LMFDB - Embedded newform 1470.2.i.i.961.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1470.961
Dual form			1470.2.i.i.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -7.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.50000 - 6.06218i) q^{26} -1.00000 q^{27} -8.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(1.50000 - 2.59808i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-3.50000 - 6.06218i) q^{39} +(0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-1.50000 + 2.59808i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(2.00000 - 3.46410i) q^{51} +(3.50000 + 6.06218i) q^{52} +(0.500000 + 0.866025i) q^{53} +(0.500000 - 0.866025i) q^{54} +1.00000 q^{55} +1.00000 q^{57} +(4.00000 - 6.92820i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-2.00000 + 3.46410i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-3.50000 + 6.06218i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{68} -1.00000 q^{69} -14.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(1.50000 + 2.59808i) q^{74} +(0.500000 - 0.866025i) q^{75} -1.00000 q^{76} +7.00000 q^{78} +(-2.00000 + 3.46410i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} -12.0000 q^{83} -4.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-1.00000 + 1.73205i) q^{89} -1.00000 q^{90} +1.00000 q^{92} +(-3.00000 + 5.19615i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(0.500000 - 0.866025i) q^{96} +16.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + q^{5} - 2 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 + q^5 - 2 * q^6 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} + q^{5} - 2 q^{6} + 2 q^{8} - q^{9} + q^{10} + q^{11} + q^{12} - 14 q^{13} + 2 q^{15} - q^{16} - 4 q^{17} - q^{18} + q^{19} - 2 q^{20} - 2 q^{22} - q^{23} + q^{24} - q^{25} + 7 q^{26} - 2 q^{27} - 16 q^{29} - q^{30} + 6 q^{31} - q^{32} - q^{33} + 8 q^{34} + 2 q^{36} + 3 q^{37} + q^{38} - 7 q^{39} + q^{40} - 18 q^{41} - 8 q^{43} + q^{44} + q^{45} - q^{46} - 3 q^{47} - 2 q^{48} + 2 q^{50} + 4 q^{51} + 7 q^{52} + q^{53} + q^{54} + 2 q^{55} + 2 q^{57} + 8 q^{58} + 12 q^{59} - q^{60} - 4 q^{61} - 12 q^{62} + 2 q^{64} - 7 q^{65} - q^{66} - 12 q^{67} - 4 q^{68} - 2 q^{69} - 28 q^{71} - q^{72} - 14 q^{73} + 3 q^{74} + q^{75} - 2 q^{76} + 14 q^{78} - 4 q^{79} + q^{80} - q^{81} + 9 q^{82} - 24 q^{83} - 8 q^{85} + 4 q^{86} - 8 q^{87} + q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{92} - 6 q^{93} - 3 q^{94} - q^{95} + q^{96} + 32 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + q^5 - 2 * q^6 + 2 * q^8 - q^9 + q^10 + q^11 + q^12 - 14 * q^13 + 2 * q^15 - q^16 - 4 * q^17 - q^18 + q^19 - 2 * q^20 - 2 * q^22 - q^23 + q^24 - q^25 + 7 * q^26 - 2 * q^27 - 16 * q^29 - q^30 + 6 * q^31 - q^32 - q^33 + 8 * q^34 + 2 * q^36 + 3 * q^37 + q^38 - 7 * q^39 + q^40 - 18 * q^41 - 8 * q^43 + q^44 + q^45 - q^46 - 3 * q^47 - 2 * q^48 + 2 * q^50 + 4 * q^51 + 7 * q^52 + q^53 + q^54 + 2 * q^55 + 2 * q^57 + 8 * q^58 + 12 * q^59 - q^60 - 4 * q^61 - 12 * q^62 + 2 * q^64 - 7 * q^65 - q^66 - 12 * q^67 - 4 * q^68 - 2 * q^69 - 28 * q^71 - q^72 - 14 * q^73 + 3 * q^74 + q^75 - 2 * q^76 + 14 * q^78 - 4 * q^79 + q^80 - q^81 + 9 * q^82 - 24 * q^83 - 8 * q^85 + 4 * q^86 - 8 * q^87 + q^88 - 2 * q^89 - 2 * q^90 + 2 * q^92 - 6 * q^93 - 3 * q^94 - q^95 + q^96 + 32 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−7.00000			−1.94145			−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000			−1.94145			−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.50000	−	6.06218i	0.686406	−	1.18889i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	4.00000			0.685994
$35$		0			0
$36$	1.00000			0.166667
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	−0.715981	−	0.698119i	$-0.754020\pi$
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	0.962580	+	0.270998i	$0.0873538\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	−3.50000	−	6.06218i	−0.560449	−	0.970725i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	1.00000			0.141421
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$	3.50000	+	6.06218i	0.485363	+	0.840673i
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	0.898321	−	0.439340i	$-0.144788\pi$
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	−0.829640	+	0.558298i	$0.811454\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	1.00000			0.134840
$56$		0			0
$57$	1.00000			0.132453
$58$	4.00000	−	6.92820i	0.525226	−	0.909718i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.50000	+	6.06218i	−0.434122	+	0.751921i
$66$	−0.500000	−	0.866025i	−0.0615457	−	0.106600i
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	−1.00000			−0.120386
$70$		0			0
$71$	−14.0000			−1.66149			−0.830747	−	0.556650i	$-0.812086\pi$
$71$	−14.0000			−1.66149			−0.830747	+	0.556650i	$0.812086\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−1.00000			−0.114708
$77$		0			0
$78$	7.00000			0.792594
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	1.00000			0.104257
$93$	−3.00000	+	5.19615i	−0.311086	+	0.538816i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	16.0000			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$98$		0			0
$99$	−1.00000			−0.100504
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$	−7.00000			−0.686406
$105$		0			0
$106$	−1.00000			−0.0971286
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.00813215	−	0.999967i	$-0.497411\pi$
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.861931	−	0.507026i	$-0.169255\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	3.00000			0.284747
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	−0.500000	+	0.866025i	−0.0468293	+	0.0811107i
$115$	0.500000	+	0.866025i	0.0466252	+	0.0807573i
$116$	4.00000	+	6.92820i	0.371391	+	0.643268i
$117$	3.50000	−	6.06218i	0.323575	−	0.560449i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	1.00000			0.0912871
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−2.00000	−	3.46410i	−0.181071	−	0.313625i
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$	−3.50000	−	6.06218i	−0.306970	−	0.531688i
$131$	−6.50000	+	11.2583i	−0.567908	+	0.983645i	0.428865	+	0.903369i	$0.358914\pi$
$131$	−6.50000	+	11.2583i	−0.567908	+	0.983645i	−0.996773	+	0.0802763i	$0.974420\pi$
$132$	1.00000			0.0870388
$133$		0			0
$134$	12.0000			1.03664
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	−2.00000	−	3.46410i	−0.171499	−	0.297044i
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	0.500000	−	0.866025i	0.0425628	−	0.0737210i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	7.00000	−	12.1244i	0.587427	−	1.01745i
$143$	−3.50000	−	6.06218i	−0.292685	−	0.506945i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.00000	+	6.92820i	−0.332182	+	0.575356i
$146$	14.0000			1.15865
$147$		0			0
$148$	−3.00000			−0.246598
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	0.500000	−	0.866025i	0.0405554	−	0.0702439i
$153$	4.00000			0.323381
$154$		0			0
$155$	6.00000			0.481932
$156$	−3.50000	+	6.06218i	−0.280224	+	0.485363i
$157$	7.50000	+	12.9904i	0.598565	+	1.03675i	0.993033	+	0.117836i	$0.0375956\pi$
$157$	7.50000	+	12.9904i	0.598565	+	1.03675i	−0.394468	+	0.918910i	$0.629071\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$	−0.500000	+	0.866025i	−0.0396526	+	0.0686803i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	1.00000			0.0785674
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$	0.500000	+	0.866025i	0.0389249	+	0.0674200i
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	5.00000			0.386912			0.193456	−	0.981109i	$-0.438030\pi$
$167$	5.00000			0.386912			0.193456	+	0.981109i	$0.438030\pi$
$168$		0			0
$169$	36.0000			2.76923
$170$	2.00000	−	3.46410i	0.153393	−	0.265684i
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872399\pi$
$174$	8.00000			0.606478
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$	−1.00000	−	1.73205i	−0.0749532	−	0.129823i
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	0.514035	−	0.857769i	$-0.328150\pi$
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	−0.999867	+	0.0162823i	$0.994817\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	12.0000			0.891953			0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000			0.891953			0.445976	+	0.895045i	$0.352856\pi$
$182$		0			0
$183$	−4.00000			−0.295689
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	3.00000			0.218797
$189$		0			0
$190$	1.00000			0.0725476
$191$	5.00000	−	8.66025i	0.361787	−	0.626634i	−0.626468	−	0.779447i	$-0.715500\pi$
$191$	5.00000	−	8.66025i	0.361787	−	0.626634i	0.988255	+	0.152813i	$0.0488333\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−13.0000	−	22.5167i	−0.935760	−	1.62078i	−0.773272	−	0.634074i	$-0.781381\pi$
$193$	−13.0000	−	22.5167i	−0.935760	−	1.62078i	−0.162488	−	0.986710i	$-0.551952\pi$
$194$	−8.00000	+	13.8564i	−0.574367	+	0.994832i
$195$	−7.00000			−0.501280
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	0.571122	−	0.820865i	$-0.306508\pi$
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	−0.996451	+	0.0841740i	$0.973175\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$		0			0
$203$		0			0
$204$	−4.00000			−0.280056
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	3.50000	−	6.06218i	0.242681	−	0.420336i
$209$	1.00000			0.0691714
$210$		0			0
$211$	−15.0000			−1.03264			−0.516321	−	0.856395i	$-0.672699\pi$
$211$	−15.0000			−1.03264			−0.516321	+	0.856395i	$0.672699\pi$
$212$	0.500000	−	0.866025i	0.0343401	−	0.0594789i
$213$	−7.00000	−	12.1244i	−0.479632	−	0.830747i
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$	−2.00000	+	3.46410i	−0.136399	+	0.236250i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−10.0000			−0.677285
$219$	7.00000	−	12.1244i	0.473016	−	0.819288i
$220$	−0.500000	−	0.866025i	−0.0337100	−	0.0583874i
$221$	14.0000	+	24.2487i	0.941742	+	1.63114i
$222$	−1.50000	+	2.59808i	−0.100673	+	0.174371i
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$	−0.500000	−	0.866025i	−0.0331133	−	0.0573539i
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$	−1.00000			−0.0659380
$231$		0			0
$232$	−8.00000			−0.525226
$233$	−13.0000	+	22.5167i	−0.851658	+	1.47512i	0.0280525	+	0.999606i	$0.491069\pi$
$233$	−13.0000	+	22.5167i	−0.851658	+	1.47512i	−0.879711	+	0.475509i	$0.842264\pi$
$234$	3.50000	+	6.06218i	0.228802	+	0.396297i
$235$	1.50000	+	2.59808i	0.0978492	+	0.169480i
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$	−4.00000			−0.259828
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$	5.00000	+	8.66025i	0.321412	+	0.556702i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.00000			0.256074
$245$		0			0
$246$	9.00000			0.573819
$247$	−3.50000	+	6.06218i	−0.222700	+	0.385727i
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	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
$253$	−1.00000			−0.0628695
$254$	−2.50000	+	4.33013i	−0.156864	+	0.271696i
$255$	−2.00000	−	3.46410i	−0.125245	−	0.216930i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	−0.963391	−	0.268101i	$-0.913604\pi$
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	0.713878	+	0.700270i	$0.246937\pi$
$258$	4.00000			0.249029
$259$		0			0
$260$	7.00000			0.434122
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	−6.50000	−	11.2583i	−0.401571	−	0.695542i
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	1.00000			0.0614295
$266$		0			0
$267$	−2.00000			−0.122398
$268$	−6.00000	+	10.3923i	−0.366508	+	0.634811i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−2.00000			−0.120824
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	0.500000	+	0.866025i	0.0300965	+	0.0521286i
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$	−6.00000			−0.359211
$280$		0			0
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	0.834772	−	0.550596i	$-0.185599\pi$
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	−0.894216	+	0.447636i	$0.852266\pi$
$284$	7.00000	+	12.1244i	0.415374	+	0.719448i
$285$	0.500000	−	0.866025i	0.0296174	−	0.0512989i
$286$	7.00000			0.413919
$287$		0			0
$288$	1.00000			0.0589256
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−4.00000	−	6.92820i	−0.234888	−	0.406838i
$291$	8.00000	+	13.8564i	0.468968	+	0.812277i
$292$	−7.00000	+	12.1244i	−0.409644	+	0.709524i
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$	12.0000			0.698667
$296$	1.50000	−	2.59808i	0.0871857	−	0.151010i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	2.00000	+	3.46410i	0.115857	+	0.200670i
$299$	3.50000	−	6.06218i	0.202410	−	0.350585i
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	−2.00000			−0.115087
$303$		0			0
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$	2.00000	+	3.46410i	0.114520	+	0.198354i
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	8.00000	+	13.8564i	0.453638	+	0.785725i	0.998609	−	0.0527306i	$-0.0167924\pi$
$311$	8.00000	+	13.8564i	0.453638	+	0.785725i	−0.544970	+	0.838455i	$0.683459\pi$
$312$	−3.50000	−	6.06218i	−0.198148	−	0.343203i
$313$	−12.0000	+	20.7846i	−0.678280	+	1.17482i	0.297218	+	0.954810i	$0.403941\pi$
$313$	−12.0000	+	20.7846i	−0.678280	+	1.17482i	−0.975499	+	0.220006i	$0.929392\pi$
$314$	−15.0000			−0.846499
$315$		0			0
$316$	4.00000			0.225018
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	−0.971589	−	0.236675i	$-0.923942\pi$
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	0.690761	+	0.723083i	$0.257276\pi$
$318$	−0.500000	−	0.866025i	−0.0280386	−	0.0485643i
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	18.0000			1.00466
$322$		0			0
$323$	−4.00000			−0.222566
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	3.50000	+	6.06218i	0.194145	+	0.336269i
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$	−5.00000	+	8.66025i	−0.276501	+	0.478913i
$328$	−9.00000			−0.496942
$329$		0			0
$330$	−1.00000			−0.0550482
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	−0.715445	−	0.698669i	$-0.753776\pi$
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	0.962788	+	0.270259i	$0.0871094\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	1.50000	+	2.59808i	0.0821995	+	0.142374i
$334$	−2.50000	+	4.33013i	−0.136794	+	0.236934i
$335$	−12.0000			−0.655630
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−18.0000	+	31.1769i	−0.979071	+	1.69580i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$	−1.00000			−0.0540738
$343$		0			0
$344$	−4.00000			−0.215666
$345$	−0.500000	+	0.866025i	−0.0269191	+	0.0466252i
$346$	−10.5000	−	18.1865i	−0.564483	−	0.977714i
$347$	17.0000	+	29.4449i	0.912608	+	1.58068i	0.810366	+	0.585923i	$0.199268\pi$
$347$	17.0000	+	29.4449i	0.912608	+	1.58068i	0.102241	+	0.994760i	$0.467399\pi$
$348$	−4.00000	+	6.92820i	−0.214423	+	0.371391i
$349$	28.0000			1.49881			0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000			1.49881			0.749403	+	0.662114i	$0.230341\pi$
$350$		0			0
$351$	7.00000			0.373632
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−4.00000	−	6.92820i	−0.212899	−	0.368751i	0.739722	−	0.672913i	$-0.234957\pi$
$353$	−4.00000	−	6.92820i	−0.212899	−	0.368751i	−0.952620	+	0.304162i	$0.901624\pi$
$354$	−6.00000	−	10.3923i	−0.318896	−	0.552345i
$355$	−7.00000	+	12.1244i	−0.371521	+	0.643494i
$356$	2.00000			0.106000
$357$		0			0
$358$	13.0000			0.687071
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.204595	+	0.978847i	$0.565588\pi$
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.745409	+	0.666608i	$0.767746\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−6.00000	+	10.3923i	−0.315353	+	0.546207i
$363$	10.0000			0.524864
$364$		0			0
$365$	−14.0000			−0.732793
$366$	2.00000	−	3.46410i	0.104542	−	0.181071i
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$	3.00000			0.155963
$371$		0			0
$372$	6.00000			0.311086
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	0.303902	+	0.952703i	$0.401711\pi$
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	−0.977016	+	0.213165i	$0.931623\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$	56.0000			2.88415
$378$		0			0
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$	−0.500000	+	0.866025i	−0.0256495	+	0.0444262i
$381$	2.50000	+	4.33013i	0.128079	+	0.221839i
$382$	5.00000	+	8.66025i	0.255822	+	0.443097i
$383$	6.50000	−	11.2583i	0.332134	−	0.575274i	−0.650796	−	0.759253i	$-0.725565\pi$
$383$	6.50000	−	11.2583i	0.332134	−	0.575274i	0.982930	+	0.183979i	$0.0588979\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	26.0000			1.32337
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$	−8.00000	−	13.8564i	−0.406138	−	0.703452i
$389$	7.00000	+	12.1244i	0.354914	+	0.614729i	0.987103	−	0.160085i	$-0.0511768\pi$
$389$	7.00000	+	12.1244i	0.354914	+	0.614729i	−0.632189	+	0.774814i	$0.717843\pi$
$390$	3.50000	−	6.06218i	0.177229	−	0.306970i
$391$	4.00000			0.202289
$392$		0			0
$393$	−13.0000			−0.655763
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$	2.00000	+	3.46410i	0.100631	+	0.174298i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	−0.546795	−	0.837267i	$-0.684152\pi$
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	0.998492	+	0.0549046i	$0.0174855\pi$
$398$	12.0000			0.601506
$399$		0			0
$400$	1.00000			0.0500000
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	−0.571901	−	0.820323i	$-0.693794\pi$
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	0.996371	+	0.0851195i	$0.0271272\pi$
$402$	6.00000	+	10.3923i	0.299253	+	0.518321i
$403$	−21.0000	−	36.3731i	−1.04608	−	1.81187i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	3.00000			0.148704
$408$	2.00000	−	3.46410i	0.0990148	−	0.171499i
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$	−4.50000	−	7.79423i	−0.222239	−	0.384930i
$411$	−1.00000	+	1.73205i	−0.0493264	+	0.0854358i
$412$	−16.0000			−0.788263
$413$		0			0
$414$	1.00000			0.0491473
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	3.50000	+	6.06218i	0.171602	+	0.297223i
$417$	2.00000	+	3.46410i	0.0979404	+	0.169638i
$418$	−0.500000	+	0.866025i	−0.0244558	+	0.0423587i
$419$	−11.0000			−0.537385			−0.268693	−	0.963226i	$-0.586592\pi$
$419$	−11.0000			−0.537385			−0.268693	+	0.963226i	$0.586592\pi$
$420$		0			0
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$	7.50000	−	12.9904i	0.365094	−	0.632362i
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$	0.500000	+	0.866025i	0.0242821	+	0.0420579i
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$	14.0000			0.678302
$427$		0			0
$428$	−18.0000			−0.870063
$429$	3.50000	−	6.06218i	0.168982	−	0.292685i
$430$	−2.00000	−	3.46410i	−0.0964486	−	0.167054i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−40.0000			−1.92228			−0.961139	−	0.276066i	$-0.910969\pi$
$433$	−40.0000			−1.92228			−0.961139	+	0.276066i	$0.910969\pi$
$434$		0			0
$435$	−8.00000			−0.383571
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	0.500000	+	0.866025i	0.0239182	+	0.0414276i
$438$	7.00000	+	12.1244i	0.334473	+	0.579324i
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$	1.00000			0.0476731
$441$		0			0
$442$	−28.0000			−1.33182
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$	−1.50000	−	2.59808i	−0.0711868	−	0.123299i
$445$	1.00000	+	1.73205i	0.0474045	+	0.0821071i
$446$	−2.00000	+	3.46410i	−0.0947027	+	0.164030i
$447$	4.00000			0.189194
$448$		0			0
$449$	−25.0000			−1.17982			−0.589911	−	0.807468i	$-0.700837\pi$
$449$	−25.0000			−1.17982			−0.589911	+	0.807468i	$0.700837\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	−1.00000	+	1.73205i	−0.0469841	+	0.0813788i
$454$	20.0000			0.938647
$455$		0			0
$456$	1.00000			0.0468293
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$	−11.0000	−	19.0526i	−0.513996	−	0.890268i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$	0.500000	−	0.866025i	0.0233126	−	0.0403786i
$461$	28.0000			1.30409			0.652045	−	0.758180i	$-0.273911\pi$
$461$	28.0000			1.30409			0.652045	+	0.758180i	$0.273911\pi$
$462$		0			0
$463$	33.0000			1.53364			0.766820	−	0.641862i	$-0.221838\pi$
$463$	33.0000			1.53364			0.766820	+	0.641862i	$0.221838\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$	3.00000	+	5.19615i	0.139122	+	0.240966i
$466$	−13.0000	−	22.5167i	−0.602213	−	1.04306i
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$	−7.00000			−0.323575
$469$		0			0
$470$	−3.00000			−0.138380
$471$	−7.50000	+	12.9904i	−0.345582	+	0.598565i
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	−2.00000	−	3.46410i	−0.0919601	−	0.159280i
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$	−1.00000			−0.0458831
$476$		0			0
$477$	−1.00000			−0.0457869
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	13.0000	+	22.5167i	0.593985	+	1.02881i	0.993689	+	0.112168i	$0.0357796\pi$
$479$	13.0000	+	22.5167i	0.593985	+	1.02881i	−0.399704	+	0.916644i	$0.630887\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	−10.5000	+	18.1865i	−0.478759	+	0.829235i
$482$	−7.00000			−0.318841
$483$		0			0
$484$	−10.0000			−0.454545
$485$	8.00000	−	13.8564i	0.363261	−	0.629187i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	0.942309	−	0.334744i	$-0.108650\pi$
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	−0.761052	+	0.648691i	$0.775317\pi$
$488$	−2.00000	+	3.46410i	−0.0905357	+	0.156813i
$489$	−8.00000			−0.361773
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−4.50000	+	7.79423i	−0.202876	+	0.351391i
$493$	16.0000	+	27.7128i	0.720604	+	1.24812i
$494$	−3.50000	−	6.06218i	−0.157472	−	0.272750i
$495$	−0.500000	+	0.866025i	−0.0224733	+	0.0389249i
$496$	−6.00000			−0.269408
$497$		0			0
$498$	12.0000			0.537733
$499$	−12.0000	+	20.7846i	−0.537194	+	0.930447i	0.461860	+	0.886953i	$0.347182\pi$
$499$	−12.0000	+	20.7846i	−0.537194	+	0.930447i	−0.999054	+	0.0434940i	$0.986151\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	2.50000	+	4.33013i	0.111692	+	0.193456i
$502$	−1.50000	+	2.59808i	−0.0669483	+	0.115958i
$503$	−28.0000			−1.24846			−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000			−1.24846			−0.624229	+	0.781241i	$0.714587\pi$
$504$		0			0
$505$		0			0
$506$	0.500000	−	0.866025i	0.0222277	−	0.0384995i
$507$	18.0000	+	31.1769i	0.799408	+	1.38462i
$508$	−2.50000	−	4.33013i	−0.110920	−	0.192118i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	4.00000			0.177123
$511$		0			0
$512$	1.00000			0.0441942
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$	−4.00000	−	6.92820i	−0.176432	−	0.305590i
$515$	−8.00000	−	13.8564i	−0.352522	−	0.610586i
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$	−3.00000			−0.131940
$518$		0			0
$519$	−21.0000			−0.921798
$520$	−3.50000	+	6.06218i	−0.153485	+	0.265844i
$521$	−10.5000	−	18.1865i	−0.460013	−	0.796766i	0.538948	−	0.842339i	$-0.318822\pi$
$521$	−10.5000	−	18.1865i	−0.460013	−	0.796766i	−0.998961	+	0.0455727i	$0.985489\pi$
$522$	4.00000	+	6.92820i	0.175075	+	0.303239i
$523$	−7.00000	+	12.1244i	−0.306089	+	0.530161i	−0.977503	−	0.210921i	$-0.932354\pi$
$523$	−7.00000	+	12.1244i	−0.306089	+	0.530161i	0.671414	+	0.741082i	$0.265687\pi$
$524$	13.0000			0.567908
$525$		0			0
$526$	−16.0000			−0.697633
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$	−0.500000	−	0.866025i	−0.0217597	−	0.0376889i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−0.500000	+	0.866025i	−0.0217186	+	0.0376177i
$531$	−12.0000			−0.520756
$532$		0			0
$533$	63.0000			2.72883
$534$	1.00000	−	1.73205i	0.0432742	−	0.0749532i
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	6.50000	−	11.2583i	0.280496	−	0.485833i
$538$		0			0
$539$		0			0
$540$	1.00000			0.0430331
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$	8.00000	+	13.8564i	0.343629	+	0.595184i
$543$	6.00000	+	10.3923i	0.257485	+	0.445976i
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$	10.0000			0.428353
$546$		0			0
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	1.00000	−	1.73205i	0.0427179	−	0.0739895i
$549$	−2.00000	−	3.46410i	−0.0853579	−	0.147844i
$550$	0.500000	+	0.866025i	0.0213201	+	0.0369274i
$551$	−4.00000	+	6.92820i	−0.170406	+	0.295151i
$552$	−1.00000			−0.0425628
$553$		0			0
$554$	−2.00000			−0.0849719
$555$	1.50000	−	2.59808i	0.0636715	−	0.110282i
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	−22.5000	−	38.9711i	−0.953356	−	1.65126i	−0.738087	−	0.674705i	$-0.764271\pi$
$557$	−22.5000	−	38.9711i	−0.953356	−	1.65126i	−0.215268	−	0.976555i	$-0.569063\pi$
$558$	3.00000	−	5.19615i	0.127000	−	0.219971i
$559$	28.0000			1.18427
$560$		0			0
$561$	4.00000			0.168880
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	7.00000	+	12.1244i	0.295015	+	0.510981i	0.974988	−	0.222256i	$-0.0713421\pi$
$563$	7.00000	+	12.1244i	0.295015	+	0.510981i	−0.679974	+	0.733237i	$0.738009\pi$
$564$	1.50000	+	2.59808i	0.0631614	+	0.109399i
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	2.00000			0.0840663
$567$		0			0
$568$	−14.0000			−0.587427
$569$	18.5000	−	32.0429i	0.775560	−	1.34331i	−0.158919	−	0.987292i	$-0.550801\pi$
$569$	18.5000	−	32.0429i	0.775560	−	1.34331i	0.934479	−	0.356018i	$-0.115866\pi$
$570$	0.500000	+	0.866025i	0.0209427	+	0.0362738i
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	0.937503	−	0.347977i	$-0.113131\pi$
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	−0.770108	+	0.637913i	$0.779798\pi$
$572$	−3.50000	+	6.06218i	−0.146342	+	0.253472i
$573$	10.0000			0.417756
$574$		0			0
$575$	1.00000			0.0417029
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	0.682730	−	0.730670i	$-0.260792\pi$
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	−0.974144	+	0.225927i	$0.927459\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$	13.0000	−	22.5167i	0.540262	−	0.935760i
$580$	8.00000			0.332182
$581$		0			0
$582$	−16.0000			−0.663221
$583$	−0.500000	+	0.866025i	−0.0207079	+	0.0358671i
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$	−3.50000	−	6.06218i	−0.144707	−	0.250640i
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$	−42.0000			−1.73353			−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000			−1.73353			−0.866763	+	0.498721i	$0.833803\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$	−6.00000	+	10.3923i	−0.247016	+	0.427844i
$591$	−1.50000	−	2.59808i	−0.0617018	−	0.106871i
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	6.00000	−	10.3923i	0.246390	−	0.426761i	−0.716131	−	0.697966i	$-0.754089\pi$
$593$	6.00000	−	10.3923i	0.246390	−	0.426761i	0.962522	+	0.271205i	$0.0874221\pi$
$594$	1.00000			0.0410305
$595$		0			0
$596$	−4.00000			−0.163846
$597$	6.00000	−	10.3923i	0.245564	−	0.425329i
$598$	3.50000	+	6.06218i	0.143126	+	0.247901i
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	0.798206	−	0.602384i	$-0.205782\pi$
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	−0.920783	+	0.390075i	$0.872449\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	1.00000	−	1.73205i	0.0406894	−	0.0704761i
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$		0			0
$607$	12.5000	−	21.6506i	0.507359	−	0.878772i	−0.492604	−	0.870253i	$-0.663955\pi$
$607$	12.5000	−	21.6506i	0.507359	−	0.878772i	0.999964	−	0.00851879i	$-0.00271165\pi$
$608$	−1.00000			−0.0405554
$609$		0			0
$610$	−4.00000			−0.161955
$611$	10.5000	−	18.1865i	0.424785	−	0.735748i
$612$	−2.00000	−	3.46410i	−0.0808452	−	0.140028i
$613$	7.50000	+	12.9904i	0.302922	+	0.524677i	0.976797	−	0.214169i	$-0.0687045\pi$
$613$	7.50000	+	12.9904i	0.302922	+	0.524677i	−0.673874	+	0.738846i	$0.735371\pi$
$614$	4.00000	−	6.92820i	0.161427	−	0.279600i
$615$	−9.00000			−0.362915
$616$		0			0
$617$	8.00000			0.322068			0.161034	−	0.986949i	$-0.448517\pi$
$617$	8.00000			0.322068			0.161034	+	0.986949i	$0.448517\pi$
$618$	−8.00000	+	13.8564i	−0.321807	+	0.557386i
$619$	−3.50000	−	6.06218i	−0.140677	−	0.243659i	0.787075	−	0.616858i	$-0.211595\pi$
$619$	−3.50000	−	6.06218i	−0.140677	−	0.243659i	−0.927752	+	0.373198i	$0.878261\pi$
$620$	−3.00000	−	5.19615i	−0.120483	−	0.208683i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	−16.0000			−0.641542
$623$		0			0
$624$	7.00000			0.280224
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−12.0000	−	20.7846i	−0.479616	−	0.830720i
$627$	0.500000	+	0.866025i	0.0199681	+	0.0345857i
$628$	7.50000	−	12.9904i	0.299283	−	0.518373i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	−2.00000	+	3.46410i	−0.0795557	+	0.137795i
$633$	−7.50000	−	12.9904i	−0.298098	−	0.516321i
$634$	−5.00000	−	8.66025i	−0.198575	−	0.343943i
$635$	2.50000	−	4.33013i	0.0992095	−	0.171836i
$636$	1.00000			0.0396526
$637$		0			0
$638$	8.00000			0.316723
$639$	7.00000	−	12.1244i	0.276916	−	0.479632i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	11.5000	+	19.9186i	0.454223	+	0.786737i	0.998643	−	0.0520757i	$-0.0165837\pi$
$641$	11.5000	+	19.9186i	0.454223	+	0.786737i	−0.544420	+	0.838812i	$0.683250\pi$
$642$	−9.00000	+	15.5885i	−0.355202	+	0.615227i
$643$	−26.0000			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$	2.00000	−	3.46410i	0.0786889	−	0.136293i
$647$	−7.50000	−	12.9904i	−0.294855	−	0.510705i	0.680096	−	0.733123i	$-0.261938\pi$
$647$	−7.50000	−	12.9904i	−0.294855	−	0.510705i	−0.974951	+	0.222419i	$0.928605\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−6.00000	+	10.3923i	−0.235521	+	0.407934i
$650$	−7.00000			−0.274563
$651$		0			0
$652$	8.00000			0.313304
$653$	−14.5000	+	25.1147i	−0.567429	+	0.982816i	0.429390	+	0.903119i	$0.358728\pi$
$653$	−14.5000	+	25.1147i	−0.567429	+	0.982816i	−0.996819	+	0.0796966i	$0.974605\pi$
$654$	−5.00000	−	8.66025i	−0.195515	−	0.338643i
$655$	6.50000	+	11.2583i	0.253976	+	0.439899i
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	14.0000			0.546192
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	0.500000	−	0.866025i	0.0194625	−	0.0337100i
$661$	4.00000	+	6.92820i	0.155582	+	0.269476i	0.933271	−	0.359174i	$-0.116941\pi$
$661$	4.00000	+	6.92820i	0.155582	+	0.269476i	−0.777689	+	0.628649i	$0.783608\pi$
$662$	4.50000	+	7.79423i	0.174897	+	0.302931i
$663$	−14.0000	+	24.2487i	−0.543715	+	0.941742i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−3.00000			−0.116248
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$	−2.50000	−	4.33013i	−0.0967279	−	0.167538i
$669$	2.00000	+	3.46410i	0.0773245	+	0.133930i
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$	−4.00000			−0.154418
$672$		0			0
$673$	−12.0000			−0.462566			−0.231283	−	0.972887i	$-0.574292\pi$
$673$	−12.0000			−0.462566			−0.231283	+	0.972887i	$0.574292\pi$
$674$		0			0
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−18.0000	−	31.1769i	−0.692308	−	1.19911i
$677$	0.500000	−	0.866025i	0.0192166	−	0.0332841i	−0.856257	−	0.516550i	$-0.827216\pi$
$677$	0.500000	−	0.866025i	0.0192166	−	0.0332841i	0.875474	+	0.483266i	$0.160549\pi$
$678$	6.00000			0.230429
$679$		0			0
$680$	−4.00000			−0.153393
$681$	10.0000	−	17.3205i	0.383201	−	0.663723i
$682$	−3.00000	−	5.19615i	−0.114876	−	0.198971i
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	0.500000	−	0.866025i	0.0191180	−	0.0331133i
$685$	2.00000			0.0764161
$686$		0			0
$687$	−22.0000			−0.839352
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−3.50000	−	6.06218i	−0.133339	−	0.230951i
$690$	−0.500000	−	0.866025i	−0.0190347	−	0.0329690i
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$	21.0000			0.798300
$693$		0			0
$694$	−34.0000			−1.29062
$695$	2.00000	−	3.46410i	0.0758643	−	0.131401i
$696$	−4.00000	−	6.92820i	−0.151620	−	0.262613i
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	−14.0000	+	24.2487i	−0.529908	+	0.917827i
$699$	−26.0000			−0.983410
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$	−3.50000	+	6.06218i	−0.132099	+	0.228802i
$703$	−1.50000	−	2.59808i	−0.0565736	−	0.0979883i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−1.50000	+	2.59808i	−0.0564933	+	0.0978492i
$706$	8.00000			0.301084
$707$		0			0
$708$	12.0000			0.450988
$709$	−2.00000	+	3.46410i	−0.0751116	+	0.130097i	−0.901135	−	0.433539i	$-0.857265\pi$
$709$	−2.00000	+	3.46410i	−0.0751116	+	0.130097i	0.826023	+	0.563636i	$0.190598\pi$
$710$	−7.00000	−	12.1244i	−0.262705	−	0.455019i
$711$	−2.00000	−	3.46410i	−0.0750059	−	0.129914i
$712$	−1.00000	+	1.73205i	−0.0374766	+	0.0649113i
$713$	−6.00000			−0.224702
$714$		0			0
$715$	−7.00000			−0.261785
$716$	−6.50000	+	11.2583i	−0.242916	+	0.420744i
$717$	−3.00000	−	5.19615i	−0.112037	−	0.194054i
$718$	−18.0000	−	31.1769i	−0.671754	−	1.16351i
$719$	13.0000	−	22.5167i	0.484818	−	0.839730i	−0.515030	−	0.857172i	$-0.672219\pi$
$719$	13.0000	−	22.5167i	0.484818	−	0.839730i	0.999848	+	0.0174426i	$0.00555244\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	−18.0000			−0.669891
$723$	−3.50000	+	6.06218i	−0.130166	+	0.225455i
$724$	−6.00000	−	10.3923i	−0.222988	−	0.386227i
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$	−5.00000	+	8.66025i	−0.185567	+	0.321412i
$727$	−17.0000			−0.630495			−0.315248	−	0.949009i	$-0.602088\pi$
$727$	−17.0000			−0.630495			−0.315248	+	0.949009i	$0.602088\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	7.00000	−	12.1244i	0.259082	−	0.448743i
$731$	8.00000	+	13.8564i	0.295891	+	0.512498i
$732$	2.00000	+	3.46410i	0.0739221	+	0.128037i
$733$	18.5000	−	32.0429i	0.683313	−	1.18353i	−0.290651	−	0.956829i	$-0.593872\pi$
$733$	18.5000	−	32.0429i	0.683313	−	1.18353i	0.973964	−	0.226704i	$-0.0727949\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$	1.00000			0.0368605
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	4.50000	+	7.79423i	0.165647	+	0.286910i
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	−0.945818	−	0.324697i	$-0.894738\pi$
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	0.191714	−	0.981451i	$-0.438596\pi$
$740$	−1.50000	+	2.59808i	−0.0551411	+	0.0955072i
$741$	−7.00000			−0.257151
$742$		0			0
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$	−3.00000	+	5.19615i	−0.109985	+	0.190500i
$745$	−2.00000	−	3.46410i	−0.0732743	−	0.126915i
$746$	−13.0000	−	22.5167i	−0.475964	−	0.824394i
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$	−4.00000			−0.146254
$749$		0			0
$750$	1.00000			0.0365148
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	−0.525193	−	0.850983i	$-0.676007\pi$
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	0.999570	+	0.0293387i	$0.00934013\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	1.50000	+	2.59808i	0.0546630	+	0.0946792i
$754$	−28.0000	+	48.4974i	−1.01970	+	1.76617i
$755$	2.00000			0.0727875
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	−0.500000	+	0.866025i	−0.0181608	+	0.0314555i
$759$	−0.500000	−	0.866025i	−0.0181489	−	0.0314347i
$760$	−0.500000	−	0.866025i	−0.0181369	−	0.0314140i
$761$	−8.50000	+	14.7224i	−0.308125	+	0.533688i	−0.977952	−	0.208829i	$-0.933035\pi$
$761$	−8.50000	+	14.7224i	−0.308125	+	0.533688i	0.669827	+	0.742517i	$0.266368\pi$
$762$	−5.00000			−0.181131
$763$		0			0
$764$	−10.0000			−0.361787
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$	6.50000	+	11.2583i	0.234855	+	0.406780i
$767$	−42.0000	−	72.7461i	−1.51653	−	2.62671i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	29.0000			1.04577			0.522883	−	0.852404i	$-0.324856\pi$
$769$	29.0000			1.04577			0.522883	+	0.852404i	$0.324856\pi$
$770$		0			0
$771$	−8.00000			−0.288113
$772$	−13.0000	+	22.5167i	−0.467880	+	0.810392i
$773$	21.5000	+	37.2391i	0.773301	+	1.33940i	0.935744	+	0.352679i	$0.114729\pi$
$773$	21.5000	+	37.2391i	0.773301	+	1.33940i	−0.162443	+	0.986718i	$0.551937\pi$
$774$	2.00000	+	3.46410i	0.0718885	+	0.124515i
$775$	3.00000	−	5.19615i	0.107763	−	0.186651i
$776$	16.0000			0.574367
$777$		0			0
$778$	−14.0000			−0.501924
$779$	−4.50000	+	7.79423i	−0.161229	+	0.279257i
$780$	3.50000	+	6.06218i	0.125320	+	0.217061i
$781$	−7.00000	−	12.1244i	−0.250480	−	0.433844i
$782$	−2.00000	+	3.46410i	−0.0715199	+	0.123876i
$783$	8.00000			0.285897
$784$		0			0
$785$	15.0000			0.535373
$786$	6.50000	−	11.2583i	0.231847	−	0.401571i
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	0.600620	−	0.799535i	$-0.294921\pi$
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	−0.992727	+	0.120384i	$0.961587\pi$
$788$	1.50000	+	2.59808i	0.0534353	+	0.0925526i
$789$	−8.00000	+	13.8564i	−0.284808	+	0.493301i
$790$	−4.00000			−0.142314
$791$		0			0
$792$	−1.00000			−0.0355335
$793$	14.0000	−	24.2487i	0.497155	−	0.861097i
$794$	9.00000	+	15.5885i	0.319398	+	0.553214i
$795$	0.500000	+	0.866025i	0.0177332	+	0.0307148i
$796$	−6.00000	+	10.3923i	−0.212664	+	0.368345i
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$		0			0
$799$	12.0000			0.424529
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−1.00000	−	1.73205i	−0.0353333	−	0.0611990i
$802$	8.50000	+	14.7224i	0.300145	+	0.519867i
$803$	7.00000	−	12.1244i	0.247025	−	0.427859i
$804$	−12.0000			−0.423207
$805$		0			0
$806$	42.0000			1.47939
$807$		0			0
$808$		0			0
$809$	−26.5000	−	45.8993i	−0.931690	−	1.61374i	−0.780432	−	0.625241i	$-0.785001\pi$
$809$	−26.5000	−	45.8993i	−0.931690	−	1.61374i	−0.151259	−	0.988494i	$-0.548333\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−37.0000			−1.29925			−0.649623	−	0.760257i	$-0.725073\pi$
$811$	−37.0000			−1.29925			−0.649623	+	0.760257i	$0.725073\pi$
$812$		0			0
$813$	16.0000			0.561144
$814$	−1.50000	+	2.59808i	−0.0525750	+	0.0910625i
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	−2.00000	+	3.46410i	−0.0699711	+	0.121194i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	9.00000			0.314294
$821$	−17.0000	+	29.4449i	−0.593304	+	1.02763i	0.400480	+	0.916306i	$0.368843\pi$
$821$	−17.0000	+	29.4449i	−0.593304	+	1.02763i	−0.993784	+	0.111327i	$0.964490\pi$
$822$	−1.00000	−	1.73205i	−0.0348790	−	0.0604122i
$823$	−24.0000	−	41.5692i	−0.836587	−	1.44901i	−0.892731	−	0.450589i	$-0.851214\pi$
$823$	−24.0000	−	41.5692i	−0.836587	−	1.44901i	0.0561440	−	0.998423i	$-0.482119\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$	1.00000			0.0348155
$826$		0			0
$827$	10.0000			0.347734			0.173867	−	0.984769i	$-0.444374\pi$
$827$	10.0000			0.347734			0.173867	+	0.984769i	$0.444374\pi$
$828$	−0.500000	+	0.866025i	−0.0173762	+	0.0300965i
$829$	6.00000	+	10.3923i	0.208389	+	0.360940i	0.951207	−	0.308553i	$-0.0998448\pi$
$829$	6.00000	+	10.3923i	0.208389	+	0.360940i	−0.742818	+	0.669493i	$0.766511\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$	−1.00000	+	1.73205i	−0.0346896	+	0.0600842i
$832$	−7.00000			−0.242681
$833$		0			0
$834$	−4.00000			−0.138509
$835$	2.50000	−	4.33013i	0.0865161	−	0.149850i
$836$	−0.500000	−	0.866025i	−0.0172929	−	0.0299521i
$837$	−3.00000	−	5.19615i	−0.103695	−	0.179605i
$838$	5.50000	−	9.52628i	0.189994	−	0.329080i
$839$	−44.0000			−1.51905			−0.759524	−	0.650479i	$-0.774568\pi$
$839$	−44.0000			−1.51905			−0.759524	+	0.650479i	$0.774568\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	7.00000	−	12.1244i	0.241236	−	0.417833i
$843$	1.50000	+	2.59808i	0.0516627	+	0.0894825i
$844$	7.50000	+	12.9904i	0.258161	+	0.447147i
$845$	18.0000	−	31.1769i	0.619219	−	1.07252i
$846$	3.00000			0.103142
$847$		0			0
$848$	−1.00000			−0.0343401
$849$	1.00000	−	1.73205i	0.0343199	−	0.0594438i
$850$	−2.00000	−	3.46410i	−0.0685994	−	0.118818i
$851$	1.50000	+	2.59808i	0.0514193	+	0.0890609i
$852$	−7.00000	+	12.1244i	−0.239816	+	0.415374i
$853$	−1.00000			−0.0342393			−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000			−0.0342393			−0.0171197	+	0.999853i	$0.505450\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$	9.00000	−	15.5885i	0.307614	−	0.532803i
$857$	−11.0000	−	19.0526i	−0.375753	−	0.650823i	0.614687	−	0.788771i	$-0.289283\pi$
$857$	−11.0000	−	19.0526i	−0.375753	−	0.650823i	−0.990439	+	0.137948i	$0.955949\pi$
$858$	3.50000	+	6.06218i	0.119488	+	0.206959i
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	−0.984655	−	0.174512i	$-0.944165\pi$
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	0.643459	+	0.765480i	$0.277499\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$	−12.0000			−0.408722
$863$	−14.5000	+	25.1147i	−0.493586	+	0.854916i	−0.999973	−	0.00739078i	$-0.997647\pi$
$863$	−14.5000	+	25.1147i	−0.493586	+	0.854916i	0.506387	+	0.862306i	$0.330981\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	10.5000	+	18.1865i	0.357011	+	0.618361i
$866$	20.0000	−	34.6410i	0.679628	−	1.17715i
$867$	1.00000			0.0339618
$868$		0			0
$869$	−4.00000			−0.135691
$870$	4.00000	−	6.92820i	0.135613	−	0.234888i
$871$	42.0000	+	72.7461i	1.42312	+	2.46491i
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$	−8.00000	+	13.8564i	−0.270759	+	0.468968i
$874$	−1.00000			−0.0338255
$875$		0			0
$876$	−14.0000			−0.473016
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$	8.00000	+	13.8564i	0.269987	+	0.467631i
$879$	−4.50000	−	7.79423i	−0.151781	−	0.262893i
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	25.0000			0.842271			0.421136	−	0.906998i	$-0.361632\pi$
$881$	25.0000			0.842271			0.421136	+	0.906998i	$0.361632\pi$
$882$		0			0
$883$	−58.0000			−1.95186			−0.975928	−	0.218094i	$-0.930016\pi$
$883$	−58.0000			−1.95186			−0.975928	+	0.218094i	$0.930016\pi$
$884$	14.0000	−	24.2487i	0.470871	−	0.815572i
$885$	6.00000	+	10.3923i	0.201688	+	0.349334i
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	−0.647865	−	0.761755i	$-0.724338\pi$
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	0.983632	+	0.180190i	$0.0576711\pi$
$888$	3.00000			0.100673
$889$		0			0
$890$	−2.00000			−0.0670402
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−2.00000	−	3.46410i	−0.0669650	−	0.115987i
$893$	1.50000	+	2.59808i	0.0501956	+	0.0869413i
$894$	−2.00000	+	3.46410i	−0.0668900	+	0.115857i
$895$	−13.0000			−0.434542
$896$		0			0
$897$	7.00000			0.233723
$898$	12.5000	−	21.6506i	0.417130	−	0.722491i
$899$	−24.0000	−	41.5692i	−0.800445	−	1.38641i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	2.00000	−	3.46410i	0.0666297	−	0.115406i
$902$	9.00000			0.299667
$903$		0			0
$904$	−6.00000			−0.199557
$905$	6.00000	−	10.3923i	0.199447	−	0.345452i
$906$	−1.00000	−	1.73205i	−0.0332228	−	0.0575435i
$907$	−23.0000	−	39.8372i	−0.763702	−	1.32277i	−0.940930	−	0.338602i	$-0.890046\pi$
$907$	−23.0000	−	39.8372i	−0.763702	−	1.32277i	0.177227	−	0.984170i	$-0.443287\pi$
$908$	−10.0000	+	17.3205i	−0.331862	+	0.574801i
$909$		0			0
$910$		0			0
$911$	−58.0000			−1.92163			−0.960813	−	0.277198i	$-0.910594\pi$
$911$	−58.0000			−1.92163			−0.960813	+	0.277198i	$0.910594\pi$
$912$	−0.500000	+	0.866025i	−0.0165567	+	0.0286770i
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$	−2.00000	+	3.46410i	−0.0661180	+	0.114520i
$916$	22.0000			0.726900
$917$		0			0
$918$	−4.00000			−0.132020
$919$	22.0000	−	38.1051i	0.725713	−	1.25697i	−0.232967	−	0.972485i	$-0.574843\pi$
$919$	22.0000	−	38.1051i	0.725713	−	1.25697i	0.958680	−	0.284487i	$-0.0918233\pi$
$920$	0.500000	+	0.866025i	0.0164845	+	0.0285520i
$921$	−4.00000	−	6.92820i	−0.131804	−	0.228292i
$922$	−14.0000	+	24.2487i	−0.461065	+	0.798589i
$923$	98.0000			3.22571
$924$		0			0
$925$	−3.00000			−0.0986394
$926$	−16.5000	+	28.5788i	−0.542224	+	0.939159i
$927$	8.00000	+	13.8564i	0.262754	+	0.455104i
$928$	4.00000	+	6.92820i	0.131306	+	0.227429i
$929$	15.5000	−	26.8468i	0.508539	−	0.880815i	−0.491413	−	0.870927i	$-0.663519\pi$
$929$	15.5000	−	26.8468i	0.508539	−	0.880815i	0.999951	−	0.00988764i	$-0.00314738\pi$
$930$	−6.00000			−0.196748
$931$		0			0
$932$	26.0000			0.851658
$933$	−8.00000	+	13.8564i	−0.261908	+	0.453638i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$	−2.00000	−	3.46410i	−0.0654070	−	0.113288i
$936$	3.50000	−	6.06218i	0.114401	−	0.198148i
$937$	−16.0000			−0.522697			−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000			−0.522697			−0.261349	+	0.965244i	$0.584167\pi$
$938$		0			0
$939$	−24.0000			−0.783210
$940$	1.50000	−	2.59808i	0.0489246	−	0.0847399i
$941$	−15.0000	−	25.9808i	−0.488986	−	0.846949i	0.510934	−	0.859620i	$-0.329300\pi$
$941$	−15.0000	−	25.9808i	−0.488986	−	0.846949i	−0.999920	+	0.0126715i	$0.995966\pi$
$942$	−7.50000	−	12.9904i	−0.244363	−	0.423249i
$943$	4.50000	−	7.79423i	0.146540	−	0.253815i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	4.00000			0.130051
$947$	−23.0000	+	39.8372i	−0.747400	+	1.29453i	0.201666	+	0.979454i	$0.435365\pi$
$947$	−23.0000	+	39.8372i	−0.747400	+	1.29453i	−0.949065	+	0.315080i	$0.897969\pi$
$948$	2.00000	+	3.46410i	0.0649570	+	0.112509i
$949$	49.0000	+	84.8705i	1.59061	+	2.75501i
$950$	0.500000	−	0.866025i	0.0162221	−	0.0280976i
$951$	−10.0000			−0.324272
$952$		0			0
$953$	44.0000			1.42530			0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000			1.42530			0.712650	+	0.701520i	$0.247495\pi$
$954$	0.500000	−	0.866025i	0.0161881	−	0.0280386i
$955$	−5.00000	−	8.66025i	−0.161796	−	0.280239i
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	4.00000	−	6.92820i	0.129302	−	0.223957i
$958$	−26.0000			−0.840022
$959$		0			0
$960$	1.00000			0.0322749
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−10.5000	−	18.1865i	−0.338534	−	0.586357i
$963$	9.00000	+	15.5885i	0.290021	+	0.502331i
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$	−26.0000			−0.836970
$966$		0			0
$967$	−20.0000			−0.643157			−0.321578	−	0.946883i	$-0.604213\pi$
$967$	−20.0000			−0.643157			−0.321578	+	0.946883i	$0.604213\pi$
$968$	5.00000	−	8.66025i	0.160706	−	0.278351i
$969$	−2.00000	−	3.46410i	−0.0642493	−	0.111283i
$970$	8.00000	+	13.8564i	0.256865	+	0.444902i
$971$	21.5000	−	37.2391i	0.689968	−	1.19506i	−0.281880	−	0.959450i	$-0.590958\pi$
$971$	21.5000	−	37.2391i	0.689968	−	1.19506i	0.971848	−	0.235610i	$-0.0757087\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−8.00000			−0.256337
$975$	−3.50000	+	6.06218i	−0.112090	+	0.194145i
$976$	−2.00000	−	3.46410i	−0.0640184	−	0.110883i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$	4.00000	−	6.92820i	0.127906	−	0.221540i
$979$	−2.00000			−0.0639203
$980$		0			0
$981$	−10.0000			−0.319275
$982$	6.00000	−	10.3923i	0.191468	−	0.331632i
$983$	−16.5000	−	28.5788i	−0.526268	−	0.911523i	−0.999532	−	0.0306024i	$-0.990257\pi$
$983$	−16.5000	−	28.5788i	−0.526268	−	0.911523i	0.473263	−	0.880921i	$-0.343076\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$	−1.50000	+	2.59808i	−0.0477940	+	0.0827816i
$986$	−32.0000			−1.01909
$987$		0			0
$988$	7.00000			0.222700
$989$	2.00000	−	3.46410i	0.0635963	−	0.110152i
$990$	−0.500000	−	0.866025i	−0.0158910	−	0.0275241i
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	0.775617	−	0.631204i	$-0.217439\pi$
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	−0.934447	+	0.356102i	$0.884106\pi$
$992$	3.00000	−	5.19615i	0.0952501	−	0.164978i
$993$	9.00000			0.285606
$994$		0			0
$995$	−12.0000			−0.380426
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	0.934274	−	0.356555i	$-0.116049\pi$
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	−0.775923	+	0.630828i	$0.782715\pi$
$998$	−12.0000	−	20.7846i	−0.379853	−	0.657925i
$999$	−1.50000	+	2.59808i	−0.0474579	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.i.961.1		2
7.2	even	3		1470.2.a.k.1.1		1
7.3	odd	6		210.2.i.a.151.1	yes	2
7.4	even	3	inner	1470.2.i.i.361.1		2
7.5	odd	6		1470.2.a.r.1.1		1
7.6	odd	2		210.2.i.a.121.1	✓	2
21.2	odd	6		4410.2.a.q.1.1		1
21.5	even	6		4410.2.a.g.1.1		1
21.17	even	6		630.2.k.h.361.1		2
21.20	even	2		630.2.k.h.541.1		2
28.3	even	6		1680.2.bg.k.1201.1		2
28.27	even	2		1680.2.bg.k.961.1		2
35.3	even	12		1050.2.o.j.949.1		4
35.9	even	6		7350.2.a.ba.1.1		1
35.13	even	4		1050.2.o.j.499.2		4
35.17	even	12		1050.2.o.j.949.2		4
35.19	odd	6		7350.2.a.j.1.1		1
35.24	odd	6		1050.2.i.s.151.1		2
35.27	even	4		1050.2.o.j.499.1		4
35.34	odd	2		1050.2.i.s.751.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.a.121.1	✓	2	7.6	odd	2
210.2.i.a.151.1	yes	2	7.3	odd	6
630.2.k.h.361.1		2	21.17	even	6
630.2.k.h.541.1		2	21.20	even	2
1050.2.i.s.151.1		2	35.24	odd	6
1050.2.i.s.751.1		2	35.34	odd	2
1050.2.o.j.499.1		4	35.27	even	4
1050.2.o.j.499.2		4	35.13	even	4
1050.2.o.j.949.1		4	35.3	even	12
1050.2.o.j.949.2		4	35.17	even	12
1470.2.a.k.1.1		1	7.2	even	3
1470.2.a.r.1.1		1	7.5	odd	6
1470.2.i.i.361.1		2	7.4	even	3	inner
1470.2.i.i.961.1		2	1.1	even	1	trivial
1680.2.bg.k.961.1		2	28.27	even	2
1680.2.bg.k.1201.1		2	28.3	even	6
4410.2.a.g.1.1		1	21.5	even	6
4410.2.a.q.1.1		1	21.2	odd	6
7350.2.a.j.1.1		1	35.19	odd	6
7350.2.a.ba.1.1		1	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
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} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -7.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.50000 - 6.06218i) q^{26} -1.00000 q^{27} -8.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(1.50000 - 2.59808i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-3.50000 - 6.06218i) q^{39} +(0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-1.50000 + 2.59808i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(2.00000 - 3.46410i) q^{51} +(3.50000 + 6.06218i) q^{52} +(0.500000 + 0.866025i) q^{53} +(0.500000 - 0.866025i) q^{54} +1.00000 q^{55} +1.00000 q^{57} +(4.00000 - 6.92820i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-2.00000 + 3.46410i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-3.50000 + 6.06218i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{68} -1.00000 q^{69} -14.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(1.50000 + 2.59808i) q^{74} +(0.500000 - 0.866025i) q^{75} -1.00000 q^{76} +7.00000 q^{78} +(-2.00000 + 3.46410i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} -12.0000 q^{83} -4.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-1.00000 + 1.73205i) q^{89} -1.00000 q^{90} +1.00000 q^{92} +(-3.00000 + 5.19615i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(0.500000 - 0.866025i) q^{96} +16.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + q^{5} - 2 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 + q^5 - 2 * q^6 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + q^{5} - 2 q^{6} + 2 q^{8} - q^{9} + q^{10} + q^{11} + q^{12} - 14 q^{13} + 2 q^{15} - q^{16} - 4 q^{17} - q^{18} + q^{19} - 2 q^{20} - 2 q^{22} - q^{23} + q^{24} - q^{25} + 7 q^{26} - 2 q^{27} - 16 q^{29} - q^{30} + 6 q^{31} - q^{32} - q^{33} + 8 q^{34} + 2 q^{36} + 3 q^{37} + q^{38} - 7 q^{39} + q^{40} - 18 q^{41} - 8 q^{43} + q^{44} + q^{45} - q^{46} - 3 q^{47} - 2 q^{48} + 2 q^{50} + 4 q^{51} + 7 q^{52} + q^{53} + q^{54} + 2 q^{55} + 2 q^{57} + 8 q^{58} + 12 q^{59} - q^{60} - 4 q^{61} - 12 q^{62} + 2 q^{64} - 7 q^{65} - q^{66} - 12 q^{67} - 4 q^{68} - 2 q^{69} - 28 q^{71} - q^{72} - 14 q^{73} + 3 q^{74} + q^{75} - 2 q^{76} + 14 q^{78} - 4 q^{79} + q^{80} - q^{81} + 9 q^{82} - 24 q^{83} - 8 q^{85} + 4 q^{86} - 8 q^{87} + q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{92} - 6 q^{93} - 3 q^{94} - q^{95} + q^{96} + 32 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + q^5 - 2 * q^6 + 2 * q^8 - q^9 + q^10 + q^11 + q^12 - 14 * q^13 + 2 * q^15 - q^16 - 4 * q^17 - q^18 + q^19 - 2 * q^20 - 2 * q^22 - q^23 + q^24 - q^25 + 7 * q^26 - 2 * q^27 - 16 * q^29 - q^30 + 6 * q^31 - q^32 - q^33 + 8 * q^34 + 2 * q^36 + 3 * q^37 + q^38 - 7 * q^39 + q^40 - 18 * q^41 - 8 * q^43 + q^44 + q^45 - q^46 - 3 * q^47 - 2 * q^48 + 2 * q^50 + 4 * q^51 + 7 * q^52 + q^53 + q^54 + 2 * q^55 + 2 * q^57 + 8 * q^58 + 12 * q^59 - q^60 - 4 * q^61 - 12 * q^62 + 2 * q^64 - 7 * q^65 - q^66 - 12 * q^67 - 4 * q^68 - 2 * q^69 - 28 * q^71 - q^72 - 14 * q^73 + 3 * q^74 + q^75 - 2 * q^76 + 14 * q^78 - 4 * q^79 + q^80 - q^81 + 9 * q^82 - 24 * q^83 - 8 * q^85 + 4 * q^86 - 8 * q^87 + q^88 - 2 * q^89 - 2 * q^90 + 2 * q^92 - 6 * q^93 - 3 * q^94 - q^95 + q^96 + 32 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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