LMFDB - Embedded newform 792.2.ce.a.283.1

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			283.1
Root			$-1.40647 + 0.147826i$ of defining polynomial
Character	$\chi$	$=$	792.283
Dual form			792.2.ce.a.403.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.575212 + 1.29195i) q^{2} +(-0.684116 + 1.59122i) q^{3} +(-1.33826 - 1.48629i) q^{4} +(-1.66226 - 1.79913i) q^{6} +(2.68999 - 0.874032i) q^{8} +(-2.06397 - 2.17716i) q^{9} +O(q^{10})$	\(q+(-0.575212 + 1.29195i) q^{2} +(-0.684116 + 1.59122i) q^{3} +(-1.33826 - 1.48629i) q^{4} +(-1.66226 - 1.79913i) q^{6} +(2.68999 - 0.874032i) q^{8} +(-2.06397 - 2.17716i) q^{9} +(0.417946 - 3.29019i) q^{11} +(3.28054 - 1.11268i) q^{12} +(-0.418114 + 3.97809i) q^{16} +(-0.395988 + 0.545030i) q^{17} +(4.00000 - 1.41421i) q^{18} +(6.81342 - 2.21381i) q^{19} +(4.01034 + 2.43252i) q^{22} +(-0.449490 + 4.87832i) q^{24} +(3.34565 - 3.71572i) q^{25} +(4.87634 - 1.79480i) q^{27} +(-4.89898 - 2.82843i) q^{32} +(4.94949 + 2.91591i) q^{33} +(-0.476374 - 0.825104i) q^{34} +(-0.473759 + 5.98127i) q^{36} +(-1.05903 + 10.0760i) q^{38} +(-1.48651 + 6.99350i) q^{41} +(10.2356 - 5.90953i) q^{43} +(-5.44949 + 3.78194i) q^{44} +(-6.04398 - 3.38679i) q^{48} +(-6.39482 + 2.84716i) q^{49} +(2.87606 + 6.45974i) q^{50} +(-0.596362 - 1.00297i) q^{51} +(-0.486138 + 7.33237i) q^{54} +(-1.13850 + 12.3562i) q^{57} +(5.89451 + 6.54651i) q^{59} +(6.47214 - 4.70228i) q^{64} +(-6.61422 + 4.71722i) q^{66} +(5.96494 - 10.3316i) q^{67} +(1.34001 - 0.140841i) q^{68} +(-7.45498 - 4.05257i) q^{72} +(-0.204607 - 0.0664810i) q^{73} +(3.62372 + 7.86566i) q^{75} +(-12.4085 - 7.16405i) q^{76} +(-0.480052 + 8.98719i) q^{81} +(-8.18018 - 5.94325i) q^{82} +(-8.24647 - 0.866738i) q^{83} +(1.74716 + 16.6231i) q^{86} +(-1.75146 - 9.21588i) q^{88} -11.2373 q^{89} +(7.85212 - 5.86039i) q^{96} +(14.6514 + 6.52324i) q^{97} -9.89949i q^{98} +(-8.02589 + 5.88091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.575212	+	1.29195i	−0.406737	+	0.913545i
$2$	−0.575212	+	1.29195i	−0.406737	+	0.913545i
$3$	−0.684116	+	1.59122i	−0.394975	+	0.918692i
$3$	−0.684116	+	1.59122i	−0.394975	+	0.918692i
$4$	−1.33826	−	1.48629i	−0.669131	−	0.743145i
$5$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$5$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$6$	−1.66226	−	1.79913i	−0.678616	−	0.734493i
$7$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$7$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$8$	2.68999	−	0.874032i	0.951057	−	0.309017i
$9$	−2.06397	−	2.17716i	−0.687990	−	0.725720i
$10$		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		0.994522	−	0.104528i	$-0.0333333\pi$
$13$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$14$		0			0
$15$		0			0
$16$	−0.418114	+	3.97809i	−0.104528	+	0.994522i
$17$	−0.395988	+	0.545030i	−0.0960411	+	0.132189i	−0.854333	−	0.519726i	$-0.826034\pi$
$17$	−0.395988	+	0.545030i	−0.0960411	+	0.132189i	0.758292	+	0.651915i	$0.226034\pi$
$18$	4.00000	−	1.41421i	0.942809	−	0.333333i
$19$	6.81342	−	2.21381i	1.56311	−	0.507884i	0.605470	−	0.795868i	$-0.292985\pi$
$19$	6.81342	−	2.21381i	1.56311	−	0.507884i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$		0			0
$22$	4.01034	+	2.43252i	0.855008	+	0.518615i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	−0.449490	+	4.87832i	−0.0917517	+	0.995782i
$25$	3.34565	−	3.71572i	0.669131	−	0.743145i
$26$		0			0
$27$	4.87634	−	1.79480i	0.938452	−	0.345410i
$28$		0			0
$29$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$29$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$30$		0			0
$31$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$31$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$32$	−4.89898	−	2.82843i	−0.866025	−	0.500000i
$33$	4.94949	+	2.91591i	0.861596	+	0.507595i
$34$	−0.476374	−	0.825104i	−0.0816975	−	0.141504i
$35$		0			0
$36$	−0.473759	+	5.98127i	−0.0789598	+	0.996878i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$	−1.05903	+	10.0760i	−0.171797	+	1.63454i
$39$		0			0
$40$		0			0
$41$	−1.48651	+	6.99350i	−0.232154	+	1.09220i	0.695432	+	0.718592i	$0.255213\pi$
$41$	−1.48651	+	6.99350i	−0.232154	+	1.09220i	−0.927586	+	0.373609i	$0.878120\pi$
$42$		0			0
$43$	10.2356	−	5.90953i	1.56091	−	0.901195i	0.563750	−	0.825945i	$-0.309358\pi$
$43$	10.2356	−	5.90953i	1.56091	−	0.901195i	0.997165	−	0.0752492i	$-0.0239752\pi$
$44$	−5.44949	+	3.78194i	−0.821541	+	0.570149i
$45$		0			0
$46$		0			0
$47$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$47$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$48$	−6.04398	−	3.38679i	−0.872373	−	0.488840i
$49$	−6.39482	+	2.84716i	−0.913545	+	0.406737i
$50$	2.87606	+	6.45974i	0.406737	+	0.913545i
$51$	−0.596362	−	1.00297i	−0.0835074	−	0.140444i
$52$		0			0
$53$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$53$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$54$	−0.486138	+	7.33237i	−0.0661549	+	0.997809i
$55$		0			0
$56$		0			0
$57$	−1.13850	+	12.3562i	−0.150798	+	1.63661i
$58$		0			0
$59$	5.89451	+	6.54651i	0.767399	+	0.852283i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	5.89451	+	6.54651i	0.767399	+	0.852283i	−0.225125	+	0.974330i	$0.572279\pi$
$60$		0			0
$61$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$61$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$62$		0			0
$63$		0			0
$64$	6.47214	−	4.70228i	0.809017	−	0.587785i
$65$		0			0
$66$	−6.61422	+	4.71722i	−0.814154	+	0.580649i
$67$	5.96494	−	10.3316i	0.728733	−	1.26220i	−0.228686	−	0.973500i	$-0.573443\pi$
$67$	5.96494	−	10.3316i	0.728733	−	1.26220i	0.957419	−	0.288703i	$-0.0932239\pi$
$68$	1.34001	−	0.140841i	0.162500	−	0.0170794i
$69$		0			0
$70$		0			0
$71$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$71$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$72$	−7.45498	−	4.05257i	−0.878577	−	0.477600i
$73$	−0.204607	−	0.0664810i	−0.0239475	−	0.00778101i	0.297019	−	0.954872i	$-0.404008\pi$
$73$	−0.204607	−	0.0664810i	−0.0239475	−	0.00778101i	−0.320966	+	0.947091i	$0.604008\pi$
$74$		0			0
$75$	3.62372	+	7.86566i	0.418432	+	0.908248i
$76$	−12.4085	−	7.16405i	−1.42335	−	0.821773i
$77$		0			0
$78$		0			0
$79$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$79$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$80$		0			0
$81$	−0.480052	+	8.98719i	−0.0533391	+	0.998576i
$82$	−8.18018	−	5.94325i	−0.903349	−	0.656322i
$83$	−8.24647	−	0.866738i	−0.905167	−	0.0951369i	−0.359506	−	0.933143i	$-0.617055\pi$
$83$	−8.24647	−	0.866738i	−0.905167	−	0.0951369i	−0.545661	+	0.838006i	$0.683721\pi$
$84$		0			0
$85$		0			0
$86$	1.74716	+	16.6231i	0.188401	+	1.79252i
$87$		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
$97$	14.6514	+	6.52324i	1.48763	+	0.662335i	0.979956	−	0.199215i	$-0.0638391\pi$
$97$	14.6514	+	6.52324i	1.48763	+	0.662335i	0.507673	+	0.861550i	$0.330506\pi$
$98$		−	9.89949i		−	1.00000i
$99$	−8.02589	+	5.88091i	−0.806632	+	0.591054i
$100$	−10.0000			−1.00000
$101$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$101$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$102$	1.63882	−	0.193550i	0.162267	−	0.0191643i
$103$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$103$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.8810	−	4.83514i	1.43860	−	0.467431i	0.517143	−	0.855899i	$-0.326996\pi$
$107$	14.8810	−	4.83514i	1.43860	−	0.467431i	0.921462	+	0.388468i	$0.126996\pi$
$108$	−9.19341	−	4.84574i	−0.884637	−	0.466281i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	15.9656	+	3.39359i	1.50192	+	0.319242i	0.884182	−	0.467143i	$-0.154717\pi$
$113$	15.9656	+	3.39359i	1.50192	+	0.319242i	0.617736	+	0.786386i	$0.288050\pi$
$114$	−15.3086	−	8.57830i	−1.43379	−	0.803432i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−11.8483	+	3.84976i	−1.09073	+	0.354399i
$119$		0			0
$120$		0			0
$121$	−10.6506	−	2.75024i	−0.968240	−	0.250022i
$122$		0			0
$123$	−10.1113	−	7.14974i	−0.911701	−	0.644670i
$124$		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	$0.700000\pi$
$128$	2.35225	+	11.0665i	0.207912	+	0.978148i
$129$	2.40103	+	20.3299i	0.211399	+	1.78995i
$130$		0			0
$131$	−11.0408	−	6.37443i	−0.964642	−	0.556936i	−0.0670435	−	0.997750i	$-0.521357\pi$
$131$	−11.0408	−	6.37443i	−0.964642	−	0.556936i	−0.897599	+	0.440814i	$0.854690\pi$
$132$	−2.28982	−	11.2586i	−0.199303	−	0.979938i
$133$		0			0
$134$	9.91676	+	13.6492i	0.856677	+	1.17912i
$135$		0			0
$136$	−0.588831	+	1.81223i	−0.0504918	+	0.155398i
$137$	2.41781	−	23.0039i	0.206567	−	1.96536i	−0.0497399	−	0.998762i	$-0.515839\pi$
$137$	2.41781	−	23.0039i	0.206567	−	1.96536i	0.256307	−	0.966595i	$-0.417494\pi$
$138$		0			0
$139$	17.3117	−	15.5875i	1.46836	−	1.32212i	0.630559	−	0.776142i	$-0.282826\pi$
$139$	17.3117	−	15.5875i	1.46836	−	1.32212i	0.837801	−	0.545976i	$-0.183841\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	9.52391	−	7.30035i	0.793659	−	0.608363i
$145$		0			0
$146$	0.203583	−	0.226102i	0.0168486	−	0.0187123i
$147$	−0.155658	−	12.1234i	−0.0128385	−	0.999918i
$148$		0			0
$149$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$149$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$150$	−12.2464	+	0.157238i	−0.999918	+	0.0128385i
$151$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$151$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$152$	16.3931	−	11.9103i	1.32966	−	0.966052i
$153$	2.00393	−	0.262798i	0.162008	−	0.0212459i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$157$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−11.3349	−	5.78975i	−0.890550	−	0.454885i
$163$	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	$-0.124958\pi$
$164$	12.3837	−	7.14974i	0.967005	−	0.558301i
$165$		0			0
$166$	5.86325	−	10.1554i	0.455077	−	0.788216i
$167$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$167$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$168$		0			0
$169$	12.7159	−	2.70285i	0.978148	−	0.207912i
$170$		0			0
$171$	−18.8825	−	10.2647i	−1.44398	−	0.784958i
$172$	−22.4812	−	7.30458i	−1.71417	−	0.556969i
$173$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$173$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$174$		0			0
$175$		0			0
$176$	12.9139	+	3.03830i	0.973422	+	0.229020i
$177$	−14.4495	+	4.90089i	−1.08609	+	0.368373i
$178$	6.46383	−	14.5180i	0.484485	−	1.08817i
$179$	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
$187$	1.62775	+	1.53067i	0.119033	+	0.111933i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$191$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$192$	3.05468	+	13.5155i	0.220452	+	0.975398i
$193$	−4.29810	−	9.65369i	−0.309384	−	0.694888i	0.690203	−	0.723615i	$-0.257521\pi$
$193$	−4.29810	−	9.65369i	−0.309384	−	0.694888i	−0.999587	+	0.0287278i	$0.990854\pi$
$194$	−16.8554	+	15.1767i	−1.21015	+	1.08962i
$195$		0			0
$196$	12.7896	+	5.69431i	0.913545	+	0.406737i
$197$		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			$\pi$
$200$	5.75212	−	12.9195i	0.406737	−	0.913545i
$201$	12.3591	+	16.5595i	0.871745	+	1.16802i
$202$		0			0
$203$		0			0
$204$	−0.692613	+	2.22860i	−0.0484926	+	0.156033i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.43622	−	23.3427i	−0.306860	−	1.61465i
$210$		0			0
$211$	−28.6653	+	3.01285i	−1.97340	+	0.207413i	−0.999784	−	0.0207756i	$-0.993386\pi$
$211$	−28.6653	+	3.01285i	−1.97340	+	0.207413i	−0.973617	+	0.228188i	$0.926720\pi$
$212$		0			0
$213$		0			0
$214$	−2.31301	+	22.0068i	−0.158114	+	1.50435i
$215$		0			0
$216$	11.5486	−	9.09009i	0.785783	−	0.618502i
$217$		0			0
$218$		0			0
$219$	0.245761	−	0.280095i	0.0166070	−	0.0189271i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$223$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$224$		0			0
$225$	−14.9951	+	0.385122i	−0.999670	+	0.0256748i
$226$	−13.5680	+	18.6747i	−0.902527	+	1.24222i
$227$	0.721606	+	3.39489i	0.0478946	+	0.225327i	0.995585	−	0.0938647i	$-0.0299221\pi$
$227$	0.721606	+	3.39489i	0.0478946	+	0.225327i	−0.947690	+	0.319191i	$0.896589\pi$
$228$	19.8884	−	14.8436i	1.31714	−	0.983043i
$229$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$229$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.13466	−	5.69087i	−0.270871	−	0.372821i	0.651813	−	0.758380i	$-0.274009\pi$
$233$	−4.13466	−	5.69087i	−0.270871	−	0.372821i	−0.922683	+	0.385558i	$0.874009\pi$
$234$		0			0
$235$		0			0
$236$	1.84162	−	17.5219i	0.119880	−	1.14058i
$237$		0			0
$238$		0			0
$239$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$239$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$240$		0			0
$241$	−9.69430	+	5.59701i	−0.624465	+	0.360535i	−0.778605	−	0.627514i	$-0.784072\pi$
$241$	−9.69430	+	5.59701i	−0.624465	+	0.360535i	0.154141	+	0.988049i	$0.450739\pi$
$242$	9.67955	−	12.1781i	0.622225	−	0.782838i
$243$	−13.9722	−	6.91215i	−0.896317	−	0.443415i
$244$		0			0
$245$		0			0
$246$	15.0532	−	8.95060i	0.959758	−	0.570669i
$247$		0			0
$248$		0			0
$249$	7.02071	−	12.5290i	0.444920	−	0.793993i
$250$		0			0
$251$	−19.3714	+	14.0742i	−1.22271	+	0.888353i	−0.996322	−	0.0856837i	$-0.972693\pi$
$251$	−19.3714	+	14.0742i	−1.22271	+	0.888353i	−0.226391	+	0.974037i	$0.572693\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−15.6504	−	3.32659i	−0.978148	−	0.207912i
$257$	15.2593	+	16.9472i	0.951849	+	1.05714i	0.998304	+	0.0582149i	$0.0185409\pi$
$257$	15.2593	+	16.9472i	0.951849	+	1.05714i	−0.0464552	+	0.998920i	$0.514792\pi$
$258$	−27.6463	−	8.59202i	−1.72118	−	0.534916i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	14.5863	−	10.5975i	0.901142	−	0.654718i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	15.8627	+	3.51778i	0.976282	+	0.216504i
$265$		0			0
$266$		0			0
$267$	7.68761	−	17.8810i	0.470474	−	1.09430i
$268$	−23.3384	+	4.96072i	−1.42562	+	0.303024i
$269$		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	$0.100000\pi$
$272$	−2.00261	−	1.80316i	−0.121426	−	0.109333i
$273$		0			0
$274$	28.3291	+	16.3558i	1.71142	+	0.988092i
$275$	−10.8271	−	12.5608i	−0.652900	−	0.757444i
$276$		0			0
$277$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$277$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$278$	10.1804	+	31.3320i	0.610578	+	1.87917i
$279$		0			0
$280$		0			0
$281$	−33.2793	−	3.49779i	−1.98528	−	0.208661i	−0.999069	−	0.0431402i	$-0.986264\pi$
$281$	−33.2793	−	3.49779i	−1.98528	−	0.208661i	−0.986206	−	0.165521i	$-0.947070\pi$
$282$		0			0
$283$	5.29257	−	24.8996i	0.314610	−	1.48013i	−0.482288	−	0.876013i	$-0.660194\pi$
$283$	5.29257	−	24.8996i	0.314610	−	1.48013i	0.796898	−	0.604113i	$-0.206473\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	3.95341	+	16.5037i	0.232957	+	0.972487i
$289$	5.11304	+	15.7363i	0.300767	+	0.925665i
$290$		0			0
$291$	−20.4032	+	18.8510i	−1.19606	+	1.10507i
$292$	0.175008	+	0.393075i	0.0102416	+	0.0230030i
$293$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$293$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$294$	15.7523	+	6.77240i	0.918692	+	0.394975i
$295$		0			0
$296$		0			0
$297$	−3.86719	−	16.7942i	−0.224397	−	0.974498i
$298$		0			0
$299$		0			0
$300$	6.84116	−	15.9122i	0.394975	−	0.918692i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	5.95796	+	28.0300i	0.341712	+	1.60763i
$305$		0			0
$306$	−0.813162	+	2.74013i	−0.0464854	+	0.156643i
$307$			32.9268i			1.87923i	0.342232	+	0.939616i	$0.388817\pi$
$307$			32.9268i			1.87923i	−0.342232	+	0.939616i	$0.611183\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$311$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$312$		0			0
$313$	−1.76007	+	16.7460i	−0.0994853	+	0.946539i	0.824951	+	0.565204i	$0.191202\pi$
$313$	−1.76007	+	16.7460i	−0.0994853	+	0.946539i	−0.924437	+	0.381336i	$0.875464\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$317$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−2.48658	+	26.9868i	−0.138787	+	1.50626i
$322$		0			0
$323$	−1.49143	+	4.59016i	−0.0829856	+	0.255403i
$324$	14.0000	−	11.3137i	0.777778	−	0.628539i
$325$		0			0
$326$	7.30021	+	34.3448i	0.404321	+	1.90218i
$327$		0			0
$328$	2.11383	+	20.1117i	0.116717	+	1.11048i
$329$		0			0
$330$		0			0
$331$	−3.03594	−	5.25840i	−0.166870	−	0.289028i	0.770448	−	0.637503i	$-0.220033\pi$
$331$	−3.03594	−	5.25840i	−0.166870	−	0.289028i	−0.937318	+	0.348476i	$0.886699\pi$
$332$	9.74770	+	13.4166i	0.534975	+	0.736329i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−26.8351	+	24.1624i	−1.46180	+	1.31621i	−0.609936	+	0.792451i	$0.708805\pi$
$337$	−26.8351	+	24.1624i	−1.46180	+	1.31621i	−0.851865	+	0.523761i	$0.824528\pi$
$338$	−3.82241	+	17.9830i	−0.207912	+	0.978148i
$339$	−16.3223	+	23.0832i	−0.886505	+	1.25371i
$340$		0			0
$341$		0			0
$342$	24.1229	−	18.4909i	1.30442	−	0.999872i
$343$		0			0
$344$	22.3686	−	24.8428i	1.20603	−	1.33944i
$345$		0			0
$346$		0			0
$347$	−15.1361	−	33.9962i	−0.812549	−	1.82501i	−0.449822	−	0.893118i	$-0.648512\pi$
$347$	−15.1361	−	33.9962i	−0.812549	−	1.82501i	−0.362727	−	0.931896i	$-0.618154\pi$
$348$		0			0
$349$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$349$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$350$		0			0
$351$		0			0
$352$	−11.3536	+	14.9364i	−0.605147	+	0.796114i
$353$	−12.3200	−	21.3388i	−0.655725	−	1.13575i	−0.981711	−	0.190375i	$-0.939030\pi$
$353$	−12.3200	−	21.3388i	−0.655725	−	1.13575i	0.325986	−	0.945375i	$-0.394304\pi$
$354$	1.97982	−	21.4870i	0.105226	−	1.14202i
$355$		0			0
$356$	15.0384	+	16.7019i	0.797035	+	0.885197i
$357$		0			0
$358$	−18.6605	−	1.96130i	−0.986238	−	0.103658i
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$		0			0
$361$	26.1504	−	18.9994i	1.37633	−	0.999966i
$362$		0			0
$363$	11.6625	−	15.0660i	0.612123	−	0.790762i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$367$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$368$		0			0
$369$	18.2941	−	11.1980i	0.952352	−	0.582944i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$373$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$374$	−2.91384	+	1.22251i	−0.150671	+	0.0632145i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	30.8769	+	22.4334i	1.58604	+	1.15233i	0.909327	+	0.416082i	$0.136597\pi$
$379$	30.8769	+	22.4334i	1.58604	+	1.15233i	0.676715	+	0.736245i	$0.263403\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$383$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$384$	−19.2184	−	3.82780i	−0.980736	−	0.195337i
$385$		0			0
$386$	14.9444			0.760649
$387$	−33.9920	−	10.0875i	−1.72791	−	0.512774i
$388$	−9.91203	−	30.5061i	−0.503207	−	1.54871i
$389$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$389$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$390$		0			0
$391$		0			0
$392$	−14.7135	+	13.2481i	−0.743145	+	0.669131i
$393$	17.6963	−	13.2076i	0.892662	−	0.666233i
$394$		0			0
$395$		0			0
$396$	19.4815	+	4.05860i	0.978981	+	0.203952i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	13.3826	+	14.8629i	0.669131	+	0.743145i
$401$	−9.70613	+	4.32145i	−0.484701	+	0.215803i	−0.634514	−	0.772912i	$-0.718800\pi$
$401$	−9.70613	+	4.32145i	−0.484701	+	0.215803i	0.149813	+	0.988714i	$0.452133\pi$
$402$	−28.5032	+	6.44209i	−1.42161	+	0.321302i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−2.48084	−	2.17674i	−0.122820	−	0.107765i
$409$	−35.8258	+	3.76544i	−1.77147	+	0.186189i	−0.933271	−	0.359174i	$-0.883059\pi$
$409$	−35.8258	+	3.76544i	−1.77147	+	0.186189i	−0.838200	+	0.545363i	$0.816392\pi$
$410$		0			0
$411$	34.9503	+	19.5846i	1.72397	+	0.966038i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	12.9600	+	38.2104i	0.634654	+	1.87117i
$418$	32.7093	+	7.69563i	1.59986	+	0.376405i
$419$	−3.52515	+	6.10573i	−0.172215	+	0.298285i	−0.939194	−	0.343387i	$-0.888426\pi$
$419$	−3.52515	+	6.10573i	−0.172215	+	0.298285i	0.766979	+	0.641672i	$0.221759\pi$
$420$		0			0
$421$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$421$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$422$	12.5962	−	38.7671i	0.613174	−	1.88715i
$423$		0			0
$424$		0			0
$425$	0.700345	+	3.29486i	0.0339717	+	0.159824i
$426$		0			0
$427$		0			0
$428$	−27.1012	−	15.6469i	−1.30998	−	0.756319i
$429$		0			0
$430$		0			0
$431$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$431$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$432$	5.10102	+	20.1489i	0.245423	+	0.969416i
$433$	−12.5764	+	38.7061i	−0.604382	+	1.86010i	−0.103396	+	0.994640i	$0.532971\pi$
$433$	−12.5764	+	38.7061i	−0.604382	+	1.86010i	−0.500986	+	0.865456i	$0.667029\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.220503	+	0.478625i	0.0105361	+	0.0228696i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	19.3974	+	8.04610i	0.923687	+	0.383147i
$442$		0			0
$443$	−26.4436	+	29.3686i	−1.25637	+	1.39534i	−0.372221	+	0.928144i	$0.621404\pi$
$443$	−26.4436	+	29.3686i	−1.25637	+	1.39534i	−0.884152	+	0.467200i	$0.845263\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	34.1877	−	24.8388i	1.61342	−	1.17222i	0.762339	−	0.647178i	$-0.224051\pi$
$449$	34.1877	−	24.8388i	1.61342	−	1.17222i	0.851078	−	0.525038i	$-0.175949\pi$
$450$	8.12778	−	19.5944i	0.383147	−	0.923687i
$451$	22.3886	+	7.81381i	1.05424	+	0.367938i
$452$	−16.3223	−	28.2710i	−0.767736	−	1.32976i
$453$		0			0
$454$	−4.80110	−	1.02050i	−0.225327	−	0.0478946i
$455$		0			0
$456$	7.73712	+	34.2331i	0.362324	+	1.60311i
$457$	−20.3197	−	2.13568i	−0.950515	−	0.0999031i	−0.383437	−	0.923567i	$-0.625260\pi$
$457$	−20.3197	−	2.13568i	−0.950515	−	0.0999031i	−0.567078	+	0.823664i	$0.691926\pi$
$458$		0			0
$459$	−0.952748	+	3.36847i	−0.0444705	+	0.157227i
$460$		0			0
$461$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$461$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$462$		0			0
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$	9.73062	−	2.06831i	0.450762	−	0.0958125i
$467$	33.9337	+	24.6543i	1.57027	+	1.14086i	0.926902	+	0.375304i	$0.122462\pi$
$467$	33.9337	+	24.6543i	1.57027	+	1.14086i	0.643364	+	0.765561i	$0.277538\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	21.5780	+	12.4581i	0.993210	+	0.573430i
$473$	−15.1655	−	36.1469i	−0.697311	−	1.66204i
$474$		0			0
$475$	14.5694	−	32.7234i	0.668490	−	1.50145i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$479$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$480$		0			0
$481$		0			0
$482$	−1.65476	−	15.7440i	−0.0753723	−	0.717120i
$483$		0			0
$484$	10.1657	+	19.5105i	0.462077	+	0.886840i
$485$		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
$489$	9.48019	+	41.9453i	0.428709	+	1.89683i
$490$		0			0
$491$	−29.9425	+	26.9604i	−1.35129	+	1.21671i	−0.396999	+	0.917819i	$0.629948\pi$
$491$	−29.9425	+	26.9604i	−1.35129	+	1.21671i	−0.954289	+	0.298886i	$0.903385\pi$
$492$	2.90492	+	24.5965i	0.130964	+	1.10889i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	12.1484	+	16.2772i	0.544384	+	0.729400i
$499$	29.2125	+	32.4438i	1.30773	+	1.45238i	0.811697	+	0.584079i	$0.198544\pi$
$499$	29.2125	+	32.4438i	1.30773	+	1.45238i	0.496034	+	0.868303i	$0.334789\pi$
$500$		0			0
$501$		0			0
$502$	−7.04040	−	33.1225i	−0.314229	−	1.47833i
$503$		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
$507$	−4.39833	+	22.0829i	−0.195337	+	0.980736i
$508$		0			0
$509$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$509$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$510$		0			0
$511$		0			0
$512$	13.3001	−	18.3060i	0.587785	−	0.809017i
$513$	29.2512	−	23.0241i	1.29147	−	1.01654i
$514$	−30.6722	+	9.96600i	−1.35289	+	0.439582i
$515$		0			0
$516$	27.0029	−	30.7754i	1.18874	−	1.35481i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.15188	−	28.1666i	0.400951	−	1.23400i	−0.523278	−	0.852162i	$-0.675291\pi$
$521$	9.15188	−	28.1666i	0.400951	−	1.23400i	0.924229	−	0.381839i	$-0.124709\pi$
$522$		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	$0.787876\pi$
$524$	5.30127	+	24.9405i	0.231587	+	1.08953i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−13.6692	+	18.4703i	−0.594876	+	0.803817i
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$		0			0
$531$	2.08672	−	26.3451i	0.0905559	−	1.14328i
$532$		0			0
$533$		0			0
$534$	18.6793	+	20.2174i	0.808334	+	0.874892i
$535$		0			0
$536$	7.01552	−	33.0054i	0.303024	−	1.42562i
$537$	−22.8833	−	2.10848i	−0.987488	−	0.0909875i
$538$		0			0
$539$	6.69498	+	22.2301i	0.288373	+	0.957518i
$540$		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
$544$	3.48151	−	1.55007i	0.149269	−	0.0664587i
$545$		0			0
$546$		0			0
$547$	−0.939395	−	0.845835i	−0.0401656	−	0.0361653i	0.648803	−	0.760956i	$-0.275270\pi$
$547$	−0.939395	−	0.845835i	−0.0401656	−	0.0361653i	−0.688969	+	0.724791i	$0.741936\pi$
$548$	−37.4261	+	27.1917i	−1.59877	+	1.16157i
$549$		0			0
$550$	22.4558	−	6.76296i	0.957518	−	0.288373i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−46.3352	−	4.87002i	−1.96505	−	0.206535i
$557$		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
$561$	−3.54920	+	1.54296i	−0.149847	+	0.0651437i
$562$	23.6616	−	40.9831i	0.998105	−	1.72877i
$563$	−25.8498	+	2.71692i	−1.08944	+	0.114505i	−0.632175	−	0.774826i	$-0.717837\pi$
$563$	−25.8498	+	2.71692i	−1.08944	+	0.114505i	−0.457265	+	0.889331i	$0.651171\pi$
$564$		0			0
$565$		0			0
$566$	29.1246	+	21.1603i	1.22420	+	0.889432i
$567$		0			0
$568$		0			0
$569$	−9.95863	−	8.96679i	−0.417488	−	0.375908i	0.433447	−	0.901179i	$-0.357297\pi$
$569$	−9.95863	−	8.96679i	−0.417488	−	0.375908i	−0.850935	+	0.525271i	$0.823964\pi$
$570$		0			0
$571$	1.87117	+	1.08032i	0.0783062	+	0.0452101i	0.538642	−	0.842535i	$-0.318938\pi$
$571$	1.87117	+	1.08032i	0.0783062	+	0.0452101i	−0.460336	+	0.887745i	$0.652271\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−23.5959	−	4.38551i	−0.983163	−	0.182729i
$577$	−38.8115	−	28.1982i	−1.61574	−	1.17391i	−0.839142	−	0.543912i	$-0.816942\pi$
$577$	−38.8115	−	28.1982i	−1.61574	−	1.17391i	−0.776600	−	0.629994i	$-0.783058\pi$
$578$	−23.2716	−	2.44594i	−0.967970	−	0.101738i
$579$	18.3016	−	0.234983i	0.760587	−	0.00976557i
$580$		0			0
$581$		0			0
$582$	−12.6184	−	37.2033i	−0.523049	−	1.54212i
$583$		0			0
$584$	−0.608499			−0.0251799
$585$		0			0
$586$		0			0
$587$	38.8790	−	8.26399i	1.60471	−	0.341091i	0.683437	−	0.730010i	$-0.260484\pi$
$587$	38.8790	−	8.26399i	1.60471	−	0.341091i	0.921272	+	0.388918i	$0.127151\pi$
$588$	−17.8105	+	16.4556i	−0.734493	+	0.678616i
$589$		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	$0.979500\pi$
$594$	23.9217	+	4.66402i	0.981519	+	0.191367i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$599$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$600$	16.6226	+	17.9913i	0.678616	+	0.734493i
$601$	−0.666670	−	3.13644i	−0.0271940	−	0.127938i	0.962457	−	0.271436i	$-0.0874984\pi$
$601$	−0.666670	−	3.13644i	−0.0271940	−	0.127938i	−0.989651	+	0.143498i	$0.954165\pi$
$602$		0			0
$603$	−34.8050	+	8.33744i	−1.41737	+	0.339527i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$607$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$608$	−39.6404	−	8.42583i	−1.60763	−	0.341712i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−3.07237	−	2.62672i	−0.124193	−	0.106179i
$613$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$613$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$614$	−42.5397	−	18.9399i	−1.71676	−	0.764352i
$615$		0			0
$616$		0			0
$617$	−4.67656	+	8.10004i	−0.188271	+	0.326095i	−0.944674	−	0.328011i	$-0.893622\pi$
$617$	−4.67656	+	8.10004i	−0.188271	+	0.326095i	0.756403	+	0.654106i	$0.226955\pi$
$618$		0			0
$619$	32.7381	−	36.3594i	1.31586	−	1.46141i	0.522514	−	0.852631i	$-0.324994\pi$
$619$	32.7381	−	36.3594i	1.31586	−	1.46141i	0.793342	−	0.608776i	$-0.208339\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−2.61321	−	24.8630i	−0.104528	−	0.994522i
$626$	−20.6225	−	11.9064i	−0.824242	−	0.475877i
$627$	40.1782	+	8.91009i	1.60456	+	0.355835i
$628$		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
$641$	−15.8846	+	17.6416i	−0.627403	+	0.696802i	−0.970117	−	0.242638i	$-0.921987\pi$
$641$	−15.8846	+	17.6416i	−0.627403	+	0.696802i	0.342714	+	0.939440i	$0.388654\pi$
$642$	−33.4353	−	18.7357i	−1.31959	−	0.739439i
$643$	2.93465	−	1.30659i	0.115731	−	0.0515269i	−0.348054	−	0.937474i	$-0.613157\pi$
$643$	2.93465	−	1.30659i	0.115731	−	0.0515269i	0.463786	+	0.885948i	$0.346491\pi$
$644$		0			0
$645$		0			0
$646$	−5.07236	−	4.56718i	−0.199569	−	0.179693i
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$	6.56375	+	24.5951i	0.257849	+	0.966185i
$649$	24.0028	−	16.6579i	0.942193	−	0.653881i
$650$		0			0
$651$		0			0
$652$	−48.5709	−	10.3241i	−1.90218	−	0.404321i
$653$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$653$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$654$		0			0
$655$		0			0
$656$	−27.1992	−	8.83756i	−1.06195	−	0.345049i
$657$	0.277564	+	0.582678i	0.0108288	+	0.0227324i
$658$		0			0
$659$	27.6934	−	15.9888i	1.07878	−	0.622834i	0.148214	−	0.988955i	$-0.452648\pi$
$659$	27.6934	−	15.9888i	1.07878	−	0.622834i	0.930567	+	0.366121i	$0.119314\pi$
$660$		0			0
$661$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$661$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$662$	8.53988	−	0.897578i	0.331912	−	0.0348854i
$663$		0			0
$664$	−22.9405	+	4.87615i	−0.890264	+	0.189231i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−10.2673	+	23.0608i	−0.395776	+	0.888927i	0.600246	+	0.799816i	$0.295069\pi$
$673$	−10.2673	+	23.0608i	−0.395776	+	0.888927i	−0.996022	+	0.0891114i	$0.971597\pi$
$674$	−15.7807	−	48.5681i	−0.607851	−	1.87077i
$675$	9.64554	−	24.1239i	0.371257	−	0.928530i
$676$	−21.0344	−	15.2824i	−0.809017	−	0.587785i
$677$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$677$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$678$	−20.4335	−	34.3653i	−0.784744	−	1.31979i
$679$		0			0
$680$		0			0
$681$	−5.89568	−	1.17426i	−0.225923	−	0.0449979i
$682$		0			0
$683$	−5.94439			−0.227456			−0.113728	−	0.993512i	$-0.536279\pi$
$683$	−5.94439			−0.227456			−0.113728	+	0.993512i	$0.536279\pi$
$684$	10.0135	+	41.8017i	0.382875	+	1.59833i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	19.2290	+	43.1890i	0.733098	+	1.64656i
$689$		0			0
$690$		0			0
$691$	−35.1027	−	15.6287i	−1.33537	−	0.594545i	−0.390082	−	0.920780i	$-0.627553\pi$
$691$	−35.1027	−	15.6287i	−1.33537	−	0.594545i	−0.945289	+	0.326235i	$0.894220\pi$
$692$		0			0
$693$		0			0
$694$	52.6279			1.99773
$695$		0			0
$696$		0			0
$697$	−3.22303	−	3.57953i	−0.122081	−	0.135585i
$698$		0			0
$699$	11.8840	−	2.68594i	0.449495	−	0.101592i
$700$		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
$706$	34.6552	−	3.64241i	1.30427	−	0.137084i
$707$		0			0
$708$	26.6213	+	14.9174i	1.00049	+	0.560632i
$709$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$709$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$710$		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
$722$	9.50417	+	44.7136i	0.353708	+	1.66407i
$723$	−2.27405	−	19.2548i	−0.0845728	−	0.716093i
$724$		0			0
$725$		0			0
$726$	12.7561	+	23.7335i	0.473424	+	0.880835i
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$		0			0
$729$	20.5574	−	17.5041i	0.761384	−	0.648301i
$730$		0			0
$731$	−0.832301	+	7.91882i	−0.0307838	+	0.292888i
$732$		0			0
$733$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$733$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−31.4998	−	23.9438i	−1.16031	−	0.881981i
$738$	3.94424	+	30.0762i	0.145190	+	1.10712i
$739$	−28.5477	−	39.2926i	−1.05014	−	1.44540i	−0.888683	−	0.458522i	$-0.848379\pi$
$739$	−28.5477	−	39.2926i	−1.05014	−	1.44540i	−0.161462	−	0.986879i	$-0.551621\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$743$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	15.1334	+	19.7428i	0.553703	+	0.722351i
$748$	0.0966596	−	4.46774i	0.00353423	−	0.163357i
$749$		0			0
$750$		0			0
$751$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$751$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$752$		0			0
$753$	−9.14280	−	40.4526i	−0.333182	−	1.47417i
$754$		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	$0.800000\pi$
$758$	−46.7436	+	26.9874i	−1.69780	+	0.980228i
$759$		0			0
$760$		0			0
$761$	47.5987	−	5.00283i	1.72545	−	0.181352i	0.810726	−	0.585426i	$-0.199073\pi$
$761$	47.5987	−	5.00283i	1.72545	−	0.181352i	0.914727	+	0.404073i	$0.132406\pi$
$762$		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	0.993313	+	0.115454i	$0.0368323\pi$
$769$	44.0908	+	25.4558i	1.58996	+	0.917961i	0.596643	+	0.802507i	$0.296501\pi$
$770$		0			0
$771$	−37.4058	+	12.6871i	−1.34714	+	0.456914i
$772$	−8.59620	+	19.3074i	−0.309384	+	0.694888i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	32.5851	−	38.1134i	1.17125	−	1.36996i
$775$		0			0
$776$	45.1138	+	4.74165i	1.61949	+	0.170215i
$777$		0			0
$778$		0			0
$779$	5.35406	+	50.9405i	0.191829	+	1.82513i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−8.65248	−	26.6296i	−0.309017	−	0.951057i
$785$		0			0
$786$	6.88433	+	30.4599i	0.245556	+	1.08647i
$787$	16.1420	+	36.2555i	0.575399	+	1.29237i	0.933464	+	0.358671i	$0.116770\pi$
$787$	16.1420	+	36.2555i	0.575399	+	1.29237i	−0.358065	+	0.933697i	$0.616563\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−16.4495	+	22.8345i	−0.584507	+	0.811389i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$797$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$798$		0			0
$799$		0			0
$800$	−26.8999	+	8.74032i	−0.951057	+	0.309017i
$801$	23.1934	+	24.4654i	0.819500	+	0.864442i
$802$		−	15.0256i		−	0.530571i
$803$	−0.304250	+	0.645411i	−0.0107367	+	0.0227761i
$804$	8.07254	−	40.5302i	0.284697	−	1.42939i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	31.7903	−	43.7556i	1.11769	−	1.53837i	0.308112	−	0.951350i	$-0.400303\pi$
$809$	31.7903	−	43.7556i	1.11769	−	1.53837i	0.809576	−	0.587015i	$-0.199697\pi$
$810$		0			0
$811$	−31.7245	+	10.3079i	−1.11400	+	0.361959i	−0.807473	−	0.589904i	$-0.799166\pi$
$811$	−31.7245	+	10.3079i	−1.11400	+	0.361959i	−0.306523	+	0.951863i	$0.599166\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	4.23924	−	1.95303i	0.148403	−	0.0683696i
$817$	56.6568	−	62.9238i	1.98217	−	2.20143i
$818$	15.7427	−	48.4510i	0.550430	−	1.69405i
$819$		0			0
$820$		0			0
$821$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$821$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$822$	−45.4061	+	33.8886i	−1.58372	+	1.18200i
$823$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$823$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$824$		0			0
$825$	27.3940	−	8.63530i	0.953737	−	0.300643i
$826$		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
$833$	0.980483	−	4.61281i	0.0339717	−	0.159824i
$834$	−56.8207	−	5.23548i	−1.96754	−	0.181290i
$835$		0			0
$836$	−28.7571	+	37.8321i	−0.994587	+	1.30845i
$837$		0			0
$838$	−5.86058	−	8.06640i	−0.202451	−	0.278649i
$839$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$839$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$840$		0			0
$841$	−26.4928	+	11.7954i	−0.913545	+	0.406737i
$842$		0			0
$843$	28.3327	−	50.5618i	0.975828	−	1.74144i
$844$	42.8396	+	38.5730i	1.47460	+	1.32774i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	36.0000	+	25.4558i	1.23552	+	0.873642i
$850$	−4.65964	−	0.990437i	−0.159824	−	0.0339717i
$851$		0			0
$852$		0			0
$853$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$853$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$854$		0			0
$855$		0			0
$856$	35.8039	−	26.0130i	1.22375	−	0.889107i
$857$	43.3414	−	25.0232i	1.48051	−	0.854776i	0.480759	−	0.876853i	$-0.340361\pi$
$857$	43.3414	−	25.0232i	1.48051	−	0.854776i	0.999756	+	0.0220773i	$0.00702798\pi$
$858$		0			0
$859$	−22.5577	+	39.0711i	−0.769658	+	1.33309i	0.168090	+	0.985772i	$0.446240\pi$
$859$	−22.5577	+	39.0711i	−0.769658	+	1.33309i	−0.937748	+	0.347316i	$0.887093\pi$
$860$		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	$0.200000\pi$
$864$	−28.9656	−	4.99966i	−0.985428	−	0.170092i
$865$		0			0
$866$	−42.7722	−	38.5122i	−1.45346	−	1.30870i
$867$	−28.5379	−	2.62949i	−0.969197	−	0.0893021i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−16.0380	−	45.3623i	−0.542804	−	1.53528i
$874$		0			0
$875$		0			0
$876$	−0.745195	+	0.00956795i	−0.0251778	+	0.000323271i
$877$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$877$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$878$		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	$0.798061\pi$
$882$	−21.5528	+	20.4323i	−0.725720	+	0.687990i
$883$	8.03012	+	24.7142i	0.270235	+	0.831698i	0.990441	+	0.137938i	$0.0440473\pi$
$883$	8.03012	+	24.7142i	0.270235	+	0.831698i	−0.720206	+	0.693760i	$0.755953\pi$
$884$		0			0
$885$		0			0
$886$	−22.7320	−	51.0569i	−0.763697	−	1.71529i
$887$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$887$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	29.3689	+	5.33562i	0.983895	+	0.178750i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	12.4253	+	58.4563i	0.414637	+	1.95071i
$899$		0			0
$900$	20.6397	+	21.7716i	0.687990	+	0.725720i
$901$		0			0
$902$	−22.9733	+	24.4303i	−0.764926	+	0.813441i
$903$		0			0
$904$	45.9135	−	4.82570i	1.52706	−	0.160500i
$905$		0			0
$906$		0			0
$907$	5.31338	−	50.5534i	0.176428	−	1.67860i	−0.445313	−	0.895375i	$-0.646908\pi$
$907$	5.31338	−	50.5534i	0.176428	−	1.67860i	0.621741	−	0.783223i	$-0.286426\pi$
$908$	4.08009	−	5.61576i	0.135403	−	0.186366i
$909$		0			0
$910$		0			0
$911$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$911$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$912$	−48.6779	−	9.69534i	−1.61189	−	0.321045i
$913$	−6.29831	+	26.7702i	−0.208444	+	0.885963i
$914$	14.4473	−	25.0235i	0.477875	−	0.827704i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−3.80386	−	3.16849i	−0.125546	−	0.104576i
$919$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$919$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$920$		0			0
$921$	−52.3938	−	22.5257i	−1.72643	−	0.742249i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.06755	+	10.1571i	−0.0350252	+	0.333243i	0.962952	+	0.269672i	$0.0869154\pi$
$929$	−1.06755	+	10.1571i	−0.0350252	+	0.333243i	−0.997977	+	0.0635704i	$0.979751\pi$
$930$		0			0
$931$	−37.2675	+	33.5558i	−1.22139	+	1.09975i
$932$	−2.92503	+	13.7612i	−0.0958125	+	0.450762i
$933$		0			0
$934$	−51.3712	+	29.6592i	−1.68092	+	0.970477i
$935$		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
$939$	−25.4425	−	14.2569i	−0.830284	−	0.465255i
$940$		0			0
$941$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$941$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$942$		0			0
$943$		0			0
$944$	−28.5072	+	20.7117i	−0.927829	+	0.674108i
$945$		0			0
$946$	55.4233	+	1.19908i	1.80197	+	0.0389856i
$947$	30.0053	+	51.9707i	0.975041	+	1.68882i	0.679799	+	0.733399i	$0.262067\pi$
$947$	30.0053	+	51.9707i	0.975041	+	1.68882i	0.295243	+	0.955422i	$0.404599\pi$
$948$		0			0
$949$		0			0
$950$	33.8965	+	37.6459i	1.09975	+	1.22139i
$951$		0			0
$952$		0			0
$953$	23.0721	+	7.49657i	0.747378	+	0.242838i	0.657852	−	0.753147i	$-0.271465\pi$
$953$	23.0721	+	7.49657i	0.747378	+	0.242838i	0.0895252	+	0.995985i	$0.471465\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−30.3226	+	6.44526i	−0.978148	+	0.207912i
$962$		0			0
$963$	−41.2409	−	22.4188i	−1.32897	−	0.722436i
$964$	21.2923	+	6.91828i	0.685778	+	0.222823i
$965$		0			0
$966$		0			0
$967$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$967$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$968$	−31.0540	+	1.91087i	−0.998112	+	0.0614178i
$969$	−6.28365	−	5.51341i	−0.201860	−	0.177116i
$970$		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	$0.566383\pi$
$972$	8.42499	+	30.0170i	0.270232	+	0.962795i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.94650	+	56.5771i	0.190245	+	1.81006i	0.507423	+	0.861697i	$0.330598\pi$
$977$	5.94650	+	56.5771i	0.190245	+	1.81006i	−0.317178	+	0.948366i	$0.602735\pi$
$978$	−59.6443	−	11.8796i	−1.90722	−	0.379867i
$979$	−4.69658	+	36.9728i	−0.150103	+	1.18165i
$980$		0			0
$981$		0			0
$982$	−17.6081	−	54.1922i	−0.561897	−	1.72934i
$983$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$983$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$984$	−33.4483	−	10.3952i	−1.06629	−	0.331386i
$985$		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
$993$	10.4442	−	1.23349i	0.331437	−	0.0391437i
$994$		0			0
$995$		0			0
$996$	−28.0173	+	6.33226i	−0.887761	+	0.200645i
$997$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$997$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$998$	−58.7191	+	19.0790i	−1.85872	+	0.603935i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.ce.a.283.1	✓	16	1.1	even	1	trivial
792.2.ce.a.283.1	✓	16	8.3	odd	2	CM
792.2.ce.a.403.1	yes	16	99.7	odd	30	inner
792.2.ce.a.403.1	yes	16	792.403	even	30	inner
792.2.ce.b.139.2	yes	16	11.7	odd	10
792.2.ce.b.139.2	yes	16	88.51	even	10
792.2.ce.b.547.2	yes	16	9.7	even	3
792.2.ce.b.547.2	yes	16	72.43	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.575212 + 1.29195i) q^{2} +(-0.684116 + 1.59122i) q^{3} +(-1.33826 - 1.48629i) q^{4} +(-1.66226 - 1.79913i) q^{6} +(2.68999 - 0.874032i) q^{8} +(-2.06397 - 2.17716i) q^{9} +O(q^{10})\)	\(q+(-0.575212 + 1.29195i) q^{2} +(-0.684116 + 1.59122i) q^{3} +(-1.33826 - 1.48629i) q^{4} +(-1.66226 - 1.79913i) q^{6} +(2.68999 - 0.874032i) q^{8} +(-2.06397 - 2.17716i) q^{9} +(0.417946 - 3.29019i) q^{11} +(3.28054 - 1.11268i) q^{12} +(-0.418114 + 3.97809i) q^{16} +(-0.395988 + 0.545030i) q^{17} +(4.00000 - 1.41421i) q^{18} +(6.81342 - 2.21381i) q^{19} +(4.01034 + 2.43252i) q^{22} +(-0.449490 + 4.87832i) q^{24} +(3.34565 - 3.71572i) q^{25} +(4.87634 - 1.79480i) q^{27} +(-4.89898 - 2.82843i) q^{32} +(4.94949 + 2.91591i) q^{33} +(-0.476374 - 0.825104i) q^{34} +(-0.473759 + 5.98127i) q^{36} +(-1.05903 + 10.0760i) q^{38} +(-1.48651 + 6.99350i) q^{41} +(10.2356 - 5.90953i) q^{43} +(-5.44949 + 3.78194i) q^{44} +(-6.04398 - 3.38679i) q^{48} +(-6.39482 + 2.84716i) q^{49} +(2.87606 + 6.45974i) q^{50} +(-0.596362 - 1.00297i) q^{51} +(-0.486138 + 7.33237i) q^{54} +(-1.13850 + 12.3562i) q^{57} +(5.89451 + 6.54651i) q^{59} +(6.47214 - 4.70228i) q^{64} +(-6.61422 + 4.71722i) q^{66} +(5.96494 - 10.3316i) q^{67} +(1.34001 - 0.140841i) q^{68} +(-7.45498 - 4.05257i) q^{72} +(-0.204607 - 0.0664810i) q^{73} +(3.62372 + 7.86566i) q^{75} +(-12.4085 - 7.16405i) q^{76} +(-0.480052 + 8.98719i) q^{81} +(-8.18018 - 5.94325i) q^{82} +(-8.24647 - 0.866738i) q^{83} +(1.74716 + 16.6231i) q^{86} +(-1.75146 - 9.21588i) q^{88} -11.2373 q^{89} +(7.85212 - 5.86039i) q^{96} +(14.6514 + 6.52324i) q^{97} -9.89949i q^{98} +(-8.02589 + 5.88091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9}+O(q^{10}) \) 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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