LMFDB - Embedded newform 675.2.r.a.181.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			181.7
Character	$\chi$	$=$	675.181
Dual form			675.2.r.a.496.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62705 - 0.345839i) q^{2} +(0.700584 + 0.311920i) q^{4} +(0.380412 - 2.20347i) q^{5} +(0.694163 - 1.20233i) q^{7} +(1.65942 + 1.20564i) q^{8} +(-1.38100 + 3.45359i) q^{10} +(4.44787 + 0.945423i) q^{11} +(-0.664131 + 0.141165i) q^{13} +(-1.54525 + 1.71617i) q^{14} +(-3.30929 - 3.67534i) q^{16} +(1.73545 + 1.26088i) q^{17} +(5.56870 + 4.04590i) q^{19} +(0.953818 - 1.42506i) q^{20} +(-6.90992 - 3.07649i) q^{22} +(0.0716950 - 0.0796254i) q^{23} +(-4.71057 - 1.67645i) q^{25} +1.12939 q^{26} +(0.861350 - 0.625807i) q^{28} +(0.214650 + 2.04226i) q^{29} +(0.675922 - 6.43096i) q^{31} +(2.06213 + 3.57172i) q^{32} +(-2.38760 - 2.65170i) q^{34} +(-2.38522 - 1.98695i) q^{35} +(-0.886060 + 2.72701i) q^{37} +(-7.66130 - 8.50874i) q^{38} +(3.28786 - 3.19785i) q^{40} +(5.31403 - 1.12953i) q^{41} +(-0.613014 + 1.06177i) q^{43} +(2.82121 + 2.04973i) q^{44} +(-0.144189 + 0.104759i) q^{46} +(-1.23665 - 11.7660i) q^{47} +(2.53627 + 4.39296i) q^{49} +(7.08454 + 4.35677i) q^{50} +(-0.509312 - 0.108258i) q^{52} +(1.07586 - 0.781661i) q^{53} +(3.77524 - 9.44110i) q^{55} +(2.60148 - 1.15825i) q^{56} +(0.357048 - 3.39709i) q^{58} +(-1.69407 + 0.360086i) q^{59} +(3.69259 + 0.784884i) q^{61} +(-3.32384 + 10.2297i) q^{62} +(0.936638 + 2.88268i) q^{64} +(0.0584104 + 1.51709i) q^{65} +(1.48608 - 14.1391i) q^{67} +(0.822536 + 1.42467i) q^{68} +(3.19370 + 4.05776i) q^{70} +(10.9600 - 7.96294i) q^{71} +(-1.83085 - 5.63478i) q^{73} +(2.38477 - 4.13054i) q^{74} +(2.63935 + 4.57148i) q^{76} +(4.22425 - 4.69151i) q^{77} +(0.938478 + 8.92902i) q^{79} +(-9.35740 + 5.89378i) q^{80} -9.03682 q^{82} +(-16.5673 + 7.37623i) q^{83} +(3.43850 - 3.34436i) q^{85} +(1.36460 - 1.51555i) q^{86} +(6.24105 + 6.93138i) q^{88} +(-2.33361 - 7.18212i) q^{89} +(-0.291288 + 0.896494i) q^{91} +(0.0750652 - 0.0334212i) q^{92} +(-2.05704 + 19.5715i) q^{94} +(11.0334 - 10.7314i) q^{95} +(-1.13640 - 10.8121i) q^{97} +(-2.60738 - 8.02469i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.62705	−	0.345839i	−1.15050	−	0.244545i	−0.407091	−	0.913388i	$-0.633457\pi$
$2$	−1.62705	−	0.345839i	−1.15050	−	0.244545i	−0.743404	+	0.668842i	$0.766790\pi$
$3$		0			0
$3$		0			0
$4$	0.700584	+	0.311920i	0.350292	+	0.155960i
$5$	0.380412	−	2.20347i	0.170126	−	0.985422i
$5$	0.380412	−	2.20347i	0.170126	−	0.985422i
$6$		0			0
$7$	0.694163	−	1.20233i	0.262369	−	0.454436i	−0.704502	−	0.709702i	$-0.748830\pi$
$7$	0.694163	−	1.20233i	0.262369	−	0.454436i	0.966871	+	0.255266i	$0.0821629\pi$
$8$	1.65942	+	1.20564i	0.586694	+	0.426258i
$9$		0			0
$10$	−1.38100	+	3.45359i	−0.436709	+	1.09212i
$11$	4.44787	+	0.945423i	1.34108	+	0.285056i	0.821912	−	0.569615i	$-0.192908\pi$
$11$	4.44787	+	0.945423i	1.34108	+	0.285056i	0.519170	+	0.854671i	$0.326241\pi$
$12$		0			0
$13$	−0.664131	+	0.141165i	−0.184197	+	0.0391522i	−0.299086	−	0.954226i	$-0.596682\pi$
$13$	−0.664131	+	0.141165i	−0.184197	+	0.0391522i	0.114890	+	0.993378i	$0.463349\pi$
$14$	−1.54525	+	1.71617i	−0.412985	+	0.458666i
$15$		0			0
$16$	−3.30929	−	3.67534i	−0.827323	−	0.918835i
$17$	1.73545	+	1.26088i	0.420909	+	0.305808i	0.778003	−	0.628260i	$-0.216233\pi$
$17$	1.73545	+	1.26088i	0.420909	+	0.305808i	−0.357095	+	0.934068i	$0.616233\pi$
$18$		0			0
$19$	5.56870	+	4.04590i	1.27755	+	0.928192i	0.999476	−	0.0323680i	$-0.0103049\pi$
$19$	5.56870	+	4.04590i	1.27755	+	0.928192i	0.278071	+	0.960560i	$0.410305\pi$
$20$	0.953818	−	1.42506i	0.213280	−	0.318653i
$21$		0			0
$22$	−6.90992	−	3.07649i	−1.47320	−	0.655911i
$23$	0.0716950	−	0.0796254i	0.0149494	−	0.0166030i	−0.735624	−	0.677390i	$-0.763111\pi$
$23$	0.0716950	−	0.0796254i	0.0149494	−	0.0166030i	0.750573	+	0.660787i	$0.229777\pi$
$24$		0			0
$25$	−4.71057	−	1.67645i	−0.942115	−	0.335291i
$26$	1.12939			0.221492
$27$		0			0
$28$	0.861350	−	0.625807i	0.162780	−	0.118266i
$29$	0.214650	+	2.04226i	0.0398595	+	0.379238i	0.996208	+	0.0870081i	$0.0277306\pi$
$29$	0.214650	+	2.04226i	0.0398595	+	0.379238i	−0.956348	+	0.292230i	$0.905603\pi$
$30$		0			0
$31$	0.675922	−	6.43096i	0.121399	−	1.15504i	−0.748959	−	0.662616i	$-0.769446\pi$
$31$	0.675922	−	6.43096i	0.121399	−	1.15504i	0.870358	−	0.492419i	$-0.163887\pi$
$32$	2.06213	+	3.57172i	0.364537	+	0.631397i
$33$		0			0
$34$	−2.38760	−	2.65170i	−0.409470	−	0.454762i
$35$	−2.38522	−	1.98695i	−0.403176	−	0.335856i
$36$		0			0
$37$	−0.886060	+	2.72701i	−0.145667	+	0.448318i	−0.997096	−	0.0761520i	$-0.975737\pi$
$37$	−0.886060	+	2.72701i	−0.145667	+	0.448318i	0.851429	+	0.524470i	$0.175737\pi$
$38$	−7.66130	−	8.50874i	−1.24283	−	1.38030i
$39$		0			0
$40$	3.28786	−	3.19785i	0.519856	−	0.505624i
$41$	5.31403	−	1.12953i	0.829913	−	0.176403i	0.226681	−	0.973969i	$-0.427213\pi$
$41$	5.31403	−	1.12953i	0.829913	−	0.176403i	0.603232	+	0.797566i	$0.293879\pi$
$42$		0			0
$43$	−0.613014	+	1.06177i	−0.0934837	+	0.161919i	−0.908975	−	0.416851i	$-0.863134\pi$
$43$	−0.613014	+	1.06177i	−0.0934837	+	0.161919i	0.815491	+	0.578770i	$0.196467\pi$
$44$	2.82121	+	2.04973i	0.425313	+	0.309008i
$45$		0			0
$46$	−0.144189	+	0.104759i	−0.0212595	+	0.0154459i
$47$	−1.23665	−	11.7660i	−0.180385	−	1.71624i	−0.592885	−	0.805287i	$-0.702011\pi$
$47$	−1.23665	−	11.7660i	−0.180385	−	1.71624i	0.412501	−	0.910957i	$-0.364655\pi$
$48$		0			0
$49$	2.53627	+	4.39296i	0.362325	+	0.627565i
$50$	7.08454	+	4.35677i	1.00190	+	0.616141i
$51$		0			0
$52$	−0.509312	−	0.108258i	−0.0706289	−	0.0150126i
$53$	1.07586	−	0.781661i	0.147781	−	0.107369i	−0.511438	−	0.859320i	$-0.670887\pi$
$53$	1.07586	−	0.781661i	0.147781	−	0.107369i	0.659219	+	0.751951i	$0.270887\pi$
$54$		0			0
$55$	3.77524	−	9.44110i	0.509053	−	1.27304i
$56$	2.60148	−	1.15825i	0.347638	−	0.154778i
$57$		0			0
$58$	0.357048	−	3.39709i	0.0468827	−	0.446059i
$59$	−1.69407	+	0.360086i	−0.220549	+	0.0468792i	−0.316861	−	0.948472i	$-0.602629\pi$
$59$	−1.69407	+	0.360086i	−0.220549	+	0.0468792i	0.0963115	+	0.995351i	$0.469295\pi$
$60$		0			0
$61$	3.69259	+	0.784884i	0.472788	+	0.100494i	0.438142	−	0.898906i	$-0.355637\pi$
$61$	3.69259	+	0.784884i	0.472788	+	0.100494i	0.0346452	+	0.999400i	$0.488970\pi$
$62$	−3.32384	+	10.2297i	−0.422128	+	1.29918i
$63$		0			0
$64$	0.936638	+	2.88268i	0.117080	+	0.360334i
$65$	0.0584104	+	1.51709i	0.00724492	+	0.188172i
$66$		0			0
$67$	1.48608	−	14.1391i	0.181553	−	1.72737i	−0.402301	−	0.915508i	$-0.631789\pi$
$67$	1.48608	−	14.1391i	0.181553	−	1.72737i	0.583854	−	0.811858i	$-0.301544\pi$
$68$	0.822536	+	1.42467i	0.0997472	+	0.172767i
$69$		0			0
$70$	3.19370	+	4.05776i	0.381721	+	0.484995i
$71$	10.9600	−	7.96294i	1.30072	−	0.945027i	0.300755	−	0.953701i	$-0.402761\pi$
$71$	10.9600	−	7.96294i	1.30072	−	0.945027i	0.999962	+	0.00867479i	$0.00276131\pi$
$72$		0			0
$73$	−1.83085	−	5.63478i	−0.214285	−	0.659501i	−0.999204	−	0.0399023i	$-0.987295\pi$
$73$	−1.83085	−	5.63478i	−0.214285	−	0.659501i	0.784919	−	0.619599i	$-0.212705\pi$
$74$	2.38477	−	4.13054i	0.277224	−	0.480166i
$75$		0			0
$76$	2.63935	+	4.57148i	0.302754	+	0.524385i
$77$	4.22425	−	4.69151i	0.481398	−	0.534647i
$78$		0			0
$79$	0.938478	+	8.92902i	0.105587	+	1.00459i	0.911148	+	0.412080i	$0.135198\pi$
$79$	0.938478	+	8.92902i	0.105587	+	1.00459i	−0.805561	+	0.592513i	$0.798136\pi$
$80$	−9.35740	+	5.89378i	−1.04619	+	0.658945i
$81$		0			0
$82$	−9.03682			−0.997950
$83$	−16.5673	+	7.37623i	−1.81850	+	0.809647i	−0.869844	+	0.493327i	$0.835781\pi$
$83$	−16.5673	+	7.37623i	−1.81850	+	0.809647i	−0.948653	+	0.316320i	$0.897553\pi$
$84$		0			0
$85$	3.43850	−	3.34436i	0.372958	−	0.362747i
$86$	1.36460	−	1.51555i	0.147149	−	0.163426i
$87$		0			0
$88$	6.24105	+	6.93138i	0.665298	+	0.738888i
$89$	−2.33361	−	7.18212i	−0.247363	−	0.761304i	−0.995239	−	0.0974656i	$-0.968926\pi$
$89$	−2.33361	−	7.18212i	−0.247363	−	0.761304i	0.747876	−	0.663838i	$-0.231074\pi$
$90$		0			0
$91$	−0.291288	+	0.896494i	−0.0305353	+	0.0939781i
$92$	0.0750652	−	0.0334212i	0.00782608	−	0.00348440i
$93$		0			0
$94$	−2.05704	+	19.5715i	−0.212168	+	2.01864i
$95$	11.0334	−	10.7314i	1.13200	−	1.10101i
$96$		0			0
$97$	−1.13640	−	10.8121i	−0.115384	−	1.09781i	−0.887017	−	0.461737i	$-0.847226\pi$
$97$	−1.13640	−	10.8121i	−0.115384	−	1.09781i	0.771633	−	0.636068i	$-0.219440\pi$
$98$	−2.60738	−	8.02469i	−0.263385	−	0.810616i
$99$		0			0
$100$	−2.77723	−	2.64382i	−0.277723	−	0.264382i
$101$	6.10657	−	10.5769i	0.607626	−	1.05244i	−0.384004	−	0.923331i	$-0.625455\pi$
$101$	6.10657	−	10.5769i	0.607626	−	1.05244i	0.991630	−	0.129108i	$-0.0412115\pi$
$102$		0			0
$103$	−0.775688	−	0.345359i	−0.0764309	−	0.0340292i	0.368165	−	0.929760i	$-0.379986\pi$
$103$	−0.775688	−	0.345359i	−0.0764309	−	0.0340292i	−0.444596	+	0.895731i	$0.646653\pi$
$104$	−1.27227	−	0.566450i	−0.124756	−	0.0555450i
$105$		0			0
$106$	−2.02081	+	0.899723i	−0.196278	+	0.0873888i
$107$	−19.0764			−1.84419			−0.922095	−	0.386964i	$-0.873524\pi$
$107$	−19.0764			−1.84419			−0.922095	+	0.386964i	$0.873524\pi$
$108$		0			0
$109$	4.05014	−	12.4651i	0.387933	−	1.19394i	−0.546397	−	0.837526i	$-0.684001\pi$
$109$	4.05014	−	12.4651i	0.387933	−	1.19394i	0.934330	−	0.356409i	$-0.115999\pi$
$110$	−9.40759	+	14.0555i	−0.896978	+	1.34014i
$111$		0			0
$112$	−6.71614	+	1.42756i	−0.634616	+	0.134892i
$113$	−6.81089	+	1.44770i	−0.640714	+	0.136188i	−0.516802	−	0.856105i	$-0.672878\pi$
$113$	−6.81089	+	1.44770i	−0.640714	+	0.136188i	−0.123913	+	0.992293i	$0.539544\pi$
$114$		0			0
$115$	−0.148179	−	0.188268i	−0.0138177	−	0.0175561i
$116$	−0.486642	+	1.49773i	−0.0451835	+	0.139061i
$117$		0			0
$118$	2.88087			0.265205
$119$	2.72067	−	1.21132i	0.249404	−	0.111042i
$120$		0			0
$121$	8.84069	+	3.93613i	0.803699	+	0.357830i
$122$	−5.73657	−	2.55409i	−0.519365	−	0.231236i
$123$		0			0
$124$	2.47949	−	4.29460i	0.222665	−	0.385666i
$125$	−5.48598	+	9.74187i	−0.490681	+	0.871339i
$126$		0			0
$127$	6.85641	+	21.1019i	0.608408	+	1.87249i	0.471407	+	0.881916i	$0.343746\pi$
$127$	6.85641	+	21.1019i	0.608408	+	1.87249i	0.137000	+	0.990571i	$0.456254\pi$
$128$	−1.38922	−	13.2175i	−0.122791	−	1.16828i
$129$		0			0
$130$	0.429635	−	2.48858i	0.0376814	−	0.218263i
$131$	−1.21480	+	11.5581i	−0.106138	+	1.00983i	0.803747	+	0.594972i	$0.202837\pi$
$131$	−1.21480	+	11.5581i	−0.106138	+	1.00983i	−0.909885	+	0.414862i	$0.863830\pi$
$132$		0			0
$133$	8.73007	−	3.88688i	0.756993	−	0.337035i
$134$	−7.30778	+	22.4910i	−0.631296	+	1.94293i
$135$		0			0
$136$	1.35968	+	4.18466i	0.116591	+	0.358832i
$137$	11.0828	+	12.3087i	0.946869	+	1.05160i	0.998598	+	0.0529430i	$0.0168602\pi$
$137$	11.0828	+	12.3087i	0.946869	+	1.05160i	−0.0517289	+	0.998661i	$0.516473\pi$
$138$		0			0
$139$	−11.2616	+	12.5073i	−0.955198	+	1.06085i	0.0428925	+	0.999080i	$0.486343\pi$
$139$	−11.2616	+	12.5073i	−0.955198	+	1.06085i	−0.998090	+	0.0617748i	$0.980324\pi$
$140$	−1.05128	−	2.13602i	−0.0888494	−	0.180527i
$141$		0			0
$142$	−20.5864	+	9.16565i	−1.72757	+	0.769164i
$143$	−3.08743			−0.258184
$144$		0			0
$145$	4.58172	+	0.303925i	0.380491	+	0.0252396i
$146$	1.03015	+	9.80123i	0.0852559	+	0.811155i
$147$		0			0
$148$	−1.47137	+	1.63412i	−0.120946	+	0.134324i
$149$	7.97992	+	13.8216i	0.653740	+	1.13231i	0.982208	+	0.187796i	$0.0601345\pi$
$149$	7.97992	+	13.8216i	0.653740	+	1.13231i	−0.328468	+	0.944515i	$0.606532\pi$
$150$		0			0
$151$	−4.20769	+	7.28793i	−0.342417	+	0.593084i	−0.984881	−	0.173232i	$-0.944579\pi$
$151$	−4.20769	+	7.28793i	−0.342417	+	0.593084i	0.642464	+	0.766316i	$0.277912\pi$
$152$	4.36292	+	13.4277i	0.353880	+	1.08913i
$153$		0			0
$154$	−8.49556	+	6.17239i	−0.684592	+	0.497385i
$155$	−13.9133	−	3.93579i	−1.11754	−	0.316130i
$156$		0			0
$157$	0.0425739	+	0.0737402i	0.00339777	+	0.00588511i	0.867719	−	0.497055i	$-0.165585\pi$
$157$	0.0425739	+	0.0737402i	0.00339777	+	0.00588511i	−0.864322	+	0.502940i	$0.832252\pi$
$158$	1.56106	−	14.8525i	0.124191	−	1.18160i
$159$		0			0
$160$	8.65465	−	3.18513i	0.684210	−	0.251806i
$161$	−0.0459676	−	0.141474i	−0.00362275	−	0.0111497i
$162$		0			0
$163$	3.81218	−	11.7327i	0.298593	−	0.918974i	−0.683398	−	0.730046i	$-0.739499\pi$
$163$	3.81218	−	11.7327i	0.298593	−	0.918974i	0.981991	−	0.188928i	$-0.0605013\pi$
$164$	4.07525	+	0.866222i	0.318224	+	0.0676406i
$165$		0			0
$166$	29.5067	−	6.27185i	2.29017	−	0.486790i
$167$	−0.700044	+	6.66047i	−0.0541710	+	0.515403i	0.933468	+	0.358660i	$0.116766\pi$
$167$	−0.700044	+	6.66047i	−0.0541710	+	0.515403i	−0.987639	+	0.156743i	$0.949901\pi$
$168$		0			0
$169$	−11.4549	+	5.10007i	−0.881150	+	0.392313i
$170$	−6.75121	+	4.25227i	−0.517794	+	0.326134i
$171$		0			0
$172$	−0.760656	+	0.552649i	−0.0579995	+	0.0421391i
$173$	11.2482	+	2.39087i	0.855181	+	0.181774i	0.614585	−	0.788851i	$-0.289324\pi$
$173$	11.2482	+	2.39087i	0.855181	+	0.181774i	0.240596	+	0.970625i	$0.422657\pi$
$174$		0			0
$175$	−5.28555	+	4.49991i	−0.399550	+	0.340161i
$176$	−11.2445	−	19.4761i	−0.847588	−	1.46807i
$177$		0			0
$178$	1.31304	+	12.4927i	0.0984162	+	0.936368i
$179$	3.97320	−	2.88670i	0.296971	−	0.215762i	−0.429315	−	0.903155i	$-0.641245\pi$
$179$	3.97320	−	2.88670i	0.296971	−	0.215762i	0.726286	+	0.687393i	$0.241245\pi$
$180$		0			0
$181$	−1.69167	−	1.22907i	−0.125741	−	0.0913562i	0.523137	−	0.852248i	$-0.324762\pi$
$181$	−1.69167	−	1.22907i	−0.125741	−	0.0913562i	−0.648878	+	0.760892i	$0.724762\pi$
$182$	0.783983	−	1.35790i	0.0581127	−	0.100654i
$183$		0			0
$184$	0.214972	−	0.0456937i	0.0158479	−	0.00336858i
$185$	5.67183	+	2.98980i	0.417001	+	0.219814i
$186$		0			0
$187$	6.52699	+	7.24896i	0.477301	+	0.530096i
$188$	2.80367	−	8.62880i	0.204478	−	0.629320i
$189$		0			0
$190$	−21.6632	+	13.6446i	−1.57161	+	0.989886i
$191$	−6.87172	−	7.63182i	−0.497220	−	0.552219i	0.441337	−	0.897341i	$-0.354504\pi$
$191$	−6.87172	−	7.63182i	−0.497220	−	0.552219i	−0.938558	+	0.345122i	$0.887838\pi$
$192$		0			0
$193$	0.879316	+	1.52302i	0.0632945	+	0.109629i	0.895936	−	0.444183i	$-0.146506\pi$
$193$	0.879316	+	1.52302i	0.0632945	+	0.109629i	−0.832642	+	0.553812i	$0.813173\pi$
$194$	−1.89028	+	17.9848i	−0.135714	+	1.29124i
$195$		0			0
$196$	0.406622	+	3.86875i	0.0290444	+	0.276339i
$197$	−1.28192	+	0.931373i	−0.0913333	+	0.0663576i	−0.632515	−	0.774548i	$-0.717977\pi$
$197$	−1.28192	+	0.931373i	−0.0913333	+	0.0663576i	0.541181	+	0.840906i	$0.317977\pi$
$198$		0			0
$199$	−4.83781			−0.342943			−0.171471	−	0.985189i	$-0.554852\pi$
$199$	−4.83781			−0.342943			−0.171471	+	0.985189i	$0.554852\pi$
$200$	−5.79563	−	8.46120i	−0.409813	−	0.598297i
$201$		0			0
$202$	−13.5936	+	15.0972i	−0.956441	+	1.06224i
$203$	2.60446	+	1.15958i	0.182798	+	0.0813867i
$204$		0			0
$205$	−0.467370	−	12.1390i	−0.0326425	−	0.847825i
$206$	1.14264	+	0.830178i	0.0796117	+	0.0578413i
$207$		0			0
$208$	2.71663	+	1.97375i	0.188365	+	0.136855i
$209$	20.9437	+	23.2604i	1.44871	+	1.60895i
$210$		0			0
$211$	−2.87300	+	3.19079i	−0.197785	+	0.219663i	−0.833877	−	0.551951i	$-0.813884\pi$
$211$	−2.87300	+	3.19079i	−0.197785	+	0.219663i	0.636091	+	0.771614i	$0.280550\pi$
$212$	0.997550	−	0.212036i	0.0685120	−	0.0145627i
$213$		0			0
$214$	31.0383	+	6.59739i	2.12173	+	0.450988i
$215$	2.10638	+	1.75467i	0.143654	+	0.119667i
$216$		0			0
$217$	−7.26291	−	5.27682i	−0.493039	−	0.358214i
$218$	−10.9007	+	18.8805i	−0.738287	+	1.27875i
$219$		0			0
$220$	5.58974	−	5.43671i	0.376860	−	0.366543i
$221$	−1.33056	−	0.592403i	−0.0895031	−	0.0398494i
$222$		0			0
$223$	−15.8538	−	3.36984i	−1.06165	−	0.225661i	−0.356193	−	0.934412i	$-0.615926\pi$
$223$	−15.8538	−	3.36984i	−1.06165	−	0.225661i	−0.705459	+	0.708751i	$0.749259\pi$
$224$	5.72583			0.382573
$225$		0			0
$226$	11.5823			0.770443
$227$	9.01077	+	1.91530i	0.598066	+	0.127123i	0.496990	−	0.867756i	$-0.334438\pi$
$227$	9.01077	+	1.91530i	0.598066	+	0.127123i	0.101075	+	0.994879i	$0.467772\pi$
$228$		0			0
$229$	−7.49545	−	3.33719i	−0.495314	−	0.220528i	0.143849	−	0.989600i	$-0.454052\pi$
$229$	−7.49545	−	3.33719i	−0.495314	−	0.220528i	−0.639162	+	0.769072i	$0.720719\pi$
$230$	0.175983	+	0.357567i	0.0116040	+	0.0235773i
$231$		0			0
$232$	−2.10604	+	3.64776i	−0.138268	+	0.239487i
$233$	6.70215	+	4.86940i	0.439073	+	0.319005i	0.785266	−	0.619158i	$-0.212526\pi$
$233$	6.70215	+	4.86940i	0.439073	+	0.319005i	−0.346194	+	0.938163i	$0.612526\pi$
$234$		0			0
$235$	−26.3964	−	1.75099i	−1.72191	−	0.114222i
$236$	−1.29916	−	0.276145i	−0.0845680	−	0.0179755i
$237$		0			0
$238$	−4.84559	+	1.02996i	−0.314093	+	0.0667625i
$239$	−0.722110	+	0.801984i	−0.0467094	+	0.0518760i	−0.766047	−	0.642785i	$-0.777779\pi$
$239$	−0.722110	+	0.801984i	−0.0467094	+	0.0518760i	0.719337	+	0.694661i	$0.244446\pi$
$240$		0			0
$241$	−16.7927	−	18.6502i	−1.08172	−	1.20137i	−0.978401	−	0.206718i	$-0.933722\pi$
$241$	−16.7927	−	18.6502i	−1.08172	−	1.20137i	−0.103315	−	0.994649i	$-0.532945\pi$
$242$	−13.0229	−	9.46173i	−0.837147	−	0.608223i
$243$		0			0
$244$	2.34215	+	1.70167i	0.149941	+	0.108938i
$245$	10.6446	−	3.91748i	0.680058	−	0.250278i
$246$		0			0
$247$	−4.26949	−	1.90090i	−0.271661	−	0.120951i
$248$	8.87507	−	9.85676i	0.563567	−	0.625905i
$249$		0			0
$250$	12.2951	−	13.9532i	0.777608	−	0.882478i
$251$	23.1900			1.46374			0.731869	−	0.681445i	$-0.238648\pi$
$251$	23.1900			1.46374			0.731869	+	0.681445i	$0.238648\pi$
$252$		0			0
$253$	0.394169	−	0.286381i	0.0247812	−	0.0180046i
$254$	−3.85784	−	36.7049i	−0.242062	−	2.30307i
$255$		0			0
$256$	−1.67716	+	15.9571i	−0.104823	+	0.997321i
$257$	10.4244	+	18.0555i	0.650253	+	1.12627i	0.983061	+	0.183277i	$0.0586705\pi$
$257$	10.4244	+	18.0555i	0.650253	+	1.12627i	−0.332808	+	0.942995i	$0.607996\pi$
$258$		0			0
$259$	2.66369	+	2.95833i	0.165514	+	0.183821i
$260$	−0.432291	+	1.08107i	−0.0268096	+	0.0670452i
$261$		0			0
$262$	5.97377	−	18.3854i	0.369061	−	1.13585i
$263$	6.07004	+	6.74146i	0.374295	+	0.415696i	0.900634	−	0.434578i	$-0.143103\pi$
$263$	6.07004	+	6.74146i	0.374295	+	0.415696i	−0.526339	+	0.850275i	$0.676436\pi$
$264$		0			0
$265$	−1.31310	−	2.66799i	−0.0806629	−	0.163893i
$266$	−15.5485	+	3.30493i	−0.953338	+	0.202638i
$267$		0			0
$268$	5.45140	−	9.44209i	0.332997	−	0.576768i
$269$	−12.0005	−	8.71886i	−0.731683	−	0.531599i	0.158413	−	0.987373i	$-0.449362\pi$
$269$	−12.0005	−	8.71886i	−0.731683	−	0.531599i	−0.890095	+	0.455774i	$0.849362\pi$
$270$		0			0
$271$	6.34725	−	4.61155i	0.385568	−	0.280132i	−0.378069	−	0.925777i	$-0.623412\pi$
$271$	6.34725	−	4.61155i	0.385568	−	0.280132i	0.763637	+	0.645646i	$0.223412\pi$
$272$	−1.10895	−	10.5510i	−0.0672402	−	0.639748i
$273$		0			0
$274$	−13.7754	−	23.8597i	−0.832203	−	1.44142i
$275$	−19.3670	−	11.9101i	−1.16788	−	0.718208i
$276$		0			0
$277$	21.7610	+	4.62545i	1.30749	+	0.277916i	0.808400	−	0.588633i	$-0.200334\pi$
$277$	21.7610	+	4.62545i	1.30749	+	0.277916i	0.499092	+	0.866549i	$0.333667\pi$
$278$	22.6487	−	16.4552i	1.35838	−	0.986919i
$279$		0			0
$280$	−1.56255	−	6.17291i	−0.0933799	−	0.368902i
$281$	−9.27859	+	4.13109i	−0.553514	+	0.246440i	−0.664380	−	0.747395i	$-0.731304\pi$
$281$	−9.27859	+	4.13109i	−0.553514	+	0.246440i	0.110866	+	0.993835i	$0.464638\pi$
$282$		0			0
$283$	−0.0797346	+	0.758624i	−0.00473973	+	0.0450955i	−0.996636	−	0.0819538i	$-0.973884\pi$
$283$	−0.0797346	+	0.758624i	−0.00473973	+	0.0450955i	0.991896	+	0.127049i	$0.0405507\pi$
$284$	10.1622	−	2.16005i	0.603018	−	0.128175i
$285$		0			0
$286$	5.02339	+	1.06775i	0.297039	+	0.0631376i
$287$	2.33074	−	7.17328i	0.137579	−	0.423425i
$288$		0			0
$289$	−3.83131	−	11.7916i	−0.225371	−	0.693622i
$290$	−7.34956	−	2.07904i	−0.431581	−	0.122085i
$291$		0			0
$292$	0.474936	−	4.51872i	0.0277935	−	0.264438i
$293$	−3.29507	−	5.70722i	−0.192500	−	0.333419i	0.753578	−	0.657358i	$-0.228326\pi$
$293$	−3.29507	−	5.70722i	−0.192500	−	0.333419i	−0.946078	+	0.323939i	$0.894993\pi$
$294$		0			0
$295$	0.148994	+	3.86982i	0.00867476	+	0.225310i
$296$	−4.75815	+	3.45699i	−0.276562	+	0.200934i
$297$		0			0
$298$	−8.20364	−	25.2482i	−0.475224	−	1.46259i
$299$	−0.0363745	+	0.0630025i	−0.00210359	+	0.00364353i
$300$		0			0
$301$	0.851063	+	1.47408i	0.0490545	+	0.0849648i
$302$	9.36656	−	10.4026i	0.538985	−	0.598604i
$303$		0			0
$304$	−3.55840	−	33.8559i	−0.204088	−	1.94177i
$305$	3.13418	−	7.83794i	0.179462	−	0.448799i
$306$		0			0
$307$	20.2069			1.15327			0.576634	−	0.817002i	$-0.304366\pi$
$307$	20.2069			1.15327			0.576634	+	0.817002i	$0.304366\pi$
$308$	4.42282	−	1.96917i	0.252014	−	0.112204i
$309$		0			0
$310$	21.2765	+	11.2155i	1.20842	+	0.636997i
$311$	−11.9608	+	13.2838i	−0.678234	+	0.753255i	−0.979754	−	0.200205i	$-0.935839\pi$
$311$	−11.9608	+	13.2838i	−0.678234	+	0.753255i	0.301520	+	0.953460i	$0.402506\pi$
$312$		0			0
$313$	12.2784	+	13.6366i	0.694019	+	0.770786i	0.982412	−	0.186726i	$-0.0597877\pi$
$313$	12.2784	+	13.6366i	0.694019	+	0.770786i	−0.288393	+	0.957512i	$0.593121\pi$
$314$	−0.0437675	−	0.134702i	−0.00246994	−	0.00760170i
$315$		0			0
$316$	−2.12766	+	6.54826i	−0.119690	+	0.368369i
$317$	−2.89860	+	1.29054i	−0.162802	+	0.0724841i	−0.486520	−	0.873670i	$-0.661734\pi$
$317$	−2.89860	+	1.29054i	−0.162802	+	0.0724841i	0.323718	+	0.946154i	$0.395067\pi$
$318$		0			0
$319$	−0.976064	+	9.28663i	−0.0546491	+	0.519952i
$320$	6.70820	−	0.967250i	0.375000	−	0.0540709i
$321$		0			0
$322$	0.0258642	+	0.246082i	0.00144136	+	0.0137136i
$323$	4.56282	+	14.0429i	0.253882	+	0.781369i
$324$		0			0
$325$	3.36509	+	0.448416i	0.186662	+	0.0248736i
$326$	−10.2602	+	17.7712i	−0.568261	+	0.984256i
$327$		0			0
$328$	10.1800	+	4.53244i	0.562098	+	0.250262i
$329$	−15.0050	−	6.68065i	−0.827251	−	0.368316i
$330$		0			0
$331$	−13.4822	+	6.00268i	−0.741051	+	0.329937i	−0.742305	−	0.670062i	$-0.766268\pi$
$331$	−13.4822	+	6.00268i	−0.741051	+	0.329937i	0.00125393	+	0.999999i	$0.499601\pi$
$332$	−13.9076			−0.763278
$333$		0			0
$334$	3.44246	−	10.5948i	0.188363	−	0.579721i
$335$	−30.5898	−	8.65322i	−1.67130	−	0.472776i
$336$		0			0
$337$	11.9319	−	2.53619i	0.649970	−	0.138155i	0.128884	−	0.991660i	$-0.458861\pi$
$337$	11.9319	−	2.53619i	0.649970	−	0.138155i	0.521086	+	0.853504i	$0.325527\pi$
$338$	20.4015	−	4.33648i	1.10970	−	0.235873i
$339$		0			0
$340$	3.45213	−	1.27047i	0.187218	−	0.0689010i
$341$	9.08639	−	27.9650i	0.492056	−	1.51439i
$342$		0			0
$343$	16.7606			0.904989
$344$	−2.29736	+	1.02285i	−0.123865	+	0.0551485i
$345$		0			0
$346$	−17.4744	−	7.78011i	−0.939430	−	0.418261i
$347$	−19.8592	−	8.84187i	−1.06610	−	0.474656i	−0.202730	−	0.979235i	$-0.564981\pi$
$347$	−19.8592	−	8.84187i	−1.06610	−	0.474656i	−0.863366	+	0.504578i	$0.831648\pi$
$348$		0			0
$349$	5.54554	−	9.60516i	0.296846	−	0.514152i	−0.678567	−	0.734539i	$-0.737399\pi$
$349$	5.54554	−	9.60516i	0.296846	−	0.514152i	0.975413	+	0.220387i	$0.0707319\pi$
$350$	10.1561	−	5.49361i	0.542866	−	0.293646i
$351$		0			0
$352$	5.79531	+	17.8361i	0.308891	+	0.950669i
$353$	0.530083	+	5.04340i	0.0282135	+	0.268433i	0.999530	+	0.0306445i	$0.00975596\pi$
$353$	0.530083	+	5.04340i	0.0282135	+	0.268433i	−0.971317	+	0.237789i	$0.923577\pi$
$354$		0			0
$355$	−13.3768	−	27.1793i	−0.709965	−	1.44253i
$356$	0.605357	−	5.75959i	0.0320838	−	0.305257i
$357$		0			0
$358$	−7.46292	+	3.32271i	−0.394427	+	0.175610i
$359$	9.46581	−	29.1328i	0.499586	−	1.53757i	−0.310099	−	0.950704i	$-0.600362\pi$
$359$	9.46581	−	29.1328i	0.499586	−	1.53757i	0.809685	−	0.586864i	$-0.199638\pi$
$360$		0			0
$361$	8.76981	+	26.9907i	0.461569	+	1.42056i
$362$	2.32737	+	2.58480i	0.122324	+	0.135854i
$363$		0			0
$364$	−0.483707	+	0.537211i	−0.0253531	+	0.0281575i
$365$	−13.1126	+	1.89069i	−0.686342	+	0.0989632i
$366$		0			0
$367$	−14.5972	+	6.49910i	−0.761968	+	0.339250i	−0.750662	−	0.660686i	$-0.770265\pi$
$367$	−14.5972	+	6.49910i	−0.761968	+	0.339250i	−0.0113057	+	0.999936i	$0.503599\pi$
$368$	−0.529910			−0.0276235
$369$		0			0
$370$	−8.19434	−	6.82608i	−0.426003	−	0.354871i
$371$	−0.192986	−	1.83614i	−0.0100193	−	0.0953276i
$372$		0			0
$373$	7.53730	−	8.37102i	0.390267	−	0.433435i	−0.515710	−	0.856763i	$-0.672472\pi$
$373$	7.53730	−	8.37102i	0.390267	−	0.433435i	0.905976	+	0.423328i	$0.139138\pi$
$374$	−8.11274	−	14.0517i	−0.419500	−	0.726595i
$375$		0			0
$376$	12.1334	−	21.0157i	0.625733	−	1.08380i
$377$	−0.430852	−	1.32603i	−0.0221900	−	0.0682938i
$378$		0			0
$379$	−17.8996	+	13.0048i	−0.919440	+	0.668012i	−0.943385	−	0.331701i	$-0.892377\pi$
$379$	−17.8996	+	13.0048i	−0.919440	+	0.668012i	0.0239446	+	0.999713i	$0.492377\pi$
$380$	11.0772	−	4.07668i	0.568247	−	0.209129i
$381$		0			0
$382$	8.54123	+	14.7938i	0.437007	+	0.756919i
$383$	0.661282	−	6.29168i	0.0337899	−	0.321490i	−0.964550	−	0.263899i	$-0.914991\pi$
$383$	0.661282	−	6.29168i	0.0337899	−	0.321490i	0.998340	−	0.0575909i	$-0.0183419\pi$
$384$		0			0
$385$	−8.73065	−	11.0927i	−0.444955	−	0.565338i
$386$	−0.903967	−	2.78213i	−0.0460107	−	0.141606i
$387$		0			0
$388$	2.57638	−	7.92927i	0.130796	−	0.402548i
$389$	32.3577	+	6.87784i	1.64060	+	0.348720i	0.933551	−	0.358444i	$-0.116693\pi$
$389$	32.3577	+	6.87784i	1.64060	+	0.348720i	0.707049	+	0.707165i	$0.250026\pi$
$390$		0			0
$391$	0.224821	−	0.0477872i	0.0113697	−	0.00241670i
$392$	−1.08758	+	10.3476i	−0.0549309	+	0.522633i
$393$		0			0
$394$	2.40786	−	1.07205i	0.121306	−	0.0540089i
$395$	20.0319	+	1.32880i	1.00791	+	0.0668591i
$396$		0			0
$397$	22.9141	−	16.6480i	1.15002	−	0.835541i	0.161540	−	0.986866i	$-0.448354\pi$
$397$	22.9141	−	16.6480i	1.15002	−	0.835541i	0.988484	+	0.151325i	$0.0483539\pi$
$398$	7.87134	+	1.67310i	0.394554	+	0.0838651i
$399$		0			0
$400$	9.42712	+	22.8608i	0.471356	+	1.14304i
$401$	4.98614	+	8.63625i	0.248996	+	0.431274i	0.963248	−	0.268615i	$-0.0865660\pi$
$401$	4.98614	+	8.63625i	0.248996	+	0.431274i	−0.714251	+	0.699889i	$0.753233\pi$
$402$		0			0
$403$	0.458929	+	4.36642i	0.0228609	+	0.217507i
$404$	7.57731	−	5.50524i	0.376985	−	0.273896i
$405$		0			0
$406$	−3.83655	−	2.78742i	−0.190405	−	0.138337i
$407$	−6.51926	+	11.2917i	−0.323148	+	0.559708i
$408$		0			0
$409$	9.44969	−	2.00859i	0.467257	−	0.0993186i	0.0317346	−	0.999496i	$-0.489897\pi$
$409$	9.44969	−	2.00859i	0.467257	−	0.0993186i	0.435523	+	0.900178i	$0.356564\pi$
$410$	−3.43772	+	19.9124i	−0.169777	+	0.983402i
$411$		0			0
$412$	−0.435711	−	0.483906i	−0.0214659	−	0.0238403i
$413$	−0.743021	+	2.28678i	−0.0365617	+	0.112525i
$414$		0			0
$415$	9.95092	+	39.3116i	0.488471	+	1.92973i
$416$	−1.87373	−	2.08099i	−0.0918672	−	0.102029i
$417$		0			0
$418$	−26.0321	−	45.0889i	−1.27327	−	2.20537i
$419$	−1.32174	+	12.5755i	−0.0645710	+	0.614352i	0.913609	+	0.406594i	$0.133283\pi$
$419$	−1.32174	+	12.5755i	−0.0645710	+	0.614352i	−0.978180	+	0.207758i	$0.933383\pi$
$420$		0			0
$421$	2.39672	+	22.8033i	0.116809	+	1.11136i	0.883202	+	0.468992i	$0.155383\pi$
$421$	2.39672	+	22.8033i	0.116809	+	1.11136i	−0.766393	+	0.642372i	$0.777951\pi$
$422$	5.77800	−	4.19797i	0.281269	−	0.204354i
$423$		0			0
$424$	2.72771			0.132470
$425$	−6.06116	−	8.84887i	−0.294010	−	0.429233i
$426$		0			0
$427$	3.50695	−	3.89486i	0.169713	−	0.188485i
$428$	−13.3647	−	5.95033i	−0.646005	−	0.287620i
$429$		0			0
$430$	−2.82035	−	3.58340i	−0.136009	−	0.172807i
$431$	−10.6124	−	7.71039i	−0.511183	−	0.371397i	0.302089	−	0.953280i	$-0.402316\pi$
$431$	−10.6124	−	7.71039i	−0.511183	−	0.371397i	−0.813272	+	0.581883i	$0.802316\pi$
$432$		0			0
$433$	−19.0904	−	13.8700i	−0.917425	−	0.666548i	0.0254569	−	0.999676i	$-0.491896\pi$
$433$	−19.0904	−	13.8700i	−0.917425	−	0.666548i	−0.942882	+	0.333128i	$0.891896\pi$
$434$	9.99217	+	11.0974i	0.479639	+	0.532694i
$435$		0			0
$436$	6.72557	−	7.46950i	0.322096	−	0.357724i
$437$	0.721404	−	0.153339i	0.0345094	−	0.00733521i
$438$		0			0
$439$	7.92866	+	1.68529i	0.378414	+	0.0804344i	0.393192	−	0.919456i	$-0.371371\pi$
$439$	7.92866	+	1.68529i	0.378414	+	0.0804344i	−0.0147778	+	0.999891i	$0.504704\pi$
$440$	17.6473	−	11.1152i	0.841301	−	0.529896i
$441$		0			0
$442$	1.96001	+	1.42403i	0.0932280	+	0.0677341i
$443$	0.254259	−	0.440389i	0.0120802	−	0.0209235i	−0.859922	−	0.510425i	$-0.829488\pi$
$443$	0.254259	−	0.440389i	0.0120802	−	0.0209235i	0.872002	+	0.489502i	$0.162821\pi$
$444$		0			0
$445$	−16.7133	+	2.40988i	−0.792288	+	0.114239i
$446$	24.6295	+	10.9658i	1.16624	+	0.519244i
$447$		0			0
$448$	4.11609	+	0.874903i	0.194467	+	0.0413353i
$449$	−7.22605			−0.341018			−0.170509	−	0.985356i	$-0.554541\pi$
$449$	−7.22605			−0.341018			−0.170509	+	0.985356i	$0.554541\pi$
$450$		0			0
$451$	24.7040			1.16327
$452$	−5.22317	−	1.11022i	−0.245677	−	0.0522203i
$453$		0			0
$454$	−13.9985	−	6.23256i	−0.656984	−	0.292508i
$455$	1.86459	+	0.982883i	0.0874132	+	0.0460783i
$456$		0			0
$457$	−7.94049	+	13.7533i	−0.371441	+	0.643354i	−0.989787	−	0.142551i	$-0.954469\pi$
$457$	−7.94049	+	13.7533i	−0.371441	+	0.643354i	0.618347	+	0.785905i	$0.287803\pi$
$458$	11.0413	+	8.02199i	0.515927	+	0.374843i
$459$		0			0
$460$	−0.0450869	−	0.178118i	−0.00210219	−	0.00830478i
$461$	32.2855	+	6.86249i	1.50369	+	0.319618i	0.884840	−	0.465895i	$-0.154267\pi$
$461$	32.2855	+	6.86249i	1.50369	+	0.319618i	0.618845	+	0.785513i	$0.287601\pi$
$462$		0			0
$463$	−18.0119	+	3.82855i	−0.837084	+	0.177928i	−0.606459	−	0.795115i	$-0.707411\pi$
$463$	−18.0119	+	3.82855i	−0.837084	+	0.177928i	−0.230625	+	0.973043i	$0.574077\pi$
$464$	6.79566	−	7.54734i	0.315480	−	0.350377i
$465$		0			0
$466$	−9.22069	−	10.2406i	−0.427140	−	0.474387i
$467$	14.9196	+	10.8397i	0.690398	+	0.501603i	0.876791	−	0.480872i	$-0.159680\pi$
$467$	14.9196	+	10.8397i	0.690398	+	0.501603i	−0.186393	+	0.982475i	$0.559680\pi$
$468$		0			0
$469$	−15.9682	−	11.6016i	−0.737344	−	0.535712i
$470$	42.3427	+	11.9779i	1.95312	+	0.552498i
$471$		0			0
$472$	−3.24531	−	1.44491i	−0.149378	−	0.0665072i
$473$	−3.73043	+	4.14306i	−0.171525	+	0.190498i
$474$		0			0
$475$	−19.4490	−	28.3942i	−0.892381	−	1.30281i
$476$	2.28390			0.104682
$477$		0			0
$478$	1.45226	−	1.05513i	0.0664250	−	0.0482606i
$479$	−2.41271	−	22.9554i	−0.110239	−	1.04886i	−0.900133	−	0.435614i	$-0.856531\pi$
$479$	−2.41271	−	22.9554i	−0.110239	−	1.04886i	0.789894	−	0.613243i	$-0.210135\pi$
$480$		0			0
$481$	0.203500	−	1.93617i	0.00927881	−	0.0882820i
$482$	20.8726	+	36.1524i	0.950720	+	1.64670i
$483$		0			0
$484$	4.96589	+	5.51518i	0.225722	+	0.250690i
$485$	−24.2565	−	1.60904i	−1.10143	−	0.0730627i
$486$		0			0
$487$	−3.52725	+	10.8558i	−0.159835	+	0.491921i	−0.998619	−	0.0525435i	$-0.983267\pi$
$487$	−3.52725	+	10.8558i	−0.159835	+	0.491921i	0.838784	+	0.544465i	$0.183267\pi$
$488$	5.18127	+	5.75439i	0.234545	+	0.260489i
$489$		0			0
$490$	−18.6741	+	2.69260i	−0.843608	+	0.121639i
$491$	−38.9241	+	8.27356i	−1.75662	+	0.373381i	−0.969818	−	0.243828i	$-0.921597\pi$
$491$	−38.9241	+	8.27356i	−1.75662	+	0.373381i	−0.786799	+	0.617209i	$0.788263\pi$
$492$		0			0
$493$	−2.20253	+	3.81489i	−0.0991969	+	0.171814i
$494$	6.28925	+	4.56941i	0.282967	+	0.205587i
$495$		0			0
$496$	−25.8728	+	18.7977i	−1.16172	+	0.844041i
$497$	−1.96599	−	18.7051i	−0.0881866	−	0.839039i
$498$		0			0
$499$	18.1188	+	31.3826i	0.811107	+	1.40488i	0.912090	+	0.409990i	$0.134468\pi$
$499$	18.1188	+	31.3826i	0.811107	+	1.40488i	−0.100983	+	0.994888i	$0.532199\pi$
$500$	−6.88208	+	5.11381i	−0.307776	+	0.228697i
$501$		0			0
$502$	−37.7312	−	8.02001i	−1.68403	−	0.357951i
$503$	−26.1554	+	19.0030i	−1.16621	+	0.847302i	−0.990550	−	0.137149i	$-0.956206\pi$
$503$	−26.1554	+	19.0030i	−1.16621	+	0.847302i	−0.175661	+	0.984451i	$0.556206\pi$
$504$		0			0
$505$	−20.9829	−	17.4792i	−0.933725	−	0.777816i
$506$	−0.740374	+	0.329636i	−0.0329136	+	0.0146541i
$507$		0			0
$508$	−1.77860	+	16.9223i	−0.0789128	+	0.750805i
$509$	−0.264168	+	0.0561506i	−0.0117090	+	0.00248883i	−0.213762	−	0.976886i	$-0.568572\pi$
$509$	−0.264168	+	0.0561506i	−0.0117090	+	0.00248883i	0.202053	+	0.979374i	$0.435239\pi$
$510$		0			0
$511$	−8.04575	−	1.71018i	−0.355923	−	0.0756538i
$512$	0.0335504	−	0.103257i	0.00148273	−	0.00456337i
$513$		0			0
$514$	−10.7166	−	32.9823i	−0.472689	−	1.45479i
$515$	−1.05607	+	1.57783i	−0.0465360	+	0.0695274i
$516$		0			0
$517$	5.62336	−	53.5027i	0.247315	−	2.35304i
$518$	−3.31084	−	5.73454i	−0.145470	−	0.251961i
$519$		0			0
$520$	−1.73214	+	2.58792i	−0.0759595	+	0.113488i
$521$	−22.4017	+	16.2758i	−0.981435	+	0.713054i	−0.958029	−	0.286672i	$-0.907451\pi$
$521$	−22.4017	+	16.2758i	−0.981435	+	0.713054i	−0.0234061	+	0.999726i	$0.507451\pi$
$522$		0			0
$523$	11.9194	+	36.6841i	0.521198	+	1.60408i	0.771713	+	0.635971i	$0.219400\pi$
$523$	11.9194	+	36.6841i	0.521198	+	1.60408i	−0.250515	+	0.968113i	$0.580600\pi$
$524$	−4.45627	+	7.71848i	−0.194673	+	0.337183i
$525$		0			0
$526$	−7.54477	−	13.0679i	−0.328968	−	0.569789i
$527$	9.28170	−	10.3084i	0.404317	−	0.449040i
$528$		0			0
$529$	2.40295	+	22.8626i	0.104476	+	0.994025i
$530$	1.21377	+	4.79506i	0.0527229	+	0.208284i
$531$		0			0
$532$	7.32855			0.317733
$533$	−3.36976	+	1.50032i	−0.145961	+	0.0649859i
$534$		0			0
$535$	−7.25691	+	42.0344i	−0.313744	+	1.81731i
$536$	19.5127	−	21.6711i	0.842820	−	0.936047i
$537$		0			0
$538$	16.5100	+	18.3362i	0.711798	+	0.790531i
$539$	7.12781	+	21.9371i	0.307016	+	0.944900i
$540$		0			0
$541$	−9.26487	+	28.5143i	−0.398328	+	1.22593i	0.528011	+	0.849237i	$0.322938\pi$
$541$	−9.26487	+	28.5143i	−0.398328	+	1.22593i	−0.926339	+	0.376690i	$0.877062\pi$
$542$	−11.9221	+	5.30808i	−0.512099	+	0.228001i
$543$		0			0
$544$	−0.924776	+	8.79865i	−0.0396494	+	0.377239i
$545$	−25.9257	−	13.6662i	−1.11053	−	0.585397i
$546$		0			0
$547$	−0.600529	−	5.71365i	−0.0256768	−	0.244298i	−0.999830	−	0.0184119i	$-0.994139\pi$
$547$	−0.600529	−	5.71365i	−0.0256768	−	0.244298i	0.974154	−	0.225886i	$-0.0725277\pi$
$548$	3.92511	+	12.0802i	0.167672	+	0.516042i
$549$		0			0
$550$	27.3921	+	26.0762i	1.16800	+	1.11189i
$551$	−7.06745	+	12.2412i	−0.301083	+	0.521492i
$552$		0			0
$553$	11.3870	+	5.06984i	0.484227	+	0.215592i
$554$	−33.8065	−	15.0516i	−1.43630	−	0.639483i
$555$		0			0
$556$	−11.7910	+	5.24969i	−0.500049	+	0.222636i
$557$	13.8510			0.586887			0.293444	−	0.955976i	$-0.405199\pi$
$557$	13.8510			0.586887			0.293444	+	0.955976i	$0.405199\pi$
$558$		0			0
$559$	0.257236	−	0.791691i	0.0108799	−	0.0334850i
$560$	0.590686	+	15.3419i	0.0249610	+	0.648313i
$561$		0			0
$562$	16.5254	−	3.51258i	0.697081	−	0.148169i
$563$	−29.1494	+	6.19591i	−1.22850	+	0.261126i	−0.776055	−	0.630665i	$-0.782782\pi$
$563$	−29.1494	+	6.19591i	−1.22850	+	0.261126i	−0.452447	+	0.891791i	$0.649449\pi$
$564$		0			0
$565$	0.599018	+	15.5583i	0.0252009	+	0.654543i
$566$	0.392094	−	1.20674i	0.0164809	−	0.0507231i
$567$		0			0
$568$	27.7878			1.16595
$569$	−14.9654	+	6.66301i	−0.627381	+	0.279328i	−0.695696	−	0.718336i	$-0.744904\pi$
$569$	−14.9654	+	6.66301i	−0.627381	+	0.279328i	0.0683159	+	0.997664i	$0.478237\pi$
$570$		0			0
$571$	−4.71944	−	2.10123i	−0.197502	−	0.0879337i	0.305602	−	0.952159i	$-0.401142\pi$
$571$	−4.71944	−	2.10123i	−0.197502	−	0.0879337i	−0.503104	+	0.864226i	$0.667809\pi$
$572$	−2.16300	−	0.963031i	−0.0904397	−	0.0402663i
$573$		0			0
$574$	−6.27303	+	10.8652i	−0.261831	+	0.453505i
$575$	−0.471213	+	0.254888i	−0.0196509	+	0.0106295i
$576$		0			0
$577$	4.99821	+	15.3829i	0.208078	+	0.640399i	0.999573	+	0.0292230i	$0.00930328\pi$
$577$	4.99821	+	15.3829i	0.208078	+	0.640399i	−0.791495	+	0.611176i	$0.790697\pi$
$578$	2.15574	+	20.5105i	0.0896668	+	0.853122i
$579$		0			0
$580$	3.11508	+	1.64206i	0.129347	+	0.0681826i
$581$	−2.63177	+	25.0396i	−0.109184	+	1.03882i
$582$		0			0
$583$	5.52430	−	2.45958i	0.228793	−	0.101865i
$584$	3.75536	−	11.5578i	0.155398	−	0.478266i
$585$		0			0
$586$	3.38744	+	10.4255i	0.139934	+	0.430672i
$587$	18.8057	+	20.8858i	0.776193	+	0.862050i	0.993474	−	0.114059i	$-0.0363854\pi$
$587$	18.8057	+	20.8858i	0.776193	+	0.862050i	−0.217281	+	0.976109i	$0.569719\pi$
$588$		0			0
$589$	29.7830	−	33.0774i	1.22719	−	1.36293i
$590$	1.09592	−	6.34790i	0.0451182	−	0.261339i
$591$		0			0
$592$	12.9549	−	5.76791i	0.532444	−	0.237060i
$593$	−3.80524			−0.156262			−0.0781312	−	0.996943i	$-0.524895\pi$
$593$	−3.80524			−0.156262			−0.0781312	+	0.996943i	$0.524895\pi$
$594$		0			0
$595$	−1.63414	−	6.45573i	−0.0669931	−	0.264659i
$596$	1.27936	+	12.1723i	0.0524047	+	0.498597i
$597$		0			0
$598$	0.0809718	−	0.0899283i	0.00331118	−	0.00367744i
$599$	−17.5681	−	30.4289i	−0.717813	−	1.24329i	−0.961864	−	0.273527i	$-0.911810\pi$
$599$	−17.5681	−	30.4289i	−0.717813	−	1.24329i	0.244051	−	0.969762i	$-0.421524\pi$
$600$		0			0
$601$	−10.6092	+	18.3758i	−0.432760	+	0.749563i	−0.997110	−	0.0759732i	$-0.975794\pi$
$601$	−10.6092	+	18.3758i	−0.432760	+	0.749563i	0.564350	+	0.825536i	$0.309127\pi$
$602$	−0.874923	−	2.69274i	−0.0356592	−	0.109748i
$603$		0			0
$604$	−5.22110	+	3.79335i	−0.212443	+	0.154349i
$605$	12.0363	−	17.9829i	0.489343	−	0.731107i
$606$		0			0
$607$	−7.55362	−	13.0833i	−0.306592	−	0.531033i	0.671023	−	0.741437i	$-0.265855\pi$
$607$	−7.55362	−	13.0833i	−0.306592	−	0.531033i	−0.977615	+	0.210404i	$0.932522\pi$
$608$	−2.96741	+	28.2330i	−0.120344	+	1.14500i
$609$		0			0
$610$	−7.81012	+	11.6688i	−0.316222	+	0.472454i
$611$	2.48225	+	7.63958i	0.100421	+	0.309064i
$612$		0			0
$613$	−0.267857	+	0.824379i	−0.0108186	+	0.0332963i	−0.956320	−	0.292321i	$-0.905572\pi$
$613$	−0.267857	+	0.824379i	−0.0108186	+	0.0332963i	0.945501	+	0.325618i	$0.105572\pi$
$614$	−32.8776	−	6.98834i	−1.32683	−	0.282026i
$615$		0			0
$616$	12.6661	−	2.69226i	0.510331	−	0.108474i
$617$	2.07726	−	19.7638i	0.0836272	−	0.795660i	−0.869671	−	0.493631i	$-0.835669\pi$
$617$	2.07726	−	19.7638i	0.0836272	−	0.795660i	0.953299	−	0.302029i	$-0.0976640\pi$
$618$		0			0
$619$	16.3619	−	7.28480i	0.657641	−	0.292801i	−0.0506549	−	0.998716i	$-0.516131\pi$
$619$	16.3619	−	7.28480i	0.657641	−	0.292801i	0.708296	+	0.705915i	$0.249464\pi$
$620$	−8.51980	−	7.09720i	−0.342163	−	0.285030i
$621$		0			0
$622$	24.0548	−	17.4768i	0.964510	−	0.700757i
$623$	−10.2552	−	2.17980i	−0.410864	−	0.0873319i
$624$		0			0
$625$	19.3790	+	15.7941i	0.775160	+	0.631765i
$626$	−15.2615	−	26.4337i	−0.609973	−	1.05650i
$627$		0			0
$628$	0.00682556	+	0.0649409i	0.000272370	+	0.00259142i
$629$	−4.97615	+	3.61538i	−0.198412	+	0.144155i
$630$		0			0
$631$	−27.5034	−	19.9824i	−1.09489	−	0.795487i	−0.114675	−	0.993403i	$-0.536583\pi$
$631$	−27.5034	−	19.9824i	−1.09489	−	0.795487i	−0.980219	+	0.197916i	$0.936583\pi$
$632$	−9.20786	+	15.9485i	−0.366269	+	0.634396i
$633$		0			0
$634$	5.16248	−	1.09732i	0.205028	−	0.0435801i
$635$	49.1056	−	7.08050i	1.94870	−	0.280981i
$636$		0			0
$637$	−2.30455	−	2.55946i	−0.0913097	−	0.101410i
$638$	4.79979	−	14.7722i	0.190025	−	0.584838i
$639$		0			0
$640$	−29.6529	−	1.96701i	−1.17213	−	0.0777527i
$641$	8.52288	+	9.46562i	0.336634	+	0.373870i	0.887566	−	0.460680i	$-0.152394\pi$
$641$	8.52288	+	9.46562i	0.336634	+	0.373870i	−0.550932	+	0.834550i	$0.685728\pi$
$642$		0			0
$643$	9.31365	+	16.1317i	0.367295	+	0.636173i	0.989142	−	0.146966i	$-0.0469507\pi$
$643$	9.31365	+	16.1317i	0.367295	+	0.636173i	−0.621847	+	0.783139i	$0.713617\pi$
$644$	0.0119243	−	0.113453i	0.000469885	−	0.00447066i
$645$		0			0
$646$	−2.56733	−	24.4265i	−0.101010	−	0.961047i
$647$	2.58476	−	1.87794i	0.101617	−	0.0738294i	−0.535816	−	0.844335i	$-0.679996\pi$
$647$	2.58476	−	1.87794i	0.101617	−	0.0738294i	0.637434	+	0.770505i	$0.279996\pi$
$648$		0			0
$649$	−7.87544			−0.309138
$650$	−5.32009	−	1.89338i	−0.208671	−	0.0742643i
$651$		0			0
$652$	6.33041	−	7.03063i	0.247918	−	0.275341i
$653$	4.61992	+	2.05692i	0.180792	+	0.0804936i	0.495136	−	0.868815i	$-0.335118\pi$
$653$	4.61992	+	2.05692i	0.180792	+	0.0804936i	−0.314345	+	0.949309i	$0.601785\pi$
$654$		0			0
$655$	25.0057	+	7.07361i	0.977055	+	0.276389i
$656$	−21.7371	−	15.7929i	−0.848691	−	0.616610i
$657$		0			0
$658$	22.1034	+	16.0590i	0.861679	+	0.626046i
$659$	−0.955484	−	1.06117i	−0.0372204	−	0.0413374i	0.724247	−	0.689540i	$-0.242187\pi$
$659$	−0.955484	−	1.06117i	−0.0372204	−	0.0413374i	−0.761468	+	0.648203i	$0.775521\pi$
$660$		0			0
$661$	−3.11002	+	3.45402i	−0.120966	+	0.134346i	−0.800586	−	0.599219i	$-0.795478\pi$
$661$	−3.11002	+	3.45402i	−0.120966	+	0.134346i	0.679620	+	0.733564i	$0.262145\pi$
$662$	24.0122	−	5.10395i	0.933261	−	0.198371i
$663$		0			0
$664$	−36.3852	−	7.73391i	−1.41202	−	0.300134i
$665$	−5.24360	−	20.7151i	−0.203338	−	0.803296i
$666$		0			0
$667$	0.178005	+	0.129328i	0.00689238	+	0.00500761i
$668$	−2.56797	+	4.44786i	−0.0993579	+	0.172093i
$669$		0			0
$670$	46.7784	+	24.6583i	1.80721	+	0.952635i
$671$	15.6821	+	6.98212i	0.605401	+	0.269542i
$672$		0			0
$673$	−18.4133	−	3.91386i	−0.709780	−	0.150868i	−0.161145	−	0.986931i	$-0.551519\pi$
$673$	−18.4133	−	3.91386i	−0.709780	−	0.150868i	−0.548634	+	0.836062i	$0.684852\pi$
$674$	−20.2908			−0.781572
$675$		0			0
$676$	−9.61597			−0.369845
$677$	−9.69731	−	2.06123i	−0.372698	−	0.0792194i	0.0177547	−	0.999842i	$-0.494348\pi$
$677$	−9.69731	−	2.06123i	−0.372698	−	0.0792194i	−0.390453	+	0.920623i	$0.627682\pi$
$678$		0			0
$679$	−13.7885	−	6.13906i	−0.529156	−	0.235595i
$680$	9.73802	−	1.40412i	0.373436	−	0.0538454i
$681$		0			0
$682$	−24.4554	+	42.3580i	−0.936445	+	1.62197i
$683$	−21.4995	−	15.6203i	−0.822655	−	0.597694i	0.0948166	−	0.995495i	$-0.469774\pi$
$683$	−21.4995	−	15.6203i	−0.822655	−	0.597694i	−0.917472	+	0.397801i	$0.869774\pi$
$684$		0			0
$685$	31.3379	−	19.7383i	1.19736	−	0.754161i
$686$	−27.2703	−	5.79649i	−1.04119	−	0.221311i
$687$		0			0
$688$	5.93101	−	1.26068i	0.226118	−	0.0480628i
$689$	−0.604171	+	0.671000i	−0.0230171	+	0.0255631i
$690$		0			0
$691$	−22.2009	−	24.6566i	−0.844563	−	0.937982i	0.154183	−	0.988042i	$-0.450725\pi$
$691$	−22.2009	−	24.6566i	−0.844563	−	0.937982i	−0.998746	+	0.0500602i	$0.984059\pi$
$692$	7.13452	+	5.18353i	0.271214	+	0.197048i
$693$		0			0
$694$	29.2539	+	21.2542i	1.11046	+	0.806799i
$695$	23.2754	+	29.5726i	0.882886	+	1.12175i
$696$		0			0
$697$	10.6465	+	4.74011i	0.403263	+	0.179544i
$698$	−12.3447	+	13.7102i	−0.467253	+	0.518938i
$699$		0			0
$700$	−5.10659	+	1.50390i	−0.193011	+	0.0568419i
$701$	−26.1441			−0.987451			−0.493725	−	0.869618i	$-0.664365\pi$
$701$	−26.1441			−0.987451			−0.493725	+	0.869618i	$0.664365\pi$
$702$		0			0
$703$	−15.9674	+	11.6010i	−0.602223	+	0.437540i
$704$	1.44069	+	13.7073i	0.0542981	+	0.516612i
$705$		0			0
$706$	0.881738	−	8.38918i	0.0331846	−	0.315731i
$707$	−8.47791	−	14.6842i	−0.318845	−	0.552255i
$708$		0			0
$709$	26.7119	+	29.6666i	1.00319	+	1.11415i	0.993458	+	0.114201i	$0.0364306\pi$
$709$	26.7119	+	29.6666i	1.00319	+	1.11415i	0.00973033	+	0.999953i	$0.496903\pi$
$710$	12.3649	+	48.8483i	0.464048	+	1.83324i
$711$		0			0
$712$	4.78661	−	14.7317i	0.179386	−	0.552093i
$713$	−0.463608	−	0.514888i	−0.0173622	−	0.0192827i
$714$		0			0
$715$	−1.17449	+	6.80306i	−0.0439236	+	0.254420i
$716$	3.68398	−	0.783055i	0.137677	−	0.0292641i
$717$		0			0
$718$	−25.4766	+	44.1267i	−0.950777	+	1.64679i
$719$	−32.4317	−	23.5630i	−1.20950	−	0.878751i	−0.214312	−	0.976765i	$-0.568751\pi$
$719$	−32.4317	−	23.5630i	−1.20950	−	0.878751i	−0.995185	+	0.0980142i	$0.968751\pi$
$720$		0			0
$721$	−0.953688	+	0.692895i	−0.0355172	+	0.0258048i
$722$	−4.93444	−	46.9481i	−0.183641	−	1.74723i
$723$		0			0
$724$	−0.801787	−	1.38874i	−0.0297982	−	0.0516120i
$725$	2.41263	−	9.98006i	0.0896029	−	0.370650i
$726$		0			0
$727$	34.5304	+	7.33967i	1.28066	+	0.272213i	0.797501	−	0.603318i	$-0.206155\pi$
$727$	34.5304	+	7.33967i	1.28066	+	0.272213i	0.483162	+	0.875531i	$0.339488\pi$
$728$	−1.56422	+	1.13647i	−0.0579738	+	0.0421204i
$729$		0			0
$730$	21.9886	+	1.45860i	0.813835	+	0.0539852i
$731$	−2.40262	+	1.06972i	−0.0888641	+	0.0395649i
$732$		0			0
$733$	−0.702668	+	6.68544i	−0.0259536	+	0.246932i	0.973851	+	0.227186i	$0.0729525\pi$
$733$	−0.702668	+	6.68544i	−0.0259536	+	0.246932i	−0.999805	+	0.0197463i	$0.993714\pi$
$734$	25.9980	−	5.52604i	0.959603	−	0.203970i
$735$		0			0
$736$	0.432244	+	0.0918764i	0.0159327	+	0.00338661i
$737$	19.9773	−	61.4839i	0.735874	−	2.26479i
$738$		0			0
$739$	−3.30815	−	10.1814i	−0.121692	−	0.374530i	0.871592	−	0.490233i	$-0.163088\pi$
$739$	−3.30815	−	10.1814i	−0.121692	−	0.374530i	−0.993284	+	0.115702i	$0.963088\pi$
$740$	3.04102	+	3.86376i	0.111790	+	0.142035i
$741$		0			0
$742$	−0.321012	+	3.05423i	−0.0117847	+	0.112124i
$743$	10.6028	+	18.3647i	0.388981	+	0.673735i	0.992313	−	0.123756i	$-0.0394939\pi$
$743$	10.6028	+	18.3647i	0.388981	+	0.673735i	−0.603332	+	0.797490i	$0.706161\pi$
$744$		0			0
$745$	33.4912	−	12.3256i	1.22702	−	0.451575i
$746$	−15.1586	+	11.0133i	−0.554995	+	0.403227i
$747$		0			0
$748$	2.31161	+	7.11441i	0.0845209	+	0.260129i
$749$	−13.2422	+	22.9361i	−0.483858	+	0.838067i
$750$		0			0
$751$	−24.6961	−	42.7750i	−0.901175	−	1.56088i	−0.825971	−	0.563713i	$-0.809372\pi$
$751$	−24.6961	−	42.7750i	−0.901175	−	1.56088i	−0.0752042	−	0.997168i	$-0.523961\pi$
$752$	−39.1515	+	43.4822i	−1.42771	+	1.58563i
$753$		0			0
$754$	0.242424	+	2.30651i	0.00882857	+	0.0839982i
$755$	14.4581	+	12.0439i	0.526184	+	0.438324i
$756$		0			0
$757$	−31.2549			−1.13598			−0.567989	−	0.823036i	$-0.692279\pi$
$757$	−31.2549			−1.13598			−0.567989	+	0.823036i	$0.692279\pi$
$758$	33.6210	−	14.9690i	1.22117	−	0.543700i
$759$		0			0
$760$	31.2473	−	4.50552i	1.13346	−	0.163432i
$761$	19.3977	−	21.5434i	0.703168	−	0.780947i	−0.280709	−	0.959793i	$-0.590570\pi$
$761$	19.3977	−	21.5434i	0.703168	−	0.780947i	0.983877	+	0.178846i	$0.0572363\pi$
$762$		0			0
$763$	−12.1756	−	13.5224i	−0.440786	−	0.489543i
$764$	−2.43370	−	7.49016i	−0.0880482	−	0.270985i
$765$		0			0
$766$	−3.25185	+	10.0082i	−0.117494	+	0.361610i
$767$	1.07425	−	0.478289i	0.0387891	−	0.0172700i
$768$		0			0
$769$	−3.56272	+	33.8970i	−0.128475	+	1.22236i	0.720322	+	0.693640i	$0.243994\pi$
$769$	−3.56272	+	33.8970i	−0.128475	+	1.22236i	−0.848797	+	0.528719i	$0.822673\pi$
$770$	10.3689	+	21.0678i	0.373668	+	0.759230i
$771$		0			0
$772$	0.140974	+	1.34128i	0.00507377	+	0.0482737i
$773$	9.44334	+	29.0636i	0.339653	+	1.04535i	0.964384	+	0.264506i	$0.0852088\pi$
$773$	9.44334	+	29.0636i	0.339653	+	1.04535i	−0.624731	+	0.780840i	$0.714791\pi$
$774$		0			0
$775$	−13.9652	+	29.1604i	−0.501645	+	1.04747i
$776$	11.1498	−	19.3120i	0.400253	−	0.693259i
$777$		0			0
$778$	−50.2688	−	22.3811i	−1.80223	−	0.802402i
$779$	34.1622	+	15.2100i	1.22399	+	0.544955i
$780$		0			0
$781$	56.2771	−	25.0562i	2.01375	−	0.896581i
$782$	−0.382321			−0.0136718
$783$		0			0
$784$	7.75234	−	23.8592i	0.276869	−	0.852116i
$785$	0.178680	−	0.0657588i	0.00637736	−	0.00234703i
$786$		0			0
$787$	22.4498	−	4.77185i	0.800249	−	0.170098i	0.210404	−	0.977615i	$-0.432522\pi$
$787$	22.4498	−	4.77185i	0.800249	−	0.170098i	0.589845	+	0.807517i	$0.299189\pi$
$788$	−1.18861	+	0.252647i	−0.0423425	+	0.00900017i
$789$		0			0
$790$	−32.1332	−	9.08982i	−1.14325	−	0.323401i
$791$	−2.98726	+	9.19384i	−0.106215	+	0.326895i
$792$		0			0
$793$	−2.56316			−0.0910205
$794$	−43.0398	+	19.1626i	−1.52743	+	0.680054i
$795$		0			0
$796$	−3.38929	−	1.50901i	−0.120130	−	0.0534854i
$797$	−39.7228	−	17.6857i	−1.40705	−	0.626461i	−0.444063	−	0.895996i	$-0.646463\pi$
$797$	−39.7228	−	17.6857i	−1.40705	−	0.626461i	−0.962991	+	0.269535i	$0.913130\pi$
$798$		0			0
$799$	12.6893	−	21.9786i	0.448916	−	0.777545i
$800$	−3.72601	−	20.2819i	−0.131734	−	0.717075i
$801$		0			0
$802$	−5.12593	−	15.7760i	−0.181003	−	0.557070i
$803$	−2.81613	−	26.7937i	−0.0993790	−	0.945528i
$804$		0			0
$805$	−0.329220	+	0.0474700i	−0.0116035	+	0.00167310i
$806$	0.763381	−	7.26308i	0.0268889	−	0.255831i
$807$		0			0
$808$	22.8853	−	10.1892i	0.805102	−	0.358455i
$809$	8.36599	−	25.7479i	0.294133	−	0.905247i	−0.689379	−	0.724401i	$-0.742116\pi$
$809$	8.36599	−	25.7479i	0.294133	−	0.905247i	0.983511	−	0.180846i	$-0.0578836\pi$
$810$		0			0
$811$	−11.3390	−	34.8979i	−0.398167	−	1.22543i	−0.926468	−	0.376375i	$-0.877171\pi$
$811$	−11.3390	−	34.8979i	−0.398167	−	1.22543i	0.528300	−	0.849058i	$-0.322829\pi$
$812$	1.46295	+	1.62477i	0.0513395	+	0.0570182i
$813$		0			0
$814$	14.5122	−	16.1175i	0.508654	−	0.564918i
$815$	−24.4024	−	12.8633i	−0.854779	−	0.450581i
$816$		0			0
$817$	−7.70951	+	3.43249i	−0.269721	+	0.120088i
$818$	−16.0697			−0.561865
$819$		0			0
$820$	3.45897	−	8.65018i	0.120793	−	0.302078i
$821$	0.158330	+	1.50641i	0.00552576	+	0.0525741i	0.996937	−	0.0782049i	$-0.0249188\pi$
$821$	0.158330	+	1.50641i	0.00552576	+	0.0525741i	−0.991412	+	0.130779i	$0.958252\pi$
$822$		0			0
$823$	−24.3576	+	27.0519i	−0.849053	+	0.942969i	−0.998954	−	0.0457319i	$-0.985438\pi$
$823$	−24.3576	+	27.0519i	−0.849053	+	0.942969i	0.149900	+	0.988701i	$0.452105\pi$
$824$	−0.870816	−	1.50830i	−0.0303363	−	0.0525440i
$825$		0			0
$826$	1.99979	−	3.46374i	0.0695816	−	0.120519i
$827$	0.131104	+	0.403496i	0.00455892	+	0.0140309i	0.953310	−	0.301993i	$-0.0976520\pi$
$827$	0.131104	+	0.403496i	0.00455892	+	0.0140309i	−0.948751	+	0.316024i	$0.897652\pi$
$828$		0			0
$829$	−15.0808	+	10.9568i	−0.523778	+	0.380547i	−0.818025	−	0.575182i	$-0.804931\pi$
$829$	−15.0808	+	10.9568i	−0.523778	+	0.380547i	0.294247	+	0.955729i	$0.404931\pi$
$830$	−2.59512	−	67.4032i	−0.0900780	−	2.33960i
$831$		0			0
$832$	−1.02898	−	1.78225i	−0.0356736	−	0.0617885i
$833$	−1.13741	+	10.8217i	−0.0394088	+	0.374950i
$834$		0			0
$835$	14.4098	+	4.07625i	0.498673	+	0.141064i
$836$	7.41748	+	22.8286i	0.256539	+	0.789545i
$837$		0			0
$838$	6.49962	−	20.0038i	0.224526	−	0.691019i
$839$	−28.4120	−	6.03916i	−0.980892	−	0.208495i	−0.310558	−	0.950554i	$-0.600516\pi$
$839$	−28.4120	−	6.03916i	−0.980892	−	0.208495i	−0.670334	+	0.742059i	$0.733849\pi$
$840$		0			0
$841$	24.2415	−	5.15270i	0.835915	−	0.177679i
$842$	3.98670	−	37.9309i	0.137391	−	1.30718i
$843$		0			0
$844$	−3.00805	+	1.33927i	−0.103541	+	0.0460996i
$845$	6.88026	+	27.1808i	0.236688	+	0.935047i
$846$		0			0
$847$	10.8694	−	7.89708i	0.373477	−	0.271347i
$848$	−6.43322	−	1.36742i	−0.220918	−	0.0469575i
$849$		0			0
$850$	6.80151	+	16.4937i	0.233290	+	0.565730i
$851$	0.153613	+	0.266066i	0.00526580	+	0.00912063i
$852$		0			0
$853$	−1.83844	−	17.4915i	−0.0629468	−	0.598899i	−0.979842	−	0.199772i	$-0.935980\pi$
$853$	−1.83844	−	17.4915i	−0.0629468	−	0.598899i	0.916896	−	0.399127i	$-0.130687\pi$
$854$	−7.05296	+	5.12428i	−0.241347	+	0.175349i
$855$		0			0
$856$	−31.6559	−	22.9993i	−1.08198	−	0.786101i
$857$	4.22020	−	7.30960i	0.144159	−	0.249691i	−0.784900	−	0.619623i	$-0.787286\pi$
$857$	4.22020	−	7.30960i	0.144159	−	0.249691i	0.929059	+	0.369932i	$0.120619\pi$
$858$		0			0
$859$	33.0228	−	7.01920i	1.12672	−	0.239492i	0.393396	−	0.919369i	$-0.371300\pi$
$859$	33.0228	−	7.01920i	1.12672	−	0.239492i	0.733326	+	0.679877i	$0.237967\pi$
$860$	0.928383	+	1.88632i	0.0316576	+	0.0643229i
$861$		0			0
$862$	14.6004	+	16.2154i	0.497291	+	0.552298i
$863$	−12.9265	+	39.7837i	−0.440023	+	1.35425i	0.447828	+	0.894120i	$0.352198\pi$
$863$	−12.9265	+	39.7837i	−0.440023	+	1.35425i	−0.887851	+	0.460132i	$0.847802\pi$
$864$		0			0
$865$	9.54714	−	23.8755i	0.324613	−	0.811790i
$866$	26.2641	+	29.1693i	0.892492	+	0.991213i
$867$		0			0
$868$	−3.44234	−	5.96231i	−0.116841	−	0.202374i
$869$	−4.26748	+	40.6024i	−0.144764	+	1.37734i
$870$		0			0
$871$	1.00900	+	9.60000i	0.0341887	+	0.325283i
$872$	21.7493	−	15.8018i	0.736523	−	0.535115i
$873$		0			0
$874$	−1.22679			−0.0414967
$875$	7.90474	+	13.3584i	0.267229	+	0.451596i
$876$		0			0
$877$	−19.1882	+	21.3106i	−0.647938	+	0.719608i	−0.974204	−	0.225670i	$-0.927543\pi$
$877$	−19.1882	+	21.3106i	−0.647938	+	0.719608i	0.326266	+	0.945278i	$0.394210\pi$
$878$	−12.3175	−	5.48408i	−0.415694	−	0.185079i
$879$		0			0
$880$	−47.1926	+	17.3681i	−1.59086	+	0.585477i
$881$	11.7352	+	8.52611i	0.395368	+	0.287252i	0.767652	−	0.640867i	$-0.221425\pi$
$881$	11.7352	+	8.52611i	0.395368	+	0.287252i	−0.372283	+	0.928119i	$0.621425\pi$
$882$		0			0
$883$	−42.8896	−	31.1611i	−1.44335	−	1.04865i	−0.987329	−	0.158684i	$-0.949275\pi$
$883$	−42.8896	−	31.1611i	−1.44335	−	1.04865i	−0.456019	−	0.889970i	$-0.650725\pi$
$884$	−0.747387	−	0.830057i	−0.0251373	−	0.0279178i
$885$		0			0
$886$	−0.565995	+	0.628601i	−0.0190150	+	0.0211183i
$887$	−8.79953	+	1.87040i	−0.295459	+	0.0628018i	−0.353256	−	0.935527i	$-0.614926\pi$
$887$	−8.79953	+	1.87040i	−0.295459	+	0.0628018i	0.0577971	+	0.998328i	$0.481592\pi$
$888$		0			0
$889$	30.1308	+	6.40449i	1.01055	+	0.214800i
$890$	28.0268	+	1.85914i	0.939461	+	0.0623185i
$891$		0			0
$892$	−10.0558	−	7.30599i	−0.336694	−	0.244623i
$893$	40.7174	−	70.5246i	1.36256	−	2.36001i
$894$		0			0
$895$	−4.84931	−	9.85297i	−0.162094	−	0.329349i
$896$	−16.8561	−	7.50483i	−0.563123	−	0.250719i
$897$		0			0
$898$	11.7571	+	2.49905i	0.392340	+	0.0833944i
$899$	13.2788			0.442872
$900$		0			0
$901$	2.85269			0.0950369
$902$	−40.1946	−	8.54362i	−1.33833	−	0.284471i
$903$		0			0
$904$	−13.0475	−	5.80914i	−0.433955	−	0.193209i
$905$	−3.35176	+	3.26000i	−0.111416	+	0.108366i
$906$		0			0
$907$	13.0147	−	22.5421i	0.432145	−	0.748498i	−0.564912	−	0.825151i	$-0.691090\pi$
$907$	13.0147	−	22.5421i	0.432145	−	0.748498i	0.997058	+	0.0766530i	$0.0244234\pi$
$908$	5.71538	+	4.15247i	0.189672	+	0.137804i
$909$		0			0
$910$	−2.69385	−	2.24404i	−0.0893003	−	0.0743893i
$911$	3.92226	+	0.833703i	0.129950	+	0.0276218i	0.272428	−	0.962176i	$-0.412173\pi$
$911$	3.92226	+	0.833703i	0.129950	+	0.0276218i	−0.142477	+	0.989798i	$0.545507\pi$
$912$		0			0
$913$	−80.6628	+	17.1454i	−2.66955	+	0.567430i
$914$	17.6760	−	19.6312i	0.584670	−	0.649342i
$915$		0			0
$916$	−4.21026	−	4.67597i	−0.139111	−	0.154498i
$917$	13.0533	+	9.48377i	0.431058	+	0.313182i
$918$		0			0
$919$	0.331871	+	0.241118i	0.0109474	+	0.00795375i	0.593245	−	0.805022i	$-0.297846\pi$
$919$	0.331871	+	0.241118i	0.0109474	+	0.00795375i	−0.582298	+	0.812975i	$0.697846\pi$
$920$	−0.0189068	−	0.491067i	−0.000623339	−	0.0161900i
$921$		0			0
$922$	−50.1567	−	22.3312i	−1.65182	−	0.735439i
$923$	−6.15481	+	6.83561i	−0.202588	+	0.224997i
$924$		0			0
$925$	8.74557	−	11.3604i	0.287552	−	0.373526i
$926$	30.6303			1.00657
$927$		0			0
$928$	−6.85175	+	4.97808i	−0.224920	+	0.163414i
$929$	−0.704207	−	6.70008i	−0.0231043	−	0.219822i	−0.999982	−	0.00602306i	$-0.998083\pi$
$929$	−0.704207	−	6.70008i	−0.0231043	−	0.219822i	0.976878	−	0.213799i	$-0.0685839\pi$
$930$		0			0
$931$	−3.64970	+	34.7246i	−0.119614	+	1.13805i
$932$	3.17656	+	5.50196i	0.104052	+	0.180223i
$933$		0			0
$934$	−20.5261	−	22.7966i	−0.671635	−	0.745926i
$935$	18.4558	−	11.6244i	0.603570	−	0.380160i
$936$		0			0
$937$	−13.0786	+	40.2519i	−0.427260	+	1.31497i	0.473554	+	0.880765i	$0.342971\pi$
$937$	−13.0786	+	40.2519i	−0.427260	+	1.31497i	−0.900814	+	0.434206i	$0.857029\pi$
$938$	21.9688	+	24.3988i	0.717305	+	0.796648i
$939$		0			0
$940$	−17.9468	−	9.46030i	−0.585359	−	0.308561i
$941$	51.2834	−	10.9006i	1.67179	−	0.355350i	0.727919	−	0.685663i	$-0.240488\pi$
$941$	51.2834	−	10.9006i	1.67179	−	0.355350i	0.943871	+	0.330314i	$0.107154\pi$
$942$		0			0
$943$	0.291050	−	0.504114i	0.00947790	−	0.0164162i
$944$	6.92961	+	5.03466i	0.225540	+	0.163864i
$945$		0			0
$946$	7.50241	−	5.45082i	0.243924	−	0.177221i
$947$	0.245164	+	2.33258i	0.00796675	+	0.0757985i	0.997783	−	0.0665533i	$-0.0212002\pi$
$947$	0.245164	+	2.33258i	0.00796675	+	0.0757985i	−0.989816	+	0.142352i	$0.954534\pi$
$948$		0			0
$949$	2.01136	+	3.48378i	0.0652915	+	0.113088i
$950$	21.8246	+	52.9249i	0.708084	+	1.71711i
$951$		0			0
$952$	5.97517	+	1.27006i	0.193656	+	0.0411629i
$953$	7.72986	−	5.61607i	0.250395	−	0.181922i	−0.455507	−	0.890232i	$-0.650542\pi$
$953$	7.72986	−	5.61607i	0.250395	−	0.181922i	0.705902	+	0.708310i	$0.250542\pi$
$954$		0			0
$955$	−19.4306	+	12.2384i	−0.628759	+	0.396026i
$956$	−0.756054	+	0.336617i	−0.0244525	+	0.0108870i
$957$		0			0
$958$	−4.01328	+	38.1839i	−0.129663	+	1.23366i
$959$	22.4924	−	4.78090i	0.726316	−	0.154383i
$960$		0			0
$961$	−10.5779	−	2.24839i	−0.341221	−	0.0725288i
$962$	−1.00071	+	3.07987i	−0.0322642	+	0.0992989i
$963$		0			0
$964$	−5.94735	−	18.3041i	−0.191551	−	0.589534i
$965$	3.69043	−	1.35817i	0.118799	−	0.0437211i
$966$		0			0
$967$	−2.15909	+	20.5424i	−0.0694318	+	0.660599i	0.903354	+	0.428895i	$0.141097\pi$
$967$	−2.15909	+	20.5424i	−0.0694318	+	0.660599i	−0.972786	+	0.231705i	$0.925570\pi$
$968$	9.92488	+	17.1904i	0.318998	+	0.552520i
$969$		0			0
$970$	38.9100	+	11.0068i	1.24932	+	0.353408i
$971$	−24.5224	+	17.8166i	−0.786962	+	0.571761i	−0.907060	−	0.421001i	$-0.861679\pi$
$971$	−24.5224	+	17.8166i	−0.786962	+	0.571761i	0.120098	+	0.992762i	$0.461679\pi$
$972$		0			0
$973$	7.22044	+	22.2222i	0.231477	+	0.712412i
$974$	9.49335	−	16.4430i	0.304186	−	0.526866i
$975$		0			0
$976$	−9.33514	−	16.1689i	−0.298810	−	0.517555i
$977$	15.7527	−	17.4951i	0.503973	−	0.559719i	−0.436448	−	0.899729i	$-0.643764\pi$
$977$	15.7527	−	17.4951i	0.503973	−	0.559719i	0.940422	+	0.340010i	$0.110430\pi$
$978$		0			0
$979$	−3.58946	−	34.1514i	−0.114719	−	1.09148i
$980$	8.67937	+	0.575740i	0.277252	+	0.0183913i
$981$		0			0
$982$	66.1926			2.11229
$983$	−17.6593	+	7.86243i	−0.563245	+	0.250773i	−0.668550	−	0.743667i	$-0.733085\pi$
$983$	−17.6593	+	7.86243i	−0.563245	+	0.250773i	0.105305	+	0.994440i	$0.466418\pi$
$984$		0			0
$985$	1.56459	+	3.17899i	0.0498521	+	0.101291i
$986$	4.90295	−	5.44528i	0.156142	−	0.173413i
$987$		0			0
$988$	−2.39821	−	2.66348i	−0.0762971	−	0.0847365i
$989$	0.0405939	+	0.124935i	0.00129081	+	0.00397271i
$990$		0			0
$991$	−0.458610	+	1.41146i	−0.0145682	+	0.0448364i	−0.958076	−	0.286513i	$-0.907504\pi$
$991$	−0.458610	+	1.41146i	−0.0145682	+	0.0448364i	0.943508	+	0.331349i	$0.107504\pi$
$992$	24.3635	−	10.8473i	0.773540	−	0.344402i
$993$		0			0
$994$	−3.27021	+	31.1140i	−0.103725	+	0.986876i
$995$	−1.84036	+	10.6600i	−0.0583433	+	0.337944i
$996$		0			0
$997$	1.65392	+	15.7360i	0.0523803	+	0.498365i	0.988989	+	0.147988i	$0.0472798\pi$
$997$	1.65392	+	15.7360i	0.0523803	+	0.498365i	−0.936609	+	0.350377i	$0.886053\pi$
$998$	−18.6267	−	57.3271i	−0.589619	−	1.81466i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.181.7		224
3.2	odd	2		225.2.q.a.106.22	yes	224
9.4	even	3	inner	675.2.r.a.631.22		224
9.5	odd	6		225.2.q.a.31.7	✓	224
25.21	even	5	inner	675.2.r.a.46.22		224
75.71	odd	10		225.2.q.a.196.7	yes	224
225.121	even	15	inner	675.2.r.a.496.7		224
225.221	odd	30		225.2.q.a.121.22	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.7	✓	224	9.5	odd	6
225.2.q.a.106.22	yes	224	3.2	odd	2
225.2.q.a.121.22	yes	224	225.221	odd	30
225.2.q.a.196.7	yes	224	75.71	odd	10
675.2.r.a.46.22		224	25.21	even	5	inner
675.2.r.a.181.7		224	1.1	even	1	trivial
675.2.r.a.496.7		224	225.121	even	15	inner
675.2.r.a.631.22		224	9.4	even	3	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.62705 - 0.345839i) q^{2} +(0.700584 + 0.311920i) q^{4} +(0.380412 - 2.20347i) q^{5} +(0.694163 - 1.20233i) q^{7} +(1.65942 + 1.20564i) q^{8} +(-1.38100 + 3.45359i) q^{10} +(4.44787 + 0.945423i) q^{11} +(-0.664131 + 0.141165i) q^{13} +(-1.54525 + 1.71617i) q^{14} +(-3.30929 - 3.67534i) q^{16} +(1.73545 + 1.26088i) q^{17} +(5.56870 + 4.04590i) q^{19} +(0.953818 - 1.42506i) q^{20} +(-6.90992 - 3.07649i) q^{22} +(0.0716950 - 0.0796254i) q^{23} +(-4.71057 - 1.67645i) q^{25} +1.12939 q^{26} +(0.861350 - 0.625807i) q^{28} +(0.214650 + 2.04226i) q^{29} +(0.675922 - 6.43096i) q^{31} +(2.06213 + 3.57172i) q^{32} +(-2.38760 - 2.65170i) q^{34} +(-2.38522 - 1.98695i) q^{35} +(-0.886060 + 2.72701i) q^{37} +(-7.66130 - 8.50874i) q^{38} +(3.28786 - 3.19785i) q^{40} +(5.31403 - 1.12953i) q^{41} +(-0.613014 + 1.06177i) q^{43} +(2.82121 + 2.04973i) q^{44} +(-0.144189 + 0.104759i) q^{46} +(-1.23665 - 11.7660i) q^{47} +(2.53627 + 4.39296i) q^{49} +(7.08454 + 4.35677i) q^{50} +(-0.509312 - 0.108258i) q^{52} +(1.07586 - 0.781661i) q^{53} +(3.77524 - 9.44110i) q^{55} +(2.60148 - 1.15825i) q^{56} +(0.357048 - 3.39709i) q^{58} +(-1.69407 + 0.360086i) q^{59} +(3.69259 + 0.784884i) q^{61} +(-3.32384 + 10.2297i) q^{62} +(0.936638 + 2.88268i) q^{64} +(0.0584104 + 1.51709i) q^{65} +(1.48608 - 14.1391i) q^{67} +(0.822536 + 1.42467i) q^{68} +(3.19370 + 4.05776i) q^{70} +(10.9600 - 7.96294i) q^{71} +(-1.83085 - 5.63478i) q^{73} +(2.38477 - 4.13054i) q^{74} +(2.63935 + 4.57148i) q^{76} +(4.22425 - 4.69151i) q^{77} +(0.938478 + 8.92902i) q^{79} +(-9.35740 + 5.89378i) q^{80} -9.03682 q^{82} +(-16.5673 + 7.37623i) q^{83} +(3.43850 - 3.34436i) q^{85} +(1.36460 - 1.51555i) q^{86} +(6.24105 + 6.93138i) q^{88} +(-2.33361 - 7.18212i) q^{89} +(-0.291288 + 0.896494i) q^{91} +(0.0750652 - 0.0334212i) q^{92} +(-2.05704 + 19.5715i) q^{94} +(11.0334 - 10.7314i) q^{95} +(-1.13640 - 10.8121i) q^{97} +(-2.60738 - 8.02469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

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