LMFDB - Embedded newform 1470.2.i.x.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:	$0$
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			961.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1470.961
Dual form			1470.2.i.x.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} +(-1.12132 - 1.94218i) q^{11} +(0.500000 - 0.866025i) q^{12} +5.65685 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.29289 - 2.23936i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.41421 - 5.91359i) q^{19} +1.00000 q^{20} -2.24264 q^{22} +(-1.58579 + 2.74666i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.82843 - 4.89898i) q^{26} -1.00000 q^{27} +2.58579 q^{29} +(-0.500000 + 0.866025i) q^{30} +(5.12132 + 8.87039i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.12132 - 1.94218i) q^{33} -2.58579 q^{34} +1.00000 q^{36} +(0.121320 - 0.210133i) q^{37} +(-3.41421 - 5.91359i) q^{38} +(2.82843 + 4.89898i) q^{39} +(0.500000 - 0.866025i) q^{40} +10.4853 q^{41} +9.07107 q^{43} +(-1.12132 + 1.94218i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(1.58579 + 2.74666i) q^{46} +(1.12132 - 1.94218i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(1.29289 - 2.23936i) q^{51} +(-2.82843 - 4.89898i) q^{52} +(-0.171573 - 0.297173i) q^{53} +(-0.500000 + 0.866025i) q^{54} +2.24264 q^{55} +6.82843 q^{57} +(1.29289 - 2.23936i) q^{58} +(1.58579 + 2.74666i) q^{59} +(0.500000 + 0.866025i) q^{60} +(5.82843 - 10.0951i) q^{61} +10.2426 q^{62} +1.00000 q^{64} +(-2.82843 + 4.89898i) q^{65} +(-1.12132 - 1.94218i) q^{66} +(-4.53553 - 7.85578i) q^{67} +(-1.29289 + 2.23936i) q^{68} -3.17157 q^{69} -4.48528 q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 + 1.73205i) q^{73} +(-0.121320 - 0.210133i) q^{74} +(0.500000 - 0.866025i) q^{75} -6.82843 q^{76} +5.65685 q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.24264 - 9.08052i) q^{82} +5.17157 q^{83} +2.58579 q^{85} +(4.53553 - 7.85578i) q^{86} +(1.29289 + 2.23936i) q^{87} +(1.12132 + 1.94218i) q^{88} +(0.414214 - 0.717439i) q^{89} -1.00000 q^{90} +3.17157 q^{92} +(-5.12132 + 8.87039i) q^{93} +(-1.12132 - 1.94218i) q^{94} +(3.41421 + 5.91359i) q^{95} +(-0.500000 + 0.866025i) q^{96} -6.48528 q^{97} +2.24264 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 $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

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

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
$11$	−1.12132	−	1.94218i	−0.338091	−	0.585590i	0.645983	−	0.763352i	$-0.276448\pi$
$11$	−1.12132	−	1.94218i	−0.338091	−	0.585590i	−0.984074	+	0.177762i	$0.943114\pi$
$12$	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
$17$	−1.29289	−	2.23936i	−0.313573	−	0.543124i	0.665560	−	0.746344i	$-0.268193\pi$
$17$	−1.29289	−	2.23936i	−0.313573	−	0.543124i	−0.979133	+	0.203220i	$0.934859\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	3.41421	−	5.91359i	0.783274	−	1.35667i	−0.146750	−	0.989174i	$-0.546881\pi$
$19$	3.41421	−	5.91359i	0.783274	−	1.35667i	0.930025	−	0.367497i	$-0.119785\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−2.24264			−0.478133
$23$	−1.58579	+	2.74666i	−0.330659	+	0.572719i	−0.982641	−	0.185516i	$-0.940604\pi$
$23$	−1.58579	+	2.74666i	−0.330659	+	0.572719i	0.651982	+	0.758234i	$0.273938\pi$
$24$	−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
$29$	2.58579			0.480168			0.240084	−	0.970752i	$-0.422825\pi$
$29$	2.58579			0.480168			0.240084	+	0.970752i	$0.422825\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	5.12132	+	8.87039i	0.919816	+	1.59317i	0.799693	+	0.600410i	$0.204996\pi$
$31$	5.12132	+	8.87039i	0.919816	+	1.59317i	0.120124	+	0.992759i	$0.461671\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.12132	−	1.94218i	0.195197	−	0.338091i
$34$	−2.58579			−0.443459
$35$		0			0
$36$	1.00000			0.166667
$37$	0.121320	−	0.210133i	0.0199449	−	0.0345457i	−0.855881	−	0.517173i	$-0.826984\pi$
$37$	0.121320	−	0.210133i	0.0199449	−	0.0345457i	0.875826	+	0.482628i	$0.160318\pi$
$38$	−3.41421	−	5.91359i	−0.553859	−	0.959311i
$39$	2.82843	+	4.89898i	0.452911	+	0.784465i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	10.4853			1.63753			0.818763	−	0.574132i	$-0.194660\pi$
$41$	10.4853			1.63753			0.818763	+	0.574132i	$0.194660\pi$
$42$		0			0
$43$	9.07107			1.38332			0.691662	−	0.722221i	$-0.256879\pi$
$43$	9.07107			1.38332			0.691662	+	0.722221i	$0.256879\pi$
$44$	−1.12132	+	1.94218i	−0.169045	+	0.292795i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	1.58579	+	2.74666i	0.233811	+	0.404973i
$47$	1.12132	−	1.94218i	0.163561	−	0.283297i	−0.772582	−	0.634915i	$-0.781035\pi$
$47$	1.12132	−	1.94218i	0.163561	−	0.283297i	0.936143	+	0.351618i	$0.114368\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$	1.29289	−	2.23936i	0.181041	−	0.313573i
$52$	−2.82843	−	4.89898i	−0.392232	−	0.679366i
$53$	−0.171573	−	0.297173i	−0.0235673	−	0.0408198i	0.854001	−	0.520271i	$-0.174169\pi$
$53$	−0.171573	−	0.297173i	−0.0235673	−	0.0408198i	−0.877569	+	0.479451i	$0.840836\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	2.24264			0.302398
$56$		0			0
$57$	6.82843			0.904447
$58$	1.29289	−	2.23936i	0.169765	−	0.294042i
$59$	1.58579	+	2.74666i	0.206452	+	0.357585i	0.950594	−	0.310436i	$-0.100475\pi$
$59$	1.58579	+	2.74666i	0.206452	+	0.357585i	−0.744143	+	0.668021i	$0.767142\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	5.82843	−	10.0951i	0.746254	−	1.29255i	−0.203353	−	0.979105i	$-0.565184\pi$
$61$	5.82843	−	10.0951i	0.746254	−	1.29255i	0.949607	−	0.313444i	$-0.101483\pi$
$62$	10.2426			1.30082
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.82843	+	4.89898i	−0.350823	+	0.607644i
$66$	−1.12132	−	1.94218i	−0.138025	−	0.239066i
$67$	−4.53553	−	7.85578i	−0.554104	−	0.959736i	−0.997973	−	0.0636440i	$-0.979728\pi$
$67$	−4.53553	−	7.85578i	−0.554104	−	0.959736i	0.443869	−	0.896092i	$-0.353606\pi$
$68$	−1.29289	+	2.23936i	−0.156786	+	0.271562i
$69$	−3.17157			−0.381813
$70$		0			0
$71$	−4.48528			−0.532305			−0.266152	−	0.963931i	$-0.585752\pi$
$71$	−4.48528			−0.532305			−0.266152	+	0.963931i	$0.585752\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	0.918594	−	0.395203i	$-0.129326\pi$
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	−0.801553	+	0.597924i	$0.795992\pi$
$74$	−0.121320	−	0.210133i	−0.0141032	−	0.0244275i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−6.82843			−0.783274
$77$		0			0
$78$	5.65685			0.640513
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.24264	−	9.08052i	0.578953	−	1.00278i
$83$	5.17157			0.567654			0.283827	−	0.958876i	$-0.408396\pi$
$83$	5.17157			0.567654			0.283827	+	0.958876i	$0.408396\pi$
$84$		0			0
$85$	2.58579			0.280468
$86$	4.53553	−	7.85578i	0.489079	−	0.847110i
$87$	1.29289	+	2.23936i	0.138613	+	0.240084i
$88$	1.12132	+	1.94218i	0.119533	+	0.207037i
$89$	0.414214	−	0.717439i	0.0439065	−	0.0760484i	−0.843237	−	0.537542i	$-0.819353\pi$
$89$	0.414214	−	0.717439i	0.0439065	−	0.0760484i	0.887144	+	0.461494i	$0.152686\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	3.17157			0.330659
$93$	−5.12132	+	8.87039i	−0.531056	+	0.919816i
$94$	−1.12132	−	1.94218i	−0.115655	−	0.200321i
$95$	3.41421	+	5.91359i	0.350291	+	0.606722i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−6.48528			−0.658481			−0.329240	−	0.944246i	$-0.606793\pi$
$97$	−6.48528			−0.658481			−0.329240	+	0.944246i	$0.606793\pi$
$98$		0			0
$99$	2.24264			0.225394
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−8.82843	−	15.2913i	−0.878461	−	1.52154i	−0.853029	−	0.521863i	$-0.825237\pi$
$101$	−8.82843	−	15.2913i	−0.878461	−	1.52154i	−0.0254321	−	0.999677i	$-0.508096\pi$
$102$	−1.29289	−	2.23936i	−0.128016	−	0.221729i
$103$	−7.41421	+	12.8418i	−0.730544	+	1.26534i	0.226107	+	0.974103i	$0.427400\pi$
$103$	−7.41421	+	12.8418i	−0.730544	+	1.26534i	−0.956651	+	0.291237i	$0.905933\pi$
$104$	−5.65685			−0.554700
$105$		0			0
$106$	−0.343146			−0.0333293
$107$	−4.82843	+	8.36308i	−0.466782	+	0.808490i	−0.999280	−	0.0379415i	$-0.987920\pi$
$107$	−4.82843	+	8.36308i	−0.466782	+	0.808490i	0.532498	+	0.846431i	$0.321253\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	1.82843	+	3.16693i	0.175132	+	0.303337i	0.940207	−	0.340604i	$-0.110632\pi$
$109$	1.82843	+	3.16693i	0.175132	+	0.303337i	−0.765075	+	0.643941i	$0.777298\pi$
$110$	1.12132	−	1.94218i	0.106914	−	0.185180i
$111$	0.242641			0.0230304
$112$		0			0
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	3.41421	−	5.91359i	0.319770	−	0.553859i
$115$	−1.58579	−	2.74666i	−0.147875	−	0.256128i
$116$	−1.29289	−	2.23936i	−0.120042	−	0.207919i
$117$	−2.82843	+	4.89898i	−0.261488	+	0.452911i
$118$	3.17157			0.291967
$119$		0			0
$120$	1.00000			0.0912871
$121$	2.98528	−	5.17066i	0.271389	−	0.470060i
$122$	−5.82843	−	10.0951i	−0.527681	−	0.913970i
$123$	5.24264	+	9.08052i	0.472713	+	0.818763i
$124$	5.12132	−	8.87039i	0.459908	−	0.796584i
$125$	1.00000			0.0894427
$126$		0			0
$127$	2.82843			0.250982			0.125491	−	0.992095i	$-0.459949\pi$
$127$	2.82843			0.250982			0.125491	+	0.992095i	$0.459949\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.53553	+	7.85578i	0.399331	+	0.691662i
$130$	2.82843	+	4.89898i	0.248069	+	0.429669i
$131$	1.58579	−	2.74666i	0.138551	−	0.239977i	−0.788397	−	0.615166i	$-0.789089\pi$
$131$	1.58579	−	2.74666i	0.138551	−	0.239977i	0.926948	+	0.375189i	$0.122422\pi$
$132$	−2.24264			−0.195197
$133$		0			0
$134$	−9.07107			−0.783621
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	1.29289	+	2.23936i	0.110865	+	0.192023i
$137$	−6.82843	−	11.8272i	−0.583392	−	1.01046i	−0.995074	−	0.0991368i	$-0.968392\pi$
$137$	−6.82843	−	11.8272i	−0.583392	−	1.01046i	0.411682	−	0.911328i	$-0.364941\pi$
$138$	−1.58579	+	2.74666i	−0.134991	+	0.233811i
$139$	−2.34315			−0.198743			−0.0993715	−	0.995050i	$-0.531683\pi$
$139$	−2.34315			−0.198743			−0.0993715	+	0.995050i	$0.531683\pi$
$140$		0			0
$141$	2.24264			0.188864
$142$	−2.24264	+	3.88437i	−0.188198	+	0.325969i
$143$	−6.34315	−	10.9867i	−0.530440	−	0.918750i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.29289	+	2.23936i	−0.107369	+	0.185968i
$146$	2.00000			0.165521
$147$		0			0
$148$	−0.242641			−0.0199449
$149$	−11.1924	+	19.3858i	−0.916916	+	1.58815i	−0.112845	+	0.993613i	$0.535996\pi$
$149$	−11.1924	+	19.3858i	−0.916916	+	1.58815i	−0.804071	+	0.594533i	$0.797337\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−10.0711	−	17.4436i	−0.819572	−	1.41954i	−0.905998	−	0.423282i	$-0.860878\pi$
$151$	−10.0711	−	17.4436i	−0.819572	−	1.41954i	0.0864262	−	0.996258i	$-0.472455\pi$
$152$	−3.41421	+	5.91359i	−0.276929	+	0.479656i
$153$	2.58579			0.209048
$154$		0			0
$155$	−10.2426			−0.822709
$156$	2.82843	−	4.89898i	0.226455	−	0.392232i
$157$	4.17157	+	7.22538i	0.332928	+	0.576648i	0.983085	−	0.183152i	$-0.0586301\pi$
$157$	4.17157	+	7.22538i	0.332928	+	0.576648i	−0.650157	+	0.759800i	$0.725297\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$	0.171573	−	0.297173i	0.0136066	−	0.0235673i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	8.53553	−	14.7840i	0.668555	−	1.15797i	−0.309754	−	0.950817i	$-0.600247\pi$
$163$	8.53553	−	14.7840i	0.668555	−	1.15797i	0.978308	−	0.207154i	$-0.0664200\pi$
$164$	−5.24264	−	9.08052i	−0.409381	−	0.709069i
$165$	1.12132	+	1.94218i	0.0872947	+	0.151199i
$166$	2.58579	−	4.47871i	0.200696	−	0.347616i
$167$	2.24264			0.173541			0.0867704	−	0.996228i	$-0.472345\pi$
$167$	2.24264			0.173541			0.0867704	+	0.996228i	$0.472345\pi$
$168$		0			0
$169$	19.0000			1.46154
$170$	1.29289	−	2.23936i	0.0991604	−	0.171751i
$171$	3.41421	+	5.91359i	0.261091	+	0.452224i
$172$	−4.53553	−	7.85578i	−0.345831	−	0.598997i
$173$	−10.4142	+	18.0379i	−0.791778	+	1.37140i	0.133087	+	0.991104i	$0.457511\pi$
$173$	−10.4142	+	18.0379i	−0.791778	+	1.37140i	−0.924865	+	0.380295i	$0.875822\pi$
$174$	2.58579			0.196028
$175$		0			0
$176$	2.24264			0.169045
$177$	−1.58579	+	2.74666i	−0.119195	+	0.206452i
$178$	−0.414214	−	0.717439i	−0.0310466	−	0.0537743i
$179$	−13.1213	−	22.7268i	−0.980734	−	1.69868i	−0.659545	−	0.751665i	$-0.729251\pi$
$179$	−13.1213	−	22.7268i	−0.980734	−	1.69868i	−0.321188	−	0.947015i	$-0.604082\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	18.4853			1.37400			0.687000	−	0.726657i	$-0.258927\pi$
$181$	18.4853			1.37400			0.687000	+	0.726657i	$0.258927\pi$
$182$		0			0
$183$	11.6569			0.861699
$184$	1.58579	−	2.74666i	0.116906	−	0.202487i
$185$	0.121320	+	0.210133i	0.00891965	+	0.0154493i
$186$	5.12132	+	8.87039i	0.375513	+	0.650408i
$187$	−2.89949	+	5.02207i	−0.212032	+	0.367250i
$188$	−2.24264			−0.163561
$189$		0			0
$190$	6.82843			0.495386
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	−0.929267	−	0.369410i	$-0.879560\pi$
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	0.784552	+	0.620063i	$0.212893\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	2.41421	+	4.18154i	0.173779	+	0.300994i	0.939738	−	0.341895i	$-0.111069\pi$
$193$	2.41421	+	4.18154i	0.173779	+	0.300994i	−0.765959	+	0.642889i	$0.777736\pi$
$194$	−3.24264	+	5.61642i	−0.232808	+	0.403235i
$195$	−5.65685			−0.405096
$196$		0			0
$197$	−25.7990			−1.83810			−0.919051	−	0.394139i	$-0.871043\pi$
$197$	−25.7990			−1.83810			−0.919051	+	0.394139i	$0.871043\pi$
$198$	1.12132	−	1.94218i	0.0796888	−	0.138025i
$199$	2.87868	+	4.98602i	0.204064	+	0.353450i	0.949834	−	0.312754i	$-0.101252\pi$
$199$	2.87868	+	4.98602i	0.204064	+	0.353450i	−0.745770	+	0.666204i	$0.767918\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	4.53553	−	7.85578i	0.319912	−	0.554104i
$202$	−17.6569			−1.24233
$203$		0			0
$204$	−2.58579			−0.181041
$205$	−5.24264	+	9.08052i	−0.366162	+	0.634211i
$206$	7.41421	+	12.8418i	0.516573	+	0.894730i
$207$	−1.58579	−	2.74666i	−0.110220	−	0.190906i
$208$	−2.82843	+	4.89898i	−0.196116	+	0.339683i
$209$	−15.3137			−1.05927
$210$		0			0
$211$	−23.3137			−1.60498			−0.802491	−	0.596664i	$-0.796492\pi$
$211$	−23.3137			−1.60498			−0.802491	+	0.596664i	$0.796492\pi$
$212$	−0.171573	+	0.297173i	−0.0117837	+	0.0204099i
$213$	−2.24264	−	3.88437i	−0.153663	−	0.266152i
$214$	4.82843	+	8.36308i	0.330064	+	0.571688i
$215$	−4.53553	+	7.85578i	−0.309321	+	0.535759i
$216$	1.00000			0.0680414
$217$		0			0
$218$	3.65685			0.247673
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$	−1.12132	−	1.94218i	−0.0755994	−	0.130942i
$221$	−7.31371	−	12.6677i	−0.491973	−	0.852123i
$222$	0.121320	−	0.210133i	0.00814249	−	0.0141032i
$223$	−7.31371			−0.489762			−0.244881	−	0.969553i	$-0.578749\pi$
$223$	−7.31371			−0.489762			−0.244881	+	0.969553i	$0.578749\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	5.00000	−	8.66025i	0.332595	−	0.576072i
$227$	12.4853	+	21.6251i	0.828677	+	1.43531i	0.899076	+	0.437792i	$0.144239\pi$
$227$	12.4853	+	21.6251i	0.828677	+	1.43531i	−0.0703990	+	0.997519i	$0.522427\pi$
$228$	−3.41421	−	5.91359i	−0.226112	−	0.391637i
$229$	8.07107	−	13.9795i	0.533351	−	0.923791i	−0.465890	−	0.884843i	$-0.654266\pi$
$229$	8.07107	−	13.9795i	0.533351	−	0.923791i	0.999241	−	0.0389487i	$-0.0124009\pi$
$230$	−3.17157			−0.209127
$231$		0			0
$232$	−2.58579			−0.169765
$233$	−9.48528	+	16.4290i	−0.621401	+	1.07630i	0.367824	+	0.929896i	$0.380103\pi$
$233$	−9.48528	+	16.4290i	−0.621401	+	1.07630i	−0.989225	+	0.146403i	$0.953230\pi$
$234$	2.82843	+	4.89898i	0.184900	+	0.320256i
$235$	1.12132	+	1.94218i	0.0731469	+	0.126694i
$236$	1.58579	−	2.74666i	0.103226	−	0.178793i
$237$	−8.00000			−0.519656
$238$		0			0
$239$	−19.3137			−1.24930			−0.624650	−	0.780905i	$-0.714758\pi$
$239$	−19.3137			−1.24930			−0.624650	+	0.780905i	$0.714758\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	9.77817	+	16.9363i	0.629868	+	1.09096i	0.987578	+	0.157130i	$0.0502242\pi$
$241$	9.77817	+	16.9363i	0.629868	+	1.09096i	−0.357710	+	0.933833i	$0.616442\pi$
$242$	−2.98528	−	5.17066i	−0.191901	−	0.332383i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−11.6569			−0.746254
$245$		0			0
$246$	10.4853			0.668517
$247$	19.3137	−	33.4523i	1.22890	−	2.12852i
$248$	−5.12132	−	8.87039i	−0.325204	−	0.563270i
$249$	2.58579	+	4.47871i	0.163868	+	0.283827i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−12.9706			−0.818695			−0.409347	−	0.912379i	$-0.634244\pi$
$251$	−12.9706			−0.818695			−0.409347	+	0.912379i	$0.634244\pi$
$252$		0			0
$253$	7.11270			0.447172
$254$	1.41421	−	2.44949i	0.0887357	−	0.153695i
$255$	1.29289	+	2.23936i	0.0809641	+	0.140234i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.29289	−	16.0958i	0.579675	−	1.00403i	−0.415842	−	0.909437i	$-0.636513\pi$
$257$	9.29289	−	16.0958i	0.579675	−	1.00403i	0.995516	−	0.0945891i	$-0.0301537\pi$
$258$	9.07107			0.564740
$259$		0			0
$260$	5.65685			0.350823
$261$	−1.29289	+	2.23936i	−0.0800281	+	0.138613i
$262$	−1.58579	−	2.74666i	−0.0979702	−	0.169689i
$263$	6.07107	+	10.5154i	0.374358	+	0.648407i	0.990231	−	0.139439i	$-0.0445298\pi$
$263$	6.07107	+	10.5154i	0.374358	+	0.648407i	−0.615873	+	0.787846i	$0.711196\pi$
$264$	−1.12132	+	1.94218i	−0.0690125	+	0.119533i
$265$	0.343146			0.0210793
$266$		0			0
$267$	0.828427			0.0506989
$268$	−4.53553	+	7.85578i	−0.277052	+	0.479868i
$269$	−6.17157	−	10.6895i	−0.376287	−	0.651749i	0.614231	−	0.789126i	$-0.289466\pi$
$269$	−6.17157	−	10.6895i	−0.376287	−	0.651749i	−0.990519	+	0.137377i	$0.956133\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−15.8492	+	27.4517i	−0.962773	+	1.66757i	−0.247290	+	0.968942i	$0.579540\pi$
$271$	−15.8492	+	27.4517i	−0.962773	+	1.66757i	−0.715483	+	0.698630i	$0.753793\pi$
$272$	2.58579			0.156786
$273$		0			0
$274$	−13.6569			−0.825041
$275$	−1.12132	+	1.94218i	−0.0676182	+	0.117118i
$276$	1.58579	+	2.74666i	0.0954531	+	0.165330i
$277$	7.77817	+	13.4722i	0.467345	+	0.809466i	0.999304	−	0.0373046i	$-0.0118772\pi$
$277$	7.77817	+	13.4722i	0.467345	+	0.809466i	−0.531959	+	0.846770i	$0.678544\pi$
$278$	−1.17157	+	2.02922i	−0.0702663	+	0.121705i
$279$	−10.2426			−0.613211
$280$		0			0
$281$	−23.4558			−1.39926			−0.699629	−	0.714506i	$-0.746651\pi$
$281$	−23.4558			−1.39926			−0.699629	+	0.714506i	$0.746651\pi$
$282$	1.12132	−	1.94218i	0.0667737	−	0.115655i
$283$	−4.75736	−	8.23999i	−0.282796	−	0.489816i	0.689277	−	0.724498i	$-0.257928\pi$
$283$	−4.75736	−	8.23999i	−0.282796	−	0.489816i	−0.972072	+	0.234682i	$0.924595\pi$
$284$	2.24264	+	3.88437i	0.133076	+	0.230495i
$285$	−3.41421	+	5.91359i	−0.202241	+	0.350291i
$286$	−12.6863			−0.750156
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	5.15685	−	8.93193i	0.303344	−	0.525408i
$290$	1.29289	+	2.23936i	0.0759213	+	0.131500i
$291$	−3.24264	−	5.61642i	−0.190087	−	0.329240i
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	21.3137			1.24516			0.622580	−	0.782556i	$-0.286084\pi$
$293$	21.3137			1.24516			0.622580	+	0.782556i	$0.286084\pi$
$294$		0			0
$295$	−3.17157			−0.184656
$296$	−0.121320	+	0.210133i	−0.00705160	+	0.0122137i
$297$	1.12132	+	1.94218i	0.0650656	+	0.112697i
$298$	11.1924	+	19.3858i	0.648358	+	1.12299i
$299$	−8.97056	+	15.5375i	−0.518781	+	0.898555i
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	−20.1421			−1.15905
$303$	8.82843	−	15.2913i	0.507180	−	0.878461i
$304$	3.41421	+	5.91359i	0.195819	+	0.339168i
$305$	5.82843	+	10.0951i	0.333735	+	0.578046i
$306$	1.29289	−	2.23936i	0.0739098	−	0.128016i
$307$	−7.31371			−0.417415			−0.208708	−	0.977978i	$-0.566926\pi$
$307$	−7.31371			−0.417415			−0.208708	+	0.977978i	$0.566926\pi$
$308$		0			0
$309$	−14.8284			−0.843560
$310$	−5.12132	+	8.87039i	−0.290871	+	0.503804i
$311$	5.41421	+	9.37769i	0.307012	+	0.531760i	0.977707	−	0.209973i	$-0.0673375\pi$
$311$	5.41421	+	9.37769i	0.307012	+	0.531760i	−0.670695	+	0.741733i	$0.734004\pi$
$312$	−2.82843	−	4.89898i	−0.160128	−	0.277350i
$313$	−15.2426	+	26.4010i	−0.861565	+	1.49227i	0.00885295	+	0.999961i	$0.497182\pi$
$313$	−15.2426	+	26.4010i	−0.861565	+	1.49227i	−0.870418	+	0.492314i	$0.836151\pi$
$314$	8.34315			0.470831
$315$		0			0
$316$	8.00000			0.450035
$317$	12.6569	−	21.9223i	0.710880	−	1.23128i	−0.253648	−	0.967297i	$-0.581630\pi$
$317$	12.6569	−	21.9223i	0.710880	−	1.23128i	0.964527	−	0.263983i	$-0.0850363\pi$
$318$	−0.171573	−	0.297173i	−0.00962133	−	0.0166646i
$319$	−2.89949	−	5.02207i	−0.162341	−	0.281182i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−9.65685			−0.538993
$322$		0			0
$323$	−17.6569			−0.982454
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.82843	−	4.89898i	−0.156893	−	0.271746i
$326$	−8.53553	−	14.7840i	−0.472740	−	0.818809i
$327$	−1.82843	+	3.16693i	−0.101112	+	0.175132i
$328$	−10.4853			−0.578953
$329$		0			0
$330$	2.24264			0.123453
$331$	3.17157	−	5.49333i	0.174325	−	0.301940i	−0.765602	−	0.643314i	$-0.777559\pi$
$331$	3.17157	−	5.49333i	0.174325	−	0.301940i	0.939928	+	0.341374i	$0.110892\pi$
$332$	−2.58579	−	4.47871i	−0.141913	−	0.245801i
$333$	0.121320	+	0.210133i	0.00664831	+	0.0115152i
$334$	1.12132	−	1.94218i	0.0613559	−	0.106272i
$335$	9.07107			0.495605
$336$		0			0
$337$	33.1127			1.80376			0.901882	−	0.431983i	$-0.142186\pi$
$337$	33.1127			1.80376			0.901882	+	0.431983i	$0.142186\pi$
$338$	9.50000	−	16.4545i	0.516732	−	0.895006i
$339$	5.00000	+	8.66025i	0.271563	+	0.470360i
$340$	−1.29289	−	2.23936i	−0.0701170	−	0.121446i
$341$	11.4853	−	19.8931i	0.621963	−	1.07727i
$342$	6.82843			0.369239
$343$		0			0
$344$	−9.07107			−0.489079
$345$	1.58579	−	2.74666i	0.0853759	−	0.147875i
$346$	10.4142	+	18.0379i	0.559872	+	0.969726i
$347$	11.1716	+	19.3497i	0.599721	+	1.03875i	0.992862	+	0.119270i	$0.0380553\pi$
$347$	11.1716	+	19.3497i	0.599721	+	1.03875i	−0.393140	+	0.919478i	$0.628611\pi$
$348$	1.29289	−	2.23936i	0.0693064	−	0.120042i
$349$	23.4558			1.25556			0.627781	−	0.778390i	$-0.283963\pi$
$349$	23.4558			1.25556			0.627781	+	0.778390i	$0.283963\pi$
$350$		0			0
$351$	−5.65685			−0.301941
$352$	1.12132	−	1.94218i	0.0597666	−	0.103519i
$353$	−8.02082	−	13.8925i	−0.426905	−	0.739421i	0.569691	−	0.821859i	$-0.307063\pi$
$353$	−8.02082	−	13.8925i	−0.426905	−	0.739421i	−0.996596	+	0.0824378i	$0.973729\pi$
$354$	1.58579	+	2.74666i	0.0842836	+	0.145983i
$355$	2.24264	−	3.88437i	0.119027	−	0.206161i
$356$	−0.828427			−0.0439065
$357$		0			0
$358$	−26.2426			−1.38697
$359$	14.2426	−	24.6690i	0.751698	−	1.30198i	−0.195301	−	0.980743i	$-0.562569\pi$
$359$	14.2426	−	24.6690i	0.751698	−	1.30198i	0.946999	−	0.321236i	$-0.104098\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	−13.8137	−	23.9260i	−0.727037	−	1.25927i
$362$	9.24264	−	16.0087i	0.485782	−	0.841400i
$363$	5.97056			0.313373
$364$		0			0
$365$	−2.00000			−0.104685
$366$	5.82843	−	10.0951i	0.304657	−	0.527681i
$367$	5.41421	+	9.37769i	0.282620	+	0.489512i	0.972029	−	0.234860i	$-0.0754632\pi$
$367$	5.41421	+	9.37769i	0.282620	+	0.489512i	−0.689410	+	0.724372i	$0.742130\pi$
$368$	−1.58579	−	2.74666i	−0.0826648	−	0.143180i
$369$	−5.24264	+	9.08052i	−0.272921	+	0.472713i
$370$	0.242641			0.0126143
$371$		0			0
$372$	10.2426			0.531056
$373$	−3.29289	+	5.70346i	−0.170500	+	0.295314i	−0.938595	−	0.345022i	$-0.887871\pi$
$373$	−3.29289	+	5.70346i	−0.170500	+	0.295314i	0.768095	+	0.640336i	$0.221205\pi$
$374$	2.89949	+	5.02207i	0.149929	+	0.259685i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−1.12132	+	1.94218i	−0.0578277	+	0.100160i
$377$	14.6274			0.753350
$378$		0			0
$379$	0.485281			0.0249272			0.0124636	−	0.999922i	$-0.496033\pi$
$379$	0.485281			0.0249272			0.0124636	+	0.999922i	$0.496033\pi$
$380$	3.41421	−	5.91359i	0.175145	−	0.303361i
$381$	1.41421	+	2.44949i	0.0724524	+	0.125491i
$382$	2.00000	+	3.46410i	0.102329	+	0.177239i
$383$	−9.70711	+	16.8132i	−0.496010	+	0.859114i	−0.999989	−	0.00460116i	$-0.998535\pi$
$383$	−9.70711	+	16.8132i	−0.496010	+	0.859114i	0.503979	+	0.863716i	$0.331869\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	4.82843			0.245760
$387$	−4.53553	+	7.85578i	−0.230554	+	0.399331i
$388$	3.24264	+	5.61642i	0.164620	+	0.285130i
$389$	14.9497	+	25.8937i	0.757982	+	1.31286i	0.943878	+	0.330294i	$0.107148\pi$
$389$	14.9497	+	25.8937i	0.757982	+	1.31286i	−0.185896	+	0.982569i	$0.559519\pi$
$390$	−2.82843	+	4.89898i	−0.143223	+	0.248069i
$391$	8.20101			0.414743
$392$		0			0
$393$	3.17157			0.159985
$394$	−12.8995	+	22.3426i	−0.649867	+	1.12560i
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$	−1.12132	−	1.94218i	−0.0563485	−	0.0975984i
$397$	−3.34315	+	5.79050i	−0.167788	+	0.290617i	−0.937642	−	0.347603i	$-0.886996\pi$
$397$	−3.34315	+	5.79050i	−0.167788	+	0.290617i	0.769854	+	0.638220i	$0.220329\pi$
$398$	5.75736			0.288590
$399$		0			0
$400$	1.00000			0.0500000
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$	−4.53553	−	7.85578i	−0.226212	−	0.391810i
$403$	28.9706	+	50.1785i	1.44313	+	2.49957i
$404$	−8.82843	+	15.2913i	−0.439231	+	0.760770i
$405$	1.00000			0.0496904
$406$		0			0
$407$	−0.544156			−0.0269728
$408$	−1.29289	+	2.23936i	−0.0640078	+	0.110865i
$409$	−2.12132	−	3.67423i	−0.104893	−	0.181679i	0.808802	−	0.588081i	$-0.200117\pi$
$409$	−2.12132	−	3.67423i	−0.104893	−	0.181679i	−0.913694	+	0.406402i	$0.866783\pi$
$410$	5.24264	+	9.08052i	0.258916	+	0.448455i
$411$	6.82843	−	11.8272i	0.336821	−	0.583392i
$412$	14.8284			0.730544
$413$		0			0
$414$	−3.17157			−0.155874
$415$	−2.58579	+	4.47871i	−0.126931	+	0.219851i
$416$	2.82843	+	4.89898i	0.138675	+	0.240192i
$417$	−1.17157	−	2.02922i	−0.0573722	−	0.0993715i
$418$	−7.65685	+	13.2621i	−0.374509	+	0.648669i
$419$	−36.9706			−1.80613			−0.903065	−	0.429504i	$-0.858689\pi$
$419$	−36.9706			−1.80613			−0.903065	+	0.429504i	$0.858689\pi$
$420$		0			0
$421$	−3.65685			−0.178224			−0.0891121	−	0.996022i	$-0.528403\pi$
$421$	−3.65685			−0.178224			−0.0891121	+	0.996022i	$0.528403\pi$
$422$	−11.6569	+	20.1903i	−0.567447	+	0.982847i
$423$	1.12132	+	1.94218i	0.0545205	+	0.0944322i
$424$	0.171573	+	0.297173i	0.00833232	+	0.0144320i
$425$	−1.29289	+	2.23936i	−0.0627145	+	0.108625i
$426$	−4.48528			−0.217313
$427$		0			0
$428$	9.65685			0.466782
$429$	6.34315	−	10.9867i	0.306250	−	0.530440i
$430$	4.53553	+	7.85578i	0.218723	+	0.378839i
$431$	−6.72792	−	11.6531i	−0.324073	−	0.561310i	0.657252	−	0.753671i	$-0.271719\pi$
$431$	−6.72792	−	11.6531i	−0.324073	−	0.561310i	−0.981324	+	0.192361i	$0.938386\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−17.7990			−0.855365			−0.427682	−	0.903929i	$-0.640670\pi$
$433$	−17.7990			−0.855365			−0.427682	+	0.903929i	$0.640670\pi$
$434$		0			0
$435$	−2.58579			−0.123979
$436$	1.82843	−	3.16693i	0.0875658	−	0.151668i
$437$	10.8284	+	18.7554i	0.517994	+	0.897192i
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	11.8492	−	20.5235i	0.565533	−	0.979533i	−0.431466	−	0.902129i	$-0.642004\pi$
$439$	11.8492	−	20.5235i	0.565533	−	0.979533i	0.997000	−	0.0774037i	$-0.0246630\pi$
$440$	−2.24264			−0.106914
$441$		0			0
$442$	−14.6274			−0.695755
$443$	−18.1421	+	31.4231i	−0.861959	+	1.49296i	0.00807656	+	0.999967i	$0.497429\pi$
$443$	−18.1421	+	31.4231i	−0.861959	+	1.49296i	−0.870035	+	0.492989i	$0.835904\pi$
$444$	−0.121320	−	0.210133i	−0.00575761	−	0.00997247i
$445$	0.414214	+	0.717439i	0.0196356	+	0.0340099i
$446$	−3.65685	+	6.33386i	−0.173157	+	0.299917i
$447$	−22.3848			−1.05876
$448$		0			0
$449$	−10.4853			−0.494831			−0.247416	−	0.968909i	$-0.579581\pi$
$449$	−10.4853			−0.494831			−0.247416	+	0.968909i	$0.579581\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$	−11.7574	−	20.3643i	−0.553632	−	0.958919i
$452$	−5.00000	−	8.66025i	−0.235180	−	0.407344i
$453$	10.0711	−	17.4436i	0.473180	−	0.819572i
$454$	24.9706			1.17193
$455$		0			0
$456$	−6.82843			−0.319770
$457$	−1.24264	+	2.15232i	−0.0581283	+	0.100681i	−0.893625	−	0.448814i	$-0.851847\pi$
$457$	−1.24264	+	2.15232i	−0.0581283	+	0.100681i	0.835497	+	0.549495i	$0.185180\pi$
$458$	−8.07107	−	13.9795i	−0.377136	−	0.653219i
$459$	1.29289	+	2.23936i	0.0603471	+	0.104524i
$460$	−1.58579	+	2.74666i	−0.0739377	+	0.128064i
$461$	2.00000			0.0931493			0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000			0.0931493			0.0465746	+	0.998915i	$0.485169\pi$
$462$		0			0
$463$	−25.6569			−1.19238			−0.596188	−	0.802845i	$-0.703319\pi$
$463$	−25.6569			−1.19238			−0.596188	+	0.802845i	$0.703319\pi$
$464$	−1.29289	+	2.23936i	−0.0600211	+	0.103960i
$465$	−5.12132	−	8.87039i	−0.237496	−	0.411354i
$466$	9.48528	+	16.4290i	0.439397	+	0.761058i
$467$	−6.24264	+	10.8126i	−0.288875	+	0.500346i	−0.973541	−	0.228510i	$-0.926615\pi$
$467$	−6.24264	+	10.8126i	−0.288875	+	0.500346i	0.684667	+	0.728856i	$0.259948\pi$
$468$	5.65685			0.261488
$469$		0			0
$470$	2.24264			0.103445
$471$	−4.17157	+	7.22538i	−0.192216	+	0.332928i
$472$	−1.58579	−	2.74666i	−0.0729917	−	0.126425i
$473$	−10.1716	−	17.6177i	−0.467689	−	0.810062i
$474$	−4.00000	+	6.92820i	−0.183726	+	0.318223i
$475$	−6.82843			−0.313310
$476$		0			0
$477$	0.343146			0.0157116
$478$	−9.65685	+	16.7262i	−0.441694	+	0.765037i
$479$	4.24264	+	7.34847i	0.193851	+	0.335760i	0.946523	−	0.322635i	$-0.104569\pi$
$479$	4.24264	+	7.34847i	0.193851	+	0.335760i	−0.752672	+	0.658396i	$0.771235\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	0.686292	−	1.18869i	0.0312922	−	0.0541997i
$482$	19.5563			0.890767
$483$		0			0
$484$	−5.97056			−0.271389
$485$	3.24264	−	5.61642i	0.147241	−	0.255028i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−5.41421	−	9.37769i	−0.245341	−	0.424944i	0.716886	−	0.697190i	$-0.245567\pi$
$487$	−5.41421	−	9.37769i	−0.245341	−	0.424944i	−0.962228	+	0.272246i	$0.912233\pi$
$488$	−5.82843	+	10.0951i	−0.263840	+	0.456985i
$489$	17.0711			0.771980
$490$		0			0
$491$	−17.0711			−0.770407			−0.385203	−	0.922832i	$-0.625869\pi$
$491$	−17.0711			−0.770407			−0.385203	+	0.922832i	$0.625869\pi$
$492$	5.24264	−	9.08052i	0.236356	−	0.409381i
$493$	−3.34315	−	5.79050i	−0.150568	−	0.260791i
$494$	−19.3137	−	33.4523i	−0.868965	−	1.50509i
$495$	−1.12132	+	1.94218i	−0.0503996	+	0.0872947i
$496$	−10.2426			−0.459908
$497$		0			0
$498$	5.17157			0.231744
$499$	−3.41421	+	5.91359i	−0.152841	+	0.264729i	−0.932271	−	0.361761i	$-0.882176\pi$
$499$	−3.41421	+	5.91359i	−0.152841	+	0.264729i	0.779430	+	0.626490i	$0.215509\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	1.12132	+	1.94218i	0.0500969	+	0.0867704i
$502$	−6.48528	+	11.2328i	−0.289452	+	0.501346i
$503$	−4.58579			−0.204470			−0.102235	−	0.994760i	$-0.532599\pi$
$503$	−4.58579			−0.204470			−0.102235	+	0.994760i	$0.532599\pi$
$504$		0			0
$505$	17.6569			0.785720
$506$	3.55635	−	6.15978i	0.158099	−	0.273836i
$507$	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	−0.614388	−	0.789004i	$-0.710597\pi$
$509$	8.48528	−	14.6969i	0.376103	−	0.651430i	0.990492	+	0.137574i	$0.0439304\pi$
$510$	2.58579			0.114501
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−3.41421	+	5.91359i	−0.150741	+	0.261091i
$514$	−9.29289	−	16.0958i	−0.409892	−	0.709954i
$515$	−7.41421	−	12.8418i	−0.326709	−	0.565877i
$516$	4.53553	−	7.85578i	0.199666	−	0.345831i
$517$	−5.02944			−0.221194
$518$		0			0
$519$	−20.8284			−0.914266
$520$	2.82843	−	4.89898i	0.124035	−	0.214834i
$521$	−19.3848	−	33.5754i	−0.849262	−	1.47097i	−0.881867	−	0.471497i	$-0.843714\pi$
$521$	−19.3848	−	33.5754i	−0.849262	−	1.47097i	0.0326050	−	0.999468i	$-0.489620\pi$
$522$	1.29289	+	2.23936i	0.0565884	+	0.0980140i
$523$	−20.8995	+	36.1990i	−0.913871	+	1.58287i	−0.105325	+	0.994438i	$0.533588\pi$
$523$	−20.8995	+	36.1990i	−0.913871	+	1.58287i	−0.808546	+	0.588433i	$0.799745\pi$
$524$	−3.17157			−0.138551
$525$		0			0
$526$	12.1421			0.529422
$527$	13.2426	−	22.9369i	0.576858	−	0.999148i
$528$	1.12132	+	1.94218i	0.0487992	+	0.0845227i
$529$	6.47056	+	11.2073i	0.281329	+	0.487276i
$530$	0.171573	−	0.297173i	0.00745265	−	0.0129084i
$531$	−3.17157			−0.137635
$532$		0			0
$533$	59.3137			2.56916
$534$	0.414214	−	0.717439i	0.0179248	−	0.0310466i
$535$	−4.82843	−	8.36308i	−0.208751	−	0.361568i
$536$	4.53553	+	7.85578i	0.195905	+	0.339318i
$537$	13.1213	−	22.7268i	0.566227	−	0.980734i
$538$	−12.3431			−0.532151
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	14.8995	−	25.8067i	0.640579	−	1.10952i	−0.344724	−	0.938704i	$-0.612028\pi$
$541$	14.8995	−	25.8067i	0.640579	−	1.10952i	0.985304	−	0.170812i	$-0.0546391\pi$
$542$	15.8492	+	27.4517i	0.680783	+	1.17915i
$543$	9.24264	+	16.0087i	0.396640	+	0.687000i
$544$	1.29289	−	2.23936i	0.0554323	−	0.0960116i
$545$	−3.65685			−0.156642
$546$		0			0
$547$	−28.3848			−1.21365			−0.606823	−	0.794837i	$-0.707556\pi$
$547$	−28.3848			−1.21365			−0.606823	+	0.794837i	$0.707556\pi$
$548$	−6.82843	+	11.8272i	−0.291696	+	0.505232i
$549$	5.82843	+	10.0951i	0.248751	+	0.430850i
$550$	1.12132	+	1.94218i	0.0478133	+	0.0828150i
$551$	8.82843	−	15.2913i	0.376104	−	0.651431i
$552$	3.17157			0.134991
$553$		0			0
$554$	15.5563			0.660926
$555$	−0.121320	+	0.210133i	−0.00514976	+	0.00891965i
$556$	1.17157	+	2.02922i	0.0496858	+	0.0860583i
$557$	19.0000	+	32.9090i	0.805056	+	1.39440i	0.916253	+	0.400599i	$0.131198\pi$
$557$	19.0000	+	32.9090i	0.805056	+	1.39440i	−0.111198	+	0.993798i	$0.535469\pi$
$558$	−5.12132	+	8.87039i	−0.216803	+	0.375513i
$559$	51.3137			2.17034
$560$		0			0
$561$	−5.79899			−0.244834
$562$	−11.7279	+	20.3134i	−0.494713	+	0.856867i
$563$	10.2426	+	17.7408i	0.431676	+	0.747684i	0.997018	−	0.0771722i	$-0.0245891\pi$
$563$	10.2426	+	17.7408i	0.431676	+	0.747684i	−0.565342	+	0.824857i	$0.691256\pi$
$564$	−1.12132	−	1.94218i	−0.0472161	−	0.0817807i
$565$	−5.00000	+	8.66025i	−0.210352	+	0.364340i
$566$	−9.51472			−0.399933
$567$		0			0
$568$	4.48528			0.188198
$569$	−4.51472	+	7.81972i	−0.189267	+	0.327820i	−0.945006	−	0.327053i	$-0.893944\pi$
$569$	−4.51472	+	7.81972i	−0.189267	+	0.327820i	0.755739	+	0.654873i	$0.227278\pi$
$570$	3.41421	+	5.91359i	0.143006	+	0.247693i
$571$	−2.34315	−	4.05845i	−0.0980576	−	0.169841i	0.812823	−	0.582511i	$-0.197930\pi$
$571$	−2.34315	−	4.05845i	−0.0980576	−	0.169841i	−0.910881	+	0.412670i	$0.864596\pi$
$572$	−6.34315	+	10.9867i	−0.265220	+	0.459375i
$573$	−4.00000			−0.167102
$574$		0			0
$575$	3.17157			0.132264
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	1.92893	+	3.34101i	0.0803025	+	0.139088i	0.903380	−	0.428841i	$-0.141078\pi$
$577$	1.92893	+	3.34101i	0.0803025	+	0.139088i	−0.823077	+	0.567929i	$0.807745\pi$
$578$	−5.15685	−	8.93193i	−0.214497	−	0.371519i
$579$	−2.41421	+	4.18154i	−0.100331	+	0.173779i
$580$	2.58579			0.107369
$581$		0			0
$582$	−6.48528			−0.268824
$583$	−0.384776	+	0.666452i	−0.0159358	+	0.0276016i
$584$	−1.00000	−	1.73205i	−0.0413803	−	0.0716728i
$585$	−2.82843	−	4.89898i	−0.116941	−	0.202548i
$586$	10.6569	−	18.4582i	0.440231	−	0.762502i
$587$	−5.17157			−0.213454			−0.106727	−	0.994288i	$-0.534037\pi$
$587$	−5.17157			−0.213454			−0.106727	+	0.994288i	$0.534037\pi$
$588$		0			0
$589$	69.9411			2.88187
$590$	−1.58579	+	2.74666i	−0.0652858	+	0.113078i
$591$	−12.8995	−	22.3426i	−0.530614	−	0.919051i
$592$	0.121320	+	0.210133i	0.00498624	+	0.00863641i
$593$	20.6066	−	35.6917i	0.846212	−	1.46568i	−0.0383530	−	0.999264i	$-0.512211\pi$
$593$	20.6066	−	35.6917i	0.846212	−	1.46568i	0.884565	−	0.466417i	$-0.154456\pi$
$594$	2.24264			0.0920167
$595$		0			0
$596$	22.3848			0.916916
$597$	−2.87868	+	4.98602i	−0.117817	+	0.204064i
$598$	8.97056	+	15.5375i	0.366834	+	0.635374i
$599$	−2.00000	−	3.46410i	−0.0817178	−	0.141539i	0.822270	−	0.569097i	$-0.192707\pi$
$599$	−2.00000	−	3.46410i	−0.0817178	−	0.141539i	−0.903988	+	0.427558i	$0.859374\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	−31.7574			−1.29541			−0.647705	−	0.761891i	$-0.724271\pi$
$601$	−31.7574			−1.29541			−0.647705	+	0.761891i	$0.724271\pi$
$602$		0			0
$603$	9.07107			0.369402
$604$	−10.0711	+	17.4436i	−0.409786	+	0.709770i
$605$	2.98528	+	5.17066i	0.121369	+	0.210217i
$606$	−8.82843	−	15.2913i	−0.358630	−	0.621166i
$607$	−2.00000	+	3.46410i	−0.0811775	+	0.140604i	−0.903756	−	0.428048i	$-0.859201\pi$
$607$	−2.00000	+	3.46410i	−0.0811775	+	0.140604i	0.822578	+	0.568652i	$0.192535\pi$
$608$	6.82843			0.276929
$609$		0			0
$610$	11.6569			0.471972
$611$	6.34315	−	10.9867i	0.256616	−	0.444472i
$612$	−1.29289	−	2.23936i	−0.0522621	−	0.0905206i
$613$	5.53553	+	9.58783i	0.223578	+	0.387249i	0.955892	−	0.293719i	$-0.0948929\pi$
$613$	5.53553	+	9.58783i	0.223578	+	0.387249i	−0.732314	+	0.680967i	$0.761560\pi$
$614$	−3.65685	+	6.33386i	−0.147579	+	0.255614i
$615$	−10.4853			−0.422807
$616$		0			0
$617$	33.9411			1.36642			0.683209	−	0.730223i	$-0.260584\pi$
$617$	33.9411			1.36642			0.683209	+	0.730223i	$0.260584\pi$
$618$	−7.41421	+	12.8418i	−0.298243	+	0.516573i
$619$	−9.55635	−	16.5521i	−0.384102	−	0.665284i	0.607542	−	0.794287i	$-0.292156\pi$
$619$	−9.55635	−	16.5521i	−0.384102	−	0.665284i	−0.991644	+	0.129003i	$0.958822\pi$
$620$	5.12132	+	8.87039i	0.205677	+	0.356243i
$621$	1.58579	−	2.74666i	0.0636354	−	0.110220i
$622$	10.8284			0.434180
$623$		0			0
$624$	−5.65685			−0.226455
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	15.2426	+	26.4010i	0.609218	+	1.05520i
$627$	−7.65685	−	13.2621i	−0.305785	−	0.529636i
$628$	4.17157	−	7.22538i	0.166464	−	0.288324i
$629$	−0.627417			−0.0250168
$630$		0			0
$631$	−8.14214			−0.324133			−0.162067	−	0.986780i	$-0.551816\pi$
$631$	−8.14214			−0.324133			−0.162067	+	0.986780i	$0.551816\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$	−11.6569	−	20.1903i	−0.463318	−	0.802491i
$634$	−12.6569	−	21.9223i	−0.502668	−	0.870646i
$635$	−1.41421	+	2.44949i	−0.0561214	+	0.0972050i
$636$	−0.343146			−0.0136066
$637$		0			0
$638$	−5.79899			−0.229584
$639$	2.24264	−	3.88437i	0.0887175	−	0.153663i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	−0.999878	−	0.0156233i	$-0.995027\pi$
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	0.486409	−	0.873731i	$-0.338307\pi$
$642$	−4.82843	+	8.36308i	−0.190563	+	0.330064i
$643$	28.8284			1.13688			0.568441	−	0.822724i	$-0.307547\pi$
$643$	28.8284			1.13688			0.568441	+	0.822724i	$0.307547\pi$
$644$		0			0
$645$	−9.07107			−0.357173
$646$	−8.82843	+	15.2913i	−0.347350	+	0.601628i
$647$	−4.43503	−	7.68170i	−0.174359	−	0.301999i	0.765580	−	0.643340i	$-0.222452\pi$
$647$	−4.43503	−	7.68170i	−0.174359	−	0.301999i	−0.939939	+	0.341342i	$0.889119\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	3.55635	−	6.15978i	0.139599	−	0.241792i
$650$	−5.65685			−0.221880
$651$		0			0
$652$	−17.0711			−0.668555
$653$	0.899495	−	1.55797i	0.0352000	−	0.0609681i	−0.847889	−	0.530174i	$-0.822127\pi$
$653$	0.899495	−	1.55797i	0.0352000	−	0.0609681i	0.883089	+	0.469206i	$0.155460\pi$
$654$	1.82843	+	3.16693i	0.0714972	+	0.123837i
$655$	1.58579	+	2.74666i	0.0619618	+	0.107321i
$656$	−5.24264	+	9.08052i	−0.204691	+	0.354535i
$657$	−2.00000			−0.0780274
$658$		0			0
$659$	20.3848			0.794078			0.397039	−	0.917802i	$-0.370038\pi$
$659$	20.3848			0.794078			0.397039	+	0.917802i	$0.370038\pi$
$660$	1.12132	−	1.94218i	0.0436473	−	0.0755994i
$661$	2.51472	+	4.35562i	0.0978112	+	0.169414i	0.910778	−	0.412895i	$-0.135483\pi$
$661$	2.51472	+	4.35562i	0.0978112	+	0.169414i	−0.812967	+	0.582309i	$0.802149\pi$
$662$	−3.17157	−	5.49333i	−0.123267	−	0.213504i
$663$	7.31371	−	12.6677i	0.284041	−	0.491973i
$664$	−5.17157			−0.200696
$665$		0			0
$666$	0.242641			0.00940214
$667$	−4.10051	+	7.10228i	−0.158772	+	0.275002i
$668$	−1.12132	−	1.94218i	−0.0433852	−	0.0751453i
$669$	−3.65685	−	6.33386i	−0.141382	−	0.244881i
$670$	4.53553	−	7.85578i	0.175223	−	0.303495i
$671$	−26.1421			−1.00921
$672$		0			0
$673$	−26.2843			−1.01318			−0.506592	−	0.862186i	$-0.669095\pi$
$673$	−26.2843			−1.01318			−0.506592	+	0.862186i	$0.669095\pi$
$674$	16.5563	−	28.6764i	0.637727	−	1.10458i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−9.50000	−	16.4545i	−0.365385	−	0.632865i
$677$	22.2132	−	38.4744i	0.853723	−	1.47869i	−0.0241021	−	0.999710i	$-0.507673\pi$
$677$	22.2132	−	38.4744i	0.853723	−	1.47869i	0.877825	−	0.478982i	$-0.158994\pi$
$678$	10.0000			0.384048
$679$		0			0
$680$	−2.58579			−0.0991604
$681$	−12.4853	+	21.6251i	−0.478437	+	0.828677i
$682$	−11.4853	−	19.8931i	−0.439794	−	0.761746i
$683$	15.8995	+	27.5387i	0.608377	+	1.05374i	0.991508	+	0.130046i	$0.0415126\pi$
$683$	15.8995	+	27.5387i	0.608377	+	1.05374i	−0.383131	+	0.923694i	$0.625154\pi$
$684$	3.41421	−	5.91359i	0.130546	−	0.226112i
$685$	13.6569			0.521802
$686$		0			0
$687$	16.1421			0.615861
$688$	−4.53553	+	7.85578i	−0.172916	+	0.299499i
$689$	−0.970563	−	1.68106i	−0.0369755	−	0.0640434i
$690$	−1.58579	−	2.74666i	−0.0603699	−	0.104564i
$691$	−1.51472	+	2.62357i	−0.0576226	+	0.0998053i	−0.893398	−	0.449267i	$-0.851685\pi$
$691$	−1.51472	+	2.62357i	−0.0576226	+	0.0998053i	0.835775	+	0.549072i	$0.185019\pi$
$692$	20.8284			0.791778
$693$		0			0
$694$	22.3431			0.848134
$695$	1.17157	−	2.02922i	0.0444403	−	0.0769728i
$696$	−1.29289	−	2.23936i	−0.0490070	−	0.0848826i
$697$	−13.5563	−	23.4803i	−0.513483	−	0.889379i
$698$	11.7279	−	20.3134i	0.443908	−	0.768872i
$699$	−18.9706			−0.717533
$700$		0			0
$701$	−17.2132			−0.650134			−0.325067	−	0.945691i	$-0.605387\pi$
$701$	−17.2132			−0.650134			−0.325067	+	0.945691i	$0.605387\pi$
$702$	−2.82843	+	4.89898i	−0.106752	+	0.184900i
$703$	−0.828427	−	1.43488i	−0.0312447	−	0.0541174i
$704$	−1.12132	−	1.94218i	−0.0422614	−	0.0731988i
$705$	−1.12132	+	1.94218i	−0.0422314	+	0.0731469i
$706$	−16.0416			−0.603735
$707$		0			0
$708$	3.17157			0.119195
$709$	−5.92893	+	10.2692i	−0.222666	+	0.385668i	−0.955617	−	0.294613i	$-0.904809\pi$
$709$	−5.92893	+	10.2692i	−0.222666	+	0.385668i	0.732951	+	0.680282i	$0.238143\pi$
$710$	−2.24264	−	3.88437i	−0.0841648	−	0.145778i
$711$	−4.00000	−	6.92820i	−0.150012	−	0.259828i
$712$	−0.414214	+	0.717439i	−0.0155233	+	0.0268872i
$713$	−32.4853			−1.21658
$714$		0			0
$715$	12.6863			0.474440
$716$	−13.1213	+	22.7268i	−0.490367	+	0.849340i
$717$	−9.65685	−	16.7262i	−0.360642	−	0.624650i
$718$	−14.2426	−	24.6690i	−0.531531	−	0.920638i
$719$	−8.97056	+	15.5375i	−0.334546	+	0.579450i	−0.983397	−	0.181465i	$-0.941916\pi$
$719$	−8.97056	+	15.5375i	−0.334546	+	0.579450i	0.648852	+	0.760915i	$0.275249\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	−27.6274			−1.02819
$723$	−9.77817	+	16.9363i	−0.363654	+	0.629868i
$724$	−9.24264	−	16.0087i	−0.343500	−	0.594960i
$725$	−1.29289	−	2.23936i	−0.0480168	−	0.0831676i
$726$	2.98528	−	5.17066i	0.110794	−	0.191901i
$727$	−30.6274			−1.13591			−0.567954	−	0.823060i	$-0.692265\pi$
$727$	−30.6274			−1.13591			−0.567954	+	0.823060i	$0.692265\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−1.00000	+	1.73205i	−0.0370117	+	0.0641061i
$731$	−11.7279	−	20.3134i	−0.433773	−	0.751317i
$732$	−5.82843	−	10.0951i	−0.215425	−	0.373127i
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	−0.360061	−	0.932929i	$-0.617244\pi$
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	0.987971	−	0.154642i	$-0.0494225\pi$
$734$	10.8284			0.399685
$735$		0			0
$736$	−3.17157			−0.116906
$737$	−10.1716	+	17.6177i	−0.374675	+	0.648956i
$738$	5.24264	+	9.08052i	0.192984	+	0.334259i
$739$	−5.55635	−	9.62388i	−0.204394	−	0.354020i	0.745546	−	0.666454i	$-0.232189\pi$
$739$	−5.55635	−	9.62388i	−0.204394	−	0.354020i	−0.949939	+	0.312434i	$0.898856\pi$
$740$	0.121320	−	0.210133i	0.00445982	−	0.00772464i
$741$	38.6274			1.41901
$742$		0			0
$743$	28.2843			1.03765			0.518825	−	0.854881i	$-0.326370\pi$
$743$	28.2843			1.03765			0.518825	+	0.854881i	$0.326370\pi$
$744$	5.12132	−	8.87039i	0.187757	−	0.325204i
$745$	−11.1924	−	19.3858i	−0.410057	−	0.710240i
$746$	3.29289	+	5.70346i	0.120561	+	0.208818i
$747$	−2.58579	+	4.47871i	−0.0946090	+	0.163868i
$748$	5.79899			0.212032
$749$		0			0
$750$	1.00000			0.0365148
$751$	−10.8995	+	18.8785i	−0.397728	+	0.688885i	−0.993445	−	0.114309i	$-0.963535\pi$
$751$	−10.8995	+	18.8785i	−0.397728	+	0.688885i	0.595717	+	0.803194i	$0.296868\pi$
$752$	1.12132	+	1.94218i	0.0408903	+	0.0708242i
$753$	−6.48528	−	11.2328i	−0.236337	−	0.409347i
$754$	7.31371	−	12.6677i	0.266350	−	0.461331i
$755$	20.1421			0.733047
$756$		0			0
$757$	25.8995			0.941333			0.470667	−	0.882311i	$-0.344013\pi$
$757$	25.8995			0.941333			0.470667	+	0.882311i	$0.344013\pi$
$758$	0.242641	−	0.420266i	0.00881311	−	0.0152647i
$759$	3.55635	+	6.15978i	0.129087	+	0.223586i
$760$	−3.41421	−	5.91359i	−0.123847	−	0.214509i
$761$	13.4853	−	23.3572i	0.488841	−	0.846698i	−0.511077	−	0.859535i	$-0.670753\pi$
$761$	13.4853	−	23.3572i	0.488841	−	0.846698i	0.999918	+	0.0128376i	$0.00408646\pi$
$762$	2.82843			0.102463
$763$		0			0
$764$	4.00000			0.144715
$765$	−1.29289	+	2.23936i	−0.0467447	+	0.0809641i
$766$	9.70711	+	16.8132i	0.350732	+	0.607486i
$767$	8.97056	+	15.5375i	0.323908	+	0.561026i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	4.72792			0.170493			0.0852466	−	0.996360i	$-0.472832\pi$
$769$	4.72792			0.170493			0.0852466	+	0.996360i	$0.472832\pi$
$770$		0			0
$771$	18.5858			0.669351
$772$	2.41421	−	4.18154i	0.0868894	−	0.150497i
$773$	11.4853	+	19.8931i	0.413097	+	0.715505i	0.995227	−	0.0975912i	$-0.0311138\pi$
$773$	11.4853	+	19.8931i	0.413097	+	0.715505i	−0.582130	+	0.813096i	$0.697780\pi$
$774$	4.53553	+	7.85578i	0.163026	+	0.282370i
$775$	5.12132	−	8.87039i	0.183963	−	0.318634i
$776$	6.48528			0.232808
$777$		0			0
$778$	29.8995			1.07195
$779$	35.7990	−	62.0057i	1.28263	−	2.22158i
$780$	2.82843	+	4.89898i	0.101274	+	0.175412i
$781$	5.02944	+	8.71124i	0.179967	+	0.311713i
$782$	4.10051	−	7.10228i	0.146634	−	0.253977i
$783$	−2.58579			−0.0924085
$784$		0			0
$785$	−8.34315			−0.297780
$786$	1.58579	−	2.74666i	0.0565631	−	0.0979702i
$787$	−19.1716	−	33.2061i	−0.683393	−	1.18367i	−0.973939	−	0.226810i	$-0.927170\pi$
$787$	−19.1716	−	33.2061i	−0.683393	−	1.18367i	0.290546	−	0.956861i	$-0.406163\pi$
$788$	12.8995	+	22.3426i	0.459525	+	0.795921i
$789$	−6.07107	+	10.5154i	−0.216136	+	0.374358i
$790$	−8.00000			−0.284627
$791$		0			0
$792$	−2.24264			−0.0796888
$793$	32.9706	−	57.1067i	1.17082	−	2.02792i
$794$	3.34315	+	5.79050i	0.118644	+	0.205497i
$795$	0.171573	+	0.297173i	0.00608506	+	0.0105396i
$796$	2.87868	−	4.98602i	0.102032	−	0.176725i
$797$	0.142136			0.00503470			0.00251735	−	0.999997i	$-0.499199\pi$
$797$	0.142136			0.00503470			0.00251735	+	0.999997i	$0.499199\pi$
$798$		0			0
$799$	−5.79899			−0.205154
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	0.414214	+	0.717439i	0.0146355	+	0.0253495i
$802$	−3.00000	−	5.19615i	−0.105934	−	0.183483i
$803$	2.24264	−	3.88437i	0.0791411	−	0.137076i
$804$	−9.07107			−0.319912
$805$		0			0
$806$	57.9411			2.04089
$807$	6.17157	−	10.6895i	0.217250	−	0.376287i
$808$	8.82843	+	15.2913i	0.310583	+	0.537946i
$809$	−17.2426	−	29.8651i	−0.606219	−	1.05000i	−0.991858	−	0.127352i	$-0.959352\pi$
$809$	−17.2426	−	29.8651i	−0.606219	−	1.05000i	0.385639	−	0.922650i	$-0.373981\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	10.3431			0.363197			0.181598	−	0.983373i	$-0.441873\pi$
$811$	10.3431			0.363197			0.181598	+	0.983373i	$0.441873\pi$
$812$		0			0
$813$	−31.6985			−1.11171
$814$	−0.272078	+	0.471253i	−0.00953633	+	0.0165174i
$815$	8.53553	+	14.7840i	0.298987	+	0.517860i
$816$	1.29289	+	2.23936i	0.0452603	+	0.0783932i
$817$	30.9706	−	53.6426i	1.08352	−	1.87672i
$818$	−4.24264			−0.148340
$819$		0			0
$820$	10.4853			0.366162
$821$	−0.606602	+	1.05066i	−0.0211705	+	0.0366685i	−0.876417	−	0.481554i	$-0.840073\pi$
$821$	−0.606602	+	1.05066i	−0.0211705	+	0.0366685i	0.855246	+	0.518222i	$0.173406\pi$
$822$	−6.82843	−	11.8272i	−0.238169	−	0.412520i
$823$	−14.4853	−	25.0892i	−0.504925	−	0.874556i	−0.999984	−	0.00569646i	$-0.998187\pi$
$823$	−14.4853	−	25.0892i	−0.504925	−	0.874556i	0.495059	−	0.868860i	$-0.335147\pi$
$824$	7.41421	−	12.8418i	0.258286	−	0.447365i
$825$	−2.24264			−0.0780787
$826$		0			0
$827$	35.5147			1.23497			0.617484	−	0.786584i	$-0.288152\pi$
$827$	35.5147			1.23497			0.617484	+	0.786584i	$0.288152\pi$
$828$	−1.58579	+	2.74666i	−0.0551099	+	0.0954531i
$829$	−16.6569	−	28.8505i	−0.578516	−	1.00202i	−0.995650	−	0.0931746i	$-0.970299\pi$
$829$	−16.6569	−	28.8505i	−0.578516	−	1.00202i	0.417133	−	0.908845i	$-0.363035\pi$
$830$	2.58579	+	4.47871i	0.0897540	+	0.155458i
$831$	−7.77817	+	13.4722i	−0.269822	+	0.467345i
$832$	5.65685			0.196116
$833$		0			0
$834$	−2.34315			−0.0811365
$835$	−1.12132	+	1.94218i	−0.0388049	+	0.0672120i
$836$	7.65685	+	13.2621i	0.264818	+	0.458678i
$837$	−5.12132	−	8.87039i	−0.177019	−	0.306605i
$838$	−18.4853	+	32.0174i	−0.638563	+	1.10602i
$839$	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
$841$	−22.3137			−0.769438
$842$	−1.82843	+	3.16693i	−0.0630118	+	0.109140i
$843$	−11.7279	−	20.3134i	−0.403931	−	0.699629i
$844$	11.6569	+	20.1903i	0.401245	+	0.694978i
$845$	−9.50000	+	16.4545i	−0.326810	+	0.566051i
$846$	2.24264			0.0771036
$847$		0			0
$848$	0.343146			0.0117837
$849$	4.75736	−	8.23999i	0.163272	−	0.282796i
$850$	1.29289	+	2.23936i	0.0443459	+	0.0768093i
$851$	0.384776	+	0.666452i	0.0131900	+	0.0228457i
$852$	−2.24264	+	3.88437i	−0.0768316	+	0.133076i
$853$	−40.6274			−1.39106			−0.695528	−	0.718499i	$-0.744830\pi$
$853$	−40.6274			−1.39106			−0.695528	+	0.718499i	$0.744830\pi$
$854$		0			0
$855$	−6.82843			−0.233527
$856$	4.82843	−	8.36308i	0.165032	−	0.285844i
$857$	−12.3640	−	21.4150i	−0.422345	−	0.731523i	0.573823	−	0.818979i	$-0.305460\pi$
$857$	−12.3640	−	21.4150i	−0.422345	−	0.731523i	−0.996168	+	0.0874562i	$0.972126\pi$
$858$	−6.34315	−	10.9867i	−0.216551	−	0.375078i
$859$	17.7990	−	30.8288i	0.607294	−	1.05186i	−0.384391	−	0.923170i	$-0.625588\pi$
$859$	17.7990	−	30.8288i	0.607294	−	1.05186i	0.991684	−	0.128693i	$-0.0410782\pi$
$860$	9.07107			0.309321
$861$		0			0
$862$	−13.4558			−0.458308
$863$	−22.8284	+	39.5400i	−0.777089	+	1.34596i	0.156524	+	0.987674i	$0.449971\pi$
$863$	−22.8284	+	39.5400i	−0.777089	+	1.34596i	−0.933613	+	0.358283i	$0.883362\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−10.4142	−	18.0379i	−0.354094	−	0.613309i
$866$	−8.89949	+	15.4144i	−0.302417	+	0.523802i
$867$	10.3137			0.350272
$868$		0			0
$869$	17.9411			0.608611
$870$	−1.29289	+	2.23936i	−0.0438332	+	0.0759213i
$871$	−25.6569	−	44.4390i	−0.869349	−	1.50576i
$872$	−1.82843	−	3.16693i	−0.0619184	−	0.107246i
$873$	3.24264	−	5.61642i	0.109747	−	0.190087i
$874$	21.6569			0.732554
$875$		0			0
$876$	2.00000			0.0675737
$877$	−2.12132	+	3.67423i	−0.0716319	+	0.124070i	−0.899617	−	0.436681i	$-0.856154\pi$
$877$	−2.12132	+	3.67423i	−0.0716319	+	0.124070i	0.827985	+	0.560751i	$0.189487\pi$
$878$	−11.8492	−	20.5235i	−0.399893	−	0.692634i
$879$	10.6569	+	18.4582i	0.359447	+	0.622580i
$880$	−1.12132	+	1.94218i	−0.0377997	+	0.0654710i
$881$	26.0000			0.875962			0.437981	−	0.898984i	$-0.355694\pi$
$881$	26.0000			0.875962			0.437981	+	0.898984i	$0.355694\pi$
$882$		0			0
$883$	−34.2426			−1.15236			−0.576178	−	0.817324i	$-0.695457\pi$
$883$	−34.2426			−1.15236			−0.576178	+	0.817324i	$0.695457\pi$
$884$	−7.31371	+	12.6677i	−0.245987	+	0.426061i
$885$	−1.58579	−	2.74666i	−0.0533056	−	0.0923281i
$886$	18.1421	+	31.4231i	0.609497	+	1.05568i
$887$	16.4350	−	28.4663i	0.551834	−	0.955805i	−0.446308	−	0.894879i	$-0.647261\pi$
$887$	16.4350	−	28.4663i	0.551834	−	0.955805i	0.998142	−	0.0609256i	$-0.0194052\pi$
$888$	−0.242641			−0.00814249
$889$		0			0
$890$	0.828427			0.0277689
$891$	−1.12132	+	1.94218i	−0.0375656	+	0.0650656i
$892$	3.65685	+	6.33386i	0.122441	+	0.212073i
$893$	−7.65685	−	13.2621i	−0.256227	−	0.443798i
$894$	−11.1924	+	19.3858i	−0.374329	+	0.648358i
$895$	26.2426			0.877195
$896$		0			0
$897$	−17.9411			−0.599037
$898$	−5.24264	+	9.08052i	−0.174949	+	0.303021i
$899$	13.2426	+	22.9369i	0.441667	+	0.764989i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−0.443651	+	0.768426i	−0.0147802	+	0.0256000i
$902$	−23.5147			−0.782954
$903$		0			0
$904$	−10.0000			−0.332595
$905$	−9.24264	+	16.0087i	−0.307236	+	0.532148i
$906$	−10.0711	−	17.4436i	−0.334589	−	0.579525i
$907$	8.43503	+	14.6099i	0.280081	+	0.485114i	0.971404	−	0.237431i	$-0.0763055\pi$
$907$	8.43503	+	14.6099i	0.280081	+	0.485114i	−0.691324	+	0.722545i	$0.742972\pi$
$908$	12.4853	−	21.6251i	0.414339	−	0.717656i
$909$	17.6569			0.585641
$910$		0			0
$911$	44.9706			1.48994			0.744971	−	0.667097i	$-0.232463\pi$
$911$	44.9706			1.48994			0.744971	+	0.667097i	$0.232463\pi$
$912$	−3.41421	+	5.91359i	−0.113056	+	0.195819i
$913$	−5.79899	−	10.0441i	−0.191919	−	0.332413i
$914$	1.24264	+	2.15232i	0.0411029	+	0.0711923i
$915$	−5.82843	+	10.0951i	−0.192682	+	0.333735i
$916$	−16.1421			−0.533351
$917$		0			0
$918$	2.58579			0.0853437
$919$	15.3848	−	26.6472i	0.507497	−	0.879010i	−0.492465	−	0.870332i	$-0.663904\pi$
$919$	15.3848	−	26.6472i	0.507497	−	0.879010i	0.999962	−	0.00867847i	$-0.00276248\pi$
$920$	1.58579	+	2.74666i	0.0522818	+	0.0905548i
$921$	−3.65685	−	6.33386i	−0.120497	−	0.208708i
$922$	1.00000	−	1.73205i	0.0329332	−	0.0570421i
$923$	−25.3726			−0.835149
$924$		0			0
$925$	−0.242641			−0.00797798
$926$	−12.8284	+	22.2195i	−0.421568	+	0.730178i
$927$	−7.41421	−	12.8418i	−0.243515	−	0.421780i
$928$	1.29289	+	2.23936i	0.0424413	+	0.0735105i
$929$	−27.8284	+	48.2002i	−0.913021	+	1.58140i	−0.103248	+	0.994656i	$0.532924\pi$
$929$	−27.8284	+	48.2002i	−0.913021	+	1.58140i	−0.809773	+	0.586743i	$0.800410\pi$
$930$	−10.2426			−0.335869
$931$		0			0
$932$	18.9706			0.621401
$933$	−5.41421	+	9.37769i	−0.177253	+	0.307012i
$934$	6.24264	+	10.8126i	0.204265	+	0.353798i
$935$	−2.89949	−	5.02207i	−0.0948236	−	0.164239i
$936$	2.82843	−	4.89898i	0.0924500	−	0.160128i
$937$	36.3431			1.18728			0.593639	−	0.804731i	$-0.297691\pi$
$937$	36.3431			1.18728			0.593639	+	0.804731i	$0.297691\pi$
$938$		0			0
$939$	−30.4853			−0.994850
$940$	1.12132	−	1.94218i	0.0365734	−	0.0633471i
$941$	14.1421	+	24.4949i	0.461020	+	0.798511i	0.999012	−	0.0444393i	$-0.0141501\pi$
$941$	14.1421	+	24.4949i	0.461020	+	0.798511i	−0.537992	+	0.842950i	$0.680817\pi$
$942$	4.17157	+	7.22538i	0.135917	+	0.235415i
$943$	−16.6274	+	28.7995i	−0.541463	+	0.937842i
$944$	−3.17157			−0.103226
$945$		0			0
$946$	−20.3431			−0.661413
$947$	4.58579	−	7.94282i	0.149018	−	0.258107i	−0.781847	−	0.623471i	$-0.785722\pi$
$947$	4.58579	−	7.94282i	0.149018	−	0.258107i	0.930865	+	0.365364i	$0.119055\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	5.65685	+	9.79796i	0.183629	+	0.318055i
$950$	−3.41421	+	5.91359i	−0.110772	+	0.191862i
$951$	25.3137			0.820853
$952$		0			0
$953$	4.68629			0.151804			0.0759019	−	0.997115i	$-0.475816\pi$
$953$	4.68629			0.151804			0.0759019	+	0.997115i	$0.475816\pi$
$954$	0.171573	−	0.297173i	0.00555488	−	0.00962133i
$955$	−2.00000	−	3.46410i	−0.0647185	−	0.112096i
$956$	9.65685	+	16.7262i	0.312325	+	0.540963i
$957$	2.89949	−	5.02207i	0.0937274	−	0.162341i
$958$	8.48528			0.274147
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	−36.9558	+	64.0094i	−1.19212	+	2.06482i
$962$	−0.686292	−	1.18869i	−0.0221269	−	0.0383250i
$963$	−4.82843	−	8.36308i	−0.155594	−	0.269497i
$964$	9.77817	−	16.9363i	0.314934	−	0.545481i
$965$	−4.82843			−0.155433
$966$		0			0
$967$	−10.3431			−0.332613			−0.166307	−	0.986074i	$-0.553184\pi$
$967$	−10.3431			−0.332613			−0.166307	+	0.986074i	$0.553184\pi$
$968$	−2.98528	+	5.17066i	−0.0959506	+	0.166191i
$969$	−8.82843	−	15.2913i	−0.283610	−	0.491227i
$970$	−3.24264	−	5.61642i	−0.104115	−	0.180332i
$971$	2.48528	−	4.30463i	0.0797565	−	0.138142i	−0.823388	−	0.567478i	$-0.807919\pi$
$971$	2.48528	−	4.30463i	0.0797565	−	0.138142i	0.903145	+	0.429336i	$0.141252\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−10.8284			−0.346965
$975$	2.82843	−	4.89898i	0.0905822	−	0.156893i
$976$	5.82843	+	10.0951i	0.186563	+	0.323137i
$977$	14.6569	+	25.3864i	0.468914	+	0.812183i	0.999369	−	0.0355301i	$-0.0113120\pi$
$977$	14.6569	+	25.3864i	0.468914	+	0.812183i	−0.530454	+	0.847714i	$0.677979\pi$
$978$	8.53553	−	14.7840i	0.272936	−	0.472740i
$979$	−1.85786			−0.0593776
$980$		0			0
$981$	−3.65685			−0.116754
$982$	−8.53553	+	14.7840i	−0.272380	+	0.471776i
$983$	8.53553	+	14.7840i	0.272241	+	0.471536i	0.969435	−	0.245347i	$-0.0789018\pi$
$983$	8.53553	+	14.7840i	0.272241	+	0.471536i	−0.697194	+	0.716882i	$0.745568\pi$
$984$	−5.24264	−	9.08052i	−0.167129	−	0.289476i
$985$	12.8995	−	22.3426i	0.411012	−	0.711894i
$986$	−6.68629			−0.212935
$987$		0			0
$988$	−38.6274			−1.22890
$989$	−14.3848	+	24.9152i	−0.457409	+	0.792256i
$990$	1.12132	+	1.94218i	0.0356379	+	0.0617267i
$991$	5.10051	+	8.83433i	0.162023	+	0.280632i	0.935594	−	0.353078i	$-0.114865\pi$
$991$	5.10051	+	8.83433i	0.162023	+	0.280632i	−0.773571	+	0.633709i	$0.781531\pi$
$992$	−5.12132	+	8.87039i	−0.162602	+	0.281635i
$993$	6.34315			0.201294
$994$		0			0
$995$	−5.75736			−0.182521
$996$	2.58579	−	4.47871i	0.0819338	−	0.141913i
$997$	28.3137	+	49.0408i	0.896704	+	1.55314i	0.831681	+	0.555253i	$0.187379\pi$
$997$	28.3137	+	49.0408i	0.896704	+	1.55314i	0.0650229	+	0.997884i	$0.479288\pi$
$998$	3.41421	+	5.91359i	0.108075	+	0.187191i
$999$	−0.121320	+	0.210133i	−0.00383841	+	0.00664831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.x.961.1		4
7.2	even	3		1470.2.a.s.1.2	✓	2
7.3	odd	6		1470.2.i.w.361.1		4
7.4	even	3	inner	1470.2.i.x.361.1		4
7.5	odd	6		1470.2.a.t.1.2	yes	2
7.6	odd	2		1470.2.i.w.961.1		4
21.2	odd	6		4410.2.a.bw.1.1		2
21.5	even	6		4410.2.a.bz.1.1		2
35.9	even	6		7350.2.a.dl.1.2		2
35.19	odd	6		7350.2.a.dh.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.a.s.1.2	✓	2	7.2	even	3
1470.2.a.t.1.2	yes	2	7.5	odd	6
1470.2.i.w.361.1		4	7.3	odd	6
1470.2.i.w.961.1		4	7.6	odd	2
1470.2.i.x.361.1		4	7.4	even	3	inner
1470.2.i.x.961.1		4	1.1	even	1	trivial
4410.2.a.bw.1.1		2	21.2	odd	6
4410.2.a.bz.1.1		2	21.5	even	6
7350.2.a.dh.1.2		2	35.19	odd	6
7350.2.a.dl.1.2		2	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} +(-1.12132 - 1.94218i) q^{11} +(0.500000 - 0.866025i) q^{12} +5.65685 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.29289 - 2.23936i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.41421 - 5.91359i) q^{19} +1.00000 q^{20} -2.24264 q^{22} +(-1.58579 + 2.74666i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.82843 - 4.89898i) q^{26} -1.00000 q^{27} +2.58579 q^{29} +(-0.500000 + 0.866025i) q^{30} +(5.12132 + 8.87039i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.12132 - 1.94218i) q^{33} -2.58579 q^{34} +1.00000 q^{36} +(0.121320 - 0.210133i) q^{37} +(-3.41421 - 5.91359i) q^{38} +(2.82843 + 4.89898i) q^{39} +(0.500000 - 0.866025i) q^{40} +10.4853 q^{41} +9.07107 q^{43} +(-1.12132 + 1.94218i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(1.58579 + 2.74666i) q^{46} +(1.12132 - 1.94218i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(1.29289 - 2.23936i) q^{51} +(-2.82843 - 4.89898i) q^{52} +(-0.171573 - 0.297173i) q^{53} +(-0.500000 + 0.866025i) q^{54} +2.24264 q^{55} +6.82843 q^{57} +(1.29289 - 2.23936i) q^{58} +(1.58579 + 2.74666i) q^{59} +(0.500000 + 0.866025i) q^{60} +(5.82843 - 10.0951i) q^{61} +10.2426 q^{62} +1.00000 q^{64} +(-2.82843 + 4.89898i) q^{65} +(-1.12132 - 1.94218i) q^{66} +(-4.53553 - 7.85578i) q^{67} +(-1.29289 + 2.23936i) q^{68} -3.17157 q^{69} -4.48528 q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 + 1.73205i) q^{73} +(-0.121320 - 0.210133i) q^{74} +(0.500000 - 0.866025i) q^{75} -6.82843 q^{76} +5.65685 q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.24264 - 9.08052i) q^{82} +5.17157 q^{83} +2.58579 q^{85} +(4.53553 - 7.85578i) q^{86} +(1.29289 + 2.23936i) q^{87} +(1.12132 + 1.94218i) q^{88} +(0.414214 - 0.717439i) q^{89} -1.00000 q^{90} +3.17157 q^{92} +(-5.12132 + 8.87039i) q^{93} +(-1.12132 - 1.94218i) q^{94} +(3.41421 + 5.91359i) q^{95} +(-0.500000 + 0.866025i) q^{96} -6.48528 q^{97} +2.24264 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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