LMFDB - Embedded newform 900.2.bj.f.487.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(127,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			487.3
Character	$\chi$	$=$	900.487
Dual form			900.2.bj.f.523.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36565 - 0.367425i) q^{2} +(1.73000 + 1.00355i) q^{4} +(-1.83777 + 1.27382i) q^{5} +(-0.338407 + 0.338407i) q^{7} +(-1.99384 - 2.00614i) q^{8} +(2.97778 - 1.06435i) q^{10} +(0.00542328 - 0.00746451i) q^{11} +(0.444902 - 2.80900i) q^{13} +(0.586484 - 0.337806i) q^{14} +(1.98578 + 3.47227i) q^{16} +(3.79071 - 1.93146i) q^{17} +(-2.23243 + 6.87071i) q^{19} +(-4.45767 + 0.359416i) q^{20} +(-0.0101489 + 0.00820125i) q^{22} +(0.917368 + 5.79204i) q^{23} +(1.75477 - 4.68196i) q^{25} +(-1.63968 + 3.67265i) q^{26} +(-0.925050 + 0.245835i) q^{28} +(-3.22482 + 1.04781i) q^{29} +(-4.34142 - 1.41061i) q^{31} +(-1.43608 - 5.47153i) q^{32} +(-5.88645 + 1.24490i) q^{34} +(0.190844 - 1.05298i) q^{35} +(-6.42204 - 1.01715i) q^{37} +(5.57319 - 8.56273i) q^{38} +(6.21967 + 1.14702i) q^{40} +(-5.70832 + 4.14734i) q^{41} +(-6.48875 - 6.48875i) q^{43} +(0.0168733 - 0.00747105i) q^{44} +(0.875337 - 8.24696i) q^{46} +(-3.91751 - 1.99607i) q^{47} +6.77096i q^{49} +(-4.11667 + 5.74917i) q^{50} +(3.58865 - 4.41309i) q^{52} +(0.604811 + 0.308167i) q^{53} +(-0.000458296 + 0.0206263i) q^{55} +(1.35362 + 0.00416215i) q^{56} +(4.78896 - 0.246057i) q^{58} +(-2.04303 + 1.48435i) q^{59} +(-7.27946 - 5.28884i) q^{61} +(5.41056 + 3.52155i) q^{62} +(-0.0491968 + 7.99985i) q^{64} +(2.76053 + 5.72902i) q^{65} +(-4.59556 - 9.01929i) q^{67} +(8.49624 + 0.462735i) q^{68} +(-0.647517 + 1.36788i) q^{70} +(-6.68849 + 2.17322i) q^{71} +(2.91467 - 0.461638i) q^{73} +(8.39652 + 3.74869i) q^{74} +(-10.7572 + 9.64596i) q^{76} +(0.000690764 + 0.00436131i) q^{77} +(-0.730993 - 2.24976i) q^{79} +(-8.07245 - 3.85170i) q^{80} +(9.31941 - 3.56643i) q^{82} +(-3.36914 + 1.71666i) q^{83} +(-4.50611 + 8.37826i) q^{85} +(6.47723 + 11.2455i) q^{86} +(-0.0257880 + 0.00400318i) q^{88} +(9.05282 - 12.4601i) q^{89} +(0.800028 + 1.10114i) q^{91} +(-4.22554 + 10.9408i) q^{92} +(4.61654 + 4.16533i) q^{94} +(-4.64936 - 15.4705i) q^{95} +(-8.12690 + 15.9499i) q^{97} +(2.48782 - 9.24676i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	−1.36565	−	0.367425i	−0.965660	−	0.259809i
$2$	−1.36565	−	0.367425i	−0.965660	−	0.259809i
$3$		0			0
$3$		0			0
$4$	1.73000	+	1.00355i	0.864999	+	0.501774i
$5$	−1.83777	+	1.27382i	−0.821874	+	0.569669i
$5$	−1.83777	+	1.27382i	−0.821874	+	0.569669i
$6$		0			0
$7$	−0.338407	+	0.338407i	−0.127906	+	0.127906i	−0.768162	−	0.640256i	$-0.778828\pi$
$7$	−0.338407	+	0.338407i	−0.127906	+	0.127906i	0.640256	+	0.768162i	$0.278828\pi$
$8$	−1.99384	−	2.00614i	−0.704929	−	0.709278i
$9$		0			0
$10$	2.97778	−	1.06435i	0.941656	−	0.336576i
$11$	0.00542328	−	0.00746451i	0.00163518	−	0.00225063i	−0.808199	−	0.588910i	$-0.799557\pi$
$11$	0.00542328	−	0.00746451i	0.00163518	−	0.00225063i	0.809834	+	0.586659i	$0.199557\pi$
$12$		0			0
$13$	0.444902	−	2.80900i	0.123394	−	0.779077i	−0.845931	−	0.533293i	$-0.820954\pi$
$13$	0.444902	−	2.80900i	0.123394	−	0.779077i	0.969324	−	0.245785i	$-0.0790456\pi$
$14$	0.586484	−	0.337806i	0.156744	−	0.0902824i
$15$		0			0
$16$	1.98578	+	3.47227i	0.496445	+	0.868068i
$17$	3.79071	−	1.93146i	0.919383	−	0.468449i	0.0707875	−	0.997491i	$-0.477449\pi$
$17$	3.79071	−	1.93146i	0.919383	−	0.468449i	0.848595	+	0.529042i	$0.177449\pi$
$18$		0			0
$19$	−2.23243	+	6.87071i	−0.512154	+	1.57625i	0.276246	+	0.961087i	$0.410910\pi$
$19$	−2.23243	+	6.87071i	−0.512154	+	1.57625i	−0.788400	+	0.615162i	$0.789090\pi$
$20$	−4.45767	+	0.359416i	−0.996765	+	0.0803678i
$21$		0			0
$22$	−0.0101489	+	0.00820125i	−0.00216376	+	0.00174851i
$23$	0.917368	+	5.79204i	0.191285	+	1.20772i	0.877230	+	0.480070i	$0.159389\pi$
$23$	0.917368	+	5.79204i	0.191285	+	1.20772i	−0.685946	+	0.727653i	$0.740611\pi$
$24$		0			0
$25$	1.75477	−	4.68196i	0.350954	−	0.936393i
$26$	−1.63968	+	3.67265i	−0.321568	+	0.720265i
$27$		0			0
$28$	−0.925050	+	0.245835i	−0.174818	+	0.0464585i
$29$	−3.22482	+	1.04781i	−0.598834	+	0.194573i	−0.592720	−	0.805409i	$-0.701946\pi$
$29$	−3.22482	+	1.04781i	−0.598834	+	0.194573i	−0.00611340	+	0.999981i	$0.501946\pi$
$30$		0			0
$31$	−4.34142	−	1.41061i	−0.779742	−	0.253353i	−0.108012	−	0.994150i	$-0.534448\pi$
$31$	−4.34142	−	1.41061i	−0.779742	−	0.253353i	−0.671730	+	0.740796i	$0.734448\pi$
$32$	−1.43608	−	5.47153i	−0.253866	−	0.967240i
$33$		0			0
$34$	−5.88645	+	1.24490i	−1.00952	+	0.213499i
$35$	0.190844	−	1.05298i	0.0322585	−	0.177986i
$36$		0			0
$37$	−6.42204	−	1.01715i	−1.05578	−	0.167219i	−0.395671	−	0.918392i	$-0.629488\pi$
$37$	−6.42204	−	1.01715i	−1.05578	−	0.167219i	−0.660105	+	0.751174i	$0.729488\pi$
$38$	5.57319	−	8.56273i	0.904091	−	1.38906i
$39$		0			0
$40$	6.21967	+	1.14702i	0.983417	+	0.181361i
$41$	−5.70832	+	4.14734i	−0.891490	+	0.647706i	−0.936266	−	0.351291i	$-0.885743\pi$
$41$	−5.70832	+	4.14734i	−0.891490	+	0.647706i	0.0447759	+	0.998997i	$0.485743\pi$
$42$		0			0
$43$	−6.48875	−	6.48875i	−0.989526	−	0.989526i	0.0104199	−	0.999946i	$-0.496683\pi$
$43$	−6.48875	−	6.48875i	−0.989526	−	0.989526i	−0.999946	+	0.0104199i	$0.996683\pi$
$44$	0.0168733	−	0.00747105i	0.00254374	−	0.00112630i
$45$		0			0
$46$	0.875337	−	8.24696i	0.129061	−	1.21595i
$47$	−3.91751	−	1.99607i	−0.571428	−	0.291157i	0.144303	−	0.989534i	$-0.453906\pi$
$47$	−3.91751	−	1.99607i	−0.571428	−	0.291157i	−0.715731	+	0.698376i	$0.753906\pi$
$48$		0			0
$49$			6.77096i			0.967280i
$50$	−4.11667	+	5.74917i	−0.582186	+	0.813056i
$51$		0			0
$52$	3.58865	−	4.41309i	0.497656	−	0.611985i
$53$	0.604811	+	0.308167i	0.0830772	+	0.0423299i	0.495035	−	0.868873i	$-0.335155\pi$
$53$	0.604811	+	0.308167i	0.0830772	+	0.0423299i	−0.411958	+	0.911203i	$0.635155\pi$
$54$		0			0
$55$	−0.000458296		0.0206263i	−6.17966e−5		0.00278125i
$56$	1.35362	+	0.00416215i	0.180885	+	0.000556191i
$57$		0			0
$58$	4.78896	−	0.246057i	0.628821	−	0.0323089i
$59$	−2.04303	+	1.48435i	−0.265979	+	0.193245i	−0.712779	−	0.701389i	$-0.752564\pi$
$59$	−2.04303	+	1.48435i	−0.265979	+	0.193245i	0.446800	+	0.894634i	$0.352564\pi$
$60$		0			0
$61$	−7.27946	−	5.28884i	−0.932039	−	0.677166i	0.0144522	−	0.999896i	$-0.495400\pi$
$61$	−7.27946	−	5.28884i	−0.932039	−	0.677166i	−0.946491	+	0.322730i	$0.895400\pi$
$62$	5.41056	+	3.52155i	0.687142	+	0.447237i
$63$		0			0
$64$	−0.0491968	+	7.99985i	−0.00614960	+	0.999981i
$65$	2.76053	+	5.72902i	0.342402	+	0.710597i
$66$		0			0
$67$	−4.59556	−	9.01929i	−0.561437	−	1.10188i	−0.980973	−	0.194143i	$-0.937807\pi$
$67$	−4.59556	−	9.01929i	−0.561437	−	1.10188i	0.419537	−	0.907738i	$-0.362193\pi$
$68$	8.49624	+	0.462735i	1.03032	+	0.0561149i
$69$		0			0
$70$	−0.647517	+	1.36788i	−0.0773931	+	0.163493i
$71$	−6.68849	+	2.17322i	−0.793777	+	0.257914i	−0.677712	−	0.735328i	$-0.737028\pi$
$71$	−6.68849	+	2.17322i	−0.793777	+	0.257914i	−0.116066	+	0.993242i	$0.537028\pi$
$72$		0			0
$73$	2.91467	−	0.461638i	0.341136	−	0.0540306i	0.0164838	−	0.999864i	$-0.494753\pi$
$73$	2.91467	−	0.461638i	0.341136	−	0.0540306i	0.324652	+	0.945834i	$0.394753\pi$
$74$	8.39652	+	3.74869i	0.976076	+	0.435776i
$75$		0			0
$76$	−10.7572	+	9.64596i	−1.23393	+	1.10647i
$77$	0.000690764		0.00436131i	7.87199e−5		0.000497018i
$78$		0			0
$79$	−0.730993	−	2.24976i	−0.0822431	−	0.253118i	0.901477	−	0.432828i	$-0.142484\pi$
$79$	−0.730993	−	2.24976i	−0.0822431	−	0.253118i	−0.983720	+	0.179710i	$0.942484\pi$
$80$	−8.07245	−	3.85170i	−0.902527	−	0.430633i
$81$		0			0
$82$	9.31941	−	3.56643i	1.02916	−	0.393846i
$83$	−3.36914	+	1.71666i	−0.369811	+	0.188428i	−0.629013	−	0.777395i	$-0.716541\pi$
$83$	−3.36914	+	1.71666i	−0.369811	+	0.188428i	0.259201	+	0.965823i	$0.416541\pi$
$84$		0			0
$85$	−4.50611	+	8.37826i	−0.488756	+	0.908750i
$86$	6.47723	+	11.2455i	0.698458	+	1.21263i
$87$		0			0
$88$	−0.0257880	+	0.00400318i	−0.00274901	+	0.000426740i
$89$	9.05282	−	12.4601i	0.959597	−	1.32077i	0.0124672	−	0.999922i	$-0.496031\pi$
$89$	9.05282	−	12.4601i	0.959597	−	1.32077i	0.947130	−	0.320850i	$-0.103969\pi$
$90$		0			0
$91$	0.800028	+	1.10114i	0.0838657	+	0.115431i
$92$	−4.22554	+	10.9408i	−0.440543	+	1.14066i
$93$		0			0
$94$	4.61654	+	4.16533i	0.476160	+	0.429621i
$95$	−4.64936	−	15.4705i	−0.477014	−	1.58724i
$96$		0			0
$97$	−8.12690	+	15.9499i	−0.825162	+	1.61947i	−0.0407999	+	0.999167i	$0.512991\pi$
$97$	−8.12690	+	15.9499i	−0.825162	+	1.61947i	−0.784362	+	0.620304i	$0.787009\pi$
$98$	2.48782	−	9.24676i	0.251308	−	0.934064i
$99$		0			0
$100$	7.73433	−	6.33879i	0.773433	−	0.633879i
$101$	−18.2367			−1.81462			−0.907310	−	0.420462i	$-0.861868\pi$
$101$	−18.2367			−1.81462			−0.907310	+	0.420462i	$0.861868\pi$
$102$		0			0
$103$	−4.91489	+	9.64602i	−0.484279	+	0.950451i	0.511554	+	0.859251i	$0.329070\pi$
$103$	−4.91489	+	9.64602i	−0.484279	+	0.950451i	−0.995833	+	0.0911996i	$0.970930\pi$
$104$	−6.52232	+	4.70817i	−0.639566	+	0.461674i
$105$		0			0
$106$	−0.712731	−	0.643070i	−0.0692266	−	0.0624605i
$107$	−3.97407	+	3.97407i	−0.384188	+	0.384188i	−0.872608	−	0.488421i	$-0.837573\pi$
$107$	−3.97407	+	3.97407i	−0.384188	+	0.384188i	0.488421	+	0.872608i	$0.337573\pi$
$108$		0			0
$109$	9.21485	+	12.6831i	0.882622	+	1.21483i	0.975688	+	0.219165i	$0.0703333\pi$
$109$	9.21485	+	12.6831i	0.882622	+	1.21483i	−0.0930657	+	0.995660i	$0.529667\pi$
$110$	0.00820449	−	0.0279999i	0.000782268	−	0.00266969i
$111$		0			0
$112$	−1.84704	−	0.503038i	−0.174529	−	0.0475327i
$113$	0.776105	−	4.90013i	0.0730098	−	0.460966i	−0.923915	−	0.382598i	$-0.875029\pi$
$113$	0.776105	−	4.90013i	0.0730098	−	0.460966i	0.996925	−	0.0783672i	$-0.0249707\pi$
$114$		0			0
$115$	−9.06391	−	9.47585i	−0.845214	−	0.883627i
$116$	−6.63045	−	1.42356i	−0.615622	−	0.132174i
$117$		0			0
$118$	3.33544	−	1.27644i	0.307052	−	0.117505i
$119$	−0.629182	+	1.93642i	−0.0576770	+	0.177512i
$120$		0			0
$121$	3.39916	+	10.4615i	0.309015	+	0.951049i
$122$	7.99794	+	9.89735i	0.724099	+	0.896064i
$123$		0			0
$124$	−6.09502	−	6.79718i	−0.547349	−	0.610405i
$125$	2.73911	+	10.8396i	0.244994	+	0.969525i
$126$		0			0
$127$	3.89805	−	0.617390i	0.345896	−	0.0547845i	0.0189303	−	0.999821i	$-0.493974\pi$
$127$	3.89805	−	0.617390i	0.345896	−	0.0547845i	0.326965	+	0.945036i	$0.393974\pi$
$128$	3.00653	−	10.9069i	0.265742	−	0.964044i
$129$		0			0
$130$	−1.66494	−	8.83812i	−0.146025	−	0.775154i
$131$	4.49851	+	1.46166i	0.393037	+	0.127705i	0.498866	−	0.866679i	$-0.333750\pi$
$131$	4.49851	+	1.46166i	0.393037	+	0.127705i	−0.105830	+	0.994384i	$0.533750\pi$
$132$		0			0
$133$	−1.56963	−	3.08056i	−0.136104	−	0.267119i
$134$	2.96201	+	14.0057i	0.255878	+	1.20991i
$135$		0			0
$136$	−11.4329	−	3.75367i	−0.980360	−	0.321874i
$137$	−2.52679	−	0.400204i	−0.215878	−	0.0341917i	0.0475584	−	0.998868i	$-0.484856\pi$
$137$	−2.52679	−	0.400204i	−0.215878	−	0.0341917i	−0.263437	+	0.964677i	$0.584856\pi$
$138$		0			0
$139$	9.10494	+	6.61513i	0.772271	+	0.561088i	0.902649	−	0.430377i	$-0.141619\pi$
$139$	9.10494	+	6.61513i	0.772271	+	0.561088i	−0.130378	+	0.991464i	$0.541619\pi$
$140$	1.38688	−	1.63013i	0.117212	−	0.137771i
$141$		0			0
$142$	9.93262	−	0.510339i	0.833527	−	0.0428267i
$143$	−0.0185550	−	0.0185550i	−0.00155165	−	0.00155165i
$144$		0			0
$145$	4.59174	−	6.03346i	0.381324	−	0.501051i
$146$	−4.15003	−	0.440487i	−0.343459	−	0.0364549i
$147$		0			0
$148$	−10.0893	−	8.20449i	−0.829339	−	0.674405i
$149$			1.04684i			0.0857604i	0.999080	+	0.0428802i	$0.0136534\pi$
$149$			1.04684i			0.0857604i	−0.999080	+	0.0428802i	$0.986347\pi$
$150$		0			0
$151$			2.66118i			0.216564i	0.994120	+	0.108282i	$0.0345349\pi$
$151$			2.66118i			0.216564i	−0.994120	+	0.108282i	$0.965465\pi$
$152$	18.2347	−	9.22054i	1.47903	−	0.747885i
$153$		0			0
$154$	0.000659115	−	0.00620983i	5.31130e−5	−	0.000500402i
$155$	9.77538	−	2.93780i	0.785177	−	0.235970i
$156$		0			0
$157$	3.72092	+	3.72092i	0.296962	+	0.296962i	0.839823	−	0.542861i	$-0.182659\pi$
$157$	3.72092	+	3.72092i	0.296962	+	0.296962i	−0.542861	+	0.839823i	$0.682659\pi$
$158$	0.171660	+	3.34098i	0.0136565	+	0.265794i
$159$		0			0
$160$	9.60892	+	8.22609i	0.759652	+	0.650330i
$161$	−2.27051	−	1.64962i	−0.178941	−	0.130008i
$162$		0			0
$163$	−18.2514	−	2.89074i	−1.42956	−	0.226420i	−0.606821	−	0.794838i	$-0.707556\pi$
$163$	−18.2514	−	2.89074i	−1.42956	−	0.226420i	−0.822740	+	0.568418i	$0.807556\pi$
$164$	−14.0374	+	1.44631i	−1.09614	+	0.112938i
$165$		0			0
$166$	5.23181	−	1.10645i	0.406068	−	0.0858774i
$167$	−9.01487	−	17.6927i	−0.697592	−	1.36910i	−0.919132	−	0.393950i	$-0.871108\pi$
$167$	−9.01487	−	17.6927i	−0.697592	−	1.36910i	0.221540	−	0.975151i	$-0.428892\pi$
$168$		0			0
$169$	4.67117	+	1.51776i	0.359321	+	0.116750i
$170$	9.23215	−	9.78611i	0.708074	−	0.750560i
$171$		0			0
$172$	−4.71375	−	17.7373i	−0.359420	−	1.35246i
$173$	5.74053	−	0.909210i	0.436444	−	0.0691260i	0.0656537	−	0.997842i	$-0.479087\pi$
$173$	5.74053	−	0.909210i	0.436444	−	0.0691260i	0.370791	+	0.928716i	$0.379087\pi$
$174$		0			0
$175$	0.990581	+	2.17823i	0.0748809	+	0.164659i
$176$	0.0366882	+	0.00400823i	0.00276548	+	0.000302132i
$177$		0			0
$178$	−16.9412	+	13.6899i	−1.26979	+	1.02611i
$179$	7.03355	+	21.6470i	0.525712	+	1.61798i	0.762903	+	0.646513i	$0.223774\pi$
$179$	7.03355	+	21.6470i	0.525712	+	1.61798i	−0.237190	+	0.971463i	$0.576226\pi$
$180$		0			0
$181$	1.43751	−	4.42421i	0.106849	−	0.328849i	−0.883311	−	0.468788i	$-0.844691\pi$
$181$	1.43751	−	4.42421i	0.106849	−	0.328849i	0.990160	+	0.139939i	$0.0446908\pi$
$182$	−0.687969	−	1.79773i	−0.0509957	−	0.133256i
$183$		0			0
$184$	9.79055	−	13.3888i	0.721769	−	0.987033i
$185$	13.0979	−	6.31122i	0.962974	−	0.464010i
$186$		0			0
$187$	0.00614067	−	0.0387707i	0.000449050	−	0.00283519i
$188$	−4.77413	−	7.38461i	−0.348189	−	0.538578i
$189$		0			0
$190$	0.665150	+	22.8355i	0.0482550	+	1.65666i
$191$	−13.5285	−	18.6203i	−0.978885	−	1.34732i	−0.937428	−	0.348179i	$-0.886800\pi$
$191$	−13.5285	−	18.6203i	−0.978885	−	1.34732i	−0.0414563	−	0.999140i	$-0.513200\pi$
$192$		0			0
$193$	16.4997	−	16.4997i	1.18767	−	1.18767i	0.209964	−	0.977709i	$-0.432665\pi$
$193$	16.4997	−	16.4997i	1.18767	−	1.18767i	0.977709	−	0.209964i	$-0.0673347\pi$
$194$	16.9589	−	18.7960i	1.21758	−	1.34947i
$195$		0			0
$196$	−6.79499	+	11.7137i	−0.485356	+	0.836696i
$197$	3.30435	−	6.48515i	0.235425	−	0.462048i	−0.742823	−	0.669488i	$-0.766513\pi$
$197$	3.30435	−	6.48515i	0.235425	−	0.462048i	0.978248	+	0.207441i	$0.0665134\pi$
$198$		0			0
$199$	18.5916			1.31793			0.658963	−	0.752175i	$-0.270995\pi$
$199$	18.5916			1.31793			0.658963	+	0.752175i	$0.270995\pi$
$200$	−12.8914	+	5.81477i	−0.911560	+	0.411167i
$201$		0			0
$202$	24.9050	+	6.70063i	1.75231	+	0.471455i
$203$	0.736715	−	1.44588i	0.0517072	−	0.101481i
$204$		0			0
$205$	5.20761	−	14.8932i	0.363715	−	1.04019i
$206$	10.2562	−	11.3672i	0.714584	−	0.791992i
$207$		0			0
$208$	10.6371	−	4.03324i	0.737550	−	0.279655i
$209$	0.0391794	+	0.0539258i	0.00271009	+	0.00373012i
$210$		0			0
$211$	14.5423	−	20.0157i	1.00113	−	1.37794i	0.0765018	−	0.997069i	$-0.475625\pi$
$211$	14.5423	−	20.0157i	1.00113	−	1.37794i	0.924629	−	0.380869i	$-0.124375\pi$
$212$	0.737061	+	1.14008i	0.0506216	+	0.0783013i
$213$		0			0
$214$	6.88736	−	3.96701i	0.470810	−	0.271179i
$215$	20.1903	+	3.65932i	1.37697	+	0.249563i
$216$		0			0
$217$	1.94653	−	0.991804i	0.132139	−	0.0673281i
$218$	−7.92414	−	20.7065i	−0.536690	−	1.40242i
$219$		0			0
$220$	−0.0214923	+	0.0352235i	−0.00144901	+	0.00237477i
$221$	−3.73899	−	11.5074i	−0.251512	−	0.774074i
$222$		0			0
$223$	1.09479	+	6.91226i	0.0733129	+	0.462879i	0.996846	+	0.0793606i	$0.0252879\pi$
$223$	1.09479	+	6.91226i	0.0733129	+	0.462879i	−0.923533	+	0.383519i	$0.874712\pi$
$224$	2.33758	+	1.36562i	0.156186	+	0.0912446i
$225$		0			0
$226$	−2.86032	+	6.40670i	−0.190266	+	0.426167i
$227$	14.5565	−	2.30553i	0.966151	−	0.153023i	0.346629	−	0.938002i	$-0.387326\pi$
$227$	14.5565	−	2.30553i	0.966151	−	0.153023i	0.619522	+	0.784979i	$0.287326\pi$
$228$		0			0
$229$	−25.5635	+	8.30610i	−1.68929	+	0.548882i	−0.986677	−	0.162693i	$-0.947982\pi$
$229$	−25.5635	+	8.30610i	−1.68929	+	0.548882i	−0.702610	+	0.711575i	$0.747982\pi$
$230$	8.89646	+	16.2710i	0.586615	+	1.07288i
$231$		0			0
$232$	8.53182	+	4.38028i	0.560141	+	0.287579i
$233$	9.83267	+	19.2977i	0.644160	+	1.26423i	0.950029	+	0.312161i	$0.101053\pi$
$233$	9.83267	+	19.2977i	0.644160	+	1.26423i	−0.305870	+	0.952073i	$0.598947\pi$
$234$		0			0
$235$	9.74211	−	1.32189i	0.635505	−	0.0862304i
$236$	−5.02404	+	0.517638i	−0.327037	+	0.0336954i
$237$		0			0
$238$	1.57073	−	2.41330i	0.101815	−	0.156431i
$239$	8.98000	+	6.52436i	0.580868	+	0.422025i	0.839037	−	0.544074i	$-0.183119\pi$
$239$	8.98000	+	6.52436i	0.580868	+	0.422025i	−0.258169	+	0.966100i	$0.583119\pi$
$240$		0			0
$241$	1.02024	−	0.741251i	0.0657197	−	0.0477481i	−0.554440	−	0.832223i	$-0.687068\pi$
$241$	1.02024	−	0.741251i	0.0657197	−	0.0477481i	0.620160	+	0.784475i	$0.287068\pi$
$242$	−0.798227	−	15.5357i	−0.0513120	−	0.998675i
$243$		0			0
$244$	−7.28584	−	16.4550i	−0.466428	−	1.05342i
$245$	−8.62498	−	12.4434i	−0.551030	−	0.794983i
$246$		0			0
$247$	18.3066	+	9.32770i	1.16482	+	0.593507i
$248$	5.82621	+	11.5220i	0.369965	+	0.731650i
$249$		0			0
$250$	0.242080	−	15.8095i	0.0153105	−	0.999883i
$251$			1.61115i			0.101695i	0.998706	+	0.0508475i	$0.0161923\pi$
$251$			1.61115i			0.101695i	−0.998706	+	0.0508475i	$0.983808\pi$
$252$		0			0
$253$	0.0482098	+	0.0245641i	0.00303093	+	0.00154433i
$254$	−5.55021	−	0.589103i	−0.348251	−	0.0369636i
$255$		0			0
$256$	−8.11335	+	13.7903i	−0.507084	+	0.861897i
$257$	21.7848	+	21.7848i	1.35890	+	1.35890i	0.875276	+	0.483624i	$0.160680\pi$
$257$	21.7848	+	21.7848i	1.35890	+	1.35890i	0.483624	+	0.875276i	$0.339320\pi$
$258$		0			0
$259$	2.51747	−	1.82905i	0.156428	−	0.113652i
$260$	−0.973629	+	12.6815i	−0.0603819	+	0.786474i
$261$		0			0
$262$	−5.60634	−	3.64898i	−0.346361	−	0.225434i
$263$	−17.8870	−	2.83302i	−1.10296	−	0.174691i	−0.421700	−	0.906735i	$-0.638567\pi$
$263$	−17.8870	−	2.83302i	−1.10296	−	0.174691i	−0.681257	+	0.732044i	$0.738567\pi$
$264$		0			0
$265$	−1.50405	+	0.204081i	−0.0923930	+	0.0125366i
$266$	1.01168	+	4.78369i	0.0620302	+	0.293307i
$267$		0			0
$268$	1.10099	−	20.2152i	0.0672537	−	1.23484i
$269$	4.11734	+	1.33780i	0.251038	+	0.0815673i	0.431833	−	0.901954i	$-0.357867\pi$
$269$	4.11734	+	1.33780i	0.251038	+	0.0815673i	−0.180795	+	0.983521i	$0.557867\pi$
$270$		0			0
$271$	−18.2185	+	5.91954i	−1.10669	+	0.359587i	−0.804675	−	0.593715i	$-0.797661\pi$
$271$	−18.2185	+	5.91954i	−1.10669	+	0.359587i	−0.302019	+	0.953302i	$0.597661\pi$
$272$	14.2341	+	9.32692i	0.863069	+	0.565528i
$273$		0			0
$274$	3.30366	+	1.47494i	0.199582	+	0.0891047i
$275$	−0.0254319	−	0.0384901i	−0.00153360	−	0.00232104i
$276$		0			0
$277$	−0.838827	−	5.29615i	−0.0504003	−	0.318215i	−0.999989	−	0.00471597i	$-0.998499\pi$
$277$	−0.838827	−	5.29615i	−0.0504003	−	0.318215i	0.949589	−	0.313499i	$-0.101501\pi$
$278$	−10.0036	−	12.3793i	−0.599976	−	0.742463i
$279$		0			0
$280$	−2.49294	+	1.71662i	−0.148982	+	0.102588i
$281$	0.313860	−	0.965962i	0.0187233	−	0.0576245i	−0.941258	−	0.337687i	$-0.890355\pi$
$281$	0.313860	−	0.965962i	0.0187233	−	0.0576245i	0.959982	+	0.280063i	$0.0903553\pi$
$282$		0			0
$283$	1.23867	−	0.631135i	0.0736314	−	0.0375171i	−0.416787	−	0.909004i	$-0.636844\pi$
$283$	1.23867	−	0.631135i	0.0736314	−	0.0375171i	0.490418	+	0.871487i	$0.336844\pi$
$284$	−13.7520	−	2.95255i	−0.816031	−	0.175202i
$285$		0			0
$286$	0.0185220	+	0.0321572i	0.00109523	+	0.00190149i
$287$	0.528247	−	3.33522i	0.0311814	−	0.196872i
$288$		0			0
$289$	0.646596	−	0.889963i	0.0380351	−	0.0523508i
$290$	−8.48756	+	6.55246i	−0.498407	+	0.384774i
$291$		0			0
$292$	5.50564	+	2.12638i	0.322193	+	0.124437i
$293$	−7.08403	+	7.08403i	−0.413853	+	0.413853i	−0.883079	−	0.469225i	$-0.844533\pi$
$293$	−7.08403	+	7.08403i	−0.413853	+	0.413853i	0.469225	+	0.883079i	$0.344533\pi$
$294$		0			0
$295$	1.86382	−	5.33033i	0.108516	−	0.310344i
$296$	10.7640	+	14.9115i	0.625643	+	0.866716i
$297$		0			0
$298$	0.384635	−	1.42961i	0.0222813	−	0.0828154i
$299$	16.6780			0.964513
$300$		0			0
$301$	4.39168			0.253132
$302$	0.977784	−	3.63424i	0.0562652	−	0.209127i
$303$		0			0
$304$	−28.2901	+	5.89213i	−1.62255	+	0.337937i
$305$	20.1150	+	0.446934i	1.15178	+	0.0255914i
$306$		0			0
$307$	−7.18265	+	7.18265i	−0.409935	+	0.409935i	−0.881716	−	0.471781i	$-0.843611\pi$
$307$	−7.18265	+	7.18265i	−0.409935	+	0.409935i	0.471781	+	0.881716i	$0.343611\pi$
$308$	−0.00318177	+	0.00823827i	−0.000181298	+	0.000469419i
$309$		0			0
$310$	−14.4292	+	0.420290i	−0.819521	+	0.0238709i
$311$	13.8607	−	19.0776i	0.785967	−	1.08179i	−0.208631	−	0.977994i	$-0.566901\pi$
$311$	13.8607	−	19.0776i	0.785967	−	1.08179i	0.994599	−	0.103797i	$-0.0330991\pi$
$312$		0			0
$313$	2.12973	−	13.4466i	0.120379	−	0.760045i	−0.851463	−	0.524414i	$-0.824284\pi$
$313$	2.12973	−	13.4466i	0.120379	−	0.760045i	0.971843	−	0.235631i	$-0.0757156\pi$
$314$	−3.71432	−	6.44864i	−0.209611	−	0.363918i
$315$		0			0
$316$	0.993132	−	4.62567i	0.0558680	−	0.260214i
$317$	−15.3739	+	7.83338i	−0.863483	+	0.439967i	−0.828875	−	0.559434i	$-0.811018\pi$
$317$	−15.3739	+	7.83338i	−0.863483	+	0.439967i	−0.0346084	+	0.999401i	$0.511018\pi$
$318$		0			0
$319$	−0.00966773	+	0.0297542i	−0.000541289	+	0.00166592i
$320$	−10.0999	−	14.7645i	−0.564604	−	0.825362i
$321$		0			0
$322$	2.49461	+	3.08704i	0.139019	+	0.172034i
$323$	4.80804	+	30.3568i	0.267526	+	1.68909i
$324$		0			0
$325$	−12.3709	−	7.01217i	−0.686217	−	0.388965i
$326$	23.8629	+	10.6538i	1.32164	+	0.590058i
$327$		0			0
$328$	19.7016	+	3.18256i	1.08784	+	0.175728i
$329$	2.00120	−	0.650228i	0.110330	−	0.0358482i
$330$		0			0
$331$	−20.8211	−	6.76518i	−1.14443	−	0.371848i	−0.325387	−	0.945581i	$-0.605495\pi$
$331$	−20.8211	−	6.76518i	−1.14443	−	0.371848i	−0.819042	+	0.573733i	$0.805495\pi$
$332$	−7.55136	−	0.411274i	−0.414435	−	0.0225716i
$333$		0			0
$334$	5.81042	+	27.4743i	0.317932	+	1.50333i
$335$	19.9345	+	10.7214i	1.08914	+	0.585775i
$336$		0			0
$337$	31.0160	+	4.91245i	1.68955	+	0.267598i	0.925826	−	0.377949i	$-0.123371\pi$
$337$	31.0160	+	4.91245i	1.68955	+	0.267598i	0.763721	+	0.645547i	$0.223371\pi$
$338$	−5.82152	−	3.78903i	−0.316649	−	0.206096i
$339$		0			0
$340$	−16.2035	+	9.97227i	−0.878761	+	0.540822i
$341$	−0.0340743	+	0.0247564i	−0.00184522	+	0.00134063i
$342$		0			0
$343$	−4.66019	−	4.66019i	−0.251626	−	0.251626i
$344$	−0.0798069	+	25.9549i	−0.00430290	+	1.39939i
$345$		0			0
$346$	−8.17362	−	0.867553i	−0.439416	−	0.0466399i
$347$	−27.9531	−	14.2428i	−1.50060	−	0.764594i	−0.505440	−	0.862862i	$-0.668670\pi$
$347$	−27.9531	−	14.2428i	−1.50060	−	0.764594i	−0.995160	+	0.0982679i	$0.968670\pi$
$348$		0			0
$349$		−	32.7545i		−	1.75331i	−0.481121	−	0.876654i	$-0.659770\pi$
$349$		−	32.7545i		−	1.75331i	0.481121	−	0.876654i	$-0.340230\pi$
$350$	−0.552449	−	3.33867i	−0.0295296	−	0.178459i
$351$		0			0
$352$	−0.0486306	−	0.0189540i	−0.00259202	−	0.00101025i
$353$	−11.6240	−	5.92270i	−0.618680	−	0.315233i	0.116411	−	0.993201i	$-0.462861\pi$
$353$	−11.6240	−	5.92270i	−0.618680	−	0.315233i	−0.735092	+	0.677968i	$0.762861\pi$
$354$		0			0
$355$	9.52358	−	12.5138i	0.505459	−	0.664163i
$356$	28.1657	−	12.4711i	1.49278	−	0.660965i
$357$		0			0
$358$	−1.65169	−	32.1466i	−0.0872948	−	1.69900i
$359$	−9.36163	+	6.80162i	−0.494088	+	0.358976i	−0.806754	−	0.590887i	$-0.798778\pi$
$359$	−9.36163	+	6.80162i	−0.494088	+	0.358976i	0.312666	+	0.949863i	$0.398778\pi$
$360$		0			0
$361$	−26.8516	−	19.5088i	−1.41324	−	1.02678i
$362$	−3.58870	+	5.51374i	−0.188618	+	0.289796i
$363$		0			0
$364$	0.278995	+	2.70784i	0.0146233	+	0.141929i
$365$	−4.76843	+	4.56114i	−0.249591	+	0.238741i
$366$		0			0
$367$	3.05019	+	5.98633i	0.159219	+	0.312484i	0.956810	−	0.290714i	$-0.0938928\pi$
$367$	3.05019	+	5.98633i	0.159219	+	0.312484i	−0.797591	+	0.603198i	$0.793893\pi$
$368$	−18.2898	+	14.6871i	−0.953423	+	0.765616i
$369$		0			0
$370$	−20.2060	+	3.80643i	−1.05046	+	0.197887i
$371$	−0.308958	+	0.100386i	−0.0160403	+	0.00521180i
$372$		0			0
$373$	−7.76622	+	1.23005i	−0.402120	+	0.0636895i	−0.354219	−	0.935163i	$-0.615253\pi$
$373$	−7.76622	+	1.23005i	−0.402120	+	0.0636895i	−0.0479009	+	0.998852i	$0.515253\pi$
$374$	−0.0226313	+	0.0506909i	−0.00117024	+	0.00262116i
$375$		0			0
$376$	3.80650	+	11.8389i	0.196305	+	0.610546i
$377$	1.50856	+	9.52469i	0.0776950	+	0.490547i
$378$		0			0
$379$	5.05817	+	15.5675i	0.259821	+	0.799646i	0.992841	+	0.119440i	$0.0381099\pi$
$379$	5.05817	+	15.5675i	0.259821	+	0.799646i	−0.733021	+	0.680206i	$0.761890\pi$
$380$	7.48199	−	31.4297i	0.383818	−	1.61231i
$381$		0			0
$382$	11.6335	+	30.3995i	0.595224	+	1.55537i
$383$	−21.7577	+	11.0861i	−1.11177	+	0.566473i	−0.910685	−	0.413102i	$-0.864445\pi$
$383$	−21.7577	+	11.0861i	−1.11177	+	0.566473i	−0.201081	+	0.979575i	$0.564445\pi$
$384$		0			0
$385$	−0.00682499	−	0.00713517i	−0.000347833	−	0.000363642i
$386$	−28.5952	+	16.4704i	−1.45546	+	0.838320i
$387$		0			0
$388$	−30.0661	+	19.4376i	−1.52637	+	0.986795i
$389$	−5.31656	+	7.31762i	−0.269560	+	0.371018i	−0.922241	−	0.386615i	$-0.873644\pi$
$389$	−5.31656	+	7.31762i	−0.269560	+	0.371018i	0.652681	+	0.757633i	$0.273644\pi$
$390$		0			0
$391$	14.6646	+	20.1841i	0.741620	+	1.02075i
$392$	13.5835	−	13.5002i	0.686070	−	0.681864i
$393$		0			0
$394$	−6.89539	+	7.64234i	−0.347385	+	0.385016i
$395$	4.20919	+	3.20339i	0.211787	+	0.161180i
$396$		0			0
$397$	−6.40609	+	12.5727i	−0.321512	+	0.631004i	−0.994034	−	0.109074i	$-0.965211\pi$
$397$	−6.40609	+	12.5727i	−0.321512	+	0.631004i	0.672521	+	0.740078i	$0.265211\pi$
$398$	−25.3897	−	6.83104i	−1.27267	−	0.342409i
$399$		0			0
$400$	19.7416	−	3.20431i	0.987082	−	0.160216i
$401$	−11.2786			−0.563225			−0.281613	−	0.959528i	$-0.590869\pi$
$401$	−11.2786			−0.563225			−0.281613	+	0.959528i	$0.590869\pi$
$402$		0			0
$403$	−5.89392	+	11.5675i	−0.293597	+	0.576217i
$404$	−31.5495	−	18.3014i	−1.56964	−	0.910530i
$405$		0			0
$406$	−1.53735	+	1.70388i	−0.0762973	+	0.0845623i
$407$	−0.0424210	+	0.0424210i	−0.00210273	+	0.00210273i
$408$		0			0
$409$	−3.93615	−	5.41764i	−0.194630	−	0.267885i	0.700537	−	0.713616i	$-0.252944\pi$
$409$	−3.93615	−	5.41764i	−0.194630	−	0.267885i	−0.895167	+	0.445731i	$0.852944\pi$
$410$	−12.5839	+	18.4255i	−0.621475	+	0.909971i
$411$		0			0
$412$	−18.1830	+	11.7553i	−0.895812	+	0.579140i
$413$	0.189061	−	1.19369i	0.00930310	−	0.0587374i
$414$		0			0
$415$	4.00498	−	7.44651i	0.196597	−	0.365535i
$416$	−16.0085	+	1.59966i	−0.784880	+	0.0784296i
$417$		0			0
$418$	−0.0336916	−	0.0880392i	−0.00164791	−	0.00430614i
$419$	5.35944	−	16.4947i	0.261826	−	0.805817i	−0.730582	−	0.682825i	$-0.760751\pi$
$419$	5.35944	−	16.4947i	0.261826	−	0.805817i	0.992408	−	0.122992i	$-0.0392490\pi$
$420$		0			0
$421$	2.27461	+	7.00054i	0.110858	+	0.341185i	0.991061	−	0.133413i	$-0.0425935\pi$
$421$	2.27461	+	7.00054i	0.110858	+	0.341185i	−0.880203	+	0.474598i	$0.842594\pi$
$422$	−27.2139	+	21.9913i	−1.32475	+	1.07052i
$423$		0			0
$424$	−0.587671	−	1.82777i	−0.0285398	−	0.0887644i
$425$	−2.39121	−	21.1373i	−0.115991	−	1.02531i
$426$		0			0
$427$	4.25319	−	0.673640i	0.205826	−	0.0325997i
$428$	−10.8633	+	2.88696i	−0.525098	+	0.139546i
$429$		0			0
$430$	−26.2284	−	12.4158i	−1.26484	−	0.598742i
$431$	27.6029	+	8.96873i	1.32959	+	0.432009i	0.885776	−	0.464113i	$-0.153627\pi$
$431$	27.6029	+	8.96873i	1.32959	+	0.432009i	0.443809	+	0.896121i	$0.353627\pi$
$432$		0			0
$433$	5.40336	+	10.6047i	0.259669	+	0.509629i	0.983627	−	0.180215i	$-0.0576793\pi$
$433$	5.40336	+	10.6047i	0.259669	+	0.509629i	−0.723959	+	0.689843i	$0.757679\pi$
$434$	−3.02269	+	0.639254i	−0.145094	+	0.0306852i
$435$		0			0
$436$	3.21351	+	31.1894i	0.153899	+	1.49370i
$437$	−41.8434	−	6.62734i	−2.00164	−	0.317029i
$438$		0			0
$439$	8.32588	+	6.04910i	0.397372	+	0.288708i	0.768470	−	0.639886i	$-0.221018\pi$
$439$	8.32588	+	6.04910i	0.397372	+	0.288708i	−0.371097	+	0.928594i	$0.621018\pi$
$440$	0.0422930	−	0.0402061i	0.00201624	−	0.00191675i
$441$		0			0
$442$	0.878030	+	17.0889i	0.0417636	+	0.812837i
$443$	−19.8963	−	19.8963i	−0.945304	−	0.945304i	0.0532759	−	0.998580i	$-0.483034\pi$
$443$	−19.8963	−	19.8963i	−0.945304	−	0.945304i	−0.998580	+	0.0532759i	$0.983034\pi$
$444$		0			0
$445$	−0.765011	+	34.4305i	−0.0362650	+	1.63216i
$446$	1.04463	−	9.84198i	0.0494649	−	0.466031i
$447$		0			0
$448$	−2.69055	−	2.72385i	−0.127117	−	0.128690i
$449$		−	3.25601i		−	0.153660i	−0.997044	−	0.0768302i	$-0.975520\pi$
$449$		−	3.25601i		−	0.153660i	0.997044	−	0.0768302i	$-0.0244799\pi$
$450$		0			0
$451$			0.0651020i			0.00306553i
$452$	6.26018	−	7.69835i	0.294454	−	0.362100i
$453$		0			0
$454$	−20.7262	−	2.19990i	−0.972730	−	0.103246i
$455$	−2.87292	−	1.00455i	−0.134685	−	0.0470942i
$456$		0			0
$457$	−7.55858	−	7.55858i	−0.353576	−	0.353576i	0.507862	−	0.861438i	$-0.330436\pi$
$457$	−7.55858	−	7.55858i	−0.353576	−	0.353576i	−0.861438	+	0.507862i	$0.830436\pi$
$458$	37.9627	−	1.95053i	1.77388	−	0.0911422i
$459$		0			0
$460$	−6.17107	−	25.4893i	−0.287728	−	1.18844i
$461$	21.9843	+	15.9725i	1.02391	+	0.743915i	0.967081	−	0.254469i	$-0.0819006\pi$
$461$	21.9843	+	15.9725i	1.02391	+	0.743915i	0.0568302	+	0.998384i	$0.481901\pi$
$462$		0			0
$463$	30.3214	+	4.80244i	1.40916	+	0.223188i	0.814207	−	0.580575i	$-0.197172\pi$
$463$	30.3214	+	4.80244i	1.40916	+	0.223188i	0.594949	+	0.803764i	$0.297172\pi$
$464$	−10.0421	−	9.11673i	−0.466191	−	0.423233i
$465$		0			0
$466$	−6.33752	−	29.9667i	−0.293580	−	1.38818i
$467$	5.34562	+	10.4914i	0.247366	+	0.485483i	0.980986	−	0.194076i	$-0.0621710\pi$
$467$	5.34562	+	10.4914i	0.247366	+	0.485483i	−0.733621	+	0.679559i	$0.762171\pi$
$468$		0			0
$469$	4.60735	+	1.49702i	0.212748	+	0.0691260i
$470$	−13.7900	−	1.77426i	−0.636085	−	0.0818407i
$471$		0			0
$472$	7.05127	+	1.13905i	0.324561	+	0.0524289i
$473$	−0.0836257	+	0.0132450i	−0.00384511	+	0.000609006i
$474$		0			0
$475$	28.2510	+	22.5087i	1.29625	+	1.03277i
$476$	−3.03178	+	2.71859i	−0.138961	+	0.124606i
$477$		0			0
$478$	−9.86633	−	12.2095i	−0.451275	−	0.558448i
$479$	9.32001	+	28.6840i	0.425842	+	1.31061i	0.902186	+	0.431348i	$0.141962\pi$
$479$	9.32001	+	28.6840i	0.425842	+	1.31061i	−0.476344	+	0.879259i	$0.658038\pi$
$480$		0			0
$481$	−5.71436	+	17.5870i	−0.260552	+	0.801898i
$482$	−1.66565	+	0.637425i	−0.0758683	+	0.0290339i
$483$		0			0
$484$	−4.61812	+	21.5097i	−0.209915	+	0.977712i
$485$	−5.38199	−	39.6645i	−0.244384	−	1.80107i
$486$		0			0
$487$	3.03505	−	19.1625i	0.137531	−	0.868337i	−0.818379	−	0.574678i	$-0.805127\pi$
$487$	3.03505	−	19.1625i	0.137531	−	0.868337i	0.955910	−	0.293659i	$-0.0948729\pi$
$488$	3.90394	+	25.1487i	0.176723	+	1.13843i
$489$		0			0
$490$	7.20666	+	20.1624i	0.325564	+	0.910845i
$491$	−1.27404	−	1.75356i	−0.0574965	−	0.0791371i	0.779301	−	0.626650i	$-0.215575\pi$
$491$	−1.27404	−	1.75356i	−0.0574965	−	0.0791371i	−0.836797	+	0.547513i	$0.815575\pi$
$492$		0			0
$493$	−10.2006	+	10.2006i	−0.459410	+	0.459410i
$494$	−21.5732	−	19.4647i	−0.970625	−	0.875758i
$495$		0			0
$496$	−3.72308	−	17.8758i	−0.167171	−	0.802645i
$497$	1.52800	−	2.99886i	0.0685400	−	0.134517i
$498$		0			0
$499$	13.9379			0.623948			0.311974	−	0.950091i	$-0.399010\pi$
$499$	13.9379			0.623948			0.311974	+	0.950091i	$0.399010\pi$
$500$	−6.13942	+	21.5013i	−0.274563	+	0.961569i
$501$		0			0
$502$	0.591978	−	2.20027i	0.0264213	−	0.0982029i
$503$	−12.6449	+	24.8171i	−0.563810	+	1.10654i	0.416511	+	0.909131i	$0.363253\pi$
$503$	−12.6449	+	24.8171i	−0.563810	+	1.10654i	−0.980321	+	0.197409i	$0.936747\pi$
$504$		0			0
$505$	33.5148	−	23.2303i	1.49139	−	1.03373i
$506$	−0.0568123	−	0.0512595i	−0.00252561	−	0.00227876i
$507$		0			0
$508$	7.36319	+	2.84380i	0.326689	+	0.126173i
$509$	−9.16632	−	12.6164i	−0.406290	−	0.559210i	0.556019	−	0.831170i	$-0.312328\pi$
$509$	−9.16632	−	12.6164i	−0.406290	−	0.559210i	−0.962309	+	0.271959i	$0.912328\pi$
$510$		0			0
$511$	−0.830121	+	1.14256i	−0.0367224	+	0.0505440i
$512$	16.1469	−	15.8517i	0.713599	−	0.700554i
$513$		0			0
$514$	−21.7461	−	37.7547i	−0.959181	−	1.66529i
$515$	−3.25486	−	23.9878i	−0.143426	−	1.05703i
$516$		0			0
$517$	−0.0361455	+	0.0184170i	−0.00158968	+	0.000809980i
$518$	−4.11002	+	1.57286i	−0.180584	+	0.0691074i
$519$		0			0
$520$	5.98914	−	16.9608i	0.262641	−	0.743779i
$521$	−7.04186	−	21.6726i	−0.308509	−	0.949494i	−0.978344	−	0.206984i	$-0.933635\pi$
$521$	−7.04186	−	21.6726i	−0.308509	−	0.949494i	0.669835	−	0.742510i	$-0.266365\pi$
$522$		0			0
$523$	2.51510	+	15.8797i	0.109977	+	0.694371i	0.979646	+	0.200734i	$0.0643327\pi$
$523$	2.51510	+	15.8797i	0.109977	+	0.694371i	−0.869668	+	0.493637i	$0.835667\pi$
$524$	6.31557	+	7.04313i	0.275897	+	0.307681i
$525$		0			0
$526$	23.3864	+	10.4410i	1.01970	+	0.455251i
$527$	−19.1816	+	3.03807i	−0.835564	+	0.132340i
$528$		0			0
$529$	−10.8318	+	3.51947i	−0.470949	+	0.153021i
$530$	2.12899	+	0.273922i	0.0924774	+	0.0118984i
$531$		0			0
$532$	0.376047	−	6.90456i	0.0163037	−	0.299351i
$533$	9.11024	+	17.8799i	0.394608	+	0.774463i
$534$		0			0
$535$	2.24117	−	12.3657i	0.0968941	−	0.534614i
$536$	−8.93115	+	27.2024i	−0.385767	+	1.17496i
$537$		0			0
$538$	−5.13130	−	3.33978i	−0.221226	−	0.143988i
$539$	0.0505419	+	0.0367208i	0.00217699	+	0.00158168i
$540$		0			0
$541$	6.37355	−	4.63066i	0.274020	−	0.199087i	−0.442285	−	0.896875i	$-0.645832\pi$
$541$	6.37355	−	4.63066i	0.274020	−	0.199087i	0.716305	+	0.697787i	$0.245832\pi$
$542$	27.0551	−	1.39009i	1.16211	−	0.0597095i
$543$		0			0
$544$	−16.0118	−	17.9673i	−0.686502	−	0.770340i
$545$	−33.0908	−	11.5706i	−1.41745	−	0.495631i
$546$		0			0
$547$	−33.1305	−	16.8808i	−1.41656	−	0.721773i	−0.432837	−	0.901472i	$-0.642488\pi$
$547$	−33.1305	−	16.8808i	−1.41656	−	0.721773i	−0.983722	+	0.179699i	$0.942488\pi$
$548$	−3.96971	−	3.22811i	−0.169578	−	0.137898i
$549$		0			0
$550$	0.0205889	+	0.0619083i	0.000877912	+	0.00263978i
$551$		−	24.4959i		−	1.04356i
$552$		0			0
$553$	1.00871	+	0.513962i	0.0428946	+	0.0218559i
$554$	−0.800394	+	7.54089i	−0.0340055	+	0.320382i
$555$		0			0
$556$	9.11292	+	20.5814i	0.386474	+	0.872846i
$557$	12.6617	+	12.6617i	0.536492	+	0.536492i	0.922497	−	0.386005i	$-0.126145\pi$
$557$	12.6617	+	12.6617i	0.536492	+	0.536492i	−0.386005	+	0.922497i	$0.626145\pi$
$558$		0			0
$559$	−21.1138	+	15.3401i	−0.893018	+	0.648816i
$560$	4.03521	−	1.42833i	0.170519	−	0.0603579i
$561$		0			0
$562$	−0.783542	+	1.20385i	−0.0330517	+	0.0507812i
$563$	29.3480	+	4.64826i	1.23687	+	0.195901i	0.740408	−	0.672158i	$-0.234632\pi$
$563$	29.3480	+	4.64826i	1.23687	+	0.195901i	0.496461	+	0.868059i	$0.334632\pi$
$564$		0			0
$565$	4.81558	+	9.99391i	0.202593	+	0.420447i
$566$	−1.92349	+	0.406790i	−0.0808502	+	0.0170986i
$567$		0			0
$568$	17.6956	+	9.08498i	0.742489	+	0.381197i
$569$	26.6584	+	8.66183i	1.11758	+	0.363123i	0.808843	−	0.588025i	$-0.200094\pi$
$569$	26.6584	+	8.66183i	1.11758	+	0.363123i	0.308735	+	0.951148i	$0.400094\pi$
$570$		0			0
$571$	8.01362	−	2.60378i	0.335360	−	0.108965i	−0.136496	−	0.990641i	$-0.543584\pi$
$571$	8.01362	−	2.60378i	0.335360	−	0.108965i	0.471856	+	0.881676i	$0.343584\pi$
$572$	−0.0134793	−	0.0507209i	−0.000563596	−	0.00212075i
$573$		0			0
$574$	−1.94685	+	4.36065i	−0.0812598	+	0.182010i
$575$	28.7279	+	5.86861i	1.19804	+	0.244738i
$576$		0			0
$577$	−1.09509	−	6.91411i	−0.0455891	−	0.287838i	0.954352	−	0.298684i	$-0.0965476\pi$
$577$	−1.09509	−	6.91411i	−0.0455891	−	0.287838i	−0.999941	+	0.0108457i	$0.996548\pi$
$578$	−1.21002	+	0.977802i	−0.0503302	+	0.0406712i
$579$		0			0
$580$	13.9986	−	5.82983i	0.581259	−	0.242070i
$581$	0.559210	−	1.72107i	0.0231999	−	0.0714021i
$582$		0			0
$583$	0.00558037	−	0.00284334i	0.000231115	−	0.000117759i
$584$	−6.73749	−	4.92680i	−0.278799	−	0.203872i
$585$		0			0
$586$	12.2772	−	7.07145i	0.507165	−	0.292119i
$587$	−7.27291	+	45.9194i	−0.300185	+	1.89530i	0.128282	+	0.991738i	$0.459054\pi$
$587$	−7.27291	+	45.9194i	−0.300185	+	1.89530i	−0.428467	+	0.903558i	$0.640946\pi$
$588$		0			0
$589$	19.3838	−	26.6795i	0.798696	−	1.09931i
$590$	−4.50382	+	6.59454i	−0.185419	+	0.271493i
$591$		0			0
$592$	−9.22093	−	24.3189i	−0.378978	−	0.999500i
$593$	23.3870	−	23.3870i	0.960388	−	0.960388i	−0.0388569	−	0.999245i	$-0.512372\pi$
$593$	23.3870	−	23.3870i	0.960388	−	0.960388i	0.999245	+	0.0388569i	$0.0123716\pi$
$594$		0			0
$595$	−1.31036	−	4.36016i	−0.0537196	−	0.178749i
$596$	−1.05055	+	1.81103i	−0.0430323	+	0.0741826i
$597$		0			0
$598$	−22.7763	−	6.12792i	−0.931392	−	0.250589i
$599$	19.0773			0.779479			0.389739	−	0.920925i	$-0.372565\pi$
$599$	19.0773			0.779479			0.389739	+	0.920925i	$0.372565\pi$
$600$		0			0
$601$	15.5584			0.634640			0.317320	−	0.948318i	$-0.397217\pi$
$601$	15.5584			0.634640			0.317320	+	0.948318i	$0.397217\pi$
$602$	−5.99749	−	1.61361i	−0.244439	−	0.0657659i
$603$		0			0
$604$	−2.67062	+	4.60383i	−0.108666	+	0.187327i
$605$	−19.5730	−	14.8960i	−0.795754	−	0.605607i
$606$		0			0
$607$	−8.69480	+	8.69480i	−0.352911	+	0.352911i	−0.861192	−	0.508281i	$-0.830281\pi$
$607$	−8.69480	+	8.69480i	−0.352911	+	0.352911i	0.508281	+	0.861192i	$0.330281\pi$
$608$	40.7993	+	2.34792i	1.65463	+	0.0952206i
$609$		0			0
$610$	−27.3058	−	8.00110i	−1.10558	−	0.323955i
$611$	−7.34989	+	10.1163i	−0.297345	+	0.409260i
$612$		0			0
$613$	−5.95915	+	37.6246i	−0.240688	+	1.51964i	0.510686	+	0.859767i	$0.329391\pi$
$613$	−5.95915	+	37.6246i	−0.240688	+	1.51964i	−0.751374	+	0.659877i	$0.770609\pi$
$614$	12.4481	−	7.16989i	0.502363	−	0.289353i
$615$		0			0
$616$	0.00737213	−	0.0100815i	0.000297032	−	0.000406197i
$617$	2.33785	−	1.19119i	0.0941182	−	0.0479556i	−0.406298	−	0.913741i	$-0.633180\pi$
$617$	2.33785	−	1.19119i	0.0941182	−	0.0479556i	0.500416	+	0.865785i	$0.333180\pi$
$618$		0			0
$619$	−0.100449	+	0.309150i	−0.00403738	+	0.0124258i	−0.953055	−	0.302798i	$-0.902079\pi$
$619$	−0.100449	+	0.309150i	−0.00403738	+	0.0124258i	0.949018	+	0.315223i	$0.102079\pi$
$620$	19.8596	+	4.72767i	0.797581	+	0.189868i
$621$		0			0
$622$	−25.9384	+	20.9605i	−1.04004	+	0.840441i
$623$	1.15306	+	7.28013i	0.0461963	+	0.291672i
$624$		0			0
$625$	−18.8416	−	16.4315i	−0.753662	−	0.657262i
$626$	−7.84907	+	17.5808i	−0.313712	+	0.702669i
$627$		0			0
$628$	2.70306	+	10.1713i	0.107864	+	0.405880i
$629$	−26.3087	+	8.54821i	−1.04900	+	0.340839i
$630$		0			0
$631$	10.0045	+	3.25066i	0.398273	+	0.129407i	0.501304	−	0.865271i	$-0.332854\pi$
$631$	10.0045	+	3.25066i	0.398273	+	0.129407i	−0.103030	+	0.994678i	$0.532854\pi$
$632$	−3.05586	+	5.95215i	−0.121556	+	0.236764i
$633$		0			0
$634$	23.8735	−	5.04890i	0.948138	−	0.200518i
$635$	−6.37726	+	6.10002i	−0.253074	+	0.242072i
$636$		0			0
$637$	19.0197	+	3.01242i	0.753586	+	0.119356i
$638$	0.0241352	−	0.0370817i	0.000955521	−	0.00146808i
$639$		0			0
$640$	8.36813	+	23.8741i	0.330779	+	0.943708i
$641$	35.5379	−	25.8198i	1.40366	−	1.01982i	0.409457	−	0.912329i	$-0.365718\pi$
$641$	35.5379	−	25.8198i	1.40366	−	1.01982i	0.994206	−	0.107492i	$-0.0342819\pi$
$642$		0			0
$643$	10.0572	+	10.0572i	0.396616	+	0.396616i	0.877037	−	0.480422i	$-0.159516\pi$
$643$	10.0572	+	10.0572i	0.396616	+	0.396616i	−0.480422	+	0.877037i	$0.659516\pi$
$644$	−2.27250	−	5.13240i	−0.0895490	−	0.202245i
$645$		0			0
$646$	4.58775	−	43.2233i	0.180502	−	1.70060i
$647$	−24.4178	−	12.4415i	−0.959963	−	0.489126i	−0.0974945	−	0.995236i	$-0.531083\pi$
$647$	−24.4178	−	12.4415i	−0.959963	−	0.489126i	−0.862469	+	0.506110i	$0.831083\pi$
$648$		0			0
$649$			0.0233002i			0.000914613i
$650$	14.3179	+	14.1216i	0.561595	+	0.553894i
$651$		0			0
$652$	−28.6739	−	23.3171i	−1.12296	−	0.913170i
$653$	4.64388	+	2.36618i	0.181729	+	0.0925956i	0.542488	−	0.840063i	$-0.317482\pi$
$653$	4.64388	+	2.36618i	0.181729	+	0.0925956i	−0.360759	+	0.932659i	$0.617482\pi$
$654$		0			0
$655$	−10.1291	+	3.04411i	−0.395777	+	0.118943i
$656$	−25.7362	−	11.5851i	−1.00483	−	0.452324i
$657$		0			0
$658$	−2.97184	+	0.152694i	−0.115855	+	0.00595261i
$659$	−3.08407	+	2.24070i	−0.120138	+	0.0872855i	−0.646232	−	0.763141i	$-0.723656\pi$
$659$	−3.08407	+	2.24070i	−0.120138	+	0.0872855i	0.526094	+	0.850427i	$0.323656\pi$
$660$		0			0
$661$	−21.1830	−	15.3904i	−0.823925	−	0.598616i	0.0939094	−	0.995581i	$-0.470064\pi$
$661$	−21.1830	−	15.3904i	−0.823925	−	0.598616i	−0.917834	+	0.396965i	$0.870064\pi$
$662$	25.9486	+	16.8891i	1.00852	+	0.656412i
$663$		0			0
$664$	10.1614	+	3.33622i	0.394339	+	0.129470i
$665$	6.80869	+	3.66194i	0.264030	+	0.142004i
$666$		0			0
$667$	−9.02728	−	17.7170i	−0.349538	−	0.686006i
$668$	2.15976	−	39.6552i	0.0835636	−	1.53430i
$669$		0			0
$670$	−23.2842	−	21.9662i	−0.899548	−	0.848627i
$671$	−0.0789571	+	0.0256547i	−0.00304810	+	0.000990389i
$672$		0			0
$673$	−25.4790	+	4.03547i	−0.982142	+	0.155556i	−0.626800	−	0.779180i	$-0.715636\pi$
$673$	−25.4790	+	4.03547i	−0.982142	+	0.155556i	−0.355342	+	0.934736i	$0.615636\pi$
$674$	−40.5520	−	18.1047i	−1.56200	−	0.697368i
$675$		0			0
$676$	6.55797	+	7.31346i	0.252230	+	0.281287i
$677$	4.12705	+	26.0571i	0.158615	+	1.00146i	0.930659	+	0.365888i	$0.119235\pi$
$677$	4.12705	+	26.0571i	0.158615	+	1.00146i	−0.772044	+	0.635570i	$0.780765\pi$
$678$		0			0
$679$	−2.64737	−	8.14776i	−0.101597	−	0.312682i
$680$	25.7924	−	7.66504i	0.989095	−	0.293941i
$681$		0			0
$682$	0.0556296	−	0.0212888i	0.00213017	−	0.000815191i
$683$	20.3220	−	10.3546i	0.777600	−	0.396207i	−0.0196878	−	0.999806i	$-0.506267\pi$
$683$	20.3220	−	10.3546i	0.777600	−	0.396207i	0.797288	+	0.603599i	$0.206267\pi$
$684$		0			0
$685$	5.15344	−	2.48319i	0.196903	−	0.0948778i
$686$	4.65191	+	8.07645i	0.177611	+	0.308360i
$687$		0			0
$688$	9.64547	−	35.4160i	0.367730	−	1.35022i
$689$	1.13472	−	1.56181i	0.0432295	−	0.0595003i
$690$		0			0
$691$	27.1958	+	37.4318i	1.03458	+	1.42397i	0.901455	+	0.432872i	$0.142500\pi$
$691$	27.1958	+	37.4318i	1.03458	+	1.42397i	0.133121	+	0.991100i	$0.457500\pi$
$692$	10.8435	+	4.18797i	0.412209	+	0.159203i
$693$		0			0
$694$	32.9409	+	29.7214i	1.25042	+	1.12821i
$695$	−25.1592	−	0.559013i	−0.954344	−	0.0212046i
$696$		0			0
$697$	−13.6282	+	26.7468i	−0.516204	+	1.01311i
$698$	−12.0348	+	44.7312i	−0.455525	+	1.69310i
$699$		0			0
$700$	−0.472260	+	4.76243i	−0.0178498	+	0.180003i
$701$	10.5399			0.398088			0.199044	−	0.979991i	$-0.436216\pi$
$701$	10.5399			0.398088			0.199044	+	0.979991i	$0.436216\pi$
$702$		0			0
$703$	21.3253	−	41.8532i	0.804299	−	1.57852i
$704$	0.0594481	+	0.0437527i	0.00224053	+	0.00164899i
$705$		0			0
$706$	13.6981	+	12.3593i	0.515535	+	0.465147i
$707$	6.17142	−	6.17142i	0.232100	−	0.232100i
$708$		0			0
$709$	−6.66013	−	9.16688i	−0.250126	−	0.344269i	0.665429	−	0.746461i	$-0.268249\pi$
$709$	−6.66013	−	9.16688i	−0.250126	−	0.344269i	−0.915556	+	0.402192i	$0.868249\pi$
$710$	−17.6038	+	13.5902i	−0.660657	+	0.510033i
$711$		0			0
$712$	−43.0467	+	6.68231i	−1.61324	+	0.250430i
$713$	4.18764	−	26.4397i	0.156828	−	0.990175i
$714$		0			0
$715$	0.0577354	+	0.0104640i	0.00215918	+	0.000391333i
$716$	−9.55583	+	44.5078i	−0.357118	+	1.66334i
$717$		0			0
$718$	15.2838	−	5.84893i	0.570386	−	0.218280i
$719$	−8.75905	+	26.9576i	−0.326658	+	1.00535i	0.644029	+	0.765001i	$0.277261\pi$
$719$	−8.75905	+	26.9576i	−0.326658	+	1.00535i	−0.970687	+	0.240348i	$0.922739\pi$
$720$		0			0
$721$	−1.60105	−	4.92751i	−0.0596261	−	0.183510i
$722$	29.5019	+	36.5082i	1.09795	+	1.35869i
$723$		0			0
$724$	6.92680	−	6.21125i	0.257432	−	0.230839i
$725$	−0.753024	+	16.9371i	−0.0279666	+	0.629029i
$726$		0			0
$727$	−43.9866	+	6.96679i	−1.63137	+	0.258384i	−0.903897	−	0.427750i	$-0.859306\pi$
$727$	−43.9866	+	6.96679i	−1.63137	+	0.258384i	−0.727475	+	0.686134i	$0.759306\pi$
$728$	0.613920	−	3.80047i	0.0227534	−	0.140855i
$729$		0			0
$730$	8.18788	−	4.47687i	0.303047	−	0.165697i
$731$	−37.1298	−	12.0642i	−1.37330	−	0.446211i
$732$		0			0
$733$	11.9095	+	23.3738i	0.439889	+	0.863331i	0.999404	+	0.0345111i	$0.0109874\pi$
$733$	11.9095	+	23.3738i	0.439889	+	0.863331i	−0.559515	+	0.828820i	$0.689013\pi$
$734$	−1.96596	−	9.29595i	−0.0725649	−	0.343120i
$735$		0			0
$736$	30.3739	−	13.3372i	1.11960	−	0.491617i
$737$	−0.0922475	−	0.0146106i	−0.00339798	−	0.000538187i
$738$		0			0
$739$	−22.6226	−	16.4363i	−0.832187	−	0.604619i	0.0879901	−	0.996121i	$-0.471956\pi$
$739$	−22.6226	−	16.4363i	−0.832187	−	0.604619i	−0.920177	+	0.391502i	$0.871956\pi$
$740$	28.9929	+	2.22594i	1.06580	+	0.0818272i
$741$		0			0
$742$	0.458812	−	0.0235738i	0.0168435	−	0.000865422i
$743$	−32.7328	−	32.7328i	−1.20085	−	1.20085i	−0.973909	−	0.226941i	$-0.927128\pi$
$743$	−32.7328	−	32.7328i	−1.20085	−	1.20085i	−0.226941	−	0.973909i	$-0.572872\pi$
$744$		0			0
$745$	−1.33348	−	1.92385i	−0.0488550	−	0.0704842i
$746$	11.0579	+	1.17369i	0.404858	+	0.0429719i
$747$		0			0
$748$	0.0495316	−	0.0609107i	0.00181105	−	0.00222712i
$749$		−	2.68970i		−	0.0982796i
$750$		0			0
$751$		−	50.2489i		−	1.83361i	−0.399338	−	0.916804i	$-0.630760\pi$
$751$		−	50.2489i		−	1.83361i	0.399338	−	0.916804i	$-0.369240\pi$
$752$	−0.848417	−	17.5664i	−0.0309386	−	0.640582i
$753$		0			0
$754$	1.43944	−	13.5617i	0.0524215	−	0.493887i
$755$	−3.38986	−	4.89062i	−0.123370	−	0.177988i
$756$		0			0
$757$	−18.7549	−	18.7549i	−0.681658	−	0.681658i	0.278716	−	0.960374i	$-0.410091\pi$
$757$	−18.7549	−	18.7549i	−0.681658	−	0.681658i	−0.960374	+	0.278716i	$0.910091\pi$
$758$	−1.18781	−	23.1182i	−0.0431434	−	0.839690i
$759$		0			0
$760$	−21.7659	+	40.1729i	−0.789531	+	1.45723i
$761$	25.1788	+	18.2935i	0.912731	+	0.663138i	0.941704	−	0.336442i	$-0.109224\pi$
$761$	25.1788	+	18.2935i	0.912731	+	0.663138i	−0.0289729	+	0.999580i	$0.509224\pi$
$762$		0			0
$763$	−7.41043	−	1.17370i	−0.268275	−	0.0424907i
$764$	−4.71780	−	45.7896i	−0.170684	−	1.65661i
$765$		0			0
$766$	33.7867	−	7.14540i	1.22076	−	0.258174i
$767$	3.26058	+	6.39926i	0.117733	+	0.231064i
$768$		0			0
$769$	27.1469	+	8.82055i	0.978941	+	0.318077i	0.754420	−	0.656392i	$-0.227918\pi$
$769$	27.1469	+	8.82055i	0.978941	+	0.318077i	0.224521	+	0.974469i	$0.427918\pi$
$770$	0.00669890	+	0.0122518i	0.000241412	+	0.000441525i
$771$		0			0
$772$	45.1026	−	11.9862i	1.62328	−	0.431392i
$773$	−35.7571	+	5.66336i	−1.28609	+	0.203697i	−0.761784	−	0.647832i	$-0.775676\pi$
$773$	−35.7571	+	5.66336i	−1.28609	+	0.203697i	−0.524308	+	0.851529i	$0.675676\pi$
$774$		0			0
$775$	−14.2226	+	17.8511i	−0.510892	+	0.641229i
$776$	48.2016	−	15.4979i	1.73034	−	0.556344i
$777$		0			0
$778$	9.94924	−	8.03986i	0.356697	−	0.288243i
$779$	−15.7517	−	48.4789i	−0.564365	−	1.73694i
$780$		0			0
$781$	−0.0200515	+	0.0617122i	−0.000717500	+	0.00220824i
$782$	−12.6106	−	32.9525i	−0.450952	−	1.17838i
$783$		0			0
$784$	−23.5106	+	13.4456i	−0.839665	+	0.480202i
$785$	−11.5780	−	2.09841i	−0.413235	−	0.0748953i
$786$		0			0
$787$	3.28931	−	20.7679i	0.117251	−	0.740294i	−0.857081	−	0.515181i	$-0.827725\pi$
$787$	3.28931	−	20.7679i	0.117251	−	0.740294i	0.974333	−	0.225113i	$-0.0722753\pi$
$788$	12.2247	−	7.90322i	0.435486	−	0.281540i
$789$		0			0
$790$	−4.57127	−	5.92127i	−0.162638	−	0.210669i
$791$	1.39560	+	1.92088i	0.0496218	+	0.0682985i
$792$		0			0
$793$	−18.0950	+	18.0950i	−0.642573	+	0.642573i
$794$	13.3680	−	14.8161i	0.474412	−	0.525803i
$795$		0			0
$796$	32.1635	+	18.6576i	1.14000	+	0.661301i
$797$	−0.286364	+	0.562022i	−0.0101435	+	0.0199078i	−0.896023	−	0.444008i	$-0.853556\pi$
$797$	−0.286364	+	0.562022i	−0.0101435	+	0.0199078i	0.885879	+	0.463916i	$0.153556\pi$
$798$		0			0
$799$	−18.7055			−0.661753
$800$	−28.1375	−	2.87761i	−0.994811	−	0.101739i
$801$		0			0
$802$	15.4026	+	4.14403i	0.543884	+	0.146331i
$803$	0.0123612	−	0.0242601i	0.000436216	−	0.000856121i
$804$		0			0
$805$	6.27398	+	0.139401i	0.221129	+	0.00491326i
$806$	12.2992	−	13.6315i	0.433221	−	0.480151i
$807$		0			0
$808$	36.3611	+	36.5854i	1.27918	+	1.28707i
$809$	10.7939	+	14.8566i	0.379495	+	0.522330i	0.955451	−	0.295151i	$-0.0953699\pi$
$809$	10.7939	+	14.8566i	0.379495	+	0.522330i	−0.575956	+	0.817481i	$0.695370\pi$
$810$		0			0
$811$	28.0972	−	38.6725i	0.986625	−	1.35797i	0.0534429	−	0.998571i	$-0.482980\pi$
$811$	28.0972	−	38.6725i	0.986625	−	1.35797i	0.933183	−	0.359403i	$-0.117020\pi$
$812$	2.72553	−	1.76205i	0.0956473	−	0.0618357i
$813$		0			0
$814$	0.0735188	−	0.0423457i	0.00257683	−	0.00148422i
$815$	37.2241	−	17.9365i	1.30390	−	0.628288i
$816$		0			0
$817$	59.0681	−	30.0967i	2.06653	−	1.05295i
$818$	3.38482	+	8.84484i	0.118347	+	0.309253i
$819$		0			0
$820$	23.9552	−	20.5391i	0.836552	−	0.717258i
$821$	12.7770	+	39.3235i	0.445919	+	1.37240i	0.881472	+	0.472236i	$0.156553\pi$
$821$	12.7770	+	39.3235i	0.445919	+	1.37240i	−0.435553	+	0.900163i	$0.643447\pi$
$822$		0			0
$823$	4.70612	+	29.7133i	0.164045	+	1.03574i	0.923057	+	0.384663i	$0.125682\pi$
$823$	4.70612	+	29.7133i	0.164045	+	1.03574i	−0.759012	+	0.651076i	$0.774318\pi$
$824$	29.1508	−	9.37267i	1.01552	−	0.326512i
$825$		0			0
$826$	−0.696782	+	1.56069i	−0.0242441	+	0.0543034i
$827$	3.42645	−	0.542696i	0.119149	−	0.0188714i	−0.0965750	−	0.995326i	$-0.530789\pi$
$827$	3.42645	−	0.542696i	0.119149	−	0.0188714i	0.215724	+	0.976454i	$0.430789\pi$
$828$		0			0
$829$	16.7607	−	5.44590i	0.582125	−	0.189144i	−0.00312747	−	0.999995i	$-0.500996\pi$
$829$	16.7607	−	5.44590i	0.582125	−	0.189144i	0.585252	+	0.810851i	$0.300996\pi$
$830$	−8.20543	+	8.69779i	−0.284815	+	0.301905i
$831$		0			0
$832$	22.4497	+	3.69735i	0.778304	+	0.128182i
$833$	13.0779	+	25.6668i	0.453121	+	0.889301i
$834$		0			0
$835$	39.1045	+	21.0317i	1.35327	+	0.727832i
$836$	0.0136631	+	0.132610i	0.000472548	+	0.00458641i
$837$		0			0
$838$	−13.3797	+	20.5567i	−0.462193	+	0.710121i
$839$	7.06575	+	5.13357i	0.243937	+	0.177231i	0.703035	−	0.711155i	$-0.251828\pi$
$839$	7.06575	+	5.13357i	0.243937	+	0.177231i	−0.459099	+	0.888385i	$0.651828\pi$
$840$		0			0
$841$	−14.1599	+	10.2878i	−0.488274	+	0.354752i
$842$	−0.534149	−	10.3960i	−0.0184080	−	0.358271i
$843$		0			0
$844$	45.2448	−	20.0333i	1.55739	−	0.689573i
$845$	−10.5179	+	3.16095i	−0.361826	+	0.108740i
$846$		0			0
$847$	−4.69055	−	2.38996i	−0.161169	−	0.0821199i
$848$	0.130984	+	2.71202i	0.00449801	+	0.0931311i
$849$		0			0
$850$	−4.50080	+	29.7447i	−0.154376	+	1.02023i
$851$		−	38.1298i		−	1.30707i
$852$		0			0
$853$	21.8126	+	11.1141i	0.746849	+	0.380539i	0.785620	−	0.618709i	$-0.212344\pi$
$853$	21.8126	+	11.1141i	0.746849	+	0.380539i	−0.0387705	+	0.999248i	$0.512344\pi$
$854$	−6.05589	−	0.642775i	−0.207228	−	0.0219953i
$855$		0			0
$856$	15.8962	+	0.0488782i	0.543321	+	0.00167062i
$857$	2.88171	+	2.88171i	0.0984373	+	0.0984373i	0.754610	−	0.656173i	$-0.227826\pi$
$857$	2.88171	+	2.88171i	0.0984373	+	0.0984373i	−0.656173	+	0.754610i	$0.727826\pi$
$858$		0			0
$859$	−39.7386	+	28.8718i	−1.35586	+	0.985092i	−0.357166	+	0.934041i	$0.616257\pi$
$859$	−39.7386	+	28.8718i	−1.35586	+	0.985092i	−0.998696	+	0.0510509i	$0.983743\pi$
$860$	31.2569	+	26.5926i	1.06585	+	0.906799i
$861$		0			0
$862$	−34.4006	−	22.3902i	−1.17169	−	0.762612i
$863$	15.4604	+	2.44868i	0.526276	+	0.0833540i	0.413919	−	0.910314i	$-0.364160\pi$
$863$	15.4604	+	2.44868i	0.526276	+	0.0833540i	0.112358	+	0.993668i	$0.464160\pi$
$864$		0			0
$865$	−9.39158	+	8.98331i	−0.319323	+	0.305442i
$866$	−3.48266	−	16.4676i	−0.118346	−	0.559592i
$867$		0			0
$868$	4.36281	+	0.237614i	0.148083	+	0.00806514i
$869$	−0.0207578	−	0.00674461i	−0.000704159	−	0.000228795i
$870$		0			0
$871$	−27.3798	+	8.89623i	−0.927729	+	0.301437i
$872$	7.07123	−	43.7744i	0.239462	−	1.48239i
$873$		0			0
$874$	54.7083	+	24.4249i	1.85054	+	0.826186i
$875$	−4.59513	−	2.74126i	−0.155344	−	0.0926716i
$876$		0			0
$877$	−8.26731	−	52.1978i	−0.279167	−	1.76259i	−0.585503	−	0.810670i	$-0.699103\pi$
$877$	−8.26731	−	52.1978i	−0.279167	−	1.76259i	0.306336	−	0.951923i	$-0.400897\pi$
$878$	−9.14763	−	11.3201i	−0.308718	−	0.382035i
$879$		0			0
$880$	−0.0725302	+	0.0393680i	−0.00244499	+	0.00132709i
$881$	−16.9137	+	52.0551i	−0.569838	+	1.75378i	0.0832834	+	0.996526i	$0.473459\pi$
$881$	−16.9137	+	52.0551i	−0.569838	+	1.75378i	−0.653121	+	0.757254i	$0.726541\pi$
$882$		0			0
$883$	−36.8694	+	18.7859i	−1.24076	+	0.632196i	−0.946245	−	0.323452i	$-0.895157\pi$
$883$	−36.8694	+	18.7859i	−1.24076	+	0.632196i	−0.294511	+	0.955648i	$0.595157\pi$
$884$	5.07982	−	23.6601i	0.170853	−	0.795775i
$885$		0			0
$886$	19.8610	+	34.4819i	0.667244	+	1.15844i
$887$	4.33280	−	27.3562i	0.145481	−	0.918532i	−0.801675	−	0.597760i	$-0.796058\pi$
$887$	4.33280	−	27.3562i	0.145481	−	0.918532i	0.947156	−	0.320772i	$-0.103942\pi$
$888$		0			0
$889$	−1.11020	+	1.52805i	−0.0372348	+	0.0512493i
$890$	13.6954	−	46.7389i	0.459070	−	1.56669i
$891$		0			0
$892$	−5.04280	+	13.0569i	−0.168845	+	0.437177i
$893$	22.4600	−	22.4600i	0.751596	−	0.751596i
$894$		0			0
$895$	−40.5004	−	30.8227i	−1.35378	−	1.03029i
$896$	2.67354	+	4.70840i	0.0893168	+	0.157297i
$897$		0			0
$898$	−1.19634	+	4.44656i	−0.0399224	+	0.148384i
$899$	15.4783			0.516231
$900$		0			0
$901$	2.88788			0.0962091
$902$	0.0239201	−	0.0889065i	0.000796453	−	0.00296026i
$903$		0			0
$904$	−11.3778	+	8.21311i	−0.378419	+	0.273164i
$905$	2.99383	+	9.96179i	0.0995182	+	0.331141i
$906$		0			0
$907$	1.04931	−	1.04931i	0.0348419	−	0.0348419i	−0.689471	−	0.724313i	$-0.742157\pi$
$907$	1.04931	−	1.04931i	0.0348419	−	0.0348419i	0.724313	+	0.689471i	$0.242157\pi$
$908$	27.4965	+	10.6196i	0.912503	+	0.352425i
$909$		0			0
$910$	3.55430	+	2.42745i	0.117824	+	0.0804693i
$911$	33.9572	−	46.7381i	1.12505	−	1.54850i	0.327911	−	0.944709i	$-0.393655\pi$
$911$	33.9572	−	46.7381i	1.12505	−	1.54850i	0.797141	−	0.603793i	$-0.206345\pi$
$912$		0			0
$913$	−0.00545776	+	0.0344589i	−0.000180625	+	0.00114042i
$914$	7.54516	+	13.0996i	0.249572	+	0.433296i
$915$		0			0
$916$	−52.5604	−	11.2847i	−1.73665	−	0.372858i
$917$	−2.01696	+	1.02769i	−0.0666059	+	0.0339374i
$918$		0			0
$919$	11.5591	−	35.5754i	0.381301	−	1.17352i	−0.557828	−	0.829957i	$-0.688365\pi$
$919$	11.5591	−	35.5754i	0.381301	−	1.17352i	0.939128	−	0.343566i	$-0.111635\pi$
$920$	−0.937879	+	37.0768i	−0.0309209	+	1.22239i
$921$		0			0
$922$	−24.1541	−	29.8905i	−0.795474	−	0.984390i
$923$	3.12886	+	19.7549i	0.102988	+	0.650239i
$924$		0			0
$925$	−16.0315	+	28.2829i	−0.527111	+	0.929935i
$926$	−39.6439	−	17.6993i	−1.30278	−	0.581635i
$927$		0			0
$928$	10.3642	+	16.1400i	0.340222	+	0.529820i
$929$	−8.87951	+	2.88513i	−0.291327	+	0.0946580i	−0.451035	−	0.892506i	$-0.648945\pi$
$929$	−8.87951	+	2.88513i	−0.291327	+	0.0946580i	0.159707	+	0.987164i	$0.448945\pi$
$930$		0			0
$931$	−46.5213	−	15.1157i	−1.52467	−	0.495397i
$932$	−2.35568	+	43.2525i	−0.0771630	+	1.41678i
$933$		0			0
$934$	−3.44545	−	16.2917i	−0.112739	−	0.533079i
$935$	0.0381017	+	0.0790735i	0.00124606	+	0.00258598i
$936$		0			0
$937$	−23.3504	−	3.69834i	−0.762825	−	0.120820i	−0.237113	−	0.971482i	$-0.576201\pi$
$937$	−23.3504	−	3.69834i	−0.762825	−	0.120820i	−0.525712	+	0.850663i	$0.676201\pi$
$938$	−5.74199	−	3.73726i	−0.187483	−	0.122026i
$939$		0			0
$940$	18.1804	+	7.48982i	0.592979	+	0.244291i
$941$	−14.7926	+	10.7475i	−0.482226	+	0.350358i	−0.802187	−	0.597073i	$-0.796330\pi$
$941$	−14.7926	+	10.7475i	−0.482226	+	0.350358i	0.319961	+	0.947431i	$0.396330\pi$
$942$		0			0
$943$	−29.2582	−	29.2582i	−0.952777	−	0.952777i
$944$	−9.21105	−	4.14636i	−0.299794	−	0.134952i
$945$		0			0
$946$	0.119070	+	0.0126382i	0.00387130	+	0.000410902i
$947$	14.5607	+	7.41904i	0.473159	+	0.241086i	0.674274	−	0.738481i	$-0.264457\pi$
$947$	14.5607	+	7.41904i	0.473159	+	0.241086i	−0.201115	+	0.979568i	$0.564457\pi$
$948$		0			0
$949$		−	8.39269i		−	0.272438i
$950$	−30.3107	−	41.1191i	−0.983410	−	1.33408i
$951$		0			0
$952$	5.13922	−	2.59869i	0.166563	−	0.0842241i
$953$	−6.96002	−	3.54631i	−0.225457	−	0.114876i	0.337614	−	0.941285i	$-0.390380\pi$
$953$	−6.96002	−	3.54631i	−0.225457	−	0.114876i	−0.563071	+	0.826409i	$0.690380\pi$
$954$		0			0
$955$	48.5810	+	16.9870i	1.57205	+	0.549686i
$956$	8.98788	+	20.2990i	0.290689	+	0.656516i
$957$		0			0
$958$	−2.18862	−	42.5967i	−0.0707112	−	1.37624i
$959$	0.990514	−	0.719650i	0.0319854	−	0.0232387i
$960$		0			0
$961$	−8.22144	−	5.97323i	−0.265208	−	0.192685i
$962$	14.2657	−	21.9181i	0.459945	−	0.706667i
$963$		0			0
$964$	2.50890	−	0.258497i	0.0808062	−	0.00832564i
$965$	−9.30496	+	51.3402i	−0.299537	+	1.65270i
$966$		0			0
$967$	15.6133	+	30.6429i	0.502091	+	0.985408i	0.993430	+	0.114440i	$0.0365074\pi$
$967$	15.6133	+	30.6429i	0.502091	+	0.985408i	−0.491340	+	0.870968i	$0.663493\pi$
$968$	14.2099	−	27.6778i	0.456725	−	0.889599i
$969$		0			0
$970$	−7.22382	+	56.1452i	−0.231943	+	1.80271i
$971$	−33.0263	+	10.7309i	−1.05986	+	0.344371i	−0.786532	−	0.617549i	$-0.788126\pi$
$971$	−33.0263	+	10.7309i	−1.05986	+	0.344371i	−0.273332	+	0.961920i	$0.588126\pi$
$972$		0			0
$973$	−5.31978	+	0.842570i	−0.170544	+	0.0270115i
$974$	−11.1856	+	25.0541i	−0.358410	+	0.802786i
$975$		0			0
$976$	3.90887	−	35.7787i	0.125120	−	1.14525i
$977$	−1.13937	−	7.19369i	−0.0364516	−	0.230147i	0.962736	−	0.270442i	$-0.0871700\pi$
$977$	−1.13937	−	7.19369i	−0.0364516	−	0.230147i	−0.999188	+	0.0402958i	$0.987170\pi$
$978$		0			0
$979$	−0.0439128	−	0.135150i	−0.00140346	−	0.00431940i
$980$	−2.43359	−	30.1827i	−0.0777382	−	0.964151i
$981$		0			0
$982$	1.09559	+	2.86286i	0.0349615	+	0.0913577i
$983$	31.7358	−	16.1702i	1.01221	−	0.515749i	0.132465	−	0.991188i	$-0.457711\pi$
$983$	31.7358	−	16.1702i	1.01221	−	0.515749i	0.879749	+	0.475439i	$0.157711\pi$
$984$		0			0
$985$	2.18828	+	16.1273i	0.0697245	+	0.513860i
$986$	17.6783	−	10.1824i	0.562992	−	0.324275i
$987$		0			0
$988$	22.3096	+	34.5085i	0.709764	+	1.09786i
$989$	31.6305	−	43.5357i	1.00579	−	1.38435i
$990$		0			0
$991$	1.17484	+	1.61702i	0.0373199	+	0.0513664i	0.827269	−	0.561806i	$-0.189893\pi$
$991$	1.17484	+	1.61702i	0.0373199	+	0.0513664i	−0.789949	+	0.613172i	$0.789893\pi$
$992$	−1.48359	+	25.7800i	−0.0471039	+	0.818515i
$993$		0			0
$994$	−3.18856	+	3.53397i	−0.101135	+	0.112091i
$995$	−34.1671	+	23.6824i	−1.08317	+	0.750782i
$996$		0			0
$997$	−16.0795	+	31.5579i	−0.509244	+	0.999447i	0.483056	+	0.875589i	$0.339527\pi$
$997$	−16.0795	+	31.5579i	−0.509244	+	0.999447i	−0.992300	+	0.123858i	$0.960473\pi$
$998$	−19.0343	−	5.12115i	−0.602521	−	0.162107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.487.3		240
3.2	odd	2		300.2.w.a.187.28	yes	240
4.3	odd	2	inner	900.2.bj.f.487.25		240
12.11	even	2		300.2.w.a.187.6	✓	240
25.23	odd	20	inner	900.2.bj.f.523.25		240
75.23	even	20		300.2.w.a.223.6	yes	240
100.23	even	20	inner	900.2.bj.f.523.3		240
300.23	odd	20		300.2.w.a.223.28	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.6	✓	240	12.11	even	2
300.2.w.a.187.28	yes	240	3.2	odd	2
300.2.w.a.223.6	yes	240	75.23	even	20
300.2.w.a.223.28	yes	240	300.23	odd	20
900.2.bj.f.487.3		240	1.1	even	1	trivial
900.2.bj.f.487.25		240	4.3	odd	2	inner
900.2.bj.f.523.3		240	100.23	even	20	inner
900.2.bj.f.523.25		240	25.23	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36565 - 0.367425i) q^{2} +(1.73000 + 1.00355i) q^{4} +(-1.83777 + 1.27382i) q^{5} +(-0.338407 + 0.338407i) q^{7} +(-1.99384 - 2.00614i) q^{8} +(2.97778 - 1.06435i) q^{10} +(0.00542328 - 0.00746451i) q^{11} +(0.444902 - 2.80900i) q^{13} +(0.586484 - 0.337806i) q^{14} +(1.98578 + 3.47227i) q^{16} +(3.79071 - 1.93146i) q^{17} +(-2.23243 + 6.87071i) q^{19} +(-4.45767 + 0.359416i) q^{20} +(-0.0101489 + 0.00820125i) q^{22} +(0.917368 + 5.79204i) q^{23} +(1.75477 - 4.68196i) q^{25} +(-1.63968 + 3.67265i) q^{26} +(-0.925050 + 0.245835i) q^{28} +(-3.22482 + 1.04781i) q^{29} +(-4.34142 - 1.41061i) q^{31} +(-1.43608 - 5.47153i) q^{32} +(-5.88645 + 1.24490i) q^{34} +(0.190844 - 1.05298i) q^{35} +(-6.42204 - 1.01715i) q^{37} +(5.57319 - 8.56273i) q^{38} +(6.21967 + 1.14702i) q^{40} +(-5.70832 + 4.14734i) q^{41} +(-6.48875 - 6.48875i) q^{43} +(0.0168733 - 0.00747105i) q^{44} +(0.875337 - 8.24696i) q^{46} +(-3.91751 - 1.99607i) q^{47} +6.77096i q^{49} +(-4.11667 + 5.74917i) q^{50} +(3.58865 - 4.41309i) q^{52} +(0.604811 + 0.308167i) q^{53} +(-0.000458296 + 0.0206263i) q^{55} +(1.35362 + 0.00416215i) q^{56} +(4.78896 - 0.246057i) q^{58} +(-2.04303 + 1.48435i) q^{59} +(-7.27946 - 5.28884i) q^{61} +(5.41056 + 3.52155i) q^{62} +(-0.0491968 + 7.99985i) q^{64} +(2.76053 + 5.72902i) q^{65} +(-4.59556 - 9.01929i) q^{67} +(8.49624 + 0.462735i) q^{68} +(-0.647517 + 1.36788i) q^{70} +(-6.68849 + 2.17322i) q^{71} +(2.91467 - 0.461638i) q^{73} +(8.39652 + 3.74869i) q^{74} +(-10.7572 + 9.64596i) q^{76} +(0.000690764 + 0.00436131i) q^{77} +(-0.730993 - 2.24976i) q^{79} +(-8.07245 - 3.85170i) q^{80} +(9.31941 - 3.56643i) q^{82} +(-3.36914 + 1.71666i) q^{83} +(-4.50611 + 8.37826i) q^{85} +(6.47723 + 11.2455i) q^{86} +(-0.0257880 + 0.00400318i) q^{88} +(9.05282 - 12.4601i) q^{89} +(0.800028 + 1.10114i) q^{91} +(-4.22554 + 10.9408i) q^{92} +(4.61654 + 4.16533i) q^{94} +(-4.64936 - 15.4705i) q^{95} +(-8.12690 + 15.9499i) q^{97} +(2.48782 - 9.24676i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Introduction

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