LMFDB - Embedded newform 60.3.f.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(19,60)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.f (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:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.389136420864.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 $ x^8 + 5x^6 + 24x^4 + 80*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$-1.52274 + 1.29664i$ of defining polynomial
Character	$\chi$	$=$	60.19
Dual form			60.3.f.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52274 + 1.29664i) q^{2} +1.73205 q^{3} +(0.637459 - 3.94888i) q^{4} +(4.27492 + 2.59328i) q^{5} +(-2.63746 + 2.24584i) q^{6} +0.837253 q^{7} +(4.14959 + 6.83966i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.52274 + 1.29664i) q^{2} +1.73205 q^{3} +(0.637459 - 3.94888i) q^{4} +(4.27492 + 2.59328i) q^{5} +(-2.63746 + 2.24584i) q^{6} +0.837253 q^{7} +(4.14959 + 6.83966i) q^{8} +3.00000 q^{9} +(-9.87212 + 1.59414i) q^{10} +15.7955i q^{11} +(1.10411 - 6.83966i) q^{12} -5.18655i q^{13} +(-1.27492 + 1.08561i) q^{14} +(7.40437 + 4.49169i) q^{15} +(-15.1873 - 5.03449i) q^{16} -27.3586i q^{17} +(-4.56821 + 3.88991i) q^{18} -17.9667i q^{19} +(12.9656 - 15.2280i) q^{20} +1.45017 q^{21} +(-20.4811 - 24.0524i) q^{22} -19.1101 q^{23} +(7.18729 + 11.8466i) q^{24} +(11.5498 + 22.1721i) q^{25} +(6.72508 + 7.89776i) q^{26} +5.19615 q^{27} +(0.533714 - 3.30621i) q^{28} -45.6495 q^{29} +(-17.0990 + 2.76113i) q^{30} -13.6243i q^{31} +(29.6542 - 12.0262i) q^{32} +27.3586i q^{33} +(35.4743 + 41.6600i) q^{34} +(3.57919 + 2.17123i) q^{35} +(1.91238 - 11.8466i) q^{36} +15.5597i q^{37} +(23.2964 + 27.3586i) q^{38} -8.98337i q^{39} +(0.00200734 + 40.0000i) q^{40} +13.2990 q^{41} +(-2.20822 + 1.88034i) q^{42} +27.9430 q^{43} +(62.3746 + 10.0690i) q^{44} +(12.8248 + 7.77983i) q^{45} +(29.0997 - 24.7789i) q^{46} -55.6558 q^{47} +(-26.3052 - 8.72000i) q^{48} -48.2990 q^{49} +(-46.3365 - 18.7863i) q^{50} -47.3865i q^{51} +(-20.4811 - 3.30621i) q^{52} +15.5597i q^{53} +(-7.91238 + 6.73753i) q^{54} +(-40.9621 + 67.5245i) q^{55} +(3.47425 + 5.72653i) q^{56} -31.1193i q^{57} +(69.5122 - 59.1909i) q^{58} -87.6625i q^{59} +(22.4571 - 26.3757i) q^{60} +38.0000 q^{61} +(17.6658 + 20.7462i) q^{62} +2.51176 q^{63} +(-29.5619 + 56.7635i) q^{64} +(13.4502 - 22.1721i) q^{65} +(-35.4743 - 41.6600i) q^{66} +92.2015 q^{67} +(-108.036 - 17.4400i) q^{68} -33.0997 q^{69} +(-8.26547 + 1.33470i) q^{70} +130.707i q^{71} +(12.4488 + 20.5190i) q^{72} -54.7173i q^{73} +(-20.1752 - 23.6933i) q^{74} +(20.0049 + 38.4032i) q^{75} +(-70.9485 - 11.4531i) q^{76} +13.2249i q^{77} +(11.6482 + 13.6793i) q^{78} +13.6243i q^{79} +(-51.8686 - 60.9069i) q^{80} +9.00000 q^{81} +(-20.2509 + 17.2440i) q^{82} +59.0048 q^{83} +(0.924421 - 5.72653i) q^{84} +(70.9485 - 116.956i) q^{85} +(-42.5498 + 36.2319i) q^{86} -79.0673 q^{87} +(-108.036 + 65.5448i) q^{88} +39.8007 q^{89} +(-29.6164 + 4.78243i) q^{90} -4.34246i q^{91} +(-12.1819 + 75.4635i) q^{92} -23.5980i q^{93} +(84.7492 - 72.1654i) q^{94} +(46.5927 - 76.8064i) q^{95} +(51.3625 - 20.8300i) q^{96} +168.821i q^{97} +(73.5467 - 62.6263i) q^{98} +47.3865i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{4} + 4 q^{5} - 6 q^{6} + 24 q^{9}+O(q^{10}) $ 8 * q - 10 * q^4 + 4 * q^5 - 6 * q^6 + 24 * q^9	$ 8 q - 10 q^{4} + 4 q^{5} - 6 q^{6} + 24 q^{9} - 42 q^{10} + 20 q^{14} - 46 q^{16} + 52 q^{20} + 72 q^{21} - 18 q^{24} + 32 q^{25} + 84 q^{26} - 184 q^{29} - 60 q^{30} + 12 q^{34} - 30 q^{36} - 6 q^{40} - 256 q^{41} + 348 q^{44} + 12 q^{45} + 112 q^{46} - 24 q^{49} + 72 q^{50} - 18 q^{54} - 244 q^{56} + 6 q^{60} + 304 q^{61} - 10 q^{64} + 168 q^{65} - 12 q^{66} - 144 q^{69} - 104 q^{70} - 252 q^{74} - 24 q^{76} - 308 q^{80} + 72 q^{81} - 204 q^{84} + 24 q^{85} - 280 q^{86} + 560 q^{89} - 126 q^{90} + 376 q^{94} + 426 q^{96}+O(q^{100}) $ 8 * q - 10 * q^4 + 4 * q^5 - 6 * q^6 + 24 * q^9 - 42 * q^10 + 20 * q^14 - 46 * q^16 + 52 * q^20 + 72 * q^21 - 18 * q^24 + 32 * q^25 + 84 * q^26 - 184 * q^29 - 60 * q^30 + 12 * q^34 - 30 * q^36 - 6 * q^40 - 256 * q^41 + 348 * q^44 + 12 * q^45 + 112 * q^46 - 24 * q^49 + 72 * q^50 - 18 * q^54 - 244 * q^56 + 6 * q^60 + 304 * q^61 - 10 * q^64 + 168 * q^65 - 12 * q^66 - 144 * q^69 - 104 * q^70 - 252 * q^74 - 24 * q^76 - 308 * q^80 + 72 * q^81 - 204 * q^84 + 24 * q^85 - 280 * q^86 + 560 * q^89 - 126 * q^90 + 376 * q^94 + 426 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.52274	+	1.29664i	−0.761369	+	0.648319i
$2$	−1.52274	+	1.29664i	−0.761369	+	0.648319i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	0.637459	−	3.94888i	0.159365	−	0.987220i
$5$	4.27492	+	2.59328i	0.854983	+	0.518655i
$5$	4.27492	+	2.59328i	0.854983	+	0.518655i
$6$	−2.63746	+	2.24584i	−0.439576	+	0.374307i
$7$	0.837253			0.119608			0.0598038	−	0.998210i	$-0.480952\pi$
$7$	0.837253			0.119608			0.0598038	+	0.998210i	$0.480952\pi$
$8$	4.14959	+	6.83966i	0.518698	+	0.854957i
$9$	3.00000			0.333333
$10$	−9.87212	+	1.59414i	−0.987212	+	0.159414i
$11$			15.7955i			1.43596i	0.696066	+	0.717978i	$0.254932\pi$
$11$			15.7955i			1.43596i	−0.696066	+	0.717978i	$0.745068\pi$
$12$	1.10411	−	6.83966i	0.0920092	−	0.569972i
$13$		−	5.18655i		−	0.398966i	−0.979901	−	0.199483i	$-0.936074\pi$
$13$		−	5.18655i		−	0.398966i	0.979901	−	0.199483i	$-0.0639262\pi$
$14$	−1.27492	+	1.08561i	−0.0910655	+	0.0775439i
$15$	7.40437	+	4.49169i	0.493625	+	0.299446i
$16$	−15.1873	−	5.03449i	−0.949206	−	0.314656i
$17$		−	27.3586i		−	1.60933i	−0.593728	−	0.804666i	$-0.702344\pi$
$17$		−	27.3586i		−	1.60933i	0.593728	−	0.804666i	$-0.297656\pi$
$18$	−4.56821	+	3.88991i	−0.253790	+	0.216106i
$19$		−	17.9667i		−	0.945618i	−0.881165	−	0.472809i	$-0.843240\pi$
$19$		−	17.9667i		−	0.945618i	0.881165	−	0.472809i	$-0.156760\pi$
$20$	12.9656	−	15.2280i	0.648281	−	0.761401i
$21$	1.45017			0.0690555
$22$	−20.4811	−	24.0524i	−0.930958	−	1.09329i
$23$	−19.1101			−0.830874			−0.415437	−	0.909622i	$-0.636371\pi$
$23$	−19.1101			−0.830874			−0.415437	+	0.909622i	$0.636371\pi$
$24$	7.18729	+	11.8466i	0.299471	+	0.493610i
$25$	11.5498	+	22.1721i	0.461993	+	0.886883i
$26$	6.72508	+	7.89776i	0.258657	+	0.303760i
$27$	5.19615			0.192450
$28$	0.533714	−	3.30621i	0.0190612	−	0.118079i
$29$	−45.6495			−1.57412			−0.787060	−	0.616876i	$-0.788398\pi$
$29$	−45.6495			−1.57412			−0.787060	+	0.616876i	$0.788398\pi$
$30$	−17.0990	+	2.76113i	−0.569967	+	0.0920378i
$31$		−	13.6243i		−	0.439493i	−0.975557	−	0.219747i	$-0.929477\pi$
$31$		−	13.6243i		−	0.439493i	0.975557	−	0.219747i	$-0.0705230\pi$
$32$	29.6542	−	12.0262i	0.926693	−	0.375819i
$33$			27.3586i			0.829050i
$34$	35.4743	+	41.6600i	1.04336	+	1.22529i
$35$	3.57919	+	2.17123i	0.102263	+	0.0620351i
$36$	1.91238	−	11.8466i	0.0531216	−	0.329073i
$37$			15.5597i			0.420531i	0.977644	+	0.210266i	$0.0674329\pi$
$37$			15.5597i			0.420531i	−0.977644	+	0.210266i	$0.932567\pi$
$38$	23.2964	+	27.3586i	0.613062	+	0.719964i
$39$		−	8.98337i		−	0.230343i
$40$	0.00200734	+	40.0000i	5.01834e−5	+	1.00000i
$41$	13.2990			0.324366			0.162183	−	0.986761i	$-0.448147\pi$
$41$	13.2990			0.324366			0.162183	+	0.986761i	$0.448147\pi$
$42$	−2.20822	+	1.88034i	−0.0525767	+	0.0447700i
$43$	27.9430			0.649837			0.324918	−	0.945742i	$-0.394663\pi$
$43$	27.9430			0.649837			0.324918	+	0.945742i	$0.394663\pi$
$44$	62.3746	+	10.0690i	1.41760	+	0.228841i
$45$	12.8248	+	7.77983i	0.284994	+	0.172885i
$46$	29.0997	−	24.7789i	0.632601	−	0.538672i
$47$	−55.6558			−1.18417			−0.592083	−	0.805877i	$-0.701694\pi$
$47$	−55.6558			−1.18417			−0.592083	+	0.805877i	$0.701694\pi$
$48$	−26.3052	−	8.72000i	−0.548024	−	0.181667i
$49$	−48.2990			−0.985694
$50$	−46.3365	−	18.7863i	−0.926731	−	0.375726i
$51$		−	47.3865i		−	0.929148i
$52$	−20.4811	−	3.30621i	−0.393867	−	0.0635810i
$53$			15.5597i			0.293578i	0.989168	+	0.146789i	$0.0468939\pi$
$53$			15.5597i			0.293578i	−0.989168	+	0.146789i	$0.953106\pi$
$54$	−7.91238	+	6.73753i	−0.146525	+	0.124769i
$55$	−40.9621	+	67.5245i	−0.744766	+	1.22772i
$56$	3.47425	+	5.72653i	0.0620403	+	0.102259i
$57$		−	31.1193i		−	0.545953i
$58$	69.5122	−	59.1909i	1.19849	−	1.02053i
$59$		−	87.6625i		−	1.48581i	−0.669400	−	0.742903i	$-0.733449\pi$
$59$		−	87.6625i		−	1.48581i	0.669400	−	0.742903i	$-0.266551\pi$
$60$	22.4571	−	26.3757i	0.374285	−	0.439595i
$61$	38.0000			0.622951			0.311475	−	0.950254i	$-0.399177\pi$
$61$	38.0000			0.622951			0.311475	+	0.950254i	$0.399177\pi$
$62$	17.6658	+	20.7462i	0.284932	+	0.334616i
$63$	2.51176			0.0398692
$64$	−29.5619	+	56.7635i	−0.461904	+	0.886930i
$65$	13.4502	−	22.1721i	0.206926	−	0.341109i
$66$	−35.4743	−	41.6600i	−0.537489	−	0.631212i
$67$	92.2015			1.37614			0.688071	−	0.725643i	$-0.258458\pi$
$67$	92.2015			1.37614			0.688071	+	0.725643i	$0.258458\pi$
$68$	−108.036	−	17.4400i	−1.58876	−	0.256471i
$69$	−33.0997			−0.479705
$70$	−8.26547	+	1.33470i	−0.118078	+	0.0190672i
$71$			130.707i			1.84094i	0.390816	+	0.920469i	$0.372193\pi$
$71$			130.707i			1.84094i	−0.390816	+	0.920469i	$0.627807\pi$
$72$	12.4488	+	20.5190i	0.172899	+	0.284986i
$73$		−	54.7173i		−	0.749552i	−0.927115	−	0.374776i	$-0.877720\pi$
$73$		−	54.7173i		−	0.749552i	0.927115	−	0.374776i	$-0.122280\pi$
$74$	−20.1752	−	23.6933i	−0.272638	−	0.320179i
$75$	20.0049	+	38.4032i	0.266732	+	0.512042i
$76$	−70.9485	−	11.4531i	−0.933533	−	0.150698i
$77$			13.2249i			0.171751i
$78$	11.6482	+	13.6793i	0.149336	+	0.175376i
$79$			13.6243i			0.172459i	0.996275	+	0.0862297i	$0.0274819\pi$
$79$			13.6243i			0.172459i	−0.996275	+	0.0862297i	$0.972518\pi$
$80$	−51.8686	−	60.9069i	−0.648357	−	0.761336i
$81$	9.00000			0.111111
$82$	−20.2509	+	17.2440i	−0.246962	+	0.210293i
$83$	59.0048			0.710901			0.355451	−	0.934695i	$-0.384327\pi$
$83$	59.0048			0.710901			0.355451	+	0.934695i	$0.384327\pi$
$84$	0.924421	−	5.72653i	0.0110050	−	0.0681730i
$85$	70.9485	−	116.956i	0.834688	−	1.37595i
$86$	−42.5498	+	36.2319i	−0.494766	+	0.421302i
$87$	−79.0673			−0.908819
$88$	−108.036	+	65.5448i	−1.22768	+	0.744828i
$89$	39.8007			0.447198			0.223599	−	0.974681i	$-0.428219\pi$
$89$	39.8007			0.447198			0.223599	+	0.974681i	$0.428219\pi$
$90$	−29.6164	+	4.78243i	−0.329071	+	0.0531381i
$91$		−	4.34246i		−	0.0477193i
$92$	−12.1819	+	75.4635i	−0.132412	+	0.820255i
$93$		−	23.5980i		−	0.253741i
$94$	84.7492	−	72.1654i	0.901587	−	0.767717i
$95$	46.5927	−	76.8064i	0.490450	−	0.808488i
$96$	51.3625	−	20.8300i	0.535026	−	0.216979i
$97$			168.821i			1.74043i	0.492675	+	0.870214i	$0.336019\pi$
$97$			168.821i			1.74043i	−0.492675	+	0.870214i	$0.663981\pi$
$98$	73.5467	−	62.6263i	0.750477	−	0.639044i
$99$			47.3865i			0.478652i
$100$	94.9174	−	31.4751i	0.949174	−	0.314751i
$101$	44.5498			0.441087			0.220544	−	0.975377i	$-0.429217\pi$
$101$	44.5498			0.441087			0.220544	+	0.975377i	$0.429217\pi$
$102$	61.4432	+	72.1573i	0.602384	+	0.707424i
$103$	−126.466			−1.22782			−0.613911	−	0.789375i	$-0.710405\pi$
$103$	−126.466			−1.22782			−0.613911	+	0.789375i	$0.710405\pi$
$104$	35.4743	−	21.5220i	0.341099	−	0.206943i
$105$	6.19934	+	3.76068i	0.0590413	+	0.0358160i
$106$	−20.1752	−	23.6933i	−0.190333	−	0.223521i
$107$	104.383			0.975546			0.487773	−	0.872971i	$-0.337809\pi$
$107$	104.383			0.975546			0.487773	+	0.872971i	$0.337809\pi$
$108$	3.31233	−	20.5190i	0.0306697	−	0.189991i
$109$	−0.501656			−0.00460235			−0.00230117	−	0.999997i	$-0.500732\pi$
$109$	−0.501656			−0.00460235			−0.00230117	+	0.999997i	$0.500732\pi$
$110$	−25.1803	−	155.935i	−0.228912	−	1.41759i
$111$			26.9501i			0.242794i
$112$	−12.7156	−	4.21515i	−0.113532	−	0.0376352i
$113$			16.9855i			0.150314i	0.997172	+	0.0751572i	$0.0239459\pi$
$113$			16.9855i			0.150314i	−0.997172	+	0.0751572i	$0.976054\pi$
$114$	40.3505	+	47.3865i	0.353952	+	0.415671i
$115$	−81.6941	−	49.5578i	−0.710384	−	0.430937i
$116$	−29.0997	+	180.264i	−0.250859	+	1.55400i
$117$		−	15.5597i		−	0.132989i
$118$	113.667	+	133.487i	0.963276	+	1.13125i
$119$		−	22.9061i		−	0.192488i
$120$	0.00347681	+	69.2820i	2.89734e−5	+	0.577350i
$121$	−128.498			−1.06197
$122$	−57.8640	+	49.2723i	−0.474295	+	0.403871i
$123$	23.0346			0.187273
$124$	−53.8007	−	8.68492i	−0.433876	−	0.0700397i
$125$	−8.12376	+	124.736i	−0.0649901	+	0.997886i
$126$	−3.82475	+	3.25684i	−0.0303552	+	0.0258480i
$127$	8.45598			0.0665825			0.0332913	−	0.999446i	$-0.489401\pi$
$127$	8.45598			0.0665825			0.0332913	+	0.999446i	$0.489401\pi$
$128$	−28.5867	−	124.767i	−0.223334	−	0.974742i
$129$	48.3987			0.375184
$130$	8.26810	+	51.2023i	0.0636008	+	0.393864i
$131$		−	51.7290i		−	0.394878i	−0.980315	−	0.197439i	$-0.936738\pi$
$131$		−	51.7290i		−	0.394878i	0.980315	−	0.197439i	$-0.0632624\pi$
$132$	108.036	+	17.4400i	0.818454	+	0.132121i
$133$		−	15.0427i		−	0.113103i
$134$	−140.399	+	119.552i	−1.04775	+	0.892179i
$135$	22.2131	+	13.4751i	0.164542	+	0.0998153i
$136$	187.124	−	113.527i	1.37591	−	0.834757i
$137$			53.8083i			0.392762i	0.980528	+	0.196381i	$0.0629189\pi$
$137$			53.8083i			0.392762i	−0.980528	+	0.196381i	$0.937081\pi$
$138$	50.4021	−	42.9183i	0.365233	−	0.311002i
$139$		−	13.6243i		−	0.0980165i	−0.998798	−	0.0490082i	$-0.984394\pi$
$139$		−	13.6243i		−	0.0980165i	0.998798	−	0.0490082i	$-0.0156061\pi$
$140$	10.8555	−	12.7497i	0.0775393	−	0.0910694i
$141$	−96.3987			−0.683679
$142$	−169.479	−	199.032i	−1.19352	−	1.40163i
$143$	81.9243			0.572897
$144$	−45.5619	−	15.1035i	−0.316402	−	0.104885i
$145$	−195.148	−	118.382i	−1.34585	−	0.816426i
$146$	70.9485	+	83.3200i	0.485949	+	0.570685i
$147$	−83.6563			−0.569091
$148$	61.4432	+	9.91864i	0.415157	+	0.0670178i
$149$	−33.6495			−0.225836			−0.112918	−	0.993604i	$-0.536020\pi$
$149$	−33.6495			−0.225836			−0.112918	+	0.993604i	$0.536020\pi$
$150$	−80.2572	−	32.5388i	−0.535048	−	0.216926i
$151$		−	139.988i		−	0.927076i	−0.886077	−	0.463538i	$-0.846580\pi$
$151$		−	139.988i		−	0.927076i	0.886077	−	0.463538i	$-0.153420\pi$
$152$	122.886	−	74.5546i	0.808463	−	0.490490i
$153$		−	82.0759i		−	0.536444i
$154$	−17.1478	−	20.1380i	−0.111350	−	0.130766i
$155$	35.3315	−	58.2427i	0.227945	−	0.375759i
$156$	−35.4743	−	5.72653i	−0.227399	−	0.0367085i
$157$		−	21.2631i		−	0.135434i	−0.997705	−	0.0677170i	$-0.978428\pi$
$157$		−	21.2631i		−	0.135434i	0.997705	−	0.0677170i	$-0.0215715\pi$
$158$	−17.6658	−	20.7462i	−0.111809	−	0.131305i
$159$			26.9501i			0.169498i
$160$	157.956	+	25.4904i	0.987228	+	0.159315i
$161$	−16.0000			−0.0993789
$162$	−13.7046	+	11.6697i	−0.0845965	+	0.0720355i
$163$	−210.211			−1.28964			−0.644819	−	0.764335i	$-0.723067\pi$
$163$	−210.211			−1.28964			−0.644819	+	0.764335i	$0.723067\pi$
$164$	8.47757	−	52.5162i	0.0516925	−	0.320221i
$165$	−70.9485	+	116.956i	−0.429991	+	0.708824i
$166$	−89.8488	+	76.5079i	−0.541258	+	0.460891i
$167$	−238.384			−1.42745			−0.713725	−	0.700426i	$-0.752994\pi$
$167$	−238.384			−1.42745			−0.713725	+	0.700426i	$0.752994\pi$
$168$	6.01759	+	9.91864i	0.0358190	+	0.0590395i
$169$	142.100			0.840826
$170$	43.6136	+	270.088i	0.256550	+	1.58875i
$171$		−	53.9002i		−	0.315206i
$172$	17.8125	−	110.343i	0.103561	−	0.641532i
$173$			2.33481i			0.0134960i	0.999977	+	0.00674800i	$0.00214797\pi$
$173$			2.33481i			0.0134960i	−0.999977	+	0.00674800i	$0.997852\pi$
$174$	120.399	−	102.522i	0.691946	−	0.589205i
$175$	9.67014	+	18.5637i	0.0552579	+	0.106078i
$176$	79.5224	−	239.891i	0.451832	−	1.36302i
$177$		−	151.836i		−	0.857830i
$178$	−60.6060	+	51.6071i	−0.340483	+	0.289927i
$179$			227.054i			1.26846i	0.773145	+	0.634229i	$0.218682\pi$
$179$			227.054i			1.26846i	−0.773145	+	0.634229i	$0.781318\pi$
$180$	38.8969	−	45.6841i	0.216094	−	0.253800i
$181$	114.096			0.630367			0.315183	−	0.949031i	$-0.397934\pi$
$181$	114.096			0.630367			0.315183	+	0.949031i	$0.397934\pi$
$182$	5.63060	+	6.61243i	0.0309374	+	0.0363320i
$183$	65.8179			0.359661
$184$	−79.2990	−	130.707i	−0.430973	−	0.710362i
$185$	−40.3505	+	66.5163i	−0.218111	+	0.359547i
$186$	30.5980	+	35.9335i	0.164505	+	0.193191i
$187$	432.144			2.31093
$188$	−35.4783	+	219.778i	−0.188714	+	1.16903i
$189$	4.35050			0.0230185
$190$	28.6415	+	177.370i	0.150745	+	0.933525i
$191$		−	139.392i		−	0.729798i	−0.931047	−	0.364899i	$-0.881103\pi$
$191$		−	139.392i		−	0.729798i	0.931047	−	0.364899i	$-0.118897\pi$
$192$	−51.2027	+	98.3173i	−0.266681	+	0.512069i
$193$			182.046i			0.943245i	0.881801	+	0.471623i	$0.156331\pi$
$193$			182.046i			0.943245i	−0.881801	+	0.471623i	$0.843669\pi$
$194$	−218.900	−	257.071i	−1.12835	−	1.32511i
$195$	23.2964	−	38.4032i	0.119469	−	0.196939i
$196$	−30.7886	+	190.727i	−0.157085	+	0.973097i
$197$		−	258.027i		−	1.30978i	−0.755724	−	0.654890i	$-0.772715\pi$
$197$		−	258.027i		−	1.30978i	0.755724	−	0.654890i	$-0.227285\pi$
$198$	−61.4432	−	72.1573i	−0.310319	−	0.364431i
$199$			256.474i			1.28881i	0.764683	+	0.644407i	$0.222896\pi$
$199$			256.474i			1.28881i	−0.764683	+	0.644407i	$0.777104\pi$
$200$	−103.722	+	171.002i	−0.518612	+	0.855009i
$201$	159.698			0.794516
$202$	−67.8377	+	57.7650i	−0.335830	+	0.285965i
$203$	−38.2202			−0.188277
$204$	−187.124	−	30.2070i	−0.917273	−	0.148073i
$205$	56.8522	+	34.4880i	0.277328	+	0.168234i
$206$	192.574	−	163.980i	0.934825	−	0.796020i
$207$	−57.3303			−0.276958
$208$	−26.1117	+	78.7697i	−0.125537	+	0.378700i
$209$	283.794			1.35787
$210$	−14.3162	+	2.31177i	−0.0681724	+	0.0110084i
$211$			211.855i			1.00405i	0.864852	+	0.502027i	$0.167412\pi$
$211$			211.855i			1.00405i	−0.864852	+	0.502027i	$0.832588\pi$
$212$	61.4432	+	9.91864i	0.289826	+	0.0467860i
$213$			226.390i			1.06287i
$214$	−158.949	+	135.348i	−0.742750	+	0.632465i
$215$	119.454	+	72.4639i	0.555600	+	0.337041i
$216$	21.5619	+	35.5399i	0.0998235	+	0.164537i
$217$		−	11.4070i		−	0.0525667i
$218$	0.763890	−	0.650466i	0.00350408	−	0.00298379i
$219$		−	94.7731i		−	0.432754i
$220$	240.535	+	204.799i	1.09334	+	0.930903i
$221$	−141.897			−0.642068
$222$	−34.9446	−	41.0380i	−0.157408	−	0.184856i
$223$	349.843			1.56880			0.784401	−	0.620255i	$-0.212971\pi$
$223$	349.843			1.56880			0.784401	+	0.620255i	$0.212971\pi$
$224$	24.8281	−	10.0690i	0.110840	−	0.0449508i
$225$	34.6495	+	66.5163i	0.153998	+	0.295628i
$226$	−22.0241	−	25.8645i	−0.0974517	−	0.114445i
$227$	−185.554			−0.817418			−0.408709	−	0.912665i	$-0.634021\pi$
$227$	−185.554			−0.817418			−0.408709	+	0.912665i	$0.634021\pi$
$228$	−122.886	−	19.8373i	−0.538976	−	0.0870056i
$229$	263.897			1.15239			0.576194	−	0.817313i	$-0.304537\pi$
$229$	263.897			1.15239			0.576194	+	0.817313i	$0.304537\pi$
$230$	188.657	−	30.4642i	0.820249	−	0.132453i
$231$			22.9061i			0.0991607i
$232$	−189.427	−	312.227i	−0.816494	−	1.34581i
$233$		−	58.4780i		−	0.250978i	−0.992095	−	0.125489i	$-0.959950\pi$
$233$		−	58.4780i		−	0.250978i	0.992095	−	0.125489i	$-0.0400500\pi$
$234$	20.1752	+	23.6933i	0.0862190	+	0.101253i
$235$	−237.924	−	144.331i	−1.01244	−	0.614174i
$236$	−346.169	−	55.8812i	−1.46682	−	0.236785i
$237$			23.5980i			0.0995694i
$238$	29.7009	+	34.8800i	0.124794	+	0.146555i
$239$			113.337i			0.474212i	0.971484	+	0.237106i	$0.0761989\pi$
$239$			113.337i			0.474212i	−0.971484	+	0.237106i	$0.923801\pi$
$240$	−89.8390	−	105.494i	−0.374329	−	0.439558i
$241$	−77.7940			−0.322797			−0.161398	−	0.986889i	$-0.551600\pi$
$241$	−77.7940			−0.322797			−0.161398	+	0.986889i	$0.551600\pi$
$242$	195.669	−	166.616i	0.808551	−	0.688495i
$243$	15.5885			0.0641500
$244$	24.2234	−	150.057i	0.0992763	−	0.614989i
$245$	−206.474	−	125.253i	−0.842752	−	0.511235i
$246$	−35.0756	+	29.8675i	−0.142584	+	0.121413i
$247$	−93.1855			−0.377269
$248$	93.1855	−	56.5351i	0.375748	−	0.227964i
$249$	102.199			0.410439
$250$	−149.367	−	200.473i	−0.597467	−	0.801893i
$251$		−	106.226i		−	0.423212i	−0.977355	−	0.211606i	$-0.932131\pi$
$251$		−	106.226i		−	0.423212i	0.977355	−	0.211606i	$-0.0678693\pi$
$252$	1.60114	−	9.91864i	0.00635374	−	0.0393597i
$253$		−	301.854i		−	1.19310i
$254$	−12.8762	+	10.9644i	−0.0506939	+	0.0431667i
$255$	122.886	−	202.574i	0.481908	−	0.794406i
$256$	205.308	+	152.921i	0.801983	+	0.597346i
$257$		−	381.078i		−	1.48279i	−0.671067	−	0.741397i	$-0.734164\pi$
$257$		−	381.078i		−	1.48279i	0.671067	−	0.741397i	$-0.265836\pi$
$258$	−73.6985	+	62.7556i	−0.285653	+	0.243239i
$259$			13.0274i			0.0502988i
$260$	−78.9810	−	67.2469i	−0.303773	−	0.258642i
$261$	−136.949			−0.524707
$262$	67.0738	+	78.7697i	0.256007	+	0.300648i
$263$	−11.4914			−0.0436934			−0.0218467	−	0.999761i	$-0.506955\pi$
$263$	−11.4914			−0.0436934			−0.0218467	+	0.999761i	$0.506955\pi$
$264$	−187.124	+	113.527i	−0.708802	+	0.430027i
$265$	−40.3505	+	66.5163i	−0.152266	+	0.251005i
$266$	19.5050	+	22.9061i	0.0733269	+	0.0861132i
$267$	68.9368			0.258190
$268$	58.7746	−	364.093i	0.219308	−	1.35855i
$269$	−77.9518			−0.289784			−0.144892	−	0.989447i	$-0.546283\pi$
$269$	−77.9518			−0.289784			−0.144892	+	0.989447i	$0.546283\pi$
$270$	−51.2970	+	8.28340i	−0.189989	+	0.0306793i
$271$			86.6851i			0.319871i	0.987127	+	0.159936i	$0.0511287\pi$
$271$			86.6851i			0.319871i	−0.987127	+	0.159936i	$0.948871\pi$
$272$	−137.737	+	415.504i	−0.506386	+	1.52759i
$273$		−	7.52136i		−	0.0275508i
$274$	−69.7700	−	81.9360i	−0.254635	−	0.299036i
$275$	−350.220	+	182.436i	−1.27353	+	0.663402i
$276$	−21.0997	+	130.707i	−0.0764481	+	0.473575i
$277$			287.328i			1.03729i	0.854991	+	0.518643i	$0.173563\pi$
$277$			287.328i			1.03729i	−0.854991	+	0.518643i	$0.826437\pi$
$278$	17.6658	+	20.7462i	0.0635459	+	0.0746267i
$279$		−	40.8729i		−	0.146498i
$280$	0.00168065	+	33.4901i	6.00232e−6	+	0.119608i
$281$	−224.598			−0.799281			−0.399641	−	0.916672i	$-0.630865\pi$
$281$	−224.598			−0.799281			−0.399641	+	0.916672i	$0.630865\pi$
$282$	146.790	−	124.994i	0.520531	−	0.443242i
$283$	−84.1224			−0.297252			−0.148626	−	0.988893i	$-0.547485\pi$
$283$	−84.1224			−0.297252			−0.148626	+	0.988893i	$0.547485\pi$
$284$	516.145	+	83.3200i	1.81741	+	0.293380i
$285$	80.7010	−	133.033i	0.283161	−	0.466781i
$286$	−124.749	+	106.226i	−0.436186	+	0.371420i
$287$	11.1346			0.0387967
$288$	88.9625	−	36.0786i	0.308898	−	0.125273i
$289$	−459.495			−1.58995
$290$	450.657	−	72.7718i	1.55399	−	0.250937i
$291$			292.407i			1.00484i
$292$	−216.072	−	34.8800i	−0.739972	−	0.119452i
$293$			246.620i			0.841706i	0.907129	+	0.420853i	$0.138269\pi$
$293$			246.620i			0.841706i	−0.907129	+	0.420853i	$0.861731\pi$
$294$	127.387	−	108.472i	0.433288	−	0.368952i
$295$	227.333	−	374.750i	0.770621	−	1.27034i
$296$	−106.423	+	64.5661i	−0.359536	+	0.218129i
$297$			82.0759i			0.276350i
$298$	51.2394	−	43.6312i	0.171944	−	0.146414i
$299$			99.1156i			0.331490i
$300$	164.402	−	54.5165i	0.548006	−	0.181722i
$301$	23.3954			0.0777255
$302$	181.514	+	213.166i	0.601041	+	0.705846i
$303$	77.1626			0.254662
$304$	−90.4535	+	272.866i	−0.297544	+	0.897586i
$305$	162.447	+	98.5445i	0.532613	+	0.323097i
$306$	106.423	+	124.980i	0.347787	+	0.408432i
$307$	−115.811			−0.377236			−0.188618	−	0.982051i	$-0.560401\pi$
$307$	−115.811			−0.377236			−0.188618	+	0.982051i	$0.560401\pi$
$308$	52.2233	+	8.43030i	0.169556	+	0.0273711i
$309$	−219.045			−0.708883
$310$	21.7190	+	134.501i	0.0700614	+	0.433873i
$311$		−	203.767i		−	0.655201i	−0.944816	−	0.327600i	$-0.893760\pi$
$311$		−	203.767i		−	0.655201i	0.944816	−	0.327600i	$-0.106240\pi$
$312$	61.4432	−	37.2773i	0.196933	−	0.119478i
$313$			99.0614i			0.316490i	0.987400	+	0.158245i	$0.0505836\pi$
$313$			99.0614i			0.316490i	−0.987400	+	0.158245i	$0.949416\pi$
$314$	27.5706	+	32.3782i	0.0878045	+	0.103115i
$315$	10.7376	+	6.51369i	0.0340875	+	0.0206784i
$316$	53.8007	+	8.68492i	0.170255	+	0.0274839i
$317$			471.192i			1.48641i	0.669063	+	0.743206i	$0.266696\pi$
$317$			471.192i			1.48641i	−0.669063	+	0.743206i	$0.733304\pi$
$318$	−34.9446	−	41.0380i	−0.109889	−	0.129050i
$319$		−	721.057i		−	2.26037i
$320$	−273.578	+	165.997i	−0.854931	+	0.518741i
$321$	180.797			0.563232
$322$	24.3638	−	20.7462i	0.0756640	−	0.0644292i
$323$	−491.546			−1.52181
$324$	5.73713	−	35.5399i	0.0177072	−	0.109691i
$325$	114.997	−	59.9038i	0.353836	−	0.184319i
$326$	320.096	−	272.568i	0.981891	−	0.836098i
$327$	−0.868893			−0.00265717
$328$	55.1854	+	90.9607i	0.168248	+	0.277319i
$329$	−46.5980			−0.141635
$330$	−43.6136	−	270.088i	−0.132162	−	0.818448i
$331$		−	270.695i		−	0.817810i	−0.912577	−	0.408905i	$-0.865911\pi$
$331$		−	270.695i		−	0.817810i	0.912577	−	0.408905i	$-0.134089\pi$
$332$	37.6131	−	233.003i	0.113293	−	0.701816i
$333$			46.6790i			0.140177i
$334$	362.997	−	309.098i	1.08682	−	0.925444i
$335$	394.154	+	239.104i	1.17658	+	0.713743i
$336$	−22.0241	−	7.30085i	−0.0655479	−	0.0217287i
$337$			377.317i			1.11964i	0.828615	+	0.559818i	$0.189129\pi$
$337$			377.317i			1.11964i	−0.828615	+	0.559818i	$0.810871\pi$
$338$	−216.380	+	184.252i	−0.640179	+	0.545124i
$339$			29.4198i			0.0867841i
$340$	−416.618	−	354.722i	−1.22535	−	1.04330i
$341$	215.203			0.631093
$342$	69.8891	+	82.0759i	0.204354	+	0.239988i
$343$	−81.4639			−0.237504
$344$	115.952	+	191.121i	0.337069	+	0.555583i
$345$	−141.498	−	85.8366i	−0.410140	−	0.248802i
$346$	−3.02740	−	3.55530i	−0.00874971	−	0.0102754i
$347$	462.222			1.33205			0.666025	−	0.745929i	$-0.267994\pi$
$347$	462.222			1.33205			0.666025	+	0.745929i	$0.267994\pi$
$348$	−50.4021	+	312.227i	−0.144834	+	0.897204i
$349$	200.598			0.574779			0.287390	−	0.957814i	$-0.407213\pi$
$349$	200.598			0.574779			0.287390	+	0.957814i	$0.407213\pi$
$350$	−38.7954	−	15.7289i	−0.110844	−	0.0449397i
$351$		−	26.9501i		−	0.0767810i
$352$	189.960	+	468.403i	0.539660	+	1.33069i
$353$		−	250.897i		−	0.710757i	−0.934722	−	0.355379i	$-0.884352\pi$
$353$		−	250.897i		−	0.710757i	0.934722	−	0.355379i	$-0.115648\pi$
$354$	196.876	+	231.206i	0.556148	+	0.653125i
$355$	−338.958	+	558.760i	−0.954812	+	1.57397i
$356$	25.3713	−	157.168i	0.0712676	−	0.441483i
$357$		−	39.6746i		−	0.111133i
$358$	−294.407	−	345.744i	−0.822366	−	0.965764i
$359$		−	215.601i		−	0.600560i	−0.953851	−	0.300280i	$-0.902920\pi$
$359$		−	215.601i		−	0.600560i	0.953851	−	0.300280i	$-0.0970801\pi$
$360$	0.00602201	+	120.000i	1.67278e−5	+	0.333333i
$361$	38.1960			0.105806
$362$	−173.739	+	147.942i	−0.479941	+	0.408679i
$363$	−222.566			−0.613129
$364$	−17.1478	−	2.76814i	−0.0471095	−	0.00760478i
$365$	141.897	−	233.912i	0.388759	−	0.640854i
$366$	−100.223	+	85.3420i	−0.273835	+	0.233175i
$367$	−67.0637			−0.182735			−0.0913675	−	0.995817i	$-0.529124\pi$
$367$	−67.0637			−0.182735			−0.0913675	+	0.995817i	$0.529124\pi$
$368$	290.231	+	96.2097i	0.788670	+	0.261439i
$369$	39.8970			0.108122
$370$	−24.8043	−	153.607i	−0.0670387	−	0.415153i
$371$			13.0274i			0.0351142i
$372$	−93.1855	−	15.0427i	−0.250499	−	0.0404374i
$373$		−	567.402i		−	1.52119i	−0.649230	−	0.760593i	$-0.724909\pi$
$373$		−	567.402i		−	1.52119i	0.649230	−	0.760593i	$-0.275091\pi$
$374$	−658.042	+	560.334i	−1.75947	+	1.49822i
$375$	−14.0708	+	216.049i	−0.0375220	+	0.576130i
$376$	−230.949	−	380.667i	−0.614225	−	1.01241i
$377$			236.764i			0.628020i
$378$	−6.62466	+	5.64102i	−0.0175256	+	0.0149233i
$379$			240.298i			0.634031i	0.948420	+	0.317016i	$0.102681\pi$
$379$			240.298i			0.634031i	−0.948420	+	0.317016i	$0.897319\pi$
$380$	−273.598	−	232.950i	−0.719995	−	0.613026i
$381$	14.6462			0.0384414
$382$	180.740	+	212.257i	0.473142	+	0.555646i
$383$	670.068			1.74952			0.874762	−	0.484553i	$-0.161018\pi$
$383$	670.068			1.74952			0.874762	+	0.484553i	$0.161018\pi$
$384$	−49.5137	−	216.103i	−0.128942	−	0.562768i
$385$	−34.2957	+	56.5351i	−0.0890797	+	0.146845i
$386$	−236.048	−	277.209i	−0.611524	−	0.718157i
$387$	83.8290			0.216612
$388$	666.655	+	107.617i	1.71818	+	0.277363i
$389$	−474.640			−1.22015			−0.610077	−	0.792342i	$-0.708861\pi$
$389$	−474.640			−1.22015			−0.610077	+	0.792342i	$0.708861\pi$
$390$	14.3208	+	88.6849i	0.0367199	+	0.227397i
$391$			522.826i			1.33715i
$392$	−200.421	−	330.349i	−0.511278	−	0.842726i
$393$		−	89.5973i		−	0.227983i
$394$	334.567	+	392.907i	0.849156	+	0.997226i
$395$	−35.3315	+	58.2427i	−0.0894469	+	0.147450i
$396$	187.124	+	30.2070i	0.472535	+	0.0762802i
$397$		−	499.460i		−	1.25809i	−0.777371	−	0.629043i	$-0.783447\pi$
$397$		−	499.460i		−	1.25809i	0.777371	−	0.629043i	$-0.216553\pi$
$398$	−332.554	−	390.542i	−0.835562	−	0.981262i
$399$		−	26.0548i		−	0.0653001i
$400$	−63.7855	−	394.882i	−0.159464	−	0.987204i
$401$	344.694			0.859587			0.429793	−	0.902927i	$-0.358586\pi$
$401$	344.694			0.859587			0.429793	+	0.902927i	$0.358586\pi$
$402$	−243.178	+	207.070i	−0.604920	+	0.515100i
$403$	−70.6631			−0.175343
$404$	28.3987	−	175.922i	0.0702938	−	0.435450i
$405$	38.4743	+	23.3395i	0.0949982	+	0.0576284i
$406$	58.1993	−	49.5578i	0.143348	−	0.122063i
$407$	−245.773			−0.603864
$408$	324.108	−	196.635i	0.794382	−	0.481947i
$409$	−501.890			−1.22712			−0.613558	−	0.789650i	$-0.710262\pi$
$409$	−501.890			−1.22712			−0.613558	+	0.789650i	$0.710262\pi$
$410$	−131.289	+	21.2005i	−0.320218	+	0.0517085i
$411$			93.1988i			0.226761i
$412$	−80.6166	+	499.397i	−0.195671	+	1.21213i
$413$		−	73.3957i		−	0.177714i
$414$	87.2990	−	74.3367i	0.210867	−	0.179557i
$415$	252.241	+	153.016i	0.607809	+	0.368713i
$416$	−62.3746	−	153.803i	−0.149939	−	0.369719i
$417$		−	23.5980i		−	0.0565898i
$418$	−432.144	+	367.978i	−1.03384	+	0.880331i
$419$		−	218.369i		−	0.521167i	−0.965451	−	0.260584i	$-0.916085\pi$
$419$		−	218.369i		−	0.521167i	0.965451	−	0.260584i	$-0.0839150\pi$
$420$	18.8023	−	22.0832i	0.0447674	−	0.0525789i
$421$	281.698			0.669116			0.334558	−	0.942375i	$-0.391413\pi$
$421$	281.698			0.669116			0.334558	+	0.942375i	$0.391413\pi$
$422$	−274.700	−	322.600i	−0.650947	−	0.764455i
$423$	−166.967			−0.394722
$424$	−106.423	+	64.5661i	−0.250997	+	0.152279i
$425$	606.598	−	315.988i	1.42729	−	0.743501i
$426$	−293.547	−	344.733i	−0.689076	−	0.809233i
$427$	31.8156			0.0745097
$428$	66.5401	−	412.197i	0.155468	−	0.963078i
$429$	141.897			0.330762
$430$	−275.856	+	44.5451i	−0.641527	+	0.103593i
$431$		−	441.081i		−	1.02339i	−0.859167	−	0.511694i	$-0.829018\pi$
$431$		−	441.081i		−	1.02339i	0.859167	−	0.511694i	$-0.170982\pi$
$432$	−78.9155	−	26.1600i	−0.182675	−	0.0605556i
$433$			123.443i			0.285089i	0.989788	+	0.142544i	$0.0455283\pi$
$433$			123.443i			0.285089i	−0.989788	+	0.142544i	$0.954472\pi$
$434$	14.7907	+	17.3698i	0.0340800	+	0.0400227i
$435$	−338.006	−	205.043i	−0.777025	−	0.471364i
$436$	−0.319785	+	1.98098i	−0.000733451	+	0.00454353i
$437$			343.346i			0.785690i
$438$	122.886	+	144.315i	0.280563	+	0.329485i
$439$			330.728i			0.753368i	0.926342	+	0.376684i	$0.122936\pi$
$439$			330.728i			0.753368i	−0.926342	+	0.376684i	$0.877064\pi$
$440$	−631.821	+	0.0317069i	−1.43596	+	7.20612e-5i
$441$	−144.897			−0.328565
$442$	216.072	−	183.989i	0.488850	−	0.416265i
$443$	154.952			0.349780			0.174890	−	0.984588i	$-0.444043\pi$
$443$	154.952			0.349780			0.174890	+	0.984588i	$0.444043\pi$
$444$	106.423	+	17.1796i	0.239691	+	0.0386928i
$445$	170.145	+	103.214i	0.382347	+	0.231942i
$446$	−532.718	+	453.619i	−1.19444	+	1.01708i
$447$	−58.2826			−0.130386
$448$	−24.7508	+	47.5254i	−0.0552473	+	0.106084i
$449$	−95.8970			−0.213579			−0.106790	−	0.994282i	$-0.534057\pi$
$449$	−95.8970			−0.213579			−0.106790	+	0.994282i	$0.534057\pi$
$450$	−139.010	−	56.3589i	−0.308910	−	0.125242i
$451$			210.065i			0.465775i
$452$	67.0738	+	10.8276i	0.148393	+	0.0239548i
$453$		−	242.467i		−	0.535247i
$454$	282.550	−	240.596i	0.622356	−	0.529948i
$455$	11.2612	−	18.5637i	0.0247499	−	0.0407992i
$456$	212.846	−	129.132i	0.466767	−	0.283185i
$457$		−	485.718i		−	1.06284i	−0.847108	−	0.531420i	$-0.821659\pi$
$457$		−	485.718i		−	1.06284i	0.847108	−	0.531420i	$-0.178341\pi$
$458$	−401.846	+	342.179i	−0.877393	+	0.747116i
$459$		−	142.160i		−	0.309716i
$460$	−247.774	+	291.009i	−0.538640	+	0.632629i
$461$	353.650			0.767136			0.383568	−	0.923513i	$-0.374695\pi$
$461$	353.650			0.767136			0.383568	+	0.923513i	$0.374695\pi$
$462$	−29.7009	−	34.8800i	−0.0642878	−	0.0754978i
$463$	421.720			0.910842			0.455421	−	0.890276i	$-0.349489\pi$
$463$	421.720			0.910842			0.455421	+	0.890276i	$0.349489\pi$
$464$	693.292	+	229.822i	1.49416	+	0.495306i
$465$	61.1960	−	100.879i	0.131604	−	0.216945i
$466$	75.8248	+	89.0466i	0.162714	+	0.191087i
$467$	640.974			1.37254			0.686268	−	0.727349i	$-0.259248\pi$
$467$	640.974			1.37254			0.686268	+	0.727349i	$0.259248\pi$
$468$	−61.4432	−	9.91864i	−0.131289	−	0.0211937i
$469$	77.1960			0.164597
$470$	549.441	−	88.7232i	1.16902	−	0.188773i
$471$		−	36.8289i		−	0.0781929i
$472$	599.582	−	363.763i	1.27030	−	0.770684i
$473$			441.374i			0.933137i
$474$	−30.5980	−	35.9335i	−0.0645528	−	0.0758091i
$475$	398.360	−	207.513i	0.838653	−	0.436869i
$476$	−90.4535	−	14.6017i	−0.190028	−	0.0306758i
$477$			46.6790i			0.0978595i
$478$	−146.957	−	172.582i	−0.307441	−	0.361050i
$479$		−	221.137i		−	0.461664i	−0.972994	−	0.230832i	$-0.925855\pi$
$479$		−	221.137i		−	0.461664i	0.972994	−	0.230832i	$-0.0741448\pi$
$480$	273.589	+	44.1507i	0.569976	+	0.0919806i
$481$	80.7010			0.167778
$482$	118.460	−	100.871i	0.245767	−	0.209275i
$483$	−27.7128			−0.0573764
$484$	−81.9124	+	507.424i	−0.169240	+	1.04840i
$485$	−437.801	+	721.698i	−0.902682	+	1.48804i
$486$	−23.7371	+	20.2126i	−0.0488418	+	0.0415897i
$487$	−889.949			−1.82741			−0.913705	−	0.406377i	$-0.866792\pi$
$487$	−889.949			−1.82741			−0.913705	+	0.406377i	$0.866792\pi$
$488$	157.684	+	259.907i	0.323123	+	0.532596i
$489$	−364.096			−0.744573
$490$	476.813	−	76.9955i	0.973089	−	0.157134i
$491$			552.843i			1.12595i	0.826473	+	0.562977i	$0.190344\pi$
$491$			552.843i			1.12595i	−0.826473	+	0.562977i	$0.809656\pi$
$492$	14.6836	−	90.9607i	0.0298447	−	0.184879i
$493$			1248.91i			2.53328i
$494$	141.897	−	120.828i	0.287241	−	0.244591i
$495$	−122.886	+	202.574i	−0.248255	+	0.409240i
$496$	−68.5914	+	206.916i	−0.138289	+	0.417169i
$497$			109.435i			0.220190i
$498$	−155.623	+	132.516i	−0.312495	+	0.266096i
$499$		−	533.302i		−	1.06874i	−0.845250	−	0.534371i	$-0.820549\pi$
$499$		−	533.302i		−	1.06874i	0.845250	−	0.534371i	$-0.179451\pi$
$500$	487.388	+	111.594i	0.974776	+	0.223187i
$501$	−412.894			−0.824139
$502$	137.737	+	161.755i	0.274376	+	0.322220i
$503$	−574.914			−1.14297			−0.571485	−	0.820612i	$-0.693633\pi$
$503$	−574.914			−1.14297			−0.571485	+	0.820612i	$0.693633\pi$
$504$	10.4228	+	17.1796i	0.0206801	+	0.0340865i
$505$	190.447	+	115.530i	0.377122	+	0.228772i
$506$	391.395	+	459.644i	0.773509	+	0.908388i
$507$	246.124			0.485451
$508$	5.39034	−	33.3917i	0.0106109	−	0.0657316i
$509$	207.547			0.407753			0.203877	−	0.978997i	$-0.434646\pi$
$509$	207.547			0.407753			0.203877	+	0.978997i	$0.434646\pi$
$510$	75.5409	+	467.806i	0.148119	+	0.917266i
$511$		−	45.8122i		−	0.0896521i
$512$	−510.913	+	33.3518i	−0.997876	+	0.0651403i
$513$		−	93.3580i		−	0.181984i
$514$	494.120	+	580.282i	0.961324	+	1.12895i
$515$	−540.630	−	327.960i	−1.04977	−	0.636816i
$516$	30.8522	−	191.121i	0.0597910	−	0.370389i
$517$		−	879.112i		−	1.70041i
$518$	−16.8918	−	19.8373i	−0.0326096	−	0.0382959i
$519$			4.04401i			0.00779192i
$520$	207.462	−	0.0104112i	0.398966	−	2.00214e-5i
$521$	−712.900			−1.36833			−0.684165	−	0.729327i	$-0.739833\pi$
$521$	−712.900			−1.36833			−0.684165	+	0.729327i	$0.739833\pi$
$522$	208.537	−	177.573i	0.399495	−	0.340178i
$523$	−139.548			−0.266822			−0.133411	−	0.991061i	$-0.542593\pi$
$523$	−139.548			−0.266822			−0.133411	+	0.991061i	$0.542593\pi$
$524$	−204.272	−	32.9751i	−0.389831	−	0.0629296i
$525$	16.7492	+	32.1532i	0.0319032	+	0.0612442i
$526$	17.4983	−	14.9002i	0.0332668	−	0.0283273i
$527$	−372.742			−0.707290
$528$	137.737	−	415.504i	0.260865	−	0.786939i
$529$	−163.804			−0.309648
$530$	−24.8043	−	153.607i	−0.0468006	−	0.289824i
$531$		−	262.988i		−	0.495268i
$532$	−59.4019	−	9.58911i	−0.111658	−	0.0180246i
$533$		−	68.9760i		−	0.129411i
$534$	−104.973	+	89.3861i	−0.196578	+	0.167390i
$535$	446.230	+	270.695i	0.834075	+	0.505972i
$536$	382.598	+	630.627i	0.713802	+	1.17654i
$537$			393.269i			0.732345i
$538$	118.700	−	101.075i	0.220632	−	0.187872i
$539$		−	762.908i		−	1.41541i
$540$	67.3713	−	79.1271i	0.124762	−	0.146532i
$541$	−946.688			−1.74988			−0.874942	−	0.484227i	$-0.839101\pi$
$541$	−946.688			−1.74988			−0.874942	+	0.484227i	$0.839101\pi$
$542$	−112.399	−	131.999i	−0.207379	−	0.243540i
$543$	197.621			0.363942
$544$	−329.021	−	811.298i	−0.604818	−	1.49136i
$545$	−2.14454	−	1.30093i	−0.00393493	−	0.00238703i
$546$	9.75248	+	11.4531i	0.0178617	+	0.0209763i
$547$	−50.3388			−0.0920271			−0.0460136	−	0.998941i	$-0.514652\pi$
$547$	−50.3388			−0.0920271			−0.0460136	+	0.998941i	$0.514652\pi$
$548$	212.483	+	34.3006i	0.387742	+	0.0625923i
$549$	114.000			0.207650
$550$	296.739	−	731.910i	0.539526	−	1.33074i
$551$			820.173i			1.48852i
$552$	−137.350	−	226.390i	−0.248822	−	0.410128i
$553$			11.4070i			0.0206275i
$554$	−372.561	−	437.525i	−0.672492	−	0.789757i
$555$	−69.8891	+	115.210i	−0.125926	+	0.207585i
$556$	−53.8007	−	8.68492i	−0.0967638	−	0.0156204i
$557$		−	790.157i		−	1.41859i	−0.704910	−	0.709297i	$-0.749013\pi$
$557$		−	790.157i		−	1.41859i	0.704910	−	0.709297i	$-0.250987\pi$
$558$	52.9973	+	62.2386i	0.0949773	+	0.111539i
$559$		−	144.928i		−	0.259263i
$560$	−43.4272	−	50.9945i	−0.0775485	−	0.0910616i
$561$	748.495			1.33422
$562$	342.004	−	291.222i	0.608548	−	0.518189i
$563$	354.133			0.629010			0.314505	−	0.949256i	$-0.398162\pi$
$563$	354.133			0.629010			0.314505	+	0.949256i	$0.398162\pi$
$564$	−61.4502	+	380.667i	−0.108954	+	0.674941i
$565$	−44.0482	+	72.6117i	−0.0779614	+	0.128516i
$566$	128.096	−	109.076i	0.226319	−	0.192714i
$567$	7.53528			0.0132897
$568$	−893.989	+	542.378i	−1.57392	+	0.954891i
$569$	55.4983			0.0975366			0.0487683	−	0.998810i	$-0.484470\pi$
$569$	55.4983			0.0975366			0.0487683	+	0.998810i	$0.484470\pi$
$570$	49.6086	+	307.214i	0.0870326	+	0.538971i
$571$		−	791.134i		−	1.38552i	−0.721167	−	0.692762i	$-0.756394\pi$
$571$		−	791.134i		−	1.38552i	0.721167	−	0.692762i	$-0.243606\pi$
$572$	52.2233	−	323.509i	0.0912995	−	0.565575i
$573$		−	241.433i		−	0.421349i
$574$	−16.9551	+	14.4376i	−0.0295386	+	0.0251526i
$575$	−220.719	−	423.711i	−0.383858	−	0.736888i
$576$	−88.6856	+	170.291i	−0.153968	+	0.295643i
$577$		−	201.759i		−	0.349668i	−0.984598	−	0.174834i	$-0.944061\pi$
$577$		−	201.759i		−	0.349668i	0.984598	−	0.174834i	$-0.0559389\pi$
$578$	699.690	−	595.799i	1.21054	−	1.03079i
$579$			315.313i			0.544583i
$580$	−591.874	+	695.152i	−1.02047	+	1.19854i
$581$	49.4020			0.0850292
$582$	−379.146	−	445.260i	−0.651454	−	0.765051i
$583$	−245.773			−0.421566
$584$	374.248	−	227.054i	0.640835	−	0.388791i
$585$	40.3505	−	66.5163i	0.0689752	−	0.113703i
$586$	−319.777	−	375.537i	−0.545694	−	0.640848i
$587$	444.556			0.757335			0.378668	−	0.925533i	$-0.376382\pi$
$587$	444.556			0.757335			0.378668	+	0.925533i	$0.376382\pi$
$588$	−53.3274	+	330.349i	−0.0906929	+	0.561818i
$589$	−244.784			−0.415593
$590$	139.746	+	865.415i	0.236858	+	1.46680i
$591$		−	446.915i		−	0.756202i
$592$	78.3350	−	236.309i	0.132323	−	0.399171i
$593$		−	563.908i		−	0.950942i	−0.879731	−	0.475471i	$-0.842278\pi$
$593$		−	563.908i		−	0.950942i	0.879731	−	0.475471i	$-0.157722\pi$
$594$	−106.423	−	124.980i	−0.179163	−	0.210404i
$595$	59.4019	−	97.9217i	0.0998351	−	0.164574i
$596$	−21.4502	+	132.878i	−0.0359902	+	0.222949i
$597$			444.226i			0.744097i
$598$	−128.517	−	150.927i	−0.214911	−	0.252386i
$599$			845.034i			1.41074i	0.708839	+	0.705371i	$0.249219\pi$
$599$			845.034i			1.41074i	−0.708839	+	0.705371i	$0.750781\pi$
$600$	−179.653	+	296.184i	−0.299421	+	0.493640i
$601$	672.296			1.11863			0.559314	−	0.828956i	$-0.311065\pi$
$601$	672.296			1.11863			0.559314	+	0.828956i	$0.311065\pi$
$602$	−35.6250	+	30.3353i	−0.0591777	+	0.0503909i
$603$	276.604			0.458714
$604$	−552.797	−	89.2368i	−0.915227	−	0.147743i
$605$	−549.320	−	333.232i	−0.907967	−	0.550796i
$606$	−117.498	+	100.052i	−0.193892	+	0.165102i
$607$	−882.664			−1.45414			−0.727071	−	0.686562i	$-0.759119\pi$
$607$	−882.664			−1.45414			−0.727071	+	0.686562i	$0.759119\pi$
$608$	−216.072	−	532.789i	−0.355381	−	0.876298i
$609$	−66.1993			−0.108702
$610$	−375.140	+	60.5774i	−0.614984	+	0.0993072i
$611$			288.662i			0.472442i
$612$	−324.108	−	52.3200i	−0.529588	−	0.0854902i
$613$			469.374i			0.765701i	0.923810	+	0.382850i	$0.125057\pi$
$613$			469.374i			0.765701i	−0.923810	+	0.382850i	$0.874943\pi$
$614$	176.350	−	150.166i	0.287216	−	0.244569i
$615$	98.4708	+	59.7350i	0.160115	+	0.0971300i
$616$	−90.4535	+	54.8777i	−0.146840	+	0.0890871i
$617$		−	218.994i		−	0.354934i	−0.984127	−	0.177467i	$-0.943210\pi$
$617$		−	218.994i		−	0.354934i	0.984127	−	0.177467i	$-0.0567902\pi$
$618$	333.548	−	284.022i	0.539721	−	0.459582i
$619$			879.610i			1.42102i	0.703689	+	0.710509i	$0.251535\pi$
$619$			879.610i			1.42102i	−0.703689	+	0.710509i	$0.748465\pi$
$620$	−207.471	−	176.647i	−0.334631	−	0.284915i
$621$	−99.2990			−0.159902
$622$	264.213	+	310.284i	0.424779	+	0.498849i
$623$	33.3232			0.0534884
$624$	−45.2267	+	136.433i	−0.0724787	+	0.218643i
$625$	−358.203	+	512.168i	−0.573124	+	0.819468i
$626$	−128.447	−	150.845i	−0.205187	−	0.240966i
$627$	491.546			0.783964
$628$	−83.9656	−	13.5544i	−0.133703	−	0.0215834i
$629$	425.691			0.676774
$630$	−24.7964	+	4.00410i	−0.0393594	+	0.00635572i
$631$		−	635.566i		−	1.00724i	−0.863926	−	0.503618i	$-0.832002\pi$
$631$		−	635.566i		−	1.00724i	0.863926	−	0.503618i	$-0.167998\pi$
$632$	−93.1855	+	56.5351i	−0.147445	+	0.0894543i
$633$			366.944i			0.579691i
$634$	−610.966	−	717.502i	−0.963669	−	1.13171i
$635$	36.1486	+	21.9287i	0.0569270	+	0.0345334i
$636$	106.423	+	17.1796i	0.167331	+	0.0270119i
$637$			250.505i			0.393258i
$638$	934.951	+	1097.98i	1.46544	+	1.72097i
$639$			392.120i			0.613646i
$640$	201.349	−	607.502i	0.314608	−	0.949222i
$641$	−296.309			−0.462260			−0.231130	−	0.972923i	$-0.574242\pi$
$641$	−296.309			−0.462260			−0.231130	+	0.972923i	$0.574242\pi$
$642$	−275.307	+	234.429i	−0.428827	+	0.365154i
$643$	591.032			0.919179			0.459590	−	0.888131i	$-0.347997\pi$
$643$	591.032			0.919179			0.459590	+	0.888131i	$0.347997\pi$
$644$	−10.1993	+	63.1821i	−0.0158375	+	0.0981088i
$645$	206.900	+	125.511i	0.320776	+	0.194591i
$646$	748.495	−	637.357i	1.15866	−	0.986621i
$647$	−166.507			−0.257352			−0.128676	−	0.991687i	$-0.541073\pi$
$647$	−166.507			−0.257352			−0.128676	+	0.991687i	$0.541073\pi$
$648$	37.3463	+	61.5569i	0.0576331	+	0.0949953i
$649$	1384.67			2.13355
$650$	−97.4362	+	240.327i	−0.149902	+	0.369734i
$651$		−	19.7575i		−	0.0303494i
$652$	−134.001	+	830.098i	−0.205523	+	1.27316i
$653$		−	621.335i		−	0.951509i	−0.879578	−	0.475754i	$-0.842175\pi$
$653$		−	621.335i		−	0.951509i	0.879578	−	0.475754i	$-0.157825\pi$
$654$	1.32310	−	1.12664i	0.00202308	−	0.00172269i
$655$	134.148	−	221.137i	0.204806	−	0.337614i
$656$	−201.976	−	66.9538i	−0.307890	−	0.102064i
$657$		−	164.152i		−	0.249851i
$658$	70.9565	−	60.4208i	0.107837	−	0.0918249i
$659$			702.113i			1.06542i	0.846297	+	0.532711i	$0.178827\pi$
$659$			702.113i			1.06542i	−0.846297	+	0.532711i	$0.821173\pi$
$660$	416.618	+	354.722i	0.631239	+	0.537457i
$661$	358.193			0.541895			0.270948	−	0.962594i	$-0.412663\pi$
$661$	358.193			0.541895			0.270948	+	0.962594i	$0.412663\pi$
$662$	350.994	+	412.197i	0.530202	+	0.622655i
$663$	−245.773			−0.370698
$664$	244.846	+	403.573i	0.368743	+	0.607790i
$665$	39.0099	−	64.3064i	0.0586616	−	0.0967013i
$666$	−60.5257	−	71.0798i	−0.0908795	−	0.106726i
$667$	872.367			1.30790
$668$	−151.960	+	941.351i	−0.227485	+	1.40921i
$669$	605.945			0.905748
$670$	−910.224	+	146.982i	−1.35854	+	0.219377i
$671$			600.230i			0.894530i
$672$	43.0035	−	17.4400i	0.0639933	−	0.0259524i
$673$		−	714.176i		−	1.06118i	−0.847628	−	0.530592i	$-0.821970\pi$
$673$		−	714.176i		−	1.06118i	0.847628	−	0.530592i	$-0.178030\pi$
$674$	−489.244	−	574.555i	−0.725882	−	0.852456i
$675$	60.0147	+	115.210i	0.0889107	+	0.170681i
$676$	90.5827	−	561.134i	0.133998	−	0.830081i
$677$			509.833i			0.753077i	0.926401	+	0.376538i	$0.122886\pi$
$677$			509.833i			0.753077i	−0.926401	+	0.376538i	$0.877114\pi$
$678$	−38.1468	−	44.7986i	−0.0562638	−	0.0660747i
$679$			141.346i			0.208168i
$680$	1094.35	−	0.0549180i	1.60933	−	8.07617e-5i
$681$	−321.389			−0.471936
$682$	−327.697	+	279.040i	−0.480494	+	0.409150i
$683$	−1263.93			−1.85055			−0.925275	−	0.379298i	$-0.876166\pi$
$683$	−1263.93			−1.85055			−0.925275	+	0.379298i	$0.876166\pi$
$684$	−212.846	−	34.3592i	−0.311178	−	0.0502327i
$685$	−139.540	+	230.026i	−0.203708	+	0.335805i
$686$	124.048	−	105.629i	0.180828	−	0.153978i
$687$	457.083			0.665332
$688$	−424.378	−	140.679i	−0.616829	−	0.204475i
$689$	80.7010			0.117128
$690$	326.764	−	52.7656i	0.473571	−	0.0764718i
$691$		−	512.351i		−	0.741463i	−0.928740	−	0.370731i	$-0.879107\pi$
$691$		−	512.351i		−	0.741463i	0.928740	−	0.370731i	$-0.120893\pi$
$692$	9.21987	+	1.48834i	0.0133235	+	0.00215078i
$693$			39.6746i			0.0572504i
$694$	−703.842	+	599.334i	−1.01418	+	0.863594i
$695$	35.3315	−	58.2427i	0.0508368	−	0.0838024i
$696$	−328.096	−	540.793i	−0.471403	−	0.777002i
$697$		−	363.843i		−	0.522012i
$698$	−305.458	+	260.103i	−0.437619	+	0.372640i
$699$		−	101.287i		−	0.144902i
$700$	79.4699	−	26.3526i	0.113528	−	0.0376466i
$701$	1092.03			1.55781			0.778907	−	0.627139i	$-0.215774\pi$
$701$	1092.03			1.55781			0.778907	+	0.627139i	$0.215774\pi$
$702$	34.9446	+	41.0380i	0.0497786	+	0.0584586i
$703$	279.556			0.397662
$704$	−896.609	−	466.945i	−1.27359	−	0.663274i
$705$	−412.096	−	249.988i	−0.584534	−	0.354593i
$706$	325.323	+	382.051i	0.460798	+	0.541148i
$707$	37.2995			0.0527574
$708$	−599.582	−	96.7891i	−0.846867	−	0.136708i
$709$	416.887			0.587993			0.293997	−	0.955806i	$-0.405015\pi$
$709$	416.887			0.587993			0.293997	+	0.955806i	$0.405015\pi$
$710$	−208.365	−	1290.35i	−0.293472	−	1.81740i
$711$			40.8729i			0.0574864i
$712$	165.156	+	272.223i	0.231961	+	0.382336i
$713$			260.362i			0.365163i
$714$	51.4435	+	60.4139i	0.0720498	+	0.0846133i
$715$	350.220	+	212.452i	0.489818	+	0.297136i
$716$	896.609	+	144.738i	1.25225	+	0.202147i
$717$			196.305i			0.273787i
$718$	279.556	+	328.304i	0.389354	+	0.457247i
$719$			395.268i			0.549747i	0.961480	+	0.274874i	$0.0886361\pi$
$719$			395.268i			0.549747i	−0.961480	+	0.274874i	$0.911364\pi$
$720$	−155.606	−	182.721i	−0.216119	−	0.253779i
$721$	−105.884			−0.146857
$722$	−58.1625	+	49.5264i	−0.0805575	+	0.0685962i
$723$	−134.743			−0.186367
$724$	72.7317	−	450.553i	0.100458	−	0.622310i
$725$	−527.244	−	1012.14i	−0.727233	−	1.39606i
$726$	338.909	−	288.587i	0.466817	−	0.397503i
$727$	−597.583			−0.821985			−0.410993	−	0.911639i	$-0.634818\pi$
$727$	−597.583			−0.821985			−0.410993	+	0.911639i	$0.634818\pi$
$728$	29.7009	−	18.0194i	0.0407980	−	0.0247519i
$729$	27.0000			0.0370370
$730$	87.2271	+	540.175i	0.119489	+	0.739966i
$731$		−	764.482i		−	1.04580i
$732$	41.9562	−	259.907i	0.0573172	−	0.355064i
$733$			23.8650i			0.0325580i	0.999867	+	0.0162790i	$0.00518200\pi$
$733$			23.8650i			0.0325580i	−0.999867	+	0.0162790i	$0.994818\pi$
$734$	102.120	−	86.9574i	0.139129	−	0.118471i
$735$	−357.624	−	216.944i	−0.486563	−	0.295162i
$736$	−566.694	+	229.822i	−0.769965	+	0.312258i
$737$			1456.37i			1.97608i
$738$	−60.7527	+	51.7320i	−0.0823207	+	0.0700976i
$739$		−	125.767i		−	0.170186i	−0.996373	−	0.0850928i	$-0.972881\pi$
$739$		−	125.767i		−	0.170186i	0.996373	−	0.0850928i	$-0.0271187\pi$
$740$	236.943	+	201.741i	0.320193	+	0.272622i
$741$	−161.402			−0.217816
$742$	−16.8918	−	19.8373i	−0.0227652	−	0.0267349i
$743$	−148.841			−0.200325			−0.100162	−	0.994971i	$-0.531936\pi$
$743$	−148.841			−0.200325			−0.100162	+	0.994971i	$0.531936\pi$
$744$	161.402	−	97.9217i	0.216938	−	0.131615i
$745$	−143.849	−	87.2625i	−0.193086	−	0.117131i
$746$	735.715	+	864.004i	0.986213	+	1.15818i
$747$	177.014			0.236967
$748$	275.474	−	1706.48i	0.368280	−	2.28140i
$749$	87.3954			0.116683
$750$	−258.711	−	347.230i	−0.344948	−	0.462973i
$751$			463.390i			0.617030i	0.951219	+	0.308515i	$0.0998321\pi$
$751$			463.390i			0.617030i	−0.951219	+	0.308515i	$0.900168\pi$
$752$	845.261	+	280.199i	1.12402	+	0.372605i
$753$		−	183.989i		−	0.244341i
$754$	−306.997	−	360.529i	−0.407157	−	0.478155i
$755$	363.029	−	598.439i	0.480833	−	0.792634i
$756$	2.77326	−	17.1796i	0.00366834	−	0.0227243i
$757$			719.363i			0.950281i	0.879910	+	0.475141i	$0.157603\pi$
$757$			719.363i			0.950281i	−0.879910	+	0.475141i	$0.842397\pi$
$758$	−311.579	−	365.910i	−0.411054	−	0.482731i
$759$		−	522.826i		−	0.688836i
$760$	718.670	−	0.0360653i	0.945618	−	4.74543e-5i
$761$	−1107.49			−1.45530			−0.727651	−	0.685947i	$-0.759388\pi$
$761$	−1107.49			−1.45530			−0.727651	+	0.685947i	$0.759388\pi$
$762$	−22.3023	+	18.9908i	−0.0292681	+	0.0249223i
$763$	−0.420013			−0.000550476
$764$	−550.440	−	88.8563i	−0.720472	−	0.116304i
$765$	212.846	−	350.868i	0.278229	−	0.458651i
$766$	−1020.34	+	868.835i	−1.33203	+	1.13425i
$767$	−454.666			−0.592785
$768$	355.603	+	264.866i	0.463025	+	0.344878i
$769$	−231.691			−0.301289			−0.150644	−	0.988588i	$-0.548135\pi$
$769$	−231.691			−0.301289			−0.150644	+	0.988588i	$0.548135\pi$
$770$	−21.0823	−	130.557i	−0.0273796	−	0.169555i
$771$		−	660.047i		−	0.856092i
$772$	718.879	+	116.047i	0.931190	+	0.150320i
$773$		−	519.956i		−	0.672647i	−0.941746	−	0.336324i	$-0.890816\pi$
$773$		−	519.956i		−	0.672647i	0.941746	−	0.336324i	$-0.109184\pi$
$774$	−127.650	+	108.696i	−0.164922	+	0.140434i
$775$	302.079	−	157.358i	0.389779	−	0.203043i
$776$	−1154.68	+	700.539i	−1.48799	+	0.902756i
$777$			22.5641i			0.0290400i
$778$	722.751	−	615.436i	0.928986	−	0.791049i
$779$		−	238.940i		−	0.306726i
$780$	−136.799	−	116.475i	−0.175383	−	0.149327i
$781$	−2064.58			−2.64351
$782$	−677.917	−	796.127i	−0.866901	−	1.01807i
$783$	−237.202			−0.302940
$784$	733.531	+	243.161i	0.935626	+	0.310154i
$785$	55.1412	−	90.8982i	0.0702436	−	0.115794i
$786$	116.175	+	136.433i	0.147806	+	0.173579i
$787$	−46.0288			−0.0584864			−0.0292432	−	0.999572i	$-0.509310\pi$
$787$	−46.0288			−0.0584864			−0.0292432	+	0.999572i	$0.509310\pi$
$788$	−1018.92	−	164.481i	−1.29304	−	0.208733i
$789$	−19.9036			−0.0252264
$790$	−21.7190	−	134.501i	−0.0274925	−	0.170254i
$791$			14.2212i			0.0179788i
$792$	−324.108	+	196.635i	−0.409227	+	0.248276i
$793$		−	197.089i		−	0.248536i
$794$	647.619	+	760.546i	0.815641	+	0.957867i
$795$	−69.8891	+	115.210i	−0.0879108	+	0.144918i
$796$	1012.78	+	163.491i	1.27234	+	0.205391i
$797$		−	15.3098i		−	0.0192093i	−0.999954	−	0.00960463i	$-0.996943\pi$
$797$		−	15.3098i		−	0.0192093i	0.999954	−	0.00960463i	$-0.00305730\pi$
$798$	33.7836	+	39.6746i	0.0423353	+	0.0497175i
$799$			1522.67i			1.90572i
$800$	609.147	+	518.594i	0.761434	+	0.648243i
$801$	119.402			0.149066
$802$	−524.879	+	446.944i	−0.654463	+	0.557287i
$803$	864.288			1.07632
$804$	101.801	−	630.627i	0.126618	−	0.784362i
$805$	−68.3987	−	41.4924i	−0.0849673	−	0.0515434i
$806$	107.601	−	91.6245i	0.133500	−	0.113678i
$807$	−135.017			−0.167307
$808$	184.863	+	304.706i	0.228791	+	0.377111i
$809$	−313.093			−0.387012			−0.193506	−	0.981099i	$-0.561986\pi$
$809$	−313.093			−0.387012			−0.193506	+	0.981099i	$0.561986\pi$
$810$	−88.8491	+	14.3473i	−0.109690	+	0.0177127i
$811$			1056.89i			1.30319i	0.758566	+	0.651596i	$0.225900\pi$
$811$			1056.89i			1.30319i	−0.758566	+	0.651596i	$0.774100\pi$
$812$	−24.3638	+	150.927i	−0.0300047	+	0.185871i
$813$			150.143i			0.184678i
$814$	374.248	−	318.678i	0.459764	−	0.391497i
$815$	−898.635	−	545.136i	−1.10262	−	0.668878i
$816$	−238.567	+	719.673i	−0.292362	+	0.881953i
$817$		−	502.045i		−	0.614498i
$818$	764.247	−	650.770i	0.934288	−	0.795563i
$819$		−	13.0274i		−	0.0159064i
$820$	172.430	−	202.518i	0.210280	−	0.246973i
$821$	308.659			0.375955			0.187978	−	0.982173i	$-0.439807\pi$
$821$	308.659			0.375955			0.187978	+	0.982173i	$0.439807\pi$
$822$	−120.845	−	141.917i	−0.147014	−	0.172649i
$823$	−109.680			−0.133269			−0.0666344	−	0.997777i	$-0.521226\pi$
$823$	−109.680			−0.133269			−0.0666344	+	0.997777i	$0.521226\pi$
$824$	−524.780	−	864.982i	−0.636869	−	1.04974i
$825$	−606.598	+	315.988i	−0.735270	+	0.383015i
$826$	95.1677	+	111.762i	0.115215	+	0.135306i
$827$	711.971			0.860908			0.430454	−	0.902613i	$-0.358354\pi$
$827$	711.971			0.860908			0.430454	+	0.902613i	$0.358354\pi$
$828$	−36.5457	+	226.390i	−0.0441373	+	0.273418i
$829$	−118.688			−0.143170			−0.0715849	−	0.997435i	$-0.522806\pi$
$829$	−118.688			−0.143170			−0.0715849	+	0.997435i	$0.522806\pi$
$830$	−582.502	+	94.0621i	−0.701810	+	0.113328i
$831$			497.667i			0.598877i
$832$	294.407	+	153.324i	0.353854	+	0.184284i
$833$			1321.40i			1.58631i
$834$	30.5980	+	35.9335i	0.0366883	+	0.0430857i
$835$	−1019.07	−	618.196i	−1.22045	−	0.740355i
$836$	180.907	−	1120.67i	0.216396	−	1.34051i
$837$		−	70.7939i		−	0.0845805i
$838$	283.146	+	332.519i	0.337883	+	0.396800i
$839$		−	1413.67i		−	1.68495i	−0.538736	−	0.842475i	$-0.681098\pi$
$839$		−	1413.67i		−	1.68495i	0.538736	−	0.842475i	$-0.318902\pi$
$840$	0.00291097	+	58.0066i	3.46544e−6	+	0.0690555i
$841$	1242.88			1.47786
$842$	−428.952	+	365.260i	−0.509444	+	0.433800i
$843$	−389.015			−0.461465
$844$	836.591	+	135.049i	0.991222	+	0.160011i
$845$	607.464	+	368.504i	0.718893	+	0.436099i
$846$	254.248	−	216.496i	0.300529	−	0.255906i
$847$	−107.586			−0.127020
$848$	78.3350	−	236.309i	0.0923762	−	0.278666i
$849$	−145.704			−0.171619
$850$	−513.968	+	1267.70i	−0.604668	+	1.49142i
$851$		−	297.347i		−	0.349409i
$852$	893.989	+	144.315i	1.04928	+	0.169383i
$853$		−	1308.03i		−	1.53344i	−0.641979	−	0.766722i	$-0.721886\pi$
$853$		−	1308.03i		−	1.53344i	0.641979	−	0.766722i	$-0.278114\pi$
$854$	−48.4469	+	41.2534i	−0.0567293	+	0.0483060i
$855$	139.778	−	230.419i	0.163483	−	0.269496i
$856$	433.148	+	713.947i	0.506014	+	0.834050i
$857$		−	719.755i		−	0.839854i	−0.907558	−	0.419927i	$-0.862056\pi$
$857$		−	719.755i		−	0.839854i	0.907558	−	0.419927i	$-0.137944\pi$
$858$	−216.072	+	183.989i	−0.251832	+	0.214440i
$859$		−	1402.44i		−	1.63264i	−0.577601	−	0.816319i	$-0.696011\pi$
$859$		−	1402.44i		−	1.63264i	0.577601	−	0.816319i	$-0.303989\pi$
$860$	362.298	−	425.517i	0.421277	−	0.494787i
$861$	19.2858			0.0223993
$862$	571.922	+	671.650i	0.663483	+	0.779176i
$863$	−72.4412			−0.0839411			−0.0419706	−	0.999119i	$-0.513364\pi$
$863$	−72.4412			−0.0839411			−0.0419706	+	0.999119i	$0.513364\pi$
$864$	154.088	−	62.4900i	0.178342	−	0.0723264i
$865$	−6.05480	+	9.98111i	−0.00699977	+	0.0115389i
$866$	−160.061	−	187.972i	−0.184828	−	0.217058i
$867$	−795.869			−0.917957
$868$	−45.0448	−	7.27148i	−0.0518949	−	0.00837728i
$869$	−215.203			−0.247644
$870$	780.561	−	126.044i	0.897197	−	0.144879i
$871$		−	478.208i		−	0.549033i
$872$	−2.08166	−	3.43115i	−0.00238723	−	0.00393481i
$873$			506.464i			0.580142i
$874$	−445.196	−	522.826i	−0.509378	−	0.598200i
$875$	−6.80164	+	104.435i	−0.00777331	+	0.119355i
$876$	−374.248	−	60.4139i	−0.427223	−	0.0689657i
$877$			1382.21i			1.57606i	0.615635	+	0.788032i	$0.288900\pi$
$877$			1382.21i			1.57606i	−0.615635	+	0.788032i	$0.711100\pi$
$878$	−428.835	−	503.613i	−0.488423	−	0.573591i
$879$			427.158i			0.485959i
$880$	962.056	−	819.291i	1.09325	−	0.931013i
$881$	−1131.38			−1.28419			−0.642097	−	0.766623i	$-0.721936\pi$
$881$	−1131.38			−1.28419			−0.642097	+	0.766623i	$0.721936\pi$
$882$	220.640	−	187.879i	0.250159	−	0.213015i
$883$	1077.39			1.22014			0.610072	−	0.792346i	$-0.291140\pi$
$883$	1077.39			1.22014			0.610072	+	0.792346i	$0.291140\pi$
$884$	−90.4535	+	560.334i	−0.102323	+	0.633862i
$885$	393.752	−	649.086i	0.444918	−	0.733430i
$886$	−235.952	+	200.917i	−0.266311	+	0.226769i
$887$	766.896			0.864595			0.432297	−	0.901731i	$-0.357703\pi$
$887$	766.896			0.864595			0.432297	+	0.901731i	$0.357703\pi$
$888$	−184.330	+	111.832i	−0.207578	+	0.125937i
$889$	7.07980			0.00796378
$890$	−392.917	+	63.4479i	−0.441480	+	0.0712898i
$891$			142.160i			0.159551i
$892$	223.010	−	1381.49i	0.250011	−	1.54875i
$893$			999.954i			1.11977i
$894$	88.7492	−	75.5715i	0.0992720	−	0.0845319i
$895$	−588.814	+	970.637i	−0.657893	+	1.08451i
$896$	−23.9344	−	104.462i	−0.0267124	−	0.116587i
$897$			171.673i			0.191386i
$898$	146.026	−	124.344i	0.162612	−	0.138467i
$899$			621.942i			0.691815i
$900$	284.752	−	94.4253i	0.316391	−	0.104917i
$901$	425.691			0.472465
$902$	−272.378	−	319.873i	−0.301971	−	0.354627i
$903$	40.5220			0.0448748
$904$	−116.175	+	70.4829i	−0.128512	+	0.0779678i
$905$	487.752	+	295.883i	0.538953	+	0.326943i
$906$	314.392	+	369.214i	0.347011	+	0.407521i
$907$	−1086.43			−1.19783			−0.598913	−	0.800814i	$-0.704400\pi$
$907$	−1086.43			−1.19783			−0.598913	+	0.800814i	$0.704400\pi$
$908$	−118.283	+	732.730i	−0.130268	+	0.806971i
$909$	133.650			0.147029
$910$	6.92250	+	42.8693i	0.00760714	+	0.0471091i
$911$		−	237.746i		−	0.260973i	−0.991450	−	0.130486i	$-0.958346\pi$
$911$		−	237.746i		−	0.260973i	0.991450	−	0.130486i	$-0.0416539\pi$
$912$	−156.670	+	472.618i	−0.171787	+	0.518222i
$913$			932.012i			1.02082i
$914$	629.801	+	739.621i	0.689060	+	0.809214i
$915$	281.366	+	170.684i	0.307504	+	0.186540i
$916$	168.223	−	1042.10i	0.183650	−	1.13766i
$917$		−	43.3103i		−	0.0472304i
$918$	184.330	+	216.472i	0.200795	+	0.235808i
$919$		−	344.517i		−	0.374882i	−0.982276	−	0.187441i	$-0.939981\pi$
$919$		−	344.517i		−	0.374882i	0.982276	−	0.187441i	$-0.0600194\pi$
$920$	−0.0383604	−	764.404i	−4.16961e−5	−	0.830874i
$921$	−200.591			−0.217797
$922$	−538.515	+	458.555i	−0.584073	+	0.497349i
$923$	677.917			0.734471
$924$	90.4535	+	14.6017i	0.0978934	+	0.0158027i
$925$	−344.990	+	179.711i	−0.372962	+	0.194283i
$926$	−642.169	+	546.818i	−0.693487	+	0.590516i
$927$	−379.397			−0.409274
$928$	−1353.70	+	548.991i	−1.45873	+	0.591585i
$929$	1478.10			1.59106			0.795531	−	0.605913i	$-0.207192\pi$
$929$	1478.10			1.59106			0.795531	+	0.605913i	$0.207192\pi$
$930$	37.6185	+	232.962i	0.0404500	+	0.250497i
$931$			867.776i			0.932090i
$932$	−230.922	−	37.2773i	−0.247771	−	0.0399971i
$933$		−	352.935i		−	0.378280i
$934$	−976.035	+	831.111i	−1.04501	+	0.889841i
$935$	1847.38	+	1120.67i	1.97581	+	1.19858i
$936$	106.423	−	64.5661i	0.113700	−	0.0689809i
$937$		−	246.887i		−	0.263486i	−0.991284	−	0.131743i	$-0.957943\pi$
$937$		−	246.887i		−	0.263486i	0.991284	−	0.131743i	$-0.0420574\pi$
$938$	−117.549	+	100.095i	−0.125319	+	0.106711i
$939$			171.579i			0.182726i
$940$	−721.612	+	847.528i	−0.767672	+	0.901625i
$941$	1658.64			1.76264			0.881318	−	0.472525i	$-0.156657\pi$
$941$	1658.64			1.76264			0.881318	+	0.472525i	$0.156657\pi$
$942$	47.7537	+	56.0807i	0.0506940	+	0.0595336i
$943$	−254.145			−0.269507
$944$	−441.336	+	1331.36i	−0.467517	+	1.41033i
$945$	18.5980	+	11.2820i	0.0196804	+	0.0119387i
$946$	−572.302	−	672.097i	−0.604971	−	0.710462i
$947$	6.00750			0.00634372			0.00317186	−	0.999995i	$-0.498990\pi$
$947$	6.00750			0.00634372			0.00317186	+	0.999995i	$0.498990\pi$
$948$	93.1855	+	15.0427i	0.0982969	+	0.0158678i
$949$	−283.794			−0.299045
$950$	−337.529	+	832.517i	−0.355293	+	0.876333i
$951$			816.129i			0.858180i
$952$	156.670	−	95.0509i	0.164569	−	0.0998434i
$953$		−	1089.55i		−	1.14329i	−0.820503	−	0.571643i	$-0.806306\pi$
$953$		−	1089.55i		−	1.14329i	0.820503	−	0.571643i	$-0.193694\pi$
$954$	−60.5257	−	71.0798i	−0.0634442	−	0.0745072i
$955$	361.481	−	595.887i	0.378514	−	0.623966i
$956$	447.553	+	72.2475i	0.468152	+	0.0755727i
$957$		−	1248.91i		−	1.30502i
$958$	286.735	+	336.734i	0.299306	+	0.351497i
$959$			45.0512i			0.0469773i
$960$	−473.851	+	287.516i	−0.493595	+	0.299495i
$961$	775.379			0.806846
$962$	−122.886	+	104.640i	−0.127741	+	0.108773i
$963$	313.150			0.325182
$964$	−49.5905	+	307.199i	−0.0514424	+	0.318671i
$965$	−472.096	+	778.233i	−0.489219	+	0.806459i
$966$	42.1993	−	35.9335i	0.0436846	−	0.0371982i
$967$	1699.27			1.75726			0.878630	−	0.477502i	$-0.158458\pi$
$967$	1699.27			1.75726			0.878630	+	0.477502i	$0.158458\pi$
$968$	−533.215	−	878.885i	−0.550842	−	0.907939i
$969$	−851.382			−0.878619
$970$	−269.125	−	1666.63i	−0.277449	−	1.71817i
$971$		−	197.851i		−	0.203760i	−0.994797	−	0.101880i	$-0.967514\pi$
$971$		−	197.851i		−	0.203760i	0.994797	−	0.101880i	$-0.0324857\pi$
$972$	9.93700	−	61.5569i	0.0102232	−	0.0633302i
$973$		−	11.4070i		−	0.0117235i
$974$	1355.16	−	1153.94i	1.39133	−	1.18475i
$975$	199.180	−	103.756i	0.204287	−	0.106417i
$976$	−577.117	−	191.311i	−0.591309	−	0.196015i
$977$		−	847.868i		−	0.867828i	−0.900954	−	0.433914i	$-0.857132\pi$
$977$		−	847.868i		−	0.867828i	0.900954	−	0.433914i	$-0.142868\pi$
$978$	554.423	−	472.101i	0.566895	−	0.482721i
$979$			628.672i			0.642157i
$980$	−626.226	+	735.498i	−0.639007	+	0.750509i
$981$	−1.50497			−0.00153412
$982$	−716.837	−	841.835i	−0.729977	−	0.857266i
$983$	96.0512			0.0977123			0.0488562	−	0.998806i	$-0.484442\pi$
$983$	96.0512			0.0977123			0.0488562	+	0.998806i	$0.484442\pi$
$984$	95.5839	+	157.549i	0.0971381	+	0.160110i
$985$	669.135	−	1103.04i	0.679324	−	1.11984i
$986$	−1619.38	−	1901.76i	−1.64238	−	1.92876i
$987$	−80.7101			−0.0817732
$988$	−59.4019	+	367.978i	−0.0601234	+	0.372448i
$989$	−533.993			−0.539933
$990$	−75.5409	−	467.806i	−0.0763039	−	0.472531i
$991$		−	1184.45i		−	1.19520i	−0.801793	−	0.597602i	$-0.796120\pi$
$991$		−	1184.45i		−	1.19520i	0.801793	−	0.597602i	$-0.203880\pi$
$992$	−163.849	−	404.017i	−0.165170	−	0.407275i
$993$		−	468.858i		−	0.472163i
$994$	−141.897	−	166.640i	−0.142754	−	0.167646i
$995$	−665.108	+	1096.40i	−0.668450	+	1.10191i
$996$	65.1478	−	403.573i	0.0654095	−	0.405194i
$997$		−	1887.35i		−	1.89303i	−0.322655	−	0.946517i	$-0.604575\pi$
$997$		−	1887.35i		−	1.89303i	0.322655	−	0.946517i	$-0.395425\pi$
$998$	691.500	+	812.079i	0.692886	+	0.813706i
$999$			80.8504i			0.0809313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.f.b.19.2	yes	8
3.2	odd	2		180.3.f.h.19.7		8
4.3	odd	2	inner	60.3.f.b.19.8	yes	8
5.2	odd	4		300.3.c.f.151.3		8
5.3	odd	4		300.3.c.f.151.6		8
5.4	even	2	inner	60.3.f.b.19.7	yes	8
8.3	odd	2		960.3.j.e.319.5		8
8.5	even	2		960.3.j.e.319.1		8
12.11	even	2		180.3.f.h.19.1		8
15.2	even	4		900.3.c.r.451.6		8
15.8	even	4		900.3.c.r.451.3		8
15.14	odd	2		180.3.f.h.19.2		8
20.3	even	4		300.3.c.f.151.5		8
20.7	even	4		300.3.c.f.151.4		8
20.19	odd	2	inner	60.3.f.b.19.1	✓	8
40.19	odd	2		960.3.j.e.319.2		8
40.29	even	2		960.3.j.e.319.6		8
60.23	odd	4		900.3.c.r.451.4		8
60.47	odd	4		900.3.c.r.451.5		8
60.59	even	2		180.3.f.h.19.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.b.19.1	✓	8	20.19	odd	2	inner
60.3.f.b.19.2	yes	8	1.1	even	1	trivial
60.3.f.b.19.7	yes	8	5.4	even	2	inner
60.3.f.b.19.8	yes	8	4.3	odd	2	inner
180.3.f.h.19.1		8	12.11	even	2
180.3.f.h.19.2		8	15.14	odd	2
180.3.f.h.19.7		8	3.2	odd	2
180.3.f.h.19.8		8	60.59	even	2
300.3.c.f.151.3		8	5.2	odd	4
300.3.c.f.151.4		8	20.7	even	4
300.3.c.f.151.5		8	20.3	even	4
300.3.c.f.151.6		8	5.3	odd	4
900.3.c.r.451.3		8	15.8	even	4
900.3.c.r.451.4		8	60.23	odd	4
900.3.c.r.451.5		8	60.47	odd	4
900.3.c.r.451.6		8	15.2	even	4
960.3.j.e.319.1		8	8.5	even	2
960.3.j.e.319.2		8	40.19	odd	2
960.3.j.e.319.5		8	8.3	odd	2
960.3.j.e.319.6		8	40.29	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52274 + 1.29664i) q^{2} +1.73205 q^{3} +(0.637459 - 3.94888i) q^{4} +(4.27492 + 2.59328i) q^{5} +(-2.63746 + 2.24584i) q^{6} +0.837253 q^{7} +(4.14959 + 6.83966i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.52274 + 1.29664i) q^{2} +1.73205 q^{3} +(0.637459 - 3.94888i) q^{4} +(4.27492 + 2.59328i) q^{5} +(-2.63746 + 2.24584i) q^{6} +0.837253 q^{7} +(4.14959 + 6.83966i) q^{8} +3.00000 q^{9} +(-9.87212 + 1.59414i) q^{10} +15.7955i q^{11} +(1.10411 - 6.83966i) q^{12} -5.18655i q^{13} +(-1.27492 + 1.08561i) q^{14} +(7.40437 + 4.49169i) q^{15} +(-15.1873 - 5.03449i) q^{16} -27.3586i q^{17} +(-4.56821 + 3.88991i) q^{18} -17.9667i q^{19} +(12.9656 - 15.2280i) q^{20} +1.45017 q^{21} +(-20.4811 - 24.0524i) q^{22} -19.1101 q^{23} +(7.18729 + 11.8466i) q^{24} +(11.5498 + 22.1721i) q^{25} +(6.72508 + 7.89776i) q^{26} +5.19615 q^{27} +(0.533714 - 3.30621i) q^{28} -45.6495 q^{29} +(-17.0990 + 2.76113i) q^{30} -13.6243i q^{31} +(29.6542 - 12.0262i) q^{32} +27.3586i q^{33} +(35.4743 + 41.6600i) q^{34} +(3.57919 + 2.17123i) q^{35} +(1.91238 - 11.8466i) q^{36} +15.5597i q^{37} +(23.2964 + 27.3586i) q^{38} -8.98337i q^{39} +(0.00200734 + 40.0000i) q^{40} +13.2990 q^{41} +(-2.20822 + 1.88034i) q^{42} +27.9430 q^{43} +(62.3746 + 10.0690i) q^{44} +(12.8248 + 7.77983i) q^{45} +(29.0997 - 24.7789i) q^{46} -55.6558 q^{47} +(-26.3052 - 8.72000i) q^{48} -48.2990 q^{49} +(-46.3365 - 18.7863i) q^{50} -47.3865i q^{51} +(-20.4811 - 3.30621i) q^{52} +15.5597i q^{53} +(-7.91238 + 6.73753i) q^{54} +(-40.9621 + 67.5245i) q^{55} +(3.47425 + 5.72653i) q^{56} -31.1193i q^{57} +(69.5122 - 59.1909i) q^{58} -87.6625i q^{59} +(22.4571 - 26.3757i) q^{60} +38.0000 q^{61} +(17.6658 + 20.7462i) q^{62} +2.51176 q^{63} +(-29.5619 + 56.7635i) q^{64} +(13.4502 - 22.1721i) q^{65} +(-35.4743 - 41.6600i) q^{66} +92.2015 q^{67} +(-108.036 - 17.4400i) q^{68} -33.0997 q^{69} +(-8.26547 + 1.33470i) q^{70} +130.707i q^{71} +(12.4488 + 20.5190i) q^{72} -54.7173i q^{73} +(-20.1752 - 23.6933i) q^{74} +(20.0049 + 38.4032i) q^{75} +(-70.9485 - 11.4531i) q^{76} +13.2249i q^{77} +(11.6482 + 13.6793i) q^{78} +13.6243i q^{79} +(-51.8686 - 60.9069i) q^{80} +9.00000 q^{81} +(-20.2509 + 17.2440i) q^{82} +59.0048 q^{83} +(0.924421 - 5.72653i) q^{84} +(70.9485 - 116.956i) q^{85} +(-42.5498 + 36.2319i) q^{86} -79.0673 q^{87} +(-108.036 + 65.5448i) q^{88} +39.8007 q^{89} +(-29.6164 + 4.78243i) q^{90} -4.34246i q^{91} +(-12.1819 + 75.4635i) q^{92} -23.5980i q^{93} +(84.7492 - 72.1654i) q^{94} +(46.5927 - 76.8064i) q^{95} +(51.3625 - 20.8300i) q^{96} +168.821i q^{97} +(73.5467 - 62.6263i) q^{98} +47.3865i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{4} + 4 q^{5} - 6 q^{6} + 24 q^{9}+O(q^{10}) \) 8 * q - 10 * q^4 + 4 * q^5 - 6 * q^6 + 24 * q^9	\( 8 q - 10 q^{4} + 4 q^{5} - 6 q^{6} + 24 q^{9} - 42 q^{10} + 20 q^{14} - 46 q^{16} + 52 q^{20} + 72 q^{21} - 18 q^{24} + 32 q^{25} + 84 q^{26} - 184 q^{29} - 60 q^{30} + 12 q^{34} - 30 q^{36} - 6 q^{40} - 256 q^{41} + 348 q^{44} + 12 q^{45} + 112 q^{46} - 24 q^{49} + 72 q^{50} - 18 q^{54} - 244 q^{56} + 6 q^{60} + 304 q^{61} - 10 q^{64} + 168 q^{65} - 12 q^{66} - 144 q^{69} - 104 q^{70} - 252 q^{74} - 24 q^{76} - 308 q^{80} + 72 q^{81} - 204 q^{84} + 24 q^{85} - 280 q^{86} + 560 q^{89} - 126 q^{90} + 376 q^{94} + 426 q^{96}+O(q^{100}) \) 8 * q - 10 * q^4 + 4 * q^5 - 6 * q^6 + 24 * q^9 - 42 * q^10 + 20 * q^14 - 46 * q^16 + 52 * q^20 + 72 * q^21 - 18 * q^24 + 32 * q^25 + 84 * q^26 - 184 * q^29 - 60 * q^30 + 12 * q^34 - 30 * q^36 - 6 * q^40 - 256 * q^41 + 348 * q^44 + 12 * q^45 + 112 * q^46 - 24 * q^49 + 72 * q^50 - 18 * q^54 - 244 * q^56 + 6 * q^60 + 304 * q^61 - 10 * q^64 + 168 * q^65 - 12 * q^66 - 144 * q^69 - 104 * q^70 - 252 * q^74 - 24 * q^76 - 308 * q^80 + 72 * q^81 - 204 * q^84 + 24 * q^85 - 280 * q^86 + 560 * q^89 - 126 * q^90 + 376 * q^94 + 426 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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