LMFDB - Embedded newform 33.5.b.a.23.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,5,Mod(23,33)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	33.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.41120878177$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 162x^{12} + 10041x^{10} + 298396x^{8} + 4418856x^{6} + 32113344x^{4} + 102865552x^{2} + 102193344 $ x^14 + 162x^12 + 10041x^10 + 298396x^8 + 4418856x^6 + 32113344x^4 + 102865552x^2 + 102193344
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{9}\cdot 11^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.12
Root			$6.24203i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.5.b.a.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.24203i q^{2} +(7.09522 - 5.53695i) q^{3} -22.9629 q^{4} +42.0693i q^{5} +(34.5618 + 44.2886i) q^{6} -11.7748 q^{7} -43.4628i q^{8} +(19.6843 - 78.5718i) q^{9} +O(q^{10})$	\(q+6.24203i q^{2} +(7.09522 - 5.53695i) q^{3} -22.9629 q^{4} +42.0693i q^{5} +(34.5618 + 44.2886i) q^{6} -11.7748 q^{7} -43.4628i q^{8} +(19.6843 - 78.5718i) q^{9} -262.598 q^{10} -36.4829i q^{11} +(-162.927 + 127.145i) q^{12} +186.682 q^{13} -73.4985i q^{14} +(232.936 + 298.491i) q^{15} -96.1107 q^{16} -216.992i q^{17} +(490.447 + 122.870i) q^{18} +579.356 q^{19} -966.034i q^{20} +(-83.5446 + 65.1964i) q^{21} +227.727 q^{22} +266.732i q^{23} +(-240.652 - 308.378i) q^{24} -1144.82 q^{25} +1165.27i q^{26} +(-295.384 - 666.475i) q^{27} +270.383 q^{28} -775.677i q^{29} +(-1863.19 + 1453.99i) q^{30} +902.204 q^{31} -1295.33i q^{32} +(-202.004 - 258.854i) q^{33} +1354.47 q^{34} -495.356i q^{35} +(-452.010 + 1804.24i) q^{36} -1100.13 q^{37} +3616.36i q^{38} +(1324.55 - 1033.65i) q^{39} +1828.45 q^{40} -682.715i q^{41} +(-406.958 - 521.488i) q^{42} -1433.48 q^{43} +837.754i q^{44} +(3305.46 + 828.105i) q^{45} -1664.95 q^{46} +3622.90i q^{47} +(-681.927 + 532.161i) q^{48} -2262.35 q^{49} -7146.03i q^{50} +(-1201.47 - 1539.60i) q^{51} -4286.76 q^{52} -987.839i q^{53} +(4160.16 - 1843.79i) q^{54} +1534.81 q^{55} +511.765i q^{56} +(4110.66 - 3207.87i) q^{57} +4841.80 q^{58} -1771.46i q^{59} +(-5348.88 - 6854.22i) q^{60} -2843.76 q^{61} +5631.59i q^{62} +(-231.778 + 925.165i) q^{63} +6547.72 q^{64} +7853.57i q^{65} +(1615.77 - 1260.91i) q^{66} -4896.10 q^{67} +4982.76i q^{68} +(1476.88 + 1892.52i) q^{69} +3092.03 q^{70} +519.758i q^{71} +(-3414.95 - 855.536i) q^{72} +7825.00 q^{73} -6867.04i q^{74} +(-8122.78 + 6338.84i) q^{75} -13303.7 q^{76} +429.578i q^{77} +(6452.07 + 8267.87i) q^{78} +416.507 q^{79} -4043.31i q^{80} +(-5786.06 - 3093.26i) q^{81} +4261.53 q^{82} +2980.79i q^{83} +(1918.43 - 1497.10i) q^{84} +9128.68 q^{85} -8947.81i q^{86} +(-4294.89 - 5503.60i) q^{87} -1585.65 q^{88} +3346.39i q^{89} +(-5169.06 + 20632.8i) q^{90} -2198.14 q^{91} -6124.96i q^{92} +(6401.34 - 4995.46i) q^{93} -22614.3 q^{94} +24373.1i q^{95} +(-7172.19 - 9190.66i) q^{96} -7544.49 q^{97} -14121.7i q^{98} +(-2866.52 - 718.140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9}+O(q^{10}) $ 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9	$ 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9} - 156 q^{10} - 100 q^{12} - 104 q^{13} + 151 q^{15} + 356 q^{16} - 34 q^{18} + 1072 q^{19} + 718 q^{21} + 1200 q^{24} - 1060 q^{25} - 1154 q^{27} - 1808 q^{28} - 3026 q^{30} + 3310 q^{31} - 605 q^{33} - 2304 q^{34} + 2644 q^{36} - 362 q^{37} + 4264 q^{39} + 1896 q^{40} - 7364 q^{42} - 6740 q^{43} + 3611 q^{45} - 4068 q^{46} - 2956 q^{48} + 7074 q^{49} - 7046 q^{51} + 13072 q^{52} + 20512 q^{54} + 726 q^{55} + 3876 q^{57} - 7848 q^{58} - 8416 q^{60} - 3560 q^{61} - 17662 q^{63} + 12020 q^{64} + 1210 q^{66} - 16514 q^{67} + 9833 q^{69} + 13320 q^{70} + 8160 q^{72} + 12664 q^{73} - 5386 q^{75} - 43736 q^{76} + 19096 q^{78} + 3052 q^{79} - 11611 q^{81} + 10200 q^{82} - 39184 q^{84} + 34884 q^{85} + 37068 q^{87} - 7260 q^{88} - 26686 q^{90} - 45856 q^{91} + 2719 q^{93} + 6120 q^{94} - 38368 q^{96} - 27854 q^{97} + 4235 q^{99}+O(q^{100}) $ 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9 - 156 * q^10 - 100 * q^12 - 104 * q^13 + 151 * q^15 + 356 * q^16 - 34 * q^18 + 1072 * q^19 + 718 * q^21 + 1200 * q^24 - 1060 * q^25 - 1154 * q^27 - 1808 * q^28 - 3026 * q^30 + 3310 * q^31 - 605 * q^33 - 2304 * q^34 + 2644 * q^36 - 362 * q^37 + 4264 * q^39 + 1896 * q^40 - 7364 * q^42 - 6740 * q^43 + 3611 * q^45 - 4068 * q^46 - 2956 * q^48 + 7074 * q^49 - 7046 * q^51 + 13072 * q^52 + 20512 * q^54 + 726 * q^55 + 3876 * q^57 - 7848 * q^58 - 8416 * q^60 - 3560 * q^61 - 17662 * q^63 + 12020 * q^64 + 1210 * q^66 - 16514 * q^67 + 9833 * q^69 + 13320 * q^70 + 8160 * q^72 + 12664 * q^73 - 5386 * q^75 - 43736 * q^76 + 19096 * q^78 + 3052 * q^79 - 11611 * q^81 + 10200 * q^82 - 39184 * q^84 + 34884 * q^85 + 37068 * q^87 - 7260 * q^88 - 26686 * q^90 - 45856 * q^91 + 2719 * q^93 + 6120 * q^94 - 38368 * q^96 - 27854 * q^97 + 4235 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

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 $

$2$			6.24203i			1.56051i	0.625463	+	0.780254i	$0.284910\pi$
$2$			6.24203i			1.56051i	−0.625463	+	0.780254i	$0.715090\pi$
$3$	7.09522	−	5.53695i	0.788358	−	0.615217i
$3$	7.09522	−	5.53695i	0.788358	−	0.615217i
$4$	−22.9629			−1.43518
$5$			42.0693i			1.68277i	0.540435	+	0.841386i	$0.318260\pi$
$5$			42.0693i			1.68277i	−0.540435	+	0.841386i	$0.681740\pi$
$6$	34.5618	+	44.2886i	0.960051	+	1.23024i
$7$	−11.7748			−0.240302			−0.120151	−	0.992756i	$-0.538338\pi$
$7$	−11.7748			−0.240302			−0.120151	+	0.992756i	$0.538338\pi$
$8$		−	43.4628i		−	0.679106i
$9$	19.6843	−	78.5718i	0.243016	−	0.970022i
$10$	−262.598			−2.62598
$11$		−	36.4829i		−	0.301511i
$11$		−	36.4829i		−	0.301511i
$12$	−162.927	+	127.145i	−1.13144	+	0.882949i
$13$	186.682			1.10463			0.552313	−	0.833637i	$-0.313745\pi$
$13$	186.682			1.10463			0.552313	+	0.833637i	$0.313745\pi$
$14$		−	73.4985i		−	0.374992i
$15$	232.936	+	298.491i	1.03527	+	1.32663i
$16$	−96.1107			−0.375433
$17$		−	216.992i		−	0.750836i	−0.926856	−	0.375418i	$-0.877499\pi$
$17$		−	216.992i		−	0.750836i	0.926856	−	0.375418i	$-0.122501\pi$
$18$	490.447	+	122.870i	1.51373	+	0.379229i
$19$	579.356			1.60487			0.802433	−	0.596743i	$-0.203539\pi$
$19$	579.356			1.60487			0.802433	+	0.596743i	$0.203539\pi$
$20$		−	966.034i		−	2.41508i
$21$	−83.5446	+	65.1964i	−0.189444	+	0.147838i
$22$	227.727			0.470511
$23$			266.732i			0.504220i	0.967699	+	0.252110i	$0.0811245\pi$
$23$			266.732i			0.504220i	−0.967699	+	0.252110i	$0.918876\pi$
$24$	−240.652	−	308.378i	−0.417798	−	0.535379i
$25$	−1144.82			−1.83172
$26$			1165.27i			1.72378i
$27$	−295.384	−	666.475i	−0.405190	−	0.914232i
$28$	270.383			0.344877
$29$		−	775.677i		−	0.922327i	−0.887315	−	0.461164i	$-0.847432\pi$
$29$		−	775.677i		−	0.922327i	0.887315	−	0.461164i	$-0.152568\pi$
$30$	−1863.19	+	1453.99i	−2.07021	+	1.61555i
$31$	902.204			0.938818			0.469409	−	0.882981i	$-0.344467\pi$
$31$	902.204			0.938818			0.469409	+	0.882981i	$0.344467\pi$
$32$		−	1295.33i		−	1.26497i
$33$	−202.004	−	258.854i	−0.185495	−	0.237699i
$34$	1354.47			1.17169
$35$		−	495.356i		−	0.404373i
$36$	−452.010	+	1804.24i	−0.348773	+	1.39216i
$37$	−1100.13			−0.803600			−0.401800	−	0.915727i	$-0.631615\pi$
$37$	−1100.13			−0.803600			−0.401800	+	0.915727i	$0.631615\pi$
$38$			3616.36i			2.50440i
$39$	1324.55	−	1033.65i	0.870841	−	0.679585i
$40$	1828.45			1.14278
$41$		−	682.715i		−	0.406136i	−0.979165	−	0.203068i	$-0.934909\pi$
$41$		−	682.715i		−	0.406136i	0.979165	−	0.203068i	$-0.0650913\pi$
$42$	−406.958	−	521.488i	−0.230702	−	0.295628i
$43$	−1433.48			−0.775272			−0.387636	−	0.921813i	$-0.626708\pi$
$43$	−1433.48			−0.775272			−0.387636	+	0.921813i	$0.626708\pi$
$44$			837.754i			0.432724i
$45$	3305.46	+	828.105i	1.63233	+	0.408941i
$46$	−1664.95			−0.786839
$47$			3622.90i			1.64007i	0.572317	+	0.820033i	$0.306045\pi$
$47$			3622.90i			1.64007i	−0.572317	+	0.820033i	$0.693955\pi$
$48$	−681.927	+	532.161i	−0.295975	+	0.230972i
$49$	−2262.35			−0.942255
$50$		−	7146.03i		−	2.85841i
$51$	−1201.47	−	1539.60i	−0.461927	−	0.591928i
$52$	−4286.76			−1.58534
$53$		−	987.839i		−	0.351669i	−0.984420	−	0.175835i	$-0.943738\pi$
$53$		−	987.839i		−	0.351669i	0.984420	−	0.175835i	$-0.0562624\pi$
$54$	4160.16	−	1843.79i	1.42667	−	0.632302i
$55$	1534.81			0.507375
$56$			511.765i			0.163190i
$57$	4110.66	−	3207.87i	1.26521	−	0.987340i
$58$	4841.80			1.43930
$59$		−	1771.46i		−	0.508895i	−0.967087	−	0.254448i	$-0.918106\pi$
$59$		−	1771.46i		−	0.508895i	0.967087	−	0.254448i	$-0.0818936\pi$
$60$	−5348.88	−	6854.22i	−1.48580	−	1.90395i
$61$	−2843.76			−0.764245			−0.382123	−	0.924112i	$-0.624807\pi$
$61$	−2843.76			−0.764245			−0.382123	+	0.924112i	$0.624807\pi$
$62$			5631.59i			1.46503i
$63$	−231.778	+	925.165i	−0.0583972	+	0.233098i
$64$	6547.72			1.59857
$65$			7853.57i			1.85883i
$66$	1615.77	−	1260.91i	0.370931	−	0.289466i
$67$	−4896.10			−1.09069			−0.545344	−	0.838212i	$-0.683601\pi$
$67$	−4896.10			−1.09069			−0.545344	+	0.838212i	$0.683601\pi$
$68$			4982.76i			1.07759i
$69$	1476.88	+	1892.52i	0.310205	+	0.397506i
$70$	3092.03			0.631026
$71$			519.758i			0.103106i	0.998670	+	0.0515531i	$0.0164171\pi$
$71$			519.758i			0.103106i	−0.998670	+	0.0515531i	$0.983583\pi$
$72$	−3414.95	−	855.536i	−0.658748	−	0.165034i
$73$	7825.00			1.46838			0.734191	−	0.678943i	$-0.237562\pi$
$73$	7825.00			1.46838			0.734191	+	0.678943i	$0.237562\pi$
$74$		−	6867.04i		−	1.25402i
$75$	−8122.78	+	6338.84i	−1.44405	+	1.12690i
$76$	−13303.7			−2.30328
$77$			429.578i			0.0724536i
$78$	6452.07	+	8267.87i	1.06050	+	1.35895i
$79$	416.507			0.0667372			0.0333686	−	0.999443i	$-0.489376\pi$
$79$	416.507			0.0667372			0.0333686	+	0.999443i	$0.489376\pi$
$80$		−	4043.31i		−	0.631767i
$81$	−5786.06	−	3093.26i	−0.881886	−	0.471462i
$82$	4261.53			0.633778
$83$			2980.79i			0.432688i	0.976317	+	0.216344i	$0.0694133\pi$
$83$			2980.79i			0.432688i	−0.976317	+	0.216344i	$0.930587\pi$
$84$	1918.43	−	1497.10i	0.271886	−	0.212174i
$85$	9128.68			1.26349
$86$		−	8947.81i		−	1.20982i
$87$	−4294.89	−	5503.60i	−0.567431	−	0.727124i
$88$	−1585.65			−0.204758
$89$			3346.39i			0.422470i	0.977435	+	0.211235i	$0.0677486\pi$
$89$			3346.39i			0.422470i	−0.977435	+	0.211235i	$0.932251\pi$
$90$	−5169.06	+	20632.8i	−0.638155	+	2.54726i
$91$	−2198.14			−0.265443
$92$		−	6124.96i		−	0.723648i
$93$	6401.34	−	4995.46i	0.740125	−	0.577577i
$94$	−22614.3			−2.55933
$95$			24373.1i			2.70062i
$96$	−7172.19	−	9190.66i	−0.778232	−	0.997250i
$97$	−7544.49			−0.801837			−0.400919	−	0.916114i	$-0.631309\pi$
$97$	−7544.49			−0.801837			−0.400919	+	0.916114i	$0.631309\pi$
$98$		−	14121.7i		−	1.47040i
$99$	−2866.52	−	718.140i	−0.292473	−	0.0732722i
$100$	26288.5			2.62885
$101$		−	15676.1i		−	1.53672i	−0.640015	−	0.768362i	$-0.721072\pi$
$101$		−	15676.1i		−	1.53672i	0.640015	−	0.768362i	$-0.278928\pi$
$102$	9610.25	−	7499.63i	0.923707	−	0.720841i
$103$	10923.7			1.02966			0.514830	−	0.857292i	$-0.327855\pi$
$103$	10923.7			1.02966			0.514830	+	0.857292i	$0.327855\pi$
$104$		−	8113.72i		−	0.750159i
$105$	−2742.76	−	3514.66i	−0.248777	−	0.318790i
$106$	6166.12			0.548782
$107$		−	775.638i		−	0.0677472i	−0.999426	−	0.0338736i	$-0.989216\pi$
$107$		−	775.638i		−	0.0677472i	0.999426	−	0.0338736i	$-0.0107844\pi$
$108$	6782.88	+	15304.2i	0.581522	+	1.31209i
$109$	4458.80			0.375288			0.187644	−	0.982237i	$-0.439915\pi$
$109$	4458.80			0.375288			0.187644	+	0.982237i	$0.439915\pi$
$110$			9580.32i			0.791762i
$111$	−7805.66	+	6091.36i	−0.633525	+	0.494389i
$112$	1131.68			0.0902170
$113$		−	15482.2i		−	1.21248i	−0.795281	−	0.606241i	$-0.792677\pi$
$113$		−	15482.2i		−	1.21248i	0.795281	−	0.606241i	$-0.207323\pi$
$114$	20023.6	+	25658.9i	1.54075	+	1.97437i
$115$	−11221.2			−0.848487
$116$			17811.8i			1.32371i
$117$	3674.71	−	14667.9i	0.268442	−	1.07151i
$118$	11057.5			0.794134
$119$			2555.03i			0.180427i
$120$	12973.3	−	10124.0i	0.900920	−	0.703058i
$121$	−1331.00			−0.0909091
$122$		−	17750.8i		−	1.19261i
$123$	−3780.16	−	4844.01i	−0.249862	−	0.320181i
$124$	−20717.3			−1.34738
$125$		−	21868.6i		−	1.39959i
$126$	−5774.91	−	1446.77i	−0.363751	−	0.0911292i
$127$	3307.23			0.205049			0.102524	−	0.994730i	$-0.467308\pi$
$127$	3307.23			0.205049			0.102524	+	0.994730i	$0.467308\pi$
$128$			20145.8i			1.22960i
$129$	−10170.8	+	7937.09i	−0.611191	+	0.476960i
$130$	−49022.2			−2.90072
$131$			6934.21i			0.404068i	0.979378	+	0.202034i	$0.0647552\pi$
$131$			6934.21i			0.404068i	−0.979378	+	0.202034i	$0.935245\pi$
$132$	4638.60	+	5944.05i	0.266219	+	0.341141i
$133$	−6821.79			−0.385652
$134$		−	30561.6i		−	1.70203i
$135$	28038.1	−	12426.6i	1.53844	−	0.681843i
$136$	−9431.07			−0.509898
$137$			51.4351i			0.00274043i	0.999999	+	0.00137022i	$0.000436153\pi$
$137$			51.4351i			0.00274043i	−0.999999	+	0.00137022i	$0.999564\pi$
$138$	−11813.2	+	9218.76i	−0.620311	+	0.484077i
$139$	−10302.8			−0.533246			−0.266623	−	0.963801i	$-0.585908\pi$
$139$	−10302.8			−0.533246			−0.266623	+	0.963801i	$0.585908\pi$
$140$			11374.8i			0.580349i
$141$	20059.8	+	25705.3i	1.00900	+	1.29296i
$142$	−3244.35			−0.160898
$143$		−	6810.69i		−	0.333057i
$144$	−1891.87	+	7551.59i	−0.0912362	+	0.364178i
$145$	32632.2			1.55207
$146$			48843.9i			2.29142i
$147$	−16051.9	+	12526.5i	−0.742834	+	0.579691i
$148$	25262.2			1.15331
$149$			15944.8i			0.718203i	0.933299	+	0.359101i	$0.116917\pi$
$149$			15944.8i			0.718203i	−0.933299	+	0.359101i	$0.883083\pi$
$150$	−39567.2	−	50702.6i	−1.75854	−	2.25345i
$151$	−26838.7			−1.17708			−0.588541	−	0.808467i	$-0.700298\pi$
$151$	−26838.7			−1.17708			−0.588541	+	0.808467i	$0.700298\pi$
$152$		−	25180.5i		−	1.08987i
$153$	−17049.4	−	4271.33i	−0.728328	−	0.182465i
$154$	−2681.44			−0.113064
$155$			37955.1i			1.57982i
$156$	−30415.5	+	23735.6i	−1.24982	+	0.975329i
$157$	46406.0			1.88267			0.941336	−	0.337470i	$-0.109571\pi$
$157$	46406.0			1.88267			0.941336	+	0.337470i	$0.109571\pi$
$158$			2599.85i			0.104144i
$159$	−5469.62	−	7008.94i	−0.216353	−	0.277241i
$160$	54493.6			2.12866
$161$		−	3140.71i		−	0.121165i
$162$	19308.2	−	36116.7i	0.735720	−	1.37619i
$163$	23680.7			0.891290			0.445645	−	0.895210i	$-0.352974\pi$
$163$	23680.7			0.891290			0.445645	+	0.895210i	$0.352974\pi$
$164$			15677.1i			0.582880i
$165$	10889.8	−	8498.16i	0.399993	−	0.312145i
$166$	−18606.2			−0.675213
$167$		−	5000.00i		−	0.179282i	−0.995974	−	0.0896411i	$-0.971428\pi$
$167$		−	5000.00i		−	0.179282i	0.995974	−	0.0896411i	$-0.0285720\pi$
$168$	2833.62	+	3631.08i	0.100397	+	0.128652i
$169$	6289.12			0.220200
$170$			56981.5i			1.97168i
$171$	11404.2	−	45521.1i	0.390008	−	1.55676i
$172$	32916.8			1.11266
$173$		−	11473.4i		−	0.383352i	−0.981458	−	0.191676i	$-0.938608\pi$
$173$		−	11473.4i		−	0.383352i	0.981458	−	0.191676i	$-0.0613924\pi$
$174$	34353.6	−	26808.8i	1.13468	−	0.885481i
$175$	13480.0			0.440165
$176$			3506.40i			0.113197i
$177$	−9808.51	−	12568.9i	−0.313081	−	0.401191i
$178$	−20888.2			−0.659268
$179$		−	22760.7i		−	0.710363i	−0.934797	−	0.355181i	$-0.884419\pi$
$179$		−	22760.7i		−	0.710363i	0.934797	−	0.355181i	$-0.115581\pi$
$180$	−75903.0	−	19015.7i	−2.34269	−	0.586905i
$181$	−38521.9			−1.17585			−0.587924	−	0.808916i	$-0.700055\pi$
$181$	−38521.9			−1.17585			−0.587924	+	0.808916i	$0.700055\pi$
$182$		−	13720.8i		−	0.414226i
$183$	−20177.1	+	15745.7i	−0.602499	+	0.470177i
$184$	11592.9			0.342419
$185$		−	46281.6i		−	1.35228i
$186$	31181.8	+	39957.3i	0.901313	+	1.15497i
$187$	−7916.48			−0.226386
$188$		−	83192.5i		−	2.35379i
$189$	3478.08	+	7847.60i	0.0973679	+	0.219691i
$190$	−152138.			−4.21434
$191$			8633.45i			0.236656i	0.992975	+	0.118328i	$0.0377534\pi$
$191$			8633.45i			0.236656i	−0.992975	+	0.118328i	$0.962247\pi$
$192$	46457.5	−	36254.4i	1.26024	−	0.983464i
$193$	−11791.3			−0.316553			−0.158277	−	0.987395i	$-0.550594\pi$
$193$	−11791.3			−0.316553			−0.158277	+	0.987395i	$0.550594\pi$
$194$		−	47092.9i		−	1.25127i
$195$	43484.9	+	55722.8i	1.14359	+	1.46543i
$196$	51950.3			1.35231
$197$			71709.3i			1.84775i	0.382697	+	0.923874i	$0.374995\pi$
$197$			71709.3i			1.84775i	−0.382697	+	0.923874i	$0.625005\pi$
$198$	4482.65	−	17892.9i	0.114342	−	0.456406i
$199$	−47291.0			−1.19419			−0.597093	−	0.802172i	$-0.703678\pi$
$199$	−47291.0			−1.19419			−0.597093	+	0.802172i	$0.703678\pi$
$200$			49757.3i			1.24393i
$201$	−34738.9	+	27109.5i	−0.859852	+	0.671009i
$202$	97850.8			2.39807
$203$			9133.43i			0.221637i
$204$	27589.3	+	35353.8i	0.662950	+	0.849524i
$205$	28721.3			0.683434
$206$			68185.8i			1.60679i
$207$	20957.6	+	5250.44i	0.489105	+	0.122534i
$208$	−17942.1			−0.414713
$209$		−	21136.6i		−	0.483885i
$210$	21938.6	−	17120.4i	0.497475	−	0.388218i
$211$	36583.9			0.821722			0.410861	−	0.911698i	$-0.365228\pi$
$211$	36583.9			0.821722			0.410861	+	0.911698i	$0.365228\pi$
$212$			22683.7i			0.504710i
$213$	2877.88	+	3687.80i	0.0634327	+	0.0812846i
$214$	4841.56			0.105720
$215$		−	60305.3i		−	1.30460i
$216$	−28966.9	+	12838.2i	−0.620861	+	0.275167i
$217$	−10623.3			−0.225600
$218$			27831.9i			0.585640i
$219$	55520.1	−	43326.7i	1.15761	−	0.903373i
$220$	−35243.7			−0.728175
$221$		−	40508.4i		−	0.829394i
$222$	−38022.5	−	48723.1i	−0.771497	−	0.988620i
$223$	−49124.9			−0.987852			−0.493926	−	0.869504i	$-0.664439\pi$
$223$	−49124.9			−0.987852			−0.493926	+	0.869504i	$0.664439\pi$
$224$			15252.2i			0.303975i
$225$	−22535.1	+	89950.9i	−0.445137	+	1.77681i
$226$	96640.2			1.89209
$227$			43131.0i			0.837024i	0.908211	+	0.418512i	$0.137448\pi$
$227$			43131.0i			0.837024i	−0.908211	+	0.418512i	$0.862552\pi$
$228$	−94392.8	+	73662.1i	−1.81581	+	1.41701i
$229$	−79943.4			−1.52444			−0.762222	−	0.647316i	$-0.775892\pi$
$229$	−79943.4			−1.52444			−0.762222	+	0.647316i	$0.775892\pi$
$230$		−	70043.3i		−	1.32407i
$231$	2378.55	+	3047.95i	0.0445747	+	0.0571194i
$232$	−33713.1			−0.626359
$233$			48365.2i			0.890883i	0.895311	+	0.445442i	$0.146953\pi$
$233$			48365.2i			0.890883i	−0.895311	+	0.445442i	$0.853047\pi$
$234$	91557.7	+	22937.6i	1.67210	+	0.418906i
$235$	−152413.			−2.75985
$236$			40678.0i			0.730358i
$237$	2955.21	−	2306.18i	0.0526128	−	0.0410579i
$238$	−15948.6			−0.281558
$239$		−	60448.7i		−	1.05826i	−0.848542	−	0.529128i	$-0.822519\pi$
$239$		−	60448.7i		−	1.05826i	0.848542	−	0.529128i	$-0.177481\pi$
$240$	−22387.6	−	28688.2i	−0.388674	−	0.498059i
$241$	−67294.4			−1.15863			−0.579315	−	0.815104i	$-0.696680\pi$
$241$	−67294.4			−1.15863			−0.579315	+	0.815104i	$0.696680\pi$
$242$		−	8308.14i		−	0.141864i
$243$	−58180.6	+	10089.7i	−0.985294	+	0.170870i
$244$	65301.0			1.09683
$245$		−	95175.6i		−	1.58560i
$246$	30236.5	−	23595.9i	0.499644	−	0.389911i
$247$	108155.			1.77278
$248$		−	39212.3i		−	0.637558i
$249$	16504.5	+	21149.4i	0.266197	+	0.341113i
$250$	136505.			2.18407
$251$			106969.i			1.69789i	0.528483	+	0.848944i	$0.322761\pi$
$251$			106969.i			1.69789i	−0.528483	+	0.848944i	$0.677239\pi$
$252$	5322.31	−	21244.5i	0.0838107	−	0.334538i
$253$	9731.16			0.152028
$254$			20643.8i			0.319980i
$255$	64770.0	−	50545.1i	0.996079	−	0.777318i
$256$	−20987.0			−0.320236
$257$		−	25616.3i		−	0.387838i	−0.981018	−	0.193919i	$-0.937880\pi$
$257$		−	25616.3i		−	0.387838i	0.981018	−	0.193919i	$-0.0621199\pi$
$258$	−49543.6	−	63486.7i	−0.744300	−	0.953769i
$259$	12953.8			0.193106
$260$		−	180341.i		−	2.66777i
$261$	−60946.4	−	15268.7i	−0.894678	−	0.224141i
$262$	−43283.6			−0.630551
$263$		−	33290.9i		−	0.481299i	−0.970612	−	0.240649i	$-0.922640\pi$
$263$		−	33290.9i		−	0.481299i	0.970612	−	0.240649i	$-0.0773604\pi$
$264$	−11250.5	+	8779.66i	−0.161423	+	0.125971i
$265$	41557.7			0.591779
$266$		−	42581.8i		−	0.601812i
$267$	18528.8	+	23743.3i	0.259911	+	0.333058i
$268$	112429.			1.56534
$269$		−	7561.06i		−	0.104491i	−0.998634	−	0.0522454i	$-0.983362\pi$
$269$		−	7561.06i		−	0.104491i	0.998634	−	0.0522454i	$-0.0166378\pi$
$270$	77567.1	+	175015.i	1.06402	+	2.40075i
$271$	25491.3			0.347100			0.173550	−	0.984825i	$-0.444476\pi$
$271$	25491.3			0.347100			0.173550	+	0.984825i	$0.444476\pi$
$272$			20855.2i			0.281888i
$273$	−15596.3	+	12171.0i	−0.209264	+	0.163305i
$274$	−321.060			−0.00427646
$275$			41766.5i			0.552284i
$276$	−33913.6	−	43457.9i	−0.445200	−	0.570494i
$277$	14441.1			0.188209			0.0941045	−	0.995562i	$-0.470001\pi$
$277$	14441.1			0.188209			0.0941045	+	0.995562i	$0.470001\pi$
$278$		−	64310.7i		−	0.832134i
$279$	17759.3	−	70887.8i	0.228148	−	0.910675i
$280$	−21529.6			−0.274612
$281$			86894.0i			1.10047i	0.835011	+	0.550234i	$0.185461\pi$
$281$			86894.0i			1.10047i	−0.835011	+	0.550234i	$0.814539\pi$
$282$	−160453.	+	125214.i	−2.01767	+	1.57455i
$283$	147937.			1.84716			0.923579	−	0.383409i	$-0.125250\pi$
$283$	147937.			1.84716			0.923579	+	0.383409i	$0.125250\pi$
$284$		−	11935.2i		−	0.147976i
$285$	134953.	+	172933.i	1.66147	+	2.12906i
$286$	42512.5			0.519739
$287$			8038.81i			0.0975951i
$288$	−101776.	−	25497.7i	−1.22705	−	0.307409i
$289$	36435.6			0.436245
$290$			203691.i			2.42201i
$291$	−53529.8	+	41773.5i	−0.632135	+	0.493304i
$292$	−179685.			−2.10740
$293$		−	98428.0i		−	1.14653i	−0.819372	−	0.573263i	$-0.805678\pi$
$293$		−	98428.0i		−	1.14653i	0.819372	−	0.573263i	$-0.194322\pi$
$294$	−78191.1	−	100196.i	−0.904613	−	1.15920i
$295$	74524.2			0.856354
$296$			47814.7i			0.545730i
$297$	−24314.9	+	10776.4i	−0.275651	+	0.122169i
$298$	−99528.1			−1.12076
$299$			49794.1i			0.556975i
$300$	186523.	−	145558.i	2.07248	−	1.61731i
$301$	16878.9			0.186299
$302$		−	167528.i		−	1.83685i
$303$	−86798.0	−	111226.i	−0.945419	−	1.21149i
$304$	−55682.4			−0.602519
$305$		−	119635.i		−	1.28605i
$306$	26661.8	−	106423.i	0.284739	−	1.13656i
$307$	−19930.4			−0.211466			−0.105733	−	0.994395i	$-0.533719\pi$
$307$	−19930.4			−0.211466			−0.105733	+	0.994395i	$0.533719\pi$
$308$		−	9864.36i		−	0.103984i
$309$	77505.8	−	60483.8i	0.811741	−	0.633464i
$310$	−236917.			−2.46532
$311$			95858.8i			0.991086i	0.868584	+	0.495543i	$0.165031\pi$
$311$			95858.8i			0.991086i	−0.868584	+	0.495543i	$0.834969\pi$
$312$	−44925.3	−	57568.6i	−0.461510	−	0.591394i
$313$	58734.4			0.599521			0.299760	−	0.954015i	$-0.403093\pi$
$313$	58734.4			0.599521			0.299760	+	0.954015i	$0.403093\pi$
$314$			289668.i			2.93792i
$315$	−38921.0	−	9750.75i	−0.392250	−	0.0982691i
$316$	−9564.22			−0.0957801
$317$			100015.i			0.995287i	0.867382	+	0.497643i	$0.165801\pi$
$317$			100015.i			0.995287i	−0.867382	+	0.497643i	$0.834199\pi$
$318$	43750.0	−	34141.5i	0.432637	−	0.337620i
$319$	−28298.9			−0.278092
$320$			275458.i			2.69002i
$321$	−4294.67	−	5503.32i	−0.0416793	−	0.0534091i
$322$	19604.4			0.189079
$323$		−	125715.i		−	1.20499i
$324$	132865.	+	71030.4i	1.26567	+	0.676635i
$325$	−213718.			−2.02337
$326$			147816.i			1.39087i
$327$	31636.2	−	24688.2i	0.295861	−	0.230884i
$328$	−29672.7			−0.275810
$329$		−	42658.9i		−	0.394110i
$330$	53045.8	+	67974.5i	0.487105	+	0.624192i
$331$	64359.9			0.587434			0.293717	−	0.955892i	$-0.405108\pi$
$331$	64359.9			0.587434			0.293717	+	0.955892i	$0.405108\pi$
$332$		−	68447.6i		−	0.620987i
$333$	−21655.3	+	86439.1i	−0.195288	+	0.779510i
$334$	31210.1			0.279771
$335$		−	205975.i		−	1.83538i
$336$	8029.54	−	6266.07i	0.0711233	−	0.0555030i
$337$	59843.0			0.526931			0.263466	−	0.964669i	$-0.415134\pi$
$337$	59843.0			0.526931			0.263466	+	0.964669i	$0.415134\pi$
$338$			39256.9i			0.343623i
$339$	−85724.1	−	109849.i	−0.745939	−	0.955869i
$340$	−209621.			−1.81333
$341$		−	32915.0i		−	0.283064i
$342$	284144.	+	71185.6i	2.42933	+	0.608611i
$343$	54910.0			0.466727
$344$			62302.9i			0.526492i
$345$	−79617.2	+	62131.5i	−0.668911	+	0.522003i
$346$	71617.0			0.598224
$347$			12845.8i			0.106685i	0.998576	+	0.0533425i	$0.0169875\pi$
$347$			12845.8i			0.106685i	−0.998576	+	0.0533425i	$0.983012\pi$
$348$	98623.2	+	126379.i	0.814368	+	1.04356i
$349$	−130947.			−1.07509			−0.537546	−	0.843234i	$-0.680649\pi$
$349$	−130947.			−1.07509			−0.537546	+	0.843234i	$0.680649\pi$
$350$			84142.9i			0.686881i
$351$	−55142.8	−	124419.i	−0.447584	−	1.00989i
$352$	−47257.4			−0.381403
$353$			15375.0i			0.123386i	0.998095	+	0.0616928i	$0.0196499\pi$
$353$			15375.0i			0.123386i	−0.998095	+	0.0616928i	$0.980350\pi$
$354$	78455.6	−	61225.0i	0.626062	−	0.488565i
$355$	−21865.9			−0.173504
$356$		−	76842.8i		−	0.606322i
$357$	14147.1	+	18128.5i	0.111002	+	0.142241i
$358$	142073.			1.10853
$359$		−	55146.4i		−	0.427886i	−0.976846	−	0.213943i	$-0.931369\pi$
$359$		−	55146.4i		−	0.427886i	0.976846	−	0.213943i	$-0.0686307\pi$
$360$	35991.8	−	143665.i	0.277714	−	1.10852i
$361$	205333.			1.57559
$362$		−	240455.i		−	1.83492i
$363$	−9443.74	+	7369.68i	−0.0716689	+	0.0559288i
$364$	50475.7			0.380960
$365$			329192.i			2.47095i
$366$	−98285.4	−	125946.i	−0.733714	−	0.940204i
$367$	160740.			1.19341			0.596706	−	0.802460i	$-0.296476\pi$
$367$	160740.			1.19341			0.596706	+	0.802460i	$0.296476\pi$
$368$		−	25635.8i		−	0.189301i
$369$	−53642.1	−	13438.8i	−0.393961	−	0.0986977i
$370$	288891.			2.11024
$371$			11631.6i			0.0845067i
$372$	−146994.	+	114710.i	−1.06221	+	0.828929i
$373$	−45525.6			−0.327219			−0.163609	−	0.986525i	$-0.552314\pi$
$373$	−45525.6			−0.327219			−0.163609	+	0.986525i	$0.552314\pi$
$374$		−	49414.9i		−	0.353276i
$375$	−121086.	−	155163.i	−0.861053	−	1.10338i
$376$	157462.			1.11378
$377$		−	144805.i		−	1.01883i
$378$	−48984.9	+	21710.3i	−0.342830	+	0.151943i
$379$	−201699.			−1.40419			−0.702093	−	0.712085i	$-0.747751\pi$
$379$	−201699.			−1.40419			−0.702093	+	0.712085i	$0.747751\pi$
$380$		−	559678.i		−	3.87589i
$381$	23465.5	−	18312.0i	0.161652	−	0.126149i
$382$	−53890.2			−0.369303
$383$			226958.i			1.54721i	0.633669	+	0.773604i	$0.281548\pi$
$383$			226958.i			1.54721i	−0.633669	+	0.773604i	$0.718452\pi$
$384$	111546.	+	142939.i	0.756471	+	0.969365i
$385$	−18072.0			−0.121923
$386$		−	73601.6i		−	0.493984i
$387$	−28217.0	+	112631.i	−0.188404	+	0.752031i
$388$	173244.			1.15078
$389$			9157.77i			0.0605188i	0.999542	+	0.0302594i	$0.00963334\pi$
$389$			9157.77i			0.0605188i	−0.999542	+	0.0302594i	$0.990367\pi$
$390$	−347824.	+	271434.i	−2.28681	+	1.78457i
$391$	57878.7			0.378587
$392$			98328.3i			0.639892i
$393$	38394.4	+	49199.8i	0.248590	+	0.318550i
$394$	−447611.			−2.88342
$395$			17522.2i			0.112303i
$396$	65823.8	+	16490.6i	0.419752	+	0.105159i
$397$	−45936.2			−0.291457			−0.145728	−	0.989325i	$-0.546553\pi$
$397$	−45936.2			−0.291457			−0.145728	+	0.989325i	$0.546553\pi$
$398$		−	295192.i		−	1.86354i
$399$	−48402.1	+	37771.9i	−0.304032	+	0.237259i
$400$	110030.			0.687687
$401$		−	87213.0i		−	0.542366i	−0.962528	−	0.271183i	$-0.912585\pi$
$401$		−	87213.0i		−	0.542366i	0.962528	−	0.271183i	$-0.0874148\pi$
$402$	−169218.	−	216841.i	−1.04712	−	1.34181i
$403$	168425.			1.03704
$404$			359970.i			2.20548i
$405$	130131.	−	243415.i	0.793363	−	1.48401i
$406$	−57011.1			−0.345866
$407$			40135.9i			0.242295i
$408$	−66915.5	+	52219.4i	−0.401982	+	0.313698i
$409$	191495.			1.14475			0.572377	−	0.819991i	$-0.306022\pi$
$409$	191495.			1.14475			0.572377	+	0.819991i	$0.306022\pi$
$410$			179279.i			1.06650i
$411$	284.794	+	364.944i	0.00168596	+	0.00216044i
$412$	−250839.			−1.47775
$413$			20858.6i			0.122288i
$414$	−32773.4	+	130818.i	−0.191215	+	0.763251i
$415$	−125400.			−0.728115
$416$		−	241815.i		−	1.39732i
$417$	−73101.0	+	57046.4i	−0.420389	+	0.328062i
$418$	131935.			0.755106
$419$		−	19793.3i		−	0.112743i	−0.998410	−	0.0563716i	$-0.982047\pi$
$419$		−	19793.3i		−	0.112743i	0.998410	−	0.0563716i	$-0.0179531\pi$
$420$	62981.9	+	80707.0i	0.357040	+	0.457522i
$421$	−215445.			−1.21555			−0.607775	−	0.794109i	$-0.707938\pi$
$421$	−215445.			−1.21555			−0.607775	+	0.794109i	$0.707938\pi$
$422$			228358.i			1.28230i
$423$	284658.	+	71314.4i	1.59090	+	0.398562i
$424$	−42934.3			−0.238821
$425$			248417.i			1.37532i
$426$	−23019.4	+	17963.8i	−0.126845	+	0.0989871i
$427$	33484.6			0.183649
$428$			17810.9i			0.0972297i
$429$	−37710.5	−	48323.4i	−0.204903	−	0.262568i
$430$	376428.			2.03584
$431$		−	69765.5i		−	0.375566i	−0.982211	−	0.187783i	$-0.939870\pi$
$431$		−	69765.5i		−	0.375566i	0.982211	−	0.187783i	$-0.0601302\pi$
$432$	28389.5	+	64055.4i	0.152122	+	0.343233i
$433$	−290735.			−1.55068			−0.775340	−	0.631544i	$-0.782421\pi$
$433$	−290735.			−1.55068			−0.775340	+	0.631544i	$0.782421\pi$
$434$		−	66310.7i		−	0.352050i
$435$	231533.	−	180683.i	1.22358	−	0.954857i
$436$	−102387.			−0.538607
$437$			154533.i			0.809205i
$438$	270446.	+	346558.i	1.40972	+	1.80646i
$439$	252609.			1.31075			0.655376	−	0.755303i	$-0.272510\pi$
$439$	252609.			1.31075			0.655376	+	0.755303i	$0.272510\pi$
$440$		−	66707.1i		−	0.344561i
$441$	−44532.9	+	177757.i	−0.228983	+	0.914008i
$442$	252855.			1.29427
$443$			383213.i			1.95269i	0.216225	+	0.976343i	$0.430625\pi$
$443$			383213.i			1.95269i	−0.216225	+	0.976343i	$0.569375\pi$
$444$	179241.	−	139876.i	0.909224	−	0.709538i
$445$	−140780.			−0.710921
$446$		−	306639.i		−	1.54155i
$447$	88285.7	+	113132.i	0.441851	+	0.566201i
$448$	−77098.0			−0.384138
$449$		−	297348.i		−	1.47493i	−0.675383	−	0.737467i	$-0.736022\pi$
$449$		−	297348.i		−	1.47493i	0.675383	−	0.737467i	$-0.263978\pi$
$450$	−561476.	−	140665.i	−2.77272	−	0.694640i
$451$	−24907.4			−0.122455
$452$			355516.i			1.74013i
$453$	−190426.	+	148604.i	−0.927962	+	0.724161i
$454$	−269225.			−1.30618
$455$		−	92474.1i		−	0.446681i
$456$	−139423.	−	178661.i	−0.670509	−	0.859211i
$457$	−109053.			−0.522161			−0.261080	−	0.965317i	$-0.584079\pi$
$457$	−109053.			−0.522161			−0.261080	+	0.965317i	$0.584079\pi$
$458$		−	499009.i		−	2.37891i
$459$	−144620.	+	64095.8i	−0.686439	+	0.304232i
$460$	257672.			1.21773
$461$		−	98599.7i		−	0.463953i	−0.972721	−	0.231976i	$-0.925481\pi$
$461$		−	98599.7i		−	0.463953i	0.972721	−	0.231976i	$-0.0745192\pi$
$462$	−19025.4	+	14847.0i	−0.0891352	+	0.0695592i
$463$	155562.			0.725674			0.362837	−	0.931853i	$-0.381808\pi$
$463$	155562.			0.725674			0.362837	+	0.931853i	$0.381808\pi$
$464$			74550.9i			0.346272i
$465$	210156.	+	269300.i	0.971930	+	1.24546i
$466$	−301897.			−1.39023
$467$			131455.i			0.602757i	0.953505	+	0.301378i	$0.0974467\pi$
$467$			131455.i			0.602757i	−0.953505	+	0.301378i	$0.902553\pi$
$468$	−84382.0	+	336819.i	−0.385264	+	1.53782i
$469$	57650.4			0.262094
$470$		−	951366.i		−	4.30677i
$471$	329261.	−	256948.i	1.48422	−	1.15825i
$472$	−76992.8			−0.345594
$473$			52297.4i			0.233753i
$474$	14395.2	+	18446.5i	0.0640711	+	0.0821027i
$475$	−663261.			−2.93966
$476$		−	58670.9i		−	0.258946i
$477$	−77616.3	−	19444.9i	−0.341127	−	0.0854613i
$478$	377322.			1.65142
$479$			123234.i			0.537104i	0.963265	+	0.268552i	$0.0865451\pi$
$479$			123234.i			0.537104i	−0.963265	+	0.268552i	$0.913455\pi$
$480$	386644.	−	301729.i	1.67814	−	1.30959i
$481$	−205374.			−0.887678
$482$		−	420053.i		−	1.80805i
$483$	−17390.0	−	22284.1i	−0.0745427	−	0.0955213i
$484$	30563.7			0.130471
$485$		−	317391.i		−	1.34931i
$486$	−62980.3	−	363165.i	−0.266644	−	1.53756i
$487$	191384.			0.806952			0.403476	−	0.914990i	$-0.367802\pi$
$487$	191384.			0.806952			0.403476	+	0.914990i	$0.367802\pi$
$488$			123598.i			0.519004i
$489$	168020.	−	131119.i	0.702656	−	0.548337i
$490$	594089.			2.47434
$491$			163093.i			0.676509i	0.941055	+	0.338254i	$0.109836\pi$
$491$			163093.i			0.676509i	−0.941055	+	0.338254i	$0.890164\pi$
$492$	86803.5	+	111233.i	0.358597	+	0.459518i
$493$	−168316.			−0.692517
$494$			675109.i			2.76643i
$495$	30211.6	−	120593.i	0.123300	−	0.492165i
$496$	−86711.5			−0.352463
$497$		−	6120.04i		−	0.0247766i
$498$	−132015.	+	103021.i	−0.532309	+	0.415402i
$499$	−158644.			−0.637120			−0.318560	−	0.947903i	$-0.603199\pi$
$499$	−158644.			−0.637120			−0.318560	+	0.947903i	$0.603199\pi$
$500$			502168.i			2.00867i
$501$	−27684.8	−	35476.1i	−0.110297	−	0.141338i
$502$	−667701.			−2.64957
$503$			386864.i			1.52905i	0.644592	+	0.764526i	$0.277027\pi$
$503$			386864.i			1.52905i	−0.644592	+	0.764526i	$0.722973\pi$
$504$	40210.3	+	10073.7i	0.158298	+	0.0396579i
$505$	659483.			2.58596
$506$			60742.2i			0.237241i
$507$	44622.7	−	34822.6i	0.173596	−	0.135471i
$508$	−75943.7			−0.294283
$509$		−	398158.i		−	1.53681i	−0.639963	−	0.768405i	$-0.721051\pi$
$509$		−	398158.i		−	1.53681i	0.639963	−	0.768405i	$-0.278949\pi$
$510$	315504.	+	404296.i	1.21301	+	1.55439i
$511$	−92137.7			−0.352854
$512$			191331.i			0.729870i
$513$	−171132.	−	386127.i	−0.650276	−	1.46722i
$514$	159898.			0.605224
$515$			459551.i			1.73268i
$516$	233552.	−	182259.i	0.877172	−	0.684525i
$517$	132174.			0.494498
$518$			80857.8i			0.301344i
$519$	−63527.4	−	81406.0i	−0.235845	−	0.302219i
$520$	341338.			1.26235
$521$		−	50104.4i		−	0.184587i	−0.995732	−	0.0922933i	$-0.970580\pi$
$521$		−	50104.4i		−	0.184587i	0.995732	−	0.0922933i	$-0.0294197\pi$
$522$	95307.5	−	380429.i	0.349773	−	1.39615i
$523$	−537778.			−1.96607			−0.983036	−	0.183415i	$-0.941285\pi$
$523$	−537778.			−1.96607			−0.983036	+	0.183415i	$0.941285\pi$
$524$		−	159230.i		−	0.579912i
$525$	95643.9	−	74638.4i	0.347007	−	0.270797i
$526$	207803.			0.751070
$527$		−	195771.i		−	0.704899i
$528$	19414.7	+	24878.7i	0.0696408	+	0.0892399i
$529$	208695.			0.745762
$530$			259404.i			0.923475i
$531$	−139187.	−	34870.0i	−0.493639	−	0.123670i
$532$	156648.			0.553481
$533$		−	127450.i		−	0.448629i
$534$	−148207.	+	115657.i	−0.519739	+	0.405593i
$535$	32630.5			0.114003
$536$			212798.i			0.740693i
$537$	−126025.	−	161492.i	−0.437027	−	0.560020i
$538$	47196.3			0.163059
$539$			82537.2i			0.284101i
$540$	−643838.	+	285351.i	−2.20795	+	0.978569i
$541$	277152.			0.946942			0.473471	−	0.880809i	$-0.343001\pi$
$541$	277152.			0.946942			0.473471	+	0.880809i	$0.343001\pi$
$542$			159118.i			0.541651i
$543$	−273322.	+	213294.i	−0.926989	+	0.723401i
$544$	−281076.			−0.949786
$545$			187578.i			0.631524i
$546$	−75971.6	−	97352.4i	−0.254839	−	0.326559i
$547$	212103.			0.708879			0.354440	−	0.935079i	$-0.384672\pi$
$547$	212103.			0.708879			0.354440	+	0.935079i	$0.384672\pi$
$548$		−	1181.10i		−	0.00393302i
$549$	−55977.4	+	223439.i	−0.185724	+	0.741335i
$550$	−260708.			−0.861843
$551$		−	449394.i		−	1.48021i
$552$	82254.5	−	64189.5i	0.269949	−	0.210662i
$553$	−4904.28			−0.0160371
$554$			90141.7i			0.293701i
$555$	−256259.	−	328378.i	−0.831943	−	1.06608i
$556$	236584.			0.765306
$557$			438459.i			1.41325i	0.707588	+	0.706625i	$0.249783\pi$
$557$			438459.i			1.41325i	−0.707588	+	0.706625i	$0.750217\pi$
$558$	442484.	+	110854.i	1.42111	+	0.356027i
$559$	−267604.			−0.856385
$560$			47609.1i			0.151815i
$561$	−56169.2	+	43833.2i	−0.178473	+	0.139276i
$562$	−542395.			−1.71729
$563$		−	390786.i		−	1.23288i	−0.787401	−	0.616442i	$-0.788574\pi$
$563$		−	390786.i		−	1.23288i	0.787401	−	0.616442i	$-0.211426\pi$
$564$	−460633.	−	590269.i	−1.44809	−	1.85563i
$565$	651324.			2.04033
$566$			923427.i			2.88250i
$567$	68129.5	+	36422.5i	0.211919	+	0.113293i
$568$	22590.2			0.0700201
$569$		−	520018.i		−	1.60618i	−0.595859	−	0.803089i	$-0.703188\pi$
$569$		−	520018.i		−	1.60618i	0.595859	−	0.803089i	$-0.296812\pi$
$570$	−1.07945e6	+	842379.i	−3.32241	+	2.59273i
$571$	−513581.			−1.57520			−0.787602	−	0.616185i	$-0.788677\pi$
$571$	−513581.			−1.57520			−0.787602	+	0.616185i	$0.788677\pi$
$572$			156393.i			0.477998i
$573$	47803.0	+	61256.2i	0.145595	+	0.186570i
$574$	−50178.5			−0.152298
$575$		−	305362.i		−	0.923589i
$576$	128887.	−	514466.i	0.388477	−	1.55064i
$577$	151067.			0.453752			0.226876	−	0.973924i	$-0.427149\pi$
$577$	151067.			0.453752			0.226876	+	0.973924i	$0.427149\pi$
$578$			227432.i			0.680764i
$579$	−83661.8	+	65287.8i	−0.249557	+	0.194749i
$580$	−749331.			−2.22750
$581$		−	35098.1i		−	0.103976i
$582$	−260751.	−	334135.i	−0.769804	−	0.986451i
$583$	−36039.2			−0.106032
$584$		−	340097.i		−	0.997187i
$585$	617069.	+	154592.i	1.80311	+	0.451727i
$586$	614391.			1.78916
$587$		−	266575.i		−	0.773648i	−0.922154	−	0.386824i	$-0.873572\pi$
$587$		−	266575.i		−	0.773648i	0.922154	−	0.386824i	$-0.126428\pi$
$588$	368599.	−	287646.i	1.06610	−	0.831963i
$589$	522698.			1.50668
$590$			465182.i			1.33635i
$591$	397051.	+	508793.i	1.13677	+	1.45669i
$592$	105734.			0.301698
$593$		−	583555.i		−	1.65948i	−0.558149	−	0.829741i	$-0.688488\pi$
$593$		−	583555.i		−	1.65948i	0.558149	−	0.829741i	$-0.311512\pi$
$594$	−67266.9	−	151775.i	−0.190646	−	0.430156i
$595$	−107488.			−0.303618
$596$		−	366140.i		−	1.03075i
$597$	−335540.	+	261848.i	−0.941446	+	0.734684i
$598$	−310816.			−0.869163
$599$			3287.16i			0.00916151i	0.999990	+	0.00458075i	$0.00145810\pi$
$599$			3287.16i			0.00916151i	−0.999990	+	0.00458075i	$0.998542\pi$
$600$	275504.	+	353039.i	0.765288	+	0.980664i
$601$	−393802.			−1.09026			−0.545128	−	0.838353i	$-0.683519\pi$
$601$	−393802.			−1.09026			−0.545128	+	0.838353i	$0.683519\pi$
$602$			105358.i			0.290721i
$603$	−96376.3	+	384695.i	−0.265055	+	1.05799i
$604$	616294.			1.68933
$605$		−	55994.2i		−	0.152979i
$606$	694273.	−	541795.i	1.89054	−	1.47533i
$607$	287851.			0.781251			0.390626	−	0.920550i	$-0.372259\pi$
$607$	287851.			0.781251			0.390626	+	0.920550i	$0.372259\pi$
$608$		−	750458.i		−	2.03011i
$609$	50571.4	+	64803.7i	0.136355	+	0.174729i
$610$	746764.			2.00689
$611$			676331.i			1.81166i
$612$	391505.	+	98082.3i	1.04528	+	0.261871i
$613$	343049.			0.912925			0.456463	−	0.889743i	$-0.349116\pi$
$613$	343049.			0.912925			0.456463	+	0.889743i	$0.349116\pi$
$614$		−	124406.i		−	0.329994i
$615$	203784.	−	159029.i	0.538791	−	0.420460i
$616$	18670.7			0.0492037
$617$			569755.i			1.49664i	0.663338	+	0.748320i	$0.269139\pi$
$617$			569755.i			1.49664i	−0.663338	+	0.748320i	$0.730861\pi$
$618$	377542.	+	483794.i	0.988526	+	1.26673i
$619$	347551.			0.907062			0.453531	−	0.891241i	$-0.350164\pi$
$619$	347551.			0.907062			0.453531	+	0.891241i	$0.350164\pi$
$620$		−	871560.i		−	2.26733i
$621$	177771.	−	78788.4i	0.460974	−	0.204305i
$622$	−598353.			−1.54660
$623$		−	39402.9i		−	0.101520i
$624$	−127303.	+	99344.7i	−0.326942	+	0.255138i
$625$	204482.			0.523475
$626$			366622.i			0.935556i
$627$	−117032.	−	149969.i	−0.297694	−	0.381475i
$628$	−1.06562e6			−2.70198
$629$			238719.i			0.603372i
$630$	60864.5	−	242946.i	0.153350	−	0.612110i
$631$	−275097.			−0.690918			−0.345459	−	0.938434i	$-0.612277\pi$
$631$	−275097.			−0.690918			−0.345459	+	0.938434i	$0.612277\pi$
$632$		−	18102.6i		−	0.0453217i
$633$	259571.	−	202563.i	0.647811	−	0.505537i
$634$	−624299.			−1.55315
$635$			139133.i			0.345050i
$636$	125598.	+	160946.i	0.310506	+	0.397892i
$637$	−422341.			−1.04084
$638$		−	176643.i		−	0.433965i
$639$	40838.3	+	10231.1i	0.100015	+	0.0250565i
$640$	−847518.			−2.06914
$641$			16424.6i			0.0399740i	0.999800	+	0.0199870i	$0.00636249\pi$
$641$			16424.6i			0.0399740i	−0.999800	+	0.0199870i	$0.993638\pi$
$642$	34351.9	−	26807.5i	0.0833453	−	0.0650408i
$643$	85020.1			0.205636			0.102818	−	0.994700i	$-0.467214\pi$
$643$	85020.1			0.205636			0.102818	+	0.994700i	$0.467214\pi$
$644$			72120.0i			0.173894i
$645$	−333908.	−	427880.i	−0.802615	−	1.02850i
$646$	784720.			1.88040
$647$			4502.05i			0.0107548i	0.999986	+	0.00537740i	$0.00171169\pi$
$647$			4502.05i			0.0107548i	−0.999986	+	0.00537740i	$0.998288\pi$
$648$	−134442.	+	251478.i	−0.320173	+	0.598895i
$649$	−64628.1			−0.153438
$650$		−	1.33403e6i		−	3.15748i
$651$	−75374.3	+	58820.5i	−0.177853	+	0.138793i
$652$	−543778.			−1.27916
$653$		−	181202.i		−	0.424950i	−0.977167	−	0.212475i	$-0.931848\pi$
$653$		−	181202.i		−	0.424950i	0.977167	−	0.212475i	$-0.0681524\pi$
$654$	154104.	+	197474.i	0.360296	+	0.461694i
$655$	−291717.			−0.679954
$656$			65616.2i			0.152477i
$657$	154030.	−	614825.i	0.356840	−	1.42436i
$658$	266278.			0.615012
$659$			584133.i			1.34506i	0.740071	+	0.672529i	$0.234792\pi$
$659$			584133.i			1.34506i	−0.740071	+	0.672529i	$0.765208\pi$
$660$	−250062.	+	195143.i	−0.574063	+	0.447986i
$661$	85750.2			0.196260			0.0981301	−	0.995174i	$-0.468714\pi$
$661$	85750.2			0.196260			0.0981301	+	0.995174i	$0.468714\pi$
$662$			401736.i			0.916695i
$663$	−224293.	−	287416.i	−0.510257	−	0.653859i
$664$	129553.			0.293841
$665$		−	286988.i		−	0.648963i
$666$	−539556.	−	135173.i	−1.21643	−	0.304748i
$667$	206898.			0.465056
$668$			114815.i			0.257303i
$669$	−348552.	+	272002.i	−0.778781	+	0.607744i
$670$	1.28570e6			2.86412
$671$			103748.i			0.230429i
$672$	84450.9	+	108218.i	0.187010	+	0.239641i
$673$	−764933.			−1.68886			−0.844429	−	0.535667i	$-0.820060\pi$
$673$	−764933.			−1.68886			−0.844429	+	0.535667i	$0.820060\pi$
$674$			373542.i			0.822280i
$675$	338162.	+	762997.i	0.742195	+	1.67462i
$676$	−144417.			−0.316027
$677$		−	394004.i		−	0.859654i	−0.902911	−	0.429827i	$-0.858575\pi$
$677$		−	394004.i		−	0.859654i	0.902911	−	0.429827i	$-0.141425\pi$
$678$	685684.	−	535092.i	1.49164	−	1.16404i
$679$	88834.6			0.192683
$680$		−	396758.i		−	0.858041i
$681$	238814.	+	306024.i	0.514951	+	0.659875i
$682$	205456.			0.441724
$683$		−	85034.7i		−	0.182287i	−0.995838	−	0.0911433i	$-0.970948\pi$
$683$		−	85034.7i		−	0.182287i	0.995838	−	0.0911433i	$-0.0290521\pi$
$684$	−261875.	+	1.04530e6i	−0.559733	+	2.23423i
$685$	−2163.84			−0.00461152
$686$			342750.i			0.728331i
$687$	−567216.	+	442643.i	−1.20181	+	0.937864i
$688$	137773.			0.291062
$689$		−	184412.i		−	0.388463i
$690$	−387826.	−	496973.i	−0.814590	−	1.04384i
$691$	362399.			0.758981			0.379491	−	0.925196i	$-0.376099\pi$
$691$	362399.			0.758981			0.379491	+	0.925196i	$0.376099\pi$
$692$			263462.i			0.550181i
$693$	33752.7	+	8455.94i	0.0702816	+	0.0176074i
$694$	−80184.1			−0.166483
$695$		−	433433.i		−	0.897331i
$696$	−239202.	+	186668.i	−0.493795	+	0.385346i
$697$	−148143.			−0.304942
$698$		−	817377.i		−	1.67769i
$699$	267796.	+	343162.i	0.548087	+	0.702335i
$700$	−309541.			−0.631717
$701$		−	431063.i		−	0.877212i	−0.898680	−	0.438606i	$-0.855472\pi$
$701$		−	431063.i		−	0.877212i	0.898680	−	0.438606i	$-0.144528\pi$
$702$	776626.	−	344203.i	1.57593	−	0.698458i
$703$	−637367.			−1.28967
$704$		−	238880.i		−	0.481985i
$705$	−1.08140e6	+	843903.i	−2.17575	+	1.69791i
$706$	−95971.0			−0.192544
$707$			184583.i			0.369277i
$708$	225232.	+	288619.i	0.449328	+	0.575783i
$709$	409134.			0.813905			0.406952	−	0.913449i	$-0.366592\pi$
$709$	409134.			0.813905			0.406952	+	0.913449i	$0.366592\pi$
$710$		−	136487.i		−	0.270754i
$711$	8198.66	−	32725.7i	0.0162182	−	0.0647366i
$712$	145443.			0.286902
$713$			240647.i			0.473371i
$714$	−113159.	+	88306.4i	−0.221968	+	0.173219i
$715$	286521.			0.560459
$716$			522653.i			1.01950i
$717$	−334701.	−	428897.i	−0.651057	−	0.834285i
$718$	344226.			0.667720
$719$		−	631414.i		−	1.22140i	−0.791863	−	0.610698i	$-0.790889\pi$
$719$		−	631414.i		−	1.22140i	0.791863	−	0.610698i	$-0.209111\pi$
$720$	−317690.	−	79589.8i	−0.612828	−	0.153530i
$721$	−128624.			−0.247429
$722$			1.28169e6i			2.45872i
$723$	−477468.	+	372606.i	−0.913415	+	0.712808i
$724$	884577.			1.68756
$725$			888014.i			1.68944i
$726$	−46001.8	−	58948.1i	−0.0872773	−	0.111840i
$727$	711266.			1.34575			0.672873	−	0.739758i	$-0.265060\pi$
$727$	711266.			1.34575			0.672873	+	0.739758i	$0.265060\pi$
$728$			95537.2i			0.180264i
$729$	−356938.	+	393732.i	−0.671642	+	0.740876i
$730$	−2.05483e6			−3.85593
$731$			311053.i			0.582102i
$732$	463325.	−	361568.i	0.864696	−	0.674789i
$733$	−36344.9			−0.0676449			−0.0338225	−	0.999428i	$-0.510768\pi$
$733$	−36344.9			−0.0676449			−0.0338225	+	0.999428i	$0.510768\pi$
$734$			1.00334e6i			1.86233i
$735$	−526983.	−	675292.i	−0.975488	−	1.25002i
$736$	345507.			0.637824
$737$			178624.i			0.328855i
$738$	83885.2	−	334836.i	0.154018	−	0.614779i
$739$	800264.			1.46536			0.732680	−	0.680574i	$-0.238269\pi$
$739$	800264.			1.46536			0.732680	+	0.680574i	$0.238269\pi$
$740$			1.06276e6i			1.94076i
$741$	767386.	−	598851.i	1.39758	−	1.09064i
$742$	−72604.7			−0.131873
$743$			41609.1i			0.0753722i	0.999290	+	0.0376861i	$0.0119987\pi$
$743$			41609.1i			0.0753722i	−0.999290	+	0.0376861i	$0.988001\pi$
$744$	−217117.	−	278220.i	−0.392236	−	0.502624i
$745$	−670787.			−1.20857
$746$		−	284172.i		−	0.510627i
$747$	234206.	+	58674.8i	0.419717	+	0.105150i
$748$	181786.			0.324905
$749$			9132.97i			0.0162798i
$750$	968530.	−	755820.i	1.72183	−	1.34368i
$751$	864924.			1.53355			0.766776	−	0.641915i	$-0.221860\pi$
$751$	864924.			1.53355			0.766776	+	0.641915i	$0.221860\pi$
$752$		−	348200.i		−	0.615734i
$753$	592280.	+	758966.i	1.04457	+	1.33854i
$754$	903877.			1.58989
$755$		−	1.12908e6i		−	1.98076i
$756$	−79866.9	−	180204.i	−0.139741	−	0.315297i
$757$	−151740.			−0.264794			−0.132397	−	0.991197i	$-0.542267\pi$
$757$	−151740.			−0.264794			−0.132397	+	0.991197i	$0.542267\pi$
$758$		−	1.25901e6i		−	2.19124i
$759$	69044.7	−	53881.0i	0.119852	−	0.0935302i
$760$	1.05932e6			1.83401
$761$		−	1.05603e6i		−	1.82351i	−0.410735	−	0.911755i	$-0.634728\pi$
$761$		−	1.05603e6i		−	1.82351i	0.410735	−	0.911755i	$-0.365272\pi$
$762$	114304.	+	146473.i	0.196857	+	0.252259i
$763$	−52501.4			−0.0901823
$764$		−	198249.i		−	0.339645i
$765$	179692.	−	717257.i	0.307047	−	1.22561i
$766$	−1.41668e6			−2.41443
$767$		−	330700.i		−	0.562139i
$768$	−148907.	+	116204.i	−0.252461	+	0.197015i
$769$	−848741.			−1.43523			−0.717617	−	0.696438i	$-0.754767\pi$
$769$	−848741.			−1.43523			−0.717617	+	0.696438i	$0.754767\pi$
$770$		−	112806.i		−	0.190262i
$771$	−141836.	−	181754.i	−0.238605	−	0.305755i
$772$	270763.			0.454312
$773$		−	296519.i		−	0.496242i	−0.968729	−	0.248121i	$-0.920187\pi$
$773$		−	296519.i		−	0.496242i	0.968729	−	0.248121i	$-0.0798130\pi$
$774$	−703045.	−	176131.i	−1.17355	−	0.294005i
$775$	−1.03287e6			−1.71965
$776$			327905.i			0.544533i
$777$	91909.9	−	71724.4i	0.152237	−	0.118802i
$778$	−57163.0			−0.0944400
$779$		−	395535.i		−	0.651794i
$780$	−998540.	−	1.27956e6i	−1.64126	−	2.10315i
$781$	18962.3			0.0310877
$782$			361280.i			0.590787i
$783$	−516970.	+	229123.i	−0.843222	+	0.373718i
$784$	217437.			0.353753
$785$			1.95227e6i			3.16811i
$786$	−307106.	+	239659.i	−0.497100	+	0.387926i
$787$	789809.			1.27518			0.637591	−	0.770375i	$-0.279931\pi$
$787$	789809.			1.27518			0.637591	+	0.770375i	$0.279931\pi$
$788$		−	1.64665e6i		−	2.65186i
$789$	−184330.	−	236207.i	−0.296103	−	0.379436i
$790$	−109374.			−0.175250
$791$			182299.i			0.291361i
$792$	−31212.4	+	124587.i	−0.0497596	+	0.198620i
$793$	−530878.			−0.844205
$794$		−	286735.i		−	0.454821i
$795$	294861.	−	230103.i	0.466534	−	0.364072i
$796$	1.08594e6			1.71388
$797$			1.22354e6i			1.92620i	0.269147	+	0.963099i	$0.413258\pi$
$797$			1.22354e6i			1.92620i	−0.269147	+	0.963099i	$0.586742\pi$
$798$	−235774.	−	302127.i	−0.370245	−	0.474443i
$799$	786140.			1.23142
$800$			1.48293e6i			2.31707i
$801$	262932.	+	65871.3i	0.409805	+	0.102667i
$802$	544386.			0.846366
$803$		−	285479.i		−	0.442734i
$804$	797707.	−	622512.i	1.23405	−	0.963021i
$805$	132128.			0.203893
$806$			1.05132e6i			1.61831i
$807$	−41865.2	−	53647.4i	−0.0642845	−	0.0823761i
$808$	−681328.			−1.04360
$809$		−	672652.i		−	1.02776i	−0.857861	−	0.513882i	$-0.828207\pi$
$809$		−	672652.i		−	1.02776i	0.857861	−	0.513882i	$-0.171793\pi$
$810$	1.51940e6	+	812284.i	2.31581	+	1.23805i
$811$	−617539.			−0.938907			−0.469453	−	0.882957i	$-0.655549\pi$
$811$	−617539.			−0.938907			−0.469453	+	0.882957i	$0.655549\pi$
$812$		−	209730.i		−	0.318089i
$813$	180867.	−	141144.i	0.273639	−	0.213542i
$814$	−250529.			−0.378103
$815$			996230.i			1.49984i
$816$	115474.	+	147972.i	0.173422	+	0.222229i
$817$	−830494.			−1.24421
$818$			1.19532e6i			1.78640i
$819$	−43268.8	+	172712.i	−0.0645071	+	0.257486i
$820$	−659526.			−0.980853
$821$			991868.i			1.47153i	0.677240	+	0.735763i	$0.263176\pi$
$821$			991868.i			1.47153i	−0.677240	+	0.735763i	$0.736824\pi$
$822$	−2277.99	+	1777.69i	−0.00337138	+	0.00263095i
$823$	−989527.			−1.46092			−0.730462	−	0.682953i	$-0.760695\pi$
$823$	−989527.			−1.46092			−0.730462	+	0.682953i	$0.760695\pi$
$824$		−	474773.i		−	0.699249i
$825$	231259.	+	296342.i	0.339774	+	0.435397i
$826$	−130200.			−0.190832
$827$		−	445972.i		−	0.652074i	−0.945357	−	0.326037i	$-0.894287\pi$
$827$		−	445972.i		−	0.652074i	0.945357	−	0.326037i	$-0.105713\pi$
$828$	−481249.	−	120566.i	−0.701955	−	0.175858i
$829$	728510.			1.06005			0.530025	−	0.847982i	$-0.322183\pi$
$829$	728510.			1.06005			0.530025	+	0.847982i	$0.322183\pi$
$830$		−	782748.i		−	1.13623i
$831$	102463.	−	79959.6i	0.148376	−	0.115789i
$832$	1.22234e6			1.76582
$833$			490912.i			0.707479i
$834$	−356085.	−	456298.i	−0.511943	−	0.656020i
$835$	210346.			0.301691
$836$			485358.i			0.694464i
$837$	−266497.	−	601297.i	−0.380400	−	0.858298i
$838$	123550.			0.175937
$839$		−	370123.i		−	0.525801i	−0.964823	−	0.262901i	$-0.915321\pi$
$839$		−	370123.i		−	0.525801i	0.964823	−	0.262901i	$-0.0846791\pi$
$840$	−152757.	+	119208.i	−0.216493	+	0.168946i
$841$	105606.			0.149312
$842$		−	1.34482e6i		−	1.89687i
$843$	481128.	+	616532.i	0.677026	+	0.867562i
$844$	−840073.			−1.17932
$845$			264579.i			0.370546i
$846$	−445146.	+	1.77684e6i	−0.621960	+	2.48261i
$847$	15672.2			0.0218456
$848$			94941.9i			0.132028i
$849$	1.04965e6	−	819120.i	1.45622	−	1.13640i
$850$	−1.55063e6			−2.14620
$851$		−	293440.i		−	0.405191i
$852$	−66084.5	−	84682.7i	−0.0910375	−	0.116658i
$853$	237569.			0.326506			0.163253	−	0.986584i	$-0.447801\pi$
$853$	237569.			0.326506			0.163253	+	0.986584i	$0.447801\pi$
$854$			209012.i			0.286586i
$855$	1.91504e6	+	479768.i	2.61966	+	0.656295i
$856$	−33711.4			−0.0460076
$857$		−	1.20972e6i		−	1.64711i	−0.567238	−	0.823554i	$-0.691988\pi$
$857$		−	1.20972e6i		−	1.64711i	0.567238	−	0.823554i	$-0.308012\pi$
$858$	301636.	−	235390.i	0.409740	−	0.319752i
$859$	31520.0			0.0427169			0.0213584	−	0.999772i	$-0.493201\pi$
$859$	31520.0			0.0427169			0.0213584	+	0.999772i	$0.493201\pi$
$860$			1.38479e6i			1.87235i
$861$	44510.5	+	57037.2i	0.0600422	+	0.0769399i
$862$	435478.			0.586073
$863$		−	965213.i		−	1.29599i	−0.761645	−	0.647995i	$-0.775608\pi$
$863$		−	965213.i		−	1.29599i	0.761645	−	0.647995i	$-0.224392\pi$
$864$	−863306.	+	382620.i	−1.15648	+	0.512554i
$865$	482676.			0.645094
$866$		−	1.81478e6i		−	2.41985i
$867$	258519.	−	201742.i	0.343917	−	0.268385i
$868$	243941.			0.323777
$869$		−	15195.4i		−	0.0201220i
$870$	1.12783e6	+	1.44523e6i	1.49006	+	1.90941i
$871$	−914012.			−1.20480
$872$		−	193792.i		−	0.254861i
$873$	−148508.	+	592784.i	−0.194859	+	0.777800i
$874$	−964600.			−1.26277
$875$			257498.i			0.336324i
$876$	−1.27490e6	+	994907.i	−1.66138	+	1.29651i
$877$	−1.33894e6			−1.74085			−0.870424	−	0.492304i	$-0.836155\pi$
$877$	−1.33894e6			−1.74085			−0.870424	+	0.492304i	$0.836155\pi$
$878$			1.57679e6i			2.04544i
$879$	−544991.	−	698369.i	−0.705362	−	0.903872i
$880$	−147512.			−0.190485
$881$			879725.i			1.13343i	0.823913	+	0.566716i	$0.191786\pi$
$881$			879725.i			1.13343i	−0.823913	+	0.566716i	$0.808214\pi$
$882$	−1.10957e6	−	277976.i	−1.42632	−	0.357330i
$883$	277527.			0.355946			0.177973	−	0.984035i	$-0.443046\pi$
$883$	277527.			0.355946			0.177973	+	0.984035i	$0.443046\pi$
$884$			930192.i			1.19033i
$885$	528766.	−	412637.i	0.675113	−	0.526843i
$886$	−2.39203e6			−3.04718
$887$		−	632003.i		−	0.803289i	−0.915796	−	0.401645i	$-0.868439\pi$
$887$		−	632003.i		−	0.803289i	0.915796	−	0.401645i	$-0.131561\pi$
$888$	264748.	+	339256.i	0.335742	+	0.430231i
$889$	−38941.9			−0.0492735
$890$		−	878753.i		−	1.10940i
$891$	−112851.	+	211092.i	−0.142151	+	0.265899i
$892$	1.12805e6			1.41775
$893$			2.09895e6i			2.63208i
$894$	−706174.	+	551082.i	−0.883561	+	0.689511i
$895$	957528.			1.19538
$896$		−	237212.i		−	0.295475i
$897$	275708.	+	353300.i	0.342660	+	0.439095i
$898$	1.85606e6			2.30164
$899$		−	699820.i		−	0.865898i
$900$	517471.	−	2.06554e6i	0.638854	−	2.55004i
$901$	−214353.			−0.264046
$902$		−	155473.i		−	0.191091i
$903$	119759.	−	93457.5i	0.146870	−	0.114614i
$904$	−672899.			−0.823404
$905$		−	1.62059e6i		−	1.97868i
$906$	−927593.	−	1.18865e6i	−1.13006	−	1.44809i
$907$	−461433.			−0.560911			−0.280455	−	0.959867i	$-0.590485\pi$
$907$	−461433.			−0.560911			−0.280455	+	0.959867i	$0.590485\pi$
$908$		−	990415.i		−	1.20128i
$909$	−1.23170e6	−	308574.i	−1.49066	−	0.373449i
$910$	577226.			0.697048
$911$			108286.i			0.130477i	0.997870	+	0.0652387i	$0.0207809\pi$
$911$			108286.i			0.130477i	−0.997870	+	0.0652387i	$0.979219\pi$
$912$	−395079.	+	308311.i	−0.475000	+	0.370680i
$913$	108748.			0.130460
$914$		−	680710.i		−	0.814835i
$915$	−662412.	−	848835.i	−0.791200	−	1.01387i
$916$	1.83573e6			2.18786
$917$		−	81648.8i		−	0.0970982i
$918$	−400088.	−	902720.i	−0.474756	−	1.07119i
$919$	1.12294e6			1.32962			0.664809	−	0.747014i	$-0.268513\pi$
$919$	1.12294e6			1.32962			0.664809	+	0.747014i	$0.268513\pi$
$920$			487707.i			0.576213i
$921$	−141411.	+	110354.i	−0.166711	+	0.130097i
$922$	615462.			0.724001
$923$			97029.4i			0.113894i
$924$	−54618.5	−	69989.8i	−0.0639729	−	0.0819768i
$925$	1.25945e6			1.47197
$926$			971023.i			1.13242i
$927$	215025.	−	858292.i	0.250224	−	0.998793i
$928$	−1.00476e6			−1.16672
$929$			748563.i			0.867355i	0.901068	+	0.433678i	$0.142784\pi$
$929$			748563.i			0.867355i	−0.901068	+	0.433678i	$0.857216\pi$
$930$	−1.68098e6	+	1.31180e6i	−1.94355	+	1.51670i
$931$	−1.31071e6			−1.51219
$932$		−	1.11061e6i		−	1.27858i
$933$	530766.	+	680139.i	0.609733	+	0.781330i
$934$	−820544.			−0.940606
$935$		−	333041.i		−	0.380955i
$936$	−637510.	−	159713.i	−0.727671	−	0.182301i
$937$	812345.			0.925255			0.462627	−	0.886553i	$-0.346907\pi$
$937$	812345.			0.925255			0.462627	+	0.886553i	$0.346907\pi$
$938$			359856.i			0.408999i
$939$	416734.	−	325210.i	0.472637	−	0.368835i
$940$	3.49985e6			3.96090
$941$			781678.i			0.882772i	0.897317	+	0.441386i	$0.145513\pi$
$941$			781678.i			0.882772i	−0.897317	+	0.441386i	$0.854487\pi$
$942$	1.60388e6	+	2.05526e6i	1.80746	+	2.31614i
$943$	182102.			0.204782
$944$			170257.i			0.191056i
$945$	−330143.	+	146320.i	−0.369690	+	0.163848i
$946$	−326442.			−0.364774
$947$		−	135861.i		−	0.151494i	−0.997127	−	0.0757468i	$-0.975866\pi$
$947$		−	135861.i		−	0.151494i	0.997127	−	0.0757468i	$-0.0241341\pi$
$948$	−67860.3	+	52956.6i	−0.0755090	+	0.0589256i
$949$	1.46079e6			1.62201
$950$		−	4.14010e6i		−	4.58736i
$951$	553780.	+	709631.i	0.612317	+	0.784642i
$952$	111049.			0.122529
$953$		−	622966.i		−	0.685928i	−0.939348	−	0.342964i	$-0.888569\pi$
$953$		−	622966.i		−	0.685928i	0.939348	−	0.342964i	$-0.111431\pi$
$954$	121376.	−	484483.i	0.133363	−	0.532331i
$955$	−363203.			−0.398238
$956$			1.38808e6i			1.51879i
$957$	−200787.	+	156690.i	−0.219236	+	0.171087i
$958$	−769228.			−0.838155
$959$		−	605.637i		−	0.000658530i
$960$	1.52520e6	+	1.95443e6i	1.65495	+	2.12070i
$961$	−109548.			−0.118620
$962$		−	1.28195e6i		−	1.38523i
$963$	−60943.3	−	15267.9i	−0.0657163	−	0.0164637i
$964$	1.54528e6			1.66285
$965$		−	496051.i		−	0.532687i
$966$	139098.	−	108549.i	0.149062	−	0.116324i
$967$	−98316.7			−0.105142			−0.0525708	−	0.998617i	$-0.516742\pi$
$967$	−98316.7			−0.105142			−0.0525708	+	0.998617i	$0.516742\pi$
$968$			57849.0i			0.0617369i
$969$	−696081.	−	891979.i	−0.741331	−	0.949964i
$970$	1.98116e6			2.10561
$971$			681994.i			0.723339i	0.932306	+	0.361670i	$0.117793\pi$
$971$			681994.i			0.723339i	−0.932306	+	0.361670i	$0.882207\pi$
$972$	1.33600e6	−	231690.i	1.41408	−	0.245230i
$973$	121314.			0.128140
$974$			1.19462e6i			1.25925i
$975$	−1.51638e6	+	1.18335e6i	−1.59514	+	1.24481i
$976$	273315.			0.286922
$977$		−	781651.i		−	0.818887i	−0.912335	−	0.409443i	$-0.865723\pi$
$977$		−	781651.i		−	0.818887i	0.912335	−	0.409443i	$-0.134277\pi$
$978$	818448.	+	1.04878e6i	0.855684	+	1.09650i
$979$	122086.			0.127380
$980$			2.18551e6i			2.27563i
$981$	87768.4	−	350336.i	0.0912011	−	0.364038i
$982$	−1.01803e6			−1.05570
$983$			1.82458e6i			1.88823i	0.329615	+	0.944116i	$0.393081\pi$
$983$			1.82458e6i			1.88823i	−0.329615	+	0.944116i	$0.606919\pi$
$984$	−210534.	+	164296.i	−0.217437	+	0.169683i
$985$	−3.01676e6			−3.10934
$986$		−	1.05063e6i		−	1.08068i
$987$	−236200.	−	302674.i	−0.242463	−	0.310700i
$988$	−2.48356e6			−2.54426
$989$		−	382355.i		−	0.390907i
$990$	752743.	+	188582.i	0.768027	+	0.192411i
$991$	847057.			0.862513			0.431256	−	0.902229i	$-0.358070\pi$
$991$	847057.			0.862513			0.431256	+	0.902229i	$0.358070\pi$
$992$		−	1.16865e6i		−	1.18758i
$993$	456647.	−	356358.i	0.463108	−	0.361399i
$994$	38201.5			0.0386640
$995$		−	1.98950e6i		−	2.00954i
$996$	−378991.	−	485651.i	−0.382041	−	0.489560i
$997$	−1.49155e6			−1.50054			−0.750271	−	0.661130i	$-0.770077\pi$
$997$	−1.49155e6			−1.50054			−0.750271	+	0.661130i	$0.770077\pi$
$998$		−	990258.i		−	0.994231i
$999$	324960.	+	733209.i	0.325611	+	0.734678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.5.b.a.23.12	yes	14
3.2	odd	2	inner	33.5.b.a.23.3	✓	14
4.3	odd	2		528.5.i.d.353.4		14
12.11	even	2		528.5.i.d.353.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.b.a.23.3	✓	14	3.2	odd	2	inner
33.5.b.a.23.12	yes	14	1.1	even	1	trivial
528.5.i.d.353.3		14	12.11	even	2
528.5.i.d.353.4		14	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.24203i q^{2} +(7.09522 - 5.53695i) q^{3} -22.9629 q^{4} +42.0693i q^{5} +(34.5618 + 44.2886i) q^{6} -11.7748 q^{7} -43.4628i q^{8} +(19.6843 - 78.5718i) q^{9} +O(q^{10})\)	\(q+6.24203i q^{2} +(7.09522 - 5.53695i) q^{3} -22.9629 q^{4} +42.0693i q^{5} +(34.5618 + 44.2886i) q^{6} -11.7748 q^{7} -43.4628i q^{8} +(19.6843 - 78.5718i) q^{9} -262.598 q^{10} -36.4829i q^{11} +(-162.927 + 127.145i) q^{12} +186.682 q^{13} -73.4985i q^{14} +(232.936 + 298.491i) q^{15} -96.1107 q^{16} -216.992i q^{17} +(490.447 + 122.870i) q^{18} +579.356 q^{19} -966.034i q^{20} +(-83.5446 + 65.1964i) q^{21} +227.727 q^{22} +266.732i q^{23} +(-240.652 - 308.378i) q^{24} -1144.82 q^{25} +1165.27i q^{26} +(-295.384 - 666.475i) q^{27} +270.383 q^{28} -775.677i q^{29} +(-1863.19 + 1453.99i) q^{30} +902.204 q^{31} -1295.33i q^{32} +(-202.004 - 258.854i) q^{33} +1354.47 q^{34} -495.356i q^{35} +(-452.010 + 1804.24i) q^{36} -1100.13 q^{37} +3616.36i q^{38} +(1324.55 - 1033.65i) q^{39} +1828.45 q^{40} -682.715i q^{41} +(-406.958 - 521.488i) q^{42} -1433.48 q^{43} +837.754i q^{44} +(3305.46 + 828.105i) q^{45} -1664.95 q^{46} +3622.90i q^{47} +(-681.927 + 532.161i) q^{48} -2262.35 q^{49} -7146.03i q^{50} +(-1201.47 - 1539.60i) q^{51} -4286.76 q^{52} -987.839i q^{53} +(4160.16 - 1843.79i) q^{54} +1534.81 q^{55} +511.765i q^{56} +(4110.66 - 3207.87i) q^{57} +4841.80 q^{58} -1771.46i q^{59} +(-5348.88 - 6854.22i) q^{60} -2843.76 q^{61} +5631.59i q^{62} +(-231.778 + 925.165i) q^{63} +6547.72 q^{64} +7853.57i q^{65} +(1615.77 - 1260.91i) q^{66} -4896.10 q^{67} +4982.76i q^{68} +(1476.88 + 1892.52i) q^{69} +3092.03 q^{70} +519.758i q^{71} +(-3414.95 - 855.536i) q^{72} +7825.00 q^{73} -6867.04i q^{74} +(-8122.78 + 6338.84i) q^{75} -13303.7 q^{76} +429.578i q^{77} +(6452.07 + 8267.87i) q^{78} +416.507 q^{79} -4043.31i q^{80} +(-5786.06 - 3093.26i) q^{81} +4261.53 q^{82} +2980.79i q^{83} +(1918.43 - 1497.10i) q^{84} +9128.68 q^{85} -8947.81i q^{86} +(-4294.89 - 5503.60i) q^{87} -1585.65 q^{88} +3346.39i q^{89} +(-5169.06 + 20632.8i) q^{90} -2198.14 q^{91} -6124.96i q^{92} +(6401.34 - 4995.46i) q^{93} -22614.3 q^{94} +24373.1i q^{95} +(-7172.19 - 9190.66i) q^{96} -7544.49 q^{97} -14121.7i q^{98} +(-2866.52 - 718.140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9}+O(q^{10}) \) 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9	\( 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9} - 156 q^{10} - 100 q^{12} - 104 q^{13} + 151 q^{15} + 356 q^{16} - 34 q^{18} + 1072 q^{19} + 718 q^{21} + 1200 q^{24} - 1060 q^{25} - 1154 q^{27} - 1808 q^{28} - 3026 q^{30} + 3310 q^{31} - 605 q^{33} - 2304 q^{34} + 2644 q^{36} - 362 q^{37} + 4264 q^{39} + 1896 q^{40} - 7364 q^{42} - 6740 q^{43} + 3611 q^{45} - 4068 q^{46} - 2956 q^{48} + 7074 q^{49} - 7046 q^{51} + 13072 q^{52} + 20512 q^{54} + 726 q^{55} + 3876 q^{57} - 7848 q^{58} - 8416 q^{60} - 3560 q^{61} - 17662 q^{63} + 12020 q^{64} + 1210 q^{66} - 16514 q^{67} + 9833 q^{69} + 13320 q^{70} + 8160 q^{72} + 12664 q^{73} - 5386 q^{75} - 43736 q^{76} + 19096 q^{78} + 3052 q^{79} - 11611 q^{81} + 10200 q^{82} - 39184 q^{84} + 34884 q^{85} + 37068 q^{87} - 7260 q^{88} - 26686 q^{90} - 45856 q^{91} + 2719 q^{93} + 6120 q^{94} - 38368 q^{96} - 27854 q^{97} + 4235 q^{99}+O(q^{100}) \) 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9 - 156 * q^10 - 100 * q^12 - 104 * q^13 + 151 * q^15 + 356 * q^16 - 34 * q^18 + 1072 * q^19 + 718 * q^21 + 1200 * q^24 - 1060 * q^25 - 1154 * q^27 - 1808 * q^28 - 3026 * q^30 + 3310 * q^31 - 605 * q^33 - 2304 * q^34 + 2644 * q^36 - 362 * q^37 + 4264 * q^39 + 1896 * q^40 - 7364 * q^42 - 6740 * q^43 + 3611 * q^45 - 4068 * q^46 - 2956 * q^48 + 7074 * q^49 - 7046 * q^51 + 13072 * q^52 + 20512 * q^54 + 726 * q^55 + 3876 * q^57 - 7848 * q^58 - 8416 * q^60 - 3560 * q^61 - 17662 * q^63 + 12020 * q^64 + 1210 * q^66 - 16514 * q^67 + 9833 * q^69 + 13320 * q^70 + 8160 * q^72 + 12664 * q^73 - 5386 * q^75 - 43736 * q^76 + 19096 * q^78 + 3052 * q^79 - 11611 * q^81 + 10200 * q^82 - 39184 * q^84 + 34884 * q^85 + 37068 * q^87 - 7260 * q^88 - 26686 * q^90 - 45856 * q^91 + 2719 * q^93 + 6120 * q^94 - 38368 * q^96 - 27854 * q^97 + 4235 * q^99

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