LMFDB - Embedded newform 1470.2.g.k.589.7

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:	$8$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.7
Root			$3.16053i$ of defining polynomial
Character	$\chi$	$=$	1470.589
Dual form			1470.2.g.k.589.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.63280 - 1.52773i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.63280 - 1.52773i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(1.52773 + 1.63280i) q^{10} +4.46967 q^{11} +1.00000i q^{12} +5.88388i q^{13} +(-1.52773 - 1.63280i) q^{15} +1.00000 q^{16} +7.73528i q^{17} -1.00000i q^{18} -6.61827 q^{19} +(-1.63280 + 1.52773i) q^{20} +4.46967i q^{22} +2.61827i q^{23} -1.00000 q^{24} +(0.332104 - 4.98896i) q^{25} -5.88388 q^{26} +1.00000i q^{27} +8.17246 q^{29} +(1.63280 - 1.52773i) q^{30} +8.46967 q^{31} +1.00000i q^{32} -4.46967i q^{33} -7.73528 q^{34} +1.00000 q^{36} -3.18719i q^{37} -6.61827i q^{38} +5.88388 q^{39} +(-1.52773 - 1.63280i) q^{40} +3.56282 q^{41} +1.43108i q^{43} -4.46967 q^{44} +(-1.63280 + 1.52773i) q^{45} -2.61827 q^{46} -6.79073i q^{47} -1.00000i q^{48} +(4.98896 + 0.332104i) q^{50} +7.73528 q^{51} -5.88388i q^{52} -1.38173i q^{53} -1.00000 q^{54} +(7.29809 - 6.82843i) q^{55} +6.61827i q^{57} +8.17246i q^{58} -4.66421 q^{59} +(1.52773 + 1.63280i) q^{60} +9.79683 q^{61} +8.46967i q^{62} -1.00000 q^{64} +(8.98896 + 9.60723i) q^{65} +4.46967 q^{66} -1.85140i q^{67} -7.73528i q^{68} +2.61827 q^{69} +2.02386 q^{71} +1.00000i q^{72} +4.01687i q^{73} +3.18719 q^{74} +(-4.98896 - 0.332104i) q^{75} +6.61827 q^{76} +5.88388i q^{78} +6.98527 q^{79} +(1.63280 - 1.52773i) q^{80} +1.00000 q^{81} +3.56282i q^{82} +5.35965i q^{83} +(11.8174 + 12.6302i) q^{85} -1.43108 q^{86} -8.17246i q^{87} -4.46967i q^{88} -14.3912 q^{89} +(-1.52773 - 1.63280i) q^{90} -2.61827i q^{92} -8.46967i q^{93} +6.79073 q^{94} +(-10.8063 + 10.1109i) q^{95} +1.00000 q^{96} +7.71966i q^{97} -4.46967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 4 * q^5 + 8 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{9} + 8 q^{16} - 24 q^{19} - 4 q^{20} - 8 q^{24} + 4 q^{25} + 16 q^{29} + 4 q^{30} + 32 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{41} - 4 q^{45} + 8 q^{46} - 4 q^{50} + 8 q^{51} - 8 q^{54} - 40 q^{59} + 24 q^{61} - 8 q^{64} + 28 q^{65} - 8 q^{69} - 40 q^{71} + 16 q^{74} + 4 q^{75} + 24 q^{76} + 16 q^{79} + 4 q^{80} + 8 q^{81} + 28 q^{85} + 8 q^{86} - 88 q^{89} - 24 q^{94} + 24 q^{95} + 8 q^{96}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^5 + 8 * q^6 - 8 * q^9 + 8 * q^16 - 24 * q^19 - 4 * q^20 - 8 * q^24 + 4 * q^25 + 16 * q^29 + 4 * q^30 + 32 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^41 - 4 * q^45 + 8 * q^46 - 4 * q^50 + 8 * q^51 - 8 * q^54 - 40 * q^59 + 24 * q^61 - 8 * q^64 + 28 * q^65 - 8 * q^69 - 40 * q^71 + 16 * q^74 + 4 * q^75 + 24 * q^76 + 16 * q^79 + 4 * q^80 + 8 * q^81 + 28 * q^85 + 8 * q^86 - 88 * q^89 - 24 * q^94 + 24 * q^95 + 8 * q^96

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
$5$	1.63280	−	1.52773i	0.730213	−	0.683220i
$5$	1.63280	−	1.52773i	0.730213	−	0.683220i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	1.52773	+	1.63280i	0.483109	+	0.516338i
$11$	4.46967			1.34766			0.673828	−	0.738889i	$-0.264649\pi$
$11$	4.46967			1.34766			0.673828	+	0.738889i	$0.264649\pi$
$12$			1.00000i			0.288675i
$13$			5.88388i			1.63189i	0.578126	+	0.815947i	$0.303784\pi$
$13$			5.88388i			1.63189i	−0.578126	+	0.815947i	$0.696216\pi$
$14$		0			0
$15$	−1.52773	−	1.63280i	−0.394457	−	0.421588i
$16$	1.00000			0.250000
$17$			7.73528i			1.87608i	0.346527	+	0.938040i	$0.387361\pi$
$17$			7.73528i			1.87608i	−0.346527	+	0.938040i	$0.612639\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−6.61827			−1.51834			−0.759168	−	0.650895i	$-0.774394\pi$
$19$	−6.61827			−1.51834			−0.759168	+	0.650895i	$0.774394\pi$
$20$	−1.63280	+	1.52773i	−0.365106	+	0.341610i
$21$		0			0
$22$			4.46967i			0.952936i
$23$			2.61827i			0.545947i	0.962022	+	0.272974i	$0.0880071\pi$
$23$			2.61827i			0.545947i	−0.962022	+	0.272974i	$0.911993\pi$
$24$	−1.00000			−0.204124
$25$	0.332104	−	4.98896i	0.0664208	−	0.997792i
$26$	−5.88388			−1.15392
$27$			1.00000i			0.192450i
$28$		0			0
$29$	8.17246			1.51759			0.758794	−	0.651331i	$-0.225789\pi$
$29$	8.17246			1.51759			0.758794	+	0.651331i	$0.225789\pi$
$30$	1.63280	−	1.52773i	0.298108	−	0.278923i
$31$	8.46967			1.52120			0.760598	−	0.649223i	$-0.224906\pi$
$31$	8.46967			1.52120			0.760598	+	0.649223i	$0.224906\pi$
$32$			1.00000i			0.176777i
$33$		−	4.46967i		−	0.778069i
$34$	−7.73528			−1.32659
$35$		0			0
$36$	1.00000			0.166667
$37$		−	3.18719i		−	0.523970i	−0.965072	−	0.261985i	$-0.915623\pi$
$37$		−	3.18719i		−	0.523970i	0.965072	−	0.261985i	$-0.0843772\pi$
$38$		−	6.61827i		−	1.07363i
$39$	5.88388			0.942175
$40$	−1.52773	−	1.63280i	−0.241555	−	0.258169i
$41$	3.56282			0.556419			0.278209	−	0.960520i	$-0.410259\pi$
$41$	3.56282			0.556419			0.278209	+	0.960520i	$0.410259\pi$
$42$		0			0
$43$			1.43108i			0.218238i	0.994029	+	0.109119i	$0.0348029\pi$
$43$			1.43108i			0.218238i	−0.994029	+	0.109119i	$0.965197\pi$
$44$	−4.46967			−0.673828
$45$	−1.63280	+	1.52773i	−0.243404	+	0.227740i
$46$	−2.61827			−0.386043
$47$		−	6.79073i		−	0.990530i	−0.868742	−	0.495265i	$-0.835071\pi$
$47$		−	6.79073i		−	0.990530i	0.868742	−	0.495265i	$-0.164929\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$	4.98896	+	0.332104i	0.705545	+	0.0469666i
$51$	7.73528			1.08316
$52$		−	5.88388i		−	0.815947i
$53$		−	1.38173i		−	0.189795i	−0.995487	−	0.0948976i	$-0.969748\pi$
$53$		−	1.38173i		−	0.189795i	0.995487	−	0.0948976i	$-0.0302524\pi$
$54$	−1.00000			−0.136083
$55$	7.29809	−	6.82843i	0.984075	−	0.920745i
$56$		0			0
$57$			6.61827i			0.876611i
$58$			8.17246i			1.07310i
$59$	−4.66421			−0.607228			−0.303614	−	0.952795i	$-0.598193\pi$
$59$	−4.66421			−0.607228			−0.303614	+	0.952795i	$0.598193\pi$
$60$	1.52773	+	1.63280i	0.197229	+	0.210794i
$61$	9.79683			1.25436			0.627178	−	0.778876i	$-0.284210\pi$
$61$	9.79683			1.25436			0.627178	+	0.778876i	$0.284210\pi$
$62$			8.46967i			1.07565i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	8.98896	+	9.60723i	1.11494	+	1.19163i
$66$	4.46967			0.550178
$67$		−	1.85140i		−	0.226184i	−0.993585	−	0.113092i	$-0.963925\pi$
$67$		−	1.85140i		−	0.226184i	0.993585	−	0.113092i	$-0.0360755\pi$
$68$		−	7.73528i		−	0.938040i
$69$	2.61827			0.315203
$70$		0			0
$71$	2.02386			0.240187			0.120094	−	0.992763i	$-0.461680\pi$
$71$	2.02386			0.240187			0.120094	+	0.992763i	$0.461680\pi$
$72$			1.00000i			0.117851i
$73$			4.01687i			0.470139i	0.971979	+	0.235069i	$0.0755318\pi$
$73$			4.01687i			0.470139i	−0.971979	+	0.235069i	$0.924468\pi$
$74$	3.18719			0.370503
$75$	−4.98896	−	0.332104i	−0.576075	−	0.0383481i
$76$	6.61827			0.759168
$77$		0			0
$78$			5.88388i			0.666218i
$79$	6.98527			0.785904			0.392952	−	0.919559i	$-0.371454\pi$
$79$	6.98527			0.785904			0.392952	+	0.919559i	$0.371454\pi$
$80$	1.63280	−	1.52773i	0.182553	−	0.170805i
$81$	1.00000			0.111111
$82$			3.56282i			0.393447i
$83$			5.35965i			0.588298i	0.955760	+	0.294149i	$0.0950361\pi$
$83$			5.35965i			0.588298i	−0.955760	+	0.294149i	$0.904964\pi$
$84$		0			0
$85$	11.8174	+	12.6302i	1.28178	+	1.36994i
$86$	−1.43108			−0.154318
$87$		−	8.17246i		−	0.876180i
$88$		−	4.46967i		−	0.476468i
$89$	−14.3912			−1.52547			−0.762734	−	0.646712i	$-0.776144\pi$
$89$	−14.3912			−1.52547			−0.762734	+	0.646712i	$0.776144\pi$
$90$	−1.52773	−	1.63280i	−0.161036	−	0.172113i
$91$		0			0
$92$		−	2.61827i		−	0.272974i
$93$		−	8.46967i		−	0.878263i
$94$	6.79073			0.700410
$95$	−10.8063	+	10.1109i	−1.10871	+	1.03736i
$96$	1.00000			0.102062
$97$			7.71966i			0.783813i	0.920005	+	0.391906i	$0.128184\pi$
$97$			7.71966i			0.783813i	−0.920005	+	0.391906i	$0.871816\pi$
$98$		0			0
$99$	−4.46967			−0.449218
$100$	−0.332104	+	4.98896i	−0.0332104	+	0.498896i
$101$	−13.3544			−1.32882			−0.664408	−	0.747370i	$-0.731316\pi$
$101$	−13.3544			−1.32882			−0.664408	+	0.747370i	$0.731316\pi$
$102$			7.73528i			0.765906i
$103$		−	9.35965i		−	0.922233i	−0.887339	−	0.461117i	$-0.847449\pi$
$103$		−	9.35965i		−	0.922233i	0.887339	−	0.461117i	$-0.152551\pi$
$104$	5.88388			0.576962
$105$		0			0
$106$	1.38173			0.134205
$107$		−	11.0165i		−	1.06501i	−0.846428	−	0.532503i	$-0.821252\pi$
$107$		−	11.0165i		−	1.06501i	0.846428	−	0.532503i	$-0.178748\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	4.69544			0.449741			0.224871	−	0.974389i	$-0.427804\pi$
$109$	4.69544			0.449741			0.224871	+	0.974389i	$0.427804\pi$
$110$	6.82843	+	7.29809i	0.651065	+	0.695846i
$111$	−3.18719			−0.302514
$112$		0			0
$113$		−	12.5723i		−	1.18271i	−0.806413	−	0.591353i	$-0.798594\pi$
$113$		−	12.5723i		−	1.18271i	0.806413	−	0.591353i	$-0.201406\pi$
$114$	−6.61827			−0.619858
$115$	4.00000	+	4.27512i	0.373002	+	0.398657i
$116$	−8.17246			−0.758794
$117$		−	5.88388i		−	0.543965i
$118$		−	4.66421i		−	0.429375i
$119$		0			0
$120$	−1.63280	+	1.52773i	−0.149054	+	0.139462i
$121$	8.97792			0.816174
$122$			9.79683i			0.886963i
$123$		−	3.56282i		−	0.321248i
$124$	−8.46967			−0.760598
$125$	−7.07950	−	8.65336i	−0.633210	−	0.773980i
$126$		0			0
$127$			6.59619i			0.585317i	0.956217	+	0.292658i	$0.0945399\pi$
$127$			6.59619i			0.585317i	−0.956217	+	0.292658i	$0.905460\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.43108			0.126000
$130$	−9.60723	+	8.98896i	−0.842610	+	0.788384i
$131$	−2.32106			−0.202792			−0.101396	−	0.994846i	$-0.532331\pi$
$131$	−2.32106			−0.202792			−0.101396	+	0.994846i	$0.532331\pi$
$132$			4.46967i			0.389035i
$133$		0			0
$134$	1.85140			0.159936
$135$	1.52773	+	1.63280i	0.131486	+	0.140529i
$136$	7.73528			0.663294
$137$			14.2751i			1.21961i	0.792553	+	0.609803i	$0.208751\pi$
$137$			14.2751i			1.21961i	−0.792553	+	0.609803i	$0.791249\pi$
$138$			2.61827i			0.222882i
$139$	14.9632			1.26916			0.634581	−	0.772857i	$-0.281173\pi$
$139$	14.9632			1.26916			0.634581	+	0.772857i	$0.281173\pi$
$140$		0			0
$141$	−6.79073			−0.571883
$142$			2.02386i			0.169838i
$143$			26.2990i			2.19923i
$144$	−1.00000			−0.0833333
$145$	13.3440	−	12.4853i	1.10816	−	1.03685i
$146$	−4.01687			−0.332438
$147$		0			0
$148$			3.18719i			0.261985i
$149$	−11.1651			−0.914681			−0.457341	−	0.889292i	$-0.651198\pi$
$149$	−11.1651			−0.914681			−0.457341	+	0.889292i	$0.651198\pi$
$150$	0.332104	−	4.98896i	0.0271162	−	0.407347i
$151$	0.664208			0.0540525			0.0270263	−	0.999635i	$-0.491396\pi$
$151$	0.664208			0.0540525			0.0270263	+	0.999635i	$0.491396\pi$
$152$			6.61827i			0.536813i
$153$		−	7.73528i		−	0.625360i
$154$		0			0
$155$	13.8293	−	12.9393i	1.11080	−	1.03931i
$156$	−5.88388			−0.471087
$157$			8.08184i			0.645001i	0.946569	+	0.322500i	$0.104523\pi$
$157$			8.08184i			0.645001i	−0.946569	+	0.322500i	$0.895477\pi$
$158$			6.98527i			0.555718i
$159$	−1.38173			−0.109578
$160$	1.52773	+	1.63280i	0.120777	+	0.129085i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$		−	0.836668i		−	0.0655329i	−0.999463	−	0.0327664i	$-0.989568\pi$
$163$		−	0.836668i		−	0.0655329i	0.999463	−	0.0327664i	$-0.0104317\pi$
$164$	−3.56282			−0.278209
$165$	−6.82843	−	7.29809i	−0.531592	−	0.568156i
$166$	−5.35965			−0.415989
$167$		−	2.66762i		−	0.206427i	−0.994659	−	0.103213i	$-0.967088\pi$
$167$		−	2.66762i		−	0.206427i	0.994659	−	0.103213i	$-0.0329125\pi$
$168$		0			0
$169$	−21.6200			−1.66308
$170$	−12.6302	+	11.8174i	−0.968692	+	0.906352i
$171$	6.61827			0.506112
$172$		−	1.43108i		−	0.109119i
$173$			0.647340i			0.0492164i	0.999697	+	0.0246082i	$0.00783382\pi$
$173$			0.647340i			0.0492164i	−0.999697	+	0.0246082i	$0.992166\pi$
$174$	8.17246			0.619553
$175$		0			0
$176$	4.46967			0.336914
$177$			4.66421i			0.350583i
$178$		−	14.3912i		−	1.07867i
$179$	25.7374			1.92371			0.961853	−	0.273566i	$-0.0882033\pi$
$179$	25.7374			1.92371			0.961853	+	0.273566i	$0.0882033\pi$
$180$	1.63280	−	1.52773i	0.121702	−	0.113870i
$181$	7.42245			0.551707			0.275853	−	0.961200i	$-0.411040\pi$
$181$	7.42245			0.551707			0.275853	+	0.961200i	$0.411040\pi$
$182$		0			0
$183$		−	9.79683i		−	0.724203i
$184$	2.61827			0.193021
$185$	−4.86915	−	5.20406i	−0.357987	−	0.382610i
$186$	8.46967			0.621026
$187$			34.5741i			2.52831i
$188$			6.79073i			0.495265i
$189$		0			0
$190$	−10.1109	−	10.8063i	−0.733522	−	0.783975i
$191$	−1.08452			−0.0784733			−0.0392367	−	0.999230i	$-0.512493\pi$
$191$	−1.08452			−0.0784733			−0.0392367	+	0.999230i	$0.512493\pi$
$192$			1.00000i			0.0721688i
$193$		−	8.93933i		−	0.643467i	−0.946830	−	0.321734i	$-0.895734\pi$
$193$		−	8.93933i		−	0.643467i	0.946830	−	0.321734i	$-0.104266\pi$
$194$	−7.71966			−0.554239
$195$	9.60723	−	8.98896i	0.687988	−	0.643713i
$196$		0			0
$197$			7.45890i			0.531425i	0.964052	+	0.265712i	$0.0856071\pi$
$197$			7.45890i			0.531425i	−0.964052	+	0.265712i	$0.914393\pi$
$198$		−	4.46967i		−	0.317645i
$199$	−25.8293			−1.83099			−0.915496	−	0.402328i	$-0.868201\pi$
$199$	−25.8293			−1.83099			−0.915496	+	0.402328i	$0.868201\pi$
$200$	−4.98896	−	0.332104i	−0.352773	−	0.0234833i
$201$	−1.85140			−0.130587
$202$		−	13.3544i		−	0.939615i
$203$		0			0
$204$	−7.73528			−0.541578
$205$	5.81739	−	5.44301i	0.406304	−	0.380156i
$206$	9.35965			0.652118
$207$		−	2.61827i		−	0.181982i
$208$			5.88388i			0.407974i
$209$	−29.5815			−2.04619
$210$		0			0
$211$	5.53375			0.380959			0.190479	−	0.981691i	$-0.438996\pi$
$211$	5.53375			0.380959			0.190479	+	0.981691i	$0.438996\pi$
$212$			1.38173i			0.0948976i
$213$		−	2.02386i		−	0.138672i
$214$	11.0165			0.753073
$215$	2.18630	+	2.33668i	0.149105	+	0.159360i
$216$	1.00000			0.0680414
$217$		0			0
$218$			4.69544i			0.318015i
$219$	4.01687			0.271435
$220$	−7.29809	+	6.82843i	−0.492037	+	0.460372i
$221$	−45.5134			−3.06157
$222$		−	3.18719i		−	0.213910i
$223$		−	3.28248i		−	0.219811i	−0.993942	−	0.109906i	$-0.964945\pi$
$223$		−	3.28248i		−	0.219811i	0.993942	−	0.109906i	$-0.0350548\pi$
$224$		0			0
$225$	−0.332104	+	4.98896i	−0.0221403	+	0.332597i
$226$	12.5723			0.836299
$227$			4.42031i			0.293387i	0.989182	+	0.146693i	$0.0468630\pi$
$227$			4.42031i			0.293387i	−0.989182	+	0.146693i	$0.953137\pi$
$228$		−	6.61827i		−	0.438306i
$229$	7.97270			0.526851			0.263426	−	0.964680i	$-0.415148\pi$
$229$	7.97270			0.526851			0.263426	+	0.964680i	$0.415148\pi$
$230$	−4.27512	+	4.00000i	−0.281893	+	0.263752i
$231$		0			0
$232$		−	8.17246i		−	0.536548i
$233$			17.9558i			1.17633i	0.808742	+	0.588163i	$0.200149\pi$
$233$			17.9558i			1.17633i	−0.808742	+	0.588163i	$0.799851\pi$
$234$	5.88388			0.384641
$235$	−10.3744	−	11.0879i	−0.676750	−	0.723297i
$236$	4.66421			0.303614
$237$		−	6.98527i		−	0.453742i
$238$		0			0
$239$	−5.41296			−0.350135			−0.175068	−	0.984556i	$-0.556014\pi$
$239$	−5.41296			−0.350135			−0.175068	+	0.984556i	$0.556014\pi$
$240$	−1.52773	−	1.63280i	−0.0986143	−	0.105397i
$241$	−4.69669			−0.302541			−0.151270	−	0.988492i	$-0.548336\pi$
$241$	−4.69669			−0.302541			−0.151270	+	0.988492i	$0.548336\pi$
$242$			8.97792i			0.577122i
$243$		−	1.00000i		−	0.0641500i
$244$	−9.79683			−0.627178
$245$		0			0
$246$	3.56282			0.227157
$247$		−	38.9411i		−	2.47776i
$248$		−	8.46967i		−	0.537824i
$249$	5.35965			0.339654
$250$	8.65336	−	7.07950i	0.547287	−	0.447747i
$251$	7.73402			0.488167			0.244084	−	0.969754i	$-0.421513\pi$
$251$	7.73402			0.488167			0.244084	+	0.969754i	$0.421513\pi$
$252$		0			0
$253$			11.7028i			0.735748i
$254$	−6.59619			−0.413882
$255$	12.6302	−	11.8174i	0.790934	−	0.740033i
$256$	1.00000			0.0625000
$257$		−	1.34442i		−	0.0838626i	−0.999120	−	0.0419313i	$-0.986649\pi$
$257$		−	1.34442i		−	0.0838626i	0.999120	−	0.0419313i	$-0.0133511\pi$
$258$			1.43108i			0.0890953i
$259$		0			0
$260$	−8.98896	−	9.60723i	−0.557472	−	0.595815i
$261$	−8.17246			−0.505863
$262$		−	2.32106i		−	0.143396i
$263$		−	4.36700i		−	0.269281i	−0.990895	−	0.134640i	$-0.957012\pi$
$263$		−	4.36700i		−	0.269281i	0.990895	−	0.134640i	$-0.0429879\pi$
$264$	−4.46967			−0.275089
$265$	−2.11091	−	2.25610i	−0.129672	−	0.138591i
$266$		0			0
$267$			14.3912i			0.880730i
$268$			1.85140i			0.113092i
$269$	−23.0671			−1.40643			−0.703213	−	0.710979i	$-0.748252\pi$
$269$	−23.0671			−1.40643			−0.703213	+	0.710979i	$0.748252\pi$
$270$	−1.63280	+	1.52773i	−0.0993693	+	0.0929745i
$271$	14.7209			0.894233			0.447117	−	0.894476i	$-0.352451\pi$
$271$	14.7209			0.894233			0.447117	+	0.894476i	$0.352451\pi$
$272$			7.73528i			0.469020i
$273$		0			0
$274$	−14.2751			−0.862392
$275$	1.48440	−	22.2990i	0.0895124	−	1.34468i
$276$	−2.61827			−0.157601
$277$			3.21104i			0.192933i	0.995336	+	0.0964665i	$0.0307541\pi$
$277$			3.21104i			0.192933i	−0.995336	+	0.0964665i	$0.969246\pi$
$278$			14.9632i			0.897432i
$279$	−8.46967			−0.507066
$280$		0			0
$281$	−7.72488			−0.460827			−0.230414	−	0.973093i	$-0.574008\pi$
$281$	−7.72488			−0.460827			−0.230414	+	0.973093i	$0.574008\pi$
$282$		−	6.79073i		−	0.404382i
$283$		−	29.5594i		−	1.75712i	−0.477630	−	0.878561i	$-0.658504\pi$
$283$		−	29.5594i		−	1.75712i	0.477630	−	0.878561i	$-0.341496\pi$
$284$	−2.02386			−0.120094
$285$	10.1109	+	10.8063i	0.598918	+	0.640113i
$286$	−26.2990			−1.55509
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−42.8345			−2.51968
$290$	12.4853	+	13.3440i	0.733161	+	0.783589i
$291$	7.71966			0.452535
$292$		−	4.01687i		−	0.235069i
$293$			1.17679i			0.0687487i	0.999409	+	0.0343743i	$0.0109438\pi$
$293$			1.17679i			0.0687487i	−0.999409	+	0.0343743i	$0.989056\pi$
$294$		0			0
$295$	−7.61574	+	7.12563i	−0.443406	+	0.414870i
$296$	−3.18719			−0.185252
$297$			4.46967i			0.259356i
$298$		−	11.1651i		−	0.646777i
$299$	−15.4056			−0.890928
$300$	4.98896	+	0.332104i	0.288038	+	0.0191740i
$301$		0			0
$302$			0.664208i			0.0382209i
$303$			13.3544i			0.767192i
$304$	−6.61827			−0.379584
$305$	15.9963	−	14.9669i	0.915946	−	0.857001i
$306$	7.73528			0.442196
$307$		−	20.3761i		−	1.16293i	−0.813572	−	0.581464i	$-0.802480\pi$
$307$		−	20.3761i		−	1.16293i	0.813572	−	0.581464i	$-0.197520\pi$
$308$		0			0
$309$	−9.35965			−0.532452
$310$	12.9393	+	13.8293i	0.734905	+	0.785452i
$311$	−18.8934			−1.07135			−0.535673	−	0.844425i	$-0.679942\pi$
$311$	−18.8934			−1.07135			−0.535673	+	0.844425i	$0.679942\pi$
$312$		−	5.88388i		−	0.333109i
$313$			16.4849i			0.931781i	0.884842	+	0.465891i	$0.154266\pi$
$313$			16.4849i			0.931781i	−0.884842	+	0.465891i	$0.845734\pi$
$314$	−8.08184			−0.456084
$315$		0			0
$316$	−6.98527			−0.392952
$317$			10.3211i			0.579689i	0.957074	+	0.289844i	$0.0936035\pi$
$317$			10.3211i			0.579689i	−0.957074	+	0.289844i	$0.906396\pi$
$318$		−	1.38173i		−	0.0774836i
$319$	36.5282			2.04518
$320$	−1.63280	+	1.52773i	−0.0912766	+	0.0854025i
$321$	−11.0165			−0.614881
$322$		0			0
$323$		−	51.1941i		−	2.84852i
$324$	−1.00000			−0.0555556
$325$	29.3544	+	1.95406i	1.62829	+	0.108392i
$326$	0.836668			0.0463387
$327$		−	4.69544i		−	0.259658i
$328$		−	3.56282i		−	0.196724i
$329$		0			0
$330$	7.29809	−	6.82843i	0.401747	−	0.375893i
$331$	−19.1906			−1.05481			−0.527405	−	0.849614i	$-0.676835\pi$
$331$	−19.1906			−1.05481			−0.527405	+	0.849614i	$0.676835\pi$
$332$		−	5.35965i		−	0.294149i
$333$			3.18719i			0.174657i
$334$	2.66762			0.145966
$335$	−2.82843	−	3.02297i	−0.154533	−	0.165162i
$336$		0			0
$337$		−	27.6035i		−	1.50366i	−0.659357	−	0.751830i	$-0.729171\pi$
$337$		−	27.6035i		−	1.50366i	0.659357	−	0.751830i	$-0.270829\pi$
$338$		−	21.6200i		−	1.17598i
$339$	−12.5723			−0.682835
$340$	−11.8174	−	12.6302i	−0.640888	−	0.684969i
$341$	37.8566			2.05005
$342$			6.61827i			0.357875i
$343$		0			0
$344$	1.43108			0.0771588
$345$	4.27512	−	4.00000i	0.230165	−	0.215353i
$346$	−0.647340			−0.0348012
$347$		−	20.3761i		−	1.09385i	−0.837182	−	0.546924i	$-0.815798\pi$
$347$		−	20.3761i		−	1.09385i	0.837182	−	0.546924i	$-0.184202\pi$
$348$			8.17246i			0.438090i
$349$	17.8281			0.954314			0.477157	−	0.878818i	$-0.341667\pi$
$349$	17.8281			0.954314			0.477157	+	0.878818i	$0.341667\pi$
$350$		0			0
$351$	−5.88388			−0.314058
$352$			4.46967i			0.238234i
$353$			3.51347i			0.187003i	0.995619	+	0.0935014i	$0.0298060\pi$
$353$			3.51347i			0.187003i	−0.995619	+	0.0935014i	$0.970194\pi$
$354$	−4.66421			−0.247900
$355$	3.30456	−	3.09190i	0.175388	−	0.164101i
$356$	14.3912			0.762734
$357$		0			0
$358$			25.7374i			1.36027i
$359$	2.19796			0.116004			0.0580018	−	0.998316i	$-0.481527\pi$
$359$	2.19796			0.116004			0.0580018	+	0.998316i	$0.481527\pi$
$360$	1.52773	+	1.63280i	0.0805182	+	0.0860564i
$361$	24.8015			1.30534
$362$			7.42245i			0.390116i
$363$		−	8.97792i		−	0.471218i
$364$		0			0
$365$	6.13668	+	6.55876i	0.321208	+	0.343301i
$366$	9.79683			0.512089
$367$		−	28.7721i		−	1.50189i	−0.660365	−	0.750945i	$-0.729598\pi$
$367$		−	28.7721i		−	1.50189i	0.660365	−	0.750945i	$-0.270402\pi$
$368$			2.61827i			0.136487i
$369$	−3.56282			−0.185473
$370$	5.20406	−	4.86915i	0.270546	−	0.253135i
$371$		0			0
$372$			8.46967i			0.439132i
$373$			14.5689i			0.754350i	0.926142	+	0.377175i	$0.123104\pi$
$373$			14.5689i			0.754350i	−0.926142	+	0.377175i	$0.876896\pi$
$374$	−34.5741			−1.78778
$375$	−8.65336	+	7.07950i	−0.446858	+	0.365584i
$376$	−6.79073			−0.350205
$377$			48.0858i			2.47654i
$378$		0			0
$379$	30.7868			1.58141			0.790705	−	0.612197i	$-0.209714\pi$
$379$	30.7868			1.58141			0.790705	+	0.612197i	$0.209714\pi$
$380$	10.8063	−	10.1109i	0.554354	−	0.518679i
$381$	6.59619			0.337933
$382$		−	1.08452i		−	0.0554890i
$383$			23.3410i			1.19267i	0.802736	+	0.596334i	$0.203377\pi$
$383$			23.3410i			1.19267i	−0.802736	+	0.596334i	$0.796623\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	8.93933			0.455000
$387$		−	1.43108i		−	0.0727460i
$388$		−	7.71966i		−	0.391906i
$389$	1.21842			0.0617762			0.0308881	−	0.999523i	$-0.490166\pi$
$389$	1.21842			0.0617762			0.0308881	+	0.999523i	$0.490166\pi$
$390$	8.98896	+	9.60723i	0.455174	+	0.486481i
$391$	−20.2530			−1.02424
$392$		0			0
$393$			2.32106i			0.117082i
$394$	−7.45890			−0.375774
$395$	11.4056	−	10.6716i	0.573877	−	0.536946i
$396$	4.46967			0.224609
$397$		−	8.40595i		−	0.421883i	−0.977499	−	0.210941i	$-0.932347\pi$
$397$		−	8.40595i		−	0.421883i	0.977499	−	0.210941i	$-0.0676529\pi$
$398$		−	25.8293i		−	1.29471i
$399$		0			0
$400$	0.332104	−	4.98896i	0.0166052	−	0.249448i
$401$	−0.664208			−0.0331690			−0.0165845	−	0.999862i	$-0.505279\pi$
$401$	−0.664208			−0.0331690			−0.0165845	+	0.999862i	$0.505279\pi$
$402$		−	1.85140i		−	0.0923393i
$403$			49.8345i			2.48243i
$404$	13.3544			0.664408
$405$	1.63280	−	1.52773i	0.0811347	−	0.0759133i
$406$		0			0
$407$		−	14.2457i		−	0.706131i
$408$		−	7.73528i		−	0.382953i
$409$	7.38476			0.365153			0.182576	−	0.983192i	$-0.441556\pi$
$409$	7.38476			0.365153			0.182576	+	0.983192i	$0.441556\pi$
$410$	5.44301	+	5.81739i	0.268811	+	0.287300i
$411$	14.2751			0.704140
$412$			9.35965i			0.461117i
$413$		0			0
$414$	2.61827			0.128681
$415$	8.18807	+	8.75126i	0.401937	+	0.429582i
$416$	−5.88388			−0.288481
$417$		−	14.9632i		−	0.732750i
$418$		−	29.5815i		−	1.44688i
$419$	−18.6274			−0.910009			−0.455004	−	0.890489i	$-0.650362\pi$
$419$	−18.6274			−0.910009			−0.455004	+	0.890489i	$0.650362\pi$
$420$		0			0
$421$	−13.5043			−0.658159			−0.329079	−	0.944302i	$-0.606738\pi$
$421$	−13.5043			−0.658159			−0.329079	+	0.944302i	$0.606738\pi$
$422$			5.53375i			0.269379i
$423$			6.79073i			0.330177i
$424$	−1.38173			−0.0671027
$425$	38.5910	+	2.56892i	1.87194	+	0.124611i
$426$	2.02386			0.0980561
$427$		0			0
$428$			11.0165i			0.532503i
$429$	26.2990			1.26973
$430$	−2.33668	+	2.18630i	−0.112685	+	0.105433i
$431$	−31.6807			−1.52601			−0.763003	−	0.646395i	$-0.776276\pi$
$431$	−31.6807			−1.52601			−0.763003	+	0.646395i	$0.776276\pi$
$432$			1.00000i			0.0481125i
$433$			25.3184i			1.21672i	0.793660	+	0.608362i	$0.208173\pi$
$433$			25.3184i			1.21672i	−0.793660	+	0.608362i	$0.791827\pi$
$434$		0			0
$435$	−12.4853	−	13.3440i	−0.598623	−	0.639797i
$436$	−4.69544			−0.224871
$437$		−	17.3284i		−	0.828931i
$438$			4.01687i			0.191933i
$439$	−32.8146			−1.56615			−0.783077	−	0.621924i	$-0.786351\pi$
$439$	−32.8146			−1.56615			−0.783077	+	0.621924i	$0.786351\pi$
$440$	−6.82843	−	7.29809i	−0.325532	−	0.347923i
$441$		0			0
$442$		−	45.5134i		−	2.16485i
$443$		−	16.6421i		−	0.790691i	−0.918532	−	0.395346i	$-0.870625\pi$
$443$		−	16.6421i		−	0.790691i	0.918532	−	0.395346i	$-0.129375\pi$
$444$	3.18719			0.151257
$445$	−23.4981	+	21.9859i	−1.11392	+	1.04223i
$446$	3.28248			0.155430
$447$			11.1651i			0.528091i
$448$		0			0
$449$	−20.1759			−0.952158			−0.476079	−	0.879402i	$-0.657942\pi$
$449$	−20.1759			−0.952158			−0.476079	+	0.879402i	$0.657942\pi$
$450$	−4.98896	−	0.332104i	−0.235182	−	0.0156555i
$451$	15.9246			0.749860
$452$			12.5723i			0.591353i
$453$		−	0.664208i		−	0.0312072i
$454$	−4.42031			−0.207456
$455$		0			0
$456$	6.61827			0.309929
$457$		−	35.4124i		−	1.65652i	−0.560342	−	0.828261i	$-0.689330\pi$
$457$		−	35.4124i		−	1.65652i	0.560342	−	0.828261i	$-0.310670\pi$
$458$			7.97270i			0.372540i
$459$	−7.73528			−0.361052
$460$	−4.00000	−	4.27512i	−0.186501	−	0.199329i
$461$	−12.5940			−0.586562			−0.293281	−	0.956026i	$-0.594747\pi$
$461$	−12.5940			−0.586562			−0.293281	+	0.956026i	$0.594747\pi$
$462$		0			0
$463$		−	32.5061i		−	1.51069i	−0.655330	−	0.755343i	$-0.727470\pi$
$463$		−	32.5061i		−	1.51069i	0.655330	−	0.755343i	$-0.272530\pi$
$464$	8.17246			0.379397
$465$	−12.9393	−	13.8293i	−0.600047	−	0.641319i
$466$	−17.9558			−0.831788
$467$			9.20531i			0.425971i	0.977055	+	0.212985i	$0.0683187\pi$
$467$			9.20531i			0.425971i	−0.977055	+	0.212985i	$0.931681\pi$
$468$			5.88388i			0.271982i
$469$		0			0
$470$	11.0879	−	10.3744i	0.511448	−	0.478534i
$471$	8.08184			0.372391
$472$			4.66421i			0.214688i
$473$			6.39646i			0.294109i
$474$	6.98527			0.320844
$475$	−2.19796	+	33.0183i	−0.100849	+	1.51498i
$476$		0			0
$477$			1.38173i			0.0632651i
$478$		−	5.41296i		−	0.247583i
$479$	39.4914			1.80441			0.902203	−	0.431312i	$-0.141949\pi$
$479$	39.4914			1.80441			0.902203	+	0.431312i	$0.141949\pi$
$480$	1.63280	−	1.52773i	0.0745270	−	0.0697308i
$481$	18.7530			0.855065
$482$		−	4.69669i		−	0.213928i
$483$		0			0
$484$	−8.97792			−0.408087
$485$	11.7935	+	12.6047i	0.535517	+	0.572350i
$486$	1.00000			0.0453609
$487$		−	29.2678i		−	1.32625i	−0.748509	−	0.663125i	$-0.769230\pi$
$487$		−	29.2678i		−	1.32625i	0.748509	−	0.663125i	$-0.230770\pi$
$488$		−	9.79683i		−	0.443482i
$489$	−0.836668			−0.0378354
$490$		0			0
$491$	15.3631			0.693325			0.346663	−	0.937990i	$-0.387315\pi$
$491$	15.3631			0.693325			0.346663	+	0.937990i	$0.387315\pi$
$492$			3.56282i			0.160624i
$493$			63.2162i			2.84712i
$494$	38.9411			1.75204
$495$	−7.29809	+	6.82843i	−0.328025	+	0.306915i
$496$	8.46967			0.380299
$497$		0			0
$498$			5.35965i			0.240172i
$499$	−20.5502			−0.919955			−0.459978	−	0.887930i	$-0.652143\pi$
$499$	−20.5502			−0.919955			−0.459978	+	0.887930i	$0.652143\pi$
$500$	7.07950	+	8.65336i	0.316605	+	0.386990i
$501$	−2.66762			−0.119181
$502$			7.73402i			0.345186i
$503$		−	20.4788i		−	0.913105i	−0.889696	−	0.456553i	$-0.849084\pi$
$503$		−	20.4788i		−	0.913105i	0.889696	−	0.456553i	$-0.150916\pi$
$504$		0			0
$505$	−21.8052	+	20.4019i	−0.970318	+	0.907873i
$506$	−11.7028			−0.520253
$507$			21.6200i			0.960180i
$508$		−	6.59619i		−	0.292658i
$509$	−12.0702			−0.535001			−0.267501	−	0.963558i	$-0.586198\pi$
$509$	−12.0702			−0.535001			−0.267501	+	0.963558i	$0.586198\pi$
$510$	11.8174	+	12.6302i	0.523283	+	0.559275i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		−	6.61827i		−	0.292204i
$514$	1.34442			0.0592998
$515$	−14.2990	−	15.2825i	−0.630088	−	0.673426i
$516$	−1.43108			−0.0629999
$517$		−	30.3523i		−	1.33489i
$518$		0			0
$519$	0.647340			0.0284151
$520$	9.60723	−	8.98896i	0.421305	−	0.394192i
$521$	14.7049			0.644235			0.322117	−	0.946700i	$-0.395605\pi$
$521$	14.7049			0.644235			0.322117	+	0.946700i	$0.395605\pi$
$522$		−	8.17246i		−	0.357699i
$523$		−	6.44417i		−	0.281784i	−0.990025	−	0.140892i	$-0.955003\pi$
$523$		−	6.44417i		−	0.281784i	0.990025	−	0.140892i	$-0.0449970\pi$
$524$	2.32106			0.101396
$525$		0			0
$526$	4.36700			0.190410
$527$			65.5152i			2.85389i
$528$		−	4.46967i		−	0.194517i
$529$	16.1447			0.701942
$530$	2.25610	−	2.11091i	0.0979985	−	0.0916919i
$531$	4.66421			0.202409
$532$		0			0
$533$			20.9632i			0.908016i
$534$	−14.3912			−0.622770
$535$	−16.8302	−	17.9878i	−0.727633	−	0.777680i
$536$	−1.85140			−0.0799681
$537$		−	25.7374i		−	1.11065i
$538$		−	23.0671i		−	0.994494i
$539$		0			0
$540$	−1.52773	−	1.63280i	−0.0657429	−	0.0702647i
$541$	−11.5815			−0.497926			−0.248963	−	0.968513i	$-0.580090\pi$
$541$	−11.5815			−0.497926			−0.248963	+	0.968513i	$0.580090\pi$
$542$			14.7209i			0.632318i
$543$		−	7.42245i		−	0.318528i
$544$	−7.73528			−0.331647
$545$	7.66674	−	7.17335i	0.328407	−	0.307272i
$546$		0			0
$547$			19.2656i			0.823737i	0.911243	+	0.411868i	$0.135124\pi$
$547$			19.2656i			0.823737i	−0.911243	+	0.411868i	$0.864876\pi$
$548$		−	14.2751i		−	0.609803i
$549$	−9.79683			−0.418119
$550$	22.2990	+	1.48440i	0.950832	+	0.0632948i
$551$	−54.0875			−2.30421
$552$		−	2.61827i		−	0.111441i
$553$		0			0
$554$	−3.21104			−0.136424
$555$	−5.20406	+	4.86915i	−0.220900	+	0.206684i
$556$	−14.9632			−0.634581
$557$			21.0404i			0.891509i	0.895155	+	0.445754i	$0.147064\pi$
$557$			21.0404i			0.891509i	−0.895155	+	0.445754i	$0.852936\pi$
$558$		−	8.46967i		−	0.358550i
$559$	−8.42031			−0.356141
$560$		0			0
$561$	34.5741			1.45972
$562$		−	7.72488i		−	0.325854i
$563$		−	3.61092i		−	0.152182i	−0.997101	−	0.0760910i	$-0.975756\pi$
$563$		−	3.61092i		−	0.152182i	0.997101	−	0.0760910i	$-0.0242439\pi$
$564$	6.79073			0.285941
$565$	−19.2071	−	20.5282i	−0.808048	−	0.863626i
$566$	29.5594			1.24247
$567$		0			0
$568$		−	2.02386i		−	0.0849191i
$569$	−33.2145			−1.39242			−0.696211	−	0.717837i	$-0.745132\pi$
$569$	−33.2145			−1.39242			−0.696211	+	0.717837i	$0.745132\pi$
$570$	−10.8063	+	10.1109i	−0.452628	+	0.423499i
$571$	−32.1776			−1.34659			−0.673296	−	0.739373i	$-0.735122\pi$
$571$	−32.1776			−1.34659			−0.673296	+	0.739373i	$0.735122\pi$
$572$		−	26.2990i		−	1.09962i
$573$			1.08452i			0.0453066i
$574$		0			0
$575$	13.0624	+	0.869539i	0.544741	+	0.0362623i
$576$	1.00000			0.0416667
$577$		−	34.1902i		−	1.42336i	−0.702505	−	0.711679i	$-0.747935\pi$
$577$		−	34.1902i		−	1.42336i	0.702505	−	0.711679i	$-0.252065\pi$
$578$		−	42.8345i		−	1.78168i
$579$	−8.93933			−0.371506
$580$	−13.3440	+	12.4853i	−0.554081	+	0.518423i
$581$		0			0
$582$			7.71966i			0.319990i
$583$		−	6.17587i		−	0.255779i
$584$	4.01687			0.166219
$585$	−8.98896	−	9.60723i	−0.371648	−	0.397210i
$586$	−1.17679			−0.0486126
$587$		−	34.5962i		−	1.42794i	−0.700178	−	0.713969i	$-0.746896\pi$
$587$		−	34.5962i		−	1.42794i	0.700178	−	0.713969i	$-0.253104\pi$
$588$		0			0
$589$	−56.0545			−2.30969
$590$	−7.12563	−	7.61574i	−0.293358	−	0.313535i
$591$	7.45890			0.306818
$592$		−	3.18719i		−	0.130993i
$593$		−	33.0845i		−	1.35862i	−0.733853	−	0.679309i	$-0.762280\pi$
$593$		−	33.0845i		−	1.35862i	0.733853	−	0.679309i	$-0.237720\pi$
$594$	−4.46967			−0.183393
$595$		0			0
$596$	11.1651			0.457341
$597$			25.8293i			1.05712i
$598$		−	15.4056i		−	0.629981i
$599$	−6.07485			−0.248212			−0.124106	−	0.992269i	$-0.539606\pi$
$599$	−6.07485			−0.248212			−0.124106	+	0.992269i	$0.539606\pi$
$600$	−0.332104	+	4.98896i	−0.0135581	+	0.203673i
$601$	−11.7469			−0.479167			−0.239584	−	0.970876i	$-0.577011\pi$
$601$	−11.7469			−0.479167			−0.239584	+	0.970876i	$0.577011\pi$
$602$		0			0
$603$			1.85140i			0.0753947i
$604$	−0.664208			−0.0270263
$605$	14.6592	−	13.7158i	0.595981	−	0.557627i
$606$	−13.3544			−0.542487
$607$			45.8180i			1.85970i	0.367944	+	0.929848i	$0.380062\pi$
$607$			45.8180i			1.85970i	−0.367944	+	0.929848i	$0.619938\pi$
$608$		−	6.61827i		−	0.268406i
$609$		0			0
$610$	14.9669	+	15.9963i	0.605991	+	0.647672i
$611$	39.9558			1.61644
$612$			7.73528i			0.312680i
$613$			34.2514i			1.38340i	0.722184	+	0.691701i	$0.243138\pi$
$613$			34.2514i			1.38340i	−0.722184	+	0.691701i	$0.756862\pi$
$614$	20.3761			0.822314
$615$	−5.44301	−	5.81739i	−0.219483	−	0.234580i
$616$		0			0
$617$			38.8106i			1.56246i	0.624245	+	0.781228i	$0.285407\pi$
$617$			38.8106i			1.56246i	−0.624245	+	0.781228i	$0.714593\pi$
$618$		−	9.35965i		−	0.376500i
$619$	4.27512			0.171832			0.0859159	−	0.996302i	$-0.472618\pi$
$619$	4.27512			0.171832			0.0859159	+	0.996302i	$0.472618\pi$
$620$	−13.8293	+	12.9393i	−0.555399	+	0.519656i
$621$	−2.61827			−0.105068
$622$		−	18.8934i		−	0.757556i
$623$		0			0
$624$	5.88388			0.235544
$625$	−24.7794	−	3.31371i	−0.991177	−	0.132548i
$626$	−16.4849			−0.658869
$627$			29.5815i			1.18137i
$628$		−	8.08184i		−	0.322500i
$629$	24.6538			0.983011
$630$		0			0
$631$	36.8419			1.46665			0.733326	−	0.679878i	$-0.237967\pi$
$631$	36.8419			1.46665			0.733326	+	0.679878i	$0.237967\pi$
$632$		−	6.98527i		−	0.277859i
$633$		−	5.53375i		−	0.219947i
$634$	−10.3211			−0.409902
$635$	10.0772	+	10.7703i	0.399900	+	0.427406i
$636$	1.38173			0.0547892
$637$		0			0
$638$			36.5282i			1.44616i
$639$	−2.02386			−0.0800625
$640$	−1.52773	−	1.63280i	−0.0603887	−	0.0645423i
$641$	49.9043			1.97110			0.985551	−	0.169382i	$-0.0541770\pi$
$641$	49.9043			1.97110			0.985551	+	0.169382i	$0.0541770\pi$
$642$		−	11.0165i		−	0.434787i
$643$			29.0091i			1.14401i	0.820251	+	0.572004i	$0.193834\pi$
$643$			29.0091i			1.14401i	−0.820251	+	0.572004i	$0.806166\pi$
$644$		0			0
$645$	2.33668	−	2.18630i	0.0920066	−	0.0860855i
$646$	51.1941			2.01421
$647$		−	4.94329i		−	0.194341i	−0.995268	−	0.0971705i	$-0.969021\pi$
$647$		−	4.94329i		−	0.194341i	0.995268	−	0.0971705i	$-0.0309792\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−20.8475			−0.818334
$650$	−1.95406	+	29.3544i	−0.0766446	+	1.15138i
$651$		0			0
$652$			0.836668i			0.0327664i
$653$			9.40559i			0.368069i	0.982920	+	0.184035i	$0.0589158\pi$
$653$			9.40559i			0.368069i	−0.982920	+	0.184035i	$0.941084\pi$
$654$	4.69544			0.183606
$655$	−3.78984	+	3.54595i	−0.148081	+	0.138552i
$656$	3.56282			0.139105
$657$		−	4.01687i		−	0.156713i
$658$		0			0
$659$	−13.4090			−0.522340			−0.261170	−	0.965293i	$-0.584108\pi$
$659$	−13.4090			−0.522340			−0.261170	+	0.965293i	$0.584108\pi$
$660$	6.82843	+	7.29809i	0.265796	+	0.284078i
$661$	13.2509			0.515400			0.257700	−	0.966225i	$-0.417035\pi$
$661$	13.2509			0.515400			0.257700	+	0.966225i	$0.417035\pi$
$662$		−	19.1906i		−	0.745864i
$663$			45.5134i			1.76760i
$664$	5.35965			0.207995
$665$		0			0
$666$	−3.18719			−0.123501
$667$			21.3977i			0.828522i
$668$			2.66762i			0.103213i
$669$	−3.28248			−0.126908
$670$	3.02297	−	2.82843i	0.116787	−	0.109272i
$671$	43.7886			1.69044
$672$		0			0
$673$			21.8236i			0.841237i	0.907238	+	0.420619i	$0.138187\pi$
$673$			21.8236i			0.841237i	−0.907238	+	0.420619i	$0.861813\pi$
$674$	27.6035			1.06325
$675$	4.98896	+	0.332104i	0.192025	+	0.0127827i
$676$	21.6200			0.831540
$677$		−	41.0572i		−	1.57796i	−0.614421	−	0.788979i	$-0.710610\pi$
$677$		−	41.0572i		−	1.57796i	0.614421	−	0.788979i	$-0.289390\pi$
$678$		−	12.5723i		−	0.482837i
$679$		0			0
$680$	12.6302	−	11.8174i	0.484346	−	0.453176i
$681$	4.42031			0.169387
$682$			37.8566i			1.44960i
$683$			31.0642i			1.18864i	0.804229	+	0.594320i	$0.202579\pi$
$683$			31.0642i			1.18864i	−0.804229	+	0.594320i	$0.797421\pi$
$684$	−6.61827			−0.253056
$685$	21.8085	+	23.3085i	0.833259	+	0.890572i
$686$		0			0
$687$		−	7.97270i		−	0.304178i
$688$			1.43108i			0.0545595i
$689$	8.12993			0.309726
$690$	4.00000	+	4.27512i	0.152277	+	0.162751i
$691$	−32.0012			−1.21738			−0.608692	−	0.793407i	$-0.708305\pi$
$691$	−32.0012			−1.21738			−0.608692	+	0.793407i	$0.708305\pi$
$692$		−	0.647340i		−	0.0246082i
$693$		0			0
$694$	20.3761			0.773468
$695$	24.4320	−	22.8597i	0.926757	−	0.867116i
$696$	−8.17246			−0.309776
$697$			27.5594i			1.04389i
$698$			17.8281i			0.674802i
$699$	17.9558			0.679152
$700$		0			0
$701$	−45.4635			−1.71713			−0.858567	−	0.512701i	$-0.828645\pi$
$701$	−45.4635			−1.71713			−0.858567	+	0.512701i	$0.828645\pi$
$702$		−	5.88388i		−	0.222073i
$703$			21.0937i			0.795563i
$704$	−4.46967			−0.168457
$705$	−11.0879	+	10.3744i	−0.417596	+	0.390722i
$706$	−3.51347			−0.132231
$707$		0			0
$708$		−	4.66421i		−	0.175292i
$709$	47.7597			1.79365			0.896826	−	0.442384i	$-0.145867\pi$
$709$	47.7597			1.79365			0.896826	+	0.442384i	$0.145867\pi$
$710$	3.09190	+	3.30456i	0.116037	+	0.124018i
$711$	−6.98527			−0.261968
$712$			14.3912i			0.539335i
$713$			22.1759i			0.830493i
$714$		0			0
$715$	40.1776	+	42.9411i	1.50256	+	1.60591i
$716$	−25.7374			−0.961853
$717$			5.41296i			0.202151i
$718$			2.19796i			0.0820270i
$719$	−13.1611			−0.490828			−0.245414	−	0.969418i	$-0.578924\pi$
$719$	−13.1611			−0.490828			−0.245414	+	0.969418i	$0.578924\pi$
$720$	−1.63280	+	1.52773i	−0.0608510	+	0.0569350i
$721$		0			0
$722$			24.8015i			0.923016i
$723$			4.69669i			0.174672i
$724$	−7.42245			−0.275853
$725$	2.71411	−	40.7721i	0.100799	−	1.51424i
$726$	8.97792			0.333202
$727$			8.17082i			0.303039i	0.988454	+	0.151519i	$0.0484166\pi$
$727$			8.17082i			0.303039i	−0.988454	+	0.151519i	$0.951583\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−6.55876	+	6.13668i	−0.242751	+	0.227129i
$731$	−11.0698			−0.409432
$732$			9.79683i			0.362101i
$733$			2.01510i			0.0744293i	0.999307	+	0.0372146i	$0.0118485\pi$
$733$			2.01510i			0.0744293i	−0.999307	+	0.0372146i	$0.988151\pi$
$734$	28.7721			1.06200
$735$		0			0
$736$	−2.61827			−0.0965107
$737$		−	8.27512i		−	0.304818i
$738$		−	3.56282i		−	0.131149i
$739$	3.82590			0.140738			0.0703690	−	0.997521i	$-0.477582\pi$
$739$	3.82590			0.140738			0.0703690	+	0.997521i	$0.477582\pi$
$740$	4.86915	+	5.20406i	0.178994	+	0.191305i
$741$	−38.9411			−1.43054
$742$		0			0
$743$			36.6654i			1.34512i	0.740041	+	0.672562i	$0.234806\pi$
$743$			36.6654i			1.34512i	−0.740041	+	0.672562i	$0.765194\pi$
$744$	−8.46967			−0.310513
$745$	−18.2304	+	17.0572i	−0.667912	+	0.624928i
$746$	−14.5689			−0.533406
$747$		−	5.35965i		−	0.196099i
$748$		−	34.5741i		−	1.26415i
$749$		0			0
$750$	−7.07950	−	8.65336i	−0.258507	−	0.315976i
$751$	−20.4657			−0.746804			−0.373402	−	0.927670i	$-0.621809\pi$
$751$	−20.4657			−0.746804			−0.373402	+	0.927670i	$0.621809\pi$
$752$		−	6.79073i		−	0.247632i
$753$		−	7.73402i		−	0.281843i
$754$	−48.0858			−1.75118
$755$	1.08452	−	1.01473i	0.0394698	−	0.0369298i
$756$		0			0
$757$		−	37.9575i		−	1.37959i	−0.724006	−	0.689794i	$-0.757701\pi$
$757$		−	37.9575i		−	1.37959i	0.724006	−	0.689794i	$-0.242299\pi$
$758$			30.7868i			1.11823i
$759$	11.7028			0.424784
$760$	10.1109	+	10.8063i	0.366761	+	0.391987i
$761$	−34.6131			−1.25472			−0.627361	−	0.778728i	$-0.715865\pi$
$761$	−34.6131			−1.25472			−0.627361	+	0.778728i	$0.715865\pi$
$762$			6.59619i			0.238955i
$763$		0			0
$764$	1.08452			0.0392367
$765$	−11.8174	−	12.6302i	−0.427258	−	0.456646i
$766$	−23.3410			−0.843344
$767$		−	27.4436i		−	0.990932i
$768$		−	1.00000i		−	0.0360844i
$769$	1.48961			0.0537167			0.0268584	−	0.999639i	$-0.491450\pi$
$769$	1.48961			0.0537167			0.0268584	+	0.999639i	$0.491450\pi$
$770$		0			0
$771$	−1.34442			−0.0484181
$772$			8.93933i			0.321734i
$773$		−	0.992258i		−	0.0356891i	−0.999841	−	0.0178445i	$-0.994320\pi$
$773$		−	0.992258i		−	0.0356891i	0.999841	−	0.0178445i	$-0.00568039\pi$
$774$	1.43108			0.0514392
$775$	2.81281	−	42.2548i	0.101039	−	1.51784i
$776$	7.71966			0.277120
$777$		0			0
$778$			1.21842i			0.0436824i
$779$	−23.5797			−0.844830
$780$	−9.60723	+	8.98896i	−0.343994	+	0.321856i
$781$	9.04596			0.323690
$782$		−	20.2530i		−	0.724247i
$783$			8.17246i			0.292060i
$784$		0			0
$785$	12.3468	+	13.1961i	0.440677	+	0.470988i
$786$	−2.32106			−0.0827896
$787$		−	10.2513i		−	0.365418i	−0.983167	−	0.182709i	$-0.941513\pi$
$787$		−	10.2513i		−	0.365418i	0.983167	−	0.182709i	$-0.0584867\pi$
$788$		−	7.45890i		−	0.265712i
$789$	−4.36700			−0.155469
$790$	10.6716	+	11.4056i	0.379678	+	0.405793i
$791$		0			0
$792$			4.46967i			0.158823i
$793$			57.6434i			2.04698i
$794$	8.40595			0.298316
$795$	−2.25610	+	2.11091i	−0.0800155	+	0.0748661i
$796$	25.8293			0.915496
$797$		−	32.6811i		−	1.15762i	−0.815461	−	0.578812i	$-0.803517\pi$
$797$		−	32.6811i		−	1.15762i	0.815461	−	0.578812i	$-0.196483\pi$
$798$		0			0
$799$	52.5282			1.85831
$800$	4.98896	+	0.332104i	0.176386	+	0.0117417i
$801$	14.3912			0.508490
$802$		−	0.664208i		−	0.0234540i
$803$			17.9541i			0.633585i
$804$	1.85140			0.0652937
$805$		0			0
$806$	−49.8345			−1.75535
$807$			23.0671i			0.812001i
$808$			13.3544i			0.469807i
$809$	−22.4515			−0.789354			−0.394677	−	0.918820i	$-0.629144\pi$
$809$	−22.4515			−0.789354			−0.394677	+	0.918820i	$0.629144\pi$
$810$	1.52773	+	1.63280i	0.0536788	+	0.0573709i
$811$	37.6581			1.32235			0.661177	−	0.750230i	$-0.270057\pi$
$811$	37.6581			1.32235			0.661177	+	0.750230i	$0.270057\pi$
$812$		0			0
$813$		−	14.7209i		−	0.516286i
$814$	14.2457			0.499310
$815$	−1.27820	−	1.36612i	−0.0447734	−	0.0478529i
$816$	7.73528			0.270789
$817$		−	9.47129i		−	0.331358i
$818$			7.38476i			0.258202i
$819$		0			0
$820$	−5.81739	+	5.44301i	−0.203152	+	0.190078i
$821$	−21.4838			−0.749791			−0.374896	−	0.927067i	$-0.622321\pi$
$821$	−21.4838			−0.749791			−0.374896	+	0.927067i	$0.622321\pi$
$822$			14.2751i			0.497902i
$823$		−	18.6127i		−	0.648797i	−0.945921	−	0.324398i	$-0.894838\pi$
$823$		−	18.6127i		−	0.648797i	0.945921	−	0.324398i	$-0.105162\pi$
$824$	−9.35965			−0.326059
$825$	−22.2990	−	1.48440i	−0.776351	−	0.0516800i
$826$		0			0
$827$			18.4254i			0.640713i	0.947297	+	0.320356i	$0.103803\pi$
$827$			18.4254i			0.640713i	−0.947297	+	0.320356i	$0.896197\pi$
$828$			2.61827i			0.0909912i
$829$	−32.0377			−1.11271			−0.556357	−	0.830943i	$-0.687801\pi$
$829$	−32.0377			−1.11271			−0.556357	+	0.830943i	$0.687801\pi$
$830$	−8.75126	+	8.18807i	−0.303761	+	0.284212i
$831$	3.21104			0.111390
$832$		−	5.88388i		−	0.203987i
$833$		0			0
$834$	14.9632			0.518133
$835$	−4.07540	−	4.35571i	−0.141035	−	0.150735i
$836$	29.5815			1.02310
$837$			8.46967i			0.292754i
$838$		−	18.6274i		−	0.643473i
$839$	−8.45154			−0.291780			−0.145890	−	0.989301i	$-0.546605\pi$
$839$	−8.45154			−0.291780			−0.145890	+	0.989301i	$0.546605\pi$
$840$		0			0
$841$	37.7891			1.30307
$842$		−	13.5043i		−	0.465389i
$843$			7.72488i			0.266059i
$844$	−5.53375			−0.190479
$845$	−35.3013	+	33.0295i	−1.21440	+	1.13625i
$846$	−6.79073			−0.233470
$847$		0			0
$848$		−	1.38173i		−	0.0474488i
$849$	−29.5594			−1.01448
$850$	−2.56892	+	38.5910i	−0.0881132	+	1.32366i
$851$	8.34492			0.286060
$852$			2.02386i			0.0693361i
$853$			50.6270i			1.73344i	0.498798	+	0.866718i	$0.333775\pi$
$853$			50.6270i			1.73344i	−0.498798	+	0.866718i	$0.666225\pi$
$854$		0			0
$855$	10.8063	−	10.1109i	0.369569	−	0.345786i
$856$	−11.0165			−0.376536
$857$		−	12.0013i		−	0.409955i	−0.978767	−	0.204978i	$-0.934288\pi$
$857$		−	12.0013i		−	0.409955i	0.978767	−	0.204978i	$-0.0657121\pi$
$858$			26.2990i			0.897832i
$859$	35.7119			1.21848			0.609238	−	0.792988i	$-0.291475\pi$
$859$	35.7119			1.21848			0.609238	+	0.792988i	$0.291475\pi$
$860$	−2.18630	−	2.33668i	−0.0745523	−	0.0796801i
$861$		0			0
$862$		−	31.6807i		−	1.07905i
$863$			1.28425i			0.0437164i	0.999761	+	0.0218582i	$0.00695824\pi$
$863$			1.28425i			0.0437164i	−0.999761	+	0.0218582i	$0.993042\pi$
$864$	−1.00000			−0.0340207
$865$	0.988958	+	1.05698i	0.0336256	+	0.0359384i
$866$	−25.3184			−0.860353
$867$			42.8345i			1.45474i
$868$		0			0
$869$	31.2218			1.05913
$870$	13.3440	−	12.4853i	0.452405	−	0.423291i
$871$	10.8934			0.369109
$872$		−	4.69544i		−	0.159008i
$873$		−	7.71966i		−	0.261271i
$874$	17.3284			0.586142
$875$		0			0
$876$	−4.01687			−0.135717
$877$			38.3501i			1.29499i	0.762069	+	0.647496i	$0.224184\pi$
$877$			38.3501i			1.29499i	−0.762069	+	0.647496i	$0.775816\pi$
$878$		−	32.8146i		−	1.10744i
$879$	1.17679			0.0396921
$880$	7.29809	−	6.82843i	0.246019	−	0.230186i
$881$	0.389472			0.0131216			0.00656082	−	0.999978i	$-0.497912\pi$
$881$	0.389472			0.0131216			0.00656082	+	0.999978i	$0.497912\pi$
$882$		0			0
$883$			18.5412i			0.623962i	0.950088	+	0.311981i	$0.100993\pi$
$883$			18.5412i			0.623962i	−0.950088	+	0.311981i	$0.899007\pi$
$884$	45.5134			1.53078
$885$	7.12563	+	7.61574i	0.239526	+	0.256000i
$886$	16.6421			0.559103
$887$		−	42.4806i		−	1.42636i	−0.700982	−	0.713179i	$-0.747255\pi$
$887$		−	42.4806i		−	1.42636i	0.700982	−	0.713179i	$-0.252745\pi$
$888$			3.18719i			0.106955i
$889$		0			0
$890$	−21.9859	−	23.4981i	−0.736968	−	0.787658i
$891$	4.46967			0.149739
$892$			3.28248i			0.109906i
$893$			44.9429i			1.50396i
$894$	−11.1651			−0.373417
$895$	42.0242	−	39.3198i	1.40471	−	1.31431i
$896$		0			0
$897$			15.4056i			0.514378i
$898$		−	20.1759i		−	0.673278i
$899$	69.2180			2.30855
$900$	0.332104	−	4.98896i	0.0110701	−	0.166299i
$901$	10.6881			0.356071
$902$			15.9246i			0.530231i
$903$		0			0
$904$	−12.5723			−0.418150
$905$	12.1194	−	11.3395i	0.402863	−	0.376937i
$906$	0.664208			0.0220668
$907$		−	41.1686i		−	1.36698i	−0.729959	−	0.683491i	$-0.760461\pi$
$907$		−	41.1686i		−	1.36698i	0.729959	−	0.683491i	$-0.239539\pi$
$908$		−	4.42031i		−	0.146693i
$909$	13.3544			0.442939
$910$		0			0
$911$	−25.1703			−0.833929			−0.416964	−	0.908923i	$-0.636906\pi$
$911$	−25.1703			−0.833929			−0.416964	+	0.908923i	$0.636906\pi$
$912$			6.61827i			0.219153i
$913$			23.9558i			0.792822i
$914$	35.4124			1.17134
$915$	−14.9669	−	15.9963i	−0.494790	−	0.528822i
$916$	−7.97270			−0.263426
$917$		0			0
$918$		−	7.73528i		−	0.255302i
$919$	5.03681			0.166149			0.0830745	−	0.996543i	$-0.473526\pi$
$919$	5.03681			0.166149			0.0830745	+	0.996543i	$0.473526\pi$
$920$	4.27512	−	4.00000i	0.140947	−	0.131876i
$921$	−20.3761			−0.671417
$922$		−	12.5940i		−	0.414762i
$923$			11.9081i			0.391961i
$924$		0			0
$925$	−15.9007	−	1.05848i	−0.522813	−	0.0348026i
$926$	32.5061			1.06822
$927$			9.35965i			0.307411i
$928$			8.17246i			0.268274i
$929$	14.2846			0.468663			0.234332	−	0.972157i	$-0.424710\pi$
$929$	14.2846			0.468663			0.234332	+	0.972157i	$0.424710\pi$
$930$	13.8293	−	12.9393i	0.453481	−	0.424297i
$931$		0			0
$932$		−	17.9558i		−	0.588163i
$933$			18.8934i			0.618542i
$934$	−9.20531			−0.301207
$935$	52.8198	+	56.4528i	1.72739	+	1.84620i
$936$	−5.88388			−0.192321
$937$		−	19.8403i		−	0.648153i	−0.946031	−	0.324077i	$-0.894946\pi$
$937$		−	19.8403i		−	0.648153i	0.946031	−	0.324077i	$-0.105054\pi$
$938$		0			0
$939$	16.4849			0.537964
$940$	10.3744	+	11.0879i	0.338375	+	0.361649i
$941$	15.9054			0.518502			0.259251	−	0.965810i	$-0.416524\pi$
$941$	15.9054			0.518502			0.259251	+	0.965810i	$0.416524\pi$
$942$			8.08184i			0.263320i
$943$			9.32842i			0.303775i
$944$	−4.66421			−0.151807
$945$		0			0
$946$	−6.39646			−0.207967
$947$			9.55815i			0.310598i	0.987867	+	0.155299i	$0.0496341\pi$
$947$			9.55815i			0.310598i	−0.987867	+	0.155299i	$0.950366\pi$
$948$			6.98527i			0.226871i
$949$	−23.6348			−0.767217
$950$	−33.0183	−	2.19796i	−1.07125	−	0.0713111i
$951$	10.3211			0.334683
$952$		0			0
$953$		−	23.7505i		−	0.769354i	−0.923051	−	0.384677i	$-0.874313\pi$
$953$		−	23.7505i		−	0.769354i	0.923051	−	0.384677i	$-0.125687\pi$
$954$	−1.38173			−0.0447352
$955$	−1.77081	+	1.65685i	−0.0573022	+	0.0536145i
$956$	5.41296			0.175068
$957$		−	36.5282i		−	1.18079i
$958$			39.4914i			1.27591i
$959$		0			0
$960$	1.52773	+	1.63280i	0.0493072	+	0.0526986i
$961$	40.7352			1.31404
$962$			18.7530i			0.604622i
$963$			11.0165i			0.355002i
$964$	4.69669			0.151270
$965$	−13.6569	−	14.5962i	−0.439630	−	0.469868i
$966$		0			0
$967$		−	56.9706i		−	1.83205i	−0.401121	−	0.916025i	$-0.631379\pi$
$967$		−	56.9706i		−	1.83205i	0.401121	−	0.916025i	$-0.368621\pi$
$968$		−	8.97792i		−	0.288561i
$969$	−51.1941			−1.64459
$970$	−12.6047	+	11.7935i	−0.404713	+	0.378667i
$971$	33.0857			1.06177			0.530886	−	0.847443i	$-0.321859\pi$
$971$	33.0857			1.06177			0.530886	+	0.847443i	$0.321859\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	29.2678			0.937800
$975$	1.95406	−	29.3544i	0.0625801	−	0.940094i
$976$	9.79683			0.313589
$977$		−	24.6127i		−	0.787429i	−0.919233	−	0.393715i	$-0.871190\pi$
$977$		−	24.6127i		−	0.787429i	0.919233	−	0.393715i	$-0.128810\pi$
$978$		−	0.836668i		−	0.0267537i
$979$	−64.3241			−2.05581
$980$		0			0
$981$	−4.69544			−0.149914
$982$			15.3631i			0.490255i
$983$		−	42.4806i		−	1.35492i	−0.735559	−	0.677460i	$-0.763081\pi$
$983$		−	42.4806i		−	1.35492i	0.735559	−	0.677460i	$-0.236919\pi$
$984$	−3.56282			−0.113578
$985$	11.3952	+	12.1789i	0.363080	+	0.388053i
$986$	−63.2162			−2.01321
$987$		0			0
$988$			38.9411i			1.23888i
$989$	−3.74696			−0.119146
$990$	−6.82843	−	7.29809i	−0.217022	−	0.231949i
$991$	−0.838308			−0.0266297			−0.0133149	−	0.999911i	$-0.504238\pi$
$991$	−0.838308			−0.0266297			−0.0133149	+	0.999911i	$0.504238\pi$
$992$			8.46967i			0.268912i
$993$			19.1906i			0.608995i
$994$		0			0
$995$	−42.1742	+	39.4601i	−1.33701	+	1.25097i
$996$	−5.35965			−0.169827
$997$		−	31.5940i		−	1.00059i	−0.865854	−	0.500297i	$-0.833224\pi$
$997$		−	31.5940i		−	1.00059i	0.865854	−	0.500297i	$-0.166776\pi$
$998$		−	20.5502i		−	0.650507i
$999$	3.18719			0.100838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.g.k.589.7	yes	8
5.2	odd	4		7350.2.a.dr.1.4		4
5.3	odd	4		7350.2.a.du.1.4		4
5.4	even	2	inner	1470.2.g.k.589.3	yes	8
7.2	even	3		1470.2.n.k.949.5		16
7.3	odd	6		1470.2.n.l.79.2		16
7.4	even	3		1470.2.n.k.79.3		16
7.5	odd	6		1470.2.n.l.949.8		16
7.6	odd	2		1470.2.g.j.589.6	yes	8
35.4	even	6		1470.2.n.k.79.5		16
35.9	even	6		1470.2.n.k.949.3		16
35.13	even	4		7350.2.a.dt.1.4		4
35.19	odd	6		1470.2.n.l.949.2		16
35.24	odd	6		1470.2.n.l.79.8		16
35.27	even	4		7350.2.a.ds.1.4		4
35.34	odd	2		1470.2.g.j.589.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.g.j.589.2	✓	8	35.34	odd	2
1470.2.g.j.589.6	yes	8	7.6	odd	2
1470.2.g.k.589.3	yes	8	5.4	even	2	inner
1470.2.g.k.589.7	yes	8	1.1	even	1	trivial
1470.2.n.k.79.3		16	7.4	even	3
1470.2.n.k.79.5		16	35.4	even	6
1470.2.n.k.949.3		16	35.9	even	6
1470.2.n.k.949.5		16	7.2	even	3
1470.2.n.l.79.2		16	7.3	odd	6
1470.2.n.l.79.8		16	35.24	odd	6
1470.2.n.l.949.2		16	35.19	odd	6
1470.2.n.l.949.8		16	7.5	odd	6
7350.2.a.dr.1.4		4	5.2	odd	4
7350.2.a.ds.1.4		4	35.27	even	4
7350.2.a.dt.1.4		4	35.13	even	4
7350.2.a.du.1.4		4	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.63280 - 1.52773i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.63280 - 1.52773i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(1.52773 + 1.63280i) q^{10} +4.46967 q^{11} +1.00000i q^{12} +5.88388i q^{13} +(-1.52773 - 1.63280i) q^{15} +1.00000 q^{16} +7.73528i q^{17} -1.00000i q^{18} -6.61827 q^{19} +(-1.63280 + 1.52773i) q^{20} +4.46967i q^{22} +2.61827i q^{23} -1.00000 q^{24} +(0.332104 - 4.98896i) q^{25} -5.88388 q^{26} +1.00000i q^{27} +8.17246 q^{29} +(1.63280 - 1.52773i) q^{30} +8.46967 q^{31} +1.00000i q^{32} -4.46967i q^{33} -7.73528 q^{34} +1.00000 q^{36} -3.18719i q^{37} -6.61827i q^{38} +5.88388 q^{39} +(-1.52773 - 1.63280i) q^{40} +3.56282 q^{41} +1.43108i q^{43} -4.46967 q^{44} +(-1.63280 + 1.52773i) q^{45} -2.61827 q^{46} -6.79073i q^{47} -1.00000i q^{48} +(4.98896 + 0.332104i) q^{50} +7.73528 q^{51} -5.88388i q^{52} -1.38173i q^{53} -1.00000 q^{54} +(7.29809 - 6.82843i) q^{55} +6.61827i q^{57} +8.17246i q^{58} -4.66421 q^{59} +(1.52773 + 1.63280i) q^{60} +9.79683 q^{61} +8.46967i q^{62} -1.00000 q^{64} +(8.98896 + 9.60723i) q^{65} +4.46967 q^{66} -1.85140i q^{67} -7.73528i q^{68} +2.61827 q^{69} +2.02386 q^{71} +1.00000i q^{72} +4.01687i q^{73} +3.18719 q^{74} +(-4.98896 - 0.332104i) q^{75} +6.61827 q^{76} +5.88388i q^{78} +6.98527 q^{79} +(1.63280 - 1.52773i) q^{80} +1.00000 q^{81} +3.56282i q^{82} +5.35965i q^{83} +(11.8174 + 12.6302i) q^{85} -1.43108 q^{86} -8.17246i q^{87} -4.46967i q^{88} -14.3912 q^{89} +(-1.52773 - 1.63280i) q^{90} -2.61827i q^{92} -8.46967i q^{93} +6.79073 q^{94} +(-10.8063 + 10.1109i) q^{95} +1.00000 q^{96} +7.71966i q^{97} -4.46967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 4 * q^5 + 8 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{9} + 8 q^{16} - 24 q^{19} - 4 q^{20} - 8 q^{24} + 4 q^{25} + 16 q^{29} + 4 q^{30} + 32 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{41} - 4 q^{45} + 8 q^{46} - 4 q^{50} + 8 q^{51} - 8 q^{54} - 40 q^{59} + 24 q^{61} - 8 q^{64} + 28 q^{65} - 8 q^{69} - 40 q^{71} + 16 q^{74} + 4 q^{75} + 24 q^{76} + 16 q^{79} + 4 q^{80} + 8 q^{81} + 28 q^{85} + 8 q^{86} - 88 q^{89} - 24 q^{94} + 24 q^{95} + 8 q^{96}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^5 + 8 * q^6 - 8 * q^9 + 8 * q^16 - 24 * q^19 - 4 * q^20 - 8 * q^24 + 4 * q^25 + 16 * q^29 + 4 * q^30 + 32 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^41 - 4 * q^45 + 8 * q^46 - 4 * q^50 + 8 * q^51 - 8 * q^54 - 40 * q^59 + 24 * q^61 - 8 * q^64 + 28 * q^65 - 8 * q^69 - 40 * q^71 + 16 * q^74 + 4 * q^75 + 24 * q^76 + 16 * q^79 + 4 * q^80 + 8 * q^81 + 28 * q^85 + 8 * q^86 - 88 * q^89 - 24 * q^94 + 24 * q^95 + 8 * q^96

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