LMFDB - Embedded newform 1470.2.d.c.1469.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1469,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.1469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.c.1469.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.68614 + 0.396143i) q^{3} +1.00000 q^{4} +(-2.18614 + 0.469882i) q^{5} +(-1.68614 + 0.396143i) q^{6} +1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.68614 + 0.396143i) q^{3} +1.00000 q^{4} +(-2.18614 + 0.469882i) q^{5} +(-1.68614 + 0.396143i) q^{6} +1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +(-2.18614 + 0.469882i) q^{10} +0.939764i q^{11} +(-1.68614 + 0.396143i) q^{12} +2.00000 q^{13} +(3.50000 - 1.65831i) q^{15} +1.00000 q^{16} -6.63325i q^{17} +(2.68614 - 1.33591i) q^{18} +3.46410i q^{19} +(-2.18614 + 0.469882i) q^{20} +0.939764i q^{22} -1.37228 q^{23} +(-1.68614 + 0.396143i) q^{24} +(4.55842 - 2.05446i) q^{25} +2.00000 q^{26} +(-4.00000 + 3.31662i) q^{27} +3.31662i q^{29} +(3.50000 - 1.65831i) q^{30} +7.57301i q^{31} +1.00000 q^{32} +(-0.372281 - 1.58457i) q^{33} -6.63325i q^{34} +(2.68614 - 1.33591i) q^{36} +8.21782i q^{37} +3.46410i q^{38} +(-3.37228 + 0.792287i) q^{39} +(-2.18614 + 0.469882i) q^{40} +7.37228 q^{41} -1.08724i q^{43} +0.939764i q^{44} +(-5.24456 + 4.18265i) q^{45} -1.37228 q^{46} +8.51278i q^{47} +(-1.68614 + 0.396143i) q^{48} +(4.55842 - 2.05446i) q^{50} +(2.62772 + 11.1846i) q^{51} +2.00000 q^{52} -4.37228 q^{53} +(-4.00000 + 3.31662i) q^{54} +(-0.441578 - 2.05446i) q^{55} +(-1.37228 - 5.84096i) q^{57} +3.31662i q^{58} +13.1168 q^{59} +(3.50000 - 1.65831i) q^{60} +12.7692i q^{61} +7.57301i q^{62} +1.00000 q^{64} +(-4.37228 + 0.939764i) q^{65} +(-0.372281 - 1.58457i) q^{66} +2.37686i q^{67} -6.63325i q^{68} +(2.31386 - 0.543620i) q^{69} +8.51278i q^{71} +(2.68614 - 1.33591i) q^{72} +2.00000 q^{73} +8.21782i q^{74} +(-6.87228 + 5.26989i) q^{75} +3.46410i q^{76} +(-3.37228 + 0.792287i) q^{78} +9.11684 q^{79} +(-2.18614 + 0.469882i) q^{80} +(5.43070 - 7.17687i) q^{81} +7.37228 q^{82} -11.8294i q^{83} +(3.11684 + 14.5012i) q^{85} -1.08724i q^{86} +(-1.31386 - 5.59230i) q^{87} +0.939764i q^{88} +1.37228 q^{89} +(-5.24456 + 4.18265i) q^{90} -1.37228 q^{92} +(-3.00000 - 12.7692i) q^{93} +8.51278i q^{94} +(-1.62772 - 7.57301i) q^{95} +(-1.68614 + 0.396143i) q^{96} +15.1168 q^{97} +(1.25544 + 2.52434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - q^{3} + 4 q^{4} - 3 q^{5} - q^{6} + 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - q^3 + 4 * q^4 - 3 * q^5 - q^6 + 4 * q^8 + 5 * q^9	$ 4 q + 4 q^{2} - q^{3} + 4 q^{4} - 3 q^{5} - q^{6} + 4 q^{8} + 5 q^{9} - 3 q^{10} - q^{12} + 8 q^{13} + 14 q^{15} + 4 q^{16} + 5 q^{18} - 3 q^{20} + 6 q^{23} - q^{24} + q^{25} + 8 q^{26} - 16 q^{27} + 14 q^{30} + 4 q^{32} + 10 q^{33} + 5 q^{36} - 2 q^{39} - 3 q^{40} + 18 q^{41} + 2 q^{45} + 6 q^{46} - q^{48} + q^{50} + 22 q^{51} + 8 q^{52} - 6 q^{53} - 16 q^{54} - 19 q^{55} + 6 q^{57} + 18 q^{59} + 14 q^{60} + 4 q^{64} - 6 q^{65} + 10 q^{66} + 15 q^{69} + 5 q^{72} + 8 q^{73} - 16 q^{75} - 2 q^{78} + 2 q^{79} - 3 q^{80} - 7 q^{81} + 18 q^{82} - 22 q^{85} - 11 q^{87} - 6 q^{89} + 2 q^{90} + 6 q^{92} - 12 q^{93} - 18 q^{95} - q^{96} + 26 q^{97} + 28 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - q^3 + 4 * q^4 - 3 * q^5 - q^6 + 4 * q^8 + 5 * q^9 - 3 * q^10 - q^12 + 8 * q^13 + 14 * q^15 + 4 * q^16 + 5 * q^18 - 3 * q^20 + 6 * q^23 - q^24 + q^25 + 8 * q^26 - 16 * q^27 + 14 * q^30 + 4 * q^32 + 10 * q^33 + 5 * q^36 - 2 * q^39 - 3 * q^40 + 18 * q^41 + 2 * q^45 + 6 * q^46 - q^48 + q^50 + 22 * q^51 + 8 * q^52 - 6 * q^53 - 16 * q^54 - 19 * q^55 + 6 * q^57 + 18 * q^59 + 14 * q^60 + 4 * q^64 - 6 * q^65 + 10 * q^66 + 15 * q^69 + 5 * q^72 + 8 * q^73 - 16 * q^75 - 2 * q^78 + 2 * q^79 - 3 * q^80 - 7 * q^81 + 18 * q^82 - 22 * q^85 - 11 * q^87 - 6 * q^89 + 2 * q^90 + 6 * q^92 - 12 * q^93 - 18 * q^95 - q^96 + 26 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

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			0.707107
$2$	1.00000			0.707107
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$4$	1.00000			0.500000
$5$	−2.18614	+	0.469882i	−0.977672	+	0.210138i
$5$	−2.18614	+	0.469882i	−0.977672	+	0.210138i
$6$	−1.68614	+	0.396143i	−0.688364	+	0.161725i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	2.68614	−	1.33591i	0.895380	−	0.445302i
$10$	−2.18614	+	0.469882i	−0.691318	+	0.148590i
$11$			0.939764i			0.283349i	0.989913	+	0.141675i	$0.0452487\pi$
$11$			0.939764i			0.283349i	−0.989913	+	0.141675i	$0.954751\pi$
$12$	−1.68614	+	0.396143i	−0.486747	+	0.114357i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	3.50000	−	1.65831i	0.903696	−	0.428174i
$16$	1.00000			0.250000
$17$		−	6.63325i		−	1.60880i	−0.594089	−	0.804400i	$-0.702487\pi$
$17$		−	6.63325i		−	1.60880i	0.594089	−	0.804400i	$-0.297513\pi$
$18$	2.68614	−	1.33591i	0.633129	−	0.314876i
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−2.18614	+	0.469882i	−0.488836	+	0.105069i
$21$		0			0
$22$			0.939764i			0.200358i
$23$	−1.37228			−0.286140			−0.143070	−	0.989713i	$-0.545697\pi$
$23$	−1.37228			−0.286140			−0.143070	+	0.989713i	$0.545697\pi$
$24$	−1.68614	+	0.396143i	−0.344182	+	0.0808625i
$25$	4.55842	−	2.05446i	0.911684	−	0.410891i
$26$	2.00000			0.392232
$27$	−4.00000	+	3.31662i	−0.769800	+	0.638285i
$28$		0			0
$29$			3.31662i			0.615882i	0.951405	+	0.307941i	$0.0996399\pi$
$29$			3.31662i			0.615882i	−0.951405	+	0.307941i	$0.900360\pi$
$30$	3.50000	−	1.65831i	0.639010	−	0.302765i
$31$			7.57301i			1.36015i	0.733141	+	0.680077i	$0.238054\pi$
$31$			7.57301i			1.36015i	−0.733141	+	0.680077i	$0.761946\pi$
$32$	1.00000			0.176777
$33$	−0.372281	−	1.58457i	−0.0648059	−	0.275839i
$34$		−	6.63325i		−	1.13759i
$35$		0			0
$36$	2.68614	−	1.33591i	0.447690	−	0.222651i
$37$			8.21782i			1.35100i	0.737359	+	0.675501i	$0.236073\pi$
$37$			8.21782i			1.35100i	−0.737359	+	0.675501i	$0.763927\pi$
$38$			3.46410i			0.561951i
$39$	−3.37228	+	0.792287i	−0.539997	+	0.126867i
$40$	−2.18614	+	0.469882i	−0.345659	+	0.0742949i
$41$	7.37228			1.15136			0.575678	−	0.817676i	$-0.304738\pi$
$41$	7.37228			1.15136			0.575678	+	0.817676i	$0.304738\pi$
$42$		0			0
$43$		−	1.08724i		−	0.165803i	−0.996558	−	0.0829013i	$-0.973581\pi$
$43$		−	1.08724i		−	0.165803i	0.996558	−	0.0829013i	$-0.0264186\pi$
$44$			0.939764i			0.141675i
$45$	−5.24456	+	4.18265i	−0.781813	+	0.623513i
$46$	−1.37228			−0.202332
$47$			8.51278i			1.24172i	0.783923	+	0.620858i	$0.213216\pi$
$47$			8.51278i			1.24172i	−0.783923	+	0.620858i	$0.786784\pi$
$48$	−1.68614	+	0.396143i	−0.243373	+	0.0571784i
$49$		0			0
$50$	4.55842	−	2.05446i	0.644658	−	0.290544i
$51$	2.62772	+	11.1846i	0.367954	+	1.56616i
$52$	2.00000			0.277350
$53$	−4.37228			−0.600579			−0.300290	−	0.953848i	$-0.597083\pi$
$53$	−4.37228			−0.600579			−0.300290	+	0.953848i	$0.597083\pi$
$54$	−4.00000	+	3.31662i	−0.544331	+	0.451335i
$55$	−0.441578	−	2.05446i	−0.0595424	−	0.277023i
$56$		0			0
$57$	−1.37228	−	5.84096i	−0.181763	−	0.773654i
$58$			3.31662i			0.435494i
$59$	13.1168			1.70767			0.853834	−	0.520546i	$-0.174271\pi$
$59$	13.1168			1.70767			0.853834	+	0.520546i	$0.174271\pi$
$60$	3.50000	−	1.65831i	0.451848	−	0.214087i
$61$			12.7692i			1.63492i	0.575982	+	0.817462i	$0.304620\pi$
$61$			12.7692i			1.63492i	−0.575982	+	0.817462i	$0.695380\pi$
$62$			7.57301i			0.961774i
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.37228	+	0.939764i	−0.542315	+	0.116563i
$66$	−0.372281	−	1.58457i	−0.0458247	−	0.195048i
$67$			2.37686i			0.290380i	0.989404	+	0.145190i	$0.0463793\pi$
$67$			2.37686i			0.290380i	−0.989404	+	0.145190i	$0.953621\pi$
$68$		−	6.63325i		−	0.804400i
$69$	2.31386	−	0.543620i	0.278556	−	0.0654442i
$70$		0			0
$71$			8.51278i			1.01028i	0.863037	+	0.505140i	$0.168559\pi$
$71$			8.51278i			1.01028i	−0.863037	+	0.505140i	$0.831441\pi$
$72$	2.68614	−	1.33591i	0.316565	−	0.157438i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$			8.21782i			0.955303i
$75$	−6.87228	+	5.26989i	−0.793543	+	0.608515i
$76$			3.46410i			0.397360i
$77$		0			0
$78$	−3.37228	+	0.792287i	−0.381836	+	0.0897088i
$79$	9.11684			1.02573			0.512863	−	0.858471i	$-0.328585\pi$
$79$	9.11684			1.02573			0.512863	+	0.858471i	$0.328585\pi$
$80$	−2.18614	+	0.469882i	−0.244418	+	0.0525344i
$81$	5.43070	−	7.17687i	0.603411	−	0.797430i
$82$	7.37228			0.814132
$83$		−	11.8294i		−	1.29845i	−0.760598	−	0.649223i	$-0.775094\pi$
$83$		−	11.8294i		−	1.29845i	0.760598	−	0.649223i	$-0.224906\pi$
$84$		0			0
$85$	3.11684	+	14.5012i	0.338069	+	1.57288i
$86$		−	1.08724i		−	0.117240i
$87$	−1.31386	−	5.59230i	−0.140861	−	0.599557i
$88$			0.939764i			0.100179i
$89$	1.37228			0.145462			0.0727308	−	0.997352i	$-0.476829\pi$
$89$	1.37228			0.145462			0.0727308	+	0.997352i	$0.476829\pi$
$90$	−5.24456	+	4.18265i	−0.552825	+	0.440890i
$91$		0			0
$92$	−1.37228			−0.143070
$93$	−3.00000	−	12.7692i	−0.311086	−	1.32410i
$94$			8.51278i			0.878026i
$95$	−1.62772	−	7.57301i	−0.167000	−	0.776975i
$96$	−1.68614	+	0.396143i	−0.172091	+	0.0404312i
$97$	15.1168			1.53488			0.767441	−	0.641119i	$-0.221530\pi$
$97$	15.1168			1.53488			0.767441	+	0.641119i	$0.221530\pi$
$98$		0			0
$99$	1.25544	+	2.52434i	0.126176	+	0.253705i
$100$	4.55842	−	2.05446i	0.455842	−	0.205446i
$101$	−10.6277			−1.05750			−0.528749	−	0.848778i	$-0.677339\pi$
$101$	−10.6277			−1.05750			−0.528749	+	0.848778i	$0.677339\pi$
$102$	2.62772	+	11.1846i	0.260183	+	1.10744i
$103$	−2.11684			−0.208579			−0.104289	−	0.994547i	$-0.533257\pi$
$103$	−2.11684			−0.208579			−0.104289	+	0.994547i	$0.533257\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	−4.37228			−0.424674
$107$	6.25544			0.604736			0.302368	−	0.953191i	$-0.402223\pi$
$107$	6.25544			0.604736			0.302368	+	0.953191i	$0.402223\pi$
$108$	−4.00000	+	3.31662i	−0.384900	+	0.319142i
$109$	−8.11684			−0.777453			−0.388726	−	0.921353i	$-0.627085\pi$
$109$	−8.11684			−0.777453			−0.388726	+	0.921353i	$0.627085\pi$
$110$	−0.441578	−	2.05446i	−0.0421028	−	0.195885i
$111$	−3.25544	−	13.8564i	−0.308992	−	1.31519i
$112$		0			0
$113$	−14.7446			−1.38705			−0.693526	−	0.720432i	$-0.743944\pi$
$113$	−14.7446			−1.38705			−0.693526	+	0.720432i	$0.743944\pi$
$114$	−1.37228	−	5.84096i	−0.128526	−	0.547056i
$115$	3.00000	−	0.644810i	0.279751	−	0.0601289i
$116$			3.31662i			0.307941i
$117$	5.37228	−	2.67181i	0.496668	−	0.247009i
$118$	13.1168			1.20750
$119$		0			0
$120$	3.50000	−	1.65831i	0.319505	−	0.151383i
$121$	10.1168			0.919713
$122$			12.7692i			1.15607i
$123$	−12.4307	+	2.92048i	−1.12084	+	0.263331i
$124$			7.57301i			0.680077i
$125$	−9.00000	+	6.63325i	−0.804984	+	0.593296i
$126$		0			0
$127$			7.57301i			0.671996i	0.941863	+	0.335998i	$0.109074\pi$
$127$			7.57301i			0.671996i	−0.941863	+	0.335998i	$0.890926\pi$
$128$	1.00000			0.0883883
$129$	0.430703	+	1.83324i	0.0379213	+	0.161408i
$130$	−4.37228	+	0.939764i	−0.383474	+	0.0824227i
$131$	−10.3723			−0.906230			−0.453115	−	0.891452i	$-0.649687\pi$
$131$	−10.3723			−0.906230			−0.453115	+	0.891452i	$0.649687\pi$
$132$	−0.372281	−	1.58457i	−0.0324029	−	0.137919i
$133$		0			0
$134$			2.37686i			0.205330i
$135$	7.18614	−	9.13014i	0.618485	−	0.785797i
$136$		−	6.63325i		−	0.568796i
$137$	−8.74456			−0.747098			−0.373549	−	0.927610i	$-0.621859\pi$
$137$	−8.74456			−0.747098			−0.373549	+	0.927610i	$0.621859\pi$
$138$	2.31386	−	0.543620i	0.196969	−	0.0462760i
$139$			8.21782i			0.697027i	0.937304	+	0.348513i	$0.113313\pi$
$139$			8.21782i			0.697027i	−0.937304	+	0.348513i	$0.886687\pi$
$140$		0			0
$141$	−3.37228	−	14.3537i	−0.283997	−	1.20880i
$142$			8.51278i			0.714376i
$143$			1.87953i			0.157174i
$144$	2.68614	−	1.33591i	0.223845	−	0.111326i
$145$	−1.55842	−	7.25061i	−0.129420	−	0.602130i
$146$	2.00000			0.165521
$147$		0			0
$148$			8.21782i			0.675501i
$149$		−	9.01011i		−	0.738137i	−0.929402	−	0.369069i	$-0.879677\pi$
$149$		−	9.01011i		−	0.738137i	0.929402	−	0.369069i	$-0.120323\pi$
$150$	−6.87228	+	5.26989i	−0.561119	+	0.430285i
$151$	9.11684			0.741918			0.370959	−	0.928649i	$-0.379029\pi$
$151$	9.11684			0.741918			0.370959	+	0.928649i	$0.379029\pi$
$152$			3.46410i			0.280976i
$153$	−8.86141	−	17.8178i	−0.716402	−	1.44049i
$154$		0			0
$155$	−3.55842	−	16.5557i	−0.285819	−	1.32978i
$156$	−3.37228	+	0.792287i	−0.269999	+	0.0634337i
$157$	8.00000			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$158$	9.11684			0.725297
$159$	7.37228	−	1.73205i	0.584660	−	0.137361i
$160$	−2.18614	+	0.469882i	−0.172830	+	0.0371474i
$161$		0			0
$162$	5.43070	−	7.17687i	0.426676	−	0.563868i
$163$			3.46410i			0.271329i	0.990755	+	0.135665i	$0.0433170\pi$
$163$			3.46410i			0.271329i	−0.990755	+	0.135665i	$0.956683\pi$
$164$	7.37228			0.575678
$165$	1.55842	+	3.28917i	0.121323	+	0.256062i
$166$		−	11.8294i		−	0.918140i
$167$		−	14.6487i		−	1.13355i	−0.823873	−	0.566775i	$-0.808191\pi$
$167$		−	14.6487i		−	1.13355i	0.823873	−	0.566775i	$-0.191809\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	3.11684	+	14.5012i	0.239051	+	1.11219i
$171$	4.62772	+	9.30506i	0.353890	+	0.711576i
$172$		−	1.08724i		−	0.0829013i
$173$		−	17.0256i		−	1.29443i	−0.762308	−	0.647214i	$-0.775934\pi$
$173$		−	17.0256i		−	1.29443i	0.762308	−	0.647214i	$-0.224066\pi$
$174$	−1.31386	−	5.59230i	−0.0996034	−	0.423951i
$175$		0			0
$176$			0.939764i			0.0708374i
$177$	−22.1168	+	5.19615i	−1.66240	+	0.390567i
$178$	1.37228			0.102857
$179$			23.6588i			1.76834i	0.467163	+	0.884171i	$0.345276\pi$
$179$			23.6588i			1.76834i	−0.467163	+	0.884171i	$0.654724\pi$
$180$	−5.24456	+	4.18265i	−0.390907	+	0.311756i
$181$			8.01544i			0.595783i	0.954600	+	0.297892i	$0.0962834\pi$
$181$			8.01544i			0.595783i	−0.954600	+	0.297892i	$0.903717\pi$
$182$		0			0
$183$	−5.05842	−	21.5306i	−0.373929	−	1.59159i
$184$	−1.37228			−0.101166
$185$	−3.86141	−	17.9653i	−0.283896	−	1.32084i
$186$	−3.00000	−	12.7692i	−0.219971	−	0.936281i
$187$	6.23369			0.455852
$188$			8.51278i			0.620858i
$189$		0			0
$190$	−1.62772	−	7.57301i	−0.118087	−	0.549404i
$191$		−	17.0256i		−	1.23193i	−0.787775	−	0.615963i	$-0.788767\pi$
$191$		−	17.0256i		−	1.23193i	0.787775	−	0.615963i	$-0.211233\pi$
$192$	−1.68614	+	0.396143i	−0.121687	+	0.0285892i
$193$		−	17.9653i		−	1.29317i	−0.762841	−	0.646586i	$-0.776196\pi$
$193$		−	17.9653i		−	1.29317i	0.762841	−	0.646586i	$-0.223804\pi$
$194$	15.1168			1.08533
$195$	7.00000	−	3.31662i	0.501280	−	0.237508i
$196$		0			0
$197$	14.2337			1.01411			0.507054	−	0.861914i	$-0.330734\pi$
$197$	14.2337			1.01411			0.507054	+	0.861914i	$0.330734\pi$
$198$	1.25544	+	2.52434i	0.0892200	+	0.179397i
$199$			1.28962i			0.0914188i	0.998955	+	0.0457094i	$0.0145548\pi$
$199$			1.28962i			0.0914188i	−0.998955	+	0.0457094i	$0.985445\pi$
$200$	4.55842	−	2.05446i	0.322329	−	0.145272i
$201$	−0.941578	−	4.00772i	−0.0664138	−	0.282683i
$202$	−10.6277			−0.747764
$203$		0			0
$204$	2.62772	+	11.1846i	0.183977	+	0.783078i
$205$	−16.1168	+	3.46410i	−1.12565	+	0.241943i
$206$	−2.11684			−0.147488
$207$	−3.68614	+	1.83324i	−0.256204	+	0.127419i
$208$	2.00000			0.138675
$209$	−3.25544			−0.225183
$210$		0			0
$211$	16.2337			1.11757			0.558787	−	0.829311i	$-0.311267\pi$
$211$	16.2337			1.11757			0.558787	+	0.829311i	$0.311267\pi$
$212$	−4.37228			−0.300290
$213$	−3.37228	−	14.3537i	−0.231065	−	0.983502i
$214$	6.25544			0.427613
$215$	0.510875	+	2.37686i	0.0348414	+	0.162101i
$216$	−4.00000	+	3.31662i	−0.272166	+	0.225668i
$217$		0			0
$218$	−8.11684			−0.549742
$219$	−3.37228	+	0.792287i	−0.227878	+	0.0535378i
$220$	−0.441578	−	2.05446i	−0.0297712	−	0.138511i
$221$		−	13.2665i		−	0.892401i
$222$	−3.25544	−	13.8564i	−0.218491	−	0.929981i
$223$	0.883156			0.0591405			0.0295703	−	0.999563i	$-0.490586\pi$
$223$	0.883156			0.0591405			0.0295703	+	0.999563i	$0.490586\pi$
$224$		0			0
$225$	9.50000	−	11.6082i	0.633333	−	0.773879i
$226$	−14.7446			−0.980794
$227$			20.8395i			1.38317i	0.722297	+	0.691584i	$0.243087\pi$
$227$			20.8395i			1.38317i	−0.722297	+	0.691584i	$0.756913\pi$
$228$	−1.37228	−	5.84096i	−0.0908816	−	0.386827i
$229$		−	13.8564i		−	0.915657i	−0.889041	−	0.457829i	$-0.848627\pi$
$229$		−	13.8564i		−	0.915657i	0.889041	−	0.457829i	$-0.151373\pi$
$230$	3.00000	−	0.644810i	0.197814	−	0.0425175i
$231$		0			0
$232$			3.31662i			0.217747i
$233$	−0.510875			−0.0334685			−0.0167343	−	0.999860i	$-0.505327\pi$
$233$	−0.510875			−0.0334685			−0.0167343	+	0.999860i	$0.505327\pi$
$234$	5.37228	−	2.67181i	0.351197	−	0.174662i
$235$	−4.00000	−	18.6101i	−0.260931	−	1.21399i
$236$	13.1168			0.853834
$237$	−15.3723	+	3.61158i	−0.998537	+	0.234597i
$238$		0			0
$239$			23.6588i			1.53036i	0.643816	+	0.765180i	$0.277350\pi$
$239$			23.6588i			1.53036i	−0.643816	+	0.765180i	$0.722650\pi$
$240$	3.50000	−	1.65831i	0.225924	−	0.107044i
$241$		−	19.2549i		−	1.24032i	−0.784475	−	0.620160i	$-0.787068\pi$
$241$		−	19.2549i		−	1.24032i	0.784475	−	0.620160i	$-0.212932\pi$
$242$	10.1168			0.650335
$243$	−6.31386	+	14.2525i	−0.405034	+	0.914302i
$244$			12.7692i			0.817462i
$245$		0			0
$246$	−12.4307	+	2.92048i	−0.792553	+	0.186203i
$247$			6.92820i			0.440831i
$248$			7.57301i			0.480887i
$249$	4.68614	+	19.9460i	0.296972	+	1.26403i
$250$	−9.00000	+	6.63325i	−0.569210	+	0.419524i
$251$	−1.11684			−0.0704946			−0.0352473	−	0.999379i	$-0.511222\pi$
$251$	−1.11684			−0.0704946			−0.0352473	+	0.999379i	$0.511222\pi$
$252$		0			0
$253$		−	1.28962i		−	0.0810777i
$254$			7.57301i			0.475173i
$255$	−11.0000	−	23.2164i	−0.688847	−	1.45387i
$256$	1.00000			0.0625000
$257$		−	1.87953i		−	0.117242i	−0.998280	−	0.0586209i	$-0.981330\pi$
$257$		−	1.87953i		−	0.117242i	0.998280	−	0.0586209i	$-0.0186703\pi$
$258$	0.430703	+	1.83324i	0.0268144	+	0.114133i
$259$		0			0
$260$	−4.37228	+	0.939764i	−0.271157	+	0.0582817i
$261$	4.43070	+	8.90892i	0.274254	+	0.551448i
$262$	−10.3723			−0.640802
$263$	7.37228			0.454594			0.227297	−	0.973825i	$-0.427011\pi$
$263$	7.37228			0.454594			0.227297	+	0.973825i	$0.427011\pi$
$264$	−0.372281	−	1.58457i	−0.0229123	−	0.0975238i
$265$	9.55842	−	2.05446i	0.587169	−	0.126204i
$266$		0			0
$267$	−2.31386	+	0.543620i	−0.141606	+	0.0332690i
$268$			2.37686i			0.145190i
$269$	25.9783			1.58392			0.791961	−	0.610572i	$-0.209060\pi$
$269$	25.9783			1.58392			0.791961	+	0.610572i	$0.209060\pi$
$270$	7.18614	−	9.13014i	0.437335	−	0.555642i
$271$		−	8.86263i		−	0.538367i	−0.963089	−	0.269183i	$-0.913246\pi$
$271$		−	8.86263i		−	0.538367i	0.963089	−	0.269183i	$-0.0867538\pi$
$272$		−	6.63325i		−	0.402200i
$273$		0			0
$274$	−8.74456			−0.528278
$275$	1.93070	+	4.28384i	0.116426	+	0.258325i
$276$	2.31386	−	0.543620i	0.139278	−	0.0327221i
$277$			9.10268i			0.546927i	0.961882	+	0.273464i	$0.0881693\pi$
$277$			9.10268i			0.546927i	−0.961882	+	0.273464i	$0.911831\pi$
$278$			8.21782i			0.492872i
$279$	10.1168	+	20.3422i	0.605680	+	1.21785i
$280$		0			0
$281$		−	11.3870i		−	0.679290i	−0.940554	−	0.339645i	$-0.889693\pi$
$281$		−	11.3870i		−	0.679290i	0.940554	−	0.339645i	$-0.110307\pi$
$282$	−3.37228	−	14.3537i	−0.200816	−	0.854753i
$283$	−16.0000			−0.951101			−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000			−0.951101			−0.475551	+	0.879688i	$0.657751\pi$
$284$			8.51278i			0.505140i
$285$	5.74456	+	12.1244i	0.340279	+	0.718185i
$286$			1.87953i			0.111139i
$287$		0			0
$288$	2.68614	−	1.33591i	0.158282	−	0.0787191i
$289$	−27.0000			−1.58824
$290$	−1.55842	−	7.25061i	−0.0915137	−	0.425770i
$291$	−25.4891	+	5.98844i	−1.49420	+	0.351049i
$292$	2.00000			0.117041
$293$			21.7244i			1.26915i	0.772861	+	0.634576i	$0.218825\pi$
$293$			21.7244i			1.26915i	−0.772861	+	0.634576i	$0.781175\pi$
$294$		0			0
$295$	−28.6753	+	6.16337i	−1.66954	+	0.358845i
$296$			8.21782i			0.477651i
$297$	−3.11684	−	3.75906i	−0.180858	−	0.218123i
$298$		−	9.01011i		−	0.521942i
$299$	−2.74456			−0.158722
$300$	−6.87228	+	5.26989i	−0.396771	+	0.304257i
$301$		0			0
$302$	9.11684			0.524615
$303$	17.9198	−	4.21010i	1.02947	−	0.241864i
$304$			3.46410i			0.198680i
$305$	−6.00000	−	27.9152i	−0.343559	−	1.59842i
$306$	−8.86141	−	17.8178i	−0.506573	−	1.01858i
$307$	24.1168			1.37642			0.688210	−	0.725511i	$-0.258397\pi$
$307$	24.1168			1.37642			0.688210	+	0.725511i	$0.258397\pi$
$308$		0			0
$309$	3.56930	−	0.838574i	0.203050	−	0.0477048i
$310$	−3.55842	−	16.5557i	−0.202105	−	0.940299i
$311$	−20.2337			−1.14735			−0.573674	−	0.819084i	$-0.694482\pi$
$311$	−20.2337			−1.14735			−0.573674	+	0.819084i	$0.694482\pi$
$312$	−3.37228	+	0.792287i	−0.190918	+	0.0448544i
$313$	3.11684			0.176174			0.0880872	−	0.996113i	$-0.471925\pi$
$313$	3.11684			0.176174			0.0880872	+	0.996113i	$0.471925\pi$
$314$	8.00000			0.451466
$315$		0			0
$316$	9.11684			0.512863
$317$	−1.11684			−0.0627282			−0.0313641	−	0.999508i	$-0.509985\pi$
$317$	−1.11684			−0.0627282			−0.0313641	+	0.999508i	$0.509985\pi$
$318$	7.37228	−	1.73205i	0.413417	−	0.0971286i
$319$	−3.11684			−0.174510
$320$	−2.18614	+	0.469882i	−0.122209	+	0.0262672i
$321$	−10.5475	+	2.47805i	−0.588707	+	0.138311i
$322$		0			0
$323$	22.9783			1.27854
$324$	5.43070	−	7.17687i	0.301706	−	0.398715i
$325$	9.11684	−	4.10891i	0.505712	−	0.227921i
$326$			3.46410i			0.191859i
$327$	13.6861	−	3.21543i	0.756845	−	0.177814i
$328$	7.37228			0.407066
$329$		0			0
$330$	1.55842	+	3.28917i	0.0857883	+	0.181063i
$331$	−24.2337			−1.33200			−0.666002	−	0.745950i	$-0.731996\pi$
$331$	−24.2337			−1.33200			−0.666002	+	0.745950i	$0.731996\pi$
$332$		−	11.8294i		−	0.649223i
$333$	10.9783	+	22.0742i	0.601604	+	1.20966i
$334$		−	14.6487i		−	0.801541i
$335$	−1.11684	−	5.19615i	−0.0610197	−	0.283896i
$336$		0			0
$337$			0.644810i			0.0351250i	0.999846	+	0.0175625i	$0.00559061\pi$
$337$			0.644810i			0.0351250i	−0.999846	+	0.0175625i	$0.994409\pi$
$338$	−9.00000			−0.489535
$339$	24.8614	−	5.84096i	1.35029	−	0.317238i
$340$	3.11684	+	14.5012i	0.169035	+	0.786439i
$341$	−7.11684			−0.385399
$342$	4.62772	+	9.30506i	0.250238	+	0.503160i
$343$		0			0
$344$		−	1.08724i		−	0.0586201i
$345$	−4.80298	+	2.27567i	−0.258584	+	0.122518i
$346$		−	17.0256i		−	0.915299i
$347$	1.88316			0.101093			0.0505466	−	0.998722i	$-0.483904\pi$
$347$	1.88316			0.101093			0.0505466	+	0.998722i	$0.483904\pi$
$348$	−1.31386	−	5.59230i	−0.0704303	−	0.299779i
$349$		−	25.7407i		−	1.37787i	−0.724824	−	0.688934i	$-0.758079\pi$
$349$		−	25.7407i		−	1.37787i	0.724824	−	0.688934i	$-0.241921\pi$
$350$		0			0
$351$	−8.00000	+	6.63325i	−0.427008	+	0.354057i
$352$			0.939764i			0.0500896i
$353$		−	12.2718i		−	0.653164i	−0.945169	−	0.326582i	$-0.894103\pi$
$353$		−	12.2718i		−	0.653164i	0.945169	−	0.326582i	$-0.105897\pi$
$354$	−22.1168	+	5.19615i	−1.17550	+	0.276172i
$355$	−4.00000	−	18.6101i	−0.212298	−	0.987723i
$356$	1.37228			0.0727308
$357$		0			0
$358$			23.6588i			1.25041i
$359$		−	27.4179i		−	1.44706i	−0.690293	−	0.723530i	$-0.742519\pi$
$359$		−	27.4179i		−	1.44706i	0.690293	−	0.723530i	$-0.257481\pi$
$360$	−5.24456	+	4.18265i	−0.276413	+	0.220445i
$361$	7.00000			0.368421
$362$			8.01544i			0.421282i
$363$	−17.0584	+	4.00772i	−0.895335	+	0.210351i
$364$		0			0
$365$	−4.37228	+	0.939764i	−0.228856	+	0.0491895i
$366$	−5.05842	−	21.5306i	−0.264408	−	1.12542i
$367$	13.2337			0.690793			0.345396	−	0.938457i	$-0.387744\pi$
$367$	13.2337			0.690793			0.345396	+	0.938457i	$0.387744\pi$
$368$	−1.37228			−0.0715351
$369$	19.8030	−	9.84868i	1.03090	−	0.512702i
$370$	−3.86141	−	17.9653i	−0.200745	−	0.933972i
$371$		0			0
$372$	−3.00000	−	12.7692i	−0.155543	−	0.662050i
$373$		−	23.3639i		−	1.20973i	−0.796326	−	0.604867i	$-0.793226\pi$
$373$		−	23.3639i		−	1.20973i	0.796326	−	0.604867i	$-0.206774\pi$
$374$	6.23369			0.322336
$375$	12.5475	−	14.7499i	0.647953	−	0.761681i
$376$			8.51278i			0.439013i
$377$			6.63325i			0.341630i
$378$		0			0
$379$	−12.2337			−0.628402			−0.314201	−	0.949356i	$-0.601737\pi$
$379$	−12.2337			−0.628402			−0.314201	+	0.949356i	$0.601737\pi$
$380$	−1.62772	−	7.57301i	−0.0835002	−	0.388487i
$381$	−3.00000	−	12.7692i	−0.153695	−	0.654184i
$382$		−	17.0256i		−	0.871103i
$383$			15.6434i			0.799338i	0.916659	+	0.399669i	$0.130875\pi$
$383$			15.6434i			0.799338i	−0.916659	+	0.399669i	$0.869125\pi$
$384$	−1.68614	+	0.396143i	−0.0860455	+	0.0202156i
$385$		0			0
$386$		−	17.9653i		−	0.914411i
$387$	−1.45245	−	2.92048i	−0.0738323	−	0.148456i
$388$	15.1168			0.767441
$389$		−	7.51811i		−	0.381183i	−0.981669	−	0.190592i	$-0.938959\pi$
$389$		−	7.51811i		−	0.381183i	0.981669	−	0.190592i	$-0.0610406\pi$
$390$	7.00000	−	3.31662i	0.354459	−	0.167944i
$391$			9.10268i			0.460343i
$392$		0			0
$393$	17.4891	−	4.10891i	0.882210	−	0.207267i
$394$	14.2337			0.717083
$395$	−19.9307	+	4.28384i	−1.00282	+	0.215543i
$396$	1.25544	+	2.52434i	0.0630881	+	0.126853i
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$			1.28962i			0.0646428i
$399$		0			0
$400$	4.55842	−	2.05446i	0.227921	−	0.102723i
$401$			16.5282i			0.825380i	0.910872	+	0.412690i	$0.135411\pi$
$401$			16.5282i			0.825380i	−0.910872	+	0.412690i	$0.864589\pi$
$402$	−0.941578	−	4.00772i	−0.0469616	−	0.199887i
$403$			15.1460i			0.754477i
$404$	−10.6277			−0.528749
$405$	−8.50000	+	18.2414i	−0.422368	+	0.906424i
$406$		0			0
$407$	−7.72281			−0.382806
$408$	2.62772	+	11.1846i	0.130091	+	0.553720i
$409$			4.31129i			0.213180i	0.994303	+	0.106590i	$0.0339932\pi$
$409$			4.31129i			0.213180i	−0.994303	+	0.106590i	$0.966007\pi$
$410$	−16.1168	+	3.46410i	−0.795954	+	0.171080i
$411$	14.7446	−	3.46410i	0.727296	−	0.170872i
$412$	−2.11684			−0.104289
$413$		0			0
$414$	−3.68614	+	1.83324i	−0.181164	+	0.0900989i
$415$	5.55842	+	25.8607i	0.272852	+	1.26945i
$416$	2.00000			0.0980581
$417$	−3.25544	−	13.8564i	−0.159419	−	0.678551i
$418$	−3.25544			−0.159229
$419$	−6.51087			−0.318077			−0.159039	−	0.987272i	$-0.550839\pi$
$419$	−6.51087			−0.318077			−0.159039	+	0.987272i	$0.550839\pi$
$420$		0			0
$421$	−2.11684			−0.103169			−0.0515843	−	0.998669i	$-0.516427\pi$
$421$	−2.11684			−0.103169			−0.0515843	+	0.998669i	$0.516427\pi$
$422$	16.2337			0.790244
$423$	11.3723	+	22.8665i	0.552939	+	1.11181i
$424$	−4.37228			−0.212337
$425$	−13.6277	−	30.2372i	−0.661041	−	1.46672i
$426$	−3.37228	−	14.3537i	−0.163388	−	0.695441i
$427$		0			0
$428$	6.25544			0.302368
$429$	−0.744563	−	3.16915i	−0.0359478	−	0.153008i
$430$	0.510875	+	2.37686i	0.0246366	+	0.114622i
$431$		−	17.0256i		−	0.820092i	−0.912065	−	0.410046i	$-0.865513\pi$
$431$		−	17.0256i		−	0.820092i	0.912065	−	0.410046i	$-0.134487\pi$
$432$	−4.00000	+	3.31662i	−0.192450	+	0.159571i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$	5.50000	+	11.6082i	0.263705	+	0.556570i
$436$	−8.11684			−0.388726
$437$		−	4.75372i		−	0.227401i
$438$	−3.37228	+	0.792287i	−0.161134	+	0.0378569i
$439$			2.81929i			0.134557i	0.997734	+	0.0672787i	$0.0214317\pi$
$439$			2.81929i			0.134557i	−0.997734	+	0.0672787i	$0.978568\pi$
$440$	−0.441578	−	2.05446i	−0.0210514	−	0.0979423i
$441$		0			0
$442$		−	13.2665i		−	0.631023i
$443$	9.00000			0.427603			0.213801	−	0.976877i	$-0.431415\pi$
$443$	9.00000			0.427603			0.213801	+	0.976877i	$0.431415\pi$
$444$	−3.25544	−	13.8564i	−0.154496	−	0.657596i
$445$	−3.00000	+	0.644810i	−0.142214	+	0.0305669i
$446$	0.883156			0.0418187
$447$	3.56930	+	15.1923i	0.168822	+	0.718572i
$448$		0			0
$449$			20.3971i			0.962598i	0.876557	+	0.481299i	$0.159835\pi$
$449$			20.3971i			0.962598i	−0.876557	+	0.481299i	$0.840165\pi$
$450$	9.50000	−	11.6082i	0.447834	−	0.547215i
$451$			6.92820i			0.326236i
$452$	−14.7446			−0.693526
$453$	−15.3723	+	3.61158i	−0.722253	+	0.169687i
$454$			20.8395i			0.978047i
$455$		0			0
$456$	−1.37228	−	5.84096i	−0.0642630	−	0.273528i
$457$		−	2.81929i		−	0.131881i	−0.997824	−	0.0659404i	$-0.978995\pi$
$457$		−	2.81929i		−	0.131881i	0.997824	−	0.0659404i	$-0.0210047\pi$
$458$		−	13.8564i		−	0.647467i
$459$	22.0000	+	26.5330i	1.02687	+	1.23845i
$460$	3.00000	−	0.644810i	0.139876	−	0.0300644i
$461$	−23.4891			−1.09400			−0.546999	−	0.837133i	$-0.684230\pi$
$461$	−23.4891			−1.09400			−0.546999	+	0.837133i	$0.684230\pi$
$462$		0			0
$463$			6.72582i			0.312576i	0.987712	+	0.156288i	$0.0499527\pi$
$463$			6.72582i			0.312576i	−0.987712	+	0.156288i	$0.950047\pi$
$464$			3.31662i			0.153970i
$465$	12.5584	+	26.5055i	0.582383	+	1.22917i
$466$	−0.510875			−0.0236658
$467$			36.4280i			1.68569i	0.538160	+	0.842843i	$0.319120\pi$
$467$			36.4280i			1.68569i	−0.538160	+	0.842843i	$0.680880\pi$
$468$	5.37228	−	2.67181i	0.248334	−	0.123505i
$469$		0			0
$470$	−4.00000	−	18.6101i	−0.184506	−	0.858421i
$471$	−13.4891	+	3.16915i	−0.621546	+	0.146027i
$472$	13.1168			0.603752
$473$	1.02175			0.0469801
$474$	−15.3723	+	3.61158i	−0.706072	+	0.165885i
$475$	7.11684	+	15.7908i	0.326543	+	0.724533i
$476$		0			0
$477$	−11.7446	+	5.84096i	−0.537747	+	0.267439i
$478$			23.6588i			1.08213i
$479$	−2.74456			−0.125402			−0.0627011	−	0.998032i	$-0.519971\pi$
$479$	−2.74456			−0.125402			−0.0627011	+	0.998032i	$0.519971\pi$
$480$	3.50000	−	1.65831i	0.159752	−	0.0756913i
$481$			16.4356i			0.749401i
$482$		−	19.2549i		−	0.877038i
$483$		0			0
$484$	10.1168			0.459857
$485$	−33.0475	+	7.10313i	−1.50061	+	0.322537i
$486$	−6.31386	+	14.2525i	−0.286402	+	0.646509i
$487$			14.5012i			0.657113i	0.944484	+	0.328556i	$0.106562\pi$
$487$			14.5012i			0.657113i	−0.944484	+	0.328556i	$0.893438\pi$
$488$			12.7692i			0.578033i
$489$	−1.37228	−	5.84096i	−0.0620567	−	0.264137i
$490$		0			0
$491$		−	30.2372i		−	1.36458i	−0.731080	−	0.682292i	$-0.760983\pi$
$491$		−	30.2372i		−	1.36458i	0.731080	−	0.682292i	$-0.239017\pi$
$492$	−12.4307	+	2.92048i	−0.560419	+	0.131665i
$493$	22.0000			0.990830
$494$			6.92820i			0.311715i
$495$	−3.93070	−	4.92865i	−0.176672	−	0.221526i
$496$			7.57301i			0.340038i
$497$		0			0
$498$	4.68614	+	19.9460i	0.209991	+	0.893803i
$499$	−6.23369			−0.279058			−0.139529	−	0.990218i	$-0.544559\pi$
$499$	−6.23369			−0.279058			−0.139529	+	0.990218i	$0.544559\pi$
$500$	−9.00000	+	6.63325i	−0.402492	+	0.296648i
$501$	5.80298	+	24.6998i	0.259258	+	1.10350i
$502$	−1.11684			−0.0498472
$503$			6.13592i			0.273587i	0.990600	+	0.136793i	$0.0436797\pi$
$503$			6.13592i			0.273587i	−0.990600	+	0.136793i	$0.956320\pi$
$504$		0			0
$505$	23.2337	−	4.99377i	1.03389	−	0.222220i
$506$		−	1.28962i		−	0.0573306i
$507$	15.1753	−	3.56529i	0.673957	−	0.158340i
$508$			7.57301i			0.335998i
$509$	11.7446			0.520569			0.260284	−	0.965532i	$-0.416184\pi$
$509$	11.7446			0.520569			0.260284	+	0.965532i	$0.416184\pi$
$510$	−11.0000	−	23.2164i	−0.487088	−	1.02804i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−11.4891	−	13.8564i	−0.507257	−	0.611775i
$514$		−	1.87953i		−	0.0829024i
$515$	4.62772	−	0.994667i	0.203922	−	0.0438303i
$516$	0.430703	+	1.83324i	0.0189607	+	0.0807039i
$517$	−8.00000			−0.351840
$518$		0			0
$519$	6.74456	+	28.7075i	0.296053	+	1.26012i
$520$	−4.37228	+	0.939764i	−0.191737	+	0.0412114i
$521$	14.7446			0.645971			0.322986	−	0.946404i	$-0.395313\pi$
$521$	14.7446			0.645971			0.322986	+	0.946404i	$0.395313\pi$
$522$	4.43070	+	8.90892i	0.193927	+	0.389933i
$523$	10.2337			0.447488			0.223744	−	0.974648i	$-0.428172\pi$
$523$	10.2337			0.447488			0.223744	+	0.974648i	$0.428172\pi$
$524$	−10.3723			−0.453115
$525$		0			0
$526$	7.37228			0.321447
$527$	50.2337			2.18821
$528$	−0.372281	−	1.58457i	−0.0162015	−	0.0689597i
$529$	−21.1168			−0.918124
$530$	9.55842	−	2.05446i	0.415191	−	0.0892399i
$531$	35.2337	−	17.5229i	1.52901	−	0.760429i
$532$		0			0
$533$	14.7446			0.638658
$534$	−2.31386	+	0.543620i	−0.100130	+	0.0235248i
$535$	−13.6753	+	2.93932i	−0.591233	+	0.127078i
$536$			2.37686i			0.102665i
$537$	−9.37228	−	39.8921i	−0.404444	−	1.72147i
$538$	25.9783			1.12000
$539$		0			0
$540$	7.18614	−	9.13014i	0.309242	−	0.392898i
$541$	38.3505			1.64882			0.824409	−	0.565994i	$-0.191508\pi$
$541$	38.3505			1.64882			0.824409	+	0.565994i	$0.191508\pi$
$542$		−	8.86263i		−	0.380683i
$543$	−3.17527	−	13.5152i	−0.136264	−	0.579991i
$544$		−	6.63325i		−	0.284398i
$545$	17.7446	−	3.81396i	0.760094	−	0.163372i
$546$		0			0
$547$			9.30506i			0.397856i	0.980014	+	0.198928i	$0.0637460\pi$
$547$			9.30506i			0.397856i	−0.980014	+	0.198928i	$0.936254\pi$
$548$	−8.74456			−0.373549
$549$	17.0584	+	34.2998i	0.728036	+	1.46388i
$550$	1.93070	+	4.28384i	0.0823255	+	0.182664i
$551$	−11.4891			−0.489453
$552$	2.31386	−	0.543620i	0.0984844	−	0.0231380i
$553$		0			0
$554$			9.10268i			0.386736i
$555$	13.6277	+	28.7624i	0.578464	+	1.22090i
$556$			8.21782i			0.348513i
$557$	27.8614			1.18053			0.590263	−	0.807211i	$-0.299024\pi$
$557$	27.8614			1.18053			0.590263	+	0.807211i	$0.299024\pi$
$558$	10.1168	+	20.3422i	0.428280	+	0.861153i
$559$		−	2.17448i		−	0.0919708i
$560$		0			0
$561$	−10.5109	+	2.46943i	−0.443769	+	0.104260i
$562$		−	11.3870i		−	0.480330i
$563$		−	1.43710i		−	0.0605664i	−0.999541	−	0.0302832i	$-0.990359\pi$
$563$		−	1.43710i		−	0.0605664i	0.999541	−	0.0302832i	$-0.00964092\pi$
$564$	−3.37228	−	14.3537i	−0.141999	−	0.604401i
$565$	32.2337	−	6.92820i	1.35608	−	0.291472i
$566$	−16.0000			−0.672530
$567$		0			0
$568$			8.51278i			0.357188i
$569$		−	11.3870i		−	0.477367i	−0.971097	−	0.238683i	$-0.923284\pi$
$569$		−	11.3870i		−	0.477367i	0.971097	−	0.238683i	$-0.0767158\pi$
$570$	5.74456	+	12.1244i	0.240613	+	0.507833i
$571$	−0.233688			−0.00977954			−0.00488977	−	0.999988i	$-0.501556\pi$
$571$	−0.233688			−0.00977954			−0.00488977	+	0.999988i	$0.501556\pi$
$572$			1.87953i			0.0785870i
$573$	6.74456	+	28.7075i	0.281758	+	1.19927i
$574$		0			0
$575$	−6.25544	+	2.81929i	−0.260870	+	0.117573i
$576$	2.68614	−	1.33591i	0.111923	−	0.0556628i
$577$	−35.1168			−1.46193			−0.730967	−	0.682413i	$-0.760931\pi$
$577$	−35.1168			−1.46193			−0.730967	+	0.682413i	$0.760931\pi$
$578$	−27.0000			−1.12305
$579$	7.11684	+	30.2921i	0.295766	+	1.25889i
$580$	−1.55842	−	7.25061i	−0.0647100	−	0.301065i
$581$		0			0
$582$	−25.4891	+	5.98844i	−1.05656	+	0.248229i
$583$		−	4.10891i		−	0.170174i
$584$	2.00000			0.0827606
$585$	−10.4891	+	8.36530i	−0.433672	+	0.345863i
$586$			21.7244i			0.897426i
$587$			0.0549029i			0.00226608i	0.999999	+	0.00113304i	$0.000360659\pi$
$587$			0.0549029i			0.00226608i	−0.999999	+	0.00113304i	$0.999639\pi$
$588$		0			0
$589$	−26.2337			−1.08094
$590$	−28.6753	+	6.16337i	−1.18054	+	0.253742i
$591$	−24.0000	+	5.63858i	−0.987228	+	0.231940i
$592$			8.21782i			0.337750i
$593$		−	27.4179i		−	1.12592i	−0.826485	−	0.562958i	$-0.809663\pi$
$593$		−	27.4179i		−	1.12592i	0.826485	−	0.562958i	$-0.190337\pi$
$594$	−3.11684	−	3.75906i	−0.127886	−	0.154236i
$595$		0			0
$596$		−	9.01011i		−	0.369069i
$597$	−0.510875	−	2.17448i	−0.0209087	−	0.0889956i
$598$	−2.74456			−0.112234
$599$		−	1.87953i		−	0.0767954i	−0.999263	−	0.0383977i	$-0.987775\pi$
$599$		−	1.87953i		−	0.0767954i	0.999263	−	0.0383977i	$-0.0122254\pi$
$600$	−6.87228	+	5.26989i	−0.280560	+	0.215142i
$601$			19.2549i			0.785425i	0.919661	+	0.392713i	$0.128463\pi$
$601$			19.2549i			0.785425i	−0.919661	+	0.392713i	$0.871537\pi$
$602$		0			0
$603$	3.17527	+	6.38458i	0.129307	+	0.260000i
$604$	9.11684			0.370959
$605$	−22.1168	+	4.75372i	−0.899178	+	0.193266i
$606$	17.9198	−	4.21010i	0.727943	−	0.171024i
$607$	−41.4674			−1.68311			−0.841554	−	0.540172i	$-0.818359\pi$
$607$	−41.4674			−1.68311			−0.841554	+	0.540172i	$0.818359\pi$
$608$			3.46410i			0.140488i
$609$		0			0
$610$	−6.00000	−	27.9152i	−0.242933	−	1.13025i
$611$			17.0256i			0.688780i
$612$	−8.86141	−	17.8178i	−0.358201	−	0.720244i
$613$			26.8280i			1.08357i	0.840517	+	0.541785i	$0.182251\pi$
$613$			26.8280i			1.08357i	−0.840517	+	0.541785i	$0.817749\pi$
$614$	24.1168			0.973277
$615$	25.8030	−	12.2255i	1.04048	−	0.492982i
$616$		0			0
$617$	−46.9783			−1.89127			−0.945637	−	0.325225i	$-0.894560\pi$
$617$	−46.9783			−1.89127			−0.945637	+	0.325225i	$0.894560\pi$
$618$	3.56930	−	0.838574i	0.143578	−	0.0337324i
$619$		−	16.4356i		−	0.660604i	−0.943875	−	0.330302i	$-0.892849\pi$
$619$		−	16.4356i		−	0.660604i	0.943875	−	0.330302i	$-0.107151\pi$
$620$	−3.55842	−	16.5557i	−0.142910	−	0.664892i
$621$	5.48913	−	4.55134i	0.220271	−	0.182639i
$622$	−20.2337			−0.811297
$623$		0			0
$624$	−3.37228	+	0.792287i	−0.134999	+	0.0317169i
$625$	16.5584	−	18.7302i	0.662337	−	0.749206i
$626$	3.11684			0.124574
$627$	5.48913	−	1.28962i	0.219215	−	0.0515025i
$628$	8.00000			0.319235
$629$	54.5109			2.17349
$630$		0			0
$631$	12.8832			0.512870			0.256435	−	0.966561i	$-0.417452\pi$
$631$	12.8832			0.512870			0.256435	+	0.966561i	$0.417452\pi$
$632$	9.11684			0.362649
$633$	−27.3723	+	6.43087i	−1.08795	+	0.255604i
$634$	−1.11684			−0.0443555
$635$	−3.55842	−	16.5557i	−0.141212	−	0.656992i
$636$	7.37228	−	1.73205i	0.292330	−	0.0686803i
$637$		0			0
$638$	−3.11684			−0.123397
$639$	11.3723	+	22.8665i	0.449880	+	0.904585i
$640$	−2.18614	+	0.469882i	−0.0864148	+	0.0185737i
$641$		−	9.01011i		−	0.355878i	−0.984042	−	0.177939i	$-0.943057\pi$
$641$		−	9.01011i		−	0.355878i	0.984042	−	0.177939i	$-0.0569430\pi$
$642$	−10.5475	+	2.47805i	−0.416278	+	0.0978009i
$643$	−18.2337			−0.719066			−0.359533	−	0.933132i	$-0.617064\pi$
$643$	−18.2337			−0.719066			−0.359533	+	0.933132i	$0.617064\pi$
$644$		0			0
$645$	−1.80298	−	3.80534i	−0.0709925	−	0.149835i
$646$	22.9783			0.904067
$647$			42.0666i			1.65381i	0.562344	+	0.826903i	$0.309900\pi$
$647$			42.0666i			1.65381i	−0.562344	+	0.826903i	$0.690100\pi$
$648$	5.43070	−	7.17687i	0.213338	−	0.281934i
$649$			12.3267i			0.483867i
$650$	9.11684	−	4.10891i	0.357592	−	0.161165i
$651$		0			0
$652$			3.46410i			0.135665i
$653$	−16.3723			−0.640697			−0.320348	−	0.947300i	$-0.603800\pi$
$653$	−16.3723			−0.640697			−0.320348	+	0.947300i	$0.603800\pi$
$654$	13.6861	−	3.21543i	0.535170	−	0.125733i
$655$	22.6753	−	4.87375i	0.885996	−	0.190433i
$656$	7.37228			0.287839
$657$	5.37228	−	2.67181i	0.209593	−	0.104237i
$658$		0			0
$659$		−	16.1407i		−	0.628752i	−0.949299	−	0.314376i	$-0.898205\pi$
$659$		−	16.1407i		−	0.628752i	0.949299	−	0.314376i	$-0.101795\pi$
$660$	1.55842	+	3.28917i	0.0606615	+	0.128031i
$661$			12.7692i			0.496663i	0.968675	+	0.248331i	$0.0798822\pi$
$661$			12.7692i			0.496663i	−0.968675	+	0.248331i	$0.920118\pi$
$662$	−24.2337			−0.941869
$663$	5.25544	+	22.3692i	0.204104	+	0.868747i
$664$		−	11.8294i		−	0.459070i
$665$		0			0
$666$	10.9783	+	22.0742i	0.425399	+	0.855359i
$667$		−	4.55134i		−	0.176229i
$668$		−	14.6487i		−	0.566775i
$669$	−1.48913	+	0.349857i	−0.0575729	+	0.0135262i
$670$	−1.11684	−	5.19615i	−0.0431474	−	0.200745i
$671$	−12.0000			−0.463255
$672$		0			0
$673$		−	46.9678i		−	1.81047i	−0.424907	−	0.905237i	$-0.639693\pi$
$673$		−	46.9678i		−	1.81047i	0.424907	−	0.905237i	$-0.360307\pi$
$674$			0.644810i			0.0248372i
$675$	−11.4198	+	23.3364i	−0.439549	+	0.898218i
$676$	−9.00000			−0.346154
$677$			1.82462i			0.0701260i	0.999385	+	0.0350630i	$0.0111632\pi$
$677$			1.82462i			0.0701260i	−0.999385	+	0.0350630i	$0.988837\pi$
$678$	24.8614	−	5.84096i	0.954797	−	0.224321i
$679$		0			0
$680$	3.11684	+	14.5012i	0.119526	+	0.556096i
$681$	−8.25544	−	35.1383i	−0.316349	−	1.34650i
$682$	−7.11684			−0.272518
$683$	31.9783			1.22361			0.611807	−	0.791007i	$-0.290443\pi$
$683$	31.9783			1.22361			0.611807	+	0.791007i	$0.290443\pi$
$684$	4.62772	+	9.30506i	0.176945	+	0.355788i
$685$	19.1168	−	4.10891i	0.730417	−	0.156993i
$686$		0			0
$687$	5.48913	+	23.3639i	0.209423	+	0.891386i
$688$		−	1.08724i		−	0.0414507i
$689$	−8.74456			−0.333141
$690$	−4.80298	+	2.27567i	−0.182847	+	0.0866333i
$691$		−	9.50744i		−	0.361680i	−0.983513	−	0.180840i	$-0.942118\pi$
$691$		−	9.50744i		−	0.361680i	0.983513	−	0.180840i	$-0.0578817\pi$
$692$		−	17.0256i		−	0.647214i
$693$		0			0
$694$	1.88316			0.0714836
$695$	−3.86141	−	17.9653i	−0.146472	−	0.681463i
$696$	−1.31386	−	5.59230i	−0.0498017	−	0.211975i
$697$		−	48.9022i		−	1.85230i
$698$		−	25.7407i		−	0.974300i
$699$	0.861407	−	0.202380i	0.0325814	−	0.00765470i
$700$		0			0
$701$			39.2473i			1.48235i	0.671313	+	0.741174i	$0.265731\pi$
$701$			39.2473i			1.48235i	−0.671313	+	0.741174i	$0.734269\pi$
$702$	−8.00000	+	6.63325i	−0.301941	+	0.250356i
$703$	−28.4674			−1.07367
$704$			0.939764i			0.0354187i
$705$	14.1168	+	29.7947i	0.531671	+	1.12213i
$706$		−	12.2718i		−	0.461857i
$707$		0			0
$708$	−22.1168	+	5.19615i	−0.831202	+	0.195283i
$709$	12.1168			0.455058			0.227529	−	0.973771i	$-0.426935\pi$
$709$	12.1168			0.455058			0.227529	+	0.973771i	$0.426935\pi$
$710$	−4.00000	−	18.6101i	−0.150117	−	0.698426i
$711$	24.4891	−	12.1793i	0.918414	−	0.456758i
$712$	1.37228			0.0514284
$713$		−	10.3923i		−	0.389195i
$714$		0			0
$715$	−0.883156	−	4.10891i	−0.0330282	−	0.153665i
$716$			23.6588i			0.884171i
$717$	−9.37228	−	39.8921i	−0.350014	−	1.48980i
$718$		−	27.4179i		−	1.02323i
$719$	−44.7446			−1.66869			−0.834345	−	0.551242i	$-0.814154\pi$
$719$	−44.7446			−1.66869			−0.834345	+	0.551242i	$0.814154\pi$
$720$	−5.24456	+	4.18265i	−0.195453	+	0.155878i
$721$		0			0
$722$	7.00000			0.260513
$723$	7.62772	+	32.4665i	0.283678	+	1.20744i
$724$			8.01544i			0.297892i
$725$	6.81386	+	15.1186i	0.253060	+	0.561490i
$726$	−17.0584	+	4.00772i	−0.633097	+	0.148741i
$727$	−19.0000			−0.704671			−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000			−0.704671			−0.352335	+	0.935874i	$0.614612\pi$
$728$		0			0
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	−4.37228	+	0.939764i	−0.161825	+	0.0347822i
$731$	−7.21194			−0.266743
$732$	−5.05842	−	21.5306i	−0.186965	−	0.795794i
$733$	−32.4674			−1.19921			−0.599605	−	0.800296i	$-0.704676\pi$
$733$	−32.4674			−1.19921			−0.599605	+	0.800296i	$0.704676\pi$
$734$	13.2337			0.488464
$735$		0			0
$736$	−1.37228			−0.0505830
$737$	−2.23369			−0.0822790
$738$	19.8030	−	9.84868i	0.728958	−	0.362535i
$739$	−1.76631			−0.0649748			−0.0324874	−	0.999472i	$-0.510343\pi$
$739$	−1.76631			−0.0649748			−0.0324874	+	0.999472i	$0.510343\pi$
$740$	−3.86141	−	17.9653i	−0.141948	−	0.660418i
$741$	−2.74456	−	11.6819i	−0.100824	−	0.429146i
$742$		0			0
$743$	21.6060			0.792646			0.396323	−	0.918111i	$-0.370286\pi$
$743$	21.6060			0.792646			0.396323	+	0.918111i	$0.370286\pi$
$744$	−3.00000	−	12.7692i	−0.109985	−	0.468140i
$745$	4.23369	+	19.6974i	0.155110	+	0.721656i
$746$		−	23.3639i		−	0.855411i
$747$	−15.8030	−	31.7754i	−0.578201	−	1.16260i
$748$	6.23369			0.227926
$749$		0			0
$750$	12.5475	−	14.7499i	0.458172	−	0.538590i
$751$	24.8832			0.907999			0.454000	−	0.891002i	$-0.349997\pi$
$751$	24.8832			0.907999			0.454000	+	0.891002i	$0.349997\pi$
$752$			8.51278i			0.310429i
$753$	1.88316	−	0.442430i	0.0686260	−	0.0161231i
$754$			6.63325i			0.241569i
$755$	−19.9307	+	4.28384i	−0.725353	+	0.155905i
$756$		0			0
$757$		−	25.5383i		−	0.928206i	−0.885781	−	0.464103i	$-0.846377\pi$
$757$		−	25.5383i		−	0.928206i	0.885781	−	0.464103i	$-0.153623\pi$
$758$	−12.2337			−0.444348
$759$	0.510875	+	2.17448i	0.0185436	+	0.0789287i
$760$	−1.62772	−	7.57301i	−0.0590436	−	0.274702i
$761$	−7.02175			−0.254538			−0.127269	−	0.991868i	$-0.540621\pi$
$761$	−7.02175			−0.254538			−0.127269	+	0.991868i	$0.540621\pi$
$762$	−3.00000	−	12.7692i	−0.108679	−	0.462578i
$763$		0			0
$764$		−	17.0256i		−	0.615963i
$765$	27.7446	+	34.7885i	1.00311	+	1.25778i
$766$			15.6434i			0.565218i
$767$	26.2337			0.947244
$768$	−1.68614	+	0.396143i	−0.0608434	+	0.0142946i
$769$		−	30.5321i		−	1.10102i	−0.834830	−	0.550508i	$-0.814434\pi$
$769$		−	30.5321i		−	1.10102i	0.834830	−	0.550508i	$-0.185566\pi$
$770$		0			0
$771$	0.744563	+	3.16915i	0.0268148	+	0.114134i
$772$		−	17.9653i		−	0.646586i
$773$			8.51278i			0.306183i	0.988212	+	0.153092i	$0.0489230\pi$
$773$			8.51278i			0.306183i	−0.988212	+	0.153092i	$0.951077\pi$
$774$	−1.45245	−	2.92048i	−0.0522073	−	0.104975i
$775$	15.5584	+	34.5210i	0.558875	+	1.24003i
$776$	15.1168			0.542663
$777$		0			0
$778$		−	7.51811i		−	0.269537i
$779$			25.5383i			0.915006i
$780$	7.00000	−	3.31662i	0.250640	−	0.118754i
$781$	−8.00000			−0.286263
$782$			9.10268i			0.325511i
$783$	−11.0000	−	13.2665i	−0.393108	−	0.474106i
$784$		0			0
$785$	−17.4891	+	3.75906i	−0.624214	+	0.134166i
$786$	17.4891	−	4.10891i	0.623816	−	0.146560i
$787$	9.88316			0.352296			0.176148	−	0.984364i	$-0.443636\pi$
$787$	9.88316			0.352296			0.176148	+	0.984364i	$0.443636\pi$
$788$	14.2337			0.507054
$789$	−12.4307	+	2.92048i	−0.442545	+	0.103972i
$790$	−19.9307	+	4.28384i	−0.709103	+	0.152412i
$791$		0			0
$792$	1.25544	+	2.52434i	0.0446100	+	0.0896984i
$793$			25.5383i			0.906893i
$794$	8.00000			0.283909
$795$	−15.3030	+	7.25061i	−0.542741	+	0.257153i
$796$			1.28962i			0.0457094i
$797$			0.939764i			0.0332881i	0.999861	+	0.0166441i	$0.00529822\pi$
$797$			0.939764i			0.0332881i	−0.999861	+	0.0166441i	$0.994702\pi$
$798$		0			0
$799$	56.4674			1.99767
$800$	4.55842	−	2.05446i	0.161165	−	0.0726360i
$801$	3.68614	−	1.83324i	0.130243	−	0.0647744i
$802$			16.5282i			0.583632i
$803$			1.87953i			0.0663271i
$804$	−0.941578	−	4.00772i	−0.0332069	−	0.141341i
$805$		0			0
$806$			15.1460i			0.533496i
$807$	−43.8030	+	10.2911i	−1.54194	+	0.362264i
$808$	−10.6277			−0.373882
$809$			42.0666i			1.47898i	0.673167	+	0.739491i	$0.264934\pi$
$809$			42.0666i			1.47898i	−0.673167	+	0.739491i	$0.735066\pi$
$810$	−8.50000	+	18.2414i	−0.298660	+	0.640939i
$811$		−	10.3923i		−	0.364923i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$		−	10.3923i		−	0.364923i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$		0			0
$813$	3.51087	+	14.9436i	0.123132	+	0.524097i
$814$	−7.72281			−0.270684
$815$	−1.62772	−	7.57301i	−0.0570165	−	0.265271i
$816$	2.62772	+	11.1846i	0.0919886	+	0.391539i
$817$	3.76631			0.131767
$818$			4.31129i			0.150741i
$819$		0			0
$820$	−16.1168	+	3.46410i	−0.562825	+	0.120972i
$821$		−	4.69882i		−	0.163990i	−0.996633	−	0.0819950i	$-0.973871\pi$
$821$		−	4.69882i		−	0.163990i	0.996633	−	0.0819950i	$-0.0261291\pi$
$822$	14.7446	−	3.46410i	0.514276	−	0.120824i
$823$			13.6540i			0.475949i	0.971271	+	0.237975i	$0.0764835\pi$
$823$			13.6540i			0.475949i	−0.971271	+	0.237975i	$0.923516\pi$
$824$	−2.11684			−0.0737438
$825$	−4.95245	−	6.45832i	−0.172422	−	0.224850i
$826$		0			0
$827$	33.0000			1.14752			0.573761	−	0.819023i	$-0.305484\pi$
$827$	33.0000			1.14752			0.573761	+	0.819023i	$0.305484\pi$
$828$	−3.68614	+	1.83324i	−0.128102	+	0.0637095i
$829$			1.28962i			0.0447904i	0.999749	+	0.0223952i	$0.00712920\pi$
$829$			1.28962i			0.0447904i	−0.999749	+	0.0223952i	$0.992871\pi$
$830$	5.55842	+	25.8607i	0.192936	+	0.897639i
$831$	−3.60597	−	15.3484i	−0.125090	−	0.532430i
$832$	2.00000			0.0693375
$833$		0			0
$834$	−3.25544	−	13.8564i	−0.112727	−	0.479808i
$835$	6.88316	+	32.0241i	0.238201	+	1.10824i
$836$	−3.25544			−0.112592
$837$	−25.1168	−	30.2921i	−0.868165	−	1.04705i
$838$	−6.51087			−0.224914
$839$	−55.7228			−1.92377			−0.961883	−	0.273463i	$-0.911831\pi$
$839$	−55.7228			−1.92377			−0.961883	+	0.273463i	$0.911831\pi$
$840$		0			0
$841$	18.0000			0.620690
$842$	−2.11684			−0.0729513
$843$	4.51087	+	19.2000i	0.155363	+	0.661284i
$844$	16.2337			0.558787
$845$	19.6753	−	4.22894i	0.676850	−	0.145480i
$846$	11.3723	+	22.8665i	0.390987	+	0.786167i
$847$		0			0
$848$	−4.37228			−0.150145
$849$	26.9783	−	6.33830i	0.925891	−	0.217530i
$850$	−13.6277	−	30.2372i	−0.467427	−	1.03713i
$851$		−	11.2772i		−	0.386576i
$852$	−3.37228	−	14.3537i	−0.115532	−	0.491751i
$853$	−38.4674			−1.31710			−0.658549	−	0.752538i	$-0.728829\pi$
$853$	−38.4674			−1.31710			−0.658549	+	0.752538i	$0.728829\pi$
$854$		0			0
$855$	−14.4891	−	18.1677i	−0.495518	−	0.621322i
$856$	6.25544			0.213806
$857$			24.5437i			0.838396i	0.907895	+	0.419198i	$0.137689\pi$
$857$			24.5437i			0.838396i	−0.907895	+	0.419198i	$0.862311\pi$
$858$	−0.744563	−	3.16915i	−0.0254189	−	0.108193i
$859$			46.7277i			1.59433i	0.603762	+	0.797164i	$0.293668\pi$
$859$			46.7277i			1.59433i	−0.603762	+	0.797164i	$0.706332\pi$
$860$	0.510875	+	2.37686i	0.0174207	+	0.0810503i
$861$		0			0
$862$		−	17.0256i		−	0.579893i
$863$	13.3723			0.455198			0.227599	−	0.973755i	$-0.426913\pi$
$863$	13.3723			0.455198			0.227599	+	0.973755i	$0.426913\pi$
$864$	−4.00000	+	3.31662i	−0.136083	+	0.112834i
$865$	8.00000	+	37.2203i	0.272008	+	1.26553i
$866$	−34.0000			−1.15537
$867$	45.5258	−	10.6959i	1.54614	−	0.363251i
$868$		0			0
$869$			8.56768i			0.290639i
$870$	5.50000	+	11.6082i	0.186467	+	0.393554i
$871$			4.75372i			0.161074i
$872$	−8.11684			−0.274871
$873$	40.6060	−	20.1947i	1.37430	−	0.683487i
$874$		−	4.75372i		−	0.160797i
$875$		0			0
$876$	−3.37228	+	0.792287i	−0.113939	+	0.0267689i
$877$		−	28.1176i		−	0.949463i	−0.880131	−	0.474731i	$-0.842545\pi$
$877$		−	28.1176i		−	0.949463i	0.880131	−	0.474731i	$-0.157455\pi$
$878$			2.81929i			0.0951465i
$879$	−8.60597	−	36.6303i	−0.290272	−	1.23551i
$880$	−0.441578	−	2.05446i	−0.0148856	−	0.0692557i
$881$	0.350532			0.0118097			0.00590486	−	0.999983i	$-0.498120\pi$
$881$	0.350532			0.0118097			0.00590486	+	0.999983i	$0.498120\pi$
$882$		0			0
$883$		−	44.5532i		−	1.49934i	−0.661815	−	0.749668i	$-0.730213\pi$
$883$		−	44.5532i		−	1.49934i	0.661815	−	0.749668i	$-0.269787\pi$
$884$		−	13.2665i		−	0.446201i
$885$	45.9090	−	21.7518i	1.54321	−	0.731180i
$886$	9.00000			0.302361
$887$		−	8.12525i		−	0.272819i	−0.990653	−	0.136410i	$-0.956444\pi$
$887$		−	8.12525i		−	0.272819i	0.990653	−	0.136410i	$-0.0435563\pi$
$888$	−3.25544	−	13.8564i	−0.109245	−	0.464991i
$889$		0			0
$890$	−3.00000	+	0.644810i	−0.100560	+	0.0216141i
$891$	6.74456	+	5.10358i	0.225951	+	0.170976i
$892$	0.883156			0.0295703
$893$	−29.4891			−0.986816
$894$	3.56930	+	15.1923i	0.119375	+	0.508107i
$895$	−11.1168	−	51.7215i	−0.371595	−	1.72886i
$896$		0			0
$897$	4.62772	−	1.08724i	0.154515	−	0.0363019i
$898$			20.3971i			0.680659i
$899$	−25.1168			−0.837694
$900$	9.50000	−	11.6082i	0.316667	−	0.386940i
$901$			29.0024i			0.966211i
$902$			6.92820i			0.230684i
$903$		0			0
$904$	−14.7446			−0.490397
$905$	−3.76631	−	17.5229i	−0.125196	−	0.582480i
$906$	−15.3723	+	3.61158i	−0.510710	+	0.119987i
$907$			4.95610i			0.164565i	0.996609	+	0.0822823i	$0.0262209\pi$
$907$			4.95610i			0.164565i	−0.996609	+	0.0822823i	$0.973779\pi$
$908$			20.8395i			0.691584i
$909$	−28.5475	+	14.1976i	−0.946862	+	0.470906i
$910$		0			0
$911$		−	37.8102i		−	1.25271i	−0.779539	−	0.626353i	$-0.784547\pi$
$911$		−	37.8102i		−	1.25271i	0.779539	−	0.626353i	$-0.215453\pi$
$912$	−1.37228	−	5.84096i	−0.0454408	−	0.193414i
$913$	11.1168			0.367914
$914$		−	2.81929i		−	0.0932539i
$915$	21.1753	+	44.6921i	0.700033	+	1.47747i
$916$		−	13.8564i		−	0.457829i
$917$		0			0
$918$	22.0000	+	26.5330i	0.726108	+	0.875719i
$919$	16.2337			0.535500			0.267750	−	0.963488i	$-0.413720\pi$
$919$	16.2337			0.535500			0.267750	+	0.963488i	$0.413720\pi$
$920$	3.00000	−	0.644810i	0.0989071	−	0.0212588i
$921$	−40.6644	+	9.55373i	−1.33994	+	0.314806i
$922$	−23.4891			−0.773573
$923$			17.0256i			0.560403i
$924$		0			0
$925$	16.8832	+	37.4603i	0.555115	+	1.23169i
$926$			6.72582i			0.221024i
$927$	−5.68614	+	2.82791i	−0.186757	+	0.0928807i
$928$			3.31662i			0.108874i
$929$	34.1168			1.11934			0.559669	−	0.828716i	$-0.310928\pi$
$929$	34.1168			1.11934			0.559669	+	0.828716i	$0.310928\pi$
$930$	12.5584	+	26.5055i	0.411807	+	0.869151i
$931$		0			0
$932$	−0.510875			−0.0167343
$933$	34.1168	−	8.01544i	1.11694	−	0.262414i
$934$			36.4280i			1.19196i
$935$	−13.6277	+	2.92910i	−0.445674	+	0.0957917i
$936$	5.37228	−	2.67181i	0.175599	−	0.0873310i
$937$	−1.35053			−0.0441200			−0.0220600	−	0.999757i	$-0.507022\pi$
$937$	−1.35053			−0.0441200			−0.0220600	+	0.999757i	$0.507022\pi$
$938$		0			0
$939$	−5.25544	+	1.23472i	−0.171505	+	0.0402935i
$940$	−4.00000	−	18.6101i	−0.130466	−	0.606995i
$941$	27.3505			0.891602			0.445801	−	0.895132i	$-0.352919\pi$
$941$	27.3505			0.891602			0.445801	+	0.895132i	$0.352919\pi$
$942$	−13.4891	+	3.16915i	−0.439499	+	0.103256i
$943$	−10.1168			−0.329450
$944$	13.1168			0.426917
$945$		0			0
$946$	1.02175			0.0332199
$947$	25.8832			0.841090			0.420545	−	0.907272i	$-0.361839\pi$
$947$	25.8832			0.841090			0.420545	+	0.907272i	$0.361839\pi$
$948$	−15.3723	+	3.61158i	−0.499268	+	0.117299i
$949$	4.00000			0.129845
$950$	7.11684	+	15.7908i	0.230901	+	0.512322i
$951$	1.88316	−	0.442430i	0.0610655	−	0.0143468i
$952$		0			0
$953$	−48.0000			−1.55487			−0.777436	−	0.628962i	$-0.783480\pi$
$953$	−48.0000			−1.55487			−0.777436	+	0.628962i	$0.783480\pi$
$954$	−11.7446	+	5.84096i	−0.380244	+	0.189108i
$955$	8.00000	+	37.2203i	0.258874	+	1.20442i
$956$			23.6588i			0.765180i
$957$	5.25544	−	1.23472i	0.169884	−	0.0399127i
$958$	−2.74456			−0.0886728
$959$		0			0
$960$	3.50000	−	1.65831i	0.112962	−	0.0535218i
$961$	−26.3505			−0.850017
$962$			16.4356i			0.529907i
$963$	16.8030	−	8.35668i	0.541469	−	0.269290i
$964$		−	19.2549i		−	0.620160i
$965$	8.44158	+	39.2747i	0.271744	+	1.26430i
$966$		0			0
$967$			27.6751i			0.889973i	0.895537	+	0.444986i	$0.146791\pi$
$967$			27.6751i			0.889973i	−0.895537	+	0.444986i	$0.853209\pi$
$968$	10.1168			0.325168
$969$	−38.7446	+	9.10268i	−1.24465	+	0.292420i
$970$	−33.0475	+	7.10313i	−1.06109	+	0.228068i
$971$	34.3723			1.10306			0.551530	−	0.834155i	$-0.314044\pi$
$971$	34.3723			1.10306			0.551530	+	0.834155i	$0.314044\pi$
$972$	−6.31386	+	14.2525i	−0.202517	+	0.457151i
$973$		0			0
$974$			14.5012i			0.464649i
$975$	−13.7446	+	10.5398i	−0.440178	+	0.337543i
$976$			12.7692i			0.408731i
$977$	28.4674			0.910752			0.455376	−	0.890299i	$-0.349505\pi$
$977$	28.4674			0.910752			0.455376	+	0.890299i	$0.349505\pi$
$978$	−1.37228	−	5.84096i	−0.0438807	−	0.186773i
$979$			1.28962i			0.0412164i
$980$		0			0
$981$	−21.8030	+	10.8434i	−0.696116	+	0.346202i
$982$		−	30.2372i		−	0.964906i
$983$		−	25.0410i		−	0.798684i	−0.916802	−	0.399342i	$-0.869239\pi$
$983$		−	25.0410i		−	0.798684i	0.916802	−	0.399342i	$-0.130761\pi$
$984$	−12.4307	+	2.92048i	−0.396276	+	0.0931015i
$985$	−31.1168	+	6.68815i	−0.991465	+	0.213102i
$986$	22.0000			0.700623
$987$		0			0
$988$			6.92820i			0.220416i
$989$			1.49200i			0.0474428i
$990$	−3.93070	−	4.92865i	−0.124926	−	0.156643i
$991$	23.3505			0.741754			0.370877	−	0.928682i	$-0.379057\pi$
$991$	23.3505			0.741754			0.370877	+	0.928682i	$0.379057\pi$
$992$			7.57301i			0.240443i
$993$	40.8614	−	9.60002i	1.29670	−	0.304647i
$994$		0			0
$995$	−0.605969	−	2.81929i	−0.0192105	−	0.0893775i
$996$	4.68614	+	19.9460i	0.148486	+	0.632014i
$997$	−38.4674			−1.21827			−0.609137	−	0.793065i	$-0.708484\pi$
$997$	−38.4674			−1.21827			−0.609137	+	0.793065i	$0.708484\pi$
$998$	−6.23369			−0.197324
$999$	−27.2554	−	32.8713i	−0.862324	−	1.04000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.c.1469.2		4
3.2	odd	2		1470.2.d.a.1469.1		4
5.4	even	2		1470.2.d.b.1469.3		4
7.4	even	3		210.2.t.b.89.2	yes	4
7.5	odd	6		210.2.t.a.59.2	✓	4
7.6	odd	2		1470.2.d.d.1469.3		4
15.14	odd	2		1470.2.d.d.1469.4		4
21.5	even	6		210.2.t.c.59.1	yes	4
21.11	odd	6		210.2.t.d.89.2	yes	4
21.20	even	2		1470.2.d.b.1469.4		4
35.4	even	6		210.2.t.c.89.1	yes	4
35.12	even	12		1050.2.s.e.101.4		8
35.18	odd	12		1050.2.s.d.551.3		8
35.19	odd	6		210.2.t.d.59.1	yes	4
35.32	odd	12		1050.2.s.d.551.2		8
35.33	even	12		1050.2.s.e.101.1		8
35.34	odd	2		1470.2.d.a.1469.2		4
105.32	even	12		1050.2.s.e.551.4		8
105.47	odd	12		1050.2.s.d.101.2		8
105.53	even	12		1050.2.s.e.551.1		8
105.68	odd	12		1050.2.s.d.101.3		8
105.74	odd	6		210.2.t.a.89.1	yes	4
105.89	even	6		210.2.t.b.59.2	yes	4
105.104	even	2	inner	1470.2.d.c.1469.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.a.59.2	✓	4	7.5	odd	6
210.2.t.a.89.1	yes	4	105.74	odd	6
210.2.t.b.59.2	yes	4	105.89	even	6
210.2.t.b.89.2	yes	4	7.4	even	3
210.2.t.c.59.1	yes	4	21.5	even	6
210.2.t.c.89.1	yes	4	35.4	even	6
210.2.t.d.59.1	yes	4	35.19	odd	6
210.2.t.d.89.2	yes	4	21.11	odd	6
1050.2.s.d.101.2		8	105.47	odd	12
1050.2.s.d.101.3		8	105.68	odd	12
1050.2.s.d.551.2		8	35.32	odd	12
1050.2.s.d.551.3		8	35.18	odd	12
1050.2.s.e.101.1		8	35.33	even	12
1050.2.s.e.101.4		8	35.12	even	12
1050.2.s.e.551.1		8	105.53	even	12
1050.2.s.e.551.4		8	105.32	even	12
1470.2.d.a.1469.1		4	3.2	odd	2
1470.2.d.a.1469.2		4	35.34	odd	2
1470.2.d.b.1469.3		4	5.4	even	2
1470.2.d.b.1469.4		4	21.20	even	2
1470.2.d.c.1469.1		4	105.104	even	2	inner
1470.2.d.c.1469.2		4	1.1	even	1	trivial
1470.2.d.d.1469.3		4	7.6	odd	2
1470.2.d.d.1469.4		4	15.14	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.68614 + 0.396143i) q^{3} +1.00000 q^{4} +(-2.18614 + 0.469882i) q^{5} +(-1.68614 + 0.396143i) q^{6} +1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.68614 + 0.396143i) q^{3} +1.00000 q^{4} +(-2.18614 + 0.469882i) q^{5} +(-1.68614 + 0.396143i) q^{6} +1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +(-2.18614 + 0.469882i) q^{10} +0.939764i q^{11} +(-1.68614 + 0.396143i) q^{12} +2.00000 q^{13} +(3.50000 - 1.65831i) q^{15} +1.00000 q^{16} -6.63325i q^{17} +(2.68614 - 1.33591i) q^{18} +3.46410i q^{19} +(-2.18614 + 0.469882i) q^{20} +0.939764i q^{22} -1.37228 q^{23} +(-1.68614 + 0.396143i) q^{24} +(4.55842 - 2.05446i) q^{25} +2.00000 q^{26} +(-4.00000 + 3.31662i) q^{27} +3.31662i q^{29} +(3.50000 - 1.65831i) q^{30} +7.57301i q^{31} +1.00000 q^{32} +(-0.372281 - 1.58457i) q^{33} -6.63325i q^{34} +(2.68614 - 1.33591i) q^{36} +8.21782i q^{37} +3.46410i q^{38} +(-3.37228 + 0.792287i) q^{39} +(-2.18614 + 0.469882i) q^{40} +7.37228 q^{41} -1.08724i q^{43} +0.939764i q^{44} +(-5.24456 + 4.18265i) q^{45} -1.37228 q^{46} +8.51278i q^{47} +(-1.68614 + 0.396143i) q^{48} +(4.55842 - 2.05446i) q^{50} +(2.62772 + 11.1846i) q^{51} +2.00000 q^{52} -4.37228 q^{53} +(-4.00000 + 3.31662i) q^{54} +(-0.441578 - 2.05446i) q^{55} +(-1.37228 - 5.84096i) q^{57} +3.31662i q^{58} +13.1168 q^{59} +(3.50000 - 1.65831i) q^{60} +12.7692i q^{61} +7.57301i q^{62} +1.00000 q^{64} +(-4.37228 + 0.939764i) q^{65} +(-0.372281 - 1.58457i) q^{66} +2.37686i q^{67} -6.63325i q^{68} +(2.31386 - 0.543620i) q^{69} +8.51278i q^{71} +(2.68614 - 1.33591i) q^{72} +2.00000 q^{73} +8.21782i q^{74} +(-6.87228 + 5.26989i) q^{75} +3.46410i q^{76} +(-3.37228 + 0.792287i) q^{78} +9.11684 q^{79} +(-2.18614 + 0.469882i) q^{80} +(5.43070 - 7.17687i) q^{81} +7.37228 q^{82} -11.8294i q^{83} +(3.11684 + 14.5012i) q^{85} -1.08724i q^{86} +(-1.31386 - 5.59230i) q^{87} +0.939764i q^{88} +1.37228 q^{89} +(-5.24456 + 4.18265i) q^{90} -1.37228 q^{92} +(-3.00000 - 12.7692i) q^{93} +8.51278i q^{94} +(-1.62772 - 7.57301i) q^{95} +(-1.68614 + 0.396143i) q^{96} +15.1168 q^{97} +(1.25544 + 2.52434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} - 3 q^{5} - q^{6} + 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 - 3 * q^5 - q^6 + 4 * q^8 + 5 * q^9	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} - 3 q^{5} - q^{6} + 4 q^{8} + 5 q^{9} - 3 q^{10} - q^{12} + 8 q^{13} + 14 q^{15} + 4 q^{16} + 5 q^{18} - 3 q^{20} + 6 q^{23} - q^{24} + q^{25} + 8 q^{26} - 16 q^{27} + 14 q^{30} + 4 q^{32} + 10 q^{33} + 5 q^{36} - 2 q^{39} - 3 q^{40} + 18 q^{41} + 2 q^{45} + 6 q^{46} - q^{48} + q^{50} + 22 q^{51} + 8 q^{52} - 6 q^{53} - 16 q^{54} - 19 q^{55} + 6 q^{57} + 18 q^{59} + 14 q^{60} + 4 q^{64} - 6 q^{65} + 10 q^{66} + 15 q^{69} + 5 q^{72} + 8 q^{73} - 16 q^{75} - 2 q^{78} + 2 q^{79} - 3 q^{80} - 7 q^{81} + 18 q^{82} - 22 q^{85} - 11 q^{87} - 6 q^{89} + 2 q^{90} + 6 q^{92} - 12 q^{93} - 18 q^{95} - q^{96} + 26 q^{97} + 28 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 - 3 * q^5 - q^6 + 4 * q^8 + 5 * q^9 - 3 * q^10 - q^12 + 8 * q^13 + 14 * q^15 + 4 * q^16 + 5 * q^18 - 3 * q^20 + 6 * q^23 - q^24 + q^25 + 8 * q^26 - 16 * q^27 + 14 * q^30 + 4 * q^32 + 10 * q^33 + 5 * q^36 - 2 * q^39 - 3 * q^40 + 18 * q^41 + 2 * q^45 + 6 * q^46 - q^48 + q^50 + 22 * q^51 + 8 * q^52 - 6 * q^53 - 16 * q^54 - 19 * q^55 + 6 * q^57 + 18 * q^59 + 14 * q^60 + 4 * q^64 - 6 * q^65 + 10 * q^66 + 15 * q^69 + 5 * q^72 + 8 * q^73 - 16 * q^75 - 2 * q^78 + 2 * q^79 - 3 * q^80 - 7 * q^81 + 18 * q^82 - 22 * q^85 - 11 * q^87 - 6 * q^89 + 2 * q^90 + 6 * q^92 - 12 * q^93 - 18 * q^95 - q^96 + 26 * q^97 + 28 * q^99

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