LMFDB - Embedded newform 864.2.bn.a.683.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			683.7
Character	$\chi$	$=$	864.683
Dual form			864.2.bn.a.611.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27367 - 0.614625i) q^{2} +(1.24447 + 1.56566i) q^{4} +(-0.0452073 - 0.343384i) q^{5} +(0.358377 + 1.33748i) q^{7} +(-0.622752 - 2.75902i) q^{8} +O(q^{10})$	\(q+(-1.27367 - 0.614625i) q^{2} +(1.24447 + 1.56566i) q^{4} +(-0.0452073 - 0.343384i) q^{5} +(0.358377 + 1.33748i) q^{7} +(-0.622752 - 2.75902i) q^{8} +(-0.153473 + 0.465143i) q^{10} +(1.53764 - 1.17987i) q^{11} +(1.07217 - 1.39728i) q^{13} +(0.365595 - 1.92378i) q^{14} +(-0.902582 + 3.89684i) q^{16} +0.574776 q^{17} +(-1.27313 + 0.527348i) q^{19} +(0.481363 - 0.498111i) q^{20} +(-2.68362 + 0.557696i) q^{22} +(-2.80438 - 0.751432i) q^{23} +(4.71376 - 1.26305i) q^{25} +(-2.22440 + 1.12069i) q^{26} +(-1.64805 + 2.22555i) q^{28} +(2.67785 + 0.352546i) q^{29} +(4.87848 - 2.81659i) q^{31} +(3.54469 - 4.40854i) q^{32} +(-0.732075 - 0.353272i) q^{34} +(0.443068 - 0.183525i) q^{35} +(0.837849 - 2.02275i) q^{37} +(1.94567 + 0.110831i) q^{38} +(-0.919249 + 0.338571i) q^{40} +(-2.97203 + 11.0918i) q^{41} +(4.52106 + 5.89196i) q^{43} +(3.76083 + 0.939103i) q^{44} +(3.11001 + 2.68072i) q^{46} +(4.21627 + 2.43427i) q^{47} +(4.40176 - 2.54136i) q^{49} +(-6.78008 - 1.28849i) q^{50} +(3.52196 - 0.0602207i) q^{52} +(3.53239 - 8.52795i) q^{53} +(-0.474662 - 0.474662i) q^{55} +(3.46695 - 1.82169i) q^{56} +(-3.19401 - 2.09490i) q^{58} +(-5.62596 + 0.740672i) q^{59} +(0.645484 - 4.90294i) q^{61} +(-7.94472 + 0.588972i) q^{62} +(-7.22436 + 3.43637i) q^{64} +(-0.528275 - 0.305000i) q^{65} +(4.11206 - 5.35894i) q^{67} +(0.715292 + 0.899903i) q^{68} +(-0.677121 - 0.0385707i) q^{70} +(5.04976 + 5.04976i) q^{71} +(8.79899 - 8.79899i) q^{73} +(-2.31038 + 2.06135i) q^{74} +(-2.41002 - 1.33702i) q^{76} +(2.12911 + 1.63372i) q^{77} +(-6.57615 + 11.3902i) q^{79} +(1.37891 + 0.133766i) q^{80} +(10.6027 - 12.3006i) q^{82} +(11.3315 + 1.49182i) q^{83} +(-0.0259841 - 0.197369i) q^{85} +(-2.13699 - 10.2832i) q^{86} +(-4.21286 - 3.50761i) q^{88} +(8.74474 - 8.74474i) q^{89} +(2.25308 + 0.933257i) q^{91} +(-2.31349 - 5.32585i) q^{92} +(-3.87398 - 5.69188i) q^{94} +(0.238638 + 0.413332i) q^{95} +(0.426263 - 0.738308i) q^{97} +(-7.16837 + 0.531418i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.27367	−	0.614625i	−0.900621	−	0.434606i
$2$	−1.27367	−	0.614625i	−0.900621	−	0.434606i
$3$		0			0
$3$		0			0
$4$	1.24447	+	1.56566i	0.622236	+	0.782830i
$5$	−0.0452073	−	0.343384i	−0.0202173	−	0.153566i	0.978358	−	0.206917i	$-0.0663430\pi$
$5$	−0.0452073	−	0.343384i	−0.0202173	−	0.153566i	−0.998576	+	0.0533512i	$0.983010\pi$
$6$		0			0
$7$	0.358377	+	1.33748i	0.135454	+	0.505520i	0.999996	+	0.00295929i	$0.000941974\pi$
$7$	0.358377	+	1.33748i	0.135454	+	0.505520i	−0.864542	+	0.502561i	$0.832391\pi$
$8$	−0.622752	−	2.75902i	−0.220176	−	0.975460i
$9$		0			0
$10$	−0.153473	+	0.465143i	−0.0485325	+	0.147091i
$11$	1.53764	−	1.17987i	0.463616	−	0.355745i	−0.350388	−	0.936605i	$-0.613950\pi$
$11$	1.53764	−	1.17987i	0.463616	−	0.355745i	0.814004	+	0.580860i	$0.197284\pi$
$12$		0			0
$13$	1.07217	−	1.39728i	0.297368	−	0.387537i	−0.620643	−	0.784094i	$-0.713128\pi$
$13$	1.07217	−	1.39728i	0.297368	−	0.387537i	0.918010	+	0.396556i	$0.129795\pi$
$14$	0.365595	−	1.92378i	0.0977095	−	0.514151i
$15$		0			0
$16$	−0.902582	+	3.89684i	−0.225645	+	0.974209i
$17$	0.574776			0.139404			0.0697018	−	0.997568i	$-0.477795\pi$
$17$	0.574776			0.139404			0.0697018	+	0.997568i	$0.477795\pi$
$18$		0			0
$19$	−1.27313	+	0.527348i	−0.292076	+	0.120982i	−0.523910	−	0.851773i	$-0.675527\pi$
$19$	−1.27313	+	0.527348i	−0.292076	+	0.120982i	0.231834	+	0.972755i	$0.425527\pi$
$20$	0.481363	−	0.498111i	0.107636	−	0.111381i
$21$		0			0
$22$	−2.68362	+	0.557696i	−0.572151	+	0.118901i
$23$	−2.80438	−	0.751432i	−0.584754	−	0.156684i	−0.0456996	−	0.998955i	$-0.514552\pi$
$23$	−2.80438	−	0.751432i	−0.584754	−	0.156684i	−0.539055	+	0.842271i	$0.681218\pi$
$24$		0			0
$25$	4.71376	−	1.26305i	0.942752	−	0.252610i
$26$	−2.22440	+	1.12069i	−0.436241	+	0.219786i
$27$		0			0
$28$	−1.64805	+	2.22555i	−0.311452	+	0.420590i
$29$	2.67785	+	0.352546i	0.497264	+	0.0654661i	0.374987	−	0.927030i	$-0.377647\pi$
$29$	2.67785	+	0.352546i	0.497264	+	0.0654661i	0.122277	+	0.992496i	$0.460980\pi$
$30$		0			0
$31$	4.87848	−	2.81659i	0.876201	−	0.505875i	0.00679713	−	0.999977i	$-0.497836\pi$
$31$	4.87848	−	2.81659i	0.876201	−	0.505875i	0.869404	+	0.494102i	$0.164503\pi$
$32$	3.54469	−	4.40854i	0.626618	−	0.779327i
$33$		0			0
$34$	−0.732075	−	0.353272i	−0.125550	−	0.0605856i
$35$	0.443068	−	0.183525i	0.0748921	−	0.0310213i
$36$		0			0
$37$	0.837849	−	2.02275i	0.137742	−	0.332538i	−0.839924	−	0.542704i	$-0.817401\pi$
$37$	0.837849	−	2.02275i	0.137742	−	0.332538i	0.977666	+	0.210166i	$0.0674006\pi$
$38$	1.94567	+	0.110831i	0.315629	+	0.0179792i
$39$		0			0
$40$	−0.919249	+	0.338571i	−0.145346	+	0.0535327i
$41$	−2.97203	+	11.0918i	−0.464154	+	1.73224i	0.195527	+	0.980698i	$0.437358\pi$
$41$	−2.97203	+	11.0918i	−0.464154	+	1.73224i	−0.659680	+	0.751546i	$0.729308\pi$
$42$		0			0
$43$	4.52106	+	5.89196i	0.689455	+	0.898515i	0.998621	−	0.0524929i	$-0.0167167\pi$
$43$	4.52106	+	5.89196i	0.689455	+	0.898515i	−0.309166	+	0.951008i	$0.600050\pi$
$44$	3.76083	+	0.939103i	0.566966	+	0.141575i
$45$		0			0
$46$	3.11001	+	2.68072i	0.458546	+	0.395251i
$47$	4.21627	+	2.43427i	0.615006	+	0.355074i	0.774922	−	0.632057i	$-0.217789\pi$
$47$	4.21627	+	2.43427i	0.615006	+	0.355074i	−0.159916	+	0.987131i	$0.551122\pi$
$48$		0			0
$49$	4.40176	−	2.54136i	0.628823	−	0.363051i
$50$	−6.78008	−	1.28849i	−0.958848	−	0.182220i
$51$		0			0
$52$	3.52196	−	0.0602207i	0.488408	−	0.00835111i
$53$	3.53239	−	8.52795i	0.485211	−	1.17140i	−0.471892	−	0.881657i	$-0.656429\pi$
$53$	3.53239	−	8.52795i	0.485211	−	1.17140i	0.957103	−	0.289748i	$-0.0935714\pi$
$54$		0			0
$55$	−0.474662	−	0.474662i	−0.0640034	−	0.0640034i
$56$	3.46695	−	1.82169i	0.463291	−	0.243433i
$57$		0			0
$58$	−3.19401	−	2.09490i	−0.419395	−	0.275074i
$59$	−5.62596	+	0.740672i	−0.732438	+	0.0964273i	−0.487514	−	0.873115i	$-0.662096\pi$
$59$	−5.62596	+	0.740672i	−0.732438	+	0.0964273i	−0.244924	+	0.969542i	$0.578763\pi$
$60$		0			0
$61$	0.645484	−	4.90294i	0.0826458	−	0.627757i	−0.899126	−	0.437691i	$-0.855796\pi$
$61$	0.645484	−	4.90294i	0.0826458	−	0.627757i	0.981771	−	0.190066i	$-0.0608702\pi$
$62$	−7.94472	+	0.588972i	−1.00898	+	0.0747995i
$63$		0			0
$64$	−7.22436	+	3.43637i	−0.903045	+	0.429546i
$65$	−0.528275	−	0.305000i	−0.0655245	−	0.0378306i
$66$		0			0
$67$	4.11206	−	5.35894i	0.502368	−	0.654699i	−0.471486	−	0.881874i	$-0.656282\pi$
$67$	4.11206	−	5.35894i	0.502368	−	0.654699i	0.973854	+	0.227175i	$0.0729489\pi$
$68$	0.715292	+	0.899903i	0.0867419	+	0.109129i
$69$		0			0
$70$	−0.677121	−	0.0385707i	−0.0809314	−	0.00461009i
$71$	5.04976	+	5.04976i	0.599296	+	0.599296i	0.940125	−	0.340829i	$-0.110708\pi$
$71$	5.04976	+	5.04976i	0.599296	+	0.599296i	−0.340829	+	0.940125i	$0.610708\pi$
$72$		0			0
$73$	8.79899	−	8.79899i	1.02984	−	1.02984i	0.0303035	−	0.999541i	$-0.490353\pi$
$73$	8.79899	−	8.79899i	1.02984	−	1.02984i	0.999541	−	0.0303035i	$-0.00964736\pi$
$74$	−2.31038	+	2.06135i	−0.268576	+	0.239627i
$75$		0			0
$76$	−2.41002	−	1.33702i	−0.276449	−	0.153367i
$77$	2.12911	+	1.63372i	0.242635	+	0.186180i
$78$		0			0
$79$	−6.57615	+	11.3902i	−0.739875	+	1.28150i	0.212676	+	0.977123i	$0.431782\pi$
$79$	−6.57615	+	11.3902i	−0.739875	+	1.28150i	−0.952551	+	0.304379i	$0.901551\pi$
$80$	1.37891	+	0.133766i	0.154167	+	0.0149555i
$81$		0			0
$82$	10.6027	−	12.3006i	1.17087	−	1.35837i
$83$	11.3315	+	1.49182i	1.24379	+	0.163749i	0.723552	−	0.690270i	$-0.242508\pi$
$83$	11.3315	+	1.49182i	1.24379	+	0.163749i	0.520242	+	0.854019i	$0.325842\pi$
$84$		0			0
$85$	−0.0259841	−	0.197369i	−0.00281837	−	0.0214076i
$86$	−2.13699	−	10.2832i	−0.230438	−	1.10886i
$87$		0			0
$88$	−4.21286	−	3.50761i	−0.449092	−	0.373912i
$89$	8.74474	−	8.74474i	0.926941	−	0.926941i	−0.0705665	−	0.997507i	$-0.522481\pi$
$89$	8.74474	−	8.74474i	0.926941	−	0.926941i	0.997507	+	0.0705665i	$0.0224807\pi$
$90$		0			0
$91$	2.25308	+	0.933257i	0.236187	+	0.0978320i
$92$	−2.31349	−	5.32585i	−0.241198	−	0.555258i
$93$		0			0
$94$	−3.87398	−	5.69188i	−0.399570	−	0.587072i
$95$	0.238638	+	0.413332i	0.0244837	+	0.0424070i
$96$		0			0
$97$	0.426263	−	0.738308i	0.0432804	−	0.0749639i	−0.843574	−	0.537013i	$-0.819552\pi$
$97$	0.426263	−	0.738308i	0.0432804	−	0.0749639i	0.886854	+	0.462050i	$0.152886\pi$
$98$	−7.16837	+	0.531418i	−0.724115	+	0.0536813i
$99$		0			0
$100$	7.84364	+	5.80832i	0.784364	+	0.580832i
$101$	13.5511	−	10.3982i	1.34839	−	1.03466i	0.353317	−	0.935504i	$-0.385054\pi$
$101$	13.5511	−	10.3982i	1.34839	−	1.03466i	0.995072	−	0.0991519i	$-0.0316130\pi$
$102$		0			0
$103$	−6.70552	−	1.79674i	−0.660714	−	0.177038i	−0.0871458	−	0.996196i	$-0.527775\pi$
$103$	−6.70552	−	1.79674i	−0.660714	−	0.177038i	−0.573568	+	0.819158i	$0.694441\pi$
$104$	−4.52283	−	2.08799i	−0.443500	−	0.204744i
$105$		0			0
$106$	−9.74060	+	8.69070i	−0.946091	+	0.844115i
$107$	−1.16034	−	0.480630i	−0.112175	−	0.0464642i	0.325890	−	0.945408i	$-0.394336\pi$
$107$	−1.16034	−	0.480630i	−0.112175	−	0.0464642i	−0.438065	+	0.898943i	$0.644336\pi$
$108$		0			0
$109$	−3.15151	−	7.60841i	−0.301860	−	0.728753i	−0.999919	−	0.0127138i	$-0.995953\pi$
$109$	−3.15151	−	7.60841i	−0.301860	−	0.728753i	0.698060	−	0.716040i	$-0.254047\pi$
$110$	0.312823	+	0.896301i	0.0298265	+	0.0854590i
$111$		0			0
$112$	−5.53541	+	0.189351i	−0.523047	+	0.0178920i
$113$	−0.963528	−	1.66888i	−0.0906411	−	0.156995i	0.817140	−	0.576439i	$-0.195558\pi$
$113$	−0.963528	−	1.66888i	−0.0906411	−	0.156995i	−0.907781	+	0.419444i	$0.862225\pi$
$114$		0			0
$115$	−0.131251	+	0.996950i	−0.0122392	+	0.0929661i
$116$	2.78054	+	4.63133i	0.258167	+	0.430009i
$117$		0			0
$118$	7.62086	+	2.51449i	0.701557	+	0.231477i
$119$	0.205986	+	0.768751i	0.0188827	+	0.0704713i
$120$		0			0
$121$	−1.87477	+	6.99675i	−0.170434	+	0.636068i
$122$	−3.83560	+	5.84800i	−0.347259	+	0.529453i
$123$		0			0
$124$	10.4810	+	4.13287i	0.941218	+	0.371143i
$125$	−1.30951	−	3.16144i	−0.117126	−	0.282768i
$126$		0			0
$127$		−	16.6034i		−	1.47332i	−0.676266	−	0.736658i	$-0.736403\pi$
$127$		−	16.6034i		−	1.47332i	0.676266	−	0.736658i	$-0.263597\pi$
$128$	11.3135	+	0.0634754i	0.999984	+	0.00561049i
$129$		0			0
$130$	0.485388	+	0.713160i	0.0425713	+	0.0625483i
$131$	10.8684	+	8.33958i	0.949573	+	0.728633i	0.962499	−	0.271284i	$-0.0874481\pi$
$131$	10.8684	+	8.33958i	0.949573	+	0.728633i	−0.0129266	+	0.999916i	$0.504115\pi$
$132$		0			0
$133$	−1.16158	−	1.51380i	−0.100722	−	0.131263i
$134$	−8.53115	+	4.29815i	−0.736979	+	0.371303i
$135$		0			0
$136$	−0.357943	−	1.58582i	−0.0306933	−	0.135983i
$137$	−20.6862	+	5.54285i	−1.76734	+	0.473558i	−0.988184	−	0.153271i	$-0.951019\pi$
$137$	−20.6862	+	5.54285i	−1.76734	+	0.473558i	−0.779157	+	0.626829i	$0.784353\pi$
$138$		0			0
$139$	1.99544	−	0.262705i	0.169251	−	0.0222823i	−0.0454242	−	0.998968i	$-0.514464\pi$
$139$	1.99544	−	0.262705i	0.169251	−	0.0222823i	0.214675	+	0.976685i	$0.431131\pi$
$140$	0.838722	+	0.465302i	0.0708850	+	0.0393252i
$141$		0			0
$142$	−3.32802	−	9.53544i	−0.279281	−	0.800196i
$143$		−	3.41355i		−	0.285455i
$144$		0			0
$145$		−	0.935468i		−	0.0776864i
$146$	−16.6151	+	5.79893i	−1.37508	+	0.479923i
$147$		0			0
$148$	4.20961	−	1.20546i	0.346028	−	0.0990885i
$149$	7.72366	−	1.01684i	0.632747	−	0.0833027i	0.192671	−	0.981263i	$-0.438285\pi$
$149$	7.72366	−	1.01684i	0.632747	−	0.0833027i	0.440076	+	0.897961i	$0.354952\pi$
$150$		0			0
$151$	−20.7464	+	5.55899i	−1.68832	+	0.452384i	−0.969955	−	0.243283i	$-0.921776\pi$
$151$	−20.7464	+	5.55899i	−1.68832	+	0.452384i	−0.718365	+	0.695667i	$0.755109\pi$
$152$	2.24781	+	3.18418i	0.182321	+	0.258271i
$153$		0			0
$154$	−1.70766	−	3.38943i	−0.137607	−	0.273128i
$155$	−1.18772	−	1.54786i	−0.0953996	−	0.124327i
$156$		0			0
$157$	−12.8538	−	9.86308i	−1.02585	−	0.787159i	−0.0485035	−	0.998823i	$-0.515445\pi$
$157$	−12.8538	−	9.86308i	−1.02585	−	0.787159i	−0.977343	+	0.211664i	$0.932112\pi$
$158$	15.3766	−	10.4655i	1.22329	−	0.832593i
$159$		0			0
$160$	−1.67407	−	1.01789i	−0.132347	−	0.0804712i
$161$		−	4.02010i		−	0.316828i
$162$		0			0
$163$	5.42994	+	13.1090i	0.425305	+	1.02678i	0.980758	+	0.195230i	$0.0625452\pi$
$163$	5.42994	+	13.1090i	0.425305	+	1.02678i	−0.555452	+	0.831548i	$0.687455\pi$
$164$	−21.0646	+	9.15021i	−1.64487	+	0.714511i
$165$		0			0
$166$	−13.5157	−	8.86471i	−1.04902	−	0.688035i
$167$	−3.82478	+	14.2743i	−0.295970	+	1.10458i	0.644474	+	0.764626i	$0.277076\pi$
$167$	−3.82478	+	14.2743i	−0.295970	+	1.10458i	−0.940444	+	0.339949i	$0.889590\pi$
$168$		0			0
$169$	2.56180	+	9.56077i	0.197062	+	0.735444i
$170$	−0.0882126	+	0.267353i	−0.00676560	+	0.0205050i
$171$		0			0
$172$	−3.59847	+	14.4108i	−0.274381	+	1.09881i
$173$	−0.270838	+	2.05722i	−0.0205915	+	0.156408i	−0.998651	−	0.0519157i	$-0.983467\pi$
$173$	−0.270838	+	2.05722i	−0.0205915	+	0.156408i	0.978060	+	0.208323i	$0.0668006\pi$
$174$		0			0
$175$	3.37860	+	5.85191i	0.255398	+	0.442363i
$176$	3.20993	+	7.05686i	0.241957	+	0.531931i
$177$		0			0
$178$	−16.5127	+	5.76318i	−1.23768	+	0.431968i
$179$	0.700228	+	1.69050i	0.0523375	+	0.126354i	0.947886	−	0.318611i	$-0.103216\pi$
$179$	0.700228	+	1.69050i	0.0523375	+	0.126354i	−0.895548	+	0.444965i	$0.853216\pi$
$180$		0			0
$181$	19.7735	+	8.19045i	1.46975	+	0.608791i	0.966803	−	0.255525i	$-0.0822482\pi$
$181$	19.7735	+	8.19045i	1.46975	+	0.608791i	0.502949	+	0.864316i	$0.332248\pi$
$182$	−2.29608	−	2.57346i	−0.170197	−	0.190758i
$183$		0			0
$184$	−0.326780	+	8.20530i	−0.0240905	+	0.604903i
$185$	−0.732455	−	0.196261i	−0.0538512	−	0.0144294i
$186$		0			0
$187$	0.883798	−	0.678162i	0.0646297	−	0.0495921i
$188$	1.43580	+	9.63062i	0.104716	+	0.702385i
$189$		0			0
$190$	−0.0499010	−	0.673122i	−0.00362020	−	0.0488334i
$191$	−1.43851	+	2.49157i	−0.104087	+	0.180284i	−0.913365	−	0.407142i	$-0.866525\pi$
$191$	−1.43851	+	2.49157i	−0.104087	+	0.180284i	0.809278	+	0.587426i	$0.199859\pi$
$192$		0			0
$193$	1.23668	+	2.14199i	0.0890182	+	0.154184i	0.907096	−	0.420923i	$-0.138294\pi$
$193$	1.23668	+	2.14199i	0.0890182	+	0.154184i	−0.818078	+	0.575107i	$0.804960\pi$
$194$	−0.996701	+	0.678370i	−0.0715589	+	0.0487041i
$195$		0			0
$196$	9.45676	+	3.72901i	0.675483	+	0.266358i
$197$	−19.5836	−	8.11179i	−1.39527	−	0.577941i	−0.446753	−	0.894657i	$-0.647420\pi$
$197$	−19.5836	−	8.11179i	−1.39527	−	0.577941i	−0.948520	+	0.316716i	$0.897420\pi$
$198$		0			0
$199$	−17.8549	+	17.8549i	−1.26570	+	1.26570i	−0.317417	+	0.948286i	$0.602815\pi$
$199$	−17.8549	+	17.8549i	−1.26570	+	1.26570i	−0.948286	+	0.317417i	$0.897185\pi$
$200$	−6.42028	−	12.2188i	−0.453982	−	0.863998i
$201$		0			0
$202$	−23.6507	+	4.91495i	−1.66405	+	0.345815i
$203$	0.488156	+	3.70791i	0.0342618	+	0.260245i
$204$		0			0
$205$	3.94309	+	0.519118i	0.275398	+	0.0362568i
$206$	7.43629	+	6.40983i	0.518111	+	0.446594i
$207$		0			0
$208$	4.47727	+	5.43925i	0.310443	+	0.377144i
$209$	−1.33541	+	2.31300i	−0.0923724	+	0.159994i
$210$		0			0
$211$	−3.60771	−	2.76830i	−0.248365	−	0.190577i	0.477075	−	0.878863i	$-0.341697\pi$
$211$	−3.60771	−	2.76830i	−0.248365	−	0.190577i	−0.725440	+	0.688285i	$0.758364\pi$
$212$	17.7478	−	5.08227i	1.21893	−	0.349051i
$213$		0			0
$214$	1.18249	+	1.32534i	0.0808331	+	0.0905984i
$215$	1.81882	−	1.81882i	0.124042	−	0.124042i
$216$		0			0
$217$	5.51547	+	5.51547i	0.374415	+	0.374415i
$218$	−0.662341	+	11.6276i	−0.0448594	+	0.787520i
$219$		0			0
$220$	0.152456	−	1.33386i	0.0102786	−	0.0899289i
$221$	0.616260	−	0.803125i	0.0414541	−	0.0540241i
$222$		0			0
$223$	−18.5810	−	10.7277i	−1.24427	−	0.718381i	−0.274311	−	0.961641i	$-0.588450\pi$
$223$	−18.5810	−	10.7277i	−1.24427	−	0.718381i	−0.969961	+	0.243260i	$0.921783\pi$
$224$	7.16666	+	3.16103i	0.478843	+	0.211205i
$225$		0			0
$226$	0.201481	+	2.71781i	0.0134023	+	0.180786i
$227$	−2.28759	+	17.3759i	−0.151832	+	1.15328i	0.730588	+	0.682819i	$0.239246\pi$
$227$	−2.28759	+	17.3759i	−0.151832	+	1.15328i	−0.882420	+	0.470462i	$0.844087\pi$
$228$		0			0
$229$	−17.3524	+	2.28449i	−1.14668	+	0.150963i	−0.679828	−	0.733372i	$-0.737945\pi$
$229$	−17.3524	+	2.28449i	−1.14668	+	0.150963i	−0.466852	+	0.884335i	$0.654612\pi$
$230$	0.779921	−	1.18912i	0.0514265	−	0.0784079i
$231$		0			0
$232$	−0.694957	−	7.60778i	−0.0456261	−	0.499475i
$233$	−1.37102	−	1.37102i	−0.0898185	−	0.0898185i	0.660770	−	0.750588i	$-0.270230\pi$
$233$	−1.37102	−	1.37102i	−0.0898185	−	0.0898185i	−0.750588	+	0.660770i	$0.770230\pi$
$234$		0			0
$235$	0.645281	−	1.55785i	0.0420935	−	0.101623i
$236$	−8.16099	−	7.88660i	−0.531235	−	0.513374i
$237$		0			0
$238$	0.210135	−	1.10574i	0.0136211	−	0.0716745i
$239$	−16.0202	+	9.24926i	−1.03626	+	0.598285i	−0.918772	−	0.394789i	$-0.870818\pi$
$239$	−16.0202	+	9.24926i	−1.03626	+	0.598285i	−0.117488	+	0.993074i	$0.537484\pi$
$240$		0			0
$241$	8.91419	+	5.14661i	0.574214	+	0.331522i	0.758830	−	0.651288i	$-0.225771\pi$
$241$	8.91419	+	5.14661i	0.574214	+	0.331522i	−0.184617	+	0.982811i	$0.559104\pi$
$242$	6.68822	−	7.75927i	0.429935	−	0.498785i
$243$		0			0
$244$	8.47962	−	5.09096i	0.542852	−	0.325915i
$245$	−1.07165	−	1.39660i	−0.0684654	−	0.0892258i
$246$		0			0
$247$	−0.628163	+	2.34434i	−0.0399690	+	0.149166i
$248$	−10.8091	−	11.7058i	−0.686379	−	0.743318i
$249$		0			0
$250$	−0.275216	+	4.83150i	−0.0174062	+	0.305571i
$251$	−7.46406	+	18.0198i	−0.471128	+	1.13740i	0.492538	+	0.870291i	$0.336069\pi$
$251$	−7.46406	+	18.0198i	−0.471128	+	1.13740i	−0.963666	+	0.267112i	$0.913931\pi$
$252$		0			0
$253$	−5.19872	+	2.15338i	−0.326841	+	0.135382i
$254$	−10.2049	+	21.1473i	−0.640311	+	1.32690i
$255$		0			0
$256$	−14.3707	−	7.03443i	−0.898168	−	0.439652i
$257$	−5.92640	+	3.42161i	−0.369679	+	0.213434i	−0.673318	−	0.739353i	$-0.735132\pi$
$257$	−5.92640	+	3.42161i	−0.369679	+	0.213434i	0.303639	+	0.952787i	$0.401798\pi$
$258$		0			0
$259$	3.00565	+	0.395701i	0.186762	+	0.0245877i
$260$	−0.179897	−	1.20666i	−0.0111568	−	0.0748340i
$261$		0			0
$262$	−8.71698	−	17.3018i	−0.538537	−	1.06891i
$263$	13.1446	−	3.52208i	0.810530	−	0.217181i	0.170328	−	0.985387i	$-0.445517\pi$
$263$	13.1446	−	3.52208i	0.810530	−	0.217181i	0.640202	+	0.768206i	$0.278851\pi$
$264$		0			0
$265$	−3.08805	−	0.827441i	−0.189697	−	0.0508293i
$266$	0.549049	+	2.64201i	0.0336643	+	0.161992i
$267$		0			0
$268$	13.5076	−	0.230962i	0.825109	−	0.0141082i
$269$	−10.4025	+	4.30886i	−0.634252	+	0.262716i	−0.676558	−	0.736389i	$-0.736529\pi$
$269$	−10.4025	+	4.30886i	−0.634252	+	0.262716i	0.0423066	+	0.999105i	$0.486529\pi$
$270$		0			0
$271$	7.69540			0.467462			0.233731	−	0.972301i	$-0.424906\pi$
$271$	7.69540			0.467462			0.233731	+	0.972301i	$0.424906\pi$
$272$	−0.518782	+	2.23981i	−0.0314558	+	0.135808i
$273$		0			0
$274$	29.7542	+	5.65450i	1.79752	+	0.341601i
$275$	5.75783	−	7.50375i	0.347210	−	0.452493i
$276$		0			0
$277$	14.2646	−	10.9456i	0.857079	−	0.657660i	−0.0837700	−	0.996485i	$-0.526696\pi$
$277$	14.2646	−	10.9456i	0.857079	−	0.657660i	0.940849	+	0.338825i	$0.110029\pi$
$278$	−2.70300	−	0.891850i	−0.162115	−	0.0534896i
$279$		0			0
$280$	−0.782269	−	1.10814i	−0.0467495	−	0.0662241i
$281$	1.39007	+	5.18783i	0.0829248	+	0.309480i	0.994913	−	0.100737i	$-0.0321199\pi$
$281$	1.39007	+	5.18783i	0.0829248	+	0.309480i	−0.911988	+	0.410216i	$0.865453\pi$
$282$		0			0
$283$	−2.38621	−	18.1250i	−0.141845	−	1.07742i	−0.903241	−	0.429134i	$-0.858819\pi$
$283$	−2.38621	−	18.1250i	−0.141845	−	1.07742i	0.761396	−	0.648288i	$-0.224515\pi$
$284$	−1.62192	+	14.1905i	−0.0962435	+	0.842051i
$285$		0			0
$286$	−2.09805	+	4.34774i	−0.124061	+	0.257087i
$287$	−15.9001			−0.938555
$288$		0			0
$289$	−16.6696			−0.980567
$290$	−0.574962	+	1.19148i	−0.0337629	+	0.0699660i
$291$		0			0
$292$	24.7263	+	2.82613i	1.44700	+	0.165387i
$293$	−2.59169	−	19.6858i	−0.151408	−	1.15006i	−0.883358	−	0.468699i	$-0.844723\pi$
$293$	−2.59169	−	19.6858i	−0.151408	−	1.15006i	0.731950	−	0.681358i	$-0.238610\pi$
$294$		0			0
$295$	0.508669	+	1.89838i	0.0296159	+	0.110528i
$296$	−6.10257	−	1.05197i	−0.354705	−	0.0611446i
$297$		0			0
$298$	−10.4624	−	3.45204i	−0.606069	−	0.199971i
$299$	−4.05675	+	3.11286i	−0.234608	+	0.180021i
$300$		0			0
$301$	−6.26013	+	8.15836i	−0.360828	+	0.470240i
$302$	29.8408	+	5.67096i	1.71714	+	0.326327i
$303$		0			0
$304$	−0.905885	−	5.43716i	−0.0519561	−	0.311842i
$305$	−1.71277			−0.0980729
$306$		0			0
$307$	−3.32430	+	1.37697i	−0.189728	+	0.0785879i	−0.475525	−	0.879702i	$-0.657742\pi$
$307$	−3.32430	+	1.37697i	−0.189728	+	0.0785879i	0.285797	+	0.958290i	$0.407742\pi$
$308$	0.0917612	+	5.36658i	0.00522858	+	0.305789i
$309$		0			0
$310$	0.561403	+	2.70146i	0.0318856	+	0.153433i
$311$	−24.9435	−	6.68359i	−1.41442	−	0.378992i	−0.530916	−	0.847424i	$-0.678152\pi$
$311$	−24.9435	−	6.68359i	−1.41442	−	0.378992i	−0.883499	+	0.468433i	$0.844819\pi$
$312$		0			0
$313$	16.3338	−	4.37664i	0.923243	−	0.247382i	0.234272	−	0.972171i	$-0.424729\pi$
$313$	16.3338	−	4.37664i	0.923243	−	0.247382i	0.688971	+	0.724789i	$0.258063\pi$
$314$	10.3094	+	20.4626i	0.581794	+	1.15477i
$315$		0			0
$316$	−26.0171	+	3.87880i	−1.46357	+	0.218199i
$317$	9.22696	+	1.21475i	0.518238	+	0.0682273i	0.385108	−	0.922871i	$-0.374164\pi$
$317$	9.22696	+	1.21475i	0.518238	+	0.0682273i	0.133129	+	0.991099i	$0.457497\pi$
$318$		0			0
$319$	4.53353	−	2.61743i	0.253829	−	0.146548i
$320$	1.50659	+	2.32538i	0.0842208	+	0.129993i
$321$		0			0
$322$	−2.47086	+	5.12028i	−0.137695	+	0.285342i
$323$	−0.731765	+	0.303107i	−0.0407165	+	0.0168653i
$324$		0			0
$325$	3.28913	−	7.94067i	0.182448	−	0.440469i
$326$	1.14119	−	20.0339i	0.0632047	−	1.10958i
$327$		0			0
$328$	32.4533	+	1.29247i	1.79193	+	0.0713645i
$329$	−1.74477	+	6.51156i	−0.0961922	+	0.358994i
$330$		0			0
$331$	−11.0885	−	14.4509i	−0.609481	−	0.794291i	0.382053	−	0.924140i	$-0.375217\pi$
$331$	−11.0885	−	14.4509i	−0.609481	−	0.794291i	−0.991534	+	0.129850i	$0.958550\pi$
$332$	11.7660	+	19.5978i	0.645745	+	1.07557i
$333$		0			0
$334$	13.6448	−	15.8299i	0.746612	−	0.866173i
$335$	−2.02607	−	1.16975i	−0.110696	−	0.0639103i
$336$		0			0
$337$	9.71791	−	5.61064i	0.529369	−	0.305631i	−0.211391	−	0.977402i	$-0.567799\pi$
$337$	9.71791	−	5.61064i	0.529369	−	0.305631i	0.740759	+	0.671771i	$0.234466\pi$
$338$	2.61340	−	13.7518i	0.142150	−	0.748000i
$339$		0			0
$340$	0.276676	−	0.286302i	0.0150048	−	0.0155269i
$341$	4.17813	−	10.0869i	0.226258	−	0.546236i
$342$		0			0
$343$	11.8302	+	11.8302i	0.638772	+	0.638772i
$344$	13.4405	−	16.1429i	0.724664	−	0.870367i
$345$		0			0
$346$	1.60938	−	2.45376i	0.0865208	−	0.131915i
$347$	7.14581	−	0.940763i	0.383607	−	0.0505028i	0.0637431	−	0.997966i	$-0.479696\pi$
$347$	7.14581	−	0.940763i	0.383607	−	0.0505028i	0.319864	+	0.947464i	$0.396363\pi$
$348$		0			0
$349$	1.22262	−	9.28675i	0.0654456	−	0.497109i	−0.927060	−	0.374912i	$-0.877673\pi$
$349$	1.22262	−	9.28675i	0.0654456	−	0.497109i	0.992506	−	0.122196i	$-0.0389938\pi$
$350$	−0.706493	−	9.52998i	−0.0377636	−	0.509399i
$351$		0			0
$352$	0.248940	−	10.9610i	0.0132685	−	0.584224i
$353$	−3.03528	−	1.75242i	−0.161552	−	0.0932720i	0.417044	−	0.908886i	$-0.363066\pi$
$353$	−3.03528	−	1.75242i	−0.161552	−	0.0932720i	−0.578596	+	0.815614i	$0.696399\pi$
$354$		0			0
$355$	1.50572	−	1.96229i	0.0799153	−	0.104148i
$356$	24.5739	+	2.80871i	1.30241	+	0.148861i
$357$		0			0
$358$	0.147165	−	2.58352i	0.00777789	−	0.136543i
$359$	−1.61533	−	1.61533i	−0.0852541	−	0.0852541i	0.663194	−	0.748448i	$-0.269201\pi$
$359$	−1.61533	−	1.61533i	−0.0852541	−	0.0852541i	−0.748448	+	0.663194i	$0.769201\pi$
$360$		0			0
$361$	−12.0923	+	12.0923i	−0.636435	+	0.636435i
$362$	−20.1508	−	22.5852i	−1.05911	−	1.18705i
$363$		0			0
$364$	1.34273	+	4.68897i	0.0703784	+	0.245769i
$365$	−3.41921	−	2.62365i	−0.178970	−	0.137328i
$366$		0			0
$367$	4.17945	−	7.23901i	0.218165	−	0.377873i	−0.736082	−	0.676893i	$-0.763326\pi$
$367$	4.17945	−	7.23901i	0.218165	−	0.377873i	0.954247	+	0.299019i	$0.0966595\pi$
$368$	5.45939	−	10.2500i	0.284591	−	0.534318i
$369$		0			0
$370$	0.812280	+	0.700157i	0.0422284	+	0.0363994i
$371$	12.6719	+	1.66829i	0.657892	+	0.0866131i
$372$		0			0
$373$	3.43521	+	26.0930i	0.177869	+	1.35105i	0.814628	+	0.579984i	$0.196941\pi$
$373$	3.43521	+	26.0930i	0.177869	+	1.35105i	−0.636759	+	0.771063i	$0.719725\pi$
$374$	−1.54248	+	0.320550i	−0.0797599	+	0.0165753i
$375$		0			0
$376$	4.09049	−	13.1487i	0.210951	−	0.678093i
$377$	3.36373	−	3.36373i	0.173241	−	0.173241i
$378$		0			0
$379$	−3.63491	−	1.50563i	−0.186713	−	0.0773389i	0.287368	−	0.957820i	$-0.407220\pi$
$379$	−3.63491	−	1.50563i	−0.186713	−	0.0773389i	−0.474081	+	0.880481i	$0.657220\pi$
$380$	−0.350160	+	0.888006i	−0.0179628	+	0.0455537i
$381$		0			0
$382$	3.36357	−	2.28930i	0.172095	−	0.117131i
$383$	−17.3414	−	30.0361i	−0.886102	−	1.53477i	−0.844445	−	0.535642i	$-0.820070\pi$
$383$	−17.3414	−	30.0361i	−0.886102	−	1.53477i	−0.0416575	−	0.999132i	$-0.513264\pi$
$384$		0			0
$385$	0.464743	−	0.804958i	0.0236855	−	0.0410245i
$386$	−0.258600	−	3.48829i	−0.0131624	−	0.177549i
$387$		0			0
$388$	1.68641	−	0.251422i	0.0856146	−	0.0127640i
$389$	11.7666	−	9.02885i	0.596592	−	0.457781i	−0.265796	−	0.964029i	$-0.585635\pi$
$389$	11.7666	−	9.02885i	0.596592	−	0.457781i	0.862388	+	0.506248i	$0.168968\pi$
$390$		0			0
$391$	−1.61189	−	0.431905i	−0.0815169	−	0.0218424i
$392$	−9.75285	−	10.5619i	−0.492593	−	0.533456i
$393$		0			0
$394$	19.9573	+	22.3683i	1.00544	+	1.12690i
$395$	4.20851	+	1.74322i	0.211753	+	0.0877110i
$396$		0			0
$397$	−11.9115	−	28.7569i	−0.597821	−	1.44327i	−0.875797	−	0.482679i	$-0.839664\pi$
$397$	−11.9115	−	28.7569i	−0.597821	−	1.44327i	0.277976	−	0.960588i	$-0.410336\pi$
$398$	33.7154	−	11.7672i	1.69000	−	0.589837i
$399$		0			0
$400$	0.667341	+	19.5088i	0.0333670	+	0.975438i
$401$	−14.6435	−	25.3633i	−0.731263	−	1.26658i	−0.956344	−	0.292245i	$-0.905598\pi$
$401$	−14.6435	−	25.3633i	−0.731263	−	1.26658i	0.225080	−	0.974340i	$-0.427736\pi$
$402$		0			0
$403$	1.29500	−	9.83651i	0.0645086	−	0.489991i
$404$	33.1440	+	8.27627i	1.64898	+	0.411760i
$405$		0			0
$406$	1.65723	−	5.02269i	0.0822469	−	0.249272i
$407$	−1.09827	−	4.09881i	−0.0544394	−	0.203171i
$408$		0			0
$409$	−8.46074	+	31.5759i	−0.418356	+	1.56133i	0.359660	+	0.933083i	$0.382893\pi$
$409$	−8.46074	+	31.5759i	−0.418356	+	1.56133i	−0.778016	+	0.628244i	$0.783774\pi$
$410$	−4.70314	−	3.08471i	−0.232271	−	0.152343i
$411$		0			0
$412$	−5.53174	−	12.7345i	−0.272529	−	0.627386i
$413$	−3.00685	−	7.25917i	−0.147957	−	0.357200i
$414$		0			0
$415$		−	3.95849i		−	0.194315i
$416$	−2.35946	−	9.67966i	−0.115682	−	0.474584i
$417$		0			0
$418$	3.12251	−	2.12522i	0.152727	−	0.103948i
$419$	26.9905	+	20.7105i	1.31857	+	1.01178i	0.997912	+	0.0645817i	$0.0205713\pi$
$419$	26.9905	+	20.7105i	1.31857	+	1.01178i	0.320660	+	0.947194i	$0.396095\pi$
$420$		0			0
$421$	−8.36658	−	10.9035i	−0.407762	−	0.531406i	0.543656	−	0.839308i	$-0.317040\pi$
$421$	−8.36658	−	10.9035i	−0.407762	−	0.531406i	−0.951418	+	0.307902i	$0.900373\pi$
$422$	2.89357	+	5.74329i	0.140857	+	0.279579i
$423$		0			0
$424$	−25.7286	−	4.43514i	−1.24949	−	0.215389i
$425$	2.70936	−	0.725970i	0.131423	−	0.0352147i
$426$		0			0
$427$	6.78891	−	0.893777i	0.328538	−	0.0432529i
$428$	−0.691511	−	2.41483i	−0.0334254	−	0.116725i
$429$		0			0
$430$	−3.43447	+	1.19868i	−0.165625	+	0.0578056i
$431$		−	15.3879i		−	0.741209i	−0.928791	−	0.370605i	$-0.879151\pi$
$431$		−	15.3879i		−	0.741209i	0.928791	−	0.370605i	$-0.120849\pi$
$432$		0			0
$433$		−	10.2006i		−	0.490209i	−0.969497	−	0.245105i	$-0.921178\pi$
$433$		−	10.2006i		−	0.490209i	0.969497	−	0.245105i	$-0.0788223\pi$
$434$	−3.63494	−	10.4148i	−0.174483	−	0.499928i
$435$		0			0
$436$	7.99022	−	14.4026i	0.382662	−	0.689761i
$437$	3.96661	−	0.522215i	0.189749	−	0.0249809i
$438$		0			0
$439$	−9.53888	+	2.55594i	−0.455266	+	0.121988i	−0.479162	−	0.877726i	$-0.659059\pi$
$439$	−9.53888	+	2.55594i	−0.455266	+	0.121988i	0.0238964	+	0.999714i	$0.492393\pi$
$440$	−1.01400	+	1.60520i	−0.0483407	+	0.0765247i
$441$		0			0
$442$	−1.27853	+	0.644148i	−0.0608136	+	0.0306390i
$443$	−10.3166	−	13.4449i	−0.490157	−	0.638786i	0.481143	−	0.876642i	$-0.340222\pi$
$443$	−10.3166	−	13.4449i	−0.490157	−	0.638786i	−0.971300	+	0.237857i	$0.923555\pi$
$444$		0			0
$445$	−3.39813	−	2.60748i	−0.161087	−	0.123606i
$446$	17.0725	+	25.0839i	0.808405	+	1.18776i
$447$		0			0
$448$	−7.18512	−	8.43092i	−0.339465	−	0.398324i
$449$			15.4753i			0.730324i	0.930944	+	0.365162i	$0.118986\pi$
$449$			15.4753i			0.730324i	−0.930944	+	0.365162i	$0.881014\pi$
$450$		0			0
$451$	8.51697	+	20.5618i	0.401048	+	0.968216i
$452$	1.41382	−	3.58543i	0.0665003	−	0.168645i
$453$		0			0
$454$	13.5933	−	20.7252i	0.637966	−	0.972682i
$455$	0.218610	−	0.815862i	0.0102486	−	0.0382482i
$456$		0			0
$457$	9.95193	+	37.1411i	0.465532	+	1.73739i	0.655120	+	0.755525i	$0.272618\pi$
$457$	9.95193	+	37.1411i	0.465532	+	1.73739i	−0.189588	+	0.981864i	$0.560715\pi$
$458$	23.5054	+	7.75555i	1.09833	+	0.362393i
$459$		0			0
$460$	−1.72422	+	1.03518i	−0.0803923	+	0.0482656i
$461$	2.92643	−	22.2284i	0.136297	−	1.03528i	−0.777434	−	0.628964i	$-0.783479\pi$
$461$	2.92643	−	22.2284i	0.136297	−	1.03528i	0.913732	−	0.406318i	$-0.133187\pi$
$462$		0			0
$463$	10.3861	+	17.9892i	0.482682	+	0.836030i	0.999802	−	0.0198831i	$-0.00632939\pi$
$463$	10.3861	+	17.9892i	0.482682	+	0.836030i	−0.517120	+	0.855913i	$0.672996\pi$
$464$	−3.79079	+	10.1169i	−0.175983	+	0.469667i
$465$		0			0
$466$	0.903563	+	2.58889i	0.0418568	+	0.119928i
$467$	−5.06780	−	12.2348i	−0.234510	−	0.566157i	0.762188	−	0.647356i	$-0.224125\pi$
$467$	−5.06780	−	12.2348i	−0.234510	−	0.566157i	−0.996698	+	0.0811986i	$0.974125\pi$
$468$		0			0
$469$	8.64114	+	3.57928i	0.399011	+	0.165276i
$470$	−1.77937	+	1.58758i	−0.0820760	+	0.0732294i
$471$		0			0
$472$	5.54711	+	15.0609i	0.255326	+	0.693233i
$473$	13.9035	+	3.72544i	0.639284	+	0.171296i
$474$		0			0
$475$	−5.33517	+	4.09382i	−0.244794	+	0.187837i
$476$	−0.947259	+	1.27919i	−0.0434175	+	0.0586317i
$477$		0			0
$478$	26.0893	−	1.93409i	1.19330	−	0.0884634i
$479$	10.2347	−	17.7270i	0.467635	−	0.809968i	−0.531681	−	0.846945i	$-0.678440\pi$
$479$	10.2347	−	17.7270i	0.467635	−	0.809968i	0.999316	+	0.0369770i	$0.0117728\pi$
$480$		0			0
$481$	−1.92803	−	3.33945i	−0.0879108	−	0.152266i
$482$	−8.19050	−	12.0340i	−0.373067	−	0.548133i
$483$		0			0
$484$	−13.2876	+	5.77200i	−0.603983	+	0.262363i
$485$	−0.272793	−	0.112995i	−0.0123869	−	0.00513082i
$486$		0			0
$487$	−24.3007	+	24.3007i	−1.10117	+	1.10117i	−0.106899	+	0.994270i	$0.534092\pi$
$487$	−24.3007	+	24.3007i	−1.10117	+	1.10117i	−0.994270	+	0.106899i	$0.965908\pi$
$488$	−13.9293	+	1.27241i	−0.630548	+	0.0575994i
$489$		0			0
$490$	0.506543	+	2.43748i	0.0228833	+	0.110114i
$491$	−0.463090	−	3.51752i	−0.0208990	−	0.158743i	0.977813	−	0.209479i	$-0.0671768\pi$
$491$	−0.463090	−	3.51752i	−0.0208990	−	0.158743i	−0.998712	+	0.0507356i	$0.983843\pi$
$492$		0			0
$493$	1.53916	+	0.202635i	0.0693204	+	0.00912621i
$494$	2.24096	−	2.59983i	0.100826	−	0.116972i
$495$		0			0
$496$	6.57258	+	21.5529i	0.295117	+	0.967752i
$497$	−4.94424	+	8.56367i	−0.221779	+	0.384133i
$498$		0			0
$499$	18.4485	+	14.1560i	0.825867	+	0.633710i	0.932735	−	0.360564i	$-0.117416\pi$
$499$	18.4485	+	14.1560i	0.825867	+	0.633710i	−0.106868	+	0.994273i	$0.534082\pi$
$500$	3.32009	−	5.98458i	0.148479	−	0.267638i
$501$		0			0
$502$	20.5822	−	18.3637i	0.918629	−	0.819614i
$503$	12.0479	−	12.0479i	0.537191	−	0.537191i	−0.385512	−	0.922703i	$-0.625975\pi$
$503$	12.0479	−	12.0479i	0.537191	−	0.537191i	0.922703	+	0.385512i	$0.125975\pi$
$504$		0			0
$505$	−4.18317	−	4.18317i	−0.186149	−	0.186149i
$506$	7.94498	+	0.452569i	0.353198	+	0.0201191i
$507$		0			0
$508$	25.9953	−	20.6625i	1.15336	−	0.916749i
$509$	−21.9860	+	28.6527i	−0.974513	+	1.27001i	−0.0116744	+	0.999932i	$0.503716\pi$
$509$	−21.9860	+	28.6527i	−0.974513	+	1.27001i	−0.962838	+	0.270078i	$0.912950\pi$
$510$		0			0
$511$	14.9218	+	8.61512i	0.660103	+	0.381111i
$512$	13.9800	+	17.7921i	0.617834	+	0.786309i
$513$		0			0
$514$	9.65129	−	0.715486i	0.425700	−	0.0315587i
$515$	−0.313832	+	2.38379i	−0.0138291	+	0.105042i
$516$		0			0
$517$	9.35523	−	1.23164i	0.411442	−	0.0541674i
$518$	−3.58500	−	2.35134i	−0.157516	−	0.103312i
$519$		0			0
$520$	−0.512515	+	1.64746i	−0.0224753	+	0.0722459i
$521$	13.4588	+	13.4588i	0.589643	+	0.589643i	0.937535	−	0.347892i	$-0.113102\pi$
$521$	13.4588	+	13.4588i	0.589643	+	0.589643i	−0.347892	+	0.937535i	$0.613102\pi$
$522$		0			0
$523$	2.77801	−	6.70671i	0.121474	−	0.293264i	−0.851432	−	0.524465i	$-0.824265\pi$
$523$	2.77801	−	6.70671i	0.121474	−	0.293264i	0.972906	+	0.231201i	$0.0742655\pi$
$524$	0.468409	+	27.3945i	0.0204625	+	1.19674i
$525$		0			0
$526$	−18.9066	−	3.59303i	−0.824369	−	0.156663i
$527$	2.80403	−	1.61891i	0.122146	−	0.0705208i
$528$		0			0
$529$	−12.6187	−	7.28539i	−0.548638	−	0.316756i
$530$	3.42459	+	2.95188i	0.148755	+	0.128221i
$531$		0			0
$532$	0.924542	−	3.70251i	0.0400840	−	0.160524i
$533$	12.3118	+	16.0451i	0.533285	+	0.694990i
$534$		0			0
$535$	−0.112584	+	0.420171i	−0.00486745	+	0.0181656i
$536$	−17.3462	−	8.00795i	−0.749242	−	0.345891i
$537$		0			0
$538$	15.8977	+	0.905578i	0.685398	+	0.0390422i
$539$	3.76984	−	9.10120i	0.162379	−	0.392017i
$540$		0			0
$541$	−25.2984	+	10.4790i	−1.08767	+	0.450526i	−0.853192	−	0.521597i	$-0.825337\pi$
$541$	−25.2984	+	10.4790i	−1.08767	+	0.450526i	−0.234473	+	0.972123i	$0.575337\pi$
$542$	−9.80140	−	4.72979i	−0.421006	−	0.203162i
$543$		0			0
$544$	2.03740	−	2.53392i	0.0873528	−	0.108641i
$545$	−2.47013	+	1.42613i	−0.105809	+	0.0610888i
$546$		0			0
$547$	−8.53332	−	1.12343i	−0.364858	−	0.0480345i	−0.0541317	−	0.998534i	$-0.517239\pi$
$547$	−8.53332	−	1.12343i	−0.364858	−	0.0480345i	−0.310727	+	0.950499i	$0.600572\pi$
$548$	−34.4216	−	25.4896i	−1.47042	−	1.08886i
$549$		0			0
$550$	−11.9456	+	6.01839i	−0.509361	+	0.256625i
$551$	−3.59517	+	0.963322i	−0.153159	+	0.0410389i
$552$		0			0
$553$	−17.5909	−	4.71348i	−0.748043	−	0.200438i
$554$	−24.8959	+	5.17373i	−1.05773	+	0.219811i
$555$		0			0
$556$	2.89458	+	2.79726i	0.122757	+	0.118630i
$557$	−12.9331	+	5.35706i	−0.547993	+	0.226986i	−0.639463	−	0.768822i	$-0.720843\pi$
$557$	−12.9331	+	5.35706i	−0.547993	+	0.226986i	0.0914705	+	0.995808i	$0.470843\pi$
$558$		0			0
$559$	13.0801			0.553229
$560$	0.315261	+	1.89221i	0.0133222	+	0.0799604i
$561$		0			0
$562$	1.41807	−	7.46195i	0.0598178	−	0.314763i
$563$	24.2298	−	31.5768i	1.02116	−	1.33080i	0.0785518	−	0.996910i	$-0.474970\pi$
$563$	24.2298	−	31.5768i	1.02116	−	1.33080i	0.942610	−	0.333895i	$-0.108363\pi$
$564$		0			0
$565$	−0.529508	+	0.406306i	−0.0222766	+	0.0170934i
$566$	−8.10087	+	24.5519i	−0.340505	+	1.03200i
$567$		0			0
$568$	10.7876	−	17.0771i	0.452639	−	0.716540i
$569$	5.63454	+	21.0284i	0.236212	+	0.881555i	0.977599	+	0.210477i	$0.0675018\pi$
$569$	5.63454	+	21.0284i	0.236212	+	0.881555i	−0.741387	+	0.671078i	$0.765832\pi$
$570$		0			0
$571$	−4.98912	−	37.8961i	−0.208788	−	1.58590i	−0.699533	−	0.714600i	$-0.746609\pi$
$571$	−4.98912	−	37.8961i	−0.208788	−	1.58590i	0.490745	−	0.871303i	$-0.336725\pi$
$572$	5.34446	−	4.24806i	0.223463	−	0.177620i
$573$		0			0
$574$	20.2515	+	9.77263i	0.845283	+	0.407902i
$575$	−14.1683			−0.590858
$576$		0			0
$577$	−20.9424			−0.871843			−0.435921	−	0.899985i	$-0.643577\pi$
$577$	−20.9424			−0.871843			−0.435921	+	0.899985i	$0.643577\pi$
$578$	21.2316	+	10.2456i	0.883119	+	0.426160i
$579$		0			0
$580$	1.46462	−	1.16416i	0.0608152	−	0.0483392i
$581$	2.06567	+	15.6903i	0.0856982	+	0.650943i
$582$		0			0
$583$	−4.63035	−	17.2807i	−0.191769	−	0.715693i
$584$	−29.7562	−	18.7970i	−1.23132	−	0.777825i
$585$		0			0
$586$	−8.79845	+	26.6662i	−0.363460	+	1.10157i
$587$	−3.70294	+	2.84136i	−0.152837	+	0.117276i	−0.682349	−	0.731027i	$-0.739042\pi$
$587$	−3.70294	+	2.84136i	−0.152837	+	0.117276i	0.529512	+	0.848302i	$0.322375\pi$
$588$		0			0
$589$	−4.72562	+	6.15855i	−0.194716	+	0.253759i
$590$	0.518915	−	2.73055i	0.0213634	−	0.112415i
$591$		0			0
$592$	7.12609	+	5.09066i	0.292881	+	0.209225i
$593$	−6.68985			−0.274719			−0.137360	−	0.990521i	$-0.543862\pi$
$593$	−6.68985			−0.274719			−0.137360	+	0.990521i	$0.543862\pi$
$594$		0			0
$595$	0.254665	−	0.105486i	0.0104402	−	0.00432448i
$596$	11.2039	+	10.8272i	0.458930	+	0.443499i
$597$		0			0
$598$	7.08020	−	1.47137i	0.289531	−	0.0601687i
$599$	−16.8748	−	4.52158i	−0.689484	−	0.184747i	−0.102969	−	0.994685i	$-0.532834\pi$
$599$	−16.8748	−	4.52158i	−0.689484	−	0.184747i	−0.586516	+	0.809938i	$0.699501\pi$
$600$		0			0
$601$	−7.02342	+	1.88192i	−0.286491	+	0.0767651i	−0.399203	−	0.916863i	$-0.630713\pi$
$601$	−7.02342	+	1.88192i	−0.286491	+	0.0767651i	0.112712	+	0.993628i	$0.464046\pi$
$602$	12.9877	−	6.54343i	0.529338	−	0.266690i
$603$		0			0
$604$	−34.5218	−	25.5638i	−1.40467	−	1.04018i
$605$	2.48732	+	0.327462i	0.101124	+	0.0133132i
$606$		0			0
$607$	−5.59768	+	3.23182i	−0.227203	+	0.131176i	−0.609281	−	0.792954i	$-0.708542\pi$
$607$	−5.59768	+	3.23182i	−0.227203	+	0.131176i	0.382078	+	0.924130i	$0.375209\pi$
$608$	−2.18802	+	7.48193i	−0.0887358	+	0.303432i
$609$		0			0
$610$	2.18150	+	1.05271i	0.0883265	+	0.0426231i
$611$	7.92194	−	3.28137i	0.320487	−	0.132750i
$612$		0			0
$613$	13.5163	−	32.6313i	0.545920	−	1.31797i	−0.374570	−	0.927199i	$-0.622209\pi$
$613$	13.5163	−	32.6313i	0.545920	−	1.31797i	0.920489	−	0.390768i	$-0.127791\pi$
$614$	5.08038	+	0.289393i	0.205028	+	0.0116790i
$615$		0			0
$616$	3.18156	−	6.89166i	0.128189	−	0.277673i
$617$	−1.49686	+	5.58635i	−0.0602613	+	0.224898i	−0.989489	−	0.144610i	$-0.953807\pi$
$617$	−1.49686	+	5.58635i	−0.0602613	+	0.224898i	0.929227	+	0.369508i	$0.120474\pi$
$618$		0			0
$619$	22.4216	+	29.2204i	0.901201	+	1.17447i	0.984048	+	0.177905i	$0.0569321\pi$
$619$	22.4216	+	29.2204i	0.901201	+	1.17447i	−0.0828470	+	0.996562i	$0.526401\pi$
$620$	0.945346	−	3.78583i	0.0379660	−	0.152042i
$621$		0			0
$622$	27.6619	+	23.8436i	1.10914	+	0.956041i
$623$	14.8298	+	8.56200i	0.594144	+	0.343029i
$624$		0			0
$625$	20.1048	−	11.6075i	0.804193	−	0.464301i
$626$	−23.4939	−	4.46480i	−0.939006	−	0.178449i
$627$		0			0
$628$	−0.553978	−	32.3990i	−0.0221061	−	1.29286i
$629$	0.481575	−	1.16263i	0.0192017	−	0.0463569i
$630$		0			0
$631$	17.9530	+	17.9530i	0.714696	+	0.714696i	0.967514	−	0.252818i	$-0.0813573\pi$
$631$	17.9530	+	17.9530i	0.714696	+	0.714696i	−0.252818	+	0.967514i	$0.581357\pi$
$632$	35.5212	+	11.0504i	1.41296	+	0.439563i
$633$		0			0
$634$	−11.0055	−	7.21832i	−0.437084	−	0.286676i
$635$	−5.70134	+	0.750596i	−0.226251	+	0.0297865i
$636$		0			0
$637$	1.16845	−	8.87529i	0.0462958	−	0.351652i
$638$	−7.38296	+	0.547326i	−0.292294	+	0.0216688i
$639$		0			0
$640$	−0.489658	−	3.88775i	−0.0193554	−	0.153677i
$641$	0.777343	+	0.448799i	0.0307032	+	0.0177265i	0.515273	−	0.857026i	$-0.327691\pi$
$641$	0.777343	+	0.448799i	0.0307032	+	0.0177265i	−0.484570	+	0.874753i	$0.661024\pi$
$642$		0			0
$643$	−3.03354	+	3.95338i	−0.119631	+	0.155906i	−0.849330	−	0.527863i	$-0.822994\pi$
$643$	−3.03354	+	3.95338i	−0.119631	+	0.155906i	0.729699	+	0.683769i	$0.239660\pi$
$644$	6.29411	−	5.00290i	0.248023	−	0.197142i
$645$		0			0
$646$	1.11832	+	0.0637029i	0.0439999	+	0.00250636i
$647$	1.28302	+	1.28302i	0.0504409	+	0.0504409i	0.731877	−	0.681436i	$-0.238644\pi$
$647$	1.28302	+	1.28302i	0.0504409	+	0.0504409i	−0.681436	+	0.731877i	$0.738644\pi$
$648$		0			0
$649$	−7.77680	+	7.77680i	−0.305266	+	0.305266i
$650$	−9.06981	+	8.09221i	−0.355747	+	0.317403i
$651$		0			0
$652$	−13.7669	+	24.8152i	−0.539152	+	0.971840i
$653$	6.65434	+	5.10605i	0.260404	+	0.199815i	0.730709	−	0.682689i	$-0.239189\pi$
$653$	6.65434	+	5.10605i	0.260404	+	0.199815i	−0.470305	+	0.882504i	$0.655856\pi$
$654$		0			0
$655$	2.37235	−	4.10903i	0.0926953	−	0.160553i
$656$	−40.5404	−	21.5928i	−1.58284	−	0.843056i
$657$		0			0
$658$	6.22443	−	7.22120i	0.242654	−	0.281512i
$659$	−35.1818	−	4.63178i	−1.37049	−	0.180428i	−0.590913	−	0.806735i	$-0.701232\pi$
$659$	−35.1818	−	4.63178i	−1.37049	−	0.180428i	−0.779577	+	0.626307i	$0.784566\pi$
$660$		0			0
$661$	−0.00813271	−	0.0617740i	−0.000316326	−	0.00240273i	0.991286	−	0.131727i	$-0.0420524\pi$
$661$	−0.00813271	−	0.0617740i	−0.000316326	−	0.00240273i	−0.991602	+	0.129325i	$0.958719\pi$
$662$	5.24127	+	25.2209i	0.203708	+	0.980238i
$663$		0			0
$664$	−2.94075	−	32.1928i	−0.114123	−	1.24932i
$665$	−0.467302	+	0.467302i	−0.0181212	+	0.0181212i
$666$		0			0
$667$	−7.24480	−	3.00090i	−0.280520	−	0.116195i
$668$	−27.1085	+	11.7756i	−1.04886	+	0.455612i
$669$		0			0
$670$	1.86158	+	2.73515i	0.0719193	+	0.105668i
$671$	−4.79232	−	8.30054i	−0.185005	−	0.320439i
$672$		0			0
$673$	−5.58320	+	9.67039i	−0.215217	+	0.372766i	−0.953340	−	0.301900i	$-0.902379\pi$
$673$	−5.58320	+	9.67039i	−0.215217	+	0.372766i	0.738123	+	0.674666i	$0.235712\pi$
$674$	−15.8259	+	1.17323i	−0.609589	+	0.0451911i
$675$		0			0
$676$	−11.7808	+	15.9090i	−0.453109	+	0.611885i
$677$	0.878057	−	0.673756i	0.0337465	−	0.0258946i	−0.591751	−	0.806121i	$-0.701563\pi$
$677$	0.878057	−	0.673756i	0.0337465	−	0.0258946i	0.625497	+	0.780227i	$0.284896\pi$
$678$		0			0
$679$	1.14024	+	0.305525i	0.0437582	+	0.0117250i
$680$	−0.528362	+	0.194602i	−0.0202618	+	0.00746266i
$681$		0			0
$682$	−11.5212	+	10.2794i	−0.441170	+	0.393618i
$683$	−27.8034	−	11.5165i	−1.06387	−	0.440668i	−0.219045	−	0.975715i	$-0.570294\pi$
$683$	−27.8034	−	11.5165i	−1.06387	−	0.440668i	−0.844823	+	0.535046i	$0.820294\pi$
$684$		0			0
$685$	2.83849	+	6.85273i	0.108453	+	0.261829i
$686$	−7.79665	−	22.3390i	−0.297677	−	0.852905i
$687$		0			0
$688$	−27.0406	+	12.2999i	−1.03091	+	0.468928i
$689$	−8.12864	−	14.0792i	−0.309676	−	0.536375i
$690$		0			0
$691$	5.47219	−	41.5654i	0.208172	−	1.58122i	−0.494158	−	0.869372i	$-0.664524\pi$
$691$	5.47219	−	41.5654i	0.208172	−	1.58122i	0.702330	−	0.711851i	$-0.252143\pi$
$692$	−3.55796	+	2.13611i	−0.135253	+	0.0812028i
$693$		0			0
$694$	−9.67962	−	3.19377i	−0.367433	−	0.121234i
$695$	−0.180417	−	0.673326i	−0.00684362	−	0.0255407i
$696$		0			0
$697$	−1.70825	+	6.37528i	−0.0647047	+	0.241481i
$698$	−7.26509	+	11.0768i	−0.274988	+	0.419263i
$699$		0			0
$700$	−4.95753	+	12.5723i	−0.187377	+	0.475188i
$701$	18.4529	+	44.5492i	0.696956	+	1.68260i	0.730274	+	0.683155i	$0.239393\pi$
$701$	18.4529	+	44.5492i	0.696956	+	1.68260i	−0.0333180	+	0.999445i	$0.510607\pi$
$702$		0			0
$703$			3.01706i			0.113791i
$704$	−7.05399	+	13.8077i	−0.265857	+	0.520398i
$705$		0			0
$706$	2.78887	+	4.09757i	0.104960	+	0.154214i
$707$	18.7637	+	14.3979i	0.705683	+	0.541490i
$708$		0			0
$709$	1.28644	+	1.67652i	0.0483133	+	0.0629631i	0.816885	−	0.576800i	$-0.195699\pi$
$709$	1.28644	+	1.67652i	0.0483133	+	0.0629631i	−0.768572	+	0.639763i	$0.779032\pi$
$710$	−3.12386	+	1.57386i	−0.117237	+	0.0590659i
$711$		0			0
$712$	−29.5727	−	18.6811i	−1.10828	−	0.700103i
$713$	−15.7976	+	4.23296i	−0.591625	+	0.158525i
$714$		0			0
$715$	−1.17216	+	0.154317i	−0.0438362	+	0.00577115i
$716$	−1.77534	+	3.20010i	−0.0663474	+	0.119593i
$717$		0			0
$718$	1.06458	+	3.05023i	0.0397297	+	0.113834i
$719$		−	49.4592i		−	1.84452i	−0.386573	−	0.922259i	$-0.626341\pi$
$719$		−	49.4592i		−	1.84452i	0.386573	−	0.922259i	$-0.373659\pi$
$720$		0			0
$721$		−	9.61240i		−	0.357985i
$722$	22.8338	−	7.96934i	0.849785	−	0.296588i
$723$		0			0
$724$	11.7841	+	41.1513i	0.437952	+	1.52938i
$725$	13.0680	−	1.72044i	0.485334	−	0.0638955i
$726$		0			0
$727$	−5.58197	+	1.49568i	−0.207024	+	0.0554719i	−0.360841	−	0.932628i	$-0.617510\pi$
$727$	−5.58197	+	1.49568i	−0.207024	+	0.0554719i	0.153817	+	0.988099i	$0.450843\pi$
$728$	1.17176	−	6.79748i	0.0434284	−	0.251932i
$729$		0			0
$730$	2.74238	+	5.44320i	0.101500	+	0.201462i
$731$	2.59859	+	3.38655i	0.0961125	+	0.125256i
$732$		0			0
$733$	−1.33408	−	1.02367i	−0.0492753	−	0.0378102i	0.583830	−	0.811876i	$-0.301553\pi$
$733$	−1.33408	−	1.02367i	−0.0492753	−	0.0378102i	−0.633105	+	0.774066i	$0.718220\pi$
$734$	−9.77252	+	6.65132i	−0.360710	+	0.245505i
$735$		0			0
$736$	−13.2534	+	9.69963i	−0.488526	+	0.357533i
$737$		−	13.0918i		−	0.482243i
$738$		0			0
$739$	6.12108	+	14.7776i	0.225168	+	0.543603i	0.995577	−	0.0939466i	$-0.0299483\pi$
$739$	6.12108	+	14.7776i	0.225168	+	0.543603i	−0.770410	+	0.637549i	$0.779948\pi$
$740$	−0.604242	−	1.39102i	−0.0222124	−	0.0511348i
$741$		0			0
$742$	−15.1144	−	9.91331i	−0.554869	−	0.363929i
$743$	−12.6215	+	47.1041i	−0.463038	+	1.72808i	0.200275	+	0.979740i	$0.435816\pi$
$743$	−12.6215	+	47.1041i	−0.463038	+	1.72808i	−0.663313	+	0.748342i	$0.730850\pi$
$744$		0			0
$745$	−0.698332	−	2.60621i	−0.0255849	−	0.0954842i
$746$	11.6621	−	35.3453i	0.426980	−	1.29408i
$747$		0			0
$748$	2.16163	+	0.539774i	0.0790371	+	0.0197361i
$749$	0.226993	−	1.72418i	0.00829414	−	0.0630002i
$750$		0			0
$751$	−1.99813	−	3.46086i	−0.0729128	−	0.126289i	0.827264	−	0.561814i	$-0.189896\pi$
$751$	−1.99813	−	3.46086i	−0.0729128	−	0.126289i	−0.900177	+	0.435525i	$0.856563\pi$
$752$	−13.2915	+	14.2330i	−0.484690	+	0.519024i
$753$		0			0
$754$	−6.35171	+	2.21685i	−0.231316	+	0.0807328i
$755$	2.84676	+	6.87268i	0.103604	+	0.250122i
$756$		0			0
$757$	−3.51002	−	1.45390i	−0.127574	−	0.0528429i	0.317983	−	0.948096i	$-0.396994\pi$
$757$	−3.51002	−	1.45390i	−0.127574	−	0.0528429i	−0.445557	+	0.895253i	$0.646994\pi$
$758$	3.70428	+	4.15178i	0.134545	+	0.150799i
$759$		0			0
$760$	0.991780	−	0.915809i	0.0359756	−	0.0332199i
$761$	32.6397	+	8.74579i	1.18319	+	0.317035i	0.796191	−	0.605046i	$-0.206845\pi$
$761$	32.6397	+	8.74579i	1.18319	+	0.317035i	0.386999	+	0.922080i	$0.373512\pi$
$762$		0			0
$763$	9.04667	−	6.94175i	0.327511	−	0.251308i
$764$	−5.69114	+	0.848473i	−0.205898	+	0.0306967i
$765$		0			0
$766$	3.62622	+	48.9146i	0.131021	+	1.76735i
$767$	−4.99708	+	8.65520i	−0.180434	+	0.312521i
$768$		0			0
$769$	21.8485	+	37.8428i	0.787879	+	1.36465i	0.927264	+	0.374408i	$0.122154\pi$
$769$	21.8485	+	37.8428i	0.787879	+	1.36465i	−0.139386	+	0.990238i	$0.544513\pi$
$770$	−1.08668	+	0.739608i	−0.0391611	+	0.0266536i
$771$		0			0
$772$	−1.81462	+	4.60187i	−0.0653096	+	0.165625i
$773$	−15.0231	−	6.22279i	−0.540345	−	0.223818i	0.0957826	−	0.995402i	$-0.469465\pi$
$773$	−15.0231	−	6.22279i	−0.540345	−	0.223818i	−0.636127	+	0.771584i	$0.719465\pi$
$774$		0			0
$775$	19.4385	−	19.4385i	0.698252	−	0.698252i
$776$	−2.30246	−	0.716283i	−0.0826536	−	0.0257131i
$777$		0			0
$778$	−20.5362	+	4.26771i	−0.736257	+	0.153005i
$779$	−2.06544	−	15.6886i	−0.0740021	−	0.562102i
$780$		0			0
$781$	13.7228	+	1.80664i	0.491040	+	0.0646466i
$782$	1.78756	+	1.54081i	0.0639230	+	0.0550994i
$783$		0			0
$784$	5.93031	+	19.4467i	0.211797	+	0.694526i
$785$	−2.80573	+	4.85967i	−0.100141	+	0.173449i
$786$		0			0
$787$	22.1614	+	17.0051i	0.789970	+	0.606165i	0.922935	−	0.384956i	$-0.125783\pi$
$787$	22.1614	+	17.0051i	0.789970	+	0.606165i	−0.132965	+	0.991121i	$0.542450\pi$
$788$	−11.6709	−	40.7562i	−0.415759	−	1.45188i
$789$		0			0
$790$	−4.28883	−	4.80695i	−0.152590	−	0.171024i
$791$	1.88679	−	1.88679i	0.0670864	−	0.0670864i
$792$		0			0
$793$	−6.15873	−	6.15873i	−0.218703	−	0.218703i
$794$	−2.50340	+	43.9479i	−0.0888423	+	1.55965i
$795$		0			0
$796$	−50.1747	−	5.73480i	−1.77840	−	0.203265i
$797$	−20.1557	+	26.2674i	−0.713952	+	0.930441i	−0.999611	−	0.0278909i	$-0.991121\pi$
$797$	−20.1557	+	26.2674i	−0.713952	+	0.930441i	0.285659	+	0.958331i	$0.407788\pi$
$798$		0			0
$799$	2.42341	+	1.39916i	0.0857341	+	0.0494986i
$800$	11.1406	−	25.2579i	0.393880	−	0.893002i
$801$		0			0
$802$	3.06208	+	41.3048i	0.108126	+	1.45852i
$803$	3.14799	−	23.9114i	0.111090	−	0.843814i
$804$		0			0
$805$	−1.38044	+	0.181738i	−0.0486540	+	0.00640543i
$806$	−7.69517	+	11.7325i	−0.271051	+	0.413261i
$807$		0			0
$808$	−37.1277	−	30.9124i	−1.30615	−	1.08749i
$809$	39.3544	+	39.3544i	1.38363	+	1.38363i	0.838083	+	0.545543i	$0.183676\pi$
$809$	39.3544	+	39.3544i	1.38363	+	1.38363i	0.545543	+	0.838083i	$0.316324\pi$
$810$		0			0
$811$	5.95460	−	14.3757i	0.209094	−	0.504798i	−0.784187	−	0.620525i	$-0.786920\pi$
$811$	5.95460	−	14.3757i	0.209094	−	0.504798i	0.993281	+	0.115727i	$0.0369196\pi$
$812$	−5.19784	+	5.37868i	−0.182408	+	0.188755i
$813$		0			0
$814$	−1.12040	+	5.89556i	−0.0392698	+	0.206639i
$815$	4.25595	−	2.45718i	0.149080	−	0.0860711i
$816$		0			0
$817$	−8.86301	−	5.11706i	−0.310077	−	0.179023i
$818$	30.1835	−	35.0171i	1.05534	−	1.22434i
$819$		0			0
$820$	4.09431	+	6.81957i	0.142979	+	0.238150i
$821$	7.15926	+	9.33013i	0.249860	+	0.325624i	0.901397	−	0.432993i	$-0.142542\pi$
$821$	7.15926	+	9.33013i	0.249860	+	0.325624i	−0.651538	+	0.758616i	$0.725876\pi$
$822$		0			0
$823$	11.6735	−	43.5662i	0.406914	−	1.51862i	−0.393585	−	0.919288i	$-0.628765\pi$
$823$	11.6735	−	43.5662i	0.406914	−	1.51862i	0.800499	−	0.599334i	$-0.204568\pi$
$824$	−0.781358	+	19.6196i	−0.0272199	+	0.683480i
$825$		0			0
$826$	−0.631939	+	11.0939i	−0.0219880	+	0.386005i
$827$	−19.2919	+	46.5749i	−0.670846	+	1.61957i	0.109329	+	0.994006i	$0.465130\pi$
$827$	−19.2919	+	46.5749i	−0.670846	+	1.61957i	−0.780175	+	0.625561i	$0.784870\pi$
$828$		0			0
$829$	−25.4354	+	10.5357i	−0.883409	+	0.365920i	−0.777818	−	0.628490i	$-0.783674\pi$
$829$	−25.4354	+	10.5357i	−0.883409	+	0.365920i	−0.105591	+	0.994410i	$0.533674\pi$
$830$	−2.43299	+	5.04182i	−0.0844503	+	0.175004i
$831$		0			0
$832$	−2.94419	+	13.7789i	−0.102071	+	0.477696i
$833$	2.53002	−	1.46071i	0.0876601	−	0.0506106i
$834$		0			0
$835$	5.07446	+	0.668065i	0.175609	+	0.0231193i
$836$	−5.28326	+	0.787664i	−0.182725	+	0.0272419i
$837$		0			0
$838$	−21.6478	−	42.9674i	−0.747810	−	1.48429i
$839$	−30.1077	+	8.06733i	−1.03943	+	0.278515i	−0.737879	−	0.674934i	$-0.764172\pi$
$839$	−30.1077	+	8.06733i	−1.03943	+	0.278515i	−0.301555	+	0.953449i	$0.597506\pi$
$840$		0			0
$841$	−20.9653	−	5.61762i	−0.722940	−	0.193711i
$842$	3.95467	+	19.0298i	0.136287	+	0.655811i
$843$		0			0
$844$	−0.155487	−	9.09352i	−0.00535207	−	0.313012i
$845$	3.16720	−	1.31190i	0.108955	−	0.0451306i
$846$		0			0
$847$	−10.0299			−0.344631
$848$	30.0438	+	21.4623i	1.03171	+	0.737020i
$849$		0			0
$850$	−3.89702	−	0.740593i	−0.133667	−	0.0254021i
$851$	−3.86961	+	5.04297i	−0.132648	+	0.172871i
$852$		0			0
$853$	−35.9469	+	27.5830i	−1.23080	+	0.944425i	−0.999594	−	0.0284809i	$-0.990933\pi$
$853$	−35.9469	+	27.5830i	−1.23080	+	0.944425i	−0.231204	+	0.972905i	$0.574266\pi$
$854$	−9.19617	−	3.03426i	−0.314686	−	0.103830i
$855$		0			0
$856$	−0.603460	+	3.50072i	−0.0206258	+	0.119652i
$857$	−1.89885	−	7.08660i	−0.0648634	−	0.242074i	0.925881	−	0.377816i	$-0.123325\pi$
$857$	−1.89885	−	7.08660i	−0.0648634	−	0.242074i	−0.990744	+	0.135742i	$0.956658\pi$
$858$		0			0
$859$	−2.36263	−	17.9459i	−0.0806118	−	0.612307i	−0.983297	−	0.182006i	$-0.941741\pi$
$859$	−2.36263	−	17.9459i	−0.0806118	−	0.612307i	0.902686	−	0.430301i	$-0.141593\pi$
$860$	5.11112	+	0.584183i	0.174288	+	0.0199205i
$861$		0			0
$862$	−9.45779	+	19.5991i	−0.322134	+	0.667548i
$863$	46.9403			1.59787			0.798934	−	0.601419i	$-0.205398\pi$
$863$	46.9403			1.59787			0.798934	+	0.601419i	$0.205398\pi$
$864$		0			0
$865$	0.718661			0.0244352
$866$	−6.26954	+	12.9922i	−0.213048	+	0.441493i
$867$		0			0
$868$	−1.77151	+	15.4992i	−0.0601288	+	0.526077i
$869$	3.32727	+	25.2731i	0.112870	+	0.857331i
$870$		0			0
$871$	−3.07912	−	11.4914i	−0.104332	−	0.389372i
$872$	−19.0291	+	13.4332i	−0.644408	+	0.454906i
$873$		0			0
$874$	−5.37312	−	1.77285i	−0.181749	−	0.0599676i
$875$	3.75907	−	2.88443i	0.127080	−	0.0975117i
$876$		0			0
$877$	−7.07932	+	9.22595i	−0.239052	+	0.311538i	−0.897437	−	0.441143i	$-0.854573\pi$
$877$	−7.07932	+	9.22595i	−0.239052	+	0.311538i	0.658385	+	0.752681i	$0.271240\pi$
$878$	13.7203	+	2.60742i	0.463039	+	0.0879961i
$879$		0			0
$880$	2.27810	−	1.42126i	0.0767947	−	0.0479106i
$881$	21.2953			0.717455			0.358728	−	0.933442i	$-0.383211\pi$
$881$	21.2953			0.717455			0.358728	+	0.933442i	$0.383211\pi$
$882$		0			0
$883$	8.06528	−	3.34075i	0.271418	−	0.112425i	−0.242823	−	0.970071i	$-0.578074\pi$
$883$	8.06528	−	3.34075i	0.271418	−	0.112425i	0.514241	+	0.857645i	$0.328074\pi$
$884$	2.02434	−	0.0346134i	0.0680859	−	0.00116417i
$885$		0			0
$886$	4.87641	+	23.4652i	0.163826	+	0.788329i
$887$	41.5311	+	11.1282i	1.39448	+	0.373649i	0.876358	−	0.481660i	$-0.159966\pi$
$887$	41.5311	+	11.1282i	1.39448	+	0.373649i	0.518119	+	0.855309i	$0.326632\pi$
$888$		0			0
$889$	22.2067	−	5.95028i	0.744790	−	0.199566i
$890$	2.72547	+	5.40964i	0.0913581	+	0.181332i
$891$		0			0
$892$	−6.32751	−	42.4418i	−0.211861	−	1.42106i
$893$	−6.65157	−	0.875696i	−0.222586	−	0.0293040i
$894$		0			0
$895$	0.548835	−	0.316870i	0.0183455	−	0.0105918i
$896$	3.96961	+	15.1544i	0.132615	+	0.506272i
$897$		0			0
$898$	9.51151	−	19.7104i	0.317403	−	0.657745i
$899$	14.0568	−	5.82252i	0.468821	−	0.194192i
$900$		0			0
$901$	2.03033	−	4.90166i	0.0676402	−	0.163298i
$902$	1.78998	−	31.4237i	0.0595999	−	1.04629i
$903$		0			0
$904$	−4.00443	+	3.69769i	−0.133185	+	0.122983i
$905$	1.91856	−	7.16016i	0.0637751	−	0.238012i
$906$		0			0
$907$	−14.6059	−	19.0348i	−0.484982	−	0.632040i	0.485205	−	0.874401i	$-0.338745\pi$
$907$	−14.6059	−	19.0348i	−0.484982	−	0.632040i	−0.970186	+	0.242360i	$0.922078\pi$
$908$	−30.0516	+	18.0423i	−0.997299	+	0.598754i
$909$		0			0
$910$	−0.779886	+	0.904776i	−0.0258530	+	0.0299930i
$911$	17.8426	+	10.3014i	0.591151	+	0.341301i	0.765553	−	0.643373i	$-0.222466\pi$
$911$	17.8426	+	10.3014i	0.591151	+	0.341301i	−0.174401	+	0.984675i	$0.555799\pi$
$912$		0			0
$913$	19.1839	−	11.0758i	0.634895	−	0.366557i
$914$	10.1524	−	53.4222i	0.335811	−	1.76705i
$915$		0			0
$916$	−25.1713	−	24.3250i	−0.831684	−	0.803721i
$917$	−7.25906	+	17.5249i	−0.239715	+	0.578724i
$918$		0			0
$919$	6.10597	+	6.10597i	0.201417	+	0.201417i	0.800607	−	0.599190i	$-0.204510\pi$
$919$	6.10597	+	6.10597i	0.201417	+	0.201417i	−0.599190	+	0.800607i	$0.704510\pi$
$920$	2.83234	−	0.258729i	0.0933795	−	0.00853004i
$921$		0			0
$922$	−17.3895	+	26.5131i	−0.572692	+	0.873161i
$923$	12.4702	−	1.64173i	0.410461	−	0.0540382i
$924$		0			0
$925$	1.39459	−	10.5930i	0.0458540	−	0.348295i
$926$	−2.17181	−	29.2959i	−0.0713701	−	0.962722i
$927$		0			0
$928$	11.0463	−	10.5557i	0.362614	−	0.346509i
$929$	−3.80199	−	2.19508i	−0.124739	−	0.0720182i	0.436332	−	0.899786i	$-0.356277\pi$
$929$	−3.80199	−	2.19508i	−0.124739	−	0.0720182i	−0.561071	+	0.827768i	$0.689611\pi$
$930$		0			0
$931$	−4.26384	+	5.55674i	−0.139742	+	0.182115i
$932$	0.440356	−	3.85274i	0.0144243	−	0.126201i
$933$		0			0
$934$	−1.06508	+	18.6979i	−0.0348506	+	0.611812i
$935$	−0.272824	−	0.272824i	−0.00892230	−	0.00892230i
$936$		0			0
$937$	1.77257	−	1.77257i	0.0579072	−	0.0579072i	−0.677560	−	0.735467i	$-0.736963\pi$
$937$	1.77257	−	1.77257i	0.0579072	−	0.0579072i	0.735467	+	0.677560i	$0.236963\pi$
$938$	−8.80605	−	9.86988i	−0.287528	−	0.322263i
$939$		0			0
$940$	3.24209	−	0.928404i	0.105745	−	0.0302812i
$941$	−28.1056	−	21.5662i	−0.916218	−	0.703039i	0.0389069	−	0.999243i	$-0.487612\pi$
$941$	−28.1056	−	21.5662i	−0.916218	−	0.703039i	−0.955125	+	0.296204i	$0.904279\pi$
$942$		0			0
$943$	16.6694	−	28.8723i	0.542832	−	0.940212i
$944$	2.19161	−	22.5920i	0.0713309	−	0.735306i
$945$		0			0
$946$	−15.4187	−	13.2904i	−0.501307	−	0.432109i
$947$	−43.8566	−	5.77383i	−1.42515	−	0.187624i	−0.621819	−	0.783161i	$-0.713606\pi$
$947$	−43.8566	−	5.77383i	−1.42515	−	0.187624i	−0.803328	+	0.595537i	$0.796939\pi$
$948$		0			0
$949$	−2.86064	−	21.7288i	−0.0928605	−	0.705345i
$950$	9.31141	−	1.93504i	0.302102	−	0.0627811i
$951$		0			0
$952$	1.99272	−	1.04706i	0.0645844	−	0.0339354i
$953$	1.30796	−	1.30796i	0.0423691	−	0.0423691i	−0.685605	−	0.727974i	$-0.740462\pi$
$953$	1.30796	−	1.30796i	0.0423691	−	0.0423691i	0.727974	+	0.685605i	$0.240462\pi$
$954$		0			0
$955$	0.920597	+	0.381324i	0.0297898	+	0.0123393i
$956$	−34.4179	−	13.5717i	−1.11315	−	0.438941i
$957$		0			0
$958$	−23.9311	+	16.2879i	−0.773178	+	0.526237i
$959$	−14.8269	−	25.6810i	−0.478786	−	0.829281i
$960$		0			0
$961$	0.366386	−	0.634599i	0.0118189	−	0.0204709i
$962$	0.403167	+	5.43838i	0.0129986	+	0.175340i
$963$		0			0
$964$	3.03562	+	20.3614i	0.0977706	+	0.655797i
$965$	0.679618	−	0.521490i	0.0218777	−	0.0167873i
$966$		0			0
$967$	−10.6279	−	2.84775i	−0.341771	−	0.0915773i	0.0838509	−	0.996478i	$-0.473278\pi$
$967$	−10.6279	−	2.84775i	−0.341771	−	0.0915773i	−0.425622	+	0.904901i	$0.639945\pi$
$968$	20.4717	+	0.815294i	0.657984	+	0.0262045i
$969$		0			0
$970$	0.277999	+	0.311584i	0.00892602	+	0.0100043i
$971$	39.4533	+	16.3421i	1.26612	+	0.524443i	0.911781	−	0.410676i	$-0.134707\pi$
$971$	39.4533	+	16.3421i	1.26612	+	0.524443i	0.354335	+	0.935119i	$0.384707\pi$
$972$		0			0
$973$	1.06648	+	2.57472i	0.0341899	+	0.0825417i
$974$	45.8869	−	16.0152i	1.47031	−	0.513161i
$975$		0			0
$976$	18.5234	+	6.94065i	0.592918	+	0.222165i
$977$	−15.0042	−	25.9880i	−0.480027	−	0.831431i	0.519711	−	0.854342i	$-0.326040\pi$
$977$	−15.0042	−	25.9880i	−0.480027	−	0.831431i	−0.999738	+	0.0229113i	$0.992706\pi$
$978$		0			0
$979$	3.12858	−	23.7639i	0.0999899	−	0.759499i
$980$	0.852967	−	3.41588i	0.0272470	−	0.109116i
$981$		0			0
$982$	−1.57213	+	4.76478i	−0.0501687	+	0.152050i
$983$	4.32695	+	16.1484i	0.138008	+	0.515053i	0.999967	+	0.00807584i	$0.00257065\pi$
$983$	4.32695	+	16.1484i	0.138008	+	0.515053i	−0.861959	+	0.506978i	$0.830763\pi$
$984$		0			0
$985$	−1.90014	+	7.09140i	−0.0605434	+	0.225951i
$986$	−1.83584	−	1.20410i	−0.0584651	−	0.0383463i
$987$		0			0
$988$	−4.45216	+	1.93397i	−0.141642	+	0.0615278i
$989$	−8.25137	−	19.9206i	−0.262378	−	0.633437i
$990$		0			0
$991$		−	50.6354i		−	1.60849i	−0.594300	−	0.804244i	$-0.702571\pi$
$991$		−	50.6354i		−	1.60849i	0.594300	−	0.804244i	$-0.297429\pi$
$992$	4.87564	−	31.4909i	0.154802	−	0.999837i
$993$		0			0
$994$	11.5608	−	7.86844i	0.366686	−	0.249572i
$995$	6.93827	+	5.32392i	0.219958	+	0.168780i
$996$		0			0
$997$	28.2085	+	36.7621i	0.893373	+	1.16427i	0.985695	+	0.168537i	$0.0539043\pi$
$997$	28.2085	+	36.7621i	0.893373	+	1.16427i	−0.0923222	+	0.995729i	$0.529429\pi$
$998$	−14.7966	−	29.3690i	−0.468379	−	0.929658i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.683.7		368
3.2	odd	2		288.2.bf.a.11.40	✓	368
9.4	even	3		288.2.bf.a.203.39	yes	368
9.5	odd	6	inner	864.2.bn.a.395.8		368
32.3	odd	8	inner	864.2.bn.a.35.8		368
96.35	even	8		288.2.bf.a.227.39	yes	368
288.67	odd	24		288.2.bf.a.131.40	yes	368
288.131	even	24	inner	864.2.bn.a.611.7		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.40	✓	368	3.2	odd	2
288.2.bf.a.131.40	yes	368	288.67	odd	24
288.2.bf.a.203.39	yes	368	9.4	even	3
288.2.bf.a.227.39	yes	368	96.35	even	8
864.2.bn.a.35.8		368	32.3	odd	8	inner
864.2.bn.a.395.8		368	9.5	odd	6	inner
864.2.bn.a.611.7		368	288.131	even	24	inner
864.2.bn.a.683.7		368	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.27367 - 0.614625i) q^{2} +(1.24447 + 1.56566i) q^{4} +(-0.0452073 - 0.343384i) q^{5} +(0.358377 + 1.33748i) q^{7} +(-0.622752 - 2.75902i) q^{8} +O(q^{10})\)	\(q+(-1.27367 - 0.614625i) q^{2} +(1.24447 + 1.56566i) q^{4} +(-0.0452073 - 0.343384i) q^{5} +(0.358377 + 1.33748i) q^{7} +(-0.622752 - 2.75902i) q^{8} +(-0.153473 + 0.465143i) q^{10} +(1.53764 - 1.17987i) q^{11} +(1.07217 - 1.39728i) q^{13} +(0.365595 - 1.92378i) q^{14} +(-0.902582 + 3.89684i) q^{16} +0.574776 q^{17} +(-1.27313 + 0.527348i) q^{19} +(0.481363 - 0.498111i) q^{20} +(-2.68362 + 0.557696i) q^{22} +(-2.80438 - 0.751432i) q^{23} +(4.71376 - 1.26305i) q^{25} +(-2.22440 + 1.12069i) q^{26} +(-1.64805 + 2.22555i) q^{28} +(2.67785 + 0.352546i) q^{29} +(4.87848 - 2.81659i) q^{31} +(3.54469 - 4.40854i) q^{32} +(-0.732075 - 0.353272i) q^{34} +(0.443068 - 0.183525i) q^{35} +(0.837849 - 2.02275i) q^{37} +(1.94567 + 0.110831i) q^{38} +(-0.919249 + 0.338571i) q^{40} +(-2.97203 + 11.0918i) q^{41} +(4.52106 + 5.89196i) q^{43} +(3.76083 + 0.939103i) q^{44} +(3.11001 + 2.68072i) q^{46} +(4.21627 + 2.43427i) q^{47} +(4.40176 - 2.54136i) q^{49} +(-6.78008 - 1.28849i) q^{50} +(3.52196 - 0.0602207i) q^{52} +(3.53239 - 8.52795i) q^{53} +(-0.474662 - 0.474662i) q^{55} +(3.46695 - 1.82169i) q^{56} +(-3.19401 - 2.09490i) q^{58} +(-5.62596 + 0.740672i) q^{59} +(0.645484 - 4.90294i) q^{61} +(-7.94472 + 0.588972i) q^{62} +(-7.22436 + 3.43637i) q^{64} +(-0.528275 - 0.305000i) q^{65} +(4.11206 - 5.35894i) q^{67} +(0.715292 + 0.899903i) q^{68} +(-0.677121 - 0.0385707i) q^{70} +(5.04976 + 5.04976i) q^{71} +(8.79899 - 8.79899i) q^{73} +(-2.31038 + 2.06135i) q^{74} +(-2.41002 - 1.33702i) q^{76} +(2.12911 + 1.63372i) q^{77} +(-6.57615 + 11.3902i) q^{79} +(1.37891 + 0.133766i) q^{80} +(10.6027 - 12.3006i) q^{82} +(11.3315 + 1.49182i) q^{83} +(-0.0259841 - 0.197369i) q^{85} +(-2.13699 - 10.2832i) q^{86} +(-4.21286 - 3.50761i) q^{88} +(8.74474 - 8.74474i) q^{89} +(2.25308 + 0.933257i) q^{91} +(-2.31349 - 5.32585i) q^{92} +(-3.87398 - 5.69188i) q^{94} +(0.238638 + 0.413332i) q^{95} +(0.426263 - 0.738308i) q^{97} +(-7.16837 + 0.531418i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

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