LMFDB - Embedded newform 405.2.r.a.368.1

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			368.1
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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	−0.821192	−	0.570652i	$-0.806690\pi$
$2$	−2.44518	−	0.213925i	−1.72900	−	0.151268i	−0.907809	+	0.419384i	$0.862246\pi$
$3$		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	−0.989406	−	0.145174i	$-0.953626\pi$
$7$	−3.87397	−	2.71258i	−1.46422	−	1.02526i	−0.474816	−	0.880085i	$-0.657485\pi$
$8$	−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	0.717682	+	0.696371i	$0.245203\pi$
$11$	−0.927704	+	2.54885i	−0.279713	+	0.768506i	−0.997395	+	0.0721346i	$0.977019\pi$
$12$		0			0
$13$	0.0885504	+	1.01214i	0.0245595	+	0.280716i	0.998537	+	0.0540717i	$0.0172200\pi$
$13$	0.0885504	+	1.01214i	0.0245595	+	0.280716i	−0.973978	+	0.226644i	$0.927224\pi$
$14$	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	−0.116240	−	0.993221i	$-0.537084\pi$
$17$	1.15325	−	0.309013i	0.279704	−	0.0749466i	0.395944	+	0.918275i	$0.370417\pi$
$18$		0			0
$19$	0.507294	−	0.292886i	0.116381	−	0.0671927i	−0.440679	−	0.897665i	$-0.645262\pi$
$19$	0.507294	−	0.292886i	0.116381	−	0.0671927i	0.557061	+	0.830472i	$0.311929\pi$
$20$	−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	0.889744	−	0.456460i	$-0.150883\pi$
$23$	0.750556	+	1.07190i	0.156502	+	0.223508i	−0.733242	+	0.679967i	$0.761994\pi$
$24$		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	−0.625400	−	0.780304i	$-0.715064\pi$
$29$	0.185521	−	0.155671i	0.0344504	−	0.0289073i	0.659850	+	0.751397i	$0.270620\pi$
$30$		0			0
$31$	−0.978463	+	5.54914i	−0.175737	+	0.996655i	0.761552	+	0.648103i	$0.224438\pi$
$31$	−0.978463	+	5.54914i	−0.175737	+	0.996655i	−0.937290	+	0.348552i	$0.886674\pi$
$32$	−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	0.944673	−	0.328013i	$-0.106379\pi$
$37$	−0.227764	−	0.850028i	−0.0374442	−	0.139744i	−0.982117	+	0.188269i	$0.939712\pi$
$38$	−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	−0.501609	−	0.865095i	$-0.667258\pi$
$41$	2.80103	−	3.33813i	0.437447	−	0.521329i	0.939055	+	0.343766i	$0.111703\pi$
$42$		0			0
$43$	4.67013	+	10.0151i	0.712188	+	1.52729i	0.844191	+	0.536043i	$0.180082\pi$
$43$	4.67013	+	10.0151i	0.712188	+	1.52729i	−0.132002	+	0.991249i	$0.542141\pi$
$44$	−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	−0.993942	−	0.109908i	$-0.964944\pi$
$47$	−3.77551	+	5.39198i	−0.550714	+	0.786501i	0.443228	+	0.896409i	$0.353833\pi$
$48$		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	−0.997397	−	0.0721125i	$-0.977026\pi$
$53$	−6.73617	+	6.73617i	−0.925284	+	0.925284i	0.0721125	+	0.997397i	$0.477026\pi$
$54$		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	−0.944495	−	0.328525i	$-0.893449\pi$
$59$	−11.1903	+	4.07292i	−1.45685	+	0.530250i	−0.512354	+	0.858775i	$0.671226\pi$
$60$		0			0
$61$	−1.40842	−	7.98754i	−0.180330	−	1.02270i	−0.931811	−	0.362945i	$-0.881771\pi$
$61$	−1.40842	−	7.98754i	−0.180330	−	1.02270i	0.751481	−	0.659755i	$-0.229340\pi$
$62$	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	−0.551458	−	0.834203i	$-0.685928\pi$
$67$	−7.77347	+	0.680090i	−0.949680	+	0.0830863i	−0.398222	+	0.917289i	$0.630373\pi$
$68$	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	0.431172	−	0.902270i	$-0.358100\pi$
$71$	−1.13442	−	0.654959i	−0.134631	−	0.0777293i	−0.565803	+	0.824541i	$0.691434\pi$
$72$		0			0
$73$	−0.567144	+	2.11661i	−0.0663792	+	0.247730i	−0.991141	−	0.132817i	$-0.957598\pi$
$73$	−0.567144	+	2.11661i	−0.0663792	+	0.247730i	0.924761	+	0.380547i	$0.124264\pi$
$74$	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	0.874513	−	0.485002i	$-0.161181\pi$
$79$	2.17780	+	2.59540i	0.245022	+	0.292006i	−0.629491	+	0.777008i	$0.716737\pi$
$80$	−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	−0.799644	−	0.600474i	$-0.794979\pi$
$83$	0.839279	−	9.59300i	0.0921228	−	1.05297i	0.891767	−	0.452495i	$-0.149466\pi$
$84$		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	0.936071	−	0.351811i	$-0.114434\pi$
$89$	1.54112	+	2.66930i	0.163359	+	0.282945i	−0.772713	+	0.634756i	$0.781101\pi$
$90$		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	−0.570886	−	0.821030i	$-0.693400\pi$
$97$	−3.04230	+	1.41865i	−0.308899	+	0.144042i	0.261987	+	0.965071i	$0.415622\pi$
$98$	−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	0.185996	−	0.982550i	$-0.440449\pi$
$101$	7.00303	−	1.23482i	0.696828	−	0.122870i	0.510831	+	0.859681i	$0.329338\pi$
$102$		0			0
$103$	−13.2831	−	6.19401i	−1.30882	−	0.610314i	−0.362032	−	0.932166i	$-0.617917\pi$
$103$	−13.2831	−	6.19401i	−1.30882	−	0.610314i	−0.946790	+	0.321852i	$0.895695\pi$
$104$	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	0.943140	−	0.332397i	$-0.107857\pi$
$107$	6.31758	+	6.31758i	0.610743	+	0.610743i	−0.332397	+	0.943140i	$0.607857\pi$
$108$		0			0
$109$		−	8.92248i		−	0.854618i	−0.904106	−	0.427309i	$-0.859462\pi$
$109$		−	8.92248i		−	0.854618i	0.904106	−	0.427309i	$-0.140538\pi$
$110$	−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	−0.960428	−	0.278527i	$-0.910154\pi$
$113$	−1.37886	+	2.95698i	−0.129713	+	0.278169i	0.830716	+	0.556697i	$0.187931\pi$
$114$		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	0.776267	−	0.630404i	$-0.217111\pi$
$127$	12.7720	+	3.42225i	1.13333	+	0.303676i	0.357065	+	0.934079i	$0.383777\pi$
$128$	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	0.199002	−	0.979999i	$-0.436230\pi$
$131$	0.581695	+	0.102569i	0.0508229	+	0.00896145i	−0.148179	+	0.988961i	$0.547341\pi$
$132$		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	−0.672875	−	0.739756i	$-0.734941\pi$
$137$	−17.1355	−	1.49916i	−1.46398	−	0.128082i	−0.791110	+	0.611674i	$0.790496\pi$
$138$		0			0
$139$	−11.8215	−	2.08444i	−1.00268	−	0.176800i	−0.351878	−	0.936046i	$-0.614457\pi$
$139$	−11.8215	−	2.08444i	−1.00268	−	0.176800i	−0.650804	+	0.759246i	$0.725568\pi$
$140$	−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	0.281367	−	0.959600i	$-0.409212\pi$
$149$	−7.50454	−	6.29706i	−0.614796	−	0.515875i	−0.896163	+	0.443725i	$0.853657\pi$
$150$		0			0
$151$	−14.4897	−	5.27382i	−1.17916	−	0.429178i	−0.323252	−	0.946313i	$-0.604776\pi$
$151$	−14.4897	−	5.27382i	−1.17916	−	0.429178i	−0.855904	+	0.517135i	$0.826998\pi$
$152$	−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	−0.383716	−	0.923451i	$-0.625356\pi$
$157$	7.14630	−	15.3253i	0.570337	−	1.22309i	0.954052	−	0.299640i	$-0.0968664\pi$
$158$	−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	0.939957	−	0.341293i	$-0.110865\pi$
$163$	7.64324	+	7.64324i	0.598665	+	0.598665i	−0.341293	+	0.939957i	$0.610865\pi$
$164$	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	0.459122	−	0.888373i	$-0.348164\pi$
$167$	0.952493	+	0.444155i	0.0737061	+	0.0343697i	−0.385416	+	0.922743i	$0.625942\pi$
$168$		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	−0.934492	−	0.355985i	$-0.884145\pi$
$173$	−16.6052	+	7.74314i	−1.26247	+	0.588700i	−0.327979	+	0.944685i	$0.606368\pi$
$174$		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	−0.979654	−	0.200694i	$-0.935680\pi$
$179$	−4.22807	+	7.32323i	−0.316021	+	0.547364i	0.663633	+	0.748058i	$0.269014\pi$
$180$		0			0
$181$	0.511902	+	0.886641i	0.0380494	+	0.0659035i	0.884423	−	0.466686i	$-0.154552\pi$
$181$	0.511902	+	0.886641i	0.0380494	+	0.0659035i	−0.846374	+	0.532590i	$0.821219\pi$
$182$	−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	0.664808	−	0.747014i	$-0.268513\pi$
$191$	−2.57471	−	3.06842i	−0.186300	−	0.222023i	−0.851108	+	0.524991i	$0.824069\pi$
$192$		0			0
$193$	0.199928	−	0.139991i	0.0143911	−	0.0100768i	−0.566359	−	0.824159i	$-0.691648\pi$
$193$	0.199928	−	0.139991i	0.0143911	−	0.0100768i	0.580750	+	0.814082i	$0.302759\pi$
$194$	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	−0.821134	−	0.570735i	$-0.806658\pi$
$197$	2.46125	−	9.18550i	0.175357	−	0.654440i	0.996491	−	0.0837043i	$-0.0266751\pi$
$198$		0			0
$199$	4.26708	+	2.46360i	0.302486	+	0.174640i	0.643559	−	0.765397i	$-0.277457\pi$
$199$	4.26708	+	2.46360i	0.302486	+	0.174640i	−0.341073	+	0.940037i	$0.610790\pi$
$200$	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	−0.996481	−	0.0838177i	$-0.973289\pi$
$211$	−24.7804	+	9.01933i	−1.70595	+	0.620916i	−0.709472	+	0.704734i	$0.751066\pi$
$212$	−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	−0.871064	−	0.491169i	$-0.836570\pi$
$223$	−1.66646	+	2.37995i	−0.111594	+	0.159373i	0.759470	+	0.650543i	$0.225459\pi$
$224$	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	0.999560	+	0.0296545i	$0.00944070\pi$
$227$	5.72184	+	12.2705i	0.379772	+	0.814424i	−0.619788	+	0.784769i	$0.712782\pi$
$228$		0			0
$229$	−6.17868	+	7.36346i	−0.408298	+	0.486591i	−0.930532	−	0.366212i	$-0.880655\pi$
$229$	−6.17868	+	7.36346i	−0.408298	+	0.486591i	0.522233	+	0.852803i	$0.325099\pi$
$230$	−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	0.935192	+	0.354142i	$0.115227\pi$
$233$	4.61537	+	17.2248i	0.302363	+	1.12843i	−0.632829	+	0.774292i	$0.718106\pi$
$234$		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	−0.471510	−	0.881861i	$-0.656291\pi$
$239$	4.22324	−	23.9512i	0.273179	−	1.54927i	0.744688	−	0.667412i	$-0.232598\pi$
$240$		0			0
$241$	5.17529	−	4.34259i	0.333370	−	0.279731i	−0.460701	−	0.887555i	$-0.652402\pi$
$241$	5.17529	−	4.34259i	0.333370	−	0.279731i	0.794071	+	0.607825i	$0.207958\pi$
$242$	−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	−0.997817	−	0.0660346i	$-0.978965\pi$
$251$	−22.8066	+	13.1674i	−1.43954	+	0.831118i	−0.441721	+	0.897152i	$0.645632\pi$
$252$		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	−0.902753	−	0.430158i	$-0.858458\pi$
$257$	−1.41734	−	16.2002i	−0.0884111	−	1.01054i	0.814342	−	0.580385i	$-0.197098\pi$
$258$		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	0.392170	−	0.919893i	$-0.371725\pi$
$263$	−5.48334	−	3.83947i	−0.338117	−	0.236752i	−0.730287	+	0.683141i	$0.760613\pi$
$264$		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	0.782050	−	0.623216i	$-0.214174\pi$
$277$	7.72074	+	5.40612i	0.463895	+	0.324822i	−0.318155	+	0.948039i	$0.603063\pi$
$278$	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	−0.963108	−	0.269115i	$-0.913269\pi$
$281$	−0.877392	+	2.41061i	−0.0523408	+	0.143805i	0.910767	+	0.412920i	$0.135491\pi$
$282$		0			0
$283$	1.56435	+	17.8806i	0.0929908	+	1.06289i	0.889093	+	0.457727i	$0.151336\pi$
$283$	1.56435	+	17.8806i	0.0929908	+	1.06289i	−0.796102	+	0.605163i	$0.793108\pi$
$284$	−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	0.982240	+	0.187630i	$0.0600807\pi$
$293$	14.0808	+	20.1095i	0.822609	+	1.17481i	−0.159631	+	0.987177i	$0.551030\pi$
$294$		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	−0.947251	−	0.320493i	$-0.896151\pi$
$307$	−5.03134	−	18.7772i	−0.287154	−	1.07167i	0.660097	−	0.751180i	$-0.270515\pi$
$308$	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	−0.651013	−	0.759067i	$-0.725656\pi$
$311$	3.69580	−	4.40448i	0.209569	−	0.249755i	0.860582	+	0.509312i	$0.170100\pi$
$312$		0			0
$313$	4.98349	+	10.6871i	0.281683	+	0.604072i	0.995340	−	0.0964234i	$-0.0307403\pi$
$313$	4.98349	+	10.6871i	0.281683	+	0.604072i	−0.713657	+	0.700495i	$0.752963\pi$
$314$	−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	−0.530366	−	0.847769i	$-0.677945\pi$
$317$	7.97058	−	11.3832i	0.447672	−	0.639342i	0.978038	+	0.208427i	$0.0668343\pi$
$318$		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	0.639658	+	0.768659i	$0.279076\pi$
$331$	5.48482	+	31.1060i	0.301473	+	1.70974i	−0.338185	+	0.941080i	$0.609813\pi$
$332$	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	0.00530714	−	0.999986i	$-0.498311\pi$
$337$	3.38108	−	0.295807i	0.184179	−	0.0161136i	0.178872	+	0.983872i	$0.442755\pi$
$338$	−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	−0.570376	+	0.821384i	$0.693202\pi$
$347$	−28.6368	+	20.0517i	−1.53730	+	1.07643i	−0.966928	+	0.255048i	$0.917909\pi$
$348$		0			0
$349$	−14.2588	−	16.9930i	−0.763258	−	0.909615i	0.234792	−	0.972046i	$-0.424559\pi$
$349$	−14.2588	−	16.9930i	−0.763258	−	0.909615i	−0.998049	+	0.0624307i	$0.980115\pi$
$350$	−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	−0.617886	−	0.786268i	$-0.712011\pi$
$353$	2.38887	−	27.3049i	0.127147	−	1.45330i	0.745033	−	0.667028i	$-0.232434\pi$
$354$		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	0.894909	−	0.446248i	$-0.147240\pi$
$359$	1.15564	+	2.00162i	0.0609923	+	0.105642i	−0.833917	+	0.551890i	$0.813907\pi$
$360$		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	0.493288	−	0.869866i	$-0.335795\pi$
$367$	28.2899	−	13.1918i	1.47672	−	0.688607i	0.983435	+	0.181259i	$0.0580172\pi$
$368$	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	−0.530721	−	0.847547i	$-0.678079\pi$
$373$	−29.3777	−	13.6991i	−1.52112	−	0.709310i	−0.990399	+	0.138237i	$0.955857\pi$
$374$	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	$0.0397282\pi$
$379$			4.84696i			0.248972i	−0.992221	+	0.124486i	$0.960272\pi$
$380$	−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	−0.993294	−	0.115618i	$-0.963115\pi$
$383$	−5.21058	+	11.1741i	−0.266248	+	0.570971i	0.727046	+	0.686589i	$0.240893\pi$
$384$		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	0.612118	−	0.790767i	$-0.290318\pi$
$389$	11.2960	+	4.11142i	0.572732	+	0.208457i	−0.0393859	+	0.999224i	$0.512540\pi$
$390$		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	−0.170488	−	0.985360i	$-0.554534\pi$
$397$	−16.1554	−	4.32882i	−0.810815	−	0.217257i	−0.640327	+	0.768103i	$0.721201\pi$
$398$	−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	−0.229905	−	0.973213i	$-0.573841\pi$
$401$	−15.5955	−	2.74991i	−0.778803	−	0.137324i	−0.548898	+	0.835889i	$0.684953\pi$
$402$		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	0.00612663	−	0.999981i	$-0.498050\pi$
$409$	−6.67646	−	1.17724i	−0.330130	−	0.0582108i	−0.336257	+	0.941770i	$0.609161\pi$
$410$	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	0.984239	−	0.176845i	$-0.0565892\pi$
$419$	20.0804	+	16.8495i	0.980992	+	0.823150i	−0.00324717	+	0.999995i	$0.501034\pi$
$420$		0			0
$421$	−8.48131	−	3.08694i	−0.413354	−	0.150448i	0.126968	−	0.991907i	$-0.459475\pi$
$421$	−8.48131	−	3.08694i	−0.413354	−	0.150448i	−0.540322	+	0.841458i	$0.681698\pi$
$422$	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	$0.224635\pi$
$431$			26.9295i			1.29715i	−0.761151	+	0.648575i	$0.775365\pi$
$432$		0			0
$433$	−0.461356	−	0.461356i	−0.0221714	−	0.0221714i	0.695934	−	0.718106i	$-0.254991\pi$
$433$	−0.461356	−	0.461356i	−0.0221714	−	0.0221714i	−0.718106	+	0.695934i	$0.754991\pi$
$434$	−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	−0.141866	−	0.989886i	$-0.545310\pi$
$439$	1.32806	−	0.234172i	0.0633847	−	0.0111764i	0.205251	+	0.978709i	$0.434199\pi$
$440$	−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	−0.955411	−	0.295278i	$-0.904588\pi$
$443$	−28.2741	+	13.1844i	−1.34334	+	0.626410i	−0.387930	+	0.921689i	$0.626810\pi$
$444$		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	−0.531631	−	0.846976i	$-0.678421\pi$
$449$	9.91012	−	17.1648i	0.467688	−	0.810059i	0.999318	+	0.0369176i	$0.0117539\pi$
$450$		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	0.920636	+	0.390422i	$0.127671\pi$
$457$	−1.15032	+	13.1482i	−0.0538096	+	0.615046i	−0.974446	+	0.224624i	$0.927885\pi$
$458$	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	0.845563	−	0.533876i	$-0.179265\pi$
$461$	3.71376	+	4.42589i	0.172967	+	0.206134i	−0.672596	+	0.740010i	$0.734821\pi$
$462$		0			0
$463$	−12.0734	+	8.45389i	−0.561099	+	0.392885i	−0.819437	−	0.573169i	$-0.805714\pi$
$463$	−12.0734	+	8.45389i	−0.561099	+	0.392885i	0.258339	+	0.966054i	$0.416825\pi$
$464$	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	−0.690663	−	0.723177i	$-0.742681\pi$
$467$	5.81437	−	21.6995i	0.269057	−	1.00413i	0.959720	−	0.280958i	$-0.0906522\pi$
$468$		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	0.934762	+	0.355274i	$0.115613\pi$
$479$	3.89318	+	22.0793i	0.177884	+	1.00883i	−0.756878	+	0.653556i	$0.773276\pi$
$480$		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	−0.967541	−	0.252714i	$-0.918677\pi$
$487$	−15.7748	+	15.7748i	−0.714827	+	0.714827i	0.252714	+	0.967541i	$0.418677\pi$
$488$	−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	0.832687	−	0.553744i	$-0.186801\pi$
$491$	−3.57036	−	9.80948i	−0.161128	−	0.442696i	−0.993815	+	0.111048i	$0.964579\pi$
$492$		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	−0.862551	−	0.505970i	$-0.831135\pi$
$499$	−4.79129	+	5.71004i	−0.214488	+	0.255617i	0.648063	+	0.761586i	$0.275579\pi$
$500$	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	−0.966127	−	0.258067i	$-0.916914\pi$
$503$	−5.79688	−	21.6342i	−0.258470	−	0.964623i	0.707657	−	0.706556i	$-0.249752\pi$
$504$		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	0.365975	+	0.930625i	$0.380736\pi$
$509$	−6.68306	+	37.9015i	−0.296221	+	1.67996i	−0.662196	+	0.749331i	$0.730375\pi$
$510$		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	0.425529	−	0.904945i	$-0.360088\pi$
$521$	32.4577	−	18.7395i	1.42200	−	0.820992i	0.996470	+	0.0839530i	$0.0267546\pi$
$522$		0			0
$523$	20.3099	−	5.44201i	0.888088	−	0.237962i	0.214195	−	0.976791i	$-0.431287\pi$
$523$	20.3099	−	5.44201i	0.888088	−	0.237962i	0.673893	+	0.738829i	$0.264621\pi$
$524$	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	0.749369	−	0.662152i	$-0.230357\pi$
$547$	8.96813	+	6.27955i	0.383449	+	0.268494i	−0.365920	+	0.930646i	$0.619246\pi$
$548$	−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	−0.277050	−	0.960856i	$-0.589357\pi$
$557$	−0.862701	+	0.231160i	−0.0365538	+	0.00979457i	0.240496	+	0.970650i	$0.422690\pi$
$558$		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	−0.967804	−	0.251706i	$-0.919008\pi$
$563$	−20.7218	−	29.5939i	−0.873322	−	1.24723i	0.0944822	−	0.995527i	$-0.469880\pi$
$564$		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	−0.529666	−	0.848206i	$-0.677683\pi$
$569$	5.09704	−	4.27692i	0.213679	−	0.179298i	0.743345	+	0.668908i	$0.233238\pi$
$570$		0			0
$571$	1.91569	−	10.8644i	0.0801693	−	0.454663i	−0.918126	−	0.396290i	$-0.870298\pi$
$571$	1.91569	−	10.8644i	0.0801693	−	0.454663i	0.998295	−	0.0583730i	$-0.0185913\pi$
$572$	−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	−0.910073	−	0.414449i	$-0.863974\pi$
$577$	−7.90648	−	29.5074i	−0.329151	−	1.22841i	0.580921	−	0.813960i	$-0.302692\pi$
$578$	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	−0.809683	−	0.586867i	$-0.800361\pi$
$587$	0.453527	−	0.647703i	0.0187191	−	0.0267336i	0.828403	+	0.560133i	$0.189250\pi$
$588$		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	0.159029	−	0.987274i	$-0.449164\pi$
$593$	27.9143	−	27.9143i	1.14630	−	1.14630i	0.987274	−	0.159029i	$-0.0508363\pi$
$594$		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	0.499925	−	0.866068i	$-0.333361\pi$
$599$	35.2332	−	12.8238i	1.43959	−	0.523967i	0.939663	+	0.342101i	$0.111139\pi$
$600$		0			0
$601$	0.988708	+	5.60724i	0.0403302	+	0.228724i	0.998310	−	0.0581113i	$-0.0185078\pi$
$601$	0.988708	+	5.60724i	0.0403302	+	0.228724i	−0.957980	+	0.286835i	$0.907397\pi$
$602$	−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	0.152589	−	0.988290i	$-0.451239\pi$
$607$	11.6898	−	1.02272i	0.474474	−	0.0415111i	0.321885	+	0.946779i	$0.395683\pi$
$608$	−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	0.819621	+	0.572906i	$0.194184\pi$
$613$	−4.37352	+	16.3222i	−0.176645	+	0.659247i	−0.996266	+	0.0863408i	$0.972483\pi$
$614$	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	0.0243643	−	0.999703i	$-0.492244\pi$
$617$	24.1467	−	16.9077i	0.972111	−	0.680679i	0.947747	+	0.319024i	$0.103355\pi$
$618$		0			0
$619$	26.5533	+	31.6450i	1.06727	+	1.27192i	0.960692	+	0.277615i	$0.0895439\pi$
$619$	26.5533	+	31.6450i	1.06727	+	1.27192i	0.106575	+	0.994305i	$0.466012\pi$
$620$	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	−0.988232	−	0.152963i	$-0.951118\pi$
$631$	−9.08444	+	15.7347i	−0.361646	+	0.626389i	0.626586	+	0.779352i	$0.284452\pi$
$632$	−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	−0.366241	−	0.930520i	$-0.619355\pi$
$641$	−9.92814	+	1.75060i	−0.392138	+	0.0691445i	−0.0258971	+	0.999665i	$0.508244\pi$
$642$		0			0
$643$	24.3420	+	11.3509i	0.959956	+	0.447635i	0.838464	−	0.544957i	$-0.183454\pi$
$643$	24.3420	+	11.3509i	0.959956	+	0.447635i	0.121492	+	0.992592i	$0.461232\pi$
$644$	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	0.134503	−	0.990913i	$-0.457056\pi$
$647$	−21.7838	−	21.7838i	−0.856411	−	0.856411i	−0.990913	+	0.134503i	$0.957056\pi$
$648$		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	0.600887	+	0.799334i	$0.294814\pi$
$653$	−10.1623	+	21.7931i	−0.397681	+	0.852830i	−0.998568	+	0.0534961i	$0.982964\pi$
$654$		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	0.488813	−	0.872389i	$-0.337430\pi$
$659$	7.76560	+	2.82645i	0.302505	+	0.110103i	−0.186308	+	0.982491i	$0.559652\pi$
$660$		0			0
$661$	16.2837	+	13.6636i	0.633361	+	0.531453i	0.901971	−	0.431796i	$-0.142120\pi$
$661$	16.2837	+	13.6636i	0.633361	+	0.531453i	−0.268610	+	0.963249i	$0.586564\pi$
$662$	−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	−0.485533	−	0.874218i	$-0.661374\pi$
$673$	−28.9385	−	2.53179i	−1.11550	−	0.0975933i	−0.629963	+	0.776625i	$0.716930\pi$
$674$	−8.33063			−0.320884
$675$		0			0
$676$	48.1660			1.85254
$677$	4.20773	+	0.368128i	0.161716	+	0.0141483i	0.167726	−	0.985834i	$-0.446358\pi$
$677$	4.20773	+	0.368128i	0.161716	+	0.0141483i	−0.00601017	+	0.999982i	$0.501913\pi$
$678$		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	−0.653130	−	0.757246i	$-0.726544\pi$
$683$	−41.7463	−	11.1859i	−1.59738	−	0.428017i	−0.944250	+	0.329230i	$0.893211\pi$
$684$		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	0.730509	−	0.682903i	$-0.239283\pi$
$691$	22.3741	+	8.14350i	0.851150	+	0.309793i	0.120641	+	0.992696i	$0.461505\pi$
$692$	−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	$-0.906814\pi$
$701$		−	15.2816i		−	0.577177i	0.957453	−	0.288588i	$-0.0931859\pi$
$702$		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	0.389561	−	0.921001i	$-0.372627\pi$
$709$	28.5077	−	5.02667i	1.07063	−	0.188781i	0.681068	+	0.732220i	$0.261516\pi$
$710$	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	−0.737008	−	0.675884i	$-0.763762\pi$
$719$	5.81410	−	10.0703i	0.216829	−	0.375559i	0.953837	+	0.300325i	$0.0970951\pi$
$720$		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	−0.570178	−	0.821521i	$-0.693126\pi$
$727$	3.61286	−	41.2951i	0.133993	−	1.53155i	0.704171	−	0.710030i	$-0.251319\pi$
$728$	−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	−0.466595	−	0.884471i	$-0.654519\pi$
$733$	5.54883	−	3.88534i	0.204951	−	0.143508i	0.671546	+	0.740963i	$0.265631\pi$
$734$	−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	−0.163197	−	0.986594i	$-0.552181\pi$
$739$	−29.8815	−	17.2521i	−1.09921	−	0.634629i	−0.936014	+	0.351964i	$0.885514\pi$
$740$	−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	0.702634	−	0.711551i	$-0.252007\pi$
$743$	41.3819	−	3.62044i	1.51815	−	0.132821i	0.815519	+	0.578730i	$0.196452\pi$
$744$		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	0.126724	−	0.991938i	$-0.459554\pi$
$751$	23.6063	−	8.59199i	0.861406	−	0.313526i	0.734682	+	0.678412i	$0.237331\pi$
$752$	−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	−0.0154328	+	0.999881i	$0.504913\pi$
$757$	−27.9350	+	27.9350i	−1.01531	+	1.01531i	−0.999881	+	0.0154328i	$0.995087\pi$
$758$	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	0.764546	+	0.644569i	$0.222963\pi$
$761$	16.3639	+	44.9594i	0.593191	+	1.62978i	−0.171355	+	0.985209i	$0.554814\pi$
$762$		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	−0.672210	−	0.740361i	$-0.734655\pi$
$769$	4.81494	−	5.73823i	0.173631	−	0.206926i	0.845841	+	0.533435i	$0.179099\pi$
$770$	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	0.908742	+	0.417358i	$0.137044\pi$
$773$	9.18683	+	34.2857i	0.330427	+	1.23317i	−0.578315	+	0.815814i	$0.696290\pi$
$774$		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	0.445433	−	0.895315i	$-0.353050\pi$
$787$	−15.3799	−	21.9648i	−0.548236	−	0.782962i	−0.993668	+	0.112354i	$0.964161\pi$
$788$	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	0.934173	+	0.356820i	$0.116139\pi$
$797$	2.14990	+	24.5735i	0.0761533	+	0.870437i	−0.858020	+	0.513617i	$0.828305\pi$
$798$		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	−0.962542	−	0.271134i	$-0.912601\pi$
$821$	−1.45874	+	4.00785i	−0.0509103	+	0.139875i	0.911631	+	0.411009i	$0.134824\pi$
$822$		0			0
$823$	−2.33570	−	26.6972i	−0.0814173	−	0.930605i	−0.921559	−	0.388238i	$-0.873084\pi$
$823$	−2.33570	−	26.6972i	−0.0814173	−	0.930605i	0.840142	−	0.542367i	$-0.182472\pi$
$824$	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	−0.385681	−	0.922632i	$-0.626033\pi$
$827$	−7.43022	+	1.99092i	−0.258374	+	0.0692311i	0.127307	+	0.991863i	$0.459367\pi$
$828$		0			0
$829$	−6.05853	+	3.49789i	−0.210421	+	0.121487i	−0.601507	−	0.798867i	$-0.705433\pi$
$829$	−6.05853	+	3.49789i	−0.210421	+	0.121487i	0.391086	+	0.920354i	$0.372100\pi$
$830$	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	−0.706612	−	0.707601i	$-0.749777\pi$
$839$	−3.83684	+	3.21949i	−0.132462	+	0.111149i	0.574149	+	0.818751i	$0.305333\pi$
$840$		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	0.991731	−	0.128336i	$-0.0409637\pi$
$853$	7.47524	+	16.0307i	0.255947	+	0.548881i	−0.735784	+	0.677217i	$0.763186\pi$
$854$	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	−0.892937	−	0.450182i	$-0.851359\pi$
$857$	−4.81571	+	6.87754i	−0.164501	+	0.234932i	0.728435	+	0.685115i	$0.240248\pi$
$858$		0			0
$859$	−0.781638	−	2.14753i	−0.0266691	−	0.0732729i	0.925644	−	0.378397i	$-0.123524\pi$
$859$	−0.781638	−	2.14753i	−0.0266691	−	0.0732729i	−0.952313	+	0.305124i	$0.901302\pi$
$860$	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	−0.748922	−	0.662658i	$-0.769428\pi$
$863$	−2.53415	+	2.53415i	−0.0862635	+	0.0862635i	0.662658	+	0.748922i	$0.269428\pi$
$864$		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	0.955796	−	0.294029i	$-0.0949962\pi$
$877$	57.6923	−	5.04742i	1.94813	−	0.170439i	0.992333	+	0.123590i	$0.0394407\pi$
$878$	−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	−0.0877038	−	0.996147i	$-0.527953\pi$
$881$	−29.5108	−	17.0381i	−0.994244	−	0.574027i	−0.906540	+	0.422120i	$0.861286\pi$
$882$		0			0
$883$	14.6479	−	54.6668i	0.492942	−	1.83969i	−0.0483207	−	0.998832i	$-0.515387\pi$
$883$	14.6479	−	54.6668i	0.492942	−	1.83969i	0.541263	−	0.840853i	$-0.317946\pi$
$884$	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	−0.328229	−	0.944598i	$-0.606452\pi$
$887$	13.3170	−	9.32467i	0.447141	−	0.313092i	0.775371	+	0.631506i	$0.217563\pi$
$888$		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	−0.0905654	−	0.995891i	$-0.528867\pi$
$907$	18.4950	−	8.62436i	0.614117	−	0.286367i	0.704682	+	0.709523i	$0.251090\pi$
$908$	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	−0.475980	−	0.879456i	$-0.657906\pi$
$911$	−18.7876	+	3.31277i	−0.622462	+	0.109757i	−0.146483	+	0.989213i	$0.546795\pi$
$912$		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	$-0.902428\pi$
$919$		−	18.2953i		−	0.603505i	0.953386	−	0.301752i	$-0.0975716\pi$
$920$	−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	−0.00138736	−	0.999999i	$-0.500442\pi$
$929$	−19.6665	−	7.15802i	−0.645237	−	0.234847i	−0.643850	+	0.765152i	$0.722664\pi$
$930$		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	−0.115827	−	0.993269i	$-0.536952\pi$
$937$	−21.8183	−	5.84618i	−0.712771	−	0.190986i	−0.596944	+	0.802283i	$0.703619\pi$
$938$	−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	−0.582975	−	0.812490i	$-0.698111\pi$
$941$	−43.2123	−	7.61949i	−1.40868	−	0.248388i	−0.825705	+	0.564102i	$0.809222\pi$
$942$		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	−0.428335	−	0.903620i	$-0.640900\pi$
$947$	−30.9911	−	2.71137i	−1.00707	−	0.0881076i	−0.578739	+	0.815513i	$0.696455\pi$
$948$		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	0.190035	−	0.981777i	$-0.439140\pi$
$953$	−4.20699	−	1.12726i	−0.136278	−	0.0365155i	−0.326313	+	0.945262i	$0.605806\pi$
$954$		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	0.168031	+	0.985782i	$0.446259\pi$
$967$	−21.6162	+	46.3561i	−0.695130	+	1.49071i	−0.863161	+	0.504929i	$0.831519\pi$
$968$	−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	$0.153135\pi$
$971$			28.8390i			0.925487i	−0.886492	+	0.462744i	$0.846865\pi$
$972$		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	0.895638	−	0.444784i	$-0.146719\pi$
$977$	35.3398	+	16.4792i	1.13062	+	0.527216i	0.234981	+	0.972000i	$0.424497\pi$
$978$		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	−0.209186	−	0.977876i	$-0.567081\pi$
$983$	12.7120	−	5.92768i	0.405448	−	0.189064i	0.614634	+	0.788812i	$0.289304\pi$
$984$		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	0.737296	−	0.675570i	$-0.236102\pi$
$991$	−6.81269	−	11.7999i	−0.216412	−	0.374837i	−0.953709	+	0.300732i	$0.902769\pi$
$992$	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	0.557886	+	0.829918i	$0.311613\pi$
$997$	−4.28282	+	48.9528i	−0.135638	+	1.55035i	−0.693524	+	0.720434i	$0.743943\pi$
$998$	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.368.1		192
3.2	odd	2		135.2.q.a.113.16	yes	192
5.2	odd	4	inner	405.2.r.a.287.16		192
15.2	even	4		135.2.q.a.32.1	✓	192
15.8	even	4		675.2.ba.b.32.16		192
15.14	odd	2		675.2.ba.b.518.1		192
27.11	odd	18	inner	405.2.r.a.278.16		192
27.16	even	9		135.2.q.a.38.1	yes	192
135.43	odd	36		675.2.ba.b.632.1		192
135.92	even	36	inner	405.2.r.a.197.1		192
135.97	odd	36		135.2.q.a.92.16	yes	192
135.124	even	18		675.2.ba.b.443.16		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.1	✓	192	15.2	even	4
135.2.q.a.38.1	yes	192	27.16	even	9
135.2.q.a.92.16	yes	192	135.97	odd	36
135.2.q.a.113.16	yes	192	3.2	odd	2
405.2.r.a.197.1		192	135.92	even	36	inner
405.2.r.a.278.16		192	27.11	odd	18	inner
405.2.r.a.287.16		192	5.2	odd	4	inner
405.2.r.a.368.1		192	1.1	even	1	trivial
675.2.ba.b.32.16		192	15.8	even	4
675.2.ba.b.443.16		192	135.124	even	18
675.2.ba.b.518.1		192	15.14	odd	2
675.2.ba.b.632.1		192	135.43	odd	36

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)

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

L-functions

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