LMFDB - Embedded newform 486.2.e.c.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [486,2,Mod(55,486)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(486, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("486.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.e (of order $9$, degree $6$, 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:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			379.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	486.379
Dual form			486.2.e.c.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(2.37939 + 0.866025i) q^{5} +(-0.407604 + 2.31164i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(2.37939 + 0.866025i) q^{5} +(-0.407604 + 2.31164i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.26604 + 2.19285i) q^{10} +(-4.03209 + 1.46756i) q^{11} +(0.581252 - 0.487728i) q^{13} +(-1.79813 + 1.50881i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(2.46064 + 4.26195i) q^{17} +(3.62449 - 6.27779i) q^{19} +(-0.439693 + 2.49362i) q^{20} +(-4.03209 - 1.46756i) q^{22} +(0.0530334 + 0.300767i) q^{23} +(1.08125 + 0.907278i) q^{25} +0.758770 q^{26} -2.34730 q^{28} +(2.37939 + 1.99654i) q^{29} +(-1.49273 - 8.46567i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.854570 + 4.84651i) q^{34} +(-2.97178 + 5.14728i) q^{35} +(3.78699 + 6.55926i) q^{37} +(6.81180 - 2.47929i) q^{38} +(-1.93969 + 1.62760i) q^{40} +(-3.75490 + 3.15074i) q^{41} +(1.53209 - 0.557635i) q^{43} +(-2.14543 - 3.71599i) q^{44} +(-0.152704 + 0.264490i) q^{46} +(0.315207 - 1.78763i) q^{47} +(1.40033 + 0.509678i) q^{49} +(0.245100 + 1.39003i) q^{50} +(0.581252 + 0.487728i) q^{52} -0.573978 q^{53} -10.8648 q^{55} +(-1.79813 - 1.50881i) q^{56} +(0.539363 + 3.05888i) q^{58} +(5.14543 + 1.87278i) q^{59} +(1.91875 - 10.8818i) q^{61} +(4.29813 - 7.44459i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(1.80541 - 0.657115i) q^{65} +(0.0320889 - 0.0269258i) q^{67} +(-3.76991 + 3.16333i) q^{68} +(-5.58512 + 2.03282i) q^{70} +(-2.10220 - 3.64111i) q^{71} +(5.54576 - 9.60554i) q^{73} +(-1.31521 + 7.45891i) q^{74} +(6.81180 + 2.47929i) q^{76} +(-1.74897 - 9.91890i) q^{77} +(-5.64930 - 4.74033i) q^{79} -2.53209 q^{80} -4.90167 q^{82} +(-5.22668 - 4.38571i) q^{83} +(2.16385 + 12.2718i) q^{85} +(1.53209 + 0.557635i) q^{86} +(0.745100 - 4.22567i) q^{88} +(3.96064 - 6.86002i) q^{89} +(0.890530 + 1.54244i) q^{91} +(-0.286989 + 0.104455i) q^{92} +(1.39053 - 1.16679i) q^{94} +(14.0608 - 11.7984i) q^{95} +(3.08512 - 1.12289i) q^{97} +(0.745100 + 1.29055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 6 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 - 6 * q^7 - 3 * q^8	$ 6 q + 3 q^{5} - 6 q^{7} - 3 q^{8} + 3 q^{10} - 15 q^{11} + 6 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} - 12 q^{23} + 9 q^{25} - 18 q^{26} - 12 q^{28} + 3 q^{29} + 9 q^{31} - 21 q^{34} - 3 q^{35} + 15 q^{37} + 6 q^{38} - 6 q^{40} - 24 q^{41} + 3 q^{44} - 3 q^{46} + 9 q^{47} - 6 q^{49} + 6 q^{52} + 12 q^{53} - 18 q^{55} + 3 q^{56} + 12 q^{58} + 15 q^{59} + 9 q^{61} + 12 q^{62} - 3 q^{64} + 15 q^{65} - 9 q^{67} + 6 q^{68} - 12 q^{70} - 12 q^{71} + 3 q^{73} - 15 q^{74} + 6 q^{76} + 15 q^{77} + 6 q^{79} - 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{85} + 3 q^{88} + 15 q^{89} - 12 q^{91} + 6 q^{92} - 9 q^{94} + 24 q^{95} - 3 q^{97} + 3 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 - 6 * q^7 - 3 * q^8 + 3 * q^10 - 15 * q^11 + 6 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 - 12 * q^23 + 9 * q^25 - 18 * q^26 - 12 * q^28 + 3 * q^29 + 9 * q^31 - 21 * q^34 - 3 * q^35 + 15 * q^37 + 6 * q^38 - 6 * q^40 - 24 * q^41 + 3 * q^44 - 3 * q^46 + 9 * q^47 - 6 * q^49 + 6 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 12 * q^58 + 15 * q^59 + 9 * q^61 + 12 * q^62 - 3 * q^64 + 15 * q^65 - 9 * q^67 + 6 * q^68 - 12 * q^70 - 12 * q^71 + 3 * q^73 - 15 * q^74 + 6 * q^76 + 15 * q^77 + 6 * q^79 - 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^85 + 3 * q^88 + 15 * q^89 - 12 * q^91 + 6 * q^92 - 9 * q^94 + 24 * q^95 - 3 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	2.37939	+	0.866025i	1.06409	+	0.387298i	0.813965	−	0.580914i	$-0.197305\pi$
$5$	2.37939	+	0.866025i	1.06409	+	0.387298i	0.250129	+	0.968213i	$0.419527\pi$
$6$		0			0
$7$	−0.407604	+	2.31164i	−0.154060	+	0.873716i	0.805581	+	0.592486i	$0.201854\pi$
$7$	−0.407604	+	2.31164i	−0.154060	+	0.873716i	−0.959640	+	0.281230i	$0.909258\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$		0			0
$10$	1.26604	+	2.19285i	0.400358	+	0.693441i
$11$	−4.03209	+	1.46756i	−1.21572	+	0.442486i	−0.868685	−	0.495366i	$-0.835034\pi$
$11$	−4.03209	+	1.46756i	−1.21572	+	0.442486i	−0.347036	+	0.937852i	$0.612812\pi$
$12$		0			0
$13$	0.581252	−	0.487728i	0.161210	−	0.135271i	−0.558614	−	0.829428i	$-0.688667\pi$
$13$	0.581252	−	0.487728i	0.161210	−	0.135271i	0.719824	+	0.694156i	$0.244222\pi$
$14$	−1.79813	+	1.50881i	−0.480571	+	0.403247i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	2.46064	+	4.26195i	0.596792	+	1.03367i	0.993291	+	0.115639i	$0.0368917\pi$
$17$	2.46064	+	4.26195i	0.596792	+	1.03367i	−0.396499	+	0.918035i	$0.629775\pi$
$18$		0			0
$19$	3.62449	−	6.27779i	0.831514	−	1.44022i	−0.0653235	−	0.997864i	$-0.520808\pi$
$19$	3.62449	−	6.27779i	0.831514	−	1.44022i	0.896837	−	0.442360i	$-0.145859\pi$
$20$	−0.439693	+	2.49362i	−0.0983183	+	0.557591i
$21$		0			0
$22$	−4.03209	−	1.46756i	−0.859644	−	0.312885i
$23$	0.0530334	+	0.300767i	0.0110582	+	0.0627144i	0.989838	−	0.142203i	$-0.0454186\pi$
$23$	0.0530334	+	0.300767i	0.0110582	+	0.0627144i	−0.978779	+	0.204917i	$0.934307\pi$
$24$		0			0
$25$	1.08125	+	0.907278i	0.216250	+	0.181456i
$26$	0.758770			0.148807
$27$		0			0
$28$	−2.34730			−0.443597
$29$	2.37939	+	1.99654i	0.441841	+	0.370748i	0.836398	−	0.548123i	$-0.184657\pi$
$29$	2.37939	+	1.99654i	0.441841	+	0.370748i	−0.394557	+	0.918871i	$0.629102\pi$
$30$		0			0
$31$	−1.49273	−	8.46567i	−0.268102	−	1.52048i	−0.760056	−	0.649858i	$-0.774828\pi$
$31$	−1.49273	−	8.46567i	−0.268102	−	1.52048i	0.491954	−	0.870621i	$-0.336283\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$		0			0
$34$	−0.854570	+	4.84651i	−0.146558	+	0.831169i
$35$	−2.97178	+	5.14728i	−0.502323	+	0.870049i
$36$		0			0
$37$	3.78699	+	6.55926i	0.622577	+	1.07834i	0.989004	+	0.147888i	$0.0472477\pi$
$37$	3.78699	+	6.55926i	0.622577	+	1.07834i	−0.366427	+	0.930447i	$0.619419\pi$
$38$	6.81180	−	2.47929i	1.10502	−	0.402195i
$39$		0			0
$40$	−1.93969	+	1.62760i	−0.306692	+	0.257345i
$41$	−3.75490	+	3.15074i	−0.586417	+	0.492062i	−0.887047	−	0.461679i	$-0.847247\pi$
$41$	−3.75490	+	3.15074i	−0.586417	+	0.492062i	0.300630	+	0.953741i	$0.402803\pi$
$42$		0			0
$43$	1.53209	−	0.557635i	0.233641	−	0.0850385i	−0.222546	−	0.974922i	$-0.571437\pi$
$43$	1.53209	−	0.557635i	0.233641	−	0.0850385i	0.456188	+	0.889884i	$0.349215\pi$
$44$	−2.14543	−	3.71599i	−0.323436	−	0.560207i
$45$		0			0
$46$	−0.152704	+	0.264490i	−0.0225149	+	0.0389970i
$47$	0.315207	−	1.78763i	0.0459777	−	0.260753i	−0.953151	−	0.302496i	$-0.902180\pi$
$47$	0.315207	−	1.78763i	0.0459777	−	0.260753i	0.999128	+	0.0417434i	$0.0132912\pi$
$48$		0			0
$49$	1.40033	+	0.509678i	0.200047	+	0.0728112i
$50$	0.245100	+	1.39003i	0.0346624	+	0.196580i
$51$		0			0
$52$	0.581252	+	0.487728i	0.0806051	+	0.0676357i
$53$	−0.573978			−0.0788419			−0.0394210	−	0.999223i	$-0.512551\pi$
$53$	−0.573978			−0.0788419			−0.0394210	+	0.999223i	$0.512551\pi$
$54$		0			0
$55$	−10.8648			−1.46501
$56$	−1.79813	−	1.50881i	−0.240286	−	0.201624i
$57$		0			0
$58$	0.539363	+	3.05888i	0.0708218	+	0.401650i
$59$	5.14543	+	1.87278i	0.669878	+	0.243816i	0.654495	−	0.756066i	$-0.272881\pi$
$59$	5.14543	+	1.87278i	0.669878	+	0.243816i	0.0153826	+	0.999882i	$0.495103\pi$
$60$		0			0
$61$	1.91875	−	10.8818i	0.245671	−	1.39327i	−0.573260	−	0.819374i	$-0.694321\pi$
$61$	1.91875	−	10.8818i	0.245671	−	1.39327i	0.818930	−	0.573893i	$-0.194567\pi$
$62$	4.29813	−	7.44459i	0.545863	−	0.945463i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.80541	−	0.657115i	0.223933	−	0.0815050i
$66$		0			0
$67$	0.0320889	−	0.0269258i	0.00392028	−	0.00328951i	−0.640825	−	0.767687i	$-0.721408\pi$
$67$	0.0320889	−	0.0269258i	0.00392028	−	0.00328951i	0.644746	+	0.764397i	$0.276963\pi$
$68$	−3.76991	+	3.16333i	−0.457169	+	0.383611i
$69$		0			0
$70$	−5.58512	+	2.03282i	−0.667550	+	0.242968i
$71$	−2.10220	−	3.64111i	−0.249485	−	0.432120i	0.713898	−	0.700250i	$-0.246928\pi$
$71$	−2.10220	−	3.64111i	−0.249485	−	0.432120i	−0.963383	+	0.268129i	$0.913595\pi$
$72$		0			0
$73$	5.54576	−	9.60554i	0.649082	−	1.12424i	−0.334260	−	0.942481i	$-0.608487\pi$
$73$	5.54576	−	9.60554i	0.649082	−	1.12424i	0.983342	−	0.181762i	$-0.0581802\pi$
$74$	−1.31521	+	7.45891i	−0.152890	+	0.867081i
$75$		0			0
$76$	6.81180	+	2.47929i	0.781367	+	0.284395i
$77$	−1.74897	−	9.91890i	−0.199314	−	1.13036i
$78$		0			0
$79$	−5.64930	−	4.74033i	−0.635596	−	0.533328i	0.267066	−	0.963678i	$-0.413946\pi$
$79$	−5.64930	−	4.74033i	−0.635596	−	0.533328i	−0.902662	+	0.430350i	$0.858390\pi$
$80$	−2.53209			−0.283096
$81$		0			0
$82$	−4.90167			−0.541299
$83$	−5.22668	−	4.38571i	−0.573703	−	0.481394i	0.309169	−	0.951007i	$-0.399949\pi$
$83$	−5.22668	−	4.38571i	−0.573703	−	0.481394i	−0.882872	+	0.469613i	$0.844393\pi$
$84$		0			0
$85$	2.16385	+	12.2718i	0.234702	+	1.33106i
$86$	1.53209	+	0.557635i	0.165209	+	0.0601313i
$87$		0			0
$88$	0.745100	−	4.22567i	0.0794279	−	0.450458i
$89$	3.96064	−	6.86002i	0.419827	−	0.727161i	−0.576095	−	0.817383i	$-0.695424\pi$
$89$	3.96064	−	6.86002i	0.419827	−	0.727161i	0.995922	+	0.0902216i	$0.0287575\pi$
$90$		0			0
$91$	0.890530	+	1.54244i	0.0933529	+	0.161692i
$92$	−0.286989	+	0.104455i	−0.0299207	+	0.0108902i
$93$		0			0
$94$	1.39053	−	1.16679i	0.143422	−	0.120345i
$95$	14.0608	−	11.7984i	1.44260	−	1.21049i
$96$		0			0
$97$	3.08512	−	1.12289i	0.313247	−	0.114012i	−0.180613	−	0.983554i	$-0.557808\pi$
$97$	3.08512	−	1.12289i	0.313247	−	0.114012i	0.493859	+	0.869542i	$0.335586\pi$
$98$	0.745100	+	1.29055i	0.0752665	+	0.130365i
$99$		0			0
$100$	−0.705737	+	1.22237i	−0.0705737	+	0.122237i
$101$	2.08260	−	11.8110i	0.207226	−	1.17524i	−0.686672	−	0.726967i	$-0.740929\pi$
$101$	2.08260	−	11.8110i	0.207226	−	1.17524i	0.893898	−	0.448270i	$-0.147960\pi$
$102$		0			0
$103$	−2.26604	−	0.824773i	−0.223280	−	0.0812673i	0.227958	−	0.973671i	$-0.426795\pi$
$103$	−2.26604	−	0.824773i	−0.223280	−	0.0812673i	−0.451238	+	0.892404i	$0.649017\pi$
$104$	0.131759	+	0.747243i	0.0129200	+	0.0732732i
$105$		0			0
$106$	−0.439693	−	0.368946i	−0.0427067	−	0.0358352i
$107$	2.42602			0.234532			0.117266	−	0.993101i	$-0.462587\pi$
$107$	2.42602			0.234532			0.117266	+	0.993101i	$0.462587\pi$
$108$		0			0
$109$	−2.32770			−0.222953			−0.111476	−	0.993767i	$-0.535558\pi$
$109$	−2.32770			−0.222953			−0.111476	+	0.993767i	$0.535558\pi$
$110$	−8.32295	−	6.98378i	−0.793562	−	0.665878i
$111$		0			0
$112$	−0.407604	−	2.31164i	−0.0385149	−	0.218429i
$113$	−16.0287	−	5.83396i	−1.50785	−	0.548813i	−0.549772	−	0.835315i	$-0.685285\pi$
$113$	−16.0287	−	5.83396i	−1.50785	−	0.548813i	−0.958080	+	0.286502i	$0.907508\pi$
$114$		0			0
$115$	−0.134285	+	0.761570i	−0.0125222	+	0.0710168i
$116$	−1.55303	+	2.68993i	−0.144196	+	0.249754i
$117$		0			0
$118$	2.73783	+	4.74205i	0.252037	+	0.436541i
$119$	−10.8550	+	3.95091i	−0.995080	+	0.362179i
$120$		0			0
$121$	5.67752	−	4.76400i	0.516138	−	0.433091i
$122$	8.46451	−	7.10257i	0.766341	−	0.643036i
$123$		0			0
$124$	8.07785	−	2.94010i	0.725412	−	0.264028i
$125$	−4.54323	−	7.86911i	−0.406359	−	0.703835i
$126$		0			0
$127$	−6.32295	+	10.9517i	−0.561071	+	0.971803i	0.436332	+	0.899786i	$0.356277\pi$
$127$	−6.32295	+	10.9517i	−0.561071	+	0.971803i	−0.997403	+	0.0720178i	$0.977056\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$		0			0
$130$	1.80541	+	0.657115i	0.158345	+	0.0576328i
$131$	0.901207	+	5.11100i	0.0787388	+	0.446550i	0.998533	+	0.0541487i	$0.0172445\pi$
$131$	0.901207	+	5.11100i	0.0787388	+	0.446550i	−0.919794	+	0.392401i	$0.871644\pi$
$132$		0			0
$133$	13.0346	+	10.9373i	1.13024	+	0.948388i
$134$	0.0418891			0.00361866
$135$		0			0
$136$	−4.92127			−0.421996
$137$	13.1099	+	11.0005i	1.12006	+	0.939840i	0.998607	−	0.0527577i	$-0.0168011\pi$
$137$	13.1099	+	11.0005i	1.12006	+	0.939840i	0.121450	+	0.992598i	$0.461246\pi$
$138$		0			0
$139$	2.11809	+	12.0123i	0.179654	+	1.01887i	0.932634	+	0.360824i	$0.117505\pi$
$139$	2.11809	+	12.0123i	0.179654	+	1.01887i	−0.752980	+	0.658044i	$0.771384\pi$
$140$	−5.58512	−	2.03282i	−0.472029	−	0.171805i
$141$		0			0
$142$	0.730085	−	4.14052i	0.0612674	−	0.347465i
$143$	−1.62789	+	2.81959i	−0.136131	+	0.235786i
$144$		0			0
$145$	3.93242	+	6.81115i	0.326570	+	0.565635i
$146$	10.4226	−	3.79352i	0.862582	−	0.313954i
$147$		0			0
$148$	−5.80200	+	4.86846i	−0.476922	+	0.400185i
$149$	−5.90033	+	4.95096i	−0.483374	+	0.405599i	−0.851645	−	0.524120i	$-0.824394\pi$
$149$	−5.90033	+	4.95096i	−0.483374	+	0.405599i	0.368271	+	0.929719i	$0.379950\pi$
$150$		0			0
$151$	0.733956	−	0.267138i	0.0597285	−	0.0217394i	−0.311983	−	0.950088i	$-0.600993\pi$
$151$	0.733956	−	0.267138i	0.0597285	−	0.0217394i	0.371712	+	0.928348i	$0.378771\pi$
$152$	3.62449	+	6.27779i	0.293985	+	0.509196i
$153$		0			0
$154$	5.03596	−	8.72254i	0.405809	−	0.702882i
$155$	3.77972	−	21.4358i	0.303594	−	1.72177i
$156$		0			0
$157$	9.78359	+	3.56093i	0.780815	+	0.284193i	0.701513	−	0.712657i	$-0.252508\pi$
$157$	9.78359	+	3.56093i	0.780815	+	0.284193i	0.0793026	+	0.996851i	$0.474731\pi$
$158$	−1.28059	−	7.26260i	−0.101878	−	0.577781i
$159$		0			0
$160$	−1.93969	−	1.62760i	−0.153346	−	0.128673i
$161$	−0.716881			−0.0564982
$162$		0			0
$163$	−10.5740			−0.828218			−0.414109	−	0.910227i	$-0.635907\pi$
$163$	−10.5740			−0.828218			−0.414109	+	0.910227i	$0.635907\pi$
$164$	−3.75490	−	3.15074i	−0.293208	−	0.246031i
$165$		0			0
$166$	−1.18479	−	6.71929i	−0.0919577	−	0.521518i
$167$	1.41235	+	0.514054i	0.109291	+	0.0397787i	0.396087	−	0.918213i	$-0.370368\pi$
$167$	1.41235	+	0.514054i	0.109291	+	0.0397787i	−0.286796	+	0.957992i	$0.592590\pi$
$168$		0			0
$169$	−2.15745	+	12.2355i	−0.165958	+	0.941193i
$170$	−6.23055	+	10.7916i	−0.477862	+	0.827680i
$171$		0			0
$172$	0.815207	+	1.41198i	0.0621590	+	0.107663i
$173$	−10.4782	+	3.81374i	−0.796641	+	0.289954i	−0.708094	−	0.706118i	$-0.750445\pi$
$173$	−10.4782	+	3.81374i	−0.796641	+	0.289954i	−0.0885473	+	0.996072i	$0.528222\pi$
$174$		0			0
$175$	−2.53802	+	2.12965i	−0.191856	+	0.160986i
$176$	3.28699	−	2.75811i	0.247766	−	0.207900i
$177$		0			0
$178$	7.44356	−	2.70924i	0.557919	−	0.203066i
$179$	3.90420	+	6.76227i	0.291814	+	0.505436i	0.974239	−	0.225520i	$-0.0724080\pi$
$179$	3.90420	+	6.76227i	0.291814	+	0.505436i	−0.682425	+	0.730956i	$0.739075\pi$
$180$		0			0
$181$	−5.23783	+	9.07218i	−0.389325	+	0.674330i	−0.992359	−	0.123385i	$-0.960625\pi$
$181$	−5.23783	+	9.07218i	−0.389325	+	0.674330i	0.603034	+	0.797715i	$0.293958\pi$
$182$	−0.309278	+	1.75400i	−0.0229252	+	0.130015i
$183$		0			0
$184$	−0.286989	−	0.104455i	−0.0211571	−	0.00770056i
$185$	3.33022	+	18.8866i	0.244843	+	1.38857i
$186$		0			0
$187$	−16.1762	−	13.5734i	−1.18292	−	0.992587i
$188$	1.81521			0.132388
$189$		0			0
$190$	18.3550			1.33161
$191$	9.36824	+	7.86089i	0.677862	+	0.568794i	0.915381	−	0.402589i	$-0.131890\pi$
$191$	9.36824	+	7.86089i	0.677862	+	0.568794i	−0.237519	+	0.971383i	$0.576334\pi$
$192$		0			0
$193$	−2.84224	−	16.1192i	−0.204589	−	1.16028i	−0.898085	−	0.439822i	$-0.855041\pi$
$193$	−2.84224	−	16.1192i	−0.204589	−	1.16028i	0.693496	−	0.720461i	$-0.256070\pi$
$194$	3.08512	+	1.12289i	0.221499	+	0.0806190i
$195$		0			0
$196$	−0.258770	+	1.46756i	−0.0184836	+	0.104826i
$197$	9.49794	−	16.4509i	0.676700	−	1.17208i	−0.299269	−	0.954169i	$-0.596743\pi$
$197$	9.49794	−	16.4509i	0.676700	−	1.17208i	0.975969	−	0.217910i	$-0.0699240\pi$
$198$		0			0
$199$	−11.5214	−	19.9557i	−0.816731	−	1.41462i	−0.908078	−	0.418801i	$-0.862451\pi$
$199$	−11.5214	−	19.9557i	−0.816731	−	1.41462i	0.0913469	−	0.995819i	$-0.470883\pi$
$200$	−1.32635	+	0.482753i	−0.0937872	+	0.0341358i
$201$		0			0
$202$	9.18732	−	7.70908i	0.646417	−	0.542409i
$203$	−5.58512	+	4.68647i	−0.391999	+	0.328926i
$204$		0			0
$205$	−11.6630	+	4.24497i	−0.814577	+	0.296482i
$206$	−1.20574	−	2.08840i	−0.0840077	−	0.145506i
$207$		0			0
$208$	−0.379385	+	0.657115i	−0.0263056	+	0.0455627i
$209$	−5.40121	+	30.6318i	−0.373609	+	2.11884i
$210$		0			0
$211$	−16.4427	−	5.98465i	−1.13196	−	0.412000i	−0.292957	−	0.956126i	$-0.594639\pi$
$211$	−16.4427	−	5.98465i	−1.13196	−	0.412000i	−0.839004	+	0.544125i	$0.816862\pi$
$212$	−0.0996702	−	0.565258i	−0.00684538	−	0.0388221i
$213$		0			0
$214$	1.85844	+	1.55942i	0.127040	+	0.106600i
$215$	4.12836			0.281552
$216$		0			0
$217$	20.1780			1.36977
$218$	−1.78312	−	1.49621i	−0.120768	−	0.101336i
$219$		0			0
$220$	−1.88666	−	10.6998i	−0.127199	−	0.721379i
$221$	3.50892	+	1.27714i	0.236036	+	0.0859100i
$222$		0			0
$223$	−0.732611	+	4.15485i	−0.0490593	+	0.278229i	−0.999462	−	0.0327924i	$-0.989560\pi$
$223$	−0.732611	+	4.15485i	−0.0490593	+	0.278229i	0.950403	+	0.311021i	$0.100671\pi$
$224$	1.17365	−	2.03282i	0.0784177	−	0.135823i
$225$		0			0
$226$	−8.52869	−	14.7721i	−0.567320	−	0.982627i
$227$	15.0030	−	5.46064i	0.995784	−	0.362436i	0.207826	−	0.978166i	$-0.433361\pi$
$227$	15.0030	−	5.46064i	0.995784	−	0.362436i	0.787957	+	0.615730i	$0.211139\pi$
$228$		0			0
$229$	−13.6721	+	11.4722i	−0.903475	+	0.758105i	−0.970866	−	0.239621i	$-0.922977\pi$
$229$	−13.6721	+	11.4722i	−0.903475	+	0.758105i	0.0673916	+	0.997727i	$0.478532\pi$
$230$	−0.592396	+	0.497079i	−0.0390615	+	0.0327765i
$231$		0			0
$232$	−2.91875	+	1.06234i	−0.191625	+	0.0697459i
$233$	−0.368241	−	0.637812i	−0.0241243	−	0.0417844i	0.853711	−	0.520747i	$-0.174346\pi$
$233$	−0.368241	−	0.637812i	−0.0241243	−	0.0417844i	−0.877835	+	0.478962i	$0.841013\pi$
$234$		0			0
$235$	2.29813	−	3.98048i	0.149914	−	0.259658i
$236$	−0.950837	+	5.39246i	−0.0618942	+	0.351020i
$237$		0			0
$238$	−10.8550	−	3.95091i	−0.703628	−	0.256099i
$239$	0.499123	+	2.83067i	0.0322856	+	0.183101i	0.996686	−	0.0813460i	$-0.0259219\pi$
$239$	0.499123	+	2.83067i	0.0322856	+	0.183101i	−0.964400	+	0.264446i	$0.914811\pi$
$240$		0			0
$241$	1.67159	+	1.40263i	0.107676	+	0.0903513i	0.695036	−	0.718975i	$-0.255388\pi$
$241$	1.67159	+	1.40263i	0.107676	+	0.0903513i	−0.587360	+	0.809326i	$0.699833\pi$
$242$	7.41147			0.476428
$243$		0			0
$244$	11.0496			0.707380
$245$	2.89053	+	2.42544i	0.184669	+	0.154956i
$246$		0			0
$247$	−0.955118	−	5.41674i	−0.0607727	−	0.344659i
$248$	8.07785	+	2.94010i	0.512944	+	0.186696i
$249$		0			0
$250$	1.57785	−	8.94842i	0.0997919	−	0.565948i
$251$	−13.0189	+	22.5494i	−0.821745	+	1.42330i	0.0826372	+	0.996580i	$0.473666\pi$
$251$	−13.0189	+	22.5494i	−0.821745	+	1.42330i	−0.904382	+	0.426724i	$0.859668\pi$
$252$		0			0
$253$	−0.655230	−	1.13489i	−0.0411939	−	0.0713500i
$254$	−11.8833	+	4.32515i	−0.745622	+	0.271384i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−7.65451	+	6.42290i	−0.477476	+	0.400650i	−0.849513	−	0.527568i	$-0.823104\pi$
$257$	−7.65451	+	6.42290i	−0.477476	+	0.400650i	0.372037	+	0.928218i	$0.378659\pi$
$258$		0			0
$259$	−16.7062	+	6.08056i	−1.03807	+	0.377828i
$260$	0.960637	+	1.66387i	0.0595762	+	0.103189i
$261$		0			0
$262$	−2.59492	+	4.49454i	−0.160315	+	0.277673i
$263$	−2.64337	+	14.9913i	−0.162997	+	0.924403i	0.788108	+	0.615537i	$0.211061\pi$
$263$	−2.64337	+	14.9913i	−0.162997	+	0.924403i	−0.951105	+	0.308866i	$0.900050\pi$
$264$		0			0
$265$	−1.36571	−	0.497079i	−0.0838952	−	0.0305354i
$266$	2.95471	+	16.7570i	0.181165	+	1.02744i
$267$		0			0
$268$	0.0320889	+	0.0269258i	0.00196014	+	0.00164475i
$269$	−30.5476			−1.86252			−0.931259	−	0.364358i	$-0.881289\pi$
$269$	−30.5476			−1.86252			−0.931259	+	0.364358i	$0.881289\pi$
$270$		0			0
$271$	25.8307			1.56910			0.784551	−	0.620064i	$-0.212893\pi$
$271$	25.8307			1.56910			0.784551	+	0.620064i	$0.212893\pi$
$272$	−3.76991	−	3.16333i	−0.228585	−	0.191805i
$273$		0			0
$274$	2.97178	+	16.8538i	0.179532	+	1.01818i
$275$	−5.69119	−	2.07142i	−0.343192	−	0.124912i
$276$		0			0
$277$	−3.89574	+	22.0939i	−0.234073	+	1.32749i	0.610485	+	0.792027i	$0.290974\pi$
$277$	−3.89574	+	22.0939i	−0.234073	+	1.32749i	−0.844558	+	0.535464i	$0.820137\pi$
$278$	−6.09879	+	10.5634i	−0.365781	+	0.633552i
$279$		0			0
$280$	−2.97178	−	5.14728i	−0.177598	−	0.307609i
$281$	5.49185	−	1.99887i	0.327616	−	0.119243i	−0.172975	−	0.984926i	$-0.555338\pi$
$281$	5.49185	−	1.99887i	0.327616	−	0.119243i	0.500592	+	0.865684i	$0.333116\pi$
$282$		0			0
$283$	−5.67752	+	4.76400i	−0.337493	+	0.283191i	−0.795745	−	0.605632i	$-0.792920\pi$
$283$	−5.67752	+	4.76400i	−0.337493	+	0.283191i	0.458251	+	0.888823i	$0.348476\pi$
$284$	3.22075	−	2.70253i	0.191116	−	0.160366i
$285$		0			0
$286$	−3.05943	+	1.11354i	−0.180908	+	0.0658451i
$287$	−5.75284	−	9.96421i	−0.339579	−	0.588169i
$288$		0			0
$289$	−3.60947	+	6.25179i	−0.212322	+	0.367752i
$290$	−1.36571	+	7.74535i	−0.0801975	+	0.454823i
$291$		0			0
$292$	10.4226	+	3.79352i	0.609938	+	0.221999i
$293$	1.54142	+	8.74184i	0.0900508	+	0.510704i	0.996152	+	0.0876426i	$0.0279333\pi$
$293$	1.54142	+	8.74184i	0.0900508	+	0.510704i	−0.906101	+	0.423061i	$0.860956\pi$
$294$		0			0
$295$	10.6211	+	8.91215i	0.618383	+	0.518885i
$296$	−7.57398			−0.440229
$297$		0			0
$298$	−7.70233			−0.446184
$299$	0.177519	+	0.148956i	0.0102662	+	0.00861433i
$300$		0			0
$301$	0.664563	+	3.76893i	0.0383048	+	0.217237i
$302$	0.733956	+	0.267138i	0.0422344	+	0.0153721i
$303$		0			0
$304$	−1.25877	+	7.13884i	−0.0721954	+	0.409441i
$305$	13.9893	−	24.2302i	0.801026	−	1.38742i
$306$		0			0
$307$	8.04963	+	13.9424i	0.459417	+	0.795733i	0.998930	−	0.0462440i	$-0.0147252\pi$
$307$	8.04963	+	13.9424i	0.459417	+	0.795733i	−0.539514	+	0.841977i	$0.681392\pi$
$308$	9.46451	−	3.44480i	0.539290	−	0.196286i
$309$		0			0
$310$	16.6741	−	13.9912i	0.947026	−	0.794649i
$311$	−10.4101	+	8.73514i	−0.590304	+	0.495324i	−0.888313	−	0.459239i	$-0.848122\pi$
$311$	−10.4101	+	8.73514i	−0.590304	+	0.495324i	0.298008	+	0.954563i	$0.403678\pi$
$312$		0			0
$313$	20.2087	−	7.35538i	1.14226	−	0.415750i	0.299534	−	0.954086i	$-0.403169\pi$
$313$	20.2087	−	7.35538i	1.14226	−	0.415750i	0.842731	+	0.538335i	$0.180947\pi$
$314$	5.20574	+	9.01660i	0.293777	+	0.508836i
$315$		0			0
$316$	3.68732	−	6.38662i	0.207428	−	0.359276i
$317$	3.66267	−	20.7720i	0.205716	−	1.16667i	−0.690594	−	0.723243i	$-0.742651\pi$
$317$	3.66267	−	20.7720i	0.205716	−	1.16667i	0.896309	−	0.443429i	$-0.146238\pi$
$318$		0			0
$319$	−12.5239	−	4.55834i	−0.701206	−	0.255218i
$320$	−0.439693	−	2.49362i	−0.0245796	−	0.139398i
$321$		0			0
$322$	−0.549163	−	0.460802i	−0.0306037	−	0.0256795i
$323$	35.6742			1.98496
$324$		0			0
$325$	1.07098			0.0594076
$326$	−8.10014	−	6.79682i	−0.448625	−	0.376441i
$327$		0			0
$328$	−0.851167	−	4.82721i	−0.0469978	−	0.266538i
$329$	4.00387	+	1.45729i	0.220741	+	0.0803430i
$330$		0			0
$331$	2.85457	−	16.1891i	0.156901	−	0.889832i	−0.800125	−	0.599833i	$-0.795234\pi$
$331$	2.85457	−	16.1891i	0.156901	−	0.889832i	0.957027	−	0.289999i	$-0.0936551\pi$
$332$	3.41147	−	5.90885i	0.187229	−	0.324290i
$333$		0			0
$334$	0.751497	+	1.30163i	0.0411201	+	0.0712220i
$335$	0.0996702	−	0.0362770i	0.00544557	−	0.00198202i
$336$		0			0
$337$	8.08306	−	6.78250i	0.440312	−	0.369466i	−0.395514	−	0.918460i	$-0.629433\pi$
$337$	8.08306	−	6.78250i	0.440312	−	0.369466i	0.835826	+	0.548994i	$0.184989\pi$
$338$	−9.51754	+	7.98617i	−0.517686	+	0.434390i
$339$		0			0
$340$	−11.7096	+	4.26195i	−0.635043	+	0.231137i
$341$	18.4427	+	31.9437i	0.998727	+	1.72985i
$342$		0			0
$343$	−9.96451	+	17.2590i	−0.538033	+	0.931900i
$344$	−0.283119	+	1.60565i	−0.0152647	+	0.0865706i
$345$		0			0
$346$	−10.4782	−	3.81374i	−0.563310	−	0.205028i
$347$	−4.92468	−	27.9292i	−0.264371	−	1.49932i	−0.770822	−	0.637051i	$-0.780154\pi$
$347$	−4.92468	−	27.9292i	−0.264371	−	1.49932i	0.506451	−	0.862269i	$-0.330957\pi$
$348$		0			0
$349$	12.0287	+	10.0933i	0.643881	+	0.540280i	0.905207	−	0.424970i	$-0.139715\pi$
$349$	12.0287	+	10.0933i	0.643881	+	0.540280i	−0.261327	+	0.965250i	$0.584160\pi$
$350$	−3.31315			−0.177095
$351$		0			0
$352$	4.29086			0.228704
$353$	1.58125	+	1.32683i	0.0841615	+	0.0706199i	0.683898	−	0.729578i	$-0.260283\pi$
$353$	1.58125	+	1.32683i	0.0841615	+	0.0706199i	−0.599736	+	0.800198i	$0.704728\pi$
$354$		0			0
$355$	−1.84864	−	10.4842i	−0.0981157	−	0.556442i
$356$	7.44356	+	2.70924i	0.394508	+	0.143589i
$357$		0			0
$358$	−1.35591	+	7.68977i	−0.0716623	+	0.406417i
$359$	−17.4820	+	30.2798i	−0.922667	+	1.59811i	−0.127397	+	0.991852i	$0.540662\pi$
$359$	−17.4820	+	30.2798i	−0.922667	+	1.59811i	−0.795271	+	0.606255i	$0.792671\pi$
$360$		0			0
$361$	−16.7738	−	29.0530i	−0.882831	−	1.52911i
$362$	−9.84389	+	3.58288i	−0.517384	+	0.188312i
$363$		0			0
$364$	−1.36437	+	1.14484i	−0.0715124	+	0.0600061i
$365$	21.5141	−	18.0525i	1.12610	−	0.944911i
$366$		0			0
$367$	0.418748	−	0.152412i	0.0218585	−	0.00795583i	−0.331068	−	0.943607i	$-0.607409\pi$
$367$	0.418748	−	0.152412i	0.0218585	−	0.00795583i	0.352926	+	0.935651i	$0.385187\pi$
$368$	−0.152704	−	0.264490i	−0.00796023	−	0.0137875i
$369$		0			0
$370$	−9.58899	+	16.6086i	−0.498508	+	0.863441i
$371$	0.233956	−	1.32683i	0.0121464	−	0.0688855i
$372$		0			0
$373$	20.7319	+	7.54579i	1.07346	+	0.390706i	0.817468	−	0.575973i	$-0.195377\pi$
$373$	20.7319	+	7.54579i	1.07346	+	0.390706i	0.255989	+	0.966680i	$0.417599\pi$
$374$	−3.66684	−	20.7957i	−0.189608	−	1.07532i
$375$		0			0
$376$	1.39053	+	1.16679i	0.0717111	+	0.0601727i
$377$	2.35679			0.121381
$378$		0			0
$379$	13.1138			0.673611			0.336806	−	0.941574i	$-0.390654\pi$
$379$	13.1138			0.673611			0.336806	+	0.941574i	$0.390654\pi$
$380$	14.0608	+	11.7984i	0.721302	+	0.605245i
$381$		0			0
$382$	2.12361	+	12.0436i	0.108653	+	0.616203i
$383$	15.1395	+	5.51033i	0.773592	+	0.281565i	0.698498	−	0.715612i	$-0.253852\pi$
$383$	15.1395	+	5.51033i	0.773592	+	0.281565i	0.0750942	+	0.997176i	$0.476074\pi$
$384$		0			0
$385$	4.42855	−	25.1155i	0.225700	−	1.28001i
$386$	8.18392	−	14.1750i	0.416550	−	0.721486i
$387$		0			0
$388$	1.64156	+	2.84326i	0.0833375	+	0.144345i
$389$	0.532966	−	0.193984i	0.0270225	−	0.00983537i	−0.328474	−	0.944513i	$-0.606534\pi$
$389$	0.532966	−	0.193984i	0.0270225	−	0.00983537i	0.355496	+	0.934678i	$0.384312\pi$
$390$		0			0
$391$	−1.15136	+	0.966105i	−0.0582268	+	0.0488580i
$392$	−1.14156	+	0.957882i	−0.0576575	+	0.0483803i
$393$		0			0
$394$	17.8503	−	6.49697i	0.899285	−	0.327313i
$395$	−9.33662	−	16.1715i	−0.469776	−	0.813676i
$396$		0			0
$397$	−18.0107	+	31.1955i	−0.903933	+	1.56566i	−0.0815894	+	0.996666i	$0.526000\pi$
$397$	−18.0107	+	31.1955i	−0.903933	+	1.56566i	−0.822343	+	0.568992i	$0.807334\pi$
$398$	4.00134	−	22.6928i	0.200569	−	1.13748i
$399$		0			0
$400$	−1.32635	−	0.482753i	−0.0663176	−	0.0241376i
$401$	−6.25015	−	35.4464i	−0.312118	−	1.77011i	−0.587946	−	0.808900i	$-0.700063\pi$
$401$	−6.25015	−	35.4464i	−0.312118	−	1.77011i	0.275828	−	0.961207i	$-0.411048\pi$
$402$		0			0
$403$	−4.99660	−	4.19264i	−0.248898	−	0.208850i
$404$	11.9932			0.596684
$405$		0			0
$406$	−7.29086			−0.361839
$407$	−24.8956	−	20.8899i	−1.23403	−	1.03547i
$408$		0			0
$409$	2.20115	+	12.4834i	0.108840	+	0.617262i	0.989617	+	0.143731i	$0.0459099\pi$
$409$	2.20115	+	12.4834i	0.108840	+	0.617262i	−0.880777	+	0.473531i	$0.842979\pi$
$410$	−11.6630	−	4.24497i	−0.575993	−	0.209644i
$411$		0			0
$412$	0.418748	−	2.37484i	0.0206302	−	0.117000i
$413$	−6.42649	+	11.1310i	−0.316227	+	0.547721i
$414$		0			0
$415$	−8.63816	−	14.9617i	−0.424030	−	0.734442i
$416$	−0.713011	+	0.259515i	−0.0349582	+	0.0127238i
$417$		0			0
$418$	−23.8273	+	19.9935i	−1.16543	+	0.977912i
$419$	−10.9231	+	9.16556i	−0.533628	+	0.447767i	−0.869352	−	0.494194i	$-0.835463\pi$
$419$	−10.9231	+	9.16556i	−0.533628	+	0.447767i	0.335724	+	0.941960i	$0.391019\pi$
$420$		0			0
$421$	−2.95811	+	1.07666i	−0.144170	+	0.0524734i	−0.413097	−	0.910687i	$-0.635553\pi$
$421$	−2.95811	+	1.07666i	−0.144170	+	0.0524734i	0.268928	+	0.963160i	$0.413331\pi$
$422$	−8.74897	−	15.1537i	−0.425893	−	0.737669i
$423$		0			0
$424$	0.286989	−	0.497079i	0.0139374	−	0.0241403i
$425$	−1.20620	+	6.84072i	−0.0585095	+	0.331824i
$426$		0			0
$427$	24.3726	+	8.87089i	1.17947	+	0.429293i
$428$	0.421274	+	2.38917i	0.0203631	+	0.115485i
$429$		0			0
$430$	3.16250	+	2.65366i	0.152509	+	0.127971i
$431$	−15.4911			−0.746182			−0.373091	−	0.927795i	$-0.621702\pi$
$431$	−15.4911			−0.746182			−0.373091	+	0.927795i	$0.621702\pi$
$432$		0			0
$433$	−2.22844			−0.107092			−0.0535459	−	0.998565i	$-0.517052\pi$
$433$	−2.22844			−0.107092			−0.0535459	+	0.998565i	$0.517052\pi$
$434$	15.4572	+	12.9702i	0.741971	+	0.622588i
$435$		0			0
$436$	−0.404200	−	2.29233i	−0.0193577	−	0.109783i
$437$	2.08037	+	0.757194i	0.0995178	+	0.0362215i
$438$		0			0
$439$	2.98246	−	16.9144i	0.142345	−	0.807279i	−0.827116	−	0.562032i	$-0.810020\pi$
$439$	2.98246	−	16.9144i	0.142345	−	0.807279i	0.969461	−	0.245247i	$-0.0788690\pi$
$440$	5.43242	−	9.40923i	0.258980	−	0.448567i
$441$		0			0
$442$	1.86706	+	3.23384i	0.0888069	+	0.153818i
$443$	−22.1964	+	8.07883i	−1.05458	+	0.383837i	−0.810391	−	0.585890i	$-0.800745\pi$
$443$	−22.1964	+	8.07883i	−1.05458	+	0.383837i	−0.244192	+	0.969727i	$0.578523\pi$
$444$		0			0
$445$	15.3648	−	12.8926i	0.728363	−	0.611169i
$446$	−3.23190	+	2.71188i	−0.153035	+	0.128411i
$447$		0			0
$448$	2.20574	−	0.802823i	0.104211	−	0.0379298i
$449$	−10.1295	−	17.5449i	−0.478042	−	0.827994i	0.521641	−	0.853165i	$-0.325320\pi$
$449$	−10.1295	−	17.5449i	−0.478042	−	0.827994i	−0.999683	+	0.0251715i	$0.991987\pi$
$450$		0			0
$451$	10.5162	−	18.2146i	0.495188	−	0.857691i
$452$	2.96198	−	16.7982i	0.139320	−	0.790122i
$453$		0			0
$454$	15.0030	+	5.46064i	0.704125	+	0.256281i
$455$	0.783119	+	4.44129i	0.0367132	+	0.208211i
$456$		0			0
$457$	−31.0710	−	26.0717i	−1.45344	−	1.21958i	−0.930020	−	0.367509i	$-0.880211\pi$
$457$	−31.0710	−	26.0717i	−1.45344	−	1.21958i	−0.523422	−	0.852074i	$-0.675345\pi$
$458$	−17.8476			−0.833964
$459$		0			0
$460$	−0.773318			−0.0360562
$461$	−10.5018	−	8.81207i	−0.489118	−	0.410419i	0.364592	−	0.931167i	$-0.381208\pi$
$461$	−10.5018	−	8.81207i	−0.489118	−	0.410419i	−0.853710	+	0.520749i	$0.825653\pi$
$462$		0			0
$463$	0.938511	+	5.32256i	0.0436163	+	0.247360i	0.998819	−	0.0485932i	$-0.0154738\pi$
$463$	0.938511	+	5.32256i	0.0436163	+	0.247360i	−0.955202	+	0.295953i	$0.904363\pi$
$464$	−2.91875	−	1.06234i	−0.135499	−	0.0493178i
$465$		0			0
$466$	0.127889	−	0.725293i	0.00592433	−	0.0335985i
$467$	15.7451	−	27.2713i	0.728596	−	1.26197i	−0.228880	−	0.973455i	$-0.573506\pi$
$467$	15.7451	−	27.2713i	0.728596	−	1.26197i	0.957477	−	0.288511i	$-0.0931603\pi$
$468$		0			0
$469$	0.0491630	+	0.0851529i	0.00227014	+	0.00393199i
$470$	4.31908	−	1.57202i	0.199224	−	0.0725117i
$471$		0			0
$472$	−4.19459	+	3.51968i	−0.193072	+	0.162006i
$473$	−5.35916	+	4.49687i	−0.246414	+	0.206766i
$474$		0			0
$475$	9.61468	−	3.49946i	0.441152	−	0.160566i
$476$	−5.77584	−	10.0041i	−0.264735	−	0.458535i
$477$		0			0
$478$	−1.43717	+	2.48925i	−0.0657345	+	0.113855i
$479$	3.64203	−	20.6550i	0.166408	−	0.943749i	−0.781192	−	0.624291i	$-0.785388\pi$
$479$	3.64203	−	20.6550i	0.166408	−	0.943749i	0.947600	−	0.319458i	$-0.103501\pi$
$480$		0			0
$481$	5.40033	+	1.96556i	0.246234	+	0.0896218i
$482$	0.378918	+	2.14895i	0.0172593	+	0.0978821i
$483$		0			0
$484$	5.67752	+	4.76400i	0.258069	+	0.216546i
$485$	8.31315			0.377481
$486$		0			0
$487$	−15.4492			−0.700072			−0.350036	−	0.936736i	$-0.613831\pi$
$487$	−15.4492			−0.700072			−0.350036	+	0.936736i	$0.613831\pi$
$488$	8.46451	+	7.10257i	0.383170	+	0.321518i
$489$		0			0
$490$	0.655230	+	3.71599i	0.0296003	+	0.167871i
$491$	14.9055	+	5.42517i	0.672678	+	0.244835i	0.655700	−	0.755021i	$-0.272373\pi$
$491$	14.9055	+	5.42517i	0.672678	+	0.244835i	0.0169774	+	0.999856i	$0.494596\pi$
$492$		0			0
$493$	−2.65435	+	15.0536i	−0.119546	+	0.677979i
$494$	2.75015	−	4.76340i	0.123735	−	0.214316i
$495$		0			0
$496$	4.29813	+	7.44459i	0.192992	+	0.334272i
$497$	9.27379	−	3.37538i	0.415986	−	0.151407i
$498$		0			0
$499$	−5.73577	+	4.81288i	−0.256768	+	0.215454i	−0.762080	−	0.647483i	$-0.775822\pi$
$499$	−5.73577	+	4.81288i	−0.256768	+	0.215454i	0.505312	+	0.862937i	$0.331377\pi$
$500$	6.96064	−	5.84067i	0.311289	−	0.261203i
$501$		0			0
$502$	−24.4675	+	8.90544i	−1.09204	+	0.397469i
$503$	−10.0667	−	17.4360i	−0.448852	−	0.777435i	0.549459	−	0.835520i	$-0.314834\pi$
$503$	−10.0667	−	17.4360i	−0.448852	−	0.777435i	−0.998312	+	0.0580857i	$0.981500\pi$
$504$		0			0
$505$	15.1839	−	26.2993i	0.675675	−	1.17030i
$506$	0.227559	−	1.29055i	0.0101162	−	0.0573720i
$507$		0			0
$508$	−11.8833	−	4.32515i	−0.527234	−	0.191898i
$509$	6.52616	+	37.0117i	0.289267	+	1.64051i	0.689633	+	0.724159i	$0.257772\pi$
$509$	6.52616	+	37.0117i	0.289267	+	1.64051i	−0.400366	+	0.916355i	$0.631117\pi$
$510$		0			0
$511$	19.9440	+	16.7350i	0.882272	+	0.740314i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−9.99226			−0.440740
$515$	−4.67752	−	3.92490i	−0.206116	−	0.172952i
$516$		0			0
$517$	1.35251	+	7.67047i	0.0594834	+	0.337347i
$518$	−16.7062	−	6.08056i	−0.734028	−	0.267165i
$519$		0			0
$520$	−0.333626	+	1.89209i	−0.0146305	+	0.0829735i
$521$	13.9645	−	24.1872i	0.611796	−	1.05966i	−0.379141	−	0.925339i	$-0.623781\pi$
$521$	13.9645	−	24.1872i	0.611796	−	1.05966i	0.990938	−	0.134323i	$-0.0428861\pi$
$522$		0			0
$523$	−3.64677	−	6.31640i	−0.159462	−	0.276197i	0.775213	−	0.631700i	$-0.217643\pi$
$523$	−3.64677	−	6.31640i	−0.159462	−	0.276197i	−0.934675	+	0.355504i	$0.884309\pi$
$524$	−4.87686	+	1.77503i	−0.213047	+	0.0775426i
$525$		0			0
$526$	−11.6612	+	9.78487i	−0.508451	+	0.426641i
$527$	32.4072	−	27.1929i	1.41168	−	1.18454i
$528$		0			0
$529$	21.5253	−	7.83456i	0.935882	−	0.340633i
$530$	−0.726682	−	1.25865i	−0.0315650	−	0.0546722i
$531$		0			0
$532$	−8.50774	+	14.7358i	−0.368857	+	0.638880i
$533$	−0.645840	+	3.66274i	−0.0279744	+	0.158651i
$534$		0			0
$535$	5.77244	+	2.10100i	0.249564	+	0.0908340i
$536$	0.00727396	+	0.0412527i	0.000314187	+	0.00178184i
$537$		0			0
$538$	−23.4008	−	19.6356i	−1.00888	−	0.846551i
$539$	−6.39424			−0.275419
$540$		0			0
$541$	−2.88444			−0.124012			−0.0620058	−	0.998076i	$-0.519750\pi$
$541$	−2.88444			−0.124012			−0.0620058	+	0.998076i	$0.519750\pi$
$542$	19.7875	+	16.6036i	0.849944	+	0.713188i
$543$		0			0
$544$	−0.854570	−	4.84651i	−0.0366394	−	0.207792i
$545$	−5.53849	−	2.01584i	−0.237243	−	0.0863493i
$546$		0			0
$547$	−1.94326	+	11.0208i	−0.0830877	+	0.471214i	0.914665	+	0.404212i	$0.132454\pi$
$547$	−1.94326	+	11.0208i	−0.0830877	+	0.471214i	−0.997753	+	0.0670015i	$0.978657\pi$
$548$	−8.55690	+	14.8210i	−0.365533	+	0.633121i
$549$		0			0
$550$	−3.02822	−	5.24503i	−0.129124	−	0.223649i
$551$	21.1579	−	7.70085i	0.901358	−	0.328067i
$552$		0			0
$553$	13.2606	−	11.1269i	0.563897	−	0.473166i
$554$	−17.1860	+	14.4207i	−0.730162	+	0.612679i
$555$		0			0
$556$	−11.4620	+	4.17182i	−0.486096	+	0.176925i
$557$	16.6741	+	28.8804i	0.706505	+	1.22370i	0.966146	+	0.257997i	$0.0830625\pi$
$557$	16.6741	+	28.8804i	0.706505	+	1.22370i	−0.259641	+	0.965705i	$0.583604\pi$
$558$		0			0
$559$	0.618555	−	1.07137i	0.0261621	−	0.0453141i
$560$	1.03209	−	5.85327i	0.0436137	−	0.247346i
$561$		0			0
$562$	5.49185	+	1.99887i	0.231660	+	0.0843172i
$563$	−3.21136	−	18.2125i	−0.135343	−	0.767567i	−0.974620	−	0.223864i	$-0.928133\pi$
$563$	−3.21136	−	18.2125i	−0.135343	−	0.767567i	0.839278	−	0.543703i	$-0.182978\pi$
$564$		0			0
$565$	−33.0861	−	27.7625i	−1.39194	−	1.16798i
$566$	−7.41147			−0.311527
$567$		0			0
$568$	4.20439			0.176412
$569$	−22.4702	−	18.8547i	−0.941999	−	0.790431i	0.0359328	−	0.999354i	$-0.488560\pi$
$569$	−22.4702	−	18.8547i	−0.941999	−	0.790431i	−0.977932	+	0.208923i	$0.933004\pi$
$570$		0			0
$571$	0.340900	+	1.93334i	0.0142662	+	0.0809077i	0.991110	−	0.133048i	$-0.0424764\pi$
$571$	0.340900	+	1.93334i	0.0142662	+	0.0809077i	−0.976843	+	0.213955i	$0.931365\pi$
$572$	−3.05943	−	1.11354i	−0.127921	−	0.0465595i
$573$		0			0
$574$	1.99794	−	11.3309i	0.0833924	−	0.472942i
$575$	−0.215537	+	0.373321i	−0.00898852	+	0.0155686i
$576$		0			0
$577$	5.52956	+	9.57748i	0.230199	+	0.398716i	0.957866	−	0.287214i	$-0.0927291\pi$
$577$	5.52956	+	9.57748i	0.230199	+	0.398716i	−0.727668	+	0.685930i	$0.759396\pi$
$578$	−6.78359	+	2.46902i	−0.282160	+	0.102698i
$579$		0			0
$580$	−6.02481	+	5.05542i	−0.250167	+	0.209915i
$581$	12.2686	−	10.2946i	0.508986	−	0.427090i
$582$		0			0
$583$	2.31433	−	0.842347i	0.0958498	−	0.0348865i
$584$	5.54576	+	9.60554i	0.229485	+	0.397480i
$585$		0			0
$586$	−4.43835	+	7.68745i	−0.183346	+	0.317565i
$587$	−5.75583	+	32.6430i	−0.237569	+	1.34732i	0.599567	+	0.800324i	$0.295339\pi$
$587$	−5.75583	+	32.6430i	−0.237569	+	1.34732i	−0.837136	+	0.546995i	$0.815772\pi$
$588$		0			0
$589$	−58.5561	−	21.3127i	−2.41276	−	0.878173i
$590$	2.40760	+	13.6542i	0.0991195	+	0.562134i
$591$		0			0
$592$	−5.80200	−	4.86846i	−0.238461	−	0.200092i
$593$	−14.8283			−0.608926			−0.304463	−	0.952524i	$-0.598477\pi$
$593$	−14.8283			−0.608926			−0.304463	+	0.952524i	$0.598477\pi$
$594$		0			0
$595$	−29.2499			−1.19913
$596$	−5.90033	−	4.95096i	−0.241687	−	0.202799i
$597$		0			0
$598$	0.0402402	+	0.228213i	0.00164554	+	0.00933234i
$599$	−44.4244	−	16.1692i	−1.81513	−	0.660654i	−0.996233	−	0.0867183i	$-0.972362\pi$
$599$	−44.4244	−	16.1692i	−1.81513	−	0.660654i	−0.818900	−	0.573936i	$-0.805416\pi$
$600$		0			0
$601$	6.39234	−	36.2528i	0.260749	−	1.47878i	−0.520124	−	0.854091i	$-0.674114\pi$
$601$	6.39234	−	36.2528i	0.260749	−	1.47878i	0.780873	−	0.624690i	$-0.214775\pi$
$602$	−1.91353	+	3.31434i	−0.0779898	+	0.135082i
$603$		0			0
$604$	0.390530	+	0.676417i	0.0158904	+	0.0275230i
$605$	17.6348	−	6.41852i	0.716955	−	0.260950i
$606$		0			0
$607$	31.6924	−	26.5931i	1.28635	−	1.07938i	0.294019	−	0.955800i	$-0.405007\pi$
$607$	31.6924	−	26.5931i	1.28635	−	1.07938i	0.992335	−	0.123579i	$-0.0394373\pi$
$608$	−5.55303	+	4.65955i	−0.225205	+	0.188970i
$609$		0			0
$610$	26.2913	−	9.56926i	1.06450	−	0.387448i
$611$	−0.688663	−	1.19280i	−0.0278603	−	0.0482555i
$612$		0			0
$613$	20.6755	−	35.8109i	0.835074	−	1.44639i	−0.0588963	−	0.998264i	$-0.518758\pi$
$613$	20.6755	−	35.8109i	0.835074	−	1.44639i	0.893970	−	0.448126i	$-0.147909\pi$
$614$	−2.79561	+	15.8547i	−0.112822	+	0.639843i
$615$		0			0
$616$	9.46451	+	3.44480i	0.381336	+	0.138795i
$617$	−4.25861	−	24.1518i	−0.171445	−	0.972314i	−0.942167	−	0.335142i	$-0.891216\pi$
$617$	−4.25861	−	24.1518i	−0.171445	−	0.972314i	0.770722	−	0.637171i	$-0.219896\pi$
$618$		0			0
$619$	30.3883	+	25.4988i	1.22141	+	1.02488i	0.998750	+	0.0499877i	$0.0159182\pi$
$619$	30.3883	+	25.4988i	1.22141	+	1.02488i	0.222659	+	0.974896i	$0.428526\pi$
$620$	21.7665			0.874164
$621$		0			0
$622$	−13.5895			−0.544888
$623$	14.2435	+	11.9517i	0.570654	+	0.478836i
$624$		0			0
$625$	−5.22075	−	29.6084i	−0.208830	−	1.18433i
$626$	20.2087	+	7.35538i	0.807703	+	0.293980i
$627$		0			0
$628$	−1.80793	+	10.2533i	−0.0721444	+	0.409151i
$629$	−18.6368	+	32.2799i	−0.743098	+	1.28708i
$630$		0			0
$631$	16.6596	+	28.8552i	0.663207	+	1.14871i	0.979768	+	0.200136i	$0.0641384\pi$
$631$	16.6596	+	28.8552i	0.663207	+	1.14871i	−0.316561	+	0.948572i	$0.602528\pi$
$632$	6.92989	−	2.52227i	0.275656	−	0.100331i
$633$		0			0
$634$	16.1578	−	13.5580i	0.641706	−	0.538456i
$635$	−24.5292	+	20.5824i	−0.973410	+	0.816788i
$636$		0			0
$637$	1.06253	−	0.386729i	0.0420989	−	0.0153228i
$638$	−6.66385	−	11.5421i	−0.263824	−	0.456957i
$639$		0			0
$640$	1.26604	−	2.19285i	0.0500448	−	0.0866801i
$641$	−1.25965	+	7.14382i	−0.0497531	+	0.282164i	−0.999526	−	0.0307751i	$-0.990202\pi$
$641$	−1.25965	+	7.14382i	−0.0497531	+	0.282164i	0.949773	+	0.312939i	$0.101314\pi$
$642$		0			0
$643$	7.25789	+	2.64166i	0.286223	+	0.104177i	0.481142	−	0.876643i	$-0.340222\pi$
$643$	7.25789	+	2.64166i	0.286223	+	0.104177i	−0.194919	+	0.980819i	$0.562444\pi$
$644$	−0.124485	−	0.705990i	−0.00490540	−	0.0278199i
$645$		0			0
$646$	27.3280	+	22.9309i	1.07521	+	0.902205i
$647$	40.9469			1.60979			0.804894	−	0.593419i	$-0.202222\pi$
$647$	40.9469			1.60979			0.804894	+	0.593419i	$0.202222\pi$
$648$		0			0
$649$	−23.4953			−0.922269
$650$	0.820422	+	0.688416i	0.0321796	+	0.0270019i
$651$		0			0
$652$	−1.83615	−	10.4133i	−0.0719093	−	0.407818i
$653$	18.6789	+	6.79855i	0.730960	+	0.266048i	0.680571	−	0.732682i	$-0.261732\pi$
$653$	18.6789	+	6.79855i	0.730960	+	0.266048i	0.0503891	+	0.998730i	$0.483954\pi$
$654$		0			0
$655$	−2.28194	+	12.9415i	−0.0891626	+	0.505666i
$656$	2.45084	−	4.24497i	0.0956891	−	0.165738i
$657$		0			0
$658$	2.13041	+	3.68999i	0.0830522	+	0.143851i
$659$	16.1532	−	5.87927i	0.629238	−	0.229024i	−0.00766151	−	0.999971i	$-0.502439\pi$
$659$	16.1532	−	5.87927i	0.629238	−	0.229024i	0.636900	+	0.770947i	$0.280217\pi$
$660$		0			0
$661$	−26.3537	+	22.1134i	−1.02504	+	0.860111i	−0.990252	−	0.139284i	$-0.955520\pi$
$661$	−26.3537	+	22.1134i	−1.02504	+	0.860111i	−0.0347874	+	0.999395i	$0.511075\pi$
$662$	12.5929	−	10.5667i	0.489436	−	0.410685i
$663$		0			0
$664$	6.41147	−	2.33359i	0.248813	−	0.0905607i
$665$	21.5424	+	37.3125i	0.835377	+	1.44691i
$666$		0			0
$667$	−0.474308	+	0.821525i	−0.0183653	+	0.0318096i
$668$	−0.260992	+	1.48016i	−0.0100981	+	0.0572691i
$669$		0			0
$670$	0.0996702	+	0.0362770i	0.00385060	+	0.00140150i
$671$	8.23308	+	46.6921i	0.317834	+	1.80253i
$672$		0			0
$673$	18.3025	+	15.3576i	0.705508	+	0.591992i	0.923335	−	0.383996i	$-0.125452\pi$
$673$	18.3025	+	15.3576i	0.705508	+	0.591992i	−0.217826	+	0.975988i	$0.569897\pi$
$674$	10.5517			0.406436
$675$		0			0
$676$	−12.4243			−0.477856
$677$	−26.5951	−	22.3160i	−1.02213	−	0.857673i	−0.0322401	−	0.999480i	$-0.510264\pi$
$677$	−26.5951	−	22.3160i	−1.02213	−	0.857673i	−0.989894	+	0.141808i	$0.954709\pi$
$678$		0			0
$679$	1.33821	+	7.58937i	0.0513558	+	0.291253i
$680$	−11.7096	−	4.26195i	−0.449043	−	0.163438i
$681$		0			0
$682$	−6.40508	+	36.3250i	−0.245263	+	1.39096i
$683$	−19.5030	+	33.7802i	−0.746261	+	1.29256i	0.203342	+	0.979108i	$0.434820\pi$
$683$	−19.5030	+	33.7802i	−0.746261	+	1.29256i	−0.949603	+	0.313455i	$0.898514\pi$
$684$		0			0
$685$	21.6668	+	37.5281i	0.827847	+	1.43387i
$686$	−18.7271	+	6.81612i	−0.715006	+	0.260241i
$687$		0			0
$688$	−1.24897	+	1.04801i	−0.0476165	+	0.0399550i
$689$	−0.333626	+	0.279945i	−0.0127101	+	0.0106651i
$690$		0			0
$691$	−23.7986	+	8.66198i	−0.905341	+	0.329517i	−0.752391	−	0.658717i	$-0.771100\pi$
$691$	−23.7986	+	8.66198i	−0.905341	+	0.329517i	−0.152950	+	0.988234i	$0.548877\pi$
$692$	−5.57532	−	9.65674i	−0.211942	−	0.367094i
$693$		0			0
$694$	14.1800	−	24.5606i	0.538267	−	0.932306i
$695$	−5.36319	+	30.4162i	−0.203437	+	1.15375i
$696$		0			0
$697$	−22.6677	−	8.25037i	−0.858601	−	0.312505i
$698$	2.72668	+	15.4638i	0.103206	+	0.585313i
$699$		0			0
$700$	−2.53802	−	2.12965i	−0.0959281	−	0.0804932i
$701$	−42.3054			−1.59785			−0.798927	−	0.601429i	$-0.794598\pi$
$701$	−42.3054			−1.59785			−0.798927	+	0.601429i	$0.794598\pi$
$702$		0			0
$703$	54.9035			2.07073
$704$	3.28699	+	2.75811i	0.123883	+	0.103950i
$705$		0			0
$706$	0.358441	+	2.03282i	0.0134901	+	0.0765061i
$707$	26.4538	+	9.62841i	0.994899	+	0.362114i
$708$		0			0
$709$	−8.32144	+	47.1932i	−0.312518	+	1.77238i	0.273292	+	0.961931i	$0.411888\pi$
$709$	−8.32144	+	47.1932i	−0.312518	+	1.77238i	−0.585810	+	0.810448i	$0.699224\pi$
$710$	5.32295	−	9.21962i	0.199767	−	0.346006i
$711$		0			0
$712$	3.96064	+	6.86002i	0.148431	+	0.257090i
$713$	2.46703	−	0.897927i	0.0923911	−	0.0336276i
$714$		0			0
$715$	−6.31521	+	5.29909i	−0.236175	+	0.198175i
$716$	−5.98158	+	5.01914i	−0.223542	+	0.187574i
$717$		0			0
$718$	−32.8555	+	11.9584i	−1.22616	+	0.446284i
$719$	6.15451	+	10.6599i	0.229525	+	0.397548i	0.957667	−	0.287877i	$-0.0929495\pi$
$719$	6.15451	+	10.6599i	0.229525	+	0.397548i	−0.728143	+	0.685426i	$0.759616\pi$
$720$		0			0
$721$	2.83022	−	4.90209i	0.105403	−	0.182563i
$722$	5.82547	−	33.0379i	0.216802	−	1.22954i
$723$		0			0
$724$	−9.84389	−	3.58288i	−0.365845	−	0.133157i
$725$	0.761297	+	4.31753i	0.0282738	+	0.160349i
$726$		0			0
$727$	−13.3320	−	11.1869i	−0.494458	−	0.414899i	0.361163	−	0.932503i	$-0.382380\pi$
$727$	−13.3320	−	11.1869i	−0.494458	−	0.414899i	−0.855621	+	0.517603i	$0.826824\pi$
$728$	−1.78106			−0.0660104
$729$		0			0
$730$	28.0847			1.03946
$731$	6.14653	+	5.15755i	0.227337	+	0.190759i
$732$		0			0
$733$	2.49953	+	14.1756i	0.0923224	+	0.523586i	0.995535	+	0.0943928i	$0.0300910\pi$
$733$	2.49953	+	14.1756i	0.0923224	+	0.523586i	−0.903213	+	0.429193i	$0.858798\pi$
$734$	0.418748	+	0.152412i	0.0154563	+	0.00562562i
$735$		0			0
$736$	0.0530334	−	0.300767i	0.00195484	−	0.0110864i
$737$	−0.0898700	+	0.155659i	−0.00331041	+	0.00573379i
$738$		0			0
$739$	6.82383	+	11.8192i	0.251018	+	0.434777i	0.963806	−	0.266603i	$-0.0859012\pi$
$739$	6.82383	+	11.8192i	0.251018	+	0.434777i	−0.712788	+	0.701380i	$0.752568\pi$
$740$	−18.0214	+	6.55926i	−0.662480	+	0.241123i
$741$		0			0
$742$	1.03209	−	0.866025i	0.0378892	−	0.0317928i
$743$	14.0590	−	11.7969i	0.515773	−	0.432785i	−0.347382	−	0.937724i	$-0.612929\pi$
$743$	14.0590	−	11.7969i	0.515773	−	0.432785i	0.863155	+	0.504938i	$0.168485\pi$
$744$		0			0
$745$	−18.3268	+	6.67042i	−0.671443	+	0.244385i
$746$	11.0312	+	19.1066i	0.403881	+	0.699543i
$747$		0			0
$748$	10.5582	−	18.2874i	0.386048	−	0.668654i
$749$	−0.988856	+	5.60808i	−0.0361320	+	0.204915i
$750$		0			0
$751$	37.9593	+	13.8161i	1.38516	+	0.504156i	0.923737	−	0.383027i	$-0.125118\pi$
$751$	37.9593	+	13.8161i	1.38516	+	0.504156i	0.461419	+	0.887182i	$0.347340\pi$
$752$	0.315207	+	1.78763i	0.0114944	+	0.0651882i
$753$		0			0
$754$	1.80541	+	1.51492i	0.0657491	+	0.0551700i
$755$	1.97771			0.0719763
$756$		0			0
$757$	3.71595			0.135058			0.0675292	−	0.997717i	$-0.478488\pi$
$757$	3.71595			0.135058			0.0675292	+	0.997717i	$0.478488\pi$
$758$	10.0458	+	8.42939i	0.364878	+	0.306169i
$759$		0			0
$760$	3.18732	+	18.0762i	0.115616	+	0.655692i
$761$	−34.6955	−	12.6281i	−1.25771	−	0.457770i	−0.374711	−	0.927142i	$-0.622258\pi$
$761$	−34.6955	−	12.6281i	−1.25771	−	0.457770i	−0.883001	+	0.469372i	$0.844480\pi$
$762$		0			0
$763$	0.948778	−	5.38079i	0.0343481	−	0.194797i
$764$	−6.11468	+	10.5909i	−0.221222	+	0.383167i
$765$		0			0
$766$	8.05556	+	13.9526i	0.291059	+	0.504129i
$767$	3.90420	−	1.42101i	0.140972	−	0.0513098i
$768$		0			0
$769$	−20.8286	+	17.4773i	−0.751100	+	0.630247i	−0.935793	−	0.352549i	$-0.885315\pi$
$769$	−20.8286	+	17.4773i	−0.751100	+	0.630247i	0.184694	+	0.982796i	$0.440871\pi$
$770$	19.5364	−	16.3930i	0.704044	−	0.590763i
$771$		0			0
$772$	15.3807	−	5.59813i	0.553565	−	0.201481i
$773$	−0.869585	−	1.50617i	−0.0312768	−	0.0541730i	0.849963	−	0.526842i	$-0.176624\pi$
$773$	−0.869585	−	1.50617i	−0.0312768	−	0.0541730i	−0.881240	+	0.472669i	$0.843291\pi$
$774$		0			0
$775$	6.06670	−	10.5078i	0.217922	−	0.377453i
$776$	−0.570108	+	3.23324i	−0.0204657	+	0.116067i
$777$		0			0
$778$	0.532966	+	0.193984i	0.0191078	+	0.00695466i
$779$	6.17008	+	34.9923i	0.221066	+	1.25373i
$780$		0			0
$781$	13.8198	+	11.5962i	0.494511	+	0.414944i
$782$	−1.50299			−0.0537469
$783$		0			0
$784$	−1.49020			−0.0532214
$785$	20.1951	+	16.9457i	0.720793	+	0.604817i
$786$		0			0
$787$	−4.01842	−	22.7896i	−0.143241	−	0.812361i	−0.968763	−	0.247990i	$-0.920230\pi$
$787$	−4.01842	−	22.7896i	−0.143241	−	0.812361i	0.825521	−	0.564371i	$-0.190881\pi$
$788$	17.8503	+	6.49697i	0.635890	+	0.231445i
$789$		0			0
$790$	3.24257	−	18.3895i	0.115366	−	0.654271i
$791$	20.0194	−	34.6745i	0.711806	−	1.23288i
$792$		0			0
$793$	−4.19207	−	7.26087i	−0.148865	−	0.257841i
$794$	−33.8491	+	12.3201i	−1.20126	+	0.437223i
$795$		0			0
$796$	17.6518	−	14.8116i	0.625652	−	0.524985i
$797$	−1.89368	+	1.58899i	−0.0670778	+	0.0562849i	−0.675710	−	0.737167i	$-0.736163\pi$
$797$	−1.89368	+	1.58899i	−0.0670778	+	0.0562849i	0.608632	+	0.793452i	$0.291718\pi$
$798$		0			0
$799$	8.39440	−	3.05531i	0.296973	−	0.108089i
$800$	−0.705737	−	1.22237i	−0.0249516	−	0.0432174i
$801$		0			0
$802$	17.9966	−	31.1710i	0.635482	−	1.10069i
$803$	−8.26429	+	46.8691i	−0.291640	+	1.65398i
$804$		0			0
$805$	−1.70574	−	0.620838i	−0.0601193	−	0.0218816i
$806$	−1.13264	−	6.42350i	−0.0398954	−	0.226258i
$807$		0			0
$808$	9.18732	+	7.70908i	0.323209	+	0.271204i
$809$	−1.04870			−0.0368702			−0.0184351	−	0.999830i	$-0.505868\pi$
$809$	−1.04870			−0.0368702			−0.0184351	+	0.999830i	$0.505868\pi$
$810$		0			0
$811$	−21.3087			−0.748250			−0.374125	−	0.927378i	$-0.622057\pi$
$811$	−21.3087			−0.748250			−0.374125	+	0.927378i	$0.622057\pi$
$812$	−5.58512	−	4.68647i	−0.195999	−	0.164463i
$813$		0			0
$814$	−5.64337	−	32.0051i	−0.197800	−	1.12178i
$815$	−25.1596	−	9.15733i	−0.881301	−	0.320767i
$816$		0			0
$817$	2.05232	−	11.6393i	0.0718015	−	0.407207i
$818$	−6.33796	+	10.9777i	−0.221602	+	0.383825i
$819$		0			0
$820$	−6.20574	−	10.7487i	−0.216714	−	0.375359i
$821$	−46.1712	+	16.8049i	−1.61139	+	0.586496i	−0.981713	−	0.190365i	$-0.939033\pi$
$821$	−46.1712	+	16.8049i	−1.61139	+	0.586496i	−0.629672	+	0.776861i	$0.716811\pi$
$822$		0			0
$823$	2.60220	−	2.18350i	0.0907069	−	0.0761121i	−0.596307	−	0.802757i	$-0.703366\pi$
$823$	2.60220	−	2.18350i	0.0907069	−	0.0761121i	0.687014	+	0.726645i	$0.258921\pi$
$824$	1.84730	−	1.55007i	0.0643536	−	0.0539991i
$825$		0			0
$826$	−12.0778	+	4.39598i	−0.420242	+	0.152956i
$827$	−23.8359	−	41.2850i	−0.828856	−	1.43562i	−0.898937	−	0.438079i	$-0.855659\pi$
$827$	−23.8359	−	41.2850i	−0.828856	−	1.43562i	0.0700811	−	0.997541i	$-0.477674\pi$
$828$		0			0
$829$	−1.71570	+	2.97168i	−0.0595887	+	0.103211i	−0.894281	−	0.447506i	$-0.852312\pi$
$829$	−1.71570	+	2.97168i	−0.0595887	+	0.103211i	0.834692	+	0.550717i	$0.185646\pi$
$830$	3.00000	−	17.0138i	0.104132	−	0.590559i
$831$		0			0
$832$	−0.713011	−	0.259515i	−0.0247192	−	0.00899706i
$833$	1.27348	+	7.22227i	0.0441235	+	0.250237i
$834$		0			0
$835$	2.91534	+	2.44626i	0.100890	+	0.0846565i
$836$	−31.1043			−1.07577
$837$		0			0
$838$	−14.2591			−0.492572
$839$	19.3439	+	16.2315i	0.667825	+	0.560372i	0.912421	−	0.409253i	$-0.134211\pi$
$839$	19.3439	+	16.2315i	0.667825	+	0.560372i	−0.244596	+	0.969625i	$0.578655\pi$
$840$		0			0
$841$	−3.36050	−	19.0583i	−0.115879	−	0.657184i
$842$	−2.95811	−	1.07666i	−0.101943	−	0.0371043i
$843$		0			0
$844$	3.03849	−	17.2321i	0.104589	−	0.593154i
$845$	−15.7297	+	27.2446i	−0.541117	+	0.937243i
$846$		0			0
$847$	8.69846	+	15.0662i	0.298883	+	0.517680i
$848$	0.539363	−	0.196312i	0.0185218	−	0.00674138i
$849$		0			0
$850$	−5.32114	+	4.46496i	−0.182514	+	0.153147i
$851$	−1.77197	+	1.48686i	−0.0607425	+	0.0509690i
$852$		0			0
$853$	−37.2388	+	13.5538i	−1.27503	+	0.464073i	−0.888786	−	0.458323i	$-0.848450\pi$
$853$	−37.2388	+	13.5538i	−1.27503	+	0.464073i	−0.386245	+	0.922396i	$0.626228\pi$
$854$	12.9684	+	22.4619i	0.443769	+	0.768630i
$855$		0			0
$856$	−1.21301	+	2.10100i	−0.0414599	+	0.0718106i
$857$	4.83140	−	27.4003i	0.165038	−	0.935975i	−0.783988	−	0.620776i	$-0.786818\pi$
$857$	4.83140	−	27.4003i	0.165038	−	0.935975i	0.949026	−	0.315199i	$-0.102071\pi$
$858$		0			0
$859$	−7.90003	−	2.87537i	−0.269545	−	0.0981065i	0.203712	−	0.979031i	$-0.434700\pi$
$859$	−7.90003	−	2.87537i	−0.269545	−	0.0981065i	−0.473257	+	0.880924i	$0.656922\pi$
$860$	0.716881	+	4.06564i	0.0244455	+	0.138637i
$861$		0			0
$862$	−11.8669	−	9.95751i	−0.404188	−	0.339154i
$863$	41.9436			1.42778			0.713888	−	0.700260i	$-0.246933\pi$
$863$	41.9436			1.42778			0.713888	+	0.700260i	$0.246933\pi$
$864$		0			0
$865$	−28.2344			−0.959999
$866$	−1.70708	−	1.43241i	−0.0580090	−	0.0486753i
$867$		0			0
$868$	3.50387	+	19.8714i	0.118929	+	0.674481i
$869$	29.7352	+	10.8227i	1.00870	+	0.367136i
$870$		0			0
$871$	0.00551927	−	0.0313013i	0.000187013	−	0.00106060i
$872$	1.16385	−	2.01584i	0.0394129	−	0.0682651i
$873$		0			0
$874$	1.10694	+	1.91728i	0.0374429	+	0.0648531i
$875$	20.0424	−	7.29482i	0.677555	−	0.246610i
$876$		0			0
$877$	−35.6373	+	29.9032i	−1.20339	+	1.00976i	−0.203859	+	0.979000i	$0.565348\pi$
$877$	−35.6373	+	29.9032i	−1.20339	+	1.00976i	−0.999527	+	0.0307599i	$0.990207\pi$
$878$	13.1570	−	11.0401i	0.444029	−	0.372584i
$879$		0			0
$880$	10.2096	−	3.71599i	0.344166	−	0.125266i
$881$	5.84611	+	10.1258i	0.196961	+	0.341146i	0.947541	−	0.319633i	$-0.103560\pi$
$881$	5.84611	+	10.1258i	0.196961	+	0.341146i	−0.750581	+	0.660779i	$0.770226\pi$
$882$		0			0
$883$	4.41400	−	7.64527i	0.148543	−	0.257284i	−0.782146	−	0.623095i	$-0.785875\pi$
$883$	4.41400	−	7.64527i	0.148543	−	0.257284i	0.930689	+	0.365811i	$0.119208\pi$
$884$	−0.648423	+	3.67739i	−0.0218088	+	0.123684i
$885$		0			0
$886$	−22.1964	−	8.07883i	−0.745703	−	0.271414i
$887$	0.728903	+	4.13381i	0.0244742	+	0.138800i	0.994596	−	0.103817i	$-0.0331055\pi$
$887$	0.728903	+	4.13381i	0.0244742	+	0.138800i	−0.970122	+	0.242616i	$0.921994\pi$
$888$		0			0
$889$	−22.7390	−	19.0803i	−0.762642	−	0.639932i
$890$	20.0574			0.672325
$891$		0			0
$892$	−4.21894			−0.141261
$893$	−10.0799	−	8.45805i	−0.337311	−	0.283038i
$894$		0			0
$895$	3.43330	+	19.4712i	0.114762	+	0.650850i
$896$	2.20574	+	0.802823i	0.0736885	+	0.0268204i
$897$		0			0
$898$	3.51795	−	19.9513i	0.117396	−	0.665783i
$899$	13.3503	−	23.1234i	0.445257	−	0.771208i
$900$		0			0
$901$	−1.41235	−	2.44626i	−0.0470522	−	0.0814969i
$902$	19.7640	−	7.19350i	0.658069	−	0.239517i
$903$		0			0
$904$	13.0667	−	10.9643i	0.434592	−	0.364666i
$905$	−20.3195	+	17.0501i	−0.675445	+	0.566765i
$906$		0			0
$907$	47.0112	−	17.1107i	1.56098	−	0.568151i	0.590020	−	0.807388i	$-0.299120\pi$
$907$	47.0112	−	17.1107i	1.56098	−	0.568151i	0.970961	+	0.239238i	$0.0768975\pi$
$908$	7.98293	+	13.8268i	0.264923	+	0.458860i
$909$		0			0
$910$	−2.25490	+	3.90560i	−0.0747492	+	0.129469i
$911$	2.80025	−	15.8810i	0.0927764	−	0.526161i	−0.902630	−	0.430418i	$-0.858366\pi$
$911$	2.80025	−	15.8810i	0.0927764	−	0.526161i	0.995406	−	0.0957431i	$-0.0305227\pi$
$912$		0			0
$913$	27.5107	+	10.0131i	0.910472	+	0.331385i
$914$	−7.04323	−	39.9442i	−0.232969	−	1.32124i
$915$		0			0
$916$	−13.6721	−	11.4722i	−0.451737	−	0.379053i
$917$	−12.1821			−0.402289
$918$		0			0
$919$	−43.4023			−1.43171			−0.715855	−	0.698249i	$-0.753963\pi$
$919$	−43.4023			−1.43171			−0.715855	+	0.698249i	$0.753963\pi$
$920$	−0.592396	−	0.497079i	−0.0195307	−	0.0163882i
$921$		0			0
$922$	−2.38057	−	13.5009i	−0.0783998	−	0.444627i
$923$	−2.99778	−	1.09110i	−0.0986731	−	0.0359141i
$924$		0			0
$925$	−1.85638	+	10.5281i	−0.0610374	+	0.346161i
$926$	−2.70233	+	4.68058i	−0.0888042	+	0.153813i
$927$		0			0
$928$	−1.55303	−	2.68993i	−0.0509808	−	0.0883014i
$929$	20.2763	−	7.37997i	0.665244	−	0.242129i	0.0127453	−	0.999919i	$-0.495943\pi$
$929$	20.2763	−	7.37997i	0.665244	−	0.242129i	0.652499	+	0.757790i	$0.273721\pi$
$930$		0			0
$931$	8.27513	−	6.94366i	0.271206	−	0.227569i
$932$	0.564178	−	0.473401i	0.0184803	−	0.0155068i
$933$		0			0
$934$	29.5911	−	10.7703i	0.968251	−	0.352414i
$935$	−26.7344	−	46.3054i	−0.874309	−	1.51435i
$936$		0			0
$937$	8.94625	−	15.4954i	0.292261	−	0.506211i	−0.682083	−	0.731275i	$-0.738926\pi$
$937$	8.94625	−	15.4954i	0.292261	−	0.506211i	0.974344	+	0.225064i	$0.0722590\pi$
$938$	−0.0170741	+	0.0968323i	−0.000557490	+	0.00316169i
$939$		0			0
$940$	4.31908	+	1.57202i	0.140873	+	0.0512735i
$941$	−5.41178	−	30.6917i	−0.176419	−	1.00052i	−0.936493	−	0.350685i	$-0.885949\pi$
$941$	−5.41178	−	30.6917i	−0.176419	−	1.00052i	0.760074	−	0.649836i	$-0.225162\pi$
$942$		0			0
$943$	−1.14677	−	0.962258i	−0.0373441	−	0.0313354i
$944$	−5.47565			−0.178217
$945$		0			0
$946$	−6.99588			−0.227456
$947$	31.0114	+	26.0217i	1.00774	+	0.845591i	0.988037	−	0.154214i	$-0.0492847\pi$
$947$	31.0114	+	26.0217i	1.00774	+	0.845591i	0.0196993	+	0.999806i	$0.493729\pi$
$948$		0			0
$949$	−1.46141	−	8.28806i	−0.0474393	−	0.269042i
$950$	9.61468	+	3.49946i	0.311942	+	0.113537i
$951$		0			0
$952$	2.00593	−	11.3762i	0.0650126	−	0.368705i
$953$	23.7040	−	41.0565i	0.767847	−	1.32995i	−0.170881	−	0.985292i	$-0.554661\pi$
$953$	23.7040	−	41.0565i	0.767847	−	1.32995i	0.938728	−	0.344659i	$-0.112005\pi$
$954$		0			0
$955$	15.4829	+	26.8172i	0.501016	+	0.867785i
$956$	−2.70099	+	0.983080i	−0.0873562	+	0.0317951i
$957$		0			0
$958$	16.0667	−	13.4816i	0.519092	−	0.435570i
$959$	−30.7729	+	25.8215i	−0.993709	+	0.833821i
$960$		0			0
$961$	−40.3089	+	14.6712i	−1.30029	+	0.473265i
$962$	2.87346	+	4.97697i	0.0926439	+	0.160464i
$963$		0			0
$964$	−1.09105	+	1.88976i	−0.0351404	+	0.0608650i
$965$	7.19681	−	40.8152i	0.231674	−	1.31389i
$966$		0			0
$967$	−10.5966	−	3.85684i	−0.340763	−	0.124028i	0.165970	−	0.986131i	$-0.446925\pi$
$967$	−10.5966	−	3.85684i	−0.340763	−	0.124028i	−0.506732	+	0.862103i	$0.669147\pi$
$968$	1.28699	+	7.29888i	0.0413654	+	0.234595i
$969$		0			0
$970$	6.36824	+	5.34359i	0.204472	+	0.171572i
$971$	−7.23442			−0.232164			−0.116082	−	0.993240i	$-0.537033\pi$
$971$	−7.23442			−0.232164			−0.116082	+	0.993240i	$0.537033\pi$
$972$		0			0
$973$	−28.6313			−0.917879
$974$	−11.8348	−	9.93058i	−0.379212	−	0.318196i
$975$		0			0
$976$	1.91875	+	10.8818i	0.0614176	+	0.348317i
$977$	21.4103	+	7.79271i	0.684976	+	0.249311i	0.660983	−	0.750401i	$-0.270140\pi$
$977$	21.4103	+	7.79271i	0.684976	+	0.249311i	0.0239934	+	0.999712i	$0.492362\pi$
$978$		0			0
$979$	−5.90214	+	33.4727i	−0.188633	+	1.06979i
$980$	−1.88666	+	3.26779i	−0.0602671	+	0.104386i
$981$		0			0
$982$	7.93107	+	13.7370i	0.253091	+	0.438366i
$983$	−1.37851	+	0.501736i	−0.0439676	+	0.0160029i	−0.363910	−	0.931434i	$-0.618559\pi$
$983$	−1.37851	+	0.501736i	−0.0439676	+	0.0160029i	0.319943	+	0.947437i	$0.396336\pi$
$984$		0			0
$985$	36.8462	−	30.9176i	1.17402	−	0.985117i
$986$	−11.7096	+	9.82553i	−0.372910	+	0.312909i
$987$		0			0
$988$	5.16860	−	1.88122i	0.164435	−	0.0598494i
$989$	0.248970	+	0.431229i	0.00791680	+	0.0137123i
$990$		0			0
$991$	1.94475	−	3.36840i	0.0617769	−	0.107001i	−0.833483	−	0.552545i	$-0.813657\pi$
$991$	1.94475	−	3.36840i	0.0617769	−	0.107001i	0.895260	+	0.445545i	$0.146990\pi$
$992$	−1.49273	+	8.46567i	−0.0473941	+	0.268785i
$993$		0			0
$994$	9.27379	+	3.37538i	0.294147	+	0.107061i
$995$	−10.1318	−	57.4601i	−0.321198	−	1.82161i
$996$		0			0
$997$	−14.6643	−	12.3048i	−0.464424	−	0.389698i	0.380332	−	0.924850i	$-0.375810\pi$
$997$	−14.6643	−	12.3048i	−0.464424	−	0.389698i	−0.844756	+	0.535152i	$0.820254\pi$
$998$	−7.48751			−0.237013
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.e.c.379.1		6
3.2	odd	2		486.2.e.b.379.1		6
9.2	odd	6		486.2.e.d.217.1		6
9.4	even	3		162.2.e.a.19.1		6
9.5	odd	6		54.2.e.a.7.1	✓	6
9.7	even	3		486.2.e.a.217.1		6
27.2	odd	18		1458.2.c.d.973.1		6
27.4	even	9		486.2.e.a.271.1		6
27.5	odd	18		486.2.e.b.109.1		6
27.7	even	9		1458.2.a.d.1.1		3
27.11	odd	18		1458.2.c.d.487.1		6
27.13	even	9		162.2.e.a.145.1		6
27.14	odd	18		54.2.e.a.31.1	yes	6
27.16	even	9		1458.2.c.a.487.3		6
27.20	odd	18		1458.2.a.a.1.3		3
27.22	even	9	inner	486.2.e.c.109.1		6
27.23	odd	18		486.2.e.d.271.1		6
27.25	even	9		1458.2.c.a.973.3		6
36.23	even	6		432.2.u.a.385.1		6
108.95	even	18		432.2.u.a.193.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.a.7.1	✓	6	9.5	odd	6
54.2.e.a.31.1	yes	6	27.14	odd	18
162.2.e.a.19.1		6	9.4	even	3
162.2.e.a.145.1		6	27.13	even	9
432.2.u.a.193.1		6	108.95	even	18
432.2.u.a.385.1		6	36.23	even	6
486.2.e.a.217.1		6	9.7	even	3
486.2.e.a.271.1		6	27.4	even	9
486.2.e.b.109.1		6	27.5	odd	18
486.2.e.b.379.1		6	3.2	odd	2
486.2.e.c.109.1		6	27.22	even	9	inner
486.2.e.c.379.1		6	1.1	even	1	trivial
486.2.e.d.217.1		6	9.2	odd	6
486.2.e.d.271.1		6	27.23	odd	18
1458.2.a.a.1.3		3	27.20	odd	18
1458.2.a.d.1.1		3	27.7	even	9
1458.2.c.a.487.3		6	27.16	even	9
1458.2.c.a.973.3		6	27.25	even	9
1458.2.c.d.487.1		6	27.11	odd	18
1458.2.c.d.973.1		6	27.2	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(2.37939 + 0.866025i) q^{5} +(-0.407604 + 2.31164i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(2.37939 + 0.866025i) q^{5} +(-0.407604 + 2.31164i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.26604 + 2.19285i) q^{10} +(-4.03209 + 1.46756i) q^{11} +(0.581252 - 0.487728i) q^{13} +(-1.79813 + 1.50881i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(2.46064 + 4.26195i) q^{17} +(3.62449 - 6.27779i) q^{19} +(-0.439693 + 2.49362i) q^{20} +(-4.03209 - 1.46756i) q^{22} +(0.0530334 + 0.300767i) q^{23} +(1.08125 + 0.907278i) q^{25} +0.758770 q^{26} -2.34730 q^{28} +(2.37939 + 1.99654i) q^{29} +(-1.49273 - 8.46567i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.854570 + 4.84651i) q^{34} +(-2.97178 + 5.14728i) q^{35} +(3.78699 + 6.55926i) q^{37} +(6.81180 - 2.47929i) q^{38} +(-1.93969 + 1.62760i) q^{40} +(-3.75490 + 3.15074i) q^{41} +(1.53209 - 0.557635i) q^{43} +(-2.14543 - 3.71599i) q^{44} +(-0.152704 + 0.264490i) q^{46} +(0.315207 - 1.78763i) q^{47} +(1.40033 + 0.509678i) q^{49} +(0.245100 + 1.39003i) q^{50} +(0.581252 + 0.487728i) q^{52} -0.573978 q^{53} -10.8648 q^{55} +(-1.79813 - 1.50881i) q^{56} +(0.539363 + 3.05888i) q^{58} +(5.14543 + 1.87278i) q^{59} +(1.91875 - 10.8818i) q^{61} +(4.29813 - 7.44459i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(1.80541 - 0.657115i) q^{65} +(0.0320889 - 0.0269258i) q^{67} +(-3.76991 + 3.16333i) q^{68} +(-5.58512 + 2.03282i) q^{70} +(-2.10220 - 3.64111i) q^{71} +(5.54576 - 9.60554i) q^{73} +(-1.31521 + 7.45891i) q^{74} +(6.81180 + 2.47929i) q^{76} +(-1.74897 - 9.91890i) q^{77} +(-5.64930 - 4.74033i) q^{79} -2.53209 q^{80} -4.90167 q^{82} +(-5.22668 - 4.38571i) q^{83} +(2.16385 + 12.2718i) q^{85} +(1.53209 + 0.557635i) q^{86} +(0.745100 - 4.22567i) q^{88} +(3.96064 - 6.86002i) q^{89} +(0.890530 + 1.54244i) q^{91} +(-0.286989 + 0.104455i) q^{92} +(1.39053 - 1.16679i) q^{94} +(14.0608 - 11.7984i) q^{95} +(3.08512 - 1.12289i) q^{97} +(0.745100 + 1.29055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 6 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 - 6 * q^7 - 3 * q^8	\( 6 q + 3 q^{5} - 6 q^{7} - 3 q^{8} + 3 q^{10} - 15 q^{11} + 6 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} - 12 q^{23} + 9 q^{25} - 18 q^{26} - 12 q^{28} + 3 q^{29} + 9 q^{31} - 21 q^{34} - 3 q^{35} + 15 q^{37} + 6 q^{38} - 6 q^{40} - 24 q^{41} + 3 q^{44} - 3 q^{46} + 9 q^{47} - 6 q^{49} + 6 q^{52} + 12 q^{53} - 18 q^{55} + 3 q^{56} + 12 q^{58} + 15 q^{59} + 9 q^{61} + 12 q^{62} - 3 q^{64} + 15 q^{65} - 9 q^{67} + 6 q^{68} - 12 q^{70} - 12 q^{71} + 3 q^{73} - 15 q^{74} + 6 q^{76} + 15 q^{77} + 6 q^{79} - 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{85} + 3 q^{88} + 15 q^{89} - 12 q^{91} + 6 q^{92} - 9 q^{94} + 24 q^{95} - 3 q^{97} + 3 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 - 6 * q^7 - 3 * q^8 + 3 * q^10 - 15 * q^11 + 6 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 - 12 * q^23 + 9 * q^25 - 18 * q^26 - 12 * q^28 + 3 * q^29 + 9 * q^31 - 21 * q^34 - 3 * q^35 + 15 * q^37 + 6 * q^38 - 6 * q^40 - 24 * q^41 + 3 * q^44 - 3 * q^46 + 9 * q^47 - 6 * q^49 + 6 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 12 * q^58 + 15 * q^59 + 9 * q^61 + 12 * q^62 - 3 * q^64 + 15 * q^65 - 9 * q^67 + 6 * q^68 - 12 * q^70 - 12 * q^71 + 3 * q^73 - 15 * q^74 + 6 * q^76 + 15 * q^77 + 6 * q^79 - 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^85 + 3 * q^88 + 15 * q^89 - 12 * q^91 + 6 * q^92 - 9 * q^94 + 24 * q^95 - 3 * q^97 + 3 * q^98

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