LMFDB - Embedded newform 1690.2.b.g.339.8

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			339.8
Root			$0.0982708i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.g.339.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +3.06821i q^{3} -1.00000 q^{4} +(-2.23031 - 0.160405i) q^{5} +3.06821 q^{6} -3.06611i q^{7} +1.00000i q^{8} -6.41393 q^{9} +(-0.160405 + 2.23031i) q^{10} +5.86077 q^{11} -3.06821i q^{12} -3.06611 q^{14} +(0.492158 - 6.84306i) q^{15} +1.00000 q^{16} +3.26418i q^{17} +6.41393i q^{18} +0.146777 q^{19} +(2.23031 + 0.160405i) q^{20} +9.40747 q^{21} -5.86077i q^{22} +0.0169460i q^{23} -3.06821 q^{24} +(4.94854 + 0.715507i) q^{25} -10.4747i q^{27} +3.06611i q^{28} +2.35939 q^{29} +(-6.84306 - 0.492158i) q^{30} -5.33352 q^{31} -1.00000i q^{32} +17.9821i q^{33} +3.26418 q^{34} +(-0.491820 + 6.83836i) q^{35} +6.41393 q^{36} +10.2495i q^{37} -0.146777i q^{38} +(0.160405 - 2.23031i) q^{40} +2.25139 q^{41} -9.40747i q^{42} +6.21583i q^{43} -5.86077 q^{44} +(14.3050 + 1.02883i) q^{45} +0.0169460 q^{46} -4.28931i q^{47} +3.06821i q^{48} -2.40101 q^{49} +(0.715507 - 4.94854i) q^{50} -10.0152 q^{51} +5.54859i q^{53} -10.4747 q^{54} +(-13.0713 - 0.940099i) q^{55} +3.06611 q^{56} +0.450342i q^{57} -2.35939i q^{58} +11.2873 q^{59} +(-0.492158 + 6.84306i) q^{60} -4.21282 q^{61} +5.33352i q^{62} +19.6658i q^{63} -1.00000 q^{64} +17.9821 q^{66} +9.43931i q^{67} -3.26418i q^{68} -0.0519941 q^{69} +(6.83836 + 0.491820i) q^{70} -11.2140 q^{71} -6.41393i q^{72} -3.17785i q^{73} +10.2495 q^{74} +(-2.19533 + 15.1832i) q^{75} -0.146777 q^{76} -17.9697i q^{77} -4.50128 q^{79} +(-2.23031 - 0.160405i) q^{80} +12.8967 q^{81} -2.25139i q^{82} -1.11696i q^{83} -9.40747 q^{84} +(0.523593 - 7.28013i) q^{85} +6.21583 q^{86} +7.23910i q^{87} +5.86077i q^{88} -7.13294 q^{89} +(1.02883 - 14.3050i) q^{90} -0.0169460i q^{92} -16.3644i q^{93} -4.28931 q^{94} +(-0.327357 - 0.0235438i) q^{95} +3.06821 q^{96} +10.0240i q^{97} +2.40101i q^{98} -37.5905 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			3.06821i			1.77143i	0.464226	+	0.885717i	$0.346332\pi$
$3$			3.06821i			1.77143i	−0.464226	+	0.885717i	$0.653668\pi$
$4$	−1.00000			−0.500000
$5$	−2.23031	−	0.160405i	−0.997424	−	0.0717355i
$5$	−2.23031	−	0.160405i	−0.997424	−	0.0717355i
$6$	3.06821			1.25259
$7$		−	3.06611i		−	1.15888i	−0.815015	−	0.579440i	$-0.803271\pi$
$7$		−	3.06611i		−	1.15888i	0.815015	−	0.579440i	$-0.196729\pi$
$8$			1.00000i			0.353553i
$9$	−6.41393			−2.13798
$10$	−0.160405	+	2.23031i	−0.0507247	+	0.705285i
$11$	5.86077			1.76709			0.883544	−	0.468348i	$-0.155151\pi$
$11$	5.86077			1.76709			0.883544	+	0.468348i	$0.155151\pi$
$12$		−	3.06821i		−	0.885717i
$13$		0			0
$13$		0			0
$14$	−3.06611			−0.819451
$15$	0.492158	−	6.84306i	0.127075	−	1.76687i
$16$	1.00000			0.250000
$17$			3.26418i			0.791680i	0.918319	+	0.395840i	$0.129547\pi$
$17$			3.26418i			0.791680i	−0.918319	+	0.395840i	$0.870453\pi$
$18$			6.41393i			1.51178i
$19$	0.146777			0.0336729			0.0168365	−	0.999858i	$-0.494641\pi$
$19$	0.146777			0.0336729			0.0168365	+	0.999858i	$0.494641\pi$
$20$	2.23031	+	0.160405i	0.498712	+	0.0358678i
$21$	9.40747			2.05288
$22$		−	5.86077i		−	1.24952i
$23$			0.0169460i			0.00353349i	0.999998	+	0.00176675i	$0.000562373\pi$
$23$			0.0169460i			0.00353349i	−0.999998	+	0.00176675i	$0.999438\pi$
$24$	−3.06821			−0.626296
$25$	4.94854	+	0.715507i	0.989708	+	0.143101i
$26$		0			0
$27$		−	10.4747i		−	2.01585i
$28$			3.06611i			0.579440i
$29$	2.35939			0.438127			0.219064	−	0.975711i	$-0.429700\pi$
$29$	2.35939			0.438127			0.219064	+	0.975711i	$0.429700\pi$
$30$	−6.84306	−	0.492158i	−1.24937	−	0.0898554i
$31$	−5.33352			−0.957929			−0.478965	−	0.877834i	$-0.658988\pi$
$31$	−5.33352			−0.957929			−0.478965	+	0.877834i	$0.658988\pi$
$32$		−	1.00000i		−	0.176777i
$33$			17.9821i			3.13028i
$34$	3.26418			0.559802
$35$	−0.491820	+	6.83836i	−0.0831328	+	1.15589i
$36$	6.41393			1.06899
$37$			10.2495i			1.68501i	0.538692	+	0.842503i	$0.318919\pi$
$37$			10.2495i			1.68501i	−0.538692	+	0.842503i	$0.681081\pi$
$38$		−	0.146777i		−	0.0238103i
$39$		0			0
$40$	0.160405	−	2.23031i	0.0253623	−	0.352643i
$41$	2.25139			0.351608			0.175804	−	0.984425i	$-0.443748\pi$
$41$	2.25139			0.351608			0.175804	+	0.984425i	$0.443748\pi$
$42$		−	9.40747i		−	1.45160i
$43$			6.21583i			0.947905i	0.880550	+	0.473952i	$0.157173\pi$
$43$			6.21583i			0.947905i	−0.880550	+	0.473952i	$0.842827\pi$
$44$	−5.86077			−0.883544
$45$	14.3050	+	1.02883i	2.13247	+	0.153369i
$46$	0.0169460			0.00249856
$47$		−	4.28931i		−	0.625660i	−0.949809	−	0.312830i	$-0.898723\pi$
$47$		−	4.28931i		−	0.625660i	0.949809	−	0.312830i	$-0.101277\pi$
$48$			3.06821i			0.442858i
$49$	−2.40101			−0.343001
$50$	0.715507	−	4.94854i	0.101188	−	0.699829i
$51$	−10.0152			−1.40241
$52$		0			0
$53$			5.54859i			0.762158i	0.924543	+	0.381079i	$0.124447\pi$
$53$			5.54859i			0.762158i	−0.924543	+	0.381079i	$0.875553\pi$
$54$	−10.4747			−1.42542
$55$	−13.0713	−	0.940099i	−1.76254	−	0.126763i
$56$	3.06611			0.409726
$57$			0.450342i			0.0596493i
$58$		−	2.35939i		−	0.309803i
$59$	11.2873			1.46948			0.734740	−	0.678349i	$-0.237304\pi$
$59$	11.2873			1.46948			0.734740	+	0.678349i	$0.237304\pi$
$60$	−0.492158	+	6.84306i	−0.0635373	+	0.883435i
$61$	−4.21282			−0.539396			−0.269698	−	0.962945i	$-0.586924\pi$
$61$	−4.21282			−0.539396			−0.269698	+	0.962945i	$0.586924\pi$
$62$			5.33352i			0.677358i
$63$			19.6658i			2.47766i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	17.9821			2.21344
$67$			9.43931i			1.15320i	0.817028	+	0.576598i	$0.195620\pi$
$67$			9.43931i			1.15320i	−0.817028	+	0.576598i	$0.804380\pi$
$68$		−	3.26418i		−	0.395840i
$69$	−0.0519941			−0.00625935
$70$	6.83836	+	0.491820i	0.817340	+	0.0587838i
$71$	−11.2140			−1.33086			−0.665429	−	0.746461i	$-0.731751\pi$
$71$	−11.2140			−1.33086			−0.665429	+	0.746461i	$0.731751\pi$
$72$		−	6.41393i		−	0.755889i
$73$		−	3.17785i		−	0.371939i	−0.982556	−	0.185970i	$-0.940457\pi$
$73$		−	3.17785i		−	0.371939i	0.982556	−	0.185970i	$-0.0595426\pi$
$74$	10.2495			1.19148
$75$	−2.19533	+	15.1832i	−0.253495	+	1.75320i
$76$	−0.146777			−0.0168365
$77$		−	17.9697i		−	2.04784i
$78$		0			0
$79$	−4.50128			−0.506433			−0.253217	−	0.967410i	$-0.581489\pi$
$79$	−4.50128			−0.506433			−0.253217	+	0.967410i	$0.581489\pi$
$80$	−2.23031	−	0.160405i	−0.249356	−	0.0179339i
$81$	12.8967			1.43297
$82$		−	2.25139i		−	0.248624i
$83$		−	1.11696i		−	0.122602i	−0.998119	−	0.0613011i	$-0.980475\pi$
$83$		−	1.11696i		−	0.122602i	0.998119	−	0.0613011i	$-0.0195250\pi$
$84$	−9.40747			−1.02644
$85$	0.523593	−	7.28013i	0.0567916	−	0.789640i
$86$	6.21583			0.670270
$87$			7.23910i			0.776113i
$88$			5.86077i			0.624760i
$89$	−7.13294			−0.756090			−0.378045	−	0.925787i	$-0.623404\pi$
$89$	−7.13294			−0.756090			−0.378045	+	0.925787i	$0.623404\pi$
$90$	1.02883	−	14.3050i	0.108448	−	1.50788i
$91$		0			0
$92$		−	0.0169460i		−	0.00176675i
$93$		−	16.3644i		−	1.69691i
$94$	−4.28931			−0.442409
$95$	−0.327357	−	0.0235438i	−0.0335862	−	0.00241554i
$96$	3.06821			0.313148
$97$			10.0240i			1.01778i	0.860831	+	0.508892i	$0.169945\pi$
$97$			10.0240i			1.01778i	−0.860831	+	0.508892i	$0.830055\pi$
$98$			2.40101i			0.242538i
$99$	−37.5905			−3.77799
$100$	−4.94854	−	0.715507i	−0.494854	−	0.0715507i
$101$	−11.3356			−1.12794			−0.563968	−	0.825796i	$-0.690726\pi$
$101$	−11.3356			−1.12794			−0.563968	+	0.825796i	$0.690726\pi$
$102$			10.0152i			0.991653i
$103$			12.1963i			1.20173i	0.799349	+	0.600866i	$0.205178\pi$
$103$			12.1963i			1.20173i	−0.799349	+	0.600866i	$0.794822\pi$
$104$		0			0
$105$	−20.9815	−	1.50901i	−2.04759	−	0.147264i
$106$	5.54859			0.538927
$107$			8.60404i			0.831784i	0.909414	+	0.415892i	$0.136531\pi$
$107$			8.60404i			0.831784i	−0.909414	+	0.415892i	$0.863469\pi$
$108$			10.4747i			1.00792i
$109$	16.5382			1.58407			0.792035	−	0.610475i	$-0.209021\pi$
$109$	16.5382			1.58407			0.792035	+	0.610475i	$0.209021\pi$
$110$	−0.940099	+	13.0713i	−0.0896349	+	1.24630i
$111$	−31.4476			−2.98487
$112$		−	3.06611i		−	0.289720i
$113$			4.79844i			0.451400i	0.974197	+	0.225700i	$0.0724668\pi$
$113$			4.79844i			0.451400i	−0.974197	+	0.225700i	$0.927533\pi$
$114$	0.450342			0.0421784
$115$	0.00271824	−	0.0377949i	0.000253477	−	0.00352439i
$116$	−2.35939			−0.219064
$117$		0			0
$118$		−	11.2873i		−	1.03908i
$119$	10.0083			0.917462
$120$	6.84306	+	0.492158i	0.624683	+	0.0449277i
$121$	23.3486			2.12260
$122$			4.21282i			0.381410i
$123$			6.90773i			0.622849i
$124$	5.33352			0.478965
$125$	−10.9220	−	2.38957i	−0.976893	−	0.213730i
$126$	19.6658			1.75197
$127$			10.1167i			0.897711i	0.893604	+	0.448855i	$0.148168\pi$
$127$			10.1167i			0.897711i	−0.893604	+	0.448855i	$0.851832\pi$
$128$			1.00000i			0.0883883i
$129$	−19.0715			−1.67915
$130$		0			0
$131$	14.8793			1.30001			0.650006	−	0.759929i	$-0.274766\pi$
$131$	14.8793			1.30001			0.650006	+	0.759929i	$0.274766\pi$
$132$		−	17.9821i		−	1.56514i
$133$		−	0.450033i		−	0.0390228i
$134$	9.43931			0.815432
$135$	−1.68019	+	23.3617i	−0.144608	+	2.01066i
$136$	−3.26418			−0.279901
$137$			19.1887i			1.63940i	0.572792	+	0.819701i	$0.305860\pi$
$137$			19.1887i			1.63940i	−0.572792	+	0.819701i	$0.694140\pi$
$138$			0.0519941i			0.00442603i
$139$	5.83295			0.494745			0.247372	−	0.968921i	$-0.420433\pi$
$139$	5.83295			0.494745			0.247372	+	0.968921i	$0.420433\pi$
$140$	0.491820	−	6.83836i	0.0415664	−	0.577947i
$141$	13.1605			1.10832
$142$			11.2140i			0.941058i
$143$		0			0
$144$	−6.41393			−0.534494
$145$	−5.26216	−	0.378459i	−0.436998	−	0.0314293i
$146$	−3.17785			−0.263001
$147$		−	7.36680i		−	0.607603i
$148$		−	10.2495i		−	0.842503i
$149$	−3.08843			−0.253014			−0.126507	−	0.991966i	$-0.540377\pi$
$149$	−3.08843			−0.253014			−0.126507	+	0.991966i	$0.540377\pi$
$150$	15.1832	+	2.19533i	1.23970	+	0.179248i
$151$	7.40695			0.602769			0.301385	−	0.953503i	$-0.402551\pi$
$151$	7.40695			0.602769			0.301385	+	0.953503i	$0.402551\pi$
$152$			0.146777i			0.0119052i
$153$		−	20.9362i		−	1.69259i
$154$	−17.9697			−1.44804
$155$	11.8954	+	0.855526i	0.955461	+	0.0687175i
$156$		0			0
$157$		−	0.979363i		−	0.0781617i	−0.999236	−	0.0390808i	$-0.987557\pi$
$157$		−	0.979363i		−	0.0781617i	0.999236	−	0.0390808i	$-0.0124430\pi$
$158$			4.50128i			0.358102i
$159$	−17.0243			−1.35011
$160$	−0.160405	+	2.23031i	−0.0126812	+	0.176321i
$161$	0.0519584			0.00409489
$162$		−	12.8967i		−	1.01326i
$163$		−	3.39574i		−	0.265975i	−0.991118	−	0.132987i	$-0.957543\pi$
$163$		−	3.39574i		−	0.265975i	0.991118	−	0.132987i	$-0.0424570\pi$
$164$	−2.25139			−0.175804
$165$	2.88442	−	40.1056i	0.224552	−	3.12221i
$166$	−1.11696			−0.0866929
$167$		−	20.2181i		−	1.56453i	−0.622949	−	0.782263i	$-0.714066\pi$
$167$		−	20.2181i		−	1.56453i	0.622949	−	0.782263i	$-0.285934\pi$
$168$			9.40747i			0.725802i
$169$		0			0
$170$	−7.28013	−	0.523593i	−0.558360	−	0.0401577i
$171$	−0.941416			−0.0719919
$172$		−	6.21583i		−	0.473952i
$173$			16.7420i			1.27287i	0.771331	+	0.636434i	$0.219591\pi$
$173$			16.7420i			1.27287i	−0.771331	+	0.636434i	$0.780409\pi$
$174$	7.23910			0.548795
$175$	2.19382	−	15.1727i	0.165837	−	1.14695i
$176$	5.86077			0.441772
$177$			34.6318i			2.60308i
$178$			7.13294i			0.534637i
$179$	−9.83274			−0.734934			−0.367467	−	0.930037i	$-0.619775\pi$
$179$	−9.83274			−0.734934			−0.367467	+	0.930037i	$0.619775\pi$
$180$	−14.3050	−	1.02883i	−1.06623	−	0.0766844i
$181$	−0.443661			−0.0329771			−0.0164885	−	0.999864i	$-0.505249\pi$
$181$	−0.443661			−0.0329771			−0.0164885	+	0.999864i	$0.505249\pi$
$182$		0			0
$183$		−	12.9258i		−	0.955504i
$184$	−0.0169460			−0.00124928
$185$	1.64407	−	22.8595i	0.120875	−	1.68066i
$186$	−16.3644			−1.19989
$187$			19.1306i			1.39897i
$188$			4.28931i			0.312830i
$189$	−32.1164			−2.33613
$190$	−0.0235438	+	0.327357i	−0.00170805	+	0.0237490i
$191$	−17.5614			−1.27070			−0.635350	−	0.772224i	$-0.719144\pi$
$191$	−17.5614			−1.27070			−0.635350	+	0.772224i	$0.719144\pi$
$192$		−	3.06821i		−	0.221429i
$193$			0.105639i			0.00760410i	0.999993	+	0.00380205i	$0.00121023\pi$
$193$			0.105639i			0.00760410i	−0.999993	+	0.00380205i	$0.998790\pi$
$194$	10.0240			0.719681
$195$		0			0
$196$	2.40101			0.171501
$197$			3.17264i			0.226041i	0.993593	+	0.113021i	$0.0360526\pi$
$197$			3.17264i			0.226041i	−0.993593	+	0.113021i	$0.963947\pi$
$198$			37.5905i			2.67144i
$199$	11.9745			0.848852			0.424426	−	0.905463i	$-0.360476\pi$
$199$	11.9745			0.848852			0.424426	+	0.905463i	$0.360476\pi$
$200$	−0.715507	+	4.94854i	−0.0505940	+	0.349915i
$201$	−28.9618			−2.04281
$202$			11.3356i			0.797572i
$203$		−	7.23413i		−	0.507736i
$204$	10.0152			0.701204
$205$	−5.02128	−	0.361135i	−0.350702	−	0.0252228i
$206$	12.1963			0.849753
$207$		−	0.108691i		−	0.00755453i
$208$		0			0
$209$	0.860225			0.0595030
$210$	−1.50901	+	20.9815i	−0.104132	+	1.44786i
$211$	24.2859			1.67191			0.835955	−	0.548798i	$-0.184914\pi$
$211$	24.2859			1.67191			0.835955	+	0.548798i	$0.184914\pi$
$212$		−	5.54859i		−	0.381079i
$213$		−	34.4070i		−	2.35753i
$214$	8.60404			0.588160
$215$	0.997053	−	13.8632i	0.0679984	−	0.945463i
$216$	10.4747			0.712710
$217$			16.3532i			1.11012i
$218$		−	16.5382i		−	1.12011i
$219$	9.75032			0.658865
$220$	13.0713	+	0.940099i	0.881268	+	0.0633815i
$221$		0			0
$222$			31.4476i			2.11063i
$223$		−	2.51878i		−	0.168670i	−0.996437	−	0.0843349i	$-0.973123\pi$
$223$		−	2.51878i		−	0.168670i	0.996437	−	0.0843349i	$-0.0268766\pi$
$224$	−3.06611			−0.204863
$225$	−31.7396	−	4.58921i	−2.11597	−	0.305947i
$226$	4.79844			0.319188
$227$		−	19.9429i		−	1.32365i	−0.749656	−	0.661827i	$-0.769781\pi$
$227$		−	19.9429i		−	1.32365i	0.749656	−	0.661827i	$-0.230219\pi$
$228$		−	0.450342i		−	0.0298247i
$229$	8.36964			0.553081			0.276541	−	0.961002i	$-0.410812\pi$
$229$	8.36964			0.553081			0.276541	+	0.961002i	$0.410812\pi$
$230$	−0.0377949	−	0.00271824i	−0.00249212	−	0.000179235i
$231$	55.1350			3.62761
$232$			2.35939i			0.154901i
$233$		−	21.9090i		−	1.43531i	−0.696399	−	0.717654i	$-0.745216\pi$
$233$		−	21.9090i		−	1.43531i	0.696399	−	0.717654i	$-0.254784\pi$
$234$		0			0
$235$	−0.688029	+	9.56648i	−0.0448821	+	0.624048i
$236$	−11.2873			−0.734740
$237$		−	13.8109i		−	0.897113i
$238$		−	10.0083i		−	0.648743i
$239$	5.67861			0.367319			0.183659	−	0.982990i	$-0.441206\pi$
$239$	5.67861			0.367319			0.183659	+	0.982990i	$0.441206\pi$
$240$	0.492158	−	6.84306i	0.0317687	−	0.441717i
$241$	20.3442			1.31049			0.655243	−	0.755419i	$-0.272566\pi$
$241$	20.3442			1.31049			0.655243	+	0.755419i	$0.272566\pi$
$242$		−	23.3486i		−	1.50090i
$243$			8.14581i			0.522554i
$244$	4.21282			0.269698
$245$	5.35498	+	0.385135i	0.342117	+	0.0246054i
$246$	6.90773			0.440421
$247$		0			0
$248$		−	5.33352i		−	0.338679i
$249$	3.42707			0.217182
$250$	−2.38957	+	10.9220i	−0.151130	+	0.690768i
$251$	4.57329			0.288664			0.144332	−	0.989529i	$-0.453897\pi$
$251$	4.57329			0.288664			0.144332	+	0.989529i	$0.453897\pi$
$252$		−	19.6658i		−	1.23883i
$253$			0.0993168i			0.00624399i
$254$	10.1167			0.634777
$255$	22.3370	+	1.60649i	1.39880	+	0.100603i
$256$	1.00000			0.0625000
$257$			12.0638i			0.752519i	0.926514	+	0.376259i	$0.122790\pi$
$257$			12.0638i			0.752519i	−0.926514	+	0.376259i	$0.877210\pi$
$258$			19.0715i			1.18734i
$259$	31.4260			1.95272
$260$		0			0
$261$	−15.1329			−0.936705
$262$		−	14.8793i		−	0.919247i
$263$			24.1283i			1.48781i	0.668283	+	0.743907i	$0.267030\pi$
$263$			24.1283i			1.48781i	−0.668283	+	0.743907i	$0.732970\pi$
$264$	−17.9821			−1.10672
$265$	0.890024	−	12.3751i	0.0546738	−	0.760194i
$266$	−0.450033			−0.0275933
$267$		−	21.8854i		−	1.33936i
$268$		−	9.43931i		−	0.576598i
$269$	14.5369			0.886333			0.443166	−	0.896439i	$-0.353855\pi$
$269$	14.5369			0.886333			0.443166	+	0.896439i	$0.353855\pi$
$270$	23.3617	+	1.68019i	1.42175	+	0.102253i
$271$	−1.41894			−0.0861947			−0.0430973	−	0.999071i	$-0.513723\pi$
$271$	−1.41894			−0.0861947			−0.0430973	+	0.999071i	$0.513723\pi$
$272$			3.26418i			0.197920i
$273$		0			0
$274$	19.1887			1.15923
$275$	29.0022	+	4.19342i	1.74890	+	0.252873i
$276$	0.0519941			0.00312967
$277$		−	22.1610i		−	1.33152i	−0.746164	−	0.665762i	$-0.768107\pi$
$277$		−	22.1610i		−	1.33152i	0.746164	−	0.665762i	$-0.231893\pi$
$278$		−	5.83295i		−	0.349837i
$279$	34.2088			2.04803
$280$	−6.83836	−	0.491820i	−0.408670	−	0.0293919i
$281$	11.2300			0.669924			0.334962	−	0.942232i	$-0.391276\pi$
$281$	11.2300			0.669924			0.334962	+	0.942232i	$0.391276\pi$
$282$		−	13.1605i		−	0.783698i
$283$			16.4081i			0.975362i	0.873022	+	0.487681i	$0.162157\pi$
$283$			16.4081i			0.975362i	−0.873022	+	0.487681i	$0.837843\pi$
$284$	11.2140			0.665429
$285$	0.0722374	−	1.00440i	0.00427897	−	0.0594956i
$286$		0			0
$287$		−	6.90299i		−	0.407471i
$288$			6.41393i			0.377944i
$289$	6.34512			0.373243
$290$	−0.378459	+	5.26216i	−0.0222239	+	0.309004i
$291$	−30.7558			−1.80294
$292$			3.17785i			0.185970i
$293$		−	24.5220i		−	1.43259i	−0.697797	−	0.716296i	$-0.745836\pi$
$293$		−	24.5220i		−	1.43259i	0.697797	−	0.716296i	$-0.254164\pi$
$294$	−7.36680			−0.429640
$295$	−25.1741	−	1.81054i	−1.46569	−	0.105414i
$296$	−10.2495			−0.595739
$297$		−	61.3895i		−	3.56218i
$298$			3.08843i			0.178908i
$299$		0			0
$300$	2.19533	−	15.1832i	0.126747	−	0.876601i
$301$	19.0584			1.09851
$302$		−	7.40695i		−	0.426222i
$303$		−	34.7801i		−	1.99806i
$304$	0.146777			0.00841823
$305$	9.39587	+	0.675759i	0.538006	+	0.0386938i
$306$	−20.9362			−1.19684
$307$			15.4206i			0.880100i	0.897973	+	0.440050i	$0.145039\pi$
$307$			15.4206i			0.880100i	−0.897973	+	0.440050i	$0.854961\pi$
$308$			17.9697i			1.02392i
$309$	−37.4207			−2.12879
$310$	0.855526	−	11.8954i	0.0485906	−	0.675613i
$311$	5.01162			0.284183			0.142091	−	0.989854i	$-0.454617\pi$
$311$	5.01162			0.284183			0.142091	+	0.989854i	$0.454617\pi$
$312$		0			0
$313$			30.6035i			1.72981i	0.501936	+	0.864905i	$0.332621\pi$
$313$			30.6035i			1.72981i	−0.501936	+	0.864905i	$0.667379\pi$
$314$	−0.979363			−0.0552687
$315$	3.15450	−	43.8607i	0.177736	−	2.47127i
$316$	4.50128			0.253217
$317$			2.06303i			0.115871i	0.998320	+	0.0579357i	$0.0184518\pi$
$317$			2.06303i			0.115871i	−0.998320	+	0.0579357i	$0.981548\pi$
$318$			17.0243i			0.954673i
$319$	13.8278			0.774209
$320$	2.23031	+	0.160405i	0.124678	+	0.00896694i
$321$	−26.3990			−1.47345
$322$		−	0.0519584i		−	0.00289553i
$323$			0.479106i			0.0266582i
$324$	−12.8967			−0.716483
$325$		0			0
$326$	−3.39574			−0.188073
$327$			50.7427i			2.80608i
$328$			2.25139i			0.124312i
$329$	−13.1515			−0.725065
$330$	−40.1056	−	2.88442i	−2.20774	−	0.158782i
$331$	32.7988			1.80279			0.901394	−	0.433000i	$-0.142545\pi$
$331$	32.7988			1.80279			0.901394	+	0.433000i	$0.142545\pi$
$332$			1.11696i			0.0613011i
$333$		−	65.7395i		−	3.60250i
$334$	−20.2181			−1.10629
$335$	1.51412	−	21.0526i	0.0827251	−	1.15022i
$336$	9.40747			0.513219
$337$		−	1.08781i		−	0.0592569i	−0.999561	−	0.0296284i	$-0.990568\pi$
$337$		−	1.08781i		−	0.0592569i	0.999561	−	0.0296284i	$-0.00943241\pi$
$338$		0			0
$339$	−14.7226			−0.799624
$340$	−0.523593	+	7.28013i	−0.0283958	+	0.394820i
$341$	−31.2585			−1.69274
$342$			0.941416i			0.0509059i
$343$		−	14.1010i		−	0.761382i
$344$	−6.21583			−0.335135
$345$	0.115963	+	0.00834013i	0.00624322	+	0.000449018i
$346$	16.7420			0.900053
$347$		−	15.7820i		−	0.847223i	−0.905844	−	0.423612i	$-0.860762\pi$
$347$		−	15.7820i		−	0.847223i	0.905844	−	0.423612i	$-0.139238\pi$
$348$		−	7.23910i		−	0.388056i
$349$	5.67847			0.303962			0.151981	−	0.988383i	$-0.451435\pi$
$349$	5.67847			0.303962			0.151981	+	0.988383i	$0.451435\pi$
$350$	−15.1727	−	2.19382i	−0.811018	−	0.117265i
$351$		0			0
$352$		−	5.86077i		−	0.312380i
$353$		−	5.40523i		−	0.287692i	−0.989600	−	0.143846i	$-0.954053\pi$
$353$		−	5.40523i		−	0.287692i	0.989600	−	0.143846i	$-0.0459469\pi$
$354$	34.6318			1.84066
$355$	25.0107	+	1.79879i	1.32743	+	0.0954698i
$356$	7.13294			0.378045
$357$			30.7077i			1.62522i
$358$			9.83274i			0.519677i
$359$	29.7756			1.57150			0.785749	−	0.618546i	$-0.212278\pi$
$359$	29.7756			1.57150			0.785749	+	0.618546i	$0.212278\pi$
$360$	−1.02883	+	14.3050i	−0.0542241	+	0.753941i
$361$	−18.9785			−0.998866
$362$			0.443661i			0.0233183i
$363$			71.6384i			3.76004i
$364$		0			0
$365$	−0.509744	+	7.08758i	−0.0266812	+	0.370981i
$366$	−12.9258			−0.675643
$367$		−	8.42416i		−	0.439738i	−0.975529	−	0.219869i	$-0.929437\pi$
$367$		−	8.42416i		−	0.439738i	0.975529	−	0.219869i	$-0.0705629\pi$
$368$			0.0169460i			0.000883374i
$369$	−14.4402			−0.751729
$370$	−22.8595	−	1.64407i	−1.18841	−	0.0854713i
$371$	17.0126			0.883249
$372$			16.3644i			0.848454i
$373$		−	7.17141i		−	0.371321i	−0.982614	−	0.185661i	$-0.940557\pi$
$373$		−	7.17141i		−	0.371321i	0.982614	−	0.185661i	$-0.0594425\pi$
$374$	19.1306			0.989220
$375$	7.33172	−	33.5110i	0.378608	−	1.73050i
$376$	4.28931			0.221204
$377$		0			0
$378$			32.1164i			1.65189i
$379$	−29.1901			−1.49940			−0.749698	−	0.661780i	$-0.769801\pi$
$379$	−29.1901			−1.49940			−0.749698	+	0.661780i	$0.769801\pi$
$380$	0.327357	+	0.0235438i	0.0167931	+	0.00120777i
$381$	−31.0401			−1.59023
$382$			17.5614i			0.898521i
$383$		−	14.8064i		−	0.756573i	−0.925689	−	0.378286i	$-0.876513\pi$
$383$		−	14.8064i		−	0.756573i	0.925689	−	0.378286i	$-0.123487\pi$
$384$	−3.06821			−0.156574
$385$	−2.88244	+	40.0780i	−0.146903	+	2.04257i
$386$	0.105639			0.00537691
$387$		−	39.8679i		−	2.02660i
$388$		−	10.0240i		−	0.508892i
$389$	−18.3462			−0.930187			−0.465094	−	0.885262i	$-0.653979\pi$
$389$	−18.3462			−0.930187			−0.465094	+	0.885262i	$0.653979\pi$
$390$		0			0
$391$	−0.0553149			−0.00279740
$392$		−	2.40101i		−	0.121269i
$393$			45.6529i			2.30288i
$394$	3.17264			0.159835
$395$	10.0392	+	0.722030i	0.505129	+	0.0363293i
$396$	37.5905			1.88900
$397$		−	12.5269i		−	0.628709i	−0.949306	−	0.314355i	$-0.898212\pi$
$397$		−	12.5269i		−	0.628709i	0.949306	−	0.314355i	$-0.101788\pi$
$398$		−	11.9745i		−	0.600229i
$399$	1.38080			0.0691264
$400$	4.94854	+	0.715507i	0.247427	+	0.0357754i
$401$	−17.0328			−0.850579			−0.425289	−	0.905057i	$-0.639828\pi$
$401$	−17.0328			−0.850579			−0.425289	+	0.905057i	$0.639828\pi$
$402$			28.9618i			1.44448i
$403$		0			0
$404$	11.3356			0.563968
$405$	−28.7636	−	2.06870i	−1.42927	−	0.102795i
$406$	−7.23413			−0.359024
$407$			60.0699i			2.97755i
$408$		−	10.0152i		−	0.495826i
$409$	−33.5842			−1.66063			−0.830317	−	0.557292i	$-0.811840\pi$
$409$	−33.5842			−1.66063			−0.830317	+	0.557292i	$0.811840\pi$
$410$	−0.361135	+	5.02128i	−0.0178352	+	0.247984i
$411$	−58.8750			−2.90409
$412$		−	12.1963i		−	0.600866i
$413$		−	34.6080i		−	1.70295i
$414$	−0.108691			−0.00534186
$415$	−0.179167	+	2.49116i	−0.00879494	+	0.122286i
$416$		0			0
$417$			17.8967i			0.876407i
$418$		−	0.860225i		−	0.0420750i
$419$	−32.5784			−1.59156			−0.795779	−	0.605587i	$-0.792938\pi$
$419$	−32.5784			−1.59156			−0.795779	+	0.605587i	$0.792938\pi$
$420$	20.9815	+	1.50901i	1.02379	+	0.0736321i
$421$	−0.993580			−0.0484241			−0.0242121	−	0.999707i	$-0.507708\pi$
$421$	−0.993580			−0.0484241			−0.0242121	+	0.999707i	$0.507708\pi$
$422$		−	24.2859i		−	1.18222i
$423$			27.5113i			1.33765i
$424$	−5.54859			−0.269463
$425$	−2.33554	+	16.1529i	−0.113291	+	0.783532i
$426$	−34.4070			−1.66702
$427$			12.9169i			0.625095i
$428$		−	8.60404i		−	0.415892i
$429$		0			0
$430$	−13.8632	−	0.997053i	−0.668543	−	0.0480822i
$431$	18.4175			0.887140			0.443570	−	0.896240i	$-0.353712\pi$
$431$	18.4175			0.887140			0.443570	+	0.896240i	$0.353712\pi$
$432$		−	10.4747i		−	0.503962i
$433$		−	15.8335i		−	0.760908i	−0.924800	−	0.380454i	$-0.875768\pi$
$433$		−	15.8335i		−	0.760908i	0.924800	−	0.380454i	$-0.124232\pi$
$434$	16.3532			0.784976
$435$	1.16119	−	16.1454i	0.0556749	−	0.774113i
$436$	−16.5382			−0.792035
$437$			0.00248729i			0.000118983i
$438$		−	9.75032i		−	0.465888i
$439$	12.9767			0.619346			0.309673	−	0.950843i	$-0.399780\pi$
$439$	12.9767			0.619346			0.309673	+	0.950843i	$0.399780\pi$
$440$	0.940099	−	13.0713i	0.0448175	−	0.623150i
$441$	15.3999			0.733328
$442$		0			0
$443$			31.3998i			1.49185i	0.666030	+	0.745925i	$0.267992\pi$
$443$			31.3998i			1.49185i	−0.666030	+	0.745925i	$0.732008\pi$
$444$	31.4476			1.49244
$445$	15.9087	+	1.14416i	0.754143	+	0.0542385i
$446$	−2.51878			−0.119268
$447$		−	9.47595i		−	0.448197i
$448$			3.06611i			0.144860i
$449$	−22.2359			−1.04938			−0.524689	−	0.851294i	$-0.675818\pi$
$449$	−22.2359			−1.04938			−0.524689	+	0.851294i	$0.675818\pi$
$450$	−4.58921	+	31.7396i	−0.216337	+	1.49622i
$451$	13.1949			0.621321
$452$		−	4.79844i		−	0.225700i
$453$			22.7261i			1.06777i
$454$	−19.9429			−0.935965
$455$		0			0
$456$	−0.450342			−0.0210892
$457$		−	3.80485i		−	0.177983i	−0.996032	−	0.0889917i	$-0.971636\pi$
$457$		−	3.80485i		−	0.177983i	0.996032	−	0.0889917i	$-0.0283645\pi$
$458$		−	8.36964i		−	0.391087i
$459$	34.1912			1.59591
$460$	−0.00271824	+	0.0377949i	−0.000126739	+	0.00176220i
$461$	−23.4158			−1.09058			−0.545292	−	0.838246i	$-0.683581\pi$
$461$	−23.4158			−1.09058			−0.545292	+	0.838246i	$0.683581\pi$
$462$		−	55.1350i		−	2.56511i
$463$			28.7667i			1.33690i	0.743756	+	0.668452i	$0.233043\pi$
$463$			28.7667i			1.33690i	−0.743756	+	0.668452i	$0.766957\pi$
$464$	2.35939			0.109532
$465$	−2.62494	+	36.4976i	−0.121729	+	1.69254i
$466$	−21.9090			−1.01492
$467$		−	27.7874i		−	1.28585i	−0.765929	−	0.642925i	$-0.777721\pi$
$467$		−	27.7874i		−	1.28585i	0.765929	−	0.642925i	$-0.222279\pi$
$468$		0			0
$469$	28.9419			1.33641
$470$	9.56648	+	0.688029i	0.441269	+	0.0317364i
$471$	3.00489			0.138458
$472$			11.2873i			0.519539i
$473$			36.4295i			1.67503i
$474$	−13.8109			−0.634355
$475$	0.726331	+	0.105020i	0.0333264	+	0.00481864i
$476$	−10.0083			−0.458731
$477$		−	35.5883i		−	1.62947i
$478$		−	5.67861i		−	0.259734i
$479$	−25.7075			−1.17460			−0.587302	−	0.809368i	$-0.699810\pi$
$479$	−25.7075			−1.17460			−0.587302	+	0.809368i	$0.699810\pi$
$480$	−6.84306	−	0.492158i	−0.312341	−	0.0224638i
$481$		0			0
$482$		−	20.3442i		−	0.926653i
$483$			0.159419i			0.00725383i
$484$	−23.3486			−1.06130
$485$	1.60791	−	22.3566i	0.0730112	−	1.01516i
$486$	8.14581			0.369502
$487$			21.4220i			0.970722i	0.874314	+	0.485361i	$0.161312\pi$
$487$			21.4220i			0.970722i	−0.874314	+	0.485361i	$0.838688\pi$
$488$		−	4.21282i		−	0.190705i
$489$	10.4188			0.471157
$490$	0.385135	−	5.35498i	0.0173986	−	0.241913i
$491$	−3.97410			−0.179349			−0.0896743	−	0.995971i	$-0.528583\pi$
$491$	−3.97410			−0.179349			−0.0896743	+	0.995971i	$0.528583\pi$
$492$		−	6.90773i		−	0.311425i
$493$			7.70146i			0.346856i
$494$		0			0
$495$	83.8384	+	6.02973i	3.76826	+	0.271016i
$496$	−5.33352			−0.239482
$497$			34.3833i			1.54230i
$498$		−	3.42707i		−	0.153571i
$499$	−2.48276			−0.111143			−0.0555717	−	0.998455i	$-0.517698\pi$
$499$	−2.48276			−0.111143			−0.0555717	+	0.998455i	$0.517698\pi$
$500$	10.9220	+	2.38957i	0.488446	+	0.106865i
$501$	62.0335			2.77145
$502$		−	4.57329i		−	0.204116i
$503$			30.2812i			1.35017i	0.737739	+	0.675086i	$0.235894\pi$
$503$			30.2812i			1.35017i	−0.737739	+	0.675086i	$0.764106\pi$
$504$	−19.6658			−0.875984
$505$	25.2819	+	1.81830i	1.12503	+	0.0809131i
$506$	0.0993168			0.00441517
$507$		0			0
$508$		−	10.1167i		−	0.448855i
$509$	−36.1968			−1.60440			−0.802198	−	0.597058i	$-0.796336\pi$
$509$	−36.1968			−1.60440			−0.802198	+	0.597058i	$0.796336\pi$
$510$	1.60649	−	22.3370i	0.0711367	−	0.989098i
$511$	−9.74362			−0.431033
$512$		−	1.00000i		−	0.0441942i
$513$		−	1.53744i		−	0.0678795i
$514$	12.0638			0.532111
$515$	1.95635	−	27.2014i	0.0862069	−	1.19864i
$516$	19.0715			0.839575
$517$		−	25.1387i		−	1.10560i
$518$		−	31.4260i		−	1.38078i
$519$	−51.3679			−2.25480
$520$		0			0
$521$	−29.7160			−1.30188			−0.650942	−	0.759128i	$-0.725626\pi$
$521$	−29.7160			−1.30188			−0.650942	+	0.759128i	$0.725626\pi$
$522$			15.1329i			0.662351i
$523$			34.3388i			1.50153i	0.660569	+	0.750765i	$0.270315\pi$
$523$			34.3388i			1.50153i	−0.660569	+	0.750765i	$0.729685\pi$
$524$	−14.8793			−0.650006
$525$	46.5532	+	6.73111i	2.03175	+	0.293770i
$526$	24.1283			1.05204
$527$		−	17.4096i		−	0.758373i
$528$			17.9821i			0.782570i
$529$	22.9997			0.999988
$530$	−12.3751	−	0.890024i	−0.537538	−	0.0386602i
$531$	−72.3958			−3.14171
$532$			0.450033i			0.0195114i
$533$		0			0
$534$	−21.8854			−0.947073
$535$	1.38014	−	19.1896i	0.0596684	−	0.829641i
$536$	−9.43931			−0.407716
$537$		−	30.1689i		−	1.30189i
$538$		−	14.5369i		−	0.626732i
$539$	−14.0717			−0.606113
$540$	1.68019	−	23.3617i	0.0723040	−	1.00533i
$541$	−14.8974			−0.640489			−0.320244	−	0.947335i	$-0.603765\pi$
$541$	−14.8974			−0.640489			−0.320244	+	0.947335i	$0.603765\pi$
$542$			1.41894i			0.0609488i
$543$		−	1.36125i		−	0.0584167i
$544$	3.26418			0.139951
$545$	−36.8852	−	2.65282i	−1.57999	−	0.113634i
$546$		0			0
$547$		−	34.0349i		−	1.45523i	−0.685987	−	0.727614i	$-0.740629\pi$
$547$		−	34.0349i		−	1.45523i	0.685987	−	0.727614i	$-0.259371\pi$
$548$		−	19.1887i		−	0.819701i
$549$	27.0207			1.15322
$550$	4.19342	−	29.0022i	0.178808	−	1.23666i
$551$	0.346303			0.0147530
$552$		−	0.0519941i		−	0.00221301i
$553$			13.8014i			0.586895i
$554$	−22.1610			−0.941529
$555$	70.1378	+	5.04437i	2.97718	+	0.214122i
$556$	−5.83295			−0.247372
$557$			14.6699i			0.621585i	0.950478	+	0.310792i	$0.100594\pi$
$557$			14.6699i			0.621585i	−0.950478	+	0.310792i	$0.899406\pi$
$558$		−	34.2088i		−	1.44818i
$559$		0			0
$560$	−0.491820	+	6.83836i	−0.0207832	+	0.288973i
$561$	−58.6968			−2.47818
$562$		−	11.2300i		−	0.473708i
$563$		−	15.6720i		−	0.660495i	−0.943894	−	0.330247i	$-0.892868\pi$
$563$		−	15.6720i		−	0.660495i	0.943894	−	0.330247i	$-0.107132\pi$
$564$	−13.1605			−0.554158
$565$	0.769697	−	10.7020i	0.0323814	−	0.450237i
$566$	16.4081			0.689685
$567$		−	39.5426i		−	1.66063i
$568$		−	11.2140i		−	0.470529i
$569$	5.49378			0.230311			0.115156	−	0.993347i	$-0.463263\pi$
$569$	5.49378			0.230311			0.115156	+	0.993347i	$0.463263\pi$
$570$	−1.00440	−	0.0722374i	−0.0420698	−	0.00302569i
$571$	−34.7053			−1.45237			−0.726186	−	0.687498i	$-0.758709\pi$
$571$	−34.7053			−1.45237			−0.726186	+	0.687498i	$0.758709\pi$
$572$		0			0
$573$		−	53.8822i		−	2.25096i
$574$	−6.90299			−0.288125
$575$	−0.0121250	+	0.0838582i	−0.000505648	+	0.00349713i
$576$	6.41393			0.267247
$577$		−	37.7135i		−	1.57003i	−0.619475	−	0.785017i	$-0.712654\pi$
$577$		−	37.7135i		−	1.57003i	0.619475	−	0.785017i	$-0.287346\pi$
$578$		−	6.34512i		−	0.263922i
$579$	−0.324124			−0.0134702
$580$	5.26216	+	0.378459i	0.218499	+	0.0157146i
$581$	−3.42472			−0.142081
$582$			30.7558i			1.27487i
$583$			32.5190i			1.34680i
$584$	3.17785			0.131500
$585$		0			0
$586$	−24.5220			−1.01300
$587$		−	31.5460i		−	1.30204i	−0.759059	−	0.651022i	$-0.774340\pi$
$587$		−	31.5460i		−	1.30204i	0.759059	−	0.651022i	$-0.225660\pi$
$588$			7.36680i			0.303802i
$589$	−0.782838			−0.0322563
$590$	−1.81054	+	25.1741i	−0.0745388	+	1.03640i
$591$	−9.73433			−0.400417
$592$			10.2495i			0.421251i
$593$		−	34.8672i		−	1.43182i	−0.698191	−	0.715912i	$-0.746011\pi$
$593$		−	34.8672i		−	1.43182i	0.698191	−	0.715912i	$-0.253989\pi$
$594$	−61.3895			−2.51884
$595$	−22.3216	−	1.60539i	−0.915098	−	0.0658146i
$596$	3.08843			0.126507
$597$			36.7404i			1.50368i
$598$		0			0
$599$	10.4498			0.426969			0.213484	−	0.976946i	$-0.431519\pi$
$599$	10.4498			0.426969			0.213484	+	0.976946i	$0.431519\pi$
$600$	−15.1832	−	2.19533i	−0.619850	−	0.0896239i
$601$	16.0656			0.655330			0.327665	−	0.944794i	$-0.393738\pi$
$601$	16.0656			0.655330			0.327665	+	0.944794i	$0.393738\pi$
$602$		−	19.0584i		−	0.776762i
$603$		−	60.5431i		−	2.46550i
$604$	−7.40695			−0.301385
$605$	−52.0745	−	3.74524i	−2.11713	−	0.152266i
$606$	−34.7801			−1.41285
$607$		−	21.7323i		−	0.882085i	−0.897486	−	0.441042i	$-0.854609\pi$
$607$		−	21.7323i		−	0.882085i	0.897486	−	0.441042i	$-0.145391\pi$
$608$		−	0.146777i		−	0.00595259i
$609$	22.1958			0.899421
$610$	0.675759	−	9.39587i	0.0273607	−	0.380428i
$611$		0			0
$612$			20.9362i			0.846297i
$613$			39.8653i			1.61014i	0.593177	+	0.805072i	$0.297873\pi$
$613$			39.8653i			1.61014i	−0.593177	+	0.805072i	$0.702127\pi$
$614$	15.4206			0.622325
$615$	1.10804	−	15.4064i	0.0446804	−	0.621245i
$616$	17.9697			0.724021
$617$		−	30.0048i		−	1.20795i	−0.797004	−	0.603974i	$-0.793583\pi$
$617$		−	30.0048i		−	1.20795i	0.797004	−	0.603974i	$-0.206417\pi$
$618$			37.4207i			1.50528i
$619$	−14.0110			−0.563150			−0.281575	−	0.959539i	$-0.590857\pi$
$619$	−14.0110			−0.563150			−0.281575	+	0.959539i	$0.590857\pi$
$620$	−11.8954	−	0.855526i	−0.477731	−	0.0343588i
$621$	0.177504			0.00712299
$622$		−	5.01162i		−	0.200948i
$623$			21.8704i			0.876218i
$624$		0			0
$625$	23.9761	+	7.08143i	0.959044	+	0.283257i
$626$	30.6035			1.22316
$627$			2.63935i			0.105406i
$628$			0.979363i			0.0390808i
$629$	−33.4562			−1.33399
$630$	−43.8607	−	3.15450i	−1.74745	−	0.125678i
$631$	−3.66957			−0.146083			−0.0730416	−	0.997329i	$-0.523271\pi$
$631$	−3.66957			−0.146083			−0.0730416	+	0.997329i	$0.523271\pi$
$632$		−	4.50128i		−	0.179051i
$633$			74.5143i			2.96168i
$634$	2.06303			0.0819335
$635$	1.62277	−	22.5633i	0.0643977	−	0.895398i
$636$	17.0243			0.675056
$637$		0			0
$638$		−	13.8278i		−	0.547448i
$639$	71.9258			2.84534
$640$	0.160405	−	2.23031i	0.00634058	−	0.0881606i
$641$	−0.743118			−0.0293514			−0.0146757	−	0.999892i	$-0.504672\pi$
$641$	−0.743118			−0.0293514			−0.0146757	+	0.999892i	$0.504672\pi$
$642$			26.3990i			1.04189i
$643$			26.7693i			1.05568i	0.849344	+	0.527839i	$0.176998\pi$
$643$			26.7693i			1.05568i	−0.849344	+	0.527839i	$0.823002\pi$
$644$	−0.0519584			−0.00204745
$645$	42.5353	+	3.05917i	1.67482	+	0.120455i
$646$	0.479106			0.0188502
$647$			7.66204i			0.301226i	0.988593	+	0.150613i	$0.0481247\pi$
$647$			7.66204i			0.301226i	−0.988593	+	0.150613i	$0.951875\pi$
$648$			12.8967i			0.506630i
$649$	66.1521			2.59670
$650$		0			0
$651$	−50.1749			−1.96651
$652$			3.39574i			0.132987i
$653$		−	30.6721i		−	1.20029i	−0.799890	−	0.600146i	$-0.795109\pi$
$653$		−	30.6721i		−	1.20029i	0.799890	−	0.600146i	$-0.204891\pi$
$654$	50.7427			1.98420
$655$	−33.1854	−	2.38672i	−1.29666	−	0.0932570i
$656$	2.25139			0.0879019
$657$			20.3825i			0.795197i
$658$			13.1515i			0.512698i
$659$	22.4254			0.873571			0.436785	−	0.899566i	$-0.356117\pi$
$659$	22.4254			0.873571			0.436785	+	0.899566i	$0.356117\pi$
$660$	−2.88442	+	40.1056i	−0.112276	+	1.56111i
$661$	−7.48529			−0.291144			−0.145572	−	0.989348i	$-0.546502\pi$
$661$	−7.48529			−0.291144			−0.145572	+	0.989348i	$0.546502\pi$
$662$		−	32.7988i		−	1.27476i
$663$		0			0
$664$	1.11696			0.0433465
$665$	−0.0721878	+	1.00371i	−0.00279932	+	0.0389223i
$666$	−65.7395			−2.54735
$667$			0.0399823i			0.00154812i
$668$			20.2181i			0.782263i
$669$	7.72814			0.298787
$670$	−21.0526	−	1.51412i	−0.813331	−	0.0584955i
$671$	−24.6903			−0.953160
$672$		−	9.40747i		−	0.362901i
$673$		−	6.32528i		−	0.243822i	−0.992541	−	0.121911i	$-0.961098\pi$
$673$		−	6.32528i		−	0.243822i	0.992541	−	0.121911i	$-0.0389022\pi$
$674$	−1.08781			−0.0419010
$675$	7.49469	−	51.8343i	0.288471	−	1.99510i
$676$		0			0
$677$			6.94316i			0.266847i	0.991059	+	0.133424i	$0.0425971\pi$
$677$			6.94316i			0.266847i	−0.991059	+	0.133424i	$0.957403\pi$
$678$			14.7226i			0.565420i
$679$	30.7347			1.17949
$680$	7.28013	+	0.523593i	0.279180	+	0.0200789i
$681$	61.1890			2.34477
$682$			31.2585i			1.19695i
$683$			32.3677i			1.23851i	0.785188	+	0.619257i	$0.212566\pi$
$683$			32.3677i			1.23851i	−0.785188	+	0.619257i	$0.787434\pi$
$684$	0.941416			0.0359959
$685$	3.07797	−	42.7967i	0.117603	−	1.63518i
$686$	−14.1010			−0.538379
$687$			25.6798i			0.979746i
$688$			6.21583i			0.236976i
$689$		0			0
$690$	0.00834013	−	0.115963i	0.000317503	−	0.00441463i
$691$	−8.94842			−0.340414			−0.170207	−	0.985408i	$-0.554444\pi$
$691$	−8.94842			−0.340414			−0.170207	+	0.985408i	$0.554444\pi$
$692$		−	16.7420i		−	0.636434i
$693$			115.257i			4.37824i
$694$	−15.7820			−0.599077
$695$	−13.0093	−	0.935637i	−0.493470	−	0.0354908i
$696$	−7.23910			−0.274397
$697$			7.34893i			0.278361i
$698$		−	5.67847i		−	0.214933i
$699$	67.2216			2.54255
$700$	−2.19382	+	15.1727i	−0.0829186	+	0.573476i
$701$	30.3913			1.14786			0.573931	−	0.818903i	$-0.305418\pi$
$701$	30.3913			1.14786			0.573931	+	0.818903i	$0.305418\pi$
$702$		0			0
$703$			1.50439i			0.0567390i
$704$	−5.86077			−0.220886
$705$	−29.3520	−	2.11102i	−1.10546	−	0.0795056i
$706$	−5.40523			−0.203429
$707$			34.7562i			1.30714i
$708$		−	34.6318i		−	1.30154i
$709$	15.8024			0.593470			0.296735	−	0.954960i	$-0.404102\pi$
$709$	15.8024			0.593470			0.296735	+	0.954960i	$0.404102\pi$
$710$	1.79879	−	25.0107i	0.0675073	−	0.938634i
$711$	28.8709			1.08274
$712$		−	7.13294i		−	0.267318i
$713$		−	0.0903821i		−	0.00338484i
$714$	30.7077			1.14921
$715$		0			0
$716$	9.83274			0.367467
$717$			17.4232i			0.650681i
$718$		−	29.7756i		−	1.11122i
$719$	−17.1490			−0.639551			−0.319775	−	0.947493i	$-0.603607\pi$
$719$	−17.1490			−0.639551			−0.319775	+	0.947493i	$0.603607\pi$
$720$	14.3050	+	1.02883i	0.533117	+	0.0383422i
$721$	37.3950			1.39266
$722$			18.9785i			0.706305i
$723$			62.4203i			2.32144i
$724$	0.443661			0.0164885
$725$	11.6755	+	1.68816i	0.433618	+	0.0626966i
$726$	71.6384			2.65875
$727$		−	26.0357i		−	0.965612i	−0.875727	−	0.482806i	$-0.839618\pi$
$727$		−	26.0357i		−	0.965612i	0.875727	−	0.482806i	$-0.160382\pi$
$728$		0			0
$729$	13.6970			0.507296
$730$	7.08758	+	0.509744i	0.262323	+	0.0188665i
$731$	−20.2896			−0.750437
$732$			12.9258i			0.477752i
$733$		−	10.3589i		−	0.382616i	−0.981530	−	0.191308i	$-0.938727\pi$
$733$		−	10.3589i		−	0.382616i	0.981530	−	0.191308i	$-0.0612729\pi$
$734$	−8.42416			−0.310941
$735$	−1.18168	+	16.4302i	−0.0435867	+	0.606038i
$736$	0.0169460			0.000624639
$737$			55.3216i			2.03780i
$738$			14.4402i			0.531552i
$739$	13.2485			0.487355			0.243677	−	0.969856i	$-0.421646\pi$
$739$	13.2485			0.487355			0.243677	+	0.969856i	$0.421646\pi$
$740$	−1.64407	+	22.8595i	−0.0604374	+	0.840332i
$741$		0			0
$742$		−	17.0126i		−	0.624551i
$743$		−	14.4666i		−	0.530729i	−0.964148	−	0.265365i	$-0.914508\pi$
$743$		−	14.4666i		−	0.530729i	0.964148	−	0.265365i	$-0.0854923\pi$
$744$	16.3644			0.599947
$745$	6.88814	+	0.495401i	0.252362	+	0.0181501i
$746$	−7.17141			−0.262564
$747$			7.16410i			0.262121i
$748$		−	19.1306i		−	0.699484i
$749$	26.3809			0.963937
$750$	−33.5110	−	7.33172i	−1.22365	−	0.267717i
$751$	12.6727			0.462432			0.231216	−	0.972902i	$-0.425730\pi$
$751$	12.6727			0.462432			0.231216	+	0.972902i	$0.425730\pi$
$752$		−	4.28931i		−	0.156415i
$753$			14.0318i			0.511348i
$754$		0			0
$755$	−16.5198	−	1.18812i	−0.601216	−	0.0432400i
$756$	32.1164			1.16806
$757$		−	8.62881i		−	0.313619i	−0.987629	−	0.156810i	$-0.949879\pi$
$757$		−	8.62881i		−	0.313619i	0.987629	−	0.156810i	$-0.0501209\pi$
$758$			29.1901i			1.06023i
$759$	−0.304725			−0.0110608
$760$	0.0235438	−	0.327357i	0.000854024	−	0.0118745i
$761$	−0.0205103			−0.000743499			−0.000371749	−	1.00000i	$-0.500118\pi$
$761$	−0.0205103			−0.000743499			−0.000371749		1.00000i	$0.500118\pi$
$762$			31.0401i			1.12447i
$763$		−	50.7078i		−	1.83575i
$764$	17.5614			0.635350
$765$	−3.35828	+	46.6942i	−0.121419	+	1.68823i
$766$	−14.8064			−0.534978
$767$		0			0
$768$			3.06821i			0.110715i
$769$	−14.9014			−0.537358			−0.268679	−	0.963230i	$-0.586587\pi$
$769$	−14.9014			−0.537358			−0.268679	+	0.963230i	$0.586587\pi$
$770$	40.0780	+	2.88244i	1.44431	+	0.103876i
$771$	−37.0143			−1.33304
$772$		−	0.105639i		−	0.00380205i
$773$		−	51.9416i		−	1.86821i	−0.357000	−	0.934105i	$-0.616200\pi$
$773$		−	51.9416i		−	1.86821i	0.357000	−	0.934105i	$-0.383800\pi$
$774$	−39.8679			−1.43302
$775$	−26.3932	−	3.81617i	−0.948070	−	0.137081i
$776$	−10.0240			−0.359841
$777$			96.4217i			3.45911i
$778$			18.3462i			0.657742i
$779$	0.330451			0.0118397
$780$		0			0
$781$	−65.7227			−2.35174
$782$			0.0553149i			0.00197806i
$783$		−	24.7138i		−	0.883198i
$784$	−2.40101			−0.0857503
$785$	−0.157095	+	2.18428i	−0.00560697	+	0.0779603i
$786$	45.6529			1.62838
$787$			40.4580i			1.44217i	0.692845	+	0.721086i	$0.256357\pi$
$787$			40.4580i			1.44217i	−0.692845	+	0.721086i	$0.743643\pi$
$788$		−	3.17264i		−	0.113021i
$789$	−74.0307			−2.63556
$790$	0.722030	−	10.0392i	0.0256887	−	0.357180i
$791$	14.7125			0.523118
$792$		−	37.5905i		−	1.33572i
$793$		0			0
$794$	−12.5269			−0.444564
$795$	37.9693	+	2.73078i	1.34663	+	0.0968509i
$796$	−11.9745			−0.424426
$797$			33.1779i			1.17522i	0.809143	+	0.587612i	$0.199932\pi$
$797$			33.1779i			1.17522i	−0.809143	+	0.587612i	$0.800068\pi$
$798$		−	1.38080i		−	0.0488797i
$799$	14.0011			0.495323
$800$	0.715507	−	4.94854i	0.0252970	−	0.174957i
$801$	45.7502			1.61650
$802$			17.0328i			0.601450i
$803$		−	18.6246i		−	0.657249i
$804$	28.9618			1.02140
$805$	−0.115883	−	0.00833441i	−0.00408434	−	0.000293749i
$806$		0			0
$807$			44.6024i			1.57008i
$808$		−	11.3356i		−	0.398786i
$809$	33.3426			1.17226			0.586132	−	0.810216i	$-0.300650\pi$
$809$	33.3426			1.17226			0.586132	+	0.810216i	$0.300650\pi$
$810$	−2.06870	+	28.7636i	−0.0726867	+	1.01065i
$811$	−18.6578			−0.655162			−0.327581	−	0.944823i	$-0.606233\pi$
$811$	−18.6578			−0.655162			−0.327581	+	0.944823i	$0.606233\pi$
$812$			7.23413i			0.253868i
$813$		−	4.35362i		−	0.152688i
$814$	60.0699			2.10545
$815$	−0.544695	+	7.57354i	−0.0190798	+	0.265290i
$816$	−10.0152			−0.350602
$817$			0.912339i			0.0319187i
$818$			33.5842i			1.17425i
$819$		0			0
$820$	5.02128	+	0.361135i	0.175351	+	0.0126114i
$821$	−32.4377			−1.13208			−0.566041	−	0.824377i	$-0.691526\pi$
$821$	−32.4377			−1.13208			−0.566041	+	0.824377i	$0.691526\pi$
$822$			58.8750i			2.05350i
$823$			28.7896i			1.00354i	0.865000	+	0.501772i	$0.167318\pi$
$823$			28.7896i			1.00354i	−0.865000	+	0.501772i	$0.832682\pi$
$824$	−12.1963			−0.424877
$825$	−12.8663	+	88.9850i	−0.447947	+	3.09806i
$826$	−34.6080			−1.20417
$827$		−	5.37264i		−	0.186825i	−0.995627	−	0.0934124i	$-0.970222\pi$
$827$		−	5.37264i		−	0.186825i	0.995627	−	0.0934124i	$-0.0297775\pi$
$828$			0.108691i			0.00377726i
$829$	16.6031			0.576650			0.288325	−	0.957533i	$-0.406902\pi$
$829$	16.6031			0.576650			0.288325	+	0.957533i	$0.406902\pi$
$830$	2.49116	+	0.179167i	0.0864696	+	0.00621896i
$831$	67.9946			2.35871
$832$		0			0
$833$		−	7.83732i		−	0.271547i
$834$	17.8967			0.619713
$835$	−3.24310	+	45.0926i	−0.112232	+	1.56049i
$836$	−0.860225			−0.0297515
$837$			55.8668i			1.93104i
$838$			32.5784i			1.12540i
$839$	23.3946			0.807670			0.403835	−	0.914832i	$-0.367677\pi$
$839$	23.3946			0.807670			0.403835	+	0.914832i	$0.367677\pi$
$840$	1.50901	−	20.9815i	0.0520658	−	0.723932i
$841$	−23.4333			−0.808045
$842$			0.993580i			0.0342410i
$843$			34.4560i			1.18673i
$844$	−24.2859			−0.835955
$845$		0			0
$846$	27.5113			0.945859
$847$		−	71.5893i		−	2.45984i
$848$			5.54859i			0.190539i
$849$	−50.3436			−1.72779
$850$	16.1529	+	2.33554i	0.554041	+	0.0801085i
$851$	−0.173688			−0.00595396
$852$			34.4070i			1.17876i
$853$		−	24.2937i		−	0.831801i	−0.909410	−	0.415901i	$-0.863466\pi$
$853$		−	24.2937i		−	0.831801i	0.909410	−	0.415901i	$-0.136534\pi$
$854$	12.9169			0.442009
$855$	2.09965	+	0.151008i	0.0718064	+	0.00516437i
$856$	−8.60404			−0.294080
$857$			13.2496i			0.452599i	0.974058	+	0.226299i	$0.0726627\pi$
$857$			13.2496i			0.452599i	−0.974058	+	0.226299i	$0.927337\pi$
$858$		0			0
$859$	25.0581			0.854973			0.427486	−	0.904022i	$-0.359399\pi$
$859$	25.0581			0.854973			0.427486	+	0.904022i	$0.359399\pi$
$860$	−0.997053	+	13.8632i	−0.0339992	+	0.472731i
$861$	21.1798			0.721807
$862$		−	18.4175i		−	0.627303i
$863$			5.39736i			0.183728i	0.995772	+	0.0918641i	$0.0292825\pi$
$863$			5.39736i			0.183728i	−0.995772	+	0.0918641i	$0.970717\pi$
$864$	−10.4747			−0.356355
$865$	2.68550	−	37.3397i	0.0913098	−	1.26959i
$866$	−15.8335			−0.538044
$867$			19.4682i			0.661174i
$868$		−	16.3532i		−	0.555062i
$869$	−26.3809			−0.894912
$870$	−16.1454	−	1.16119i	−0.547381	−	0.0393681i
$871$		0			0
$872$			16.5382i			0.560054i
$873$		−	64.2932i		−	2.17600i
$874$	0.00248729			8.41337e−5
$875$	−7.32669	+	33.4880i	−0.247687	+	1.13210i
$876$	−9.75032			−0.329433
$877$		−	5.51023i		−	0.186067i	−0.995663	−	0.0930337i	$-0.970344\pi$
$877$		−	5.51023i		−	0.186067i	0.995663	−	0.0930337i	$-0.0296564\pi$
$878$		−	12.9767i		−	0.437944i
$879$	75.2388			2.53774
$880$	−13.0713	−	0.940099i	−0.440634	−	0.0316907i
$881$	17.3675			0.585126			0.292563	−	0.956246i	$-0.405492\pi$
$881$	17.3675			0.585126			0.292563	+	0.956246i	$0.405492\pi$
$882$		−	15.3999i		−	0.518541i
$883$		−	44.8753i		−	1.51017i	−0.655625	−	0.755087i	$-0.727595\pi$
$883$		−	44.8753i		−	1.51017i	0.655625	−	0.755087i	$-0.272405\pi$
$884$		0			0
$885$	5.55513	−	77.2395i	0.186734	−	2.59638i
$886$	31.3998			1.05490
$887$		−	48.4709i		−	1.62749i	−0.581219	−	0.813747i	$-0.697424\pi$
$887$		−	48.4709i		−	1.62749i	0.581219	−	0.813747i	$-0.302576\pi$
$888$		−	31.4476i		−	1.05531i
$889$	31.0188			1.04034
$890$	1.14416	−	15.9087i	0.0383524	−	0.533259i
$891$	75.5845			2.53218
$892$			2.51878i			0.0843349i
$893$		−	0.629571i		−	0.0210678i
$894$	−9.47595			−0.316923
$895$	21.9300	+	1.57723i	0.733040	+	0.0527209i
$896$	3.06611			0.102431
$897$		0			0
$898$			22.2359i			0.742023i
$899$	−12.5838			−0.419695
$900$	31.7396	+	4.58921i	1.05799	+	0.152974i
$901$	−18.1116			−0.603385
$902$		−	13.1949i		−	0.439341i
$903$			58.4752i			1.94593i
$904$	−4.79844			−0.159594
$905$	0.989500	+	0.0711657i	0.0328921	+	0.00236563i
$906$	22.7261			0.755024
$907$			23.2156i			0.770862i	0.922737	+	0.385431i	$0.125947\pi$
$907$			23.2156i			0.770862i	−0.922737	+	0.385431i	$0.874053\pi$
$908$			19.9429i			0.661827i
$909$	72.7059			2.41150
$910$		0			0
$911$	16.1288			0.534370			0.267185	−	0.963645i	$-0.413907\pi$
$911$	16.1288			0.534370			0.267185	+	0.963645i	$0.413907\pi$
$912$			0.450342i			0.0149123i
$913$		−	6.54624i		−	0.216649i
$914$	−3.80485			−0.125853
$915$	−2.07337	+	28.8285i	−0.0685436	+	0.953042i
$916$	−8.36964			−0.276541
$917$		−	45.6215i		−	1.50656i
$918$		−	34.1912i		−	1.12848i
$919$	34.2809			1.13082			0.565411	−	0.824809i	$-0.308718\pi$
$919$	34.2809			1.13082			0.565411	+	0.824809i	$0.308718\pi$
$920$	0.0377949	+	0.00271824i	0.00124606	+	8.96177e-5i
$921$	−47.3137			−1.55904
$922$			23.4158i			0.771159i
$923$		0			0
$924$	−55.1350			−1.81381
$925$	−7.33358	+	50.7200i	−0.241127	+	1.66766i
$926$	28.7667			0.945333
$927$		−	78.2259i		−	2.56928i
$928$		−	2.35939i		−	0.0774507i
$929$	38.2009			1.25333			0.626666	−	0.779288i	$-0.284419\pi$
$929$	38.2009			1.25333			0.626666	+	0.779288i	$0.284419\pi$
$930$	36.4976	+	2.62494i	1.19680	+	0.0860751i
$931$	−0.352412			−0.0115498
$932$			21.9090i			0.717654i
$933$			15.3767i			0.503411i
$934$	−27.7874			−0.909233
$935$	3.06865	−	42.6671i	0.100356	−	1.39536i
$936$		0			0
$937$		−	48.7978i		−	1.59416i	−0.603876	−	0.797078i	$-0.706378\pi$
$937$		−	48.7978i		−	1.59416i	0.603876	−	0.797078i	$-0.293622\pi$
$938$		−	28.9419i		−	0.944987i
$939$	−93.8979			−3.06424
$940$	0.688029	−	9.56648i	0.0224410	−	0.312024i
$941$	−13.5563			−0.441922			−0.220961	−	0.975283i	$-0.570919\pi$
$941$	−13.5563			−0.441922			−0.220961	+	0.975283i	$0.570919\pi$
$942$		−	3.00489i		−	0.0979048i
$943$			0.0381521i			0.00124240i
$944$	11.2873			0.367370
$945$	71.6295	+	5.15165i	2.33011	+	0.167583i
$946$	36.4295			1.18443
$947$		−	18.0780i		−	0.587456i	−0.955889	−	0.293728i	$-0.905104\pi$
$947$		−	18.0780i		−	0.587456i	0.955889	−	0.293728i	$-0.0948961\pi$
$948$			13.8109i			0.448556i
$949$		0			0
$950$	0.105020	−	0.726331i	0.00340729	−	0.0235653i
$951$	−6.32982			−0.205259
$952$			10.0083i			0.324372i
$953$		−	24.3013i		−	0.787196i	−0.919283	−	0.393598i	$-0.871230\pi$
$953$		−	24.3013i		−	0.787196i	0.919283	−	0.393598i	$-0.128770\pi$
$954$	−35.5883			−1.15221
$955$	39.1674	+	2.81695i	1.26743	+	0.0911543i
$956$	−5.67861			−0.183659
$957$			42.4267i			1.37146i
$958$			25.7075i			0.830571i
$959$	58.8346			1.89987
$960$	−0.492158	+	6.84306i	−0.0158843	+	0.220859i
$961$	−2.55352			−0.0823718
$962$		0			0
$963$		−	55.1857i		−	1.77833i
$964$	−20.3442			−0.655243
$965$	0.0169452	−	0.235609i	0.000545484	−	0.00758451i
$966$	0.159419			0.00512923
$967$			0.452528i			0.0145523i	0.999974	+	0.00727616i	$0.00231609\pi$
$967$			0.452528i			0.0145523i	−0.999974	+	0.00727616i	$0.997684\pi$
$968$			23.3486i			0.750452i
$969$	−1.47000			−0.0472232
$970$	−22.3566	−	1.60791i	−0.717827	−	0.0516267i
$971$	−36.8572			−1.18280			−0.591402	−	0.806377i	$-0.701425\pi$
$971$	−36.8572			−1.18280			−0.591402	+	0.806377i	$0.701425\pi$
$972$		−	8.14581i		−	0.261277i
$973$		−	17.8844i		−	0.573349i
$974$	21.4220			0.686404
$975$		0			0
$976$	−4.21282			−0.134849
$977$		−	33.3976i		−	1.06848i	−0.845332	−	0.534242i	$-0.820597\pi$
$977$		−	33.3976i		−	1.06848i	0.845332	−	0.534242i	$-0.179403\pi$
$978$		−	10.4188i		−	0.333158i
$979$	−41.8045			−1.33608
$980$	−5.35498	−	0.385135i	−0.171059	−	0.0123027i
$981$	−106.075			−3.38671
$982$			3.97410i			0.126819i
$983$		−	18.0751i		−	0.576507i	−0.957554	−	0.288253i	$-0.906925\pi$
$983$		−	18.0751i		−	0.576507i	0.957554	−	0.288253i	$-0.0930745\pi$
$984$	−6.90773			−0.220211
$985$	0.508909	−	7.07596i	0.0162152	−	0.225459i
$986$	7.70146			0.245265
$987$		−	40.3515i		−	1.28440i
$988$		0			0
$989$	−0.105334			−0.00334942
$990$	6.02973	−	83.8384i	0.191637	−	2.66456i
$991$	25.8715			0.821834			0.410917	−	0.911673i	$-0.365209\pi$
$991$	25.8715			0.821834			0.410917	+	0.911673i	$0.365209\pi$
$992$			5.33352i			0.169340i
$993$			100.634i			3.19352i
$994$	34.3833			1.09057
$995$	−26.7069	−	1.92078i	−0.846665	−	0.0608928i
$996$	−3.42707			−0.108591
$997$		−	10.8765i		−	0.344461i	−0.985057	−	0.172231i	$-0.944903\pi$
$997$		−	10.8765i		−	0.344461i	0.985057	−	0.172231i	$-0.0550975\pi$
$998$			2.48276i			0.0785903i
$999$	107.360			3.39672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.g.339.8	yes	18
5.2	odd	4		8450.2.a.da.1.8		9
5.3	odd	4		8450.2.a.ct.1.2		9
5.4	even	2	inner	1690.2.b.g.339.11	yes	18
13.5	odd	4		1690.2.c.g.1689.17		18
13.8	odd	4		1690.2.c.h.1689.17		18
13.12	even	2		1690.2.b.f.339.17	yes	18
65.12	odd	4		8450.2.a.cw.1.8		9
65.34	odd	4		1690.2.c.g.1689.2		18
65.38	odd	4		8450.2.a.cx.1.2		9
65.44	odd	4		1690.2.c.h.1689.2		18
65.64	even	2		1690.2.b.f.339.2	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.2	✓	18	65.64	even	2
1690.2.b.f.339.17	yes	18	13.12	even	2
1690.2.b.g.339.8	yes	18	1.1	even	1	trivial
1690.2.b.g.339.11	yes	18	5.4	even	2	inner
1690.2.c.g.1689.2		18	65.34	odd	4
1690.2.c.g.1689.17		18	13.5	odd	4
1690.2.c.h.1689.2		18	65.44	odd	4
1690.2.c.h.1689.17		18	13.8	odd	4
8450.2.a.ct.1.2		9	5.3	odd	4
8450.2.a.cw.1.8		9	65.12	odd	4
8450.2.a.cx.1.2		9	65.38	odd	4
8450.2.a.da.1.8		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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +3.06821i q^{3} -1.00000 q^{4} +(-2.23031 - 0.160405i) q^{5} +3.06821 q^{6} -3.06611i q^{7} +1.00000i q^{8} -6.41393 q^{9} +(-0.160405 + 2.23031i) q^{10} +5.86077 q^{11} -3.06821i q^{12} -3.06611 q^{14} +(0.492158 - 6.84306i) q^{15} +1.00000 q^{16} +3.26418i q^{17} +6.41393i q^{18} +0.146777 q^{19} +(2.23031 + 0.160405i) q^{20} +9.40747 q^{21} -5.86077i q^{22} +0.0169460i q^{23} -3.06821 q^{24} +(4.94854 + 0.715507i) q^{25} -10.4747i q^{27} +3.06611i q^{28} +2.35939 q^{29} +(-6.84306 - 0.492158i) q^{30} -5.33352 q^{31} -1.00000i q^{32} +17.9821i q^{33} +3.26418 q^{34} +(-0.491820 + 6.83836i) q^{35} +6.41393 q^{36} +10.2495i q^{37} -0.146777i q^{38} +(0.160405 - 2.23031i) q^{40} +2.25139 q^{41} -9.40747i q^{42} +6.21583i q^{43} -5.86077 q^{44} +(14.3050 + 1.02883i) q^{45} +0.0169460 q^{46} -4.28931i q^{47} +3.06821i q^{48} -2.40101 q^{49} +(0.715507 - 4.94854i) q^{50} -10.0152 q^{51} +5.54859i q^{53} -10.4747 q^{54} +(-13.0713 - 0.940099i) q^{55} +3.06611 q^{56} +0.450342i q^{57} -2.35939i q^{58} +11.2873 q^{59} +(-0.492158 + 6.84306i) q^{60} -4.21282 q^{61} +5.33352i q^{62} +19.6658i q^{63} -1.00000 q^{64} +17.9821 q^{66} +9.43931i q^{67} -3.26418i q^{68} -0.0519941 q^{69} +(6.83836 + 0.491820i) q^{70} -11.2140 q^{71} -6.41393i q^{72} -3.17785i q^{73} +10.2495 q^{74} +(-2.19533 + 15.1832i) q^{75} -0.146777 q^{76} -17.9697i q^{77} -4.50128 q^{79} +(-2.23031 - 0.160405i) q^{80} +12.8967 q^{81} -2.25139i q^{82} -1.11696i q^{83} -9.40747 q^{84} +(0.523593 - 7.28013i) q^{85} +6.21583 q^{86} +7.23910i q^{87} +5.86077i q^{88} -7.13294 q^{89} +(1.02883 - 14.3050i) q^{90} -0.0169460i q^{92} -16.3644i q^{93} -4.28931 q^{94} +(-0.327357 - 0.0235438i) q^{95} +3.06821 q^{96} +10.0240i q^{97} +2.40101i q^{98} -37.5905 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{4} + 14 q^{6} - 16 q^{9} + 2 q^{10} + 8 q^{11} - 2 q^{14} + 8 q^{15} + 18 q^{16} - 12 q^{19} + 16 q^{21} - 14 q^{24} + 22 q^{25} - 30 q^{29} - 14 q^{30} - 12 q^{31} - 24 q^{34} - 4 q^{35} + 16 q^{36}+ \cdots - 32 q^{99}+O(q^{100}) \) 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

Groups

Database

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