LMFDB - Embedded newform 1470.2.i.w.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(361,1470)]

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, 0, 4]))

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

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

chi := DirichletCharacter("1470.361");

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.i (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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1470.361
Dual form			1470.2.i.w.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(3.12132 - 5.40629i) q^{11} +(-0.500000 - 0.866025i) q^{12} +5.65685 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.70711 - 4.68885i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.585786 - 1.01461i) q^{19} -1.00000 q^{20} +6.24264 q^{22} +(-4.41421 - 7.64564i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.82843 + 4.89898i) q^{26} +1.00000 q^{27} +5.41421 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.878680 + 1.52192i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.12132 + 5.40629i) q^{33} +5.41421 q^{34} +1.00000 q^{36} +(-4.12132 - 7.13834i) q^{37} +(0.585786 - 1.01461i) q^{38} +(-2.82843 + 4.89898i) q^{39} +(-0.500000 - 0.866025i) q^{40} +6.48528 q^{41} -5.07107 q^{43} +(3.12132 + 5.40629i) q^{44} +(0.500000 - 0.866025i) q^{45} +(4.41421 - 7.64564i) q^{46} +(3.12132 + 5.40629i) q^{47} +1.00000 q^{48} -1.00000 q^{50} +(2.70711 + 4.68885i) q^{51} +(-2.82843 + 4.89898i) q^{52} +(-5.82843 + 10.0951i) q^{53} +(0.500000 + 0.866025i) q^{54} +6.24264 q^{55} +1.17157 q^{57} +(2.70711 + 4.68885i) q^{58} +(-4.41421 + 7.64564i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-0.171573 - 0.297173i) q^{61} -1.75736 q^{62} +1.00000 q^{64} +(2.82843 + 4.89898i) q^{65} +(-3.12132 + 5.40629i) q^{66} +(2.53553 - 4.39167i) q^{67} +(2.70711 + 4.68885i) q^{68} +8.82843 q^{69} +12.4853 q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(4.12132 - 7.13834i) q^{74} +(-0.500000 - 0.866025i) q^{75} +1.17157 q^{76} -5.65685 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.24264 + 5.61642i) q^{82} -10.8284 q^{83} +5.41421 q^{85} +(-2.53553 - 4.39167i) q^{86} +(-2.70711 + 4.68885i) q^{87} +(-3.12132 + 5.40629i) q^{88} +(2.41421 + 4.18154i) q^{89} +1.00000 q^{90} +8.82843 q^{92} +(-0.878680 - 1.52192i) q^{93} +(-3.12132 + 5.40629i) q^{94} +(0.585786 - 1.01461i) q^{95} +(0.500000 + 0.866025i) q^{96} -10.4853 q^{97} -6.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} - 8 q^{19} - 4 q^{20} + 8 q^{22} - 12 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{27} + 16 q^{29} - 2 q^{30} - 12 q^{31} + 2 q^{32} + 4 q^{33} + 16 q^{34} + 4 q^{36} - 8 q^{37} + 8 q^{38} - 2 q^{40} - 8 q^{41} + 8 q^{43} + 4 q^{44} + 2 q^{45} + 12 q^{46} + 4 q^{47} + 4 q^{48} - 4 q^{50} + 8 q^{51} - 12 q^{53} + 2 q^{54} + 8 q^{55} + 16 q^{57} + 8 q^{58} - 12 q^{59} + 2 q^{60} - 12 q^{61} - 24 q^{62} + 4 q^{64} - 4 q^{66} - 4 q^{67} + 8 q^{68} + 24 q^{69} + 16 q^{71} + 2 q^{72} - 4 q^{73} + 8 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{79} + 2 q^{80} - 2 q^{81} - 4 q^{82} - 32 q^{83} + 16 q^{85} + 4 q^{86} - 8 q^{87} - 4 q^{88} + 4 q^{89} + 4 q^{90} + 24 q^{92} - 12 q^{93} - 4 q^{94} + 8 q^{95} + 2 q^{96} - 8 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 - 4 * q^15 - 2 * q^16 + 8 * q^17 + 2 * q^18 - 8 * q^19 - 4 * q^20 + 8 * q^22 - 12 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^27 + 16 * q^29 - 2 * q^30 - 12 * q^31 + 2 * q^32 + 4 * q^33 + 16 * q^34 + 4 * q^36 - 8 * q^37 + 8 * q^38 - 2 * q^40 - 8 * q^41 + 8 * q^43 + 4 * q^44 + 2 * q^45 + 12 * q^46 + 4 * q^47 + 4 * q^48 - 4 * q^50 + 8 * q^51 - 12 * q^53 + 2 * q^54 + 8 * q^55 + 16 * q^57 + 8 * q^58 - 12 * q^59 + 2 * q^60 - 12 * q^61 - 24 * q^62 + 4 * q^64 - 4 * q^66 - 4 * q^67 + 8 * q^68 + 24 * q^69 + 16 * q^71 + 2 * q^72 - 4 * q^73 + 8 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^79 + 2 * q^80 - 2 * q^81 - 4 * q^82 - 32 * q^83 + 16 * q^85 + 4 * q^86 - 8 * q^87 - 4 * q^88 + 4 * q^89 + 4 * q^90 + 24 * q^92 - 12 * q^93 - 4 * q^94 + 8 * q^95 + 2 * q^96 - 8 * q^97 - 8 * 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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	3.12132	−	5.40629i	0.941113	−	1.63006i	0.177762	−	0.984074i	$-0.443114\pi$
$11$	3.12132	−	5.40629i	0.941113	−	1.63006i	0.763352	−	0.645983i	$-0.223552\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	5.65685			1.56893			0.784465	−	0.620174i	$-0.212938\pi$
$13$	5.65685			1.56893			0.784465	+	0.620174i	$0.212938\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.70711	−	4.68885i	0.656570	−	1.13721i	−0.324928	−	0.945739i	$-0.605340\pi$
$17$	2.70711	−	4.68885i	0.656570	−	1.13721i	0.981498	−	0.191474i	$-0.0613266\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−0.585786	−	1.01461i	−0.134389	−	0.232768i	0.790975	−	0.611848i	$-0.209574\pi$
$19$	−0.585786	−	1.01461i	−0.134389	−	0.232768i	−0.925364	+	0.379080i	$0.876240\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	6.24264			1.33094
$23$	−4.41421	−	7.64564i	−0.920427	−	1.59423i	−0.798755	−	0.601656i	$-0.794508\pi$
$23$	−4.41421	−	7.64564i	−0.920427	−	1.59423i	−0.121672	−	0.992570i	$-0.538826\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.82843	+	4.89898i	0.554700	+	0.960769i
$27$	1.00000			0.192450
$28$		0			0
$29$	5.41421			1.00539			0.502697	−	0.864463i	$-0.332341\pi$
$29$	5.41421			1.00539			0.502697	+	0.864463i	$0.332341\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−0.878680	+	1.52192i	−0.157816	+	0.273345i	−0.934081	−	0.357062i	$-0.883778\pi$
$31$	−0.878680	+	1.52192i	−0.157816	+	0.273345i	0.776265	+	0.630407i	$0.217112\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.12132	+	5.40629i	0.543352	+	0.941113i
$34$	5.41421			0.928530
$35$		0			0
$36$	1.00000			0.166667
$37$	−4.12132	−	7.13834i	−0.677541	−	1.17354i	−0.975719	−	0.219025i	$-0.929712\pi$
$37$	−4.12132	−	7.13834i	−0.677541	−	1.17354i	0.298178	−	0.954510i	$-0.403621\pi$
$38$	0.585786	−	1.01461i	0.0950271	−	0.164592i
$39$	−2.82843	+	4.89898i	−0.452911	+	0.784465i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	6.48528			1.01283			0.506415	−	0.862290i	$-0.330970\pi$
$41$	6.48528			1.01283			0.506415	+	0.862290i	$0.330970\pi$
$42$		0			0
$43$	−5.07107			−0.773331			−0.386665	−	0.922220i	$-0.626373\pi$
$43$	−5.07107			−0.773331			−0.386665	+	0.922220i	$0.626373\pi$
$44$	3.12132	+	5.40629i	0.470557	+	0.815028i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	4.41421	−	7.64564i	0.650840	−	1.12729i
$47$	3.12132	+	5.40629i	0.455291	+	0.788588i	0.998705	−	0.0508774i	$-0.0162018\pi$
$47$	3.12132	+	5.40629i	0.455291	+	0.788588i	−0.543414	+	0.839465i	$0.682868\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$	2.70711	+	4.68885i	0.379071	+	0.656570i
$52$	−2.82843	+	4.89898i	−0.392232	+	0.679366i
$53$	−5.82843	+	10.0951i	−0.800596	+	1.38667i	0.118628	+	0.992939i	$0.462150\pi$
$53$	−5.82843	+	10.0951i	−0.800596	+	1.38667i	−0.919224	+	0.393734i	$0.871183\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	6.24264			0.841757
$56$		0			0
$57$	1.17157			0.155179
$58$	2.70711	+	4.68885i	0.355461	+	0.615676i
$59$	−4.41421	+	7.64564i	−0.574682	+	0.995378i	0.421394	+	0.906877i	$0.361541\pi$
$59$	−4.41421	+	7.64564i	−0.574682	+	0.995378i	−0.996076	+	0.0885004i	$0.971793\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	−0.171573	−	0.297173i	−0.0219677	−	0.0380491i	0.854833	−	0.518904i	$-0.173660\pi$
$61$	−0.171573	−	0.297173i	−0.0219677	−	0.0380491i	−0.876800	+	0.480855i	$0.840326\pi$
$62$	−1.75736			−0.223185
$63$		0			0
$64$	1.00000			0.125000
$65$	2.82843	+	4.89898i	0.350823	+	0.607644i
$66$	−3.12132	+	5.40629i	−0.384208	+	0.665468i
$67$	2.53553	−	4.39167i	0.309765	−	0.536528i	−0.668546	−	0.743671i	$-0.733083\pi$
$67$	2.53553	−	4.39167i	0.309765	−	0.536528i	0.978311	+	0.207142i	$0.0664164\pi$
$68$	2.70711	+	4.68885i	0.328285	+	0.568606i
$69$	8.82843			1.06282
$70$		0			0
$71$	12.4853			1.48173			0.740865	−	0.671654i	$-0.234416\pi$
$71$	12.4853			1.48173			0.740865	+	0.671654i	$0.234416\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	4.12132	−	7.13834i	0.479094	−	0.829815i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	1.17157			0.134389
$77$		0			0
$78$	−5.65685			−0.640513
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.24264	+	5.61642i	0.358090	+	0.620230i
$83$	−10.8284			−1.18857			−0.594287	−	0.804253i	$-0.702566\pi$
$83$	−10.8284			−1.18857			−0.594287	+	0.804253i	$0.702566\pi$
$84$		0			0
$85$	5.41421			0.587254
$86$	−2.53553	−	4.39167i	−0.273414	−	0.473566i
$87$	−2.70711	+	4.68885i	−0.290232	+	0.502697i
$88$	−3.12132	+	5.40629i	−0.332734	+	0.576312i
$89$	2.41421	+	4.18154i	0.255906	+	0.443242i	0.965141	−	0.261730i	$-0.0842929\pi$
$89$	2.41421	+	4.18154i	0.255906	+	0.443242i	−0.709235	+	0.704972i	$0.750960\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	8.82843			0.920427
$93$	−0.878680	−	1.52192i	−0.0911148	−	0.157816i
$94$	−3.12132	+	5.40629i	−0.321940	+	0.557616i
$95$	0.585786	−	1.01461i	0.0601004	−	0.104097i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−10.4853			−1.06462			−0.532310	−	0.846550i	$-0.678676\pi$
$97$	−10.4853			−1.06462			−0.532310	+	0.846550i	$0.678676\pi$
$98$		0			0
$99$	−6.24264			−0.627409
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.17157	−	5.49333i	0.315583	−	0.546606i	−0.663978	−	0.747752i	$-0.731133\pi$
$101$	3.17157	−	5.49333i	0.315583	−	0.546606i	0.979561	+	0.201146i	$0.0644665\pi$
$102$	−2.70711	+	4.68885i	−0.268044	+	0.464265i
$103$	4.58579	+	7.94282i	0.451851	+	0.782629i	0.998501	−	0.0547323i	$-0.0174305\pi$
$103$	4.58579	+	7.94282i	0.451851	+	0.782629i	−0.546650	+	0.837361i	$0.684097\pi$
$104$	−5.65685			−0.554700
$105$		0			0
$106$	−11.6569			−1.13221
$107$	0.828427	+	1.43488i	0.0800871	+	0.138715i	0.903287	−	0.429036i	$-0.141147\pi$
$107$	0.828427	+	1.43488i	0.0800871	+	0.138715i	−0.823200	+	0.567751i	$0.807813\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−3.82843	+	6.63103i	−0.366697	+	0.635138i	−0.989047	−	0.147601i	$-0.952845\pi$
$109$	−3.82843	+	6.63103i	−0.366697	+	0.635138i	0.622350	+	0.782739i	$0.286178\pi$
$110$	3.12132	+	5.40629i	0.297606	+	0.515469i
$111$	8.24264			0.782357
$112$		0			0
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	0.585786	+	1.01461i	0.0548639	+	0.0950271i
$115$	4.41421	−	7.64564i	0.411628	−	0.712960i
$116$	−2.70711	+	4.68885i	−0.251349	+	0.435348i
$117$	−2.82843	−	4.89898i	−0.261488	−	0.452911i
$118$	−8.82843			−0.812723
$119$		0			0
$120$	1.00000			0.0912871
$121$	−13.9853	−	24.2232i	−1.27139	−	2.20211i
$122$	0.171573	−	0.297173i	0.0155335	−	0.0269048i
$123$	−3.24264	+	5.61642i	−0.292379	+	0.506415i
$124$	−0.878680	−	1.52192i	−0.0789078	−	0.136672i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.82843			−0.250982			−0.125491	−	0.992095i	$-0.540051\pi$
$127$	−2.82843			−0.250982			−0.125491	+	0.992095i	$0.540051\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	2.53553	−	4.39167i	0.223241	−	0.386665i
$130$	−2.82843	+	4.89898i	−0.248069	+	0.429669i
$131$	−4.41421	−	7.64564i	−0.385672	−	0.668003i	0.606190	−	0.795319i	$-0.292697\pi$
$131$	−4.41421	−	7.64564i	−0.385672	−	0.668003i	−0.991862	+	0.127317i	$0.959364\pi$
$132$	−6.24264			−0.543352
$133$		0			0
$134$	5.07107			0.438074
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−2.70711	+	4.68885i	−0.232132	+	0.402065i
$137$	−1.17157	+	2.02922i	−0.100094	+	0.173368i	−0.911723	−	0.410805i	$-0.865248\pi$
$137$	−1.17157	+	2.02922i	−0.100094	+	0.173368i	0.811629	+	0.584173i	$0.198581\pi$
$138$	4.41421	+	7.64564i	0.375763	+	0.650840i
$139$	13.6569			1.15836			0.579180	−	0.815200i	$-0.303373\pi$
$139$	13.6569			1.15836			0.579180	+	0.815200i	$0.303373\pi$
$140$		0			0
$141$	−6.24264			−0.525725
$142$	6.24264	+	10.8126i	0.523871	+	0.907371i
$143$	17.6569	−	30.5826i	1.47654	−	2.55744i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.70711	+	4.68885i	0.224813	+	0.389388i
$146$	−2.00000			−0.165521
$147$		0			0
$148$	8.24264			0.677541
$149$	7.19239	+	12.4576i	0.589223	+	1.02056i	0.994334	+	0.106297i	$0.0338995\pi$
$149$	7.19239	+	12.4576i	0.589223	+	1.02056i	−0.405111	+	0.914268i	$0.632767\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	4.07107	−	7.05130i	0.331299	−	0.573826i	−0.651468	−	0.758676i	$-0.725847\pi$
$151$	4.07107	−	7.05130i	0.331299	−	0.573826i	0.982767	+	0.184850i	$0.0591799\pi$
$152$	0.585786	+	1.01461i	0.0475136	+	0.0822959i
$153$	−5.41421			−0.437713
$154$		0			0
$155$	−1.75736			−0.141154
$156$	−2.82843	−	4.89898i	−0.226455	−	0.392232i
$157$	−9.82843	+	17.0233i	−0.784394	+	1.35861i	0.144967	+	0.989437i	$0.453693\pi$
$157$	−9.82843	+	17.0233i	−0.784394	+	1.35861i	−0.929360	+	0.369174i	$0.879641\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$	−5.82843	−	10.0951i	−0.462224	−	0.800596i
$160$	1.00000			0.0790569
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	1.46447	+	2.53653i	0.114706	+	0.198676i	0.917662	−	0.397362i	$-0.130074\pi$
$163$	1.46447	+	2.53653i	0.114706	+	0.198676i	−0.802956	+	0.596038i	$0.796741\pi$
$164$	−3.24264	+	5.61642i	−0.253208	+	0.438569i
$165$	−3.12132	+	5.40629i	−0.242994	+	0.420879i
$166$	−5.41421	−	9.37769i	−0.420224	−	0.727850i
$167$	6.24264			0.483070			0.241535	−	0.970392i	$-0.422349\pi$
$167$	6.24264			0.483070			0.241535	+	0.970392i	$0.422349\pi$
$168$		0			0
$169$	19.0000			1.46154
$170$	2.70711	+	4.68885i	0.207626	+	0.359618i
$171$	−0.585786	+	1.01461i	−0.0447962	+	0.0775893i
$172$	2.53553	−	4.39167i	0.193333	−	0.334862i
$173$	7.58579	+	13.1390i	0.576737	+	0.998937i	0.995851	+	0.0910035i	$0.0290075\pi$
$173$	7.58579	+	13.1390i	0.576737	+	0.998937i	−0.419114	+	0.907934i	$0.637659\pi$
$174$	−5.41421			−0.410450
$175$		0			0
$176$	−6.24264			−0.470557
$177$	−4.41421	−	7.64564i	−0.331793	−	0.574682i
$178$	−2.41421	+	4.18154i	−0.180953	+	0.313420i
$179$	−8.87868	+	15.3783i	−0.663624	+	1.14943i	0.316033	+	0.948748i	$0.397649\pi$
$179$	−8.87868	+	15.3783i	−0.663624	+	1.14943i	−0.979657	+	0.200682i	$0.935684\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−1.51472			−0.112588			−0.0562941	−	0.998414i	$-0.517928\pi$
$181$	−1.51472			−0.112588			−0.0562941	+	0.998414i	$0.517928\pi$
$182$		0			0
$183$	0.343146			0.0253661
$184$	4.41421	+	7.64564i	0.325420	+	0.563644i
$185$	4.12132	−	7.13834i	0.303005	−	0.524821i
$186$	0.878680	−	1.52192i	0.0644279	−	0.111592i
$187$	−16.8995	−	29.2708i	−1.23581	−	2.14049i
$188$	−6.24264			−0.455291
$189$		0			0
$190$	1.17157			0.0849948
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−0.414214	+	0.717439i	−0.0298157	+	0.0516424i	−0.880548	−	0.473957i	$-0.842825\pi$
$193$	−0.414214	+	0.717439i	−0.0298157	+	0.0516424i	0.850733	+	0.525599i	$0.176159\pi$
$194$	−5.24264	−	9.08052i	−0.376400	−	0.651943i
$195$	−5.65685			−0.405096
$196$		0			0
$197$	13.7990			0.983137			0.491569	−	0.870839i	$-0.336424\pi$
$197$	13.7990			0.983137			0.491569	+	0.870839i	$0.336424\pi$
$198$	−3.12132	−	5.40629i	−0.221823	−	0.384208i
$199$	−7.12132	+	12.3345i	−0.504817	+	0.874369i	0.495167	+	0.868798i	$0.335107\pi$
$199$	−7.12132	+	12.3345i	−0.504817	+	0.874369i	−0.999984	+	0.00557117i	$0.998227\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	2.53553	+	4.39167i	0.178843	+	0.309765i
$202$	6.34315			0.446302
$203$		0			0
$204$	−5.41421			−0.379071
$205$	3.24264	+	5.61642i	0.226476	+	0.392268i
$206$	−4.58579	+	7.94282i	−0.319507	+	0.553402i
$207$	−4.41421	+	7.64564i	−0.306809	+	0.531409i
$208$	−2.82843	−	4.89898i	−0.196116	−	0.339683i
$209$	−7.31371			−0.505900
$210$		0			0
$211$	−0.686292			−0.0472463			−0.0236231	−	0.999721i	$-0.507520\pi$
$211$	−0.686292			−0.0472463			−0.0236231	+	0.999721i	$0.507520\pi$
$212$	−5.82843	−	10.0951i	−0.400298	−	0.693337i
$213$	−6.24264	+	10.8126i	−0.427739	+	0.740865i
$214$	−0.828427	+	1.43488i	−0.0566301	+	0.0980862i
$215$	−2.53553	−	4.39167i	−0.172922	−	0.299510i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−7.65685			−0.518588
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$	−3.12132	+	5.40629i	−0.210439	+	0.364492i
$221$	15.3137	−	26.5241i	1.03011	−	1.78421i
$222$	4.12132	+	7.13834i	0.276605	+	0.479094i
$223$	−15.3137			−1.02548			−0.512741	−	0.858543i	$-0.671370\pi$
$223$	−15.3137			−1.02548			−0.512741	+	0.858543i	$0.671370\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	5.00000	+	8.66025i	0.332595	+	0.576072i
$227$	4.48528	−	7.76874i	0.297699	−	0.515629i	−0.677910	−	0.735144i	$-0.737114\pi$
$227$	4.48528	−	7.76874i	0.297699	−	0.515629i	0.975609	+	0.219515i	$0.0704476\pi$
$228$	−0.585786	+	1.01461i	−0.0387947	+	0.0671943i
$229$	6.07107	+	10.5154i	0.401187	+	0.694877i	0.993870	−	0.110559i	$-0.0352643\pi$
$229$	6.07107	+	10.5154i	0.401187	+	0.694877i	−0.592682	+	0.805437i	$0.701931\pi$
$230$	8.82843			0.582129
$231$		0			0
$232$	−5.41421			−0.355461
$233$	7.48528	+	12.9649i	0.490377	+	0.849358i	0.999939	−	0.0110762i	$-0.00352573\pi$
$233$	7.48528	+	12.9649i	0.490377	+	0.849358i	−0.509562	+	0.860434i	$0.670192\pi$
$234$	2.82843	−	4.89898i	0.184900	−	0.320256i
$235$	−3.12132	+	5.40629i	−0.203612	+	0.352667i
$236$	−4.41421	−	7.64564i	−0.287341	−	0.497689i
$237$	8.00000			0.519656
$238$		0			0
$239$	3.31371			0.214346			0.107173	−	0.994240i	$-0.465820\pi$
$239$	3.31371			0.214346			0.107173	+	0.994240i	$0.465820\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	5.77817	−	10.0081i	0.372205	−	0.644678i	−0.617699	−	0.786414i	$-0.711935\pi$
$241$	5.77817	−	10.0081i	0.372205	−	0.644678i	0.989904	+	0.141736i	$0.0452685\pi$
$242$	13.9853	−	24.2232i	0.899008	−	1.55713i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.343146			0.0219677
$245$		0			0
$246$	−6.48528			−0.413486
$247$	−3.31371	−	5.73951i	−0.210846	−	0.365196i
$248$	0.878680	−	1.52192i	0.0557962	−	0.0966419i
$249$	5.41421	−	9.37769i	0.343112	−	0.594287i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−20.9706			−1.32365			−0.661825	−	0.749658i	$-0.730218\pi$
$251$	−20.9706			−1.32365			−0.661825	+	0.749658i	$0.730218\pi$
$252$		0			0
$253$	−55.1127			−3.46491
$254$	−1.41421	−	2.44949i	−0.0887357	−	0.153695i
$255$	−2.70711	+	4.68885i	−0.169526	+	0.293627i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.7071	−	18.5453i	−0.667891	−	1.15682i	−0.978493	−	0.206281i	$-0.933864\pi$
$257$	−10.7071	−	18.5453i	−0.667891	−	1.15682i	0.310602	−	0.950540i	$-0.399469\pi$
$258$	5.07107			0.315711
$259$		0			0
$260$	−5.65685			−0.350823
$261$	−2.70711	−	4.68885i	−0.167566	−	0.290232i
$262$	4.41421	−	7.64564i	0.272711	−	0.472349i
$263$	−8.07107	+	13.9795i	−0.497683	+	0.862013i	−0.999996	−	0.00267296i	$-0.999149\pi$
$263$	−8.07107	+	13.9795i	−0.497683	+	0.862013i	0.502313	+	0.864686i	$0.332483\pi$
$264$	−3.12132	−	5.40629i	−0.192104	−	0.332734i
$265$	−11.6569			−0.716075
$266$		0			0
$267$	−4.82843			−0.295495
$268$	2.53553	+	4.39167i	0.154882	+	0.268264i
$269$	11.8284	−	20.4874i	0.721192	−	1.24914i	−0.239330	−	0.970938i	$-0.576928\pi$
$269$	11.8284	−	20.4874i	0.721192	−	1.24914i	0.960522	−	0.278203i	$-0.0897388\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−13.8492	−	23.9876i	−0.841282	−	1.45714i	−0.888812	−	0.458273i	$-0.848468\pi$
$271$	−13.8492	−	23.9876i	−0.841282	−	1.45714i	0.0475301	−	0.998870i	$-0.484865\pi$
$272$	−5.41421			−0.328285
$273$		0			0
$274$	−2.34315			−0.141555
$275$	3.12132	+	5.40629i	0.188223	+	0.326011i
$276$	−4.41421	+	7.64564i	−0.265704	+	0.460214i
$277$	−7.77817	+	13.4722i	−0.467345	+	0.809466i	−0.999304	−	0.0373046i	$-0.988123\pi$
$277$	−7.77817	+	13.4722i	−0.467345	+	0.809466i	0.531959	+	0.846770i	$0.321456\pi$
$278$	6.82843	+	11.8272i	0.409542	+	0.709347i
$279$	1.75736			0.105210
$280$		0			0
$281$	27.4558			1.63788			0.818939	−	0.573880i	$-0.194563\pi$
$281$	27.4558			1.63788			0.818939	+	0.573880i	$0.194563\pi$
$282$	−3.12132	−	5.40629i	−0.185872	−	0.321940i
$283$	13.2426	−	22.9369i	0.787193	−	1.36346i	−0.140487	−	0.990083i	$-0.544867\pi$
$283$	13.2426	−	22.9369i	0.787193	−	1.36346i	0.927680	−	0.373376i	$-0.121800\pi$
$284$	−6.24264	+	10.8126i	−0.370433	+	0.641608i
$285$	0.585786	+	1.01461i	0.0346990	+	0.0601004i
$286$	35.3137			2.08814
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−6.15685	−	10.6640i	−0.362168	−	0.627293i
$290$	−2.70711	+	4.68885i	−0.158967	+	0.275339i
$291$	5.24264	−	9.08052i	0.307329	−	0.532310i
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	1.31371			0.0767477			0.0383738	−	0.999263i	$-0.487782\pi$
$293$	1.31371			0.0767477			0.0383738	+	0.999263i	$0.487782\pi$
$294$		0			0
$295$	−8.82843			−0.514011
$296$	4.12132	+	7.13834i	0.239547	+	0.414907i
$297$	3.12132	−	5.40629i	0.181117	−	0.313704i
$298$	−7.19239	+	12.4576i	−0.416644	+	0.721648i
$299$	−24.9706	−	43.2503i	−1.44408	−	2.50123i
$300$	1.00000			0.0577350
$301$		0			0
$302$	8.14214			0.468527
$303$	3.17157	+	5.49333i	0.182202	+	0.315583i
$304$	−0.585786	+	1.01461i	−0.0335972	+	0.0581920i
$305$	0.171573	−	0.297173i	0.00982423	−	0.0170161i
$306$	−2.70711	−	4.68885i	−0.154755	−	0.268044i
$307$	−15.3137			−0.874000			−0.437000	−	0.899462i	$-0.643959\pi$
$307$	−15.3137			−0.874000			−0.437000	+	0.899462i	$0.643959\pi$
$308$		0			0
$309$	−9.17157			−0.521753
$310$	−0.878680	−	1.52192i	−0.0499057	−	0.0864391i
$311$	−2.58579	+	4.47871i	−0.146626	+	0.253965i	−0.929979	−	0.367614i	$-0.880175\pi$
$311$	−2.58579	+	4.47871i	−0.146626	+	0.253965i	0.783352	+	0.621578i	$0.213508\pi$
$312$	2.82843	−	4.89898i	0.160128	−	0.277350i
$313$	6.75736	+	11.7041i	0.381949	+	0.661554i	0.991341	−	0.131315i	$-0.0419198\pi$
$313$	6.75736	+	11.7041i	0.381949	+	0.661554i	−0.609392	+	0.792869i	$0.708586\pi$
$314$	−19.6569			−1.10930
$315$		0			0
$316$	8.00000			0.450035
$317$	1.34315	+	2.32640i	0.0754386	+	0.130663i	0.901277	−	0.433243i	$-0.142631\pi$
$317$	1.34315	+	2.32640i	0.0754386	+	0.130663i	−0.825838	+	0.563907i	$0.809298\pi$
$318$	5.82843	−	10.0951i	0.326842	−	0.566107i
$319$	16.8995	−	29.2708i	0.946190	−	1.63885i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−1.65685			−0.0924766
$322$		0			0
$323$	−6.34315			−0.352942
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−2.82843	+	4.89898i	−0.156893	+	0.271746i
$326$	−1.46447	+	2.53653i	−0.0811093	+	0.140485i
$327$	−3.82843	−	6.63103i	−0.211713	−	0.366697i
$328$	−6.48528			−0.358090
$329$		0			0
$330$	−6.24264			−0.343646
$331$	8.82843	+	15.2913i	0.485254	+	0.840485i	0.999856	−	0.0169441i	$-0.00539372\pi$
$331$	8.82843	+	15.2913i	0.485254	+	0.840485i	−0.514602	+	0.857429i	$0.672060\pi$
$332$	5.41421	−	9.37769i	0.297144	−	0.514668i
$333$	−4.12132	+	7.13834i	−0.225847	+	0.391178i
$334$	3.12132	+	5.40629i	0.170791	+	0.295819i
$335$	5.07107			0.277062
$336$		0			0
$337$	−29.1127			−1.58587			−0.792935	−	0.609306i	$-0.791448\pi$
$337$	−29.1127			−1.58587			−0.792935	+	0.609306i	$0.791448\pi$
$338$	9.50000	+	16.4545i	0.516732	+	0.895006i
$339$	−5.00000	+	8.66025i	−0.271563	+	0.470360i
$340$	−2.70711	+	4.68885i	−0.146813	+	0.254288i
$341$	5.48528	+	9.50079i	0.297045	+	0.514496i
$342$	−1.17157			−0.0633514
$343$		0			0
$344$	5.07107			0.273414
$345$	4.41421	+	7.64564i	0.237653	+	0.411628i
$346$	−7.58579	+	13.1390i	−0.407814	+	0.706355i
$347$	16.8284	−	29.1477i	0.903397	−	1.56473i	0.0803430	−	0.996767i	$-0.474398\pi$
$347$	16.8284	−	29.1477i	0.903397	−	1.56473i	0.823054	−	0.567963i	$-0.192268\pi$
$348$	−2.70711	−	4.68885i	−0.145116	−	0.251349i
$349$	27.4558			1.46968			0.734839	−	0.678242i	$-0.237258\pi$
$349$	27.4558			1.46968			0.734839	+	0.678242i	$0.237258\pi$
$350$		0			0
$351$	5.65685			0.301941
$352$	−3.12132	−	5.40629i	−0.166367	−	0.288156i
$353$	−16.0208	+	27.7489i	−0.852702	+	1.47692i	0.0260587	+	0.999660i	$0.491704\pi$
$353$	−16.0208	+	27.7489i	−0.852702	+	1.47692i	−0.878761	+	0.477263i	$0.841629\pi$
$354$	4.41421	−	7.64564i	0.234613	−	0.406361i
$355$	6.24264	+	10.8126i	0.331325	+	0.573872i
$356$	−4.82843			−0.255906
$357$		0			0
$358$	−17.7574			−0.938506
$359$	5.75736	+	9.97204i	0.303862	+	0.526304i	0.977007	−	0.213206i	$-0.0683906\pi$
$359$	5.75736	+	9.97204i	0.303862	+	0.526304i	−0.673145	+	0.739510i	$0.735057\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	8.81371	−	15.2658i	0.463879	−	0.803463i
$362$	−0.757359	−	1.31178i	−0.0398059	−	0.0689459i
$363$	27.9706			1.46807
$364$		0			0
$365$	−2.00000			−0.104685
$366$	0.171573	+	0.297173i	0.00896826	+	0.0155335i
$367$	−2.58579	+	4.47871i	−0.134977	+	0.233787i	−0.925589	−	0.378531i	$-0.876429\pi$
$367$	−2.58579	+	4.47871i	−0.134977	+	0.233787i	0.790612	+	0.612318i	$0.209763\pi$
$368$	−4.41421	+	7.64564i	−0.230107	+	0.398557i
$369$	−3.24264	−	5.61642i	−0.168805	−	0.292379i
$370$	8.24264			0.428514
$371$		0			0
$372$	1.75736			0.0911148
$373$	−4.70711	−	8.15295i	−0.243725	−	0.422144i	0.718048	−	0.695994i	$-0.245036\pi$
$373$	−4.70711	−	8.15295i	−0.243725	−	0.422144i	−0.961772	+	0.273850i	$0.911703\pi$
$374$	16.8995	−	29.2708i	0.873852	−	1.51356i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−3.12132	−	5.40629i	−0.160970	−	0.278808i
$377$	30.6274			1.57739
$378$		0			0
$379$	−16.4853			−0.846792			−0.423396	−	0.905945i	$-0.639162\pi$
$379$	−16.4853			−0.846792			−0.423396	+	0.905945i	$0.639162\pi$
$380$	0.585786	+	1.01461i	0.0300502	+	0.0520485i
$381$	1.41421	−	2.44949i	0.0724524	−	0.125491i
$382$	2.00000	−	3.46410i	0.102329	−	0.177239i
$383$	8.29289	+	14.3637i	0.423747	+	0.733951i	0.996303	−	0.0859146i	$-0.0273812\pi$
$383$	8.29289	+	14.3637i	0.423747	+	0.733951i	−0.572555	+	0.819866i	$0.694048\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−0.828427			−0.0421658
$387$	2.53553	+	4.39167i	0.128888	+	0.223241i
$388$	5.24264	−	9.08052i	0.266155	−	0.460994i
$389$	5.05025	−	8.74729i	0.256058	−	0.443505i	−0.709124	−	0.705083i	$-0.750910\pi$
$389$	5.05025	−	8.74729i	0.256058	−	0.443505i	0.965182	+	0.261578i	$0.0842429\pi$
$390$	−2.82843	−	4.89898i	−0.143223	−	0.248069i
$391$	−47.7990			−2.41730
$392$		0			0
$393$	8.82843			0.445335
$394$	6.89949	+	11.9503i	0.347592	+	0.602046i
$395$	4.00000	−	6.92820i	0.201262	−	0.348596i
$396$	3.12132	−	5.40629i	0.156852	−	0.271676i
$397$	14.6569	+	25.3864i	0.735606	+	1.27411i	0.954457	+	0.298349i	$0.0964360\pi$
$397$	14.6569	+	25.3864i	0.735606	+	1.27411i	−0.218850	+	0.975758i	$0.570231\pi$
$398$	−14.2426			−0.713919
$399$		0			0
$400$	1.00000			0.0500000
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$	−2.53553	+	4.39167i	−0.126461	+	0.219037i
$403$	−4.97056	+	8.60927i	−0.247601	+	0.428858i
$404$	3.17157	+	5.49333i	0.157792	+	0.273303i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−51.4558			−2.55057
$408$	−2.70711	−	4.68885i	−0.134022	−	0.232132i
$409$	−2.12132	+	3.67423i	−0.104893	+	0.181679i	−0.913694	−	0.406402i	$-0.866783\pi$
$409$	−2.12132	+	3.67423i	−0.104893	+	0.181679i	0.808802	+	0.588081i	$0.200117\pi$
$410$	−3.24264	+	5.61642i	−0.160143	+	0.277375i
$411$	−1.17157	−	2.02922i	−0.0577894	−	0.100094i
$412$	−9.17157			−0.451851
$413$		0			0
$414$	−8.82843			−0.433894
$415$	−5.41421	−	9.37769i	−0.265773	−	0.460333i
$416$	2.82843	−	4.89898i	0.138675	−	0.240192i
$417$	−6.82843	+	11.8272i	−0.334390	+	0.579180i
$418$	−3.65685	−	6.33386i	−0.178863	−	0.309799i
$419$	3.02944			0.147998			0.0739988	−	0.997258i	$-0.476424\pi$
$419$	3.02944			0.147998			0.0739988	+	0.997258i	$0.476424\pi$
$420$		0			0
$421$	7.65685			0.373172			0.186586	−	0.982439i	$-0.440258\pi$
$421$	7.65685			0.373172			0.186586	+	0.982439i	$0.440258\pi$
$422$	−0.343146	−	0.594346i	−0.0167041	−	0.0289323i
$423$	3.12132	−	5.40629i	0.151764	−	0.262863i
$424$	5.82843	−	10.0951i	0.283053	−	0.490263i
$425$	2.70711	+	4.68885i	0.131314	+	0.227442i
$426$	−12.4853			−0.604914
$427$		0			0
$428$	−1.65685			−0.0800871
$429$	17.6569	+	30.5826i	0.852481	+	1.47654i
$430$	2.53553	−	4.39167i	0.122274	−	0.211785i
$431$	18.7279	−	32.4377i	0.902092	−	1.56247i	0.0773187	−	0.997006i	$-0.475364\pi$
$431$	18.7279	−	32.4377i	0.902092	−	1.56247i	0.824774	−	0.565463i	$-0.191303\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−21.7990			−1.04759			−0.523796	−	0.851844i	$-0.675485\pi$
$433$	−21.7990			−1.04759			−0.523796	+	0.851844i	$0.675485\pi$
$434$		0			0
$435$	−5.41421			−0.259592
$436$	−3.82843	−	6.63103i	−0.183348	−	0.317569i
$437$	−5.17157	+	8.95743i	−0.247390	+	0.428492i
$438$	1.00000	−	1.73205i	0.0477818	−	0.0827606i
$439$	17.8492	+	30.9158i	0.851898	+	1.47553i	0.879493	+	0.475911i	$0.157882\pi$
$439$	17.8492	+	30.9158i	0.851898	+	1.47553i	−0.0275955	+	0.999619i	$0.508785\pi$
$440$	−6.24264			−0.297606
$441$		0			0
$442$	30.6274			1.45680
$443$	10.1421	+	17.5667i	0.481867	+	0.834619i	0.999783	−	0.0208127i	$-0.00662535\pi$
$443$	10.1421	+	17.5667i	0.481867	+	0.834619i	−0.517916	+	0.855431i	$0.673292\pi$
$444$	−4.12132	+	7.13834i	−0.195589	+	0.338770i
$445$	−2.41421	+	4.18154i	−0.114445	+	0.198224i
$446$	−7.65685	−	13.2621i	−0.362563	−	0.627977i
$447$	−14.3848			−0.680377
$448$		0			0
$449$	6.48528			0.306059			0.153030	−	0.988222i	$-0.451097\pi$
$449$	6.48528			0.306059			0.153030	+	0.988222i	$0.451097\pi$
$450$	0.500000	+	0.866025i	0.0235702	+	0.0408248i
$451$	20.2426	−	35.0613i	0.953189	−	1.65097i
$452$	−5.00000	+	8.66025i	−0.235180	+	0.407344i
$453$	4.07107	+	7.05130i	0.191275	+	0.331299i
$454$	8.97056			0.421009
$455$		0			0
$456$	−1.17157			−0.0548639
$457$	7.24264	+	12.5446i	0.338796	+	0.586813i	0.984207	−	0.177024i	$-0.0566469\pi$
$457$	7.24264	+	12.5446i	0.338796	+	0.586813i	−0.645410	+	0.763836i	$0.723314\pi$
$458$	−6.07107	+	10.5154i	−0.283682	+	0.491352i
$459$	2.70711	−	4.68885i	0.126357	−	0.218857i
$460$	4.41421	+	7.64564i	0.205814	+	0.356480i
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$		0			0
$463$	−14.3431			−0.666583			−0.333291	−	0.942824i	$-0.608159\pi$
$463$	−14.3431			−0.666583			−0.333291	+	0.942824i	$0.608159\pi$
$464$	−2.70711	−	4.68885i	−0.125674	−	0.217674i
$465$	0.878680	−	1.52192i	0.0407478	−	0.0705772i
$466$	−7.48528	+	12.9649i	−0.346749	+	0.600587i
$467$	−2.24264	−	3.88437i	−0.103777	−	0.179747i	0.809461	−	0.587174i	$-0.199760\pi$
$467$	−2.24264	−	3.88437i	−0.103777	−	0.179747i	−0.913238	+	0.407427i	$0.866426\pi$
$468$	5.65685			0.261488
$469$		0			0
$470$	−6.24264			−0.287952
$471$	−9.82843	−	17.0233i	−0.452870	−	0.784394i
$472$	4.41421	−	7.64564i	0.203181	−	0.351919i
$473$	−15.8284	+	27.4156i	−0.727792	+	1.26057i
$474$	4.00000	+	6.92820i	0.183726	+	0.318223i
$475$	1.17157			0.0537555
$476$		0			0
$477$	11.6569			0.533731
$478$	1.65685	+	2.86976i	0.0757827	+	0.131260i
$479$	4.24264	−	7.34847i	0.193851	−	0.335760i	−0.752672	−	0.658396i	$-0.771235\pi$
$479$	4.24264	−	7.34847i	0.193851	−	0.335760i	0.946523	+	0.322635i	$0.104569\pi$
$480$	−0.500000	+	0.866025i	−0.0228218	+	0.0395285i
$481$	−23.3137	−	40.3805i	−1.06301	−	1.84119i
$482$	11.5563			0.526377
$483$		0			0
$484$	27.9706			1.27139
$485$	−5.24264	−	9.08052i	−0.238056	−	0.412325i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−2.58579	+	4.47871i	−0.117173	+	0.202950i	−0.918646	−	0.395081i	$-0.870717\pi$
$487$	−2.58579	+	4.47871i	−0.117173	+	0.202950i	0.801473	+	0.598031i	$0.204050\pi$
$488$	0.171573	+	0.297173i	0.00776674	+	0.0134524i
$489$	−2.92893			−0.132451
$490$		0			0
$491$	−2.92893			−0.132181			−0.0660904	−	0.997814i	$-0.521053\pi$
$491$	−2.92893			−0.132181			−0.0660904	+	0.997814i	$0.521053\pi$
$492$	−3.24264	−	5.61642i	−0.146190	−	0.253208i
$493$	14.6569	−	25.3864i	0.660112	−	1.14335i
$494$	3.31371	−	5.73951i	0.149091	−	0.258233i
$495$	−3.12132	−	5.40629i	−0.140293	−	0.242994i
$496$	1.75736			0.0789078
$497$		0			0
$498$	10.8284			0.485233
$499$	−0.585786	−	1.01461i	−0.0262234	−	0.0454203i	0.852616	−	0.522538i	$-0.175015\pi$
$499$	−0.585786	−	1.01461i	−0.0262234	−	0.0454203i	−0.878839	+	0.477118i	$0.841681\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−3.12132	+	5.40629i	−0.139450	+	0.241535i
$502$	−10.4853	−	18.1610i	−0.467981	−	0.810567i
$503$	7.41421			0.330583			0.165292	−	0.986245i	$-0.447143\pi$
$503$	7.41421			0.330583			0.165292	+	0.986245i	$0.447143\pi$
$504$		0			0
$505$	6.34315			0.282266
$506$	−27.5563	−	47.7290i	−1.22503	−	2.12181i
$507$	−9.50000	+	16.4545i	−0.421910	+	0.730769i
$508$	1.41421	−	2.44949i	0.0627456	−	0.108679i
$509$	8.48528	+	14.6969i	0.376103	+	0.651430i	0.990492	−	0.137574i	$-0.0439304\pi$
$509$	8.48528	+	14.6969i	0.376103	+	0.651430i	−0.614388	+	0.789004i	$0.710597\pi$
$510$	−5.41421			−0.239745
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−0.585786	−	1.01461i	−0.0258631	−	0.0447962i
$514$	10.7071	−	18.5453i	0.472270	−	0.817996i
$515$	−4.58579	+	7.94282i	−0.202074	+	0.350002i
$516$	2.53553	+	4.39167i	0.111621	+	0.193333i
$517$	38.9706			1.71392
$518$		0			0
$519$	−15.1716			−0.665958
$520$	−2.82843	−	4.89898i	−0.124035	−	0.214834i
$521$	−17.3848	+	30.1113i	−0.761641	+	1.31920i	0.180363	+	0.983600i	$0.442273\pi$
$521$	−17.3848	+	30.1113i	−0.761641	+	1.31920i	−0.942004	+	0.335601i	$0.891061\pi$
$522$	2.70711	−	4.68885i	0.118487	−	0.205225i
$523$	1.10051	+	1.90613i	0.0481217	+	0.0833493i	0.889083	−	0.457746i	$-0.151343\pi$
$523$	1.10051	+	1.90613i	0.0481217	+	0.0833493i	−0.840961	+	0.541095i	$0.818010\pi$
$524$	8.82843			0.385672
$525$		0			0
$526$	−16.1421			−0.703831
$527$	4.75736	+	8.23999i	0.207234	+	0.358940i
$528$	3.12132	−	5.40629i	0.135838	−	0.235278i
$529$	−27.4706	+	47.5804i	−1.19437	+	2.06871i
$530$	−5.82843	−	10.0951i	−0.253171	−	0.438505i
$531$	8.82843			0.383121
$532$		0			0
$533$	36.6863			1.58906
$534$	−2.41421	−	4.18154i	−0.104473	−	0.180953i
$535$	−0.828427	+	1.43488i	−0.0358160	+	0.0620352i
$536$	−2.53553	+	4.39167i	−0.109518	+	0.189691i
$537$	−8.87868	−	15.3783i	−0.383143	−	0.663624i
$538$	23.6569			1.01992
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	−4.89949	−	8.48617i	−0.210646	−	0.364849i	0.741271	−	0.671206i	$-0.234223\pi$
$541$	−4.89949	−	8.48617i	−0.210646	−	0.364849i	−0.951917	+	0.306357i	$0.900890\pi$
$542$	13.8492	−	23.9876i	0.594876	−	1.03036i
$543$	0.757359	−	1.31178i	0.0325014	−	0.0562941i
$544$	−2.70711	−	4.68885i	−0.116066	−	0.201033i
$545$	−7.65685			−0.327984
$546$		0			0
$547$	8.38478			0.358507			0.179254	−	0.983803i	$-0.442632\pi$
$547$	8.38478			0.358507			0.179254	+	0.983803i	$0.442632\pi$
$548$	−1.17157	−	2.02922i	−0.0500471	−	0.0866841i
$549$	−0.171573	+	0.297173i	−0.00732255	+	0.0126830i
$550$	−3.12132	+	5.40629i	−0.133094	+	0.230525i
$551$	−3.17157	−	5.49333i	−0.135114	−	0.234024i
$552$	−8.82843			−0.375763
$553$		0			0
$554$	−15.5563			−0.660926
$555$	4.12132	+	7.13834i	0.174940	+	0.303005i
$556$	−6.82843	+	11.8272i	−0.289590	+	0.501584i
$557$	19.0000	−	32.9090i	0.805056	−	1.39440i	−0.111198	−	0.993798i	$-0.535469\pi$
$557$	19.0000	−	32.9090i	0.805056	−	1.39440i	0.916253	−	0.400599i	$-0.131198\pi$
$558$	0.878680	+	1.52192i	0.0371975	+	0.0644279i
$559$	−28.6863			−1.21330
$560$		0			0
$561$	33.7990			1.42699
$562$	13.7279	+	23.7775i	0.579077	+	1.00299i
$563$	−1.75736	+	3.04384i	−0.0740639	+	0.128282i	−0.900679	−	0.434486i	$-0.856930\pi$
$563$	−1.75736	+	3.04384i	−0.0740639	+	0.128282i	0.826615	+	0.562768i	$0.190264\pi$
$564$	3.12132	−	5.40629i	0.131431	−	0.227646i
$565$	5.00000	+	8.66025i	0.210352	+	0.364340i
$566$	26.4853			1.11326
$567$		0			0
$568$	−12.4853			−0.523871
$569$	−21.4853	−	37.2136i	−0.900710	−	1.56008i	−0.826575	−	0.562827i	$-0.809714\pi$
$569$	−21.4853	−	37.2136i	−0.900710	−	1.56008i	−0.0741351	−	0.997248i	$-0.523620\pi$
$570$	−0.585786	+	1.01461i	−0.0245359	+	0.0424974i
$571$	−13.6569	+	23.6544i	−0.571522	+	0.989904i	0.424888	+	0.905246i	$0.360313\pi$
$571$	−13.6569	+	23.6544i	−0.571522	+	0.989904i	−0.996410	+	0.0846587i	$0.973020\pi$
$572$	17.6569	+	30.5826i	0.738270	+	1.27872i
$573$	4.00000			0.167102
$574$		0			0
$575$	8.82843			0.368171
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−16.0711	+	27.8359i	−0.669047	+	1.15882i	0.309124	+	0.951022i	$0.399964\pi$
$577$	−16.0711	+	27.8359i	−0.669047	+	1.15882i	−0.978171	+	0.207802i	$0.933369\pi$
$578$	6.15685	−	10.6640i	0.256091	−	0.443563i
$579$	−0.414214	−	0.717439i	−0.0172141	−	0.0298157i
$580$	−5.41421			−0.224813
$581$		0			0
$582$	10.4853			0.434629
$583$	36.3848	+	63.0203i	1.50690	+	2.61003i
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$	2.82843	−	4.89898i	0.116941	−	0.202548i
$586$	0.656854	+	1.13770i	0.0271344	+	0.0469982i
$587$	10.8284			0.446937			0.223469	−	0.974711i	$-0.428262\pi$
$587$	10.8284			0.446937			0.223469	+	0.974711i	$0.428262\pi$
$588$		0			0
$589$	2.05887			0.0848344
$590$	−4.41421	−	7.64564i	−0.181730	−	0.314766i
$591$	−6.89949	+	11.9503i	−0.283807	+	0.491569i
$592$	−4.12132	+	7.13834i	−0.169385	+	0.293384i
$593$	0.606602	+	1.05066i	0.0249101	+	0.0431456i	0.878212	−	0.478272i	$-0.158737\pi$
$593$	0.606602	+	1.05066i	0.0249101	+	0.0431456i	−0.853302	+	0.521418i	$0.825403\pi$
$594$	6.24264			0.256139
$595$		0			0
$596$	−14.3848			−0.589223
$597$	−7.12132	−	12.3345i	−0.291456	−	0.504817i
$598$	24.9706	−	43.2503i	1.02112	−	1.76864i
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	−0.903988	−	0.427558i	$-0.859374\pi$
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	0.822270	+	0.569097i	$0.192707\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	40.2426			1.64153			0.820766	−	0.571265i	$-0.193547\pi$
$601$	40.2426			1.64153			0.820766	+	0.571265i	$0.193547\pi$
$602$		0			0
$603$	−5.07107			−0.206510
$604$	4.07107	+	7.05130i	0.165649	+	0.286913i
$605$	13.9853	−	24.2232i	0.568583	−	0.984814i
$606$	−3.17157	+	5.49333i	−0.128836	+	0.223151i
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	0.903756	−	0.428048i	$-0.140799\pi$
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	−0.822578	+	0.568652i	$0.807465\pi$
$608$	−1.17157			−0.0475136
$609$		0			0
$610$	0.343146			0.0138936
$611$	17.6569	+	30.5826i	0.714320	+	1.23724i
$612$	2.70711	−	4.68885i	0.109428	−	0.189535i
$613$	−1.53553	+	2.65962i	−0.0620196	+	0.107421i	−0.895368	−	0.445327i	$-0.853087\pi$
$613$	−1.53553	+	2.65962i	−0.0620196	+	0.107421i	0.833348	+	0.552748i	$0.186421\pi$
$614$	−7.65685	−	13.2621i	−0.309005	−	0.535213i
$615$	−6.48528			−0.261512
$616$		0			0
$617$	−33.9411			−1.36642			−0.683209	−	0.730223i	$-0.739416\pi$
$617$	−33.9411			−1.36642			−0.683209	+	0.730223i	$0.739416\pi$
$618$	−4.58579	−	7.94282i	−0.184467	−	0.319507i
$619$	−21.5563	+	37.3367i	−0.866423	+	1.50069i	−0.000795393		1.00000i	$0.500253\pi$
$619$	−21.5563	+	37.3367i	−0.866423	+	1.50069i	−0.865627	+	0.500689i	$0.833080\pi$
$620$	0.878680	−	1.52192i	0.0352886	−	0.0611217i
$621$	−4.41421	−	7.64564i	−0.177136	−	0.306809i
$622$	−5.17157			−0.207361
$623$		0			0
$624$	5.65685			0.226455
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−6.75736	+	11.7041i	−0.270078	+	0.467790i
$627$	3.65685	−	6.33386i	0.146041	−	0.252950i
$628$	−9.82843	−	17.0233i	−0.392197	−	0.679305i
$629$	−44.6274			−1.77941
$630$		0			0
$631$	20.1421			0.801846			0.400923	−	0.916112i	$-0.368690\pi$
$631$	20.1421			0.801846			0.400923	+	0.916112i	$0.368690\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$	0.343146	−	0.594346i	0.0136388	−	0.0236231i
$634$	−1.34315	+	2.32640i	−0.0533431	+	0.0923930i
$635$	−1.41421	−	2.44949i	−0.0561214	−	0.0972050i
$636$	11.6569			0.462224
$637$		0			0
$638$	33.7990			1.33811
$639$	−6.24264	−	10.8126i	−0.246955	−	0.427739i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	0.486409	+	0.873731i	$0.338307\pi$
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	−0.999878	+	0.0156233i	$0.995027\pi$
$642$	−0.828427	−	1.43488i	−0.0326954	−	0.0566301i
$643$	−23.1716			−0.913798			−0.456899	−	0.889519i	$-0.651040\pi$
$643$	−23.1716			−0.913798			−0.456899	+	0.889519i	$0.651040\pi$
$644$		0			0
$645$	5.07107			0.199673
$646$	−3.17157	−	5.49333i	−0.124784	−	0.216132i
$647$	−22.4350	+	38.8586i	−0.882012	+	1.52769i	−0.0329115	+	0.999458i	$0.510478\pi$
$647$	−22.4350	+	38.8586i	−0.882012	+	1.52769i	−0.849101	+	0.528231i	$0.822855\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	27.5563	+	47.7290i	1.08168	+	1.87353i
$650$	−5.65685			−0.221880
$651$		0			0
$652$	−2.92893			−0.114706
$653$	−18.8995	−	32.7349i	−0.739594	−	1.28102i	−0.952678	−	0.303981i	$-0.901684\pi$
$653$	−18.8995	−	32.7349i	−0.739594	−	1.28102i	0.213084	−	0.977034i	$-0.431649\pi$
$654$	3.82843	−	6.63103i	0.149703	−	0.259294i
$655$	4.41421	−	7.64564i	0.172478	−	0.298740i
$656$	−3.24264	−	5.61642i	−0.126604	−	0.219284i
$657$	2.00000			0.0780274
$658$		0			0
$659$	−16.3848			−0.638260			−0.319130	−	0.947711i	$-0.603391\pi$
$659$	−16.3848			−0.638260			−0.319130	+	0.947711i	$0.603391\pi$
$660$	−3.12132	−	5.40629i	−0.121497	−	0.210439i
$661$	−19.4853	+	33.7495i	−0.757890	+	1.31270i	0.186035	+	0.982543i	$0.440436\pi$
$661$	−19.4853	+	33.7495i	−0.757890	+	1.31270i	−0.943925	+	0.330160i	$0.892897\pi$
$662$	−8.82843	+	15.2913i	−0.343127	+	0.594313i
$663$	15.3137	+	26.5241i	0.594735	+	1.03011i
$664$	10.8284			0.420224
$665$		0			0
$666$	−8.24264			−0.319396
$667$	−23.8995	−	41.3951i	−0.925392	−	1.60283i
$668$	−3.12132	+	5.40629i	−0.120768	+	0.209175i
$669$	7.65685	−	13.2621i	0.296031	−	0.512741i
$670$	2.53553	+	4.39167i	0.0979562	+	0.169665i
$671$	−2.14214			−0.0826962
$672$		0			0
$673$	30.2843			1.16737			0.583686	−	0.811979i	$-0.301610\pi$
$673$	30.2843			1.16737			0.583686	+	0.811979i	$0.301610\pi$
$674$	−14.5563	−	25.2123i	−0.560690	−	0.971143i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−9.50000	+	16.4545i	−0.365385	+	0.632865i
$677$	20.2132	+	35.0103i	0.776857	+	1.34555i	0.933745	+	0.357939i	$0.116520\pi$
$677$	20.2132	+	35.0103i	0.776857	+	1.34555i	−0.156889	+	0.987616i	$0.550146\pi$
$678$	−10.0000			−0.384048
$679$		0			0
$680$	−5.41421			−0.207626
$681$	4.48528	+	7.76874i	0.171876	+	0.297699i
$682$	−5.48528	+	9.50079i	−0.210042	+	0.363804i
$683$	−3.89949	+	6.75412i	−0.149210	+	0.258439i	−0.930936	−	0.365183i	$-0.881006\pi$
$683$	−3.89949	+	6.75412i	−0.149210	+	0.258439i	0.781726	+	0.623622i	$0.214340\pi$
$684$	−0.585786	−	1.01461i	−0.0223981	−	0.0387947i
$685$	−2.34315			−0.0895270
$686$		0			0
$687$	−12.1421			−0.463251
$688$	2.53553	+	4.39167i	0.0966663	+	0.167431i
$689$	−32.9706	+	57.1067i	−1.25608	+	2.17559i
$690$	−4.41421	+	7.64564i	−0.168046	+	0.291065i
$691$	18.4853	+	32.0174i	0.703213	+	1.21800i	0.967332	+	0.253511i	$0.0815854\pi$
$691$	18.4853	+	32.0174i	0.703213	+	1.21800i	−0.264119	+	0.964490i	$0.585081\pi$
$692$	−15.1716			−0.576737
$693$		0			0
$694$	33.6569			1.27760
$695$	6.82843	+	11.8272i	0.259017	+	0.448631i
$696$	2.70711	−	4.68885i	0.102613	−	0.177730i
$697$	17.5563	−	30.4085i	0.664994	−	1.15180i
$698$	13.7279	+	23.7775i	0.519610	+	0.899990i
$699$	−14.9706			−0.566239
$700$		0			0
$701$	25.2132			0.952290			0.476145	−	0.879367i	$-0.342034\pi$
$701$	25.2132			0.952290			0.476145	+	0.879367i	$0.342034\pi$
$702$	2.82843	+	4.89898i	0.106752	+	0.184900i
$703$	−4.82843	+	8.36308i	−0.182108	+	0.315420i
$704$	3.12132	−	5.40629i	0.117639	−	0.203757i
$705$	−3.12132	−	5.40629i	−0.117556	−	0.203612i
$706$	−32.0416			−1.20590
$707$		0			0
$708$	8.82843			0.331793
$709$	−20.0711	−	34.7641i	−0.753785	−	1.30559i	−0.945976	−	0.324236i	$-0.894893\pi$
$709$	−20.0711	−	34.7641i	−0.753785	−	1.30559i	0.192191	−	0.981357i	$-0.438441\pi$
$710$	−6.24264	+	10.8126i	−0.234282	+	0.405789i
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	−2.41421	−	4.18154i	−0.0904765	−	0.156710i
$713$	15.5147			0.581031
$714$		0			0
$715$	35.3137			1.32066
$716$	−8.87868	−	15.3783i	−0.331812	−	0.574715i
$717$	−1.65685	+	2.86976i	−0.0618764	+	0.107173i
$718$	−5.75736	+	9.97204i	−0.214863	+	0.372153i
$719$	−24.9706	−	43.2503i	−0.931245	−	1.61296i	−0.781197	−	0.624285i	$-0.785391\pi$
$719$	−24.9706	−	43.2503i	−0.931245	−	1.61296i	−0.150048	−	0.988679i	$-0.547943\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	17.6274			0.656025
$723$	5.77817	+	10.0081i	0.214893	+	0.372205i
$724$	0.757359	−	1.31178i	0.0281470	−	0.0487521i
$725$	−2.70711	+	4.68885i	−0.100539	+	0.174139i
$726$	13.9853	+	24.2232i	0.519042	+	0.899008i
$727$	−14.6274			−0.542501			−0.271250	−	0.962509i	$-0.587437\pi$
$727$	−14.6274			−0.542501			−0.271250	+	0.962509i	$0.587437\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−1.00000	−	1.73205i	−0.0370117	−	0.0641061i
$731$	−13.7279	+	23.7775i	−0.507746	+	0.879441i
$732$	−0.171573	+	0.297173i	−0.00634152	+	0.0109838i
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	−0.987971	−	0.154642i	$-0.950578\pi$
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	0.360061	−	0.932929i	$-0.382756\pi$
$734$	−5.17157			−0.190886
$735$		0			0
$736$	−8.82843			−0.325420
$737$	−15.8284	−	27.4156i	−0.583048	−	1.00987i
$738$	3.24264	−	5.61642i	0.119363	−	0.206743i
$739$	25.5563	−	44.2649i	0.940106	−	1.62831i	0.174839	−	0.984597i	$-0.444060\pi$
$739$	25.5563	−	44.2649i	0.940106	−	1.62831i	0.765267	−	0.643713i	$-0.222607\pi$
$740$	4.12132	+	7.13834i	0.151503	+	0.262410i
$741$	6.62742			0.243464
$742$		0			0
$743$	−28.2843			−1.03765			−0.518825	−	0.854881i	$-0.673630\pi$
$743$	−28.2843			−1.03765			−0.518825	+	0.854881i	$0.673630\pi$
$744$	0.878680	+	1.52192i	0.0322140	+	0.0557962i
$745$	−7.19239	+	12.4576i	−0.263509	+	0.456410i
$746$	4.70711	−	8.15295i	0.172339	−	0.298501i
$747$	5.41421	+	9.37769i	0.198096	+	0.343112i
$748$	33.7990			1.23581
$749$		0			0
$750$	1.00000			0.0365148
$751$	8.89949	+	15.4144i	0.324747	+	0.562479i	0.981461	−	0.191661i	$-0.0613875\pi$
$751$	8.89949	+	15.4144i	0.324747	+	0.562479i	−0.656714	+	0.754140i	$0.728054\pi$
$752$	3.12132	−	5.40629i	0.113823	−	0.197147i
$753$	10.4853	−	18.1610i	0.382105	−	0.661825i
$754$	15.3137	+	26.5241i	0.557692	+	0.965952i
$755$	8.14214			0.296323
$756$		0			0
$757$	6.10051			0.221727			0.110863	−	0.993836i	$-0.464638\pi$
$757$	6.10051			0.221727			0.110863	+	0.993836i	$0.464638\pi$
$758$	−8.24264	−	14.2767i	−0.299386	−	0.518552i
$759$	27.5563	−	47.7290i	1.00023	−	1.73245i
$760$	−0.585786	+	1.01461i	−0.0212487	+	0.0368038i
$761$	3.48528	+	6.03668i	0.126341	+	0.218830i	0.922256	−	0.386579i	$-0.126343\pi$
$761$	3.48528	+	6.03668i	0.126341	+	0.218830i	−0.795915	+	0.605408i	$0.793010\pi$
$762$	2.82843			0.102463
$763$		0			0
$764$	4.00000			0.144715
$765$	−2.70711	−	4.68885i	−0.0978757	−	0.169526i
$766$	−8.29289	+	14.3637i	−0.299634	+	0.518982i
$767$	−24.9706	+	43.2503i	−0.901635	+	1.56168i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	20.7279			0.747468			0.373734	−	0.927536i	$-0.378077\pi$
$769$	20.7279			0.747468			0.373734	+	0.927536i	$0.378077\pi$
$770$		0			0
$771$	21.4142			0.771214
$772$	−0.414214	−	0.717439i	−0.0149079	−	0.0258212i
$773$	5.48528	−	9.50079i	0.197292	−	0.341720i	−0.750358	−	0.661032i	$-0.770119\pi$
$773$	5.48528	−	9.50079i	0.197292	−	0.341720i	0.947649	+	0.319313i	$0.103452\pi$
$774$	−2.53553	+	4.39167i	−0.0911379	+	0.157855i
$775$	−0.878680	−	1.52192i	−0.0315631	−	0.0546689i
$776$	10.4853			0.376400
$777$		0			0
$778$	10.1005			0.362121
$779$	−3.79899	−	6.58004i	−0.136113	−	0.235755i
$780$	2.82843	−	4.89898i	0.101274	−	0.175412i
$781$	38.9706	−	67.4990i	1.39448	−	2.41530i
$782$	−23.8995	−	41.3951i	−0.854644	−	1.48029i
$783$	5.41421			0.193488
$784$		0			0
$785$	−19.6569			−0.701583
$786$	4.41421	+	7.64564i	0.157450	+	0.272711i
$787$	24.8284	−	43.0041i	0.885038	−	1.53293i	0.0393676	−	0.999225i	$-0.487466\pi$
$787$	24.8284	−	43.0041i	0.885038	−	1.53293i	0.845670	−	0.533706i	$-0.179201\pi$
$788$	−6.89949	+	11.9503i	−0.245784	+	0.425711i
$789$	−8.07107	−	13.9795i	−0.287338	−	0.497683i
$790$	8.00000			0.284627
$791$		0			0
$792$	6.24264			0.221823
$793$	−0.970563	−	1.68106i	−0.0344657	−	0.0596963i
$794$	−14.6569	+	25.3864i	−0.520152	+	0.900930i
$795$	5.82843	−	10.0951i	0.206713	−	0.358037i
$796$	−7.12132	−	12.3345i	−0.252409	−	0.437184i
$797$	28.1421			0.996846			0.498423	−	0.866934i	$-0.333913\pi$
$797$	28.1421			0.996846			0.498423	+	0.866934i	$0.333913\pi$
$798$		0			0
$799$	33.7990			1.19572
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	2.41421	−	4.18154i	0.0853020	−	0.147747i
$802$	−3.00000	+	5.19615i	−0.105934	+	0.183483i
$803$	6.24264	+	10.8126i	0.220298	+	0.381567i
$804$	−5.07107			−0.178843
$805$		0			0
$806$	−9.94113			−0.350161
$807$	11.8284	+	20.4874i	0.416380	+	0.721192i
$808$	−3.17157	+	5.49333i	−0.111576	+	0.193255i
$809$	−8.75736	+	15.1682i	−0.307892	+	0.533285i	−0.977901	−	0.209068i	$-0.932957\pi$
$809$	−8.75736	+	15.1682i	−0.307892	+	0.533285i	0.670009	+	0.742353i	$0.266290\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−21.6569			−0.760475			−0.380238	−	0.924889i	$-0.624158\pi$
$811$	−21.6569			−0.760475			−0.380238	+	0.924889i	$0.624158\pi$
$812$		0			0
$813$	27.6985			0.971428
$814$	−25.7279	−	44.5621i	−0.901763	−	1.56190i
$815$	−1.46447	+	2.53653i	−0.0512980	+	0.0888508i
$816$	2.70711	−	4.68885i	0.0947677	−	0.164142i
$817$	2.97056	+	5.14517i	0.103927	+	0.180007i
$818$	−4.24264			−0.148340
$819$		0			0
$820$	−6.48528			−0.226476
$821$	20.6066	+	35.6917i	0.719175	+	1.24565i	0.961327	+	0.275410i	$0.0888135\pi$
$821$	20.6066	+	35.6917i	0.719175	+	1.24565i	−0.242152	+	0.970238i	$0.577853\pi$
$822$	1.17157	−	2.02922i	0.0408633	−	0.0707773i
$823$	2.48528	−	4.30463i	0.0866315	−	0.150050i	−0.819454	−	0.573145i	$-0.805723\pi$
$823$	2.48528	−	4.30463i	0.0866315	−	0.150050i	0.906085	+	0.423095i	$0.139056\pi$
$824$	−4.58579	−	7.94282i	−0.159753	−	0.276701i
$825$	−6.24264			−0.217341
$826$		0			0
$827$	52.4853			1.82509			0.912546	−	0.408974i	$-0.134113\pi$
$827$	52.4853			1.82509			0.912546	+	0.408974i	$0.134113\pi$
$828$	−4.41421	−	7.64564i	−0.153405	−	0.265704i
$829$	5.34315	−	9.25460i	0.185575	−	0.321426i	−0.758195	−	0.652028i	$-0.773919\pi$
$829$	5.34315	−	9.25460i	0.185575	−	0.321426i	0.943770	+	0.330602i	$0.107252\pi$
$830$	5.41421	−	9.37769i	0.187930	−	0.325504i
$831$	−7.77817	−	13.4722i	−0.269822	−	0.467345i
$832$	5.65685			0.196116
$833$		0			0
$834$	−13.6569			−0.472898
$835$	3.12132	+	5.40629i	0.108018	+	0.187092i
$836$	3.65685	−	6.33386i	0.126475	−	0.219061i
$837$	−0.878680	+	1.52192i	−0.0303716	+	0.0526052i
$838$	1.51472	+	2.62357i	0.0523251	+	0.0906297i
$839$	8.48528			0.292944			0.146472	−	0.989215i	$-0.453208\pi$
$839$	8.48528			0.292944			0.146472	+	0.989215i	$0.453208\pi$
$840$		0			0
$841$	0.313708			0.0108175
$842$	3.82843	+	6.63103i	0.131936	+	0.228520i
$843$	−13.7279	+	23.7775i	−0.472815	+	0.818939i
$844$	0.343146	−	0.594346i	0.0118116	−	0.0204582i
$845$	9.50000	+	16.4545i	0.326810	+	0.566051i
$846$	6.24264			0.214626
$847$		0			0
$848$	11.6569			0.400298
$849$	13.2426	+	22.9369i	0.454486	+	0.787193i
$850$	−2.70711	+	4.68885i	−0.0928530	+	0.160826i
$851$	−36.3848	+	63.0203i	−1.24725	+	2.16031i
$852$	−6.24264	−	10.8126i	−0.213869	−	0.370433i
$853$	−4.62742			−0.158440			−0.0792199	−	0.996857i	$-0.525243\pi$
$853$	−4.62742			−0.158440			−0.0792199	+	0.996857i	$0.525243\pi$
$854$		0			0
$855$	−1.17157			−0.0400669
$856$	−0.828427	−	1.43488i	−0.0283151	−	0.0490431i
$857$	−0.363961	+	0.630399i	−0.0124327	+	0.0215340i	−0.872175	−	0.489194i	$-0.837291\pi$
$857$	−0.363961	+	0.630399i	−0.0124327	+	0.0215340i	0.859742	+	0.510728i	$0.170624\pi$
$858$	−17.6569	+	30.5826i	−0.602795	+	1.04407i
$859$	21.7990	+	37.7570i	0.743772	+	1.28825i	0.950766	+	0.309909i	$0.100298\pi$
$859$	21.7990	+	37.7570i	0.743772	+	1.28825i	−0.206994	+	0.978342i	$0.566368\pi$
$860$	5.07107			0.172922
$861$		0			0
$862$	37.4558			1.27575
$863$	−17.1716	−	29.7420i	−0.584527	−	1.01243i	−0.994934	−	0.100528i	$-0.967947\pi$
$863$	−17.1716	−	29.7420i	−0.584527	−	1.01243i	0.410407	−	0.911902i	$-0.365387\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−7.58579	+	13.1390i	−0.257924	+	0.446738i
$866$	−10.8995	−	18.8785i	−0.370380	−	0.641517i
$867$	12.3137			0.418195
$868$		0			0
$869$	−49.9411			−1.69414
$870$	−2.70711	−	4.68885i	−0.0917795	−	0.158967i
$871$	14.3431	−	24.8431i	0.485999	−	0.841775i
$872$	3.82843	−	6.63103i	0.129647	−	0.224555i
$873$	5.24264	+	9.08052i	0.177437	+	0.307329i
$874$	−10.3431			−0.349862
$875$		0			0
$876$	2.00000			0.0675737
$877$	2.12132	+	3.67423i	0.0716319	+	0.124070i	0.899617	−	0.436681i	$-0.143846\pi$
$877$	2.12132	+	3.67423i	0.0716319	+	0.124070i	−0.827985	+	0.560751i	$0.810513\pi$
$878$	−17.8492	+	30.9158i	−0.602383	+	1.04336i
$879$	−0.656854	+	1.13770i	−0.0221551	+	0.0383738i
$880$	−3.12132	−	5.40629i	−0.105220	−	0.182246i
$881$	−26.0000			−0.875962			−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000			−0.875962			−0.437981	+	0.898984i	$0.644306\pi$
$882$		0			0
$883$	−25.7574			−0.866804			−0.433402	−	0.901201i	$-0.642687\pi$
$883$	−25.7574			−0.866804			−0.433402	+	0.901201i	$0.642687\pi$
$884$	15.3137	+	26.5241i	0.515056	+	0.892103i
$885$	4.41421	−	7.64564i	0.148382	−	0.257005i
$886$	−10.1421	+	17.5667i	−0.340732	+	0.590165i
$887$	10.4350	+	18.0740i	0.350374	+	0.606866i	0.986315	−	0.164872i	$-0.0527212\pi$
$887$	10.4350	+	18.0740i	0.350374	+	0.606866i	−0.635941	+	0.771738i	$0.719388\pi$
$888$	−8.24264			−0.276605
$889$		0			0
$890$	−4.82843			−0.161849
$891$	3.12132	+	5.40629i	0.104568	+	0.181117i
$892$	7.65685	−	13.2621i	0.256370	−	0.444047i
$893$	3.65685	−	6.33386i	0.122372	−	0.211954i
$894$	−7.19239	−	12.4576i	−0.240549	−	0.416644i
$895$	−17.7574			−0.593563
$896$		0			0
$897$	49.9411			1.66749
$898$	3.24264	+	5.61642i	0.108208	+	0.187422i
$899$	−4.75736	+	8.23999i	−0.158667	+	0.274819i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	31.5563	+	54.6572i	1.05129	+	1.82090i
$902$	40.4853			1.34801
$903$		0			0
$904$	−10.0000			−0.332595
$905$	−0.757359	−	1.31178i	−0.0251755	−	0.0436052i
$906$	−4.07107	+	7.05130i	−0.135252	+	0.234264i
$907$	−18.4350	+	31.9304i	−0.612125	+	1.06023i	0.378757	+	0.925496i	$0.376352\pi$
$907$	−18.4350	+	31.9304i	−0.612125	+	1.06023i	−0.990882	+	0.134735i	$0.956982\pi$
$908$	4.48528	+	7.76874i	0.148849	+	0.257815i
$909$	−6.34315			−0.210389
$910$		0			0
$911$	11.0294			0.365422			0.182711	−	0.983167i	$-0.441513\pi$
$911$	11.0294			0.365422			0.182711	+	0.983167i	$0.441513\pi$
$912$	−0.585786	−	1.01461i	−0.0193973	−	0.0335972i
$913$	−33.7990	+	58.5416i	−1.11858	+	1.93744i
$914$	−7.24264	+	12.5446i	−0.239565	+	0.414939i
$915$	0.171573	+	0.297173i	0.00567202	+	0.00982423i
$916$	−12.1421			−0.401187
$917$		0			0
$918$	5.41421			0.178696
$919$	−21.3848	−	37.0395i	−0.705419	−	1.22182i	−0.966540	−	0.256515i	$-0.917426\pi$
$919$	−21.3848	−	37.0395i	−0.705419	−	1.22182i	0.261122	−	0.965306i	$-0.415908\pi$
$920$	−4.41421	+	7.64564i	−0.145532	+	0.252069i
$921$	7.65685	−	13.2621i	0.252302	−	0.437000i
$922$	−1.00000	−	1.73205i	−0.0329332	−	0.0570421i
$923$	70.6274			2.32473
$924$		0			0
$925$	8.24264			0.271016
$926$	−7.17157	−	12.4215i	−0.235673	−	0.408197i
$927$	4.58579	−	7.94282i	0.150617	−	0.260876i
$928$	2.70711	−	4.68885i	0.0888651	−	0.153919i
$929$	22.1716	+	38.4023i	0.727426	+	1.25994i	0.957968	+	0.286876i	$0.0926167\pi$
$929$	22.1716	+	38.4023i	0.727426	+	1.25994i	−0.230542	+	0.973062i	$0.574050\pi$
$930$	1.75736			0.0576261
$931$		0			0
$932$	−14.9706			−0.490377
$933$	−2.58579	−	4.47871i	−0.0846548	−	0.146626i
$934$	2.24264	−	3.88437i	0.0733814	−	0.127100i
$935$	16.8995	−	29.2708i	0.552673	−	0.957257i
$936$	2.82843	+	4.89898i	0.0924500	+	0.160128i
$937$	−47.6569			−1.55688			−0.778441	−	0.627718i	$-0.783989\pi$
$937$	−47.6569			−1.55688			−0.778441	+	0.627718i	$0.783989\pi$
$938$		0			0
$939$	−13.5147			−0.441036
$940$	−3.12132	−	5.40629i	−0.101806	−	0.176334i
$941$	14.1421	−	24.4949i	0.461020	−	0.798511i	−0.537992	−	0.842950i	$-0.680817\pi$
$941$	14.1421	−	24.4949i	0.461020	−	0.798511i	0.999012	+	0.0444393i	$0.0141501\pi$
$942$	9.82843	−	17.0233i	0.320227	−	0.554650i
$943$	−28.6274	−	49.5841i	−0.932237	−	1.61468i
$944$	8.82843			0.287341
$945$		0			0
$946$	−31.6569			−1.02925
$947$	7.41421	+	12.8418i	0.240930	+	0.417302i	0.960979	−	0.276620i	$-0.0892144\pi$
$947$	7.41421	+	12.8418i	0.240930	+	0.417302i	−0.720050	+	0.693922i	$0.755881\pi$
$948$	−4.00000	+	6.92820i	−0.129914	+	0.225018i
$949$	−5.65685	+	9.79796i	−0.183629	+	0.318055i
$950$	0.585786	+	1.01461i	0.0190054	+	0.0329184i
$951$	−2.68629			−0.0871090
$952$		0			0
$953$	27.3137			0.884778			0.442389	−	0.896823i	$-0.354131\pi$
$953$	27.3137			0.884778			0.442389	+	0.896823i	$0.354131\pi$
$954$	5.82843	+	10.0951i	0.188702	+	0.326842i
$955$	2.00000	−	3.46410i	0.0647185	−	0.112096i
$956$	−1.65685	+	2.86976i	−0.0535865	+	0.0928145i
$957$	16.8995	+	29.2708i	0.546283	+	0.946190i
$958$	8.48528			0.274147
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	13.9558	+	24.1722i	0.450189	+	0.779749i
$962$	23.3137	−	40.3805i	0.751664	−	1.30192i
$963$	0.828427	−	1.43488i	0.0266957	−	0.0462383i
$964$	5.77817	+	10.0081i	0.186102	+	0.322339i
$965$	−0.828427			−0.0266680
$966$		0			0
$967$	−21.6569			−0.696437			−0.348219	−	0.937413i	$-0.613213\pi$
$967$	−21.6569			−0.696437			−0.348219	+	0.937413i	$0.613213\pi$
$968$	13.9853	+	24.2232i	0.449504	+	0.778564i
$969$	3.17157	−	5.49333i	0.101886	−	0.176471i
$970$	5.24264	−	9.08052i	0.168331	−	0.291558i
$971$	14.4853	+	25.0892i	0.464855	+	0.805152i	0.999195	−	0.0401174i	$-0.0127732\pi$
$971$	14.4853	+	25.0892i	0.464855	+	0.805152i	−0.534340	+	0.845270i	$0.679440\pi$
$972$	1.00000			0.0320750
$973$		0			0
$974$	−5.17157			−0.165708
$975$	−2.82843	−	4.89898i	−0.0905822	−	0.156893i
$976$	−0.171573	+	0.297173i	−0.00549191	+	0.00951227i
$977$	3.34315	−	5.79050i	0.106957	−	0.185254i	−0.807579	−	0.589759i	$-0.799223\pi$
$977$	3.34315	−	5.79050i	0.106957	−	0.185254i	0.914536	+	0.404505i	$0.132556\pi$
$978$	−1.46447	−	2.53653i	−0.0468285	−	0.0811093i
$979$	30.1421			0.963347
$980$		0			0
$981$	7.65685			0.244465
$982$	−1.46447	−	2.53653i	−0.0467330	−	0.0809439i
$983$	−1.46447	+	2.53653i	−0.0467092	+	0.0809027i	−0.888435	−	0.459003i	$-0.848207\pi$
$983$	−1.46447	+	2.53653i	−0.0467092	+	0.0809027i	0.841726	+	0.539906i	$0.181540\pi$
$984$	3.24264	−	5.61642i	0.103372	−	0.179045i
$985$	6.89949	+	11.9503i	0.219836	+	0.380767i
$986$	29.3137			0.933539
$987$		0			0
$988$	6.62742			0.210846
$989$	22.3848	+	38.7716i	0.711794	+	1.23286i
$990$	3.12132	−	5.40629i	0.0992021	−	0.171823i
$991$	24.8995	−	43.1272i	0.790959	−	1.36998i	−0.134416	−	0.990925i	$-0.542916\pi$
$991$	24.8995	−	43.1272i	0.790959	−	1.36998i	0.925374	−	0.379055i	$-0.123751\pi$
$992$	0.878680	+	1.52192i	0.0278981	+	0.0483209i
$993$	−17.6569			−0.560323
$994$		0			0
$995$	−14.2426			−0.451522
$996$	5.41421	+	9.37769i	0.171556	+	0.297144i
$997$	−5.68629	+	9.84895i	−0.180087	+	0.311919i	−0.941910	−	0.335866i	$-0.890971\pi$
$997$	−5.68629	+	9.84895i	−0.180087	+	0.311919i	0.761823	+	0.647785i	$0.224304\pi$
$998$	0.585786	−	1.01461i	0.0185427	−	0.0321170i
$999$	−4.12132	−	7.13834i	−0.130393	−	0.225847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.w.361.2		4
7.2	even	3	inner	1470.2.i.w.961.2		4
7.3	odd	6		1470.2.a.s.1.1	✓	2
7.4	even	3		1470.2.a.t.1.1	yes	2
7.5	odd	6		1470.2.i.x.961.2		4
7.6	odd	2		1470.2.i.x.361.2		4
21.11	odd	6		4410.2.a.bz.1.2		2
21.17	even	6		4410.2.a.bw.1.2		2
35.4	even	6		7350.2.a.dh.1.1		2
35.24	odd	6		7350.2.a.dl.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.a.s.1.1	✓	2	7.3	odd	6
1470.2.a.t.1.1	yes	2	7.4	even	3
1470.2.i.w.361.2		4	1.1	even	1	trivial
1470.2.i.w.961.2		4	7.2	even	3	inner
1470.2.i.x.361.2		4	7.6	odd	2
1470.2.i.x.961.2		4	7.5	odd	6
4410.2.a.bw.1.2		2	21.17	even	6
4410.2.a.bz.1.2		2	21.11	odd	6
7350.2.a.dh.1.1		2	35.4	even	6
7350.2.a.dl.1.1		2	35.24	odd	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(3.12132 - 5.40629i) q^{11} +(-0.500000 - 0.866025i) q^{12} +5.65685 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.70711 - 4.68885i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.585786 - 1.01461i) q^{19} -1.00000 q^{20} +6.24264 q^{22} +(-4.41421 - 7.64564i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.82843 + 4.89898i) q^{26} +1.00000 q^{27} +5.41421 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.878680 + 1.52192i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.12132 + 5.40629i) q^{33} +5.41421 q^{34} +1.00000 q^{36} +(-4.12132 - 7.13834i) q^{37} +(0.585786 - 1.01461i) q^{38} +(-2.82843 + 4.89898i) q^{39} +(-0.500000 - 0.866025i) q^{40} +6.48528 q^{41} -5.07107 q^{43} +(3.12132 + 5.40629i) q^{44} +(0.500000 - 0.866025i) q^{45} +(4.41421 - 7.64564i) q^{46} +(3.12132 + 5.40629i) q^{47} +1.00000 q^{48} -1.00000 q^{50} +(2.70711 + 4.68885i) q^{51} +(-2.82843 + 4.89898i) q^{52} +(-5.82843 + 10.0951i) q^{53} +(0.500000 + 0.866025i) q^{54} +6.24264 q^{55} +1.17157 q^{57} +(2.70711 + 4.68885i) q^{58} +(-4.41421 + 7.64564i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-0.171573 - 0.297173i) q^{61} -1.75736 q^{62} +1.00000 q^{64} +(2.82843 + 4.89898i) q^{65} +(-3.12132 + 5.40629i) q^{66} +(2.53553 - 4.39167i) q^{67} +(2.70711 + 4.68885i) q^{68} +8.82843 q^{69} +12.4853 q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(4.12132 - 7.13834i) q^{74} +(-0.500000 - 0.866025i) q^{75} +1.17157 q^{76} -5.65685 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.24264 + 5.61642i) q^{82} -10.8284 q^{83} +5.41421 q^{85} +(-2.53553 - 4.39167i) q^{86} +(-2.70711 + 4.68885i) q^{87} +(-3.12132 + 5.40629i) q^{88} +(2.41421 + 4.18154i) q^{89} +1.00000 q^{90} +8.82843 q^{92} +(-0.878680 - 1.52192i) q^{93} +(-3.12132 + 5.40629i) q^{94} +(0.585786 - 1.01461i) q^{95} +(0.500000 + 0.866025i) q^{96} -10.4853 q^{97} -6.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} - 8 q^{19} - 4 q^{20} + 8 q^{22} - 12 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{27} + 16 q^{29} - 2 q^{30} - 12 q^{31} + 2 q^{32} + 4 q^{33} + 16 q^{34} + 4 q^{36} - 8 q^{37} + 8 q^{38} - 2 q^{40} - 8 q^{41} + 8 q^{43} + 4 q^{44} + 2 q^{45} + 12 q^{46} + 4 q^{47} + 4 q^{48} - 4 q^{50} + 8 q^{51} - 12 q^{53} + 2 q^{54} + 8 q^{55} + 16 q^{57} + 8 q^{58} - 12 q^{59} + 2 q^{60} - 12 q^{61} - 24 q^{62} + 4 q^{64} - 4 q^{66} - 4 q^{67} + 8 q^{68} + 24 q^{69} + 16 q^{71} + 2 q^{72} - 4 q^{73} + 8 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{79} + 2 q^{80} - 2 q^{81} - 4 q^{82} - 32 q^{83} + 16 q^{85} + 4 q^{86} - 8 q^{87} - 4 q^{88} + 4 q^{89} + 4 q^{90} + 24 q^{92} - 12 q^{93} - 4 q^{94} + 8 q^{95} + 2 q^{96} - 8 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 - 4 * q^15 - 2 * q^16 + 8 * q^17 + 2 * q^18 - 8 * q^19 - 4 * q^20 + 8 * q^22 - 12 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^27 + 16 * q^29 - 2 * q^30 - 12 * q^31 + 2 * q^32 + 4 * q^33 + 16 * q^34 + 4 * q^36 - 8 * q^37 + 8 * q^38 - 2 * q^40 - 8 * q^41 + 8 * q^43 + 4 * q^44 + 2 * q^45 + 12 * q^46 + 4 * q^47 + 4 * q^48 - 4 * q^50 + 8 * q^51 - 12 * q^53 + 2 * q^54 + 8 * q^55 + 16 * q^57 + 8 * q^58 - 12 * q^59 + 2 * q^60 - 12 * q^61 - 24 * q^62 + 4 * q^64 - 4 * q^66 - 4 * q^67 + 8 * q^68 + 24 * q^69 + 16 * q^71 + 2 * q^72 - 4 * q^73 + 8 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^79 + 2 * q^80 - 2 * q^81 - 4 * q^82 - 32 * q^83 + 16 * q^85 + 4 * q^86 - 8 * q^87 - 4 * q^88 + 4 * q^89 + 4 * q^90 + 24 * q^92 - 12 * q^93 - 4 * q^94 + 8 * q^95 + 2 * q^96 - 8 * q^97 - 8 * q^99

Introduction

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