	0.456623i	$0.150941\pi$
$773$			1.51718e7i			0.913246i	−0.889660	+	0.456623i	$0.849059\pi$
$774$		0			0
$775$	4.83417e6			0.289113
$776$	825855.	+	7.04988e6i	0.0492322	+	0.420269i
$777$		0			0
$778$	−1.42067e7	−	2.25362e7i	−0.841483	−	1.33485i
$779$		−	2.98438e7i		−	1.76202i
$780$		0			0
$781$			2.13758e6i			0.125399i
$782$	−2.30799e7	+	1.45494e7i	−1.34963	+	0.850804i
$783$		0			0
$784$	8.75682e6	+	1.08491e7i	0.508811	+	0.630383i
$785$	−6.31050e6			−0.365502
$786$		0			0
$787$		−	1.46106e7i		−	0.840874i	−0.907322	−	0.420437i	$-0.861877\pi$
$787$		−	1.46106e7i		−	0.840874i	0.907322	−	0.420437i	$-0.138123\pi$
$788$	−1.02064e7	−	4.87820e6i	−0.585541	−	0.279862i
$789$		0			0
$790$	3.49375e6	+	5.54216e6i	0.199170	+	0.315945i
$791$	−1.25359e7			−0.712384
$792$		0			0
$793$	−3.20839e7			−1.81177
$794$	−1.46435e6	−	2.32291e6i	−0.0824318	−	0.130762i
$795$		0			0
$796$	3.21563e6	−	6.72789e6i	0.179880	−	0.376354i
$797$		−	4.81785e6i		−	0.268663i	−0.990936	−	0.134331i	$-0.957111\pi$
$797$		−	4.81785e6i		−	0.268663i	0.990936	−	0.134331i	$-0.0428887\pi$
$798$		0			0
$799$	−4.01753e6			−0.222634
$800$	3.42593e6	+	1.17057e6i	0.189257	+	0.0646655i
$801$		0			0
$802$	−8.29790e6	+	5.23096e6i	−0.455546	+	0.287174i
$803$			1.07234e7i			0.586870i
$804$		0			0
$805$			3.63014e6i			0.197440i
$806$	1.68145e7	+	2.66729e7i	0.911686	+	1.44621i
$807$		0			0
$808$	−7.53194e6	+	882326.i	−0.405862	+	0.0475445i
$809$	267715.			0.0143814			0.00719072	−	0.999974i	$-0.497711\pi$
$809$	267715.			0.0143814			0.00719072	+	0.999974i	$0.497711\pi$
$810$		0			0
$811$		−	1.10232e7i		−	0.588514i	−0.955726	−	0.294257i	$-0.904928\pi$
$811$		−	1.10232e7i		−	0.588514i	0.955726	−	0.294257i	$-0.0950722\pi$
$812$	−2.77308e6	−	1.32541e6i	−0.147595	−	0.0705440i
$813$		0			0
$814$	−1.52738e7	+	9.62851e6i	−0.807951	+	0.509329i
$815$	−9.58044e6			−0.505233
$816$		0			0
$817$	3.60889e7			1.89155
$818$	−4.08472e6	+	2.57499e6i	−0.213442	+	0.134553i
$819$		0			0
$820$	−1.08120e7	−	5.16765e6i	−0.561528	−	0.268385i
$821$		−	7.52183e6i		−	0.389462i	−0.980857	−	0.194731i	$-0.937617\pi$
$821$		−	7.52183e6i		−	0.389462i	0.980857	−	0.194731i	$-0.0623834\pi$
$822$		0			0
$823$	−2.86933e7			−1.47666			−0.738331	−	0.674439i	$-0.764386\pi$
$823$	−2.86933e7			−1.47666			−0.738331	+	0.674439i	$0.764386\pi$
$824$	2.49278e6	+	2.12796e7i	0.127899	+	1.09180i
$825$		0			0
$826$	−456888.	−	724764.i	−0.0233002	−	0.0369613i
$827$		−	1.90830e7i		−	0.970248i	−0.874445	−	0.485124i	$-0.838774\pi$
$827$		−	1.90830e7i		−	0.970248i	0.874445	−	0.485124i	$-0.161226\pi$
$828$		0			0
$829$		−	2.31916e7i		−	1.17205i	−0.810295	−	0.586023i	$-0.800693\pi$
$829$		−	2.31916e7i		−	1.17205i	0.810295	−	0.586023i	$-0.199307\pi$
$830$	−7.37608e6	+	4.64985e6i	−0.371647	+	0.234285i
$831$		0			0
$832$	5.45752e6	+	2.29743e7i	0.273330	+	1.15063i
$833$	−2.55486e7			−1.27572
$834$		0			0
$835$		−	2.71044e6i		−	0.134531i
$836$	7.17617e6	−	1.50143e7i	0.355122	−	0.743002i
$837$		0			0
$838$	−1.16716e7	−	1.85147e7i	−0.574143	−	0.910766i
$839$	887580.			0.0435314			0.0217657	−	0.999763i	$-0.493071\pi$
$839$	887580.			0.0435314			0.0217657	+	0.999763i	$0.493071\pi$
$840$		0			0
$841$	1.76206e7			0.859075
$842$	−3.46958e6	−	5.50382e6i	−0.168654	−	0.267537i
$843$		0			0
$844$	1.15840e7	+	5.53663e6i	0.559760	+	0.267540i
$845$		−	3.70040e6i		−	0.178282i
$846$		0			0
$847$	−5.24942e6			−0.251422
$848$	1.27947e6	−	1.03271e6i	0.0610997	−	0.0493163i
$849$		0			0
$850$	−5.61216e6	+	3.53788e6i	−0.266430	+	0.167956i
$851$			3.14299e7i			1.48771i
$852$		0			0
$853$		−	1.39449e7i		−	0.656208i	−0.944642	−	0.328104i	$-0.893590\pi$
$853$		−	1.39449e7i		−	0.656208i	0.944642	−	0.328104i	$-0.106410\pi$
$854$	7.58758e6	+	1.20362e7i	0.356007	+	0.564736i
$855$		0			0
$856$	−2.66050e7	+	3.11663e6i	−1.24102	+	0.145379i
$857$	3.58423e7			1.66703			0.833516	−	0.552495i	$-0.186324\pi$
$857$	3.58423e7			1.66703			0.833516	+	0.552495i	$0.186324\pi$
$858$		0			0
$859$			767053.i			0.0354685i	0.999843	+	0.0177342i	$0.00564528\pi$
$859$			767053.i			0.0354685i	−0.999843	+	0.0177342i	$0.994355\pi$
$860$	6.24903e6	−	1.30745e7i	0.288115	−	0.602808i
$861$		0			0
$862$	1.47905e7	−	9.32387e6i	0.677977	−	0.427394i
$863$	2.90420e7			1.32739			0.663697	−	0.748002i	$-0.268987\pi$
$863$	2.90420e7			1.32739			0.663697	+	0.748002i	$0.268987\pi$
$864$		0			0
$865$	−7.64829e6			−0.347555
$866$	1.18625e7	−	7.47809e6i	0.537506	−	0.338841i
$867$		0			0
$868$	6.02980e6	−	1.26158e7i	0.271646	−	0.568351i
$869$		−	1.20919e7i		−	0.543183i
$870$		0			0
$871$	8.99778e6			0.401874
$872$	−2.27503e7	+	2.66508e6i	−1.01320	+	0.118691i
$873$		0			0
$874$	−1.54480e7	−	2.45052e7i	−0.684059	−	1.08513i
$875$			882716.i			0.0389763i
$876$		0			0
$877$		−	9.62715e6i		−	0.422667i	−0.977414	−	0.211334i	$-0.932219\pi$
$877$		−	9.62715e6i		−	0.422667i	0.977414	−	0.211334i	$-0.0677807\pi$
$878$	4.77177e6	−	3.00810e6i	0.208902	−	0.131691i
$879$		0			0
$880$	−4.19688e6	−	5.19965e6i	−0.182692	−	0.226343i
$881$	−3.88627e7			−1.68691			−0.843457	−	0.537196i	$-0.819483\pi$
$881$	−3.88627e7			−1.68691			−0.843457	+	0.537196i	$0.819483\pi$
$882$		0			0
$883$			4.29023e6i			0.185173i	0.995705	+	0.0925867i	$0.0295135\pi$
$883$			4.29023e6i			0.185173i	−0.995705	+	0.0925867i	$0.970486\pi$
$884$	−3.90410e7	−	1.86599e7i	−1.68031	−	0.803115i
$885$		0			0
$886$	6.36416e6	+	1.00955e7i	0.272368	+	0.432059i
$887$	1.30883e7			0.558564			0.279282	−	0.960209i	$-0.409904\pi$
$887$	1.30883e7			0.558564			0.279282	+	0.960209i	$0.409904\pi$
$888$		0			0
$889$	−1.34356e7			−0.570170
$890$	−4.01258e6	−	6.36518e6i	−0.169804	−	0.269361i
$891$		0			0
$892$	−6.56380e6	+	1.37331e7i	−0.276212	+	0.577905i
$893$		−	4.26564e6i		−	0.179001i
$894$		0			0
$895$	5.24669e6			0.218941
$896$	7.32812e6	−	7.48062e6i	0.304946	−	0.311292i
$897$		0			0
$898$	−2.99068e7	+	1.88531e7i	−1.23760	+	0.780174i
$899$		−	1.31502e7i		−	0.542665i
$900$		0			0
$901$			3.01301e6i			0.123649i
$902$	1.17949e7	+	1.87102e7i	0.482699	+	0.765708i
$903$		0			0
$904$	−4.67349e6	−	3.98951e7i	−0.190204	−	1.62367i
$905$	5.32474e6			0.216111
$906$		0			0
$907$		−	2.36895e7i		−	0.956175i	−0.878312	−	0.478087i	$-0.841330\pi$
$907$		−	2.36895e7i		−	0.956175i	0.878312	−	0.478087i	$-0.158670\pi$
$908$	−824547.	−	394096.i	−0.0331895	−	0.0158631i
$909$		0			0
$910$	−4.87045e6	+	3.07031e6i	−0.194969	+	0.122908i
$911$	−1.27323e7			−0.508289			−0.254144	−	0.967166i	$-0.581794\pi$
$911$	−1.27323e7			−0.508289			−0.254144	+	0.967166i	$0.581794\pi$
$912$		0			0
$913$	1.60932e7			0.638948
$914$	8.98062e6	−	5.66135e6i	0.355583	−	0.224158i
$915$		0			0
$916$	−2.79980e7	−	1.33818e7i	−1.10252	−	0.526957i
$917$		−	8.54258e6i		−	0.335479i
$918$		0			0
$919$	3.36064e7			1.31260			0.656302	−	0.754499i	$-0.272120\pi$
$919$	3.36064e7			1.31260			0.656302	+	0.754499i	$0.272120\pi$
$920$	−1.15528e7	+	1.35335e6i	−0.450006	+	0.0527158i
$921$		0			0
$922$	−2.57858e7	−	4.09042e7i	−0.998972	−	1.58467i
$923$			5.90152e6i			0.228013i
$924$		0			0
$925$			7.64257e6i			0.293687i
$926$	−3.61711e7	+	2.28021e7i	−1.38623	+	0.873871i
$927$		0			0
$928$	3.18425e6	−	9.31938e6i	0.121377	−	0.355236i
$929$	−2.44326e7			−0.928816			−0.464408	−	0.885621i	$-0.653733\pi$
$929$	−2.44326e7			−0.928816			−0.464408	+	0.885621i	$0.653733\pi$
$930$		0			0
$931$		−	2.71265e7i		−	1.02570i
$932$	220869.	−	462112.i	0.00832904	−	0.0174264i
$933$		0			0
$934$	9.92867e6	+	1.57499e7i	0.372412	+	0.590760i
$935$	1.22447e7			0.458055
$936$		0			0
$937$	−2.46226e7			−0.916188			−0.458094	−	0.888904i	$-0.651468\pi$
$937$	−2.46226e7			−0.916188			−0.458094	+	0.888904i	$0.651468\pi$
$938$	−2.12790e6	−	3.37550e6i	−0.0789667	−	0.125265i
$939$		0			0
$940$	−1.54538e6	−	738624.i	−0.0570449	−	0.0272649i
$941$		−	3.64578e7i		−	1.34220i	−0.741368	−	0.671098i	$-0.765823\pi$
$941$		−	3.64578e7i		−	1.34220i	0.741368	−	0.671098i	$-0.234177\pi$
$942$		0			0
$943$	3.85013e7			1.40993
$944$	2.13621e6	−	1.72423e6i	0.0780214	−	0.0629746i
$945$		0			0
$946$	−2.26255e7	+	1.42630e7i	−0.821999	+	0.518184i
$947$		−	1.49302e7i		−	0.540992i	−0.962721	−	0.270496i	$-0.912812\pi$
$947$		−	1.49302e7i		−	0.540992i	0.962721	−	0.270496i	$-0.0871876\pi$
$948$		0			0
$949$			2.96055e7i			1.06710i
$950$	−3.75638e6	−	5.95876e6i	−0.135039	−	0.214214i
$951$		0			0
$952$	2.23267e6	+	1.90591e7i	0.0798420	+	0.681568i
$953$	−2.82853e7			−1.00885			−0.504426	−	0.863455i	$-0.668296\pi$
$953$	−2.82853e7			−1.00885			−0.504426	+	0.863455i	$0.668296\pi$
$954$		0			0
$955$			4.43115e6i			0.157220i
$956$	−1.74698e7	+	3.65510e7i	−0.618219	+	1.29347i
$957$		0			0
$958$	−2.37168e7	+	1.49509e7i	−0.834914	+	0.526326i
$959$	9.22071e6			0.323756
$960$		0			0
$961$	3.11960e7			1.08966
$962$	−4.21684e7	+	2.65828e7i	−1.46909	+	0.926110i
$963$		0			0
$964$	5.72109e6	−	1.19699e7i	0.198283	−	0.414857i
$965$			1.89529e7i			0.655176i
$966$		0			0
$967$	3.47503e7			1.19507			0.597533	−	0.801844i	$-0.296148\pi$
$967$	3.47503e7			1.19507			0.597533	+	0.801844i	$0.296148\pi$
$968$	−1.95703e6	−	1.67061e7i	−0.0671288	−	0.573043i
$969$		0			0
$970$	−2.95723e6	−	4.69106e6i	−0.100915	−	0.160082i
$971$		−	4.65499e7i		−	1.58442i	−0.610247	−	0.792211i	$-0.708930\pi$
$971$		−	4.65499e7i		−	1.58442i	0.610247	−	0.792211i	$-0.291070\pi$
$972$		0			0
$973$		−	423158.i		−	0.0143291i
$974$	−3.62224e7	+	2.28345e7i	−1.22343	+	0.771247i
$975$		0			0
$976$	−3.54762e7	+	2.86344e7i	−1.19210	+	0.962198i
$977$	−4.15712e7			−1.39334			−0.696668	−	0.717394i	$-0.745335\pi$
$977$	−4.15712e7			−1.39334			−0.696668	+	0.717394i	$0.745335\pi$
$978$		0			0
$979$			1.38876e7i			0.463096i
$980$	−9.82754e6	−	4.69712e6i	−0.326873	−	0.156231i
$981$		0			0
$982$	3.77130e6	+	5.98243e6i	0.124799	+	0.197970i
$983$	2.55186e7			0.842313			0.421157	−	0.906988i	$-0.361624\pi$
$983$	2.55186e7			0.842313			0.421157	+	0.906988i	$0.361624\pi$
$984$		0			0
$985$	8.83771e6			0.290235
$986$	9.62393e6	+	1.52665e7i	0.315254	+	0.500089i
$987$		0			0
$988$	1.98123e7	−	4.14521e7i	0.645716	−	1.35100i
$989$			4.65581e7i			1.51358i
$990$		0			0
$991$	−3.10296e7			−1.00367			−0.501836	−	0.864963i	$-0.667342\pi$
$991$	−3.10296e7			−1.00367			−0.501836	+	0.864963i	$0.667342\pi$
$992$	4.23975e7	+	1.44864e7i	1.36792	+	0.467391i
$993$		0			0
$994$	2.21395e6	−	1.39566e6i	0.0710724	−	0.0448037i
$995$			5.82567e6i			0.186547i
$996$		0			0
$997$			1.66036e7i			0.529011i	0.964384	+	0.264505i	$0.0852087\pi$
$997$			1.66036e7i			0.529011i	−0.964384	+	0.264505i	$0.914791\pi$
$998$	−1.68721e7	−	2.67643e7i	−0.536219	−	0.850607i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.6.k.b.181.17		20
3.2	odd	2		40.6.d.a.21.4	yes	20
8.5	even	2	inner	360.6.k.b.181.18		20
12.11	even	2		160.6.d.a.81.19		20
15.2	even	4		200.6.f.c.149.7		20
15.8	even	4		200.6.f.b.149.14		20
15.14	odd	2		200.6.d.b.101.17		20
24.5	odd	2		40.6.d.a.21.3	✓	20
24.11	even	2		160.6.d.a.81.2		20
60.23	odd	4		800.6.f.c.49.1		20
60.47	odd	4		800.6.f.b.49.20		20
60.59	even	2		800.6.d.c.401.2		20
120.29	odd	2		200.6.d.b.101.18		20
120.53	even	4		200.6.f.c.149.8		20
120.59	even	2		800.6.d.c.401.19		20
120.77	even	4		200.6.f.b.149.13		20
120.83	odd	4		800.6.f.b.49.19		20
120.107	odd	4		800.6.f.c.49.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.3	✓	20	24.5	odd	2
40.6.d.a.21.4	yes	20	3.2	odd	2
160.6.d.a.81.2		20	24.11	even	2
160.6.d.a.81.19		20	12.11	even	2
200.6.d.b.101.17		20	15.14	odd	2
200.6.d.b.101.18		20	120.29	odd	2
200.6.f.b.149.13		20	120.77	even	4
200.6.f.b.149.14		20	15.8	even	4
200.6.f.c.149.7		20	15.2	even	4
200.6.f.c.149.8		20	120.53	even	4
360.6.k.b.181.17		20	1.1	even	1	trivial
360.6.k.b.181.18		20	8.5	even	2	inner
800.6.d.c.401.2		20	60.59	even	2
800.6.d.c.401.19		20	120.59	even	2
800.6.f.b.49.19		20	120.83	odd	4
800.6.f.b.49.20		20	60.47	odd	4
800.6.f.c.49.1		20	60.23	odd	4
800.6.f.c.49.2		20	120.107	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.78536 - 3.01667i) q^{2} +(13.7994 - 28.8717i) q^{4} +25.0000i q^{5} -56.4938 q^{7} +(-21.0614 - 179.790i) q^{8} +(75.4168 + 119.634i) q^{10} -261.019i q^{11} -720.631i q^{13} +(-270.343 + 170.423i) q^{14} +(-643.154 - 796.825i) q^{16} +1876.44 q^{17} +1992.33i q^{19} +(721.793 + 344.985i) q^{20} +(-787.408 - 1249.07i) q^{22} -2570.29 q^{23} -625.000 q^{25} +(-2173.91 - 3448.48i) q^{26} +(-779.581 + 1631.07i) q^{28} +1700.16i q^{29} -7734.68 q^{31} +(-5481.48 - 1872.91i) q^{32} +(8979.46 - 5660.61i) q^{34} -1412.35i q^{35} -12228.1i q^{37} +(6010.20 + 9534.02i) q^{38} +(4494.75 - 526.535i) q^{40} -14979.3 q^{41} -18113.9i q^{43} +(-7536.06 - 3601.90i) q^{44} +(-12299.8 + 7753.73i) q^{46} -2141.03 q^{47} -13615.4 q^{49} +(-2990.85 + 1885.42i) q^{50} +(-20805.9 - 9944.27i) q^{52} +1605.71i q^{53} +6525.47 q^{55} +(1189.84 + 10157.0i) q^{56} +(5128.81 + 8135.87i) q^{58} +2680.90i q^{59} -44521.9i q^{61} +(-37013.2 + 23333.0i) q^{62} +(-31880.8 + 7573.26i) q^{64} +18015.8 q^{65} +12486.0i q^{67} +(25893.8 - 54176.2i) q^{68} +(-4260.58 - 6758.59i) q^{70} -8189.38 q^{71} -41082.7 q^{73} +(-36888.2 - 58516.0i) q^{74} +(57522.0 + 27492.9i) q^{76} +14746.0i q^{77} +46325.9 q^{79} +(19920.6 - 16078.8i) q^{80} +(-71681.6 + 45187.8i) q^{82} +61655.4i q^{83} +46911.1i q^{85} +(-54643.7 - 86681.7i) q^{86} +(-46928.5 + 5497.42i) q^{88} -53205.4 q^{89} +40711.2i q^{91} +(-35468.5 + 74208.8i) q^{92} +(-10245.6 + 6458.79i) q^{94} -49808.2 q^{95} -39211.8 q^{97} +(-65154.8 + 41073.3i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32}+ \cdots - 216942 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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