LMFDB - Embedded newform 490.2.e.a.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("490.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.91266969904$
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 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.361
Dual form			490.2.e.a.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-1.00000 - 1.73205i) q^{12} -5.00000 q^{13} +2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +1.00000 q^{20} +3.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.50000 + 4.33013i) q^{26} -4.00000 q^{27} -6.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(-5.50000 - 9.52628i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(5.00000 - 8.66025i) q^{39} +(-0.500000 - 0.866025i) q^{40} -3.00000 q^{41} -10.0000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-1.50000 + 2.59808i) q^{46} +(1.50000 + 2.59808i) q^{47} +2.00000 q^{48} +1.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(2.50000 - 4.33013i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(2.00000 + 3.46410i) q^{54} +3.00000 q^{55} +2.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(-1.00000 + 1.73205i) q^{60} +(-2.00000 - 3.46410i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(-3.00000 + 5.19615i) q^{66} +(2.00000 - 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +6.00000 q^{69} +12.0000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(-5.50000 + 9.52628i) q^{74} +(-1.00000 - 1.73205i) q^{75} +1.00000 q^{76} -10.0000 q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(1.50000 + 2.59808i) q^{82} +12.0000 q^{83} -6.00000 q^{85} +(5.00000 + 8.66025i) q^{86} +(6.00000 - 10.3923i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +1.00000 q^{90} +3.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-0.500000 + 0.866025i) q^{95} +(-1.00000 - 1.73205i) q^{96} -14.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 4 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 - q^5 + 4 * q^6 + 2 * q^8 - q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 4 q^{6} + 2 q^{8} - q^{9} - q^{10} - 3 q^{11} - 2 q^{12} - 10 q^{13} + 4 q^{15} - q^{16} + 6 q^{17} - q^{18} - q^{19} + 2 q^{20} + 6 q^{22} - 3 q^{23} - 2 q^{24} - q^{25} + 5 q^{26} - 8 q^{27} - 12 q^{29} - 2 q^{30} - 4 q^{31} - q^{32} - 6 q^{33} - 12 q^{34} + 2 q^{36} - 11 q^{37} - q^{38} + 10 q^{39} - q^{40} - 6 q^{41} - 20 q^{43} - 3 q^{44} - q^{45} - 3 q^{46} + 3 q^{47} + 4 q^{48} + 2 q^{50} + 12 q^{51} + 5 q^{52} - 3 q^{53} + 4 q^{54} + 6 q^{55} + 4 q^{57} + 6 q^{58} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{64} + 5 q^{65} - 6 q^{66} + 4 q^{67} + 6 q^{68} + 12 q^{69} + 24 q^{71} - q^{72} - 4 q^{73} - 11 q^{74} - 2 q^{75} + 2 q^{76} - 20 q^{78} + 10 q^{79} - q^{80} + 11 q^{81} + 3 q^{82} + 24 q^{83} - 12 q^{85} + 10 q^{86} + 12 q^{87} - 3 q^{88} + 6 q^{89} + 2 q^{90} + 6 q^{92} - 8 q^{93} + 3 q^{94} - q^{95} - 2 q^{96} - 28 q^{97} + 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 - q^5 + 4 * q^6 + 2 * q^8 - q^9 - q^10 - 3 * q^11 - 2 * q^12 - 10 * q^13 + 4 * q^15 - q^16 + 6 * q^17 - q^18 - q^19 + 2 * q^20 + 6 * q^22 - 3 * q^23 - 2 * q^24 - q^25 + 5 * q^26 - 8 * q^27 - 12 * q^29 - 2 * q^30 - 4 * q^31 - q^32 - 6 * q^33 - 12 * q^34 + 2 * q^36 - 11 * q^37 - q^38 + 10 * q^39 - q^40 - 6 * q^41 - 20 * q^43 - 3 * q^44 - q^45 - 3 * q^46 + 3 * q^47 + 4 * q^48 + 2 * q^50 + 12 * q^51 + 5 * q^52 - 3 * q^53 + 4 * q^54 + 6 * q^55 + 4 * q^57 + 6 * q^58 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^64 + 5 * q^65 - 6 * q^66 + 4 * q^67 + 6 * q^68 + 12 * q^69 + 24 * q^71 - q^72 - 4 * q^73 - 11 * q^74 - 2 * q^75 + 2 * q^76 - 20 * q^78 + 10 * q^79 - q^80 + 11 * q^81 + 3 * q^82 + 24 * q^83 - 12 * q^85 + 10 * q^86 + 12 * q^87 - 3 * q^88 + 6 * q^89 + 2 * q^90 + 6 * q^92 - 8 * q^93 + 3 * q^94 - q^95 - 2 * q^96 - 28 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−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
$6$	2.00000			0.816497
$7$		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
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	3.00000			0.639602
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.00000	−	1.73205i	−0.182574	−	0.316228i
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.0821995	−	0.996616i	$-0.526194\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	5.00000	−	8.66025i	0.800641	−	1.38675i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$	2.00000			0.288675
$49$		0			0
$50$	1.00000			0.141421
$51$	6.00000	+	10.3923i	0.840168	+	1.45521i
$52$	2.50000	−	4.33013i	0.346688	−	0.600481i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	3.00000			0.404520
$56$		0			0
$57$	2.00000			0.264906
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	−1.00000	+	1.73205i	−0.129099	+	0.223607i
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	2.50000	+	4.33013i	0.310087	+	0.537086i
$66$	−3.00000	+	5.19615i	−0.369274	+	0.639602i
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$	6.00000			0.722315
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	−0.959006	−	0.283387i	$-0.908542\pi$
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	0.724923	+	0.688830i	$0.241875\pi$
$74$	−5.50000	+	9.52628i	−0.639362	+	1.10741i
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$	1.00000			0.114708
$77$		0			0
$78$	−10.0000			−1.13228
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$	5.00000	+	8.66025i	0.539164	+	0.933859i
$87$	6.00000	−	10.3923i	0.643268	−	1.11417i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	3.00000			0.312772
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	−0.500000	+	0.866025i	−0.0512989	+	0.0888523i
$96$	−1.00000	−	1.73205i	−0.102062	−	0.176777i
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$	3.00000			0.301511
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$	6.00000	−	10.3923i	0.594089	−	1.02899i
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	0.750510	−	0.660859i	$-0.229808\pi$
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	−0.947576	+	0.319531i	$0.896475\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	3.00000			0.291386
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	−0.754204	−	0.656640i	$-0.771977\pi$
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	0.945769	+	0.324840i	$0.105310\pi$
$110$	−1.50000	−	2.59808i	−0.143019	−	0.247717i
$111$	22.0000			2.08815
$112$		0			0
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	2.50000	+	4.33013i	0.231125	+	0.400320i
$118$		0			0
$119$		0			0
$120$	2.00000			0.182574
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−2.00000	+	3.46410i	−0.181071	+	0.313625i
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−19.0000			−1.68598			−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	10.0000	−	17.3205i	0.880451	−	1.52499i
$130$	2.50000	−	4.33013i	0.219265	−	0.379777i
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	0.924084	−	0.382190i	$-0.124830\pi$
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	−0.793028	+	0.609185i	$0.791497\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$	−4.00000			−0.345547
$135$	2.00000	+	3.46410i	0.172133	+	0.298142i
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$	−3.00000	−	5.19615i	−0.255377	−	0.442326i
$139$	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
$141$	−6.00000			−0.505291
$142$	−6.00000	−	10.3923i	−0.503509	−	0.872103i
$143$	7.50000	−	12.9904i	0.627182	−	1.08631i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	4.00000			0.331042
$147$		0			0
$148$	11.0000			0.904194
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$	−1.00000	+	1.73205i	−0.0816497	+	0.141421i
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	0.426948	+	0.904276i	$0.359589\pi$
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	−0.996600	+	0.0823900i	$0.973745\pi$
$152$	−0.500000	−	0.866025i	−0.0405554	−	0.0702439i
$153$	−6.00000			−0.485071
$154$		0			0
$155$	4.00000			0.321288
$156$	5.00000	+	8.66025i	0.400320	+	0.693375i
$157$	2.50000	−	4.33013i	0.199522	−	0.345582i	−0.748852	−	0.662738i	$-0.769394\pi$
$157$	2.50000	−	4.33013i	0.199522	−	0.345582i	0.948373	+	0.317156i	$0.102728\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	1.00000			0.0790569
$161$		0			0
$162$	−11.0000			−0.864242
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	−9.00000			−0.696441			−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000			−0.696441			−0.348220	+	0.937413i	$0.613214\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	3.00000	+	5.19615i	0.230089	+	0.398527i
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$	5.00000	−	8.66025i	0.381246	−	0.660338i
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	0.917397	−	0.397974i	$-0.130287\pi$
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	−0.803354	+	0.595502i	$0.796953\pi$
$174$	−12.0000			−0.909718
$175$		0			0
$176$	3.00000			0.226134
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	1.50000	−	2.59808i	0.112115	−	0.194189i	−0.804508	−	0.593942i	$-0.797571\pi$
$179$	1.50000	−	2.59808i	0.112115	−	0.194189i	0.916623	+	0.399753i	$0.130904\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	−5.50000	+	9.52628i	−0.404368	+	0.700386i
$186$	−4.00000	+	6.92820i	−0.293294	+	0.508001i
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$	−3.00000			−0.218797
$189$		0			0
$190$	1.00000			0.0725476
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$	7.00000	+	12.1244i	0.502571	+	0.870478i
$195$	−10.0000			−0.716115
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	4.00000	+	6.92820i	0.282138	+	0.488678i
$202$	12.0000			0.844317
$203$		0			0
$204$	−12.0000			−0.840168
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$	−2.00000	+	3.46410i	−0.139347	+	0.241355i
$207$	−1.50000	+	2.59808i	−0.104257	+	0.180579i
$208$	2.50000	+	4.33013i	0.173344	+	0.300240i
$209$	3.00000			0.207514
$210$		0			0
$211$	−1.00000			−0.0688428			−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000			−0.0688428			−0.0344214	+	0.999407i	$0.510959\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	−12.0000	+	20.7846i	−0.822226	+	1.42414i
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$	−4.00000			−0.272166
$217$		0			0
$218$	−4.00000			−0.270914
$219$	−4.00000	−	6.92820i	−0.270295	−	0.468165i
$220$	−1.50000	+	2.59808i	−0.101130	+	0.175162i
$221$	−15.0000	+	25.9808i	−1.00901	+	1.74766i
$222$	−11.0000	−	19.0526i	−0.738272	−	1.27872i
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	0.125435	+	0.992102i	$0.459967\pi$
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	−0.921903	+	0.387421i	$0.873366\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	−14.0000	−	24.2487i	−0.925146	−	1.60240i	−0.791326	−	0.611394i	$-0.790609\pi$
$229$	−14.0000	−	24.2487i	−0.925146	−	1.60240i	−0.133820	−	0.991006i	$-0.542724\pi$
$230$	3.00000			0.197814
$231$		0			0
$232$	−6.00000			−0.393919
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	2.50000	−	4.33013i	0.163430	−	0.283069i
$235$	1.50000	−	2.59808i	0.0978492	−	0.169480i
$236$		0			0
$237$	−20.0000			−1.29914
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	−1.00000	−	1.73205i	−0.0645497	−	0.111803i
$241$	−12.5000	+	21.6506i	−0.805196	+	1.39464i	0.110963	+	0.993825i	$0.464606\pi$
$241$	−12.5000	+	21.6506i	−0.805196	+	1.39464i	−0.916159	+	0.400815i	$0.868727\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	4.00000			0.256074
$245$		0			0
$246$	−6.00000			−0.382546
$247$	2.50000	+	4.33013i	0.159071	+	0.275519i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	−12.0000	+	20.7846i	−0.760469	+	1.31717i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	15.0000			0.946792			0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000			0.946792			0.473396	+	0.880850i	$0.343028\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$	9.50000	+	16.4545i	0.596083	+	1.03245i
$255$	6.00000	−	10.3923i	0.375735	−	0.650791i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	0.615948	−	0.787787i	$-0.288773\pi$
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	−0.990217	+	0.139533i	$0.955440\pi$
$258$	−20.0000			−1.24515
$259$		0			0
$260$	−5.00000			−0.310087
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	1.50000	−	2.59808i	0.0926703	−	0.160510i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$	3.00000			0.184289
$266$		0			0
$267$	−12.0000			−0.734388
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$	2.00000	−	3.46410i	0.121716	−	0.210819i
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	12.0000			0.724947
$275$	−1.50000	−	2.59808i	−0.0904534	−	0.156670i
$276$	−3.00000	+	5.19615i	−0.180579	+	0.312772i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$	4.00000			0.239474
$280$		0			0
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$	3.00000	+	5.19615i	0.178647	+	0.309426i
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	−0.163270	−	0.986581i	$-0.552204\pi$
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	0.936039	−	0.351895i	$-0.114463\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$	−1.00000	−	1.73205i	−0.0592349	−	0.102598i
$286$	−15.0000			−0.886969
$287$		0			0
$288$	1.00000			0.0589256
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	3.00000	−	5.19615i	0.176166	−	0.305129i
$291$	14.0000	−	24.2487i	0.820695	−	1.42148i
$292$	−2.00000	−	3.46410i	−0.117041	−	0.202721i
$293$	27.0000			1.57736			0.788678	−	0.614806i	$-0.210766\pi$
$293$	27.0000			1.57736			0.788678	+	0.614806i	$0.210766\pi$
$294$		0			0
$295$		0			0
$296$	−5.50000	−	9.52628i	−0.319681	−	0.553704i
$297$	6.00000	−	10.3923i	0.348155	−	0.603023i
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$	7.50000	+	12.9904i	0.433736	+	0.751253i
$300$	2.00000			0.115470
$301$		0			0
$302$	14.0000			0.805609
$303$	−12.0000	−	20.7846i	−0.689382	−	1.19404i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$	−2.00000	+	3.46410i	−0.114520	+	0.198354i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$	5.00000	−	8.66025i	0.283069	−	0.490290i
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	0.956647	−	0.291250i	$-0.0940712\pi$
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	−0.730554	+	0.682855i	$0.760738\pi$
$314$	−5.00000			−0.282166
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−24.0000			−1.33955
$322$		0			0
$323$	−6.00000			−0.333849
$324$	5.50000	+	9.52628i	0.305556	+	0.529238i
$325$	2.50000	−	4.33013i	0.138675	−	0.240192i
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	4.00000	+	6.92820i	0.221201	+	0.383131i
$328$	−3.00000			−0.165647
$329$		0			0
$330$	6.00000			0.330289
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	0.946038	−	0.324057i	$-0.105047\pi$
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	−0.753660	+	0.657264i	$0.771714\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	−5.50000	+	9.52628i	−0.301398	+	0.522037i
$334$	4.50000	+	7.79423i	0.246229	+	0.426481i
$335$	−4.00000			−0.218543
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	−12.0000	+	20.7846i	−0.651751	+	1.12887i
$340$	3.00000	−	5.19615i	0.162698	−	0.281801i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	1.00000			0.0540738
$343$		0			0
$344$	−10.0000			−0.539164
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$	1.50000	−	2.59808i	0.0806405	−	0.139673i
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	0.340293	+	0.940319i	$0.389474\pi$
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	−0.984487	+	0.175457i	$0.943860\pi$
$348$	6.00000	+	10.3923i	0.321634	+	0.557086i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	−0.661004	−	0.750382i	$-0.729870\pi$
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	0.980352	+	0.197256i	$0.0632029\pi$
$354$		0			0
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−3.00000			−0.158555
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	0.775934	−	0.630814i	$-0.217279\pi$
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	−0.934268	+	0.356572i	$0.883946\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	1.00000	+	1.73205i	0.0525588	+	0.0910346i
$363$	−4.00000			−0.209946
$364$		0			0
$365$	4.00000			0.209370
$366$	−4.00000	−	6.92820i	−0.209083	−	0.362143i
$367$	−0.500000	+	0.866025i	−0.0260998	+	0.0452062i	−0.878780	−	0.477227i	$-0.841642\pi$
$367$	−0.500000	+	0.866025i	−0.0260998	+	0.0452062i	0.852680	+	0.522433i	$0.174975\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$	1.50000	+	2.59808i	0.0780869	+	0.135250i
$370$	11.0000			0.571863
$371$		0			0
$372$	8.00000			0.414781
$373$	17.0000	+	29.4449i	0.880227	+	1.52460i	0.851089	+	0.525022i	$0.175943\pi$
$373$	17.0000	+	29.4449i	0.880227	+	1.52460i	0.0291379	+	0.999575i	$0.490724\pi$
$374$	9.00000	−	15.5885i	0.465379	−	0.806060i
$375$	−1.00000	+	1.73205i	−0.0516398	+	0.0894427i
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$	30.0000			1.54508
$378$		0			0
$379$	−25.0000			−1.28416			−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000			−1.28416			−0.642082	+	0.766636i	$0.721929\pi$
$380$	−0.500000	−	0.866025i	−0.0256495	−	0.0444262i
$381$	19.0000	−	32.9090i	0.973399	−	1.68598i
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$	2.00000			0.102062
$385$		0			0
$386$	−4.00000			−0.203595
$387$	5.00000	+	8.66025i	0.254164	+	0.440225i
$388$	7.00000	−	12.1244i	0.355371	−	0.615521i
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	−0.383076	−	0.923717i	$-0.625135\pi$
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	0.991500	−	0.130105i	$-0.0415314\pi$
$390$	5.00000	+	8.66025i	0.253185	+	0.438529i
$391$	−18.0000			−0.910299
$392$		0			0
$393$	−6.00000			−0.302660
$394$	1.50000	+	2.59808i	0.0755689	+	0.130889i
$395$	5.00000	−	8.66025i	0.251577	−	0.435745i
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	0.890028	−	0.455905i	$-0.150684\pi$
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	−0.839840	+	0.542834i	$0.817351\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	1.00000			0.0500000
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	−0.999598	−	0.0283431i	$-0.990977\pi$
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	0.475253	−	0.879849i	$-0.342356\pi$
$402$	4.00000	−	6.92820i	0.199502	−	0.345547i
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	−6.00000	−	10.3923i	−0.298511	−	0.517036i
$405$	−11.0000			−0.546594
$406$		0			0
$407$	33.0000			1.63575
$408$	6.00000	+	10.3923i	0.297044	+	0.514496i
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	0.454759	+	0.890614i	$0.349725\pi$
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	−0.998674	+	0.0514740i	$0.983608\pi$
$410$	1.50000	−	2.59808i	0.0740797	−	0.128310i
$411$	−12.0000	−	20.7846i	−0.591916	−	1.02523i
$412$	4.00000			0.197066
$413$		0			0
$414$	3.00000			0.147442
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$	−4.00000	+	6.92820i	−0.195881	+	0.339276i
$418$	−1.50000	−	2.59808i	−0.0733674	−	0.127076i
$419$	−15.0000			−0.732798			−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000			−0.732798			−0.366399	+	0.930458i	$0.619409\pi$
$420$		0			0
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	0.500000	+	0.866025i	0.0243396	+	0.0421575i
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$	24.0000			1.16280
$427$		0			0
$428$	−12.0000			−0.580042
$429$	15.0000	+	25.9808i	0.724207	+	1.25436i
$430$	5.00000	−	8.66025i	0.241121	−	0.417635i
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	16.0000			0.768911			0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000			0.768911			0.384455	+	0.923144i	$0.374389\pi$
$434$		0			0
$435$	−12.0000			−0.575356
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	−1.50000	+	2.59808i	−0.0717547	+	0.124283i
$438$	−4.00000	+	6.92820i	−0.191127	+	0.331042i
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$	3.00000			0.143019
$441$		0			0
$442$	30.0000			1.42695
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	0.996551	+	0.0829786i	$0.0264433\pi$
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	−0.426414	+	0.904528i	$0.640223\pi$
$444$	−11.0000	+	19.0526i	−0.522037	+	0.904194i
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$	36.0000			1.70274
$448$		0			0
$449$	−3.00000			−0.141579			−0.0707894	−	0.997491i	$-0.522552\pi$
$449$	−3.00000			−0.141579			−0.0707894	+	0.997491i	$0.522552\pi$
$450$	−0.500000	−	0.866025i	−0.0235702	−	0.0408248i
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	−14.0000	−	24.2487i	−0.657777	−	1.13930i
$454$	24.0000			1.12638
$455$		0			0
$456$	2.00000			0.0936586
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$	−14.0000	+	24.2487i	−0.654177	+	1.13307i
$459$	−12.0000	+	20.7846i	−0.560112	+	0.970143i
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$	−4.00000	+	6.92820i	−0.185496	+	0.321288i
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	−9.00000	−	15.5885i	−0.416470	−	0.721348i	0.579111	−	0.815249i	$-0.303400\pi$
$467$	−9.00000	−	15.5885i	−0.416470	−	0.721348i	−0.995582	+	0.0939008i	$0.970066\pi$
$468$	−5.00000			−0.231125
$469$		0			0
$470$	−3.00000			−0.138380
$471$	5.00000	+	8.66025i	0.230388	+	0.399043i
$472$		0			0
$473$	15.0000	−	25.9808i	0.689701	−	1.19460i
$474$	10.0000	+	17.3205i	0.459315	+	0.795557i
$475$	1.00000			0.0458831
$476$		0			0
$477$	3.00000			0.137361
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	−1.00000	+	1.73205i	−0.0456435	+	0.0790569i
$481$	27.5000	+	47.6314i	1.25389	+	2.17180i
$482$	25.0000			1.13872
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	7.00000	+	12.1244i	0.317854	+	0.550539i
$486$	5.00000	−	8.66025i	0.226805	−	0.392837i
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	−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	$0.587280\pi$
$492$	3.00000	+	5.19615i	0.135250	+	0.234261i
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$	2.50000	−	4.33013i	0.112480	−	0.194822i
$495$	−1.50000	−	2.59808i	−0.0674200	−	0.116775i
$496$	4.00000			0.179605
$497$		0			0
$498$	24.0000			1.07547
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	0.988204	+	0.153141i	$0.0489388\pi$
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	−0.361478	+	0.932381i	$0.617728\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$	−7.50000	−	12.9904i	−0.334741	−	0.579789i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	−4.50000	−	7.79423i	−0.200049	−	0.346496i
$507$	−12.0000	+	20.7846i	−0.532939	+	0.923077i
$508$	9.50000	−	16.4545i	0.421494	−	0.730050i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$	−12.0000			−0.531369
$511$		0			0
$512$	1.00000			0.0441942
$513$	2.00000	+	3.46410i	0.0883022	+	0.152944i
$514$	−6.00000	+	10.3923i	−0.264649	+	0.458385i
$515$	−2.00000	+	3.46410i	−0.0881305	+	0.152647i
$516$	10.0000	+	17.3205i	0.440225	+	0.762493i
$517$	−9.00000			−0.395820
$518$		0			0
$519$	−6.00000			−0.263371
$520$	2.50000	+	4.33013i	0.109632	+	0.189889i
$521$	16.5000	−	28.5788i	0.722878	−	1.25206i	−0.236963	−	0.971519i	$-0.576152\pi$
$521$	16.5000	−	28.5788i	0.722878	−	1.25206i	0.959841	−	0.280543i	$-0.0905145\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$	−3.00000			−0.131056
$525$		0			0
$526$		0			0
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$	−3.00000	+	5.19615i	−0.130558	+	0.226134i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−1.50000	−	2.59808i	−0.0651558	−	0.112853i
$531$		0			0
$532$		0			0
$533$	15.0000			0.649722
$534$	6.00000	+	10.3923i	0.259645	+	0.449719i
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$	2.00000	−	3.46410i	0.0863868	−	0.149626i
$537$	3.00000	+	5.19615i	0.129460	+	0.224231i
$538$	12.0000			0.517357
$539$		0			0
$540$	−4.00000			−0.172133
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	2.00000	−	3.46410i	0.0858282	−	0.148659i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$	−2.00000	+	3.46410i	−0.0853579	+	0.147844i
$550$	−1.50000	+	2.59808i	−0.0639602	+	0.110782i
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$	6.00000			0.255377
$553$		0			0
$554$	2.00000			0.0849719
$555$	−11.0000	−	19.0526i	−0.466924	−	0.808736i
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	13.5000	−	23.3827i	0.572013	−	0.990756i	−0.424346	−	0.905500i	$-0.639496\pi$
$557$	13.5000	−	23.3827i	0.572013	−	0.990756i	0.996359	−	0.0852559i	$-0.0271708\pi$
$558$	−2.00000	−	3.46410i	−0.0846668	−	0.146647i
$559$	50.0000			2.11477
$560$		0			0
$561$	−36.0000			−1.51992
$562$	1.50000	+	2.59808i	0.0632737	+	0.109593i
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$	3.00000	−	5.19615i	0.126323	−	0.218797i
$565$	−6.00000	−	10.3923i	−0.252422	−	0.437208i
$566$	−26.0000			−1.09286
$567$		0			0
$568$	12.0000			0.503509
$569$	1.50000	+	2.59808i	0.0628833	+	0.108917i	0.895753	−	0.444552i	$-0.146637\pi$
$569$	1.50000	+	2.59808i	0.0628833	+	0.108917i	−0.832870	+	0.553469i	$0.813304\pi$
$570$	−1.00000	+	1.73205i	−0.0418854	+	0.0725476i
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	7.50000	+	12.9904i	0.313591	+	0.543155i
$573$	24.0000			1.00261
$574$		0			0
$575$	3.00000			0.125109
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	10.0000	−	17.3205i	0.416305	−	0.721062i	−0.579259	−	0.815144i	$-0.696658\pi$
$577$	10.0000	−	17.3205i	0.416305	−	0.721062i	0.995565	+	0.0940813i	$0.0299914\pi$
$578$	−9.50000	+	16.4545i	−0.395148	+	0.684416i
$579$	4.00000	+	6.92820i	0.166234	+	0.287926i
$580$	−6.00000			−0.249136
$581$		0			0
$582$	−28.0000			−1.16064
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$	−2.00000	+	3.46410i	−0.0827606	+	0.143346i
$585$	2.50000	−	4.33013i	0.103362	−	0.179029i
$586$	−13.5000	−	23.3827i	−0.557680	−	0.965930i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	4.00000			0.164817
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	−5.50000	+	9.52628i	−0.226049	+	0.391528i
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	−0.952869	−	0.303383i	$-0.901884\pi$
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	0.213697	−	0.976900i	$-0.431449\pi$
$594$	−12.0000			−0.492366
$595$		0			0
$596$	18.0000			0.737309
$597$	−4.00000	−	6.92820i	−0.163709	−	0.283552i
$598$	7.50000	−	12.9904i	0.306698	−	0.531216i
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	0.0157622	+	0.999876i	$0.494983\pi$
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	−0.873799	+	0.486287i	$0.838351\pi$
$600$	−1.00000	−	1.73205i	−0.0408248	−	0.0707107i
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$	−12.0000	+	20.7846i	−0.487467	+	0.844317i
$607$	−9.50000	−	16.4545i	−0.385593	−	0.667867i	0.606258	−	0.795268i	$-0.292670\pi$
$607$	−9.50000	−	16.4545i	−0.385593	−	0.667867i	−0.991851	+	0.127401i	$0.959336\pi$
$608$	1.00000			0.0405554
$609$		0			0
$610$	4.00000			0.161955
$611$	−7.50000	−	12.9904i	−0.303418	−	0.525535i
$612$	3.00000	−	5.19615i	0.121268	−	0.210042i
$613$	−23.5000	+	40.7032i	−0.949156	+	1.64399i	−0.201948	+	0.979396i	$0.564727\pi$
$613$	−23.5000	+	40.7032i	−0.949156	+	1.64399i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$	−4.00000	−	6.92820i	−0.160904	−	0.278693i
$619$	−0.500000	+	0.866025i	−0.0200967	+	0.0348085i	−0.875899	−	0.482495i	$-0.839731\pi$
$619$	−0.500000	+	0.866025i	−0.0200967	+	0.0348085i	0.855802	+	0.517303i	$0.173064\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$	6.00000	+	10.3923i	0.240772	+	0.417029i
$622$	−12.0000			−0.481156
$623$		0			0
$624$	−10.0000			−0.400320
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.00000	−	6.92820i	0.159872	−	0.276907i
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$	2.50000	+	4.33013i	0.0997609	+	0.172791i
$629$	−66.0000			−2.63159
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$	1.00000	−	1.73205i	0.0397464	−	0.0688428i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	9.50000	+	16.4545i	0.376996	+	0.652976i
$636$	6.00000			0.237915
$637$		0			0
$638$	−18.0000			−0.712627
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	22.5000	−	38.9711i	0.888697	−	1.53927i	0.0472793	−	0.998882i	$-0.484945\pi$
$641$	22.5000	−	38.9711i	0.888697	−	1.53927i	0.841417	−	0.540386i	$-0.181722\pi$
$642$	12.0000	+	20.7846i	0.473602	+	0.820303i
$643$	−38.0000			−1.49857			−0.749287	−	0.662246i	$-0.769604\pi$
$643$	−38.0000			−1.49857			−0.749287	+	0.662246i	$0.769604\pi$
$644$		0			0
$645$	−20.0000			−0.787499
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	−10.5000	+	18.1865i	−0.412798	+	0.714986i	−0.995194	−	0.0979182i	$-0.968782\pi$
$647$	−10.5000	+	18.1865i	−0.412798	+	0.714986i	0.582397	+	0.812905i	$0.302115\pi$
$648$	5.50000	−	9.52628i	0.216060	−	0.374228i
$649$		0			0
$650$	−5.00000			−0.196116
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	0.584091	−	0.811688i	$-0.301451\pi$
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	−0.994988	+	0.0999939i	$0.968118\pi$
$654$	4.00000	−	6.92820i	0.156412	−	0.270914i
$655$	1.50000	−	2.59808i	0.0586098	−	0.101515i
$656$	1.50000	+	2.59808i	0.0585652	+	0.101438i
$657$	4.00000			0.156055
$658$		0			0
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	22.0000	−	38.1051i	0.855701	−	1.48212i	−0.0202925	−	0.999794i	$-0.506460\pi$
$661$	22.0000	−	38.1051i	0.855701	−	1.48212i	0.875993	−	0.482323i	$-0.160207\pi$
$662$	3.50000	−	6.06218i	0.136031	−	0.235613i
$663$	−30.0000	−	51.9615i	−1.16510	−	2.01802i
$664$	12.0000			0.465690
$665$		0			0
$666$	11.0000			0.426241
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	4.50000	−	7.79423i	0.174110	−	0.301568i
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$	2.00000	+	3.46410i	0.0772667	+	0.133830i
$671$	12.0000			0.463255
$672$		0			0
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	−1.50000	−	2.59808i	−0.0576497	−	0.0998522i	0.835760	−	0.549095i	$-0.185027\pi$
$677$	−1.50000	−	2.59808i	−0.0576497	−	0.0998522i	−0.893410	+	0.449242i	$0.851694\pi$
$678$	24.0000			0.921714
$679$		0			0
$680$	−6.00000			−0.230089
$681$	−24.0000	−	41.5692i	−0.919682	−	1.59294i
$682$	−6.00000	+	10.3923i	−0.229752	+	0.397942i
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$	−0.500000	−	0.866025i	−0.0191180	−	0.0331133i
$685$	12.0000			0.458496
$686$		0			0
$687$	56.0000			2.13653
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$	7.50000	−	12.9904i	0.285727	−	0.494894i
$690$	−3.00000	+	5.19615i	−0.114208	+	0.197814i
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$	−3.00000			−0.114043
$693$		0			0
$694$	24.0000			0.911028
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$	6.00000	−	10.3923i	0.227429	−	0.393919i
$697$	−9.00000	+	15.5885i	−0.340899	+	0.590455i
$698$	−5.00000	−	8.66025i	−0.189253	−	0.327795i
$699$	−12.0000			−0.453882
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−10.0000	−	17.3205i	−0.377426	−	0.653720i
$703$	−5.50000	+	9.52628i	−0.207436	+	0.359290i
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$	3.00000	+	5.19615i	0.112987	+	0.195698i
$706$	−12.0000			−0.451626
$707$		0			0
$708$		0			0
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$	−6.00000	+	10.3923i	−0.225176	+	0.390016i
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	12.0000			0.449404
$714$		0			0
$715$	−15.0000			−0.560968
$716$	1.50000	+	2.59808i	0.0560576	+	0.0970947i
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	−0.977539	−	0.210752i	$-0.932409\pi$
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	0.306253	−	0.951950i	$-0.400925\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	−18.0000			−0.669891
$723$	−25.0000	−	43.3013i	−0.929760	−	1.61039i
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	2.00000	+	3.46410i	0.0742270	+	0.128565i
$727$	−29.0000			−1.07555			−0.537775	−	0.843088i	$-0.680735\pi$
$727$	−29.0000			−1.07555			−0.537775	+	0.843088i	$0.680735\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−2.00000	−	3.46410i	−0.0740233	−	0.128212i
$731$	−30.0000	+	51.9615i	−1.10959	+	1.92187i
$732$	−4.00000	+	6.92820i	−0.147844	+	0.256074i
$733$	23.5000	+	40.7032i	0.867992	+	1.50341i	0.864045	+	0.503415i	$0.167923\pi$
$733$	23.5000	+	40.7032i	0.867992	+	1.50341i	0.00394730	+	0.999992i	$0.498744\pi$
$734$	1.00000			0.0369107
$735$		0			0
$736$	3.00000			0.110581
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$	1.50000	−	2.59808i	0.0552158	−	0.0956365i
$739$	18.5000	−	32.0429i	0.680534	−	1.17872i	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	18.5000	−	32.0429i	0.680534	−	1.17872i	0.974818	−	0.223001i	$-0.0715853\pi$
$740$	−5.50000	−	9.52628i	−0.202184	−	0.350193i
$741$	−10.0000			−0.367359
$742$		0			0
$743$	9.00000			0.330178			0.165089	−	0.986279i	$-0.447209\pi$
$743$	9.00000			0.330178			0.165089	+	0.986279i	$0.447209\pi$
$744$	−4.00000	−	6.92820i	−0.146647	−	0.254000i
$745$	−9.00000	+	15.5885i	−0.329734	+	0.571117i
$746$	17.0000	−	29.4449i	0.622414	−	1.07805i
$747$	−6.00000	−	10.3923i	−0.219529	−	0.380235i
$748$	−18.0000			−0.658145
$749$		0			0
$750$	2.00000			0.0730297
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	0.525193	−	0.850983i	$-0.323993\pi$
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	−0.999570	+	0.0293387i	$0.990660\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	−15.0000	+	25.9808i	−0.546630	+	0.946792i
$754$	−15.0000	−	25.9808i	−0.546268	−	0.946164i
$755$	14.0000			0.509512
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	12.5000	+	21.6506i	0.454020	+	0.786386i
$759$	−9.00000	+	15.5885i	−0.326679	+	0.565825i
$760$	−0.500000	+	0.866025i	−0.0181369	+	0.0314140i
$761$	−25.5000	−	44.1673i	−0.924374	−	1.60106i	−0.792564	−	0.609788i	$-0.791255\pi$
$761$	−25.5000	−	44.1673i	−0.924374	−	1.60106i	−0.131810	−	0.991275i	$-0.542079\pi$
$762$	−38.0000			−1.37659
$763$		0			0
$764$	12.0000			0.434145
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$	7.50000	−	12.9904i	0.270986	−	0.469362i
$767$		0			0
$768$	−1.00000	−	1.73205i	−0.0360844	−	0.0625000i
$769$	49.0000			1.76699			0.883493	−	0.468445i	$-0.155186\pi$
$769$	49.0000			1.76699			0.883493	+	0.468445i	$0.155186\pi$
$770$		0			0
$771$	24.0000			0.864339
$772$	2.00000	+	3.46410i	0.0719816	+	0.124676i
$773$	19.5000	−	33.7750i	0.701366	−	1.21480i	−0.266621	−	0.963802i	$-0.585907\pi$
$773$	19.5000	−	33.7750i	0.701366	−	1.21480i	0.967987	−	0.251000i	$-0.0807596\pi$
$774$	5.00000	−	8.66025i	0.179721	−	0.311286i
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$	−14.0000			−0.502571
$777$		0			0
$778$	−24.0000			−0.860442
$779$	1.50000	+	2.59808i	0.0537431	+	0.0930857i
$780$	5.00000	−	8.66025i	0.179029	−	0.310087i
$781$	−18.0000	+	31.1769i	−0.644091	+	1.11560i
$782$	9.00000	+	15.5885i	0.321839	+	0.557442i
$783$	24.0000			0.857690
$784$		0			0
$785$	−5.00000			−0.178458
$786$	3.00000	+	5.19615i	0.107006	+	0.185341i
$787$	−17.0000	+	29.4449i	−0.605985	+	1.04960i	0.385911	+	0.922536i	$0.373887\pi$
$787$	−17.0000	+	29.4449i	−0.605985	+	1.04960i	−0.991895	+	0.127060i	$0.959446\pi$
$788$	1.50000	−	2.59808i	0.0534353	−	0.0925526i
$789$		0			0
$790$	−10.0000			−0.355784
$791$		0			0
$792$	3.00000			0.106600
$793$	10.0000	+	17.3205i	0.355110	+	0.615069i
$794$	1.00000	−	1.73205i	0.0354887	−	0.0614682i
$795$	−3.00000	+	5.19615i	−0.106399	+	0.184289i
$796$	−2.00000	−	3.46410i	−0.0708881	−	0.122782i
$797$	30.0000			1.06265			0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000			1.06265			0.531327	+	0.847167i	$0.321693\pi$
$798$		0			0
$799$	18.0000			0.636794
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	−10.5000	+	18.1865i	−0.370768	+	0.642189i
$803$	−6.00000	−	10.3923i	−0.211735	−	0.366736i
$804$	−8.00000			−0.282138
$805$		0			0
$806$	−20.0000			−0.704470
$807$	−12.0000	−	20.7846i	−0.422420	−	0.731653i
$808$	−6.00000	+	10.3923i	−0.211079	+	0.365600i
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	0.287670	+	0.957730i	$0.407120\pi$
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	−0.973253	+	0.229736i	$0.926214\pi$
$810$	5.50000	+	9.52628i	0.193250	+	0.334719i
$811$	−47.0000			−1.65039			−0.825197	−	0.564846i	$-0.808936\pi$
$811$	−47.0000			−1.65039			−0.825197	+	0.564846i	$0.808936\pi$
$812$		0			0
$813$	32.0000			1.12229
$814$	−16.5000	−	28.5788i	−0.578325	−	1.00169i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$	6.00000	−	10.3923i	0.210042	−	0.363803i
$817$	5.00000	+	8.66025i	0.174928	+	0.302984i
$818$	22.0000			0.769212
$819$		0			0
$820$	−3.00000			−0.104765
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$	−12.0000	+	20.7846i	−0.418548	+	0.724947i
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	0.172379	+	0.985031i	$0.444854\pi$
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	−0.939251	+	0.343230i	$0.888479\pi$
$824$	−2.00000	−	3.46410i	−0.0696733	−	0.120678i
$825$	6.00000			0.208893
$826$		0			0
$827$	−54.0000			−1.87776			−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−54.0000			−1.87776			−0.938882	+	0.344239i	$0.888137\pi$
$828$	−1.50000	−	2.59808i	−0.0521286	−	0.0902894i
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$	−2.00000	−	3.46410i	−0.0693792	−	0.120168i
$832$	−5.00000			−0.173344
$833$		0			0
$834$	8.00000			0.277017
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	−1.50000	+	2.59808i	−0.0518786	+	0.0898563i
$837$	8.00000	−	13.8564i	0.276520	−	0.478947i
$838$	7.50000	+	12.9904i	0.259083	+	0.448745i
$839$	6.00000			0.207143			0.103572	−	0.994622i	$-0.466973\pi$
$839$	6.00000			0.207143			0.103572	+	0.994622i	$0.466973\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	17.0000	+	29.4449i	0.585859	+	1.01474i
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$	0.500000	−	0.866025i	0.0172107	−	0.0298098i
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$	−3.00000			−0.103142
$847$		0			0
$848$	3.00000			0.103020
$849$	26.0000	+	45.0333i	0.892318	+	1.54554i
$850$	3.00000	−	5.19615i	0.102899	−	0.178227i
$851$	−16.5000	+	28.5788i	−0.565613	+	0.979670i
$852$	−12.0000	−	20.7846i	−0.411113	−	0.712069i
$853$	1.00000			0.0342393			0.0171197	−	0.999853i	$-0.494550\pi$
$853$	1.00000			0.0342393			0.0171197	+	0.999853i	$0.494550\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$	15.0000	−	25.9808i	0.512092	−	0.886969i
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	0.998549	+	0.0538535i	$0.0171504\pi$
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	−0.452636	+	0.891695i	$0.649516\pi$
$860$	−10.0000			−0.340997
$861$		0			0
$862$		0			0
$863$	−19.5000	−	33.7750i	−0.663788	−	1.14971i	−0.979612	−	0.200897i	$-0.935615\pi$
$863$	−19.5000	−	33.7750i	−0.663788	−	1.14971i	0.315825	−	0.948818i	$-0.397719\pi$
$864$	2.00000	−	3.46410i	0.0680414	−	0.117851i
$865$	1.50000	−	2.59808i	0.0510015	−	0.0883372i
$866$	−8.00000	−	13.8564i	−0.271851	−	0.470860i
$867$	38.0000			1.29055
$868$		0			0
$869$	−30.0000			−1.01768
$870$	6.00000	+	10.3923i	0.203419	+	0.352332i
$871$	−10.0000	+	17.3205i	−0.338837	+	0.586883i
$872$	2.00000	−	3.46410i	0.0677285	−	0.117309i
$873$	7.00000	+	12.1244i	0.236914	+	0.410347i
$874$	3.00000			0.101477
$875$		0			0
$876$	8.00000			0.270295
$877$	3.50000	+	6.06218i	0.118187	+	0.204705i	0.919049	−	0.394143i	$-0.128959\pi$
$877$	3.50000	+	6.06218i	0.118187	+	0.204705i	−0.800862	+	0.598848i	$0.795625\pi$
$878$	−5.00000	+	8.66025i	−0.168742	+	0.292269i
$879$	−27.0000	+	46.7654i	−0.910687	+	1.57736i
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	−15.0000	−	25.9808i	−0.504505	−	0.873828i
$885$		0			0
$886$	12.0000	−	20.7846i	0.403148	−	0.698273i
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$	22.0000			0.738272
$889$		0			0
$890$	−6.00000			−0.201120
$891$	16.5000	+	28.5788i	0.552771	+	0.957427i
$892$	4.00000	−	6.92820i	0.133930	−	0.231973i
$893$	1.50000	−	2.59808i	0.0501956	−	0.0869413i
$894$	−18.0000	−	31.1769i	−0.602010	−	1.04271i
$895$	−3.00000			−0.100279
$896$		0			0
$897$	−30.0000			−1.00167
$898$	1.50000	+	2.59808i	0.0500556	+	0.0866989i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$	−9.00000			−0.299667
$903$		0			0
$904$	12.0000			0.399114
$905$	1.00000	+	1.73205i	0.0332411	+	0.0575753i
$906$	−14.0000	+	24.2487i	−0.465119	+	0.805609i
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	−0.770996	−	0.636841i	$-0.780241\pi$
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	0.937018	+	0.349281i	$0.113574\pi$
$908$	−12.0000	−	20.7846i	−0.398234	−	0.689761i
$909$	12.0000			0.398015
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	−18.0000	+	31.1769i	−0.595713	+	1.03181i
$914$	11.0000	−	19.0526i	0.363848	−	0.630203i
$915$	−4.00000	−	6.92820i	−0.132236	−	0.229039i
$916$	28.0000			0.925146
$917$		0			0
$918$	24.0000			0.792118
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	−0.988199	−	0.153174i	$-0.951051\pi$
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	0.361447	−	0.932393i	$-0.382283\pi$
$920$	−1.50000	+	2.59808i	−0.0494535	+	0.0856560i
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$	3.00000	+	5.19615i	0.0987997	+	0.171126i
$923$	−60.0000			−1.97492
$924$		0			0
$925$	11.0000			0.361678
$926$	9.50000	+	16.4545i	0.312189	+	0.540728i
$927$	−2.00000	+	3.46410i	−0.0656886	+	0.113776i
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	0.998827	+	0.0484211i	$0.0154190\pi$
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	−0.457480	+	0.889220i	$0.651248\pi$
$930$	8.00000			0.262330
$931$		0			0
$932$	−6.00000			−0.196537
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$	−9.00000	+	15.5885i	−0.294489	+	0.510070i
$935$	9.00000	−	15.5885i	0.294331	−	0.509797i
$936$	2.50000	+	4.33013i	0.0817151	+	0.141535i
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	−16.0000			−0.522140
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	−0.601418	−	0.798935i	$-0.705397\pi$
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	0.992607	+	0.121376i	$0.0387306\pi$
$942$	5.00000	−	8.66025i	0.162909	−	0.282166i
$943$	4.50000	+	7.79423i	0.146540	+	0.253815i
$944$		0			0
$945$		0			0
$946$	−30.0000			−0.975384
$947$	−15.0000	−	25.9808i	−0.487435	−	0.844261i	0.512461	−	0.858710i	$-0.328734\pi$
$947$	−15.0000	−	25.9808i	−0.487435	−	0.844261i	−0.999896	+	0.0144491i	$0.995401\pi$
$948$	10.0000	−	17.3205i	0.324785	−	0.562544i
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$	−0.500000	−	0.866025i	−0.0162221	−	0.0280976i
$951$	36.0000			1.16738
$952$		0			0
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$	−1.50000	−	2.59808i	−0.0485643	−	0.0841158i
$955$	−6.00000	+	10.3923i	−0.194155	+	0.336287i
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	18.0000	+	31.1769i	0.581857	+	1.00781i
$958$	−24.0000			−0.775405
$959$		0			0
$960$	2.00000			0.0645497
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	27.5000	−	47.6314i	0.886636	−	1.53570i
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	−12.5000	−	21.6506i	−0.402598	−	0.697320i
$965$	−4.00000			−0.128765
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	6.00000	−	10.3923i	0.192748	−	0.333849i
$970$	7.00000	−	12.1244i	0.224756	−	0.389290i
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	0.997150	−	0.0754473i	$-0.0240385\pi$
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	−0.563914	+	0.825833i	$0.690705\pi$
$972$	−10.0000			−0.320750
$973$		0			0
$974$	−16.0000			−0.512673
$975$	5.00000	+	8.66025i	0.160128	+	0.277350i
$976$	−2.00000	+	3.46410i	−0.0640184	+	0.110883i
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$	4.00000	+	6.92820i	0.127906	+	0.221540i
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−4.00000			−0.127710
$982$	6.00000	+	10.3923i	0.191468	+	0.331632i
$983$	28.5000	−	49.3634i	0.909009	−	1.57445i	0.0935651	−	0.995613i	$-0.470174\pi$
$983$	28.5000	−	49.3634i	0.909009	−	1.57445i	0.815444	−	0.578836i	$-0.196493\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$	1.50000	+	2.59808i	0.0477940	+	0.0827816i
$986$	36.0000			1.14647
$987$		0			0
$988$	−5.00000			−0.159071
$989$	15.0000	+	25.9808i	0.476972	+	0.826140i
$990$	−1.50000	+	2.59808i	−0.0476731	+	0.0825723i
$991$	−10.0000	+	17.3205i	−0.317660	+	0.550204i	−0.979999	−	0.199000i	$-0.936231\pi$
$991$	−10.0000	+	17.3205i	−0.317660	+	0.550204i	0.662339	+	0.749204i	$0.269564\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	−14.0000			−0.444277
$994$		0			0
$995$	4.00000			0.126809
$996$	−12.0000	−	20.7846i	−0.380235	−	0.658586i
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	−0.733630	−	0.679549i	$-0.762175\pi$
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	0.955322	+	0.295567i	$0.0955086\pi$
$998$	14.0000	−	24.2487i	0.443162	−	0.767580i
$999$	22.0000	+	38.1051i	0.696049	+	1.20559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.e.a.361.1		2
7.2	even	3	inner	490.2.e.a.471.1		2
7.3	odd	6		490.2.a.g.1.1		1
7.4	even	3		490.2.a.j.1.1		1
7.5	odd	6		70.2.e.b.51.1	yes	2
7.6	odd	2		70.2.e.b.11.1	✓	2
21.5	even	6		630.2.k.e.541.1		2
21.11	odd	6		4410.2.a.c.1.1		1
21.17	even	6		4410.2.a.m.1.1		1
21.20	even	2		630.2.k.e.361.1		2
28.3	even	6		3920.2.a.be.1.1		1
28.11	odd	6		3920.2.a.g.1.1		1
28.19	even	6		560.2.q.d.401.1		2
28.27	even	2		560.2.q.d.81.1		2
35.3	even	12		2450.2.c.f.99.1		2
35.4	even	6		2450.2.a.f.1.1		1
35.12	even	12		350.2.j.a.149.1		4
35.13	even	4		350.2.j.a.249.1		4
35.17	even	12		2450.2.c.f.99.2		2
35.18	odd	12		2450.2.c.p.99.1		2
35.19	odd	6		350.2.e.h.51.1		2
35.24	odd	6		2450.2.a.p.1.1		1
35.27	even	4		350.2.j.a.249.2		4
35.32	odd	12		2450.2.c.p.99.2		2
35.33	even	12		350.2.j.a.149.2		4
35.34	odd	2		350.2.e.h.151.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.b.11.1	✓	2	7.6	odd	2
70.2.e.b.51.1	yes	2	7.5	odd	6
350.2.e.h.51.1		2	35.19	odd	6
350.2.e.h.151.1		2	35.34	odd	2
350.2.j.a.149.1		4	35.12	even	12
350.2.j.a.149.2		4	35.33	even	12
350.2.j.a.249.1		4	35.13	even	4
350.2.j.a.249.2		4	35.27	even	4
490.2.a.g.1.1		1	7.3	odd	6
490.2.a.j.1.1		1	7.4	even	3
490.2.e.a.361.1		2	1.1	even	1	trivial
490.2.e.a.471.1		2	7.2	even	3	inner
560.2.q.d.81.1		2	28.27	even	2
560.2.q.d.401.1		2	28.19	even	6
630.2.k.e.361.1		2	21.20	even	2
630.2.k.e.541.1		2	21.5	even	6
2450.2.a.f.1.1		1	35.4	even	6
2450.2.a.p.1.1		1	35.24	odd	6
2450.2.c.f.99.1		2	35.3	even	12
2450.2.c.f.99.2		2	35.17	even	12
2450.2.c.p.99.1		2	35.18	odd	12
2450.2.c.p.99.2		2	35.32	odd	12
3920.2.a.g.1.1		1	28.11	odd	6
3920.2.a.be.1.1		1	28.3	even	6
4410.2.a.c.1.1		1	21.11	odd	6
4410.2.a.m.1.1		1	21.17	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-1.00000 - 1.73205i) q^{12} -5.00000 q^{13} +2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +1.00000 q^{20} +3.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.50000 + 4.33013i) q^{26} -4.00000 q^{27} -6.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(-5.50000 - 9.52628i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(5.00000 - 8.66025i) q^{39} +(-0.500000 - 0.866025i) q^{40} -3.00000 q^{41} -10.0000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-1.50000 + 2.59808i) q^{46} +(1.50000 + 2.59808i) q^{47} +2.00000 q^{48} +1.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(2.50000 - 4.33013i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(2.00000 + 3.46410i) q^{54} +3.00000 q^{55} +2.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(-1.00000 + 1.73205i) q^{60} +(-2.00000 - 3.46410i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(-3.00000 + 5.19615i) q^{66} +(2.00000 - 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +6.00000 q^{69} +12.0000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(-5.50000 + 9.52628i) q^{74} +(-1.00000 - 1.73205i) q^{75} +1.00000 q^{76} -10.0000 q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(1.50000 + 2.59808i) q^{82} +12.0000 q^{83} -6.00000 q^{85} +(5.00000 + 8.66025i) q^{86} +(6.00000 - 10.3923i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +1.00000 q^{90} +3.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-0.500000 + 0.866025i) q^{95} +(-1.00000 - 1.73205i) q^{96} -14.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 4 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 - q^5 + 4 * q^6 + 2 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 4 q^{6} + 2 q^{8} - q^{9} - q^{10} - 3 q^{11} - 2 q^{12} - 10 q^{13} + 4 q^{15} - q^{16} + 6 q^{17} - q^{18} - q^{19} + 2 q^{20} + 6 q^{22} - 3 q^{23} - 2 q^{24} - q^{25} + 5 q^{26} - 8 q^{27} - 12 q^{29} - 2 q^{30} - 4 q^{31} - q^{32} - 6 q^{33} - 12 q^{34} + 2 q^{36} - 11 q^{37} - q^{38} + 10 q^{39} - q^{40} - 6 q^{41} - 20 q^{43} - 3 q^{44} - q^{45} - 3 q^{46} + 3 q^{47} + 4 q^{48} + 2 q^{50} + 12 q^{51} + 5 q^{52} - 3 q^{53} + 4 q^{54} + 6 q^{55} + 4 q^{57} + 6 q^{58} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{64} + 5 q^{65} - 6 q^{66} + 4 q^{67} + 6 q^{68} + 12 q^{69} + 24 q^{71} - q^{72} - 4 q^{73} - 11 q^{74} - 2 q^{75} + 2 q^{76} - 20 q^{78} + 10 q^{79} - q^{80} + 11 q^{81} + 3 q^{82} + 24 q^{83} - 12 q^{85} + 10 q^{86} + 12 q^{87} - 3 q^{88} + 6 q^{89} + 2 q^{90} + 6 q^{92} - 8 q^{93} + 3 q^{94} - q^{95} - 2 q^{96} - 28 q^{97} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - q^5 + 4 * q^6 + 2 * q^8 - q^9 - q^10 - 3 * q^11 - 2 * q^12 - 10 * q^13 + 4 * q^15 - q^16 + 6 * q^17 - q^18 - q^19 + 2 * q^20 + 6 * q^22 - 3 * q^23 - 2 * q^24 - q^25 + 5 * q^26 - 8 * q^27 - 12 * q^29 - 2 * q^30 - 4 * q^31 - q^32 - 6 * q^33 - 12 * q^34 + 2 * q^36 - 11 * q^37 - q^38 + 10 * q^39 - q^40 - 6 * q^41 - 20 * q^43 - 3 * q^44 - q^45 - 3 * q^46 + 3 * q^47 + 4 * q^48 + 2 * q^50 + 12 * q^51 + 5 * q^52 - 3 * q^53 + 4 * q^54 + 6 * q^55 + 4 * q^57 + 6 * q^58 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^64 + 5 * q^65 - 6 * q^66 + 4 * q^67 + 6 * q^68 + 12 * q^69 + 24 * q^71 - q^72 - 4 * q^73 - 11 * q^74 - 2 * q^75 + 2 * q^76 - 20 * q^78 + 10 * q^79 - q^80 + 11 * q^81 + 3 * q^82 + 24 * q^83 - 12 * q^85 + 10 * q^86 + 12 * q^87 - 3 * q^88 + 6 * q^89 + 2 * q^90 + 6 * q^92 - 8 * q^93 + 3 * q^94 - q^95 - 2 * q^96 - 28 * q^97 + 6 * q^99

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