LMFDB - Embedded newform 405.2.r.a.8.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			8.16
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18018 - 1.52658i) q^{2} +(1.73870 - 4.77703i) q^{4} +(-1.64880 + 1.51045i) q^{5} +(1.30062 - 2.78918i) q^{7} +(-2.12414 - 7.92739i) q^{8} +O(q^{10})$	\(q+(2.18018 - 1.52658i) q^{2} +(1.73870 - 4.77703i) q^{4} +(-1.64880 + 1.51045i) q^{5} +(1.30062 - 2.78918i) q^{7} +(-2.12414 - 7.92739i) q^{8} +(-1.28885 + 5.81007i) q^{10} +(0.426793 - 0.508631i) q^{11} +(-0.269123 + 0.384347i) q^{13} +(-1.42232 - 8.06640i) q^{14} +(-8.94423 - 7.50510i) q^{16} +(-1.20591 + 4.50051i) q^{17} +(4.80938 + 2.77670i) q^{19} +(4.34871 + 10.5026i) q^{20} +(0.154018 - 1.76044i) q^{22} +(0.0602123 - 0.0280775i) q^{23} +(0.437073 - 4.98086i) q^{25} +1.24878i q^{26} +(-11.0626 - 11.0626i) q^{28} +(-0.434735 + 2.46551i) q^{29} +(1.76652 + 0.642961i) q^{31} +(-14.6055 - 1.27781i) q^{32} +(4.24128 + 11.6528i) q^{34} +(2.06847 + 6.56331i) q^{35} +(-2.44933 - 0.656295i) q^{37} +(14.7241 - 1.28820i) q^{38} +(15.4762 + 9.86226i) q^{40} +(-1.62695 + 0.286875i) q^{41} +(0.732214 + 8.36925i) q^{43} +(-1.68769 - 2.92316i) q^{44} +(0.0884111 - 0.153133i) q^{46} +(3.71355 + 1.73166i) q^{47} +(-1.58841 - 1.89299i) q^{49} +(-6.65077 - 11.5264i) q^{50} +(1.36812 + 1.95387i) q^{52} +(-7.52870 + 7.52870i) q^{53} +(0.0645683 + 1.48328i) q^{55} +(-24.8736 - 4.38589i) q^{56} +(2.81598 + 6.03890i) q^{58} +(3.49452 - 2.93225i) q^{59} +(-5.84534 + 2.12753i) q^{61} +(4.83286 - 1.29496i) q^{62} +(-13.5701 + 7.83468i) q^{64} +(-0.136808 - 1.04021i) q^{65} +(-4.48268 - 3.13881i) q^{67} +(19.4024 + 13.5857i) q^{68} +(14.5290 + 11.1515i) q^{70} +(5.33043 - 3.07752i) q^{71} +(13.6146 - 3.64803i) q^{73} +(-6.34185 + 2.30824i) q^{74} +(21.6264 - 18.1467i) q^{76} +(-0.863572 - 1.85194i) q^{77} +(-5.34198 - 0.941936i) q^{79} +(26.0833 - 1.13543i) q^{80} +(-3.10910 + 3.10910i) q^{82} +(-3.25316 - 4.64599i) q^{83} +(-4.80950 - 9.24190i) q^{85} +(14.3727 + 17.1287i) q^{86} +(-4.93869 - 2.30295i) q^{88} +(3.08131 - 5.33699i) q^{89} +(0.721988 + 1.25052i) q^{91} +(-0.0294359 - 0.336454i) q^{92} +(10.7397 - 1.89370i) q^{94} +(-12.1238 + 2.68612i) q^{95} +(-13.5821 + 1.18828i) q^{97} +(-6.35281 - 1.70223i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.18018	−	1.52658i	1.54162	−	1.07945i	0.576682	−	0.816969i	$-0.304347\pi$
$2$	2.18018	−	1.52658i	1.54162	−	1.07945i	0.964936	−	0.262484i	$-0.0845416\pi$
$3$		0			0
$3$		0			0
$4$	1.73870	−	4.77703i	0.869348	−	2.38851i
$5$	−1.64880	+	1.51045i	−0.737365	+	0.675494i
$5$	−1.64880	+	1.51045i	−0.737365	+	0.675494i
$6$		0			0
$7$	1.30062	−	2.78918i	0.491587	−	1.05421i	−0.491468	−	0.870896i	$-0.663539\pi$
$7$	1.30062	−	2.78918i	0.491587	−	1.05421i	0.983054	−	0.183315i	$-0.0586829\pi$
$8$	−2.12414	−	7.92739i	−0.750996	−	2.80276i
$9$		0			0
$10$	−1.28885	+	5.81007i	−0.407571	+	1.83731i
$11$	0.426793	−	0.508631i	0.128683	−	0.153358i	−0.697856	−	0.716238i	$-0.745862\pi$
$11$	0.426793	−	0.508631i	0.128683	−	0.153358i	0.826538	+	0.562880i	$0.190307\pi$
$12$		0			0
$13$	−0.269123	+	0.384347i	−0.0746412	+	0.106599i	−0.854737	−	0.519062i	$-0.826282\pi$
$13$	−0.269123	+	0.384347i	−0.0746412	+	0.106599i	0.780096	+	0.625660i	$0.215170\pi$
$14$	−1.42232	−	8.06640i	−0.380132	−	2.15584i
$15$		0			0
$16$	−8.94423	−	7.50510i	−2.23606	−	1.87627i
$17$	−1.20591	+	4.50051i	−0.292476	+	1.09153i	0.650726	+	0.759313i	$0.274465\pi$
$17$	−1.20591	+	4.50051i	−0.292476	+	1.09153i	−0.943201	+	0.332221i	$0.892202\pi$
$18$		0			0
$19$	4.80938	+	2.77670i	1.10335	+	0.637018i	0.937098	−	0.349066i	$-0.113501\pi$
$19$	4.80938	+	2.77670i	1.10335	+	0.637018i	0.166249	+	0.986084i	$0.446834\pi$
$20$	4.34871	+	10.5026i	0.972401	+	2.34845i
$21$		0			0
$22$	0.154018	−	1.76044i	0.0328368	−	0.375327i
$23$	0.0602123	−	0.0280775i	0.0125551	−	0.00585456i	−0.416331	−	0.909213i	$-0.636684\pi$
$23$	0.0602123	−	0.0280775i	0.0125551	−	0.00585456i	0.428886	+	0.903359i	$0.358906\pi$
$24$		0			0
$25$	0.437073	−	4.98086i	0.0874146	−	0.996172i
$26$			1.24878i			0.244906i
$27$		0			0
$28$	−11.0626	−	11.0626i	−2.09064	−	2.09064i
$29$	−0.434735	+	2.46551i	−0.0807283	+	0.457833i	0.917469	+	0.397808i	$0.130229\pi$
$29$	−0.434735	+	2.46551i	−0.0807283	+	0.457833i	−0.998197	+	0.0600247i	$0.980882\pi$
$30$		0			0
$31$	1.76652	+	0.642961i	0.317276	+	0.115479i	0.495749	−	0.868466i	$-0.334893\pi$
$31$	1.76652	+	0.642961i	0.317276	+	0.115479i	−0.178473	+	0.983945i	$0.557116\pi$
$32$	−14.6055	−	1.27781i	−2.58191	−	0.225888i
$33$		0			0
$34$	4.24128	+	11.6528i	0.727373	+	1.99844i
$35$	2.06847	+	6.56331i	0.349635	+	1.10940i
$36$		0			0
$37$	−2.44933	−	0.656295i	−0.402667	−	0.107894i	0.0518010	−	0.998657i	$-0.483504\pi$
$37$	−2.44933	−	0.656295i	−0.402667	−	0.107894i	−0.454468	+	0.890763i	$0.650170\pi$
$38$	14.7241	−	1.28820i	2.38857	−	0.208973i
$39$		0			0
$40$	15.4762	+	9.86226i	2.44700	+	1.55936i
$41$	−1.62695	+	0.286875i	−0.254087	+	0.0448023i	−0.299241	−	0.954178i	$-0.596733\pi$
$41$	−1.62695	+	0.286875i	−0.254087	+	0.0448023i	0.0451539	+	0.998980i	$0.485622\pi$
$42$		0			0
$43$	0.732214	+	8.36925i	0.111662	+	1.27630i	0.820794	+	0.571224i	$0.193531\pi$
$43$	0.732214	+	8.36925i	0.111662	+	1.27630i	−0.709133	+	0.705075i	$0.750913\pi$
$44$	−1.68769	−	2.92316i	−0.254428	−	0.440682i
$45$		0			0
$46$	0.0884111	−	0.153133i	0.0130355	−	0.0225782i
$47$	3.71355	+	1.73166i	0.541677	+	0.252588i	0.674145	−	0.738599i	$-0.264512\pi$
$47$	3.71355	+	1.73166i	0.541677	+	0.252588i	−0.132468	+	0.991187i	$0.542290\pi$
$48$		0			0
$49$	−1.58841	−	1.89299i	−0.226916	−	0.270428i
$50$	−6.65077	−	11.5264i	−0.940561	−	1.63008i
$51$		0			0
$52$	1.36812	+	1.95387i	0.189723	+	0.270953i
$53$	−7.52870	+	7.52870i	−1.03415	+	1.03415i	−0.0347509	+	0.999396i	$0.511064\pi$
$53$	−7.52870	+	7.52870i	−1.03415	+	1.03415i	−0.999396	+	0.0347509i	$0.988936\pi$
$54$		0			0
$55$	0.0645683	+	1.48328i	0.00870639	+	0.200005i
$56$	−24.8736	−	4.38589i	−3.32388	−	0.586089i
$57$		0			0
$58$	2.81598	+	6.03890i	0.369757	+	0.792946i
$59$	3.49452	−	2.93225i	0.454948	−	0.381747i	−0.386320	−	0.922365i	$-0.626254\pi$
$59$	3.49452	−	2.93225i	0.454948	−	0.381747i	0.841268	+	0.540618i	$0.181810\pi$
$60$		0			0
$61$	−5.84534	+	2.12753i	−0.748419	+	0.272402i	−0.687940	−	0.725767i	$-0.741485\pi$
$61$	−5.84534	+	2.12753i	−0.748419	+	0.272402i	−0.0604785	+	0.998169i	$0.519263\pi$
$62$	4.83286	−	1.29496i	0.613773	−	0.164460i
$63$		0			0
$64$	−13.5701	+	7.83468i	−1.69626	+	0.979335i
$65$	−0.136808	−	1.04021i	−0.0169690	−	0.129022i
$66$		0			0
$67$	−4.48268	−	3.13881i	−0.547646	−	0.383466i	0.266758	−	0.963763i	$-0.414047\pi$
$67$	−4.48268	−	3.13881i	−0.547646	−	0.383466i	−0.814405	+	0.580297i	$0.802936\pi$
$68$	19.4024	+	13.5857i	2.35288	+	1.64751i
$69$		0			0
$70$	14.5290	+	11.1515i	1.73655	+	1.33286i
$71$	5.33043	−	3.07752i	0.632605	−	0.365235i	−0.149155	−	0.988814i	$-0.547655\pi$
$71$	5.33043	−	3.07752i	0.632605	−	0.365235i	0.781760	+	0.623579i	$0.214322\pi$
$72$		0			0
$73$	13.6146	−	3.64803i	1.59347	−	0.426970i	0.650410	−	0.759583i	$-0.274597\pi$
$73$	13.6146	−	3.64803i	1.59347	−	0.426970i	0.943063	+	0.332613i	$0.107930\pi$
$74$	−6.34185	+	2.30824i	−0.737225	+	0.268328i
$75$		0			0
$76$	21.6264	−	18.1467i	2.48072	−	2.08157i
$77$	−0.863572	−	1.85194i	−0.0984131	−	0.211048i
$78$		0			0
$79$	−5.34198	−	0.941936i	−0.601020	−	0.105976i	−0.135144	−	0.990826i	$-0.543150\pi$
$79$	−5.34198	−	0.941936i	−0.601020	−	0.105976i	−0.465876	+	0.884850i	$0.654261\pi$
$80$	26.0833	−	1.13543i	2.91620	−	0.126945i
$81$		0			0
$82$	−3.10910	+	3.10910i	−0.343343	+	0.343343i
$83$	−3.25316	−	4.64599i	−0.357081	−	0.509964i	0.599916	−	0.800063i	$-0.295201\pi$
$83$	−3.25316	−	4.64599i	−0.357081	−	0.509964i	−0.956997	+	0.290099i	$0.906312\pi$
$84$		0			0
$85$	−4.80950	−	9.24190i	−0.521664	−	1.00242i
$86$	14.3727	+	17.1287i	1.54984	+	1.84703i
$87$		0			0
$88$	−4.93869	−	2.30295i	−0.526466	−	0.245495i
$89$	3.08131	−	5.33699i	0.326619	−	0.565720i	−0.655220	−	0.755438i	$-0.727424\pi$
$89$	3.08131	−	5.33699i	0.326619	−	0.565720i	0.981839	+	0.189718i	$0.0607574\pi$
$90$		0			0
$91$	0.721988	+	1.25052i	0.0756849	+	0.131090i
$92$	−0.0294359	−	0.336454i	−0.00306891	−	0.0350778i
$93$		0			0
$94$	10.7397	−	1.89370i	1.10772	−	0.195320i
$95$	−12.1238	+	2.68612i	−1.24387	+	0.275590i
$96$		0			0
$97$	−13.5821	+	1.18828i	−1.37906	+	0.120652i	−0.752433	−	0.658669i	$-0.771120\pi$
$97$	−13.5821	+	1.18828i	−1.37906	+	0.120652i	−0.626625	+	0.779321i	$0.715564\pi$
$98$	−6.35281	−	1.70223i	−0.641731	−	0.171951i
$99$		0			0
$100$	−23.0338	−	10.7481i	−2.30338	−	1.07481i
$101$	0.629841	+	1.73048i	0.0626716	+	0.172189i	0.967076	−	0.254487i	$-0.0819067\pi$
$101$	0.629841	+	1.73048i	0.0626716	+	0.172189i	−0.904405	+	0.426676i	$0.859684\pi$
$102$		0			0
$103$	−16.2704	−	1.42347i	−1.60317	−	0.140259i	−0.749833	−	0.661627i	$-0.769866\pi$
$103$	−16.2704	−	1.42347i	−1.60317	−	0.140259i	−0.853332	+	0.521368i	$0.825422\pi$
$104$	3.61852	+	1.31704i	0.354826	+	0.129146i
$105$		0			0
$106$	−4.92077	+	27.9071i	−0.477947	+	2.71057i
$107$	−10.4880	−	10.4880i	−1.01391	−	1.01391i	−0.999902	−	0.0140087i	$-0.995541\pi$
$107$	−10.4880	−	10.4880i	−1.01391	−	1.01391i	−0.0140087	−	0.999902i	$-0.504459\pi$
$108$		0			0
$109$		−	9.34913i		−	0.895484i	−0.894163	−	0.447742i	$-0.852228\pi$
$109$		−	9.34913i		−	0.895484i	0.894163	−	0.447742i	$-0.147772\pi$
$110$	2.40511	+	3.13525i	0.229318	+	0.298934i
$111$		0			0
$112$	−32.5661	+	15.1858i	−3.07721	+	1.43492i
$113$	1.81095	−	20.6993i	0.170360	−	1.94722i	−0.125734	−	0.992064i	$-0.540129\pi$
$113$	1.81095	−	20.6993i	0.170360	−	1.94722i	0.296094	−	0.955159i	$-0.404316\pi$
$114$		0			0
$115$	−0.0568683	+	0.137242i	−0.00530300	+	0.0127979i
$116$	11.0219	+	6.36351i	1.02336	+	0.590837i
$117$		0			0
$118$	3.14237	−	11.7275i	0.289278	−	1.07960i
$119$	10.9843	+	9.21693i	1.00693	+	0.844915i
$120$		0			0
$121$	1.83358	+	10.3987i	0.166689	+	0.945339i
$122$	−9.49604	+	13.5617i	−0.859731	+	1.22782i
$123$		0			0
$124$	6.14289	−	7.32081i	0.551648	−	0.657428i
$125$	6.80270	+	8.87261i	0.608452	+	0.793591i
$126$		0			0
$127$	−1.97054	−	7.35416i	−0.174857	−	0.652576i	−0.996576	−	0.0826829i	$-0.973651\pi$
$127$	−1.97054	−	7.35416i	−0.174857	−	0.652576i	0.821719	−	0.569893i	$-0.193016\pi$
$128$	−5.23265	+	11.2214i	−0.462505	+	0.991845i
$129$		0			0
$130$	−1.88622	−	2.05899i	−0.165433	−	0.180585i
$131$	−4.01388	+	11.0280i	−0.350694	+	0.963524i	0.631454	+	0.775414i	$0.282459\pi$
$131$	−4.01388	+	11.0280i	−0.350694	+	0.963524i	−0.982148	+	0.188111i	$0.939764\pi$
$132$		0			0
$133$	13.9999	−	9.80281i	1.21394	−	0.850012i
$134$	−14.5647			−1.25820
$135$		0			0
$136$	38.2388			3.27895
$137$	−5.50755	+	3.85643i	−0.470542	+	0.329477i	−0.784681	−	0.619900i	$-0.787173\pi$
$137$	−5.50755	+	3.85643i	−0.470542	+	0.329477i	0.314139	+	0.949377i	$0.398284\pi$
$138$		0			0
$139$	−0.519349	+	1.42690i	−0.0440506	+	0.121028i	−0.959767	−	0.280796i	$-0.909402\pi$
$139$	−0.519349	+	1.42690i	−0.0440506	+	0.121028i	0.915717	+	0.401824i	$0.131624\pi$
$140$	34.9496	+	1.53048i	2.95378	+	0.129349i
$141$		0			0
$142$	6.92320	−	14.8468i	0.580982	−	1.24592i
$143$	0.0806315	+	0.300921i	0.00674274	+	0.0251643i
$144$		0			0
$145$	−3.00724	−	4.72177i	−0.249737	−	0.392122i
$146$	24.1133	−	28.7372i	1.99563	−	2.37830i
$147$		0			0
$148$	−7.39377	+	10.5594i	−0.607764	+	0.867978i
$149$	−3.69731	−	20.9685i	−0.302895	−	1.71780i	−0.633250	−	0.773947i	$-0.718280\pi$
$149$	−3.69731	−	20.9685i	−0.302895	−	1.71780i	0.330355	−	0.943857i	$-0.392832\pi$
$150$		0			0
$151$	6.08208	+	5.10347i	0.494952	+	0.415314i	0.855797	−	0.517312i	$-0.173067\pi$
$151$	6.08208	+	5.10347i	0.494952	+	0.415314i	−0.360845	+	0.932626i	$0.617512\pi$
$152$	11.7962	−	44.0239i	0.956797	−	3.57081i
$153$		0			0
$154$	−4.70986	−	2.71924i	−0.379531	−	0.219123i
$155$	−3.88380	+	1.60813i	−0.311954	+	0.129168i
$156$		0			0
$157$	−1.19160	+	13.6200i	−0.0950997	+	1.08699i	0.787324	+	0.616539i	$0.211466\pi$
$157$	−1.19160	+	13.6200i	−0.0950997	+	1.08699i	−0.882424	+	0.470455i	$0.844090\pi$
$158$	−13.0844	+	6.10136i	−1.04094	+	0.485398i
$159$		0			0
$160$	26.0116	−	19.9540i	2.05640	−	1.57750i
$161$		−	0.204461i		−	0.0161138i
$162$		0			0
$163$	13.8462	+	13.8462i	1.08452	+	1.08452i	0.996082	+	0.0884330i	$0.0281859\pi$
$163$	13.8462	+	13.8462i	1.08452	+	1.08452i	0.0884330	+	0.996082i	$0.471814\pi$
$164$	−1.45836	+	8.27077i	−0.113879	+	0.645839i
$165$		0			0
$166$	−14.1849	−	5.16289i	−1.10096	−	0.400718i
$167$	−21.8892	−	1.91506i	−1.69384	−	0.148192i	−0.801028	−	0.598627i	$-0.795713\pi$
$167$	−21.8892	−	1.91506i	−1.69384	−	0.148192i	−0.892809	+	0.450435i	$0.851269\pi$
$168$		0			0
$169$	4.37097	+	12.0091i	0.336228	+	0.923779i
$170$	−24.5940	−	12.8069i	−1.88628	−	0.982245i
$171$		0			0
$172$	41.2533	+	11.0538i	3.14553	+	0.842842i
$173$	−3.73833	+	0.327061i	−0.284220	+	0.0248660i	−0.228374	−	0.973573i	$-0.573341\pi$
$173$	−3.73833	+	0.327061i	−0.284220	+	0.0248660i	−0.0558456	+	0.998439i	$0.517785\pi$
$174$		0			0
$175$	−13.3241	−	7.69726i	−1.00720	−	0.581858i
$176$	−7.63466	+	1.34620i	−0.575484	+	0.101473i
$177$		0			0
$178$	−1.42952	−	16.3394i	−0.107147	−	1.22469i
$179$	7.21345	+	12.4941i	0.539158	+	0.933850i	0.998950	+	0.0458226i	$0.0145909\pi$
$179$	7.21345	+	12.4941i	0.539158	+	0.933850i	−0.459791	+	0.888027i	$0.652076\pi$
$180$		0			0
$181$	−7.06370	+	12.2347i	−0.525041	+	0.909397i	0.474534	+	0.880237i	$0.342617\pi$
$181$	−7.06370	+	12.2347i	−0.525041	+	0.909397i	−0.999575	+	0.0291599i	$0.990717\pi$
$182$	3.48308	+	1.62419i	0.258183	+	0.120393i
$183$		0			0
$184$	−0.350480	−	0.417686i	−0.0258378	−	0.0307922i
$185$	5.02975	−	2.61749i	0.369794	−	0.192442i
$186$		0			0
$187$	1.77443	+	2.53415i	0.129759	+	0.185315i
$188$	14.7289	−	14.7289i	1.07422	−	1.07422i
$189$		0			0
$190$	−22.3314	+	24.3641i	−1.62009	+	1.76756i
$191$	2.54718	+	0.449136i	0.184307	+	0.0324983i	0.265040	−	0.964237i	$-0.414615\pi$
$191$	2.54718	+	0.449136i	0.184307	+	0.0324983i	−0.0807326	+	0.996736i	$0.525726\pi$
$192$		0			0
$193$	−6.02445	−	12.9195i	−0.433649	−	0.929963i	−0.994761	−	0.102224i	$-0.967404\pi$
$193$	−6.02445	−	12.9195i	−0.433649	−	0.929963i	0.561112	−	0.827740i	$-0.310374\pi$
$194$	−27.7975	+	23.3248i	−1.99574	+	1.67463i
$195$		0			0
$196$	−11.8046	+	4.29654i	−0.843189	+	0.306896i
$197$	8.06170	−	2.16013i	0.574372	−	0.153903i	0.0400711	−	0.999197i	$-0.487242\pi$
$197$	8.06170	−	2.16013i	0.574372	−	0.153903i	0.534301	+	0.845294i	$0.320575\pi$
$198$		0			0
$199$	3.27312	−	1.88973i	0.232025	−	0.133960i	−0.379481	−	0.925200i	$-0.623897\pi$
$199$	3.27312	−	1.88973i	0.232025	−	0.133960i	0.611506	+	0.791240i	$0.290564\pi$
$200$	−40.4136	+	7.11519i	−2.85768	+	0.503120i
$201$		0			0
$202$	4.01487	+	2.81124i	0.282485	+	0.197798i
$203$	6.31132	+	4.41923i	0.442968	+	0.310169i
$204$		0			0
$205$	2.24920	−	2.93043i	0.157091	−	0.204670i
$206$	−37.6453	+	21.7345i	−2.62287	+	1.51432i
$207$		0			0
$208$	5.29166	−	1.41790i	0.366911	−	0.0983134i
$209$	3.46492	−	1.26113i	0.239674	−	0.0872341i
$210$		0			0
$211$	−13.6392	+	11.4447i	−0.938964	+	0.787885i	−0.977405	−	0.211376i	$-0.932205\pi$
$211$	−13.6392	+	11.4447i	−0.938964	+	0.787885i	0.0384403	+	0.999261i	$0.487761\pi$
$212$	22.8747	+	49.0550i	1.57104	+	3.36911i
$213$		0			0
$214$	−38.8763	−	6.85495i	−2.65753	−	0.468594i
$215$	−13.8486	−	12.6932i	−0.944468	−	0.865671i
$216$		0			0
$217$	4.09090	−	4.09090i	0.277708	−	0.277708i
$218$	−14.2722	−	20.3828i	−0.966633	−	1.38049i
$219$		0			0
$220$	7.19794	+	2.27053i	0.485285	+	0.153079i
$221$	−1.40522	−	1.67468i	−0.0945254	−	0.112651i
$222$		0			0
$223$	−17.3515	−	8.09113i	−1.16194	−	0.541822i	−0.256605	−	0.966516i	$-0.582604\pi$
$223$	−17.3515	−	8.09113i	−1.16194	−	0.541822i	−0.905337	+	0.424694i	$0.860382\pi$
$224$	−22.5602	+	39.0754i	−1.50737	+	2.61083i
$225$		0			0
$226$	−27.6508	−	47.8926i	−1.83930	−	3.18577i
$227$	0.0420779	+	0.480953i	0.00279281	+	0.0319220i	0.997463	−	0.0711836i	$-0.0226776\pi$
$227$	0.0420779	+	0.480953i	0.00279281	+	0.0319220i	−0.994670	+	0.103106i	$0.967122\pi$
$228$		0			0
$229$	14.7979	−	2.60927i	0.977875	−	0.172426i	0.338203	−	0.941073i	$-0.390181\pi$
$229$	14.7979	−	2.60927i	0.977875	−	0.172426i	0.639672	+	0.768648i	$0.279070\pi$
$230$	0.0855272	+	0.386026i	0.00563950	+	0.0254538i
$231$		0			0
$232$	20.4685	−	1.79076i	1.34382	−	0.117569i
$233$	0.534587	+	0.143242i	0.0350220	+	0.00938411i	0.276287	−	0.961075i	$-0.410896\pi$
$233$	0.534587	+	0.143242i	0.0350220	+	0.00938411i	−0.241266	+	0.970459i	$0.577562\pi$
$234$		0			0
$235$	−8.73847	+	2.75398i	−0.570035	+	0.179650i
$236$	−7.93154	−	21.7917i	−0.516299	−	1.41852i
$237$		0			0
$238$	38.0181	+	3.32615i	2.46435	+	0.215602i
$239$	5.32354	+	1.93761i	0.344351	+	0.125334i	0.508406	−	0.861118i	$-0.330235\pi$
$239$	5.32354	+	1.93761i	0.344351	+	0.125334i	−0.164054	+	0.986451i	$0.552457\pi$
$240$		0			0
$241$	0.317967	−	1.80328i	0.0204821	−	0.116160i	−0.972853	−	0.231426i	$-0.925661\pi$
$241$	0.317967	−	1.80328i	0.0204821	−	0.116160i	0.993335	+	0.115266i	$0.0367721\pi$
$242$	19.8720	+	19.8720i	1.27742	+	1.27742i
$243$		0			0
$244$			31.6225i			2.02442i
$245$	5.47824	+	0.721948i	0.349992	+	0.0461236i
$246$		0			0
$247$	−2.36153	+	1.10120i	−0.150261	+	0.0700677i
$248$	1.34467	−	15.3696i	0.0853866	−	0.975973i
$249$		0			0
$250$	28.3758	+	8.95902i	1.79464	+	0.566618i
$251$	16.8470	+	9.72663i	1.06337	+	0.613939i	0.926364	−	0.376630i	$-0.122917\pi$
$251$	16.8470	+	9.72663i	1.06337	+	0.613939i	0.137011	+	0.990570i	$0.456251\pi$
$252$		0			0
$253$	0.0114171	−	0.0426091i	0.000717786	−	0.00267881i
$254$	−15.5228	−	13.0252i	−0.973988	−	0.817273i
$255$		0			0
$256$	0.280392	+	1.59018i	0.0175245	+	0.0993864i
$257$	17.1627	−	24.5109i	1.07058	−	1.52895i	0.241027	−	0.970518i	$-0.422516\pi$
$257$	17.1627	−	24.5109i	1.07058	−	1.52895i	0.829553	−	0.558428i	$-0.188595\pi$
$258$		0			0
$259$	−5.01616	+	5.97802i	−0.311689	+	0.371456i
$260$	−5.20697	−	1.15507i	−0.322923	−	0.0716343i
$261$		0			0
$262$	8.08418	+	30.1706i	0.499442	+	1.86394i
$263$	3.54766	−	7.60797i	0.218758	−	0.469128i	−0.766049	−	0.642782i	$-0.777780\pi$
$263$	3.54766	−	7.60797i	0.218758	−	0.469128i	0.984807	+	0.173655i	$0.0555577\pi$
$264$		0			0
$265$	1.04157	−	23.7851i	0.0639834	−	1.46110i
$266$	15.5574	−	42.7437i	0.953888	−	2.62079i
$267$		0			0
$268$	−22.7882	+	15.9565i	−1.39201	+	0.974696i
$269$	2.21545			0.135079			0.0675393	−	0.997717i	$-0.478485\pi$
$269$	2.21545			0.135079			0.0675393	+	0.997717i	$0.478485\pi$
$270$		0			0
$271$	−5.87725			−0.357017			−0.178509	−	0.983938i	$-0.557127\pi$
$271$	−5.87725			−0.357017			−0.178509	+	0.983938i	$0.557127\pi$
$272$	44.5627	−	31.2031i	2.70201	−	1.89197i
$273$		0			0
$274$	−6.12031	+	16.8154i	−0.369741	+	1.01586i
$275$	−2.34688	−	2.34810i	−0.141522	−	0.141596i
$276$		0			0
$277$	4.78156	−	10.2541i	0.287296	−	0.616108i	−0.708700	−	0.705510i	$-0.750718\pi$
$277$	4.78156	−	10.2541i	0.287296	−	0.616108i	0.995996	+	0.0894020i	$0.0284956\pi$
$278$	1.04600	+	3.90372i	0.0627348	+	0.234130i
$279$		0			0
$280$	47.6362	−	30.3389i	2.84681	−	1.81310i
$281$	−13.9719	+	16.6511i	−0.833496	+	0.993322i	0.166478	+	0.986045i	$0.446761\pi$
$281$	−13.9719	+	16.6511i	−0.833496	+	0.993322i	−0.999974	+	0.00727642i	$0.997684\pi$
$282$		0			0
$283$	−7.52820	+	10.7514i	−0.447505	+	0.639103i	−0.978005	−	0.208582i	$-0.933115\pi$
$283$	−7.52820	+	10.7514i	−0.447505	+	0.639103i	0.530500	+	0.847685i	$0.322004\pi$
$284$	−5.43342	−	30.8145i	−0.322414	−	1.82850i
$285$		0			0
$286$	0.635170	+	0.532971i	0.0375584	+	0.0315152i
$287$	−1.31589	+	4.91097i	−0.0776745	+	0.289885i
$288$		0			0
$289$	−4.07794	−	2.35440i	−0.239879	−	0.138494i
$290$	−13.7645	−	5.70352i	−0.808276	−	0.334922i
$291$		0			0
$292$	6.24497	−	71.3804i	0.365460	−	4.17722i
$293$	3.86399	−	1.80181i	0.225736	−	0.105263i	−0.306460	−	0.951884i	$-0.599145\pi$
$293$	3.86399	−	1.80181i	0.225736	−	0.105263i	0.532196	+	0.846621i	$0.321367\pi$
$294$		0			0
$295$	−1.33274	+	10.1130i	−0.0775950	+	0.588801i
$296$			20.8108i			1.20960i
$297$		0			0
$298$	−40.0708	−	40.0708i	−2.32124	−	2.32124i
$299$	−0.00541301	+	0.0306987i	−0.000313043	+	0.00177535i
$300$		0			0
$301$	24.2957	+	8.84290i	1.40038	+	0.509696i
$302$	21.0508	+	1.84171i	1.21134	+	0.105978i
$303$		0			0
$304$	−22.1768	−	60.9303i	−1.27193	−	3.49459i
$305$	6.42425	−	12.3370i	0.367852	−	0.706413i
$306$		0			0
$307$	17.9955	+	4.82189i	1.02706	+	0.275200i	0.732741	−	0.680508i	$-0.238241\pi$
$307$	17.9955	+	4.82189i	1.02706	+	0.275200i	0.294318	+	0.955707i	$0.404907\pi$
$308$	−10.3482	+	0.905354i	−0.589646	+	0.0515873i
$309$		0			0
$310$	−6.01243	+	9.43492i	−0.341483	+	0.535868i
$311$	8.07539	−	1.42391i	0.457913	−	0.0807425i	0.0600667	−	0.998194i	$-0.480869\pi$
$311$	8.07539	−	1.42391i	0.457913	−	0.0807425i	0.397847	+	0.917452i	$0.369758\pi$
$312$		0			0
$313$	−1.66176	−	18.9940i	−0.0939283	−	1.07360i	−0.886158	−	0.463382i	$-0.846636\pi$
$313$	−1.66176	−	18.9940i	−0.0939283	−	1.07360i	0.792230	−	0.610222i	$-0.208920\pi$
$314$	18.1941	+	31.5131i	1.02675	+	1.77839i
$315$		0			0
$316$	−13.7877	+	23.8811i	−0.775621	+	1.34342i
$317$	−15.3899	−	7.17642i	−0.864382	−	0.403068i	−0.0607206	−	0.998155i	$-0.519340\pi$
$317$	−15.3899	−	7.17642i	−0.864382	−	0.403068i	−0.803661	+	0.595087i	$0.797118\pi$
$318$		0			0
$319$	1.06849	+	1.27338i	0.0598241	+	0.0712956i
$320$	10.5404	−	33.4147i	0.589226	−	1.86794i
$321$		0			0
$322$	−0.312125	−	0.445761i	−0.0173941	−	0.0248413i
$323$	−18.2962	+	18.2962i	−1.01803	+	1.01803i
$324$		0			0
$325$	1.79675	+	1.50845i	0.0996659	+	0.0836738i
$326$	51.3243	+	9.04986i	2.84259	+	0.501225i
$327$		0			0
$328$	5.73003	+	12.2881i	0.316388	+	0.678497i
$329$	9.65980	−	8.10554i	0.532562	−	0.446873i
$330$		0			0
$331$	13.3657	−	4.86470i	0.734643	−	0.267388i	0.0525142	−	0.998620i	$-0.483277\pi$
$331$	13.3657	−	4.86470i	0.734643	−	0.267388i	0.682129	+	0.731232i	$0.261054\pi$
$332$	−27.8503	+	7.46247i	−1.52848	+	0.409556i
$333$		0			0
$334$	−50.6458	+	29.2404i	−2.77122	+	1.59996i
$335$	12.1320	−	1.59561i	0.662845	−	0.0871775i
$336$		0			0
$337$	5.58245	+	3.90887i	0.304095	+	0.212930i	0.715657	−	0.698452i	$-0.246128\pi$
$337$	5.58245	+	3.90887i	0.304095	+	0.212930i	−0.411561	+	0.911382i	$0.635016\pi$
$338$	27.8623	+	19.5094i	1.51551	+	1.06117i
$339$		0			0
$340$	−52.5111	+	6.90628i	−2.84781	+	0.374545i
$341$	1.08097	−	0.624097i	0.0585377	−	0.0337968i
$342$		0			0
$343$	13.4628	−	3.60734i	0.726922	−	0.194778i
$344$	64.7910	−	23.5820i	3.49330	−	1.27146i
$345$		0			0
$346$	−7.65094	+	6.41990i	−0.411317	+	0.345136i
$347$	−5.81216	−	12.4642i	−0.312013	−	0.669114i	0.686291	−	0.727327i	$-0.259238\pi$
$347$	−5.81216	−	12.4642i	−0.312013	−	0.669114i	−0.998304	+	0.0582130i	$0.981460\pi$
$348$		0			0
$349$	26.3484	+	4.64594i	1.41040	+	0.248691i	0.826409	−	0.563070i	$-0.190380\pi$
$349$	26.3484	+	4.64594i	1.41040	+	0.248691i	0.583990	+	0.811761i	$0.301491\pi$
$350$	−40.7993	+	3.55879i	−2.18081	+	0.190225i
$351$		0			0
$352$	−6.88345	+	6.88345i	−0.366889	+	0.366889i
$353$	0.0271374	+	0.0387563i	0.00144438	+	0.00206279i	0.819874	−	0.572545i	$-0.194044\pi$
$353$	0.0271374	+	0.0387563i	0.00144438	+	0.00206279i	−0.818429	+	0.574607i	$0.805155\pi$
$354$		0			0
$355$	−4.14035	+	13.1256i	−0.219747	+	0.696633i
$356$	−20.1375	−	23.9989i	−1.06729	−	1.27194i
$357$		0			0
$358$	34.7997	+	16.2274i	1.83922	+	0.857644i
$359$	9.42597	−	16.3263i	0.497484	−	0.861667i	−0.502512	−	0.864570i	$-0.667591\pi$
$359$	9.42597	−	16.3263i	0.497484	−	0.861667i	0.999996	+	0.00290290i	$0.000924023\pi$
$360$		0			0
$361$	5.92010	+	10.2539i	0.311584	+	0.539680i
$362$	3.27707	+	37.4571i	0.172239	+	1.96870i
$363$		0			0
$364$	7.22909	−	1.27468i	0.378907	−	0.0668116i
$365$	−16.9376	+	26.5791i	−0.886556	+	1.39122i
$366$		0			0
$367$	−19.7504	+	1.72794i	−1.03096	+	0.0901977i	−0.590063	−	0.807357i	$-0.700897\pi$
$367$	−19.7504	+	1.72794i	−1.03096	+	0.0901977i	−0.440902	+	0.897555i	$0.645341\pi$
$368$	−0.749277	−	0.200768i	−0.0390588	−	0.0104658i
$369$		0			0
$370$	6.96994	−	13.3849i	0.362350	−	0.695847i
$371$	11.2070	+	30.7909i	0.581836	+	1.59858i
$372$		0			0
$373$	21.1273	+	1.84840i	1.09393	+	0.0957063i	0.619808	−	0.784754i	$-0.287211\pi$
$373$	21.1273	+	1.84840i	1.09393	+	0.0957063i	0.474120	+	0.880460i	$0.342766\pi$
$374$	7.73714	+	2.81609i	0.400078	+	0.145616i
$375$		0			0
$376$	5.83943	−	33.1170i	0.301145	−	1.70788i
$377$	−0.830613	−	0.830613i	−0.0427788	−	0.0427788i
$378$		0			0
$379$		−	4.95221i		−	0.254378i	−0.991878	−	0.127189i	$-0.959405\pi$
$379$		−	4.95221i		−	0.254378i	0.991878	−	0.127189i	$-0.0405955\pi$
$380$	−8.24787	+	62.5860i	−0.423107	+	3.21059i
$381$		0			0
$382$	6.23894	−	2.90926i	0.319212	−	0.148851i
$383$	−2.46502	+	28.1753i	−0.125957	+	1.43969i	0.625663	+	0.780093i	$0.284828\pi$
$383$	−2.46502	+	28.1753i	−0.125957	+	1.43969i	−0.751620	+	0.659596i	$0.770727\pi$
$384$		0			0
$385$	4.22111	+	1.74909i	0.215128	+	0.0891416i
$386$	−32.8569	−	18.9699i	−1.67237	−	0.965545i
$387$		0			0
$388$	−17.9388	+	66.9484i	−0.910703	+	3.39879i
$389$	−22.5434	−	18.9162i	−1.14300	−	0.959088i	−0.143463	−	0.989656i	$-0.545824\pi$
$389$	−22.5434	−	18.9162i	−1.14300	−	0.959088i	−0.999533	+	0.0305681i	$0.990268\pi$
$390$		0			0
$391$	0.0537524	+	0.304845i	0.00271838	+	0.0154167i
$392$	−11.6325	+	16.6129i	−0.587530	+	0.839080i
$393$		0			0
$394$	14.2783	−	17.0163i	0.719332	−	0.857267i
$395$	10.2306	−	6.51574i	0.514757	−	0.327843i
$396$		0			0
$397$	−5.07320	−	18.9334i	−0.254616	−	0.950242i	−0.968303	−	0.249777i	$-0.919643\pi$
$397$	−5.07320	−	18.9334i	−0.254616	−	0.950242i	0.713687	−	0.700465i	$-0.247024\pi$
$398$	4.25115	−	9.11662i	0.213091	−	0.456975i
$399$		0			0
$400$	−41.2911	+	41.2697i	−2.06456	+	2.06348i
$401$	0.0115561	−	0.0317502i	0.000577086	−	0.00158553i	−0.939404	−	0.342813i	$-0.888620\pi$
$401$	0.0115561	−	0.0317502i	0.000577086	−	0.00158553i	0.939981	+	0.341227i	$0.110843\pi$
$402$		0			0
$403$	−0.722531	+	0.505922i	−0.0359918	+	0.0252018i
$404$	9.36163			0.465759
$405$		0			0
$406$	20.5061			1.01770
$407$	−1.37917	+	0.965702i	−0.0683627	+	0.0478681i
$408$		0			0
$409$	3.01485	−	8.28322i	0.149075	−	0.409579i	−0.842569	−	0.538589i	$-0.818958\pi$
$409$	3.01485	−	8.28322i	0.149075	−	0.409579i	0.991643	+	0.129010i	$0.0411799\pi$
$410$	0.430135	−	9.82242i	0.0212428	−	0.485095i
$411$		0			0
$412$	−35.0892	+	75.2490i	−1.72872	+	3.70725i
$413$	−3.63355	−	13.5606i	−0.178795	−	0.667272i
$414$		0			0
$415$	12.3814	+	2.74657i	0.607777	+	0.134824i
$416$	4.42180	−	5.26969i	0.216796	−	0.258368i
$417$		0			0
$418$	5.62894	−	8.03896i	0.275320	−	0.393198i
$419$	5.75122	+	32.6168i	0.280966	+	1.59344i	0.719350	+	0.694648i	$0.244440\pi$
$419$	5.75122	+	32.6168i	0.280966	+	1.59344i	−0.438384	+	0.898788i	$0.644449\pi$
$420$		0			0
$421$	12.7180	+	10.6716i	0.619835	+	0.520104i	0.897752	−	0.440502i	$-0.145199\pi$
$421$	12.7180	+	10.6716i	0.619835	+	0.520104i	−0.277916	+	0.960605i	$0.589644\pi$
$422$	−12.2648	+	45.7728i	−0.597040	+	2.22819i
$423$		0			0
$424$	75.6750	+	43.6910i	3.67510	+	2.12182i
$425$	21.8893	+	7.97351i	1.06179	+	0.386772i
$426$		0			0
$427$	−1.66848	+	19.0708i	−0.0807433	+	0.922901i
$428$	−68.3368	+	31.8660i	−3.30318	+	1.54030i
$429$		0			0
$430$	−49.5696	−	6.53252i	−2.39046	−	0.315026i
$431$		−	14.4385i		−	0.695480i	−0.937591	−	0.347740i	$-0.886949\pi$
$431$		−	14.4385i		−	0.695480i	0.937591	−	0.347740i	$-0.113051\pi$
$432$		0			0
$433$	16.4822	+	16.4822i	0.792085	+	0.792085i	0.981833	−	0.189748i	$-0.0607670\pi$
$433$	16.4822	+	16.4822i	0.792085	+	0.792085i	−0.189748	+	0.981833i	$0.560767\pi$
$434$	2.67381	−	15.1640i	0.128347	−	0.727893i
$435$		0			0
$436$	−44.6611	−	16.2553i	−2.13888	−	0.778488i
$437$	0.367547	+	0.0321562i	0.0175821	+	0.00153824i
$438$		0			0
$439$	−10.9388	−	30.0541i	−0.522080	−	1.43440i	−0.868201	−	0.496213i	$-0.834723\pi$
$439$	−10.9388	−	30.0541i	−0.522080	−	1.43440i	0.346121	−	0.938190i	$-0.387499\pi$
$440$	11.6214	−	3.66255i	0.554028	−	0.174605i
$441$		0			0
$442$	−5.62015	−	1.50592i	−0.267323	−	0.0716291i
$443$	−17.8910	+	1.56526i	−0.850027	+	0.0743677i	−0.503839	−	0.863798i	$-0.668080\pi$
$443$	−17.8910	+	1.56526i	−0.850027	+	0.0743677i	−0.346188	+	0.938165i	$0.612524\pi$
$444$		0			0
$445$	2.98080	+	13.4538i	0.141304	+	0.637771i
$446$	−50.1811	+	8.84827i	−2.37614	+	0.418978i
$447$		0			0
$448$	4.20289	+	48.0392i	0.198568	+	2.26964i
$449$	6.63475	+	11.4917i	0.313113	+	0.542328i	0.979035	−	0.203694i	$-0.0652947\pi$
$449$	6.63475	+	11.4917i	0.313113	+	0.542328i	−0.665921	+	0.746022i	$0.731961\pi$
$450$		0			0
$451$	−0.548456	+	0.949953i	−0.0258258	+	0.0447316i
$452$	−95.7323	−	44.6407i	−4.50287	−	2.09972i
$453$		0			0
$454$	0.825948	+	0.984327i	0.0387637	+	0.0461968i
$455$	−3.07926	−	0.971328i	−0.144358	−	0.0455365i
$456$		0			0
$457$	−4.61784	−	6.59496i	−0.216013	−	0.308499i	0.696491	−	0.717565i	$-0.254743\pi$
$457$	−4.61784	−	6.59496i	−0.216013	−	0.308499i	−0.912505	+	0.409066i	$0.865855\pi$
$458$	28.2789	−	28.2789i	1.32138	−	1.32138i
$459$		0			0
$460$	0.556732	+	0.510284i	0.0259578	+	0.0237921i
$461$	14.1578	+	2.49640i	0.659393	+	0.116269i	0.493324	−	0.869846i	$-0.335782\pi$
$461$	14.1578	+	2.49640i	0.659393	+	0.116269i	0.166068	+	0.986114i	$0.446893\pi$
$462$		0			0
$463$	8.79261	+	18.8558i	0.408627	+	0.876304i	0.997671	+	0.0682032i	$0.0217266\pi$
$463$	8.79261	+	18.8558i	0.408627	+	0.876304i	−0.589044	+	0.808101i	$0.700496\pi$
$464$	22.3922	−	18.7893i	1.03953	−	0.872272i
$465$		0			0
$466$	1.38417	−	0.503795i	0.0641202	−	0.0233378i
$467$	23.8222	−	6.38314i	1.10236	−	0.295376i	0.338635	−	0.940918i	$-0.390035\pi$
$467$	23.8222	−	6.38314i	1.10236	−	0.295376i	0.763725	+	0.645542i	$0.223368\pi$
$468$		0			0
$469$	−14.5849	+	8.42062i	−0.673470	+	0.388828i
$470$	−14.8473	+	19.3441i	−0.684853	+	0.892278i
$471$		0			0
$472$	−30.6679	−	21.4739i	−1.41161	−	0.988418i
$473$	4.56937	+	3.19951i	0.210100	+	0.147113i
$474$		0			0
$475$	15.9324	−	22.7412i	0.731028	−	1.04344i
$476$	63.1279	−	36.4469i	2.89346	−	1.67054i
$477$		0			0
$478$	14.5642	−	3.90246i	0.666150	−	0.178494i
$479$	−25.2593	+	9.19362i	−1.15412	+	0.420067i	−0.846995	−	0.531601i	$-0.821591\pi$
$479$	−25.2593	+	9.19362i	−1.15412	+	0.420067i	−0.307130	+	0.951668i	$0.599368\pi$
$480$		0			0
$481$	0.911414	−	0.764768i	0.0415569	−	0.0348704i
$482$	−2.05962	−	4.41687i	−0.0938132	−	0.201183i
$483$		0			0
$484$	52.8631	+	9.32118i	2.40287	+	0.423690i
$485$	20.5994	−	22.4744i	0.935369	−	1.02051i
$486$		0			0
$487$	1.39406	−	1.39406i	0.0631711	−	0.0631711i	−0.674815	−	0.737987i	$-0.735777\pi$
$487$	1.39406	−	1.39406i	0.0631711	−	0.0631711i	0.737987	+	0.674815i	$0.235777\pi$
$488$	29.2821	+	41.8191i	1.32554	+	1.89306i
$489$		0			0
$490$	13.0456	−	6.78898i	0.589342	−	0.306695i
$491$	15.2423	+	18.1651i	0.687875	+	0.819777i	0.991097	−	0.133143i	$-0.0425068\pi$
$491$	15.2423	+	18.1651i	0.687875	+	0.819777i	−0.303222	+	0.952920i	$0.598062\pi$
$492$		0			0
$493$	−10.5718	−	4.92970i	−0.476129	−	0.222023i
$494$	−3.46749	+	6.00587i	−0.156010	+	0.270217i
$495$		0			0
$496$	−10.9747	−	19.0087i	−0.492778	−	0.853516i
$497$	−1.65093	−	18.8702i	−0.0740542	−	0.846444i
$498$		0			0
$499$	30.8900	−	5.44673i	1.38282	−	0.243829i	0.567758	−	0.823196i	$-0.307811\pi$
$499$	30.8900	−	5.44673i	1.38282	−	0.243829i	0.815067	+	0.579366i	$0.196700\pi$
$500$	54.2126	−	17.0699i	2.42446	−	0.763390i
$501$		0			0
$502$	51.5779	−	4.51248i	2.30204	−	0.201402i
$503$	5.95437	+	1.59547i	0.265492	+	0.0711385i	0.389109	−	0.921192i	$-0.372783\pi$
$503$	5.95437	+	1.59547i	0.265492	+	0.0711385i	−0.123617	+	0.992330i	$0.539449\pi$
$504$		0			0
$505$	−3.65228	−	1.90186i	−0.162524	−	0.0846317i
$506$	−0.0401548	−	0.110325i	−0.00178510	−	0.00490452i
$507$		0			0
$508$	−38.5572	−	3.37332i	−1.71070	−	0.149667i
$509$	−18.3832	−	6.69092i	−0.814819	−	0.296570i	−0.0992061	−	0.995067i	$-0.531630\pi$
$509$	−18.3832	−	6.69092i	−0.814819	−	0.296570i	−0.715613	+	0.698497i	$0.753853\pi$
$510$		0			0
$511$	7.53240	−	42.7184i	0.333214	−	1.88975i
$512$	−14.4712	−	14.4712i	−0.639545	−	0.639545i
$513$		0			0
$514$		−	79.6382i		−	3.51269i
$515$	28.9766	−	22.2286i	1.27686	−	0.979507i
$516$		0			0
$517$	2.46569	−	1.14977i	0.108441	−	0.0505668i
$518$	−1.81020	+	20.6907i	−0.0795357	+	0.909097i
$519$		0			0
$520$	−7.95554	+	3.29408i	−0.348873	+	0.144455i
$521$	−1.02507	−	0.591824i	−0.0449091	−	0.0259283i	0.477377	−	0.878698i	$-0.341587\pi$
$521$	−1.02507	−	0.591824i	−0.0449091	−	0.0259283i	−0.522286	+	0.852770i	$0.674921\pi$
$522$		0			0
$523$	−11.5734	+	43.1925i	−0.506069	+	1.88868i	−0.0499636	+	0.998751i	$0.515911\pi$
$523$	−11.5734	+	43.1925i	−0.506069	+	1.88868i	−0.456106	+	0.889926i	$0.650756\pi$
$524$	45.7023	+	38.3488i	1.99652	+	1.67528i
$525$		0			0
$526$	−3.87963	−	22.0025i	−0.169160	−	0.959354i
$527$	−5.02391	+	7.17489i	−0.218845	+	0.312543i
$528$		0			0
$529$	−14.7813	+	17.6156i	−0.642664	+	0.765897i
$530$	−34.0389	−	53.4457i	−1.47856	−	2.32153i
$531$		0			0
$532$	−22.4868	−	83.9219i	−0.974927	−	3.63848i
$533$	0.327589	−	0.702518i	0.0141895	−	0.0304294i
$534$		0			0
$535$	33.1341	+	1.45098i	1.43251	+	0.0627313i
$536$	−15.3607	+	42.2032i	−0.663482	+	1.82290i
$537$		0			0
$538$	4.83008	−	3.38206i	0.208240	−	0.145811i
$539$	−1.64076			−0.0706724
$540$		0			0
$541$	−0.781277			−0.0335897			−0.0167949	−	0.999859i	$-0.505346\pi$
$541$	−0.781277			−0.0335897			−0.0167949	+	0.999859i	$0.505346\pi$
$542$	−12.8134	+	8.97207i	−0.550384	+	0.385383i
$543$		0			0
$544$	23.3637	−	64.1912i	1.00171	−	2.75218i
$545$	14.1214	+	15.4148i	0.604895	+	0.660299i
$546$		0			0
$547$	−4.68743	+	10.0522i	−0.200420	+	0.429802i	−0.980671	−	0.195665i	$-0.937314\pi$
$547$	−4.68743	+	10.0522i	−0.200420	+	0.429802i	0.780251	+	0.625467i	$0.215091\pi$
$548$	8.84632	+	33.0149i	0.377896	+	1.41033i
$549$		0			0
$550$	−8.70118	−	1.53658i	−0.371020	−	0.0655202i
$551$	−8.93677	+	10.6504i	−0.380719	+	0.453724i
$552$		0			0
$553$	−9.57510	+	13.6747i	−0.407175	+	0.581505i
$554$	−5.22900	−	29.6551i	−0.222159	−	1.25993i
$555$		0			0
$556$	5.91335	+	4.96189i	0.250782	+	0.210431i
$557$	−3.48849	+	13.0192i	−0.147812	+	0.551642i	0.851802	+	0.523864i	$0.175510\pi$
$557$	−3.48849	+	13.0192i	−0.147812	+	0.551642i	−0.999614	+	0.0277782i	$0.991157\pi$
$558$		0			0
$559$	−3.41375	−	1.97093i	−0.144386	−	0.0833615i
$560$	30.7575	−	74.2278i	1.29974	−	3.13670i
$561$		0			0
$562$	−5.04211	+	57.6316i	−0.212689	+	2.43104i
$563$	34.0720	−	15.8881i	1.43596	−	0.669601i	0.460078	−	0.887878i	$-0.347821\pi$
$563$	34.0720	−	15.8881i	1.43596	−	0.669601i	0.975887	+	0.218277i	$0.0700436\pi$
$564$		0			0
$565$	28.2793	+	36.8643i	1.18972	+	1.55089i
$566$			34.9323i			1.46831i
$567$		0			0
$568$	−35.7193	−	35.7193i	−1.49875	−	1.49875i
$569$	−2.09817	+	11.8993i	−0.0879598	+	0.498845i	0.908719	+	0.417409i	$0.137062\pi$
$569$	−2.09817	+	11.8993i	−0.0879598	+	0.498845i	−0.996679	+	0.0814360i	$0.974049\pi$
$570$		0			0
$571$	0.672547	+	0.244787i	0.0281452	+	0.0102440i	0.356054	−	0.934465i	$-0.384122\pi$
$571$	0.672547	+	0.244787i	0.0281452	+	0.0102440i	−0.327909	+	0.944709i	$0.606344\pi$
$572$	1.57770	+	0.138031i	0.0659670	+	0.00577137i
$573$		0			0
$574$	4.62809	+	12.7156i	0.193173	+	0.530738i
$575$	−0.113533	−	0.312181i	−0.00473464	−	0.0130189i
$576$		0			0
$577$	−36.1045	−	9.67417i	−1.50305	−	0.402741i	−0.588930	−	0.808184i	$-0.700451\pi$
$577$	−36.1045	−	9.67417i	−1.50305	−	0.402741i	−0.914120	+	0.405443i	$0.867117\pi$
$578$	−12.4848	+	1.09228i	−0.519300	+	0.0454328i
$579$		0			0
$580$	−27.7847	+	6.15593i	−1.15370	+	0.255611i
$581$	−17.1896	+	3.03100i	−0.713146	+	0.125747i
$582$		0			0
$583$	0.616142	+	7.04253i	0.0255180	+	0.291672i
$584$	−57.8388	−	100.180i	−2.39339	−	4.14547i
$585$		0			0
$586$	5.67358	−	9.82693i	0.234373	−	0.405947i
$587$	8.34577	+	3.89170i	0.344467	+	0.160628i	0.587150	−	0.809478i	$-0.300250\pi$
$587$	8.34577	+	3.89170i	0.344467	+	0.160628i	−0.242683	+	0.970106i	$0.578028\pi$
$588$		0			0
$589$	6.71056	+	7.99734i	0.276504	+	0.329525i
$590$	12.5327	+	24.0826i	0.515961	+	0.991467i
$591$		0			0
$592$	16.9818	+	24.2525i	0.697946	+	0.996771i
$593$	−9.96484	+	9.96484i	−0.409207	+	0.409207i	−0.881462	−	0.472255i	$-0.843440\pi$
$593$	−9.96484	+	9.96484i	−0.409207	+	0.409207i	0.472255	+	0.881462i	$0.343440\pi$
$594$		0			0
$595$	−32.0326	+	1.39441i	−1.31321	+	0.0571651i
$596$	−106.595	−	18.7957i	−4.36632	−	0.769900i
$597$		0			0
$598$	0.0350626	+	0.0751920i	0.00143382	+	0.00307483i
$599$	5.73610	−	4.81316i	0.234371	−	0.196660i	−0.518037	−	0.855358i	$-0.673337\pi$
$599$	5.73610	−	4.81316i	0.234371	−	0.196660i	0.752407	+	0.658698i	$0.228893\pi$
$600$		0			0
$601$	−20.4882	+	7.45708i	−0.835730	+	0.304181i	−0.724208	−	0.689581i	$-0.757795\pi$
$601$	−20.4882	+	7.45708i	−0.835730	+	0.304181i	−0.111522	+	0.993762i	$0.535572\pi$
$602$	66.4682	−	17.8101i	2.70904	−	0.725886i
$603$		0			0
$604$	34.9543	−	20.1809i	1.42227	−	0.821148i
$605$	−18.7300	−	14.3759i	−0.761481	−	0.584462i
$606$		0			0
$607$	−18.7469	−	13.1267i	−0.760912	−	0.532796i	0.127503	−	0.991838i	$-0.459304\pi$
$607$	−18.7469	−	13.1267i	−0.760912	−	0.532796i	−0.888415	+	0.459042i	$0.848193\pi$
$608$	−66.6953	−	46.7005i	−2.70485	−	1.89396i
$609$		0			0
$610$	−4.82731	−	36.7039i	−0.195452	−	1.48610i
$611$	−1.66496	+	0.961264i	−0.0673570	+	0.0388886i
$612$		0			0
$613$	−14.4667	+	3.87633i	−0.584303	+	0.156564i	−0.538848	−	0.842403i	$-0.681140\pi$
$613$	−14.4667	+	3.87633i	−0.584303	+	0.156564i	−0.0454549	+	0.998966i	$0.514474\pi$
$614$	46.5944	−	16.9590i	1.88040	−	0.684409i
$615$		0			0
$616$	−12.8467	+	10.7796i	−0.517607	+	0.434324i
$617$	−0.200538	−	0.430054i	−0.00807334	−	0.0173133i	0.902230	−	0.431256i	$-0.141929\pi$
$617$	−0.200538	−	0.430054i	−0.00807334	−	0.0173133i	−0.910303	+	0.413942i	$0.864152\pi$
$618$		0			0
$619$	−10.1152	−	1.78359i	−0.406565	−	0.0716885i	−0.0333743	−	0.999443i	$-0.510625\pi$
$619$	−10.1152	−	1.78359i	−0.406565	−	0.0716885i	−0.373191	+	0.927754i	$0.621736\pi$
$620$	0.929342	+	21.3491i	0.0373233	+	0.857399i
$621$		0			0
$622$	15.4321	−	15.4321i	0.618770	−	0.618770i
$623$	−10.8782	−	15.5357i	−0.435827	−	0.622425i
$624$		0			0
$625$	−24.6179	−	4.35400i	−0.984717	−	0.174160i
$626$	−32.6187	−	38.8735i	−1.30371	−	1.55370i
$627$		0			0
$628$	62.9913	+	29.3733i	2.51363	+	1.17212i
$629$	5.90732	−	10.2318i	0.235540	−	0.407968i
$630$		0			0
$631$	−6.48152	−	11.2263i	−0.258025	−	0.446913i	0.707688	−	0.706526i	$-0.249738\pi$
$631$	−6.48152	−	11.2263i	−0.258025	−	0.446913i	−0.965713	+	0.259613i	$0.916405\pi$
$632$	3.88002	+	44.3488i	0.154339	+	1.76410i
$633$		0			0
$634$	−44.5080	+	7.84797i	−1.76764	+	0.311683i
$635$	14.3571	+	9.14912i	0.569745	+	0.363072i
$636$		0			0
$637$	1.15504	−	0.101053i	0.0457645	−	0.00400388i
$638$	4.27341	+	1.14506i	0.169186	+	0.0453333i
$639$		0			0
$640$	−8.32187	−	26.4056i	−0.328951	−	1.04377i
$641$	−16.0051	−	43.9737i	−0.632164	−	1.73686i	−0.675045	−	0.737777i	$-0.735876\pi$
$641$	−16.0051	−	43.9737i	−0.632164	−	1.73686i	0.0428806	−	0.999080i	$-0.486347\pi$
$642$		0			0
$643$	−22.0886	−	1.93250i	−0.871088	−	0.0762103i	−0.357160	−	0.934043i	$-0.616255\pi$
$643$	−22.0886	−	1.93250i	−0.871088	−	0.0762103i	−0.513928	+	0.857833i	$0.671810\pi$
$644$	−0.976716	−	0.355496i	−0.0384880	−	0.0140085i
$645$		0			0
$646$	−11.9584	+	67.8196i	−0.470498	+	2.66833i
$647$	23.9696	+	23.9696i	0.942341	+	0.942341i	0.998426	−	0.0560849i	$-0.0178617\pi$
$647$	23.9696	+	23.9696i	0.942341	+	0.942341i	−0.0560849	+	0.998426i	$0.517862\pi$
$648$		0			0
$649$		−	3.02889i		−	0.118894i
$650$	6.22001	+	0.545809i	0.243969	+	0.0214084i
$651$		0			0
$652$	90.2178	−	42.0693i	3.53320	−	1.64756i
$653$	0.846075	−	9.67068i	0.0331095	−	0.378443i	−0.961504	−	0.274791i	$-0.911391\pi$
$653$	0.846075	−	9.67068i	0.0331095	−	0.378443i	0.994614	−	0.103652i	$-0.0330530\pi$
$654$		0			0
$655$	−10.0392	−	24.2458i	−0.392266	−	0.947361i
$656$	16.7048	+	9.64453i	0.652214	+	0.376556i
$657$		0			0
$658$	8.68636	−	32.4179i	0.338629	−	1.26378i
$659$	15.9731	+	13.4030i	0.622224	+	0.522108i	0.898502	−	0.438970i	$-0.144657\pi$
$659$	15.9731	+	13.4030i	0.622224	+	0.522108i	−0.276278	+	0.961078i	$0.589101\pi$
$660$		0			0
$661$	−6.68365	−	37.9049i	−0.259964	−	1.47433i	−0.783002	−	0.622020i	$-0.786312\pi$
$661$	−6.68365	−	37.9049i	−0.259964	−	1.47433i	0.523038	−	0.852310i	$-0.324799\pi$
$662$	21.7132	−	31.0096i	0.843906	−	1.20522i
$663$		0			0
$664$	−29.9205	+	35.6578i	−1.16114	+	1.38379i
$665$	−8.27629	+	37.3090i	−0.320941	+	1.44678i
$666$		0			0
$667$	0.0430488	+	0.160660i	0.00166685	+	0.00622079i
$668$	−47.2070	+	101.236i	−1.82649	+	3.91693i
$669$		0			0
$670$	24.0142	−	21.9992i	0.927749	−	0.849904i
$671$	−1.41262	+	3.88114i	−0.0545335	+	0.149830i
$672$		0			0
$673$	16.8631	−	11.8077i	0.650026	−	0.455153i	−0.201484	−	0.979492i	$-0.564576\pi$
$673$	16.8631	−	11.8077i	0.650026	−	0.455153i	0.851510	+	0.524339i	$0.175687\pi$
$674$	18.1379			0.698646
$675$		0			0
$676$	64.9678			2.49876
$677$	−18.5670	+	13.0007i	−0.713588	+	0.499659i	−0.873103	−	0.487536i	$-0.837896\pi$
$677$	−18.5670	+	13.0007i	−0.713588	+	0.499659i	0.159515	+	0.987195i	$0.449007\pi$
$678$		0			0
$679$	−14.3508	+	39.4285i	−0.550734	+	1.51313i
$680$	−63.0481	+	57.7579i	−2.41778	+	2.21491i
$681$		0			0
$682$	1.40397	−	3.01082i	0.0537608	−	0.115290i
$683$	−2.12172	−	7.91835i	−0.0811852	−	0.302987i	0.913379	−	0.407110i	$-0.133463\pi$
$683$	−2.12172	−	7.91835i	−0.0811852	−	0.302987i	−0.994564	+	0.104122i	$0.966797\pi$
$684$		0			0
$685$	3.25589	−	14.6774i	0.124401	−	0.560793i
$686$	23.8444	−	28.4166i	0.910382	−	1.08495i
$687$		0			0
$688$	56.2630	−	80.3518i	2.14500	−	3.06338i
$689$	−0.867490	−	4.91978i	−0.0330487	−	0.187429i
$690$		0			0
$691$	2.09562	+	1.75844i	0.0797212	+	0.0668941i	0.681777	−	0.731560i	$-0.261207\pi$
$691$	2.09562	+	1.75844i	0.0797212	+	0.0668941i	−0.602056	+	0.798454i	$0.705652\pi$
$692$	−4.93744	+	18.4268i	−0.187693	+	0.700481i
$693$		0			0
$694$	−31.6991	−	18.3015i	−1.20328	−	0.694715i
$695$	−1.29896	−	3.13712i	−0.0492724	−	0.118998i
$696$		0			0
$697$	0.670867	−	7.66804i	0.0254109	−	0.290448i
$698$	64.5366	−	30.0939i	2.44275	−	1.13907i
$699$		0			0
$700$	−59.9365	+	50.2662i	−2.26539	+	1.89988i
$701$		−	45.2015i		−	1.70724i	−0.520899	−	0.853618i	$-0.674403\pi$
$701$		−	45.2015i		−	1.70724i	0.520899	−	0.853618i	$-0.325597\pi$
$702$		0			0
$703$	−9.95741	−	9.95741i	−0.375551	−	0.375551i
$704$	−1.80664	+	10.2459i	−0.0680901	+	0.386158i
$705$		0			0
$706$	0.118329	+	0.0430682i	0.00445337	+	0.00162089i
$707$	5.64579	+	0.493942i	0.212332	+	0.0185766i
$708$		0			0
$709$	−6.90171	−	18.9623i	−0.259199	−	0.712144i	−0.999217	−	0.0395569i	$-0.987405\pi$
$709$	−6.90171	−	18.9623i	−0.259199	−	0.712144i	0.740018	−	0.672587i	$-0.234817\pi$
$710$	11.0105	+	34.9366i	0.413216	+	1.31115i
$711$		0			0
$712$	−48.8536	−	13.0903i	−1.83086	−	0.490579i
$713$	0.124419	−	0.0108853i	0.00465953	−	0.000407656i
$714$		0			0
$715$	−0.587471	−	0.374368i	−0.0219702	−	0.0140006i
$716$	72.2265	−	12.7355i	2.69923	−	0.475947i
$717$		0			0
$718$	−4.37300	−	49.9836i	−0.163199	−	1.86537i
$719$	−18.2157	−	31.5505i	−0.679331	−	1.17664i	−0.975183	−	0.221402i	$-0.928937\pi$
$719$	−18.2157	−	31.5505i	−0.679331	−	1.17664i	0.295852	−	0.955234i	$-0.404396\pi$
$720$		0			0
$721$	−25.1318	+	43.5295i	−0.935957	+	1.62113i
$722$	28.5603	+	13.3179i	1.06290	+	0.495640i
$723$		0			0
$724$	46.1638	+	55.0159i	1.71566	+	2.04465i
$725$	12.0903	+	3.24296i	0.449024	+	0.120441i
$726$		0			0
$727$	−7.67153	−	10.9561i	−0.284521	−	0.406338i	0.651296	−	0.758824i	$-0.274226\pi$
$727$	−7.67153	−	10.9561i	−0.284521	−	0.406338i	−0.935817	+	0.352485i	$0.885337\pi$
$728$	8.37976	−	8.37976i	0.310575	−	0.310575i
$729$		0			0
$730$	3.64805	+	83.8038i	0.135020	+	3.10172i
$731$	−38.5489	−	6.79721i	−1.42578	−	0.251404i
$732$		0			0
$733$	−17.7462	−	38.0568i	−0.655470	−	1.40566i	−0.899944	−	0.436005i	$-0.856393\pi$
$733$	−17.7462	−	38.0568i	−0.655470	−	1.40566i	0.244474	−	0.969656i	$-0.421385\pi$
$734$	−40.4216	+	33.9178i	−1.49199	+	1.25193i
$735$		0			0
$736$	−0.915308	+	0.333145i	−0.0337387	+	0.0122799i
$737$	−3.50967	+	0.940413i	−0.129280	+	0.0346406i
$738$		0			0
$739$	34.0711	−	19.6709i	1.25332	−	0.723607i	0.281556	−	0.959545i	$-0.409150\pi$
$739$	34.0711	−	19.6709i	1.25332	−	0.723607i	0.971768	+	0.235938i	$0.0758162\pi$
$740$	−3.75862	−	28.5783i	−0.138170	−	1.05056i
$741$		0			0
$742$	71.4378	+	50.0213i	2.62256	+	1.83634i
$743$	−10.6136	−	7.43173i	−0.389376	−	0.272644i	0.362453	−	0.932002i	$-0.381939\pi$
$743$	−10.6136	−	7.43173i	−0.389376	−	0.272644i	−0.751829	+	0.659358i	$0.770828\pi$
$744$		0			0
$745$	37.7680	+	28.9882i	1.38371	+	1.06204i
$746$	48.8829	−	28.2225i	1.78973	−	1.03330i
$747$		0			0
$748$	15.1909	−	4.07039i	0.555434	−	0.148828i
$749$	−42.8937	+	15.6120i	−1.56730	+	0.570451i
$750$		0			0
$751$	30.6700	−	25.7352i	1.11916	−	0.939089i	0.120601	−	0.992701i	$-0.461518\pi$
$751$	30.6700	−	25.7352i	1.11916	−	0.939089i	0.998562	+	0.0536119i	$0.0170734\pi$
$752$	−20.2186	−	43.3589i	−0.737296	−	1.58114i
$753$		0			0
$754$	−3.07888	−	0.542889i	−0.112126	−	0.0197709i
$755$	−17.7367	+	0.772091i	−0.645503	+	0.0280993i
$756$		0			0
$757$	0.846964	−	0.846964i	0.0307834	−	0.0307834i	−0.691548	−	0.722331i	$-0.743071\pi$
$757$	0.846964	−	0.846964i	0.0307834	−	0.0307834i	0.722331	+	0.691548i	$0.243071\pi$
$758$	−7.55993	−	10.7967i	−0.274589	−	0.392154i
$759$		0			0
$760$	47.0465	+	90.4042i	1.70656	+	3.27930i
$761$	3.25980	+	3.88488i	0.118168	+	0.140827i	0.821885	−	0.569653i	$-0.192922\pi$
$761$	3.25980	+	3.88488i	0.118168	+	0.140827i	−0.703718	+	0.710480i	$0.748478\pi$
$762$		0			0
$763$	−26.0764	−	12.1596i	−0.944029	−	0.440208i
$764$	6.57430	−	11.3870i	0.237850	−	0.411968i
$765$		0			0
$766$	37.6375	+	65.1901i	1.35990	+	2.35542i
$767$	0.186547	+	2.13224i	0.00673583	+	0.0769909i
$768$		0			0
$769$	26.0795	−	4.59852i	0.940451	−	0.165827i	0.317651	−	0.948208i	$-0.397106\pi$
$769$	26.0795	−	4.59852i	0.940451	−	0.165827i	0.622800	+	0.782381i	$0.285995\pi$
$770$	11.8729	−	2.63054i	0.427869	−	0.0947980i
$771$		0			0
$772$	−72.1914	+	6.31593i	−2.59822	+	0.227315i
$773$	10.4941	+	2.81189i	0.377447	+	0.101137i	0.442555	−	0.896742i	$-0.354072\pi$
$773$	10.4941	+	2.81189i	0.377447	+	0.101137i	−0.0651074	+	0.997878i	$0.520739\pi$
$774$		0			0
$775$	3.97460	−	8.51777i	0.142772	−	0.305967i
$776$	38.2703	+	105.147i	1.37383	+	3.77455i
$777$		0			0
$778$	−78.0256	−	6.82635i	−2.79735	−	0.244737i
$779$	−8.62118	−	3.13785i	−0.308886	−	0.112425i
$780$		0			0
$781$	0.709661	−	4.02469i	0.0253937	−	0.144015i
$782$	0.582559	+	0.582559i	0.0208323	+	0.0208323i
$783$		0			0
$784$			28.8525i			1.03045i
$785$	−18.6076	−	24.2565i	−0.664135	−	0.865751i
$786$		0			0
$787$	7.22332	−	3.36829i	0.257484	−	0.120067i	−0.289591	−	0.957151i	$-0.593519\pi$
$787$	7.22332	−	3.36829i	0.257484	−	0.120067i	0.547074	+	0.837084i	$0.315741\pi$
$788$	3.69786	−	42.2668i	0.131731	−	1.50569i
$789$		0			0
$790$	12.3577	−	29.8233i	0.439669	−	1.06106i
$791$	−55.3786	−	31.9729i	−1.96904	−	1.13682i
$792$		0			0
$793$	0.755404	−	2.81921i	0.0268252	−	0.100113i
$794$	−39.9638	−	33.5336i	−1.41826	−	1.19006i
$795$		0			0
$796$	−3.33636	−	18.9215i	−0.118254	−	0.670653i
$797$	0.435383	−	0.621792i	0.0154221	−	0.0220250i	−0.811367	−	0.584537i	$-0.801276\pi$
$797$	0.435383	−	0.621792i	0.0154221	−	0.0220250i	0.826789	+	0.562512i	$0.190165\pi$
$798$		0			0
$799$	−12.2715	+	14.6246i	−0.434136	+	0.517383i
$800$	−12.7483	+	72.1894i	−0.450720	+	2.55228i
$801$		0			0
$802$	−0.0232747	−	0.0868625i	−0.000821859	−	0.00306722i
$803$	3.95512	−	8.48179i	0.139573	−	0.299316i
$804$		0			0
$805$	0.308828	+	0.337115i	0.0108848	+	0.0118817i
$806$	−0.802918	+	2.20600i	−0.0282816	+	0.0777030i
$807$		0			0
$808$	12.3803	−	8.66877i	0.435537	−	0.304966i
$809$	3.88327			0.136528			0.0682642	−	0.997667i	$-0.478254\pi$
$809$	3.88327			0.136528			0.0682642	+	0.997667i	$0.478254\pi$
$810$		0			0
$811$	−22.9810			−0.806974			−0.403487	−	0.914985i	$-0.632202\pi$
$811$	−22.9810			−0.806974			−0.403487	+	0.914985i	$0.632202\pi$
$812$	32.0843	−	22.4656i	1.12594	−	0.788390i
$813$		0			0
$814$	−1.53261	+	4.21081i	−0.0537179	+	0.147589i
$815$	−43.7435	−	1.91558i	−1.53227	−	0.0670997i
$816$		0			0
$817$	−19.7174	+	42.2840i	−0.689824	+	1.47933i
$818$	−6.07207	−	22.6613i	−0.212305	−	0.792333i
$819$		0			0
$820$	−10.0881	−	15.8396i	−0.352290	−	0.553143i
$821$	1.59034	−	1.89529i	0.0555031	−	0.0661461i	−0.737579	−	0.675261i	$-0.764031\pi$
$821$	1.59034	−	1.89529i	0.0555031	−	0.0661461i	0.793082	+	0.609115i	$0.208475\pi$
$822$		0			0
$823$	−18.8527	+	26.9245i	−0.657164	+	0.938528i	−1.00000		0.000867529i	$-0.999724\pi$
$823$	−18.8527	+	26.9245i	−0.657164	+	0.938528i	0.342835	+	0.939396i	$0.388613\pi$
$824$	23.2761	+	132.005i	0.810860	+	4.59862i
$825$		0			0
$826$	−28.6230	−	24.0176i	−0.995923	−	0.835678i
$827$	−2.22968	+	8.32126i	−0.0775334	+	0.289359i	−0.993796	−	0.111220i	$-0.964524\pi$
$827$	−2.22968	+	8.32126i	−0.0775334	+	0.289359i	0.916262	+	0.400579i	$0.131191\pi$
$828$		0			0
$829$	−7.38409	−	4.26321i	−0.256460	−	0.148067i	0.366259	−	0.930513i	$-0.380639\pi$
$829$	−7.38409	−	4.26321i	−0.256460	−	0.148067i	−0.622719	+	0.782446i	$0.713972\pi$
$830$	31.1864	−	12.9131i	1.08250	−	0.448220i
$831$		0			0
$832$	0.640776	−	7.32410i	0.0222149	−	0.253918i
$833$	10.4349	−	4.86588i	0.361548	−	0.168593i
$834$		0			0
$835$	38.9835	−	29.9050i	1.34908	−	1.03491i
$836$		−	18.7448i		−	0.648301i
$837$		0			0
$838$	62.3307	+	62.3307i	2.15318	+	2.15318i
$839$	−8.06541	+	45.7412i	−0.278449	+	1.57916i	0.449340	+	0.893361i	$0.351659\pi$
$839$	−8.06541	+	45.7412i	−0.278449	+	1.57916i	−0.727789	+	0.685802i	$0.759452\pi$
$840$		0			0
$841$	21.3614	+	7.77490i	0.736599	+	0.268100i
$842$	44.0185	+	3.85112i	1.51698	+	0.132718i
$843$		0			0
$844$	30.9571	+	85.0539i	1.06559	+	2.92768i
$845$	−25.3461	−	13.1985i	−0.871931	−	0.454042i
$846$		0			0
$847$	31.3887	+	8.41058i	1.07853	+	0.288991i
$848$	123.842	−	10.8348i	4.25276	−	0.372068i
$849$		0			0
$850$	59.8948	−	16.0321i	2.05438	−	0.549896i
$851$	−0.165907	+	0.0292538i	−0.00568721	+	0.00100281i
$852$		0			0
$853$	1.80662	+	20.6498i	0.0618575	+	0.707035i	0.962288	+	0.272034i	$0.0876964\pi$
$853$	1.80662	+	20.6498i	0.0618575	+	0.707035i	−0.900430	+	0.435001i	$0.856748\pi$
$854$	25.4755	+	44.1248i	0.871752	+	1.50992i
$855$		0			0
$856$	−60.8644	+	105.420i	−2.08030	+	3.60319i
$857$	−3.98725	−	1.85929i	−0.136202	−	0.0635120i	0.353322	−	0.935502i	$-0.385052\pi$
$857$	−3.98725	−	1.85929i	−0.136202	−	0.0635120i	−0.489524	+	0.871990i	$0.662830\pi$
$858$		0			0
$859$	−27.5782	−	32.8664i	−0.940956	−	1.12139i	−0.992442	−	0.122714i	$-0.960840\pi$
$859$	−27.5782	−	32.8664i	−0.940956	−	1.12139i	0.0514862	−	0.998674i	$-0.483604\pi$
$860$	−84.7145	+	44.0856i	−2.88874	+	1.50331i
$861$		0			0
$862$	−22.0415	−	31.4786i	−0.750738	−	1.07217i
$863$	−29.7115	+	29.7115i	−1.01139	+	1.01139i	−0.0114553	+	0.999934i	$0.503646\pi$
$863$	−29.7115	+	29.7115i	−1.01139	+	1.01139i	−0.999934	+	0.0114553i	$0.996354\pi$
$864$		0			0
$865$	5.66974	−	6.18582i	0.192777	−	0.210324i
$866$	61.0955	+	10.7728i	2.07611	+	0.366074i
$867$		0			0
$868$	−12.4295	−	26.6552i	−0.421885	−	0.904736i
$869$	−2.75902	+	2.31509i	−0.0935932	+	0.0785340i
$870$		0			0
$871$	2.41278	−	0.878181i	0.0817540	−	0.0297560i
$872$	−74.1142	+	19.8588i	−2.50982	+	0.672505i
$873$		0			0
$874$	0.850406	−	0.490982i	0.0287654	−	0.0166077i
$875$	33.5950	−	7.43410i	1.13572	−	0.251318i
$876$		0			0
$877$	−9.47306	−	6.63310i	−0.319882	−	0.223984i	0.402596	−	0.915378i	$-0.368108\pi$
$877$	−9.47306	−	6.63310i	−0.319882	−	0.223984i	−0.722478	+	0.691394i	$0.756997\pi$
$878$	−69.7284	−	48.8243i	−2.35322	−	1.64774i
$879$		0			0
$880$	10.5547	−	13.7514i	0.355797	−	0.463559i
$881$	−12.7653	+	7.37007i	−0.430075	+	0.248304i	−0.699379	−	0.714751i	$-0.746540\pi$
$881$	−12.7653	+	7.37007i	−0.430075	+	0.248304i	0.269304	+	0.963055i	$0.413206\pi$
$882$		0			0
$883$	−15.3517	+	4.11349i	−0.516627	+	0.138430i	−0.507706	−	0.861530i	$-0.669506\pi$
$883$	−15.3517	+	4.11349i	−0.516627	+	0.138430i	−0.00892106	+	0.999960i	$0.502840\pi$
$884$	−10.4432	+	3.80103i	−0.351244	+	0.127842i
$885$		0			0
$886$	−36.6160	+	30.7245i	−1.23014	+	1.03221i
$887$	−3.15396	−	6.76369i	−0.105900	−	0.227102i	0.846216	−	0.532839i	$-0.178875\pi$
$887$	−3.15396	−	6.76369i	−0.105900	−	0.227102i	−0.952116	+	0.305737i	$0.901097\pi$
$888$		0			0
$889$	−23.0750	−	4.06875i	−0.773911	−	0.136461i
$890$	27.0369	+	24.7812i	0.906280	+	0.830669i
$891$		0			0
$892$	−68.8206	+	68.8206i	−2.30428	+	2.30428i
$893$	13.0516	+	18.6396i	0.436755	+	0.623750i
$894$		0			0
$895$	−30.7652	−	9.70462i	−1.02837	−	0.324390i
$896$	24.4930	+	29.1896i	0.818253	+	0.975156i
$897$		0			0
$898$	32.0079	+	14.9255i	1.06812	+	0.498072i
$899$	−2.35319	+	4.07585i	−0.0784834	+	0.135937i
$900$		0			0
$901$	−24.8041	−	42.9619i	−0.826344	−	1.43127i
$902$	0.254446	+	2.90833i	0.00847211	+	0.0968367i
$903$		0			0
$904$	−167.938	+	29.6120i	−5.58553	+	0.984880i
$905$	−6.83328	−	30.8419i	−0.227146	−	1.02522i
$906$		0			0
$907$	16.3212	−	1.42792i	0.541937	−	0.0474134i	0.187099	−	0.982341i	$-0.440092\pi$
$907$	16.3212	−	1.42792i	0.541937	−	0.0474134i	0.354838	+	0.934928i	$0.384536\pi$
$908$	2.37069	+	0.635223i	0.0786740	+	0.0210806i
$909$		0			0
$910$	−8.19614	+	2.58306i	−0.271700	+	0.0856277i
$911$	0.825532	+	2.26813i	0.0273511	+	0.0751465i	0.952617	−	0.304173i	$-0.0983802\pi$
$911$	0.825532	+	2.26813i	0.0273511	+	0.0751465i	−0.925266	+	0.379320i	$0.876158\pi$
$912$		0			0
$913$	−3.75152	−	0.328216i	−0.124157	−	0.0108624i
$914$	−20.1354	−	7.32869i	−0.666020	−	0.242412i
$915$		0			0
$916$	13.2645	−	75.2269i	0.438273	−	2.48557i
$917$	25.5387	+	25.5387i	0.843361	+	0.843361i
$918$		0			0
$919$			5.68243i			0.187446i	0.995598	+	0.0937230i	$0.0298768\pi$
$919$			5.68243i			0.187446i	−0.995598	+	0.0937230i	$0.970123\pi$
$920$	1.20877	+	0.159297i	0.0398519	+	0.00525186i
$921$		0			0
$922$	34.6774	−	16.1703i	1.14204	−	0.532541i
$923$	−0.251702	+	2.87697i	−0.00828487	+	0.0946965i
$924$		0			0
$925$	−4.33945	+	11.9129i	−0.142680	+	0.391694i
$926$	47.9543	+	27.6864i	1.57588	+	0.909832i
$927$		0			0
$928$	9.49998	−	35.4544i	0.311852	−	1.16385i
$929$	31.5686	+	26.4892i	1.03573	+	0.869082i	0.991522	−	0.129941i	$-0.0414787\pi$
$929$	31.5686	+	26.4892i	1.03573	+	0.869082i	0.0442093	+	0.999022i	$0.485923\pi$
$930$		0			0
$931$	−2.38300	−	13.5147i	−0.0780996	−	0.442925i
$932$	1.61376	−	2.30468i	0.0528604	−	0.0754924i
$933$		0			0
$934$	42.1923	−	50.2828i	1.38057	−	1.64530i
$935$	−6.75338	−	1.49811i	−0.220859	−	0.0489934i
$936$		0			0
$937$	−2.09031	−	7.80116i	−0.0682876	−	0.254853i	0.923340	−	0.383983i	$-0.125448\pi$
$937$	−2.09031	−	7.80116i	−0.0682876	−	0.254853i	−0.991628	+	0.129131i	$0.958781\pi$
$938$	−18.9430	+	40.6235i	−0.618512	+	1.32640i
$939$		0			0
$940$	−2.03770	+	46.5323i	−0.0664625	+	1.51772i
$941$	−17.0461	+	46.8337i	−0.555686	+	1.52673i	0.270147	+	0.962819i	$0.412928\pi$
$941$	−17.0461	+	46.8337i	−0.555686	+	1.52673i	−0.825833	+	0.563915i	$0.809294\pi$
$942$		0			0
$943$	−0.0899076	+	0.0629540i	−0.00292780	+	0.00205006i
$944$	−53.2626			−1.73355
$945$		0			0
$946$	14.8463			0.482696
$947$	39.8496	−	27.9030i	1.29494	−	0.906726i	0.296112	−	0.955153i	$-0.404310\pi$
$947$	39.8496	−	27.9030i	1.29494	−	0.906726i	0.998827	+	0.0484276i	$0.0154210\pi$
$948$		0			0
$949$	−2.26190	+	6.21452i	−0.0734244	+	0.201732i
$950$	0.0192021	−	73.9019i	0.000622999	−	2.39770i
$951$		0			0
$952$	49.7340	−	106.655i	1.61189	−	3.45671i
$953$	13.0100	+	48.5541i	0.421436	+	1.57282i	0.771584	+	0.636127i	$0.219465\pi$
$953$	13.0100	+	48.5541i	0.421436	+	1.57282i	−0.350148	+	0.936694i	$0.613869\pi$
$954$		0			0
$955$	−4.87818	+	3.10685i	−0.157854	+	0.100535i
$956$	18.5120	−	22.0618i	0.598722	−	0.713529i
$957$		0			0
$958$	−41.0349	+	58.6039i	−1.32578	+	1.89341i
$959$	3.59307	+	20.3773i	0.116026	+	0.658017i
$960$		0			0
$961$	−21.0402	−	17.6548i	−0.678716	−	0.569510i
$962$	0.819569	−	3.05867i	0.0264240	−	0.0986156i
$963$		0			0
$964$	−8.06148	−	4.65430i	−0.259643	−	0.149905i
$965$	29.4473	+	12.2020i	0.947943	+	0.392795i
$966$		0			0
$967$	−4.33600	+	49.5607i	−0.139436	+	1.59377i	0.528096	+	0.849185i	$0.322906\pi$
$967$	−4.33600	+	49.5607i	−0.139436	+	1.59377i	−0.667533	+	0.744581i	$0.732650\pi$
$968$	78.5400	−	36.6238i	2.52437	−	1.17713i
$969$		0			0
$970$	10.6014	−	80.4447i	0.340390	−	2.58292i
$971$		−	40.2818i		−	1.29270i	−0.763039	−	0.646352i	$-0.776294\pi$
$971$		−	40.2818i		−	1.29270i	0.763039	−	0.646352i	$-0.223706\pi$
$972$		0			0
$973$	3.30441	+	3.30441i	0.105934	+	0.105934i
$974$	0.911162	−	5.16745i	0.0291955	−	0.165576i
$975$		0			0
$976$	68.2493	+	24.8407i	2.18461	+	0.795132i
$977$	37.7958	+	3.30670i	1.20919	+	0.105791i	0.673866	−	0.738854i	$-0.264633\pi$
$977$	37.7958	+	3.30670i	1.20919	+	0.105791i	0.535328	+	0.844644i	$0.320188\pi$
$978$		0			0
$979$	−1.39948	−	3.84504i	−0.0447276	−	0.122888i
$980$	12.9738	−	24.9145i	0.414432	−	0.795864i
$981$		0			0
$982$	60.9612	+	16.3345i	1.94535	+	0.521255i
$983$	35.6886	−	3.12235i	1.13829	−	0.0995874i	0.497614	−	0.867399i	$-0.334210\pi$
$983$	35.6886	−	3.12235i	1.13829	−	0.0995874i	0.640676	+	0.767811i	$0.278654\pi$
$984$		0			0
$985$	−10.0294	+	15.7384i	−0.319562	+	0.501468i
$986$	−30.5739	+	5.39101i	−0.973672	+	0.171685i
$987$		0			0
$988$	1.15448	+	13.1958i	0.0367289	+	0.419813i
$989$	0.279076	+	0.483373i	0.00887409	+	0.0153704i
$990$		0			0
$991$	21.8850	−	37.9060i	0.695201	−	1.20412i	−0.274912	−	0.961469i	$-0.588649\pi$
$991$	21.8850	−	37.9060i	0.695201	−	1.20412i	0.970113	−	0.242654i	$-0.0780179\pi$
$992$	−24.9793	−	11.6480i	−0.793094	−	0.369826i
$993$		0			0
$994$	−32.4061	−	38.6201i	−1.02786	−	1.22495i
$995$	−2.54236	+	8.05968i	−0.0805981	+	0.255509i
$996$		0			0
$997$	13.9764	+	19.9603i	0.442636	+	0.632150i	0.977034	−	0.213083i	$-0.0683505\pi$
$997$	13.9764	+	19.9603i	0.442636	+	0.632150i	−0.534398	+	0.845233i	$0.679462\pi$
$998$	59.0307	−	59.0307i	1.86859	−	1.86859i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.8.16		192
3.2	odd	2		135.2.q.a.83.1	yes	192
5.2	odd	4	inner	405.2.r.a.332.16		192
15.2	even	4		135.2.q.a.2.1	✓	192
15.8	even	4		675.2.ba.b.407.16		192
15.14	odd	2		675.2.ba.b.218.16		192
27.13	even	9		135.2.q.a.68.1	yes	192
27.14	odd	18	inner	405.2.r.a.233.16		192
135.13	odd	36		675.2.ba.b.257.16		192
135.67	odd	36		135.2.q.a.122.1	yes	192
135.94	even	18		675.2.ba.b.68.16		192
135.122	even	36	inner	405.2.r.a.152.16		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.1	✓	192	15.2	even	4
135.2.q.a.68.1	yes	192	27.13	even	9
135.2.q.a.83.1	yes	192	3.2	odd	2
135.2.q.a.122.1	yes	192	135.67	odd	36
405.2.r.a.8.16		192	1.1	even	1	trivial
405.2.r.a.152.16		192	135.122	even	36	inner
405.2.r.a.233.16		192	27.14	odd	18	inner
405.2.r.a.332.16		192	5.2	odd	4	inner
675.2.ba.b.68.16		192	135.94	even	18
675.2.ba.b.218.16		192	15.14	odd	2
675.2.ba.b.257.16		192	135.13	odd	36
675.2.ba.b.407.16		192	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.18018 - 1.52658i) q^{2} +(1.73870 - 4.77703i) q^{4} +(-1.64880 + 1.51045i) q^{5} +(1.30062 - 2.78918i) q^{7} +(-2.12414 - 7.92739i) q^{8} +O(q^{10})\)	\(q+(2.18018 - 1.52658i) q^{2} +(1.73870 - 4.77703i) q^{4} +(-1.64880 + 1.51045i) q^{5} +(1.30062 - 2.78918i) q^{7} +(-2.12414 - 7.92739i) q^{8} +(-1.28885 + 5.81007i) q^{10} +(0.426793 - 0.508631i) q^{11} +(-0.269123 + 0.384347i) q^{13} +(-1.42232 - 8.06640i) q^{14} +(-8.94423 - 7.50510i) q^{16} +(-1.20591 + 4.50051i) q^{17} +(4.80938 + 2.77670i) q^{19} +(4.34871 + 10.5026i) q^{20} +(0.154018 - 1.76044i) q^{22} +(0.0602123 - 0.0280775i) q^{23} +(0.437073 - 4.98086i) q^{25} +1.24878i q^{26} +(-11.0626 - 11.0626i) q^{28} +(-0.434735 + 2.46551i) q^{29} +(1.76652 + 0.642961i) q^{31} +(-14.6055 - 1.27781i) q^{32} +(4.24128 + 11.6528i) q^{34} +(2.06847 + 6.56331i) q^{35} +(-2.44933 - 0.656295i) q^{37} +(14.7241 - 1.28820i) q^{38} +(15.4762 + 9.86226i) q^{40} +(-1.62695 + 0.286875i) q^{41} +(0.732214 + 8.36925i) q^{43} +(-1.68769 - 2.92316i) q^{44} +(0.0884111 - 0.153133i) q^{46} +(3.71355 + 1.73166i) q^{47} +(-1.58841 - 1.89299i) q^{49} +(-6.65077 - 11.5264i) q^{50} +(1.36812 + 1.95387i) q^{52} +(-7.52870 + 7.52870i) q^{53} +(0.0645683 + 1.48328i) q^{55} +(-24.8736 - 4.38589i) q^{56} +(2.81598 + 6.03890i) q^{58} +(3.49452 - 2.93225i) q^{59} +(-5.84534 + 2.12753i) q^{61} +(4.83286 - 1.29496i) q^{62} +(-13.5701 + 7.83468i) q^{64} +(-0.136808 - 1.04021i) q^{65} +(-4.48268 - 3.13881i) q^{67} +(19.4024 + 13.5857i) q^{68} +(14.5290 + 11.1515i) q^{70} +(5.33043 - 3.07752i) q^{71} +(13.6146 - 3.64803i) q^{73} +(-6.34185 + 2.30824i) q^{74} +(21.6264 - 18.1467i) q^{76} +(-0.863572 - 1.85194i) q^{77} +(-5.34198 - 0.941936i) q^{79} +(26.0833 - 1.13543i) q^{80} +(-3.10910 + 3.10910i) q^{82} +(-3.25316 - 4.64599i) q^{83} +(-4.80950 - 9.24190i) q^{85} +(14.3727 + 17.1287i) q^{86} +(-4.93869 - 2.30295i) q^{88} +(3.08131 - 5.33699i) q^{89} +(0.721988 + 1.25052i) q^{91} +(-0.0294359 - 0.336454i) q^{92} +(10.7397 - 1.89370i) q^{94} +(-12.1238 + 2.68612i) q^{95} +(-13.5821 + 1.18828i) q^{97} +(-6.35281 - 1.70223i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more