LMFDB - Embedded newform 405.2.r.a.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			197.1
Character	$\chi$	$=$	405.197
Dual form			405.2.r.a.368.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44518 + 0.213925i) q^{2} +(3.96351 - 0.698873i) q^{4} +(-1.02222 + 1.98874i) q^{5} +(-3.87397 + 2.71258i) q^{7} +(-4.80021 + 1.28621i) q^{8} +O(q^{10})$	\(q+(-2.44518 + 0.213925i) q^{2} +(3.96351 - 0.698873i) q^{4} +(-1.02222 + 1.98874i) q^{5} +(-3.87397 + 2.71258i) q^{7} +(-4.80021 + 1.28621i) q^{8} +(2.07406 - 5.08149i) q^{10} +(-0.927704 - 2.54885i) q^{11} +(0.0885504 - 1.01214i) q^{13} +(8.89224 - 7.46148i) q^{14} +(3.89833 - 1.41887i) q^{16} +(1.15325 + 0.309013i) q^{17} +(0.507294 + 0.292886i) q^{19} +(-2.66169 + 8.59677i) q^{20} +(2.81366 + 6.03392i) q^{22} +(0.750556 - 1.07190i) q^{23} +(-2.91015 - 4.06584i) q^{25} +2.49379i q^{26} +(-13.4587 + 13.4587i) q^{28} +(0.185521 + 0.155671i) q^{29} +(-0.978463 - 5.54914i) q^{31} +(-0.220700 + 0.102914i) q^{32} +(-2.88601 - 0.508881i) q^{34} +(-1.43458 - 10.4771i) q^{35} +(-0.227764 + 0.850028i) q^{37} +(-1.30308 - 0.607636i) q^{38} +(2.34891 - 10.8611i) q^{40} +(2.80103 + 3.33813i) q^{41} +(4.67013 - 10.0151i) q^{43} +(-5.45828 - 9.45402i) q^{44} +(-1.60593 + 2.78156i) q^{46} +(-3.77551 - 5.39198i) q^{47} +(5.25539 - 14.4391i) q^{49} +(7.98561 + 9.31914i) q^{50} +(-0.356385 - 4.07349i) q^{52} +(-6.73617 - 6.73617i) q^{53} +(6.01730 + 0.760513i) q^{55} +(15.1069 - 18.0037i) q^{56} +(-0.486933 - 0.340954i) q^{58} +(-11.1903 - 4.07292i) q^{59} +(-1.40842 + 7.98754i) q^{61} +(3.57962 + 13.3593i) q^{62} +(-6.66780 + 3.84966i) q^{64} +(1.92235 + 1.21073i) q^{65} +(-7.77347 - 0.680090i) q^{67} +(4.78688 + 0.418798i) q^{68} +(5.74912 + 25.3116i) q^{70} +(-1.13442 + 0.654959i) q^{71} +(-0.567144 - 2.11661i) q^{73} +(0.375082 - 2.12719i) q^{74} +(2.21535 + 0.806323i) q^{76} +(10.5078 + 7.35767i) q^{77} +(2.17780 - 2.59540i) q^{79} +(-1.16316 + 9.20314i) q^{80} +(-7.56311 - 7.56311i) q^{82} +(0.839279 + 9.59300i) q^{83} +(-1.79342 + 1.97763i) q^{85} +(-9.27680 + 25.4878i) q^{86} +(7.73153 + 11.0418i) q^{88} +(1.54112 - 2.66930i) q^{89} +(2.40246 + 4.16118i) q^{91} +(2.22571 - 4.77305i) q^{92} +(10.3853 + 12.3767i) q^{94} +(-1.10104 + 0.709481i) q^{95} +(-3.04230 - 1.41865i) q^{97} +(-9.76147 + 36.4303i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−2.44518	+	0.213925i	−1.72900	+	0.151268i	−0.907809	−	0.419384i	$-0.862246\pi$
$2$	−2.44518	+	0.213925i	−1.72900	+	0.151268i	−0.821192	+	0.570652i	$0.806690\pi$
$3$		0			0
$3$		0			0
$4$	3.96351	−	0.698873i	1.98175	−	0.349437i
$5$	−1.02222	+	1.98874i	−0.457149	+	0.889390i
$5$	−1.02222	+	1.98874i	−0.457149	+	0.889390i
$6$		0			0
$7$	−3.87397	+	2.71258i	−1.46422	+	1.02526i	−0.474816	+	0.880085i	$0.657485\pi$
$7$	−3.87397	+	2.71258i	−1.46422	+	1.02526i	−0.989406	+	0.145174i	$0.953626\pi$
$8$	−4.80021	+	1.28621i	−1.69713	+	0.454744i
$9$		0			0
$10$	2.07406	−	5.08149i	0.655875	−	1.60691i
$11$	−0.927704	−	2.54885i	−0.279713	−	0.768506i	−0.997395	−	0.0721346i	$-0.977019\pi$
$11$	−0.927704	−	2.54885i	−0.279713	−	0.768506i	0.717682	−	0.696371i	$-0.245203\pi$
$12$		0			0
$13$	0.0885504	−	1.01214i	0.0245595	−	0.280716i	−0.973978	−	0.226644i	$-0.927224\pi$
$13$	0.0885504	−	1.01214i	0.0245595	−	0.280716i	0.998537	−	0.0540717i	$-0.0172200\pi$
$14$	8.89224	−	7.46148i	2.37655	−	1.99416i
$15$		0			0
$16$	3.89833	−	1.41887i	0.974582	−	0.354719i
$17$	1.15325	+	0.309013i	0.279704	+	0.0749466i	0.395944	−	0.918275i	$-0.370417\pi$
$17$	1.15325	+	0.309013i	0.279704	+	0.0749466i	−0.116240	+	0.993221i	$0.537084\pi$
$18$		0			0
$19$	0.507294	+	0.292886i	0.116381	+	0.0671927i	0.557061	−	0.830472i	$-0.311929\pi$
$19$	0.507294	+	0.292886i	0.116381	+	0.0671927i	−0.440679	+	0.897665i	$0.645262\pi$
$20$	−2.66169	+	8.59677i	−0.595171	+	1.92230i
$21$		0			0
$22$	2.81366	+	6.03392i	0.599875	+	1.28644i
$23$	0.750556	−	1.07190i	0.156502	−	0.223508i	−0.733242	−	0.679967i	$-0.761994\pi$
$23$	0.750556	−	1.07190i	0.156502	−	0.223508i	0.889744	+	0.456460i	$0.150883\pi$
$24$		0			0
$25$	−2.91015	−	4.06584i	−0.582030	−	0.813168i
$26$			2.49379i			0.489073i
$27$		0			0
$28$	−13.4587	+	13.4587i	−2.54346	+	2.54346i
$29$	0.185521	+	0.155671i	0.0344504	+	0.0289073i	0.659850	−	0.751397i	$-0.270620\pi$
$29$	0.185521	+	0.155671i	0.0344504	+	0.0289073i	−0.625400	+	0.780304i	$0.715064\pi$
$30$		0			0
$31$	−0.978463	−	5.54914i	−0.175737	−	0.996655i	−0.937290	−	0.348552i	$-0.886674\pi$
$31$	−0.978463	−	5.54914i	−0.175737	−	0.996655i	0.761552	−	0.648103i	$-0.224438\pi$
$32$	−0.220700	+	0.102914i	−0.0390146	+	0.0181928i
$33$		0			0
$34$	−2.88601	−	0.508881i	−0.494946	−	0.0872724i
$35$	−1.43458	−	10.4771i	−0.242488	−	1.77096i
$36$		0			0
$37$	−0.227764	+	0.850028i	−0.0374442	+	0.139744i	−0.982117	−	0.188269i	$-0.939712\pi$
$37$	−0.227764	+	0.850028i	−0.0374442	+	0.139744i	0.944673	+	0.328013i	$0.106379\pi$
$38$	−1.30308	−	0.607636i	−0.211387	−	0.0985715i
$39$		0			0
$40$	2.34891	−	10.8611i	0.371396	−	1.71730i
$41$	2.80103	+	3.33813i	0.437447	+	0.521329i	0.939055	−	0.343766i	$-0.111703\pi$
$41$	2.80103	+	3.33813i	0.437447	+	0.521329i	−0.501609	+	0.865095i	$0.667258\pi$
$42$		0			0
$43$	4.67013	−	10.0151i	0.712188	−	1.52729i	−0.132002	−	0.991249i	$-0.542141\pi$
$43$	4.67013	−	10.0151i	0.712188	−	1.52729i	0.844191	−	0.536043i	$-0.180082\pi$
$44$	−5.45828	−	9.45402i	−0.822867	−	1.42525i
$45$		0			0
$46$	−1.60593	+	2.78156i	−0.236782	+	0.410118i
$47$	−3.77551	−	5.39198i	−0.550714	−	0.786501i	0.443228	−	0.896409i	$-0.353833\pi$
$47$	−3.77551	−	5.39198i	−0.550714	−	0.786501i	−0.993942	+	0.109908i	$0.964944\pi$
$48$		0			0
$49$	5.25539	−	14.4391i	0.750770	−	2.06272i
$50$	7.98561	+	9.31914i	1.12934	+	1.31793i
$51$		0			0
$52$	−0.356385	−	4.07349i	−0.0494217	−	0.564892i
$53$	−6.73617	−	6.73617i	−0.925284	−	0.925284i	0.0721125	−	0.997397i	$-0.477026\pi$
$53$	−6.73617	−	6.73617i	−0.925284	−	0.925284i	−0.997397	+	0.0721125i	$0.977026\pi$
$54$		0			0
$55$	6.01730	+	0.760513i	0.811372	+	0.102548i
$56$	15.1069	−	18.0037i	2.01874	−	2.40584i
$57$		0			0
$58$	−0.486933	−	0.340954i	−0.0639375	−	0.0447695i
$59$	−11.1903	−	4.07292i	−1.45685	−	0.530250i	−0.512354	−	0.858775i	$-0.671226\pi$
$59$	−11.1903	−	4.07292i	−1.45685	−	0.530250i	−0.944495	+	0.328525i	$0.893449\pi$
$60$		0			0
$61$	−1.40842	+	7.98754i	−0.180330	+	1.02270i	0.751481	+	0.659755i	$0.229340\pi$
$61$	−1.40842	+	7.98754i	−0.180330	+	1.02270i	−0.931811	+	0.362945i	$0.881771\pi$
$62$	3.57962	+	13.3593i	0.454612	+	1.69663i
$63$		0			0
$64$	−6.66780	+	3.84966i	−0.833475	+	0.481207i
$65$	1.92235	+	1.21073i	0.238439	+	0.150172i
$66$		0			0
$67$	−7.77347	−	0.680090i	−0.949680	−	0.0830863i	−0.398222	−	0.917289i	$-0.630373\pi$
$67$	−7.77347	−	0.680090i	−0.949680	−	0.0830863i	−0.551458	+	0.834203i	$0.685928\pi$
$68$	4.78688	+	0.418798i	0.580494	+	0.0507867i
$69$		0			0
$70$	5.74912	+	25.3116i	0.687151	+	3.02531i
$71$	−1.13442	+	0.654959i	−0.134631	+	0.0777293i	−0.565803	−	0.824541i	$-0.691434\pi$
$71$	−1.13442	+	0.654959i	−0.134631	+	0.0777293i	0.431172	+	0.902270i	$0.358100\pi$
$72$		0			0
$73$	−0.567144	−	2.11661i	−0.0663792	−	0.247730i	0.924761	−	0.380547i	$-0.124264\pi$
$73$	−0.567144	−	2.11661i	−0.0663792	−	0.247730i	−0.991141	+	0.132817i	$0.957598\pi$
$74$	0.375082	−	2.12719i	0.0436024	−	0.247281i
$75$		0			0
$76$	2.21535	+	0.806323i	0.254119	+	0.0924916i
$77$	10.5078	+	7.35767i	1.19748	+	0.838485i
$78$		0			0
$79$	2.17780	−	2.59540i	0.245022	−	0.292006i	−0.629491	−	0.777008i	$-0.716737\pi$
$79$	2.17780	−	2.59540i	0.245022	−	0.292006i	0.874513	+	0.485002i	$0.161181\pi$
$80$	−1.16316	+	9.20314i	−0.130046	+	1.02894i
$81$		0			0
$82$	−7.56311	−	7.56311i	−0.835206	−	0.835206i
$83$	0.839279	+	9.59300i	0.0921228	+	1.05297i	0.891767	+	0.452495i	$0.149466\pi$
$83$	0.839279	+	9.59300i	0.0921228	+	1.05297i	−0.799644	+	0.600474i	$0.794979\pi$
$84$		0			0
$85$	−1.79342	+	1.97763i	−0.194523	+	0.214505i
$86$	−9.27680	+	25.4878i	−1.00034	+	2.74842i
$87$		0			0
$88$	7.73153	+	11.0418i	0.824183	+	1.17706i
$89$	1.54112	−	2.66930i	0.163359	−	0.282945i	−0.772713	−	0.634756i	$-0.781101\pi$
$89$	1.54112	−	2.66930i	0.163359	−	0.282945i	0.936071	+	0.351811i	$0.114434\pi$
$90$		0			0
$91$	2.40246	+	4.16118i	0.251846	+	0.436211i
$92$	2.22571	−	4.77305i	0.232046	−	0.497624i
$93$		0			0
$94$	10.3853	+	12.3767i	1.07116	+	1.27656i
$95$	−1.10104	+	0.709481i	−0.112964	+	0.0727912i
$96$		0			0
$97$	−3.04230	−	1.41865i	−0.308899	−	0.144042i	0.261987	−	0.965071i	$-0.415622\pi$
$97$	−3.04230	−	1.41865i	−0.308899	−	0.144042i	−0.570886	+	0.821030i	$0.693400\pi$
$98$	−9.76147	+	36.4303i	−0.986057	+	3.68002i
$99$		0			0
$100$	−14.3759	−	14.0812i	−1.43759	−	1.40812i
$101$	7.00303	+	1.23482i	0.696828	+	0.122870i	0.510831	−	0.859681i	$-0.329338\pi$
$101$	7.00303	+	1.23482i	0.696828	+	0.122870i	0.185996	+	0.982550i	$0.440449\pi$
$102$		0			0
$103$	−13.2831	+	6.19401i	−1.30882	+	0.610314i	−0.946790	−	0.321852i	$-0.895695\pi$
$103$	−13.2831	+	6.19401i	−1.30882	+	0.610314i	−0.362032	+	0.932166i	$0.617917\pi$
$104$	0.876761	+	4.97236i	0.0859735	+	0.487580i
$105$		0			0
$106$	17.9122	+	15.0301i	1.73978	+	1.45985i
$107$	6.31758	−	6.31758i	0.610743	−	0.610743i	−0.332397	−	0.943140i	$-0.607857\pi$
$107$	6.31758	−	6.31758i	0.610743	−	0.610743i	0.943140	+	0.332397i	$0.107857\pi$
$108$		0			0
$109$			8.92248i			0.854618i	0.904106	+	0.427309i	$0.140538\pi$
$109$			8.92248i			0.854618i	−0.904106	+	0.427309i	$0.859462\pi$
$110$	−14.8760	−	0.572336i	−1.41838	−	0.0545701i
$111$		0			0
$112$	−11.2532	+	16.0712i	−1.06333	+	1.51859i
$113$	−1.37886	−	2.95698i	−0.129713	−	0.278169i	0.830716	−	0.556697i	$-0.187931\pi$
$113$	−1.37886	−	2.95698i	−0.129713	−	0.278169i	−0.960428	+	0.278527i	$0.910154\pi$
$114$		0			0
$115$	1.36451	+	2.58838i	0.127241	+	0.241367i
$116$	0.844108	+	0.487346i	0.0783734	+	0.0452489i
$117$		0			0
$118$	28.2335	+	7.56514i	2.59910	+	0.696427i
$119$	−5.30588	+	1.93118i	−0.486389	+	0.177031i
$120$		0			0
$121$	2.79051	−	2.34151i	0.253683	−	0.212865i
$122$	1.73510	−	19.8322i	0.157088	−	1.79553i
$123$		0			0
$124$	−7.75629	−	21.3102i	−0.696536	−	1.91372i
$125$	11.0607	−	1.63135i	0.989298	−	0.145912i
$126$		0			0
$127$	12.7720	−	3.42225i	1.13333	−	0.303676i	0.357065	−	0.934079i	$-0.383777\pi$
$127$	12.7720	−	3.42225i	1.13333	−	0.303676i	0.776267	+	0.630404i	$0.217111\pi$
$128$	15.8794	−	11.1188i	1.40355	−	0.982777i
$129$		0			0
$130$	−4.95950	−	2.54920i	−0.434977	−	0.223579i
$131$	0.581695	−	0.102569i	0.0508229	−	0.00896145i	−0.148179	−	0.988961i	$-0.547341\pi$
$131$	0.581695	−	0.102569i	0.0508229	−	0.00896145i	0.199002	+	0.979999i	$0.436230\pi$
$132$		0			0
$133$	−2.75972	+	0.241444i	−0.239298	+	0.0209359i
$134$	19.1530			1.65457
$135$		0			0
$136$	−5.93330			−0.508776
$137$	−17.1355	+	1.49916i	−1.46398	+	0.128082i	−0.791110	−	0.611674i	$-0.790496\pi$
$137$	−17.1355	+	1.49916i	−1.46398	+	0.128082i	−0.672875	+	0.739756i	$0.734941\pi$
$138$		0			0
$139$	−11.8215	+	2.08444i	−1.00268	+	0.176800i	−0.650804	−	0.759246i	$-0.725568\pi$
$139$	−11.8215	+	2.08444i	−1.00268	+	0.176800i	−0.351878	+	0.936046i	$0.614457\pi$
$140$	−13.0082	−	40.5237i	−1.09939	−	3.42487i
$141$		0			0
$142$	2.63375	−	1.84417i	0.221019	−	0.154759i
$143$	−2.66193	+	0.713261i	−0.222602	+	0.0596459i
$144$		0			0
$145$	−0.499230	+	0.209823i	−0.0414588	+	0.0174249i
$146$	1.83956	+	5.05416i	0.152243	+	0.418285i
$147$		0			0
$148$	−0.308684	+	3.52827i	−0.0253737	+	0.290022i
$149$	−7.50454	+	6.29706i	−0.614796	+	0.515875i	−0.896163	−	0.443725i	$-0.853657\pi$
$149$	−7.50454	+	6.29706i	−0.614796	+	0.515875i	0.281367	+	0.959600i	$0.409212\pi$
$150$		0			0
$151$	−14.4897	+	5.27382i	−1.17916	+	0.429178i	−0.855904	−	0.517135i	$-0.826998\pi$
$151$	−14.4897	+	5.27382i	−1.17916	+	0.429178i	−0.323252	+	0.946313i	$0.604776\pi$
$152$	−2.81183	−	0.753427i	−0.228069	−	0.0611110i
$153$		0			0
$154$	−27.2675	−	15.7429i	−2.19728	−	1.26860i
$155$	12.0360	+	3.72652i	0.966753	+	0.299321i
$156$		0			0
$157$	7.14630	+	15.3253i	0.570337	+	1.22309i	0.954052	+	0.299640i	$0.0968664\pi$
$157$	7.14630	+	15.3253i	0.570337	+	1.22309i	−0.383716	+	0.923451i	$0.625356\pi$
$158$	−4.76989	+	6.81211i	−0.379472	+	0.541942i
$159$		0			0
$160$	0.0209341	−	0.544114i	0.00165498	−	0.0430160i
$161$			6.18847i			0.487720i
$162$		0			0
$163$	7.64324	−	7.64324i	0.598665	−	0.598665i	−0.341293	−	0.939957i	$-0.610865\pi$
$163$	7.64324	−	7.64324i	0.598665	−	0.598665i	0.939957	+	0.341293i	$0.110865\pi$
$164$	13.4348	+	11.2731i	1.04908	+	0.880285i
$165$		0			0
$166$	−4.10437	−	23.2770i	−0.318561	−	1.80665i
$167$	0.952493	−	0.444155i	0.0737061	−	0.0343697i	−0.385416	−	0.922743i	$-0.625942\pi$
$167$	0.952493	−	0.444155i	0.0737061	−	0.0343697i	0.459122	+	0.888373i	$0.348164\pi$
$168$		0			0
$169$	11.7859	+	2.07818i	0.906609	+	0.159860i
$170$	3.96215	−	5.21932i	0.303883	−	0.400304i
$171$		0			0
$172$	11.5108	−	42.9589i	0.877690	−	3.27558i
$173$	−16.6052	−	7.74314i	−1.26247	−	0.588700i	−0.327979	−	0.944685i	$-0.606368\pi$
$173$	−16.6052	−	7.74314i	−1.26247	−	0.588700i	−0.934492	+	0.355985i	$0.884145\pi$
$174$		0			0
$175$	22.3027	+	7.85691i	1.68593	+	0.593927i
$176$	−7.23299	−	8.61994i	−0.545207	−	0.649752i
$177$		0			0
$178$	−3.19728	+	6.85659i	−0.239646	+	0.513923i
$179$	−4.22807	−	7.32323i	−0.316021	−	0.547364i	0.663633	−	0.748058i	$-0.269014\pi$
$179$	−4.22807	−	7.32323i	−0.316021	−	0.547364i	−0.979654	+	0.200694i	$0.935680\pi$
$180$		0			0
$181$	0.511902	−	0.886641i	0.0380494	−	0.0659035i	−0.846374	−	0.532590i	$-0.821219\pi$
$181$	0.511902	−	0.886641i	0.0380494	−	0.0659035i	0.884423	+	0.466686i	$0.154552\pi$
$182$	−6.76462	−	9.66088i	−0.501427	−	0.716112i
$183$		0			0
$184$	−2.22413	+	6.11074i	−0.163965	+	0.450489i
$185$	−1.45766	−	1.32188i	−0.107169	−	0.0971863i
$186$		0			0
$187$	−0.282250	−	3.22613i	−0.0206402	−	0.235918i
$188$	−18.7326	−	18.7326i	−1.36621	−	1.36621i
$189$		0			0
$190$	2.54046	−	1.97035i	0.184304	−	0.142944i
$191$	−2.57471	+	3.06842i	−0.186300	+	0.222023i	−0.851108	−	0.524991i	$-0.824069\pi$
$191$	−2.57471	+	3.06842i	−0.186300	+	0.222023i	0.664808	+	0.747014i	$0.268513\pi$
$192$		0			0
$193$	0.199928	+	0.139991i	0.0143911	+	0.0100768i	0.580750	−	0.814082i	$-0.302759\pi$
$193$	0.199928	+	0.139991i	0.0143911	+	0.0100768i	−0.566359	+	0.824159i	$0.691648\pi$
$194$	7.74244	+	2.81802i	0.555875	+	0.202322i
$195$		0			0
$196$	10.7387	−	60.9022i	0.767050	−	4.35015i
$197$	2.46125	+	9.18550i	0.175357	+	0.654440i	0.996491	+	0.0837043i	$0.0266751\pi$
$197$	2.46125	+	9.18550i	0.175357	+	0.654440i	−0.821134	+	0.570735i	$0.806658\pi$
$198$		0			0
$199$	4.26708	−	2.46360i	0.302486	−	0.174640i	−0.341073	−	0.940037i	$-0.610790\pi$
$199$	4.26708	−	2.46360i	0.302486	−	0.174640i	0.643559	+	0.765397i	$0.277457\pi$
$200$	19.1988	+	15.7738i	1.35756	+	1.11538i
$201$		0			0
$202$	−17.3878	−	1.52124i	−1.22340	−	0.107034i
$203$	−1.14097	−	0.0998220i	−0.0800805	−	0.00700613i
$204$		0			0
$205$	−9.50192	+	2.15821i	−0.663643	+	0.150736i
$206$	31.1544	−	17.9870i	2.17063	−	1.25322i
$207$		0			0
$208$	−1.09090	−	4.07128i	−0.0756400	−	0.282292i
$209$	0.275903	−	1.56473i	0.0190846	−	0.108234i
$210$		0			0
$211$	−24.7804	−	9.01933i	−1.70595	−	0.620916i	−0.709472	−	0.704734i	$-0.751066\pi$
$211$	−24.7804	−	9.01933i	−1.70595	−	0.620916i	−0.996481	+	0.0838177i	$0.973289\pi$
$212$	−31.4066	−	21.9911i	−2.15701	−	1.51036i
$213$		0			0
$214$	−14.0961	+	16.7991i	−0.963589	+	1.14836i
$215$	15.1436	+	19.5253i	1.03278	+	1.33161i
$216$		0			0
$217$	18.8430	+	18.8430i	1.27915	+	1.27915i
$218$	−1.90874	−	21.8170i	−0.129276	−	1.47764i
$219$		0			0
$220$	24.3811	−	1.19103i	1.64377	−	0.0802993i
$221$	0.414884	−	1.13988i	0.0279081	−	0.0766769i
$222$		0			0
$223$	−1.66646	−	2.37995i	−0.111594	−	0.159373i	0.759470	−	0.650543i	$-0.225459\pi$
$223$	−1.66646	−	2.37995i	−0.111594	−	0.159373i	−0.871064	+	0.491169i	$0.836570\pi$
$224$	0.575821	−	0.997351i	0.0384737	−	0.0666383i
$225$		0			0
$226$	4.00414	+	6.93537i	0.266351	+	0.461334i
$227$	5.72184	−	12.2705i	0.379772	−	0.814424i	−0.619788	−	0.784769i	$-0.712782\pi$
$227$	5.72184	−	12.2705i	0.379772	−	0.814424i	0.999560	−	0.0296545i	$-0.00944070\pi$
$228$		0			0
$229$	−6.17868	−	7.36346i	−0.408298	−	0.486591i	0.522233	−	0.852803i	$-0.325099\pi$
$229$	−6.17868	−	7.36346i	−0.408298	−	0.486591i	−0.930532	+	0.366212i	$0.880655\pi$
$230$	−3.89018	−	6.03713i	−0.256511	−	0.398077i
$231$		0			0
$232$	−1.09076	−	0.508632i	−0.0716122	−	0.0333933i
$233$	4.61537	−	17.2248i	0.302363	−	1.12843i	−0.632829	−	0.774292i	$-0.718106\pi$
$233$	4.61537	−	17.2248i	0.302363	−	1.12843i	0.935192	−	0.354142i	$-0.115227\pi$
$234$		0			0
$235$	14.5826	−	1.99672i	0.951265	−	0.130251i
$236$	−47.1992	−	8.32249i	−3.07240	−	0.541748i
$237$		0			0
$238$	12.5607	−	5.85714i	0.814188	−	0.379662i
$239$	4.22324	+	23.9512i	0.273179	+	1.54927i	0.744688	+	0.667412i	$0.232598\pi$
$239$	4.22324	+	23.9512i	0.273179	+	1.54927i	−0.471510	+	0.881861i	$0.656291\pi$
$240$		0			0
$241$	5.17529	+	4.34259i	0.333370	+	0.279731i	0.794071	−	0.607825i	$-0.207958\pi$
$241$	5.17529	+	4.34259i	0.333370	+	0.279731i	−0.460701	+	0.887555i	$0.652402\pi$
$242$	−6.32237	+	6.32237i	−0.406418	+	0.406418i
$243$		0			0
$244$			32.6430i			2.08975i
$245$	23.3433	+	25.2114i	1.49135	+	1.61070i
$246$		0			0
$247$	0.341362	−	0.487515i	0.0217203	−	0.0310199i
$248$	11.8342	+	25.3785i	0.751472	+	1.61154i
$249$		0			0
$250$	−26.6963	+	6.35510i	−1.68842	+	0.401932i
$251$	−22.8066	−	13.1674i	−1.43954	−	0.831118i	−0.441721	−	0.897152i	$-0.645632\pi$
$251$	−22.8066	−	13.1674i	−1.43954	−	0.831118i	−0.997817	+	0.0660346i	$0.978965\pi$
$252$		0			0
$253$	−3.42841	−	0.918641i	−0.215543	−	0.0577544i
$254$	−30.4977	+	11.1003i	−1.91360	+	0.696492i
$255$		0			0
$256$	−24.6532	+	20.6865i	−1.54083	+	1.29291i
$257$	−1.41734	+	16.2002i	−0.0884111	+	1.01054i	0.814342	+	0.580385i	$0.197098\pi$
$257$	−1.41734	+	16.2002i	−0.0884111	+	1.01054i	−0.902753	+	0.430158i	$0.858458\pi$
$258$		0			0
$259$	−1.42342	−	3.91081i	−0.0884470	−	0.243006i
$260$	8.46541	+	3.45524i	0.525003	+	0.214285i
$261$		0			0
$262$	−1.40040	+	0.375237i	−0.0865173	+	0.0231822i
$263$	−5.48334	+	3.83947i	−0.338117	+	0.236752i	−0.730287	−	0.683141i	$-0.760613\pi$
$263$	−5.48334	+	3.83947i	−0.338117	+	0.236752i	0.392170	+	0.919893i	$0.371725\pi$
$264$		0			0
$265$	20.2823	−	6.51065i	1.24593	−	0.399946i
$266$	6.69635	−	1.18075i	0.410579	−	0.0723962i
$267$		0			0
$268$	−31.2855	+	2.73713i	−1.91107	+	0.167197i
$269$	−3.20425			−0.195366			−0.0976832	−	0.995218i	$-0.531143\pi$
$269$	−3.20425			−0.195366			−0.0976832	+	0.995218i	$0.531143\pi$
$270$		0			0
$271$	−29.5892			−1.79742			−0.898709	−	0.438546i	$-0.855494\pi$
$271$	−29.5892			−1.79742			−0.898709	+	0.438546i	$0.855494\pi$
$272$	4.93420	−	0.431686i	0.299180	−	0.0261748i
$273$		0			0
$274$	41.5786	−	7.33143i	2.51186	−	0.442908i
$275$	−7.66344	+	11.1894i	−0.462123	+	0.674747i
$276$		0			0
$277$	7.72074	−	5.40612i	0.463895	−	0.324822i	−0.318155	−	0.948039i	$-0.603063\pi$
$277$	7.72074	−	5.40612i	0.463895	−	0.324822i	0.782050	+	0.623216i	$0.214174\pi$
$278$	28.4596	−	7.62573i	1.70689	−	0.457361i
$279$		0			0
$280$	20.3621	+	48.4473i	1.21687	+	2.89528i
$281$	−0.877392	−	2.41061i	−0.0523408	−	0.143805i	0.910767	−	0.412920i	$-0.135491\pi$
$281$	−0.877392	−	2.41061i	−0.0523408	−	0.143805i	−0.963108	+	0.269115i	$0.913269\pi$
$282$		0			0
$283$	1.56435	−	17.8806i	0.0929908	−	1.06289i	−0.796102	−	0.605163i	$-0.793108\pi$
$283$	1.56435	−	17.8806i	0.0929908	−	1.06289i	0.889093	−	0.457727i	$-0.151336\pi$
$284$	−4.03856	+	3.38875i	−0.239644	+	0.201085i
$285$		0			0
$286$	6.35630	−	2.31350i	0.375856	−	0.136800i
$287$	−19.9060	−	5.33381i	−1.17502	−	0.314845i
$288$		0			0
$289$	−13.4879	−	7.78726i	−0.793408	−	0.458074i
$290$	1.17582	−	0.619853i	0.0690465	−	0.0363990i
$291$		0			0
$292$	−3.72712	−	7.99284i	−0.218113	−	0.467745i
$293$	14.0808	−	20.1095i	0.822609	−	1.17481i	−0.159631	−	0.987177i	$-0.551030\pi$
$293$	14.0808	−	20.1095i	0.822609	−	1.17481i	0.982240	−	0.187630i	$-0.0600807\pi$
$294$		0			0
$295$	19.5389	−	18.0911i	1.13760	−	1.05330i
$296$		−	4.37326i		−	0.254191i
$297$		0			0
$298$	17.0028	−	17.0028i	0.984947	−	0.984947i
$299$	−1.01845	−	0.854582i	−0.0588986	−	0.0494218i
$300$		0			0
$301$	9.07491	+	51.4664i	0.523069	+	2.96647i
$302$	34.3017	−	15.9951i	1.97384	−	0.920417i
$303$		0			0
$304$	2.39317	+	0.421980i	0.137258	+	0.0242022i
$305$	−14.4454	−	10.9660i	−0.827142	−	0.627910i
$306$		0			0
$307$	−5.03134	+	18.7772i	−0.287154	+	1.07167i	0.660097	+	0.751180i	$0.270515\pi$
$307$	−5.03134	+	18.7772i	−0.287154	+	1.07167i	−0.947251	+	0.320493i	$0.896151\pi$
$308$	46.7900	+	21.8185i	2.66611	+	1.24323i
$309$		0			0
$310$	−30.2273	−	6.53719i	−1.71680	−	0.371287i
$311$	3.69580	+	4.40448i	0.209569	+	0.249755i	0.860582	−	0.509312i	$-0.170100\pi$
$311$	3.69580	+	4.40448i	0.209569	+	0.249755i	−0.651013	+	0.759067i	$0.725656\pi$
$312$		0			0
$313$	4.98349	−	10.6871i	0.281683	−	0.604072i	−0.713657	−	0.700495i	$-0.752963\pi$
$313$	4.98349	−	10.6871i	0.281683	−	0.604072i	0.995340	+	0.0964234i	$0.0307403\pi$
$314$	−20.7524	−	35.9442i	−1.17113	−	2.02845i
$315$		0			0
$316$	6.81788	−	11.8089i	0.383536	−	0.664303i
$317$	7.97058	+	11.3832i	0.447672	+	0.639342i	0.978038	−	0.208427i	$-0.0668343\pi$
$317$	7.97058	+	11.3832i	0.447672	+	0.639342i	−0.530366	+	0.847769i	$0.677945\pi$
$318$		0			0
$319$	0.224672	−	0.617281i	0.0125792	−	0.0345611i
$320$	−0.840019	−	17.1957i	−0.0469585	−	0.961268i
$321$		0			0
$322$	−1.32387	−	15.1319i	−0.0737763	−	0.843268i
$323$	0.494532	+	0.494532i	0.0275165	+	0.0275165i
$324$		0			0
$325$	−4.37288	+	2.58543i	−0.242564	+	0.143414i
$326$	−17.0540	+	20.3241i	−0.944533	+	1.12565i
$327$		0			0
$328$	−17.7390	−	12.4210i	−0.979475	−	0.685836i
$329$	29.2524	+	10.6470i	1.61274	+	0.586988i
$330$		0			0
$331$	5.48482	−	31.1060i	0.301473	−	1.70974i	−0.338185	−	0.941080i	$-0.609813\pi$
$331$	5.48482	−	31.1060i	0.301473	−	1.70974i	0.639658	−	0.768659i	$-0.279076\pi$
$332$	10.0308	+	37.4354i	0.550511	+	2.05453i
$333$		0			0
$334$	−2.23400	+	1.28980i	−0.122239	+	0.0705747i
$335$	9.29869	−	14.7642i	0.508041	−	0.806653i
$336$		0			0
$337$	3.38108	+	0.295807i	0.184179	+	0.0161136i	0.178872	−	0.983872i	$-0.442755\pi$
$337$	3.38108	+	0.295807i	0.184179	+	0.0161136i	0.00530714	+	0.999986i	$0.498311\pi$
$338$	−29.2632	−	2.56020i	−1.59171	−	0.139257i
$339$		0			0
$340$	−5.72610	+	9.09174i	−0.310542	+	0.493069i
$341$	−13.2362	+	7.64191i	−0.716779	+	0.413833i
$342$		0			0
$343$	10.2398	+	38.2154i	0.552897	+	2.06344i
$344$	−9.53602	+	54.0814i	−0.514148	+	2.91588i
$345$		0			0
$346$	42.2591	+	15.3811i	2.27186	+	0.826891i
$347$	−28.6368	−	20.0517i	−1.53730	−	1.07643i	−0.966928	−	0.255048i	$-0.917909\pi$
$347$	−28.6368	−	20.0517i	−1.53730	−	1.07643i	−0.570376	−	0.821384i	$-0.693202\pi$
$348$		0			0
$349$	−14.2588	+	16.9930i	−0.763258	+	0.909615i	−0.998049	−	0.0624307i	$-0.980115\pi$
$349$	−14.2588	+	16.9930i	−0.763258	+	0.909615i	0.234792	+	0.972046i	$0.424559\pi$
$350$	−56.2149	−	14.4404i	−3.00481	−	0.771873i
$351$		0			0
$352$	0.467056	+	0.467056i	0.0248942	+	0.0248942i
$353$	2.38887	+	27.3049i	0.127147	+	1.45330i	0.745033	+	0.667028i	$0.232434\pi$
$353$	2.38887	+	27.3049i	0.127147	+	1.45330i	−0.617886	+	0.786268i	$0.712011\pi$
$354$		0			0
$355$	−0.142916	−	2.92558i	−0.00758520	−	0.155274i
$356$	4.24274	−	11.6568i	0.224865	−	0.617811i
$357$		0			0
$358$	11.9050	+	17.0021i	0.629199	+	0.898589i
$359$	1.15564	−	2.00162i	0.0609923	−	0.105642i	−0.833917	−	0.551890i	$-0.813907\pi$
$359$	1.15564	−	2.00162i	0.0609923	−	0.105642i	0.894909	+	0.446248i	$0.147240\pi$
$360$		0			0
$361$	−9.32844	−	16.1573i	−0.490970	−	0.850385i
$362$	−1.06202	+	2.27750i	−0.0558184	+	0.119703i
$363$		0			0
$364$	12.4303	+	14.8139i	0.651525	+	0.776458i
$365$	4.78912	+	1.03573i	0.250674	+	0.0542128i
$366$		0			0
$367$	28.2899	+	13.1918i	1.47672	+	0.688607i	0.983435	−	0.181259i	$-0.0580172\pi$
$367$	28.2899	+	13.1918i	1.47672	+	0.688607i	0.493288	+	0.869866i	$0.335795\pi$
$368$	1.40501	−	5.24358i	0.0732414	−	0.273340i
$369$		0			0
$370$	3.84701	+	2.92039i	0.199997	+	0.151824i
$371$	44.3681	+	7.82330i	2.30348	+	0.406165i
$372$		0			0
$373$	−29.3777	+	13.6991i	−1.52112	+	0.709310i	−0.990399	−	0.138237i	$-0.955857\pi$
$373$	−29.3777	+	13.6991i	−1.52112	+	0.709310i	−0.530721	+	0.847547i	$0.678079\pi$
$374$	1.38030	+	7.82808i	0.0713737	+	0.404780i
$375$		0			0
$376$	25.0584	+	21.0265i	1.29229	+	1.08436i
$377$	0.173988	−	0.173988i	0.00896083	−	0.00896083i
$378$		0			0
$379$		−	4.84696i		−	0.248972i	−0.992221	−	0.124486i	$-0.960272\pi$
$379$		−	4.84696i		−	0.248972i	0.992221	−	0.124486i	$-0.0397282\pi$
$380$	−3.86814	+	3.58152i	−0.198431	+	0.183728i
$381$		0			0
$382$	5.63921	−	8.05362i	0.288527	−	0.412059i
$383$	−5.21058	−	11.1741i	−0.266248	−	0.570971i	0.727046	−	0.686589i	$-0.240893\pi$
$383$	−5.21058	−	11.1741i	−0.266248	−	0.570971i	−0.993294	+	0.115618i	$0.963115\pi$
$384$		0			0
$385$	−25.3738	+	13.3762i	−1.29317	+	0.681715i
$386$	−0.518806	−	0.299533i	−0.0264065	−	0.0152458i
$387$		0			0
$388$	−13.0496	−	3.49664i	−0.662495	−	0.177515i
$389$	11.2960	−	4.11142i	0.572732	−	0.208457i	−0.0393859	−	0.999224i	$-0.512540\pi$
$389$	11.2960	−	4.11142i	0.572732	−	0.208457i	0.612118	+	0.790767i	$0.290318\pi$
$390$		0			0
$391$	1.19681	−	1.00424i	0.0605253	−	0.0507868i
$392$	−6.65526	+	76.0700i	−0.336141	+	3.84211i
$393$		0			0
$394$	−7.98319	−	21.9336i	−0.402187	−	1.10500i
$395$	2.93539	+	6.98414i	0.147696	+	0.351410i
$396$		0			0
$397$	−16.1554	+	4.32882i	−0.810815	+	0.217257i	−0.640327	−	0.768103i	$-0.721201\pi$
$397$	−16.1554	+	4.32882i	−0.810815	+	0.217257i	−0.170488	+	0.985360i	$0.554534\pi$
$398$	−9.90675	+	6.93678i	−0.496580	+	0.347709i
$399$		0			0
$400$	−17.1136	−	11.7208i	−0.855681	−	0.586042i
$401$	−15.5955	+	2.74991i	−0.778803	+	0.137324i	−0.548898	−	0.835889i	$-0.684953\pi$
$401$	−15.5955	+	2.74991i	−0.778803	+	0.137324i	−0.229905	+	0.973213i	$0.573841\pi$
$402$		0			0
$403$	−5.70313	+	0.498959i	−0.284093	+	0.0248549i
$404$	28.6196			1.42388
$405$		0			0
$406$	2.81123			0.139519
$407$	2.37789	−	0.208038i	0.117868	−	0.0103121i
$408$		0			0
$409$	−6.67646	+	1.17724i	−0.330130	+	0.0582108i	−0.336257	−	0.941770i	$-0.609161\pi$
$409$	−6.67646	+	1.17724i	−0.330130	+	0.0582108i	0.00612663	+	0.999981i	$0.498050\pi$
$410$	22.7722	−	7.30990i	1.12464	−	0.361010i
$411$		0			0
$412$	−48.3188	+	33.8332i	−2.38050	+	1.66684i
$413$	54.3989	−	14.5761i	2.67679	−	0.717245i
$414$		0			0
$415$	−19.9359	−	8.13702i	−0.978614	−	0.399431i
$416$	0.0846199	+	0.232491i	0.00414883	+	0.0113988i
$417$		0			0
$418$	−0.339898	+	3.88505i	−0.0166250	+	0.190024i
$419$	20.0804	−	16.8495i	0.980992	−	0.823150i	−0.00324717	−	0.999995i	$-0.501034\pi$
$419$	20.0804	−	16.8495i	0.980992	−	0.823150i	0.984239	+	0.176845i	$0.0565892\pi$
$420$		0			0
$421$	−8.48131	+	3.08694i	−0.413354	+	0.150448i	−0.540322	−	0.841458i	$-0.681698\pi$
$421$	−8.48131	+	3.08694i	−0.413354	+	0.150448i	0.126968	+	0.991907i	$0.459475\pi$
$422$	62.5219	+	16.7527i	3.04352	+	0.815508i
$423$		0			0
$424$	40.9991	+	23.6709i	1.99109	+	1.14956i
$425$	−2.09973	−	5.58820i	−0.101852	−	0.271068i
$426$		0			0
$427$	−16.2107	−	34.7639i	−0.784490	−	1.68234i
$428$	20.6246	−	29.4549i	0.996926	−	1.42376i
$429$		0			0
$430$	−41.2056	−	44.5032i	−1.98711	−	2.14613i
$431$		−	26.9295i		−	1.29715i	−0.761151	−	0.648575i	$-0.775365\pi$
$431$		−	26.9295i		−	1.29715i	0.761151	−	0.648575i	$-0.224635\pi$
$432$		0			0
$433$	−0.461356	+	0.461356i	−0.0221714	+	0.0221714i	−0.718106	−	0.695934i	$-0.754991\pi$
$433$	−0.461356	+	0.461356i	−0.0221714	+	0.0221714i	0.695934	+	0.718106i	$0.254991\pi$
$434$	−50.1055	−	42.0435i	−2.40514	−	2.01815i
$435$		0			0
$436$	6.23568	+	35.3643i	0.298635	+	1.69364i
$437$	0.694699	−	0.323943i	0.0332319	−	0.0154963i
$438$		0			0
$439$	1.32806	+	0.234172i	0.0633847	+	0.0111764i	0.205251	−	0.978709i	$-0.434199\pi$
$439$	1.32806	+	0.234172i	0.0633847	+	0.0111764i	−0.141866	+	0.989886i	$0.545310\pi$
$440$	−29.8624	+	4.08890i	−1.42364	+	0.194931i
$441$		0			0
$442$	−0.770614	+	2.87597i	−0.0366544	+	0.136796i
$443$	−28.2741	−	13.1844i	−1.34334	−	0.626410i	−0.387930	−	0.921689i	$-0.626810\pi$
$443$	−28.2741	−	13.1844i	−1.34334	−	0.626410i	−0.955411	+	0.295278i	$0.904588\pi$
$444$		0			0
$445$	3.73318	+	5.79349i	0.176970	+	0.274638i
$446$	4.58392	+	5.46290i	0.217055	+	0.258676i
$447$		0			0
$448$	15.3883	−	33.0004i	0.727031	−	1.55912i
$449$	9.91012	+	17.1648i	0.467688	+	0.810059i	0.999318	−	0.0369176i	$-0.0117539\pi$
$449$	9.91012	+	17.1648i	0.467688	+	0.810059i	−0.531631	+	0.846976i	$0.678421\pi$
$450$		0			0
$451$	5.90986	−	10.2362i	0.278285	−	0.482003i
$452$	−7.53169	−	10.7564i	−0.354261	−	0.505937i
$453$		0			0
$454$	−11.3659	+	31.2276i	−0.533430	+	1.46559i
$455$	−10.7313	+	0.524232i	−0.503093	+	0.0245764i
$456$		0			0
$457$	−1.15032	−	13.1482i	−0.0538096	−	0.615046i	−0.974446	−	0.224624i	$-0.927885\pi$
$457$	−1.15032	−	13.1482i	−0.0538096	−	0.615046i	0.920636	−	0.390422i	$-0.127671\pi$
$458$	16.6832	+	16.6832i	0.779554	+	0.779554i
$459$		0			0
$460$	7.21718	+	9.30543i	0.336503	+	0.433868i
$461$	3.71376	−	4.42589i	0.172967	−	0.206134i	−0.672596	−	0.740010i	$-0.734821\pi$
$461$	3.71376	−	4.42589i	0.172967	−	0.206134i	0.845563	+	0.533876i	$0.179265\pi$
$462$		0			0
$463$	−12.0734	−	8.45389i	−0.561099	−	0.392885i	0.258339	−	0.966054i	$-0.416825\pi$
$463$	−12.0734	−	8.45389i	−0.561099	−	0.392885i	−0.819437	+	0.573169i	$0.805714\pi$
$464$	0.944098	+	0.343624i	0.0438287	+	0.0159523i
$465$		0			0
$466$	−7.60057	+	43.1050i	−0.352090	+	1.99680i
$467$	5.81437	+	21.6995i	0.269057	+	1.00413i	0.959720	+	0.280958i	$0.0906522\pi$
$467$	5.81437	+	21.6995i	0.269057	+	1.00413i	−0.690663	+	0.723177i	$0.742681\pi$
$468$		0			0
$469$	31.9590	−	18.4515i	1.47573	−	0.852012i
$470$	−35.2299	+	8.00191i	−1.62503	+	0.369101i
$471$		0			0
$472$	58.9542	+	5.15783i	2.71359	+	0.237408i
$473$	−29.8595	−	2.61237i	−1.37294	−	0.120117i
$474$		0			0
$475$	−0.285472	−	2.91492i	−0.0130984	−	0.133746i
$476$	−19.6802	+	11.3624i	−0.902042	+	0.520794i
$477$		0			0
$478$	−15.4503	−	57.6614i	−0.706682	−	2.63737i
$479$	3.89318	−	22.0793i	0.177884	−	1.00883i	−0.756878	−	0.653556i	$-0.773276\pi$
$479$	3.89318	−	22.0793i	0.177884	−	1.00883i	0.934762	−	0.355274i	$-0.115613\pi$
$480$		0			0
$481$	0.840176	+	0.305799i	0.0383087	+	0.0139432i
$482$	−13.5835	−	9.51126i	−0.618711	−	0.433226i
$483$		0			0
$484$	9.42378	−	11.2308i	0.428353	−	0.510492i
$485$	5.93120	−	4.60017i	0.269322	−	0.208883i
$486$		0			0
$487$	−15.7748	−	15.7748i	−0.714827	−	0.714827i	0.252714	−	0.967541i	$-0.418677\pi$
$487$	−15.7748	−	15.7748i	−0.714827	−	0.714827i	−0.967541	+	0.252714i	$0.918677\pi$
$488$	−3.51296	−	40.1534i	−0.159024	−	1.81766i
$489$		0			0
$490$	−62.4719	−	56.6526i	−2.82219	−	2.55931i
$491$	−3.57036	+	9.80948i	−0.161128	+	0.442696i	−0.993815	−	0.111048i	$-0.964579\pi$
$491$	−3.57036	+	9.80948i	−0.161128	+	0.442696i	0.832687	+	0.553744i	$0.186801\pi$
$492$		0			0
$493$	0.165848	+	0.236855i	0.00746942	+	0.0106674i
$494$	−0.730398	+	1.26509i	−0.0328622	+	0.0569190i
$495$		0			0
$496$	−11.6879	−	20.2441i	−0.524803	−	0.908985i
$497$	2.61809	−	5.61450i	0.117437	−	0.251845i
$498$		0			0
$499$	−4.79129	−	5.71004i	−0.214488	−	0.255617i	0.648063	−	0.761586i	$-0.275579\pi$
$499$	−4.79129	−	5.71004i	−0.214488	−	0.255617i	−0.862551	+	0.505970i	$0.831135\pi$
$500$	42.6990	−	14.1959i	1.90956	−	0.634859i
$501$		0			0
$502$	58.5829	+	27.3177i	2.61468	+	1.21925i
$503$	−5.79688	+	21.6342i	−0.258470	+	0.964623i	0.707657	+	0.706556i	$0.249752\pi$
$503$	−5.79688	+	21.6342i	−0.258470	+	0.964623i	−0.966127	+	0.258067i	$0.916914\pi$
$504$		0			0
$505$	−9.61435	+	12.6649i	−0.427833	+	0.563582i
$506$	8.57960	+	1.51281i	0.381410	+	0.0672528i
$507$		0			0
$508$	48.2303	−	22.4901i	2.13987	−	0.997838i
$509$	−6.68306	−	37.9015i	−0.296221	−	1.67996i	−0.662196	−	0.749331i	$-0.730375\pi$
$509$	−6.68306	−	37.9015i	−0.296221	−	1.67996i	0.365975	−	0.930625i	$-0.380736\pi$
$510$		0			0
$511$	7.93857	+	6.66126i	0.351182	+	0.294677i
$512$	28.4414	−	28.4414i	1.25694	−	1.25694i
$513$		0			0
$514$		−	39.9156i		−	1.76060i
$515$	1.25994	−	32.7482i	0.0555197	−	1.44306i
$516$		0			0
$517$	−10.2408	+	14.6253i	−0.450389	+	0.643222i
$518$	4.31713	+	9.25812i	0.189684	+	0.406778i
$519$		0			0
$520$	−10.7849	−	3.33918i	−0.472951	−	0.146433i
$521$	32.4577	+	18.7395i	1.42200	+	0.820992i	0.996470	−	0.0839530i	$-0.0267546\pi$
$521$	32.4577	+	18.7395i	1.42200	+	0.820992i	0.425529	+	0.904945i	$0.360088\pi$
$522$		0			0
$523$	20.3099	+	5.44201i	0.888088	+	0.237962i	0.673893	−	0.738829i	$-0.264621\pi$
$523$	20.3099	+	5.44201i	0.888088	+	0.237962i	0.214195	+	0.976791i	$0.431287\pi$
$524$	2.23387	−	0.813062i	0.0975871	−	0.0355188i
$525$		0			0
$526$	12.5864	−	10.5612i	0.548791	−	0.460491i
$527$	0.586341	−	6.70191i	0.0255414	−	0.291940i
$528$		0			0
$529$	7.28082	+	20.0039i	0.316557	+	0.869734i
$530$	−48.2010	+	20.2586i	−2.09372	+	0.879976i
$531$		0			0
$532$	−10.7694	+	2.88566i	−0.466914	+	0.125109i
$533$	3.62668	−	2.53943i	0.157089	−	0.109995i
$534$		0			0
$535$	6.10607	+	19.0219i	0.263988	+	0.822389i
$536$	38.1890	−	6.73375i	1.64951	−	0.290854i
$537$		0			0
$538$	7.83495	−	0.685470i	0.337789	−	0.0295527i
$539$	−41.6784			−1.79521
$540$		0			0
$541$	4.57481			0.196686			0.0983432	−	0.995153i	$-0.468646\pi$
$541$	4.57481			0.196686			0.0983432	+	0.995153i	$0.468646\pi$
$542$	72.3509	−	6.32988i	3.10774	−	0.271892i
$543$		0			0
$544$	−0.286324	+	0.0504866i	−0.0122760	+	0.00216460i
$545$	−17.7445	−	9.12070i	−0.760089	−	0.390688i
$546$		0			0
$547$	8.96813	−	6.27955i	0.383449	−	0.268494i	−0.365920	−	0.930646i	$-0.619246\pi$
$547$	8.96813	−	6.27955i	0.383449	−	0.268494i	0.749369	+	0.662152i	$0.230357\pi$
$548$	−66.8690	+	17.9175i	−2.85650	+	0.765397i
$549$		0			0
$550$	16.3448	−	28.9995i	0.696943	−	1.23654i
$551$	0.0485199	+	0.133307i	0.00206702	+	0.00567908i
$552$		0			0
$553$	−1.39649	+	15.9620i	−0.0593849	+	0.678772i
$554$	−17.7221	+	14.8706i	−0.752939	+	0.631791i
$555$		0			0
$556$	−45.3977	+	16.5234i	−1.92529	+	0.700748i
$557$	−0.862701	−	0.231160i	−0.0365538	−	0.00979457i	0.240496	−	0.970650i	$-0.422690\pi$
$557$	−0.862701	−	0.231160i	−0.0365538	−	0.00979457i	−0.277050	+	0.960856i	$0.589357\pi$
$558$		0			0
$559$	−9.72313	−	5.61365i	−0.411245	−	0.237432i
$560$	−20.4582	−	38.8079i	−0.864517	−	1.63993i
$561$		0			0
$562$	2.66107	+	5.70668i	0.112250	+	0.240722i
$563$	−20.7218	+	29.5939i	−0.873322	+	1.24723i	0.0944822	+	0.995527i	$0.469880\pi$
$563$	−20.7218	+	29.5939i	−0.873322	+	1.24723i	−0.967804	+	0.251706i	$0.919008\pi$
$564$		0			0
$565$	7.29015	+	0.280479i	0.306699	+	0.0117998i
$566$			44.0558i			1.85180i
$567$		0			0
$568$	4.60305	−	4.60305i	0.193139	−	0.193139i
$569$	5.09704	+	4.27692i	0.213679	+	0.179298i	0.743345	−	0.668908i	$-0.233238\pi$
$569$	5.09704	+	4.27692i	0.213679	+	0.179298i	−0.529666	+	0.848206i	$0.677683\pi$
$570$		0			0
$571$	1.91569	+	10.8644i	0.0801693	+	0.454663i	0.998295	+	0.0583730i	$0.0185913\pi$
$571$	1.91569	+	10.8644i	0.0801693	+	0.454663i	−0.918126	+	0.396290i	$0.870298\pi$
$572$	−10.0521	+	4.68737i	−0.420299	+	0.195989i
$573$		0			0
$574$	49.8148	+	8.78369i	2.07923	+	0.366624i
$575$	−6.54242	+	0.0677626i	−0.272838	+	0.00282590i
$576$		0			0
$577$	−7.90648	+	29.5074i	−0.329151	+	1.22841i	0.580921	+	0.813960i	$0.302692\pi$
$577$	−7.90648	+	29.5074i	−0.329151	+	1.22841i	−0.910073	+	0.414449i	$0.863974\pi$
$578$	34.6463	+	16.1558i	1.44109	+	0.671993i
$579$		0			0
$580$	−1.83206	+	1.18053i	−0.0760723	+	0.0490190i
$581$	−29.2731	−	34.8864i	−1.21445	−	1.44733i
$582$		0			0
$583$	−10.9203	+	23.4186i	−0.452272	+	0.969901i
$584$	5.44482	+	9.43070i	0.225308	+	0.390245i
$585$		0			0
$586$	−30.1281	+	52.1834i	−1.24458	+	2.15568i
$587$	0.453527	+	0.647703i	0.0187191	+	0.0267336i	0.828403	−	0.560133i	$-0.189250\pi$
$587$	0.453527	+	0.647703i	0.0187191	+	0.0267336i	−0.809683	+	0.586867i	$0.800361\pi$
$588$		0			0
$589$	1.12890	−	3.10162i	0.0465155	−	0.127800i
$590$	−43.9058	+	48.4158i	−1.80757	+	1.99325i
$591$		0			0
$592$	0.318184	+	3.63686i	0.0130773	+	0.149474i
$593$	27.9143	+	27.9143i	1.14630	+	1.14630i	0.987274	+	0.159029i	$0.0508363\pi$
$593$	27.9143	+	27.9143i	1.14630	+	1.14630i	0.159029	+	0.987274i	$0.449164\pi$
$594$		0			0
$595$	1.58314	−	12.5261i	0.0649025	−	0.513519i
$596$	−25.3435	+	30.2032i	−1.03811	+	1.23717i
$597$		0			0
$598$	2.67311	+	1.87173i	0.109312	+	0.0765408i
$599$	35.2332	+	12.8238i	1.43959	+	0.523967i	0.939663	−	0.342101i	$-0.111139\pi$
$599$	35.2332	+	12.8238i	1.43959	+	0.523967i	0.499925	+	0.866068i	$0.333361\pi$
$600$		0			0
$601$	0.988708	−	5.60724i	0.0403302	−	0.228724i	−0.957980	−	0.286835i	$-0.907397\pi$
$601$	0.988708	−	5.60724i	0.0403302	−	0.228724i	0.998310	+	0.0581113i	$0.0185078\pi$
$602$	−33.1997	−	123.903i	−1.35312	−	5.04991i
$603$		0			0
$604$	−53.7443	+	31.0293i	−2.18683	+	1.26256i
$605$	1.80415	+	7.94312i	0.0733492	+	0.322934i
$606$		0			0
$607$	11.6898	+	1.02272i	0.474474	+	0.0415111i	0.321885	−	0.946779i	$-0.395683\pi$
$607$	11.6898	+	1.02272i	0.474474	+	0.0415111i	0.152589	+	0.988290i	$0.451239\pi$
$608$	−0.142102	−	0.0124323i	−0.00576299	−	0.000504196i
$609$		0			0
$610$	37.6675	+	23.7235i	1.52511	+	0.960536i
$611$	−5.79174	+	3.34386i	−0.234309	+	0.135278i
$612$		0			0
$613$	−4.37352	−	16.3222i	−0.176645	−	0.659247i	−0.996266	−	0.0863408i	$-0.972483\pi$
$613$	−4.37352	−	16.3222i	−0.176645	−	0.659247i	0.819621	−	0.572906i	$-0.194184\pi$
$614$	8.28560	−	46.9900i	0.334380	−	1.89636i
$615$		0			0
$616$	−59.9034	−	21.8030i	−2.41358	−	0.878469i
$617$	24.1467	+	16.9077i	0.972111	+	0.680679i	0.947747	−	0.319024i	$-0.103355\pi$
$617$	24.1467	+	16.9077i	0.972111	+	0.680679i	0.0243643	+	0.999703i	$0.492244\pi$
$618$		0			0
$619$	26.5533	−	31.6450i	1.06727	−	1.27192i	0.106575	−	0.994305i	$-0.466012\pi$
$619$	26.5533	−	31.6450i	1.06727	−	1.27192i	0.960692	−	0.277615i	$-0.0895439\pi$
$620$	50.3091	+	6.35845i	2.02046	+	0.255362i
$621$		0			0
$622$	−9.97910	−	9.97910i	−0.400126	−	0.400126i
$623$	1.27044	+	14.5212i	0.0508991	+	0.581780i
$624$		0			0
$625$	−8.06208	+	23.6644i	−0.322483	+	0.946575i
$626$	−9.89926	+	27.1980i	−0.395654	+	1.08705i
$627$		0			0
$628$	39.0348	+	55.7475i	1.55766	+	2.22457i
$629$	−0.525339	+	0.909914i	−0.0209466	+	0.0362806i
$630$		0			0
$631$	−9.08444	−	15.7347i	−0.361646	−	0.626389i	0.626586	−	0.779352i	$-0.284452\pi$
$631$	−9.08444	−	15.7347i	−0.361646	−	0.626389i	−0.988232	+	0.152963i	$0.951118\pi$
$632$	−7.11566	+	15.2596i	−0.283046	+	0.606994i
$633$		0			0
$634$	−21.9246	−	26.1287i	−0.870738	−	1.03770i
$635$	−6.24981	+	28.8985i	−0.248016	+	1.14680i
$636$		0			0
$637$	−14.1489	−	6.59775i	−0.560601	−	0.261412i
$638$	−0.417310	+	1.55742i	−0.0165215	+	0.0616589i
$639$		0			0
$640$	5.88032	+	42.9457i	0.232440	+	1.69758i
$641$	−9.92814	−	1.75060i	−0.392138	−	0.0691445i	−0.0258971	−	0.999665i	$-0.508244\pi$
$641$	−9.92814	−	1.75060i	−0.392138	−	0.0691445i	−0.366241	+	0.930520i	$0.619355\pi$
$642$		0			0
$643$	24.3420	−	11.3509i	0.959956	−	0.447635i	0.121492	−	0.992592i	$-0.461232\pi$
$643$	24.3420	−	11.3509i	0.959956	−	0.447635i	0.838464	+	0.544957i	$0.183454\pi$
$644$	4.32495	+	24.5280i	0.170427	+	0.966540i
$645$		0			0
$646$	−1.31501	−	1.10342i	−0.0517384	−	0.0434136i
$647$	−21.7838	+	21.7838i	−0.856411	+	0.856411i	−0.990913	−	0.134503i	$-0.957056\pi$
$647$	−21.7838	+	21.7838i	−0.856411	+	0.856411i	0.134503	+	0.990913i	$0.457056\pi$
$648$		0			0
$649$			32.3007i			1.26792i
$650$	10.1394	−	7.25731i	0.397699	−	0.284655i
$651$		0			0
$652$	24.9524	−	35.6357i	0.977210	−	1.39560i
$653$	−10.1623	−	21.7931i	−0.397681	−	0.852830i	−0.998568	−	0.0534961i	$-0.982964\pi$
$653$	−10.1623	−	21.7931i	−0.397681	−	0.852830i	0.600887	−	0.799334i	$-0.294814\pi$
$654$		0			0
$655$	−0.390636	+	1.26169i	−0.0152634	+	0.0492981i
$656$	15.6557	+	9.03883i	0.611253	+	0.352907i
$657$		0			0
$658$	−73.8049	−	19.7760i	−2.87721	−	0.770947i
$659$	7.76560	−	2.82645i	0.302505	−	0.110103i	−0.186308	−	0.982491i	$-0.559652\pi$
$659$	7.76560	−	2.82645i	0.302505	−	0.110103i	0.488813	+	0.872389i	$0.337430\pi$
$660$		0			0
$661$	16.2837	−	13.6636i	0.633361	−	0.531453i	−0.268610	−	0.963249i	$-0.586564\pi$
$661$	16.2837	−	13.6636i	0.633361	−	0.531453i	0.901971	+	0.431796i	$0.142120\pi$
$662$	−6.75701	+	77.2329i	−0.262618	+	3.00174i
$663$		0			0
$664$	−16.3673	−	44.9689i	−0.635176	−	1.74513i
$665$	2.34086	−	5.73516i	0.0907747	−	0.222400i
$666$		0			0
$667$	0.306108	−	0.0820213i	0.0118525	−	0.00317588i
$668$	3.46481	−	2.42608i	0.134057	−	0.0938680i
$669$		0			0
$670$	−19.5785	+	38.0902i	−0.756383	+	1.47155i
$671$	21.6656	−	3.82023i	0.836392	−	0.147478i
$672$		0			0
$673$	−28.9385	+	2.53179i	−1.11550	+	0.0975933i	−0.629963	−	0.776625i	$-0.716930\pi$
$673$	−28.9385	+	2.53179i	−1.11550	+	0.0975933i	−0.485533	+	0.874218i	$0.661374\pi$
$674$	−8.33063			−0.320884
$675$		0			0
$676$	48.1660			1.85254
$677$	4.20773	−	0.368128i	0.161716	−	0.0141483i	−0.00601017	−	0.999982i	$-0.501913\pi$
$677$	4.20773	−	0.368128i	0.161716	−	0.0141483i	0.167726	+	0.985834i	$0.446358\pi$
$678$		0			0
$679$	15.6340	−	2.75669i	0.599977	−	0.105792i
$680$	6.06511	−	11.7998i	0.232586	−	0.452500i
$681$		0			0
$682$	30.7300	−	21.5174i	1.17671	−	0.823943i
$683$	−41.7463	+	11.1859i	−1.59738	+	0.428017i	−0.944250	−	0.329230i	$-0.893211\pi$
$683$	−41.7463	+	11.1859i	−1.59738	+	0.428017i	−0.653130	+	0.757246i	$0.726544\pi$
$684$		0			0
$685$	14.5348	−	35.6105i	0.555344	−	1.36061i
$686$	−33.2133	−	91.2529i	−1.26809	−	3.48405i
$687$		0			0
$688$	3.99548	−	45.6686i	0.152326	−	1.74110i
$689$	−7.41441	+	6.22143i	−0.282467	+	0.237018i
$690$		0			0
$691$	22.3741	−	8.14350i	0.851150	−	0.309793i	0.120641	−	0.992696i	$-0.461505\pi$
$691$	22.3741	−	8.14350i	0.851150	−	0.309793i	0.730509	+	0.682903i	$0.239283\pi$
$692$	−71.2264	−	19.0850i	−2.70762	−	0.725505i
$693$		0			0
$694$	74.3116	+	42.9038i	2.82083	+	1.62861i
$695$	7.93868	−	25.6405i	0.301131	−	0.972600i
$696$		0			0
$697$	2.19876	+	4.71526i	0.0832840	+	0.178603i
$698$	31.2301	−	44.6012i	1.18208	−	1.68818i
$699$		0			0
$700$	93.8880	+	15.5542i	3.54863	+	0.587892i
$701$			15.2816i			0.577177i	0.957453	+	0.288588i	$0.0931859\pi$
$701$			15.2816i			0.577177i	−0.957453	+	0.288588i	$0.906814\pi$
$702$		0			0
$703$	−0.364505	+	0.364505i	−0.0137476	+	0.0137476i
$704$	15.9979	+	13.4239i	0.602945	+	0.505931i
$705$		0			0
$706$	−11.6824	−	66.2543i	−0.439674	−	2.49352i
$707$	−30.4791	+	14.2126i	−1.14628	+	0.534521i
$708$		0			0
$709$	28.5077	+	5.02667i	1.07063	+	0.188781i	0.681068	−	0.732220i	$-0.261516\pi$
$709$	28.5077	+	5.02667i	1.07063	+	0.188781i	0.389561	+	0.921001i	$0.372627\pi$
$710$	0.975310	+	7.12298i	0.0366027	+	0.267321i
$711$		0			0
$712$	−3.96442	+	14.7954i	−0.148573	+	0.554481i
$713$	−6.68254	−	3.11612i	−0.250263	−	0.116700i
$714$		0			0
$715$	1.30258	−	6.02298i	0.0487136	−	0.225247i
$716$	−21.8760	−	26.0708i	−0.817544	−	0.974311i
$717$		0			0
$718$	−2.39754	+	5.14154i	−0.0894755	+	0.191881i
$719$	5.81410	+	10.0703i	0.216829	+	0.375559i	0.953837	−	0.300325i	$-0.0970951\pi$
$719$	5.81410	+	10.0703i	0.216829	+	0.375559i	−0.737008	+	0.675884i	$0.763762\pi$
$720$		0			0
$721$	34.6565	−	60.0268i	1.29068	−	2.23552i
$722$	26.2661	+	37.5119i	0.977524	+	1.39605i
$723$		0			0
$724$	1.40928	−	3.87196i	0.0523755	−	0.143900i
$725$	0.0930380	−	1.20732i	0.00345534	−	0.0448388i
$726$		0			0
$727$	3.61286	+	41.2951i	0.133993	+	1.53155i	0.704171	+	0.710030i	$0.251319\pi$
$727$	3.61286	+	41.2951i	0.133993	+	1.53155i	−0.570178	+	0.821521i	$0.693126\pi$
$728$	−16.8845	−	16.8845i	−0.625780	−	0.625780i
$729$		0			0
$730$	−11.9318	−	1.50804i	−0.441617	−	0.0558149i
$731$	8.48063	−	10.1068i	0.313668	−	0.373814i
$732$		0			0
$733$	5.54883	+	3.88534i	0.204951	+	0.143508i	0.671546	−	0.740963i	$-0.265631\pi$
$733$	5.54883	+	3.88534i	0.204951	+	0.143508i	−0.466595	+	0.884471i	$0.654519\pi$
$734$	−71.9960	−	26.2044i	−2.65742	−	0.967222i
$735$		0			0
$736$	−0.0553335	+	0.313812i	−0.00203962	+	0.0115673i
$737$	5.47803	+	20.4443i	0.201786	+	0.753075i
$738$		0			0
$739$	−29.8815	+	17.2521i	−1.09921	+	0.634629i	−0.936014	−	0.351964i	$-0.885514\pi$
$739$	−29.8815	+	17.2521i	−1.09921	+	0.634629i	−0.163197	+	0.986594i	$0.552181\pi$
$740$	−6.70126	−	4.22055i	−0.246343	−	0.155150i
$741$		0			0
$742$	−110.161	−	9.63788i	−4.04415	−	0.353818i
$743$	41.3819	+	3.62044i	1.51815	+	0.132821i	0.815519	−	0.578730i	$-0.196452\pi$
$743$	41.3819	+	3.62044i	1.51815	+	0.132821i	0.702634	+	0.711551i	$0.252007\pi$
$744$		0			0
$745$	−4.85193	−	21.3615i	−0.177761	−	0.782625i
$746$	68.9031	−	39.7812i	2.52272	−	1.45649i
$747$		0			0
$748$	−3.37336	−	12.5895i	−0.123342	−	0.460319i
$749$	−7.33715	+	41.6110i	−0.268093	+	1.52043i
$750$		0			0
$751$	23.6063	+	8.59199i	0.861406	+	0.313526i	0.734682	−	0.678412i	$-0.237331\pi$
$751$	23.6063	+	8.59199i	0.861406	+	0.313526i	0.126724	+	0.991938i	$0.459554\pi$
$752$	−22.3687	−	15.6627i	−0.815703	−	0.571161i
$753$		0			0
$754$	−0.388210	+	0.462651i	−0.0141378	+	0.0168488i
$755$	4.32337	−	34.2072i	0.157344	−	1.24493i
$756$		0			0
$757$	−27.9350	−	27.9350i	−1.01531	−	1.01531i	−0.999881	−	0.0154328i	$-0.995087\pi$
$757$	−27.9350	−	27.9350i	−1.01531	−	1.01531i	−0.0154328	−	0.999881i	$-0.504913\pi$
$758$	1.03689	+	11.8517i	0.0376615	+	0.430473i
$759$		0			0
$760$	4.37267	−	4.82182i	0.158613	−	0.174906i
$761$	16.3639	−	44.9594i	0.593191	−	1.62978i	−0.171355	−	0.985209i	$-0.554814\pi$
$761$	16.3639	−	44.9594i	0.593191	−	1.62978i	0.764546	−	0.644569i	$-0.222963\pi$
$762$		0			0
$763$	−24.2029	−	34.5654i	−0.876205	−	1.25135i
$764$	−8.06045	+	13.9611i	−0.291617	+	0.505095i
$765$		0			0
$766$	15.1312	+	26.2080i	0.546713	+	0.946935i
$767$	−5.11326	+	10.9654i	−0.184629	+	0.395938i
$768$		0			0
$769$	4.81494	+	5.73823i	0.173631	+	0.206926i	0.845841	−	0.533435i	$-0.179099\pi$
$769$	4.81494	+	5.73823i	0.173631	+	0.206926i	−0.672210	+	0.740361i	$0.734655\pi$
$770$	59.1818	−	38.1353i	2.13277	−	1.37430i
$771$		0			0
$772$	0.890250	+	0.415130i	0.0320408	+	0.0149409i
$773$	9.18683	−	34.2857i	0.330427	−	1.23317i	−0.578315	−	0.815814i	$-0.696290\pi$
$773$	9.18683	−	34.2857i	0.330427	−	1.23317i	0.908742	−	0.417358i	$-0.137044\pi$
$774$		0			0
$775$	−19.7144	+	20.1271i	−0.708164	+	0.722987i
$776$	16.4283	+	2.89676i	0.589743	+	0.103988i
$777$		0			0
$778$	−26.7413	+	12.4697i	−0.958721	+	0.447059i
$779$	0.443250	+	2.51380i	0.0158811	+	0.0900661i
$780$		0			0
$781$	2.72180	+	2.28386i	0.0973936	+	0.0817229i
$782$	−2.71158	+	2.71158i	−0.0969659	+	0.0969659i
$783$		0			0
$784$		−	63.7449i		−	2.27660i
$785$	−37.7830	−	1.45365i	−1.34853	−	0.0518830i
$786$		0			0
$787$	−15.3799	+	21.9648i	−0.548236	+	0.782962i	−0.993668	−	0.112354i	$-0.964161\pi$
$787$	−15.3799	+	21.9648i	−0.548236	+	0.782962i	0.445433	+	0.895315i	$0.353050\pi$
$788$	16.1747	+	34.6867i	0.576199	+	1.23566i
$789$		0			0
$790$	−8.67163	−	16.4495i	−0.308523	−	0.585247i
$791$	13.3627	+	7.71497i	0.475124	+	0.274313i
$792$		0			0
$793$	7.95976	+	2.13281i	0.282660	+	0.0757384i
$794$	38.5767	−	14.0408i	1.36904	−	0.498288i
$795$		0			0
$796$	15.1909	−	12.7467i	0.538426	−	0.451793i
$797$	2.14990	−	24.5735i	0.0761533	−	0.870437i	−0.858020	−	0.513617i	$-0.828305\pi$
$797$	2.14990	−	24.5735i	0.0761533	−	0.870437i	0.934173	−	0.356820i	$-0.116139\pi$
$798$		0			0
$799$	−2.68791	−	7.38499i	−0.0950916	−	0.261262i
$800$	1.06070	+	0.597835i	0.0375014	+	0.0211366i
$801$		0			0
$802$	37.5455	−	10.0603i	1.32578	−	0.355241i
$803$	−4.86877	+	3.40915i	−0.171815	+	0.120306i
$804$		0			0
$805$	−12.3072	−	6.32595i	−0.433773	−	0.222961i
$806$	13.8384	−	2.44009i	0.487438	−	0.0859484i
$807$		0			0
$808$	−35.2042	+	3.07997i	−1.23848	+	0.108353i
$809$	−11.7095			−0.411684			−0.205842	−	0.978585i	$-0.565993\pi$
$809$	−11.7095			−0.411684			−0.205842	+	0.978585i	$0.565993\pi$
$810$		0			0
$811$	−18.5512			−0.651422			−0.325711	−	0.945469i	$-0.605604\pi$
$811$	−18.5512			−0.651422			−0.325711	+	0.945469i	$0.605604\pi$
$812$	−4.59201	+	0.401749i	−0.161148	+	0.0140986i
$813$		0			0
$814$	−5.76985	+	1.01738i	−0.202233	+	0.0356592i
$815$	7.38734	+	23.0134i	0.258767	+	0.806125i
$816$		0			0
$817$	5.30242	−	3.71280i	0.185508	−	0.129894i
$818$	16.0733	−	4.30683i	0.561989	−	0.150585i
$819$		0			0
$820$	−36.1526	+	15.1947i	−1.26250	+	0.530622i
$821$	−1.45874	−	4.00785i	−0.0509103	−	0.139875i	0.911631	−	0.411009i	$-0.134824\pi$
$821$	−1.45874	−	4.00785i	−0.0509103	−	0.139875i	−0.962542	+	0.271134i	$0.912601\pi$
$822$		0			0
$823$	−2.33570	+	26.6972i	−0.0814173	+	0.930605i	0.840142	+	0.542367i	$0.182472\pi$
$823$	−2.33570	+	26.6972i	−0.0814173	+	0.930605i	−0.921559	+	0.388238i	$0.873084\pi$
$824$	55.7948	−	46.8174i	1.94370	−	1.63096i
$825$		0			0
$826$	−129.897	+	47.2785i	−4.51968	+	1.64503i
$827$	−7.43022	−	1.99092i	−0.258374	−	0.0692311i	0.127307	−	0.991863i	$-0.459367\pi$
$827$	−7.43022	−	1.99092i	−0.258374	−	0.0692311i	−0.385681	+	0.922632i	$0.626033\pi$
$828$		0			0
$829$	−6.05853	−	3.49789i	−0.210421	−	0.121487i	0.391086	−	0.920354i	$-0.372100\pi$
$829$	−6.05853	−	3.49789i	−0.210421	−	0.121487i	−0.601507	+	0.798867i	$0.705433\pi$
$830$	50.4875	+	15.6317i	1.75245	+	0.542583i
$831$		0			0
$832$	3.30594	+	7.08961i	0.114613	+	0.245788i
$833$	10.5226	−	15.0279i	0.364588	−	0.520685i
$834$		0			0
$835$	−0.0903470	+	2.34828i	−0.00312659	+	0.0812656i
$836$		−	6.39463i		−	0.221163i
$837$		0			0
$838$	−45.4956	+	45.4956i	−1.57162	+	1.57162i
$839$	−3.83684	−	3.21949i	−0.132462	−	0.111149i	0.574149	−	0.818751i	$-0.305333\pi$
$839$	−3.83684	−	3.21949i	−0.132462	−	0.111149i	−0.706612	+	0.707601i	$0.749777\pi$
$840$		0			0
$841$	−5.02561	−	28.5017i	−0.173297	−	0.982816i
$842$	20.0779	−	9.36249i	0.691931	−	0.322653i
$843$		0			0
$844$	−104.521	−	18.4298i	−3.59775	−	0.634380i
$845$	−16.1807	+	21.3148i	−0.556633	+	0.733250i
$846$		0			0
$847$	−4.45879	+	16.6404i	−0.153206	+	0.571772i
$848$	−35.8176	−	16.7020i	−1.22998	−	0.573549i
$849$		0			0
$850$	6.32968	+	13.2150i	0.217106	+	0.453269i
$851$	0.740200	+	0.882136i	0.0253737	+	0.0302392i
$852$		0			0
$853$	7.47524	−	16.0307i	0.255947	−	0.548881i	−0.735784	−	0.677217i	$-0.763186\pi$
$853$	7.47524	−	16.0307i	0.255947	−	0.548881i	0.991731	+	0.128336i	$0.0409637\pi$
$854$	47.0749	+	81.5361i	1.61087	+	2.79011i
$855$		0			0
$856$	−22.1999	+	38.4514i	−0.758778	+	1.31424i
$857$	−4.81571	−	6.87754i	−0.164501	−	0.234932i	0.728435	−	0.685115i	$-0.240248\pi$
$857$	−4.81571	−	6.87754i	−0.164501	−	0.234932i	−0.892937	+	0.450182i	$0.851359\pi$
$858$		0			0
$859$	−0.781638	+	2.14753i	−0.0266691	+	0.0732729i	−0.952313	−	0.305124i	$-0.901302\pi$
$859$	−0.781638	+	2.14753i	−0.0266691	+	0.0732729i	0.925644	+	0.378397i	$0.123524\pi$
$860$	73.6673	+	66.8052i	2.51204	+	2.27804i
$861$		0			0
$862$	5.76090	+	65.8474i	0.196217	+	2.24277i
$863$	−2.53415	−	2.53415i	−0.0862635	−	0.0862635i	0.662658	−	0.748922i	$-0.269428\pi$
$863$	−2.53415	−	2.53415i	−0.0862635	−	0.0862635i	−0.748922	+	0.662658i	$0.769428\pi$
$864$		0			0
$865$	32.3732	−	25.1082i	1.10072	−	0.853706i
$866$	1.02940	−	1.22679i	0.0349805	−	0.0416881i
$867$		0			0
$868$	87.8534	+	61.5156i	2.98194	+	2.08798i
$869$	−8.63564	−	3.14312i	−0.292944	−	0.106623i
$870$		0			0
$871$	−1.37669	+	7.80759i	−0.0466473	+	0.264550i
$872$	−11.4762	−	42.8297i	−0.388633	−	1.45040i
$873$		0			0
$874$	−1.62936	+	0.940712i	−0.0551140	+	0.0318201i
$875$	−38.4236	+	36.3228i	−1.29895	+	1.22793i
$876$		0			0
$877$	57.6923	+	5.04742i	1.94813	+	0.170439i	0.992333	−	0.123590i	$-0.0394407\pi$
$877$	57.6923	+	5.04742i	1.94813	+	0.170439i	0.955796	+	0.294029i	$0.0949962\pi$
$878$	−3.29743	−	0.288488i	−0.111283	−	0.00973599i
$879$		0			0
$880$	24.5365	−	5.57307i	0.827124	−	0.187868i
$881$	−29.5108	+	17.0381i	−0.994244	+	0.574027i	−0.906540	−	0.422120i	$-0.861286\pi$
$881$	−29.5108	+	17.0381i	−0.994244	+	0.574027i	−0.0877038	+	0.996147i	$0.527953\pi$
$882$		0			0
$883$	14.6479	+	54.6668i	0.492942	+	1.83969i	0.541263	+	0.840853i	$0.317946\pi$
$883$	14.6479	+	54.6668i	0.492942	+	1.83969i	−0.0483207	+	0.998832i	$0.515387\pi$
$884$	0.847760	−	4.80789i	0.0285133	−	0.161707i
$885$		0			0
$886$	71.9556	+	26.1897i	2.41739	+	0.879860i
$887$	13.3170	+	9.32467i	0.447141	+	0.313092i	0.775371	−	0.631506i	$-0.217563\pi$
$887$	13.3170	+	9.32467i	0.447141	+	0.313092i	−0.328229	+	0.944598i	$0.606452\pi$
$888$		0			0
$889$	−40.1952	+	47.9028i	−1.34810	+	1.60661i
$890$	−10.3676	−	13.3675i	−0.347524	−	0.448079i
$891$		0			0
$892$	−8.26831	−	8.26831i	−0.276844	−	0.276844i
$893$	−0.336054	−	3.84111i	−0.0112456	−	0.128538i
$894$		0			0
$895$	18.8860	−	0.922590i	0.631289	−	0.0308388i
$896$	−31.3554	+	86.1481i	−1.04751	+	2.87801i
$897$		0			0
$898$	−27.9040	−	39.8510i	−0.931168	−	1.32985i
$899$	0.682312	−	1.18180i	0.0227564	−	0.0394152i
$900$		0			0
$901$	−5.68693	−	9.85005i	−0.189459	−	0.328153i
$902$	−12.2609	+	26.2935i	−0.408243	+	0.875479i
$903$		0			0
$904$	10.4221	+	12.4206i	0.346635	+	0.413103i
$905$	1.24002	+	1.92438i	0.0412197	+	0.0639685i
$906$		0			0
$907$	18.4950	+	8.62436i	0.614117	+	0.286367i	0.704682	−	0.709523i	$-0.251090\pi$
$907$	18.4950	+	8.62436i	0.614117	+	0.286367i	−0.0905654	+	0.995891i	$0.528867\pi$
$908$	14.1030	−	52.6332i	0.468025	−	1.74669i
$909$		0			0
$910$	26.1279	−	3.57754i	0.866130	−	0.118594i
$911$	−18.7876	−	3.31277i	−0.622462	−	0.109757i	−0.146483	−	0.989213i	$-0.546795\pi$
$911$	−18.7876	−	3.31277i	−0.622462	−	0.109757i	−0.475980	+	0.879456i	$0.657906\pi$
$912$		0			0
$913$	23.6725	−	11.0387i	0.783445	−	0.365326i
$914$	5.62546	+	31.9035i	0.186074	+	1.05528i
$915$		0			0
$916$	−29.6354	−	24.8670i	−0.979180	−	0.821629i
$917$	−1.97524	+	1.97524i	−0.0652282	+	0.0652282i
$918$		0			0
$919$			18.2953i			0.603505i	0.953386	+	0.301752i	$0.0975716\pi$
$919$			18.2953i			0.603505i	−0.953386	+	0.301752i	$0.902428\pi$
$920$	−9.87911	−	10.6697i	−0.325705	−	0.351769i
$921$		0			0
$922$	−8.13399	+	11.6165i	−0.267879	+	0.382570i
$923$	0.562454	+	1.20619i	0.0185134	+	0.0397021i
$924$		0			0
$925$	4.11891	−	1.54765i	0.135429	−	0.0508866i
$926$	31.3301	+	18.0884i	1.02957	+	0.594423i
$927$		0			0
$928$	−0.0569651	−	0.0152638i	−0.00186997	−	0.000501057i
$929$	−19.6665	+	7.15802i	−0.645237	+	0.234847i	−0.643850	−	0.765152i	$-0.722664\pi$
$929$	−19.6665	+	7.15802i	−0.645237	+	0.234847i	−0.00138736	+	0.999999i	$0.500442\pi$
$930$		0			0
$931$	6.89503	−	5.78562i	0.225975	−	0.189616i
$932$	6.25510	−	71.4961i	0.204893	−	2.34193i
$933$		0			0
$934$	−18.8592	−	51.8154i	−0.617093	−	1.69545i
$935$	6.70445	+	2.73648i	0.219259	+	0.0894926i
$936$		0			0
$937$	−21.8183	+	5.84618i	−0.712771	+	0.190986i	−0.596944	−	0.802283i	$-0.703619\pi$
$937$	−21.8183	+	5.84618i	−0.712771	+	0.190986i	−0.115827	+	0.993269i	$0.536952\pi$
$938$	−74.1980	+	51.9540i	−2.42265	+	1.69636i
$939$		0			0
$940$	56.4028	−	18.1054i	1.83966	−	0.590533i
$941$	−43.2123	+	7.61949i	−1.40868	+	0.248388i	−0.825705	−	0.564102i	$-0.809222\pi$
$941$	−43.2123	+	7.61949i	−1.40868	+	0.248388i	−0.582975	+	0.812490i	$0.698111\pi$
$942$		0			0
$943$	5.68049	−	0.496978i	0.184982	−	0.0161838i
$944$	−49.4023			−1.60791
$945$		0			0
$946$	73.5706			2.39199
$947$	−30.9911	+	2.71137i	−1.00707	+	0.0881076i	−0.578739	−	0.815513i	$-0.696455\pi$
$947$	−30.9911	+	2.71137i	−1.00707	+	0.0881076i	−0.428335	+	0.903620i	$0.640900\pi$
$948$		0			0
$949$	−2.19252	+	0.386600i	−0.0711722	+	0.0125496i
$950$	1.32160	+	7.06642i	0.0428785	+	0.229265i
$951$		0			0
$952$	22.9854	−	16.0946i	0.744961	−	0.521627i
$953$	−4.20699	+	1.12726i	−0.136278	+	0.0365155i	−0.326313	−	0.945262i	$-0.605806\pi$
$953$	−4.20699	+	1.12726i	−0.136278	+	0.0365155i	0.190035	+	0.981777i	$0.439140\pi$
$954$		0			0
$955$	−3.47037	−	8.25701i	−0.112299	−	0.267191i
$956$	33.4777	+	91.9792i	1.08275	+	2.97482i
$957$		0			0
$958$	−4.79619	+	54.8207i	−0.154958	+	1.77118i
$959$	62.3158	−	52.2892i	2.01228	−	1.68850i
$960$		0			0
$961$	−0.705110	+	0.256639i	−0.0227455	+	0.00827868i
$962$	−2.11980	−	0.567998i	−0.0683450	−	0.0183130i
$963$		0			0
$964$	23.5472	+	13.5950i	0.758405	+	0.437865i
$965$	−0.482774	+	0.254502i	−0.0155410	+	0.00819272i
$966$		0			0
$967$	−21.6162	−	46.3561i	−0.695130	−	1.49071i	−0.863161	−	0.504929i	$-0.831519\pi$
$967$	−21.6162	−	46.3561i	−0.695130	−	1.49071i	0.168031	−	0.985782i	$-0.446259\pi$
$968$	−10.3833	+	14.8289i	−0.333733	+	0.476620i
$969$		0			0
$970$	−13.5187	+	12.5171i	−0.434061	+	0.401898i
$971$		−	28.8390i		−	0.925487i	−0.886492	−	0.462744i	$-0.846865\pi$
$971$		−	28.8390i		−	0.925487i	0.886492	−	0.462744i	$-0.153135\pi$
$972$		0			0
$973$	40.1417	−	40.1417i	1.28688	−	1.28688i
$974$	41.9469	+	35.1976i	1.34407	+	1.12781i
$975$		0			0
$976$	5.84285	+	33.1364i	0.187025	+	1.06067i
$977$	35.3398	−	16.4792i	1.13062	−	0.527216i	0.234981	−	0.972000i	$-0.424497\pi$
$977$	35.3398	−	16.4792i	1.13062	−	0.527216i	0.895638	+	0.444784i	$0.146719\pi$
$978$		0			0
$979$	−8.23334	−	1.45176i	−0.263139	−	0.0463985i
$980$	110.141	+	83.6116i	3.51833	+	2.67088i
$981$		0			0
$982$	6.63166	−	24.7497i	0.211625	−	0.789795i
$983$	12.7120	+	5.92768i	0.405448	+	0.189064i	0.614634	−	0.788812i	$-0.289304\pi$
$983$	12.7120	+	5.92768i	0.405448	+	0.189064i	−0.209186	+	0.977876i	$0.567081\pi$
$984$		0			0
$985$	−20.7835	−	4.49479i	−0.662216	−	0.143216i
$986$	−0.456197	−	0.543674i	−0.0145283	−	0.0173141i
$987$		0			0
$988$	1.01228	−	2.17084i	0.0322049	−	0.0690636i
$989$	−7.23007	−	12.5228i	−0.229903	−	0.398203i
$990$		0			0
$991$	−6.81269	+	11.7999i	−0.216412	+	0.374837i	−0.953709	−	0.300732i	$-0.902769\pi$
$991$	−6.81269	+	11.7999i	−0.216412	+	0.374837i	0.737296	+	0.675570i	$0.236102\pi$
$992$	0.787031	+	1.12400i	0.0249883	+	0.0356869i
$993$		0			0
$994$	−5.20060	+	14.2885i	−0.164953	+	0.453204i
$995$	0.537573	+	11.0044i	0.0170422	+	0.348864i
$996$		0			0
$997$	−4.28282	−	48.9528i	−0.135638	−	1.55035i	−0.693524	−	0.720434i	$-0.743943\pi$
$997$	−4.28282	−	48.9528i	−0.135638	−	1.55035i	0.557886	−	0.829918i	$-0.311613\pi$
$998$	12.9371	+	12.9371i	0.409516	+	0.409516i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.197.1		192
3.2	odd	2		135.2.q.a.92.16	yes	192
5.3	odd	4	inner	405.2.r.a.278.16		192
15.2	even	4		675.2.ba.b.443.16		192
15.8	even	4		135.2.q.a.38.1	yes	192
15.14	odd	2		675.2.ba.b.632.1		192
27.5	odd	18	inner	405.2.r.a.287.16		192
27.22	even	9		135.2.q.a.32.1	✓	192
135.22	odd	36		675.2.ba.b.518.1		192
135.49	even	18		675.2.ba.b.32.16		192
135.103	odd	36		135.2.q.a.113.16	yes	192
135.113	even	36	inner	405.2.r.a.368.1		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.1	✓	192	27.22	even	9
135.2.q.a.38.1	yes	192	15.8	even	4
135.2.q.a.92.16	yes	192	3.2	odd	2
135.2.q.a.113.16	yes	192	135.103	odd	36
405.2.r.a.197.1		192	1.1	even	1	trivial
405.2.r.a.278.16		192	5.3	odd	4	inner
405.2.r.a.287.16		192	27.5	odd	18	inner
405.2.r.a.368.1		192	135.113	even	36	inner
675.2.ba.b.32.16		192	135.49	even	18
675.2.ba.b.443.16		192	15.2	even	4
675.2.ba.b.518.1		192	135.22	odd	36
675.2.ba.b.632.1		192	15.14	odd	2

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.44518 + 0.213925i) q^{2} +(3.96351 - 0.698873i) q^{4} +(-1.02222 + 1.98874i) q^{5} +(-3.87397 + 2.71258i) q^{7} +(-4.80021 + 1.28621i) q^{8} +O(q^{10})\)	\(q+(-2.44518 + 0.213925i) q^{2} +(3.96351 - 0.698873i) q^{4} +(-1.02222 + 1.98874i) q^{5} +(-3.87397 + 2.71258i) q^{7} +(-4.80021 + 1.28621i) q^{8} +(2.07406 - 5.08149i) q^{10} +(-0.927704 - 2.54885i) q^{11} +(0.0885504 - 1.01214i) q^{13} +(8.89224 - 7.46148i) q^{14} +(3.89833 - 1.41887i) q^{16} +(1.15325 + 0.309013i) q^{17} +(0.507294 + 0.292886i) q^{19} +(-2.66169 + 8.59677i) q^{20} +(2.81366 + 6.03392i) q^{22} +(0.750556 - 1.07190i) q^{23} +(-2.91015 - 4.06584i) q^{25} +2.49379i q^{26} +(-13.4587 + 13.4587i) q^{28} +(0.185521 + 0.155671i) q^{29} +(-0.978463 - 5.54914i) q^{31} +(-0.220700 + 0.102914i) q^{32} +(-2.88601 - 0.508881i) q^{34} +(-1.43458 - 10.4771i) q^{35} +(-0.227764 + 0.850028i) q^{37} +(-1.30308 - 0.607636i) q^{38} +(2.34891 - 10.8611i) q^{40} +(2.80103 + 3.33813i) q^{41} +(4.67013 - 10.0151i) q^{43} +(-5.45828 - 9.45402i) q^{44} +(-1.60593 + 2.78156i) q^{46} +(-3.77551 - 5.39198i) q^{47} +(5.25539 - 14.4391i) q^{49} +(7.98561 + 9.31914i) q^{50} +(-0.356385 - 4.07349i) q^{52} +(-6.73617 - 6.73617i) q^{53} +(6.01730 + 0.760513i) q^{55} +(15.1069 - 18.0037i) q^{56} +(-0.486933 - 0.340954i) q^{58} +(-11.1903 - 4.07292i) q^{59} +(-1.40842 + 7.98754i) q^{61} +(3.57962 + 13.3593i) q^{62} +(-6.66780 + 3.84966i) q^{64} +(1.92235 + 1.21073i) q^{65} +(-7.77347 - 0.680090i) q^{67} +(4.78688 + 0.418798i) q^{68} +(5.74912 + 25.3116i) q^{70} +(-1.13442 + 0.654959i) q^{71} +(-0.567144 - 2.11661i) q^{73} +(0.375082 - 2.12719i) q^{74} +(2.21535 + 0.806323i) q^{76} +(10.5078 + 7.35767i) q^{77} +(2.17780 - 2.59540i) q^{79} +(-1.16316 + 9.20314i) q^{80} +(-7.56311 - 7.56311i) q^{82} +(0.839279 + 9.59300i) q^{83} +(-1.79342 + 1.97763i) q^{85} +(-9.27680 + 25.4878i) q^{86} +(7.73153 + 11.0418i) q^{88} +(1.54112 - 2.66930i) q^{89} +(2.40246 + 4.16118i) q^{91} +(2.22571 - 4.77305i) q^{92} +(10.3853 + 12.3767i) q^{94} +(-1.10104 + 0.709481i) q^{95} +(-3.04230 - 1.41865i) q^{97} +(-9.76147 + 36.4303i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

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