LMFDB - Embedded newform 342.2.u.d.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(55,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("342.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.u (of order $9$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	342.289
Dual form			342.2.u.d.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(2.97178 - 2.49362i) q^{5} +(-0.613341 + 1.06234i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(2.97178 - 2.49362i) q^{5} +(-0.613341 + 1.06234i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.64543 - 1.32683i) q^{10} +(-1.06031 - 1.83651i) q^{11} +(0.0851223 - 0.482753i) q^{13} +(-0.939693 + 0.788496i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-5.19846 - 1.89209i) q^{17} +(2.77719 + 3.35965i) q^{19} +3.87939 q^{20} +(-0.368241 - 2.08840i) q^{22} +(6.85117 + 5.74881i) q^{23} +(1.74510 - 9.89695i) q^{25} +(0.245100 - 0.424525i) q^{26} +(-1.15270 + 0.419550i) q^{28} +(-7.96451 + 2.89884i) q^{29} +(-1.20574 + 2.08840i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-4.23783 - 3.55596i) q^{34} +(0.826352 + 4.68647i) q^{35} +1.69459 q^{37} +(1.46064 + 4.10689i) q^{38} +(3.64543 + 1.32683i) q^{40} +(-0.277189 - 1.57202i) q^{41} +(-5.08512 + 4.26692i) q^{43} +(0.368241 - 2.08840i) q^{44} +(4.47178 + 7.74535i) q^{46} +(2.03936 - 0.742267i) q^{47} +(2.74763 + 4.75903i) q^{49} +(5.02481 - 8.70323i) q^{50} +(0.375515 - 0.315094i) q^{52} +(-6.80793 - 5.71253i) q^{53} +(-7.73055 - 2.81369i) q^{55} -1.22668 q^{56} -8.47565 q^{58} +(-10.7306 - 3.90560i) q^{59} +(0.0320889 + 0.0269258i) q^{61} +(-1.84730 + 1.55007i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.950837 - 1.64690i) q^{65} +(-4.20574 + 1.53076i) q^{67} +(-2.76604 - 4.79093i) q^{68} +(-0.826352 + 4.68647i) q^{70} +(-2.02094 + 1.69577i) q^{71} +(-2.66772 - 15.1294i) q^{73} +(1.59240 + 0.579585i) q^{74} +(-0.0320889 + 4.35878i) q^{76} +2.60132 q^{77} +(-0.809278 - 4.58964i) q^{79} +(2.97178 + 2.49362i) q^{80} +(0.277189 - 1.57202i) q^{82} +(6.24035 - 10.8086i) q^{83} +(-20.1668 + 7.34013i) q^{85} +(-6.23783 + 2.27038i) q^{86} +(1.06031 - 1.83651i) q^{88} +(-1.46838 + 8.32759i) q^{89} +(0.460637 + 0.386520i) q^{91} +(1.55303 + 8.80769i) q^{92} +2.17024 q^{94} +(16.6309 + 3.05888i) q^{95} +(13.5103 + 4.91734i) q^{97} +(0.954241 + 5.41177i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8	$ 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8} + 6 q^{10} - 12 q^{11} - 21 q^{13} - 3 q^{17} + 6 q^{19} + 12 q^{20} + 3 q^{22} + 15 q^{23} + 9 q^{25} - 9 q^{28} - 15 q^{29} + 3 q^{31} - 6 q^{34} + 6 q^{35} + 6 q^{37} + 6 q^{40} + 9 q^{41} - 9 q^{43} - 3 q^{44} + 12 q^{46} + 21 q^{47} + 3 q^{50} + 15 q^{52} - 30 q^{53} - 9 q^{55} + 6 q^{56} - 12 q^{58} - 27 q^{59} - 9 q^{61} - 9 q^{62} - 3 q^{64} + 6 q^{65} - 15 q^{67} - 12 q^{68} - 6 q^{70} - 9 q^{71} + 12 q^{73} + 6 q^{74} + 9 q^{76} - 42 q^{77} + 15 q^{79} + 3 q^{80} - 9 q^{82} + 3 q^{83} - 36 q^{85} - 18 q^{86} + 12 q^{88} + 48 q^{89} - 6 q^{91} - 3 q^{92} - 30 q^{94} + 48 q^{95} + 18 q^{97} + 36 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8 + 6 * q^10 - 12 * q^11 - 21 * q^13 - 3 * q^17 + 6 * q^19 + 12 * q^20 + 3 * q^22 + 15 * q^23 + 9 * q^25 - 9 * q^28 - 15 * q^29 + 3 * q^31 - 6 * q^34 + 6 * q^35 + 6 * q^37 + 6 * q^40 + 9 * q^41 - 9 * q^43 - 3 * q^44 + 12 * q^46 + 21 * q^47 + 3 * q^50 + 15 * q^52 - 30 * q^53 - 9 * q^55 + 6 * q^56 - 12 * q^58 - 27 * q^59 - 9 * q^61 - 9 * q^62 - 3 * q^64 + 6 * q^65 - 15 * q^67 - 12 * q^68 - 6 * q^70 - 9 * q^71 + 12 * q^73 + 6 * q^74 + 9 * q^76 - 42 * q^77 + 15 * q^79 + 3 * q^80 - 9 * q^82 + 3 * q^83 - 36 * q^85 - 18 * q^86 + 12 * q^88 + 48 * q^89 - 6 * q^91 - 3 * q^92 - 30 * q^94 + 48 * q^95 + 18 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	2.97178	−	2.49362i	1.32902	−	1.11518i	0.344716	−	0.938707i	$-0.387975\pi$
$5$	2.97178	−	2.49362i	1.32902	−	1.11518i	0.984305	−	0.176474i	$-0.0564692\pi$
$6$		0			0
$7$	−0.613341	+	1.06234i	−0.231821	+	0.401526i	−0.958344	−	0.285616i	$-0.907802\pi$
$7$	−0.613341	+	1.06234i	−0.231821	+	0.401526i	0.726523	+	0.687142i	$0.241135\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	3.64543	−	1.32683i	1.15279	−	0.419580i
$11$	−1.06031	−	1.83651i	−0.319695	−	0.553727i	0.660730	−	0.750624i	$-0.270247\pi$
$11$	−1.06031	−	1.83651i	−0.319695	−	0.553727i	−0.980424	+	0.196897i	$0.936914\pi$
$12$		0			0
$13$	0.0851223	−	0.482753i	0.0236087	−	0.133891i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	0.0851223	−	0.482753i	0.0236087	−	0.133891i	0.994334	+	0.106301i	$0.0339006\pi$
$14$	−0.939693	+	0.788496i	−0.251143	+	0.210734i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−5.19846	−	1.89209i	−1.26081	−	0.458898i	−0.376771	−	0.926306i	$-0.622966\pi$
$17$	−5.19846	−	1.89209i	−1.26081	−	0.458898i	−0.884042	+	0.467408i	$0.845188\pi$
$18$		0			0
$19$	2.77719	+	3.35965i	0.637131	+	0.770756i
$19$	2.77719	+	3.35965i	0.637131	+	0.770756i
$20$	3.87939			0.867457
$21$		0			0
$22$	−0.368241	−	2.08840i	−0.0785092	−	0.445248i
$23$	6.85117	+	5.74881i	1.42857	+	1.19871i	0.946554	+	0.322546i	$0.104539\pi$
$23$	6.85117	+	5.74881i	1.42857	+	1.19871i	0.482013	+	0.876164i	$0.339906\pi$
$24$		0			0
$25$	1.74510	−	9.89695i	0.349020	−	1.97939i
$26$	0.245100	−	0.424525i	0.0480680	−	0.0832563i
$27$		0			0
$28$	−1.15270	+	0.419550i	−0.217841	+	0.0792875i
$29$	−7.96451	+	2.89884i	−1.47897	+	0.538302i	−0.950521	−	0.310662i	$-0.899449\pi$
$29$	−7.96451	+	2.89884i	−1.47897	+	0.538302i	−0.528451	+	0.848964i	$0.677227\pi$
$30$		0			0
$31$	−1.20574	+	2.08840i	−0.216557	+	0.375087i	−0.953753	−	0.300591i	$-0.902816\pi$
$31$	−1.20574	+	2.08840i	−0.216557	+	0.375087i	0.737196	+	0.675679i	$0.236149\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$		0			0
$34$	−4.23783	−	3.55596i	−0.726781	−	0.609842i
$35$	0.826352	+	4.68647i	0.139679	+	0.792159i
$36$		0			0
$37$	1.69459			0.278589			0.139295	−	0.990251i	$-0.455516\pi$
$37$	1.69459			0.278589			0.139295	+	0.990251i	$0.455516\pi$
$38$	1.46064	+	4.10689i	0.236947	+	0.666225i
$39$		0			0
$40$	3.64543	+	1.32683i	0.576393	+	0.209790i
$41$	−0.277189	−	1.57202i	−0.0432896	−	0.245508i	0.955483	−	0.295048i	$-0.0953355\pi$
$41$	−0.277189	−	1.57202i	−0.0432896	−	0.245508i	−0.998772	+	0.0495401i	$0.984224\pi$
$42$		0			0
$43$	−5.08512	+	4.26692i	−0.775474	+	0.650700i	−0.942104	−	0.335320i	$-0.891156\pi$
$43$	−5.08512	+	4.26692i	−0.775474	+	0.650700i	0.166631	+	0.986019i	$0.446711\pi$
$44$	0.368241	−	2.08840i	0.0555144	−	0.314838i
$45$		0			0
$46$	4.47178	+	7.74535i	0.659328	+	1.14199i
$47$	2.03936	−	0.742267i	0.297472	−	0.108271i	−0.188973	−	0.981982i	$-0.560516\pi$
$47$	2.03936	−	0.742267i	0.297472	−	0.108271i	0.486444	+	0.873711i	$0.338294\pi$
$48$		0			0
$49$	2.74763	+	4.75903i	0.392518	+	0.679861i
$50$	5.02481	−	8.70323i	0.710616	−	1.23082i
$51$		0			0
$52$	0.375515	−	0.315094i	0.0520745	−	0.0436957i
$53$	−6.80793	−	5.71253i	−0.935142	−	0.784677i	0.0415917	−	0.999135i	$-0.486757\pi$
$53$	−6.80793	−	5.71253i	−0.935142	−	0.784677i	−0.976733	+	0.214458i	$0.931202\pi$
$54$		0			0
$55$	−7.73055	−	2.81369i	−1.04239	−	0.379398i
$56$	−1.22668			−0.163922
$57$		0			0
$58$	−8.47565			−1.11291
$59$	−10.7306	−	3.90560i	−1.39700	−	0.508466i	−0.469713	−	0.882819i	$-0.655643\pi$
$59$	−10.7306	−	3.90560i	−1.39700	−	0.508466i	−0.927286	+	0.374353i	$0.877865\pi$
$60$		0			0
$61$	0.0320889	+	0.0269258i	0.00410856	+	0.00344749i	0.644840	−	0.764318i	$-0.276924\pi$
$61$	0.0320889	+	0.0269258i	0.00410856	+	0.00344749i	−0.640731	+	0.767765i	$0.721369\pi$
$62$	−1.84730	+	1.55007i	−0.234607	+	0.196859i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.950837	−	1.64690i	−0.117937	−	0.204273i
$66$		0			0
$67$	−4.20574	+	1.53076i	−0.513813	+	0.187012i	−0.585896	−	0.810386i	$-0.699257\pi$
$67$	−4.20574	+	1.53076i	−0.513813	+	0.187012i	0.0720836	+	0.997399i	$0.477035\pi$
$68$	−2.76604	−	4.79093i	−0.335432	−	0.580986i
$69$		0			0
$70$	−0.826352	+	4.68647i	−0.0987679	+	0.560141i
$71$	−2.02094	+	1.69577i	−0.239842	+	0.201251i	−0.754783	−	0.655974i	$-0.772258\pi$
$71$	−2.02094	+	1.69577i	−0.239842	+	0.201251i	0.514941	+	0.857225i	$0.327814\pi$
$72$		0			0
$73$	−2.66772	−	15.1294i	−0.312233	−	1.77076i	−0.587334	−	0.809345i	$-0.699822\pi$
$73$	−2.66772	−	15.1294i	−0.312233	−	1.77076i	0.275101	−	0.961415i	$-0.411289\pi$
$74$	1.59240	+	0.579585i	0.185112	+	0.0673754i
$75$		0			0
$76$	−0.0320889	+	4.35878i	−0.00368085	+	0.499986i
$77$	2.60132			0.296448
$78$		0			0
$79$	−0.809278	−	4.58964i	−0.0910509	−	0.516375i	−0.995886	−	0.0906133i	$-0.971117\pi$
$79$	−0.809278	−	4.58964i	−0.0910509	−	0.516375i	0.904835	−	0.425762i	$-0.139994\pi$
$80$	2.97178	+	2.49362i	0.332255	+	0.278795i
$81$		0			0
$82$	0.277189	−	1.57202i	0.0306104	−	0.173600i
$83$	6.24035	−	10.8086i	0.684968	−	1.18640i	−0.288479	−	0.957486i	$-0.593150\pi$
$83$	6.24035	−	10.8086i	0.684968	−	1.18640i	0.973447	−	0.228913i	$-0.0735170\pi$
$84$		0			0
$85$	−20.1668	+	7.34013i	−2.18740	+	0.796149i
$86$	−6.23783	+	2.27038i	−0.672642	+	0.244822i
$87$		0			0
$88$	1.06031	−	1.83651i	0.113029	−	0.195772i
$89$	−1.46838	+	8.32759i	−0.155648	+	0.882722i	0.802543	+	0.596594i	$0.203480\pi$
$89$	−1.46838	+	8.32759i	−0.155648	+	0.882722i	−0.958191	+	0.286129i	$0.907632\pi$
$90$		0			0
$91$	0.460637	+	0.386520i	0.0482879	+	0.0405184i
$92$	1.55303	+	8.80769i	0.161915	+	0.918265i
$93$		0			0
$94$	2.17024			0.223844
$95$	16.6309	+	3.05888i	1.70629	+	0.313834i
$96$		0			0
$97$	13.5103	+	4.91734i	1.37176	+	0.499280i	0.919670	−	0.392693i	$-0.128456\pi$
$97$	13.5103	+	4.91734i	1.37176	+	0.499280i	0.452090	+	0.891972i	$0.350679\pi$
$98$	0.954241	+	5.41177i	0.0963929	+	0.546671i
$99$		0			0
$100$	7.69846	−	6.45978i	0.769846	−	0.645978i
$101$	−0.988856	+	5.60808i	−0.0983948	+	0.558025i	0.895259	+	0.445546i	$0.146990\pi$
$101$	−0.988856	+	5.60808i	−0.0983948	+	0.558025i	−0.993654	+	0.112479i	$0.964121\pi$
$102$		0			0
$103$	0.156574	+	0.271194i	0.0154277	+	0.0267216i	0.873636	−	0.486580i	$-0.161756\pi$
$103$	0.156574	+	0.271194i	0.0154277	+	0.0267216i	−0.858208	+	0.513301i	$0.828422\pi$
$104$	0.460637	−	0.167658i	0.0451692	−	0.0164402i
$105$		0			0
$106$	−4.44356	−	7.69648i	−0.431597	−	0.747548i
$107$	−8.41400	+	14.5735i	−0.813412	+	1.40887i	0.0970504	+	0.995279i	$0.469059\pi$
$107$	−8.41400	+	14.5735i	−0.813412	+	1.40887i	−0.910462	+	0.413592i	$0.864274\pi$
$108$		0			0
$109$	−7.97565	+	6.69237i	−0.763929	+	0.641012i	−0.939146	−	0.343517i	$-0.888382\pi$
$109$	−7.97565	+	6.69237i	−0.763929	+	0.641012i	0.175217	+	0.984530i	$0.443937\pi$
$110$	−6.30200	−	5.28801i	−0.600872	−	0.504192i
$111$		0			0
$112$	−1.15270	−	0.419550i	−0.108920	−	0.0396437i
$113$	17.3824			1.63520			0.817598	−	0.575789i	$-0.195305\pi$
$113$	17.3824			1.63520			0.817598	+	0.575789i	$0.195305\pi$
$114$		0			0
$115$	34.6955			3.23537
$116$	−7.96451	−	2.89884i	−0.739486	−	0.269151i
$117$		0			0
$118$	−8.74763	−	7.34013i	−0.805284	−	0.675714i
$119$	5.19846	−	4.36203i	0.476542	−	0.399866i
$120$		0			0
$121$	3.25150	−	5.63176i	0.295591	−	0.511978i
$122$	0.0209445	+	0.0362770i	0.00189623	+	0.00328436i
$123$		0			0
$124$	−2.26604	+	0.824773i	−0.203497	+	0.0740668i
$125$	−9.79473	−	16.9650i	−0.876067	−	1.51739i
$126$		0			0
$127$	−0.283119	+	1.60565i	−0.0251227	+	0.142478i	−0.994789	−	0.101954i	$-0.967490\pi$
$127$	−0.283119	+	1.60565i	−0.0251227	+	0.142478i	0.969666	+	0.244432i	$0.0786016\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$		0			0
$130$	−0.330222	−	1.87278i	−0.0289624	−	0.164254i
$131$	5.60354	+	2.03952i	0.489584	+	0.178194i	0.575003	−	0.818151i	$-0.305001\pi$
$131$	5.60354	+	2.03952i	0.489584	+	0.178194i	−0.0854195	+	0.996345i	$0.527223\pi$
$132$		0			0
$133$	−5.27244	+	0.889704i	−0.457179	+	0.0771471i
$134$	−4.47565			−0.386637
$135$		0			0
$136$	−0.960637	−	5.44804i	−0.0823740	−	0.467166i
$137$	0.0150147	+	0.0125989i	0.00128280	+	0.00107639i	0.643429	−	0.765506i	$-0.277511\pi$
$137$	0.0150147	+	0.0125989i	0.00128280	+	0.00107639i	−0.642146	+	0.766582i	$0.721956\pi$
$138$		0			0
$139$	0.780592	−	4.42696i	0.0662090	−	0.375490i	−0.933642	−	0.358208i	$-0.883388\pi$
$139$	0.780592	−	4.42696i	0.0662090	−	0.375490i	0.999851	−	0.0172815i	$-0.00550113\pi$
$140$	−2.37939	+	4.12122i	−0.201095	+	0.348306i
$141$		0			0
$142$	−2.47906	+	0.902302i	−0.208038	+	0.0757195i
$143$	−0.976834	+	0.355538i	−0.0816870	+	0.0297316i
$144$		0			0
$145$	−16.4402	+	28.4752i	−1.36528	+	2.36474i
$146$	2.66772	−	15.1294i	0.220782	−	1.25212i
$147$		0			0
$148$	1.29813	+	1.08926i	0.106706	+	0.0895369i
$149$	−2.08899	−	11.8473i	−0.171137	−	0.970566i	−0.942509	−	0.334181i	$-0.891540\pi$
$149$	−2.08899	−	11.8473i	−0.171137	−	0.970566i	0.771372	−	0.636385i	$-0.219571\pi$
$150$		0			0
$151$	0.0591253			0.00481155			0.00240578	−	0.999997i	$-0.499234\pi$
$151$	0.0591253			0.00481155			0.00240578	+	0.999997i	$0.499234\pi$
$152$	−1.52094	+	4.08494i	−0.123365	+	0.331332i
$153$		0			0
$154$	2.44444	+	0.889704i	0.196979	+	0.0716944i
$155$	1.62449	+	9.21291i	0.130482	+	0.739999i
$156$		0			0
$157$	9.92649	−	8.32931i	0.792220	−	0.664752i	−0.154074	−	0.988059i	$-0.549239\pi$
$157$	9.92649	−	8.32931i	0.792220	−	0.664752i	0.946294	+	0.323308i	$0.104795\pi$
$158$	0.809278	−	4.58964i	0.0643827	−	0.365132i
$159$		0			0
$160$	1.93969	+	3.35965i	0.153346	+	0.265603i
$161$	−10.3093	+	3.75227i	−0.812485	+	0.295720i
$162$		0			0
$163$	−7.53596	−	13.0527i	−0.590262	−	1.02236i	−0.994197	−	0.107576i	$-0.965691\pi$
$163$	−7.53596	−	13.0527i	−0.590262	−	1.02236i	0.403935	−	0.914788i	$-0.367642\pi$
$164$	0.798133	−	1.38241i	0.0623237	−	0.107948i
$165$		0			0
$166$	9.56077	−	8.02244i	0.742060	−	0.622662i
$167$	1.48680	+	1.24757i	0.115052	+	0.0965399i	0.698499	−	0.715612i	$-0.253852\pi$
$167$	1.48680	+	1.24757i	0.115052	+	0.0965399i	−0.583447	+	0.812151i	$0.698296\pi$
$168$		0			0
$169$	11.9902	+	4.36408i	0.922323	+	0.335698i
$170$	−21.4611			−1.64599
$171$		0			0
$172$	−6.63816			−0.506155
$173$	15.1027	+	5.49692i	1.14823	+	0.417923i	0.844881	−	0.534955i	$-0.179671\pi$
$173$	15.1027	+	5.49692i	1.14823	+	0.417923i	0.303354	+	0.952878i	$0.401894\pi$
$174$		0			0
$175$	9.44356	+	7.92409i	0.713866	+	0.599005i
$176$	1.62449	−	1.36310i	0.122450	−	0.102748i
$177$		0			0
$178$	−4.22803	+	7.32316i	−0.316904	+	0.548894i
$179$	7.38713	+	12.7949i	0.552140	+	0.956334i	0.998120	+	0.0612912i	$0.0195218\pi$
$179$	7.38713	+	12.7949i	0.552140	+	0.956334i	−0.445980	+	0.895043i	$0.647145\pi$
$180$		0			0
$181$	17.1275	−	6.23389i	1.27308	−	0.463362i	0.384939	−	0.922942i	$-0.374222\pi$
$181$	17.1275	−	6.23389i	1.27308	−	0.463362i	0.888136	+	0.459580i	$0.152000\pi$
$182$	0.300660	+	0.520758i	0.0222864	+	0.0386011i
$183$		0			0
$184$	−1.55303	+	8.80769i	−0.114491	+	0.649312i
$185$	5.03596	−	4.22567i	0.370251	−	0.310678i
$186$		0			0
$187$	2.03714	+	11.5532i	0.148971	+	0.844854i
$188$	2.03936	+	0.742267i	0.148736	+	0.0541354i
$189$		0			0
$190$	14.5817	+	8.56250i	1.05787	+	0.621189i
$191$	−1.29086			−0.0934033			−0.0467017	−	0.998909i	$-0.514871\pi$
$191$	−1.29086			−0.0934033			−0.0467017	+	0.998909i	$0.514871\pi$
$192$		0			0
$193$	−1.58378	−	8.98205i	−0.114003	−	0.646542i	−0.987239	−	0.159245i	$-0.949094\pi$
$193$	−1.58378	−	8.98205i	−0.114003	−	0.646542i	0.873236	−	0.487297i	$-0.162017\pi$
$194$	11.0137	+	9.24157i	0.790735	+	0.663506i
$195$		0			0
$196$	−0.954241	+	5.41177i	−0.0681600	+	0.386555i
$197$	9.31180	−	16.1285i	0.663439	−	1.14911i	−0.316268	−	0.948670i	$-0.602430\pi$
$197$	9.31180	−	16.1285i	0.663439	−	1.14911i	0.979706	−	0.200439i	$-0.0642369\pi$
$198$		0			0
$199$	−7.92262	+	2.88360i	−0.561620	+	0.204413i	−0.607202	−	0.794548i	$-0.707708\pi$
$199$	−7.92262	+	2.88360i	−0.561620	+	0.204413i	0.0455821	+	0.998961i	$0.485486\pi$
$200$	9.44356	−	3.43718i	0.667761	−	0.243045i
$201$		0			0
$202$	−2.84730	+	4.93166i	−0.200335	+	0.346991i
$203$	1.80541	−	10.2390i	0.126715	−	0.718635i
$204$		0			0
$205$	−4.74376	−	3.98048i	−0.331318	−	0.278009i
$206$	0.0543776	+	0.308391i	0.00378867	+	0.0214866i
$207$		0			0
$208$	0.490200			0.0339892
$209$	3.22534	−	8.66258i	0.223101	−	0.599203i
$210$		0			0
$211$	1.37939	+	0.502055i	0.0949608	+	0.0345629i	0.389064	−	0.921211i	$-0.372799\pi$
$211$	1.37939	+	0.502055i	0.0949608	+	0.0345629i	−0.294103	+	0.955774i	$0.595021\pi$
$212$	−1.54323	−	8.75211i	−0.105990	−	0.601097i
$213$		0			0
$214$	−12.8910	+	10.8168i	−0.881210	+	0.739423i
$215$	−4.47178	+	25.3607i	−0.304973	+	1.72959i
$216$		0			0
$217$	−1.47906	−	2.56180i	−0.100405	−	0.173906i
$218$	−9.78359	+	3.56093i	−0.662628	+	0.241177i
$219$		0			0
$220$	−4.11334	−	7.12452i	−0.277321	−	0.480335i
$221$	−1.35591	+	2.34851i	−0.0912087	+	0.157978i
$222$		0			0
$223$	20.1229	−	16.8851i	1.34753	−	1.13071i	0.367906	−	0.929863i	$-0.380075\pi$
$223$	20.1229	−	16.8851i	1.34753	−	1.13071i	0.979622	−	0.200848i	$-0.0643697\pi$
$224$	−0.939693	−	0.788496i	−0.0627859	−	0.0526836i
$225$		0			0
$226$	16.3341	+	5.94512i	1.08653	+	0.395464i
$227$	−18.3678			−1.21912			−0.609558	−	0.792742i	$-0.708653\pi$
$227$	−18.3678			−1.21912			−0.609558	+	0.792742i	$0.708653\pi$
$228$		0			0
$229$	3.87164			0.255845			0.127923	−	0.991784i	$-0.459169\pi$
$229$	3.87164			0.255845			0.127923	+	0.991784i	$0.459169\pi$
$230$	32.6031	+	11.8666i	2.14979	+	0.782458i
$231$		0			0
$232$	−6.49273	−	5.44804i	−0.426268	−	0.357682i
$233$	−12.5988	+	10.5716i	−0.825374	+	0.692571i	−0.954224	−	0.299093i	$-0.903316\pi$
$233$	−12.5988	+	10.5716i	−0.825374	+	0.692571i	0.128850	+	0.991664i	$0.458872\pi$
$234$		0			0
$235$	4.20961	−	7.29125i	0.274605	−	0.475629i
$236$	−5.70961	−	9.88933i	−0.371664	−	0.643741i
$237$		0			0
$238$	6.37686	−	2.32099i	0.413350	−	0.150447i
$239$	1.65270	+	2.86257i	0.106905	+	0.185164i	0.914515	−	0.404553i	$-0.132573\pi$
$239$	1.65270	+	2.86257i	0.106905	+	0.185164i	−0.807610	+	0.589717i	$0.799239\pi$
$240$		0			0
$241$	0.523633	−	2.96967i	0.0337302	−	0.191293i	−0.963287	−	0.268474i	$-0.913481\pi$
$241$	0.523633	−	2.96967i	0.0337302	−	0.191293i	0.997017	+	0.0771806i	$0.0245918\pi$
$242$	4.98158	−	4.18004i	0.320228	−	0.268703i
$243$		0			0
$244$	0.00727396	+	0.0412527i	0.000465668	+	0.00264093i
$245$	20.0326	+	7.29125i	1.27983	+	0.465821i
$246$		0			0
$247$	1.85828	−	1.05471i	0.118239	−	0.0671099i
$248$	−2.41147			−0.153129
$249$		0			0
$250$	−3.40167	−	19.2919i	−0.215141	−	1.22012i
$251$	2.70780	+	2.27211i	0.170915	+	0.143414i	0.724233	−	0.689556i	$-0.242194\pi$
$251$	2.70780	+	2.27211i	0.170915	+	0.143414i	−0.553318	+	0.832970i	$0.686639\pi$
$252$		0			0
$253$	3.29339	−	18.6777i	0.207053	−	1.17426i
$254$	−0.815207	+	1.41198i	−0.0511507	+	0.0885956i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−4.41875	+	1.60829i	−0.275634	+	0.100323i	−0.476139	−	0.879370i	$-0.657964\pi$
$257$	−4.41875	+	1.60829i	−0.275634	+	0.100323i	0.200505	+	0.979693i	$0.435742\pi$
$258$		0			0
$259$	−1.03936	+	1.80023i	−0.0645829	+	0.111861i
$260$	0.330222	−	1.87278i	0.0204795	−	0.116145i
$261$		0			0
$262$	4.56805	+	3.83305i	0.282215	+	0.236806i
$263$	−3.65745	−	20.7424i	−0.225528	−	1.27903i	−0.861673	−	0.507464i	$-0.830583\pi$
$263$	−3.65745	−	20.7424i	−0.225528	−	1.27903i	0.636145	−	0.771570i	$-0.280528\pi$
$264$		0			0
$265$	−34.4766			−2.11788
$266$	−5.25877	−	0.967233i	−0.322436	−	0.0593049i
$267$		0			0
$268$	−4.20574	−	1.53076i	−0.256906	−	0.0935062i
$269$	−1.75015	−	9.92561i	−0.106709	−	0.605175i	−0.990524	−	0.137339i	$-0.956145\pi$
$269$	−1.75015	−	9.92561i	−0.106709	−	0.605175i	0.883815	−	0.467836i	$-0.154966\pi$
$270$		0			0
$271$	−7.47952	+	6.27606i	−0.454349	+	0.381244i	−0.841047	−	0.540963i	$-0.818060\pi$
$271$	−7.47952	+	6.27606i	−0.454349	+	0.381244i	0.386698	+	0.922206i	$0.373616\pi$
$272$	0.960637	−	5.44804i	0.0582472	−	0.330336i
$273$		0			0
$274$	0.00980018	+	0.0169744i	0.000592051	+	0.00102546i
$275$	−20.0262	+	7.28893i	−1.20762	+	0.439539i
$276$		0			0
$277$	−8.42855	−	14.5987i	−0.506422	−	0.877149i	−0.999972	−	0.00743188i	$-0.997634\pi$
$277$	−8.42855	−	14.5987i	−0.506422	−	0.877149i	0.493550	−	0.869717i	$-0.335699\pi$
$278$	2.24763	−	3.89300i	0.134804	−	0.233487i
$279$		0			0
$280$	−3.64543	+	3.05888i	−0.217856	+	0.182803i
$281$	8.98158	+	7.53644i	0.535796	+	0.449586i	0.870097	−	0.492880i	$-0.164056\pi$
$281$	8.98158	+	7.53644i	0.535796	+	0.449586i	−0.334301	+	0.942466i	$0.608500\pi$
$282$		0			0
$283$	20.2456	+	7.36878i	1.20347	+	0.438029i	0.864435	−	0.502744i	$-0.167676\pi$
$283$	20.2456	+	7.36878i	1.20347	+	0.438029i	0.339039	+	0.940772i	$0.389898\pi$
$284$	−2.63816			−0.156546
$285$		0			0
$286$	−1.03952			−0.0614684
$287$	1.84002	+	0.669713i	0.108613	+	0.0395319i
$288$		0			0
$289$	10.4213	+	8.74449i	0.613016	+	0.514382i
$290$	−25.1878	+	21.1351i	−1.47908	+	1.24109i
$291$		0			0
$292$	7.68139	−	13.3046i	0.449519	−	0.778590i
$293$	−5.56031	−	9.63073i	−0.324837	−	0.562634i	0.656643	−	0.754202i	$-0.271976\pi$
$293$	−5.56031	−	9.63073i	−0.324837	−	0.562634i	−0.981479	+	0.191568i	$0.938643\pi$
$294$		0			0
$295$	−41.6279	+	15.1513i	−2.42367	+	0.882145i
$296$	0.847296	+	1.46756i	0.0492481	+	0.0853002i
$297$		0			0
$298$	2.08899	−	11.8473i	0.121012	−	0.686294i
$299$	3.35844	−	2.81807i	0.194224	−	0.162973i
$300$		0			0
$301$	−1.41400	−	8.01919i	−0.0815016	−	0.462219i
$302$	0.0555596	+	0.0202221i	0.00319710	+	0.00116365i
$303$		0			0
$304$	−2.82635	+	3.31839i	−0.162102	+	0.190323i
$305$	0.162504			0.00930494
$306$		0			0
$307$	4.34817	+	24.6597i	0.248163	+	1.40740i	0.813030	+	0.582222i	$0.197817\pi$
$307$	4.34817	+	24.6597i	0.248163	+	1.40740i	−0.564866	+	0.825182i	$0.691072\pi$
$308$	1.99273	+	1.67210i	0.113546	+	0.0952765i
$309$		0			0
$310$	−1.62449	+	9.21291i	−0.0922646	+	0.523258i
$311$	0.0282185	−	0.0488759i	0.00160012	−	0.00277150i	−0.865224	−	0.501385i	$-0.832824\pi$
$311$	0.0282185	−	0.0488759i	0.00160012	−	0.00277150i	0.866824	+	0.498614i	$0.166157\pi$
$312$		0			0
$313$	−12.9338	+	4.70750i	−0.731059	+	0.266084i	−0.680613	−	0.732643i	$-0.738287\pi$
$313$	−12.9338	+	4.70750i	−0.731059	+	0.266084i	−0.0504462	+	0.998727i	$0.516064\pi$
$314$	12.1766	−	4.43193i	0.687168	−	0.250109i
$315$		0			0
$316$	2.33022	−	4.03606i	0.131085	−	0.227046i
$317$	−1.89347	+	10.7384i	−0.106348	+	0.603128i	0.884326	+	0.466870i	$0.154619\pi$
$317$	−1.89347	+	10.7384i	−0.106348	+	0.603128i	−0.990673	+	0.136257i	$0.956493\pi$
$318$		0			0
$319$	13.7686	+	11.5532i	0.770892	+	0.646855i
$320$	0.673648	+	3.82045i	0.0376581	+	0.213570i
$321$		0			0
$322$	−10.9709			−0.611385
$323$	−8.08037	−	22.7197i	−0.449604	−	1.26416i
$324$		0			0
$325$	−4.62923	−	1.68490i	−0.256784	−	0.0934616i
$326$	−2.61721	−	14.8429i	−0.144954	−	0.822075i
$327$		0			0
$328$	1.22281	−	1.02606i	0.0675185	−	0.0566547i
$329$	−0.462286	+	2.62175i	−0.0254867	+	0.144542i
$330$		0			0
$331$	−4.29561	−	7.44021i	−0.236108	−	0.408951i	0.723486	−	0.690339i	$-0.242539\pi$
$331$	−4.29561	−	7.44021i	−0.236108	−	0.408951i	−0.959594	+	0.281388i	$0.909205\pi$
$332$	11.7280	−	4.26865i	0.643659	−	0.234273i
$333$		0			0
$334$	0.970437	+	1.68085i	0.0531000	+	0.0919718i
$335$	−8.68139	+	15.0366i	−0.474315	+	0.821538i
$336$		0			0
$337$	−1.76991	+	1.48513i	−0.0964134	+	0.0809005i	−0.689720	−	0.724076i	$-0.742267\pi$
$337$	−1.76991	+	1.48513i	−0.0964134	+	0.0809005i	0.593307	+	0.804976i	$0.297822\pi$
$338$	9.77450	+	8.20178i	0.531663	+	0.446118i
$339$		0			0
$340$	−20.1668	−	7.34013i	−1.09370	−	0.398074i
$341$	5.11381			0.276928
$342$		0			0
$343$	−15.3277			−0.827618
$344$	−6.23783	−	2.27038i	−0.336321	−	0.122411i
$345$		0			0
$346$	12.3118	+	10.3308i	0.661887	+	0.555389i
$347$	2.51707	−	2.11208i	0.135124	−	0.113382i	−0.572721	−	0.819750i	$-0.694112\pi$
$347$	2.51707	−	2.11208i	0.135124	−	0.113382i	0.707845	+	0.706368i	$0.249668\pi$
$348$		0			0
$349$	−14.6741	+	25.4163i	−0.785487	+	1.36050i	0.143220	+	0.989691i	$0.454254\pi$
$349$	−14.6741	+	25.4163i	−0.785487	+	1.36050i	−0.928707	+	0.370813i	$0.879079\pi$
$350$	6.16385	+	10.6761i	0.329472	+	0.570661i
$351$		0			0
$352$	1.99273	−	0.725293i	0.106213	−	0.0386582i
$353$	−3.86959	−	6.70232i	−0.205957	−	0.356728i	0.744480	−	0.667645i	$-0.232697\pi$
$353$	−3.86959	−	6.70232i	−0.205957	−	0.356728i	−0.950437	+	0.310916i	$0.899364\pi$
$354$		0			0
$355$	−1.77719	+	10.0789i	−0.0943234	+	0.534935i
$356$	−6.47771	+	5.43545i	−0.343318	+	0.288078i
$357$		0			0
$358$	2.56552	+	14.5498i	0.135592	+	0.768981i
$359$	2.69459	+	0.980752i	0.142215	+	0.0517621i	0.412147	−	0.911117i	$-0.364779\pi$
$359$	2.69459	+	0.980752i	0.142215	+	0.0517621i	−0.269932	+	0.962879i	$0.587001\pi$
$360$		0			0
$361$	−3.57444	+	18.6607i	−0.188129	+	0.982144i
$362$	18.2267			0.957973
$363$		0			0
$364$	0.104418	+	0.592184i	0.00547299	+	0.0310389i
$365$	−45.6548	−	38.3089i	−2.38968	−	2.00518i
$366$		0			0
$367$	−3.98798	+	22.6169i	−0.208171	+	1.18060i	0.684201	+	0.729294i	$0.260151\pi$
$367$	−3.98798	+	22.6169i	−0.208171	+	1.18060i	−0.892372	+	0.451301i	$0.850960\pi$
$368$	−4.47178	+	7.74535i	−0.233108	+	0.403754i
$369$		0			0
$370$	6.17752	−	2.24843i	0.321154	−	0.116890i
$371$	10.2442	−	3.72859i	0.531854	−	0.193579i
$372$		0			0
$373$	11.5954	−	20.0838i	0.600387	−	1.03990i	−0.392376	−	0.919805i	$-0.628347\pi$
$373$	11.5954	−	20.0838i	0.600387	−	1.03990i	0.992762	−	0.120095i	$-0.0383199\pi$
$374$	−2.03714	+	11.5532i	−0.105338	+	0.597402i
$375$		0			0
$376$	1.66250	+	1.39501i	0.0857371	+	0.0719420i
$377$	0.721467	+	4.09164i	0.0371574	+	0.210730i
$378$		0			0
$379$	−33.5185			−1.72173			−0.860864	−	0.508835i	$-0.830076\pi$
$379$	−33.5185			−1.72173			−0.860864	+	0.508835i	$0.830076\pi$
$380$	10.7738	+	13.0334i	0.552684	+	0.668597i
$381$		0			0
$382$	−1.21301	−	0.441500i	−0.0620630	−	0.0225891i
$383$	−1.16860	−	6.62744i	−0.0597125	−	0.338646i	0.940286	−	0.340385i	$-0.110558\pi$
$383$	−1.16860	−	6.62744i	−0.0597125	−	0.338646i	−0.999998	+	0.00173918i	$0.999446\pi$
$384$		0			0
$385$	7.73055	−	6.48670i	0.393985	−	0.330593i
$386$	1.58378	−	8.98205i	0.0806122	−	0.457174i
$387$		0			0
$388$	7.18866	+	12.4511i	0.364949	+	0.632110i
$389$	−17.8751	+	6.50601i	−0.906304	+	0.329868i	−0.752776	−	0.658277i	$-0.771286\pi$
$389$	−17.8751	+	6.50601i	−0.906304	+	0.329868i	−0.153528	+	0.988144i	$0.549063\pi$
$390$		0			0
$391$	−24.7383	−	42.8480i	−1.25107	−	2.16692i
$392$	−2.74763	+	4.75903i	−0.138776	+	0.240367i
$393$		0			0
$394$	14.2665	−	11.9710i	0.718736	−	0.603091i
$395$	−13.8498	−	11.6214i	−0.696860	−	0.584735i
$396$		0			0
$397$	25.2913	+	9.20529i	1.26934	+	0.462000i	0.886891	−	0.461978i	$-0.152860\pi$
$397$	25.2913	+	9.20529i	1.26934	+	0.462000i	0.382444	+	0.923979i	$0.375082\pi$
$398$	−8.43107			−0.422612
$399$		0			0
$400$	10.0496			0.502481
$401$	−5.35756	−	1.94999i	−0.267544	−	0.0973780i	0.204765	−	0.978811i	$-0.434357\pi$
$401$	−5.35756	−	1.94999i	−0.267544	−	0.0973780i	−0.472309	+	0.881433i	$0.656579\pi$
$402$		0			0
$403$	0.905544	+	0.759842i	0.0451084	+	0.0378504i
$404$	−4.36231	+	3.66041i	−0.217033	+	0.182112i
$405$		0			0
$406$	5.19846	−	9.00400i	0.257995	−	0.446861i
$407$	−1.79679	−	3.11213i	−0.0890635	−	0.154263i
$408$		0			0
$409$	0.758770	−	0.276170i	0.0375188	−	0.0136557i	−0.323193	−	0.946333i	$-0.604756\pi$
$409$	0.758770	−	0.276170i	0.0375188	−	0.0136557i	0.360711	+	0.932677i	$0.382534\pi$
$410$	−3.09627	−	5.36289i	−0.152914	−	0.264854i
$411$		0			0
$412$	−0.0543776	+	0.308391i	−0.00267899	+	0.0151933i
$413$	10.7306	−	9.00400i	0.528016	−	0.443058i
$414$		0			0
$415$	−8.40760	−	47.6819i	−0.412713	−	2.34061i
$416$	0.460637	+	0.167658i	0.0225846	+	0.00822012i
$417$		0			0
$418$	5.99360	−	7.03703i	0.293157	−	0.344193i
$419$	19.1215			0.934149			0.467074	−	0.884218i	$-0.345308\pi$
$419$	19.1215			0.934149			0.467074	+	0.884218i	$0.345308\pi$
$420$		0			0
$421$	−4.86618	−	27.5975i	−0.237163	−	1.34502i	−0.838010	−	0.545655i	$-0.816281\pi$
$421$	−4.86618	−	27.5975i	−0.237163	−	1.34502i	0.600847	−	0.799364i	$-0.294830\pi$
$422$	1.12449	+	0.943555i	0.0547391	+	0.0459315i
$423$		0			0
$424$	1.54323	−	8.75211i	0.0749460	−	0.425040i
$425$	−27.7977	+	48.1471i	−1.34839	+	2.33548i
$426$		0			0
$427$	−0.0482857	+	0.0175745i	−0.00233671	+	0.000850492i
$428$	−15.8131	+	5.75552i	−0.764357	+	0.278203i
$429$		0			0
$430$	−12.8760	+	22.3019i	−0.620935	+	1.07549i
$431$	1.56923	−	8.89955i	0.0755872	−	0.428676i	−0.923406	−	0.383824i	$-0.874607\pi$
$431$	1.56923	−	8.89955i	0.0755872	−	0.428676i	0.998994	−	0.0448525i	$-0.0142818\pi$
$432$		0			0
$433$	1.12061	+	0.940307i	0.0538533	+	0.0451883i	0.669317	−	0.742977i	$-0.266587\pi$
$433$	1.12061	+	0.940307i	0.0538533	+	0.0451883i	−0.615464	+	0.788165i	$0.711031\pi$
$434$	−0.513671	−	2.91317i	−0.0246570	−	0.139837i
$435$		0			0
$436$	−10.4115			−0.498619
$437$	−0.286989	+	38.9830i	−0.0137285	+	1.86481i
$438$		0			0
$439$	5.08987	+	1.85256i	0.242926	+	0.0884179i	0.460614	−	0.887601i	$-0.347629\pi$
$439$	5.08987	+	1.85256i	0.242926	+	0.0884179i	−0.217688	+	0.976018i	$0.569851\pi$
$440$	−1.42855	−	8.10170i	−0.0681034	−	0.386233i
$441$		0			0
$442$	−2.07738	+	1.74313i	−0.0988110	+	0.0829122i
$443$	4.94310	−	28.0337i	0.234854	−	1.33192i	−0.608068	−	0.793885i	$-0.708055\pi$
$443$	4.94310	−	28.0337i	0.234854	−	1.33192i	0.842922	−	0.538036i	$-0.180834\pi$
$444$		0			0
$445$	16.4021	+	28.4093i	0.777536	+	1.34673i
$446$	24.6844	−	8.98438i	1.16884	−	0.425423i
$447$		0			0
$448$	−0.613341	−	1.06234i	−0.0289776	−	0.0501907i
$449$	−11.3824	+	19.7149i	−0.537168	+	0.930402i	0.461887	+	0.886939i	$0.347172\pi$
$449$	−11.3824	+	19.7149i	−0.537168	+	0.930402i	−0.999055	+	0.0434631i	$0.986161\pi$
$450$		0			0
$451$	−2.59311	+	2.17588i	−0.122105	+	0.102458i
$452$	13.3157	+	11.1732i	0.626317	+	0.525542i
$453$		0			0
$454$	−17.2601	−	6.28217i	−0.810057	−	0.294837i
$455$	2.33275			0.109361
$456$		0			0
$457$	−1.13011			−0.0528643			−0.0264322	−	0.999651i	$-0.508415\pi$
$457$	−1.13011			−0.0528643			−0.0264322	+	0.999651i	$0.508415\pi$
$458$	3.63816	+	1.32418i	0.170000	+	0.0618749i
$459$		0			0
$460$	26.5783	+	22.3019i	1.23922	+	1.03983i
$461$	9.94562	−	8.34537i	0.463214	−	0.388683i	−0.381098	−	0.924535i	$-0.624454\pi$
$461$	9.94562	−	8.34537i	0.463214	−	0.388683i	0.844312	+	0.535852i	$0.180010\pi$
$462$		0			0
$463$	15.3123	−	26.5216i	0.711622	−	1.23256i	−0.252627	−	0.967564i	$-0.581294\pi$
$463$	15.3123	−	26.5216i	0.711622	−	1.23256i	0.964248	−	0.265001i	$-0.0853722\pi$
$464$	−4.23783	−	7.34013i	−0.196736	−	0.340757i
$465$		0			0
$466$	−15.4547	+	5.62505i	−0.715925	+	0.260576i
$467$	5.52869	+	9.57596i	0.255837	+	0.443123i	0.965123	−	0.261799i	$-0.0843156\pi$
$467$	5.52869	+	9.57596i	0.255837	+	0.443123i	−0.709285	+	0.704921i	$0.750982\pi$
$468$		0			0
$469$	0.953363	−	5.40679i	0.0440222	−	0.249662i
$470$	6.44949	−	5.41177i	0.297493	−	0.249626i
$471$		0			0
$472$	−1.98293	−	11.2457i	−0.0912716	−	0.517627i
$473$	13.2280	+	4.81461i	0.608225	+	0.221376i
$474$		0			0
$475$	38.0967	−	21.6228i	1.74800	−	0.992122i
$476$	6.78611			0.311041
$477$		0			0
$478$	0.573978	+	3.25519i	0.0262531	+	0.148889i
$479$	13.5116	+	11.3376i	0.617361	+	0.518028i	0.896973	−	0.442086i	$-0.145761\pi$
$479$	13.5116	+	11.3376i	0.617361	+	0.518028i	−0.279612	+	0.960113i	$0.590206\pi$
$480$		0			0
$481$	0.144248	−	0.818069i	0.00657713	−	0.0373007i
$482$	1.50774	−	2.61148i	0.0686757	−	0.118950i
$483$		0			0
$484$	6.11081	−	2.22415i	0.277764	−	0.101098i
$485$	52.4115	−	19.0762i	2.37989	−	0.866207i
$486$		0			0
$487$	7.64677	−	13.2446i	0.346508	−	0.600170i	−0.639118	−	0.769109i	$-0.720701\pi$
$487$	7.64677	−	13.2446i	0.346508	−	0.600170i	0.985627	+	0.168938i	$0.0540339\pi$
$488$	−0.00727396	+	0.0412527i	−0.000329277	+	0.00186742i
$489$		0			0
$490$	16.3307	+	13.7031i	0.737745	+	0.619042i
$491$	0.308811	+	1.75135i	0.0139364	+	0.0790375i	0.990983	−	0.133990i	$-0.0427789\pi$
$491$	0.308811	+	1.75135i	0.0139364	+	0.0790375i	−0.977046	+	0.213027i	$0.931668\pi$
$492$		0			0
$493$	46.8881			2.11173
$494$	2.10694	−	0.355538i	0.0947959	−	0.0159964i
$495$		0			0
$496$	−2.26604	−	0.824773i	−0.101748	−	0.0370334i
$497$	−0.561956	−	3.18701i	−0.0252072	−	0.142957i
$498$		0			0
$499$	−0.0825961	+	0.0693063i	−0.00369751	+	0.00310258i	−0.644634	−	0.764491i	$-0.722990\pi$
$499$	−0.0825961	+	0.0693063i	−0.00369751	+	0.00310258i	0.640937	+	0.767594i	$0.278546\pi$
$500$	3.40167	−	19.2919i	0.152127	−	0.862758i
$501$		0			0
$502$	1.76739	+	3.06121i	0.0788824	+	0.136628i
$503$	−22.2615	+	8.10251i	−0.992589	+	0.361273i	−0.786722	−	0.617307i	$-0.788224\pi$
$503$	−22.2615	+	8.10251i	−0.992589	+	0.361273i	−0.205867	+	0.978580i	$0.566001\pi$
$504$		0			0
$505$	11.0458	+	19.1318i	0.491530	+	0.851355i
$506$	9.48293	−	16.4249i	0.421567	−	0.730176i
$507$		0			0
$508$	−1.24897	+	1.04801i	−0.0554141	+	0.0464979i
$509$	2.73783	+	2.29731i	0.121352	+	0.101826i	0.701444	−	0.712724i	$-0.252539\pi$
$509$	2.73783	+	2.29731i	0.121352	+	0.101826i	−0.580092	+	0.814551i	$0.696983\pi$
$510$		0			0
$511$	17.7087	+	6.44545i	0.783388	+	0.285130i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−4.70233			−0.207411
$515$	1.14156	+	0.415494i	0.0503031	+	0.0183088i
$516$		0			0
$517$	−3.52553	−	2.95827i	−0.155053	−	0.130105i
$518$	−1.59240	+	1.33618i	−0.0699659	+	0.0587083i
$519$		0			0
$520$	0.950837	−	1.64690i	0.0416970	−	0.0722213i
$521$	17.0608	+	29.5501i	0.747446	+	1.29461i	0.949043	+	0.315146i	$0.102054\pi$
$521$	17.0608	+	29.5501i	0.747446	+	1.29461i	−0.201597	+	0.979469i	$0.564613\pi$
$522$		0			0
$523$	−16.0376	+	5.83721i	−0.701276	+	0.255243i	−0.667955	−	0.744201i	$-0.732830\pi$
$523$	−16.0376	+	5.83721i	−0.701276	+	0.255243i	−0.0333202	+	0.999445i	$0.510608\pi$
$524$	2.98158	+	5.16425i	0.130251	+	0.225601i
$525$		0			0
$526$	3.65745	−	20.7424i	0.159472	−	0.904413i
$527$	10.2194	−	8.57510i	0.445164	−	0.373537i
$528$		0			0
$529$	9.89574	+	56.1216i	0.430250	+	2.44007i
$530$	−32.3974	−	11.7917i	−1.40725	−	0.512198i
$531$		0			0
$532$	−4.61081	−	2.70751i	−0.199904	−	0.117385i
$533$	−0.782490			−0.0338934
$534$		0			0
$535$	11.3362	+	64.2905i	0.490105	+	2.77952i
$536$	−3.42855	−	2.87689i	−0.148091	−	0.124263i
$537$		0			0
$538$	1.75015	−	9.92561i	0.0754544	−	0.427923i
$539$	5.82666	−	10.0921i	0.250972	−	0.434696i
$540$		0			0
$541$	−24.7841	+	9.02066i	−1.06555	+	0.387828i	−0.814511	−	0.580149i	$-0.802994\pi$
$541$	−24.7841	+	9.02066i	−1.06555	+	0.387828i	−0.251039	+	0.967977i	$0.580772\pi$
$542$	−9.17499	+	3.33942i	−0.394100	+	0.143441i
$543$		0			0
$544$	2.76604	−	4.79093i	0.118593	−	0.205409i
$545$	−7.01367	+	39.7765i	−0.300433	+	1.70384i
$546$		0			0
$547$	−26.7317	−	22.4306i	−1.14297	−	0.959063i	−0.143435	−	0.989660i	$-0.545815\pi$
$547$	−26.7317	−	22.4306i	−1.14297	−	0.959063i	−0.999532	+	0.0305971i	$0.990259\pi$
$548$	0.00340357	+	0.0193026i	0.000145393	+	0.000824566i
$549$		0			0
$550$	−21.3114			−0.908721
$551$	−31.8580	−	18.7073i	−1.35720	−	0.796957i
$552$		0			0
$553$	5.37211	+	1.95529i	0.228445	+	0.0831473i
$554$	−2.92720	−	16.6010i	−0.124365	−	0.705309i
$555$		0			0
$556$	3.44356	−	2.88949i	0.146040	−	0.122542i
$557$	5.65957	−	32.0970i	0.239804	−	1.35999i	−0.592454	−	0.805604i	$-0.701841\pi$
$557$	5.65957	−	32.0970i	0.239804	−	1.35999i	0.832258	−	0.554389i	$-0.187048\pi$
$558$		0			0
$559$	1.62701	+	2.81807i	0.0688152	+	0.119192i
$560$	−4.47178	+	1.62760i	−0.188967	+	0.0687785i
$561$		0			0
$562$	5.86231	+	10.1538i	0.247287	+	0.428313i
$563$	−2.39780	+	4.15312i	−0.101055	+	0.175033i	−0.912120	−	0.409924i	$-0.865555\pi$
$563$	−2.39780	+	4.15312i	−0.101055	+	0.175033i	0.811064	+	0.584957i	$0.198889\pi$
$564$		0			0
$565$	51.6566	−	43.3451i	2.17321	−	1.82354i
$566$	16.5043	+	13.8488i	0.693729	+	0.582108i
$567$		0			0
$568$	−2.47906	−	0.902302i	−0.104019	−	0.0378598i
$569$	32.7006			1.37088			0.685440	−	0.728129i	$-0.259610\pi$
$569$	32.7006			1.37088			0.685440	+	0.728129i	$0.259610\pi$
$570$		0			0
$571$	−10.9531			−0.458371			−0.229186	−	0.973383i	$-0.573606\pi$
$571$	−10.9531			−0.458371			−0.229186	+	0.973383i	$0.573606\pi$
$572$	−0.976834	−	0.355538i	−0.0408435	−	0.0148658i
$573$		0			0
$574$	1.50000	+	1.25865i	0.0626088	+	0.0525350i
$575$	68.8517	−	57.7734i	2.87131	−	2.40932i
$576$		0			0
$577$	9.15136	−	15.8506i	0.380976	−	0.659870i	−0.610226	−	0.792227i	$-0.708921\pi$
$577$	9.15136	−	15.8506i	0.380976	−	0.659870i	0.991202	+	0.132357i	$0.0422547\pi$
$578$	6.80200	+	11.7814i	0.282926	+	0.490042i
$579$		0			0
$580$	−30.8974	+	11.2457i	−1.28294	+	0.466954i
$581$	7.65493	+	13.2587i	0.317580	+	0.550064i
$582$		0			0
$583$	−3.27260	+	18.5599i	−0.135537	+	0.768671i
$584$	11.7686	−	9.87500i	0.486987	−	0.408631i
$585$		0			0
$586$	−1.93107	−	10.9517i	−0.0797720	−	0.452409i
$587$	−5.34137	−	1.94410i	−0.220462	−	0.0802415i	0.229428	−	0.973326i	$-0.426314\pi$
$587$	−5.34137	−	1.94410i	−0.220462	−	0.0802415i	−0.449890	+	0.893084i	$0.648537\pi$
$588$		0			0
$589$	−10.3648	+	1.74903i	−0.427076	+	0.0720673i
$590$	−44.2995			−1.82378
$591$		0			0
$592$	0.294263	+	1.66885i	0.0120941	+	0.0685892i
$593$	8.05097	+	6.75557i	0.330614	+	0.277418i	0.792950	−	0.609287i	$-0.208544\pi$
$593$	8.05097	+	6.75557i	0.330614	+	0.277418i	−0.462336	+	0.886705i	$0.652989\pi$
$594$		0			0
$595$	4.57145	−	25.9260i	0.187411	−	1.06286i
$596$	6.01501	−	10.4183i	0.246385	−	0.426751i
$597$		0			0
$598$	4.11974	−	1.49946i	0.168469	−	0.0613176i
$599$	−42.0146	+	15.2921i	−1.71667	+	0.624817i	−0.997543	−	0.0700613i	$-0.977681\pi$
$599$	−42.0146	+	15.2921i	−1.71667	+	0.624817i	−0.719128	+	0.694878i	$0.755458\pi$
$600$		0			0
$601$	−16.4363	+	28.4685i	−0.670450	+	1.16125i	0.307326	+	0.951604i	$0.400566\pi$
$601$	−16.4363	+	28.4685i	−0.670450	+	1.16125i	−0.977777	+	0.209650i	$0.932768\pi$
$602$	1.41400	−	8.01919i	0.0576304	−	0.326838i
$603$		0			0
$604$	0.0452926	+	0.0380050i	0.00184293	+	0.00154640i
$605$	−4.38073	−	24.8444i	−0.178102	−	1.01007i
$606$		0			0
$607$	29.9486			1.21558			0.607788	−	0.794099i	$-0.292057\pi$
$607$	29.9486			1.21558			0.607788	+	0.794099i	$0.292057\pi$
$608$	−3.79086	+	2.15160i	−0.153740	+	0.0872589i
$609$		0			0
$610$	0.152704	+	0.0555796i	0.00618279	+	0.00225035i
$611$	−0.184736	−	1.04769i	−0.00747363	−	0.0423850i
$612$		0			0
$613$	4.47384	−	3.75400i	0.180697	−	0.151623i	−0.547953	−	0.836509i	$-0.684593\pi$
$613$	4.47384	−	3.75400i	0.180697	−	0.151623i	0.728650	+	0.684887i	$0.240148\pi$
$614$	−4.34817	+	24.6597i	−0.175478	+	0.995185i
$615$		0			0
$616$	1.30066	+	2.25281i	0.0524051	+	0.0907682i
$617$	−11.8135	+	4.29975i	−0.475592	+	0.173101i	−0.568684	−	0.822556i	$-0.692547\pi$
$617$	−11.8135	+	4.29975i	−0.475592	+	0.173101i	0.0930920	+	0.995658i	$0.470325\pi$
$618$		0			0
$619$	−4.14290	−	7.17572i	−0.166517	−	0.288417i	0.770676	−	0.637228i	$-0.219919\pi$
$619$	−4.14290	−	7.17572i	−0.166517	−	0.288417i	−0.937193	+	0.348811i	$0.886586\pi$
$620$	−4.67752	+	8.10170i	−0.187854	+	0.325372i
$621$		0			0
$622$	0.0432332	−	0.0362770i	0.00173349	−	0.00145457i
$623$	−7.94609	−	6.66756i	−0.318353	−	0.267130i
$624$		0			0
$625$	−24.1942	−	8.80596i	−0.967767	−	0.352238i
$626$	−13.7638			−0.550113
$627$		0			0
$628$	12.9581			0.517085
$629$	−8.80928	−	3.20631i	−0.351249	−	0.127844i
$630$		0			0
$631$	5.23055	+	4.38895i	0.208225	+	0.174722i	0.740936	−	0.671576i	$-0.234382\pi$
$631$	5.23055	+	4.38895i	0.208225	+	0.174722i	−0.532711	+	0.846297i	$0.678827\pi$
$632$	3.57011	−	2.99568i	0.142011	−	0.119162i
$633$		0			0
$634$	−5.45202	+	9.44317i	−0.216527	+	0.375036i
$635$	3.16250	+	5.47762i	0.125500	+	0.217373i
$636$		0			0
$637$	2.53132	−	0.921324i	0.100294	−	0.0365042i
$638$	8.98680	+	15.5656i	0.355791	+	0.616248i
$639$		0			0
$640$	−0.673648	+	3.82045i	−0.0266283	+	0.151016i
$641$	−29.6544	+	24.8830i	−1.17128	+	0.982818i	−0.999997	−	0.00240481i	$-0.999235\pi$
$641$	−29.6544	+	24.8830i	−1.17128	+	0.982818i	−0.171279	+	0.985222i	$0.554790\pi$
$642$		0			0
$643$	−2.18820	−	12.4099i	−0.0862940	−	0.489398i	−0.997070	−	0.0764965i	$-0.975627\pi$
$643$	−2.18820	−	12.4099i	−0.0862940	−	0.489398i	0.910776	−	0.412901i	$-0.135485\pi$
$644$	−10.3093	−	3.75227i	−0.406242	−	0.147860i
$645$		0			0
$646$	0.177519	−	24.1132i	0.00698437	−	0.948720i
$647$	−8.41241			−0.330726			−0.165363	−	0.986233i	$-0.552880\pi$
$647$	−8.41241			−0.330726			−0.165363	+	0.986233i	$0.552880\pi$
$648$		0			0
$649$	4.20502	+	23.8479i	0.165062	+	0.936111i
$650$	−3.77379	−	3.16658i	−0.148020	−	0.124204i
$651$		0			0
$652$	2.61721	−	14.8429i	0.102498	−	0.581294i
$653$	13.1900	−	22.8458i	0.516165	−	0.894024i	−0.483659	−	0.875257i	$-0.660693\pi$
$653$	13.1900	−	22.8458i	0.516165	−	0.894024i	0.999824	−	0.0187673i	$-0.00597416\pi$
$654$		0			0
$655$	21.7383	−	7.91209i	0.849385	−	0.309151i
$656$	1.50000	−	0.545955i	0.0585652	−	0.0213160i
$657$		0			0
$658$	−1.33110	+	2.30553i	−0.0518917	+	0.0898790i
$659$	−5.55794	+	31.5207i	−0.216507	+	1.22787i	0.661766	+	0.749711i	$0.269807\pi$
$659$	−5.55794	+	31.5207i	−0.216507	+	1.22787i	−0.878273	+	0.478160i	$0.841304\pi$
$660$		0			0
$661$	−31.0462	−	26.0509i	−1.20756	−	1.01326i	−0.999381	−	0.0351705i	$-0.988803\pi$
$661$	−31.0462	−	26.0509i	−1.20756	−	1.01326i	−0.208177	−	0.978091i	$-0.566753\pi$
$662$	−1.49185	−	8.46069i	−0.0579823	−	0.328834i
$663$		0			0
$664$	12.4807			0.484345
$665$	−13.4500	+	15.7915i	−0.521567	+	0.612367i
$666$		0			0
$667$	−71.2311	−	25.9260i	−2.75808	−	1.00386i
$668$	0.337029	+	1.91139i	0.0130401	+	0.0739538i
$669$		0			0
$670$	−13.3007	+	11.1606i	−0.513849	+	0.431171i
$671$	0.0154253	−	0.0874810i	0.000595486	−	0.00337717i
$672$		0			0
$673$	2.28059	+	3.95010i	0.0879104	+	0.152265i	0.906628	−	0.421932i	$-0.138648\pi$
$673$	2.28059	+	3.95010i	0.0879104	+	0.152265i	−0.818717	+	0.574197i	$0.805314\pi$
$674$	−2.17112	+	0.790224i	−0.0836285	+	0.0304383i
$675$		0			0
$676$	6.37985	+	11.0502i	0.245379	+	0.425009i
$677$	16.7208	−	28.9612i	0.642631	−	1.11307i	−0.342213	−	0.939623i	$-0.611176\pi$
$677$	16.7208	−	28.9612i	0.642631	−	1.11307i	0.984843	−	0.173446i	$-0.0554904\pi$
$678$		0			0
$679$	−13.5103	+	11.3365i	−0.518476	+	0.435053i
$680$	−16.4402	−	13.7949i	−0.630451	−	0.529011i
$681$		0			0
$682$	4.80541	+	1.74903i	0.184009	+	0.0669736i
$683$	26.4825			1.01332			0.506662	−	0.862145i	$-0.330879\pi$
$683$	26.4825			1.01332			0.506662	+	0.862145i	$0.330879\pi$
$684$		0			0
$685$	0.0760373			0.00290524
$686$	−14.4033	−	5.24238i	−0.549921	−	0.200155i
$687$		0			0
$688$	−5.08512	−	4.26692i	−0.193868	−	0.162675i
$689$	−3.33725	+	2.80028i	−0.127139	+	0.106682i
$690$		0			0
$691$	−16.7003	+	28.9257i	−0.635308	+	1.10039i	0.351141	+	0.936322i	$0.385794\pi$
$691$	−16.7003	+	28.9257i	−0.635308	+	1.10039i	−0.986450	+	0.164064i	$0.947540\pi$
$692$	8.03596	+	13.9187i	0.305481	+	0.529109i
$693$		0			0
$694$	3.08765	−	1.12381i	0.117206	−	0.0426593i
$695$	−8.71941	−	15.1025i	−0.330746	−	0.572869i
$696$		0			0
$697$	−1.53343	+	8.69653i	−0.0580829	+	0.329405i
$698$	−22.4820	+	18.8647i	−0.850958	+	0.714039i
$699$		0			0
$700$	2.14068	+	12.1404i	0.0809102	+	0.458864i
$701$	17.7408	+	6.45713i	0.670061	+	0.243882i	0.654574	−	0.755998i	$-0.272848\pi$
$701$	17.7408	+	6.45713i	0.670061	+	0.243882i	0.0154871	+	0.999880i	$0.495070\pi$
$702$		0			0
$703$	4.70620	+	5.69323i	0.177498	+	0.214724i
$704$	2.12061			0.0799237
$705$		0			0
$706$	−1.34389	−	7.62159i	−0.0505781	−	0.286843i
$707$	−5.35117	−	4.49016i	−0.201251	−	0.168870i
$708$		0			0
$709$	−0.0369988	+	0.209830i	−0.00138952	+	0.00788034i	−0.985495	−	0.169707i	$-0.945718\pi$
$709$	−0.0369988	+	0.209830i	−0.00138952	+	0.00788034i	0.984105	+	0.177587i	$0.0568291\pi$
$710$	−5.11721	+	8.86327i	−0.192046	+	0.332633i
$711$		0			0
$712$	−7.94609	+	2.89214i	−0.297792	+	0.108388i
$713$	−20.2665	+	7.37641i	−0.758987	+	0.276249i
$714$		0			0
$715$	−2.01636	+	3.49244i	−0.0754075	+	0.130610i
$716$	−2.56552	+	14.5498i	−0.0958781	+	0.543751i
$717$		0			0
$718$	2.19665	+	1.84321i	0.0819783	+	0.0687880i
$719$	2.25150	+	12.7689i	0.0839667	+	0.476199i	0.997575	+	0.0696027i	$0.0221732\pi$
$719$	2.25150	+	12.7689i	0.0839667	+	0.476199i	−0.913608	+	0.406596i	$0.866716\pi$
$720$		0			0
$721$	−0.384133			−0.0143059
$722$	−9.74123	+	16.3128i	−0.362531	+	0.607101i
$723$		0			0
$724$	17.1275	+	6.23389i	0.636538	+	0.231681i
$725$	14.7909	+	83.8831i	0.549319	+	3.11534i
$726$		0			0
$727$	19.7062	−	16.5355i	0.730863	−	0.613267i	−0.199504	−	0.979897i	$-0.563933\pi$
$727$	19.7062	−	16.5355i	0.730863	−	0.613267i	0.930367	+	0.366630i	$0.119489\pi$
$728$	−0.104418	+	0.592184i	−0.00386999	+	0.0219478i
$729$		0			0
$730$	−29.7991	−	51.6135i	−1.10291	−	1.91030i
$731$	34.5082	−	12.5600i	1.27633	−	0.464547i
$732$		0			0
$733$	−4.25995	−	7.37845i	−0.157345	−	0.272529i	0.776565	−	0.630037i	$-0.216960\pi$
$733$	−4.25995	−	7.37845i	−0.157345	−	0.272529i	−0.933910	+	0.357507i	$0.883627\pi$
$734$	−11.4829	+	19.8890i	−0.423843	+	0.734117i
$735$		0			0
$736$	−6.85117	+	5.74881i	−0.252537	+	0.211904i
$737$	7.27063	+	6.10078i	0.267817	+	0.224725i
$738$		0			0
$739$	12.5030	+	4.55072i	0.459930	+	0.167401i	0.561585	−	0.827419i	$-0.310192\pi$
$739$	12.5030	+	4.55072i	0.459930	+	0.167401i	−0.101655	+	0.994820i	$0.532414\pi$
$740$	6.57398			0.241664
$741$		0			0
$742$	10.9017			0.400213
$743$	−25.3307	−	9.21962i	−0.929293	−	0.338235i	−0.167364	−	0.985895i	$-0.553525\pi$
$743$	−25.3307	−	9.21962i	−0.929293	−	0.338235i	−0.761929	+	0.647660i	$0.775748\pi$
$744$		0			0
$745$	−35.7506	−	29.9983i	−1.30980	−	1.09905i
$746$	17.7652	−	14.9067i	0.650429	−	0.545775i
$747$		0			0
$748$	−5.86571	+	10.1597i	−0.214472	+	0.371476i
$749$	−10.3213	−	17.8770i	−0.377132	−	0.653212i
$750$		0			0
$751$	−17.3277	+	6.30677i	−0.632297	+	0.230137i	−0.638231	−	0.769845i	$-0.720333\pi$
$751$	−17.3277	+	6.30677i	−0.632297	+	0.230137i	0.00593399	+	0.999982i	$0.498111\pi$
$752$	1.08512	+	1.87949i	0.0395703	+	0.0685378i
$753$		0			0
$754$	−0.721467	+	4.09164i	−0.0262743	+	0.149009i
$755$	0.175708	−	0.147436i	0.00639465	−	0.00536575i
$756$		0			0
$757$	5.19490	+	29.4617i	0.188812	+	1.07080i	0.920959	+	0.389659i	$0.127407\pi$
$757$	5.19490	+	29.4617i	0.188812	+	1.07080i	−0.732148	+	0.681146i	$0.761482\pi$
$758$	−31.4971	−	11.4640i	−1.14402	−	0.416391i
$759$		0			0
$760$	5.66637	+	15.9322i	0.205541	+	0.577922i
$761$	28.6691			1.03925			0.519627	−	0.854393i	$-0.326071\pi$
$761$	28.6691			1.03925			0.519627	+	0.854393i	$0.326071\pi$
$762$		0			0
$763$	−2.21776	−	12.5775i	−0.0802883	−	0.455337i
$764$	−0.988856	−	0.829748i	−0.0357755	−	0.0300192i
$765$		0			0
$766$	1.16860	−	6.62744i	0.0422231	−	0.239459i
$767$	−2.79885	+	4.84775i	−0.101061	+	0.175042i
$768$		0			0
$769$	9.17277	−	3.33862i	0.330779	−	0.120394i	−0.171292	−	0.985220i	$-0.554794\pi$
$769$	9.17277	−	3.33862i	0.330779	−	0.120394i	0.502070	+	0.864827i	$0.332572\pi$
$770$	9.48293	−	3.45150i	0.341741	−	0.124384i
$771$		0			0
$772$	4.56031	−	7.89868i	0.164129	−	0.284280i
$773$	0.676641	−	3.83742i	0.0243371	−	0.138023i	−0.970218	−	0.242233i	$-0.922120\pi$
$773$	0.676641	−	3.83742i	0.0243371	−	0.138023i	0.994555	+	0.104210i	$0.0332314\pi$
$774$		0			0
$775$	18.5646	+	15.5776i	0.666862	+	0.559563i
$776$	2.49660	+	14.1589i	0.0896226	+	0.508275i
$777$		0			0
$778$	−19.0223			−0.681982
$779$	4.51161	−	5.29704i	0.161645	−	0.189786i
$780$		0			0
$781$	5.25712	+	1.91344i	0.188115	+	0.0684681i
$782$	−8.59152	−	48.7249i	−0.307232	−	1.74240i
$783$		0			0
$784$	−4.20961	+	3.53228i	−0.150343	+	0.126153i
$785$	8.72921	−	49.5058i	0.311559	−	1.76694i
$786$		0			0
$787$	1.47044	+	2.54687i	0.0524154	+	0.0907862i	0.891043	−	0.453920i	$-0.149975\pi$
$787$	1.47044	+	2.54687i	0.0524154	+	0.0907862i	−0.838627	+	0.544706i	$0.816641\pi$
$788$	17.5005	−	6.36965i	0.623428	−	0.226909i
$789$		0			0
$790$	−9.03983	−	15.6574i	−0.321623	−	0.557067i
$791$	−10.6613	+	18.4660i	−0.379073	+	0.656574i
$792$		0			0
$793$	0.0157300	−	0.0131990i	0.000558587	−	0.000468711i
$794$	20.6177	+	17.3003i	0.731694	+	0.613964i
$795$		0			0
$796$	−7.92262	−	2.88360i	−0.280810	−	0.102206i
$797$	−8.26950			−0.292921			−0.146460	−	0.989217i	$-0.546788\pi$
$797$	−8.26950			−0.292921			−0.146460	+	0.989217i	$0.546788\pi$
$798$		0			0
$799$	−12.0060			−0.424741
$800$	9.44356	+	3.43718i	0.333880	+	0.121523i
$801$		0			0
$802$	−4.36753	−	3.66479i	−0.154223	−	0.129408i
$803$	−24.9566	+	20.9411i	−0.880699	+	0.738995i
$804$		0			0
$805$	−21.2802	+	36.8584i	−0.750028	+	1.29909i
$806$	0.591052	+	1.02373i	0.0208189	+	0.0360594i
$807$		0			0
$808$	−5.35117	+	1.94767i	−0.188253	+	0.0685186i
$809$	−1.04529	−	1.81050i	−0.0367505	−	0.0636538i	0.847065	−	0.531489i	$-0.178367\pi$
$809$	−1.04529	−	1.81050i	−0.0367505	−	0.0636538i	−0.883816	+	0.467835i	$0.845034\pi$
$810$		0			0
$811$	0.150177	−	0.851698i	0.00527344	−	0.0299072i	−0.982057	−	0.188582i	$-0.939611\pi$
$811$	0.150177	−	0.851698i	0.00527344	−	0.0299072i	0.987331	+	0.158675i	$0.0507221\pi$
$812$	7.96451	−	6.68302i	0.279499	−	0.234528i
$813$		0			0
$814$	−0.624018	−	3.53898i	−0.0218718	−	0.124041i
$815$	−54.9436	−	19.9978i	−1.92459	−	0.700494i
$816$		0			0
$817$	−28.4577	−	5.23416i	−0.995609	−	0.183120i
$818$	0.807467			0.0282324
$819$		0			0
$820$	−1.07532	−	6.09845i	−0.0375519	−	0.212967i
$821$	−17.4394	−	14.6334i	−0.608641	−	0.510710i	0.285569	−	0.958358i	$-0.407817\pi$
$821$	−17.4394	−	14.6334i	−0.608641	−	0.510710i	−0.894210	+	0.447648i	$0.852262\pi$
$822$		0			0
$823$	−5.75056	+	32.6131i	−0.200452	+	1.13682i	0.703986	+	0.710214i	$0.251402\pi$
$823$	−5.75056	+	32.6131i	−0.200452	+	1.13682i	−0.904438	+	0.426606i	$0.859709\pi$
$824$	−0.156574	+	0.271194i	−0.00545452	+	0.00944750i
$825$		0			0
$826$	13.1630	−	4.79093i	0.457998	−	0.166698i
$827$	−24.9158	+	9.06861i	−0.866408	+	0.315347i	−0.736712	−	0.676207i	$-0.763622\pi$
$827$	−24.9158	+	9.06861i	−0.866408	+	0.315347i	−0.129696	+	0.991554i	$0.541400\pi$
$828$		0			0
$829$	1.57873	−	2.73443i	0.0548314	−	0.0949708i	−0.837307	−	0.546733i	$-0.815871\pi$
$829$	1.57873	−	2.73443i	0.0548314	−	0.0949708i	0.892138	+	0.451762i	$0.149205\pi$
$830$	8.40760	−	47.6819i	0.291832	−	1.65506i
$831$		0			0
$832$	0.375515	+	0.315094i	0.0130186	+	0.0109239i
$833$	−5.27894	−	29.9384i	−0.182905	−	1.03730i
$834$		0			0
$835$	7.52940			0.260566
$836$	8.03895	−	4.56272i	0.278033	−	0.157805i
$837$		0			0
$838$	17.9684	+	6.53995i	0.620707	+	0.225919i
$839$	7.31386	+	41.4790i	0.252503	+	1.43201i	0.802403	+	0.596783i	$0.203555\pi$
$839$	7.31386	+	41.4790i	0.252503	+	1.43201i	−0.549900	+	0.835230i	$0.685334\pi$
$840$		0			0
$841$	32.8148	−	27.5349i	1.13154	−	0.949479i
$842$	4.86618	−	27.5975i	0.167700	−	0.951072i
$843$		0			0
$844$	0.733956	+	1.27125i	0.0252638	+	0.0437582i
$845$	46.5146	−	16.9299i	1.60015	−	0.582407i
$846$		0			0
$847$	3.98855	+	6.90837i	0.137048	+	0.237375i
$848$	4.44356	−	7.69648i	0.152593	−	0.264298i
$849$		0			0
$850$	−42.5886	+	35.7361i	−1.46078	+	1.22574i
$851$	11.6099	+	9.74189i	0.397984	+	0.333948i
$852$		0			0
$853$	−53.1147	−	19.3322i	−1.81861	−	0.661921i	−0.995579	−	0.0939314i	$-0.970057\pi$
$853$	−53.1147	−	19.3322i	−1.81861	−	0.661921i	−0.823035	−	0.567990i	$-0.807721\pi$
$854$	−0.0513845			−0.00175834
$855$		0			0
$856$	−16.8280			−0.575169
$857$	12.3960	+	4.51179i	0.423441	+	0.154120i	0.544946	−	0.838471i	$-0.316550\pi$
$857$	12.3960	+	4.51179i	0.423441	+	0.154120i	−0.121505	+	0.992591i	$0.538772\pi$
$858$		0			0
$859$	−16.6623	−	13.9813i	−0.568509	−	0.477036i	0.312642	−	0.949871i	$-0.398786\pi$
$859$	−16.6623	−	13.9813i	−0.568509	−	0.477036i	−0.881151	+	0.472836i	$0.843230\pi$
$860$	−19.7271	+	16.5530i	−0.672690	+	0.564454i
$861$		0			0
$862$	4.51842	−	7.82613i	0.153898	−	0.266559i
$863$	−23.4550	−	40.6253i	−0.798418	−	1.38290i	−0.920646	−	0.390398i	$-0.872337\pi$
$863$	−23.4550	−	40.6253i	−0.798418	−	1.38290i	0.122228	−	0.992502i	$-0.460996\pi$
$864$		0			0
$865$	58.5890	−	21.3247i	1.99209	−	0.725061i
$866$	0.731429	+	1.26687i	0.0248550	+	0.0430501i
$867$		0			0
$868$	0.513671	−	2.91317i	0.0174351	−	0.0988795i
$869$	−7.57082	+	6.35267i	−0.256823	+	0.215500i
$870$		0			0
$871$	0.380978	+	2.16063i	0.0129089	+	0.0732102i
$872$	−9.78359	−	3.56093i	−0.331314	−	0.120588i
$873$		0			0
$874$	−13.6027	+	36.5339i	−0.460117	+	1.23578i
$875$	24.0300			0.812363
$876$		0			0
$877$	−0.464451	−	2.63403i	−0.0156834	−	0.0889450i	0.975961	−	0.217944i	$-0.0699349\pi$
$877$	−0.464451	−	2.63403i	−0.0156834	−	0.0889450i	−0.991645	+	0.128999i	$0.958824\pi$
$878$	4.14930	+	3.48168i	0.140032	+	0.117501i
$879$		0			0
$880$	1.42855	−	8.10170i	0.0481564	−	0.273108i
$881$	−13.5548	+	23.4777i	−0.456674	+	0.790983i	−0.998783	−	0.0493254i	$-0.984293\pi$
$881$	−13.5548	+	23.4777i	−0.456674	+	0.790983i	0.542108	+	0.840309i	$0.317626\pi$
$882$		0			0
$883$	40.8055	−	14.8520i	1.37321	−	0.499809i	0.453099	−	0.891460i	$-0.350318\pi$
$883$	40.8055	−	14.8520i	1.37321	−	0.499809i	0.920114	+	0.391651i	$0.128096\pi$
$884$	−2.54829	+	0.927500i	−0.0857081	+	0.0311952i
$885$		0			0
$886$	14.2331	−	24.6524i	0.478170	−	0.828214i
$887$	3.72251	−	21.1114i	0.124990	−	0.708851i	−0.856325	−	0.516438i	$-0.827258\pi$
$887$	3.72251	−	21.1114i	0.124990	−	0.708851i	0.981314	−	0.192413i	$-0.0616313\pi$
$888$		0			0
$889$	−1.53209	−	1.28558i	−0.0513846	−	0.0431168i
$890$	5.69640	+	32.3059i	0.190944	+	1.08290i
$891$		0			0
$892$	26.2686			0.879537
$893$	8.15745	+	4.79012i	0.272979	+	0.160295i
$894$		0			0
$895$	53.8585	+	19.6029i	1.80029	+	0.655252i
$896$	−0.213011	−	1.20805i	−0.00711620	−	0.0403580i
$897$		0			0
$898$	−17.4388	+	14.6329i	−0.581941	+	0.488306i
$899$	3.54916	−	20.1283i	0.118371	−	0.671317i
$900$		0			0
$901$	24.5822	+	42.5776i	0.818951	+	1.41847i
$902$	−3.18092	+	1.15776i	−0.105913	+	0.0385492i
$903$		0			0
$904$	8.69119	+	15.0536i	0.289065	+	0.500675i
$905$	35.3542	−	61.2352i	1.17521	−	2.03553i
$906$		0			0
$907$	−12.5471	+	10.5283i	−0.416620	+	0.349585i	−0.826875	−	0.562385i	$-0.809884\pi$
$907$	−12.5471	+	10.5283i	−0.416620	+	0.349585i	0.410256	+	0.911971i	$0.365439\pi$
$908$	−14.0706	−	11.8066i	−0.466948	−	0.391816i
$909$		0			0
$910$	2.19207	+	0.797847i	0.0726663	+	0.0264484i
$911$	−28.4502			−0.942596			−0.471298	−	0.881974i	$-0.656214\pi$
$911$	−28.4502			−0.942596			−0.471298	+	0.881974i	$0.656214\pi$
$912$		0			0
$913$	−26.4668			−0.875922
$914$	−1.06196	−	0.386520i	−0.0351264	−	0.0127850i
$915$		0			0
$916$	2.96585	+	2.48865i	0.0979945	+	0.0822271i
$917$	−5.60354	+	4.70193i	−0.185045	+	0.155271i
$918$		0			0
$919$	25.6268	−	44.3869i	0.845349	−	1.46419i	−0.0399689	−	0.999201i	$-0.512726\pi$
$919$	25.6268	−	44.3869i	0.845349	−	1.46419i	0.885318	−	0.464986i	$-0.153941\pi$
$920$	17.3478	+	30.0472i	0.571939	+	0.990627i
$921$		0			0
$922$	12.2001	−	4.44048i	0.401789	−	0.146239i
$923$	0.646612	+	1.11996i	0.0212835	+	0.0368641i
$924$		0			0
$925$	2.95723	−	16.7713i	0.0972332	−	0.551437i
$926$	23.4598	−	19.6851i	0.770936	−	0.646892i
$927$		0			0
$928$	−1.47178	−	8.34689i	−0.0483136	−	0.274000i
$929$	48.4445	+	17.6324i	1.58941	+	0.578499i	0.977223	−	0.212213i	$-0.0680670\pi$
$929$	48.4445	+	17.6324i	1.58941	+	0.578499i	0.612189	+	0.790712i	$0.290289\pi$
$930$		0			0
$931$	−8.35797	+	22.4478i	−0.273922	+	0.735696i
$932$	−16.4466			−0.538725
$933$		0			0
$934$	1.92009	+	10.8894i	0.0628273	+	0.356312i
$935$	34.8632	+	29.2537i	1.14015	+	0.956699i
$936$		0			0
$937$	−2.51161	+	14.2441i	−0.0820508	+	0.465333i	0.915903	+	0.401399i	$0.131476\pi$
$937$	−2.51161	+	14.2441i	−0.0820508	+	0.465333i	−0.997954	+	0.0639341i	$0.979635\pi$
$938$	2.74510	−	4.75465i	0.0896307	−	0.155245i
$939$		0			0
$940$	7.91147	−	2.87954i	0.258044	−	0.0939203i
$941$	−12.3855	+	4.50795i	−0.403755	+	0.146955i	−0.535912	−	0.844274i	$-0.680032\pi$
$941$	−12.3855	+	4.50795i	−0.403755	+	0.146955i	0.132157	+	0.991229i	$0.457810\pi$
$942$		0			0
$943$	7.13816	−	12.3636i	0.232450	−	0.402616i
$944$	1.98293	−	11.2457i	0.0645387	−	0.366017i
$945$		0			0
$946$	10.7836	+	9.04850i	0.350605	+	0.294192i
$947$	7.43676	+	42.1759i	0.241662	+	1.37053i	0.828119	+	0.560553i	$0.189411\pi$
$947$	7.43676	+	42.1759i	0.241662	+	1.37053i	−0.586456	+	0.809981i	$0.699477\pi$
$948$		0			0
$949$	−7.53083			−0.244461
$950$	43.1946	−	7.28893i	1.40142	−	0.236484i
$951$		0			0
$952$	6.37686	+	2.32099i	0.206675	+	0.0752236i
$953$	5.59451	+	31.7281i	0.181224	+	1.02777i	0.930712	+	0.365754i	$0.119189\pi$
$953$	5.59451	+	31.7281i	0.181224	+	1.02777i	−0.749488	+	0.662018i	$0.769700\pi$
$954$		0			0
$955$	−3.83615	+	3.21891i	−0.124135	+	0.104162i
$956$	−0.573978	+	3.25519i	−0.0185638	+	0.105280i
$957$		0			0
$958$	8.81908	+	15.2751i	0.284931	+	0.493516i
$959$	−0.0225934	+	0.00822333i	−0.000729579	+	0.000265545i
$960$		0			0
$961$	12.5924	+	21.8107i	0.406206	+	0.703570i
$962$	0.415345	−	0.719398i	0.0133912	−	0.0231943i
$963$		0			0
$964$	2.30999	−	1.93831i	0.0743999	−	0.0624289i
$965$	−27.1045	−	22.7434i	−0.872524	−	0.732134i
$966$		0			0
$967$	−32.4650	−	11.8163i	−1.04400	−	0.379986i	−0.237607	−	0.971361i	$-0.576363\pi$
$967$	−32.4650	−	11.8163i	−1.04400	−	0.379986i	−0.806396	+	0.591375i	$0.798585\pi$
$968$	6.50299			0.209014
$969$		0			0
$970$	55.7752			1.79083
$971$	−1.11556	−	0.406031i	−0.0358001	−	0.0130302i	0.324058	−	0.946037i	$-0.394953\pi$
$971$	−1.11556	−	0.406031i	−0.0358001	−	0.0130302i	−0.359858	+	0.933007i	$0.617175\pi$
$972$		0			0
$973$	4.22416	+	3.54449i	0.135420	+	0.113631i
$974$	11.7155	−	9.83050i	0.375390	−	0.314990i
$975$		0			0
$976$	−0.0209445	+	0.0362770i	−0.000670418	+	0.00116120i
$977$	10.4413	+	18.0849i	0.334048	+	0.578588i	0.983302	−	0.181984i	$-0.0582519\pi$
$977$	10.4413	+	18.0849i	0.334048	+	0.578588i	−0.649253	+	0.760572i	$0.724919\pi$
$978$		0			0
$979$	16.8506	−	6.13311i	0.538547	−	0.196015i
$980$	10.6591	+	18.4621i	0.340492	+	0.589750i
$981$		0			0
$982$	−0.308811	+	1.75135i	−0.00985455	+	0.0558879i
$983$	26.8855	−	22.5596i	0.857515	−	0.719541i	−0.103916	−	0.994586i	$-0.533137\pi$
$983$	26.8855	−	22.5596i	0.857515	−	0.719541i	0.961431	+	0.275045i	$0.0886928\pi$
$984$		0			0
$985$	−12.5458	−	71.1505i	−0.399741	−	2.26704i
$986$	44.0604	+	16.0367i	1.40317	+	0.510711i
$987$		0			0
$988$	2.10148	+	0.386520i	0.0668570	+	0.0122969i
$989$	−59.3688			−1.88782
$990$		0			0
$991$	−8.63651	−	48.9801i	−0.274348	−	1.55590i	−0.741026	−	0.671476i	$-0.765661\pi$
$991$	−8.63651	−	48.9801i	−0.274348	−	1.55590i	0.466679	−	0.884427i	$-0.345450\pi$
$992$	−1.84730	−	1.55007i	−0.0586517	−	0.0492146i
$993$		0			0
$994$	0.561956	−	3.18701i	0.0178242	−	0.101086i
$995$	−16.3537	+	28.3254i	−0.518447	+	0.897976i
$996$		0			0
$997$	−39.3105	+	14.3079i	−1.24498	+	0.453134i	−0.878701	−	0.477372i	$-0.841589\pi$
$997$	−39.3105	+	14.3079i	−1.24498	+	0.453134i	−0.366275	+	0.930507i	$0.619367\pi$
$998$	−0.101319	+	0.0368771i	−0.00320720	+	0.00116733i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.d.289.1		6
3.2	odd	2		114.2.i.b.61.1	yes	6
12.11	even	2		912.2.bo.c.289.1		6
19.5	even	9	inner	342.2.u.d.271.1		6
19.9	even	9		6498.2.a.bo.1.3		3
19.10	odd	18		6498.2.a.bt.1.3		3
57.5	odd	18		114.2.i.b.43.1	✓	6
57.29	even	18		2166.2.a.n.1.1		3
57.47	odd	18		2166.2.a.t.1.1		3
228.119	even	18		912.2.bo.c.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.43.1	✓	6	57.5	odd	18
114.2.i.b.61.1	yes	6	3.2	odd	2
342.2.u.d.271.1		6	19.5	even	9	inner
342.2.u.d.289.1		6	1.1	even	1	trivial
912.2.bo.c.289.1		6	12.11	even	2
912.2.bo.c.385.1		6	228.119	even	18
2166.2.a.n.1.1		3	57.29	even	18
2166.2.a.t.1.1		3	57.47	odd	18
6498.2.a.bo.1.3		3	19.9	even	9
6498.2.a.bt.1.3		3	19.10	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(2.97178 - 2.49362i) q^{5} +(-0.613341 + 1.06234i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(2.97178 - 2.49362i) q^{5} +(-0.613341 + 1.06234i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.64543 - 1.32683i) q^{10} +(-1.06031 - 1.83651i) q^{11} +(0.0851223 - 0.482753i) q^{13} +(-0.939693 + 0.788496i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-5.19846 - 1.89209i) q^{17} +(2.77719 + 3.35965i) q^{19} +3.87939 q^{20} +(-0.368241 - 2.08840i) q^{22} +(6.85117 + 5.74881i) q^{23} +(1.74510 - 9.89695i) q^{25} +(0.245100 - 0.424525i) q^{26} +(-1.15270 + 0.419550i) q^{28} +(-7.96451 + 2.89884i) q^{29} +(-1.20574 + 2.08840i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-4.23783 - 3.55596i) q^{34} +(0.826352 + 4.68647i) q^{35} +1.69459 q^{37} +(1.46064 + 4.10689i) q^{38} +(3.64543 + 1.32683i) q^{40} +(-0.277189 - 1.57202i) q^{41} +(-5.08512 + 4.26692i) q^{43} +(0.368241 - 2.08840i) q^{44} +(4.47178 + 7.74535i) q^{46} +(2.03936 - 0.742267i) q^{47} +(2.74763 + 4.75903i) q^{49} +(5.02481 - 8.70323i) q^{50} +(0.375515 - 0.315094i) q^{52} +(-6.80793 - 5.71253i) q^{53} +(-7.73055 - 2.81369i) q^{55} -1.22668 q^{56} -8.47565 q^{58} +(-10.7306 - 3.90560i) q^{59} +(0.0320889 + 0.0269258i) q^{61} +(-1.84730 + 1.55007i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.950837 - 1.64690i) q^{65} +(-4.20574 + 1.53076i) q^{67} +(-2.76604 - 4.79093i) q^{68} +(-0.826352 + 4.68647i) q^{70} +(-2.02094 + 1.69577i) q^{71} +(-2.66772 - 15.1294i) q^{73} +(1.59240 + 0.579585i) q^{74} +(-0.0320889 + 4.35878i) q^{76} +2.60132 q^{77} +(-0.809278 - 4.58964i) q^{79} +(2.97178 + 2.49362i) q^{80} +(0.277189 - 1.57202i) q^{82} +(6.24035 - 10.8086i) q^{83} +(-20.1668 + 7.34013i) q^{85} +(-6.23783 + 2.27038i) q^{86} +(1.06031 - 1.83651i) q^{88} +(-1.46838 + 8.32759i) q^{89} +(0.460637 + 0.386520i) q^{91} +(1.55303 + 8.80769i) q^{92} +2.17024 q^{94} +(16.6309 + 3.05888i) q^{95} +(13.5103 + 4.91734i) q^{97} +(0.954241 + 5.41177i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8	\( 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8} + 6 q^{10} - 12 q^{11} - 21 q^{13} - 3 q^{17} + 6 q^{19} + 12 q^{20} + 3 q^{22} + 15 q^{23} + 9 q^{25} - 9 q^{28} - 15 q^{29} + 3 q^{31} - 6 q^{34} + 6 q^{35} + 6 q^{37} + 6 q^{40} + 9 q^{41} - 9 q^{43} - 3 q^{44} + 12 q^{46} + 21 q^{47} + 3 q^{50} + 15 q^{52} - 30 q^{53} - 9 q^{55} + 6 q^{56} - 12 q^{58} - 27 q^{59} - 9 q^{61} - 9 q^{62} - 3 q^{64} + 6 q^{65} - 15 q^{67} - 12 q^{68} - 6 q^{70} - 9 q^{71} + 12 q^{73} + 6 q^{74} + 9 q^{76} - 42 q^{77} + 15 q^{79} + 3 q^{80} - 9 q^{82} + 3 q^{83} - 36 q^{85} - 18 q^{86} + 12 q^{88} + 48 q^{89} - 6 q^{91} - 3 q^{92} - 30 q^{94} + 48 q^{95} + 18 q^{97} + 36 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8 + 6 * q^10 - 12 * q^11 - 21 * q^13 - 3 * q^17 + 6 * q^19 + 12 * q^20 + 3 * q^22 + 15 * q^23 + 9 * q^25 - 9 * q^28 - 15 * q^29 + 3 * q^31 - 6 * q^34 + 6 * q^35 + 6 * q^37 + 6 * q^40 + 9 * q^41 - 9 * q^43 - 3 * q^44 + 12 * q^46 + 21 * q^47 + 3 * q^50 + 15 * q^52 - 30 * q^53 - 9 * q^55 + 6 * q^56 - 12 * q^58 - 27 * q^59 - 9 * q^61 - 9 * q^62 - 3 * q^64 + 6 * q^65 - 15 * q^67 - 12 * q^68 - 6 * q^70 - 9 * q^71 + 12 * q^73 + 6 * q^74 + 9 * q^76 - 42 * q^77 + 15 * q^79 + 3 * q^80 - 9 * q^82 + 3 * q^83 - 36 * q^85 - 18 * q^86 + 12 * q^88 + 48 * q^89 - 6 * q^91 - 3 * q^92 - 30 * q^94 + 48 * q^95 + 18 * q^97 + 36 * q^98

Introduction

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