LMFDB - Embedded newform 1690.2.c.h.1689.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(1689,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.1689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18,18,0,18,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 29x^{16} + 336x^{14} + 1977x^{12} + 6147x^{10} + 9369x^{8} + 5559x^{6} + 1342x^{4} + 116x^{2} + 1 $ x^18 + 29x^16 + 336x^14 + 1977x^12 + 6147x^10 + 9369x^8 + 5559x^6 + 1342x^4 + 116x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1689.16
Root			$-0.430845i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.h.1689.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.55203i q^{3} +1.00000 q^{4} +(1.57226 - 1.58997i) q^{5} +2.55203i q^{6} -1.86919 q^{7} +1.00000 q^{8} -3.51288 q^{9} +(1.57226 - 1.58997i) q^{10} +4.42801i q^{11} +2.55203i q^{12} -1.86919 q^{14} +(4.05765 + 4.01247i) q^{15} +1.00000 q^{16} +4.16688i q^{17} -3.51288 q^{18} +4.52055i q^{19} +(1.57226 - 1.58997i) q^{20} -4.77024i q^{21} +4.42801i q^{22} -7.56163i q^{23} +2.55203i q^{24} +(-0.0559819 - 4.99969i) q^{25} -1.30889i q^{27} -1.86919 q^{28} -3.22160 q^{29} +(4.05765 + 4.01247i) q^{30} +8.51124i q^{31} +1.00000 q^{32} -11.3004 q^{33} +4.16688i q^{34} +(-2.93886 + 2.97195i) q^{35} -3.51288 q^{36} +0.488194 q^{37} +4.52055i q^{38} +(1.57226 - 1.58997i) q^{40} +10.9095i q^{41} -4.77024i q^{42} -4.38872i q^{43} +4.42801i q^{44} +(-5.52317 + 5.58536i) q^{45} -7.56163i q^{46} +12.5176 q^{47} +2.55203i q^{48} -3.50612 q^{49} +(-0.0559819 - 4.99969i) q^{50} -10.6340 q^{51} -0.191394i q^{53} -1.30889i q^{54} +(7.04039 + 6.96200i) q^{55} -1.86919 q^{56} -11.5366 q^{57} -3.22160 q^{58} +11.2785i q^{59} +(4.05765 + 4.01247i) q^{60} +6.28685 q^{61} +8.51124i q^{62} +6.56625 q^{63} +1.00000 q^{64} -11.3004 q^{66} +5.69785 q^{67} +4.16688i q^{68} +19.2975 q^{69} +(-2.93886 + 2.97195i) q^{70} -10.1438i q^{71} -3.51288 q^{72} -4.10663 q^{73} +0.488194 q^{74} +(12.7594 - 0.142868i) q^{75} +4.52055i q^{76} -8.27681i q^{77} +2.33064 q^{79} +(1.57226 - 1.58997i) q^{80} -7.19832 q^{81} +10.9095i q^{82} -2.49654 q^{83} -4.77024i q^{84} +(6.62519 + 6.55143i) q^{85} -4.38872i q^{86} -8.22163i q^{87} +4.42801i q^{88} -11.9415i q^{89} +(-5.52317 + 5.58536i) q^{90} -7.56163i q^{92} -21.7210 q^{93} +12.5176 q^{94} +(7.18752 + 7.10749i) q^{95} +2.55203i q^{96} -1.91384 q^{97} -3.50612 q^{98} -15.5551i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 18 q^{2} + 18 q^{4} - 2 q^{5} - 2 q^{7} + 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} + 14 q^{15} + 18 q^{16} - 16 q^{18} - 2 q^{20} - 22 q^{25} - 2 q^{28} - 30 q^{29} + 14 q^{30} + 18 q^{32} - 28 q^{33}+ \cdots - 20 q^{98}+O(q^{100}) $ 18 * q + 18 * q^2 + 18 * q^4 - 2 * q^5 - 2 * q^7 + 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 + 14 * q^15 + 18 * q^16 - 16 * q^18 - 2 * q^20 - 22 * q^25 - 2 * q^28 - 30 * q^29 + 14 * q^30 + 18 * q^32 - 28 * q^33 - 4 * q^35 - 16 * q^36 + 20 * q^37 - 2 * q^40 + 20 * q^45 - 10 * q^47 - 20 * q^49 - 22 * q^50 - 24 * q^51 - 2 * q^56 - 24 * q^57 - 30 * q^58 + 14 * q^60 - 38 * q^61 + 78 * q^63 + 18 * q^64 - 28 * q^66 - 2 * q^67 - 28 * q^69 - 4 * q^70 - 16 * q^72 - 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 - 2 * q^80 + 106 * q^81 - 2 * q^83 - 16 * q^85 + 20 * q^90 + 56 * q^93 - 10 * q^94 + 54 * q^95 + 12 * q^97 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$			2.55203i			1.47342i	0.676210	+	0.736709i	$0.263621\pi$
$3$			2.55203i			1.47342i	−0.676210	+	0.736709i	$0.736379\pi$
$4$	1.00000			0.500000
$5$	1.57226	−	1.58997i	0.703137	−	0.711054i
$5$	1.57226	−	1.58997i	0.703137	−	0.711054i
$6$			2.55203i			1.04186i
$7$	−1.86919			−0.706488			−0.353244	−	0.935531i	$-0.614922\pi$
$7$	−1.86919			−0.706488			−0.353244	+	0.935531i	$0.614922\pi$
$8$	1.00000			0.353553
$9$	−3.51288			−1.17096
$10$	1.57226	−	1.58997i	0.497193	−	0.502791i
$11$			4.42801i			1.33510i	0.744567	+	0.667548i	$0.232656\pi$
$11$			4.42801i			1.33510i	−0.744567	+	0.667548i	$0.767344\pi$
$12$			2.55203i			0.736709i
$13$		0			0
$13$		0			0
$14$	−1.86919			−0.499563
$15$	4.05765	+	4.01247i	1.04768	+	1.03601i
$16$	1.00000			0.250000
$17$			4.16688i			1.01062i	0.862939	+	0.505308i	$0.168621\pi$
$17$			4.16688i			1.01062i	−0.862939	+	0.505308i	$0.831379\pi$
$18$	−3.51288			−0.827994
$19$			4.52055i			1.03709i	0.855052	+	0.518543i	$0.173525\pi$
$19$			4.52055i			1.03709i	−0.855052	+	0.518543i	$0.826475\pi$
$20$	1.57226	−	1.58997i	0.351569	−	0.355527i
$21$		−	4.77024i		−	1.04095i
$22$			4.42801i			0.944056i
$23$		−	7.56163i		−	1.57671i	−0.615221	−	0.788354i	$-0.710933\pi$
$23$		−	7.56163i		−	1.57671i	0.615221	−	0.788354i	$-0.289067\pi$
$24$			2.55203i			0.520932i
$25$	−0.0559819	−	4.99969i	−0.0111964	−	0.999937i
$26$		0			0
$27$		−	1.30889i		−	0.251895i
$28$	−1.86919			−0.353244
$29$	−3.22160			−0.598236			−0.299118	−	0.954216i	$-0.596692\pi$
$29$	−3.22160			−0.598236			−0.299118	+	0.954216i	$0.596692\pi$
$30$	4.05765	+	4.01247i	0.740822	+	0.732573i
$31$			8.51124i			1.52866i	0.644823	+	0.764332i	$0.276931\pi$
$31$			8.51124i			1.52866i	−0.644823	+	0.764332i	$0.723069\pi$
$32$	1.00000			0.176777
$33$	−11.3004			−1.96715
$34$			4.16688i			0.714614i
$35$	−2.93886	+	2.97195i	−0.496758	+	0.502352i
$36$	−3.51288			−0.585480
$37$	0.488194			0.0802585			0.0401293	−	0.999194i	$-0.487223\pi$
$37$	0.488194			0.0802585			0.0401293	+	0.999194i	$0.487223\pi$
$38$			4.52055i			0.733330i
$39$		0			0
$40$	1.57226	−	1.58997i	0.248597	−	0.251396i
$41$			10.9095i			1.70378i	0.523724	+	0.851888i	$0.324542\pi$
$41$			10.9095i			1.70378i	−0.523724	+	0.851888i	$0.675458\pi$
$42$		−	4.77024i		−	0.736065i
$43$		−	4.38872i		−	0.669274i	−0.942347	−	0.334637i	$-0.891386\pi$
$43$		−	4.38872i		−	0.669274i	0.942347	−	0.334637i	$-0.108614\pi$
$44$			4.42801i			0.667548i
$45$	−5.52317	+	5.58536i	−0.823345	+	0.832616i
$46$		−	7.56163i		−	1.11490i
$47$	12.5176			1.82587			0.912937	−	0.408101i	$-0.133809\pi$
$47$	12.5176			1.82587			0.912937	+	0.408101i	$0.133809\pi$
$48$			2.55203i			0.368354i
$49$	−3.50612			−0.500874
$50$	−0.0559819	−	4.99969i	−0.00791703	−	0.707062i
$51$	−10.6340			−1.48906
$52$		0			0
$53$		−	0.191394i		−	0.0262900i	−0.999914	−	0.0131450i	$-0.995816\pi$
$53$		−	0.191394i		−	0.0262900i	0.999914	−	0.0131450i	$-0.00418430\pi$
$54$		−	1.30889i		−	0.178117i
$55$	7.04039	+	6.96200i	0.949326	+	0.938756i
$56$	−1.86919			−0.249781
$57$	−11.5366			−1.52806
$58$	−3.22160			−0.423016
$59$			11.2785i			1.46833i	0.678970	+	0.734166i	$0.262427\pi$
$59$			11.2785i			1.46833i	−0.678970	+	0.734166i	$0.737573\pi$
$60$	4.05765	+	4.01247i	0.523840	+	0.518007i
$61$	6.28685			0.804949			0.402474	−	0.915431i	$-0.368150\pi$
$61$	6.28685			0.804949			0.402474	+	0.915431i	$0.368150\pi$
$62$			8.51124i			1.08093i
$63$	6.56625			0.827270
$64$	1.00000			0.125000
$65$		0			0
$66$	−11.3004			−1.39099
$67$	5.69785			0.696103			0.348051	−	0.937475i	$-0.386843\pi$
$67$	5.69785			0.696103			0.348051	+	0.937475i	$0.386843\pi$
$68$			4.16688i			0.505308i
$69$	19.2975			2.32315
$70$	−2.93886	+	2.97195i	−0.351261	+	0.355216i
$71$		−	10.1438i		−	1.20384i	−0.798555	−	0.601922i	$-0.794402\pi$
$71$		−	10.1438i		−	1.20384i	0.798555	−	0.601922i	$-0.205598\pi$
$72$	−3.51288			−0.413997
$73$	−4.10663			−0.480645			−0.240323	−	0.970693i	$-0.577253\pi$
$73$	−4.10663			−0.480645			−0.240323	+	0.970693i	$0.577253\pi$
$74$	0.488194			0.0567514
$75$	12.7594	−	0.142868i	1.47333	−	0.0164969i
$76$			4.52055i			0.518543i
$77$		−	8.27681i		−	0.943230i
$78$		0			0
$79$	2.33064			0.262217			0.131108	−	0.991368i	$-0.458146\pi$
$79$	2.33064			0.262217			0.131108	+	0.991368i	$0.458146\pi$
$80$	1.57226	−	1.58997i	0.175784	−	0.177764i
$81$	−7.19832			−0.799813
$82$			10.9095i			1.20475i
$83$	−2.49654			−0.274031			−0.137016	−	0.990569i	$-0.543751\pi$
$83$	−2.49654			−0.274031			−0.137016	+	0.990569i	$0.543751\pi$
$84$		−	4.77024i		−	0.520476i
$85$	6.62519	+	6.55143i	0.718603	+	0.710602i
$86$		−	4.38872i		−	0.473248i
$87$		−	8.22163i		−	0.881451i
$88$			4.42801i			0.472028i
$89$		−	11.9415i		−	1.26579i	−0.774237	−	0.632896i	$-0.781866\pi$
$89$		−	11.9415i		−	1.26579i	0.774237	−	0.632896i	$-0.218134\pi$
$90$	−5.52317	+	5.58536i	−0.582193	+	0.588748i
$91$		0			0
$92$		−	7.56163i		−	0.788354i
$93$	−21.7210			−2.25236
$94$	12.5176			1.29109
$95$	7.18752	+	7.10749i	0.737424	+	0.729213i
$96$			2.55203i			0.260466i
$97$	−1.91384			−0.194322			−0.0971608	−	0.995269i	$-0.530976\pi$
$97$	−1.91384			−0.194322			−0.0971608	+	0.995269i	$0.530976\pi$
$98$	−3.50612			−0.354171
$99$		−	15.5551i		−	1.56334i
$100$	−0.0559819	−	4.99969i	−0.00559819	−	0.499969i
$101$	−16.3092			−1.62282			−0.811411	−	0.584476i	$-0.801300\pi$
$101$	−16.3092			−1.62282			−0.811411	+	0.584476i	$0.801300\pi$
$102$	−10.6340			−1.05292
$103$		−	14.5800i		−	1.43661i	−0.695728	−	0.718305i	$-0.744918\pi$
$103$		−	14.5800i		−	1.43661i	0.695728	−	0.718305i	$-0.255082\pi$
$104$		0			0
$105$	−7.58452	−	7.50008i	−0.740174	−	0.731932i
$106$		−	0.191394i		−	0.0185898i
$107$			11.4218i			1.10418i	0.833784	+	0.552091i	$0.186170\pi$
$107$			11.4218i			1.10418i	−0.833784	+	0.552091i	$0.813830\pi$
$108$		−	1.30889i		−	0.125948i
$109$		−	10.3606i		−	0.992363i	−0.868219	−	0.496181i	$-0.834735\pi$
$109$		−	10.3606i		−	0.992363i	0.868219	−	0.496181i	$-0.165265\pi$
$110$	7.04039	+	6.96200i	0.671275	+	0.663801i
$111$			1.24589i			0.118254i
$112$	−1.86919			−0.176622
$113$		−	0.559115i		−	0.0525971i	−0.999654	−	0.0262985i	$-0.991628\pi$
$113$		−	0.559115i		−	0.0525971i	0.999654	−	0.0262985i	$-0.00837205\pi$
$114$	−11.5366			−1.08050
$115$	−12.0227	−	11.8889i	−1.12113	−	1.10864i
$116$	−3.22160			−0.299118
$117$		0			0
$118$			11.2785i			1.03827i
$119$		−	7.78870i		−	0.713989i
$120$	4.05765	+	4.01247i	0.370411	+	0.366287i
$121$	−8.60730			−0.782482
$122$	6.28685			0.569185
$123$	−27.8414			−2.51037
$124$			8.51124i			0.764332i
$125$	−8.03735	−	7.77181i	−0.718882	−	0.695132i
$126$	6.56625			0.584968
$127$		−	1.52200i		−	0.135055i	−0.997717	−	0.0675277i	$-0.978489\pi$
$127$		−	1.52200i		−	0.135055i	0.997717	−	0.0675277i	$-0.0215111\pi$
$128$	1.00000			0.0883883
$129$	11.2002			0.986120
$130$		0			0
$131$	7.16465			0.625979			0.312989	−	0.949757i	$-0.398670\pi$
$131$	7.16465			0.625979			0.312989	+	0.949757i	$0.398670\pi$
$132$	−11.3004			−0.983577
$133$		−	8.44978i		−	0.732689i
$134$	5.69785			0.492219
$135$	−2.08108	−	2.05791i	−0.179111	−	0.177117i
$136$			4.16688i			0.357307i
$137$	16.0494			1.37119			0.685596	−	0.727983i	$-0.259542\pi$
$137$	16.0494			1.37119			0.685596	+	0.727983i	$0.259542\pi$
$138$	19.2975			1.64272
$139$	17.7302			1.50386			0.751930	−	0.659243i	$-0.229123\pi$
$139$	17.7302			1.50386			0.751930	+	0.659243i	$0.229123\pi$
$140$	−2.93886	+	2.97195i	−0.248379	+	0.251176i
$141$			31.9452i			2.69027i
$142$		−	10.1438i		−	0.851246i
$143$		0			0
$144$	−3.51288			−0.292740
$145$	−5.06520	+	5.12223i	−0.420642	+	0.425378i
$146$	−4.10663			−0.339867
$147$		−	8.94773i		−	0.737997i
$148$	0.488194			0.0401293
$149$		−	9.94873i		−	0.815032i	−0.913198	−	0.407516i	$-0.866395\pi$
$149$		−	9.94873i		−	0.815032i	0.913198	−	0.407516i	$-0.133605\pi$
$150$	12.7594	−	0.142868i	1.04180	−	0.0116651i
$151$		−	11.9580i		−	0.973130i	−0.873644	−	0.486565i	$-0.838250\pi$
$151$		−	11.9580i		−	0.973130i	0.873644	−	0.486565i	$-0.161750\pi$
$152$			4.52055i			0.366665i
$153$		−	14.6377i		−	1.18339i
$154$		−	8.27681i		−	0.666964i
$155$	13.5326	+	13.3819i	1.08696	+	1.07486i
$156$		0			0
$157$		−	6.72590i		−	0.536785i	−0.963310	−	0.268392i	$-0.913508\pi$
$157$		−	6.72590i		−	0.536785i	0.963310	−	0.268392i	$-0.0864924\pi$
$158$	2.33064			0.185415
$159$	0.488443			0.0387361
$160$	1.57226	−	1.58997i	0.124298	−	0.125698i
$161$			14.1341i			1.11393i
$162$	−7.19832			−0.565553
$163$	−0.00838925			−0.000657097			−0.000328549	−	1.00000i	$-0.500105\pi$
$163$	−0.00838925			−0.000657097			−0.000328549		1.00000i	$0.500105\pi$
$164$			10.9095i			0.851888i
$165$	−17.7673	+	17.9673i	−1.38318	+	1.39875i
$166$	−2.49654			−0.193769
$167$	8.77138			0.678749			0.339375	−	0.940651i	$-0.389785\pi$
$167$	8.77138			0.678749			0.339375	+	0.940651i	$0.389785\pi$
$168$		−	4.77024i		−	0.368032i
$169$		0			0
$170$	6.62519	+	6.55143i	0.508129	+	0.502471i
$171$		−	15.8801i		−	1.21439i
$172$		−	4.38872i		−	0.334637i
$173$			5.17428i			0.393393i	0.980464	+	0.196697i	$0.0630214\pi$
$173$			5.17428i			0.393393i	−0.980464	+	0.196697i	$0.936979\pi$
$174$		−	8.22163i		−	0.623280i
$175$	0.104641	+	9.34538i	0.00791011	+	0.706444i
$176$			4.42801i			0.333774i
$177$	−28.7831			−2.16347
$178$		−	11.9415i		−	0.895050i
$179$	−7.82042			−0.584526			−0.292263	−	0.956338i	$-0.594408\pi$
$179$	−7.82042			−0.584526			−0.292263	+	0.956338i	$0.594408\pi$
$180$	−5.52317	+	5.58536i	−0.411673	+	0.416308i
$181$	12.2270			0.908823			0.454411	−	0.890792i	$-0.349850\pi$
$181$	12.2270			0.908823			0.454411	+	0.890792i	$0.349850\pi$
$182$		0			0
$183$			16.0443i			1.18603i
$184$		−	7.56163i		−	0.557451i
$185$	0.767568	−	0.776211i	0.0564328	−	0.0570682i
$186$	−21.7210			−1.59266
$187$	−18.4510			−1.34927
$188$	12.5176			0.912937
$189$			2.44656i			0.177961i
$190$	7.18752	+	7.10749i	0.521437	+	0.515632i
$191$	18.1313			1.31194			0.655968	−	0.754789i	$-0.272261\pi$
$191$	18.1313			1.31194			0.655968	+	0.754789i	$0.272261\pi$
$192$			2.55203i			0.184177i
$193$	6.34605			0.456799			0.228399	−	0.973568i	$-0.426651\pi$
$193$	6.34605			0.456799			0.228399	+	0.973568i	$0.426651\pi$
$194$	−1.91384			−0.137406
$195$		0			0
$196$	−3.50612			−0.250437
$197$	2.19339			0.156273			0.0781364	−	0.996943i	$-0.475103\pi$
$197$	2.19339			0.156273			0.0781364	+	0.996943i	$0.475103\pi$
$198$		−	15.5551i		−	1.10545i
$199$	−4.80668			−0.340737			−0.170368	−	0.985380i	$-0.554496\pi$
$199$	−4.80668			−0.340737			−0.170368	+	0.985380i	$0.554496\pi$
$200$	−0.0559819	−	4.99969i	−0.00395852	−	0.353531i
$201$			14.5411i			1.02565i
$202$	−16.3092			−1.14751
$203$	6.02179			0.422646
$204$	−10.6340			−0.744530
$205$	17.3457	+	17.1526i	1.21148	+	1.19799i
$206$		−	14.5800i		−	1.01584i
$207$			26.5631i			1.84626i
$208$		0			0
$209$	−20.0171			−1.38461
$210$	−7.58452	−	7.50008i	−0.523382	−	0.517554i
$211$	−1.98463			−0.136628			−0.0683139	−	0.997664i	$-0.521762\pi$
$211$	−1.98463			−0.136628			−0.0683139	+	0.997664i	$0.521762\pi$
$212$		−	0.191394i		−	0.0131450i
$213$	25.8872			1.77376
$214$			11.4218i			0.780775i
$215$	−6.97792	−	6.90022i	−0.475890	−	0.470591i
$216$		−	1.30889i		−	0.0890584i
$217$		−	15.9092i		−	1.07998i
$218$		−	10.3606i		−	0.701706i
$219$		−	10.4803i		−	0.708191i
$220$	7.04039	+	6.96200i	0.474663	+	0.469378i
$221$		0			0
$222$			1.24589i			0.0836185i
$223$	6.23337			0.417417			0.208709	−	0.977978i	$-0.433074\pi$
$223$	6.23337			0.417417			0.208709	+	0.977978i	$0.433074\pi$
$224$	−1.86919			−0.124891
$225$	0.196658	+	17.5633i	0.0131105	+	1.17089i
$226$		−	0.559115i		−	0.0371917i
$227$	13.3667			0.887180			0.443590	−	0.896230i	$-0.353705\pi$
$227$	13.3667			0.887180			0.443590	+	0.896230i	$0.353705\pi$
$228$	−11.5366			−0.764030
$229$			5.10916i			0.337623i	0.985648	+	0.168811i	$0.0539928\pi$
$229$			5.10916i			0.337623i	−0.985648	+	0.168811i	$0.946007\pi$
$230$	−12.0227	−	11.8889i	−0.792755	−	0.783929i
$231$	21.1227			1.38977
$232$	−3.22160			−0.211508
$233$		−	25.7364i		−	1.68605i	−0.537874	−	0.843025i	$-0.680772\pi$
$233$		−	25.7364i		−	1.68605i	0.537874	−	0.843025i	$-0.319228\pi$
$234$		0			0
$235$	19.6809	−	19.9025i	1.28384	−	1.29830i
$236$			11.2785i			0.734166i
$237$			5.94786i			0.386355i
$238$		−	7.78870i		−	0.504866i
$239$			9.42688i			0.609774i	0.952389	+	0.304887i	$0.0986187\pi$
$239$			9.42688i			0.609774i	−0.952389	+	0.304887i	$0.901381\pi$
$240$	4.05765	+	4.01247i	0.261920	+	0.259004i
$241$		−	8.55884i		−	0.551324i	−0.961255	−	0.275662i	$-0.911103\pi$
$241$		−	8.55884i		−	0.551324i	0.961255	−	0.275662i	$-0.0888970\pi$
$242$	−8.60730			−0.553298
$243$		−	22.2970i		−	1.43035i
$244$	6.28685			0.402474
$245$	−5.51254	+	5.57461i	−0.352183	+	0.356149i
$246$	−27.8414			−1.77510
$247$		0			0
$248$			8.51124i			0.540464i
$249$		−	6.37126i		−	0.403762i
$250$	−8.03735	−	7.77181i	−0.508327	−	0.491532i
$251$	2.91331			0.183887			0.0919433	−	0.995764i	$-0.470692\pi$
$251$	2.91331			0.183887			0.0919433	+	0.995764i	$0.470692\pi$
$252$	6.56625			0.413635
$253$	33.4830			2.10506
$254$		−	1.52200i		−	0.0954986i
$255$	−16.7195	+	16.9077i	−1.04701	+	1.05880i
$256$	1.00000			0.0625000
$257$		−	28.3335i		−	1.76740i	−0.468057	−	0.883698i	$-0.655046\pi$
$257$		−	28.3335i		−	1.76740i	0.468057	−	0.883698i	$-0.344954\pi$
$258$	11.2002			0.697292
$259$	−0.912528			−0.0567017
$260$		0			0
$261$	11.3171			0.700510
$262$	7.16465			0.442634
$263$		−	6.57342i		−	0.405335i	−0.979248	−	0.202667i	$-0.935039\pi$
$263$		−	6.57342i		−	0.405335i	0.979248	−	0.202667i	$-0.0649610\pi$
$264$	−11.3004			−0.695494
$265$	−0.304309	−	0.300921i	−0.0186936	−	0.0184854i
$266$		−	8.44978i		−	0.518089i
$267$	30.4750			1.86504
$268$	5.69785			0.348051
$269$	−13.1504			−0.801797			−0.400898	−	0.916123i	$-0.631302\pi$
$269$	−13.1504			−0.801797			−0.400898	+	0.916123i	$0.631302\pi$
$270$	−2.08108	−	2.05791i	−0.126651	−	0.125241i
$271$			22.3779i			1.35936i	0.733507	+	0.679682i	$0.237882\pi$
$271$			22.3779i			1.35936i	−0.733507	+	0.679682i	$0.762118\pi$
$272$			4.16688i			0.252654i
$273$		0			0
$274$	16.0494			0.969579
$275$	22.1387	−	0.247888i	1.33501	−	0.0149482i
$276$	19.2975			1.16158
$277$			11.0451i			0.663634i	0.943344	+	0.331817i	$0.107662\pi$
$277$			11.0451i			0.663634i	−0.943344	+	0.331817i	$0.892338\pi$
$278$	17.7302			1.06339
$279$		−	29.8990i		−	1.79000i
$280$	−2.93886	+	2.97195i	−0.175631	+	0.177608i
$281$			20.1064i			1.19945i	0.800207	+	0.599724i	$0.204723\pi$
$281$			20.1064i			1.19945i	−0.800207	+	0.599724i	$0.795277\pi$
$282$			31.9452i			1.90231i
$283$			20.2670i			1.20475i	0.798215	+	0.602373i	$0.205778\pi$
$283$			20.2670i			1.20475i	−0.798215	+	0.602373i	$0.794222\pi$
$284$		−	10.1438i		−	0.601922i
$285$	−18.1386	+	18.3428i	−1.07444	+	1.08653i
$286$		0			0
$287$		−	20.3919i		−	1.20370i
$288$	−3.51288			−0.206998
$289$	−0.362874			−0.0213455
$290$	−5.06520	+	5.12223i	−0.297439	+	0.300788i
$291$		−	4.88420i		−	0.286317i
$292$	−4.10663			−0.240323
$293$	−29.8007			−1.74097			−0.870487	−	0.492191i	$-0.836196\pi$
$293$	−29.8007			−1.74097			−0.870487	+	0.492191i	$0.836196\pi$
$294$		−	8.94773i		−	0.521842i
$295$	17.9324	+	17.7327i	1.04406	+	1.03244i
$296$	0.488194			0.0283757
$297$	5.79577			0.336304
$298$		−	9.94873i		−	0.576315i
$299$		0			0
$300$	12.7594	−	0.142868i	0.736663	−	0.00824847i
$301$			8.20337i			0.472834i
$302$		−	11.9580i		−	0.688107i
$303$		−	41.6215i		−	2.39109i
$304$			4.52055i			0.259271i
$305$	9.88458	−	9.99588i	0.565989	−	0.572362i
$306$		−	14.6377i		−	0.836784i
$307$	9.13426			0.521320			0.260660	−	0.965431i	$-0.416060\pi$
$307$	9.13426			0.521320			0.260660	+	0.965431i	$0.416060\pi$
$308$		−	8.27681i		−	0.471615i
$309$	37.2087			2.11673
$310$	13.5326	+	13.3819i	0.768599	+	0.760041i
$311$	5.34622			0.303157			0.151578	−	0.988445i	$-0.451564\pi$
$311$	5.34622			0.303157			0.151578	+	0.988445i	$0.451564\pi$
$312$		0			0
$313$			1.32226i			0.0747385i	0.999302	+	0.0373692i	$0.0118978\pi$
$313$			1.32226i			0.0747385i	−0.999302	+	0.0373692i	$0.988102\pi$
$314$		−	6.72590i		−	0.379564i
$315$	10.3239	−	10.4401i	0.581684	−	0.588234i
$316$	2.33064			0.131108
$317$	3.84953			0.216211			0.108106	−	0.994139i	$-0.465522\pi$
$317$	3.84953			0.216211			0.108106	+	0.994139i	$0.465522\pi$
$318$	0.488443			0.0273905
$319$		−	14.2653i		−	0.798702i
$320$	1.57226	−	1.58997i	0.0878921	−	0.0888818i
$321$	−29.1487			−1.62692
$322$			14.1341i			0.787665i
$323$	−18.8366			−1.04810
$324$	−7.19832			−0.399906
$325$		0			0
$326$	−0.00838925			−0.000464638
$327$	26.4405			1.46216
$328$			10.9095i			0.602376i
$329$	−23.3977			−1.28996
$330$	−17.7673	+	17.9673i	−0.978055	+	0.989068i
$331$		−	4.96398i		−	0.272845i	−0.990651	−	0.136423i	$-0.956439\pi$
$331$		−	4.96398i		−	0.272845i	0.990651	−	0.136423i	$-0.0435605\pi$
$332$	−2.49654			−0.137016
$333$	−1.71497			−0.0939795
$334$	8.77138			0.479948
$335$	8.95851	−	9.05938i	0.489456	−	0.494967i
$336$		−	4.77024i		−	0.260238i
$337$			11.2699i			0.613911i	0.951724	+	0.306956i	$0.0993103\pi$
$337$			11.2699i			0.613911i	−0.951724	+	0.306956i	$0.900690\pi$
$338$		0			0
$339$	1.42688			0.0774975
$340$	6.62519	+	6.55143i	0.359302	+	0.355301i
$341$	−37.6879			−2.04091
$342$		−	15.8801i		−	0.858700i
$343$	19.6380			1.06035
$344$		−	4.38872i		−	0.236624i
$345$	30.3408	−	30.6824i	1.63349	−	1.65189i
$346$			5.17428i			0.278171i
$347$			15.6806i			0.841781i	0.907112	+	0.420890i	$0.138282\pi$
$347$			15.6806i			0.841781i	−0.907112	+	0.420890i	$0.861718\pi$
$348$		−	8.22163i		−	0.440725i
$349$			0.557452i			0.0298397i	0.999889	+	0.0149198i	$0.00474931\pi$
$349$			0.557452i			0.0298397i	−0.999889	+	0.0149198i	$0.995251\pi$
$350$	0.104641	+	9.34538i	0.00559329	+	0.499531i
$351$		0			0
$352$			4.42801i			0.236014i
$353$	24.1725			1.28657			0.643285	−	0.765627i	$-0.277571\pi$
$353$	24.1725			1.28657			0.643285	+	0.765627i	$0.277571\pi$
$354$	−28.7831			−1.52980
$355$	−16.1282	−	15.9487i	−0.855998	−	0.846467i
$356$		−	11.9415i		−	0.632896i
$357$	19.8770			1.05200
$358$	−7.82042			−0.413322
$359$		−	0.910208i		−	0.0480389i	−0.999711	−	0.0240195i	$-0.992354\pi$
$359$		−	0.910208i		−	0.0480389i	0.999711	−	0.0240195i	$-0.00764637\pi$
$360$	−5.52317	+	5.58536i	−0.291097	+	0.294374i
$361$	−1.43537			−0.0755457
$362$	12.2270			0.642635
$363$		−	21.9661i		−	1.15292i
$364$		0			0
$365$	−6.45671	+	6.52941i	−0.337959	+	0.341765i
$366$			16.0443i			0.838647i
$367$		−	4.41148i		−	0.230277i	−0.993349	−	0.115139i	$-0.963269\pi$
$367$		−	4.41148i		−	0.230277i	0.993349	−	0.115139i	$-0.0367312\pi$
$368$		−	7.56163i		−	0.394177i
$369$		−	38.3237i		−	1.99505i
$370$	0.767568	−	0.776211i	0.0399040	−	0.0403533i
$371$			0.357752i			0.0185735i
$372$	−21.7210			−1.12618
$373$			7.59431i			0.393219i	0.980482	+	0.196609i	$0.0629931\pi$
$373$			7.59431i			0.393219i	−0.980482	+	0.196609i	$0.937007\pi$
$374$	−18.4510			−0.954078
$375$	19.8339	−	20.5116i	1.02422	−	1.05921i
$376$	12.5176			0.645544
$377$		0			0
$378$			2.44656i			0.125838i
$379$			30.3412i			1.55852i	0.626698	+	0.779262i	$0.284406\pi$
$379$			30.3412i			1.55852i	−0.626698	+	0.779262i	$0.715594\pi$
$380$	7.18752	+	7.10749i	0.368712	+	0.364607i
$381$	3.88419			0.198993
$382$	18.1313			0.927679
$383$	−7.99851			−0.408705			−0.204352	−	0.978897i	$-0.565509\pi$
$383$	−7.99851			−0.408705			−0.204352	+	0.978897i	$0.565509\pi$
$384$			2.55203i			0.130233i
$385$	−13.1598	−	13.0133i	−0.670688	−	0.663220i
$386$	6.34605			0.323006
$387$			15.4170i			0.783693i
$388$	−1.91384			−0.0971608
$389$	22.4951			1.14055			0.570273	−	0.821455i	$-0.306837\pi$
$389$	22.4951			1.14055			0.570273	+	0.821455i	$0.306837\pi$
$390$		0			0
$391$	31.5084			1.59345
$392$	−3.50612			−0.177086
$393$			18.2844i			0.922328i
$394$	2.19339			0.110502
$395$	3.66437	−	3.70563i	0.184374	−	0.186451i
$396$		−	15.5551i		−	0.781672i
$397$	29.6953			1.49036			0.745181	−	0.666862i	$-0.232363\pi$
$397$	29.6953			1.49036			0.745181	+	0.666862i	$0.232363\pi$
$398$	−4.80668			−0.240937
$399$	21.5641			1.07956
$400$	−0.0559819	−	4.99969i	−0.00279909	−	0.249984i
$401$		−	26.3944i		−	1.31807i	−0.752110	−	0.659037i	$-0.770964\pi$
$401$		−	26.3944i		−	1.31807i	0.752110	−	0.659037i	$-0.229036\pi$
$402$			14.5411i			0.725244i
$403$		0			0
$404$	−16.3092			−0.811411
$405$	−11.3176	+	11.4451i	−0.562378	+	0.568710i
$406$	6.02179			0.298856
$407$			2.16173i			0.107153i
$408$	−10.6340			−0.526462
$409$			9.89433i			0.489243i	0.969619	+	0.244622i	$0.0786637\pi$
$409$			9.89433i			0.489243i	−0.969619	+	0.244622i	$0.921336\pi$
$410$	17.3457	+	17.1526i	0.856644	+	0.847106i
$411$			40.9586i			2.02034i
$412$		−	14.5800i		−	0.718305i
$413$		−	21.0817i		−	1.03736i
$414$			26.5631i			1.30550i
$415$	−3.92522	+	3.96942i	−0.192681	+	0.194851i
$416$		0			0
$417$			45.2482i			2.21581i
$418$	−20.0171			−0.979066
$419$	17.9386			0.876359			0.438179	−	0.898888i	$-0.355623\pi$
$419$	17.9386			0.876359			0.438179	+	0.898888i	$0.355623\pi$
$420$	−7.58452	−	7.50008i	−0.370087	−	0.365966i
$421$		−	15.5977i		−	0.760184i	−0.924949	−	0.380092i	$-0.875892\pi$
$421$		−	15.5977i		−	0.760184i	0.924949	−	0.380092i	$-0.124108\pi$
$422$	−1.98463			−0.0966105
$423$	−43.9727			−2.13802
$424$		−	0.191394i		−	0.00929490i
$425$	20.8331	−	0.233270i	1.01055	−	0.0113152i
$426$	25.8872			1.25424
$427$	−11.7513			−0.568687
$428$			11.4218i			0.552091i
$429$		0			0
$430$	−6.97792	−	6.90022i	−0.336505	−	0.332758i
$431$		−	30.0631i		−	1.44809i	−0.689753	−	0.724045i	$-0.742281\pi$
$431$		−	30.0631i		−	1.44809i	0.689753	−	0.724045i	$-0.257719\pi$
$432$		−	1.30889i		−	0.0629738i
$433$		−	22.5878i		−	1.08550i	−0.839894	−	0.542750i	$-0.817383\pi$
$433$		−	22.5878i		−	1.08550i	0.839894	−	0.542750i	$-0.182617\pi$
$434$		−	15.9092i		−	0.763664i
$435$	−13.0721	−	12.9266i	−0.626759	−	0.619781i
$436$		−	10.3606i		−	0.496181i
$437$	34.1827			1.63518
$438$		−	10.4803i		−	0.500767i
$439$	−34.8184			−1.66179			−0.830895	−	0.556429i	$-0.812171\pi$
$439$	−34.8184			−1.66179			−0.830895	+	0.556429i	$0.812171\pi$
$440$	7.04039	+	6.96200i	0.335637	+	0.331900i
$441$	12.3166			0.586503
$442$		0			0
$443$			15.5022i			0.736533i	0.929720	+	0.368267i	$0.120049\pi$
$443$			15.5022i			0.736533i	−0.929720	+	0.368267i	$0.879951\pi$
$444$			1.24589i			0.0591272i
$445$	−18.9865	−	18.7751i	−0.900047	−	0.890025i
$446$	6.23337			0.295159
$447$	25.3895			1.20088
$448$	−1.86919			−0.0883111
$449$			0.894606i			0.0422191i	0.999777	+	0.0211095i	$0.00671987\pi$
$449$			0.894606i			0.0422191i	−0.999777	+	0.0211095i	$0.993280\pi$
$450$	0.196658	+	17.5633i	0.00927053	+	0.827942i
$451$	−48.3074			−2.27471
$452$		−	0.559115i		−	0.0262985i
$453$	30.5173			1.43383
$454$	13.3667			0.627331
$455$		0			0
$456$	−11.5366			−0.540251
$457$	−10.7958			−0.505007			−0.252504	−	0.967596i	$-0.581254\pi$
$457$	−10.7958			−0.505007			−0.252504	+	0.967596i	$0.581254\pi$
$458$			5.10916i			0.238735i
$459$	5.45397			0.254570
$460$	−12.0227	−	11.8889i	−0.560563	−	0.554321i
$461$			10.8827i			0.506859i	0.967354	+	0.253429i	$0.0815585\pi$
$461$			10.8827i			0.506859i	−0.967354	+	0.253429i	$0.918441\pi$
$462$	21.1227			0.982717
$463$	−3.15999			−0.146857			−0.0734287	−	0.997300i	$-0.523394\pi$
$463$	−3.15999			−0.146857			−0.0734287	+	0.997300i	$0.523394\pi$
$464$	−3.22160			−0.149559
$465$	−34.1511	+	34.5356i	−1.58372	+	1.60155i
$466$		−	25.7364i		−	1.19222i
$467$			23.0475i			1.06651i	0.845954	+	0.533256i	$0.179032\pi$
$467$			23.0475i			1.06651i	−0.845954	+	0.533256i	$0.820968\pi$
$468$		0			0
$469$	−10.6504			−0.491789
$470$	19.6809	−	19.9025i	0.907812	−	0.918033i
$471$	17.1647			0.790908
$472$			11.2785i			0.519134i
$473$	19.4333			0.893545
$474$			5.94786i			0.273194i
$475$	22.6013	−	0.253069i	1.03702	−	0.0116116i
$476$		−	7.78870i		−	0.356994i
$477$			0.672343i			0.0307845i
$478$			9.42688i			0.431175i
$479$			9.16688i			0.418845i	0.977825	+	0.209423i	$0.0671584\pi$
$479$			9.16688i			0.418845i	−0.977825	+	0.209423i	$0.932842\pi$
$480$	4.05765	+	4.01247i	0.185205	+	0.183143i
$481$		0			0
$482$		−	8.55884i		−	0.389845i
$483$	−36.0708			−1.64128
$484$	−8.60730			−0.391241
$485$	−3.00907	+	3.04295i	−0.136635	+	0.138173i
$486$		−	22.2970i		−	1.01141i
$487$	−24.1155			−1.09278			−0.546389	−	0.837531i	$-0.683998\pi$
$487$	−24.1155			−1.09278			−0.546389	+	0.837531i	$0.683998\pi$
$488$	6.28685			0.284592
$489$		−	0.0214097i		−	0.000968178i
$490$	−5.51254	+	5.57461i	−0.249031	+	0.251835i
$491$	−5.68528			−0.256573			−0.128286	−	0.991737i	$-0.540948\pi$
$491$	−5.68528			−0.256573			−0.128286	+	0.991737i	$0.540948\pi$
$492$	−27.8414			−1.25519
$493$		−	13.4240i		−	0.604587i
$494$		0			0
$495$	−24.7320	−	24.4567i	−1.11162	−	1.09925i
$496$			8.51124i			0.382166i
$497$			18.9607i			0.850501i
$498$		−	6.37126i		−	0.285503i
$499$			6.68270i			0.299159i	0.988750	+	0.149579i	$0.0477920\pi$
$499$			6.68270i			0.299159i	−0.988750	+	0.149579i	$0.952208\pi$
$500$	−8.03735	−	7.77181i	−0.359441	−	0.347566i
$501$			22.3849i			1.00008i
$502$	2.91331			0.130027
$503$		−	17.4365i		−	0.777455i	−0.921353	−	0.388727i	$-0.872915\pi$
$503$		−	17.4365i		−	0.777455i	0.921353	−	0.388727i	$-0.127085\pi$
$504$	6.56625			0.292484
$505$	−25.6423	+	25.9310i	−1.14107	+	1.15391i
$506$	33.4830			1.48850
$507$		0			0
$508$		−	1.52200i		−	0.0675277i
$509$		−	28.6424i		−	1.26955i	−0.772696	−	0.634776i	$-0.781092\pi$
$509$		−	28.6424i		−	1.26955i	0.772696	−	0.634776i	$-0.218908\pi$
$510$	−16.7195	+	16.9077i	−0.740350	+	0.748686i
$511$	7.67609			0.339570
$512$	1.00000			0.0441942
$513$	5.91689			0.261237
$514$		−	28.3335i		−	1.24974i
$515$	−23.1817	−	22.9236i	−1.02151	−	1.01013i
$516$	11.2002			0.493060
$517$			55.4279i			2.43772i
$518$	−0.912528			−0.0400942
$519$	−13.2049			−0.579632
$520$		0			0
$521$	−24.2436			−1.06213			−0.531066	−	0.847331i	$-0.678208\pi$
$521$	−24.2436			−1.06213			−0.531066	+	0.847331i	$0.678208\pi$
$522$	11.3171			0.495335
$523$		−	7.25966i		−	0.317443i	−0.987323	−	0.158721i	$-0.949263\pi$
$523$		−	7.25966i		−	0.317443i	0.987323	−	0.158721i	$-0.0507372\pi$
$524$	7.16465			0.312989
$525$	−23.8497	+	0.267047i	−1.04089	+	0.0116549i
$526$		−	6.57342i		−	0.286615i
$527$	−35.4653			−1.54489
$528$	−11.3004			−0.491789
$529$	−34.1782			−1.48601
$530$	−0.304309	−	0.300921i	−0.0132184	−	0.0130712i
$531$		−	39.6199i		−	1.71936i
$532$		−	8.44978i		−	0.366344i
$533$		0			0
$534$	30.4750			1.31878
$535$	18.1602	+	17.9580i	0.785134	+	0.776392i
$536$	5.69785			0.246109
$537$		−	19.9580i		−	0.861251i
$538$	−13.1504			−0.566956
$539$		−	15.5251i		−	0.668715i
$540$	−2.08108	−	2.05791i	−0.0895556	−	0.0885585i
$541$		−	9.90908i		−	0.426025i	−0.977049	−	0.213012i	$-0.931673\pi$
$541$		−	9.90908i		−	0.426025i	0.977049	−	0.213012i	$-0.0683275\pi$
$542$			22.3779i			0.961215i
$543$			31.2036i			1.33908i
$544$			4.16688i			0.178653i
$545$	−16.4730	−	16.2895i	−0.705624	−	0.697767i
$546$		0			0
$547$			15.7348i			0.672769i	0.941725	+	0.336385i	$0.109204\pi$
$547$			15.7348i			0.672769i	−0.941725	+	0.336385i	$0.890796\pi$
$548$	16.0494			0.685596
$549$	−22.0850			−0.942563
$550$	22.1387	−	0.247888i	0.943996	−	0.0105700i
$551$		−	14.5634i		−	0.620421i
$552$	19.2975			0.821358
$553$	−4.35641			−0.185253
$554$			11.0451i			0.469260i
$555$	1.98092	+	1.95886i	0.0840853	+	0.0831490i
$556$	17.7302			0.751930
$557$	−11.6684			−0.494408			−0.247204	−	0.968963i	$-0.579512\pi$
$557$	−11.6684			−0.494408			−0.247204	+	0.968963i	$0.579512\pi$
$558$		−	29.8990i		−	1.26572i
$559$		0			0
$560$	−2.93886	+	2.97195i	−0.124190	+	0.125588i
$561$		−	47.0876i		−	1.98804i
$562$			20.1064i			0.848138i
$563$		−	34.0262i		−	1.43403i	−0.697056	−	0.717017i	$-0.745507\pi$
$563$		−	34.0262i		−	1.43403i	0.697056	−	0.717017i	$-0.254493\pi$
$564$			31.9452i			1.34514i
$565$	−0.888973	−	0.879075i	−0.0373994	−	0.0369830i
$566$			20.2670i			0.851884i
$567$	13.4550			0.565059
$568$		−	10.1438i		−	0.425623i
$569$	−44.3266			−1.85827			−0.929135	−	0.369741i	$-0.879446\pi$
$569$	−44.3266			−1.85827			−0.929135	+	0.369741i	$0.879446\pi$
$570$	−18.1386	+	18.3428i	−0.759741	+	0.768295i
$571$	−15.3587			−0.642740			−0.321370	−	0.946954i	$-0.604143\pi$
$571$	−15.3587			−0.642740			−0.321370	+	0.946954i	$0.604143\pi$
$572$		0			0
$573$			46.2717i			1.93303i
$574$		−	20.3919i		−	0.851143i
$575$	−37.8058	+	0.423314i	−1.57661	+	0.0176534i
$576$	−3.51288			−0.146370
$577$	−31.5537			−1.31360			−0.656799	−	0.754065i	$-0.728090\pi$
$577$	−31.5537			−1.31360			−0.656799	+	0.754065i	$0.728090\pi$
$578$	−0.362874			−0.0150936
$579$			16.1953i			0.673056i
$580$	−5.06520	+	5.12223i	−0.210321	+	0.212689i
$581$	4.66652			0.193600
$582$		−	4.88420i		−	0.202457i
$583$	0.847494			0.0350996
$584$	−4.10663			−0.169934
$585$		0			0
$586$	−29.8007			−1.23106
$587$	−22.9587			−0.947607			−0.473803	−	0.880631i	$-0.657119\pi$
$587$	−22.9587			−0.947607			−0.473803	+	0.880631i	$0.657119\pi$
$588$		−	8.94773i		−	0.368998i
$589$	−38.4755			−1.58535
$590$	17.9324	+	17.7327i	0.738265	+	0.730045i
$591$			5.59761i			0.230255i
$592$	0.488194			0.0200646
$593$	27.6241			1.13439			0.567194	−	0.823584i	$-0.308029\pi$
$593$	27.6241			1.13439			0.567194	+	0.823584i	$0.308029\pi$
$594$	5.79577			0.237803
$595$	−12.3838	−	12.2459i	−0.507685	−	0.502032i
$596$		−	9.94873i		−	0.407516i
$597$		−	12.2668i		−	0.502048i
$598$		0			0
$599$	1.54774			0.0632389			0.0316194	−	0.999500i	$-0.489934\pi$
$599$	1.54774			0.0632389			0.0316194	+	0.999500i	$0.489934\pi$
$600$	12.7594	−	0.142868i	0.520899	−	0.00583255i
$601$	25.3606			1.03448			0.517241	−	0.855840i	$-0.326959\pi$
$601$	25.3606			1.03448			0.517241	+	0.855840i	$0.326959\pi$
$602$			8.20337i			0.334344i
$603$	−20.0158			−0.815108
$604$		−	11.9580i		−	0.486565i
$605$	−13.5329	+	13.6853i	−0.550192	+	0.556387i
$606$		−	41.6215i		−	1.69076i
$607$		−	19.1839i		−	0.778652i	−0.921100	−	0.389326i	$-0.872708\pi$
$607$		−	19.1839i		−	0.778652i	0.921100	−	0.389326i	$-0.127292\pi$
$608$			4.52055i			0.183332i
$609$			15.3678i			0.622735i
$610$	9.88458	−	9.99588i	0.400215	−	0.404721i
$611$		0			0
$612$		−	14.6377i		−	0.591696i
$613$	3.32275			0.134205			0.0671024	−	0.997746i	$-0.478625\pi$
$613$	3.32275			0.134205			0.0671024	+	0.997746i	$0.478625\pi$
$614$	9.13426			0.368629
$615$	−43.7740	+	44.2669i	−1.76514	+	1.78501i
$616$		−	8.27681i		−	0.333482i
$617$	13.7220			0.552425			0.276213	−	0.961097i	$-0.410921\pi$
$617$	13.7220			0.552425			0.276213	+	0.961097i	$0.410921\pi$
$618$	37.2087			1.49675
$619$			40.9597i			1.64631i	0.567817	+	0.823155i	$0.307788\pi$
$619$			40.9597i			1.64631i	−0.567817	+	0.823155i	$0.692212\pi$
$620$	13.5326	+	13.3819i	0.543482	+	0.537430i
$621$	−9.89731			−0.397166
$622$	5.34622			0.214364
$623$			22.3209i			0.894267i
$624$		0			0
$625$	−24.9937	+	0.559784i	−0.999749	+	0.0223913i
$626$			1.32226i			0.0528481i
$627$		−	51.0842i		−	2.04011i
$628$		−	6.72590i		−	0.268392i
$629$			2.03424i			0.0811106i
$630$	10.3239	−	10.4401i	0.411313	−	0.415944i
$631$			14.9553i			0.595361i	0.954666	+	0.297680i	$0.0962130\pi$
$631$			14.9553i			0.595361i	−0.954666	+	0.297680i	$0.903787\pi$
$632$	2.33064			0.0927077
$633$		−	5.06485i		−	0.201310i
$634$	3.84953			0.152885
$635$	−2.41992	−	2.39298i	−0.0960317	−	0.0949624i
$636$	0.488443			0.0193680
$637$		0			0
$638$		−	14.2653i		−	0.564768i
$639$			35.6338i			1.40965i
$640$	1.57226	−	1.58997i	0.0621491	−	0.0628489i
$641$	36.5876			1.44512			0.722562	−	0.691306i	$-0.242964\pi$
$641$	36.5876			1.44512			0.722562	+	0.691306i	$0.242964\pi$
$642$	−29.1487			−1.15041
$643$	−43.3819			−1.71082			−0.855408	−	0.517954i	$-0.826694\pi$
$643$	−43.3819			−1.71082			−0.855408	+	0.517954i	$0.826694\pi$
$644$			14.1341i			0.556963i
$645$	17.6096	−	17.8079i	0.693377	−	0.701185i
$646$	−18.8366			−0.741115
$647$		−	42.6622i		−	1.67722i	−0.544730	−	0.838611i	$-0.683368\pi$
$647$		−	42.6622i		−	1.67722i	0.544730	−	0.838611i	$-0.316632\pi$
$648$	−7.19832			−0.282777
$649$	−49.9413			−1.96037
$650$		0			0
$651$	40.6007			1.59127
$652$	−0.00838925			−0.000328549
$653$		−	44.8543i		−	1.75528i	−0.479316	−	0.877642i	$-0.659115\pi$
$653$		−	44.8543i		−	1.75528i	0.479316	−	0.877642i	$-0.340885\pi$
$654$	26.4405			1.03391
$655$	11.2647	−	11.3916i	0.440149	−	0.445105i
$656$			10.9095i			0.425944i
$657$	14.4261			0.562816
$658$	−23.3977			−0.912138
$659$	28.7835			1.12125			0.560624	−	0.828071i	$-0.310561\pi$
$659$	28.7835			1.12125			0.560624	+	0.828071i	$0.310561\pi$
$660$	−17.7673	+	17.9673i	−0.691590	+	0.699377i
$661$		−	9.90351i		−	0.385202i	−0.981277	−	0.192601i	$-0.938308\pi$
$661$		−	9.90351i		−	0.385202i	0.981277	−	0.192601i	$-0.0616923\pi$
$662$		−	4.96398i		−	0.192931i
$663$		0			0
$664$	−2.49654			−0.0968846
$665$	−13.4349	−	13.2853i	−0.520981	−	0.515181i
$666$	−1.71497			−0.0664536
$667$			24.3605i			0.943243i
$668$	8.77138			0.339375
$669$			15.9078i			0.615030i
$670$	8.95851	−	9.05938i	0.346097	−	0.349994i
$671$			27.8383i			1.07468i
$672$		−	4.77024i		−	0.184016i
$673$		−	46.6987i		−	1.80010i	−0.435784	−	0.900051i	$-0.643529\pi$
$673$		−	46.6987i		−	1.80010i	0.435784	−	0.900051i	$-0.356471\pi$
$674$			11.2699i			0.434101i
$675$	−6.54402	+	0.0732739i	−0.251880	+	0.00282031i
$676$		0			0
$677$		−	15.1897i		−	0.583787i	−0.956451	−	0.291893i	$-0.905715\pi$
$677$		−	15.1897i		−	0.583787i	0.956451	−	0.291893i	$-0.0942852\pi$
$678$	1.42688			0.0547990
$679$	3.57735			0.137286
$680$	6.62519	+	6.55143i	0.254065	+	0.251236i
$681$			34.1123i			1.30719i
$682$	−37.6879			−1.44314
$683$	−5.91381			−0.226286			−0.113143	−	0.993579i	$-0.536092\pi$
$683$	−5.91381			−0.226286			−0.113143	+	0.993579i	$0.536092\pi$
$684$		−	15.8801i		−	0.607193i
$685$	25.2338	−	25.5180i	0.964135	−	0.974991i
$686$	19.6380			0.749781
$687$	−13.0387			−0.497459
$688$		−	4.38872i		−	0.167318i
$689$		0			0
$690$	30.3408	−	30.6824i	1.15505	−	1.16806i
$691$			23.5531i			0.896004i	0.894033	+	0.448002i	$0.147864\pi$
$691$			23.5531i			0.896004i	−0.894033	+	0.448002i	$0.852136\pi$
$692$			5.17428i			0.196697i
$693$			29.0754i			1.10448i
$694$			15.6806i			0.595229i
$695$	27.8766	−	28.1905i	1.05742	−	1.06933i
$696$		−	8.22163i		−	0.311640i
$697$	−45.4585			−1.72186
$698$			0.557452i			0.0210999i
$699$	65.6803			2.48426
$700$	0.104641	+	9.34538i	0.00395505	+	0.353222i
$701$	39.9205			1.50778			0.753888	−	0.657003i	$-0.228176\pi$
$701$	39.9205			1.50778			0.753888	+	0.657003i	$0.228176\pi$
$702$		0			0
$703$			2.20690i			0.0832349i
$704$			4.42801i			0.166887i
$705$	50.7918	+	50.2263i	1.91293	+	1.89163i
$706$	24.1725			0.909742
$707$	30.4850			1.14650
$708$	−28.7831			−1.08173
$709$		−	8.96987i		−	0.336870i	−0.985713	−	0.168435i	$-0.946129\pi$
$709$		−	8.96987i		−	0.336870i	0.985713	−	0.168435i	$-0.0538714\pi$
$710$	−16.1282	−	15.9487i	−0.605282	−	0.598543i
$711$	−8.18724			−0.307046
$712$		−	11.9415i		−	0.447525i
$713$	64.3589			2.41026
$714$	19.8770			0.743879
$715$		0			0
$716$	−7.82042			−0.292263
$717$	−24.0577			−0.898452
$718$		−	0.910208i		−	0.0339687i
$719$	19.5515			0.729149			0.364575	−	0.931174i	$-0.381214\pi$
$719$	19.5515			0.729149			0.364575	+	0.931174i	$0.381214\pi$
$720$	−5.52317	+	5.58536i	−0.205836	+	0.208154i
$721$			27.2528i			1.01495i
$722$	−1.43537			−0.0534189
$723$	21.8425			0.812330
$724$	12.2270			0.454411
$725$	0.180351	+	16.1070i	0.00669807	+	0.598198i
$726$		−	21.9661i		−	0.815240i
$727$			21.2591i			0.788458i	0.919012	+	0.394229i	$0.128988\pi$
$727$			21.2591i			0.788458i	−0.919012	+	0.394229i	$0.871012\pi$
$728$		0			0
$729$	35.3078			1.30770
$730$	−6.45671	+	6.52941i	−0.238973	+	0.241664i
$731$	18.2873			0.676379
$732$			16.0443i			0.593013i
$733$	−51.7515			−1.91149			−0.955743	−	0.294203i	$-0.904946\pi$
$733$	−51.7515			−1.91149			−0.955743	+	0.294203i	$0.904946\pi$
$734$		−	4.41148i		−	0.162831i
$735$	−14.2266	−	14.0682i	−0.524756	−	0.518913i
$736$		−	7.56163i		−	0.278725i
$737$			25.2301i			0.929364i
$738$		−	38.3237i		−	1.41072i
$739$			2.48566i			0.0914364i	0.998954	+	0.0457182i	$0.0145576\pi$
$739$			2.48566i			0.0914364i	−0.998954	+	0.0457182i	$0.985442\pi$
$740$	0.767568	−	0.776211i	0.0282164	−	0.0285341i
$741$		0			0
$742$			0.357752i			0.0131335i
$743$	−41.9532			−1.53911			−0.769557	−	0.638578i	$-0.779523\pi$
$743$	−41.9532			−1.53911			−0.769557	+	0.638578i	$0.779523\pi$
$744$	−21.7210			−0.796330
$745$	−15.8181	−	15.6420i	−0.579532	−	0.573079i
$746$			7.59431i			0.278048i
$747$	8.77005			0.320879
$748$	−18.4510			−0.674635
$749$		−	21.3495i		−	0.780092i
$750$	19.8339	−	20.5116i	0.724233	−	0.748977i
$751$	−4.26126			−0.155496			−0.0777478	−	0.996973i	$-0.524773\pi$
$751$	−4.26126			−0.155496			−0.0777478	+	0.996973i	$0.524773\pi$
$752$	12.5176			0.456468
$753$			7.43487i			0.270942i
$754$		0			0
$755$	−19.0128	−	18.8011i	−0.691948	−	0.684244i
$756$			2.44656i			0.0889806i
$757$			32.1223i			1.16750i	0.811932	+	0.583752i	$0.198416\pi$
$757$			32.1223i			1.16750i	−0.811932	+	0.583752i	$0.801584\pi$
$758$			30.3412i			1.10204i
$759$			85.4498i			3.10163i
$760$	7.18752	+	7.10749i	0.260719	+	0.257816i
$761$			50.8769i			1.84429i	0.386850	+	0.922143i	$0.373563\pi$
$761$			50.8769i			1.84429i	−0.386850	+	0.922143i	$0.626437\pi$
$762$	3.88419			0.140709
$763$			19.3659i			0.701093i
$764$	18.1313			0.655968
$765$	−23.2735	−	23.0144i	−0.841455	−	0.832086i
$766$	−7.99851			−0.288998
$767$		0			0
$768$			2.55203i			0.0920886i
$769$			10.8452i			0.391089i	0.980695	+	0.195545i	$0.0626475\pi$
$769$			10.8452i			0.391089i	−0.980695	+	0.195545i	$0.937353\pi$
$770$	−13.1598	−	13.0133i	−0.474248	−	0.468967i
$771$	72.3081			2.60411
$772$	6.34605			0.228399
$773$	17.0142			0.611959			0.305979	−	0.952038i	$-0.401016\pi$
$773$	17.0142			0.611959			0.305979	+	0.952038i	$0.401016\pi$
$774$			15.4170i			0.554154i
$775$	42.5535	−	0.476475i	1.52857	−	0.0171155i
$776$	−1.91384			−0.0687030
$777$		−	2.32880i		−	0.0835453i
$778$	22.4951			0.806488
$779$	−49.3169			−1.76696
$780$		0			0
$781$	44.9167			1.60725
$782$	31.5084			1.12674
$783$			4.21670i			0.150693i
$784$	−3.50612			−0.125219
$785$	−10.6939	−	10.5749i	−0.381683	−	0.377433i
$786$			18.2844i			0.652184i
$787$	−27.0297			−0.963505			−0.481752	−	0.876307i	$-0.660000\pi$
$787$	−27.0297			−0.963505			−0.481752	+	0.876307i	$0.660000\pi$
$788$	2.19339			0.0781364
$789$	16.7756			0.597227
$790$	3.66437	−	3.70563i	0.130372	−	0.131840i
$791$			1.04509i			0.0371592i
$792$		−	15.5551i		−	0.552726i
$793$		0			0
$794$	29.6953			1.05385
$795$	0.767961	−	0.776608i	0.0272368	−	0.0275435i
$796$	−4.80668			−0.170368
$797$			15.1585i			0.536942i	0.963288	+	0.268471i	$0.0865183\pi$
$797$			15.1585i			0.536942i	−0.963288	+	0.268471i	$0.913482\pi$
$798$	21.5641			0.763362
$799$			52.1591i			1.84526i
$800$	−0.0559819	−	4.99969i	−0.00197926	−	0.176766i
$801$			41.9489i			1.48219i
$802$		−	26.3944i		−	0.932019i
$803$		−	18.1842i		−	0.641708i
$804$			14.5411i			0.512825i
$805$	22.4728	+	22.2226i	0.792062	+	0.783243i
$806$		0			0
$807$		−	33.5604i		−	1.18138i
$808$	−16.3092			−0.573754
$809$	39.3369			1.38301			0.691506	−	0.722371i	$-0.256948\pi$
$809$	39.3369			1.38301			0.691506	+	0.722371i	$0.256948\pi$
$810$	−11.3176	+	11.4451i	−0.397661	+	0.402139i
$811$		−	9.57933i		−	0.336376i	−0.985755	−	0.168188i	$-0.946208\pi$
$811$		−	9.57933i		−	0.336376i	0.985755	−	0.168188i	$-0.0537915\pi$
$812$	6.02179			0.211323
$813$	−57.1093			−2.00291
$814$			2.16173i			0.0757685i
$815$	−0.0131901	+	0.0133386i	−0.000462029	+	0.000467232i
$816$	−10.6340			−0.372265
$817$	19.8394			0.694094
$818$			9.89433i			0.345947i
$819$		0			0
$820$	17.3457	+	17.1526i	0.605739	+	0.598994i
$821$			7.82037i			0.272933i	0.990645	+	0.136466i	$0.0435745\pi$
$821$			7.82037i			0.272933i	−0.990645	+	0.136466i	$0.956425\pi$
$822$			40.9586i			1.42859i
$823$			34.1839i			1.19158i	0.803142	+	0.595788i	$0.203160\pi$
$823$			34.1839i			1.19158i	−0.803142	+	0.595788i	$0.796840\pi$
$824$		−	14.5800i		−	0.507919i
$825$	0.632620	+	56.4987i	0.0220250	+	1.96703i
$826$		−	21.0817i		−	0.733524i
$827$	−3.47145			−0.120714			−0.0603570	−	0.998177i	$-0.519224\pi$
$827$	−3.47145			−0.120714			−0.0603570	+	0.998177i	$0.519224\pi$
$828$			26.5631i			0.923131i
$829$	13.3557			0.463864			0.231932	−	0.972732i	$-0.425495\pi$
$829$	13.3557			0.463864			0.231932	+	0.972732i	$0.425495\pi$
$830$	−3.92522	+	3.96942i	−0.136246	+	0.137780i
$831$	−28.1874			−0.977811
$832$		0			0
$833$		−	14.6096i		−	0.506192i
$834$			45.2482i			1.56682i
$835$	13.7909	−	13.9462i	0.477254	−	0.482628i
$836$	−20.0171			−0.692304
$837$	11.1402			0.385063
$838$	17.9386			0.619679
$839$		−	47.9304i		−	1.65474i	−0.561657	−	0.827370i	$-0.689836\pi$
$839$		−	47.9304i		−	1.65474i	0.561657	−	0.827370i	$-0.310164\pi$
$840$	−7.58452	−	7.50008i	−0.261691	−	0.258777i
$841$	−18.6213			−0.642114
$842$		−	15.5977i		−	0.537532i
$843$	−51.3123			−1.76729
$844$	−1.98463			−0.0683139
$845$		0			0
$846$	−43.9727			−1.51181
$847$	16.0887			0.552814
$848$		−	0.191394i		−	0.00657249i
$849$	−51.7220			−1.77509
$850$	20.8331	−	0.233270i	0.714569	−	0.00800108i
$851$		−	3.69154i		−	0.126544i
$852$	25.8872			0.886882
$853$	36.4405			1.24770			0.623850	−	0.781544i	$-0.285568\pi$
$853$	36.4405			1.24770			0.623850	+	0.781544i	$0.285568\pi$
$854$	−11.7513			−0.402123
$855$	−25.2489	−	24.9678i	−0.863494	−	0.853879i
$856$			11.4218i			0.390388i
$857$		−	29.9745i		−	1.02391i	−0.859013	−	0.511954i	$-0.828922\pi$
$857$		−	29.9745i		−	1.02391i	0.859013	−	0.511954i	$-0.171078\pi$
$858$		0			0
$859$	−34.8453			−1.18891			−0.594454	−	0.804130i	$-0.702632\pi$
$859$	−34.8453			−1.18891			−0.594454	+	0.804130i	$0.702632\pi$
$860$	−6.97792	−	6.90022i	−0.237945	−	0.235296i
$861$	52.0409			1.77355
$862$		−	30.0631i		−	1.02395i
$863$	25.2753			0.860381			0.430190	−	0.902738i	$-0.358446\pi$
$863$	25.2753			0.860381			0.430190	+	0.902738i	$0.358446\pi$
$864$		−	1.30889i		−	0.0445292i
$865$	8.22692	+	8.13532i	0.279724	+	0.276609i
$866$		−	22.5878i		−	0.767565i
$867$		−	0.926067i		−	0.0314509i
$868$		−	15.9092i		−	0.539992i
$869$			10.3201i			0.350085i
$870$	−13.0721	−	12.9266i	−0.443186	−	0.438251i
$871$		0			0
$872$		−	10.3606i		−	0.350853i
$873$	6.72311			0.227543
$874$	34.1827			1.15625
$875$	15.0234	+	14.5270i	0.507882	+	0.491103i
$876$		−	10.4803i		−	0.354096i
$877$	−6.44566			−0.217654			−0.108827	−	0.994061i	$-0.534710\pi$
$877$	−6.44566			−0.217654			−0.108827	+	0.994061i	$0.534710\pi$
$878$	−34.8184			−1.17506
$879$		−	76.0524i		−	2.56518i
$880$	7.04039	+	6.96200i	0.237331	+	0.234689i
$881$	12.5890			0.424133			0.212066	−	0.977255i	$-0.431981\pi$
$881$	12.5890			0.424133			0.212066	+	0.977255i	$0.431981\pi$
$882$	12.3166			0.414721
$883$		−	17.7501i		−	0.597339i	−0.954357	−	0.298669i	$-0.903457\pi$
$883$		−	17.7501i		−	0.597339i	0.954357	−	0.298669i	$-0.0965428\pi$
$884$		0			0
$885$	−45.2545	+	45.7641i	−1.52121	+	1.53834i
$886$			15.5022i			0.520808i
$887$		−	6.79925i		−	0.228296i	−0.993464	−	0.114148i	$-0.963586\pi$
$887$		−	6.79925i		−	0.228296i	0.993464	−	0.114148i	$-0.0364139\pi$
$888$			1.24589i			0.0418092i
$889$			2.84491i			0.0954151i
$890$	−18.9865	−	18.7751i	−0.636429	−	0.629343i
$891$		−	31.8742i		−	1.06783i
$892$	6.23337			0.208709
$893$			56.5862i			1.89359i
$894$	25.3895			0.849152
$895$	−12.2958	+	12.4342i	−0.411002	+	0.415630i
$896$	−1.86919			−0.0624453
$897$		0			0
$898$			0.894606i			0.0298534i
$899$		−	27.4198i		−	0.914501i
$900$	0.196658	+	17.5633i	0.00655525	+	0.585443i
$901$	0.797514			0.0265691
$902$	−48.3074			−1.60846
$903$	−20.9353			−0.696682
$904$		−	0.559115i		−	0.0185959i
$905$	19.2240	−	19.4404i	0.639027	−	0.646222i
$906$	30.5173			1.01387
$907$		−	10.4184i		−	0.345937i	−0.984927	−	0.172969i	$-0.944664\pi$
$907$		−	10.4184i		−	0.345937i	0.984927	−	0.172969i	$-0.0553359\pi$
$908$	13.3667			0.443590
$909$	57.2921			1.90026
$910$		0			0
$911$	−9.38030			−0.310783			−0.155392	−	0.987853i	$-0.549664\pi$
$911$	−9.38030			−0.310783			−0.155392	+	0.987853i	$0.549664\pi$
$912$	−11.5366			−0.382015
$913$		−	11.0547i		−	0.365858i
$914$	−10.7958			−0.357094
$915$	25.5098	+	25.2258i	0.843329	+	0.833939i
$916$			5.10916i			0.168811i
$917$	−13.3921			−0.442247
$918$	5.45397			0.180008
$919$	−39.0419			−1.28787			−0.643937	−	0.765078i	$-0.722700\pi$
$919$	−39.0419			−1.28787			−0.643937	+	0.765078i	$0.722700\pi$
$920$	−12.0227	−	11.8889i	−0.396378	−	0.391964i
$921$			23.3109i			0.768121i
$922$			10.8827i			0.358403i
$923$		0			0
$924$	21.1227			0.694886
$925$	−0.0273300	−	2.44081i	−0.000898605	−	0.0802535i
$926$	−3.15999			−0.103844
$927$			51.2178i			1.68221i
$928$	−3.22160			−0.105754
$929$			29.3209i			0.961988i	0.876724	+	0.480994i	$0.159724\pi$
$929$			29.3209i			0.961988i	−0.876724	+	0.480994i	$0.840276\pi$
$930$	−34.1511	+	34.5356i	−1.11986	+	1.13247i
$931$		−	15.8496i		−	0.519449i
$932$		−	25.7364i		−	0.843025i
$933$			13.6437i			0.446676i
$934$			23.0475i			0.754138i
$935$	−29.0098	+	29.3364i	−0.948722	+	0.959404i
$936$		0			0
$937$		−	55.0322i		−	1.79782i	−0.438130	−	0.898911i	$-0.644359\pi$
$937$		−	55.0322i		−	1.79782i	0.438130	−	0.898911i	$-0.355641\pi$
$938$	−10.6504			−0.347747
$939$	−3.37445			−0.110121
$940$	19.6809	−	19.9025i	0.641920	−	0.649148i
$941$			12.9833i			0.423243i	0.977352	+	0.211621i	$0.0678744\pi$
$941$			12.9833i			0.423243i	−0.977352	+	0.211621i	$0.932126\pi$
$942$	17.1647			0.559257
$943$	82.4935			2.68636
$944$			11.2785i			0.367083i
$945$	3.88995	+	3.84664i	0.126540	+	0.125131i
$946$	19.4333			0.631832
$947$	−43.0090			−1.39760			−0.698802	−	0.715316i	$-0.746283\pi$
$947$	−43.0090			−1.39760			−0.698802	+	0.715316i	$0.746283\pi$
$948$			5.94786i			0.193178i
$949$		0			0
$950$	22.6013	−	0.253069i	0.733284	−	0.00821064i
$951$			9.82414i			0.318570i
$952$		−	7.78870i		−	0.252433i
$953$			26.9615i			0.873369i	0.899615	+	0.436684i	$0.143847\pi$
$953$			26.9615i			0.873369i	−0.899615	+	0.436684i	$0.856153\pi$
$954$			0.672343i			0.0217679i
$955$	28.5072	−	28.8282i	0.922471	−	0.932858i
$956$			9.42688i			0.304887i
$957$	36.4055			1.17682
$958$			9.16688i			0.296168i
$959$	−29.9994			−0.968731
$960$	4.05765	+	4.01247i	0.130960	+	0.129502i
$961$	−41.4412			−1.33681
$962$		0			0
$963$		−	40.1232i		−	1.29295i
$964$		−	8.55884i		−	0.275662i
$965$	9.97766	−	10.0900i	0.321192	−	0.324809i
$966$	−36.0708			−1.16056
$967$	−3.03699			−0.0976630			−0.0488315	−	0.998807i	$-0.515550\pi$
$967$	−3.03699			−0.0976630			−0.0488315	+	0.998807i	$0.515550\pi$
$968$	−8.60730			−0.276649
$969$		−	48.0716i		−	1.54428i
$970$	−3.00907	+	3.04295i	−0.0966153	+	0.0977032i
$971$	29.5149			0.947180			0.473590	−	0.880746i	$-0.342958\pi$
$971$	29.5149			0.947180			0.473590	+	0.880746i	$0.342958\pi$
$972$		−	22.2970i		−	0.715177i
$973$	−33.1412			−1.06246
$974$	−24.1155			−0.772711
$975$		0			0
$976$	6.28685			0.201237
$977$	38.3621			1.22731			0.613656	−	0.789574i	$-0.289698\pi$
$977$	38.3621			1.22731			0.613656	+	0.789574i	$0.289698\pi$
$978$		−	0.0214097i		−	0.000684606i
$979$	52.8769			1.68995
$980$	−5.51254	+	5.57461i	−0.176092	+	0.178074i
$981$			36.3954i			1.16202i
$982$	−5.68528			−0.181424
$983$	−30.0081			−0.957109			−0.478554	−	0.878058i	$-0.658839\pi$
$983$	−30.0081			−0.957109			−0.478554	+	0.878058i	$0.658839\pi$
$984$	−27.8414			−0.887551
$985$	3.44859	−	3.48742i	0.109881	−	0.111118i
$986$		−	13.4240i		−	0.427507i
$987$		−	59.7118i		−	1.90065i
$988$		0			0
$989$	−33.1859			−1.05525
$990$	−24.7320	−	24.4567i	−0.786036	−	0.777284i
$991$	−24.3851			−0.774618			−0.387309	−	0.921950i	$-0.626595\pi$
$991$	−24.3851			−0.774618			−0.387309	+	0.921950i	$0.626595\pi$
$992$			8.51124i			0.270232i
$993$	12.6683			0.402015
$994$			18.9607i			0.601395i
$995$	−7.55737	+	7.64246i	−0.239585	+	0.242282i
$996$		−	6.37126i		−	0.201881i
$997$			29.2603i			0.926681i	0.886180	+	0.463341i	$0.153349\pi$
$997$			29.2603i			0.926681i	−0.886180	+	0.463341i	$0.846651\pi$
$998$			6.68270i			0.211537i
$999$		−	0.638990i		−	0.0202167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.c.h.1689.16		18
5.4	even	2		1690.2.c.g.1689.3		18
13.5	odd	4		1690.2.b.g.339.7	yes	18
13.8	odd	4		1690.2.b.f.339.16	yes	18
13.12	even	2		1690.2.c.g.1689.16		18
65.8	even	4		8450.2.a.cx.1.3		9
65.18	even	4		8450.2.a.ct.1.3		9
65.34	odd	4		1690.2.b.f.339.3	✓	18
65.44	odd	4		1690.2.b.g.339.12	yes	18
65.47	even	4		8450.2.a.cw.1.7		9
65.57	even	4		8450.2.a.da.1.7		9
65.64	even	2	inner	1690.2.c.h.1689.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.3	✓	18	65.34	odd	4
1690.2.b.f.339.16	yes	18	13.8	odd	4
1690.2.b.g.339.7	yes	18	13.5	odd	4
1690.2.b.g.339.12	yes	18	65.44	odd	4
1690.2.c.g.1689.3		18	5.4	even	2
1690.2.c.g.1689.16		18	13.12	even	2
1690.2.c.h.1689.3		18	65.64	even	2	inner
1690.2.c.h.1689.16		18	1.1	even	1	trivial
8450.2.a.ct.1.3		9	65.18	even	4
8450.2.a.cw.1.7		9	65.47	even	4
8450.2.a.cx.1.3		9	65.8	even	4
8450.2.a.da.1.7		9	65.57	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.55203i q^{3} +1.00000 q^{4} +(1.57226 - 1.58997i) q^{5} +2.55203i q^{6} -1.86919 q^{7} +1.00000 q^{8} -3.51288 q^{9} +(1.57226 - 1.58997i) q^{10} +4.42801i q^{11} +2.55203i q^{12} -1.86919 q^{14} +(4.05765 + 4.01247i) q^{15} +1.00000 q^{16} +4.16688i q^{17} -3.51288 q^{18} +4.52055i q^{19} +(1.57226 - 1.58997i) q^{20} -4.77024i q^{21} +4.42801i q^{22} -7.56163i q^{23} +2.55203i q^{24} +(-0.0559819 - 4.99969i) q^{25} -1.30889i q^{27} -1.86919 q^{28} -3.22160 q^{29} +(4.05765 + 4.01247i) q^{30} +8.51124i q^{31} +1.00000 q^{32} -11.3004 q^{33} +4.16688i q^{34} +(-2.93886 + 2.97195i) q^{35} -3.51288 q^{36} +0.488194 q^{37} +4.52055i q^{38} +(1.57226 - 1.58997i) q^{40} +10.9095i q^{41} -4.77024i q^{42} -4.38872i q^{43} +4.42801i q^{44} +(-5.52317 + 5.58536i) q^{45} -7.56163i q^{46} +12.5176 q^{47} +2.55203i q^{48} -3.50612 q^{49} +(-0.0559819 - 4.99969i) q^{50} -10.6340 q^{51} -0.191394i q^{53} -1.30889i q^{54} +(7.04039 + 6.96200i) q^{55} -1.86919 q^{56} -11.5366 q^{57} -3.22160 q^{58} +11.2785i q^{59} +(4.05765 + 4.01247i) q^{60} +6.28685 q^{61} +8.51124i q^{62} +6.56625 q^{63} +1.00000 q^{64} -11.3004 q^{66} +5.69785 q^{67} +4.16688i q^{68} +19.2975 q^{69} +(-2.93886 + 2.97195i) q^{70} -10.1438i q^{71} -3.51288 q^{72} -4.10663 q^{73} +0.488194 q^{74} +(12.7594 - 0.142868i) q^{75} +4.52055i q^{76} -8.27681i q^{77} +2.33064 q^{79} +(1.57226 - 1.58997i) q^{80} -7.19832 q^{81} +10.9095i q^{82} -2.49654 q^{83} -4.77024i q^{84} +(6.62519 + 6.55143i) q^{85} -4.38872i q^{86} -8.22163i q^{87} +4.42801i q^{88} -11.9415i q^{89} +(-5.52317 + 5.58536i) q^{90} -7.56163i q^{92} -21.7210 q^{93} +12.5176 q^{94} +(7.18752 + 7.10749i) q^{95} +2.55203i q^{96} -1.91384 q^{97} -3.50612 q^{98} -15.5551i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{2} + 18 q^{4} - 2 q^{5} - 2 q^{7} + 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} + 14 q^{15} + 18 q^{16} - 16 q^{18} - 2 q^{20} - 22 q^{25} - 2 q^{28} - 30 q^{29} + 14 q^{30} + 18 q^{32} - 28 q^{33}+ \cdots - 20 q^{98}+O(q^{100}) \) 18 * q + 18 * q^2 + 18 * q^4 - 2 * q^5 - 2 * q^7 + 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 + 14 * q^15 + 18 * q^16 - 16 * q^18 - 2 * q^20 - 22 * q^25 - 2 * q^28 - 30 * q^29 + 14 * q^30 + 18 * q^32 - 28 * q^33 - 4 * q^35 - 16 * q^36 + 20 * q^37 - 2 * q^40 + 20 * q^45 - 10 * q^47 - 20 * q^49 - 22 * q^50 - 24 * q^51 - 2 * q^56 - 24 * q^57 - 30 * q^58 + 14 * q^60 - 38 * q^61 + 78 * q^63 + 18 * q^64 - 28 * q^66 - 2 * q^67 - 28 * q^69 - 4 * q^70 - 16 * q^72 - 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 - 2 * q^80 + 106 * q^81 - 2 * q^83 - 16 * q^85 + 20 * q^90 + 56 * q^93 - 10 * q^94 + 54 * q^95 + 12 * q^97 - 20 * q^98

Introduction

L-functions

Modular forms

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Database

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