LMFDB - Embedded newform 819.2.fn.e.460.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			460.5
Character	$\chi$	$=$	819.460
Dual form			819.2.fn.e.73.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.186083 + 0.694471i) q^{2} +(1.28439 - 0.741542i) q^{4} +(1.87130 - 0.501414i) q^{5} +(-0.783278 + 2.52715i) q^{7} +(1.77076 + 1.77076i) q^{8} +O(q^{10})$	\(q+(0.186083 + 0.694471i) q^{2} +(1.28439 - 0.741542i) q^{4} +(1.87130 - 0.501414i) q^{5} +(-0.783278 + 2.52715i) q^{7} +(1.77076 + 1.77076i) q^{8} +(0.696434 + 1.20626i) q^{10} +(-0.825667 + 3.08143i) q^{11} +(0.846120 + 3.50487i) q^{13} +(-1.90079 - 0.0737047i) q^{14} +(0.582851 - 1.00953i) q^{16} +(0.254148 + 0.440197i) q^{17} +(-2.65082 + 0.710286i) q^{19} +(2.03166 - 2.03166i) q^{20} -2.29361 q^{22} +(-2.49648 - 1.44134i) q^{23} +(-1.07978 + 0.623409i) q^{25} +(-2.27658 + 1.23980i) q^{26} +(0.867953 + 3.82667i) q^{28} +2.40426 q^{29} +(0.827581 - 3.08857i) q^{31} +(5.64735 + 1.51320i) q^{32} +(-0.258412 + 0.258412i) q^{34} +(-0.198602 + 5.12180i) q^{35} +(9.40142 - 2.51910i) q^{37} +(-0.986546 - 1.70875i) q^{38} +(4.20150 + 2.42574i) q^{40} +(5.34023 + 5.34023i) q^{41} -12.5736i q^{43} +(1.22453 + 4.57002i) q^{44} +(0.536419 - 2.00194i) q^{46} +(-2.88879 - 10.7811i) q^{47} +(-5.77295 - 3.95892i) q^{49} +(-0.633867 - 0.633867i) q^{50} +(3.68575 + 3.87417i) q^{52} +(3.42477 + 5.93187i) q^{53} +6.18029i q^{55} +(-5.86196 + 3.08797i) q^{56} +(0.447392 + 1.66969i) q^{58} +(-3.74520 - 1.00352i) q^{59} +(-5.51719 - 3.18535i) q^{61} +2.29892 q^{62} +1.87209i q^{64} +(3.34073 + 6.13440i) q^{65} +(6.56281 + 1.75850i) q^{67} +(0.652849 + 0.376923i) q^{68} +(-3.59390 + 0.815156i) q^{70} +(1.90492 - 1.90492i) q^{71} +(0.252451 + 0.0676442i) q^{73} +(3.49889 + 6.06025i) q^{74} +(-2.87798 + 2.87798i) q^{76} +(-7.14051 - 4.50020i) q^{77} +(-2.78380 + 4.82168i) q^{79} +(0.584499 - 2.18138i) q^{80} +(-2.71491 + 4.70236i) q^{82} +(-5.86182 - 5.86182i) q^{83} +(0.696309 + 0.696309i) q^{85} +(8.73203 - 2.33974i) q^{86} +(-6.91853 + 3.99441i) q^{88} +(3.17139 + 11.8358i) q^{89} +(-9.52006 - 0.607013i) q^{91} -4.27526 q^{92} +(6.94962 - 4.01237i) q^{94} +(-4.60434 + 2.65832i) q^{95} +(-7.04713 - 7.04713i) q^{97} +(1.67511 - 4.74583i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.186083	+	0.694471i	0.131581	+	0.491065i	0.999989	−	0.00478511i	$-0.00152315\pi$
$2$	0.186083	+	0.694471i	0.131581	+	0.491065i	−0.868408	+	0.495850i	$0.834856\pi$
$3$		0			0
$3$		0			0
$4$	1.28439	−	0.741542i	0.642194	−	0.370771i
$5$	1.87130	−	0.501414i	0.836871	−	0.224239i	0.185162	−	0.982708i	$-0.440719\pi$
$5$	1.87130	−	0.501414i	0.836871	−	0.224239i	0.651709	+	0.758469i	$0.274052\pi$
$6$		0			0
$7$	−0.783278	+	2.52715i	−0.296051	+	0.955172i
$7$	−0.783278	+	2.52715i	−0.296051	+	0.955172i
$8$	1.77076	+	1.77076i	0.626057	+	0.626057i
$9$		0			0
$10$	0.696434	+	1.20626i	0.220232	+	0.381453i
$11$	−0.825667	+	3.08143i	−0.248948	+	0.929087i	0.722410	+	0.691465i	$0.243034\pi$
$11$	−0.825667	+	3.08143i	−0.248948	+	0.929087i	−0.971358	+	0.237621i	$0.923632\pi$
$12$		0			0
$13$	0.846120	+	3.50487i	0.234671	+	0.972075i
$13$	0.846120	+	3.50487i	0.234671	+	0.972075i
$14$	−1.90079	−	0.0737047i	−0.508006	−	0.0196984i
$15$		0			0
$16$	0.582851	−	1.00953i	0.145713	−	0.252382i
$17$	0.254148	+	0.440197i	0.0616400	+	0.106764i	0.895199	−	0.445667i	$-0.147034\pi$
$17$	0.254148	+	0.440197i	0.0616400	+	0.106764i	−0.833559	+	0.552431i	$0.813700\pi$
$18$		0			0
$19$	−2.65082	+	0.710286i	−0.608141	+	0.162951i	−0.549731	−	0.835342i	$-0.685270\pi$
$19$	−2.65082	+	0.710286i	−0.608141	+	0.162951i	−0.0584100	+	0.998293i	$0.518603\pi$
$20$	2.03166	−	2.03166i	0.454292	−	0.454292i
$21$		0			0
$22$	−2.29361			−0.488999
$23$	−2.49648	−	1.44134i	−0.520552	−	0.300541i	0.216609	−	0.976259i	$-0.430500\pi$
$23$	−2.49648	−	1.44134i	−0.520552	−	0.300541i	−0.737160	+	0.675718i	$0.763834\pi$
$24$		0			0
$25$	−1.07978	+	0.623409i	−0.215955	+	0.124682i
$26$	−2.27658	+	1.23980i	−0.446474	+	0.243145i
$27$		0			0
$28$	0.867953	+	3.82667i	0.164028	+	0.723173i
$29$	2.40426			0.446460			0.223230	−	0.974766i	$-0.428340\pi$
$29$	2.40426			0.446460			0.223230	+	0.974766i	$0.428340\pi$
$30$		0			0
$31$	0.827581	−	3.08857i	0.148638	−	0.554724i	−0.850929	−	0.525281i	$-0.823960\pi$
$31$	0.827581	−	3.08857i	0.148638	−	0.554724i	0.999566	−	0.0294427i	$-0.00937326\pi$
$32$	5.64735	+	1.51320i	0.998319	+	0.267499i
$33$		0			0
$34$	−0.258412	+	0.258412i	−0.0443172	+	0.0443172i
$35$	−0.198602	+	5.12180i	−0.0335699	+	0.865742i
$36$		0			0
$37$	9.40142	−	2.51910i	1.54558	−	0.414138i	0.617519	−	0.786556i	$-0.288138\pi$
$37$	9.40142	−	2.51910i	1.54558	−	0.414138i	0.928065	+	0.372418i	$0.121471\pi$
$38$	−0.986546	−	1.70875i	−0.160039	−	0.277196i
$39$		0			0
$40$	4.20150	+	2.42574i	0.664316	+	0.383543i
$41$	5.34023	+	5.34023i	0.834004	+	0.834004i	0.988062	−	0.154058i	$-0.0492342\pi$
$41$	5.34023	+	5.34023i	0.834004	+	0.834004i	−0.154058	+	0.988062i	$0.549234\pi$
$42$		0			0
$43$		−	12.5736i		−	1.91746i	−0.284313	−	0.958732i	$-0.591765\pi$
$43$		−	12.5736i		−	1.91746i	0.284313	−	0.958732i	$-0.408235\pi$
$44$	1.22453	+	4.57002i	0.184605	+	0.688956i
$45$		0			0
$46$	0.536419	−	2.00194i	0.0790906	−	0.295170i
$47$	−2.88879	−	10.7811i	−0.421374	−	1.57259i	−0.771716	−	0.635967i	$-0.780601\pi$
$47$	−2.88879	−	10.7811i	−0.421374	−	1.57259i	0.350342	−	0.936622i	$-0.386065\pi$
$48$		0			0
$49$	−5.77295	−	3.95892i	−0.824707	−	0.565560i
$50$	−0.633867	−	0.633867i	−0.0896423	−	0.0896423i
$51$		0			0
$52$	3.68575	+	3.87417i	0.511122	+	0.537251i
$53$	3.42477	+	5.93187i	0.470428	+	0.814805i	0.999428	−	0.0338167i	$-0.0107663\pi$
$53$	3.42477	+	5.93187i	0.470428	+	0.814805i	−0.529000	+	0.848622i	$0.677433\pi$
$54$		0			0
$55$			6.18029i			0.833350i
$56$	−5.86196	+	3.08797i	−0.783338	+	0.412648i
$57$		0			0
$58$	0.447392	+	1.66969i	0.0587454	+	0.219241i
$59$	−3.74520	−	1.00352i	−0.487583	−	0.130647i	0.00664837	−	0.999978i	$-0.497884\pi$
$59$	−3.74520	−	1.00352i	−0.487583	−	0.130647i	−0.494231	+	0.869330i	$0.664550\pi$
$60$		0			0
$61$	−5.51719	−	3.18535i	−0.706404	−	0.407843i	0.103324	−	0.994648i	$-0.467052\pi$
$61$	−5.51719	−	3.18535i	−0.706404	−	0.407843i	−0.809728	+	0.586805i	$0.800386\pi$
$62$	2.29892			0.291963
$63$		0			0
$64$			1.87209i			0.234012i
$65$	3.34073	+	6.13440i	0.414367	+	0.760879i
$66$		0			0
$67$	6.56281	+	1.75850i	0.801775	+	0.214835i	0.636363	−	0.771390i	$-0.280438\pi$
$67$	6.56281	+	1.75850i	0.801775	+	0.214835i	0.165412	+	0.986225i	$0.447105\pi$
$68$	0.652849	+	0.376923i	0.0791696	+	0.0457086i
$69$		0			0
$70$	−3.59390	+	0.815156i	−0.429553	+	0.0974298i
$71$	1.90492	−	1.90492i	0.226072	−	0.226072i	−0.584978	−	0.811049i	$-0.698897\pi$
$71$	1.90492	−	1.90492i	0.226072	−	0.226072i	0.811049	+	0.584978i	$0.198897\pi$
$72$		0			0
$73$	0.252451	+	0.0676442i	0.0295472	+	0.00791715i	0.273562	−	0.961854i	$-0.411798\pi$
$73$	0.252451	+	0.0676442i	0.0295472	+	0.00791715i	−0.244015	+	0.969771i	$0.578465\pi$
$74$	3.49889	+	6.06025i	0.406738	+	0.704490i
$75$		0			0
$76$	−2.87798	+	2.87798i	−0.330127	+	0.330127i
$77$	−7.14051	−	4.50020i	−0.813736	−	0.512845i
$78$		0			0
$79$	−2.78380	+	4.82168i	−0.313202	+	0.542481i	−0.979054	−	0.203603i	$-0.934735\pi$
$79$	−2.78380	+	4.82168i	−0.313202	+	0.542481i	0.665852	+	0.746084i	$0.268068\pi$
$80$	0.584499	−	2.18138i	0.0653490	−	0.243886i
$81$		0			0
$82$	−2.71491	+	4.70236i	−0.299812	+	0.519289i
$83$	−5.86182	−	5.86182i	−0.643419	−	0.643419i	0.307975	−	0.951394i	$-0.400349\pi$
$83$	−5.86182	−	5.86182i	−0.643419	−	0.643419i	−0.951394	+	0.307975i	$0.900349\pi$
$84$		0			0
$85$	0.696309	+	0.696309i	0.0755253	+	0.0755253i
$86$	8.73203	−	2.33974i	0.941599	−	0.252301i
$87$		0			0
$88$	−6.91853	+	3.99441i	−0.737517	+	0.425806i
$89$	3.17139	+	11.8358i	0.336166	+	1.25459i	0.902599	+	0.430482i	$0.141656\pi$
$89$	3.17139	+	11.8358i	0.336166	+	1.25459i	−0.566433	+	0.824108i	$0.691677\pi$
$90$		0			0
$91$	−9.52006	−	0.607013i	−0.997973	−	0.0636323i
$92$	−4.27526			−0.445727
$93$		0			0
$94$	6.94962	−	4.01237i	0.716799	−	0.413844i
$95$	−4.60434	+	2.65832i	−0.472396	+	0.272738i
$96$		0			0
$97$	−7.04713	−	7.04713i	−0.715528	−	0.715528i	0.252158	−	0.967686i	$-0.418860\pi$
$97$	−7.04713	−	7.04713i	−0.715528	−	0.715528i	−0.967686	+	0.252158i	$0.918860\pi$
$98$	1.67511	−	4.74583i	0.169211	−	0.479402i
$99$		0			0
$100$	−0.924567	+	1.60140i	−0.0924567	+	0.160140i
$101$	2.35974	+	4.08719i	0.234803	+	0.406691i	0.959215	−	0.282676i	$-0.0912222\pi$
$101$	2.35974	+	4.08719i	0.234803	+	0.406691i	−0.724412	+	0.689367i	$0.757889\pi$
$102$		0			0
$103$	2.22971	−	3.86197i	0.219700	−	0.380531i	−0.735016	−	0.678049i	$-0.762826\pi$
$103$	2.22971	−	3.86197i	0.219700	−	0.380531i	0.954716	+	0.297518i	$0.0961589\pi$
$104$	−4.70799	+	7.70454i	−0.461657	+	0.755492i
$105$		0			0
$106$	−3.48222	+	3.48222i	−0.338223	+	0.338223i
$107$	9.65530	−	16.7235i	0.933413	−	1.61672i	0.155973	−	0.987761i	$-0.450149\pi$
$107$	9.65530	−	16.7235i	0.933413	−	1.61672i	0.777440	−	0.628957i	$-0.216518\pi$
$108$		0			0
$109$	10.5129	+	2.81694i	1.00696	+	0.269813i	0.724358	−	0.689424i	$-0.242136\pi$
$109$	10.5129	+	2.81694i	1.00696	+	0.269813i	0.282600	+	0.959238i	$0.408803\pi$
$110$	−4.29203	+	1.15005i	−0.409229	+	0.109653i
$111$		0			0
$112$	2.09469	+	2.26369i	0.197930	+	0.213899i
$113$	−11.1771			−1.05145			−0.525726	−	0.850654i	$-0.676206\pi$
$113$	−11.1771			−1.05145			−0.525726	+	0.850654i	$0.676206\pi$
$114$		0			0
$115$	−5.39437	−	1.44542i	−0.503028	−	0.134786i
$116$	3.08800	−	1.78286i	0.286714	−	0.165534i
$117$		0			0
$118$		−	2.78767i		−	0.256626i
$119$	−1.31151	+	0.297473i	−0.120226	+	0.0272693i
$120$		0			0
$121$	0.712785	+	0.411527i	0.0647987	+	0.0374115i
$122$	1.18548	−	4.42427i	0.107328	−	0.400555i
$123$		0			0
$124$	−1.22737	−	4.58061i	−0.110221	−	0.411351i
$125$	−8.55744	+	8.55744i	−0.765400	+	0.765400i
$126$		0			0
$127$			14.7463i			1.30852i	0.756269	+	0.654261i	$0.227020\pi$
$127$			14.7463i			1.30852i	−0.756269	+	0.654261i	$0.772980\pi$
$128$	9.99458	−	2.67804i	0.883404	−	0.236707i
$129$		0			0
$130$	−3.63851	+	3.46155i	−0.319118	+	0.303598i
$131$	−17.5068	−	10.1075i	−1.52957	−	0.883100i	−0.999379	−	0.0352230i	$-0.988786\pi$
$131$	−17.5068	−	10.1075i	−1.52957	−	0.883100i	−0.530194	−	0.847877i	$-0.677881\pi$
$132$		0			0
$133$	0.281334	−	7.25538i	0.0243947	−	0.629121i
$134$			4.88491i			0.421992i
$135$		0			0
$136$	−0.329448	+	1.22952i	−0.0282500	+	0.105430i
$137$	2.19304	−	8.18452i	0.187364	−	0.699251i	−0.806748	−	0.590895i	$-0.798775\pi$
$137$	2.19304	−	8.18452i	0.187364	−	0.699251i	0.994112	−	0.108356i	$-0.0345586\pi$
$138$		0			0
$139$		−	2.42919i		−	0.206041i	−0.994679	−	0.103021i	$-0.967149\pi$
$139$		−	2.42919i		−	0.206041i	0.994679	−	0.103021i	$-0.0328507\pi$
$140$	3.54295	+	6.72565i	0.299434	+	0.568421i
$141$		0			0
$142$	1.67738	+	0.968436i	0.140763	+	0.0812694i
$143$	−11.4986	−	0.286591i	−0.961563	−	0.0239659i
$144$		0			0
$145$	4.49909	−	1.20553i	0.373629	−	0.100114i
$146$			0.187908i			0.0155513i
$147$		0			0
$148$	10.2071	−	10.2071i	0.839015	−	0.839015i
$149$	−1.53590	−	5.73207i	−0.125826	−	0.469590i	0.874042	−	0.485851i	$-0.161490\pi$
$149$	−1.53590	−	5.73207i	−0.125826	−	0.469590i	−0.999868	+	0.0162614i	$0.994824\pi$
$150$		0			0
$151$	1.67388	−	6.24701i	0.136219	−	0.508374i	−0.863771	−	0.503884i	$-0.831904\pi$
$151$	1.67388	−	6.24701i	0.136219	−	0.508374i	0.999990	−	0.00449055i	$-0.00142939\pi$
$152$	−5.95171	−	3.43622i	−0.482748	−	0.278715i
$153$		0			0
$154$	1.79653	−	5.79628i	0.144769	−	0.467078i
$155$		−	6.19461i		−	0.497563i
$156$		0			0
$157$	5.54969	−	3.20411i	0.442913	−	0.255716i	−0.261919	−	0.965090i	$-0.584355\pi$
$157$	5.54969	−	3.20411i	0.442913	−	0.255716i	0.704833	+	0.709374i	$0.251022\pi$
$158$	−3.86653	−	1.03603i	−0.307605	−	0.0824225i
$159$		0			0
$160$	11.3266			0.895448
$161$	5.59792	−	5.18000i	0.441178	−	0.408241i
$162$		0			0
$163$	−0.660995	+	0.177113i	−0.0517731	+	0.0138726i	−0.284613	−	0.958643i	$-0.591865\pi$
$163$	−0.660995	+	0.177113i	−0.0517731	+	0.0138726i	0.232840	+	0.972515i	$0.425198\pi$
$164$	10.8189	+	2.89892i	0.844816	+	0.226368i
$165$		0			0
$166$	2.98008	−	5.16165i	0.231299	−	0.400622i
$167$	2.47505	−	2.47505i	0.191525	−	0.191525i	−0.604830	−	0.796355i	$-0.706759\pi$
$167$	2.47505	−	2.47505i	0.191525	−	0.191525i	0.796355	+	0.604830i	$0.206759\pi$
$168$		0			0
$169$	−11.5682	+	5.93107i	−0.889859	+	0.456236i
$170$	−0.353995	+	0.613137i	−0.0271502	+	0.0470255i
$171$		0			0
$172$	−9.32388	−	16.1494i	−0.710939	−	1.23138i
$173$	12.3860	−	21.4531i	0.941687	−	1.63105i	0.179435	−	0.983770i	$-0.442573\pi$
$173$	12.3860	−	21.4531i	0.941687	−	1.63105i	0.762252	−	0.647280i	$-0.224094\pi$
$174$		0			0
$175$	−0.729681	−	3.21705i	−0.0551587	−	0.243186i
$176$	2.62955	+	2.62955i	0.198210	+	0.198210i
$177$		0			0
$178$	−7.62946	+	4.40487i	−0.571852	+	0.330159i
$179$	−16.6184	+	9.59464i	−1.24212	+	0.717137i	−0.969525	−	0.244992i	$-0.921215\pi$
$179$	−16.6184	+	9.59464i	−1.24212	+	0.717137i	−0.272593	+	0.962129i	$0.587881\pi$
$180$		0			0
$181$	−11.0428			−0.820803			−0.410401	−	0.911905i	$-0.634611\pi$
$181$	−11.0428			−0.820803			−0.410401	+	0.911905i	$0.634611\pi$
$182$	−1.34997	−	6.72436i	−0.100066	−	0.498443i
$183$		0			0
$184$	−1.86839	−	6.97293i	−0.137740	−	0.514051i
$185$	16.3298	−	9.42800i	1.20059	−	0.693161i
$186$		0			0
$187$	−1.56628	+	0.419683i	−0.114538	+	0.0306903i
$188$	−11.7050	−	11.7050i	−0.853674	−	0.853674i
$189$		0			0
$190$	−2.70291	−	2.70291i	−0.196090	−	0.196090i
$191$	5.68132	−	9.84033i	0.411086	−	0.712022i	−0.583923	−	0.811809i	$-0.698483\pi$
$191$	5.68132	−	9.84033i	0.411086	−	0.712022i	0.995009	+	0.0997875i	$0.0318163\pi$
$192$		0			0
$193$	−3.22844	+	12.0487i	−0.232388	+	0.867286i	0.746920	+	0.664914i	$0.231532\pi$
$193$	−3.22844	+	12.0487i	−0.232388	+	0.867286i	−0.979309	+	0.202372i	$0.935135\pi$
$194$	3.58268	−	6.20538i	0.257221	−	0.445520i
$195$		0			0
$196$	−10.3504	−	0.803902i	−0.739315	−	0.0574216i
$197$	13.9343	−	13.9343i	0.992775	−	0.992775i	−0.00719943	−	0.999974i	$-0.502292\pi$
$197$	13.9343	−	13.9343i	0.992775	−	0.992775i	0.999974	+	0.00719943i	$0.00229167\pi$
$198$		0			0
$199$	0.413742	+	0.716622i	0.0293294	+	0.0508000i	0.880318	−	0.474385i	$-0.157329\pi$
$199$	0.413742	+	0.716622i	0.0293294	+	0.0508000i	−0.850988	+	0.525185i	$0.823996\pi$
$200$	−3.01593	−	0.808115i	−0.213258	−	0.0571424i
$201$		0			0
$202$	−2.39933	+	2.39933i	−0.168816	+	0.168816i
$203$	−1.88320	+	6.07592i	−0.132175	+	0.426446i
$204$		0			0
$205$	12.6708	+	7.31551i	0.884970	+	0.510938i
$206$	3.09694	+	0.829821i	0.215774	+	0.0578164i
$207$		0			0
$208$	4.03142	+	1.18863i	0.279529	+	0.0824169i
$209$		−	8.75479i		−	0.605582i
$210$		0			0
$211$	18.8543			1.29798			0.648992	−	0.760795i	$-0.275191\pi$
$211$	18.8543			1.29798			0.648992	+	0.760795i	$0.275191\pi$
$212$	8.79746	+	5.07921i	0.604212	+	0.348842i
$213$		0			0
$214$	13.4106	+	3.59337i	0.916733	+	0.245638i
$215$	−6.30460	−	23.5291i	−0.429970	−	1.60467i
$216$		0			0
$217$	7.15705	+	4.51063i	0.485853	+	0.306201i
$218$			7.82512i			0.529984i
$219$		0			0
$220$	4.58294	+	7.93788i	0.308982	+	0.535172i
$221$	−1.32779	+	1.26321i	−0.0893170	+	0.0849730i
$222$		0			0
$223$	−9.83194	−	9.83194i	−0.658396	−	0.658396i	0.296605	−	0.955000i	$-0.404146\pi$
$223$	−9.83194	−	9.83194i	−0.658396	−	0.658396i	−0.955000	+	0.296605i	$0.904146\pi$
$224$	−8.24753	+	13.0864i	−0.551061	+	0.874373i
$225$		0			0
$226$	−2.07987	−	7.76216i	−0.138351	−	0.516332i
$227$	−4.05207	+	15.1225i	−0.268945	+	1.00372i	0.690846	+	0.723002i	$0.257238\pi$
$227$	−4.05207	+	15.1225i	−0.268945	+	1.00372i	−0.959791	+	0.280715i	$0.909428\pi$
$228$		0			0
$229$	−1.23889	−	4.62362i	−0.0818684	−	0.305537i	0.912834	−	0.408330i	$-0.133889\pi$
$229$	−1.23889	−	4.62362i	−0.0818684	−	0.305537i	−0.994703	+	0.102793i	$0.967222\pi$
$230$		−	4.01520i		−	0.264755i
$231$		0			0
$232$	4.25736	+	4.25736i	0.279509	+	0.279509i
$233$	2.74537	+	1.58504i	0.179855	+	0.103839i	0.587225	−	0.809424i	$-0.300221\pi$
$233$	2.74537	+	1.58504i	0.179855	+	0.103839i	−0.407369	+	0.913263i	$0.633554\pi$
$234$		0			0
$235$	−10.8116	−	18.7263i	−0.705271	−	1.22157i
$236$	−5.55444	+	1.48831i	−0.361563	+	0.0968805i
$237$		0			0
$238$	−0.450636	−	0.855453i	−0.0292104	−	0.0554508i
$239$	−7.52256	+	7.52256i	−0.486594	+	0.486594i	−0.907230	−	0.420636i	$-0.861807\pi$
$239$	−7.52256	+	7.52256i	−0.486594	+	0.486594i	0.420636	+	0.907230i	$0.361807\pi$
$240$		0			0
$241$	−1.89421	−	0.507552i	−0.122017	−	0.0326943i	0.197294	−	0.980344i	$-0.436785\pi$
$241$	−1.89421	−	0.507552i	−0.122017	−	0.0326943i	−0.319311	+	0.947650i	$0.603451\pi$
$242$	−0.153156	+	0.571587i	−0.00984526	+	0.0367430i
$243$		0			0
$244$	−9.44829			−0.604865
$245$	−12.7880	−	4.51369i	−0.816994	−	0.288369i
$246$		0			0
$247$	−4.73237	−	8.68980i	−0.301114	−	0.552918i
$248$	6.93456	−	4.00367i	0.440345	−	0.254233i
$249$		0			0
$250$	−7.53528	−	4.35050i	−0.476573	−	0.275150i
$251$	1.64155			0.103614			0.0518070	−	0.998657i	$-0.483502\pi$
$251$	1.64155			0.103614			0.0518070	+	0.998657i	$0.483502\pi$
$252$		0			0
$253$	6.50266	−	6.50266i	0.408819	−	0.408819i
$254$	−10.2409	+	2.74403i	−0.642570	+	0.172176i
$255$		0			0
$256$	5.59174	+	9.68517i	0.349483	+	0.605323i
$257$	−10.9118	+	18.8997i	−0.680657	+	1.17893i	0.294124	+	0.955767i	$0.404972\pi$
$257$	−10.9118	+	18.8997i	−0.680657	+	1.17893i	−0.974781	+	0.223165i	$0.928361\pi$
$258$		0			0
$259$	−0.997779	+	25.7319i	−0.0619990	+	1.59891i
$260$	8.83971	+	5.40166i	0.548216	+	0.334997i
$261$		0			0
$262$	3.76168	−	14.0388i	0.232397	−	0.867319i
$263$	8.33334	+	14.4338i	0.513856	+	0.890024i	0.999871	+	0.0160740i	$0.00511672\pi$
$263$	8.33334	+	14.4338i	0.513856	+	0.890024i	−0.486015	+	0.873950i	$0.661550\pi$
$264$		0			0
$265$	9.38309	+	9.38309i	0.576399	+	0.576399i
$266$	5.09100	−	1.15472i	0.312149	−	0.0708007i
$267$		0			0
$268$	9.73319	−	2.60800i	0.594549	−	0.159309i
$269$	−14.6567	+	8.46207i	−0.893637	+	0.515942i	−0.875130	−	0.483887i	$-0.839225\pi$
$269$	−14.6567	+	8.46207i	−0.893637	+	0.515942i	−0.0185068	+	0.999829i	$0.505891\pi$
$270$		0			0
$271$	−3.59627	−	13.4215i	−0.218458	−	0.815295i	−0.984921	−	0.173007i	$-0.944652\pi$
$271$	−3.59627	−	13.4215i	−0.218458	−	0.815295i	0.766463	−	0.642289i	$-0.222015\pi$
$272$	0.592522			0.0359269
$273$		0			0
$274$	6.09200			0.368031
$275$	−1.02946	−	3.84198i	−0.0620785	−	0.231680i
$276$		0			0
$277$	−17.0084	+	9.81980i	−1.02194	+	0.590015i	−0.914664	−	0.404215i	$-0.867545\pi$
$277$	−17.0084	+	9.81980i	−1.02194	+	0.590015i	−0.107272	+	0.994230i	$0.534211\pi$
$278$	1.68700	−	0.452030i	0.101180	−	0.0271110i
$279$		0			0
$280$	−9.42114	+	8.71779i	−0.563021	+	0.520988i
$281$	17.2002	+	17.2002i	1.02608	+	1.02608i	0.999651	+	0.0264298i	$0.00841385\pi$
$281$	17.2002	+	17.2002i	1.02608	+	1.02608i	0.0264298	+	0.999651i	$0.491586\pi$
$282$		0			0
$283$	5.89745	+	10.2147i	0.350567	+	0.607200i	0.986349	−	0.164669i	$-0.0526555\pi$
$283$	5.89745	+	10.2147i	0.350567	+	0.607200i	−0.635782	+	0.771869i	$0.719322\pi$
$284$	1.03408	−	3.85922i	0.0613611	−	0.229003i
$285$		0			0
$286$	−1.94067	−	8.03878i	−0.114754	−	0.475343i
$287$	−17.6784	+	9.31267i	−1.04353	+	0.549709i
$288$		0			0
$289$	8.37082	−	14.4987i	0.492401	−	0.852864i
$290$	1.67441	+	2.90016i	0.0983247	+	0.170303i
$291$		0			0
$292$	0.374406	−	0.100322i	0.0219105	−	0.00587090i
$293$	−18.5497	+	18.5497i	−1.08368	+	1.08368i	−0.0875204	+	0.996163i	$0.527894\pi$
$293$	−18.5497	+	18.5497i	−1.08368	+	1.08368i	−0.996163	+	0.0875204i	$0.972106\pi$
$294$		0			0
$295$	−7.51157			−0.437340
$296$	21.1084	+	12.1869i	1.22690	+	0.708350i
$297$		0			0
$298$	3.69495	−	2.13328i	0.214043	−	0.123578i
$299$	2.93939	−	9.96937i	0.169989	−	0.576544i
$300$		0			0
$301$	31.7755	+	9.84866i	1.83151	+	0.567667i
$302$	4.64985			0.267569
$303$		0			0
$304$	−0.827982	+	3.09007i	−0.0474880	+	0.177228i
$305$	−11.9215	−	3.19436i	−0.682624	−	0.182908i
$306$		0			0
$307$	1.29211	−	1.29211i	0.0737445	−	0.0737445i	−0.669273	−	0.743017i	$-0.733394\pi$
$307$	1.29211	−	1.29211i	0.0737445	−	0.0737445i	0.743017	+	0.669273i	$0.233394\pi$
$308$	−12.5083	−	0.485019i	−0.712724	−	0.0276365i
$309$		0			0
$310$	4.30198	−	1.15271i	0.244336	−	0.0654696i
$311$	1.35809	+	2.35229i	0.0770104	+	0.133386i	0.901959	−	0.431822i	$-0.142129\pi$
$311$	1.35809	+	2.35229i	0.0770104	+	0.133386i	−0.824948	+	0.565208i	$0.808796\pi$
$312$		0			0
$313$	−22.0145	−	12.7101i	−1.24433	−	0.718415i	−0.274359	−	0.961627i	$-0.588466\pi$
$313$	−22.0145	−	12.7101i	−1.24433	−	0.718415i	−0.969973	+	0.243212i	$0.921799\pi$
$314$	3.25787	+	3.25787i	0.183852	+	0.183852i
$315$		0			0
$316$			8.25721i			0.464504i
$317$	−7.86887	−	29.3670i	−0.441960	−	1.64942i	−0.723841	−	0.689967i	$-0.757625\pi$
$317$	−7.86887	−	29.3670i	−0.441960	−	1.64942i	0.281882	−	0.959449i	$-0.409041\pi$
$318$		0			0
$319$	−1.98512	+	7.40856i	−0.111145	+	0.414800i
$320$	0.938694	+	3.50325i	0.0524746	+	0.195838i
$321$		0			0
$322$	4.63904	+	2.92369i	0.258523	+	0.162931i
$323$	−0.986368	−	0.986368i	−0.0548830	−	0.0548830i
$324$		0			0
$325$	−3.09858	−	3.25699i	−0.171878	−	0.180665i
$326$	−0.246000	−	0.426084i	−0.0136247	−	0.0235986i
$327$		0			0
$328$			18.9125i			1.04427i
$329$	29.5082	+	1.14421i	1.62684	+	0.0630822i
$330$		0			0
$331$	0.489966	+	1.82858i	0.0269310	+	0.100508i	0.978083	−	0.208215i	$-0.0667652\pi$
$331$	0.489966	+	1.82858i	0.0269310	+	0.100508i	−0.951152	+	0.308722i	$0.900099\pi$
$332$	−11.8756	−	3.18207i	−0.651761	−	0.174639i
$333$		0			0
$334$	2.17942	+	1.25829i	0.119252	+	0.0688504i
$335$	13.1627			0.719157
$336$		0			0
$337$		−	15.8664i		−	0.864300i	−0.901802	−	0.432150i	$-0.857755\pi$
$337$		−	15.8664i		−	0.864300i	0.901802	−	0.432150i	$-0.142245\pi$
$338$	−6.27160	−	6.93008i	−0.341130	−	0.376947i
$339$		0			0
$340$	1.41067	+	0.377988i	0.0765044	+	0.0204993i
$341$	8.83392	+	5.10027i	0.478384	+	0.276195i
$342$		0			0
$343$	14.5266	−	11.4882i	0.784362	−	0.620303i
$344$	22.2649	−	22.2649i	1.20044	−	1.20044i
$345$		0			0
$346$	17.2034	+	4.60963i	0.924860	+	0.247815i
$347$	8.10074	+	14.0309i	0.434871	+	0.753218i	0.997285	−	0.0736374i	$-0.0234608\pi$
$347$	8.10074	+	14.0309i	0.434871	+	0.753218i	−0.562414	+	0.826856i	$0.690127\pi$
$348$		0			0
$349$	−18.7058	+	18.7058i	−1.00130	+	1.00130i	−0.00129933	+	0.999999i	$0.500414\pi$
$349$	−18.7058	+	18.7058i	−1.00130	+	1.00130i	−0.999999	+	0.00129933i	$0.999586\pi$
$350$	2.09837	−	1.10538i	0.112163	−	0.0590851i
$351$		0			0
$352$	−9.32566	+	16.1525i	−0.497059	+	0.860932i
$353$	5.93777	−	22.1601i	0.316036	−	1.17946i	−0.606986	−	0.794712i	$-0.707622\pi$
$353$	5.93777	−	22.1601i	0.316036	−	1.17946i	0.923022	−	0.384748i	$-0.125712\pi$
$354$		0			0
$355$	2.60952	−	4.51982i	0.138499	−	0.239887i
$356$	12.8500	+	12.8500i	0.681049	+	0.681049i
$357$		0			0
$358$	−9.75560	−	9.75560i	−0.515600	−	0.515600i
$359$	7.19663	−	1.92833i	0.379824	−	0.101773i	−0.0638554	−	0.997959i	$-0.520340\pi$
$359$	7.19663	−	1.92833i	0.379824	−	0.101773i	0.443679	+	0.896186i	$0.353673\pi$
$360$		0			0
$361$	−9.93212	+	5.73431i	−0.522743	+	0.301806i
$362$	−2.05487	−	7.66889i	−0.108002	−	0.403068i
$363$		0			0
$364$	−12.6776	+	6.27988i	−0.664485	+	0.329155i
$365$	0.506330			0.0265025
$366$		0			0
$367$	−30.3981	+	17.5504i	−1.58677	+	0.916122i	−0.592934	+	0.805251i	$0.702031\pi$
$367$	−30.3981	+	17.5504i	−1.58677	+	0.916122i	−0.993835	+	0.110871i	$0.964636\pi$
$368$	−2.91015	+	1.68018i	−0.151702	+	0.0875853i
$369$		0			0
$370$	9.58617	+	9.58617i	0.498361	+	0.498361i
$371$	−17.6733	+	4.00859i	−0.917550	+	0.208116i
$372$		0			0
$373$	7.82695	−	13.5567i	0.405264	−	0.701938i	−0.589088	−	0.808069i	$-0.700513\pi$
$373$	7.82695	−	13.5567i	0.405264	−	0.701938i	0.994352	+	0.106131i	$0.0338462\pi$
$374$	−0.582916	−	1.00964i	−0.0301419	−	0.0522072i
$375$		0			0
$376$	13.9754	−	24.2061i	0.720727	−	1.24834i
$377$	2.03429	+	8.42660i	0.104771	+	0.433992i
$378$		0			0
$379$	−17.5478	+	17.5478i	−0.901371	+	0.901371i	−0.995555	−	0.0941840i	$-0.969976\pi$
$379$	−17.5478	+	17.5478i	−0.901371	+	0.901371i	0.0941840	+	0.995555i	$0.469976\pi$
$380$	−3.94251	+	6.82862i	−0.202246	+	0.350301i
$381$		0			0
$382$	7.89102	+	2.11439i	0.403740	+	0.108182i
$383$	−0.951971	+	0.255080i	−0.0486435	+	0.0130340i	−0.283059	−	0.959103i	$-0.591349\pi$
$383$	−0.951971	+	0.255080i	−0.0486435	+	0.0130340i	0.234415	+	0.972137i	$0.424682\pi$
$384$		0			0
$385$	−15.6185	−	4.84088i	−0.795992	−	0.246714i
$386$	−8.96824			−0.456471
$387$		0			0
$388$	−14.2770	−	3.82551i	−0.724805	−	0.194211i
$389$	−4.37916	+	2.52831i	−0.222032	+	0.128190i	−0.606891	−	0.794785i	$-0.707584\pi$
$389$	−4.37916	+	2.52831i	−0.222032	+	0.128190i	0.384859	+	0.922976i	$0.374250\pi$
$390$		0			0
$391$		−	1.46526i		−	0.0741013i
$392$	−3.21221	−	17.2328i	−0.162241	−	0.870387i
$393$		0			0
$394$	12.2699	+	7.08401i	0.618147	+	0.356887i
$395$	−2.79167	+	10.4186i	−0.140464	+	0.524219i
$396$		0			0
$397$	−0.301304	−	1.12448i	−0.0151220	−	0.0564361i	0.957953	−	0.286927i	$-0.0926336\pi$
$397$	−0.301304	−	1.12448i	−0.0151220	−	0.0564361i	−0.973075	+	0.230491i	$0.925967\pi$
$398$	−0.420683	+	0.420683i	−0.0210869	+	0.0210869i
$399$		0			0
$400$			1.45342i			0.0726709i
$401$	1.48151	−	0.396969i	0.0739830	−	0.0198237i	−0.221638	−	0.975129i	$-0.571140\pi$
$401$	1.48151	−	0.396969i	0.0739830	−	0.0198237i	0.295621	+	0.955305i	$0.404474\pi$
$402$		0			0
$403$	11.5253	+	0.287255i	0.574114	+	0.0143092i
$404$	6.06164	+	3.49969i	0.301578	+	0.174116i
$405$		0			0
$406$	−4.56998	−	0.177205i	−0.226804	−	0.00879454i
$407$			31.0498i			1.53908i
$408$		0			0
$409$	2.76317	−	10.3123i	0.136630	−	0.509910i	−0.863356	−	0.504595i	$-0.831642\pi$
$409$	2.76317	−	10.3123i	0.136630	−	0.509910i	0.999986	−	0.00531434i	$-0.00169161\pi$
$410$	−2.72258	+	10.1608i	−0.134459	+	0.501807i
$411$		0			0
$412$		−	6.61369i		−	0.325833i
$413$	5.46958	−	8.67863i	0.269140	−	0.427047i
$414$		0			0
$415$	−13.9084	−	8.03004i	−0.682738	−	0.394179i
$416$	−0.525236	+	21.0735i	−0.0257518	+	1.03322i
$417$		0			0
$418$	6.07995	−	1.62912i	0.297380	−	0.0796828i
$419$		−	11.8652i		−	0.579653i	−0.957079	−	0.289826i	$-0.906402\pi$
$419$		−	11.8652i		−	0.579653i	0.957079	−	0.289826i	$-0.0935976\pi$
$420$		0			0
$421$	3.15236	−	3.15236i	0.153636	−	0.153636i	−0.626103	−	0.779740i	$-0.715351\pi$
$421$	3.15236	−	3.15236i	0.153636	−	0.153636i	0.779740	+	0.626103i	$0.215351\pi$
$422$	3.50847	+	13.0938i	0.170789	+	0.637395i
$423$		0			0
$424$	−4.43947	+	16.5683i	−0.215600	+	0.804630i
$425$	−0.548846	−	0.316876i	−0.0266229	−	0.0153708i
$426$		0			0
$427$	12.3714	−	11.4477i	0.598692	−	0.553995i
$428$		−	28.6392i		−	1.38433i
$429$		0			0
$430$	15.1671	−	8.75672i	0.731422	−	0.422286i
$431$	1.18005	+	0.316193i	0.0568410	+	0.0152305i	0.287127	−	0.957892i	$-0.407300\pi$
$431$	1.18005	+	0.316193i	0.0568410	+	0.0152305i	−0.230286	+	0.973123i	$0.573966\pi$
$432$		0			0
$433$	18.1346			0.871493			0.435747	−	0.900069i	$-0.356484\pi$
$433$	18.1346			0.871493			0.435747	+	0.900069i	$0.356484\pi$
$434$	−1.80070	+	5.80972i	−0.0864361	+	0.278875i
$435$		0			0
$436$	15.5916	−	4.17775i	0.746701	−	0.200078i
$437$	7.64149	+	2.04753i	0.365542	+	0.0979467i
$438$		0			0
$439$	−15.6253	+	27.0638i	−0.745755	+	1.29169i	0.204087	+	0.978953i	$0.434578\pi$
$439$	−15.6253	+	27.0638i	−0.745755	+	1.29169i	−0.949841	+	0.312732i	$0.898756\pi$
$440$	−10.9438	+	10.9438i	−0.521725	+	0.521725i
$441$		0			0
$442$	−1.12435	−	0.687051i	−0.0534797	−	0.0326797i
$443$	−12.3867	+	21.4544i	−0.588510	+	1.01933i	0.405918	+	0.913910i	$0.366952\pi$
$443$	−12.3867	+	21.4544i	−0.588510	+	1.01933i	−0.994428	+	0.105420i	$0.966381\pi$
$444$		0			0
$445$	11.8692	+	20.5581i	0.562656	+	0.974549i
$446$	4.99844	−	8.65756i	0.236683	−	0.409947i
$447$		0			0
$448$	−4.73106	−	1.46637i	−0.223522	−	0.0692795i
$449$	−7.07560	−	7.07560i	−0.333918	−	0.333918i	0.520154	−	0.854072i	$-0.325874\pi$
$449$	−7.07560	−	7.07560i	−0.333918	−	0.333918i	−0.854072	+	0.520154i	$0.825874\pi$
$450$		0			0
$451$	−20.8648	+	12.0463i	−0.982485	+	0.567238i
$452$	−14.3557	+	8.28828i	−0.675236	+	0.389848i
$453$		0			0
$454$	−11.2562			−0.528278
$455$	−18.1193	+	3.63758i	−0.849444	+	0.170533i
$456$		0			0
$457$	−5.42349	−	20.2407i	−0.253700	−	0.946821i	−0.968809	−	0.247808i	$-0.920290\pi$
$457$	−5.42349	−	20.2407i	−0.253700	−	0.946821i	0.715109	−	0.699013i	$-0.246377\pi$
$458$	2.98043	−	1.72075i	0.139266	−	0.0804055i
$459$		0			0
$460$	−8.00030	+	2.14367i	−0.373016	+	0.0999494i
$461$	8.07954	+	8.07954i	0.376302	+	0.376302i	0.869766	−	0.493464i	$-0.164270\pi$
$461$	8.07954	+	8.07954i	0.376302	+	0.376302i	−0.493464	+	0.869766i	$0.664270\pi$
$462$		0			0
$463$	−0.417027	−	0.417027i	−0.0193809	−	0.0193809i	0.697350	−	0.716731i	$-0.254362\pi$
$463$	−0.417027	−	0.417027i	−0.0193809	−	0.0193809i	−0.716731	+	0.697350i	$0.754362\pi$
$464$	1.40133	−	2.42717i	0.0650549	−	0.112678i
$465$		0			0
$466$	−0.589898	+	2.20153i	−0.0273265	+	0.101984i
$467$	−2.80499	+	4.85839i	−0.129800	+	0.224819i	−0.923599	−	0.383360i	$-0.874767\pi$
$467$	−2.80499	+	4.85839i	−0.129800	+	0.224819i	0.793799	+	0.608180i	$0.208100\pi$
$468$		0			0
$469$	−9.58449	+	15.2078i	−0.442571	+	0.702231i
$470$	10.9930	−	10.9930i	0.507069	−	0.507069i
$471$		0			0
$472$	−4.85484	−	8.40883i	−0.223462	−	0.387048i
$473$	38.7448	+	10.3816i	1.78149	+	0.477349i
$474$		0			0
$475$	2.41950	−	2.41950i	0.111014	−	0.111014i
$476$	−1.46390	+	1.35461i	−0.0670978	+	0.0620885i
$477$		0			0
$478$	−6.62402	−	3.82438i	−0.302976	−	0.174923i
$479$	13.8255	+	3.70453i	0.631703	+	0.169264i	0.560442	−	0.828193i	$-0.310631\pi$
$479$	13.8255	+	3.70453i	0.631703	+	0.169264i	0.0712606	+	0.997458i	$0.477298\pi$
$480$		0			0
$481$	16.7839	+	30.8193i	0.765278	+	1.40524i
$482$		−	1.40992i		−	0.0642201i
$483$		0			0
$484$	1.22066			0.0554844
$485$	−16.7208	−	9.65378i	−0.759254	−	0.438356i
$486$		0			0
$487$	15.2331	+	4.08170i	0.690278	+	0.184959i	0.586872	−	0.809680i	$-0.300359\pi$
$487$	15.2331	+	4.08170i	0.690278	+	0.184959i	0.103406	+	0.994639i	$0.467026\pi$
$488$	−4.12913	−	15.4101i	−0.186917	−	0.697583i
$489$		0			0
$490$	0.755001	−	9.72081i	0.0341075	−	0.439141i
$491$			25.0495i			1.13047i	0.824930	+	0.565234i	$0.191214\pi$
$491$			25.0495i			1.13047i	−0.824930	+	0.565234i	$0.808786\pi$
$492$		0			0
$493$	0.611038	+	1.05835i	0.0275198	+	0.0476656i
$494$	5.15420	−	4.90352i	0.231898	−	0.220620i
$495$		0			0
$496$	−2.63564	−	2.63564i	−0.118344	−	0.118344i
$497$	3.32192	+	6.30608i	0.149009	+	0.282866i
$498$		0			0
$499$	6.06736	+	22.6437i	0.271612	+	1.01367i	0.958078	+	0.286508i	$0.0924946\pi$
$499$	6.06736	+	22.6437i	0.271612	+	1.01367i	−0.686466	+	0.727162i	$0.740839\pi$
$500$	−4.64537	+	17.3368i	−0.207747	+	0.775324i
$501$		0			0
$502$	0.305465	+	1.14001i	0.0136336	+	0.0508812i
$503$			0.879009i			0.0391931i	0.999808	+	0.0195965i	$0.00623817\pi$
$503$			0.879009i			0.0391931i	−0.999808	+	0.0195965i	$0.993762\pi$
$504$		0			0
$505$	6.46516	+	6.46516i	0.287696	+	0.287696i
$506$	5.72594	+	3.30587i	0.254549	+	0.146964i
$507$		0			0
$508$	10.9350	+	18.9400i	0.485162	+	0.840325i
$509$	9.64356	−	2.58398i	0.427443	−	0.114533i	−0.0386826	−	0.999252i	$-0.512316\pi$
$509$	9.64356	−	2.58398i	0.427443	−	0.114533i	0.466126	+	0.884719i	$0.345649\pi$
$510$		0			0
$511$	−0.368686	+	0.584998i	−0.0163097	+	0.0258788i
$512$	8.94753	−	8.94753i	0.395429	−	0.395429i
$513$		0			0
$514$	−15.1558	−	4.06099i	−0.668494	−	0.179122i
$515$	2.23601	−	8.34491i	0.0985305	−	0.367721i
$516$		0			0
$517$	35.6065			1.56597
$518$	−18.0558	+	4.09535i	−0.793325	+	0.179939i
$519$		0			0
$520$	−4.94691	+	16.7782i	−0.216936	+	0.735771i
$521$	13.4841	−	7.78505i	0.590749	−	0.341069i	−0.174644	−	0.984632i	$-0.555878\pi$
$521$	13.4841	−	7.78505i	0.590749	−	0.341069i	0.765394	+	0.643562i	$0.222544\pi$
$522$		0			0
$523$	11.1498	+	6.43737i	0.487549	+	0.281486i	0.723557	−	0.690265i	$-0.242506\pi$
$523$	11.1498	+	6.43737i	0.487549	+	0.281486i	−0.236008	+	0.971751i	$0.575839\pi$
$524$	−29.9806			−1.30971
$525$		0			0
$526$	−8.47314	+	8.47314i	−0.369447	+	0.369447i
$527$	1.56991	−	0.420656i	0.0683864	−	0.0183241i
$528$		0			0
$529$	−7.34506	−	12.7220i	−0.319351	−	0.553131i
$530$	−4.77025	+	8.26232i	−0.207206	+	0.358892i
$531$		0			0
$532$	−5.01882	−	9.52734i	−0.217594	−	0.413062i
$533$	−14.1983	+	23.2353i	−0.614997	+	1.00643i
$534$		0			0
$535$	9.68260	−	36.1359i	0.418615	−	1.56229i
$536$	8.50727	+	14.7350i	0.367458	+	0.636456i
$537$		0			0
$538$	−8.60403	−	8.60403i	−0.370946	−	0.370946i
$539$	16.9657	−	14.5202i	0.730763	−	0.625430i
$540$		0			0
$541$	15.3392	−	4.11014i	0.659485	−	0.176709i	0.0864715	−	0.996254i	$-0.472441\pi$
$541$	15.3392	−	4.11014i	0.659485	−	0.176709i	0.573014	+	0.819546i	$0.305774\pi$
$542$	8.65161	−	4.99501i	0.371618	−	0.214554i
$543$		0			0
$544$	0.769155	+	2.87053i	0.0329772	+	0.123073i
$545$	21.0853			0.903197
$546$		0			0
$547$	29.5180			1.26210			0.631048	−	0.775743i	$-0.282625\pi$
$547$	29.5180			1.26210			0.631048	+	0.775743i	$0.282625\pi$
$548$	−3.25245	−	12.1383i	−0.138938	−	0.518524i
$549$		0			0
$550$	2.47658	−	1.42985i	0.105602	−	0.0609692i
$551$	−6.37327	+	1.70771i	−0.271510	+	0.0727510i
$552$		0			0
$553$	−10.0046	−	10.8118i	−0.425439	−	0.459764i
$554$	−9.98454	−	9.98454i	−0.424203	−	0.424203i
$555$		0			0
$556$	−1.80134	−	3.12002i	−0.0763940	−	0.132318i
$557$	0.525477	−	1.96111i	0.0222652	−	0.0830947i	−0.953899	−	0.300127i	$-0.902971\pi$
$557$	0.525477	−	1.96111i	0.0222652	−	0.0830947i	0.976164	+	0.217032i	$0.0696376\pi$
$558$		0			0
$559$	44.0689	−	10.6388i	1.86392	−	0.449974i
$560$	5.05484	+	3.18574i	0.213606	+	0.134622i
$561$		0			0
$562$	−8.74440	+	15.1457i	−0.368860	+	0.638885i
$563$	−11.9044	−	20.6190i	−0.501711	−	0.868988i	−0.999998	−	0.00197638i	$-0.999371\pi$
$563$	−11.9044	−	20.6190i	−0.501711	−	0.868988i	0.498287	−	0.867012i	$-0.333962\pi$
$564$		0			0
$565$	−20.9157	+	5.60434i	−0.879930	+	0.235777i
$566$	−5.99639	+	5.99639i	−0.252047	+	0.252047i
$567$		0			0
$568$	6.74629			0.283068
$569$	19.7784	+	11.4191i	0.829154	+	0.478712i	0.853563	−	0.520990i	$-0.174437\pi$
$569$	19.7784	+	11.4191i	0.829154	+	0.478712i	−0.0244092	+	0.999702i	$0.507770\pi$
$570$		0			0
$571$	−14.3799	+	8.30223i	−0.601779	+	0.347437i	−0.769741	−	0.638356i	$-0.779615\pi$
$571$	−14.3799	+	8.30223i	−0.601779	+	0.347437i	0.167962	+	0.985793i	$0.446281\pi$
$572$	−14.9812	+	8.15861i	−0.626395	+	0.341129i
$573$		0			0
$574$	−9.75703	−	10.5442i	−0.407251	−	0.440108i
$575$	3.59418			0.149888
$576$		0			0
$577$	−6.37286	+	23.7838i	−0.265306	+	0.990134i	0.696757	+	0.717307i	$0.254625\pi$
$577$	−6.37286	+	23.7838i	−0.265306	+	0.990134i	−0.962063	+	0.272827i	$0.912041\pi$
$578$	11.6266	+	3.11533i	0.483602	+	0.129581i
$579$		0			0
$580$	4.88463	−	4.88463i	0.202823	−	0.202823i
$581$	19.4051	−	10.2223i	0.805061	−	0.424091i
$582$		0			0
$583$	−21.1064	+	5.65543i	−0.874136	+	0.234224i
$584$	0.327249	+	0.566812i	0.0135417	+	0.0234548i
$585$		0			0
$586$	−16.3340	−	9.43043i	−0.674751	−	0.389567i
$587$	30.7522	+	30.7522i	1.26928	+	1.26928i	0.946461	+	0.322819i	$0.104631\pi$
$587$	30.7522	+	30.7522i	1.26928	+	1.26928i	0.322819	+	0.946461i	$0.395369\pi$
$588$		0			0
$589$			8.77508i			0.361571i
$590$	−1.39777	−	5.21657i	−0.0575455	−	0.214763i
$591$		0			0
$592$	2.93653	−	10.9593i	0.120690	−	0.450423i
$593$	−2.54948	−	9.51478i	−0.104694	−	0.390725i	0.893616	−	0.448833i	$-0.148160\pi$
$593$	−2.54948	−	9.51478i	−0.104694	−	0.390725i	−0.998310	+	0.0581076i	$0.981493\pi$
$594$		0			0
$595$	−2.30508	+	1.21427i	−0.0944990	+	0.0497803i
$596$	−6.22327	−	6.22327i	−0.254915	−	0.254915i
$597$		0			0
$598$	7.47041	+	0.186192i	0.305488	+	0.00761396i
$599$	−20.3493	−	35.2461i	−0.831452	−	1.44012i	−0.896887	−	0.442260i	$-0.854177\pi$
$599$	−20.3493	−	35.2461i	−0.831452	−	1.44012i	0.0654350	−	0.997857i	$-0.479156\pi$
$600$		0			0
$601$		−	10.7311i		−	0.437731i	−0.975755	−	0.218865i	$-0.929764\pi$
$601$		−	10.7311i		−	0.437731i	0.975755	−	0.218865i	$-0.0702356\pi$
$602$	−0.926736	+	23.8998i	−0.0377710	+	0.974083i
$603$		0			0
$604$	−2.48251	−	9.26484i	−0.101012	−	0.376981i
$605$	1.54018	+	0.412690i	0.0626173	+	0.0167782i
$606$		0			0
$607$	−10.0602	−	5.80826i	−0.408331	−	0.235750i	0.281742	−	0.959490i	$-0.409088\pi$
$607$	−10.0602	−	5.80826i	−0.408331	−	0.235750i	−0.690072	+	0.723741i	$0.742421\pi$
$608$	−16.0449			−0.650708
$609$		0			0
$610$		−	8.87356i		−	0.359280i
$611$	35.3421	−	19.2470i	1.42979	−	0.778649i
$612$		0			0
$613$	−19.3947	−	5.19678i	−0.783343	−	0.209896i	−0.155085	−	0.987901i	$-0.549565\pi$
$613$	−19.3947	−	5.19678i	−0.783343	−	0.209896i	−0.628258	+	0.778005i	$0.716232\pi$
$614$	1.13777	+	0.656892i	0.0459167	+	0.0265100i
$615$		0			0
$616$	−4.67534	−	20.6129i	−0.188375	−	0.830516i
$617$	2.09240	−	2.09240i	0.0842369	−	0.0842369i	−0.663733	−	0.747970i	$-0.731029\pi$
$617$	2.09240	−	2.09240i	0.0842369	−	0.0842369i	0.747970	+	0.663733i	$0.231029\pi$
$618$		0			0
$619$	34.4009	+	9.21770i	1.38269	+	0.370491i	0.872098	−	0.489332i	$-0.162759\pi$
$619$	34.4009	+	9.21770i	1.38269	+	0.370491i	0.510593	+	0.859823i	$0.329426\pi$
$620$	−4.59356	−	7.95628i	−0.184482	−	0.319532i
$621$		0			0
$622$	−1.38088	+	1.38088i	−0.0553681	+	0.0553681i
$623$	−32.3948	−	1.25614i	−1.29787	−	0.0503262i
$624$		0			0
$625$	−8.60568	+	14.9055i	−0.344227	+	0.596219i
$626$	4.73025	−	17.6535i	0.189059	−	0.705578i
$627$		0			0
$628$	4.75197	−	8.23065i	0.189624	−	0.328439i
$629$	3.49826	+	3.49826i	0.139485	+	0.139485i
$630$		0			0
$631$	9.03483	+	9.03483i	0.359671	+	0.359671i	0.863692	−	0.504021i	$-0.168146\pi$
$631$	9.03483	+	9.03483i	0.359671	+	0.359671i	−0.504021	+	0.863692i	$0.668146\pi$
$632$	−13.4675	+	3.60859i	−0.535707	+	0.143542i
$633$		0			0
$634$	18.9303	−	10.9294i	0.751817	−	0.434062i
$635$	7.39399	+	27.5948i	0.293422	+	1.09506i
$636$		0			0
$637$	8.99086	−	23.5831i	0.356231	−	0.934398i
$638$	−5.51443			−0.218318
$639$		0			0
$640$	17.3601	−	10.0228i	0.686217	−	0.396187i
$641$	−15.8985	+	9.17899i	−0.627952	+	0.362548i	−0.779958	−	0.625831i	$-0.784760\pi$
$641$	−15.8985	+	9.17899i	−0.627952	+	0.362548i	0.152007	+	0.988379i	$0.451426\pi$
$642$		0			0
$643$	−29.9544	−	29.9544i	−1.18129	−	1.18129i	−0.979412	−	0.201874i	$-0.935297\pi$
$643$	−29.9544	−	29.9544i	−1.18129	−	1.18129i	−0.201874	−	0.979412i	$-0.564703\pi$
$644$	3.34872	−	10.8042i	0.131958	−	0.425746i
$645$		0			0
$646$	0.501458	−	0.868551i	0.0197296	−	0.0341727i
$647$	9.86908	+	17.0937i	0.387993	+	0.672024i	0.992180	−	0.124819i	$-0.0398350\pi$
$647$	9.86908	+	17.0937i	0.387993	+	0.672024i	−0.604186	+	0.796843i	$0.706502\pi$
$648$		0			0
$649$	6.18457	−	10.7120i	0.242766	−	0.420482i
$650$	1.68529	−	2.75795i	0.0661025	−	0.108176i
$651$		0			0
$652$	−0.717637	+	0.717637i	−0.0281049	+	0.0281049i
$653$	−0.0419432	+	0.0726478i	−0.00164136	+	0.00284293i	−0.866845	−	0.498578i	$-0.833856\pi$
$653$	−0.0419432	+	0.0726478i	−0.00164136	+	0.00284293i	0.865204	+	0.501421i	$0.167189\pi$
$654$		0			0
$655$	−37.8285	−	10.1361i	−1.47808	−	0.396051i
$656$	8.50367	−	2.27855i	0.332013	−	0.0889625i
$657$		0			0
$658$	4.69636	+	20.7055i	0.183083	+	0.807185i
$659$	−40.2054			−1.56618			−0.783089	−	0.621909i	$-0.786357\pi$
$659$	−40.2054			−1.56618			−0.783089	+	0.621909i	$0.786357\pi$
$660$		0			0
$661$	25.7149	+	6.89030i	1.00020	+	0.268001i	0.721527	−	0.692386i	$-0.243440\pi$
$661$	25.7149	+	6.89030i	1.00020	+	0.268001i	0.278668	+	0.960388i	$0.410107\pi$
$662$	−1.17872	+	0.680535i	−0.0458123	+	0.0264497i
$663$		0			0
$664$		−	20.7597i		−	0.805634i
$665$	−3.11148	−	13.7181i	−0.120658	−	0.531963i
$666$		0			0
$667$	−6.00218	−	3.46536i	−0.232405	−	0.134179i
$668$	1.34357	−	5.01428i	0.0519844	−	0.194008i
$669$		0			0
$670$	2.44936	+	9.14113i	0.0946270	+	0.353153i
$671$	14.3708	−	14.3708i	0.554779	−	0.554779i
$672$		0			0
$673$		−	2.18487i		−	0.0842204i	−0.999113	−	0.0421102i	$-0.986592\pi$
$673$		−	2.18487i		−	0.0842204i	0.999113	−	0.0421102i	$-0.0134081\pi$
$674$	11.0188	−	2.95247i	0.424428	−	0.113725i
$675$		0			0
$676$	−10.4599	+	16.1961i	−0.402303	+	0.622926i
$677$	3.62597	+	2.09346i	0.139357	+	0.0804580i	0.568058	−	0.822989i	$-0.307695\pi$
$677$	3.62597	+	2.09346i	0.139357	+	0.0804580i	−0.428700	+	0.903447i	$0.641028\pi$
$678$		0			0
$679$	23.3290	−	12.2893i	0.895285	−	0.471619i
$680$			2.46599i			0.0945663i
$681$		0			0
$682$	−1.89814	+	7.08397i	−0.0726837	+	0.271259i
$683$	3.07935	−	11.4923i	0.117828	−	0.439740i	−0.881655	−	0.471895i	$-0.843570\pi$
$683$	3.07935	−	11.4923i	0.117828	−	0.439740i	0.999483	+	0.0321547i	$0.0102369\pi$
$684$		0			0
$685$		−	16.4153i		−	0.627197i
$686$	10.6814	+	7.95055i	0.407816	+	0.303553i
$687$		0			0
$688$	−12.6934	−	7.32856i	−0.483933	−	0.279399i
$689$	−17.8926	+	17.0224i	−0.681655	+	0.648503i
$690$		0			0
$691$	36.2075	−	9.70177i	1.37740	−	0.369073i	0.507223	−	0.861815i	$-0.330672\pi$
$691$	36.2075	−	9.70177i	1.37740	−	0.369073i	0.870175	+	0.492742i	$0.164005\pi$
$692$		−	36.7388i		−	1.39660i
$693$		0			0
$694$	−8.23664	+	8.23664i	−0.312659	+	0.312659i
$695$	−1.21803	−	4.54574i	−0.0462024	−	0.172430i
$696$		0			0
$697$	−0.993546	+	3.70797i	−0.0376333	+	0.140449i
$698$	−16.4715	−	9.50980i	−0.623454	−	0.359951i
$699$		0			0
$700$	−3.32277	−	3.59086i	−0.125589	−	0.135722i
$701$			31.0974i			1.17453i	0.809394	+	0.587266i	$0.199796\pi$
$701$			31.0974i			1.17453i	−0.809394	+	0.587266i	$0.800204\pi$
$702$		0			0
$703$	−23.1322	+	13.3554i	−0.872449	+	0.503709i
$704$	−5.76873	−	1.54573i	−0.217417	−	0.0582568i
$705$		0			0
$706$	16.4944			0.620776
$707$	−12.1773	+	2.76201i	−0.457973	+	0.103876i
$708$		0			0
$709$	−14.6318	+	3.92057i	−0.549508	+	0.147240i	−0.522882	−	0.852405i	$-0.675143\pi$
$709$	−14.6318	+	3.92057i	−0.549508	+	0.147240i	−0.0266262	+	0.999645i	$0.508476\pi$
$710$	3.62447	+	0.971174i	0.136024	+	0.0364475i
$711$		0			0
$712$	−15.3425	+	26.5741i	−0.574986	+	0.995905i
$713$	−6.51773	+	6.51773i	−0.244091	+	0.244091i
$714$		0			0
$715$	−21.6611	+	5.22926i	−0.810078	+	0.195563i
$716$	−14.2297	+	24.6465i	−0.531787	+	0.921082i
$717$		0			0
$718$	2.67834	+	4.63902i	0.0999548	+	0.173127i
$719$	−10.7088	+	18.5482i	−0.399371	+	0.691732i	−0.993648	−	0.112529i	$-0.964105\pi$
$719$	−10.7088	+	18.5482i	−0.399371	+	0.691732i	0.594277	+	0.804260i	$0.297438\pi$
$720$		0			0
$721$	8.01328	+	8.65980i	0.298430	+	0.322508i
$722$	−5.83051	−	5.83051i	−0.216989	−	0.216989i
$723$		0			0
$724$	−14.1832	+	8.18868i	−0.527115	+	0.304330i
$725$	−2.59606	+	1.49884i	−0.0964152	+	0.0556654i
$726$		0			0
$727$	39.0080			1.44673			0.723363	−	0.690468i	$-0.242595\pi$
$727$	39.0080			1.44673			0.723363	+	0.690468i	$0.242595\pi$
$728$	−15.7828	−	17.9326i	−0.584951	−	0.664626i
$729$		0			0
$730$	0.0942194	+	0.351632i	0.00348722	+	0.0130145i
$731$	5.53489	−	3.19557i	0.204715	−	0.118192i
$732$		0			0
$733$	1.60598	−	0.430322i	0.0593183	−	0.0158943i	−0.229038	−	0.973418i	$-0.573558\pi$
$733$	1.60598	−	0.430322i	0.0593183	−	0.0158943i	0.288356	+	0.957523i	$0.406891\pi$
$734$	−17.8448	−	17.8448i	−0.658663	−	0.658663i
$735$		0			0
$736$	−11.9174	−	11.9174i	−0.439283	−	0.439283i
$737$	−10.8374	+	18.7709i	−0.399200	+	0.691435i
$738$		0			0
$739$	9.36946	−	34.9673i	0.344661	−	1.28629i	−0.548346	−	0.836251i	$-0.684742\pi$
$739$	9.36946	−	34.9673i	0.344661	−	1.28629i	0.893008	−	0.450042i	$-0.148591\pi$
$740$	13.9825	−	24.2184i	0.514007	−	0.890287i
$741$		0			0
$742$	−6.07254	−	11.5276i	−0.222930	−	0.423193i
$743$	2.82866	−	2.82866i	0.103773	−	0.103773i	−0.653314	−	0.757087i	$-0.726622\pi$
$743$	2.82866	−	2.82866i	0.103773	−	0.103773i	0.757087	+	0.653314i	$0.226622\pi$
$744$		0			0
$745$	−5.74828	−	9.95631i	−0.210601	−	0.364771i
$746$	10.8712	+	2.91292i	0.398022	+	0.106650i
$747$		0			0
$748$	−1.70050	+	1.70050i	−0.0621764	+	0.0621764i
$749$	34.6999	+	37.4995i	1.26791	+	1.37020i
$750$		0			0
$751$	−11.5377	−	6.66132i	−0.421018	−	0.243075i	0.274495	−	0.961589i	$-0.411489\pi$
$751$	−11.5377	−	6.66132i	−0.421018	−	0.243075i	−0.695513	+	0.718514i	$0.744823\pi$
$752$	−12.5676	−	3.36747i	−0.458293	−	0.122799i
$753$		0			0
$754$	−5.47348	+	2.98080i	−0.199333	+	0.108554i
$755$		−	12.5293i		−	0.455989i
$756$		0			0
$757$	16.0291			0.582587			0.291294	−	0.956634i	$-0.405914\pi$
$757$	16.0291			0.582587			0.291294	+	0.956634i	$0.405914\pi$
$758$	−15.4518	−	8.92110i	−0.561235	−	0.324029i
$759$		0			0
$760$	−12.8604	−	3.44594i	−0.466496	−	0.124997i
$761$	1.79513	+	6.69953i	0.0650735	+	0.242858i	0.990800	−	0.135337i	$-0.0432117\pi$
$761$	1.79513	+	6.69953i	0.0650735	+	0.242858i	−0.925726	+	0.378195i	$0.876545\pi$
$762$		0			0
$763$	−15.3534	+	24.3613i	−0.555829	+	0.881939i
$764$		−	16.8517i		−	0.609675i
$765$		0			0
$766$	−0.354291	−	0.613650i	−0.0128011	−	0.0221721i
$767$	0.348325	−	13.9755i	0.0125773	−	0.504626i
$768$		0			0
$769$	12.5271	+	12.5271i	0.451740	+	0.451740i	0.895932	−	0.444192i	$-0.146509\pi$
$769$	12.5271	+	12.5271i	0.451740	+	0.451740i	−0.444192	+	0.895932i	$0.646509\pi$
$770$	0.455516	−	11.7474i	0.0164157	−	0.423347i
$771$		0			0
$772$	4.78805	+	17.8692i	0.172326	+	0.643128i
$773$	12.6706	−	47.2874i	0.455730	−	1.70081i	−0.230202	−	0.973143i	$-0.573939\pi$
$773$	12.6706	−	47.2874i	0.455730	−	1.70081i	0.685932	−	0.727665i	$-0.259395\pi$
$774$		0			0
$775$	1.03184	+	3.85089i	0.0370648	+	0.138328i
$776$		−	24.9575i		−	0.895923i
$777$		0			0
$778$	−2.57073	−	2.57073i	−0.0921650	−	0.0921650i
$779$	−17.9491	−	10.3629i	−0.643093	−	0.371290i
$780$		0			0
$781$	4.29704	+	7.44269i	0.153760	+	0.266320i
$782$	1.01758	−	0.272660i	0.0363886	−	0.00975029i
$783$		0			0
$784$	−7.36141	+	3.52050i	−0.262907	+	0.125732i
$785$	8.77855	−	8.77855i	0.313320	−	0.313320i
$786$		0			0
$787$	−14.0046	−	3.75252i	−0.499210	−	0.133763i	0.000423598	−	1.00000i	$-0.499865\pi$
$787$	−14.0046	−	3.75252i	−0.499210	−	0.133763i	−0.499633	+	0.866237i	$0.666532\pi$
$788$	7.56416	−	28.2298i	0.269462	−	1.00565i
$789$		0			0
$790$	−7.75493			−0.275908
$791$	8.75477	−	28.2462i	0.311284	−	1.00432i
$792$		0			0
$793$	6.49603	−	22.0322i	0.230681	−	0.782387i
$794$	0.724851	−	0.418493i	0.0257240	−	0.0148518i
$795$		0			0
$796$	1.06281	+	0.613614i	0.0376703	+	0.0217490i
$797$	25.6379			0.908139			0.454070	−	0.890966i	$-0.349972\pi$
$797$	25.6379			0.908139			0.454070	+	0.890966i	$0.349972\pi$
$798$		0			0
$799$	4.01164	−	4.01164i	0.141922	−	0.141922i
$800$	−7.04121	+	1.88669i	−0.248944	+	0.0667044i
$801$		0			0
$802$	0.551367	+	0.954996i	0.0194694	+	0.0337221i
$803$	−0.416882	+	0.722060i	−0.0147114	+	0.0254810i
$804$		0			0
$805$	7.87808	−	12.5002i	0.277666	−	0.440575i
$806$	1.94516	+	8.05742i	0.0685155	+	0.283810i
$807$		0			0
$808$	−3.05890	+	11.4160i	−0.107612	+	0.401612i
$809$	−19.7540	−	34.2150i	−0.694515	−	1.20293i	−0.970344	−	0.241728i	$-0.922286\pi$
$809$	−19.7540	−	34.2150i	−0.694515	−	1.20293i	0.275829	−	0.961207i	$-0.411048\pi$
$810$		0			0
$811$	17.7080	+	17.7080i	0.621813	+	0.621813i	0.945995	−	0.324182i	$-0.105089\pi$
$811$	17.7080	+	17.7080i	0.621813	+	0.621813i	−0.324182	+	0.945995i	$0.605089\pi$
$812$	2.08678	+	9.20031i	0.0732317	+	0.322868i
$813$		0			0
$814$	−21.5632	+	5.77784i	−0.755789	+	0.202513i
$815$	−1.14811	+	0.662864i	−0.0402167	+	0.0232191i
$816$		0			0
$817$	8.93089	+	33.3305i	0.312452	+	1.16609i
$818$	7.67576			0.268377
$819$		0			0
$820$	21.6990			0.757763
$821$	−5.07462	−	18.9387i	−0.177105	−	0.660966i	−0.996183	−	0.0872842i	$-0.972181\pi$
$821$	−5.07462	−	18.9387i	−0.177105	−	0.660966i	0.819078	−	0.573682i	$-0.194486\pi$
$822$		0			0
$823$	−17.8932	+	10.3306i	−0.623717	+	0.360103i	−0.778315	−	0.627874i	$-0.783925\pi$
$823$	−17.8932	+	10.3306i	−0.623717	+	0.360103i	0.154598	+	0.987978i	$0.450592\pi$
$824$	10.7869	−	2.89034i	0.375779	−	0.100690i
$825$		0			0
$826$	7.04485	+	2.18352i	0.245122	+	0.0759743i
$827$	18.0688	+	18.0688i	0.628315	+	0.628315i	0.947644	−	0.319329i	$-0.103457\pi$
$827$	18.0688	+	18.0688i	0.628315	+	0.628315i	−0.319329	+	0.947644i	$0.603457\pi$
$828$		0			0
$829$	−20.2612	−	35.0934i	−0.703700	−	1.21884i	−0.967159	−	0.254173i	$-0.918197\pi$
$829$	−20.2612	−	35.0934i	−0.703700	−	1.21884i	0.263459	−	0.964671i	$-0.415137\pi$
$830$	2.98851	−	11.1533i	0.103733	−	0.387135i
$831$		0			0
$832$	−6.56144	+	1.58402i	−0.227477	+	0.0549159i
$833$	0.275521	−	3.54739i	0.00954623	−	0.122910i
$834$		0			0
$835$	3.39054	−	5.87259i	0.117335	−	0.203229i
$836$	−6.49204	−	11.2446i	−0.224532	−	0.388901i
$837$		0			0
$838$	8.24004	−	2.20791i	0.284647	−	0.0762710i
$839$	2.12585	−	2.12585i	0.0733926	−	0.0733926i	−0.669458	−	0.742850i	$-0.733473\pi$
$839$	2.12585	−	2.12585i	0.0733926	−	0.0733926i	0.742850	+	0.669458i	$0.233473\pi$
$840$		0			0
$841$	−23.2195			−0.800674
$842$	2.77582	+	1.60262i	0.0956611	+	0.0552299i
$843$		0			0
$844$	24.2162	−	13.9813i	0.833557	−	0.481255i
$845$	−18.6736	+	16.8993i	−0.642391	+	0.581352i
$846$		0			0
$847$	−1.59830	+	1.47897i	−0.0549182	+	0.0508182i
$848$	7.98452			0.274189
$849$		0			0
$850$	0.117931	−	0.440123i	0.00404498	−	0.0150961i
$851$	−27.1014	−	7.26178i	−0.929022	−	0.248931i
$852$		0			0
$853$	−38.1991	+	38.1991i	−1.30791	+	1.30791i	−0.384992	+	0.922920i	$0.625796\pi$
$853$	−38.1991	+	38.1991i	−1.30791	+	1.30791i	−0.922920	+	0.384992i	$0.874204\pi$
$854$	10.2522	+	6.46132i	0.350824	+	0.221102i
$855$		0			0
$856$	46.7104	−	12.5160i	1.59653	−	0.427789i
$857$	−10.7700	−	18.6543i	−0.367898	−	0.637218i	0.621339	−	0.783542i	$-0.286589\pi$
$857$	−10.7700	−	18.6543i	−0.367898	−	0.637218i	−0.989237	+	0.146324i	$0.953256\pi$
$858$		0			0
$859$	0.937124	+	0.541049i	0.0319743	+	0.0184603i	0.515902	−	0.856648i	$-0.327457\pi$
$859$	0.937124	+	0.541049i	0.0319743	+	0.0184603i	−0.483928	+	0.875108i	$0.660790\pi$
$860$	−25.5453	−	25.5453i	−0.871089	−	0.871089i
$861$		0			0
$862$			0.878348i			0.0299167i
$863$	0.839713	+	3.13385i	0.0285842	+	0.106678i	0.978744	−	0.205085i	$-0.0657472\pi$
$863$	0.839713	+	3.13385i	0.0285842	+	0.106678i	−0.950160	+	0.311763i	$0.899081\pi$
$864$		0			0
$865$	12.4210	−	46.3557i	0.422326	−	1.57614i
$866$	3.37454	+	12.5939i	0.114671	+	0.427960i
$867$		0			0
$868$	12.5373	+	0.486143i	0.425542	+	0.0165008i
$869$	−12.5592	−	12.5592i	−0.426041	−	0.426041i
$870$		0			0
$871$	−0.610379	+	24.4897i	−0.0206819	+	0.829801i
$872$	13.6278	+	23.6040i	0.461495	+	0.799332i
$873$		0			0
$874$			5.68781i			0.192393i
$875$	−14.9231	−	28.3288i	−0.504491	−	0.957687i
$876$		0			0
$877$	5.50863	+	20.5585i	0.186013	+	0.694211i	0.994411	+	0.105575i	$0.0336682\pi$
$877$	5.50863	+	20.5585i	0.186013	+	0.694211i	−0.808398	+	0.588636i	$0.799665\pi$
$878$	−21.7026	−	5.81520i	−0.732428	−	0.196254i
$879$		0			0
$880$	6.23917	+	3.60219i	0.210322	+	0.121430i
$881$	34.2796			1.15491			0.577455	−	0.816423i	$-0.304046\pi$
$881$	34.2796			1.15491			0.577455	+	0.816423i	$0.304046\pi$
$882$		0			0
$883$			8.76503i			0.294967i	0.989065	+	0.147483i	$0.0471173\pi$
$883$			8.76503i			0.294967i	−0.989065	+	0.147483i	$0.952883\pi$
$884$	−0.768675	+	2.60707i	−0.0258533	+	0.0876853i
$885$		0			0
$886$	−17.2044	−	4.60991i	−0.577994	−	0.154873i
$887$	7.22277	+	4.17007i	0.242517	+	0.140017i	0.616333	−	0.787486i	$-0.288618\pi$
$887$	7.22277	+	4.17007i	0.242517	+	0.140017i	−0.373816	+	0.927503i	$0.621951\pi$
$888$		0			0
$889$	−37.2661	−	11.5504i	−1.24986	−	0.387390i
$890$	−12.0684	+	12.0684i	−0.404532	+	0.404532i
$891$		0			0
$892$	−19.9188	−	5.33723i	−0.666932	−	0.178704i
$893$	15.3154	+	26.5270i	0.512509	+	0.887692i
$894$		0			0
$895$	−26.2872	+	26.2872i	−0.878683	+	0.878683i
$896$	−1.06073	+	27.3554i	−0.0354365	+	0.913881i
$897$		0			0
$898$	3.59715	−	6.23045i	0.120038	−	0.207913i
$899$	1.98972	−	7.42573i	0.0663608	−	0.247662i
$900$		0			0
$901$	−1.74080	+	3.01515i	−0.0579943	+	0.100449i
$902$	−12.2484	−	12.2484i	−0.407827	−	0.407827i
$903$		0			0
$904$	−19.7919	−	19.7919i	−0.658269	−	0.658269i
$905$	−20.6644	+	5.53700i	−0.686906	+	0.184056i
$906$		0			0
$907$	−3.67167	+	2.11984i	−0.121916	+	0.0703882i	−0.559718	−	0.828683i	$-0.689090\pi$
$907$	−3.67167	+	2.11984i	−0.121916	+	0.0703882i	0.437802	+	0.899071i	$0.355757\pi$
$908$	6.00955	+	22.4280i	0.199434	+	0.744298i
$909$		0			0
$910$	−5.89788	−	11.9064i	−0.195513	−	0.394694i
$911$	1.59871			0.0529676			0.0264838	−	0.999649i	$-0.491569\pi$
$911$	1.59871			0.0529676			0.0264838	+	0.999649i	$0.491569\pi$
$912$		0			0
$913$	22.9027	−	13.2229i	0.757970	−	0.437614i
$914$	13.0474	−	7.53291i	0.431569	−	0.249166i
$915$		0			0
$916$	−5.01982	−	5.01982i	−0.165860	−	0.165860i
$917$	39.2559	−	36.3252i	1.29634	−	1.19956i
$918$		0			0
$919$	6.09990	−	10.5653i	0.201217	−	0.348518i	−0.747704	−	0.664032i	$-0.768844\pi$
$919$	6.09990	−	10.5653i	0.201217	−	0.348518i	0.948921	+	0.315514i	$0.102177\pi$
$920$	−6.99264	−	12.1116i	−0.230541	−	0.399308i
$921$		0			0
$922$	−4.10754	+	7.11447i	−0.135275	+	0.234303i
$923$	8.28826	+	5.06469i	0.272811	+	0.166706i
$924$		0			0
$925$	−8.58099	+	8.58099i	−0.282141	+	0.282141i
$926$	0.212012	−	0.367215i	0.00696714	−	0.0120674i
$927$		0			0
$928$	13.5777	+	3.63813i	0.445709	+	0.119427i
$929$	0.590349	−	0.158183i	0.0193687	−	0.00518983i	−0.249122	−	0.968472i	$-0.580142\pi$
$929$	0.590349	−	0.158183i	0.0193687	−	0.00518983i	0.268490	+	0.963282i	$0.413475\pi$
$930$		0			0
$931$	18.1150	+	6.39395i	0.593697	+	0.209553i
$932$	4.70149			0.154002
$933$		0			0
$934$	−3.89597	−	1.04392i	−0.127480	−	0.0341582i
$935$	−2.72055	+	1.57071i	−0.0889714	+	0.0513677i
$936$		0			0
$937$		−	5.03265i		−	0.164410i	−0.996615	−	0.0822048i	$-0.973804\pi$
$937$		−	5.03265i		−	0.164410i	0.996615	−	0.0822048i	$-0.0261961\pi$
$938$	−12.3449	−	3.82624i	−0.403075	−	0.124931i
$939$		0			0
$940$	−27.7726	−	16.0345i	−0.905842	−	0.522988i
$941$	−12.4703	+	46.5400i	−0.406522	+	1.51716i	0.394711	+	0.918805i	$0.370845\pi$
$941$	−12.4703	+	46.5400i	−0.406522	+	1.51716i	−0.801232	+	0.598354i	$0.795822\pi$
$942$		0			0
$943$	−5.63467	−	21.0289i	−0.183490	−	0.684794i
$944$	−3.19597	+	3.19597i	−0.104020	+	0.104020i
$945$		0			0
$946$			28.8390i			0.937637i
$947$	11.2196	−	3.00627i	0.364586	−	0.0976907i	−0.0718749	−	0.997414i	$-0.522898\pi$
$947$	11.2196	−	3.00627i	0.364586	−	0.0976907i	0.436461	+	0.899723i	$0.356232\pi$
$948$		0			0
$949$	−0.0234794	+	0.942043i	−0.000762175	+	0.0305800i
$950$	2.13050	+	1.23004i	0.0691224	+	0.0399079i
$951$		0			0
$952$	−2.84912	−	1.79562i	−0.0923406	−	0.0581963i
$953$		−	12.7370i		−	0.412592i	−0.978490	−	0.206296i	$-0.933859\pi$
$953$		−	12.7370i		−	0.412592i	0.978490	−	0.206296i	$-0.0661409\pi$
$954$		0			0
$955$	5.69738	−	21.2629i	0.184363	−	0.688052i
$956$	−4.08359	+	15.2402i	−0.132073	+	0.492903i
$957$		0			0
$958$			10.2908i			0.332479i
$959$	18.9657	+	11.9529i	0.612436	+	0.385979i
$960$		0			0
$961$	17.9924	+	10.3879i	0.580400	+	0.335094i
$962$	−18.2799	+	17.3908i	−0.589367	+	0.560703i
$963$		0			0
$964$	−2.80927	+	0.752742i	−0.0904805	+	0.0242442i
$965$			24.1656i			0.777917i
$966$		0			0
$967$	1.70551	−	1.70551i	0.0548455	−	0.0548455i	−0.679152	−	0.733998i	$-0.737652\pi$
$967$	1.70551	−	1.70551i	0.0548455	−	0.0548455i	0.733998	+	0.679152i	$0.237652\pi$
$968$	0.533456	+	1.99088i	0.0171459	+	0.0639895i
$969$		0			0
$970$	3.59281	−	13.4085i	0.115358	−	0.430522i
$971$	−21.9961	−	12.6994i	−0.705887	−	0.407544i	0.103649	−	0.994614i	$-0.466948\pi$
$971$	−21.9961	−	12.6994i	−0.705887	−	0.407544i	−0.809536	+	0.587070i	$0.800281\pi$
$972$		0			0
$973$	6.13892	+	1.90273i	0.196805	+	0.0609987i
$974$			11.3385i			0.363309i
$975$		0			0
$976$	−6.43141	+	3.71317i	−0.205864	+	0.118856i
$977$	20.7685	+	5.56490i	0.664443	+	0.178037i	0.575250	−	0.817977i	$-0.304905\pi$
$977$	20.7685	+	5.56490i	0.664443	+	0.178037i	0.0891927	+	0.996014i	$0.471571\pi$
$978$		0			0
$979$	−39.0897			−1.24931
$980$	−19.7718	+	3.68549i	−0.631588	+	0.117729i
$981$		0			0
$982$	−17.3962	+	4.66129i	−0.555134	+	0.148748i
$983$	−34.6856	−	9.29397i	−1.10630	−	0.296431i	−0.340971	−	0.940074i	$-0.610756\pi$
$983$	−34.6856	−	9.29397i	−1.10630	−	0.296431i	−0.765326	+	0.643642i	$0.777422\pi$
$984$		0			0
$985$	19.0884	−	33.0620i	0.608206	−	1.05344i
$986$	−0.621289	+	0.621289i	−0.0197859	+	0.0197859i
$987$		0			0
$988$	−12.5220	−	7.65181i	−0.398379	−	0.243437i
$989$	−18.1229	+	31.3898i	−0.576276	+	0.998139i
$990$		0			0
$991$	−21.3172	−	36.9225i	−0.677164	−	1.17288i	−0.975831	−	0.218525i	$-0.929876\pi$
$991$	−21.3172	−	36.9225i	−0.677164	−	1.17288i	0.298668	−	0.954357i	$-0.403458\pi$
$992$	9.34727	−	16.1899i	0.296776	−	0.514031i
$993$		0			0
$994$	−3.76124	+	3.48043i	−0.119299	+	0.110393i
$995$	1.13356	+	1.13356i	0.0359363	+	0.0359363i
$996$		0			0
$997$	49.9716	−	28.8511i	1.58262	−	0.913724i	0.588141	−	0.808759i	$-0.299860\pi$
$997$	49.9716	−	28.8511i	1.58262	−	0.913724i	0.994476	−	0.104966i	$-0.0334732\pi$
$998$	−14.5964	+	8.42721i	−0.462039	+	0.266759i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.e.460.5		32
3.2	odd	2		91.2.bb.a.5.4	✓	32
7.3	odd	6	inner	819.2.fn.e.577.4		32
13.8	odd	4	inner	819.2.fn.e.775.4		32
21.2	odd	6		637.2.i.a.538.8		32
21.5	even	6		637.2.i.a.538.7		32
21.11	odd	6		637.2.bc.b.31.5		32
21.17	even	6		91.2.bb.a.31.5	yes	32
21.20	even	2		637.2.bc.b.460.4		32
39.8	even	4		91.2.bb.a.47.5	yes	32
91.73	even	12	inner	819.2.fn.e.73.5		32
273.47	odd	12		637.2.i.a.489.7		32
273.86	even	12		637.2.i.a.489.8		32
273.125	odd	4		637.2.bc.b.411.5		32
273.164	odd	12		91.2.bb.a.73.4	yes	32
273.242	even	12		637.2.bc.b.619.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.4	✓	32	3.2	odd	2
91.2.bb.a.31.5	yes	32	21.17	even	6
91.2.bb.a.47.5	yes	32	39.8	even	4
91.2.bb.a.73.4	yes	32	273.164	odd	12
637.2.i.a.489.7		32	273.47	odd	12
637.2.i.a.489.8		32	273.86	even	12
637.2.i.a.538.7		32	21.5	even	6
637.2.i.a.538.8		32	21.2	odd	6
637.2.bc.b.31.5		32	21.11	odd	6
637.2.bc.b.411.5		32	273.125	odd	4
637.2.bc.b.460.4		32	21.20	even	2
637.2.bc.b.619.4		32	273.242	even	12
819.2.fn.e.73.5		32	91.73	even	12	inner
819.2.fn.e.460.5		32	1.1	even	1	trivial
819.2.fn.e.577.4		32	7.3	odd	6	inner
819.2.fn.e.775.4		32	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.186083 + 0.694471i) q^{2} +(1.28439 - 0.741542i) q^{4} +(1.87130 - 0.501414i) q^{5} +(-0.783278 + 2.52715i) q^{7} +(1.77076 + 1.77076i) q^{8} +O(q^{10})\)	\(q+(0.186083 + 0.694471i) q^{2} +(1.28439 - 0.741542i) q^{4} +(1.87130 - 0.501414i) q^{5} +(-0.783278 + 2.52715i) q^{7} +(1.77076 + 1.77076i) q^{8} +(0.696434 + 1.20626i) q^{10} +(-0.825667 + 3.08143i) q^{11} +(0.846120 + 3.50487i) q^{13} +(-1.90079 - 0.0737047i) q^{14} +(0.582851 - 1.00953i) q^{16} +(0.254148 + 0.440197i) q^{17} +(-2.65082 + 0.710286i) q^{19} +(2.03166 - 2.03166i) q^{20} -2.29361 q^{22} +(-2.49648 - 1.44134i) q^{23} +(-1.07978 + 0.623409i) q^{25} +(-2.27658 + 1.23980i) q^{26} +(0.867953 + 3.82667i) q^{28} +2.40426 q^{29} +(0.827581 - 3.08857i) q^{31} +(5.64735 + 1.51320i) q^{32} +(-0.258412 + 0.258412i) q^{34} +(-0.198602 + 5.12180i) q^{35} +(9.40142 - 2.51910i) q^{37} +(-0.986546 - 1.70875i) q^{38} +(4.20150 + 2.42574i) q^{40} +(5.34023 + 5.34023i) q^{41} -12.5736i q^{43} +(1.22453 + 4.57002i) q^{44} +(0.536419 - 2.00194i) q^{46} +(-2.88879 - 10.7811i) q^{47} +(-5.77295 - 3.95892i) q^{49} +(-0.633867 - 0.633867i) q^{50} +(3.68575 + 3.87417i) q^{52} +(3.42477 + 5.93187i) q^{53} +6.18029i q^{55} +(-5.86196 + 3.08797i) q^{56} +(0.447392 + 1.66969i) q^{58} +(-3.74520 - 1.00352i) q^{59} +(-5.51719 - 3.18535i) q^{61} +2.29892 q^{62} +1.87209i q^{64} +(3.34073 + 6.13440i) q^{65} +(6.56281 + 1.75850i) q^{67} +(0.652849 + 0.376923i) q^{68} +(-3.59390 + 0.815156i) q^{70} +(1.90492 - 1.90492i) q^{71} +(0.252451 + 0.0676442i) q^{73} +(3.49889 + 6.06025i) q^{74} +(-2.87798 + 2.87798i) q^{76} +(-7.14051 - 4.50020i) q^{77} +(-2.78380 + 4.82168i) q^{79} +(0.584499 - 2.18138i) q^{80} +(-2.71491 + 4.70236i) q^{82} +(-5.86182 - 5.86182i) q^{83} +(0.696309 + 0.696309i) q^{85} +(8.73203 - 2.33974i) q^{86} +(-6.91853 + 3.99441i) q^{88} +(3.17139 + 11.8358i) q^{89} +(-9.52006 - 0.607013i) q^{91} -4.27526 q^{92} +(6.94962 - 4.01237i) q^{94} +(-4.60434 + 2.65832i) q^{95} +(-7.04713 - 7.04713i) q^{97} +(1.67511 - 4.74583i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

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