LMFDB - Embedded newform 39.4.b.b.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(25,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("39.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.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:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.1362828.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 23x^{2} + 48 $ x^4 + 23*x^2 + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			25.4
Root			$4.54739i$ of defining polynomial
Character	$\chi$	$=$	39.25
Dual form			39.4.b.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.54739i q^{2} +3.00000 q^{3} -12.6788 q^{4} +12.9118i q^{5} +13.6422i q^{6} -16.7289i q^{7} -21.2762i q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.54739i q^{2} +3.00000 q^{3} -12.6788 q^{4} +12.9118i q^{5} +13.6422i q^{6} -16.7289i q^{7} -21.2762i q^{8} +9.00000 q^{9} -58.7151 q^{10} -24.9280i q^{11} -38.0363 q^{12} +(33.7151 + 32.5621i) q^{13} +76.0727 q^{14} +38.7355i q^{15} -4.67878 q^{16} +134.145 q^{17} +40.9265i q^{18} -14.9376i q^{19} -163.706i q^{20} -50.1866i q^{21} +113.358 q^{22} -72.0000 q^{23} -63.8287i q^{24} -41.7151 q^{25} +(-148.073 + 153.316i) q^{26} +27.0000 q^{27} +212.101i q^{28} -206.145 q^{29} -176.145 q^{30} -249.142i q^{31} -191.486i q^{32} -74.7841i q^{33} +610.012i q^{34} +216.000 q^{35} -114.109 q^{36} -293.955i q^{37} +67.9273 q^{38} +(101.145 + 97.6863i) q^{39} +274.715 q^{40} +250.506i q^{41} +228.218 q^{42} -432.145 q^{43} +316.057i q^{44} +116.206i q^{45} -327.412i q^{46} +159.889i q^{47} -14.0363 q^{48} +63.1454 q^{49} -189.695i q^{50} +402.436 q^{51} +(-427.467 - 412.848i) q^{52} -194.581 q^{53} +122.780i q^{54} +321.866 q^{55} -355.927 q^{56} -44.8129i q^{57} -937.424i q^{58} -232.647i q^{59} -491.118i q^{60} -185.006 q^{61} +1132.94 q^{62} -150.560i q^{63} +833.333 q^{64} +(-420.436 + 435.324i) q^{65} +340.073 q^{66} -39.4393i q^{67} -1700.80 q^{68} -216.000 q^{69} +982.237i q^{70} +920.460i q^{71} -191.486i q^{72} +549.078i q^{73} +1336.73 q^{74} -125.145 q^{75} +189.391i q^{76} -417.018 q^{77} +(-444.218 + 459.948i) q^{78} +933.140 q^{79} -60.4116i q^{80} +81.0000 q^{81} -1139.15 q^{82} -1095.38i q^{83} +636.304i q^{84} +1732.06i q^{85} -1965.13i q^{86} -618.436 q^{87} -530.375 q^{88} +532.114i q^{89} -528.436 q^{90} +(544.727 - 564.015i) q^{91} +912.872 q^{92} -747.425i q^{93} -727.079 q^{94} +192.872 q^{95} -574.459i q^{96} -362.661i q^{97} +287.147i q^{98} -224.352i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{3} - 14 q^{4} + 36 q^{9}+O(q^{10}) $ 4 * q + 12 * q^3 - 14 * q^4 + 36 * q^9	$ 4 q + 12 q^{3} - 14 q^{4} + 36 q^{9} - 88 q^{10} - 42 q^{12} - 12 q^{13} + 84 q^{14} + 18 q^{16} + 96 q^{17} + 380 q^{22} - 288 q^{23} - 20 q^{25} - 372 q^{26} + 108 q^{27} - 384 q^{29} - 264 q^{30} + 864 q^{35} - 126 q^{36} + 492 q^{38} - 36 q^{39} + 952 q^{40} + 252 q^{42} - 1288 q^{43} + 54 q^{48} - 188 q^{49} + 288 q^{51} - 1306 q^{52} + 984 q^{53} - 328 q^{55} - 1644 q^{56} + 288 q^{61} + 1668 q^{62} + 1314 q^{64} - 360 q^{65} + 1140 q^{66} - 4380 q^{68} - 864 q^{69} + 3144 q^{74} - 60 q^{75} + 1416 q^{77} - 1116 q^{78} + 4320 q^{79} + 324 q^{81} - 3088 q^{82} - 1152 q^{87} + 1036 q^{88} - 792 q^{90} - 24 q^{91} + 1008 q^{92} - 1660 q^{94} - 1872 q^{95}+O(q^{100}) $ 4 * q + 12 * q^3 - 14 * q^4 + 36 * q^9 - 88 * q^10 - 42 * q^12 - 12 * q^13 + 84 * q^14 + 18 * q^16 + 96 * q^17 + 380 * q^22 - 288 * q^23 - 20 * q^25 - 372 * q^26 + 108 * q^27 - 384 * q^29 - 264 * q^30 + 864 * q^35 - 126 * q^36 + 492 * q^38 - 36 * q^39 + 952 * q^40 + 252 * q^42 - 1288 * q^43 + 54 * q^48 - 188 * q^49 + 288 * q^51 - 1306 * q^52 + 984 * q^53 - 328 * q^55 - 1644 * q^56 + 288 * q^61 + 1668 * q^62 + 1314 * q^64 - 360 * q^65 + 1140 * q^66 - 4380 * q^68 - 864 * q^69 + 3144 * q^74 - 60 * q^75 + 1416 * q^77 - 1116 * q^78 + 4320 * q^79 + 324 * q^81 - 3088 * q^82 - 1152 * q^87 + 1036 * q^88 - 792 * q^90 - 24 * q^91 + 1008 * q^92 - 1660 * q^94 - 1872 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$-1$

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 $

$2$			4.54739i			1.60775i	0.594801	+	0.803873i	$0.297231\pi$
$2$			4.54739i			1.60775i	−0.594801	+	0.803873i	$0.702769\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	−12.6788			−1.58485
$5$			12.9118i			1.15487i	0.816437	+	0.577434i	$0.195946\pi$
$5$			12.9118i			1.15487i	−0.816437	+	0.577434i	$0.804054\pi$
$6$			13.6422i			0.928233i
$7$		−	16.7289i		−	0.903273i	−0.892202	−	0.451637i	$-0.850840\pi$
$7$		−	16.7289i		−	0.903273i	0.892202	−	0.451637i	$-0.149160\pi$
$8$		−	21.2762i		−	0.940286i
$9$	9.00000			0.333333
$10$	−58.7151			−1.85674
$11$		−	24.9280i		−	0.683280i	−0.939831	−	0.341640i	$-0.889018\pi$
$11$		−	24.9280i		−	0.683280i	0.939831	−	0.341640i	$-0.110982\pi$
$12$	−38.0363			−0.915012
$13$	33.7151	+	32.5621i	0.719299	+	0.694700i
$13$	33.7151	+	32.5621i	0.719299	+	0.694700i
$14$	76.0727			1.45223
$15$			38.7355i			0.666764i
$16$	−4.67878			−0.0731059
$17$	134.145			1.91383			0.956913	−	0.290376i	$-0.0937804\pi$
$17$	134.145			1.91383			0.956913	+	0.290376i	$0.0937804\pi$
$18$			40.9265i			0.535915i
$19$		−	14.9376i		−	0.180365i	−0.995925	−	0.0901824i	$-0.971255\pi$
$19$		−	14.9376i		−	0.180365i	0.995925	−	0.0901824i	$-0.0287450\pi$
$20$		−	163.706i		−	1.83029i
$21$		−	50.1866i		−	0.521505i
$22$	113.358			1.09854
$23$	−72.0000			−0.652741			−0.326370	−	0.945242i	$-0.605826\pi$
$23$	−72.0000			−0.652741			−0.326370	+	0.945242i	$0.605826\pi$
$24$		−	63.8287i		−	0.542875i
$25$	−41.7151			−0.333721
$26$	−148.073	+	153.316i	−1.11690	+	1.15645i
$27$	27.0000			0.192450
$28$			212.101i			1.43155i
$29$	−206.145			−1.32001			−0.660004	−	0.751262i	$-0.729445\pi$
$29$	−206.145			−1.32001			−0.660004	+	0.751262i	$0.729445\pi$
$30$	−176.145			−1.07199
$31$		−	249.142i		−	1.44346i	−0.692176	−	0.721728i	$-0.743348\pi$
$31$		−	249.142i		−	1.44346i	0.692176	−	0.721728i	$-0.256652\pi$
$32$		−	191.486i		−	1.05782i
$33$		−	74.7841i		−	0.394492i
$34$			610.012i			3.07694i
$35$	216.000			1.04316
$36$	−114.109			−0.528282
$37$		−	293.955i		−	1.30610i	−0.757313	−	0.653052i	$-0.773488\pi$
$37$		−	293.955i		−	1.30610i	0.757313	−	0.653052i	$-0.226512\pi$
$38$	67.9273			0.289981
$39$	101.145	+	97.6863i	0.415288	+	0.401085i
$40$	274.715			1.08591
$41$			250.506i			0.954208i	0.878847	+	0.477104i	$0.158314\pi$
$41$			250.506i			0.954208i	−0.878847	+	0.477104i	$0.841686\pi$
$42$	228.218			0.838448
$43$	−432.145			−1.53259			−0.766297	−	0.642486i	$-0.777903\pi$
$43$	−432.145			−1.53259			−0.766297	+	0.642486i	$0.777903\pi$
$44$			316.057i			1.08290i
$45$			116.206i			0.384956i
$46$		−	327.412i		−	1.04944i
$47$			159.889i			0.496217i	0.968732	+	0.248109i	$0.0798090\pi$
$47$			159.889i			0.496217i	−0.968732	+	0.248109i	$0.920191\pi$
$48$	−14.0363			−0.0422077
$49$	63.1454			0.184097
$50$		−	189.695i		−	0.536539i
$51$	402.436			1.10495
$52$	−427.467	−	412.848i	−1.13998	−	1.10099i
$53$	−194.581			−0.504298			−0.252149	−	0.967688i	$-0.581137\pi$
$53$	−194.581			−0.504298			−0.252149	+	0.967688i	$0.581137\pi$
$54$			122.780i			0.309411i
$55$	321.866			0.789099
$56$	−355.927			−0.849336
$57$		−	44.8129i		−	0.104134i
$58$		−	937.424i		−	2.12224i
$59$		−	232.647i		−	0.513358i	−0.966497	−	0.256679i	$-0.917372\pi$
$59$		−	232.647i		−	0.513358i	0.966497	−	0.256679i	$-0.0826283\pi$
$60$		−	491.118i		−	1.05672i
$61$	−185.006			−0.388321			−0.194160	−	0.980970i	$-0.562198\pi$
$61$	−185.006			−0.388321			−0.194160	+	0.980970i	$0.562198\pi$
$62$	1132.94			2.32071
$63$		−	150.560i		−	0.301091i
$64$	833.333			1.62760
$65$	−420.436	+	435.324i	−0.802287	+	0.830696i
$66$	340.073			0.634243
$67$		−	39.4393i		−	0.0719145i	−0.999353	−	0.0359573i	$-0.988552\pi$
$67$		−	39.4393i		−	0.0719145i	0.999353	−	0.0359573i	$-0.0114480\pi$
$68$	−1700.80			−3.03312
$69$	−216.000			−0.376860
$70$			982.237i			1.67714i
$71$			920.460i			1.53857i	0.638905	+	0.769286i	$0.279388\pi$
$71$			920.460i			1.53857i	−0.638905	+	0.769286i	$0.720612\pi$
$72$		−	191.486i		−	0.313429i
$73$			549.078i			0.880338i	0.897915	+	0.440169i	$0.145082\pi$
$73$			549.078i			0.880338i	−0.897915	+	0.440169i	$0.854918\pi$
$74$	1336.73			2.09988
$75$	−125.145			−0.192674
$76$			189.391i			0.285851i
$77$	−417.018			−0.617189
$78$	−444.218	+	459.948i	−0.644843	+	0.667677i
$79$	933.140			1.32894			0.664471	−	0.747314i	$-0.268657\pi$
$79$	933.140			1.32894			0.664471	+	0.747314i	$0.268657\pi$
$80$		−	60.4116i		−	0.0844277i
$81$	81.0000			0.111111
$82$	−1139.15			−1.53412
$83$		−	1095.38i		−	1.44860i	−0.689484	−	0.724301i	$-0.742163\pi$
$83$		−	1095.38i		−	1.44860i	0.689484	−	0.724301i	$-0.257837\pi$
$84$			636.304i			0.826506i
$85$			1732.06i			2.21022i
$86$		−	1965.13i		−	2.46402i
$87$	−618.436			−0.762107
$88$	−530.375			−0.642479
$89$			532.114i			0.633753i	0.948467	+	0.316876i	$0.102634\pi$
$89$			532.114i			0.633753i	−0.948467	+	0.316876i	$0.897366\pi$
$90$	−528.436			−0.618912
$91$	544.727	−	564.015i	0.627504	−	0.649724i
$92$	912.872			1.03449
$93$		−	747.425i		−	0.833380i
$94$	−727.079			−0.797792
$95$	192.872			0.208298
$96$		−	574.459i		−	0.610734i
$97$		−	362.661i		−	0.379615i	−0.981821	−	0.189808i	$-0.939214\pi$
$97$		−	362.661i		−	0.379615i	0.981821	−	0.189808i	$-0.0607864\pi$
$98$			287.147i			0.295982i
$99$		−	224.352i		−	0.227760i
$100$	528.897			0.528897
$101$	−1490.58			−1.46850			−0.734249	−	0.678880i	$-0.762466\pi$
$101$	−1490.58			−1.46850			−0.734249	+	0.678880i	$0.762466\pi$
$102$			1830.03i			1.77648i
$103$	−628.436			−0.601181			−0.300591	−	0.953753i	$-0.597184\pi$
$103$	−628.436			−0.601181			−0.300591	+	0.953753i	$0.597184\pi$
$104$	692.799	−	717.331i	0.653217	−	0.676347i
$105$	648.000			0.602270
$106$		−	884.838i		−	0.810784i
$107$	477.454			0.431376			0.215688	−	0.976462i	$-0.430801\pi$
$107$	477.454			0.431376			0.215688	+	0.976462i	$0.430801\pi$
$108$	−342.327			−0.305004
$109$		−	378.207i		−	0.332345i	−0.986097	−	0.166173i	$-0.946859\pi$
$109$		−	378.207i		−	0.332345i	0.986097	−	0.166173i	$-0.0531409\pi$
$110$			1463.65i			1.26867i
$111$		−	881.864i		−	0.754079i
$112$			78.2706i			0.0660346i
$113$	13.2732			0.0110499			0.00552495	−	0.999985i	$-0.498241\pi$
$113$	13.2732			0.0110499			0.00552495	+	0.999985i	$0.498241\pi$
$114$	203.782			0.167420
$115$		−	929.651i		−	0.753830i
$116$	2613.67			2.09201
$117$	303.436	+	293.059i	0.239766	+	0.231567i
$118$	1057.94			0.825349
$119$		−	2244.10i		−	1.72871i
$120$	824.145			0.626949
$121$	709.593			0.533128
$122$		−	841.294i		−	0.624321i
$123$			751.519i			0.550912i
$124$			3158.81i			2.28766i
$125$			1075.36i			0.769465i
$126$	684.654			0.484078
$127$	−145.988			−0.102003			−0.0510015	−	0.998699i	$-0.516241\pi$
$127$	−145.988			−0.102003			−0.0510015	+	0.998699i	$0.516241\pi$
$128$			2257.60i			1.55895i
$129$	−1296.44			−0.884844
$130$	−1979.59	−	1911.89i	−1.33555	−	1.28987i
$131$	317.163			0.211532			0.105766	−	0.994391i	$-0.466271\pi$
$131$	317.163			0.211532			0.105766	+	0.994391i	$0.466271\pi$
$132$			948.171i			0.625210i
$133$	−249.890			−0.162919
$134$	179.346			0.115620
$135$			348.619i			0.222255i
$136$		−	2854.11i		−	1.79954i
$137$		−	443.149i		−	0.276356i	−0.990407	−	0.138178i	$-0.955875\pi$
$137$		−	443.149i		−	0.276356i	0.990407	−	0.138178i	$-0.0441247\pi$
$138$		−	982.237i		−	0.605895i
$139$	785.018			0.479024			0.239512	−	0.970893i	$-0.423013\pi$
$139$	785.018			0.479024			0.239512	+	0.970893i	$0.423013\pi$
$140$	−2738.62			−1.65325
$141$			479.667i			0.286491i
$142$	−4185.69			−2.47363
$143$	811.709	−	840.452i	0.474675	−	0.491483i
$144$	−42.1090			−0.0243686
$145$		−	2661.71i		−	1.52444i
$146$	−2496.87			−1.41536
$147$	189.436			0.106289
$148$			3726.99i			2.06997i
$149$			135.420i			0.0744566i	0.999307	+	0.0372283i	$0.0118529\pi$
$149$			135.420i			0.0744566i	−0.999307	+	0.0372283i	$0.988147\pi$
$150$		−	569.085i		−	0.309771i
$151$			2373.74i			1.27929i	0.768672	+	0.639643i	$0.220918\pi$
$151$			2373.74i			1.27929i	−0.768672	+	0.639643i	$0.779082\pi$
$152$	−317.817			−0.169594
$153$	1207.31			0.637942
$154$		−	1896.34i		−	0.992283i
$155$	3216.87			1.66700
$156$	−1282.40	−	1238.54i	−0.658168	−	0.635659i
$157$	−1166.73			−0.593089			−0.296544	−	0.955019i	$-0.595834\pi$
$157$	−1166.73			−0.593089			−0.296544	+	0.955019i	$0.595834\pi$
$158$			4243.35i			2.13660i
$159$	−583.744			−0.291157
$160$	2472.44			1.22165
$161$			1204.48i			0.589603i
$162$			368.339i			0.178638i
$163$			2309.19i			1.10963i	0.831974	+	0.554815i	$0.187211\pi$
$163$			2309.19i			1.10963i	−0.831974	+	0.554815i	$0.812789\pi$
$164$		−	3176.12i		−	1.51227i
$165$	965.599			0.455587
$166$	4981.14			2.32898
$167$			600.788i			0.278386i	0.990265	+	0.139193i	$0.0444508\pi$
$167$			600.788i			0.278386i	−0.990265	+	0.139193i	$0.955549\pi$
$168$	−1067.78			−0.490364
$169$	76.4186	+	2195.67i	0.0347831	+	0.999395i
$170$	−7876.36			−3.55347
$171$		−	134.439i		−	0.0601216i
$172$	5479.08			2.42893
$173$	−3430.36			−1.50755			−0.753773	−	0.657135i	$-0.771768\pi$
$173$	−3430.36			−1.50755			−0.753773	+	0.657135i	$0.771768\pi$
$174$		−	2812.27i		−	1.22527i
$175$			697.846i			0.301441i
$176$			116.633i			0.0499519i
$177$		−	697.942i		−	0.296387i
$178$	−2419.73			−1.01891
$179$	−978.837			−0.408725			−0.204362	−	0.978895i	$-0.565512\pi$
$179$	−978.837			−0.408725			−0.204362	+	0.978895i	$0.565512\pi$
$180$		−	1473.36i		−	0.610097i
$181$	3839.09			1.57656			0.788279	−	0.615318i	$-0.210972\pi$
$181$	3839.09			1.57656			0.788279	+	0.615318i	$0.210972\pi$
$182$	2564.80	+	2477.09i	1.04459	+	1.00887i
$183$	−555.018			−0.224197
$184$			1531.89i			0.613763i
$185$	3795.49			1.50838
$186$	3398.83			1.33986
$187$		−	3343.98i		−	1.30768i
$188$		−	2027.20i		−	0.786429i
$189$		−	451.679i		−	0.173835i
$190$			877.065i			0.334890i
$191$	−487.709			−0.184761			−0.0923806	−	0.995724i	$-0.529448\pi$
$191$	−487.709			−0.184761			−0.0923806	+	0.995724i	$0.529448\pi$
$192$	2500.00			0.939697
$193$		−	4245.61i		−	1.58345i	−0.610878	−	0.791725i	$-0.709183\pi$
$193$		−	4245.61i		−	1.58345i	0.610878	−	0.791725i	$-0.290817\pi$
$194$	1649.16			0.610325
$195$	−1261.31	+	1305.97i	−0.463201	+	0.479603i
$196$	−800.606			−0.291766
$197$		−	2712.71i		−	0.981079i	−0.871419	−	0.490539i	$-0.836800\pi$
$197$		−	2712.71i		−	0.981079i	0.871419	−	0.490539i	$-0.163200\pi$
$198$	1020.22			0.366180
$199$	−3116.90			−1.11031			−0.555153	−	0.831748i	$-0.687340\pi$
$199$	−3116.90			−1.11031			−0.555153	+	0.831748i	$0.687340\pi$
$200$			887.541i			0.313793i
$201$		−	118.318i		−	0.0415199i
$202$		−	6778.26i		−	2.36097i
$203$			3448.58i			1.19233i
$204$	−5102.40			−1.75117
$205$	−3234.49			−1.10198
$206$		−	2857.75i		−	0.966546i
$207$	−648.000			−0.217580
$208$	−157.746	−	152.351i	−0.0525851	−	0.0507867i
$209$	−372.366			−0.123240
$210$			2946.71i			0.968297i
$211$	−1051.22			−0.342981			−0.171491	−	0.985186i	$-0.554858\pi$
$211$	−1051.22			−0.342981			−0.171491	+	0.985186i	$0.554858\pi$
$212$	2467.06			0.799236
$213$			2761.38i			0.888294i
$214$			2171.17i			0.693542i
$215$		−	5579.78i		−	1.76994i
$216$		−	574.459i		−	0.180958i
$217$	−4167.85			−1.30384
$218$	1719.85			0.534327
$219$			1647.23i			0.508264i
$220$	−4080.87			−1.25060
$221$	4522.73	+	4368.06i	1.37661	+	1.32953i
$222$	4010.18			1.21237
$223$			5496.12i			1.65044i	0.564814	+	0.825218i	$0.308948\pi$
$223$			5496.12i			1.65044i	−0.564814	+	0.825218i	$0.691052\pi$
$224$	−3203.35			−0.955502
$225$	−375.436			−0.111240
$226$			60.3585i			0.0177654i
$227$		−	921.570i		−	0.269457i	−0.990883	−	0.134729i	$-0.956984\pi$
$227$		−	921.570i		−	0.269457i	0.990883	−	0.134729i	$-0.0430162\pi$
$228$			568.173i			0.165036i
$229$		−	192.941i		−	0.0556764i	−0.999612	−	0.0278382i	$-0.991138\pi$
$229$		−	192.941i		−	0.0556764i	0.999612	−	0.0278382i	$-0.00886232\pi$
$230$	4227.49			1.21197
$231$	−1251.05			−0.356334
$232$			4386.00i			1.24119i
$233$	−913.779			−0.256926			−0.128463	−	0.991714i	$-0.541004\pi$
$233$	−913.779			−0.256926			−0.128463	+	0.991714i	$0.541004\pi$
$234$	−1332.65	+	1379.84i	−0.372301	+	0.385484i
$235$	−2064.46			−0.573066
$236$			2949.68i			0.813594i
$237$	2799.42			0.767265
$238$	10204.8			2.77932
$239$		−	1976.86i		−	0.535032i	−0.963553	−	0.267516i	$-0.913797\pi$
$239$		−	1976.86i		−	0.535032i	0.963553	−	0.267516i	$-0.0862028\pi$
$240$		−	181.235i		−	0.0487444i
$241$		−	3904.45i		−	1.04360i	−0.853068	−	0.521800i	$-0.825261\pi$
$241$		−	3904.45i		−	1.04360i	0.853068	−	0.521800i	$-0.174739\pi$
$242$			3226.80i			0.857134i
$243$	243.000			0.0641500
$244$	2345.65			0.615429
$245$			815.322i			0.212608i
$246$	−3417.45			−0.885727
$247$	486.401	−	503.624i	0.125299	−	0.129736i
$248$	−5300.80			−1.35726
$249$		−	3286.15i		−	0.836350i
$250$	−4890.08			−1.23710
$251$	942.035			0.236895			0.118448	−	0.992960i	$-0.462208\pi$
$251$	942.035			0.236895			0.118448	+	0.992960i	$0.462208\pi$
$252$			1908.91i			0.477183i
$253$			1794.82i			0.446005i
$254$		−	663.866i		−	0.163995i
$255$			5196.18i			1.27607i
$256$	−3599.54			−0.878794
$257$	812.616			0.197236			0.0986179	−	0.995125i	$-0.468558\pi$
$257$	812.616			0.197236			0.0986179	+	0.995125i	$0.468558\pi$
$258$		−	5895.40i		−	1.42260i
$259$	−4917.52			−1.17977
$260$	5330.62	−	5519.37i	1.27150	−	1.31653i
$261$	−1855.31			−0.440003
$262$			1442.26i			0.340089i
$263$	−2608.29			−0.611536			−0.305768	−	0.952106i	$-0.598913\pi$
$263$	−2608.29			−0.611536			−0.305768	+	0.952106i	$0.598913\pi$
$264$	−1591.13			−0.370936
$265$		−	2512.40i		−	0.582398i
$266$		−	1136.35i		−	0.261932i
$267$			1596.34i			0.365897i
$268$			500.042i			0.113974i
$269$	−4791.02			−1.08592			−0.542962	−	0.839757i	$-0.682697\pi$
$269$	−4791.02			−1.08592			−0.542962	+	0.839757i	$0.682697\pi$
$270$	−1585.31			−0.357329
$271$			3663.62i			0.821214i	0.911812	+	0.410607i	$0.134683\pi$
$271$			3663.62i			0.821214i	−0.911812	+	0.410607i	$0.865317\pi$
$272$	−627.637			−0.139912
$273$	1634.18	−	1692.05i	0.362290	−	0.375118i
$274$	2015.17			0.444311
$275$			1039.88i			0.228025i
$276$	2738.62			0.597266
$277$	624.326			0.135423			0.0677114	−	0.997705i	$-0.478430\pi$
$277$	624.326			0.135423			0.0677114	+	0.997705i	$0.478430\pi$
$278$			3569.78i			0.770149i
$279$		−	2242.27i		−	0.481152i
$280$		−	4595.67i		−	0.980871i
$281$		−	5535.12i		−	1.17508i	−0.809195	−	0.587540i	$-0.800096\pi$
$281$		−	5535.12i		−	1.17508i	0.809195	−	0.587540i	$-0.199904\pi$
$282$	−2181.24			−0.460605
$283$	−175.151			−0.0367903			−0.0183952	−	0.999831i	$-0.505856\pi$
$283$	−175.151			−0.0367903			−0.0183952	+	0.999831i	$0.505856\pi$
$284$		−	11670.3i		−	2.43840i
$285$	578.616			0.120261
$286$	3821.86	+	3691.16i	0.790180	+	0.763157i
$287$	4190.69			0.861911
$288$		−	1723.38i		−	0.352607i
$289$	13082.0			2.66273
$290$	12103.8			2.45091
$291$		−	1087.98i		−	0.219171i
$292$		−	6961.64i		−	1.39520i
$293$			7774.33i			1.55011i	0.631895	+	0.775054i	$0.282277\pi$
$293$			7774.33i			1.55011i	−0.631895	+	0.775054i	$0.717723\pi$
$294$			861.440i			0.170885i
$295$	3003.90			0.592861
$296$	−6254.25			−1.22811
$297$		−	673.057i		−	0.131497i
$298$	−615.808			−0.119707
$299$	−2427.49	−	2344.47i	−0.469516	−	0.453459i
$300$	1586.69			0.305359
$301$			7229.30i			1.38435i
$302$	−10794.3			−2.05677
$303$	−4471.74			−0.847838
$304$			69.8899i			0.0131857i
$305$		−	2388.76i		−	0.448459i
$306$			5490.10i			1.02565i
$307$		−	8022.85i		−	1.49149i	−0.666230	−	0.745746i	$-0.732093\pi$
$307$		−	8022.85i		−	1.49149i	0.666230	−	0.745746i	$-0.267907\pi$
$308$	5287.27			0.978150
$309$	−1885.31			−0.347092
$310$			14628.4i			2.68012i
$311$	9264.87			1.68927			0.844635	−	0.535343i	$-0.179818\pi$
$311$	9264.87			1.68927			0.844635	+	0.535343i	$0.179818\pi$
$312$	2078.40	−	2151.99i	0.377135	−	0.390489i
$313$	7423.57			1.34059			0.670296	−	0.742094i	$-0.266167\pi$
$313$	7423.57			1.34059			0.670296	+	0.742094i	$0.266167\pi$
$314$		−	5305.56i		−	0.953536i
$315$	1944.00			0.347721
$316$	−11831.1			−2.10617
$317$			2641.04i			0.467935i	0.972244	+	0.233968i	$0.0751710\pi$
$317$			2641.04i			0.467935i	−0.972244	+	0.233968i	$0.924829\pi$
$318$		−	2654.51i		−	0.468106i
$319$			5138.80i			0.901936i
$320$			10759.8i			1.87967i
$321$	1432.36			0.249055
$322$	−5477.23			−0.947932
$323$		−	2003.82i		−	0.345187i
$324$	−1026.98			−0.176094
$325$	−1406.43	−	1358.33i	−0.240045	−	0.231836i
$326$	−10500.8			−1.78400
$327$		−	1134.62i		−	0.191880i
$328$	5329.84			0.897229
$329$	2674.76			0.448220
$330$			4390.96i			0.732467i
$331$			10779.5i			1.79001i	0.446052	+	0.895007i	$0.352830\pi$
$331$			10779.5i			1.79001i	−0.446052	+	0.895007i	$0.647170\pi$
$332$			13888.1i			2.29581i
$333$		−	2645.59i		−	0.435368i
$334$	−2732.02			−0.447573
$335$	509.233			0.0830518
$336$			234.812i			0.0381251i
$337$	313.465			0.0506693			0.0253346	−	0.999679i	$-0.491935\pi$
$337$	313.465			0.0506693			0.0253346	+	0.999679i	$0.491935\pi$
$338$	−9984.58	+	347.505i	−1.60677	+	0.0559225i
$339$	39.8196			0.00637966
$340$		−	21960.4i		−	3.50286i
$341$	−6210.61			−0.986286
$342$	611.346			0.0966602
$343$		−	6794.35i		−	1.06956i
$344$			9194.43i			1.44108i
$345$		−	2788.95i		−	0.435224i
$346$		−	15599.2i		−	2.42375i
$347$	−2849.23			−0.440792			−0.220396	−	0.975410i	$-0.570735\pi$
$347$	−2849.23			−0.440792			−0.220396	+	0.975410i	$0.570735\pi$
$348$	7841.01			1.20782
$349$		−	6466.94i		−	0.991883i	−0.868356	−	0.495941i	$-0.834823\pi$
$349$		−	6466.94i		−	0.991883i	0.868356	−	0.495941i	$-0.165177\pi$
$350$	−3173.38			−0.484641
$351$	910.308	+	879.177i	0.138429	+	0.133695i
$352$	−4773.38			−0.722789
$353$		−	2773.10i		−	0.418122i	−0.977903	−	0.209061i	$-0.932959\pi$
$353$		−	2773.10i		−	0.418122i	0.977903	−	0.209061i	$-0.0670408\pi$
$354$	3173.82			0.476515
$355$	−11884.8			−1.77685
$356$		−	6746.56i		−	1.00440i
$357$		−	6732.30i		−	0.998070i
$358$		−	4451.16i		−	0.657126i
$359$			1467.11i			0.215685i	0.994168	+	0.107843i	$0.0343942\pi$
$359$			1467.11i			0.215685i	−0.994168	+	0.107843i	$0.965606\pi$
$360$	2472.44			0.361969
$361$	6635.87			0.967469
$362$			17457.8i			2.53471i
$363$	2128.78			0.307801
$364$	−6906.47	+	7151.03i	−0.994498	+	1.02971i
$365$	−7089.59			−1.01667
$366$		−	2523.88i		−	0.360452i
$367$	4648.22			0.661130			0.330565	−	0.943783i	$-0.392761\pi$
$367$	4648.22			0.661130			0.330565	+	0.943783i	$0.392761\pi$
$368$	336.872			0.0477192
$369$			2254.56i			0.318069i
$370$			17259.6i			2.42509i
$371$			3255.12i			0.455519i
$372$			9476.44i			1.32078i
$373$	1763.72			0.244831			0.122416	−	0.992479i	$-0.460936\pi$
$373$	1763.72			0.244831			0.122416	+	0.992479i	$0.460936\pi$
$374$	15206.4			2.10242
$375$			3226.08i			0.444251i
$376$	3401.84			0.466586
$377$	−6950.22	−	6712.53i	−0.949481	−	0.917010i
$378$	2053.96			0.279483
$379$			1930.47i			0.261640i	0.991406	+	0.130820i	$0.0417611\pi$
$379$			1930.47i			0.261640i	−0.991406	+	0.130820i	$0.958239\pi$
$380$	−2445.38			−0.330120
$381$	−437.965			−0.0588914
$382$		−	2217.81i		−	0.297049i
$383$		−	8845.93i		−	1.18017i	−0.807340	−	0.590086i	$-0.799094\pi$
$383$		−	8845.93i		−	1.18017i	0.807340	−	0.590086i	$-0.200906\pi$
$384$			6772.81i			0.900061i
$385$		−	5384.46i		−	0.712772i
$386$	19306.5			2.54579
$387$	−3889.31			−0.510865
$388$			4598.10i			0.601632i
$389$	1598.08			0.208292			0.104146	−	0.994562i	$-0.466789\pi$
$389$	1598.08			0.208292			0.104146	+	0.994562i	$0.466789\pi$
$390$	−5938.76	−	5735.66i	−0.771079	−	0.744709i
$391$	−9658.47			−1.24923
$392$		−	1343.50i		−	0.173104i
$393$	951.489			0.122128
$394$	12335.8			1.57733
$395$			12048.5i			1.53475i
$396$			2844.51i			0.360965i
$397$		−	3578.82i		−	0.452433i	−0.974077	−	0.226217i	$-0.927364\pi$
$397$		−	3578.82i		−	0.452433i	0.974077	−	0.226217i	$-0.0726357\pi$
$398$		−	14173.7i		−	1.78509i
$399$	−749.669			−0.0940611
$400$	195.176			0.0243970
$401$			3485.99i			0.434120i	0.976158	+	0.217060i	$0.0696467\pi$
$401$			3485.99i			0.434120i	−0.976158	+	0.217060i	$0.930353\pi$
$402$	538.038			0.0667534
$403$	8112.58	−	8399.84i	1.00277	−	1.03828i
$404$	18898.8			2.32735
$405$			1045.86i			0.128319i
$406$	−15682.0			−1.91696
$407$	−7327.71			−0.892435
$408$		−	8562.33i		−	1.03897i
$409$			14709.1i			1.77828i	0.457637	+	0.889139i	$0.348696\pi$
$409$			14709.1i			1.77828i	−0.457637	+	0.889139i	$0.651304\pi$
$410$		−	14708.5i		−	1.77171i
$411$		−	1329.45i		−	0.159554i
$412$	7967.80			0.952780
$413$	−3891.92			−0.463702
$414$		−	2946.71i		−	0.349814i
$415$	14143.4			1.67294
$416$	6235.20	−	6455.98i	0.734869	−	0.760891i
$417$	2355.05			0.276565
$418$		−	1693.29i		−	0.198138i
$419$	3709.01			0.432451			0.216226	−	0.976343i	$-0.430625\pi$
$419$	3709.01			0.432451			0.216226	+	0.976343i	$0.430625\pi$
$420$	−8215.85			−0.954506
$421$			794.029i			0.0919207i	0.998943	+	0.0459603i	$0.0146348\pi$
$421$			794.029i			0.0919207i	−0.998943	+	0.0459603i	$0.985365\pi$
$422$		−	4780.32i		−	0.551427i
$423$			1439.00i			0.165406i
$424$			4139.96i			0.474185i
$425$	−5595.89			−0.638684
$426$	−12557.1			−1.42815
$427$			3094.94i			0.350760i
$428$	−6053.53			−0.683664
$429$	2435.13	−	2521.35i	0.274054	−	0.283758i
$430$	25373.5			2.84562
$431$			2891.52i			0.323155i	0.986860	+	0.161577i	$0.0516582\pi$
$431$			2891.52i			0.323155i	−0.986860	+	0.161577i	$0.948342\pi$
$432$	−126.327			−0.0140692
$433$	−5560.94			−0.617186			−0.308593	−	0.951194i	$-0.599858\pi$
$433$	−5560.94			−0.617186			−0.308593	+	0.951194i	$0.599858\pi$
$434$		−	18952.9i		−	2.09624i
$435$		−	7985.14i		−	0.880133i
$436$			4795.20i			0.526717i
$437$			1075.51i			0.117731i
$438$	−7490.62			−0.817159
$439$	−15127.2			−1.64460			−0.822302	−	0.569051i	$-0.807311\pi$
$439$	−15127.2			−1.64460			−0.822302	+	0.569051i	$0.807311\pi$
$440$		−	6848.11i		−	0.741979i
$441$	568.308			0.0613658
$442$	−19863.3	+	20566.6i	−2.13755	+	2.21324i
$443$	2357.89			0.252883			0.126441	−	0.991974i	$-0.459644\pi$
$443$	2357.89			0.252883			0.126441	+	0.991974i	$0.459644\pi$
$444$			11181.0i			1.19510i
$445$	−6870.56			−0.731901
$446$	−24993.0			−2.65348
$447$			406.260i			0.0429876i
$448$		−	13940.7i		−	1.47017i
$449$			7165.06i			0.753096i	0.926397	+	0.376548i	$0.122889\pi$
$449$			7165.06i			0.753096i	−0.926397	+	0.376548i	$0.877111\pi$
$450$		−	1707.26i		−	0.178846i
$451$	6244.63			0.651992
$452$	−168.288			−0.0175124
$453$			7121.22i			0.738596i
$454$	4190.74			0.433219
$455$	7282.47	+	7033.41i	0.750346	+	0.724685i
$456$	−953.451			−0.0979154
$457$			8020.96i			0.821017i	0.911857	+	0.410508i	$0.134649\pi$
$457$			8020.96i			0.821017i	−0.911857	+	0.410508i	$0.865351\pi$
$458$	877.378			0.0895135
$459$	3621.92			0.368316
$460$			11786.8i			1.19471i
$461$		−	4146.59i		−	0.418928i	−0.977816	−	0.209464i	$-0.932828\pi$
$461$		−	4146.59i		−	0.418928i	0.977816	−	0.209464i	$-0.0671720\pi$
$462$		−	5689.03i		−	0.572895i
$463$		−	7118.21i		−	0.714495i	−0.934010	−	0.357248i	$-0.883715\pi$
$463$		−	7118.21i		−	0.714495i	0.934010	−	0.357248i	$-0.116285\pi$
$464$	964.509			0.0965004
$465$	9650.62			0.962444
$466$		−	4155.31i		−	0.413071i
$467$	2128.22			0.210883			0.105441	−	0.994426i	$-0.466374\pi$
$467$	2128.22			0.210883			0.105441	+	0.994426i	$0.466374\pi$
$468$	−3847.20	−	3715.63i	−0.379993	−	0.366998i
$469$	−659.774			−0.0649585
$470$		−	9387.91i		−	0.921344i
$471$	−3500.18			−0.342420
$472$	−4949.86			−0.482703
$473$			10772.5i			1.04719i
$474$			12730.1i			1.23357i
$475$			623.125i			0.0601915i
$476$			28452.4i			2.73974i
$477$	−1751.23			−0.168099
$478$	8989.57			0.860196
$479$			3715.30i			0.354397i	0.984175	+	0.177199i	$0.0567035\pi$
$479$			3715.30i			0.354397i	−0.984175	+	0.177199i	$0.943296\pi$
$480$	7417.31			0.705317
$481$	9571.78	−	9910.71i	0.907350	−	0.939479i
$482$	17755.0			1.67784
$483$			3613.43i			0.340408i
$484$	−8996.77			−0.844926
$485$	4682.62			0.438405
$486$			1105.02i			0.103137i
$487$		−	8139.28i		−	0.757343i	−0.925531	−	0.378671i	$-0.876381\pi$
$487$		−	8139.28i		−	0.757343i	0.925531	−	0.378671i	$-0.123619\pi$
$488$			3936.23i			0.365133i
$489$			6927.57i			0.640645i
$490$	−3707.59			−0.341820
$491$	−18081.7			−1.66194			−0.830972	−	0.556315i	$-0.812215\pi$
$491$	−18081.7			−1.66194			−0.830972	+	0.556315i	$0.812215\pi$
$492$		−	9528.35i		−	0.873112i
$493$	−27653.4			−2.52626
$494$	2290.18	+	2211.86i	0.208583	+	0.201450i
$495$	2896.80			0.263033
$496$			1165.68i			0.105525i
$497$	15398.3			1.38975
$498$	14943.4			1.34464
$499$			11031.5i			0.989659i	0.868990	+	0.494829i	$0.164769\pi$
$499$			11031.5i			0.989659i	−0.868990	+	0.494829i	$0.835231\pi$
$500$		−	13634.2i		−	1.21948i
$501$			1802.37i			0.160726i
$502$			4283.80i			0.380868i
$503$	8016.14			0.710581			0.355290	−	0.934756i	$-0.384382\pi$
$503$	8016.14			0.710581			0.355290	+	0.934756i	$0.384382\pi$
$504$	−3203.35			−0.283112
$505$		−	19246.1i		−	1.69592i
$506$	−8161.74			−0.717063
$507$	229.256	+	6587.01i	0.0200821	+	0.577001i
$508$	1850.95			0.161659
$509$			20173.9i			1.75676i	0.477959	+	0.878382i	$0.341377\pi$
$509$			20173.9i			1.75676i	−0.477959	+	0.878382i	$0.658623\pi$
$510$	−23629.1			−2.05159
$511$	9185.44			0.795186
$512$			1692.30i			0.146074i
$513$		−	403.316i		−	0.0347112i
$514$			3695.29i			0.317105i
$515$		−	8114.25i		−	0.694285i
$516$	16437.2			1.40234
$517$	3985.72			0.339056
$518$		−	22361.9i		−	1.89677i
$519$	−10291.1			−0.870382
$520$	9262.05	+	8945.30i	0.781092	+	0.754380i
$521$	9746.95			0.819619			0.409810	−	0.912171i	$-0.365595\pi$
$521$	9746.95			0.819619			0.409810	+	0.912171i	$0.365595\pi$
$522$		−	8436.81i		−	0.707413i
$523$	−18929.3			−1.58264			−0.791320	−	0.611402i	$-0.790606\pi$
$523$	−18929.3			−1.58264			−0.791320	+	0.611402i	$0.790606\pi$
$524$	−4021.24			−0.335245
$525$			2093.54i			0.174037i
$526$		−	11860.9i		−	0.983195i
$527$		−	33421.2i		−	2.76252i
$528$			349.898i			0.0288397i
$529$	−6983.00			−0.573929
$530$	11424.9			0.936349
$531$		−	2093.83i		−	0.171119i
$532$	3168.30			0.258201
$533$	−8157.02	+	8445.85i	−0.662889	+	0.686361i
$534$	−7259.20			−0.588270
$535$			6164.80i			0.498182i
$536$	−839.120			−0.0676203
$537$	−2936.51			−0.235977
$538$		−	21786.6i		−	1.74589i
$539$		−	1574.09i		−	0.125790i
$540$		−	4420.07i		−	0.352240i
$541$			11366.8i			0.903321i	0.892190	+	0.451661i	$0.149168\pi$
$541$			11366.8i			0.903321i	−0.892190	+	0.451661i	$0.850832\pi$
$542$	−16659.9			−1.32030
$543$	11517.3			0.910227
$544$		−	25687.0i		−	2.02449i
$545$	4883.34			0.383815
$546$	7694.40	+	7431.26i	0.603095	+	0.582470i
$547$	17495.4			1.36755			0.683775	−	0.729693i	$-0.260337\pi$
$547$	17495.4			1.36755			0.683775	+	0.729693i	$0.260337\pi$
$548$			5618.59i			0.437983i
$549$	−1665.05			−0.129440
$550$	−4728.72			−0.366606
$551$			3079.33i			0.238083i
$552$			4595.67i			0.354356i
$553$		−	15610.4i		−	1.20040i
$554$			2839.05i			0.217725i
$555$	11386.5			0.870862
$556$	−9953.06			−0.759180
$557$			11873.1i			0.903192i	0.892223	+	0.451596i	$0.149145\pi$
$557$			11873.1i			0.903192i	−0.892223	+	0.451596i	$0.850855\pi$
$558$	10196.5			0.773571
$559$	−14569.8	−	14071.6i	−1.10239	−	1.06469i
$560$	−1010.62			−0.0762613
$561$		−	10031.9i		−	0.754989i
$562$	25170.4			1.88923
$563$	2829.31			0.211796			0.105898	−	0.994377i	$-0.466228\pi$
$563$	2829.31			0.211796			0.105898	+	0.994377i	$0.466228\pi$
$564$		−	6081.60i		−	0.454045i
$565$			171.381i			0.0127612i
$566$		−	796.481i		−	0.0591495i
$567$		−	1355.04i		−	0.100364i
$568$	19583.9			1.44670
$569$	−16136.8			−1.18891			−0.594453	−	0.804130i	$-0.702632\pi$
$569$	−16136.8			−1.18891			−0.594453	+	0.804130i	$0.702632\pi$
$570$			2631.20i			0.193349i
$571$	17840.5			1.30754			0.653769	−	0.756695i	$-0.273187\pi$
$571$	17840.5			1.30754			0.653769	+	0.756695i	$0.273187\pi$
$572$	−10291.5	+	10655.9i	−0.752288	+	0.778926i
$573$	−1463.13			−0.106672
$574$			19056.7i			1.38573i
$575$	3003.49			0.217833
$576$	7500.00			0.542534
$577$			8516.17i			0.614442i	0.951638	+	0.307221i	$0.0993990\pi$
$577$			8516.17i			0.614442i	−0.951638	+	0.307221i	$0.900601\pi$
$578$			59488.9i			4.28099i
$579$		−	12736.8i		−	0.914205i
$580$			33747.3i			2.41600i
$581$	−18324.5			−1.30848
$582$	4947.49			0.352371
$583$			4850.53i			0.344577i
$584$	11682.3			0.827770
$585$	−3783.92	+	3917.91i	−0.267429	+	0.276899i
$586$	−35352.9			−2.49218
$587$		−	20688.3i		−	1.45468i	−0.686277	−	0.727340i	$-0.740756\pi$
$587$		−	20688.3i		−	1.45468i	0.686277	−	0.727340i	$-0.259244\pi$
$588$	−2401.82			−0.168451
$589$	−3721.59			−0.260349
$590$			13659.9i			0.953169i
$591$		−	8138.13i		−	0.566426i
$592$			1375.35i			0.0954839i
$593$		−	11435.9i		−	0.791933i	−0.918265	−	0.395966i	$-0.870410\pi$
$593$		−	11435.9i		−	0.791933i	0.918265	−	0.395966i	$-0.129590\pi$
$594$	3060.65			0.211414
$595$	28975.4			1.99643
$596$		−	1716.96i		−	0.118002i
$597$	−9350.69			−0.641035
$598$	10661.2	−	11038.7i	0.729047	−	0.754863i
$599$	1260.80			0.0860016			0.0430008	−	0.999075i	$-0.486308\pi$
$599$	1260.80			0.0860016			0.0430008	+	0.999075i	$0.486308\pi$
$600$			2662.62i			0.181169i
$601$	6261.10			0.424951			0.212476	−	0.977166i	$-0.431847\pi$
$601$	6261.10			0.424951			0.212476	+	0.977166i	$0.431847\pi$
$602$	−32874.5			−2.22569
$603$		−	354.954i		−	0.0239715i
$604$		−	30096.1i		−	2.02747i
$605$			9162.14i			0.615692i
$606$		−	20334.8i		−	1.36311i
$607$	3230.33			0.216005			0.108003	−	0.994151i	$-0.465555\pi$
$607$	3230.33			0.216005			0.108003	+	0.994151i	$0.465555\pi$
$608$	−2860.35			−0.190794
$609$			10345.7i			0.688391i
$610$	10862.6			0.721009
$611$	−5206.33	+	5390.68i	−0.344722	+	0.356929i
$612$	−15307.2			−1.01104
$613$			14868.5i			0.979660i	0.871818	+	0.489830i	$0.162941\pi$
$613$			14868.5i			0.979660i	−0.871818	+	0.489830i	$0.837059\pi$
$614$	36483.0			2.39794
$615$	−9703.48			−0.636231
$616$			8872.57i			0.580334i
$617$		−	19952.8i		−	1.30190i	−0.759121	−	0.650949i	$-0.774371\pi$
$617$		−	19952.8i		−	1.30190i	0.759121	−	0.650949i	$-0.225629\pi$
$618$		−	8573.24i		−	0.558036i
$619$		−	8316.48i		−	0.540012i	−0.962859	−	0.270006i	$-0.912974\pi$
$619$		−	8316.48i		−	0.540012i	0.962859	−	0.270006i	$-0.0870257\pi$
$620$	−40786.0			−2.64194
$621$	−1944.00			−0.125620
$622$			42131.0i			2.71592i
$623$	8901.66			0.572452
$624$	−473.237	−	457.053i	−0.0303600	−	0.0293217i
$625$	−19099.2			−1.22235
$626$			33757.9i			2.15533i
$627$	−1117.10			−0.0711525
$628$	14792.7			0.939955
$629$		−	39432.6i		−	2.49965i
$630$			8840.13i			0.559046i
$631$			12605.9i			0.795299i	0.917537	+	0.397649i	$0.130174\pi$
$631$			12605.9i			0.795299i	−0.917537	+	0.397649i	$0.869826\pi$
$632$		−	19853.7i		−	1.24959i
$633$	−3153.66			−0.198020
$634$	−12009.8			−0.752321
$635$		−	1884.98i		−	0.117800i
$636$	7401.17			0.461439
$637$	2128.95	+	2056.15i	0.132421	+	0.127892i
$638$	−23368.1			−1.45008
$639$			8284.14i			0.512857i
$640$	−29149.8			−1.80038
$641$	9224.04			0.568374			0.284187	−	0.958769i	$-0.408276\pi$
$641$	9224.04			0.568374			0.284187	+	0.958769i	$0.408276\pi$
$642$			6513.51i			0.400417i
$643$			4439.16i			0.272260i	0.990691	+	0.136130i	$0.0434665\pi$
$643$			4439.16i			0.272260i	−0.990691	+	0.136130i	$0.956533\pi$
$644$		−	15271.3i		−	0.934431i
$645$		−	16739.4i		−	1.02188i
$646$	9112.13			0.554972
$647$	9601.15			0.583401			0.291700	−	0.956510i	$-0.405779\pi$
$647$	9601.15			0.583401			0.291700	+	0.956510i	$0.405779\pi$
$648$		−	1723.38i		−	0.104476i
$649$	−5799.44			−0.350767
$650$	6176.87	−	6395.59i	0.372733	−	0.385932i
$651$	−12503.6			−0.752770
$652$		−	29277.7i		−	1.75859i
$653$	27112.8			1.62482			0.812410	−	0.583087i	$-0.198155\pi$
$653$	27112.8			1.62482			0.812410	+	0.583087i	$0.198155\pi$
$654$	5159.56			0.308494
$655$			4095.15i			0.244291i
$656$		−	1172.06i		−	0.0697583i
$657$			4941.70i			0.293446i
$658$			12163.2i			0.720624i
$659$	5587.26			0.330271			0.165136	−	0.986271i	$-0.447194\pi$
$659$	5587.26			0.330271			0.165136	+	0.986271i	$0.447194\pi$
$660$	−12242.6			−0.722035
$661$			3060.13i			0.180069i	0.995939	+	0.0900343i	$0.0286977\pi$
$661$			3060.13i			0.180069i	−0.995939	+	0.0900343i	$0.971302\pi$
$662$	−49018.6			−2.87789
$663$	13568.2	+	13104.2i	0.794788	+	0.767607i
$664$	−23305.6			−1.36210
$665$		−	3226.53i		−	0.188150i
$666$	12030.5			0.699961
$667$	14842.5			0.861623
$668$		−	7617.26i		−	0.441199i
$669$			16488.4i			0.952880i
$670$			2315.68i			0.133526i
$671$			4611.83i			0.265332i
$672$	−9610.04			−0.551660
$673$	−4121.55			−0.236069			−0.118034	−	0.993010i	$-0.537659\pi$
$673$	−4121.55			−0.236069			−0.118034	+	0.993010i	$0.537659\pi$
$674$			1425.45i			0.0814633i
$675$	−1126.31			−0.0642246
$676$	−968.894	−	27838.4i	−0.0551260	−	1.58389i
$677$	22889.5			1.29943			0.649715	−	0.760178i	$-0.274888\pi$
$677$	22889.5			1.29943			0.649715	+	0.760178i	$0.274888\pi$
$678$			181.075i			0.0102569i
$679$	−6066.91			−0.342896
$680$	36851.8			2.07824
$681$		−	2764.71i		−	0.155571i
$682$		−	28242.1i		−	1.58570i
$683$			19297.9i			1.08113i	0.841301	+	0.540566i	$0.181790\pi$
$683$			19297.9i			1.08113i	−0.841301	+	0.540566i	$0.818210\pi$
$684$			1704.52i			0.0952835i
$685$	5721.87			0.319155
$686$	30896.6			1.71959
$687$		−	578.823i		−	0.0321448i
$688$	2021.91			0.112042
$689$	−6560.34	−	6335.98i	−0.362742	−	0.350336i
$690$	12682.5			0.699729
$691$		−	30317.8i		−	1.66910i	−0.550935	−	0.834548i	$-0.685729\pi$
$691$		−	30317.8i		−	1.66910i	0.550935	−	0.834548i	$-0.314271\pi$
$692$	43492.8			2.38923
$693$	−3753.16			−0.205730
$694$		−	12956.6i		−	0.708682i
$695$			10136.0i			0.553210i
$696$			13158.0i			0.716599i
$697$			33604.3i			1.82619i
$698$	29407.7			1.59470
$699$	−2741.34			−0.148336
$700$		−	8847.84i		−	0.477738i
$701$	−9606.16			−0.517574			−0.258787	−	0.965934i	$-0.583323\pi$
$701$	−9606.16			−0.517574			−0.258787	+	0.965934i	$0.583323\pi$
$702$	−3997.96	+	4139.53i	−0.214948	+	0.222559i
$703$	−4390.99			−0.235575
$704$		−	20773.4i		−	1.11211i
$705$	−6193.38			−0.330860
$706$	12610.4			0.672235
$707$			24935.7i			1.32646i
$708$			8849.05i			0.469729i
$709$			23398.8i			1.23944i	0.784825	+	0.619718i	$0.212753\pi$
$709$			23398.8i			1.23944i	−0.784825	+	0.619718i	$0.787247\pi$
$710$		−	54044.9i		−	2.85672i
$711$	8398.26			0.442981
$712$	11321.4			0.595909
$713$			17938.2i			0.942203i
$714$	30614.4			1.60464
$715$	10851.8	+	10480.6i	0.567598	+	0.548187i
$716$	12410.5			0.647766
$717$		−	5930.59i		−	0.308901i
$718$	−6671.51			−0.346767
$719$	23588.7			1.22352			0.611758	−	0.791045i	$-0.290463\pi$
$719$	23588.7			1.22352			0.611758	+	0.791045i	$0.290463\pi$
$720$		−	543.704i		−	0.0281426i
$721$			10513.0i			0.543031i
$722$			30175.9i			1.55544i
$723$		−	11713.3i		−	0.602522i
$724$	−48674.9			−2.49861
$725$	8599.38			0.440514
$726$			9680.40i			0.494867i
$727$	−15733.5			−0.802644			−0.401322	−	0.915937i	$-0.631449\pi$
$727$	−15733.5			−0.802644			−0.401322	+	0.915937i	$0.631449\pi$
$728$	−12000.1	−	11589.7i	−0.610926	−	0.590034i
$729$	729.000			0.0370370
$730$		−	32239.2i		−	1.63455i
$731$	−57970.3			−2.93312
$732$	7036.94			0.355318
$733$		−	17297.1i		−	0.871598i	−0.900044	−	0.435799i	$-0.856466\pi$
$733$		−	17297.1i		−	0.871598i	0.900044	−	0.435799i	$-0.143534\pi$
$734$			21137.3i			1.06293i
$735$			2445.96i			0.122749i
$736$			13787.0i			0.690484i
$737$	−983.144			−0.0491378
$738$	−10252.4			−0.511375
$739$		−	38749.2i		−	1.92884i	−0.264377	−	0.964419i	$-0.585166\pi$
$739$		−	38749.2i		−	1.92884i	0.264377	−	0.964419i	$-0.414834\pi$
$740$	−48122.2			−2.39055
$741$	1459.20	−	1510.87i	0.0723417	−	0.0749033i
$742$	−14802.3			−0.732359
$743$		−	3139.76i		−	0.155029i	−0.996991	−	0.0775144i	$-0.975302\pi$
$743$		−	3139.76i		−	0.155029i	0.996991	−	0.0775144i	$-0.0246984\pi$
$744$	−15902.4			−0.783616
$745$	−1748.52			−0.0859876
$746$			8020.33i			0.393626i
$747$		−	9858.45i		−	0.482867i
$748$			42397.6i			2.07247i
$749$		−	7987.25i		−	0.389650i
$750$	−14670.2			−0.714242
$751$	−40628.6			−1.97411			−0.987055	−	0.160380i	$-0.948728\pi$
$751$	−40628.6			−1.97411			−0.987055	+	0.160380i	$0.948728\pi$
$752$		−	748.086i		−	0.0362764i
$753$	2826.11			0.136772
$754$	30524.5	−	31605.4i	1.47432	−	1.52652i
$755$	−30649.3			−1.47741
$756$			5726.74i			0.275502i
$757$	24004.9			1.15254			0.576271	−	0.817259i	$-0.304507\pi$
$757$	24004.9			1.15254			0.576271	+	0.817259i	$0.304507\pi$
$758$	−8778.62			−0.420651
$759$			5384.46i			0.257501i
$760$		−	4103.60i		−	0.195859i
$761$		−	29540.1i		−	1.40713i	−0.710630	−	0.703566i	$-0.751590\pi$
$761$		−	29540.1i		−	1.40713i	0.710630	−	0.703566i	$-0.248410\pi$
$762$		−	1991.60i		−	0.0946824i
$763$	−6326.97			−0.300199
$764$	6183.56			0.292818
$765$			15588.5i			0.736739i
$766$	40225.9			1.89742
$767$	7575.49	−	7843.73i	0.356630	−	0.369258i
$768$	−10798.6			−0.507372
$769$			7585.63i			0.355715i	0.984056	+	0.177857i	$0.0569166\pi$
$769$			7585.63i			0.355715i	−0.984056	+	0.177857i	$0.943083\pi$
$770$	24485.2			1.14596
$771$	2437.85			0.113874
$772$			53829.2i			2.50953i
$773$			3284.29i			0.152817i	0.997077	+	0.0764086i	$0.0243453\pi$
$773$			3284.29i			0.152817i	−0.997077	+	0.0764086i	$0.975655\pi$
$774$		−	17686.2i		−	0.821341i
$775$			10393.0i			0.481712i
$776$	−7716.07			−0.356947
$777$	−14752.6			−0.681140
$778$			7267.08i			0.334881i
$779$	3741.98			0.172106
$780$	15991.8	−	16558.1i	0.734103	−	0.760097i
$781$	22945.3			1.05128
$782$		−	43920.8i		−	2.00845i
$783$	−5565.92			−0.254036
$784$	−295.443			−0.0134586
$785$		−	15064.6i		−	0.684939i
$786$			4326.79i			0.196351i
$787$			41624.1i			1.88531i	0.333772	+	0.942654i	$0.391679\pi$
$787$			41624.1i			1.88531i	−0.333772	+	0.942654i	$0.608321\pi$
$788$			34393.8i			1.55486i
$789$	−7824.87			−0.353071
$790$	−54789.4			−2.46749
$791$		−	222.046i		−	0.00998108i
$792$	−4773.38			−0.214160
$793$	−6237.49	−	6024.18i	−0.279319	−	0.269767i
$794$	16274.3			0.727398
$795$		−	7537.20i		−	0.336248i
$796$	39518.4			1.75967
$797$	30333.3			1.34813			0.674066	−	0.738671i	$-0.264546\pi$
$797$	30333.3			1.34813			0.674066	+	0.738671i	$0.264546\pi$
$798$		−	3409.04i		−	0.151226i
$799$			21448.4i			0.949674i
$800$			7987.87i			0.353017i
$801$			4789.03i			0.211251i
$802$	−15852.2			−0.697954
$803$	13687.4			0.601518
$804$			1500.13i			0.0658027i
$805$	−15552.0			−0.680914
$806$	38197.4	+	36891.1i	1.66929	+	1.61220i
$807$	−14373.1			−0.626958
$808$			31714.0i			1.38081i
$809$	−24853.9			−1.08012			−0.540060	−	0.841627i	$-0.681598\pi$
$809$	−24853.9			−1.08012			−0.540060	+	0.841627i	$0.681598\pi$
$810$	−4755.92			−0.206304
$811$		−	17383.5i		−	0.752674i	−0.926483	−	0.376337i	$-0.877184\pi$
$811$		−	17383.5i		−	0.752674i	0.926483	−	0.376337i	$-0.122816\pi$
$812$		−	43723.7i		−	1.88966i
$813$			10990.9i			0.474128i
$814$		−	33322.0i		−	1.43481i
$815$	−29815.8			−1.28148
$816$	−1882.91			−0.0807782
$817$			6455.23i			0.276426i
$818$	−66887.8			−2.85902
$819$	4902.54	−	5076.14i	0.209168	−	0.216575i
$820$	41009.4			1.74648
$821$		−	31169.4i		−	1.32499i	−0.749065	−	0.662496i	$-0.769497\pi$
$821$		−	31169.4i		−	1.32499i	0.749065	−	0.662496i	$-0.230503\pi$
$822$	6045.52			0.256523
$823$	−5512.79			−0.233492			−0.116746	−	0.993162i	$-0.537246\pi$
$823$	−5512.79			−0.233492			−0.116746	+	0.993162i	$0.537246\pi$
$824$			13370.8i			0.565282i
$825$			3119.63i			0.131650i
$826$		−	17698.1i		−	0.745516i
$827$			13335.8i			0.560738i	0.959892	+	0.280369i	$0.0904568\pi$
$827$			13335.8i			0.560738i	−0.959892	+	0.280369i	$0.909543\pi$
$828$	8215.85			0.344832
$829$	28338.5			1.18726			0.593628	−	0.804739i	$-0.297695\pi$
$829$	28338.5			1.18726			0.593628	+	0.804739i	$0.297695\pi$
$830$			64315.5i			2.68967i
$831$	1872.98			0.0781864
$832$	28095.9	+	27135.1i	1.17073	+	1.13070i
$833$	8470.66			0.352330
$834$			10709.3i			0.444646i
$835$	−7757.27			−0.321499
$836$	4721.15			0.195316
$837$		−	6726.82i		−	0.277793i
$838$			16866.3i			0.695272i
$839$			27149.5i			1.11717i	0.829447	+	0.558585i	$0.188656\pi$
$839$			27149.5i			1.11717i	−0.829447	+	0.558585i	$0.811344\pi$
$840$		−	13787.0i		−	0.566306i
$841$	18106.9			0.742421
$842$	−3610.76			−0.147785
$843$		−	16605.4i		−	0.678433i
$844$	13328.2			0.543573
$845$	−28350.1	+	986.703i	−1.15417	+	0.0401700i
$846$	−6543.71			−0.265931
$847$		−	11870.7i		−	0.481560i
$848$	910.404			0.0368672
$849$	−525.454			−0.0212409
$850$		−	25446.7i		−	1.02684i
$851$			21164.7i			0.852547i
$852$		−	35010.9i		−	1.40781i
$853$		−	7978.22i		−	0.320245i	−0.987097	−	0.160123i	$-0.948811\pi$
$853$		−	7978.22i		−	0.320245i	0.987097	−	0.160123i	$-0.0511889\pi$
$854$	−14073.9			−0.563933
$855$	1735.85			0.0694325
$856$		−	10158.4i		−	0.405616i
$857$	13614.4			0.542657			0.271329	−	0.962487i	$-0.412537\pi$
$857$	13614.4			0.542657			0.271329	+	0.962487i	$0.412537\pi$
$858$	11465.6	+	11073.5i	0.456211	+	0.440609i
$859$	−35007.7			−1.39051			−0.695255	−	0.718763i	$-0.744709\pi$
$859$	−35007.7			−1.39051			−0.695255	+	0.718763i	$0.744709\pi$
$860$			70744.8i			2.80509i
$861$	12572.1			0.497624
$862$	−13148.9			−0.519551
$863$		−	24461.5i		−	0.964867i	−0.875933	−	0.482434i	$-0.839753\pi$
$863$		−	24461.5i		−	0.964867i	0.875933	−	0.482434i	$-0.160247\pi$
$864$		−	5170.13i		−	0.203578i
$865$		−	44292.2i		−	1.74102i
$866$		−	25287.8i		−	0.992278i
$867$	39245.9			1.53733
$868$	52843.3			2.06638
$869$		−	23261.3i		−	0.908040i
$870$	36311.5			1.41503
$871$	1284.23	−	1329.70i	0.0499591	−	0.0517281i
$872$	−8046.82			−0.312500
$873$		−	3263.95i		−	0.126538i
$874$	−4890.77			−0.189282
$875$	17989.5			0.695037
$876$		−	20884.9i		−	0.805520i
$877$		−	43121.6i		−	1.66034i	−0.557514	−	0.830168i	$-0.688245\pi$
$877$		−	43121.6i		−	1.66034i	0.557514	−	0.830168i	$-0.311755\pi$
$878$		−	68789.3i		−	2.64411i
$879$			23323.0i			0.894955i
$880$	−1505.94			−0.0576878
$881$	40824.5			1.56120			0.780598	−	0.625034i	$-0.214915\pi$
$881$	40824.5			1.56120			0.780598	+	0.625034i	$0.214915\pi$
$882$			2584.32i			0.0986605i
$883$	−8262.14			−0.314885			−0.157442	−	0.987528i	$-0.550325\pi$
$883$	−8262.14			−0.314885			−0.157442	+	0.987528i	$0.550325\pi$
$884$	−57342.7	−	55381.6i	−2.18172	−	2.10711i
$885$	9011.70			0.342288
$886$			10722.3i			0.406571i
$887$	−40858.6			−1.54667			−0.773336	−	0.633997i	$-0.781413\pi$
$887$	−40858.6			−1.54667			−0.773336	+	0.633997i	$0.781413\pi$
$888$	−18762.8			−0.709050
$889$			2442.22i			0.0921365i
$890$		−	31243.2i		−	1.17671i
$891$		−	2019.17i		−	0.0759201i
$892$		−	69684.1i		−	2.61569i
$893$	2388.37			0.0895001
$894$	−1847.42			−0.0691131
$895$		−	12638.6i		−	0.472023i
$896$	37767.1			1.40816
$897$	−7282.47	−	7033.41i	−0.271075	−	0.261805i
$898$	−32582.3			−1.21079
$899$			51359.4i			1.90537i
$900$	4760.07			0.176299
$901$	−26102.2			−0.965139
$902$			28396.8i			1.04824i
$903$			21687.9i			0.799256i
$904$		−	282.404i		−	0.0103901i
$905$			49569.6i			1.82072i
$906$	−32383.0			−1.18747
$907$	32729.3			1.19819			0.599095	−	0.800678i	$-0.295527\pi$
$907$	32729.3			1.19819			0.599095	+	0.800678i	$0.295527\pi$
$908$			11684.4i			0.427048i
$909$	−13415.2			−0.489500
$910$	−31983.7	+	33116.2i	−1.16511	+	1.20637i
$911$	11065.9			0.402447			0.201223	−	0.979545i	$-0.435508\pi$
$911$	11065.9			0.402447			0.201223	+	0.979545i	$0.435508\pi$
$912$			209.670i			0.00761279i
$913$	−27305.7			−0.989801
$914$	−36474.5			−1.31999
$915$		−	7166.29i		−	0.258918i
$916$			2446.26i			0.0882386i
$917$		−	5305.77i		−	0.191071i
$918$			16470.3i			0.592158i
$919$	50682.2			1.81921			0.909604	−	0.415477i	$-0.136385\pi$
$919$	50682.2			1.81921			0.909604	+	0.415477i	$0.136385\pi$
$920$	−19779.5			−0.708816
$921$		−	24068.5i		−	0.861114i
$922$	18856.2			0.673531
$923$	−29972.1	+	31033.4i	−1.06885	+	1.10669i
$924$	15861.8			0.564735
$925$			12262.3i			0.435874i
$926$	32369.3			1.14873
$927$	−5655.92			−0.200394
$928$			39474.0i			1.39633i
$929$			41045.5i			1.44958i	0.688970	+	0.724790i	$0.258063\pi$
$929$			41045.5i			1.44958i	−0.688970	+	0.724790i	$0.741937\pi$
$930$			43885.1i			1.54737i
$931$		−	943.243i		−	0.0332047i
$932$	11585.6			0.407188
$933$	27794.6			0.975300
$934$			9677.86i			0.339046i
$935$	43176.9			1.51020
$936$	6235.20	−	6455.98i	0.217739	−	0.225449i
$937$	−788.985			−0.0275080			−0.0137540	−	0.999905i	$-0.504378\pi$
$937$	−788.985			−0.0275080			−0.0137540	+	0.999905i	$0.504378\pi$
$938$		−	3000.25i		−	0.104437i
$939$	22270.7			0.773991
$940$	26174.8			0.908222
$941$		−	25676.2i		−	0.889499i	−0.895655	−	0.444750i	$-0.853293\pi$
$941$		−	25676.2i		−	0.889499i	0.895655	−	0.444750i	$-0.146707\pi$
$942$		−	15916.7i		−	0.550524i
$943$		−	18036.5i		−	0.622851i
$944$			1088.51i			0.0375295i
$945$	5832.00			0.200757
$946$	−48986.9			−1.68362
$947$			679.352i			0.0233115i	0.999932	+	0.0116557i	$0.00371022\pi$
$947$			679.352i			0.0233115i	−0.999932	+	0.0116557i	$0.996290\pi$
$948$	−35493.2			−1.21600
$949$	−17879.1	+	18512.2i	−0.611571	+	0.633227i
$950$	−2833.60			−0.0967726
$951$			7923.12i			0.270163i
$952$	−47746.0			−1.62548
$953$	20238.4			0.687917			0.343958	−	0.938985i	$-0.388232\pi$
$953$	20238.4			0.687917			0.343958	+	0.938985i	$0.388232\pi$
$954$		−	7963.54i		−	0.270261i
$955$		−	6297.21i		−	0.213375i
$956$			25064.2i			0.847944i
$957$			15416.4i			0.520733i
$958$	−16894.9			−0.569781
$959$	−7413.38			−0.249625
$960$			32279.5i			1.08523i
$961$	−32280.6			−1.08357
$962$	45067.9	+	43526.6i	1.51044	+	1.45879i
$963$	4297.08			0.143792
$964$			49503.6i			1.65395i
$965$	54818.6			1.82868
$966$	−16431.7			−0.547289
$967$		−	6161.63i		−	0.204906i	−0.994738	−	0.102453i	$-0.967331\pi$
$967$		−	6161.63i		−	0.204906i	0.994738	−	0.102453i	$-0.0326692\pi$
$968$		−	15097.5i		−	0.501293i
$969$		−	6011.45i		−	0.199294i
$970$			21293.7i			0.704845i
$971$	−48569.5			−1.60522			−0.802610	−	0.596504i	$-0.796556\pi$
$971$	−48569.5			−1.60522			−0.802610	+	0.596504i	$0.796556\pi$
$972$	−3080.94			−0.101668
$973$		−	13132.4i		−	0.432689i
$974$	37012.5			1.21761
$975$	−4219.29	−	4075.00i	−0.138590	−	0.133851i
$976$	865.602			0.0283886
$977$		−	44595.8i		−	1.46033i	−0.683269	−	0.730167i	$-0.739442\pi$
$977$		−	44595.8i		−	1.46033i	0.683269	−	0.730167i	$-0.260558\pi$
$978$	−31502.4			−1.03000
$979$	13264.6			0.433031
$980$		−	10337.3i		−	0.336951i
$981$		−	3403.86i		−	0.110782i
$982$		−	82224.4i		−	2.67198i
$983$			29599.0i			0.960389i	0.877162	+	0.480195i	$0.159434\pi$
$983$			29599.0i			0.960389i	−0.877162	+	0.480195i	$0.840566\pi$
$984$	15989.5			0.518015
$985$	35026.0			1.13302
$986$		−	125751.i		−	4.06159i
$987$	8024.29			0.258780
$988$	−6166.97	+	6385.34i	−0.198580	+	0.205612i
$989$	31114.5			1.00039
$990$			13172.9i			0.422890i
$991$	5718.45			0.183302			0.0916511	−	0.995791i	$-0.470786\pi$
$991$	5718.45			0.183302			0.0916511	+	0.995791i	$0.470786\pi$
$992$	−47707.2			−1.52692
$993$			32338.5i			1.03347i
$994$			70021.9i			2.23437i
$995$		−	40244.8i		−	1.28226i
$996$			41664.4i			1.32549i
$997$	−1491.44			−0.0473766			−0.0236883	−	0.999719i	$-0.507541\pi$
$997$	−1491.44			−0.0473766			−0.0236883	+	0.999719i	$0.507541\pi$
$998$	−50164.8			−1.59112
$999$		−	7936.77i		−	0.251360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.b.b.25.4	yes	4
3.2	odd	2		117.4.b.e.64.1		4
4.3	odd	2		624.4.c.c.337.4		4
13.5	odd	4		507.4.a.l.1.4		4
13.8	odd	4		507.4.a.l.1.1		4
13.12	even	2	inner	39.4.b.b.25.1	✓	4
39.5	even	4		1521.4.a.w.1.1		4
39.8	even	4		1521.4.a.w.1.4		4
39.38	odd	2		117.4.b.e.64.4		4
52.51	odd	2		624.4.c.c.337.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.b.b.25.1	✓	4	13.12	even	2	inner
39.4.b.b.25.4	yes	4	1.1	even	1	trivial
117.4.b.e.64.1		4	3.2	odd	2
117.4.b.e.64.4		4	39.38	odd	2
507.4.a.l.1.1		4	13.8	odd	4
507.4.a.l.1.4		4	13.5	odd	4
624.4.c.c.337.1		4	52.51	odd	2
624.4.c.c.337.4		4	4.3	odd	2
1521.4.a.w.1.1		4	39.5	even	4
1521.4.a.w.1.4		4	39.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.54739i q^{2} +3.00000 q^{3} -12.6788 q^{4} +12.9118i q^{5} +13.6422i q^{6} -16.7289i q^{7} -21.2762i q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.54739i q^{2} +3.00000 q^{3} -12.6788 q^{4} +12.9118i q^{5} +13.6422i q^{6} -16.7289i q^{7} -21.2762i q^{8} +9.00000 q^{9} -58.7151 q^{10} -24.9280i q^{11} -38.0363 q^{12} +(33.7151 + 32.5621i) q^{13} +76.0727 q^{14} +38.7355i q^{15} -4.67878 q^{16} +134.145 q^{17} +40.9265i q^{18} -14.9376i q^{19} -163.706i q^{20} -50.1866i q^{21} +113.358 q^{22} -72.0000 q^{23} -63.8287i q^{24} -41.7151 q^{25} +(-148.073 + 153.316i) q^{26} +27.0000 q^{27} +212.101i q^{28} -206.145 q^{29} -176.145 q^{30} -249.142i q^{31} -191.486i q^{32} -74.7841i q^{33} +610.012i q^{34} +216.000 q^{35} -114.109 q^{36} -293.955i q^{37} +67.9273 q^{38} +(101.145 + 97.6863i) q^{39} +274.715 q^{40} +250.506i q^{41} +228.218 q^{42} -432.145 q^{43} +316.057i q^{44} +116.206i q^{45} -327.412i q^{46} +159.889i q^{47} -14.0363 q^{48} +63.1454 q^{49} -189.695i q^{50} +402.436 q^{51} +(-427.467 - 412.848i) q^{52} -194.581 q^{53} +122.780i q^{54} +321.866 q^{55} -355.927 q^{56} -44.8129i q^{57} -937.424i q^{58} -232.647i q^{59} -491.118i q^{60} -185.006 q^{61} +1132.94 q^{62} -150.560i q^{63} +833.333 q^{64} +(-420.436 + 435.324i) q^{65} +340.073 q^{66} -39.4393i q^{67} -1700.80 q^{68} -216.000 q^{69} +982.237i q^{70} +920.460i q^{71} -191.486i q^{72} +549.078i q^{73} +1336.73 q^{74} -125.145 q^{75} +189.391i q^{76} -417.018 q^{77} +(-444.218 + 459.948i) q^{78} +933.140 q^{79} -60.4116i q^{80} +81.0000 q^{81} -1139.15 q^{82} -1095.38i q^{83} +636.304i q^{84} +1732.06i q^{85} -1965.13i q^{86} -618.436 q^{87} -530.375 q^{88} +532.114i q^{89} -528.436 q^{90} +(544.727 - 564.015i) q^{91} +912.872 q^{92} -747.425i q^{93} -727.079 q^{94} +192.872 q^{95} -574.459i q^{96} -362.661i q^{97} +287.147i q^{98} -224.352i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{3} - 14 q^{4} + 36 q^{9}+O(q^{10}) \) 4 * q + 12 * q^3 - 14 * q^4 + 36 * q^9	\( 4 q + 12 q^{3} - 14 q^{4} + 36 q^{9} - 88 q^{10} - 42 q^{12} - 12 q^{13} + 84 q^{14} + 18 q^{16} + 96 q^{17} + 380 q^{22} - 288 q^{23} - 20 q^{25} - 372 q^{26} + 108 q^{27} - 384 q^{29} - 264 q^{30} + 864 q^{35} - 126 q^{36} + 492 q^{38} - 36 q^{39} + 952 q^{40} + 252 q^{42} - 1288 q^{43} + 54 q^{48} - 188 q^{49} + 288 q^{51} - 1306 q^{52} + 984 q^{53} - 328 q^{55} - 1644 q^{56} + 288 q^{61} + 1668 q^{62} + 1314 q^{64} - 360 q^{65} + 1140 q^{66} - 4380 q^{68} - 864 q^{69} + 3144 q^{74} - 60 q^{75} + 1416 q^{77} - 1116 q^{78} + 4320 q^{79} + 324 q^{81} - 3088 q^{82} - 1152 q^{87} + 1036 q^{88} - 792 q^{90} - 24 q^{91} + 1008 q^{92} - 1660 q^{94} - 1872 q^{95}+O(q^{100}) \) 4 * q + 12 * q^3 - 14 * q^4 + 36 * q^9 - 88 * q^10 - 42 * q^12 - 12 * q^13 + 84 * q^14 + 18 * q^16 + 96 * q^17 + 380 * q^22 - 288 * q^23 - 20 * q^25 - 372 * q^26 + 108 * q^27 - 384 * q^29 - 264 * q^30 + 864 * q^35 - 126 * q^36 + 492 * q^38 - 36 * q^39 + 952 * q^40 + 252 * q^42 - 1288 * q^43 + 54 * q^48 - 188 * q^49 + 288 * q^51 - 1306 * q^52 + 984 * q^53 - 328 * q^55 - 1644 * q^56 + 288 * q^61 + 1668 * q^62 + 1314 * q^64 - 360 * q^65 + 1140 * q^66 - 4380 * q^68 - 864 * q^69 + 3144 * q^74 - 60 * q^75 + 1416 * q^77 - 1116 * q^78 + 4320 * q^79 + 324 * q^81 - 3088 * q^82 - 1152 * q^87 + 1036 * q^88 - 792 * q^90 - 24 * q^91 + 1008 * q^92 - 1660 * q^94 - 1872 * q^95

Introduction

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