LMFDB - Embedded newform 792.2.ce.a.547.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [792,2,Mod(139,792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(792, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 15, 10, 21]))

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

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

chi := DirichletCharacter("792.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.ce (of order $30$, degree $8$, 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:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{30})$
Coefficient field:	16.0.26873856000000000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 8x^{10} - 16x^{8} - 32x^{6} + 128x^{2} + 256 $ x^16 + 2x^14 - 8x^10 - 16x^8 - 32x^6 + 128*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{30}]$

Embedding invariants

Embedding label			547.2
Root			$0.575212 - 1.29195i$ of defining polynomial
Character	$\chi$	$=$	792.547
Dual form			792.2.ce.a.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40647 - 0.147826i) q^{2} +(1.72010 - 0.203149i) q^{3} +(1.95630 - 0.415823i) q^{4} +(2.38923 - 0.539996i) q^{6} +(2.68999 - 0.874032i) q^{8} +(2.91746 - 0.698871i) q^{9} +O(q^{10})$	\(q+(1.40647 - 0.147826i) q^{2} +(1.72010 - 0.203149i) q^{3} +(1.95630 - 0.415823i) q^{4} +(2.38923 - 0.539996i) q^{6} +(2.68999 - 0.874032i) q^{8} +(2.91746 - 0.698871i) q^{9} +(0.417946 - 3.29019i) q^{11} +(3.28054 - 1.11268i) q^{12} +(3.65418 - 1.62695i) q^{16} +(-3.98560 + 5.48571i) q^{17} +(4.00000 - 1.41421i) q^{18} +(-7.49816 + 2.43630i) q^{19} +(0.101453 - 4.68932i) q^{22} +(4.44949 - 2.04989i) q^{24} +(-4.89074 - 1.03956i) q^{25} +(4.87634 - 1.79480i) q^{27} +(4.89898 - 2.82843i) q^{32} +(0.0505103 - 5.74434i) q^{33} +(-4.79469 + 8.30464i) q^{34} +(5.41681 - 2.58035i) q^{36} +(-10.1858 + 4.53499i) q^{38} +(9.49442 + 8.54882i) q^{41} +(9.38094 + 5.41609i) q^{43} +(-0.550510 - 6.61037i) q^{44} +(5.95503 - 3.54085i) q^{48} +(0.731699 - 6.96165i) q^{49} +(-7.03233 - 0.739128i) q^{50} +(-5.74120 + 10.2456i) q^{51} +(6.59309 - 3.24518i) q^{54} +(-12.4026 + 5.71391i) q^{57} +(-6.35294 + 1.35036i) q^{59} +(6.47214 - 4.70228i) q^{64} +(-0.778119 - 8.08669i) q^{66} +(-7.83681 - 13.5738i) q^{67} +(-5.51593 + 12.3890i) q^{68} +(7.23712 - 4.42991i) q^{72} +(-13.9709 - 4.53943i) q^{73} +(-8.62372 - 0.794593i) q^{75} +(-13.6555 + 7.88403i) q^{76} +(8.02316 - 4.07786i) q^{81} +(14.6173 + 10.6201i) q^{82} +(3.37262 + 7.57502i) q^{83} +(13.9946 + 6.23080i) q^{86} +(-1.75146 - 9.21588i) q^{88} -11.2373 q^{89} +(7.85212 - 5.86039i) q^{96} +(1.87345 + 17.8247i) q^{97} -9.89949i q^{98} +(-1.08007 - 9.89108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 - 4 * q^4 + 4 * q^6 - 2 * q^9	$ 16 q + 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9} + 12 q^{11} + 8 q^{12} + 8 q^{16} + 64 q^{18} + 10 q^{19} + 4 q^{22} + 32 q^{24} + 10 q^{25} + 20 q^{27} + 40 q^{33} + 8 q^{34} + 4 q^{36} - 12 q^{38} + 18 q^{41} + 30 q^{43} - 48 q^{44} + 8 q^{48} - 14 q^{49} + 10 q^{51} + 4 q^{54} + 18 q^{57} + 36 q^{59} + 32 q^{64} - 8 q^{66} - 14 q^{67} + 36 q^{68} - 16 q^{72} - 40 q^{75} + 12 q^{76} - 14 q^{81} + 48 q^{82} - 90 q^{83} + 72 q^{86} + 16 q^{88} - 72 q^{89} - 32 q^{96} + 90 q^{97} - 2 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - 4 * q^4 + 4 * q^6 - 2 * q^9 + 12 * q^11 + 8 * q^12 + 8 * q^16 + 64 * q^18 + 10 * q^19 + 4 * q^22 + 32 * q^24 + 10 * q^25 + 20 * q^27 + 40 * q^33 + 8 * q^34 + 4 * q^36 - 12 * q^38 + 18 * q^41 + 30 * q^43 - 48 * q^44 + 8 * q^48 - 14 * q^49 + 10 * q^51 + 4 * q^54 + 18 * q^57 + 36 * q^59 + 32 * q^64 - 8 * q^66 - 14 * q^67 + 36 * q^68 - 16 * q^72 - 40 * q^75 + 12 * q^76 - 14 * q^81 + 48 * q^82 - 90 * q^83 + 72 * q^86 + 16 * q^88 - 72 * q^89 - 32 * q^96 + 90 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.40647	−	0.147826i	0.994522	−	0.104528i
$2$	1.40647	−	0.147826i	0.994522	−	0.104528i
$3$	1.72010	−	0.203149i	0.993098	−	0.117288i
$3$	1.72010	−	0.203149i	0.993098	−	0.117288i
$4$	1.95630	−	0.415823i	0.978148	−	0.207912i
$5$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$5$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$6$	2.38923	−	0.539996i	0.975398	−	0.220452i
$7$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$7$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$8$	2.68999	−	0.874032i	0.951057	−	0.309017i
$9$	2.91746	−	0.698871i	0.972487	−	0.232957i
$10$		0			0
$11$	0.417946	−	3.29019i	0.126015	−	0.992028i
$11$	0.417946	−	3.29019i	0.126015	−	0.992028i
$12$	3.28054	−	1.11268i	0.947011	−	0.321202i
$13$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$13$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$14$		0			0
$15$		0			0
$16$	3.65418	−	1.62695i	0.913545	−	0.406737i
$17$	−3.98560	+	5.48571i	−0.966650	+	1.33048i	−0.0229291	+	0.999737i	$0.507299\pi$
$17$	−3.98560	+	5.48571i	−0.966650	+	1.33048i	−0.943721	+	0.330743i	$0.892701\pi$
$18$	4.00000	−	1.41421i	0.942809	−	0.333333i
$19$	−7.49816	+	2.43630i	−1.72020	+	0.558926i	−0.991977	−	0.126418i	$-0.959652\pi$
$19$	−7.49816	+	2.43630i	−1.72020	+	0.558926i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$		0			0
$22$	0.101453	−	4.68932i	0.0216300	−	0.999766i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	4.44949	−	2.04989i	0.908248	−	0.418432i
$25$	−4.89074	−	1.03956i	−0.978148	−	0.207912i
$26$		0			0
$27$	4.87634	−	1.79480i	0.938452	−	0.345410i
$28$		0			0
$29$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$29$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$30$		0			0
$31$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$31$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$32$	4.89898	−	2.82843i	0.866025	−	0.500000i
$33$	0.0505103	−	5.74434i	0.00879271	−	0.999961i
$34$	−4.79469	+	8.30464i	−0.822282	+	1.42423i
$35$		0			0
$36$	5.41681	−	2.58035i	0.902801	−	0.430058i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$	−10.1858	+	4.53499i	−1.65235	+	0.735673i
$39$		0			0
$40$		0			0
$41$	9.49442	+	8.54882i	1.48278	+	1.33510i	0.787348	+	0.616509i	$0.211454\pi$
$41$	9.49442	+	8.54882i	1.48278	+	1.33510i	0.695432	+	0.718592i	$0.255213\pi$
$42$		0			0
$43$	9.38094	+	5.41609i	1.43058	+	0.825945i	0.997165	−	0.0752492i	$-0.0239752\pi$
$43$	9.38094	+	5.41609i	1.43058	+	0.825945i	0.433415	+	0.901195i	$0.357309\pi$
$44$	−0.550510	−	6.61037i	−0.0829925	−	0.996550i
$45$		0			0
$46$		0			0
$47$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$47$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$48$	5.95503	−	3.54085i	0.859535	−	0.511077i
$49$	0.731699	−	6.96165i	0.104528	−	0.994522i
$50$	−7.03233	−	0.739128i	−0.994522	−	0.104528i
$51$	−5.74120	+	10.2456i	−0.803929	+	1.43467i
$52$		0			0
$53$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$53$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$54$	6.59309	−	3.24518i	0.897206	−	0.441613i
$55$		0			0
$56$		0			0
$57$	−12.4026	+	5.71391i	−1.64277	+	0.756826i
$58$		0			0
$59$	−6.35294	+	1.35036i	−0.827083	+	0.175802i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	−6.35294	+	1.35036i	−0.827083	+	0.175802i	−0.225125	+	0.974330i	$0.572279\pi$
$60$		0			0
$61$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$61$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$62$		0			0
$63$		0			0
$64$	6.47214	−	4.70228i	0.809017	−	0.587785i
$65$		0			0
$66$	−0.778119	−	8.08669i	−0.0957799	−	0.995403i
$67$	−7.83681	−	13.5738i	−0.957419	−	1.65830i	−0.728733	−	0.684798i	$-0.759891\pi$
$67$	−7.83681	−	13.5738i	−0.957419	−	1.65830i	−0.228686	−	0.973500i	$-0.573443\pi$
$68$	−5.51593	+	12.3890i	−0.668904	+	1.50238i
$69$		0			0
$70$		0			0
$71$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$71$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$72$	7.23712	−	4.42991i	0.852903	−	0.522070i
$73$	−13.9709	−	4.53943i	−1.63517	−	0.531300i	−0.659721	−	0.751510i	$-0.729326\pi$
$73$	−13.9709	−	4.53943i	−1.63517	−	0.531300i	−0.975452	+	0.220210i	$0.929326\pi$
$74$		0			0
$75$	−8.62372	−	0.794593i	−0.995782	−	0.0917517i
$76$	−13.6555	+	7.88403i	−1.56640	+	0.904361i
$77$		0			0
$78$		0			0
$79$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$79$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$80$		0			0
$81$	8.02316	−	4.07786i	0.891462	−	0.453095i
$82$	14.6173	+	10.6201i	1.61421	+	1.17279i
$83$	3.37262	+	7.57502i	0.370193	+	0.831466i	0.998565	+	0.0535535i	$0.0170548\pi$
$83$	3.37262	+	7.57502i	0.370193	+	0.831466i	−0.628372	+	0.777913i	$0.716279\pi$
$84$		0			0
$85$		0			0
$86$	13.9946	+	6.23080i	1.50908	+	0.671885i
$87$		0			0
$88$	−1.75146	−	9.21588i	−0.186706	−	0.982416i
$89$	−11.2373			−1.19115			−0.595575	−	0.803300i	$-0.703076\pi$
$89$	−11.2373			−1.19115			−0.595575	+	0.803300i	$0.703076\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	7.85212	−	5.86039i	0.801404	−	0.598123i
$97$	1.87345	+	17.8247i	0.190220	+	1.80982i	0.507673	+	0.861550i	$0.330506\pi$
$97$	1.87345	+	17.8247i	0.190220	+	1.80982i	−0.317453	+	0.948274i	$0.602828\pi$
$98$		−	9.89949i		−	1.00000i
$99$	−1.08007	−	9.89108i	−0.108551	−	0.994091i
$100$	−10.0000			−1.00000
$101$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$101$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$102$	−6.56024	+	15.2588i	−0.649561	+	1.51085i
$103$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$103$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.70681	−	1.20442i	0.358351	−	0.116435i	−0.124308	−	0.992244i	$-0.539671\pi$
$107$	3.70681	−	1.20442i	0.358351	−	0.116435i	0.482659	+	0.875808i	$0.339671\pi$
$108$	8.79324	−	5.53886i	0.846130	−	0.532977i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−10.9217	+	12.1298i	−1.02743	+	1.14108i	−0.0375328	+	0.999295i	$0.511950\pi$
$113$	−10.9217	+	12.1298i	−1.02743	+	1.14108i	−0.989898	+	0.141782i	$0.954717\pi$
$114$	−16.5992	+	9.86985i	−1.55466	+	0.924396i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−8.73558	+	2.83836i	−0.804176	+	0.261292i
$119$		0			0
$120$		0			0
$121$	−10.6506	−	2.75024i	−0.968240	−	0.250022i
$122$		0			0
$123$	18.0680	+	12.7760i	1.62914	+	1.15197i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$127$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$128$	8.40772	−	7.57035i	0.743145	−	0.669131i
$129$	17.2364	+	7.41046i	1.51758	+	0.652455i
$130$		0			0
$131$	11.0408	−	6.37443i	0.964642	−	0.556936i	0.0670435	−	0.997750i	$-0.478643\pi$
$131$	11.0408	−	6.37443i	0.964642	−	0.556936i	0.897599	+	0.440814i	$0.145310\pi$
$132$	−2.28982	−	11.2586i	−0.199303	−	0.979938i
$133$		0			0
$134$	−13.0288	−	17.9325i	−1.12551	−	1.54914i
$135$		0			0
$136$	−5.92656	+	18.2401i	−0.508198	+	1.56407i
$137$	13.4151	−	5.97279i	1.14613	−	0.510290i	0.256307	−	0.966595i	$-0.417494\pi$
$137$	13.4151	−	5.97279i	1.14613	−	0.510290i	0.889823	+	0.456305i	$0.150827\pi$
$138$		0			0
$139$	−3.07916	−	14.4863i	−0.261171	−	1.22871i	−0.891729	−	0.452569i	$-0.850508\pi$
$139$	−3.07916	−	14.4863i	−0.261171	−	1.22871i	0.630559	−	0.776142i	$-0.282826\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	9.52391	−	7.30035i	0.793659	−	0.608363i
$145$		0			0
$146$	−20.3207	−	4.31930i	−1.68175	−	0.357467i
$147$	−0.155658	−	12.1234i	−0.0128385	−	0.999918i
$148$		0			0
$149$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$149$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$150$	−12.2464	+	0.157238i	−0.999918	+	0.0128385i
$151$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$151$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$152$	−18.0406	+	13.1073i	−1.46329	+	1.06314i
$153$	−7.79403	+	18.7898i	−0.630110	+	1.51906i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$157$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	10.6815	−	6.92140i	0.839217	−	0.543796i
$163$	20.0863	−	14.5935i	1.57328	−	1.14305i	0.649347	−	0.760493i	$-0.275042\pi$
$163$	20.0863	−	14.5935i	1.57328	−	1.14305i	0.923931	−	0.382560i	$-0.124958\pi$
$164$	22.1287	+	12.7760i	1.72796	+	0.997639i
$165$		0			0
$166$	5.86325	+	10.1554i	0.455077	+	0.788216i
$167$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$167$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$168$		0			0
$169$	−8.69870	−	9.66088i	−0.669131	−	0.743145i
$170$		0			0
$171$	−20.1729	+	12.3481i	−1.54266	+	0.944280i
$172$	20.6040	+	6.69465i	1.57104	+	0.510462i
$173$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$173$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$174$		0			0
$175$		0			0
$176$	−3.82571	−	12.7029i	−0.288373	−	0.957518i
$177$	−10.6533	+	3.61334i	−0.800755	+	0.271595i
$178$	−15.8049	+	1.66116i	−1.18463	+	0.124509i
$179$	4.09993	+	12.6183i	0.306443	+	0.943135i	0.979135	+	0.203212i	$0.0651381\pi$
$179$	4.09993	+	12.6183i	0.306443	+	0.943135i	−0.672692	+	0.739923i	$0.734862\pi$
$180$		0			0
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	16.3832	+	15.4061i	1.19806	+	1.12661i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$191$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$192$	10.1774	−	9.40318i	0.734493	−	0.678616i
$193$	−27.3870	−	2.87849i	−1.97136	−	0.207198i	−0.971771	−	0.235926i	$-0.924188\pi$
$193$	−27.3870	−	2.87849i	−1.97136	−	0.207198i	−0.999587	+	0.0287278i	$0.990854\pi$
$194$	5.26989	+	24.7929i	0.378356	+	1.78003i
$195$		0			0
$196$	−1.46340	−	13.9233i	−0.104528	−	0.994522i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−2.98124	−	13.7518i	−0.211868	−	0.977298i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−14.0647	+	1.47826i	−0.994522	+	0.104528i
$201$	−16.2376	−	21.7561i	−1.14531	−	1.53456i
$202$		0			0
$203$		0			0
$204$	−6.97112	+	22.4308i	−0.488076	+	1.57047i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.88205	+	25.6886i	0.337699	+	1.77692i
$210$		0			0
$211$	11.7235	−	26.3313i	0.807076	−	1.81272i	0.289192	−	0.957271i	$-0.406614\pi$
$211$	11.7235	−	26.3313i	0.807076	−	1.81272i	0.517884	−	0.855451i	$-0.326720\pi$
$212$		0			0
$213$		0			0
$214$	5.03546	−	2.24193i	0.344217	−	0.153255i
$215$		0			0
$216$	11.5486	−	9.09009i	0.785783	−	0.618502i
$217$		0			0
$218$		0			0
$219$	−24.9535	−	4.97008i	−1.68620	−	0.335847i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$223$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$224$		0			0
$225$	−14.9951	+	0.385122i	−0.999670	+	0.0256748i
$226$	−13.5680	+	18.6747i	−0.902527	+	1.24222i
$227$	17.9744	−	16.1842i	1.19300	−	1.07418i	0.197417	−	0.980320i	$-0.436745\pi$
$227$	17.9744	−	16.1842i	1.19300	−	1.07418i	0.995585	−	0.0938647i	$-0.0299221\pi$
$228$	−21.8872	+	16.3354i	−1.44952	+	1.08184i
$229$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$229$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	17.1894	+	23.6592i	1.12612	+	1.54996i	0.795245	+	0.606288i	$0.207342\pi$
$233$	17.1894	+	23.6592i	1.12612	+	1.54996i	0.330870	+	0.943676i	$0.392658\pi$
$234$		0			0
$235$		0			0
$236$	−11.8667	+	5.28340i	−0.772458	+	0.343920i
$237$		0			0
$238$		0			0
$239$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$239$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$240$		0			0
$241$	−26.5673	−	15.3386i	−1.71135	−	0.988049i	−0.932746	−	0.360535i	$-0.882594\pi$
$241$	−26.5673	−	15.3386i	−1.71135	−	0.988049i	−0.778605	−	0.627514i	$-0.784072\pi$
$242$	−15.3863	−	2.29368i	−0.989070	−	0.147444i
$243$	12.9722	−	8.64420i	0.832167	−	0.554526i
$244$		0			0
$245$		0			0
$246$	27.3007	+	15.2981i	1.74063	+	0.975372i
$247$		0			0
$248$		0			0
$249$	7.34008	+	12.3446i	0.465159	+	0.782308i
$250$		0			0
$251$	24.2255	−	17.6009i	1.52910	−	1.11096i	0.572365	−	0.819999i	$-0.306026\pi$
$251$	24.2255	−	17.6009i	1.52910	−	1.11096i	0.956736	−	0.290958i	$-0.0939741\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	10.7061	−	11.8903i	0.669131	−	0.743145i
$257$	−7.93853	+	1.68739i	−0.495192	+	0.105256i	−0.448736	−	0.893664i	$-0.648126\pi$
$257$	−7.93853	+	1.68739i	−0.495192	+	0.105256i	−0.0464552	+	0.998920i	$0.514792\pi$
$258$	25.3378	+	7.87459i	1.57747	+	0.490250i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	14.5863	−	10.5975i	0.901142	−	0.654718i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	−4.88487	−	15.4964i	−0.300643	−	0.953737i
$265$		0			0
$266$		0			0
$267$	−19.3292	+	2.28284i	−1.18293	+	0.139708i
$268$	−20.9754	−	23.2955i	−1.28128	−	1.42300i
$269$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$269$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$270$		0			0
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$	−5.63915	+	26.5301i	−0.341924	+	1.60863i
$273$		0			0
$274$	17.9850	−	10.3836i	1.08651	−	0.627298i
$275$	−5.46440	+	15.6570i	−0.329516	+	0.944150i
$276$		0			0
$277$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$277$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$278$	−6.47217	−	19.9193i	−0.388175	−	1.19468i
$279$		0			0
$280$		0			0
$281$	13.6105	+	30.5696i	0.811932	+	1.82363i	0.462174	+	0.886789i	$0.347070\pi$
$281$	13.6105	+	30.5696i	0.811932	+	1.82363i	0.349758	+	0.936840i	$0.386264\pi$
$282$		0			0
$283$	18.9174	+	17.0333i	1.12452	+	1.01252i	0.999793	+	0.0203327i	$0.00647255\pi$
$283$	18.9174	+	17.0333i	1.12452	+	1.01252i	0.124728	+	0.992191i	$0.460194\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	12.3159	−	11.6756i	0.725720	−	0.687990i
$289$	−8.95470	−	27.5597i	−0.526747	−	1.62116i
$290$		0			0
$291$	6.84358	+	30.2796i	0.401178	+	1.77502i
$292$	−29.2189	−	3.07103i	−1.70990	−	0.179718i
$293$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$293$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$294$	−2.01107	−	17.0281i	−0.117288	−	0.993098i
$295$		0			0
$296$		0			0
$297$	−3.86719	−	16.7942i	−0.224397	−	0.974498i
$298$		0			0
$299$		0			0
$300$	−17.2010	+	2.03149i	−0.993098	+	0.117288i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−23.4359	+	21.1018i	−1.34414	+	1.21027i
$305$		0			0
$306$	−8.18444	+	27.5793i	−0.467873	+	1.57661i
$307$		−	6.07736i		−	0.346853i	−0.984847	−	0.173427i	$-0.944516\pi$
$307$		−	6.07736i		−	0.346853i	0.984847	−	0.173427i	$-0.0554839\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$311$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$312$		0			0
$313$	16.9297	−	7.53759i	0.956923	−	0.426050i	0.131972	−	0.991253i	$-0.457869\pi$
$313$	16.9297	−	7.53759i	0.956923	−	0.426050i	0.824951	+	0.565204i	$0.191202\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$317$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	6.13140	−	2.82475i	0.342221	−	0.157662i
$322$		0			0
$323$	16.5198	−	50.8429i	0.919189	−	2.82897i
$324$	14.0000	−	11.3137i	0.777778	−	0.628539i
$325$		0			0
$326$	26.0934	−	23.4946i	1.44518	−	1.30124i
$327$		0			0
$328$	33.0119	+	14.6978i	1.82278	+	0.811552i
$329$		0			0
$330$		0			0
$331$	−3.03594	+	5.25840i	−0.166870	+	0.289028i	−0.937318	−	0.348476i	$-0.886699\pi$
$331$	−3.03594	+	5.25840i	−0.166870	+	0.289028i	0.770448	+	0.637503i	$0.220033\pi$
$332$	9.74770	+	13.4166i	0.534975	+	0.736329i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.55877	+	12.0381i	0.139385	+	0.655756i	0.991250	+	0.131995i	$0.0421382\pi$
$337$	2.55877	+	12.0381i	0.139385	+	0.655756i	−0.851865	+	0.523761i	$0.824528\pi$
$338$	−13.6626	−	12.3018i	−0.743145	−	0.669131i
$339$	−16.3223	+	23.0832i	−0.886505	+	1.25371i
$340$		0			0
$341$		0			0
$342$	−26.5472	+	20.3492i	−1.43551	+	1.10036i
$343$		0			0
$344$	29.9685	+	6.37000i	1.61579	+	0.343447i
$345$		0			0
$346$		0			0
$347$	−20.0344	−	2.10570i	−1.07550	−	0.113040i	−0.449822	−	0.893118i	$-0.648512\pi$
$347$	−20.0344	−	2.10570i	−1.07550	−	0.113040i	−0.625682	+	0.780078i	$0.715179\pi$
$348$		0			0
$349$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$349$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$350$		0			0
$351$		0			0
$352$	−7.25854	−	17.3007i	−0.386882	−	0.922129i
$353$	18.4447	−	31.9471i	0.981711	−	1.70037i	0.325986	−	0.945375i	$-0.394304\pi$
$353$	18.4447	−	31.9471i	0.981711	−	1.70037i	0.655725	−	0.754999i	$-0.272363\pi$
$354$	−14.4494	+	6.65688i	−0.767979	+	0.353809i
$355$		0			0
$356$	−21.9835	+	4.67273i	−1.16512	+	0.247654i
$357$		0			0
$358$	7.63172	+	17.1411i	0.403349	+	0.905936i
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$		0			0
$361$	34.9156	−	25.3676i	1.83766	−	1.33514i
$362$		0			0
$363$	−18.8788	−	2.56701i	−0.990882	−	0.134733i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$367$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$368$		0			0
$369$	33.6741	+	18.3055i	1.75301	+	0.952945i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$373$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$374$	25.3199	+	19.2463i	1.30926	+	0.995202i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−10.0406	−	7.29493i	−0.515752	−	0.374715i	0.299249	−	0.954175i	$-0.403264\pi$
$379$	−10.0406	−	7.29493i	−0.515752	−	0.374715i	−0.815001	+	0.579459i	$0.803264\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$383$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$384$	12.9242	−	14.7297i	0.659535	−	0.751674i
$385$		0			0
$386$	−38.9444			−1.98222
$387$	31.1537	+	9.24516i	1.58363	+	0.469958i
$388$	11.0769	+	34.0913i	0.562347	+	1.73073i
$389$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$389$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$390$		0			0
$391$		0			0
$392$	−4.11644	−	19.3663i	−0.207912	−	0.978148i
$393$	17.6963	−	13.2076i	0.892662	−	0.666233i
$394$		0			0
$395$		0			0
$396$	−6.22588	−	18.9008i	−0.312862	−	0.949798i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	−19.5630	+	4.15823i	−0.978148	+	0.207912i
$401$	−4.05088	+	38.5416i	−0.202292	+	1.92468i	0.149813	+	0.988714i	$0.452133\pi$
$401$	−4.05088	+	38.5416i	−0.202292	+	1.92468i	−0.352104	+	0.935961i	$0.614534\pi$
$402$	−26.0537	−	28.1989i	−1.29944	−	1.40643i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−6.48880	+	32.5786i	−0.321243	+	1.61288i
$409$	−0.846824	+	1.90200i	−0.0418728	+	0.0940478i	−0.933271	−	0.359174i	$-0.883059\pi$
$409$	−0.846824	+	1.90200i	−0.0418728	+	0.0940478i	0.891398	+	0.453221i	$0.149725\pi$
$410$		0			0
$411$	21.8619	−	12.9990i	1.07837	−	0.641196i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−8.23931	−	24.2923i	−0.403481	−	1.18960i
$418$	10.6639	+	35.4084i	0.521587	+	1.73188i
$419$	−3.52515	−	6.10573i	−0.172215	−	0.298285i	0.766979	−	0.641672i	$-0.221759\pi$
$419$	−3.52515	−	6.10573i	−0.172215	−	0.298285i	−0.939194	+	0.343387i	$0.888426\pi$
$420$		0			0
$421$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$421$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$422$	12.5962	−	38.7671i	0.613174	−	1.88715i
$423$		0			0
$424$		0			0
$425$	25.1952	−	22.6859i	1.22215	−	1.10043i
$426$		0			0
$427$		0			0
$428$	6.75080	−	3.89757i	0.326312	−	0.188396i
$429$		0			0
$430$		0			0
$431$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$431$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$432$	14.8990	−	14.4921i	0.716827	−	0.697251i
$433$	3.96017	−	12.1881i	0.190314	−	0.585725i	−0.809686	−	0.586864i	$-0.800362\pi$
$433$	3.96017	−	12.1881i	0.190314	−	0.585725i	0.999999	+	0.00113866i	$0.000362448\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−35.8310	−	3.30148i	−1.71207	−	0.157751i
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−2.73059	−	20.8217i	−0.130028	−	0.991510i
$442$		0			0
$443$	−7.04572	−	1.49761i	−0.334752	−	0.0711538i	0.0374690	−	0.999298i	$-0.488070\pi$
$443$	−7.04572	−	1.49761i	−0.334752	−	0.0711538i	−0.372221	+	0.928144i	$0.621404\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−19.3352	+	14.0478i	−0.912485	+	0.662959i	−0.941642	−	0.336616i	$-0.890718\pi$
$449$	−19.3352	+	14.0478i	−0.912485	+	0.662959i	0.0291574	+	0.999575i	$0.490718\pi$
$450$	−21.0331	+	2.75831i	−0.991510	+	0.130028i
$451$	32.0954	−	27.6655i	1.51131	−	1.30272i
$452$	−16.3223	+	28.2710i	−0.767736	+	1.32976i
$453$		0			0
$454$	22.8879	−	25.4196i	1.07418	−	1.19300i
$455$		0			0
$456$	−28.3689	+	26.2107i	−1.32849	+	1.22743i
$457$	9.07420	+	20.3810i	0.424473	+	0.953382i	0.991551	+	0.129718i	$0.0414071\pi$
$457$	9.07420	+	20.3810i	0.424473	+	0.953382i	−0.567078	+	0.823664i	$0.691926\pi$
$458$		0			0
$459$	−9.58937	+	33.9035i	−0.447593	+	1.58248i
$460$		0			0
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$		0			0
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$		0			0
$466$	27.6737	+	30.7348i	1.28196	+	1.42376i
$467$	−9.66321	−	7.02073i	−0.447160	−	0.324881i	0.341313	−	0.939950i	$-0.389128\pi$
$467$	−9.66321	−	7.02073i	−0.447160	−	0.324881i	−0.788474	+	0.615069i	$0.789128\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−15.9091	+	9.18514i	−0.732277	+	0.422780i
$473$	21.7407	−	28.6014i	0.999636	−	1.31509i
$474$		0			0
$475$	39.2042	−	4.12053i	1.79881	−	0.189063i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$479$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$480$		0			0
$481$		0			0
$482$	−39.6335	−	17.6460i	−1.80526	−	0.803751i
$483$		0			0
$484$	−21.9794	−	0.951495i	−0.999064	−	0.0432498i
$485$		0			0
$486$	16.9671	−	14.0754i	0.769644	−	0.638473i
$487$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$487$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$488$		0			0
$489$	31.5856	−	29.1828i	1.42835	−	1.31969i
$490$		0			0
$491$	0.865631	+	4.07247i	0.0390654	+	0.183788i	0.993354	−	0.115098i	$-0.0367182\pi$
$491$	0.865631	+	4.07247i	0.0390654	+	0.183788i	−0.954289	+	0.298886i	$0.903385\pi$
$492$	40.6589	+	17.4805i	1.83305	+	0.788084i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	12.1484	+	16.2772i	0.544384	+	0.729400i
$499$	29.3894	−	6.24692i	1.31565	−	0.279650i	0.503955	−	0.863730i	$-0.331878\pi$
$499$	29.3894	−	6.24692i	1.31565	−	0.279650i	0.811697	+	0.584079i	$0.198544\pi$
$500$		0			0
$501$		0			0
$502$	31.4705	−	28.3362i	1.40460	−	1.26471i
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−16.9252	−	14.8505i	−0.751674	−	0.659535i
$508$		0			0
$509$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$509$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$510$		0			0
$511$		0			0
$512$	13.3001	−	18.3060i	0.587785	−	0.809017i
$513$	−32.1909	+	25.3380i	−1.42126	+	1.11870i
$514$	−10.9158	+	3.54677i	−0.481477	+	0.156441i
$515$		0			0
$516$	36.8009	+	7.32976i	1.62007	+	0.322675i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.72113	−	14.5301i	0.206836	−	0.636577i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$	4.72113	−	14.5301i	0.206836	−	0.636577i	0.999633	−	0.0270907i	$-0.00862429\pi$
$522$		0			0
$523$	−25.8663	+	35.6020i	−1.13106	+	1.55676i	−0.345007	+	0.938600i	$0.612124\pi$
$523$	−25.8663	+	35.6020i	−1.13106	+	1.55676i	−0.786049	+	0.618165i	$0.787876\pi$
$524$	18.9485	−	17.0613i	0.827769	−	0.745326i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−9.16116	−	21.0730i	−0.398688	−	0.917086i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$	−17.5907	+	8.37951i	−0.763373	+	0.363640i
$532$		0			0
$533$		0			0
$534$	−26.8484	+	6.06809i	−1.16185	+	0.262592i
$535$		0			0
$536$	−32.9449	−	29.6637i	−1.42300	−	1.28128i
$537$	9.61566	+	20.8718i	0.414946	+	0.900683i
$538$		0			0
$539$	−22.5993	−	5.31702i	−0.973422	−	0.229020i
$540$		0			0
$541$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$541$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$542$		0			0
$543$		0			0
$544$	−4.00945	+	38.1474i	−0.171904	+	1.63555i
$545$		0			0
$546$		0			0
$547$	−8.28786	+	38.9913i	−0.354363	+	1.66715i	0.334606	+	0.942358i	$0.391397\pi$
$547$	−8.28786	+	38.9913i	−0.354363	+	1.66715i	−0.688969	+	0.724791i	$0.741936\pi$
$548$	23.7603	−	17.2629i	1.01499	−	0.737433i
$549$		0			0
$550$	−5.37100	+	22.8288i	−0.229020	+	0.973422i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−12.0475	−	27.0591i	−0.510927	−	1.14756i
$557$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$557$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	31.3105	+	23.1717i	1.32193	+	0.978311i
$562$	23.6616	+	40.9831i	0.998105	+	1.72877i
$563$	8.69951	−	19.5394i	0.366641	−	0.823488i	−0.632175	−	0.774826i	$-0.717837\pi$
$563$	8.69951	−	19.5394i	0.366641	−	0.823488i	0.998815	−	0.0486624i	$-0.0154959\pi$
$564$		0			0
$565$		0			0
$566$	29.1246	+	21.1603i	1.22420	+	0.889432i
$567$		0			0
$568$		0			0
$569$	9.63728	−	45.3399i	0.404016	−	1.90075i	−0.0294311	−	0.999567i	$-0.509370\pi$
$569$	9.63728	−	45.3399i	0.404016	−	1.90075i	0.433447	−	0.901179i	$-0.357297\pi$
$570$		0			0
$571$	−34.8712	+	20.1329i	−1.45931	+	0.842535i	−0.998978	−	0.0452101i	$-0.985604\pi$
$571$	−34.8712	+	20.1329i	−1.45931	+	0.842535i	−0.460336	+	0.887745i	$0.652271\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	15.5959	−	18.2419i	0.649830	−	0.760080i
$577$	21.1965	+	15.4001i	0.882420	+	0.641116i	0.933891	−	0.357559i	$-0.116391\pi$
$577$	21.1965	+	15.4001i	0.882420	+	0.641116i	−0.0514706	+	0.998675i	$0.516391\pi$
$578$	−16.6685	−	37.4381i	−0.693319	−	1.55722i
$579$	−47.6930	+	0.612356i	−1.98205	+	0.0254486i
$580$		0			0
$581$		0			0
$582$	14.1014	+	41.5756i	0.584520	+	1.72336i
$583$		0			0
$584$	−41.5493			−1.71932
$585$		0			0
$586$		0			0
$587$	−2.76230	−	3.06784i	−0.114012	−	0.126623i	0.683437	−	0.730010i	$-0.260484\pi$
$587$	−2.76230	−	3.06784i	−0.114012	−	0.126623i	−0.797449	+	0.603386i	$0.793818\pi$
$588$	−5.34569	−	23.6521i	−0.220452	−	0.975398i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$			3.13450i			0.128719i	0.997927	+	0.0643593i	$0.0205004\pi$
$593$			3.13450i			0.128719i	−0.997927	+	0.0643593i	$0.979500\pi$
$594$	−7.92168	−	23.0488i	−0.325031	−	0.945703i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$599$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$600$	−23.8923	+	5.39996i	−0.975398	+	0.220452i
$601$	32.6791	−	29.4244i	1.33301	−	1.20025i	0.370553	−	0.928811i	$-0.379168\pi$
$601$	32.6791	−	29.4244i	1.33301	−	1.20025i	0.962457	−	0.271436i	$-0.0874984\pi$
$602$		0			0
$603$	−32.3499	−	34.1240i	−1.31739	−	1.38964i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$607$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$608$	−29.8424	+	33.1434i	−1.21027	+	1.34414i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−7.43421	+	39.9993i	−0.300510	+	1.61687i
$613$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$613$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$614$	−0.898389	−	8.54760i	−0.0362560	−	0.344953i
$615$		0			0
$616$		0			0
$617$	−18.7887	−	32.5429i	−0.756403	−	1.31013i	−0.944674	−	0.328011i	$-0.893622\pi$
$617$	−18.7887	−	32.5429i	−0.756403	−	1.31013i	0.188271	−	0.982117i	$-0.439712\pi$
$618$		0			0
$619$	16.2479	+	3.45360i	0.653058	+	0.138812i	0.522514	−	0.852631i	$-0.324994\pi$
$619$	16.2479	+	3.45360i	0.653058	+	0.138812i	0.130544	+	0.991442i	$0.458328\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	22.8386	+	10.1684i	0.913545	+	0.406737i
$626$	22.6968	−	13.1040i	0.907147	−	0.523741i
$627$	13.6162	+	43.1951i	0.543779	+	1.72504i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$631$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$632$		0			0
$633$	14.8163	−	47.6740i	0.588895	−	1.89487i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	26.2776	+	5.58548i	1.03790	+	0.220613i	0.695189	−	0.718827i	$-0.255321\pi$
$641$	26.2776	+	5.58548i	1.03790	+	0.220613i	0.342714	+	0.939440i	$0.388654\pi$
$642$	8.20604	−	4.87929i	0.323866	−	0.192570i
$643$	−4.41382	+	41.9947i	−0.174064	+	1.65611i	0.463786	+	0.885948i	$0.346491\pi$
$643$	−4.41382	+	41.9947i	−0.174064	+	1.65611i	−0.637850	+	0.770161i	$0.720176\pi$
$644$		0			0
$645$		0			0
$646$	15.7187	−	73.9508i	0.618445	−	2.90956i
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$	18.0181	−	17.9819i	0.707817	−	0.706396i
$649$	1.78775	+	21.4667i	0.0701752	+	0.842643i
$650$		0			0
$651$		0			0
$652$	33.2263	−	36.9016i	1.30124	−	1.44518i
$653$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$653$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$654$		0			0
$655$		0			0
$656$	48.6028	+	15.7920i	1.89762	+	0.616575i
$657$	−43.9321	−	3.47974i	−1.71396	−	0.135758i
$658$		0			0
$659$	−27.6934	−	15.9888i	−1.07878	−	0.622834i	−0.148214	−	0.988955i	$-0.547352\pi$
$659$	−27.6934	−	15.9888i	−1.07878	−	0.622834i	−0.930567	+	0.366121i	$0.880686\pi$
$660$		0			0
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$	−3.49262	+	7.84455i	−0.135744	+	0.304887i
$663$		0			0
$664$	15.6931	+	17.4290i	0.609011	+	0.676376i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	25.1049	−	2.63863i	0.967721	−	0.101712i	0.392538	−	0.919736i	$-0.371597\pi$
$673$	25.1049	−	2.63863i	0.967721	−	0.101712i	0.575184	+	0.818024i	$0.304931\pi$
$674$	5.37836	+	16.5529i	0.207167	+	0.637594i
$675$	−25.7147	+	3.70867i	−0.989759	+	0.142747i
$676$	−21.0344	−	15.2824i	−0.809017	−	0.587785i
$677$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$677$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$678$	−19.5445	+	34.8786i	−0.750600	+	1.33950i
$679$		0			0
$680$		0			0
$681$	27.6299	−	31.4899i	1.05878	−	1.20669i
$682$		0			0
$683$	47.9444			1.83454			0.917270	−	0.398265i	$-0.130387\pi$
$683$	47.9444			1.83454			0.917270	+	0.398265i	$0.130387\pi$
$684$	−34.3296	+	32.5448i	−1.31263	+	1.24438i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	43.0913	+	4.52908i	1.64284	+	0.172670i
$689$		0			0
$690$		0			0
$691$	4.01648	+	38.2142i	0.152794	+	1.45374i	0.755172	+	0.655527i	$0.227553\pi$
$691$	4.01648	+	38.2142i	0.152794	+	1.45374i	−0.602378	+	0.798211i	$0.705780\pi$
$692$		0			0
$693$		0			0
$694$	−28.4890			−1.08143
$695$		0			0
$696$		0			0
$697$	−84.7373	+	18.0115i	−3.20965	+	0.682233i
$698$		0			0
$699$	34.3738	+	37.2041i	1.30013	+	1.40719i
$700$		0			0
$701$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$701$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$702$		0			0
$703$		0			0
$704$	−12.7664	−	23.2598i	−0.481151	−	0.876638i
$705$		0			0
$706$	21.2192	−	47.6592i	0.798596	−	1.79368i
$707$		0			0
$708$	−19.3386	+	11.4987i	−0.726788	+	0.432147i
$709$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$709$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$710$		0			0
$711$		0			0
$712$	−30.2282	+	9.82175i	−1.13285	+	0.368086i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	13.2677	+	22.9802i	0.495835	+	0.858812i
$717$		0			0
$718$		0			0
$719$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$719$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$720$		0			0
$721$		0			0
$722$	45.3576	−	40.8401i	1.68803	−	1.51991i
$723$	−48.8144	−	20.9868i	−1.81543	−	0.780508i
$724$		0			0
$725$		0			0
$726$	−26.9319	−	0.819642i	−0.999537	−	0.0304198i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	20.5574	−	17.5041i	0.761384	−	0.648301i
$730$		0			0
$731$	−67.0997	+	29.8747i	−2.48177	+	1.10496i
$732$		0			0
$733$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$733$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−47.9355	+	20.1115i	−1.76573	+	0.740815i
$738$	50.0675	+	20.7681i	1.84301	+	0.764485i
$739$	1.83500	+	2.52566i	0.0675015	+	0.0929078i	0.841433	−	0.540362i	$-0.181713\pi$
$739$	1.83500	+	2.52566i	0.0675015	+	0.0929078i	−0.773931	+	0.633269i	$0.781713\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$743$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	15.1334	+	19.7428i	0.553703	+	0.722351i
$748$	38.4567	+	23.3263i	1.40611	+	0.852895i
$749$		0			0
$750$		0			0
$751$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$751$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$752$		0			0
$753$	38.0946	−	35.1966i	1.38825	−	1.28263i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$757$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$758$	−15.2002	−	8.77582i	−0.552095	−	0.318752i
$759$		0			0
$760$		0			0
$761$	−19.4668	+	43.7231i	−0.705671	+	1.58496i	0.101630	+	0.994822i	$0.467594\pi$
$761$	−19.4668	+	43.7231i	−0.705671	+	1.58496i	−0.807301	+	0.590140i	$0.799073\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	16.0000	−	22.6274i	0.577350	−	0.816497i
$769$	−44.0908	+	25.4558i	−1.58996	+	0.917961i	−0.596643	+	0.802507i	$0.703499\pi$
$769$	−44.0908	+	25.4558i	−1.58996	+	0.917961i	−0.993313	+	0.115454i	$0.963168\pi$
$770$		0			0
$771$	−13.3122	+	4.51517i	−0.479428	+	0.162610i
$772$	−54.7740	+	5.75698i	−1.97136	+	0.207198i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	45.1832	+	8.39770i	1.62408	+	0.301849i
$775$		0			0
$776$	20.6189	+	46.3109i	0.740176	+	1.66246i
$777$		0			0
$778$		0			0
$779$	−92.0182	−	40.9691i	−3.29689	−	1.46787i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−8.65248	−	26.6296i	−0.309017	−	0.951057i
$785$		0			0
$786$	22.9369	−	21.1920i	0.818132	−	0.755892i
$787$	−39.4691	−	4.14837i	−1.40692	−	0.147874i	−0.629572	−	0.776942i	$-0.716770\pi$
$787$	−39.4691	−	4.14837i	−1.40692	−	0.147874i	−0.777350	+	0.629068i	$0.783437\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−11.5505	−	25.6629i	−0.410430	−	0.911892i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$797$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$798$		0			0
$799$		0			0
$800$	−26.8999	+	8.74032i	−0.951057	+	0.309017i
$801$	−32.7844	+	7.85341i	−1.15838	+	0.277487i
$802$			54.8063i			1.93528i
$803$	−20.7747	+	44.0697i	−0.733122	+	1.55519i
$804$	−40.8122	−	35.8094i	−1.43933	−	1.26290i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−24.8696	+	34.2300i	−0.874367	+	1.20346i	0.103582	+	0.994621i	$0.466969\pi$
$809$	−24.8696	+	34.2300i	−0.874367	+	1.20346i	−0.977949	+	0.208842i	$0.933031\pi$
$810$		0			0
$811$	−22.1620	+	7.20086i	−0.778212	+	0.252856i	−0.671076	−	0.741388i	$-0.734168\pi$
$811$	−22.1620	+	7.20086i	−0.778212	+	0.252856i	−0.107135	+	0.994244i	$0.534168\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−4.31032	+	46.7800i	−0.150892	+	1.63763i
$817$	−83.5350	−	17.7559i	−2.92252	−	0.621201i
$818$	−0.909866	+	2.80028i	−0.0318127	+	0.0979094i
$819$		0			0
$820$		0			0
$821$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$821$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$822$	28.8265	−	21.5145i	1.00544	−	0.750403i
$823$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$823$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$824$		0			0
$825$	−6.21861	+	28.0416i	−0.216504	+	0.976282i
$826$		0			0
$827$	−33.7831	−	46.4985i	−1.17475	−	1.61691i	−0.617521	−	0.786554i	$-0.711863\pi$
$827$	−33.7831	−	46.4985i	−1.17475	−	1.61691i	−0.557233	−	0.830356i	$-0.688137\pi$
$828$		0			0
$829$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$829$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	35.2733	+	31.7603i	1.22215	+	1.10043i
$834$	−15.1793	−	32.9483i	−0.525617	−	1.14091i
$835$		0			0
$836$	20.2327	+	48.2244i	0.699761	+	1.66788i
$837$		0			0
$838$	−5.86058	−	8.06640i	−0.202451	−	0.278649i
$839$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$839$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$840$		0			0
$841$	3.03133	−	28.8411i	0.104528	−	0.994522i
$842$		0			0
$843$	29.6215	+	49.8177i	1.02022	+	1.71581i
$844$	11.9854	−	56.3867i	0.412553	−	1.94091i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	36.0000	+	25.4558i	1.23552	+	0.873642i
$850$	32.0827	−	35.6315i	1.10043	−	1.22215i
$851$		0			0
$852$		0			0
$853$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$853$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$854$		0			0
$855$		0			0
$856$	8.91861	−	6.47975i	0.304832	−	0.221473i
$857$	−43.3414	−	25.0232i	−1.48051	−	0.854776i	−0.480759	−	0.876853i	$-0.659639\pi$
$857$	−43.3414	−	25.0232i	−1.48051	−	0.854776i	−0.999756	+	0.0220773i	$0.992972\pi$
$858$		0			0
$859$	27.4842	+	47.6040i	0.937748	+	1.62423i	0.769658	+	0.638456i	$0.220427\pi$
$859$	27.4842	+	47.6040i	0.937748	+	1.62423i	0.168090	+	0.985772i	$0.446240\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$863$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$864$	18.8126	−	22.5851i	0.640018	−	0.768360i
$865$		0			0
$866$	3.76812	−	17.7276i	0.128046	−	0.602410i
$867$	−21.0017	−	45.5862i	−0.713254	−	1.54819i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	17.9229	+	50.6936i	0.606598	+	1.71572i
$874$		0			0
$875$		0			0
$876$	−50.8831	+	0.653315i	−1.71918	+	0.0220735i
$877$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$877$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−47.8125			−1.61084			−0.805421	−	0.592703i	$-0.798061\pi$
$881$	−47.8125			−1.61084			−0.805421	+	0.592703i	$0.798061\pi$
$882$	−6.91847	−	28.8814i	−0.232957	−	0.972487i
$883$	−18.3187	−	56.3792i	−0.616474	−	1.89731i	−0.375763	−	0.926716i	$-0.622619\pi$
$883$	−18.3187	−	56.3792i	−0.616474	−	1.89731i	−0.240711	−	0.970597i	$-0.577381\pi$
$884$		0			0
$885$		0			0
$886$	−10.1310	−	1.06481i	−0.340356	−	0.0357729i
$887$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$887$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−10.0637	−	28.1020i	−0.337145	−	0.941453i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−25.1177	+	22.6161i	−0.838188	+	0.754708i
$899$		0			0
$900$	−29.1746	+	6.98871i	−0.972487	+	0.232957i
$901$		0			0
$902$	41.0514	−	43.6551i	1.36686	−	1.45355i
$903$		0			0
$904$	−18.7776	+	42.1751i	−0.624532	+	1.40272i
$905$		0			0
$906$		0			0
$907$	−2.34585	+	1.04444i	−0.0778925	+	0.0346800i	−0.445313	−	0.895375i	$-0.646908\pi$
$907$	−2.34585	+	1.04444i	−0.0778925	+	0.0346800i	0.367421	+	0.930055i	$0.380241\pi$
$908$	28.4334	−	39.1353i	0.943597	−	1.29875i
$909$		0			0
$910$		0			0
$911$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$911$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$912$	−36.0252	+	41.0581i	−1.19291	+	1.35957i
$913$	26.3328	−	7.93058i	0.871488	−	0.262464i
$914$	15.7754	+	27.3238i	0.521803	+	0.903790i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−8.47532	+	49.1017i	−0.279727	+	1.62060i
$919$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$919$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$920$		0			0
$921$	−1.23461	−	10.4536i	−0.0406817	−	0.344459i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	9.33006	−	4.15401i	0.306109	−	0.136289i	−0.247933	−	0.968777i	$-0.579751\pi$
$929$	9.33006	−	4.15401i	0.306109	−	0.136289i	0.554042	+	0.832489i	$0.313085\pi$
$930$		0			0
$931$	11.4743	+	53.9822i	0.376054	+	1.76920i
$932$	43.4656	+	39.1366i	1.42376	+	1.28196i
$933$		0			0
$934$	−14.6288	−	8.44596i	−0.478670	−	0.276360i
$935$		0			0
$936$		0			0
$937$	9.75920	+	13.4324i	0.318819	+	0.438817i	0.938106	−	0.346348i	$-0.112578\pi$
$937$	9.75920	+	13.4324i	0.318819	+	0.438817i	−0.619287	+	0.785165i	$0.712578\pi$
$938$		0			0
$939$	27.5895	−	16.4046i	0.900348	−	0.535345i
$940$		0			0
$941$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$941$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$942$		0			0
$943$		0			0
$944$	−21.0178	+	15.2704i	−0.684073	+	0.497008i
$945$		0			0
$946$	26.3495	−	43.4407i	0.856696	−	1.41238i
$947$	−9.08561	+	15.7367i	−0.295243	+	0.511376i	−0.975041	−	0.222023i	$-0.928734\pi$
$947$	−9.08561	+	15.7367i	−0.295243	+	0.511376i	0.679799	+	0.733399i	$0.262067\pi$
$948$		0			0
$949$		0			0
$950$	54.5303	−	11.5908i	1.76920	−	0.376054i
$951$		0			0
$952$		0			0
$953$	35.2267	+	11.4458i	1.14110	+	0.370767i	0.817785	−	0.575523i	$-0.195202\pi$
$953$	35.2267	+	11.4458i	1.14110	+	0.370767i	0.323318	+	0.946290i	$0.395202\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	20.7430	+	23.0375i	0.669131	+	0.743145i
$962$		0			0
$963$	9.97275	−	6.10442i	0.321367	−	0.196712i
$964$	−58.3517	−	18.9596i	−1.87938	−	0.610648i
$965$		0			0
$966$		0			0
$967$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$967$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$968$	−31.0540	+	1.91087i	−0.998112	+	0.0614178i
$969$	18.0871	−	90.8106i	0.581040	−	2.91726i
$970$		0			0
$971$	16.6869	+	51.3571i	0.535509	+	1.64813i	0.742547	+	0.669793i	$0.233617\pi$
$971$	16.6869	+	51.3571i	0.535509	+	1.64813i	−0.207039	+	0.978333i	$0.566383\pi$
$972$	21.7830	−	22.3047i	0.698689	−	0.715425i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	46.4892	+	20.6983i	1.48732	+	0.662198i	0.979898	−	0.199499i	$-0.0639313\pi$
$977$	46.4892	+	20.6983i	1.48732	+	0.662198i	0.507423	+	0.861697i	$0.330598\pi$
$978$	40.1102	−	45.7137i	1.28258	−	1.46176i
$979$	−4.69658	+	36.9728i	−0.150103	+	1.18165i
$980$		0			0
$981$		0			0
$982$	1.81950	+	5.59983i	0.0580625	+	0.178698i
$983$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$983$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$984$	59.7695	+	18.5754i	1.90538	+	0.592161i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$	−4.15387	+	9.66169i	−0.131819	+	0.306605i
$994$		0			0
$995$		0			0
$996$	19.4925	+	21.0975i	0.617645	+	0.668501i
$997$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$997$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$998$	40.4118	−	13.1306i	1.27921	−	0.415642i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.ce.a.547.2	yes	16
8.3	odd	2	CM	792.2.ce.a.547.2	yes	16
9.4	even	3		792.2.ce.b.283.1	yes	16
11.7	odd	10		792.2.ce.b.403.1	yes	16
72.67	odd	6		792.2.ce.b.283.1	yes	16
88.51	even	10		792.2.ce.b.403.1	yes	16
99.40	odd	30	inner	792.2.ce.a.139.2	✓	16
792.139	even	30	inner	792.2.ce.a.139.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.ce.a.139.2	✓	16	99.40	odd	30	inner
792.2.ce.a.139.2	✓	16	792.139	even	30	inner
792.2.ce.a.547.2	yes	16	1.1	even	1	trivial
792.2.ce.a.547.2	yes	16	8.3	odd	2	CM
792.2.ce.b.283.1	yes	16	9.4	even	3
792.2.ce.b.283.1	yes	16	72.67	odd	6
792.2.ce.b.403.1	yes	16	11.7	odd	10
792.2.ce.b.403.1	yes	16	88.51	even	10

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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.ce (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40647 - 0.147826i) q^{2} +(1.72010 - 0.203149i) q^{3} +(1.95630 - 0.415823i) q^{4} +(2.38923 - 0.539996i) q^{6} +(2.68999 - 0.874032i) q^{8} +(2.91746 - 0.698871i) q^{9} +O(q^{10})\)	\(q+(1.40647 - 0.147826i) q^{2} +(1.72010 - 0.203149i) q^{3} +(1.95630 - 0.415823i) q^{4} +(2.38923 - 0.539996i) q^{6} +(2.68999 - 0.874032i) q^{8} +(2.91746 - 0.698871i) q^{9} +(0.417946 - 3.29019i) q^{11} +(3.28054 - 1.11268i) q^{12} +(3.65418 - 1.62695i) q^{16} +(-3.98560 + 5.48571i) q^{17} +(4.00000 - 1.41421i) q^{18} +(-7.49816 + 2.43630i) q^{19} +(0.101453 - 4.68932i) q^{22} +(4.44949 - 2.04989i) q^{24} +(-4.89074 - 1.03956i) q^{25} +(4.87634 - 1.79480i) q^{27} +(4.89898 - 2.82843i) q^{32} +(0.0505103 - 5.74434i) q^{33} +(-4.79469 + 8.30464i) q^{34} +(5.41681 - 2.58035i) q^{36} +(-10.1858 + 4.53499i) q^{38} +(9.49442 + 8.54882i) q^{41} +(9.38094 + 5.41609i) q^{43} +(-0.550510 - 6.61037i) q^{44} +(5.95503 - 3.54085i) q^{48} +(0.731699 - 6.96165i) q^{49} +(-7.03233 - 0.739128i) q^{50} +(-5.74120 + 10.2456i) q^{51} +(6.59309 - 3.24518i) q^{54} +(-12.4026 + 5.71391i) q^{57} +(-6.35294 + 1.35036i) q^{59} +(6.47214 - 4.70228i) q^{64} +(-0.778119 - 8.08669i) q^{66} +(-7.83681 - 13.5738i) q^{67} +(-5.51593 + 12.3890i) q^{68} +(7.23712 - 4.42991i) q^{72} +(-13.9709 - 4.53943i) q^{73} +(-8.62372 - 0.794593i) q^{75} +(-13.6555 + 7.88403i) q^{76} +(8.02316 - 4.07786i) q^{81} +(14.6173 + 10.6201i) q^{82} +(3.37262 + 7.57502i) q^{83} +(13.9946 + 6.23080i) q^{86} +(-1.75146 - 9.21588i) q^{88} -11.2373 q^{89} +(7.85212 - 5.86039i) q^{96} +(1.87345 + 17.8247i) q^{97} -9.89949i q^{98} +(-1.08007 - 9.89108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 - 4 * q^4 + 4 * q^6 - 2 * q^9	\( 16 q + 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9} + 12 q^{11} + 8 q^{12} + 8 q^{16} + 64 q^{18} + 10 q^{19} + 4 q^{22} + 32 q^{24} + 10 q^{25} + 20 q^{27} + 40 q^{33} + 8 q^{34} + 4 q^{36} - 12 q^{38} + 18 q^{41} + 30 q^{43} - 48 q^{44} + 8 q^{48} - 14 q^{49} + 10 q^{51} + 4 q^{54} + 18 q^{57} + 36 q^{59} + 32 q^{64} - 8 q^{66} - 14 q^{67} + 36 q^{68} - 16 q^{72} - 40 q^{75} + 12 q^{76} - 14 q^{81} + 48 q^{82} - 90 q^{83} + 72 q^{86} + 16 q^{88} - 72 q^{89} - 32 q^{96} + 90 q^{97} - 2 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - 4 * q^4 + 4 * q^6 - 2 * q^9 + 12 * q^11 + 8 * q^12 + 8 * q^16 + 64 * q^18 + 10 * q^19 + 4 * q^22 + 32 * q^24 + 10 * q^25 + 20 * q^27 + 40 * q^33 + 8 * q^34 + 4 * q^36 - 12 * q^38 + 18 * q^41 + 30 * q^43 - 48 * q^44 + 8 * q^48 - 14 * q^49 + 10 * q^51 + 4 * q^54 + 18 * q^57 + 36 * q^59 + 32 * q^64 - 8 * q^66 - 14 * q^67 + 36 * q^68 - 16 * q^72 - 40 * q^75 + 12 * q^76 - 14 * q^81 + 48 * q^82 - 90 * q^83 + 72 * q^86 + 16 * q^88 - 72 * q^89 - 32 * q^96 + 90 * q^97 - 2 * q^99

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