LMFDB - Embedded newform 650.2.m.e.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(101,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("650.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.m (of order $6$, degree $2$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 60 x^{13} + 92 x^{12} + 292 x^{11} - 104 x^{10} + 936 x^{9} + 664 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 8x^14 - 60x^13 + 92x^12 + 292x^11 - 104x^10 + 936x^9 + 664x^8 - 2376x^7 + 232x^6 - 4216x^5 + 3812x^4 + 3408x^3 + 800x^2 + 640*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.4
Root			$1.23451 - 0.330787i$ of defining polynomial
Character	$\chi$	$=$	650.251
Dual form			650.2.m.e.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.20493 - 2.08700i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.08700 + 1.20493i) q^{6} +(1.21729 - 0.702803i) q^{7} -1.00000i q^{8} +(-1.40373 - 2.43133i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.20493 - 2.08700i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.08700 + 1.20493i) q^{6} +(1.21729 - 0.702803i) q^{7} -1.00000i q^{8} +(-1.40373 - 2.43133i) q^{9} +(-4.59726 - 2.65423i) q^{11} +2.40987 q^{12} +(3.23750 + 1.58700i) q^{13} -1.40561 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.52026 - 6.09726i) q^{17} +2.80745i q^{18} +(-2.28793 + 1.32094i) q^{19} -3.38732i q^{21} +(2.65423 + 4.59726i) q^{22} +(1.33329 - 2.30933i) q^{23} +(-2.08700 - 1.20493i) q^{24} +(-2.01026 - 2.99314i) q^{26} +0.464013 q^{27} +(1.21729 + 0.702803i) q^{28} +(2.10653 - 3.64862i) q^{29} -5.07645i q^{31} +(0.866025 - 0.500000i) q^{32} +(-11.0788 + 6.39634i) q^{33} +7.04051i q^{34} +(1.40373 - 2.43133i) q^{36} +(0.715328 + 0.412995i) q^{37} +2.64187 q^{38} +(7.21306 - 4.84445i) q^{39} +(2.43440 + 1.40550i) q^{41} +(-1.69366 + 2.93351i) q^{42} +(-2.64187 - 4.57586i) q^{43} -5.30846i q^{44} +(-2.30933 + 1.33329i) q^{46} +1.79070i q^{47} +(1.20493 + 2.08700i) q^{48} +(-2.51214 + 4.35115i) q^{49} -16.9667 q^{51} +(0.244364 + 3.59726i) q^{52} +7.93952 q^{53} +(-0.401847 - 0.232006i) q^{54} +(-0.702803 - 1.21729i) q^{56} +6.36656i q^{57} +(-3.64862 + 2.10653i) q^{58} +(-5.59815 + 3.23210i) q^{59} +(7.36754 + 12.7610i) q^{61} +(-2.53823 + 4.39634i) q^{62} +(-3.41749 - 1.97309i) q^{63} -1.00000 q^{64} +12.7927 q^{66} +(-3.46410 - 2.00000i) q^{67} +(3.52026 - 6.09726i) q^{68} +(-3.21306 - 5.56518i) q^{69} +(-8.34802 + 4.81973i) q^{71} +(-2.43133 + 1.40373i) q^{72} -7.04281i q^{73} +(-0.412995 - 0.715328i) q^{74} +(-2.28793 - 1.32094i) q^{76} -7.46160 q^{77} +(-8.66892 + 0.588885i) q^{78} -4.05956 q^{79} +(4.77028 - 8.26237i) q^{81} +(-1.40550 - 2.43440i) q^{82} +8.55910i q^{83} +(2.93351 - 1.69366i) q^{84} +5.28374i q^{86} +(-5.07645 - 8.79268i) q^{87} +(-2.65423 + 4.59726i) q^{88} +(13.1289 + 7.57999i) q^{89} +(5.05633 - 0.343480i) q^{91} +2.66659 q^{92} +(-10.5946 - 6.11679i) q^{93} +(0.895350 - 1.55079i) q^{94} -2.40987i q^{96} +(3.78155 - 2.18328i) q^{97} +(4.35115 - 2.51214i) q^{98} +14.9033i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 16 * q^9	$ 16 q + 8 q^{4} - 16 q^{9} - 6 q^{11} + 20 q^{14} - 8 q^{16} - 18 q^{19} + 2 q^{26} + 6 q^{29} + 16 q^{36} + 60 q^{39} + 42 q^{41} + 12 q^{46} + 30 q^{49} - 40 q^{51} - 36 q^{54} + 10 q^{56} - 60 q^{59} - 10 q^{61} - 16 q^{64} + 40 q^{66} + 4 q^{69} - 40 q^{74} - 18 q^{76} - 8 q^{79} + 16 q^{81} + 12 q^{84} + 78 q^{89} + 38 q^{91} + 6 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 - 16 * q^9 - 6 * q^11 + 20 * q^14 - 8 * q^16 - 18 * q^19 + 2 * q^26 + 6 * q^29 + 16 * q^36 + 60 * q^39 + 42 * q^41 + 12 * q^46 + 30 * q^49 - 40 * q^51 - 36 * q^54 + 10 * q^56 - 60 * q^59 - 10 * q^61 - 16 * q^64 + 40 * q^66 + 4 * q^69 - 40 * q^74 - 18 * q^76 - 8 * q^79 + 16 * q^81 + 12 * q^84 + 78 * q^89 + 38 * q^91 + 6 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.20493	−	2.08700i	0.695668	−	1.20493i	−0.274287	−	0.961648i	$-0.588442\pi$
$3$	1.20493	−	2.08700i	0.695668	−	1.20493i	0.969955	−	0.243285i	$-0.0782250\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−2.08700	+	1.20493i	−0.852016	+	0.491912i
$7$	1.21729	−	0.702803i	0.460093	−	0.265635i	−0.251991	−	0.967730i	$-0.581085\pi$
$7$	1.21729	−	0.702803i	0.460093	−	0.265635i	0.712083	+	0.702095i	$0.247752\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.40373	−	2.43133i	−0.467909	−	0.810442i
$10$		0			0
$11$	−4.59726	−	2.65423i	−1.38613	−	0.800280i	−0.393250	−	0.919432i	$-0.628649\pi$
$11$	−4.59726	−	2.65423i	−1.38613	−	0.800280i	−0.992876	+	0.119151i	$0.961983\pi$
$12$	2.40987			0.695668
$13$	3.23750	+	1.58700i	0.897921	+	0.440156i
$13$	3.23750	+	1.58700i	0.897921	+	0.440156i
$14$	−1.40561			−0.375664
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.52026	−	6.09726i	−0.853787	−	1.47880i	−0.877766	−	0.479091i	$-0.840967\pi$
$17$	−3.52026	−	6.09726i	−0.853787	−	1.47880i	0.0239782	−	0.999712i	$-0.492367\pi$
$18$			2.80745i			0.661723i
$19$	−2.28793	+	1.32094i	−0.524887	+	0.303044i	−0.738932	−	0.673780i	$-0.764669\pi$
$19$	−2.28793	+	1.32094i	−0.524887	+	0.303044i	0.214045	+	0.976824i	$0.431336\pi$
$20$		0			0
$21$		−	3.38732i		−	0.739174i
$22$	2.65423	+	4.59726i	0.565884	+	0.980139i
$23$	1.33329	−	2.30933i	0.278011	−	0.481529i	−0.692879	−	0.721054i	$-0.743658\pi$
$23$	1.33329	−	2.30933i	0.278011	−	0.481529i	0.970890	+	0.239524i	$0.0769915\pi$
$24$	−2.08700	−	1.20493i	−0.426008	−	0.245956i
$25$		0			0
$26$	−2.01026	−	2.99314i	−0.394244	−	0.587003i
$27$	0.464013			0.0892993
$28$	1.21729	+	0.702803i	0.230046	+	0.132817i
$29$	2.10653	−	3.64862i	0.391173	−	0.677531i	−0.601432	−	0.798924i	$-0.705403\pi$
$29$	2.10653	−	3.64862i	0.391173	−	0.677531i	0.992605	+	0.121393i	$0.0387362\pi$
$30$		0			0
$31$		−	5.07645i		−	0.911758i	−0.890042	−	0.455879i	$-0.849325\pi$
$31$		−	5.07645i		−	0.911758i	0.890042	−	0.455879i	$-0.150675\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−11.0788	+	6.39634i	−1.92857	+	1.11346i
$34$			7.04051i			1.20744i
$35$		0			0
$36$	1.40373	−	2.43133i	0.233954	−	0.405221i
$37$	0.715328	+	0.412995i	0.117599	+	0.0678960i	0.557646	−	0.830079i	$-0.311705\pi$
$37$	0.715328	+	0.412995i	0.117599	+	0.0678960i	−0.440047	+	0.897975i	$0.645038\pi$
$38$	2.64187			0.428568
$39$	7.21306	−	4.84445i	1.15501	−	0.775732i
$40$		0			0
$41$	2.43440	+	1.40550i	0.380189	+	0.219502i	0.677901	−	0.735154i	$-0.262890\pi$
$41$	2.43440	+	1.40550i	0.380189	+	0.219502i	−0.297711	+	0.954656i	$0.596223\pi$
$42$	−1.69366	+	2.93351i	−0.261338	+	0.452650i
$43$	−2.64187	−	4.57586i	−0.402882	−	0.697812i	0.591191	−	0.806532i	$-0.298658\pi$
$43$	−2.64187	−	4.57586i	−0.402882	−	0.697812i	−0.994072	+	0.108720i	$0.965325\pi$
$44$		−	5.30846i		−	0.800280i
$45$		0			0
$46$	−2.30933	+	1.33329i	−0.340493	+	0.196583i
$47$			1.79070i			0.261200i	0.991435	+	0.130600i	$0.0416904\pi$
$47$			1.79070i			0.261200i	−0.991435	+	0.130600i	$0.958310\pi$
$48$	1.20493	+	2.08700i	0.173917	+	0.301233i
$49$	−2.51214	+	4.35115i	−0.358877	+	0.621592i
$50$		0			0
$51$	−16.9667			−2.37581
$52$	0.244364	+	3.59726i	0.0338872	+	0.498850i
$53$	7.93952			1.09058			0.545288	−	0.838248i	$-0.316420\pi$
$53$	7.93952			1.09058			0.545288	+	0.838248i	$0.316420\pi$
$54$	−0.401847	−	0.232006i	−0.0546844	−	0.0315721i
$55$		0			0
$56$	−0.702803	−	1.21729i	−0.0939160	−	0.162667i
$57$			6.36656i			0.843271i
$58$	−3.64862	+	2.10653i	−0.479087	+	0.276601i
$59$	−5.59815	+	3.23210i	−0.728817	+	0.420783i	−0.817989	−	0.575233i	$-0.804911\pi$
$59$	−5.59815	+	3.23210i	−0.728817	+	0.420783i	0.0891719	+	0.996016i	$0.471578\pi$
$60$		0			0
$61$	7.36754	+	12.7610i	0.943317	+	1.63387i	0.759086	+	0.650991i	$0.225646\pi$
$61$	7.36754	+	12.7610i	0.943317	+	1.63387i	0.184232	+	0.982883i	$0.441020\pi$
$62$	−2.53823	+	4.39634i	−0.322355	+	0.558335i
$63$	−3.41749	−	1.97309i	−0.430563	−	0.248586i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	12.7927			1.57467
$67$	−3.46410	−	2.00000i	−0.423207	−	0.244339i	0.273241	−	0.961946i	$-0.411904\pi$
$67$	−3.46410	−	2.00000i	−0.423207	−	0.244339i	−0.696449	+	0.717607i	$0.745238\pi$
$68$	3.52026	−	6.09726i	0.426894	−	0.739401i
$69$	−3.21306	−	5.56518i	−0.386807	−	0.669969i
$70$		0			0
$71$	−8.34802	+	4.81973i	−0.990728	+	0.571997i	−0.905492	−	0.424364i	$-0.860498\pi$
$71$	−8.34802	+	4.81973i	−0.990728	+	0.571997i	−0.0852359	+	0.996361i	$0.527164\pi$
$72$	−2.43133	+	1.40373i	−0.286534	+	0.165431i
$73$		−	7.04281i		−	0.824298i	−0.911116	−	0.412149i	$-0.864778\pi$
$73$		−	7.04281i		−	0.824298i	0.911116	−	0.412149i	$-0.135222\pi$
$74$	−0.412995	−	0.715328i	−0.0480097	−	0.0831552i
$75$		0			0
$76$	−2.28793	−	1.32094i	−0.262443	−	0.151522i
$77$	−7.46160			−0.850329
$78$	−8.66892	+	0.588885i	−0.981561	+	0.0666781i
$79$	−4.05956			−0.456736			−0.228368	−	0.973575i	$-0.573339\pi$
$79$	−4.05956			−0.456736			−0.228368	+	0.973575i	$0.573339\pi$
$80$		0			0
$81$	4.77028	−	8.26237i	0.530031	−	0.918041i
$82$	−1.40550	−	2.43440i	−0.155212	−	0.268834i
$83$			8.55910i			0.939484i	0.882804	+	0.469742i	$0.155653\pi$
$83$			8.55910i			0.939484i	−0.882804	+	0.469742i	$0.844347\pi$
$84$	2.93351	−	1.69366i	0.320072	−	0.184794i
$85$		0			0
$86$			5.28374i			0.569761i
$87$	−5.07645	−	8.79268i	−0.544253	−	0.942674i
$88$	−2.65423	+	4.59726i	−0.282942	+	0.490070i
$89$	13.1289	+	7.57999i	1.39166	+	0.803477i	0.993499	−	0.113838i	$-0.0363143\pi$
$89$	13.1289	+	7.57999i	1.39166	+	0.803477i	0.398163	+	0.917314i	$0.369648\pi$
$90$		0			0
$91$	5.05633	−	0.343480i	0.530048	−	0.0360065i
$92$	2.66659			0.278011
$93$	−10.5946	−	6.11679i	−1.09861	−	0.634281i
$94$	0.895350	−	1.55079i	0.0923483	−	0.159952i
$95$		0			0
$96$		−	2.40987i		−	0.245956i
$97$	3.78155	−	2.18328i	0.383958	−	0.221678i	−0.295581	−	0.955318i	$-0.595513\pi$
$97$	3.78155	−	2.18328i	0.383958	−	0.221678i	0.679539	+	0.733639i	$0.262180\pi$
$98$	4.35115	−	2.51214i	0.439532	−	0.253764i
$99$			14.9033i			1.49783i
$100$		0			0
$101$	4.19353	−	7.26341i	0.417272	−	0.722737i	−0.578392	−	0.815759i	$-0.696319\pi$
$101$	4.19353	−	7.26341i	0.417272	−	0.722737i	0.995664	+	0.0930224i	$0.0296528\pi$
$102$	14.6936	+	8.48334i	1.45488	+	0.839976i
$103$	5.56518			0.548354			0.274177	−	0.961679i	$-0.411595\pi$
$103$	5.56518			0.548354			0.274177	+	0.961679i	$0.411595\pi$
$104$	1.58700	−	3.23750i	0.155619	−	0.317463i
$105$		0			0
$106$	−6.87583	−	3.96976i	−0.667839	−	0.385577i
$107$	7.59234	−	13.1503i	0.733980	−	1.27129i	−0.221190	−	0.975231i	$-0.570994\pi$
$107$	7.59234	−	13.1503i	0.733980	−	1.27129i	0.955170	−	0.296059i	$-0.0956726\pi$
$108$	0.232006	+	0.401847i	0.0223248	+	0.0386677i
$109$		−	0.667003i		−	0.0638873i	−0.999490	−	0.0319436i	$-0.989830\pi$
$109$		−	0.667003i		−	0.0638873i	0.999490	−	0.0319436i	$-0.0101697\pi$
$110$		0			0
$111$	1.72385	−	0.995263i	0.163620	−	0.0944661i
$112$			1.40561i			0.132817i
$113$	1.68456	+	2.91774i	0.158470	+	0.274478i	0.934317	−	0.356443i	$-0.116011\pi$
$113$	1.68456	+	2.91774i	0.158470	+	0.274478i	−0.775847	+	0.630921i	$0.782677\pi$
$114$	3.18328	−	5.51360i	0.298141	−	0.516396i
$115$		0			0
$116$	4.21306			0.391173
$117$	−0.686041	−	10.0991i	−0.0634245	−	0.933666i
$118$	6.46419			0.595077
$119$	−8.57035	−	4.94809i	−0.785642	−	0.453591i
$120$		0			0
$121$	8.58987	+	14.8781i	0.780897	+	1.35255i
$122$		−	14.7351i		−	1.33405i
$123$	5.86658	−	3.38707i	0.528971	−	0.305402i
$124$	4.39634	−	2.53823i	0.394803	−	0.227939i
$125$		0			0
$126$	1.97309	+	3.41749i	0.175777	+	0.304454i
$127$	5.42446	−	9.39545i	0.481343	−	0.833711i	−0.518428	−	0.855122i	$-0.673482\pi$
$127$	5.42446	−	9.39545i	0.481343	−	0.833711i	0.999771	+	0.0214106i	$0.00681573\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−12.7331			−1.12109
$130$		0			0
$131$	15.3500			1.34114			0.670568	−	0.741848i	$-0.266051\pi$
$131$	15.3500			1.34114			0.670568	+	0.741848i	$0.266051\pi$
$132$	−11.0788	−	6.39634i	−0.964284	−	0.556730i
$133$	−1.85672	+	3.21593i	−0.160998	+	0.278856i
$134$	2.00000	+	3.46410i	0.172774	+	0.299253i
$135$		0			0
$136$	−6.09726	+	3.52026i	−0.522836	+	0.301859i
$137$	−9.86475	+	5.69541i	−0.842802	+	0.486592i	−0.858216	−	0.513289i	$-0.828427\pi$
$137$	−9.86475	+	5.69541i	−0.842802	+	0.486592i	0.0154136	+	0.999881i	$0.495094\pi$
$138$			6.42612i			0.547028i
$139$	5.67500	+	9.82938i	0.481347	+	0.833717i	0.999771	−	0.0214063i	$-0.00681437\pi$
$139$	5.67500	+	9.82938i	0.481347	+	0.833717i	−0.518424	+	0.855124i	$0.673481\pi$
$140$		0			0
$141$	3.73720	+	2.15767i	0.314729	+	0.181709i
$142$	9.63946			0.808926
$143$	−10.6714	−	15.8889i	−0.892384	−	1.32870i
$144$	2.80745			0.233954
$145$		0			0
$146$	−3.52140	+	6.09925i	−0.291433	+	0.504778i
$147$	6.05391	+	10.4857i	0.499318	+	0.864844i
$148$			0.825990i			0.0678960i
$149$	−1.70092	+	0.982029i	−0.139345	+	0.0804509i	−0.568052	−	0.822993i	$-0.692303\pi$
$149$	−1.70092	+	0.982029i	−0.139345	+	0.0804509i	0.428707	+	0.903444i	$0.358969\pi$
$150$		0			0
$151$			10.3602i			0.843101i	0.906805	+	0.421550i	$0.138514\pi$
$151$			10.3602i			0.843101i	−0.906805	+	0.421550i	$0.861486\pi$
$152$	1.32094	+	2.28793i	0.107142	+	0.185575i
$153$	−9.88295	+	17.1178i	−0.798989	+	1.38389i
$154$	6.46194	+	3.73080i	0.520718	+	0.300637i
$155$		0			0
$156$	7.80194	+	3.82447i	0.624655	+	0.306203i
$157$	5.83105			0.465368			0.232684	−	0.972552i	$-0.425249\pi$
$157$	5.83105			0.465368			0.232684	+	0.972552i	$0.425249\pi$
$158$	3.51568	+	2.02978i	0.279693	+	0.161481i
$159$	9.56659	−	16.5698i	0.758680	−	1.31407i
$160$		0			0
$161$		−	3.74817i		−	0.295397i
$162$	−8.26237	+	4.77028i	−0.649153	+	0.374789i
$163$	10.1774	−	5.87592i	0.797155	−	0.460238i	−0.0453204	−	0.998973i	$-0.514431\pi$
$163$	10.1774	−	5.87592i	0.797155	−	0.460238i	0.842475	+	0.538735i	$0.181098\pi$
$164$			2.81100i			0.219502i
$165$		0			0
$166$	4.27955	−	7.41240i	0.332158	−	0.575314i
$167$	−9.67869	−	5.58799i	−0.748959	−	0.432412i	0.0763585	−	0.997080i	$-0.475671\pi$
$167$	−9.67869	−	5.58799i	−0.748959	−	0.432412i	−0.825318	+	0.564669i	$0.809004\pi$
$168$	−3.38732			−0.261338
$169$	7.96283	+	10.2759i	0.612525	+	0.790451i
$170$		0			0
$171$	6.42325	+	3.70847i	0.491198	+	0.283593i
$172$	2.64187	−	4.57586i	0.201441	−	0.348906i
$173$	0.266700	+	0.461938i	0.0202768	+	0.0351205i	0.875986	−	0.482337i	$-0.160212\pi$
$173$	0.266700	+	0.461938i	0.0202768	+	0.0351205i	−0.855709	+	0.517457i	$0.826879\pi$
$174$			10.1529i			0.769690i
$175$		0			0
$176$	4.59726	−	2.65423i	0.346532	−	0.200070i
$177$			15.5778i			1.17090i
$178$	−7.57999	−	13.1289i	−0.568144	−	0.984054i
$179$	4.61867	−	7.99976i	0.345215	−	0.597930i	−0.640178	−	0.768227i	$-0.721139\pi$
$179$	4.61867	−	7.99976i	0.345215	−	0.597930i	0.985393	+	0.170297i	$0.0544726\pi$
$180$		0			0
$181$	−4.76464			−0.354153			−0.177077	−	0.984197i	$-0.556664\pi$
$181$	−4.76464			−0.354153			−0.177077	+	0.984197i	$0.556664\pi$
$182$	−4.55065	−	2.23070i	−0.337317	−	0.165351i
$183$	35.5096			2.62494
$184$	−2.30933	−	1.33329i	−0.170246	−	0.0982917i
$185$		0			0
$186$	6.11679	+	10.5946i	0.448504	+	0.776833i
$187$			37.3743i			2.73308i
$188$	−1.55079	+	0.895350i	−0.113103	+	0.0653001i
$189$	0.564838	−	0.326110i	0.0410859	−	0.0237210i
$190$		0			0
$191$	8.97219	+	15.5403i	0.649205	+	1.12446i	0.983313	+	0.181922i	$0.0582317\pi$
$191$	8.97219	+	15.5403i	0.649205	+	1.12446i	−0.334108	+	0.942535i	$0.608435\pi$
$192$	−1.20493	+	2.08700i	−0.0869585	+	0.150617i
$193$	18.1399	+	10.4731i	1.30574	+	0.753869i	0.981382	−	0.192065i	$-0.0615185\pi$
$193$	18.1399	+	10.4731i	1.30574	+	0.753869i	0.324358	+	0.945934i	$0.394852\pi$
$194$	−4.36656			−0.313501
$195$		0			0
$196$	−5.02427			−0.358877
$197$	23.1855	+	13.3862i	1.65190	+	0.953726i	0.976290	+	0.216468i	$0.0694536\pi$
$197$	23.1855	+	13.3862i	1.65190	+	0.953726i	0.675611	+	0.737258i	$0.263880\pi$
$198$	7.45163	−	12.9066i	0.529564	−	0.917232i
$199$	7.19452	+	12.4613i	0.510006	+	0.883357i	0.999933	+	0.0115929i	$0.00369021\pi$
$199$	7.19452	+	12.4613i	0.510006	+	0.883357i	−0.489927	+	0.871764i	$0.662976\pi$
$200$		0			0
$201$	−8.34802	+	4.81973i	−0.588824	+	0.339958i
$202$	−7.26341	+	4.19353i	−0.511052	+	0.295056i
$203$		−	5.92190i		−	0.415636i
$204$	−8.48334	−	14.6936i	−0.593953	−	1.02876i
$205$		0			0
$206$	−4.81959	−	2.78259i	−0.335797	−	0.193872i
$207$	−7.48632			−0.520335
$208$	−2.99314	+	2.01026i	−0.207537	+	0.139386i
$209$	14.0243			0.970079
$210$		0			0
$211$	12.1954	−	21.1231i	0.839567	−	1.45417i	−0.0506903	−	0.998714i	$-0.516142\pi$
$211$	12.1954	−	21.1231i	0.839567	−	1.45417i	0.890257	−	0.455458i	$-0.150525\pi$
$212$	3.96976	+	6.87583i	0.272644	+	0.472234i
$213$			23.2298i			1.59168i
$214$	−13.1503	+	7.59234i	−0.898938	+	0.519002i
$215$		0			0
$216$		−	0.464013i		−	0.0315721i
$217$	−3.56775	−	6.17952i	−0.242194	−	0.419493i
$218$	−0.333501	+	0.577641i	−0.0225876	+	0.0391228i
$219$	−14.6984	−	8.48611i	−0.993224	−	0.573438i
$220$		0			0
$221$	−1.72045	−	25.3266i	−0.115730	−	1.70365i
$222$	−1.99053			−0.133595
$223$	−2.58031	−	1.48974i	−0.172790	−	0.0997606i	0.411110	−	0.911586i	$-0.365141\pi$
$223$	−2.58031	−	1.48974i	−0.172790	−	0.0997606i	−0.583901	+	0.811825i	$0.698474\pi$
$224$	0.702803	−	1.21729i	0.0469580	−	0.0813337i
$225$		0			0
$226$		−	3.36912i		−	0.224110i
$227$	3.43199	−	1.98146i	0.227789	−	0.131514i	−0.381762	−	0.924260i	$-0.624683\pi$
$227$	3.43199	−	1.98146i	0.227789	−	0.131514i	0.609552	+	0.792746i	$0.291349\pi$
$228$	−5.51360	+	3.18328i	−0.365147	+	0.210818i
$229$		−	9.85151i		−	0.651006i	−0.945541	−	0.325503i	$-0.894466\pi$
$229$		−	9.85151i		−	0.651006i	0.945541	−	0.325503i	$-0.105534\pi$
$230$		0			0
$231$	−8.99073	+	15.5724i	−0.591547	+	1.02459i
$232$	−3.64862	−	2.10653i	−0.239543	−	0.138300i
$233$	−19.3821			−1.26976			−0.634881	−	0.772610i	$-0.718951\pi$
$233$	−19.3821			−1.26976			−0.634881	+	0.772610i	$0.718951\pi$
$234$	−4.45544	+	9.08913i	−0.291261	+	0.594175i
$235$		0			0
$236$	−5.59815	−	3.23210i	−0.364409	−	0.210391i
$237$	−4.89150	+	8.47232i	−0.317737	+	0.550337i
$238$	4.94809	+	8.57035i	0.320737	+	0.555533i
$239$		−	30.0138i		−	1.94143i	−0.240232	−	0.970715i	$-0.577224\pi$
$239$		−	30.0138i		−	1.94143i	0.240232	−	0.970715i	$-0.422776\pi$
$240$		0			0
$241$	−16.5815	+	9.57333i	−1.06811	+	0.616672i	−0.927664	−	0.373416i	$-0.878186\pi$
$241$	−16.5815	+	9.57333i	−1.06811	+	0.616672i	−0.140444	+	0.990089i	$0.544853\pi$
$242$		−	17.1797i		−	1.10436i
$243$	−10.7997	−	18.7057i	−0.692803	−	1.19997i
$244$	−7.36754	+	12.7610i	−0.471659	+	0.816937i
$245$		0			0
$246$	−6.77414			−0.431903
$247$	−9.50350	+	0.645579i	−0.604693	+	0.0410772i
$248$	−5.07645			−0.322355
$249$	17.8629	+	10.3131i	1.13201	+	0.653569i
$250$		0			0
$251$	−8.52150	−	14.7597i	−0.537872	−	0.931622i	−0.999018	−	0.0442979i	$-0.985895\pi$
$251$	−8.52150	−	14.7597i	−0.537872	−	0.931622i	0.461146	−	0.887324i	$-0.347438\pi$
$252$		−	3.94617i		−	0.248586i
$253$	−12.2590	+	7.07774i	−0.770717	+	0.444973i
$254$	−9.39545	+	5.42446i	−0.589523	+	0.340361i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.11263	+	7.12328i	−0.256539	+	0.444338i	−0.965312	−	0.261098i	$-0.915915\pi$
$257$	−4.11263	+	7.12328i	−0.256539	+	0.444338i	0.708774	+	0.705436i	$0.249249\pi$
$258$	11.0272	+	6.36656i	0.686523	+	0.396365i
$259$	1.16102			0.0721421
$260$		0			0
$261$	−11.8280			−0.732133
$262$	−13.2935	−	7.67500i	−0.821274	−	0.474163i
$263$	−5.21479	+	9.03229i	−0.321558	+	0.556955i	−0.980810	−	0.194968i	$-0.937540\pi$
$263$	−5.21479	+	9.03229i	−0.321558	+	0.556955i	0.659252	+	0.751922i	$0.270873\pi$
$264$	6.39634	+	11.0788i	0.393667	+	0.681852i
$265$		0			0
$266$	3.21593	−	1.85672i	0.197181	−	0.113843i
$267$	31.6389	−	18.2667i	1.93627	−	1.11791i
$268$		−	4.00000i		−	0.244339i
$269$	−11.3206	−	19.6078i	−0.690228	−	1.19551i	−0.971763	−	0.235959i	$-0.924177\pi$
$269$	−11.3206	−	19.6078i	−0.690228	−	1.19551i	0.281535	−	0.959551i	$-0.409156\pi$
$270$		0			0
$271$	0.218603	+	0.126211i	0.0132792	+	0.00766675i	0.506625	−	0.862167i	$-0.330893\pi$
$271$	0.218603	+	0.126211i	0.0132792	+	0.00766675i	−0.493346	+	0.869833i	$0.664226\pi$
$272$	7.04051			0.426894
$273$	5.37570	−	10.9665i	0.325352	−	0.663720i
$274$	11.3908			0.688145
$275$		0			0
$276$	3.21306	−	5.56518i	0.193403	−	0.334985i
$277$	−2.32768	−	4.03166i	−0.139857	−	0.242239i	0.787586	−	0.616205i	$-0.211331\pi$
$277$	−2.32768	−	4.03166i	−0.139857	−	0.242239i	−0.927442	+	0.373966i	$0.877998\pi$
$278$		−	11.3500i		−	0.680727i
$279$	−12.3425	+	7.12595i	−0.738927	+	0.426620i
$280$		0			0
$281$			3.70262i			0.220880i	0.993883	+	0.110440i	$0.0352260\pi$
$281$			3.70262i			0.220880i	−0.993883	+	0.110440i	$0.964774\pi$
$282$	−2.15767	−	3.73720i	−0.128488	−	0.222547i
$283$	−2.67398	+	4.63147i	−0.158952	+	0.275312i	−0.934491	−	0.355987i	$-0.884145\pi$
$283$	−2.67398	+	4.63147i	−0.158952	+	0.275312i	0.775539	+	0.631299i	$0.217478\pi$
$284$	−8.34802	−	4.81973i	−0.495364	−	0.285998i
$285$		0			0
$286$	1.29720	+	19.0959i	0.0767049	+	1.12917i
$287$	3.95116			0.233230
$288$	−2.43133	−	1.40373i	−0.143267	−	0.0827154i
$289$	−16.2844	+	28.2054i	−0.957906	+	1.65914i
$290$		0			0
$291$		−	10.5228i		−	0.616858i
$292$	6.09925	−	3.52140i	0.356932	−	0.206075i
$293$	−20.9355	+	12.0871i	−1.22306	+	0.706136i	−0.965570	−	0.260144i	$-0.916230\pi$
$293$	−20.9355	+	12.0871i	−1.22306	+	0.706136i	−0.257493	+	0.966280i	$0.582897\pi$
$294$		−	12.1078i		−	0.706142i
$295$		0			0
$296$	0.412995	−	0.715328i	0.0240048	−	0.0415776i
$297$	−2.13319	−	1.23160i	−0.123780	−	0.0714645i
$298$	1.96406			0.113775
$299$	7.98146	−	5.36052i	0.461580	−	0.310007i
$300$		0			0
$301$	−6.43185	−	3.71343i	−0.370726	−	0.214039i
$302$	5.18010	−	8.97219i	0.298081	−	0.516292i
$303$	−10.1059	−	17.5039i	−0.580566	−	1.00557i
$304$		−	2.64187i		−	0.151522i
$305$		0			0
$306$	17.1178	−	9.88295i	0.978558	−	0.564971i
$307$		−	27.5443i		−	1.57204i	−0.618203	−	0.786019i	$-0.712139\pi$
$307$		−	27.5443i		−	1.57204i	0.618203	−	0.786019i	$-0.287861\pi$
$308$	−3.73080	−	6.46194i	−0.212582	−	0.368203i
$309$	6.70567	−	11.6146i	0.381472	−	0.660729i
$310$		0			0
$311$	12.8262			0.727306			0.363653	−	0.931534i	$-0.381529\pi$
$311$	12.8262			0.727306			0.363653	+	0.931534i	$0.381529\pi$
$312$	−4.84445	−	7.21306i	−0.274263	−	0.408359i
$313$	2.72604			0.154085			0.0770425	−	0.997028i	$-0.475452\pi$
$313$	2.72604			0.154085			0.0770425	+	0.997028i	$0.475452\pi$
$314$	−5.04984	−	2.91552i	−0.284979	−	0.164533i
$315$		0			0
$316$	−2.02978	−	3.51568i	−0.114184	−	0.197773i
$317$			1.89961i			0.106692i	0.998576	+	0.0533462i	$0.0169887\pi$
$317$			1.89961i			0.106692i	−0.998576	+	0.0533462i	$0.983011\pi$
$318$	−16.5698	+	9.56659i	−0.929189	+	0.536468i
$319$	−19.3685	+	11.1824i	−1.08443	+	0.626096i
$320$		0			0
$321$	−18.2965	−	31.6905i	−1.02121	−	1.76879i
$322$	−1.87409	+	3.24601i	−0.104439	+	0.180893i
$323$	16.1082	+	9.30006i	0.896283	+	0.517469i
$324$	9.54057			0.530031
$325$		0			0
$326$	−11.7518			−0.650874
$327$	−1.39204	−	0.803694i	−0.0769799	−	0.0444444i
$328$	1.40550	−	2.43440i	0.0776058	−	0.134417i
$329$	1.25851	+	2.17980i	0.0693839	+	0.120176i
$330$		0			0
$331$	7.78318	−	4.49362i	0.427802	−	0.246992i	−0.270608	−	0.962690i	$-0.587225\pi$
$331$	7.78318	−	4.49362i	0.427802	−	0.246992i	0.698410	+	0.715698i	$0.253891\pi$
$332$	−7.41240	+	4.27955i	−0.406808	+	0.234871i
$333$		−	2.31893i		−	0.127076i
$334$	5.58799	+	9.67869i	0.305761	+	0.529594i
$335$		0			0
$336$	2.93351	+	1.69366i	0.160036	+	0.0923968i
$337$	1.37859			0.0750967			0.0375484	−	0.999295i	$-0.488045\pi$
$337$	1.37859			0.0750967			0.0375484	+	0.999295i	$0.488045\pi$
$338$	−1.75808	−	12.8806i	−0.0956271	−	0.700611i
$339$	8.11912			0.440970
$340$		0			0
$341$	−13.4741	+	23.3378i	−0.729662	+	1.26381i
$342$	−3.70847	−	6.42325i	−0.200531	−	0.347330i
$343$			16.9014i			0.912589i
$344$	−4.57586	+	2.64187i	−0.246714	+	0.142440i
$345$		0			0
$346$		−	0.533400i		−	0.0286758i
$347$	5.94788	+	10.3020i	0.319299	+	0.553042i	0.980342	−	0.197306i	$-0.0632192\pi$
$347$	5.94788	+	10.3020i	0.319299	+	0.553042i	−0.661043	+	0.750348i	$0.729886\pi$
$348$	5.07645	−	8.79268i	0.272126	−	0.471337i
$349$	−3.95580	−	2.28388i	−0.211749	−	0.122254i	0.390375	−	0.920656i	$-0.372345\pi$
$349$	−3.95580	−	2.28388i	−0.211749	−	0.122254i	−0.602124	+	0.798403i	$0.705679\pi$
$350$		0			0
$351$	1.50224	+	0.736390i	0.0801837	+	0.0393056i
$352$	−5.30846			−0.282942
$353$	0.729210	+	0.421009i	0.0388119	+	0.0224081i	0.519280	−	0.854604i	$-0.326200\pi$
$353$	0.729210	+	0.421009i	0.0388119	+	0.0224081i	−0.480468	+	0.877012i	$0.659533\pi$
$354$	7.78892	−	13.4908i	0.413976	−	0.717028i
$355$		0			0
$356$			15.1600i			0.803477i
$357$	−20.6534	+	11.9242i	−1.09309	+	0.631098i
$358$	−7.99976	+	4.61867i	−0.422801	+	0.244104i
$359$			8.05922i			0.425349i	0.977123	+	0.212675i	$0.0682174\pi$
$359$			8.05922i			0.425349i	−0.977123	+	0.212675i	$0.931783\pi$
$360$		0			0
$361$	−6.01026	+	10.4101i	−0.316329	+	0.547898i
$362$	4.12630	+	2.38232i	0.216874	+	0.125212i
$363$	41.4009			2.17298
$364$	2.82563	+	4.20717i	0.148103	+	0.220516i
$365$		0			0
$366$	−30.7522	−	17.7548i	−1.60744	−	0.928058i
$367$	−8.25912	+	14.3052i	−0.431122	+	0.746726i	−0.996970	−	0.0777837i	$-0.975216\pi$
$367$	−8.25912	+	14.3052i	−0.431122	+	0.746726i	0.565848	+	0.824510i	$0.308549\pi$
$368$	1.33329	+	2.30933i	0.0695027	+	0.120382i
$369$		−	7.89176i		−	0.410828i
$370$		0			0
$371$	9.66470	−	5.57992i	0.501766	−	0.289695i
$372$		−	12.2336i		−	0.634281i
$373$	−13.2773	−	22.9969i	−0.687471	−	1.19073i	−0.972653	−	0.232261i	$-0.925388\pi$
$373$	−13.2773	−	22.9969i	−0.687471	−	1.19073i	0.285183	−	0.958473i	$-0.407946\pi$
$374$	18.6871	−	32.3671i	0.966289	−	1.67366i
$375$		0			0
$376$	1.79070			0.0923483
$377$	12.6103	−	8.46933i	0.649462	−	0.436193i
$378$	−0.652219			−0.0335465
$379$	1.00089	+	0.577865i	0.0514124	+	0.0296830i	0.525486	−	0.850802i	$-0.323884\pi$
$379$	1.00089	+	0.577865i	0.0514124	+	0.0296830i	−0.474073	+	0.880485i	$0.657217\pi$
$380$		0			0
$381$	−13.0722	−	22.6418i	−0.669710	−	1.15997i
$382$		−	17.9444i		−	0.918115i
$383$	−30.3176	+	17.5039i	−1.54916	+	0.894405i	−0.550949	+	0.834539i	$0.685734\pi$
$383$	−30.3176	+	17.5039i	−1.54916	+	0.894405i	−0.998206	+	0.0598661i	$0.980933\pi$
$384$	2.08700	−	1.20493i	0.106502	−	0.0614890i
$385$		0			0
$386$	−10.4731	−	18.1399i	−0.533066	−	0.923298i
$387$	−7.41693	+	12.8465i	−0.377024	+	0.653024i
$388$	3.78155	+	2.18328i	0.191979	+	0.110839i
$389$	−11.3135			−0.573615			−0.286807	−	0.957988i	$-0.592594\pi$
$389$	−11.3135			−0.573615			−0.286807	+	0.957988i	$0.592594\pi$
$390$		0			0
$391$	−18.7741			−0.949449
$392$	4.35115	+	2.51214i	0.219766	+	0.126882i
$393$	18.4957	−	32.0355i	0.932985	−	1.61598i
$394$	−13.3862	−	23.1855i	−0.674386	−	1.16807i
$395$		0			0
$396$	−12.9066	+	7.45163i	−0.648581	+	0.374458i
$397$	−15.5934	+	9.00287i	−0.782611	+	0.451841i	−0.837355	−	0.546660i	$-0.815899\pi$
$397$	−15.5934	+	9.00287i	−0.782611	+	0.451841i	0.0547435	+	0.998500i	$0.482566\pi$
$398$		−	14.3890i		−	0.721258i
$399$	4.47444	+	7.74995i	0.224002	+	0.387983i
$400$		0			0
$401$	3.97385	+	2.29430i	0.198445	+	0.114572i	0.595930	−	0.803037i	$-0.296784\pi$
$401$	3.97385	+	2.29430i	0.198445	+	0.114572i	−0.397485	+	0.917609i	$0.630117\pi$
$402$	9.63946			0.480773
$403$	8.05636	−	16.4350i	0.401316	−	0.818687i
$404$	8.38707			0.417272
$405$		0			0
$406$	−2.96095	+	5.12852i	−0.146950	+	0.254524i
$407$	−2.19237	−	3.79729i	−0.108672	−	0.188225i
$408$			16.9667i			0.839976i
$409$	22.7332	−	13.1250i	1.12408	−	0.648991i	0.181644	−	0.983364i	$-0.441858\pi$
$409$	22.7332	−	13.1250i	1.12408	−	0.648991i	0.942441	+	0.334374i	$0.108525\pi$
$410$		0			0
$411$			27.4504i			1.35403i
$412$	2.78259	+	4.81959i	0.137088	+	0.237444i
$413$	−4.54305	+	7.86880i	−0.223549	+	0.387198i
$414$	6.48334	+	3.74316i	0.318639	+	0.183966i
$415$		0			0
$416$	3.59726	−	0.244364i	0.176370	−	0.0119809i
$417$	27.3520			1.33943
$418$	−12.1454	−	7.01214i	−0.594050	−	0.342975i
$419$	−6.03869	+	10.4593i	−0.295009	+	0.510971i	−0.974987	−	0.222262i	$-0.928656\pi$
$419$	−6.03869	+	10.4593i	−0.295009	+	0.510971i	0.679978	+	0.733233i	$0.261989\pi$
$420$		0			0
$421$		−	3.11716i		−	0.151921i	−0.997111	−	0.0759604i	$-0.975798\pi$
$421$		−	3.11716i		−	0.151921i	0.997111	−	0.0759604i	$-0.0242023\pi$
$422$	−21.1231	+	12.1954i	−1.02826	+	0.593663i
$423$	4.35378	−	2.51365i	0.211688	−	0.122218i
$424$		−	7.93952i		−	0.385577i
$425$		0			0
$426$	11.6149	−	20.1176i	0.562744	−	0.974701i
$427$	17.9369	+	10.3559i	0.868027	+	0.501155i
$428$	15.1847			0.733980
$429$	−46.0186	+	3.12607i	−2.22180	+	0.150928i
$430$		0			0
$431$	4.52932	+	2.61501i	0.218170	+	0.125960i	0.605103	−	0.796148i	$-0.293132\pi$
$431$	4.52932	+	2.61501i	0.218170	+	0.125960i	−0.386933	+	0.922108i	$0.626465\pi$
$432$	−0.232006	+	0.401847i	−0.0111624	+	0.0193339i
$433$	11.1531	+	19.3178i	0.535986	+	0.928354i	0.999115	+	0.0420637i	$0.0133932\pi$
$433$	11.1531	+	19.3178i	0.535986	+	0.928354i	−0.463129	+	0.886291i	$0.653273\pi$
$434$			7.13549i			0.342515i
$435$		0			0
$436$	0.577641	−	0.333501i	0.0276640	−	0.0159718i
$437$			7.04478i			0.336998i
$438$	8.48611	+	14.6984i	0.405482	+	0.702316i
$439$	−2.62417	+	4.54520i	−0.125245	+	0.216931i	−0.921829	−	0.387598i	$-0.873305\pi$
$439$	−2.62417	+	4.54520i	−0.125245	+	0.216931i	0.796584	+	0.604528i	$0.206638\pi$
$440$		0			0
$441$	14.1054			0.671686
$442$	−11.1733	+	22.7937i	−0.531461	+	1.08418i
$443$	−1.11623			−0.0530338			−0.0265169	−	0.999648i	$-0.508442\pi$
$443$	−1.11623			−0.0530338			−0.0265169	+	0.999648i	$0.508442\pi$
$444$	1.72385	+	0.995263i	0.0818101	+	0.0472331i
$445$		0			0
$446$	1.48974	+	2.58031i	0.0705414	+	0.122181i
$447$			4.73311i			0.223869i
$448$	−1.21729	+	0.702803i	−0.0575116	+	0.0332043i
$449$	−29.8678	+	17.2442i	−1.40955	+	0.813802i	−0.995344	−	0.0963822i	$-0.969273\pi$
$449$	−29.8678	+	17.2442i	−1.40955	+	0.813802i	−0.414203	+	0.910185i	$0.635940\pi$
$450$		0			0
$451$	−7.46105	−	12.9229i	−0.351327	−	0.608516i
$452$	−1.68456	+	2.91774i	−0.0792350	+	0.137239i
$453$	21.6218	+	12.4833i	1.01588	+	0.586519i
$454$	−3.96293			−0.185989
$455$		0			0
$456$	6.36656			0.298141
$457$	3.52940	+	2.03770i	0.165098	+	0.0953196i	0.580273	−	0.814422i	$-0.302946\pi$
$457$	3.52940	+	2.03770i	0.165098	+	0.0953196i	−0.415174	+	0.909742i	$0.636279\pi$
$458$	−4.92576	+	8.53166i	−0.230165	+	0.398658i
$459$	−1.63344	−	2.82921i	−0.0762426	−	0.132056i
$460$		0			0
$461$	26.2766	−	15.1708i	1.22383	−	0.706576i	0.258094	−	0.966120i	$-0.416906\pi$
$461$	26.2766	−	15.1708i	1.22383	−	0.706576i	0.965731	+	0.259544i	$0.0835722\pi$
$462$	15.5724	−	8.99073i	0.724494	−	0.418287i
$463$		−	25.2291i		−	1.17250i	−0.810132	−	0.586248i	$-0.800605\pi$
$463$		−	25.2291i		−	1.17250i	0.810132	−	0.586248i	$-0.199395\pi$
$464$	2.10653	+	3.64862i	0.0977932	+	0.169383i
$465$		0			0
$466$	16.7854	+	9.69104i	0.777568	+	0.448929i
$467$	−21.9997			−1.01802			−0.509012	−	0.860759i	$-0.669989\pi$
$467$	−21.9997			−1.01802			−0.509012	+	0.860759i	$0.669989\pi$
$468$	8.40309	−	5.64370i	0.388433	−	0.260880i
$469$	−5.62242			−0.259619
$470$		0			0
$471$	7.02602	−	12.1694i	0.323742	−	0.560738i
$472$	3.23210	+	5.59815i	0.148769	+	0.257676i
$473$			28.0485i			1.28967i
$474$	8.47232	−	4.89150i	0.389147	−	0.224674i
$475$		0			0
$476$		−	9.89618i		−	0.453591i
$477$	−11.1449	−	19.3036i	−0.510291	−	0.883849i
$478$	−15.0069	+	25.9927i	−0.686399	+	1.18888i
$479$	19.1462	+	11.0541i	0.874812	+	0.505073i	0.868944	−	0.494910i	$-0.164799\pi$
$479$	19.1462	+	11.0541i	0.874812	+	0.505073i	0.00586793	+	0.999983i	$0.498132\pi$
$480$		0			0
$481$	1.66045	+	2.47230i	0.0757101	+	0.112727i
$482$	19.1467			0.872107
$483$	−7.82245	−	4.51630i	−0.355934	−	0.205499i
$484$	−8.58987	+	14.8781i	−0.390449	+	0.676277i
$485$		0			0
$486$			21.5994i			0.979771i
$487$	3.17722	−	1.83437i	0.143973	−	0.0831231i	−0.426283	−	0.904590i	$-0.640177\pi$
$487$	3.17722	−	1.83437i	0.143973	−	0.0831231i	0.570256	+	0.821467i	$0.306844\pi$
$488$	12.7610	−	7.36754i	0.577662	−	0.333513i
$489$		−	28.3204i		−	1.28069i
$490$		0			0
$491$	−13.2345	+	22.9228i	−0.597263	+	1.03449i	0.395960	+	0.918268i	$0.370412\pi$
$491$	−13.2345	+	22.9228i	−0.597263	+	1.03449i	−0.993223	+	0.116222i	$0.962922\pi$
$492$	5.86658	+	3.38707i	0.264486	+	0.152701i
$493$	−29.6621			−1.33591
$494$	8.55306	+	4.19266i	0.384821	+	0.188637i
$495$		0			0
$496$	4.39634	+	2.53823i	0.197401	+	0.113970i
$497$	−6.77464	+	11.7340i	−0.303884	+	0.526343i
$498$	−10.3131	−	17.8629i	−0.462143	−	0.800455i
$499$			37.0404i			1.65816i	0.559133	+	0.829078i	$0.311134\pi$
$499$			37.0404i			1.65816i	−0.559133	+	0.829078i	$0.688866\pi$
$500$		0			0
$501$	−23.3243	+	13.4663i	−1.04205	+	0.601630i
$502$			17.0430i			0.760666i
$503$	17.0098	+	29.4618i	0.758429	+	1.31364i	0.943652	+	0.330940i	$0.107366\pi$
$503$	17.0098	+	29.4618i	0.758429	+	1.31364i	−0.185223	+	0.982696i	$0.559301\pi$
$504$	−1.97309	+	3.41749i	−0.0878883	+	0.152227i
$505$		0			0
$506$	14.1555			0.629288
$507$	31.0405	−	4.23674i	1.37855	−	0.188160i
$508$	10.8489			0.481343
$509$	13.9811	+	8.07197i	0.619700	+	0.357784i	0.776752	−	0.629806i	$-0.216866\pi$
$509$	13.9811	+	8.07197i	0.619700	+	0.357784i	−0.157052	+	0.987590i	$0.550199\pi$
$510$		0			0
$511$	−4.94971	−	8.57314i	−0.218962	−	0.379254i
$512$			1.00000i			0.0441942i
$513$	−1.06163	+	0.612931i	−0.0468720	+	0.0270616i
$514$	7.12328	−	4.11263i	0.314195	−	0.181400i
$515$		0			0
$516$	−6.36656	−	11.0272i	−0.280272	−	0.485445i
$517$	4.75293	−	8.23232i	0.209034	−	0.362057i
$518$	−1.00547	−	0.580508i	−0.0441778	−	0.0255061i
$519$	1.28542			0.0564238
$520$		0			0
$521$	−36.5483			−1.60121			−0.800605	−	0.599193i	$-0.795488\pi$
$521$	−36.5483			−1.60121			−0.800605	+	0.599193i	$0.795488\pi$
$522$	10.2433	+	5.91398i	0.448338	+	0.258848i
$523$	0.333501	−	0.577641i	0.0145830	−	0.0252585i	−0.858642	−	0.512576i	$-0.828691\pi$
$523$	0.333501	−	0.577641i	0.0145830	−	0.0252585i	0.873225	+	0.487318i	$0.162025\pi$
$524$	7.67500	+	13.2935i	0.335284	+	0.580729i
$525$		0			0
$526$	9.03229	−	5.21479i	0.393826	−	0.227376i
$527$	−30.9525	+	17.8704i	−1.34831	+	0.778447i
$528$		−	12.7927i		−	0.556730i
$529$	7.94466	+	13.7605i	0.345420	+	0.598285i
$530$		0			0
$531$	15.7166	+	9.07396i	0.682040	+	0.393776i
$532$	−3.71343			−0.160998
$533$	5.65083	+	8.41372i	0.244765	+	0.364438i
$534$	−36.5335			−1.58096
$535$		0			0
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	−11.1304	−	19.2784i	−0.480311	−	0.831922i
$538$			22.6412i			0.976129i
$539$	23.0979	−	13.3356i	0.994896	−	0.574404i
$540$		0			0
$541$		−	7.70275i		−	0.331167i	−0.986196	−	0.165584i	$-0.947049\pi$
$541$		−	7.70275i		−	0.331167i	0.986196	−	0.165584i	$-0.0529508\pi$
$542$	−0.126211	−	0.218603i	−0.00542121	−	0.00938981i
$543$	−5.74108	+	9.94384i	−0.246373	+	0.426731i
$544$	−6.09726	−	3.52026i	−0.261418	−	0.150930i
$545$		0			0
$546$	−10.1387	+	6.80938i	−0.433897	+	0.291415i
$547$	27.5445			1.17772			0.588858	−	0.808236i	$-0.299578\pi$
$547$	27.5445			1.17772			0.588858	+	0.808236i	$0.299578\pi$
$548$	−9.86475	−	5.69541i	−0.421401	−	0.243296i
$549$	20.6840	−	35.8258i	0.882773	−	1.52901i
$550$		0			0
$551$			11.1304i			0.474169i
$552$	−5.56518	+	3.21306i	−0.236870	+	0.136757i
$553$	−4.94167	+	2.85307i	−0.210141	+	0.121325i
$554$			4.65536i			0.197787i
$555$		0			0
$556$	−5.67500	+	9.82938i	−0.240673	+	0.416859i
$557$	−3.60503	−	2.08137i	−0.152750	−	0.0881903i	0.421677	−	0.906746i	$-0.361442\pi$
$557$	−3.60503	−	2.08137i	−0.152750	−	0.0881903i	−0.574427	+	0.818556i	$0.694775\pi$
$558$	14.2519			0.603331
$559$	−1.29116	−	19.0070i	−0.0546101	−	0.803911i
$560$		0			0
$561$	78.0003	+	45.0335i	3.29317	+	1.90132i
$562$	1.85131	−	3.20656i	0.0780928	−	0.135261i
$563$	−15.7949	−	27.3575i	−0.665674	−	1.15298i	−0.979102	−	0.203370i	$-0.934811\pi$
$563$	−15.7949	−	27.3575i	−0.665674	−	1.15298i	0.313428	−	0.949612i	$-0.398523\pi$
$564$			4.31535i			0.181709i
$565$		0			0
$566$	4.63147	−	2.67398i	0.194675	−	0.112396i
$567$		−	13.4103i		−	0.563179i
$568$	4.81973	+	8.34802i	0.202231	+	0.350275i
$569$	−11.9583	+	20.7124i	−0.501318	+	0.868309i	0.498680	+	0.866786i	$0.333818\pi$
$569$	−11.9583	+	20.7124i	−0.501318	+	0.868309i	−0.999999	+	0.00152301i	$0.999515\pi$
$570$		0			0
$571$	0.653231			0.0273369			0.0136684	−	0.999907i	$-0.495649\pi$
$571$	0.653231			0.0273369			0.0136684	+	0.999907i	$0.495649\pi$
$572$	8.42455	−	17.1861i	0.352248	−	0.718589i
$573$	43.2436			1.80653
$574$	−3.42181	−	1.97558i	−0.142823	−	0.0824592i
$575$		0			0
$576$	1.40373	+	2.43133i	0.0584886	+	0.101305i
$577$		−	21.3167i		−	0.887425i	−0.896169	−	0.443712i	$-0.853661\pi$
$577$		−	21.3167i		−	0.887425i	0.896169	−	0.443712i	$-0.146339\pi$
$578$	28.2054	−	16.2844i	1.17319	−	0.677341i
$579$	43.7148	−	25.2387i	1.81672	−	1.04889i
$580$		0			0
$581$	6.01536	+	10.4189i	0.249559	+	0.432250i
$582$	−5.26141	+	9.11303i	−0.218092	+	0.377747i
$583$	−36.5000	−	21.0733i	−1.51168	−	0.872767i
$584$	−7.04281			−0.291433
$585$		0			0
$586$	24.1742			0.998627
$587$	−13.1894	−	7.61491i	−0.544385	−	0.314301i	0.202469	−	0.979289i	$-0.435103\pi$
$587$	−13.1894	−	7.61491i	−0.544385	−	0.314301i	−0.746854	+	0.664988i	$0.768437\pi$
$588$	−6.05391	+	10.4857i	−0.249659	+	0.432422i
$589$	6.70567	+	11.6146i	0.276302	+	0.478570i
$590$		0			0
$591$	55.8740	−	32.2589i	2.29835	−	1.32695i
$592$	−0.715328	+	0.412995i	−0.0293998	+	0.0169740i
$593$			9.70527i			0.398548i	0.979944	+	0.199274i	$0.0638583\pi$
$593$			9.70527i			0.398548i	−0.979944	+	0.199274i	$0.936142\pi$
$594$	1.23160	+	2.13319i	0.0505330	+	0.0875257i
$595$		0			0
$596$	−1.70092	−	0.982029i	−0.0696725	−	0.0402255i
$597$	34.6757			1.41918
$598$	−9.59241	+	0.651618i	−0.392263	+	0.0266467i
$599$	1.20026			0.0490411			0.0245206	−	0.999699i	$-0.492194\pi$
$599$	1.20026			0.0490411			0.0245206	+	0.999699i	$0.492194\pi$
$600$		0			0
$601$	−7.03681	+	12.1881i	−0.287037	+	0.497163i	−0.973101	−	0.230378i	$-0.926004\pi$
$601$	−7.03681	+	12.1881i	−0.287037	+	0.497163i	0.686064	+	0.727541i	$0.259337\pi$
$602$	3.71343	+	6.43185i	0.151348	+	0.262143i
$603$			11.2298i			0.457313i
$604$	−8.97219	+	5.18010i	−0.365073	+	0.210775i
$605$		0			0
$606$			20.2117i			0.821045i
$607$	−15.7647	−	27.3053i	−0.639870	−	1.10829i	−0.985461	−	0.169902i	$-0.945655\pi$
$607$	−15.7647	−	27.3053i	−0.639870	−	1.10829i	0.345591	−	0.938385i	$-0.387678\pi$
$608$	−1.32094	+	2.28793i	−0.0535710	+	0.0927877i
$609$	−12.3590	−	7.13549i	−0.500814	−	0.289145i
$610$		0			0
$611$	−2.84185	+	5.79739i	−0.114969	+	0.234537i
$612$	−19.7659			−0.798989
$613$	2.45389	+	1.41675i	0.0991117	+	0.0572222i	0.548737	−	0.835995i	$-0.315109\pi$
$613$	2.45389	+	1.41675i	0.0991117	+	0.0572222i	−0.449625	+	0.893217i	$0.648442\pi$
$614$	−13.7722	+	23.8541i	−0.555799	+	0.962673i
$615$		0			0
$616$			7.46160i			0.300637i
$617$	1.95209	−	1.12704i	0.0785883	−	0.0453730i	−0.460191	−	0.887820i	$-0.652219\pi$
$617$	1.95209	−	1.12704i	0.0785883	−	0.0453730i	0.538779	+	0.842447i	$0.318886\pi$
$618$	−11.6146	+	6.70567i	−0.467206	+	0.269742i
$619$		−	6.37526i		−	0.256243i	−0.991758	−	0.128122i	$-0.959105\pi$
$619$		−	6.37526i		−	0.256243i	0.991758	−	0.128122i	$-0.0408948\pi$
$620$		0			0
$621$	0.618665	−	1.07156i	0.0248262	−	0.0430002i
$622$	−11.1078	−	6.41309i	−0.445382	−	0.257141i
$623$	21.3090			0.853725
$624$	0.588885	+	8.66892i	0.0235743	+	0.347034i
$625$		0			0
$626$	−2.36082	−	1.36302i	−0.0943575	−	0.0544773i
$627$	16.8983	−	29.2687i	0.674853	−	1.16888i
$628$	2.91552	+	5.04984i	0.116342	+	0.201510i
$629$		−	5.81539i		−	0.231875i
$630$		0			0
$631$	−26.7025	+	15.4167i	−1.06301	+	0.613729i	−0.926263	−	0.376877i	$-0.876998\pi$
$631$	−26.7025	+	15.4167i	−1.06301	+	0.613729i	−0.136746	+	0.990606i	$0.543665\pi$
$632$			4.05956i			0.161481i
$633$	−29.3893	−	50.9038i	−1.16812	−	2.02324i
$634$	0.949803	−	1.64511i	0.0377215	−	0.0653355i
$635$		0			0
$636$	19.1332			0.758680
$637$	−15.0383	+	10.1001i	−0.595840	+	0.400179i
$638$	22.3649			0.885433
$639$	23.4367	+	13.5312i	0.927140	+	0.535285i
$640$		0			0
$641$	9.59449	+	16.6181i	0.378960	+	0.656377i	0.990911	−	0.134518i	$-0.0429486\pi$
$641$	9.59449	+	16.6181i	0.378960	+	0.656377i	−0.611952	+	0.790895i	$0.709615\pi$
$642$			36.5931i			1.44421i
$643$	21.2657	−	12.2778i	0.838638	−	0.484188i	−0.0181630	−	0.999835i	$-0.505782\pi$
$643$	21.2657	−	12.2778i	0.838638	−	0.484188i	0.856801	+	0.515647i	$0.172448\pi$
$644$	3.24601	−	1.87409i	0.127911	−	0.0738493i
$645$		0			0
$646$	−9.30006	−	16.1082i	−0.365906	−	0.633768i
$647$	−14.6834	+	25.4323i	−0.577263	+	0.999849i	0.418529	+	0.908204i	$0.362546\pi$
$647$	−14.6834	+	25.4323i	−0.577263	+	0.999849i	−0.995792	+	0.0916452i	$0.970787\pi$
$648$	−8.26237	−	4.77028i	−0.324577	−	0.187394i
$649$	34.3149			1.34698
$650$		0			0
$651$	−17.1956			−0.673948
$652$	10.1774	+	5.87592i	0.398577	+	0.230119i
$653$	12.5257	−	21.6951i	0.490168	−	0.848997i	−0.509767	−	0.860312i	$-0.670269\pi$
$653$	12.5257	−	21.6951i	0.490168	−	0.848997i	0.999936	+	0.0113155i	$0.00360191\pi$
$654$	0.803694	+	1.39204i	0.0314269	+	0.0544330i
$655$		0			0
$656$	−2.43440	+	1.40550i	−0.0950473	+	0.0548756i
$657$	−17.1234	+	9.88618i	−0.668046	+	0.385696i
$658$		−	2.51702i		−	0.0981236i
$659$	−17.5467	−	30.3917i	−0.683521	−	1.18389i	−0.973899	−	0.226981i	$-0.927114\pi$
$659$	−17.5467	−	30.3917i	−0.683521	−	1.18389i	0.290378	−	0.956912i	$-0.406219\pi$
$660$		0			0
$661$	26.9586	+	15.5646i	1.04857	+	0.605392i	0.922248	−	0.386598i	$-0.126350\pi$
$661$	26.9586	+	15.5646i	1.04857	+	0.605392i	0.126321	+	0.991989i	$0.459683\pi$
$662$	−8.98724			−0.349299
$663$	−54.9297	−	26.9262i	−2.13329	−	1.04573i
$664$	8.55910			0.332158
$665$		0			0
$666$	−1.15946	+	2.00825i	−0.0449283	+	0.0778181i
$667$	−5.61725	−	9.72935i	−0.217501	−	0.376722i
$668$		−	11.1760i		−	0.432412i
$669$	−6.21821	+	3.59008i	−0.240410	+	0.138801i
$670$		0			0
$671$		−	78.2206i		−	3.01967i
$672$	−1.69366	−	2.93351i	−0.0653344	−	0.113162i
$673$	−0.0969228	+	0.167875i	−0.00373610	+	0.00647112i	−0.867887	−	0.496761i	$-0.834523\pi$
$673$	−0.0969228	+	0.167875i	−0.00373610	+	0.00647112i	0.864151	+	0.503232i	$0.167856\pi$
$674$	−1.19390	−	0.689296i	−0.0459872	−	0.0265507i
$675$		0			0
$676$	−4.91774	+	12.0339i	−0.189144	+	0.462844i
$677$	21.9008			0.841718			0.420859	−	0.907126i	$-0.361729\pi$
$677$	21.9008			0.841718			0.420859	+	0.907126i	$0.361729\pi$
$678$	−7.03137	−	4.05956i	−0.270038	−	0.155907i
$679$	3.06883	−	5.31537i	0.117771	−	0.203985i
$680$		0			0
$681$		−	9.55012i		−	0.365961i
$682$	23.3378	−	13.4741i	0.893650	−	0.515949i
$683$	4.43250	−	2.55910i	0.169605	−	0.0979214i	−0.412795	−	0.910824i	$-0.635447\pi$
$683$	4.43250	−	2.55910i	0.169605	−	0.0979214i	0.582399	+	0.812903i	$0.302114\pi$
$684$			7.41693i			0.283593i
$685$		0			0
$686$	8.45069	−	14.6370i	0.322649	−	0.558845i
$687$	−20.5602	−	11.8704i	−0.784419	−	0.452884i
$688$	5.28374			0.201441
$689$	25.7042	+	12.6001i	0.979252	+	0.480024i
$690$		0			0
$691$	−1.66003	−	0.958418i	−0.0631505	−	0.0364600i	0.468092	−	0.883680i	$-0.344941\pi$
$691$	−1.66003	−	0.958418i	−0.0631505	−	0.0364600i	−0.531243	+	0.847220i	$0.678275\pi$
$692$	−0.266700	+	0.461938i	−0.0101384	+	0.0175603i
$693$	10.4741	+	18.1416i	0.397876	+	0.689142i
$694$		−	11.8958i		−	0.451557i
$695$		0			0
$696$	−8.79268	+	5.07645i	−0.333285	+	0.192422i
$697$		−	19.7909i		−	0.749633i
$698$	2.28388	+	3.95580i	0.0864463	+	0.149729i
$699$	−23.3541	+	40.4505i	−0.883334	+	1.52998i
$700$		0			0
$701$	−23.4448			−0.885500			−0.442750	−	0.896645i	$-0.645997\pi$
$701$	−23.4448			−0.885500			−0.442750	+	0.896645i	$0.645997\pi$
$702$	−0.932784	−	1.38885i	−0.0352057	−	0.0524189i
$703$	−2.18216			−0.0823017
$704$	4.59726	+	2.65423i	0.173266	+	0.100035i
$705$		0			0
$706$	−0.421009	−	0.729210i	−0.0158449	−	0.0274442i
$707$		−	11.7889i		−	0.443368i
$708$	−13.4908	+	7.78892i	−0.507015	+	0.292725i
$709$	4.33100	−	2.50051i	0.162654	−	0.0939085i	−0.416463	−	0.909153i	$-0.636731\pi$
$709$	4.33100	−	2.50051i	0.162654	−	0.0939085i	0.579118	+	0.815244i	$0.303397\pi$
$710$		0			0
$711$	5.69851	+	9.87011i	0.213711	+	0.370158i
$712$	7.57999	−	13.1289i	0.284072	−	0.492027i
$713$	−11.7232	−	6.76840i	−0.439038	−	0.253479i
$714$	23.8485			0.892507
$715$		0			0
$716$	9.23733			0.345215
$717$	−62.6389	−	36.1646i	−2.33929	−	1.35059i
$718$	4.02961	−	6.97949i	0.150384	−	0.260472i
$719$	−22.7388	−	39.3848i	−0.848016	−	1.46881i	−0.882976	−	0.469418i	$-0.844464\pi$
$719$	−22.7388	−	39.3848i	−0.848016	−	1.46881i	0.0349601	−	0.999389i	$-0.488870\pi$
$720$		0			0
$721$	6.77444	−	3.91123i	0.252293	−	0.145662i
$722$	10.4101	−	6.01026i	0.387423	−	0.223679i
$723$			46.1409i			1.71600i
$724$	−2.38232	−	4.12630i	−0.0885383	−	0.153353i
$725$		0			0
$726$	−35.8542	−	20.7004i	−1.33067	−	0.768265i
$727$	−6.38432			−0.236781			−0.118391	−	0.992967i	$-0.537774\pi$
$727$	−6.38432			−0.236781			−0.118391	+	0.992967i	$0.537774\pi$
$728$	−0.343480	−	5.05633i	−0.0127302	−	0.187400i
$729$	−23.4301			−0.867780
$730$		0			0
$731$	−18.6001	+	32.2164i	−0.687951	+	1.19157i
$732$	17.7548	+	30.7522i	0.656236	+	1.13663i
$733$		−	46.0006i		−	1.69907i	−0.527530	−	0.849536i	$-0.676882\pi$
$733$		−	46.0006i		−	1.69907i	0.527530	−	0.849536i	$-0.323118\pi$
$734$	14.3052	−	8.25912i	0.528015	−	0.304850i
$735$		0			0
$736$		−	2.66659i		−	0.0982917i
$737$	10.6169	+	18.3890i	0.391079	+	0.677369i
$738$	−3.94588	+	6.83446i	−0.145250	+	0.251580i
$739$	4.14392	+	2.39250i	0.152437	+	0.0880094i	0.574278	−	0.818660i	$-0.305283\pi$
$739$	4.14392	+	2.39250i	0.152437	+	0.0880094i	−0.421841	+	0.906670i	$0.638616\pi$
$740$		0			0
$741$	−10.1038	+	20.6117i	−0.371171	+	0.757191i
$742$	−11.1598			−0.409691
$743$	13.6962	+	7.90749i	0.502464	+	0.290098i	0.729730	−	0.683735i	$-0.239646\pi$
$743$	13.6962	+	7.90749i	0.502464	+	0.290098i	−0.227267	+	0.973833i	$0.572979\pi$
$744$	−6.11679	+	10.5946i	−0.224252	+	0.388416i
$745$		0			0
$746$			26.5545i			0.972231i
$747$	20.8100	−	12.0146i	0.761397	−	0.439593i
$748$	−32.3671	+	18.6871i	−1.18346	+	0.683269i
$749$		−	21.3437i		−	0.779881i
$750$		0			0
$751$	−4.94420	+	8.56360i	−0.180416	+	0.312490i	−0.942022	−	0.335550i	$-0.891078\pi$
$751$	−4.94420	+	8.56360i	−0.180416	+	0.312490i	0.761606	+	0.648040i	$0.224411\pi$
$752$	−1.55079	−	0.895350i	−0.0565516	−	0.0326501i
$753$	−41.0713			−1.49672
$754$	−15.1555	+	1.02952i	−0.551930	+	0.0374929i
$755$		0			0
$756$	0.564838	+	0.326110i	0.0205430	+	0.0118605i
$757$	−4.37046	+	7.56985i	−0.158847	+	0.275131i	−0.934453	−	0.356086i	$-0.884111\pi$
$757$	−4.37046	+	7.56985i	−0.158847	+	0.275131i	0.775606	+	0.631217i	$0.217444\pi$
$758$	−0.577865	−	1.00089i	−0.0209890	−	0.0363540i
$759$			34.1128i			1.23822i
$760$		0			0
$761$	42.8460	−	24.7372i	1.55317	−	0.896721i	0.555286	−	0.831659i	$-0.312609\pi$
$761$	42.8460	−	24.7372i	1.55317	−	0.896721i	0.997881	−	0.0650620i	$-0.0207245\pi$
$762$			26.1445i			0.947114i
$763$	−0.468772	−	0.811936i	−0.0169707	−	0.0293941i
$764$	−8.97219	+	15.5403i	−0.324603	+	0.562228i
$765$		0			0
$766$	35.0077			1.26488
$767$	−23.2534	+	1.57962i	−0.839631	+	0.0570366i
$768$	−2.40987			−0.0869585
$769$	−20.2409	−	11.6861i	−0.729906	−	0.421412i	0.0884817	−	0.996078i	$-0.471799\pi$
$769$	−20.2409	−	11.6861i	−0.729906	−	0.421412i	−0.818388	+	0.574666i	$0.805132\pi$
$770$		0			0
$771$	9.91088	+	17.1662i	0.356932	+	0.618224i
$772$			20.9462i			0.753869i
$773$	1.43562	−	0.828857i	0.0516358	−	0.0298119i	−0.473960	−	0.880546i	$-0.657176\pi$
$773$	1.43562	−	0.828857i	0.0516358	−	0.0298119i	0.525596	+	0.850735i	$0.323842\pi$
$774$	12.8465	−	7.41693i	0.461758	−	0.266596i
$775$		0			0
$776$	−2.18328	−	3.78155i	−0.0783751	−	0.135750i
$777$	1.39895	−	2.42305i	0.0501870	−	0.0869264i
$778$	9.79774	+	5.65673i	0.351266	+	0.202803i
$779$	−7.42631			−0.266075
$780$		0			0
$781$	51.1707			1.83103
$782$	16.2589	+	9.38707i	0.581416	+	0.335681i
$783$	0.977456	−	1.69300i	0.0349314	−	0.0605030i
$784$	−2.51214	−	4.35115i	−0.0897191	−	0.155398i
$785$		0			0
$786$	−32.0355	+	18.4957i	−1.14267	+	0.659720i
$787$	37.5376	−	21.6724i	1.33807	−	0.772536i	0.351550	−	0.936169i	$-0.385655\pi$
$787$	37.5376	−	21.6724i	1.33807	−	0.772536i	0.986521	+	0.163633i	$0.0523213\pi$
$788$			26.7724i			0.953726i
$789$	12.5669	+	21.7666i	0.447395	+	0.774911i
$790$		0			0
$791$	4.10120	+	2.36783i	0.145822	+	0.0841902i
$792$	14.9033			0.529564
$793$	3.60073	+	53.0060i	0.127866	+	1.88230i
$794$	18.0057			0.639000
$795$		0			0
$796$	−7.19452	+	12.4613i	−0.255003	+	0.441678i
$797$	10.2117	+	17.6871i	0.361715	+	0.626509i	0.988243	−	0.152890i	$-0.0488579\pi$
$797$	10.2117	+	17.6871i	0.361715	+	0.626509i	−0.626528	+	0.779399i	$0.715525\pi$
$798$		−	8.94887i		−	0.316787i
$799$	10.9184	−	6.30372i	0.386264	−	0.223010i
$800$		0			0
$801$		−	42.5609i		−	1.50382i
$802$	−2.29430	−	3.97385i	−0.0810146	−	0.140321i
$803$	−18.6932	+	32.3776i	−0.659670	+	1.14258i
$804$	−8.34802	−	4.81973i	−0.294412	−	0.169979i
$805$		0			0
$806$	−15.1945	+	10.2050i	−0.535204	+	0.359455i
$807$	−54.5621			−1.92068
$808$	−7.26341	−	4.19353i	−0.255526	−	0.147528i
$809$	−11.5118	+	19.9390i	−0.404732	+	0.701017i	−0.994290	−	0.106709i	$-0.965969\pi$
$809$	−11.5118	+	19.9390i	−0.404732	+	0.701017i	0.589558	+	0.807726i	$0.299302\pi$
$810$		0			0
$811$			5.67837i			0.199395i	0.995018	+	0.0996973i	$0.0317874\pi$
$811$			5.67837i			0.199395i	−0.995018	+	0.0996973i	$0.968213\pi$
$812$	5.12852	−	2.96095i	0.179976	−	0.103909i
$813$	0.526804	−	0.304150i	0.0184758	−	0.0106670i
$814$			4.38474i			0.153685i
$815$		0			0
$816$	8.48334	−	14.6936i	0.296976	−	0.514378i
$817$	12.0888	+	6.97949i	0.422935	+	0.244181i
$818$	−26.2500			−0.917811
$819$	−7.93282	−	11.8114i	−0.277195	−	0.412725i
$820$		0			0
$821$	−11.2259	−	6.48129i	−0.391787	−	0.226198i	0.291147	−	0.956678i	$-0.405963\pi$
$821$	−11.2259	−	6.48129i	−0.391787	−	0.226198i	−0.682934	+	0.730480i	$0.739296\pi$
$822$	13.7252	−	23.7727i	0.478721	−	0.829169i
$823$	4.09355	+	7.09023i	0.142692	+	0.247150i	0.928510	−	0.371309i	$-0.121091\pi$
$823$	4.09355	+	7.09023i	0.142692	+	0.247150i	−0.785817	+	0.618459i	$0.787757\pi$
$824$		−	5.56518i		−	0.193872i
$825$		0			0
$826$	7.86880	−	4.54305i	0.273791	−	0.158073i
$827$			9.13747i			0.317741i	0.987299	+	0.158870i	$0.0507852\pi$
$827$			9.13747i			0.317741i	−0.987299	+	0.158870i	$0.949215\pi$
$828$	−3.74316	−	6.48334i	−0.130084	−	0.225312i
$829$	−2.45257	+	4.24798i	−0.0851814	+	0.147539i	−0.905469	−	0.424413i	$-0.860480\pi$
$829$	−2.45257	+	4.24798i	−0.0851814	+	0.147539i	0.820287	+	0.571952i	$0.193814\pi$
$830$		0			0
$831$	−11.2188			−0.389176
$832$	−3.23750	−	1.58700i	−0.112240	−	0.0550195i
$833$	35.3734			1.22562
$834$	−23.6875	−	13.6760i	−0.820231	−	0.473561i
$835$		0			0
$836$	7.01214	+	12.1454i	0.242520	+	0.420057i
$837$		−	2.35554i		−	0.0814193i
$838$	10.4593	−	6.03869i	0.361311	−	0.208603i
$839$	1.95525	−	1.12887i	0.0675028	−	0.0389727i	−0.465869	−	0.884854i	$-0.654258\pi$
$839$	1.95525	−	1.12887i	0.0675028	−	0.0389727i	0.533372	+	0.845881i	$0.320925\pi$
$840$		0			0
$841$	5.62507	+	9.74290i	0.193968	+	0.335962i
$842$	−1.55858	+	2.69954i	−0.0537121	+	0.0930321i
$843$	7.72739	+	4.46141i	0.266145	+	0.153659i
$844$	24.3908			0.839567
$845$		0			0
$846$	−5.02731			−0.172842
$847$	20.9127	+	12.0740i	0.718570	+	0.414867i
$848$	−3.96976	+	6.87583i	−0.136322	+	0.236117i
$849$	6.44393	+	11.1612i	0.221155	+	0.383052i
$850$		0			0
$851$	1.90749	−	1.10129i	0.0653878	−	0.0377516i
$852$	−20.1176	+	11.6149i	−0.689218	+	0.397920i
$853$		−	14.7832i		−	0.506166i	−0.967445	−	0.253083i	$-0.918555\pi$
$853$		−	14.7832i		−	0.506166i	0.967445	−	0.253083i	$-0.0814447\pi$
$854$	−10.3559	−	17.9369i	−0.354370	−	0.613788i
$855$		0			0
$856$	−13.1503	−	7.59234i	−0.449469	−	0.259501i
$857$	19.3235			0.660079			0.330039	−	0.943967i	$-0.392938\pi$
$857$	19.3235			0.660079			0.330039	+	0.943967i	$0.392938\pi$
$858$	41.4163	+	20.3020i	1.41393	+	0.693100i
$859$	−48.8245			−1.66587			−0.832935	−	0.553371i	$-0.813341\pi$
$859$	−48.8245			−1.66587			−0.832935	+	0.553371i	$0.813341\pi$
$860$		0			0
$861$	4.76088	−	8.24609i	0.162251	−	0.281026i
$862$	−2.61501	−	4.52932i	−0.0890675	−	0.154269i
$863$			15.2366i			0.518660i	0.965789	+	0.259330i	$0.0835017\pi$
$863$			15.2366i			0.518660i	−0.965789	+	0.259330i	$0.916498\pi$
$864$	0.401847	−	0.232006i	0.0136711	−	0.00789302i
$865$		0			0
$866$		−	22.3063i		−	0.757998i
$867$	39.2432	+	67.9712i	1.33277	+	2.30842i
$868$	3.56775	−	6.17952i	0.121097	−	0.209747i
$869$	18.6629	+	10.7750i	0.633094	+	0.365517i
$870$		0			0
$871$	−8.04102	−	11.9725i	−0.272460	−	0.405674i
$872$	−0.667003			−0.0225876
$873$	−10.6165	−	6.12945i	−0.359315	−	0.207451i
$874$	3.52239	−	6.10096i	0.119147	−	0.206368i
$875$		0			0
$876$		−	16.9722i		−	0.573438i
$877$	−0.386166	+	0.222953i	−0.0130399	+	0.00752859i	−0.506506	−	0.862237i	$-0.669063\pi$
$877$	−0.386166	+	0.222953i	−0.0130399	+	0.00752859i	0.493466	+	0.869765i	$0.335730\pi$
$878$	4.54520	−	2.62417i	0.153393	−	0.0885616i
$879$			58.2566i			1.96495i
$880$		0			0
$881$	−19.4053	+	33.6110i	−0.653782	+	1.13238i	0.328415	+	0.944534i	$0.393486\pi$
$881$	−19.4053	+	33.6110i	−0.653782	+	1.13238i	−0.982198	+	0.187851i	$0.939848\pi$
$882$	−12.2156	−	7.05270i	−0.411322	−	0.237477i
$883$	25.2239			0.848853			0.424427	−	0.905462i	$-0.360476\pi$
$883$	25.2239			0.848853			0.424427	+	0.905462i	$0.360476\pi$
$884$	21.0732	−	14.1532i	0.708769	−	0.476025i
$885$		0			0
$886$	0.966685	+	0.558116i	0.0324764	+	0.0187503i
$887$	−0.130947	+	0.226808i	−0.00439678	+	0.00761545i	−0.868215	−	0.496187i	$-0.834733\pi$
$887$	−0.130947	+	0.226808i	−0.00439678	+	0.00761545i	0.863819	+	0.503803i	$0.168066\pi$
$888$	−0.995263	−	1.72385i	−0.0333988	−	0.0578485i
$889$		−	15.2493i		−	0.511446i
$890$		0			0
$891$	−43.8605	+	25.3229i	−1.46938	+	0.848348i
$892$		−	2.97949i		−	0.0997606i
$893$	−2.36540	−	4.09699i	−0.0791551	−	0.137101i
$894$	2.36656	−	4.09900i	0.0791495	−	0.137091i
$895$		0			0
$896$	1.40561			0.0469580
$897$	−1.57031	−	23.1164i	−0.0524312	−	0.771835i
$898$	34.4883			1.15089
$899$	−18.5220	−	10.6937i	−0.617744	−	0.356655i
$900$		0			0
$901$	−27.9491	−	48.4093i	−0.931121	−	1.61275i
$902$			14.9221i			0.496851i
$903$	−15.4999	+	8.94887i	−0.515804	+	0.297800i
$904$	2.91774	−	1.68456i	0.0970426	−	0.0560276i
$905$		0			0
$906$	−12.4833	−	21.6218i	−0.414731	−	0.718336i
$907$	−19.0315	+	32.9635i	−0.631930	+	1.09454i	0.355226	+	0.934780i	$0.384404\pi$
$907$	−19.0315	+	32.9635i	−0.631930	+	1.09454i	−0.987157	+	0.159755i	$0.948930\pi$
$908$	3.43199	+	1.98146i	0.113895	+	0.0657572i
$909$	−23.5463			−0.780982
$910$		0			0
$911$	−50.4261			−1.67069			−0.835346	−	0.549725i	$-0.814733\pi$
$911$	−50.4261			−1.67069			−0.835346	+	0.549725i	$0.814733\pi$
$912$	−5.51360	−	3.18328i	−0.182574	−	0.105409i
$913$	22.7178	−	39.3484i	0.751850	−	1.30224i
$914$	−2.03770	−	3.52940i	−0.0674011	−	0.116742i
$915$		0			0
$916$	8.53166	−	4.92576i	0.281894	−	0.162752i
$917$	18.6854	−	10.7880i	0.617046	−	0.356252i
$918$			3.26689i			0.107823i
$919$	3.36458	+	5.82763i	0.110987	+	0.192236i	0.916169	−	0.400793i	$-0.131265\pi$
$919$	3.36458	+	5.82763i	0.110987	+	0.192236i	−0.805181	+	0.593029i	$0.797932\pi$
$920$		0			0
$921$	−57.4851	−	33.1891i	−1.89420	−	1.09362i
$922$	−30.3417			−0.999249
$923$	−34.6757	+	2.35554i	−1.14136	+	0.0775335i
$924$	−17.9815			−0.591547
$925$		0			0
$926$	−12.6145	+	21.8490i	−0.414540	+	0.718004i
$927$	−7.81199	−	13.5308i	−0.256579	−	0.444409i
$928$		−	4.21306i		−	0.138300i
$929$	−13.8526	+	7.99782i	−0.454490	+	0.262400i	−0.709725	−	0.704479i	$-0.751181\pi$
$929$	−13.8526	+	7.99782i	−0.454490	+	0.262400i	0.255234	+	0.966879i	$0.417847\pi$
$930$		0			0
$931$		−	13.2735i		−	0.435021i
$932$	−9.69104	−	16.7854i	−0.317441	−	0.549823i
$933$	15.4547	−	26.7683i	0.505964	−	0.876355i
$934$	19.0523	+	10.9999i	0.623410	+	0.359926i
$935$		0			0
$936$	−10.0991	+	0.686041i	−0.330101	+	0.0224239i
$937$	−32.2129			−1.05235			−0.526176	−	0.850376i	$-0.676375\pi$
$937$	−32.2129			−1.05235			−0.526176	+	0.850376i	$0.676375\pi$
$938$	4.86916	+	2.81121i	0.158984	+	0.0917893i
$939$	3.28470	−	5.68927i	0.107192	−	0.185662i
$940$		0			0
$941$		−	14.9874i		−	0.488576i	−0.969703	−	0.244288i	$-0.921446\pi$
$941$		−	14.9874i		−	0.488576i	0.969703	−	0.244288i	$-0.0785542\pi$
$942$	−12.1694	+	7.02602i	−0.396501	+	0.228920i
$943$	6.49154	−	3.74789i	0.211394	−	0.122048i
$944$		−	6.46419i		−	0.210391i
$945$		0			0
$946$	14.0243	−	24.2908i	0.455968	−	0.789760i
$947$	12.8844	+	7.43878i	0.418685	+	0.241728i	0.694515	−	0.719479i	$-0.255619\pi$
$947$	12.8844	+	7.43878i	0.418685	+	0.241728i	−0.275829	+	0.961207i	$0.588952\pi$
$948$	−9.78300			−0.317737
$949$	11.1770	−	22.8011i	0.362820	−	0.740155i
$950$		0			0
$951$	3.96449	+	2.28890i	0.128557	+	0.0742226i
$952$	−4.94809	+	8.57035i	−0.160369	+	0.277767i
$953$	−3.31103	−	5.73486i	−0.107255	−	0.185770i	0.807402	−	0.590001i	$-0.200873\pi$
$953$	−3.31103	−	5.73486i	−0.107255	−	0.185770i	−0.914657	+	0.404231i	$0.867539\pi$
$954$			22.2898i			0.721660i
$955$		0			0
$956$	25.9927	−	15.0069i	0.840664	−	0.485358i
$957$			53.8963i			1.74222i
$958$	−11.0541	−	19.1462i	−0.357141	−	0.618586i
$959$	−8.00551	+	13.8659i	−0.258511	+	0.447755i
$960$		0			0
$961$	5.22962			0.168697
$962$	−0.201842	−	2.97130i	−0.00650766	−	0.0957986i
$963$	−42.6303			−1.37374
$964$	−16.5815	−	9.57333i	−0.534054	−	0.308336i
$965$		0			0
$966$	4.51630	+	7.82245i	0.145309	+	0.251683i
$967$			24.8355i			0.798655i	0.916808	+	0.399328i	$0.130756\pi$
$967$			24.8355i			0.798655i	−0.916808	+	0.399328i	$0.869244\pi$
$968$	14.8781	−	8.58987i	0.478200	−	0.276089i
$969$	38.8186	−	22.4119i	1.24703	−	0.719974i
$970$		0			0
$971$	11.5415	+	19.9904i	0.370383	+	0.641522i	0.989624	−	0.143678i	$-0.0458931\pi$
$971$	11.5415	+	19.9904i	0.370383	+	0.641522i	−0.619241	+	0.785201i	$0.712560\pi$
$972$	10.7997	−	18.7057i	0.346401	−	0.599985i
$973$	13.8162	+	7.97681i	0.442928	+	0.255725i
$974$	−3.66873			−0.117554
$975$		0			0
$976$	−14.7351			−0.471659
$977$	6.94534	+	4.00989i	0.222201	+	0.128288i	0.606969	−	0.794725i	$-0.292385\pi$
$977$	6.94534	+	4.00989i	0.222201	+	0.128288i	−0.384768	+	0.923013i	$0.625719\pi$
$978$	−14.1602	+	24.5262i	−0.452793	+	0.784260i
$979$	−40.2381	−	69.6943i	−1.28601	−	2.22744i
$980$		0			0
$981$	−1.62170	+	0.936289i	−0.0517769	+	0.0298934i
$982$	22.9228	−	13.2345i	0.731495	−	0.422329i
$983$		−	16.0606i		−	0.512254i	−0.966643	−	0.256127i	$-0.917553\pi$
$983$		−	16.0606i		−	0.512254i	0.966643	−	0.256127i	$-0.0824466\pi$
$984$	−3.38707	−	5.86658i	−0.107976	−	0.187020i
$985$		0			0
$986$	25.6881	+	14.8310i	0.818076	+	0.472317i
$987$	6.06568			0.193073
$988$	−5.31084	−	7.90749i	−0.168960	−	0.251571i
$989$	−14.0896			−0.448022
$990$		0			0
$991$	17.2373	−	29.8559i	0.547562	−	0.948405i	−0.450879	−	0.892585i	$-0.648889\pi$
$991$	17.2373	−	29.8559i	0.547562	−	0.948405i	0.998441	−	0.0558199i	$-0.0177773\pi$
$992$	−2.53823	−	4.39634i	−0.0805888	−	0.139584i
$993$		−	21.6581i		−	0.687297i
$994$	11.7340	−	6.77464i	0.372181	−	0.214879i
$995$		0			0
$996$			20.6263i			0.653569i
$997$	−22.1233	−	38.3187i	−0.700652	−	1.21357i	−0.968238	−	0.250031i	$-0.919559\pi$
$997$	−22.1233	−	38.3187i	−0.700652	−	1.21357i	0.267586	−	0.963534i	$-0.413774\pi$
$998$	18.5202	−	32.0779i	0.586247	−	1.01541i
$999$	0.331921	+	0.191635i	0.0105015	+	0.00606306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.m.e.251.4		16
5.2	odd	4		130.2.m.b.69.1	yes	8
5.3	odd	4		130.2.m.a.69.4	yes	8
5.4	even	2	inner	650.2.m.e.251.5		16
13.6	odd	12		8450.2.a.cs.1.2		8
13.7	odd	12		8450.2.a.cr.1.2		8
13.10	even	6	inner	650.2.m.e.101.4		16
15.2	even	4		1170.2.bj.a.199.4		8
15.8	even	4		1170.2.bj.b.199.1		8
20.3	even	4		1040.2.df.c.849.1		8
20.7	even	4		1040.2.df.a.849.4		8
65.7	even	12		1690.2.b.e.339.7		16
65.17	odd	12		1690.2.c.f.1689.7		8
65.19	odd	12		8450.2.a.cr.1.7		8
65.22	odd	12		1690.2.c.e.1689.7		8
65.23	odd	12		130.2.m.b.49.1	yes	8
65.32	even	12		1690.2.b.e.339.15		16
65.33	even	12		1690.2.b.e.339.10		16
65.43	odd	12		1690.2.c.e.1689.2		8
65.48	odd	12		1690.2.c.f.1689.2		8
65.49	even	6	inner	650.2.m.e.101.5		16
65.58	even	12		1690.2.b.e.339.2		16
65.59	odd	12		8450.2.a.cs.1.7		8
65.62	odd	12		130.2.m.a.49.4	✓	8
195.23	even	12		1170.2.bj.a.829.4		8
195.62	even	12		1170.2.bj.b.829.1		8
260.23	even	12		1040.2.df.a.49.4		8
260.127	even	12		1040.2.df.c.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.4	✓	8	65.62	odd	12
130.2.m.a.69.4	yes	8	5.3	odd	4
130.2.m.b.49.1	yes	8	65.23	odd	12
130.2.m.b.69.1	yes	8	5.2	odd	4
650.2.m.e.101.4		16	13.10	even	6	inner
650.2.m.e.101.5		16	65.49	even	6	inner
650.2.m.e.251.4		16	1.1	even	1	trivial
650.2.m.e.251.5		16	5.4	even	2	inner
1040.2.df.a.49.4		8	260.23	even	12
1040.2.df.a.849.4		8	20.7	even	4
1040.2.df.c.49.1		8	260.127	even	12
1040.2.df.c.849.1		8	20.3	even	4
1170.2.bj.a.199.4		8	15.2	even	4
1170.2.bj.a.829.4		8	195.23	even	12
1170.2.bj.b.199.1		8	15.8	even	4
1170.2.bj.b.829.1		8	195.62	even	12
1690.2.b.e.339.2		16	65.58	even	12
1690.2.b.e.339.7		16	65.7	even	12
1690.2.b.e.339.10		16	65.33	even	12
1690.2.b.e.339.15		16	65.32	even	12
1690.2.c.e.1689.2		8	65.43	odd	12
1690.2.c.e.1689.7		8	65.22	odd	12
1690.2.c.f.1689.2		8	65.48	odd	12
1690.2.c.f.1689.7		8	65.17	odd	12
8450.2.a.cr.1.2		8	13.7	odd	12
8450.2.a.cr.1.7		8	65.19	odd	12
8450.2.a.cs.1.2		8	13.6	odd	12
8450.2.a.cs.1.7		8	65.59	odd	12

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.20493 - 2.08700i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.08700 + 1.20493i) q^{6} +(1.21729 - 0.702803i) q^{7} -1.00000i q^{8} +(-1.40373 - 2.43133i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.20493 - 2.08700i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.08700 + 1.20493i) q^{6} +(1.21729 - 0.702803i) q^{7} -1.00000i q^{8} +(-1.40373 - 2.43133i) q^{9} +(-4.59726 - 2.65423i) q^{11} +2.40987 q^{12} +(3.23750 + 1.58700i) q^{13} -1.40561 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.52026 - 6.09726i) q^{17} +2.80745i q^{18} +(-2.28793 + 1.32094i) q^{19} -3.38732i q^{21} +(2.65423 + 4.59726i) q^{22} +(1.33329 - 2.30933i) q^{23} +(-2.08700 - 1.20493i) q^{24} +(-2.01026 - 2.99314i) q^{26} +0.464013 q^{27} +(1.21729 + 0.702803i) q^{28} +(2.10653 - 3.64862i) q^{29} -5.07645i q^{31} +(0.866025 - 0.500000i) q^{32} +(-11.0788 + 6.39634i) q^{33} +7.04051i q^{34} +(1.40373 - 2.43133i) q^{36} +(0.715328 + 0.412995i) q^{37} +2.64187 q^{38} +(7.21306 - 4.84445i) q^{39} +(2.43440 + 1.40550i) q^{41} +(-1.69366 + 2.93351i) q^{42} +(-2.64187 - 4.57586i) q^{43} -5.30846i q^{44} +(-2.30933 + 1.33329i) q^{46} +1.79070i q^{47} +(1.20493 + 2.08700i) q^{48} +(-2.51214 + 4.35115i) q^{49} -16.9667 q^{51} +(0.244364 + 3.59726i) q^{52} +7.93952 q^{53} +(-0.401847 - 0.232006i) q^{54} +(-0.702803 - 1.21729i) q^{56} +6.36656i q^{57} +(-3.64862 + 2.10653i) q^{58} +(-5.59815 + 3.23210i) q^{59} +(7.36754 + 12.7610i) q^{61} +(-2.53823 + 4.39634i) q^{62} +(-3.41749 - 1.97309i) q^{63} -1.00000 q^{64} +12.7927 q^{66} +(-3.46410 - 2.00000i) q^{67} +(3.52026 - 6.09726i) q^{68} +(-3.21306 - 5.56518i) q^{69} +(-8.34802 + 4.81973i) q^{71} +(-2.43133 + 1.40373i) q^{72} -7.04281i q^{73} +(-0.412995 - 0.715328i) q^{74} +(-2.28793 - 1.32094i) q^{76} -7.46160 q^{77} +(-8.66892 + 0.588885i) q^{78} -4.05956 q^{79} +(4.77028 - 8.26237i) q^{81} +(-1.40550 - 2.43440i) q^{82} +8.55910i q^{83} +(2.93351 - 1.69366i) q^{84} +5.28374i q^{86} +(-5.07645 - 8.79268i) q^{87} +(-2.65423 + 4.59726i) q^{88} +(13.1289 + 7.57999i) q^{89} +(5.05633 - 0.343480i) q^{91} +2.66659 q^{92} +(-10.5946 - 6.11679i) q^{93} +(0.895350 - 1.55079i) q^{94} -2.40987i q^{96} +(3.78155 - 2.18328i) q^{97} +(4.35115 - 2.51214i) q^{98} +14.9033i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 16 * q^9	\( 16 q + 8 q^{4} - 16 q^{9} - 6 q^{11} + 20 q^{14} - 8 q^{16} - 18 q^{19} + 2 q^{26} + 6 q^{29} + 16 q^{36} + 60 q^{39} + 42 q^{41} + 12 q^{46} + 30 q^{49} - 40 q^{51} - 36 q^{54} + 10 q^{56} - 60 q^{59} - 10 q^{61} - 16 q^{64} + 40 q^{66} + 4 q^{69} - 40 q^{74} - 18 q^{76} - 8 q^{79} + 16 q^{81} + 12 q^{84} + 78 q^{89} + 38 q^{91} + 6 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 - 16 * q^9 - 6 * q^11 + 20 * q^14 - 8 * q^16 - 18 * q^19 + 2 * q^26 + 6 * q^29 + 16 * q^36 + 60 * q^39 + 42 * q^41 + 12 * q^46 + 30 * q^49 - 40 * q^51 - 36 * q^54 + 10 * q^56 - 60 * q^59 - 10 * q^61 - 16 * q^64 + 40 * q^66 + 4 * q^69 - 40 * q^74 - 18 * q^76 - 8 * q^79 + 16 * q^81 + 12 * q^84 + 78 * q^89 + 38 * q^91 + 6 * q^94

Introduction

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