LMFDB - Embedded newform 1470.2.n.i.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(79,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1470.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.n (of order $6$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1470.949
Dual form			1470.2.n.i.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.23205 - 1.86603i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-0.866025 + 0.500000i) q^{12} +1.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(2.00000 + 1.00000i) q^{20} +5.00000i q^{22} +(-2.59808 + 1.50000i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(-0.500000 - 0.866025i) q^{26} -1.00000i q^{27} +(0.133975 + 2.23205i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.33013 + 2.50000i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-4.33013 + 2.50000i) q^{37} +(6.06218 + 3.50000i) q^{38} +(0.500000 - 0.866025i) q^{39} +(-2.23205 + 0.133975i) q^{40} +9.00000 q^{41} -10.0000i q^{43} +(-2.50000 - 4.33013i) q^{44} +(-1.86603 + 1.23205i) q^{45} +(1.50000 - 2.59808i) q^{46} +(11.2583 - 6.50000i) q^{47} +1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} +(1.00000 + 1.73205i) q^{51} +(0.866025 + 0.500000i) q^{52} +(-0.866025 - 0.500000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(10.0000 + 5.00000i) q^{55} +7.00000i q^{57} +(-2.00000 + 3.46410i) q^{59} +(-1.23205 - 1.86603i) q^{60} +(-1.00000 - 1.73205i) q^{61} -6.00000i q^{62} -1.00000 q^{64} +(-2.23205 + 0.133975i) q^{65} +(2.50000 - 4.33013i) q^{66} +(-5.19615 - 3.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(2.50000 - 4.33013i) q^{74} +(4.59808 + 1.96410i) q^{75} -7.00000 q^{76} +1.00000i q^{78} +(-7.00000 - 12.1244i) q^{79} +(1.86603 - 1.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.79423 + 4.50000i) q^{82} -10.0000i q^{83} +(2.00000 - 4.00000i) q^{85} +(5.00000 + 8.66025i) q^{86} +(4.33013 + 2.50000i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(1.00000 - 2.00000i) q^{90} +3.00000i q^{92} +(5.19615 - 3.00000i) q^{93} +(-6.50000 + 11.2583i) q^{94} +(13.0622 - 8.62436i) q^{95} +(-0.500000 - 0.866025i) q^{96} -8.00000i q^{97} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{9} + 2 q^{10} + 10 q^{11} + 4 q^{15} - 2 q^{16} - 14 q^{19} + 8 q^{20} + 2 q^{24} - 6 q^{25} - 2 q^{26} + 4 q^{30} - 12 q^{31} + 8 q^{34} + 4 q^{36} + 2 q^{39} - 2 q^{40} + 36 q^{41} - 10 q^{44} - 4 q^{45} + 6 q^{46} + 16 q^{50} + 4 q^{51} + 2 q^{54} + 40 q^{55} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 4 q^{64} - 2 q^{65} + 10 q^{66} + 12 q^{69} - 8 q^{71} + 10 q^{74} + 8 q^{75} - 28 q^{76} - 28 q^{79} + 4 q^{80} - 2 q^{81} + 8 q^{85} + 20 q^{86} - 20 q^{89} + 4 q^{90} - 26 q^{94} + 28 q^{95} - 2 q^{96} + 20 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^9 + 2 * q^10 + 10 * q^11 + 4 * q^15 - 2 * q^16 - 14 * q^19 + 8 * q^20 + 2 * q^24 - 6 * q^25 - 2 * q^26 + 4 * q^30 - 12 * q^31 + 8 * q^34 + 4 * q^36 + 2 * q^39 - 2 * q^40 + 36 * q^41 - 10 * q^44 - 4 * q^45 + 6 * q^46 + 16 * q^50 + 4 * q^51 + 2 * q^54 + 40 * q^55 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 4 * q^64 - 2 * q^65 + 10 * q^66 + 12 * q^69 - 8 * q^71 + 10 * q^74 + 8 * q^75 - 28 * q^76 - 28 * q^79 + 4 * q^80 - 2 * q^81 + 8 * q^85 + 20 * q^86 - 20 * q^89 + 4 * q^90 - 26 * q^94 + 28 * q^95 - 2 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.23205	−	1.86603i	−0.389609	−	0.590089i
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$		0			0
$15$	1.00000	−	2.00000i	0.258199	−	0.516398i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$		0			0
$22$			5.00000i			1.06600i
$23$	−2.59808	+	1.50000i	−0.541736	+	0.312772i	−0.745782	−	0.666190i	$-0.767924\pi$
$23$	−2.59808	+	1.50000i	−0.541736	+	0.312772i	0.204046	+	0.978961i	$0.434591\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	0.133975	+	2.23205i	0.0244603	+	0.407515i
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.33013	+	2.50000i	−0.753778	+	0.435194i
$34$	2.00000			0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	−4.33013	+	2.50000i	−0.711868	+	0.410997i	−0.811752	−	0.584002i	$-0.801486\pi$
$37$	−4.33013	+	2.50000i	−0.711868	+	0.410997i	0.0998840	+	0.994999i	$0.468153\pi$
$38$	6.06218	+	3.50000i	0.983415	+	0.567775i
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	−2.23205	+	0.133975i	−0.352918	+	0.0211832i
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$		0			0
$43$		−	10.0000i		−	1.52499i	−0.646997	−	0.762493i	$-0.723975\pi$
$43$		−	10.0000i		−	1.52499i	0.646997	−	0.762493i	$-0.276025\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$	−1.86603	+	1.23205i	−0.278171	+	0.183663i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	11.2583	−	6.50000i	1.64220	−	0.948122i	0.662145	−	0.749375i	$-0.269646\pi$
$47$	11.2583	−	6.50000i	1.64220	−	0.948122i	0.980051	−	0.198747i	$-0.0636872\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	0.866025	+	0.500000i	0.120096	+	0.0693375i
$53$	−0.866025	−	0.500000i	−0.118958	−	0.0686803i	0.439340	−	0.898321i	$-0.355212\pi$
$53$	−0.866025	−	0.500000i	−0.118958	−	0.0686803i	−0.558298	+	0.829640i	$0.688546\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	10.0000	+	5.00000i	1.34840	+	0.674200i
$56$		0			0
$57$			7.00000i			0.927173i
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$	−1.23205	−	1.86603i	−0.159057	−	0.240903i
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		−	6.00000i		−	0.762001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.23205	+	0.133975i	−0.276852	+	0.0166175i
$66$	2.50000	−	4.33013i	0.307729	−	0.533002i
$67$	−5.19615	−	3.00000i	−0.634811	−	0.366508i	0.147802	−	0.989017i	$-0.452780\pi$
$67$	−5.19615	−	3.00000i	−0.634811	−	0.366508i	−0.782613	+	0.622509i	$0.786114\pi$
$68$	−1.73205	+	1.00000i	−0.210042	+	0.121268i
$69$	3.00000			0.361158
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	0.283387	−	0.959006i	$-0.408542\pi$
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	−0.688830	+	0.724923i	$0.741875\pi$
$74$	2.50000	−	4.33013i	0.290619	−	0.503367i
$75$	4.59808	+	1.96410i	0.530940	+	0.226795i
$76$	−7.00000			−0.802955
$77$		0			0
$78$			1.00000i			0.113228i
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$	1.86603	−	1.23205i	0.208628	−	0.137747i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−7.79423	+	4.50000i	−0.860729	+	0.496942i
$83$		−	10.0000i		−	1.09764i	−0.835940	−	0.548821i	$-0.815077\pi$
$83$		−	10.0000i		−	1.09764i	0.835940	−	0.548821i	$-0.184923\pi$
$84$		0			0
$85$	2.00000	−	4.00000i	0.216930	−	0.433861i
$86$	5.00000	+	8.66025i	0.539164	+	0.933859i
$87$		0			0
$88$	4.33013	+	2.50000i	0.461593	+	0.266501i
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$	1.00000	−	2.00000i	0.105409	−	0.210819i
$91$		0			0
$92$			3.00000i			0.312772i
$93$	5.19615	−	3.00000i	0.538816	−	0.311086i
$94$	−6.50000	+	11.2583i	−0.670424	+	1.16121i
$95$	13.0622	−	8.62436i	1.34015	−	0.884840i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$		−	8.00000i		−	0.812277i	−0.913812	−	0.406138i	$-0.866875\pi$
$97$		−	8.00000i		−	0.812277i	0.913812	−	0.406138i	$-0.133125\pi$
$98$		0			0
$99$	5.00000			0.502519
$100$	−1.96410	+	4.59808i	−0.196410	+	0.459808i
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	−0.595466	−	0.803380i	$-0.703033\pi$
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	0.993481	+	0.113998i	$0.0363659\pi$
$102$	−1.73205	−	1.00000i	−0.171499	−	0.0990148i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	1.00000			0.0971286
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.0950377	−	0.995474i	$-0.469703\pi$
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.909624	+	0.415432i	$0.136370\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−9.00000	+	15.5885i	−0.862044	+	1.49310i	0.00790932	+	0.999969i	$0.497482\pi$
$109$	−9.00000	+	15.5885i	−0.862044	+	1.49310i	−0.869953	+	0.493135i	$0.835851\pi$
$110$	−11.1603	+	0.669873i	−1.06409	+	0.0638699i
$111$	5.00000			0.474579
$112$		0			0
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−3.50000	−	6.06218i	−0.327805	−	0.567775i
$115$	−3.69615	−	5.59808i	−0.344668	−	0.522023i
$116$		0			0
$117$	−0.866025	+	0.500000i	−0.0800641	+	0.0462250i
$118$		−	4.00000i		−	0.368230i
$119$		0			0
$120$	2.00000	+	1.00000i	0.182574	+	0.0912871i
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	1.73205	+	1.00000i	0.156813	+	0.0905357i
$123$	−7.79423	−	4.50000i	−0.702782	−	0.405751i
$124$	3.00000	+	5.19615i	0.269408	+	0.466628i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$			9.00000i			0.798621i	0.916816	+	0.399310i	$0.130750\pi$
$127$			9.00000i			0.798621i	−0.916816	+	0.399310i	$0.869250\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−5.00000	+	8.66025i	−0.440225	+	0.762493i
$130$	1.86603	−	1.23205i	0.163661	−	0.108058i
$131$	−8.50000	−	14.7224i	−0.742648	−	1.28630i	−0.951285	−	0.308312i	$-0.900236\pi$
$131$	−8.50000	−	14.7224i	−0.742648	−	1.28630i	0.208637	−	0.977993i	$-0.433097\pi$
$132$			5.00000i			0.435194i
$133$		0			0
$134$	6.00000			0.518321
$135$	2.23205	−	0.133975i	0.192104	−	0.0115307i
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	3.46410	+	2.00000i	0.295958	+	0.170872i	0.640626	−	0.767853i	$-0.278675\pi$
$137$	3.46410	+	2.00000i	0.295958	+	0.170872i	−0.344668	+	0.938725i	$0.612008\pi$
$138$	−2.59808	+	1.50000i	−0.221163	+	0.127688i
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−13.0000			−1.09480
$142$	1.73205	−	1.00000i	0.145350	−	0.0839181i
$143$	4.33013	+	2.50000i	0.362103	+	0.209061i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$		0			0
$146$	4.00000			0.331042
$147$		0			0
$148$			5.00000i			0.410997i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$	−4.96410	+	0.598076i	−0.405317	+	0.0488327i
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.0615699	−	0.998103i	$-0.480389\pi$
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.833597	−	0.552372i	$-0.186277\pi$
$152$	6.06218	−	3.50000i	0.491708	−	0.283887i
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	−12.0000	−	6.00000i	−0.963863	−	0.481932i
$156$	−0.500000	−	0.866025i	−0.0400320	−	0.0693375i
$157$	11.2583	+	6.50000i	0.898513	+	0.518756i	0.876717	−	0.481006i	$-0.159728\pi$
$157$	11.2583	+	6.50000i	0.898513	+	0.518756i	0.0217953	+	0.999762i	$0.493062\pi$
$158$	12.1244	+	7.00000i	0.964562	+	0.556890i
$159$	0.500000	+	0.866025i	0.0396526	+	0.0686803i
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	10.3923	−	6.00000i	0.813988	−	0.469956i	−0.0343508	−	0.999410i	$-0.510936\pi$
$163$	10.3923	−	6.00000i	0.813988	−	0.469956i	0.848339	+	0.529454i	$0.177603\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$	−6.16025	−	9.33013i	−0.479575	−	0.726349i
$166$	5.00000	+	8.66025i	0.388075	+	0.672166i
$167$			19.0000i			1.47026i	0.677924	+	0.735132i	$0.262880\pi$
$167$			19.0000i			1.47026i	−0.677924	+	0.735132i	$0.737120\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	0.267949	+	4.46410i	0.0205508	+	0.342381i
$171$	3.50000	−	6.06218i	0.267652	−	0.463586i
$172$	−8.66025	−	5.00000i	−0.660338	−	0.381246i
$173$	6.06218	−	3.50000i	0.460899	−	0.266100i	−0.251523	−	0.967851i	$-0.580932\pi$
$173$	6.06218	−	3.50000i	0.460899	−	0.266100i	0.712422	+	0.701751i	$0.247598\pi$
$174$		0			0
$175$		0			0
$176$	−5.00000			−0.376889
$177$	3.46410	−	2.00000i	0.260378	−	0.150329i
$178$	8.66025	+	5.00000i	0.649113	+	0.374766i
$179$	−5.50000	+	9.52628i	−0.411089	+	0.712028i	−0.995009	−	0.0997838i	$-0.968185\pi$
$179$	−5.50000	+	9.52628i	−0.411089	+	0.712028i	0.583920	+	0.811811i	$0.301518\pi$
$180$	0.133975	+	2.23205i	0.00998588	+	0.166367i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$			2.00000i			0.147844i
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	−6.16025	−	9.33013i	−0.452911	−	0.685965i
$186$	−3.00000	+	5.19615i	−0.219971	+	0.381000i
$187$	−8.66025	+	5.00000i	−0.633300	+	0.365636i
$188$		−	13.0000i		−	0.948122i
$189$		0			0
$190$	−7.00000	+	14.0000i	−0.507833	+	1.01567i
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−15.5885	−	9.00000i	−1.12208	−	0.647834i	−0.180150	−	0.983639i	$-0.557658\pi$
$193$	−15.5885	−	9.00000i	−1.12208	−	0.647834i	−0.941932	+	0.335805i	$0.890992\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$	2.00000	+	1.00000i	0.143223	+	0.0716115i
$196$		0			0
$197$		−	27.0000i		−	1.92367i	−0.273629	−	0.961835i	$-0.588224\pi$
$197$		−	27.0000i		−	1.92367i	0.273629	−	0.961835i	$-0.411776\pi$
$198$	−4.33013	+	2.50000i	−0.307729	+	0.177667i
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$	−0.598076	−	4.96410i	−0.0422904	−	0.351015i
$201$	3.00000	+	5.19615i	0.211604	+	0.366508i
$202$			8.00000i			0.562878i
$203$		0			0
$204$	2.00000			0.140028
$205$	1.20577	+	20.0885i	0.0842147	+	1.40304i
$206$		0			0
$207$	−2.59808	−	1.50000i	−0.180579	−	0.104257i
$208$	0.866025	−	0.500000i	0.0600481	−	0.0346688i
$209$	−35.0000			−2.42100
$210$		0			0
$211$	19.0000			1.30801			0.654007	−	0.756489i	$-0.273087\pi$
$211$	19.0000			1.30801			0.654007	+	0.756489i	$0.273087\pi$
$212$	−0.866025	+	0.500000i	−0.0594789	+	0.0343401i
$213$	1.73205	+	1.00000i	0.118678	+	0.0685189i
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	22.3205	−	1.33975i	1.52225	−	0.0913699i
$216$	1.00000			0.0680414
$217$		0			0
$218$		−	18.0000i		−	1.21911i
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$	9.33013	−	6.16025i	0.629037	−	0.415324i
$221$	1.00000	−	1.73205i	0.0672673	−	0.116510i
$222$	−4.33013	+	2.50000i	−0.290619	+	0.167789i
$223$			16.0000i			1.07144i	0.844396	+	0.535720i	$0.179960\pi$
$223$			16.0000i			1.07144i	−0.844396	+	0.535720i	$0.820040\pi$
$224$		0			0
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	12.1244	+	7.00000i	0.804722	+	0.464606i	0.845120	−	0.534577i	$-0.179529\pi$
$227$	12.1244	+	7.00000i	0.804722	+	0.464606i	−0.0403978	+	0.999184i	$0.512863\pi$
$228$	6.06218	+	3.50000i	0.401478	+	0.231793i
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$	6.00000	+	3.00000i	0.395628	+	0.197814i
$231$		0			0
$232$		0			0
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$	16.0167	+	24.2583i	1.04481	+	1.58244i
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$			14.0000i			0.909398i
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$	−2.23205	+	0.133975i	−0.144078	+	0.00864802i
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	−0.881680	−	0.471848i	$-0.843587\pi$
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	0.849472	+	0.527633i	$0.176921\pi$
$242$	12.1244	+	7.00000i	0.779383	+	0.449977i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	9.00000			0.573819
$247$	6.06218	−	3.50000i	0.385727	−	0.222700i
$248$	−5.19615	−	3.00000i	−0.329956	−	0.190500i
$249$	−5.00000	+	8.66025i	−0.316862	+	0.548821i
$250$	7.23205	+	8.52628i	0.457395	+	0.539249i
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$			15.0000i			0.943042i
$254$	−4.50000	−	7.79423i	−0.282355	−	0.489053i
$255$	−3.73205	+	2.46410i	−0.233710	+	0.154308i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.66025	−	5.00000i	0.540212	−	0.311891i	−0.204953	−	0.978772i	$-0.565704\pi$
$257$	8.66025	−	5.00000i	0.540212	−	0.311891i	0.745165	+	0.666880i	$0.232371\pi$
$258$		−	10.0000i		−	0.622573i
$259$		0			0
$260$	−1.00000	+	2.00000i	−0.0620174	+	0.124035i
$261$		0			0
$262$	14.7224	+	8.50000i	0.909555	+	0.525132i
$263$	20.7846	+	12.0000i	1.28163	+	0.739952i	0.977147	−	0.212565i	$-0.0681817\pi$
$263$	20.7846	+	12.0000i	1.28163	+	0.739952i	0.304487	+	0.952517i	$0.401515\pi$
$264$	−2.50000	−	4.33013i	−0.153864	−	0.266501i
$265$	1.00000	−	2.00000i	0.0614295	−	0.122859i
$266$		0			0
$267$			10.0000i			0.611990i
$268$	−5.19615	+	3.00000i	−0.317406	+	0.183254i
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	−0.996586	−	0.0825561i	$-0.973692\pi$
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	0.569789	+	0.821791i	$0.307025\pi$
$270$	−1.86603	+	1.23205i	−0.113563	+	0.0749802i
$271$	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	$0.755208\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$	−4.00000			−0.241649
$275$	−9.82051	+	22.9904i	−0.592199	+	1.38637i
$276$	1.50000	−	2.59808i	0.0902894	−	0.156386i
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	0.447062	−	0.894503i	$-0.352470\pi$
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	−0.551131	+	0.834419i	$0.685804\pi$
$278$	6.92820	−	4.00000i	0.415526	−	0.239904i
$279$	−6.00000			−0.359211
$280$		0			0
$281$	−11.0000			−0.656205			−0.328102	−	0.944642i	$-0.606409\pi$
$281$	−11.0000			−0.656205			−0.328102	+	0.944642i	$0.606409\pi$
$282$	11.2583	−	6.50000i	0.670424	−	0.387069i
$283$	−22.5167	−	13.0000i	−1.33848	−	0.772770i	−0.351895	−	0.936039i	$-0.614463\pi$
$283$	−22.5167	−	13.0000i	−1.33848	−	0.772770i	−0.986581	+	0.163270i	$0.947796\pi$
$284$	−1.00000	+	1.73205i	−0.0593391	+	0.102778i
$285$	−15.6244	+	0.937822i	−0.925507	+	0.0555518i
$286$	−5.00000			−0.295656
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$	−3.46410	+	2.00000i	−0.202721	+	0.117041i
$293$			1.00000i			0.0584206i	0.999573	+	0.0292103i	$0.00929925\pi$
$293$			1.00000i			0.0584206i	−0.999573	+	0.0292103i	$0.990701\pi$
$294$		0			0
$295$	−8.00000	−	4.00000i	−0.465778	−	0.232889i
$296$	−2.50000	−	4.33013i	−0.145310	−	0.251684i
$297$	−4.33013	−	2.50000i	−0.251259	−	0.145065i
$298$	5.19615	+	3.00000i	0.301005	+	0.173785i
$299$	−1.50000	−	2.59808i	−0.0867472	−	0.150251i
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$		0			0
$302$			22.0000i			1.26596i
$303$	−6.92820	+	4.00000i	−0.398015	+	0.229794i
$304$	−3.50000	+	6.06218i	−0.200739	+	0.347690i
$305$	3.73205	−	2.46410i	0.213697	−	0.141094i
$306$	1.00000	+	1.73205i	0.0571662	+	0.0990148i
$307$		−	2.00000i		−	0.114146i	−0.998370	−	0.0570730i	$-0.981823\pi$
$307$		−	2.00000i		−	0.114146i	0.998370	−	0.0570730i	$-0.0181768\pi$
$308$		0			0
$309$		0			0
$310$	13.3923	−	0.803848i	0.760632	−	0.0456555i
$311$	−13.0000	+	22.5167i	−0.737162	+	1.27680i	0.216606	+	0.976259i	$0.430501\pi$
$311$	−13.0000	+	22.5167i	−0.737162	+	1.27680i	−0.953768	+	0.300544i	$0.902832\pi$
$312$	0.866025	+	0.500000i	0.0490290	+	0.0283069i
$313$	−8.66025	+	5.00000i	−0.489506	+	0.282617i	−0.724370	−	0.689412i	$-0.757869\pi$
$313$	−8.66025	+	5.00000i	−0.489506	+	0.282617i	0.234863	+	0.972028i	$0.424536\pi$
$314$	−13.0000			−0.733632
$315$		0			0
$316$	−14.0000			−0.787562
$317$	1.73205	−	1.00000i	0.0972817	−	0.0561656i	−0.450570	−	0.892741i	$-0.648779\pi$
$317$	1.73205	−	1.00000i	0.0972817	−	0.0561656i	0.547852	+	0.836576i	$0.315446\pi$
$318$	−0.866025	−	0.500000i	−0.0485643	−	0.0280386i
$319$		0			0
$320$	−0.133975	−	2.23205i	−0.00748941	−	0.124775i
$321$	−12.0000			−0.669775
$322$		0			0
$323$			14.0000i			0.778981i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−0.598076	−	4.96410i	−0.0331753	−	0.275359i
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	15.5885	−	9.00000i	0.862044	−	0.497701i
$328$			9.00000i			0.496942i
$329$		0			0
$330$	10.0000	+	5.00000i	0.550482	+	0.275241i
$331$	7.50000	+	12.9904i	0.412237	+	0.714016i	0.995134	−	0.0985303i	$-0.0314141\pi$
$331$	7.50000	+	12.9904i	0.412237	+	0.714016i	−0.582897	+	0.812546i	$0.698081\pi$
$332$	−8.66025	−	5.00000i	−0.475293	−	0.274411i
$333$	−4.33013	−	2.50000i	−0.237289	−	0.136999i
$334$	−9.50000	−	16.4545i	−0.519817	−	0.900349i
$335$	6.00000	−	12.0000i	0.327815	−	0.655630i
$336$		0			0
$337$		−	14.0000i		−	0.762629i	−0.924445	−	0.381314i	$-0.875472\pi$
$337$		−	14.0000i		−	0.762629i	0.924445	−	0.381314i	$-0.124528\pi$
$338$	−10.3923	+	6.00000i	−0.565267	+	0.326357i
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$	−2.46410	−	3.73205i	−0.133635	−	0.202399i
$341$	15.0000	+	25.9808i	0.812296	+	1.40694i
$342$			7.00000i			0.378517i
$343$		0			0
$344$	10.0000			0.539164
$345$	0.401924	+	6.69615i	0.0216388	+	0.360509i
$346$	−3.50000	+	6.06218i	−0.188161	+	0.325905i
$347$	13.8564	+	8.00000i	0.743851	+	0.429463i	0.823468	−	0.567363i	$-0.192036\pi$
$347$	13.8564	+	8.00000i	0.743851	+	0.429463i	−0.0796169	+	0.996826i	$0.525370\pi$
$348$		0			0
$349$	−24.0000			−1.28469			−0.642345	−	0.766415i	$-0.722038\pi$
$349$	−24.0000			−1.28469			−0.642345	+	0.766415i	$0.722038\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$	4.33013	−	2.50000i	0.230797	−	0.133250i
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$	−2.00000	+	3.46410i	−0.106299	+	0.184115i
$355$	−0.267949	−	4.46410i	−0.0142213	−	0.236930i
$356$	−10.0000			−0.529999
$357$		0			0
$358$		−	11.0000i		−	0.581368i
$359$	−14.0000	−	24.2487i	−0.738892	−	1.27980i	−0.952995	−	0.302987i	$-0.902016\pi$
$359$	−14.0000	−	24.2487i	−0.738892	−	1.27980i	0.214103	−	0.976811i	$-0.431317\pi$
$360$	−1.23205	−	1.86603i	−0.0649348	−	0.0983482i
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	−1.73205	+	1.00000i	−0.0910346	+	0.0525588i
$363$			14.0000i			0.734809i
$364$		0			0
$365$	4.00000	−	8.00000i	0.209370	−	0.418739i
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	−32.0429	−	18.5000i	−1.67263	−	0.965692i	−0.966159	−	0.257948i	$-0.916954\pi$
$367$	−32.0429	−	18.5000i	−1.67263	−	0.965692i	−0.706469	−	0.707744i	$-0.749713\pi$
$368$	2.59808	+	1.50000i	0.135434	+	0.0781929i
$369$	4.50000	+	7.79423i	0.234261	+	0.405751i
$370$	10.0000	+	5.00000i	0.519875	+	0.259938i
$371$		0			0
$372$		−	6.00000i		−	0.311086i
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	−0.628454	−	0.777847i	$-0.716312\pi$
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	0.359408	+	0.933181i	$0.382979\pi$
$374$	5.00000	−	8.66025i	0.258544	−	0.447811i
$375$	−3.76795	+	10.5263i	−0.194576	+	0.543575i
$376$	6.50000	+	11.2583i	0.335212	+	0.580604i
$377$		0			0
$378$		0			0
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$	−0.937822	−	15.6244i	−0.0481093	−	0.801513i
$381$	4.50000	−	7.79423i	0.230542	−	0.399310i
$382$	−13.8564	−	8.00000i	−0.708955	−	0.409316i
$383$	−7.79423	+	4.50000i	−0.398266	+	0.229939i	−0.685736	−	0.727851i	$-0.740519\pi$
$383$	−7.79423	+	4.50000i	−0.398266	+	0.229939i	0.287469	+	0.957790i	$0.407186\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	18.0000			0.916176
$387$	8.66025	−	5.00000i	0.440225	−	0.254164i
$388$	−6.92820	−	4.00000i	−0.351726	−	0.203069i
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$	−2.23205	+	0.133975i	−0.113024	+	0.00678407i
$391$	6.00000			0.303433
$392$		0			0
$393$			17.0000i			0.857537i
$394$	13.5000	+	23.3827i	0.680120	+	1.17800i
$395$	26.1244	−	17.2487i	1.31446	−	0.867877i
$396$	2.50000	−	4.33013i	0.125630	−	0.217597i
$397$	1.73205	−	1.00000i	0.0869291	−	0.0501886i	−0.455905	−	0.890028i	$-0.650684\pi$
$397$	1.73205	−	1.00000i	0.0869291	−	0.0501886i	0.542834	+	0.839840i	$0.317351\pi$
$398$			14.0000i			0.701757i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$	−5.19615	−	3.00000i	−0.259161	−	0.149626i
$403$	−5.19615	−	3.00000i	−0.258839	−	0.149441i
$404$	−4.00000	−	6.92820i	−0.199007	−	0.344691i
$405$	−2.00000	−	1.00000i	−0.0993808	−	0.0496904i
$406$		0			0
$407$			25.0000i			1.23920i
$408$	−1.73205	+	1.00000i	−0.0857493	+	0.0495074i
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	−11.0885	−	16.7942i	−0.547620	−	0.829408i
$411$	−2.00000	−	3.46410i	−0.0986527	−	0.170872i
$412$		0			0
$413$		0			0
$414$	3.00000			0.147442
$415$	22.3205	−	1.33975i	1.09567	−	0.0657655i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	6.92820	+	4.00000i	0.339276	+	0.195881i
$418$	30.3109	−	17.5000i	1.48255	−	0.855953i
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	−16.4545	+	9.50000i	−0.800992	+	0.462453i
$423$	11.2583	+	6.50000i	0.547399	+	0.316041i
$424$	0.500000	−	0.866025i	0.0242821	−	0.0420579i
$425$	9.19615	+	3.92820i	0.446079	+	0.190546i
$426$	−2.00000			−0.0969003
$427$		0			0
$428$		−	12.0000i		−	0.580042i
$429$	−2.50000	−	4.33013i	−0.120701	−	0.209061i
$430$	−18.6603	+	12.3205i	−0.899877	+	0.594148i
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	−0.997173	−	0.0751385i	$-0.976060\pi$
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	0.563658	+	0.826008i	$0.309393\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$			4.00000i			0.192228i	0.995370	+	0.0961139i	$0.0306413\pi$
$433$			4.00000i			0.192228i	−0.995370	+	0.0961139i	$0.969359\pi$
$434$		0			0
$435$		0			0
$436$	9.00000	+	15.5885i	0.431022	+	0.746552i
$437$	18.1865	+	10.5000i	0.869980	+	0.502283i
$438$	−3.46410	−	2.00000i	−0.165521	−	0.0955637i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	−5.00000	+	10.0000i	−0.238366	+	0.476731i
$441$		0			0
$442$			2.00000i			0.0951303i
$443$	5.19615	−	3.00000i	0.246877	−	0.142534i	−0.371457	−	0.928450i	$-0.621142\pi$
$443$	5.19615	−	3.00000i	0.246877	−	0.142534i	0.618333	+	0.785916i	$0.287808\pi$
$444$	2.50000	−	4.33013i	0.118645	−	0.205499i
$445$	18.6603	−	12.3205i	0.884581	−	0.584048i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$			6.00000i			0.283790i
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$	4.59808	+	1.96410i	0.216755	+	0.0925886i
$451$	22.5000	−	38.9711i	1.05948	−	1.83508i
$452$	−5.19615	−	3.00000i	−0.244406	−	0.141108i
$453$	−19.0526	+	11.0000i	−0.895167	+	0.516825i
$454$	−14.0000			−0.657053
$455$		0			0
$456$	−7.00000			−0.327805
$457$	−32.9090	+	19.0000i	−1.53942	+	0.888783i	−0.540544	+	0.841316i	$0.681781\pi$
$457$	−32.9090	+	19.0000i	−1.53942	+	0.888783i	−0.998873	+	0.0474665i	$0.984885\pi$
$458$	−3.46410	−	2.00000i	−0.161867	−	0.0934539i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	−6.69615	+	0.401924i	−0.312210	+	0.0187398i
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$			15.0000i			0.697109i	0.937288	+	0.348555i	$0.113327\pi$
$463$			15.0000i			0.697109i	−0.937288	+	0.348555i	$0.886673\pi$
$464$		0			0
$465$	7.39230	+	11.1962i	0.342810	+	0.519209i
$466$		0			0
$467$	−1.73205	+	1.00000i	−0.0801498	+	0.0462745i	−0.539539	−	0.841960i	$-0.681402\pi$
$467$	−1.73205	+	1.00000i	−0.0801498	+	0.0462745i	0.459390	+	0.888235i	$0.348068\pi$
$468$			1.00000i			0.0462250i
$469$		0			0
$470$	−26.0000	−	13.0000i	−1.19929	−	0.599645i
$471$	−6.50000	−	11.2583i	−0.299504	−	0.518756i
$472$	−3.46410	−	2.00000i	−0.159448	−	0.0920575i
$473$	−43.3013	−	25.0000i	−1.99099	−	1.14950i
$474$	−7.00000	−	12.1244i	−0.321521	−	0.556890i
$475$	21.0000	+	28.0000i	0.963546	+	1.28473i
$476$		0			0
$477$		−	1.00000i		−	0.0457869i
$478$	17.3205	−	10.0000i	0.792222	−	0.457389i
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	−0.942821	−	0.333300i	$-0.891838\pi$
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	0.760056	+	0.649857i	$0.225171\pi$
$480$	1.86603	−	1.23205i	0.0851720	−	0.0562352i
$481$	−2.50000	−	4.33013i	−0.113990	−	0.197437i
$482$		−	1.00000i		−	0.0455488i
$483$		0			0
$484$	−14.0000			−0.636364
$485$	17.8564	−	1.07180i	0.810818	−	0.0486678i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.0513038	−	0.998683i	$-0.516338\pi$
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.890537	+	0.454911i	$0.849671\pi$
$488$	1.73205	−	1.00000i	0.0784063	−	0.0452679i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$	−7.79423	+	4.50000i	−0.351391	+	0.202876i
$493$		0			0
$494$	−3.50000	+	6.06218i	−0.157472	+	0.272750i
$495$	0.669873	+	11.1603i	0.0301086	+	0.501616i
$496$	6.00000			0.269408
$497$		0			0
$498$		−	10.0000i		−	0.448111i
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	−0.988204	−	0.153141i	$-0.951061\pi$
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	0.361478	−	0.932381i	$-0.382272\pi$
$500$	−10.5263	−	3.76795i	−0.470750	−	0.168508i
$501$	9.50000	−	16.4545i	0.424429	−	0.735132i
$502$	−2.59808	+	1.50000i	−0.115958	+	0.0669483i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$		0			0
$505$	16.0000	+	8.00000i	0.711991	+	0.355995i
$506$	−7.50000	−	12.9904i	−0.333416	−	0.577493i
$507$	−10.3923	−	6.00000i	−0.461538	−	0.266469i
$508$	7.79423	+	4.50000i	0.345813	+	0.199655i
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	0.668151	−	0.744026i	$-0.267086\pi$
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	−0.978421	+	0.206623i	$0.933753\pi$
$510$	2.00000	−	4.00000i	0.0885615	−	0.177123i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−6.06218	+	3.50000i	−0.267652	+	0.154529i
$514$	−5.00000	+	8.66025i	−0.220541	+	0.381987i
$515$		0			0
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$		−	65.0000i		−	2.85870i
$518$		0			0
$519$	−7.00000			−0.307266
$520$	−0.133975	−	2.23205i	−0.00587517	−	0.0978819i
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	−0.982231	−	0.187678i	$-0.939904\pi$
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	0.653650	+	0.756797i	$0.273237\pi$
$522$		0			0
$523$	10.3923	−	6.00000i	0.454424	−	0.262362i	−0.255273	−	0.966869i	$-0.582165\pi$
$523$	10.3923	−	6.00000i	0.454424	−	0.262362i	0.709697	+	0.704507i	$0.248832\pi$
$524$	−17.0000			−0.742648
$525$		0			0
$526$	−24.0000			−1.04645
$527$	10.3923	−	6.00000i	0.452696	−	0.261364i
$528$	4.33013	+	2.50000i	0.188445	+	0.108799i
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$	0.133975	+	2.23205i	0.00581948	+	0.0969541i
$531$	−4.00000			−0.173585
$532$		0			0
$533$			9.00000i			0.389833i
$534$	−5.00000	−	8.66025i	−0.216371	−	0.374766i
$535$	14.7846	+	22.3923i	0.639194	+	0.968104i
$536$	3.00000	−	5.19615i	0.129580	−	0.224440i
$537$	9.52628	−	5.50000i	0.411089	−	0.237343i
$538$		−	14.0000i		−	0.603583i
$539$		0			0
$540$	1.00000	−	2.00000i	0.0430331	−	0.0860663i
$541$	−2.00000	−	3.46410i	−0.0859867	−	0.148933i	0.819825	−	0.572615i	$-0.194071\pi$
$541$	−2.00000	−	3.46410i	−0.0859867	−	0.148933i	−0.905811	+	0.423681i	$0.860738\pi$
$542$	−6.92820	−	4.00000i	−0.297592	−	0.171815i
$543$	−1.73205	−	1.00000i	−0.0743294	−	0.0429141i
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	−36.0000	−	18.0000i	−1.54207	−	0.771035i
$546$		0			0
$547$		−	14.0000i		−	0.598597i	−0.954160	−	0.299298i	$-0.903247\pi$
$547$		−	14.0000i		−	0.598597i	0.954160	−	0.299298i	$-0.0967526\pi$
$548$	3.46410	−	2.00000i	0.147979	−	0.0854358i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	−2.99038	−	24.8205i	−0.127510	−	1.05835i
$551$		0			0
$552$			3.00000i			0.127688i
$553$		0			0
$554$	2.00000			0.0849719
$555$	0.669873	+	11.1603i	0.0284345	+	0.473726i
$556$	−4.00000	+	6.92820i	−0.169638	+	0.293821i
$557$	33.7750	+	19.5000i	1.43109	+	0.826242i	0.997204	−	0.0747252i	$-0.0238080\pi$
$557$	33.7750	+	19.5000i	1.43109	+	0.826242i	0.433888	+	0.900967i	$0.357141\pi$
$558$	5.19615	−	3.00000i	0.219971	−	0.127000i
$559$	10.0000			0.422955
$560$		0			0
$561$	10.0000			0.422200
$562$	9.52628	−	5.50000i	0.401842	−	0.232003i
$563$	−25.9808	−	15.0000i	−1.09496	−	0.632175i	−0.160066	−	0.987106i	$-0.551171\pi$
$563$	−25.9808	−	15.0000i	−1.09496	−	0.632175i	−0.934892	+	0.354932i	$0.884504\pi$
$564$	−6.50000	+	11.2583i	−0.273699	+	0.474061i
$565$	13.3923	−	0.803848i	0.563418	−	0.0338181i
$566$	26.0000			1.09286
$567$		0			0
$568$		−	2.00000i		−	0.0839181i
$569$	−1.50000	−	2.59808i	−0.0628833	−	0.108917i	0.832870	−	0.553469i	$-0.186696\pi$
$569$	−1.50000	−	2.59808i	−0.0628833	−	0.108917i	−0.895753	+	0.444552i	$0.853363\pi$
$570$	13.0622	−	8.62436i	0.547114	−	0.361235i
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	−0.770108	−	0.637913i	$-0.779798\pi$
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	0.937503	+	0.347977i	$0.113131\pi$
$572$	4.33013	−	2.50000i	0.181052	−	0.104530i
$573$		−	16.0000i		−	0.668410i
$574$		0			0
$575$	12.0000	−	9.00000i	0.500435	−	0.375326i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	20.7846	+	12.0000i	0.865275	+	0.499567i	0.865775	−	0.500433i	$-0.166826\pi$
$577$	20.7846	+	12.0000i	0.865275	+	0.499567i	−0.000500448		1.00000i	$0.500159\pi$
$578$	11.2583	+	6.50000i	0.468285	+	0.270364i
$579$	9.00000	+	15.5885i	0.374027	+	0.647834i
$580$		0			0
$581$		0			0
$582$		−	8.00000i		−	0.331611i
$583$	−4.33013	+	2.50000i	−0.179336	+	0.103539i
$584$	2.00000	−	3.46410i	0.0827606	−	0.143346i
$585$	−1.23205	−	1.86603i	−0.0509390	−	0.0771507i
$586$	−0.500000	−	0.866025i	−0.0206548	−	0.0357752i
$587$		−	2.00000i		−	0.0825488i	−0.999148	−	0.0412744i	$-0.986858\pi$
$587$		−	2.00000i		−	0.0825488i	0.999148	−	0.0412744i	$-0.0131418\pi$
$588$		0			0
$589$	42.0000			1.73058
$590$	8.92820	−	0.535898i	0.367568	−	0.0220626i
$591$	−13.5000	+	23.3827i	−0.555316	+	0.961835i
$592$	4.33013	+	2.50000i	0.177967	+	0.102749i
$593$	−29.4449	+	17.0000i	−1.20916	+	0.698106i	−0.962575	−	0.271016i	$-0.912640\pi$
$593$	−29.4449	+	17.0000i	−1.20916	+	0.698106i	−0.246581	+	0.969122i	$0.579307\pi$
$594$	5.00000			0.205152
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−12.1244	+	7.00000i	−0.496217	+	0.286491i
$598$	2.59808	+	1.50000i	0.106243	+	0.0613396i
$599$	−14.0000	+	24.2487i	−0.572024	+	0.990775i	0.424333	+	0.905506i	$0.360508\pi$
$599$	−14.0000	+	24.2487i	−0.572024	+	0.990775i	−0.996358	+	0.0852695i	$0.972825\pi$
$600$	−1.96410	+	4.59808i	−0.0801841	+	0.187716i
$601$	30.0000			1.22373			0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000			1.22373			0.611863	+	0.790964i	$0.290420\pi$
$602$		0			0
$603$		−	6.00000i		−	0.244339i
$604$	−11.0000	−	19.0526i	−0.447584	−	0.775238i
$605$	26.1244	−	17.2487i	1.06211	−	0.701260i
$606$	4.00000	−	6.92820i	0.162489	−	0.281439i
$607$	−11.2583	+	6.50000i	−0.456962	+	0.263827i	−0.710766	−	0.703429i	$-0.751651\pi$
$607$	−11.2583	+	6.50000i	−0.456962	+	0.263827i	0.253804	+	0.967256i	$0.418318\pi$
$608$		−	7.00000i		−	0.283887i
$609$		0			0
$610$	−2.00000	+	4.00000i	−0.0809776	+	0.161955i
$611$	6.50000	+	11.2583i	0.262962	+	0.455463i
$612$	−1.73205	−	1.00000i	−0.0700140	−	0.0404226i
$613$	16.4545	+	9.50000i	0.664590	+	0.383701i	0.794024	−	0.607887i	$-0.207983\pi$
$613$	16.4545	+	9.50000i	0.664590	+	0.383701i	−0.129433	+	0.991588i	$0.541316\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$	9.00000	−	18.0000i	0.362915	−	0.725830i
$616$		0			0
$617$			30.0000i			1.20775i	0.797077	+	0.603877i	$0.206378\pi$
$617$			30.0000i			1.20775i	−0.797077	+	0.603877i	$0.793622\pi$
$618$		0			0
$619$	−7.50000	+	12.9904i	−0.301450	+	0.522127i	−0.976465	−	0.215677i	$-0.930804\pi$
$619$	−7.50000	+	12.9904i	−0.301450	+	0.522127i	0.675014	+	0.737805i	$0.264137\pi$
$620$	−11.1962	+	7.39230i	−0.449648	+	0.296882i
$621$	1.50000	+	2.59808i	0.0601929	+	0.104257i
$622$		−	26.0000i		−	1.04251i
$623$		0			0
$624$	−1.00000			−0.0400320
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	5.00000	−	8.66025i	0.199840	−	0.346133i
$627$	30.3109	+	17.5000i	1.21050	+	0.698883i
$628$	11.2583	−	6.50000i	0.449256	−	0.259378i
$629$	10.0000			0.398726
$630$		0			0
$631$	18.0000			0.716569			0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000			0.716569			0.358284	+	0.933613i	$0.383362\pi$
$632$	12.1244	−	7.00000i	0.482281	−	0.278445i
$633$	−16.4545	−	9.50000i	−0.654007	−	0.377591i
$634$	−1.00000	+	1.73205i	−0.0397151	+	0.0687885i
$635$	−20.0885	+	1.20577i	−0.797186	+	0.0478496i
$636$	1.00000			0.0396526
$637$		0			0
$638$		0			0
$639$	−1.00000	−	1.73205i	−0.0395594	−	0.0685189i
$640$	1.23205	+	1.86603i	0.0487011	+	0.0737611i
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$	10.3923	−	6.00000i	0.410152	−	0.236801i
$643$			38.0000i			1.49857i	0.662246	+	0.749287i	$0.269604\pi$
$643$			38.0000i			1.49857i	−0.662246	+	0.749287i	$0.730396\pi$
$644$		0			0
$645$	−20.0000	−	10.0000i	−0.787499	−	0.393750i
$646$	−7.00000	−	12.1244i	−0.275411	−	0.477026i
$647$	−0.866025	−	0.500000i	−0.0340470	−	0.0196570i	0.482880	−	0.875687i	$-0.339591\pi$
$647$	−0.866025	−	0.500000i	−0.0340470	−	0.0196570i	−0.516927	+	0.856030i	$0.672924\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	10.0000	+	17.3205i	0.392534	+	0.679889i
$650$	3.00000	+	4.00000i	0.117670	+	0.156893i
$651$		0			0
$652$		−	12.0000i		−	0.469956i
$653$	−4.33013	+	2.50000i	−0.169451	+	0.0978326i	−0.582327	−	0.812955i	$-0.697858\pi$
$653$	−4.33013	+	2.50000i	−0.169451	+	0.0978326i	0.412876	+	0.910787i	$0.364524\pi$
$654$	−9.00000	+	15.5885i	−0.351928	+	0.609557i
$655$	31.7224	−	20.9449i	1.23950	−	0.818384i
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$		−	4.00000i		−	0.156055i
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	−11.1603	+	0.669873i	−0.434412	+	0.0260748i
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$	−12.9904	−	7.50000i	−0.504885	−	0.291496i
$663$	−1.73205	+	1.00000i	−0.0672673	+	0.0388368i
$664$	10.0000			0.388075
$665$		0			0
$666$	5.00000			0.193746
$667$		0			0
$668$	16.4545	+	9.50000i	0.636643	+	0.367566i
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$	0.803848	+	13.3923i	0.0310553	+	0.517390i
$671$	−10.0000			−0.386046
$672$		0			0
$673$		−	36.0000i		−	1.38770i	−0.720121	−	0.693849i	$-0.755914\pi$
$673$		−	36.0000i		−	1.38770i	0.720121	−	0.693849i	$-0.244086\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$	0.598076	+	4.96410i	0.0230200	+	0.191068i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−28.5788	+	16.5000i	−1.09837	+	0.634147i	−0.935793	−	0.352549i	$-0.885315\pi$
$677$	−28.5788	+	16.5000i	−1.09837	+	0.634147i	−0.162581	+	0.986695i	$0.551982\pi$
$678$		−	6.00000i		−	0.230429i
$679$		0			0
$680$	4.00000	+	2.00000i	0.153393	+	0.0766965i
$681$	−7.00000	−	12.1244i	−0.268241	−	0.464606i
$682$	−25.9808	−	15.0000i	−0.994855	−	0.574380i
$683$	−3.46410	−	2.00000i	−0.132550	−	0.0765279i	0.432259	−	0.901750i	$-0.357717\pi$
$683$	−3.46410	−	2.00000i	−0.132550	−	0.0765279i	−0.564809	+	0.825222i	$0.691050\pi$
$684$	−3.50000	−	6.06218i	−0.133826	−	0.231793i
$685$	−4.00000	+	8.00000i	−0.152832	+	0.305664i
$686$		0			0
$687$		−	4.00000i		−	0.152610i
$688$	−8.66025	+	5.00000i	−0.330169	+	0.190623i
$689$	0.500000	−	0.866025i	0.0190485	−	0.0329929i
$690$	−3.69615	−	5.59808i	−0.140710	−	0.213115i
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	0.610704	−	0.791859i	$-0.290887\pi$
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	−0.991122	+	0.132956i	$0.957553\pi$
$692$		−	7.00000i		−	0.266100i
$693$		0			0
$694$	−16.0000			−0.607352
$695$	−1.07180	−	17.8564i	−0.0406556	−	0.677332i
$696$		0			0
$697$	−15.5885	−	9.00000i	−0.590455	−	0.340899i
$698$	20.7846	−	12.0000i	0.786709	−	0.454207i
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−0.866025	+	0.500000i	−0.0326860	+	0.0188713i
$703$	30.3109	+	17.5000i	1.14320	+	0.660025i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$	−1.74167	−	29.0167i	−0.0655951	−	1.09283i
$706$		0			0
$707$		0			0
$708$		−	4.00000i		−	0.150329i
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	0.976237	−	0.216705i	$-0.0695310\pi$
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	−0.675791	+	0.737093i	$0.736198\pi$
$710$	2.46410	+	3.73205i	0.0924761	+	0.140061i
$711$	7.00000	−	12.1244i	0.262521	−	0.454699i
$712$	8.66025	−	5.00000i	0.324557	−	0.187383i
$713$		−	18.0000i		−	0.674105i
$714$		0			0
$715$	−5.00000	+	10.0000i	−0.186989	+	0.373979i
$716$	5.50000	+	9.52628i	0.205545	+	0.356014i
$717$	17.3205	+	10.0000i	0.646846	+	0.373457i
$718$	24.2487	+	14.0000i	0.904954	+	0.522475i
$719$	1.00000	+	1.73205i	0.0372937	+	0.0645946i	0.884070	−	0.467355i	$-0.154793\pi$
$719$	1.00000	+	1.73205i	0.0372937	+	0.0645946i	−0.846776	+	0.531949i	$0.821460\pi$
$720$	2.00000	+	1.00000i	0.0745356	+	0.0372678i
$721$		0			0
$722$		−	30.0000i		−	1.11648i
$723$	0.866025	−	0.500000i	0.0322078	−	0.0185952i
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$		0			0
$726$	−7.00000	−	12.1244i	−0.259794	−	0.449977i
$727$		−	53.0000i		−	1.96566i	−0.184510	−	0.982831i	$-0.559070\pi$
$727$		−	53.0000i		−	1.96566i	0.184510	−	0.982831i	$-0.440930\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	0.535898	+	8.92820i	0.0198345	+	0.330448i
$731$	−10.0000	+	17.3205i	−0.369863	+	0.640622i
$732$	1.73205	+	1.00000i	0.0640184	+	0.0369611i
$733$	−18.1865	+	10.5000i	−0.671735	+	0.387826i	−0.796734	−	0.604331i	$-0.793441\pi$
$733$	−18.1865	+	10.5000i	−0.671735	+	0.387826i	0.124999	+	0.992157i	$0.460107\pi$
$734$	37.0000			1.36569
$735$		0			0
$736$	−3.00000			−0.110581
$737$	−25.9808	+	15.0000i	−0.957014	+	0.552532i
$738$	−7.79423	−	4.50000i	−0.286910	−	0.165647i
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	−0.00311943	−	0.999995i	$-0.500993\pi$
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	0.867581	−	0.497296i	$-0.165674\pi$
$740$	−11.1603	+	0.669873i	−0.410259	+	0.0246250i
$741$	−7.00000			−0.257151
$742$		0			0
$743$			31.0000i			1.13728i	0.822587	+	0.568640i	$0.192530\pi$
$743$			31.0000i			1.13728i	−0.822587	+	0.568640i	$0.807470\pi$
$744$	3.00000	+	5.19615i	0.109985	+	0.190500i
$745$	11.1962	−	7.39230i	0.410195	−	0.270833i
$746$	3.00000	−	5.19615i	0.109838	−	0.190245i
$747$	8.66025	−	5.00000i	0.316862	−	0.182940i
$748$			10.0000i			0.365636i
$749$		0			0
$750$	−2.00000	−	11.0000i	−0.0730297	−	0.401663i
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$	−11.2583	−	6.50000i	−0.410549	−	0.237031i
$753$	−2.59808	−	1.50000i	−0.0946792	−	0.0546630i
$754$		0			0
$755$	44.0000	+	22.0000i	1.60132	+	0.800662i
$756$		0			0
$757$		−	26.0000i		−	0.944986i	−0.881334	−	0.472493i	$-0.843354\pi$
$757$		−	26.0000i		−	0.944986i	0.881334	−	0.472493i	$-0.156646\pi$
$758$	−0.866025	+	0.500000i	−0.0314555	+	0.0181608i
$759$	7.50000	−	12.9904i	0.272233	−	0.471521i
$760$	8.62436	+	13.0622i	0.312838	+	0.473815i
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	0.837557	−	0.546350i	$-0.183983\pi$
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	−0.891932	+	0.452170i	$0.850650\pi$
$762$			9.00000i			0.326036i
$763$		0			0
$764$	16.0000			0.578860
$765$	4.46410	−	0.267949i	0.161400	−	0.00968772i
$766$	4.50000	−	7.79423i	0.162592	−	0.281617i
$767$	−3.46410	−	2.00000i	−0.125081	−	0.0722158i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	51.0000			1.83911			0.919554	−	0.392965i	$-0.128551\pi$
$769$	51.0000			1.83911			0.919554	+	0.392965i	$0.128551\pi$
$770$		0			0
$771$	−10.0000			−0.360141
$772$	−15.5885	+	9.00000i	−0.561041	+	0.323917i
$773$	32.0429	+	18.5000i	1.15250	+	0.665399i	0.949496	−	0.313778i	$-0.101595\pi$
$773$	32.0429	+	18.5000i	1.15250	+	0.665399i	0.203008	+	0.979177i	$0.434928\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$	11.7846	−	27.5885i	0.423316	−	0.991007i
$776$	8.00000			0.287183
$777$		0			0
$778$			6.00000i			0.215110i
$779$	−31.5000	−	54.5596i	−1.12860	−	1.95480i
$780$	1.86603	−	1.23205i	0.0668144	−	0.0441145i
$781$	−5.00000	+	8.66025i	−0.178914	+	0.309888i
$782$	−5.19615	+	3.00000i	−0.185814	+	0.107280i
$783$		0			0
$784$		0			0
$785$	−13.0000	+	26.0000i	−0.463990	+	0.927980i
$786$	−8.50000	−	14.7224i	−0.303185	−	0.525132i
$787$	32.9090	+	19.0000i	1.17308	+	0.677277i	0.954403	−	0.298521i	$-0.0964933\pi$
$787$	32.9090	+	19.0000i	1.17308	+	0.677277i	0.218675	+	0.975798i	$0.429827\pi$
$788$	−23.3827	−	13.5000i	−0.832974	−	0.480918i
$789$	−12.0000	−	20.7846i	−0.427211	−	0.739952i
$790$	−14.0000	+	28.0000i	−0.498098	+	0.996195i
$791$		0			0
$792$			5.00000i			0.177667i
$793$	1.73205	−	1.00000i	0.0615069	−	0.0355110i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$	−1.86603	+	1.23205i	−0.0661811	+	0.0436963i
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$			30.0000i			1.06265i	0.847167	+	0.531327i	$0.178307\pi$
$797$			30.0000i			1.06265i	−0.847167	+	0.531327i	$0.821693\pi$
$798$		0			0
$799$	−26.0000			−0.919814
$800$	−4.59808	−	1.96410i	−0.162567	−	0.0694415i
$801$	5.00000	−	8.66025i	0.176666	−	0.305995i
$802$	−23.3827	−	13.5000i	−0.825671	−	0.476702i
$803$	−17.3205	+	10.0000i	−0.611227	+	0.352892i
$804$	6.00000			0.211604
$805$		0			0
$806$	6.00000			0.211341
$807$	12.1244	−	7.00000i	0.426798	−	0.246412i
$808$	6.92820	+	4.00000i	0.243733	+	0.140720i
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$	2.23205	−	0.133975i	0.0784263	−	0.00470739i
$811$	−11.0000			−0.386262			−0.193131	−	0.981173i	$-0.561864\pi$
$811$	−11.0000			−0.386262			−0.193131	+	0.981173i	$0.561864\pi$
$812$		0			0
$813$		−	8.00000i		−	0.280572i
$814$	−12.5000	−	21.6506i	−0.438125	−	0.758854i
$815$	14.7846	+	22.3923i	0.517882	+	0.784368i
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	−60.6218	+	35.0000i	−2.12089	+	1.22449i
$818$		−	10.0000i		−	0.349642i
$819$		0			0
$820$	18.0000	+	9.00000i	0.628587	+	0.314294i
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	0.808915	−	0.587925i	$-0.200055\pi$
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	−0.913616	+	0.406578i	$0.866722\pi$
$822$	3.46410	+	2.00000i	0.120824	+	0.0697580i
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	0.374365	−	0.927281i	$-0.377861\pi$
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	−0.615867	+	0.787850i	$0.711194\pi$
$824$		0			0
$825$	20.0000	−	15.0000i	0.696311	−	0.522233i
$826$		0			0
$827$		−	42.0000i		−	1.46048i	−0.683189	−	0.730242i	$-0.739408\pi$
$827$		−	42.0000i		−	1.46048i	0.683189	−	0.730242i	$-0.260592\pi$
$828$	−2.59808	+	1.50000i	−0.0902894	+	0.0521286i
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$	−18.6603	+	12.3205i	−0.647707	+	0.427651i
$831$	1.00000	+	1.73205i	0.0346896	+	0.0600842i
$832$		−	1.00000i		−	0.0346688i
$833$		0			0
$834$	−8.00000			−0.277017
$835$	−42.4090	+	2.54552i	−1.46762	+	0.0880913i
$836$	−17.5000	+	30.3109i	−0.605250	+	1.04832i
$837$	5.19615	+	3.00000i	0.179605	+	0.103695i
$838$	−2.59808	+	1.50000i	−0.0897491	+	0.0518166i
$839$	2.00000			0.0690477			0.0345238	−	0.999404i	$-0.489009\pi$
$839$	2.00000			0.0690477			0.0345238	+	0.999404i	$0.489009\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	17.3205	−	10.0000i	0.596904	−	0.344623i
$843$	9.52628	+	5.50000i	0.328102	+	0.189430i
$844$	9.50000	−	16.4545i	0.327003	−	0.566387i
$845$	1.60770	+	26.7846i	0.0553064	+	0.921419i
$846$	−13.0000			−0.446949
$847$		0			0
$848$			1.00000i			0.0343401i
$849$	13.0000	+	22.5167i	0.446159	+	0.772770i
$850$	−9.92820	+	1.19615i	−0.340535	+	0.0410277i
$851$	7.50000	−	12.9904i	0.257097	−	0.445305i
$852$	1.73205	−	1.00000i	0.0593391	−	0.0342594i
$853$		−	49.0000i		−	1.67773i	−0.544341	−	0.838864i	$-0.683220\pi$
$853$		−	49.0000i		−	1.67773i	0.544341	−	0.838864i	$-0.316780\pi$
$854$		0			0
$855$	14.0000	+	7.00000i	0.478790	+	0.239395i
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−48.4974	−	28.0000i	−1.65664	−	0.956462i	−0.974249	−	0.225475i	$-0.927607\pi$
$857$	−48.4974	−	28.0000i	−1.65664	−	0.956462i	−0.682391	−	0.730987i	$-0.739060\pi$
$858$	4.33013	+	2.50000i	0.147828	+	0.0853486i
$859$	−18.0000	−	31.1769i	−0.614152	−	1.06374i	−0.990533	−	0.137277i	$-0.956165\pi$
$859$	−18.0000	−	31.1769i	−0.614152	−	1.06374i	0.376381	−	0.926465i	$-0.377169\pi$
$860$	10.0000	−	20.0000i	0.340997	−	0.681994i
$861$		0			0
$862$		−	18.0000i		−	0.613082i
$863$	−12.9904	+	7.50000i	−0.442198	+	0.255303i	−0.704529	−	0.709675i	$-0.748842\pi$
$863$	−12.9904	+	7.50000i	−0.442198	+	0.255303i	0.262332	+	0.964978i	$0.415509\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	8.62436	+	13.0622i	0.293237	+	0.444127i
$866$	−2.00000	−	3.46410i	−0.0679628	−	0.117715i
$867$			13.0000i			0.441503i
$868$		0			0
$869$	−70.0000			−2.37459
$870$		0			0
$871$	3.00000	−	5.19615i	0.101651	−	0.176065i
$872$	−15.5885	−	9.00000i	−0.527892	−	0.304778i
$873$	6.92820	−	4.00000i	0.234484	−	0.135379i
$874$	−21.0000			−0.710336
$875$		0			0
$876$	4.00000			0.135147
$877$	−23.3827	+	13.5000i	−0.789577	+	0.455863i	−0.839814	−	0.542875i	$-0.817336\pi$
$877$	−23.3827	+	13.5000i	−0.789577	+	0.455863i	0.0502365	+	0.998737i	$0.484002\pi$
$878$		0			0
$879$	0.500000	−	0.866025i	0.0168646	−	0.0292103i
$880$	−0.669873	−	11.1603i	−0.0225814	−	0.376212i
$881$	3.00000			0.101073			0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000			0.101073			0.0505363	+	0.998722i	$0.483907\pi$
$882$		0			0
$883$			52.0000i			1.74994i	0.484178	+	0.874970i	$0.339119\pi$
$883$			52.0000i			1.74994i	−0.484178	+	0.874970i	$0.660881\pi$
$884$	−1.00000	−	1.73205i	−0.0336336	−	0.0582552i
$885$	4.92820	+	7.46410i	0.165660	+	0.250903i
$886$	−3.00000	+	5.19615i	−0.100787	+	0.174568i
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	−0.315279	−	0.948999i	$-0.602098\pi$
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	0.664218	+	0.747539i	$0.268765\pi$
$888$			5.00000i			0.167789i
$889$		0			0
$890$	−10.0000	+	20.0000i	−0.335201	+	0.670402i
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$	13.8564	+	8.00000i	0.463947	+	0.267860i
$893$	−78.8083	−	45.5000i	−2.63722	−	1.52260i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$	−22.0000	−	11.0000i	−0.735379	−	0.367689i
$896$		0			0
$897$			3.00000i			0.100167i
$898$	7.79423	−	4.50000i	0.260097	−	0.150167i
$899$		0			0
$900$	−4.96410	+	0.598076i	−0.165470	+	0.0199359i
$901$	1.00000	+	1.73205i	0.0333148	+	0.0577030i
$902$			45.0000i			1.49834i
$903$		0			0
$904$	6.00000			0.199557
$905$	0.267949	+	4.46410i	0.00890693	+	0.148392i
$906$	11.0000	−	19.0526i	0.365451	−	0.632979i
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	0.712084	−	0.702094i	$-0.247752\pi$
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	−0.251990	+	0.967730i	$0.581085\pi$
$908$	12.1244	−	7.00000i	0.402361	−	0.232303i
$909$	8.00000			0.265343
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	6.06218	−	3.50000i	0.200739	−	0.115897i
$913$	−43.3013	−	25.0000i	−1.43306	−	0.827379i
$914$	19.0000	−	32.9090i	0.628464	−	1.08853i
$915$	−4.46410	+	0.267949i	−0.147579	+	0.00885813i
$916$	4.00000			0.132164
$917$		0			0
$918$		−	2.00000i		−	0.0660098i
$919$	28.0000	+	48.4974i	0.923635	+	1.59978i	0.793742	+	0.608254i	$0.208130\pi$
$919$	28.0000	+	48.4974i	0.923635	+	1.59978i	0.129893	+	0.991528i	$0.458537\pi$
$920$	5.59808	−	3.69615i	0.184563	−	0.121859i
$921$	−1.00000	+	1.73205i	−0.0329511	+	0.0570730i
$922$	−10.3923	+	6.00000i	−0.342252	+	0.197599i
$923$		−	2.00000i		−	0.0658308i
$924$		0			0
$925$	20.0000	−	15.0000i	0.657596	−	0.493197i
$926$	−7.50000	−	12.9904i	−0.246465	−	0.426890i
$927$		0			0
$928$		0			0
$929$	−16.5000	−	28.5788i	−0.541347	−	0.937641i	−0.998827	−	0.0484211i	$-0.984581\pi$
$929$	−16.5000	−	28.5788i	−0.541347	−	0.937641i	0.457480	−	0.889220i	$-0.348752\pi$
$930$	−12.0000	−	6.00000i	−0.393496	−	0.196748i
$931$		0			0
$932$		0			0
$933$	22.5167	−	13.0000i	0.737162	−	0.425601i
$934$	1.00000	−	1.73205i	0.0327210	−	0.0566744i
$935$	−12.3205	−	18.6603i	−0.402924	−	0.610256i
$936$	−0.500000	−	0.866025i	−0.0163430	−	0.0283069i
$937$			34.0000i			1.11073i	0.831606	+	0.555366i	$0.187422\pi$
$937$			34.0000i			1.11073i	−0.831606	+	0.555366i	$0.812578\pi$
$938$		0			0
$939$	10.0000			0.326338
$940$	29.0167	−	1.74167i	0.946419	−	0.0568070i
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$	11.2583	+	6.50000i	0.366816	+	0.211781i
$943$	−23.3827	+	13.5000i	−0.761445	+	0.439620i
$944$	4.00000			0.130189
$945$		0			0
$946$	50.0000			1.62564
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	−0.321552	−	0.946892i	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$	12.1244	+	7.00000i	0.393781	+	0.227349i
$949$	2.00000	−	3.46410i	0.0649227	−	0.112449i
$950$	−32.1865	−	13.7487i	−1.04427	−	0.446067i
$951$	−2.00000			−0.0648544
$952$		0			0
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$	0.500000	+	0.866025i	0.0161881	+	0.0280386i
$955$	−29.8564	+	19.7128i	−0.966131	+	0.637892i
$956$	−10.0000	+	17.3205i	−0.323423	+	0.560185i
$957$		0			0
$958$		−	8.00000i		−	0.258468i
$959$		0			0
$960$	−1.00000	+	2.00000i	−0.0322749	+	0.0645497i
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$	4.33013	+	2.50000i	0.139609	+	0.0806032i
$963$	10.3923	+	6.00000i	0.334887	+	0.193347i
$964$	0.500000	+	0.866025i	0.0161039	+	0.0278928i
$965$	18.0000	−	36.0000i	0.579441	−	1.15888i
$966$		0			0
$967$		−	24.0000i		−	0.771788i	−0.922543	−	0.385894i	$-0.873893\pi$
$967$		−	24.0000i		−	0.771788i	0.922543	−	0.385894i	$-0.126107\pi$
$968$	12.1244	−	7.00000i	0.389692	−	0.224989i
$969$	7.00000	−	12.1244i	0.224872	−	0.389490i
$970$	−14.9282	+	9.85641i	−0.479316	+	0.316470i
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	0.988389	+	0.151948i	$0.0485545\pi$
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	−0.362604	+	0.931943i	$0.618112\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	24.0000			0.769010
$975$	−1.96410	+	4.59808i	−0.0629016	+	0.147256i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.211495	−	0.977379i	$-0.567833\pi$
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.952183	+	0.305530i	$0.901167\pi$
$978$	10.3923	−	6.00000i	0.332309	−	0.191859i
$979$	−50.0000			−1.59801
$980$		0			0
$981$	−18.0000			−0.574696
$982$	−20.7846	+	12.0000i	−0.663264	+	0.382935i
$983$	−28.5788	−	16.5000i	−0.911523	−	0.526268i	−0.0306024	−	0.999532i	$-0.509743\pi$
$983$	−28.5788	−	16.5000i	−0.911523	−	0.526268i	−0.880921	+	0.473263i	$0.843076\pi$
$984$	4.50000	−	7.79423i	0.143455	−	0.248471i
$985$	60.2654	−	3.61731i	1.92021	−	0.115257i
$986$		0			0
$987$		0			0
$988$		−	7.00000i		−	0.222700i
$989$	15.0000	+	25.9808i	0.476972	+	0.826140i
$990$	−6.16025	−	9.33013i	−0.195786	−	0.296531i
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	−0.424594	−	0.905384i	$-0.639583\pi$
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	0.996382	−	0.0849833i	$-0.0270837\pi$
$992$	−5.19615	+	3.00000i	−0.164978	+	0.0952501i
$993$		−	15.0000i		−	0.476011i
$994$		0			0
$995$	28.0000	+	14.0000i	0.887660	+	0.443830i
$996$	5.00000	+	8.66025i	0.158431	+	0.274411i
$997$	−8.66025	−	5.00000i	−0.274273	−	0.158352i	0.356555	−	0.934274i	$-0.383951\pi$
$997$	−8.66025	−	5.00000i	−0.274273	−	0.158352i	−0.630828	+	0.775923i	$0.717285\pi$
$998$	24.2487	+	14.0000i	0.767580	+	0.443162i
$999$	2.50000	+	4.33013i	0.0790965	+	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.n.i.949.1		4
5.4	even	2	inner	1470.2.n.i.949.2		4
7.2	even	3	inner	1470.2.n.i.79.2		4
7.3	odd	6		1470.2.g.f.589.1		2
7.4	even	3		1470.2.g.a.589.1		2
7.5	odd	6		210.2.n.a.79.2	yes	4
7.6	odd	2		210.2.n.a.109.1	yes	4
21.5	even	6		630.2.u.c.289.1		4
21.20	even	2		630.2.u.c.109.2		4
28.19	even	6		1680.2.di.a.289.2		4
28.27	even	2		1680.2.di.a.529.1		4
35.3	even	12		7350.2.a.t.1.1		1
35.4	even	6		1470.2.g.a.589.2		2
35.9	even	6	inner	1470.2.n.i.79.1		4
35.12	even	12		1050.2.i.f.751.1		2
35.13	even	4		1050.2.i.o.151.1		2
35.17	even	12		7350.2.a.bn.1.1		1
35.18	odd	12		7350.2.a.b.1.1		1
35.19	odd	6		210.2.n.a.79.1	✓	4
35.24	odd	6		1470.2.g.f.589.2		2
35.27	even	4		1050.2.i.f.151.1		2
35.32	odd	12		7350.2.a.ch.1.1		1
35.33	even	12		1050.2.i.o.751.1		2
35.34	odd	2		210.2.n.a.109.2	yes	4
105.89	even	6		630.2.u.c.289.2		4
105.104	even	2		630.2.u.c.109.1		4
140.19	even	6		1680.2.di.a.289.1		4
140.139	even	2		1680.2.di.a.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.a.79.1	✓	4	35.19	odd	6
210.2.n.a.79.2	yes	4	7.5	odd	6
210.2.n.a.109.1	yes	4	7.6	odd	2
210.2.n.a.109.2	yes	4	35.34	odd	2
630.2.u.c.109.1		4	105.104	even	2
630.2.u.c.109.2		4	21.20	even	2
630.2.u.c.289.1		4	21.5	even	6
630.2.u.c.289.2		4	105.89	even	6
1050.2.i.f.151.1		2	35.27	even	4
1050.2.i.f.751.1		2	35.12	even	12
1050.2.i.o.151.1		2	35.13	even	4
1050.2.i.o.751.1		2	35.33	even	12
1470.2.g.a.589.1		2	7.4	even	3
1470.2.g.a.589.2		2	35.4	even	6
1470.2.g.f.589.1		2	7.3	odd	6
1470.2.g.f.589.2		2	35.24	odd	6
1470.2.n.i.79.1		4	35.9	even	6	inner
1470.2.n.i.79.2		4	7.2	even	3	inner
1470.2.n.i.949.1		4	1.1	even	1	trivial
1470.2.n.i.949.2		4	5.4	even	2	inner
1680.2.di.a.289.1		4	140.19	even	6
1680.2.di.a.289.2		4	28.19	even	6
1680.2.di.a.529.1		4	28.27	even	2
1680.2.di.a.529.2		4	140.139	even	2
7350.2.a.b.1.1		1	35.18	odd	12
7350.2.a.t.1.1		1	35.3	even	12
7350.2.a.bn.1.1		1	35.17	even	12
7350.2.a.ch.1.1		1	35.32	odd	12

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.23205 - 1.86603i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-0.866025 + 0.500000i) q^{12} +1.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(2.00000 + 1.00000i) q^{20} +5.00000i q^{22} +(-2.59808 + 1.50000i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(-0.500000 - 0.866025i) q^{26} -1.00000i q^{27} +(0.133975 + 2.23205i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.33013 + 2.50000i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-4.33013 + 2.50000i) q^{37} +(6.06218 + 3.50000i) q^{38} +(0.500000 - 0.866025i) q^{39} +(-2.23205 + 0.133975i) q^{40} +9.00000 q^{41} -10.0000i q^{43} +(-2.50000 - 4.33013i) q^{44} +(-1.86603 + 1.23205i) q^{45} +(1.50000 - 2.59808i) q^{46} +(11.2583 - 6.50000i) q^{47} +1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} +(1.00000 + 1.73205i) q^{51} +(0.866025 + 0.500000i) q^{52} +(-0.866025 - 0.500000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(10.0000 + 5.00000i) q^{55} +7.00000i q^{57} +(-2.00000 + 3.46410i) q^{59} +(-1.23205 - 1.86603i) q^{60} +(-1.00000 - 1.73205i) q^{61} -6.00000i q^{62} -1.00000 q^{64} +(-2.23205 + 0.133975i) q^{65} +(2.50000 - 4.33013i) q^{66} +(-5.19615 - 3.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(2.50000 - 4.33013i) q^{74} +(4.59808 + 1.96410i) q^{75} -7.00000 q^{76} +1.00000i q^{78} +(-7.00000 - 12.1244i) q^{79} +(1.86603 - 1.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.79423 + 4.50000i) q^{82} -10.0000i q^{83} +(2.00000 - 4.00000i) q^{85} +(5.00000 + 8.66025i) q^{86} +(4.33013 + 2.50000i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(1.00000 - 2.00000i) q^{90} +3.00000i q^{92} +(5.19615 - 3.00000i) q^{93} +(-6.50000 + 11.2583i) q^{94} +(13.0622 - 8.62436i) q^{95} +(-0.500000 - 0.866025i) q^{96} -8.00000i q^{97} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{9} + 2 q^{10} + 10 q^{11} + 4 q^{15} - 2 q^{16} - 14 q^{19} + 8 q^{20} + 2 q^{24} - 6 q^{25} - 2 q^{26} + 4 q^{30} - 12 q^{31} + 8 q^{34} + 4 q^{36} + 2 q^{39} - 2 q^{40} + 36 q^{41} - 10 q^{44} - 4 q^{45} + 6 q^{46} + 16 q^{50} + 4 q^{51} + 2 q^{54} + 40 q^{55} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 4 q^{64} - 2 q^{65} + 10 q^{66} + 12 q^{69} - 8 q^{71} + 10 q^{74} + 8 q^{75} - 28 q^{76} - 28 q^{79} + 4 q^{80} - 2 q^{81} + 8 q^{85} + 20 q^{86} - 20 q^{89} + 4 q^{90} - 26 q^{94} + 28 q^{95} - 2 q^{96} + 20 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^9 + 2 * q^10 + 10 * q^11 + 4 * q^15 - 2 * q^16 - 14 * q^19 + 8 * q^20 + 2 * q^24 - 6 * q^25 - 2 * q^26 + 4 * q^30 - 12 * q^31 + 8 * q^34 + 4 * q^36 + 2 * q^39 - 2 * q^40 + 36 * q^41 - 10 * q^44 - 4 * q^45 + 6 * q^46 + 16 * q^50 + 4 * q^51 + 2 * q^54 + 40 * q^55 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 4 * q^64 - 2 * q^65 + 10 * q^66 + 12 * q^69 - 8 * q^71 + 10 * q^74 + 8 * q^75 - 28 * q^76 - 28 * q^79 + 4 * q^80 - 2 * q^81 + 8 * q^85 + 20 * q^86 - 20 * q^89 + 4 * q^90 - 26 * q^94 + 28 * q^95 - 2 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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