LMFDB - Embedded newform 369.2.ba.a.350.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [369,2,Mod(17,369)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("369.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(369, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [112,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$7$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			350.5
Character	$\chi$	$=$	369.350
Dual form			369.2.ba.a.233.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.626663 + 1.22990i) q^{2} +(0.0556331 - 0.0765724i) q^{4} +(0.501789 + 3.16817i) q^{5} +(-0.983319 - 1.15132i) q^{7} +(2.85574 + 0.452305i) q^{8} +(-3.58207 + 2.60253i) q^{10} +(-0.369033 + 0.602207i) q^{11} +(0.346766 + 4.40607i) q^{13} +(0.799793 - 1.93087i) q^{14} +(1.17480 + 3.61567i) q^{16} +(0.0916972 + 0.381946i) q^{17} +(0.318106 - 4.04192i) q^{19} +(0.270511 + 0.137832i) q^{20} +(-0.971911 - 0.0764911i) q^{22} +(1.07861 - 3.31961i) q^{23} +(-5.03024 + 1.63442i) q^{25} +(-5.20171 + 3.18761i) q^{26} +(-0.142864 + 0.0112437i) q^{28} +(-1.58190 + 6.58910i) q^{29} +(0.487790 + 0.671385i) q^{31} +(0.378272 - 0.378272i) q^{32} +(-0.412291 + 0.352130i) q^{34} +(3.15416 - 3.69304i) q^{35} +(-7.31688 - 5.31603i) q^{37} +(5.17049 - 2.14169i) q^{38} +9.27444i q^{40} +(6.26427 - 1.32625i) q^{41} +(5.53886 - 2.82219i) q^{43} +(0.0255820 + 0.0617604i) q^{44} +(4.75870 - 0.753704i) q^{46} +(-6.09893 - 5.20898i) q^{47} +(0.736423 - 4.64959i) q^{49} +(-5.16244 - 5.16244i) q^{50} +(0.356675 + 0.218571i) q^{52} +(-6.54598 - 1.57155i) q^{53} +(-2.09307 - 0.866979i) q^{55} +(-2.28736 - 3.73263i) q^{56} +(-9.09523 + 2.18357i) q^{58} +(13.3068 + 4.32366i) q^{59} +(5.69224 - 11.1716i) q^{61} +(-0.520054 + 1.02066i) q^{62} +(7.93363 + 2.57779i) q^{64} +(-13.7852 + 3.30953i) q^{65} +(1.09943 + 1.79411i) q^{67} +(0.0343479 + 0.0142274i) q^{68} +(6.51866 + 1.56499i) q^{70} +(-7.80591 - 4.78347i) q^{71} +(-0.723298 - 0.723298i) q^{73} +(1.95294 - 12.3304i) q^{74} +(-0.291802 - 0.249223i) q^{76} +(1.05621 - 0.167287i) q^{77} +(-4.02725 - 9.72264i) q^{79} +(-10.8656 + 5.53629i) q^{80} +(5.55674 + 6.87329i) q^{82} +2.39159i q^{83} +(-1.16406 + 0.482169i) q^{85} +(6.94200 + 5.04366i) q^{86} +(-1.32624 + 1.55283i) q^{88} +(-7.24033 + 6.18383i) q^{89} +(4.73182 - 4.73182i) q^{91} +(-0.194184 - 0.267272i) q^{92} +(2.58453 - 10.7653i) q^{94} +(12.9651 - 1.02038i) q^{95} +(15.2104 - 9.32092i) q^{97} +(6.18000 - 2.00800i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 4 q^{5} + 24 q^{8} - 12 q^{11} - 4 q^{13} - 4 q^{14} + 28 q^{16} - 4 q^{17} + 88 q^{20} + 8 q^{22} + 24 q^{23} - 60 q^{26} + 8 q^{29} + 48 q^{32} - 152 q^{35} + 8 q^{37} - 56 q^{38} + 12 q^{41}+ \cdots + 60 q^{98}+O(q^{100}) $ 112 * q - 4 * q^5 + 24 * q^8 - 12 * q^11 - 4 * q^13 - 4 * q^14 + 28 * q^16 - 4 * q^17 + 88 * q^20 + 8 * q^22 + 24 * q^23 - 60 * q^26 + 8 * q^29 + 48 * q^32 - 152 * q^35 + 8 * q^37 - 56 * q^38 + 12 * q^41 - 24 * q^43 - 60 * q^44 - 56 * q^46 - 28 * q^47 + 64 * q^52 + 16 * q^53 - 8 * q^55 + 72 * q^56 - 16 * q^58 + 40 * q^59 + 28 * q^61 + 68 * q^62 + 172 * q^65 + 48 * q^67 - 36 * q^68 - 232 * q^70 - 32 * q^71 - 72 * q^73 - 4 * q^74 - 176 * q^76 - 60 * q^77 - 72 * q^79 - 128 * q^80 - 192 * q^82 + 16 * q^85 - 40 * q^86 - 112 * q^88 + 48 * q^89 - 80 * q^91 - 64 * q^94 + 20 * q^95 - 72 * q^97 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$-1$	$e\left(\frac{29}{40}\right)$

Coefficient data

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

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

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

$2$	0.626663	+	1.22990i	0.443118	+	0.869668i	0.999256	+	0.0385777i	$0.0122827\pi$
$2$	0.626663	+	1.22990i	0.443118	+	0.869668i	−0.556138	+	0.831090i	$0.687717\pi$
$3$		0			0
$3$		0			0
$4$	0.0556331	−	0.0765724i	0.0278165	−	0.0382862i
$5$	0.501789	+	3.16817i	0.224407	+	1.41685i	0.800435	+	0.599420i	$0.204602\pi$
$5$	0.501789	+	3.16817i	0.224407	+	1.41685i	−0.576028	+	0.817430i	$0.695398\pi$
$6$		0			0
$7$	−0.983319	−	1.15132i	−0.371660	−	0.435158i	0.542783	−	0.839873i	$-0.317371\pi$
$7$	−0.983319	−	1.15132i	−0.371660	−	0.435158i	−0.914443	+	0.404715i	$0.867371\pi$
$8$	2.85574	+	0.452305i	1.00966	+	0.159914i
$9$		0			0
$10$	−3.58207	+	2.60253i	−1.13275	+	0.822991i
$11$	−0.369033	+	0.602207i	−0.111268	+	0.181572i	−0.903427	−	0.428742i	$-0.858957\pi$
$11$	−0.369033	+	0.602207i	−0.111268	+	0.181572i	0.792159	+	0.610314i	$0.208957\pi$
$12$		0			0
$13$	0.346766	+	4.40607i	0.0961755	+	1.22203i	0.835811	+	0.549017i	$0.184998\pi$
$13$	0.346766	+	4.40607i	0.0961755	+	1.22203i	−0.739635	+	0.673008i	$0.765002\pi$
$14$	0.799793	−	1.93087i	0.213754	−	0.516047i
$15$		0			0
$16$	1.17480	+	3.61567i	0.293701	+	0.903918i
$17$	0.0916972	+	0.381946i	0.0222398	+	0.0926356i	0.982386	−	0.186863i	$-0.0598319\pi$
$17$	0.0916972	+	0.381946i	0.0222398	+	0.0926356i	−0.960146	+	0.279498i	$0.909832\pi$
$18$		0			0
$19$	0.318106	−	4.04192i	0.0729786	−	0.927281i	−0.846054	−	0.533098i	$-0.821028\pi$
$19$	0.318106	−	4.04192i	0.0729786	−	0.927281i	0.919032	−	0.394183i	$-0.128972\pi$
$20$	0.270511	+	0.137832i	0.0604880	+	0.0308202i
$21$		0			0
$22$	−0.971911	−	0.0764911i	−0.207212	−	0.0163080i
$23$	1.07861	−	3.31961i	0.224905	−	0.692187i	−0.773396	−	0.633923i	$-0.781444\pi$
$23$	1.07861	−	3.31961i	0.224905	−	0.692187i	0.998301	−	0.0582639i	$-0.0185565\pi$
$24$		0			0
$25$	−5.03024	+	1.63442i	−1.00605	+	0.326885i
$26$	−5.20171	+	3.18761i	−1.02014	+	0.625142i
$27$		0			0
$28$	−0.142864	+	0.0112437i	−0.0269988	+	0.00212485i
$29$	−1.58190	+	6.58910i	−0.293752	+	1.22357i	0.608918	+	0.793233i	$0.291604\pi$
$29$	−1.58190	+	6.58910i	−0.293752	+	1.22357i	−0.902670	+	0.430333i	$0.858396\pi$
$30$		0			0
$31$	0.487790	+	0.671385i	0.0876096	+	0.120584i	0.850572	−	0.525859i	$-0.176256\pi$
$31$	0.487790	+	0.671385i	0.0876096	+	0.120584i	−0.762962	+	0.646443i	$0.776256\pi$
$32$	0.378272	−	0.378272i	0.0668696	−	0.0668696i
$33$		0			0
$34$	−0.412291	+	0.352130i	−0.0707073	+	0.0603897i
$35$	3.15416	−	3.69304i	0.533150	−	0.624238i
$36$		0			0
$37$	−7.31688	−	5.31603i	−1.20289	−	0.873949i	−0.208322	−	0.978060i	$-0.566800\pi$
$37$	−7.31688	−	5.31603i	−1.20289	−	0.873949i	−0.994566	+	0.104111i	$0.966800\pi$
$38$	5.17049	−	2.14169i	0.838764	−	0.347428i
$39$		0			0
$40$			9.27444i			1.46642i
$41$	6.26427	−	1.32625i	0.978314	−	0.207126i
$41$	6.26427	−	1.32625i	0.978314	−	0.207126i
$42$		0			0
$43$	5.53886	−	2.82219i	0.844668	−	0.430380i	0.0225831	−	0.999745i	$-0.492811\pi$
$43$	5.53886	−	2.82219i	0.844668	−	0.430380i	0.822085	+	0.569365i	$0.192811\pi$
$44$	0.0255820	+	0.0617604i	0.00385663	+	0.00931072i
$45$		0			0
$46$	4.75870	−	0.753704i	0.701632	−	0.111128i
$47$	−6.09893	−	5.20898i	−0.889620	−	0.759807i	0.0819309	−	0.996638i	$-0.473891\pi$
$47$	−6.09893	−	5.20898i	−0.889620	−	0.759807i	−0.971551	+	0.236831i	$0.923891\pi$
$48$		0			0
$49$	0.736423	−	4.64959i	0.105203	−	0.664227i
$50$	−5.16244	−	5.16244i	−0.730079	−	0.730079i
$51$		0			0
$52$	0.356675	+	0.218571i	0.0494620	+	0.0303103i
$53$	−6.54598	−	1.57155i	−0.899160	−	0.215869i	−0.242585	−	0.970130i	$-0.577995\pi$
$53$	−6.54598	−	1.57155i	−0.899160	−	0.215869i	−0.656575	+	0.754261i	$0.727995\pi$
$54$		0			0
$55$	−2.09307	−	0.866979i	−0.282230	−	0.116903i
$56$	−2.28736	−	3.73263i	−0.305661	−	0.498793i
$57$		0			0
$58$	−9.09523	+	2.18357i	−1.19426	+	0.286717i
$59$	13.3068	+	4.32366i	1.73240	+	0.562892i	0.993794	−	0.111241i	$-0.0354824\pi$
$59$	13.3068	+	4.32366i	1.73240	+	0.562892i	0.738610	+	0.674133i	$0.235482\pi$
$60$		0			0
$61$	5.69224	−	11.1716i	0.728816	−	1.43038i	−0.167000	−	0.985957i	$-0.553408\pi$
$61$	5.69224	−	11.1716i	0.728816	−	1.43038i	0.895816	−	0.444425i	$-0.146592\pi$
$62$	−0.520054	+	1.02066i	−0.0660469	+	0.129624i
$63$		0			0
$64$	7.93363	+	2.57779i	0.991704	+	0.322224i
$65$	−13.7852	+	3.30953i	−1.70984	+	0.410497i
$66$		0			0
$67$	1.09943	+	1.79411i	0.134317	+	0.219186i	0.912726	−	0.408572i	$-0.133973\pi$
$67$	1.09943	+	1.79411i	0.134317	+	0.219186i	−0.778409	+	0.627757i	$0.783973\pi$
$68$	0.0343479	+	0.0142274i	0.00416530	+	0.00172532i
$69$		0			0
$70$	6.51866	+	1.56499i	0.779128	+	0.187052i
$71$	−7.80591	−	4.78347i	−0.926392	−	0.567694i	−0.0245208	−	0.999699i	$-0.507806\pi$
$71$	−7.80591	−	4.78347i	−0.926392	−	0.567694i	−0.901871	+	0.432006i	$0.857806\pi$
$72$		0			0
$73$	−0.723298	−	0.723298i	−0.0846557	−	0.0846557i	0.663511	−	0.748167i	$-0.269066\pi$
$73$	−0.723298	−	0.723298i	−0.0846557	−	0.0846557i	−0.748167	+	0.663511i	$0.769066\pi$
$74$	1.95294	−	12.3304i	0.227024	−	1.43338i
$75$		0			0
$76$	−0.291802	−	0.249223i	−0.0334720	−	0.0285878i
$77$	1.05621	−	0.167287i	0.120366	−	0.0190641i
$78$		0			0
$79$	−4.02725	−	9.72264i	−0.453101	−	1.09388i	−0.971137	−	0.238523i	$-0.923337\pi$
$79$	−4.02725	−	9.72264i	−0.453101	−	1.09388i	0.518036	−	0.855359i	$-0.326663\pi$
$80$	−10.8656	+	5.53629i	−1.21481	+	0.618976i
$81$		0			0
$82$	5.55674	+	6.87329i	0.613639	+	0.759027i
$83$			2.39159i			0.262511i	0.991349	+	0.131255i	$0.0419008\pi$
$83$			2.39159i			0.262511i	−0.991349	+	0.131255i	$0.958099\pi$
$84$		0			0
$85$	−1.16406	+	0.482169i	−0.126260	+	0.0522986i
$86$	6.94200	+	5.04366i	0.748575	+	0.543872i
$87$		0			0
$88$	−1.32624	+	1.55283i	−0.141378	+	0.165532i
$89$	−7.24033	+	6.18383i	−0.767474	+	0.655484i	−0.944422	−	0.328736i	$-0.893377\pi$
$89$	−7.24033	+	6.18383i	−0.767474	+	0.655484i	0.176948	+	0.984220i	$0.443377\pi$
$90$		0			0
$91$	4.73182	−	4.73182i	0.496029	−	0.496029i
$92$	−0.194184	−	0.267272i	−0.0202451	−	0.0278650i
$93$		0			0
$94$	2.58453	−	10.7653i	0.266573	−	1.11036i
$95$	12.9651	−	1.02038i	1.33019	−	0.104689i
$96$		0			0
$97$	15.2104	−	9.32092i	1.54438	−	0.946396i	0.550629	−	0.834750i	$-0.314388\pi$
$97$	15.2104	−	9.32092i	1.54438	−	0.946396i	0.993748	−	0.111646i	$-0.0356122\pi$
$98$	6.18000	−	2.00800i	0.624274	−	0.202839i
$99$		0			0
$100$	−0.154696	+	0.476105i	−0.0154696	+	0.0476105i
$101$	7.31744	+	0.575895i	0.728113	+	0.0573037i	0.437097	−	0.899414i	$-0.356007\pi$
$101$	7.31744	+	0.575895i	0.728113	+	0.0573037i	0.291016	+	0.956718i	$0.406007\pi$
$102$		0			0
$103$	−0.148091	−	0.0754562i	−0.0145919	−	0.00743492i	0.446679	−	0.894694i	$-0.352606\pi$
$103$	−0.148091	−	0.0754562i	−0.0145919	−	0.00743492i	−0.461271	+	0.887259i	$0.652606\pi$
$104$	−1.00262	+	12.7394i	−0.0983146	+	1.24921i
$105$		0			0
$106$	−2.16928	−	9.03571i	−0.210699	−	0.877626i
$107$	−2.63626	−	8.11358i	−0.254857	−	0.784369i	−0.993858	−	0.110665i	$-0.964702\pi$
$107$	−2.63626	−	8.11358i	−0.254857	−	0.784369i	0.739001	−	0.673705i	$-0.235298\pi$
$108$		0			0
$109$	2.27143	−	5.48372i	0.217564	−	0.525245i	−0.776985	−	0.629519i	$-0.783252\pi$
$109$	2.27143	−	5.48372i	0.217564	−	0.525245i	0.994549	+	0.104274i	$0.0332519\pi$
$110$	−0.245358	−	3.11756i	−0.0233939	−	0.297248i
$111$		0			0
$112$	3.00759	−	4.90794i	0.284190	−	0.463756i
$113$	−6.41054	+	4.65753i	−0.603053	+	0.438144i	−0.846961	−	0.531655i	$-0.821570\pi$
$113$	−6.41054	+	4.65753i	−0.603053	+	0.438144i	0.243908	+	0.969798i	$0.421570\pi$
$114$		0			0
$115$	11.0583	+	1.75147i	1.03120	+	0.163325i
$116$	0.416537	+	0.487702i	0.0386745	+	0.0452820i
$117$		0			0
$118$	3.02126	+	19.0755i	0.278130	+	1.75604i
$119$	0.349574	−	0.481148i	0.0320454	−	0.0441068i
$120$		0			0
$121$	4.76743	+	9.35660i	0.433403	+	0.850600i
$122$	17.3071			1.56691
$123$		0			0
$124$	0.0785468			0.00705371
$125$	−0.421008	−	0.826275i	−0.0376561	−	0.0739043i
$126$		0			0
$127$	−3.55138	+	4.88806i	−0.315134	+	0.433745i	−0.936974	−	0.349400i	$-0.886386\pi$
$127$	−3.55138	+	4.88806i	−0.315134	+	0.433745i	0.621840	+	0.783145i	$0.286386\pi$
$128$	1.63393	+	10.3162i	0.144420	+	0.911833i
$129$		0			0
$130$	−12.7091	−	14.8804i	−1.11466	−	1.30510i
$131$	−15.8526	−	2.51081i	−1.38505	−	0.219371i	−0.580987	−	0.813913i	$-0.697333\pi$
$131$	−15.8526	−	2.51081i	−1.38505	−	0.219371i	−0.804065	+	0.594542i	$0.797333\pi$
$132$		0			0
$133$	−4.96634	+	3.60826i	−0.430637	+	0.312876i
$134$	−1.51760	+	2.47649i	−0.131100	+	0.213936i
$135$		0			0
$136$	0.0891072	+	1.13221i	0.00764088	+	0.0970866i
$137$	−2.32085	+	5.60304i	−0.198284	+	0.478700i	−0.991479	−	0.130268i	$-0.958416\pi$
$137$	−2.32085	+	5.60304i	−0.198284	+	0.478700i	0.793195	+	0.608968i	$0.208416\pi$
$138$		0			0
$139$	6.81303	+	20.9684i	0.577874	+	1.77851i	0.626178	+	0.779680i	$0.284618\pi$
$139$	6.81303	+	20.9684i	0.577874	+	1.77851i	−0.0483036	+	0.998833i	$0.515382\pi$
$140$	−0.107310	−	0.446977i	−0.00906932	−	0.0377764i
$141$		0			0
$142$	0.991491	−	12.5981i	0.0832041	−	1.05721i
$143$	−2.78134	−	1.41716i	−0.232587	−	0.118509i
$144$		0			0
$145$	−21.6692	−	1.70540i	−1.79953	−	0.141626i
$146$	0.436317	−	1.34285i	0.0361099	−	0.111135i
$147$		0			0
$148$	−0.814121	+	0.264524i	−0.0669204	+	0.0217437i
$149$	−1.86668	+	1.14390i	−0.152924	+	0.0937121i	−0.596855	−	0.802349i	$-0.703583\pi$
$149$	−1.86668	+	1.14390i	−0.152924	+	0.0937121i	0.443931	+	0.896061i	$0.353583\pi$
$150$		0			0
$151$	−18.0731	+	1.42238i	−1.47077	+	0.115752i	−0.788357	−	0.615218i	$-0.789068\pi$
$151$	−18.0731	+	1.42238i	−1.47077	+	0.115752i	−0.682409	+	0.730970i	$0.739068\pi$
$152$	2.73661	−	11.3988i	0.221968	−	0.924565i
$153$		0			0
$154$	0.867634	+	1.19420i	0.0699159	+	0.0962310i
$155$	−1.88229	+	1.88229i	−0.151190	+	0.151190i
$156$		0			0
$157$	−7.65640	+	6.53918i	−0.611047	+	0.521884i	−0.900244	−	0.435386i	$-0.856612\pi$
$157$	−7.65640	+	6.53918i	−0.611047	+	0.521884i	0.289197	+	0.957270i	$0.406612\pi$
$158$	9.43410	−	11.0459i	0.750537	−	0.878766i
$159$		0			0
$160$	1.38824	+	1.00862i	0.109750	+	0.0797382i
$161$	−4.88255	+	2.02242i	−0.384799	+	0.159389i
$162$		0			0
$163$			15.6240i			1.22377i	0.790948	+	0.611883i	$0.209588\pi$
$163$			15.6240i			1.22377i	−0.790948	+	0.611883i	$0.790412\pi$
$164$	0.246946	−	0.553453i	0.0192833	−	0.0432175i
$165$		0			0
$166$	−2.94140	+	1.49872i	−0.228297	+	0.116323i
$167$	−4.82565	−	11.6501i	−0.373420	−	0.901515i	−0.993166	−	0.116713i	$-0.962764\pi$
$167$	−4.82565	−	11.6501i	−0.373420	−	0.901515i	0.619746	−	0.784802i	$-0.287236\pi$
$168$		0			0
$169$	−6.45330	+	1.02210i	−0.496407	+	0.0786232i
$170$	−1.32249	−	1.12951i	−0.101430	−	0.0866297i
$171$		0			0
$172$	0.0920420	−	0.581131i	0.00701814	−	0.0443108i
$173$	−5.02432	−	5.02432i	−0.381992	−	0.381992i	0.489828	−	0.871819i	$-0.337060\pi$
$173$	−5.02432	−	5.02432i	−0.381992	−	0.381992i	−0.871819	+	0.489828i	$0.837060\pi$
$174$		0			0
$175$	6.82807	+	4.18425i	0.516154	+	0.316299i
$176$	−2.61092	−	0.626828i	−0.196806	−	0.0472489i
$177$		0			0
$178$	−12.1427	−	5.02968i	−0.910135	−	0.376990i
$179$	3.95369	+	6.45184i	0.295513	+	0.482233i	0.965594	−	0.260055i	$-0.0837406\pi$
$179$	3.95369	+	6.45184i	0.295513	+	0.482233i	−0.670081	+	0.742288i	$0.733741\pi$
$180$		0			0
$181$	−14.0815	+	3.38067i	−1.04667	+	0.251283i	−0.720086	−	0.693885i	$-0.755898\pi$
$181$	−14.0815	+	3.38067i	−1.04667	+	0.251283i	−0.326585	+	0.945168i	$0.605898\pi$
$182$	8.78490	+	2.85439i	0.651180	+	0.211581i
$183$		0			0
$184$	4.58170	−	8.99209i	0.337767	−	0.662906i
$185$	13.1706	−	25.8487i	0.968318	−	1.90043i
$186$		0			0
$187$	−0.263850	−	0.0857300i	−0.0192946	−	0.00626920i
$188$	−0.738166	+	0.177218i	−0.0538363	+	0.0129249i
$189$		0			0
$190$	9.37973	+	15.3063i	0.680477	+	1.11044i
$191$	−10.5888	−	4.38602i	−0.766178	−	0.317361i	−0.0348546	−	0.999392i	$-0.511097\pi$
$191$	−10.5888	−	4.38602i	−0.766178	−	0.317361i	−0.731323	+	0.682031i	$0.761097\pi$
$192$		0			0
$193$	−26.3732	−	6.33165i	−1.89838	−	0.455762i	−0.999858	−	0.0168424i	$-0.994639\pi$
$193$	−26.3732	−	6.33165i	−1.89838	−	0.455762i	−0.898526	−	0.438919i	$-0.855361\pi$
$194$	20.9955	+	12.8661i	1.50739	+	0.923730i
$195$		0			0
$196$	−0.315061	−	0.315061i	−0.0225043	−	0.0225043i
$197$	−2.39369	+	15.1132i	−0.170543	+	1.07677i	0.742781	+	0.669535i	$0.233507\pi$
$197$	−2.39369	+	15.1132i	−0.170543	+	1.07677i	−0.913324	+	0.407234i	$0.866493\pi$
$198$		0			0
$199$	4.94666	+	4.22484i	0.350659	+	0.299491i	0.807278	−	0.590171i	$-0.200940\pi$
$199$	4.94666	+	4.22484i	0.350659	+	0.299491i	−0.456619	+	0.889662i	$0.650940\pi$
$200$	−15.1043	+	2.39229i	−1.06804	+	0.169160i
$201$		0			0
$202$	3.87728	+	9.36059i	0.272805	+	0.658609i
$203$	9.14168	−	4.65792i	0.641620	−	0.326922i
$204$		0			0
$205$	7.34513	+	19.1808i	0.513006	+	1.33964i
$206$		−	0.229422i		−	0.0159846i
$207$		0			0
$208$	−15.5235	+	6.43006i	−1.07636	+	0.445845i
$209$	2.31668	+	1.68317i	0.160248	+	0.116427i
$210$		0			0
$211$	16.0303	−	18.7690i	1.10357	−	1.29211i	0.150749	−	0.988572i	$-0.451831\pi$
$211$	16.0303	−	18.7690i	1.10357	−	1.29211i	0.952819	−	0.303540i	$-0.0981686\pi$
$212$	−0.484511	+	0.413811i	−0.0332763	+	0.0284207i
$213$		0			0
$214$	8.32681	−	8.32681i	0.569209	−	0.569209i
$215$	11.7205	+	16.1319i	0.799333	+	1.10019i
$216$		0			0
$217$	0.293325	−	1.22179i	0.0199122	−	0.0829403i
$218$	8.16783	−	0.642822i	0.553195	−	0.0435374i
$219$		0			0
$220$	−0.182831	+	0.112039i	−0.0123264	+	0.00755365i
$221$	−1.65109	+	0.536470i	−0.111064	+	0.0360869i
$222$		0			0
$223$	−6.30536	+	19.4059i	−0.422238	+	1.29952i	0.483376	+	0.875413i	$0.339410\pi$
$223$	−6.30536	+	19.4059i	−0.422238	+	1.29952i	−0.905614	+	0.424103i	$0.860590\pi$
$224$	−0.807473	−	0.0635495i	−0.0539516	−	0.00424608i
$225$		0			0
$226$	−9.74553	−	4.96560i	−0.648263	−	0.330307i
$227$	−2.21227	+	28.1096i	−0.146834	+	1.86570i	0.278206	+	0.960522i	$0.410260\pi$
$227$	−2.21227	+	28.1096i	−0.146834	+	1.86570i	−0.425039	+	0.905175i	$0.639740\pi$
$228$		0			0
$229$	1.98635	+	8.27376i	0.131262	+	0.546745i	0.998782	+	0.0493430i	$0.0157128\pi$
$229$	1.98635	+	8.27376i	0.131262	+	0.546745i	−0.867520	+	0.497402i	$0.834287\pi$
$230$	4.77573	+	14.6982i	0.314902	+	0.969170i
$231$		0			0
$232$	−7.49779	+	18.1013i	−0.492254	+	1.18841i
$233$	−0.256186	−	3.25515i	−0.0167833	−	0.213252i	−0.999590	−	0.0286170i	$-0.990890\pi$
$233$	−0.256186	−	3.25515i	−0.0167833	−	0.213252i	0.982807	−	0.184635i	$-0.0591103\pi$
$234$		0			0
$235$	13.4426	−	21.9363i	0.876896	−	1.43096i
$236$	1.07137	−	0.778399i	0.0697405	−	0.0506694i
$237$		0			0
$238$	0.810827	+	0.128422i	0.0525581	+	0.00832439i
$239$	10.4264	+	12.2078i	0.674430	+	0.789656i	0.987083	−	0.160212i	$-0.0512177\pi$
$239$	10.4264	+	12.2078i	0.674430	+	0.789656i	−0.312653	+	0.949867i	$0.601218\pi$
$240$		0			0
$241$	−1.80293	−	11.3833i	−0.116137	−	0.733260i	−0.975189	−	0.221372i	$-0.928946\pi$
$241$	−1.80293	−	11.3833i	−0.116137	−	0.733260i	0.859052	−	0.511888i	$-0.171054\pi$
$242$	−8.52008	+	11.7269i	−0.547691	+	0.753832i
$243$		0			0
$244$	−0.538763	−	1.05738i	−0.0344907	−	0.0676919i
$245$	15.1002			0.964718
$246$		0			0
$247$	17.9193			1.14018
$248$	1.08933	+	2.13793i	0.0691725	+	0.135759i
$249$		0			0
$250$	0.752402	−	1.03559i	0.0475861	−	0.0654967i
$251$	−3.94201	−	24.8888i	−0.248817	−	1.57097i	−0.723192	−	0.690647i	$-0.757326\pi$
$251$	−3.94201	−	24.8888i	−0.248817	−	1.57097i	0.474375	−	0.880323i	$-0.342674\pi$
$252$		0			0
$253$	1.60105	+	1.87459i	0.100657	+	0.117855i
$254$	−8.23733	−	1.30466i	−0.516856	−	0.0818619i
$255$		0			0
$256$	1.83356	−	1.33216i	0.114597	−	0.0832598i
$257$	−4.78295	+	7.80507i	−0.298352	+	0.486867i	−0.966327	−	0.257317i	$-0.917161\pi$
$257$	−4.78295	+	7.80507i	−0.298352	+	0.486867i	0.667975	+	0.744184i	$0.267161\pi$
$258$		0			0
$259$	1.07439	+	13.6514i	0.0667593	+	0.848258i
$260$	−0.513494	+	1.23968i	−0.0318456	+	0.0768820i
$261$		0			0
$262$	−6.84623	−	21.0705i	−0.422962	−	1.30174i
$263$	−2.10293	−	8.75934i	−0.129672	−	0.540124i	−0.998951	−	0.0458009i	$-0.985416\pi$
$263$	−2.10293	−	8.75934i	−0.129672	−	0.540124i	0.869278	−	0.494323i	$-0.164584\pi$
$264$		0			0
$265$	1.69424	−	21.5274i	0.104076	−	1.32242i
$266$	−7.55001	−	3.84692i	−0.462921	−	0.235870i
$267$		0			0
$268$	0.198544	+	0.0156258i	0.0121280	+	0.000954496i
$269$	4.64304	−	14.2898i	0.283091	−	0.871266i	−0.703873	−	0.710326i	$-0.748548\pi$
$269$	4.64304	−	14.2898i	0.283091	−	0.871266i	0.986964	−	0.160940i	$-0.0514525\pi$
$270$		0			0
$271$	−1.08985	+	0.354114i	−0.0662038	+	0.0215109i	−0.341932	−	0.939725i	$-0.611081\pi$
$271$	−1.08985	+	0.354114i	−0.0662038	+	0.0215109i	0.275728	+	0.961236i	$0.411081\pi$
$272$	−1.27327	+	0.780259i	−0.0772031	+	0.0473101i
$273$		0			0
$274$	−8.34555	+	0.656809i	−0.504173	+	0.0396793i
$275$	0.872062	−	3.63240i	0.0525873	−	0.219042i
$276$		0			0
$277$	−9.66393	−	13.3013i	−0.580649	−	0.799195i	0.413117	−	0.910678i	$-0.364440\pi$
$277$	−9.66393	−	13.3013i	−0.580649	−	0.799195i	−0.993766	+	0.111483i	$0.964440\pi$
$278$	−21.5194	+	21.5194i	−1.29065	+	1.29065i
$279$		0			0
$280$	10.6778	−	9.11973i	0.638123	−	0.545008i
$281$	−0.651019	+	0.762246i	−0.0388366	+	0.0454718i	−0.779484	−	0.626422i	$-0.784519\pi$
$281$	−0.651019	+	0.762246i	−0.0388366	+	0.0454718i	0.740648	+	0.671894i	$0.234519\pi$
$282$		0			0
$283$	21.1156	+	15.3414i	1.25519	+	0.911952i	0.998511	−	0.0545438i	$-0.0173705\pi$
$283$	21.1156	+	15.3414i	1.25519	+	0.911952i	0.256683	+	0.966496i	$0.417370\pi$
$284$	−0.800549	+	0.331598i	−0.0475038	+	0.0196767i
$285$		0			0
$286$		−	4.30884i		−	0.254787i
$287$	−7.68672	−	5.90804i	−0.453732	−	0.348741i
$288$		0			0
$289$	15.0096	−	7.64779i	0.882920	−	0.449870i
$290$	−11.4818	−	27.7196i	−0.674236	−	1.62775i
$291$		0			0
$292$	−0.0956240	+	0.0151454i	−0.00559597	+	0.000886315i
$293$	14.0903	+	12.0343i	0.823166	+	0.703050i	0.957672	−	0.287863i	$-0.0929448\pi$
$293$	14.0903	+	12.0343i	0.823166	+	0.703050i	−0.134506	+	0.990913i	$0.542945\pi$
$294$		0			0
$295$	−7.02086	+	44.3279i	−0.408770	+	2.58087i
$296$	−18.4906	−	18.4906i	−1.07475	−	1.07475i
$297$		0			0
$298$	−2.57666	−	1.57898i	−0.149262	−	0.0914678i
$299$	15.0005	+	3.60130i	0.867500	+	0.208268i
$300$		0			0
$301$	−8.69571	−	3.60188i	−0.501212	−	0.207609i
$302$	−13.0751	−	21.3367i	−0.752388	−	1.22779i
$303$		0			0
$304$	14.9880	−	3.59830i	0.859620	−	0.206377i
$305$	38.2500	+	12.4282i	2.19019	+	0.711635i
$306$		0			0
$307$	5.90452	−	11.5883i	0.336989	−	0.661378i	−0.658873	−	0.752254i	$-0.728967\pi$
$307$	5.90452	−	11.5883i	0.336989	−	0.661378i	0.995862	+	0.0908759i	$0.0289667\pi$
$308$	0.0459506	−	0.0901832i	0.00261828	−	0.00513866i
$309$		0			0
$310$	−3.49459	−	1.13546i	−0.198479	−	0.0644899i
$311$	26.3432	−	6.32443i	1.49378	−	0.358626i	0.597414	−	0.801933i	$-0.296195\pi$
$311$	26.3432	−	6.32443i	1.49378	−	0.358626i	0.896370	+	0.443308i	$0.146195\pi$
$312$		0			0
$313$	9.09284	+	14.8382i	0.513958	+	0.838703i	0.999367	−	0.0355842i	$-0.0113292\pi$
$313$	9.09284	+	14.8382i	0.513958	+	0.838703i	−0.485409	+	0.874287i	$0.661329\pi$
$314$	−12.8405	−	5.31871i	−0.724631	−	0.300152i
$315$		0			0
$316$	−0.968534	−	0.232524i	−0.0544843	−	0.0130805i
$317$	−11.3149	−	6.93375i	−0.635506	−	0.389438i	0.167107	−	0.985939i	$-0.446557\pi$
$317$	−11.3149	−	6.93375i	−0.635506	−	0.389438i	−0.802613	+	0.596500i	$0.796557\pi$
$318$		0			0
$319$	−3.38423	−	3.38423i	−0.189480	−	0.189480i
$320$	−4.18588	+	26.4286i	−0.233998	+	1.47740i
$321$		0			0
$322$	−5.54708	−	4.73765i	−0.309127	−	0.264019i
$323$	1.57297	−	0.249133i	0.0875222	−	0.0138622i
$324$		0			0
$325$	−8.94570	−	21.5968i	−0.496218	−	1.19798i
$326$	−19.2159	+	9.79099i	−1.06427	+	0.542273i
$327$		0			0
$328$	18.4890	−	0.954072i	1.02088	−	0.0526798i
$329$			12.1439i			0.669515i
$330$		0			0
$331$	19.3900	−	8.03161i	1.06577	−	0.441457i	0.220275	−	0.975438i	$-0.429304\pi$
$331$	19.3900	−	8.03161i	1.06577	−	0.441457i	0.845497	+	0.533980i	$0.179304\pi$
$332$	0.183129	+	0.133051i	0.0100505	+	0.00730214i
$333$		0			0
$334$	11.3044	−	13.2358i	0.618550	−	0.724229i
$335$	−5.13237	+	4.38346i	−0.280411	+	0.239494i
$336$		0			0
$337$	−8.35710	+	8.35710i	−0.455240	+	0.455240i	−0.897089	−	0.441849i	$-0.854323\pi$
$337$	−8.35710	+	8.35710i	−0.455240	+	0.455240i	0.441849	+	0.897089i	$0.354323\pi$
$338$	−5.30112	−	7.29637i	−0.288343	−	0.396870i
$339$		0			0
$340$	−0.0278394	+	0.115959i	−0.00150980	+	0.00628878i
$341$	−0.584323	+	0.0459872i	−0.0316429	+	0.00249035i
$342$		0			0
$343$	−15.1141	+	9.26192i	−0.816084	+	0.500097i
$344$	17.0940	−	5.55419i	0.921648	−	0.299462i
$345$		0			0
$346$	3.03083	−	9.32794i	0.162939	−	0.501473i
$347$	−14.5206	−	1.14280i	−0.779507	−	0.0613485i	−0.317539	−	0.948245i	$-0.602856\pi$
$347$	−14.5206	−	1.14280i	−0.779507	−	0.0613485i	−0.461968	+	0.886897i	$0.652856\pi$
$348$		0			0
$349$	−8.84082	−	4.50462i	−0.473238	−	0.241127i	0.201070	−	0.979577i	$-0.435558\pi$
$349$	−8.84082	−	4.50462i	−0.473238	−	0.241127i	−0.674308	+	0.738450i	$0.735558\pi$
$350$	−0.867288	+	11.0199i	−0.0463585	+	0.589040i
$351$		0			0
$352$	0.0882031	+	0.367392i	0.00470124	+	0.0195821i
$353$	−1.74660	−	5.37548i	−0.0929621	−	0.286108i	0.893755	−	0.448555i	$-0.148061\pi$
$353$	−1.74660	−	5.37548i	−0.0929621	−	0.286108i	−0.986717	+	0.162447i	$0.948061\pi$
$354$		0			0
$355$	11.2379	−	27.1308i	0.596448	−	1.43995i
$356$	0.0707084	+	0.898435i	0.00374754	+	0.0476170i
$357$		0			0
$358$	−5.45746	+	8.90577i	−0.288436	+	0.470684i
$359$	−16.0221	+	11.6408i	−0.845615	+	0.614375i	−0.923934	−	0.382553i	$-0.875045\pi$
$359$	−16.0221	+	11.6408i	−0.845615	+	0.614375i	0.0783183	+	0.996928i	$0.475045\pi$
$360$		0			0
$361$	2.53013	+	0.400733i	0.133165	+	0.0210912i
$362$	−12.9822	−	15.2003i	−0.682332	−	0.798908i
$363$		0			0
$364$	−0.0990809	−	0.625572i	−0.00519325	−	0.0327889i
$365$	1.92859	−	2.65448i	0.100947	−	0.138942i
$366$		0			0
$367$	4.28343	+	8.40670i	0.223593	+	0.438826i	0.975365	−	0.220597i	$-0.0708005\pi$
$367$	4.28343	+	8.40670i	0.223593	+	0.438826i	−0.751772	+	0.659423i	$0.770801\pi$
$368$	13.2698			0.691736
$369$		0			0
$370$	40.0447			2.08182
$371$	4.62743	+	9.08185i	0.240244	+	0.471506i
$372$		0			0
$373$	−11.5758	+	15.9328i	−0.599373	+	0.824967i	−0.995651	−	0.0931642i	$-0.970302\pi$
$373$	−11.5758	+	15.9328i	−0.599373	+	0.824967i	0.396277	+	0.918131i	$0.370302\pi$
$374$	−0.0599060	−	0.378232i	−0.00309767	−	0.0195579i
$375$		0			0
$376$	−15.0609	−	17.6341i	−0.776707	−	0.909407i
$377$	−29.5806	−	4.68511i	−1.52348	−	0.241296i
$378$		0			0
$379$	30.6033	−	22.2346i	1.57199	−	1.14212i	0.646765	−	0.762689i	$-0.276121\pi$
$379$	30.6033	−	22.2346i	1.57199	−	1.14212i	0.925222	−	0.379426i	$-0.123879\pi$
$380$	0.643157	−	1.04954i	0.0329933	−	0.0538401i
$381$		0			0
$382$	−1.24126	−	15.7717i	−0.0635082	−	0.806948i
$383$	10.7674	−	25.9947i	0.550186	−	1.32827i	−0.367153	−	0.930161i	$-0.619667\pi$
$383$	10.7674	−	25.9947i	0.550186	−	1.32827i	0.917339	−	0.398107i	$-0.130333\pi$
$384$		0			0
$385$	1.05999	+	3.26231i	0.0540220	+	0.166263i
$386$	−8.73985	−	36.4041i	−0.444847	−	1.85292i
$387$		0			0
$388$	0.132474	−	1.68324i	0.00672536	−	0.0854538i
$389$	1.70386	+	0.868162i	0.0863893	+	0.0440175i	0.496651	−	0.867950i	$-0.334563\pi$
$389$	1.70386	+	0.868162i	0.0863893	+	0.0440175i	−0.410262	+	0.911968i	$0.634563\pi$
$390$		0			0
$391$	1.36682	+	0.107571i	0.0691230	+	0.00544010i
$392$	4.20606	−	12.9449i	0.212438	−	0.653818i
$393$		0			0
$394$	−20.0877	+	6.52688i	−1.01200	+	0.328819i
$395$	28.7822	−	17.6377i	1.44819	−	0.887450i
$396$		0			0
$397$	15.5147	−	1.22104i	0.778663	−	0.0612821i	0.317103	−	0.948391i	$-0.397290\pi$
$397$	15.5147	−	1.22104i	0.778663	−	0.0612821i	0.461560	+	0.887109i	$0.347290\pi$
$398$	−2.09623	+	8.73143i	−0.105075	+	0.437667i
$399$		0			0
$400$	−11.8191	−	16.2676i	−0.590954	−	0.813379i
$401$	2.51506	−	2.51506i	0.125596	−	0.125596i	−0.641515	−	0.767111i	$-0.721694\pi$
$401$	2.51506	−	2.51506i	0.125596	−	0.125596i	0.767111	+	0.641515i	$0.221694\pi$
$402$		0			0
$403$	−2.78902	+	2.38205i	−0.138931	+	0.118658i
$404$	0.451190	−	0.528275i	0.0224475	−	0.0262827i
$405$		0			0
$406$	11.4575	+	8.32437i	0.568627	+	0.413131i
$407$	5.90152	−	2.44449i	0.292527	−	0.121169i
$408$		0			0
$409$			7.86984i			0.389138i	0.980889	+	0.194569i	$0.0623309\pi$
$409$			7.86984i			0.389138i	−0.980889	+	0.194569i	$0.937669\pi$
$410$	−18.9874	+	21.0536i	−0.937723	+	1.03977i
$411$		0			0
$412$	−0.0140166	+	0.00714183i	−0.000690550	+	0.000351853i
$413$	−8.10697	−	19.5720i	−0.398918	−	0.963073i
$414$		0			0
$415$	−7.57696	+	1.20007i	−0.371938	+	0.0589092i
$416$	1.79786	+	1.53552i	0.0881475	+	0.0752851i
$417$		0			0
$418$	−0.618342	+	3.90406i	−0.0302441	+	0.190954i
$419$	−23.0073	−	23.0073i	−1.12398	−	1.12398i	−0.991137	−	0.132844i	$-0.957589\pi$
$419$	−23.0073	−	23.0073i	−1.12398	−	1.12398i	−0.132844	−	0.991137i	$-0.542411\pi$
$420$		0			0
$421$	33.6837	+	20.6414i	1.64165	+	1.00600i	0.962226	+	0.272251i	$0.0877680\pi$
$421$	33.6837	+	20.6414i	1.64165	+	1.00600i	0.679419	+	0.733751i	$0.262232\pi$
$422$	33.1295	+	7.95369i	1.61272	+	0.387180i
$423$		0			0
$424$	−17.9828	−	7.44872i	−0.873322	−	0.361742i
$425$	−1.08552	−	1.77141i	−0.0526555	−	0.0859259i
$426$		0			0
$427$	−18.4594	+	4.43171i	−0.893314	+	0.214466i
$428$	−0.767940	−	0.249519i	−0.0371198	−	0.0120609i
$429$		0			0
$430$	−12.4958	+	24.5243i	−0.602599	+	1.18267i
$431$	5.13903	−	10.0859i	0.247539	−	0.485822i	−0.733486	−	0.679704i	$-0.762108\pi$
$431$	5.13903	−	10.0859i	0.247539	−	0.485822i	0.981025	+	0.193883i	$0.0621081\pi$
$432$		0			0
$433$	−34.9045	−	11.3412i	−1.67740	−	0.545021i	−0.692999	−	0.720939i	$-0.743711\pi$
$433$	−34.9045	−	11.3412i	−1.67740	−	0.545021i	−0.984405	+	0.175917i	$0.943711\pi$
$434$	1.68649	−	0.404890i	0.0809540	−	0.0194353i
$435$		0			0
$436$	−0.293535	−	0.479005i	−0.0140578	−	0.0229402i
$437$	−13.0745	−	5.41564i	−0.625438	−	0.259065i
$438$		0			0
$439$	−8.50499	−	2.04187i	−0.405921	−	0.0974530i	0.0253430	−	0.999679i	$-0.491932\pi$
$439$	−8.50499	−	2.04187i	−0.405921	−	0.0974530i	−0.431264	+	0.902226i	$0.641932\pi$
$440$	−5.58513	−	3.42257i	−0.266261	−	0.163165i
$441$		0			0
$442$	−1.69448	−	1.69448i	−0.0805981	−	0.0805981i
$443$	−4.22809	+	26.6951i	−0.200883	+	1.26832i	0.656768	+	0.754092i	$0.271923\pi$
$443$	−4.22809	+	26.6951i	−0.200883	+	1.26832i	−0.857651	+	0.514232i	$0.828077\pi$
$444$		0			0
$445$	−23.2245	−	19.8356i	−1.10095	−	0.940299i
$446$	−27.8186	+	4.40603i	−1.31725	+	0.208632i
$447$		0			0
$448$	−4.83343	−	11.6689i	−0.228358	−	0.551305i
$449$	−6.77390	+	3.45148i	−0.319680	+	0.162885i	−0.606466	−	0.795110i	$-0.707413\pi$
$449$	−6.77390	+	3.45148i	−0.319680	+	0.162885i	0.286785	+	0.957995i	$0.407413\pi$
$450$		0			0
$451$	−1.51304	+	4.26182i	−0.0712464	+	0.200681i
$452$			0.749984i			0.0352763i
$453$		0			0
$454$	−35.9582	+	14.8944i	−1.68760	+	0.699027i
$455$	17.3656	+	12.6168i	0.814111	+	0.591486i
$456$		0			0
$457$	−7.88006	+	9.22637i	−0.368614	+	0.431591i	−0.913450	−	0.406951i	$-0.866592\pi$
$457$	−7.88006	+	9.22637i	−0.368614	+	0.431591i	0.544836	+	0.838543i	$0.316592\pi$
$458$	−8.93109	+	7.62787i	−0.417322	+	0.356427i
$459$		0			0
$460$	0.749324	−	0.749324i	0.0349374	−	0.0349374i
$461$	−11.4128	−	15.7084i	−0.531547	−	0.731612i	0.455818	−	0.890073i	$-0.349347\pi$
$461$	−11.4128	−	15.7084i	−0.531547	−	0.731612i	−0.987365	+	0.158461i	$0.949347\pi$
$462$		0			0
$463$	−3.12164	+	13.0026i	−0.145075	+	0.604281i	0.851700	+	0.524030i	$0.175572\pi$
$463$	−3.12164	+	13.0026i	−0.145075	+	0.604281i	−0.996775	+	0.0802508i	$0.974428\pi$
$464$	−25.6825	+	2.02125i	−1.19228	+	0.0938344i
$465$		0			0
$466$	3.84296	−	2.35497i	0.178021	−	0.109092i
$467$	1.72751	−	0.561303i	0.0799397	−	0.0259740i	−0.268774	−	0.963203i	$-0.586619\pi$
$467$	1.72751	−	0.561303i	0.0799397	−	0.0259740i	0.348714	+	0.937229i	$0.386619\pi$
$468$		0			0
$469$	0.984501	−	3.02998i	0.0454600	−	0.139912i
$470$	35.4033	+	2.78630i	1.63303	+	0.128522i
$471$		0			0
$472$	36.0453	+	18.3660i	1.65912	+	0.845363i
$473$	−0.344479	+	4.37702i	−0.0158392	+	0.201256i
$474$		0			0
$475$	5.00606	+	20.8518i	0.229694	+	0.956744i
$476$	−0.0173947	−	0.0535355i	−0.000797286	−	0.00245380i
$477$		0			0
$478$	−8.48044	+	20.4736i	−0.387886	+	0.936441i
$479$	−1.51817	−	19.2901i	−0.0693668	−	0.881389i	−0.928905	−	0.370317i	$-0.879249\pi$
$479$	−1.51817	−	19.2901i	−0.0693668	−	0.881389i	0.859538	−	0.511071i	$-0.170751\pi$
$480$		0			0
$481$	20.8856	−	34.0821i	0.952300	−	1.55401i
$482$	12.8704	−	9.35088i	0.586230	−	0.425921i
$483$		0			0
$484$	0.981684	+	0.155483i	0.0446220	+	0.00706743i
$485$	37.1627	+	43.5119i	1.68747	+	1.97577i
$486$		0			0
$487$	0.174854	+	1.10399i	0.00792339	+	0.0500263i	0.991333	−	0.131371i	$-0.0419380\pi$
$487$	0.174854	+	1.10399i	0.00792339	+	0.0500263i	−0.983410	+	0.181397i	$0.941938\pi$
$488$	21.3085	−	29.3287i	0.964592	−	1.32765i
$489$		0			0
$490$	9.46276	+	18.5717i	0.427484	+	0.838984i
$491$	−38.4365			−1.73461			−0.867307	−	0.497773i	$-0.834151\pi$
$491$	−38.4365			−1.73461			−0.867307	+	0.497773i	$0.834151\pi$
$492$		0			0
$493$	−2.66174			−0.119879
$494$	11.2294	+	22.0389i	0.505234	+	0.991577i
$495$		0			0
$496$	−1.85445	+	2.55243i	−0.0832673	+	0.114608i
$497$	2.16841	+	13.6908i	0.0972663	+	0.614115i
$498$		0			0
$499$	18.3489	+	21.4838i	0.821408	+	0.961745i	0.999753	−	0.0222231i	$-0.00707442\pi$
$499$	18.3489	+	21.4838i	0.821408	+	0.961745i	−0.178345	+	0.983968i	$0.557074\pi$
$500$	−0.0866919	−	0.0137306i	−0.00387698	−	0.000614053i
$501$		0			0
$502$	28.1404	−	20.4452i	1.25597	−	0.912513i
$503$	3.57462	−	5.83325i	0.159384	−	0.260092i	−0.762972	−	0.646431i	$-0.776261\pi$
$503$	3.57462	−	5.83325i	0.159384	−	0.260092i	0.922357	+	0.386340i	$0.126261\pi$
$504$		0			0
$505$	1.84728	+	23.4719i	0.0822028	+	1.04449i
$506$	−1.30223	+	3.14387i	−0.0578913	+	0.139762i
$507$		0			0
$508$	0.176716	+	0.543876i	0.00784050	+	0.0241306i
$509$	2.63332	+	10.9686i	0.116720	+	0.486173i	0.999855	+	0.0170539i	$0.00542868\pi$
$509$	2.63332	+	10.9686i	0.116720	+	0.486173i	−0.883135	+	0.469120i	$0.844571\pi$
$510$		0			0
$511$	−0.121514	+	1.54398i	−0.00537546	+	0.0683017i
$512$	21.4002	+	10.9040i	0.945765	+	0.481891i
$513$		0			0
$514$	−12.5967	−	0.991384i	−0.555618	−	0.0437281i
$515$	0.164748	−	0.507041i	0.00725965	−	0.0223429i
$516$		0			0
$517$	5.38759	−	1.75053i	0.236946	−	0.0769883i
$518$	−16.1165	+	9.87623i	−0.708120	+	0.433937i
$519$		0			0
$520$	−40.8639	+	3.21606i	−1.79200	+	0.141033i
$521$	−4.80365	+	20.0086i	−0.210452	+	0.876595i	0.762760	+	0.646682i	$0.223844\pi$
$521$	−4.80365	+	20.0086i	−0.210452	+	0.876595i	−0.973211	+	0.229912i	$0.926156\pi$
$522$		0			0
$523$	−9.41472	−	12.9583i	−0.411677	−	0.566625i	0.551949	−	0.833878i	$-0.313884\pi$
$523$	−9.41472	−	12.9583i	−0.411677	−	0.566625i	−0.963626	+	0.267253i	$0.913884\pi$
$524$	−1.07419	+	1.07419i	−0.0469262	+	0.0469262i
$525$		0			0
$526$	9.45525	−	8.07554i	0.412268	−	0.352110i
$527$	−0.211704	+	0.247873i	−0.00922197	+	0.0107975i
$528$		0			0
$529$	8.75096	+	6.35794i	0.380476	+	0.276432i
$530$	27.5382	−	11.4067i	1.19618	−	0.495474i
$531$		0			0
$532$			0.581023i			0.0251906i
$533$	8.01580	+	27.1409i	0.347203	+	1.17560i
$534$		0			0
$535$	24.3824	−	12.4234i	1.05414	−	0.537112i
$536$	2.32821	+	5.62080i	0.100563	+	0.242781i
$537$		0			0
$538$	20.4846	−	3.24445i	0.883155	−	0.139878i
$539$	2.52825	+	2.15933i	0.108899	+	0.0930089i
$540$		0			0
$541$	−0.622281	+	3.92893i	−0.0267539	+	0.168918i	−0.997448	−	0.0714026i	$-0.977252\pi$
$541$	−0.622281	+	3.92893i	−0.0267539	+	0.168918i	0.970694	+	0.240320i	$0.0772525\pi$
$542$	−1.11849	−	1.11849i	−0.0480434	−	0.0480434i
$543$		0			0
$544$	0.179166	+	0.109793i	0.00768167	+	0.00470733i
$545$	18.5132	+	4.44461i	0.793016	+	0.190386i
$546$		0			0
$547$	−38.8125	−	16.0766i	−1.65950	−	0.687388i	−0.661462	−	0.749979i	$-0.730064\pi$
$547$	−38.8125	−	16.0766i	−1.65950	−	0.687388i	−0.998039	+	0.0625912i	$0.980064\pi$
$548$	0.299922	+	0.489428i	0.0128120	+	0.0209073i
$549$		0			0
$550$	5.01396	−	1.20375i	0.213796	−	0.0513279i
$551$	26.1294	+	8.48997i	1.11315	+	0.361685i
$552$		0			0
$553$	−7.23379	+	14.1971i	−0.307612	+	0.603722i
$554$	10.3031	−	20.2210i	0.437738	−	0.859110i
$555$		0			0
$556$	1.98463	+	0.644845i	0.0841670	+	0.0273475i
$557$	−32.7419	+	7.86064i	−1.38732	+	0.333066i	−0.857255	−	0.514892i	$-0.827832\pi$
$557$	−32.7419	+	7.86064i	−1.38732	+	0.333066i	−0.530064	+	0.847958i	$0.677832\pi$
$558$		0			0
$559$	14.3555	+	23.4260i	0.607171	+	0.990813i
$560$	17.0584	+	7.06580i	0.720847	+	0.298585i
$561$		0			0
$562$	−1.34545	−	0.323015i	−0.0567545	−	0.0136255i
$563$	26.4753	+	16.2241i	1.11580	+	0.683763i	0.953022	−	0.302900i	$-0.0979547\pi$
$563$	26.4753	+	16.2241i	1.11580	+	0.683763i	0.162778	+	0.986663i	$0.447955\pi$
$564$		0			0
$565$	−17.9726	−	17.9726i	−0.756113	−	0.756113i
$566$	−5.63594	+	35.5839i	−0.236896	+	1.49570i
$567$		0			0
$568$	−20.1281	−	17.1910i	−0.844555	−	0.721318i
$569$	−9.29108	+	1.47156i	−0.389502	+	0.0616911i	−0.348114	−	0.937452i	$-0.613178\pi$
$569$	−9.29108	+	1.47156i	−0.389502	+	0.0616911i	−0.0413878	+	0.999143i	$0.513178\pi$
$570$		0			0
$571$	−9.53367	−	23.0163i	−0.398972	−	0.963202i	−0.987911	−	0.155025i	$-0.950454\pi$
$571$	−9.53367	−	23.0163i	−0.398972	−	0.963202i	0.588939	−	0.808177i	$-0.299546\pi$
$572$	−0.263250	+	0.134132i	−0.0110070	+	0.00560836i
$573$		0			0
$574$	2.44930	−	13.1562i	0.102232	−	0.549130i
$575$			18.4613i			0.769891i
$576$		0			0
$577$	−4.84247	+	2.00582i	−0.201595	+	0.0835033i	−0.481196	−	0.876613i	$-0.659798\pi$
$577$	−4.84247	+	2.00582i	−0.201595	+	0.0835033i	0.279602	+	0.960116i	$0.409798\pi$
$578$	18.8120	+	13.6677i	0.782475	+	0.568501i
$579$		0			0
$580$	−1.33611	+	1.56439i	−0.0554790	+	0.0649576i
$581$	2.75348	−	2.35169i	0.114234	−	0.0975647i
$582$		0			0
$583$	3.36208	−	3.36208i	0.139243	−	0.139243i
$584$	−1.73840	−	2.39270i	−0.0719355	−	0.0990108i
$585$		0			0
$586$	−5.97102	+	24.8711i	−0.246660	+	1.02741i
$587$	7.62789	−	0.600328i	0.314837	−	0.0247782i	0.0799437	−	0.996799i	$-0.474526\pi$
$587$	7.62789	−	0.600328i	0.314837	−	0.0247782i	0.234893	+	0.972021i	$0.424526\pi$
$588$		0			0
$589$	2.86885	−	1.75804i	0.118209	−	0.0724386i
$590$	−58.9185	+	19.1438i	−2.42564	+	0.788137i
$591$		0			0
$592$	10.6251	−	32.7007i	0.436690	−	1.34399i
$593$	39.5471	+	3.11243i	1.62401	+	0.127812i	0.857521	−	0.514450i	$-0.172004\pi$
$593$	39.5471	+	3.11243i	1.62401	+	0.127812i	0.766486	+	0.642262i	$0.222004\pi$
$594$		0			0
$595$	1.69977	+	0.866077i	0.0696838	+	0.0355057i
$596$	−0.0162578	+	0.206575i	−0.000665945	+	0.00846163i
$597$		0			0
$598$	4.97103	+	20.7058i	0.203281	+	0.846725i
$599$	−1.77363	−	5.45868i	−0.0724687	−	0.223036i	0.908261	−	0.418403i	$-0.137410\pi$
$599$	−1.77363	−	5.45868i	−0.0724687	−	0.223036i	−0.980730	+	0.195367i	$0.937410\pi$
$600$		0			0
$601$	−7.24802	+	17.4983i	−0.295653	+	0.713769i	0.704339	+	0.709863i	$0.251243\pi$
$601$	−7.24802	+	17.4983i	−0.295653	+	0.713769i	−0.999992	+	0.00390608i	$0.998757\pi$
$602$	−1.01934	−	12.9520i	−0.0415453	−	0.527883i
$603$		0			0
$604$	−0.896546	+	1.46303i	−0.0364799	+	0.0595298i
$605$	−27.2511	+	19.7991i	−1.10791	+	0.804947i
$606$		0			0
$607$	−44.9704	−	7.12261i	−1.82529	−	0.289098i	−0.852835	−	0.522180i	$-0.825119\pi$
$607$	−44.9704	−	7.12261i	−1.82529	−	0.289098i	−0.972457	+	0.233083i	$0.925119\pi$
$608$	−1.40861	−	1.64928i	−0.0571268	−	0.0668869i
$609$		0			0
$610$	8.68450	+	54.8318i	0.351625	+	2.22007i
$611$	20.8362	−	28.6786i	0.842944	−	1.16021i
$612$		0			0
$613$	10.0783	+	19.7797i	0.407057	+	0.798894i	0.999980	−	0.00636491i	$-0.00202603\pi$
$613$	10.0783	+	19.7797i	0.407057	+	0.798894i	−0.592923	+	0.805259i	$0.702026\pi$
$614$	17.9525			0.724505
$615$		0			0
$616$	3.09192			0.124577
$617$	−7.26558	−	14.2595i	−0.292501	−	0.574066i	0.697257	−	0.716821i	$-0.254404\pi$
$617$	−7.26558	−	14.2595i	−0.292501	−	0.574066i	−0.989758	+	0.142756i	$0.954404\pi$
$618$		0			0
$619$	−2.13229	+	2.93485i	−0.0857040	+	0.117961i	−0.849716	−	0.527240i	$-0.823227\pi$
$619$	−2.13229	+	2.93485i	−0.0857040	+	0.117961i	0.764012	+	0.645202i	$0.223227\pi$
$620$	0.0394139	+	0.248850i	0.00158290	+	0.00999404i
$621$		0			0
$622$	24.2867	+	28.4361i	0.973807	+	1.14018i
$623$	14.2391	+	2.25525i	0.570478	+	0.0903549i
$624$		0			0
$625$	−18.9884	+	13.7958i	−0.759534	+	0.551834i
$626$	−12.5513	+	20.4818i	−0.501649	+	0.818617i
$627$		0			0
$628$	0.0747716	+	0.950064i	0.00298371	+	0.0379117i
$629$	1.35950	−	3.28212i	0.0542068	−	0.130867i
$630$		0			0
$631$	2.40812	+	7.41143i	0.0958657	+	0.295044i	0.987478	−	0.157755i	$-0.0504255\pi$
$631$	2.40812	+	7.41143i	0.0958657	+	0.295044i	−0.891613	+	0.452799i	$0.850426\pi$
$632$	−7.10318	−	29.5869i	−0.282549	−	1.17690i
$633$		0			0
$634$	1.43719	−	18.2612i	0.0570781	−	0.725246i
$635$	−17.2683	−	8.79862i	−0.685270	−	0.349162i
$636$		0			0
$637$	20.7418	+	1.63242i	0.821820	+	0.0646786i
$638$	2.04148	−	6.28302i	0.0808229	−	0.248747i
$639$		0			0
$640$	−31.8636	+	10.3531i	−1.25952	+	0.409243i
$641$	−20.3995	+	12.5008i	−0.805733	+	0.493754i	−0.863362	−	0.504584i	$-0.831646\pi$
$641$	−20.3995	+	12.5008i	−0.805733	+	0.493754i	0.0576297	+	0.998338i	$0.481646\pi$
$642$		0			0
$643$	16.1444	−	1.27059i	0.636672	−	0.0501071i	0.243984	−	0.969779i	$-0.421545\pi$
$643$	16.1444	−	1.27059i	0.636672	−	0.0501071i	0.392687	+	0.919672i	$0.371545\pi$
$644$	−0.116770	+	0.486382i	−0.00460138	+	0.0191661i
$645$		0			0
$646$	1.29213	+	1.77846i	0.0508381	+	0.0699727i
$647$	24.0389	−	24.0389i	0.945067	−	0.945067i	−0.0535006	−	0.998568i	$-0.517038\pi$
$647$	24.0389	−	24.0389i	0.945067	−	0.945067i	0.998568	+	0.0535006i	$0.0170379\pi$
$648$		0			0
$649$	−7.51440	+	6.41790i	−0.294966	+	0.251925i
$650$	20.9559	−	24.5362i	0.821959	−	0.962390i
$651$		0			0
$652$	1.19637	+	0.869211i	0.0468533	+	0.0340409i
$653$	−29.8930	+	12.3821i	−1.16980	+	0.484548i	−0.881127	−	0.472879i	$-0.843215\pi$
$653$	−29.8930	+	12.3821i	−1.16980	+	0.484548i	−0.288675	+	0.957427i	$0.593215\pi$
$654$		0			0
$655$		−	51.4838i		−	2.01164i
$656$	12.1546	+	21.0915i	0.474557	+	0.823483i
$657$		0			0
$658$	−14.9357	+	7.61014i	−0.582256	+	0.296674i
$659$	−17.9858	−	43.4215i	−0.700626	−	1.69146i	−0.722190	−	0.691694i	$-0.756865\pi$
$659$	−17.9858	−	43.4215i	−0.700626	−	1.69146i	0.0215639	−	0.999767i	$-0.493135\pi$
$660$		0			0
$661$	17.8322	−	2.82434i	0.693592	−	0.109854i	0.200322	−	0.979730i	$-0.435801\pi$
$661$	17.8322	−	2.82434i	0.693592	−	0.109854i	0.493271	+	0.869876i	$0.335801\pi$
$662$	22.0291	+	18.8146i	0.856184	+	0.731250i
$663$		0			0
$664$	−1.08173	+	6.82975i	−0.0419791	+	0.265046i
$665$	−13.9236	−	13.9236i	−0.539936	−	0.539936i
$666$		0			0
$667$	20.1670	+	12.3584i	0.780870	+	0.478518i
$668$	−1.16054	−	0.278622i	−0.0449028	−	0.0107802i
$669$		0			0
$670$	−8.60747	−	3.56533i	−0.332536	−	0.137741i
$671$	4.62702	+	7.55061i	0.178624	+	0.291488i
$672$		0			0
$673$	42.4556	−	10.1927i	1.63654	−	0.392899i	0.692159	−	0.721745i	$-0.256660\pi$
$673$	42.4556	−	10.1927i	1.63654	−	0.392899i	0.944383	+	0.328846i	$0.106660\pi$
$674$	−15.5155	−	5.04128i	−0.597633	−	0.194183i
$675$		0			0
$676$	−0.280752	+	0.551007i	−0.0107982	+	0.0211926i
$677$	13.8628	−	27.2072i	0.532790	−	1.04566i	−0.455091	−	0.890445i	$-0.650393\pi$
$677$	13.8628	−	27.2072i	0.532790	−	1.04566i	0.987881	−	0.155214i	$-0.0496067\pi$
$678$		0			0
$679$	−25.6880	−	8.34653i	−0.985814	−	0.320311i
$680$	−3.54234	+	0.850440i	−0.135842	+	0.0326129i
$681$		0			0
$682$	−0.422733	−	0.689838i	−0.0161873	−	0.0264153i
$683$	−30.8111	−	12.7624i	−1.17896	−	0.488339i	−0.294812	−	0.955555i	$-0.595257\pi$
$683$	−30.8111	−	12.7624i	−1.17896	−	0.488339i	−0.884143	+	0.467216i	$0.845257\pi$
$684$		0			0
$685$	−18.9160	−	4.54132i	−0.722742	−	0.173515i
$686$	−20.8626	−	12.7846i	−0.796540	−	0.488120i
$687$		0			0
$688$	16.7112	+	16.7112i	0.637108	+	0.637108i
$689$	4.65445	−	29.3870i	0.177320	−	1.11956i
$690$		0			0
$691$	−23.5638	−	20.1254i	−0.896408	−	0.765605i	0.0764339	−	0.997075i	$-0.475647\pi$
$691$	−23.5638	−	20.1254i	−0.896408	−	0.765605i	−0.972842	+	0.231470i	$0.925647\pi$
$692$	−0.664242	+	0.105206i	−0.0252507	+	0.00399932i
$693$		0			0
$694$	−7.69401	−	18.5750i	−0.292061	−	0.705096i
$695$	−63.0127	+	32.1066i	−2.39021	+	1.21787i
$696$		0			0
$697$	1.08097	+	2.27100i	0.0409448	+	0.0860203i
$698$		−	13.6962i		−	0.518408i
$699$		0			0
$700$	0.700265	−	0.290059i	0.0264675	−	0.0109632i
$701$	0.349064	+	0.253610i	0.0131840	+	0.00957871i	0.594358	−	0.804201i	$-0.297406\pi$
$701$	0.349064	+	0.253610i	0.0131840	+	0.00957871i	−0.581174	+	0.813779i	$0.697406\pi$
$702$		0			0
$703$	−23.8145	+	27.8832i	−0.898181	+	1.05164i
$704$	−4.48014	+	3.82640i	−0.168851	+	0.144213i
$705$		0			0
$706$	5.51675	−	5.51675i	0.207626	−	0.207626i
$707$	−6.53234	−	8.99100i	−0.245674	−	0.338141i
$708$		0			0
$709$	4.26392	−	17.7605i	0.160135	−	0.667009i	−0.833321	−	0.552790i	$-0.813563\pi$
$709$	4.26392	−	17.7605i	0.160135	−	0.667009i	0.993456	−	0.114220i	$-0.0364368\pi$
$710$	40.4104	−	3.18037i	1.51658	−	0.119357i
$711$		0			0
$712$	−23.4735	+	14.3846i	−0.879706	+	0.539084i
$713$	2.75487	−	0.895112i	0.103171	−	0.0335222i
$714$		0			0
$715$	3.09417	−	9.52287i	0.115715	−	0.356135i
$716$	0.713989	+	0.0561922i	0.0266830	+	0.00210000i
$717$		0			0
$718$	−24.3574	−	12.4107i	−0.909010	−	0.463164i
$719$	−0.931727	+	11.8387i	−0.0347475	+	0.441509i	0.954795	+	0.297266i	$0.0960748\pi$
$719$	−0.931727	+	11.8387i	−0.0347475	+	0.441509i	−0.989542	+	0.144243i	$0.953925\pi$
$720$		0			0
$721$	0.0587467	+	0.244698i	0.00218784	+	0.00911302i
$722$	1.09268	+	3.36292i	0.0406653	+	0.125155i
$723$		0			0
$724$	−0.524532	+	1.26633i	−0.0194941	+	0.0470629i
$725$	−2.81203	−	35.7303i	−0.104436	−	1.32699i
$726$		0			0
$727$	6.44010	−	10.5093i	0.238850	−	0.389768i	−0.710645	−	0.703551i	$-0.751597\pi$
$727$	6.44010	−	10.5093i	0.238850	−	0.389768i	0.949495	+	0.313783i	$0.101597\pi$
$728$	15.6531	−	11.3726i	0.580141	−	0.421497i
$729$		0			0
$730$	4.47331	+	0.708502i	0.165565	+	0.0262228i
$731$	1.58582	+	1.85676i	0.0586537	+	0.0686747i
$732$		0			0
$733$	0.595077	+	3.75717i	0.0219797	+	0.138774i	0.996238	−	0.0866609i	$-0.0276197\pi$
$733$	0.595077	+	3.75717i	0.0219797	+	0.138774i	−0.974258	+	0.225435i	$0.927620\pi$
$734$	−7.65510	+	10.5363i	−0.282555	+	0.388904i
$735$		0			0
$736$	−0.847709	−	1.66372i	−0.0312470	−	0.0613256i
$737$	−1.48615			−0.0547432
$738$		0			0
$739$	1.23408			0.0453964			0.0226982	−	0.999742i	$-0.492774\pi$
$739$	1.23408			0.0453964			0.0226982	+	0.999742i	$0.492774\pi$
$740$	−1.24658	−	2.44654i	−0.0458250	−	0.0899366i
$741$		0			0
$742$	−8.26989	+	11.3825i	−0.303597	+	0.417866i
$743$	4.40873	+	27.8356i	0.161741	+	1.02119i	0.926341	+	0.376686i	$0.122936\pi$
$743$	4.40873	+	27.8356i	0.161741	+	1.02119i	−0.764601	+	0.644504i	$0.777064\pi$
$744$		0			0
$745$	−4.56076	−	5.33996i	−0.167093	−	0.195641i
$746$	−26.8498	−	4.25259i	−0.983040	−	0.155698i
$747$		0			0
$748$	−0.0212433	+	0.0154342i	−0.000776733	+	0.000564330i
$749$	−6.74903	+	11.0134i	−0.246604	+	0.402422i
$750$		0			0
$751$	−2.86246	−	36.3710i	−0.104453	−	1.32720i	−0.796190	−	0.605047i	$-0.793154\pi$
$751$	−2.86246	−	36.3710i	−0.104453	−	1.32720i	0.691737	−	0.722149i	$-0.256846\pi$
$752$	11.6689	−	28.1713i	0.425522	−	1.02730i
$753$		0			0
$754$	−12.7749	−	39.3171i	−0.465234	−	1.43184i
$755$	−13.5752	−	56.5449i	−0.494053	−	2.05788i
$756$		0			0
$757$	4.03529	−	51.2732i	0.146665	−	1.86356i	−0.281115	−	0.959674i	$-0.590704\pi$
$757$	4.03529	−	51.2732i	0.146665	−	1.86356i	0.427780	−	0.903883i	$-0.359296\pi$
$758$	46.5242	+	23.7053i	1.68984	+	0.861015i
$759$		0			0
$760$	37.4866	+	2.95026i	1.35978	+	0.107017i
$761$	−0.243367	+	0.749007i	−0.00882205	+	0.0271515i	−0.955371	−	0.295410i	$-0.904544\pi$
$761$	−0.243367	+	0.749007i	−0.00882205	+	0.0271515i	0.946549	+	0.322561i	$0.104544\pi$
$762$		0			0
$763$	−8.54706	+	2.77711i	−0.309424	+	0.100538i
$764$	−0.924935	+	0.566801i	−0.0334630	+	0.0205061i
$765$		0			0
$766$	38.7183	−	3.04720i	1.39895	−	0.110100i
$767$	−14.4360	+	60.1302i	−0.521254	+	2.17118i
$768$		0			0
$769$	13.1839	+	18.1460i	0.475422	+	0.654362i	0.977617	−	0.210392i	$-0.0674741\pi$
$769$	13.1839	+	18.1460i	0.475422	+	0.654362i	−0.502195	+	0.864754i	$0.667474\pi$
$770$	−3.34805	+	3.34805i	−0.120655	+	0.120655i
$771$		0			0
$772$	−1.95205	+	1.66721i	−0.0702559	+	0.0600042i
$773$	0.811712	−	0.950393i	0.0291952	−	0.0341832i	−0.745616	−	0.666376i	$-0.767845\pi$
$773$	0.811712	−	0.950393i	0.0291952	−	0.0341832i	0.774811	+	0.632192i	$0.217845\pi$
$774$		0			0
$775$	−3.55102	−	2.57997i	−0.127557	−	0.0926753i
$776$	47.6527	−	19.7384i	1.71063	−	0.708567i
$777$		0			0
$778$			2.63962i			0.0946350i
$779$	−3.36790	−	25.7416i	−0.120668	−	0.922288i
$780$		0			0
$781$	5.76128	−	2.93552i	0.206155	−	0.105041i
$782$	0.724234	+	1.74846i	0.0258986	+	0.0625247i
$783$		0			0
$784$	17.6765	−	2.79969i	0.631305	−	0.0999889i
$785$	−24.5592	−	20.9755i	−0.876554	−	0.748648i
$786$		0			0
$787$	0.454509	−	2.86965i	0.0162015	−	0.102292i	−0.978262	−	0.207371i	$-0.933509\pi$
$787$	0.454509	−	2.86965i	0.0162015	−	0.102292i	0.994464	+	0.105079i	$0.0335094\pi$
$788$	1.02408	+	1.02408i	0.0364814	+	0.0364814i
$789$		0			0
$790$	39.7293	+	24.3461i	1.41350	+	0.866197i
$791$	11.6659	+	2.80074i	0.414792	+	0.0995828i
$792$		0			0
$793$	51.1970	+	21.2065i	1.81806	+	0.753064i
$794$	11.2243	+	18.3163i	0.398335	+	0.650023i
$795$		0			0
$796$	0.598704	−	0.143736i	0.0212205	−	0.00509459i
$797$	−5.51385	−	1.79156i	−0.195311	−	0.0634603i	0.209728	−	0.977760i	$-0.432742\pi$
$797$	−5.51385	−	1.79156i	−0.195311	−	0.0634603i	−0.405039	+	0.914299i	$0.632742\pi$
$798$		0			0
$799$	1.43029	−	2.80711i	0.0506002	−	0.0993084i
$800$	−1.28454	+	2.52105i	−0.0454153	+	0.0891326i
$801$		0			0
$802$	4.66936	+	1.51717i	0.164881	+	0.0535730i
$803$	0.702496	−	0.168654i	0.0247906	−	0.00595169i
$804$		0			0
$805$	−8.85738	−	14.4539i	−0.312182	−	0.509434i
$806$	−4.67745	−	1.93746i	−0.164756	−	0.0682443i
$807$		0			0
$808$	20.6362	+	4.95432i	0.725980	+	0.174292i
$809$	−24.0581	−	14.7428i	−0.845838	−	0.518330i	0.0307752	−	0.999526i	$-0.490202\pi$
$809$	−24.0581	−	14.7428i	−0.845838	−	0.518330i	−0.876613	+	0.481196i	$0.840202\pi$
$810$		0			0
$811$	−4.39928	−	4.39928i	−0.154480	−	0.154480i	0.625636	−	0.780115i	$-0.284840\pi$
$811$	−4.39928	−	4.39928i	−0.154480	−	0.154480i	−0.780115	+	0.625636i	$0.784840\pi$
$812$	0.151912	−	0.959135i	0.00533107	−	0.0336590i
$813$		0			0
$814$	6.70473	+	5.72638i	0.235001	+	0.200710i
$815$	−49.4995	+	7.83995i	−1.73389	+	0.274622i
$816$		0			0
$817$	−9.64513	−	23.2854i	−0.337440	−	0.814653i
$818$	−9.67908	+	4.93174i	−0.338421	+	0.172434i
$819$		0			0
$820$	1.87735	+	0.504652i	0.0655599	+	0.0176232i
$821$			8.62347i			0.300961i	0.988613	+	0.150481i	$0.0480821\pi$
$821$			8.62347i			0.300961i	−0.988613	+	0.150481i	$0.951918\pi$
$822$		0			0
$823$	−25.0623	+	10.3812i	−0.873618	+	0.361865i	−0.774018	−	0.633163i	$-0.781756\pi$
$823$	−25.0623	+	10.3812i	−0.873618	+	0.361865i	−0.0995998	+	0.995028i	$0.531756\pi$
$824$	−0.388781	−	0.282466i	−0.0135438	−	0.00984016i
$825$		0			0
$826$	18.9911	−	22.2358i	0.660786	−	0.773681i
$827$	18.9518	−	16.1864i	0.659019	−	0.562856i	−0.255795	−	0.966731i	$-0.582337\pi$
$827$	18.9518	−	16.1864i	0.659019	−	0.562856i	0.914814	+	0.403876i	$0.132337\pi$
$828$		0			0
$829$	−28.9863	+	28.9863i	−1.00674	+	1.00674i	−0.00675804	+	0.999977i	$0.502151\pi$
$829$	−28.9863	+	28.9863i	−1.00674	+	1.00674i	−0.999977	+	0.00675804i	$0.997849\pi$
$830$	−6.22416	−	8.56683i	−0.216044	−	0.297359i
$831$		0			0
$832$	−8.60684	+	35.8501i	−0.298388	+	1.24288i
$833$	1.84342	−	0.145080i	0.0638708	−	0.00502674i
$834$		0			0
$835$	34.4882	−	21.1344i	1.19351	−	0.731386i
$836$	0.257768	−	0.0837540i	0.00891511	−	0.00289669i
$837$		0			0
$838$	13.8788	−	42.7144i	0.479434	−	1.47555i
$839$	11.5601	+	0.909800i	0.399099	+	0.0314098i	0.276421	−	0.961037i	$-0.410852\pi$
$839$	11.5601	+	0.909800i	0.399099	+	0.0314098i	0.122678	+	0.992446i	$0.460852\pi$
$840$		0			0
$841$	−15.0747	−	7.68094i	−0.519817	−	0.264860i
$842$	−4.27844	+	54.3627i	−0.147445	+	1.87346i
$843$		0			0
$844$	−0.545376	−	2.27165i	−0.0187726	−	0.0781935i
$845$	−6.47639	−	19.9323i	−0.222795	−	0.685691i
$846$		0			0
$847$	6.08453	−	14.6894i	0.209067	−	0.504732i
$848$	−2.00803	−	25.5144i	−0.0689559	−	0.876168i
$849$		0			0
$850$	1.49839	−	2.44515i	0.0513944	−	0.0838681i
$851$	−25.5392	+	18.5553i	−0.875472	+	0.636068i
$852$		0			0
$853$	3.18240	+	0.504042i	0.108963	+	0.0172581i	0.210678	−	0.977556i	$-0.432433\pi$
$853$	3.18240	+	0.504042i	0.108963	+	0.0172581i	−0.101715	+	0.994814i	$0.532433\pi$
$854$	−17.0184	−	19.9260i	−0.582357	−	0.681853i
$855$		0			0
$856$	−3.85867	−	24.3627i	−0.131887	−	0.832699i
$857$	−16.6351	+	22.8963i	−0.568245	+	0.782122i	−0.992345	−	0.123493i	$-0.960590\pi$
$857$	−16.6351	+	22.8963i	−0.568245	+	0.782122i	0.424101	+	0.905615i	$0.360590\pi$
$858$		0			0
$859$	18.5467	+	36.4000i	0.632806	+	1.24195i	0.955372	+	0.295404i	$0.0954544\pi$
$859$	18.5467	+	36.4000i	0.632806	+	1.24195i	−0.322567	+	0.946547i	$0.604546\pi$
$860$	1.88731			0.0643566
$861$		0			0
$862$	15.6251			0.532192
$863$	17.6587	+	34.6572i	0.601111	+	1.17975i	0.968345	+	0.249617i	$0.0803049\pi$
$863$	17.6587	+	34.6572i	0.601111	+	1.17975i	−0.367234	+	0.930129i	$0.619695\pi$
$864$		0			0
$865$	13.3967	−	18.4390i	0.455503	−	0.626946i
$866$	−7.92492	−	50.0360i	−0.269300	−	1.70029i
$867$		0			0
$868$	−0.0772366	−	0.0904324i	−0.00262158	−	0.00306948i
$869$	7.34122	+	1.16274i	0.249034	+	0.0394431i
$870$		0			0
$871$	−7.52374	+	5.46632i	−0.254932	+	0.185219i
$872$	8.96693	−	14.6327i	0.303659	−	0.495526i
$873$		0			0
$874$	−1.53264	−	19.4741i	−0.0518424	−	0.658720i
$875$	−0.537321	+	1.29721i	−0.0181648	+	0.0438536i
$876$		0			0
$877$	3.22536	+	9.92663i	0.108913	+	0.335198i	0.990629	−	0.136582i	$-0.0436116\pi$
$877$	3.22536	+	9.92663i	0.108913	+	0.335198i	−0.881716	+	0.471780i	$0.843612\pi$
$878$	−2.81848	−	11.7398i	−0.0951191	−	0.396199i
$879$		0			0
$880$	0.675764	−	8.58639i	0.0227800	−	0.289447i
$881$	46.6686	+	23.7788i	1.57230	+	0.801129i	0.999823	−	0.0187887i	$-0.00598099\pi$
$881$	46.6686	+	23.7788i	1.57230	+	0.801129i	0.572481	+	0.819918i	$0.305981\pi$
$882$		0			0
$883$	22.9017	+	1.80240i	0.770703	+	0.0606556i	0.457712	−	0.889101i	$-0.348669\pi$
$883$	22.9017	+	1.80240i	0.770703	+	0.0606556i	0.312991	+	0.949756i	$0.398669\pi$
$884$	−0.0507762	+	0.156273i	−0.00170779	+	0.00525603i
$885$		0			0
$886$	−35.4818	+	11.5287i	−1.19204	+	0.387316i
$887$	−46.0326	+	28.2088i	−1.54562	+	0.947159i	−0.552069	+	0.833798i	$0.686161\pi$
$887$	−46.0326	+	28.2088i	−1.54562	+	0.947159i	−0.993554	+	0.113360i	$0.963839\pi$
$888$		0			0
$889$	9.11986	−	0.717748i	0.305870	−	0.0240725i
$890$	9.84180	−	40.9940i	0.329898	−	1.37412i
$891$		0			0
$892$	1.13517	+	1.56243i	0.0380083	+	0.0523139i
$893$	−22.9944	+	22.9944i	−0.769478	+	0.769478i
$894$		0			0
$895$	−18.4566	+	15.7634i	−0.616937	+	0.526914i
$896$	10.2706	−	12.0253i	0.343116	−	0.401737i
$897$		0			0
$898$	−8.48992	−	6.16828i	−0.283312	−	0.205838i
$899$	−5.19546	+	2.15203i	−0.173278	+	0.0717742i
$900$		0			0
$901$		−	2.64432i		−	0.0880950i
$902$	−6.18976	+	0.809838i	−0.206096	+	0.0269647i
$903$		0			0
$904$	−20.4135	+	10.4012i	−0.678942	+	0.345938i
$905$	−17.7765	−	42.9163i	−0.590911	−	1.42659i
$906$		0			0
$907$	−22.4641	+	3.55797i	−0.745909	+	0.118140i	−0.517808	−	0.855497i	$-0.673252\pi$
$907$	−22.4641	+	3.55797i	−0.745909	+	0.118140i	−0.228101	+	0.973637i	$0.573252\pi$
$908$	2.02934	+	1.73322i	0.0673460	+	0.0575189i
$909$		0			0
$910$	−4.63502	+	29.2644i	−0.153649	+	0.970104i
$911$	38.7532	+	38.7532i	1.28395	+	1.28395i	0.938401	+	0.345549i	$0.112307\pi$
$911$	38.7532	+	38.7532i	1.28395	+	1.28395i	0.345549	+	0.938401i	$0.387693\pi$
$912$		0			0
$913$	−1.44023	−	0.882574i	−0.0476646	−	0.0292089i
$914$	−16.2856	−	3.90983i	−0.538680	−	0.129326i
$915$		0			0
$916$	0.744049	+	0.308195i	0.0245841	+	0.0101830i
$917$	12.6975	+	20.7204i	0.419307	+	0.684247i
$918$		0			0
$919$	−44.2164	+	10.6154i	−1.45856	+	0.350170i	−0.883690	−	0.468073i	$-0.844949\pi$
$919$	−44.2164	+	10.6154i	−1.45856	+	0.350170i	−0.574873	+	0.818243i	$0.694949\pi$
$920$	30.7875	+	10.0035i	1.01504	+	0.329805i
$921$		0			0
$922$	12.1677	−	23.8804i	0.400721	−	0.786460i
$923$	18.3695	−	36.0522i	0.604640	−	1.18667i
$924$		0			0
$925$	45.4943	+	14.7820i	1.49584	+	0.486029i
$926$	−17.9480	+	4.30894i	−0.589809	+	0.141601i
$927$		0			0
$928$	1.89408	+	3.09086i	0.0621763	+	0.101462i
$929$	13.3056	+	5.51136i	0.436542	+	0.180822i	0.590121	−	0.807315i	$-0.299080\pi$
$929$	13.3056	+	5.51136i	0.436542	+	0.180822i	−0.153579	+	0.988136i	$0.549080\pi$
$930$		0			0
$931$	−18.5590	−	4.45563i	−0.608247	−	0.146027i
$932$	−0.263507	−	0.161477i	−0.00863146	−	0.00528937i
$933$		0			0
$934$	1.77291	+	1.77291i	0.0580115	+	0.0580115i
$935$	0.139210	−	0.878940i	0.00455267	−	0.0287444i
$936$		0			0
$937$	12.1305	+	10.3605i	0.396287	+	0.338461i	0.825155	−	0.564906i	$-0.191087\pi$
$937$	12.1305	+	10.3605i	0.396287	+	0.338461i	−0.428868	+	0.903367i	$0.641087\pi$
$938$	4.34352	−	0.687945i	0.141821	−	0.0224622i
$939$		0			0
$940$	−0.931861	−	2.24971i	−0.0303939	−	0.0733775i
$941$	−4.65315	+	2.37090i	−0.151688	+	0.0772890i	−0.528187	−	0.849128i	$-0.677128\pi$
$941$	−4.65315	+	2.37090i	−0.151688	+	0.0772890i	0.376499	+	0.926417i	$0.377128\pi$
$942$		0			0
$943$	2.35405	−	22.2254i	0.0766583	−	0.723760i
$944$			53.1927i			1.73127i
$945$		0			0
$946$	−5.59915	+	2.31924i	−0.182044	+	0.0754051i
$947$	−35.8206	−	26.0252i	−1.16401	−	0.845704i	−0.173732	−	0.984793i	$-0.555583\pi$
$947$	−35.8206	−	26.0252i	−1.16401	−	0.845704i	−0.990280	+	0.139089i	$0.955583\pi$
$948$		0			0
$949$	2.93609	−	3.43772i	0.0953096	−	0.111593i
$950$	−22.5084	+	19.2240i	−0.730268	+	0.623708i
$951$		0			0
$952$	1.21592	−	1.21592i	0.0394082	−	0.0394082i
$953$	21.0410	+	28.9604i	0.681584	+	0.938120i	0.999952	−	0.00984752i	$-0.00313461\pi$
$953$	21.0410	+	28.9604i	0.681584	+	0.938120i	−0.318368	+	0.947967i	$0.603135\pi$
$954$		0			0
$955$	8.58232	−	35.7479i	0.277717	−	1.15678i
$956$	1.51483	−	0.119220i	0.0489932	−	0.00385585i
$957$		0			0
$958$	22.7735	−	13.9556i	0.735778	−	0.450885i
$959$	8.73303	−	2.83753i	0.282004	−	0.0916287i
$960$		0			0
$961$	9.36671	−	28.8278i	0.302152	−	0.929928i
$962$	55.0057	+	4.32904i	1.77346	+	0.139574i
$963$		0			0
$964$	−0.971945	−	0.495231i	−0.0313042	−	0.0159503i
$965$	6.82596	−	86.7320i	0.219735	−	2.79200i
$966$		0			0
$967$	2.80051	+	11.6650i	0.0900583	+	0.375120i	0.999138	−	0.0415015i	$-0.0132141\pi$
$967$	2.80051	+	11.6650i	0.0900583	+	0.375120i	−0.909080	+	0.416621i	$0.863214\pi$
$968$	9.38250	+	28.8764i	0.301565	+	0.928121i
$969$		0			0
$970$	−30.2266	+	72.9735i	−0.970518	+	2.34304i
$971$	2.43288	+	30.9127i	0.0780748	+	0.992035i	0.903798	+	0.427959i	$0.140767\pi$
$971$	2.43288	+	30.9127i	0.0780748	+	0.992035i	−0.825723	+	0.564075i	$0.809233\pi$
$972$		0			0
$973$	17.4419	−	28.4626i	0.559161	−	0.912468i
$974$	−1.24821	+	0.906879i	−0.0399953	+	0.0290583i
$975$		0			0
$976$	47.0803	+	7.45678i	1.50700	+	0.238686i
$977$	9.44565	+	11.0594i	0.302193	+	0.353823i	0.890637	−	0.454716i	$-0.150259\pi$
$977$	9.44565	+	11.0594i	0.302193	+	0.353823i	−0.588444	+	0.808538i	$0.700259\pi$
$978$		0			0
$979$	−1.05202	−	6.64221i	−0.0336228	−	0.212286i
$980$	0.840072	−	1.15626i	0.0268351	−	0.0369354i
$981$		0			0
$982$	−24.0867	−	47.2729i	−0.768639	−	1.50854i
$983$	27.8004			0.886696			0.443348	−	0.896350i	$-0.353791\pi$
$983$	27.8004			0.886696			0.443348	+	0.896350i	$0.353791\pi$
$984$		0			0
$985$	−49.0822			−1.56389
$986$	−1.66801	−	3.27366i	−0.0531204	−	0.104255i
$987$		0			0
$988$	0.996907	−	1.37213i	0.0317158	−	0.0436531i
$989$	−3.39432	−	21.4309i	−0.107933	−	0.681463i
$990$		0			0
$991$	5.70258	+	6.67686i	0.181148	+	0.212097i	0.843549	−	0.537052i	$-0.180462\pi$
$991$	5.70258	+	6.67686i	0.181148	+	0.212097i	−0.662401	+	0.749150i	$0.730462\pi$
$992$	0.438483	+	0.0694488i	0.0139218	+	0.00220500i
$993$		0			0
$994$	−15.4794	+	11.2464i	−0.490976	+	0.356715i
$995$	−10.9029	+	17.7918i	−0.345644	+	0.564039i
$996$		0			0
$997$	1.77966	+	22.6127i	0.0563624	+	0.716152i	0.958571	+	0.284853i	$0.0919447\pi$
$997$	1.77966	+	22.6127i	0.0563624	+	0.716152i	−0.902209	+	0.431299i	$0.858055\pi$
$998$	−14.9242	+	36.0303i	−0.472418	+	1.14052i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.ba.a.350.5	yes	112
3.2	odd	2		369.2.ba.b.350.3	yes	112
41.28	odd	40		369.2.ba.b.233.3	yes	112
123.110	even	40	inner	369.2.ba.a.233.5	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
369.2.ba.a.233.5	✓	112	123.110	even	40	inner
369.2.ba.a.350.5	yes	112	1.1	even	1	trivial
369.2.ba.b.233.3	yes	112	41.28	odd	40
369.2.ba.b.350.3	yes	112	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.626663 + 1.22990i) q^{2} +(0.0556331 - 0.0765724i) q^{4} +(0.501789 + 3.16817i) q^{5} +(-0.983319 - 1.15132i) q^{7} +(2.85574 + 0.452305i) q^{8} +(-3.58207 + 2.60253i) q^{10} +(-0.369033 + 0.602207i) q^{11} +(0.346766 + 4.40607i) q^{13} +(0.799793 - 1.93087i) q^{14} +(1.17480 + 3.61567i) q^{16} +(0.0916972 + 0.381946i) q^{17} +(0.318106 - 4.04192i) q^{19} +(0.270511 + 0.137832i) q^{20} +(-0.971911 - 0.0764911i) q^{22} +(1.07861 - 3.31961i) q^{23} +(-5.03024 + 1.63442i) q^{25} +(-5.20171 + 3.18761i) q^{26} +(-0.142864 + 0.0112437i) q^{28} +(-1.58190 + 6.58910i) q^{29} +(0.487790 + 0.671385i) q^{31} +(0.378272 - 0.378272i) q^{32} +(-0.412291 + 0.352130i) q^{34} +(3.15416 - 3.69304i) q^{35} +(-7.31688 - 5.31603i) q^{37} +(5.17049 - 2.14169i) q^{38} +9.27444i q^{40} +(6.26427 - 1.32625i) q^{41} +(5.53886 - 2.82219i) q^{43} +(0.0255820 + 0.0617604i) q^{44} +(4.75870 - 0.753704i) q^{46} +(-6.09893 - 5.20898i) q^{47} +(0.736423 - 4.64959i) q^{49} +(-5.16244 - 5.16244i) q^{50} +(0.356675 + 0.218571i) q^{52} +(-6.54598 - 1.57155i) q^{53} +(-2.09307 - 0.866979i) q^{55} +(-2.28736 - 3.73263i) q^{56} +(-9.09523 + 2.18357i) q^{58} +(13.3068 + 4.32366i) q^{59} +(5.69224 - 11.1716i) q^{61} +(-0.520054 + 1.02066i) q^{62} +(7.93363 + 2.57779i) q^{64} +(-13.7852 + 3.30953i) q^{65} +(1.09943 + 1.79411i) q^{67} +(0.0343479 + 0.0142274i) q^{68} +(6.51866 + 1.56499i) q^{70} +(-7.80591 - 4.78347i) q^{71} +(-0.723298 - 0.723298i) q^{73} +(1.95294 - 12.3304i) q^{74} +(-0.291802 - 0.249223i) q^{76} +(1.05621 - 0.167287i) q^{77} +(-4.02725 - 9.72264i) q^{79} +(-10.8656 + 5.53629i) q^{80} +(5.55674 + 6.87329i) q^{82} +2.39159i q^{83} +(-1.16406 + 0.482169i) q^{85} +(6.94200 + 5.04366i) q^{86} +(-1.32624 + 1.55283i) q^{88} +(-7.24033 + 6.18383i) q^{89} +(4.73182 - 4.73182i) q^{91} +(-0.194184 - 0.267272i) q^{92} +(2.58453 - 10.7653i) q^{94} +(12.9651 - 1.02038i) q^{95} +(15.2104 - 9.32092i) q^{97} +(6.18000 - 2.00800i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 4 q^{5} + 24 q^{8} - 12 q^{11} - 4 q^{13} - 4 q^{14} + 28 q^{16} - 4 q^{17} + 88 q^{20} + 8 q^{22} + 24 q^{23} - 60 q^{26} + 8 q^{29} + 48 q^{32} - 152 q^{35} + 8 q^{37} - 56 q^{38} + 12 q^{41}+ \cdots + 60 q^{98}+O(q^{100}) \) 112 * q - 4 * q^5 + 24 * q^8 - 12 * q^11 - 4 * q^13 - 4 * q^14 + 28 * q^16 - 4 * q^17 + 88 * q^20 + 8 * q^22 + 24 * q^23 - 60 * q^26 + 8 * q^29 + 48 * q^32 - 152 * q^35 + 8 * q^37 - 56 * q^38 + 12 * q^41 - 24 * q^43 - 60 * q^44 - 56 * q^46 - 28 * q^47 + 64 * q^52 + 16 * q^53 - 8 * q^55 + 72 * q^56 - 16 * q^58 + 40 * q^59 + 28 * q^61 + 68 * q^62 + 172 * q^65 + 48 * q^67 - 36 * q^68 - 232 * q^70 - 32 * q^71 - 72 * q^73 - 4 * q^74 - 176 * q^76 - 60 * q^77 - 72 * q^79 - 128 * q^80 - 192 * q^82 + 16 * q^85 - 40 * q^86 - 112 * q^88 + 48 * q^89 - 80 * q^91 - 64 * q^94 + 20 * q^95 - 72 * q^97 + 60 * q^98

Introduction

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