LMFDB - Embedded newform 819.2.et.b.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.1
Character	$\chi$	$=$	819.145
Dual form			819.2.et.b.514.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51485 + 1.51485i) q^{2} -2.58954i q^{4} +(1.34505 - 0.360406i) q^{5} +(-0.246373 + 2.63426i) q^{7} +(0.893066 + 0.893066i) q^{8} +O(q^{10})$	\(q+(-1.51485 + 1.51485i) q^{2} -2.58954i q^{4} +(1.34505 - 0.360406i) q^{5} +(-0.246373 + 2.63426i) q^{7} +(0.893066 + 0.893066i) q^{8} +(-1.49159 + 2.58351i) q^{10} +(-0.336721 + 0.0902242i) q^{11} +(-1.32860 + 3.35184i) q^{13} +(-3.61728 - 4.36372i) q^{14} +2.47336 q^{16} +0.982239 q^{17} +(1.19250 - 4.45046i) q^{19} +(-0.933286 - 3.48307i) q^{20} +(0.373406 - 0.646758i) q^{22} +3.30540i q^{23} +(-2.65085 + 1.53047i) q^{25} +(-3.06491 - 7.09016i) q^{26} +(6.82151 + 0.637994i) q^{28} +(0.941928 + 1.63147i) q^{29} +(-0.755562 + 2.81980i) q^{31} +(-5.53290 + 5.53290i) q^{32} +(-1.48794 + 1.48794i) q^{34} +(0.618016 + 3.63201i) q^{35} +(5.79522 + 5.79522i) q^{37} +(4.93532 + 8.54823i) q^{38} +(1.52309 + 0.879355i) q^{40} +(-0.580331 + 2.16583i) q^{41} +(-6.47031 - 3.73564i) q^{43} +(0.233639 + 0.871953i) q^{44} +(-5.00718 - 5.00718i) q^{46} +(2.83465 + 10.5791i) q^{47} +(-6.87860 - 1.29802i) q^{49} +(1.69721 - 6.33408i) q^{50} +(8.67973 + 3.44045i) q^{52} +(-3.77305 - 6.53511i) q^{53} +(-0.420391 + 0.242713i) q^{55} +(-2.57259 + 2.13254i) q^{56} +(-3.89831 - 1.04455i) q^{58} +(-10.7864 + 10.7864i) q^{59} +(-5.59044 + 3.22764i) q^{61} +(-3.12700 - 5.41613i) q^{62} -11.8163i q^{64} +(-0.579009 + 4.98724i) q^{65} +(2.61216 + 9.74870i) q^{67} -2.54355i q^{68} +(-6.43815 - 4.56574i) q^{70} +(-2.43186 - 9.07582i) q^{71} +(10.3048 + 2.76117i) q^{73} -17.5578 q^{74} +(-11.5246 - 3.08802i) q^{76} +(-0.154714 - 0.909238i) q^{77} +(0.890418 - 1.54225i) q^{79} +(3.32680 - 0.891413i) q^{80} +(-2.40179 - 4.16002i) q^{82} +(-8.33002 - 8.33002i) q^{83} +(1.32116 - 0.354005i) q^{85} +(15.4605 - 4.14262i) q^{86} +(-0.381291 - 0.220138i) q^{88} +(9.61466 - 9.61466i) q^{89} +(-8.50227 - 4.32566i) q^{91} +8.55946 q^{92} +(-20.3198 - 11.7316i) q^{94} -6.41589i q^{95} +(-12.6772 + 3.39684i) q^{97} +(12.3864 - 8.45374i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.51485	+	1.51485i	−1.07116	+	1.07116i	−0.0738947	+	0.997266i	$0.523543\pi$
$2$	−1.51485	+	1.51485i	−1.07116	+	1.07116i	−0.997266	+	0.0738947i	$0.976457\pi$
$3$		0			0
$3$		0			0
$4$		−	2.58954i		−	1.29477i
$5$	1.34505	−	0.360406i	0.601526	−	0.161178i	0.0548104	−	0.998497i	$-0.482545\pi$
$5$	1.34505	−	0.360406i	0.601526	−	0.161178i	0.546716	+	0.837318i	$0.315878\pi$
$6$		0			0
$7$	−0.246373	+	2.63426i	−0.0931204	+	0.995655i
$7$	−0.246373	+	2.63426i	−0.0931204	+	0.995655i
$8$	0.893066	+	0.893066i	0.315747	+	0.315747i
$9$		0			0
$10$	−1.49159	+	2.58351i	−0.471683	+	0.816979i
$11$	−0.336721	+	0.0902242i	−0.101525	+	0.0272036i	−0.309224	−	0.950989i	$-0.600069\pi$
$11$	−0.336721	+	0.0902242i	−0.101525	+	0.0272036i	0.207699	+	0.978193i	$0.433403\pi$
$12$		0			0
$13$	−1.32860	+	3.35184i	−0.368486	+	0.929633i
$13$	−1.32860	+	3.35184i	−0.368486	+	0.929633i
$14$	−3.61728	−	4.36372i	−0.966759	−	1.16625i
$15$		0			0
$16$	2.47336			0.618340
$17$	0.982239			0.238228			0.119114	−	0.992881i	$-0.461995\pi$
$17$	0.982239			0.238228			0.119114	+	0.992881i	$0.461995\pi$
$18$		0			0
$19$	1.19250	−	4.45046i	0.273578	−	1.02101i	−0.683211	−	0.730221i	$-0.739417\pi$
$19$	1.19250	−	4.45046i	0.273578	−	1.02101i	0.956789	−	0.290784i	$-0.0939162\pi$
$20$	−0.933286	−	3.48307i	−0.208689	−	0.778838i
$21$		0			0
$22$	0.373406	−	0.646758i	0.0796104	−	0.137889i
$23$			3.30540i			0.689223i	0.938745	+	0.344612i	$0.111989\pi$
$23$			3.30540i			0.689223i	−0.938745	+	0.344612i	$0.888011\pi$
$24$		0			0
$25$	−2.65085	+	1.53047i	−0.530170	+	0.306094i
$26$	−3.06491	−	7.09016i	−0.601079	−	1.39049i
$27$		0			0
$28$	6.82151	+	0.637994i	1.28914	+	0.120570i
$29$	0.941928	+	1.63147i	0.174912	+	0.302956i	0.940131	−	0.340814i	$-0.110703\pi$
$29$	0.941928	+	1.63147i	0.174912	+	0.302956i	−0.765219	+	0.643770i	$0.777369\pi$
$30$		0			0
$31$	−0.755562	+	2.81980i	−0.135703	+	0.506450i	0.864291	+	0.502992i	$0.167767\pi$
$31$	−0.755562	+	2.81980i	−0.135703	+	0.506450i	−0.999994	+	0.00345828i	$0.998899\pi$
$32$	−5.53290	+	5.53290i	−0.978088	+	0.978088i
$33$		0			0
$34$	−1.48794	+	1.48794i	−0.255180	+	0.255180i
$35$	0.618016	+	3.63201i	0.104464	+	0.613921i
$36$		0			0
$37$	5.79522	+	5.79522i	0.952728	+	0.952728i	0.998932	−	0.0462036i	$-0.0147123\pi$
$37$	5.79522	+	5.79522i	0.952728	+	0.952728i	−0.0462036	+	0.998932i	$0.514712\pi$
$38$	4.93532	+	8.54823i	0.800615	+	1.38671i
$39$		0			0
$40$	1.52309	+	0.879355i	0.240821	+	0.139038i
$41$	−0.580331	+	2.16583i	−0.0906326	+	0.338245i	−0.996321	−	0.0856983i	$-0.972688\pi$
$41$	−0.580331	+	2.16583i	−0.0906326	+	0.338245i	0.905689	+	0.423944i	$0.139355\pi$
$42$		0			0
$43$	−6.47031	−	3.73564i	−0.986714	−	0.569679i	−0.0824233	−	0.996597i	$-0.526266\pi$
$43$	−6.47031	−	3.73564i	−0.986714	−	0.569679i	−0.904290	+	0.426918i	$0.859599\pi$
$44$	0.233639	+	0.871953i	0.0352224	+	0.131452i
$45$		0			0
$46$	−5.00718	−	5.00718i	−0.738269	−	0.738269i
$47$	2.83465	+	10.5791i	0.413476	+	1.54311i	0.787868	+	0.615844i	$0.211185\pi$
$47$	2.83465	+	10.5791i	0.413476	+	1.54311i	−0.374392	+	0.927271i	$0.622148\pi$
$48$		0			0
$49$	−6.87860	−	1.29802i	−0.982657	−	0.185432i
$50$	1.69721	−	6.33408i	0.240022	−	0.895774i
$51$		0			0
$52$	8.67973	+	3.44045i	1.20366	+	0.477105i
$53$	−3.77305	−	6.53511i	−0.518268	−	0.897667i	−0.999775	−	0.0212243i	$-0.993244\pi$
$53$	−3.77305	−	6.53511i	−0.518268	−	0.897667i	0.481507	−	0.876442i	$-0.340090\pi$
$54$		0			0
$55$	−0.420391	+	0.242713i	−0.0566855	+	0.0327274i
$56$	−2.57259	+	2.13254i	−0.343777	+	0.284972i
$57$		0			0
$58$	−3.89831	−	1.04455i	−0.511873	−	0.137156i
$59$	−10.7864	+	10.7864i	−1.40426	+	1.40426i	−0.618405	+	0.785860i	$0.712221\pi$
$59$	−10.7864	+	10.7864i	−1.40426	+	1.40426i	−0.785860	+	0.618405i	$0.787779\pi$
$60$		0			0
$61$	−5.59044	+	3.22764i	−0.715782	+	0.413257i	−0.813198	−	0.581987i	$-0.802276\pi$
$61$	−5.59044	+	3.22764i	−0.715782	+	0.413257i	0.0974163	+	0.995244i	$0.468942\pi$
$62$	−3.12700	−	5.41613i	−0.397130	−	0.687849i
$63$		0			0
$64$		−	11.8163i		−	1.47704i
$65$	−0.579009	+	4.98724i	−0.0718172	+	0.618591i
$66$		0			0
$67$	2.61216	+	9.74870i	0.319126	+	1.19099i	0.920087	+	0.391715i	$0.128118\pi$
$67$	2.61216	+	9.74870i	0.319126	+	1.19099i	−0.600961	+	0.799279i	$0.705215\pi$
$68$		−	2.54355i		−	0.308450i
$69$		0			0
$70$	−6.43815	−	4.56574i	−0.769506	−	0.545711i
$71$	−2.43186	−	9.07582i	−0.288608	−	1.07710i	−0.946162	−	0.323693i	$-0.895075\pi$
$71$	−2.43186	−	9.07582i	−0.288608	−	1.07710i	0.657554	−	0.753408i	$-0.271591\pi$
$72$		0			0
$73$	10.3048	+	2.76117i	1.20609	+	0.323170i	0.805226	−	0.592968i	$-0.202044\pi$
$73$	10.3048	+	2.76117i	1.20609	+	0.323170i	0.400862	+	0.916138i	$0.368711\pi$
$74$	−17.5578			−2.04105
$75$		0			0
$76$	−11.5246	−	3.08802i	−1.32197	−	0.354220i
$77$	−0.154714	−	0.909238i	−0.0176313	−	0.103617i
$78$		0			0
$79$	0.890418	−	1.54225i	0.100180	−	0.173517i	−0.811579	−	0.584243i	$-0.801392\pi$
$79$	0.890418	−	1.54225i	0.100180	−	0.173517i	0.911759	+	0.410726i	$0.134725\pi$
$80$	3.32680	−	0.891413i	0.371947	−	0.0996630i
$81$		0			0
$82$	−2.40179	−	4.16002i	−0.265233	−	0.459397i
$83$	−8.33002	−	8.33002i	−0.914339	−	0.914339i	0.0822710	−	0.996610i	$-0.473783\pi$
$83$	−8.33002	−	8.33002i	−0.914339	−	0.914339i	−0.996610	+	0.0822710i	$0.973783\pi$
$84$		0			0
$85$	1.32116	−	0.354005i	0.143300	−	0.0383972i
$86$	15.4605	−	4.14262i	1.66715	−	0.446711i
$87$		0			0
$88$	−0.381291	−	0.220138i	−0.0406457	−	0.0234668i
$89$	9.61466	−	9.61466i	1.01915	−	1.01915i	0.0193394	−	0.999813i	$-0.493844\pi$
$89$	9.61466	−	9.61466i	1.01915	−	1.01915i	0.999813	−	0.0193394i	$-0.00615630\pi$
$90$		0			0
$91$	−8.50227	−	4.32566i	−0.891280	−	0.453453i
$92$	8.55946			0.892386
$93$		0			0
$94$	−20.3198	−	11.7316i	−2.09582	−	1.21002i
$95$		−	6.41589i		−	0.658256i
$96$		0			0
$97$	−12.6772	+	3.39684i	−1.28717	+	0.344897i	−0.836587	−	0.547835i	$-0.815452\pi$
$97$	−12.6772	+	3.39684i	−1.28717	+	0.344897i	−0.450588	+	0.892732i	$0.648786\pi$
$98$	12.3864	−	8.45374i	1.25121	−	0.853957i
$99$		0			0
$100$	3.96321	+	6.86449i	0.396321	+	0.686449i
$101$	−0.556688	+	0.964211i	−0.0553925	+	0.0959426i	−0.892392	−	0.451261i	$-0.850974\pi$
$101$	−0.556688	+	0.964211i	−0.0553925	+	0.0959426i	0.837000	+	0.547204i	$0.184308\pi$
$102$		0			0
$103$	3.57913	−	6.19923i	0.352662	−	0.610828i	−0.634053	−	0.773290i	$-0.718610\pi$
$103$	3.57913	−	6.19923i	0.352662	−	0.610828i	0.986715	+	0.162461i	$0.0519432\pi$
$104$	−4.17994	+	1.80689i	−0.409877	+	0.177180i
$105$		0			0
$106$	15.6153	+	4.18411i	1.51669	+	0.406397i
$107$	−13.4520			−1.30046			−0.650229	−	0.759738i	$-0.725327\pi$
$107$	−13.4520			−1.30046			−0.650229	+	0.759738i	$0.725327\pi$
$108$		0			0
$109$	8.41418	+	2.25457i	0.805932	+	0.215949i	0.638187	−	0.769881i	$-0.279685\pi$
$109$	8.41418	+	2.25457i	0.805932	+	0.215949i	0.167745	+	0.985830i	$0.446351\pi$
$110$	0.269155	−	1.00450i	0.0256630	−	0.0957755i
$111$		0			0
$112$	−0.609370	+	6.51546i	−0.0575800	+	0.615653i
$113$	−1.70049	+	2.94534i	−0.159969	+	0.277074i	−0.934857	−	0.355024i	$-0.884473\pi$
$113$	−1.70049	+	2.94534i	−0.159969	+	0.277074i	0.774888	+	0.632098i	$0.217806\pi$
$114$		0			0
$115$	1.19128	+	4.44594i	0.111088	+	0.414586i
$116$	4.22475	−	2.43916i	0.392258	−	0.226470i
$117$		0			0
$118$		−	32.6794i		−	3.00839i
$119$	−0.241997	+	2.58747i	−0.0221839	+	0.237193i
$120$		0			0
$121$	−9.42104	+	5.43924i	−0.856458	+	0.494476i
$122$	3.57928	−	13.3581i	0.324053	−	1.20938i
$123$		0			0
$124$	7.30198	+	1.95656i	0.655737	+	0.175704i
$125$	−7.93718	+	7.93718i	−0.709923	+	0.709923i
$126$		0			0
$127$	4.20085	−	2.42536i	0.372765	−	0.215216i	−0.301901	−	0.953339i	$-0.597621\pi$
$127$	4.20085	−	2.42536i	0.372765	−	0.215216i	0.674666	+	0.738123i	$0.264288\pi$
$128$	6.83414	+	6.83414i	0.604058	+	0.604058i
$129$		0			0
$130$	−6.67780	−	8.43203i	−0.585682	−	0.739538i
$131$	1.98825	+	1.14792i	0.173714	+	0.100294i	0.584336	−	0.811512i	$-0.301355\pi$
$131$	1.98825	+	1.14792i	0.173714	+	0.100294i	−0.410622	+	0.911806i	$0.634688\pi$
$132$		0			0
$133$	11.4298	+	4.23782i	0.991093	+	0.367465i
$134$	−18.7249	−	10.8108i	−1.61758	−	0.933911i
$135$		0			0
$136$	0.877204	+	0.877204i	0.0752196	+	0.0752196i
$137$	13.3241	+	13.3241i	1.13835	+	1.13835i	0.988745	+	0.149609i	$0.0478015\pi$
$137$	13.3241	+	13.3241i	1.13835	+	1.13835i	0.149609	+	0.988745i	$0.452198\pi$
$138$		0			0
$139$	−13.0999	−	7.56325i	−1.11112	−	0.641506i	−0.172002	−	0.985097i	$-0.555024\pi$
$139$	−13.0999	−	7.56325i	−1.11112	−	0.641506i	−0.939120	+	0.343590i	$0.888357\pi$
$140$	9.40523	−	1.60038i	0.794887	−	0.135257i
$141$		0			0
$142$	17.4324	+	10.0646i	1.46289	+	0.844602i
$143$	0.144949	−	1.24851i	0.0121213	−	0.104405i
$144$		0			0
$145$	1.85493	+	1.85493i	0.154044	+	0.154044i
$146$	−19.7930	+	11.4275i	−1.63808	+	0.945747i
$147$		0			0
$148$	15.0070	−	15.0070i	1.23356	−	1.23356i
$149$	15.1677	+	4.06418i	1.24259	+	0.332951i	0.819469	−	0.573123i	$-0.194268\pi$
$149$	15.1677	+	4.06418i	1.24259	+	0.332951i	0.423120	+	0.906074i	$0.360935\pi$
$150$		0			0
$151$	1.15543	−	4.31214i	0.0940279	−	0.350917i	−0.902842	−	0.429972i	$-0.858524\pi$
$151$	1.15543	−	4.31214i	0.0940279	−	0.350917i	0.996870	+	0.0790547i	$0.0251902\pi$
$152$	5.03953	−	2.90958i	0.408760	−	0.235998i
$153$		0			0
$154$	1.61173	+	1.14299i	0.129877	+	0.0921048i
$155$			4.06508i			0.326515i
$156$		0			0
$157$	−3.77401	+	2.17892i	−0.301198	+	0.173897i	−0.642981	−	0.765882i	$-0.722303\pi$
$157$	−3.77401	+	2.17892i	−0.301198	+	0.173897i	0.341783	+	0.939779i	$0.388969\pi$
$158$	0.987426	+	3.68513i	0.0785554	+	0.293173i
$159$		0			0
$160$	−5.44796	+	9.43613i	−0.430699	+	0.745992i
$161$	−8.70726	−	0.814362i	−0.686228	−	0.0641807i
$162$		0			0
$163$	−4.03483	+	15.0582i	−0.316032	+	1.17945i	0.606992	+	0.794708i	$0.292376\pi$
$163$	−4.03483	+	15.0582i	−0.316032	+	1.17945i	−0.923025	+	0.384741i	$0.874291\pi$
$164$	5.60850	+	1.50279i	0.437950	+	0.117348i
$165$		0			0
$166$	25.2375			1.95881
$167$	12.6263	+	3.38321i	0.977053	+	0.261800i	0.711803	−	0.702379i	$-0.247879\pi$
$167$	12.6263	+	3.38321i	0.977053	+	0.261800i	0.265250	+	0.964180i	$0.414546\pi$
$168$		0			0
$169$	−9.46967	−	8.90648i	−0.728436	−	0.685114i
$170$	−1.46510	+	2.53763i	−0.112368	+	0.194627i
$171$		0			0
$172$	−9.67359	+	16.7551i	−0.737604	+	1.27757i
$173$	2.22746	+	3.85808i	0.169351	+	0.293324i	0.938192	−	0.346116i	$-0.112500\pi$
$173$	2.22746	+	3.85808i	0.169351	+	0.293324i	−0.768841	+	0.639440i	$0.779166\pi$
$174$		0			0
$175$	−3.37855	−	7.36009i	−0.255394	−	0.556370i
$176$	−0.832833	+	0.223157i	−0.0627771	+	0.0168211i
$177$		0			0
$178$			29.1295i			2.18335i
$179$	10.4308	+	6.02223i	0.779636	+	0.450123i	0.836301	−	0.548270i	$-0.184713\pi$
$179$	10.4308	+	6.02223i	0.779636	+	0.450123i	−0.0566654	+	0.998393i	$0.518047\pi$
$180$		0			0
$181$	23.4597			1.74374			0.871871	−	0.489735i	$-0.162907\pi$
$181$	23.4597			1.74374			0.871871	+	0.489735i	$0.162907\pi$
$182$	19.4324	−	6.32693i	1.44043	−	0.468984i
$183$		0			0
$184$	−2.95194	+	2.95194i	−0.217620	+	0.217620i
$185$	9.88351	+	5.70625i	0.726650	+	0.419532i
$186$		0			0
$187$	−0.330741	+	0.0886217i	−0.0241862	+	0.00648066i
$188$	27.3949	−	7.34044i	1.99798	−	0.535357i
$189$		0			0
$190$	9.71910	+	9.71910i	0.705098	+	0.705098i
$191$	5.04478	+	8.73782i	0.365028	+	0.632247i	0.988781	−	0.149375i	$-0.0477262\pi$
$191$	5.04478	+	8.73782i	0.365028	+	0.632247i	−0.623753	+	0.781622i	$0.714393\pi$
$192$		0			0
$193$	14.5144	−	3.88911i	1.04477	−	0.279944i	0.304679	−	0.952455i	$-0.401451\pi$
$193$	14.5144	−	3.88911i	1.04477	−	0.279944i	0.740087	+	0.672511i	$0.234784\pi$
$194$	14.0583	−	24.3498i	1.00933	−	1.74821i
$195$		0			0
$196$	−3.36128	+	17.8124i	−0.240091	+	1.27232i
$197$	8.74176	+	2.34235i	0.622825	+	0.166885i	0.556412	−	0.830907i	$-0.312178\pi$
$197$	8.74176	+	2.34235i	0.622825	+	0.166885i	0.0664131	+	0.997792i	$0.478844\pi$
$198$		0			0
$199$	−5.73738			−0.406712			−0.203356	−	0.979105i	$-0.565185\pi$
$199$	−5.73738			−0.406712			−0.203356	+	0.979105i	$0.565185\pi$
$200$	−3.73420	−	1.00058i	−0.264048	−	0.0707513i
$201$		0			0
$202$	−0.617337	−	2.30393i	−0.0434357	−	0.162104i
$203$	−4.52977	+	2.07933i	−0.317927	+	0.145940i
$204$		0			0
$205$			3.12231i			0.218071i
$206$	3.96906	+	14.8127i	0.276538	+	1.03205i
$207$		0			0
$208$	−3.28609	+	8.29031i	−0.227850	+	0.574829i
$209$			1.60616i			0.111100i
$210$		0			0
$211$	−1.22030	−	2.11362i	−0.0840090	−	0.145508i	0.820959	−	0.570986i	$-0.193439\pi$
$211$	−1.22030	−	2.11362i	−0.0840090	−	0.145508i	−0.904969	+	0.425479i	$0.860106\pi$
$212$	−16.9229	+	9.77047i	−1.16227	+	0.671038i
$213$		0			0
$214$	20.3778	−	20.3778i	1.39300	−	1.39300i
$215$	−10.0493	−	2.69269i	−0.685354	−	0.183640i
$216$		0			0
$217$	−7.24191	−	2.68507i	−0.491613	−	0.182274i
$218$	−16.1616	+	9.33088i	−1.09460	+	0.631967i
$219$		0			0
$220$	0.628514	+	1.08862i	0.0423744	+	0.0733947i
$221$	−1.30500	+	3.29231i	−0.0877837	+	0.221465i
$222$		0			0
$223$	−1.13460	+	4.23437i	−0.0759782	+	0.283554i	−0.993453	−	0.114239i	$-0.963557\pi$
$223$	−1.13460	+	4.23437i	−0.0759782	+	0.283554i	0.917475	+	0.397793i	$0.130224\pi$
$224$	−13.2119	−	15.9382i	−0.882758	−	1.06492i
$225$		0			0
$226$	−1.88575	−	7.03773i	−0.125439	−	0.468143i
$227$	−13.1360	−	13.1360i	−0.871866	−	0.871866i	0.120809	−	0.992676i	$-0.461451\pi$
$227$	−13.1360	−	13.1360i	−0.871866	−	0.871866i	−0.992676	+	0.120809i	$0.961451\pi$
$228$		0			0
$229$	2.42113	+	9.03577i	0.159993	+	0.597100i	0.998626	+	0.0524040i	$0.0166884\pi$
$229$	2.42113	+	9.03577i	0.159993	+	0.597100i	−0.838633	+	0.544696i	$0.816645\pi$
$230$	−8.53954	−	4.93031i	−0.563081	−	0.325095i
$231$		0			0
$232$	−0.615804	+	2.29821i	−0.0404295	+	0.150885i
$233$	16.7047	+	9.64448i	1.09436	+	0.631831i	0.934735	−	0.355347i	$-0.115637\pi$
$233$	16.7047	+	9.64448i	1.09436	+	0.631831i	0.159628	+	0.987177i	$0.448970\pi$
$234$		0			0
$235$	7.62551	+	13.2078i	0.497434	+	0.861580i
$236$	27.9317	+	27.9317i	1.81820	+	1.81820i
$237$		0			0
$238$	−3.55304	−	4.28621i	−0.230309	−	0.277834i
$239$	0.192645	−	0.192645i	0.0124612	−	0.0124612i	−0.700849	−	0.713310i	$-0.747195\pi$
$239$	0.192645	−	0.192645i	0.0124612	−	0.0124612i	0.713310	+	0.700849i	$0.247195\pi$
$240$		0			0
$241$	14.3156	−	14.3156i	0.922151	−	0.922151i	−0.0750302	−	0.997181i	$-0.523905\pi$
$241$	14.3156	−	14.3156i	0.922151	−	0.922151i	0.997181	+	0.0750302i	$0.0239053\pi$
$242$	6.03183	−	22.5111i	0.387741	−	1.44707i
$243$		0			0
$244$	8.35810	+	14.4767i	0.535073	+	0.926773i
$245$	−9.71990	+	0.733182i	−0.620981	+	0.0468413i
$246$		0			0
$247$	13.3329	+	9.90992i	0.848351	+	0.630553i
$248$	−3.19303	+	1.84350i	−0.202758	+	0.117062i
$249$		0			0
$250$		−	24.0473i		−	1.52088i
$251$	−0.965416	+	1.67215i	−0.0609365	+	0.105545i	−0.894884	−	0.446298i	$-0.852742\pi$
$251$	−0.965416	+	1.67215i	−0.0609365	+	0.105545i	0.833948	+	0.551843i	$0.186075\pi$
$252$		0			0
$253$	−0.298227	−	1.11300i	−0.0187494	−	0.0699736i
$254$	−2.68960	+	10.0377i	−0.168760	+	0.629822i
$255$		0			0
$256$	2.92724			0.182952
$257$	12.5547			0.783143			0.391572	−	0.920148i	$-0.371932\pi$
$257$	12.5547			0.783143			0.391572	+	0.920148i	$0.371932\pi$
$258$		0			0
$259$	−16.6939	+	13.8383i	−1.03731	+	0.859870i
$260$	12.9147	+	1.49937i	0.800933	+	0.0929868i
$261$		0			0
$262$	−4.75083	+	1.27298i	−0.293507	+	0.0786450i
$263$	5.54102	−	9.59734i	0.341674	−	0.591797i	−0.643070	−	0.765808i	$-0.722339\pi$
$263$	5.54102	−	9.59734i	0.341674	−	0.591797i	0.984744	+	0.174011i	$0.0556727\pi$
$264$		0			0
$265$	−7.43024	−	7.43024i	−0.456436	−	0.456436i
$266$	−23.7342	+	10.8948i	−1.45523	+	0.668006i
$267$		0			0
$268$	25.2447	−	6.76429i	1.54206	−	0.413195i
$269$		−	16.4027i		−	1.00009i	−0.866000	−	0.500044i	$-0.833317\pi$
$269$		−	16.4027i		−	1.00009i	0.866000	−	0.500044i	$-0.166683\pi$
$270$		0			0
$271$	0.381486	−	0.381486i	0.0231736	−	0.0231736i	−0.695425	−	0.718599i	$-0.744784\pi$
$271$	0.381486	−	0.381486i	0.0231736	−	0.0231736i	0.718599	+	0.695425i	$0.244784\pi$
$272$	2.42943			0.147306
$273$		0			0
$274$	−40.3680			−2.43872
$275$	0.754513	−	0.754513i	0.0454988	−	0.0454988i
$276$		0			0
$277$		−	10.4856i		−	0.630016i	−0.949089	−	0.315008i	$-0.897993\pi$
$277$		−	10.4856i		−	0.630016i	0.949089	−	0.315008i	$-0.102007\pi$
$278$	31.3016	−	8.38724i	1.87735	−	0.503033i
$279$		0			0
$280$	−2.69169	+	3.79555i	−0.160859	+	0.226828i
$281$	11.0310	+	11.0310i	0.658057	+	0.658057i	0.954920	−	0.296863i	$-0.0959405\pi$
$281$	11.0310	+	11.0310i	0.658057	+	0.658057i	−0.296863	+	0.954920i	$0.595941\pi$
$282$		0			0
$283$	14.1670	−	24.5380i	0.842144	−	1.45864i	−0.0459352	−	0.998944i	$-0.514627\pi$
$283$	14.1670	−	24.5380i	0.842144	−	1.45864i	0.888079	−	0.459691i	$-0.152040\pi$
$284$	−23.5022	+	6.29739i	−1.39460	+	0.373682i
$285$		0			0
$286$	1.67172	+	2.11088i	0.0988512	+	0.124819i
$287$	−5.56236	−	2.06234i	−0.328336	−	0.121736i
$288$		0			0
$289$	−16.0352			−0.943247
$290$	−5.61989			−0.330011
$291$		0			0
$292$	7.15016	−	26.6848i	0.418432	−	1.56161i
$293$	−5.59897	−	20.8956i	−0.327095	−	1.22074i	−0.912189	−	0.409770i	$-0.865609\pi$
$293$	−5.59897	−	20.8956i	−0.327095	−	1.22074i	0.585094	−	0.810966i	$-0.301058\pi$
$294$		0			0
$295$	−10.6208	+	18.3957i	−0.618364	+	1.07104i
$296$			10.3510i			0.601642i
$297$		0			0
$298$	−29.1335	+	16.8202i	−1.68766	+	0.974369i
$299$	−11.0792	−	4.39154i	−0.640725	−	0.253969i
$300$		0			0
$301$	11.4347	−	16.1241i	0.659087	−	0.929377i
$302$	4.78194	+	8.28256i	0.275170	+	0.476608i
$303$		0			0
$304$	2.94947	−	11.0076i	0.169164	−	0.631328i
$305$	−6.35617	+	6.35617i	−0.363953	+	0.363953i
$306$		0			0
$307$	−7.12305	+	7.12305i	−0.406534	+	0.406534i	−0.880528	−	0.473994i	$-0.842812\pi$
$307$	−7.12305	+	7.12305i	−0.406534	+	0.406534i	0.473994	+	0.880528i	$0.342812\pi$
$308$	−2.35451	+	0.400639i	−0.134161	+	0.0228285i
$309$		0			0
$310$	−6.15799	−	6.15799i	−0.349750	−	0.349750i
$311$	−8.27116	−	14.3261i	−0.469015	−	0.812357i	0.530358	−	0.847774i	$-0.322058\pi$
$311$	−8.27116	−	14.3261i	−0.469015	−	0.812357i	−0.999373	+	0.0354166i	$0.988724\pi$
$312$		0			0
$313$	29.9497	+	17.2915i	1.69286	+	0.977372i	0.952193	+	0.305496i	$0.0988223\pi$
$313$	29.9497	+	17.2915i	1.69286	+	0.977372i	0.740664	+	0.671876i	$0.234511\pi$
$314$	2.41631	−	9.01780i	0.136360	−	0.508904i
$315$		0			0
$316$	−3.99372	−	2.30577i	−0.224664	−	0.129710i
$317$	−3.19887	−	11.9384i	−0.179667	−	0.670525i	−0.995710	−	0.0925337i	$-0.970503\pi$
$317$	−3.19887	−	11.9384i	−0.179667	−	0.670525i	0.816043	−	0.577991i	$-0.196163\pi$
$318$		0			0
$319$	−0.464365	−	0.464365i	−0.0259994	−	0.0259994i
$320$	−4.25867	−	15.8936i	−0.238067	−	0.888477i
$321$		0			0
$322$	14.4238	−	11.9566i	0.803809	−	0.666313i
$323$	1.17132	−	4.37141i	0.0651738	−	0.243232i
$324$		0			0
$325$	−1.60798	−	10.9186i	−0.0891947	−	0.605655i
$326$	−16.6987	−	28.9231i	−0.924857	−	1.60190i
$327$		0			0
$328$	−2.45250	+	1.41595i	−0.135417	+	0.0781829i
$329$	−28.5663	+	4.86079i	−1.57491	+	0.267984i
$330$		0			0
$331$	19.1095	+	5.12036i	1.05035	+	0.281441i	0.742397	−	0.669961i	$-0.233689\pi$
$331$	19.1095	+	5.12036i	1.05035	+	0.281441i	0.307954	+	0.951401i	$0.400356\pi$
$332$	−21.5709	+	21.5709i	−1.18386	+	1.18386i
$333$		0			0
$334$	−24.2520	+	14.0019i	−1.32701	+	0.766150i
$335$	7.02698	+	12.1711i	0.383925	+	0.664978i
$336$		0			0
$337$			6.72576i			0.366376i	0.983078	+	0.183188i	$0.0586416\pi$
$337$			6.72576i			0.366376i	−0.983078	+	0.183188i	$0.941358\pi$
$338$	27.8371	−	0.853141i	1.51414	−	0.0464047i
$339$		0			0
$340$	−0.916709	−	3.42121i	−0.0497156	−	0.185541i
$341$		−	1.01766i		−	0.0551091i
$342$		0			0
$343$	5.11402	−	17.8002i	0.276131	−	0.961120i
$344$	−2.44225	−	9.11459i	−0.131677	−	0.491426i
$345$		0			0
$346$	−9.21869	−	2.47014i	−0.495600	−	0.132796i
$347$	13.2991			0.713932			0.356966	−	0.934117i	$-0.383811\pi$
$347$	13.2991			0.713932			0.356966	+	0.934117i	$0.383811\pi$
$348$		0			0
$349$	1.99671	+	0.535016i	0.106881	+	0.0286387i	0.311863	−	0.950127i	$-0.399047\pi$
$349$	1.99671	+	0.535016i	0.106881	+	0.0286387i	−0.204982	+	0.978766i	$0.565714\pi$
$350$	16.2674	+	6.03143i	0.869530	+	0.322394i
$351$		0			0
$352$	1.36384	−	2.36225i	0.0726931	−	0.125908i
$353$	12.3813	−	3.31755i	0.658988	−	0.176575i	0.0861986	−	0.996278i	$-0.472528\pi$
$353$	12.3813	−	3.31755i	0.658988	−	0.176575i	0.572789	+	0.819703i	$0.305861\pi$
$354$		0			0
$355$	−6.54195	−	11.3310i	−0.347211	−	0.601387i
$356$	−24.8976	−	24.8976i	−1.31957	−	1.31957i
$357$		0			0
$358$	−24.9239	+	6.67834i	−1.31727	+	0.352961i
$359$	−2.75160	+	0.737290i	−0.145224	+	0.0389127i	−0.330699	−	0.943736i	$-0.607284\pi$
$359$	−2.75160	+	0.737290i	−0.145224	+	0.0389127i	0.185475	+	0.982649i	$0.440618\pi$
$360$		0			0
$361$	−1.93005	−	1.11432i	−0.101582	−	0.0586482i
$362$	−35.5379	+	35.5379i	−1.86783	+	1.86783i
$363$		0			0
$364$	−11.2015	+	22.0170i	−0.587117	+	1.15400i
$365$	14.8557			0.777582
$366$		0			0
$367$	5.51927	+	3.18655i	0.288104	+	0.166337i	0.637086	−	0.770792i	$-0.280139\pi$
$367$	5.51927	+	3.18655i	0.288104	+	0.166337i	−0.348983	+	0.937129i	$0.613473\pi$
$368$			8.17544i			0.426174i
$369$		0			0
$370$	−23.6161	+	6.32793i	−1.22775	+	0.328973i
$371$	18.1447	−	8.32910i	0.942028	−	0.432425i
$372$		0			0
$373$	−0.522080	−	0.904268i	−0.0270323	−	0.0468212i	0.852193	−	0.523228i	$-0.175272\pi$
$373$	−0.522080	−	0.904268i	−0.0270323	−	0.0468212i	−0.879225	+	0.476407i	$0.841939\pi$
$374$	0.366774	−	0.635271i	0.0189654	−	0.0328491i
$375$		0			0
$376$	−6.91627	+	11.9793i	−0.356679	+	0.617787i
$377$	−6.71986	+	0.989632i	−0.346090	+	0.0509686i
$378$		0			0
$379$	14.6260	+	3.91904i	0.751289	+	0.201307i	0.614090	−	0.789236i	$-0.289523\pi$
$379$	14.6260	+	3.91904i	0.751289	+	0.201307i	0.137199	+	0.990543i	$0.456190\pi$
$380$	−16.6142			−0.852290
$381$		0			0
$382$	−20.8786	−	5.59440i	−1.06824	−	0.286234i
$383$	2.58499	−	9.64730i	0.132087	−	0.492954i	−0.867906	−	0.496728i	$-0.834535\pi$
$383$	2.58499	−	9.64730i	0.132087	−	0.492954i	0.999993	+	0.00377402i	$0.00120131\pi$
$384$		0			0
$385$	−0.535794	−	1.16721i	−0.0273066	−	0.0594867i
$386$	−16.0957	+	27.8785i	−0.819247	+	1.41898i
$387$		0			0
$388$	8.79627	+	32.8281i	0.446563	+	1.66660i
$389$	−15.4988	+	8.94824i	−0.785821	+	0.453694i	−0.838489	−	0.544918i	$-0.816561\pi$
$389$	−15.4988	+	8.94824i	−0.785821	+	0.453694i	0.0526685	+	0.998612i	$0.483227\pi$
$390$		0			0
$391$			3.24669i			0.164192i
$392$	−4.98383	−	7.30226i	−0.251721	−	0.368820i
$393$		0			0
$394$	−16.7908	+	9.69415i	−0.845906	+	0.488384i
$395$	0.641824	−	2.39532i	0.0322937	−	0.120522i
$396$		0			0
$397$	8.46474	+	2.26812i	0.424833	+	0.113834i	0.464900	−	0.885363i	$-0.346090\pi$
$397$	8.46474	+	2.26812i	0.424833	+	0.113834i	−0.0400665	+	0.999197i	$0.512757\pi$
$398$	8.69128	−	8.69128i	0.435654	−	0.435654i
$399$		0			0
$400$	−6.55651	+	3.78540i	−0.327825	+	0.189270i
$401$	11.9210	+	11.9210i	0.595305	+	0.595305i	0.939059	−	0.343755i	$-0.111699\pi$
$401$	11.9210	+	11.9210i	0.595305	+	0.595305i	−0.343755	+	0.939059i	$0.611699\pi$
$402$		0			0
$403$	−8.44767	−	6.27889i	−0.420808	−	0.312774i
$404$	2.49686	+	1.44157i	0.124224	+	0.0717206i
$405$		0			0
$406$	3.71205	−	10.0118i	0.184226	−	0.496877i
$407$	−2.47424	−	1.42850i	−0.122644	−	0.0708084i
$408$		0			0
$409$	−20.7606	−	20.7606i	−1.02654	−	1.02654i	−0.999638	−	0.0269065i	$-0.991434\pi$
$409$	−20.7606	−	20.7606i	−1.02654	−	1.02654i	−0.0269065	−	0.999638i	$-0.508566\pi$
$410$	−4.72983	−	4.72983i	−0.233589	−	0.233589i
$411$		0			0
$412$	−16.0532	−	9.26830i	−0.790883	−	0.456616i
$413$	−25.7566	−	31.0715i	−1.26740	−	1.52893i
$414$		0			0
$415$	−14.2065	−	8.20213i	−0.697370	−	0.402627i
$416$	−11.1944	−	25.8964i	−0.548851	−	1.26967i
$417$		0			0
$418$	−2.43309	−	2.43309i	−0.119006	−	0.119006i
$419$	−1.94150	+	1.12093i	−0.0948486	+	0.0547609i	−0.546674	−	0.837345i	$-0.684106\pi$
$419$	−1.94150	+	1.12093i	−0.0948486	+	0.0547609i	0.451825	+	0.892106i	$0.350773\pi$
$420$		0			0
$421$	5.33907	−	5.33907i	0.260210	−	0.260210i	−0.564929	−	0.825139i	$-0.691096\pi$
$421$	5.33907	−	5.33907i	0.260210	−	0.260210i	0.825139	+	0.564929i	$0.191096\pi$
$422$	5.05040	+	1.35325i	0.245849	+	0.0658752i
$423$		0			0
$424$	2.46671	−	9.20587i	0.119794	−	0.447077i
$425$	−2.60377	+	1.50329i	−0.126301	+	0.0729201i
$426$		0			0
$427$	−7.12509	−	15.5218i	−0.344807	−	0.751154i
$428$			34.8346i			1.68380i
$429$		0			0
$430$	19.3021	−	11.1441i	0.930832	−	0.537416i
$431$	2.24648	+	8.38396i	0.108209	+	0.403841i	0.998689	−	0.0511801i	$-0.0162983\pi$
$431$	2.24648	+	8.38396i	0.108209	+	0.403841i	−0.890480	+	0.455021i	$0.849632\pi$
$432$		0			0
$433$	12.7738	−	22.1248i	0.613869	−	1.06325i	−0.376713	−	0.926330i	$-0.622946\pi$
$433$	12.7738	−	22.1248i	0.613869	−	1.06325i	0.990582	−	0.136922i	$-0.0437210\pi$
$434$	15.0379	−	6.90294i	0.721841	−	0.331352i
$435$		0			0
$436$	5.83831	−	21.7889i	0.279604	−	1.04350i
$437$	14.7105	+	3.94168i	0.703700	+	0.188556i
$438$		0			0
$439$	−34.4632			−1.64484			−0.822421	−	0.568880i	$-0.807377\pi$
$439$	−34.4632			−1.64484			−0.822421	+	0.568880i	$0.807377\pi$
$440$	−0.592195	−	0.158678i	−0.0282318	−	0.00756469i
$441$		0			0
$442$	−3.01048	−	6.96423i	−0.143194	−	0.331255i
$443$	−17.8457	+	30.9097i	−0.847876	+	1.46857i	0.0352231	+	0.999379i	$0.488786\pi$
$443$	−17.8457	+	30.9097i	−0.847876	+	1.46857i	−0.883100	+	0.469186i	$0.844548\pi$
$444$		0			0
$445$	9.46705	−	16.3974i	0.448781	−	0.777312i
$446$	−4.69569	−	8.13318i	−0.222348	−	0.385117i
$447$		0			0
$448$	31.1272	+	2.91122i	1.47062	+	0.137542i
$449$	−5.75740	+	1.54269i	−0.271709	+	0.0728041i	−0.392101	−	0.919922i	$-0.628252\pi$
$449$	−5.75740	+	1.54269i	−0.271709	+	0.0728041i	0.120392	+	0.992726i	$0.461585\pi$
$450$		0			0
$451$		−	0.781640i		−	0.0368060i
$452$	7.62707	+	4.40349i	0.358747	+	0.207123i
$453$		0			0
$454$	39.7981			1.86782
$455$	−12.9950	−	2.75398i	−0.609215	−	0.129109i
$456$		0			0
$457$	19.3234	−	19.3234i	0.903910	−	0.903910i	−0.0918622	−	0.995772i	$-0.529282\pi$
$457$	19.3234	−	19.3234i	0.903910	−	0.903910i	0.995772	+	0.0918622i	$0.0292819\pi$
$458$	−17.3555	−	10.0202i	−0.810968	−	0.468213i
$459$		0			0
$460$	11.5129	−	3.08488i	0.536793	−	0.143833i
$461$	25.4470	−	6.81851i	1.18519	−	0.317570i	0.388205	−	0.921573i	$-0.373095\pi$
$461$	25.4470	−	6.81851i	1.18519	−	0.317570i	0.796982	+	0.604004i	$0.206429\pi$
$462$		0			0
$463$	20.1763	+	20.1763i	0.937671	+	0.937671i	0.998168	−	0.0604970i	$-0.0192686\pi$
$463$	20.1763	+	20.1763i	0.937671	+	0.937671i	−0.0604970	+	0.998168i	$0.519269\pi$
$464$	2.32973	+	4.03520i	0.108155	+	0.187330i
$465$		0			0
$466$	−39.9151	+	10.6952i	−1.84903	+	0.495446i
$467$	−11.1697	+	19.3465i	−0.516873	+	0.895251i	0.482935	+	0.875656i	$0.339571\pi$
$467$	−11.1697	+	19.3465i	−0.516873	+	0.895251i	−0.999808	+	0.0195946i	$0.993762\pi$
$468$		0			0
$469$	−26.3241	+	4.47927i	−1.21554	+	0.206833i
$470$	−31.5593	−	8.45629i	−1.45572	−	0.390060i
$471$		0			0
$472$	−19.2659			−0.886783
$473$	2.51574	+	0.674090i	0.115674	+	0.0309947i
$474$		0			0
$475$	3.65016	+	13.6226i	0.167481	+	0.625047i
$476$	6.70035	+	0.626662i	0.307110	+	0.0287230i
$477$		0			0
$478$			0.583657i			0.0266959i
$479$	3.98443	+	14.8701i	0.182053	+	0.679432i	0.995242	+	0.0974319i	$0.0310628\pi$
$479$	3.98443	+	14.8701i	0.182053	+	0.679432i	−0.813189	+	0.582000i	$0.802271\pi$
$480$		0			0
$481$	−27.1242	+	11.7251i	−1.23676	+	0.534621i
$482$			43.3721i			1.97554i
$483$		0			0
$484$	14.0851	+	24.3962i	0.640233	+	1.10892i
$485$	−15.8273	+	9.13787i	−0.718679	+	0.414929i
$486$		0			0
$487$	−12.8093	+	12.8093i	−0.580444	+	0.580444i	−0.935025	−	0.354581i	$-0.884623\pi$
$487$	−12.8093	+	12.8093i	−0.580444	+	0.580444i	0.354581	+	0.935025i	$0.384623\pi$
$488$	−7.87512	−	2.11013i	−0.356490	−	0.0955212i
$489$		0			0
$490$	13.6135	−	15.8348i	0.614996	−	0.715345i
$491$	−17.3469	+	10.0153i	−0.782857	+	0.451983i	−0.837442	−	0.546527i	$-0.815950\pi$
$491$	−17.3469	+	10.0153i	−0.782857	+	0.451983i	0.0545850	+	0.998509i	$0.482616\pi$
$492$		0			0
$493$	0.925198	+	1.60249i	0.0416688	+	0.0721725i
$494$	−35.2094	+	5.18527i	−1.58414	+	0.233296i
$495$		0			0
$496$	−1.86878	+	6.97437i	−0.0839105	+	0.313158i
$497$	24.5072	−	4.17009i	1.09930	−	0.187054i
$498$		0			0
$499$	2.03847	+	7.60769i	0.0912546	+	0.340567i	0.996425	−	0.0844820i	$-0.0269236\pi$
$499$	2.03847	+	7.60769i	0.0912546	+	0.340567i	−0.905170	+	0.425049i	$0.860257\pi$
$500$	20.5537	+	20.5537i	0.919188	+	0.919188i
$501$		0			0
$502$	−1.07060	−	3.99552i	−0.0477830	−	0.178329i
$503$	−36.6569	−	21.1639i	−1.63445	−	0.943650i	−0.982698	−	0.185217i	$-0.940701\pi$
$503$	−36.6569	−	21.1639i	−1.63445	−	0.943650i	−0.651752	−	0.758432i	$-0.725966\pi$
$504$		0			0
$505$	−0.401267	+	1.49755i	−0.0178561	+	0.0666400i
$506$	2.13779	+	1.23426i	0.0950365	+	0.0548694i
$507$		0			0
$508$	−6.28057	−	10.8783i	−0.278655	−	0.482645i
$509$	−26.6734	−	26.6734i	−1.18228	−	1.18228i	−0.979153	−	0.203126i	$-0.934890\pi$
$509$	−26.6734	−	26.6734i	−1.18228	−	1.18228i	−0.203126	−	0.979153i	$-0.565110\pi$
$510$		0			0
$511$	−9.81246	+	26.4653i	−0.434078	+	1.17075i
$512$	−18.1026	+	18.1026i	−0.800029	+	0.800029i
$513$		0			0
$514$	−19.0185	+	19.0185i	−0.838872	+	0.838872i
$515$	2.57988	−	9.62823i	0.113683	−	0.424271i
$516$		0			0
$517$	−1.90897	−	3.30644i	−0.0839566	−	0.145417i
$518$	4.32577	−	46.2517i	0.190063	−	2.03218i
$519$		0			0
$520$	−4.97103	+	3.93684i	−0.217994	+	0.172642i
$521$	22.8432	−	13.1885i	1.00078	−	0.577800i	0.0923008	−	0.995731i	$-0.470578\pi$
$521$	22.8432	−	13.1885i	1.00078	−	0.577800i	0.908479	+	0.417931i	$0.137245\pi$
$522$		0			0
$523$		−	14.9301i		−	0.652846i	−0.945224	−	0.326423i	$-0.894157\pi$
$523$		−	14.9301i		−	0.652846i	0.945224	−	0.326423i	$-0.105843\pi$
$524$	2.97258	−	5.14866i	0.129858	−	0.224920i
$525$		0			0
$526$	6.14470	+	22.9323i	0.267922	+	0.999898i
$527$	−0.742142	+	2.76971i	−0.0323282	+	0.120651i
$528$		0			0
$529$	12.0743			0.524971
$530$	22.5114			0.977833
$531$		0			0
$532$	10.9740	−	29.5981i	0.475783	−	1.28324i
$533$	−6.48848	−	4.82269i	−0.281047	−	0.208894i
$534$		0			0
$535$	−18.0937	+	4.84820i	−0.782260	+	0.209606i
$536$	−6.37341	+	11.0391i	−0.275289	+	0.476815i
$537$		0			0
$538$	24.8476	+	24.8476i	1.07126	+	1.07126i
$539$	2.43328	−	0.183545i	0.104809	−	0.00790584i
$540$		0			0
$541$	−17.8662	+	4.78723i	−0.768127	+	0.205819i	−0.621544	−	0.783379i	$-0.713494\pi$
$541$	−17.8662	+	4.78723i	−0.768127	+	0.205819i	−0.146583	+	0.989198i	$0.546828\pi$
$542$			1.15579i			0.0496454i
$543$		0			0
$544$	−5.43463	+	5.43463i	−0.233008	+	0.233008i
$545$	12.1301			0.519596
$546$		0			0
$547$	−12.6324			−0.540123			−0.270062	−	0.962843i	$-0.587044\pi$
$547$	−12.6324			−0.540123			−0.270062	+	0.962843i	$0.587044\pi$
$548$	34.5033	−	34.5033i	1.47391	−	1.47391i
$549$		0			0
$550$			2.28595i			0.0974731i
$551$	8.38402	−	2.24649i	0.357171	−	0.0957038i
$552$		0			0
$553$	3.84330	+	2.72556i	0.163434	+	0.115902i
$554$	15.8841	+	15.8841i	0.674849	+	0.674849i
$555$		0			0
$556$	−19.5853	+	33.9228i	−0.830603	+	1.43865i
$557$	−0.590694	+	0.158276i	−0.0250285	+	0.00670637i	−0.271312	−	0.962492i	$-0.587457\pi$
$557$	−0.590694	+	0.158276i	−0.0250285	+	0.00670637i	0.246283	+	0.969198i	$0.420791\pi$
$558$		0			0
$559$	21.1177	−	16.7243i	0.893183	−	0.707363i
$560$	1.52858	+	8.98326i	0.0645941	+	0.379612i
$561$		0			0
$562$	−33.4208			−1.40977
$563$	10.8225			0.456113			0.228057	−	0.973648i	$-0.426763\pi$
$563$	10.8225			0.456113			0.228057	+	0.973648i	$0.426763\pi$
$564$		0			0
$565$	−1.22573	+	4.57450i	−0.0515670	+	0.192451i
$566$	15.7105	+	58.6324i	0.660362	+	2.46450i
$567$		0			0
$568$	5.93349	−	10.2771i	0.248964	−	0.431218i
$569$		−	29.0842i		−	1.21927i	−0.792680	−	0.609637i	$-0.791315\pi$
$569$		−	29.0842i		−	1.21927i	0.792680	−	0.609637i	$-0.208685\pi$
$570$		0			0
$571$	11.7038	−	6.75719i	0.489788	−	0.282779i	−0.234698	−	0.972068i	$-0.575410\pi$
$571$	11.7038	−	6.75719i	0.489788	−	0.282779i	0.724487	+	0.689289i	$0.242077\pi$
$572$	−3.23306	−	0.375352i	−0.135181	−	0.0156943i
$573$		0			0
$574$	11.5503	−	5.30200i	0.482100	−	0.221301i
$575$	−5.05881	−	8.76212i	−0.210967	−	0.365406i
$576$		0			0
$577$	2.83216	−	10.5697i	0.117904	−	0.440024i	−0.881584	−	0.472028i	$-0.843522\pi$
$577$	2.83216	−	10.5697i	0.117904	−	0.440024i	0.999488	+	0.0320036i	$0.0101888\pi$
$578$	24.2909	−	24.2909i	1.01037	−	1.01037i
$579$		0			0
$580$	4.80343	−	4.80343i	0.199451	−	0.199451i
$581$	23.9957	−	19.8911i	0.995510	−	0.825222i
$582$		0			0
$583$	1.86009	+	1.86009i	0.0770371	+	0.0770371i
$584$	6.73698	+	11.6688i	0.278778	+	0.482858i
$585$		0			0
$586$	40.1353	+	23.1721i	1.65798	+	0.957232i
$587$	7.06382	−	26.3625i	0.291555	−	1.08810i	−0.652360	−	0.757909i	$-0.726221\pi$
$587$	7.06382	−	26.3625i	0.291555	−	1.08810i	0.943915	−	0.330188i	$-0.107112\pi$
$588$		0			0
$589$	11.6484	+	6.72519i	0.479963	+	0.277107i
$590$	−11.7779	−	43.9556i	−0.484887	−	1.80962i
$591$		0			0
$592$	14.3337	+	14.3337i	0.589110	+	0.589110i
$593$	2.29583	+	8.56816i	0.0942785	+	0.351852i	0.996909	−	0.0785641i	$-0.0250335\pi$
$593$	2.29583	+	8.56816i	0.0942785	+	0.351852i	−0.902631	+	0.430416i	$0.858367\pi$
$594$		0			0
$595$	0.607039	+	3.56750i	0.0248862	+	0.146253i
$596$	10.5244	−	39.2775i	0.431095	−	1.60887i
$597$		0			0
$598$	23.4358	−	10.1308i	0.958361	−	0.414277i
$599$	10.0430	+	17.3949i	0.410344	+	0.710737i	0.994927	−	0.100597i	$-0.0320752\pi$
$599$	10.0430	+	17.3949i	0.410344	+	0.710737i	−0.584583	+	0.811334i	$0.698742\pi$
$600$		0			0
$601$	−10.0979	+	5.83002i	−0.411902	+	0.237811i	−0.691606	−	0.722275i	$-0.743097\pi$
$601$	−10.0979	+	5.83002i	−0.411902	+	0.237811i	0.279705	+	0.960086i	$0.409763\pi$
$602$	7.10368	+	41.7475i	0.289524	+	1.70150i
$603$		0			0
$604$	−11.1665	−	2.99205i	−0.454357	−	0.121745i
$605$	−10.7115	+	10.7115i	−0.435483	+	0.435483i
$606$		0			0
$607$	36.7395	−	21.2116i	1.49121	−	0.860952i	0.491263	−	0.871011i	$-0.336536\pi$
$607$	36.7395	−	21.2116i	1.49121	−	0.860952i	0.999949	+	0.0100597i	$0.00320217\pi$
$608$	18.0260	+	31.2219i	0.731050	+	1.26622i
$609$		0			0
$610$		−	19.2573i		−	0.779705i
$611$	−39.2254	−	4.55400i	−1.58689	−	0.184235i
$612$		0			0
$613$	4.55495	+	16.9993i	0.183973	+	0.686595i	0.994848	+	0.101376i	$0.0323246\pi$
$613$	4.55495	+	16.9993i	0.183973	+	0.686595i	−0.810876	+	0.585219i	$0.801009\pi$
$614$		−	21.5807i		−	0.870926i
$615$		0			0
$616$	0.673840	−	0.950180i	0.0271498	−	0.0382839i
$617$	−2.26503	−	8.45319i	−0.0911865	−	0.340313i	0.905227	−	0.424928i	$-0.139701\pi$
$617$	−2.26503	−	8.45319i	−0.0911865	−	0.340313i	−0.996414	+	0.0846152i	$0.973034\pi$
$618$		0			0
$619$	−5.89711	−	1.58013i	−0.237025	−	0.0635107i	0.138351	−	0.990383i	$-0.455820\pi$
$619$	−5.89711	−	1.58013i	−0.237025	−	0.0635107i	−0.375376	+	0.926873i	$0.622486\pi$
$620$	10.5267			0.422762
$621$		0			0
$622$	34.2314	+	9.17228i	1.37256	+	0.367775i
$623$	22.9587	+	27.6963i	0.919820	+	1.10963i
$624$		0			0
$625$	−0.162973	+	0.282278i	−0.00651893	+	0.0112911i
$626$	−71.5633	+	19.1753i	−2.86024	+	0.766400i
$627$		0			0
$628$	5.64241	+	9.77294i	0.225157	+	0.389983i
$629$	5.69229	+	5.69229i	0.226966	+	0.226966i
$630$		0			0
$631$	−12.1554	+	3.25704i	−0.483900	+	0.129661i	−0.492518	−	0.870302i	$-0.663923\pi$
$631$	−12.1554	+	3.25704i	−0.483900	+	0.129661i	0.00861795	+	0.999963i	$0.497257\pi$
$632$	2.17253	−	0.582128i	0.0864187	−	0.0231558i
$633$		0			0
$634$	22.9306	+	13.2390i	0.910692	+	0.525788i
$635$	4.77625	−	4.77625i	0.189540	−	0.189540i
$636$		0			0
$637$	13.4896	−	21.3314i	0.534479	−	0.845182i
$638$	1.40689			0.0556992
$639$		0			0
$640$	11.6553	+	6.72921i	0.460718	+	0.265996i
$641$		−	6.78631i		−	0.268043i	−0.990978	−	0.134022i	$-0.957211\pi$
$641$		−	6.78631i		−	0.268043i	0.990978	−	0.134022i	$-0.0427892\pi$
$642$		0			0
$643$	16.9779	−	4.54920i	0.669541	−	0.179403i	0.0919931	−	0.995760i	$-0.470676\pi$
$643$	16.9779	−	4.54920i	0.669541	−	0.179403i	0.577548	+	0.816357i	$0.304010\pi$
$644$	−2.10882	+	22.5478i	−0.0830993	+	0.888508i
$645$		0			0
$646$	4.84767	+	8.39640i	0.190729	+	0.330352i
$647$	−9.12424	+	15.8037i	−0.358711	+	0.621306i	−0.987746	−	0.156071i	$-0.950117\pi$
$647$	−9.12424	+	15.8037i	−0.358711	+	0.621306i	0.629035	+	0.777377i	$0.283450\pi$
$648$		0			0
$649$	2.65881	−	4.60519i	0.104367	−	0.180769i
$650$	18.9759	+	14.1042i	0.744296	+	0.553212i
$651$		0			0
$652$	38.9938	+	10.4484i	1.52711	+	0.409189i
$653$	26.8238			1.04970			0.524849	−	0.851195i	$-0.324122\pi$
$653$	26.8238			1.04970			0.524849	+	0.851195i	$0.324122\pi$
$654$		0			0
$655$	3.08802	+	0.827433i	0.120659	+	0.0323305i
$656$	−1.43537	+	5.35687i	−0.0560417	+	0.209151i
$657$		0			0
$658$	35.9103	−	50.6371i	1.39993	−	1.97404i
$659$	8.29277	−	14.3635i	0.323040	−	0.559522i	−0.658073	−	0.752954i	$-0.728628\pi$
$659$	8.29277	−	14.3635i	0.323040	−	0.559522i	0.981114	+	0.193431i	$0.0619617\pi$
$660$		0			0
$661$	2.18176	+	8.14245i	0.0848607	+	0.316704i	0.995288	−	0.0969651i	$-0.0309135\pi$
$661$	2.18176	+	8.14245i	0.0848607	+	0.316704i	−0.910427	+	0.413670i	$0.864247\pi$
$662$	−36.7045	+	21.1914i	−1.42656	+	0.823626i
$663$		0			0
$664$		−	14.8785i		−	0.577399i
$665$	16.9011	+	1.58070i	0.655396	+	0.0612970i
$666$		0			0
$667$	−5.39265	+	3.11345i	−0.208804	+	0.120553i
$668$	8.76095	−	32.6963i	0.338972	−	1.26506i
$669$		0			0
$670$	−29.0822	−	7.79255i	−1.12354	−	0.301052i
$671$	1.59121	−	1.59121i	0.0614279	−	0.0614279i
$672$		0			0
$673$	−26.7116	+	15.4220i	−1.02966	+	0.594473i	−0.916887	−	0.399148i	$-0.869306\pi$
$673$	−26.7116	+	15.4220i	−1.02966	+	0.594473i	−0.112771	+	0.993621i	$0.535973\pi$
$674$	−10.1885	−	10.1885i	−0.392447	−	0.392447i
$675$		0			0
$676$	−23.0637	+	24.5221i	−0.887065	+	0.943157i
$677$	23.6241	+	13.6394i	0.907947	+	0.524203i	0.879770	−	0.475400i	$-0.157697\pi$
$677$	23.6241	+	13.6394i	0.907947	+	0.524203i	0.0281768	+	0.999603i	$0.491030\pi$
$678$		0			0
$679$	−5.82483	−	34.2319i	−0.223537	−	1.31370i
$680$	1.49604	+	0.863737i	0.0573704	+	0.0331228i
$681$		0			0
$682$	1.54159	+	1.54159i	0.0590307	+	0.0590307i
$683$	−2.04428	−	2.04428i	−0.0782222	−	0.0782222i	0.666913	−	0.745135i	$-0.267615\pi$
$683$	−2.04428	−	2.04428i	−0.0782222	−	0.0782222i	−0.745135	+	0.666913i	$0.767615\pi$
$684$		0			0
$685$	22.7237	+	13.1195i	0.868228	+	0.501272i
$686$	19.2176	+	34.7116i	0.733733	+	1.32529i
$687$		0			0
$688$	−16.0034	−	9.23957i	−0.610124	−	0.352255i
$689$	26.9175	−	3.96414i	1.02548	−	0.151022i
$690$		0			0
$691$	−12.0266	−	12.0266i	−0.457515	−	0.457515i	0.440324	−	0.897839i	$-0.354864\pi$
$691$	−12.0266	−	12.0266i	−0.457515	−	0.457515i	−0.897839	+	0.440324i	$0.854864\pi$
$692$	9.99066	−	5.76811i	0.379788	−	0.219271i
$693$		0			0
$694$	−20.1461	+	20.1461i	−0.764736	+	0.764736i
$695$	−20.3459	−	5.45168i	−0.771765	−	0.206794i
$696$		0			0
$697$	−0.570024	+	2.12736i	−0.0215912	+	0.0805795i
$698$	−3.83518	+	2.21424i	−0.145164	+	0.0838103i
$699$		0			0
$700$	−19.0592	+	8.74889i	−0.720372	+	0.330677i
$701$		−	9.25014i		−	0.349373i	−0.984624	−	0.174687i	$-0.944109\pi$
$701$		−	9.25014i		−	0.349373i	0.984624	−	0.174687i	$-0.0558912\pi$
$702$		0			0
$703$	32.7022	−	18.8806i	1.23339	−	0.712096i
$704$	1.06612	+	3.97880i	0.0401808	+	0.149957i
$705$		0			0
$706$	−13.7302	+	23.7813i	−0.516741	+	0.895022i
$707$	−2.40283	−	1.70401i	−0.0903675	−	0.0640860i
$708$		0			0
$709$	0.0570187	−	0.212797i	0.00214138	−	0.00799175i	−0.964847	−	0.262813i	$-0.915350\pi$
$709$	0.0570187	−	0.212797i	0.00214138	−	0.00799175i	0.966988	+	0.254821i	$0.0820165\pi$
$710$	27.0748	+	7.25468i	1.01610	+	0.272263i
$711$		0			0
$712$	17.1731			0.643588
$713$	−9.32055	−	2.49743i	−0.349057	−	0.0935296i
$714$		0			0
$715$	−0.255005	−	1.73155i	−0.00953664	−	0.0647563i
$716$	15.5948	−	27.0110i	0.582806	−	1.00945i
$717$		0			0
$718$	3.05138	−	5.28515i	0.113877	−	0.197240i
$719$	13.1959	+	22.8560i	0.492125	+	0.852385i	0.999959	−	0.00906953i	$-0.00288696\pi$
$719$	13.1959	+	22.8560i	0.492125	+	0.852385i	−0.507834	+	0.861455i	$0.669554\pi$
$720$		0			0
$721$	15.4486	+	10.9557i	0.575334	+	0.408010i
$722$	4.61176	−	1.23572i	0.171632	−	0.0459886i
$723$		0			0
$724$		−	60.7497i		−	2.25775i
$725$	−4.99382	−	2.88319i	−0.185466	−	0.107079i
$726$		0			0
$727$	11.9152			0.441910			0.220955	−	0.975284i	$-0.429083\pi$
$727$	11.9152			0.441910			0.220955	+	0.975284i	$0.429083\pi$
$728$	−3.72999	−	11.4562i	−0.138243	−	0.424595i
$729$		0			0
$730$	−22.5041	+	22.5041i	−0.832915	+	0.832915i
$731$	−6.35539	−	3.66929i	−0.235063	−	0.135714i
$732$		0			0
$733$	−38.3067	+	10.2643i	−1.41489	+	0.379119i	−0.883669	−	0.468113i	$-0.844934\pi$
$733$	−38.3067	+	10.2643i	−1.41489	+	0.379119i	−0.531223	+	0.847232i	$0.678267\pi$
$734$	−13.1880	+	3.53372i	−0.486779	+	0.130432i
$735$		0			0
$736$	−18.2884	−	18.2884i	−0.674121	−	0.674121i
$737$	−1.75914	−	3.04692i	−0.0647987	−	0.112235i
$738$		0			0
$739$	17.3308	−	4.64377i	0.637523	−	0.170824i	0.0744418	−	0.997225i	$-0.476282\pi$
$739$	17.3308	−	4.64377i	0.637523	−	0.170824i	0.563081	+	0.826402i	$0.309616\pi$
$740$	14.7766	−	25.5938i	0.543197	−	0.940845i
$741$		0			0
$742$	−14.8692	+	40.1039i	−0.545866	+	1.47226i
$743$	13.8438	+	3.70943i	0.507880	+	0.136086i	0.503655	−	0.863905i	$-0.331988\pi$
$743$	13.8438	+	3.70943i	0.507880	+	0.136086i	0.00422503	+	0.999991i	$0.498655\pi$
$744$		0			0
$745$	21.8662			0.801114
$746$	2.16070	+	0.578959i	0.0791090	+	0.0211972i
$747$		0			0
$748$	0.229489	+	0.856466i	0.00839097	+	0.0313155i
$749$	3.31423	−	35.4361i	0.121099	−	1.29481i
$750$		0			0
$751$		−	14.8260i		−	0.541008i	−0.962719	−	0.270504i	$-0.912810\pi$
$751$		−	14.8260i		−	0.541008i	0.962719	−	0.270504i	$-0.0871904\pi$
$752$	7.01111	+	26.1658i	0.255669	+	0.954169i
$753$		0			0
$754$	8.68043	−	11.6787i	0.316123	−	0.425314i
$755$		−	6.21648i		−	0.226241i
$756$		0			0
$757$	16.7856	+	29.0735i	0.610082	+	1.05669i	0.991226	+	0.132177i	$0.0421968\pi$
$757$	16.7856	+	29.0735i	0.610082	+	1.05669i	−0.381144	+	0.924516i	$0.624470\pi$
$758$	−28.0930	+	16.2195i	−1.02038	+	0.589119i
$759$		0			0
$760$	5.72981	−	5.72981i	0.207842	−	0.207842i
$761$	−0.530277	−	0.142087i	−0.0192225	−	0.00515066i	0.249195	−	0.968453i	$-0.419834\pi$
$761$	−0.530277	−	0.142087i	−0.0192225	−	0.00515066i	−0.268418	+	0.963303i	$0.586501\pi$
$762$		0			0
$763$	−8.01215	+	21.6096i	−0.290059	+	0.782321i
$764$	22.6269	−	13.0637i	0.818614	−	0.472627i
$765$		0			0
$766$	10.6983	+	18.5301i	0.386547	+	0.669519i
$767$	−21.8234	−	50.4849i	−0.787999	−	1.82290i
$768$		0			0
$769$	−5.27369	+	19.6817i	−0.190174	+	0.709739i	0.803289	+	0.595589i	$0.203081\pi$
$769$	−5.27369	+	19.6817i	−0.190174	+	0.709739i	−0.993463	+	0.114150i	$0.963585\pi$
$770$	2.57980	+	0.956507i	0.0929696	+	0.0344701i
$771$		0			0
$772$	−10.0710	−	37.5855i	−0.362464	−	1.35273i
$773$	19.7884	+	19.7884i	0.711740	+	0.711740i	0.966899	−	0.255159i	$-0.0821279\pi$
$773$	19.7884	+	19.7884i	0.711740	+	0.711740i	−0.255159	+	0.966899i	$0.582128\pi$
$774$		0			0
$775$	−2.31273	−	8.63123i	−0.0830757	−	0.310043i
$776$	−14.3552	−	8.28797i	−0.515321	−	0.297521i
$777$		0			0
$778$	9.92313	−	37.0336i	0.355761	−	1.32772i
$779$	8.94688	+	5.16548i	0.320555	+	0.185073i
$780$		0			0
$781$	1.63772	+	2.83661i	0.0586021	+	0.101502i
$782$	−4.91825	−	4.91825i	−0.175876	−	0.175876i
$783$		0			0
$784$	−17.0133	−	3.21047i	−0.607616	−	0.114660i
$785$	−4.29094	+	4.29094i	−0.153150	+	0.153150i
$786$		0			0
$787$	−21.6945	+	21.6945i	−0.773326	+	0.773326i	−0.978686	−	0.205361i	$-0.934163\pi$
$787$	−21.6945	+	21.6945i	−0.773326	+	0.773326i	0.205361	+	0.978686i	$0.434163\pi$
$788$	6.06560	−	22.6371i	0.216078	−	0.806415i
$789$		0			0
$790$	2.65628	+	4.60081i	0.0945063	+	0.163690i
$791$	−7.33981	−	5.20518i	−0.260974	−	0.185075i
$792$		0			0
$793$	−3.39110	−	23.0265i	−0.120422	−	0.817694i
$794$	−16.2587	+	9.38695i	−0.576999	+	0.333131i
$795$		0			0
$796$			14.8572i			0.526599i
$797$	−11.4398	+	19.8143i	−0.405219	+	0.701860i	−0.994347	−	0.106180i	$-0.966138\pi$
$797$	−11.4398	+	19.8143i	−0.405219	+	0.701860i	0.589128	+	0.808040i	$0.299471\pi$
$798$		0			0
$799$	2.78430	+	10.3912i	0.0985016	+	0.367613i
$800$	6.19896	−	23.1348i	0.219166	−	0.817940i
$801$		0			0
$802$	−36.1170			−1.27533
$803$	−3.71898			−0.131240
$804$		0			0
$805$	−12.0052	+	2.04279i	−0.423129	+	0.0719988i
$806$	22.3085	−	3.28537i	0.785784	−	0.115722i
$807$		0			0
$808$	−1.35826	+	0.363946i	−0.0477835	+	0.0128036i
$809$	−22.0767	+	38.2379i	−0.776175	+	1.34437i	0.157957	+	0.987446i	$0.449509\pi$
$809$	−22.0767	+	38.2379i	−0.776175	+	1.34437i	−0.934132	+	0.356928i	$0.883824\pi$
$810$		0			0
$811$	−32.3569	−	32.3569i	−1.13620	−	1.13620i	−0.989125	−	0.147078i	$-0.953013\pi$
$811$	−32.3569	−	32.3569i	−1.13620	−	1.13620i	−0.147078	−	0.989125i	$-0.546987\pi$
$812$	5.38451	+	11.7300i	0.188959	+	0.411643i
$813$		0			0
$814$	5.91208	−	1.58414i	0.207218	−	0.0555240i
$815$			21.7082i			0.760406i
$816$		0			0
$817$	−24.3411	+	24.3411i	−0.851588	+	0.851588i
$818$	62.8983			2.19919
$819$		0			0
$820$	8.08534			0.282352
$821$	−30.5876	+	30.5876i	−1.06752	+	1.06752i	−0.0699661	+	0.997549i	$0.522289\pi$
$821$	−30.5876	+	30.5876i	−1.06752	+	1.06752i	−0.997549	+	0.0699661i	$0.977711\pi$
$822$		0			0
$823$			25.3047i			0.882067i	0.897491	+	0.441033i	$0.145388\pi$
$823$			25.3047i			0.882067i	−0.897491	+	0.441033i	$0.854612\pi$
$824$	8.73272	−	2.33993i	0.304219	−	0.0815152i
$825$		0			0
$826$	86.0860	+	8.05134i	2.99531	+	0.280142i
$827$	0.367751	+	0.367751i	0.0127880	+	0.0127880i	0.713472	−	0.700684i	$-0.247122\pi$
$827$	0.367751	+	0.367751i	0.0127880	+	0.0127880i	−0.700684	+	0.713472i	$0.747122\pi$
$828$		0			0
$829$	−7.50113	+	12.9923i	−0.260525	+	0.451243i	−0.966382	−	0.257112i	$-0.917229\pi$
$829$	−7.50113	+	12.9923i	−0.260525	+	0.451243i	0.705856	+	0.708355i	$0.250562\pi$
$830$	33.9457	−	9.09573i	1.17827	−	0.315718i
$831$		0			0
$832$	39.6064	+	15.6991i	1.37310	+	0.544268i
$833$	−6.75643	−	1.27497i	−0.234096	−	0.0441750i
$834$		0			0
$835$	18.2024			0.629919
$836$	4.15921			0.143849
$837$		0			0
$838$	1.24305	−	4.63912i	0.0429404	−	0.160256i
$839$	−2.91549	−	10.8808i	−0.100654	−	0.375646i	0.897162	−	0.441702i	$-0.145625\pi$
$839$	−2.91549	−	10.8808i	−0.100654	−	0.375646i	−0.997816	+	0.0660560i	$0.978958\pi$
$840$		0			0
$841$	12.7255	−	22.0413i	0.438812	−	0.760044i
$842$			16.1758i			0.557454i
$843$		0			0
$844$	−5.47332	+	3.16002i	−0.188399	+	0.108772i
$845$	−15.9472	−	8.56677i	−0.548599	−	0.294706i
$846$		0			0
$847$	−12.0073	−	26.1575i	−0.412574	−	0.898782i
$848$	−9.33211	−	16.1637i	−0.320466	−	0.555063i
$849$		0			0
$850$	1.66707	−	6.22157i	0.0571799	−	0.213398i
$851$	−19.1555	+	19.1555i	−0.656643	+	0.656643i
$852$		0			0
$853$	−11.2202	+	11.2202i	−0.384171	+	0.384171i	−0.872602	−	0.488431i	$-0.837569\pi$
$853$	−11.2202	+	11.2202i	−0.384171	+	0.384171i	0.488431	+	0.872602i	$0.337569\pi$
$854$	34.3067	+	12.7198i	1.17395	+	0.435263i
$855$		0			0
$856$	−12.0136	−	12.0136i	−0.410615	−	0.410615i
$857$	−22.2843	−	38.5976i	−0.761219	−	1.31847i	−0.942223	−	0.334987i	$-0.891268\pi$
$857$	−22.2843	−	38.5976i	−0.761219	−	1.31847i	0.181004	−	0.983482i	$-0.442065\pi$
$858$		0			0
$859$	16.5887	+	9.57747i	0.565998	+	0.326779i	0.755549	−	0.655092i	$-0.227370\pi$
$859$	16.5887	+	9.57747i	0.565998	+	0.326779i	−0.189552	+	0.981871i	$0.560703\pi$
$860$	−6.97283	+	26.0230i	−0.237772	+	0.887376i
$861$		0			0
$862$	−16.1035	−	9.29737i	−0.548488	−	0.316670i
$863$	4.99275	+	18.6332i	0.169955	+	0.634282i	0.997356	+	0.0726698i	$0.0231519\pi$
$863$	4.99275	+	18.6332i	0.169955	+	0.634282i	−0.827401	+	0.561612i	$0.810181\pi$
$864$		0			0
$865$	4.38653	+	4.38653i	0.149147	+	0.149147i
$866$	14.1655	+	52.8662i	0.481362	+	1.79647i
$867$		0			0
$868$	−6.95309	+	18.7532i	−0.236003	+	0.636526i
$869$	−0.160674	+	0.599645i	−0.00545051	+	0.0203416i
$870$		0			0
$871$	−36.1466	−	4.19655i	−1.22478	−	0.142195i
$872$	5.50094	+	9.52790i	0.186285	+	0.322656i
$873$		0			0
$874$	−28.2553	+	16.3132i	−0.955750	+	0.551803i
$875$	−18.9531	−	22.8641i	−0.640730	−	0.772947i
$876$		0			0
$877$	−9.50026	−	2.54559i	−0.320801	−	0.0859584i	0.0948250	−	0.995494i	$-0.469771\pi$
$877$	−9.50026	−	2.54559i	−0.320801	−	0.0859584i	−0.415626	+	0.909536i	$0.636438\pi$
$878$	52.2067	−	52.2067i	1.76189	−	1.76189i
$879$		0			0
$880$	−1.03978	+	0.600316i	−0.0350509	+	0.0202366i
$881$	−23.9382	−	41.4622i	−0.806500	−	1.39690i	−0.915274	−	0.402832i	$-0.868026\pi$
$881$	−23.9382	−	41.4622i	−0.806500	−	1.39690i	0.108774	−	0.994066i	$-0.465307\pi$
$882$		0			0
$883$		−	12.8094i		−	0.431069i	−0.976496	−	0.215535i	$-0.930851\pi$
$883$		−	12.8094i		−	0.431069i	0.976496	−	0.215535i	$-0.0691495\pi$
$884$	8.52557	+	3.37935i	0.286746	+	0.113660i
$885$		0			0
$886$	−19.7900	−	73.8572i	−0.664857	−	2.48128i
$887$		−	36.6972i		−	1.23217i	−0.787679	−	0.616086i	$-0.788717\pi$
$887$		−	36.6972i		−	1.23217i	0.787679	−	0.616086i	$-0.211283\pi$
$888$		0			0
$889$	5.35404	+	11.6637i	0.179569	+	0.391186i
$890$	10.4985	+	39.1808i	0.351909	+	1.31334i
$891$		0			0
$892$	10.9651	+	2.93808i	0.367138	+	0.0983743i
$893$	50.4620			1.68865
$894$		0			0
$895$	16.2004	+	4.34090i	0.541521	+	0.145100i
$896$	−19.6866	+	16.3191i	−0.657683	+	0.545183i
$897$		0			0
$898$	6.38466	−	11.0586i	0.213059	−	0.369029i
$899$	−5.31209	+	1.42337i	−0.177168	+	0.0474720i
$900$		0			0
$901$	−3.70604	−	6.41904i	−0.123466	−	0.213849i
$902$	1.18407	+	1.18407i	0.0394251	+	0.0394251i
$903$		0			0
$904$	−4.14903	+	1.11173i	−0.137995	+	0.0369756i
$905$	31.5545	−	8.45500i	1.04891	−	0.281054i
$906$		0			0
$907$	−24.7443	−	14.2861i	−0.821622	−	0.474364i	0.0293537	−	0.999569i	$-0.490655\pi$
$907$	−24.7443	−	14.2861i	−0.821622	−	0.474364i	−0.850975	+	0.525206i	$0.823988\pi$
$908$	−34.0162	+	34.0162i	−1.12887	+	1.12887i
$909$		0			0
$910$	23.8573	−	15.5136i	0.790863	−	0.514271i
$911$	−12.2854			−0.407034			−0.203517	−	0.979071i	$-0.565237\pi$
$911$	−12.2854			−0.407034			−0.203517	+	0.979071i	$0.565237\pi$
$912$		0			0
$913$	3.55647	+	2.05333i	0.117702	+	0.0679552i
$914$			58.5440i			1.93646i
$915$		0			0
$916$	23.3985	−	6.26961i	0.773108	−	0.207154i
$917$	−3.51376	+	4.95475i	−0.116035	+	0.163620i
$918$		0			0
$919$	0.388793	+	0.673409i	0.0128251	+	0.0222137i	0.872367	−	0.488852i	$-0.162584\pi$
$919$	0.388793	+	0.673409i	0.0128251	+	0.0222137i	−0.859542	+	0.511066i	$0.829251\pi$
$920$	−2.90662	+	5.03441i	−0.0958284	+	0.165980i
$921$		0			0
$922$	−28.2194	+	48.8774i	−0.929357	+	1.60969i
$923$	33.6516	+	3.90689i	1.10766	+	0.128597i
$924$		0			0
$925$	−24.2317	−	6.49286i	−0.796733	−	0.213484i
$926$	−61.1281			−2.00879
$927$		0			0
$928$	−14.2383	−	3.81515i	−0.467396	−	0.125238i
$929$	−3.47052	+	12.9521i	−0.113864	+	0.424946i	−0.999199	−	0.0400068i	$-0.987262\pi$
$929$	−3.47052	+	12.9521i	−0.113864	+	0.424946i	0.885335	+	0.464953i	$0.153929\pi$
$930$		0			0
$931$	−13.9795	+	29.0650i	−0.458159	+	0.952568i
$932$	24.9748	−	43.2576i	0.818076	−	1.41695i
$933$		0			0
$934$	−12.3866	−	46.2276i	−0.405303	−	1.51261i
$935$	−0.412924	+	0.238402i	−0.0135041	+	0.00779657i
$936$		0			0
$937$		−	1.11894i		−	0.0365542i	−0.999833	−	0.0182771i	$-0.994182\pi$
$937$		−	1.11894i		−	0.0365542i	0.999833	−	0.0182771i	$-0.00581811\pi$
$938$	33.0917	−	46.6625i	1.08048	−	1.52359i
$939$		0			0
$940$	34.2021	−	19.7466i	1.11555	−	0.644062i
$941$	2.54413	−	9.49482i	0.0829363	−	0.309522i	−0.911979	−	0.410237i	$-0.865446\pi$
$941$	2.54413	−	9.49482i	0.0829363	−	0.309522i	0.994915	+	0.100714i	$0.0321128\pi$
$942$		0			0
$943$	−7.15892	−	1.91823i	−0.233126	−	0.0624661i
$944$	−26.6785	+	26.6785i	−0.868313	+	0.868313i
$945$		0			0
$946$	−4.83211	+	2.78982i	−0.157105	+	0.0907048i
$947$	−25.3868	−	25.3868i	−0.824959	−	0.824959i	0.161855	−	0.986815i	$-0.448252\pi$
$947$	−25.3868	−	25.3868i	−0.824959	−	0.824959i	−0.986815	+	0.161855i	$0.948252\pi$
$948$		0			0
$949$	−22.9459	+	30.8717i	−0.744857	+	1.00214i
$950$	−26.1656	−	15.1067i	−0.848925	−	0.490127i
$951$		0			0
$952$	−2.52690	+	2.09466i	−0.0818973	+	0.0678883i
$953$	1.55852	+	0.899814i	0.0504855	+	0.0291478i	0.525030	−	0.851084i	$-0.324054\pi$
$953$	1.55852	+	0.899814i	0.0504855	+	0.0291478i	−0.474545	+	0.880231i	$0.657387\pi$
$954$		0			0
$955$	9.93466	+	9.93466i	0.321478	+	0.321478i
$956$	−0.498863	−	0.498863i	−0.0161344	−	0.0161344i
$957$		0			0
$958$	−28.5618	−	16.4901i	−0.922789	−	0.532772i
$959$	−38.3818	+	31.8164i	−1.23941	+	1.02740i
$960$		0			0
$961$	19.4664	+	11.2389i	0.627949	+	0.362546i
$962$	23.3272	−	58.8509i	0.752099	−	1.89743i
$963$		0			0
$964$	−37.0709	−	37.0709i	−1.19397	−	1.19397i
$965$	18.1209	−	10.4621i	0.583333	−	0.336788i
$966$		0			0
$967$	−40.2608	+	40.2608i	−1.29470	+	1.29470i	−0.362857	+	0.931845i	$0.618198\pi$
$967$	−40.2608	+	40.2608i	−1.29470	+	1.29470i	−0.931845	+	0.362857i	$0.881802\pi$
$968$	−13.2712	−	3.55601i	−0.426553	−	0.114295i
$969$		0			0
$970$	10.1334	−	37.8184i	0.325364	−	1.21428i
$971$	−25.7522	+	14.8680i	−0.826427	+	0.477138i	−0.852628	−	0.522519i	$-0.824992\pi$
$971$	−25.7522	+	14.8680i	−0.826427	+	0.477138i	0.0262007	+	0.999657i	$0.491659\pi$
$972$		0			0
$973$	23.1510	−	32.6452i	0.742187	−	1.04656i
$974$		−	38.8083i		−	1.24350i
$975$		0			0
$976$	−13.8272	+	7.98311i	−0.442596	+	0.255533i
$977$	11.7430	+	43.8253i	0.375690	+	1.40210i	0.852333	+	0.522999i	$0.175187\pi$
$977$	11.7430	+	43.8253i	0.375690	+	1.40210i	−0.476643	+	0.879097i	$0.658147\pi$
$978$		0			0
$979$	−2.36999	+	4.10494i	−0.0757451	+	0.131194i
$980$	1.89860	+	25.1701i	0.0606487	+	0.804028i
$981$		0			0
$982$	11.1064	−	41.4496i	0.354419	−	1.32271i
$983$	−44.7741	−	11.9972i	−1.42807	−	0.382651i	−0.539732	−	0.841837i	$-0.681474\pi$
$983$	−44.7741	−	11.9972i	−1.42807	−	0.382651i	−0.888340	+	0.459187i	$0.848141\pi$
$984$		0			0
$985$	12.6023			0.401543
$986$	−3.82907	−	1.02600i	−0.121942	−	0.0326744i
$987$		0			0
$988$	25.6621	−	34.5260i	0.816422	−	1.09842i
$989$	12.3478	−	21.3870i	0.392636	−	0.680066i
$990$		0			0
$991$	17.4610	−	30.2434i	0.554668	−	0.960713i	−0.443262	−	0.896392i	$-0.646179\pi$
$991$	17.4610	−	30.2434i	0.554668	−	0.960713i	0.997929	−	0.0643204i	$-0.0204880\pi$
$992$	−11.4212	−	19.7821i	−0.362623	−	0.628082i
$993$		0			0
$994$	−30.8076	+	43.4417i	−0.977158	+	1.37789i
$995$	−7.71709	+	2.06779i	−0.244648	+	0.0655533i
$996$		0			0
$997$		−	39.9473i		−	1.26514i	−0.774502	−	0.632572i	$-0.781999\pi$
$997$		−	39.9473i		−	1.26514i	0.774502	−	0.632572i	$-0.218001\pi$
$998$	−14.6125	−	8.43652i	−0.462550	−	0.267054i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.b.145.1		28
3.2	odd	2		91.2.ba.a.54.7	yes	28
7.3	odd	6		819.2.gh.b.262.1		28
13.7	odd	12		819.2.gh.b.397.1		28
21.2	odd	6		637.2.bd.b.587.1		28
21.5	even	6		637.2.bd.a.587.1		28
21.11	odd	6		637.2.x.a.80.7		28
21.17	even	6		91.2.w.a.80.7	yes	28
21.20	even	2		637.2.bb.a.509.7		28
39.20	even	12		91.2.w.a.33.7	✓	28
91.59	even	12	inner	819.2.et.b.514.1		28
273.20	odd	12		637.2.x.a.215.7		28
273.59	odd	12		91.2.ba.a.59.7	yes	28
273.137	even	12		637.2.bb.a.423.7		28
273.215	odd	12		637.2.bd.b.293.1		28
273.254	even	12		637.2.bd.a.293.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.7	✓	28	39.20	even	12
91.2.w.a.80.7	yes	28	21.17	even	6
91.2.ba.a.54.7	yes	28	3.2	odd	2
91.2.ba.a.59.7	yes	28	273.59	odd	12
637.2.x.a.80.7		28	21.11	odd	6
637.2.x.a.215.7		28	273.20	odd	12
637.2.bb.a.423.7		28	273.137	even	12
637.2.bb.a.509.7		28	21.20	even	2
637.2.bd.a.293.1		28	273.254	even	12
637.2.bd.a.587.1		28	21.5	even	6
637.2.bd.b.293.1		28	273.215	odd	12
637.2.bd.b.587.1		28	21.2	odd	6
819.2.et.b.145.1		28	1.1	even	1	trivial
819.2.et.b.514.1		28	91.59	even	12	inner
819.2.gh.b.262.1		28	7.3	odd	6
819.2.gh.b.397.1		28	13.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51485 + 1.51485i) q^{2} -2.58954i q^{4} +(1.34505 - 0.360406i) q^{5} +(-0.246373 + 2.63426i) q^{7} +(0.893066 + 0.893066i) q^{8} +O(q^{10})\)	\(q+(-1.51485 + 1.51485i) q^{2} -2.58954i q^{4} +(1.34505 - 0.360406i) q^{5} +(-0.246373 + 2.63426i) q^{7} +(0.893066 + 0.893066i) q^{8} +(-1.49159 + 2.58351i) q^{10} +(-0.336721 + 0.0902242i) q^{11} +(-1.32860 + 3.35184i) q^{13} +(-3.61728 - 4.36372i) q^{14} +2.47336 q^{16} +0.982239 q^{17} +(1.19250 - 4.45046i) q^{19} +(-0.933286 - 3.48307i) q^{20} +(0.373406 - 0.646758i) q^{22} +3.30540i q^{23} +(-2.65085 + 1.53047i) q^{25} +(-3.06491 - 7.09016i) q^{26} +(6.82151 + 0.637994i) q^{28} +(0.941928 + 1.63147i) q^{29} +(-0.755562 + 2.81980i) q^{31} +(-5.53290 + 5.53290i) q^{32} +(-1.48794 + 1.48794i) q^{34} +(0.618016 + 3.63201i) q^{35} +(5.79522 + 5.79522i) q^{37} +(4.93532 + 8.54823i) q^{38} +(1.52309 + 0.879355i) q^{40} +(-0.580331 + 2.16583i) q^{41} +(-6.47031 - 3.73564i) q^{43} +(0.233639 + 0.871953i) q^{44} +(-5.00718 - 5.00718i) q^{46} +(2.83465 + 10.5791i) q^{47} +(-6.87860 - 1.29802i) q^{49} +(1.69721 - 6.33408i) q^{50} +(8.67973 + 3.44045i) q^{52} +(-3.77305 - 6.53511i) q^{53} +(-0.420391 + 0.242713i) q^{55} +(-2.57259 + 2.13254i) q^{56} +(-3.89831 - 1.04455i) q^{58} +(-10.7864 + 10.7864i) q^{59} +(-5.59044 + 3.22764i) q^{61} +(-3.12700 - 5.41613i) q^{62} -11.8163i q^{64} +(-0.579009 + 4.98724i) q^{65} +(2.61216 + 9.74870i) q^{67} -2.54355i q^{68} +(-6.43815 - 4.56574i) q^{70} +(-2.43186 - 9.07582i) q^{71} +(10.3048 + 2.76117i) q^{73} -17.5578 q^{74} +(-11.5246 - 3.08802i) q^{76} +(-0.154714 - 0.909238i) q^{77} +(0.890418 - 1.54225i) q^{79} +(3.32680 - 0.891413i) q^{80} +(-2.40179 - 4.16002i) q^{82} +(-8.33002 - 8.33002i) q^{83} +(1.32116 - 0.354005i) q^{85} +(15.4605 - 4.14262i) q^{86} +(-0.381291 - 0.220138i) q^{88} +(9.61466 - 9.61466i) q^{89} +(-8.50227 - 4.32566i) q^{91} +8.55946 q^{92} +(-20.3198 - 11.7316i) q^{94} -6.41589i q^{95} +(-12.6772 + 3.39684i) q^{97} +(12.3864 - 8.45374i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

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