LMFDB - Embedded newform 637.2.e.d.508.1

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			508.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.d.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +(3.00000 - 5.19615i) q^{10} +(3.00000 - 5.19615i) q^{11} +1.00000 q^{13} +(2.00000 + 3.46410i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(2.50000 + 4.33013i) q^{19} +6.00000 q^{20} +12.0000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} -5.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(-4.00000 + 6.92820i) q^{32} +8.00000 q^{34} -6.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-5.00000 + 8.66025i) q^{38} +6.00000 q^{41} -1.00000 q^{43} +(6.00000 + 10.3923i) q^{44} +(4.50000 - 7.79423i) q^{45} +(3.00000 - 5.19615i) q^{46} +(3.50000 + 6.06218i) q^{47} -8.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(4.50000 - 7.79423i) q^{53} -18.0000 q^{55} +(-5.00000 - 8.66025i) q^{58} +(4.00000 - 6.92820i) q^{59} +(-5.00000 - 8.66025i) q^{61} -6.00000 q^{62} -8.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(3.00000 - 5.19615i) q^{67} +(4.00000 + 6.92820i) q^{68} -8.00000 q^{71} +(-6.50000 + 11.2583i) q^{73} +(-4.00000 + 6.92820i) q^{74} -10.0000 q^{76} +(-1.50000 - 2.59808i) q^{79} +(6.00000 - 10.3923i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 + 10.3923i) q^{82} -15.0000 q^{83} -12.0000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(1.50000 + 2.59808i) q^{89} +18.0000 q^{90} +6.00000 q^{92} +(-7.00000 + 12.1244i) q^{94} +(7.50000 - 12.9904i) q^{95} -7.00000 q^{97} +18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{4} - 3 q^{5} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^4 - 3 * q^5 + 3 * q^9	$ 2 q + 2 q^{2} - 2 q^{4} - 3 q^{5} + 3 q^{9} + 6 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 12 q^{20} + 24 q^{22} - 3 q^{23} - 4 q^{25} + 2 q^{26} - 10 q^{29} - 3 q^{31} - 8 q^{32} + 16 q^{34} - 12 q^{36} + 4 q^{37} - 10 q^{38} + 12 q^{41} - 2 q^{43} + 12 q^{44} + 9 q^{45} + 6 q^{46} + 7 q^{47} - 16 q^{50} - 2 q^{52} + 9 q^{53} - 36 q^{55} - 10 q^{58} + 8 q^{59} - 10 q^{61} - 12 q^{62} - 16 q^{64} - 3 q^{65} + 6 q^{67} + 8 q^{68} - 16 q^{71} - 13 q^{73} - 8 q^{74} - 20 q^{76} - 3 q^{79} + 12 q^{80} - 9 q^{81} + 12 q^{82} - 30 q^{83} - 24 q^{85} - 2 q^{86} + 3 q^{89} + 36 q^{90} + 12 q^{92} - 14 q^{94} + 15 q^{95} - 14 q^{97} + 36 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^4 - 3 * q^5 + 3 * q^9 + 6 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 12 * q^20 + 24 * q^22 - 3 * q^23 - 4 * q^25 + 2 * q^26 - 10 * q^29 - 3 * q^31 - 8 * q^32 + 16 * q^34 - 12 * q^36 + 4 * q^37 - 10 * q^38 + 12 * q^41 - 2 * q^43 + 12 * q^44 + 9 * q^45 + 6 * q^46 + 7 * q^47 - 16 * q^50 - 2 * q^52 + 9 * q^53 - 36 * q^55 - 10 * q^58 + 8 * q^59 - 10 * q^61 - 12 * q^62 - 16 * q^64 - 3 * q^65 + 6 * q^67 + 8 * q^68 - 16 * q^71 - 13 * q^73 - 8 * q^74 - 20 * q^76 - 3 * q^79 + 12 * q^80 - 9 * q^81 + 12 * q^82 - 30 * q^83 - 24 * q^85 - 2 * q^86 + 3 * q^89 + 36 * q^90 + 12 * q^92 - 14 * q^94 + 15 * q^95 - 14 * q^97 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	3.00000	−	5.19615i	0.948683	−	1.64317i
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$	−3.00000	+	5.19615i	−0.707107	+	1.22474i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	6.00000			1.34164
$21$		0			0
$22$	12.0000			2.55841
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$		0			0
$28$		0			0
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$	−4.00000	+	6.92820i	−0.707107	+	1.22474i
$33$		0			0
$34$	8.00000			1.37199
$35$		0			0
$36$	−6.00000			−1.00000
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	−5.00000	+	8.66025i	−0.811107	+	1.40488i
$39$		0			0
$40$		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	$0.524294\pi$
$44$	6.00000	+	10.3923i	0.904534	+	1.56670i
$45$	4.50000	−	7.79423i	0.670820	−	1.16190i
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	0.999926	+	0.0121990i	$0.00388317\pi$
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	−0.489398	+	0.872060i	$0.662783\pi$
$48$		0			0
$49$		0			0
$50$	−8.00000			−1.13137
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$		0			0
$55$	−18.0000			−2.42712
$56$		0			0
$57$		0			0
$58$	−5.00000	−	8.66025i	−0.656532	−	1.13715i
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−1.50000	−	2.59808i	−0.186052	−	0.322252i
$66$		0			0
$67$	3.00000	−	5.19615i	0.366508	−	0.634811i	−0.622509	−	0.782613i	$-0.713886\pi$
$67$	3.00000	−	5.19615i	0.366508	−	0.634811i	0.989017	+	0.147802i	$0.0472198\pi$
$68$	4.00000	+	6.92820i	0.485071	+	0.840168i
$69$		0			0
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	0.181688	+	0.983356i	$0.441844\pi$
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	−0.942455	+	0.334332i	$0.891489\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	−10.0000			−1.14708
$77$		0			0
$78$		0			0
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	0.769222	−	0.638982i	$-0.220644\pi$
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	−0.937985	+	0.346675i	$0.887311\pi$
$80$	6.00000	−	10.3923i	0.670820	−	1.16190i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	6.00000	+	10.3923i	0.662589	+	1.14764i
$83$	−15.0000			−1.64646			−0.823232	−	0.567705i	$-0.807831\pi$
$83$	−15.0000			−1.64646			−0.823232	+	0.567705i	$0.807831\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$		0			0
$88$		0			0
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	0.934508	−	0.355942i	$-0.115840\pi$
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	−0.775509	+	0.631337i	$0.782506\pi$
$90$	18.0000			1.89737
$91$		0			0
$92$	6.00000			0.625543
$93$		0			0
$94$	−7.00000	+	12.1244i	−0.721995	+	1.25053i
$95$	7.50000	−	12.9904i	0.769484	−	1.33278i
$96$		0			0
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$		0			0
$99$	18.0000			1.80907
$100$	−4.00000	−	6.92820i	−0.400000	−	0.692820i
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$		0			0
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	0.750510	−	0.660859i	$-0.229808\pi$
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	−0.947576	+	0.319531i	$0.896475\pi$
$104$		0			0
$105$		0			0
$106$	18.0000			1.74831
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−18.0000	−	31.1769i	−1.71623	−	2.97260i
$111$		0			0
$112$		0			0
$113$	−3.00000			−0.282216			−0.141108	−	0.989994i	$-0.545067\pi$
$113$	−3.00000			−0.282216			−0.141108	+	0.989994i	$0.545067\pi$
$114$		0			0
$115$	−4.50000	+	7.79423i	−0.419627	+	0.726816i
$116$	5.00000	−	8.66025i	0.464238	−	0.804084i
$117$	1.50000	+	2.59808i	0.138675	+	0.240192i
$118$	16.0000			1.47292
$119$		0			0
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	10.0000	−	17.3205i	0.905357	−	1.56813i
$123$		0			0
$124$	−3.00000	−	5.19615i	−0.269408	−	0.466628i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$		0			0
$129$		0			0
$130$	3.00000	−	5.19615i	0.263117	−	0.455733i
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	0.986157	−	0.165812i	$-0.0530244\pi$
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	−0.636676	+	0.771132i	$0.719691\pi$
$132$		0			0
$133$		0			0
$134$	12.0000			1.03664
$135$		0			0
$136$		0			0
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$		0			0
$139$	18.0000			1.52674			0.763370	−	0.645961i	$-0.223543\pi$
$139$	18.0000			1.52674			0.763370	+	0.645961i	$0.223543\pi$
$140$		0			0
$141$		0			0
$142$	−8.00000	−	13.8564i	−0.671345	−	1.16280i
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	−6.00000	+	10.3923i	−0.500000	+	0.866025i
$145$	7.50000	+	12.9904i	0.622841	+	1.07879i
$146$	−26.0000			−2.15178
$147$		0			0
$148$	−8.00000			−0.657596
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	9.00000			0.722897
$156$		0			0
$157$	−4.00000	+	6.92820i	−0.319235	+	0.552931i	−0.980329	−	0.197372i	$-0.936759\pi$
$157$	−4.00000	+	6.92820i	−0.319235	+	0.552931i	0.661094	+	0.750303i	$0.270093\pi$
$158$	3.00000	−	5.19615i	0.238667	−	0.413384i
$159$		0			0
$160$	24.0000			1.89737
$161$		0			0
$162$	−18.0000			−1.41421
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	−6.00000	+	10.3923i	−0.468521	+	0.811503i
$165$		0			0
$166$	−15.0000	−	25.9808i	−1.16423	−	2.01650i
$167$	−5.00000			−0.386912			−0.193456	−	0.981109i	$-0.561970\pi$
$167$	−5.00000			−0.386912			−0.193456	+	0.981109i	$0.561970\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−12.0000	−	20.7846i	−0.920358	−	1.59411i
$171$	−7.50000	+	12.9904i	−0.573539	+	0.993399i
$172$	1.00000	−	1.73205i	0.0762493	−	0.132068i
$173$	−4.00000	−	6.92820i	−0.304114	−	0.526742i	0.672949	−	0.739689i	$-0.265027\pi$
$173$	−4.00000	−	6.92820i	−0.304114	−	0.526742i	−0.977064	+	0.212947i	$0.931694\pi$
$174$		0			0
$175$		0			0
$176$	24.0000			1.80907
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−11.5000	+	19.9186i	−0.859550	+	1.48878i	0.0128080	+	0.999918i	$0.495923\pi$
$179$	−11.5000	+	19.9186i	−0.859550	+	1.48878i	−0.872358	+	0.488867i	$0.837410\pi$
$180$	9.00000	+	15.5885i	0.670820	+	1.16190i
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.00000	−	10.3923i	0.441129	−	0.764057i
$186$		0			0
$187$	−12.0000	−	20.7846i	−0.877527	−	1.51992i
$188$	−14.0000			−1.02105
$189$		0			0
$190$	30.0000			2.17643
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		0			0
$193$	−11.0000	+	19.0526i	−0.791797	+	1.37143i	0.133056	+	0.991109i	$0.457521\pi$
$193$	−11.0000	+	19.0526i	−0.791797	+	1.37143i	−0.924853	+	0.380325i	$0.875812\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$		0			0
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	18.0000	+	31.1769i	1.27920	+	2.21565i
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$		0			0
$201$		0			0
$202$	−28.0000			−1.97007
$203$		0			0
$204$		0			0
$205$	−9.00000	−	15.5885i	−0.628587	−	1.08875i
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$	4.50000	−	7.79423i	0.312772	−	0.541736i
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	30.0000			2.07514
$210$		0			0
$211$	−5.00000			−0.344214			−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000			−0.344214			−0.172107	+	0.985078i	$0.555058\pi$
$212$	9.00000	+	15.5885i	0.618123	+	1.07062i
$213$		0			0
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	1.50000	+	2.59808i	0.102299	+	0.177187i
$216$		0			0
$217$		0			0
$218$	4.00000			0.270914
$219$		0			0
$220$	18.0000	−	31.1769i	1.21356	−	2.10195i
$221$	2.00000	−	3.46410i	0.134535	−	0.233021i
$222$		0			0
$223$	−15.0000			−1.00447			−0.502237	−	0.864730i	$-0.667490\pi$
$223$	−15.0000			−1.00447			−0.502237	+	0.864730i	$0.667490\pi$
$224$		0			0
$225$	−12.0000			−0.800000
$226$	−3.00000	−	5.19615i	−0.199557	−	0.345643i
$227$	10.0000	−	17.3205i	0.663723	−	1.14960i	−0.315906	−	0.948790i	$-0.602309\pi$
$227$	10.0000	−	17.3205i	0.663723	−	1.14960i	0.979630	−	0.200812i	$-0.0643581\pi$
$228$		0			0
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$	−18.0000			−1.18688
$231$		0			0
$232$		0			0
$233$	−7.50000	−	12.9904i	−0.491341	−	0.851028i	0.508609	−	0.860998i	$-0.330160\pi$
$233$	−7.50000	−	12.9904i	−0.491341	−	0.851028i	−0.999950	+	0.00996947i	$0.996827\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$	10.5000	−	18.1865i	0.684944	−	1.18636i
$236$	8.00000	+	13.8564i	0.520756	+	0.901975i
$237$		0			0
$238$		0			0
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$		0			0
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	0.450910	+	0.892570i	$0.351100\pi$
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	25.0000	−	43.3013i	1.60706	−	2.78351i
$243$		0			0
$244$	20.0000			1.28037
$245$		0			0
$246$		0			0
$247$	2.50000	+	4.33013i	0.159071	+	0.275519i
$248$		0			0
$249$		0			0
$250$	−3.00000	−	5.19615i	−0.189737	−	0.328634i
$251$	26.0000			1.64111			0.820553	−	0.571571i	$-0.193666\pi$
$251$	26.0000			1.64111			0.820553	+	0.571571i	$0.193666\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	0.833150	−	0.553047i	$-0.186535\pi$
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	−0.895528	+	0.445005i	$0.853202\pi$
$258$		0			0
$259$		0			0
$260$	6.00000			0.372104
$261$	−7.50000	−	12.9904i	−0.464238	−	0.804084i
$262$	−8.00000	+	13.8564i	−0.494242	+	0.856052i
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	−0.536614	−	0.843828i	$-0.680297\pi$
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	0.999083	+	0.0428069i	$0.0136300\pi$
$264$		0			0
$265$	−27.0000			−1.65860
$266$		0			0
$267$		0			0
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$	16.0000			0.970143
$273$		0			0
$274$	−8.00000			−0.483298
$275$	12.0000	+	20.7846i	0.723627	+	1.25336i
$276$		0			0
$277$	−0.500000	+	0.866025i	−0.0300421	+	0.0520344i	−0.880656	−	0.473757i	$-0.842897\pi$
$277$	−0.500000	+	0.866025i	−0.0300421	+	0.0520344i	0.850613	+	0.525792i	$0.176231\pi$
$278$	18.0000	+	31.1769i	1.07957	+	1.86987i
$279$	−9.00000			−0.538816
$280$		0			0
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$		0			0
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	−0.524057	−	0.851683i	$-0.675582\pi$
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	0.999608	+	0.0280052i	$0.00891551\pi$
$284$	8.00000	−	13.8564i	0.474713	−	0.822226i
$285$		0			0
$286$	12.0000			0.709575
$287$		0			0
$288$	−24.0000			−1.41421
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−15.0000	+	25.9808i	−0.880830	+	1.52564i
$291$		0			0
$292$	−13.0000	−	22.5167i	−0.760767	−	1.31769i
$293$	19.0000			1.10999			0.554996	−	0.831853i	$-0.312720\pi$
$293$	19.0000			1.10999			0.554996	+	0.831853i	$0.312720\pi$
$294$		0			0
$295$	−24.0000			−1.39733
$296$		0			0
$297$		0			0
$298$	−18.0000	+	31.1769i	−1.04271	+	1.80603i
$299$	−1.50000	−	2.59808i	−0.0867472	−	0.150251i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−10.0000	+	17.3205i	−0.573539	+	0.993399i
$305$	−15.0000	+	25.9808i	−0.858898	+	1.48765i
$306$	12.0000	+	20.7846i	0.685994	+	1.18818i
$307$	33.0000			1.88341			0.941705	−	0.336440i	$-0.109223\pi$
$307$	33.0000			1.88341			0.941705	+	0.336440i	$0.109223\pi$
$308$		0			0
$309$		0			0
$310$	9.00000	+	15.5885i	0.511166	+	0.885365i
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	−0.938460	−	0.345389i	$-0.887747\pi$
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	0.768345	+	0.640036i	$0.221080\pi$
$312$		0			0
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	0.989158	+	0.146852i	$0.0469141\pi$
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	−0.367402	+	0.930062i	$0.619753\pi$
$314$	−16.0000			−0.902932
$315$		0			0
$316$	6.00000			0.337526
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	0.976764	+	0.214318i	$0.0687530\pi$
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	−0.302777	+	0.953062i	$0.597914\pi$
$318$		0			0
$319$	−15.0000	+	25.9808i	−0.839839	+	1.45464i
$320$	12.0000	+	20.7846i	0.670820	+	1.16190i
$321$		0			0
$322$		0			0
$323$	20.0000			1.11283
$324$	−9.00000	−	15.5885i	−0.500000	−	0.866025i
$325$	−2.00000	+	3.46410i	−0.110940	+	0.192154i
$326$	−4.00000	+	6.92820i	−0.221540	+	0.383718i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−11.0000	−	19.0526i	−0.604615	−	1.04722i	−0.992112	−	0.125353i	$-0.959994\pi$
$331$	−11.0000	−	19.0526i	−0.604615	−	1.04722i	0.387498	−	0.921871i	$-0.373340\pi$
$332$	15.0000	−	25.9808i	0.823232	−	1.42588i
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$	−5.00000	−	8.66025i	−0.273588	−	0.473868i
$335$	−18.0000			−0.983445
$336$		0			0
$337$	17.0000			0.926049			0.463025	−	0.886345i	$-0.346764\pi$
$337$	17.0000			0.926049			0.463025	+	0.886345i	$0.346764\pi$
$338$	1.00000	+	1.73205i	0.0543928	+	0.0942111i
$339$		0			0
$340$	12.0000	−	20.7846i	0.650791	−	1.12720i
$341$	9.00000	+	15.5885i	0.487377	+	0.844162i
$342$	−30.0000			−1.62221
$343$		0			0
$344$		0			0
$345$		0			0
$346$	8.00000	−	13.8564i	0.430083	−	0.744925i
$347$	16.0000	−	27.7128i	0.858925	−	1.48770i	−0.0140303	−	0.999902i	$-0.504466\pi$
$347$	16.0000	−	27.7128i	0.858925	−	1.48770i	0.872955	−	0.487800i	$-0.162201\pi$
$348$		0			0
$349$	−11.0000			−0.588817			−0.294408	−	0.955680i	$-0.595123\pi$
$349$	−11.0000			−0.588817			−0.294408	+	0.955680i	$0.595123\pi$
$350$		0			0
$351$		0			0
$352$	24.0000	+	41.5692i	1.27920	+	2.21565i
$353$	−5.00000	+	8.66025i	−0.266123	+	0.460939i	−0.967857	−	0.251500i	$-0.919076\pi$
$353$	−5.00000	+	8.66025i	−0.266123	+	0.460939i	0.701734	+	0.712439i	$0.252409\pi$
$354$		0			0
$355$	12.0000	+	20.7846i	0.636894	+	1.10313i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−46.0000			−2.43118
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−14.0000	−	24.2487i	−0.735824	−	1.27448i
$363$		0			0
$364$		0			0
$365$	39.0000			2.04135
$366$		0			0
$367$	7.00000	−	12.1244i	0.365397	−	0.632886i	−0.623443	−	0.781869i	$-0.714267\pi$
$367$	7.00000	−	12.1244i	0.365397	−	0.632886i	0.988840	+	0.148983i	$0.0475999\pi$
$368$	6.00000	−	10.3923i	0.312772	−	0.541736i
$369$	9.00000	+	15.5885i	0.468521	+	0.811503i
$370$	24.0000			1.24770
$371$		0			0
$372$		0			0
$373$	−15.0000	−	25.9808i	−0.776671	−	1.34523i	−0.933851	−	0.357663i	$-0.883574\pi$
$373$	−15.0000	−	25.9808i	−0.776671	−	1.34523i	0.157180	−	0.987570i	$-0.449760\pi$
$374$	24.0000	−	41.5692i	1.24101	−	2.14949i
$375$		0			0
$376$		0			0
$377$	−5.00000			−0.257513
$378$		0			0
$379$	−6.00000			−0.308199			−0.154100	−	0.988055i	$-0.549248\pi$
$379$	−6.00000			−0.308199			−0.154100	+	0.988055i	$0.549248\pi$
$380$	15.0000	+	25.9808i	0.769484	+	1.33278i
$381$		0			0
$382$	−8.00000	+	13.8564i	−0.409316	+	0.708955i
$383$	−18.0000	−	31.1769i	−0.919757	−	1.59307i	−0.799783	−	0.600289i	$-0.795052\pi$
$383$	−18.0000	−	31.1769i	−0.919757	−	1.59307i	−0.119974	−	0.992777i	$-0.538281\pi$
$384$		0			0
$385$		0			0
$386$	−44.0000			−2.23954
$387$	−1.50000	−	2.59808i	−0.0762493	−	0.132068i
$388$	7.00000	−	12.1244i	0.355371	−	0.615521i
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$		0			0
$393$		0			0
$394$	2.00000	+	3.46410i	0.100759	+	0.174519i
$395$	−4.50000	+	7.79423i	−0.226420	+	0.392170i
$396$	−18.0000	+	31.1769i	−0.904534	+	1.56670i
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	0.655534	−	0.755166i	$-0.272444\pi$
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	−0.981760	+	0.190126i	$0.939110\pi$
$398$	8.00000			0.401004
$399$		0			0
$400$	−16.0000			−0.800000
$401$	16.0000	+	27.7128i	0.799002	+	1.38391i	0.920267	+	0.391292i	$0.127972\pi$
$401$	16.0000	+	27.7128i	0.799002	+	1.38391i	−0.121265	+	0.992620i	$0.538695\pi$
$402$		0			0
$403$	−1.50000	+	2.59808i	−0.0747203	+	0.129419i
$404$	−14.0000	−	24.2487i	−0.696526	−	1.20642i
$405$	27.0000			1.34164
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	−6.50000	+	11.2583i	−0.321404	+	0.556689i	−0.980778	−	0.195127i	$-0.937488\pi$
$409$	−6.50000	+	11.2583i	−0.321404	+	0.556689i	0.659374	+	0.751815i	$0.270822\pi$
$410$	18.0000	−	31.1769i	0.888957	−	1.53972i
$411$		0			0
$412$	8.00000			0.394132
$413$		0			0
$414$	18.0000			0.884652
$415$	22.5000	+	38.9711i	1.10448	+	1.91302i
$416$	−4.00000	+	6.92820i	−0.196116	+	0.339683i
$417$		0			0
$418$	30.0000	+	51.9615i	1.46735	+	2.54152i
$419$	10.0000			0.488532			0.244266	−	0.969708i	$-0.421453\pi$
$419$	10.0000			0.488532			0.244266	+	0.969708i	$0.421453\pi$
$420$		0			0
$421$	−12.0000			−0.584844			−0.292422	−	0.956289i	$-0.594461\pi$
$421$	−12.0000			−0.584844			−0.292422	+	0.956289i	$0.594461\pi$
$422$	−5.00000	−	8.66025i	−0.243396	−	0.421575i
$423$	−10.5000	+	18.1865i	−0.510527	+	0.884260i
$424$		0			0
$425$	8.00000	+	13.8564i	0.388057	+	0.672134i
$426$		0			0
$427$		0			0
$428$	−8.00000			−0.386695
$429$		0			0
$430$	−3.00000	+	5.19615i	−0.144673	+	0.250581i
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	−0.929188	−	0.369607i	$-0.879492\pi$
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	0.784683	+	0.619897i	$0.212826\pi$
$432$		0			0
$433$	−12.0000			−0.576683			−0.288342	−	0.957528i	$-0.593104\pi$
$433$	−12.0000			−0.576683			−0.288342	+	0.957528i	$0.593104\pi$
$434$		0			0
$435$		0			0
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	7.50000	−	12.9904i	0.358774	−	0.621414i
$438$		0			0
$439$	−11.0000	−	19.0526i	−0.525001	−	0.909329i	−0.999576	−	0.0291138i	$-0.990731\pi$
$439$	−11.0000	−	19.0526i	−0.525001	−	0.909329i	0.474575	−	0.880215i	$-0.342602\pi$
$440$		0			0
$441$		0			0
$442$	8.00000			0.380521
$443$	−9.50000	−	16.4545i	−0.451359	−	0.781776i	0.547112	−	0.837059i	$-0.315727\pi$
$443$	−9.50000	−	16.4545i	−0.451359	−	0.781776i	−0.998471	+	0.0552833i	$0.982394\pi$
$444$		0			0
$445$	4.50000	−	7.79423i	0.213320	−	0.369482i
$446$	−15.0000	−	25.9808i	−0.710271	−	1.23022i
$447$		0			0
$448$		0			0
$449$	36.0000			1.69895			0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000			1.69895			0.849473	+	0.527633i	$0.176920\pi$
$450$	−12.0000	−	20.7846i	−0.565685	−	0.979796i
$451$	18.0000	−	31.1769i	0.847587	−	1.46806i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$		0			0
$454$	40.0000			1.87729
$455$		0			0
$456$		0			0
$457$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$457$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$458$	−14.0000	+	24.2487i	−0.654177	+	1.13307i
$459$		0			0
$460$	−9.00000	−	15.5885i	−0.419627	−	0.726816i
$461$	22.0000			1.02464			0.512321	−	0.858794i	$-0.328786\pi$
$461$	22.0000			1.02464			0.512321	+	0.858794i	$0.328786\pi$
$462$		0			0
$463$	−14.0000			−0.650635			−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000			−0.650635			−0.325318	+	0.945605i	$0.605471\pi$
$464$	−10.0000	−	17.3205i	−0.464238	−	0.804084i
$465$		0			0
$466$	15.0000	−	25.9808i	0.694862	−	1.20354i
$467$	−11.0000	−	19.0526i	−0.509019	−	0.881647i	−0.999945	−	0.0104461i	$-0.996675\pi$
$467$	−11.0000	−	19.0526i	−0.509019	−	0.881647i	0.490926	−	0.871201i	$-0.336658\pi$
$468$	−6.00000			−0.277350
$469$		0			0
$470$	42.0000			1.93732
$471$		0			0
$472$		0			0
$473$	−3.00000	+	5.19615i	−0.137940	+	0.238919i
$474$		0			0
$475$	−20.0000			−0.917663
$476$		0			0
$477$	27.0000			1.23625
$478$	−4.00000	−	6.92820i	−0.182956	−	0.316889i
$479$	−5.50000	+	9.52628i	−0.251301	+	0.435267i	−0.963884	−	0.266321i	$-0.914192\pi$
$479$	−5.50000	+	9.52628i	−0.251301	+	0.435267i	0.712583	+	0.701588i	$0.247525\pi$
$480$		0			0
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$	−34.0000			−1.54866
$483$		0			0
$484$	50.0000			2.27273
$485$	10.5000	+	18.1865i	0.476780	+	0.825808i
$486$		0			0
$487$	13.0000	−	22.5167i	0.589086	−	1.02033i	−0.405266	−	0.914199i	$-0.632821\pi$
$487$	13.0000	−	22.5167i	0.589086	−	1.02033i	0.994352	−	0.106129i	$-0.0338455\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	−10.0000	+	17.3205i	−0.450377	+	0.780076i
$494$	−5.00000	+	8.66025i	−0.224961	+	0.389643i
$495$	−27.0000	−	46.7654i	−1.21356	−	2.10195i
$496$	−12.0000			−0.538816
$497$		0			0
$498$		0			0
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	0.987648	−	0.156687i	$-0.0500814\pi$
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	−0.629519	+	0.776985i	$0.716748\pi$
$500$	3.00000	−	5.19615i	0.134164	−	0.232379i
$501$		0			0
$502$	26.0000	+	45.0333i	1.16044	+	2.00994i
$503$	−2.00000			−0.0891756			−0.0445878	−	0.999005i	$-0.514197\pi$
$503$	−2.00000			−0.0891756			−0.0445878	+	0.999005i	$0.514197\pi$
$504$		0			0
$505$	42.0000			1.86898
$506$	−18.0000	−	31.1769i	−0.800198	−	1.38598i
$507$		0			0
$508$	4.00000	−	6.92820i	0.177471	−	0.307389i
$509$	−9.50000	−	16.4545i	−0.421080	−	0.729332i	0.574965	−	0.818178i	$-0.305016\pi$
$509$	−9.50000	−	16.4545i	−0.421080	−	0.729332i	−0.996045	+	0.0888457i	$0.971682\pi$
$510$		0			0
$511$		0			0
$512$	−32.0000			−1.41421
$513$		0			0
$514$	2.00000	−	3.46410i	0.0882162	−	0.152795i
$515$	−6.00000	+	10.3923i	−0.264392	+	0.457940i
$516$		0			0
$517$	42.0000			1.84716
$518$		0			0
$519$		0			0
$520$		0			0
$521$	20.0000	−	34.6410i	0.876216	−	1.51765i	0.0207541	−	0.999785i	$-0.493393\pi$
$521$	20.0000	−	34.6410i	0.876216	−	1.51765i	0.855462	−	0.517866i	$-0.173273\pi$
$522$	15.0000	−	25.9808i	0.656532	−	1.13715i
$523$	5.00000	+	8.66025i	0.218635	+	0.378686i	0.954391	−	0.298560i	$-0.0965063\pi$
$523$	5.00000	+	8.66025i	0.218635	+	0.378686i	−0.735756	+	0.677247i	$0.763173\pi$
$524$	−16.0000			−0.698963
$525$		0			0
$526$	30.0000			1.30806
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−27.0000	−	46.7654i	−1.17281	−	2.03136i
$531$	24.0000			1.04151
$532$		0			0
$533$	6.00000			0.259889
$534$		0			0
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	20.0000	+	34.6410i	0.859867	+	1.48933i	0.872055	+	0.489408i	$0.162787\pi$
$541$	20.0000	+	34.6410i	0.859867	+	1.48933i	−0.0121878	+	0.999926i	$0.503880\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$		0			0
$544$	16.0000	+	27.7128i	0.685994	+	1.18818i
$545$	−6.00000			−0.257012
$546$		0			0
$547$	−7.00000			−0.299298			−0.149649	−	0.988739i	$-0.547814\pi$
$547$	−7.00000			−0.299298			−0.149649	+	0.988739i	$0.547814\pi$
$548$	−4.00000	−	6.92820i	−0.170872	−	0.295958i
$549$	15.0000	−	25.9808i	0.640184	−	1.10883i
$550$	−24.0000	+	41.5692i	−1.02336	+	1.77252i
$551$	−12.5000	−	21.6506i	−0.532518	−	0.922348i
$552$		0			0
$553$		0			0
$554$	−2.00000			−0.0849719
$555$		0			0
$556$	−18.0000	+	31.1769i	−0.763370	+	1.32220i
$557$	6.00000	−	10.3923i	0.254228	−	0.440336i	−0.710457	−	0.703740i	$-0.751512\pi$
$557$	6.00000	−	10.3923i	0.254228	−	0.440336i	0.964686	+	0.263404i	$0.0848453\pi$
$558$	−9.00000	−	15.5885i	−0.381000	−	0.659912i
$559$	−1.00000			−0.0422955
$560$		0			0
$561$		0			0
$562$	−30.0000	−	51.9615i	−1.26547	−	2.19186i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		0			0
$565$	4.50000	+	7.79423i	0.189316	+	0.327906i
$566$	32.0000			1.34506
$567$		0			0
$568$		0			0
$569$	−3.50000	−	6.06218i	−0.146728	−	0.254140i	0.783289	−	0.621658i	$-0.213541\pi$
$569$	−3.50000	−	6.06218i	−0.146728	−	0.254140i	−0.930016	+	0.367519i	$0.880207\pi$
$570$		0			0
$571$	8.50000	−	14.7224i	0.355714	−	0.616115i	−0.631526	−	0.775355i	$-0.717571\pi$
$571$	8.50000	−	14.7224i	0.355714	−	0.616115i	0.987240	+	0.159240i	$0.0509044\pi$
$572$	6.00000	+	10.3923i	0.250873	+	0.434524i
$573$		0			0
$574$		0			0
$575$	12.0000			0.500435
$576$	−12.0000	−	20.7846i	−0.500000	−	0.866025i
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	−0.844459	−	0.535620i	$-0.820078\pi$
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	0.886090	+	0.463513i	$0.153411\pi$
$578$	−1.00000	+	1.73205i	−0.0415945	+	0.0720438i
$579$		0			0
$580$	−30.0000			−1.24568
$581$		0			0
$582$		0			0
$583$	−27.0000	−	46.7654i	−1.11823	−	1.93682i
$584$		0			0
$585$	4.50000	−	7.79423i	0.186052	−	0.322252i
$586$	19.0000	+	32.9090i	0.784883	+	1.35946i
$587$	−39.0000			−1.60970			−0.804851	−	0.593477i	$-0.797755\pi$
$587$	−39.0000			−1.60970			−0.804851	+	0.593477i	$0.797755\pi$
$588$		0			0
$589$	−15.0000			−0.618064
$590$	−24.0000	−	41.5692i	−0.988064	−	1.71138i
$591$		0			0
$592$	−8.00000	+	13.8564i	−0.328798	+	0.569495i
$593$	−13.5000	−	23.3827i	−0.554379	−	0.960212i	−0.997952	−	0.0639736i	$-0.979623\pi$
$593$	−13.5000	−	23.3827i	−0.554379	−	0.960212i	0.443573	−	0.896238i	$-0.353711\pi$
$594$		0			0
$595$		0			0
$596$	−36.0000			−1.47462
$597$		0			0
$598$	3.00000	−	5.19615i	0.122679	−	0.212486i
$599$	−5.50000	+	9.52628i	−0.224724	+	0.389233i	−0.956237	−	0.292595i	$-0.905481\pi$
$599$	−5.50000	+	9.52628i	−0.224724	+	0.389233i	0.731513	+	0.681828i	$0.238815\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	18.0000			0.733017
$604$		0			0
$605$	−37.5000	+	64.9519i	−1.52459	+	2.64067i
$606$		0			0
$607$	1.00000	+	1.73205i	0.0405887	+	0.0703018i	0.885606	−	0.464437i	$-0.153743\pi$
$607$	1.00000	+	1.73205i	0.0405887	+	0.0703018i	−0.845017	+	0.534739i	$0.820410\pi$
$608$	−40.0000			−1.62221
$609$		0			0
$610$	−60.0000			−2.42933
$611$	3.50000	+	6.06218i	0.141595	+	0.245249i
$612$	−12.0000	+	20.7846i	−0.485071	+	0.840168i
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	−0.935428	−	0.353518i	$-0.884985\pi$
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	0.773869	+	0.633345i	$0.218319\pi$
$614$	33.0000	+	57.1577i	1.33177	+	2.30670i
$615$		0			0
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$	−9.00000	+	15.5885i	−0.361449	+	0.626048i
$621$		0			0
$622$	−12.0000			−0.481156
$623$		0			0
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−22.0000	+	38.1051i	−0.879297	+	1.52299i
$627$		0			0
$628$	−8.00000	−	13.8564i	−0.319235	−	0.552931i
$629$	16.0000			0.637962
$630$		0			0
$631$	22.0000			0.875806			0.437903	−	0.899022i	$-0.355721\pi$
$631$	22.0000			0.875806			0.437903	+	0.899022i	$0.355721\pi$
$632$		0			0
$633$		0			0
$634$	−24.0000	+	41.5692i	−0.953162	+	1.65092i
$635$	6.00000	+	10.3923i	0.238103	+	0.412406i
$636$		0			0
$637$		0			0
$638$	−60.0000			−2.37542
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$		0			0
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$		0			0
$643$	−8.00000			−0.315489			−0.157745	−	0.987480i	$-0.550422\pi$
$643$	−8.00000			−0.315489			−0.157745	+	0.987480i	$0.550422\pi$
$644$		0			0
$645$		0			0
$646$	20.0000	+	34.6410i	0.786889	+	1.36293i
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	−0.633090	−	0.774078i	$-0.718214\pi$
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	0.986916	+	0.161233i	$0.0515470\pi$
$648$		0			0
$649$	−24.0000	−	41.5692i	−0.942082	−	1.63173i
$650$	−8.00000			−0.313786
$651$		0			0
$652$	−8.00000			−0.313304
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$		0			0
$655$	12.0000	−	20.7846i	0.468879	−	0.812122i
$656$	12.0000	+	20.7846i	0.468521	+	0.811503i
$657$	−39.0000			−1.52153
$658$		0			0
$659$	17.0000			0.662226			0.331113	−	0.943591i	$-0.392576\pi$
$659$	17.0000			0.662226			0.331113	+	0.943591i	$0.392576\pi$
$660$		0			0
$661$	−16.5000	+	28.5788i	−0.641776	+	1.11159i	0.343261	+	0.939240i	$0.388469\pi$
$661$	−16.5000	+	28.5788i	−0.641776	+	1.11159i	−0.985036	+	0.172348i	$0.944865\pi$
$662$	22.0000	−	38.1051i	0.855054	−	1.48100i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−24.0000			−0.929981
$667$	7.50000	+	12.9904i	0.290401	+	0.502990i
$668$	5.00000	−	8.66025i	0.193456	−	0.335075i
$669$		0			0
$670$	−18.0000	−	31.1769i	−0.695401	−	1.20447i
$671$	−60.0000			−2.31627
$672$		0			0
$673$	1.00000			0.0385472			0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000			0.0385472			0.0192736	+	0.999814i	$0.493865\pi$
$674$	17.0000	+	29.4449i	0.654816	+	1.13417i
$675$		0			0
$676$	−1.00000	+	1.73205i	−0.0384615	+	0.0666173i
$677$	11.0000	+	19.0526i	0.422764	+	0.732249i	0.996209	−	0.0869952i	$-0.0277265\pi$
$677$	11.0000	+	19.0526i	0.422764	+	0.732249i	−0.573444	+	0.819244i	$0.694393\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−18.0000	+	31.1769i	−0.689256	+	1.19383i
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$	−15.0000	−	25.9808i	−0.573539	−	0.993399i
$685$	12.0000			0.458496
$686$		0			0
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	4.50000	−	7.79423i	0.171436	−	0.296936i
$690$		0			0
$691$	5.50000	+	9.52628i	0.209230	+	0.362397i	0.951472	−	0.307735i	$-0.0995710\pi$
$691$	5.50000	+	9.52628i	0.209230	+	0.362397i	−0.742242	+	0.670132i	$0.766238\pi$
$692$	16.0000			0.608229
$693$		0			0
$694$	64.0000			2.42941
$695$	−27.0000	−	46.7654i	−1.02417	−	1.77391i
$696$		0			0
$697$	12.0000	−	20.7846i	0.454532	−	0.787273i
$698$	−11.0000	−	19.0526i	−0.416356	−	0.721150i
$699$		0			0
$700$		0			0
$701$	−27.0000			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$702$		0			0
$703$	−10.0000	+	17.3205i	−0.377157	+	0.653255i
$704$	−24.0000	+	41.5692i	−0.904534	+	1.56670i
$705$		0			0
$706$	−20.0000			−0.752710
$707$		0			0
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	−24.0000	+	41.5692i	−0.900704	+	1.56007i
$711$	4.50000	−	7.79423i	0.168763	−	0.292306i
$712$		0			0
$713$	9.00000			0.337053
$714$		0			0
$715$	−18.0000			−0.673162
$716$	−23.0000	−	39.8372i	−0.859550	−	1.48878i
$717$		0			0
$718$	20.0000	−	34.6410i	0.746393	−	1.29279i
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	0.983608	−	0.180319i	$-0.0577130\pi$
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	−0.647965	+	0.761670i	$0.724380\pi$
$720$	36.0000			1.34164
$721$		0			0
$722$	−12.0000			−0.446594
$723$		0			0
$724$	14.0000	−	24.2487i	0.520306	−	0.901196i
$725$	10.0000	−	17.3205i	0.371391	−	0.643268i
$726$		0			0
$727$	−46.0000			−1.70605			−0.853023	−	0.521874i	$-0.825233\pi$
$727$	−46.0000			−1.70605			−0.853023	+	0.521874i	$0.825233\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	39.0000	+	67.5500i	1.44345	+	2.50014i
$731$	−2.00000	+	3.46410i	−0.0739727	+	0.128124i
$732$		0			0
$733$	25.5000	+	44.1673i	0.941864	+	1.63136i	0.761912	+	0.647681i	$0.224261\pi$
$733$	25.5000	+	44.1673i	0.941864	+	1.63136i	0.179952	+	0.983675i	$0.442406\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$	24.0000			0.884652
$737$	−18.0000	−	31.1769i	−0.663039	−	1.14842i
$738$	−18.0000	+	31.1769i	−0.662589	+	1.14764i
$739$	13.0000	−	22.5167i	0.478213	−	0.828289i	−0.521475	−	0.853266i	$-0.674618\pi$
$739$	13.0000	−	22.5167i	0.478213	−	0.828289i	0.999688	+	0.0249776i	$0.00795146\pi$
$740$	12.0000	+	20.7846i	0.441129	+	0.764057i
$741$		0			0
$742$		0			0
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$		0			0
$745$	27.0000	−	46.7654i	0.989203	−	1.71335i
$746$	30.0000	−	51.9615i	1.09838	−	1.90245i
$747$	−22.5000	−	38.9711i	−0.823232	−	1.42588i
$748$	48.0000			1.75505
$749$		0			0
$750$		0			0
$751$	8.50000	+	14.7224i	0.310169	+	0.537229i	0.978399	−	0.206726i	$-0.0662809\pi$
$751$	8.50000	+	14.7224i	0.310169	+	0.537229i	−0.668229	+	0.743955i	$0.732948\pi$
$752$	−14.0000	+	24.2487i	−0.510527	+	0.884260i
$753$		0			0
$754$	−5.00000	−	8.66025i	−0.182089	−	0.315388i
$755$		0			0
$756$		0			0
$757$	−15.0000			−0.545184			−0.272592	−	0.962130i	$-0.587881\pi$
$757$	−15.0000			−0.545184			−0.272592	+	0.962130i	$0.587881\pi$
$758$	−6.00000	−	10.3923i	−0.217930	−	0.377466i
$759$		0			0
$760$		0			0
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	0.935988	−	0.352032i	$-0.114509\pi$
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	−0.772863	+	0.634573i	$0.781176\pi$
$762$		0			0
$763$		0			0
$764$	−16.0000			−0.578860
$765$	−18.0000	−	31.1769i	−0.650791	−	1.12720i
$766$	36.0000	−	62.3538i	1.30073	−	2.25294i
$767$	4.00000	−	6.92820i	0.144432	−	0.250163i
$768$		0			0
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$		0			0
$771$		0			0
$772$	−22.0000	−	38.1051i	−0.791797	−	1.37143i
$773$	27.0000	−	46.7654i	0.971123	−	1.68203i	0.278944	−	0.960307i	$-0.410016\pi$
$773$	27.0000	−	46.7654i	0.971123	−	1.68203i	0.692179	−	0.721726i	$-0.256651\pi$
$774$	3.00000	−	5.19615i	0.107833	−	0.186772i
$775$	−6.00000	−	10.3923i	−0.215526	−	0.373303i
$776$		0			0
$777$		0			0
$778$	−60.0000			−2.15110
$779$	15.0000	+	25.9808i	0.537431	+	0.930857i
$780$		0			0
$781$	−24.0000	+	41.5692i	−0.858788	+	1.48746i
$782$	−12.0000	−	20.7846i	−0.429119	−	0.743256i
$783$		0			0
$784$		0			0
$785$	24.0000			0.856597
$786$		0			0
$787$	18.5000	−	32.0429i	0.659454	−	1.14221i	−0.321303	−	0.946976i	$-0.604121\pi$
$787$	18.5000	−	32.0429i	0.659454	−	1.14221i	0.980757	−	0.195231i	$-0.0625457\pi$
$788$	−2.00000	+	3.46410i	−0.0712470	+	0.123404i
$789$		0			0
$790$	−18.0000			−0.640411
$791$		0			0
$792$		0			0
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$	13.0000	−	22.5167i	0.461353	−	0.799086i
$795$		0			0
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$	28.0000			0.990569
$800$	−16.0000	−	27.7128i	−0.565685	−	0.979796i
$801$	−4.50000	+	7.79423i	−0.159000	+	0.275396i
$802$	−32.0000	+	55.4256i	−1.12996	+	1.95715i
$803$	39.0000	+	67.5500i	1.37628	+	2.38379i
$804$		0			0
$805$		0			0
$806$	−6.00000			−0.211341
$807$		0			0
$808$		0			0
$809$	15.5000	−	26.8468i	0.544951	−	0.943883i	−0.453659	−	0.891175i	$-0.649882\pi$
$809$	15.5000	−	26.8468i	0.544951	−	0.943883i	0.998610	−	0.0527074i	$-0.0167851\pi$
$810$	27.0000	+	46.7654i	0.948683	+	1.64317i
$811$	52.0000			1.82597			0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000			1.82597			0.912983	+	0.407997i	$0.133772\pi$
$812$		0			0
$813$		0			0
$814$	24.0000	+	41.5692i	0.841200	+	1.45700i
$815$	6.00000	−	10.3923i	0.210171	−	0.364027i
$816$		0			0
$817$	−2.50000	−	4.33013i	−0.0874639	−	0.151492i
$818$	−26.0000			−0.909069
$819$		0			0
$820$	36.0000			1.25717
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$		0			0
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.00000			0.139094			0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000			0.139094			0.0695468	+	0.997579i	$0.477845\pi$
$828$	9.00000	+	15.5885i	0.312772	+	0.541736i
$829$	−5.00000	+	8.66025i	−0.173657	+	0.300783i	−0.939696	−	0.342012i	$-0.888892\pi$
$829$	−5.00000	+	8.66025i	−0.173657	+	0.300783i	0.766039	+	0.642795i	$0.222225\pi$
$830$	−45.0000	+	77.9423i	−1.56197	+	2.70542i
$831$		0			0
$832$	−8.00000			−0.277350
$833$		0			0
$834$		0			0
$835$	7.50000	+	12.9904i	0.259548	+	0.449551i
$836$	−30.0000	+	51.9615i	−1.03757	+	1.79713i
$837$		0			0
$838$	10.0000	+	17.3205i	0.345444	+	0.598327i
$839$	8.00000			0.276191			0.138095	−	0.990419i	$-0.455902\pi$
$839$	8.00000			0.276191			0.138095	+	0.990419i	$0.455902\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	−12.0000	−	20.7846i	−0.413547	−	0.716285i
$843$		0			0
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$	−1.50000	−	2.59808i	−0.0516016	−	0.0893765i
$846$	−42.0000			−1.44399
$847$		0			0
$848$	36.0000			1.23625
$849$		0			0
$850$	−16.0000	+	27.7128i	−0.548795	+	0.950542i
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$		0			0
$853$	−45.0000			−1.54077			−0.770385	−	0.637579i	$-0.779936\pi$
$853$	−45.0000			−1.54077			−0.770385	+	0.637579i	$0.779936\pi$
$854$		0			0
$855$	45.0000			1.53897
$856$		0			0
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	−0.912705	−	0.408619i	$-0.866010\pi$
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	0.810227	+	0.586116i	$0.199344\pi$
$858$		0			0
$859$	−1.00000	−	1.73205i	−0.0341196	−	0.0590968i	0.848461	−	0.529257i	$-0.177529\pi$
$859$	−1.00000	−	1.73205i	−0.0341196	−	0.0590968i	−0.882581	+	0.470160i	$0.844196\pi$
$860$	−6.00000			−0.204598
$861$		0			0
$862$	−12.0000			−0.408722
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	0.998629	+	0.0523446i	$0.0166694\pi$
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	−0.453983	+	0.891010i	$0.649997\pi$
$864$		0			0
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$	−12.0000	−	20.7846i	−0.407777	−	0.706290i
$867$		0			0
$868$		0			0
$869$	−18.0000			−0.610608
$870$		0			0
$871$	3.00000	−	5.19615i	0.101651	−	0.176065i
$872$		0			0
$873$	−10.5000	−	18.1865i	−0.355371	−	0.615521i
$874$	30.0000			1.01477
$875$		0			0
$876$		0			0
$877$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$877$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$878$	22.0000	−	38.1051i	0.742464	−	1.28599i
$879$		0			0
$880$	−36.0000	−	62.3538i	−1.21356	−	2.10195i
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	4.00000	+	6.92820i	0.134535	+	0.233021i
$885$		0			0
$886$	19.0000	−	32.9090i	0.638317	−	1.10560i
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	0.747539	−	0.664218i	$-0.231235\pi$
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	−0.948999	+	0.315279i	$0.897902\pi$
$888$		0			0
$889$		0			0
$890$	18.0000			0.603361
$891$	27.0000	+	46.7654i	0.904534	+	1.56670i
$892$	15.0000	−	25.9808i	0.502237	−	0.869900i
$893$	−17.5000	+	30.3109i	−0.585615	+	1.01432i
$894$		0			0
$895$	69.0000			2.30642
$896$		0			0
$897$		0			0
$898$	36.0000	+	62.3538i	1.20134	+	2.08077i
$899$	7.50000	−	12.9904i	0.250139	−	0.433253i
$900$	12.0000	−	20.7846i	0.400000	−	0.692820i
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$	72.0000			2.39734
$903$		0			0
$904$		0			0
$905$	21.0000	+	36.3731i	0.698064	+	1.20908i
$906$		0			0
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$	20.0000	+	34.6410i	0.663723	+	1.14960i
$909$	−42.0000			−1.39305
$910$		0			0
$911$	−15.0000			−0.496972			−0.248486	−	0.968635i	$-0.579933\pi$
$911$	−15.0000			−0.496972			−0.248486	+	0.968635i	$0.579933\pi$
$912$		0			0
$913$	−45.0000	+	77.9423i	−1.48928	+	2.57951i
$914$		0			0
$915$		0			0
$916$	−28.0000			−0.925146
$917$		0			0
$918$		0			0
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$		0			0
$921$		0			0
$922$	22.0000	+	38.1051i	0.724531	+	1.25493i
$923$	−8.00000			−0.263323
$924$		0			0
$925$	−16.0000			−0.526077
$926$	−14.0000	−	24.2487i	−0.460069	−	0.796862i
$927$	6.00000	−	10.3923i	0.197066	−	0.341328i
$928$	20.0000	−	34.6410i	0.656532	−	1.13715i
$929$	2.50000	+	4.33013i	0.0820223	+	0.142067i	0.904118	−	0.427282i	$-0.140529\pi$
$929$	2.50000	+	4.33013i	0.0820223	+	0.142067i	−0.822096	+	0.569349i	$0.807195\pi$
$930$		0			0
$931$		0			0
$932$	30.0000			0.982683
$933$		0			0
$934$	22.0000	−	38.1051i	0.719862	−	1.24684i
$935$	−36.0000	+	62.3538i	−1.17733	+	2.03919i
$936$		0			0
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$		0			0
$939$		0			0
$940$	21.0000	+	36.3731i	0.684944	+	1.18636i
$941$	27.5000	−	47.6314i	0.896474	−	1.55274i	0.0645052	−	0.997917i	$-0.479453\pi$
$941$	27.5000	−	47.6314i	0.896474	−	1.55274i	0.831969	−	0.554822i	$-0.187214\pi$
$942$		0			0
$943$	−9.00000	−	15.5885i	−0.293080	−	0.507630i
$944$	32.0000			1.04151
$945$		0			0
$946$	−12.0000			−0.390154
$947$	9.00000	+	15.5885i	0.292461	+	0.506557i	0.974391	−	0.224860i	$-0.0721926\pi$
$947$	9.00000	+	15.5885i	0.292461	+	0.506557i	−0.681930	+	0.731417i	$0.738859\pi$
$948$		0			0
$949$	−6.50000	+	11.2583i	−0.210999	+	0.365461i
$950$	−20.0000	−	34.6410i	−0.648886	−	1.12390i
$951$		0			0
$952$		0			0
$953$	−39.0000			−1.26333			−0.631667	−	0.775240i	$-0.717629\pi$
$953$	−39.0000			−1.26333			−0.631667	+	0.775240i	$0.717629\pi$
$954$	27.0000	+	46.7654i	0.874157	+	1.51408i
$955$	12.0000	−	20.7846i	0.388311	−	0.672574i
$956$	4.00000	−	6.92820i	0.129369	−	0.224074i
$957$		0			0
$958$	−22.0000			−0.710788
$959$		0			0
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$	−4.00000	+	6.92820i	−0.128965	+	0.223374i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	−17.0000	−	29.4449i	−0.547533	−	0.948355i
$965$	66.0000			2.12462
$966$		0			0
$967$	22.0000			0.707472			0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000			0.707472			0.353736	+	0.935345i	$0.384911\pi$
$968$		0			0
$969$		0			0
$970$	−21.0000	+	36.3731i	−0.674269	+	1.16787i
$971$	19.0000	+	32.9090i	0.609739	+	1.05610i	0.991283	+	0.131748i	$0.0420591\pi$
$971$	19.0000	+	32.9090i	0.609739	+	1.05610i	−0.381544	+	0.924351i	$0.624608\pi$
$972$		0			0
$973$		0			0
$974$	52.0000			1.66619
$975$		0			0
$976$	20.0000	−	34.6410i	0.640184	−	1.10883i
$977$	−5.00000	+	8.66025i	−0.159964	+	0.277066i	−0.934856	−	0.355028i	$-0.884471\pi$
$977$	−5.00000	+	8.66025i	−0.159964	+	0.277066i	0.774891	+	0.632094i	$0.217805\pi$
$978$		0			0
$979$	18.0000			0.575282
$980$		0			0
$981$	6.00000			0.191565
$982$	−12.0000	−	20.7846i	−0.382935	−	0.663264i
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	−0.698038	−	0.716061i	$-0.745943\pi$
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	0.969146	+	0.246488i	$0.0792766\pi$
$984$		0			0
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$	−40.0000			−1.27386
$987$		0			0
$988$	−10.0000			−0.318142
$989$	1.50000	+	2.59808i	0.0476972	+	0.0826140i
$990$	54.0000	−	93.5307i	1.71623	−	2.97260i
$991$	−2.00000	+	3.46410i	−0.0635321	+	0.110041i	−0.896042	−	0.443969i	$-0.853570\pi$
$991$	−2.00000	+	3.46410i	−0.0635321	+	0.110041i	0.832510	+	0.554010i	$0.186903\pi$
$992$	−12.0000	−	20.7846i	−0.381000	−	0.659912i
$993$		0			0
$994$		0			0
$995$	−12.0000			−0.380426
$996$		0			0
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	−0.997938	−	0.0641836i	$-0.979556\pi$
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	0.554554	+	0.832148i	$0.312889\pi$
$998$	−16.0000	+	27.7128i	−0.506471	+	0.877234i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.d.508.1		2
7.2	even	3	inner	637.2.e.d.79.1		2
7.3	odd	6		91.2.a.a.1.1	✓	1
7.4	even	3		637.2.a.a.1.1		1
7.5	odd	6		637.2.e.e.79.1		2
7.6	odd	2		637.2.e.e.508.1		2
21.11	odd	6		5733.2.a.l.1.1		1
21.17	even	6		819.2.a.f.1.1		1
28.3	even	6		1456.2.a.g.1.1		1
35.24	odd	6		2275.2.a.h.1.1		1
56.3	even	6		5824.2.a.t.1.1		1
56.45	odd	6		5824.2.a.s.1.1		1
91.25	even	6		8281.2.a.l.1.1		1
91.31	even	12		1183.2.c.b.337.2		2
91.38	odd	6		1183.2.a.b.1.1		1
91.73	even	12		1183.2.c.b.337.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.a.1.1	✓	1	7.3	odd	6
637.2.a.a.1.1		1	7.4	even	3
637.2.e.d.79.1		2	7.2	even	3	inner
637.2.e.d.508.1		2	1.1	even	1	trivial
637.2.e.e.79.1		2	7.5	odd	6
637.2.e.e.508.1		2	7.6	odd	2
819.2.a.f.1.1		1	21.17	even	6
1183.2.a.b.1.1		1	91.38	odd	6
1183.2.c.b.337.1		2	91.73	even	12
1183.2.c.b.337.2		2	91.31	even	12
1456.2.a.g.1.1		1	28.3	even	6
2275.2.a.h.1.1		1	35.24	odd	6
5733.2.a.l.1.1		1	21.11	odd	6
5824.2.a.s.1.1		1	56.45	odd	6
5824.2.a.t.1.1		1	56.3	even	6
8281.2.a.l.1.1		1	91.25	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +(3.00000 - 5.19615i) q^{10} +(3.00000 - 5.19615i) q^{11} +1.00000 q^{13} +(2.00000 + 3.46410i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(2.50000 + 4.33013i) q^{19} +6.00000 q^{20} +12.0000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} -5.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(-4.00000 + 6.92820i) q^{32} +8.00000 q^{34} -6.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-5.00000 + 8.66025i) q^{38} +6.00000 q^{41} -1.00000 q^{43} +(6.00000 + 10.3923i) q^{44} +(4.50000 - 7.79423i) q^{45} +(3.00000 - 5.19615i) q^{46} +(3.50000 + 6.06218i) q^{47} -8.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(4.50000 - 7.79423i) q^{53} -18.0000 q^{55} +(-5.00000 - 8.66025i) q^{58} +(4.00000 - 6.92820i) q^{59} +(-5.00000 - 8.66025i) q^{61} -6.00000 q^{62} -8.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(3.00000 - 5.19615i) q^{67} +(4.00000 + 6.92820i) q^{68} -8.00000 q^{71} +(-6.50000 + 11.2583i) q^{73} +(-4.00000 + 6.92820i) q^{74} -10.0000 q^{76} +(-1.50000 - 2.59808i) q^{79} +(6.00000 - 10.3923i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 + 10.3923i) q^{82} -15.0000 q^{83} -12.0000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(1.50000 + 2.59808i) q^{89} +18.0000 q^{90} +6.00000 q^{92} +(-7.00000 + 12.1244i) q^{94} +(7.50000 - 12.9904i) q^{95} -7.00000 q^{97} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} - 3 q^{5} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^4 - 3 * q^5 + 3 * q^9	\( 2 q + 2 q^{2} - 2 q^{4} - 3 q^{5} + 3 q^{9} + 6 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 12 q^{20} + 24 q^{22} - 3 q^{23} - 4 q^{25} + 2 q^{26} - 10 q^{29} - 3 q^{31} - 8 q^{32} + 16 q^{34} - 12 q^{36} + 4 q^{37} - 10 q^{38} + 12 q^{41} - 2 q^{43} + 12 q^{44} + 9 q^{45} + 6 q^{46} + 7 q^{47} - 16 q^{50} - 2 q^{52} + 9 q^{53} - 36 q^{55} - 10 q^{58} + 8 q^{59} - 10 q^{61} - 12 q^{62} - 16 q^{64} - 3 q^{65} + 6 q^{67} + 8 q^{68} - 16 q^{71} - 13 q^{73} - 8 q^{74} - 20 q^{76} - 3 q^{79} + 12 q^{80} - 9 q^{81} + 12 q^{82} - 30 q^{83} - 24 q^{85} - 2 q^{86} + 3 q^{89} + 36 q^{90} + 12 q^{92} - 14 q^{94} + 15 q^{95} - 14 q^{97} + 36 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^4 - 3 * q^5 + 3 * q^9 + 6 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 12 * q^20 + 24 * q^22 - 3 * q^23 - 4 * q^25 + 2 * q^26 - 10 * q^29 - 3 * q^31 - 8 * q^32 + 16 * q^34 - 12 * q^36 + 4 * q^37 - 10 * q^38 + 12 * q^41 - 2 * q^43 + 12 * q^44 + 9 * q^45 + 6 * q^46 + 7 * q^47 - 16 * q^50 - 2 * q^52 + 9 * q^53 - 36 * q^55 - 10 * q^58 + 8 * q^59 - 10 * q^61 - 12 * q^62 - 16 * q^64 - 3 * q^65 + 6 * q^67 + 8 * q^68 - 16 * q^71 - 13 * q^73 - 8 * q^74 - 20 * q^76 - 3 * q^79 + 12 * q^80 - 9 * q^81 + 12 * q^82 - 30 * q^83 - 24 * q^85 - 2 * q^86 + 3 * q^89 + 36 * q^90 + 12 * q^92 - 14 * q^94 + 15 * q^95 - 14 * q^97 + 36 * q^99

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