LMFDB - Embedded newform 1690.2.b.g.339.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(339,1690)] 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, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.339"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0,-18,0,14,0,0,-16,2,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == 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			339.7
Root			$-0.430845i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.g.339.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			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
$5$	−1.58997	−	1.57226i	−0.711054	−	0.703137i
$5$	−1.58997	−	1.57226i	−0.711054	−	0.703137i
$6$	2.55203			1.04186
$7$		−	1.86919i		−	0.706488i	−0.935531	−	0.353244i	$-0.885078\pi$
$7$		−	1.86919i		−	0.706488i	0.935531	−	0.353244i	$-0.114922\pi$
$8$			1.00000i			0.353553i
$9$	−3.51288			−1.17096
$10$	−1.57226	+	1.58997i	−0.497193	+	0.502791i
$11$	−4.42801			−1.33510			−0.667548	−	0.744567i	$-0.732656\pi$
$11$	−4.42801			−1.33510			−0.667548	+	0.744567i	$0.732656\pi$
$12$		−	2.55203i		−	0.736709i
$13$		0			0
$13$		0			0
$14$	−1.86919			−0.499563
$15$	4.01247	−	4.05765i	1.03601	−	1.04768i
$16$	1.00000			0.250000
$17$		−	4.16688i		−	1.01062i	−0.862939	−	0.505308i	$-0.831379\pi$
$17$		−	4.16688i		−	1.01062i	0.862939	−	0.505308i	$-0.168621\pi$
$18$			3.51288i			0.827994i
$19$	4.52055			1.03709			0.518543	−	0.855052i	$-0.326475\pi$
$19$	4.52055			1.03709			0.518543	+	0.855052i	$0.326475\pi$
$20$	1.58997	+	1.57226i	0.355527	+	0.351569i
$21$	4.77024			1.04095
$22$			4.42801i			0.944056i
$23$			7.56163i			1.57671i	0.615221	+	0.788354i	$0.289067\pi$
$23$			7.56163i			1.57671i	−0.615221	+	0.788354i	$0.710933\pi$
$24$	−2.55203			−0.520932
$25$	0.0559819	+	4.99969i	0.0111964	+	0.999937i
$26$		0			0
$27$		−	1.30889i		−	0.251895i
$28$			1.86919i			0.353244i
$29$	−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
$31$	8.51124			1.52866			0.764332	−	0.644823i	$-0.223069\pi$
$31$	8.51124			1.52866			0.764332	+	0.644823i	$0.223069\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	11.3004i		−	1.96715i
$34$	−4.16688			−0.714614
$35$	−2.93886	+	2.97195i	−0.496758	+	0.502352i
$36$	3.51288			0.585480
$37$			0.488194i			0.0802585i	0.999194	+	0.0401293i	$0.0127770\pi$
$37$			0.488194i			0.0802585i	−0.999194	+	0.0401293i	$0.987223\pi$
$38$		−	4.52055i		−	0.733330i
$39$		0			0
$40$	1.57226	−	1.58997i	0.248597	−	0.251396i
$41$	10.9095			1.70378			0.851888	−	0.523724i	$-0.175458\pi$
$41$	10.9095			1.70378			0.851888	+	0.523724i	$0.175458\pi$
$42$		−	4.77024i		−	0.736065i
$43$			4.38872i			0.669274i	0.942347	+	0.334637i	$0.108614\pi$
$43$			4.38872i			0.669274i	−0.942347	+	0.334637i	$0.891386\pi$
$44$	4.42801			0.667548
$45$	5.58536	+	5.52317i	0.832616	+	0.823345i
$46$	7.56163			1.11490
$47$			12.5176i			1.82587i	0.408101	+	0.912937i	$0.366191\pi$
$47$			12.5176i			1.82587i	−0.408101	+	0.912937i	$0.633809\pi$
$48$			2.55203i			0.368354i
$49$	3.50612			0.500874
$50$	4.99969	−	0.0559819i	0.707062	−	0.00791703i
$51$	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	$-0.00418430\pi$
$54$	−1.30889			−0.178117
$55$	7.04039	+	6.96200i	0.949326	+	0.938756i
$56$	1.86919			0.249781
$57$			11.5366i			1.52806i
$58$			3.22160i			0.423016i
$59$	−11.2785			−1.46833			−0.734166	−	0.678970i	$-0.762427\pi$
$59$	−11.2785			−1.46833			−0.734166	+	0.678970i	$0.762427\pi$
$60$	−4.01247	+	4.05765i	−0.518007	+	0.523840i
$61$	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
$63$			6.56625i			0.827270i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−11.3004			−1.39099
$67$		−	5.69785i		−	0.696103i	−0.937475	−	0.348051i	$-0.886843\pi$
$67$		−	5.69785i		−	0.696103i	0.937475	−	0.348051i	$-0.113157\pi$
$68$			4.16688i			0.505308i
$69$	−19.2975			−2.32315
$70$	2.97195	+	2.93886i	0.355216	+	0.351261i
$71$	−10.1438			−1.20384			−0.601922	−	0.798555i	$-0.705598\pi$
$71$	−10.1438			−1.20384			−0.601922	+	0.798555i	$0.705598\pi$
$72$		−	3.51288i		−	0.413997i
$73$		−	4.10663i		−	0.480645i	−0.970693	−	0.240323i	$-0.922747\pi$
$73$		−	4.10663i		−	0.480645i	0.970693	−	0.240323i	$-0.0772532\pi$
$74$	0.488194			0.0567514
$75$	−12.7594	+	0.142868i	−1.47333	+	0.0164969i
$76$	−4.52055			−0.518543
$77$			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	$0.458146\pi$
$80$	−1.58997	−	1.57226i	−0.177764	−	0.175784i
$81$	−7.19832			−0.799813
$82$		−	10.9095i		−	1.20475i
$83$			2.49654i			0.274031i	0.990569	+	0.137016i	$0.0437510\pi$
$83$			2.49654i			0.274031i	−0.990569	+	0.137016i	$0.956249\pi$
$84$	−4.77024			−0.520476
$85$	−6.55143	+	6.62519i	−0.710602	+	0.718603i
$86$	4.38872			0.473248
$87$		−	8.22163i		−	0.881451i
$88$		−	4.42801i		−	0.472028i
$89$	11.9415			1.26579			0.632896	−	0.774237i	$-0.281866\pi$
$89$	11.9415			1.26579			0.632896	+	0.774237i	$0.281866\pi$
$90$	5.52317	−	5.58536i	0.582193	−	0.588748i
$91$		0			0
$92$		−	7.56163i		−	0.788354i
$93$			21.7210i			2.25236i
$94$	12.5176			1.29109
$95$	−7.18752	−	7.10749i	−0.737424	−	0.729213i
$96$	2.55203			0.260466
$97$			1.91384i			0.194322i	0.995269	+	0.0971608i	$0.0309761\pi$
$97$			1.91384i			0.194322i	−0.995269	+	0.0971608i	$0.969024\pi$
$98$		−	3.50612i		−	0.354171i
$99$	15.5551			1.56334
$100$	−0.0559819	−	4.99969i	−0.00559819	−	0.499969i
$101$	16.3092			1.62282			0.811411	−	0.584476i	$-0.198700\pi$
$101$	16.3092			1.62282			0.811411	+	0.584476i	$0.198700\pi$
$102$		−	10.6340i		−	1.05292i
$103$			14.5800i			1.43661i	0.695728	+	0.718305i	$0.255082\pi$
$103$			14.5800i			1.43661i	−0.695728	+	0.718305i	$0.744918\pi$
$104$		0			0
$105$	−7.58452	−	7.50008i	−0.740174	−	0.731932i
$106$	−0.191394			−0.0185898
$107$			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
$109$	−10.3606			−0.992363			−0.496181	−	0.868219i	$-0.665265\pi$
$109$	−10.3606			−0.992363			−0.496181	+	0.868219i	$0.665265\pi$
$110$	6.96200	−	7.04039i	0.663801	−	0.671275i
$111$	−1.24589			−0.118254
$112$		−	1.86919i		−	0.176622i
$113$		−	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
$115$	11.8889	−	12.0227i	1.10864	−	1.12113i
$116$	3.22160			0.299118
$117$		0			0
$118$			11.2785i			1.03827i
$119$	−7.78870			−0.713989
$120$	4.05765	+	4.01247i	0.370411	+	0.366287i
$121$	8.60730			0.782482
$122$		−	6.28685i		−	0.569185i
$123$			27.8414i			2.51037i
$124$	−8.51124			−0.764332
$125$	7.77181	−	8.03735i	0.695132	−	0.718882i
$126$	6.56625			0.584968
$127$			1.52200i			0.135055i	0.997717	+	0.0675277i	$0.0215111\pi$
$127$			1.52200i			0.135055i	−0.997717	+	0.0675277i	$0.978489\pi$
$128$			1.00000i			0.0883883i
$129$	−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	$0.398670\pi$
$132$			11.3004i			0.983577i
$133$		−	8.44978i		−	0.732689i
$134$	−5.69785			−0.492219
$135$	−2.05791	+	2.08108i	−0.177117	+	0.179111i
$136$	4.16688			0.357307
$137$			16.0494i			1.37119i	0.727983	+	0.685596i	$0.240458\pi$
$137$			16.0494i			1.37119i	−0.727983	+	0.685596i	$0.759542\pi$
$138$			19.2975i			1.64272i
$139$	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
$141$	−31.9452			−2.69027
$142$			10.1438i			0.851246i
$143$		0			0
$144$	−3.51288			−0.292740
$145$	5.12223	+	5.06520i	0.425378	+	0.420642i
$146$	−4.10663			−0.339867
$147$			8.94773i			0.737997i
$148$		−	0.488194i		−	0.0401293i
$149$	−9.94873			−0.815032			−0.407516	−	0.913198i	$-0.633605\pi$
$149$	−9.94873			−0.815032			−0.407516	+	0.913198i	$0.633605\pi$
$150$	0.142868	+	12.7594i	0.0116651	+	1.04180i
$151$	11.9580			0.973130			0.486565	−	0.873644i	$-0.338250\pi$
$151$	11.9580			0.973130			0.486565	+	0.873644i	$0.338250\pi$
$152$			4.52055i			0.366665i
$153$			14.6377i			1.18339i
$154$	8.27681			0.666964
$155$	−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	$-0.0864924\pi$
$158$		−	2.33064i		−	0.185415i
$159$	0.488443			0.0387361
$160$	−1.57226	+	1.58997i	−0.124298	+	0.125698i
$161$	14.1341			1.11393
$162$			7.19832i			0.565553i
$163$		−	0.00838925i		−	0.000657097i	−1.00000		0.000328549i	$-0.999895\pi$
$163$		−	0.00838925i		−	0.000657097i	1.00000		0.000328549i	$-0.000104580\pi$
$164$	−10.9095			−0.851888
$165$	−17.7673	+	17.9673i	−1.38318	+	1.39875i
$166$	2.49654			0.193769
$167$			8.77138i			0.678749i	0.940651	+	0.339375i	$0.110215\pi$
$167$			8.77138i			0.678749i	−0.940651	+	0.339375i	$0.889785\pi$
$168$			4.77024i			0.368032i
$169$		0			0
$170$	6.62519	+	6.55143i	0.508129	+	0.502471i
$171$	−15.8801			−1.21439
$172$		−	4.38872i		−	0.334637i
$173$		−	5.17428i		−	0.393393i	−0.980464	−	0.196697i	$-0.936979\pi$
$173$		−	5.17428i		−	0.393393i	0.980464	−	0.196697i	$-0.0630214\pi$
$174$	−8.22163			−0.623280
$175$	9.34538	−	0.104641i	0.706444	−	0.00791011i
$176$	−4.42801			−0.333774
$177$		−	28.7831i		−	2.16347i
$178$		−	11.9415i		−	0.895050i
$179$	7.82042			0.584526			0.292263	−	0.956338i	$-0.405592\pi$
$179$	7.82042			0.584526			0.292263	+	0.956338i	$0.405592\pi$
$180$	−5.58536	−	5.52317i	−0.416308	−	0.411673i
$181$	−12.2270			−0.908823			−0.454411	−	0.890792i	$-0.650150\pi$
$181$	−12.2270			−0.908823			−0.454411	+	0.890792i	$0.650150\pi$
$182$		0			0
$183$			16.0443i			1.18603i
$184$	−7.56163			−0.557451
$185$	0.767568	−	0.776211i	0.0564328	−	0.0570682i
$186$	21.7210			1.59266
$187$			18.4510i			1.34927i
$188$		−	12.5176i		−	0.912937i
$189$	−2.44656			−0.177961
$190$	−7.10749	+	7.18752i	−0.515632	+	0.521437i
$191$	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
$193$			6.34605i			0.456799i	0.973568	+	0.228399i	$0.0733492\pi$
$193$			6.34605i			0.456799i	−0.973568	+	0.228399i	$0.926651\pi$
$194$	1.91384			0.137406
$195$		0			0
$196$	−3.50612			−0.250437
$197$		−	2.19339i		−	0.156273i	−0.996943	−	0.0781364i	$-0.975103\pi$
$197$		−	2.19339i		−	0.156273i	0.996943	−	0.0781364i	$-0.0248970\pi$
$198$		−	15.5551i		−	1.10545i
$199$	4.80668			0.340737			0.170368	−	0.985380i	$-0.445504\pi$
$199$	4.80668			0.340737			0.170368	+	0.985380i	$0.445504\pi$
$200$	−4.99969	+	0.0559819i	−0.353531	+	0.00395852i
$201$	14.5411			1.02565
$202$		−	16.3092i		−	1.14751i
$203$			6.02179i			0.422646i
$204$	−10.6340			−0.744530
$205$	−17.3457	−	17.1526i	−1.21148	−	1.19799i
$206$	14.5800			1.01584
$207$		−	26.5631i		−	1.84626i
$208$		0			0
$209$	−20.0171			−1.38461
$210$	−7.50008	+	7.58452i	−0.517554	+	0.523382i
$211$	−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
$213$		−	25.8872i		−	1.77376i
$214$	11.4218			0.780775
$215$	6.90022	−	6.97792i	0.470591	−	0.475890i
$216$	1.30889			0.0890584
$217$		−	15.9092i		−	1.07998i
$218$			10.3606i			0.701706i
$219$	10.4803			0.708191
$220$	−7.04039	−	6.96200i	−0.474663	−	0.469378i
$221$		0			0
$222$			1.24589i			0.0836185i
$223$		−	6.23337i		−	0.417417i	−0.977978	−	0.208709i	$-0.933074\pi$
$223$		−	6.23337i		−	0.417417i	0.977978	−	0.208709i	$-0.0669260\pi$
$224$	−1.86919			−0.124891
$225$	−0.196658	−	17.5633i	−0.0131105	−	1.17089i
$226$	−0.559115			−0.0371917
$227$		−	13.3667i		−	0.887180i	−0.896230	−	0.443590i	$-0.853705\pi$
$227$		−	13.3667i		−	0.887180i	0.896230	−	0.443590i	$-0.146295\pi$
$228$		−	11.5366i		−	0.764030i
$229$	−5.10916			−0.337623			−0.168811	−	0.985648i	$-0.553993\pi$
$229$	−5.10916			−0.337623			−0.168811	+	0.985648i	$0.553993\pi$
$230$	−12.0227	−	11.8889i	−0.792755	−	0.783929i
$231$	−21.1227			−1.38977
$232$		−	3.22160i		−	0.211508i
$233$			25.7364i			1.68605i	0.537874	+	0.843025i	$0.319228\pi$
$233$			25.7364i			1.68605i	−0.537874	+	0.843025i	$0.680772\pi$
$234$		0			0
$235$	19.6809	−	19.9025i	1.28384	−	1.29830i
$236$	11.2785			0.734166
$237$			5.94786i			0.386355i
$238$			7.78870i			0.504866i
$239$	9.42688			0.609774			0.304887	−	0.952389i	$-0.401381\pi$
$239$	9.42688			0.609774			0.304887	+	0.952389i	$0.401381\pi$
$240$	4.01247	−	4.05765i	0.259004	−	0.261920i
$241$	8.55884			0.551324			0.275662	−	0.961255i	$-0.411103\pi$
$241$	8.55884			0.551324			0.275662	+	0.961255i	$0.411103\pi$
$242$		−	8.60730i		−	0.553298i
$243$		−	22.2970i		−	1.43035i
$244$	−6.28685			−0.402474
$245$	−5.57461	−	5.51254i	−0.356149	−	0.352183i
$246$	27.8414			1.77510
$247$		0			0
$248$			8.51124i			0.540464i
$249$	−6.37126			−0.403762
$250$	−8.03735	−	7.77181i	−0.508327	−	0.491532i
$251$	−2.91331			−0.183887			−0.0919433	−	0.995764i	$-0.529308\pi$
$251$	−2.91331			−0.183887			−0.0919433	+	0.995764i	$0.529308\pi$
$252$		−	6.56625i		−	0.413635i
$253$		−	33.4830i		−	2.10506i
$254$	1.52200			0.0954986
$255$	−16.9077	−	16.7195i	−1.05880	−	1.04701i
$256$	1.00000			0.0625000
$257$			28.3335i			1.76740i	0.468057	+	0.883698i	$0.344954\pi$
$257$			28.3335i			1.76740i	−0.468057	+	0.883698i	$0.655046\pi$
$258$			11.2002i			0.697292i
$259$	0.912528			0.0567017
$260$		0			0
$261$	11.3171			0.700510
$262$		−	7.16465i		−	0.442634i
$263$		−	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
$265$	−0.300921	+	0.304309i	−0.0184854	+	0.0186936i
$266$	−8.44978			−0.518089
$267$			30.4750i			1.86504i
$268$			5.69785i			0.348051i
$269$	−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
$271$	−22.3779			−1.35936			−0.679682	−	0.733507i	$-0.737882\pi$
$271$	−22.3779			−1.35936			−0.679682	+	0.733507i	$0.737882\pi$
$272$		−	4.16688i		−	0.252654i
$273$		0			0
$274$	16.0494			0.969579
$275$	−0.247888	−	22.1387i	−0.0149482	−	1.33501i
$276$	19.2975			1.16158
$277$		−	11.0451i		−	0.663634i	−0.943344	−	0.331817i	$-0.892338\pi$
$277$		−	11.0451i		−	0.663634i	0.943344	−	0.331817i	$-0.107662\pi$
$278$		−	17.7302i		−	1.06339i
$279$	−29.8990			−1.79000
$280$	−2.97195	−	2.93886i	−0.177608	−	0.175631i
$281$	−20.1064			−1.19945			−0.599724	−	0.800207i	$-0.704723\pi$
$281$	−20.1064			−1.19945			−0.599724	+	0.800207i	$0.704723\pi$
$282$			31.9452i			1.90231i
$283$		−	20.2670i		−	1.20475i	−0.798215	−	0.602373i	$-0.794222\pi$
$283$		−	20.2670i		−	1.20475i	0.798215	−	0.602373i	$-0.205778\pi$
$284$	10.1438			0.601922
$285$	18.1386	−	18.3428i	1.07444	−	1.08653i
$286$		0			0
$287$		−	20.3919i		−	1.20370i
$288$			3.51288i			0.206998i
$289$	−0.362874			−0.0213455
$290$	5.06520	−	5.12223i	0.297439	−	0.300788i
$291$	−4.88420			−0.286317
$292$			4.10663i			0.240323i
$293$		−	29.8007i		−	1.74097i	−0.492191	−	0.870487i	$-0.663804\pi$
$293$		−	29.8007i		−	1.74097i	0.492191	−	0.870487i	$-0.336196\pi$
$294$	8.94773			0.521842
$295$	17.9324	+	17.7327i	1.04406	+	1.03244i
$296$	−0.488194			−0.0283757
$297$			5.79577i			0.336304i
$298$			9.94873i			0.576315i
$299$		0			0
$300$	12.7594	−	0.142868i	0.736663	−	0.00824847i
$301$	8.20337			0.472834
$302$		−	11.9580i		−	0.688107i
$303$			41.6215i			2.39109i
$304$	4.52055			0.259271
$305$	−9.99588	−	9.88458i	−0.572362	−	0.565989i
$306$	14.6377			0.836784
$307$			9.13426i			0.521320i	0.965431	+	0.260660i	$0.0839401\pi$
$307$			9.13426i			0.521320i	−0.965431	+	0.260660i	$0.916060\pi$
$308$		−	8.27681i		−	0.471615i
$309$	−37.2087			−2.11673
$310$	−13.3819	+	13.5326i	−0.760041	+	0.768599i
$311$	−5.34622			−0.303157			−0.151578	−	0.988445i	$-0.548436\pi$
$311$	−5.34622			−0.303157			−0.151578	+	0.988445i	$0.548436\pi$
$312$		0			0
$313$			1.32226i			0.0747385i	0.999302	+	0.0373692i	$0.0118978\pi$
$313$			1.32226i			0.0747385i	−0.999302	+	0.0373692i	$0.988102\pi$
$314$	−6.72590			−0.379564
$315$	10.3239	−	10.4401i	0.581684	−	0.588234i
$316$	−2.33064			−0.131108
$317$		−	3.84953i		−	0.216211i	−0.994139	−	0.108106i	$-0.965522\pi$
$317$		−	3.84953i		−	0.216211i	0.994139	−	0.108106i	$-0.0344785\pi$
$318$		−	0.488443i		−	0.0273905i
$319$	14.2653			0.798702
$320$	1.58997	+	1.57226i	0.0888818	+	0.0878921i
$321$	−29.1487			−1.62692
$322$		−	14.1341i		−	0.787665i
$323$		−	18.8366i		−	1.04810i
$324$	7.19832			0.399906
$325$		0			0
$326$	−0.00838925			−0.000464638
$327$		−	26.4405i		−	1.46216i
$328$			10.9095i			0.602376i
$329$	23.3977			1.28996
$330$	17.9673	+	17.7673i	0.989068	+	0.978055i
$331$	−4.96398			−0.272845			−0.136423	−	0.990651i	$-0.543561\pi$
$331$	−4.96398			−0.272845			−0.136423	+	0.990651i	$0.543561\pi$
$332$		−	2.49654i		−	0.137016i
$333$		−	1.71497i		−	0.0939795i
$334$	8.77138			0.479948
$335$	−8.95851	+	9.05938i	−0.489456	+	0.494967i
$336$	4.77024			0.260238
$337$		−	11.2699i		−	0.613911i	−0.951724	−	0.306956i	$-0.900690\pi$
$337$		−	11.2699i		−	0.613911i	0.951724	−	0.306956i	$-0.0993103\pi$
$338$		0			0
$339$	1.42688			0.0774975
$340$	6.55143	−	6.62519i	0.355301	−	0.359302i
$341$	−37.6879			−2.04091
$342$			15.8801i			0.858700i
$343$		−	19.6380i		−	1.06035i
$344$	−4.38872			−0.236624
$345$	30.6824	+	30.3408i	1.65189	+	1.63349i
$346$	−5.17428			−0.278171
$347$			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
$349$	−0.557452			−0.0298397			−0.0149198	−	0.999889i	$-0.504749\pi$
$349$	−0.557452			−0.0298397			−0.0149198	+	0.999889i	$0.504749\pi$
$350$	−0.104641	−	9.34538i	−0.00559329	−	0.499531i
$351$		0			0
$352$			4.42801i			0.236014i
$353$		−	24.1725i		−	1.28657i	−0.765627	−	0.643285i	$-0.777571\pi$
$353$		−	24.1725i		−	1.28657i	0.765627	−	0.643285i	$-0.222429\pi$
$354$	−28.7831			−1.52980
$355$	16.1282	+	15.9487i	0.855998	+	0.846467i
$356$	−11.9415			−0.632896
$357$		−	19.8770i		−	1.05200i
$358$		−	7.82042i		−	0.413322i
$359$	0.910208			0.0480389			0.0240195	−	0.999711i	$-0.492354\pi$
$359$	0.910208			0.0480389			0.0240195	+	0.999711i	$0.492354\pi$
$360$	−5.52317	+	5.58536i	−0.291097	+	0.294374i
$361$	1.43537			0.0755457
$362$			12.2270i			0.642635i
$363$			21.9661i			1.15292i
$364$		0			0
$365$	−6.45671	+	6.52941i	−0.337959	+	0.341765i
$366$	16.0443			0.838647
$367$		−	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
$369$	−38.3237			−1.99505
$370$	−0.776211	−	0.767568i	−0.0403533	−	0.0399040i
$371$	−0.357752			−0.0185735
$372$		−	21.7210i		−	1.12618i
$373$			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
$375$	20.5116	+	19.8339i	1.05921	+	1.02422i
$376$	−12.5176			−0.645544
$377$		0			0
$378$			2.44656i			0.125838i
$379$	30.3412			1.55852			0.779262	−	0.626698i	$-0.215594\pi$
$379$	30.3412			1.55852			0.779262	+	0.626698i	$0.215594\pi$
$380$	7.18752	+	7.10749i	0.368712	+	0.364607i
$381$	−3.88419			−0.198993
$382$		−	18.1313i		−	0.927679i
$383$			7.99851i			0.408705i	0.978897	+	0.204352i	$0.0655088\pi$
$383$			7.99851i			0.408705i	−0.978897	+	0.204352i	$0.934491\pi$
$384$	−2.55203			−0.130233
$385$	13.0133	−	13.1598i	0.663220	−	0.670688i
$386$	6.34605			0.323006
$387$		−	15.4170i		−	0.783693i
$388$		−	1.91384i		−	0.0971608i
$389$	−22.4951			−1.14055			−0.570273	−	0.821455i	$-0.693163\pi$
$389$	−22.4951			−1.14055			−0.570273	+	0.821455i	$0.693163\pi$
$390$		0			0
$391$	31.5084			1.59345
$392$			3.50612i			0.177086i
$393$			18.2844i			0.922328i
$394$	−2.19339			−0.110502
$395$	−3.70563	−	3.66437i	−0.186451	−	0.184374i
$396$	−15.5551			−0.781672
$397$			29.6953i			1.49036i	0.666862	+	0.745181i	$0.267637\pi$
$397$			29.6953i			1.49036i	−0.666862	+	0.745181i	$0.732363\pi$
$398$		−	4.80668i		−	0.240937i
$399$	21.5641			1.07956
$400$	0.0559819	+	4.99969i	0.00279909	+	0.249984i
$401$	26.3944			1.31807			0.659037	−	0.752110i	$-0.270964\pi$
$401$	26.3944			1.31807			0.659037	+	0.752110i	$0.270964\pi$
$402$		−	14.5411i		−	0.725244i
$403$		0			0
$404$	−16.3092			−0.811411
$405$	11.4451	+	11.3176i	0.568710	+	0.562378i
$406$	6.02179			0.298856
$407$		−	2.16173i		−	0.107153i
$408$			10.6340i			0.526462i
$409$	9.89433			0.489243			0.244622	−	0.969619i	$-0.421336\pi$
$409$	9.89433			0.489243			0.244622	+	0.969619i	$0.421336\pi$
$410$	−17.1526	+	17.3457i	−0.847106	+	0.856644i
$411$	−40.9586			−2.02034
$412$		−	14.5800i		−	0.718305i
$413$			21.0817i			1.03736i
$414$	−26.5631			−1.30550
$415$	3.92522	−	3.96942i	0.192681	−	0.194851i
$416$		0			0
$417$			45.2482i			2.21581i
$418$			20.0171i			0.979066i
$419$	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
$421$	−15.5977			−0.760184			−0.380092	−	0.924949i	$-0.624108\pi$
$421$	−15.5977			−0.760184			−0.380092	+	0.924949i	$0.624108\pi$
$422$			1.98463i			0.0966105i
$423$		−	43.9727i		−	2.13802i
$424$	0.191394			0.00929490
$425$	20.8331	−	0.233270i	1.01055	−	0.0113152i
$426$	−25.8872			−1.25424
$427$		−	11.7513i		−	0.568687i
$428$		−	11.4218i		−	0.552091i
$429$		0			0
$430$	−6.97792	−	6.90022i	−0.336505	−	0.332758i
$431$	−30.0631			−1.44809			−0.724045	−	0.689753i	$-0.757719\pi$
$431$	−30.0631			−1.44809			−0.724045	+	0.689753i	$0.757719\pi$
$432$		−	1.30889i		−	0.0629738i
$433$			22.5878i			1.08550i	0.839894	+	0.542750i	$0.182617\pi$
$433$			22.5878i			1.08550i	−0.839894	+	0.542750i	$0.817383\pi$
$434$	−15.9092			−0.763664
$435$	−12.9266	+	13.0721i	−0.619781	+	0.626759i
$436$	10.3606			0.496181
$437$			34.1827i			1.63518i
$438$		−	10.4803i		−	0.500767i
$439$	34.8184			1.66179			0.830895	−	0.556429i	$-0.187829\pi$
$439$	34.8184			1.66179			0.830895	+	0.556429i	$0.187829\pi$
$440$	−6.96200	+	7.04039i	−0.331900	+	0.335637i
$441$	−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	$0.879951\pi$
$444$	1.24589			0.0591272
$445$	−18.9865	−	18.7751i	−0.900047	−	0.890025i
$446$	−6.23337			−0.295159
$447$		−	25.3895i		−	1.20088i
$448$			1.86919i			0.0883111i
$449$	−0.894606			−0.0422191			−0.0211095	−	0.999777i	$-0.506720\pi$
$449$	−0.894606			−0.0422191			−0.0211095	+	0.999777i	$0.506720\pi$
$450$	−17.5633	+	0.196658i	−0.827942	+	0.00927053i
$451$	−48.3074			−2.27471
$452$			0.559115i			0.0262985i
$453$			30.5173i			1.43383i
$454$	−13.3667			−0.627331
$455$		0			0
$456$	−11.5366			−0.540251
$457$			10.7958i			0.505007i	0.967596	+	0.252504i	$0.0812540\pi$
$457$			10.7958i			0.505007i	−0.967596	+	0.252504i	$0.918746\pi$
$458$			5.10916i			0.238735i
$459$	−5.45397			−0.254570
$460$	−11.8889	+	12.0227i	−0.554321	+	0.560563i
$461$	10.8827			0.506859			0.253429	−	0.967354i	$-0.418441\pi$
$461$	10.8827			0.506859			0.253429	+	0.967354i	$0.418441\pi$
$462$			21.1227i			0.982717i
$463$		−	3.15999i		−	0.146857i	−0.997300	−	0.0734287i	$-0.976606\pi$
$463$		−	3.15999i		−	0.146857i	0.997300	−	0.0734287i	$-0.0233941\pi$
$464$	−3.22160			−0.149559
$465$	34.1511	−	34.5356i	1.58372	−	1.60155i
$466$	25.7364			1.19222
$467$		−	23.0475i		−	1.06651i	−0.845954	−	0.533256i	$-0.820968\pi$
$467$		−	23.0475i		−	1.06651i	0.845954	−	0.533256i	$-0.179032\pi$
$468$		0			0
$469$	−10.6504			−0.491789
$470$	−19.9025	−	19.6809i	−0.918033	−	0.907812i
$471$	17.1647			0.790908
$472$		−	11.2785i		−	0.519134i
$473$		−	19.4333i		−	0.893545i
$474$	5.94786			0.273194
$475$	0.253069	+	22.6013i	0.0116116	+	1.03702i
$476$	7.78870			0.356994
$477$			0.672343i			0.0307845i
$478$		−	9.42688i		−	0.431175i
$479$	−9.16688			−0.418845			−0.209423	−	0.977825i	$-0.567158\pi$
$479$	−9.16688			−0.418845			−0.209423	+	0.977825i	$0.567158\pi$
$480$	−4.05765	−	4.01247i	−0.185205	−	0.183143i
$481$		0			0
$482$		−	8.55884i		−	0.389845i
$483$			36.0708i			1.64128i
$484$	−8.60730			−0.391241
$485$	3.00907	−	3.04295i	0.136635	−	0.138173i
$486$	−22.2970			−1.01141
$487$			24.1155i			1.09278i	0.837531	+	0.546389i	$0.183998\pi$
$487$			24.1155i			1.09278i	−0.837531	+	0.546389i	$0.816002\pi$
$488$			6.28685i			0.284592i
$489$	0.0214097			0.000968178
$490$	−5.51254	+	5.57461i	−0.249031	+	0.251835i
$491$	5.68528			0.256573			0.128286	−	0.991737i	$-0.459052\pi$
$491$	5.68528			0.256573			0.128286	+	0.991737i	$0.459052\pi$
$492$		−	27.8414i		−	1.25519i
$493$			13.4240i			0.604587i
$494$		0			0
$495$	−24.7320	−	24.4567i	−1.11162	−	1.09925i
$496$	8.51124			0.382166
$497$			18.9607i			0.850501i
$498$			6.37126i			0.285503i
$499$	6.68270			0.299159			0.149579	−	0.988750i	$-0.452208\pi$
$499$	6.68270			0.299159			0.149579	+	0.988750i	$0.452208\pi$
$500$	−7.77181	+	8.03735i	−0.347566	+	0.359441i
$501$	−22.3849			−1.00008
$502$			2.91331i			0.130027i
$503$		−	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
$505$	−25.9310	−	25.6423i	−1.15391	−	1.14107i
$506$	−33.4830			−1.48850
$507$		0			0
$508$		−	1.52200i		−	0.0675277i
$509$	−28.6424			−1.26955			−0.634776	−	0.772696i	$-0.718908\pi$
$509$	−28.6424			−1.26955			−0.634776	+	0.772696i	$0.718908\pi$
$510$	−16.7195	+	16.9077i	−0.740350	+	0.748686i
$511$	−7.67609			−0.339570
$512$		−	1.00000i		−	0.0441942i
$513$		−	5.91689i		−	0.261237i
$514$	28.3335			1.24974
$515$	22.9236	−	23.1817i	1.01013	−	1.02151i
$516$	11.2002			0.493060
$517$		−	55.4279i		−	2.43772i
$518$		−	0.912528i		−	0.0400942i
$519$	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	$0.678208\pi$
$522$		−	11.3171i		−	0.495335i
$523$		−	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
$525$	0.267047	+	23.8497i	0.0116549	+	1.04089i
$526$	−6.57342			−0.286615
$527$		−	35.4653i		−	1.54489i
$528$		−	11.3004i		−	0.491789i
$529$	−34.1782			−1.48601
$530$	0.304309	+	0.300921i	0.0132184	+	0.0130712i
$531$	39.6199			1.71936
$532$			8.44978i			0.366344i
$533$		0			0
$534$	30.4750			1.31878
$535$	17.9580	−	18.1602i	0.776392	−	0.785134i
$536$	5.69785			0.246109
$537$			19.9580i			0.861251i
$538$			13.1504i			0.566956i
$539$	−15.5251			−0.668715
$540$	2.05791	−	2.08108i	0.0885585	−	0.0895556i
$541$	9.90908			0.426025			0.213012	−	0.977049i	$-0.431673\pi$
$541$	9.90908			0.426025			0.213012	+	0.977049i	$0.431673\pi$
$542$			22.3779i			0.961215i
$543$		−	31.2036i		−	1.33908i
$544$	−4.16688			−0.178653
$545$	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	$0.890796\pi$
$548$		−	16.0494i		−	0.685596i
$549$	−22.0850			−0.942563
$550$	−22.1387	+	0.247888i	−0.943996	+	0.0105700i
$551$	−14.5634			−0.620421
$552$		−	19.2975i		−	0.821358i
$553$		−	4.35641i		−	0.185253i
$554$	−11.0451			−0.469260
$555$	1.98092	+	1.95886i	0.0840853	+	0.0831490i
$556$	−17.7302			−0.751930
$557$		−	11.6684i		−	0.494408i	−0.968963	−	0.247204i	$-0.920488\pi$
$557$		−	11.6684i		−	0.494408i	0.968963	−	0.247204i	$-0.0795117\pi$
$558$			29.8990i			1.26572i
$559$		0			0
$560$	−2.93886	+	2.97195i	−0.124190	+	0.125588i
$561$	−47.0876			−1.98804
$562$			20.1064i			0.848138i
$563$			34.0262i			1.43403i	0.697056	+	0.717017i	$0.254493\pi$
$563$			34.0262i			1.43403i	−0.697056	+	0.717017i	$0.745507\pi$
$564$	31.9452			1.34514
$565$	−0.879075	+	0.888973i	−0.0369830	+	0.0373994i
$566$	−20.2670			−0.851884
$567$			13.4550i			0.565059i
$568$		−	10.1438i		−	0.425623i
$569$	44.3266			1.85827			0.929135	−	0.369741i	$-0.120554\pi$
$569$	44.3266			1.85827			0.929135	+	0.369741i	$0.120554\pi$
$570$	−18.3428	−	18.1386i	−0.768295	−	0.759741i
$571$	15.3587			0.642740			0.321370	−	0.946954i	$-0.395857\pi$
$571$	15.3587			0.642740			0.321370	+	0.946954i	$0.395857\pi$
$572$		0			0
$573$			46.2717i			1.93303i
$574$	−20.3919			−0.851143
$575$	−37.8058	+	0.423314i	−1.57661	+	0.0176534i
$576$	3.51288			0.146370
$577$			31.5537i			1.31360i	0.754065	+	0.656799i	$0.228090\pi$
$577$			31.5537i			1.31360i	−0.754065	+	0.656799i	$0.771910\pi$
$578$			0.362874i			0.0150936i
$579$	−16.1953			−0.673056
$580$	−5.12223	−	5.06520i	−0.212689	−	0.210321i
$581$	4.66652			0.193600
$582$			4.88420i			0.202457i
$583$			0.847494i			0.0350996i
$584$	4.10663			0.169934
$585$		0			0
$586$	−29.8007			−1.23106
$587$			22.9587i			0.947607i	0.880631	+	0.473803i	$0.157119\pi$
$587$			22.9587i			0.947607i	−0.880631	+	0.473803i	$0.842881\pi$
$588$		−	8.94773i		−	0.368998i
$589$	38.4755			1.58535
$590$	17.7327	−	17.9324i	0.730045	−	0.738265i
$591$	5.59761			0.230255
$592$			0.488194i			0.0200646i
$593$			27.6241i			1.13439i	0.823584	+	0.567194i	$0.191971\pi$
$593$			27.6241i			1.13439i	−0.823584	+	0.567194i	$0.808029\pi$
$594$	5.79577			0.237803
$595$	12.3838	+	12.2459i	0.507685	+	0.502032i
$596$	9.94873			0.407516
$597$			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	$0.489934\pi$
$600$	−0.142868	−	12.7594i	−0.00583255	−	0.520899i
$601$	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
$603$			20.0158i			0.815108i
$604$	−11.9580			−0.486565
$605$	−13.6853	−	13.5329i	−0.556387	−	0.550192i
$606$	41.6215			1.69076
$607$		−	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
$609$	−15.3678			−0.622735
$610$	−9.88458	+	9.99588i	−0.400215	+	0.404721i
$611$		0			0
$612$		−	14.6377i		−	0.591696i
$613$		−	3.32275i		−	0.134205i	−0.997746	−	0.0671024i	$-0.978625\pi$
$613$		−	3.32275i		−	0.134205i	0.997746	−	0.0671024i	$-0.0213754\pi$
$614$	9.13426			0.368629
$615$	43.7740	−	44.2669i	1.76514	−	1.78501i
$616$	−8.27681			−0.333482
$617$		−	13.7220i		−	0.552425i	−0.961097	−	0.276213i	$-0.910921\pi$
$617$		−	13.7220i		−	0.552425i	0.961097	−	0.276213i	$-0.0890794\pi$
$618$			37.2087i			1.49675i
$619$	−40.9597			−1.64631			−0.823155	−	0.567817i	$-0.807788\pi$
$619$	−40.9597			−1.64631			−0.823155	+	0.567817i	$0.807788\pi$
$620$	13.5326	+	13.3819i	0.543482	+	0.537430i
$621$	9.89731			0.397166
$622$			5.34622i			0.214364i
$623$		−	22.3209i		−	0.894267i
$624$		0			0
$625$	−24.9937	+	0.559784i	−0.999749	+	0.0223913i
$626$	1.32226			0.0528481
$627$		−	51.0842i		−	2.04011i
$628$			6.72590i			0.268392i
$629$	2.03424			0.0811106
$630$	−10.4401	−	10.3239i	−0.415944	−	0.411313i
$631$	−14.9553			−0.595361			−0.297680	−	0.954666i	$-0.596213\pi$
$631$	−14.9553			−0.595361			−0.297680	+	0.954666i	$0.596213\pi$
$632$			2.33064i			0.0927077i
$633$		−	5.06485i		−	0.201310i
$634$	−3.84953			−0.152885
$635$	2.39298	−	2.41992i	0.0949624	−	0.0960317i
$636$	−0.488443			−0.0193680
$637$		0			0
$638$		−	14.2653i		−	0.564768i
$639$	35.6338			1.40965
$640$	1.57226	−	1.58997i	0.0621491	−	0.0628489i
$641$	−36.5876			−1.44512			−0.722562	−	0.691306i	$-0.757036\pi$
$641$	−36.5876			−1.44512			−0.722562	+	0.691306i	$0.757036\pi$
$642$			29.1487i			1.15041i
$643$			43.3819i			1.71082i	0.517954	+	0.855408i	$0.326694\pi$
$643$			43.3819i			1.71082i	−0.517954	+	0.855408i	$0.673306\pi$
$644$	−14.1341			−0.556963
$645$	17.8079	+	17.6096i	0.701185	+	0.693377i
$646$	−18.8366			−0.741115
$647$			42.6622i			1.67722i	0.544730	+	0.838611i	$0.316632\pi$
$647$			42.6622i			1.67722i	−0.544730	+	0.838611i	$0.683368\pi$
$648$		−	7.19832i		−	0.282777i
$649$	49.9413			1.96037
$650$		0			0
$651$	40.6007			1.59127
$652$			0.00838925i			0.000328549i
$653$		−	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
$655$	−11.3916	−	11.2647i	−0.445105	−	0.440149i
$656$	10.9095			0.425944
$657$			14.4261i			0.562816i
$658$		−	23.3977i		−	0.912138i
$659$	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
$661$	9.90351			0.385202			0.192601	−	0.981277i	$-0.438308\pi$
$661$	9.90351			0.385202			0.192601	+	0.981277i	$0.438308\pi$
$662$			4.96398i			0.192931i
$663$		0			0
$664$	−2.49654			−0.0968846
$665$	−13.2853	+	13.4349i	−0.515181	+	0.520981i
$666$	−1.71497			−0.0664536
$667$		−	24.3605i		−	0.943243i
$668$		−	8.77138i		−	0.339375i
$669$	15.9078			0.615030
$670$	9.05938	+	8.95851i	0.349994	+	0.346097i
$671$	−27.8383			−1.07468
$672$		−	4.77024i		−	0.184016i
$673$			46.6987i			1.80010i	0.435784	+	0.900051i	$0.356471\pi$
$673$			46.6987i			1.80010i	−0.435784	+	0.900051i	$0.643529\pi$
$674$	−11.2699			−0.434101
$675$	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	$-0.0942852\pi$
$678$		−	1.42688i		−	0.0547990i
$679$	3.57735			0.137286
$680$	−6.62519	−	6.55143i	−0.254065	−	0.251236i
$681$	34.1123			1.30719
$682$			37.6879i			1.44314i
$683$		−	5.91381i		−	0.226286i	−0.993579	−	0.113143i	$-0.963908\pi$
$683$		−	5.91381i		−	0.226286i	0.993579	−	0.113143i	$-0.0360918\pi$
$684$	15.8801			0.607193
$685$	25.2338	−	25.5180i	0.964135	−	0.974991i
$686$	−19.6380			−0.749781
$687$		−	13.0387i		−	0.497459i
$688$			4.38872i			0.167318i
$689$		0			0
$690$	30.3408	−	30.6824i	1.15505	−	1.16806i
$691$	23.5531			0.896004			0.448002	−	0.894033i	$-0.352136\pi$
$691$	23.5531			0.896004			0.448002	+	0.894033i	$0.352136\pi$
$692$			5.17428i			0.196697i
$693$		−	29.0754i		−	1.10448i
$694$	15.6806			0.595229
$695$	−28.1905	−	27.8766i	−1.06933	−	1.05742i
$696$	8.22163			0.311640
$697$		−	45.4585i		−	1.72186i
$698$			0.557452i			0.0210999i
$699$	−65.6803			−2.48426
$700$	−9.34538	+	0.104641i	−0.353222	+	0.00395505i
$701$	−39.9205			−1.50778			−0.753888	−	0.657003i	$-0.771824\pi$
$701$	−39.9205			−1.50778			−0.753888	+	0.657003i	$0.771824\pi$
$702$		0			0
$703$			2.20690i			0.0832349i
$704$	4.42801			0.166887
$705$	50.7918	+	50.2263i	1.91293	+	1.89163i
$706$	−24.1725			−0.909742
$707$		−	30.4850i		−	1.14650i
$708$			28.7831i			1.08173i
$709$	8.96987			0.336870			0.168435	−	0.985713i	$-0.446129\pi$
$709$	8.96987			0.336870			0.168435	+	0.985713i	$0.446129\pi$
$710$	15.9487	−	16.1282i	0.598543	−	0.605282i
$711$	−8.18724			−0.307046
$712$			11.9415i			0.447525i
$713$			64.3589i			2.41026i
$714$	−19.8770			−0.743879
$715$		0			0
$716$	−7.82042			−0.292263
$717$			24.0577i			0.898452i
$718$		−	0.910208i		−	0.0339687i
$719$	−19.5515			−0.729149			−0.364575	−	0.931174i	$-0.618786\pi$
$719$	−19.5515			−0.729149			−0.364575	+	0.931174i	$0.618786\pi$
$720$	5.58536	+	5.52317i	0.208154	+	0.205836i
$721$	27.2528			1.01495
$722$		−	1.43537i		−	0.0534189i
$723$			21.8425i			0.812330i
$724$	12.2270			0.454411
$725$	−0.180351	−	16.1070i	−0.00669807	−	0.598198i
$726$	21.9661			0.815240
$727$		−	21.2591i		−	0.788458i	−0.919012	−	0.394229i	$-0.871012\pi$
$727$		−	21.2591i		−	0.788458i	0.919012	−	0.394229i	$-0.128988\pi$
$728$		0			0
$729$	35.3078			1.30770
$730$	6.52941	+	6.45671i	0.241664	+	0.238973i
$731$	18.2873			0.676379
$732$		−	16.0443i		−	0.593013i
$733$			51.7515i			1.91149i	0.294203	+	0.955743i	$0.404946\pi$
$733$			51.7515i			1.91149i	−0.294203	+	0.955743i	$0.595054\pi$
$734$	−4.41148			−0.162831
$735$	14.0682	−	14.2266i	0.518913	−	0.524756i
$736$	7.56163			0.278725
$737$			25.2301i			0.929364i
$738$			38.3237i			1.41072i
$739$	−2.48566			−0.0914364			−0.0457182	−	0.998954i	$-0.514558\pi$
$739$	−2.48566			−0.0914364			−0.0457182	+	0.998954i	$0.514558\pi$
$740$	−0.767568	+	0.776211i	−0.0282164	+	0.0285341i
$741$		0			0
$742$			0.357752i			0.0131335i
$743$			41.9532i			1.53911i	0.638578	+	0.769557i	$0.279523\pi$
$743$			41.9532i			1.53911i	−0.638578	+	0.769557i	$0.720477\pi$
$744$	−21.7210			−0.796330
$745$	15.8181	+	15.6420i	0.579532	+	0.573079i
$746$	7.59431			0.278048
$747$		−	8.77005i		−	0.320879i
$748$		−	18.4510i		−	0.674635i
$749$	21.3495			0.780092
$750$	19.8339	−	20.5116i	0.724233	−	0.748977i
$751$	4.26126			0.155496			0.0777478	−	0.996973i	$-0.475227\pi$
$751$	4.26126			0.155496			0.0777478	+	0.996973i	$0.475227\pi$
$752$			12.5176i			0.456468i
$753$		−	7.43487i		−	0.270942i
$754$		0			0
$755$	−19.0128	−	18.8011i	−0.691948	−	0.684244i
$756$	2.44656			0.0889806
$757$			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
$759$	85.4498			3.10163
$760$	7.10749	−	7.18752i	0.257816	−	0.260719i
$761$	−50.8769			−1.84429			−0.922143	−	0.386850i	$-0.873563\pi$
$761$	−50.8769			−1.84429			−0.922143	+	0.386850i	$0.873563\pi$
$762$			3.88419i			0.140709i
$763$			19.3659i			0.701093i
$764$	−18.1313			−0.655968
$765$	23.0144	−	23.2735i	0.832086	−	0.841455i
$766$	7.99851			0.288998
$767$		0			0
$768$			2.55203i			0.0920886i
$769$	10.8452			0.391089			0.195545	−	0.980695i	$-0.437353\pi$
$769$	10.8452			0.391089			0.195545	+	0.980695i	$0.437353\pi$
$770$	−13.1598	−	13.0133i	−0.474248	−	0.468967i
$771$	−72.3081			−2.60411
$772$		−	6.34605i		−	0.228399i
$773$		−	17.0142i		−	0.611959i	−0.952038	−	0.305979i	$-0.901016\pi$
$773$		−	17.0142i		−	0.611959i	0.952038	−	0.305979i	$-0.0989838\pi$
$774$	−15.4170			−0.554154
$775$	0.476475	+	42.5535i	0.0171155	+	1.52857i
$776$	−1.91384			−0.0687030
$777$			2.32880i			0.0835453i
$778$			22.4951i			0.806488i
$779$	49.3169			1.76696
$780$		0			0
$781$	44.9167			1.60725
$782$		−	31.5084i		−	1.12674i
$783$			4.21670i			0.150693i
$784$	3.50612			0.125219
$785$	−10.5749	+	10.6939i	−0.377433	+	0.381683i
$786$	18.2844			0.652184
$787$		−	27.0297i		−	0.963505i	−0.876307	−	0.481752i	$-0.840000\pi$
$787$		−	27.0297i		−	0.963505i	0.876307	−	0.481752i	$-0.160000\pi$
$788$			2.19339i			0.0781364i
$789$	16.7756			0.597227
$790$	−3.66437	+	3.70563i	−0.130372	+	0.131840i
$791$	−1.04509			−0.0371592
$792$			15.5551i			0.552726i
$793$		0			0
$794$	29.6953			1.05385
$795$	−0.776608	−	0.767961i	−0.0275435	−	0.0272368i
$796$	−4.80668			−0.170368
$797$		−	15.1585i		−	0.536942i	−0.963288	−	0.268471i	$-0.913482\pi$
$797$		−	15.1585i		−	0.536942i	0.963288	−	0.268471i	$-0.0865183\pi$
$798$		−	21.5641i		−	0.763362i
$799$	52.1591			1.84526
$800$	4.99969	−	0.0559819i	0.176766	−	0.00197926i
$801$	−41.9489			−1.48219
$802$		−	26.3944i		−	0.932019i
$803$			18.1842i			0.641708i
$804$	−14.5411			−0.512825
$805$	−22.4728	−	22.2226i	−0.792062	−	0.783243i
$806$		0			0
$807$		−	33.5604i		−	1.18138i
$808$			16.3092i			0.573754i
$809$	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
$811$	−9.57933			−0.336376			−0.168188	−	0.985755i	$-0.553792\pi$
$811$	−9.57933			−0.336376			−0.168188	+	0.985755i	$0.553792\pi$
$812$		−	6.02179i		−	0.211323i
$813$		−	57.1093i		−	2.00291i
$814$	−2.16173			−0.0757685
$815$	−0.0131901	+	0.0133386i	−0.000462029	+	0.000467232i
$816$	10.6340			0.372265
$817$			19.8394i			0.694094i
$818$		−	9.89433i		−	0.345947i
$819$		0			0
$820$	17.3457	+	17.1526i	0.605739	+	0.598994i
$821$	7.82037			0.272933			0.136466	−	0.990645i	$-0.456425\pi$
$821$	7.82037			0.272933			0.136466	+	0.990645i	$0.456425\pi$
$822$			40.9586i			1.42859i
$823$		−	34.1839i		−	1.19158i	−0.803142	−	0.595788i	$-0.796840\pi$
$823$		−	34.1839i		−	1.19158i	0.803142	−	0.595788i	$-0.203160\pi$
$824$	−14.5800			−0.507919
$825$	56.4987	−	0.632620i	1.96703	−	0.0220250i
$826$	21.0817			0.733524
$827$		−	3.47145i		−	0.120714i	−0.998177	−	0.0603570i	$-0.980776\pi$
$827$		−	3.47145i		−	0.120714i	0.998177	−	0.0603570i	$-0.0192239\pi$
$828$			26.5631i			0.923131i
$829$	−13.3557			−0.463864			−0.231932	−	0.972732i	$-0.574505\pi$
$829$	−13.3557			−0.463864			−0.231932	+	0.972732i	$0.574505\pi$
$830$	−3.96942	−	3.92522i	−0.137780	−	0.136246i
$831$	28.1874			0.977811
$832$		0			0
$833$		−	14.6096i		−	0.506192i
$834$	45.2482			1.56682
$835$	13.7909	−	13.9462i	0.477254	−	0.482628i
$836$	20.0171			0.692304
$837$		−	11.1402i		−	0.385063i
$838$		−	17.9386i		−	0.619679i
$839$	47.9304			1.65474			0.827370	−	0.561657i	$-0.189836\pi$
$839$	47.9304			1.65474			0.827370	+	0.561657i	$0.189836\pi$
$840$	7.50008	−	7.58452i	0.258777	−	0.261691i
$841$	−18.6213			−0.642114
$842$			15.5977i			0.537532i
$843$		−	51.3123i		−	1.76729i
$844$	1.98463			0.0683139
$845$		0			0
$846$	−43.9727			−1.51181
$847$		−	16.0887i		−	0.552814i
$848$		−	0.191394i		−	0.00657249i
$849$	51.7220			1.77509
$850$	−0.233270	−	20.8331i	−0.00800108	−	0.714569i
$851$	−3.69154			−0.126544
$852$			25.8872i			0.886882i
$853$			36.4405i			1.24770i	0.781544	+	0.623850i	$0.214432\pi$
$853$			36.4405i			1.24770i	−0.781544	+	0.623850i	$0.785568\pi$
$854$	−11.7513			−0.402123
$855$	25.2489	+	24.9678i	0.863494	+	0.853879i
$856$	−11.4218			−0.390388
$857$			29.9745i			1.02391i	0.859013	+	0.511954i	$0.171078\pi$
$857$			29.9745i			1.02391i	−0.859013	+	0.511954i	$0.828922\pi$
$858$		0			0
$859$	−34.8453			−1.18891			−0.594454	−	0.804130i	$-0.702632\pi$
$859$	−34.8453			−1.18891			−0.594454	+	0.804130i	$0.702632\pi$
$860$	−6.90022	+	6.97792i	−0.235296	+	0.237945i
$861$	52.0409			1.77355
$862$			30.0631i			1.02395i
$863$		−	25.2753i		−	0.860381i	−0.902738	−	0.430190i	$-0.858446\pi$
$863$		−	25.2753i		−	0.860381i	0.902738	−	0.430190i	$-0.141554\pi$
$864$	−1.30889			−0.0445292
$865$	−8.13532	+	8.22692i	−0.276609	+	0.279724i
$866$	22.5878			0.767565
$867$		−	0.926067i		−	0.0314509i
$868$			15.9092i			0.539992i
$869$	−10.3201			−0.350085
$870$	13.0721	+	12.9266i	0.443186	+	0.438251i
$871$		0			0
$872$		−	10.3606i		−	0.350853i
$873$		−	6.72311i		−	0.227543i
$874$	34.1827			1.15625
$875$	−15.0234	−	14.5270i	−0.507882	−	0.491103i
$876$	−10.4803			−0.354096
$877$			6.44566i			0.217654i	0.994061	+	0.108827i	$0.0347095\pi$
$877$			6.44566i			0.217654i	−0.994061	+	0.108827i	$0.965290\pi$
$878$		−	34.8184i		−	1.17506i
$879$	76.0524			2.56518
$880$	7.04039	+	6.96200i	0.237331	+	0.234689i
$881$	−12.5890			−0.424133			−0.212066	−	0.977255i	$-0.568019\pi$
$881$	−12.5890			−0.424133			−0.212066	+	0.977255i	$0.568019\pi$
$882$			12.3166i			0.414721i
$883$			17.7501i			0.597339i	0.954357	+	0.298669i	$0.0965428\pi$
$883$			17.7501i			0.597339i	−0.954357	+	0.298669i	$0.903457\pi$
$884$		0			0
$885$	−45.2545	+	45.7641i	−1.52121	+	1.53834i
$886$	15.5022			0.520808
$887$		−	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
$889$	2.84491			0.0954151
$890$	−18.7751	+	18.9865i	−0.629343	+	0.636429i
$891$	31.8742			1.06783
$892$			6.23337i			0.208709i
$893$			56.5862i			1.89359i
$894$	−25.3895			−0.849152
$895$	−12.4342	−	12.2958i	−0.415630	−	0.411002i
$896$	1.86919			0.0624453
$897$		0			0
$898$			0.894606i			0.0298534i
$899$	−27.4198			−0.914501
$900$	0.196658	+	17.5633i	0.00655525	+	0.585443i
$901$	−0.797514			−0.0265691
$902$			48.3074i			1.60846i
$903$			20.9353i			0.696682i
$904$	0.559115			0.0185959
$905$	19.4404	+	19.2240i	0.646222	+	0.639027i
$906$	30.5173			1.01387
$907$			10.4184i			0.345937i	0.984927	+	0.172969i	$0.0553359\pi$
$907$			10.4184i			0.345937i	−0.984927	+	0.172969i	$0.944664\pi$
$908$			13.3667i			0.443590i
$909$	−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	$0.549664\pi$
$912$			11.5366i			0.382015i
$913$		−	11.0547i		−	0.365858i
$914$	10.7958			0.357094
$915$	25.2258	−	25.5098i	0.833939	−	0.843329i
$916$	5.10916			0.168811
$917$		−	13.3921i		−	0.442247i
$918$			5.45397i			0.180008i
$919$	−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
$921$	−23.3109			−0.768121
$922$		−	10.8827i		−	0.358403i
$923$		0			0
$924$	21.1227			0.694886
$925$	−2.44081	+	0.0273300i	−0.0802535	+	0.000898605i
$926$	−3.15999			−0.103844
$927$		−	51.2178i		−	1.68221i
$928$			3.22160i			0.105754i
$929$	29.3209			0.961988			0.480994	−	0.876724i	$-0.340276\pi$
$929$	29.3209			0.961988			0.480994	+	0.876724i	$0.340276\pi$
$930$	−34.5356	−	34.1511i	−1.13247	−	1.11986i
$931$	15.8496			0.519449
$932$		−	25.7364i		−	0.843025i
$933$		−	13.6437i		−	0.446676i
$934$	−23.0475			−0.754138
$935$	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	$-0.355641\pi$
$938$			10.6504i			0.347747i
$939$	−3.37445			−0.110121
$940$	−19.6809	+	19.9025i	−0.641920	+	0.649148i
$941$	12.9833			0.423243			0.211621	−	0.977352i	$-0.432126\pi$
$941$	12.9833			0.423243			0.211621	+	0.977352i	$0.432126\pi$
$942$		−	17.1647i		−	0.559257i
$943$			82.4935i			2.68636i
$944$	−11.2785			−0.367083
$945$	3.88995	+	3.84664i	0.126540	+	0.125131i
$946$	−19.4333			−0.631832
$947$		−	43.0090i		−	1.39760i	−0.715316	−	0.698802i	$-0.753717\pi$
$947$		−	43.0090i		−	1.39760i	0.715316	−	0.698802i	$-0.246283\pi$
$948$		−	5.94786i		−	0.193178i
$949$		0			0
$950$	22.6013	−	0.253069i	0.733284	−	0.00821064i
$951$	9.82414			0.318570
$952$		−	7.78870i		−	0.252433i
$953$		−	26.9615i		−	0.873369i	−0.899615	−	0.436684i	$-0.856153\pi$
$953$		−	26.9615i		−	0.873369i	0.899615	−	0.436684i	$-0.143847\pi$
$954$	0.672343			0.0217679
$955$	−28.8282	−	28.5072i	−0.932858	−	0.922471i
$956$	−9.42688			−0.304887
$957$			36.4055i			1.17682i
$958$			9.16688i			0.296168i
$959$	29.9994			0.968731
$960$	−4.01247	+	4.05765i	−0.129502	+	0.130960i
$961$	41.4412			1.33681
$962$		0			0
$963$		−	40.1232i		−	1.29295i
$964$	−8.55884			−0.275662
$965$	9.97766	−	10.0900i	0.321192	−	0.324809i
$966$	36.0708			1.16056
$967$			3.03699i			0.0976630i	0.998807	+	0.0488315i	$0.0155497\pi$
$967$			3.03699i			0.0976630i	−0.998807	+	0.0488315i	$0.984450\pi$
$968$			8.60730i			0.276649i
$969$	48.0716			1.54428
$970$	−3.04295	−	3.00907i	−0.0977032	−	0.0966153i
$971$	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
$973$		−	33.1412i		−	1.06246i
$974$	24.1155			0.772711
$975$		0			0
$976$	6.28685			0.201237
$977$		−	38.3621i		−	1.22731i	−0.789574	−	0.613656i	$-0.789698\pi$
$977$		−	38.3621i		−	1.22731i	0.789574	−	0.613656i	$-0.210302\pi$
$978$		−	0.0214097i		−	0.000684606i
$979$	−52.8769			−1.68995
$980$	5.57461	+	5.51254i	0.178074	+	0.176092i
$981$	36.3954			1.16202
$982$		−	5.68528i		−	0.181424i
$983$		−	30.0081i		−	0.957109i	−0.878058	−	0.478554i	$-0.841161\pi$
$983$		−	30.0081i		−	0.957109i	0.878058	−	0.478554i	$-0.158839\pi$
$984$	−27.8414			−0.887551
$985$	−3.44859	+	3.48742i	−0.109881	+	0.111118i
$986$	13.4240			0.427507
$987$			59.7118i			1.90065i
$988$		0			0
$989$	−33.1859			−1.05525
$990$	−24.4567	+	24.7320i	−0.777284	+	0.786036i
$991$	−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
$993$		−	12.6683i		−	0.402015i
$994$	18.9607			0.601395
$995$	−7.64246	−	7.55737i	−0.242282	−	0.239585i
$996$	6.37126			0.201881
$997$			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
$999$	0.638990			0.0202167

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.3	✓	18	65.64	even	2
1690.2.b.f.339.16	yes	18	13.12	even	2
1690.2.b.g.339.7	yes	18	1.1	even	1	trivial
1690.2.b.g.339.12	yes	18	5.4	even	2	inner
1690.2.c.g.1689.3		18	65.34	odd	4
1690.2.c.g.1689.16		18	13.5	odd	4
1690.2.c.h.1689.3		18	65.44	odd	4
1690.2.c.h.1689.16		18	13.8	odd	4
8450.2.a.ct.1.3		9	5.3	odd	4
8450.2.a.cw.1.7		9	65.12	odd	4
8450.2.a.cx.1.3		9	65.38	odd	4
8450.2.a.da.1.7		9	5.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.b (of order \(2\), degree \(1\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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