LMFDB - Embedded newform 405.2.r.a.8.6

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			8.6
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.490069 + 0.343150i) q^{2} +(-0.561625 + 1.54305i) q^{4} +(1.25284 - 1.85213i) q^{5} +(-0.0636379 + 0.136472i) q^{7} +(-0.563947 - 2.10468i) q^{8} +O(q^{10})$	\(q+(-0.490069 + 0.343150i) q^{2} +(-0.561625 + 1.54305i) q^{4} +(1.25284 - 1.85213i) q^{5} +(-0.0636379 + 0.136472i) q^{7} +(-0.563947 - 2.10468i) q^{8} +(0.0215816 + 1.33758i) q^{10} +(3.54970 - 4.23037i) q^{11} +(1.08490 - 1.54940i) q^{13} +(-0.0156434 - 0.0887180i) q^{14} +(-1.51722 - 1.27310i) q^{16} +(-1.18141 + 4.40907i) q^{17} +(6.55178 + 3.78267i) q^{19} +(2.15431 + 2.97340i) q^{20} +(-0.287947 + 3.29125i) q^{22} +(0.883698 - 0.412075i) q^{23} +(-1.86079 - 4.64085i) q^{25} +1.13159i q^{26} +(-0.174843 - 0.174843i) q^{28} +(0.486461 - 2.75886i) q^{29} +(1.70974 + 0.622294i) q^{31} +(5.52167 + 0.483084i) q^{32} +(-0.934001 - 2.56615i) q^{34} +(0.173036 + 0.288843i) q^{35} +(5.71298 + 1.53079i) q^{37} +(-4.50885 + 0.394473i) q^{38} +(-4.60468 - 1.59232i) q^{40} +(0.682276 - 0.120304i) q^{41} +(0.151755 + 1.73456i) q^{43} +(4.53407 + 7.85325i) q^{44} +(-0.291669 + 0.505186i) q^{46} +(-10.0941 - 4.70696i) q^{47} +(4.48494 + 5.34494i) q^{49} +(2.50442 + 1.63581i) q^{50} +(1.78149 + 2.54423i) q^{52} +(-0.204978 + 0.204978i) q^{53} +(-3.38800 - 11.8745i) q^{55} +(0.323118 + 0.0569745i) q^{56} +(0.708303 + 1.51896i) q^{58} +(-0.796564 + 0.668396i) q^{59} +(9.12620 - 3.32167i) q^{61} +(-1.05143 + 0.281730i) q^{62} +(0.558711 - 0.322572i) q^{64} +(-1.51048 - 3.95052i) q^{65} +(-8.96216 - 6.27537i) q^{67} +(-6.13991 - 4.29921i) q^{68} +(-0.183916 - 0.0821758i) q^{70} +(2.53024 - 1.46084i) q^{71} +(-9.95358 + 2.66706i) q^{73} +(-3.32505 + 1.21022i) q^{74} +(-9.51649 + 7.98529i) q^{76} +(0.351431 + 0.753647i) q^{77} +(-11.9179 - 2.10144i) q^{79} +(-4.25878 + 1.21510i) q^{80} +(-0.293080 + 0.293080i) q^{82} +(-4.10306 - 5.85978i) q^{83} +(6.68606 + 7.71197i) q^{85} +(-0.669585 - 0.797981i) q^{86} +(-10.9054 - 5.08528i) q^{88} +(-6.74192 + 11.6773i) q^{89} +(0.142409 + 0.246659i) q^{91} +(0.139546 + 1.59502i) q^{92} +(6.56201 - 1.15706i) q^{94} +(15.2143 - 7.39568i) q^{95} +(3.56471 - 0.311872i) q^{97} +(-4.03205 - 1.08038i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−0.490069	+	0.343150i	−0.346531	+	0.242644i	−0.733864	−	0.679296i	$-0.762285\pi$
$2$	−0.490069	+	0.343150i	−0.346531	+	0.242644i	0.387333	+	0.921940i	$0.373396\pi$
$3$		0			0
$3$		0			0
$4$	−0.561625	+	1.54305i	−0.280812	+	0.771525i
$5$	1.25284	−	1.85213i	0.560287	−	0.828299i
$5$	1.25284	−	1.85213i	0.560287	−	0.828299i
$6$		0			0
$7$	−0.0636379	+	0.136472i	−0.0240529	+	0.0515816i	−0.917967	−	0.396656i	$-0.870170\pi$
$7$	−0.0636379	+	0.136472i	−0.0240529	+	0.0515816i	0.893914	+	0.448238i	$0.147948\pi$
$8$	−0.563947	−	2.10468i	−0.199385	−	0.744117i
$9$		0			0
$10$	0.0215816	+	1.33758i	0.00682471	+	0.422981i
$11$	3.54970	−	4.23037i	1.07027	−	1.27550i	0.110760	−	0.993847i	$-0.464672\pi$
$11$	3.54970	−	4.23037i	1.07027	−	1.27550i	0.959515	−	0.281657i	$-0.0908840\pi$
$12$		0			0
$13$	1.08490	−	1.54940i	0.300897	−	0.429725i	−0.640022	−	0.768356i	$-0.721075\pi$
$13$	1.08490	−	1.54940i	0.300897	−	0.429725i	0.940919	+	0.338631i	$0.109964\pi$
$14$	−0.0156434	−	0.0887180i	−0.00418087	−	0.0237109i
$15$		0			0
$16$	−1.51722	−	1.27310i	−0.379305	−	0.318275i
$17$	−1.18141	+	4.40907i	−0.286533	+	1.06936i	0.661179	+	0.750228i	$0.270056\pi$
$17$	−1.18141	+	4.40907i	−0.286533	+	1.06936i	−0.947712	+	0.319127i	$0.896610\pi$
$18$		0			0
$19$	6.55178	+	3.78267i	1.50308	+	0.867804i	0.999994	+	0.00356839i	$0.00113586\pi$
$19$	6.55178	+	3.78267i	1.50308	+	0.867804i	0.503087	+	0.864236i	$0.332197\pi$
$20$	2.15431	+	2.97340i	0.481718	+	0.664872i
$21$		0			0
$22$	−0.287947	+	3.29125i	−0.0613906	+	0.701697i
$23$	0.883698	−	0.412075i	0.184264	−	0.0859236i	−0.328297	−	0.944575i	$-0.606475\pi$
$23$	0.883698	−	0.412075i	0.184264	−	0.0859236i	0.512561	+	0.858651i	$0.328697\pi$
$24$		0			0
$25$	−1.86079	−	4.64085i	−0.372158	−	0.928170i
$26$			1.13159i			0.221924i
$27$		0			0
$28$	−0.174843	−	0.174843i	−0.0330421	−	0.0330421i
$29$	0.486461	−	2.75886i	0.0903336	−	0.512307i	−0.905744	−	0.423825i	$-0.860687\pi$
$29$	0.486461	−	2.75886i	0.0903336	−	0.512307i	0.996078	−	0.0884824i	$-0.0282017\pi$
$30$		0			0
$31$	1.70974	+	0.622294i	0.307078	+	0.111767i	0.490963	−	0.871181i	$-0.336645\pi$
$31$	1.70974	+	0.622294i	0.307078	+	0.111767i	−0.183885	+	0.982948i	$0.558867\pi$
$32$	5.52167	+	0.483084i	0.976103	+	0.0853979i
$33$		0			0
$34$	−0.934001	−	2.56615i	−0.160180	−	0.440090i
$35$	0.173036	+	0.288843i	0.0292484	+	0.0488234i
$36$		0			0
$37$	5.71298	+	1.53079i	0.939209	+	0.251660i	0.695777	−	0.718258i	$-0.255060\pi$
$37$	5.71298	+	1.53079i	0.939209	+	0.251660i	0.243432	+	0.969918i	$0.421727\pi$
$38$	−4.50885	+	0.394473i	−0.731431	+	0.0639920i
$39$		0			0
$40$	−4.60468	−	1.59232i	−0.728064	−	0.251768i
$41$	0.682276	−	0.120304i	0.106554	−	0.0187883i	−0.120117	−	0.992760i	$-0.538327\pi$
$41$	0.682276	−	0.120304i	0.106554	−	0.0187883i	0.226671	+	0.973971i	$0.427216\pi$
$42$		0			0
$43$	0.151755	+	1.73456i	0.0231424	+	0.264518i	0.998947	+	0.0458750i	$0.0146076\pi$
$43$	0.151755	+	1.73456i	0.0231424	+	0.264518i	−0.975805	+	0.218643i	$0.929837\pi$
$44$	4.53407	+	7.85325i	0.683537	+	1.18392i
$45$		0			0
$46$	−0.291669	+	0.505186i	−0.0430043	+	0.0744856i
$47$	−10.0941	−	4.70696i	−1.47238	−	0.686581i	−0.489698	−	0.871892i	$-0.662893\pi$
$47$	−10.0941	−	4.70696i	−1.47238	−	0.686581i	−0.982680	+	0.185311i	$0.940671\pi$
$48$		0			0
$49$	4.48494	+	5.34494i	0.640705	+	0.763563i
$50$	2.50442	+	1.63581i	0.354179	+	0.231338i
$51$		0			0
$52$	1.78149	+	2.54423i	0.247049	+	0.352822i
$53$	−0.204978	+	0.204978i	−0.0281559	+	0.0281559i	−0.721045	−	0.692889i	$-0.756338\pi$
$53$	−0.204978	+	0.204978i	−0.0281559	+	0.0281559i	0.692889	+	0.721045i	$0.256338\pi$
$54$		0			0
$55$	−3.38800	−	11.8745i	−0.456838	−	1.60116i
$56$	0.323118	+	0.0569745i	0.0431785	+	0.00761353i
$57$		0			0
$58$	0.708303	+	1.51896i	0.0930047	+	0.199449i
$59$	−0.796564	+	0.668396i	−0.103704	+	0.0870178i	−0.693165	−	0.720779i	$-0.743784\pi$
$59$	−0.796564	+	0.668396i	−0.103704	+	0.0870178i	0.589462	+	0.807796i	$0.299340\pi$
$60$		0			0
$61$	9.12620	−	3.32167i	1.16849	−	0.425296i	0.316367	−	0.948637i	$-0.397537\pi$
$61$	9.12620	−	3.32167i	1.16849	−	0.425296i	0.852123	+	0.523341i	$0.175315\pi$
$62$	−1.05143	+	0.281730i	−0.133532	+	0.0357797i
$63$		0			0
$64$	0.558711	−	0.322572i	0.0698389	−	0.0403215i
$65$	−1.51048	−	3.95052i	−0.187352	−	0.490002i
$66$		0			0
$67$	−8.96216	−	6.27537i	−1.09490	−	0.766659i	−0.120780	−	0.992679i	$-0.538539\pi$
$67$	−8.96216	−	6.27537i	−1.09490	−	0.766659i	−0.974122	+	0.226021i	$0.927428\pi$
$68$	−6.13991	−	4.29921i	−0.744573	−	0.521356i
$69$		0			0
$70$	−0.183916	−	0.0821758i	−0.0219822	−	0.00982189i
$71$	2.53024	−	1.46084i	0.300285	−	0.173369i	−0.342286	−	0.939596i	$-0.611201\pi$
$71$	2.53024	−	1.46084i	0.300285	−	0.173369i	0.642571	+	0.766226i	$0.277868\pi$
$72$		0			0
$73$	−9.95358	+	2.66706i	−1.16498	+	0.312155i	−0.788953	−	0.614454i	$-0.789376\pi$
$73$	−9.95358	+	2.66706i	−1.16498	+	0.312155i	−0.376026	+	0.926609i	$0.622710\pi$
$74$	−3.32505	+	1.21022i	−0.386529	+	0.140685i
$75$		0			0
$76$	−9.51649	+	7.98529i	−1.09162	+	0.915975i
$77$	0.351431	+	0.753647i	0.0400493	+	0.0858860i
$78$		0			0
$79$	−11.9179	−	2.10144i	−1.34086	−	0.236430i	−0.543236	−	0.839580i	$-0.682801\pi$
$79$	−11.9179	−	2.10144i	−1.34086	−	0.236430i	−0.797628	+	0.603150i	$0.793912\pi$
$80$	−4.25878	+	1.21510i	−0.476146	+	0.135853i
$81$		0			0
$82$	−0.293080	+	0.293080i	−0.0323653	+	0.0323653i
$83$	−4.10306	−	5.85978i	−0.450370	−	0.643194i	0.528198	−	0.849121i	$-0.322868\pi$
$83$	−4.10306	−	5.85978i	−0.450370	−	0.643194i	−0.978567	+	0.205927i	$0.933979\pi$
$84$		0			0
$85$	6.68606	+	7.71197i	0.725205	+	0.836481i
$86$	−0.669585	−	0.797981i	−0.0722033	−	0.0860485i
$87$		0			0
$88$	−10.9054	−	5.08528i	−1.16252	−	0.542092i
$89$	−6.74192	+	11.6773i	−0.714642	+	1.23780i	0.248455	+	0.968643i	$0.420077\pi$
$89$	−6.74192	+	11.6773i	−0.714642	+	1.23780i	−0.963097	+	0.269153i	$0.913256\pi$
$90$		0			0
$91$	0.142409	+	0.246659i	0.0149285	+	0.0258569i
$92$	0.139546	+	1.59502i	0.0145487	+	0.166293i
$93$		0			0
$94$	6.56201	−	1.15706i	0.676819	−	0.119341i
$95$	15.2143	−	7.39568i	1.56096	−	0.758781i
$96$		0			0
$97$	3.56471	−	0.311872i	0.361941	−	0.0316658i	0.0952651	−	0.995452i	$-0.469630\pi$
$97$	3.56471	−	0.311872i	0.361941	−	0.0316658i	0.266676	+	0.963786i	$0.414075\pi$
$98$	−4.03205	−	1.08038i	−0.407298	−	0.109135i
$99$		0			0
$100$	8.20613	−	0.264877i	0.820613	−	0.0264877i
$101$	1.31720	+	3.61898i	0.131067	+	0.360102i	0.987815	−	0.155632i	$-0.0497414\pi$
$101$	1.31720	+	3.61898i	0.131067	+	0.360102i	−0.856749	+	0.515734i	$0.827519\pi$
$102$		0			0
$103$	−12.2709	−	1.07356i	−1.20909	−	0.105781i	−0.535270	−	0.844681i	$-0.679790\pi$
$103$	−12.2709	−	1.07356i	−1.20909	−	0.105781i	−0.673816	+	0.738900i	$0.735346\pi$
$104$	−3.87281	−	1.40959i	−0.379760	−	0.138221i
$105$		0			0
$106$	0.0301151	−	0.170791i	0.00292504	−	0.0165887i
$107$	−0.874553	−	0.874553i	−0.0845462	−	0.0845462i	0.663569	−	0.748115i	$-0.269041\pi$
$107$	−0.874553	−	0.874553i	−0.0845462	−	0.0845462i	−0.748115	+	0.663569i	$0.769041\pi$
$108$		0			0
$109$			8.22348i			0.787666i	0.919182	+	0.393833i	$0.128851\pi$
$109$			8.22348i			0.787666i	−0.919182	+	0.393833i	$0.871149\pi$
$110$	5.73508	+	4.65673i	0.546819	+	0.444001i
$111$		0			0
$112$	0.270295	−	0.126041i	0.0255405	−	0.0119097i
$113$	−0.174058	+	1.98949i	−0.0163740	+	0.187156i	0.983603	+	0.180348i	$0.0577225\pi$
$113$	−0.174058	+	1.98949i	−0.0163740	+	0.187156i	−0.999977	+	0.00680753i	$0.997833\pi$
$114$		0			0
$115$	0.343914	−	2.15299i	0.0320701	−	0.200767i
$116$	3.98385	+	2.30008i	0.369891	+	0.213557i
$117$		0			0
$118$	0.161011	−	0.600901i	0.0148223	−	0.0553174i
$119$	−0.526532	−	0.441813i	−0.0482671	−	0.0405009i
$120$		0			0
$121$	−3.38551	−	19.2002i	−0.307774	−	1.74547i
$122$	−3.33264	+	4.75950i	−0.301723	+	0.430905i
$123$		0			0
$124$	−1.92046	+	2.28872i	−0.172463	+	0.205533i
$125$	−10.9267	−	2.36781i	−0.977317	−	0.211783i
$126$		0			0
$127$	−1.72156	−	6.42494i	−0.152764	−	0.570121i	−0.999286	−	0.0377691i	$-0.987975\pi$
$127$	−1.72156	−	6.42494i	−0.152764	−	0.570121i	0.846523	−	0.532352i	$-0.178692\pi$
$128$	−4.84806	+	10.3967i	−0.428512	+	0.918948i
$129$		0			0
$130$	2.09586	+	1.41771i	0.183819	+	0.124341i
$131$	−4.62535	+	12.7080i	−0.404119	+	1.11031i	0.556114	+	0.831106i	$0.312292\pi$
$131$	−4.62535	+	12.7080i	−0.404119	+	1.11031i	−0.960233	+	0.279201i	$0.909930\pi$
$132$		0			0
$133$	−0.933170	+	0.653413i	−0.0809161	+	0.0566581i
$134$	6.54547			0.565442
$135$		0			0
$136$	9.94592			0.852856
$137$	−6.70575	+	4.69542i	−0.572911	+	0.401156i	−0.823818	−	0.566855i	$-0.808160\pi$
$137$	−6.70575	+	4.69542i	−0.572911	+	0.401156i	0.250907	+	0.968011i	$0.419271\pi$
$138$		0			0
$139$	6.24384	−	17.1548i	0.529596	−	1.45505i	−0.329952	−	0.943998i	$-0.607033\pi$
$139$	6.24384	−	17.1548i	0.529596	−	1.45505i	0.859548	−	0.511055i	$-0.170745\pi$
$140$	−0.542881	+	0.104782i	−0.0458818	+	0.00885569i
$141$		0			0
$142$	−0.738707	+	1.58416i	−0.0619909	+	0.132940i
$143$	−2.70345	−	10.0894i	−0.226074	−	0.843720i
$144$		0			0
$145$	−4.50031	−	4.35740i	−0.373731	−	0.361862i
$146$	3.96274	−	4.72261i	0.327959	−	0.390846i
$147$		0			0
$148$	−5.57064	+	7.95570i	−0.457904	+	0.653954i
$149$	0.725914	+	4.11686i	0.0594692	+	0.337266i	0.999997	−	0.00245028i	$-0.000779950\pi$
$149$	0.725914	+	4.11686i	0.0594692	+	0.337266i	−0.940528	+	0.339717i	$0.889669\pi$
$150$		0			0
$151$	3.72470	+	3.12540i	0.303112	+	0.254341i	0.781638	−	0.623732i	$-0.214384\pi$
$151$	3.72470	+	3.12540i	0.303112	+	0.254341i	−0.478526	+	0.878073i	$0.658829\pi$
$152$	4.26645	−	15.9226i	0.346055	−	1.29149i
$153$		0			0
$154$	−0.430839	−	0.248745i	−0.0347180	−	0.0200445i
$155$	3.29460	−	2.38703i	0.264628	−	0.191731i
$156$		0			0
$157$	−1.51739	+	17.3439i	−0.121101	+	1.38419i	0.655974	+	0.754783i	$0.272258\pi$
$157$	−1.51739	+	17.3439i	−0.121101	+	1.38419i	−0.777075	+	0.629407i	$0.783298\pi$
$158$	6.56168	−	3.05976i	0.522019	−	0.243422i
$159$		0			0
$160$	7.81250	−	9.62164i	0.617633	−	0.760658i
$161$			0.146824i			0.0115713i
$162$		0			0
$163$	2.64439	+	2.64439i	0.207124	+	0.207124i	0.803044	−	0.595920i	$-0.203212\pi$
$163$	2.64439	+	2.64439i	0.207124	+	0.207124i	−0.595920	+	0.803044i	$0.703212\pi$
$164$	−0.197548	+	1.12035i	−0.0154259	+	0.0874848i
$165$		0			0
$166$	4.02157	+	1.46373i	0.312134	+	0.113608i
$167$	−0.523503	−	0.0458006i	−0.0405099	−	0.00354415i	0.0668828	−	0.997761i	$-0.478695\pi$
$167$	−0.523503	−	0.0458006i	−0.0405099	−	0.00354415i	−0.107393	+	0.994217i	$0.534250\pi$
$168$		0			0
$169$	3.22264	+	8.85412i	0.247895	+	0.681086i
$170$	−5.92299	−	1.48507i	−0.454273	−	0.113900i
$171$		0			0
$172$	−2.76175	−	0.740008i	−0.210581	−	0.0564251i
$173$	17.5306	−	1.53373i	1.33282	−	0.116607i	0.601629	−	0.798776i	$-0.294519\pi$
$173$	17.5306	−	1.53373i	1.33282	−	0.116607i	0.731195	+	0.682169i	$0.238963\pi$
$174$		0			0
$175$	0.751762	+	0.0413885i	0.0568279	+	0.00312867i
$176$	−10.7714	+	1.89928i	−0.811921	+	0.143164i
$177$		0			0
$178$	−0.703076	−	8.03619i	−0.0526978	−	0.602338i
$179$	0.435152	+	0.753705i	0.0325248	+	0.0563346i	0.881830	−	0.471568i	$-0.156312\pi$
$179$	0.435152	+	0.753705i	0.0325248	+	0.0563346i	−0.849305	+	0.527903i	$0.822979\pi$
$180$		0			0
$181$	5.47447	−	9.48206i	0.406914	−	0.704796i	−0.587628	−	0.809131i	$-0.699938\pi$
$181$	5.47447	−	9.48206i	0.406914	−	0.704796i	0.994542	+	0.104335i	$0.0332715\pi$
$182$	−0.154431	−	0.0720123i	−0.0114472	−	0.00533791i
$183$		0			0
$184$	−1.36565	−	1.62751i	−0.100677	−	0.119982i
$185$	9.99267	−	8.66337i	0.734676	−	0.636943i
$186$		0			0
$187$	14.4583	+	20.6486i	1.05730	+	1.50998i
$188$	12.9322	−	12.9322i	0.943177	−	0.943177i
$189$		0			0
$190$	−4.91824	+	8.84519i	−0.356807	+	0.641698i
$191$	−14.0251	−	2.47300i	−1.01482	−	0.178940i	−0.358585	−	0.933497i	$-0.616741\pi$
$191$	−14.0251	−	2.47300i	−1.01482	−	0.178940i	−0.656234	+	0.754557i	$0.727852\pi$
$192$		0			0
$193$	5.12102	+	10.9821i	0.368619	+	0.790506i	0.999888	+	0.0149426i	$0.00475655\pi$
$193$	5.12102	+	10.9821i	0.368619	+	0.790506i	−0.631269	+	0.775564i	$0.717466\pi$
$194$	−1.63993	+	1.37607i	−0.117740	+	0.0987960i
$195$		0			0
$196$	−10.7664	+	3.91864i	−0.769026	+	0.279903i
$197$	10.7112	−	2.87005i	0.763138	−	0.204482i	0.143800	−	0.989607i	$-0.454068\pi$
$197$	10.7112	−	2.87005i	0.763138	−	0.204482i	0.619338	+	0.785124i	$0.287401\pi$
$198$		0			0
$199$	3.29595	−	1.90292i	0.233644	−	0.134894i	−0.378608	−	0.925557i	$-0.623597\pi$
$199$	3.29595	−	1.90292i	0.233644	−	0.134894i	0.612252	+	0.790663i	$0.290264\pi$
$200$	−8.71811	+	6.53356i	−0.616464	+	0.461992i
$201$		0			0
$202$	−1.88737	−	1.32155i	−0.132795	−	0.0929842i
$203$	0.345550	+	0.241956i	0.0242528	+	0.0169820i
$204$		0			0
$205$	0.631964	−	1.41439i	0.0441383	−	0.0987851i
$206$	6.38197	−	3.68463i	0.444653	−	0.256720i
$207$		0			0
$208$	−3.61857	+	0.969592i	−0.250902	+	0.0672291i
$209$	39.2589	−	14.2891i	2.71560	−	0.988397i
$210$		0			0
$211$	−0.117333	+	0.0984540i	−0.00807753	+	0.00677785i	−0.646817	−	0.762645i	$-0.723900\pi$
$211$	−0.117333	+	0.0984540i	−0.00807753	+	0.00677785i	0.638740	+	0.769423i	$0.279456\pi$
$212$	−0.201171	−	0.431412i	−0.0138165	−	0.0296295i
$213$		0			0
$214$	0.728694	+	0.128488i	0.0498125	+	0.00878329i
$215$	3.40276	+	1.89206i	0.232067	+	0.129037i
$216$		0			0
$217$	−0.193730	+	0.193730i	−0.0131512	+	0.0131512i
$218$	−2.82189	−	4.03007i	−0.191122	−	0.272951i
$219$		0			0
$220$	20.2257	+	1.44115i	1.36362	+	0.0971623i
$221$	5.54969	+	6.61386i	0.373312	+	0.444896i
$222$		0			0
$223$	24.0272	+	11.2041i	1.60898	+	0.750281i	0.999108	−	0.0422168i	$-0.0134420\pi$
$223$	24.0272	+	11.2041i	1.60898	+	0.750281i	0.609875	+	0.792498i	$0.291220\pi$
$224$	−0.417315	+	0.722811i	−0.0278830	+	0.0482948i
$225$		0			0
$226$	−0.597394	−	1.03472i	−0.0397381	−	0.0688283i
$227$	1.41372	+	16.1589i	0.0938320	+	1.07250i	0.886462	+	0.462802i	$0.153156\pi$
$227$	1.41372	+	16.1589i	0.0938320	+	1.07250i	−0.792630	+	0.609703i	$0.791289\pi$
$228$		0			0
$229$	2.26795	−	0.399901i	0.149871	−	0.0264262i	−0.0982095	−	0.995166i	$-0.531312\pi$
$229$	2.26795	−	0.399901i	0.149871	−	0.0264262i	0.248080	+	0.968740i	$0.420200\pi$
$230$	0.570257	+	1.17313i	0.0376016	+	0.0773537i
$231$		0			0
$232$	−6.08085	+	0.532006i	−0.399228	+	0.0349279i
$233$	−5.48640	−	1.47008i	−0.359426	−	0.0963080i	0.0745868	−	0.997215i	$-0.476236\pi$
$233$	−5.48640	−	1.47008i	−0.359426	−	0.0963080i	−0.434013	+	0.900907i	$0.642903\pi$
$234$		0			0
$235$	−21.3642	+	12.7986i	−1.39365	+	0.834886i
$236$	−0.584000	−	1.60453i	−0.0380152	−	0.104446i
$237$		0			0
$238$	0.409645	+	0.0358393i	0.0265533	+	0.00232312i
$239$	−27.4639	−	9.99603i	−1.77649	−	0.646589i	−0.999862	−	0.0166299i	$-0.994706\pi$
$239$	−27.4639	−	9.99603i	−1.77649	−	0.646589i	−0.776628	−	0.629960i	$-0.783071\pi$
$240$		0			0
$241$	−1.09121	+	6.18855i	−0.0702909	+	0.398639i	0.929281	+	0.369374i	$0.120428\pi$
$241$	−1.09121	+	6.18855i	−0.0702909	+	0.398639i	−0.999572	+	0.0292653i	$0.990683\pi$
$242$	8.24768	+	8.24768i	0.530181	+	0.530181i
$243$		0			0
$244$			15.9477i			1.02095i
$245$	15.5184	−	1.61035i	0.991437	−	0.102881i
$246$		0			0
$247$	12.9689	−	6.04749i	0.825190	−	0.384792i
$248$	0.345527	−	3.94939i	0.0219410	−	0.250787i
$249$		0			0
$250$	6.16737	−	2.58912i	0.390058	−	0.163750i
$251$	7.99676	+	4.61693i	0.504751	+	0.291418i	0.730673	−	0.682727i	$-0.239206\pi$
$251$	7.99676	+	4.61693i	0.504751	+	0.291418i	−0.225923	+	0.974145i	$0.572540\pi$
$252$		0			0
$253$	1.39363	−	5.20111i	0.0876170	−	0.326991i
$254$	3.04840	+	2.55791i	0.191274	+	0.160498i
$255$		0			0
$256$	−0.967687	−	5.48803i	−0.0604805	−	0.343002i
$257$	−9.43754	+	13.4782i	−0.588697	+	0.840747i	−0.997411	−	0.0719158i	$-0.977089\pi$
$257$	−9.43754	+	13.4782i	−0.588697	+	0.840747i	0.408713	+	0.912663i	$0.365978\pi$
$258$		0			0
$259$	−0.572472	+	0.682246i	−0.0355717	+	0.0423927i
$260$	6.94418	−	0.112043i	0.430660	−	0.00694860i
$261$		0			0
$262$	−2.09402	−	7.81501i	−0.129369	−	0.482813i
$263$	−5.18376	+	11.1166i	−0.319644	+	0.685480i	−0.998824	−	0.0484930i	$-0.984558\pi$
$263$	−5.18376	+	11.1166i	−0.319644	+	0.685480i	0.679179	+	0.733973i	$0.262336\pi$
$264$		0			0
$265$	0.122842	+	0.636450i	0.00754611	+	0.0390968i
$266$	0.233099	−	0.640435i	0.0142922	−	0.0392676i
$267$		0			0
$268$	14.7166	−	10.3047i	0.898959	−	0.629458i
$269$	−18.4528			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$269$	−18.4528			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$270$		0			0
$271$	−13.3622			−0.811695			−0.405848	−	0.913941i	$-0.633024\pi$
$271$	−13.3622			−0.811695			−0.405848	+	0.913941i	$0.633024\pi$
$272$	7.40563	−	5.18548i	0.449032	−	0.314416i
$273$		0			0
$274$	1.67505	−	4.60215i	0.101193	−	0.278026i
$275$	−26.2377	−	8.60180i	−1.58220	−	0.518708i
$276$		0			0
$277$	−9.07810	+	19.4680i	−0.545450	+	1.16972i	0.419613	+	0.907703i	$0.362166\pi$
$277$	−9.07810	+	19.4680i	−0.545450	+	1.16972i	−0.965063	+	0.262018i	$0.915612\pi$
$278$	2.82676	+	10.5496i	0.169538	+	0.632724i
$279$		0			0
$280$	0.510339	−	0.527078i	0.0304986	−	0.0314989i
$281$	−4.46928	+	5.32628i	−0.266615	+	0.317739i	−0.882697	−	0.469943i	$-0.844275\pi$
$281$	−4.46928	+	5.32628i	−0.266615	+	0.317739i	0.616082	+	0.787682i	$0.288719\pi$
$282$		0			0
$283$	13.8553	−	19.7874i	0.823612	−	1.17624i	−0.158391	−	0.987376i	$-0.550631\pi$
$283$	13.8553	−	19.7874i	0.823612	−	1.17624i	0.982003	−	0.188864i	$-0.0604805\pi$
$284$	0.833098	+	4.72473i	0.0494353	+	0.280361i
$285$		0			0
$286$	4.78706	+	4.01682i	0.283065	+	0.237520i
$287$	−0.0270006	+	0.100767i	−0.00159379	+	0.00594811i
$288$		0			0
$289$	−3.32171	−	1.91779i	−0.195395	−	0.112811i
$290$	3.70071	+	0.591142i	0.217313	+	0.0347131i
$291$		0			0
$292$	1.47478	−	16.8568i	0.0863048	−	0.986468i
$293$	14.5847	−	6.80096i	0.852048	−	0.397316i	0.0530076	−	0.998594i	$-0.483119\pi$
$293$	14.5847	−	6.80096i	0.852048	−	0.397316i	0.799040	+	0.601278i	$0.205341\pi$
$294$		0			0
$295$	0.239992	+	2.31273i	0.0139729	+	0.134653i
$296$		−	12.8873i		−	0.749058i
$297$		0			0
$298$	−1.76845	−	1.76845i	−0.102443	−	0.102443i
$299$	0.320256	−	1.81626i	0.0185209	−	0.105037i
$300$		0			0
$301$	−0.246377	−	0.0896737i	−0.0142009	−	0.00516871i
$302$	−2.89784	−	0.253528i	−0.166752	−	0.0145889i
$303$		0			0
$304$	−5.12477	−	14.0802i	−0.293926	−	0.807555i
$305$	5.28150	−	21.0645i	0.302418	−	1.20615i
$306$		0			0
$307$	−30.9704	−	8.29849i	−1.76757	−	0.473620i	−0.779343	−	0.626598i	$-0.784447\pi$
$307$	−30.9704	−	8.29849i	−1.76757	−	0.473620i	−0.988230	+	0.152978i	$0.951114\pi$
$308$	−1.36029	+	0.119010i	−0.0775096	+	0.00678121i
$309$		0			0
$310$	−0.795471	+	2.30035i	−0.0451797	+	0.130651i
$311$	17.6839	−	3.11815i	1.00276	−	0.176814i	0.351922	−	0.936029i	$-0.385528\pi$
$311$	17.6839	−	3.11815i	1.00276	−	0.176814i	0.650840	+	0.759215i	$0.274417\pi$
$312$		0			0
$313$	−0.0467556	−	0.534419i	−0.00264278	−	0.0302071i	0.994759	−	0.102249i	$-0.0326039\pi$
$313$	−0.0467556	−	0.534419i	−0.00264278	−	0.0302071i	−0.997402	+	0.0720422i	$0.977048\pi$
$314$	−5.20792	−	9.02038i	−0.293900	−	0.509049i
$315$		0			0
$316$	9.93599	−	17.2096i	0.558943	−	0.968118i
$317$	−26.8041	−	12.4989i	−1.50547	−	0.702011i	−0.517358	−	0.855769i	$-0.673085\pi$
$317$	−26.8041	−	12.4989i	−1.50547	−	0.702011i	−0.988109	+	0.153758i	$0.950862\pi$
$318$		0			0
$319$	−9.94420	−	11.8510i	−0.556768	−	0.663531i
$320$	0.102529	−	1.43894i	0.00573155	−	0.0804391i
$321$		0			0
$322$	−0.0503825	−	0.0719537i	−0.00280771	−	0.00400982i
$323$	−24.4183	+	24.4183i	−1.35867	+	1.35867i
$324$		0			0
$325$	−9.20928	−	2.15175i	−0.510839	−	0.119358i
$326$	−2.20335	−	0.388511i	−0.122032	−	0.0215176i
$327$		0			0
$328$	−0.637968	−	1.36813i	−0.0352259	−	0.0755422i
$329$	1.28474	−	1.07802i	0.0708298	−	0.0594333i
$330$		0			0
$331$	−24.8454	+	9.04298i	−1.36563	+	0.497047i	−0.917789	−	0.397068i	$-0.870028\pi$
$331$	−24.8454	+	9.04298i	−1.36563	+	0.497047i	−0.447837	+	0.894115i	$0.647805\pi$
$332$	11.3463	−	3.04024i	0.622710	−	0.166855i
$333$		0			0
$334$	0.272269	−	0.157195i	0.0148979	−	0.00860130i
$335$	−22.8510	+	8.73707i	−1.24848	+	0.477357i
$336$		0			0
$337$	−14.1961	−	9.94021i	−0.773310	−	0.541478i	0.119003	−	0.992894i	$-0.462030\pi$
$337$	−14.1961	−	9.94021i	−0.773310	−	0.541478i	−0.892314	+	0.451416i	$0.850919\pi$
$338$	−4.61761	−	3.23328i	−0.251165	−	0.175867i
$339$		0			0
$340$	−15.6550	+	5.98570i	−0.849013	+	0.324620i
$341$	8.70159	−	5.02387i	0.471218	−	0.272058i
$342$		0			0
$343$	−2.03299	+	0.544739i	−0.109771	+	0.0294131i
$344$	3.56512	−	1.29760i	0.192218	−	0.0699617i
$345$		0			0
$346$	−8.06488	+	6.76724i	−0.433571	+	0.363809i
$347$	3.53574	+	7.58241i	0.189808	+	0.407045i	0.978065	−	0.208302i	$-0.0667937\pi$
$347$	3.53574	+	7.58241i	0.189808	+	0.407045i	−0.788256	+	0.615347i	$0.789016\pi$
$348$		0			0
$349$	−21.0838	−	3.71764i	−1.12859	−	0.199000i	−0.421979	−	0.906605i	$-0.638665\pi$
$349$	−21.0838	−	3.71764i	−1.12859	−	0.199000i	−0.706608	+	0.707605i	$0.749776\pi$
$350$	−0.382618	+	0.237684i	−0.0204518	+	0.0127047i
$351$		0			0
$352$	21.6439	−	21.6439i	1.15362	−	1.15362i
$353$	16.6830	+	23.8257i	0.887944	+	1.26812i	0.962606	+	0.270907i	$0.0873236\pi$
$353$	16.6830	+	23.8257i	0.887944	+	1.26812i	−0.0746612	+	0.997209i	$0.523788\pi$
$354$		0			0
$355$	0.464325	−	6.51654i	0.0246438	−	0.345862i
$356$	−14.2323	−	16.9614i	−0.754311	−	0.898953i
$357$		0			0
$358$	−0.471889	−	0.220045i	−0.0249401	−	0.0116298i
$359$	5.32734	−	9.22723i	0.281166	−	0.486995i	−0.690506	−	0.723327i	$-0.742612\pi$
$359$	5.32734	−	9.22723i	0.281166	−	0.486995i	0.971672	+	0.236332i	$0.0759454\pi$
$360$		0			0
$361$	19.1172	+	33.1119i	1.00617	+	1.74273i
$362$	0.570901	+	6.52543i	0.0300059	+	0.342969i
$363$		0			0
$364$	−0.460587	+	0.0812140i	−0.0241413	+	0.00425677i
$365$	−7.53050	+	21.7767i	−0.394164	+	1.13985i
$366$		0			0
$367$	21.4206	−	1.87406i	1.11814	−	0.0978249i	0.486935	−	0.873438i	$-0.338115\pi$
$367$	21.4206	−	1.87406i	1.11814	−	0.0978249i	0.631209	+	0.775613i	$0.282559\pi$
$368$	−1.86538	−	0.499826i	−0.0972395	−	0.0260552i
$369$		0			0
$370$	−1.92426	+	7.67463i	−0.100038	+	0.398985i
$371$	−0.0149294	−	0.0410181i	−0.000775094	−	0.00212955i
$372$		0			0
$373$	10.9407	+	0.957189i	0.566489	+	0.0495614i	0.366803	−	0.930299i	$-0.380452\pi$
$373$	10.9407	+	0.957189i	0.566489	+	0.0495614i	0.199686	+	0.979860i	$0.436008\pi$
$374$	−14.1712	−	5.15788i	−0.732773	−	0.266708i
$375$		0			0
$376$	−4.21410	+	23.8994i	−0.217326	+	1.23252i
$377$	−3.74681	−	3.74681i	−0.192970	−	0.192970i
$378$		0			0
$379$			9.48980i			0.487458i	0.969843	+	0.243729i	$0.0783708\pi$
$379$			9.48980i			0.487458i	−0.969843	+	0.243729i	$0.921629\pi$
$380$	2.86717	+	27.6301i	0.147083	+	1.41739i
$381$		0			0
$382$	7.72187	−	3.60077i	0.395085	−	0.184231i
$383$	−2.27956	+	26.0555i	−0.116480	+	1.33137i	0.682884	+	0.730526i	$0.260725\pi$
$383$	−2.27956	+	26.0555i	−0.116480	+	1.33137i	−0.799364	+	0.600846i	$0.794830\pi$
$384$		0			0
$385$	1.83614	+	0.293301i	0.0935783	+	0.0149480i
$386$	−6.27815	−	3.62469i	−0.319549	−	0.184492i
$387$		0			0
$388$	−1.52079	+	5.67568i	−0.0772066	+	0.288139i
$389$	−2.90227	−	2.43529i	−0.147151	−	0.123474i	0.566240	−	0.824240i	$-0.308397\pi$
$389$	−2.90227	−	2.43529i	−0.147151	−	0.123474i	−0.713391	+	0.700766i	$0.752842\pi$
$390$		0			0
$391$	0.772861	+	4.38311i	0.0390852	+	0.221663i
$392$	8.72012	−	12.4536i	0.440433	−	0.629003i
$393$		0			0
$394$	−4.26435	+	5.08205i	−0.214835	+	0.256030i
$395$	−18.8233	+	19.4407i	−0.947103	+	0.978167i
$396$		0			0
$397$	4.76915	+	17.7987i	0.239357	+	0.893292i	0.976136	+	0.217159i	$0.0696789\pi$
$397$	4.76915	+	17.7987i	0.239357	+	0.893292i	−0.736779	+	0.676133i	$0.763654\pi$
$398$	−0.962257	+	2.06357i	−0.0482336	+	0.103437i
$399$		0			0
$400$	−3.08503	+	9.41015i	−0.154252	+	0.470508i
$401$	−3.20835	+	8.81488i	−0.160217	+	0.440194i	−0.993662	−	0.112409i	$-0.964143\pi$
$401$	−3.20835	+	8.81488i	−0.160217	+	0.440194i	0.833445	+	0.552603i	$0.186365\pi$
$402$		0			0
$403$	2.81907	−	1.97394i	0.140428	−	0.0983288i
$404$	−6.32405			−0.314633
$405$		0			0
$406$	−0.252370			−0.0125249
$407$	26.7552	−	18.7342i	1.32621	−	0.928619i
$408$		0			0
$409$	6.70343	−	18.4175i	0.331464	−	0.910689i	−0.656268	−	0.754528i	$-0.727866\pi$
$409$	6.70343	−	18.4175i	0.331464	−	0.910689i	0.987732	−	0.156161i	$-0.0499118\pi$
$410$	0.175641	+	0.910005i	0.00867429	+	0.0449420i
$411$		0			0
$412$	8.54819	−	18.3317i	0.421139	−	0.903136i
$413$	−0.0405257	−	0.151244i	−0.00199414	−	0.00744223i
$414$		0			0
$415$	−15.9936	+	0.258052i	−0.785093	+	0.0126673i
$416$	6.73895	−	8.03117i	0.330404	−	0.393760i
$417$		0			0
$418$	−14.3363	+	20.4743i	−0.701211	+	1.00143i
$419$	−4.78282	−	27.1247i	−0.233656	−	1.32513i	−0.845426	−	0.534092i	$-0.820653\pi$
$419$	−4.78282	−	27.1247i	−0.233656	−	1.32513i	0.611770	−	0.791035i	$-0.290458\pi$
$420$		0			0
$421$	−7.89176	−	6.62197i	−0.384621	−	0.322735i	0.429892	−	0.902880i	$-0.358551\pi$
$421$	−7.89176	−	6.62197i	−0.384621	−	0.322735i	−0.814513	+	0.580145i	$0.802996\pi$
$422$	0.0237167	−	0.0885121i	0.00115451	−	0.00430870i
$423$		0			0
$424$	0.547009	+	0.315816i	0.0265651	+	0.0153374i
$425$	22.6601	−	2.72161i	1.09918	−	0.132018i
$426$		0			0
$427$	−0.127458	+	1.45686i	−0.00616814	+	0.0705022i
$428$	1.84065	−	0.858309i	0.0889712	−	0.0414879i
$429$		0			0
$430$	−2.31685	+	0.240419i	−0.111728	+	0.0115940i
$431$		−	0.427248i		−	0.0205798i	−0.999947	−	0.0102899i	$-0.996725\pi$
$431$		−	0.427248i		−	0.0205798i	0.999947	−	0.0102899i	$-0.00327543\pi$
$432$		0			0
$433$	−12.7271	−	12.7271i	−0.611625	−	0.611625i	0.331744	−	0.943369i	$-0.392363\pi$
$433$	−12.7271	−	12.7271i	−0.611625	−	0.611625i	−0.943369	+	0.331744i	$0.892363\pi$
$434$	0.0284626	−	0.161419i	0.00136625	−	0.00774838i
$435$		0			0
$436$	−12.6892	−	4.61851i	−0.607705	−	0.221186i
$437$	7.34854	+	0.642914i	0.351528	+	0.0307547i
$438$		0			0
$439$	−2.87705	−	7.90463i	−0.137314	−	0.377267i	0.851908	−	0.523692i	$-0.175446\pi$
$439$	−2.87705	−	7.90463i	−0.137314	−	0.377267i	−0.989222	+	0.146425i	$0.953223\pi$
$440$	−23.0813	+	13.8272i	−1.10036	+	0.659188i
$441$		0			0
$442$	−4.98928	−	1.33687i	−0.237316	−	0.0635885i
$443$	8.73772	−	0.764452i	0.415142	−	0.0363202i	0.122328	−	0.992490i	$-0.460964\pi$
$443$	8.73772	−	0.764452i	0.415142	−	0.0363202i	0.292814	+	0.956170i	$0.405408\pi$
$444$		0			0
$445$	13.1815	+	27.1168i	0.624861	+	1.28546i
$446$	−15.6197	+	2.75417i	−0.739614	+	0.130414i
$447$		0			0
$448$	0.00846683	+	0.0967763i	0.000400020	+	0.00457225i
$449$	12.5244	+	21.6930i	0.591065	+	1.02375i	0.994089	+	0.108565i	$0.0346255\pi$
$449$	12.5244	+	21.6930i	0.591065	+	1.02375i	−0.403025	+	0.915189i	$0.632041\pi$
$450$		0			0
$451$	1.91295	−	3.31332i	0.0900772	−	0.156018i
$452$	−2.97213	−	1.38593i	−0.139797	−	0.0651886i
$453$		0			0
$454$	−6.23775	−	7.43386i	−0.292752	−	0.348888i
$455$	0.635260	+	0.0452644i	0.0297814	+	0.00212203i
$456$		0			0
$457$	−19.0426	−	27.1956i	−0.890775	−	1.27216i	−0.961540	−	0.274666i	$-0.911433\pi$
$457$	−19.0426	−	27.1956i	−0.890775	−	1.27216i	0.0707647	−	0.997493i	$-0.477456\pi$
$458$	−0.974227	+	0.974227i	−0.0455226	+	0.0455226i
$459$		0			0
$460$	3.12902	+	1.73985i	0.145891	+	0.0811208i
$461$	−33.1856	−	5.85151i	−1.54561	−	0.272532i	−0.665169	−	0.746693i	$-0.731640\pi$
$461$	−33.1856	−	5.85151i	−1.54561	−	0.272532i	−0.880438	+	0.474161i	$0.842751\pi$
$462$		0			0
$463$	4.31391	+	9.25121i	0.200484	+	0.429940i	0.980686	−	0.195588i	$-0.0626614\pi$
$463$	4.31391	+	9.25121i	0.200484	+	0.429940i	−0.780202	+	0.625528i	$0.784884\pi$
$464$	−4.25037	+	3.56648i	−0.197318	+	0.165570i
$465$		0			0
$466$	3.19317	−	1.16222i	0.147921	−	0.0538388i
$467$	7.55151	−	2.02342i	0.349442	−	0.0936327i	−0.0798287	−	0.996809i	$-0.525437\pi$
$467$	7.55151	−	2.02342i	0.349442	−	0.0936327i	0.429271	+	0.903176i	$0.358771\pi$
$468$		0			0
$469$	1.42675	−	0.823732i	0.0658810	−	0.0380364i
$470$	6.07811	−	13.6033i	0.280362	−	0.627474i
$471$		0			0
$472$	1.85598	+	1.29957i	0.0854284	+	0.0598176i
$473$	7.87652	+	5.51520i	0.362163	+	0.253589i
$474$		0			0
$475$	5.36333	−	37.4445i	0.246086	−	1.71807i
$476$	0.977453	−	0.564332i	0.0448015	−	0.0258661i
$477$		0			0
$478$	16.8893	−	4.52548i	0.772500	−	0.206991i
$479$	−12.4057	+	4.51531i	−0.566831	+	0.206310i	−0.609509	−	0.792779i	$-0.708633\pi$
$479$	−12.4057	+	4.51531i	−0.566831	+	0.206310i	0.0426779	+	0.999089i	$0.486411\pi$
$480$		0			0
$481$	8.56981	−	7.19093i	0.390750	−	0.327878i
$482$	−1.58883	−	3.40726i	−0.0723693	−	0.155197i
$483$		0			0
$484$	31.5283	+	5.55928i	1.43310	+	0.252695i
$485$	3.88838	−	6.99304i	0.176562	−	0.317537i
$486$		0			0
$487$	12.1497	−	12.1497i	0.550553	−	0.550553i	−0.376047	−	0.926601i	$-0.622717\pi$
$487$	12.1497	−	12.1497i	0.550553	−	0.550553i	0.926601	+	0.376047i	$0.122717\pi$
$488$	−12.1377	−	17.3345i	−0.549450	−	0.784696i
$489$		0			0
$490$	−7.05252	+	6.11434i	−0.318600	+	0.276218i
$491$	11.2054	+	13.3541i	0.505693	+	0.602661i	0.957136	−	0.289639i	$-0.0935352\pi$
$491$	11.2054	+	13.3541i	0.505693	+	0.602661i	−0.451443	+	0.892300i	$0.649091\pi$
$492$		0			0
$493$	11.5893	+	5.40417i	0.521955	+	0.243392i
$494$	−4.28045	+	7.41396i	−0.192587	+	0.333570i
$495$		0			0
$496$	−1.80181	−	3.12082i	−0.0809035	−	0.140129i
$497$	0.0383438	+	0.438272i	0.00171995	+	0.0196592i
$498$		0			0
$499$	−3.01325	+	0.531318i	−0.134892	+	0.0237851i	−0.240686	−	0.970603i	$-0.577373\pi$
$499$	−3.01325	+	0.531318i	−0.134892	+	0.0237851i	0.105795	+	0.994388i	$0.466261\pi$
$500$	9.79037	−	15.5307i	0.437839	−	0.694553i
$501$		0			0
$502$	−5.50326	+	0.481473i	−0.245623	+	0.0214892i
$503$	6.64016	+	1.77923i	0.296070	+	0.0793318i	0.403797	−	0.914849i	$-0.367690\pi$
$503$	6.64016	+	1.77923i	0.296070	+	0.0793318i	−0.107726	+	0.994181i	$0.534357\pi$
$504$		0			0
$505$	8.35308	+	2.09437i	0.371707	+	0.0931983i
$506$	1.10178	+	3.02713i	0.0489803	+	0.134572i
$507$		0			0
$508$	10.8809	+	0.951954i	0.482761	+	0.0422361i
$509$	28.5486	+	10.3908i	1.26540	+	0.460566i	0.885576	−	0.464495i	$-0.153764\pi$
$509$	28.5486	+	10.3908i	1.26540	+	0.460566i	0.379819	+	0.925061i	$0.375986\pi$
$510$		0			0
$511$	0.269447	−	1.52811i	0.0119196	−	0.0675997i
$512$	−13.8657	−	13.8657i	−0.612783	−	0.612783i
$513$		0			0
$514$		−	9.84374i		−	0.434189i
$515$	−17.3618	+	21.3823i	−0.765053	+	0.942216i
$516$		0			0
$517$	−55.7433	+	25.9935i	−2.45159	+	1.14319i
$518$	0.0464382	−	0.530791i	0.00204038	−	0.0233216i
$519$		0			0
$520$	−7.46275	+	5.40697i	−0.327263	+	0.237111i
$521$	1.31724	+	0.760511i	0.0577095	+	0.0333186i	0.528577	−	0.848885i	$-0.322726\pi$
$521$	1.31724	+	0.760511i	0.0577095	+	0.0333186i	−0.470868	+	0.882204i	$0.656059\pi$
$522$		0			0
$523$	3.57368	−	13.3371i	0.156266	−	0.583192i	−0.842728	−	0.538340i	$-0.819052\pi$
$523$	3.57368	−	13.3371i	0.156266	−	0.583192i	0.998994	−	0.0448523i	$-0.0142817\pi$
$524$	−17.0114	−	14.2743i	−0.743148	−	0.623576i
$525$		0			0
$526$	−1.27426	−	7.22671i	−0.0555606	−	0.315100i
$527$	−4.76363	+	6.80317i	−0.207507	+	0.296351i
$528$		0			0
$529$	−14.1730	+	16.8907i	−0.616217	+	0.734379i
$530$	−0.278599	−	0.269751i	−0.0121016	−	0.0117173i
$531$		0			0
$532$	−0.484158	−	1.80690i	−0.0209909	−	0.0783391i
$533$	0.553803	−	1.18763i	0.0239879	−	0.0514421i
$534$		0			0
$535$	−2.71546	+	0.524114i	−0.117400	+	0.0226594i
$536$	−8.15346	+	22.4015i	−0.352176	+	0.967595i
$537$		0			0
$538$	9.04315	−	6.33208i	0.389878	−	0.272995i
$539$	38.5313			1.65966
$540$		0			0
$541$	0.376014			0.0161661			0.00808305	−	0.999967i	$-0.497427\pi$
$541$	0.376014			0.0161661			0.00808305	+	0.999967i	$0.497427\pi$
$542$	6.54839	−	4.58523i	0.281278	−	0.196953i
$543$		0			0
$544$	−8.65328	+	23.7747i	−0.371006	+	1.01933i
$545$	15.2310	+	10.3027i	0.652423	+	0.441319i
$546$		0			0
$547$	5.56415	−	11.9323i	0.237906	−	0.510190i	−0.750714	−	0.660627i	$-0.770290\pi$
$547$	5.56415	−	11.9323i	0.237906	−	0.510190i	0.988620	+	0.150437i	$0.0480681\pi$
$548$	−3.47915	−	12.9844i	−0.148622	−	0.554665i
$549$		0			0
$550$	15.8100	−	4.78800i	0.674141	−	0.204161i
$551$	13.6230	−	16.2353i	0.580361	−	0.691647i
$552$		0			0
$553$	1.04522	−	1.49272i	0.0444471	−	0.0634770i
$554$	−2.23156	−	12.6558i	−0.0948101	−	0.537695i
$555$		0			0
$556$	22.9641	+	19.2691i	0.973893	+	0.817193i
$557$	7.60724	−	28.3906i	0.322329	−	1.20295i	−0.594641	−	0.803991i	$-0.702706\pi$
$557$	7.60724	−	28.3906i	0.322329	−	1.20295i	0.916970	−	0.398957i	$-0.130628\pi$
$558$		0			0
$559$	2.85217	+	1.64670i	0.120634	+	0.0696479i
$560$	0.105192	−	0.658531i	0.00444518	−	0.0278280i
$561$		0			0
$562$	0.362542	−	4.14388i	0.0152929	−	0.174799i
$563$	−7.92028	+	3.69329i	−0.333800	+	0.155653i	−0.582290	−	0.812981i	$-0.697843\pi$
$563$	−7.92028	+	3.69329i	−0.333800	+	0.155653i	0.248490	+	0.968634i	$0.420066\pi$
$564$		0			0
$565$	3.46674	+	2.81489i	0.145847	+	0.118423i
$566$			14.4516i			0.607448i
$567$		0			0
$568$	−4.50151	−	4.50151i	−0.188879	−	0.188879i
$569$	0.230736	−	1.30857i	0.00967296	−	0.0548581i	−0.979589	−	0.201010i	$-0.935578\pi$
$569$	0.230736	−	1.30857i	0.00967296	−	0.0548581i	0.989262	+	0.146152i	$0.0466888\pi$
$570$		0			0
$571$	−14.3584	−	5.22603i	−0.600881	−	0.218703i	0.0236277	−	0.999721i	$-0.492478\pi$
$571$	−14.3584	−	5.22603i	−0.600881	−	0.218703i	−0.624508	+	0.781018i	$0.714701\pi$
$572$	17.0868	+	1.49490i	0.714436	+	0.0625050i
$573$		0			0
$574$	−0.0213462	−	0.0586482i	−0.000890974	−	0.00244793i
$575$	−3.55675	−	3.33432i	−0.148327	−	0.139051i
$576$		0			0
$577$	33.8078	+	9.05878i	1.40744	+	0.377122i	0.881010	−	0.473098i	$-0.156864\pi$
$577$	33.8078	+	9.05878i	1.40744	+	0.377122i	0.526428	+	0.850220i	$0.323531\pi$
$578$	2.28596	−	0.199995i	0.0950833	−	0.00831871i
$579$		0			0
$580$	9.25117	−	4.49699i	0.384134	−	0.186727i
$581$	1.06081	−	0.187049i	0.0440097	−	0.00776009i
$582$		0			0
$583$	0.139522	+	1.59474i	0.00577840	+	0.0660475i
$584$	11.2266	+	19.4450i	0.464560	+	0.804641i
$585$		0			0
$586$	−4.81376	+	8.33768i	−0.198855	+	0.344426i
$587$	−28.8395	−	13.4481i	−1.19033	−	0.555061i	−0.276446	−	0.961030i	$-0.589157\pi$
$587$	−28.8395	−	13.4481i	−1.19033	−	0.555061i	−0.913887	+	0.405968i	$0.866934\pi$
$588$		0			0
$589$	8.84789	+	10.5445i	0.364571	+	0.434479i
$590$	−0.911228	−	1.05105i	−0.0375146	−	0.0432709i
$591$		0			0
$592$	−6.71900	−	9.59573i	−0.276149	−	0.394382i
$593$	14.3845	−	14.3845i	0.590702	−	0.590702i	−0.347119	−	0.937821i	$-0.612840\pi$
$593$	14.3845	−	14.3845i	0.590702	−	0.590702i	0.937821	+	0.347119i	$0.112840\pi$
$594$		0			0
$595$	−1.47795	+	0.421686i	−0.0605902	+	0.0172875i
$596$	−6.76022	−	1.19201i	−0.276909	−	0.0488266i
$597$		0			0
$598$	0.466302	+	0.999988i	0.0190685	+	0.0408925i
$599$	30.6931	−	25.7546i	1.25409	−	1.05230i	0.257801	−	0.966198i	$-0.417002\pi$
$599$	30.6931	−	25.7546i	1.25409	−	1.05230i	0.996286	−	0.0861056i	$-0.0274423\pi$
$600$		0			0
$601$	30.8662	−	11.2344i	1.25906	−	0.458260i	0.375606	−	0.926779i	$-0.377435\pi$
$601$	30.8662	−	11.2344i	1.25906	−	0.458260i	0.883453	+	0.468519i	$0.155212\pi$
$602$	0.151513	−	0.0405978i	0.00617521	−	0.00165464i
$603$		0			0
$604$	−6.91453	+	3.99211i	−0.281348	+	0.162436i
$605$	−39.8028	−	17.7843i	−1.61821	−	0.723036i
$606$		0			0
$607$	19.8141	+	13.8740i	0.804231	+	0.563129i	0.901827	−	0.432097i	$-0.142226\pi$
$607$	19.8141	+	13.8740i	0.804231	+	0.563129i	−0.0975958	+	0.995226i	$0.531115\pi$
$608$	34.3494	+	24.0517i	1.39305	+	0.975426i
$609$		0			0
$610$	4.63997	+	12.1354i	0.187867	+	0.491347i
$611$	−18.2441	+	10.5332i	−0.738075	+	0.426128i
$612$		0			0
$613$	21.4554	−	5.74896i	0.866575	−	0.232198i	0.201969	−	0.979392i	$-0.435266\pi$
$613$	21.4554	−	5.74896i	0.866575	−	0.232198i	0.664606	+	0.747194i	$0.268599\pi$
$614$	18.0252	−	6.56065i	0.727440	−	0.264766i
$615$		0			0
$616$	1.38800	−	1.16467i	0.0559239	−	0.0469258i
$617$	4.95167	+	10.6189i	0.199347	+	0.427500i	0.980414	−	0.196946i	$-0.0631024\pi$
$617$	4.95167	+	10.6189i	0.199347	+	0.427500i	−0.781068	+	0.624446i	$0.785325\pi$
$618$		0			0
$619$	−28.3482	−	4.99855i	−1.13941	−	0.200909i	−0.428062	−	0.903749i	$-0.640803\pi$
$619$	−28.3482	−	4.99855i	−1.13941	−	0.200909i	−0.711347	+	0.702841i	$0.751915\pi$
$620$	1.83298	+	6.42434i	0.0736142	+	0.258008i
$621$		0			0
$622$	−7.59634	+	7.59634i	−0.304585	+	0.304585i
$623$	−1.16459	−	1.66321i	−0.0466583	−	0.0666349i
$624$		0			0
$625$	−18.0749	+	17.2713i	−0.722997	+	0.690851i
$626$	0.206299	+	0.245858i	0.00824538	+	0.00982646i
$627$		0			0
$628$	−25.9103	−	12.0821i	−1.03393	−	0.482130i
$629$	−13.4987	+	23.3804i	−0.538228	+	0.932239i
$630$		0			0
$631$	−8.26145	−	14.3093i	−0.328883	−	0.569643i	0.653407	−	0.757007i	$-0.273339\pi$
$631$	−8.26145	−	14.3093i	−0.328883	−	0.569643i	−0.982291	+	0.187364i	$0.940006\pi$
$632$	2.29819	+	26.2684i	0.0914169	+	1.04490i
$633$		0			0
$634$	17.4249	−	3.07247i	0.692029	−	0.122023i
$635$	−14.0567	−	4.86086i	−0.557822	−	0.192898i
$636$		0			0
$637$	13.1471	−	1.15023i	0.520909	−	0.0455736i
$638$	8.94003	+	2.39547i	0.353939	+	0.0948377i
$639$		0			0
$640$	13.1822	+	22.0047i	0.521073	+	0.869810i
$641$	6.11791	+	16.8088i	0.241643	+	0.663909i	0.999928	+	0.0119858i	$0.00381528\pi$
$641$	6.11791	+	16.8088i	0.241643	+	0.663909i	−0.758285	+	0.651923i	$0.773962\pi$
$642$		0			0
$643$	21.1290	+	1.84855i	0.833247	+	0.0728997i	0.495791	−	0.868442i	$-0.334878\pi$
$643$	21.1290	+	1.84855i	0.833247	+	0.0728997i	0.337456	+	0.941341i	$0.390434\pi$
$644$	−0.226556	−	0.0824598i	−0.00892757	−	0.00324937i
$645$		0			0
$646$	3.58752	−	20.3458i	0.141149	−	0.800496i
$647$	7.44855	+	7.44855i	0.292833	+	0.292833i	0.838198	−	0.545366i	$-0.183609\pi$
$647$	7.44855	+	7.44855i	0.292833	+	0.292833i	−0.545366	+	0.838198i	$0.683609\pi$
$648$		0			0
$649$			5.74237i			0.225408i
$650$	5.25156	−	2.10566i	0.205983	−	0.0825907i
$651$		0			0
$652$	−5.56558	+	2.59527i	−0.217965	+	0.101639i
$653$	4.00398	−	45.7657i	0.156688	−	1.79095i	−0.358150	−	0.933664i	$-0.616592\pi$
$653$	4.00398	−	45.7657i	0.156688	−	1.79095i	0.514838	−	0.857288i	$-0.327852\pi$
$654$		0			0
$655$	17.7422	+	24.4879i	0.693243	+	0.956821i
$656$	−1.18832	−	0.686078i	−0.0463961	−	0.0267868i
$657$		0			0
$658$	−0.259686	+	0.969163i	−0.0101236	+	0.0377819i
$659$	3.34888	+	2.81004i	0.130454	+	0.109464i	0.705680	−	0.708531i	$-0.250642\pi$
$659$	3.34888	+	2.81004i	0.130454	+	0.109464i	−0.575226	+	0.817994i	$0.695086\pi$
$660$		0			0
$661$	6.57135	+	37.2680i	0.255596	+	1.44956i	0.794539	+	0.607214i	$0.207713\pi$
$661$	6.57135	+	37.2680i	0.255596	+	1.44956i	−0.538943	+	0.842342i	$0.681176\pi$
$662$	9.07285	−	12.9574i	0.352626	−	0.503603i
$663$		0			0
$664$	−10.0190	+	11.9402i	−0.388815	+	0.463371i
$665$	0.0410949	+	2.54698i	0.00159359	+	0.0987675i
$666$		0			0
$667$	−0.706972	−	2.63846i	−0.0273741	−	0.102161i
$668$	0.364685	−	0.782069i	0.0141101	−	0.0302592i
$669$		0			0
$670$	8.20042	−	12.1231i	0.316810	−	0.468355i
$671$	18.3434	−	50.3981i	0.708140	−	1.94560i
$672$		0			0
$673$	−35.3130	+	24.7264i	−1.36122	+	0.953134i	−0.361431	+	0.932399i	$0.617712\pi$
$673$	−35.3130	+	24.7264i	−1.36122	+	0.953134i	−0.999785	+	0.0207353i	$0.993399\pi$
$674$	10.3680			0.399362
$675$		0			0
$676$	−15.4723			−0.595088
$677$	32.2989	−	22.6160i	1.24135	−	0.869202i	0.246359	−	0.969179i	$-0.420766\pi$
$677$	32.2989	−	22.6160i	1.24135	−	0.869202i	0.994990	+	0.0999769i	$0.0318769\pi$
$678$		0			0
$679$	−0.184289	+	0.506330i	−0.00707236	+	0.0194312i
$680$	12.4606	−	18.4212i	0.477844	−	0.706419i
$681$		0			0
$682$	−2.54044	+	5.44799i	−0.0972785	+	0.208614i
$683$	7.98000	+	29.7818i	0.305346	+	1.13957i	0.932647	+	0.360791i	$0.117493\pi$
$683$	7.98000	+	29.7818i	0.305346	+	1.13957i	−0.627301	+	0.778777i	$0.715840\pi$
$684$		0			0
$685$	0.295307	+	18.3025i	0.0112831	+	0.699304i
$686$	0.809379	−	0.964580i	0.0309022	−	0.0368279i
$687$		0			0
$688$	1.97802	−	2.82491i	0.0754115	−	0.107699i
$689$	0.0952117	+	0.539972i	0.00362728	+	0.0205713i
$690$		0			0
$691$	−14.5283	−	12.1907i	−0.552681	−	0.463755i	0.323166	−	0.946342i	$-0.395253\pi$
$691$	−14.5283	−	12.1907i	−0.552681	−	0.463755i	−0.875848	+	0.482587i	$0.839697\pi$
$692$	−7.47898	+	27.9119i	−0.284308	+	1.06105i
$693$		0			0
$694$	−4.33466	−	2.50262i	−0.164541	−	0.0949980i
$695$	−23.9505	−	33.0566i	−0.908493	−	1.25391i
$696$		0			0
$697$	−0.275618	+	3.15033i	−0.0104398	+	0.119327i
$698$	11.6082	−	5.41299i	0.439377	−	0.204885i
$699$		0			0
$700$	−0.486073	+	1.13676i	−0.0183718	+	0.0429656i
$701$		−	10.8100i		−	0.408288i	−0.978941	−	0.204144i	$-0.934559\pi$
$701$		−	10.8100i		−	0.408288i	0.978941	−	0.204144i	$-0.0654410\pi$
$702$		0			0
$703$	31.6397	+	31.6397i	1.19331	+	1.19331i
$704$	0.618659	−	3.50859i	0.0233166	−	0.132235i
$705$		0			0
$706$	−16.3516	−	5.95150i	−0.615401	−	0.223987i
$707$	−0.577714	−	0.0505434i	−0.0217272	−	0.00190088i
$708$		0			0
$709$	−11.3780	−	31.2608i	−0.427310	−	1.17403i	−0.947439	−	0.319937i	$-0.896338\pi$
$709$	−11.3780	−	31.2608i	−0.427310	−	1.17403i	0.520129	−	0.854088i	$-0.325884\pi$
$710$	2.00860	+	3.35289i	0.0753813	+	0.125832i
$711$		0			0
$712$	28.3792	+	7.60417i	1.06355	+	0.284978i
$713$	1.76732	−	0.154621i	0.0661868	−	0.00579060i
$714$		0			0
$715$	−22.0739	−	7.63327i	−0.825518	−	0.285468i
$716$	−1.40740	+	0.248162i	−0.0525969	+	0.00927426i
$717$		0			0
$718$	0.555558	+	6.35006i	0.0207332	+	0.236982i
$719$	−20.7377	−	35.9188i	−0.773387	−	1.33955i	−0.935697	−	0.352806i	$-0.885228\pi$
$719$	−20.7377	−	35.9188i	−0.773387	−	1.33955i	0.162310	−	0.986740i	$-0.448106\pi$
$720$		0			0
$721$	0.927405	−	1.60631i	0.0345384	−	0.0598222i
$722$	−20.7311	−	9.66707i	−0.771532	−	0.359771i
$723$		0			0
$724$	11.5567	+	13.7727i	0.429501	+	0.511860i
$725$	−13.7086	+	2.87606i	−0.509126	+	0.106814i
$726$		0			0
$727$	7.46713	+	10.6642i	0.276940	+	0.395512i	0.933393	−	0.358855i	$-0.116833\pi$
$727$	7.46713	+	10.6642i	0.276940	+	0.395512i	−0.656453	+	0.754367i	$0.727944\pi$
$728$	0.438827	−	0.438827i	0.0162640	−	0.0162640i
$729$		0			0
$730$	−3.78223	−	13.2562i	−0.139986	−	0.490634i
$731$	−7.82709	−	1.38013i	−0.289495	−	0.0510458i
$732$		0			0
$733$	−13.8950	−	29.7979i	−0.513223	−	1.10061i	−0.976721	−	0.214512i	$-0.931184\pi$
$733$	−13.8950	−	29.7979i	−0.513223	−	1.10061i	0.463499	−	0.886098i	$-0.346594\pi$
$734$	−9.85447	+	8.26888i	−0.363735	+	0.305210i
$735$		0			0
$736$	5.07856	−	1.84844i	0.187198	−	0.0681345i
$737$	−58.3601	+	15.6375i	−2.14972	+	0.576016i
$738$		0			0
$739$	13.4399	−	7.75952i	0.494394	−	0.285439i	−0.232001	−	0.972715i	$-0.574527\pi$
$739$	13.4399	−	7.75952i	0.494394	−	0.285439i	0.726396	+	0.687277i	$0.241194\pi$
$740$	7.75589	+	20.2848i	0.285112	+	0.745683i
$741$		0			0
$742$	0.0213918	+	0.0149787i	0.000785317	+	0.000549885i
$743$	−25.3533	−	17.7526i	−0.930122	−	0.651279i	0.00711360	−	0.999975i	$-0.497736\pi$
$743$	−25.3533	−	17.7526i	−0.930122	−	0.651279i	−0.937236	+	0.348696i	$0.886625\pi$
$744$		0			0
$745$	8.53442	+	3.81328i	0.312677	+	0.139708i
$746$	−5.69017	+	3.28522i	−0.208332	+	0.120280i
$747$		0			0
$748$	−39.9821	+	10.7132i	−1.46189	+	0.391712i
$749$	0.175007	−	0.0636972i	0.00639460	−	0.00232745i
$750$		0			0
$751$	36.7847	−	30.8660i	1.34229	−	1.12632i	0.361263	−	0.932464i	$-0.382346\pi$
$751$	36.7847	−	30.8660i	1.34229	−	1.12632i	0.981030	−	0.193854i	$-0.0620989\pi$
$752$	9.32256	+	19.9923i	0.339959	+	0.729044i
$753$		0			0
$754$	3.12191	+	0.550477i	0.113693	+	0.0200472i
$755$	10.4551	−	2.98302i	0.380500	−	0.108563i
$756$		0			0
$757$	2.53936	−	2.53936i	0.0922948	−	0.0922948i	−0.659452	−	0.751747i	$-0.729212\pi$
$757$	2.53936	−	2.53936i	0.0922948	−	0.0922948i	0.751747	+	0.659452i	$0.229212\pi$
$758$	−3.25643	−	4.65066i	−0.118279	−	0.168919i
$759$		0			0
$760$	−24.1456	−	27.8505i	−0.875854	−	1.01024i
$761$	12.6924	+	15.1262i	0.460099	+	0.548324i	0.945353	−	0.326049i	$-0.105717\pi$
$761$	12.6924	+	15.1262i	0.460099	+	0.548324i	−0.485254	+	0.874373i	$0.661273\pi$
$762$		0			0
$763$	−1.12227	−	0.523325i	−0.0406291	−	0.0189456i
$764$	11.6928	−	20.2525i	0.423030	−	0.732710i
$765$		0			0
$766$	−7.82380	−	13.5512i	−0.282685	−	0.489625i
$767$	0.171420	+	1.95934i	0.00618961	+	0.0707475i
$768$		0			0
$769$	−12.6400	+	2.22877i	−0.455810	+	0.0803717i	−0.396839	−	0.917888i	$-0.629893\pi$
$769$	−12.6400	+	2.22877i	−0.455810	+	0.0803717i	−0.0589709	+	0.998260i	$0.518782\pi$
$770$	−1.00048	+	0.486334i	−0.0360548	+	0.0175262i
$771$		0			0
$772$	−19.8220	+	1.73420i	−0.713409	+	0.0624152i
$773$	13.0368	+	3.49320i	0.468901	+	0.125642i	0.485530	−	0.874220i	$-0.338627\pi$
$773$	13.0368	+	3.49320i	0.468901	+	0.125642i	−0.0166290	+	0.999862i	$0.505293\pi$
$774$		0			0
$775$	−0.293490	−	9.09259i	−0.0105425	−	0.326616i
$776$	−2.66670	−	7.32669i	−0.0957289	−	0.263013i
$777$		0			0
$778$	2.25798	+	0.197548i	0.0809526	+	0.00708244i
$779$	4.92519	+	1.79262i	0.176463	+	0.0642274i
$780$		0			0
$781$	2.80173	−	15.8894i	0.100254	−	0.568567i
$782$	−1.88282	−	1.88282i	−0.0673295	−	0.0673295i
$783$		0			0
$784$		−	13.8192i		−	0.493544i
$785$	30.2221	+	24.5395i	1.07867	+	0.875851i
$786$		0			0
$787$	−11.5978	+	5.40813i	−0.413416	+	0.192779i	−0.618187	−	0.786031i	$-0.712133\pi$
$787$	−11.5978	+	5.40813i	−0.413416	+	0.192779i	0.204771	+	0.978810i	$0.434355\pi$
$788$	−1.58702	+	18.1397i	−0.0565353	+	0.646202i
$789$		0			0
$790$	2.55365	−	15.9865i	0.0908547	−	0.568774i
$791$	−0.260433	−	0.150361i	−0.00925995	−	0.00534623i
$792$		0			0
$793$	4.75443	−	17.7438i	0.168835	−	0.630100i
$794$	−8.44484	−	7.08606i	−0.299696	−	0.251475i
$795$		0			0
$796$	1.08521	+	6.15455i	0.0384643	+	0.218142i
$797$	−6.45753	+	9.22231i	−0.228738	+	0.326671i	−0.917071	−	0.398723i	$-0.869454\pi$
$797$	−6.45753	+	9.22231i	−0.228738	+	0.326671i	0.688334	+	0.725394i	$0.258342\pi$
$798$		0			0
$799$	32.6786	−	38.9448i	1.15608	−	1.37777i
$800$	−8.03275	−	26.5242i	−0.284000	−	0.937771i
$801$		0			0
$802$	−1.45251	−	5.42084i	−0.0512899	−	0.191417i
$803$	−24.0496	+	51.5746i	−0.848693	+	1.82003i
$804$		0			0
$805$	0.271937	+	0.183946i	0.00958451	+	0.00648326i
$806$	−0.704184	+	1.93473i	−0.0248038	+	0.0681480i
$807$		0			0
$808$	6.87397	−	4.81320i	0.241825	−	0.169328i
$809$	−28.7457			−1.01065			−0.505323	−	0.862930i	$-0.668627\pi$
$809$	−28.7457			−1.01065			−0.505323	+	0.862930i	$0.668627\pi$
$810$		0			0
$811$	9.97816			0.350380			0.175190	−	0.984535i	$-0.443946\pi$
$811$	9.97816			0.350380			0.175190	+	0.984535i	$0.443946\pi$
$812$	−0.567420	+	0.397312i	−0.0199125	+	0.0139429i
$813$		0			0
$814$	−6.68325	+	18.3621i	−0.234248	+	0.643591i
$815$	8.21075	−	1.58476i	0.287610	−	0.0555118i
$816$		0			0
$817$	−5.56702	+	11.9385i	−0.194765	+	0.417676i
$818$	3.03483	+	11.3261i	0.106110	+	0.396009i
$819$		0			0
$820$	1.82754	+	1.76951i	0.0638206	+	0.0617939i
$821$	18.8449	−	22.4584i	0.657691	−	0.783805i	−0.329362	−	0.944204i	$-0.606834\pi$
$821$	18.8449	−	22.4584i	0.657691	−	0.783805i	0.987052	+	0.160399i	$0.0512780\pi$
$822$		0			0
$823$	−8.12702	+	11.6066i	−0.283290	+	0.404580i	−0.935426	−	0.353522i	$-0.884984\pi$
$823$	−8.12702	+	11.6066i	−0.283290	+	0.404580i	0.652136	+	0.758102i	$0.273873\pi$
$824$	4.66062	+	26.4317i	0.162360	+	0.920792i
$825$		0			0
$826$	0.0717598	+	0.0602136i	0.00249684	+	0.00209510i
$827$	−6.25009	+	23.3257i	−0.217337	+	0.811113i	0.767994	+	0.640457i	$0.221255\pi$
$827$	−6.25009	+	23.3257i	−0.217337	+	0.811113i	−0.985331	+	0.170656i	$0.945411\pi$
$828$		0			0
$829$	3.60048	+	2.07874i	0.125050	+	0.0721976i	0.561220	−	0.827667i	$-0.310332\pi$
$829$	3.60048	+	2.07874i	0.125050	+	0.0721976i	−0.436170	+	0.899864i	$0.643665\pi$
$830$	7.74940	−	5.61465i	0.268986	−	0.194888i
$831$		0			0
$832$	0.106353	−	1.21562i	0.00368714	−	0.0421442i
$833$	−28.8647	+	13.4598i	−1.00010	+	0.466356i
$834$		0			0
$835$	−0.740694	+	0.912216i	−0.0256328	+	0.0315685i
$836$			68.6036i			2.37271i
$837$		0			0
$838$	11.6517	+	11.6517i	0.402503	+	0.402503i
$839$	−8.22992	+	46.6742i	−0.284128	+	1.61137i	0.424255	+	0.905543i	$0.360536\pi$
$839$	−8.22992	+	46.6742i	−0.284128	+	1.61137i	−0.708383	+	0.705828i	$0.750575\pi$
$840$		0			0
$841$	19.8764	+	7.23443i	0.685394	+	0.249463i
$842$	6.13984	+	0.537166i	0.211593	+	0.0185120i
$843$		0			0
$844$	−0.0860225	−	0.236345i	−0.00296102	−	0.00813533i
$845$	20.4365	+	5.12404i	0.703035	+	0.176272i
$846$		0			0
$847$	2.83574	+	0.759833i	0.0974370	+	0.0261082i
$848$	0.571953	−	0.0500394i	0.0196410	−	0.00171836i
$849$		0			0
$850$	−10.1711	+	9.10961i	−0.348866	+	0.312457i
$851$	5.67935	−	1.00142i	0.194686	−	0.0343283i
$852$		0			0
$853$	−1.91338	−	21.8701i	−0.0655130	−	0.748817i	−0.955915	−	0.293643i	$-0.905132\pi$
$853$	−1.91338	−	21.8701i	−0.0655130	−	0.748817i	0.890402	−	0.455174i	$-0.150423\pi$
$854$	−0.437456	−	0.757697i	−0.0149695	−	0.0259279i
$855$		0			0
$856$	−1.34745	+	2.33385i	−0.0460550	+	0.0797695i
$857$	18.4106	+	8.58498i	0.628893	+	0.293257i	0.710813	−	0.703381i	$-0.248327\pi$
$857$	18.4106	+	8.58498i	0.628893	+	0.293257i	−0.0819200	+	0.996639i	$0.526105\pi$
$858$		0			0
$859$	−21.1435	−	25.1978i	−0.721405	−	0.859737i	0.273361	−	0.961911i	$-0.411865\pi$
$859$	−21.1435	−	25.1978i	−0.721405	−	0.859737i	−0.994767	+	0.102174i	$0.967420\pi$
$860$	−4.83062	+	4.18801i	−0.164723	+	0.142810i
$861$		0			0
$862$	0.146610	+	0.209381i	0.00499356	+	0.00713154i
$863$	8.90068	−	8.90068i	0.302983	−	0.302983i	−0.539197	−	0.842180i	$-0.681272\pi$
$863$	8.90068	−	8.90068i	0.302983	−	0.302983i	0.842180	+	0.539197i	$0.181272\pi$
$864$		0			0
$865$	19.1223	−	34.3904i	0.650178	−	1.16931i
$866$	10.6045	+	1.86985i	0.360354	+	0.0635402i
$867$		0			0
$868$	−0.190132	−	0.407738i	−0.00645349	−	0.0138395i
$869$	−51.1947	+	42.9575i	−1.73666	+	1.45723i
$870$		0			0
$871$	−19.4461	+	7.07780i	−0.658905	+	0.239822i
$872$	17.3078	−	4.63761i	0.586116	−	0.157049i
$873$		0			0
$874$	−3.82191	+	2.20658i	−0.129278	+	0.0746386i
$875$	1.01849	−	1.34051i	0.0344314	−	0.0453175i
$876$		0			0
$877$	32.9173	+	23.0489i	1.11154	+	0.778307i	0.977135	−	0.212620i	$-0.0681995\pi$
$877$	32.9173	+	23.0489i	1.11154	+	0.778307i	0.134403	+	0.990927i	$0.457088\pi$
$878$	4.12243	+	2.88655i	0.139125	+	0.0974165i
$879$		0			0
$880$	−9.97705	+	22.3295i	−0.336326	+	0.752726i
$881$	−5.14179	+	2.96862i	−0.173231	+	0.100015i	−0.584109	−	0.811675i	$-0.698556\pi$
$881$	−5.14179	+	2.96862i	−0.173231	+	0.100015i	0.410877	+	0.911691i	$0.365222\pi$
$882$		0			0
$883$	−22.3002	+	5.97531i	−0.750460	+	0.201085i	−0.613722	−	0.789522i	$-0.710329\pi$
$883$	−22.3002	+	5.97531i	−0.750460	+	0.201085i	−0.136738	+	0.990607i	$0.543662\pi$
$884$	−13.3224	+	4.84894i	−0.448080	+	0.163088i
$885$		0			0
$886$	−4.01977	+	3.37298i	−0.135047	+	0.113318i
$887$	−11.5426	−	24.7531i	−0.387561	−	0.831127i	−0.999200	−	0.0399903i	$-0.987267\pi$
$887$	−11.5426	−	24.7531i	−0.387561	−	0.831127i	0.611639	−	0.791137i	$-0.290510\pi$
$888$		0			0
$889$	0.986381	+	0.173926i	0.0330822	+	0.00583328i
$890$	−15.7649	−	8.76587i	−0.528442	−	0.293833i
$891$		0			0
$892$	−30.7828	+	30.7828i	−1.03068	+	1.03068i
$893$	−48.3295	−	69.0217i	−1.61728	−	2.30972i
$894$		0			0
$895$	1.94114	+	0.138312i	0.0648851	+	0.00462328i
$896$	−1.11034	−	1.32325i	−0.0370938	−	0.0442067i
$897$		0			0
$898$	−13.5818	−	6.33328i	−0.453230	−	0.211344i
$899$	2.54854	−	4.41421i	0.0849987	−	0.147222i
$900$		0			0
$901$	−0.661599	−	1.14592i	−0.0220411	−	0.0381762i
$902$	0.199490	+	2.28018i	0.00664230	+	0.0759218i
$903$		0			0
$904$	4.28541	−	0.755633i	0.142530	−	0.0251320i
$905$	−10.7034	−	22.0189i	−0.355793	−	0.731934i
$906$		0			0
$907$	−22.9269	+	2.00584i	−0.761275	+	0.0666030i	−0.461180	−	0.887306i	$-0.652574\pi$
$907$	−22.9269	+	2.00584i	−0.761275	+	0.0666030i	−0.300095	+	0.953909i	$0.597018\pi$
$908$	−25.7280	−	6.89380i	−0.853814	−	0.228779i
$909$		0			0
$910$	−0.326854	+	0.195807i	−0.0108351	+	0.00649093i
$911$	14.7689	+	40.5773i	0.489316	+	1.34439i	0.901301	+	0.433194i	$0.142614\pi$
$911$	14.7689	+	40.5773i	0.489316	+	1.34439i	−0.411984	+	0.911191i	$0.635164\pi$
$912$		0			0
$913$	−39.3537	−	3.44300i	−1.30242	−	0.113947i
$914$	18.6644	+	6.79328i	0.617363	+	0.224702i
$915$		0			0
$916$	−0.656670	+	3.72416i	−0.0216970	+	0.123050i
$917$	−1.43994	−	1.43994i	−0.0475511	−	0.0475511i
$918$		0			0
$919$			4.18974i			0.138207i	0.997609	+	0.0691034i	$0.0220139\pi$
$919$			4.18974i			0.138207i	−0.997609	+	0.0691034i	$0.977986\pi$
$920$	−4.72530	+	0.490344i	−0.155789	+	0.0161662i
$921$		0			0
$922$	18.2712	−	8.51999i	0.601729	−	0.280591i
$923$	0.481644	−	5.50521i	0.0158535	−	0.181206i
$924$		0			0
$925$	−3.52649	−	29.3616i	−0.115950	−	0.965402i
$926$	−5.28866	−	3.05341i	−0.173796	−	0.100341i
$927$		0			0
$928$	4.01884	−	14.9985i	0.131925	−	0.492350i
$929$	−30.3026	−	25.4269i	−0.994196	−	0.834229i	−0.00802588	−	0.999968i	$-0.502555\pi$
$929$	−30.3026	−	25.4269i	−0.994196	−	0.834229i	−0.986170	+	0.165739i	$0.946999\pi$
$930$		0			0
$931$	9.16617	+	51.9839i	0.300409	+	1.70370i
$932$	5.34970	−	7.64017i	0.175235	−	0.250262i
$933$		0			0
$934$	−3.00642	+	3.58291i	−0.0983731	+	0.117237i
$935$	56.3580	−	0.909323i	1.84310	−	0.0297380i
$936$		0			0
$937$	−4.18203	−	15.6076i	−0.136621	−	0.509877i	−0.999986	−	0.00529663i	$-0.998314\pi$
$937$	−4.18203	−	15.6076i	−0.136621	−	0.509877i	0.863365	−	0.504580i	$-0.168353\pi$
$938$	−0.416540	+	0.893273i	−0.0136005	+	0.0291664i
$939$		0			0
$940$	−7.75017	−	40.1541i	−0.252783	−	1.30968i
$941$	1.64321	−	4.51470i	0.0535673	−	0.147175i	−0.910023	−	0.414557i	$-0.863936\pi$
$941$	1.64321	−	4.51470i	0.0535673	−	0.147175i	0.963591	+	0.267382i	$0.0861587\pi$
$942$		0			0
$943$	0.553352	−	0.387461i	0.0180196	−	0.0126175i
$944$	2.05950			0.0670309
$945$		0			0
$946$	−5.75258			−0.187033
$947$	−6.82062	+	4.77585i	−0.221640	+	0.155194i	−0.679124	−	0.734024i	$-0.737640\pi$
$947$	−6.82062	+	4.77585i	−0.221640	+	0.155194i	0.457483	+	0.889218i	$0.348751\pi$
$948$		0			0
$949$	−6.66631	+	18.3155i	−0.216398	+	0.594548i
$950$	10.2207	+	20.1908i	0.331603	+	0.655077i
$951$		0			0
$952$	−0.632938	+	1.35734i	−0.0205136	+	0.0439916i
$953$	−13.0697	−	48.7769i	−0.423370	−	1.58004i	−0.767456	−	0.641101i	$-0.778478\pi$
$953$	−13.0697	−	48.7769i	−0.423370	−	1.58004i	0.344086	−	0.938938i	$-0.388189\pi$
$954$		0			0
$955$	−22.1515	+	22.8780i	−0.716805	+	0.740316i
$956$	30.8488	−	36.7641i	0.997720	−	1.18904i
$957$		0			0
$958$	4.53022	−	6.46983i	0.146365	−	0.209031i
$959$	−0.214053	−	1.21395i	−0.00691212	−	0.0392006i
$960$		0			0
$961$	−21.2114	−	17.7985i	−0.684239	−	0.574145i
$962$	−1.73223	+	6.46478i	−0.0558494	+	0.208433i
$963$		0			0
$964$	−8.93639	−	5.15943i	−0.287822	−	0.166174i
$965$	26.7561	+	4.27395i	0.861308	+	0.137583i
$966$		0			0
$967$	4.27628	−	48.8782i	0.137516	−	1.57182i	−0.543413	−	0.839466i	$-0.682868\pi$
$967$	4.27628	−	48.8782i	0.137516	−	1.57182i	0.680929	−	0.732350i	$-0.261576\pi$
$968$	−38.5010	+	17.9533i	−1.23747	+	0.577041i
$969$		0			0
$970$	0.494087	+	4.76137i	0.0158642	+	0.152878i
$971$		−	49.8235i		−	1.59891i	−0.600725	−	0.799456i	$-0.705121\pi$
$971$		−	49.8235i		−	1.59891i	0.600725	−	0.799456i	$-0.294879\pi$
$972$		0			0
$973$	1.94381	+	1.94381i	0.0623156	+	0.0623156i
$974$	−1.78501	+	10.1233i	−0.0571956	+	0.324372i
$975$		0			0
$976$	−18.0753	−	6.57886i	−0.578575	−	0.210584i
$977$	−55.2362	−	4.83254i	−1.76716	−	0.154607i	−0.843328	−	0.537400i	$-0.819407\pi$
$977$	−55.2362	−	4.83254i	−1.76716	−	0.154607i	−0.923834	+	0.382793i	$0.874962\pi$
$978$		0			0
$979$	25.4677	+	69.9719i	0.813951	+	2.23631i
$980$	−6.23069	+	24.8502i	−0.199032	+	0.793809i
$981$		0			0
$982$	−10.0739	−	2.69929i	−0.321470	−	0.0861377i
$983$	61.1731	−	5.35195i	1.95112	−	0.170701i	0.957912	−	0.287061i	$-0.0926781\pi$
$983$	61.1731	−	5.35195i	1.95112	−	0.170701i	0.993207	+	0.116360i	$0.0371225\pi$
$984$		0			0
$985$	8.10365	−	23.4342i	0.258204	−	0.746675i
$986$	−7.53399	+	1.32845i	−0.239931	+	0.0423063i
$987$		0			0
$988$	2.04794	+	23.4081i	0.0651536	+	0.744710i
$989$	0.848876	+	1.47030i	0.0269927	+	0.0467527i
$990$		0			0
$991$	−23.2830	+	40.3274i	−0.739609	+	1.28104i	0.213062	+	0.977039i	$0.431656\pi$
$991$	−23.2830	+	40.3274i	−0.739609	+	1.28104i	−0.952671	+	0.304002i	$0.901677\pi$
$992$	9.13999	+	4.26205i	0.290195	+	0.135320i
$993$		0			0
$994$	−0.169184	−	0.201626i	−0.00536619	−	0.00639518i
$995$	0.604840	−	8.48859i	0.0191747	−	0.269106i
$996$		0			0
$997$	−10.7055	−	15.2890i	−0.339046	−	0.484208i	0.613034	−	0.790056i	$-0.289949\pi$
$997$	−10.7055	−	15.2890i	−0.339046	−	0.484208i	−0.952080	+	0.305848i	$0.901060\pi$
$998$	1.29438	−	1.29438i	0.0409729	−	0.0409729i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.8.6		192
3.2	odd	2		135.2.q.a.83.11	yes	192
5.2	odd	4	inner	405.2.r.a.332.6		192
15.2	even	4		135.2.q.a.2.11	✓	192
15.8	even	4		675.2.ba.b.407.6		192
15.14	odd	2		675.2.ba.b.218.6		192
27.13	even	9		135.2.q.a.68.11	yes	192
27.14	odd	18	inner	405.2.r.a.233.6		192
135.13	odd	36		675.2.ba.b.257.6		192
135.67	odd	36		135.2.q.a.122.11	yes	192
135.94	even	18		675.2.ba.b.68.6		192
135.122	even	36	inner	405.2.r.a.152.6		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.11	✓	192	15.2	even	4
135.2.q.a.68.11	yes	192	27.13	even	9
135.2.q.a.83.11	yes	192	3.2	odd	2
135.2.q.a.122.11	yes	192	135.67	odd	36
405.2.r.a.8.6		192	1.1	even	1	trivial
405.2.r.a.152.6		192	135.122	even	36	inner
405.2.r.a.233.6		192	27.14	odd	18	inner
405.2.r.a.332.6		192	5.2	odd	4	inner
675.2.ba.b.68.6		192	135.94	even	18
675.2.ba.b.218.6		192	15.14	odd	2
675.2.ba.b.257.6		192	135.13	odd	36
675.2.ba.b.407.6		192	15.8	even	4

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)

\(f(q)\)	\(=\)	\(q+(-0.490069 + 0.343150i) q^{2} +(-0.561625 + 1.54305i) q^{4} +(1.25284 - 1.85213i) q^{5} +(-0.0636379 + 0.136472i) q^{7} +(-0.563947 - 2.10468i) q^{8} +O(q^{10})\)	\(q+(-0.490069 + 0.343150i) q^{2} +(-0.561625 + 1.54305i) q^{4} +(1.25284 - 1.85213i) q^{5} +(-0.0636379 + 0.136472i) q^{7} +(-0.563947 - 2.10468i) q^{8} +(0.0215816 + 1.33758i) q^{10} +(3.54970 - 4.23037i) q^{11} +(1.08490 - 1.54940i) q^{13} +(-0.0156434 - 0.0887180i) q^{14} +(-1.51722 - 1.27310i) q^{16} +(-1.18141 + 4.40907i) q^{17} +(6.55178 + 3.78267i) q^{19} +(2.15431 + 2.97340i) q^{20} +(-0.287947 + 3.29125i) q^{22} +(0.883698 - 0.412075i) q^{23} +(-1.86079 - 4.64085i) q^{25} +1.13159i q^{26} +(-0.174843 - 0.174843i) q^{28} +(0.486461 - 2.75886i) q^{29} +(1.70974 + 0.622294i) q^{31} +(5.52167 + 0.483084i) q^{32} +(-0.934001 - 2.56615i) q^{34} +(0.173036 + 0.288843i) q^{35} +(5.71298 + 1.53079i) q^{37} +(-4.50885 + 0.394473i) q^{38} +(-4.60468 - 1.59232i) q^{40} +(0.682276 - 0.120304i) q^{41} +(0.151755 + 1.73456i) q^{43} +(4.53407 + 7.85325i) q^{44} +(-0.291669 + 0.505186i) q^{46} +(-10.0941 - 4.70696i) q^{47} +(4.48494 + 5.34494i) q^{49} +(2.50442 + 1.63581i) q^{50} +(1.78149 + 2.54423i) q^{52} +(-0.204978 + 0.204978i) q^{53} +(-3.38800 - 11.8745i) q^{55} +(0.323118 + 0.0569745i) q^{56} +(0.708303 + 1.51896i) q^{58} +(-0.796564 + 0.668396i) q^{59} +(9.12620 - 3.32167i) q^{61} +(-1.05143 + 0.281730i) q^{62} +(0.558711 - 0.322572i) q^{64} +(-1.51048 - 3.95052i) q^{65} +(-8.96216 - 6.27537i) q^{67} +(-6.13991 - 4.29921i) q^{68} +(-0.183916 - 0.0821758i) q^{70} +(2.53024 - 1.46084i) q^{71} +(-9.95358 + 2.66706i) q^{73} +(-3.32505 + 1.21022i) q^{74} +(-9.51649 + 7.98529i) q^{76} +(0.351431 + 0.753647i) q^{77} +(-11.9179 - 2.10144i) q^{79} +(-4.25878 + 1.21510i) q^{80} +(-0.293080 + 0.293080i) q^{82} +(-4.10306 - 5.85978i) q^{83} +(6.68606 + 7.71197i) q^{85} +(-0.669585 - 0.797981i) q^{86} +(-10.9054 - 5.08528i) q^{88} +(-6.74192 + 11.6773i) q^{89} +(0.142409 + 0.246659i) q^{91} +(0.139546 + 1.59502i) q^{92} +(6.56201 - 1.15706i) q^{94} +(15.2143 - 7.39568i) q^{95} +(3.56471 - 0.311872i) q^{97} +(-4.03205 - 1.08038i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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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