LMFDB - Embedded newform 33.5.b.a.23.11

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			23.11
Root			$3.64872i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.5.b.a.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.64872i q^{2} +(1.72713 - 8.83273i) q^{3} +2.68684 q^{4} -34.1690i q^{5} +(32.2281 + 6.30180i) q^{6} +45.8062 q^{7} +68.1830i q^{8} +(-75.0341 - 30.5105i) q^{9} +O(q^{10})$	\(q+3.64872i q^{2} +(1.72713 - 8.83273i) q^{3} +2.68684 q^{4} -34.1690i q^{5} +(32.2281 + 6.30180i) q^{6} +45.8062 q^{7} +68.1830i q^{8} +(-75.0341 - 30.5105i) q^{9} +124.673 q^{10} +36.4829i q^{11} +(4.64050 - 23.7321i) q^{12} +161.054 q^{13} +167.134i q^{14} +(-301.805 - 59.0141i) q^{15} -205.792 q^{16} -35.8678i q^{17} +(111.324 - 273.778i) q^{18} -549.055 q^{19} -91.8064i q^{20} +(79.1131 - 404.594i) q^{21} -133.116 q^{22} +363.395i q^{23} +(602.242 + 117.761i) q^{24} -542.520 q^{25} +587.642i q^{26} +(-399.084 + 610.060i) q^{27} +123.074 q^{28} +969.087i q^{29} +(215.326 - 1101.20i) q^{30} +1810.89 q^{31} +340.053i q^{32} +(322.243 + 63.0105i) q^{33} +130.872 q^{34} -1565.15i q^{35} +(-201.604 - 81.9766i) q^{36} -1599.42 q^{37} -2003.35i q^{38} +(278.161 - 1422.55i) q^{39} +2329.75 q^{40} +917.476i q^{41} +(1476.25 + 288.662i) q^{42} -542.393 q^{43} +98.0235i q^{44} +(-1042.51 + 2563.84i) q^{45} -1325.93 q^{46} +1641.86i q^{47} +(-355.428 + 1817.70i) q^{48} -302.789 q^{49} -1979.50i q^{50} +(-316.810 - 61.9482i) q^{51} +432.727 q^{52} -3069.85i q^{53} +(-2225.94 - 1456.15i) q^{54} +1246.58 q^{55} +3123.21i q^{56} +(-948.287 + 4849.65i) q^{57} -3535.93 q^{58} -4257.21i q^{59} +(-810.901 - 158.561i) q^{60} +2624.21 q^{61} +6607.43i q^{62} +(-3437.03 - 1397.57i) q^{63} -4533.42 q^{64} -5503.06i q^{65} +(-229.908 + 1175.78i) q^{66} +3871.47 q^{67} -96.3708i q^{68} +(3209.77 + 627.628i) q^{69} +5710.80 q^{70} -2894.42i q^{71} +(2080.30 - 5116.05i) q^{72} -4852.92 q^{73} -5835.84i q^{74} +(-937.000 + 4791.93i) q^{75} -1475.22 q^{76} +1671.14i q^{77} +(5190.48 + 1014.93i) q^{78} +7174.45 q^{79} +7031.69i q^{80} +(4699.22 + 4578.65i) q^{81} -3347.61 q^{82} -8352.54i q^{83} +(212.564 - 1087.08i) q^{84} -1225.57 q^{85} -1979.04i q^{86} +(8559.68 + 1673.74i) q^{87} -2487.51 q^{88} +8540.30i q^{89} +(-9354.73 - 3803.83i) q^{90} +7377.29 q^{91} +976.382i q^{92} +(3127.64 - 15995.1i) q^{93} -5990.67 q^{94} +18760.6i q^{95} +(3003.59 + 587.314i) q^{96} -10869.6 q^{97} -1104.79i q^{98} +(1113.11 - 2737.46i) 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 $

$2$			3.64872i			0.912180i	0.889934	+	0.456090i	$0.150751\pi$
$2$			3.64872i			0.912180i	−0.889934	+	0.456090i	$0.849249\pi$
$3$	1.72713	−	8.83273i	0.191903	−	0.981414i
$3$	1.72713	−	8.83273i	0.191903	−	0.981414i
$4$	2.68684			0.167927
$5$		−	34.1690i		−	1.36676i	−0.730063	−	0.683380i	$-0.760509\pi$
$5$		−	34.1690i		−	1.36676i	0.730063	−	0.683380i	$-0.239491\pi$
$6$	32.2281	+	6.30180i	0.895226	+	0.175050i
$7$	45.8062			0.934821			0.467410	−	0.884040i	$-0.345187\pi$
$7$	45.8062			0.934821			0.467410	+	0.884040i	$0.345187\pi$
$8$			68.1830i			1.06536i
$9$	−75.0341	−	30.5105i	−0.926347	−	0.376672i
$10$	124.673			1.24673
$11$			36.4829i			0.301511i
$11$			36.4829i			0.301511i
$12$	4.64050	−	23.7321i	0.0322257	−	0.164806i
$13$	161.054			0.952984			0.476492	−	0.879179i	$-0.341908\pi$
$13$	161.054			0.952984			0.476492	+	0.879179i	$0.341908\pi$
$14$			167.134i			0.852725i
$15$	−301.805	−	59.0141i	−1.34136	−	0.262285i
$16$	−205.792			−0.803873
$17$		−	35.8678i		−	0.124110i	−0.998073	−	0.0620550i	$-0.980235\pi$
$17$		−	35.8678i		−	0.124110i	0.998073	−	0.0620550i	$-0.0197654\pi$
$18$	111.324	−	273.778i	0.343593	−	0.844995i
$19$	−549.055			−1.52093			−0.760464	−	0.649380i	$-0.775028\pi$
$19$	−549.055			−1.52093			−0.760464	+	0.649380i	$0.775028\pi$
$20$		−	91.8064i		−	0.229516i
$21$	79.1131	−	404.594i	0.179395	−	0.917446i
$22$	−133.116			−0.275033
$23$			363.395i			0.686946i	0.939162	+	0.343473i	$0.111603\pi$
$23$			363.395i			0.686946i	−0.939162	+	0.343473i	$0.888397\pi$
$24$	602.242	+	117.761i	1.04556	+	0.204446i
$25$	−542.520			−0.868031
$26$			587.642i			0.869294i
$27$	−399.084	+	610.060i	−0.547440	+	0.836845i
$28$	123.074			0.156982
$29$			969.087i			1.15230i	0.817343	+	0.576152i	$0.195446\pi$
$29$			969.087i			1.15230i	−0.817343	+	0.576152i	$0.804554\pi$
$30$	215.326	−	1101.20i	0.239251	−	1.22356i
$31$	1810.89			1.88438			0.942191	−	0.335077i	$-0.108762\pi$
$31$	1810.89			1.88438			0.942191	+	0.335077i	$0.108762\pi$
$32$			340.053i			0.332083i
$33$	322.243	+	63.0105i	0.295907	+	0.0578609i
$34$	130.872			0.113211
$35$		−	1565.15i		−	1.27768i
$36$	−201.604	−	81.9766i	−0.155559	−	0.0632535i
$37$	−1599.42			−1.16831			−0.584156	−	0.811641i	$-0.698574\pi$
$37$	−1599.42			−1.16831			−0.584156	+	0.811641i	$0.698574\pi$
$38$		−	2003.35i		−	1.38736i
$39$	278.161	−	1422.55i	0.182880	−	0.935272i
$40$	2329.75			1.45609
$41$			917.476i			0.545792i	0.962044	+	0.272896i	$0.0879815\pi$
$41$			917.476i			0.545792i	−0.962044	+	0.272896i	$0.912019\pi$
$42$	1476.25	+	288.662i	0.836876	+	0.163640i
$43$	−542.393			−0.293344			−0.146672	−	0.989185i	$-0.546856\pi$
$43$	−542.393			−0.293344			−0.146672	+	0.989185i	$0.546856\pi$
$44$			98.0235i			0.0506320i
$45$	−1042.51	+	2563.84i	−0.514821	+	1.26609i
$46$	−1325.93			−0.626619
$47$			1641.86i			0.743257i	0.928381	+	0.371629i	$0.121201\pi$
$47$			1641.86i			0.743257i	−0.928381	+	0.371629i	$0.878799\pi$
$48$	−355.428	+	1817.70i	−0.154266	+	0.788932i
$49$	−302.789			−0.126110
$50$		−	1979.50i		−	0.791801i
$51$	−316.810	−	61.9482i	−0.121803	−	0.0238171i
$52$	432.727			0.160032
$53$		−	3069.85i		−	1.09286i	−0.837504	−	0.546432i	$-0.815986\pi$
$53$		−	3069.85i		−	1.09286i	0.837504	−	0.546432i	$-0.184014\pi$
$54$	−2225.94	−	1456.15i	−0.763353	−	0.499364i
$55$	1246.58			0.412093
$56$			3123.21i			0.995921i
$57$	−948.287	+	4849.65i	−0.291870	+	1.49266i
$58$	−3535.93			−1.05111
$59$		−	4257.21i		−	1.22298i	−0.791251	−	0.611492i	$-0.790570\pi$
$59$		−	4257.21i		−	1.22298i	0.791251	−	0.611492i	$-0.209430\pi$
$60$	−810.901	−	158.561i	−0.225250	−	0.0440448i
$61$	2624.21			0.705244			0.352622	−	0.935766i	$-0.385290\pi$
$61$	2624.21			0.705244			0.352622	+	0.935766i	$0.385290\pi$
$62$			6607.43i			1.71890i
$63$	−3437.03	−	1397.57i	−0.865968	−	0.352121i
$64$	−4533.42			−1.10679
$65$		−	5503.06i		−	1.30250i
$66$	−229.908	+	1175.78i	−0.0527796	+	0.269921i
$67$	3871.47			0.862434			0.431217	−	0.902248i	$-0.358084\pi$
$67$	3871.47			0.862434			0.431217	+	0.902248i	$0.358084\pi$
$68$		−	96.3708i		−	0.0208414i
$69$	3209.77	+	627.628i	0.674179	+	0.131827i
$70$	5710.80			1.16547
$71$		−	2894.42i		−	0.574175i	−0.957904	−	0.287088i	$-0.907313\pi$
$71$		−	2894.42i		−	0.574175i	0.957904	−	0.287088i	$-0.0926871\pi$
$72$	2080.30	−	5116.05i	0.401292	−	0.986893i
$73$	−4852.92			−0.910663			−0.455331	−	0.890322i	$-0.650479\pi$
$73$	−4852.92			−0.910663			−0.455331	+	0.890322i	$0.650479\pi$
$74$		−	5835.84i		−	1.06571i
$75$	−937.000	+	4791.93i	−0.166578	+	0.851898i
$76$	−1475.22			−0.255405
$77$			1671.14i			0.281859i
$78$	5190.48	+	1014.93i	0.853137	+	0.166820i
$79$	7174.45			1.14957			0.574783	−	0.818306i	$-0.305086\pi$
$79$	7174.45			1.14957			0.574783	+	0.818306i	$0.305086\pi$
$80$			7031.69i			1.09870i
$81$	4699.22	+	4578.65i	0.716236	+	0.697858i
$82$	−3347.61			−0.497860
$83$		−	8352.54i		−	1.21245i	−0.795295	−	0.606223i	$-0.792684\pi$
$83$		−	8352.54i		−	1.21245i	0.795295	−	0.606223i	$-0.207316\pi$
$84$	212.564	−	1087.08i	0.0301253	−	0.154064i
$85$	−1225.57			−0.169628
$86$		−	1979.04i		−	0.267582i
$87$	8559.68	+	1673.74i	1.13089	+	0.221130i
$88$	−2487.51			−0.321218
$89$			8540.30i			1.07818i	0.842247	+	0.539092i	$0.181233\pi$
$89$			8540.30i			1.07818i	−0.842247	+	0.539092i	$0.818767\pi$
$90$	−9354.73	−	3803.83i	−1.15490	−	0.469609i
$91$	7377.29			0.890870
$92$			976.382i			0.115357i
$93$	3127.64	−	15995.1i	0.361618	−	1.84936i
$94$	−5990.67			−0.677985
$95$			18760.6i			2.07874i
$96$	3003.59	+	587.314i	0.325911	+	0.0637277i
$97$	−10869.6			−1.15523			−0.577617	−	0.816308i	$-0.696017\pi$
$97$	−10869.6			−1.15523			−0.577617	+	0.816308i	$0.696017\pi$
$98$		−	1104.79i		−	0.115035i
$99$	1113.11	−	2737.46i	0.113571	−	0.279304i
$100$	−1457.66			−0.145766
$101$		−	4872.29i		−	0.477628i	−0.971065	−	0.238814i	$-0.923241\pi$
$101$		−	4872.29i		−	0.477628i	0.971065	−	0.238814i	$-0.0767587\pi$
$102$	226.032	−	1155.95i	0.0217255	−	0.111107i
$103$	3924.42			0.369914			0.184957	−	0.982747i	$-0.440785\pi$
$103$	3924.42			0.369914			0.184957	+	0.982747i	$0.440785\pi$
$104$			10981.2i			1.01527i
$105$	−13824.6	−	2703.22i	−1.25393	−	0.245190i
$106$	11201.0			0.996889
$107$		−	9698.45i		−	0.847101i	−0.905873	−	0.423550i	$-0.860784\pi$
$107$		−	9698.45i		−	0.847101i	0.905873	−	0.423550i	$-0.139216\pi$
$108$	−1072.27	+	1639.13i	−0.0919301	+	0.140529i
$109$	−13683.9			−1.15174			−0.575872	−	0.817540i	$-0.695337\pi$
$109$	−13683.9			−1.15174			−0.575872	+	0.817540i	$0.695337\pi$
$110$			4548.43i			0.375904i
$111$	−2762.40	+	14127.2i	−0.224203	+	1.14660i
$112$	−9426.53			−0.751478
$113$		−	5006.62i		−	0.392092i	−0.980595	−	0.196046i	$-0.937190\pi$
$113$		−	5006.62i		−	0.392092i	0.980595	−	0.196046i	$-0.0628102\pi$
$114$	−17695.0	−	3460.03i	−1.36157	−	0.266238i
$115$	12416.8			0.938891
$116$			2603.78i			0.193503i
$117$	−12084.6	−	4913.84i	−0.882794	−	0.358963i
$118$	15533.4			1.11558
$119$		−	1642.97i		−	0.116021i
$120$	4023.76	−	20578.0i	0.279428	−	1.42903i
$121$	−1331.00			−0.0909091
$122$			9575.02i			0.643310i
$123$	8103.81	+	1584.60i	0.535648	+	0.104739i
$124$	4865.56			0.316439
$125$		−	2818.27i		−	0.180369i
$126$	5099.34	−	12540.8i	0.321198	−	0.789919i
$127$	−23115.6			−1.43317			−0.716586	−	0.697499i	$-0.754296\pi$
$127$	−23115.6			−1.43317			−0.716586	+	0.697499i	$0.754296\pi$
$128$		−	11100.3i		−	0.677512i
$129$	−936.780	+	4790.80i	−0.0562935	+	0.287892i
$130$	20079.1			1.18812
$131$			13163.0i			0.767027i	0.923535	+	0.383514i	$0.125286\pi$
$131$			13163.0i			0.767027i	−0.923535	+	0.383514i	$0.874714\pi$
$132$	865.814	+	169.299i	0.0496909	+	0.00971642i
$133$	−25150.1			−1.42179
$134$			14125.9i			0.786696i
$135$	20845.1	+	13636.3i	1.14377	+	0.748219i
$136$	2445.57			0.132222
$137$			14535.7i			0.774453i	0.921985	+	0.387226i	$0.126567\pi$
$137$			14535.7i			0.774453i	−0.921985	+	0.387226i	$0.873433\pi$
$138$	−2290.04	+	11711.5i	−0.120250	+	0.614973i
$139$	20081.9			1.03938			0.519692	−	0.854354i	$-0.326047\pi$
$139$	20081.9			1.03938			0.519692	+	0.854354i	$0.326047\pi$
$140$		−	4205.31i		−	0.214556i
$141$	14502.1	+	2835.69i	0.729443	+	0.142633i
$142$	10560.9			0.523751
$143$			5875.73i			0.287336i
$144$	15441.4	+	6278.79i	0.744665	+	0.302797i
$145$	33112.7			1.57492
$146$		−	17707.0i		−	0.830688i
$147$	−522.956	+	2674.46i	−0.0242008	+	0.123766i
$148$	−4297.38			−0.196191
$149$		−	9591.21i		−	0.432017i	−0.976391	−	0.216009i	$-0.930696\pi$
$149$		−	9591.21i		−	0.432017i	0.976391	−	0.216009i	$-0.0693039\pi$
$150$	−17484.4	−	3418.85i	−0.777085	−	0.151949i
$151$	5897.15			0.258635			0.129318	−	0.991603i	$-0.458721\pi$
$151$	5897.15			0.258635			0.129318	+	0.991603i	$0.458721\pi$
$152$		−	37436.2i		−	1.62034i
$153$	−1094.34	+	2691.31i	−0.0467488	+	0.114969i
$154$	−6097.53			−0.257106
$155$		−	61876.3i		−	2.57550i
$156$	747.373	−	3822.16i	0.0307106	−	0.157058i
$157$	−45950.7			−1.86420			−0.932100	−	0.362200i	$-0.882026\pi$
$157$	−45950.7			−1.86420			−0.932100	+	0.362200i	$0.882026\pi$
$158$			26177.6i			1.04861i
$159$	−27115.2	−	5302.02i	−1.07255	−	0.209724i
$160$	11619.3			0.453877
$161$			16645.7i			0.642172i
$162$	−16706.2	+	17146.2i	−0.636573	+	0.653336i
$163$	−29132.6			−1.09649			−0.548245	−	0.836318i	$-0.684704\pi$
$163$	−29132.6			−1.09649			−0.548245	+	0.836318i	$0.684704\pi$
$164$			2465.11i			0.0916533i
$165$	2153.01	−	11010.7i	0.0790819	−	0.404434i
$166$	30476.1			1.10597
$167$		−	19658.7i		−	0.704890i	−0.935833	−	0.352445i	$-0.885350\pi$
$167$		−	19658.7i		−	0.704890i	0.935833	−	0.352445i	$-0.114650\pi$
$168$	27586.4	+	5394.17i	0.977411	+	0.191120i
$169$	−2622.49			−0.0918207
$170$		−	4471.75i		−	0.154732i
$171$	41197.8	+	16751.9i	1.40891	+	0.572891i
$172$	−1457.32			−0.0492604
$173$			14798.3i			0.494448i	0.968958	+	0.247224i	$0.0795184\pi$
$173$			14798.3i			0.494448i	−0.968958	+	0.247224i	$0.920482\pi$
$174$	−6107.00	+	31231.9i	−0.201711	+	1.03157i
$175$	−24850.8			−0.811454
$176$		−	7507.87i		−	0.242377i
$177$	−37602.7	−	7352.73i	−1.20025	−	0.234694i
$178$	−31161.2			−0.983499
$179$			6458.03i			0.201555i	0.994909	+	0.100778i	$0.0321330\pi$
$179$			6458.03i			0.201555i	−0.994909	+	0.100778i	$0.967867\pi$
$180$	−2801.06	+	6888.61i	−0.0864524	+	0.212611i
$181$	−4358.65			−0.133044			−0.0665219	−	0.997785i	$-0.521190\pi$
$181$	−4358.65			−0.133044			−0.0665219	+	0.997785i	$0.521190\pi$
$182$			26917.7i			0.812634i
$183$	4532.35	−	23179.0i	0.135338	−	0.692136i
$184$	−24777.4			−0.731845
$185$			54650.6i			1.59680i
$186$	58361.6	+	11411.9i	1.68695	+	0.329861i
$187$	1308.56			0.0374206
$188$			4411.39i			0.124813i
$189$	−18280.5	+	27944.5i	−0.511758	+	0.782300i
$190$	−68452.4			−1.89619
$191$		−	67555.0i		−	1.85179i	−0.377785	−	0.925893i	$-0.623314\pi$
$191$		−	67555.0i		−	1.85179i	0.377785	−	0.925893i	$-0.376686\pi$
$192$	−7829.79	+	40042.5i	−0.212397	+	1.08622i
$193$	66551.1			1.78665			0.893327	−	0.449407i	$-0.148365\pi$
$193$	66551.1			1.78665			0.893327	+	0.449407i	$0.148365\pi$
$194$		−	39660.1i		−	1.05378i
$195$	−48607.1	−	9504.49i	−1.27829	−	0.249954i
$196$	−813.545			−0.0211773
$197$			17475.8i			0.450302i	0.974324	+	0.225151i	$0.0722875\pi$
$197$			17475.8i			0.450302i	−0.974324	+	0.225151i	$0.927712\pi$
$198$	9988.22	+	4061.43i	0.254776	+	0.103597i
$199$	28119.7			0.710075			0.355037	−	0.934852i	$-0.384468\pi$
$199$	28119.7			0.710075			0.355037	+	0.934852i	$0.384468\pi$
$200$		−	36990.6i		−	0.924766i
$201$	6686.51	−	34195.6i	0.165504	−	0.846405i
$202$	17777.6			0.435683
$203$			44390.2i			1.07720i
$204$	−851.217	−	166.445i	−0.0204541	−	0.00399953i
$205$	31349.2			0.745966
$206$			14319.1i			0.337429i
$207$	11087.3	−	27267.0i	0.258754	−	0.636350i
$208$	−33143.6			−0.766079
$209$		−	20031.1i		−	0.458577i
$210$	9863.28	−	50442.0i	0.223657	−	1.14381i
$211$	36526.0			0.820423			0.410211	−	0.911991i	$-0.365455\pi$
$211$	36526.0			0.820423			0.410211	+	0.911991i	$0.365455\pi$
$212$		−	8248.19i		−	0.183522i
$213$	−25565.6	−	4999.02i	−0.563504	−	0.110186i
$214$	35387.0			0.772708
$215$			18533.0i			0.400930i
$216$	−41595.7	−	27210.8i	−0.891541	−	0.583221i
$217$	82950.1			1.76156
$218$		−	49928.6i		−	1.05060i
$219$	−8381.61	+	42864.5i	−0.174759	+	0.893737i
$220$	3349.36			0.0692017
$221$		−	5776.66i		−	0.118275i
$222$	−51546.3	−	10079.2i	−1.04590	−	0.204513i
$223$	−21025.7			−0.422806			−0.211403	−	0.977399i	$-0.567803\pi$
$223$	−21025.7			−0.422806			−0.211403	+	0.977399i	$0.567803\pi$
$224$			15576.5i			0.310438i
$225$	40707.5	+	16552.5i	0.804098	+	0.326963i
$226$	18267.8			0.357659
$227$		−	30600.0i		−	0.593841i	−0.954902	−	0.296921i	$-0.904040\pi$
$227$		−	30600.0i		−	0.593841i	0.954902	−	0.296921i	$-0.0959596\pi$
$228$	−2547.89	+	13030.2i	−0.0490130	+	0.250658i
$229$	44513.2			0.848824			0.424412	−	0.905469i	$-0.360481\pi$
$229$	44513.2			0.848824			0.424412	+	0.905469i	$0.360481\pi$
$230$			45305.5i			0.856437i
$231$	14760.7	+	2886.27i	0.276620	+	0.0540896i
$232$	−66075.3			−1.22762
$233$			84153.0i			1.55009i	0.631905	+	0.775046i	$0.282273\pi$
$233$			84153.0i			1.55009i	−0.631905	+	0.775046i	$0.717727\pi$
$234$	17929.2	−	44093.2i	0.327439	−	0.805267i
$235$	56100.5			1.01585
$236$		−	11438.4i		−	0.205372i
$237$	12391.2	−	63369.9i	0.220605	−	1.12820i
$238$	5994.73			0.105832
$239$			91062.7i			1.59421i	0.603843	+	0.797103i	$0.293635\pi$
$239$			91062.7i			1.59421i	−0.603843	+	0.797103i	$0.706365\pi$
$240$	62109.0	+	12144.6i	1.07828	+	0.210844i
$241$	−47911.3			−0.824905			−0.412453	−	0.910979i	$-0.635328\pi$
$241$	−47911.3			−0.824905			−0.412453	+	0.910979i	$0.635328\pi$
$242$		−	4856.45i		−	0.0829255i
$243$	48558.1	−	33599.0i	0.822336	−	0.569003i
$244$	7050.83			0.118430
$245$			10346.0i			0.172362i
$246$	−5781.75	+	29568.6i	−0.0955409	+	0.488607i
$247$	−88427.7			−1.44942
$248$			123472.i			2.00754i
$249$	−73775.7	−	14425.9i	−1.18991	−	0.232672i
$250$	10283.1			0.164529
$251$			64860.7i			1.02952i	0.857335	+	0.514759i	$0.172119\pi$
$251$			64860.7i			1.02952i	−0.857335	+	0.514759i	$0.827881\pi$
$252$	−9234.73	−	3755.04i	−0.145420	−	0.0591307i
$253$	−13257.7			−0.207122
$254$		−	84342.5i		−	1.30731i
$255$	−2116.71	+	10825.1i	−0.0325522	+	0.166476i
$256$	−32032.7			−0.488780
$257$		−	38779.5i		−	0.587132i	−0.955939	−	0.293566i	$-0.905158\pi$
$257$		−	38779.5i		−	0.587132i	0.955939	−	0.293566i	$-0.0948421\pi$
$258$	−17480.3	−	3418.05i	−0.262609	−	0.0513498i
$259$	−73263.4			−1.09216
$260$		−	14785.8i		−	0.218725i
$261$	29567.3	−	72714.6i	0.434041	−	1.06743i
$262$	−48027.9			−0.699667
$263$		−	24750.4i		−	0.357825i	−0.983865	−	0.178912i	$-0.942742\pi$
$263$		−	24750.4i		−	0.357825i	0.983865	−	0.178912i	$-0.0572578\pi$
$264$	−4296.25	+	21971.5i	−0.0616427	+	0.315248i
$265$	−104894.			−1.49368
$266$		−	91765.8i		−	1.29693i
$267$	75434.1	+	14750.2i	1.05815	+	0.206907i
$268$	10402.0			0.144826
$269$		−	69516.8i		−	0.960694i	−0.877079	−	0.480347i	$-0.840511\pi$
$269$		−	69516.8i		−	0.960694i	0.877079	−	0.480347i	$-0.159489\pi$
$270$	−49755.0	+	76058.1i	−0.682511	+	1.04332i
$271$	60460.5			0.823253			0.411627	−	0.911353i	$-0.364961\pi$
$271$	60460.5			0.823253			0.411627	+	0.911353i	$0.364961\pi$
$272$			7381.29i			0.0997687i
$273$	12741.5	−	65161.6i	0.170961	−	0.874312i
$274$	−53036.7			−0.706440
$275$		−	19792.7i		−	0.261721i
$276$	8624.11	+	1686.33i	0.113213	+	0.0221373i
$277$	8072.92			0.105213			0.0526067	−	0.998615i	$-0.483247\pi$
$277$	8072.92			0.105213			0.0526067	+	0.998615i	$0.483247\pi$
$278$			73273.4i			0.948105i
$279$	−135878.	−	55251.1i	−1.74559	−	0.709794i
$280$	106717.			1.36118
$281$			28173.9i			0.356807i	0.983957	+	0.178404i	$0.0570933\pi$
$281$			28173.9i			0.356807i	−0.983957	+	0.178404i	$0.942907\pi$
$282$	−10346.6	+	52914.0i	−0.130107	+	0.665383i
$283$	−27222.4			−0.339902			−0.169951	−	0.985453i	$-0.554361\pi$
$283$	−27222.4			−0.339902			−0.169951	+	0.985453i	$0.554361\pi$
$284$		−	7776.82i		−	0.0964197i
$285$	165708.	+	32402.0i	2.04011	+	0.398917i
$286$	−21438.9			−0.262102
$287$			42026.1i			0.510218i
$288$	10375.2	−	25515.5i	0.125086	−	0.307624i
$289$	82234.5			0.984597
$290$			120819.i			1.43661i
$291$	−18773.2	+	96008.1i	−0.221693	+	1.13376i
$292$	−13039.0			−0.152925
$293$		−	35825.8i		−	0.417312i	−0.977989	−	0.208656i	$-0.933091\pi$
$293$		−	35825.8i		−	0.417312i	0.977989	−	0.208656i	$-0.0669089\pi$
$294$	−9758.34	−	1908.12i	−0.112897	−	0.0220755i
$295$	−145464.			−1.67153
$296$		−	109053.i		−	1.24467i
$297$	−22256.7	−	14559.7i	−0.252318	−	0.165059i
$298$	34995.7			0.394078
$299$			58526.3i			0.654649i
$300$	−2517.56	+	12875.1i	−0.0279729	+	0.143057i
$301$	−24845.0			−0.274224
$302$			21517.0i			0.235922i
$303$	−43035.6	−	8415.05i	−0.468751	−	0.0916583i
$304$	112991.			1.22263
$305$		−	89666.7i		−	0.963899i
$306$	−9819.82	−	3992.95i	−0.104872	−	0.0426433i
$307$	97652.0			1.03611			0.518053	−	0.855349i	$-0.326657\pi$
$307$	97652.0			1.03611			0.518053	+	0.855349i	$0.326657\pi$
$308$			4490.09i			0.0473318i
$309$	6777.97	−	34663.3i	0.0709876	−	0.363039i
$310$	225769.			2.34932
$311$		−	171213.i		−	1.77018i	−0.465425	−	0.885088i	$-0.654098\pi$
$311$		−	171213.i		−	1.77018i	0.465425	−	0.885088i	$-0.345902\pi$
$312$	96993.7	+	18965.9i	0.996402	+	0.194834i
$313$	59924.8			0.611671			0.305835	−	0.952084i	$-0.401064\pi$
$313$	59924.8			0.611671			0.305835	+	0.952084i	$0.401064\pi$
$314$		−	167661.i		−	1.70049i
$315$	−47753.5	+	117440.i	−0.481265	+	1.18357i
$316$	19276.6			0.193044
$317$			112960.i			1.12410i	0.827104	+	0.562049i	$0.189987\pi$
$317$			112960.i			1.12410i	−0.827104	+	0.562049i	$0.810013\pi$
$318$	19345.6	−	98935.7i	0.191306	−	0.978360i
$319$	−35355.1			−0.347433
$320$			154902.i			1.51272i
$321$	−85663.8	−	16750.5i	−0.831356	−	0.162561i
$322$	−60735.7			−0.585777
$323$			19693.4i			0.188762i
$324$	12626.0	+	12302.1i	0.120276	+	0.117189i
$325$	−87375.2			−0.827220
$326$		−	106297.i		−	1.00020i
$327$	−23633.8	+	120866.i	−0.221023	+	1.13034i
$328$	−62556.3			−0.581465
$329$			75207.2i			0.694812i
$330$	40175.1	+	7855.72i	0.368917	+	0.0721370i
$331$	135469.			1.23647			0.618233	−	0.785995i	$-0.287849\pi$
$331$	135469.			1.23647			0.618233	+	0.785995i	$0.287849\pi$
$332$		−	22441.9i		−	0.203603i
$333$	120011.	+	48799.0i	1.08226	+	0.440071i
$334$	71729.0			0.642987
$335$		−	132284.i		−	1.17874i
$336$	−16280.8	+	83262.0i	−0.144211	+	0.737511i
$337$	−50721.7			−0.446615			−0.223308	−	0.974748i	$-0.571685\pi$
$337$	−50721.7			−0.446615			−0.223308	+	0.974748i	$0.571685\pi$
$338$		−	9568.73i		−	0.0837570i
$339$	−44222.1	−	8647.07i	−0.384805	−	0.0752436i
$340$	−3292.89			−0.0284852
$341$			66066.5i			0.568162i
$342$	−61123.1	+	150319.i	−0.522580	+	1.28518i
$343$	−123850.			−1.05271
$344$		−	36982.0i		−	0.312517i
$345$	21445.4	−	109674.i	0.180176	−	0.921440i
$346$	−53995.0			−0.451026
$347$		−	200897.i		−	1.66846i	−0.551418	−	0.834229i	$-0.685913\pi$
$347$		−	200897.i		−	1.66846i	0.551418	−	0.834229i	$-0.314087\pi$
$348$	22998.5	+	4497.05i	0.189907	+	0.0371338i
$349$	69031.1			0.566753			0.283376	−	0.959009i	$-0.408545\pi$
$349$	69031.1			0.566753			0.283376	+	0.959009i	$0.408545\pi$
$350$		−	90673.6i		−	0.740192i
$351$	−64274.2	+	98252.8i	−0.521702	+	0.797500i
$352$	−12406.1			−0.100127
$353$		−	30190.0i		−	0.242278i	−0.992636	−	0.121139i	$-0.961345\pi$
$353$		−	30190.0i		−	0.242278i	0.992636	−	0.121139i	$-0.0386547\pi$
$354$	26828.1	−	137202.i	0.214083	−	1.09485i
$355$	−98899.3			−0.784759
$356$			22946.4i			0.181057i
$357$	−14511.9	−	2837.61i	−0.113864	−	0.0222647i
$358$	−23563.5			−0.183855
$359$			172843.i			1.34110i	0.741863	+	0.670551i	$0.233942\pi$
$359$			172843.i			1.34110i	−0.741863	+	0.670551i	$0.766058\pi$
$360$	−174810.	−	71081.6i	−1.34884	−	0.548469i
$361$	171140.			1.31322
$362$		−	15903.5i		−	0.121360i
$363$	−2298.80	+	11756.4i	−0.0174457	+	0.0892194i
$364$	19821.6			0.149601
$365$			165819.i			1.24466i
$366$	84573.5	+	16537.3i	0.631353	+	0.123453i
$367$	−11930.2			−0.0885756			−0.0442878	−	0.999019i	$-0.514102\pi$
$367$	−11930.2			−0.0885756			−0.0442878	+	0.999019i	$0.514102\pi$
$368$		−	74783.6i		−	0.552218i
$369$	27992.6	−	68842.0i	0.205585	−	0.505592i
$370$	−199405.			−1.45657
$371$		−	140618.i		−	1.02163i
$372$	8403.44	−	42976.2i	0.0607255	−	0.310558i
$373$	−147869.			−1.06282			−0.531410	−	0.847115i	$-0.678338\pi$
$373$	−147869.			−1.06282			−0.531410	+	0.847115i	$0.678338\pi$
$374$			4774.57i			0.0341343i
$375$	−24893.0	−	4867.51i	−0.177017	−	0.0346134i
$376$	−111947.			−0.791837
$377$			156076.i			1.09813i
$378$	−101962.	−	66700.5i	−0.713599	−	0.466816i
$379$	−116762.			−0.812873			−0.406436	−	0.913679i	$-0.633229\pi$
$379$	−116762.			−0.812873			−0.406436	+	0.913679i	$0.633229\pi$
$380$			50406.8i			0.349077i
$381$	−39923.6	+	204174.i	−0.275030	+	1.40654i
$382$	246489.			1.68916
$383$			83723.4i			0.570754i	0.958415	+	0.285377i	$0.0921188\pi$
$383$			83723.4i			0.570754i	−0.958415	+	0.285377i	$0.907881\pi$
$384$	−98046.3	−	19171.7i	−0.664919	−	0.130016i
$385$	57101.3			0.385234
$386$			242826.i			1.62975i
$387$	40697.9	+	16548.6i	0.271738	+	0.110494i
$388$	−29204.8			−0.193995
$389$			29315.9i			0.193733i	0.995297	+	0.0968667i	$0.0308821\pi$
$389$			29315.9i			0.193733i	−0.995297	+	0.0968667i	$0.969118\pi$
$390$	34679.2	−	177354.i	0.228003	−	1.16603i
$391$	13034.2			0.0852569
$392$		−	20645.1i		−	0.134352i
$393$	116265.	+	22734.1i	0.752771	+	0.147195i
$394$	−63764.2			−0.410757
$395$		−	245144.i		−	1.57118i
$396$	2990.74	−	7355.10i	0.0190717	−	0.0469027i
$397$	25535.6			0.162019			0.0810093	−	0.996713i	$-0.474186\pi$
$397$	25535.6			0.162019			0.0810093	+	0.996713i	$0.474186\pi$
$398$			102601.i			0.647716i
$399$	−43437.4	+	222144.i	−0.272847	+	1.39537i
$400$	111646.			0.697787
$401$		−	984.068i		−	0.00611979i	−0.999995	−	0.00305990i	$-0.999026\pi$
$401$		−	984.068i		−	0.00611979i	0.999995	−	0.00305990i	$-0.000973996\pi$
$402$	124770.	+	24397.2i	0.772074	+	0.150969i
$403$	291652.			1.79579
$404$		−	13091.0i		−	0.0802068i
$405$	156448.	−	160568.i	0.953804	−	0.978922i
$406$	−161968.			−0.982598
$407$		−	58351.4i		−	0.352259i
$408$	4223.82	−	21601.1i	0.0253738	−	0.129764i
$409$	−144168.			−0.861832			−0.430916	−	0.902392i	$-0.641809\pi$
$409$	−144168.			−0.861832			−0.430916	+	0.902392i	$0.641809\pi$
$410$			114385.i			0.680456i
$411$	128390.	+	25105.0i	0.760059	+	0.148620i
$412$	10544.3			0.0621187
$413$		−	195007.i		−	1.14327i
$414$	99489.6	+	40454.6i	0.580466	+	0.236030i
$415$	−285398.			−1.65712
$416$			54767.0i			0.316470i
$417$	34684.0	−	177378.i	0.199461	−	1.02007i
$418$	73087.9			0.418305
$419$			2714.59i			0.0154624i	0.999970	+	0.00773119i	$0.00246094\pi$
$419$			2714.59i			0.0154624i	−0.999970	+	0.00773119i	$0.997539\pi$
$420$	−37144.3	−	7263.10i	−0.210569	−	0.0411740i
$421$	−79271.8			−0.447254			−0.223627	−	0.974675i	$-0.571790\pi$
$421$	−79271.8			−0.447254			−0.223627	+	0.974675i	$0.571790\pi$
$422$			133273.i			0.748373i
$423$	50093.8	−	123195.i	0.279964	−	0.688514i
$424$	209312.			1.16429
$425$			19459.0i			0.107731i
$426$	18240.0	−	93281.7i	0.100509	−	0.514017i
$427$	120205.			0.659277
$428$		−	26058.2i		−	0.142251i
$429$	51898.7	+	10148.1i	0.281995	+	0.0551405i
$430$	−67621.8			−0.365721
$431$			67828.9i			0.365141i	0.983193	+	0.182570i	$0.0584418\pi$
$431$			67828.9i			0.365141i	−0.983193	+	0.182570i	$0.941558\pi$
$432$	82128.1	−	125545.i	0.440072	−	0.672717i
$433$	−11248.2			−0.0599940			−0.0299970	−	0.999550i	$-0.509550\pi$
$433$	−11248.2			−0.0599940			−0.0299970	+	0.999550i	$0.509550\pi$
$434$			302662.i			1.60686i
$435$	57189.9	−	292476.i	0.302232	−	1.54565i
$436$	−36766.3			−0.193409
$437$		−	199524.i		−	1.04480i
$438$	−156401.	−	30582.1i	−0.815249	−	0.159412i
$439$	104609.			0.542801			0.271401	−	0.962466i	$-0.412513\pi$
$439$	104609.			0.542801			0.271401	+	0.962466i	$0.412513\pi$
$440$			84995.8i			0.439028i
$441$	22719.5	+	9238.24i	0.116821	+	0.0475020i
$442$	21077.4			0.107888
$443$			65873.7i			0.335664i	0.985816	+	0.167832i	$0.0536766\pi$
$443$			65873.7i			0.335664i	−0.985816	+	0.167832i	$0.946323\pi$
$444$	−7422.11	+	37957.6i	−0.0376497	+	0.192545i
$445$	291813.			1.47362
$446$		−	76717.1i		−	0.385676i
$447$	−84716.6	−	16565.2i	−0.423988	−	0.0829054i
$448$	−207659.			−1.03465
$449$		−	29595.0i		−	0.146800i	−0.997303	−	0.0733999i	$-0.976615\pi$
$449$		−	29595.0i		−	0.146800i	0.997303	−	0.0733999i	$-0.0233849\pi$
$450$	−60395.5	+	148530.i	−0.298250	+	0.733482i
$451$	−33472.2			−0.164562
$452$		−	13452.0i		−	0.0658429i
$453$	10185.1	−	52087.9i	0.0496329	−	0.253828i
$454$	111651.			0.541690
$455$		−	252075.i		−	1.21760i
$456$	−330664.	−	64657.1i	−1.59022	−	0.310947i
$457$	107042.			0.512531			0.256265	−	0.966606i	$-0.417508\pi$
$457$	107042.			0.512531			0.256265	+	0.966606i	$0.417508\pi$
$458$			162416.i			0.774281i
$459$	21881.5	+	14314.3i	0.103861	+	0.0679428i
$460$	33362.0			0.157665
$461$			272357.i			1.28155i	0.767727	+	0.640777i	$0.221388\pi$
$461$			272357.i			1.28155i	−0.767727	+	0.640777i	$0.778612\pi$
$462$	−10531.2	+	53857.8i	−0.0493395	+	0.252328i
$463$	177162.			0.826433			0.413216	−	0.910633i	$-0.364405\pi$
$463$	177162.			0.826433			0.413216	+	0.910633i	$0.364405\pi$
$464$		−	199430.i		−	0.926306i
$465$	−546536.	−	106868.i	−2.52763	−	0.494245i
$466$	−307051.			−1.41396
$467$		−	290967.i		−	1.33417i	−0.744983	−	0.667084i	$-0.767542\pi$
$467$		−	290967.i		−	1.33417i	0.744983	−	0.667084i	$-0.232458\pi$
$468$	−32469.2	−	13202.7i	−0.148245	−	0.0602796i
$469$	177337.			0.806222
$470$			204695.i			0.926642i
$471$	−79362.6	+	405870.i	−0.357746	+	1.82955i
$472$	290269.			1.30292
$473$		−	19788.0i		−	0.0884465i
$474$	231219.	+	45211.9i	1.02912	+	0.201232i
$475$	297873.			1.32021
$476$		−	4414.38i		−	0.0194830i
$477$	−93662.7	+	230344.i	−0.411652	+	1.01237i
$478$	−332262.			−1.45420
$479$			337860.i			1.47253i	0.676691	+	0.736267i	$0.263413\pi$
$479$			337860.i			1.47253i	−0.676691	+	0.736267i	$0.736587\pi$
$480$	20067.9	−	102630.i	0.0871004	−	0.445442i
$481$	−257594.			−1.11338
$482$		−	174815.i		−	0.752462i
$483$	147027.	+	28749.3i	0.630237	+	0.123235i
$484$	−3576.18			−0.0152661
$485$			371403.i			1.57893i
$486$	122594.	+	177175.i	0.519033	+	0.750118i
$487$	−79838.3			−0.336631			−0.168315	−	0.985733i	$-0.553833\pi$
$487$	−79838.3			−0.336631			−0.168315	+	0.985733i	$0.553833\pi$
$488$			178927.i			0.751339i
$489$	−50315.7	+	257320.i	−0.210419	+	1.07611i
$490$	−37749.7			−0.157225
$491$			41586.5i			0.172500i	0.996274	+	0.0862501i	$0.0274884\pi$
$491$			41586.5i			0.172500i	−0.996274	+	0.0862501i	$0.972512\pi$
$492$	21773.6	+	4257.55i	0.0899498	+	0.0175885i
$493$	34759.0			0.143012
$494$		−	322648.i		−	1.32213i
$495$	−93536.2	−	38033.8i	−0.381741	−	0.155224i
$496$	−372666.			−1.51480
$497$		−	132582.i		−	0.536751i
$498$	52636.0	−	269187.i	0.212239	−	1.08541i
$499$	64373.4			0.258527			0.129263	−	0.991610i	$-0.458739\pi$
$499$	64373.4			0.258527			0.129263	+	0.991610i	$0.458739\pi$
$500$		−	7572.23i		−	0.0302889i
$501$	−173640.	−	33953.0i	−0.691789	−	0.135270i
$502$	−236658.			−0.939106
$503$			150986.i			0.596760i	0.954447	+	0.298380i	$0.0964463\pi$
$503$			150986.i			0.596760i	−0.954447	+	0.298380i	$0.903554\pi$
$504$	95290.5	−	234347.i	0.375136	−	0.922568i
$505$	−166481.			−0.652803
$506$		−	48373.6i		−	0.188933i
$507$	−4529.37	+	23163.7i	−0.0176206	+	0.0901141i
$508$	−62107.9			−0.240669
$509$		−	190850.i		−	0.736641i	−0.929699	−	0.368321i	$-0.879933\pi$
$509$		−	190850.i		−	0.736641i	0.929699	−	0.368321i	$-0.120067\pi$
$510$	−39497.7	−	7723.27i	−0.151856	−	0.0296935i
$511$	−222294.			−0.851307
$512$		−	294484.i		−	1.12337i
$513$	219119.	−	334956.i	0.832617	−	1.27278i
$514$	141496.			0.535570
$515$		−	134094.i		−	0.505584i
$516$	−2516.98	+	12872.1i	−0.00945321	+	0.0483448i
$517$	−59899.6			−0.224100
$518$		−	267318.i		−	0.996250i
$519$	130710.	+	25558.6i	0.485258	+	0.0948861i
$520$	375216.			1.38763
$521$		−	425668.i		−	1.56818i	−0.620647	−	0.784090i	$-0.713130\pi$
$521$		−	425668.i		−	1.56818i	0.620647	−	0.784090i	$-0.286870\pi$
$522$	265315.	+	107883.i	0.973691	+	0.395924i
$523$	−92792.6			−0.339242			−0.169621	−	0.985509i	$-0.554254\pi$
$523$	−92792.6			−0.339242			−0.169621	+	0.985509i	$0.554254\pi$
$524$			35366.7i			0.128805i
$525$	−42920.4	+	219500.i	−0.155720	+	0.796372i
$526$	90307.2			0.326400
$527$		−	64952.6i		−	0.233871i
$528$	−66314.9	−	12967.0i	−0.237872	−	0.0465128i
$529$	147785.			0.528105
$530$		−	382728.i		−	1.36251i
$531$	−129889.	+	319436.i	−0.460664	+	1.13291i
$532$	−67574.3			−0.238758
$533$			147764.i			0.520131i
$534$	−53819.3	+	275238.i	−0.188736	+	0.965219i
$535$	−331386.			−1.15778
$536$			263968.i			0.918803i
$537$	57042.0	+	11153.8i	0.197809	+	0.0386790i
$538$	253647.			0.876326
$539$		−	11046.6i		−	0.0380235i
$540$	56007.4	+	36638.5i	0.192069	+	0.125646i
$541$	62513.0			0.213588			0.106794	−	0.994281i	$-0.465942\pi$
$541$	62513.0			0.213588			0.106794	+	0.994281i	$0.465942\pi$
$542$			220604.i			0.750955i
$543$	−7527.93	+	38498.7i	−0.0255315	+	0.130571i
$544$	12196.9			0.0412148
$545$			467564.i			1.57416i
$546$	237757.	+	46490.2i	0.797530	+	0.155947i
$547$	301354.			1.00717			0.503584	−	0.863946i	$-0.332014\pi$
$547$	301354.			1.00717			0.503584	+	0.863946i	$0.332014\pi$
$548$			39055.0i			0.130052i
$549$	−196905.	−	80065.9i	−0.653300	−	0.265646i
$550$	72217.9			0.238737
$551$		−	532082.i		−	1.75257i
$552$	−42793.6	+	218852.i	−0.140443	+	0.718243i
$553$	328634.			1.07464
$554$			29455.8i			0.0959736i
$555$	482713.	+	94388.4i	1.56712	+	0.306431i
$556$	53956.9			0.174541
$557$			170860.i			0.550719i	0.961341	+	0.275360i	$0.0887969\pi$
$557$			170860.i			0.550719i	−0.961341	+	0.275360i	$0.911203\pi$
$558$	201596.	−	495783.i	0.647460	−	1.59229i
$559$	−87354.7			−0.279552
$560$			322095.i			1.02709i
$561$	2260.05	−	11558.1i	0.00718112	−	0.0367251i
$562$	−102799.			−0.325473
$563$			18592.4i			0.0586568i	0.999570	+	0.0293284i	$0.00933686\pi$
$563$			18592.4i			0.0586568i	−0.999570	+	0.0293284i	$0.990663\pi$
$564$	38964.6	+	7619.04i	0.122493	+	0.0239520i
$565$	−171071.			−0.535896
$566$		−	99327.0i		−	0.310052i
$567$	215254.	+	209731.i	0.669552	+	0.652373i
$568$	197350.			0.611703
$569$		−	243140.i		−	0.750987i	−0.926825	−	0.375493i	$-0.877473\pi$
$569$		−	243140.i		−	0.750987i	0.926825	−	0.375493i	$-0.122527\pi$
$570$	−118226.	+	604621.i	−0.363884	+	1.86094i
$571$	179456.			0.550409			0.275204	−	0.961386i	$-0.411254\pi$
$571$	179456.			0.550409			0.275204	+	0.961386i	$0.411254\pi$
$572$			15787.1i			0.0482515i
$573$	−596695.	−	116676.i	−1.81737	−	0.355363i
$574$	−153342.			−0.465410
$575$		−	197149.i		−	0.596291i
$576$	340161.	+	138317.i	1.02527	+	0.416898i
$577$	190429.			0.571980			0.285990	−	0.958233i	$-0.407678\pi$
$577$	190429.			0.571980			0.285990	+	0.958233i	$0.407678\pi$
$578$			300051.i			0.898130i
$579$	114942.	−	587827.i	0.342864	−	1.75345i
$580$	88968.5			0.264472
$581$		−	382598.i		−	1.13342i
$582$	−350307.	−	68498.0i	−1.03420	−	0.202224i
$583$	111997.			0.329511
$584$		−	330887.i		−	0.970184i
$585$	−167901.	+	412917.i	−0.490616	+	1.20657i
$586$	130718.			0.380664
$587$			216065.i			0.627059i	0.949578	+	0.313530i	$0.101511\pi$
$587$			216065.i			0.627059i	−0.949578	+	0.313530i	$0.898489\pi$
$588$	−1405.10	+	7185.82i	−0.00406398	+	0.0207837i
$589$	−994278.			−2.86601
$590$		−	530759.i		−	1.52473i
$591$	154359.	+	30182.9i	0.441933	+	0.0864142i
$592$	329147.			0.939175
$593$			648046.i			1.84288i	0.388525	+	0.921438i	$0.372985\pi$
$593$			648046.i			1.84288i	−0.388525	+	0.921438i	$0.627015\pi$
$594$	53124.4	−	81208.6i	0.150564	−	0.230160i
$595$	−56138.5			−0.158572
$596$		−	25770.0i		−	0.0725474i
$597$	48566.2	−	248373.i	0.136265	−	0.696877i
$598$	−213546.			−0.597158
$599$		−	85198.6i		−	0.237454i	−0.992927	−	0.118727i	$-0.962119\pi$
$599$		−	85198.6i		−	0.237454i	0.992927	−	0.118727i	$-0.0378813\pi$
$600$	−326728.	−	63887.5i	−0.907578	−	0.177465i
$601$	−644198.			−1.78349			−0.891745	−	0.452538i	$-0.850519\pi$
$601$	−644198.			−1.78349			−0.891745	+	0.452538i	$0.850519\pi$
$602$		−	90652.3i		−	0.250142i
$603$	−290492.	−	118120.i	−0.798913	−	0.324855i
$604$	15844.7			0.0434319
$605$			45478.9i			0.124251i
$606$	30704.2	−	157025.i	0.0836089	−	0.427586i
$607$	−213448.			−0.579316			−0.289658	−	0.957130i	$-0.593542\pi$
$607$	−213448.			−0.579316			−0.289658	+	0.957130i	$0.593542\pi$
$608$		−	186708.i		−	0.505074i
$609$	392087.	+	76667.5i	1.05718	+	0.206717i
$610$	327169.			0.879249
$611$			264428.i			0.708313i
$612$	−2940.32	+	7231.10i	−0.00785040	+	0.0193064i
$613$	467.669			0.00124457			0.000622283	−	1.00000i	$-0.499802\pi$
$613$	467.669			0.00124457			0.000622283		1.00000i	$0.499802\pi$
$614$			356305.i			0.945115i
$615$	54144.1	−	276899.i	0.143153	−	0.732102i
$616$	−113944.			−0.300281
$617$		−	489554.i		−	1.28597i	−0.765880	−	0.642984i	$-0.777696\pi$
$617$		−	489554.i		−	1.28597i	0.765880	−	0.642984i	$-0.222304\pi$
$618$	126477.	+	24730.9i	0.331157	+	0.0647535i
$619$	272830.			0.712050			0.356025	−	0.934476i	$-0.384132\pi$
$619$	272830.			0.712050			0.356025	+	0.934476i	$0.384132\pi$
$620$		−	166251.i		−	0.432496i
$621$	−221693.	−	145025.i	−0.574868	−	0.376062i
$622$	624709.			1.61472
$623$			391199.i			1.00791i
$624$	−57243.2	+	292749.i	−0.147013	+	0.751840i
$625$	−435372.			−1.11455
$626$			218649.i			0.557954i
$627$	−176929.	−	34596.2i	−0.450054	−	0.0880022i
$628$	−123462.			−0.313050
$629$			57367.6i			0.144999i
$630$	−428505.	−	174239.i	−1.07963	−	0.439000i
$631$	51022.3			0.128145			0.0640725	−	0.997945i	$-0.479591\pi$
$631$	51022.3			0.128145			0.0640725	+	0.997945i	$0.479591\pi$
$632$			489176.i			1.22470i
$633$	63085.1	−	322624.i	0.157441	−	0.805174i
$634$	−412158.			−1.02538
$635$			789838.i			1.95880i
$636$	−72854.0	−	14245.7i	−0.180111	−	0.0352183i
$637$	−48765.6			−0.120181
$638$		−	129001.i		−	0.316921i
$639$	−88310.0	+	217180.i	−0.216276	+	0.531885i
$640$	−379288.			−0.925995
$641$		−	47989.0i		−	0.116795i	−0.998293	−	0.0583976i	$-0.981401\pi$
$641$		−	47989.0i		−	0.116795i	0.998293	−	0.0583976i	$-0.0185991\pi$
$642$	61117.7	−	312563.i	0.148285	−	0.758347i
$643$	375824.			0.908997			0.454499	−	0.890747i	$-0.349818\pi$
$643$	375824.			0.908997			0.454499	+	0.890747i	$0.349818\pi$
$644$			44724.4i			0.107838i
$645$	163697.	+	32008.8i	0.393479	+	0.0769397i
$646$	−71855.6			−0.172185
$647$		−	58903.1i		−	0.140712i	−0.997522	−	0.0703558i	$-0.977587\pi$
$647$		−	58903.1i		−	0.140712i	0.997522	−	0.0703558i	$-0.0224135\pi$
$648$	−312186.	+	320407.i	−0.743470	+	0.763049i
$649$	155315.			0.368744
$650$		−	318808.i		−	0.754574i
$651$	143265.	−	732675.i	0.338048	−	1.72882i
$652$	−78274.6			−0.184130
$653$		−	229827.i		−	0.538984i	−0.963003	−	0.269492i	$-0.913144\pi$
$653$		−	229827.i		−	0.538984i	0.963003	−	0.269492i	$-0.0868557\pi$
$654$	−441006.	−	86233.0i	−1.03107	−	0.201613i
$655$	449765.			1.04834
$656$		−	188809.i		−	0.438747i
$657$	364134.	+	148065.i	0.843589	+	0.343021i
$658$	−274410.			−0.633794
$659$			109817.i			0.252870i	0.991975	+	0.126435i	$0.0403535\pi$
$659$			109817.i			0.252870i	−0.991975	+	0.126435i	$0.959646\pi$
$660$	5784.77	−	29584.0i	0.0132800	−	0.0679155i
$661$	729297.			1.66917			0.834587	−	0.550876i	$-0.185706\pi$
$661$	729297.			1.66917			0.834587	+	0.550876i	$0.185706\pi$
$662$			494287.i			1.12788i
$663$	−51023.7	−	9977.03i	−0.116077	−	0.0226973i
$664$	569502.			1.29169
$665$			859354.i			1.94325i
$666$	−178054.	+	437887.i	−0.401424	+	0.987218i
$667$	−352161.			−0.791571
$668$		−	52819.6i		−	0.118370i
$669$	−36314.1	+	185715.i	−0.0811378	+	0.414948i
$670$	482668.			1.07522
$671$			95738.8i			0.212639i
$672$	137583.	+	26902.6i	0.304668	+	0.0595740i
$673$	−392075.			−0.865643			−0.432821	−	0.901480i	$-0.642482\pi$
$673$	−392075.			−0.865643			−0.432821	+	0.901480i	$0.642482\pi$
$674$		−	185069.i		−	0.407394i
$675$	216511.	−	330969.i	0.475195	−	0.726408i
$676$	−7046.20			−0.0154192
$677$			110401.i			0.240877i	0.992721	+	0.120438i	$0.0384300\pi$
$677$			110401.i			0.240877i	−0.992721	+	0.120438i	$0.961570\pi$
$678$	31550.7	−	161354.i	0.0686357	−	0.351011i
$679$	−497895.			−1.07994
$680$		−	83562.8i		−	0.180715i
$681$	−270282.	−	52850.1i	−0.582804	−	0.113960i
$682$	−241058.			−0.518266
$683$			645787.i			1.38436i	0.721726	+	0.692178i	$0.243349\pi$
$683$			645787.i			1.38436i	−0.721726	+	0.692178i	$0.756651\pi$
$684$	110692.	+	45009.6i	0.236594	+	0.0962041i
$685$	496670.			1.05849
$686$		−	451896.i		−	0.960262i
$687$	76879.9	−	393173.i	0.162892	−	0.833048i
$688$	111620.			0.235811
$689$		−	494413.i		−	1.04148i
$690$	400171.	+	78248.4i	0.840520	+	0.164353i
$691$	332137.			0.695602			0.347801	−	0.937568i	$-0.386928\pi$
$691$	332137.			0.695602			0.347801	+	0.937568i	$0.386928\pi$
$692$			39760.7i			0.0830313i
$693$	50987.3	−	125393.i	0.106169	−	0.261099i
$694$	733018.			1.52193
$695$		−	686179.i		−	1.42059i
$696$	−114120.	+	583625.i	−0.235584	+	1.20480i
$697$	32907.8			0.0677382
$698$			251875.i			0.516981i
$699$	743300.	+	145343.i	1.52128	+	0.297467i
$700$	−66770.0			−0.136265
$701$		−	539203.i		−	1.09728i	−0.836060	−	0.548639i	$-0.815146\pi$
$701$		−	539203.i		−	1.09728i	0.836060	−	0.548639i	$-0.184854\pi$
$702$	−358497.	−	234519.i	−0.727464	−	0.475886i
$703$	878169.			1.77692
$704$		−	165392.i		−	0.333711i
$705$	96892.7	−	495521.i	0.194945	−	0.996973i
$706$	110155.			0.221001
$707$		−	223181.i		−	0.446497i
$708$	−101032.	−	19755.6i	−0.201555	−	0.0394115i
$709$	−989881.			−1.96920			−0.984602	−	0.174814i	$-0.944068\pi$
$709$	−989881.			−1.96920			−0.984602	+	0.174814i	$0.944068\pi$
$710$		−	360856.i		−	0.715842i
$711$	−538328.	−	218896.i	−1.06490	−	0.433010i
$712$	−582304.			−1.14865
$713$			658068.i			1.29447i
$714$	10353.7	−	52949.8i	0.0203094	−	0.103865i
$715$	200768.			0.392719
$716$			17351.7i			0.0338466i
$717$	804332.	+	157277.i	1.56458	+	0.305933i
$718$	−630655.			−1.22333
$719$			509120.i			0.984832i	0.870360	+	0.492416i	$0.163886\pi$
$719$			509120.i			0.984832i	−0.870360	+	0.492416i	$0.836114\pi$
$720$	214540.	−	527616.i	0.413850	−	1.01778i
$721$	179763.			0.345804
$722$			624443.i			1.19789i
$723$	−82748.9	+	423188.i	−0.158302	+	0.809574i
$724$	−11711.0			−0.0223417
$725$		−	525749.i		−	1.00024i
$726$	−42895.7	−	8387.70i	−0.0813842	−	0.0159136i
$727$	−793797.			−1.50190			−0.750950	−	0.660359i	$-0.770404\pi$
$727$	−793797.			−1.50190			−0.750950	+	0.660359i	$0.770404\pi$
$728$			503006.i			0.949097i
$729$	−212905.	−	486930.i	−0.400619	−	0.916245i
$730$	−605029.			−1.13535
$731$			19454.4i			0.0364069i
$732$	12177.7	−	62278.0i	0.0227270	−	0.116229i
$733$	1.01077e6			1.88123			0.940617	−	0.339470i	$-0.110248\pi$
$733$	1.01077e6			1.88123			0.940617	+	0.339470i	$0.110248\pi$
$734$		−	43529.8i		−	0.0807969i
$735$	91383.4	+	17868.9i	0.169158	+	0.0330767i
$736$	−123573.			−0.228123
$737$			141242.i			0.260034i
$738$	251185.	+	102137.i	0.461191	+	0.187530i
$739$	−178883.			−0.327552			−0.163776	−	0.986498i	$-0.552368\pi$
$739$	−178883.			−0.327552			−0.163776	+	0.986498i	$0.552368\pi$
$740$			146837.i			0.268147i
$741$	−152726.	+	781057.i	−0.278148	+	1.42248i
$742$	513077.			0.931912
$743$			174754.i			0.316555i	0.987395	+	0.158278i	$0.0505941\pi$
$743$			174754.i			0.316555i	−0.987395	+	0.158278i	$0.949406\pi$
$744$	1.09059e6	+	213252.i	1.97023	+	0.385254i
$745$	−327722.			−0.590464
$746$		−	539533.i		−	0.969484i
$747$	−254840.	+	626725.i	−0.456695	+	1.12314i
$748$	3515.88			0.00628393
$749$		−	444250.i		−	0.791887i
$750$	17760.2	−	90827.6i	0.0315737	−	0.161471i
$751$	414298.			0.734570			0.367285	−	0.930109i	$-0.380287\pi$
$751$	414298.			0.734570			0.367285	+	0.930109i	$0.380287\pi$
$752$		−	337880.i		−	0.597485i
$753$	572896.	+	112023.i	1.01038	+	0.197567i
$754$	−569477.			−1.00169
$755$		−	201500.i		−	0.353493i
$756$	−49116.8	+	75082.4i	−0.0859382	+	0.131369i
$757$	593298.			1.03534			0.517668	−	0.855582i	$-0.326800\pi$
$757$	593298.			1.03534			0.517668	+	0.855582i	$0.326800\pi$
$758$		−	426031.i		−	0.741486i
$759$	−22897.7	+	117101.i	−0.0397473	+	0.203273i
$760$	−1.27916e6			−2.21461
$761$			504689.i			0.871475i	0.900074	+	0.435737i	$0.143512\pi$
$761$			504689.i			0.871475i	−0.900074	+	0.435737i	$0.856488\pi$
$762$	−744974.	−	145670.i	−1.28301	−	0.250877i
$763$	−626806.			−1.07667
$764$		−	181509.i		−	0.310965i
$765$	91959.2	+	37392.6i	0.157135	+	0.0638944i
$766$	−305483.			−0.520631
$767$		−	685642.i		−	1.16548i
$768$	−55324.5	+	282936.i	−0.0937983	+	0.479696i
$769$	−464827.			−0.786029			−0.393015	−	0.919532i	$-0.628568\pi$
$769$	−464827.			−0.786029			−0.393015	+	0.919532i	$0.628568\pi$
$770$			208347.i			0.351403i
$771$	−342529.	−	66977.1i	−0.576220	−	0.112672i
$772$	178812.			0.300028
$773$		−	66302.8i		−	0.110962i	−0.998460	−	0.0554808i	$-0.982331\pi$
$773$		−	66302.8i		−	0.110962i	0.998460	−	0.0554808i	$-0.0176692\pi$
$774$	−60381.4	+	148495.i	−0.100791	+	0.247874i
$775$	−982444.			−1.63570
$776$		−	741122.i		−	1.23074i
$777$	−126535.	+	647115.i	−0.209589	+	1.07186i
$778$	−106966.			−0.176720
$779$		−	503745.i		−	0.830110i
$780$	−130599.	−	25537.0i	−0.214660	−	0.0419740i
$781$	105597.			0.173120
$782$			47558.0i			0.0777697i
$783$	−591201.	−	386747.i	−0.964299	−	0.630817i
$784$	62311.5			0.101376
$785$			1.57009e6i			2.54791i
$786$	−82950.3	+	424218.i	−0.134268	+	0.686663i
$787$	420094.			0.678261			0.339131	−	0.940739i	$-0.389867\pi$
$787$	420094.			0.678261			0.339131	+	0.940739i	$0.389867\pi$
$788$			46954.5i			0.0756180i
$789$	−218613.	−	42747.0i	−0.351174	−	0.0686676i
$790$	894461.			1.43320
$791$		−	229335.i		−	0.366536i
$792$	186648.	+	75895.2i	0.297559	+	0.120994i
$793$	422641.			0.672087
$794$			93172.2i			0.147790i
$795$	−181165.	+	926498.i	−0.286642	+	1.46592i
$796$	75552.9			0.119241
$797$		−	232990.i		−	0.366793i	−0.983039	−	0.183396i	$-0.941291\pi$
$797$		−	232990.i		−	0.366793i	0.983039	−	0.183396i	$-0.0587091\pi$
$798$	−810542.	−	158491.i	−1.27283	−	0.248885i
$799$	58889.7			0.0922456
$800$		−	184485.i		−	0.288258i
$801$	260568.	−	640813.i	0.406122	−	0.998773i
$802$	3590.59			0.00558235
$803$		−	177049.i		−	0.274575i
$804$	17965.6	−	91878.0i	0.0277926	−	0.142134i
$805$	568768.			0.877695
$806$			1.06416e6i			1.63808i
$807$	−614022.	−	120064.i	−0.942838	−	0.184360i
$808$	332207.			0.508846
$809$		−	60807.5i		−	0.0929095i	−0.998920	−	0.0464547i	$-0.985208\pi$
$809$		−	60807.5i		−	0.0929095i	0.998920	−	0.0464547i	$-0.0147923\pi$
$810$	585867.	+	570834.i	0.892953	+	0.870042i
$811$	965384.			1.46777			0.733886	−	0.679273i	$-0.237705\pi$
$811$	965384.			1.46777			0.733886	+	0.679273i	$0.237705\pi$
$812$			119269.i			0.180891i
$813$	104423.	−	534031.i	0.157985	−	0.807952i
$814$	212908.			0.321324
$815$			995432.i			1.49864i
$816$	65196.9	+	12748.4i	0.0979144	+	0.0191459i
$817$	297803.			0.446155
$818$		−	526029.i		−	0.786146i
$819$	−553548.	−	225085.i	−0.825254	−	0.335566i
$820$	84230.2			0.125268
$821$		−	1.15600e6i		−	1.71503i	−0.514458	−	0.857516i	$-0.672007\pi$
$821$		−	1.15600e6i		−	1.71503i	0.514458	−	0.857516i	$-0.327993\pi$
$822$	−91601.1	+	468459.i	−0.135568	+	0.693310i
$823$	80741.5			0.119206			0.0596029	−	0.998222i	$-0.481017\pi$
$823$	80741.5			0.119206			0.0596029	+	0.998222i	$0.481017\pi$
$824$			267579.i			0.394092i
$825$	−174823.	−	34184.4i	−0.256857	−	0.0502251i
$826$	711525.			1.04287
$827$		−	557870.i		−	0.815684i	−0.913053	−	0.407842i	$-0.866281\pi$
$827$		−	557870.i		−	0.815684i	0.913053	−	0.407842i	$-0.133719\pi$
$828$	29789.9	−	73261.9i	0.0434518	−	0.106861i
$829$	−451247.			−0.656606			−0.328303	−	0.944572i	$-0.606477\pi$
$829$	−451247.			−0.656606			−0.328303	+	0.944572i	$0.606477\pi$
$830$		−	1.04134e6i		−	1.51159i
$831$	13942.9	−	71305.9i	0.0201907	−	0.103258i
$832$	−730128.			−1.05476
$833$			10860.4i			0.0156515i
$834$	647204.	+	126552.i	0.930484	+	0.181944i
$835$	−671717.			−0.963415
$836$		−	53820.3i		−	0.0770075i
$837$	−722697.	+	1.10475e6i	−1.03159	+	1.57693i
$838$	−9904.78			−0.0141045
$839$			73632.1i			0.104603i	0.998631	+	0.0523014i	$0.0166557\pi$
$839$			73632.1i			0.104603i	−0.998631	+	0.0523014i	$0.983344\pi$
$840$	184313.	−	942601.i	0.261215	−	1.33589i
$841$	−231849.			−0.327804
$842$		−	289241.i		−	0.407977i
$843$	248852.	+	48659.8i	0.350176	+	0.0684724i
$844$	98139.4			0.137771
$845$			89607.8i			0.125497i
$846$	449504.	+	182778.i	0.628049	+	0.255378i
$847$	−60968.1			−0.0849837
$848$			631750.i			0.878524i
$849$	−47016.6	+	240448.i	−0.0652282	+	0.333585i
$850$	−71000.4			−0.0982704
$851$		−	581221.i		−	0.802568i
$852$	−68690.5	−	13431.6i	−0.0946276	−	0.0185032i
$853$	229339.			0.315196			0.157598	−	0.987503i	$-0.449625\pi$
$853$	229339.			0.315196			0.157598	+	0.987503i	$0.449625\pi$
$854$			438596.i			0.601379i
$855$	572396.	−	1.40769e6i	0.783005	−	1.92564i
$856$	661270.			0.902467
$857$		−	1.26091e6i		−	1.71681i	−0.512976	−	0.858403i	$-0.671457\pi$
$857$		−	1.26091e6i		−	1.71681i	0.512976	−	0.858403i	$-0.328543\pi$
$858$	−37027.7	+	189364.i	−0.0502981	+	0.257230i
$859$	96295.7			0.130503			0.0652515	−	0.997869i	$-0.479215\pi$
$859$	96295.7			0.130503			0.0652515	+	0.997869i	$0.479215\pi$
$860$			49795.1i			0.0673271i
$861$	371205.	+	72584.4i	0.500735	+	0.0979122i
$862$	−247489.			−0.333074
$863$		−	369410.i		−	0.496006i	−0.968759	−	0.248003i	$-0.920226\pi$
$863$		−	369410.i		−	0.496006i	0.968759	−	0.248003i	$-0.0797742\pi$
$864$	−207453.	−	135710.i	−0.277902	−	0.181795i
$865$	505644.			0.675792
$866$		−	41041.6i		−	0.0547254i
$867$	142029.	−	726355.i	0.188947	−	0.966297i
$868$	222873.			0.295814
$869$			261744.i			0.346607i
$870$	1.06716e6	+	208670.i	1.40991	+	0.275690i
$871$	623517.			0.821886
$872$		−	933008.i		−	1.22702i
$873$	815590.	+	331636.i	1.07015	+	0.435145i
$874$	728006.			0.953042
$875$		−	129094.i		−	0.168613i
$876$	−22520.0	+	115170.i	−0.0293468	+	0.150083i
$877$	−874908.			−1.13753			−0.568765	−	0.822500i	$-0.692579\pi$
$877$	−874908.			−1.13753			−0.568765	+	0.822500i	$0.692579\pi$
$878$			381690.i			0.495133i
$879$	−316440.	−	61875.7i	−0.409556	−	0.0800834i
$880$	−256536.			−0.331271
$881$			1.00825e6i			1.29903i	0.760350	+	0.649514i	$0.225028\pi$
$881$			1.00825e6i			1.29903i	−0.760350	+	0.649514i	$0.774972\pi$
$882$	−33707.8	+	82897.2i	−0.0433304	+	0.106562i
$883$	−13066.0			−0.0167579			−0.00837897	−	0.999965i	$-0.502667\pi$
$883$	−13066.0			−0.0167579			−0.00837897	+	0.999965i	$0.502667\pi$
$884$		−	15520.9i		−	0.0198616i
$885$	−251236.	+	1.28485e6i	−0.320771	+	1.64046i
$886$	−240355.			−0.306186
$887$			1.51856e6i			1.93012i	0.262026	+	0.965061i	$0.415610\pi$
$887$			1.51856e6i			1.93012i	−0.262026	+	0.965061i	$0.584390\pi$
$888$	−963238.	−	188349.i	−1.22154	−	0.238856i
$889$	−1.05884e6			−1.33976
$890$			1.06475e6i			1.34421i
$891$	−167042.	+	171441.i	−0.210412	+	0.215953i
$892$	−56492.7			−0.0710007
$893$		−	901469.i		−	1.13044i
$894$	60441.9	−	309107.i	0.0756246	−	0.386753i
$895$	220664.			0.275477
$896$		−	508465.i		−	0.633352i
$897$	516947.	+	101082.i	0.642482	+	0.125629i
$898$	107984.			0.133908
$899$			1.75491e6i			2.17138i
$900$	109374.	+	44473.9i	0.135030	+	0.0549061i
$901$	−110109.			−0.135635
$902$		−	122131.i		−	0.150111i
$903$	−42910.4	+	219449.i	−0.0526244	+	0.269127i
$904$	341367.			0.417719
$905$			148930.i			0.181839i
$906$	190054.	+	37162.7i	0.231537	+	0.0452742i
$907$	−675022.			−0.820546			−0.410273	−	0.911963i	$-0.634567\pi$
$907$	−675022.			−0.820546			−0.410273	+	0.911963i	$0.634567\pi$
$908$		−	82217.3i		−	0.0997221i
$909$	−148656.	+	365588.i	−0.179909	+	0.442449i
$910$	919750.			1.11068
$911$			404273.i			0.487122i	0.969886	+	0.243561i	$0.0783157\pi$
$911$			404273.i			0.487122i	−0.969886	+	0.243561i	$0.921684\pi$
$912$	195149.	−	998017.i	0.234627	−	1.19991i
$913$	304725.			0.365566
$914$			390565.i			0.467521i
$915$	−792001.	−	154866.i	−0.945984	−	0.184975i
$916$	119600.			0.142541
$917$			602945.i			0.717033i
$918$	−52228.7	+	79839.5i	−0.0619761	+	0.0947398i
$919$	−1.34517e6			−1.59275			−0.796373	−	0.604806i	$-0.793251\pi$
$919$	−1.34517e6			−1.59275			−0.796373	+	0.604806i	$0.793251\pi$
$920$			846617.i			1.00026i
$921$	168657.	−	862533.i	0.198832	−	1.01685i
$922$	−993755.			−1.16901
$923$		−	466159.i		−	0.547180i
$924$	39659.7	+	7754.94i	0.0464521	+	0.00908311i
$925$	867717.			1.01413
$926$			646413.i			0.753856i
$927$	−294465.	−	119736.i	−0.342669	−	0.139337i
$928$	−329541.			−0.382660
$929$		−	841093.i		−	0.974569i	−0.873243	−	0.487284i	$-0.837988\pi$
$929$		−	841093.i		−	0.974569i	0.873243	−	0.487284i	$-0.162012\pi$
$930$	389932.	−	1.99416e6i	0.450841	−	2.30565i
$931$	166248.			0.191804
$932$			226105.i			0.260303i
$933$	−1.51228e6	−	295707.i	−1.73727	−	0.339702i
$934$	1.06166e6			1.21700
$935$		−	44712.2i		−	0.0511449i
$936$	335041.	−	823962.i	0.382425	−	0.940493i
$937$	−738908.			−0.841611			−0.420805	−	0.907151i	$-0.638253\pi$
$937$	−738908.			−0.841611			−0.420805	+	0.907151i	$0.638253\pi$
$938$			647054.i			0.735419i
$939$	103498.	−	529299.i	0.117381	−	0.600302i
$940$	150733.			0.170590
$941$		−	1.42573e6i		−	1.61012i	−0.593191	−	0.805062i	$-0.702132\pi$
$941$		−	1.42573e6i		−	1.61012i	0.593191	−	0.805062i	$-0.297868\pi$
$942$	−1.48091e6	−	289572.i	−1.66888	−	0.326328i
$943$	−333406.			−0.374930
$944$			876097.i			0.983124i
$945$	954837.	+	624627.i	1.06922	+	0.699451i
$946$	72201.0			0.0806791
$947$		−	229285.i		−	0.255667i	−0.991796	−	0.127834i	$-0.959198\pi$
$947$		−	229285.i		−	0.255667i	0.991796	−	0.127834i	$-0.0408024\pi$
$948$	33293.1	−	170265.i	0.0370456	−	0.189456i
$949$	−781584.			−0.867847
$950$			1.08686e6i			1.20427i
$951$	997741.	+	195095.i	1.10321	+	0.215718i
$952$	112023.			0.123604
$953$		−	1.47835e6i		−	1.62776i	−0.581034	−	0.813879i	$-0.697352\pi$
$953$		−	1.47835e6i		−	1.62776i	0.581034	−	0.813879i	$-0.302648\pi$
$954$	−840460.	−	341749.i	−0.923464	−	0.375500i
$955$	−2.30829e6			−2.53095
$956$			244670.i			0.267711i
$957$	−61062.7	+	312282.i	−0.0666733	+	0.340975i
$958$	−1.23276e6			−1.34322
$959$			665826.i			0.723975i
$960$	1.36821e6	+	267536.i	1.48460	+	0.290295i
$961$	2.35580e6			2.55089
$962$		−	939887.i		−	1.01561i
$963$	−295904.	+	727714.i	−0.319079	+	0.784709i
$964$	−128730.			−0.138524
$965$		−	2.27398e6i		−	2.44193i
$966$	−104898.	+	536461.i	−0.112412	+	0.574889i
$967$	−991862.			−1.06071			−0.530357	−	0.847774i	$-0.677942\pi$
$967$	−991862.			−1.06071			−0.530357	+	0.847774i	$0.677942\pi$
$968$		−	90751.6i		−	0.0968509i
$969$	173946.	+	34012.9i	0.185254	+	0.0362240i
$970$	−1.35515e6			−1.44027
$971$			1.17951e6i			1.25101i	0.780219	+	0.625506i	$0.215107\pi$
$971$			1.17951e6i			1.25101i	−0.780219	+	0.625506i	$0.784893\pi$
$972$	130468.	−	90275.1i	0.138093	−	0.0955511i
$973$	919878.			0.971638
$974$		−	291308.i		−	0.307068i
$975$	−150908.	+	771761.i	−0.158746	+	0.811846i
$976$	−540041.			−0.566927
$977$			483877.i			0.506928i	0.967345	+	0.253464i	$0.0815699\pi$
$977$			483877.i			0.506928i	−0.967345	+	0.253464i	$0.918430\pi$
$978$	−938891.	−	183588.i	−0.981606	−	0.191941i
$979$	−311575.			−0.325085
$980$			27798.0i			0.0289442i
$981$	1.02676e6	+	417501.i	1.06691	+	0.433830i
$982$	−151738.			−0.157351
$983$			546998.i			0.566081i	0.959108	+	0.283040i	$0.0913431\pi$
$983$			546998.i			0.566081i	−0.959108	+	0.283040i	$0.908657\pi$
$984$	−108043.	+	552543.i	−0.111585	+	0.570658i
$985$	597129.			0.615454
$986$			126826.i			0.130453i
$987$	664284.	+	129892.i	0.681899	+	0.133337i
$988$	−237591.			−0.243397
$989$		−	197103.i		−	0.201511i
$990$	138775.	−	341287.i	0.141592	−	0.348217i
$991$	382123.			0.389095			0.194548	−	0.980893i	$-0.437676\pi$
$991$	382123.			0.389095			0.194548	+	0.980893i	$0.437676\pi$
$992$			615798.i			0.625771i
$993$	233971.	−	1.19656e6i	0.237282	−	1.21349i
$994$	483756.			0.489614
$995$		−	960821.i		−	0.970501i
$996$	−198223.	−	38760.0i	−0.199818	−	0.0390719i
$997$	−121193.			−0.121923			−0.0609617	−	0.998140i	$-0.519417\pi$
$997$	−121193.			−0.121923			−0.0609617	+	0.998140i	$0.519417\pi$
$998$			234881.i			0.235823i
$999$	638303.	−	975742.i	0.639581	−	0.977696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.5.b.a.23.11	yes	14
3.2	odd	2	inner	33.5.b.a.23.4	✓	14
4.3	odd	2		528.5.i.d.353.6		14
12.11	even	2		528.5.i.d.353.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.b.a.23.4	✓	14	3.2	odd	2	inner
33.5.b.a.23.11	yes	14	1.1	even	1	trivial
528.5.i.d.353.5		14	12.11	even	2
528.5.i.d.353.6		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)

\(f(q)\)	\(=\)	\(q+3.64872i q^{2} +(1.72713 - 8.83273i) q^{3} +2.68684 q^{4} -34.1690i q^{5} +(32.2281 + 6.30180i) q^{6} +45.8062 q^{7} +68.1830i q^{8} +(-75.0341 - 30.5105i) q^{9} +O(q^{10})\)	\(q+3.64872i q^{2} +(1.72713 - 8.83273i) q^{3} +2.68684 q^{4} -34.1690i q^{5} +(32.2281 + 6.30180i) q^{6} +45.8062 q^{7} +68.1830i q^{8} +(-75.0341 - 30.5105i) q^{9} +124.673 q^{10} +36.4829i q^{11} +(4.64050 - 23.7321i) q^{12} +161.054 q^{13} +167.134i q^{14} +(-301.805 - 59.0141i) q^{15} -205.792 q^{16} -35.8678i q^{17} +(111.324 - 273.778i) q^{18} -549.055 q^{19} -91.8064i q^{20} +(79.1131 - 404.594i) q^{21} -133.116 q^{22} +363.395i q^{23} +(602.242 + 117.761i) q^{24} -542.520 q^{25} +587.642i q^{26} +(-399.084 + 610.060i) q^{27} +123.074 q^{28} +969.087i q^{29} +(215.326 - 1101.20i) q^{30} +1810.89 q^{31} +340.053i q^{32} +(322.243 + 63.0105i) q^{33} +130.872 q^{34} -1565.15i q^{35} +(-201.604 - 81.9766i) q^{36} -1599.42 q^{37} -2003.35i q^{38} +(278.161 - 1422.55i) q^{39} +2329.75 q^{40} +917.476i q^{41} +(1476.25 + 288.662i) q^{42} -542.393 q^{43} +98.0235i q^{44} +(-1042.51 + 2563.84i) q^{45} -1325.93 q^{46} +1641.86i q^{47} +(-355.428 + 1817.70i) q^{48} -302.789 q^{49} -1979.50i q^{50} +(-316.810 - 61.9482i) q^{51} +432.727 q^{52} -3069.85i q^{53} +(-2225.94 - 1456.15i) q^{54} +1246.58 q^{55} +3123.21i q^{56} +(-948.287 + 4849.65i) q^{57} -3535.93 q^{58} -4257.21i q^{59} +(-810.901 - 158.561i) q^{60} +2624.21 q^{61} +6607.43i q^{62} +(-3437.03 - 1397.57i) q^{63} -4533.42 q^{64} -5503.06i q^{65} +(-229.908 + 1175.78i) q^{66} +3871.47 q^{67} -96.3708i q^{68} +(3209.77 + 627.628i) q^{69} +5710.80 q^{70} -2894.42i q^{71} +(2080.30 - 5116.05i) q^{72} -4852.92 q^{73} -5835.84i q^{74} +(-937.000 + 4791.93i) q^{75} -1475.22 q^{76} +1671.14i q^{77} +(5190.48 + 1014.93i) q^{78} +7174.45 q^{79} +7031.69i q^{80} +(4699.22 + 4578.65i) q^{81} -3347.61 q^{82} -8352.54i q^{83} +(212.564 - 1087.08i) q^{84} -1225.57 q^{85} -1979.04i q^{86} +(8559.68 + 1673.74i) q^{87} -2487.51 q^{88} +8540.30i q^{89} +(-9354.73 - 3803.83i) q^{90} +7377.29 q^{91} +976.382i q^{92} +(3127.64 - 15995.1i) q^{93} -5990.67 q^{94} +18760.6i q^{95} +(3003.59 + 587.314i) q^{96} -10869.6 q^{97} -1104.79i q^{98} +(1113.11 - 2737.46i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more