LMFDB - Embedded newform 39.4.b.a.25.1

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:	4.0.5054412.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 29x^{2} + 48 $ x^4 + 29*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			25.1
Root			$-5.21898i$ of defining polynomial
Character	$\chi$	$=$	39.25
Dual form			39.4.b.a.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.21898i q^{2} -3.00000 q^{3} -19.2377 q^{4} +5.83936i q^{5} +15.6569i q^{6} -31.3139i q^{7} +58.6495i q^{8} +9.00000 q^{9} +30.4755 q^{10} -16.2773i q^{11} +57.7132 q^{12} +(-43.4755 - 17.5181i) q^{13} -163.426 q^{14} -17.5181i q^{15} +152.189 q^{16} +54.0000 q^{17} -46.9708i q^{18} -66.3500i q^{19} -112.336i q^{20} +93.9416i q^{21} -84.9510 q^{22} +182.853 q^{23} -175.949i q^{24} +90.9019 q^{25} +(-91.4264 + 226.898i) q^{26} -27.0000 q^{27} +602.408i q^{28} -164.853 q^{29} -91.4264 q^{30} +58.9055i q^{31} -325.073i q^{32} +48.8319i q^{33} -281.825i q^{34} +182.853 q^{35} -173.140 q^{36} -110.366i q^{37} -346.279 q^{38} +(130.426 + 52.5542i) q^{39} -342.475 q^{40} -55.0357i q^{41} +490.279 q^{42} +113.147 q^{43} +313.139i q^{44} +52.5542i q^{45} -954.305i q^{46} +514.089i q^{47} -456.566 q^{48} -637.559 q^{49} -474.415i q^{50} -162.000 q^{51} +(836.370 + 337.008i) q^{52} +242.559 q^{53} +140.912i q^{54} +95.0490 q^{55} +1836.54 q^{56} +199.050i q^{57} +860.364i q^{58} -265.036i q^{59} +337.008i q^{60} -468.098 q^{61} +307.426 q^{62} -281.825i q^{63} -479.042 q^{64} +(102.294 - 253.869i) q^{65} +254.853 q^{66} -852.919i q^{67} -1038.84 q^{68} -548.559 q^{69} -954.305i q^{70} -165.619i q^{71} +527.846i q^{72} +315.325i q^{73} -576.000 q^{74} -272.706 q^{75} +1276.42i q^{76} -509.706 q^{77} +(274.279 - 680.693i) q^{78} +479.608 q^{79} +888.684i q^{80} +81.0000 q^{81} -287.230 q^{82} -574.235i q^{83} -1807.22i q^{84} +315.325i q^{85} -590.512i q^{86} +494.559 q^{87} +954.657 q^{88} +66.7144i q^{89} +274.279 q^{90} +(-548.559 + 1361.39i) q^{91} -3517.68 q^{92} -176.716i q^{93} +2683.02 q^{94} +387.441 q^{95} +975.220i q^{96} +1438.25i q^{97} +3327.40i q^{98} -146.496i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{3} - 26 q^{4} + 36 q^{9} + 20 q^{10} + 78 q^{12} - 72 q^{13} - 348 q^{14} + 354 q^{16} + 216 q^{17} - 136 q^{22} + 120 q^{23} - 44 q^{25} - 60 q^{26} - 108 q^{27} - 48 q^{29} - 60 q^{30} + 120 q^{35}+ \cdots + 3384 q^{95}+O(q^{100}) $ 4 * q - 12 * q^3 - 26 * q^4 + 36 * q^9 + 20 * q^10 + 78 * q^12 - 72 * q^13 - 348 * q^14 + 354 * q^16 + 216 * q^17 - 136 * q^22 + 120 * q^23 - 44 * q^25 - 60 * q^26 - 108 * q^27 - 48 * q^29 - 60 * q^30 + 120 * q^35 - 234 * q^36 - 468 * q^38 + 216 * q^39 - 1268 * q^40 + 1044 * q^42 + 1064 * q^43 - 1062 * q^48 - 716 * q^49 - 648 * q^51 + 1766 * q^52 - 864 * q^53 + 584 * q^55 + 3372 * q^56 - 2280 * q^61 + 924 * q^62 - 1050 * q^64 + 1632 * q^65 + 408 * q^66 - 1404 * q^68 - 360 * q^69 - 2304 * q^74 + 132 * q^75 - 816 * q^77 + 180 * q^78 + 288 * q^79 + 324 * q^81 - 28 * q^82 + 144 * q^87 + 2392 * q^88 + 180 * q^90 - 360 * q^91 - 8568 * q^92 + 6656 * q^94 + 3384 * 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 $

$2$		−	5.21898i		−	1.84519i	−0.385773	−	0.922594i	$-0.626065\pi$
$2$		−	5.21898i		−	1.84519i	0.385773	−	0.922594i	$-0.373935\pi$
$3$	−3.00000			−0.577350
$3$	−3.00000			−0.577350
$4$	−19.2377			−2.40472
$5$			5.83936i			0.522288i	0.965300	+	0.261144i	$0.0840997\pi$
$5$			5.83936i			0.522288i	−0.965300	+	0.261144i	$0.915900\pi$
$6$			15.6569i			1.06532i
$7$		−	31.3139i		−	1.69079i	−0.534141	−	0.845395i	$-0.679365\pi$
$7$		−	31.3139i		−	1.69079i	0.534141	−	0.845395i	$-0.320635\pi$
$8$			58.6495i			2.59197i
$9$	9.00000			0.333333
$10$	30.4755			0.963719
$11$		−	16.2773i		−	0.446163i	−0.974800	−	0.223082i	$-0.928388\pi$
$11$		−	16.2773i		−	0.446163i	0.974800	−	0.223082i	$-0.0716116\pi$
$12$	57.7132			1.38836
$13$	−43.4755	−	17.5181i	−0.927533	−	0.373741i
$13$	−43.4755	−	17.5181i	−0.927533	−	0.373741i
$14$	−163.426			−3.11983
$15$		−	17.5181i		−	0.301543i
$16$	152.189			2.37795
$17$	54.0000			0.770407			0.385204	−	0.922832i	$-0.374131\pi$
$17$	54.0000			0.770407			0.385204	+	0.922832i	$0.374131\pi$
$18$		−	46.9708i		−	0.615063i
$19$		−	66.3500i		−	0.801144i	−0.916265	−	0.400572i	$-0.868811\pi$
$19$		−	66.3500i		−	0.801144i	0.916265	−	0.400572i	$-0.131189\pi$
$20$		−	112.336i		−	1.25595i
$21$			93.9416i			0.976178i
$22$	−84.9510			−0.823255
$23$	182.853			1.65772			0.828858	−	0.559459i	$-0.188991\pi$
$23$	182.853			1.65772			0.828858	+	0.559459i	$0.188991\pi$
$24$		−	175.949i		−	1.49647i
$25$	90.9019			0.727215
$26$	−91.4264	+	226.898i	−0.689623	+	1.71147i
$27$	−27.0000			−0.192450
$28$			602.408i			4.06587i
$29$	−164.853			−1.05560			−0.527800	−	0.849369i	$-0.676983\pi$
$29$	−164.853			−1.05560			−0.527800	+	0.849369i	$0.676983\pi$
$30$	−91.4264			−0.556404
$31$			58.9055i			0.341282i	0.985333	+	0.170641i	$0.0545838\pi$
$31$			58.9055i			0.341282i	−0.985333	+	0.170641i	$0.945416\pi$
$32$		−	325.073i		−	1.79579i
$33$			48.8319i			0.257592i
$34$		−	281.825i		−	1.42155i
$35$	182.853			0.883079
$36$	−173.140			−0.801572
$37$		−	110.366i		−	0.490382i	−0.969475	−	0.245191i	$-0.921149\pi$
$37$		−	110.366i		−	0.490382i	0.969475	−	0.245191i	$-0.0788506\pi$
$38$	−346.279			−1.47826
$39$	130.426	+	52.5542i	0.535511	+	0.215780i
$40$	−342.475			−1.35375
$41$		−	55.0357i		−	0.209637i	−0.994491	−	0.104819i	$-0.966574\pi$
$41$		−	55.0357i		−	0.209637i	0.994491	−	0.104819i	$-0.0334262\pi$
$42$	490.279			1.80123
$43$	113.147			0.401274			0.200637	−	0.979666i	$-0.435699\pi$
$43$	113.147			0.401274			0.200637	+	0.979666i	$0.435699\pi$
$44$			313.139i			1.07290i
$45$			52.5542i			0.174096i
$46$		−	954.305i		−	3.05880i
$47$			514.089i			1.59548i	0.603001	+	0.797740i	$0.293971\pi$
$47$			514.089i			1.59548i	−0.603001	+	0.797740i	$0.706029\pi$
$48$	−456.566			−1.37291
$49$	−637.559			−1.85877
$50$		−	474.415i		−	1.34185i
$51$	−162.000			−0.444795
$52$	836.370	+	337.008i	2.23045	+	0.898742i
$53$	242.559			0.628641			0.314321	−	0.949317i	$-0.398223\pi$
$53$	242.559			0.628641			0.314321	+	0.949317i	$0.398223\pi$
$54$			140.912i			0.355107i
$55$	95.0490			0.233026
$56$	1836.54			4.38247
$57$			199.050i			0.462541i
$58$			860.364i			1.94778i
$59$		−	265.036i		−	0.584825i	−0.956292	−	0.292413i	$-0.905542\pi$
$59$		−	265.036i		−	0.584825i	0.956292	−	0.292413i	$-0.0944581\pi$
$60$			337.008i			0.725126i
$61$	−468.098			−0.982522			−0.491261	−	0.871013i	$-0.663464\pi$
$61$	−468.098			−0.982522			−0.491261	+	0.871013i	$0.663464\pi$
$62$	307.426			0.629729
$63$		−	281.825i		−	0.563597i
$64$	−479.042			−0.935628
$65$	102.294	−	253.869i	0.195201	−	0.484439i
$66$	254.853			0.475306
$67$		−	852.919i		−	1.55523i	−0.628739	−	0.777617i	$-0.716428\pi$
$67$		−	852.919i		−	1.55523i	0.628739	−	0.777617i	$-0.283572\pi$
$68$	−1038.84			−1.85261
$69$	−548.559			−0.957083
$70$		−	954.305i		−	1.62945i
$71$		−	165.619i		−	0.276836i	−0.990374	−	0.138418i	$-0.955798\pi$
$71$		−	165.619i		−	0.276836i	0.990374	−	0.138418i	$-0.0442018\pi$
$72$			527.846i			0.863989i
$73$			315.325i			0.505562i	0.967524	+	0.252781i	$0.0813452\pi$
$73$			315.325i			0.505562i	−0.967524	+	0.252781i	$0.918655\pi$
$74$	−576.000			−0.904846
$75$	−272.706			−0.419858
$76$			1276.42i			1.92653i
$77$	−509.706			−0.754368
$78$	274.279	−	680.693i	0.398154	−	0.988119i
$79$	479.608			0.683039			0.341519	−	0.939875i	$-0.389058\pi$
$79$	479.608			0.683039			0.341519	+	0.939875i	$0.389058\pi$
$80$			888.684i			1.24197i
$81$	81.0000			0.111111
$82$	−287.230			−0.386820
$83$		−	574.235i		−	0.759404i	−0.925109	−	0.379702i	$-0.876027\pi$
$83$		−	574.235i		−	0.759404i	0.925109	−	0.379702i	$-0.123973\pi$
$84$		−	1807.22i		−	2.34743i
$85$			315.325i			0.402374i
$86$		−	590.512i		−	0.740426i
$87$	494.559			0.609451
$88$	954.657			1.15644
$89$			66.7144i			0.0794575i	0.999211	+	0.0397287i	$0.0126494\pi$
$89$			66.7144i			0.0794575i	−0.999211	+	0.0397287i	$0.987351\pi$
$90$	274.279			0.321240
$91$	−548.559	+	1361.39i	−0.631918	+	1.56826i
$92$	−3517.68			−3.98634
$93$		−	176.716i		−	0.197039i
$94$	2683.02			2.94396
$95$	387.441			0.418428
$96$			975.220i			1.03680i
$97$			1438.25i			1.50549i	0.658313	+	0.752744i	$0.271270\pi$
$97$			1438.25i			1.50549i	−0.658313	+	0.752744i	$0.728730\pi$
$98$			3327.40i			3.42978i
$99$		−	146.496i		−	0.148721i
$100$	−1748.75			−1.74875
$101$	896.264			0.882986			0.441493	−	0.897265i	$-0.354449\pi$
$101$	896.264			0.882986			0.441493	+	0.897265i	$0.354449\pi$
$102$			845.475i			0.820730i
$103$	22.2644			0.0212988			0.0106494	−	0.999943i	$-0.496610\pi$
$103$	22.2644			0.0212988			0.0106494	+	0.999943i	$0.496610\pi$
$104$	1027.43	−	2549.82i	0.968725	−	2.40413i
$105$	−548.559			−0.509846
$106$		−	1265.91i		−	1.15996i
$107$	−351.441			−0.317524			−0.158762	−	0.987317i	$-0.550750\pi$
$107$	−351.441			−0.317524			−0.158762	+	0.987317i	$0.550750\pi$
$108$	519.419			0.462788
$109$		−	967.008i		−	0.849748i	−0.905252	−	0.424874i	$-0.860318\pi$
$109$		−	967.008i		−	0.849748i	0.905252	−	0.424874i	$-0.139682\pi$
$110$		−	496.059i		−	0.429976i
$111$			331.099i			0.283122i
$112$		−	4765.62i		−	4.02061i
$113$	48.2943			0.0402048			0.0201024	−	0.999798i	$-0.493601\pi$
$113$	48.2943			0.0402048			0.0201024	+	0.999798i	$0.493601\pi$
$114$	1038.84			0.853474
$115$			1067.74i			0.865805i
$116$	3171.40			2.53842
$117$	−391.279	−	157.663i	−0.309178	−	0.124580i
$118$	−1383.22			−1.07911
$119$		−	1690.95i		−	1.30260i
$120$	1027.43			0.781590
$121$	1066.05			0.800938
$122$			2442.99i			1.81294i
$123$			165.107i			0.121034i
$124$		−	1133.21i		−	0.820686i
$125$			1260.73i			0.902104i
$126$	−1470.84			−1.03994
$127$	1763.02			1.23183			0.615916	−	0.787812i	$-0.288786\pi$
$127$	1763.02			1.23183			0.615916	+	0.787812i	$0.288786\pi$
$128$		−	100.479i		−	0.0693844i
$129$	−339.441			−0.231676
$130$	−1324.94	−	533.872i	−0.893881	−	0.360182i
$131$	955.970			0.637584			0.318792	−	0.947825i	$-0.396723\pi$
$131$	955.970			0.637584			0.318792	+	0.947825i	$0.396723\pi$
$132$		−	939.416i		−	0.619437i
$133$	−2077.68			−1.35457
$134$	−4451.37			−2.86970
$135$		−	157.663i		−	0.100514i
$136$			3167.07i			1.99687i
$137$			15.9215i			0.00992894i	0.999988	+	0.00496447i	$0.00158025\pi$
$137$			15.9215i			0.00992894i	−0.999988	+	0.00496447i	$0.998420\pi$
$138$			2862.92i			1.76600i
$139$	2074.26			1.26573			0.632866	−	0.774261i	$-0.281878\pi$
$139$	2074.26			1.26573			0.632866	+	0.774261i	$0.281878\pi$
$140$	−3517.68			−2.12356
$141$		−	1542.27i		−	0.921151i
$142$	−864.362			−0.510815
$143$	−285.147	+	707.664i	−0.166750	+	0.413831i
$144$	1369.70			0.792649
$145$		−	962.635i		−	0.551327i
$146$	1645.68			0.932857
$147$	1912.68			1.07316
$148$			2123.20i			1.17923i
$149$			2764.08i			1.51975i	0.650071	+	0.759873i	$0.274739\pi$
$149$			2764.08i			1.51975i	−0.650071	+	0.759873i	$0.725261\pi$
$150$			1423.25i			0.774717i
$151$		−	1618.46i		−	0.872239i	−0.899889	−	0.436120i	$-0.856352\pi$
$151$		−	1618.46i		−	0.872239i	0.899889	−	0.436120i	$-0.143648\pi$
$152$	3891.40			2.07654
$153$	486.000			0.256802
$154$			2660.14i			1.39195i
$155$	−343.970			−0.178247
$156$	−2509.11	−	1011.02i	−1.28775	−	0.518889i
$157$	−1109.97			−0.564237			−0.282119	−	0.959380i	$-0.591037\pi$
$157$	−1109.97			−0.564237			−0.282119	+	0.959380i	$0.591037\pi$
$158$		−	2503.06i		−	1.26034i
$159$	−727.676			−0.362946
$160$	1898.22			0.937921
$161$		−	5725.83i		−	2.80285i
$162$		−	422.737i		−	0.205021i
$163$			233.201i			0.112060i	0.998429	+	0.0560299i	$0.0178442\pi$
$163$			233.201i			0.112060i	−0.998429	+	0.0560299i	$0.982156\pi$
$164$			1058.76i			0.504119i
$165$	−285.147			−0.134537
$166$	−2996.92			−1.40124
$167$			215.405i			0.0998118i	0.998754	+	0.0499059i	$0.0158921\pi$
$167$			215.405i			0.0998118i	−0.998754	+	0.0499059i	$0.984108\pi$
$168$	−5509.63			−2.53022
$169$	1583.23	+	1523.21i	0.720635	+	0.693315i
$170$	1645.68			0.742456
$171$		−	597.150i		−	0.267048i
$172$	−2176.69			−0.964950
$173$	1383.15			0.607854			0.303927	−	0.952695i	$-0.401702\pi$
$173$	1383.15			0.607854			0.303927	+	0.952695i	$0.401702\pi$
$174$		−	2581.09i		−	1.12455i
$175$		−	2846.49i		−	1.22957i
$176$		−	2477.22i		−	1.06095i
$177$			795.107i			0.337649i
$178$	348.181			0.146614
$179$	−3642.79			−1.52109			−0.760545	−	0.649285i	$-0.775068\pi$
$179$	−3642.79			−1.52109			−0.760545	+	0.649285i	$0.775068\pi$
$180$		−	1011.02i		−	0.418652i
$181$	−2621.97			−1.07674			−0.538369	−	0.842709i	$-0.680959\pi$
$181$	−2621.97			−1.07674			−0.538369	+	0.842709i	$0.680959\pi$
$182$	7105.04	+	2862.92i	2.89374	+	1.16601i
$183$	1404.29			0.567259
$184$			10724.2i			4.29674i
$185$	644.469			0.256121
$186$	−922.279			−0.363574
$187$		−	878.975i		−	0.343727i
$188$		−	9889.91i		−	3.83668i
$189$			845.475i			0.325393i
$190$		−	2022.05i		−	0.772078i
$191$	−3419.32			−1.29536			−0.647679	−	0.761913i	$-0.724260\pi$
$191$	−3419.32			−1.29536			−0.647679	+	0.761913i	$0.724260\pi$
$192$	1437.12			0.540185
$193$		−	1698.39i		−	0.633435i	−0.948520	−	0.316718i	$-0.897419\pi$
$193$		−	1698.39i		−	0.633435i	0.948520	−	0.316718i	$-0.102581\pi$
$194$	7506.20			2.77791
$195$	−306.883	+	761.606i	−0.112699	+	0.279691i
$196$	12265.2			4.46982
$197$			2293.72i			0.829548i	0.909925	+	0.414774i	$0.136139\pi$
$197$			2293.72i			0.829548i	−0.909925	+	0.414774i	$0.863861\pi$
$198$	−764.559			−0.274418
$199$	−900.981			−0.320949			−0.160474	−	0.987040i	$-0.551302\pi$
$199$	−900.981			−0.320949			−0.160474	+	0.987040i	$0.551302\pi$
$200$			5331.35i			1.88492i
$201$			2558.76i			0.897915i
$202$		−	4677.58i		−	1.62928i
$203$			5162.18i			1.78480i
$204$	3116.51			1.06961
$205$	321.373			0.109491
$206$		−	116.197i		−	0.0393002i
$207$	1645.68			0.552572
$208$	−6616.48	−	2666.05i	−2.20563	−	0.888738i
$209$	−1080.00			−0.357441
$210$			2862.92i			0.940762i
$211$	431.019			0.140628			0.0703142	−	0.997525i	$-0.477600\pi$
$211$	431.019			0.140628			0.0703142	+	0.997525i	$0.477600\pi$
$212$	−4666.28			−1.51170
$213$			496.857i			0.159831i
$214$			1834.17i			0.585892i
$215$			660.706i			0.209580i
$216$		−	1583.54i		−	0.498824i
$217$	1844.56			0.577036
$218$	−5046.79			−1.56794
$219$		−	945.976i		−	0.291886i
$220$	−1828.53			−0.560361
$221$	−2347.68	−	945.976i	−0.714578	−	0.287933i
$222$	1728.00			0.522413
$223$		−	4104.30i		−	1.23249i	−0.787556	−	0.616243i	$-0.788654\pi$
$223$		−	4104.30i		−	1.23249i	0.787556	−	0.616243i	$-0.211346\pi$
$224$	−10179.3			−3.03631
$225$	818.117			0.242405
$226$		−	252.047i		−	0.0741854i
$227$			1809.11i			0.528963i	0.964391	+	0.264482i	$0.0852009\pi$
$227$			1809.11i			0.528963i	−0.964391	+	0.264482i	$0.914799\pi$
$228$		−	3829.27i		−	1.11228i
$229$			5249.33i			1.51478i	0.652961	+	0.757392i	$0.273527\pi$
$229$			5249.33i			1.51478i	−0.652961	+	0.757392i	$0.726473\pi$
$230$	5572.53			1.59757
$231$	1529.12			0.435535
$232$		−	9668.54i		−	2.73608i
$233$	2808.88			0.789768			0.394884	−	0.918731i	$-0.370785\pi$
$233$	2808.88			0.789768			0.394884	+	0.918731i	$0.370785\pi$
$234$	−822.838	+	2042.08i	−0.229874	+	0.570491i
$235$	−3001.95			−0.833300
$236$			5098.69i			1.40634i
$237$	−1438.82			−0.394353
$238$	−8825.03			−2.40354
$239$			6712.01i			1.81659i	0.418334	+	0.908293i	$0.362614\pi$
$239$			6712.01i			1.81659i	−0.418334	+	0.908293i	$0.637386\pi$
$240$		−	2666.05i		−	0.717054i
$241$		−	2519.11i		−	0.673321i	−0.941626	−	0.336661i	$-0.890703\pi$
$241$		−	2519.11i		−	0.673321i	0.941626	−	0.336661i	$-0.109297\pi$
$242$		−	5563.69i		−	1.47788i
$243$	−243.000			−0.0641500
$244$	9005.15			2.36269
$245$		−	3722.93i		−	0.970814i
$246$	861.691			0.223331
$247$	−1162.32	+	2884.60i	−0.299421	+	0.743087i
$248$	−3454.78			−0.884591
$249$			1722.71i			0.438442i
$250$	6579.71			1.66455
$251$	−828.000			−0.208219			−0.104109	−	0.994566i	$-0.533199\pi$
$251$	−828.000			−0.208219			−0.104109	+	0.994566i	$0.533199\pi$
$252$			5421.67i			1.35529i
$253$		−	2976.35i		−	0.739612i
$254$		−	9201.16i		−	2.27296i
$255$		−	945.976i		−	0.232311i
$256$	−4356.73			−1.06366
$257$	5840.76			1.41765			0.708826	−	0.705383i	$-0.249225\pi$
$257$	5840.76			1.41765			0.708826	+	0.705383i	$0.249225\pi$
$258$			1771.54i			0.427485i
$259$	−3456.00			−0.829133
$260$	−1967.91	+	4883.86i	−0.469402	+	1.16494i
$261$	−1483.68			−0.351867
$262$		−	4989.19i		−	1.17646i
$263$	−4064.06			−0.952854			−0.476427	−	0.879214i	$-0.658068\pi$
$263$	−4064.06			−0.952854			−0.476427	+	0.879214i	$0.658068\pi$
$264$	−2863.97			−0.667671
$265$			1416.39i			0.328332i
$266$			10843.3i			2.49943i
$267$		−	200.143i		−	0.0458748i
$268$			16408.2i			3.73990i
$269$	1845.44			0.418285			0.209142	−	0.977885i	$-0.432933\pi$
$269$	1845.44			0.418285			0.209142	+	0.977885i	$0.432933\pi$
$270$	−822.838			−0.185468
$271$			2106.78i			0.472242i	0.971724	+	0.236121i	$0.0758761\pi$
$271$			2106.78i			0.472242i	−0.971724	+	0.236121i	$0.924124\pi$
$272$	8218.19			1.83199
$273$	1645.68	−	4084.16i	0.364838	−	0.905437i
$274$	83.0939			0.0183208
$275$		−	1479.64i		−	0.324457i
$276$	10553.0			2.30151
$277$	4781.94			1.03725			0.518626	−	0.855001i	$-0.326444\pi$
$277$	4781.94			1.03725			0.518626	+	0.855001i	$0.326444\pi$
$278$		−	10825.5i		−	2.33551i
$279$			530.149i			0.113761i
$280$			10724.2i			2.28891i
$281$		−	5865.81i		−	1.24528i	−0.782507	−	0.622642i	$-0.786059\pi$
$281$		−	5865.81i		−	1.24528i	0.782507	−	0.622642i	$-0.213941\pi$
$282$	−8049.06			−1.69970
$283$	6407.02			1.34579			0.672894	−	0.739739i	$-0.265051\pi$
$283$	6407.02			1.34579			0.672894	+	0.739739i	$0.265051\pi$
$284$			3186.14i			0.665713i
$285$	−1162.32			−0.241579
$286$	3693.28	+	1488.18i	0.763596	+	0.307684i
$287$	−1723.38			−0.354453
$288$		−	2925.66i		−	0.598598i
$289$	−1997.00			−0.406473
$290$	−5023.97			−1.01730
$291$		−	4314.75i		−	0.869194i
$292$		−	6066.15i		−	1.21573i
$293$			3010.24i			0.600204i	0.953907	+	0.300102i	$0.0970208\pi$
$293$			3010.24i			0.600204i	−0.953907	+	0.300102i	$0.902979\pi$
$294$		−	9982.21i		−	1.98019i
$295$	1547.64			0.305447
$296$	6472.94			1.27105
$297$			439.487i			0.0858641i
$298$	14425.7			2.80422
$299$	−7949.62	−	3203.23i	−1.53759	−	0.619557i
$300$	5246.24			1.00964
$301$		−	3543.07i		−	0.678470i
$302$	−8446.69			−1.60944
$303$	−2688.79			−0.509792
$304$		−	10097.7i		−	1.90508i
$305$		−	2733.39i		−	0.513159i
$306$		−	2536.42i		−	0.473849i
$307$			3341.84i			0.621266i	0.950530	+	0.310633i	$0.100541\pi$
$307$			3341.84i			0.621266i	−0.950530	+	0.310633i	$0.899459\pi$
$308$	9805.59			1.81404
$309$	−66.7931			−0.0122968
$310$			1795.17i			0.328900i
$311$	−8755.20			−1.59634			−0.798170	−	0.602432i	$-0.794199\pi$
$311$	−8755.20			−1.59634			−0.798170	+	0.602432i	$0.794199\pi$
$312$	−3082.28	+	7649.45i	−0.559294	+	1.38803i
$313$	1948.93			0.351949			0.175974	−	0.984395i	$-0.443692\pi$
$313$	1948.93			0.351949			0.175974	+	0.984395i	$0.443692\pi$
$314$			5792.91i			1.04112i
$315$	1645.68			0.294360
$316$	−9226.57			−1.64252
$317$		−	1940.43i		−	0.343802i	−0.985114	−	0.171901i	$-0.945009\pi$
$317$		−	1940.43i		−	0.343802i	0.985114	−	0.171901i	$-0.0549909\pi$
$318$			3797.72i			0.669704i
$319$			2683.36i			0.470970i
$320$		−	2797.29i		−	0.488667i
$321$	1054.32			0.183323
$322$	−29883.0			−5.17178
$323$		−	3582.90i		−	0.617207i
$324$	−1558.26			−0.267191
$325$	−3952.00	−	1592.43i	−0.674516	−	0.271790i
$326$	1217.07			0.206771
$327$			2901.02i			0.490602i
$328$	3227.82			0.543373
$329$	16098.1			2.69762
$330$			1488.18i			0.248247i
$331$		−	7402.13i		−	1.22918i	−0.788848	−	0.614589i	$-0.789322\pi$
$331$		−	7402.13i		−	1.22918i	0.788848	−	0.614589i	$-0.210678\pi$
$332$			11047.0i			1.82615i
$333$		−	993.298i		−	0.163461i
$334$	1124.20			0.184171
$335$	4980.50			0.812280
$336$			14296.9i			2.32130i
$337$	5494.05			0.888071			0.444035	−	0.896009i	$-0.353546\pi$
$337$	5494.05			0.888071			0.444035	+	0.896009i	$0.353546\pi$
$338$	7949.62	−	8262.87i	1.27930	−	1.32971i
$339$	−144.883			−0.0232122
$340$		−	6066.15i		−	0.967597i
$341$	958.823			0.152267
$342$	−3116.51			−0.492754
$343$			9223.77i			1.45200i
$344$			6636.03i			1.04009i
$345$		−	3203.23i		−	0.499873i
$346$		−	7218.62i		−	1.12160i
$347$	3410.76			0.527664			0.263832	−	0.964569i	$-0.415014\pi$
$347$	3410.76			0.527664			0.263832	+	0.964569i	$0.415014\pi$
$348$	−9514.19			−1.46556
$349$			12629.8i			1.93712i	0.248773	+	0.968562i	$0.419973\pi$
$349$			12629.8i			1.93712i	−0.248773	+	0.968562i	$0.580027\pi$
$350$	−14855.8			−2.26878
$351$	1173.84	+	472.988i	0.178504	+	0.0719266i
$352$	−5291.32			−0.801217
$353$			2981.78i			0.449586i	0.974407	+	0.224793i	$0.0721706\pi$
$353$			2981.78i			0.449586i	−0.974407	+	0.224793i	$0.927829\pi$
$354$	4149.65			0.623026
$355$	967.109			0.144588
$356$		−	1283.43i		−	0.191073i
$357$			5072.85i			0.752055i
$358$			19011.7i			2.80670i
$359$		−	8942.30i		−	1.31464i	−0.753611	−	0.657321i	$-0.771690\pi$
$359$		−	8942.30i		−	1.31464i	0.753611	−	0.657321i	$-0.228310\pi$
$360$	−3082.28			−0.451251
$361$	2456.68			0.358168
$362$			13684.0i			1.98678i
$363$	−3198.15			−0.462422
$364$	10553.0	−	26190.0i	1.51958	−	3.77123i
$365$	−1841.30			−0.264049
$366$		−	7328.98i		−	1.04670i
$367$	−4735.26			−0.673511			−0.336756	−	0.941592i	$-0.609330\pi$
$367$	−4735.26			−0.673511			−0.336756	+	0.941592i	$0.609330\pi$
$368$	27828.1			3.94196
$369$		−	495.321i		−	0.0698792i
$370$		−	3363.47i		−	0.472590i
$371$		−	7595.45i		−	1.06290i
$372$			3399.62i			0.473823i
$373$	−8304.01			−1.15272			−0.576361	−	0.817195i	$-0.695528\pi$
$373$	−8304.01			−1.15272			−0.576361	+	0.817195i	$0.695528\pi$
$374$	−4587.35			−0.634241
$375$		−	3782.18i		−	0.520830i
$376$	−30151.1			−4.13543
$377$	7167.06	+	2887.90i	0.979104	+	0.394522i
$378$	4412.51			0.600411
$379$			4088.11i			0.554069i	0.960860	+	0.277035i	$0.0893517\pi$
$379$			4088.11i			0.554069i	−0.960860	+	0.277035i	$0.910648\pi$
$380$	−7453.50			−1.00620
$381$	−5289.06			−0.711198
$382$			17845.4i			2.39018i
$383$			13951.5i			1.86132i	0.365879	+	0.930662i	$0.380768\pi$
$383$			13951.5i			1.86132i	−0.365879	+	0.930662i	$0.619232\pi$
$384$			301.438i			0.0400591i
$385$		−	2976.35i		−	0.393997i
$386$	−8863.88			−1.16881
$387$	1018.32			0.133758
$388$		−	27668.7i		−	3.62027i
$389$	2804.26			0.365506			0.182753	−	0.983159i	$-0.441499\pi$
$389$	2804.26			0.365506			0.182753	+	0.983159i	$0.441499\pi$
$390$	3974.81	+	1601.61i	0.516083	+	0.207951i
$391$	9874.06			1.27712
$392$		−	37392.5i		−	4.81787i
$393$	−2867.91			−0.368109
$394$	11970.9			1.53067
$395$			2800.60i			0.356743i
$396$			2818.25i			0.357632i
$397$		−	6556.18i		−	0.828830i	−0.910088	−	0.414415i	$-0.863986\pi$
$397$		−	6556.18i		−	0.828830i	0.910088	−	0.414415i	$-0.136014\pi$
$398$			4702.20i			0.592211i
$399$	6233.03			0.782059
$400$	13834.2			1.72928
$401$			4730.95i			0.589157i	0.955627	+	0.294579i	$0.0951793\pi$
$401$			4730.95i			0.589157i	−0.955627	+	0.294579i	$0.904821\pi$
$402$	13354.1			1.65682
$403$	1031.91	−	2560.94i	0.127551	−	0.316550i
$404$	−17242.1			−2.12333
$405$			472.988i			0.0580320i
$406$	26941.3			3.29329
$407$	−1796.47			−0.218790
$408$		−	9501.22i		−	1.15289i
$409$		−	12314.4i		−	1.48878i	−0.667746	−	0.744389i	$-0.732741\pi$
$409$		−	12314.4i		−	1.48878i	0.667746	−	0.744389i	$-0.267259\pi$
$410$		−	1677.24i		−	0.202032i
$411$		−	47.7645i		−	0.00573247i
$412$	−428.316			−0.0512175
$413$	−8299.29			−0.988817
$414$		−	8588.75i		−	1.01960i
$415$	3353.16			0.396627
$416$	−5694.66	+	14132.7i	−0.671163	+	1.66566i
$417$	−6222.79			−0.730771
$418$			5636.50i			0.659546i
$419$	−5499.85			−0.641254			−0.320627	−	0.947206i	$-0.603894\pi$
$419$	−5499.85			−0.641254			−0.320627	+	0.947206i	$0.603894\pi$
$420$	10553.0			1.22604
$421$			12629.7i			1.46208i	0.682336	+	0.731039i	$0.260964\pi$
$421$			12629.7i			1.46208i	−0.682336	+	0.731039i	$0.739036\pi$
$422$		−	2249.48i		−	0.259486i
$423$			4626.80i			0.531827i
$424$			14225.9i			1.62942i
$425$	4908.70			0.560252
$426$	2593.09			0.294919
$427$			14658.0i			1.66124i
$428$	6760.94			0.763557
$429$	855.441	−	2122.99i	0.0962730	−	0.238925i
$430$	3448.21			0.386715
$431$			7191.15i			0.803679i	0.915710	+	0.401840i	$0.131629\pi$
$431$			7191.15i			0.803679i	−0.915710	+	0.401840i	$0.868371\pi$
$432$	−4109.09			−0.457636
$433$	−6062.68			−0.672873			−0.336436	−	0.941706i	$-0.609222\pi$
$433$	−6062.68			−0.672873			−0.336436	+	0.941706i	$0.609222\pi$
$434$		−	9626.71i		−	1.06474i
$435$			2887.90i			0.318309i
$436$			18603.0i			2.04340i
$437$		−	12132.3i		−	1.32807i
$438$	−4937.03			−0.538585
$439$	−11864.3			−1.28986			−0.644932	−	0.764240i	$-0.723114\pi$
$439$	−11864.3			−1.28986			−0.644932	+	0.764240i	$0.723114\pi$
$440$			5574.58i			0.603995i
$441$	−5738.03			−0.619590
$442$	−4937.03	+	12252.5i	−0.531291	+	1.31853i
$443$	10560.5			1.13261			0.566303	−	0.824197i	$-0.308373\pi$
$443$	10560.5			1.13261			0.566303	+	0.824197i	$0.308373\pi$
$444$		−	6369.60i		−	0.680829i
$445$	−389.569			−0.0414997
$446$	−21420.3			−2.27417
$447$		−	8292.24i		−	0.877426i
$448$			15000.6i			1.58195i
$449$			12659.7i			1.33062i	0.746569	+	0.665308i	$0.231700\pi$
$449$			12659.7i			1.33062i	−0.746569	+	0.665308i	$0.768300\pi$
$450$		−	4269.74i		−	0.447283i
$451$	−895.834			−0.0935325
$452$	−929.072			−0.0966812
$453$			4855.37i			0.503587i
$454$	9441.69			0.976037
$455$	−7949.62	−	3203.23i	−0.819085	−	0.330043i
$456$	−11674.2			−1.19889
$457$		−	1544.24i		−	0.158067i	−0.996872	−	0.0790336i	$-0.974817\pi$
$457$		−	1544.24i		−	0.158067i	0.996872	−	0.0790336i	$-0.0251834\pi$
$458$	27396.1			2.79506
$459$	−1458.00			−0.148265
$460$		−	20541.0i		−	2.08202i
$461$		−	13196.8i		−	1.33327i	−0.745384	−	0.666635i	$-0.767734\pi$
$461$		−	13196.8i		−	1.33327i	0.745384	−	0.666635i	$-0.232266\pi$
$462$		−	7980.43i		−	0.803643i
$463$		−	16309.2i		−	1.63705i	−0.574472	−	0.818524i	$-0.694792\pi$
$463$		−	16309.2i		−	1.63705i	0.574472	−	0.818524i	$-0.305208\pi$
$464$	−25088.7			−2.51016
$465$	1031.91			0.102911
$466$		−	14659.5i		−	1.45727i
$467$	14260.8			1.41308			0.706541	−	0.707672i	$-0.250255\pi$
$467$	14260.8			1.41308			0.706541	+	0.707672i	$0.250255\pi$
$468$	7527.33	+	3033.07i	0.743485	+	0.299581i
$469$	−26708.2			−2.62957
$470$			15667.1i			1.53760i
$471$	3329.91			0.325763
$472$	15544.2			1.51585
$473$		−	1841.73i		−	0.179034i
$474$			7509.19i			0.727655i
$475$		−	6031.34i		−	0.582604i
$476$			32530.0i			3.13238i
$477$	2183.03			0.209547
$478$	35029.9			3.35194
$479$		−	18011.5i		−	1.71809i	−0.511899	−	0.859046i	$-0.671058\pi$
$479$		−	18011.5i		−	1.71809i	0.511899	−	0.859046i	$-0.328942\pi$
$480$	−5694.66			−0.541509
$481$	−1933.41	+	4798.23i	−0.183276	+	0.454845i
$482$	−13147.2			−1.24240
$483$			17177.5i			1.61823i
$484$	−20508.4			−1.92603
$485$	−8398.46			−0.786298
$486$			1268.21i			0.118369i
$487$		−	14043.3i		−	1.30670i	−0.757055	−	0.653351i	$-0.773363\pi$
$487$		−	14043.3i		−	1.30670i	0.757055	−	0.653351i	$-0.226637\pi$
$488$		−	27453.7i		−	2.54666i
$489$		−	699.604i		−	0.0646977i
$490$	−19429.9			−1.79133
$491$	12966.1			1.19176			0.595878	−	0.803075i	$-0.296804\pi$
$491$	12966.1			1.19176			0.595878	+	0.803075i	$0.296804\pi$
$492$		−	3176.29i		−	0.291053i
$493$	−8902.06			−0.813242
$494$	15054.7	+	6066.15i	1.37114	+	0.552487i
$495$	855.441			0.0776752
$496$			8964.75i			0.811551i
$497$	−5186.17			−0.468072
$498$	8990.76			0.809007
$499$		−	10215.5i		−	0.916453i	−0.888835	−	0.458227i	$-0.848485\pi$
$499$		−	10215.5i		−	0.916453i	0.888835	−	0.458227i	$-0.151515\pi$
$500$		−	24253.6i		−	2.16930i
$501$		−	646.216i		−	0.0576264i
$502$			4321.31i			0.384203i
$503$	−16632.0			−1.47432			−0.737161	−	0.675717i	$-0.763834\pi$
$503$	−16632.0			−1.47432			−0.737161	+	0.675717i	$0.763834\pi$
$504$	16528.9			1.46082
$505$			5233.61i			0.461173i
$506$	−15533.5			−1.36472
$507$	−4749.70	−	4569.64i	−0.416059	−	0.400286i
$508$	−33916.5			−2.96221
$509$			15235.3i			1.32671i	0.748306	+	0.663354i	$0.230868\pi$
$509$			15235.3i			1.32671i	−0.748306	+	0.663354i	$0.769132\pi$
$510$	−4937.03			−0.428657
$511$	9874.06			0.854799
$512$			21933.9i			1.89326i
$513$			1791.45i			0.154180i
$514$		−	30482.8i		−	2.61584i
$515$			130.009i			0.0111241i
$516$	6530.08			0.557114
$517$	8367.99			0.711845
$518$			18036.8i			1.52991i
$519$	−4149.44			−0.350945
$520$	14889.3	+	5999.51i	1.25565	+	0.505954i
$521$	2680.23			0.225380			0.112690	−	0.993630i	$-0.464053\pi$
$521$	2680.23			0.225380			0.112690	+	0.993630i	$0.464053\pi$
$522$			7743.27i			0.649260i
$523$	−2410.38			−0.201527			−0.100764	−	0.994910i	$-0.532129\pi$
$523$	−2410.38			−0.201527			−0.100764	+	0.994910i	$0.532129\pi$
$524$	−18390.7			−1.53321
$525$			8539.47i			0.709892i
$526$			21210.2i			1.75819i
$527$			3180.90i			0.262926i
$528$			7431.67i			0.612541i
$529$	21268.2			1.74802
$530$	7392.09			0.605834
$531$		−	2385.32i		−	0.194942i
$532$	39969.8			3.25735
$533$	−964.120	+	2392.70i	−0.0783502	+	0.194446i
$534$	−1044.54			−0.0846476
$535$		−	2052.19i		−	0.165839i
$536$	50023.3			4.03111
$537$	10928.4			0.878202
$538$		−	9631.32i		−	0.771814i
$539$			10377.7i			0.829315i
$540$			3033.07i			0.241709i
$541$			9969.58i			0.792284i	0.918189	+	0.396142i	$0.129651\pi$
$541$			9969.58i			0.792284i	−0.918189	+	0.396142i	$0.870349\pi$
$542$	10995.2			0.871375
$543$	7865.91			0.621655
$544$		−	17554.0i		−	1.38349i
$545$	5646.70			0.443813
$546$	−21315.1	−	8588.75i	−1.67070	−	0.673195i
$547$	16848.8			1.31701			0.658505	−	0.752576i	$-0.271189\pi$
$547$	16848.8			1.31701			0.658505	+	0.752576i	$0.271189\pi$
$548$		−	306.293i		−	0.0238763i
$549$	−4212.88			−0.327507
$550$	−7722.20			−0.598683
$551$			10938.0i			0.845688i
$552$		−	32172.7i		−	2.48073i
$553$		−	15018.4i		−	1.15488i
$554$		−	24956.8i		−	1.91393i
$555$	−1933.41			−0.147871
$556$	−39904.2			−3.04373
$557$		−	3800.83i		−	0.289132i	−0.989495	−	0.144566i	$-0.953821\pi$
$557$		−	3800.83i		−	0.289132i	0.989495	−	0.144566i	$-0.0461786\pi$
$558$	2766.84			0.209910
$559$	−4919.13	−	1982.12i	−0.372195	−	0.149973i
$560$	27828.1			2.09992
$561$			2636.92i			0.198451i
$562$	−30613.5			−2.29778
$563$	15750.2			1.17903			0.589513	−	0.807759i	$-0.299320\pi$
$563$	15750.2			1.17903			0.589513	+	0.807759i	$0.299320\pi$
$564$			29669.7i			2.21511i
$565$			282.007i			0.0209985i
$566$		−	33438.1i		−	2.48323i
$567$		−	2536.42i		−	0.187866i
$568$	9713.48			0.717550
$569$	−17753.2			−1.30800			−0.654002	−	0.756493i	$-0.726911\pi$
$569$	−17753.2			−1.30800			−0.654002	+	0.756493i	$0.726911\pi$
$570$			6066.15i			0.445759i
$571$	−25293.1			−1.85374			−0.926868	−	0.375388i	$-0.877509\pi$
$571$	−25293.1			−1.85374			−0.926868	+	0.375388i	$0.877509\pi$
$572$	5485.59	−	13613.9i	0.400986	−	0.995147i
$573$	10258.0			0.747875
$574$			8994.29i			0.654032i
$575$	16621.7			1.20552
$576$	−4311.37			−0.311876
$577$			18488.8i			1.33396i	0.745073	+	0.666982i	$0.232414\pi$
$577$			18488.8i			1.33396i	−0.745073	+	0.666982i	$0.767586\pi$
$578$			10422.3i			0.750018i
$579$			5095.18i			0.365714i
$580$			18518.9i			1.32579i
$581$	−17981.5			−1.28399
$582$	−22518.6			−1.60383
$583$		−	3948.20i		−	0.280477i
$584$	−18493.7			−1.31040
$585$	920.648	−	2284.82i	0.0650669	−	0.161480i
$586$	15710.4			1.10749
$587$			17376.7i			1.22183i	0.791697	+	0.610914i	$0.209198\pi$
$587$			17376.7i			1.22183i	−0.791697	+	0.610914i	$0.790802\pi$
$588$	−36795.6			−2.58065
$589$	3908.38			0.273416
$590$		−	8077.09i		−	0.563608i
$591$		−	6881.16i		−	0.478940i
$592$		−	16796.5i		−	1.16610i
$593$			7991.09i			0.553381i	0.960959	+	0.276690i	$0.0892377\pi$
$593$			7991.09i			0.553381i	−0.960959	+	0.276690i	$0.910762\pi$
$594$	2293.68			0.158435
$595$	9874.06			0.680331
$596$		−	53174.7i		−	3.65456i
$597$	2702.94			0.185300
$598$	−16717.6	+	41488.9i	−1.14320	+	2.83713i
$599$	10386.5			0.708480			0.354240	−	0.935154i	$-0.384740\pi$
$599$	10386.5			0.708480			0.354240	+	0.935154i	$0.384740\pi$
$600$		−	15994.1i		−	1.08826i
$601$	−9241.77			−0.627254			−0.313627	−	0.949546i	$-0.601544\pi$
$601$	−9241.77			−0.627254			−0.313627	+	0.949546i	$0.601544\pi$
$602$	−18491.2			−1.25190
$603$		−	7676.27i		−	0.518411i
$604$			31135.4i			2.09749i
$605$			6225.04i			0.418320i
$606$			14032.8i			0.940663i
$607$	18921.5			1.26524			0.632619	−	0.774463i	$-0.281980\pi$
$607$	18921.5			1.26524			0.632619	+	0.774463i	$0.281980\pi$
$608$	−21568.6			−1.43869
$609$		−	15486.5i		−	1.03045i
$610$	−14265.5			−0.946875
$611$	9005.85	−	22350.3i	0.596297	−	1.47986i
$612$	−9349.54			−0.617537
$613$		−	17138.1i		−	1.12921i	−0.825363	−	0.564603i	$-0.809029\pi$
$613$		−	17138.1i		−	1.12921i	0.825363	−	0.564603i	$-0.190971\pi$
$614$	17441.0			1.14635
$615$	−964.120			−0.0632147
$616$		−	29894.0i		−	1.95530i
$617$		−	18825.8i		−	1.22836i	−0.789166	−	0.614180i	$-0.789487\pi$
$617$		−	18825.8i		−	1.22836i	0.789166	−	0.614180i	$-0.210513\pi$
$618$			348.592i			0.0226900i
$619$			1392.83i			0.0904404i	0.998977	+	0.0452202i	$0.0143989\pi$
$619$			1392.83i			0.0904404i	−0.998977	+	0.0452202i	$0.985601\pi$
$620$	6617.21			0.428635
$621$	−4937.03			−0.319028
$622$			45693.2i			2.94555i
$623$	2089.09			0.134346
$624$	19849.4	+	7998.16i	1.27342	+	0.513113i
$625$	4000.90			0.256057
$626$		−	10171.4i		−	0.649412i
$627$	3240.00			0.206369
$628$	21353.3			1.35683
$629$		−	5959.79i		−	0.377794i
$630$		−	8588.75i		−	0.543149i
$631$			25488.4i			1.60804i	0.594599	+	0.804022i	$0.297311\pi$
$631$			25488.4i			1.60804i	−0.594599	+	0.804022i	$0.702689\pi$
$632$			28128.8i			1.77041i
$633$	−1293.06			−0.0811918
$634$	−10127.1			−0.634379
$635$			10294.9i			0.643371i
$636$	13998.8			0.872783
$637$	27718.2	+	11168.8i	1.72407	+	0.694700i
$638$	14004.4			0.869028
$639$		−	1490.57i		−	0.0922787i
$640$	586.735			0.0362387
$641$	6066.41			0.373805			0.186902	−	0.982379i	$-0.440155\pi$
$641$	6066.41			0.373805			0.186902	+	0.982379i	$0.440155\pi$
$642$		−	5502.50i		−	0.338265i
$643$			1598.78i			0.0980554i	0.998797	+	0.0490277i	$0.0156123\pi$
$643$			1598.78i			0.0980554i	−0.998797	+	0.0490277i	$0.984388\pi$
$644$			110152.i			6.74006i
$645$		−	1982.12i		−	0.121001i
$646$	−18699.1			−1.13886
$647$	−23067.2			−1.40164			−0.700822	−	0.713336i	$-0.747183\pi$
$647$	−23067.2			−1.40164			−0.700822	+	0.713336i	$0.747183\pi$
$648$			4750.61i			0.287996i
$649$	−4314.07			−0.260928
$650$	−8310.84	+	20625.4i	−0.501504	+	1.24461i
$651$	−5533.68			−0.333152
$652$		−	4486.26i		−	0.269472i
$653$	−23743.9			−1.42293			−0.711463	−	0.702723i	$-0.751967\pi$
$653$	−23743.9			−1.42293			−0.711463	+	0.702723i	$0.751967\pi$
$654$	15140.4			0.905253
$655$			5582.25i			0.333002i
$656$		−	8375.81i		−	0.498507i
$657$			2837.93i			0.168521i
$658$		−	84015.7i		−	4.97762i
$659$	−7497.65			−0.443197			−0.221598	−	0.975138i	$-0.571127\pi$
$659$	−7497.65			−0.443197			−0.221598	+	0.975138i	$0.571127\pi$
$660$	5485.59			0.323524
$661$			1255.26i			0.0738638i	0.999318	+	0.0369319i	$0.0117585\pi$
$661$			1255.26i			0.0738638i	−0.999318	+	0.0369319i	$0.988242\pi$
$662$	−38631.5			−2.26806
$663$	7043.03	+	2837.93i	0.412562	+	0.166238i
$664$	33678.6			1.96835
$665$		−	12132.3i		−	0.707474i
$666$	−5184.00			−0.301615
$667$	−30143.8			−1.74989
$668$		−	4143.91i		−	0.240019i
$669$			12312.9i			0.711576i
$670$		−	25993.1i		−	1.49881i
$671$			7619.38i			0.438365i
$672$	30537.9			1.75301
$673$	−1505.97			−0.0862569			−0.0431284	−	0.999070i	$-0.513732\pi$
$673$	−1505.97			−0.0862569			−0.0431284	+	0.999070i	$0.513732\pi$
$674$		−	28673.3i		−	1.63866i
$675$	−2454.35			−0.139953
$676$	−30457.9	−	29303.2i	−1.73292	−	1.66723i
$677$	−16201.4			−0.919751			−0.459876	−	0.887983i	$-0.652106\pi$
$677$	−16201.4			−0.919751			−0.459876	+	0.887983i	$0.652106\pi$
$678$			756.140i			0.0428310i
$679$	45037.2			2.54546
$680$	−18493.7			−1.04294
$681$		−	5427.32i		−	0.305397i
$682$		−	5004.08i		−	0.280962i
$683$		−	29090.4i		−	1.62974i	−0.579644	−	0.814870i	$-0.696808\pi$
$683$		−	29090.4i		−	1.62974i	0.579644	−	0.814870i	$-0.303192\pi$
$684$			11487.8i			0.642175i
$685$	−92.9712			−0.00518576
$686$	48138.7			2.67922
$687$		−	15748.0i		−	0.874561i
$688$	17219.7			0.954208
$689$	−10545.4	−	4249.16i	−0.583085	−	0.234949i
$690$	−16717.6			−0.922359
$691$			940.952i			0.0518025i	0.999665	+	0.0259012i	$0.00824554\pi$
$691$			940.952i			0.0518025i	−0.999665	+	0.0259012i	$0.991754\pi$
$692$	−26608.6			−1.46172
$693$	−4587.35			−0.251456
$694$		−	17800.7i		−	0.973639i
$695$			12112.4i			0.661077i
$696$			29005.6i			1.57968i
$697$		−	2971.93i		−	0.161506i
$698$	65914.5			3.57436
$699$	−8426.65			−0.455973
$700$			54760.1i			2.95676i
$701$	30713.9			1.65485			0.827424	−	0.561578i	$-0.189805\pi$
$701$	30713.9			1.65485			0.827424	+	0.561578i	$0.189805\pi$
$702$	2468.51	−	6126.24i	0.132718	−	0.329373i
$703$	−7322.81			−0.392866
$704$			7797.51i			0.417443i
$705$	9005.85			0.481106
$706$	15561.8			0.829571
$707$		−	28065.5i		−	1.49294i
$708$		−	15296.1i		−	0.811951i
$709$		−	25640.5i		−	1.35818i	−0.734056	−	0.679089i	$-0.762375\pi$
$709$		−	25640.5i		−	1.35818i	0.734056	−	0.679089i	$-0.237625\pi$
$710$		−	5047.32i		−	0.266792i
$711$	4316.47			0.227680
$712$	−3912.77			−0.205951
$713$			10771.0i			0.565748i
$714$	26475.1			1.38768
$715$	−4132.30	−	1665.08i	−0.216139	−	0.0870913i
$716$	70079.1			3.65779
$717$		−	20136.0i		−	1.04881i
$718$	−46669.7			−2.42576
$719$	−20842.5			−1.08108			−0.540538	−	0.841319i	$-0.681779\pi$
$719$	−20842.5			−1.08108			−0.540538	+	0.841319i	$0.681779\pi$
$720$			7998.16i			0.413991i
$721$		−	697.183i		−	0.0360117i
$722$		−	12821.3i		−	0.660888i
$723$			7557.34i			0.388742i
$724$	50440.8			2.58925
$725$	−14985.4			−0.767649
$726$			16691.1i			0.853255i
$727$	263.608			0.0134480			0.00672398	−	0.999977i	$-0.497860\pi$
$727$	263.608			0.0134480			0.00672398	+	0.999977i	$0.497860\pi$
$728$	−79844.6	−	32172.7i	−4.06489	−	1.63791i
$729$	729.000			0.0370370
$730$			9609.69i			0.487220i
$731$	6109.94			0.309144
$732$	−27015.4			−1.36410
$733$			21835.5i			1.10029i	0.835069	+	0.550146i	$0.185428\pi$
$733$			21835.5i			1.10029i	−0.835069	+	0.550146i	$0.814572\pi$
$734$			24713.2i			1.24275i
$735$			11168.8i			0.560500i
$736$		−	59440.6i		−	2.97692i
$737$	−13883.2			−0.693888
$738$	−2585.07			−0.128940
$739$			19536.4i			0.972476i	0.873826	+	0.486238i	$0.161631\pi$
$739$			19536.4i			0.972476i	−0.873826	+	0.486238i	$0.838369\pi$
$740$	−12398.1			−0.615897
$741$	3486.97	−	8653.80i	0.172871	−	0.429022i
$742$	−39640.5			−1.96125
$743$		−	30353.1i		−	1.49872i	−0.662163	−	0.749360i	$-0.730361\pi$
$743$		−	30353.1i		−	1.49872i	0.662163	−	0.749360i	$-0.269639\pi$
$744$	10364.3			0.510719
$745$	−16140.5			−0.793746
$746$			43338.4i			2.12699i
$747$		−	5168.12i		−	0.253135i
$748$			16909.5i			0.826567i
$749$			11005.0i			0.536867i
$750$	−19739.1			−0.961029
$751$	3904.20			0.189702			0.0948510	−	0.995491i	$-0.469763\pi$
$751$	3904.20			0.189702			0.0948510	+	0.995491i	$0.469763\pi$
$752$			78238.5i			3.79397i
$753$	2484.00			0.120215
$754$	15071.9	−	37404.7i	0.727966	−	1.80663i
$755$	9450.74			0.455560
$756$		−	16265.0i		−	0.782478i
$757$	−2900.52			−0.139262			−0.0696308	−	0.997573i	$-0.522182\pi$
$757$	−2900.52			−0.139262			−0.0696308	+	0.997573i	$0.522182\pi$
$758$	21335.8			1.02236
$759$			8929.06i			0.427015i
$760$			22723.3i			1.08455i
$761$			33518.7i			1.59665i	0.602227	+	0.798325i	$0.294280\pi$
$761$			33518.7i			1.59665i	−0.602227	+	0.798325i	$0.705720\pi$
$762$			27603.5i			1.31229i
$763$	−30280.8			−1.43675
$764$	65780.0			3.11497
$765$			2837.93i			0.134125i
$766$	72812.5			3.43449
$767$	−4642.91	+	11522.6i	−0.218573	+	0.542445i
$768$	13070.2			0.614102
$769$		−	552.769i		−	0.0259211i	−0.999916	−	0.0129606i	$-0.995874\pi$
$769$		−	552.769i		−	0.0259211i	0.999916	−	0.0129606i	$-0.00412559\pi$
$770$	−15533.5			−0.726999
$771$	−17522.3			−0.818482
$772$			32673.3i			1.52323i
$773$			36498.8i			1.69828i	0.528166	+	0.849141i	$0.322880\pi$
$773$			36498.8i			1.69828i	−0.528166	+	0.849141i	$0.677120\pi$
$774$		−	5314.61i		−	0.246809i
$775$			5354.62i			0.248185i
$776$	−84352.8			−3.90218
$777$	10368.0			0.478700
$778$		−	14635.4i		−	0.674427i
$779$	−3651.62			−0.167950
$780$	5903.73	−	14651.6i	0.271010	−	0.672578i
$781$	−2695.83			−0.123514
$782$		−	51532.5i		−	2.35652i
$783$	4451.03			0.203150
$784$	−97029.2			−4.42006
$785$		−	6481.51i		−	0.294694i
$786$			14967.6i			0.679231i
$787$		−	4284.79i		−	0.194074i	−0.995281	−	0.0970371i	$-0.969063\pi$
$787$		−	4284.79i		−	0.194074i	0.995281	−	0.0970371i	$-0.0309366\pi$
$788$		−	44126.0i		−	1.99483i
$789$	12192.2			0.550131
$790$	14616.3			0.658258
$791$		−	1512.28i		−	0.0679779i
$792$	8591.91			0.385480
$793$	20350.8	+	8200.18i	0.911321	+	0.367209i
$794$	−34216.6			−1.52935
$795$		−	4249.16i		−	0.189562i
$796$	17332.8			0.771792
$797$	29538.5			1.31281			0.656405	−	0.754409i	$-0.272076\pi$
$797$	29538.5			1.31281			0.656405	+	0.754409i	$0.272076\pi$
$798$		−	32530.0i		−	1.44305i
$799$			27760.8i			1.22917i
$800$		−	29549.8i		−	1.30593i
$801$			600.430i			0.0264858i
$802$	24690.7			1.08711
$803$	5132.65			0.225563
$804$		−	49224.7i		−	2.15923i
$805$	33435.2			1.46389
$806$	−13365.5	−	5385.52i	−0.584094	−	0.235356i
$807$	−5536.32			−0.241497
$808$			52565.5i			2.28867i
$809$	−895.586			−0.0389211			−0.0194605	−	0.999811i	$-0.506195\pi$
$809$	−895.586			−0.0389211			−0.0194605	+	0.999811i	$0.506195\pi$
$810$	2468.51			0.107080
$811$		−	20139.7i		−	0.872011i	−0.899944	−	0.436006i	$-0.856393\pi$
$811$		−	20139.7i		−	0.872011i	0.899944	−	0.436006i	$-0.143607\pi$
$812$		−	99308.7i		−	4.29194i
$813$		−	6320.33i		−	0.272649i
$814$			9375.73i			0.403709i
$815$	−1361.75			−0.0585274
$816$	−24654.6			−1.05770
$817$		−	7507.31i		−	0.321478i
$818$	−64268.8			−2.74707
$819$	−4937.03	+	12252.5i	−0.210639	+	0.522755i
$820$	−6182.49			−0.263295
$821$			17263.2i			0.733848i	0.930251	+	0.366924i	$0.119589\pi$
$821$			17263.2i			0.733848i	−0.930251	+	0.366924i	$0.880411\pi$
$822$	−249.282			−0.0105775
$823$	−12114.5			−0.513104			−0.256552	−	0.966530i	$-0.582587\pi$
$823$	−12114.5			−0.513104			−0.256552	+	0.966530i	$0.582587\pi$
$824$			1305.79i			0.0552057i
$825$			4438.92i			0.187325i
$826$			43313.8i			1.82455i
$827$			31450.9i			1.32243i	0.750194	+	0.661217i	$0.229960\pi$
$827$			31450.9i			1.32243i	−0.750194	+	0.661217i	$0.770040\pi$
$828$	−31659.1			−1.32878
$829$	−13760.4			−0.576499			−0.288250	−	0.957555i	$-0.593073\pi$
$829$	−13760.4			−0.576499			−0.288250	+	0.957555i	$0.593073\pi$
$830$		−	17500.1i		−	0.731852i
$831$	−14345.8			−0.598858
$832$	20826.6	+	8391.88i	0.867826	+	0.349683i
$833$	−34428.2			−1.43201
$834$			32476.6i			1.34841i
$835$	−1257.83			−0.0521305
$836$	20776.8			0.859545
$837$		−	1590.45i		−	0.0656797i
$838$			28703.6i			1.18323i
$839$		−	9846.21i		−	0.405160i	−0.979266	−	0.202580i	$-0.935067\pi$
$839$		−	9846.21i		−	0.405160i	0.979266	−	0.202580i	$-0.0649326\pi$
$840$		−	32172.7i		−	1.32150i
$841$	2787.47			0.114292
$842$	65914.2			2.69781
$843$			17597.4i			0.718965i
$844$	−8291.83			−0.338171
$845$	−8894.58	+	9245.07i	−0.362110	+	0.376379i
$846$	24147.2			0.981320
$847$		−	33382.1i		−	1.35422i
$848$	36914.7			1.49488
$849$	−19221.1			−0.776991
$850$		−	25618.4i		−	1.03377i
$851$		−	20180.8i		−	0.812914i
$852$		−	9558.41i		−	0.384349i
$853$		−	27574.5i		−	1.10684i	−0.832903	−	0.553420i	$-0.813323\pi$
$853$		−	27574.5i		−	1.10684i	0.832903	−	0.553420i	$-0.186677\pi$
$854$	76499.6			3.06530
$855$	3486.97			0.139476
$856$		−	20611.9i		−	0.823013i
$857$	8046.95			0.320745			0.160373	−	0.987057i	$-0.448730\pi$
$857$	8046.95			0.320745			0.160373	+	0.987057i	$0.448730\pi$
$858$	−11079.9	−	4464.53i	−0.440862	−	0.177642i
$859$	2898.13			0.115114			0.0575570	−	0.998342i	$-0.481669\pi$
$859$	2898.13			0.115114			0.0575570	+	0.998342i	$0.481669\pi$
$860$		−	12710.5i		−	0.503982i
$861$	5170.14			0.204644
$862$	37530.5			1.48294
$863$			4961.16i			0.195689i	0.995202	+	0.0978447i	$0.0311948\pi$
$863$			4961.16i			0.195689i	−0.995202	+	0.0978447i	$0.968805\pi$
$864$			8776.98i			0.345601i
$865$			8076.69i			0.317475i
$866$			31641.0i			1.24158i
$867$	5991.00			0.234677
$868$	−35485.1			−1.38761
$869$		−	7806.72i		−	0.304747i
$870$	15071.9			0.587340
$871$	−14941.5	+	37081.1i	−0.581255	+	1.44253i
$872$	56714.5			2.20252
$873$			12944.3i			0.501829i
$874$	−63318.2			−2.45054
$875$	39478.3			1.52527
$876$			18198.4i			0.701904i
$877$			1386.66i			0.0533913i	0.999644	+	0.0266957i	$0.00849850\pi$
$877$			1386.66i			0.0533913i	−0.999644	+	0.0266957i	$0.991502\pi$
$878$			61919.3i			2.38004i
$879$		−	9030.71i		−	0.346528i
$880$	14465.4			0.554123
$881$	−9030.36			−0.345335			−0.172668	−	0.984980i	$-0.555239\pi$
$881$	−9030.36			−0.345335			−0.172668	+	0.984980i	$0.555239\pi$
$882$			29946.6i			1.14326i
$883$	−15512.7			−0.591216			−0.295608	−	0.955309i	$-0.595522\pi$
$883$	−15512.7			−0.591216			−0.295608	+	0.955309i	$0.595522\pi$
$884$	45164.0	+	18198.4i	1.71836	+	0.692398i
$885$	−4642.91			−0.176350
$886$		−	55115.0i		−	2.08987i
$887$	7431.21			0.281303			0.140651	−	0.990059i	$-0.455080\pi$
$887$	7431.21			0.281303			0.140651	+	0.990059i	$0.455080\pi$
$888$	−19418.8			−0.733843
$889$		−	55207.0i		−	2.08277i
$890$			2033.15i			0.0765747i
$891$		−	1318.46i		−	0.0495737i
$892$			78957.5i			2.96378i
$893$	34109.8			1.27821
$894$	−43277.0			−1.61902
$895$		−	21271.6i		−	0.794447i
$896$	−3146.40			−0.117315
$897$	23848.8	+	9609.69i	0.887726	+	0.357701i
$898$	66070.5			2.45524
$899$		−	9710.74i		−	0.360257i
$900$	−15738.7			−0.582916
$901$	13098.2			0.484310
$902$			4675.34i			0.172585i
$903$			10629.2i			0.391715i
$904$			2832.44i			0.104210i
$905$		−	15310.6i		−	0.562367i
$906$	25340.1			0.929213
$907$	−10550.2			−0.386234			−0.193117	−	0.981176i	$-0.561860\pi$
$907$	−10550.2			−0.386234			−0.193117	+	0.981176i	$0.561860\pi$
$908$		−	34803.1i		−	1.27201i
$909$	8066.38			0.294329
$910$	−16717.6	+	41488.9i	−0.608992	+	1.51137i
$911$	35703.3			1.29847			0.649234	−	0.760589i	$-0.275090\pi$
$911$	35703.3			1.29847			0.649234	+	0.760589i	$0.275090\pi$
$912$			30293.2i			1.09990i
$913$	−9347.01			−0.338818
$914$	−8059.38			−0.291664
$915$			8200.18i			0.296273i
$916$		−	100985.i		−	3.64263i
$917$		−	29935.1i		−	1.07802i
$918$			7609.27i			0.273577i
$919$	−42896.6			−1.53975			−0.769873	−	0.638197i	$-0.779681\pi$
$919$	−42896.6			−1.53975			−0.769873	+	0.638197i	$0.779681\pi$
$920$	−62622.6			−2.24414
$921$		−	10025.5i		−	0.358688i
$922$	−68874.0			−2.46013
$923$	−2901.33	+	7200.37i	−0.103465	+	0.256775i
$924$	−29416.8			−1.04734
$925$		−	10032.5i		−	0.356613i
$926$	−85117.5			−3.02066
$927$	200.379			0.00709959
$928$			53589.3i			1.89564i
$929$			10366.7i			0.366114i	0.983102	+	0.183057i	$0.0585993\pi$
$929$			10366.7i			0.366114i	−0.983102	+	0.183057i	$0.941401\pi$
$930$		−	5385.52i		−	0.189890i
$931$			42302.0i			1.48914i
$932$	−54036.6			−1.89917
$933$	26265.6			0.921648
$934$		−	74426.6i		−	2.60740i
$935$	5132.65			0.179525
$936$	9246.84	−	22948.3i	0.322908	−	0.801378i
$937$	20289.8			0.707405			0.353702	−	0.935358i	$-0.384923\pi$
$937$	20289.8			0.707405			0.353702	+	0.935358i	$0.384923\pi$
$938$			139390.i			4.85206i
$939$	−5846.79			−0.203198
$940$	57750.7			2.00385
$941$		−	37089.1i		−	1.28488i	−0.766337	−	0.642438i	$-0.777923\pi$
$941$		−	37089.1i		−	1.28488i	0.766337	−	0.642438i	$-0.222077\pi$
$942$		−	17378.7i		−	0.601093i
$943$		−	10063.4i		−	0.347519i
$944$		−	40335.4i		−	1.39068i
$945$	−4937.03			−0.169949
$946$	−9611.96			−0.330351
$947$			23458.2i			0.804952i	0.915430	+	0.402476i	$0.131850\pi$
$947$			23458.2i			0.804952i	−0.915430	+	0.402476i	$0.868150\pi$
$948$	27679.7			0.948307
$949$	5523.89	−	13708.9i	0.188949	−	0.468925i
$950$	−31477.5			−1.07501
$951$			5821.28i			0.198494i
$952$	99173.4			3.37629
$953$	−34695.5			−1.17933			−0.589663	−	0.807649i	$-0.700740\pi$
$953$	−34695.5			−1.17933			−0.589663	+	0.807649i	$0.700740\pi$
$954$		−	11393.2i		−	0.386654i
$955$		−	19966.6i		−	0.676550i
$956$		−	129124.i		−	4.36838i
$957$		−	8050.09i		−	0.271915i
$958$	−94001.6			−3.17020
$959$	498.563			0.0167878
$960$			8391.88i			0.282132i
$961$	26321.1			0.883527
$962$	25041.9	+	10090.4i	0.839275	+	0.338179i
$963$	−3162.97			−0.105841
$964$			48462.1i			1.61915i
$965$	9917.53			0.330836
$966$	89649.0			2.98593
$967$		−	6289.66i		−	0.209164i	−0.994516	−	0.104582i	$-0.966649\pi$
$967$		−	6289.66i		−	0.209164i	0.994516	−	0.104582i	$-0.0333505\pi$
$968$			62523.3i			2.07601i
$969$			10748.7i			0.356345i
$970$			43831.4i			1.45087i
$971$	−20185.9			−0.667145			−0.333573	−	0.942724i	$-0.608254\pi$
$971$	−20185.9			−0.667145			−0.333573	+	0.942724i	$0.608254\pi$
$972$	4674.77			0.154263
$973$		−	64953.2i		−	2.14009i
$974$	−73291.8			−2.41111
$975$	11856.0	+	4777.28i	0.389432	+	0.156918i
$976$	−71239.2			−2.33639
$977$		−	44244.0i		−	1.44881i	−0.689373	−	0.724406i	$-0.742114\pi$
$977$		−	44244.0i		−	1.44881i	0.689373	−	0.724406i	$-0.257886\pi$
$978$	−3651.22			−0.119379
$979$	1085.93			0.0354510
$980$			71620.8i			2.33453i
$981$		−	8703.07i		−	0.283249i
$982$		−	67669.9i		−	2.19901i
$983$			8835.11i			0.286670i	0.989674	+	0.143335i	$0.0457826\pi$
$983$			8835.11i			0.286670i	−0.989674	+	0.143335i	$0.954217\pi$
$984$	−9683.46			−0.313717
$985$	−13393.9			−0.433263
$986$			46459.6i			1.50058i
$987$	−48294.3			−1.55747
$988$	22360.5	−	55493.2i	0.720022	−	1.78692i
$989$	20689.3			0.665198
$990$		−	4464.53i		−	0.143325i
$991$	34915.1			1.11919			0.559594	−	0.828767i	$-0.310957\pi$
$991$	34915.1			1.11919			0.559594	+	0.828767i	$0.310957\pi$
$992$	19148.6			0.612872
$993$			22206.4i			0.709666i
$994$			27066.5i			0.863680i
$995$		−	5261.15i		−	0.167628i
$996$		−	33141.0i		−	1.05433i
$997$	37962.8			1.20591			0.602956	−	0.797774i	$-0.293989\pi$
$997$	37962.8			1.20591			0.602956	+	0.797774i	$0.293989\pi$
$998$	−53314.6			−1.69103
$999$			2979.89i			0.0943740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.b.a.25.1	✓	4
3.2	odd	2		117.4.b.d.64.4		4
4.3	odd	2		624.4.c.e.337.3		4
13.5	odd	4		507.4.a.j.1.1		4
13.8	odd	4		507.4.a.j.1.4		4
13.12	even	2	inner	39.4.b.a.25.4	yes	4
39.5	even	4		1521.4.a.x.1.4		4
39.8	even	4		1521.4.a.x.1.1		4
39.38	odd	2		117.4.b.d.64.1		4
52.51	odd	2		624.4.c.e.337.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.b.a.25.1	✓	4	1.1	even	1	trivial
39.4.b.a.25.4	yes	4	13.12	even	2	inner
117.4.b.d.64.1		4	39.38	odd	2
117.4.b.d.64.4		4	3.2	odd	2
507.4.a.j.1.1		4	13.5	odd	4
507.4.a.j.1.4		4	13.8	odd	4
624.4.c.e.337.2		4	52.51	odd	2
624.4.c.e.337.3		4	4.3	odd	2
1521.4.a.x.1.1		4	39.8	even	4
1521.4.a.x.1.4		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)

\(f(q)\)	\(=\)	\(q-5.21898i q^{2} -3.00000 q^{3} -19.2377 q^{4} +5.83936i q^{5} +15.6569i q^{6} -31.3139i q^{7} +58.6495i q^{8} +9.00000 q^{9} +30.4755 q^{10} -16.2773i q^{11} +57.7132 q^{12} +(-43.4755 - 17.5181i) q^{13} -163.426 q^{14} -17.5181i q^{15} +152.189 q^{16} +54.0000 q^{17} -46.9708i q^{18} -66.3500i q^{19} -112.336i q^{20} +93.9416i q^{21} -84.9510 q^{22} +182.853 q^{23} -175.949i q^{24} +90.9019 q^{25} +(-91.4264 + 226.898i) q^{26} -27.0000 q^{27} +602.408i q^{28} -164.853 q^{29} -91.4264 q^{30} +58.9055i q^{31} -325.073i q^{32} +48.8319i q^{33} -281.825i q^{34} +182.853 q^{35} -173.140 q^{36} -110.366i q^{37} -346.279 q^{38} +(130.426 + 52.5542i) q^{39} -342.475 q^{40} -55.0357i q^{41} +490.279 q^{42} +113.147 q^{43} +313.139i q^{44} +52.5542i q^{45} -954.305i q^{46} +514.089i q^{47} -456.566 q^{48} -637.559 q^{49} -474.415i q^{50} -162.000 q^{51} +(836.370 + 337.008i) q^{52} +242.559 q^{53} +140.912i q^{54} +95.0490 q^{55} +1836.54 q^{56} +199.050i q^{57} +860.364i q^{58} -265.036i q^{59} +337.008i q^{60} -468.098 q^{61} +307.426 q^{62} -281.825i q^{63} -479.042 q^{64} +(102.294 - 253.869i) q^{65} +254.853 q^{66} -852.919i q^{67} -1038.84 q^{68} -548.559 q^{69} -954.305i q^{70} -165.619i q^{71} +527.846i q^{72} +315.325i q^{73} -576.000 q^{74} -272.706 q^{75} +1276.42i q^{76} -509.706 q^{77} +(274.279 - 680.693i) q^{78} +479.608 q^{79} +888.684i q^{80} +81.0000 q^{81} -287.230 q^{82} -574.235i q^{83} -1807.22i q^{84} +315.325i q^{85} -590.512i q^{86} +494.559 q^{87} +954.657 q^{88} +66.7144i q^{89} +274.279 q^{90} +(-548.559 + 1361.39i) q^{91} -3517.68 q^{92} -176.716i q^{93} +2683.02 q^{94} +387.441 q^{95} +975.220i q^{96} +1438.25i q^{97} +3327.40i q^{98} -146.496i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{3} - 26 q^{4} + 36 q^{9} + 20 q^{10} + 78 q^{12} - 72 q^{13} - 348 q^{14} + 354 q^{16} + 216 q^{17} - 136 q^{22} + 120 q^{23} - 44 q^{25} - 60 q^{26} - 108 q^{27} - 48 q^{29} - 60 q^{30} + 120 q^{35}+ \cdots + 3384 q^{95}+O(q^{100}) \) 4 * q - 12 * q^3 - 26 * q^4 + 36 * q^9 + 20 * q^10 + 78 * q^12 - 72 * q^13 - 348 * q^14 + 354 * q^16 + 216 * q^17 - 136 * q^22 + 120 * q^23 - 44 * q^25 - 60 * q^26 - 108 * q^27 - 48 * q^29 - 60 * q^30 + 120 * q^35 - 234 * q^36 - 468 * q^38 + 216 * q^39 - 1268 * q^40 + 1044 * q^42 + 1064 * q^43 - 1062 * q^48 - 716 * q^49 - 648 * q^51 + 1766 * q^52 - 864 * q^53 + 584 * q^55 + 3372 * q^56 - 2280 * q^61 + 924 * q^62 - 1050 * q^64 + 1632 * q^65 + 408 * q^66 - 1404 * q^68 - 360 * q^69 - 2304 * q^74 + 132 * q^75 - 816 * q^77 + 180 * q^78 + 288 * q^79 + 324 * q^81 - 28 * q^82 + 144 * q^87 + 2392 * q^88 + 180 * q^90 - 360 * q^91 - 8568 * q^92 + 6656 * q^94 + 3384 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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