LMFDB - Embedded newform 792.2.ce.a.547.1

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			547.1
Root			$-0.575212 + 1.29195i$ of defining polynomial
Character	$\chi$	$=$	792.547
Dual form			792.2.ce.a.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40647 + 0.147826i) q^{2} +(-0.381835 + 1.68944i) q^{3} +(1.95630 - 0.415823i) q^{4} +(0.287296 - 2.43258i) q^{6} +(-2.68999 + 0.874032i) q^{8} +(-2.70840 - 1.29017i) q^{9} +O(q^{10})$	\(q+(-1.40647 + 0.147826i) q^{2} +(-0.381835 + 1.68944i) q^{3} +(1.95630 - 0.415823i) q^{4} +(0.287296 - 2.43258i) q^{6} +(-2.68999 + 0.874032i) q^{8} +(-2.70840 - 1.29017i) q^{9} +(-2.27205 - 2.41615i) q^{11} +(-0.0444738 + 3.46382i) q^{12} +(3.65418 - 1.62695i) q^{16} +(2.51911 - 3.46726i) q^{17} +(4.00000 + 1.41421i) q^{18} +(8.28911 - 2.69329i) q^{19} +(3.55273 + 3.06237i) q^{22} +(-0.449490 - 4.87832i) q^{24} +(-4.89074 - 1.03956i) q^{25} +(3.21383 - 4.08305i) q^{27} +(-4.89898 + 2.82843i) q^{32} +(4.94949 - 2.91591i) q^{33} +(-3.03050 + 5.24897i) q^{34} +(-5.83492 - 1.39774i) q^{36} +(-11.2602 + 5.01337i) q^{38} +(-5.86725 - 5.28290i) q^{41} +(7.84469 + 4.52913i) q^{43} +(-5.44949 - 3.78194i) q^{44} +(1.35333 + 6.79474i) q^{48} +(0.731699 - 6.96165i) q^{49} +(7.03233 + 0.739128i) q^{50} +(4.89584 + 5.57980i) q^{51} +(-3.91657 + 6.21776i) q^{54} +(1.38508 + 15.0323i) q^{57} +(14.2070 - 3.01980i) q^{59} +(6.47214 - 4.70228i) q^{64} +(-6.53024 + 4.83280i) q^{66} +(-1.53102 - 2.65180i) q^{67} +(3.48636 - 7.83049i) q^{68} +(8.41324 + 1.10333i) q^{72} +(15.5183 + 5.04219i) q^{73} +(3.62372 - 7.86566i) q^{75} +(15.0960 - 8.71568i) q^{76} +(5.67091 + 6.98862i) q^{81} +(9.03304 + 6.56289i) q^{82} +(5.23404 + 11.7559i) q^{83} +(-11.7028 - 5.21043i) q^{86} +(8.22359 + 4.51360i) q^{88} -17.8873 q^{89} +(-2.90785 - 9.35652i) q^{96} +(-1.65493 - 15.7456i) q^{97} +9.89949i q^{98} +(3.03637 + 9.47526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.381835	+	1.68944i	−0.220452	+	0.975398i
$3$	−0.381835	+	1.68944i	−0.220452	+	0.975398i
$4$	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	$0.533333\pi$
$6$	0.287296	−	2.43258i	0.117288	−	0.993098i
$7$		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
$9$	−2.70840	−	1.29017i	−0.902801	−	0.430058i
$10$		0			0
$11$	−2.27205	−	2.41615i	−0.685048	−	0.728498i
$11$	−2.27205	−	2.41615i	−0.685048	−	0.728498i
$12$	−0.0444738	+	3.46382i	−0.0128385	+	0.999918i
$13$		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
$17$	2.51911	−	3.46726i	0.610974	−	0.840934i	−0.385683	−	0.922631i	$-0.626034\pi$
$17$	2.51911	−	3.46726i	0.610974	−	0.840934i	0.996657	+	0.0816975i	$0.0260341\pi$
$18$	4.00000	+	1.41421i	0.942809	+	0.333333i
$19$	8.28911	−	2.69329i	1.90165	−	0.617884i	0.944016	−	0.329900i	$-0.107015\pi$
$19$	8.28911	−	2.69329i	1.90165	−	0.617884i	0.957635	−	0.287984i	$-0.0929851\pi$
$20$		0			0
$21$		0			0
$22$	3.55273	+	3.06237i	0.757444	+	0.652900i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−0.449490	−	4.87832i	−0.0917517	−	0.995782i
$25$	−4.89074	−	1.03956i	−0.978148	−	0.207912i
$26$		0			0
$27$	3.21383	−	4.08305i	0.618502	−	0.785783i
$28$		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
$33$	4.94949	−	2.91591i	0.861596	−	0.507595i
$34$	−3.03050	+	5.24897i	−0.519726	+	0.900191i
$35$		0			0
$36$	−5.83492	−	1.39774i	−0.972487	−	0.232957i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$	−11.2602	+	5.01337i	−1.82665	+	0.813276i
$39$		0			0
$40$		0			0
$41$	−5.86725	−	5.28290i	−0.916311	−	0.825050i	0.0686831	−	0.997639i	$-0.478120\pi$
$41$	−5.86725	−	5.28290i	−0.916311	−	0.825050i	−0.984994	+	0.172588i	$0.944787\pi$
$42$		0			0
$43$	7.84469	+	4.52913i	1.19630	+	0.690686i	0.959729	−	0.280927i	$-0.0906419\pi$
$43$	7.84469	+	4.52913i	1.19630	+	0.690686i	0.236575	+	0.971613i	$0.423975\pi$
$44$	−5.44949	−	3.78194i	−0.821541	−	0.570149i
$45$		0			0
$46$		0			0
$47$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$47$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$48$	1.35333	+	6.79474i	0.195337	+	0.980736i
$49$	0.731699	−	6.96165i	0.104528	−	0.994522i
$50$	7.03233	+	0.739128i	0.994522	+	0.104528i
$51$	4.89584	+	5.57980i	0.685554	+	0.781329i
$52$		0			0
$53$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$53$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$54$	−3.91657	+	6.21776i	−0.532977	+	0.846130i
$55$		0			0
$56$		0			0
$57$	1.38508	+	15.0323i	0.183459	+	1.99108i
$58$		0			0
$59$	14.2070	−	3.01980i	1.84960	−	0.393145i	0.857075	−	0.515191i	$-0.172279\pi$
$59$	14.2070	−	3.01980i	1.84960	−	0.393145i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		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
$66$	−6.53024	+	4.83280i	−0.803817	+	0.594876i
$67$	−1.53102	−	2.65180i	−0.187044	−	0.323969i	0.757220	−	0.653160i	$-0.226557\pi$
$67$	−1.53102	−	2.65180i	−0.187044	−	0.323969i	−0.944263	+	0.329191i	$0.893224\pi$
$68$	3.48636	−	7.83049i	0.422783	−	0.949586i
$69$		0			0
$70$		0			0
$71$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$71$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$72$	8.41324	+	1.10333i	0.991510	+	0.130028i
$73$	15.5183	+	5.04219i	1.81627	+	0.590143i	0.999921	+	0.0125899i	$0.00400761\pi$
$73$	15.5183	+	5.04219i	1.81627	+	0.590143i	0.816353	+	0.577553i	$0.195992\pi$
$74$		0			0
$75$	3.62372	−	7.86566i	0.418432	−	0.908248i
$76$	15.0960	−	8.71568i	1.73163	−	0.999757i
$77$		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
$81$	5.67091	+	6.98862i	0.630101	+	0.776513i
$82$	9.03304	+	6.56289i	0.997532	+	0.724750i
$83$	5.23404	+	11.7559i	0.574511	+	1.29037i	0.934017	+	0.357229i	$0.116279\pi$
$83$	5.23404	+	11.7559i	0.574511	+	1.29037i	−0.359506	+	0.933143i	$0.617055\pi$
$84$		0			0
$85$		0			0
$86$	−11.7028	−	5.21043i	−1.26195	−	0.561855i
$87$		0			0
$88$	8.22359	+	4.51360i	0.876638	+	0.481151i
$89$	−17.8873			−1.89605			−0.948026	−	0.318192i	$-0.896924\pi$
$89$	−17.8873			−1.89605			−0.948026	+	0.318192i	$0.896924\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−2.90785	−	9.35652i	−0.296781	−	0.954945i
$97$	−1.65493	−	15.7456i	−0.168032	−	1.59872i	−0.675705	−	0.737172i	$-0.736161\pi$
$97$	−1.65493	−	15.7456i	−0.168032	−	1.59872i	0.507673	−	0.861550i	$-0.330506\pi$
$98$			9.89949i			1.00000i
$99$	3.03637	+	9.47526i	0.305166	+	0.952299i
$100$	−10.0000			−1.00000
$101$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$101$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$102$	−7.71067	−	7.12408i	−0.763470	−	0.705389i
$103$		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
$107$	7.64335	−	2.48347i	0.738910	−	0.240086i	0.0847076	−	0.996406i	$-0.473004\pi$
$107$	7.64335	−	2.48347i	0.738910	−	0.240086i	0.654203	+	0.756319i	$0.273004\pi$
$108$	4.58938	−	9.32404i	0.441613	−	0.897206i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.47792	−	3.86262i	0.327175	−	0.363365i	−0.557006	−	0.830508i	$-0.688050\pi$
$113$	3.47792	−	3.86262i	0.327175	−	0.363365i	0.884182	+	0.467143i	$0.154717\pi$
$114$	−4.17024	−	20.9377i	−0.390578	−	1.96100i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−19.5353	+	6.34741i	−1.79837	+	0.584327i
$119$		0			0
$120$		0			0
$121$	−0.675596	+	10.9792i	−0.0614178	+	0.998112i
$122$		0			0
$123$	11.1655	−	7.89517i	1.00675	−	0.711883i
$124$		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
$129$	−10.6471	+	11.5237i	−0.937422	+	1.01461i
$130$		0			0
$131$	18.6102	−	10.7446i	1.62598	−	0.938759i	0.640702	−	0.767790i	$-0.278643\pi$
$131$	18.6102	−	10.7446i	1.62598	−	0.938759i	0.985276	−	0.170970i	$-0.0546900\pi$
$132$	8.47016	−	7.76250i	0.737233	−	0.675639i
$133$		0			0
$134$	2.54533	+	3.50334i	0.219883	+	0.302643i
$135$		0			0
$136$	−3.74590	+	11.5287i	−0.321208	+	0.988577i
$137$	−3.40033	+	1.51393i	−0.290510	+	0.129343i	−0.546817	−	0.837252i	$-0.684161\pi$
$137$	−3.40033	+	1.51393i	−0.290510	+	0.129343i	0.256307	+	0.966595i	$0.417494\pi$
$138$		0			0
$139$	−4.84334	−	22.7861i	−0.410807	−	1.93270i	−0.356879	−	0.934151i	$-0.616159\pi$
$139$	−4.84334	−	22.7861i	−0.410807	−	1.93270i	−0.0539282	−	0.998545i	$-0.517174\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−11.9960	−	0.308098i	−0.999670	−	0.0256748i
$145$		0			0
$146$	−22.5713	−	4.79767i	−1.86801	−	0.397058i
$147$	11.4819	+	3.89436i	0.947011	+	0.321202i
$148$		0			0
$149$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$149$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$150$	−3.93390	+	11.5985i	−0.321202	+	0.947011i
$151$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$151$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$152$	−19.9436	+	14.4899i	−1.61764	+	1.17529i
$153$	−11.2961	+	6.14065i	−0.913239	+	0.496442i
$154$		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
$162$	−9.00904	−	8.99095i	−0.707817	−	0.706396i
$163$	−19.0863	+	13.8670i	−1.49495	+	1.08615i	−0.522612	+	0.852570i	$0.675042\pi$
$163$	−19.0863	+	13.8670i	−1.49495	+	1.08615i	−0.972339	+	0.233575i	$0.924958\pi$
$164$	−13.6748	−	7.89517i	−1.06782	−	0.616509i
$165$		0			0
$166$	−9.09932	−	15.7605i	−0.706244	−	1.22325i
$167$		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
$171$	−25.9251	−	3.39985i	−1.98254	−	0.259993i
$172$	17.2298	+	5.59832i	1.31376	+	0.426868i
$173$		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
$176$	−12.2334	−	5.13256i	−0.922129	−	0.386882i
$177$	−0.322978	+	25.1550i	−0.0242765	+	1.89076i
$178$	25.1579	−	2.64420i	1.88567	−	0.198191i
$179$	−7.53762	−	23.1984i	−0.563388	−	1.73393i	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−7.53762	−	23.1984i	−0.563388	−	1.73393i	0.109303	−	0.994008i	$-0.465138\pi$
$180$		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
$187$	−14.1010	+	1.79122i	−1.03117	+	0.130987i
$188$		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	$0.266667\pi$
$192$	5.47293	+	12.7298i	0.394975	+	0.918692i
$193$	−10.5094	−	1.10458i	−0.756482	−	0.0795095i	−0.281568	−	0.959541i	$-0.590854\pi$
$193$	−10.5094	−	1.10458i	−0.756482	−	0.0795095i	−0.474915	+	0.880032i	$0.657521\pi$
$194$	4.65520	+	21.9010i	0.334224	+	1.57240i
$195$		0			0
$196$	−1.46340	−	13.9233i	−0.104528	−	0.994522i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−5.67123	−	12.8778i	−0.403037	−	0.915184i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	14.0647	−	1.47826i	0.994522	−	0.104528i
$201$	5.06465	−	1.57401i	0.357233	−	0.111022i
$202$		0			0
$203$		0			0
$204$	11.8979	+	8.87994i	0.833021	+	0.621720i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−25.3407	−	13.9085i	−1.75285	−	0.962068i
$210$		0			0
$211$	−5.02939	+	11.2962i	−0.346237	+	0.777662i	0.653547	+	0.756886i	$0.273280\pi$
$211$	−5.02939	+	11.2962i	−0.346237	+	0.777662i	−0.999784	+	0.0207756i	$0.993386\pi$
$212$		0			0
$213$		0			0
$214$	−10.3830	+	4.62280i	−0.709766	+	0.316008i
$215$		0			0
$216$	−5.07647	+	13.7924i	−0.345410	+	0.938452i
$217$		0			0
$218$		0			0
$219$	−14.4439	+	24.2918i	−0.976026	+	1.64149i
$220$		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
$225$	11.9049	+	9.12544i	0.793659	+	0.608363i
$226$	−4.32058	+	5.94677i	−0.287401	+	0.395573i
$227$	15.1615	−	13.6514i	1.00630	−	0.906078i	0.0107165	−	0.999943i	$-0.496589\pi$
$227$	15.1615	−	13.6514i	1.00630	−	0.906078i	0.995585	+	0.0938647i	$0.0299221\pi$
$228$	8.96043	+	28.8317i	0.593419	+	1.90943i
$229$		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
$233$	17.8845	+	24.6159i	1.17165	+	1.61264i	0.651813	+	0.758380i	$0.274009\pi$
$233$	17.8845	+	24.6159i	1.17165	+	1.61264i	0.519841	+	0.854263i	$0.325991\pi$
$234$		0			0
$235$		0			0
$236$	26.5375	−	11.8152i	1.72744	−	0.769107i
$237$		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
$241$	−6.89897	−	3.98312i	−0.444402	−	0.256575i	0.261061	−	0.965322i	$-0.415928\pi$
$241$	−6.89897	−	3.98312i	−0.444402	−	0.256575i	−0.705463	+	0.708747i	$0.749261\pi$
$242$	−0.672809	−	15.5418i	−0.0432498	−	0.999064i
$243$	−13.9722	+	6.91215i	−0.896317	+	0.443415i
$244$		0			0
$245$		0			0
$246$	−14.5367	+	12.7548i	−0.926828	+	0.813218i
$247$		0			0
$248$		0			0
$249$	−21.8593	+	4.35380i	−1.38528	+	0.275911i
$250$		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
$256$	10.7061	−	11.8903i	0.669131	−	0.743145i
$257$	14.0732	−	2.99135i	0.877861	−	0.186595i	0.253127	−	0.967433i	$-0.418541\pi$
$257$	14.0732	−	2.99135i	0.877861	−	0.186595i	0.624734	+	0.780838i	$0.285208\pi$
$258$	13.2712	−	17.7817i	0.826231	−	1.10704i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−24.5863	+	17.8630i	−1.51894	+	1.10358i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	−10.7655	+	12.1698i	−0.662570	+	0.749000i
$265$		0			0
$266$		0			0
$267$	6.83000	−	30.2195i	0.417989	−	1.84941i
$268$	−4.09780	−	4.55107i	−0.250313	−	0.278001i
$269$		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	$0.100000\pi$
$272$	3.56425	−	16.7685i	0.216114	−	1.01674i
$273$		0			0
$274$	4.55866	−	2.63194i	0.275398	−	0.159001i
$275$	8.60026	+	14.1787i	0.518615	+	0.855008i
$276$		0			0
$277$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$277$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$278$	10.1804	+	31.3320i	0.610578	+	1.87917i
$279$		0			0
$280$		0			0
$281$	−5.00380	−	11.2387i	−0.298502	−	0.670446i	0.700567	−	0.713587i	$-0.252930\pi$
$281$	−5.00380	−	11.2387i	−0.298502	−	0.670446i	−0.999069	+	0.0431402i	$0.986264\pi$
$282$		0			0
$283$	−18.9174	−	17.0333i	−1.12452	−	1.01252i	−0.999793	−	0.0203327i	$-0.993527\pi$
$283$	−18.9174	−	17.0333i	−1.12452	−	1.01252i	−0.124728	−	0.992191i	$-0.539806\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	16.9176	−	1.33999i	0.996878	−	0.0789598i
$289$	−0.422676	−	1.30086i	−0.0248633	−	0.0765214i
$290$		0			0
$291$	27.2331	+	3.21631i	1.59643	+	0.188544i
$292$	32.4549	+	3.41115i	1.89928	+	0.199623i
$293$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$293$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$294$	−16.7246	−	3.77997i	−0.975398	−	0.220452i
$295$		0			0
$296$		0			0
$297$	−17.1673	+	1.51177i	−0.996145	+	0.0877220i
$298$		0			0
$299$		0			0
$300$	3.81835	−	16.8944i	0.220452	−	0.975398i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	25.9081	−	23.3277i	1.48593	−	1.33794i
$305$		0			0
$306$	14.9799	−	10.3065i	0.856343	−	0.589182i
$307$		−	21.5807i		−	1.23168i	−0.787872	−	0.615839i	$-0.788817\pi$
$307$		−	21.5807i		−	1.23168i	0.787872	−	0.615839i	$-0.211183\pi$
$308$		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
$313$	−29.1553	+	12.9808i	−1.64796	+	0.733717i	−0.999618	−	0.0276348i	$-0.991202\pi$
$313$	−29.1553	+	12.9808i	−1.64796	+	0.733717i	−0.648338	+	0.761352i	$0.724536\pi$
$314$		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
$321$	1.27718	+	13.8612i	0.0712852	+	0.773659i
$322$		0			0
$323$	11.5428	−	35.5252i	0.642260	−	1.97667i
$324$	14.0000	+	11.3137i	0.777778	+	0.628539i
$325$		0			0
$326$	24.7943	−	22.3249i	1.37323	−	1.23646i
$327$		0			0
$328$	20.4003	+	9.08280i	1.12642	+	0.501514i
$329$		0			0
$330$		0			0
$331$	−17.9985	+	31.1743i	−0.989287	+	1.71350i	−0.368220	+	0.929739i	$0.620033\pi$
$331$	−17.9985	+	31.1743i	−0.989287	+	1.71350i	−0.621067	+	0.783757i	$0.713301\pi$
$332$	15.1277	+	20.8215i	0.830240	+	1.14273i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−6.88501	−	32.3914i	−0.375050	−	1.76447i	−0.609936	−	0.792451i	$-0.708805\pi$
$337$	−6.88501	−	32.3914i	−0.375050	−	1.76447i	0.234886	−	0.972023i	$-0.424528\pi$
$338$	13.6626	+	12.3018i	0.743145	+	0.669131i
$339$	5.19767	+	7.35062i	0.282299	+	0.399231i
$340$		0			0
$341$		0			0
$342$	36.9653	+	0.949391i	1.99886	+	0.0513372i
$343$		0			0
$344$	−25.0608	−	5.32683i	−1.35119	−	0.287204i
$345$		0			0
$346$		0			0
$347$	28.9033	+	3.03786i	1.55161	+	0.163081i	0.841207	−	0.540714i	$-0.181846\pi$
$347$	28.9033	+	3.03786i	1.55161	+	0.163081i	0.710404	+	0.703795i	$0.248512\pi$
$348$		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
$352$	17.9646	+	5.41036i	0.957518	+	0.288373i
$353$	1.62924	−	2.82192i	0.0867154	−	0.150196i	−0.819405	−	0.573214i	$-0.805696\pi$
$353$	1.62924	−	2.82192i	0.0867154	−	0.150196i	0.906121	+	0.423019i	$0.139030\pi$
$354$	−3.26429	−	35.4274i	−0.173495	−	1.88294i
$355$		0			0
$356$	−34.9929	+	7.43797i	−1.85462	+	0.394211i
$357$		0			0
$358$	14.0307	+	31.5135i	0.741547	+	1.66554i
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$		0			0
$361$	46.0841	−	33.4821i	2.42548	−	1.76221i
$362$		0			0
$363$	−18.2908	−	5.33363i	−0.960017	−	0.279943i
$364$		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
$369$	9.07504	+	21.8780i	0.472428	+	1.13892i
$370$		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	$0.833333\pi$
$374$	19.5678	−	4.60377i	1.01182	−	0.238056i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	3.61365	+	2.62547i	0.185621	+	0.134861i	0.676715	−	0.736245i	$-0.263403\pi$
$379$	3.61365	+	2.62547i	0.185621	+	0.134861i	−0.491094	+	0.871106i	$0.663403\pi$
$380$		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	$0.133333\pi$
$384$	−9.57928	−	17.0950i	−0.488840	−	0.872373i
$385$		0			0
$386$	14.9444			0.760649
$387$	−15.4032	−	22.3877i	−0.782990	−	1.13803i
$388$	−9.78491	−	30.1148i	−0.496753	−	1.52885i
$389$		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
$393$	11.0463	+	35.5434i	0.557212	+	1.79293i
$394$		0			0
$395$		0			0
$396$	9.88007	+	17.2738i	0.496492	+	0.868041i
$397$		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
$401$	4.18200	−	39.7891i	0.208839	−	1.98697i	0.0590262	−	0.998256i	$-0.481200\pi$
$401$	4.18200	−	39.7891i	0.208839	−	1.98697i	0.149813	−	0.988714i	$-0.452133\pi$
$402$	−6.89058	+	2.96248i	−0.343671	+	0.147755i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−18.0467	−	10.7305i	−0.893445	−	0.531240i
$409$	−14.6519	+	32.9088i	−0.724491	+	1.62723i	0.0531978	+	0.998584i	$0.483059\pi$
$409$	−14.6519	+	32.9088i	−0.724491	+	1.62723i	−0.777689	+	0.628649i	$0.783608\pi$
$410$		0			0
$411$	−1.25932	−	6.32272i	−0.0621176	−	0.311877i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	40.3451	+	0.518013i	1.97571	+	0.0253672i
$418$	37.6968	+	15.8158i	1.84381	+	0.773575i
$419$	18.0875	+	31.3284i	0.883630	+	1.53049i	0.847276	+	0.531153i	$0.178241\pi$
$419$	18.0875	+	31.3284i	0.883630	+	1.53049i	0.0363540	+	0.999339i	$0.488426\pi$
$420$		0			0
$421$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$421$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$422$	5.40380	−	16.6312i	0.263053	−	0.809593i
$423$		0			0
$424$		0			0
$425$	−15.9247	+	14.3387i	−0.772463	+	0.695529i
$426$		0			0
$427$		0			0
$428$	13.9200	−	8.03669i	0.672846	−	0.388468i
$429$		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
$433$	11.7546	−	36.1768i	0.564888	−	1.73855i	−0.103396	−	0.994640i	$-0.532971\pi$
$433$	11.7546	−	36.1768i	0.564888	−	1.73855i	0.668284	−	0.743906i	$-0.267029\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	16.7239	−	36.3008i	0.799097	−	1.73452i
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−10.9635	+	17.9110i	−0.522070	+	0.852903i
$442$		0			0
$443$	−1.54280	−	0.327931i	−0.0733004	−	0.0155805i	0.171115	−	0.985251i	$-0.445263\pi$
$443$	−1.54280	−	0.327931i	−0.0733004	−	0.0155805i	−0.244416	+	0.969670i	$0.578596\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−26.1372	+	18.9898i	−1.23349	+	0.896183i	−0.997147	−	0.0754863i	$-0.975949\pi$
$449$	−26.1372	+	18.9898i	−1.23349	+	0.896183i	−0.236344	+	0.971670i	$0.575949\pi$
$450$	−18.0928	−	11.0748i	−0.852903	−	0.522070i
$451$	0.566387	+	26.1792i	0.0266701	+	1.23273i
$452$	5.19767	−	9.00263i	0.244478	−	0.423448i
$453$		0			0
$454$	−19.3061	+	21.4415i	−0.906078	+	1.00630i
$455$		0			0
$456$	−16.8646	−	39.2263i	−0.789757	−	1.83694i
$457$	11.9602	+	26.8632i	0.559477	+	1.25661i	0.942913	+	0.333038i	$0.108074\pi$
$457$	11.9602	+	26.8632i	0.559477	+	1.25661i	−0.383437	+	0.923567i	$0.625260\pi$
$458$		0			0
$459$	−6.06099	−	21.4288i	−0.282903	−	1.00021i
$460$		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
$466$	−28.7928	−	31.9777i	−1.33380	−	1.48134i
$467$	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
$472$	−35.5775	+	20.5407i	−1.63759	+	0.945460i
$473$	−6.88043	−	29.2444i	−0.316362	−	1.34466i
$474$		0			0
$475$	−43.3397	+	4.55518i	−1.98856	+	0.209006i
$476$		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
$482$	10.2920	+	4.58228i	0.468787	+	0.208717i
$483$		0			0
$484$	3.24376	+	21.7596i	0.147444	+	0.989070i
$485$		0			0
$486$	18.6296	−	11.7872i	0.845057	−	0.534676i
$487$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$487$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$488$		0			0
$489$	−16.1396	−	37.5400i	−0.729858	−	1.69762i
$490$		0			0
$491$	6.23785	+	29.3468i	0.281510	+	1.32440i	0.860660	+	0.509181i	$0.170052\pi$
$491$	6.23785	+	29.3468i	0.281510	+	1.32440i	−0.579149	+	0.815222i	$0.696615\pi$
$492$	18.5599	−	20.0881i	0.836746	−	0.905643i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	30.1008	−	9.35484i	1.34885	−	0.419200i
$499$	−4.36913	+	0.928687i	−0.195589	+	0.0415737i	−0.304664	−	0.952460i	$-0.598544\pi$
$499$	−4.36913	+	0.928687i	−0.195589	+	0.0415737i	0.109075	+	0.994033i	$0.465211\pi$
$500$		0			0
$501$		0			0
$502$	25.1647	−	22.6584i	1.12316	−	1.01129i
$503$		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
$507$	19.6429	−	11.0071i	0.872373	−	0.488840i
$508$		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
$513$	15.6429	−	42.5006i	0.690652	−	1.87645i
$514$	−19.3513	+	6.28761i	−0.853547	+	0.277334i
$515$		0			0
$516$	−16.0370	+	26.9711i	−0.705988	+	1.18734i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.09396	+	3.36686i	−0.0479272	+	0.147505i	−0.972156	−	0.234334i	$-0.924709\pi$
$521$	−1.09396	+	3.36686i	−0.0479272	+	0.147505i	0.924229	+	0.381839i	$0.124709\pi$
$522$		0			0
$523$	−16.6190	+	22.8740i	−0.726696	+	1.00021i	0.272578	+	0.962134i	$0.412124\pi$
$523$	−16.6190	+	22.8740i	−0.726696	+	1.00021i	−0.999275	+	0.0380781i	$0.987876\pi$
$524$	31.9391	−	28.7581i	1.39527	−	1.25630i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	13.3423	−	18.7078i	0.580649	−	0.814154i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$	−42.3745	−	10.1507i	−1.83890	−	0.440503i
$532$		0			0
$533$		0			0
$534$	−5.13895	+	43.5124i	−0.222384	+	1.88297i
$535$		0			0
$536$	6.43619	+	5.79517i	0.278001	+	0.250313i
$537$	42.0704	−	3.87639i	1.81547	−	0.167278i
$538$		0			0
$539$	−18.4829	+	14.0493i	−0.796114	+	0.605147i
$540$		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
$544$	−2.53418	+	24.1112i	−0.108652	+	1.03376i
$545$		0			0
$546$		0			0
$547$	−5.92692	+	27.8840i	−0.253417	+	1.19223i	0.648803	+	0.760956i	$0.275270\pi$
$547$	−5.92692	+	27.8840i	−0.253417	+	1.19223i	−0.902220	+	0.431276i	$0.858064\pi$
$548$	−6.02253	+	4.37562i	−0.257270	+	0.186917i
$549$		0			0
$550$	−14.1919	−	18.6705i	−0.605147	−	0.796114i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−18.9500	−	42.5624i	−0.803660	−	1.80505i
$557$		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
$561$	2.35809	−	24.5067i	0.0995585	−	1.03467i
$562$	8.69906	+	15.0672i	0.366947	+	0.635572i
$563$	−18.6256	+	41.8338i	−0.784975	+	1.76308i	−0.152800	+	0.988257i	$0.548829\pi$
$563$	−18.6256	+	41.8338i	−0.784975	+	1.76308i	−0.632175	+	0.774826i	$0.717837\pi$
$564$		0			0
$565$		0			0
$566$	29.1246	+	21.1603i	1.22420	+	0.889432i
$567$		0			0
$568$		0			0
$569$	3.34143	−	15.7202i	0.140080	−	0.659025i	−0.850935	−	0.525271i	$-0.823964\pi$
$569$	3.34143	−	15.7202i	0.140080	−	0.659025i	0.991015	−	0.133753i	$-0.0427029\pi$
$570$		0			0
$571$	1.87117	−	1.08032i	0.0783062	−	0.0452101i	−0.460336	−	0.887745i	$-0.652271\pi$
$571$	1.87117	−	1.08032i	0.0783062	−	0.0452101i	0.538642	+	0.842535i	$0.318938\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−23.5959	+	4.38551i	−0.983163	+	0.182729i
$577$	32.6145	+	23.6958i	1.35776	+	0.986471i	0.998584	+	0.0532013i	$0.0169425\pi$
$577$	32.6145	+	23.6958i	1.35776	+	0.986471i	0.359177	+	0.933270i	$0.383058\pi$
$578$	0.786781	+	1.76714i	0.0327258	+	0.0735033i
$579$	5.87897	−	17.3332i	0.244322	−	0.720343i
$580$		0			0
$581$		0			0
$582$	−38.7779	−	0.497890i	−1.60740	−	0.0206382i
$583$		0			0
$584$	−46.1510			−1.90974
$585$		0			0
$586$		0			0
$587$	10.6164	+	11.7907i	0.438186	+	0.486654i	0.921272	−	0.388918i	$-0.127151\pi$
$587$	10.6164	+	11.7907i	0.438186	+	0.486654i	−0.483087	+	0.875573i	$0.660484\pi$
$588$	24.0813	+	2.84408i	0.993098	+	0.117288i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$			31.1035i			1.27727i	0.769510	+	0.638634i	$0.220500\pi$
$593$			31.1035i			1.27727i	−0.769510	+	0.638634i	$0.779500\pi$
$594$	23.9217	−	4.66402i	0.981519	−	0.191367i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$599$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$600$	−2.87296	+	24.3258i	−0.117288	+	0.993098i
$601$	35.3157	−	31.7984i	1.44056	−	1.29708i	0.555566	−	0.831472i	$-0.312502\pi$
$601$	35.3157	−	31.7984i	1.44056	−	1.29708i	0.884990	−	0.465610i	$-0.154165\pi$
$602$		0			0
$603$	0.725333	+	9.15743i	0.0295379	+	0.372919i
$604$		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	$0.633333\pi$
$608$	−32.9904	+	36.6395i	−1.33794	+	1.48593i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−19.5452	+	16.7101i	−0.790066	+	0.675467i
$613$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$613$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$614$	3.19018	+	30.3526i	0.128745	+	1.22493i
$615$		0			0
$616$		0			0
$617$	−10.5558	−	18.2831i	−0.424959	−	0.736051i	0.571457	−	0.820632i	$-0.306378\pi$
$617$	−10.5558	−	18.2831i	−0.424959	−	0.736051i	−0.996417	+	0.0845806i	$0.973045\pi$
$618$		0			0
$619$	33.5043	+	7.12155i	1.34665	+	0.286239i	0.824137	−	0.566391i	$-0.191661\pi$
$619$	33.5043	+	7.12155i	1.34665	+	0.286239i	0.522514	+	0.852631i	$0.324994\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	22.8386	+	10.1684i	0.913545	+	0.406737i
$626$	39.0871	−	22.5669i	1.56223	−	0.901956i
$627$	33.1734	−	37.5007i	1.32482	−	1.49764i
$628$		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
$633$	−17.1638	−	12.8101i	−0.682201	−	0.509156i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	48.7833	+	10.3692i	1.92682	+	0.409559i	0.999365	+	0.0356372i	$0.0113461\pi$
$641$	48.7833	+	10.3692i	1.92682	+	0.409559i	0.927460	+	0.373922i	$0.121987\pi$
$642$	−3.84536	−	19.3066i	−0.151764	−	0.761969i
$643$	−5.13533	+	48.8594i	−0.202518	+	1.92683i	0.145537	+	0.989353i	$0.453509\pi$
$643$	−5.13533	+	48.8594i	−0.202518	+	1.92683i	−0.348054	+	0.937474i	$0.613157\pi$
$644$		0			0
$645$		0			0
$646$	−10.9831	+	51.6713i	−0.432123	+	2.03298i
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$	−21.3630	−	13.8428i	−0.839217	−	0.543796i
$649$	−39.5754	−	27.4653i	−1.55347	−	1.07811i
$650$		0			0
$651$		0			0
$652$	−31.5721	+	35.0644i	−1.23646	+	1.37323i
$653$		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
$656$	−30.0350	−	9.75896i	−1.17267	−	0.381024i
$657$	−35.5244	−	33.6775i	−1.38594	−	1.31388i
$658$		0			0
$659$	−1.95763	−	1.13024i	−0.0762583	−	0.0440278i	0.461386	−	0.887200i	$-0.347352\pi$
$659$	−1.95763	−	1.13024i	−0.0762583	−	0.0440278i	−0.537644	+	0.843172i	$0.680686\pi$
$660$		0			0
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$	20.7059	−	46.5063i	0.804759	−	1.80752i
$663$		0			0
$664$	−24.3545	−	27.0484i	−0.945139	−	1.04968i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−6.18793	+	0.650377i	−0.238527	+	0.0250702i	−0.223038	−	0.974810i	$-0.571597\pi$
$673$	−6.18793	+	0.650377i	−0.238527	+	0.0250702i	−0.0154894	+	0.999880i	$0.504931\pi$
$674$	14.4718	+	44.5397i	0.557434	+	1.71560i
$675$	−19.9626	+	16.6282i	−0.768360	+	0.640018i
$676$	−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	$0.366667\pi$
$678$	−8.39696	−	9.57005i	−0.322483	−	0.367535i
$679$		0			0
$680$		0			0
$681$	17.2741	+	30.8269i	0.661945	+	1.18129i
$682$		0			0
$683$	−5.94439			−0.227456			−0.113728	−	0.993512i	$-0.536279\pi$
$683$	−5.94439			−0.227456			−0.113728	+	0.993512i	$0.536279\pi$
$684$	−52.1308	+	4.12913i	−1.99327	+	0.157881i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	36.0346	+	3.78739i	1.37381	+	0.144393i
$689$		0			0
$690$		0			0
$691$	−1.04478	−	9.94041i	−0.0397453	−	0.378151i	−0.996256	−	0.0864535i	$-0.972447\pi$
$691$	−1.04478	−	9.94041i	−0.0397453	−	0.378151i	0.956511	−	0.291698i	$-0.0942201\pi$
$692$		0			0
$693$		0			0
$694$	−41.1006			−1.56016
$695$		0			0
$696$		0			0
$697$	−33.0974	+	7.03508i	−1.25365	+	0.266473i
$698$		0			0
$699$	−48.4160	+	20.8156i	−1.83126	+	0.787317i
$700$		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
$704$	−26.0664	−	4.95386i	−0.982416	−	0.186706i
$705$		0			0
$706$	−1.87431	+	4.20978i	−0.0705407	+	0.158437i
$707$		0			0
$708$	9.82819	+	49.3449i	0.369366	+	1.85449i
$709$		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
$712$	48.1168	−	15.6341i	1.80325	−	0.585912i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−24.3923	−	42.2486i	−0.911582	−	1.57891i
$717$		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
$722$	−59.8662	+	53.9038i	−2.22799	+	2.00609i
$723$	9.36350	−	10.1345i	0.348232	−	0.376906i
$724$		0			0
$725$		0			0
$726$	26.5138	+	4.79773i	0.984020	+	0.178060i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	−6.34258	−	26.2445i	−0.234910	−	0.972017i
$730$		0			0
$731$	35.4653	−	15.7902i	1.31173	−	0.584021i
$732$		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
$737$	−2.92861	+	9.72419i	−0.107877	+	0.358195i
$738$	−15.9979	−	29.4291i	−0.588890	−	1.08330i
$739$	−31.5380	−	43.4084i	−1.16015	−	1.59680i	−0.710698	−	0.703497i	$-0.751621\pi$
$739$	−31.5380	−	43.4084i	−1.16015	−	1.59680i	−0.449448	−	0.893307i	$-0.648379\pi$
$740$		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
$747$	0.991180	−	38.5924i	0.0362654	−	1.41202i
$748$	−26.8408	+	9.36767i	−0.981398	+	0.342516i
$749$		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
$753$	−16.3807	−	38.1008i	−0.596947	−	1.38847i
$754$		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	$0.800000\pi$
$758$	−5.47059	−	3.15845i	−0.198701	−	0.114720i
$759$		0			0
$760$		0			0
$761$	−22.3108	+	50.1109i	−0.808766	+	1.81652i	−0.306245	+	0.951953i	$0.599073\pi$
$761$	−22.3108	+	50.1109i	−0.808766	+	1.81652i	−0.502521	+	0.864565i	$0.667594\pi$
$762$		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	$-0.296501\pi$
$769$	44.0908	−	25.4558i	1.58996	−	0.917961i	0.993313	−	0.115454i	$-0.0368323\pi$
$770$		0			0
$771$	−0.319935	+	24.9180i	−0.0115222	+	0.897399i
$772$	−21.0188	+	2.20916i	−0.756482	+	0.0795095i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	24.9736	+	29.2106i	0.897657	+	1.04995i
$775$		0			0
$776$	18.2139	+	40.9091i	0.653840	+	1.46855i
$777$		0			0
$778$		0			0
$779$	−62.8627	−	27.9883i	−2.25229	−	1.00278i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−8.65248	−	26.6296i	−0.309017	−	0.951057i
$785$		0			0
$786$	−20.7905	−	48.3577i	−0.741572	−	1.72486i
$787$	−55.1155	−	5.79287i	−1.96466	−	0.206494i	−0.966010	−	0.258506i	$-0.916770\pi$
$787$	−55.1155	−	5.79287i	−1.96466	−	0.206494i	−0.998646	+	0.0520120i	$0.983437\pi$
$788$		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		0.104528	−	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
$801$	48.4461	+	23.0777i	1.71176	+	0.815412i
$802$			56.5802i			1.99792i
$803$	−23.0755	−	48.9506i	−0.814317	−	1.72743i
$804$	9.25344	−	5.18523i	0.326344	−	0.182869i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	19.6278	−	27.0154i	0.690078	−	0.949811i	−0.309921	−	0.950762i	$-0.600303\pi$
$809$	19.6278	−	27.0154i	0.690078	−	0.949811i	1.00000		0.000951178i	$0.000302769\pi$
$810$		0			0
$811$	51.5610	−	16.7532i	1.81055	−	0.588284i	0.810555	−	0.585662i	$-0.199166\pi$
$811$	51.5610	−	16.7532i	1.81055	−	0.588284i	0.999997	−	0.00262139i	$-0.000834414\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	26.9683	+	12.4244i	0.944080	+	0.434939i
$817$	77.2237	+	16.4144i	2.70172	+	0.574268i
$818$	15.7427	−	48.4510i	0.550430	−	1.69405i
$819$		0			0
$820$		0			0
$821$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$821$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$822$	2.70585	+	8.70654i	0.0943773	+	0.303675i
$823$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$823$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$824$		0			0
$825$	−27.2379	+	9.11568i	−0.948303	+	0.317367i
$826$		0			0
$827$	−26.5907	−	36.5990i	−0.924650	−	1.27267i	−0.961910	−	0.273366i	$-0.911863\pi$
$827$	−26.5907	−	36.5990i	−0.924650	−	1.27267i	0.0372604	−	0.999306i	$-0.488137\pi$
$828$		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
$833$	−22.2946	−	20.0742i	−0.772463	−	0.695529i
$834$	−56.8207	+	5.23548i	−1.96754	+	0.181290i
$835$		0			0
$836$	−55.3573	−	16.6718i	−1.91457	−	0.576607i
$837$		0			0
$838$	−30.0705	−	41.3885i	−1.03877	−	1.42974i
$839$		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
$843$	20.8978	−	4.16228i	0.719757	−	0.143357i
$844$	−5.14175	+	24.1900i	−0.176986	+	0.832655i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	36.0000	−	25.4558i	1.23552	−	0.873642i
$850$	20.2780	−	22.5210i	0.695529	−	0.772463i
$851$		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
$856$	−18.3899	+	13.3611i	−0.628554	+	0.456672i
$857$	−11.6346	−	6.71722i	−0.397429	−	0.229456i	0.287945	−	0.957647i	$-0.407028\pi$
$857$	−11.6346	−	6.71722i	−0.397429	−	0.229456i	−0.685374	+	0.728191i	$0.740361\pi$
$858$		0			0
$859$	29.2484	+	50.6597i	0.997942	+	1.72849i	0.554507	+	0.832179i	$0.312907\pi$
$859$	29.2484	+	50.6597i	0.997942	+	1.72849i	0.443434	+	0.896307i	$0.353760\pi$
$860$		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	$0.200000\pi$
$864$	−4.19589	+	29.0929i	−0.142747	+	0.989759i
$865$		0			0
$866$	−11.1845	+	52.6191i	−0.380066	+	1.78807i
$867$	2.35912	−	0.217370i	0.0801200	−	0.00738229i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−15.8323	+	44.7805i	−0.535843	+	1.51559i
$874$		0			0
$875$		0			0
$876$	−18.1554	+	53.5281i	−0.613413	+	1.80855i
$877$		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
$881$	18.6878			0.629610			0.314805	−	0.949156i	$-0.398061\pi$
$881$	18.6878			0.629610			0.314805	+	0.949156i	$0.398061\pi$
$882$	12.7721	−	26.8118i	0.430058	−	0.902801i
$883$	18.1895	+	55.9816i	0.612126	+	1.88393i	0.437250	+	0.899340i	$0.355953\pi$
$883$	18.1895	+	55.9816i	0.612126	+	1.88393i	0.174877	+	0.984590i	$0.444047\pi$
$884$		0			0
$885$		0			0
$886$	2.21837	+	0.233160i	0.0745275	+	0.00783316i
$887$		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
$891$	4.00101	−	29.5803i	0.134039	−	0.990976i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	33.9539	−	30.5722i	1.13306	−	1.02021i
$899$		0			0
$900$	27.0840	+	12.9017i	0.902801	+	0.430058i
$901$		0			0
$902$	−4.66656	−	36.7364i	−0.155379	−	1.22319i
$903$		0			0
$904$	−5.97953	+	13.4302i	−0.198876	+	0.446683i
$905$		0			0
$906$		0			0
$907$	20.2175	−	9.00141i	0.671311	−	0.298887i	−0.0426320	−	0.999091i	$-0.513574\pi$
$907$	20.2175	−	9.00141i	0.671311	−	0.298887i	0.713943	+	0.700204i	$0.246908\pi$
$908$	23.9837	−	33.0107i	0.795927	−	1.09550i
$909$		0			0
$910$		0			0
$911$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$911$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$912$	29.5181	+	52.6774i	0.977443	+	1.74432i
$913$	16.5119	−	39.3561i	0.546466	−	1.30250i
$914$	−20.7927	−	36.0141i	−0.687763	−	1.19124i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	11.6923	+	29.2430i	0.385904	+	0.965162i
$919$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$919$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$920$		0			0
$921$	36.4593	+	8.24028i	1.20138	+	0.271526i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−39.8186	+	17.7284i	−1.30641	+	0.581649i	−0.937554	−	0.347840i	$-0.886915\pi$
$929$	−39.8186	+	17.7284i	−1.30641	+	0.581649i	−0.368851	+	0.929489i	$0.620249\pi$
$930$		0			0
$931$	−12.6846	−	59.6766i	−0.415722	−	1.95582i
$932$	45.2233	+	40.7192i	1.48134	+	1.33380i
$933$		0			0
$934$	−51.3712	−	29.6592i	−1.68092	−	0.970477i
$935$		0			0
$936$		0			0
$937$	28.2540	+	38.8882i	0.923016	+	1.27042i	0.962522	+	0.271204i	$0.0874217\pi$
$937$	28.2540	+	38.8882i	0.923016	+	1.27042i	−0.0395055	+	0.999219i	$0.512578\pi$
$938$		0			0
$939$	−10.7977	−	54.2126i	−0.352370	−	1.76916i
$940$		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
$944$	47.0021	−	34.1490i	1.52979	−	1.11146i
$945$		0			0
$946$	14.0002	+	40.1141i	0.455184	+	1.30422i
$947$	−20.2588	+	35.0893i	−0.658323	+	1.14025i	0.322727	+	0.946492i	$0.395401\pi$
$947$	−20.2588	+	35.0893i	−0.658323	+	1.14025i	−0.981050	+	0.193757i	$0.937933\pi$
$948$		0			0
$949$		0			0
$950$	60.2824	−	12.8134i	1.95582	−	0.415722i
$951$		0			0
$952$		0			0
$953$	44.2244	+	14.3694i	1.43257	+	0.465470i	0.919573	−	0.392920i	$-0.128535\pi$
$953$	44.2244	+	14.3694i	1.43257	+	0.465470i	0.512998	+	0.858390i	$0.328535\pi$
$954$		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
$963$	−23.9054	−	3.13499i	−0.770340	−	0.101024i
$964$	−15.1527	−	4.92341i	−0.488035	−	0.158572i
$965$		0			0
$966$		0			0
$967$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$967$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$968$	−7.77885	−	30.1246i	−0.250022	−	0.968240i
$969$	55.6102	+	33.0657i	1.78646	+	1.06222i
$970$		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	$0.566383\pi$
$972$	−24.4595	+	19.3322i	−0.784539	+	0.620080i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−51.9705	−	23.1387i	−1.66268	−	0.740274i	−0.662720	−	0.748867i	$-0.730598\pi$
$977$	−51.9705	−	23.1387i	−1.66268	−	0.740274i	−0.999963	+	0.00859317i	$0.997265\pi$
$978$	28.2492	+	50.4128i	0.903309	+	1.61202i
$979$	40.6409	+	43.2185i	1.29889	+	1.38127i
$980$		0			0
$981$		0			0
$982$	−13.1115	−	40.3532i	−0.418406	−	1.28772i
$983$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$983$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$984$	−23.1344	+	30.9969i	−0.737497	+	0.988146i
$985$		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
$993$	−45.7946	−	42.3108i	−1.45325	−	1.34269i
$994$		0			0
$995$		0			0
$996$	−40.9529	+	17.6069i	−1.29764	+	0.557897i
$997$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$997$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$998$	6.00775	−	1.95204i	0.190172	−	0.0617906i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.ce.a.547.1	yes	16
8.3	odd	2	CM	792.2.ce.a.547.1	yes	16
9.4	even	3		792.2.ce.b.283.2	yes	16
11.7	odd	10		792.2.ce.b.403.2	yes	16
72.67	odd	6		792.2.ce.b.283.2	yes	16
88.51	even	10		792.2.ce.b.403.2	yes	16
99.40	odd	30	inner	792.2.ce.a.139.1	✓	16
792.139	even	30	inner	792.2.ce.a.139.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.ce.a.139.1	✓	16	99.40	odd	30	inner
792.2.ce.a.139.1	✓	16	792.139	even	30	inner
792.2.ce.a.547.1	yes	16	1.1	even	1	trivial
792.2.ce.a.547.1	yes	16	8.3	odd	2	CM
792.2.ce.b.283.2	yes	16	9.4	even	3
792.2.ce.b.283.2	yes	16	72.67	odd	6
792.2.ce.b.403.2	yes	16	11.7	odd	10
792.2.ce.b.403.2	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)

\(f(q)\)	\(=\)	\(q+(-1.40647 + 0.147826i) q^{2} +(-0.381835 + 1.68944i) q^{3} +(1.95630 - 0.415823i) q^{4} +(0.287296 - 2.43258i) q^{6} +(-2.68999 + 0.874032i) q^{8} +(-2.70840 - 1.29017i) q^{9} +O(q^{10})\)	\(q+(-1.40647 + 0.147826i) q^{2} +(-0.381835 + 1.68944i) q^{3} +(1.95630 - 0.415823i) q^{4} +(0.287296 - 2.43258i) q^{6} +(-2.68999 + 0.874032i) q^{8} +(-2.70840 - 1.29017i) q^{9} +(-2.27205 - 2.41615i) q^{11} +(-0.0444738 + 3.46382i) q^{12} +(3.65418 - 1.62695i) q^{16} +(2.51911 - 3.46726i) q^{17} +(4.00000 + 1.41421i) q^{18} +(8.28911 - 2.69329i) q^{19} +(3.55273 + 3.06237i) q^{22} +(-0.449490 - 4.87832i) q^{24} +(-4.89074 - 1.03956i) q^{25} +(3.21383 - 4.08305i) q^{27} +(-4.89898 + 2.82843i) q^{32} +(4.94949 - 2.91591i) q^{33} +(-3.03050 + 5.24897i) q^{34} +(-5.83492 - 1.39774i) q^{36} +(-11.2602 + 5.01337i) q^{38} +(-5.86725 - 5.28290i) q^{41} +(7.84469 + 4.52913i) q^{43} +(-5.44949 - 3.78194i) q^{44} +(1.35333 + 6.79474i) q^{48} +(0.731699 - 6.96165i) q^{49} +(7.03233 + 0.739128i) q^{50} +(4.89584 + 5.57980i) q^{51} +(-3.91657 + 6.21776i) q^{54} +(1.38508 + 15.0323i) q^{57} +(14.2070 - 3.01980i) q^{59} +(6.47214 - 4.70228i) q^{64} +(-6.53024 + 4.83280i) q^{66} +(-1.53102 - 2.65180i) q^{67} +(3.48636 - 7.83049i) q^{68} +(8.41324 + 1.10333i) q^{72} +(15.5183 + 5.04219i) q^{73} +(3.62372 - 7.86566i) q^{75} +(15.0960 - 8.71568i) q^{76} +(5.67091 + 6.98862i) q^{81} +(9.03304 + 6.56289i) q^{82} +(5.23404 + 11.7559i) q^{83} +(-11.7028 - 5.21043i) q^{86} +(8.22359 + 4.51360i) q^{88} -17.8873 q^{89} +(-2.90785 - 9.35652i) q^{96} +(-1.65493 - 15.7456i) q^{97} +9.89949i q^{98} +(3.03637 + 9.47526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more