LMFDB - Embedded newform 637.2.e.b.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.b.508.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{12} -1.00000 q^{13} +6.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-3.50000 + 6.06218i) q^{19} -6.00000 q^{20} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -4.00000 q^{27} -9.00000 q^{29} +(2.50000 + 4.33013i) q^{31} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -1.00000 q^{43} +(-1.50000 - 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{47} +8.00000 q^{48} +(-6.00000 + 10.3923i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(4.50000 + 7.79423i) q^{53} +14.0000 q^{57} +(6.00000 + 10.3923i) q^{60} +(-5.00000 + 8.66025i) q^{61} -8.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-7.00000 - 12.1244i) q^{67} +(6.00000 - 10.3923i) q^{68} +6.00000 q^{69} -6.00000 q^{71} +(5.50000 + 9.52628i) q^{73} +(-4.00000 + 6.92820i) q^{75} -14.0000 q^{76} +(0.500000 - 0.866025i) q^{79} +(-6.00000 - 10.3923i) q^{80} +(5.50000 + 9.52628i) q^{81} -3.00000 q^{83} +18.0000 q^{85} +(9.00000 + 15.5885i) q^{87} +(7.50000 - 12.9904i) q^{89} -6.00000 q^{92} +(5.00000 - 8.66025i) q^{93} +(-10.5000 - 18.1865i) q^{95} +1.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{4} - 3 q^{5} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 2 * q^4 - 3 * q^5 - q^9	$ 2 q - 2 q^{3} + 2 q^{4} - 3 q^{5} - q^{9} + 4 q^{12} - 2 q^{13} + 12 q^{15} - 4 q^{16} - 6 q^{17} - 7 q^{19} - 12 q^{20} - 3 q^{23} - 4 q^{25} - 8 q^{27} - 18 q^{29} + 5 q^{31} - 4 q^{36} - 2 q^{37} + 2 q^{39} + 12 q^{41} - 2 q^{43} - 3 q^{45} + 3 q^{47} + 16 q^{48} - 12 q^{51} - 2 q^{52} + 9 q^{53} + 28 q^{57} + 12 q^{60} - 10 q^{61} - 16 q^{64} + 3 q^{65} - 14 q^{67} + 12 q^{68} + 12 q^{69} - 12 q^{71} + 11 q^{73} - 8 q^{75} - 28 q^{76} + q^{79} - 12 q^{80} + 11 q^{81} - 6 q^{83} + 36 q^{85} + 18 q^{87} + 15 q^{89} - 12 q^{92} + 10 q^{93} - 21 q^{95} + 2 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^4 - 3 * q^5 - q^9 + 4 * q^12 - 2 * q^13 + 12 * q^15 - 4 * q^16 - 6 * q^17 - 7 * q^19 - 12 * q^20 - 3 * q^23 - 4 * q^25 - 8 * q^27 - 18 * q^29 + 5 * q^31 - 4 * q^36 - 2 * q^37 + 2 * q^39 + 12 * q^41 - 2 * q^43 - 3 * q^45 + 3 * q^47 + 16 * q^48 - 12 * q^51 - 2 * q^52 + 9 * q^53 + 28 * q^57 + 12 * q^60 - 10 * q^61 - 16 * q^64 + 3 * q^65 - 14 * q^67 + 12 * q^68 + 12 * q^69 - 12 * q^71 + 11 * q^73 - 8 * q^75 - 28 * q^76 + q^79 - 12 * q^80 + 11 * q^81 - 6 * q^83 + 36 * q^85 + 18 * q^87 + 15 * q^89 - 12 * q^92 + 10 * q^93 - 21 * q^95 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	2.00000	−	3.46410i	0.577350	−	1.00000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	6.00000			1.54919
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−6.00000			−1.34164
$21$		0			0
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	0.998322	−	0.0579057i	$-0.0184423\pi$
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	−0.549309	+	0.835619i	$0.685109\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$	1.00000	+	1.73205i	0.160128	+	0.277350i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		0			0
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$		0			0
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$	8.00000			1.15470
$49$		0			0
$50$		0			0
$51$	−6.00000	+	10.3923i	−0.840168	+	1.45521i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	14.0000			1.85435
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	6.00000	+	10.3923i	0.774597	+	1.34164i
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	1.50000	−	2.59808i	0.186052	−	0.322252i
$66$		0			0
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$	6.00000	−	10.3923i	0.727607	−	1.26025i
$69$	6.00000			0.722315
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$		0			0
$75$	−4.00000	+	6.92820i	−0.461880	+	0.800000i
$76$	−14.0000			−1.60591
$77$		0			0
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	−6.00000	−	10.3923i	−0.670820	−	1.16190i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$		0			0
$85$	18.0000			1.95237
$86$		0			0
$87$	9.00000	+	15.5885i	0.964901	+	1.67126i
$88$		0			0
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	−0.127842	−	0.991795i	$-0.540805\pi$
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	0.922840	−	0.385183i	$-0.125862\pi$
$90$		0			0
$91$		0			0
$92$	−6.00000			−0.625543
$93$	5.00000	−	8.66025i	0.518476	−	0.898027i
$94$		0			0
$95$	−10.5000	−	18.1865i	−1.07728	−	1.86590i
$96$		0			0
$97$	1.00000			0.101535			0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000			0.101535			0.0507673	+	0.998711i	$0.483833\pi$
$98$		0			0
$99$		0			0
$100$	4.00000	−	6.92820i	0.400000	−	0.692820i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	−4.00000	−	6.92820i	−0.384900	−	0.666667i
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$	9.00000			0.846649			0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000			0.846649			0.423324	+	0.905978i	$0.360863\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$	−9.00000	−	15.5885i	−0.835629	−	1.44735i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$		0			0
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	6.00000	−	10.3923i	0.516398	−	0.894427i
$136$		0			0
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$		0			0
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	13.5000	−	23.3827i	1.12111	−	1.94183i
$146$		0			0
$147$		0			0
$148$	−4.00000			−0.328798
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	−15.0000			−1.20483
$156$	−2.00000	+	3.46410i	−0.160128	+	0.277350i
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$		0			0
$159$	9.00000	−	15.5885i	0.713746	−	1.23625i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$		0			0
$166$		0			0
$167$	15.0000			1.16073			0.580367	−	0.814355i	$-0.302909\pi$
$167$	15.0000			1.16073			0.580367	+	0.814355i	$0.302909\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−3.50000	−	6.06218i	−0.267652	−	0.463586i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	−0.997446	−	0.0714220i	$-0.977246\pi$
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	0.436870	−	0.899525i	$-0.356087\pi$
$180$	3.00000	−	5.19615i	0.223607	−	0.387298i
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$		0			0
$183$	20.0000			1.47844
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$		0			0
$188$	6.00000			0.437595
$189$		0			0
$190$		0			0
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$	8.00000	+	13.8564i	0.577350	+	1.00000i
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	0.924853	+	0.380325i	$0.124188\pi$
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	−0.133056	+	0.991109i	$0.542479\pi$
$194$		0			0
$195$	−6.00000			−0.429669
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	0.899291	−	0.437351i	$-0.144083\pi$
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	−0.828403	+	0.560133i	$0.810750\pi$
$200$		0			0
$201$	−14.0000	+	24.2487i	−0.987484	+	1.71037i
$202$		0			0
$203$		0			0
$204$	−24.0000			−1.68034
$205$	−9.00000	+	15.5885i	−0.628587	+	1.08875i
$206$		0			0
$207$	−1.50000	−	2.59808i	−0.104257	−	0.180579i
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$		0			0
$210$		0			0
$211$	23.0000			1.58339			0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000			1.58339			0.791693	+	0.610920i	$0.209200\pi$
$212$	−9.00000	+	15.5885i	−0.618123	+	1.07062i
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$		0			0
$215$	1.50000	−	2.59808i	0.102299	−	0.177187i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	11.0000	−	19.0526i	0.743311	−	1.28745i
$220$		0			0
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$		0			0
$223$	1.00000			0.0669650			0.0334825	−	0.999439i	$-0.489340\pi$
$223$	1.00000			0.0669650			0.0334825	+	0.999439i	$0.489340\pi$
$224$		0			0
$225$	4.00000			0.266667
$226$		0			0
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	0.921903	+	0.387421i	$0.126634\pi$
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	−0.125435	+	0.992102i	$0.540033\pi$
$228$	14.0000	+	24.2487i	0.927173	+	1.60591i
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.50000	−	7.79423i	0.294805	−	0.510617i	−0.680135	−	0.733087i	$-0.738079\pi$
$233$	4.50000	−	7.79423i	0.294805	−	0.510617i	0.974939	+	0.222470i	$0.0714120\pi$
$234$		0			0
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$		0			0
$237$	−2.00000			−0.129914
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	−12.0000	+	20.7846i	−0.774597	+	1.34164i
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	0.849472	−	0.527633i	$-0.176921\pi$
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	−0.881680	+	0.471848i	$0.843587\pi$
$242$		0			0
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−20.0000			−1.28037
$245$		0			0
$246$		0			0
$247$	3.50000	−	6.06218i	0.222700	−	0.385727i
$248$		0			0
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−18.0000	−	31.1769i	−1.12720	−	1.95237i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−12.0000	+	20.7846i	−0.748539	+	1.29651i	0.199983	+	0.979799i	$0.435911\pi$
$257$	−12.0000	+	20.7846i	−0.748539	+	1.29651i	−0.948523	+	0.316709i	$0.897422\pi$
$258$		0			0
$259$		0			0
$260$	6.00000			0.372104
$261$	4.50000	−	7.79423i	0.278543	−	0.482451i
$262$		0			0
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$	−27.0000			−1.65860
$266$		0			0
$267$	−30.0000			−1.83597
$268$	14.0000	−	24.2487i	0.855186	−	1.48123i
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$		0			0
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$	24.0000			1.45521
$273$		0			0
$274$		0			0
$275$		0			0
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$		0			0
$279$	−5.00000			−0.299342
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	−21.0000	+	36.3731i	−1.24393	+	2.15455i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−1.00000	−	1.73205i	−0.0586210	−	0.101535i
$292$	−11.0000	+	19.0526i	−0.643726	+	1.11497i
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.50000	−	2.59808i	0.0867472	−	0.150251i
$300$	−16.0000			−0.923760
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−14.0000	−	24.2487i	−0.802955	−	1.39076i
$305$	−15.0000	−	25.9808i	−0.858898	−	1.48765i
$306$		0			0
$307$	−11.0000			−0.627803			−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000			−0.627803			−0.313902	+	0.949456i	$0.601636\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	−0.730554	−	0.682855i	$-0.760738\pi$
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	0.956647	+	0.291250i	$0.0940712\pi$
$314$		0			0
$315$		0			0
$316$	2.00000			0.112509
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$		0			0
$319$		0			0
$320$	12.0000	−	20.7846i	0.670820	−	1.16190i
$321$	−24.0000			−1.33955
$322$		0			0
$323$	42.0000			2.33694
$324$	−11.0000	+	19.0526i	−0.611111	+	1.05848i
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$		0			0
$327$	16.0000	−	27.7128i	0.884802	−	1.53252i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	0.248590	+	0.968609i	$0.420033\pi$
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	−0.963135	+	0.269019i	$0.913301\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	−1.00000	−	1.73205i	−0.0547997	−	0.0949158i
$334$		0			0
$335$	42.0000			2.29471
$336$		0			0
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$		0			0
$339$	−9.00000	−	15.5885i	−0.488813	−	0.846649i
$340$	18.0000	+	31.1769i	0.976187	+	1.69081i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−9.00000	+	15.5885i	−0.484544	+	0.839254i
$346$		0			0
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	−18.0000	+	31.1769i	−0.964901	+	1.67126i
$349$	1.00000			0.0535288			0.0267644	−	0.999642i	$-0.491480\pi$
$349$	1.00000			0.0535288			0.0267644	+	0.999642i	$0.491480\pi$
$350$		0			0
$351$	4.00000			0.213504
$352$		0			0
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$		0			0
$355$	9.00000	−	15.5885i	0.477670	−	0.827349i
$356$	30.0000			1.59000
$357$		0			0
$358$		0			0
$359$	−9.00000	+	15.5885i	−0.475002	+	0.822727i	−0.999590	−	0.0286287i	$-0.990886\pi$
$359$	−9.00000	+	15.5885i	−0.475002	+	0.822727i	0.524588	+	0.851356i	$0.324219\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$	−22.0000			−1.15470
$364$		0			0
$365$	−33.0000			−1.72730
$366$		0			0
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	−0.956544	−	0.291587i	$-0.905817\pi$
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	0.225750	−	0.974185i	$-0.427517\pi$
$368$	−6.00000	−	10.3923i	−0.312772	−	0.541736i
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$		0			0
$371$		0			0
$372$	20.0000			1.03695
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$		0			0
$375$	3.00000	+	5.19615i	0.154919	+	0.268328i
$376$		0			0
$377$	9.00000			0.463524
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	21.0000	−	36.3731i	1.07728	−	1.86590i
$381$	16.0000	+	27.7128i	0.819705	+	1.41977i
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.500000	−	0.866025i	0.0254164	−	0.0440225i
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$		0			0
$393$	24.0000			1.21064
$394$		0			0
$395$	1.50000	+	2.59808i	0.0754732	+	0.130723i
$396$		0			0
$397$	5.50000	−	9.52628i	0.276037	−	0.478110i	−0.694359	−	0.719629i	$-0.744312\pi$
$397$	5.50000	−	9.52628i	0.276037	−	0.478110i	0.970396	+	0.241518i	$0.0776454\pi$
$398$		0			0
$399$		0			0
$400$	16.0000			0.800000
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	−0.976050	−	0.217545i	$-0.930195\pi$
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	0.676425	+	0.736512i	$0.263528\pi$
$402$		0			0
$403$	−2.50000	−	4.33013i	−0.124534	−	0.215699i
$404$		0			0
$405$	−33.0000			−1.63978
$406$		0			0
$407$		0			0
$408$		0			0
$409$	11.5000	+	19.9186i	0.568638	+	0.984911i	0.996701	+	0.0811615i	$0.0258630\pi$
$409$	11.5000	+	19.9186i	0.568638	+	0.984911i	−0.428063	+	0.903749i	$0.640804\pi$
$410$		0			0
$411$	−6.00000	+	10.3923i	−0.295958	+	0.512615i
$412$	−8.00000			−0.394132
$413$		0			0
$414$		0			0
$415$	4.50000	−	7.79423i	0.220896	−	0.382604i
$416$		0			0
$417$	−4.00000	−	6.92820i	−0.195881	−	0.339276i
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$	1.50000	+	2.59808i	0.0729325	+	0.126323i
$424$		0			0
$425$	−12.0000	+	20.7846i	−0.582086	+	1.00820i
$426$		0			0
$427$		0			0
$428$	24.0000			1.16008
$429$		0			0
$430$		0			0
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$	8.00000	−	13.8564i	0.384900	−	0.666667i
$433$	16.0000			0.768911			0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000			0.768911			0.384455	+	0.923144i	$0.374389\pi$
$434$		0			0
$435$	−54.0000			−2.58910
$436$	−16.0000	+	27.7128i	−0.766261	+	1.32720i
$437$	−10.5000	−	18.1865i	−0.502283	−	0.869980i
$438$		0			0
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.5000	+	33.7750i	−0.926473	+	1.60470i	−0.137298	+	0.990530i	$0.543842\pi$
$443$	−19.5000	+	33.7750i	−0.926473	+	1.60470i	−0.789175	+	0.614168i	$0.789492\pi$
$444$	4.00000	+	6.92820i	0.189832	+	0.328798i
$445$	22.5000	+	38.9711i	1.06660	+	1.84741i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−24.0000			−1.13263			−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000			−1.13263			−0.566315	+	0.824189i	$0.691631\pi$
$450$		0			0
$451$		0			0
$452$	9.00000	+	15.5885i	0.423324	+	0.733219i
$453$	10.0000	−	17.3205i	0.469841	−	0.813788i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$		0			0
$459$	12.0000	+	20.7846i	0.560112	+	0.970143i
$460$	9.00000	−	15.5885i	0.419627	−	0.726816i
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	18.0000	−	31.1769i	0.835629	−	1.44735i
$465$	15.0000	+	25.9808i	0.695608	+	1.20483i
$466$		0			0
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	0.0627555	+	0.998029i	$0.480011\pi$
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	−0.895696	+	0.444667i	$0.853322\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$		0			0
$471$	14.0000	−	24.2487i	0.645086	−	1.11732i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	28.0000			1.28473
$476$		0			0
$477$	−9.00000			−0.412082
$478$		0			0
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	0.950327	−	0.311253i	$-0.100749\pi$
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	−0.744717	+	0.667381i	$0.767415\pi$
$480$		0			0
$481$	1.00000	−	1.73205i	0.0455961	−	0.0789747i
$482$		0			0
$483$		0			0
$484$	22.0000			1.00000
$485$	−1.50000	+	2.59808i	−0.0681115	+	0.117973i
$486$		0			0
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$		0			0
$489$	−32.0000			−1.44709
$490$		0			0
$491$	−24.0000			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$492$	12.0000	−	20.7846i	0.541002	−	0.937043i
$493$	27.0000	+	46.7654i	1.21602	+	2.10621i
$494$		0			0
$495$		0			0
$496$	−20.0000			−0.898027
$497$		0			0
$498$		0			0
$499$	−7.00000	+	12.1244i	−0.313363	+	0.542761i	−0.979088	−	0.203436i	$-0.934789\pi$
$499$	−7.00000	+	12.1244i	−0.313363	+	0.542761i	0.665725	+	0.746197i	$0.268122\pi$
$500$	−3.00000	−	5.19615i	−0.134164	−	0.232379i
$501$	−15.0000	−	25.9808i	−0.670151	−	1.16073i
$502$		0			0
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.00000	−	1.73205i	−0.0444116	−	0.0769231i
$508$	−16.0000	−	27.7128i	−0.709885	−	1.22956i
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	−0.533815	−	0.845601i	$-0.679242\pi$
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	0.999220	+	0.0394971i	$0.0125756\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	14.0000	−	24.2487i	0.618115	−	1.07061i
$514$		0			0
$515$	−6.00000	−	10.3923i	−0.264392	−	0.457940i
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$		0			0
$518$		0			0
$519$	−12.0000			−0.526742
$520$		0			0
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$		0			0
$523$	1.00000	−	1.73205i	0.0437269	−	0.0757373i	−0.843334	−	0.537390i	$-0.819410\pi$
$523$	1.00000	−	1.73205i	0.0437269	−	0.0757373i	0.887061	+	0.461653i	$0.152744\pi$
$524$	−24.0000			−1.04844
$525$		0			0
$526$		0			0
$527$	15.0000	−	25.9808i	0.653410	−	1.13174i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.00000			−0.259889
$534$		0			0
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$		0			0
$537$	−15.0000	+	25.9808i	−0.647298	+	1.12115i
$538$		0			0
$539$		0			0
$540$	24.0000			1.03280
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$		0			0
$543$	−16.0000	−	27.7128i	−0.686626	−	1.18927i
$544$		0			0
$545$	−48.0000			−2.05609
$546$		0			0
$547$	17.0000			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$		0			0
$551$	31.5000	−	54.5596i	1.34195	−	2.32432i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−6.00000	+	10.3923i	−0.254686	+	0.441129i
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$		0			0
$559$	1.00000			0.0422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$	−6.00000	−	10.3923i	−0.252646	−	0.437595i
$565$	−13.5000	+	23.3827i	−0.567949	+	0.983717i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.5000	+	23.3827i	−0.565949	+	0.980253i	0.431011	+	0.902347i	$0.358157\pi$
$569$	−13.5000	+	23.3827i	−0.565949	+	0.980253i	−0.996961	+	0.0779066i	$0.975176\pi$
$570$		0			0
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	0.518509	−	0.855072i	$-0.326487\pi$
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	−0.999769	+	0.0215055i	$0.993154\pi$
$572$		0			0
$573$	48.0000			2.00523
$574$		0			0
$575$	12.0000			0.500435
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	−17.0000	−	29.4449i	−0.707719	−	1.22581i	−0.965701	−	0.259656i	$-0.916391\pi$
$577$	−17.0000	−	29.4449i	−0.707719	−	1.22581i	0.257982	−	0.966150i	$-0.416942\pi$
$578$		0			0
$579$	22.0000	−	38.1051i	0.914289	−	1.58359i
$580$	54.0000			2.24223
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.50000	+	2.59808i	0.0620174	+	0.107417i
$586$		0			0
$587$	9.00000			0.371470			0.185735	−	0.982600i	$-0.440533\pi$
$587$	9.00000			0.371470			0.185735	+	0.982600i	$0.440533\pi$
$588$		0			0
$589$	−35.0000			−1.44215
$590$		0			0
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	4.50000	−	7.79423i	0.184793	−	0.320071i	−0.758714	−	0.651424i	$-0.774172\pi$
$593$	4.50000	−	7.79423i	0.184793	−	0.320071i	0.943507	+	0.331353i	$0.107505\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$		0			0
$599$	−7.50000	−	12.9904i	−0.306442	−	0.530773i	0.671140	−	0.741331i	$-0.265805\pi$
$599$	−7.50000	−	12.9904i	−0.306442	−	0.530773i	−0.977581	+	0.210558i	$0.932472\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	14.0000			0.570124
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	16.5000	+	28.5788i	0.670820	+	1.16190i
$606$		0			0
$607$	−2.00000	+	3.46410i	−0.0811775	+	0.140604i	−0.903756	−	0.428048i	$-0.859201\pi$
$607$	−2.00000	+	3.46410i	−0.0811775	+	0.140604i	0.822578	+	0.568652i	$0.192535\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.50000	+	2.59808i	−0.0606835	+	0.105107i
$612$	6.00000	+	10.3923i	0.242536	+	0.420084i
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$		0			0
$615$	36.0000			1.45166
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	−0.997259	−	0.0739910i	$-0.976426\pi$
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	0.434551	−	0.900647i	$-0.356907\pi$
$620$	−15.0000	−	25.9808i	−0.602414	−	1.04341i
$621$	6.00000	−	10.3923i	0.240772	−	0.417029i
$622$		0			0
$623$		0			0
$624$	−8.00000			−0.320256
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$	−14.0000	+	24.2487i	−0.558661	+	0.967629i
$629$	12.0000			0.478471
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$		0			0
$633$	−23.0000	−	39.8372i	−0.914168	−	1.58339i
$634$		0			0
$635$	24.0000	−	41.5692i	0.952411	−	1.64962i
$636$	36.0000			1.42749
$637$		0			0
$638$		0			0
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$		0			0
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$	−6.00000			−0.236250
$646$		0			0
$647$	−24.0000	−	41.5692i	−0.943537	−	1.63425i	−0.758654	−	0.651494i	$-0.774142\pi$
$647$	−24.0000	−	41.5692i	−0.943537	−	1.63425i	−0.184884	−	0.982760i	$-0.559191\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	32.0000			1.25322
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$		0			0
$655$	−18.0000	−	31.1769i	−0.703318	−	1.21818i
$656$	−12.0000	+	20.7846i	−0.468521	+	0.811503i
$657$	−11.0000			−0.429151
$658$		0			0
$659$	−3.00000			−0.116863			−0.0584317	−	0.998291i	$-0.518610\pi$
$659$	−3.00000			−0.116863			−0.0584317	+	0.998291i	$0.518610\pi$
$660$		0			0
$661$	−6.50000	−	11.2583i	−0.252821	−	0.437898i	0.711481	−	0.702706i	$-0.248025\pi$
$661$	−6.50000	−	11.2583i	−0.252821	−	0.437898i	−0.964301	+	0.264807i	$0.914692\pi$
$662$		0			0
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	13.5000	−	23.3827i	0.522722	−	0.905381i
$668$	15.0000	+	25.9808i	0.580367	+	1.00523i
$669$	−1.00000	−	1.73205i	−0.0386622	−	0.0669650i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$		0			0
$675$	8.00000	+	13.8564i	0.307920	+	0.533333i
$676$	1.00000	+	1.73205i	0.0384615	+	0.0666173i
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	−0.727386	−	0.686229i	$-0.759265\pi$
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	0.957984	+	0.286820i	$0.0925982\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	24.0000	−	41.5692i	0.919682	−	1.59294i
$682$		0			0
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	7.00000	−	12.1244i	0.267652	−	0.463586i
$685$	18.0000			0.687745
$686$		0			0
$687$	−28.0000			−1.06827
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−4.50000	−	7.79423i	−0.171436	−	0.296936i
$690$		0			0
$691$	−18.5000	+	32.0429i	−0.703773	+	1.21897i	0.263359	+	0.964698i	$0.415170\pi$
$691$	−18.5000	+	32.0429i	−0.703773	+	1.21897i	−0.967132	+	0.254273i	$0.918164\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$		0			0
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$		0			0
$697$	−18.0000	−	31.1769i	−0.681799	−	1.18091i
$698$		0			0
$699$	−18.0000			−0.680823
$700$		0			0
$701$	9.00000			0.339925			0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000			0.339925			0.169963	+	0.985451i	$0.445635\pi$
$702$		0			0
$703$	−7.00000	−	12.1244i	−0.264010	−	0.457279i
$704$		0			0
$705$	9.00000	−	15.5885i	0.338960	−	0.587095i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	−0.931309	−	0.364229i	$-0.881333\pi$
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	0.781086	+	0.624423i	$0.214666\pi$
$710$		0			0
$711$	0.500000	+	0.866025i	0.0187515	+	0.0324785i
$712$		0			0
$713$	−15.0000			−0.561754
$714$		0			0
$715$		0			0
$716$	15.0000	−	25.9808i	0.560576	−	0.970947i
$717$	12.0000	+	20.7846i	0.448148	+	0.776215i
$718$		0			0
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	−0.732185	−	0.681106i	$-0.761499\pi$
$719$	6.00000	−	10.3923i	0.223762	−	0.387568i	0.955947	+	0.293538i	$0.0948328\pi$
$720$	12.0000			0.447214
$721$		0			0
$722$		0			0
$723$	−1.00000	+	1.73205i	−0.0371904	+	0.0644157i
$724$	16.0000	+	27.7128i	0.594635	+	1.02994i
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$		0			0
$727$	−26.0000			−0.964287			−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000			−0.964287			−0.482143	+	0.876092i	$0.660142\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	3.00000	+	5.19615i	0.110959	+	0.192187i
$732$	20.0000	+	34.6410i	0.739221	+	1.28037i
$733$	−24.5000	+	42.4352i	−0.904928	+	1.56738i	−0.0839145	+	0.996473i	$0.526742\pi$
$733$	−24.5000	+	42.4352i	−0.904928	+	1.56738i	−0.821014	+	0.570909i	$0.806591\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	6.00000	−	10.3923i	0.220564	−	0.382029i
$741$	−14.0000			−0.514303
$742$		0			0
$743$	48.0000			1.76095			0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000			1.76095			0.880475	+	0.474093i	$0.157224\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.50000	−	2.59808i	0.0548821	−	0.0950586i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$	6.00000	+	10.3923i	0.218797	+	0.378968i
$753$	12.0000	+	20.7846i	0.437304	+	0.757433i
$754$		0			0
$755$	−30.0000			−1.09181
$756$		0			0
$757$	−43.0000			−1.56286			−0.781431	−	0.623992i	$-0.785510\pi$
$757$	−43.0000			−1.56286			−0.781431	+	0.623992i	$0.785510\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$		0			0
$763$		0			0
$764$	−48.0000			−1.73658
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$		0			0
$767$		0			0
$768$	−16.0000	+	27.7128i	−0.577350	+	1.00000i
$769$	−5.00000			−0.180305			−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000			−0.180305			−0.0901523	+	0.995928i	$0.528735\pi$
$770$		0			0
$771$	48.0000			1.72868
$772$	−22.0000	+	38.1051i	−0.791797	+	1.37143i
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	0.998930	+	0.0462427i	$0.0147248\pi$
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	−0.459418	+	0.888220i	$0.651942\pi$
$774$		0			0
$775$	10.0000	−	17.3205i	0.359211	−	0.622171i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−21.0000	+	36.3731i	−0.752403	+	1.30320i
$780$	−6.00000	−	10.3923i	−0.214834	−	0.372104i
$781$		0			0
$782$		0			0
$783$	36.0000			1.28654
$784$		0			0
$785$	−42.0000			−1.49904
$786$		0			0
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	0.907137	−	0.420834i	$-0.138263\pi$
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	−0.818022	+	0.575187i	$0.804929\pi$
$788$	6.00000	+	10.3923i	0.213741	+	0.370211i
$789$	−9.00000	+	15.5885i	−0.320408	+	0.554964i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	5.00000	−	8.66025i	0.177555	−	0.307535i
$794$		0			0
$795$	27.0000	+	46.7654i	0.957591	+	1.65860i
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	−54.0000			−1.91278			−0.956389	−	0.292096i	$-0.905647\pi$
$797$	−54.0000			−1.91278			−0.956389	+	0.292096i	$0.905647\pi$
$798$		0			0
$799$	−18.0000			−0.636794
$800$		0			0
$801$	7.50000	+	12.9904i	0.264999	+	0.458993i
$802$		0			0
$803$		0			0
$804$	−56.0000			−1.97497
$805$		0			0
$806$		0			0
$807$	−24.0000	+	41.5692i	−0.844840	+	1.46331i
$808$		0			0
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	0.891189	−	0.453632i	$-0.149872\pi$
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	−0.838452	+	0.544976i	$0.816539\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	32.0000			1.12229
$814$		0			0
$815$	24.0000	+	41.5692i	0.840683	+	1.45611i
$816$	−24.0000	−	41.5692i	−0.840168	−	1.45521i
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$		0			0
$819$		0			0
$820$	−36.0000			−1.25717
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.181250	−	0.983437i	$-0.441986\pi$
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.761056	−	0.648686i	$-0.224681\pi$
$822$		0			0
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	3.00000	−	5.19615i	0.104257	−	0.180579i
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	0.985771	−	0.168091i	$-0.0537604\pi$
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	−0.638457	+	0.769657i	$0.720427\pi$
$830$		0			0
$831$	19.0000	−	32.9090i	0.659103	−	1.14160i
$832$	8.00000			0.277350
$833$		0			0
$834$		0			0
$835$	−22.5000	+	38.9711i	−0.778645	+	1.34865i
$836$		0			0
$837$	−10.0000	−	17.3205i	−0.345651	−	0.598684i
$838$		0			0
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$		0			0
$843$	−12.0000	−	20.7846i	−0.413302	−	0.715860i
$844$	23.0000	+	39.8372i	0.791693	+	1.37125i
$845$	−1.50000	+	2.59808i	−0.0516016	+	0.0893765i
$846$		0			0
$847$		0			0
$848$	−36.0000			−1.23625
$849$	−4.00000	+	6.92820i	−0.137280	+	0.237775i
$850$		0			0
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$	−12.0000	+	20.7846i	−0.411113	+	0.712069i
$853$	−17.0000			−0.582069			−0.291034	−	0.956713i	$-0.593999\pi$
$853$	−17.0000			−0.582069			−0.291034	+	0.956713i	$0.593999\pi$
$854$		0			0
$855$	21.0000			0.718185
$856$		0			0
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	−0.962048	−	0.272882i	$-0.912023\pi$
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	0.244701	−	0.969599i	$-0.421310\pi$
$858$		0			0
$859$	25.0000	−	43.3013i	0.852989	−	1.47742i	−0.0255092	−	0.999675i	$-0.508121\pi$
$859$	25.0000	−	43.3013i	0.852989	−	1.47742i	0.878498	−	0.477746i	$-0.158546\pi$
$860$	6.00000			0.204598
$861$		0			0
$862$		0			0
$863$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$863$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$		0			0
$867$	38.0000			1.29055
$868$		0			0
$869$		0			0
$870$		0			0
$871$	7.00000	+	12.1244i	0.237186	+	0.410818i
$872$		0			0
$873$	−0.500000	+	0.866025i	−0.0169224	+	0.0293105i
$874$		0			0
$875$		0			0
$876$	44.0000			1.48662
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$		0			0
$879$	9.00000	+	15.5885i	0.303562	+	0.525786i
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$		0			0
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	1.00000	+	1.73205i	0.0334825	+	0.0579934i
$893$	10.5000	+	18.1865i	0.351369	+	0.608589i
$894$		0			0
$895$	45.0000			1.50418
$896$		0			0
$897$	−6.00000			−0.200334
$898$		0			0
$899$	−22.5000	−	38.9711i	−0.750417	−	1.29976i
$900$	4.00000	+	6.92820i	0.133333	+	0.230940i
$901$	27.0000	−	46.7654i	0.899500	−	1.55798i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−24.0000	+	41.5692i	−0.797787	+	1.38181i
$906$		0			0
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	0.990510	+	0.137441i	$0.0438878\pi$
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	−0.376228	+	0.926527i	$0.622779\pi$
$908$	−24.0000	+	41.5692i	−0.796468	+	1.37952i
$909$		0			0
$910$		0			0
$911$	−15.0000			−0.496972			−0.248486	−	0.968635i	$-0.579933\pi$
$911$	−15.0000			−0.496972			−0.248486	+	0.968635i	$0.579933\pi$
$912$	−28.0000	+	48.4974i	−0.927173	+	1.60591i
$913$		0			0
$914$		0			0
$915$	−30.0000	+	51.9615i	−0.991769	+	1.71780i
$916$	28.0000			0.925146
$917$		0			0
$918$		0			0
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	11.0000	+	19.0526i	0.362462	+	0.627803i
$922$		0			0
$923$	6.00000			0.197492
$924$		0			0
$925$	8.00000			0.263038
$926$		0			0
$927$	−2.00000	−	3.46410i	−0.0656886	−	0.113776i
$928$		0			0
$929$	−1.50000	+	2.59808i	−0.0492134	+	0.0852401i	−0.889583	−	0.456774i	$-0.849005\pi$
$929$	−1.50000	+	2.59808i	−0.0492134	+	0.0852401i	0.840369	+	0.542014i	$0.182338\pi$
$930$		0			0
$931$		0			0
$932$	18.0000			0.589610
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	−16.0000			−0.522140
$940$	−9.00000	+	15.5885i	−0.293548	+	0.508439i
$941$	7.50000	+	12.9904i	0.244493	+	0.423474i	0.961989	−	0.273088i	$-0.0880451\pi$
$941$	7.50000	+	12.9904i	0.244493	+	0.423474i	−0.717496	+	0.696563i	$0.754712\pi$
$942$		0			0
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−27.0000	+	46.7654i	−0.877382	+	1.51967i	−0.0231788	+	0.999731i	$0.507379\pi$
$947$	−27.0000	+	46.7654i	−0.877382	+	1.51967i	−0.854203	+	0.519939i	$0.825955\pi$
$948$	−2.00000	−	3.46410i	−0.0649570	−	0.112509i
$949$	−5.50000	−	9.52628i	−0.178538	−	0.309236i
$950$		0			0
$951$	24.0000			0.778253
$952$		0			0
$953$	21.0000			0.680257			0.340128	−	0.940379i	$-0.389529\pi$
$953$	21.0000			0.680257			0.340128	+	0.940379i	$0.389529\pi$
$954$		0			0
$955$	−36.0000	−	62.3538i	−1.16493	−	2.01772i
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−48.0000			−1.54919
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	1.00000	−	1.73205i	0.0322078	−	0.0557856i
$965$	−66.0000			−2.12462
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$		0			0
$969$	−42.0000	−	72.7461i	−1.34923	−	2.33694i
$970$		0			0
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	−0.910140	−	0.414301i	$-0.864026\pi$
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	0.813865	+	0.581054i	$0.197359\pi$
$972$	20.0000			0.641500
$973$		0			0
$974$		0			0
$975$	4.00000	−	6.92820i	0.128103	−	0.221880i
$976$	−20.0000	−	34.6410i	−0.640184	−	1.10883i
$977$	−24.0000	−	41.5692i	−0.767828	−	1.32992i	−0.938738	−	0.344631i	$-0.888004\pi$
$977$	−24.0000	−	41.5692i	−0.767828	−	1.32992i	0.170910	−	0.985287i	$-0.445329\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−16.0000			−0.510841
$982$		0			0
$983$	28.5000	+	49.3634i	0.909009	+	1.57445i	0.815444	+	0.578836i	$0.196493\pi$
$983$	28.5000	+	49.3634i	0.909009	+	1.57445i	0.0935651	+	0.995613i	$0.470174\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$	14.0000			0.445399
$989$	1.50000	−	2.59808i	0.0476972	−	0.0826140i
$990$		0			0
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$		0			0
$993$	52.0000			1.65017
$994$		0			0
$995$	−6.00000			−0.190213
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	4.00000	+	6.92820i	0.126681	+	0.219418i	0.922389	−	0.386263i	$-0.126234\pi$
$997$	4.00000	+	6.92820i	0.126681	+	0.219418i	−0.795708	+	0.605681i	$0.792901\pi$
$998$		0			0
$999$	4.00000	−	6.92820i	0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.b.79.1		2
7.2	even	3		637.2.a.b.1.1		1
7.3	odd	6		637.2.e.c.508.1		2
7.4	even	3	inner	637.2.e.b.508.1		2
7.5	odd	6		91.2.a.b.1.1	✓	1
7.6	odd	2		637.2.e.c.79.1		2
21.2	odd	6		5733.2.a.f.1.1		1
21.5	even	6		819.2.a.c.1.1		1
28.19	even	6		1456.2.a.k.1.1		1
35.19	odd	6		2275.2.a.d.1.1		1
56.5	odd	6		5824.2.a.bd.1.1		1
56.19	even	6		5824.2.a.f.1.1		1
91.5	even	12		1183.2.c.a.337.2		2
91.12	odd	6		1183.2.a.a.1.1		1
91.47	even	12		1183.2.c.a.337.1		2
91.51	even	6		8281.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.b.1.1	✓	1	7.5	odd	6
637.2.a.b.1.1		1	7.2	even	3
637.2.e.b.79.1		2	1.1	even	1	trivial
637.2.e.b.508.1		2	7.4	even	3	inner
637.2.e.c.79.1		2	7.6	odd	2
637.2.e.c.508.1		2	7.3	odd	6
819.2.a.c.1.1		1	21.5	even	6
1183.2.a.a.1.1		1	91.12	odd	6
1183.2.c.a.337.1		2	91.47	even	12
1183.2.c.a.337.2		2	91.5	even	12
1456.2.a.k.1.1		1	28.19	even	6
2275.2.a.d.1.1		1	35.19	odd	6
5733.2.a.f.1.1		1	21.2	odd	6
5824.2.a.f.1.1		1	56.19	even	6
5824.2.a.bd.1.1		1	56.5	odd	6
8281.2.a.h.1.1		1	91.51	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{12} -1.00000 q^{13} +6.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-3.50000 + 6.06218i) q^{19} -6.00000 q^{20} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -4.00000 q^{27} -9.00000 q^{29} +(2.50000 + 4.33013i) q^{31} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -1.00000 q^{43} +(-1.50000 - 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{47} +8.00000 q^{48} +(-6.00000 + 10.3923i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(4.50000 + 7.79423i) q^{53} +14.0000 q^{57} +(6.00000 + 10.3923i) q^{60} +(-5.00000 + 8.66025i) q^{61} -8.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-7.00000 - 12.1244i) q^{67} +(6.00000 - 10.3923i) q^{68} +6.00000 q^{69} -6.00000 q^{71} +(5.50000 + 9.52628i) q^{73} +(-4.00000 + 6.92820i) q^{75} -14.0000 q^{76} +(0.500000 - 0.866025i) q^{79} +(-6.00000 - 10.3923i) q^{80} +(5.50000 + 9.52628i) q^{81} -3.00000 q^{83} +18.0000 q^{85} +(9.00000 + 15.5885i) q^{87} +(7.50000 - 12.9904i) q^{89} -6.00000 q^{92} +(5.00000 - 8.66025i) q^{93} +(-10.5000 - 18.1865i) q^{95} +1.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{4} - 3 q^{5} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^4 - 3 * q^5 - q^9	\( 2 q - 2 q^{3} + 2 q^{4} - 3 q^{5} - q^{9} + 4 q^{12} - 2 q^{13} + 12 q^{15} - 4 q^{16} - 6 q^{17} - 7 q^{19} - 12 q^{20} - 3 q^{23} - 4 q^{25} - 8 q^{27} - 18 q^{29} + 5 q^{31} - 4 q^{36} - 2 q^{37} + 2 q^{39} + 12 q^{41} - 2 q^{43} - 3 q^{45} + 3 q^{47} + 16 q^{48} - 12 q^{51} - 2 q^{52} + 9 q^{53} + 28 q^{57} + 12 q^{60} - 10 q^{61} - 16 q^{64} + 3 q^{65} - 14 q^{67} + 12 q^{68} + 12 q^{69} - 12 q^{71} + 11 q^{73} - 8 q^{75} - 28 q^{76} + q^{79} - 12 q^{80} + 11 q^{81} - 6 q^{83} + 36 q^{85} + 18 q^{87} + 15 q^{89} - 12 q^{92} + 10 q^{93} - 21 q^{95} + 2 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^4 - 3 * q^5 - q^9 + 4 * q^12 - 2 * q^13 + 12 * q^15 - 4 * q^16 - 6 * q^17 - 7 * q^19 - 12 * q^20 - 3 * q^23 - 4 * q^25 - 8 * q^27 - 18 * q^29 + 5 * q^31 - 4 * q^36 - 2 * q^37 + 2 * q^39 + 12 * q^41 - 2 * q^43 - 3 * q^45 + 3 * q^47 + 16 * q^48 - 12 * q^51 - 2 * q^52 + 9 * q^53 + 28 * q^57 + 12 * q^60 - 10 * q^61 - 16 * q^64 + 3 * q^65 - 14 * q^67 + 12 * q^68 + 12 * q^69 - 12 * q^71 + 11 * q^73 - 8 * q^75 - 28 * q^76 + q^79 - 12 * q^80 + 11 * q^81 - 6 * q^83 + 36 * q^85 + 18 * q^87 + 15 * q^89 - 12 * q^92 + 10 * q^93 - 21 * q^95 + 2 * q^97

Introduction

L-functions

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