LMFDB - Embedded newform 729.2.g.a.217.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,-9,0,9,-9,0,9,18,0,-18,-9,0,9,-9,0,9,18,0,-18,-45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			217.1
Character	$\chi$	$=$	729.217
Dual form			729.2.g.a.514.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.155231 + 2.66522i) q^{2} +(-5.09281 - 0.595264i) q^{4} +(2.46694 - 0.584676i) q^{5} +(0.305106 + 0.409828i) q^{7} +(1.44988 - 8.22270i) q^{8} +(1.17534 + 6.66569i) q^{10} +(1.05464 - 1.11785i) q^{11} +(5.04127 + 2.53182i) q^{13} +(-1.13964 + 0.749555i) q^{14} +(11.7117 + 2.77572i) q^{16} +(1.33086 + 0.484393i) q^{17} +(0.986977 - 0.359230i) q^{19} +(-12.9117 + 1.50916i) q^{20} +(2.81561 + 2.98437i) q^{22} +(-0.155479 + 0.208844i) q^{23} +(1.27579 - 0.640725i) q^{25} +(-7.53041 + 13.0431i) q^{26} +(-1.30989 - 2.26880i) q^{28} +(1.48594 + 0.977316i) q^{29} +(2.04644 + 4.74419i) q^{31} +(-4.42655 + 14.7857i) q^{32} +(-1.49760 + 3.47184i) q^{34} +(0.992294 + 0.832634i) q^{35} +(-5.04999 + 4.23745i) q^{37} +(0.804217 + 2.68627i) q^{38} +(-1.23083 - 21.1326i) q^{40} +(-0.392910 - 6.74600i) q^{41} +(1.75232 + 5.85315i) q^{43} +(-6.03650 + 5.06523i) q^{44} +(-0.532481 - 0.446804i) q^{46} +(-2.89593 + 6.71353i) q^{47} +(1.93275 - 6.45584i) q^{49} +(1.50963 + 3.49971i) q^{50} +(-24.1671 - 15.8950i) q^{52} +(-4.74440 - 8.21755i) q^{53} +(1.94815 - 3.37430i) q^{55} +(3.81226 - 1.91459i) q^{56} +(-2.83542 + 3.80864i) q^{58} +(-3.40033 - 3.60414i) q^{59} +(12.8136 - 1.49769i) q^{61} +(-12.9620 + 4.71777i) q^{62} +(-16.0995 - 5.85975i) q^{64} +(13.9168 + 3.29834i) q^{65} +(-5.36299 + 3.52730i) q^{67} +(-6.48947 - 3.25914i) q^{68} +(-2.37319 + 2.51543i) q^{70} +(0.896716 + 5.08553i) q^{71} +(-1.03528 + 5.87137i) q^{73} +(-10.5098 - 14.1171i) q^{74} +(-5.24032 + 1.24198i) q^{76} +(0.779905 + 0.0911578i) q^{77} +(-0.578079 + 9.92524i) q^{79} +30.5149 q^{80} +18.0405 q^{82} +(0.753098 - 12.9302i) q^{83} +(3.56636 + 0.416848i) q^{85} +(-15.8719 + 3.76171i) q^{86} +(-7.66266 - 10.2927i) q^{88} +(1.71260 - 9.71264i) q^{89} +(0.500509 + 2.83853i) q^{91} +(0.916142 - 0.971054i) q^{92} +(-17.4435 - 8.76045i) q^{94} +(2.22478 - 1.46326i) q^{95} +(-3.50004 - 0.829525i) q^{97} +(16.9062 + 6.15336i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{14}{27}\right)$

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 $

$2$	−0.155231	+	2.66522i	−0.109765	+	1.88459i	0.274808	+	0.961499i	$0.411386\pi$
$2$	−0.155231	+	2.66522i	−0.109765	+	1.88459i	−0.384573	+	0.923094i	$0.625651\pi$
$3$		0			0
$3$		0			0
$4$	−5.09281	−	0.595264i	−2.54641	−	0.297632i
$5$	2.46694	−	0.584676i	1.10325	−	0.261475i	0.361647	−	0.932315i	$-0.382214\pi$
$5$	2.46694	−	0.584676i	1.10325	−	0.261475i	0.741602	+	0.670840i	$0.234066\pi$
$6$		0			0
$7$	0.305106	+	0.409828i	0.115319	+	0.154900i	0.856035	−	0.516918i	$-0.172921\pi$
$7$	0.305106	+	0.409828i	0.115319	+	0.154900i	−0.740716	+	0.671819i	$0.765513\pi$
$8$	1.44988	−	8.22270i	0.512611	−	2.90716i
$9$		0			0
$10$	1.17534	+	6.66569i	0.371676	+	2.10788i
$11$	1.05464	−	1.11785i	0.317986	−	0.337046i	−0.548589	−	0.836092i	$-0.684835\pi$
$11$	1.05464	−	1.11785i	0.317986	−	0.337046i	0.866575	+	0.499047i	$0.166316\pi$
$12$		0			0
$13$	5.04127	+	2.53182i	1.39820	+	0.702200i	0.978650	−	0.205534i	$-0.0658931\pi$
$13$	5.04127	+	2.53182i	1.39820	+	0.702200i	0.419546	+	0.907734i	$0.362189\pi$
$14$	−1.13964	+	0.749555i	−0.304582	+	0.200327i
$15$		0			0
$16$	11.7117	+	2.77572i	2.92792	+	0.693929i
$17$	1.33086	+	0.484393i	0.322781	+	0.117483i	0.498328	−	0.866988i	$-0.333947\pi$
$17$	1.33086	+	0.484393i	0.322781	+	0.117483i	−0.175548	+	0.984471i	$0.556170\pi$
$18$		0			0
$19$	0.986977	−	0.359230i	0.226428	−	0.0824131i	−0.226315	−	0.974054i	$-0.572668\pi$
$19$	0.986977	−	0.359230i	0.226428	−	0.0824131i	0.452743	+	0.891641i	$0.350446\pi$
$20$	−12.9117	+	1.50916i	−2.88714	+	0.337459i
$21$		0			0
$22$	2.81561	+	2.98437i	0.600290	+	0.636270i
$23$	−0.155479	+	0.208844i	−0.0324196	+	0.0435471i	−0.818037	−	0.575165i	$-0.804938\pi$
$23$	−0.155479	+	0.208844i	−0.0324196	+	0.0435471i	0.785618	+	0.618712i	$0.212345\pi$
$24$		0			0
$25$	1.27579	−	0.640725i	0.255157	−	0.128145i
$26$	−7.53041	+	13.0431i	−1.47684	+	2.55795i
$27$		0			0
$28$	−1.30989	−	2.26880i	−0.247546	−	0.428762i
$29$	1.48594	+	0.977316i	0.275932	+	0.181483i	0.679931	−	0.733276i	$-0.262010\pi$
$29$	1.48594	+	0.977316i	0.275932	+	0.181483i	−0.403999	+	0.914759i	$0.632380\pi$
$30$		0			0
$31$	2.04644	+	4.74419i	0.367552	+	0.852081i	0.997170	+	0.0751766i	$0.0239521\pi$
$31$	2.04644	+	4.74419i	0.367552	+	0.852081i	−0.629618	+	0.776905i	$0.716789\pi$
$32$	−4.42655	+	14.7857i	−0.782511	+	2.61377i
$33$		0			0
$34$	−1.49760	+	3.47184i	−0.256837	+	0.595415i
$35$	0.992294	+	0.832634i	0.167728	+	0.140741i
$36$		0			0
$37$	−5.04999	+	4.23745i	−0.830214	+	0.696632i	−0.955340	−	0.295509i	$-0.904511\pi$
$37$	−5.04999	+	4.23745i	−0.830214	+	0.696632i	0.125126	+	0.992141i	$0.460066\pi$
$38$	0.804217	+	2.68627i	0.130461	+	0.435771i
$39$		0			0
$40$	−1.23083	−	21.1326i	−0.194612	−	3.34136i
$41$	−0.392910	−	6.74600i	−0.0613622	−	1.05355i	−0.878695	−	0.477383i	$-0.841586\pi$
$41$	−0.392910	−	6.74600i	−0.0613622	−	1.05355i	0.817333	−	0.576165i	$-0.195452\pi$
$42$		0			0
$43$	1.75232	+	5.85315i	0.267226	+	0.892597i	0.981293	+	0.192519i	$0.0616658\pi$
$43$	1.75232	+	5.85315i	0.267226	+	0.892597i	−0.714067	+	0.700077i	$0.753149\pi$
$44$	−6.03650	+	5.06523i	−0.910037	+	0.763612i
$45$		0			0
$46$	−0.532481	−	0.446804i	−0.0785100	−	0.0658777i
$47$	−2.89593	+	6.71353i	−0.422416	+	0.979269i	0.565567	+	0.824702i	$0.308657\pi$
$47$	−2.89593	+	6.71353i	−0.422416	+	0.979269i	−0.987982	+	0.154567i	$0.950602\pi$
$48$		0			0
$49$	1.93275	−	6.45584i	0.276108	−	0.922264i
$50$	1.50963	+	3.49971i	0.213494	+	0.494934i
$51$		0			0
$52$	−24.1671	−	15.8950i	−3.35138	−	2.20423i
$53$	−4.74440	−	8.21755i	−0.651694	−	1.12877i	−0.982712	−	0.185142i	$-0.940725\pi$
$53$	−4.74440	−	8.21755i	−0.651694	−	1.12877i	0.331018	−	0.943624i	$-0.392608\pi$
$54$		0			0
$55$	1.94815	−	3.37430i	0.262689	−	0.454991i
$56$	3.81226	−	1.91459i	0.509435	−	0.255848i
$57$		0			0
$58$	−2.83542	+	3.80864i	−0.372309	+	0.500098i
$59$	−3.40033	−	3.60414i	−0.442685	−	0.469219i	0.467156	−	0.884175i	$-0.345279\pi$
$59$	−3.40033	−	3.60414i	−0.442685	−	0.469219i	−0.909842	+	0.414956i	$0.863797\pi$
$60$		0			0
$61$	12.8136	−	1.49769i	1.64061	−	0.191760i	0.754847	−	0.655901i	$-0.227711\pi$
$61$	12.8136	−	1.49769i	1.64061	−	0.191760i	0.885761	+	0.464142i	$0.153637\pi$
$62$	−12.9620	+	4.71777i	−1.64617	+	0.599157i
$63$		0			0
$64$	−16.0995	−	5.85975i	−2.01244	−	0.732468i
$65$	13.9168	+	3.29834i	1.72617	+	0.409109i
$66$		0			0
$67$	−5.36299	+	3.52730i	−0.655194	+	0.430928i	−0.833102	−	0.553119i	$-0.813437\pi$
$67$	−5.36299	+	3.52730i	−0.655194	+	0.430928i	0.177908	+	0.984047i	$0.443067\pi$
$68$	−6.48947	−	3.25914i	−0.786964	−	0.395228i
$69$		0			0
$70$	−2.37319	+	2.51543i	−0.283650	+	0.300651i
$71$	0.896716	+	5.08553i	0.106421	+	0.603541i	0.990643	+	0.136476i	$0.0435776\pi$
$71$	0.896716	+	5.08553i	0.106421	+	0.603541i	−0.884223	+	0.467065i	$0.845311\pi$
$72$		0			0
$73$	−1.03528	+	5.87137i	−0.121171	+	0.687192i	0.862338	+	0.506332i	$0.168999\pi$
$73$	−1.03528	+	5.87137i	−0.121171	+	0.687192i	−0.983509	+	0.180860i	$0.942112\pi$
$74$	−10.5098	−	14.1171i	−1.22174	−	1.64108i
$75$		0			0
$76$	−5.24032	+	1.24198i	−0.601106	+	0.142465i
$77$	0.779905	+	0.0911578i	0.0888784	+	0.0103884i
$78$		0			0
$79$	−0.578079	+	9.92524i	−0.0650390	+	1.11668i	0.795054	+	0.606539i	$0.207443\pi$
$79$	−0.578079	+	9.92524i	−0.0650390	+	1.11668i	−0.860093	+	0.510138i	$0.829594\pi$
$80$	30.5149			3.41167
$81$		0			0
$82$	18.0405			1.99224
$83$	0.753098	−	12.9302i	0.0826632	−	1.41927i	−0.660833	−	0.750533i	$-0.729797\pi$
$83$	0.753098	−	12.9302i	0.0826632	−	1.41927i	0.743496	−	0.668740i	$-0.233166\pi$
$84$		0			0
$85$	3.56636	+	0.416848i	0.386826	+	0.0452135i
$86$	−15.8719	+	3.76171i	−1.71151	+	0.405636i
$87$		0			0
$88$	−7.66266	−	10.2927i	−0.816843	−	1.09721i
$89$	1.71260	−	9.71264i	0.181535	−	1.02954i	−0.748791	−	0.662806i	$-0.769366\pi$
$89$	1.71260	−	9.71264i	0.181535	−	1.02954i	0.930327	−	0.366732i	$-0.119523\pi$
$90$		0			0
$91$	0.500509	+	2.83853i	0.0524676	+	0.297558i
$92$	0.916142	−	0.971054i	0.0955144	−	0.101239i
$93$		0			0
$94$	−17.4435	−	8.76045i	−1.79916	−	0.903571i
$95$	2.22478	−	1.46326i	0.228258	−	0.150127i
$96$		0			0
$97$	−3.50004	−	0.829525i	−0.355375	−	0.0842255i	0.0490505	−	0.998796i	$-0.484380\pi$
$97$	−3.50004	−	0.829525i	−0.355375	−	0.0842255i	−0.404426	+	0.914571i	$0.632529\pi$
$98$	16.9062	+	6.15336i	1.70778	+	0.621583i
$99$		0			0
$100$	−6.87874	+	2.50366i	−0.687874	+	0.250366i
$101$	17.7029	−	2.06917i	1.76150	−	0.205890i	0.827086	−	0.562076i	$-0.189997\pi$
$101$	17.7029	−	2.06917i	1.76150	−	0.205890i	0.934415	+	0.356186i	$0.115923\pi$
$102$		0			0
$103$	−2.96285	−	3.14044i	−0.291939	−	0.309437i	0.564759	−	0.825256i	$-0.308969\pi$
$103$	−2.96285	−	3.14044i	−0.291939	−	0.309437i	−0.856698	+	0.515819i	$0.827488\pi$
$104$	28.1276	−	37.7820i	2.75814	−	3.70483i
$105$		0			0
$106$	22.6380	−	11.3692i	2.19880	−	1.10428i
$107$	−3.98940	+	6.90985i	−0.385670	+	0.668000i	−0.991862	−	0.127318i	$-0.959363\pi$
$107$	−3.98940	+	6.90985i	−0.385670	+	0.668000i	0.606192	+	0.795319i	$0.292696\pi$
$108$		0			0
$109$	0.106432	+	0.184345i	0.0101943	+	0.0176571i	0.871078	−	0.491145i	$-0.163422\pi$
$109$	0.106432	+	0.184345i	0.0101943	+	0.0176571i	−0.860883	+	0.508803i	$0.830088\pi$
$110$	8.69083	+	5.71605i	0.828638	+	0.545004i
$111$		0			0
$112$	2.43573	+	5.64666i	0.230155	+	0.533559i
$113$	1.59069	−	5.31329i	0.149640	−	0.499832i	−0.849997	−	0.526788i	$-0.823396\pi$
$113$	1.59069	−	5.31329i	0.149640	−	0.499832i	0.999637	+	0.0269560i	$0.00858140\pi$
$114$		0			0
$115$	−0.261451	+	0.606112i	−0.0243804	+	0.0565202i
$116$	−6.98584	−	5.86181i	−0.648619	−	0.544256i
$117$		0			0
$118$	10.1337	−	8.50315i	0.932878	−	0.782778i
$119$	0.207535	+	0.693215i	0.0190247	+	0.0635469i
$120$		0			0
$121$	0.502263	+	8.62352i	0.0456603	+	0.783957i
$122$	2.00260	+	34.3834i	0.181307	+	3.11293i
$123$		0			0
$124$	−7.59810	−	25.3794i	−0.682330	−	2.27914i
$125$	−6.93801	+	5.82168i	−0.620554	+	0.520707i
$126$		0			0
$127$	−13.9870	−	11.7365i	−1.24115	−	1.04145i	−0.997434	−	0.0715979i	$-0.977190\pi$
$127$	−13.9870	−	11.7365i	−1.24115	−	1.04145i	−0.243713	−	0.969847i	$-0.578365\pi$
$128$	5.89038	−	13.6554i	0.520641	−	1.20698i
$129$		0			0
$130$	−10.9511	+	36.5793i	−0.960477	+	3.20822i
$131$	−3.18462	−	7.38277i	−0.278241	−	0.645035i	0.720591	−	0.693361i	$-0.243871\pi$
$131$	−3.18462	−	7.38277i	−0.278241	−	0.645035i	−0.998832	+	0.0483254i	$0.984612\pi$
$132$		0			0
$133$	0.448355	+	0.294888i	0.0388773	+	0.0255700i
$134$	−8.56851	−	14.8411i	−0.740206	−	1.28207i
$135$		0			0
$136$	5.91261	−	10.2409i	0.507002	−	0.878153i
$137$	−7.62496	+	3.82940i	−0.651444	+	0.327168i	−0.743647	−	0.668573i	$-0.766906\pi$
$137$	−7.62496	+	3.82940i	−0.651444	+	0.327168i	0.0922025	+	0.995740i	$0.470609\pi$
$138$		0			0
$139$	7.79256	−	10.4672i	0.660956	−	0.887818i	−0.337614	−	0.941285i	$-0.609620\pi$
$139$	7.79256	−	10.4672i	0.660956	−	0.887818i	0.998570	+	0.0534669i	$0.0170272\pi$
$140$	−4.55793	−	4.83112i	−0.385215	−	0.408304i
$141$		0			0
$142$	−13.6932	+	1.60051i	−1.14911	+	0.134312i
$143$	8.14693	−	2.96524i	0.681280	−	0.247966i
$144$		0			0
$145$	4.23713	+	1.54219i	0.351875	+	0.128072i
$146$	−15.4878	−	3.67067i	−1.28178	−	0.303787i
$147$		0			0
$148$	28.2411	−	18.5744i	2.32140	−	1.52681i
$149$	14.5793	+	7.32201i	1.19438	+	0.599842i	0.931060	−	0.364865i	$-0.118885\pi$
$149$	14.5793	+	7.32201i	1.19438	+	0.599842i	0.263324	+	0.964708i	$0.415181\pi$
$150$		0			0
$151$	−14.8615	+	15.7523i	−1.20941	+	1.28190i	−0.260826	+	0.965386i	$0.583995\pi$
$151$	−14.8615	+	15.7523i	−1.20941	+	1.28190i	−0.948587	+	0.316517i	$0.897487\pi$
$152$	−1.52284	−	8.63645i	−0.123519	−	0.700509i
$153$		0			0
$154$	−0.364021	+	2.06446i	−0.0293336	+	0.166359i
$155$	7.82226	+	10.5071i	0.628299	+	0.843953i
$156$		0			0
$157$	−2.45596	+	0.582074i	−0.196007	+	0.0464546i	−0.327447	−	0.944870i	$-0.606188\pi$
$157$	−2.45596	+	0.582074i	−0.196007	+	0.0464546i	0.131440	+	0.991324i	$0.458040\pi$
$158$	−26.3632	−	3.08141i	−2.09734	−	0.245144i
$159$		0			0
$160$	−2.27519	+	39.0636i	−0.179870	+	3.08825i
$161$	−0.133028			−0.0104841
$162$		0			0
$163$	7.30888			0.572476			0.286238	−	0.958159i	$-0.407595\pi$
$163$	7.30888			0.572476			0.286238	+	0.958159i	$0.407595\pi$
$164$	−2.01464	+	34.5900i	−0.157317	+	2.70102i
$165$		0			0
$166$	34.3449	+	4.01434i	2.66568	+	0.311573i
$167$	6.23897	−	1.47866i	0.482786	−	0.114422i	0.0179862	−	0.999838i	$-0.494274\pi$
$167$	6.23897	−	1.47866i	0.482786	−	0.114422i	0.464800	+	0.885416i	$0.346126\pi$
$168$		0			0
$169$	11.2412	+	15.0995i	0.864708	+	1.16150i
$170$	−1.66460	+	9.44043i	−0.127669	+	0.724048i
$171$		0			0
$172$	−5.44005	−	30.8521i	−0.414800	−	2.35245i
$173$	−3.35472	+	3.55580i	−0.255055	+	0.270343i	−0.842231	−	0.539117i	$-0.818758\pi$
$173$	−3.35472	+	3.55580i	−0.255055	+	0.270343i	0.587176	+	0.809459i	$0.300240\pi$
$174$		0			0
$175$	0.651837	+	0.327365i	0.0492742	+	0.0247465i
$176$	15.4544	−	10.1645i	1.16492	−	0.766181i
$177$		0			0
$178$	25.6204	+	6.07216i	1.92033	+	0.455127i
$179$	−0.481678	−	0.175316i	−0.0360023	−	0.0131038i	0.323956	−	0.946072i	$-0.394987\pi$
$179$	−0.481678	−	0.175316i	−0.0360023	−	0.0131038i	−0.359959	+	0.932968i	$0.617209\pi$
$180$		0			0
$181$	3.55046	−	1.29226i	0.263904	−	0.0960531i	−0.206680	−	0.978409i	$-0.566266\pi$
$181$	3.55046	−	1.29226i	0.263904	−	0.0960531i	0.470583	+	0.882356i	$0.344044\pi$
$182$	−7.64298	+	0.893336i	−0.566536	+	0.0662185i
$183$		0			0
$184$	1.49184	+	1.58126i	0.109980	+	0.116572i
$185$	−9.98050	+	13.4061i	−0.733781	+	0.985639i
$186$		0			0
$187$	1.94506	−	0.976845i	0.142237	−	0.0714340i
$188$	18.7448	−	32.4669i	1.36710	−	2.36789i
$189$		0			0
$190$	3.55455	+	6.15667i	0.257874	+	0.446652i
$191$	−18.9332	−	12.4525i	−1.36996	−	0.901034i	−0.370345	−	0.928894i	$-0.620760\pi$
$191$	−18.9332	−	12.4525i	−1.36996	−	0.901034i	−0.999612	+	0.0278600i	$0.991131\pi$
$192$		0			0
$193$	−2.26697	−	5.25543i	−0.163180	−	0.378294i	0.816933	−	0.576732i	$-0.195672\pi$
$193$	−2.26697	−	5.25543i	−0.163180	−	0.378294i	−0.980113	+	0.198438i	$0.936413\pi$
$194$	2.75418	−	9.19960i	0.197739	−	0.660493i
$195$		0			0
$196$	−13.6861	+	31.7279i	−0.977577	+	2.26628i
$197$	1.85381	+	1.55553i	0.132078	+	0.110827i	0.706434	−	0.707779i	$-0.250303\pi$
$197$	1.85381	+	1.55553i	0.132078	+	0.110827i	−0.574356	+	0.818606i	$0.694747\pi$
$198$		0			0
$199$	−7.49610	+	6.28997i	−0.531384	+	0.445884i	−0.868579	−	0.495550i	$-0.834966\pi$
$199$	−7.49610	+	6.28997i	−0.531384	+	0.445884i	0.337195	+	0.941435i	$0.390522\pi$
$200$	−3.41874	−	11.4194i	−0.241741	−	0.807473i
$201$		0			0
$202$	2.76674	+	47.5032i	0.194667	+	3.34231i
$203$	0.0528363	+	0.907164i	0.00370838	+	0.0636704i
$204$		0			0
$205$	−4.91351	−	16.4123i	−0.343174	−	1.14628i
$206$	8.82988	−	7.40915i	0.615207	−	0.516220i
$207$		0			0
$208$	52.0140	+	43.6449i	3.60652	+	3.02623i
$209$	0.639339	−	1.48215i	0.0442240	−	0.102523i
$210$		0			0
$211$	5.62474	−	18.7879i	0.387223	−	1.29341i	−0.513151	−	0.858298i	$-0.671522\pi$
$211$	5.62474	−	18.7879i	0.387223	−	1.29341i	0.900374	−	0.435116i	$-0.143293\pi$
$212$	19.2707	+	44.6746i	1.32352	+	3.06826i
$213$		0			0
$214$	−17.7970	−	11.7053i	−1.21658	−	0.800155i
$215$	7.74505	+	13.4148i	0.528208	+	0.914884i
$216$		0			0
$217$	−1.31992	+	2.28617i	−0.0896020	+	0.155195i
$218$	−0.507842	+	0.255048i	−0.0343954	+	0.0172740i
$219$		0			0
$220$	−11.9302	+	16.0250i	−0.804332	+	1.08041i
$221$	5.48282	+	5.81145i	0.368814	+	0.390920i
$222$		0			0
$223$	−2.60234	+	0.304170i	−0.174266	+	0.0203687i	−0.202778	−	0.979225i	$-0.564997\pi$
$223$	−2.60234	+	0.304170i	−0.174266	+	0.0203687i	0.0285125	+	0.999593i	$0.490923\pi$
$224$	−7.41017	+	2.69708i	−0.495113	+	0.180206i
$225$		0			0
$226$	13.9141	+	5.06433i	0.925555	+	0.336874i
$227$	−1.20184	−	0.284840i	−0.0797686	−	0.0189055i	0.190538	−	0.981680i	$-0.438977\pi$
$227$	−1.20184	−	0.284840i	−0.0797686	−	0.0189055i	−0.270306	+	0.962774i	$0.587125\pi$
$228$		0			0
$229$	−4.09317	+	2.69212i	−0.270484	+	0.177900i	−0.677504	−	0.735519i	$-0.736938\pi$
$229$	−4.09317	+	2.69212i	−0.270484	+	0.177900i	0.407020	+	0.913419i	$0.366568\pi$
$230$	−1.57483	−	0.790911i	−0.103841	−	0.0521511i
$231$		0			0
$232$	10.1906	−	10.8014i	0.669046	−	0.709148i
$233$	0.664049	+	3.76601i	0.0435033	+	0.246719i	0.998803	−	0.0489208i	$-0.0155782\pi$
$233$	0.664049	+	3.76601i	0.0435033	+	0.246719i	−0.955299	+	0.295640i	$0.904467\pi$
$234$		0			0
$235$	−3.21886	+	18.2551i	−0.209975	+	1.19083i
$236$	15.1718	+	20.3793i	0.987602	+	1.32658i
$237$		0			0
$238$	−1.87978	+	0.445517i	−0.121848	+	0.0288786i
$239$	−8.98593	−	1.05030i	−0.581251	−	0.0679385i	−0.179614	−	0.983737i	$-0.557485\pi$
$239$	−8.98593	−	1.05030i	−0.581251	−	0.0679385i	−0.401638	+	0.915799i	$0.631559\pi$
$240$		0			0
$241$	1.36210	−	23.3864i	0.0877407	−	1.50645i	−0.611318	−	0.791385i	$-0.709360\pi$
$241$	1.36210	−	23.3864i	0.0877407	−	1.50645i	0.699058	−	0.715065i	$-0.253603\pi$
$242$	−23.0615			−1.48245
$243$		0			0
$244$	−66.1485			−4.23473
$245$	0.993412	−	17.0562i	0.0634667	−	1.08968i
$246$		0			0
$247$	5.88512	+	0.687872i	0.374461	+	0.0437682i
$248$	41.9771	−	9.94876i	2.66555	−	0.631747i
$249$		0			0
$250$	−14.4390	−	19.3950i	−0.913206	−	1.22665i
$251$	2.14133	−	12.1441i	0.135160	−	0.766530i	−0.839588	−	0.543223i	$-0.817204\pi$
$251$	2.14133	−	12.1441i	0.135160	−	0.766530i	0.974748	−	0.223307i	$-0.0716851\pi$
$252$		0			0
$253$	0.0694831	+	0.394058i	0.00436837	+	0.0247742i
$254$	33.4515	−	35.4565i	2.09894	−	2.22474i
$255$		0			0
$256$	4.85954	+	2.44055i	0.303721	+	0.152535i
$257$	24.6302	−	16.1995i	1.53639	−	1.01050i	0.552132	−	0.833757i	$-0.313815\pi$
$257$	24.6302	−	16.1995i	1.53639	−	1.01050i	0.984257	−	0.176742i	$-0.0565558\pi$
$258$		0			0
$259$	−3.27741	−	0.776760i	−0.203648	−	0.0482655i
$260$	−68.9122	−	25.0820i	−4.27376	−	1.55552i
$261$		0			0
$262$	20.1710	−	7.34166i	1.24617	−	0.453569i
$263$	−20.4500	+	2.39027i	−1.26100	+	0.147390i	−0.720205	−	0.693762i	$-0.755952\pi$
$263$	−20.4500	+	2.39027i	−1.26100	+	0.147390i	−0.540799	+	0.841152i	$0.681878\pi$
$264$		0			0
$265$	−16.5088	−	17.4983i	−1.01412	−	1.07491i
$266$	−0.855539	+	1.14919i	−0.0524564	+	0.0704612i
$267$		0			0
$268$	29.4124	−	14.7715i	1.79665	−	0.902310i
$269$	6.08593	−	10.5411i	0.371066	−	0.642705i	−0.618664	−	0.785656i	$-0.712326\pi$
$269$	6.08593	−	10.5411i	0.371066	−	0.642705i	0.989730	+	0.142951i	$0.0456591\pi$
$270$		0			0
$271$	−11.5577	−	20.0185i	−0.702078	−	1.21603i	−0.967736	−	0.251967i	$-0.918922\pi$
$271$	−11.5577	−	20.0185i	−0.702078	−	1.21603i	0.265658	−	0.964067i	$-0.414411\pi$
$272$	14.2420	+	9.36714i	0.863550	+	0.567966i
$273$		0			0
$274$	−9.02255	−	20.9166i	−0.545072	−	1.26362i
$275$	0.629261	−	2.10188i	0.0379459	−	0.126748i
$276$		0			0
$277$	0.542133	−	1.25681i	0.0325736	−	0.0755142i	−0.901153	−	0.433502i	$-0.857278\pi$
$277$	0.542133	−	1.25681i	0.0325736	−	0.0755142i	0.933726	+	0.357988i	$0.116537\pi$
$278$	26.6878	+	22.3937i	1.60063	+	1.34308i
$279$		0			0
$280$	8.28520	−	6.95211i	0.495136	−	0.415468i
$281$	−5.13509	−	17.1524i	−0.306334	−	1.02323i	−0.963103	−	0.269134i	$-0.913263\pi$
$281$	−5.13509	−	17.1524i	−0.306334	−	1.02323i	0.656769	−	0.754092i	$-0.271923\pi$
$282$		0			0
$283$	−0.567297	−	9.74010i	−0.0337223	−	0.578989i	−0.972273	−	0.233848i	$-0.924868\pi$
$283$	−0.567297	−	9.74010i	−0.0337223	−	0.578989i	0.938551	−	0.345141i	$-0.112169\pi$
$284$	−1.53957	−	26.4334i	−0.0913568	−	1.56853i
$285$		0			0
$286$	6.63835	+	22.1736i	0.392534	+	1.31115i
$287$	2.64482	−	2.21927i	0.156119	−	0.130999i
$288$		0			0
$289$	−11.4862	−	9.63807i	−0.675659	−	0.566945i
$290$	−4.76801	+	11.0535i	−0.279987	+	0.649083i
$291$		0			0
$292$	8.76751	−	29.2855i	0.513080	−	1.71381i
$293$	−1.21673	−	2.82069i	−0.0710819	−	0.164786i	0.878971	−	0.476875i	$-0.158231\pi$
$293$	−1.21673	−	2.82069i	−0.0710819	−	0.164786i	−0.950053	+	0.312089i	$0.898971\pi$
$294$		0			0
$295$	−10.4957	−	6.90311i	−0.611081	−	0.401915i
$296$	27.5213	+	47.6684i	1.59965	+	2.77067i
$297$		0			0
$298$	−21.7779	+	37.7204i	−1.26156	+	2.18509i
$299$	−1.31257	+	0.659196i	−0.0759077	+	0.0381223i
$300$		0			0
$301$	−1.86414	+	2.50398i	−0.107447	+	0.144327i
$302$	−39.6763	−	42.0544i	−2.28311	−	2.41996i
$303$		0			0
$304$	12.5563	−	1.46762i	0.720151	−	0.0841736i
$305$	30.7346	−	11.1865i	1.75986	−	0.640536i
$306$		0			0
$307$	5.34825	+	1.94660i	0.305241	+	0.111099i	0.490099	−	0.871667i	$-0.336960\pi$
$307$	5.34825	+	1.94660i	0.305241	+	0.111099i	−0.184859	+	0.982765i	$0.559183\pi$
$308$	−3.91764	−	0.928499i	−0.223228	−	0.0529061i
$309$		0			0
$310$	−29.2180	+	19.2170i	−1.65947	+	1.09145i
$311$	2.90565	+	1.45927i	0.164764	+	0.0827476i	0.529270	−	0.848453i	$-0.322466\pi$
$311$	2.90565	+	1.45927i	0.164764	+	0.0827476i	−0.364506	+	0.931201i	$0.618762\pi$
$312$		0			0
$313$	6.49142	−	6.88051i	0.366917	−	0.388909i	−0.517441	−	0.855719i	$-0.673115\pi$
$313$	6.49142	−	6.88051i	0.366917	−	0.388909i	0.884358	+	0.466810i	$0.154597\pi$
$314$	−1.17011	−	6.63603i	−0.0660332	−	0.374493i
$315$		0			0
$316$	8.85219	−	50.2032i	0.497974	−	2.82415i
$317$	−12.2475	−	16.4513i	−0.687889	−	0.923996i	0.311768	−	0.950158i	$-0.399079\pi$
$317$	−12.2475	−	16.4513i	−0.687889	−	0.923996i	−0.999658	+	0.0261623i	$0.991671\pi$
$318$		0			0
$319$	2.65963	−	0.630343i	0.148910	−	0.0352924i
$320$	−43.1426	−	5.04265i	−2.41175	−	0.281893i
$321$		0			0
$322$	0.0206501	−	0.354548i	0.00115078	−	0.0197582i
$323$	1.48754			0.0827687
$324$		0			0
$325$	8.05378			0.446744
$326$	−1.13457	+	19.4798i	−0.0628378	+	1.07888i
$327$		0			0
$328$	−56.0400	−	6.55013i	−3.09429	−	0.361671i
$329$	−3.63496	+	0.861501i	−0.200402	+	0.0474961i
$330$		0			0
$331$	−4.12134	−	5.53592i	−0.226529	−	0.304281i	0.674298	−	0.738459i	$-0.264446\pi$
$331$	−4.12134	−	5.53592i	−0.226529	−	0.304281i	−0.900827	+	0.434178i	$0.857039\pi$
$332$	−11.5323	+	65.4027i	−0.632915	+	3.58944i
$333$		0			0
$334$	2.97247	+	16.8577i	0.162647	+	0.922415i
$335$	−11.1679	+	11.8372i	−0.610165	+	0.646738i
$336$		0			0
$337$	24.2352	+	12.1714i	1.32017	+	0.663016i	0.962615	−	0.270874i	$-0.0873126\pi$
$337$	24.2352	+	12.1714i	1.32017	+	0.663016i	0.357560	+	0.933890i	$0.383609\pi$
$338$	−41.9886	+	27.6163i	−2.28388	+	1.50213i
$339$		0			0
$340$	−17.9147	−	4.24586i	−0.971560	−	0.230264i
$341$	7.46157	+	2.71579i	0.404067	+	0.147068i
$342$		0			0
$343$	6.59630	−	2.40086i	0.356166	−	0.129634i
$344$	50.6693	−	5.92239i	2.73191	−	0.319314i
$345$		0			0
$346$	−8.95622	−	9.49304i	−0.481490	−	0.510349i
$347$	−13.8619	+	18.6198i	−0.744148	+	0.999565i	0.255317	+	0.966857i	$0.417820\pi$
$347$	−13.8619	+	18.6198i	−0.744148	+	0.999565i	−0.999465	+	0.0327071i	$0.989587\pi$
$348$		0			0
$349$	2.74329	−	1.37773i	0.146845	−	0.0737484i	−0.373859	−	0.927485i	$-0.621966\pi$
$349$	2.74329	−	1.37773i	0.146845	−	0.0737484i	0.520704	+	0.853737i	$0.325669\pi$
$350$	−0.973684	+	1.68647i	−0.0520456	+	0.0901456i
$351$		0			0
$352$	11.8598	+	20.5418i	0.632131	+	1.09488i
$353$	8.77373	+	5.77057i	0.466978	+	0.307137i	0.761104	−	0.648630i	$-0.224658\pi$
$353$	8.77373	+	5.77057i	0.466978	+	0.307137i	−0.294125	+	0.955767i	$0.595028\pi$
$354$		0			0
$355$	5.18553	+	12.0214i	0.275219	+	0.638030i
$356$	−14.5035	+	48.4452i	−0.768686	+	2.56759i
$357$		0			0
$358$	0.542028	−	1.25656i	0.0286471	−	0.0664114i
$359$	−23.6540	−	19.8481i	−1.24841	−	1.04754i	−0.996818	−	0.0797090i	$-0.974601\pi$
$359$	−23.6540	−	19.8481i	−1.24841	−	1.04754i	−0.251594	−	0.967833i	$-0.580955\pi$
$360$		0			0
$361$	−13.7098	+	11.5039i	−0.721567	+	0.605466i
$362$	2.89302	+	9.66335i	0.152054	+	0.507895i
$363$		0			0
$364$	−0.859323	−	14.7540i	−0.0450408	−	0.773320i
$365$	0.878871	+	15.0896i	0.0460022	+	0.789828i
$366$		0			0
$367$	−4.36626	−	14.5843i	−0.227917	−	0.761295i	−0.993078	−	0.117457i	$-0.962526\pi$
$367$	−4.36626	−	14.5843i	−0.227917	−	0.761295i	0.765161	−	0.643839i	$-0.222659\pi$
$368$	−2.40061	+	2.01435i	−0.125140	+	0.105005i
$369$		0			0
$370$	−34.1810	−	28.6813i	−1.77699	−	1.49107i
$371$	1.92024	−	4.45161i	0.0996937	−	0.231116i
$372$		0			0
$373$	0.267683	−	0.894124i	0.0138601	−	0.0462960i	−0.950780	−	0.309867i	$-0.899715\pi$
$373$	0.267683	−	0.894124i	0.0138601	−	0.0462960i	0.964640	+	0.263572i	$0.0849005\pi$
$374$	2.30157	+	5.33564i	0.119011	+	0.275899i
$375$		0			0
$376$	51.0046	+	33.5462i	2.63036	+	1.73001i
$377$	5.01662	+	8.68904i	0.258369	+	0.447508i
$378$		0			0
$379$	19.2328	−	33.3122i	0.987924	−	1.71113i	0.359781	−	0.933037i	$-0.382851\pi$
$379$	19.2328	−	33.3122i	0.987924	−	1.71113i	0.628143	−	0.778098i	$-0.283815\pi$
$380$	−12.2014	+	6.12778i	−0.625919	+	0.314348i
$381$		0			0
$382$	36.1278	−	48.5280i	1.84846	−	2.48291i
$383$	10.1239	+	10.7307i	0.517306	+	0.548312i	0.932382	−	0.361475i	$-0.117727\pi$
$383$	10.1239	+	10.7307i	0.517306	+	0.548312i	−0.415076	+	0.909787i	$0.636245\pi$
$384$		0			0
$385$	1.97728	−	0.231110i	0.100771	−	0.0117785i
$386$	14.3588	−	5.22616i	0.730841	−	0.266005i
$387$		0			0
$388$	17.3313	+	6.30806i	0.879862	+	0.320243i
$389$	16.6281	+	3.94094i	0.843079	+	0.199814i	0.629391	−	0.777088i	$-0.283304\pi$
$389$	16.6281	+	3.94094i	0.843079	+	0.199814i	0.213688	+	0.976902i	$0.431452\pi$
$390$		0			0
$391$	−0.308083	+	0.202630i	−0.0155804	+	0.0102474i
$392$	−50.2822	−	25.2527i	−2.53963	−	1.27545i
$393$		0			0
$394$	−4.43359	+	4.69933i	−0.223361	+	0.236749i
$395$	4.37696	+	24.8230i	0.220229	+	1.24898i
$396$		0			0
$397$	−4.37414	+	24.8070i	−0.219532	+	1.24503i	0.653335	+	0.757069i	$0.273369\pi$
$397$	−4.37414	+	24.8070i	−0.219532	+	1.24503i	−0.872867	+	0.487958i	$0.837742\pi$
$398$	−15.6005	−	20.9551i	−0.781983	−	1.05039i
$399$		0			0
$400$	16.7201	−	3.96273i	0.836003	−	0.198136i
$401$	−20.4909	−	2.39504i	−1.02327	−	0.119603i	−0.412128	−	0.911126i	$-0.635214\pi$
$401$	−20.4909	−	2.39504i	−1.02327	−	0.119603i	−0.611139	+	0.791523i	$0.709288\pi$
$402$		0			0
$403$	−1.69476	+	29.0979i	−0.0844221	+	1.44947i
$404$	−91.3890			−4.54677
$405$		0			0
$406$	−2.42599			−0.120400
$407$	−0.589081	+	10.1141i	−0.0291997	+	0.501339i
$408$		0			0
$409$	−34.9426	−	4.08420i	−1.72780	−	0.201951i	−0.806616	−	0.591076i	$-0.798703\pi$
$409$	−34.9426	−	4.08420i	−1.72780	−	0.201951i	−0.921185	+	0.389125i	$0.872777\pi$
$410$	44.5050	−	10.5479i	2.19794	−	0.520922i
$411$		0			0
$412$	13.2199	+	17.7573i	0.651296	+	0.874842i
$413$	0.439618	−	2.49319i	0.0216322	−	0.122682i
$414$		0			0
$415$	−5.70212	−	32.3383i	−0.279906	−	1.58743i
$416$	−59.7502	+	63.3315i	−2.92949	+	3.10508i
$417$		0			0
$418$	3.85102	+	1.93405i	0.188359	+	0.0945977i
$419$	−22.6465	+	14.8948i	−1.10635	+	0.727659i	−0.964987	−	0.262299i	$-0.915519\pi$
$419$	−22.6465	+	14.8948i	−1.10635	+	0.727659i	−0.141365	+	0.989958i	$0.545149\pi$
$420$		0			0
$421$	−29.6178	−	7.01956i	−1.44349	−	0.342112i	−0.567071	−	0.823669i	$-0.691923\pi$
$421$	−29.6178	−	7.01956i	−1.44349	−	0.342112i	−0.876415	+	0.481557i	$0.840072\pi$
$422$	49.2008	+	17.9076i	2.39506	+	0.871729i
$423$		0			0
$424$	−74.4492	+	27.0973i	−3.61557	+	1.31596i
$425$	2.00826	−	0.234731i	0.0974147	−	0.0113861i
$426$		0			0
$427$	4.52328	+	4.79440i	0.218897	+	0.232017i
$428$	24.4305	−	32.8158i	1.18089	−	1.58621i
$429$		0			0
$430$	−36.9557	+	18.5599i	−1.78216	+	0.895036i
$431$	4.50933	−	7.81039i	0.217207	−	0.376213i	−0.736746	−	0.676170i	$-0.763639\pi$
$431$	4.50933	−	7.81039i	0.217207	−	0.376213i	0.953953	+	0.299956i	$0.0969720\pi$
$432$		0			0
$433$	−11.8523	−	20.5287i	−0.569584	−	0.986548i	−0.996607	−	0.0823075i	$-0.973771\pi$
$433$	−11.8523	−	20.5287i	−0.569584	−	0.986548i	0.427023	−	0.904241i	$-0.359562\pi$
$434$	−5.88824	−	3.87276i	−0.282645	−	0.185898i
$435$		0			0
$436$	−0.432303	−	1.00219i	−0.0207036	−	0.0479963i
$437$	−0.0784309	+	0.261977i	−0.00375186	+	0.0125321i
$438$		0			0
$439$	1.59411	−	3.69557i	0.0760828	−	0.176380i	−0.875930	−	0.482439i	$-0.839751\pi$
$439$	1.59411	−	3.69557i	0.0760828	−	0.176380i	0.952013	+	0.306059i	$0.0990104\pi$
$440$	−24.9213	−	20.9114i	−1.18807	−	0.996913i
$441$		0			0
$442$	−16.3399	+	13.7108i	−0.777209	+	0.652156i
$443$	2.28228	+	7.62333i	0.108434	+	0.362195i	0.994934	−	0.100534i	$-0.0320552\pi$
$443$	2.28228	+	7.62333i	0.108434	+	0.362195i	−0.886499	+	0.462730i	$0.846870\pi$
$444$		0			0
$445$	−1.45386	−	24.9618i	−0.0689196	−	1.18330i
$446$	−0.406715	−	6.98303i	−0.0192585	−	0.330656i
$447$		0			0
$448$	−2.51057	−	8.38588i	−0.118613	−	0.396196i
$449$	11.2889	−	9.47253i	0.532757	−	0.447037i	−0.336295	−	0.941757i	$-0.609174\pi$
$449$	11.2889	−	9.47253i	0.532757	−	0.447037i	0.869052	+	0.494720i	$0.164729\pi$
$450$		0			0
$451$	−7.95542	−	6.67539i	−0.374606	−	0.314332i
$452$	−11.2639	+	26.1127i	−0.529810	+	1.22824i
$453$		0			0
$454$	0.945724	−	3.15894i	0.0443850	−	0.148256i
$455$	2.89434	+	6.70984i	0.135689	+	0.314562i
$456$		0			0
$457$	6.56749	+	4.31950i	0.307214	+	0.202058i	0.693749	−	0.720217i	$-0.255958\pi$
$457$	6.56749	+	4.31950i	0.307214	+	0.202058i	−0.386535	+	0.922275i	$0.626328\pi$
$458$	−6.53970	−	11.3271i	−0.305580	−	0.529280i
$459$		0			0
$460$	1.69232	−	2.93118i	0.0789047	−	0.136667i
$461$	−2.95240	+	1.48275i	−0.137507	+	0.0690586i	−0.516222	−	0.856455i	$-0.672662\pi$
$461$	−2.95240	+	1.48275i	−0.137507	+	0.0690586i	0.378715	+	0.925513i	$0.376366\pi$
$462$		0			0
$463$	−10.5706	+	14.1988i	−0.491257	+	0.659873i	−0.976753	−	0.214366i	$-0.931231\pi$
$463$	−10.5706	+	14.1988i	−0.491257	+	0.659873i	0.485497	+	0.874239i	$0.338639\pi$
$464$	14.6900	+	15.5705i	0.681968	+	0.722844i
$465$		0			0
$466$	−10.1403	+	1.18523i	−0.469741	+	0.0549048i
$467$	−37.4545	+	13.6323i	−1.73319	+	0.630829i	−0.998849	−	0.0479555i	$-0.984729\pi$
$467$	−37.4545	+	13.6323i	−1.73319	+	0.630829i	−0.734338	+	0.678784i	$0.762507\pi$
$468$		0			0
$469$	−3.08187	−	1.12171i	−0.142307	−	0.0517956i
$470$	−48.1541	−	11.4127i	−2.22118	−	0.526430i
$471$		0			0
$472$	−34.5658	+	22.7343i	−1.59102	+	1.04643i
$473$	8.39102	+	4.21413i	0.385820	+	0.193766i
$474$		0			0
$475$	1.02901	−	1.09068i	0.0472140	−	0.0500439i
$476$	−0.644290	−	3.65395i	−0.0295310	−	0.167478i
$477$		0			0
$478$	4.19419	−	23.7864i	0.191838	−	1.08797i
$479$	23.4031	+	31.4359i	1.06932	+	1.43634i	0.891915	+	0.452203i	$0.149362\pi$
$479$	23.4031	+	31.4359i	1.06932	+	1.43634i	0.177402	+	0.984139i	$0.443231\pi$
$480$		0			0
$481$	−36.1868	+	8.57643i	−1.64998	+	0.391052i
$482$	62.1184	+	7.26060i	2.82941	+	0.330711i
$483$		0			0
$484$	2.57534	−	44.2170i	0.117061	−	2.00986i
$485$	−9.11940			−0.414091
$486$		0			0
$487$	35.0579			1.58863			0.794313	−	0.607509i	$-0.207831\pi$
$487$	35.0579			1.58863			0.794313	+	0.607509i	$0.207831\pi$
$488$	6.26311	−	107.533i	0.283518	−	4.86781i
$489$		0			0
$490$	45.3043	+	5.29532i	2.04664	+	0.239218i
$491$	−20.0273	+	4.74656i	−0.903821	+	0.214209i	−0.656146	−	0.754634i	$-0.727815\pi$
$491$	−20.0273	+	4.74656i	−0.903821	+	0.214209i	−0.247675	+	0.968843i	$0.579666\pi$
$492$		0			0
$493$	1.50417	+	2.02045i	0.0677443	+	0.0909964i
$494$	−2.74688	+	15.5783i	−0.123588	+	0.700903i
$495$		0			0
$496$	10.7987	+	61.2427i	0.484878	+	2.74988i
$497$	−1.81060	+	1.91912i	−0.0812165	+	0.0860845i
$498$		0			0
$499$	7.36824	+	3.70047i	0.329848	+	0.165656i	0.606014	−	0.795454i	$-0.292768\pi$
$499$	7.36824	+	3.70047i	0.329848	+	0.165656i	−0.276166	+	0.961110i	$0.589064\pi$
$500$	38.7994	−	25.5188i	1.73516	−	1.14123i
$501$		0			0
$502$	32.0343	+	7.59227i	1.42976	+	0.338860i
$503$	−15.9904	−	5.82003i	−0.712977	−	0.259503i	−0.0400358	−	0.999198i	$-0.512747\pi$
$503$	−15.9904	−	5.82003i	−0.712977	−	0.259503i	−0.672941	+	0.739696i	$0.734969\pi$
$504$		0			0
$505$	42.4621	−	15.4549i	1.88954	−	0.687736i
$506$	−1.06104	+	0.124017i	−0.0471689	+	0.00551325i
$507$		0			0
$508$	64.2469	+	68.0977i	2.85049	+	3.02135i
$509$	9.79652	−	13.1590i	0.434223	−	0.583263i	−0.530118	−	0.847924i	$-0.677853\pi$
$509$	9.79652	−	13.1590i	0.434223	−	0.583263i	0.964342	+	0.264661i	$0.0852599\pi$
$510$		0			0
$511$	−2.72212	+	1.36710i	−0.120420	+	0.0604770i
$512$	7.61274	−	13.1856i	0.336439	−	0.582729i
$513$		0			0
$514$	39.3519	+	68.1595i	1.73574	+	3.00639i
$515$	−9.14532	−	6.01497i	−0.402991	−	0.265051i
$516$		0			0
$517$	4.45057	+	10.3176i	0.195736	+	0.453767i
$518$	2.57899	−	8.61442i	0.113314	−	0.378496i
$519$		0			0
$520$	47.2990	−	109.651i	2.07420	−	4.80853i
$521$	9.25237	+	7.76366i	0.405354	+	0.340132i	0.822559	−	0.568680i	$-0.192546\pi$
$521$	9.25237	+	7.76366i	0.405354	+	0.340132i	−0.417205	+	0.908812i	$0.636990\pi$
$522$		0			0
$523$	−5.53110	+	4.64114i	−0.241858	+	0.202943i	−0.755657	−	0.654968i	$-0.772682\pi$
$523$	−5.53110	+	4.64114i	−0.241858	+	0.202943i	0.513799	+	0.857911i	$0.328238\pi$
$524$	11.8239	+	39.4947i	0.516531	+	1.72534i
$525$		0			0
$526$	−3.19610	−	54.8748i	−0.139356	−	2.39266i
$527$	0.425475	+	7.30513i	0.0185340	+	0.318216i
$528$		0			0
$529$	6.57703	+	21.9688i	0.285958	+	0.955166i
$530$	49.1993	−	41.2832i	2.13708	−	1.79323i
$531$		0			0
$532$	−2.10785	−	1.76870i	−0.0913869	−	0.0766827i
$533$	15.0989	−	35.0032i	0.654005	−	1.51615i
$534$		0			0
$535$	−5.80160	+	19.3787i	−0.250825	+	0.837814i
$536$	21.2282	+	49.2124i	0.916917	+	2.12565i
$537$		0			0
$538$	27.1497	+	17.8567i	1.17051	+	0.769855i
$539$	−5.17833	−	8.96913i	−0.223046	−	0.386328i
$540$		0			0
$541$	−19.0806	+	33.0486i	−0.820339	+	1.42087i	0.0850910	+	0.996373i	$0.472882\pi$
$541$	−19.0806	+	33.0486i	−0.820339	+	1.42087i	−0.905430	+	0.424496i	$0.860451\pi$
$542$	55.1476	−	27.6962i	2.36879	−	1.18965i
$543$		0			0
$544$	−13.0532	+	17.5335i	−0.559652	+	0.751743i
$545$	0.370343	+	0.392541i	0.0158638	+	0.0168146i
$546$		0			0
$547$	36.9317	−	4.31670i	1.57909	−	0.184569i	0.719107	−	0.694899i	$-0.244551\pi$
$547$	36.9317	−	4.31670i	1.57909	−	0.184569i	0.859978	+	0.510331i	$0.170477\pi$
$548$	41.1120	−	14.9635i	1.75622	−	0.639211i
$549$		0			0
$550$	5.50428	+	2.00339i	0.234703	+	0.0854250i
$551$	1.81767	+	0.430795i	0.0774352	+	0.0183525i
$552$		0			0
$553$	−4.24402	+	2.79133i	−0.180474	+	0.118700i
$554$	3.26551	+	1.64000i	0.138738	+	0.0696769i
$555$		0			0
$556$	−45.9168	+	48.6689i	−1.94730	+	2.06402i
$557$	−4.26215	−	24.1719i	−0.180593	−	1.02420i	−0.931488	−	0.363773i	$-0.881488\pi$
$557$	−4.26215	−	24.1719i	−0.180593	−	1.02420i	0.750894	−	0.660422i	$-0.229623\pi$
$558$		0			0
$559$	−5.98521	+	33.9438i	−0.253147	+	1.43567i
$560$	9.31026	+	12.5059i	0.393430	+	0.528469i
$561$		0			0
$562$	46.5120	−	11.0235i	1.96199	−	0.465000i
$563$	7.01231	+	0.819622i	0.295534	+	0.0345429i	0.262568	−	0.964914i	$-0.415431\pi$
$563$	7.01231	+	0.819622i	0.295534	+	0.0345429i	0.0329659	+	0.999456i	$0.489505\pi$
$564$		0			0
$565$	0.817597	−	14.0376i	0.0343966	−	0.590566i
$566$	26.0476			1.09486
$567$		0			0
$568$	43.1169			1.80914
$569$	−0.491975	+	8.44688i	−0.0206247	+	0.354112i	0.972169	+	0.234279i	$0.0752729\pi$
$569$	−0.491975	+	8.44688i	−0.0206247	+	0.354112i	−0.992794	+	0.119833i	$0.961764\pi$
$570$		0			0
$571$	0.438888	+	0.0512987i	0.0183669	+	0.00214678i	0.125271	−	0.992123i	$-0.460020\pi$
$571$	0.438888	+	0.0512987i	0.0183669	+	0.00214678i	−0.106905	+	0.994269i	$0.534094\pi$
$572$	−43.2559	+	10.2518i	−1.80862	+	0.428650i
$573$		0			0
$574$	5.50427	+	7.39352i	0.229744	+	0.308600i
$575$	−0.0645463	+	0.366060i	−0.00269177	+	0.0152658i
$576$		0			0
$577$	1.80812	+	10.2544i	0.0752730	+	0.426894i	0.999035	+	0.0439266i	$0.0139868\pi$
$577$	1.80812	+	10.2544i	0.0752730	+	0.426894i	−0.923762	+	0.382968i	$0.874902\pi$
$578$	27.4706	−	29.1171i	1.14263	−	1.21111i
$579$		0			0
$580$	−20.6609	−	10.3763i	−0.857897	−	0.430852i
$581$	5.52893	−	3.63643i	0.229379	−	0.150865i
$582$		0			0
$583$	−14.1896	−	3.36301i	−0.587675	−	0.139282i
$584$	46.7775	+	17.0256i	1.93567	+	0.704525i
$585$		0			0
$586$	7.70663	−	2.80498i	0.318358	−	0.115873i
$587$	−36.6788	+	4.28713i	−1.51389	+	0.176949i	−0.832112	−	0.554607i	$-0.812869\pi$
$587$	−36.6788	+	4.28713i	−1.51389	+	0.176949i	−0.681782	+	0.731556i	$0.738795\pi$
$588$		0			0
$589$	3.72405	+	3.94726i	0.153447	+	0.162644i
$590$	20.0275	−	26.9017i	0.824521	−	1.10752i
$591$		0			0
$592$	−70.9058	+	35.6102i	−2.91421	+	1.46357i
$593$	−1.15692	+	2.00385i	−0.0475091	+	0.0822881i	−0.888802	−	0.458291i	$-0.848462\pi$
$593$	−1.15692	+	2.00385i	−0.0475091	+	0.0822881i	0.841293	+	0.540579i	$0.181795\pi$
$594$		0			0
$595$	0.917282	+	1.58878i	0.0376049	+	0.0651336i
$596$	−69.8912	−	45.9681i	−2.86285	−	1.88293i
$597$		0			0
$598$	−1.55315	−	3.60060i	−0.0635130	−	0.147240i
$599$	2.31454	−	7.73110i	0.0945695	−	0.315884i	−0.897595	−	0.440821i	$-0.854688\pi$
$599$	2.31454	−	7.73110i	0.0945695	−	0.315884i	0.992165	+	0.124936i	$0.0398727\pi$
$600$		0			0
$601$	6.03525	−	13.9913i	0.246183	−	0.570717i	−0.749658	−	0.661826i	$-0.769782\pi$
$601$	6.03525	−	13.9913i	0.246183	−	0.570717i	0.995841	+	0.0911091i	$0.0290412\pi$
$602$	−6.38427	−	5.35704i	−0.260203	−	0.218337i
$603$		0			0
$604$	85.0636	−	71.3769i	3.46119	−	2.90428i
$605$	6.28102	+	20.9801i	0.255360	+	0.852961i
$606$		0			0
$607$	1.70295	+	29.2385i	0.0691205	+	1.18675i	0.837382	+	0.546617i	$0.184085\pi$
$607$	1.70295	+	29.2385i	0.0691205	+	1.18675i	−0.768262	+	0.640136i	$0.778878\pi$
$608$	0.942570	+	16.1833i	0.0382263	+	0.656320i
$609$		0			0
$610$	25.0434	+	83.6509i	1.01398	+	3.38693i
$611$	−31.5966	+	26.5127i	−1.27826	+	1.07259i
$612$		0			0
$613$	5.16392	+	4.33305i	0.208569	+	0.175010i	0.741088	−	0.671408i	$-0.234310\pi$
$613$	5.16392	+	4.33305i	0.208569	+	0.175010i	−0.532519	+	0.846418i	$0.678755\pi$
$614$	−6.01834	+	13.9521i	−0.242880	+	0.563060i
$615$		0			0
$616$	1.88033	−	6.28075i	0.0757608	−	0.253059i
$617$	−4.77035	−	11.0589i	−0.192047	−	0.445215i	0.794800	−	0.606871i	$-0.207576\pi$
$617$	−4.77035	−	11.0589i	−0.192047	−	0.445215i	−0.986847	+	0.161656i	$0.948316\pi$
$618$		0			0
$619$	11.2250	+	7.38281i	0.451172	+	0.296740i	0.754685	−	0.656087i	$-0.227790\pi$
$619$	11.2250	+	7.38281i	0.451172	+	0.296740i	−0.303514	+	0.952827i	$0.598160\pi$
$620$	−33.5828	−	58.1671i	−1.34872	−	2.33605i
$621$		0			0
$622$	−4.34032	+	7.51765i	−0.174031	+	0.301430i
$623$	4.50304	−	2.26151i	0.180410	−	0.0906055i
$624$		0			0
$625$	−17.9745	+	24.1439i	−0.718980	+	0.965758i
$626$	17.3304	+	18.3691i	0.692661	+	0.734178i
$627$		0			0
$628$	12.8542	−	1.50245i	0.512940	−	0.0599541i
$629$	−8.77342	+	3.19326i	−0.349819	+	0.127324i
$630$		0			0
$631$	−0.571023	−	0.207835i	−0.0227321	−	0.00827379i	0.330629	−	0.943761i	$-0.392739\pi$
$631$	−0.571023	−	0.207835i	−0.0227321	−	0.00827379i	−0.353361	+	0.935487i	$0.614961\pi$
$632$	80.7741	+	19.1438i	3.21302	+	0.761500i
$633$		0			0
$634$	45.7474	−	30.0886i	1.81686	−	1.19497i
$635$	−41.3672	−	20.7754i	−1.64161	−	0.824445i
$636$		0			0
$637$	26.0886	−	27.6523i	1.03367	−	1.09562i
$638$	1.26714	+	7.18633i	0.0501667	+	0.284510i
$639$		0			0
$640$	6.54721	−	37.1311i	0.258801	−	1.46774i
$641$	13.5276	+	18.1707i	0.534307	+	0.717699i	0.984530	−	0.175217i	$-0.0560627\pi$
$641$	13.5276	+	18.1707i	0.534307	+	0.717699i	−0.450222	+	0.892916i	$0.648655\pi$
$642$		0			0
$643$	47.4241	−	11.2397i	1.87022	−	0.443251i	0.871347	−	0.490667i	$-0.163247\pi$
$643$	47.4241	−	11.2397i	1.87022	−	0.443251i	0.998875	+	0.0474161i	$0.0150987\pi$
$644$	0.677486	+	0.0791867i	0.0266967	+	0.00312039i
$645$		0			0
$646$	−0.230912	+	3.96461i	−0.00908511	+	0.155985i
$647$	20.1953			0.793960			0.396980	−	0.917827i	$-0.370058\pi$
$647$	20.1953			0.793960			0.396980	+	0.917827i	$0.370058\pi$
$648$		0			0
$649$	−7.61503			−0.298916
$650$	−1.25020	+	21.4651i	−0.0490368	+	0.841930i
$651$		0			0
$652$	−37.2227	−	4.35071i	−1.45775	−	0.170387i
$653$	−18.6280	+	4.41491i	−0.728969	+	0.172769i	−0.578310	−	0.815817i	$-0.696288\pi$
$653$	−18.6280	+	4.41491i	−0.728969	+	0.172769i	−0.150659	+	0.988586i	$0.548139\pi$
$654$		0			0
$655$	−12.1728	−	16.3509i	−0.475630	−	0.638882i
$656$	14.1233	−	80.0975i	0.551424	−	3.12728i
$657$		0			0
$658$	−1.73183	−	9.82169i	−0.0675137	−	0.382889i
$659$	−28.2425	+	29.9353i	−1.10017	+	1.16611i	−0.115208	+	0.993341i	$0.536754\pi$
$659$	−28.2425	+	29.9353i	−1.10017	+	1.16611i	−0.984962	+	0.172771i	$0.944728\pi$
$660$		0			0
$661$	−25.4494	−	12.7812i	−0.989868	−	0.497130i	−0.121255	−	0.992621i	$-0.538692\pi$
$661$	−25.4494	−	12.7812i	−0.989868	−	0.497130i	−0.868613	+	0.495491i	$0.834988\pi$
$662$	15.3942	−	10.1249i	0.598312	−	0.393516i
$663$		0			0
$664$	−105.229	−	24.9398i	−4.08368	−	0.967850i
$665$	1.27848	+	0.465328i	0.0495773	+	0.0180447i
$666$		0			0
$667$	−0.435139	+	0.158378i	−0.0168486	+	0.00613241i
$668$	−32.6541	+	3.81671i	−1.26342	+	0.147673i
$669$		0			0
$670$	−29.8152	−	31.6023i	−1.15186	−	1.22090i
$671$	11.8395	−	15.9032i	0.457059	−	0.613936i
$672$		0			0
$673$	−32.6287	+	16.3867i	−1.25774	+	0.631662i	−0.947731	−	0.319071i	$-0.896629\pi$
$673$	−32.6287	+	16.3867i	−1.25774	+	0.631662i	−0.310011	+	0.950733i	$0.600333\pi$
$674$	−36.2014	+	62.7027i	−1.39443	+	2.41522i
$675$		0			0
$676$	−48.2611	−	83.5906i	−1.85620	−	3.21502i
$677$	1.47886	+	0.972660i	0.0568371	+	0.0373824i	0.577610	−	0.816313i	$-0.303986\pi$
$677$	1.47886	+	0.972660i	0.0568371	+	0.0373824i	−0.520772	+	0.853696i	$0.674356\pi$
$678$		0			0
$679$	−0.727920	−	1.68751i	−0.0279350	−	0.0647606i
$680$	8.59842	−	28.7207i	0.329735	−	1.10139i
$681$		0			0
$682$	−8.39644	+	19.4651i	−0.321516	+	0.745358i
$683$	−17.5030	−	14.6868i	−0.669734	−	0.561973i	0.243253	−	0.969963i	$-0.421786\pi$
$683$	−17.5030	−	14.6868i	−0.669734	−	0.561973i	−0.912987	+	0.407989i	$0.866230\pi$
$684$		0			0
$685$	−16.5714	+	13.9050i	−0.633159	+	0.531284i
$686$	5.37485	+	17.9532i	0.205213	+	0.685458i
$687$		0			0
$688$	4.27588	+	73.4140i	0.163016	+	2.79888i
$689$	−3.11246	−	53.4388i	−0.118575	−	2.03586i
$690$		0			0
$691$	−1.62241	−	5.41921i	−0.0617192	−	0.206157i	0.921568	−	0.388216i	$-0.126909\pi$
$691$	−1.62241	−	5.41921i	−0.0617192	−	0.206157i	−0.983287	+	0.182060i	$0.941724\pi$
$692$	19.2016	−	16.1121i	0.729936	−	0.612489i
$693$		0			0
$694$	−47.4741	−	39.8355i	−1.80209	−	1.51213i
$695$	13.1038	−	30.3781i	0.497057	−	1.15231i
$696$		0			0
$697$	2.74481	−	9.16830i	0.103967	−	0.347274i
$698$	3.24611	+	7.52534i	0.122867	+	0.284838i
$699$		0			0
$700$	−3.12481	−	2.05522i	−0.118107	−	0.0776801i
$701$	12.8656	+	22.2838i	0.485926	+	0.841648i	0.999869	−	0.0161763i	$-0.00514928\pi$
$701$	12.8656	+	22.2838i	0.485926	+	0.841648i	−0.513944	+	0.857824i	$0.671816\pi$
$702$		0			0
$703$	−3.46201	+	5.99637i	−0.130572	+	0.226157i
$704$	−23.5295	+	11.8170i	−0.886803	+	0.445369i
$705$		0			0
$706$	−16.7418	+	22.4881i	−0.630085	+	0.846352i
$707$	6.24925	+	6.62382i	0.235027	+	0.249114i
$708$		0			0
$709$	−33.2813	+	3.89003i	−1.24991	+	0.146093i	−0.715185	−	0.698935i	$-0.753658\pi$
$709$	−33.2813	+	3.89003i	−1.24991	+	0.146093i	−0.534721	+	0.845028i	$0.679583\pi$
$710$	−32.8446	+	11.9545i	−1.23264	+	0.448643i
$711$		0			0
$712$	−77.3810	−	28.1644i	−2.89997	−	1.05550i
$713$	−1.30898	−	0.310233i	−0.0490215	−	0.0116183i
$714$		0			0
$715$	18.3643	−	12.0784i	0.686785	−	0.451706i
$716$	2.34874	+	1.17958i	0.0877764	+	0.0440829i
$717$		0			0
$718$	56.5713	−	59.9621i	2.11122	−	2.23777i
$719$	0.373099	+	2.11595i	0.0139143	+	0.0789116i	0.990974	−	0.134053i	$-0.0427992\pi$
$719$	0.373099	+	2.11595i	0.0139143	+	0.0789116i	−0.977060	+	0.212965i	$0.931688\pi$
$720$		0			0
$721$	0.383057	−	2.17243i	0.0142658	−	0.0809054i
$722$	−28.5321	−	38.3253i	−1.06186	−	1.42632i
$723$		0			0
$724$	−18.8511	+	4.46779i	−0.700594	+	0.166044i
$725$	2.52193	+	0.294771i	0.0936621	+	0.0109475i
$726$		0			0
$727$	−0.643271	+	11.0445i	−0.0238576	+	0.409619i	0.965144	+	0.261718i	$0.0842889\pi$
$727$	−0.643271	+	11.0445i	−0.0238576	+	0.409619i	−0.989002	+	0.147902i	$0.952748\pi$
$728$	24.0660			0.891946
$729$		0			0
$730$	−40.3536			−1.49355
$731$	−0.503137	+	8.63852i	−0.0186092	+	0.319507i
$732$		0			0
$733$	16.8882	+	1.97394i	0.623778	+	0.0729092i	0.422110	−	0.906545i	$-0.361290\pi$
$733$	16.8882	+	1.97394i	0.623778	+	0.0729092i	0.201668	+	0.979454i	$0.435364\pi$
$734$	39.5482	−	9.37309i	1.45975	−	0.345967i
$735$		0			0
$736$	−2.39968	−	3.22333i	−0.0884533	−	0.118813i
$737$	−1.71303	+	9.71507i	−0.0631002	+	0.357859i
$738$		0			0
$739$	−4.23694	−	24.0289i	−0.155858	−	0.883917i	−0.957997	−	0.286779i	$-0.907416\pi$
$739$	−4.23694	−	24.0289i	−0.155858	−	0.883917i	0.802138	−	0.597138i	$-0.203696\pi$
$740$	58.8090	−	62.3339i	2.16186	−	2.29144i
$741$		0			0
$742$	11.5664	+	5.80888i	0.424617	+	0.213251i
$743$	−4.93235	+	3.24406i	−0.180951	+	0.119013i	−0.636753	−	0.771068i	$-0.719723\pi$
$743$	−4.93235	+	3.24406i	−0.180951	+	0.119013i	0.455802	+	0.890081i	$0.349352\pi$
$744$		0			0
$745$	40.2473	+	9.53879i	1.47455	+	0.349474i
$746$	2.34148	+	0.852230i	0.0857277	+	0.0312023i
$747$		0			0
$748$	−10.4873	+	3.81706i	−0.383453	+	0.139566i
$749$	−4.04904	+	0.473265i	−0.147949	+	0.0172927i
$750$		0			0
$751$	23.7112	+	25.1324i	0.865234	+	0.917095i	0.997247	−	0.0741534i	$-0.0236255\pi$
$751$	23.7112	+	25.1324i	0.865234	+	0.917095i	−0.132013	+	0.991248i	$0.542144\pi$
$752$	−52.5511	+	70.5884i	−1.91634	+	2.57409i
$753$		0			0
$754$	−23.9369	+	12.0216i	−0.871731	+	0.437800i
$755$	−27.4525	+	47.5491i	−0.999099	+	1.73049i
$756$		0			0
$757$	19.4091	+	33.6176i	0.705437	+	1.22185i	0.966534	+	0.256540i	$0.0825824\pi$
$757$	19.4091	+	33.6176i	0.705437	+	1.22185i	−0.261097	+	0.965313i	$0.584084\pi$
$758$	85.7988	+	56.4308i	3.11635	+	2.04966i
$759$		0			0
$760$	−8.80628	−	20.4152i	−0.319437	−	0.740539i
$761$	−11.7222	+	39.1550i	−0.424931	+	1.41937i	0.431035	+	0.902335i	$0.358149\pi$
$761$	−11.7222	+	39.1550i	−0.424931	+	1.41937i	−0.855966	+	0.517033i	$0.827036\pi$
$762$		0			0
$763$	−0.0430770	+	0.0998636i	−0.00155949	+	0.00361531i
$764$	89.0105	+	74.6887i	3.22029	+	2.70214i
$765$		0			0
$766$	−30.1711	+	25.3166i	−1.09013	+	0.914725i
$767$	−8.01694	−	26.7785i	−0.289475	−	0.966914i
$768$		0			0
$769$	1.79697	+	30.8528i	0.0648004	+	1.11258i	0.861352	+	0.508009i	$0.169618\pi$
$769$	1.79697	+	30.8528i	0.0648004	+	1.11258i	−0.796551	+	0.604571i	$0.793345\pi$
$770$	0.309025	+	5.30575i	0.0111365	+	0.191206i
$771$		0			0
$772$	8.41688	+	28.1143i	0.302930	+	1.01186i
$773$	−22.5762	+	18.9437i	−0.812009	+	0.681356i	−0.951086	−	0.308925i	$-0.900031\pi$
$773$	−22.5762	+	18.9437i	−0.812009	+	0.681356i	0.139077	+	0.990282i	$0.455586\pi$
$774$		0			0
$775$	5.65054	+	4.74137i	0.202974	+	0.170315i
$776$	−11.8956	+	27.5771i	−0.427027	+	0.989959i
$777$		0			0
$778$	−13.0847	+	43.7058i	−0.469108	+	1.56693i
$779$	−2.81116	−	6.51700i	−0.100720	−	0.233496i
$780$		0			0
$781$	6.63059	+	4.36101i	0.237261	+	0.156049i
$782$	−0.492228	−	0.852563i	−0.0176020	−	0.0304876i
$783$		0			0
$784$	40.5553	−	70.2439i	1.44841	−	2.50871i
$785$	−5.71839	+	2.87188i	−0.204098	+	0.102502i
$786$		0			0
$787$	9.81231	−	13.1802i	0.349771	−	0.469824i	−0.592068	−	0.805888i	$-0.701688\pi$
$787$	9.81231	−	13.1802i	0.349771	−	0.469824i	0.941839	+	0.336064i	$0.109096\pi$
$788$	−8.51513	−	9.02551i	−0.303339	−	0.321521i
$789$		0			0
$790$	−66.8380	+	7.81224i	−2.37799	+	0.277947i
$791$	2.66286	−	0.969203i	0.0946805	−	0.0344609i
$792$		0			0
$793$	68.3884	+	24.8914i	2.42854	+	0.883918i
$794$	−65.4370	−	15.5089i	−2.32227	−	0.550389i
$795$		0			0
$796$	41.9204	−	27.5715i	1.48583	−	0.977245i
$797$	7.51505	+	3.77420i	0.266197	+	0.133689i	0.576892	−	0.816821i	$-0.304265\pi$
$797$	7.51505	+	3.77420i	0.266197	+	0.133689i	−0.310695	+	0.950510i	$0.600562\pi$
$798$		0			0
$799$	−7.10607	+	7.53199i	−0.251395	+	0.266463i
$800$	3.82623	+	21.6996i	0.135278	+	0.767198i
$801$		0			0
$802$	9.56414	−	54.2409i	0.337721	−	1.91531i
$803$	5.47149	+	7.34948i	0.193085	+	0.259358i
$804$		0			0
$805$	−0.328172	+	0.0777781i	−0.0115665	+	0.00274132i
$806$	−77.2893	−	9.03382i	−2.72240	−	0.318203i
$807$		0			0
$808$	8.65294	−	148.565i	0.304409	−	5.22651i
$809$	1.83823			0.0646289			0.0323144	−	0.999478i	$-0.489712\pi$
$809$	1.83823			0.0646289			0.0323144	+	0.999478i	$0.489712\pi$
$810$		0			0
$811$	−8.25761			−0.289964			−0.144982	−	0.989434i	$-0.546312\pi$
$811$	−8.25761			−0.289964			−0.144982	+	0.989434i	$0.546312\pi$
$812$	0.270917	−	4.65146i	0.00950732	−	0.163234i
$813$		0			0
$814$	−26.8649	−	3.14006i	−0.941615	−	0.110059i
$815$	18.0306	−	4.27332i	0.631583	−	0.149688i
$816$		0			0
$817$	3.83212	+	5.14744i	0.134069	+	0.180086i
$818$	16.3095	−	92.4956i	0.570248	−	3.23403i
$819$		0			0
$820$	15.2539	+	86.5093i	0.532690	+	3.02104i
$821$	−17.5206	+	18.5707i	−0.611472	+	0.648122i	−0.956932	−	0.290311i	$-0.906241\pi$
$821$	−17.5206	+	18.5707i	−0.611472	+	0.648122i	0.345460	+	0.938433i	$0.387723\pi$
$822$		0			0
$823$	−3.13825	−	1.57609i	−0.109392	−	0.0549390i	0.393261	−	0.919427i	$-0.371347\pi$
$823$	−3.13825	−	1.57609i	−0.109392	−	0.0549390i	−0.502654	+	0.864488i	$0.667643\pi$
$824$	−30.1187	+	19.8094i	−1.04923	+	0.690092i
$825$		0			0
$826$	6.57666	+	1.55870i	0.228831	+	0.0542340i
$827$	−29.3726	−	10.6908i	−1.02139	−	0.371754i	−0.223591	−	0.974683i	$-0.571778\pi$
$827$	−29.3726	−	10.6908i	−1.02139	−	0.371754i	−0.797795	+	0.602929i	$0.794000\pi$
$828$		0			0
$829$	44.5589	−	16.2181i	1.54759	−	0.563278i	0.579743	−	0.814800i	$-0.303153\pi$
$829$	44.5589	−	16.2181i	1.54759	−	0.563278i	0.967852	+	0.251521i	$0.0809308\pi$
$830$	87.0738	−	10.1775i	3.02238	−	0.353265i
$831$		0			0
$832$	−66.3262	−	70.3016i	−2.29945	−	2.43727i
$833$	5.69939	−	7.65561i	0.197472	−	0.265251i
$834$		0			0
$835$	14.5266	−	7.29555i	0.502715	−	0.252473i
$836$	−4.13831	+	7.16776i	−0.143126	+	0.247902i
$837$		0			0
$838$	−36.1825	−	62.6699i	−1.24990	−	2.16489i
$839$	24.8318	+	16.3321i	0.857288	+	0.563847i	0.900321	−	0.435227i	$-0.143332\pi$
$839$	24.8318	+	16.3321i	0.857288	+	0.563847i	−0.0430333	+	0.999074i	$0.513702\pi$
$840$		0			0
$841$	−10.2335	−	23.7238i	−0.352878	−	0.818062i
$842$	23.3063	−	77.8483i	0.803187	−	2.68283i
$843$		0			0
$844$	−39.8295	+	92.3352i	−1.37099	+	3.17831i
$845$	36.5597	+	30.6772i	1.25769	+	1.05533i
$846$		0			0
$847$	−3.38092	+	2.83693i	−0.116170	+	0.0974780i
$848$	−32.7553	−	109.410i	−1.12482	−	3.75716i
$849$		0			0
$850$	0.313866	+	5.38888i	0.0107655	+	0.184837i
$851$	−0.0997998	−	1.71350i	−0.00342109	−	0.0587379i
$852$		0			0
$853$	−3.02404	−	10.1010i	−0.103541	−	0.345852i	0.890482	−	0.455018i	$-0.150367\pi$
$853$	−3.02404	−	10.1010i	−0.103541	−	0.345852i	−0.994024	+	0.109166i	$0.965182\pi$
$854$	−13.4803	+	11.3113i	−0.461286	+	0.387065i
$855$		0			0
$856$	51.0334	+	42.8221i	1.74429	+	1.46363i
$857$	−5.87391	+	13.6172i	−0.200649	+	0.465156i	−0.988597	−	0.150585i	$-0.951884\pi$
$857$	−5.87391	+	13.6172i	−0.200649	+	0.465156i	0.787948	+	0.615742i	$0.211143\pi$
$858$		0			0
$859$	−9.06592	+	30.2823i	−0.309325	+	1.03322i	0.652096	+	0.758137i	$0.273890\pi$
$859$	−9.06592	+	30.2823i	−0.309325	+	1.03322i	−0.961421	+	0.275082i	$0.911295\pi$
$860$	−31.4587	−	72.9295i	−1.07273	−	2.48688i
$861$		0			0
$862$	20.1164	+	13.2308i	0.685168	+	0.450642i
$863$	−1.64562	−	2.85030i	−0.0560177	−	0.0970255i	0.836657	−	0.547728i	$-0.184507\pi$
$863$	−1.64562	−	2.85030i	−0.0560177	−	0.0970255i	−0.892674	+	0.450702i	$0.851174\pi$
$864$		0			0
$865$	−6.19692	+	10.7334i	−0.210701	+	0.364946i
$866$	56.5534	−	28.4022i	1.92176	−	0.965145i
$867$		0			0
$868$	8.08298	−	10.8573i	0.274354	−	0.368522i
$869$	10.4853	+	11.1138i	0.355689	+	0.377009i
$870$		0			0
$871$	−35.9668	+	4.20391i	−1.21869	+	0.142444i
$872$	1.67013	−	0.607878i	0.0565577	−	0.0205853i
$873$		0			0
$874$	−0.686052	−	0.249702i	−0.0232060	−	0.00844631i
$875$	−4.50271	−	1.06716i	−0.152220	−	0.0360767i
$876$		0			0
$877$	30.8592	−	20.2964i	1.04204	−	0.685361i	0.0914509	−	0.995810i	$-0.470850\pi$
$877$	30.8592	−	20.2964i	1.04204	−	0.685361i	0.950590	+	0.310448i	$0.100479\pi$
$878$	9.60203	+	4.82232i	0.324053	+	0.162745i
$879$		0			0
$880$	32.1822	−	34.1112i	1.08486	−	1.14989i
$881$	−5.05857	−	28.6886i	−0.170427	−	0.966542i	−0.943290	−	0.331969i	$-0.892287\pi$
$881$	−5.05857	−	28.6886i	−0.170427	−	0.966542i	0.772863	−	0.634573i	$-0.218824\pi$
$882$		0			0
$883$	−3.27904	+	18.5963i	−0.110348	+	0.625817i	0.878600	+	0.477558i	$0.158478\pi$
$883$	−3.27904	+	18.5963i	−0.110348	+	0.625817i	−0.988949	+	0.148259i	$0.952633\pi$
$884$	−24.4636	−	32.8603i	−0.822800	−	1.10521i
$885$		0			0
$886$	−20.6721	+	4.89938i	−0.694493	+	0.164598i
$887$	24.1255	+	2.81987i	0.810055	+	0.0946818i	0.511029	−	0.859563i	$-0.329264\pi$
$887$	24.1255	+	2.81987i	0.810055	+	0.0946818i	0.299026	+	0.954245i	$0.403338\pi$
$888$		0			0
$889$	0.542429	−	9.31314i	0.0181925	−	0.312353i
$890$	66.7543			2.23761
$891$		0			0
$892$	13.4343			0.449814
$893$	−0.446517	+	7.66641i	−0.0149421	+	0.256547i
$894$		0			0
$895$	−1.29077	−	0.150870i	−0.0431458	−	0.00504302i
$896$	7.39357	−	1.75231i	0.247002	−	0.0585405i
$897$		0			0
$898$	23.4940	+	31.5579i	0.784004	+	1.05310i
$899$	−1.59569	+	9.04959i	−0.0532191	+	0.301821i
$900$		0			0
$901$	−2.33361	−	13.2346i	−0.0777438	−	0.440907i
$902$	19.0263	−	20.1667i	0.633506	−	0.671477i
$903$		0			0
$904$	−41.3832	−	20.7834i	−1.37639	−	0.691247i
$905$	8.00322	−	5.26380i	0.266036	−	0.174975i
$906$		0			0
$907$	38.3630	+	9.09219i	1.27382	+	0.301901i	0.811260	−	0.584686i	$-0.198782\pi$
$907$	38.3630	+	9.09219i	1.27382	+	0.301901i	0.462561	+	0.886587i	$0.346931\pi$
$908$	5.95117	+	2.16605i	0.197496	+	0.0718828i
$909$		0			0
$910$	−18.3325	+	6.67247i	−0.607715	+	0.221190i
$911$	41.1013	−	4.80405i	1.36175	−	0.159165i	0.596350	−	0.802724i	$-0.296617\pi$
$911$	41.1013	−	4.80405i	1.36175	−	0.159165i	0.765397	+	0.643559i	$0.222543\pi$
$912$		0			0
$913$	−13.6598	−	14.4786i	−0.452074	−	0.479170i
$914$	−12.5319	+	16.8333i	−0.414518	+	0.556795i
$915$		0			0
$916$	22.4483	−	11.2739i	0.741711	−	0.372501i
$917$	2.05402	−	3.55767i	0.0678298	−	0.117485i
$918$		0			0
$919$	0.677038	+	1.17266i	0.0223334	+	0.0386826i	0.876976	−	0.480534i	$-0.159557\pi$
$919$	0.677038	+	1.17266i	0.0223334	+	0.0386826i	−0.854643	+	0.519217i	$0.826224\pi$
$920$	4.60480	+	3.02862i	0.151816	+	0.0998507i
$921$		0			0
$922$	−3.49355	−	8.09896i	−0.115054	−	0.266725i
$923$	−8.35506	+	27.9078i	−0.275010	+	0.918597i
$924$		0			0
$925$	−3.72768	+	8.64174i	−0.122565	+	0.284139i
$926$	−36.2019	−	30.3770i	−1.18967	−	0.998250i
$927$		0			0
$928$	−21.0279	+	17.6445i	−0.690274	+	0.579209i
$929$	−7.66343	−	25.5976i	−0.251429	−	0.839831i	−0.986769	−	0.162133i	$-0.948163\pi$
$929$	−7.66343	−	25.5976i	−0.251429	−	0.839831i	0.735340	−	0.677698i	$-0.237022\pi$
$930$		0			0
$931$	−0.411552	−	7.06607i	−0.0134881	−	0.231581i
$932$	−1.14011	−	19.5748i	−0.0373454	−	0.641195i
$933$		0			0
$934$	−30.5190	−	101.941i	−0.998612	−	3.33560i
$935$	4.22721	−	3.54705i	0.138244	−	0.116001i
$936$		0			0
$937$	−2.08507	−	1.74958i	−0.0681162	−	0.0571563i	0.608094	−	0.793865i	$-0.291934\pi$
$937$	−2.08507	−	1.74958i	−0.0681162	−	0.0571563i	−0.676210	+	0.736709i	$0.736379\pi$
$938$	3.46800	−	8.03972i	0.113234	−	0.262506i
$939$		0			0
$940$	27.2596	−	91.0535i	0.889111	−	2.96984i
$941$	−9.03193	−	20.9384i	−0.294433	−	0.682571i	0.705218	−	0.708990i	$-0.250849\pi$
$941$	−9.03193	−	20.9384i	−0.294433	−	0.682571i	−0.999651	+	0.0264187i	$0.991590\pi$
$942$		0			0
$943$	1.46995	+	0.966803i	0.0478683	+	0.0314835i
$944$	−29.8195	−	51.6488i	−0.970541	−	1.68103i
$945$		0			0
$946$	−12.5341	+	21.7097i	−0.407520	+	0.705845i
$947$	−14.6434	+	7.35420i	−0.475847	+	0.238980i	−0.670524	−	0.741888i	$-0.733931\pi$
$947$	−14.6434	+	7.35420i	−0.475847	+	0.238980i	0.194677	+	0.980868i	$0.437634\pi$
$948$		0			0
$949$	−20.0844	+	26.9780i	−0.651967	+	0.875743i
$950$	2.74717	+	2.91183i	0.0891300	+	0.0944723i
$951$		0			0
$952$	6.00099	−	0.701416i	0.194493	−	0.0227330i
$953$	−33.5144	+	12.1982i	−1.08564	+	0.395140i	−0.822003	−	0.569483i	$-0.807143\pi$
$953$	−33.5144	+	12.1982i	−1.08564	+	0.395140i	−0.263634	+	0.964623i	$0.584921\pi$
$954$		0			0
$955$	−53.9877	−	19.6499i	−1.74700	−	0.635857i
$956$	45.1384	+	10.6980i	1.45988	+	0.345998i
$957$		0			0
$958$	−87.4163	+	57.4946i	−2.82429	+	1.85757i
$959$	−3.89581	−	1.95655i	−0.125802	−	0.0631803i
$960$		0			0
$961$	2.95410	−	3.13116i	0.0952935	−	0.101005i
$962$	−17.2407	−	97.7770i	−0.555863	−	3.15246i
$963$		0			0
$964$	−20.8580	+	118.292i	−0.671791	+	3.80992i
$965$	−8.66520	−	11.6394i	−0.278943	−	0.374685i
$966$		0			0
$967$	−7.83011	+	1.85577i	−0.251799	+	0.0596775i	−0.354577	−	0.935027i	$-0.615375\pi$
$967$	−7.83011	+	1.85577i	−0.251799	+	0.0596775i	0.102778	+	0.994704i	$0.467227\pi$
$968$	71.6368	+	8.37314i	2.30249	+	0.269123i
$969$		0			0
$970$	1.41562	−	24.3052i	0.0454527	−	0.780392i
$971$	44.9410			1.44223			0.721113	−	0.692818i	$-0.243631\pi$
$971$	44.9410			1.44223			0.721113	+	0.692818i	$0.243631\pi$
$972$		0			0
$973$	6.66731			0.213744
$974$	−5.44208	+	93.4369i	−0.174376	+	2.99391i
$975$		0			0
$976$	154.225	+	18.0263i	4.93663	+	0.577009i
$977$	27.0205	−	6.40398i	0.864463	−	0.204881i	0.225617	−	0.974216i	$-0.427560\pi$
$977$	27.0205	−	6.40398i	0.864463	−	0.204881i	0.638846	+	0.769335i	$0.279412\pi$
$978$		0			0
$979$	−9.05113	−	12.1578i	−0.289275	−	0.388564i
$980$	−15.2122	+	86.2728i	−0.485936	+	2.75588i
$981$		0			0
$982$	−9.54176	−	54.1140i	−0.304490	−	1.72685i
$983$	−4.80513	+	5.09314i	−0.153260	+	0.162446i	−0.799454	−	0.600727i	$-0.794878\pi$
$983$	−4.80513	+	5.09314i	−0.153260	+	0.162446i	0.646195	+	0.763173i	$0.276359\pi$
$984$		0			0
$985$	5.48271	+	2.75352i	0.174694	+	0.0877344i
$986$	−5.61843	+	3.69530i	−0.178927	+	0.117682i
$987$		0			0
$988$	−29.5623	−	7.00640i	−0.940503	−	0.222903i
$989$	−1.49485	−	0.544079i	−0.0475333	−	0.0173007i
$990$		0			0
$991$	55.0238	−	20.0270i	1.74789	−	0.636179i	0.748259	−	0.663407i	$-0.230890\pi$
$991$	55.0238	−	20.0270i	1.74789	−	0.636179i	0.999629	+	0.0272280i	$0.00866800\pi$
$992$	−79.2049	+	9.25772i	−2.51476	+	0.293933i
$993$		0			0
$994$	−4.83382	−	5.12355i	−0.153319	−	0.162509i
$995$	−14.8148	+	19.8998i	−0.469662	+	0.630865i
$996$		0			0
$997$	−34.4025	+	17.2776i	−1.08954	+	0.547187i	−0.900532	−	0.434789i	$-0.856823\pi$
$997$	−34.4025	+	17.2776i	−1.08954	+	0.547187i	−0.189006	+	0.981976i	$0.560527\pi$
$998$	−11.0063	+	19.0635i	−0.348400	+	0.603446i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.217.1		144
3.2	odd	2		729.2.g.d.217.8		144
9.2	odd	6		81.2.g.a.25.1	yes	144
9.4	even	3		729.2.g.b.703.1		144
9.5	odd	6		729.2.g.c.703.8		144
9.7	even	3		243.2.g.a.73.8		144
81.11	odd	54		6561.2.a.c.1.2		72
81.13	even	27		729.2.g.b.28.1		144
81.14	odd	54		81.2.g.a.13.1	✓	144
81.40	even	27	inner	729.2.g.a.514.1		144
81.41	odd	54		729.2.g.d.514.8		144
81.67	even	27		243.2.g.a.10.8		144
81.68	odd	54		729.2.g.c.28.8		144
81.70	even	27		6561.2.a.d.1.71		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.1	✓	144	81.14	odd	54
81.2.g.a.25.1	yes	144	9.2	odd	6
243.2.g.a.10.8		144	81.67	even	27
243.2.g.a.73.8		144	9.7	even	3
729.2.g.a.217.1		144	1.1	even	1	trivial
729.2.g.a.514.1		144	81.40	even	27	inner
729.2.g.b.28.1		144	81.13	even	27
729.2.g.b.703.1		144	9.4	even	3
729.2.g.c.28.8		144	81.68	odd	54
729.2.g.c.703.8		144	9.5	odd	6
729.2.g.d.217.8		144	3.2	odd	2
729.2.g.d.514.8		144	81.41	odd	54
6561.2.a.c.1.2		72	81.11	odd	54
6561.2.a.d.1.71		72	81.70	even	27

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.155231 + 2.66522i) q^{2} +(-5.09281 - 0.595264i) q^{4} +(2.46694 - 0.584676i) q^{5} +(0.305106 + 0.409828i) q^{7} +(1.44988 - 8.22270i) q^{8} +(1.17534 + 6.66569i) q^{10} +(1.05464 - 1.11785i) q^{11} +(5.04127 + 2.53182i) q^{13} +(-1.13964 + 0.749555i) q^{14} +(11.7117 + 2.77572i) q^{16} +(1.33086 + 0.484393i) q^{17} +(0.986977 - 0.359230i) q^{19} +(-12.9117 + 1.50916i) q^{20} +(2.81561 + 2.98437i) q^{22} +(-0.155479 + 0.208844i) q^{23} +(1.27579 - 0.640725i) q^{25} +(-7.53041 + 13.0431i) q^{26} +(-1.30989 - 2.26880i) q^{28} +(1.48594 + 0.977316i) q^{29} +(2.04644 + 4.74419i) q^{31} +(-4.42655 + 14.7857i) q^{32} +(-1.49760 + 3.47184i) q^{34} +(0.992294 + 0.832634i) q^{35} +(-5.04999 + 4.23745i) q^{37} +(0.804217 + 2.68627i) q^{38} +(-1.23083 - 21.1326i) q^{40} +(-0.392910 - 6.74600i) q^{41} +(1.75232 + 5.85315i) q^{43} +(-6.03650 + 5.06523i) q^{44} +(-0.532481 - 0.446804i) q^{46} +(-2.89593 + 6.71353i) q^{47} +(1.93275 - 6.45584i) q^{49} +(1.50963 + 3.49971i) q^{50} +(-24.1671 - 15.8950i) q^{52} +(-4.74440 - 8.21755i) q^{53} +(1.94815 - 3.37430i) q^{55} +(3.81226 - 1.91459i) q^{56} +(-2.83542 + 3.80864i) q^{58} +(-3.40033 - 3.60414i) q^{59} +(12.8136 - 1.49769i) q^{61} +(-12.9620 + 4.71777i) q^{62} +(-16.0995 - 5.85975i) q^{64} +(13.9168 + 3.29834i) q^{65} +(-5.36299 + 3.52730i) q^{67} +(-6.48947 - 3.25914i) q^{68} +(-2.37319 + 2.51543i) q^{70} +(0.896716 + 5.08553i) q^{71} +(-1.03528 + 5.87137i) q^{73} +(-10.5098 - 14.1171i) q^{74} +(-5.24032 + 1.24198i) q^{76} +(0.779905 + 0.0911578i) q^{77} +(-0.578079 + 9.92524i) q^{79} +30.5149 q^{80} +18.0405 q^{82} +(0.753098 - 12.9302i) q^{83} +(3.56636 + 0.416848i) q^{85} +(-15.8719 + 3.76171i) q^{86} +(-7.66266 - 10.2927i) q^{88} +(1.71260 - 9.71264i) q^{89} +(0.500509 + 2.83853i) q^{91} +(0.916142 - 0.971054i) q^{92} +(-17.4435 - 8.76045i) q^{94} +(2.22478 - 1.46326i) q^{95} +(-3.50004 - 0.829525i) q^{97} +(16.9062 + 6.15336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

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