LMFDB - Embedded newform 1470.2.g.h.589.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(589,1470)]

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([0, 1, 0]))

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

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

chi := DirichletCharacter("1470.589");

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.g (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:	$6$
Coefficient field:	6.0.29160000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 20x^{3} + 125 $ x^6 - 20*x^3 + 125
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.5
Root			$-0.806615 + 2.08551i$ of defining polynomial
Character	$\chi$	$=$	1470.589
Dual form			1470.2.g.h.589.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.806615 + 2.08551i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.806615 + 2.08551i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(-2.08551 + 0.806615i) q^{10} -4.78426 q^{11} -1.00000i q^{12} -3.17103i q^{13} +(-2.08551 + 0.806615i) q^{15} +1.00000 q^{16} -5.22646i q^{17} -1.00000i q^{18} -3.17103 q^{19} +(-0.806615 - 2.08551i) q^{20} -4.78426i q^{22} -7.17103i q^{23} +1.00000 q^{24} +(-3.69874 + 3.36441i) q^{25} +3.17103 q^{26} -1.00000i q^{27} -2.38677 q^{29} +(-0.806615 - 2.08551i) q^{30} -4.17103 q^{31} +1.00000i q^{32} -4.78426i q^{33} +5.22646 q^{34} +1.00000 q^{36} +7.17103i q^{37} -3.17103i q^{38} +3.17103 q^{39} +(2.08551 - 0.806615i) q^{40} +2.05543 q^{41} +2.00000i q^{43} +4.78426 q^{44} +(-0.806615 - 2.08551i) q^{45} +7.17103 q^{46} -11.5131i q^{47} +1.00000i q^{48} +(-3.36441 - 3.69874i) q^{50} +5.22646 q^{51} +3.17103i q^{52} +8.11560i q^{53} +1.00000 q^{54} +(-3.85906 - 9.97764i) q^{55} -3.17103i q^{57} -2.38677i q^{58} -10.7288 q^{59} +(2.08551 - 0.806615i) q^{60} -7.11560 q^{61} -4.17103i q^{62} -1.00000 q^{64} +(6.61323 - 2.55780i) q^{65} +4.78426 q^{66} +9.56852i q^{67} +5.22646i q^{68} +7.17103 q^{69} +6.00000 q^{71} +1.00000i q^{72} +4.00000i q^{73} -7.17103 q^{74} +(-3.36441 - 3.69874i) q^{75} +3.17103 q^{76} +3.17103i q^{78} -12.1710 q^{79} +(0.806615 + 2.08551i) q^{80} +1.00000 q^{81} +2.05543i q^{82} -3.39749i q^{83} +(10.8999 - 4.21574i) q^{85} -2.00000 q^{86} -2.38677i q^{87} +4.78426i q^{88} +9.56852 q^{89} +(2.08551 - 0.806615i) q^{90} +7.17103i q^{92} -4.17103i q^{93} +11.5131 q^{94} +(-2.55780 - 6.61323i) q^{95} -1.00000 q^{96} +1.27117i q^{97} +4.78426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 6 q^{11} + 6 q^{16} + 6 q^{19} + 6 q^{24} - 6 q^{26} - 24 q^{29} + 12 q^{34} + 6 q^{36} - 6 q^{39} + 18 q^{41} - 6 q^{44} + 18 q^{46} + 12 q^{51} + 6 q^{54} - 30 q^{55} - 24 q^{59} - 12 q^{61} - 6 q^{64} + 30 q^{65} - 6 q^{66} + 18 q^{69} + 36 q^{71} - 18 q^{74} - 6 q^{76} - 48 q^{79} + 6 q^{81} - 12 q^{86} - 12 q^{89} - 6 q^{94} - 6 q^{96} - 6 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 6 * q^11 + 6 * q^16 + 6 * q^19 + 6 * q^24 - 6 * q^26 - 24 * q^29 + 12 * q^34 + 6 * q^36 - 6 * q^39 + 18 * q^41 - 6 * q^44 + 18 * q^46 + 12 * q^51 + 6 * q^54 - 30 * q^55 - 24 * q^59 - 12 * q^61 - 6 * q^64 + 30 * q^65 - 6 * q^66 + 18 * q^69 + 36 * q^71 - 18 * q^74 - 6 * q^76 - 48 * q^79 + 6 * q^81 - 12 * q^86 - 12 * q^89 - 6 * q^94 - 6 * q^96 - 6 * 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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	0.806615	+	2.08551i	0.360729	+	0.932671i
$5$	0.806615	+	2.08551i	0.360729	+	0.932671i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−2.08551	+	0.806615i	−0.659498	+	0.255074i
$11$	−4.78426			−1.44251			−0.721254	−	0.692670i	$-0.756434\pi$
$11$	−4.78426			−1.44251			−0.721254	+	0.692670i	$0.756434\pi$
$12$		−	1.00000i		−	0.288675i
$13$		−	3.17103i		−	0.879485i	−0.898124	−	0.439743i	$-0.855070\pi$
$13$		−	3.17103i		−	0.879485i	0.898124	−	0.439743i	$-0.144930\pi$
$14$		0			0
$15$	−2.08551	+	0.806615i	−0.538478	+	0.208267i
$16$	1.00000			0.250000
$17$		−	5.22646i		−	1.26760i	−0.773496	−	0.633801i	$-0.781494\pi$
$17$		−	5.22646i		−	1.26760i	0.773496	−	0.633801i	$-0.218506\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−3.17103			−0.727484			−0.363742	−	0.931500i	$-0.618501\pi$
$19$	−3.17103			−0.727484			−0.363742	+	0.931500i	$0.618501\pi$
$20$	−0.806615	−	2.08551i	−0.180365	−	0.466335i
$21$		0			0
$22$		−	4.78426i		−	1.02001i
$23$		−	7.17103i		−	1.49526i	−0.664114	−	0.747632i	$-0.731191\pi$
$23$		−	7.17103i		−	1.49526i	0.664114	−	0.747632i	$-0.268809\pi$
$24$	1.00000			0.204124
$25$	−3.69874	+	3.36441i	−0.739749	+	0.672883i
$26$	3.17103			0.621890
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−2.38677			−0.443212			−0.221606	−	0.975136i	$-0.571130\pi$
$29$	−2.38677			−0.443212			−0.221606	+	0.975136i	$0.571130\pi$
$30$	−0.806615	−	2.08551i	−0.147267	−	0.380761i
$31$	−4.17103			−0.749139			−0.374570	−	0.927199i	$-0.622209\pi$
$31$	−4.17103			−0.749139			−0.374570	+	0.927199i	$0.622209\pi$
$32$			1.00000i			0.176777i
$33$		−	4.78426i		−	0.832833i
$34$	5.22646			0.896330
$35$		0			0
$36$	1.00000			0.166667
$37$			7.17103i			1.17891i	0.807801	+	0.589455i	$0.200657\pi$
$37$			7.17103i			1.17891i	−0.807801	+	0.589455i	$0.799343\pi$
$38$		−	3.17103i		−	0.514409i
$39$	3.17103			0.507771
$40$	2.08551	−	0.806615i	0.329749	−	0.127537i
$41$	2.05543			0.321004			0.160502	−	0.987035i	$-0.448689\pi$
$41$	2.05543			0.321004			0.160502	+	0.987035i	$0.448689\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	4.78426			0.721254
$45$	−0.806615	−	2.08551i	−0.120243	−	0.310890i
$46$	7.17103			1.05731
$47$		−	11.5131i		−	1.67936i	−0.543084	−	0.839678i	$-0.682744\pi$
$47$		−	11.5131i		−	1.67936i	0.543084	−	0.839678i	$-0.317256\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$	−3.36441	−	3.69874i	−0.475800	−	0.523081i
$51$	5.22646			0.731851
$52$			3.17103i			0.439743i
$53$			8.11560i			1.11476i	0.830256	+	0.557382i	$0.188194\pi$
$53$			8.11560i			1.11476i	−0.830256	+	0.557382i	$0.811806\pi$
$54$	1.00000			0.136083
$55$	−3.85906	−	9.97764i	−0.520355	−	1.34539i
$56$		0			0
$57$		−	3.17103i		−	0.420013i
$58$		−	2.38677i		−	0.313398i
$59$	−10.7288			−1.39677			−0.698387	−	0.715720i	$-0.746099\pi$
$59$	−10.7288			−1.39677			−0.698387	+	0.715720i	$0.746099\pi$
$60$	2.08551	−	0.806615i	0.269239	−	0.104134i
$61$	−7.11560			−0.911059			−0.455530	−	0.890221i	$-0.650550\pi$
$61$	−7.11560			−0.911059			−0.455530	+	0.890221i	$0.650550\pi$
$62$		−	4.17103i		−	0.529721i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.61323	−	2.55780i	0.820270	−	0.317256i
$66$	4.78426			0.588902
$67$			9.56852i			1.16898i	0.811401	+	0.584490i	$0.198706\pi$
$67$			9.56852i			1.16898i	−0.811401	+	0.584490i	$0.801294\pi$
$68$			5.22646i			0.633801i
$69$	7.17103			0.863291
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$			1.00000i			0.117851i
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	−7.17103			−0.833615
$75$	−3.36441	−	3.69874i	−0.388489	−	0.427094i
$76$	3.17103			0.363742
$77$		0			0
$78$			3.17103i			0.359048i
$79$	−12.1710			−1.36935			−0.684674	−	0.728850i	$-0.740055\pi$
$79$	−12.1710			−1.36935			−0.684674	+	0.728850i	$0.740055\pi$
$80$	0.806615	+	2.08551i	0.0901823	+	0.233168i
$81$	1.00000			0.111111
$82$			2.05543i			0.226984i
$83$		−	3.39749i		−	0.372923i	−0.982462	−	0.186461i	$-0.940298\pi$
$83$		−	3.39749i		−	0.372923i	0.982462	−	0.186461i	$-0.0597019\pi$
$84$		0			0
$85$	10.8999	−	4.21574i	1.18226	−	0.457261i
$86$	−2.00000			−0.215666
$87$		−	2.38677i		−	0.255889i
$88$			4.78426i			0.510004i
$89$	9.56852			1.01426			0.507131	−	0.861869i	$-0.330706\pi$
$89$	9.56852			1.01426			0.507131	+	0.861869i	$0.330706\pi$
$90$	2.08551	−	0.806615i	0.219833	−	0.0850247i
$91$		0			0
$92$			7.17103i			0.747632i
$93$		−	4.17103i		−	0.432516i
$94$	11.5131			1.18748
$95$	−2.55780	−	6.61323i	−0.262425	−	0.678503i
$96$	−1.00000			−0.102062
$97$			1.27117i			0.129068i	0.997916	+	0.0645339i	$0.0205561\pi$
$97$			1.27117i			0.129068i	−0.997916	+	0.0645339i	$0.979444\pi$
$98$		0			0
$99$	4.78426			0.480836
$100$	3.69874	−	3.36441i	0.369874	−	0.336441i
$101$	8.00000			0.796030			0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000			0.796030			0.398015	+	0.917379i	$0.369699\pi$
$102$			5.22646i			0.517497i
$103$		−	11.2265i		−	1.10618i	−0.833123	−	0.553088i	$-0.813449\pi$
$103$		−	11.2265i		−	1.10618i	0.833123	−	0.553088i	$-0.186551\pi$
$104$	−3.17103			−0.310945
$105$		0			0
$106$	−8.11560			−0.788257
$107$		−	1.39749i		−	0.135100i	−0.997716	−	0.0675502i	$-0.978482\pi$
$107$		−	1.39749i		−	0.135100i	0.997716	−	0.0675502i	$-0.0215183\pi$
$108$			1.00000i			0.0962250i
$109$	−12.4529			−1.19277			−0.596387	−	0.802697i	$-0.703397\pi$
$109$	−12.4529			−1.19277			−0.596387	+	0.802697i	$0.703397\pi$
$110$	9.97764	−	3.85906i	0.951331	−	0.367946i
$111$	−7.17103			−0.680644
$112$		0			0
$113$		−	6.34206i		−	0.596611i	−0.954470	−	0.298305i	$-0.903579\pi$
$113$		−	6.34206i		−	0.596611i	0.954470	−	0.298305i	$-0.0964214\pi$
$114$	3.17103			0.296994
$115$	14.9553	−	5.78426i	1.39459	−	0.539385i
$116$	2.38677			0.221606
$117$			3.17103i			0.293162i
$118$		−	10.7288i		−	0.987669i
$119$		0			0
$120$	0.806615	+	2.08551i	0.0736335	+	0.190381i
$121$	11.8891			1.08083
$122$		−	7.11560i		−	0.644216i
$123$			2.05543i			0.185332i
$124$	4.17103			0.374570
$125$	−10.0000	−	5.00000i	−0.894427	−	0.447214i
$126$		0			0
$127$			18.0107i			1.59819i	0.601203	+	0.799096i	$0.294688\pi$
$127$			18.0107i			1.59819i	−0.601203	+	0.799096i	$0.705312\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.00000			−0.176090
$130$	2.55780	+	6.61323i	0.224334	+	0.580019i
$131$	5.55780			0.485587			0.242794	−	0.970078i	$-0.421936\pi$
$131$	5.55780			0.485587			0.242794	+	0.970078i	$0.421936\pi$
$132$			4.78426i			0.416416i
$133$		0			0
$134$	−9.56852			−0.826594
$135$	2.08551	−	0.806615i	0.179493	−	0.0694224i
$136$	−5.22646			−0.448165
$137$		−	14.7950i		−	1.26402i	−0.774960	−	0.632010i	$-0.782230\pi$
$137$		−	14.7950i		−	1.26402i	0.774960	−	0.632010i	$-0.217770\pi$
$138$			7.17103i			0.610439i
$139$	3.65794			0.310262			0.155131	−	0.987894i	$-0.450420\pi$
$139$	3.65794			0.310262			0.155131	+	0.987894i	$0.450420\pi$
$140$		0			0
$141$	11.5131			0.969577
$142$			6.00000i			0.503509i
$143$			15.1710i			1.26867i
$144$	−1.00000			−0.0833333
$145$	−1.92520	−	4.97764i	−0.159880	−	0.413371i
$146$	−4.00000			−0.331042
$147$		0			0
$148$		−	7.17103i		−	0.589455i
$149$	−22.3421			−1.83033			−0.915166	−	0.403076i	$-0.867941\pi$
$149$	−22.3421			−1.83033			−0.915166	+	0.403076i	$0.867941\pi$
$150$	3.69874	−	3.36441i	0.302001	−	0.274703i
$151$	16.5131			1.34382			0.671908	−	0.740635i	$-0.265475\pi$
$151$	16.5131			1.34382			0.671908	+	0.740635i	$0.265475\pi$
$152$			3.17103i			0.257204i
$153$			5.22646i			0.422534i
$154$		0			0
$155$	−3.36441	−	8.69874i	−0.270236	−	0.698700i
$156$	−3.17103			−0.253886
$157$		−	9.94457i		−	0.793663i	−0.917891	−	0.396832i	$-0.870110\pi$
$157$		−	9.94457i		−	0.793663i	0.917891	−	0.396832i	$-0.129890\pi$
$158$		−	12.1710i		−	0.968275i
$159$	−8.11560			−0.643609
$160$	−2.08551	+	0.806615i	−0.164874	+	0.0637685i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$		−	2.88440i		−	0.225924i	−0.993599	−	0.112962i	$-0.963966\pi$
$163$		−	2.88440i		−	0.225924i	0.993599	−	0.112962i	$-0.0360338\pi$
$164$	−2.05543			−0.160502
$165$	9.97764	−	3.85906i	0.776759	−	0.300427i
$166$	3.39749			0.263696
$167$		−	4.05543i		−	0.313819i	−0.987613	−	0.156909i	$-0.949847\pi$
$167$		−	4.05543i		−	0.313819i	0.987613	−	0.156909i	$-0.0501530\pi$
$168$		0			0
$169$	2.94457			0.226505
$170$	4.21574	+	10.8999i	0.323333	+	0.835981i
$171$	3.17103			0.242495
$172$		−	2.00000i		−	0.152499i
$173$			6.39749i			0.486392i	0.969977	+	0.243196i	$0.0781958\pi$
$173$			6.39749i			0.486392i	−0.969977	+	0.243196i	$0.921804\pi$
$174$	2.38677			0.180941
$175$		0			0
$176$	−4.78426			−0.360627
$177$		−	10.7288i		−	0.806428i
$178$			9.56852i			0.717191i
$179$	−19.5131			−1.45848			−0.729238	−	0.684260i	$-0.760125\pi$
$179$	−19.5131			−1.45848			−0.729238	+	0.684260i	$0.760125\pi$
$180$	0.806615	+	2.08551i	0.0601215	+	0.155445i
$181$	23.0262			1.71152			0.855761	−	0.517371i	$-0.173089\pi$
$181$	23.0262			1.71152			0.855761	+	0.517371i	$0.173089\pi$
$182$		0			0
$183$		−	7.11560i		−	0.526000i
$184$	−7.17103			−0.528655
$185$	−14.9553	+	5.78426i	−1.09953	+	0.425267i
$186$	4.17103			0.305835
$187$			25.0047i			1.82853i
$188$			11.5131i			0.839678i
$189$		0			0
$190$	6.61323	−	2.55780i	0.479774	−	0.185562i
$191$	−10.2312			−0.740304			−0.370152	−	0.928971i	$-0.620694\pi$
$191$	−10.2312			−0.740304			−0.370152	+	0.928971i	$0.620694\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			11.6132i			0.835939i	0.908461	+	0.417969i	$0.137258\pi$
$193$			11.6132i			0.835939i	−0.908461	+	0.417969i	$0.862742\pi$
$194$	−1.27117			−0.0912647
$195$	2.55780	+	6.61323i	0.183168	+	0.473583i
$196$		0			0
$197$		−	2.39749i		−	0.170814i	−0.996346	−	0.0854070i	$-0.972781\pi$
$197$		−	2.39749i		−	0.170814i	0.996346	−	0.0854070i	$-0.0272191\pi$
$198$			4.78426i			0.340003i
$199$	−18.3421			−1.30023			−0.650117	−	0.759834i	$-0.725280\pi$
$199$	−18.3421			−1.30023			−0.650117	+	0.759834i	$0.725280\pi$
$200$	3.36441	+	3.69874i	0.237900	+	0.261541i
$201$	−9.56852			−0.674911
$202$			8.00000i			0.562878i
$203$		0			0
$204$	−5.22646			−0.365925
$205$	1.65794	+	4.28663i	0.115796	+	0.299391i
$206$	11.2265			0.782185
$207$			7.17103i			0.498421i
$208$		−	3.17103i		−	0.219871i
$209$	15.1710			1.04940
$210$		0			0
$211$	−2.82897			−0.194754			−0.0973772	−	0.995248i	$-0.531045\pi$
$211$	−2.82897			−0.194754			−0.0973772	+	0.995248i	$0.531045\pi$
$212$		−	8.11560i		−	0.557382i
$213$			6.00000i			0.411113i
$214$	1.39749			0.0955304
$215$	−4.17103	+	1.61323i	−0.284462	+	0.110021i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$		−	12.4529i		−	0.843418i
$219$	−4.00000			−0.270295
$220$	3.85906	+	9.97764i	0.260177	+	0.672693i
$221$	−16.5733			−1.11484
$222$		−	7.17103i		−	0.481288i
$223$			14.2973i			0.957421i	0.877973	+	0.478711i	$0.158896\pi$
$223$			14.2973i			0.957421i	−0.877973	+	0.478711i	$0.841104\pi$
$224$		0			0
$225$	3.69874	−	3.36441i	0.246583	−	0.224294i
$226$	6.34206			0.421868
$227$		−	11.0554i		−	0.733775i	−0.930265	−	0.366887i	$-0.880423\pi$
$227$		−	11.0554i		−	0.733775i	0.930265	−	0.366887i	$-0.119577\pi$
$228$			3.17103i			0.210007i
$229$	−18.4529			−1.21940			−0.609702	−	0.792631i	$-0.708711\pi$
$229$	−18.4529			−1.21940			−0.609702	+	0.792631i	$0.708711\pi$
$230$	5.78426	+	14.9553i	0.381403	+	0.986123i
$231$		0			0
$232$			2.38677i			0.156699i
$233$			9.11560i			0.597183i	0.954381	+	0.298591i	$0.0965168\pi$
$233$			9.11560i			0.597183i	−0.954381	+	0.298591i	$0.903483\pi$
$234$	−3.17103			−0.207297
$235$	24.0107	−	9.28663i	1.56629	−	0.605793i
$236$	10.7288			0.698387
$237$		−	12.1710i		−	0.790593i
$238$		0			0
$239$	−13.1156			−0.848378			−0.424189	−	0.905574i	$-0.639441\pi$
$239$	−13.1156			−0.848378			−0.424189	+	0.905574i	$0.639441\pi$
$240$	−2.08551	+	0.806615i	−0.134619	+	0.0520668i
$241$	5.34206			0.344112			0.172056	−	0.985087i	$-0.444959\pi$
$241$	5.34206			0.344112			0.172056	+	0.985087i	$0.444959\pi$
$242$			11.8891i			0.764263i
$243$			1.00000i			0.0641500i
$244$	7.11560			0.455530
$245$		0			0
$246$	−2.05543			−0.131049
$247$			10.0554i			0.639812i
$248$			4.17103i			0.264861i
$249$	3.39749			0.215307
$250$	5.00000	−	10.0000i	0.316228	−	0.632456i
$251$	−27.9213			−1.76238			−0.881188	−	0.472765i	$-0.843256\pi$
$251$	−27.9213			−1.76238			−0.881188	+	0.472765i	$0.843256\pi$
$252$		0			0
$253$			34.3081i			2.15693i
$254$	−18.0107			−1.13009
$255$	4.21574	+	10.8999i	0.264000	+	0.682576i
$256$	1.00000			0.0625000
$257$			21.1370i			1.31849i	0.751927	+	0.659246i	$0.229124\pi$
$257$			21.1370i			1.31849i	−0.751927	+	0.659246i	$0.770876\pi$
$258$		−	2.00000i		−	0.124515i
$259$		0			0
$260$	−6.61323	+	2.55780i	−0.410135	+	0.158628i
$261$	2.38677			0.147737
$262$			5.55780i			0.343362i
$263$		−	11.9106i		−	0.734438i	−0.930135	−	0.367219i	$-0.880310\pi$
$263$		−	11.9106i		−	0.734438i	0.930135	−	0.367219i	$-0.119690\pi$
$264$	−4.78426			−0.294451
$265$	−16.9252	+	6.54616i	−1.03971	+	0.402128i
$266$		0			0
$267$			9.56852i			0.585584i
$268$		−	9.56852i		−	0.584490i
$269$	−3.27117			−0.199447			−0.0997234	−	0.995015i	$-0.531796\pi$
$269$	−3.27117			−0.199447			−0.0997234	+	0.995015i	$0.531796\pi$
$270$	0.806615	+	2.08551i	0.0490890	+	0.126920i
$271$	−0.623949			−0.0379022			−0.0189511	−	0.999820i	$-0.506033\pi$
$271$	−0.623949			−0.0379022			−0.0189511	+	0.999820i	$0.506033\pi$
$272$		−	5.22646i		−	0.316901i
$273$		0			0
$274$	14.7950			0.893797
$275$	17.6958	−	16.0962i	1.06709	−	0.970639i
$276$	−7.17103			−0.431645
$277$		−	28.7950i		−	1.73012i	−0.501666	−	0.865061i	$-0.667279\pi$
$277$		−	28.7950i		−	1.73012i	0.501666	−	0.865061i	$-0.332721\pi$
$278$			3.65794i			0.219389i
$279$	4.17103			0.249713
$280$		0			0
$281$	2.82897			0.168762			0.0843811	−	0.996434i	$-0.473109\pi$
$281$	2.82897			0.168762			0.0843811	+	0.996434i	$0.473109\pi$
$282$			11.5131i			0.685594i
$283$		−	25.1370i		−	1.49424i	−0.664688	−	0.747121i	$-0.731436\pi$
$283$		−	25.1370i		−	1.49424i	0.664688	−	0.747121i	$-0.268564\pi$
$284$	−6.00000			−0.356034
$285$	6.61323	−	2.55780i	0.391734	−	0.151511i
$286$	−15.1710			−0.897082
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−10.3159			−0.606817
$290$	4.97764	−	1.92520i	0.292297	−	0.113052i
$291$	−1.27117			−0.0745173
$292$		−	4.00000i		−	0.234082i
$293$			10.2265i			0.597436i	0.954341	+	0.298718i	$0.0965590\pi$
$293$			10.2265i			0.597436i	−0.954341	+	0.298718i	$0.903441\pi$
$294$		0			0
$295$	−8.65403	−	22.3751i	−0.503857	−	1.30273i
$296$	7.17103			0.416808
$297$			4.78426i			0.277611i
$298$		−	22.3421i		−	1.29424i
$299$	−22.7395			−1.31506
$300$	3.36441	+	3.69874i	0.194245	+	0.213547i
$301$		0			0
$302$			16.5131i			0.950222i
$303$			8.00000i			0.459588i
$304$	−3.17103			−0.181871
$305$	−5.73955	−	14.8397i	−0.328646	−	0.849718i
$306$	−5.22646			−0.298777
$307$			23.4577i			1.33880i	0.742902	+	0.669400i	$0.233449\pi$
$307$			23.4577i			1.33880i	−0.742902	+	0.669400i	$0.766551\pi$
$308$		0			0
$309$	11.2265			0.638651
$310$	8.69874	−	3.36441i	0.494056	−	0.191086i
$311$	5.65794			0.320832			0.160416	−	0.987049i	$-0.448716\pi$
$311$	5.65794			0.320832			0.160416	+	0.987049i	$0.448716\pi$
$312$		−	3.17103i		−	0.179524i
$313$		−	16.3868i		−	0.926235i	−0.886297	−	0.463118i	$-0.846731\pi$
$313$		−	16.3868i		−	0.926235i	0.886297	−	0.463118i	$-0.153269\pi$
$314$	9.94457			0.561205
$315$		0			0
$316$	12.1710			0.684674
$317$			4.51309i			0.253480i	0.991936	+	0.126740i	$0.0404514\pi$
$317$			4.51309i			0.253480i	−0.991936	+	0.126740i	$0.959549\pi$
$318$		−	8.11560i		−	0.455100i
$319$	11.4189			0.639337
$320$	−0.806615	−	2.08551i	−0.0450911	−	0.116584i
$321$	1.39749			0.0780003
$322$		0			0
$323$			16.5733i			0.922161i
$324$	−1.00000			−0.0555556
$325$	10.6687	+	11.7288i	0.591791	+	0.650598i
$326$	2.88440			0.159752
$327$		−	12.4529i		−	0.688648i
$328$		−	2.05543i		−	0.113492i
$329$		0			0
$330$	3.85906	+	9.97764i	0.212434	+	0.549251i
$331$	−13.0816			−0.719030			−0.359515	−	0.933139i	$-0.617058\pi$
$331$	−13.0816			−0.719030			−0.359515	+	0.933139i	$0.617058\pi$
$332$			3.39749i			0.186461i
$333$		−	7.17103i		−	0.392970i
$334$	4.05543			0.221903
$335$	−19.9553	+	7.71811i	−1.09027	+	0.421685i
$336$		0			0
$337$			20.2973i			1.10567i	0.833292	+	0.552834i	$0.186453\pi$
$337$			20.2973i			1.10567i	−0.833292	+	0.552834i	$0.813547\pi$
$338$			2.94457i			0.160163i
$339$	6.34206			0.344453
$340$	−10.8999	+	4.21574i	−0.591128	+	0.228631i
$341$	19.9553			1.08064
$342$			3.17103i			0.171470i
$343$		0			0
$344$	2.00000			0.107833
$345$	5.78426	+	14.9553i	0.311414	+	0.805166i
$346$	−6.39749			−0.343931
$347$			14.4529i			0.775873i	0.921686	+	0.387937i	$0.126812\pi$
$347$			14.4529i			0.775873i	−0.921686	+	0.387937i	$0.873188\pi$
$348$			2.38677i			0.127944i
$349$	13.8891			0.743469			0.371734	−	0.928339i	$-0.378763\pi$
$349$	13.8891			0.743469			0.371734	+	0.928339i	$0.378763\pi$
$350$		0			0
$351$	−3.17103			−0.169257
$352$		−	4.78426i		−	0.255002i
$353$		−	6.45292i		−	0.343454i	−0.985145	−	0.171727i	$-0.945065\pi$
$353$		−	6.45292i		−	0.343454i	0.985145	−	0.171727i	$-0.0549347\pi$
$354$	10.7288			0.570231
$355$	4.83969	+	12.5131i	0.256864	+	0.664126i
$356$	−9.56852			−0.507131
$357$		0			0
$358$		−	19.5131i		−	1.03130i
$359$	−7.22646			−0.381398			−0.190699	−	0.981649i	$-0.561075\pi$
$359$	−7.22646			−0.381398			−0.190699	+	0.981649i	$0.561075\pi$
$360$	−2.08551	+	0.806615i	−0.109916	+	0.0425123i
$361$	−8.94457			−0.470767
$362$			23.0262i			1.21023i
$363$			11.8891i			0.624018i
$364$		0			0
$365$	−8.34206	+	3.22646i	−0.436643	+	0.168881i
$366$	7.11560			0.371938
$367$			2.10014i			0.109626i	0.998497	+	0.0548132i	$0.0174563\pi$
$367$			2.10014i			0.109626i	−0.998497	+	0.0548132i	$0.982544\pi$
$368$		−	7.17103i		−	0.373816i
$369$	−2.05543			−0.107001
$370$	−5.78426	−	14.9553i	−0.300709	−	0.777488i
$371$		0			0
$372$			4.17103i			0.216258i
$373$			23.2479i			1.20373i	0.798598	+	0.601865i	$0.205576\pi$
$373$			23.2479i			1.20373i	−0.798598	+	0.601865i	$0.794424\pi$
$374$	−25.0047			−1.29296
$375$	5.00000	−	10.0000i	0.258199	−	0.516398i
$376$	−11.5131			−0.593742
$377$			7.56852i			0.389799i
$378$		0			0
$379$	−2.16629			−0.111275			−0.0556374	−	0.998451i	$-0.517719\pi$
$379$	−2.16629			−0.111275			−0.0556374	+	0.998451i	$0.517719\pi$
$380$	2.55780	+	6.61323i	0.131212	+	0.339252i
$381$	−18.0107			−0.922717
$382$		−	10.2312i		−	0.523474i
$383$		−	8.05543i		−	0.411613i	−0.978593	−	0.205807i	$-0.934018\pi$
$383$		−	8.05543i		−	0.411613i	0.978593	−	0.205807i	$-0.0659818\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−11.6132			−0.591098
$387$		−	2.00000i		−	0.101666i
$388$		−	1.27117i		−	0.0645339i
$389$	−11.8891			−0.602803			−0.301402	−	0.953497i	$-0.597455\pi$
$389$	−11.8891			−0.602803			−0.301402	+	0.953497i	$0.597455\pi$
$390$	−6.61323	+	2.55780i	−0.334874	+	0.129519i
$391$	−37.4791			−1.89540
$392$		0			0
$393$			5.55780i			0.280354i
$394$	2.39749			0.120784
$395$	−9.81733	−	25.3829i	−0.493964	−	1.27715i
$396$	−4.78426			−0.240418
$397$			16.1109i			0.808581i	0.914631	+	0.404290i	$0.132481\pi$
$397$			16.1109i			0.808581i	−0.914631	+	0.404290i	$0.867519\pi$
$398$		−	18.3421i		−	0.919404i
$399$		0			0
$400$	−3.69874	+	3.36441i	−0.184937	+	0.168221i
$401$	24.9707			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$401$	24.9707			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$402$		−	9.56852i		−	0.477234i
$403$			13.2265i			0.658857i
$404$	−8.00000			−0.398015
$405$	0.806615	+	2.08551i	0.0400810	+	0.103630i
$406$		0			0
$407$		−	34.3081i		−	1.70059i
$408$		−	5.22646i		−	0.258748i
$409$	3.05543			0.151081			0.0755406	−	0.997143i	$-0.475932\pi$
$409$	3.05543			0.151081			0.0755406	+	0.997143i	$0.475932\pi$
$410$	−4.28663	+	1.65794i	−0.211702	+	0.0818798i
$411$	14.7950			0.729782
$412$			11.2265i			0.553088i
$413$		0			0
$414$	−7.17103			−0.352437
$415$	7.08551	−	2.74047i	0.347814	−	0.134524i
$416$	3.17103			0.155473
$417$			3.65794i			0.179130i
$418$			15.1710i			0.742039i
$419$	−20.1972			−0.986698			−0.493349	−	0.869831i	$-0.664227\pi$
$419$	−20.1972			−0.986698			−0.493349	+	0.869831i	$0.664227\pi$
$420$		0			0
$421$	−30.3635			−1.47983			−0.739913	−	0.672702i	$-0.765133\pi$
$421$	−30.3635			−1.47983			−0.739913	+	0.672702i	$0.765133\pi$
$422$		−	2.82897i		−	0.137712i
$423$			11.5131i			0.559786i
$424$	8.11560			0.394128
$425$	17.5840	+	19.3313i	0.852948	+	0.937708i
$426$	−6.00000			−0.290701
$427$		0			0
$428$			1.39749i			0.0675502i
$429$	−15.1710			−0.732464
$430$	−1.61323	−	4.17103i	−0.0777969	−	0.201145i
$431$	24.5733			1.18365			0.591826	−	0.806066i	$-0.298407\pi$
$431$	24.5733			1.18365			0.591826	+	0.806066i	$0.298407\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			4.68412i			0.225104i	0.993646	+	0.112552i	$0.0359026\pi$
$433$			4.68412i			0.225104i	−0.993646	+	0.112552i	$0.964097\pi$
$434$		0			0
$435$	4.97764	−	1.92520i	0.238660	−	0.0923065i
$436$	12.4529			0.596387
$437$			22.7395i			1.08778i
$438$		−	4.00000i		−	0.191127i
$439$	−30.5131			−1.45631			−0.728155	−	0.685412i	$-0.759622\pi$
$439$	−30.5131			−1.45631			−0.728155	+	0.685412i	$0.759622\pi$
$440$	−9.97764	+	3.85906i	−0.475666	+	0.183973i
$441$		0			0
$442$		−	16.5733i		−	0.788310i
$443$			9.50835i			0.451755i	0.974156	+	0.225878i	$0.0725250\pi$
$443$			9.50835i			0.451755i	−0.974156	+	0.225878i	$0.927475\pi$
$444$	7.17103			0.340322
$445$	7.71811	+	19.9553i	0.365874	+	0.945971i
$446$	−14.2973			−0.676999
$447$		−	22.3421i		−	1.05674i
$448$		0			0
$449$	−17.6239			−0.831726			−0.415863	−	0.909427i	$-0.636520\pi$
$449$	−17.6239			−0.831726			−0.415863	+	0.909427i	$0.636520\pi$
$450$	3.36441	+	3.69874i	0.158600	+	0.174360i
$451$	−9.83371			−0.463051
$452$			6.34206i			0.298305i
$453$			16.5131i			0.775853i
$454$	11.0554			0.518857
$455$		0			0
$456$	−3.17103			−0.148497
$457$			0.386770i			0.0180923i	0.999959	+	0.00904617i	$0.00287953\pi$
$457$			0.386770i			0.0180923i	−0.999959	+	0.00904617i	$0.997120\pi$
$458$		−	18.4529i		−	0.862248i
$459$	−5.22646			−0.243950
$460$	−14.9553	+	5.78426i	−0.697294	+	0.269692i
$461$	37.3682			1.74041			0.870206	−	0.492688i	$-0.163986\pi$
$461$	37.3682			1.74041			0.870206	+	0.492688i	$0.163986\pi$
$462$		0			0
$463$		−	24.3081i		−	1.12969i	−0.825196	−	0.564846i	$-0.808936\pi$
$463$		−	24.3081i		−	1.12969i	0.825196	−	0.564846i	$-0.191064\pi$
$464$	−2.38677			−0.110803
$465$	8.69874	−	3.36441i	0.403395	−	0.156021i
$466$	−9.11560			−0.422272
$467$		−	28.5733i		−	1.32221i	−0.750292	−	0.661106i	$-0.770087\pi$
$467$		−	28.5733i		−	1.32221i	0.750292	−	0.661106i	$-0.229913\pi$
$468$		−	3.17103i		−	0.146581i
$469$		0			0
$470$	9.28663	+	24.0107i	0.428360	+	1.10753i
$471$	9.94457			0.458222
$472$			10.7288i			0.493834i
$473$		−	9.56852i		−	0.439961i
$474$	12.1710			0.559034
$475$	11.7288	−	10.6687i	0.538156	−	0.489512i
$476$		0			0
$477$		−	8.11560i		−	0.371588i
$478$		−	13.1156i		−	0.599894i
$479$	−8.56378			−0.391289			−0.195645	−	0.980675i	$-0.562680\pi$
$479$	−8.56378			−0.391289			−0.195645	+	0.980675i	$0.562680\pi$
$480$	−0.806615	−	2.08551i	−0.0368168	−	0.0951903i
$481$	22.7395			1.03683
$482$			5.34206i			0.243324i
$483$		0			0
$484$	−11.8891			−0.540415
$485$	−2.65104	+	1.02534i	−0.120378	+	0.0465585i
$486$	−1.00000			−0.0453609
$487$		−	31.8444i		−	1.44301i	−0.692410	−	0.721504i	$-0.743451\pi$
$487$		−	31.8444i		−	1.44301i	0.692410	−	0.721504i	$-0.256549\pi$
$488$			7.11560i			0.322108i
$489$	2.88440			0.130437
$490$		0			0
$491$	4.49763			0.202975			0.101488	−	0.994837i	$-0.467640\pi$
$491$	4.49763			0.202975			0.101488	+	0.994837i	$0.467640\pi$
$492$		−	2.05543i		−	0.0926659i
$493$			12.4744i			0.561817i
$494$	−10.0554			−0.452415
$495$	3.85906	+	9.97764i	0.173452	+	0.448462i
$496$	−4.17103			−0.187285
$497$		0			0
$498$			3.39749i			0.152245i
$499$	0.342060			0.0153127			0.00765634	−	0.999971i	$-0.497563\pi$
$499$	0.342060			0.0153127			0.00765634	+	0.999971i	$0.497563\pi$
$500$	10.0000	+	5.00000i	0.447214	+	0.223607i
$501$	4.05543			0.181183
$502$		−	27.9213i		−	1.24619i
$503$		−	7.56852i		−	0.337464i	−0.985662	−	0.168732i	$-0.946033\pi$
$503$		−	7.56852i		−	0.337464i	0.985662	−	0.168732i	$-0.0539672\pi$
$504$		0			0
$505$	6.45292	+	16.6841i	0.287151	+	0.742434i
$506$	−34.3081			−1.52518
$507$			2.94457i			0.130773i
$508$		−	18.0107i		−	0.799096i
$509$	30.9600			1.37228			0.686140	−	0.727470i	$-0.259304\pi$
$509$	30.9600			1.37228			0.686140	+	0.727470i	$0.259304\pi$
$510$	−10.8999	+	4.21574i	−0.482654	+	0.186676i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			3.17103i			0.140004i
$514$	−21.1370			−0.932315
$515$	23.4129	−	9.05543i	1.03170	−	0.399030i
$516$	2.00000			0.0880451
$517$			55.0816i			2.42249i
$518$		0			0
$519$	−6.39749			−0.280819
$520$	−2.55780	−	6.61323i	−0.112167	−	0.290009i
$521$	−4.85041			−0.212500			−0.106250	−	0.994339i	$-0.533884\pi$
$521$	−4.85041			−0.212500			−0.106250	+	0.994339i	$0.533884\pi$
$522$			2.38677i			0.104466i
$523$			4.25264i			0.185955i	0.995668	+	0.0929774i	$0.0296384\pi$
$523$			4.25264i			0.185955i	−0.995668	+	0.0929774i	$0.970362\pi$
$524$	−5.55780			−0.242794
$525$		0			0
$526$	11.9106			0.519326
$527$			21.7997i			0.949611i
$528$		−	4.78426i		−	0.208208i
$529$	−28.4237			−1.23581
$530$	−6.54616	−	16.9252i	−0.284347	−	0.735184i
$531$	10.7288			0.465592
$532$		0			0
$533$		−	6.51783i		−	0.282319i
$534$	−9.56852			−0.414070
$535$	2.91449	−	1.12724i	0.126004	−	0.0487347i
$536$	9.56852			0.413297
$537$		−	19.5131i		−	0.842052i
$538$		−	3.27117i		−	0.141030i
$539$		0			0
$540$	−2.08551	+	0.806615i	−0.0897463	+	0.0347112i
$541$	38.3635			1.64938			0.824688	−	0.565588i	$-0.191351\pi$
$541$	38.3635			1.64938			0.824688	+	0.565588i	$0.191351\pi$
$542$		−	0.623949i		−	0.0268009i
$543$			23.0262i			0.988148i
$544$	5.22646			0.224083
$545$	−10.0447	−	25.9707i	−0.430268	−	1.11246i
$546$		0			0
$547$		−	1.44818i		−	0.0619197i	−0.999521	−	0.0309598i	$-0.990144\pi$
$547$		−	1.44818i		−	0.0619197i	0.999521	−	0.0309598i	$-0.00985640\pi$
$548$			14.7950i			0.632010i
$549$	7.11560			0.303686
$550$	16.0962	+	17.6958i	0.686346	+	0.754550i
$551$	7.56852			0.322430
$552$		−	7.17103i		−	0.305219i
$553$		0			0
$554$	28.7950			1.22338
$555$	−5.78426	−	14.9553i	−0.245528	−	0.634817i
$556$	−3.65794			−0.155131
$557$			13.0214i			0.551736i	0.961196	+	0.275868i	$0.0889653\pi$
$557$			13.0214i			0.551736i	−0.961196	+	0.275868i	$0.911035\pi$
$558$			4.17103i			0.176574i
$559$	6.34206			0.268241
$560$		0			0
$561$	−25.0047			−1.05570
$562$			2.82897i			0.119333i
$563$			5.85041i			0.246565i	0.992372	+	0.123283i	$0.0393422\pi$
$563$			5.85041i			0.246565i	−0.992372	+	0.123283i	$0.960658\pi$
$564$	−11.5131			−0.484789
$565$	13.2265	−	5.11560i	0.556441	−	0.215215i
$566$	25.1370			1.05659
$567$		0			0
$568$		−	6.00000i		−	0.251754i
$569$	40.6501			1.70414			0.852071	−	0.523426i	$-0.175346\pi$
$569$	40.6501			1.70414			0.852071	+	0.523426i	$0.175346\pi$
$570$	2.55780	+	6.61323i	0.107134	+	0.276998i
$571$	−3.22646			−0.135023			−0.0675116	−	0.997718i	$-0.521506\pi$
$571$	−3.22646			−0.135023			−0.0675116	+	0.997718i	$0.521506\pi$
$572$		−	15.1710i		−	0.634333i
$573$		−	10.2312i		−	0.427415i
$574$		0			0
$575$	24.1263	+	26.5238i	1.00614	+	1.10612i
$576$	1.00000			0.0416667
$577$		−	11.6347i		−	0.484358i	−0.970232	−	0.242179i	$-0.922138\pi$
$577$		−	11.6347i		−	0.484358i	0.970232	−	0.242179i	$-0.0778621\pi$
$578$		−	10.3159i		−	0.429084i
$579$	−11.6132			−0.482629
$580$	1.92520	+	4.97764i	0.0799398	+	0.206685i
$581$		0			0
$582$		−	1.27117i		−	0.0526917i
$583$		−	38.8271i		−	1.60806i
$584$	4.00000			0.165521
$585$	−6.61323	+	2.55780i	−0.273423	+	0.105752i
$586$	−10.2265			−0.422451
$587$		−	28.9446i		−	1.19467i	−0.801992	−	0.597335i	$-0.796226\pi$
$587$		−	28.9446i		−	1.19467i	0.801992	−	0.597335i	$-0.203774\pi$
$588$		0			0
$589$	13.2265			0.544987
$590$	22.3751	−	8.65403i	0.921170	−	0.356281i
$591$	2.39749			0.0986195
$592$			7.17103i			0.294728i
$593$		−	11.4577i		−	0.470510i	−0.971934	−	0.235255i	$-0.924408\pi$
$593$		−	11.4577i		−	0.470510i	0.971934	−	0.235255i	$-0.0755925\pi$
$594$	−4.78426			−0.196301
$595$		0			0
$596$	22.3421			0.915166
$597$		−	18.3421i		−	0.750691i
$598$		−	22.7395i		−	0.929889i
$599$	3.00474			0.122770			0.0613852	−	0.998114i	$-0.480448\pi$
$599$	3.00474			0.122770			0.0613852	+	0.998114i	$0.480448\pi$
$600$	−3.69874	+	3.36441i	−0.151001	+	0.137352i
$601$	−40.0816			−1.63496			−0.817481	−	0.575955i	$-0.804630\pi$
$601$	−40.0816			−1.63496			−0.817481	+	0.575955i	$0.804630\pi$
$602$		0			0
$603$		−	9.56852i		−	0.389660i
$604$	−16.5131			−0.671908
$605$	9.58996	+	24.7950i	0.389887	+	1.00806i
$606$	−8.00000			−0.324978
$607$			26.1216i			1.06024i	0.847922	+	0.530121i	$0.177854\pi$
$607$			26.1216i			1.06024i	−0.847922	+	0.530121i	$0.822146\pi$
$608$		−	3.17103i		−	0.128602i
$609$		0			0
$610$	14.8397	−	5.73955i	0.600841	−	0.232388i
$611$	−36.5083			−1.47697
$612$		−	5.22646i		−	0.211267i
$613$			41.5131i			1.67670i	0.545134	+	0.838349i	$0.316479\pi$
$613$			41.5131i			1.67670i	−0.545134	+	0.838349i	$0.683521\pi$
$614$	−23.4577			−0.946674
$615$	−4.28663	+	1.65794i	−0.172854	+	0.0668546i
$616$		0			0
$617$		−	31.1156i		−	1.25267i	−0.779555	−	0.626333i	$-0.784555\pi$
$617$		−	31.1156i		−	1.25267i	0.779555	−	0.626333i	$-0.215445\pi$
$618$			11.2265i			0.451594i
$619$	32.9922			1.32607			0.663034	−	0.748589i	$-0.269268\pi$
$619$	32.9922			1.32607			0.663034	+	0.748589i	$0.269268\pi$
$620$	3.36441	+	8.69874i	0.135118	+	0.349350i
$621$	−7.17103			−0.287764
$622$			5.65794i			0.226863i
$623$		0			0
$624$	3.17103			0.126943
$625$	2.36143	−	24.8882i	0.0944570	−	0.995529i
$626$	16.3868			0.654947
$627$			15.1710i			0.605873i
$628$			9.94457i			0.396832i
$629$	37.4791			1.49439
$630$		0			0
$631$	47.6501			1.89692			0.948461	−	0.316894i	$-0.102640\pi$
$631$	47.6501			1.89692			0.948461	+	0.316894i	$0.102640\pi$
$632$			12.1710i			0.484138i
$633$		−	2.82897i		−	0.112441i
$634$	−4.51309			−0.179238
$635$	−37.5616	+	14.5277i	−1.49059	+	0.576515i
$636$	8.11560			0.321804
$637$		0			0
$638$			11.4189i			0.452080i
$639$	−6.00000			−0.237356
$640$	2.08551	−	0.806615i	0.0824372	−	0.0318843i
$641$	10.2866			0.406297			0.203149	−	0.979148i	$-0.434883\pi$
$641$	10.2866			0.406297			0.203149	+	0.979148i	$0.434883\pi$
$642$			1.39749i			0.0551545i
$643$		−	38.9368i		−	1.53552i	−0.640740	−	0.767758i	$-0.721372\pi$
$643$		−	38.9368i		−	1.53552i	0.640740	−	0.767758i	$-0.278628\pi$
$644$		0			0
$645$	−1.61323	−	4.17103i	−0.0635209	−	0.164234i
$646$	−16.5733			−0.652066
$647$			33.8551i			1.33098i	0.746405	+	0.665492i	$0.231778\pi$
$647$			33.8551i			1.33098i	−0.746405	+	0.665492i	$0.768222\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	51.3295			2.01486
$650$	−11.7288	+	10.6687i	−0.460043	+	0.418459i
$651$		0			0
$652$			2.88440i			0.112962i
$653$		−	5.36350i		−	0.209890i	−0.994478	−	0.104945i	$-0.966533\pi$
$653$		−	5.36350i		−	0.209890i	0.994478	−	0.104945i	$-0.0334666\pi$
$654$	12.4529			0.486948
$655$	4.48300	+	11.5909i	0.175165	+	0.452893i
$656$	2.05543			0.0802511
$657$		−	4.00000i		−	0.156055i
$658$		0			0
$659$	−23.2265			−0.904774			−0.452387	−	0.891822i	$-0.649427\pi$
$659$	−23.2265			−0.904774			−0.452387	+	0.891822i	$0.649427\pi$
$660$	−9.97764	+	3.85906i	−0.388379	+	0.150214i
$661$	36.5947			1.42337			0.711684	−	0.702499i	$-0.247933\pi$
$661$	36.5947			1.42337			0.711684	+	0.702499i	$0.247933\pi$
$662$		−	13.0816i		−	0.508431i
$663$		−	16.5733i		−	0.643652i
$664$	−3.39749			−0.131848
$665$		0			0
$666$	7.17103			0.277872
$667$			17.1156i			0.662719i
$668$			4.05543i			0.156909i
$669$	−14.2973			−0.552767
$670$	−7.71811	−	19.9553i	−0.298177	−	0.770940i
$671$	34.0429			1.31421
$672$		0			0
$673$			17.7336i			0.683579i	0.939777	+	0.341789i	$0.111033\pi$
$673$			17.7336i			0.683579i	−0.939777	+	0.341789i	$0.888967\pi$
$674$	−20.2973			−0.781825
$675$	3.36441	+	3.69874i	0.129496	+	0.142365i
$676$	−2.94457			−0.113253
$677$		−	26.2265i		−	1.00796i	−0.863714	−	0.503982i	$-0.831868\pi$
$677$		−	26.2265i		−	1.00796i	0.863714	−	0.503982i	$-0.168132\pi$
$678$			6.34206i			0.243565i
$679$		0			0
$680$	−4.21574	−	10.8999i	−0.161666	−	0.417991i
$681$	11.0554			0.423645
$682$			19.9553i			0.764128i
$683$			49.2186i			1.88330i	0.336595	+	0.941650i	$0.390725\pi$
$683$			49.2186i			1.88330i	−0.336595	+	0.941650i	$0.609275\pi$
$684$	−3.17103			−0.121247
$685$	30.8551	−	11.9339i	1.17891	−	0.455969i
$686$		0			0
$687$		−	18.4529i		−	0.704023i
$688$			2.00000i			0.0762493i
$689$	25.7348			0.980418
$690$	−14.9553	+	5.78426i	−0.569338	+	0.220203i
$691$	−8.90584			−0.338794			−0.169397	−	0.985548i	$-0.554182\pi$
$691$	−8.90584			−0.338794			−0.169397	+	0.985548i	$0.554182\pi$
$692$		−	6.39749i		−	0.243196i
$693$		0			0
$694$	−14.4529			−0.548625
$695$	2.95055	+	7.62869i	0.111921	+	0.289373i
$696$	−2.38677			−0.0904703
$697$		−	10.7426i		−	0.406906i
$698$			13.8891i			0.525712i
$699$	−9.11560			−0.344784
$700$		0			0
$701$	11.9553			0.451545			0.225773	−	0.974180i	$-0.427509\pi$
$701$	11.9553			0.451545			0.225773	+	0.974180i	$0.427509\pi$
$702$		−	3.17103i		−	0.119683i
$703$		−	22.7395i		−	0.857638i
$704$	4.78426			0.180314
$705$	9.28663	+	24.0107i	0.349755	+	0.904296i
$706$	6.45292			0.242859
$707$		0			0
$708$			10.7288i			0.403214i
$709$	−52.1632			−1.95903			−0.979515	−	0.201369i	$-0.935461\pi$
$709$	−52.1632			−1.95903			−0.979515	+	0.201369i	$0.935461\pi$
$710$	−12.5131	+	4.83969i	−0.469608	+	0.181630i
$711$	12.1710			0.456449
$712$		−	9.56852i		−	0.358595i
$713$			29.9106i			1.12016i
$714$		0			0
$715$	−31.6394	+	12.2372i	−1.18325	+	0.457645i
$716$	19.5131			0.729238
$717$		−	13.1156i		−	0.489811i
$718$		−	7.22646i		−	0.269689i
$719$	25.7902			0.961814			0.480907	−	0.876772i	$-0.340308\pi$
$719$	25.7902			0.961814			0.480907	+	0.876772i	$0.340308\pi$
$720$	−0.806615	−	2.08551i	−0.0300608	−	0.0777226i
$721$		0			0
$722$		−	8.94457i		−	0.332882i
$723$			5.34206i			0.198673i
$724$	−23.0262			−0.855761
$725$	8.82805	−	8.03008i	0.327866	−	0.298230i
$726$	−11.8891			−0.441247
$727$		−	34.6054i		−	1.28344i	−0.766937	−	0.641722i	$-0.778220\pi$
$727$		−	34.6054i		−	1.28344i	0.766937	−	0.641722i	$-0.221780\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−3.22646	−	8.34206i	−0.119417	−	0.308753i
$731$	10.4529			0.386615
$732$			7.11560i			0.263000i
$733$		−	30.9707i		−	1.14393i	−0.820278	−	0.571965i	$-0.806181\pi$
$733$		−	30.9707i		−	1.14393i	0.820278	−	0.571965i	$-0.193819\pi$
$734$	−2.10014			−0.0775176
$735$		0			0
$736$	7.17103			0.264328
$737$		−	45.7783i		−	1.68626i
$738$		−	2.05543i		−	0.0756614i
$739$	2.17577			0.0800370			0.0400185	−	0.999199i	$-0.487258\pi$
$739$	2.17577			0.0800370			0.0400185	+	0.999199i	$0.487258\pi$
$740$	14.9553	−	5.78426i	0.549767	−	0.212634i
$741$	−10.0554			−0.369395
$742$		0			0
$743$			31.9446i			1.17193i	0.810335	+	0.585966i	$0.199285\pi$
$743$			31.9446i			1.17193i	−0.810335	+	0.585966i	$0.800715\pi$
$744$	−4.17103			−0.152917
$745$	−18.0214	−	46.5947i	−0.660254	−	1.70710i
$746$	−23.2479			−0.851166
$747$			3.39749i			0.124308i
$748$		−	25.0047i		−	0.914264i
$749$		0			0
$750$	10.0000	+	5.00000i	0.365148	+	0.182574i
$751$	−5.60725			−0.204611			−0.102306	−	0.994753i	$-0.532622\pi$
$751$	−5.60725			−0.204611			−0.102306	+	0.994753i	$0.532622\pi$
$752$		−	11.5131i		−	0.419839i
$753$		−	27.9213i		−	1.01751i
$754$	−7.56852			−0.275629
$755$	13.3197	+	34.4383i	0.484754	+	1.25334i
$756$		0			0
$757$		−	24.2312i		−	0.880698i	−0.897827	−	0.440349i	$-0.854855\pi$
$757$		−	24.2312i		−	0.880698i	0.897827	−	0.440349i	$-0.145145\pi$
$758$		−	2.16629i		−	0.0786832i
$759$	−34.3081			−1.24530
$760$	−6.61323	+	2.55780i	−0.239887	+	0.0927812i
$761$	−39.8551			−1.44475			−0.722374	−	0.691503i	$-0.756949\pi$
$761$	−39.8551			−1.44475			−0.722374	+	0.691503i	$0.756949\pi$
$762$		−	18.0107i		−	0.652460i
$763$		0			0
$764$	10.2312			0.370152
$765$	−10.8999	+	4.21574i	−0.394085	+	0.152420i
$766$	8.05543			0.291055
$767$			34.0214i			1.22844i
$768$			1.00000i			0.0360844i
$769$	29.7950			1.07443			0.537217	−	0.843444i	$-0.319476\pi$
$769$	29.7950			1.07443			0.537217	+	0.843444i	$0.319476\pi$
$770$		0			0
$771$	−21.1370			−0.761232
$772$		−	11.6132i		−	0.417969i
$773$			0.166290i			0.00598102i	0.999996	+	0.00299051i	$0.000951911\pi$
$773$			0.166290i			0.00598102i	−0.999996	+	0.00299051i	$0.999048\pi$
$774$	2.00000			0.0718885
$775$	15.4276	−	14.0331i	0.554175	−	0.504083i
$776$	1.27117			0.0456324
$777$		0			0
$778$		−	11.8891i		−	0.426246i
$779$	−6.51783			−0.233525
$780$	−2.55780	−	6.61323i	−0.0915839	−	0.236792i
$781$	−28.7056			−1.02717
$782$		−	37.4791i		−	1.34025i
$783$			2.38677i			0.0852962i
$784$		0			0
$785$	20.7395	−	8.02144i	0.740226	−	0.286297i
$786$	−5.55780			−0.198240
$787$			28.4529i			1.01424i	0.861876	+	0.507119i	$0.169289\pi$
$787$			28.4529i			1.01424i	−0.861876	+	0.507119i	$0.830711\pi$
$788$			2.39749i			0.0854070i
$789$	11.9106			0.424028
$790$	25.3829	−	9.81733i	0.903082	−	0.349285i
$791$		0			0
$792$		−	4.78426i		−	0.170001i
$793$			22.5638i			0.801263i
$794$	−16.1109			−0.571753
$795$	−6.54616	−	16.9252i	−0.232169	−	0.600275i
$796$	18.3421			0.650117
$797$		−	36.6334i		−	1.29762i	−0.760949	−	0.648811i	$-0.775266\pi$
$797$		−	36.6334i		−	1.29762i	0.760949	−	0.648811i	$-0.224734\pi$
$798$		0			0
$799$	−60.1727			−2.12876
$800$	−3.36441	−	3.69874i	−0.118950	−	0.130770i
$801$	−9.56852			−0.338087
$802$			24.9707i			0.881748i
$803$		−	19.1370i		−	0.675331i
$804$	9.56852			0.337456
$805$		0			0
$806$	−13.2265			−0.465882
$807$		−	3.27117i		−	0.115151i
$808$		−	8.00000i		−	0.281439i
$809$	20.2866			0.713240			0.356620	−	0.934250i	$-0.383929\pi$
$809$	20.2866			0.713240			0.356620	+	0.934250i	$0.383929\pi$
$810$	−2.08551	+	0.806615i	−0.0732775	+	0.0283416i
$811$	−1.38079			−0.0484861			−0.0242431	−	0.999706i	$-0.507718\pi$
$811$	−1.38079			−0.0484861			−0.0242431	+	0.999706i	$0.507718\pi$
$812$		0			0
$813$		−	0.623949i		−	0.0218829i
$814$	34.3081			1.20250
$815$	6.01546	−	2.32660i	0.210712	−	0.0814972i
$816$	5.22646			0.182963
$817$		−	6.34206i		−	0.221881i
$818$			3.05543i			0.106831i
$819$		0			0
$820$	−1.65794	−	4.28663i	−0.0578978	−	0.149696i
$821$	−17.4129			−0.607716			−0.303858	−	0.952717i	$-0.598275\pi$
$821$	−17.4129			−0.607716			−0.303858	+	0.952717i	$0.598275\pi$
$822$			14.7950i			0.516034i
$823$		−	20.5947i		−	0.717886i	−0.933359	−	0.358943i	$-0.883137\pi$
$823$		−	20.5947i		−	0.717886i	0.933359	−	0.358943i	$-0.116863\pi$
$824$	−11.2265			−0.391092
$825$	16.0962	+	17.6958i	0.560399	+	0.616087i
$826$		0			0
$827$			13.8504i			0.481626i	0.970572	+	0.240813i	$0.0774140\pi$
$827$			13.8504i			0.481626i	−0.970572	+	0.240813i	$0.922586\pi$
$828$		−	7.17103i		−	0.249211i
$829$	−1.22646			−0.0425967			−0.0212984	−	0.999773i	$-0.506780\pi$
$829$	−1.22646			−0.0425967			−0.0212984	+	0.999773i	$0.506780\pi$
$830$	2.74047	+	7.08551i	0.0951230	+	0.245942i
$831$	28.7950			0.998887
$832$			3.17103i			0.109936i
$833$		0			0
$834$	−3.65794			−0.126664
$835$	8.45766	−	3.27117i	0.292689	−	0.113204i
$836$	−15.1710			−0.524701
$837$			4.17103i			0.144172i
$838$		−	20.1972i		−	0.697701i
$839$	29.9106			1.03263			0.516314	−	0.856399i	$-0.327304\pi$
$839$	29.9106			1.03263			0.516314	+	0.856399i	$0.327304\pi$
$840$		0			0
$841$	−23.3033			−0.803563
$842$		−	30.3635i		−	1.04640i
$843$			2.82897i			0.0974349i
$844$	2.82897			0.0973772
$845$	2.37513	+	6.14094i	0.0817071	+	0.211255i
$846$	−11.5131			−0.395828
$847$		0			0
$848$			8.11560i			0.278691i
$849$	25.1370			0.862701
$850$	−19.3313	+	17.5840i	−0.663060	+	0.603125i
$851$	51.4237			1.76278
$852$		−	6.00000i		−	0.205557i
$853$		−	10.7181i		−	0.366981i	−0.983021	−	0.183491i	$-0.941260\pi$
$853$		−	10.7181i		−	0.366981i	0.983021	−	0.183491i	$-0.0587397\pi$
$854$		0			0
$855$	2.55780	+	6.61323i	0.0874749	+	0.226168i
$856$	−1.39749			−0.0477652
$857$		−	39.6889i		−	1.35575i	−0.735179	−	0.677873i	$-0.762902\pi$
$857$		−	39.6889i		−	1.35575i	0.735179	−	0.677873i	$-0.237098\pi$
$858$		−	15.1710i		−	0.517930i
$859$	11.0047			0.375477			0.187738	−	0.982219i	$-0.439884\pi$
$859$	11.0047			0.375477			0.187738	+	0.982219i	$0.439884\pi$
$860$	4.17103	−	1.61323i	0.142231	−	0.0550107i
$861$		0			0
$862$			24.5733i			0.836969i
$863$		−	8.62869i		−	0.293724i	−0.989157	−	0.146862i	$-0.953083\pi$
$863$		−	8.62869i		−	0.293724i	0.989157	−	0.146862i	$-0.0469173\pi$
$864$	1.00000			0.0340207
$865$	−13.3421	+	5.16031i	−0.453644	+	0.175456i
$866$	−4.68412			−0.159173
$867$		−	10.3159i		−	0.350346i
$868$		0			0
$869$	58.2294			1.97530
$870$	1.92520	+	4.97764i	0.0652705	+	0.168758i
$871$	30.3421			1.02810
$872$			12.4529i			0.421709i
$873$		−	1.27117i		−	0.0430226i
$874$	−22.7395			−0.769177
$875$		0			0
$876$	4.00000			0.135147
$877$		−	38.7395i		−	1.30814i	−0.756433	−	0.654071i	$-0.773060\pi$
$877$		−	38.7395i		−	1.30814i	0.756433	−	0.654071i	$-0.226940\pi$
$878$		−	30.5131i		−	1.02977i
$879$	−10.2265			−0.344930
$880$	−3.85906	−	9.97764i	−0.130089	−	0.336346i
$881$	6.03399			0.203290			0.101645	−	0.994821i	$-0.467589\pi$
$881$	6.03399			0.203290			0.101645	+	0.994821i	$0.467589\pi$
$882$		0			0
$883$		−	7.77828i		−	0.261760i	−0.991398	−	0.130880i	$-0.958220\pi$
$883$		−	7.77828i		−	0.261760i	0.991398	−	0.130880i	$-0.0417803\pi$
$884$	16.5733			0.557419
$885$	22.3751	−	8.65403i	0.752132	−	0.290902i
$886$	−9.50835			−0.319439
$887$			24.8939i			0.835855i	0.908480	+	0.417927i	$0.137243\pi$
$887$			24.8939i			0.835855i	−0.908480	+	0.417927i	$0.862757\pi$
$888$			7.17103i			0.240644i
$889$		0			0
$890$	−19.9553	+	7.71811i	−0.668903	+	0.258712i
$891$	−4.78426			−0.160279
$892$		−	14.2973i		−	0.478711i
$893$			36.5083i			1.22171i
$894$	22.3421			0.747230
$895$	−15.7395	−	40.6948i	−0.526115	−	1.36028i
$896$		0			0
$897$		−	22.7395i		−	0.759251i
$898$		−	17.6239i		−	0.588119i
$899$	9.95529			0.332027
$900$	−3.69874	+	3.36441i	−0.123291	+	0.112147i
$901$	42.4159			1.41308
$902$		−	9.83371i		−	0.327427i
$903$		0			0
$904$	−6.34206			−0.210934
$905$	18.5733	+	48.0214i	0.617396	+	1.59629i
$906$	−16.5131			−0.548611
$907$		−	46.7056i		−	1.55083i	−0.631450	−	0.775416i	$-0.717540\pi$
$907$		−	46.7056i		−	1.55083i	0.631450	−	0.775416i	$-0.282460\pi$
$908$			11.0554i			0.366887i
$909$	−8.00000			−0.265343
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		−	3.17103i		−	0.105003i
$913$			16.2545i			0.537944i
$914$	−0.386770			−0.0127932
$915$	14.8397	−	5.73955i	0.490585	−	0.189744i
$916$	18.4529			0.609702
$917$		0			0
$918$		−	5.22646i		−	0.172499i
$919$	34.2312			1.12918			0.564592	−	0.825370i	$-0.309034\pi$
$919$	34.2312			1.12918			0.564592	+	0.825370i	$0.309034\pi$
$920$	−5.78426	−	14.9553i	−0.190701	−	0.493061i
$921$	−23.4577			−0.772956
$922$			37.3682i			1.23066i
$923$		−	19.0262i		−	0.626254i
$924$		0			0
$925$	−24.1263	−	26.5238i	−0.793268	−	0.872097i
$926$	24.3081			0.798813
$927$			11.2265i			0.368725i
$928$		−	2.38677i		−	0.0783496i
$929$	−27.6549			−0.907327			−0.453663	−	0.891173i	$-0.649883\pi$
$929$	−27.6549			−0.907327			−0.453663	+	0.891173i	$0.649883\pi$
$930$	3.36441	+	8.69874i	0.110324	+	0.285243i
$931$		0			0
$932$		−	9.11560i		−	0.298591i
$933$			5.65794i			0.185233i
$934$	28.5733			0.934946
$935$	−52.1478	+	20.1692i	−1.70541	+	0.659603i
$936$	3.17103			0.103648
$937$			38.8397i			1.26884i	0.772990	+	0.634419i	$0.218760\pi$
$937$			38.8397i			1.26884i	−0.772990	+	0.634419i	$0.781240\pi$
$938$		0			0
$939$	16.3868			0.534762
$940$	−24.0107	+	9.28663i	−0.783143	+	0.302896i
$941$	19.7550			0.643995			0.321997	−	0.946741i	$-0.395646\pi$
$941$	19.7550			0.643995			0.321997	+	0.946741i	$0.395646\pi$
$942$			9.94457i			0.324012i
$943$		−	14.7395i		−	0.479986i
$944$	−10.7288			−0.349194
$945$		0			0
$946$	9.56852			0.311099
$947$		−	38.0524i		−	1.23654i	−0.785968	−	0.618268i	$-0.787835\pi$
$947$		−	38.0524i		−	1.23654i	0.785968	−	0.618268i	$-0.212165\pi$
$948$			12.1710i			0.395297i
$949$	12.6841			0.411744
$950$	10.6687	+	11.7288i	0.346137	+	0.380533i
$951$	−4.51309			−0.146347
$952$		0			0
$953$		−	52.5947i		−	1.70371i	−0.523778	−	0.851855i	$-0.675478\pi$
$953$		−	52.5947i		−	1.70371i	0.523778	−	0.851855i	$-0.324522\pi$
$954$	8.11560			0.262752
$955$	−8.25264	−	21.3373i	−0.267049	−	0.690459i
$956$	13.1156			0.424189
$957$			11.4189i			0.369122i
$958$		−	8.56378i		−	0.276683i
$959$		0			0
$960$	2.08551	−	0.806615i	0.0673097	−	0.0260334i
$961$	−13.6025			−0.438791
$962$			22.7395i			0.733152i
$963$			1.39749i			0.0450335i
$964$	−5.34206			−0.172056
$965$	−24.2196	+	9.36740i	−0.779655	+	0.301547i
$966$		0			0
$967$		−	4.61797i		−	0.148504i	−0.997240	−	0.0742520i	$-0.976343\pi$
$967$		−	4.61797i		−	0.148504i	0.997240	−	0.0742520i	$-0.0236569\pi$
$968$		−	11.8891i		−	0.382131i
$969$	−16.5733			−0.532410
$970$	−1.02534	−	2.65104i	−0.0329218	−	0.0851199i
$971$	−38.9046			−1.24851			−0.624254	−	0.781221i	$-0.714597\pi$
$971$	−38.9046			−1.24851			−0.624254	+	0.781221i	$0.714597\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	31.8444			1.02036
$975$	−11.7288	+	10.6687i	−0.375623	+	0.341671i
$976$	−7.11560			−0.227765
$977$		−	16.0214i		−	0.512571i	−0.966601	−	0.256286i	$-0.917501\pi$
$977$		−	16.0214i		−	0.512571i	0.966601	−	0.256286i	$-0.0824988\pi$
$978$			2.88440i			0.0922329i
$979$	−45.7783			−1.46308
$980$		0			0
$981$	12.4529			0.397591
$982$			4.49763i			0.143525i
$983$		−	2.05543i		−	0.0655580i	−0.999463	−	0.0327790i	$-0.989564\pi$
$983$		−	2.05543i		−	0.0655580i	0.999463	−	0.0327790i	$-0.0104358\pi$
$984$	2.05543			0.0655247
$985$	5.00000	−	1.93385i	0.159313	−	0.0616176i
$986$	−12.4744			−0.397264
$987$		0			0
$988$		−	10.0554i		−	0.319906i
$989$	14.3421			0.456051
$990$	−9.97764	+	3.85906i	−0.317110	+	0.122649i
$991$	−27.1972			−0.863948			−0.431974	−	0.901886i	$-0.642183\pi$
$991$	−27.1972			−0.863948			−0.431974	+	0.901886i	$0.642183\pi$
$992$		−	4.17103i		−	0.132430i
$993$		−	13.0816i		−	0.415132i
$994$		0			0
$995$	−14.7950	−	38.2526i	−0.469032	−	1.21269i
$996$	−3.39749			−0.107654
$997$			18.4744i			0.585089i	0.956252	+	0.292544i	$0.0945019\pi$
$997$			18.4744i			0.585089i	−0.956252	+	0.292544i	$0.905498\pi$
$998$			0.342060i			0.0108277i
$999$	7.17103			0.226881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.g.h.589.5		6
5.2	odd	4		7350.2.a.do.1.1		3
5.3	odd	4		7350.2.a.dp.1.1		3
5.4	even	2	inner	1470.2.g.h.589.2		6
7.2	even	3		1470.2.n.j.949.6		12
7.3	odd	6		210.2.n.b.79.3	✓	12
7.4	even	3		1470.2.n.j.79.1		12
7.5	odd	6		210.2.n.b.109.4	yes	12
7.6	odd	2		1470.2.g.i.589.5		6
21.5	even	6		630.2.u.f.109.3		12
21.17	even	6		630.2.u.f.289.4		12
28.3	even	6		1680.2.di.c.289.6		12
28.19	even	6		1680.2.di.c.529.1		12
35.3	even	12		1050.2.i.u.751.2		6
35.4	even	6		1470.2.n.j.79.6		12
35.9	even	6		1470.2.n.j.949.1		12
35.12	even	12		1050.2.i.v.151.2		6
35.13	even	4		7350.2.a.dq.1.1		3
35.17	even	12		1050.2.i.v.751.2		6
35.19	odd	6		210.2.n.b.109.3	yes	12
35.24	odd	6		210.2.n.b.79.4	yes	12
35.27	even	4		7350.2.a.dn.1.1		3
35.33	even	12		1050.2.i.u.151.2		6
35.34	odd	2		1470.2.g.i.589.2		6
105.59	even	6		630.2.u.f.289.3		12
105.89	even	6		630.2.u.f.109.4		12
140.19	even	6		1680.2.di.c.529.6		12
140.59	even	6		1680.2.di.c.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.b.79.3	✓	12	7.3	odd	6
210.2.n.b.79.4	yes	12	35.24	odd	6
210.2.n.b.109.3	yes	12	35.19	odd	6
210.2.n.b.109.4	yes	12	7.5	odd	6
630.2.u.f.109.3		12	21.5	even	6
630.2.u.f.109.4		12	105.89	even	6
630.2.u.f.289.3		12	105.59	even	6
630.2.u.f.289.4		12	21.17	even	6
1050.2.i.u.151.2		6	35.33	even	12
1050.2.i.u.751.2		6	35.3	even	12
1050.2.i.v.151.2		6	35.12	even	12
1050.2.i.v.751.2		6	35.17	even	12
1470.2.g.h.589.2		6	5.4	even	2	inner
1470.2.g.h.589.5		6	1.1	even	1	trivial
1470.2.g.i.589.2		6	35.34	odd	2
1470.2.g.i.589.5		6	7.6	odd	2
1470.2.n.j.79.1		12	7.4	even	3
1470.2.n.j.79.6		12	35.4	even	6
1470.2.n.j.949.1		12	35.9	even	6
1470.2.n.j.949.6		12	7.2	even	3
1680.2.di.c.289.1		12	140.59	even	6
1680.2.di.c.289.6		12	28.3	even	6
1680.2.di.c.529.1		12	28.19	even	6
1680.2.di.c.529.6		12	140.19	even	6
7350.2.a.dn.1.1		3	35.27	even	4
7350.2.a.do.1.1		3	5.2	odd	4
7350.2.a.dp.1.1		3	5.3	odd	4
7350.2.a.dq.1.1		3	35.13	even	4

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.806615 + 2.08551i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.806615 + 2.08551i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(-2.08551 + 0.806615i) q^{10} -4.78426 q^{11} -1.00000i q^{12} -3.17103i q^{13} +(-2.08551 + 0.806615i) q^{15} +1.00000 q^{16} -5.22646i q^{17} -1.00000i q^{18} -3.17103 q^{19} +(-0.806615 - 2.08551i) q^{20} -4.78426i q^{22} -7.17103i q^{23} +1.00000 q^{24} +(-3.69874 + 3.36441i) q^{25} +3.17103 q^{26} -1.00000i q^{27} -2.38677 q^{29} +(-0.806615 - 2.08551i) q^{30} -4.17103 q^{31} +1.00000i q^{32} -4.78426i q^{33} +5.22646 q^{34} +1.00000 q^{36} +7.17103i q^{37} -3.17103i q^{38} +3.17103 q^{39} +(2.08551 - 0.806615i) q^{40} +2.05543 q^{41} +2.00000i q^{43} +4.78426 q^{44} +(-0.806615 - 2.08551i) q^{45} +7.17103 q^{46} -11.5131i q^{47} +1.00000i q^{48} +(-3.36441 - 3.69874i) q^{50} +5.22646 q^{51} +3.17103i q^{52} +8.11560i q^{53} +1.00000 q^{54} +(-3.85906 - 9.97764i) q^{55} -3.17103i q^{57} -2.38677i q^{58} -10.7288 q^{59} +(2.08551 - 0.806615i) q^{60} -7.11560 q^{61} -4.17103i q^{62} -1.00000 q^{64} +(6.61323 - 2.55780i) q^{65} +4.78426 q^{66} +9.56852i q^{67} +5.22646i q^{68} +7.17103 q^{69} +6.00000 q^{71} +1.00000i q^{72} +4.00000i q^{73} -7.17103 q^{74} +(-3.36441 - 3.69874i) q^{75} +3.17103 q^{76} +3.17103i q^{78} -12.1710 q^{79} +(0.806615 + 2.08551i) q^{80} +1.00000 q^{81} +2.05543i q^{82} -3.39749i q^{83} +(10.8999 - 4.21574i) q^{85} -2.00000 q^{86} -2.38677i q^{87} +4.78426i q^{88} +9.56852 q^{89} +(2.08551 - 0.806615i) q^{90} +7.17103i q^{92} -4.17103i q^{93} +11.5131 q^{94} +(-2.55780 - 6.61323i) q^{95} -1.00000 q^{96} +1.27117i q^{97} +4.78426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 6 q^{11} + 6 q^{16} + 6 q^{19} + 6 q^{24} - 6 q^{26} - 24 q^{29} + 12 q^{34} + 6 q^{36} - 6 q^{39} + 18 q^{41} - 6 q^{44} + 18 q^{46} + 12 q^{51} + 6 q^{54} - 30 q^{55} - 24 q^{59} - 12 q^{61} - 6 q^{64} + 30 q^{65} - 6 q^{66} + 18 q^{69} + 36 q^{71} - 18 q^{74} - 6 q^{76} - 48 q^{79} + 6 q^{81} - 12 q^{86} - 12 q^{89} - 6 q^{94} - 6 q^{96} - 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 6 * q^11 + 6 * q^16 + 6 * q^19 + 6 * q^24 - 6 * q^26 - 24 * q^29 + 12 * q^34 + 6 * q^36 - 6 * q^39 + 18 * q^41 - 6 * q^44 + 18 * q^46 + 12 * q^51 + 6 * q^54 - 30 * q^55 - 24 * q^59 - 12 * q^61 - 6 * q^64 + 30 * q^65 - 6 * q^66 + 18 * q^69 + 36 * q^71 - 18 * q^74 - 6 * q^76 - 48 * q^79 + 6 * q^81 - 12 * q^86 - 12 * q^89 - 6 * q^94 - 6 * q^96 - 6 * q^99

Introduction

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