LMFDB - Embedded newform 138.5.b.a.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,5,Mod(91,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("138.91");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	138.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:	$14.2650549056$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1428 x^{14} - 600 x^{13} + 788282 x^{12} - 529464 x^{11} + 213396724 x^{10} + \cdots + 274129967370817 $ x^16 + 1428x^14 - 600x^13 + 788282x^12 - 529464x^11 + 213396724x^10 - 175079484x^9 + 29130946113x^8 - 26553654912x^7 + 1790717926120x^6 - 1672125302460x^5 + 32715955056348x^4 - 11255739266544x^3 + 140972261417692x^2 - 70961983286748x + 274129967370817
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.3
Root			$-0.707107 - 11.7850i$ of defining polynomial
Character	$\chi$	$=$	138.91
Dual form			138.5.b.a.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843 q^{2} -5.19615 q^{3} +8.00000 q^{4} +26.7045i q^{5} +14.6969 q^{6} -66.7315i q^{7} -22.6274 q^{8} +27.0000 q^{9} +O(q^{10})$	\(q-2.82843 q^{2} -5.19615 q^{3} +8.00000 q^{4} +26.7045i q^{5} +14.6969 q^{6} -66.7315i q^{7} -22.6274 q^{8} +27.0000 q^{9} -75.5318i q^{10} -8.81477i q^{11} -41.5692 q^{12} -136.925 q^{13} +188.745i q^{14} -138.761i q^{15} +64.0000 q^{16} +184.077i q^{17} -76.3675 q^{18} -33.2701i q^{19} +213.636i q^{20} +346.747i q^{21} +24.9319i q^{22} +(493.509 - 190.498i) q^{23} +117.576 q^{24} -88.1308 q^{25} +387.283 q^{26} -140.296 q^{27} -533.852i q^{28} +1221.54 q^{29} +392.475i q^{30} +1220.45 q^{31} -181.019 q^{32} +45.8029i q^{33} -520.649i q^{34} +1782.03 q^{35} +216.000 q^{36} +2059.16i q^{37} +94.1019i q^{38} +711.485 q^{39} -604.254i q^{40} +884.746 q^{41} -980.749i q^{42} +1572.25i q^{43} -70.5181i q^{44} +721.022i q^{45} +(-1395.86 + 538.810i) q^{46} +564.292 q^{47} -332.554 q^{48} -2052.10 q^{49} +249.272 q^{50} -956.493i q^{51} -1095.40 q^{52} +3033.20i q^{53} +396.817 q^{54} +235.394 q^{55} +1509.96i q^{56} +172.876i q^{57} -3455.04 q^{58} +5664.52 q^{59} -1110.09i q^{60} -3378.10i q^{61} -3451.96 q^{62} -1801.75i q^{63} +512.000 q^{64} -3656.52i q^{65} -129.550i q^{66} -6983.41i q^{67} +1472.62i q^{68} +(-2564.35 + 989.856i) q^{69} -5040.35 q^{70} -3482.47 q^{71} -610.940 q^{72} +406.423 q^{73} -5824.17i q^{74} +457.941 q^{75} -266.160i q^{76} -588.223 q^{77} -2012.38 q^{78} +103.984i q^{79} +1709.09i q^{80} +729.000 q^{81} -2502.44 q^{82} +10105.6i q^{83} +2773.98i q^{84} -4915.69 q^{85} -4446.99i q^{86} -6347.32 q^{87} +199.455i q^{88} +7418.94i q^{89} -2039.36i q^{90} +9137.24i q^{91} +(3948.08 - 1523.98i) q^{92} -6341.66 q^{93} -1596.06 q^{94} +888.461 q^{95} +940.604 q^{96} -16181.4i q^{97} +5804.21 q^{98} -237.999i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 128 q^{4} + 432 q^{9}+O(q^{10}) $ 16 * q + 128 * q^4 + 432 * q^9	$ 16 q + 128 q^{4} + 432 q^{9} - 208 q^{13} + 1024 q^{16} + 840 q^{23} + 1056 q^{25} + 1920 q^{26} + 3600 q^{29} + 224 q^{31} - 3264 q^{35} + 3456 q^{36} - 2016 q^{39} - 6144 q^{41} + 1280 q^{46} + 8880 q^{47} - 13888 q^{49} + 7296 q^{50} - 1664 q^{52} + 832 q^{55} + 2944 q^{58} - 18240 q^{59} + 8192 q^{64} + 10584 q^{69} + 19584 q^{70} - 30048 q^{71} + 9536 q^{73} - 4176 q^{75} + 14160 q^{77} + 6912 q^{78} + 11664 q^{81} - 19584 q^{82} - 32496 q^{85} - 8064 q^{87} + 6720 q^{92} - 11952 q^{93} - 21248 q^{94} - 20064 q^{95} + 21504 q^{98}+O(q^{100}) $ 16 * q + 128 * q^4 + 432 * q^9 - 208 * q^13 + 1024 * q^16 + 840 * q^23 + 1056 * q^25 + 1920 * q^26 + 3600 * q^29 + 224 * q^31 - 3264 * q^35 + 3456 * q^36 - 2016 * q^39 - 6144 * q^41 + 1280 * q^46 + 8880 * q^47 - 13888 * q^49 + 7296 * q^50 - 1664 * q^52 + 832 * q^55 + 2944 * q^58 - 18240 * q^59 + 8192 * q^64 + 10584 * q^69 + 19584 * q^70 - 30048 * q^71 + 9536 * q^73 - 4176 * q^75 + 14160 * q^77 + 6912 * q^78 + 11664 * q^81 - 19584 * q^82 - 32496 * q^85 - 8064 * q^87 + 6720 * q^92 - 11952 * q^93 - 21248 * q^94 - 20064 * q^95 + 21504 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.82843			−0.707107
$2$	−2.82843			−0.707107
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	8.00000			0.500000
$5$			26.7045i			1.06818i	0.845428	+	0.534090i	$0.179346\pi$
$5$			26.7045i			1.06818i	−0.845428	+	0.534090i	$0.820654\pi$
$6$	14.6969			0.408248
$7$		−	66.7315i		−	1.36187i	−0.732345	−	0.680934i	$-0.761574\pi$
$7$		−	66.7315i		−	1.36187i	0.732345	−	0.680934i	$-0.238426\pi$
$8$	−22.6274			−0.353553
$9$	27.0000			0.333333
$10$		−	75.5318i		−	0.755318i
$11$		−	8.81477i		−	0.0728493i	−0.999336	−	0.0364247i	$-0.988403\pi$
$11$		−	8.81477i		−	0.0728493i	0.999336	−	0.0364247i	$-0.0115969\pi$
$12$	−41.5692			−0.288675
$13$	−136.925			−0.810209			−0.405105	−	0.914270i	$-0.632765\pi$
$13$	−136.925			−0.810209			−0.405105	+	0.914270i	$0.632765\pi$
$14$			188.745i			0.962986i
$15$		−	138.761i		−	0.616714i
$16$	64.0000			0.250000
$17$			184.077i			0.636946i	0.947932	+	0.318473i	$0.103170\pi$
$17$			184.077i			0.636946i	−0.947932	+	0.318473i	$0.896830\pi$
$18$	−76.3675			−0.235702
$19$		−	33.2701i		−	0.0921608i	−0.998938	−	0.0460804i	$-0.985327\pi$
$19$		−	33.2701i		−	0.0921608i	0.998938	−	0.0460804i	$-0.0146730\pi$
$20$			213.636i			0.534090i
$21$			346.747i			0.786275i
$22$			24.9319i			0.0515122i
$23$	493.509	−	190.498i	0.932910	−	0.360110i
$23$	493.509	−	190.498i	0.932910	−	0.360110i
$24$	117.576			0.204124
$25$	−88.1308			−0.141009
$26$	387.283			0.572904
$27$	−140.296			−0.192450
$28$		−	533.852i		−	0.680934i
$29$	1221.54			1.45249			0.726244	−	0.687437i	$-0.241264\pi$
$29$	1221.54			1.45249			0.726244	+	0.687437i	$0.241264\pi$
$30$			392.475i			0.436083i
$31$	1220.45			1.26998			0.634991	−	0.772519i	$-0.281004\pi$
$31$	1220.45			1.26998			0.634991	+	0.772519i	$0.281004\pi$
$32$	−181.019			−0.176777
$33$			45.8029i			0.0420596i
$34$		−	520.649i		−	0.450389i
$35$	1782.03			1.45472
$36$	216.000			0.166667
$37$			2059.16i			1.50413i	0.659088	+	0.752066i	$0.270942\pi$
$37$			2059.16i			1.50413i	−0.659088	+	0.752066i	$0.729058\pi$
$38$			94.1019i			0.0651676i
$39$	711.485			0.467774
$40$		−	604.254i		−	0.377659i
$41$	884.746			0.526321			0.263160	−	0.964752i	$-0.415235\pi$
$41$	884.746			0.526321			0.263160	+	0.964752i	$0.415235\pi$
$42$		−	980.749i		−	0.555980i
$43$			1572.25i			0.850323i	0.905117	+	0.425162i	$0.139783\pi$
$43$			1572.25i			0.850323i	−0.905117	+	0.425162i	$0.860217\pi$
$44$		−	70.5181i		−	0.0364247i
$45$			721.022i			0.356060i
$46$	−1395.86	+	538.810i	−0.659667	+	0.254636i
$47$	564.292			0.255451			0.127726	−	0.991810i	$-0.459232\pi$
$47$	564.292			0.255451			0.127726	+	0.991810i	$0.459232\pi$
$48$	−332.554			−0.144338
$49$	−2052.10			−0.854685
$50$	249.272			0.0997086
$51$		−	956.493i		−	0.367741i
$52$	−1095.40			−0.405105
$53$			3033.20i			1.07982i	0.841724	+	0.539908i	$0.181541\pi$
$53$			3033.20i			1.07982i	−0.841724	+	0.539908i	$0.818459\pi$
$54$	396.817			0.136083
$55$	235.394			0.0778162
$56$			1509.96i			0.481493i
$57$			172.876i			0.0532091i
$58$	−3455.04			−1.02706
$59$	5664.52			1.62727			0.813633	−	0.581378i	$-0.197486\pi$
$59$	5664.52			1.62727			0.813633	+	0.581378i	$0.197486\pi$
$60$		−	1110.09i		−	0.308357i
$61$		−	3378.10i		−	0.907847i	−0.891041	−	0.453924i	$-0.850024\pi$
$61$		−	3378.10i		−	0.907847i	0.891041	−	0.453924i	$-0.149976\pi$
$62$	−3451.96			−0.898013
$63$		−	1801.75i		−	0.453956i
$64$	512.000			0.125000
$65$		−	3656.52i		−	0.865449i
$66$		−	129.550i		−	0.0297406i
$67$		−	6983.41i		−	1.55567i	−0.628468	−	0.777836i	$-0.716318\pi$
$67$		−	6983.41i		−	1.55567i	0.628468	−	0.777836i	$-0.283682\pi$
$68$			1472.62i			0.318473i
$69$	−2564.35	+	989.856i	−0.538616	+	0.207909i
$70$	−5040.35			−1.02864
$71$	−3482.47			−0.690829			−0.345415	−	0.938450i	$-0.612262\pi$
$71$	−3482.47			−0.690829			−0.345415	+	0.938450i	$0.612262\pi$
$72$	−610.940			−0.117851
$73$	406.423			0.0762663			0.0381331	−	0.999273i	$-0.487859\pi$
$73$	406.423			0.0762663			0.0381331	+	0.999273i	$0.487859\pi$
$74$		−	5824.17i		−	1.06358i
$75$	457.941			0.0814118
$76$		−	266.160i		−	0.0460804i
$77$	−588.223			−0.0992112
$78$	−2012.38			−0.330766
$79$			103.984i			0.0166614i	0.999965	+	0.00833069i	$0.00265177\pi$
$79$			103.984i			0.0166614i	−0.999965	+	0.00833069i	$0.997348\pi$
$80$			1709.09i			0.267045i
$81$	729.000			0.111111
$82$	−2502.44			−0.372165
$83$			10105.6i			1.46692i	0.679733	+	0.733460i	$0.262096\pi$
$83$			10105.6i			1.46692i	−0.679733	+	0.733460i	$0.737904\pi$
$84$			2773.98i			0.393138i
$85$	−4915.69			−0.680373
$86$		−	4446.99i		−	0.601269i
$87$	−6347.32			−0.838594
$88$			199.455i			0.0257561i
$89$			7418.94i			0.936617i	0.883565	+	0.468308i	$0.155136\pi$
$89$			7418.94i			0.936617i	−0.883565	+	0.468308i	$0.844864\pi$
$90$		−	2039.36i		−	0.251773i
$91$			9137.24i			1.10340i
$92$	3948.08	−	1523.98i	0.466455	−	0.180055i
$93$	−6341.66			−0.733225
$94$	−1596.06			−0.180631
$95$	888.461			0.0984444
$96$	940.604			0.102062
$97$		−	16181.4i		−	1.71978i	−0.510481	−	0.859889i	$-0.670533\pi$
$97$		−	16181.4i		−	1.71978i	0.510481	−	0.859889i	$-0.329467\pi$
$98$	5804.21			0.604354
$99$		−	237.999i		−	0.0242831i
$100$	−705.047			−0.0705047
$101$	2091.11			0.204991			0.102496	−	0.994733i	$-0.467317\pi$
$101$	2091.11			0.204991			0.102496	+	0.994733i	$0.467317\pi$
$102$			2705.37i			0.260032i
$103$			9021.54i			0.850367i	0.905107	+	0.425184i	$0.139790\pi$
$103$			9021.54i			0.850367i	−0.905107	+	0.425184i	$0.860210\pi$
$104$	3098.27			0.286452
$105$	−9259.72			−0.839884
$106$		−	8579.19i		−	0.763545i
$107$			635.992i			0.0555500i	0.999614	+	0.0277750i	$0.00884219\pi$
$107$			635.992i			0.0555500i	−0.999614	+	0.0277750i	$0.991158\pi$
$108$	−1122.37			−0.0962250
$109$		−	5742.50i		−	0.483334i	−0.970359	−	0.241667i	$-0.922306\pi$
$109$		−	5742.50i		−	0.483334i	0.970359	−	0.241667i	$-0.0776942\pi$
$110$	−665.795			−0.0550244
$111$		−	10699.7i		−	0.868411i
$112$		−	4270.82i		−	0.340467i
$113$		−	21000.0i		−	1.64461i	−0.569049	−	0.822303i	$-0.692689\pi$
$113$		−	21000.0i		−	1.64461i	0.569049	−	0.822303i	$-0.307311\pi$
$114$		−	488.968i		−	0.0376245i
$115$	5087.15	+	13178.9i	0.384662	+	0.996516i
$116$	9772.34			0.726244
$117$	−3696.98			−0.270070
$118$	−16021.7			−1.15065
$119$	12283.8			0.867436
$120$			3139.80i			0.218041i
$121$	14563.3			0.994693
$122$			9554.71i			0.641945i
$123$	−4597.27			−0.303872
$124$	9763.62			0.634991
$125$			14336.8i			0.917557i
$126$			5096.12i			0.320995i
$127$	−9865.08			−0.611636			−0.305818	−	0.952090i	$-0.598930\pi$
$127$	−9865.08			−0.611636			−0.305818	+	0.952090i	$0.598930\pi$
$128$	−1448.15			−0.0883883
$129$		−	8169.64i		−	0.490934i
$130$			10342.2i			0.611965i
$131$	6324.59			0.368545			0.184272	−	0.982875i	$-0.441007\pi$
$131$	6324.59			0.368545			0.184272	+	0.982875i	$0.441007\pi$
$132$			366.423i			0.0210298i
$133$	−2220.16			−0.125511
$134$			19752.1i			1.10003i
$135$		−	3746.54i		−	0.205571i
$136$		−	4165.19i		−	0.225194i
$137$		−	11350.4i		−	0.604739i	−0.953191	−	0.302370i	$-0.902222\pi$
$137$		−	11350.4i		−	0.604739i	0.953191	−	0.302370i	$-0.0977777\pi$
$138$	7253.08	−	2799.74i	0.380859	−	0.147014i
$139$	19799.1			1.02474			0.512372	−	0.858764i	$-0.328767\pi$
$139$	19799.1			1.02474			0.512372	+	0.858764i	$0.328767\pi$
$140$	14256.3			0.727361
$141$	−2932.15			−0.147485
$142$	9849.92			0.488490
$143$			1206.96i			0.0590232i
$144$	1728.00			0.0833333
$145$			32620.7i			1.55152i
$146$	−1149.54			−0.0539284
$147$	10663.0			0.493453
$148$			16473.2i			0.752066i
$149$		−	1082.56i		−	0.0487616i	−0.999703	−	0.0243808i	$-0.992239\pi$
$149$		−	1082.56i		−	0.0487616i	0.999703	−	0.0243808i	$-0.00776142\pi$
$150$	−1295.25			−0.0575668
$151$	34090.1			1.49512			0.747558	−	0.664197i	$-0.231226\pi$
$151$	34090.1			1.49512			0.747558	+	0.664197i	$0.231226\pi$
$152$			752.816i			0.0325838i
$153$			4970.09i			0.212315i
$154$	1663.75			0.0701529
$155$			32591.6i			1.35657i
$156$	5691.88			0.233887
$157$		−	5006.67i		−	0.203119i	−0.994829	−	0.101559i	$-0.967617\pi$
$157$		−	5006.67i		−	0.203119i	0.994829	−	0.101559i	$-0.0323832\pi$
$158$		−	294.110i		−	0.0117814i
$159$		−	15761.0i		−	0.623432i
$160$		−	4834.03i		−	0.188829i
$161$	−12712.2	−	32932.6i	−0.490422	−	1.27050i
$162$	−2061.92			−0.0785674
$163$	−13052.4			−0.491265			−0.245632	−	0.969363i	$-0.578996\pi$
$163$	−13052.4			−0.491265			−0.245632	+	0.969363i	$0.578996\pi$
$164$	7077.96			0.263160
$165$	−1223.14			−0.0449272
$166$		−	28583.0i		−	1.03727i
$167$	30628.9			1.09824			0.549122	−	0.835742i	$-0.314962\pi$
$167$	30628.9			1.09824			0.549122	+	0.835742i	$0.314962\pi$
$168$		−	7846.00i		−	0.277990i
$169$	−9812.45			−0.343561
$170$	13903.7			0.481096
$171$		−	898.292i		−	0.0307203i
$172$			12578.0i			0.425162i
$173$	−11185.9			−0.373747			−0.186873	−	0.982384i	$-0.559835\pi$
$173$	−11185.9			−0.373747			−0.186873	+	0.982384i	$0.559835\pi$
$174$	17952.9			0.592976
$175$			5881.11i			0.192036i
$176$		−	564.145i		−	0.0182123i
$177$	−29433.7			−0.939503
$178$		−	20983.9i		−	0.662288i
$179$	−47448.9			−1.48088			−0.740440	−	0.672123i	$-0.765383\pi$
$179$	−47448.9			−1.48088			−0.740440	+	0.672123i	$0.765383\pi$
$180$			5768.17i			0.178030i
$181$			16174.1i			0.493700i	0.969054	+	0.246850i	$0.0793955\pi$
$181$			16174.1i			0.493700i	−0.969054	+	0.246850i	$0.920605\pi$
$182$		−	25844.0i		−	0.780220i
$183$			17553.1i			0.524146i
$184$	−11166.8	+	4310.48i	−0.329833	+	0.127318i
$185$	−54988.7			−1.60668
$186$	17936.9			0.518468
$187$	1622.60			0.0464010
$188$	4514.34			0.127726
$189$			9362.18i			0.262092i
$190$	−2512.95			−0.0696107
$191$		−	3552.05i		−	0.0973672i	−0.998814	−	0.0486836i	$-0.984497\pi$
$191$		−	3552.05i		−	0.0973672i	0.998814	−	0.0486836i	$-0.0155026\pi$
$192$	−2660.43			−0.0721688
$193$	28418.4			0.762929			0.381465	−	0.924383i	$-0.375420\pi$
$193$	28418.4			0.762929			0.381465	+	0.924383i	$0.375420\pi$
$194$			45767.9i			1.21607i
$195$			18999.9i			0.499668i
$196$	−16416.8			−0.427343
$197$	−14923.4			−0.384534			−0.192267	−	0.981343i	$-0.561584\pi$
$197$	−14923.4			−0.384534			−0.192267	+	0.981343i	$0.561584\pi$
$198$			673.162i			0.0171707i
$199$		−	71331.2i		−	1.80125i	−0.434599	−	0.900624i	$-0.643110\pi$
$199$		−	71331.2i		−	1.80125i	0.434599	−	0.900624i	$-0.356890\pi$
$200$	1994.17			0.0498543
$201$			36286.9i			0.898167i
$202$	−5914.57			−0.144951
$203$		−	81515.4i		−	1.97810i
$204$		−	7651.95i		−	0.183870i
$205$			23626.7i			0.562206i
$206$		−	25516.8i		−	0.601300i
$207$	13324.8	−	5143.45i	0.310970	−	0.120037i
$208$	−8763.22			−0.202552
$209$	−293.268			−0.00671385
$210$	26190.4			0.593887
$211$	−20415.9			−0.458568			−0.229284	−	0.973360i	$-0.573638\pi$
$211$	−20415.9			−0.458568			−0.229284	+	0.973360i	$0.573638\pi$
$212$			24265.6i			0.539908i
$213$	18095.5			0.398851
$214$		−	1798.86i		−	0.0392798i
$215$	−41986.1			−0.908299
$216$	3174.54			0.0680414
$217$		−	81442.7i		−	1.72955i
$218$			16242.2i			0.341769i
$219$	−2111.84			−0.0440323
$220$	1883.15			0.0389081
$221$		−	25204.8i		−	0.516059i
$222$			30263.3i			0.614059i
$223$	10531.8			0.211783			0.105892	−	0.994378i	$-0.466230\pi$
$223$	10531.8			0.211783			0.105892	+	0.994378i	$0.466230\pi$
$224$			12079.7i			0.240747i
$225$	−2379.53			−0.0470031
$226$			59396.9i			1.16291i
$227$			43696.8i			0.848004i	0.905661	+	0.424002i	$0.139375\pi$
$227$			43696.8i			0.848004i	−0.905661	+	0.424002i	$0.860625\pi$
$228$			1383.01i			0.0266045i
$229$			71464.4i			1.36276i	0.731931	+	0.681379i	$0.238619\pi$
$229$			71464.4i			1.36276i	−0.731931	+	0.681379i	$0.761381\pi$
$230$	−14388.6	−	37275.6i	−0.271997	−	0.704643i
$231$	3056.50			0.0572796
$232$	−27640.4			−0.513532
$233$	−26628.4			−0.490494			−0.245247	−	0.969461i	$-0.578869\pi$
$233$	−26628.4			−0.490494			−0.245247	+	0.969461i	$0.578869\pi$
$234$	10456.7			0.190968
$235$			15069.1i			0.272868i
$236$	45316.1			0.813633
$237$		−	540.315i		−	0.00961945i
$238$	−34743.7			−0.613370
$239$	23532.5			0.411977			0.205988	−	0.978554i	$-0.433959\pi$
$239$	23532.5			0.411977			0.205988	+	0.978554i	$0.433959\pi$
$240$		−	8880.68i		−	0.154179i
$241$			6120.68i			0.105382i	0.998611	+	0.0526909i	$0.0167798\pi$
$241$			6120.68i			0.105382i	−0.998611	+	0.0526909i	$0.983220\pi$
$242$	−41191.2			−0.703354
$243$	−3788.00			−0.0641500
$244$		−	27024.8i		−	0.453924i
$245$		−	54800.3i		−	0.912958i
$246$	13003.1			0.214870
$247$			4555.51i			0.0746696i
$248$	−27615.7			−0.449007
$249$		−	52510.3i		−	0.846927i
$250$		−	40550.7i		−	0.648811i
$251$			124768.i			1.98041i	0.139627	+	0.990204i	$0.455410\pi$
$251$			124768.i			1.98041i	−0.139627	+	0.990204i	$0.544590\pi$
$252$		−	14414.0i		−	0.226978i
$253$	−1679.19	−	4350.17i	−0.0262337	−	0.0679618i
$254$	27902.7			0.432492
$255$	25542.7			0.392813
$256$	4096.00			0.0625000
$257$	−67049.4			−1.01515			−0.507573	−	0.861608i	$-0.669457\pi$
$257$	−67049.4			−1.01515			−0.507573	+	0.861608i	$0.669457\pi$
$258$			23107.2i			0.347143i
$259$	137411.			2.04843
$260$		−	29252.2i		−	0.432725i
$261$	32981.6			0.484163
$262$	−17888.6			−0.260600
$263$		−	50313.6i		−	0.727402i	−0.931516	−	0.363701i	$-0.881513\pi$
$263$		−	50313.6i		−	0.727402i	0.931516	−	0.363701i	$-0.118487\pi$
$264$		−	1036.40i		−	0.0148703i
$265$	−81000.2			−1.15344
$266$	6279.57			0.0887496
$267$		−	38550.0i		−	0.540756i
$268$		−	55867.3i		−	0.777836i
$269$	−31067.8			−0.429344			−0.214672	−	0.976686i	$-0.568868\pi$
$269$	−31067.8			−0.429344			−0.214672	+	0.976686i	$0.568868\pi$
$270$			10596.8i			0.145361i
$271$	10.6034			0.000144379			7.21896e−5	−	1.00000i	$-0.499977\pi$
$271$	10.6034			0.000144379			7.21896e−5		1.00000i	$0.499977\pi$
$272$			11780.9i			0.159236i
$273$		−	47478.5i		−	0.637047i
$274$			32103.6i			0.427615i
$275$			776.852i			0.0102724i
$276$	−20514.8	+	7918.85i	−0.269308	+	0.103955i
$277$	−110743.			−1.44330			−0.721650	−	0.692258i	$-0.756616\pi$
$277$	−110743.			−1.44330			−0.721650	+	0.692258i	$0.756616\pi$
$278$	−56000.3			−0.724604
$279$	32952.2			0.423327
$280$	−40322.8			−0.514322
$281$			95523.4i			1.20975i	0.796319	+	0.604877i	$0.206778\pi$
$281$			95523.4i			1.20975i	−0.796319	+	0.604877i	$0.793222\pi$
$282$	8293.36			0.104288
$283$		−	39396.5i		−	0.491910i	−0.969281	−	0.245955i	$-0.920899\pi$
$283$		−	39396.5i		−	0.491910i	0.969281	−	0.245955i	$-0.0791015\pi$
$284$	−27859.8			−0.345415
$285$	−4616.58			−0.0568369
$286$		−	3413.81i		−	0.0417357i
$287$		−	59040.4i		−	0.716780i
$288$	−4887.52			−0.0589256
$289$	49636.6			0.594300
$290$		−	92265.3i		−	1.09709i
$291$			84081.0i			0.992914i
$292$	3251.38			0.0381331
$293$		−	81900.7i		−	0.954009i	−0.878901	−	0.477005i	$-0.841722\pi$
$293$		−	81900.7i		−	0.954009i	0.878901	−	0.477005i	$-0.158278\pi$
$294$	−30159.6			−0.348924
$295$			151268.i			1.73821i
$296$		−	46593.4i		−	0.531791i
$297$			1236.68i			0.0140199i
$298$			3061.93i			0.0344796i
$299$	−67573.9	+	26084.0i	−0.755852	+	0.291764i
$300$	3663.53			0.0407059
$301$	104919.			1.15803
$302$	−96421.5			−1.05721
$303$	−10865.8			−0.118352
$304$		−	2129.28i		−	0.0230402i
$305$	90210.5			0.969744
$306$		−	14057.5i		−	0.150130i
$307$	160322.			1.70105			0.850524	−	0.525936i	$-0.176285\pi$
$307$	160322.			1.70105			0.850524	+	0.525936i	$0.176285\pi$
$308$	−4705.78			−0.0496056
$309$		−	46877.3i		−	0.490960i
$310$		−	92183.0i		−	0.959240i
$311$	−50635.7			−0.523523			−0.261762	−	0.965133i	$-0.584303\pi$
$311$	−50635.7			−0.523523			−0.261762	+	0.965133i	$0.584303\pi$
$312$	−16099.1			−0.165383
$313$			175913.i			1.79560i	0.440408	+	0.897798i	$0.354834\pi$
$313$			175913.i			1.79560i	−0.440408	+	0.897798i	$0.645166\pi$
$314$			14161.0i			0.143627i
$315$	48114.9			0.484907
$316$			831.869i			0.00833069i
$317$	−15238.4			−0.151642			−0.0758212	−	0.997121i	$-0.524158\pi$
$317$	−15238.4			−0.151642			−0.0758212	+	0.997121i	$0.524158\pi$
$318$			44578.8i			0.440833i
$319$		−	10767.6i		−	0.105813i
$320$			13672.7i			0.133523i
$321$		−	3304.71i		−	0.0320718i
$322$	35955.6	+	93147.6i	0.346781	+	0.898380i
$323$	6124.26			0.0587014
$324$	5832.00			0.0555556
$325$	12067.3			0.114247
$326$	36917.8			0.347376
$327$			29838.9i			0.279053i
$328$	−20019.5			−0.186083
$329$		−	37656.1i		−	0.347891i
$330$	3459.57			0.0317683
$331$	−10413.5			−0.0950473			−0.0475237	−	0.998870i	$-0.515133\pi$
$331$	−10413.5			−0.0950473			−0.0475237	+	0.998870i	$0.515133\pi$
$332$			80844.9i			0.733460i
$333$			55597.2i			0.501377i
$334$	−86631.6			−0.776575
$335$	186488.			1.66174
$336$			22191.8i			0.196569i
$337$		−	45745.9i		−	0.402802i	−0.979509	−	0.201401i	$-0.935451\pi$
$337$		−	45745.9i		−	0.402802i	0.979509	−	0.201401i	$-0.0645495\pi$
$338$	27753.8			0.242934
$339$			109119.i			0.949514i
$340$	−39325.5			−0.340186
$341$		−	10758.0i		−	0.0925173i
$342$			2540.75i			0.0217225i
$343$		−	23282.7i		−	0.197899i
$344$		−	35575.9i		−	0.300635i
$345$	−26433.6	−	68479.7i	−0.222085	−	0.575339i
$346$	31638.4			0.264279
$347$	202424.			1.68114			0.840570	−	0.541704i	$-0.182220\pi$
$347$	202424.			1.68114			0.840570	+	0.541704i	$0.182220\pi$
$348$	−50778.6			−0.419297
$349$	160230.			1.31550			0.657752	−	0.753234i	$-0.271507\pi$
$349$	160230.			1.31550			0.657752	+	0.753234i	$0.271507\pi$
$350$		−	16634.3i		−	0.135790i
$351$	19210.1			0.155925
$352$			1595.64i			0.0128781i
$353$	−96178.5			−0.771842			−0.385921	−	0.922532i	$-0.626116\pi$
$353$	−96178.5			−0.771842			−0.385921	+	0.922532i	$0.626116\pi$
$354$	83251.0			0.664329
$355$		−	92997.7i		−	0.737930i
$356$			59351.5i			0.468308i
$357$	−63828.3			−0.500814
$358$	134206.			1.04714
$359$			14946.4i			0.115970i	0.998317	+	0.0579851i	$0.0184676\pi$
$359$			14946.4i			0.115970i	−0.998317	+	0.0579851i	$0.981532\pi$
$360$		−	16314.9i		−	0.125886i
$361$	129214.			0.991506
$362$		−	45747.3i		−	0.349099i
$363$	−75673.1			−0.574286
$364$			73097.9i			0.551699i
$365$			10853.3i			0.0814661i
$366$		−	49647.7i		−	0.370627i
$367$			133014.i			0.987566i	0.869585	+	0.493783i	$0.164386\pi$
$367$			133014.i			0.987566i	−0.869585	+	0.493783i	$0.835614\pi$
$368$	31584.6	−	12191.9i	0.233228	−	0.0900274i
$369$	23888.1			0.175440
$370$	155532.			1.13610
$371$	202410.			1.47057
$372$	−50733.3			−0.366612
$373$		−	178722.i		−	1.28458i	−0.766462	−	0.642290i	$-0.777984\pi$
$373$		−	178722.i		−	1.28458i	0.766462	−	0.642290i	$-0.222016\pi$
$374$	−4589.40			−0.0328105
$375$		−	74496.3i		−	0.529752i
$376$	−12768.5			−0.0903157
$377$	−167260.			−1.17682
$378$		−	26480.2i		−	0.185327i
$379$		−	199044.i		−	1.38571i	−0.721079	−	0.692853i	$-0.756353\pi$
$379$		−	199044.i		−	1.38571i	0.721079	−	0.692853i	$-0.243647\pi$
$380$	7107.69			0.0492222
$381$	51260.4			0.353128
$382$			10046.7i			0.0688490i
$383$			116619.i			0.795007i	0.917601	+	0.397504i	$0.130123\pi$
$383$			116619.i			0.795007i	−0.917601	+	0.397504i	$0.869877\pi$
$384$	7524.83			0.0510310
$385$		−	15708.2i		−	0.105975i
$386$	−80379.3			−0.539473
$387$			42450.7i			0.283441i
$388$		−	129451.i		−	0.859889i
$389$			283865.i			1.87591i	0.346758	+	0.937955i	$0.387283\pi$
$389$			283865.i			1.87591i	−0.346758	+	0.937955i	$0.612717\pi$
$390$		−	53739.7i		−	0.353318i
$391$	35066.3	+	90843.9i	0.229370	+	0.594213i
$392$	46433.7			0.302177
$393$	−32863.5			−0.212779
$394$	42209.6			0.271906
$395$	−2776.83			−0.0177973
$396$		−	1903.99i		−	0.0121416i
$397$	161458.			1.02442			0.512212	−	0.858859i	$-0.328826\pi$
$397$	161458.			1.02442			0.512212	+	0.858859i	$0.328826\pi$
$398$			201755.i			1.27368i
$399$	11536.3			0.0724638
$400$	−5640.37			−0.0352523
$401$			172741.i			1.07426i	0.843501	+	0.537128i	$0.180491\pi$
$401$			172741.i			1.07426i	−0.843501	+	0.537128i	$0.819509\pi$
$402$		−	102635.i		−	0.635100i
$403$	−167111.			−1.02895
$404$	16728.9			0.102496
$405$			19467.6i			0.118687i
$406$			230560.i			1.39873i
$407$	18151.0			0.109575
$408$			21643.0i			0.130016i
$409$	−305480.			−1.82615			−0.913073	−	0.407796i	$-0.866297\pi$
$409$	−305480.			−1.82615			−0.913073	+	0.407796i	$0.866297\pi$
$410$		−	66826.4i		−	0.397539i
$411$			58978.2i			0.349146i
$412$			72172.3i			0.425184i
$413$		−	378002.i		−	2.21612i
$414$	−37688.1	+	14547.9i	−0.219889	+	0.0848786i
$415$	−269865.			−1.56694
$416$	24786.1			0.143226
$417$	−102879.			−0.591636
$418$	829.487			0.00474741
$419$			181747.i			1.03524i	0.855612	+	0.517619i	$0.173181\pi$
$419$			181747.i			1.03524i	−0.855612	+	0.517619i	$0.826819\pi$
$420$	−74077.7			−0.419942
$421$		−	92369.5i		−	0.521152i	−0.965453	−	0.260576i	$-0.916088\pi$
$421$		−	92369.5i		−	0.521152i	0.965453	−	0.260576i	$-0.0839125\pi$
$422$	57744.9			0.324257
$423$	15235.9			0.0851504
$424$		−	68633.5i		−	0.381772i
$425$		−	16222.9i		−	0.0898152i
$426$	−51181.7			−0.282030
$427$	−225426.			−1.23637
$428$			5087.93i			0.0277750i
$429$		−	6271.57i		−	0.0340770i
$430$	118755.			0.642264
$431$		−	313163.i		−	1.68584i	−0.538041	−	0.842918i	$-0.680836\pi$
$431$		−	313163.i		−	1.68584i	0.538041	−	0.842918i	$-0.319164\pi$
$432$	−8978.95			−0.0481125
$433$			102902.i			0.548844i	0.961609	+	0.274422i	$0.0884865\pi$
$433$			102902.i			0.548844i	−0.961609	+	0.274422i	$0.911514\pi$
$434$			230355.i			1.22298i
$435$		−	169502.i		−	0.895770i
$436$		−	45940.0i		−	0.241667i
$437$	−6337.88	−	16419.1i	−0.0331880	−	0.0859778i
$438$	5973.17			0.0311356
$439$	−195379.			−1.01379			−0.506895	−	0.862008i	$-0.669207\pi$
$439$	−195379.			−1.01379			−0.506895	+	0.862008i	$0.669207\pi$
$440$	−5326.36			−0.0275122
$441$	−55406.7			−0.284895
$442$			71290.1i			0.364909i
$443$	228229.			1.16296			0.581478	−	0.813562i	$-0.302475\pi$
$443$	228229.			1.16296			0.581478	+	0.813562i	$0.302475\pi$
$444$		−	85597.5i		−	0.434205i
$445$	−198119.			−1.00048
$446$	−29788.3			−0.149753
$447$			5625.13i			0.0281525i
$448$		−	34166.6i		−	0.170234i
$449$	−201941.			−1.00169			−0.500843	−	0.865538i	$-0.666976\pi$
$449$	−201941.			−1.00169			−0.500843	+	0.865538i	$0.666976\pi$
$450$	6730.33			0.0332362
$451$		−	7798.82i		−	0.0383421i
$452$		−	168000.i		−	0.822303i
$453$	−177138.			−0.863206
$454$		−	123593.i		−	0.599629i
$455$	−244006.			−1.17863
$456$		−	3911.74i		−	0.0188123i
$457$		−	126293.i		−	0.604711i	−0.953195	−	0.302356i	$-0.902227\pi$
$457$		−	126293.i		−	0.604711i	0.953195	−	0.302356i	$-0.0977730\pi$
$458$		−	202132.i		−	0.963615i
$459$		−	25825.3i		−	0.122580i
$460$	40697.2	+	105431.i	0.192331	+	0.498258i
$461$	329484.			1.55036			0.775180	−	0.631740i	$-0.217659\pi$
$461$	329484.			1.55036			0.775180	+	0.631740i	$0.217659\pi$
$462$	−8645.08			−0.0405028
$463$	−188711.			−0.880311			−0.440155	−	0.897922i	$-0.645077\pi$
$463$	−188711.			−0.880311			−0.440155	+	0.897922i	$0.645077\pi$
$464$	78178.7			0.363122
$465$		−	169351.i		−	0.783216i
$466$	75316.5			0.346832
$467$		−	164612.i		−	0.754792i	−0.926052	−	0.377396i	$-0.876820\pi$
$467$		−	164612.i		−	0.754792i	0.926052	−	0.377396i	$-0.123180\pi$
$468$	−29575.9			−0.135035
$469$	−466014.			−2.11862
$470$		−	42622.0i		−	0.192947i
$471$			26015.4i			0.117271i
$472$	−128173.			−0.575326
$473$	13859.0			0.0619455
$474$			1528.24i			0.00680198i
$475$			2932.12i			0.0129955i
$476$	98270.1			0.433718
$477$			81896.5i			0.359939i
$478$	−66560.0			−0.291311
$479$		−	306234.i		−	1.33470i	−0.744745	−	0.667349i	$-0.767429\pi$
$479$		−	306234.i		−	1.33470i	0.744745	−	0.667349i	$-0.232571\pi$
$480$			25118.4i			0.109021i
$481$		−	281951.i		−	1.21866i
$482$		−	17311.9i		−	0.0745162i
$483$	66054.7	+	171123.i	0.283145	+	0.733524i
$484$	116506.			0.497346
$485$	432116.			1.83703
$486$	10714.1			0.0453609
$487$	−365176.			−1.53973			−0.769864	−	0.638208i	$-0.779676\pi$
$487$	−365176.			−1.53973			−0.769864	+	0.638208i	$0.779676\pi$
$488$			76437.6i			0.320972i
$489$	67822.3			0.283632
$490$			154999.i			0.645559i
$491$	380595.			1.57870			0.789351	−	0.613942i	$-0.210417\pi$
$491$	380595.			1.57870			0.789351	+	0.613942i	$0.210417\pi$
$492$	−36778.2			−0.151936
$493$			224858.i			0.925156i
$494$		−	12884.9i		−	0.0527993i
$495$	6355.64			0.0259387
$496$	78109.0			0.317496
$497$			232391.i			0.940819i
$498$			148522.i			0.598868i
$499$	−15929.0			−0.0639716			−0.0319858	−	0.999488i	$-0.510183\pi$
$499$	−15929.0			−0.0639716			−0.0319858	+	0.999488i	$0.510183\pi$
$500$			114695.i			0.458779i
$501$	−159152.			−0.634071
$502$		−	352896.i		−	1.40036i
$503$			239167.i			0.945289i	0.881253	+	0.472645i	$0.156701\pi$
$503$			239167.i			0.945289i	−0.881253	+	0.472645i	$0.843299\pi$
$504$			40769.0i			0.160498i
$505$			55842.2i			0.218968i
$506$	4749.48	+	12304.1i	0.0185500	+	0.0480563i
$507$	50987.0			0.198355
$508$	−78920.6			−0.305818
$509$	−297194.			−1.14711			−0.573555	−	0.819167i	$-0.694436\pi$
$509$	−297194.			−1.14711			−0.573555	+	0.819167i	$0.694436\pi$
$510$	−72245.6			−0.277761
$511$		−	27121.2i		−	0.103865i
$512$	−11585.2			−0.0441942
$513$			4667.66i			0.0177364i
$514$	189644.			0.717817
$515$	−240916.			−0.908345
$516$		−	65357.1i		−	0.245467i
$517$		−	4974.10i		−	0.0186094i
$518$	−388656.			−1.44846
$519$	58123.5			0.215783
$520$			82737.7i			0.305983i
$521$			490440.i			1.80680i	0.428797	+	0.903401i	$0.358938\pi$
$521$			490440.i			1.80680i	−0.428797	+	0.903401i	$0.641062\pi$
$522$	−93286.2			−0.342355
$523$		−	54355.5i		−	0.198719i	−0.995052	−	0.0993596i	$-0.968321\pi$
$523$		−	54355.5i		−	0.198719i	0.995052	−	0.0993596i	$-0.0316794\pi$
$524$	50596.7			0.184272
$525$		−	30559.1i		−	0.110872i
$526$			142308.i			0.514351i
$527$			224658.i			0.808910i
$528$			2931.38i			0.0105149i
$529$	207262.	−	188025.i	0.740642	−	0.671900i
$530$	229103.			0.815604
$531$	152942.			0.542422
$532$	−17761.3			−0.0627555
$533$	−121144.			−0.426430
$534$			109036.i			0.382372i
$535$	−16983.8			−0.0593374
$536$			158016.i			0.550013i
$537$	246552.			0.854986
$538$	87873.0			0.303592
$539$			18088.8i			0.0622632i
$540$		−	29972.3i		−	0.102786i
$541$	290778.			0.993498			0.496749	−	0.867894i	$-0.334527\pi$
$541$	290778.			0.993498			0.496749	+	0.867894i	$0.334527\pi$
$542$	−29.9908			−0.000102092
$543$		−	84043.1i		−	0.285038i
$544$		−	33321.5i		−	0.112597i
$545$	153351.			0.516288
$546$			134289.i			0.450460i
$547$	−361239.			−1.20731			−0.603656	−	0.797245i	$-0.706290\pi$
$547$	−361239.			−1.20731			−0.603656	+	0.797245i	$0.706290\pi$
$548$		−	90802.8i		−	0.302370i
$549$		−	91208.7i		−	0.302616i
$550$		−	2197.27i		−	0.00726370i
$551$		−	40640.8i		−	0.133863i
$552$	58024.6	−	22397.9i	0.190429	−	0.0735071i
$553$	6938.99			0.0226906
$554$	313229.			1.02057
$555$	285730.			0.927619
$556$	158393.			0.512372
$557$		−	423652.i		−	1.36552i	−0.730641	−	0.682762i	$-0.760779\pi$
$557$		−	423652.i		−	1.36552i	0.730641	−	0.682762i	$-0.239221\pi$
$558$	−93203.0			−0.299338
$559$		−	215281.i		−	0.688940i
$560$	114050.			0.363680
$561$	−8431.27			−0.0267897
$562$		−	270181.i		−	0.855425i
$563$			278440.i			0.878446i	0.898378	+	0.439223i	$0.144746\pi$
$563$			278440.i			0.878446i	−0.898378	+	0.439223i	$0.855254\pi$
$564$	−23457.2			−0.0737424
$565$	560794.			1.75674
$566$			111430.i			0.347833i
$567$		−	48647.3i		−	0.151319i
$568$	78799.3			0.244245
$569$		−	22300.7i		−	0.0688803i	−0.999407	−	0.0344401i	$-0.989035\pi$
$569$		−	22300.7i		−	0.0688803i	0.999407	−	0.0344401i	$-0.0109648\pi$
$570$	13057.7			0.0401898
$571$		−	351483.i		−	1.07803i	−0.842295	−	0.539017i	$-0.818796\pi$
$571$		−	351483.i		−	1.07803i	0.842295	−	0.539017i	$-0.181204\pi$
$572$			9655.72i			0.0295116i
$573$			18457.0i			0.0562150i
$574$			166992.i			0.506840i
$575$	−43493.4	+	16788.7i	−0.131549	+	0.0507788i
$576$	13824.0			0.0416667
$577$	331198.			0.994801			0.497401	−	0.867521i	$-0.334288\pi$
$577$	331198.			0.994801			0.497401	+	0.867521i	$0.334288\pi$
$578$	−140393.			−0.420234
$579$	−147666.			−0.440478
$580$			260966.i			0.775760i
$581$	674363.			1.99775
$582$		−	237817.i		−	0.702096i
$583$	26737.0			0.0786638
$584$	−9196.30			−0.0269642
$585$		−	98726.2i		−	0.288483i
$586$			231650.i			0.674586i
$587$	243067.			0.705423			0.352711	−	0.935732i	$-0.385260\pi$
$587$	243067.			0.705423			0.352711	+	0.935732i	$0.385260\pi$
$588$	85304.2			0.246726
$589$		−	40604.5i		−	0.117043i
$590$		−	427851.i		−	1.22910i
$591$	77544.1			0.222011
$592$			131786.i			0.376033i
$593$	−103094.			−0.293172			−0.146586	−	0.989198i	$-0.546829\pi$
$593$	−103094.			−0.293172			−0.146586	+	0.989198i	$0.546829\pi$
$594$		−	3497.85i		−	0.00991353i
$595$			328032.i			0.926578i
$596$		−	8660.45i		−	0.0243808i
$597$			370648.i			1.03995i
$598$	191128.	−	73776.7i	0.534468	−	0.206308i
$599$	−354671.			−0.988490			−0.494245	−	0.869323i	$-0.664555\pi$
$599$	−354671.			−0.988490			−0.494245	+	0.869323i	$0.664555\pi$
$600$	−10362.0			−0.0287834
$601$	681636.			1.88714			0.943569	−	0.331175i	$-0.107445\pi$
$601$	681636.			1.88714			0.943569	+	0.331175i	$0.107445\pi$
$602$	−296754.			−0.818850
$603$		−	188552.i		−	0.518557i
$604$	272721.			0.747558
$605$			388906.i			1.06251i
$606$	30733.0			0.0836873
$607$	−674049.			−1.82942			−0.914711	−	0.404109i	$-0.867582\pi$
$607$	−674049.			−1.82942			−0.914711	+	0.404109i	$0.867582\pi$
$608$			6022.52i			0.0162919i
$609$			423567.i			1.14206i
$610$	−255154.			−0.685713
$611$	−77265.9			−0.206969
$612$			39760.7i			0.106158i
$613$			432868.i			1.15195i	0.817467	+	0.575976i	$0.195378\pi$
$613$			432868.i			1.15195i	−0.817467	+	0.575976i	$0.804622\pi$
$614$	−453459.			−1.20282
$615$		−	122768.i		−	0.324590i
$616$	13310.0			0.0350764
$617$			366413.i			0.962500i	0.876583	+	0.481250i	$0.159817\pi$
$617$			366413.i			0.962500i	−0.876583	+	0.481250i	$0.840183\pi$
$618$			132589.i			0.347161i
$619$		−	575223.i		−	1.50126i	−0.660724	−	0.750629i	$-0.729751\pi$
$619$		−	575223.i		−	1.50126i	0.660724	−	0.750629i	$-0.270249\pi$
$620$			260733.i			0.678285i
$621$	−69237.5	+	26726.1i	−0.179539	+	0.0693031i
$622$	143219.			0.370187
$623$	495078.			1.27555
$624$	45535.0			0.116944
$625$	−437940.			−1.12113
$626$		−	497556.i		−	1.26968i
$627$	1523.86			0.00387624
$628$		−	40053.4i		−	0.101559i
$629$	−379044.			−0.958050
$630$	−136089.			−0.342881
$631$			544431.i			1.36736i	0.729780	+	0.683682i	$0.239622\pi$
$631$			544431.i			1.36736i	−0.729780	+	0.683682i	$0.760378\pi$
$632$		−	2352.88i		−	0.00589068i
$633$	106084.			0.264754
$634$	43100.7			0.107227
$635$		−	263442.i		−	0.653338i
$636$		−	126088.i		−	0.311716i
$637$	280984.			0.692474
$638$			30455.4i			0.0748209i
$639$	−94026.7			−0.230276
$640$		−	38672.3i		−	0.0944147i
$641$		−	437564.i		−	1.06494i	−0.846449	−	0.532470i	$-0.821264\pi$
$641$		−	437564.i		−	1.06494i	0.846449	−	0.532470i	$-0.178736\pi$
$642$			9347.13i			0.0226782i
$643$			9226.04i			0.0223148i	0.999938	+	0.0111574i	$0.00355159\pi$
$643$			9226.04i			0.0223148i	−0.999938	+	0.0111574i	$0.996448\pi$
$644$	−101698.	−	263461.i	−0.245211	−	0.635250i
$645$	218166.			0.524406
$646$	−17322.0			−0.0415082
$647$	−78818.7			−0.188287			−0.0941436	−	0.995559i	$-0.530011\pi$
$647$	−78818.7			−0.188287			−0.0941436	+	0.995559i	$0.530011\pi$
$648$	−16495.4			−0.0392837
$649$		−	49931.4i		−	0.118545i
$650$	−34131.6			−0.0807848
$651$			423189.i			0.998555i
$652$	−104419.			−0.245632
$653$	−483227.			−1.13325			−0.566624	−	0.823977i	$-0.691751\pi$
$653$	−483227.			−1.13325			−0.566624	+	0.823977i	$0.691751\pi$
$654$		−	84397.1i		−	0.197320i
$655$			168895.i			0.393672i
$656$	56623.7			0.131580
$657$	10973.4			0.0254221
$658$			106507.i			0.245996i
$659$		−	657389.i		−	1.51374i	−0.653564	−	0.756871i	$-0.726727\pi$
$659$		−	657389.i		−	1.51374i	0.653564	−	0.756871i	$-0.273273\pi$
$660$	−9785.14			−0.0224636
$661$			783821.i			1.79397i	0.442066	+	0.896983i	$0.354246\pi$
$661$			783821.i			1.79397i	−0.442066	+	0.896983i	$0.645754\pi$
$662$	29453.8			0.0672086
$663$			130968.i			0.297947i
$664$		−	228664.i		−	0.518635i
$665$		−	59288.4i		−	0.134068i
$666$		−	157253.i		−	0.354527i
$667$	602843.	−	232701.i	1.35504	−	0.523055i
$668$	245031.			0.549122
$669$	−54724.7			−0.122273
$670$	−527469.			−1.17503
$671$	−29777.1			−0.0661360
$672$		−	62768.0i		−	0.138995i
$673$	626018.			1.38215			0.691077	−	0.722781i	$-0.257136\pi$
$673$	626018.			1.38215			0.691077	+	0.722781i	$0.257136\pi$
$674$			129389.i			0.284824i
$675$	12364.4			0.0271373
$676$	−78499.6			−0.171781
$677$		−	2298.21i		−	0.00501432i	−0.999997	−	0.00250716i	$-0.999202\pi$
$677$		−	2298.21i		−	0.00501432i	0.999997	−	0.00250716i	$-0.000798054\pi$
$678$		−	308635.i		−	0.671408i
$679$	−1.07981e6			−2.34211
$680$	111229.			0.240548
$681$		−	227055.i		−	0.489595i
$682$			30428.2i			0.0654196i
$683$	−815691.			−1.74857			−0.874287	−	0.485409i	$-0.838671\pi$
$683$	−815691.			−1.74857			−0.874287	+	0.485409i	$0.838671\pi$
$684$		−	7186.33i		−	0.0153601i
$685$	303106.			0.645971
$686$			65853.3i			0.139936i
$687$		−	371340.i		−	0.786789i
$688$			100624.i			0.212581i
$689$		−	415322.i		−	0.874876i
$690$	74765.6	+	193690.i	0.157038	+	0.406826i
$691$	849576.			1.77929			0.889644	−	0.456655i	$-0.150953\pi$
$691$	849576.			1.77929			0.889644	+	0.456655i	$0.150953\pi$
$692$	−89486.9			−0.186873
$693$	−15882.0			−0.0330704
$694$	−572542.			−1.18874
$695$			528725.i			1.09461i
$696$	143623.			0.296488
$697$			162862.i			0.335238i
$698$	−453198.			−0.930202
$699$	138365.			0.283187
$700$			47048.8i			0.0960181i
$701$		−	488828.i		−	0.994763i	−0.867532	−	0.497382i	$-0.834295\pi$
$701$		−	488828.i		−	0.994763i	0.867532	−	0.497382i	$-0.165705\pi$
$702$	−54334.4			−0.110255
$703$	68508.2			0.138622
$704$		−	4513.16i		−	0.00910616i
$705$		−	78301.5i		−	0.157540i
$706$	272034.			0.545775
$707$		−	139543.i		−	0.279171i
$708$	−235470.			−0.469751
$709$			932925.i			1.85590i	0.372706	+	0.927950i	$0.378430\pi$
$709$			932925.i			1.85590i	−0.372706	+	0.927950i	$0.621570\pi$
$710$			263037.i			0.521796i
$711$			2807.56i			0.00555379i
$712$		−	167872.i		−	0.331144i
$713$	602305.	−	232494.i	1.18478	−	0.457333i
$714$	180534.			0.354129
$715$	−32231.4			−0.0630474
$716$	−379591.			−0.740440
$717$	−122279.			−0.237855
$718$		−	42274.7i		−	0.0820033i
$719$	−74115.8			−0.143368			−0.0716841	−	0.997427i	$-0.522837\pi$
$719$	−74115.8			−0.143368			−0.0716841	+	0.997427i	$0.522837\pi$
$720$			46145.4i			0.0890150i
$721$	602022.			1.15809
$722$	−365473.			−0.701101
$723$		−	31804.0i		−	0.0608422i
$724$			129393.i			0.246850i
$725$	−107656.			−0.204814
$726$	214036.			0.406082
$727$		−	864443.i		−	1.63556i	−0.575528	−	0.817782i	$-0.695204\pi$
$727$		−	864443.i		−	1.63556i	0.575528	−	0.817782i	$-0.304796\pi$
$728$		−	206752.i		−	0.390110i
$729$	19683.0			0.0370370
$730$		−	30697.8i		−	0.0576052i
$731$	−289415.			−0.541610
$732$			140425.i			0.262073i
$733$		−	526886.i		−	0.980637i	−0.871543	−	0.490319i	$-0.836880\pi$
$733$		−	526886.i		−	0.980637i	0.871543	−	0.490319i	$-0.163120\pi$
$734$		−	376221.i		−	0.698314i
$735$			284751.i			0.527097i
$736$	−89334.7	+	34483.8i	−0.164917	+	0.0636590i
$737$	−61557.1			−0.113330
$738$	−67565.8			−0.124055
$739$	90319.3			0.165383			0.0826917	−	0.996575i	$-0.473648\pi$
$739$	90319.3			0.165383			0.0826917	+	0.996575i	$0.473648\pi$
$740$	−439910.			−0.803342
$741$		−	23671.1i		−	0.0431105i
$742$	−572503.			−1.03985
$743$		−	79340.7i		−	0.143720i	−0.997415	−	0.0718602i	$-0.977106\pi$
$743$		−	79340.7i		−	0.143720i	0.997415	−	0.0718602i	$-0.0228935\pi$
$744$	143495.			0.259234
$745$	28909.1			0.0520862
$746$			505503.i			0.908335i
$747$			272852.i			0.488973i
$748$	12980.8			0.0232005
$749$	42440.7			0.0756518
$750$			210707.i			0.374591i
$751$		−	825836.i		−	1.46424i	−0.681173	−	0.732122i	$-0.738530\pi$
$751$		−	825836.i		−	1.46424i	0.681173	−	0.732122i	$-0.261470\pi$
$752$	36114.7			0.0638628
$753$		−	648312.i		−	1.14339i
$754$	473083.			0.832137
$755$			910360.i			1.59705i
$756$			74897.4i			0.131046i
$757$			391369.i			0.682960i	0.939889	+	0.341480i	$0.110928\pi$
$757$			391369.i			0.682960i	−0.939889	+	0.341480i	$0.889072\pi$
$758$			562982.i			0.979842i
$759$	8725.35	+	22604.1i	0.0151461	+	0.0392378i
$760$	−20103.6			−0.0348053
$761$	48843.0			0.0843398			0.0421699	−	0.999110i	$-0.486573\pi$
$761$	48843.0			0.0843398			0.0421699	+	0.999110i	$0.486573\pi$
$762$	−144986.			−0.249699
$763$	−383206.			−0.658238
$764$		−	28416.4i		−	0.0486836i
$765$	−132724.			−0.226791
$766$		−	329848.i		−	0.562155i
$767$	−775616.			−1.31843
$768$	−21283.4			−0.0360844
$769$			32257.6i			0.0545480i	0.999628	+	0.0272740i	$0.00868266\pi$
$769$			32257.6i			0.0545480i	−0.999628	+	0.0272740i	$0.991317\pi$
$770$			44429.5i			0.0749359i
$771$	348399.			0.586095
$772$	227347.			0.381465
$773$		−	261048.i		−	0.436879i	−0.975850	−	0.218440i	$-0.929903\pi$
$773$		−	261048.i		−	0.436879i	0.975850	−	0.218440i	$-0.0700967\pi$
$774$		−	120069.i		−	0.200423i
$775$	−107560.			−0.179079
$776$			366143.i			0.608033i
$777$	−714007.			−1.18266
$778$		−	802890.i		−	1.32647i
$779$		−	29435.5i		−	0.0485062i
$780$			151999.i			0.249834i
$781$			30697.2i			0.0503264i
$782$	−99182.6	−	256945.i	−0.162189	−	0.420172i
$783$	−171378.			−0.279531
$784$	−131334.			−0.213671
$785$	133701.			0.216967
$786$	92952.1			0.150458
$787$			769153.i			1.24183i	0.783877	+	0.620917i	$0.213239\pi$
$787$			769153.i			1.24183i	−0.783877	+	0.620917i	$0.786761\pi$
$788$	−119387.			−0.192267
$789$			261437.i			0.419966i
$790$	7854.07			0.0125846
$791$	−1.40136e6			−2.23974
$792$			5385.30i			0.00858537i
$793$			462547.i			0.735546i
$794$	−456673.			−0.724377
$795$	420889.			0.665938
$796$		−	570650.i		−	0.900624i
$797$		−	358409.i		−	0.564238i	−0.959379	−	0.282119i	$-0.908963\pi$
$797$		−	358409.i		−	0.564238i	0.959379	−	0.282119i	$-0.0910373\pi$
$798$	−32629.6			−0.0512396
$799$			103873.i			0.162709i
$800$	15953.4			0.0249272
$801$			200311.i			0.312206i
$802$		−	488586.i		−	0.759613i
$803$		−	3582.52i		−	0.00555594i
$804$			290295.i			0.449084i
$805$	879450.	−	339474.i	1.35712	−	0.523859i
$806$	472661.			0.727578
$807$	161433.			0.247882
$808$	−47316.5			−0.0724753
$809$	427855.			0.653732			0.326866	−	0.945071i	$-0.394007\pi$
$809$	427855.			0.653732			0.326866	+	0.945071i	$0.394007\pi$
$810$		−	55062.7i		−	0.0839242i
$811$	364799.			0.554641			0.277321	−	0.960777i	$-0.410554\pi$
$811$	364799.			0.554641			0.277321	+	0.960777i	$0.410554\pi$
$812$		−	652123.i		−	0.989049i
$813$	−55.0966			−8.33574e−5
$814$	−51338.7			−0.0774812
$815$		−	348558.i		−	0.524759i
$816$		−	61215.6i		−	0.0919352i
$817$	52308.8			0.0783665
$818$	864027.			1.29128
$819$			246705.i			0.367799i
$820$			189014.i			0.281103i
$821$	−1.11083e6			−1.64801			−0.824006	−	0.566581i	$-0.808266\pi$
$821$	−1.11083e6			−1.64801			−0.824006	+	0.566581i	$0.808266\pi$
$822$		−	166815.i		−	0.246884i
$823$	−775829.			−1.14542			−0.572712	−	0.819756i	$-0.694109\pi$
$823$	−775829.			−1.14542			−0.572712	+	0.819756i	$0.694109\pi$
$824$		−	204134.i		−	0.300650i
$825$		−	4036.64i		−	0.00593079i
$826$			1.06915e6i			1.56704i
$827$			671515.i			0.981848i	0.871202	+	0.490924i	$0.163341\pi$
$827$			671515.i			0.981848i	−0.871202	+	0.490924i	$0.836659\pi$
$828$	106598.	−	41147.6i	0.155485	−	0.0600183i
$829$	−1.00171e6			−1.45758			−0.728789	−	0.684739i	$-0.759916\pi$
$829$	−1.00171e6			−1.45758			−0.728789	+	0.684739i	$0.759916\pi$
$830$	763295.			1.10799
$831$	575438.			0.833290
$832$	−70105.8			−0.101276
$833$		−	377745.i		−	0.544388i
$834$	290986.			0.418350
$835$			817930.i			1.17312i
$836$	−2346.14			−0.00335693
$837$	−171225.			−0.244408
$838$		−	514059.i		−	0.732023i
$839$		−	704933.i		−	1.00144i	−0.865610	−	0.500719i	$-0.833069\pi$
$839$		−	704933.i		−	1.00144i	0.865610	−	0.500719i	$-0.166931\pi$
$840$	209523.			0.296944
$841$	784885.			1.10972
$842$			261260.i			0.368510i
$843$		−	496354.i		−	0.698452i
$844$	−163327.			−0.229284
$845$		−	262037.i		−	0.366985i
$846$	−43093.6			−0.0602104
$847$		−	971832.i		−	1.35464i
$848$			194125.i			0.269954i
$849$			204710.i			0.284004i
$850$			45885.2i			0.0635090i
$851$	392265.	+	1.01621e6i	0.541652	+	1.40322i
$852$	144764.			0.199425
$853$	412976.			0.567579			0.283790	−	0.958887i	$-0.408408\pi$
$853$	412976.			0.567579			0.283790	+	0.958887i	$0.408408\pi$
$854$	637600.			0.874244
$855$	23988.4			0.0328148
$856$		−	14390.8i		−	0.0196399i
$857$	−566697.			−0.771595			−0.385798	−	0.922583i	$-0.626074\pi$
$857$	−566697.			−0.771595			−0.385798	+	0.922583i	$0.626074\pi$
$858$			17738.7i			0.0240961i
$859$	−1.36198e6			−1.84580			−0.922901	−	0.385036i	$-0.874189\pi$
$859$	−1.36198e6			−1.84580			−0.922901	+	0.385036i	$0.874189\pi$
$860$	−335889.			−0.454149
$861$			306783.i			0.413833i
$862$			885758.i			1.19207i
$863$	64405.4			0.0864771			0.0432385	−	0.999065i	$-0.486232\pi$
$863$	64405.4			0.0864771			0.0432385	+	0.999065i	$0.486232\pi$
$864$	25396.3			0.0340207
$865$		−	298713.i		−	0.399229i
$866$		−	291051.i		−	0.388091i
$867$	−257919.			−0.343119
$868$		−	651542.i		−	0.864774i
$869$	916.591			0.00121377
$870$			479424.i			0.633405i
$871$			956206.i			1.26042i
$872$			129938.i			0.170885i
$873$		−	436897.i		−	0.573259i
$874$	17926.2	+	46440.2i	0.0234675	+	0.0607955i
$875$	956719.			1.24959
$876$	−16894.7			−0.0220162
$877$	335218.			0.435841			0.217921	−	0.975967i	$-0.430073\pi$
$877$	335218.			0.435841			0.217921	+	0.975967i	$0.430073\pi$
$878$	552614.			0.716858
$879$			425569.i			0.550798i
$880$	15065.2			0.0194540
$881$			168848.i			0.217543i	0.994067	+	0.108771i	$0.0346916\pi$
$881$			168848.i			0.217543i	−0.994067	+	0.108771i	$0.965308\pi$
$882$	156714.			0.201451
$883$	155798.			0.199821			0.0999103	−	0.994996i	$-0.468144\pi$
$883$	155798.			0.199821			0.0999103	+	0.994996i	$0.468144\pi$
$884$		−	201639.i		−	0.258030i
$885$		−	786012.i		−	1.00356i
$886$	−645529.			−0.822334
$887$	817194.			1.03867			0.519335	−	0.854570i	$-0.326180\pi$
$887$	817194.			1.03867			0.519335	+	0.854570i	$0.326180\pi$
$888$			242106.i			0.307029i
$889$			658312.i			0.832968i
$890$	560366.			0.707443
$891$		−	6425.96i		−	0.00809437i
$892$	84254.1			0.105892
$893$		−	18774.0i		−	0.0235426i
$894$		−	15910.3i		−	0.0199068i
$895$		−	1.26710e6i		−	1.58185i
$896$			96637.6i			0.120373i
$897$	351125.	−	135536.i	0.436391	−	0.168450i
$898$	571175.			0.708298
$899$	1.49084e6			1.84463
$900$	−19036.3			−0.0235016
$901$	−558344.			−0.687784
$902$			22058.4i			0.0271120i
$903$	−545173.			−0.668588
$904$			475175.i			0.581456i
$905$	−431922.			−0.527361
$906$	501021.			0.610378
$907$		−	426923.i		−	0.518961i	−0.965748	−	0.259481i	$-0.916449\pi$
$907$		−	426923.i		−	0.518961i	0.965748	−	0.259481i	$-0.0835514\pi$
$908$			349574.i			0.424002i
$909$	56460.1			0.0683304
$910$	690152.			0.833416
$911$			120577.i			0.145288i	0.997358	+	0.0726438i	$0.0231436\pi$
$911$			120577.i			0.145288i	−0.997358	+	0.0726438i	$0.976856\pi$
$912$			11064.1i			0.0133023i
$913$	89078.6			0.106864
$914$			357212.i			0.427595i
$915$	−468747.			−0.559882
$916$			571715.i			0.681379i
$917$		−	422050.i		−	0.501909i
$918$			73045.0i			0.0866773i
$919$		−	1.26268e6i		−	1.49507i	−0.664221	−	0.747537i	$-0.731236\pi$
$919$		−	1.26268e6i		−	1.49507i	0.664221	−	0.747537i	$-0.268764\pi$
$920$	−115109.	−	298205.i	−0.135999	−	0.352322i
$921$	−833058.			−0.982100
$922$	−931922.			−1.09627
$923$	476839.			0.559716
$924$	24452.0			0.0286398
$925$		−	181475.i		−	0.212096i
$926$	533756.			0.622474
$927$			243582.i			0.283456i
$928$	−221123.			−0.256766
$929$	−778978.			−0.902597			−0.451298	−	0.892373i	$-0.649039\pi$
$929$	−778978.			−0.902597			−0.451298	+	0.892373i	$0.649039\pi$
$930$			478997.i			0.553817i
$931$			68273.5i			0.0787685i
$932$	−213027.			−0.245247
$933$	263111.			0.302256
$934$			465592.i			0.533718i
$935$			43330.7i			0.0495647i
$936$	83653.2			0.0954841
$937$			1.53056e6i			1.74329i	0.490137	+	0.871645i	$0.336947\pi$
$937$			1.53056e6i			1.74329i	−0.490137	+	0.871645i	$0.663053\pi$
$938$	1.31809e6			1.49809
$939$		−	914069.i		−	1.03669i
$940$			120553.i			0.136434i
$941$			230300.i			0.260084i	0.991508	+	0.130042i	$0.0415113\pi$
$941$			230300.i			0.260084i	−0.991508	+	0.130042i	$0.958489\pi$
$942$		−	73582.7i		−	0.0829228i
$943$	436630.	−	168542.i	0.491010	−	0.189533i
$944$	362529.			0.406817
$945$	−250012.			−0.279961
$946$	−39199.2			−0.0438021
$947$	301394.			0.336074			0.168037	−	0.985781i	$-0.446257\pi$
$947$	301394.			0.336074			0.168037	+	0.985781i	$0.446257\pi$
$948$		−	4322.52i		−	0.00480972i
$949$	−55649.6			−0.0617916
$950$		−	8293.28i		−	0.00918923i
$951$	79181.0			0.0875508
$952$	−277950.			−0.306685
$953$		−	178700.i		−	0.196761i	−0.995149	−	0.0983803i	$-0.968634\pi$
$953$		−	178700.i		−	0.196761i	0.995149	−	0.0983803i	$-0.0313662\pi$
$954$		−	231638.i		−	0.254515i
$955$	94855.8			0.104006
$956$	188260.			0.205988
$957$			55950.2i			0.0610910i
$958$			866162.i			0.943774i
$959$	−757427.			−0.823575
$960$		−	71045.5i		−	0.0770893i
$961$	565985.			0.612855
$962$			797477.i			0.861723i
$963$			17171.8i			0.0185167i
$964$			48965.5i			0.0526909i
$965$			758898.i			0.814946i
$966$	−186831.	−	484009.i	−0.200214	−	0.518680i
$967$	−331589.			−0.354607			−0.177304	−	0.984156i	$-0.556737\pi$
$967$	−331589.			−0.354607			−0.177304	+	0.984156i	$0.556737\pi$
$968$	−329530.			−0.351677
$969$	−31822.6			−0.0338913
$970$	−1.22221e6			−1.29898
$971$			1.13672e6i			1.20563i	0.797881	+	0.602815i	$0.205954\pi$
$971$			1.13672e6i			1.20563i	−0.797881	+	0.602815i	$0.794046\pi$
$972$	−30304.0			−0.0320750
$973$		−	1.32122e6i		−	1.39557i
$974$	1.03287e6			1.08875
$975$	−62703.7			−0.0659606
$976$		−	216198.i		−	0.226962i
$977$		−	123255.i		−	0.129126i	−0.997914	−	0.0645631i	$-0.979435\pi$
$977$		−	123255.i		−	0.129126i	0.997914	−	0.0645631i	$-0.0205654\pi$
$978$	−191830.			−0.200558
$979$	65396.2			0.0682319
$980$		−	438403.i		−	0.456479i
$981$		−	155047.i		−	0.161111i
$982$	−1.07649e6			−1.11631
$983$			381404.i			0.394710i	0.980332	+	0.197355i	$0.0632351\pi$
$983$			381404.i			0.394710i	−0.980332	+	0.197355i	$0.936765\pi$
$984$	104024.			0.107435
$985$		−	398521.i		−	0.410751i
$986$		−	635995.i		−	0.654184i
$987$			195667.i			0.200855i
$988$			36444.1i			0.0373348i
$989$	299510.	+	775919.i	0.306210	+	0.793275i
$990$	−17976.5			−0.0183415
$991$	−551610.			−0.561675			−0.280837	−	0.959755i	$-0.590612\pi$
$991$	−551610.			−0.561675			−0.280837	+	0.959755i	$0.590612\pi$
$992$	−220926.			−0.224503
$993$	54110.0			0.0548756
$994$		−	657300.i		−	0.665259i
$995$	1.90487e6			1.92406
$996$		−	420082.i		−	0.423463i
$997$	−443006.			−0.445676			−0.222838	−	0.974856i	$-0.571532\pi$
$997$	−443006.			−0.445676			−0.222838	+	0.974856i	$0.571532\pi$
$998$	45054.0			0.0452348
$999$		−	288892.i		−	0.289470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.5.b.a.91.3	yes	16
3.2	odd	2		414.5.b.b.91.11		16
4.3	odd	2		1104.5.c.a.1057.15		16
23.22	odd	2	inner	138.5.b.a.91.2	✓	16
69.68	even	2		414.5.b.b.91.14		16
92.91	even	2		1104.5.c.a.1057.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.5.b.a.91.2	✓	16	23.22	odd	2	inner
138.5.b.a.91.3	yes	16	1.1	even	1	trivial
414.5.b.b.91.11		16	3.2	odd	2
414.5.b.b.91.14		16	69.68	even	2
1104.5.c.a.1057.10		16	92.91	even	2
1104.5.c.a.1057.15		16	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	138.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843 q^{2} -5.19615 q^{3} +8.00000 q^{4} +26.7045i q^{5} +14.6969 q^{6} -66.7315i q^{7} -22.6274 q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q-2.82843 q^{2} -5.19615 q^{3} +8.00000 q^{4} +26.7045i q^{5} +14.6969 q^{6} -66.7315i q^{7} -22.6274 q^{8} +27.0000 q^{9} -75.5318i q^{10} -8.81477i q^{11} -41.5692 q^{12} -136.925 q^{13} +188.745i q^{14} -138.761i q^{15} +64.0000 q^{16} +184.077i q^{17} -76.3675 q^{18} -33.2701i q^{19} +213.636i q^{20} +346.747i q^{21} +24.9319i q^{22} +(493.509 - 190.498i) q^{23} +117.576 q^{24} -88.1308 q^{25} +387.283 q^{26} -140.296 q^{27} -533.852i q^{28} +1221.54 q^{29} +392.475i q^{30} +1220.45 q^{31} -181.019 q^{32} +45.8029i q^{33} -520.649i q^{34} +1782.03 q^{35} +216.000 q^{36} +2059.16i q^{37} +94.1019i q^{38} +711.485 q^{39} -604.254i q^{40} +884.746 q^{41} -980.749i q^{42} +1572.25i q^{43} -70.5181i q^{44} +721.022i q^{45} +(-1395.86 + 538.810i) q^{46} +564.292 q^{47} -332.554 q^{48} -2052.10 q^{49} +249.272 q^{50} -956.493i q^{51} -1095.40 q^{52} +3033.20i q^{53} +396.817 q^{54} +235.394 q^{55} +1509.96i q^{56} +172.876i q^{57} -3455.04 q^{58} +5664.52 q^{59} -1110.09i q^{60} -3378.10i q^{61} -3451.96 q^{62} -1801.75i q^{63} +512.000 q^{64} -3656.52i q^{65} -129.550i q^{66} -6983.41i q^{67} +1472.62i q^{68} +(-2564.35 + 989.856i) q^{69} -5040.35 q^{70} -3482.47 q^{71} -610.940 q^{72} +406.423 q^{73} -5824.17i q^{74} +457.941 q^{75} -266.160i q^{76} -588.223 q^{77} -2012.38 q^{78} +103.984i q^{79} +1709.09i q^{80} +729.000 q^{81} -2502.44 q^{82} +10105.6i q^{83} +2773.98i q^{84} -4915.69 q^{85} -4446.99i q^{86} -6347.32 q^{87} +199.455i q^{88} +7418.94i q^{89} -2039.36i q^{90} +9137.24i q^{91} +(3948.08 - 1523.98i) q^{92} -6341.66 q^{93} -1596.06 q^{94} +888.461 q^{95} +940.604 q^{96} -16181.4i q^{97} +5804.21 q^{98} -237.999i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 128 q^{4} + 432 q^{9}+O(q^{10}) \) 16 * q + 128 * q^4 + 432 * q^9	\( 16 q + 128 q^{4} + 432 q^{9} - 208 q^{13} + 1024 q^{16} + 840 q^{23} + 1056 q^{25} + 1920 q^{26} + 3600 q^{29} + 224 q^{31} - 3264 q^{35} + 3456 q^{36} - 2016 q^{39} - 6144 q^{41} + 1280 q^{46} + 8880 q^{47} - 13888 q^{49} + 7296 q^{50} - 1664 q^{52} + 832 q^{55} + 2944 q^{58} - 18240 q^{59} + 8192 q^{64} + 10584 q^{69} + 19584 q^{70} - 30048 q^{71} + 9536 q^{73} - 4176 q^{75} + 14160 q^{77} + 6912 q^{78} + 11664 q^{81} - 19584 q^{82} - 32496 q^{85} - 8064 q^{87} + 6720 q^{92} - 11952 q^{93} - 21248 q^{94} - 20064 q^{95} + 21504 q^{98}+O(q^{100}) \) 16 * q + 128 * q^4 + 432 * q^9 - 208 * q^13 + 1024 * q^16 + 840 * q^23 + 1056 * q^25 + 1920 * q^26 + 3600 * q^29 + 224 * q^31 - 3264 * q^35 + 3456 * q^36 - 2016 * q^39 - 6144 * q^41 + 1280 * q^46 + 8880 * q^47 - 13888 * q^49 + 7296 * q^50 - 1664 * q^52 + 832 * q^55 + 2944 * q^58 - 18240 * q^59 + 8192 * q^64 + 10584 * q^69 + 19584 * q^70 - 30048 * q^71 + 9536 * q^73 - 4176 * q^75 + 14160 * q^77 + 6912 * q^78 + 11664 * q^81 - 19584 * q^82 - 32496 * q^85 - 8064 * q^87 + 6720 * q^92 - 11952 * q^93 - 21248 * q^94 - 20064 * q^95 + 21504 * q^98

Introduction

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