LMFDB - Embedded newform 441.2.bg.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	441.17
Dual form			441.2.bg.a.26.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.859142 + 0.0643838i) q^{2} +(-1.24368 + 0.187455i) q^{4} +(0.593873 - 0.551034i) q^{5} +(-2.64451 - 0.0809471i) q^{7} +(2.73633 - 0.624550i) q^{8} +O(q^{10})$	\(q+(-0.859142 + 0.0643838i) q^{2} +(-1.24368 + 0.187455i) q^{4} +(0.593873 - 0.551034i) q^{5} +(-2.64451 - 0.0809471i) q^{7} +(2.73633 - 0.624550i) q^{8} +(-0.474744 + 0.511652i) q^{10} +(1.38741 + 2.03495i) q^{11} +(0.765584 - 1.58975i) q^{13} +(2.27722 - 0.100719i) q^{14} +(0.0930170 - 0.0286919i) q^{16} +(1.82925 + 4.66086i) q^{17} +(-7.17650 + 4.14336i) q^{19} +(-0.635295 + 0.796635i) q^{20} +(-1.32300 - 1.65899i) q^{22} +(8.61741 + 3.38208i) q^{23} +(-0.324603 + 4.33153i) q^{25} +(-0.555391 + 1.41511i) q^{26} +(3.30411 - 0.395054i) q^{28} +(-5.72992 - 4.56946i) q^{29} +(8.45706 + 4.88268i) q^{31} +(-5.30344 + 2.08145i) q^{32} +(-1.87167 - 3.88657i) q^{34} +(-1.61511 + 1.40914i) q^{35} +(-2.83761 - 0.427702i) q^{37} +(5.89887 - 4.02178i) q^{38} +(1.28089 - 1.87871i) q^{40} +(0.489533 + 2.14478i) q^{41} +(-1.60041 + 7.01184i) q^{43} +(-2.10696 - 2.27076i) q^{44} +(-7.62133 - 2.35087i) q^{46} +(0.512020 + 6.83244i) q^{47} +(6.98690 + 0.428131i) q^{49} -3.74230i q^{50} +(-0.654136 + 2.12066i) q^{52} +(0.166100 + 1.10200i) q^{53} +(1.94527 + 0.443996i) q^{55} +(-7.28682 + 1.43013i) q^{56} +(5.21701 + 3.55690i) q^{58} +(2.89579 + 2.68690i) q^{59} +(1.16627 - 7.73769i) q^{61} +(-7.58018 - 3.65042i) q^{62} +(4.24699 - 2.04524i) q^{64} +(-0.421347 - 1.36597i) q^{65} +(0.774142 - 1.34085i) q^{67} +(-3.14871 - 5.45372i) q^{68} +(1.29688 - 1.31464i) q^{70} +(10.1939 - 8.12937i) q^{71} +(-10.2762 - 0.770098i) q^{73} +(2.46545 + 0.184760i) q^{74} +(8.14859 - 6.49829i) q^{76} +(-3.50429 - 5.49377i) q^{77} +(1.36987 + 2.37268i) q^{79} +(0.0394300 - 0.0682948i) q^{80} +(-0.558668 - 1.81116i) q^{82} +(-13.7776 + 6.63496i) q^{83} +(3.65463 + 1.75998i) q^{85} +(0.923528 - 6.12721i) q^{86} +(5.06734 + 4.70180i) q^{88} +(2.84048 + 1.93661i) q^{89} +(-2.15328 + 4.14215i) q^{91} +(-11.3513 - 2.59086i) q^{92} +(-0.879797 - 5.83707i) q^{94} +(-1.97880 + 6.41512i) q^{95} -10.2541i q^{97} +(-6.03030 + 0.0820171i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{25}{42}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.859142	+	0.0643838i	−0.607505	+	0.0455262i	−0.374932	−	0.927053i	$-0.622334\pi$
$2$	−0.859142	+	0.0643838i	−0.607505	+	0.0455262i	−0.232574	+	0.972579i	$0.574715\pi$
$3$		0			0
$3$		0			0
$4$	−1.24368	+	0.187455i	−0.621841	+	0.0937274i
$5$	0.593873	−	0.551034i	0.265588	−	0.246430i	−0.536125	−	0.844138i	$-0.680113\pi$
$5$	0.593873	−	0.551034i	0.265588	−	0.246430i	0.801713	+	0.597709i	$0.203922\pi$
$6$		0			0
$7$	−2.64451	−	0.0809471i	−0.999532	−	0.0305951i
$7$	−2.64451	−	0.0809471i	−0.999532	−	0.0305951i
$8$	2.73633	−	0.624550i	0.967439	−	0.220812i
$9$		0			0
$10$	−0.474744	+	0.511652i	−0.150127	+	0.161799i
$11$	1.38741	+	2.03495i	0.418319	+	0.613562i	0.976334	−	0.216270i	$-0.0693890\pi$
$11$	1.38741	+	2.03495i	0.418319	+	0.613562i	−0.558014	+	0.829831i	$0.688437\pi$
$12$		0			0
$13$	0.765584	−	1.58975i	0.212335	−	0.440918i	−0.767413	−	0.641153i	$-0.778456\pi$
$13$	0.765584	−	1.58975i	0.212335	−	0.440918i	0.979748	+	0.200235i	$0.0641707\pi$
$14$	2.27722	−	0.100719i	0.608614	−	0.0269182i
$15$		0			0
$16$	0.0930170	−	0.0286919i	0.0232542	−	0.00717298i
$17$	1.82925	+	4.66086i	0.443659	+	1.13042i	0.961465	+	0.274927i	$0.0886536\pi$
$17$	1.82925	+	4.66086i	0.443659	+	1.13042i	−0.517806	+	0.855498i	$0.673251\pi$
$18$		0			0
$19$	−7.17650	+	4.14336i	−1.64640	+	0.950551i	−0.667918	+	0.744235i	$0.732814\pi$
$19$	−7.17650	+	4.14336i	−1.64640	+	0.950551i	−0.978485	+	0.206316i	$0.933853\pi$
$20$	−0.635295	+	0.796635i	−0.142056	+	0.178133i
$21$		0			0
$22$	−1.32300	−	1.65899i	−0.282064	−	0.353697i
$23$	8.61741	+	3.38208i	1.79685	+	0.705213i	0.994044	+	0.108979i	$0.0347581\pi$
$23$	8.61741	+	3.38208i	1.79685	+	0.705213i	0.802810	+	0.596234i	$0.203337\pi$
$24$		0			0
$25$	−0.324603	+	4.33153i	−0.0649207	+	0.866306i
$26$	−0.555391	+	1.41511i	−0.108921	+	0.277527i
$27$		0			0
$28$	3.30411	−	0.395054i	0.624417	−	0.0746582i
$29$	−5.72992	−	4.56946i	−1.06402	−	0.848527i	−0.0751288	−	0.997174i	$-0.523937\pi$
$29$	−5.72992	−	4.56946i	−1.06402	−	0.848527i	−0.988890	+	0.148647i	$0.952508\pi$
$30$		0			0
$31$	8.45706	+	4.88268i	1.51893	+	0.876956i	0.999752	+	0.0222913i	$0.00709614\pi$
$31$	8.45706	+	4.88268i	1.51893	+	0.876956i	0.519181	+	0.854665i	$0.326237\pi$
$32$	−5.30344	+	2.08145i	−0.937524	+	0.367951i
$33$		0			0
$34$	−1.87167	−	3.88657i	−0.320989	−	0.666541i
$35$	−1.61511	+	1.40914i	−0.273003	+	0.238189i
$36$		0			0
$37$	−2.83761	−	0.427702i	−0.466501	−	0.0703137i	−0.0884141	−	0.996084i	$-0.528180\pi$
$37$	−2.83761	−	0.427702i	−0.466501	−	0.0703137i	−0.378087	+	0.925770i	$0.623418\pi$
$38$	5.89887	−	4.02178i	0.956924	−	0.652419i
$39$		0			0
$40$	1.28089	−	1.87871i	0.202526	−	0.297051i
$41$	0.489533	+	2.14478i	0.0764522	+	0.334959i	0.998661	−	0.0517336i	$-0.0164747\pi$
$41$	0.489533	+	2.14478i	0.0764522	+	0.334959i	−0.922209	+	0.386692i	$0.873618\pi$
$42$		0			0
$43$	−1.60041	+	7.01184i	−0.244060	+	1.06930i	0.693222	+	0.720724i	$0.256190\pi$
$43$	−1.60041	+	7.01184i	−0.244060	+	1.06930i	−0.937282	+	0.348572i	$0.886667\pi$
$44$	−2.10696	−	2.27076i	−0.317635	−	0.342330i
$45$		0			0
$46$	−7.62133	−	2.35087i	−1.12370	−	0.346617i
$47$	0.512020	+	6.83244i	0.0746858	+	0.996613i	0.901117	+	0.433576i	$0.142748\pi$
$47$	0.512020	+	6.83244i	0.0746858	+	0.996613i	−0.826431	+	0.563038i	$0.809633\pi$
$48$		0			0
$49$	6.98690	+	0.428131i	0.998128	+	0.0611616i
$50$		−	3.74230i		−	0.529241i
$51$		0			0
$52$	−0.654136	+	2.12066i	−0.0907124	+	0.294082i
$53$	0.166100	+	1.10200i	0.0228155	+	0.151371i	0.997338	−	0.0729194i	$-0.0232316\pi$
$53$	0.166100	+	1.10200i	0.0228155	+	0.151371i	−0.974522	+	0.224291i	$0.927994\pi$
$54$		0			0
$55$	1.94527	+	0.443996i	0.262300	+	0.0598684i
$56$	−7.28682	+	1.43013i	−0.973742	+	0.191109i
$57$		0			0
$58$	5.21701	+	3.55690i	0.685028	+	0.467044i
$59$	2.89579	+	2.68690i	0.377000	+	0.349805i	0.845801	−	0.533499i	$-0.179123\pi$
$59$	2.89579	+	2.68690i	0.377000	+	0.349805i	−0.468800	+	0.883304i	$0.655314\pi$
$60$		0			0
$61$	1.16627	−	7.73769i	0.149325	−	0.990710i	−0.781147	−	0.624347i	$-0.785365\pi$
$61$	1.16627	−	7.73769i	0.149325	−	0.990710i	0.930472	−	0.366362i	$-0.119397\pi$
$62$	−7.58018	−	3.65042i	−0.962684	−	0.463604i
$63$		0			0
$64$	4.24699	−	2.04524i	0.530874	−	0.255655i
$65$	−0.421347	−	1.36597i	−0.0522616	−	0.169428i
$66$		0			0
$67$	0.774142	−	1.34085i	0.0945765	−	0.163811i	−0.814855	−	0.579664i	$-0.803184\pi$
$67$	0.774142	−	1.34085i	0.0945765	−	0.163811i	0.909432	+	0.415853i	$0.136517\pi$
$68$	−3.14871	−	5.45372i	−0.381837	−	0.661361i
$69$		0			0
$70$	1.29688	−	1.31464i	0.155007	−	0.157130i
$71$	10.1939	−	8.12937i	1.20979	−	0.964778i	0.209877	−	0.977728i	$-0.432694\pi$
$71$	10.1939	−	8.12937i	1.20979	−	0.964778i	0.999916	+	0.0129496i	$0.00412209\pi$
$72$		0			0
$73$	−10.2762	−	0.770098i	−1.20274	−	0.0901332i	−0.541760	−	0.840533i	$-0.682242\pi$
$73$	−10.2762	−	0.770098i	−1.20274	−	0.0901332i	−0.660984	+	0.750400i	$0.729861\pi$
$74$	2.46545	+	0.184760i	0.286603	+	0.0214779i
$75$		0			0
$76$	8.14859	−	6.49829i	0.934708	−	0.745405i
$77$	−3.50429	−	5.49377i	−0.399351	−	0.626073i
$78$		0			0
$79$	1.36987	+	2.37268i	0.154122	+	0.266947i	0.932739	−	0.360552i	$-0.117412\pi$
$79$	1.36987	+	2.37268i	0.154122	+	0.266947i	−0.778617	+	0.627500i	$0.784078\pi$
$80$	0.0394300	−	0.0682948i	0.00440841	−	0.00763560i
$81$		0			0
$82$	−0.558668	−	1.81116i	−0.0616945	−	0.200009i
$83$	−13.7776	+	6.63496i	−1.51229	+	0.728281i	−0.992062	−	0.125746i	$-0.959868\pi$
$83$	−13.7776	+	6.63496i	−1.51229	+	0.728281i	−0.520228	+	0.854027i	$0.674153\pi$
$84$		0			0
$85$	3.65463	+	1.75998i	0.396401	+	0.190897i
$86$	0.923528	−	6.12721i	0.0995866	−	0.660714i
$87$		0			0
$88$	5.06734	+	4.70180i	0.540180	+	0.501214i
$89$	2.84048	+	1.93661i	0.301090	+	0.205280i	0.704436	−	0.709768i	$-0.251200\pi$
$89$	2.84048	+	1.93661i	0.301090	+	0.205280i	−0.403345	+	0.915048i	$0.632153\pi$
$90$		0			0
$91$	−2.15328	+	4.14215i	−0.225725	+	0.434215i
$92$	−11.3513	−	2.59086i	−1.18346	−	0.270116i
$93$		0			0
$94$	−0.879797	−	5.83707i	−0.0907441	−	0.602048i
$95$	−1.97880	+	6.41512i	−0.203021	+	0.658178i
$96$		0			0
$97$		−	10.2541i		−	1.04115i	−0.853817	−	0.520574i	$-0.825718\pi$
$97$		−	10.2541i		−	1.04115i	0.853817	−	0.520574i	$-0.174282\pi$
$98$	−6.03030	+	0.0820171i	−0.609152	+	0.00828498i
$99$		0			0
$100$	−0.408263	−	5.44789i	−0.0408263	−	0.544789i
$101$	4.90328	+	1.51246i	0.487895	+	0.150496i	0.528936	−	0.848662i	$-0.322591\pi$
$101$	4.90328	+	1.51246i	0.487895	+	0.150496i	−0.0410410	+	0.999157i	$0.513067\pi$
$102$		0			0
$103$	−4.88896	−	5.26904i	−0.481723	−	0.519174i	0.444689	−	0.895685i	$-0.353314\pi$
$103$	−4.88896	−	5.26904i	−0.481723	−	0.519174i	−0.926412	+	0.376511i	$0.877124\pi$
$104$	1.10201	−	4.82823i	0.108061	−	0.473447i
$105$		0			0
$106$	−0.213654	−	0.936080i	−0.0207519	−	0.0909201i
$107$	9.16617	−	13.4443i	0.886128	−	1.29971i	−0.0671898	−	0.997740i	$-0.521403\pi$
$107$	9.16617	−	13.4443i	0.886128	−	1.29971i	0.953317	−	0.301970i	$-0.0976443\pi$
$108$		0			0
$109$	−7.56272	+	5.15617i	−0.724377	+	0.493872i	−0.868501	−	0.495688i	$-0.834916\pi$
$109$	−7.56272	+	5.15617i	−0.724377	+	0.493872i	0.144124	+	0.989560i	$0.453964\pi$
$110$	−1.69985	−	0.256211i	−0.162074	−	0.0244288i
$111$		0			0
$112$	−0.248307	+	0.0683467i	−0.0234628	+	0.00645816i
$113$	−4.23491	−	8.79389i	−0.398387	−	0.827260i	−0.999603	−	0.0281729i	$-0.991031\pi$
$113$	−4.23491	−	8.79389i	−0.398387	−	0.827260i	0.601216	−	0.799087i	$-0.294683\pi$
$114$		0			0
$115$	6.98129	−	2.73995i	0.651009	−	0.255502i
$116$	7.98276	+	4.60885i	0.741181	+	0.427921i
$117$		0			0
$118$	−2.66089	−	2.12199i	−0.244955	−	0.195345i
$119$	−4.46020	−	12.4738i	−0.408866	−	1.14347i
$120$		0			0
$121$	1.80262	−	4.59299i	0.163874	−	0.417545i
$122$	−0.503809	+	6.72287i	−0.0456127	+	0.608660i
$123$		0			0
$124$	−11.4332	−	4.48719i	−1.02673	−	0.402961i
$125$	4.71961	+	5.91820i	0.422135	+	0.529340i
$126$		0			0
$127$	1.51347	−	1.89783i	0.134299	−	0.168405i	−0.710135	−	0.704066i	$-0.751366\pi$
$127$	1.51347	−	1.89783i	0.134299	−	0.168405i	0.844433	+	0.535661i	$0.179937\pi$
$128$	6.35087	−	3.66667i	0.561343	−	0.324091i
$129$		0			0
$130$	0.449943	+	1.14644i	0.0394627	+	0.100549i
$131$	−4.74729	+	1.46434i	−0.414772	+	0.127940i	−0.495116	−	0.868827i	$-0.664874\pi$
$131$	−4.74729	+	1.46434i	−0.414772	+	0.127940i	0.0803437	+	0.996767i	$0.474398\pi$
$132$		0			0
$133$	19.3137	−	10.3762i	1.67471	−	0.899734i
$134$	−0.578769	+	1.20183i	−0.0499980	+	0.103822i
$135$		0			0
$136$	7.91638	+	11.6112i	0.678824	+	0.995652i
$137$	−5.26836	+	5.67794i	−0.450106	+	0.485099i	−0.916815	−	0.399312i	$-0.869249\pi$
$137$	−5.26836	+	5.67794i	−0.450106	+	0.485099i	0.466709	+	0.884411i	$0.345440\pi$
$138$		0			0
$139$	−2.19460	+	0.500904i	−0.186144	+	0.0424861i	−0.314576	−	0.949232i	$-0.601862\pi$
$139$	−2.19460	+	0.500904i	−0.186144	+	0.0424861i	0.128433	+	0.991718i	$0.459005\pi$
$140$	1.74453	−	2.05529i	0.147440	−	0.173703i
$141$		0			0
$142$	−8.23461	+	7.64060i	−0.691033	+	0.641185i
$143$	4.29725	−	0.647706i	0.359354	−	0.0541639i
$144$		0			0
$145$	−5.92077	+	0.443700i	−0.491693	+	0.0368473i
$146$	8.87834			0.734777
$147$		0			0
$148$	3.60926			0.296680
$149$	6.31947	−	0.473579i	0.517711	−	0.0387971i	0.186687	−	0.982419i	$-0.440225\pi$
$149$	6.31947	−	0.473579i	0.517711	−	0.0387971i	0.331024	+	0.943622i	$0.392606\pi$
$150$		0			0
$151$	−12.0259	+	1.81261i	−0.978651	+	0.147508i	−0.618840	−	0.785517i	$-0.712397\pi$
$151$	−12.0259	+	1.81261i	−0.978651	+	0.147508i	−0.359811	+	0.933025i	$0.617159\pi$
$152$	−17.0496	+	15.8197i	−1.38290	+	1.28315i
$153$		0			0
$154$	3.36440	+	4.49431i	0.271111	+	0.362162i
$155$	7.71294	−	1.76043i	0.619518	−	0.141401i
$156$		0			0
$157$	−10.9494	+	11.8007i	−0.873860	+	0.941797i	−0.998730	−	0.0503757i	$-0.983958\pi$
$157$	−10.9494	+	11.8007i	−0.873860	+	0.941797i	0.124870	+	0.992173i	$0.460149\pi$
$158$	−1.32967	−	1.95027i	−0.105783	−	0.155155i
$159$		0			0
$160$	−2.00262	+	4.15849i	−0.158321	+	0.328757i
$161$	−22.5151	−	9.64152i	−1.77444	−	0.759858i
$162$		0			0
$163$	−2.61562	+	0.806812i	−0.204871	+	0.0631944i	−0.395492	−	0.918469i	$-0.629426\pi$
$163$	−2.61562	+	0.806812i	−0.204871	+	0.0631944i	0.190621	+	0.981664i	$0.438950\pi$
$164$	−1.01087	−	2.57566i	−0.0789359	−	0.201125i
$165$		0			0
$166$	11.4098	−	6.58743i	0.885569	−	0.511283i
$167$	−1.60920	+	2.01788i	−0.124524	+	0.156148i	−0.840185	−	0.542299i	$-0.817554\pi$
$167$	−1.60920	+	2.01788i	−0.124524	+	0.156148i	0.715662	+	0.698447i	$0.246125\pi$
$168$		0			0
$169$	6.16418	+	7.72963i	0.474167	+	0.594587i
$170$	−3.25316	−	1.27677i	−0.249506	−	0.0979240i
$171$		0			0
$172$	0.675993	−	9.02050i	0.0515440	−	0.687807i
$173$	0.542447	−	1.38213i	0.0412415	−	0.105082i	−0.908769	−	0.417299i	$-0.862977\pi$
$173$	0.542447	−	1.38213i	0.0412415	−	0.105082i	0.950011	+	0.312218i	$0.101072\pi$
$174$		0			0
$175$	1.20904	−	11.4285i	0.0913950	−	0.863914i
$176$	0.187439	+	0.149478i	0.0141288	+	0.0112673i
$177$		0			0
$178$	−2.56506	−	1.48094i	−0.192260	−	0.111001i
$179$	11.1848	−	4.38970i	0.835989	−	0.328102i	0.0915573	−	0.995800i	$-0.470816\pi$
$179$	11.1848	−	4.38970i	0.835989	−	0.328102i	0.744432	+	0.667698i	$0.232720\pi$
$180$		0			0
$181$	−3.30660	−	6.86622i	−0.245778	−	0.510362i	0.741187	−	0.671298i	$-0.234263\pi$
$181$	−3.30660	−	6.86622i	−0.245778	−	0.510362i	−0.986965	+	0.160936i	$0.948549\pi$
$182$	1.58329	−	3.69733i	0.117361	−	0.274064i
$183$		0			0
$184$	25.6924	+	3.87250i	1.89407	+	0.285485i
$185$	−1.92086	+	1.30962i	−0.141224	+	0.0962852i
$186$		0			0
$187$	−6.94671	+	10.1890i	−0.507994	+	0.745090i
$188$	−1.91756	−	8.40139i	−0.139853	−	0.612735i
$189$		0			0
$190$	1.28704	−	5.63891i	0.0933719	−	0.409089i
$191$	15.4513	+	16.6525i	1.11802	+	1.20494i	0.976618	+	0.214983i	$0.0689697\pi$
$191$	15.4513	+	16.6525i	1.11802	+	1.20494i	0.141399	+	0.989953i	$0.454840\pi$
$192$		0			0
$193$	12.9810	+	4.00410i	0.934391	+	0.288222i	0.724320	−	0.689464i	$-0.242154\pi$
$193$	12.9810	+	4.00410i	0.934391	+	0.288222i	0.210072	+	0.977686i	$0.432630\pi$
$194$	0.660199	+	8.80974i	0.0473995	+	0.632503i
$195$		0			0
$196$	−8.76973	+	0.777268i	−0.626409	+	0.0555191i
$197$			12.0796i			0.860635i	0.902678	+	0.430317i	$0.141598\pi$
$197$			12.0796i			0.860635i	−0.902678	+	0.430317i	$0.858402\pi$
$198$		0			0
$199$	−5.17381	+	16.7731i	−0.366762	+	1.18901i	0.564738	+	0.825271i	$0.308977\pi$
$199$	−5.17381	+	16.7731i	−0.366762	+	1.18901i	−0.931500	+	0.363743i	$0.881499\pi$
$200$	1.81703	+	12.0552i	0.128484	+	0.852434i
$201$		0			0
$202$	−4.31000	−	0.983728i	−0.303250	−	0.0692149i
$203$	14.7830	+	12.5478i	1.03756	+	0.880684i
$204$		0			0
$205$	1.47257	+	1.00398i	0.102849	+	0.0701210i
$206$	4.53955	+	4.21209i	0.316286	+	0.293470i
$207$		0			0
$208$	0.0255993	−	0.169840i	0.00177499	−	0.0117763i
$209$	−18.3883	−	8.85533i	−1.27194	−	0.612536i
$210$		0			0
$211$	11.2776	−	5.43099i	0.776380	−	0.373885i	−0.00335491	−	0.999994i	$-0.501068\pi$
$211$	11.2776	−	5.43099i	0.776380	−	0.373885i	0.779735	+	0.626109i	$0.215354\pi$
$212$	−0.413150	−	1.33940i	−0.0283753	−	0.0919903i
$213$		0			0
$214$	−7.00945	+	12.1407i	−0.479156	+	0.829923i
$215$	2.91332	+	5.04602i	0.198687	+	0.344136i
$216$		0			0
$217$	−21.9696	−	13.5969i	−1.49139	−	0.923017i
$218$	6.16548	−	4.91680i	0.417579	−	0.333008i
$219$		0			0
$220$	−2.50253	−	0.187539i	−0.168720	−	0.0126438i
$221$	8.81006	+	0.660222i	0.592628	+	0.0444114i
$222$		0			0
$223$	−12.4101	+	9.89675i	−0.831044	+	0.662736i	−0.943665	−	0.330902i	$-0.892647\pi$
$223$	−12.4101	+	9.89675i	−0.831044	+	0.662736i	0.112621	+	0.993638i	$0.464075\pi$
$224$	14.1935	−	5.07511i	0.948343	−	0.339095i
$225$		0			0
$226$	4.20458	+	7.28254i	0.279684	+	0.484428i
$227$	−8.19543	+	14.1949i	−0.543950	+	0.942149i	0.454722	+	0.890633i	$0.349739\pi$
$227$	−8.19543	+	14.1949i	−0.543950	+	0.942149i	−0.998672	+	0.0515156i	$0.983595\pi$
$228$		0			0
$229$	2.29235	+	7.43162i	0.151483	+	0.491096i	0.999227	−	0.0393098i	$-0.0125159\pi$
$229$	2.29235	+	7.43162i	0.151483	+	0.491096i	−0.847744	+	0.530405i	$0.822040\pi$
$230$	−5.82151	+	2.80349i	−0.383859	+	0.184857i
$231$		0			0
$232$	−18.5328	−	8.92493i	−1.21674	−	0.585950i
$233$	1.84181	−	12.2196i	0.120661	−	0.800534i	−0.843867	−	0.536553i	$-0.819726\pi$
$233$	1.84181	−	12.2196i	0.120661	−	0.800534i	0.964528	−	0.263981i	$-0.0850356\pi$
$234$		0			0
$235$	4.06898	+	3.77546i	0.265431	+	0.246284i
$236$	−4.10512	−	2.79882i	−0.267220	−	0.182188i
$237$		0			0
$238$	4.63505	+	10.4296i	0.300446	+	0.676049i
$239$	16.6387	+	3.79768i	1.07627	+	0.245652i	0.723687	−	0.690129i	$-0.242446\pi$
$239$	16.6387	+	3.79768i	1.07627	+	0.245652i	0.352584	+	0.935780i	$0.385303\pi$
$240$		0			0
$241$	−1.72358	−	11.4352i	−0.111026	−	0.736608i	−0.973194	−	0.229986i	$-0.926132\pi$
$241$	−1.72358	−	11.4352i	−0.111026	−	0.736608i	0.862168	−	0.506622i	$-0.169106\pi$
$242$	−1.25299	+	4.06209i	−0.0805452	+	0.261121i
$243$		0			0
$244$			9.84184i			0.630060i
$245$	4.38524	−	3.59576i	0.280163	−	0.229725i
$246$		0			0
$247$	1.09269	+	14.5809i	0.0695263	+	0.927763i
$248$	26.1908	+	8.07879i	1.66312	+	0.513004i
$249$		0			0
$250$	−4.43585	−	4.78071i	−0.280548	−	0.302359i
$251$	−5.18904	+	22.7347i	−0.327529	+	1.43500i	0.496295	+	0.868154i	$0.334693\pi$
$251$	−5.18904	+	22.7347i	−0.327529	+	1.43500i	−0.823825	+	0.566845i	$0.808164\pi$
$252$		0			0
$253$	5.07348	+	22.2284i	0.318967	+	1.39749i
$254$	−1.17810	+	1.72795i	−0.0739203	+	0.108421i
$255$		0			0
$256$	−13.0097	+	8.86985i	−0.813105	+	0.554366i
$257$	−5.07474	−	0.764893i	−0.316553	−	0.0477127i	−0.0111560	−	0.999938i	$-0.503551\pi$
$257$	−5.07474	−	0.764893i	−0.316553	−	0.0477127i	−0.305397	+	0.952225i	$0.598789\pi$
$258$		0			0
$259$	7.46949	+	1.36076i	0.464131	+	0.0845535i
$260$	0.780080	+	1.61985i	0.0483785	+	0.100459i
$261$		0			0
$262$	3.98431	−	1.56373i	0.246152	−	0.0966074i
$263$	10.3656	+	5.98457i	0.639169	+	0.369025i	0.784294	−	0.620389i	$-0.213025\pi$
$263$	10.3656	+	5.98457i	0.639169	+	0.369025i	−0.145125	+	0.989413i	$0.546359\pi$
$264$		0			0
$265$	0.705881	+	0.562921i	0.0433619	+	0.0345800i
$266$	−15.9252	+	10.1582i	−0.976436	+	0.622837i
$267$		0			0
$268$	−0.711437	+	1.81271i	−0.0434579	+	0.110729i
$269$	−0.0151990	+	0.202817i	−0.000926702	+	0.0123660i	−0.997648	−	0.0685457i	$-0.978164\pi$
$269$	−0.0151990	+	0.202817i	−0.000926702	+	0.0123660i	0.996721	+	0.0809116i	$0.0257832\pi$
$270$		0			0
$271$	−2.03185	−	0.797442i	−0.123426	−	0.0484411i	0.302824	−	0.953046i	$-0.402070\pi$
$271$	−2.03185	−	0.797442i	−0.123426	−	0.0484411i	−0.426250	+	0.904605i	$0.640166\pi$
$272$	0.303881	+	0.381054i	0.0184255	+	0.0231048i
$273$		0			0
$274$	4.16070	−	5.21736i	0.251357	−	0.315192i
$275$	−9.26482	+	5.34905i	−0.558690	+	0.322560i
$276$		0			0
$277$	−1.45119	−	3.69758i	−0.0871937	−	0.222166i	0.880625	−	0.473813i	$-0.157123\pi$
$277$	−1.45119	−	3.69758i	−0.0871937	−	0.222166i	−0.967819	+	0.251647i	$0.919028\pi$
$278$	1.85323	−	0.571644i	0.111149	−	0.0342850i
$279$		0			0
$280$	−3.53939	+	4.86460i	−0.211519	+	0.290715i
$281$	2.09431	−	4.34887i	0.124936	−	0.259432i	−0.829114	−	0.559079i	$-0.811155\pi$
$281$	2.09431	−	4.34887i	0.124936	−	0.259432i	0.954050	+	0.299647i	$0.0968690\pi$
$282$		0			0
$283$	−9.17239	−	13.4534i	−0.545242	−	0.799723i	0.450415	−	0.892819i	$-0.351276\pi$
$283$	−9.17239	−	13.4534i	−0.545242	−	0.799723i	−0.995657	+	0.0930959i	$0.970324\pi$
$284$	−11.1541	+	12.0212i	−0.661873	+	0.713329i
$285$		0			0
$286$	−3.65025	+	0.833145i	−0.215844	+	0.0492649i
$287$	−1.12096	−	5.71153i	−0.0661683	−	0.337141i
$288$		0			0
$289$	−5.91557	+	5.48884i	−0.347974	+	0.322873i
$290$	5.05821	−	0.762403i	0.297029	−	0.0447699i
$291$		0			0
$292$	12.9247	−	0.968575i	0.756363	−	0.0566816i
$293$	7.90646			0.461900			0.230950	−	0.972966i	$-0.425817\pi$
$293$	7.90646			0.461900			0.230950	+	0.972966i	$0.425817\pi$
$294$		0			0
$295$	3.20031			0.186329
$296$	−8.03177	+	0.601898i	−0.466837	+	0.0349846i
$297$		0			0
$298$	−5.39883	+	0.813743i	−0.312746	+	0.0471389i
$299$	11.9740	−	11.1103i	0.692476	−	0.642524i
$300$		0			0
$301$	4.79988	−	18.4133i	0.276661	−	1.06133i
$302$	10.2152	−	2.33156i	0.587820	−	0.134166i
$303$		0			0
$304$	−0.548656	+	0.591310i	−0.0314676	+	0.0339140i
$305$	−3.57111	−	5.23786i	−0.204481	−	0.299919i
$306$		0			0
$307$	12.8354	−	26.6529i	0.732554	−	1.52116i	−0.116693	−	0.993168i	$-0.537229\pi$
$307$	12.8354	−	26.6529i	0.732554	−	1.52116i	0.849247	−	0.527996i	$-0.177056\pi$
$308$	5.38806	+	6.17560i	0.307013	+	0.351887i
$309$		0			0
$310$	−6.51317	+	2.00905i	−0.369923	+	0.114106i
$311$	−12.4989	−	31.8466i	−0.708745	−	1.80585i	−0.580755	−	0.814079i	$-0.697242\pi$
$311$	−12.4989	−	31.8466i	−0.708745	−	1.80585i	−0.127991	−	0.991775i	$-0.540853\pi$
$312$		0			0
$313$	−5.89721	+	3.40475i	−0.333330	+	0.192448i	−0.657319	−	0.753613i	$-0.728309\pi$
$313$	−5.89721	+	3.40475i	−0.333330	+	0.192448i	0.323989	+	0.946061i	$0.394976\pi$
$314$	8.64735	−	10.8434i	0.487998	−	0.611930i
$315$		0			0
$316$	−2.14845	−	2.69407i	−0.120860	−	0.151553i
$317$	−8.30964	−	3.26129i	−0.466716	−	0.183173i	0.120317	−	0.992736i	$-0.461609\pi$
$317$	−8.30964	−	3.26129i	−0.466716	−	0.183173i	−0.587033	+	0.809563i	$0.699704\pi$
$318$		0			0
$319$	1.34890	−	17.9998i	0.0755239	−	1.00780i
$320$	1.39518	−	3.55485i	0.0779927	−	0.198722i
$321$		0			0
$322$	19.9644	+	6.83383i	1.11257	+	0.380835i
$323$	−32.4392	−	25.8694i	−1.80497	−	1.43941i
$324$		0			0
$325$	6.63755	+	3.83219i	0.368185	+	0.212572i
$326$	2.19524	−	0.861570i	0.121583	−	0.0477179i
$327$		0			0
$328$	2.67905	+	5.56310i	0.147926	+	0.307171i
$329$	−0.800978	−	18.1099i	−0.0441594	−	0.998432i
$330$		0			0
$331$	0.236178	+	0.0355981i	0.0129815	+	0.00195665i	0.155530	−	0.987831i	$-0.450292\pi$
$331$	0.236178	+	0.0355981i	0.0129815	+	0.00195665i	−0.142548	+	0.989788i	$0.545530\pi$
$332$	15.8912	−	10.8345i	0.872144	−	0.594618i
$333$		0			0
$334$	1.25262	−	1.83725i	0.0685401	−	0.100530i
$335$	−0.279113	−	1.22288i	−0.0152496	−	0.0668128i
$336$		0			0
$337$	3.17938	−	13.9298i	0.173192	−	0.758803i	−0.811479	−	0.584381i	$-0.801337\pi$
$337$	3.17938	−	13.9298i	0.173192	−	0.758803i	0.984671	−	0.174422i	$-0.0558056\pi$
$338$	−5.79357	−	6.24398i	−0.315129	−	0.339628i
$339$		0			0
$340$	−4.87512	−	1.50377i	−0.264390	−	0.0815536i
$341$	1.79735	+	23.9840i	0.0973320	+	1.29881i
$342$		0			0
$343$	−18.4423	−	1.69777i	−0.995789	−	0.0916709i
$344$			20.1862i			1.08837i
$345$		0			0
$346$	−0.377052	+	1.22237i	−0.0202704	+	0.0657152i
$347$	−2.95258	−	19.5891i	−0.158503	−	1.05160i	−0.916701	−	0.399574i	$-0.869158\pi$
$347$	−2.95258	−	19.5891i	−0.158503	−	1.05160i	0.758198	−	0.652025i	$-0.226080\pi$
$348$		0			0
$349$	2.59908	+	0.593223i	0.139125	+	0.0317545i	0.291517	−	0.956566i	$-0.405840\pi$
$349$	2.59908	+	0.593223i	0.139125	+	0.0317545i	−0.152391	+	0.988320i	$0.548697\pi$
$350$	−0.302929	+	9.89656i	−0.0161922	+	0.528993i
$351$		0			0
$352$	−11.5937	−	7.90443i	−0.617945	−	0.421308i
$353$	−6.84795	−	6.35397i	−0.364480	−	0.338188i	0.476579	−	0.879132i	$-0.341877\pi$
$353$	−6.84795	−	6.35397i	−0.364480	−	0.338188i	−0.841059	+	0.540944i	$0.818067\pi$
$354$		0			0
$355$	1.57433	−	10.4450i	0.0835567	−	0.554363i
$356$	−3.89568	−	1.87606i	−0.206471	−	0.0994310i
$357$		0			0
$358$	−9.32669	+	4.49150i	−0.492931	+	0.237383i
$359$	6.22804	+	20.1908i	0.328703	+	1.06563i	0.957590	+	0.288133i	$0.0930347\pi$
$359$	6.22804	+	20.1908i	0.328703	+	1.06563i	−0.628887	+	0.777497i	$0.716489\pi$
$360$		0			0
$361$	24.8348	−	43.0152i	1.30710	−	2.26396i
$362$	3.28291	+	5.68617i	0.172546	+	0.298859i
$363$		0			0
$364$	1.90153	−	5.55515i	0.0996674	−	0.291169i
$365$	−6.52714	+	5.20522i	−0.341646	+	0.272453i
$366$		0			0
$367$	−25.9930	−	1.94791i	−1.35683	−	0.101680i	−0.623642	−	0.781710i	$-0.714348\pi$
$367$	−25.9930	−	1.94791i	−1.35683	−	0.101680i	−0.733184	+	0.680030i	$0.761967\pi$
$368$	0.898604	+	0.0673411i	0.0468430	+	0.00351040i
$369$		0			0
$370$	1.56597	−	1.24882i	0.0814111	−	0.0649232i
$371$	−0.350049	−	2.92770i	−0.0181736	−	0.151998i
$372$		0			0
$373$	−0.813019	−	1.40819i	−0.0420965	−	0.0729133i	0.844209	−	0.536013i	$-0.180070\pi$
$373$	−0.813019	−	1.40819i	−0.0420965	−	0.0729133i	−0.886306	+	0.463100i	$0.846737\pi$
$374$	5.31221	−	9.20102i	0.274688	−	0.475773i
$375$		0			0
$376$	5.66825	+	18.3760i	0.292318	+	0.947671i
$377$	−11.6510	+	5.61084i	−0.600059	+	0.288973i
$378$		0			0
$379$	12.2610	+	5.90457i	0.629804	+	0.303297i	0.721421	−	0.692497i	$-0.243489\pi$
$379$	12.2610	+	5.90457i	0.629804	+	0.303297i	−0.0916173	+	0.995794i	$0.529204\pi$
$380$	1.25846	−	8.34931i	0.0645574	−	0.428310i
$381$		0			0
$382$	−14.3470	−	13.3121i	−0.734058	−	0.681106i
$383$	7.59847	+	5.18055i	0.388264	+	0.264714i	0.741682	−	0.670752i	$-0.234028\pi$
$383$	7.59847	+	5.18055i	0.388264	+	0.264714i	−0.353418	+	0.935465i	$0.614981\pi$
$384$		0			0
$385$	−5.10836	−	1.33162i	−0.260346	−	0.0678654i
$386$	−11.4103	−	2.60433i	−0.580769	−	0.132557i
$387$		0			0
$388$	1.92218	+	12.7529i	0.0975841	+	0.647428i
$389$	6.24131	−	20.2338i	0.316447	−	1.02590i	−0.648005	−	0.761636i	$-0.724396\pi$
$389$	6.24131	−	20.2338i	0.316447	−	1.02590i	0.964452	−	0.264259i	$-0.0851274\pi$
$390$		0			0
$391$			46.3512i			2.34408i
$392$	19.3858	−	3.19215i	0.979133	−	0.161228i
$393$		0			0
$394$	−0.777730	−	10.3781i	−0.0391814	−	0.522840i
$395$	2.12095	+	0.654228i	0.106717	+	0.0329178i
$396$		0			0
$397$	7.39644	+	7.97146i	0.371217	+	0.400076i	0.890839	−	0.454320i	$-0.150118\pi$
$397$	7.39644	+	7.97146i	0.371217	+	0.400076i	−0.519622	+	0.854396i	$0.673927\pi$
$398$	3.36513	−	14.7436i	0.168679	−	0.739029i
$399$		0			0
$400$	0.0940864	+	0.412219i	0.00470432	+	0.0206110i
$401$	−3.95834	+	5.80581i	−0.197670	+	0.289929i	−0.912257	−	0.409618i	$-0.865662\pi$
$401$	−3.95834	+	5.80581i	−0.197670	+	0.289929i	0.714587	+	0.699546i	$0.246614\pi$
$402$		0			0
$403$	14.2368	−	9.70651i	0.709188	−	0.483516i
$404$	−6.38164	−	0.961878i	−0.317498	−	0.0478552i
$405$		0			0
$406$	−13.5085	−	9.82857i	−0.670418	−	0.487784i
$407$	−3.06658	−	6.36781i	−0.152005	−	0.315641i
$408$		0			0
$409$	20.6149	−	8.09077i	1.01934	−	0.400063i	0.203957	−	0.978980i	$-0.434620\pi$
$409$	20.6149	−	8.09077i	1.01934	−	0.400063i	0.815386	+	0.578917i	$0.196525\pi$
$410$	−1.32979	−	0.767752i	−0.0656734	−	0.0379166i
$411$		0			0
$412$	7.06801	+	5.63655i	0.348216	+	0.277693i
$413$	−7.44047	−	7.33996i	−0.366121	−	0.361176i
$414$		0			0
$415$	−4.52608	+	11.5323i	−0.222176	+	0.566096i
$416$	−0.751245	+	10.0247i	−0.0368328	+	0.491500i
$417$		0			0
$418$	16.3683	+	6.42408i	0.800599	+	0.314212i
$419$	−14.8904	−	18.6719i	−0.727442	−	0.912184i	0.271291	−	0.962497i	$-0.412549\pi$
$419$	−14.8904	−	18.6719i	−0.727442	−	0.912184i	−0.998733	+	0.0503136i	$0.983978\pi$
$420$		0			0
$421$	11.5324	−	14.4612i	0.562056	−	0.704796i	−0.416881	−	0.908961i	$-0.636877\pi$
$421$	11.5324	−	14.4612i	0.562056	−	0.704796i	0.978936	+	0.204166i	$0.0654481\pi$
$422$	−9.33937	+	5.39209i	−0.454634	+	0.262483i
$423$		0			0
$424$	1.14276	+	2.91170i	0.0554972	+	0.141405i
$425$	−20.7824	+	6.41053i	−1.00810	+	0.310957i
$426$		0			0
$427$	−3.71056	+	20.3680i	−0.179566	+	0.985677i
$428$	−8.87960	+	18.4387i	−0.429212	+	0.891267i
$429$		0			0
$430$	−2.82784	−	4.14768i	−0.136371	−	0.200019i
$431$	−0.575410	+	0.620145i	−0.0277165	+	0.0298713i	−0.746758	−	0.665096i	$-0.768391\pi$
$431$	−0.575410	+	0.620145i	−0.0277165	+	0.0298713i	0.719041	+	0.694967i	$0.244581\pi$
$432$		0			0
$433$	7.94629	−	1.81369i	0.381874	−	0.0871603i	−0.0272745	−	0.999628i	$-0.508683\pi$
$433$	7.94629	−	1.81369i	0.381874	−	0.0871603i	0.409149	+	0.912468i	$0.365826\pi$
$434$	19.7504	+	10.2672i	0.948049	+	0.492841i
$435$		0			0
$436$	8.43906	−	7.83030i	0.404158	−	0.375004i
$437$	−75.8561	+	11.4335i	−3.62869	+	0.546937i
$438$		0			0
$439$	27.1836	−	2.03713i	1.29740	−	0.0972270i	0.591946	−	0.805978i	$-0.298360\pi$
$439$	27.1836	−	2.03713i	1.29740	−	0.0972270i	0.705459	+	0.708751i	$0.250741\pi$
$440$	5.60020			0.266979
$441$		0			0
$442$	−7.61160			−0.362047
$443$	−21.1386	+	1.58412i	−1.00432	+	0.0752637i	−0.566725	−	0.823907i	$-0.691790\pi$
$443$	−21.1386	+	1.58412i	−1.00432	+	0.0752637i	−0.437599	+	0.899170i	$0.644171\pi$
$444$		0			0
$445$	2.75402	−	0.415102i	0.130553	−	0.0196777i
$446$	10.0249	−	9.30173i	0.474692	−	0.440450i
$447$		0			0
$448$	−11.3968	+	5.06489i	−0.538447	+	0.239294i
$449$	33.7634	−	7.70628i	1.59339	−	0.363682i	0.668442	−	0.743764i	$-0.266962\pi$
$449$	33.7634	−	7.70628i	1.59339	−	0.363682i	0.924953	+	0.380083i	$0.124104\pi$
$450$		0			0
$451$	−3.68535	+	3.97187i	−0.173536	+	0.187028i
$452$	6.91534	+	10.1429i	0.325270	+	0.477084i
$453$		0			0
$454$	6.12712	−	12.7231i	0.287560	−	0.597124i
$455$	1.00369	+	3.64644i	0.0470535	+	0.170948i
$456$		0			0
$457$	14.8667	−	4.58577i	0.695435	−	0.214513i	0.0731697	−	0.997320i	$-0.476689\pi$
$457$	14.8667	−	4.58577i	0.695435	−	0.214513i	0.622266	+	0.782806i	$0.286212\pi$
$458$	−2.44793	−	6.23723i	−0.114384	−	0.291447i
$459$		0			0
$460$	−8.16888	+	4.71631i	−0.380876	+	0.219899i
$461$	−0.992274	+	1.24427i	−0.0462148	+	0.0579515i	−0.804402	−	0.594086i	$-0.797514\pi$
$461$	−0.992274	+	1.24427i	−0.0462148	+	0.0579515i	0.758187	+	0.652037i	$0.226085\pi$
$462$		0			0
$463$	7.27627	+	9.12416i	0.338157	+	0.424035i	0.921614	−	0.388109i	$-0.126872\pi$
$463$	7.27627	+	9.12416i	0.338157	+	0.424035i	−0.583457	+	0.812144i	$0.698300\pi$
$464$	−0.664086	−	0.260635i	−0.0308294	−	0.0120997i
$465$		0			0
$466$	−0.795632	+	10.6170i	−0.0368569	+	0.491822i
$467$	10.6898	−	27.2371i	0.494664	−	1.26038i	−0.437785	−	0.899080i	$-0.644237\pi$
$467$	10.6898	−	27.2371i	0.494664	−	1.26038i	0.932448	−	0.361303i	$-0.117668\pi$
$468$		0			0
$469$	−2.15577	+	3.48324i	−0.0995441	+	0.160841i
$470$	−3.73891	−	2.98168i	−0.172463	−	0.137535i
$471$		0			0
$472$	9.60196	+	5.54369i	0.441966	+	0.255169i
$473$	−16.4892	+	6.47153i	−0.758173	+	0.297561i
$474$		0			0
$475$	−15.6176	−	32.4302i	−0.716583	−	1.48800i
$476$	7.88534	+	14.6773i	0.361424	+	0.672734i
$477$		0			0
$478$	−14.5395	−	2.19148i	−0.665023	−	0.100236i
$479$	29.2845	−	19.9658i	1.33804	−	0.912262i	0.338455	−	0.940983i	$-0.390096\pi$
$479$	29.2845	−	19.9658i	1.33804	−	0.912262i	0.999587	+	0.0287208i	$0.00914339\pi$
$480$		0			0
$481$	−2.85237	+	4.18366i	−0.130057	+	0.190759i
$482$	2.21705	+	9.71352i	0.100984	+	0.442439i
$483$		0			0
$484$	−1.38090	+	6.05013i	−0.0627683	+	0.275006i
$485$	−5.65036	−	6.08964i	−0.256570	−	0.276516i
$486$		0			0
$487$	−16.5739	−	5.11237i	−0.751035	−	0.231663i	−0.104476	−	0.994527i	$-0.533316\pi$
$487$	−16.5739	−	5.11237i	−0.751035	−	0.231663i	−0.646559	+	0.762864i	$0.723793\pi$
$488$	−1.64127	−	21.9013i	−0.0742970	−	0.991424i
$489$		0			0
$490$	−3.53604	+	3.37161i	−0.159742	+	0.152314i
$491$			15.2630i			0.688811i	0.938821	+	0.344405i	$0.111919\pi$
$491$			15.2630i			0.688811i	−0.938821	+	0.344405i	$0.888081\pi$
$492$		0			0
$493$	10.8161	−	35.0650i	0.487134	−	1.57925i
$494$	−1.87755	−	12.4568i	−0.0844751	−	0.560456i
$495$		0			0
$496$	0.926743	+	0.211523i	0.0416120	+	0.00949767i
$497$	−27.6160	+	20.6730i	−1.23874	+	0.927313i
$498$		0			0
$499$	−9.23399	−	6.29563i	−0.413370	−	0.281831i	0.338725	−	0.940885i	$-0.390004\pi$
$499$	−9.23399	−	6.29563i	−0.413370	−	0.281831i	−0.752095	+	0.659054i	$0.770957\pi$
$500$	−6.97909	−	6.47565i	−0.312114	−	0.289600i
$501$		0			0
$502$	2.99438	−	19.8664i	0.133646	−	0.886680i
$503$	13.8231	+	6.65685i	0.616341	+	0.296814i	0.715884	−	0.698219i	$-0.246024\pi$
$503$	13.8231	+	6.65685i	0.616341	+	0.296814i	−0.0995430	+	0.995033i	$0.531738\pi$
$504$		0			0
$505$	3.74534	−	1.80366i	0.166666	−	0.0802619i
$506$	−5.78999	−	18.7707i	−0.257396	−	0.834458i
$507$		0			0
$508$	−1.52652	+	2.64400i	−0.0677282	+	0.117309i
$509$	−19.4988	−	33.7729i	−0.864268	−	1.49696i	−0.867773	−	0.496961i	$-0.834449\pi$
$509$	−19.4988	−	33.7729i	−0.864268	−	1.49696i	0.00350504	−	0.999994i	$-0.498884\pi$
$510$		0			0
$511$	27.1133	+	2.86837i	1.19942	+	0.126889i
$512$	−0.860795	+	0.686461i	−0.0380421	+	0.0303376i
$513$		0			0
$514$	4.40917	+	0.330421i	0.194480	+	0.0145743i
$515$	−5.80684	−	0.435162i	−0.255880	−	0.0191755i
$516$		0			0
$517$	−13.1933	+	10.5213i	−0.580241	+	0.462727i
$518$	−6.50496	−	0.688172i	−0.285812	−	0.0302365i
$519$		0			0
$520$	−2.00606	−	3.47460i	−0.0879717	−	0.152371i
$521$	9.94044	−	17.2173i	0.435498	−	0.754305i	−0.561838	−	0.827247i	$-0.689905\pi$
$521$	9.94044	−	17.2173i	0.435498	−	0.754305i	0.997336	+	0.0729420i	$0.0232388\pi$
$522$		0			0
$523$	10.2290	+	33.1617i	0.447284	+	1.45006i	0.846097	+	0.533028i	$0.178946\pi$
$523$	10.2290	+	33.1617i	0.447284	+	1.45006i	−0.398813	+	0.917032i	$0.630578\pi$
$524$	5.62961	−	2.71108i	0.245931	−	0.118434i
$525$		0			0
$526$	−9.29082	−	4.47422i	−0.405099	−	0.195085i
$527$	−7.28741	+	48.3488i	−0.317445	+	2.10611i
$528$		0			0
$529$	45.9611	+	42.6457i	1.99831	+	1.85416i
$530$	−0.642695	−	0.438182i	−0.0279169	−	0.0190334i
$531$		0			0
$532$	−22.0751	+	16.5252i	−0.957076	+	0.716458i
$533$	3.78445	+	0.863776i	0.163923	+	0.0374143i
$534$		0			0
$535$	−1.96472	−	13.0351i	−0.0849424	−	0.563556i
$536$	1.28088	−	4.15251i	0.0553256	−	0.179361i
$537$		0			0
$538$		−	0.175227i		−	0.00755458i
$539$	8.82245	+	14.8120i	0.380010	+	0.637998i
$540$		0			0
$541$	−0.920507	−	12.2833i	−0.0395757	−	0.528101i	−0.981397	−	0.191988i	$-0.938507\pi$
$541$	−0.920507	−	12.2833i	−0.0395757	−	0.528101i	0.941822	−	0.336113i	$-0.109112\pi$
$542$	1.79699	+	0.554298i	0.0771873	+	0.0238091i
$543$		0			0
$544$	−19.4026	−	20.9111i	−0.831882	−	0.896555i
$545$	−1.65007	+	7.22942i	−0.0706812	+	0.309674i
$546$		0			0
$547$	2.99366	+	13.1161i	0.127999	+	0.560802i	0.997734	+	0.0672825i	$0.0214329\pi$
$547$	2.99366	+	13.1161i	0.127999	+	0.560802i	−0.869734	+	0.493520i	$0.835710\pi$
$548$	5.48780	−	8.04913i	0.234427	−	0.343842i
$549$		0			0
$550$	7.61541	−	5.19210i	0.324722	−	0.221392i
$551$	60.0537	+	9.05164i	2.55837	+	0.385613i
$552$		0			0
$553$	−3.43057	−	6.38547i	−0.145883	−	0.271538i
$554$	1.48485	+	3.08331i	0.0630850	+	0.130997i
$555$		0			0
$556$	2.63549	−	1.03435i	0.111770	−	0.0438664i
$557$	−18.8697	−	10.8944i	−0.799536	−	0.461613i	0.0437726	−	0.999042i	$-0.486062\pi$
$557$	−18.8697	−	10.8944i	−0.799536	−	0.461613i	−0.843309	+	0.537429i	$0.819396\pi$
$558$		0			0
$559$	9.92184	+	7.91240i	0.419649	+	0.334659i
$560$	−0.109802	+	0.177415i	−0.00463996	+	0.00749714i
$561$		0			0
$562$	−1.51931	+	3.87114i	−0.0640882	+	0.163294i
$563$	−3.11383	+	41.5512i	−0.131232	+	1.75117i	0.411629	+	0.911352i	$0.364960\pi$
$563$	−3.11383	+	41.5512i	−0.131232	+	1.75117i	−0.542861	+	0.839822i	$0.682659\pi$
$564$		0			0
$565$	−7.36073	−	2.88887i	−0.309668	−	0.121536i
$566$	8.74657	+	10.9679i	0.367646	+	0.461013i
$567$		0			0
$568$	22.8167	−	28.6112i	0.957367	−	1.20050i
$569$	0.737473	−	0.425780i	0.0309165	−	0.0178496i	−0.484462	−	0.874812i	$-0.660985\pi$
$569$	0.737473	−	0.425780i	0.0309165	−	0.0178496i	0.515379	+	0.856963i	$0.327651\pi$
$570$		0			0
$571$	10.7689	+	27.4388i	0.450666	+	1.14828i	0.958061	+	0.286565i	$0.0925133\pi$
$571$	10.7689	+	27.4388i	0.450666	+	1.14828i	−0.507395	+	0.861714i	$0.669391\pi$
$572$	−5.22299	+	1.61108i	−0.218384	+	0.0673626i
$573$		0			0
$574$	1.33080	+	4.83485i	0.0555463	+	0.201803i
$575$	−17.4468	+	36.2287i	−0.727584	+	1.51084i
$576$		0			0
$577$	8.62611	+	12.6522i	0.359109	+	0.526717i	0.962698	−	0.270579i	$-0.0872153\pi$
$577$	8.62611	+	12.6522i	0.359109	+	0.526717i	−0.603588	+	0.797296i	$0.706263\pi$
$578$	4.72892	−	5.09656i	0.196697	−	0.211989i
$579$		0			0
$580$	7.28038	−	1.66170i	0.302301	−	0.0689983i
$581$	36.9722	−	16.4310i	1.53386	−	0.681671i
$582$		0			0
$583$	−2.01207	+	1.86693i	−0.0833314	+	0.0773202i
$584$	−28.6002	+	4.31078i	−1.18348	+	0.178381i
$585$		0			0
$586$	−6.79278	+	0.509048i	−0.280607	+	0.0210286i
$587$	26.2007			1.08142			0.540710	−	0.841209i	$-0.318156\pi$
$587$	26.2007			1.08142			0.540710	+	0.841209i	$0.318156\pi$
$588$		0			0
$589$	−80.9228			−3.33437
$590$	−2.74952	+	0.206048i	−0.113196	+	0.00848286i
$591$		0			0
$592$	−0.276218	+	0.0416332i	−0.0113525	+	0.00171111i
$593$	4.06154	−	3.76856i	0.166787	−	0.154756i	−0.592363	−	0.805671i	$-0.701805\pi$
$593$	4.06154	−	3.76856i	0.166787	−	0.154756i	0.759151	+	0.650915i	$0.225614\pi$
$594$		0			0
$595$	−9.52226	−	4.95012i	−0.390375	−	0.202935i
$596$	−7.77063	+	1.77360i	−0.318298	+	0.0726493i
$597$		0			0
$598$	−9.57207	+	10.3162i	−0.391431	+	0.421862i
$599$	−11.3843	−	16.6977i	−0.465149	−	0.682249i	0.519958	−	0.854192i	$-0.325948\pi$
$599$	−11.3843	−	16.6977i	−0.465149	−	0.682249i	−0.985107	+	0.171943i	$0.944995\pi$
$600$		0			0
$601$	−11.6840	+	24.2620i	−0.476599	+	0.989667i	0.514618	+	0.857420i	$0.327934\pi$
$601$	−11.6840	+	24.2620i	−0.476599	+	0.989667i	−0.991217	+	0.132248i	$0.957781\pi$
$602$	−2.93826	+	16.1287i	−0.119755	+	0.657358i
$603$		0			0
$604$	14.6166	−	4.50861i	0.594739	−	0.183453i
$605$	−1.46037	−	3.72095i	−0.0593724	−	0.151278i
$606$		0			0
$607$	−12.0607	+	6.96327i	−0.489530	+	0.282631i	−0.724380	−	0.689401i	$-0.757874\pi$
$607$	−12.0607	+	6.96327i	−0.489530	+	0.282631i	0.234849	+	0.972032i	$0.424540\pi$
$608$	29.4360	−	36.9115i	1.19379	−	1.49696i
$609$		0			0
$610$	3.40533	+	4.27014i	0.137878	+	0.172893i
$611$	11.2539	+	4.41682i	0.455283	+	0.178685i
$612$		0			0
$613$	1.47868	−	19.7317i	0.0597235	−	0.796955i	−0.884267	−	0.466982i	$-0.845341\pi$
$613$	1.47868	−	19.7317i	0.0597235	−	0.796955i	0.943990	−	0.329973i	$-0.107040\pi$
$614$	−9.31140	+	23.7251i	−0.375778	+	0.957466i
$615$		0			0
$616$	−13.0200	−	12.8442i	−0.524592	−	0.517506i
$617$	26.9583	+	21.4986i	1.08530	+	0.865499i	0.991502	−	0.130092i	$-0.0415272\pi$
$617$	26.9583	+	21.4986i	1.08530	+	0.865499i	0.0937997	+	0.995591i	$0.470099\pi$
$618$		0			0
$619$	7.27183	+	4.19839i	0.292279	+	0.168748i	0.638969	−	0.769232i	$-0.279361\pi$
$619$	7.27183	+	4.19839i	0.292279	+	0.168748i	−0.346690	+	0.937980i	$0.612694\pi$
$620$	−9.26244	+	3.63524i	−0.371989	+	0.145995i
$621$		0			0
$622$	12.7887	+	26.5560i	0.512780	+	1.06480i
$623$	−7.35492	−	5.35131i	−0.294669	−	0.214396i
$624$		0			0
$625$	−15.4118	−	2.32296i	−0.616473	−	0.0929184i
$626$	4.84733	−	3.30485i	0.193738	−	0.132088i
$627$		0			0
$628$	11.4055	−	16.7288i	0.455130	−	0.667553i
$629$	−3.19726	−	14.0081i	−0.127483	−	0.558539i
$630$		0			0
$631$	2.38108	−	10.4322i	0.0947895	−	0.415300i	−0.905163	−	0.425065i	$-0.860251\pi$
$631$	2.38108	−	10.4322i	0.0947895	−	0.415300i	0.999952	+	0.00976515i	$0.00310839\pi$
$632$	5.23027	+	5.63689i	0.208049	+	0.224223i
$633$		0			0
$634$	7.34914	+	2.26691i	0.291872	+	0.0900305i
$635$	−0.146960	−	1.96104i	−0.00583193	−	0.0778216i
$636$		0			0
$637$	6.02968	−	10.7797i	0.238905	−	0.427106i
$638$			15.5513i			0.615680i
$639$		0			0
$640$	1.75115	−	5.67708i	0.0692202	−	0.224406i
$641$	−4.46068	−	29.5947i	−0.176186	−	1.16892i	−0.885710	−	0.464239i	$-0.846328\pi$
$641$	−4.46068	−	29.5947i	−0.176186	−	1.16892i	0.709524	−	0.704681i	$-0.248910\pi$
$642$		0			0
$643$	−29.8887	−	6.82189i	−1.17869	−	0.269029i	−0.412086	−	0.911145i	$-0.635200\pi$
$643$	−29.8887	−	6.82189i	−1.17869	−	0.269029i	−0.766608	+	0.642116i	$0.778057\pi$
$644$	29.8089	+	7.77042i	1.17464	+	0.306197i
$645$		0			0
$646$	29.5355	+	20.1370i	1.16206	+	0.792278i
$647$	−6.27882	−	5.82589i	−0.246846	−	0.229039i	0.547040	−	0.837107i	$-0.315755\pi$
$647$	−6.27882	−	5.82589i	−0.246846	−	0.229039i	−0.793886	+	0.608067i	$0.791945\pi$
$648$		0			0
$649$	−1.45008	+	9.62064i	−0.0569205	+	0.377643i
$650$	−5.94933	−	2.86505i	−0.233352	−	0.112376i
$651$		0			0
$652$	3.10176	−	1.49373i	0.121474	−	0.0584989i
$653$	4.52050	+	14.6551i	0.176901	+	0.573498i	0.999984	+	0.00557820i	$0.00177561\pi$
$653$	4.52050	+	14.6551i	0.176901	+	0.573498i	−0.823084	+	0.567920i	$0.807748\pi$
$654$		0			0
$655$	−2.01238	+	3.48555i	−0.0786303	+	0.136192i
$656$	0.107073	+	0.185456i	0.00418049	+	0.00724082i
$657$		0			0
$658$	1.85414	+	15.5074i	0.0722819	+	0.604542i
$659$	9.96466	−	7.94655i	0.388168	−	0.309554i	−0.409889	−	0.912135i	$-0.634433\pi$
$659$	9.96466	−	7.94655i	0.388168	−	0.309554i	0.798057	+	0.602582i	$0.205861\pi$
$660$		0			0
$661$	−29.5178	−	2.21205i	−1.14811	−	0.0860389i	−0.512949	−	0.858419i	$-0.671447\pi$
$661$	−29.5178	−	2.21205i	−1.14811	−	0.0860389i	−0.635160	+	0.772380i	$0.719066\pi$
$662$	−0.205202	−	0.0153778i	−0.00797542	−	0.000597675i
$663$		0			0
$664$	−33.5563	+	26.7602i	−1.30224	+	1.03850i
$665$	5.75226	−	16.8047i	0.223063	−	0.651658i
$666$		0			0
$667$	−33.9228	−	58.7560i	−1.31349	−	2.27504i
$668$	1.62307	−	2.81125i	0.0627986	−	0.108770i
$669$		0			0
$670$	0.318531	+	1.03265i	0.0123059	+	0.0398949i
$671$	17.3639	−	8.36203i	0.670327	−	0.322813i
$672$		0			0
$673$	−36.4046	−	17.5316i	−1.40330	−	0.675792i	−0.429469	−	0.903082i	$-0.641299\pi$
$673$	−36.4046	−	17.5316i	−1.40330	−	0.675792i	−0.973827	+	0.227290i	$0.927014\pi$
$674$	−1.83469	+	12.1724i	−0.0706695	+	0.468861i
$675$		0			0
$676$	−9.11523	−	8.45770i	−0.350586	−	0.325296i
$677$	−0.947328	−	0.645877i	−0.0364088	−	0.0248231i	0.544979	−	0.838450i	$-0.316538\pi$
$677$	−0.947328	−	0.645877i	−0.0364088	−	0.0248231i	−0.581388	+	0.813627i	$0.697490\pi$
$678$		0			0
$679$	−0.830041	+	27.1171i	−0.0318541	+	1.04066i
$680$	11.0995	+	2.53338i	0.425646	+	0.0971509i
$681$		0			0
$682$	−3.08836	−	20.4899i	−0.118259	−	0.784600i
$683$	−7.31713	+	23.7216i	−0.279982	+	0.907680i	0.700930	+	0.713230i	$0.252768\pi$
$683$	−7.31713	+	23.7216i	−0.279982	+	0.907680i	−0.980912	+	0.194450i	$0.937708\pi$
$684$		0			0
$685$			6.27502i			0.239756i
$686$	15.9538	+	0.271240i	0.609121	+	0.0103560i
$687$		0			0
$688$	0.0523183	+	0.698139i	0.00199462	+	0.0266163i
$689$	1.87907	+	0.579616i	0.0715868	+	0.0220816i
$690$		0			0
$691$	16.1556	+	17.4116i	0.614590	+	0.662370i	0.961269	−	0.275614i	$-0.0888810\pi$
$691$	16.1556	+	17.4116i	0.614590	+	0.662370i	−0.346679	+	0.937984i	$0.612691\pi$
$692$	−0.415544	+	1.82062i	−0.0157966	+	0.0692094i
$693$		0			0
$694$	3.79791	+	16.6397i	0.144167	+	0.631636i
$695$	−1.02730	+	1.50677i	−0.0389677	+	0.0571551i
$696$		0			0
$697$	−9.10105	+	6.20499i	−0.344727	+	0.235031i
$698$	−2.27117	−	0.342324i	−0.0859651	−	0.0129572i
$699$		0			0
$700$	0.638666	+	14.4401i	0.0241393	+	0.545783i
$701$	−5.65702	−	11.7469i	−0.213663	−	0.443675i	0.766400	−	0.642364i	$-0.222046\pi$
$701$	−5.65702	−	11.7469i	−0.213663	−	0.443675i	−0.980063	+	0.198689i	$0.936332\pi$
$702$		0			0
$703$	22.1363	−	8.68785i	0.834885	−	0.327668i
$704$	10.0543	+	5.80484i	0.378935	+	0.218778i
$705$		0			0
$706$	6.29246	+	5.01807i	0.236820	+	0.188858i
$707$	−12.8444	−	4.39663i	−0.483062	−	0.165352i
$708$		0			0
$709$	1.09679	−	2.79458i	0.0411909	−	0.104953i	−0.908798	−	0.417236i	$-0.862999\pi$
$709$	1.09679	−	2.79458i	0.0411909	−	0.104953i	0.949989	+	0.312284i	$0.101094\pi$
$710$	−0.680084	+	9.07510i	−0.0255231	+	0.340582i
$711$		0			0
$712$	8.98200	+	3.52518i	0.336615	+	0.132112i
$713$	56.3643	+	70.6786i	2.11086	+	2.64693i
$714$		0			0
$715$	2.19511	−	2.75258i	0.0820925	−	0.102941i
$716$	−13.0874	+	7.55603i	−0.489100	+	0.282382i
$717$		0			0
$718$	−6.65073	−	16.9458i	−0.248203	−	0.632411i
$719$	36.5054	−	11.2604i	1.36142	−	0.419943i	0.473847	−	0.880607i	$-0.342865\pi$
$719$	36.5054	−	11.2604i	1.36142	−	0.419943i	0.887574	+	0.460664i	$0.152389\pi$
$720$		0			0
$721$	12.5024	+	14.3298i	0.465614	+	0.533670i
$722$	−18.5672	+	38.5551i	−0.690998	+	1.43487i
$723$		0			0
$724$	5.39946	+	7.91956i	0.200669	+	0.294328i
$725$	21.6527	−	23.3361i	0.804161	−	0.866679i
$726$		0			0
$727$	14.6295	−	3.33910i	0.542580	−	0.123840i	0.0575578	−	0.998342i	$-0.481669\pi$
$727$	14.6295	−	3.33910i	0.542580	−	0.123840i	0.485022	+	0.874502i	$0.338812\pi$
$728$	−3.30512	+	12.6791i	−0.122496	+	0.469919i
$729$		0			0
$730$	5.27261	−	4.89226i	0.195148	−	0.181071i
$731$	−35.6087	+	5.36715i	−1.31704	+	0.198511i
$732$		0			0
$733$	17.2286	−	1.29110i	0.636351	−	0.0476879i	0.247351	−	0.968926i	$-0.420440\pi$
$733$	17.2286	−	1.29110i	0.636351	−	0.0476879i	0.389000	+	0.921238i	$0.372821\pi$
$734$	22.4571			0.828908
$735$		0			0
$736$	−52.7415			−1.94408
$737$	3.80263	−	0.284967i	0.140072	−	0.0104969i
$738$		0			0
$739$	−9.31553	+	1.40409i	−0.342677	+	0.0516503i	−0.318126	−	0.948048i	$-0.603054\pi$
$739$	−9.31553	+	1.40409i	−0.342677	+	0.0516503i	−0.0245508	+	0.999699i	$0.507816\pi$
$740$	2.14344	−	1.98883i	0.0787946	−	0.0731107i
$741$		0			0
$742$	0.489238	+	2.49277i	0.0179605	+	0.0915125i
$743$	22.9729	−	5.24341i	0.842793	−	0.192362i	0.220736	−	0.975334i	$-0.429154\pi$
$743$	22.9729	−	5.24341i	0.842793	−	0.192362i	0.622057	+	0.782972i	$0.286297\pi$
$744$		0			0
$745$	3.49200	−	3.76349i	0.127937	−	0.137883i
$746$	0.789164	+	1.15749i	0.0288933	+	0.0423787i
$747$		0			0
$748$	6.72953	−	13.9740i	0.246056	−	0.510941i
$749$	−25.3283	+	34.8117i	−0.925478	+	1.27199i
$750$		0			0
$751$	−8.40251	+	2.59183i	−0.306612	+	0.0945773i	−0.444243	−	0.895906i	$-0.646527\pi$
$751$	−8.40251	+	2.59183i	−0.306612	+	0.0945773i	0.137631	+	0.990484i	$0.456051\pi$
$752$	0.243662	+	0.620842i	0.00888545	+	0.0226398i
$753$		0			0
$754$	9.64865	−	5.57065i	0.351383	−	0.202871i
$755$	−6.14303	+	7.70311i	−0.223568	+	0.280345i
$756$		0			0
$757$	29.5264	+	37.0250i	1.07316	+	1.34570i	0.934744	+	0.355321i	$0.115629\pi$
$757$	29.5264	+	37.0250i	1.07316	+	1.34570i	0.138413	+	0.990375i	$0.455800\pi$
$758$	−10.9141	−	4.28346i	−0.396417	−	0.155582i
$759$		0			0
$760$	−1.40810	+	18.7898i	−0.0510771	+	0.681576i
$761$	6.67922	−	17.0184i	0.242122	−	0.616916i	−0.757222	−	0.653158i	$-0.773444\pi$
$761$	6.67922	−	17.0184i	0.242122	−	0.616916i	0.999343	+	0.0362426i	$0.0115389\pi$
$762$		0			0
$763$	20.4171	−	13.0234i	0.739148	−	0.471478i
$764$	−22.3381	−	17.8140i	−0.808164	−	0.644489i
$765$		0			0
$766$	−6.86171	−	3.96161i	−0.247924	−	0.143139i
$767$	6.48848	−	2.54654i	0.234286	−	0.0919503i
$768$		0			0
$769$	−2.71870	−	5.64544i	−0.0980388	−	0.203580i	0.846181	−	0.532896i	$-0.178896\pi$
$769$	−2.71870	−	5.64544i	−0.0980388	−	0.203580i	−0.944220	+	0.329316i	$0.893182\pi$
$770$	4.47454	+	0.815152i	0.161251	+	0.0293760i
$771$		0			0
$772$	−16.8948	−	2.54648i	−0.608057	−	0.0916498i
$773$	−24.2077	+	16.5045i	−0.870691	+	0.593627i	−0.914127	−	0.405429i	$-0.867122\pi$
$773$	−24.2077	+	16.5045i	−0.870691	+	0.593627i	0.0434354	+	0.999056i	$0.486170\pi$
$774$		0			0
$775$	−23.8947	+	35.0471i	−0.858322	+	1.25893i
$776$	−6.40420	−	28.0587i	−0.229898	−	1.00725i
$777$		0			0
$778$	−4.05944	+	17.7856i	−0.145538	+	0.637643i
$779$	−12.3997	−	13.3637i	−0.444267	−	0.478806i
$780$		0			0
$781$	30.6860	+	9.46537i	1.09803	+	0.338698i
$782$	−2.98427	−	39.8223i	−0.106717	−	1.42404i
$783$		0			0
$784$	0.662184	−	0.160644i	0.0236494	−	0.00573729i
$785$			13.0416i			0.465475i
$786$		0			0
$787$	4.57434	−	14.8296i	0.163058	−	0.528620i	−0.836763	−	0.547565i	$-0.815555\pi$
$787$	4.57434	−	14.8296i	0.163058	−	0.528620i	0.999821	+	0.0189457i	$0.00603096\pi$
$788$	−2.26438	−	15.0232i	−0.0806651	−	0.535178i
$789$		0			0
$790$	−1.86432	−	0.425520i	−0.0663296	−	0.0151393i
$791$	10.4874	+	23.5984i	0.372891	+	0.839061i
$792$		0			0
$793$	−11.4081	−	7.77793i	−0.405114	−	0.276202i
$794$	−6.86783	−	6.37241i	−0.243730	−	0.226148i
$795$		0			0
$796$	3.29038	−	21.8302i	0.116624	−	0.773752i
$797$	16.3882	+	7.89216i	0.580501	+	0.279554i	0.701003	−	0.713159i	$-0.252736\pi$
$797$	16.3882	+	7.89216i	0.580501	+	0.279554i	−0.120502	+	0.992713i	$0.538450\pi$
$798$		0			0
$799$	−30.9084	+	14.8847i	−1.09346	+	0.526583i
$800$	−7.29433	−	23.6476i	−0.257894	−	0.836070i
$801$		0			0
$802$	3.02697	−	5.24287i	0.106886	−	0.185132i
$803$	−12.6902	−	21.9801i	−0.447829	−	0.775662i
$804$		0			0
$805$	−18.6839	+	6.68073i	−0.658521	+	0.235465i
$806$	−11.6065	+	9.25590i	−0.408823	+	0.326025i
$807$		0			0
$808$	14.3616	+	1.07625i	0.505240	+	0.0378625i
$809$	43.4636	+	3.25715i	1.52810	+	0.114515i	0.812072	−	0.583557i	$-0.198340\pi$
$809$	43.4636	+	3.25715i	1.52810	+	0.114515i	0.716027	+	0.698073i	$0.245959\pi$
$810$		0			0
$811$	26.7073	−	21.2984i	0.937821	−	0.747887i	−0.0299939	−	0.999550i	$-0.509549\pi$
$811$	26.7073	−	21.2984i	0.937821	−	0.747887i	0.967815	+	0.251663i	$0.0809774\pi$
$812$	−20.7374	−	12.8343i	−0.727741	−	0.450397i
$813$		0			0
$814$	3.04461	+	5.27342i	0.106713	+	0.184833i
$815$	−1.10877	+	1.92044i	−0.0388384	+	0.0672700i
$816$		0			0
$817$	−17.5672	−	56.9515i	−0.614599	−	1.99248i
$818$	−17.1903	+	8.27839i	−0.601043	+	0.289447i
$819$		0			0
$820$	−2.01961	−	0.972591i	−0.0705277	−	0.0339644i
$821$	5.05503	−	33.5379i	0.176422	−	1.17048i	−0.708833	−	0.705376i	$-0.750778\pi$
$821$	5.05503	−	33.5379i	0.176422	−	1.17048i	0.885255	−	0.465106i	$-0.153984\pi$
$822$		0			0
$823$	4.22589	+	3.92105i	0.147305	+	0.136679i	0.750383	−	0.661003i	$-0.229869\pi$
$823$	4.22589	+	3.92105i	0.147305	+	0.136679i	−0.603078	+	0.797682i	$0.706059\pi$
$824$	−16.6686	−	11.3644i	−0.580678	−	0.395899i
$825$		0			0
$826$	6.86499	+	5.82702i	0.238864	+	0.202748i
$827$	−15.6291	−	3.56724i	−0.543476	−	0.124045i	−0.0580357	−	0.998315i	$-0.518484\pi$
$827$	−15.6291	−	3.56724i	−0.543476	−	0.124045i	−0.485441	+	0.874270i	$0.661341\pi$
$828$		0			0
$829$	−1.63202	−	10.8277i	−0.0566823	−	0.376062i	−0.999130	−	0.0417084i	$-0.986720\pi$
$829$	−1.63202	−	10.8277i	−0.0566823	−	0.376062i	0.942448	−	0.334354i	$-0.108518\pi$
$830$	3.14605	−	10.1993i	0.109201	−	0.354021i
$831$		0			0
$832$		−	8.31747i		−	0.288356i
$833$	10.7853	+	33.3481i	0.373690	+	1.15544i
$834$		0			0
$835$	0.156256	+	2.08509i	0.00540745	+	0.0721574i
$836$	24.5291	+	7.56624i	0.848358	+	0.261684i
$837$		0			0
$838$	13.9951	+	15.0831i	0.483453	+	0.521039i
$839$	−6.59770	+	28.9064i	−0.227778	+	0.997959i	0.723669	+	0.690147i	$0.242454\pi$
$839$	−6.59770	+	28.9064i	−0.227778	+	0.997959i	−0.951447	+	0.307813i	$0.900403\pi$
$840$		0			0
$841$	5.49892	+	24.0923i	0.189618	+	0.830770i
$842$	−8.97692	+	13.1667i	−0.309365	+	0.453755i
$843$		0			0
$844$	−13.0076	+	8.86846i	−0.447742	+	0.305265i
$845$	7.92002	+	1.19375i	0.272457	+	0.0410663i
$846$		0			0
$847$	−5.13883	+	12.0003i	−0.176572	+	0.412335i
$848$	0.0470686	+	0.0977389i	0.00161634	+	0.00335637i
$849$		0			0
$850$	17.4423	−	6.84561i	0.598267	−	0.234803i
$851$	−23.0064	−	13.2827i	−0.788648	−	0.455326i
$852$		0			0
$853$	32.4102	+	25.8463i	1.10970	+	0.884959i	0.994114	−	0.108338i	$-0.0345530\pi$
$853$	32.4102	+	25.8463i	1.10970	+	0.884959i	0.115589	+	0.993297i	$0.463124\pi$
$854$	1.87653	−	17.7379i	0.0642134	−	0.606979i
$855$		0			0
$856$	16.6851	−	42.5128i	0.570283	−	1.45306i
$857$	−2.79048	+	37.2364i	−0.0953210	+	1.27197i	0.720414	+	0.693545i	$0.243952\pi$
$857$	−2.79048	+	37.2364i	−0.0953210	+	1.27197i	−0.815735	+	0.578426i	$0.803667\pi$
$858$		0			0
$859$	−7.11666	−	2.79308i	−0.242817	−	0.0952988i	0.240812	−	0.970572i	$-0.422586\pi$
$859$	−7.11666	−	2.79308i	−0.242817	−	0.0952988i	−0.483629	+	0.875273i	$0.660682\pi$
$860$	−4.56914	−	5.72953i	−0.155807	−	0.195375i
$861$		0			0
$862$	0.454432	−	0.569840i	0.0154780	−	0.0194088i
$863$	24.9307	−	14.3938i	0.848652	−	0.489969i	−0.0115441	−	0.999933i	$-0.503675\pi$
$863$	24.9307	−	14.3938i	0.848652	−	0.489969i	0.860196	+	0.509964i	$0.170341\pi$
$864$		0			0
$865$	−0.439457	−	1.11972i	−0.0149420	−	0.0380715i
$866$	−6.71022	+	2.06983i	−0.228023	+	0.0703357i
$867$		0			0
$868$	29.8719	+	12.7919i	1.01392	+	0.434186i
$869$	−2.92773	+	6.07949i	−0.0993164	+	0.206233i
$870$		0			0
$871$	−1.53895	−	2.25723i	−0.0521454	−	0.0764833i
$872$	−17.4738	+	18.8323i	−0.591738	+	0.637742i
$873$		0			0
$874$	64.4350	−	14.7069i	2.17955	−	0.497467i
$875$	−12.0020	−	16.0328i	−0.405742	−	0.542008i
$876$		0			0
$877$	5.16662	−	4.79392i	0.174464	−	0.161879i	−0.588108	−	0.808783i	$-0.700127\pi$
$877$	5.16662	−	4.79392i	0.174464	−	0.161879i	0.762572	+	0.646903i	$0.223936\pi$
$878$	−23.2235	+	3.50037i	−0.783754	+	0.118132i
$879$		0			0
$880$	0.193682	−	0.0145145i	0.00652903	−	0.000489283i
$881$	−5.03384			−0.169595			−0.0847973	−	0.996398i	$-0.527024\pi$
$881$	−5.03384			−0.169595			−0.0847973	+	0.996398i	$0.527024\pi$
$882$		0			0
$883$	36.6086			1.23198			0.615989	−	0.787755i	$-0.288757\pi$
$883$	36.6086			1.23198			0.615989	+	0.787755i	$0.288757\pi$
$884$	−11.0807	+	0.830381i	−0.372683	+	0.0279287i
$885$		0			0
$886$	18.0591	−	2.72196i	0.606706	−	0.0914462i
$887$	−5.45928	+	5.06547i	−0.183305	+	0.170082i	−0.766488	−	0.642259i	$-0.777997\pi$
$887$	−5.45928	+	5.06547i	−0.183305	+	0.170082i	0.583183	+	0.812341i	$0.301807\pi$
$888$		0			0
$889$	−4.15601	+	4.89633i	−0.139388	+	0.164218i
$890$	−2.33937	+	0.533946i	−0.0784158	+	0.0178979i
$891$		0			0
$892$	13.5791	−	14.6347i	0.454661	−	0.490008i
$893$	−31.9837	−	46.9115i	−1.07030	−	1.56983i
$894$		0			0
$895$	4.22346	−	8.77011i	0.141175	−	0.293153i
$896$	−17.0918	+	9.18248i	−0.570995	+	0.306765i
$897$		0			0
$898$	−28.5114	+	8.79461i	−0.951438	+	0.293480i
$899$	−26.1470	−	66.6215i	−0.872052	−	2.22195i
$900$		0			0
$901$	−4.83242	+	2.79000i	−0.160991	+	0.0929484i
$902$	2.91052	−	3.64967i	0.0969097	−	0.121521i
$903$		0			0
$904$	−17.0804	−	21.4181i	−0.568084	−	0.712355i
$905$	−5.74722	−	2.25562i	−0.191044	−	0.0749793i
$906$		0			0
$907$	2.29198	−	30.5843i	0.0761038	−	1.01554i	−0.820195	−	0.572084i	$-0.806135\pi$
$907$	2.29198	−	30.5843i	0.0761038	−	1.01554i	0.896299	−	0.443451i	$-0.146246\pi$
$908$	7.53160	−	19.1902i	0.249945	−	0.636850i
$909$		0			0
$910$	−1.09708	−	3.06819i	−0.0363679	−	0.101709i
$911$	−39.9167	−	31.8325i	−1.32250	−	1.05466i	−0.993911	−	0.110184i	$-0.964856\pi$
$911$	−39.9167	−	31.8325i	−1.32250	−	1.05466i	−0.328587	−	0.944474i	$-0.606573\pi$
$912$		0			0
$913$	−32.6170	−	18.8314i	−1.07947	−	0.623230i
$914$	−12.4774	+	4.89701i	−0.412715	+	0.161979i
$915$		0			0
$916$	−4.24405	−	8.81286i	−0.140227	−	0.291185i
$917$	12.6728	−	3.48820i	0.418492	−	0.115190i
$918$		0			0
$919$	−9.57219	−	1.44278i	−0.315757	−	0.0475928i	−0.0107484	−	0.999942i	$-0.503421\pi$
$919$	−9.57219	−	1.44278i	−0.315757	−	0.0475928i	−0.305009	+	0.952349i	$0.598659\pi$
$920$	17.3919	−	11.8576i	0.573393	−	0.390933i
$921$		0			0
$922$	0.772394	−	1.13289i	0.0254374	−	0.0373099i
$923$	−5.11938	−	22.4295i	−0.168507	−	0.738275i
$924$		0			0
$925$	2.77370	−	12.1524i	0.0911988	−	0.399568i
$926$	−6.83880	−	7.37047i	−0.224737	−	0.242209i
$927$		0			0
$928$	39.8993	+	12.3073i	1.30976	+	0.404007i
$929$	2.47739	+	33.0584i	0.0812804	+	1.08461i	0.877491	+	0.479592i	$0.159215\pi$
$929$	2.47739	+	33.0584i	0.0812804	+	1.08461i	−0.796211	+	0.605019i	$0.793166\pi$
$930$		0			0
$931$	−51.9154	+	25.8767i	−1.70146	+	0.848075i
$932$			15.5426i			0.509114i
$933$		0			0
$934$	−7.43041	+	24.0888i	−0.243130	+	0.788209i
$935$	1.48899	+	9.87882i	0.0486953	+	0.323072i
$936$		0			0
$937$	−8.06607	−	1.84103i	−0.263507	−	0.0601438i	0.0887260	−	0.996056i	$-0.471720\pi$
$937$	−8.06607	−	1.84103i	−0.263507	−	0.0601438i	−0.352233	+	0.935912i	$0.614578\pi$
$938$	1.62785	−	3.13140i	0.0531511	−	0.102244i
$939$		0			0
$940$	−5.76824	−	3.93272i	−0.188139	−	0.128271i
$941$	28.4133	+	26.3637i	0.926248	+	0.859432i	0.990361	−	0.138510i	$-0.0442314\pi$
$941$	28.4133	+	26.3637i	0.926248	+	0.859432i	−0.0641131	+	0.997943i	$0.520422\pi$
$942$		0			0
$943$	−3.03533	+	20.1381i	−0.0988440	+	0.655787i
$944$	0.346450	+	0.166842i	0.0112760	+	0.00543024i
$945$		0			0
$946$	13.7499	−	6.62160i	0.447048	−	0.215287i
$947$	10.0121	+	32.4583i	0.325349	+	1.05475i	0.959539	+	0.281577i	$0.0908575\pi$
$947$	10.0121	+	32.4583i	0.325349	+	1.05475i	−0.634190	+	0.773177i	$0.718666\pi$
$948$		0			0
$949$	−9.09160	+	15.7471i	−0.295126	+	0.511173i
$950$	15.5057	+	26.8566i	0.503071	+	0.871344i
$951$		0			0
$952$	−19.9951	−	31.3468i	−0.648044	−	1.01595i
$953$	20.6388	−	16.4589i	0.668556	−	0.533156i	−0.229349	−	0.973344i	$-0.573660\pi$
$953$	20.6388	−	16.4589i	0.668556	−	0.533156i	0.897905	+	0.440189i	$0.145088\pi$
$954$		0			0
$955$	18.3522	+	1.37531i	0.593864	+	0.0445040i
$956$	−21.4052	−	1.60410i	−0.692293	−	0.0518802i
$957$		0			0
$958$	−23.8741	+	19.0389i	−0.771336	+	0.615120i
$959$	14.3919	−	14.5889i	0.464737	−	0.471101i
$960$		0			0
$961$	32.1812	+	55.7395i	1.03810	+	1.79805i
$962$	2.18123	−	3.77801i	0.0703258	−	0.121808i
$963$		0			0
$964$	4.28718	+	13.8987i	0.138081	+	0.447647i
$965$	9.91545	−	4.77503i	0.319190	−	0.153714i
$966$		0			0
$967$	−32.5434	−	15.6721i	−1.04653	−	0.503980i	−0.170054	−	0.985435i	$-0.554394\pi$
$967$	−32.5434	−	15.6721i	−1.04653	−	0.503980i	−0.876471	+	0.481455i	$0.840109\pi$
$968$	2.06400	−	13.6938i	0.0663396	−	0.440134i
$969$		0			0
$970$	5.24654	+	4.86808i	0.168456	+	0.156304i
$971$	−4.44161	−	3.02824i	−0.142538	−	0.0971809i	0.489951	−	0.871750i	$-0.337015\pi$
$971$	−4.44161	−	3.02824i	−0.142538	−	0.0971809i	−0.632490	+	0.774569i	$0.717967\pi$
$972$		0			0
$973$	5.84420	−	1.14700i	0.187356	−	0.0367711i
$974$	14.5685	+	3.32516i	0.466804	+	0.106545i
$975$		0			0
$976$	−0.113526	−	0.753199i	−0.00363389	−	0.0241093i
$977$	6.00157	−	19.4566i	0.192007	−	0.622472i	−0.807463	−	0.589919i	$-0.799160\pi$
$977$	6.00157	−	19.4566i	0.192007	−	0.622472i	0.999470	−	0.0325537i	$-0.0103640\pi$
$978$		0			0
$979$			8.46711i			0.270610i
$980$	−4.77980	+	5.29401i	−0.152685	+	0.169111i
$981$		0			0
$982$	−0.982692	−	13.1131i	−0.0313590	−	0.418456i
$983$	−0.868828	−	0.267998i	−0.0277113	−	0.00854780i	0.280869	−	0.959746i	$-0.409378\pi$
$983$	−0.868828	−	0.267998i	−0.0277113	−	0.00854780i	−0.308580	+	0.951198i	$0.599854\pi$
$984$		0			0
$985$	6.65626	+	7.17374i	0.212086	+	0.228574i
$986$	−7.03497	+	30.8222i	−0.224039	+	0.981580i
$987$		0			0
$988$	−4.09223	−	17.9292i	−0.130191	−	0.570405i
$989$	−37.5060	+	55.0112i	−1.19262	+	1.74925i
$990$		0			0
$991$	17.2680	−	11.7731i	0.548535	−	0.373985i	−0.257111	−	0.966382i	$-0.582771\pi$
$991$	17.2680	−	11.7731i	0.548535	−	0.373985i	0.805646	+	0.592397i	$0.201818\pi$
$992$	−55.0145	−	8.29210i	−1.74671	−	0.263274i
$993$		0			0
$994$	22.3950	−	19.5391i	0.710327	−	0.619743i
$995$	6.16995	+	12.8120i	0.195601	+	0.406169i
$996$		0			0
$997$	41.0258	−	16.1014i	1.29930	−	0.509938i	0.387992	−	0.921663i	$-0.373169\pi$
$997$	41.0258	−	16.1014i	1.29930	−	0.509938i	0.911308	+	0.411725i	$0.135074\pi$
$998$	8.33864	+	4.81432i	0.263955	+	0.152395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.17.7	✓	216
3.2	odd	2	inner	441.2.bg.a.17.12	yes	216
49.26	odd	42	inner	441.2.bg.a.26.12	yes	216
147.26	even	42	inner	441.2.bg.a.26.7	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.17.7	✓	216	1.1	even	1	trivial
441.2.bg.a.17.12	yes	216	3.2	odd	2	inner
441.2.bg.a.26.7	yes	216	147.26	even	42	inner
441.2.bg.a.26.12	yes	216	49.26	odd	42	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.859142 + 0.0643838i) q^{2} +(-1.24368 + 0.187455i) q^{4} +(0.593873 - 0.551034i) q^{5} +(-2.64451 - 0.0809471i) q^{7} +(2.73633 - 0.624550i) q^{8} +O(q^{10})\)	\(q+(-0.859142 + 0.0643838i) q^{2} +(-1.24368 + 0.187455i) q^{4} +(0.593873 - 0.551034i) q^{5} +(-2.64451 - 0.0809471i) q^{7} +(2.73633 - 0.624550i) q^{8} +(-0.474744 + 0.511652i) q^{10} +(1.38741 + 2.03495i) q^{11} +(0.765584 - 1.58975i) q^{13} +(2.27722 - 0.100719i) q^{14} +(0.0930170 - 0.0286919i) q^{16} +(1.82925 + 4.66086i) q^{17} +(-7.17650 + 4.14336i) q^{19} +(-0.635295 + 0.796635i) q^{20} +(-1.32300 - 1.65899i) q^{22} +(8.61741 + 3.38208i) q^{23} +(-0.324603 + 4.33153i) q^{25} +(-0.555391 + 1.41511i) q^{26} +(3.30411 - 0.395054i) q^{28} +(-5.72992 - 4.56946i) q^{29} +(8.45706 + 4.88268i) q^{31} +(-5.30344 + 2.08145i) q^{32} +(-1.87167 - 3.88657i) q^{34} +(-1.61511 + 1.40914i) q^{35} +(-2.83761 - 0.427702i) q^{37} +(5.89887 - 4.02178i) q^{38} +(1.28089 - 1.87871i) q^{40} +(0.489533 + 2.14478i) q^{41} +(-1.60041 + 7.01184i) q^{43} +(-2.10696 - 2.27076i) q^{44} +(-7.62133 - 2.35087i) q^{46} +(0.512020 + 6.83244i) q^{47} +(6.98690 + 0.428131i) q^{49} -3.74230i q^{50} +(-0.654136 + 2.12066i) q^{52} +(0.166100 + 1.10200i) q^{53} +(1.94527 + 0.443996i) q^{55} +(-7.28682 + 1.43013i) q^{56} +(5.21701 + 3.55690i) q^{58} +(2.89579 + 2.68690i) q^{59} +(1.16627 - 7.73769i) q^{61} +(-7.58018 - 3.65042i) q^{62} +(4.24699 - 2.04524i) q^{64} +(-0.421347 - 1.36597i) q^{65} +(0.774142 - 1.34085i) q^{67} +(-3.14871 - 5.45372i) q^{68} +(1.29688 - 1.31464i) q^{70} +(10.1939 - 8.12937i) q^{71} +(-10.2762 - 0.770098i) q^{73} +(2.46545 + 0.184760i) q^{74} +(8.14859 - 6.49829i) q^{76} +(-3.50429 - 5.49377i) q^{77} +(1.36987 + 2.37268i) q^{79} +(0.0394300 - 0.0682948i) q^{80} +(-0.558668 - 1.81116i) q^{82} +(-13.7776 + 6.63496i) q^{83} +(3.65463 + 1.75998i) q^{85} +(0.923528 - 6.12721i) q^{86} +(5.06734 + 4.70180i) q^{88} +(2.84048 + 1.93661i) q^{89} +(-2.15328 + 4.14215i) q^{91} +(-11.3513 - 2.59086i) q^{92} +(-0.879797 - 5.83707i) q^{94} +(-1.97880 + 6.41512i) q^{95} -10.2541i q^{97} +(-6.03030 + 0.0820171i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

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