LMFDB - Embedded newform 728.2.ds.a.293.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(293,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 6, 11]))

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

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

chi := DirichletCharacter("728.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.ds (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 8x^{12} + 40x^{10} - 161x^{8} + 360x^{6} + 648x^{4} - 2916x^{2} + 6561 $ x^16 - 4x^14 + 8x^12 + 40x^10 - 161x^8 + 360x^6 + 648x^4 - 2916*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			293.4
Root			$-0.197958 + 1.72070i$ of defining polynomial
Character	$\chi$	$=$	728.293
Dual form			728.2.ds.a.405.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 + 0.366025i) q^{2} +(1.58915 - 2.75249i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.54117 + 2.54117i) q^{5} +(-1.16334 + 4.34164i) q^{6} +(2.55560 + 0.684771i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-3.55080 - 6.15016i) q^{9} +(-4.40143 - 2.54117i) q^{10} -6.35660i q^{12} +(-2.47602 + 2.62094i) q^{13} -3.74166 q^{14} +(11.0328 - 2.95624i) q^{15} +(2.00000 - 3.46410i) q^{16} +(7.10159 + 7.10159i) q^{18} +(2.16840 - 8.09257i) q^{19} +(6.94259 + 1.86026i) q^{20} +(5.94606 - 5.94606i) q^{21} +(3.01441 + 1.74037i) q^{23} +(2.32668 + 8.68328i) q^{24} +7.91505i q^{25} +(2.42298 - 4.48655i) q^{26} -13.0361 q^{27} +(5.11120 - 1.36954i) q^{28} +(-13.9891 + 8.07659i) q^{30} +(-1.46410 + 5.46410i) q^{32} +(4.75409 + 8.23432i) q^{35} +(-12.3003 - 7.10159i) q^{36} +11.8483i q^{38} +(3.27933 + 10.9803i) q^{39} -10.1647 q^{40} +(-5.94606 + 10.2989i) q^{42} +(6.60541 - 24.6517i) q^{45} +(-4.75478 - 1.27404i) q^{46} +(-6.35660 - 11.0100i) q^{48} +(6.06218 + 3.50000i) q^{49} +(-2.89711 - 10.8122i) q^{50} +(-1.66766 + 7.01562i) q^{52} +(17.8076 - 4.77154i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(-18.8288 - 18.8288i) q^{57} +(14.4778 + 3.87931i) q^{59} +(16.1532 - 16.1532i) q^{60} +(-4.96731 - 8.60363i) q^{61} +(-4.86296 - 18.1488i) q^{63} -8.00000i q^{64} +(-12.9522 + 0.368255i) q^{65} +(9.58070 - 5.53142i) q^{69} +(-9.50817 - 9.50817i) q^{70} +(-4.29022 + 16.0113i) q^{71} +(19.4019 + 5.19873i) q^{72} +(21.7861 + 12.5782i) q^{75} +(-4.33679 - 16.1851i) q^{76} +(-8.49871 - 13.7990i) q^{78} -15.7417 q^{79} +(13.8852 - 3.72052i) q^{80} +(-10.0639 + 17.4312i) q^{81} +(-5.83132 - 5.83132i) q^{83} +(4.35281 - 16.2449i) q^{84} +36.0926i q^{90} +(-8.12246 + 5.00256i) q^{91} +6.96148 q^{92} +(26.0748 - 15.0543i) q^{95} +(12.7132 + 12.7132i) q^{96} +(-9.56218 - 2.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 32 q^{8} - 32 q^{9} + 40 q^{15} + 32 q^{16} + 64 q^{18} - 96 q^{30} + 32 q^{32} - 48 q^{36} + 8 q^{39} + 24 q^{46} + 136 q^{50} - 72 q^{57} - 32 q^{60} - 112 q^{63} - 16 q^{65} + 16 q^{71}+ \cdots - 56 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 32 * q^8 - 32 * q^9 + 40 * q^15 + 32 * q^16 + 64 * q^18 - 96 * q^30 + 32 * q^32 - 48 * q^36 + 8 * q^39 + 24 * q^46 + 136 * q^50 - 72 * q^57 - 32 * q^60 - 112 * q^63 - 16 * q^65 + 16 * q^71 + 112 * q^72 - 144 * q^78 - 192 * q^79 - 96 * q^81 - 96 * q^92 + 312 * q^95 - 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$	1.58915	−	2.75249i	0.917496	−	1.58915i	0.114291	−	0.993447i	$-0.463540\pi$
$3$	1.58915	−	2.75249i	0.917496	−	1.58915i	0.803205	−	0.595703i	$-0.203126\pi$
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	2.54117	+	2.54117i	1.13644	+	1.13644i	0.989083	+	0.147361i	$0.0470779\pi$
$5$	2.54117	+	2.54117i	1.13644	+	1.13644i	0.147361	+	0.989083i	$0.452922\pi$
$6$	−1.16334	+	4.34164i	−0.474931	+	1.77247i
$7$	2.55560	+	0.684771i	0.965926	+	0.258819i
$7$	2.55560	+	0.684771i	0.965926	+	0.258819i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−3.55080	−	6.15016i	−1.18360	−	2.05005i
$10$	−4.40143	−	2.54117i	−1.39185	−	0.803587i
$11$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$11$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$12$		−	6.35660i		−	1.83499i
$13$	−2.47602	+	2.62094i	−0.686725	+	0.726917i
$13$	−2.47602	+	2.62094i	−0.686725	+	0.726917i
$14$	−3.74166			−1.00000
$15$	11.0328	−	2.95624i	2.84866	−	0.763297i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	7.10159	+	7.10159i	1.67386	+	1.67386i
$19$	2.16840	−	8.09257i	0.497464	−	1.85656i	−0.0183009	−	0.999833i	$-0.505826\pi$
$19$	2.16840	−	8.09257i	0.497464	−	1.85656i	0.515765	−	0.856730i	$-0.327508\pi$
$20$	6.94259	+	1.86026i	1.55241	+	0.415967i
$21$	5.94606	−	5.94606i	1.29754	−	1.29754i
$22$		0			0
$23$	3.01441	+	1.74037i	0.628548	+	0.362892i	0.780189	−	0.625543i	$-0.215123\pi$
$23$	3.01441	+	1.74037i	0.628548	+	0.362892i	−0.151642	+	0.988436i	$0.548456\pi$
$24$	2.32668	+	8.68328i	0.474931	+	1.77247i
$25$			7.91505i			1.58301i
$26$	2.42298	−	4.48655i	0.475185	−	0.879886i
$27$	−13.0361			−2.50880
$28$	5.11120	−	1.36954i	0.965926	−	0.258819i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$	−13.9891	+	8.07659i	−2.55404	+	1.47458i
$31$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$31$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$		0			0
$34$		0			0
$35$	4.75409	+	8.23432i	0.803587	+	1.39185i
$36$	−12.3003	−	7.10159i	−2.05005	−	1.18360i
$37$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$37$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$38$			11.8483i			1.92205i
$39$	3.27933	+	10.9803i	0.525113	+	1.75825i
$40$	−10.1647			−1.60717
$41$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$41$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$42$	−5.94606	+	10.2989i	−0.917496	+	1.58915i
$43$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$43$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$44$		0			0
$45$	6.60541	−	24.6517i	0.984677	−	3.67486i
$46$	−4.75478	−	1.27404i	−0.701054	−	0.187847i
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$	−6.35660	−	11.0100i	−0.917496	−	1.58915i
$49$	6.06218	+	3.50000i	0.866025	+	0.500000i
$50$	−2.89711	−	10.8122i	−0.409713	−	1.52907i
$51$		0			0
$52$	−1.66766	+	7.01562i	−0.231263	+	0.972891i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	17.8076	−	4.77154i	2.42331	−	0.649324i
$55$		0			0
$56$	−6.48074	+	3.74166i	−0.866025	+	0.500000i
$57$	−18.8288	−	18.8288i	−2.49393	−	2.49393i
$58$		0			0
$59$	14.4778	+	3.87931i	1.88485	+	0.505044i	0.999170	+	0.0407464i	$0.0129736\pi$
$59$	14.4778	+	3.87931i	1.88485	+	0.505044i	0.885679	+	0.464297i	$0.153693\pi$
$60$	16.1532	−	16.1532i	2.08537	−	2.08537i
$61$	−4.96731	−	8.60363i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$61$	−4.96731	−	8.60363i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$62$		0			0
$63$	−4.86296	−	18.1488i	−0.612676	−	2.28654i
$64$		−	8.00000i		−	1.00000i
$65$	−12.9522	+	0.368255i	−1.60653	+	0.0456764i
$66$		0			0
$67$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$67$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$68$		0			0
$69$	9.58070	−	5.53142i	1.15338	−	0.665905i
$70$	−9.50817	−	9.50817i	−1.13644	−	1.13644i
$71$	−4.29022	+	16.0113i	−0.509156	+	1.90020i	−0.0804327	+	0.996760i	$0.525630\pi$
$71$	−4.29022	+	16.0113i	−0.509156	+	1.90020i	−0.428723	+	0.903436i	$0.641036\pi$
$72$	19.4019	+	5.19873i	2.28654	+	0.612676i
$73$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$		0			0
$75$	21.7861	+	12.5782i	2.51564	+	1.45241i
$76$	−4.33679	−	16.1851i	−0.497464	−	1.85656i
$77$		0			0
$78$	−8.49871	−	13.7990i	−0.962290	−	1.56243i
$79$	−15.7417			−1.77107			−0.885537	−	0.464568i	$-0.846210\pi$
$79$	−15.7417			−1.77107			−0.885537	+	0.464568i	$0.846210\pi$
$80$	13.8852	−	3.72052i	1.55241	−	0.415967i
$81$	−10.0639	+	17.4312i	−1.11821	+	1.93680i
$82$		0			0
$83$	−5.83132	−	5.83132i	−0.640071	−	0.640071i	0.310502	−	0.950573i	$-0.399503\pi$
$83$	−5.83132	−	5.83132i	−0.640071	−	0.640071i	−0.950573	+	0.310502i	$0.899503\pi$
$84$	4.35281	−	16.2449i	0.474931	−	1.77247i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$89$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$90$			36.0926i			3.80450i
$91$	−8.12246	+	5.00256i	−0.851465	+	0.524411i
$92$	6.96148			0.725785
$93$		0			0
$94$		0			0
$95$	26.0748	−	15.0543i	2.67522	−	1.54454i
$96$	12.7132	+	12.7132i	1.29754	+	1.29754i
$97$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$97$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$98$	−9.56218	−	2.56218i	−0.965926	−	0.258819i
$99$		0			0
$100$	7.91505	+	13.7093i	0.791505	+	1.37093i
$101$	−13.1323	−	7.58192i	−1.30671	−	0.754429i	−0.325164	−	0.945658i	$-0.605419\pi$
$101$	−13.1323	−	7.58192i	−1.30671	−	0.754429i	−0.981546	+	0.191229i	$0.938753\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−0.289831	−	10.1939i	−0.0284203	−	0.999596i
$105$	30.2198			2.94915
$106$		0			0
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	−22.5792	+	13.0361i	−2.17268	+	1.25440i
$109$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$		0			0
$111$		0			0
$112$	7.48331	−	7.48331i	0.707107	−	0.707107i
$113$	10.6125	+	18.3814i	0.998339	+	1.72917i	0.549068	+	0.835778i	$0.314983\pi$
$113$	10.6125	+	18.3814i	0.998339	+	1.72917i	0.449271	+	0.893396i	$0.351684\pi$
$114$	32.6124	+	18.8288i	3.05443	+	1.76348i
$115$	3.23755	+	12.0827i	0.301903	+	1.12672i
$116$		0			0
$117$	24.9110	+	5.92152i	2.30303	+	0.547444i
$118$	−21.1970			−1.95134
$119$		0			0
$120$	−16.1532	+	27.9781i	−1.47458	+	2.55404i
$121$	−9.52628	+	5.50000i	−0.866025	+	0.500000i
$122$	9.93462	+	9.93462i	0.899438	+	0.899438i
$123$		0			0
$124$		0			0
$125$	−7.40762	+	7.40762i	−0.662557	+	0.662557i
$126$	13.2859	+	23.0118i	1.18360	+	2.05005i
$127$	8.22111	+	4.74646i	0.729506	+	0.421180i	0.818241	−	0.574875i	$-0.194949\pi$
$127$	8.22111	+	4.74646i	0.729506	+	0.421180i	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$		0			0
$130$	17.5583	−	5.24389i	1.53996	−	0.459919i
$131$	−21.8267			−1.90701			−0.953505	−	0.301377i	$-0.902554\pi$
$131$	−21.8267			−1.90701			−0.953505	+	0.301377i	$0.902554\pi$
$132$		0			0
$133$	11.0831	−	19.1965i	0.961027	−	1.66455i
$134$		0			0
$135$	−33.1269	−	33.1269i	−2.85111	−	2.85111i
$136$		0			0
$137$	−13.0526	−	3.49743i	−1.11516	−	0.298805i	−0.346235	−	0.938148i	$-0.612540\pi$
$137$	−13.0526	−	3.49743i	−1.11516	−	0.298805i	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−11.0628	+	11.0628i	−0.941731	+	0.941731i
$139$	−6.23715	−	10.8031i	−0.529028	−	0.916304i	−0.999427	−	0.0338497i	$-0.989223\pi$
$139$	−6.23715	−	10.8031i	−0.529028	−	0.916304i	0.470399	−	0.882454i	$-0.344110\pi$
$140$	16.4686	+	9.50817i	1.39185	+	0.803587i
$141$		0			0
$142$		−	23.4422i		−	1.96723i
$143$		0			0
$144$	−28.4064			−2.36720
$145$		0			0
$146$		0			0
$147$	19.2674	−	11.1241i	1.58915	−	0.917496i
$148$		0			0
$149$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$149$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$150$	−34.3643	−	9.20788i	−2.80583	−	0.751820i
$151$	−13.5035	+	13.5035i	−1.09890	+	1.09890i	−0.104357	+	0.994540i	$0.533278\pi$
$151$	−13.5035	+	13.5035i	−1.09890	+	1.09890i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	11.8483	+	20.5219i	0.961027	+	1.66455i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	16.6603	+	15.7391i	1.33389	+	1.26014i
$157$	−23.0707			−1.84124			−0.920622	−	0.390455i	$-0.872318\pi$
$157$	−23.0707			−1.84124			−0.920622	+	0.390455i	$0.872318\pi$
$158$	21.5035	−	5.76185i	1.71073	−	0.458388i
$159$		0			0
$160$	−17.6057	+	10.1647i	−1.39185	+	0.803587i
$161$	6.51187	+	6.51187i	0.513207	+	0.513207i
$162$	7.36730	−	27.4951i	0.578830	−	2.16022i
$163$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$163$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$164$		0			0
$165$		0			0
$166$	10.1001	+	5.83132i	0.783923	+	0.452598i
$167$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$167$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$168$			23.7842i			1.83499i
$169$	−0.738629	−	12.9790i	−0.0568176	−	0.998385i
$170$		0			0
$171$	−57.4701	+	15.3991i	−4.39485	+	1.17760i
$172$		0			0
$173$	11.9941	−	6.92480i	0.911895	−	0.526483i	0.0308546	−	0.999524i	$-0.490177\pi$
$173$	11.9941	−	6.92480i	0.911895	−	0.526483i	0.881040	+	0.473041i	$0.156844\pi$
$174$		0			0
$175$	−5.41999	+	20.2277i	−0.409713	+	1.52907i
$176$		0			0
$177$	33.6852	−	33.6852i	2.53193	−	2.53193i
$178$		0			0
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	−13.2108	−	49.3035i	−0.984677	−	3.67486i
$181$			7.32755i			0.544652i	0.962205	+	0.272326i	$0.0877929\pi$
$181$			7.32755i			0.544652i	−0.962205	+	0.272326i	$0.912207\pi$
$182$	9.26443	−	9.80665i	0.686725	−	0.726917i
$183$	−31.5752			−2.33411
$184$	−9.50956	+	2.54808i	−0.701054	+	0.187847i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−33.3150	−	8.92674i	−2.42331	−	0.649324i
$190$	−30.1086	+	30.1086i	−2.18431	+	2.18431i
$191$	−2.38751	−	4.13530i	−0.172754	−	0.299219i	0.766627	−	0.642092i	$-0.221933\pi$
$191$	−2.38751	−	4.13530i	−0.172754	−	0.299219i	−0.939382	+	0.342873i	$0.888600\pi$
$192$	−22.0199	−	12.7132i	−1.58915	−	0.917496i
$193$	1.52193	+	5.67992i	0.109551	+	0.408850i	0.998822	−	0.0485316i	$-0.0154541\pi$
$193$	1.52193	+	5.67992i	0.109551	+	0.408850i	−0.889271	+	0.457381i	$0.848787\pi$
$194$		0			0
$195$	−19.5694	+	36.2361i	−1.40139	+	2.59492i
$196$	14.0000			1.00000
$197$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$197$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	−15.8301	−	15.8301i	−1.11936	−	1.11936i
$201$		0			0
$202$	20.7142	+	5.55035i	1.45744	+	0.390521i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	24.7188i		−	1.71808i
$208$	4.12715	+	13.8191i	0.286166	+	0.958180i
$209$		0			0
$210$	−41.2810	+	11.0612i	−2.84866	+	0.763297i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	37.2532	+	37.2532i	2.55255	+	2.55255i
$214$		0			0
$215$		0			0
$216$	26.0722	−	26.0722i	1.77399	−	1.77399i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$223$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$224$	−7.48331	+	12.9615i	−0.500000	+	0.866025i
$225$	48.6788	−	28.1047i	3.24525	−	1.87365i
$226$	−21.2250	−	21.2250i	−1.41186	−	1.41186i
$227$	−2.89290	+	10.7964i	−0.192008	+	0.716585i	0.801013	+	0.598647i	$0.204295\pi$
$227$	−2.89290	+	10.7964i	−0.192008	+	0.716585i	−0.993021	+	0.117938i	$0.962372\pi$
$228$	−51.4412	−	13.7836i	−3.40678	−	0.912843i
$229$	2.33013	−	2.33013i	0.153979	−	0.153979i	−0.625913	−	0.779893i	$-0.715274\pi$
$229$	2.33013	−	2.33013i	0.153979	−	0.153979i	0.779893	+	0.625913i	$0.215274\pi$
$230$	−8.84514	−	15.3202i	−0.583231	−	1.01019i
$231$		0			0
$232$		0			0
$233$			20.1628i			1.32091i	0.750867	+	0.660454i	$0.229636\pi$
$233$			20.1628i			1.32091i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	−36.1965	+	1.02913i	−2.36624	+	0.0672764i
$235$		0			0
$236$	28.9556	−	7.75863i	1.88485	−	0.505044i
$237$	−25.0159	+	43.3287i	−1.62495	+	2.81450i
$238$		0			0
$239$	21.8599	+	21.8599i	1.41400	+	1.41400i	0.719264	+	0.694737i	$0.244479\pi$
$239$	21.8599	+	21.8599i	1.41400	+	1.41400i	0.694737	+	0.719264i	$0.255521\pi$
$240$	11.8249	−	44.1313i	0.763297	−	2.84866i
$241$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$241$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$242$	11.0000	−	11.0000i	0.707107	−	0.707107i
$243$	12.4320	+	21.5329i	0.797514	+	1.38134i
$244$	−17.2073	−	9.93462i	−1.10158	−	0.635999i
$245$	6.51092	+	24.2991i	0.415967	+	1.55241i
$246$		0			0
$247$	15.8411	+	25.7206i	1.00795	+	1.63656i
$248$		0			0
$249$	−25.3175	+	6.78380i	−1.60443	+	0.429906i
$250$	7.40762	−	12.8304i	0.468499	−	0.811464i
$251$	21.1387	−	12.2045i	1.33426	−	0.770338i	0.348315	−	0.937378i	$-0.386754\pi$
$251$	21.1387	−	12.2045i	1.33426	−	0.770338i	0.985950	+	0.167039i	$0.0534207\pi$
$252$	−26.5717	−	26.5717i	−1.67386	−	1.67386i
$253$		0			0
$254$	−12.9676	−	3.47465i	−0.813658	−	0.218019i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$		0			0
$260$	−22.0656	+	13.5901i	−1.36845	+	0.842819i
$261$		0			0
$262$	29.8159	−	7.98914i	1.84203	−	0.493571i
$263$	11.6059	−	20.1021i	0.715653	−	1.23955i	−0.247054	−	0.969002i	$-0.579463\pi$
$263$	11.6059	−	20.1021i	0.715653	−	1.23955i	0.962707	−	0.270546i	$-0.0872041\pi$
$264$		0			0
$265$		0			0
$266$	−8.11340	+	30.2796i	−0.497464	+	1.85656i
$267$		0			0
$268$		0			0
$269$	4.58095	+	7.93445i	0.279306	+	0.483772i	0.971212	−	0.238215i	$-0.0765624\pi$
$269$	4.58095	+	7.93445i	0.279306	+	0.483772i	−0.691907	+	0.721987i	$0.743229\pi$
$270$	57.3774	+	33.1269i	3.49188	+	2.01604i
$271$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$271$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$272$		0			0
$273$	0.861676	+	30.3068i	0.0521510	+	1.83425i
$274$	19.1103			1.15449
$275$		0			0
$276$	11.0628	−	19.1614i	0.665905	−	1.15338i
$277$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$277$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$278$	12.4743	+	12.4743i	0.748159	+	0.748159i
$279$		0			0
$280$	−25.9768	−	6.96046i	−1.55241	−	0.415967i
$281$	−7.51669	+	7.51669i	−0.448408	+	0.448408i	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−7.51669	+	7.51669i	−0.448408	+	0.448408i	0.446417	+	0.894825i	$0.352700\pi$
$282$		0			0
$283$	12.0113	+	6.93471i	0.713996	+	0.412226i	0.812539	−	0.582907i	$-0.198085\pi$
$283$	12.0113	+	6.93471i	0.713996	+	0.412226i	−0.0985428	+	0.995133i	$0.531418\pi$
$284$	8.58045	+	32.0227i	0.509156	+	1.90020i
$285$		−	95.6942i		−	5.66843i
$286$		0			0
$287$		0			0
$288$	38.8038	−	10.3975i	2.28654	−	0.612676i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−22.3139	−	5.97899i	−1.30359	−	0.349296i	−0.460784	−	0.887512i	$-0.652432\pi$
$293$	−22.3139	−	5.97899i	−1.30359	−	0.349296i	−0.842807	+	0.538216i	$0.819098\pi$
$294$	−22.2481	+	22.2481i	−1.29754	+	1.29754i
$295$	26.9325	+	46.6485i	1.56807	+	2.71598i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−12.0251	+	3.59139i	−0.695432	+	0.207695i
$300$	50.3128			2.90481
$301$		0			0
$302$	13.5035	−	23.3887i	0.777037	−	1.34587i
$303$	−41.7383	+	24.0976i	−2.39780	+	1.38437i
$304$	−23.6967	−	23.6967i	−1.35910	−	1.35910i
$305$	9.24050	−	34.4860i	0.529110	−	1.97466i
$306$		0			0
$307$	12.7791	−	12.7791i	0.729342	−	0.729342i	−0.241146	−	0.970489i	$-0.577523\pi$
$307$	12.7791	−	12.7791i	0.729342	−	0.729342i	0.970489	+	0.241146i	$0.0775234\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	−28.5192	−	15.4019i	−1.61458	−	0.871962i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	31.5152	−	8.44447i	1.77851	−	0.476549i
$315$	33.7616	−	58.4768i	1.90225	−	3.29479i
$316$	−27.2654	+	15.7417i	−1.53380	+	0.885537i
$317$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$317$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$318$		0			0
$319$		0			0
$320$	20.3293	−	20.3293i	1.13644	−	1.13644i
$321$		0			0
$322$	−11.2789	−	6.51187i	−0.628548	−	0.362892i
$323$		0			0
$324$			40.2557i			2.23643i
$325$	−20.7448	−	19.5978i	−1.15072	−	1.08709i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$331$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$332$	−15.9315	−	4.26882i	−0.874353	−	0.234282i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−8.70563	−	32.4899i	−0.474931	−	1.77247i
$337$		−	0.708287i		−	0.0385828i	−0.999814	−	0.0192914i	$-0.993859\pi$
$337$		−	0.708287i		−	0.0385828i	0.999814	−	0.0192914i	$-0.00614103\pi$
$338$	5.75963	+	17.4593i	0.313283	+	0.949660i
$339$	67.4593			3.66389
$340$		0			0
$341$		0			0
$342$	72.8692	−	42.0710i	3.94031	−	2.27494i
$343$	13.0958	+	13.0958i	0.707107	+	0.707107i
$344$		0			0
$345$	38.4024	+	10.2899i	2.06752	+	0.553989i
$346$	−13.8496	+	13.8496i	−0.744559	+	0.744559i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$		0			0
$349$	8.15771	+	30.4450i	0.436672	+	1.62968i	0.737032	+	0.675857i	$0.236226\pi$
$349$	8.15771	+	30.4450i	0.436672	+	1.62968i	−0.300360	+	0.953826i	$0.597107\pi$
$350$		−	29.6154i		−	1.58301i
$351$	32.2777	−	34.1668i	1.72285	−	1.82369i
$352$		0			0
$353$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$353$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$354$	−33.6852	+	58.3444i	−1.79035	+	3.10097i
$355$	−51.5896	+	29.7853i	−2.73809	+	1.58084i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.74963	+	2.74963i	−0.145120	+	0.145120i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	−2.74963	+	2.74963i	−0.145120	+	0.145120i	0.630814	+	0.775934i	$0.282721\pi$
$360$	36.0926	+	62.5143i	1.90225	+	3.29479i
$361$	−44.3332	−	25.5958i	−2.33333	−	1.34715i
$362$	−2.68207	−	10.0096i	−0.140966	−	0.526094i
$363$			34.9613i			1.83499i
$364$	−9.06596	+	16.7871i	−0.475185	+	0.879886i
$365$		0			0
$366$	43.1325	−	11.5573i	2.25457	−	0.604111i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	12.0576	−	6.96148i	0.628548	−	0.362892i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	8.61757	+	32.1612i	0.445009	+	1.66080i
$376$		0			0
$377$		0			0
$378$	48.7766			2.50880
$379$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$379$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$380$	30.1086	−	52.1496i	1.54454	−	2.67522i
$381$	26.1292	−	15.0857i	1.33864	−	0.772863i
$382$	4.77503	+	4.77503i	0.244312	+	0.244312i
$383$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$383$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$384$	34.7331	+	9.30671i	1.77247	+	0.474931i
$385$		0			0
$386$	−4.15799	−	7.20185i	−0.211636	−	0.366565i
$387$		0			0
$388$		0			0
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$	13.4690	−	56.6623i	0.682029	−	2.86921i
$391$		0			0
$392$	−19.1244	+	5.12436i	−0.965926	+	0.258819i
$393$	−34.6860	+	60.0778i	−1.74967	+	3.03053i
$394$		0			0
$395$	−40.0022	−	40.0022i	−2.01273	−	2.01273i
$396$		0			0
$397$	12.3640	+	3.31292i	0.620531	+	0.166271i	0.555369	−	0.831604i	$-0.312577\pi$
$397$	12.3640	+	3.31292i	0.620531	+	0.166271i	0.0651619	+	0.997875i	$0.479244\pi$
$398$		0			0
$399$	−35.2254	−	61.0123i	−1.76348	−	3.05443i
$400$	27.4185	+	15.8301i	1.37093	+	0.791505i
$401$	−4.10862	−	15.3336i	−0.205175	−	0.765723i	−0.989396	−	0.145242i	$-0.953604\pi$
$401$	−4.10862	−	15.3336i	−0.205175	−	0.765723i	0.784221	−	0.620481i	$-0.213063\pi$
$402$		0			0
$403$		0			0
$404$	−30.3277			−1.50886
$405$	−69.8697	+	18.7215i	−3.47185	+	0.930280i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$409$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$410$		0			0
$411$	−30.3691	+	30.3691i	−1.49800	+	1.49800i
$412$		0			0
$413$	34.3430	+	19.8279i	1.68991	+	0.975670i
$414$	9.04771	+	33.7665i	0.444671	+	1.65953i
$415$		−	29.6367i		−	1.45481i
$416$	−10.6959	−	17.3666i	−0.524411	−	0.851465i
$417$	−39.6471			−1.94153
$418$		0			0
$419$	−20.4156	+	35.3609i	−0.997368	+	1.72749i	−0.435897	+	0.899996i	$0.643569\pi$
$419$	−20.4156	+	35.3609i	−0.997368	+	1.72749i	−0.561471	+	0.827496i	$0.689764\pi$
$420$	52.3423	−	30.2198i	2.55404	−	1.47458i
$421$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$421$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−64.5245	−	37.2532i	−3.12622	−	1.80492i
$427$	−6.80294	−	25.3889i	−0.329217	−	1.22866i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	39.4101	−	10.5599i	1.89832	−	0.508653i	0.901146	−	0.433515i	$-0.142727\pi$
$431$	39.4101	−	10.5599i	1.89832	−	0.508653i	0.997173	−	0.0751385i	$-0.0239399\pi$
$432$	−26.0722	+	45.1583i	−1.25440	+	2.17268i
$433$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$433$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	20.6205	−	20.6205i	0.986412	−	0.986412i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$		−	49.7111i		−	2.36720i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	5.47817	−	20.4448i	0.258819	−	0.965926i
$449$	−35.4281	−	9.49293i	−1.67196	−	0.447999i	−0.706319	−	0.707894i	$-0.749646\pi$
$449$	−35.4281	−	9.49293i	−1.67196	−	0.447999i	−0.965637	+	0.259895i	$0.916312\pi$
$450$	−56.2094	+	56.2094i	−2.64974	+	2.64974i
$451$		0			0
$452$	36.7627	+	21.2250i	1.72917	+	0.998339i
$453$	15.7091	+	58.6272i	0.738078	+	2.75455i
$454$		−	15.8071i		−	0.741863i
$455$	−33.3529	−	7.92819i	−1.56361	−	0.371679i
$456$	75.3152			3.52696
$457$	38.0460	−	10.1944i	1.77972	−	0.476873i	0.789184	−	0.614157i	$-0.210504\pi$
$457$	38.0460	−	10.1944i	1.77972	−	0.476873i	0.990532	+	0.137283i	$0.0438371\pi$
$458$	−2.33013	+	4.03590i	−0.108880	+	0.188585i
$459$		0			0
$460$	17.6903	+	17.6903i	0.824813	+	0.824813i
$461$	7.96628	−	29.7306i	0.371027	−	1.38469i	−0.488038	−	0.872822i	$-0.662287\pi$
$461$	7.96628	−	29.7306i	0.371027	−	1.38469i	0.859064	−	0.511867i	$-0.171046\pi$
$462$		0			0
$463$	28.2019	−	28.2019i	1.31065	−	1.31065i	0.389716	−	0.920935i	$-0.372573\pi$
$463$	28.2019	−	28.2019i	1.31065	−	1.31065i	0.920935	−	0.389716i	$-0.127427\pi$
$464$		0			0
$465$		0			0
$466$	−7.38009	−	27.5429i	−0.341876	−	1.27590i
$467$		−	6.08508i		−	0.281584i	−0.990039	−	0.140792i	$-0.955035\pi$
$467$		−	6.08508i		−	0.281584i	0.990039	−	0.140792i	$-0.0449649\pi$
$468$	49.0687	−	14.6547i	2.26820	−	0.677412i
$469$		0			0
$470$		0			0
$471$	−36.6628	+	63.5019i	−1.68933	+	2.92601i
$472$	−36.7142	+	21.1970i	−1.68991	+	0.975670i
$473$		0			0
$474$	18.3129	−	68.3446i	0.841138	−	3.13917i
$475$	64.0531	+	17.1630i	2.93896	+	0.787491i
$476$		0			0
$477$		0			0
$478$	−37.8625	−	21.8599i	−1.73179	−	0.999850i
$479$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$479$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$480$			64.6127i			2.94915i
$481$		0			0
$482$		0			0
$483$	28.2722	−	7.57551i	1.28643	−	0.344698i
$484$	−11.0000	+	19.0526i	−0.500000	+	0.866025i
$485$		0			0
$486$	−24.8640	−	24.8640i	−1.12786	−	1.12786i
$487$	11.0039	−	41.0670i	0.498633	−	1.86092i	−0.0100195	−	0.999950i	$-0.503189\pi$
$487$	11.0039	−	41.0670i	0.498633	−	1.86092i	0.508652	−	0.860972i	$-0.330144\pi$
$488$	27.1419	+	7.27265i	1.22866	+	0.329217i
$489$		0			0
$490$	−17.7882	−	30.8100i	−0.803587	−	1.39185i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$		0			0
$494$	−31.0538	−	29.3368i	−1.39717	−	1.31992i
$495$		0			0
$496$		0			0
$497$	−21.9282	+	37.9807i	−0.983614	+	1.70367i
$498$	32.1013	−	18.5337i	1.43849	−	0.830515i
$499$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$499$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$500$	−5.42275	+	20.2380i	−0.242513	+	0.905070i
$501$		0			0
$502$	−24.4089	+	24.4089i	−1.08942	+	1.08942i
$503$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$503$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$504$	46.0236	+	26.5717i	2.05005	+	1.18360i
$505$	−14.1044	−	52.6382i	−0.627636	−	2.34237i
$506$		0			0
$507$	−36.8983	−	18.5925i	−1.63871	−	0.825722i
$508$	18.9858			0.842361
$509$	2.77450	−	0.743425i	0.122978	−	0.0329518i	−0.196805	−	0.980443i	$-0.563057\pi$
$509$	2.77450	−	0.743425i	0.122978	−	0.0329518i	0.319783	+	0.947491i	$0.396390\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−28.2674	+	105.495i	−1.24804	+	4.65774i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		−	44.0182i		−	1.93218i
$520$	25.1679	−	26.6409i	1.10369	−	1.16828i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	22.8055	−	39.5002i	0.997214	−	1.72723i	0.434005	−	0.900910i	$-0.357100\pi$
$523$	22.8055	−	39.5002i	0.997214	−	1.72723i	0.563209	−	0.826315i	$-0.309567\pi$
$524$	−37.8050	+	21.8267i	−1.65152	+	0.953505i
$525$	47.0633	+	47.0633i	2.05401	+	2.05401i
$526$	−8.49614	+	31.7080i	−0.370449	+	1.38254i
$527$		0			0
$528$		0			0
$529$	−5.44222	−	9.42621i	−0.236618	−	0.409835i
$530$		0			0
$531$	−27.5493	−	102.815i	−1.19554	−	4.46181i
$532$		−	44.3324i		−	1.92205i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−9.16191	−	9.16191i	−0.394998	−	0.394998i
$539$		0			0
$540$	−90.5043	−	24.2506i	−3.89468	−	1.04358i
$541$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$541$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$542$		0			0
$543$	20.1690	+	11.6446i	0.865534	+	0.499716i
$544$		0			0
$545$		0			0
$546$	−12.2701	−	41.0845i	−0.525113	−	1.75825i
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	−26.1051	+	6.99485i	−1.11516	+	0.298805i
$549$	−35.2758	+	61.0995i	−1.50554	+	2.60766i
$550$		0			0
$551$		0			0
$552$	−8.09856	+	30.2242i	−0.344698	+	1.28643i
$553$	−40.2294	−	10.7794i	−1.71073	−	0.458388i
$554$		0			0
$555$		0			0
$556$	−21.6061	−	12.4743i	−0.916304	−	0.529028i
$557$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$557$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$558$		0			0
$559$		0			0
$560$	38.0327			1.60717
$561$		0			0
$562$	7.51669	−	13.0193i	0.317072	−	0.549185i
$563$	−8.63468	+	4.98523i	−0.363908	+	0.210103i	−0.670794	−	0.741644i	$-0.734046\pi$
$563$	−8.63468	+	4.98523i	−0.363908	+	0.210103i	0.306886	+	0.951746i	$0.400713\pi$
$564$		0			0
$565$	−19.7420	+	73.6782i	−0.830553	+	3.09966i
$566$	−18.9460	−	5.07656i	−0.796359	−	0.213384i
$567$	−37.6557	+	37.6557i	−1.58139	+	1.58139i
$568$	−23.4422	−	40.6031i	−0.983614	−	1.70367i
$569$	−39.2039	−	22.6344i	−1.64351	−	0.948882i	−0.979571	−	0.201097i	$-0.935549\pi$
$569$	−39.2039	−	22.6344i	−1.64351	−	0.948882i	−0.663941	−	0.747785i	$-0.731117\pi$
$570$	35.0265	+	130.721i	1.46710	+	5.47529i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	−15.1765			−0.634006
$574$		0			0
$575$	−13.7751	+	23.8592i	−0.574462	+	0.994997i
$576$	−49.2013	+	28.4064i	−2.05005	+	1.18360i
$577$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$577$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$578$	−6.22243	+	23.2224i	−0.258819	+	0.965926i
$579$	18.0525	+	4.83715i	0.750236	+	0.201025i
$580$		0			0
$581$	−10.9094	−	18.8956i	−0.452598	−	0.783923i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	48.2555	+	78.3506i	1.99512	+	3.23940i
$586$	32.6698			1.34958
$587$	−9.34420	+	2.50377i	−0.385676	+	0.103342i	−0.446447	−	0.894810i	$-0.647311\pi$
$587$	−9.34420	+	2.50377i	−0.385676	+	0.103342i	0.0607706	+	0.998152i	$0.480644\pi$
$588$	22.2481	−	38.5348i	0.917496	−	1.58915i
$589$		0			0
$590$	−53.8650	−	53.8650i	−2.21759	−	2.21759i
$591$		0			0
$592$		0			0
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	15.1121	−	9.30743i	0.617981	−	0.380609i
$599$	1.39767			0.0571073			0.0285537	−	0.999592i	$-0.490910\pi$
$599$	1.39767			0.0571073			0.0285537	+	0.999592i	$0.490910\pi$
$600$	−68.7285	+	18.4158i	−2.80583	+	0.751820i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	−9.88523	+	36.8922i	−0.402224	+	1.50112i
$605$	−38.1843	−	10.2314i	−1.55241	−	0.415967i
$606$	48.1952	−	48.1952i	1.95780	−	1.95780i
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$	41.0439	+	23.6967i	1.66455	+	0.961027i
$609$		0			0
$610$			50.4910i			2.04432i
$611$		0			0
$612$		0			0
$613$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$613$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$614$	−12.7791	+	22.1341i	−0.515723	+	0.893258i
$615$		0			0
$616$		0			0
$617$	−9.33281	+	34.8305i	−0.375725	+	1.40222i	0.476558	+	0.879143i	$0.341884\pi$
$617$	−9.33281	+	34.8305i	−0.375725	+	1.40222i	−0.852283	+	0.523081i	$0.824782\pi$
$618$		0			0
$619$	32.0324	−	32.0324i	1.28749	−	1.28749i	0.351185	−	0.936306i	$-0.385779\pi$
$619$	32.0324	−	32.0324i	1.28749	−	1.28749i	0.936306	−	0.351185i	$-0.114221\pi$
$620$		0			0
$621$	−39.2961	−	22.6876i	−1.57690	−	0.910423i
$622$		0			0
$623$		0			0
$624$	44.5955	+	10.6006i	1.78525	+	0.424365i
$625$	1.92727			0.0770908
$626$		0			0
$627$		0			0
$628$	−39.9597	+	23.0707i	−1.59456	+	0.920622i
$629$		0			0
$630$	−24.7152	+	92.2384i	−0.984677	+	3.67486i
$631$	−10.5031	−	2.81430i	−0.418122	−	0.112035i	0.0436231	−	0.999048i	$-0.486110\pi$
$631$	−10.5031	−	2.81430i	−0.418122	−	0.112035i	−0.461745	+	0.887013i	$0.652777\pi$
$632$	31.4833	−	31.4833i	1.25234	−	1.25234i
$633$		0			0
$634$		0			0
$635$	8.82966	+	32.9527i	0.350394	+	1.30769i
$636$		0			0
$637$	−24.1834	+	7.22251i	−0.958180	+	0.286166i
$638$		0			0
$639$	113.706	−	30.4674i	4.49814	−	1.20527i
$640$	−20.3293	+	35.2114i	−0.803587	+	1.39185i
$641$	24.0569	−	13.8892i	0.950189	−	0.548592i	0.0570491	−	0.998371i	$-0.481831\pi$
$641$	24.0569	−	13.8892i	0.950189	−	0.548592i	0.893140	+	0.449780i	$0.148498\pi$
$642$		0			0
$643$	2.28299	−	8.52022i	0.0900322	−	0.336005i	−0.906187	−	0.422876i	$-0.861020\pi$
$643$	2.28299	−	8.52022i	0.0900322	−	0.336005i	0.996219	+	0.0868719i	$0.0276871\pi$
$644$	17.7908	+	4.76702i	0.701054	+	0.187847i
$645$		0			0
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−14.7346	−	54.9903i	−0.578830	−	2.16022i
$649$		0			0
$650$	35.5113	+	19.1780i	1.39287	+	0.752223i
$651$		0			0
$652$		0			0
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$	−55.4653	−	55.4653i	−2.16721	−	2.16721i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	−3.66711	−	13.6858i	−0.142634	−	0.532317i	−0.999849	−	0.0173592i	$-0.994474\pi$
$661$	−3.66711	−	13.6858i	−0.142634	−	0.532317i	0.857215	−	0.514958i	$-0.172193\pi$
$662$		0			0
$663$		0			0
$664$	23.3253			0.905197
$665$	76.9455	−	20.6175i	2.98382	−	0.799512i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	23.7842	+	41.1955i	0.917496	+	1.58915i
$673$	38.8844	+	22.4499i	1.49889	+	0.865382i	0.999999	−	0.00128586i	$-0.000409302\pi$
$673$	38.8844	+	22.4499i	1.49889	+	0.865382i	0.498886	+	0.866668i	$0.333743\pi$
$674$	0.259251	+	0.967538i	0.00998598	+	0.0372682i
$675$		−	103.181i		−	3.97145i
$676$	−14.2583	−	21.7417i	−0.548398	−	0.836218i
$677$	−16.0501			−0.616854			−0.308427	−	0.951248i	$-0.599802\pi$
$677$	−16.0501			−0.616854			−0.308427	+	0.951248i	$0.599802\pi$
$678$	−92.1512	+	24.6918i	−3.53904	+	0.948284i
$679$		0			0
$680$		0			0
$681$	25.1198	+	25.1198i	0.962594	+	0.962594i
$682$		0			0
$683$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$683$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$684$	−84.1421	+	84.1421i	−3.21725	+	3.21725i
$685$	−24.2812	−	42.0563i	−0.927737	−	1.60689i
$686$	−22.6826	−	13.0958i	−0.866025	−	0.500000i
$687$	−2.71073	−	10.1166i	−0.103421	−	0.385972i
$688$		0			0
$689$		0			0
$690$	−56.2250			−2.14045
$691$	−2.10151	+	0.563098i	−0.0799452	+	0.0214213i	−0.298570	−	0.954388i	$-0.596510\pi$
$691$	−2.10151	+	0.563098i	−0.0799452	+	0.0214213i	0.218625	+	0.975809i	$0.429843\pi$
$692$	13.8496	−	23.9882i	0.526483	−	0.911895i
$693$		0			0
$694$		0			0
$695$	11.6027	−	43.3020i	0.440117	−	1.64254i
$696$		0			0
$697$		0			0
$698$	−22.2873	−	38.6027i	−0.843586	−	1.46113i
$699$	55.4978	+	32.0417i	2.09912	+	1.21193i
$700$	10.8400	+	40.4554i	0.409713	+	1.52907i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−31.5862	+	58.4871i	−1.19214	+	2.20745i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−28.3689	−	28.3689i	−1.06692	−	1.06692i
$708$	24.6593	−	92.0296i	0.926751	−	3.45868i
$709$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$709$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$710$	59.5706	−	59.5706i	2.23564	−	2.23564i
$711$	55.8954	+	96.8137i	2.09624	+	3.63080i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	94.9079	−	25.4305i	3.54440	−	0.949719i
$718$	2.74963	−	4.76250i	0.102615	−	0.177735i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−72.1853	−	72.1853i	−2.69019	−	2.69019i
$721$		0			0
$722$	69.9290	+	18.7374i	2.60249	+	0.697335i
$723$		0			0
$724$	7.32755	+	12.6917i	0.272326	+	0.471683i
$725$		0			0
$726$	−12.7967	−	47.7580i	−0.474931	−	1.77247i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	6.23981	−	26.2500i	0.231263	−	0.972891i
$729$	18.6419			0.690439
$730$		0			0
$731$		0			0
$732$	−54.6899	+	31.5752i	−2.02140	+	1.16705i
$733$	−9.86103	−	9.86103i	−0.364226	−	0.364226i	0.501140	−	0.865366i	$-0.332914\pi$
$733$	−9.86103	−	9.86103i	−0.364226	−	0.364226i	−0.865366	+	0.501140i	$0.832914\pi$
$734$		0			0
$735$	77.2298	+	20.6937i	2.84866	+	0.763297i
$736$	−13.9230	+	13.9230i	−0.513207	+	0.513207i
$737$		0			0
$738$		0			0
$739$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$739$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$740$		0			0
$741$	95.9696	−	2.72859i	3.52553	−	0.100237i
$742$		0			0
$743$	−31.7715	+	8.51314i	−1.16558	+	0.312317i	−0.789193	−	0.614145i	$-0.789501\pi$
$743$	−31.7715	+	8.51314i	−1.16558	+	0.312317i	−0.376389	+	0.926462i	$0.622834\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−15.1577	+	56.5694i	−0.554592	+	2.06977i
$748$		0			0
$749$		0			0
$750$	−23.5436	−	40.7788i	−0.859692	−	1.48903i
$751$	47.2211	+	27.2631i	1.72312	+	0.994845i	0.912263	+	0.409605i	$0.134333\pi$
$751$	47.2211	+	27.2631i	1.72312	+	0.994845i	0.810860	+	0.585240i	$0.199000\pi$
$752$		0			0
$753$		−	77.5788i		−	2.82713i
$754$		0			0
$755$	−68.6291			−2.49767
$756$	−66.6301	+	17.8535i	−2.42331	+	0.649324i
$757$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$757$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$758$		0			0
$759$		0			0
$760$	−22.0410	+	82.2582i	−0.799512	+	2.98382i
$761$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$761$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$762$	−30.1714	+	30.1714i	−1.09299	+	1.09299i
$763$		0			0
$764$	−8.27059	−	4.77503i	−0.299219	−	0.172754i
$765$		0			0
$766$		0			0
$767$	−46.0148	+	28.3401i	−1.66150	+	1.02330i
$768$	−50.8528			−1.83499
$769$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$769$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$770$		0			0
$771$		0			0
$772$	8.31598	+	8.31598i	0.299299	+	0.299299i
$773$	−11.0711	+	41.3179i	−0.398200	+	1.48610i	0.418061	+	0.908419i	$0.362710\pi$
$773$	−11.0711	+	41.3179i	−0.398200	+	1.48610i	−0.816261	+	0.577683i	$0.803957\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	2.34085	+	82.3321i	0.0838158	+	2.94796i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	24.2487	−	14.0000i	0.866025	−	0.500000i
$785$	−58.6265	−	58.6265i	−2.09247	−	2.09247i
$786$	25.3919	−	94.7638i	0.905698	−	3.38011i
$787$	54.1833	+	14.5184i	1.93142	+	0.517524i	0.971154	+	0.238451i	$0.0766398\pi$
$787$	54.1833	+	14.5184i	1.93142	+	0.517524i	0.960270	+	0.279072i	$0.0900269\pi$
$788$		0			0
$789$	−36.8872	−	63.8904i	−1.31322	−	2.27456i
$790$	69.2858	+	40.0022i	2.46508	+	1.42321i
$791$	14.5342	+	54.2425i	0.516778	+	1.92864i
$792$		0			0
$793$	34.8488	+	8.28378i	1.23752	+	0.294166i
$794$	−18.1021			−0.642421
$795$		0			0
$796$		0			0
$797$	−23.9344	+	13.8185i	−0.847799	+	0.489477i	−0.859908	−	0.510449i	$-0.829479\pi$
$797$	−23.9344	+	13.8185i	−0.847799	+	0.489477i	0.0121083	+	0.999927i	$0.496146\pi$
$798$	70.4509	+	70.4509i	2.49393	+	2.49393i
$799$		0			0
$800$	−43.2486	−	11.5884i	−1.52907	−	0.409713i
$801$		0			0
$802$	11.2250	+	19.4422i	0.396368	+	0.686529i
$803$		0			0
$804$		0			0
$805$			33.0955i			1.16646i
$806$		0			0
$807$	29.1193			1.02505
$808$	41.4284	−	11.1007i	1.45744	−	0.390521i
$809$	5.83746	−	10.1108i	0.205234	−	0.355476i	−0.744973	−	0.667094i	$-0.767538\pi$
$809$	5.83746	−	10.1108i	0.205234	−	0.355476i	0.950207	+	0.311619i	$0.100871\pi$
$810$	88.5912	−	51.1482i	3.11278	−	1.79716i
$811$	37.6558	+	37.6558i	1.32227	+	1.32227i	0.911932	+	0.410341i	$0.134590\pi$
$811$	37.6558	+	37.6558i	1.32227	+	1.32227i	0.410341	+	0.911932i	$0.365410\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	59.6077	+	32.1914i	2.08286	+	1.12486i
$820$		0			0
$821$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$821$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$822$	30.3691	−	52.6009i	1.05924	−	1.83467i
$823$	48.5187	−	28.0123i	1.69126	−	0.976448i	0.737752	−	0.675072i	$-0.235888\pi$
$823$	48.5187	−	28.0123i	1.69126	−	0.976448i	0.953506	−	0.301376i	$-0.0974458\pi$
$824$		0			0
$825$		0			0
$826$	−54.1710	−	14.5151i	−1.88485	−	0.505044i
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$	−24.7188	−	42.8142i	−0.859038	−	1.48790i
$829$	−29.4394	−	16.9968i	−1.02247	−	0.590324i	−0.107653	−	0.994189i	$-0.534333\pi$
$829$	−29.4394	−	16.9968i	−1.02247	−	0.590324i	−0.914819	+	0.403864i	$0.867667\pi$
$830$	10.8478	+	40.4845i	0.376532	+	1.40524i
$831$		0			0
$832$	20.9675	+	19.8082i	0.726917	+	0.686725i
$833$		0			0
$834$	54.1589	−	14.5118i	1.87537	−	0.502504i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	14.9453	−	55.7765i	0.516276	−	1.92677i
$839$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$839$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$840$	−60.4396	+	60.4396i	−2.08537	+	2.08537i
$841$	−14.5000	−	25.1147i	−0.500000	−	0.866025i
$842$		0			0
$843$	8.74445	+	32.6347i	0.301175	+	1.12400i
$844$		0			0
$845$	31.1048	−	34.8588i	1.07004	−	1.19918i
$846$		0			0
$847$	−28.1116	+	7.53248i	−0.965926	+	0.258819i
$848$		0			0
$849$	38.1754	−	22.0406i	1.31018	−	0.756431i
$850$		0			0
$851$		0			0
$852$	101.778	+	27.2712i	3.48685	+	0.934297i
$853$	−41.3036	+	41.3036i	−1.41421	+	1.41421i	−0.705350	+	0.708860i	$0.749210\pi$
$853$	−41.3036	+	41.3036i	−1.41421	+	1.41421i	−0.708860	+	0.705350i	$0.750790\pi$
$854$	18.5860	+	32.1919i	0.635999	+	1.10158i
$855$	−185.173	−	106.910i	−6.33277	−	3.65623i
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	58.6158			1.99994			0.999972	−	0.00751074i	$-0.00239076\pi$
$859$	58.6158			1.99994			0.999972	+	0.00751074i	$0.00239076\pi$
$860$		0			0
$861$		0			0
$862$	−49.9701	+	28.8502i	−1.70199	+	0.982643i
$863$	29.0285	+	29.0285i	0.988143	+	0.988143i	0.999931	−	0.0117879i	$-0.00375228\pi$
$863$	29.0285	+	29.0285i	0.988143	+	0.988143i	−0.0117879	+	0.999931i	$0.503752\pi$
$864$	19.0862	−	71.2305i	0.649324	−	2.42331i
$865$	48.0761	+	12.8819i	1.63464	+	0.437999i
$866$		0			0
$867$	−27.0156	−	46.7923i	−0.917496	−	1.58915i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−20.6205	+	35.7158i	−0.697499	+	1.20810i
$875$	−24.0034	+	13.8584i	−0.811464	+	0.468499i
$876$		0			0
$877$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$877$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$878$		0			0
$879$	−51.9172	+	51.9172i	−1.75112	+	1.75112i
$880$		0			0
$881$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$881$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$882$	18.1955	+	67.9067i	0.612676	+	2.28654i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$	171.199			5.75480
$886$		0			0
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$	17.7596	+	17.7596i	0.595639	+	0.595639i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$			29.9333i			1.00000i
$897$	−9.22452	+	38.8063i	−0.307998	+	1.29571i
$898$	51.8704			1.73094
$899$		0			0
$900$	56.2094	−	97.3576i	1.87365	−	3.24525i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−57.9877	−	15.5378i	−1.92864	−	0.516778i
$905$	−18.6205	+	18.6205i	−0.618967	+	0.618967i
$906$	−42.9181	−	74.3363i	−1.42586	−	2.46966i
$907$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$907$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$908$	5.78580	+	21.5929i	0.192008	+	0.716585i
$909$			107.687i			3.57176i
$910$	48.4628	−	1.37788i	1.60653	−	0.0456764i
$911$	−52.1724			−1.72855			−0.864274	−	0.503022i	$-0.832222\pi$
$911$	−52.1724			−1.72855			−0.864274	+	0.503022i	$0.832222\pi$
$912$	−102.882	+	27.5673i	−3.40678	+	0.912843i
$913$		0			0
$914$	−48.2404	+	27.8516i	−1.59565	+	0.921249i
$915$	−80.2378	−	80.2378i	−2.65258	−	2.65258i
$916$	1.70577	−	6.36603i	0.0563603	−	0.210340i
$917$	−55.7804	−	14.9463i	−1.84203	−	0.493571i
$918$		0			0
$919$	−30.3077	−	52.4946i	−0.999760	−	1.73164i	−0.518840	−	0.854872i	$-0.673636\pi$
$919$	−30.3077	−	52.4946i	−0.999760	−	1.73164i	−0.480921	−	0.876764i	$-0.659697\pi$
$920$	−30.6405	−	17.6903i	−1.01019	−	0.583231i
$921$	−14.8664	−	55.4823i	−0.489866	−	1.82820i
$922$			43.5285i			1.43354i
$923$	−31.3420	−	50.8888i	−1.03164	−	1.67503i
$924$		0			0
$925$		0			0
$926$	−28.2019	+	48.8470i	−0.926770	+	1.60521i
$927$		0			0
$928$		0			0
$929$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$929$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$930$		0			0
$931$	41.4692	−	41.4692i	1.35910	−	1.35910i
$932$	20.1628	+	34.9230i	0.660454	+	1.14394i
$933$		0			0
$934$	2.22730	+	8.31238i	0.0728793	+	0.271989i
$935$		0			0
$936$	−61.6651	+	37.9790i	−2.01559	+	1.24138i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−39.1230	−	39.1230i	−1.27537	−	1.27537i	−0.943228	−	0.332145i	$-0.892228\pi$
$941$	−39.1230	−	39.1230i	−1.27537	−	1.27537i	−0.332145	−	0.943228i	$-0.607772\pi$
$942$	26.8391	−	100.165i	0.874464	−	3.26354i
$943$		0			0
$944$	42.3939	−	42.3939i	1.37981	−	1.37981i
$945$	−61.9747	−	107.343i	−2.01604	−	3.49188i
$946$		0			0
$947$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$947$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$948$			100.063i			3.24991i
$949$		0			0
$950$	−93.7802			−3.04263
$951$		0			0
$952$		0			0
$953$	45.8326	−	26.4615i	1.48466	−	0.857171i	0.484817	−	0.874616i	$-0.338886\pi$
$953$	45.8326	−	26.4615i	1.48466	−	0.857171i	0.999848	+	0.0174443i	$0.00555298\pi$
$954$		0			0
$955$	4.44140	−	16.5755i	0.143720	−	0.536372i
$956$	59.7224	+	16.0026i	1.93156	+	0.517560i
$957$		0			0
$958$		0			0
$959$	−30.9622	−	17.8760i	−0.999822	−	0.577247i
$960$	−23.6499	−	88.2626i	−0.763297	−	2.84866i
$961$			31.0000i			1.00000i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−10.5661	+	18.3011i	−0.340136	+	0.589133i
$966$	−35.8477	+	20.6967i	−1.15338	+	0.665905i
$967$	17.7750	+	17.7750i	0.571606	+	0.571606i	0.932577	−	0.360971i	$-0.117555\pi$
$967$	17.7750	+	17.7750i	0.571606	+	0.571606i	−0.360971	+	0.932577i	$0.617555\pi$
$968$	8.05256	−	30.0526i	0.258819	−	0.965926i
$969$		0			0
$970$		0			0
$971$	−24.7630	−	42.8907i	−0.794681	−	1.37643i	−0.923041	−	0.384701i	$-0.874305\pi$
$971$	−24.7630	−	42.8907i	−0.794681	−	1.37643i	0.128360	−	0.991728i	$-0.459029\pi$
$972$	43.0658	+	24.8640i	1.38134	+	0.797514i
$973$	−8.54204	−	31.8793i	−0.273845	−	1.02200i
$974$			60.1262i			1.92657i
$975$	−86.9095	+	25.9561i	−2.78333	+	0.831259i
$976$	−39.7385			−1.27200
$977$	−51.3562	+	13.7609i	−1.64303	+	0.440249i	−0.957650	−	0.287936i	$-0.907031\pi$
$977$	−51.3562	+	13.7609i	−1.64303	+	0.440249i	−0.685381	+	0.728184i	$0.740364\pi$
$978$		0			0
$979$		0			0
$980$	35.5763	+	35.5763i	1.13644	+	1.13644i
$981$		0			0
$982$		0			0
$983$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$983$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	53.1582	+	28.7083i	1.69119	+	0.913332i
$989$		0			0
$990$		0			0
$991$	−24.4777	+	42.3965i	−0.777558	+	1.34677i	0.155787	+	0.987791i	$0.450209\pi$
$991$	−24.4777	+	42.3965i	−0.777558	+	1.34677i	−0.933345	+	0.358980i	$0.883125\pi$
$992$		0			0
$993$		0			0
$994$	16.0525	−	59.9089i	0.509156	−	1.90020i
$995$		0			0
$996$	−37.0674	+	37.0674i	−1.17452	+	1.17452i
$997$	−2.07298	−	3.59050i	−0.0656519	−	0.113712i	0.831331	−	0.555777i	$-0.187579\pi$
$997$	−2.07298	−	3.59050i	−0.0656519	−	0.113712i	−0.896983	+	0.442065i	$0.854246\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.ds.a.293.4	yes	16
7.6	odd	2	inner	728.2.ds.a.293.1	✓	16
8.5	even	2	inner	728.2.ds.a.293.1	✓	16
13.2	odd	12	inner	728.2.ds.a.405.4	yes	16
56.13	odd	2	CM	728.2.ds.a.293.4	yes	16
91.41	even	12	inner	728.2.ds.a.405.1	yes	16
104.93	odd	12	inner	728.2.ds.a.405.1	yes	16
728.405	even	12	inner	728.2.ds.a.405.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.ds.a.293.1	✓	16	7.6	odd	2	inner
728.2.ds.a.293.1	✓	16	8.5	even	2	inner
728.2.ds.a.293.4	yes	16	1.1	even	1	trivial
728.2.ds.a.293.4	yes	16	56.13	odd	2	CM
728.2.ds.a.405.1	yes	16	91.41	even	12	inner
728.2.ds.a.405.1	yes	16	104.93	odd	12	inner
728.2.ds.a.405.4	yes	16	13.2	odd	12	inner
728.2.ds.a.405.4	yes	16	728.405	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.ds (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.58915 - 2.75249i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.54117 + 2.54117i) q^{5} +(-1.16334 + 4.34164i) q^{6} +(2.55560 + 0.684771i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-3.55080 - 6.15016i) q^{9} +(-4.40143 - 2.54117i) q^{10} -6.35660i q^{12} +(-2.47602 + 2.62094i) q^{13} -3.74166 q^{14} +(11.0328 - 2.95624i) q^{15} +(2.00000 - 3.46410i) q^{16} +(7.10159 + 7.10159i) q^{18} +(2.16840 - 8.09257i) q^{19} +(6.94259 + 1.86026i) q^{20} +(5.94606 - 5.94606i) q^{21} +(3.01441 + 1.74037i) q^{23} +(2.32668 + 8.68328i) q^{24} +7.91505i q^{25} +(2.42298 - 4.48655i) q^{26} -13.0361 q^{27} +(5.11120 - 1.36954i) q^{28} +(-13.9891 + 8.07659i) q^{30} +(-1.46410 + 5.46410i) q^{32} +(4.75409 + 8.23432i) q^{35} +(-12.3003 - 7.10159i) q^{36} +11.8483i q^{38} +(3.27933 + 10.9803i) q^{39} -10.1647 q^{40} +(-5.94606 + 10.2989i) q^{42} +(6.60541 - 24.6517i) q^{45} +(-4.75478 - 1.27404i) q^{46} +(-6.35660 - 11.0100i) q^{48} +(6.06218 + 3.50000i) q^{49} +(-2.89711 - 10.8122i) q^{50} +(-1.66766 + 7.01562i) q^{52} +(17.8076 - 4.77154i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(-18.8288 - 18.8288i) q^{57} +(14.4778 + 3.87931i) q^{59} +(16.1532 - 16.1532i) q^{60} +(-4.96731 - 8.60363i) q^{61} +(-4.86296 - 18.1488i) q^{63} -8.00000i q^{64} +(-12.9522 + 0.368255i) q^{65} +(9.58070 - 5.53142i) q^{69} +(-9.50817 - 9.50817i) q^{70} +(-4.29022 + 16.0113i) q^{71} +(19.4019 + 5.19873i) q^{72} +(21.7861 + 12.5782i) q^{75} +(-4.33679 - 16.1851i) q^{76} +(-8.49871 - 13.7990i) q^{78} -15.7417 q^{79} +(13.8852 - 3.72052i) q^{80} +(-10.0639 + 17.4312i) q^{81} +(-5.83132 - 5.83132i) q^{83} +(4.35281 - 16.2449i) q^{84} +36.0926i q^{90} +(-8.12246 + 5.00256i) q^{91} +6.96148 q^{92} +(26.0748 - 15.0543i) q^{95} +(12.7132 + 12.7132i) q^{96} +(-9.56218 - 2.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 32 q^{8} - 32 q^{9} + 40 q^{15} + 32 q^{16} + 64 q^{18} - 96 q^{30} + 32 q^{32} - 48 q^{36} + 8 q^{39} + 24 q^{46} + 136 q^{50} - 72 q^{57} - 32 q^{60} - 112 q^{63} - 16 q^{65} + 16 q^{71}+ \cdots - 56 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 32 * q^8 - 32 * q^9 + 40 * q^15 + 32 * q^16 + 64 * q^18 - 96 * q^30 + 32 * q^32 - 48 * q^36 + 8 * q^39 + 24 * q^46 + 136 * q^50 - 72 * q^57 - 32 * q^60 - 112 * q^63 - 16 * q^65 + 16 * q^71 + 112 * q^72 - 144 * q^78 - 192 * q^79 - 96 * q^81 - 96 * q^92 + 312 * q^95 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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