LMFDB - Embedded newform 21.3.d.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,3,Mod(13,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("21.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	21.d (of order $2$, degree $1$, 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:	$0.572208555157$
Analytic rank:	$0$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.2
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	21.13
Dual form			21.3.d.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.73205i q^{3} -3.00000 q^{4} -6.92820i q^{5} +1.73205i q^{6} +(1.00000 + 6.92820i) q^{7} -7.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.73205i q^{3} -3.00000 q^{4} -6.92820i q^{5} +1.73205i q^{6} +(1.00000 + 6.92820i) q^{7} -7.00000 q^{8} -3.00000 q^{9} -6.92820i q^{10} +10.0000 q^{11} -5.19615i q^{12} +6.92820i q^{13} +(1.00000 + 6.92820i) q^{14} +12.0000 q^{15} +5.00000 q^{16} -3.00000 q^{18} -20.7846i q^{19} +20.7846i q^{20} +(-12.0000 + 1.73205i) q^{21} +10.0000 q^{22} -14.0000 q^{23} -12.1244i q^{24} -23.0000 q^{25} +6.92820i q^{26} -5.19615i q^{27} +(-3.00000 - 20.7846i) q^{28} -38.0000 q^{29} +12.0000 q^{30} +27.7128i q^{31} +33.0000 q^{32} +17.3205i q^{33} +(48.0000 - 6.92820i) q^{35} +9.00000 q^{36} +26.0000 q^{37} -20.7846i q^{38} -12.0000 q^{39} +48.4974i q^{40} -69.2820i q^{41} +(-12.0000 + 1.73205i) q^{42} +26.0000 q^{43} -30.0000 q^{44} +20.7846i q^{45} -14.0000 q^{46} +27.7128i q^{47} +8.66025i q^{48} +(-47.0000 + 13.8564i) q^{49} -23.0000 q^{50} -20.7846i q^{52} +10.0000 q^{53} -5.19615i q^{54} -69.2820i q^{55} +(-7.00000 - 48.4974i) q^{56} +36.0000 q^{57} -38.0000 q^{58} +76.2102i q^{59} -36.0000 q^{60} +34.6410i q^{61} +27.7128i q^{62} +(-3.00000 - 20.7846i) q^{63} +13.0000 q^{64} +48.0000 q^{65} +17.3205i q^{66} +74.0000 q^{67} -24.2487i q^{69} +(48.0000 - 6.92820i) q^{70} -62.0000 q^{71} +21.0000 q^{72} -41.5692i q^{73} +26.0000 q^{74} -39.8372i q^{75} +62.3538i q^{76} +(10.0000 + 69.2820i) q^{77} -12.0000 q^{78} -46.0000 q^{79} -34.6410i q^{80} +9.00000 q^{81} -69.2820i q^{82} +90.0666i q^{83} +(36.0000 - 5.19615i) q^{84} +26.0000 q^{86} -65.8179i q^{87} -70.0000 q^{88} -41.5692i q^{89} +20.7846i q^{90} +(-48.0000 + 6.92820i) q^{91} +42.0000 q^{92} -48.0000 q^{93} +27.7128i q^{94} -144.000 q^{95} +57.1577i q^{96} +55.4256i q^{97} +(-47.0000 + 13.8564i) q^{98} -30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 6 q^{4} + 2 q^{7} - 14 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 6 * q^4 + 2 * q^7 - 14 * q^8 - 6 * q^9	$ 2 q + 2 q^{2} - 6 q^{4} + 2 q^{7} - 14 q^{8} - 6 q^{9} + 20 q^{11} + 2 q^{14} + 24 q^{15} + 10 q^{16} - 6 q^{18} - 24 q^{21} + 20 q^{22} - 28 q^{23} - 46 q^{25} - 6 q^{28} - 76 q^{29} + 24 q^{30} + 66 q^{32} + 96 q^{35} + 18 q^{36} + 52 q^{37} - 24 q^{39} - 24 q^{42} + 52 q^{43} - 60 q^{44} - 28 q^{46} - 94 q^{49} - 46 q^{50} + 20 q^{53} - 14 q^{56} + 72 q^{57} - 76 q^{58} - 72 q^{60} - 6 q^{63} + 26 q^{64} + 96 q^{65} + 148 q^{67} + 96 q^{70} - 124 q^{71} + 42 q^{72} + 52 q^{74} + 20 q^{77} - 24 q^{78} - 92 q^{79} + 18 q^{81} + 72 q^{84} + 52 q^{86} - 140 q^{88} - 96 q^{91} + 84 q^{92} - 96 q^{93} - 288 q^{95} - 94 q^{98} - 60 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 6 * q^4 + 2 * q^7 - 14 * q^8 - 6 * q^9 + 20 * q^11 + 2 * q^14 + 24 * q^15 + 10 * q^16 - 6 * q^18 - 24 * q^21 + 20 * q^22 - 28 * q^23 - 46 * q^25 - 6 * q^28 - 76 * q^29 + 24 * q^30 + 66 * q^32 + 96 * q^35 + 18 * q^36 + 52 * q^37 - 24 * q^39 - 24 * q^42 + 52 * q^43 - 60 * q^44 - 28 * q^46 - 94 * q^49 - 46 * q^50 + 20 * q^53 - 14 * q^56 + 72 * q^57 - 76 * q^58 - 72 * q^60 - 6 * q^63 + 26 * q^64 + 96 * q^65 + 148 * q^67 + 96 * q^70 - 124 * q^71 + 42 * q^72 + 52 * q^74 + 20 * q^77 - 24 * q^78 - 92 * q^79 + 18 * q^81 + 72 * q^84 + 52 * q^86 - 140 * q^88 - 96 * q^91 + 84 * q^92 - 96 * q^93 - 288 * q^95 - 94 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.00000			0.500000			0.250000	−	0.968246i	$-0.419569\pi$
$2$	1.00000			0.500000			0.250000	+	0.968246i	$0.419569\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−3.00000			−0.750000
$5$		−	6.92820i		−	1.38564i	−0.721110	−	0.692820i	$-0.756368\pi$
$5$		−	6.92820i		−	1.38564i	0.721110	−	0.692820i	$-0.243632\pi$
$6$			1.73205i			0.288675i
$7$	1.00000	+	6.92820i	0.142857	+	0.989743i
$7$	1.00000	+	6.92820i	0.142857	+	0.989743i
$8$	−7.00000			−0.875000
$9$	−3.00000			−0.333333
$10$		−	6.92820i		−	0.692820i
$11$	10.0000			0.909091			0.454545	−	0.890724i	$-0.349802\pi$
$11$	10.0000			0.909091			0.454545	+	0.890724i	$0.349802\pi$
$12$		−	5.19615i		−	0.433013i
$13$			6.92820i			0.532939i	0.963843	+	0.266469i	$0.0858571\pi$
$13$			6.92820i			0.532939i	−0.963843	+	0.266469i	$0.914143\pi$
$14$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$15$	12.0000			0.800000
$16$	5.00000			0.312500
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−3.00000			−0.166667
$19$		−	20.7846i		−	1.09393i	−0.837157	−	0.546963i	$-0.815784\pi$
$19$		−	20.7846i		−	1.09393i	0.837157	−	0.546963i	$-0.184216\pi$
$20$			20.7846i			1.03923i
$21$	−12.0000	+	1.73205i	−0.571429	+	0.0824786i
$22$	10.0000			0.454545
$23$	−14.0000			−0.608696			−0.304348	−	0.952561i	$-0.598439\pi$
$23$	−14.0000			−0.608696			−0.304348	+	0.952561i	$0.598439\pi$
$24$		−	12.1244i		−	0.505181i
$25$	−23.0000			−0.920000
$26$			6.92820i			0.266469i
$27$		−	5.19615i		−	0.192450i
$28$	−3.00000	−	20.7846i	−0.107143	−	0.742307i
$29$	−38.0000			−1.31034			−0.655172	−	0.755479i	$-0.727404\pi$
$29$	−38.0000			−1.31034			−0.655172	+	0.755479i	$0.727404\pi$
$30$	12.0000			0.400000
$31$			27.7128i			0.893962i	0.894544	+	0.446981i	$0.147501\pi$
$31$			27.7128i			0.893962i	−0.894544	+	0.446981i	$0.852499\pi$
$32$	33.0000			1.03125
$33$			17.3205i			0.524864i
$34$		0			0
$35$	48.0000	−	6.92820i	1.37143	−	0.197949i
$36$	9.00000			0.250000
$37$	26.0000			0.702703			0.351351	−	0.936244i	$-0.385722\pi$
$37$	26.0000			0.702703			0.351351	+	0.936244i	$0.385722\pi$
$38$		−	20.7846i		−	0.546963i
$39$	−12.0000			−0.307692
$40$			48.4974i			1.21244i
$41$		−	69.2820i		−	1.68981i	−0.534920	−	0.844903i	$-0.679658\pi$
$41$		−	69.2820i		−	1.68981i	0.534920	−	0.844903i	$-0.320342\pi$
$42$	−12.0000	+	1.73205i	−0.285714	+	0.0412393i
$43$	26.0000			0.604651			0.302326	−	0.953205i	$-0.402237\pi$
$43$	26.0000			0.604651			0.302326	+	0.953205i	$0.402237\pi$
$44$	−30.0000			−0.681818
$45$			20.7846i			0.461880i
$46$	−14.0000			−0.304348
$47$			27.7128i			0.589634i	0.955554	+	0.294817i	$0.0952587\pi$
$47$			27.7128i			0.589634i	−0.955554	+	0.294817i	$0.904741\pi$
$48$			8.66025i			0.180422i
$49$	−47.0000	+	13.8564i	−0.959184	+	0.282784i
$50$	−23.0000			−0.460000
$51$		0			0
$52$		−	20.7846i		−	0.399704i
$53$	10.0000			0.188679			0.0943396	−	0.995540i	$-0.469926\pi$
$53$	10.0000			0.188679			0.0943396	+	0.995540i	$0.469926\pi$
$54$		−	5.19615i		−	0.0962250i
$55$		−	69.2820i		−	1.25967i
$56$	−7.00000	−	48.4974i	−0.125000	−	0.866025i
$57$	36.0000			0.631579
$58$	−38.0000			−0.655172
$59$			76.2102i			1.29170i	0.763465	+	0.645849i	$0.223497\pi$
$59$			76.2102i			1.29170i	−0.763465	+	0.645849i	$0.776503\pi$
$60$	−36.0000			−0.600000
$61$			34.6410i			0.567886i	0.958841	+	0.283943i	$0.0916426\pi$
$61$			34.6410i			0.567886i	−0.958841	+	0.283943i	$0.908357\pi$
$62$			27.7128i			0.446981i
$63$	−3.00000	−	20.7846i	−0.0476190	−	0.329914i
$64$	13.0000			0.203125
$65$	48.0000			0.738462
$66$			17.3205i			0.262432i
$67$	74.0000			1.10448			0.552239	−	0.833686i	$-0.313774\pi$
$67$	74.0000			1.10448			0.552239	+	0.833686i	$0.313774\pi$
$68$		0			0
$69$		−	24.2487i		−	0.351431i
$70$	48.0000	−	6.92820i	0.685714	−	0.0989743i
$71$	−62.0000			−0.873239			−0.436620	−	0.899646i	$-0.643824\pi$
$71$	−62.0000			−0.873239			−0.436620	+	0.899646i	$0.643824\pi$
$72$	21.0000			0.291667
$73$		−	41.5692i		−	0.569441i	−0.958611	−	0.284721i	$-0.908099\pi$
$73$		−	41.5692i		−	0.569441i	0.958611	−	0.284721i	$-0.0919009\pi$
$74$	26.0000			0.351351
$75$		−	39.8372i		−	0.531162i
$76$			62.3538i			0.820445i
$77$	10.0000	+	69.2820i	0.129870	+	0.899767i
$78$	−12.0000			−0.153846
$79$	−46.0000			−0.582278			−0.291139	−	0.956681i	$-0.594034\pi$
$79$	−46.0000			−0.582278			−0.291139	+	0.956681i	$0.594034\pi$
$80$		−	34.6410i		−	0.433013i
$81$	9.00000			0.111111
$82$		−	69.2820i		−	0.844903i
$83$			90.0666i			1.08514i	0.840011	+	0.542570i	$0.182549\pi$
$83$			90.0666i			1.08514i	−0.840011	+	0.542570i	$0.817451\pi$
$84$	36.0000	−	5.19615i	0.428571	−	0.0618590i
$85$		0			0
$86$	26.0000			0.302326
$87$		−	65.8179i		−	0.756528i
$88$	−70.0000			−0.795455
$89$		−	41.5692i		−	0.467070i	−0.972348	−	0.233535i	$-0.924971\pi$
$89$		−	41.5692i		−	0.467070i	0.972348	−	0.233535i	$-0.0750293\pi$
$90$			20.7846i			0.230940i
$91$	−48.0000	+	6.92820i	−0.527473	+	0.0761341i
$92$	42.0000			0.456522
$93$	−48.0000			−0.516129
$94$			27.7128i			0.294817i
$95$	−144.000			−1.51579
$96$			57.1577i			0.595392i
$97$			55.4256i			0.571398i	0.958319	+	0.285699i	$0.0922258\pi$
$97$			55.4256i			0.571398i	−0.958319	+	0.285699i	$0.907774\pi$
$98$	−47.0000	+	13.8564i	−0.479592	+	0.141392i
$99$	−30.0000			−0.303030
$100$	69.0000			0.690000
$101$		−	117.779i		−	1.16613i	−0.812424	−	0.583067i	$-0.801853\pi$
$101$		−	117.779i		−	1.16613i	0.812424	−	0.583067i	$-0.198147\pi$
$102$		0			0
$103$		−	96.9948i		−	0.941698i	−0.882214	−	0.470849i	$-0.843948\pi$
$103$		−	96.9948i		−	0.941698i	0.882214	−	0.470849i	$-0.156052\pi$
$104$		−	48.4974i		−	0.466321i
$105$	12.0000	+	83.1384i	0.114286	+	0.791795i
$106$	10.0000			0.0943396
$107$	10.0000			0.0934579			0.0467290	−	0.998908i	$-0.485120\pi$
$107$	10.0000			0.0934579			0.0467290	+	0.998908i	$0.485120\pi$
$108$			15.5885i			0.144338i
$109$	74.0000			0.678899			0.339450	−	0.940624i	$-0.389759\pi$
$109$	74.0000			0.678899			0.339450	+	0.940624i	$0.389759\pi$
$110$		−	69.2820i		−	0.629837i
$111$			45.0333i			0.405706i
$112$	5.00000	+	34.6410i	0.0446429	+	0.309295i
$113$	178.000			1.57522			0.787611	−	0.616173i	$-0.211318\pi$
$113$	178.000			1.57522			0.787611	+	0.616173i	$0.211318\pi$
$114$	36.0000			0.315789
$115$			96.9948i			0.843433i
$116$	114.000			0.982759
$117$		−	20.7846i		−	0.177646i
$118$			76.2102i			0.645849i
$119$		0			0
$120$	−84.0000			−0.700000
$121$	−21.0000			−0.173554
$122$			34.6410i			0.283943i
$123$	120.000			0.975610
$124$		−	83.1384i		−	0.670471i
$125$		−	13.8564i		−	0.110851i
$126$	−3.00000	−	20.7846i	−0.0238095	−	0.164957i
$127$	−190.000			−1.49606			−0.748031	−	0.663663i	$-0.769001\pi$
$127$	−190.000			−1.49606			−0.748031	+	0.663663i	$0.769001\pi$
$128$	−119.000			−0.929688
$129$			45.0333i			0.349096i
$130$	48.0000			0.369231
$131$		−	48.4974i		−	0.370209i	−0.982719	−	0.185105i	$-0.940738\pi$
$131$		−	48.4974i		−	0.370209i	0.982719	−	0.185105i	$-0.0592624\pi$
$132$		−	51.9615i		−	0.393648i
$133$	144.000	−	20.7846i	1.08271	−	0.156275i
$134$	74.0000			0.552239
$135$	−36.0000			−0.266667
$136$		0			0
$137$	−206.000			−1.50365			−0.751825	−	0.659363i	$-0.770826\pi$
$137$	−206.000			−1.50365			−0.751825	+	0.659363i	$0.770826\pi$
$138$		−	24.2487i		−	0.175715i
$139$		−	117.779i		−	0.847334i	−0.905818	−	0.423667i	$-0.860743\pi$
$139$		−	117.779i		−	0.847334i	0.905818	−	0.423667i	$-0.139257\pi$
$140$	−144.000	+	20.7846i	−1.02857	+	0.148461i
$141$	−48.0000			−0.340426
$142$	−62.0000			−0.436620
$143$			69.2820i			0.484490i
$144$	−15.0000			−0.104167
$145$			263.272i			1.81567i
$146$		−	41.5692i		−	0.284721i
$147$	−24.0000	−	81.4064i	−0.163265	−	0.553785i
$148$	−78.0000			−0.527027
$149$	106.000			0.711409			0.355705	−	0.934598i	$-0.384241\pi$
$149$	106.000			0.711409			0.355705	+	0.934598i	$0.384241\pi$
$150$		−	39.8372i		−	0.265581i
$151$	−46.0000			−0.304636			−0.152318	−	0.988332i	$-0.548674\pi$
$151$	−46.0000			−0.304636			−0.152318	+	0.988332i	$0.548674\pi$
$152$			145.492i			0.957186i
$153$		0			0
$154$	10.0000	+	69.2820i	0.0649351	+	0.449883i
$155$	192.000			1.23871
$156$	36.0000			0.230769
$157$		−	242.487i		−	1.54450i	−0.635316	−	0.772252i	$-0.719130\pi$
$157$		−	242.487i		−	1.54450i	0.635316	−	0.772252i	$-0.280870\pi$
$158$	−46.0000			−0.291139
$159$			17.3205i			0.108934i
$160$		−	228.631i		−	1.42894i
$161$	−14.0000	−	96.9948i	−0.0869565	−	0.602452i
$162$	9.00000			0.0555556
$163$	170.000			1.04294			0.521472	−	0.853268i	$-0.325383\pi$
$163$	170.000			1.04294			0.521472	+	0.853268i	$0.325383\pi$
$164$			207.846i			1.26735i
$165$	120.000			0.727273
$166$			90.0666i			0.542570i
$167$			96.9948i			0.580807i	0.956904	+	0.290404i	$0.0937896\pi$
$167$			96.9948i			0.580807i	−0.956904	+	0.290404i	$0.906210\pi$
$168$	84.0000	−	12.1244i	0.500000	−	0.0721688i
$169$	121.000			0.715976
$170$		0			0
$171$			62.3538i			0.364642i
$172$	−78.0000			−0.453488
$173$			173.205i			1.00119i	0.865683	+	0.500593i	$0.166885\pi$
$173$			173.205i			1.00119i	−0.865683	+	0.500593i	$0.833115\pi$
$174$		−	65.8179i		−	0.378264i
$175$	−23.0000	−	159.349i	−0.131429	−	0.910564i
$176$	50.0000			0.284091
$177$	−132.000			−0.745763
$178$		−	41.5692i		−	0.233535i
$179$	−38.0000			−0.212291			−0.106145	−	0.994351i	$-0.533851\pi$
$179$	−38.0000			−0.212291			−0.106145	+	0.994351i	$0.533851\pi$
$180$		−	62.3538i		−	0.346410i
$181$			187.061i			1.03349i	0.856140	+	0.516744i	$0.172856\pi$
$181$			187.061i			1.03349i	−0.856140	+	0.516744i	$0.827144\pi$
$182$	−48.0000	+	6.92820i	−0.263736	+	0.0380671i
$183$	−60.0000			−0.327869
$184$	98.0000			0.532609
$185$		−	180.133i		−	0.973693i
$186$	−48.0000			−0.258065
$187$		0			0
$188$		−	83.1384i		−	0.442226i
$189$	36.0000	−	5.19615i	0.190476	−	0.0274929i
$190$	−144.000			−0.757895
$191$	82.0000			0.429319			0.214660	−	0.976689i	$-0.431136\pi$
$191$	82.0000			0.429319			0.214660	+	0.976689i	$0.431136\pi$
$192$			22.5167i			0.117274i
$193$	50.0000			0.259067			0.129534	−	0.991575i	$-0.458652\pi$
$193$	50.0000			0.259067			0.129534	+	0.991575i	$0.458652\pi$
$194$			55.4256i			0.285699i
$195$			83.1384i			0.426351i
$196$	141.000	−	41.5692i	0.719388	−	0.212088i
$197$	−278.000			−1.41117			−0.705584	−	0.708627i	$-0.749315\pi$
$197$	−278.000			−1.41117			−0.705584	+	0.708627i	$0.749315\pi$
$198$	−30.0000			−0.151515
$199$			290.985i			1.46223i	0.682252	+	0.731117i	$0.261001\pi$
$199$			290.985i			1.46223i	−0.682252	+	0.731117i	$0.738999\pi$
$200$	161.000			0.805000
$201$			128.172i			0.637670i
$202$		−	117.779i		−	0.583067i
$203$	−38.0000	−	263.272i	−0.187192	−	1.29691i
$204$		0			0
$205$	−480.000			−2.34146
$206$		−	96.9948i		−	0.470849i
$207$	42.0000			0.202899
$208$			34.6410i			0.166543i
$209$		−	207.846i		−	0.994479i
$210$	12.0000	+	83.1384i	0.0571429	+	0.395897i
$211$	74.0000			0.350711			0.175355	−	0.984505i	$-0.443893\pi$
$211$	74.0000			0.350711			0.175355	+	0.984505i	$0.443893\pi$
$212$	−30.0000			−0.141509
$213$		−	107.387i		−	0.504165i
$214$	10.0000			0.0467290
$215$		−	180.133i		−	0.837829i
$216$			36.3731i			0.168394i
$217$	−192.000	+	27.7128i	−0.884793	+	0.127709i
$218$	74.0000			0.339450
$219$	72.0000			0.328767
$220$			207.846i			0.944755i
$221$		0			0
$222$			45.0333i			0.202853i
$223$			304.841i			1.36700i	0.729951	+	0.683500i	$0.239543\pi$
$223$			304.841i			1.36700i	−0.729951	+	0.683500i	$0.760457\pi$
$224$	33.0000	+	228.631i	0.147321	+	1.02067i
$225$	69.0000			0.306667
$226$	178.000			0.787611
$227$			6.92820i			0.0305207i	0.999884	+	0.0152604i	$0.00485771\pi$
$227$			6.92820i			0.0305207i	−0.999884	+	0.0152604i	$0.995142\pi$
$228$	−108.000			−0.473684
$229$		−	284.056i		−	1.24042i	−0.784436	−	0.620210i	$-0.787047\pi$
$229$		−	284.056i		−	1.24042i	0.784436	−	0.620210i	$-0.212953\pi$
$230$			96.9948i			0.421717i
$231$	−120.000	+	17.3205i	−0.519481	+	0.0749806i
$232$	266.000			1.14655
$233$	178.000			0.763948			0.381974	−	0.924173i	$-0.375244\pi$
$233$	178.000			0.763948			0.381974	+	0.924173i	$0.375244\pi$
$234$		−	20.7846i		−	0.0888231i
$235$	192.000			0.817021
$236$		−	228.631i		−	0.968774i
$237$		−	79.6743i		−	0.336179i
$238$		0			0
$239$	34.0000			0.142259			0.0711297	−	0.997467i	$-0.477340\pi$
$239$	34.0000			0.142259			0.0711297	+	0.997467i	$0.477340\pi$
$240$	60.0000			0.250000
$241$		−	193.990i		−	0.804936i	−0.915434	−	0.402468i	$-0.868152\pi$
$241$		−	193.990i		−	0.804936i	0.915434	−	0.402468i	$-0.131848\pi$
$242$	−21.0000			−0.0867769
$243$			15.5885i			0.0641500i
$244$		−	103.923i		−	0.425914i
$245$	96.0000	+	325.626i	0.391837	+	1.32908i
$246$	120.000			0.487805
$247$	144.000			0.582996
$248$		−	193.990i		−	0.782216i
$249$	−156.000			−0.626506
$250$		−	13.8564i		−	0.0554256i
$251$			187.061i			0.745265i	0.927979	+	0.372632i	$0.121545\pi$
$251$			187.061i			0.745265i	−0.927979	+	0.372632i	$0.878455\pi$
$252$	9.00000	+	62.3538i	0.0357143	+	0.247436i
$253$	−140.000			−0.553360
$254$	−190.000			−0.748031
$255$		0			0
$256$	−171.000			−0.667969
$257$			138.564i			0.539160i	0.962978	+	0.269580i	$0.0868848\pi$
$257$			138.564i			0.539160i	−0.962978	+	0.269580i	$0.913115\pi$
$258$			45.0333i			0.174548i
$259$	26.0000	+	180.133i	0.100386	+	0.695495i
$260$	−144.000			−0.553846
$261$	114.000			0.436782
$262$		−	48.4974i		−	0.185105i
$263$	−62.0000			−0.235741			−0.117871	−	0.993029i	$-0.537607\pi$
$263$	−62.0000			−0.235741			−0.117871	+	0.993029i	$0.537607\pi$
$264$		−	121.244i		−	0.459256i
$265$		−	69.2820i		−	0.261442i
$266$	144.000	−	20.7846i	0.541353	−	0.0781376i
$267$	72.0000			0.269663
$268$	−222.000			−0.828358
$269$			228.631i			0.849928i	0.905210	+	0.424964i	$0.139713\pi$
$269$			228.631i			0.849928i	−0.905210	+	0.424964i	$0.860287\pi$
$270$	−36.0000			−0.133333
$271$		−	332.554i		−	1.22714i	−0.789642	−	0.613568i	$-0.789734\pi$
$271$		−	332.554i		−	1.22714i	0.789642	−	0.613568i	$-0.210266\pi$
$272$		0			0
$273$	−12.0000	−	83.1384i	−0.0439560	−	0.304536i
$274$	−206.000			−0.751825
$275$	−230.000			−0.836364
$276$			72.7461i			0.263573i
$277$	26.0000			0.0938628			0.0469314	−	0.998898i	$-0.485056\pi$
$277$	26.0000			0.0938628			0.0469314	+	0.998898i	$0.485056\pi$
$278$		−	117.779i		−	0.423667i
$279$		−	83.1384i		−	0.297987i
$280$	−336.000	+	48.4974i	−1.20000	+	0.173205i
$281$	−494.000			−1.75801			−0.879004	−	0.476815i	$-0.841791\pi$
$281$	−494.000			−1.75801			−0.879004	+	0.476815i	$0.841791\pi$
$282$	−48.0000			−0.170213
$283$		−	200.918i		−	0.709957i	−0.934874	−	0.354979i	$-0.884488\pi$
$283$		−	200.918i		−	0.709957i	0.934874	−	0.354979i	$-0.115512\pi$
$284$	186.000			0.654930
$285$		−	249.415i		−	0.875141i
$286$			69.2820i			0.242245i
$287$	480.000	−	69.2820i	1.67247	−	0.241401i
$288$	−99.0000			−0.343750
$289$	289.000			1.00000
$290$			263.272i			0.907834i
$291$	−96.0000			−0.329897
$292$			124.708i			0.427081i
$293$			491.902i			1.67885i	0.543477	+	0.839424i	$0.317107\pi$
$293$			491.902i			1.67885i	−0.543477	+	0.839424i	$0.682893\pi$
$294$	−24.0000	−	81.4064i	−0.0816327	−	0.276892i
$295$	528.000			1.78983
$296$	−182.000			−0.614865
$297$		−	51.9615i		−	0.174955i
$298$	106.000			0.355705
$299$		−	96.9948i		−	0.324397i
$300$			119.512i			0.398372i
$301$	26.0000	+	180.133i	0.0863787	+	0.598449i
$302$	−46.0000			−0.152318
$303$	204.000			0.673267
$304$		−	103.923i		−	0.341852i
$305$	240.000			0.786885
$306$		0			0
$307$		−	20.7846i		−	0.0677023i	−0.999427	−	0.0338512i	$-0.989223\pi$
$307$		−	20.7846i		−	0.0677023i	0.999427	−	0.0338512i	$-0.0107772\pi$
$308$	−30.0000	−	207.846i	−0.0974026	−	0.674825i
$309$	168.000			0.543689
$310$	192.000			0.619355
$311$			13.8564i			0.0445544i	0.999752	+	0.0222772i	$0.00709163\pi$
$311$			13.8564i			0.0445544i	−0.999752	+	0.0222772i	$0.992908\pi$
$312$	84.0000			0.269231
$313$			263.272i			0.841124i	0.907264	+	0.420562i	$0.138167\pi$
$313$			263.272i			0.841124i	−0.907264	+	0.420562i	$0.861833\pi$
$314$		−	242.487i		−	0.772252i
$315$	−144.000	+	20.7846i	−0.457143	+	0.0659829i
$316$	138.000			0.436709
$317$	250.000			0.788644			0.394322	−	0.918972i	$-0.370980\pi$
$317$	250.000			0.788644			0.394322	+	0.918972i	$0.370980\pi$
$318$			17.3205i			0.0544670i
$319$	−380.000			−1.19122
$320$		−	90.0666i		−	0.281458i
$321$			17.3205i			0.0539580i
$322$	−14.0000	−	96.9948i	−0.0434783	−	0.301226i
$323$		0			0
$324$	−27.0000			−0.0833333
$325$		−	159.349i		−	0.490304i
$326$	170.000			0.521472
$327$			128.172i			0.391963i
$328$			484.974i			1.47858i
$329$	−192.000	+	27.7128i	−0.583587	+	0.0842335i
$330$	120.000			0.363636
$331$	−646.000			−1.95166			−0.975831	−	0.218527i	$-0.929875\pi$
$331$	−646.000			−1.95166			−0.975831	+	0.218527i	$0.929875\pi$
$332$		−	270.200i		−	0.813855i
$333$	−78.0000			−0.234234
$334$			96.9948i			0.290404i
$335$		−	512.687i		−	1.53041i
$336$	−60.0000	+	8.66025i	−0.178571	+	0.0257746i
$337$	146.000			0.433234			0.216617	−	0.976257i	$-0.430498\pi$
$337$	146.000			0.433234			0.216617	+	0.976257i	$0.430498\pi$
$338$	121.000			0.357988
$339$			308.305i			0.909454i
$340$		0			0
$341$			277.128i			0.812692i
$342$			62.3538i			0.182321i
$343$	−143.000	−	311.769i	−0.416910	−	0.908948i
$344$	−182.000			−0.529070
$345$	−168.000			−0.486957
$346$			173.205i			0.500593i
$347$	106.000			0.305476			0.152738	−	0.988267i	$-0.451191\pi$
$347$	106.000			0.305476			0.152738	+	0.988267i	$0.451191\pi$
$348$			197.454i			0.567396i
$349$		−	630.466i		−	1.80649i	−0.429121	−	0.903247i	$-0.641177\pi$
$349$		−	630.466i		−	1.80649i	0.429121	−	0.903247i	$-0.358823\pi$
$350$	−23.0000	−	159.349i	−0.0657143	−	0.455282i
$351$	36.0000			0.102564
$352$	330.000			0.937500
$353$		−	304.841i		−	0.863572i	−0.901976	−	0.431786i	$-0.857884\pi$
$353$		−	304.841i		−	0.863572i	0.901976	−	0.431786i	$-0.142116\pi$
$354$	−132.000			−0.372881
$355$			429.549i			1.21000i
$356$			124.708i			0.350302i
$357$		0			0
$358$	−38.0000			−0.106145
$359$	−494.000			−1.37604			−0.688022	−	0.725690i	$-0.741521\pi$
$359$	−494.000			−1.37604			−0.688022	+	0.725690i	$0.741521\pi$
$360$		−	145.492i		−	0.404145i
$361$	−71.0000			−0.196676
$362$			187.061i			0.516744i
$363$		−	36.3731i		−	0.100201i
$364$	144.000	−	20.7846i	0.395604	−	0.0571006i
$365$	−288.000			−0.789041
$366$	−60.0000			−0.163934
$367$			554.256i			1.51024i	0.655589	+	0.755118i	$0.272420\pi$
$367$			554.256i			1.51024i	−0.655589	+	0.755118i	$0.727580\pi$
$368$	−70.0000			−0.190217
$369$			207.846i			0.563269i
$370$		−	180.133i		−	0.486847i
$371$	10.0000	+	69.2820i	0.0269542	+	0.186744i
$372$	144.000			0.387097
$373$	218.000			0.584450			0.292225	−	0.956350i	$-0.405604\pi$
$373$	218.000			0.584450			0.292225	+	0.956350i	$0.405604\pi$
$374$		0			0
$375$	24.0000			0.0640000
$376$		−	193.990i		−	0.515930i
$377$		−	263.272i		−	0.698333i
$378$	36.0000	−	5.19615i	0.0952381	−	0.0137464i
$379$	−550.000			−1.45119			−0.725594	−	0.688123i	$-0.758435\pi$
$379$	−550.000			−1.45119			−0.725594	+	0.688123i	$0.758435\pi$
$380$	432.000			1.13684
$381$		−	329.090i		−	0.863752i
$382$	82.0000			0.214660
$383$			55.4256i			0.144714i	0.997379	+	0.0723572i	$0.0230522\pi$
$383$			55.4256i			0.144714i	−0.997379	+	0.0723572i	$0.976948\pi$
$384$		−	206.114i		−	0.536755i
$385$	480.000	−	69.2820i	1.24675	−	0.179953i
$386$	50.0000			0.129534
$387$	−78.0000			−0.201550
$388$		−	166.277i		−	0.428549i
$389$	394.000			1.01285			0.506427	−	0.862283i	$-0.330966\pi$
$389$	394.000			1.01285			0.506427	+	0.862283i	$0.330966\pi$
$390$			83.1384i			0.213175i
$391$		0			0
$392$	329.000	−	96.9948i	0.839286	−	0.247436i
$393$	84.0000			0.213740
$394$	−278.000			−0.705584
$395$			318.697i			0.806829i
$396$	90.0000			0.227273
$397$		−	103.923i		−	0.261771i	−0.991397	−	0.130885i	$-0.958218\pi$
$397$		−	103.923i		−	0.261771i	0.991397	−	0.130885i	$-0.0417820\pi$
$398$			290.985i			0.731117i
$399$	36.0000	+	249.415i	0.0902256	+	0.625101i
$400$	−115.000			−0.287500
$401$	178.000			0.443890			0.221945	−	0.975059i	$-0.428759\pi$
$401$	178.000			0.443890			0.221945	+	0.975059i	$0.428759\pi$
$402$			128.172i			0.318835i
$403$	−192.000			−0.476427
$404$			353.338i			0.874600i
$405$		−	62.3538i		−	0.153960i
$406$	−38.0000	−	263.272i	−0.0935961	−	0.648453i
$407$	260.000			0.638821
$408$		0			0
$409$			651.251i			1.59230i	0.605099	+	0.796150i	$0.293134\pi$
$409$			651.251i			1.59230i	−0.605099	+	0.796150i	$0.706866\pi$
$410$	−480.000			−1.17073
$411$		−	356.802i		−	0.868133i
$412$			290.985i			0.706273i
$413$	−528.000	+	76.2102i	−1.27845	+	0.184528i
$414$	42.0000			0.101449
$415$	624.000			1.50361
$416$			228.631i			0.549593i
$417$	204.000			0.489209
$418$		−	207.846i		−	0.497239i
$419$		−	713.605i		−	1.70311i	−0.524262	−	0.851557i	$-0.675659\pi$
$419$		−	713.605i		−	1.70311i	0.524262	−	0.851557i	$-0.324341\pi$
$420$	−36.0000	−	249.415i	−0.0857143	−	0.593846i
$421$	602.000			1.42993			0.714964	−	0.699161i	$-0.246443\pi$
$421$	602.000			1.42993			0.714964	+	0.699161i	$0.246443\pi$
$422$	74.0000			0.175355
$423$		−	83.1384i		−	0.196545i
$424$	−70.0000			−0.165094
$425$		0			0
$426$		−	107.387i		−	0.252083i
$427$	−240.000	+	34.6410i	−0.562061	+	0.0811265i
$428$	−30.0000			−0.0700935
$429$	−120.000			−0.279720
$430$		−	180.133i		−	0.418915i
$431$	34.0000			0.0788863			0.0394432	−	0.999222i	$-0.487442\pi$
$431$	34.0000			0.0788863			0.0394432	+	0.999222i	$0.487442\pi$
$432$		−	25.9808i		−	0.0601407i
$433$		−	415.692i		−	0.960028i	−0.877261	−	0.480014i	$-0.840632\pi$
$433$		−	415.692i		−	0.960028i	0.877261	−	0.480014i	$-0.159368\pi$
$434$	−192.000	+	27.7128i	−0.442396	+	0.0638544i
$435$	−456.000			−1.04828
$436$	−222.000			−0.509174
$437$			290.985i			0.665869i
$438$	72.0000			0.164384
$439$			96.9948i			0.220945i	0.993879	+	0.110472i	$0.0352364\pi$
$439$			96.9948i			0.220945i	−0.993879	+	0.110472i	$0.964764\pi$
$440$			484.974i			1.10221i
$441$	141.000	−	41.5692i	0.319728	−	0.0942613i
$442$		0			0
$443$	−470.000			−1.06095			−0.530474	−	0.847701i	$-0.677986\pi$
$443$	−470.000			−1.06095			−0.530474	+	0.847701i	$0.677986\pi$
$444$		−	135.100i		−	0.304279i
$445$	−288.000			−0.647191
$446$			304.841i			0.683500i
$447$			183.597i			0.410732i
$448$	13.0000	+	90.0666i	0.0290179	+	0.201042i
$449$	514.000			1.14477			0.572383	−	0.819986i	$-0.306019\pi$
$449$	514.000			1.14477			0.572383	+	0.819986i	$0.306019\pi$
$450$	69.0000			0.153333
$451$		−	692.820i		−	1.53619i
$452$	−534.000			−1.18142
$453$		−	79.6743i		−	0.175882i
$454$			6.92820i			0.0152604i
$455$	48.0000	+	332.554i	0.105495	+	0.730887i
$456$	−252.000			−0.552632
$457$	−478.000			−1.04595			−0.522976	−	0.852347i	$-0.675178\pi$
$457$	−478.000			−1.04595			−0.522976	+	0.852347i	$0.675178\pi$
$458$		−	284.056i		−	0.620210i
$459$		0			0
$460$		−	290.985i		−	0.632575i
$461$			672.036i			1.45778i	0.684632	+	0.728889i	$0.259963\pi$
$461$			672.036i			1.45778i	−0.684632	+	0.728889i	$0.740037\pi$
$462$	−120.000	+	17.3205i	−0.259740	+	0.0374903i
$463$	−430.000			−0.928726			−0.464363	−	0.885645i	$-0.653717\pi$
$463$	−430.000			−0.928726			−0.464363	+	0.885645i	$0.653717\pi$
$464$	−190.000			−0.409483
$465$			332.554i			0.715169i
$466$	178.000			0.381974
$467$		−	852.169i		−	1.82477i	−0.409330	−	0.912387i	$-0.634237\pi$
$467$		−	852.169i		−	1.82477i	0.409330	−	0.912387i	$-0.365763\pi$
$468$			62.3538i			0.133235i
$469$	74.0000	+	512.687i	0.157783	+	1.09315i
$470$	192.000			0.408511
$471$	420.000			0.891720
$472$		−	533.472i		−	1.13024i
$473$	260.000			0.549683
$474$		−	79.6743i		−	0.168089i
$475$			478.046i			1.00641i
$476$		0			0
$477$	−30.0000			−0.0628931
$478$	34.0000			0.0711297
$479$		−	387.979i		−	0.809978i	−0.914322	−	0.404989i	$-0.867275\pi$
$479$		−	387.979i		−	0.809978i	0.914322	−	0.404989i	$-0.132725\pi$
$480$	396.000			0.825000
$481$			180.133i			0.374497i
$482$		−	193.990i		−	0.402468i
$483$	168.000	−	24.2487i	0.347826	−	0.0502044i
$484$	63.0000			0.130165
$485$	384.000			0.791753
$486$			15.5885i			0.0320750i
$487$	818.000			1.67967			0.839836	−	0.542841i	$-0.182651\pi$
$487$	818.000			1.67967			0.839836	+	0.542841i	$0.182651\pi$
$488$		−	242.487i		−	0.496900i
$489$			294.449i			0.602144i
$490$	96.0000	+	325.626i	0.195918	+	0.664542i
$491$	490.000			0.997963			0.498982	−	0.866613i	$-0.333707\pi$
$491$	490.000			0.997963			0.498982	+	0.866613i	$0.333707\pi$
$492$	−360.000			−0.731707
$493$		0			0
$494$	144.000			0.291498
$495$			207.846i			0.419891i
$496$			138.564i			0.279363i
$497$	−62.0000	−	429.549i	−0.124748	−	0.864283i
$498$	−156.000			−0.313253
$499$	554.000			1.11022			0.555110	−	0.831777i	$-0.312676\pi$
$499$	554.000			1.11022			0.555110	+	0.831777i	$0.312676\pi$
$500$			41.5692i			0.0831384i
$501$	−168.000			−0.335329
$502$			187.061i			0.372632i
$503$			290.985i			0.578498i	0.957254	+	0.289249i	$0.0934056\pi$
$503$			290.985i			0.578498i	−0.957254	+	0.289249i	$0.906594\pi$
$504$	21.0000	+	145.492i	0.0416667	+	0.288675i
$505$	−816.000			−1.61584
$506$	−140.000			−0.276680
$507$			209.578i			0.413369i
$508$	570.000			1.12205
$509$		−	963.020i		−	1.89198i	−0.324189	−	0.945992i	$-0.605091\pi$
$509$		−	963.020i		−	1.89198i	0.324189	−	0.945992i	$-0.394909\pi$
$510$		0			0
$511$	288.000	−	41.5692i	0.563601	−	0.0813488i
$512$	305.000			0.595703
$513$	−108.000			−0.210526
$514$			138.564i			0.269580i
$515$	−672.000			−1.30485
$516$		−	135.100i		−	0.261822i
$517$			277.128i			0.536031i
$518$	26.0000	+	180.133i	0.0501931	+	0.347748i
$519$	−300.000			−0.578035
$520$	−336.000			−0.646154
$521$		−	124.708i		−	0.239362i	−0.992812	−	0.119681i	$-0.961813\pi$
$521$		−	124.708i		−	0.239362i	0.992812	−	0.119681i	$-0.0381872\pi$
$522$	114.000			0.218391
$523$		−	62.3538i		−	0.119223i	−0.998222	−	0.0596117i	$-0.981014\pi$
$523$		−	62.3538i		−	0.119223i	0.998222	−	0.0596117i	$-0.0189862\pi$
$524$			145.492i			0.277657i
$525$	276.000	−	39.8372i	0.525714	−	0.0758803i
$526$	−62.0000			−0.117871
$527$		0			0
$528$			86.6025i			0.164020i
$529$	−333.000			−0.629490
$530$		−	69.2820i		−	0.130721i
$531$		−	228.631i		−	0.430566i
$532$	−432.000	+	62.3538i	−0.812030	+	0.117206i
$533$	480.000			0.900563
$534$	72.0000			0.134831
$535$		−	69.2820i		−	0.129499i
$536$	−518.000			−0.966418
$537$		−	65.8179i		−	0.122566i
$538$			228.631i			0.424964i
$539$	−470.000	+	138.564i	−0.871985	+	0.257076i
$540$	108.000			0.200000
$541$	−118.000			−0.218115			−0.109057	−	0.994035i	$-0.534783\pi$
$541$	−118.000			−0.218115			−0.109057	+	0.994035i	$0.534783\pi$
$542$		−	332.554i		−	0.613568i
$543$	−324.000			−0.596685
$544$		0			0
$545$		−	512.687i		−	0.940710i
$546$	−12.0000	−	83.1384i	−0.0219780	−	0.152268i
$547$	−406.000			−0.742230			−0.371115	−	0.928587i	$-0.621024\pi$
$547$	−406.000			−0.742230			−0.371115	+	0.928587i	$0.621024\pi$
$548$	618.000			1.12774
$549$		−	103.923i		−	0.189295i
$550$	−230.000			−0.418182
$551$			789.815i			1.43342i
$552$			169.741i			0.307502i
$553$	−46.0000	−	318.697i	−0.0831826	−	0.576306i
$554$	26.0000			0.0469314
$555$	312.000			0.562162
$556$			353.338i			0.635501i
$557$	−998.000			−1.79174			−0.895871	−	0.444315i	$-0.853447\pi$
$557$	−998.000			−1.79174			−0.895871	+	0.444315i	$0.853447\pi$
$558$		−	83.1384i		−	0.148994i
$559$			180.133i			0.322242i
$560$	240.000	−	34.6410i	0.428571	−	0.0618590i
$561$		0			0
$562$	−494.000			−0.879004
$563$			367.195i			0.652211i	0.945333	+	0.326105i	$0.105736\pi$
$563$			367.195i			0.652211i	−0.945333	+	0.326105i	$0.894264\pi$
$564$	144.000			0.255319
$565$		−	1233.22i		−	2.18269i
$566$		−	200.918i		−	0.354979i
$567$	9.00000	+	62.3538i	0.0158730	+	0.109971i
$568$	434.000			0.764085
$569$	−62.0000			−0.108963			−0.0544815	−	0.998515i	$-0.517351\pi$
$569$	−62.0000			−0.108963			−0.0544815	+	0.998515i	$0.517351\pi$
$570$		−	249.415i		−	0.437571i
$571$	410.000			0.718039			0.359019	−	0.933330i	$-0.383111\pi$
$571$	410.000			0.718039			0.359019	+	0.933330i	$0.383111\pi$
$572$		−	207.846i		−	0.363367i
$573$			142.028i			0.247868i
$574$	480.000	−	69.2820i	0.836237	−	0.120700i
$575$	322.000			0.560000
$576$	−39.0000			−0.0677083
$577$			831.384i			1.44087i	0.693520	+	0.720437i	$0.256059\pi$
$577$			831.384i			1.44087i	−0.693520	+	0.720437i	$0.743941\pi$
$578$	289.000			0.500000
$579$			86.6025i			0.149573i
$580$		−	789.815i		−	1.36175i
$581$	−624.000	+	90.0666i	−1.07401	+	0.155020i
$582$	−96.0000			−0.164948
$583$	100.000			0.171527
$584$			290.985i			0.498261i
$585$	−144.000			−0.246154
$586$			491.902i			0.839424i
$587$			547.328i			0.932416i	0.884675	+	0.466208i	$0.154380\pi$
$587$			547.328i			0.932416i	−0.884675	+	0.466208i	$0.845620\pi$
$588$	72.0000	+	244.219i	0.122449	+	0.415339i
$589$	576.000			0.977929
$590$	528.000			0.894915
$591$		−	481.510i		−	0.814738i
$592$	130.000			0.219595
$593$			997.661i			1.68240i	0.540727	+	0.841198i	$0.318149\pi$
$593$			997.661i			1.68240i	−0.540727	+	0.841198i	$0.681851\pi$
$594$		−	51.9615i		−	0.0874773i
$595$		0			0
$596$	−318.000			−0.533557
$597$	−504.000			−0.844221
$598$		−	96.9948i		−	0.162199i
$599$	1186.00			1.97997			0.989983	−	0.141184i	$-0.0450911\pi$
$599$	1186.00			1.97997			0.989983	+	0.141184i	$0.0450911\pi$
$600$			278.860i			0.464767i
$601$		−	401.836i		−	0.668612i	−0.942465	−	0.334306i	$-0.891498\pi$
$601$		−	401.836i		−	0.668612i	0.942465	−	0.334306i	$-0.108502\pi$
$602$	26.0000	+	180.133i	0.0431894	+	0.299225i
$603$	−222.000			−0.368159
$604$	138.000			0.228477
$605$			145.492i			0.240483i
$606$	204.000			0.336634
$607$		−	138.564i		−	0.228277i	−0.993465	−	0.114138i	$-0.963589\pi$
$607$		−	138.564i		−	0.228277i	0.993465	−	0.114138i	$-0.0364107\pi$
$608$		−	685.892i		−	1.12811i
$609$	456.000	−	65.8179i	0.748768	−	0.108075i
$610$	240.000			0.393443
$611$	−192.000			−0.314239
$612$		0			0
$613$	26.0000			0.0424144			0.0212072	−	0.999775i	$-0.493249\pi$
$613$	26.0000			0.0424144			0.0212072	+	0.999775i	$0.493249\pi$
$614$		−	20.7846i		−	0.0338512i
$615$		−	831.384i		−	1.35184i
$616$	−70.0000	−	484.974i	−0.113636	−	0.787296i
$617$	−734.000			−1.18963			−0.594814	−	0.803864i	$-0.702774\pi$
$617$	−734.000			−1.18963			−0.594814	+	0.803864i	$0.702774\pi$
$618$	168.000			0.271845
$619$		−	838.313i		−	1.35430i	−0.735844	−	0.677151i	$-0.763215\pi$
$619$		−	838.313i		−	1.35430i	0.735844	−	0.677151i	$-0.236785\pi$
$620$	−576.000			−0.929032
$621$			72.7461i			0.117144i
$622$			13.8564i			0.0222772i
$623$	288.000	−	41.5692i	0.462279	−	0.0667243i
$624$	−60.0000			−0.0961538
$625$	−671.000			−1.07360
$626$			263.272i			0.420562i
$627$	360.000			0.574163
$628$			727.461i			1.15838i
$629$		0			0
$630$	−144.000	+	20.7846i	−0.228571	+	0.0329914i
$631$	−286.000			−0.453249			−0.226624	−	0.973982i	$-0.572769\pi$
$631$	−286.000			−0.453249			−0.226624	+	0.973982i	$0.572769\pi$
$632$	322.000			0.509494
$633$			128.172i			0.202483i
$634$	250.000			0.394322
$635$			1316.36i			2.07301i
$636$		−	51.9615i		−	0.0817005i
$637$	−96.0000	−	325.626i	−0.150706	−	0.511186i
$638$	−380.000			−0.595611
$639$	186.000			0.291080
$640$			824.456i			1.28821i
$641$	658.000			1.02652			0.513261	−	0.858233i	$-0.328437\pi$
$641$	658.000			1.02652			0.513261	+	0.858233i	$0.328437\pi$
$642$			17.3205i			0.0269790i
$643$		−	325.626i		−	0.506416i	−0.967412	−	0.253208i	$-0.918514\pi$
$643$		−	325.626i		−	0.506416i	0.967412	−	0.253208i	$-0.0814857\pi$
$644$	42.0000	+	290.985i	0.0652174	+	0.451839i
$645$	312.000			0.483721
$646$		0			0
$647$		−	457.261i		−	0.706741i	−0.935483	−	0.353370i	$-0.885036\pi$
$647$		−	457.261i		−	0.706741i	0.935483	−	0.353370i	$-0.114964\pi$
$648$	−63.0000			−0.0972222
$649$			762.102i			1.17427i
$650$		−	159.349i		−	0.245152i
$651$	−48.0000	−	332.554i	−0.0737327	−	0.510835i
$652$	−510.000			−0.782209
$653$	−614.000			−0.940276			−0.470138	−	0.882593i	$-0.655796\pi$
$653$	−614.000			−0.940276			−0.470138	+	0.882593i	$0.655796\pi$
$654$			128.172i			0.195981i
$655$	−336.000			−0.512977
$656$		−	346.410i		−	0.528064i
$657$			124.708i			0.189814i
$658$	−192.000	+	27.7128i	−0.291793	+	0.0421167i
$659$	442.000			0.670713			0.335357	−	0.942091i	$-0.391143\pi$
$659$	442.000			0.670713			0.335357	+	0.942091i	$0.391143\pi$
$660$	−360.000			−0.545455
$661$		−	34.6410i		−	0.0524070i	−0.999657	−	0.0262035i	$-0.991658\pi$
$661$		−	34.6410i		−	0.0524070i	0.999657	−	0.0262035i	$-0.00834179\pi$
$662$	−646.000			−0.975831
$663$		0			0
$664$		−	630.466i		−	0.949498i
$665$	−144.000	−	997.661i	−0.216541	−	1.50024i
$666$	−78.0000			−0.117117
$667$	532.000			0.797601
$668$		−	290.985i		−	0.435606i
$669$	−528.000			−0.789238
$670$		−	512.687i		−	0.765205i
$671$			346.410i			0.516260i
$672$	−396.000	+	57.1577i	−0.589286	+	0.0850561i
$673$	386.000			0.573551			0.286776	−	0.957998i	$-0.407417\pi$
$673$	386.000			0.573551			0.286776	+	0.957998i	$0.407417\pi$
$674$	146.000			0.216617
$675$			119.512i			0.177054i
$676$	−363.000			−0.536982
$677$		−	782.887i		−	1.15641i	−0.815893	−	0.578203i	$-0.803754\pi$
$677$		−	782.887i		−	1.15641i	0.815893	−	0.578203i	$-0.196246\pi$
$678$			308.305i			0.454727i
$679$	−384.000	+	55.4256i	−0.565538	+	0.0816283i
$680$		0			0
$681$	−12.0000			−0.0176211
$682$			277.128i			0.406346i
$683$	298.000			0.436310			0.218155	−	0.975914i	$-0.429996\pi$
$683$	298.000			0.436310			0.218155	+	0.975914i	$0.429996\pi$
$684$		−	187.061i		−	0.273482i
$685$			1427.21i			2.08352i
$686$	−143.000	−	311.769i	−0.208455	−	0.454474i
$687$	492.000			0.716157
$688$	130.000			0.188953
$689$			69.2820i			0.100554i
$690$	−168.000			−0.243478
$691$			866.025i			1.25329i	0.779304	+	0.626646i	$0.215573\pi$
$691$			866.025i			1.25329i	−0.779304	+	0.626646i	$0.784427\pi$
$692$		−	519.615i		−	0.750889i
$693$	−30.0000	−	207.846i	−0.0432900	−	0.299922i
$694$	106.000			0.152738
$695$	−816.000			−1.17410
$696$			460.726i			0.661962i
$697$		0			0
$698$		−	630.466i		−	0.903247i
$699$			308.305i			0.441066i
$700$	69.0000	+	478.046i	0.0985714	+	0.682923i
$701$	154.000			0.219686			0.109843	−	0.993949i	$-0.464965\pi$
$701$	154.000			0.219686			0.109843	+	0.993949i	$0.464965\pi$
$702$	36.0000			0.0512821
$703$		−	540.400i		−	0.768705i
$704$	130.000			0.184659
$705$			332.554i			0.471707i
$706$		−	304.841i		−	0.431786i
$707$	816.000	−	117.779i	1.15417	−	0.166590i
$708$	396.000			0.559322
$709$	890.000			1.25529			0.627645	−	0.778500i	$-0.284019\pi$
$709$	890.000			1.25529			0.627645	+	0.778500i	$0.284019\pi$
$710$			429.549i			0.604998i
$711$	138.000			0.194093
$712$			290.985i			0.408686i
$713$		−	387.979i		−	0.544151i
$714$		0			0
$715$	480.000			0.671329
$716$	114.000			0.159218
$717$			58.8897i			0.0821335i
$718$	−494.000			−0.688022
$719$			83.1384i			0.115631i	0.998327	+	0.0578153i	$0.0184135\pi$
$719$			83.1384i			0.115631i	−0.998327	+	0.0578153i	$0.981587\pi$
$720$			103.923i			0.144338i
$721$	672.000	−	96.9948i	0.932039	−	0.134528i
$722$	−71.0000			−0.0983380
$723$	336.000			0.464730
$724$		−	561.184i		−	0.775117i
$725$	874.000			1.20552
$726$		−	36.3731i		−	0.0501006i
$727$		−	235.559i		−	0.324015i	−0.986790	−	0.162008i	$-0.948203\pi$
$727$		−	235.559i		−	0.324015i	0.986790	−	0.162008i	$-0.0517969\pi$
$728$	336.000	−	48.4974i	0.461538	−	0.0666173i
$729$	−27.0000			−0.0370370
$730$	−288.000			−0.394521
$731$		0			0
$732$	180.000			0.245902
$733$		−	76.2102i		−	0.103970i	−0.998648	−	0.0519852i	$-0.983445\pi$
$733$		−	76.2102i		−	0.103970i	0.998648	−	0.0519852i	$-0.0165549\pi$
$734$			554.256i			0.755118i
$735$	−564.000	+	166.277i	−0.767347	+	0.226227i
$736$	−462.000			−0.627717
$737$	740.000			1.00407
$738$			207.846i			0.281634i
$739$	−982.000			−1.32882			−0.664411	−	0.747367i	$-0.731318\pi$
$739$	−982.000			−1.32882			−0.664411	+	0.747367i	$0.731318\pi$
$740$			540.400i			0.730270i
$741$			249.415i			0.336593i
$742$	10.0000	+	69.2820i	0.0134771	+	0.0933720i
$743$	−686.000			−0.923284			−0.461642	−	0.887066i	$-0.652740\pi$
$743$	−686.000			−0.923284			−0.461642	+	0.887066i	$0.652740\pi$
$744$	336.000			0.451613
$745$		−	734.390i		−	0.985758i
$746$	218.000			0.292225
$747$		−	270.200i		−	0.361713i
$748$		0			0
$749$	10.0000	+	69.2820i	0.0133511	+	0.0924994i
$750$	24.0000			0.0320000
$751$	290.000			0.386152			0.193076	−	0.981184i	$-0.438154\pi$
$751$	290.000			0.386152			0.193076	+	0.981184i	$0.438154\pi$
$752$			138.564i			0.184261i
$753$	−324.000			−0.430279
$754$		−	263.272i		−	0.349167i
$755$			318.697i			0.422116i
$756$	−108.000	+	15.5885i	−0.142857	+	0.0206197i
$757$	−358.000			−0.472919			−0.236460	−	0.971641i	$-0.575987\pi$
$757$	−358.000			−0.472919			−0.236460	+	0.971641i	$0.575987\pi$
$758$	−550.000			−0.725594
$759$		−	242.487i		−	0.319482i
$760$	1008.00			1.32632
$761$		−	651.251i		−	0.855783i	−0.903830	−	0.427892i	$-0.859256\pi$
$761$		−	651.251i		−	0.855783i	0.903830	−	0.427892i	$-0.140744\pi$
$762$		−	329.090i		−	0.431876i
$763$	74.0000	+	512.687i	0.0969856	+	0.671936i
$764$	−246.000			−0.321990
$765$		0			0
$766$			55.4256i			0.0723572i
$767$	−528.000			−0.688396
$768$		−	296.181i		−	0.385652i
$769$			775.959i			1.00905i	0.863397	+	0.504525i	$0.168332\pi$
$769$			775.959i			1.00905i	−0.863397	+	0.504525i	$0.831668\pi$
$770$	480.000	−	69.2820i	0.623377	−	0.0899767i
$771$	−240.000			−0.311284
$772$	−150.000			−0.194301
$773$		−	228.631i		−	0.295771i	−0.989005	−	0.147885i	$-0.952753\pi$
$773$		−	228.631i		−	0.295771i	0.989005	−	0.147885i	$-0.0472467\pi$
$774$	−78.0000			−0.100775
$775$		−	637.395i		−	0.822445i
$776$		−	387.979i		−	0.499973i
$777$	−312.000	+	45.0333i	−0.401544	+	0.0579579i
$778$	394.000			0.506427
$779$	−1440.00			−1.84852
$780$		−	249.415i		−	0.319763i
$781$	−620.000			−0.793854
$782$		0			0
$783$			197.454i			0.252176i
$784$	−235.000	+	69.2820i	−0.299745	+	0.0883699i
$785$	−1680.00			−2.14013
$786$	84.0000			0.106870
$787$		−	76.2102i		−	0.0968364i	−0.998827	−	0.0484182i	$-0.984582\pi$
$787$		−	76.2102i		−	0.0968364i	0.998827	−	0.0484182i	$-0.0154180\pi$
$788$	834.000			1.05838
$789$		−	107.387i		−	0.136105i
$790$			318.697i			0.403414i
$791$	178.000	+	1233.22i	0.225032	+	1.55906i
$792$	210.000			0.265152
$793$	−240.000			−0.302648
$794$		−	103.923i		−	0.130885i
$795$	120.000			0.150943
$796$		−	872.954i		−	1.09668i
$797$			866.025i			1.08661i	0.839537	+	0.543303i	$0.182827\pi$
$797$			866.025i			1.08661i	−0.839537	+	0.543303i	$0.817173\pi$
$798$	36.0000	+	249.415i	0.0451128	+	0.312551i
$799$		0			0
$800$	−759.000			−0.948750
$801$			124.708i			0.155690i
$802$	178.000			0.221945
$803$		−	415.692i		−	0.517674i
$804$		−	384.515i		−	0.478253i
$805$	−672.000	+	96.9948i	−0.834783	+	0.120490i
$806$	−192.000			−0.238213
$807$	−396.000			−0.490706
$808$			824.456i			1.02037i
$809$	802.000			0.991347			0.495674	−	0.868509i	$-0.334921\pi$
$809$	802.000			0.991347			0.495674	+	0.868509i	$0.334921\pi$
$810$		−	62.3538i		−	0.0769800i
$811$		−	893.738i		−	1.10202i	−0.834499	−	0.551010i	$-0.814243\pi$
$811$		−	893.738i		−	1.10202i	0.834499	−	0.551010i	$-0.185757\pi$
$812$	114.000	+	789.815i	0.140394	+	0.972679i
$813$	576.000			0.708487
$814$	260.000			0.319410
$815$		−	1177.79i		−	1.44515i
$816$		0			0
$817$		−	540.400i		−	0.661444i
$818$			651.251i			0.796150i
$819$	144.000	−	20.7846i	0.175824	−	0.0253780i
$820$	1440.00			1.75610
$821$	1450.00			1.76614			0.883069	−	0.469242i	$-0.155473\pi$
$821$	1450.00			1.76614			0.883069	+	0.469242i	$0.155473\pi$
$822$		−	356.802i		−	0.434066i
$823$	−1246.00			−1.51397			−0.756987	−	0.653430i	$-0.773329\pi$
$823$	−1246.00			−1.51397			−0.756987	+	0.653430i	$0.773329\pi$
$824$			678.964i			0.823985i
$825$		−	398.372i		−	0.482875i
$826$	−528.000	+	76.2102i	−0.639225	+	0.0922642i
$827$	586.000			0.708585			0.354293	−	0.935135i	$-0.384722\pi$
$827$	586.000			0.708585			0.354293	+	0.935135i	$0.384722\pi$
$828$	−126.000			−0.152174
$829$			810.600i			0.977804i	0.872339	+	0.488902i	$0.162602\pi$
$829$			810.600i			0.977804i	−0.872339	+	0.488902i	$0.837398\pi$
$830$	624.000			0.751807
$831$			45.0333i			0.0541917i
$832$			90.0666i			0.108253i
$833$		0			0
$834$	204.000			0.244604
$835$	672.000			0.804790
$836$			623.538i			0.745859i
$837$	144.000			0.172043
$838$		−	713.605i		−	0.851557i
$839$		−	13.8564i		−	0.0165154i	−0.999966	−	0.00825769i	$-0.997371\pi$
$839$		−	13.8564i		−	0.0165154i	0.999966	−	0.00825769i	$-0.00262853\pi$
$840$	−84.0000	−	581.969i	−0.100000	−	0.692820i
$841$	603.000			0.717004
$842$	602.000			0.714964
$843$		−	855.633i		−	1.01499i
$844$	−222.000			−0.263033
$845$		−	838.313i		−	0.992086i
$846$		−	83.1384i		−	0.0982724i
$847$	−21.0000	−	145.492i	−0.0247934	−	0.171774i
$848$	50.0000			0.0589623
$849$	348.000			0.409894
$850$		0			0
$851$	−364.000			−0.427732
$852$			322.161i			0.378124i
$853$			242.487i			0.284276i	0.989847	+	0.142138i	$0.0453976\pi$
$853$			242.487i			0.284276i	−0.989847	+	0.142138i	$0.954602\pi$
$854$	−240.000	+	34.6410i	−0.281030	+	0.0405633i
$855$	432.000			0.505263
$856$	−70.0000			−0.0817757
$857$			1399.50i			1.63302i	0.577332	+	0.816509i	$0.304094\pi$
$857$			1399.50i			1.63302i	−0.577332	+	0.816509i	$0.695906\pi$
$858$	−120.000			−0.139860
$859$			297.913i			0.346813i	0.984850	+	0.173407i	$0.0554775\pi$
$859$			297.913i			0.346813i	−0.984850	+	0.173407i	$0.944522\pi$
$860$			540.400i			0.628372i
$861$	120.000	+	831.384i	0.139373	+	0.965603i
$862$	34.0000			0.0394432
$863$	−1070.00			−1.23986			−0.619930	−	0.784657i	$-0.712839\pi$
$863$	−1070.00			−1.23986			−0.619930	+	0.784657i	$0.712839\pi$
$864$		−	171.473i		−	0.198464i
$865$	1200.00			1.38728
$866$		−	415.692i		−	0.480014i
$867$			500.563i			0.577350i
$868$	576.000	−	83.1384i	0.663594	−	0.0957816i
$869$	−460.000			−0.529344
$870$	−456.000			−0.524138
$871$			512.687i			0.588619i
$872$	−518.000			−0.594037
$873$		−	166.277i		−	0.190466i
$874$			290.985i			0.332934i
$875$	96.0000	−	13.8564i	0.109714	−	0.0158359i
$876$	−216.000			−0.246575
$877$	−502.000			−0.572406			−0.286203	−	0.958169i	$-0.592393\pi$
$877$	−502.000			−0.572406			−0.286203	+	0.958169i	$0.592393\pi$
$878$			96.9948i			0.110472i
$879$	−852.000			−0.969283
$880$		−	346.410i		−	0.393648i
$881$		−	997.661i		−	1.13242i	−0.824261	−	0.566210i	$-0.808409\pi$
$881$		−	997.661i		−	1.13242i	0.824261	−	0.566210i	$-0.191591\pi$
$882$	141.000	−	41.5692i	0.159864	−	0.0471306i
$883$	−118.000			−0.133635			−0.0668177	−	0.997765i	$-0.521285\pi$
$883$	−118.000			−0.133635			−0.0668177	+	0.997765i	$0.521285\pi$
$884$		0			0
$885$			914.523i			1.03336i
$886$	−470.000			−0.530474
$887$			512.687i			0.578001i	0.957329	+	0.289001i	$0.0933230\pi$
$887$			512.687i			0.578001i	−0.957329	+	0.289001i	$0.906677\pi$
$888$		−	315.233i		−	0.354992i
$889$	−190.000	−	1316.36i	−0.213723	−	1.48072i
$890$	−288.000			−0.323596
$891$	90.0000			0.101010
$892$		−	914.523i		−	1.02525i
$893$	576.000			0.645017
$894$			183.597i			0.205366i
$895$			263.272i			0.294158i
$896$	−119.000	−	824.456i	−0.132812	−	0.920152i
$897$	168.000			0.187291
$898$	514.000			0.572383
$899$		−	1053.09i		−	1.17140i
$900$	−207.000			−0.230000
$901$		0			0
$902$		−	692.820i		−	0.768093i
$903$	−312.000	+	45.0333i	−0.345515	+	0.0498708i
$904$	−1246.00			−1.37832
$905$	1296.00			1.43204
$906$		−	79.6743i		−	0.0879408i
$907$	1466.00			1.61632			0.808159	−	0.588965i	$-0.200464\pi$
$907$	1466.00			1.61632			0.808159	+	0.588965i	$0.200464\pi$
$908$		−	20.7846i		−	0.0228905i
$909$			353.338i			0.388711i
$910$	48.0000	+	332.554i	0.0527473	+	0.365444i
$911$	−542.000			−0.594951			−0.297475	−	0.954730i	$-0.596145\pi$
$911$	−542.000			−0.594951			−0.297475	+	0.954730i	$0.596145\pi$
$912$	180.000			0.197368
$913$			900.666i			0.986491i
$914$	−478.000			−0.522976
$915$			415.692i			0.454308i
$916$			852.169i			0.930315i
$917$	336.000	−	48.4974i	0.366412	−	0.0528870i
$918$		0			0
$919$	−1630.00			−1.77367			−0.886834	−	0.462089i	$-0.847100\pi$
$919$	−1630.00			−1.77367			−0.886834	+	0.462089i	$0.847100\pi$
$920$		−	678.964i		−	0.738004i
$921$	36.0000			0.0390879
$922$			672.036i			0.728889i
$923$		−	429.549i		−	0.465383i
$924$	360.000	−	51.9615i	0.389610	−	0.0562354i
$925$	−598.000			−0.646486
$926$	−430.000			−0.464363
$927$			290.985i			0.313899i
$928$	−1254.00			−1.35129
$929$			193.990i			0.208816i	0.994535	+	0.104408i	$0.0332947\pi$
$929$			193.990i			0.208816i	−0.994535	+	0.104408i	$0.966705\pi$
$930$			332.554i			0.357585i
$931$	288.000	+	976.877i	0.309345	+	1.04928i
$932$	−534.000			−0.572961
$933$	−24.0000			−0.0257235
$934$		−	852.169i		−	0.912387i
$935$		0			0
$936$			145.492i			0.155440i
$937$		−	1205.51i		−	1.28656i	−0.765631	−	0.643280i	$-0.777573\pi$
$937$		−	1205.51i		−	1.28656i	0.765631	−	0.643280i	$-0.222427\pi$
$938$	74.0000	+	512.687i	0.0788913	+	0.546575i
$939$	−456.000			−0.485623
$940$	−576.000			−0.612766
$941$		−	879.882i		−	0.935050i	−0.883980	−	0.467525i	$-0.845146\pi$
$941$		−	879.882i		−	0.935050i	0.883980	−	0.467525i	$-0.154854\pi$
$942$	420.000			0.445860
$943$			969.948i			1.02858i
$944$			381.051i			0.403656i
$945$	−36.0000	−	249.415i	−0.0380952	−	0.263932i
$946$	260.000			0.274841
$947$	1402.00			1.48046			0.740232	−	0.672351i	$-0.234716\pi$
$947$	1402.00			1.48046			0.740232	+	0.672351i	$0.234716\pi$
$948$			239.023i			0.252134i
$949$	288.000			0.303477
$950$			478.046i			0.503206i
$951$			433.013i			0.455324i
$952$		0			0
$953$	−110.000			−0.115425			−0.0577125	−	0.998333i	$-0.518381\pi$
$953$	−110.000			−0.115425			−0.0577125	+	0.998333i	$0.518381\pi$
$954$	−30.0000			−0.0314465
$955$		−	568.113i		−	0.594882i
$956$	−102.000			−0.106695
$957$		−	658.179i		−	0.687753i
$958$		−	387.979i		−	0.404989i
$959$	−206.000	−	1427.21i	−0.214807	−	1.48823i
$960$	156.000			0.162500
$961$	193.000			0.200832
$962$			180.133i			0.187249i
$963$	−30.0000			−0.0311526
$964$			581.969i			0.603702i
$965$		−	346.410i		−	0.358974i
$966$	168.000	−	24.2487i	0.173913	−	0.0251022i
$967$	1202.00			1.24302			0.621510	−	0.783406i	$-0.286520\pi$
$967$	1202.00			1.24302			0.621510	+	0.783406i	$0.286520\pi$
$968$	147.000			0.151860
$969$		0			0
$970$	384.000			0.395876
$971$			270.200i			0.278270i	0.990273	+	0.139135i	$0.0444322\pi$
$971$			270.200i			0.278270i	−0.990273	+	0.139135i	$0.955568\pi$
$972$		−	46.7654i		−	0.0481125i
$973$	816.000	−	117.779i	0.838643	−	0.121048i
$974$	818.000			0.839836
$975$	276.000			0.283077
$976$			173.205i			0.177464i
$977$	−1310.00			−1.34084			−0.670420	−	0.741982i	$-0.733886\pi$
$977$	−1310.00			−1.34084			−0.670420	+	0.741982i	$0.733886\pi$
$978$			294.449i			0.301072i
$979$		−	415.692i		−	0.424609i
$980$	−288.000	−	976.877i	−0.293878	−	0.996813i
$981$	−222.000			−0.226300
$982$	490.000			0.498982
$983$			1565.77i			1.59285i	0.604736	+	0.796426i	$0.293279\pi$
$983$			1565.77i			1.59285i	−0.604736	+	0.796426i	$0.706721\pi$
$984$	−840.000			−0.853659
$985$			1926.04i			1.95537i
$986$		0			0
$987$	−48.0000	−	332.554i	−0.0486322	−	0.336934i
$988$	−432.000			−0.437247
$989$	−364.000			−0.368049
$990$			207.846i			0.209946i
$991$	818.000			0.825429			0.412714	−	0.910860i	$-0.364581\pi$
$991$	818.000			0.825429			0.412714	+	0.910860i	$0.364581\pi$
$992$			914.523i			0.921898i
$993$		−	1118.90i		−	1.12679i
$994$	−62.0000	−	429.549i	−0.0623742	−	0.432141i
$995$	2016.00			2.02613
$996$	468.000			0.469880
$997$		−	173.205i		−	0.173726i	−0.996220	−	0.0868631i	$-0.972316\pi$
$997$		−	173.205i		−	0.173726i	0.996220	−	0.0868631i	$-0.0276843\pi$
$998$	554.000			0.555110
$999$		−	135.100i		−	0.135235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.3.d.a.13.2	yes	2
3.2	odd	2		63.3.d.b.55.2		2
4.3	odd	2		336.3.f.a.97.1		2
5.2	odd	4		525.3.e.a.349.4		4
5.3	odd	4		525.3.e.a.349.1		4
5.4	even	2		525.3.h.a.76.1		2
7.2	even	3		147.3.f.b.31.1		2
7.3	odd	6		147.3.f.b.19.1		2
7.4	even	3		147.3.f.d.19.1		2
7.5	odd	6		147.3.f.d.31.1		2
7.6	odd	2	inner	21.3.d.a.13.1	✓	2
8.3	odd	2		1344.3.f.b.769.2		2
8.5	even	2		1344.3.f.c.769.1		2
12.11	even	2		1008.3.f.d.433.2		2
21.2	odd	6		441.3.m.f.325.1		2
21.5	even	6		441.3.m.d.325.1		2
21.11	odd	6		441.3.m.d.19.1		2
21.17	even	6		441.3.m.f.19.1		2
21.20	even	2		63.3.d.b.55.1		2
28.27	even	2		336.3.f.a.97.2		2
35.13	even	4		525.3.e.a.349.2		4
35.27	even	4		525.3.e.a.349.3		4
35.34	odd	2		525.3.h.a.76.2		2
56.13	odd	2		1344.3.f.c.769.2		2
56.27	even	2		1344.3.f.b.769.1		2
84.83	odd	2		1008.3.f.d.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.d.a.13.1	✓	2	7.6	odd	2	inner
21.3.d.a.13.2	yes	2	1.1	even	1	trivial
63.3.d.b.55.1		2	21.20	even	2
63.3.d.b.55.2		2	3.2	odd	2
147.3.f.b.19.1		2	7.3	odd	6
147.3.f.b.31.1		2	7.2	even	3
147.3.f.d.19.1		2	7.4	even	3
147.3.f.d.31.1		2	7.5	odd	6
336.3.f.a.97.1		2	4.3	odd	2
336.3.f.a.97.2		2	28.27	even	2
441.3.m.d.19.1		2	21.11	odd	6
441.3.m.d.325.1		2	21.5	even	6
441.3.m.f.19.1		2	21.17	even	6
441.3.m.f.325.1		2	21.2	odd	6
525.3.e.a.349.1		4	5.3	odd	4
525.3.e.a.349.2		4	35.13	even	4
525.3.e.a.349.3		4	35.27	even	4
525.3.e.a.349.4		4	5.2	odd	4
525.3.h.a.76.1		2	5.4	even	2
525.3.h.a.76.2		2	35.34	odd	2
1008.3.f.d.433.1		2	84.83	odd	2
1008.3.f.d.433.2		2	12.11	even	2
1344.3.f.b.769.1		2	56.27	even	2
1344.3.f.b.769.2		2	8.3	odd	2
1344.3.f.c.769.1		2	8.5	even	2
1344.3.f.c.769.2		2	56.13	odd	2

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	21.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.73205i q^{3} -3.00000 q^{4} -6.92820i q^{5} +1.73205i q^{6} +(1.00000 + 6.92820i) q^{7} -7.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.73205i q^{3} -3.00000 q^{4} -6.92820i q^{5} +1.73205i q^{6} +(1.00000 + 6.92820i) q^{7} -7.00000 q^{8} -3.00000 q^{9} -6.92820i q^{10} +10.0000 q^{11} -5.19615i q^{12} +6.92820i q^{13} +(1.00000 + 6.92820i) q^{14} +12.0000 q^{15} +5.00000 q^{16} -3.00000 q^{18} -20.7846i q^{19} +20.7846i q^{20} +(-12.0000 + 1.73205i) q^{21} +10.0000 q^{22} -14.0000 q^{23} -12.1244i q^{24} -23.0000 q^{25} +6.92820i q^{26} -5.19615i q^{27} +(-3.00000 - 20.7846i) q^{28} -38.0000 q^{29} +12.0000 q^{30} +27.7128i q^{31} +33.0000 q^{32} +17.3205i q^{33} +(48.0000 - 6.92820i) q^{35} +9.00000 q^{36} +26.0000 q^{37} -20.7846i q^{38} -12.0000 q^{39} +48.4974i q^{40} -69.2820i q^{41} +(-12.0000 + 1.73205i) q^{42} +26.0000 q^{43} -30.0000 q^{44} +20.7846i q^{45} -14.0000 q^{46} +27.7128i q^{47} +8.66025i q^{48} +(-47.0000 + 13.8564i) q^{49} -23.0000 q^{50} -20.7846i q^{52} +10.0000 q^{53} -5.19615i q^{54} -69.2820i q^{55} +(-7.00000 - 48.4974i) q^{56} +36.0000 q^{57} -38.0000 q^{58} +76.2102i q^{59} -36.0000 q^{60} +34.6410i q^{61} +27.7128i q^{62} +(-3.00000 - 20.7846i) q^{63} +13.0000 q^{64} +48.0000 q^{65} +17.3205i q^{66} +74.0000 q^{67} -24.2487i q^{69} +(48.0000 - 6.92820i) q^{70} -62.0000 q^{71} +21.0000 q^{72} -41.5692i q^{73} +26.0000 q^{74} -39.8372i q^{75} +62.3538i q^{76} +(10.0000 + 69.2820i) q^{77} -12.0000 q^{78} -46.0000 q^{79} -34.6410i q^{80} +9.00000 q^{81} -69.2820i q^{82} +90.0666i q^{83} +(36.0000 - 5.19615i) q^{84} +26.0000 q^{86} -65.8179i q^{87} -70.0000 q^{88} -41.5692i q^{89} +20.7846i q^{90} +(-48.0000 + 6.92820i) q^{91} +42.0000 q^{92} -48.0000 q^{93} +27.7128i q^{94} -144.000 q^{95} +57.1577i q^{96} +55.4256i q^{97} +(-47.0000 + 13.8564i) q^{98} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 6 q^{4} + 2 q^{7} - 14 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 6 * q^4 + 2 * q^7 - 14 * q^8 - 6 * q^9	\( 2 q + 2 q^{2} - 6 q^{4} + 2 q^{7} - 14 q^{8} - 6 q^{9} + 20 q^{11} + 2 q^{14} + 24 q^{15} + 10 q^{16} - 6 q^{18} - 24 q^{21} + 20 q^{22} - 28 q^{23} - 46 q^{25} - 6 q^{28} - 76 q^{29} + 24 q^{30} + 66 q^{32} + 96 q^{35} + 18 q^{36} + 52 q^{37} - 24 q^{39} - 24 q^{42} + 52 q^{43} - 60 q^{44} - 28 q^{46} - 94 q^{49} - 46 q^{50} + 20 q^{53} - 14 q^{56} + 72 q^{57} - 76 q^{58} - 72 q^{60} - 6 q^{63} + 26 q^{64} + 96 q^{65} + 148 q^{67} + 96 q^{70} - 124 q^{71} + 42 q^{72} + 52 q^{74} + 20 q^{77} - 24 q^{78} - 92 q^{79} + 18 q^{81} + 72 q^{84} + 52 q^{86} - 140 q^{88} - 96 q^{91} + 84 q^{92} - 96 q^{93} - 288 q^{95} - 94 q^{98} - 60 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 6 * q^4 + 2 * q^7 - 14 * q^8 - 6 * q^9 + 20 * q^11 + 2 * q^14 + 24 * q^15 + 10 * q^16 - 6 * q^18 - 24 * q^21 + 20 * q^22 - 28 * q^23 - 46 * q^25 - 6 * q^28 - 76 * q^29 + 24 * q^30 + 66 * q^32 + 96 * q^35 + 18 * q^36 + 52 * q^37 - 24 * q^39 - 24 * q^42 + 52 * q^43 - 60 * q^44 - 28 * q^46 - 94 * q^49 - 46 * q^50 + 20 * q^53 - 14 * q^56 + 72 * q^57 - 76 * q^58 - 72 * q^60 - 6 * q^63 + 26 * q^64 + 96 * q^65 + 148 * q^67 + 96 * q^70 - 124 * q^71 + 42 * q^72 + 52 * q^74 + 20 * q^77 - 24 * q^78 - 92 * q^79 + 18 * q^81 + 72 * q^84 + 52 * q^86 - 140 * q^88 - 96 * q^91 + 84 * q^92 - 96 * q^93 - 288 * q^95 - 94 * q^98 - 60 * q^99

Introduction

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