LMFDB - Embedded newform 60.3.f.b.19.7

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			19.7
Root			$1.52274 - 1.29664i$ of defining polynomial
Character	$\chi$	$=$	60.19
Dual form			60.3.f.b.19.8

$q$-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} +(3.14704 - 9.49190i) 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} +(-7.51545 - 18.5342i) 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} +(-5.45082 + 16.4405i) 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} +(-35.4763 - 18.4780i) 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} +(-11.1618 - 48.7382i) 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} +(13.0171 + 32.1022i) 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} +(-2.63487 + 7.94713i) 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} +(-77.9803 + 17.8628i) 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} +(9.44111 - 28.4757i) 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	$-0.519048\pi$
$7$	−0.837253			−0.119608			−0.0598038	+	0.998210i	$0.519048\pi$
$8$	−4.14959	−	6.83966i	−0.518698	−	0.854957i
$9$	3.00000			0.333333
$10$	3.14704	−	9.49190i	0.314704	−	0.949190i
$11$			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	$0.0639262\pi$
$13$			5.18655i			0.398966i	−0.979901	+	0.199483i	$0.936074\pi$
$14$	−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	$0.297656\pi$
$17$			27.3586i			1.60933i	−0.593728	+	0.804666i	$0.702344\pi$
$18$	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	$-0.156760\pi$
$20$	−7.51545	−	18.5342i	−0.375773	−	0.926712i
$21$	1.45017			0.0690555
$22$	20.4811	+	24.0524i	0.930958	+	1.09329i
$23$	19.1101			0.830874			0.415437	−	0.909622i	$-0.363629\pi$
$23$	19.1101			0.830874			0.415437	+	0.909622i	$0.363629\pi$
$24$	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	$0.788398\pi$
$30$	−5.45082	+	16.4405i	−0.181694	+	0.548015i
$31$		−	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	$-0.932567\pi$
$37$		−	15.5597i		−	0.420531i	0.977644	−	0.210266i	$-0.0674329\pi$
$38$	−23.2964	−	27.3586i	−0.613062	−	0.719964i
$39$		−	8.98337i		−	0.230343i
$40$	−35.4763	−	18.4780i	−0.886907	−	0.461949i
$41$	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	$-0.605337\pi$
$43$	−27.9430			−0.649837			−0.324918	+	0.945742i	$0.605337\pi$
$44$	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	$-0.298306\pi$
$47$	55.6558			1.18417			0.592083	+	0.805877i	$0.298306\pi$
$48$	26.3052	+	8.72000i	0.548024	+	0.181667i
$49$	−48.2990			−0.985694
$50$	−11.1618	−	48.7382i	−0.223236	−	0.974764i
$51$		−	47.3865i		−	0.929148i
$52$	20.4811	+	3.30621i	0.393867	+	0.0635810i
$53$		−	15.5597i		−	0.293578i	−0.989168	−	0.146789i	$-0.953106\pi$
$53$		−	15.5597i		−	0.293578i	0.989168	−	0.146789i	$-0.0468939\pi$
$54$	−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	$-0.266551\pi$
$60$	13.0171	+	32.1022i	0.216952	+	0.535037i
$61$	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	$-0.741542\pi$
$67$	−92.2015			−1.37614			−0.688071	+	0.725643i	$0.741542\pi$
$68$	108.036	+	17.4400i	1.58876	+	0.256471i
$69$	−33.0997			−0.479705
$70$	−2.63487	+	7.94713i	−0.0376409	+	0.113530i
$71$			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	$0.122280\pi$
$73$			54.7173i			0.749552i	−0.927115	+	0.374776i	$0.877720\pi$
$74$	−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	$0.972518\pi$
$80$	−77.9803	+	17.8628i	−0.974753	+	0.223285i
$81$	9.00000			0.111111
$82$	20.2509	−	17.2440i	0.246962	−	0.210293i
$83$	−59.0048			−0.710901			−0.355451	−	0.934695i	$-0.615673\pi$
$83$	−59.0048			−0.710901			−0.355451	+	0.934695i	$0.615673\pi$
$84$	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	$0.428219\pi$
$90$	9.44111	−	28.4757i	0.104901	−	0.316397i
$91$		−	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	$-0.663981\pi$
$97$		−	168.821i		−	1.74043i	0.492675	−	0.870214i	$-0.336019\pi$
$98$	−73.5467	+	62.6263i	−0.750477	+	0.639044i
$99$			47.3865i			0.478652i
$100$	−80.1923	−	59.7427i	−0.801923	−	0.597427i
$101$	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	$-0.289595\pi$
$103$	126.466			1.22782			0.613911	+	0.789375i	$0.289595\pi$
$104$	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	$-0.662191\pi$
$107$	−104.383			−0.975546			−0.487773	+	0.872971i	$0.662191\pi$
$108$	−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	$0.500732\pi$
$110$	149.929	+	49.7090i	1.36300	+	0.451900i
$111$			26.9501i			0.242794i
$112$	12.7156	+	4.21515i	0.113532	+	0.0376352i
$113$		−	16.9855i		−	0.150314i	−0.997172	−	0.0751572i	$-0.976054\pi$
$113$		−	16.9855i		−	0.150314i	0.997172	−	0.0751572i	$-0.0239459\pi$
$114$	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
$120$	61.4467	+	32.0048i	0.512056	+	0.266706i
$121$	−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	$-0.510599\pi$
$127$	−8.45598			−0.0665825			−0.0332913	+	0.999446i	$0.510599\pi$
$128$	28.5867	+	124.767i	0.223334	+	0.974742i
$129$	48.3987			0.375184
$130$	49.2302	+	16.3223i	0.378694	+	0.125556i
$131$		−	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	$-0.937081\pi$
$137$		−	53.8083i		−	0.392762i	0.980528	−	0.196381i	$-0.0629189\pi$
$138$	−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	$-0.0156061\pi$
$140$	6.29234	+	15.5179i	0.0449453	+	0.110842i
$141$	−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	$0.536020\pi$
$150$	19.3328	+	84.4171i	0.128885	+	0.562780i
$151$		−	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	$0.0215715\pi$
$157$			21.2631i			0.135434i	−0.997705	+	0.0677170i	$0.978428\pi$
$158$	17.6658	+	20.7462i	0.111809	+	0.131305i
$159$			26.9501i			0.169498i
$160$	−95.5819	+	128.313i	−0.597387	+	0.801953i
$161$	−16.0000			−0.0993789
$162$	13.7046	−	11.6697i	0.0845965	−	0.0720355i
$163$	210.211			1.28964			0.644819	−	0.764335i	$-0.276933\pi$
$163$	210.211			1.28964			0.644819	+	0.764335i	$0.276933\pi$
$164$	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	$-0.247006\pi$
$167$	238.384			1.42745			0.713725	+	0.700426i	$0.247006\pi$
$168$	−6.01759	−	9.91864i	−0.0358190	−	0.0590395i
$169$	142.100			0.840826
$170$	259.685	+	86.0986i	1.52756	+	0.506462i
$171$		−	53.9002i		−	0.315206i
$172$	−17.8125	+	110.343i	−0.103561	+	0.641532i
$173$		−	2.33481i		−	0.0134960i	−0.999977	−	0.00674800i	$-0.997852\pi$
$173$		−	2.33481i		−	0.0134960i	0.999977	−	0.00674800i	$-0.00214797\pi$
$174$	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	$0.781318\pi$
$180$	−22.5464	−	55.6027i	−0.125258	−	0.308904i
$181$	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
$190$	−170.539	−	56.5420i	−0.897571	−	0.297589i
$191$		−	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	$-0.843669\pi$
$193$		−	182.046i		−	0.943245i	0.881801	−	0.471623i	$-0.156331\pi$
$194$	−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	$0.227285\pi$
$197$			258.027i			1.30978i	−0.755724	+	0.654890i	$0.772715\pi$
$198$	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	$0.777104\pi$
$200$	−199.577	+	13.0080i	−0.997883	+	0.0650401i
$201$	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
$210$	4.56372	−	13.7648i	0.0217320	−	0.0655468i
$211$			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
$220$	292.758	−	118.710i	1.33072	−	0.539593i
$221$	−141.897			−0.642068
$222$	34.9446	+	41.0380i	0.157408	+	0.184856i
$223$	−349.843			−1.56880			−0.784401	−	0.620255i	$-0.787029\pi$
$223$	−349.843			−1.56880			−0.784401	+	0.620255i	$0.787029\pi$
$224$	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	$-0.365979\pi$
$227$	185.554			0.817418			0.408709	+	0.912665i	$0.365979\pi$
$228$	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	$0.304537\pi$
$230$	60.1402	−	181.391i	0.261479	−	0.788657i
$231$			22.9061i			0.0991607i
$232$	189.427	+	312.227i	0.816494	+	1.34581i
$233$			58.4780i			0.250978i	0.992095	+	0.125489i	$0.0400500\pi$
$233$			58.4780i			0.250978i	−0.992095	+	0.125489i	$0.959950\pi$
$234$	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	$0.923801\pi$
$240$	135.066	−	30.9393i	0.562774	−	0.128914i
$241$	−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
$250$	−174.107	−	179.406i	−0.696430	−	0.717625i
$251$		−	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	$0.265836\pi$
$257$			381.078i			1.48279i	−0.671067	+	0.741397i	$0.734164\pi$
$258$	73.6985	−	62.7556i	0.285653	−	0.243239i
$259$			13.0274i			0.0502988i
$260$	96.1288	−	38.9793i	0.369726	−	0.149920i
$261$	−136.949			−0.524707
$262$	−67.0738	−	78.7697i	−0.256007	−	0.300648i
$263$	11.4914			0.0436934			0.0218467	−	0.999761i	$-0.493045\pi$
$263$	11.4914			0.0436934			0.0218467	+	0.999761i	$0.493045\pi$
$264$	−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	$0.546283\pi$
$270$	−16.3525	+	49.3214i	−0.0605647	+	0.182672i
$271$			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	$-0.826437\pi$
$277$		−	287.328i		−	1.03729i	0.854991	−	0.518643i	$-0.173563\pi$
$278$	−17.6658	−	20.7462i	−0.0635459	−	0.0746267i
$279$		−	40.8729i		−	0.146498i
$280$	29.7026	+	15.4707i	0.106081	+	0.0552526i
$281$	−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	$-0.452515\pi$
$283$	84.1224			0.297252			0.148626	+	0.988893i	$0.452515\pi$
$284$	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
$290$	−143.661	+	433.301i	−0.495381	+	1.49414i
$291$			292.407i			1.00484i
$292$	216.072	+	34.8800i	0.739972	+	0.119452i
$293$		−	246.620i		−	0.841706i	−0.907129	−	0.420853i	$-0.861731\pi$
$293$		−	246.620i		−	0.841706i	0.907129	−	0.420853i	$-0.138269\pi$
$294$	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
$300$	138.897	+	103.477i	0.462991	+	0.344925i
$301$	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	$-0.439599\pi$
$307$	115.811			0.377236			0.188618	+	0.982051i	$0.439599\pi$
$308$	−52.2233	−	8.43030i	−0.169556	−	0.0273711i
$309$	−219.045			−0.708883
$310$	−129.320	−	42.8761i	−0.417162	−	0.138310i
$311$		−	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	$-0.949416\pi$
$313$		−	99.0614i		−	0.316490i	0.987400	−	0.158245i	$-0.0505836\pi$
$314$	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	$-0.733304\pi$
$317$		−	471.192i		−	1.48641i	0.669063	−	0.743206i	$-0.266696\pi$
$318$	34.9446	+	41.0380i	0.109889	+	0.129050i
$319$		−	721.057i		−	2.26037i
$320$	20.8289	+	319.321i	0.0650902	+	0.997879i
$321$	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
$330$	−259.685	−	86.0986i	−0.786926	−	0.260905i
$331$		−	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	$-0.810871\pi$
$337$		−	377.317i		−	1.11964i	0.828615	−	0.559818i	$-0.189129\pi$
$338$	216.380	−	184.252i	0.640179	−	0.545124i
$339$			29.4198i			0.0867841i
$340$	507.071	−	205.613i	1.49139	−	0.604743i
$341$	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	$-0.732006\pi$
$347$	−462.222			−1.33205			−0.666025	+	0.745929i	$0.732006\pi$
$348$	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	$0.407213\pi$
$350$	9.34526	+	40.8062i	0.0267007	+	0.116589i
$351$		−	26.9501i		−	0.0767810i
$352$	−189.960	−	468.403i	−0.539660	−	1.33069i
$353$			250.897i			0.710757i	0.934722	+	0.355379i	$0.115648\pi$
$353$			250.897i			0.710757i	−0.934722	+	0.355379i	$0.884352\pi$
$354$	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	$-0.0970801\pi$
$360$	−106.429	−	55.4339i	−0.295636	−	0.153983i
$361$	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	$-0.470876\pi$
$367$	67.0637			0.182735			0.0913675	+	0.995817i	$0.470876\pi$
$368$	−290.231	−	96.2097i	−0.788670	−	0.261439i
$369$	39.8970			0.108122
$370$	−147.691	−	48.9668i	−0.399164	−	0.132343i
$371$			13.0274i			0.0351142i
$372$	93.1855	+	15.0427i	0.250499	+	0.0404374i
$373$			567.402i			1.52119i	0.649230	+	0.760593i	$0.275091\pi$
$373$			567.402i			1.52119i	−0.649230	+	0.760593i	$0.724909\pi$
$374$	−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	$0.897319\pi$
$380$	−333.000	+	135.028i	−0.876316	+	0.355337i
$381$	14.6462			0.0384414
$382$	−180.740	−	212.257i	−0.473142	−	0.555646i
$383$	−670.068			−1.74952			−0.874762	−	0.484553i	$-0.838982\pi$
$383$	−670.068			−1.74952			−0.874762	+	0.484553i	$0.838982\pi$
$384$	−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	$0.708861\pi$
$390$	−85.2693	−	28.2710i	−0.218639	−	0.0724897i
$391$			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	$0.216553\pi$
$397$			499.460i			1.25809i	−0.777371	+	0.629043i	$0.783447\pi$
$398$	332.554	+	390.542i	0.835562	+	0.981262i
$399$		−	26.0548i		−	0.0653001i
$400$	−287.036	+	278.586i	−0.717590	+	0.696466i
$401$	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	$0.710262\pi$
$410$	41.8524	−	126.233i	0.102079	−	0.307885i
$411$			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	$-0.0839150\pi$
$420$	−10.8987	−	26.8777i	−0.0259492	−	0.0639946i
$421$	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
$430$	−87.9376	+	265.232i	−0.204506	+	0.616819i
$431$		−	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	$-0.954472\pi$
$433$		−	123.443i		−	0.285089i	0.989788	−	0.142544i	$-0.0455283\pi$
$434$	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	$0.877064\pi$
$440$	291.869	−	560.366i	0.663338	−	1.27356i
$441$	−144.897			−0.328565
$442$	−216.072	+	183.989i	−0.488850	+	0.416265i
$443$	−154.952			−0.349780			−0.174890	−	0.984588i	$-0.555957\pi$
$443$	−154.952			−0.349780			−0.174890	+	0.984588i	$0.555957\pi$
$444$	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	$0.534057\pi$
$450$	−33.4854	−	146.215i	−0.0744120	−	0.324921i
$451$			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	$0.178341\pi$
$457$			485.718i			1.06284i	−0.847108	+	0.531420i	$0.821659\pi$
$458$	401.846	−	342.179i	0.877393	−	0.747116i
$459$		−	142.160i		−	0.309716i
$460$	−143.621	−	354.191i	−0.312220	−	0.769981i
$461$	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	$-0.650511\pi$
$463$	−421.720			−0.910842			−0.455421	+	0.890276i	$0.650511\pi$
$464$	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	$-0.740752\pi$
$467$	−640.974			−1.37254			−0.686268	+	0.727349i	$0.740752\pi$
$468$	61.4432	+	9.91864i	0.131289	+	0.0211937i
$469$	77.1960			0.164597
$470$	175.151	−	528.279i	0.372661	−	1.12400i
$471$		−	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	$-0.0741448\pi$
$480$	165.553	−	222.244i	0.344901	−	0.463008i
$481$	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	$-0.133208\pi$
$487$	889.949			1.82741			0.913705	+	0.406377i	$0.133208\pi$
$488$	−157.684	−	259.907i	−0.323123	−	0.532596i
$489$	−364.096			−0.744573
$490$	−151.999	+	458.449i	−0.310201	+	0.935611i
$491$			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	$-0.179451\pi$
$500$	−497.745	−	47.4341i	−0.995490	−	0.0948683i
$501$	−412.894			−0.824139
$502$	−137.737	−	161.755i	−0.274376	−	0.322220i
$503$	574.914			1.14297			0.571485	−	0.820612i	$-0.306367\pi$
$503$	574.914			1.14297			0.571485	+	0.820612i	$0.306367\pi$
$504$	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	$0.434646\pi$
$510$	−449.788	−	149.127i	−0.881938	−	0.292406i
$511$		−	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
$520$	95.8369	−	184.000i	0.184302	−	0.353845i
$521$	−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	$-0.457407\pi$
$523$	139.548			0.266822			0.133411	+	0.991061i	$0.457407\pi$
$524$	−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
$530$	−147.691	−	48.9668i	−0.278662	−	0.0923902i
$531$		−	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
$540$	39.0514	+	96.3067i	0.0723175	+	0.178346i
$541$	−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	$-0.485348\pi$
$547$	50.3388			0.0920271			0.0460136	+	0.998941i	$0.485348\pi$
$548$	−212.483	−	34.3006i	−0.387742	−	0.0625923i
$549$	114.000			0.207650
$550$	769.845	−	176.307i	1.39972	−	0.320557i
$551$			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	$0.250987\pi$
$557$			790.157i			1.41859i	−0.704910	+	0.709297i	$0.749013\pi$
$558$	−52.9973	−	62.2386i	−0.0949773	−	0.111539i
$559$		−	144.928i		−	0.259263i
$560$	65.2892	−	14.9557i	0.116588	−	0.0267066i
$561$	748.495			1.33422
$562$	−342.004	+	291.222i	−0.608548	+	0.518189i
$563$	−354.133			−0.629010			−0.314505	−	0.949256i	$-0.601838\pi$
$563$	−354.133			−0.629010			−0.314505	+	0.949256i	$0.601838\pi$
$564$	−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	$0.484470\pi$
$570$	295.381	+	97.9336i	0.518213	+	0.171813i
$571$		−	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	$0.0559389\pi$
$577$			201.759i			0.349668i	−0.984598	+	0.174834i	$0.944061\pi$
$578$	−699.690	+	595.799i	−1.21054	+	1.03079i
$579$			315.313i			0.544583i
$580$	343.077	+	846.079i	0.591512	+	1.45876i
$581$	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	$-0.623618\pi$
$587$	−444.556			−0.757335			−0.378668	+	0.925533i	$0.623618\pi$
$588$	53.3274	−	330.349i	0.0906929	−	0.561818i
$589$	−244.784			−0.415593
$590$	−832.084	−	275.877i	−1.41031	−	0.467588i
$591$		−	446.915i		−	0.756202i
$592$	−78.3350	+	236.309i	−0.132323	+	0.399171i
$593$			563.908i			0.950942i	0.879731	+	0.475471i	$0.157722\pi$
$593$			563.908i			0.950942i	−0.879731	+	0.475471i	$0.842278\pi$
$594$	−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	$0.750781\pi$
$600$	345.677	−	22.5306i	0.576128	−	0.0375509i
$601$	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	$-0.240881\pi$
$607$	882.664			1.45414			0.727071	+	0.686562i	$0.240881\pi$
$608$	216.072	+	532.789i	0.355381	+	0.876298i
$609$	−66.1993			−0.108702
$610$	119.587	−	360.692i	0.196045	−	0.591299i
$611$			288.662i			0.472442i
$612$	324.108	+	52.3200i	0.529588	+	0.0854902i
$613$		−	469.374i		−	0.765701i	−0.923810	−	0.382850i	$-0.874943\pi$
$613$		−	469.374i		−	0.765701i	0.923810	−	0.382850i	$-0.125057\pi$
$614$	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	$0.0567902\pi$
$617$			218.994i			0.354934i	−0.984127	+	0.177467i	$0.943210\pi$
$618$	−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	$0.748465\pi$
$620$	−252.516	+	102.393i	−0.407284	+	0.165149i
$621$	−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
$630$	−7.90460	+	23.8414i	−0.0125470	+	0.0378435i
$631$		−	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
$640$	445.761	+	459.235i	0.696502	+	0.717555i
$641$	−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	$-0.652003\pi$
$643$	−591.032			−0.919179			−0.459590	+	0.888131i	$0.652003\pi$
$644$	−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	$-0.458927\pi$
$647$	166.507			0.257352			0.128676	+	0.991687i	$0.458927\pi$
$648$	−37.3463	−	61.5569i	−0.0576331	−	0.0949953i
$649$	1384.67			2.13355
$650$	252.783	−	57.8913i	0.388897	−	0.0890635i
$651$		−	19.7575i		−	0.0303494i
$652$	134.001	−	830.098i	0.205523	−	1.27316i
$653$			621.335i			0.951509i	0.879578	+	0.475754i	$0.157825\pi$
$653$			621.335i			0.951509i	−0.879578	+	0.475754i	$0.842175\pi$
$654$	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	$0.821173\pi$
$660$	−507.071	+	205.613i	−0.768290	+	0.311534i
$661$	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
$670$	−290.161	+	875.167i	−0.433077	+	1.30622i
$671$			600.230i			0.894530i
$672$	−43.0035	+	17.4400i	−0.0639933	+	0.0259524i
$673$			714.176i			1.06118i	0.847628	+	0.530592i	$0.178030\pi$
$673$			714.176i			1.06118i	−0.847628	+	0.530592i	$0.821970\pi$
$674$	−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	$-0.877114\pi$
$677$		−	509.833i		−	0.753077i	0.926401	−	0.376538i	$-0.122886\pi$
$678$	38.1468	+	44.7986i	0.0562638	+	0.0660747i
$679$			141.346i			0.208168i
$680$	505.532	−	970.582i	0.743429	−	1.42733i
$681$	−321.389			−0.471936
$682$	327.697	−	279.040i	0.480494	−	0.409150i
$683$	1263.93			1.85055			0.925275	−	0.379298i	$-0.123834\pi$
$683$	1263.93			1.85055			0.925275	+	0.379298i	$0.123834\pi$
$684$	−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
$690$	−104.166	+	314.179i	−0.150965	+	0.455332i
$691$		−	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
$700$	67.1413	+	50.0198i	0.0959162	+	0.0714568i
$701$	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	$0.405015\pi$
$710$	1240.65	+	411.338i	1.74740	+	0.579350i
$711$			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	$0.911364\pi$
$720$	−233.941	+	53.5884i	−0.324918	+	0.0744284i
$721$	−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	$-0.365182\pi$
$727$	597.583			0.821985			0.410993	+	0.911639i	$0.365182\pi$
$728$	−29.7009	+	18.0194i	−0.0407980	+	0.0247519i
$729$	27.0000			0.0370370
$730$	519.371	+	172.197i	0.711467	+	0.235887i
$731$		−	764.482i		−	1.04580i
$732$	−41.9562	+	259.907i	−0.0573172	+	0.355064i
$733$		−	23.8650i		−	0.0325580i	−0.999867	−	0.0162790i	$-0.994818\pi$
$733$		−	23.8650i		−	0.0325580i	0.999867	−	0.0162790i	$-0.00518200\pi$
$734$	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	$-0.0271187\pi$
$740$	−288.386	+	116.938i	−0.389711	+	0.158024i
$741$	−161.402			−0.217816
$742$	16.8918	+	19.8373i	0.0227652	+	0.0267349i
$743$	148.841			0.200325			0.100162	−	0.994971i	$-0.468064\pi$
$743$	148.841			0.200325			0.100162	+	0.994971i	$0.468064\pi$
$744$	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
$750$	301.563	+	310.741i	0.402084	+	0.414321i
$751$			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	$-0.842397\pi$
$757$		−	719.363i		−	0.950281i	0.879910	−	0.475141i	$-0.157603\pi$
$758$	311.579	+	365.910i	0.411054	+	0.482731i
$759$		−	522.826i		−	0.688836i
$760$	−331.989	+	637.393i	−0.436827	+	0.838675i
$761$	−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	$0.548135\pi$
$770$	−125.529	−	41.6191i	−0.163025	−	0.0540507i
$771$		−	660.047i		−	0.856092i
$772$	−718.879	−	116.047i	−0.931190	−	0.150320i
$773$			519.956i			0.672647i	0.941746	+	0.336324i	$0.109184\pi$
$773$			519.956i			0.672647i	−0.941746	+	0.336324i	$0.890816\pi$
$774$	−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
$780$	−166.500	+	67.5141i	−0.213462	+	0.0865566i
$781$	−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	$-0.490690\pi$
$787$	46.0288			0.0584864			0.0292432	+	0.999572i	$0.490690\pi$
$788$	1018.92	+	164.481i	1.29304	+	0.208733i
$789$	−19.9036			−0.0252264
$790$	129.320	+	42.8761i	0.163697	+	0.0542736i
$791$			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	$0.00305730\pi$
$797$			15.3098i			0.0192093i	−0.999954	+	0.00960463i	$0.996943\pi$
$798$	−33.7836	−	39.6746i	−0.0423353	−	0.0497175i
$799$			1522.67i			1.90572i
$800$	−75.8546	+	796.396i	−0.0948183	+	0.995495i
$801$	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	$0.561986\pi$
$810$	28.3233	−	85.4271i	0.0349671	−	0.105466i
$811$			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
$820$	−99.9481	−	246.487i	−0.121888	−	0.300594i
$821$	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	$-0.478774\pi$
$823$	109.680			0.133269			0.0666344	+	0.997777i	$0.478774\pi$
$824$	−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	$-0.641646\pi$
$827$	−711.971			−0.860908			−0.430454	+	0.902613i	$0.641646\pi$
$828$	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	$0.522806\pi$
$830$	−185.690	+	560.068i	−0.223723	+	0.674781i
$831$			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	$-0.318902\pi$
$840$	−51.4465	−	26.7961i	−0.0612458	−	0.0319001i
$841$	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
$850$	1333.41	−	305.372i	1.56872	−	0.359261i
$851$		−	297.347i		−	0.349409i
$852$	−893.989	−	144.315i	−1.04928	−	0.169383i
$853$			1308.03i			1.53344i	0.641979	+	0.766722i	$0.278114\pi$
$853$			1308.03i			1.53344i	−0.641979	+	0.766722i	$0.721886\pi$
$854$	−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	$0.137944\pi$
$857$			719.755i			0.839854i	−0.907558	+	0.419927i	$0.862056\pi$
$858$	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	$-0.303989\pi$
$860$	210.004	+	517.902i	0.244191	+	0.602212i
$861$	19.2858			0.0223993
$862$	−571.922	−	671.650i	−0.663483	−	0.779176i
$863$	72.4412			0.0839411			0.0419706	−	0.999119i	$-0.486636\pi$
$863$	72.4412			0.0839411			0.0419706	+	0.999119i	$0.486636\pi$
$864$	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
$870$	248.827	−	750.499i	0.286009	−	0.862642i
$871$		−	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	$-0.711100\pi$
$877$		−	1382.21i		−	1.57606i	0.615635	−	0.788032i	$-0.288900\pi$
$878$	428.835	+	503.613i	0.488423	+	0.573591i
$879$			427.158i			0.485959i
$880$	−282.152	−	1231.74i	−0.320628	−	1.39970i
$881$	−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	$-0.708860\pi$
$883$	−1077.39			−1.22014			−0.610072	+	0.792346i	$0.708860\pi$
$884$	−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	$-0.642297\pi$
$887$	−766.896			−0.864595			−0.432297	+	0.901731i	$0.642297\pi$
$888$	184.330	−	111.832i	0.207578	−	0.125937i
$889$	7.07980			0.00796378
$890$	125.254	−	377.784i	0.140735	−	0.424476i
$891$			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
$900$	−240.577	−	179.228i	−0.267308	−	0.199142i
$901$	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	$-0.295600\pi$
$907$	1086.43			1.19783			0.598913	+	0.800814i	$0.295600\pi$
$908$	118.283	−	732.730i	0.130268	−	0.806971i
$909$	133.650			0.147029
$910$	−41.2182	−	13.6659i	−0.0452947	−	0.0150174i
$911$		−	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	$-0.0600194\pi$
$920$	−677.955	−	353.116i	−0.736908	−	0.383821i
$921$	−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	$0.207192\pi$
$930$	223.989	+	74.2636i	0.240849	+	0.0798533i
$931$			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	$0.0420574\pi$
$937$			246.887i			0.263486i	−0.991284	+	0.131743i	$0.957943\pi$
$938$	117.549	−	100.095i	0.125319	−	0.106711i
$939$			171.579i			0.182726i
$940$	−418.279	−	1031.54i	−0.444977	−	1.09738i
$941$	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	$-0.501010\pi$
$947$	−6.00750			−0.00634372			−0.00317186	+	0.999995i	$0.501010\pi$
$948$	−93.1855	−	15.0427i	−0.0982969	−	0.0158678i
$949$	−283.794			−0.299045
$950$	−875.667	+	200.541i	−0.921755	+	0.211096i
$951$			816.129i			0.858180i
$952$	−156.670	+	95.0509i	−0.164569	+	0.0998434i
$953$			1089.55i			1.14329i	0.820503	+	0.571643i	$0.193694\pi$
$953$			1089.55i			1.14329i	−0.820503	+	0.571643i	$0.806306\pi$
$954$	−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
$960$	−36.0767	−	553.081i	−0.0375799	−	0.576126i
$961$	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	$-0.841542\pi$
$967$	−1699.27			−1.75726			−0.878630	+	0.477502i	$0.841542\pi$
$968$	533.215	+	878.885i	0.550842	+	0.907939i
$969$	−851.382			−0.878619
$970$	−1602.44	−	531.287i	−1.65200	−	0.547719i
$971$		−	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	$0.142868\pi$
$977$			847.868i			0.867828i	−0.900954	+	0.433914i	$0.857132\pi$
$978$	−554.423	+	472.101i	−0.566895	+	0.482721i
$979$			628.672i			0.642157i
$980$	362.989	+	895.185i	0.370397	+	0.913454i
$981$	−1.50497			−0.00153412
$982$	716.837	+	841.835i	0.729977	+	0.857266i
$983$	−96.0512			−0.0977123			−0.0488562	−	0.998806i	$-0.515558\pi$
$983$	−96.0512			−0.0977123			−0.0488562	+	0.998806i	$0.515558\pi$
$984$	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
$990$	449.788	+	149.127i	0.454332	+	0.150633i
$991$		−	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	$0.395425\pi$
$997$			1887.35i			1.89303i	−0.322655	+	0.946517i	$0.604575\pi$
$998$	−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.19.7	yes	8
3.2	odd	2		180.3.f.h.19.2		8
4.3	odd	2	inner	60.3.f.b.19.1	✓	8
5.2	odd	4		300.3.c.f.151.6		8
5.3	odd	4		300.3.c.f.151.3		8
5.4	even	2	inner	60.3.f.b.19.2	yes	8
8.3	odd	2		960.3.j.e.319.2		8
8.5	even	2		960.3.j.e.319.6		8
12.11	even	2		180.3.f.h.19.8		8
15.2	even	4		900.3.c.r.451.3		8
15.8	even	4		900.3.c.r.451.6		8
15.14	odd	2		180.3.f.h.19.7		8
20.3	even	4		300.3.c.f.151.4		8
20.7	even	4		300.3.c.f.151.5		8
20.19	odd	2	inner	60.3.f.b.19.8	yes	8
40.19	odd	2		960.3.j.e.319.5		8
40.29	even	2		960.3.j.e.319.1		8
60.23	odd	4		900.3.c.r.451.5		8
60.47	odd	4		900.3.c.r.451.4		8
60.59	even	2		180.3.f.h.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.b.19.1	✓	8	4.3	odd	2	inner
60.3.f.b.19.2	yes	8	5.4	even	2	inner
60.3.f.b.19.7	yes	8	1.1	even	1	trivial
60.3.f.b.19.8	yes	8	20.19	odd	2	inner
180.3.f.h.19.1		8	60.59	even	2
180.3.f.h.19.2		8	3.2	odd	2
180.3.f.h.19.7		8	15.14	odd	2
180.3.f.h.19.8		8	12.11	even	2
300.3.c.f.151.3		8	5.3	odd	4
300.3.c.f.151.4		8	20.3	even	4
300.3.c.f.151.5		8	20.7	even	4
300.3.c.f.151.6		8	5.2	odd	4
900.3.c.r.451.3		8	15.2	even	4
900.3.c.r.451.4		8	60.47	odd	4
900.3.c.r.451.5		8	60.23	odd	4
900.3.c.r.451.6		8	15.8	even	4
960.3.j.e.319.1		8	40.29	even	2
960.3.j.e.319.2		8	8.3	odd	2
960.3.j.e.319.5		8	40.19	odd	2
960.3.j.e.319.6		8	8.5	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} +(3.14704 - 9.49190i) 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} +(-7.51545 - 18.5342i) 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} +(-5.45082 + 16.4405i) 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} +(-35.4763 - 18.4780i) 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} +(-11.1618 - 48.7382i) 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} +(13.0171 + 32.1022i) 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} +(-2.63487 + 7.94713i) 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} +(-77.9803 + 17.8628i) 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} +(9.44111 - 28.4757i) 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

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Database

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