LMFDB - Embedded newform 39.4.b.b.25.2

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			25.2
Root			$-1.52356i$ of defining polynomial
Character	$\chi$	$=$	39.25
Dual form			39.4.b.b.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.52356i q^{2} +3.00000 q^{3} +5.67878 q^{4} +9.65841i q^{5} -4.57067i q^{6} -22.3639i q^{7} -20.8404i q^{8} +9.00000 q^{9} +14.7151 q^{10} +50.3050i q^{11} +17.0363 q^{12} +(-39.7151 - 24.8940i) q^{13} -34.0727 q^{14} +28.9752i q^{15} +13.6788 q^{16} -86.1454 q^{17} -13.7120i q^{18} +116.880i q^{19} +54.8480i q^{20} -67.0918i q^{21} +76.6424 q^{22} -72.0000 q^{23} -62.5211i q^{24} +31.7151 q^{25} +(-37.9273 + 60.5082i) q^{26} +27.0000 q^{27} -127.000i q^{28} +14.1454 q^{29} +44.1454 q^{30} -196.215i q^{31} -187.563i q^{32} +150.915i q^{33} +131.247i q^{34} +216.000 q^{35} +51.1090 q^{36} +154.424i q^{37} +178.073 q^{38} +(-119.145 - 74.6819i) q^{39} +201.285 q^{40} -265.726i q^{41} -102.218 q^{42} -211.855 q^{43} +285.671i q^{44} +86.9257i q^{45} +109.696i q^{46} -67.5535i q^{47} +41.0363 q^{48} -157.145 q^{49} -48.3197i q^{50} -258.436 q^{51} +(-225.533 - 141.367i) q^{52} +686.581 q^{53} -41.1360i q^{54} -485.866 q^{55} -466.073 q^{56} +350.639i q^{57} -21.5512i q^{58} +91.9304i q^{59} +164.544i q^{60} +329.006 q^{61} -298.945 q^{62} -201.275i q^{63} -176.333 q^{64} +(240.436 - 383.585i) q^{65} +229.927 q^{66} +768.370i q^{67} -489.201 q^{68} -216.000 q^{69} -329.088i q^{70} +264.969i q^{71} -187.563i q^{72} -771.306i q^{73} +235.273 q^{74} +95.1454 q^{75} +663.734i q^{76} +1125.02 q^{77} +(-113.782 + 181.525i) q^{78} +1226.86 q^{79} +132.115i q^{80} +81.0000 q^{81} -404.849 q^{82} -514.019i q^{83} -381.000i q^{84} -832.027i q^{85} +322.772i q^{86} +42.4361 q^{87} +1048.38 q^{88} -527.889i q^{89} +132.436 q^{90} +(-556.727 + 888.186i) q^{91} -408.872 q^{92} -588.646i q^{93} -102.921 q^{94} -1128.87 q^{95} -562.690i q^{96} -74.2755i q^{97} +239.420i q^{98} +452.745i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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 $

$2$		−	1.52356i		−	0.538658i	−0.963048	−	0.269329i	$-0.913198\pi$
$2$		−	1.52356i		−	0.538658i	0.963048	−	0.269329i	$-0.0868019\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	5.67878			0.709847
$5$			9.65841i			0.863874i	0.901904	+	0.431937i	$0.142170\pi$
$5$			9.65841i			0.863874i	−0.901904	+	0.431937i	$0.857830\pi$
$6$		−	4.57067i		−	0.310994i
$7$		−	22.3639i		−	1.20754i	−0.797159	−	0.603769i	$-0.793665\pi$
$7$		−	22.3639i		−	1.20754i	0.797159	−	0.603769i	$-0.206335\pi$
$8$		−	20.8404i		−	0.921023i
$9$	9.00000			0.333333
$10$	14.7151			0.465333
$11$			50.3050i			1.37887i	0.724349	+	0.689433i	$0.242140\pi$
$11$			50.3050i			1.37887i	−0.724349	+	0.689433i	$0.757860\pi$
$12$	17.0363			0.409831
$13$	−39.7151	−	24.8940i	−0.847307	−	0.531103i
$13$	−39.7151	−	24.8940i	−0.847307	−	0.531103i
$14$	−34.0727			−0.650450
$15$			28.9752i			0.498758i
$16$	13.6788			0.213731
$17$	−86.1454			−1.22902			−0.614509	−	0.788910i	$-0.710646\pi$
$17$	−86.1454			−1.22902			−0.614509	+	0.788910i	$0.710646\pi$
$18$		−	13.7120i		−	0.179553i
$19$			116.880i			1.41127i	0.708578	+	0.705633i	$0.249337\pi$
$19$			116.880i			1.41127i	−0.708578	+	0.705633i	$0.750663\pi$
$20$			54.8480i			0.613219i
$21$		−	67.0918i		−	0.697173i
$22$	76.6424			0.742737
$23$	−72.0000			−0.652741			−0.326370	−	0.945242i	$-0.605826\pi$
$23$	−72.0000			−0.652741			−0.326370	+	0.945242i	$0.605826\pi$
$24$		−	62.5211i		−	0.531753i
$25$	31.7151			0.253721
$26$	−37.9273	+	60.5082i	−0.286083	+	0.456409i
$27$	27.0000			0.192450
$28$		−	127.000i		−	0.857168i
$29$	14.1454			0.0905768			0.0452884	−	0.998974i	$-0.485579\pi$
$29$	14.1454			0.0905768			0.0452884	+	0.998974i	$0.485579\pi$
$30$	44.1454			0.268660
$31$		−	196.215i		−	1.13682i	−0.822747	−	0.568408i	$-0.807559\pi$
$31$		−	196.215i		−	1.13682i	0.822747	−	0.568408i	$-0.192441\pi$
$32$		−	187.563i		−	1.03615i
$33$			150.915i			0.796089i
$34$			131.247i			0.662021i
$35$	216.000			1.04316
$36$	51.1090			0.236616
$37$			154.424i			0.686138i	0.939310	+	0.343069i	$0.111467\pi$
$37$			154.424i			0.686138i	−0.939310	+	0.343069i	$0.888533\pi$
$38$	178.073			0.760190
$39$	−119.145	−	74.6819i	−0.489193	−	0.306633i
$40$	201.285			0.795648
$41$		−	265.726i		−	1.01218i	−0.862480	−	0.506091i	$-0.831090\pi$
$41$		−	265.726i		−	1.01218i	0.862480	−	0.506091i	$-0.168910\pi$
$42$	−102.218			−0.375538
$43$	−211.855			−0.751338			−0.375669	−	0.926754i	$-0.622587\pi$
$43$	−211.855			−0.751338			−0.375669	+	0.926754i	$0.622587\pi$
$44$			285.671i			0.978785i
$45$			86.9257i			0.287958i
$46$			109.696i			0.351604i
$47$		−	67.5535i		−	0.209653i	−0.994491	−	0.104827i	$-0.966571\pi$
$47$		−	67.5535i		−	0.209653i	0.994491	−	0.104827i	$-0.0334287\pi$
$48$	41.0363			0.123398
$49$	−157.145			−0.458150
$50$		−	48.3197i		−	0.136669i
$51$	−258.436			−0.709574
$52$	−225.533	−	141.367i	−0.601459	−	0.377002i
$53$	686.581			1.77942			0.889710	−	0.456527i	$-0.150907\pi$
$53$	686.581			1.77942			0.889710	+	0.456527i	$0.150907\pi$
$54$		−	41.1360i		−	0.103665i
$55$	−485.866			−1.19117
$56$	−466.073			−1.11217
$57$			350.639i			0.814795i
$58$		−	21.5512i		−	0.0487899i
$59$			91.9304i			0.202853i	0.994843	+	0.101426i	$0.0323406\pi$
$59$			91.9304i			0.202853i	−0.994843	+	0.101426i	$0.967659\pi$
$60$			164.544i			0.354042i
$61$	329.006			0.690572			0.345286	−	0.938498i	$-0.387782\pi$
$61$	329.006			0.690572			0.345286	+	0.938498i	$0.387782\pi$
$62$	−298.945			−0.612355
$63$		−	201.275i		−	0.402513i
$64$	−176.333			−0.344400
$65$	240.436	−	383.585i	0.458807	−	0.731967i
$66$	229.927			0.428820
$67$			768.370i			1.40106i	0.713621	+	0.700532i	$0.247054\pi$
$67$			768.370i			1.40106i	−0.713621	+	0.700532i	$0.752946\pi$
$68$	−489.201			−0.872416
$69$	−216.000			−0.376860
$70$		−	329.088i		−	0.561908i
$71$			264.969i			0.442902i	0.975171	+	0.221451i	$0.0710793\pi$
$71$			264.969i			0.442902i	−0.975171	+	0.221451i	$0.928921\pi$
$72$		−	187.563i		−	0.307008i
$73$		−	771.306i		−	1.23664i	−0.785927	−	0.618319i	$-0.787814\pi$
$73$		−	771.306i		−	1.23664i	0.785927	−	0.618319i	$-0.212186\pi$
$74$	235.273			0.369594
$75$	95.1454			0.146486
$76$			663.734i			1.00178i
$77$	1125.02			1.66503
$78$	−113.782	+	181.525i	−0.165170	+	0.263508i
$79$	1226.86			1.74725			0.873624	−	0.486602i	$-0.161764\pi$
$79$	1226.86			1.74725			0.873624	+	0.486602i	$0.161764\pi$
$80$			132.115i			0.184637i
$81$	81.0000			0.111111
$82$	−404.849			−0.545220
$83$		−	514.019i		−	0.679771i	−0.940467	−	0.339885i	$-0.889612\pi$
$83$		−	514.019i		−	0.679771i	0.940467	−	0.339885i	$-0.110388\pi$
$84$		−	381.000i		−	0.494886i
$85$		−	832.027i		−	1.06172i
$86$			322.772i			0.404714i
$87$	42.4361			0.0522945
$88$	1048.38			1.26997
$89$		−	527.889i		−	0.628720i	−0.949304	−	0.314360i	$-0.898210\pi$
$89$		−	527.889i		−	0.628720i	0.949304	−	0.314360i	$-0.101790\pi$
$90$	132.436			0.155111
$91$	−556.727	+	888.186i	−0.641328	+	1.02316i
$92$	−408.872			−0.463346
$93$		−	588.646i		−	0.656341i
$94$	−102.921			−0.112931
$95$	−1128.87			−1.21916
$96$		−	562.690i		−	0.598222i
$97$		−	74.2755i		−	0.0777478i	−0.999244	−	0.0388739i	$-0.987623\pi$
$97$		−	74.2755i		−	0.0777478i	0.999244	−	0.0388739i	$-0.0123771\pi$
$98$			239.420i			0.246786i
$99$			452.745i			0.459622i
$100$	180.103			0.180103
$101$	−609.419			−0.600390			−0.300195	−	0.953878i	$-0.597052\pi$
$101$	−609.419			−0.600390			−0.300195	+	0.953878i	$0.597052\pi$
$102$			393.742i			0.382218i
$103$	32.4361			0.0310293			0.0155147	−	0.999880i	$-0.495061\pi$
$103$	32.4361			0.0310293			0.0155147	+	0.999880i	$0.495061\pi$
$104$	−518.799	+	827.678i	−0.489158	+	0.780389i
$105$	648.000			0.602270
$106$		−	1046.04i		−	0.958498i
$107$	−1725.45			−1.55893			−0.779467	−	0.626444i	$-0.784510\pi$
$107$	−1725.45			−1.55893			−0.779467	+	0.626444i	$0.784510\pi$
$108$	153.327			0.136610
$109$			1273.43i			1.11902i	0.828825	+	0.559508i	$0.189010\pi$
$109$			1273.43i			1.11902i	−0.828825	+	0.559508i	$0.810990\pi$
$110$			740.244i			0.641632i
$111$			463.271i			0.396142i
$112$		−	305.911i		−	0.258088i
$113$	1114.73			0.928006			0.464003	−	0.885834i	$-0.346413\pi$
$113$	1114.73			0.928006			0.464003	+	0.885834i	$0.346413\pi$
$114$	534.218			0.438896
$115$		−	695.406i		−	0.563886i
$116$	80.3284			0.0642957
$117$	−357.436	−	224.046i	−0.282436	−	0.177034i
$118$	140.061			0.109268
$119$			1926.55i			1.48409i
$120$	603.855			0.459368
$121$	−1199.59			−0.901272
$122$		−	501.259i		−	0.371982i
$123$		−	797.179i		−	0.584384i
$124$		−	1114.26i		−	0.806966i
$125$			1513.62i			1.08306i
$126$	−306.654			−0.216817
$127$	−1174.01			−0.820289			−0.410144	−	0.912021i	$-0.634522\pi$
$127$	−1174.01			−0.820289			−0.410144	+	0.912021i	$0.634522\pi$
$128$		−	1231.85i		−	0.850637i
$129$	−635.564			−0.433785
$130$	−584.413	−	366.318i	−0.394280	−	0.247140i
$131$	−1445.16			−0.963851			−0.481925	−	0.876212i	$-0.660062\pi$
$131$	−1445.16			−0.963851			−0.481925	+	0.876212i	$0.660062\pi$
$132$			857.013i			0.565102i
$133$	2613.89			1.70416
$134$	1170.65			0.754695
$135$			260.777i			0.166253i
$136$			1795.30i			1.13195i
$137$		−	508.793i		−	0.317293i	−0.987335	−	0.158646i	$-0.949287\pi$
$137$		−	508.793i		−	0.317293i	0.987335	−	0.158646i	$-0.0507130\pi$
$138$			329.088i			0.202999i
$139$	−757.018			−0.461938			−0.230969	−	0.972961i	$-0.574190\pi$
$139$	−757.018			−0.461938			−0.230969	+	0.972961i	$0.574190\pi$
$140$	1226.62			0.740486
$141$		−	202.661i		−	0.121043i
$142$	403.695			0.238573
$143$	1252.29	−	1997.87i	0.732320	−	1.16832i
$144$	123.109			0.0712436
$145$			136.622i			0.0782470i
$146$	−1175.13			−0.666125
$147$	−471.436			−0.264513
$148$			876.939i			0.487054i
$149$		−	3247.79i		−	1.78570i	−0.450352	−	0.892851i	$-0.648702\pi$
$149$		−	3247.79i		−	1.78570i	0.450352	−	0.892851i	$-0.351298\pi$
$150$		−	144.959i		−	0.0789058i
$151$		−	795.296i		−	0.428611i	−0.976767	−	0.214305i	$-0.931251\pi$
$151$		−	795.296i		−	0.428611i	0.976767	−	0.214305i	$-0.0687488\pi$
$152$	2435.82			1.29981
$153$	−775.308			−0.409673
$154$		−	1714.03i		−	0.896884i
$155$	1895.13			0.982067
$156$	−676.600	−	424.102i	−0.347252	−	0.217662i
$157$	−65.2732			−0.0331807			−0.0165903	−	0.999862i	$-0.505281\pi$
$157$	−65.2732			−0.0331807			−0.0165903	+	0.999862i	$0.505281\pi$
$158$		−	1869.19i		−	0.941169i
$159$	2059.74			1.02735
$160$	1811.56			0.895104
$161$			1610.20i			0.788210i
$162$		−	123.408i		−	0.0598509i
$163$			1855.39i			0.891568i	0.895140	+	0.445784i	$0.147075\pi$
$163$			1855.39i			0.891568i	−0.895140	+	0.445784i	$0.852925\pi$
$164$		−	1509.00i		−	0.718495i
$165$	−1457.60			−0.687721
$166$	−783.137			−0.366164
$167$			3532.54i			1.63686i	0.574604	+	0.818432i	$0.305156\pi$
$167$			3532.54i			1.63686i	−0.574604	+	0.818432i	$0.694844\pi$
$168$	−1398.22			−0.642112
$169$	957.581	+	1977.33i	0.435859	+	0.900015i
$170$	−1267.64			−0.571903
$171$			1051.92i			0.470422i
$172$	−1203.08			−0.533335
$173$	3178.36			1.39680			0.698400	−	0.715708i	$-0.253896\pi$
$173$	3178.36			1.39680			0.698400	+	0.715708i	$0.253896\pi$
$174$		−	64.6537i		−	0.0281689i
$175$		−	709.275i		−	0.306378i
$176$			688.111i			0.294706i
$177$			275.791i			0.117117i
$178$	−804.267			−0.338665
$179$	−2741.16			−1.14460			−0.572302	−	0.820043i	$-0.693950\pi$
$179$	−2741.16			−1.14460			−0.572302	+	0.820043i	$0.693950\pi$
$180$			493.632i			0.204406i
$181$	−3871.09			−1.58970			−0.794850	−	0.606806i	$-0.792450\pi$
$181$	−3871.09			−1.58970			−0.794850	+	0.606806i	$0.792450\pi$
$182$	1353.20	+	848.204i	0.551131	+	0.345456i
$183$	987.018			0.398702
$184$			1500.51i			0.601189i
$185$	−1491.49			−0.592737
$186$	−896.834			−0.353544
$187$		−	4333.54i		−	1.69465i
$188$		−	383.621i		−	0.148822i
$189$		−	603.826i		−	0.232391i
$190$			1719.90i			0.656708i
$191$	−928.291			−0.351669			−0.175834	−	0.984420i	$-0.556262\pi$
$191$	−928.291			−0.351669			−0.175834	+	0.984420i	$0.556262\pi$
$192$	−528.999			−0.198840
$193$			2261.51i			0.843456i	0.906722	+	0.421728i	$0.138576\pi$
$193$			2261.51i			0.843456i	−0.906722	+	0.421728i	$0.861424\pi$
$194$	−113.163			−0.0418795
$195$	721.308	−	1150.75i	0.264892	−	0.422601i
$196$	−892.394			−0.325216
$197$		−	2265.59i		−	0.819374i	−0.912226	−	0.409687i	$-0.865638\pi$
$197$		−	2265.59i		−	0.819374i	0.912226	−	0.409687i	$-0.134362\pi$
$198$	689.782			0.247579
$199$	260.895			0.0929366			0.0464683	−	0.998920i	$-0.485203\pi$
$199$	260.895			0.0929366			0.0464683	+	0.998920i	$0.485203\pi$
$200$		−	660.955i		−	0.233683i
$201$			2305.11i			0.808905i
$202$			928.483i			0.323405i
$203$		−	316.346i		−	0.109375i
$204$	−1467.60			−0.503690
$205$	2566.49			0.874399
$206$		−	49.4181i		−	0.0167142i
$207$	−648.000			−0.217580
$208$	−543.254	−	340.519i	−0.181096	−	0.113513i
$209$	−5879.63			−1.94595
$210$		−	987.264i		−	0.324417i
$211$	5851.22			1.90907			0.954537	−	0.298092i	$-0.0963502\pi$
$211$	5851.22			1.90907			0.954537	+	0.298092i	$0.0963502\pi$
$212$	3898.94			1.26312
$213$			794.907i			0.255710i
$214$			2628.82i			0.839732i
$215$		−	2046.18i		−	0.649062i
$216$		−	562.690i		−	0.177251i
$217$	−4388.15			−1.37275
$218$	1940.15			0.602767
$219$		−	2313.92i		−	0.713973i
$220$	−2759.13			−0.845547
$221$	3421.27	+	2144.50i	1.04136	+	0.652736i
$222$	705.820			0.213385
$223$		−	3463.60i		−	1.04009i	−0.854139	−	0.520045i	$-0.825915\pi$
$223$		−	3463.60i		−	1.04009i	0.854139	−	0.520045i	$-0.174085\pi$
$224$	−4194.65			−1.25119
$225$	285.436			0.0845737
$226$		−	1698.35i		−	0.499878i
$227$			5329.15i			1.55819i	0.626908	+	0.779093i	$0.284320\pi$
$227$			5329.15i			1.55819i	−0.626908	+	0.779093i	$0.715680\pi$
$228$			1991.20i			0.578380i
$229$		−	4773.95i		−	1.37761i	−0.724949	−	0.688803i	$-0.758137\pi$
$229$		−	4773.95i		−	1.37761i	0.724949	−	0.688803i	$-0.241863\pi$
$230$	−1059.49			−0.303742
$231$	3375.05			0.961308
$232$		−	294.795i		−	0.0834233i
$233$	4813.78			1.35348			0.676741	−	0.736221i	$-0.263392\pi$
$233$	4813.78			1.35348			0.676741	+	0.736221i	$0.263392\pi$
$234$	−341.346	+	544.574i	−0.0953610	+	0.152136i
$235$	652.459			0.181114
$236$			522.052i			0.143995i
$237$	3680.58			1.00877
$238$	2935.20			0.799416
$239$			1683.19i			0.455549i	0.973714	+	0.227775i	$0.0731449\pi$
$239$			1683.19i			0.455549i	−0.973714	+	0.227775i	$0.926855\pi$
$240$			396.346i			0.106600i
$241$			664.861i			0.177707i	0.996045	+	0.0888537i	$0.0283204\pi$
$241$			664.861i			0.177707i	−0.996045	+	0.0888537i	$0.971680\pi$
$242$			1827.65i			0.485477i
$243$	243.000			0.0641500
$244$	1868.35			0.490201
$245$		−	1517.77i		−	0.395784i
$246$	−1214.55			−0.314783
$247$	2909.60	−	4641.89i	0.749528	−	1.19578i
$248$	−4089.20			−1.04703
$249$		−	1542.06i		−	0.392466i
$250$	2306.08			0.583398
$251$	−2142.04			−0.538662			−0.269331	−	0.963048i	$-0.586802\pi$
$251$	−2142.04			−0.538662			−0.269331	+	0.963048i	$0.586802\pi$
$252$		−	1143.00i		−	0.285723i
$253$		−	3621.96i		−	0.900042i
$254$			1788.67i			0.441855i
$255$		−	2496.08i		−	0.612983i
$256$	−3287.46			−0.802603
$257$	−3152.62			−0.765194			−0.382597	−	0.923915i	$-0.624970\pi$
$257$	−3152.62			−0.765194			−0.382597	+	0.923915i	$0.624970\pi$
$258$			968.317i			0.233662i
$259$	3453.52			0.828539
$260$	1365.38	−	2178.29i	0.325683	−	0.519585i
$261$	127.308			0.0301923
$262$			2201.79i			0.519186i
$263$	−2167.71			−0.508238			−0.254119	−	0.967173i	$-0.581786\pi$
$263$	−2167.71			−0.508238			−0.254119	+	0.967173i	$0.581786\pi$
$264$	3145.13			0.733216
$265$			6631.28i			1.53719i
$266$		−	3982.40i		−	0.917958i
$267$		−	1583.67i		−	0.362992i
$268$			4363.40i			0.994542i
$269$	−3248.98			−0.736409			−0.368204	−	0.929745i	$-0.620027\pi$
$269$	−3248.98			−0.736409			−0.368204	+	0.929745i	$0.620027\pi$
$270$	397.308			0.0895534
$271$			4897.70i			1.09784i	0.835876	+	0.548919i	$0.184960\pi$
$271$			4897.70i			1.09784i	−0.835876	+	0.548919i	$0.815040\pi$
$272$	−1178.36			−0.262679
$273$	−1670.18	+	2664.56i	−0.370271	+	0.590719i
$274$	−775.175			−0.170912
$275$			1595.43i			0.349847i
$276$	−1226.62			−0.267513
$277$	−2900.33			−0.629111			−0.314555	−	0.949239i	$-0.601855\pi$
$277$	−2900.33			−0.629111			−0.314555	+	0.949239i	$0.601855\pi$
$278$			1153.36i			0.248827i
$279$		−	1765.94i		−	0.378939i
$280$		−	4501.52i		−	0.960776i
$281$		−	4396.53i		−	0.933364i	−0.884425	−	0.466682i	$-0.845449\pi$
$281$		−	4396.53i		−	0.933364i	0.884425	−	0.466682i	$-0.154551\pi$
$282$	−308.764			−0.0652009
$283$	559.151			0.117449			0.0587245	−	0.998274i	$-0.481297\pi$
$283$	559.151			0.117449			0.0587245	+	0.998274i	$0.481297\pi$
$284$			1504.70i			0.314393i
$285$	−3386.62			−0.703880
$286$	−3043.86	−	1907.93i	−0.629327	−	0.394470i
$287$	−5942.69			−1.22225
$288$		−	1688.07i		−	0.345384i
$289$	2508.02			0.510487
$290$	208.151			0.0421484
$291$		−	222.827i		−	0.0448877i
$292$		−	4380.08i		−	0.877825i
$293$			6918.65i			1.37950i	0.724050	+	0.689748i	$0.242278\pi$
$293$			6918.65i			1.37950i	−0.724050	+	0.689748i	$0.757722\pi$
$294$			718.259i			0.142482i
$295$	−887.901			−0.175239
$296$	3218.25			0.631949
$297$			1358.24i			0.265363i
$298$	−4948.19			−0.961883
$299$	2859.49	+	1792.37i	0.553072	+	0.346673i
$300$	540.310			0.103983
$301$			4737.90i			0.907270i
$302$	−1211.68			−0.230875
$303$	−1828.26			−0.346635
$304$			1598.77i			0.301631i
$305$			3177.67i			0.596567i
$306$			1181.22i			0.220674i
$307$			8980.94i			1.66961i	0.550548	+	0.834803i	$0.314419\pi$
$307$			8980.94i			1.66961i	−0.550548	+	0.834803i	$0.685581\pi$
$308$	6388.73			1.18192
$309$	97.3082			0.0179148
$310$		−	2887.33i		−	0.528998i
$311$	7943.13			1.44827			0.724137	−	0.689656i	$-0.242238\pi$
$311$	7943.13			1.44827			0.724137	+	0.689656i	$0.242238\pi$
$312$	−1556.40	+	2483.03i	−0.282416	+	0.450558i
$313$	−5059.57			−0.913686			−0.456843	−	0.889547i	$-0.651020\pi$
$313$	−5059.57			−0.913686			−0.456843	+	0.889547i	$0.651020\pi$
$314$			99.4473i			0.0178730i
$315$	1944.00			0.347721
$316$	6967.07			1.24028
$317$		−	8702.12i		−	1.54183i	−0.636939	−	0.770914i	$-0.719800\pi$
$317$		−	8702.12i		−	1.54183i	0.636939	−	0.770914i	$-0.280200\pi$
$318$		−	3138.13i		−	0.553389i
$319$			711.582i			0.124893i
$320$		−	1703.10i		−	0.297519i
$321$	−5176.36			−0.900051
$322$	2453.23			0.424576
$323$		−	10068.6i		−	1.73447i
$324$	459.981			0.0788719
$325$	−1259.57	−	789.515i	−0.214980	−	0.134752i
$326$	2826.79			0.480250
$327$			3820.30i			0.646064i
$328$	−5537.84			−0.932244
$329$	−1510.76			−0.253164
$330$			2220.73i			0.370446i
$331$		−	1737.65i		−	0.288549i	−0.989538	−	0.144275i	$-0.953915\pi$
$331$		−	1737.65i		−	0.288549i	0.989538	−	0.144275i	$-0.0460848\pi$
$332$		−	2919.00i		−	0.482533i
$333$			1389.81i			0.228713i
$334$	5382.02			0.881710
$335$	−7421.23			−1.21034
$336$		−	917.734i		−	0.149007i
$337$	−2917.47			−0.471586			−0.235793	−	0.971803i	$-0.575769\pi$
$337$	−2917.47			−0.471586			−0.235793	+	0.971803i	$0.575769\pi$
$338$	3012.58	−	1458.93i	0.484800	−	0.234779i
$339$	3344.18			0.535785
$340$		−	4724.90i		−	0.753658i
$341$	9870.61			1.56752
$342$	1602.65			0.253397
$343$		−	4156.44i		−	0.654305i
$344$			4415.13i			0.692000i
$345$		−	2086.22i		−	0.325560i
$346$		−	4842.41i		−	0.752397i
$347$	5081.23			0.786095			0.393047	−	0.919518i	$-0.371421\pi$
$347$	5081.23			0.786095			0.393047	+	0.919518i	$0.371421\pi$
$348$	240.985			0.0371211
$349$		−	4266.14i		−	0.654330i	−0.944967	−	0.327165i	$-0.893907\pi$
$349$		−	4266.14i		−	0.654330i	0.944967	−	0.327165i	$-0.106093\pi$
$350$	−1080.62			−0.165033
$351$	−1072.31	−	672.137i	−0.163064	−	0.102211i
$352$	9435.38			1.42871
$353$			3264.49i			0.492213i	0.969243	+	0.246106i	$0.0791513\pi$
$353$			3264.49i			0.492213i	−0.969243	+	0.246106i	$0.920849\pi$
$354$	420.183			0.0630861
$355$	−2559.18			−0.382612
$356$		−	2997.76i		−	0.446295i
$357$			5779.65i			0.856838i
$358$			4176.31i			0.616550i
$359$			4416.98i			0.649357i	0.945824	+	0.324679i	$0.105256\pi$
$359$			4416.98i			0.649357i	−0.945824	+	0.324679i	$0.894744\pi$
$360$	1811.56			0.265216
$361$	−6801.87			−0.991670
$362$			5897.82i			0.856305i
$363$	−3598.78			−0.520350
$364$	−3161.53	+	5043.81i	−0.455245	+	0.726285i
$365$	7449.59			1.06830
$366$		−	1503.78i		−	0.214764i
$367$	−1740.22			−0.247516			−0.123758	−	0.992312i	$-0.539495\pi$
$367$	−1740.22			−0.247516			−0.123758	+	0.992312i	$0.539495\pi$
$368$	−984.872			−0.139511
$369$		−	2391.54i		−	0.337394i
$370$			2272.37i			0.319283i
$371$		−	15354.7i		−	2.14872i
$372$		−	3342.79i		−	0.465902i
$373$	1176.28			0.163285			0.0816427	−	0.996662i	$-0.473983\pi$
$373$	1176.28			0.163285			0.0816427	+	0.996662i	$0.473983\pi$
$374$	−6602.39			−0.912838
$375$			4540.86i			0.625304i
$376$	−1407.84			−0.193095
$377$	−561.785	−	352.134i	−0.0767464	−	0.0481056i
$378$	−919.962			−0.125179
$379$		−	7135.54i		−	0.967092i	−0.875319	−	0.483546i	$-0.839349\pi$
$379$		−	7135.54i		−	0.967092i	0.875319	−	0.483546i	$-0.160651\pi$
$380$	−6410.62			−0.865415
$381$	−3522.04			−0.473594
$382$			1414.30i			0.189429i
$383$			1942.87i			0.259207i	0.991566	+	0.129603i	$0.0413704\pi$
$383$			1942.87i			0.259207i	−0.991566	+	0.129603i	$0.958630\pi$
$384$		−	3695.56i		−	0.491116i
$385$			10865.9i			1.43838i
$386$	3445.53			0.454334
$387$	−1906.69			−0.250446
$388$		−	421.794i		−	0.0551891i
$389$	7545.92			0.983531			0.491766	−	0.870728i	$-0.336352\pi$
$389$	7545.92			0.983531			0.491766	+	0.870728i	$0.336352\pi$
$390$	−1753.24	−	1098.95i	−0.227638	−	0.142686i
$391$	6202.47			0.802231
$392$			3274.97i			0.421967i
$393$	−4335.49			−0.556480
$394$	−3451.75			−0.441362
$395$			11849.5i			1.50940i
$396$			2571.04i			0.326262i
$397$			415.922i			0.0525806i	0.999654	+	0.0262903i	$0.00836943\pi$
$397$			415.922i			0.0525806i	−0.999654	+	0.0262903i	$0.991631\pi$
$398$		−	397.489i		−	0.0500611i
$399$	7841.67			0.983896
$400$	433.824			0.0542280
$401$		−	958.178i		−	0.119324i	−0.998219	−	0.0596622i	$-0.980998\pi$
$401$		−	958.178i		−	0.119324i	0.998219	−	0.0596622i	$-0.0190024\pi$
$402$	3511.96			0.435723
$403$	−4884.58	+	7792.71i	−0.603767	+	0.963233i
$404$	−3460.75			−0.426185
$405$			782.331i			0.0959860i
$406$	−481.970			−0.0589157
$407$	−7768.29			−0.946093
$408$			5385.90i			0.653534i
$409$		−	4284.83i		−	0.518022i	−0.965874	−	0.259011i	$-0.916603\pi$
$409$		−	4284.83i		−	0.518022i	0.965874	−	0.259011i	$-0.0833966\pi$
$410$		−	3910.20i		−	0.471002i
$411$		−	1526.38i		−	0.183189i
$412$	184.197			0.0220261
$413$	2055.92			0.244953
$414$			987.264i			0.117201i
$415$	4964.61			0.587236
$416$	−4669.20	+	7449.10i	−0.550303	+	0.877938i
$417$	−2271.05			−0.266700
$418$			8957.95i			1.04820i
$419$	−9949.01			−1.16000			−0.580001	−	0.814616i	$-0.696948\pi$
$419$	−9949.01			−1.16000			−0.580001	+	0.814616i	$0.696948\pi$
$420$	3679.85			0.427520
$421$			377.250i			0.0436724i	0.999762	+	0.0218362i	$0.00695122\pi$
$421$			377.250i			0.0436724i	−0.999762	+	0.0218362i	$0.993049\pi$
$422$		−	8914.66i		−	1.02834i
$423$		−	607.982i		−	0.0698843i
$424$		−	14308.6i		−	1.63889i
$425$	−2732.11			−0.311828
$426$	1211.08			0.137740
$427$		−	7357.86i		−	0.833892i
$428$	−9798.47			−1.10661
$429$	3756.87	−	5993.61i	0.422805	−	0.674532i
$430$	−3117.47			−0.349622
$431$		−	2437.13i		−	0.272373i	−0.990683	−	0.136186i	$-0.956515\pi$
$431$		−	2437.13i		−	0.272373i	0.990683	−	0.136186i	$-0.0434846\pi$
$432$	369.327			0.0411325
$433$	−11215.1			−1.24471			−0.622357	−	0.782733i	$-0.713825\pi$
$433$	−11215.1			−1.24471			−0.622357	+	0.782733i	$0.713825\pi$
$434$			6685.58i			0.739443i
$435$			409.865i			0.0451759i
$436$			7231.55i			0.794331i
$437$		−	8415.34i		−	0.921191i
$438$	−3525.38			−0.384588
$439$	1835.19			0.199519			0.0997596	−	0.995012i	$-0.468193\pi$
$439$	1835.19			0.199519			0.0997596	+	0.995012i	$0.468193\pi$
$440$			10125.6i			1.09709i
$441$	−1414.31			−0.152717
$442$	3267.26	−	5212.50i	0.351601	−	0.560935i
$443$	11610.1			1.24518			0.622588	−	0.782550i	$-0.286081\pi$
$443$	11610.1			1.24518			0.622588	+	0.782550i	$0.286081\pi$
$444$			2630.82i			0.281201i
$445$	5098.56			0.543135
$446$	−5276.99			−0.560253
$447$		−	9743.38i		−	1.03098i
$448$			3943.50i			0.415877i
$449$			14087.0i			1.48064i	0.672255	+	0.740319i	$0.265326\pi$
$449$			14087.0i			1.48064i	−0.672255	+	0.740319i	$0.734674\pi$
$450$		−	434.878i		−	0.0455563i
$451$	13367.4			1.39566
$452$	6330.29			0.658743
$453$		−	2385.89i		−	0.247459i
$454$	8119.26			0.839330
$455$	−8578.47	−	5377.10i	−0.883878	−	0.554027i
$456$	7307.45			0.750445
$457$			2375.01i			0.243103i	0.992585	+	0.121552i	$0.0387870\pi$
$457$			2375.01i			0.243103i	−0.992585	+	0.121552i	$0.961213\pi$
$458$	−7273.38			−0.742058
$459$	−2325.92			−0.236525
$460$		−	3949.05i		−	0.400273i
$461$		−	6372.06i		−	0.643766i	−0.946779	−	0.321883i	$-0.895684\pi$
$461$		−	6372.06i		−	0.643766i	0.946779	−	0.321883i	$-0.104316\pi$
$462$		−	5142.08i		−	0.517816i
$463$			63.4732i			0.00637117i	0.999995	+	0.00318558i	$0.00101400\pi$
$463$			63.4732i			0.00637117i	−0.999995	+	0.00318558i	$0.998986\pi$
$464$	193.491			0.0193591
$465$	5685.38			0.566996
$466$		−	7334.06i		−	0.729064i
$467$	7855.78			0.778420			0.389210	−	0.921149i	$-0.372748\pi$
$467$	7855.78			0.778420			0.389210	+	0.921149i	$0.372748\pi$
$468$	−2029.80	−	1272.31i	−0.200486	−	0.125667i
$469$	17183.8			1.69184
$470$		−	994.058i		−	0.0975584i
$471$	−195.820			−0.0191569
$472$	1915.86			0.186832
$473$		−	10657.3i		−	1.03599i
$474$		−	5607.57i		−	0.543384i
$475$			3706.85i			0.358068i
$476$			10940.4i			1.05348i
$477$	6179.23			0.593140
$478$	2564.43			0.245385
$479$			13033.3i			1.24323i	0.783324	+	0.621613i	$0.213523\pi$
$479$			13033.3i			1.24323i	−0.783324	+	0.621613i	$0.786477\pi$
$480$	5434.69			0.516789
$481$	3844.22	−	6132.96i	0.364410	−	0.581370i
$482$	1012.95			0.0957235
$483$			4830.61i			0.455073i
$484$	−6812.23			−0.639766
$485$	717.384			0.0671643
$486$		−	370.224i		−	0.0345549i
$487$		−	69.8976i		−	0.00650383i	−0.999995	−	0.00325191i	$-0.998965\pi$
$487$		−	69.8976i		−	0.00650383i	0.999995	−	0.00325191i	$-0.00103512\pi$
$488$		−	6856.60i		−	0.636033i
$489$			5566.18i			0.514747i
$490$	−2312.41			−0.213192
$491$	2625.66			0.241333			0.120667	−	0.992693i	$-0.461497\pi$
$491$	2625.66			0.241333			0.120667	+	0.992693i	$0.461497\pi$
$492$		−	4527.01i		−	0.414823i
$493$	−1218.56			−0.111321
$494$	−7072.18	−	4432.93i	−0.644114	−	0.403739i
$495$	−4372.80			−0.397056
$496$		−	2683.99i		−	0.242973i
$497$	5925.75			0.534821
$498$	−2349.41			−0.211405
$499$			7631.34i			0.684621i	0.939587	+	0.342310i	$0.111209\pi$
$499$			7631.34i			0.684621i	−0.939587	+	0.342310i	$0.888791\pi$
$500$			8595.51i			0.768806i
$501$			10597.6i			0.945044i
$502$			3263.51i			0.290154i
$503$	−4320.14			−0.382953			−0.191477	−	0.981497i	$-0.561328\pi$
$503$	−4320.14			−0.382953			−0.191477	+	0.981497i	$0.561328\pi$
$504$	−4194.65			−0.370724
$505$		−	5886.01i		−	0.518662i
$506$	−5518.26			−0.484815
$507$	2872.74	+	5932.00i	0.251643	+	0.519624i
$508$	−6666.95			−0.582280
$509$		−	12450.7i		−	1.08422i	−0.840308	−	0.542109i	$-0.817626\pi$
$509$		−	12450.7i		−	1.08422i	0.840308	−	0.542109i	$-0.182374\pi$
$510$	−3802.92			−0.330188
$511$	−17249.4			−1.49329
$512$		−	4846.21i		−	0.418309i
$513$			3155.75i			0.271598i
$514$			4803.18i			0.412178i
$515$			313.281i			0.0268054i
$516$	−3609.23			−0.307921
$517$	3398.28			0.289083
$518$		−	5261.63i		−	0.446299i
$519$	9535.08			0.806443
$520$	−7994.05	−	5010.78i	−0.674158	−	0.422571i
$521$	14373.1			1.20863			0.604314	−	0.796746i	$-0.293447\pi$
$521$	14373.1			1.20863			0.604314	+	0.796746i	$0.293447\pi$
$522$		−	193.961i		−	0.0162633i
$523$	−16946.7			−1.41688			−0.708439	−	0.705772i	$-0.750600\pi$
$523$	−16946.7			−1.41688			−0.708439	+	0.705772i	$0.750600\pi$
$524$	−8206.76			−0.684187
$525$		−	2127.82i		−	0.176887i
$526$			3302.62i			0.273767i
$527$			16903.0i			1.39717i
$528$			2064.33i			0.170149i
$529$	−6983.00			−0.573929
$530$	10103.1			0.828022
$531$			827.373i			0.0676176i
$532$	14843.7			1.20969
$533$	−6614.98	+	10553.4i	−0.537574	+	0.857630i
$534$	−2412.80			−0.195528
$535$		−	16665.1i		−	1.34672i
$536$	16013.1			1.29041
$537$	−8223.49			−0.660837
$538$			4950.00i			0.396673i
$539$		−	7905.20i		−	0.631727i
$540$			1480.90i			0.118014i
$541$		−	815.667i		−	0.0648212i	−0.999475	−	0.0324106i	$-0.989682\pi$
$541$		−	815.667i		−	0.0648212i	0.999475	−	0.0324106i	$-0.0103184\pi$
$542$	7461.92			0.591359
$543$	−11613.3			−0.917814
$544$			16157.7i			1.27345i
$545$	−12299.3			−0.966689
$546$	4059.60	+	2544.61i	0.318196	+	0.199449i
$547$	−17971.4			−1.40476			−0.702378	−	0.711804i	$-0.747878\pi$
$547$	−17971.4			−1.40476			−0.702378	+	0.711804i	$0.747878\pi$
$548$		−	2889.32i		−	0.225230i
$549$	2961.05			0.230191
$550$	2430.72			0.188448
$551$			1653.31i			0.127828i
$552$			4501.52i			0.347097i
$553$		−	27437.4i		−	2.10987i
$554$			4418.81i			0.338876i
$555$	−4474.47			−0.342217
$556$	−4298.94			−0.327906
$557$		−	6760.83i		−	0.514301i	−0.966371	−	0.257151i	$-0.917216\pi$
$557$		−	6760.83i		−	0.514301i	0.966371	−	0.257151i	$-0.0827836\pi$
$558$	−2690.50			−0.204118
$559$	8413.83	+	5273.90i	0.636614	+	0.399038i
$560$	2954.62			0.222956
$561$		−	13000.6i		−	0.978408i
$562$	−6698.36			−0.502764
$563$	12962.7			0.970359			0.485179	−	0.874415i	$-0.338754\pi$
$563$	12962.7			0.970359			0.485179	+	0.874415i	$0.338754\pi$
$564$		−	1150.86i		−	0.0859222i
$565$			10766.5i			0.801681i
$566$		−	851.898i		−	0.0632649i
$567$		−	1811.48i		−	0.134171i
$568$	5522.05			0.407923
$569$	164.757			0.0121388			0.00606938	−	0.999982i	$-0.498068\pi$
$569$	164.757			0.0121388			0.00606938	+	0.999982i	$0.498068\pi$
$570$			5159.70i			0.379151i
$571$	−5216.55			−0.382322			−0.191161	−	0.981559i	$-0.561225\pi$
$571$	−5216.55			−0.382322			−0.191161	+	0.981559i	$0.561225\pi$
$572$	7111.48	−	11345.5i	0.519836	−	0.829331i
$573$	−2784.87			−0.203036
$574$			9054.01i			0.658375i
$575$	−2283.49			−0.165614
$576$	−1587.00			−0.114800
$577$			12753.3i			0.920151i	0.887880	+	0.460076i	$0.152178\pi$
$577$			12753.3i			0.920151i	−0.887880	+	0.460076i	$0.847822\pi$
$578$		−	3821.11i		−	0.274978i
$579$			6784.53i			0.486970i
$580$			775.844i			0.0555434i
$581$	−11495.5			−0.820849
$582$	−339.489			−0.0241791
$583$			34538.5i			2.45358i
$584$	−16074.3			−1.13897
$585$	2163.92	−	3452.26i	0.152936	−	0.243989i
$586$	10540.9			0.743076
$587$			1575.38i			0.110771i	0.998465	+	0.0553857i	$0.0176388\pi$
$587$			1575.38i			0.110771i	−0.998465	+	0.0553857i	$0.982361\pi$
$588$	−2677.18			−0.187764
$589$	22933.6			1.60435
$590$			1352.77i			0.0943941i
$591$		−	6796.77i		−	0.473066i
$592$			2112.33i			0.146649i
$593$		−	3845.95i		−	0.266331i	−0.991094	−	0.133165i	$-0.957486\pi$
$593$		−	3845.95i		−	0.266331i	0.991094	−	0.133165i	$-0.0425142\pi$
$594$	2069.35			0.142940
$595$	−18607.4			−1.28207
$596$		−	18443.5i		−	1.26758i
$597$	782.686			0.0536570
$598$	2730.77	−	4356.59i	0.186738	−	0.297917i
$599$	6107.20			0.416583			0.208292	−	0.978067i	$-0.433210\pi$
$599$	6107.20			0.416583			0.208292	+	0.978067i	$0.433210\pi$
$600$		−	1982.86i		−	0.134917i
$601$	9638.90			0.654208			0.327104	−	0.944988i	$-0.393927\pi$
$601$	9638.90			0.654208			0.327104	+	0.944988i	$0.393927\pi$
$602$	7218.46			0.488708
$603$			6915.33i			0.467022i
$604$		−	4516.31i		−	0.304248i
$605$		−	11586.2i		−	0.778586i
$606$			2785.45i			0.186718i
$607$	11821.7			0.790489			0.395244	−	0.918576i	$-0.370660\pi$
$607$	11821.7			0.790489			0.395244	+	0.918576i	$0.370660\pi$
$608$	21922.4			1.46228
$609$		−	949.037i		−	0.0631477i
$610$	4841.36			0.321346
$611$	−1681.67	+	2682.90i	−0.111347	+	0.177640i
$612$	−4402.80			−0.290805
$613$			8107.86i			0.534214i	0.963667	+	0.267107i	$0.0860677\pi$
$613$			8107.86i			0.534214i	−0.963667	+	0.267107i	$0.913932\pi$
$614$	13683.0			0.899347
$615$	7699.48			0.504834
$616$		−	23445.8i		−	1.53354i
$617$			27647.6i			1.80397i	0.431768	+	0.901985i	$0.357890\pi$
$617$			27647.6i			1.80397i	−0.431768	+	0.901985i	$0.642110\pi$
$618$		−	148.254i		−	0.00964995i
$619$		−	29181.9i		−	1.89486i	−0.319956	−	0.947432i	$-0.603668\pi$
$619$		−	29181.9i		−	1.89486i	0.319956	−	0.947432i	$-0.396332\pi$
$620$	10762.0			0.697118
$621$	−1944.00			−0.125620
$622$		−	12101.8i		−	0.780125i
$623$	−11805.7			−0.759204
$624$	−1629.76	−	1021.56i	−0.104556	−	0.0655369i
$625$	−10654.8			−0.681905
$626$			7708.53i			0.492165i
$627$	−17638.9			−1.12349
$628$	−370.672			−0.0235532
$629$		−	13302.9i		−	0.843277i
$630$		−	2961.79i		−	0.187303i
$631$			2209.34i			0.139386i	0.997569	+	0.0696928i	$0.0222019\pi$
$631$			2209.34i			0.139386i	−0.997569	+	0.0696928i	$0.977798\pi$
$632$		−	25568.2i		−	1.60926i
$633$	17553.7			1.10220
$634$	−13258.2			−0.830518
$635$		−	11339.1i		−	0.708627i
$636$	11696.8			0.729260
$637$	6241.05	+	3911.97i	0.388194	+	0.243325i
$638$	1084.13			0.0672748
$639$			2384.72i			0.147634i
$640$	11897.8			0.734844
$641$	18256.0			1.12491			0.562455	−	0.826828i	$-0.309857\pi$
$641$	18256.0			1.12491			0.562455	+	0.826828i	$0.309857\pi$
$642$			7886.47i			0.484820i
$643$			1281.61i			0.0786033i	0.999227	+	0.0393016i	$0.0125133\pi$
$643$			1281.61i			0.0786033i	−0.999227	+	0.0393016i	$0.987487\pi$
$644$			9143.99i			0.559509i
$645$		−	6138.54i		−	0.374736i
$646$	−15340.1			−0.934287
$647$	−16393.2			−0.996107			−0.498054	−	0.867146i	$-0.665952\pi$
$647$	−16393.2			−0.996107			−0.498054	+	0.867146i	$0.665952\pi$
$648$		−	1688.07i		−	0.102336i
$649$	−4624.56			−0.279707
$650$	−1202.87	+	1919.02i	−0.0725853	+	0.115800i
$651$	−13164.4			−0.792557
$652$			10536.4i			0.632878i
$653$	16759.2			1.00434			0.502172	−	0.864768i	$-0.332534\pi$
$653$	16759.2			1.00434			0.502172	+	0.864768i	$0.332534\pi$
$654$	5820.44			0.348008
$655$		−	13958.0i		−	0.832646i
$656$		−	3634.81i		−	0.216335i
$657$		−	6941.76i		−	0.412213i
$658$			2301.73i			0.136369i
$659$	−29659.3			−1.75320			−0.876601	−	0.481217i	$-0.840195\pi$
$659$	−29659.3			−1.75320			−0.876601	+	0.481217i	$0.840195\pi$
$660$	−8277.38			−0.488177
$661$			10386.0i			0.611147i	0.952169	+	0.305573i	$0.0988481\pi$
$661$			10386.0i			0.611147i	−0.952169	+	0.305573i	$0.901152\pi$
$662$	−2647.40			−0.155429
$663$	10263.8	+	6433.50i	0.601227	+	0.376857i
$664$	−10712.4			−0.626084
$665$			25246.0i			1.47218i
$666$	2117.46			0.123198
$667$	−1018.47			−0.0591232
$668$			20060.5i			1.16192i
$669$		−	10390.8i		−	0.600496i
$670$			11306.7i			0.651962i
$671$			16550.6i			0.952206i
$672$	−12584.0			−0.722376
$673$	19449.6			1.11400			0.557002	−	0.830511i	$-0.311951\pi$
$673$	19449.6			1.11400			0.557002	+	0.830511i	$0.311951\pi$
$674$			4444.92i			0.254024i
$675$	856.308			0.0488286
$676$	5437.89	+	11228.8i	0.309393	+	0.638873i
$677$	−6629.48			−0.376354			−0.188177	−	0.982135i	$-0.560258\pi$
$677$	−6629.48			−0.376354			−0.188177	+	0.982135i	$0.560258\pi$
$678$		−	5095.04i		−	0.288605i
$679$	−1661.09			−0.0938835
$680$	−17339.8			−0.977867
$681$			15987.5i			0.899619i
$682$		−	15038.4i		−	0.844356i
$683$			2526.40i			0.141537i	0.997493	+	0.0707687i	$0.0225452\pi$
$683$			2526.40i			0.141537i	−0.997493	+	0.0707687i	$0.977455\pi$
$684$			5973.61i			0.333928i
$685$	4914.13			0.274101
$686$	−6332.57			−0.352447
$687$		−	14321.9i		−	0.795361i
$688$	−2897.91			−0.160584
$689$	−27267.7	−	17091.7i	−1.50771	−	0.945055i
$690$	−3178.47			−0.175365
$691$			3808.76i			0.209685i	0.994489	+	0.104842i	$0.0334338\pi$
$691$			3808.76i			0.209685i	−0.994489	+	0.104842i	$0.966566\pi$
$692$	18049.2			0.991515
$693$	10125.2			0.555011
$694$		−	7741.54i		−	0.423436i
$695$		−	7311.59i		−	0.399056i
$696$		−	884.384i		−	0.0481645i
$697$			22891.1i			1.24399i
$698$	−6499.69			−0.352460
$699$	14441.3			0.781433
$700$		−	4027.81i		−	0.217482i
$701$	−33617.8			−1.81131			−0.905655	−	0.424015i	$-0.860620\pi$
$701$	−33617.8			−1.81131			−0.905655	+	0.424015i	$0.860620\pi$
$702$	−1024.04	+	1633.72i	−0.0550567	+	0.0878359i
$703$	−18049.0			−0.968323
$704$		−	8870.43i		−	0.474882i
$705$	1957.38			0.104566
$706$	4973.63			0.265134
$707$			13629.0i			0.724994i
$708$			1566.16i			0.0831353i
$709$		−	26606.5i		−	1.40935i	−0.709530	−	0.704675i	$-0.751093\pi$
$709$		−	26606.5i		−	1.40935i	0.709530	−	0.704675i	$-0.248907\pi$
$710$			3899.05i			0.206097i
$711$	11041.7			0.582416
$712$	−11001.4			−0.579066
$713$			14127.5i			0.742046i
$714$	8805.61			0.461543
$715$	19296.2	+	12095.1i	1.00928	+	0.632633i
$716$	−15566.5			−0.812494
$717$			5049.56i			0.263011i
$718$	6729.51			0.349781
$719$	16539.3			0.857877			0.428939	−	0.903334i	$-0.358888\pi$
$719$	16539.3			0.857877			0.428939	+	0.903334i	$0.358888\pi$
$720$			1189.04i			0.0615456i
$721$		−	725.398i		−	0.0374691i
$722$			10363.0i			0.534171i
$723$			1994.58i			0.102599i
$724$	−21983.1			−1.12844
$725$	448.622			0.0229812
$726$			5482.94i			0.280291i
$727$	12757.5			0.650823			0.325411	−	0.945573i	$-0.394497\pi$
$727$	12757.5			0.650823			0.325411	+	0.945573i	$0.394497\pi$
$728$	18510.1	+	11602.4i	0.942350	+	0.590678i
$729$	729.000			0.0370370
$730$		−	11349.9i		−	0.575448i
$731$	18250.3			0.923408
$732$	5605.06			0.283017
$733$		−	20523.4i		−	1.03417i	−0.855933	−	0.517087i	$-0.827016\pi$
$733$		−	20523.4i		−	1.03417i	0.855933	−	0.517087i	$-0.172984\pi$
$734$			2651.31i			0.133327i
$735$		−	4553.32i		−	0.228506i
$736$			13504.6i			0.676338i
$737$	−38652.9			−1.93188
$738$	−3643.64			−0.181740
$739$		−	7462.66i		−	0.371473i	−0.982600	−	0.185736i	$-0.940533\pi$
$739$		−	7462.66i		−	0.371473i	0.982600	−	0.185736i	$-0.0594670\pi$
$740$	−8469.84			−0.420753
$741$	8728.80	−	13925.7i	0.432740	−	0.690381i
$742$	−23393.7			−1.15742
$743$		−	18847.8i		−	0.930632i	−0.885145	−	0.465316i	$-0.845941\pi$
$743$		−	18847.8i		−	0.930632i	0.885145	−	0.465316i	$-0.154059\pi$
$744$	−12267.6			−0.604506
$745$	31368.5			1.54262
$746$		−	1792.13i		−	0.0879549i
$747$		−	4626.17i		−	0.226590i
$748$		−	24609.2i		−	1.20294i
$749$			38587.9i			1.88247i
$750$	6918.25			0.336825
$751$	20832.6			1.01224			0.506119	−	0.862464i	$-0.331080\pi$
$751$	20832.6			1.01224			0.506119	+	0.862464i	$0.331080\pi$
$752$		−	924.050i		−	0.0448093i
$753$	−6426.11			−0.310996
$754$	−536.496	+	855.910i	−0.0259125	+	0.0413400i
$755$	7681.29			0.370266
$756$		−	3429.00i		−	0.164962i
$757$	−20860.9			−1.00159			−0.500795	−	0.865566i	$-0.666959\pi$
$757$	−20860.9			−1.00159			−0.500795	+	0.865566i	$0.666959\pi$
$758$	−10871.4			−0.520932
$759$		−	10865.9i		−	0.519640i
$760$			23526.1i			1.12287i
$761$		−	4464.86i		−	0.212682i	−0.994330	−	0.106341i	$-0.966086\pi$
$761$		−	4464.86i		−	0.212682i	0.994330	−	0.106341i	$-0.0339135\pi$
$762$			5366.01i			0.255105i
$763$	28479.0			1.35126
$764$	−5271.56			−0.249631
$765$		−	7488.24i		−	0.353906i
$766$	2960.08			0.139624
$767$	2288.51	−	3651.03i	0.107736	−	0.171879i
$768$	−9862.38			−0.463383
$769$		−	23797.7i		−	1.11595i	−0.829857	−	0.557977i	$-0.811578\pi$
$769$		−	23797.7i		−	1.11595i	0.829857	−	0.557977i	$-0.188422\pi$
$770$	16554.8			0.774795
$771$	−9457.85			−0.441785
$772$			12842.6i			0.598725i
$773$		−	29418.7i		−	1.36885i	−0.729085	−	0.684423i	$-0.760054\pi$
$773$		−	29418.7i		−	1.36885i	0.729085	−	0.684423i	$-0.239946\pi$
$774$			2904.95i			0.134905i
$775$		−	6222.99i		−	0.288434i
$776$	−1547.93			−0.0716075
$777$	10360.6			0.478357
$778$		−	11496.6i		−	0.529787i
$779$	31058.0			1.42846
$780$	4096.15	−	6534.88i	0.188033	−	0.299982i
$781$	−13329.3			−0.610703
$782$		−	9449.80i		−	0.432128i
$783$	381.925			0.0174315
$784$	−2149.56			−0.0979208
$785$		−	630.435i		−	0.0286640i
$786$			6605.36i			0.299752i
$787$			23896.0i			1.08234i	0.840913	+	0.541170i	$0.182018\pi$
$787$			23896.0i			1.08234i	−0.840913	+	0.541170i	$0.817982\pi$
$788$		−	12865.8i		−	0.581630i
$789$	−6503.13			−0.293432
$790$	18053.4			0.813052
$791$		−	24929.7i		−	1.12060i
$792$	9435.38			0.423323
$793$	−13066.5	−	8190.26i	−0.585126	−	0.366765i
$794$	633.680			0.0283230
$795$			19893.9i			0.887500i
$796$	1481.57			0.0659708
$797$	1034.67			0.0459847			0.0229923	−	0.999736i	$-0.492681\pi$
$797$	1034.67			0.0459847			0.0229923	+	0.999736i	$0.492681\pi$
$798$		−	11947.2i		−	0.529983i
$799$			5819.42i			0.257667i
$800$		−	5948.59i		−	0.262893i
$801$		−	4751.00i		−	0.209573i
$802$	−1459.84			−0.0642751
$803$	38800.6			1.70516
$804$			13090.2i			0.574199i
$805$	−15552.0			−0.680914
$806$	11872.6	+	7441.92i	0.518853	+	0.325224i
$807$	−9746.95			−0.425166
$808$			12700.5i			0.552973i
$809$	29557.9			1.28455			0.642275	−	0.766474i	$-0.277991\pi$
$809$	29557.9			1.28455			0.642275	+	0.766474i	$0.277991\pi$
$810$	1191.92			0.0517037
$811$			30268.9i			1.31058i	0.755376	+	0.655292i	$0.227454\pi$
$811$			30268.9i			1.31058i	−0.755376	+	0.655292i	$0.772546\pi$
$812$		−	1796.46i		−	0.0776396i
$813$			14693.1i			0.633837i
$814$			11835.4i			0.509621i
$815$	−17920.2			−0.770203
$816$	−3535.09			−0.151658
$817$		−	24761.5i		−	1.06034i
$818$	−6528.17			−0.279037
$819$	−5010.54	+	7993.68i	−0.213776	+	0.341052i
$820$	14574.6			0.620690
$821$			39292.7i			1.67031i	0.550013	+	0.835156i	$0.314623\pi$
$821$			39292.7i			1.67031i	−0.550013	+	0.835156i	$0.685377\pi$
$822$	−2325.52			−0.0986763
$823$	25988.8			1.10074			0.550372	−	0.834920i	$-0.314486\pi$
$823$	25988.8			1.10074			0.550372	+	0.834920i	$0.314486\pi$
$824$		−	675.980i		−	0.0285787i
$825$			4786.29i			0.201984i
$826$		−	3132.31i		−	0.131946i
$827$		−	19585.1i		−	0.823508i	−0.911295	−	0.411754i	$-0.864916\pi$
$827$		−	19585.1i		−	0.823508i	0.911295	−	0.411754i	$-0.135084\pi$
$828$	−3679.85			−0.154449
$829$	−666.472			−0.0279222			−0.0139611	−	0.999903i	$-0.504444\pi$
$829$	−666.472			−0.0279222			−0.0139611	+	0.999903i	$0.504444\pi$
$830$		−	7563.86i		−	0.316320i
$831$	−8700.98			−0.363217
$832$	7003.08	+	4389.62i	0.291813	+	0.182912i
$833$	13537.3			0.563075
$834$			3460.07i			0.143660i
$835$	−34118.7			−1.41404
$836$	−33389.1			−1.38133
$837$		−	5297.81i		−	0.218780i
$838$			15157.9i			0.624845i
$839$		−	36379.7i		−	1.49698i	−0.663146	−	0.748490i	$-0.730779\pi$
$839$		−	36379.7i		−	1.49698i	0.663146	−	0.748490i	$-0.269221\pi$
$840$		−	13504.6i		−	0.554704i
$841$	−24188.9			−0.991796
$842$	574.762			0.0235245
$843$		−	13189.6i		−	0.538878i
$844$	33227.8			1.35515
$845$	−19097.9	+	9248.71i	−0.777500	+	0.376527i
$846$	−926.293			−0.0376438
$847$			26827.6i			1.08832i
$848$	9391.60			0.380317
$849$	1677.45			0.0678093
$850$			4162.52i			0.167969i
$851$		−	11118.5i		−	0.447871i
$852$			4514.10i			0.181515i
$853$		−	39951.4i		−	1.60364i	−0.597563	−	0.801822i	$-0.703864\pi$
$853$		−	39951.4i		−	1.60364i	0.597563	−	0.801822i	$-0.296136\pi$
$854$	−11210.1			−0.449183
$855$	−10159.8			−0.406385
$856$			35959.1i			1.43581i
$857$	−17226.4			−0.686629			−0.343314	−	0.939221i	$-0.611550\pi$
$857$	−17226.4			−0.686629			−0.343314	+	0.939221i	$0.611550\pi$
$858$	−9131.59	−	5723.80i	−0.363342	−	0.227748i
$859$	−33392.3			−1.32634			−0.663172	−	0.748467i	$-0.730790\pi$
$859$	−33392.3			−1.32634			−0.663172	+	0.748467i	$0.730790\pi$
$860$		−	11619.8i		−	0.460735i
$861$	−17828.1			−0.705666
$862$	−3713.11			−0.146716
$863$		−	17381.9i		−	0.685614i	−0.939406	−	0.342807i	$-0.888622\pi$
$863$		−	17381.9i		−	0.685614i	0.939406	−	0.342807i	$-0.111378\pi$
$864$		−	5064.21i		−	0.199407i
$865$			30697.9i			1.20666i
$866$			17086.8i			0.670476i
$867$	7524.07			0.294730
$868$	−24919.3			−0.974443
$869$			61717.2i			2.40922i
$870$	624.452			0.0243344
$871$	19127.8	−	30515.9i	0.744110	−	1.18713i
$872$	26538.8			1.03064
$873$		−	668.480i		−	0.0259159i
$874$	−12821.2			−0.496207
$875$	33850.5			1.30783
$876$		−	13140.2i		−	0.506812i
$877$			14335.6i			0.551970i	0.961162	+	0.275985i	$0.0890040\pi$
$877$			14335.6i			0.551970i	−0.961162	+	0.275985i	$0.910996\pi$
$878$		−	2796.02i		−	0.107473i
$879$			20756.0i			0.796452i
$880$	−6646.06			−0.254589
$881$	−5436.53			−0.207901			−0.103951	−	0.994582i	$-0.533148\pi$
$881$	−5436.53			−0.207901			−0.103951	+	0.994582i	$0.533148\pi$
$882$			2154.78i			0.0822620i
$883$	−21185.9			−0.807430			−0.403715	−	0.914885i	$-0.632281\pi$
$883$	−21185.9			−0.807430			−0.403715	+	0.914885i	$0.632281\pi$
$884$	19428.7	+	12178.1i	0.739204	+	0.463343i
$885$	−2663.70			−0.101174
$886$		−	17688.6i		−	0.670724i
$887$	−12661.4			−0.479287			−0.239644	−	0.970861i	$-0.577031\pi$
$887$	−12661.4			−0.479287			−0.239644	+	0.970861i	$0.577031\pi$
$888$	9654.75			0.364856
$889$			26255.5i			0.990531i
$890$		−	7767.94i		−	0.292564i
$891$			4074.71i			0.153207i
$892$		−	19669.0i		−	0.738305i
$893$	7895.63			0.295876
$894$	−14844.6			−0.555343
$895$		−	26475.3i		−	0.988794i
$896$	−27549.1			−1.02718
$897$	8578.47	+	5377.10i	0.319316	+	0.200152i
$898$	21462.3			0.797558
$899$		−	2775.54i		−	0.102969i
$900$	1620.93			0.0600344
$901$	−59145.8			−2.18694
$902$		−	20365.9i		−	0.751786i
$903$			14213.7i			0.523812i
$904$		−	23231.3i		−	0.854715i
$905$		−	37388.6i		−	1.37330i
$906$	−3635.03			−0.133296
$907$	−3545.27			−0.129789			−0.0648946	−	0.997892i	$-0.520671\pi$
$907$	−3545.27			−0.129789			−0.0648946	+	0.997892i	$0.520671\pi$
$908$			30263.1i			1.10607i
$909$	−5484.77			−0.200130
$910$	−8192.30	+	13069.8i	−0.298431	+	0.476108i
$911$	−3913.88			−0.142341			−0.0711706	−	0.997464i	$-0.522673\pi$
$911$	−3913.88			−0.142341			−0.0711706	+	0.997464i	$0.522673\pi$
$912$			4796.32i			0.174147i
$913$	25857.7			0.937313
$914$	3618.46			0.130950
$915$			9533.02i			0.344428i
$916$		−	27110.2i		−	0.977890i
$917$			32319.5i			1.16389i
$918$			3543.67i			0.127406i
$919$	6917.79			0.248310			0.124155	−	0.992263i	$-0.460378\pi$
$919$	6917.79			0.248310			0.124155	+	0.992263i	$0.460378\pi$
$920$	−14492.5			−0.519352
$921$			26942.8i			0.963948i
$922$	−9708.18			−0.346770
$923$	6596.13	−	10523.3i	0.235227	−	0.375274i
$924$	19166.2			0.682382
$925$			4897.57i			0.174088i
$926$	96.7050			0.00343188
$927$	291.925			0.0103431
$928$		−	2653.15i		−	0.0938512i
$929$		−	3753.03i		−	0.132543i	−0.997802	−	0.0662717i	$-0.978890\pi$
$929$		−	3753.03i		−	0.132543i	0.997802	−	0.0662717i	$-0.0211104\pi$
$930$		−	8662.00i		−	0.305417i
$931$		−	18367.1i		−	0.646571i
$932$	27336.4			0.960765
$933$	23829.4			0.836162
$934$		−	11968.7i		−	0.419302i
$935$	41855.1			1.46397
$936$	−4669.20	+	7449.10i	−0.163053	+	0.260130i
$937$	48189.0			1.68011			0.840056	−	0.542499i	$-0.182522\pi$
$937$	48189.0			1.68011			0.840056	+	0.542499i	$0.182522\pi$
$938$		−	26180.4i		−	0.911323i
$939$	−15178.7			−0.527517
$940$	3705.17			0.128563
$941$			26656.4i			0.923456i	0.887022	+	0.461728i	$0.152770\pi$
$941$			26656.4i			0.923456i	−0.887022	+	0.461728i	$0.847230\pi$
$942$			298.342i			0.0103190i
$943$			19132.3i			0.660693i
$944$			1257.50i			0.0433559i
$945$	5832.00			0.200757
$946$	−16237.1			−0.558047
$947$		−	31258.9i		−	1.07263i	−0.844018	−	0.536314i	$-0.819816\pi$
$947$		−	31258.9i		−	1.07263i	0.844018	−	0.536314i	$-0.180184\pi$
$948$	20901.2			0.716076
$949$	−19200.9	+	30632.5i	−0.656783	+	1.04781i
$950$	5647.60			0.192876
$951$		−	26106.4i		−	0.890175i
$952$	40150.0			1.36688
$953$	−10602.4			−0.360382			−0.180191	−	0.983632i	$-0.557672\pi$
$953$	−10602.4			−0.360382			−0.180191	+	0.983632i	$0.557672\pi$
$954$		−	9414.40i		−	0.319499i
$955$		−	8965.81i		−	0.303798i
$956$			9558.44i			0.323370i
$957$			2134.75i			0.0721072i
$958$	19856.9			0.669674
$959$	−11378.6			−0.383144
$960$		−	5109.29i		−	0.171772i
$961$	−8709.45			−0.292352
$962$	−9343.90	−	5856.88i	−0.313160	−	0.196293i
$963$	−15529.1			−0.519645
$964$			3775.60i			0.126145i
$965$	−21842.6			−0.728640
$966$	7359.70			0.245129
$967$		−	4815.93i		−	0.160155i	−0.996789	−	0.0800774i	$-0.974483\pi$
$967$		−	4815.93i		−	0.160155i	0.996789	−	0.0800774i	$-0.0255168\pi$
$968$			25000.0i			0.830092i
$969$		−	30205.9i		−	1.00140i
$970$		−	1092.97i		−	0.0361786i
$971$	56729.5			1.87491			0.937454	−	0.348109i	$-0.113176\pi$
$971$	56729.5			1.87491			0.937454	+	0.348109i	$0.113176\pi$
$972$	1379.94			0.0455367
$973$			16929.9i			0.557808i
$974$	−106.493			−0.00350334
$975$	−3778.71	−	2368.54i	−0.124119	−	0.0777991i
$976$	4500.40			0.147597
$977$		−	55246.2i		−	1.80909i	−0.426375	−	0.904546i	$-0.640210\pi$
$977$		−	55246.2i		−	1.80909i	0.426375	−	0.904546i	$-0.359790\pi$
$978$	8480.38			0.277273
$979$	26555.4			0.866921
$980$		−	8619.11i		−	0.280946i
$981$			11460.9i			0.373005i
$982$		−	4000.34i		−	0.129996i
$983$			22820.6i			0.740451i	0.928942	+	0.370226i	$0.120720\pi$
$983$			22820.6i			0.740451i	−0.928942	+	0.370226i	$0.879280\pi$
$984$	−16613.5			−0.538231
$985$	21882.0			0.707836
$986$			1856.54i			0.0599637i
$987$	−4532.29			−0.146164
$988$	16523.0	−	26360.3i	0.532050	−	0.848818i
$989$	15253.5			0.490429
$990$			6662.20i			0.213877i
$991$	−46490.4			−1.49023			−0.745115	−	0.666936i	$-0.767605\pi$
$991$	−46490.4			−1.49023			−0.745115	+	0.666936i	$0.767605\pi$
$992$	−36802.8			−1.17791
$993$		−	5212.94i		−	0.166594i
$994$		−	9028.21i		−	0.288086i
$995$			2519.84i			0.0802856i
$996$		−	8757.01i		−	0.278591i
$997$	24943.4			0.792344			0.396172	−	0.918176i	$-0.370338\pi$
$997$	24943.4			0.792344			0.396172	+	0.918176i	$0.370338\pi$
$998$	11626.8			0.368777
$999$			4169.44i			0.132047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.b.b.25.2	✓	4
3.2	odd	2		117.4.b.e.64.3		4
4.3	odd	2		624.4.c.c.337.3		4
13.5	odd	4		507.4.a.l.1.2		4
13.8	odd	4		507.4.a.l.1.3		4
13.12	even	2	inner	39.4.b.b.25.3	yes	4
39.5	even	4		1521.4.a.w.1.3		4
39.8	even	4		1521.4.a.w.1.2		4
39.38	odd	2		117.4.b.e.64.2		4
52.51	odd	2		624.4.c.c.337.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.b.b.25.2	✓	4	1.1	even	1	trivial
39.4.b.b.25.3	yes	4	13.12	even	2	inner
117.4.b.e.64.2		4	39.38	odd	2
117.4.b.e.64.3		4	3.2	odd	2
507.4.a.l.1.2		4	13.5	odd	4
507.4.a.l.1.3		4	13.8	odd	4
624.4.c.c.337.2		4	52.51	odd	2
624.4.c.c.337.3		4	4.3	odd	2
1521.4.a.w.1.2		4	39.8	even	4
1521.4.a.w.1.3		4	39.5	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)

\(f(q)\)	\(=\)	\(q-1.52356i q^{2} +3.00000 q^{3} +5.67878 q^{4} +9.65841i q^{5} -4.57067i q^{6} -22.3639i q^{7} -20.8404i q^{8} +9.00000 q^{9} +14.7151 q^{10} +50.3050i q^{11} +17.0363 q^{12} +(-39.7151 - 24.8940i) q^{13} -34.0727 q^{14} +28.9752i q^{15} +13.6788 q^{16} -86.1454 q^{17} -13.7120i q^{18} +116.880i q^{19} +54.8480i q^{20} -67.0918i q^{21} +76.6424 q^{22} -72.0000 q^{23} -62.5211i q^{24} +31.7151 q^{25} +(-37.9273 + 60.5082i) q^{26} +27.0000 q^{27} -127.000i q^{28} +14.1454 q^{29} +44.1454 q^{30} -196.215i q^{31} -187.563i q^{32} +150.915i q^{33} +131.247i q^{34} +216.000 q^{35} +51.1090 q^{36} +154.424i q^{37} +178.073 q^{38} +(-119.145 - 74.6819i) q^{39} +201.285 q^{40} -265.726i q^{41} -102.218 q^{42} -211.855 q^{43} +285.671i q^{44} +86.9257i q^{45} +109.696i q^{46} -67.5535i q^{47} +41.0363 q^{48} -157.145 q^{49} -48.3197i q^{50} -258.436 q^{51} +(-225.533 - 141.367i) q^{52} +686.581 q^{53} -41.1360i q^{54} -485.866 q^{55} -466.073 q^{56} +350.639i q^{57} -21.5512i q^{58} +91.9304i q^{59} +164.544i q^{60} +329.006 q^{61} -298.945 q^{62} -201.275i q^{63} -176.333 q^{64} +(240.436 - 383.585i) q^{65} +229.927 q^{66} +768.370i q^{67} -489.201 q^{68} -216.000 q^{69} -329.088i q^{70} +264.969i q^{71} -187.563i q^{72} -771.306i q^{73} +235.273 q^{74} +95.1454 q^{75} +663.734i q^{76} +1125.02 q^{77} +(-113.782 + 181.525i) q^{78} +1226.86 q^{79} +132.115i q^{80} +81.0000 q^{81} -404.849 q^{82} -514.019i q^{83} -381.000i q^{84} -832.027i q^{85} +322.772i q^{86} +42.4361 q^{87} +1048.38 q^{88} -527.889i q^{89} +132.436 q^{90} +(-556.727 + 888.186i) q^{91} -408.872 q^{92} -588.646i q^{93} -102.921 q^{94} -1128.87 q^{95} -562.690i q^{96} -74.2755i q^{97} +239.420i q^{98} +452.745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{3} - 14 q^{4} + 36 q^{9} - 88 q^{10} - 42 q^{12} - 12 q^{13} + 84 q^{14} + 18 q^{16} + 96 q^{17} + 380 q^{22} - 288 q^{23} - 20 q^{25} - 372 q^{26} + 108 q^{27} - 384 q^{29} - 264 q^{30} + 864 q^{35}+ \cdots - 1872 q^{95}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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