LMFDB - Embedded newform 119.5.c.a.69.39

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [119,5,Mod(69,119)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("119.69"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(119, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	119.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.3010256070$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.39
Character	$\chi$	$=$	119.69
Dual form			119.5.c.a.69.40

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+6.58903 q^{2} -5.18871i q^{3} +27.4153 q^{4} +26.0235i q^{5} -34.1886i q^{6} +(14.9357 - 46.6683i) q^{7} +75.2159 q^{8} +54.0773 q^{9} +171.470i q^{10} +159.995 q^{11} -142.250i q^{12} -89.9878i q^{13} +(98.4115 - 307.499i) q^{14} +135.028 q^{15} +56.9547 q^{16} +70.0928i q^{17} +356.317 q^{18} +272.253i q^{19} +713.443i q^{20} +(-242.148 - 77.4968i) q^{21} +1054.21 q^{22} -918.510 q^{23} -390.273i q^{24} -52.2225 q^{25} -592.932i q^{26} -700.877i q^{27} +(409.466 - 1279.43i) q^{28} -403.212 q^{29} +889.706 q^{30} +166.296i q^{31} -828.178 q^{32} -830.165i q^{33} +461.844i q^{34} +(1214.47 + 388.678i) q^{35} +1482.55 q^{36} -1010.92 q^{37} +1793.88i q^{38} -466.921 q^{39} +1957.38i q^{40} +1431.34i q^{41} +(-1595.52 - 510.628i) q^{42} +256.675 q^{43} +4386.30 q^{44} +1407.28i q^{45} -6052.09 q^{46} +2009.34i q^{47} -295.521i q^{48} +(-1954.85 - 1394.04i) q^{49} -344.096 q^{50} +363.691 q^{51} -2467.04i q^{52} -2286.71 q^{53} -4618.10i q^{54} +4163.62i q^{55} +(1123.40 - 3510.20i) q^{56} +1412.64 q^{57} -2656.78 q^{58} +5112.51i q^{59} +3701.85 q^{60} -4872.10i q^{61} +1095.73i q^{62} +(807.679 - 2523.69i) q^{63} -6368.17 q^{64} +2341.80 q^{65} -5469.98i q^{66} +4689.48 q^{67} +1921.62i q^{68} +4765.88i q^{69} +(8002.19 + 2561.01i) q^{70} +4255.15 q^{71} +4067.47 q^{72} -8799.21i q^{73} -6660.99 q^{74} +270.967i q^{75} +7463.91i q^{76} +(2389.62 - 7466.66i) q^{77} -3076.55 q^{78} -11112.7 q^{79} +1482.16i q^{80} +743.614 q^{81} +9431.15i q^{82} +1229.58i q^{83} +(-6638.57 - 2124.60i) q^{84} -1824.06 q^{85} +1691.24 q^{86} +2092.15i q^{87} +12034.1 q^{88} +5476.97i q^{89} +9272.61i q^{90} +(-4199.57 - 1344.03i) q^{91} -25181.2 q^{92} +862.864 q^{93} +13239.6i q^{94} -7084.98 q^{95} +4297.18i q^{96} -14912.8i q^{97} +(-12880.6 - 9185.38i) q^{98} +8652.07 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{2} + 378 q^{4} - 130 q^{7} - 6 q^{8} - 1232 q^{9} + 192 q^{11} - 294 q^{14} - 128 q^{15} + 3178 q^{16} + 682 q^{18} + 312 q^{21} + 336 q^{22} + 876 q^{23} - 3800 q^{25} - 2426 q^{28} - 3372 q^{29}+ \cdots - 19620 q^{99}+O(q^{100}) $ 44 * q - 6 * q^2 + 378 * q^4 - 130 * q^7 - 6 * q^8 - 1232 * q^9 + 192 * q^11 - 294 * q^14 - 128 * q^15 + 3178 * q^16 + 682 * q^18 + 312 * q^21 + 336 * q^22 + 876 * q^23 - 3800 * q^25 - 2426 * q^28 - 3372 * q^29 + 2866 * q^30 + 2808 * q^32 - 2904 * q^35 - 6288 * q^36 - 488 * q^37 - 1156 * q^39 + 2494 * q^42 + 2676 * q^43 - 8376 * q^44 + 2492 * q^46 - 3216 * q^49 + 3660 * q^50 + 7668 * q^53 + 3126 * q^56 - 8940 * q^57 + 6420 * q^58 - 7530 * q^60 + 13934 * q^63 + 22394 * q^64 + 16440 * q^65 - 25844 * q^67 - 1216 * q^70 - 11364 * q^71 + 5620 * q^72 + 15600 * q^74 - 276 * q^77 + 38692 * q^78 + 2168 * q^79 + 37180 * q^81 + 13384 * q^84 - 61026 * q^86 - 23564 * q^88 - 14604 * q^91 + 7068 * q^92 - 60464 * q^93 + 16164 * q^95 - 16710 * q^98 - 19620 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/119\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$1$

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 $

$2$	6.58903			1.64726			0.823629	−	0.567129i	$-0.191946\pi$
$2$	6.58903			1.64726			0.823629	+	0.567129i	$0.191946\pi$
$3$		−	5.18871i		−	0.576523i	−0.957552	−	0.288262i	$-0.906923\pi$
$3$		−	5.18871i		−	0.576523i	0.957552	−	0.288262i	$-0.0930773\pi$
$4$	27.4153			1.71346
$5$			26.0235i			1.04094i	0.853880	+	0.520470i	$0.174243\pi$
$5$			26.0235i			1.04094i	−0.853880	+	0.520470i	$0.825757\pi$
$6$		−	34.1886i		−	0.949682i
$7$	14.9357	−	46.6683i	0.304809	−	0.952413i
$7$	14.9357	−	46.6683i	0.304809	−	0.952413i
$8$	75.2159			1.17525
$9$	54.0773			0.667621
$10$			171.470i			1.71470i
$11$	159.995			1.32227			0.661134	−	0.750268i	$-0.270075\pi$
$11$	159.995			1.32227			0.661134	+	0.750268i	$0.270075\pi$
$12$		−	142.250i		−	0.987848i
$13$		−	89.9878i		−	0.532472i	−0.963908	−	0.266236i	$-0.914220\pi$
$13$		−	89.9878i		−	0.532472i	0.963908	−	0.266236i	$-0.0857801\pi$
$14$	98.4115	−	307.499i	0.502099	−	1.56887i
$15$	135.028			0.600126
$16$	56.9547			0.222479
$17$			70.0928i			0.242536i
$17$			70.0928i			0.242536i
$18$	356.317			1.09974
$19$			272.253i			0.754164i	0.926180	+	0.377082i	$0.123073\pi$
$19$			272.253i			0.754164i	−0.926180	+	0.377082i	$0.876927\pi$
$20$			713.443i			1.78361i
$21$	−242.148	−	77.4968i	−0.549089	−	0.175730i
$22$	1054.21			2.17812
$23$	−918.510			−1.73631			−0.868157	−	0.496290i	$-0.834695\pi$
$23$	−918.510			−1.73631			−0.868157	+	0.496290i	$0.834695\pi$
$24$		−	390.273i		−	0.677558i
$25$	−52.2225			−0.0835560
$26$		−	592.932i		−	0.877119i
$27$		−	700.877i		−	0.961422i
$28$	409.466	−	1279.43i	0.522278	−	1.63192i
$29$	−403.212			−0.479444			−0.239722	−	0.970842i	$-0.577056\pi$
$29$	−403.212			−0.479444			−0.239722	+	0.970842i	$0.577056\pi$
$30$	889.706			0.988562
$31$			166.296i			0.173045i	0.996250	+	0.0865226i	$0.0275755\pi$
$31$			166.296i			0.173045i	−0.996250	+	0.0865226i	$0.972425\pi$
$32$	−828.178			−0.808768
$33$		−	830.165i		−	0.762319i
$34$			461.844i			0.399519i
$35$	1214.47	+	388.678i	0.991405	+	0.317288i
$36$	1482.55			1.14394
$37$	−1010.92			−0.738437			−0.369219	−	0.929343i	$-0.620375\pi$
$37$	−1010.92			−0.738437			−0.369219	+	0.929343i	$0.620375\pi$
$38$			1793.88i			1.24230i
$39$	−466.921			−0.306983
$40$			1957.38i			1.22336i
$41$			1431.34i			0.851482i	0.904845	+	0.425741i	$0.139986\pi$
$41$			1431.34i			0.851482i	−0.904845	+	0.425741i	$0.860014\pi$
$42$	−1595.52	−	510.628i	−0.904490	−	0.289472i
$43$	256.675			0.138818			0.0694090	−	0.997588i	$-0.477889\pi$
$43$	256.675			0.138818			0.0694090	+	0.997588i	$0.477889\pi$
$44$	4386.30			2.26565
$45$			1407.28i			0.694953i
$46$	−6052.09			−2.86016
$47$			2009.34i			0.909617i	0.890589	+	0.454809i	$0.150292\pi$
$47$			2009.34i			0.909617i	−0.890589	+	0.454809i	$0.849708\pi$
$48$		−	295.521i		−	0.128265i
$49$	−1954.85	−	1394.04i	−0.814183	−	0.580609i
$50$	−344.096			−0.137638
$51$	363.691			0.139827
$52$		−	2467.04i		−	0.912369i
$53$	−2286.71			−0.814065			−0.407033	−	0.913414i	$-0.633437\pi$
$53$	−2286.71			−0.814065			−0.407033	+	0.913414i	$0.633437\pi$
$54$		−	4618.10i		−	1.58371i
$55$			4163.62i			1.37640i
$56$	1123.40	−	3510.20i	0.358227	−	1.11932i
$57$	1412.64			0.434793
$58$	−2656.78			−0.789767
$59$			5112.51i			1.46869i	0.678776	+	0.734345i	$0.262511\pi$
$59$			5112.51i			1.46869i	−0.678776	+	0.734345i	$0.737489\pi$
$60$	3701.85			1.02829
$61$		−	4872.10i		−	1.30935i	−0.755909	−	0.654677i	$-0.772805\pi$
$61$		−	4872.10i		−	1.30935i	0.755909	−	0.654677i	$-0.227195\pi$
$62$			1095.73i			0.285050i
$63$	807.679	−	2523.69i	0.203497	−	0.635851i
$64$	−6368.17			−1.55473
$65$	2341.80			0.554272
$66$		−	5469.98i		−	1.25574i
$67$	4689.48			1.04466			0.522330	−	0.852744i	$-0.325063\pi$
$67$	4689.48			1.04466			0.522330	+	0.852744i	$0.325063\pi$
$68$			1921.62i			0.415575i
$69$			4765.88i			1.00103i
$70$	8002.19	+	2561.01i	1.63310	+	0.522655i
$71$	4255.15			0.844109			0.422054	−	0.906571i	$-0.361309\pi$
$71$	4255.15			0.844109			0.422054	+	0.906571i	$0.361309\pi$
$72$	4067.47			0.784620
$73$		−	8799.21i		−	1.65119i	−0.564261	−	0.825597i	$-0.690839\pi$
$73$		−	8799.21i		−	1.65119i	0.564261	−	0.825597i	$-0.309161\pi$
$74$	−6660.99			−1.21640
$75$			270.967i			0.0481720i
$76$			7463.91i			1.29223i
$77$	2389.62	−	7466.66i	0.403040	−	1.25935i
$78$	−3076.55			−0.505680
$79$	−11112.7			−1.78060			−0.890300	−	0.455374i	$-0.849506\pi$
$79$	−11112.7			−1.78060			−0.890300	+	0.455374i	$0.849506\pi$
$80$			1482.16i			0.231588i
$81$	743.614			0.113338
$82$			9431.15i			1.40261i
$83$			1229.58i			0.178484i	0.996010	+	0.0892421i	$0.0284445\pi$
$83$			1229.58i			0.178484i	−0.996010	+	0.0892421i	$0.971556\pi$
$84$	−6638.57	−	2124.60i	−0.940840	−	0.301105i
$85$	−1824.06			−0.252465
$86$	1691.24			0.228669
$87$			2092.15i			0.276410i
$88$	12034.1			1.55399
$89$			5476.97i			0.691449i	0.938336	+	0.345725i	$0.112367\pi$
$89$			5476.97i			0.691449i	−0.938336	+	0.345725i	$0.887633\pi$
$90$			9272.61i			1.14477i
$91$	−4199.57	−	1344.03i	−0.507134	−	0.162302i
$92$	−25181.2			−2.97510
$93$	862.864			0.0997646
$94$			13239.6i			1.49837i
$95$	−7084.98			−0.785039
$96$			4297.18i			0.466273i
$97$		−	14912.8i		−	1.58495i	−0.609902	−	0.792477i	$-0.708791\pi$
$97$		−	14912.8i		−	1.58495i	0.609902	−	0.792477i	$-0.291209\pi$
$98$	−12880.6	−	9185.38i	−1.34117	−	0.956412i
$99$	8652.07			0.882774
$100$	−1431.70			−0.143170
$101$		−	9085.72i		−	0.890670i	−0.895364	−	0.445335i	$-0.853085\pi$
$101$		−	9085.72i		−	0.890670i	0.895364	−	0.445335i	$-0.146915\pi$
$102$	2396.37			0.230332
$103$			17131.0i			1.61476i	0.590031	+	0.807381i	$0.299116\pi$
$103$			17131.0i			1.61476i	−0.590031	+	0.807381i	$0.700884\pi$
$104$		−	6768.51i		−	0.625787i
$105$	2016.74	−	6301.54i	0.182924	−	0.571568i
$106$	−15067.2			−1.34098
$107$	−26.0786			−0.00227780			−0.00113890	−	0.999999i	$-0.500363\pi$
$107$	−26.0786			−0.00227780			−0.00113890	+	0.999999i	$0.500363\pi$
$108$		−	19214.8i		−	1.64736i
$109$	4390.60			0.369548			0.184774	−	0.982781i	$-0.440845\pi$
$109$	4390.60			0.369548			0.184774	+	0.982781i	$0.440845\pi$
$110$			27434.2i			2.26729i
$111$			5245.37i			0.425726i
$112$	850.656	−	2657.98i	0.0678137	−	0.211892i
$113$	1888.59			0.147904			0.0739522	−	0.997262i	$-0.476439\pi$
$113$	1888.59			0.147904			0.0739522	+	0.997262i	$0.476439\pi$
$114$	9307.95			0.716216
$115$		−	23902.8i		−	1.80740i
$116$	−11054.2			−0.821506
$117$		−	4866.30i		−	0.355490i
$118$			33686.5i			2.41931i
$119$	3271.11	+	1046.88i	0.230994	+	0.0739271i
$120$	10156.3			0.705297
$121$	10957.2			0.748394
$122$		−	32102.4i		−	2.15684i
$123$	7426.81			0.490899
$124$			4559.07i			0.296506i
$125$			14905.7i			0.953963i
$126$	5321.82	−	16628.7i	0.335212	−	1.04741i
$127$	30348.3			1.88160			0.940799	−	0.338964i	$-0.110076\pi$
$127$	30348.3			1.88160			0.940799	+	0.338964i	$0.110076\pi$
$128$	−28709.2			−1.75227
$129$		−	1331.81i		−	0.0800318i
$130$	15430.2			0.913028
$131$			14817.9i			0.863463i	0.902002	+	0.431731i	$0.142097\pi$
$131$			14817.9i			0.863463i	−0.902002	+	0.431731i	$0.857903\pi$
$132$		−	22759.2i		−	1.30620i
$133$	12705.6	+	4066.28i	0.718276	+	0.229876i
$134$	30899.1			1.72082
$135$	18239.3			1.00078
$136$			5272.09i			0.285040i
$137$	15001.0			0.799241			0.399621	−	0.916681i	$-0.369142\pi$
$137$	15001.0			0.799241			0.399621	+	0.916681i	$0.369142\pi$
$138$			31402.5i			1.64895i
$139$		−	26905.9i		−	1.39257i	−0.717765	−	0.696285i	$-0.754835\pi$
$139$		−	26905.9i		−	1.39257i	0.717765	−	0.696285i	$-0.245165\pi$
$140$	33295.1	+	10655.7i	1.69873	+	0.543660i
$141$	10425.9			0.524415
$142$	28037.3			1.39046
$143$		−	14397.6i		−	0.704071i
$144$	3079.96			0.148532
$145$		−	10493.0i		−	0.499072i
$146$		−	57978.3i		−	2.71994i
$147$	−7233.28	+	10143.2i	−0.334734	+	0.469395i
$148$	−27714.7			−1.26528
$149$	−22381.1			−1.00811			−0.504056	−	0.863671i	$-0.668159\pi$
$149$	−22381.1			−1.00811			−0.504056	+	0.863671i	$0.668159\pi$
$150$			1785.41i			0.0793517i
$151$	4139.51			0.181550			0.0907748	−	0.995871i	$-0.471066\pi$
$151$	4139.51			0.181550			0.0907748	+	0.995871i	$0.471066\pi$
$152$			20477.8i			0.886330i
$153$			3790.43i			0.161922i
$154$	15745.3	−	49198.1i	0.663910	−	2.07447i
$155$	−4327.62			−0.180130
$156$	−12800.8			−0.526002
$157$		−	7394.03i		−	0.299973i	−0.988688	−	0.149986i	$-0.952077\pi$
$157$		−	7394.03i		−	0.299973i	0.988688	−	0.149986i	$-0.0479230\pi$
$158$	−73222.1			−2.93311
$159$			11865.1i			0.469328i
$160$		−	21552.1i		−	0.841879i
$161$	−13718.5	+	42865.3i	−0.529244	+	1.65369i
$162$	4899.69			0.186698
$163$	−1784.24			−0.0671549			−0.0335775	−	0.999436i	$-0.510690\pi$
$163$	−1784.24			−0.0671549			−0.0335775	+	0.999436i	$0.510690\pi$
$164$			39240.7i			1.45898i
$165$	21603.8			0.793528
$166$			8101.72i			0.294009i
$167$		−	15792.2i		−	0.566252i	−0.959083	−	0.283126i	$-0.908629\pi$
$167$		−	15792.2i		−	0.566252i	0.959083	−	0.283126i	$-0.0913715\pi$
$168$	−18213.4	−	5828.99i	−0.645315	−	0.206526i
$169$	20463.2			0.716473
$170$	−12018.8			−0.415875
$171$			14722.7i			0.503496i
$172$	7036.82			0.237859
$173$		−	14592.4i		−	0.487569i	−0.969829	−	0.243784i	$-0.921611\pi$
$173$		−	14592.4i		−	0.487569i	0.969829	−	0.243784i	$-0.0783889\pi$
$174$			13785.2i			0.455319i
$175$	−779.977	+	2437.13i	−0.0254686	+	0.0795798i
$176$	9112.44			0.294177
$177$	26527.3			0.846735
$178$			36087.9i			1.13900i
$179$	32441.3			1.01249			0.506247	−	0.862389i	$-0.331032\pi$
$179$	32441.3			1.01249			0.506247	+	0.862389i	$0.331032\pi$
$180$			38581.0i			1.19077i
$181$			25152.4i			0.767753i	0.923384	+	0.383876i	$0.125411\pi$
$181$			25152.4i			0.767753i	−0.923384	+	0.383876i	$0.874589\pi$
$182$	−27671.1	−	8855.83i	−0.835380	−	0.267354i
$183$	−25279.9			−0.754873
$184$	−69086.5			−2.04060
$185$		−	26307.7i		−	0.768669i
$186$	5685.44			0.164338
$187$			11214.5i			0.320697i
$188$			55086.8i			1.55859i
$189$	−32708.7	−	10468.1i	−0.915672	−	0.293050i
$190$	−46683.2			−1.29316
$191$	−5621.37			−0.154090			−0.0770452	−	0.997028i	$-0.524549\pi$
$191$	−5621.37			−0.154090			−0.0770452	+	0.997028i	$0.524549\pi$
$192$			33042.6i			0.896337i
$193$	−13494.5			−0.362279			−0.181140	−	0.983457i	$-0.557979\pi$
$193$	−13494.5			−0.362279			−0.181140	+	0.983457i	$0.557979\pi$
$194$		−	98261.1i		−	2.61083i
$195$		−	12150.9i		−	0.319551i
$196$	−53592.9	−	38218.1i	−1.39507	−	0.994848i
$197$	60193.2			1.55101			0.775505	−	0.631341i	$-0.217495\pi$
$197$	60193.2			1.55101			0.775505	+	0.631341i	$0.217495\pi$
$198$	57008.7			1.45416
$199$			47479.3i			1.19894i	0.800397	+	0.599471i	$0.204622\pi$
$199$			47479.3i			1.19894i	−0.800397	+	0.599471i	$0.795378\pi$
$200$	−3927.96			−0.0981990
$201$		−	24332.3i		−	0.602270i
$202$		−	59866.1i		−	1.46716i
$203$	−6022.23	+	18817.2i	−0.146139	+	0.456629i
$204$	9970.71			0.239588
$205$	−37248.5			−0.886341
$206$			112877.i			2.65993i
$207$	−49670.5			−1.15920
$208$		−	5125.23i		−	0.118464i
$209$			43559.0i			0.997207i
$210$	13288.3	−	41521.0i	0.301323	−	0.941520i
$211$	−51384.0			−1.15415			−0.577076	−	0.816690i	$-0.695806\pi$
$211$	−51384.0			−1.15415			−0.577076	+	0.816690i	$0.695806\pi$
$212$	−62690.9			−1.39487
$213$		−	22078.7i		−	0.486648i
$214$	−171.832			−0.00375213
$215$			6679.57i			0.144501i
$216$		−	52717.1i		−	1.12991i
$217$	7760.77	+	2483.75i	0.164811	+	0.0527458i
$218$	28929.8			0.608740
$219$	−45656.5			−0.951951
$220$			114147.i			2.35841i
$221$	6307.50			0.129144
$222$			34561.9i			0.701281i
$223$		−	56849.6i		−	1.14319i	−0.820537	−	0.571594i	$-0.806325\pi$
$223$		−	56849.6i		−	1.14319i	0.820537	−	0.571594i	$-0.193675\pi$
$224$	−12369.4	+	38649.6i	−0.246520	+	0.770281i
$225$	−2824.05			−0.0557837
$226$	12444.0			0.243637
$227$		−	62497.3i		−	1.21286i	−0.795138	−	0.606428i	$-0.792602\pi$
$227$		−	62497.3i		−	1.21286i	0.795138	−	0.606428i	$-0.207398\pi$
$228$	38728.1			0.745000
$229$		−	16873.7i		−	0.321766i	−0.986973	−	0.160883i	$-0.948566\pi$
$229$		−	16873.7i		−	0.321766i	0.986973	−	0.160883i	$-0.0514342\pi$
$230$		−	157497.i		−	2.97725i
$231$	−38742.4	−	12399.1i	−0.726043	−	0.232362i
$232$	−30328.0			−0.563465
$233$	24525.1			0.451750			0.225875	−	0.974156i	$-0.427476\pi$
$233$	24525.1			0.451750			0.225875	+	0.974156i	$0.427476\pi$
$234$		−	32064.2i		−	0.585583i
$235$	−52290.2			−0.946857
$236$			140161.i			2.51654i
$237$			57660.7i			1.02656i
$238$	21553.4	+	6897.93i	0.380507	+	0.121777i
$239$	−32608.9			−0.570873			−0.285437	−	0.958398i	$-0.592139\pi$
$239$	−32608.9			−0.570873			−0.285437	+	0.958398i	$0.592139\pi$
$240$	7690.50			0.133516
$241$			71825.8i			1.23665i	0.785923	+	0.618325i	$0.212188\pi$
$241$			71825.8i			1.23665i	−0.785923	+	0.618325i	$0.787812\pi$
$242$	72197.6			1.23280
$243$		−	60629.4i		−	1.02676i
$244$		−	133570.i		−	2.24352i
$245$	36277.8	−	50872.1i	0.604379	−	0.847515i
$246$	48935.5			0.808637
$247$	24499.5			0.401571
$248$			12508.1i			0.203371i
$249$	6379.92			0.102900
$250$			98213.9i			1.57142i
$251$		−	22527.0i		−	0.357566i	−0.983889	−	0.178783i	$-0.942784\pi$
$251$		−	22527.0i		−	0.357566i	0.983889	−	0.178783i	$-0.0572160\pi$
$252$	22142.8	−	69187.9i	0.348683	−	1.08950i
$253$	−146957.			−2.29587
$254$	199966.			3.09948
$255$			9464.52i			0.145552i
$256$	−87275.1			−1.33171
$257$			94252.2i			1.42700i	0.700653	+	0.713502i	$0.252892\pi$
$257$			94252.2i			1.42700i	−0.700653	+	0.713502i	$0.747108\pi$
$258$		−	8775.33i		−	0.131833i
$259$	−15098.8	+	47177.9i	−0.225082	+	0.703298i
$260$	64201.1			0.949721
$261$	−21804.6			−0.320087
$262$			97635.5i			1.42235i
$263$	−38602.9			−0.558095			−0.279048	−	0.960277i	$-0.590019\pi$
$263$	−38602.9			−0.558095			−0.279048	+	0.960277i	$0.590019\pi$
$264$		−	62441.6i		−	0.895914i
$265$		−	59508.2i		−	0.847393i
$266$	83717.5	+	26792.8i	1.18319	+	0.378665i
$267$	28418.4			0.398637
$268$	128563.			1.78998
$269$		−	118537.i		−	1.63814i	−0.573695	−	0.819069i	$-0.694490\pi$
$269$		−	118537.i		−	1.63814i	0.573695	−	0.819069i	$-0.305510\pi$
$270$	120179.			1.64855
$271$			101988.i			1.38871i	0.719634	+	0.694354i	$0.244310\pi$
$271$			101988.i			1.38871i	−0.719634	+	0.694354i	$0.755690\pi$
$272$			3992.11i			0.0539592i
$273$	−6973.76	+	21790.4i	−0.0935711	+	0.292374i
$274$	98841.8			1.31656
$275$	−8355.31			−0.110483
$276$			130658.i			1.71521i
$277$	38937.2			0.507464			0.253732	−	0.967275i	$-0.418342\pi$
$277$	38937.2			0.507464			0.253732	+	0.967275i	$0.418342\pi$
$278$		−	177284.i		−	2.29392i
$279$			8992.86i			0.115529i
$280$	91347.6	+	29234.8i	1.16515	+	0.372892i
$281$	52914.4			0.670134			0.335067	−	0.942194i	$-0.391241\pi$
$281$	52914.4			0.670134			0.335067	+	0.942194i	$0.391241\pi$
$282$	68696.6			0.863847
$283$			119650.i			1.49396i	0.664846	+	0.746980i	$0.268497\pi$
$283$			119650.i			1.49396i	−0.664846	+	0.746980i	$0.731503\pi$
$284$	116656.			1.44634
$285$			36761.9i			0.452594i
$286$		−	94865.9i		−	1.15979i
$287$	66798.2	+	21378.0i	0.810963	+	0.259539i
$288$	−44785.6			−0.539950
$289$	−4913.00			−0.0588235
$290$		−	69138.6i		−	0.822100i
$291$	−77378.4			−0.913763
$292$		−	241233.i		−	2.82925i
$293$		−	26642.3i		−	0.310339i	−0.987888	−	0.155169i	$-0.950408\pi$
$293$		−	26642.3i		−	0.310339i	0.987888	−	0.155169i	$-0.0495923\pi$
$294$	−47660.3	+	66833.6i	−0.551394	+	0.773215i
$295$	−133045.			−1.52882
$296$	−76037.3			−0.867847
$297$		−	112136.i		−	1.27126i
$298$	−147470.			−1.66062
$299$			82654.7i			0.924539i
$300$			7428.66i			0.0825406i
$301$	3833.60	−	11978.6i	0.0423130	−	0.132212i
$302$	27275.4			0.299059
$303$	−47143.2			−0.513492
$304$			15506.1i			0.167786i
$305$	126789.			1.36296
$306$			24975.2i			0.266727i
$307$		−	50393.0i		−	0.534679i	−0.963602	−	0.267340i	$-0.913855\pi$
$307$		−	50393.0i		−	0.534679i	0.963602	−	0.267340i	$-0.0861445\pi$
$308$	65512.3	−	204701.i	0.690591	−	2.15784i
$309$	88887.8			0.930948
$310$	−28514.8			−0.296720
$311$		−	70479.9i		−	0.728693i	−0.931264	−	0.364346i	$-0.881292\pi$
$311$		−	70479.9i		−	0.728693i	0.931264	−	0.364346i	$-0.118708\pi$
$312$	−35119.9			−0.360781
$313$			118402.i			1.20856i	0.796771	+	0.604281i	$0.206540\pi$
$313$			118402.i			1.20856i	−0.796771	+	0.604281i	$0.793460\pi$
$314$		−	48719.5i		−	0.494132i
$315$	65675.3	+	21018.6i	0.661883	+	0.211828i
$316$	−304659.			−3.05098
$317$	−141311.			−1.40623			−0.703117	−	0.711075i	$-0.748209\pi$
$317$	−141311.			−1.40623			−0.703117	+	0.711075i	$0.748209\pi$
$318$			78179.3i			0.773104i
$319$	−64511.7			−0.633953
$320$		−	165722.i		−	1.61838i
$321$			135.314i			0.00131321i
$322$	−90391.9	+	282440.i	−0.871802	+	2.72405i
$323$	−19083.0			−0.182912
$324$	20386.4			0.194201
$325$			4699.39i			0.0444912i
$326$	−11756.4			−0.110621
$327$		−	22781.5i		−	0.213053i
$328$			107660.i			1.00070i
$329$	93772.6	+	30010.9i	0.866332	+	0.277260i
$330$	142348.			1.30715
$331$	−123071.			−1.12331			−0.561657	−	0.827370i	$-0.689836\pi$
$331$	−123071.			−1.12331			−0.561657	+	0.827370i	$0.689836\pi$
$332$			33709.3i			0.305825i
$333$	−54667.9			−0.492996
$334$		−	104055.i		−	0.932763i
$335$			122037.i			1.08743i
$336$	−13791.5	−	4413.81i	−0.122161	−	0.0390962i
$337$	−131496.			−1.15785			−0.578924	−	0.815381i	$-0.696527\pi$
$337$	−131496.			−1.15785			−0.578924	+	0.815381i	$0.696527\pi$
$338$	134833.			1.18022
$339$		−	9799.35i		−	0.0852704i
$340$	−50007.2			−0.432588
$341$			26606.5i			0.228812i
$342$			97008.4i			0.829387i
$343$	−94254.5	+	70408.7i	−0.801150	+	0.598464i
$344$	19306.0			0.163146
$345$	−124025.			−1.04201
$346$		−	96150.1i		−	0.803151i
$347$	−129949.			−1.07923			−0.539615	−	0.841912i	$-0.681430\pi$
$347$	−129949.			−1.07923			−0.539615	+	0.841912i	$0.681430\pi$
$348$			57357.0i			0.473618i
$349$		−	103853.i		−	0.852647i	−0.904571	−	0.426324i	$-0.859808\pi$
$349$		−	103853.i		−	0.852647i	0.904571	−	0.426324i	$-0.140192\pi$
$350$	−5139.29	+	16058.3i	−0.0419534	+	0.131089i
$351$	−63070.4			−0.511931
$352$	−132504.			−1.06941
$353$		−	68143.3i		−	0.546857i	−0.961892	−	0.273429i	$-0.911842\pi$
$353$		−	68143.3i		−	0.546857i	0.961892	−	0.273429i	$-0.0881577\pi$
$354$	174789.			1.39479
$355$			110734.i			0.878666i
$356$			150153.i			1.18477i
$357$	5431.96	−	16972.8i	0.0426207	−	0.133174i
$358$	213757.			1.66784
$359$	231390.			1.79538			0.897690	−	0.440627i	$-0.145244\pi$
$359$	231390.			1.79538			0.897690	+	0.440627i	$0.145244\pi$
$360$			105850.i			0.816743i
$361$	56199.2			0.431237
$362$			165730.i			1.26469i
$363$		−	56853.9i		−	0.431467i
$364$	−115133.	−	36846.9i	−0.868952	−	0.278098i
$365$	228986.			1.71879
$366$	−166570.			−1.24347
$367$		−	230663.i		−	1.71256i	−0.516511	−	0.856281i	$-0.672769\pi$
$367$		−	230663.i		−	1.71256i	0.516511	−	0.856281i	$-0.327231\pi$
$368$	−52313.5			−0.386294
$369$			77403.0i			0.568467i
$370$		−	173342.i		−	1.26620i
$371$	−34153.5	+	106717.i	−0.248135	+	0.775327i
$372$	23655.7			0.170942
$373$	−51324.0			−0.368895			−0.184447	−	0.982842i	$-0.559050\pi$
$373$	−51324.0			−0.368895			−0.184447	+	0.982842i	$0.559050\pi$
$374$			73892.4i			0.528271i
$375$	77341.2			0.549982
$376$			151135.i			1.06903i
$377$			36284.2i			0.255290i
$378$	−215519.	−	68974.3i	−1.50835	−	0.482729i
$379$	255626.			1.77962			0.889810	−	0.456332i	$-0.150837\pi$
$379$	255626.			1.77962			0.889810	+	0.456332i	$0.150837\pi$
$380$	−194237.			−1.34513
$381$		−	157469.i		−	1.08479i
$382$	−37039.4			−0.253826
$383$		−	96361.4i		−	0.656910i	−0.944520	−	0.328455i	$-0.893472\pi$
$383$		−	96361.4i		−	0.656910i	0.944520	−	0.328455i	$-0.106528\pi$
$384$			148964.i			1.01022i
$385$	194309.	+	62186.3i	1.31090	+	0.419540i
$386$	−88915.9			−0.596767
$387$	13880.3			0.0926778
$388$		−	408840.i		−	2.71575i
$389$	7743.98			0.0511759			0.0255879	−	0.999673i	$-0.491854\pi$
$389$	7743.98			0.0511759			0.0255879	+	0.999673i	$0.491854\pi$
$390$		−	80062.7i		−	0.526382i
$391$		−	64380.9i		−	0.421118i
$392$	−147036.	−	104854.i	−0.956867	−	0.682360i
$393$	76885.7			0.497806
$394$	396615.			2.55491
$395$		−	289192.i		−	1.85350i
$396$	237199.			1.51260
$397$			9358.50i			0.0593779i	0.999559	+	0.0296890i	$0.00945168\pi$
$397$			9358.50i			0.0593779i	−0.999559	+	0.0296890i	$0.990548\pi$
$398$			312842.i			1.97497i
$399$	21098.7	−	65925.6i	0.132529	−	0.414103i
$400$	−2974.32			−0.0185895
$401$	313553.			1.94994			0.974971	−	0.222332i	$-0.0713669\pi$
$401$	313553.			1.94994			0.974971	+	0.222332i	$0.0713669\pi$
$402$		−	160326.i		−	0.992094i
$403$	14964.7			0.0921418
$404$		−	249088.i		−	1.52613i
$405$			19351.4i			0.117979i
$406$	−39680.7	+	123987.i	−0.240728	+	0.752185i
$407$	−161742.			−0.976413
$408$	27355.4			0.164332
$409$			28317.5i			0.169281i	0.996412	+	0.0846405i	$0.0269742\pi$
$409$			28317.5i			0.169281i	−0.996412	+	0.0846405i	$0.973026\pi$
$410$	−245431.			−1.46003
$411$		−	77835.6i		−	0.460781i
$412$			469652.i			2.76683i
$413$	238592.	+	76358.7i	1.39880	+	0.447670i
$414$	−327281.			−1.90950
$415$	−31997.9			−0.185791
$416$			74525.9i			0.430646i
$417$	−139607.			−0.802850
$418$			287012.i			1.64266i
$419$			220178.i			1.25414i	0.778964	+	0.627069i	$0.215745\pi$
$419$			220178.i			1.25414i	−0.778964	+	0.627069i	$0.784255\pi$
$420$	55289.5	−	172759.i	0.313432	−	0.979358i
$421$	176205.			0.994154			0.497077	−	0.867706i	$-0.334407\pi$
$421$	176205.			0.994154			0.497077	+	0.867706i	$0.334407\pi$
$422$	−338571.			−1.90119
$423$			108660.i			0.607279i
$424$	−171997.			−0.956729
$425$		−	3660.42i		−	0.0202653i
$426$		−	145478.i		−	0.801635i
$427$	−227373.	−	72768.0i	−1.24705	−	0.399103i
$428$	−714.952			−0.00390292
$429$	−74704.7			−0.405914
$430$			44011.9i			0.238031i
$431$	178574.			0.961311			0.480656	−	0.876909i	$-0.340399\pi$
$431$	178574.			0.961311			0.480656	+	0.876909i	$0.340399\pi$
$432$		−	39918.2i		−	0.213897i
$433$			63507.0i			0.338724i	0.985554	+	0.169362i	$0.0541706\pi$
$433$			63507.0i			0.338724i	−0.985554	+	0.169362i	$0.945829\pi$
$434$	51135.9	+	16365.5i	0.271486	+	0.0868859i
$435$	−54445.1			−0.287727
$436$	120370.			0.633204
$437$		−	250067.i		−	1.30946i
$438$	−300832.			−1.56811
$439$			128385.i			0.666170i	0.942897	+	0.333085i	$0.108090\pi$
$439$			128385.i			0.666170i	−0.942897	+	0.333085i	$0.891910\pi$
$440$			313170.i			1.61761i
$441$	−105713.	−	75386.0i	−0.543565	−	0.387627i
$442$	41560.3			0.212733
$443$	−10947.7			−0.0557850			−0.0278925	−	0.999611i	$-0.508880\pi$
$443$	−10947.7			−0.0557850			−0.0278925	+	0.999611i	$0.508880\pi$
$444$			143804.i			0.729464i
$445$	−142530.			−0.719757
$446$		−	374584.i		−	1.88313i
$447$			116129.i			0.581200i
$448$	−95112.7	+	297191.i	−0.473895	+	1.48074i
$449$	−1853.11			−0.00919198			−0.00459599	−	0.999989i	$-0.501463\pi$
$449$	−1853.11			−0.00919198			−0.00459599	+	0.999989i	$0.501463\pi$
$450$	−18607.8			−0.0918902
$451$			229007.i			1.12589i
$452$	51776.4			0.253428
$453$		−	21478.7i		−	0.104668i
$454$		−	411796.i		−	1.99789i
$455$	34976.3	−	109288.i	0.168947	−	0.527896i
$456$	106253.			0.510990
$457$	−33867.6			−0.162163			−0.0810815	−	0.996707i	$-0.525837\pi$
$457$	−33867.6			−0.162163			−0.0810815	+	0.996707i	$0.525837\pi$
$458$		−	111181.i		−	0.530031i
$459$	49126.4			0.233179
$460$		−	655304.i		−	3.09690i
$461$			316325.i			1.48844i	0.667933	+	0.744221i	$0.267179\pi$
$461$			316325.i			1.48844i	−0.667933	+	0.744221i	$0.732821\pi$
$462$	−255275.	−	81697.7i	−1.19598	−	0.382760i
$463$	41525.0			0.193708			0.0968541	−	0.995299i	$-0.469122\pi$
$463$	41525.0			0.193708			0.0968541	+	0.995299i	$0.469122\pi$
$464$	−22964.8			−0.106666
$465$			22454.7i			0.103849i
$466$	161596.			0.744149
$467$			171791.i			0.787708i	0.919173	+	0.393854i	$0.128858\pi$
$467$			171791.i			0.787708i	−0.919173	+	0.393854i	$0.871142\pi$
$468$		−	133411.i		−	0.609116i
$469$	70040.4	−	218850.i	0.318422	−	0.994947i
$470$	−344541.			−1.55972
$471$	−38365.5			−0.172941
$472$			384542.i			1.72608i
$473$	41066.5			0.183555
$474$			379928.i			1.69101i
$475$		−	14217.7i		−	0.0630149i
$476$	89678.5	+	28700.6i	0.395799	+	0.126671i
$477$	−123659.			−0.543487
$478$	−214861.			−0.940376
$479$		−	167966.i		−	0.732068i	−0.930601	−	0.366034i	$-0.880715\pi$
$479$		−	167966.i		−	0.732068i	0.930601	−	0.366034i	$-0.119285\pi$
$480$	−111828.			−0.485363
$481$			90970.6i			0.393197i
$482$			473263.i			2.03708i
$483$	222415.	+	71181.5i	0.953390	+	0.305122i
$484$	300396.			1.28234
$485$	388084.			1.64984
$486$		−	399489.i		−	1.69135i
$487$	208154.			0.877660			0.438830	−	0.898570i	$-0.355393\pi$
$487$	208154.			0.877660			0.438830	+	0.898570i	$0.355393\pi$
$488$		−	366460.i		−	1.53882i
$489$			9257.90i			0.0387164i
$490$	239036.	−	335198.i	0.995568	−	1.39608i
$491$	−404286.			−1.67697			−0.838485	−	0.544925i	$-0.816558\pi$
$491$	−404286.			−1.67697			−0.838485	+	0.544925i	$0.816558\pi$
$492$	203608.			0.841135
$493$		−	28262.3i		−	0.116282i
$494$	161428.			0.661492
$495$			225157.i			0.918915i
$496$			9471.37i			0.0384990i
$497$	63553.5	−	198581.i	0.257292	−	0.803940i
$498$	42037.5			0.169503
$499$	383335.			1.53949			0.769745	−	0.638351i	$-0.220383\pi$
$499$	383335.			1.53949			0.769745	+	0.638351i	$0.220383\pi$
$500$			408644.i			1.63458i
$501$	−81941.2			−0.326458
$502$		−	148431.i		−	0.589004i
$503$			25407.1i			0.100420i	0.998739	+	0.0502099i	$0.0159890\pi$
$503$			25407.1i			0.100420i	−0.998739	+	0.0502099i	$0.984011\pi$
$504$	60750.3	−	189822.i	0.239159	−	0.747283i
$505$	236442.			0.927134
$506$	−968301.			−3.78189
$507$		−	106178.i		−	0.413064i
$508$	832009.			3.22404
$509$		−	369143.i		−	1.42482i	−0.701765	−	0.712408i	$-0.747604\pi$
$509$		−	369143.i		−	1.42482i	0.701765	−	0.712408i	$-0.252396\pi$
$510$			62362.0i			0.239762i
$511$	−410644.	−	131422.i	−1.57262	−	0.503299i
$512$	−115711.			−0.441403
$513$	190816.			0.725070
$514$			621031.i			2.35064i
$515$	−445809.			−1.68087
$516$		−	36512.0i		−	0.137131i
$517$			321484.i			1.20276i
$518$	−99486.2	+	310857.i	−0.370769	+	1.15851i
$519$	−75716.0			−0.281095
$520$	176140.			0.651407
$521$		−	230936.i		−	0.850780i	−0.905010	−	0.425390i	$-0.860137\pi$
$521$		−	230936.i		−	0.850780i	0.905010	−	0.425390i	$-0.139863\pi$
$522$	−143671.			−0.527265
$523$		−	382943.i		−	1.40001i	−0.714139	−	0.700004i	$-0.753182\pi$
$523$		−	382943.i		−	1.40001i	0.714139	−	0.700004i	$-0.246818\pi$
$524$			406237.i			1.47951i
$525$	12645.6	+	4047.07i	0.0458796	+	0.0146833i
$526$	−254356.			−0.919327
$527$	−11656.2			−0.0419696
$528$		−	47281.8i		−	0.169600i
$529$	563819.			2.01478
$530$		−	392101.i		−	1.39587i
$531$			276471.i			0.980529i
$532$	348328.	+	111478.i	1.23074	+	0.393883i
$533$	128803.			0.453390
$534$	187250.			0.656657
$535$		−	678.655i		−	0.00237105i
$536$	352723.			1.22773
$537$		−	168329.i		−	0.583726i
$538$		−	781046.i		−	2.69844i
$539$	−312766.	−	223039.i	−1.07657	−	0.767721i
$540$	500035.			1.71480
$541$	51686.7			0.176597			0.0882987	−	0.996094i	$-0.471857\pi$
$541$	51686.7			0.176597			0.0882987	+	0.996094i	$0.471857\pi$
$542$			672003.i			2.28756i
$543$	130508.			0.442627
$544$		−	58049.3i		−	0.196155i
$545$			114259.i			0.384677i
$546$	−45950.3	+	143577.i	−0.154136	+	0.481616i
$547$	−74882.5			−0.250268			−0.125134	−	0.992140i	$-0.539936\pi$
$547$	−74882.5			−0.250268			−0.125134	+	0.992140i	$0.539936\pi$
$548$	411256.			1.36947
$549$		−	263470.i		−	0.874152i
$550$	−55053.4			−0.181995
$551$		−	109776.i		−	0.361579i
$552$			358470.i			1.17645i
$553$	−165976.	+	518612.i	−0.542743	+	1.69587i
$554$	256559.			0.835925
$555$	−136503.			−0.443156
$556$		−	737633.i		−	2.38611i
$557$	2145.72			0.00691612			0.00345806	−	0.999994i	$-0.498899\pi$
$557$	2145.72			0.00691612			0.00345806	+	0.999994i	$0.498899\pi$
$558$			59254.2i			0.190305i
$559$		−	23097.6i		−	0.0739168i
$560$	69169.9	+	22137.0i	0.220567	+	0.0705900i
$561$	58188.6			0.184889
$562$	348655.			1.10388
$563$		−	18179.6i		−	0.0573544i	−0.999589	−	0.0286772i	$-0.990871\pi$
$563$		−	18179.6i		−	0.0573544i	0.999589	−	0.0286772i	$-0.00912949\pi$
$564$	285830.			0.898564
$565$			49147.8i			0.153960i
$566$			788376.i			2.46094i
$567$	11106.4	−	34703.2i	0.0345466	−	0.107945i
$568$	320055.			0.992037
$569$	−413942.			−1.27854			−0.639272	−	0.768981i	$-0.720764\pi$
$569$	−413942.			−1.27854			−0.639272	+	0.768981i	$0.720764\pi$
$570$			242225.i			0.745538i
$571$	−436476.			−1.33872			−0.669358	−	0.742940i	$-0.733431\pi$
$571$	−436476.			−1.33872			−0.669358	+	0.742940i	$0.733431\pi$
$572$		−	394714.i		−	1.20640i
$573$			29167.7i			0.0888367i
$574$	440135.	+	140860.i	1.33586	+	0.427528i
$575$	47966.9			0.145079
$576$	−344373.			−1.03797
$577$		−	481056.i		−	1.44492i	−0.691413	−	0.722460i	$-0.743011\pi$
$577$		−	481056.i		−	1.44492i	0.691413	−	0.722460i	$-0.256989\pi$
$578$	−32371.9			−0.0968975
$579$			70019.3i			0.208862i
$580$		−	287669.i		−	0.855139i
$581$	57382.2	+	18364.5i	0.169991	+	0.0544036i
$582$	−509848.			−1.50520
$583$	−365861.			−1.07641
$584$		−	661840.i		−	1.94056i
$585$	126638.			0.370043
$586$		−	175547.i		−	0.511208i
$587$			475026.i			1.37861i	0.724472	+	0.689304i	$0.242084\pi$
$587$			475026.i			1.37861i	−0.724472	+	0.689304i	$0.757916\pi$
$588$	−198303.	+	278078.i	−0.573553	+	0.804289i
$589$	−45274.7			−0.130504
$590$	−876641.			−2.51836
$591$		−	312325.i		−	0.894194i
$592$	−57576.7			−0.164287
$593$		−	335743.i		−	0.954768i	−0.878695	−	0.477384i	$-0.841585\pi$
$593$		−	335743.i		−	0.954768i	0.878695	−	0.477384i	$-0.158415\pi$
$594$		−	738870.i		−	2.09409i
$595$	−27243.5	+	85125.7i	−0.0769537	+	0.240451i
$596$	−613585.			−1.72736
$597$	246356.			0.691218
$598$			544614.i			1.52295i
$599$	67850.0			0.189102			0.0945510	−	0.995520i	$-0.469858\pi$
$599$	67850.0			0.189102			0.0945510	+	0.995520i	$0.469858\pi$
$600$			20381.1i			0.0566140i
$601$		−	396974.i		−	1.09904i	−0.835481	−	0.549520i	$-0.814811\pi$
$601$		−	396974.i		−	1.09904i	0.835481	−	0.549520i	$-0.185189\pi$
$602$	25259.7	−	78927.1i	0.0697004	−	0.217787i
$603$	253594.			0.697436
$604$	113486.			0.311077
$605$			285146.i			0.779034i
$606$	−310628.			−0.845854
$607$		−	206429.i		−	0.560265i	−0.959961	−	0.280133i	$-0.909622\pi$
$607$		−	206429.i		−	0.560265i	0.959961	−	0.280133i	$-0.0903784\pi$
$608$		−	225474.i		−	0.609943i
$609$	97637.0	+	31247.6i	0.263257	+	0.0842524i
$610$	835418.			2.24514
$611$	180816.			0.484346
$612$			103916.i			0.277446i
$613$	−255556.			−0.680089			−0.340044	−	0.940409i	$-0.610442\pi$
$613$	−255556.			−0.680089			−0.340044	+	0.940409i	$0.610442\pi$
$614$		−	332041.i		−	0.880754i
$615$			193272.i			0.510996i
$616$	179738.	−	561612.i	0.473672	−	1.48004i
$617$	454159.			1.19299			0.596496	−	0.802616i	$-0.296559\pi$
$617$	454159.			1.19299			0.596496	+	0.802616i	$0.296559\pi$
$618$	585684.			1.53351
$619$			617532.i			1.61168i	0.592135	+	0.805839i	$0.298285\pi$
$619$			617532.i			1.61168i	−0.592135	+	0.805839i	$0.701715\pi$
$620$	−118643.			−0.308645
$621$			643762.i			1.66933i
$622$		−	464394.i		−	1.20034i
$623$	255601.	+	81802.1i	0.658546	+	0.210760i
$624$	−26593.3			−0.0682973
$625$	−420537.			−1.07657
$626$			780152.i			1.99081i
$627$	226015.			0.574913
$628$		−	202710.i		−	0.513991i
$629$		−	70858.3i		−	0.179097i
$630$	432737.	+	138492.i	1.09029	+	0.348935i
$631$	−610459.			−1.53320			−0.766598	−	0.642127i	$-0.778052\pi$
$631$	−610459.			−1.53320			−0.766598	+	0.642127i	$0.778052\pi$
$632$	−835854.			−2.09265
$633$			266617.i			0.665396i
$634$	−931102.			−2.31643
$635$			789769.i			1.95863i
$636$			325285.i			0.804173i
$637$	−125447.	+	175913.i	−0.309158	+	0.433530i
$638$	−425070.			−1.04428
$639$	230107.			0.563545
$640$		−	747114.i		−	1.82401i
$641$	252745.			0.615129			0.307564	−	0.951527i	$-0.400486\pi$
$641$	252745.			0.615129			0.307564	+	0.951527i	$0.400486\pi$
$642$			891.588i			0.00216319i
$643$		−	157343.i		−	0.380563i	−0.981730	−	0.190282i	$-0.939060\pi$
$643$		−	157343.i		−	0.380563i	0.981730	−	0.190282i	$-0.0609401\pi$
$644$	−376098.	+	1.17516e6i	−0.906838	+	2.83352i
$645$	34658.3			0.0833083
$646$	−125738.			−0.301303
$647$		−	533657.i		−	1.27483i	−0.770519	−	0.637417i	$-0.780003\pi$
$647$		−	533657.i		−	1.27483i	0.770519	−	0.637417i	$-0.219997\pi$
$648$	55931.6			0.133201
$649$			817974.i			1.94200i
$650$			30964.4i			0.0732885i
$651$	12887.4	−	40268.4i	0.0304092	−	0.0950172i
$652$	−48915.5			−0.115067
$653$	148297.			0.347781			0.173891	−	0.984765i	$-0.444366\pi$
$653$	148297.			0.347781			0.173891	+	0.984765i	$0.444366\pi$
$654$		−	150108.i		−	0.350953i
$655$	−385613.			−0.898813
$656$			81521.6i			0.189437i
$657$		−	475837.i		−	1.10237i
$658$	617870.	+	197742.i	1.42707	+	0.456718i
$659$	56743.2			0.130660			0.0653301	−	0.997864i	$-0.479190\pi$
$659$	56743.2			0.130660			0.0653301	+	0.997864i	$0.479190\pi$
$660$	592275.			1.35968
$661$		−	372082.i		−	0.851600i	−0.904817	−	0.425800i	$-0.859993\pi$
$661$		−	372082.i		−	0.851600i	0.904817	−	0.425800i	$-0.140007\pi$
$662$	−810921.			−1.85039
$663$		−	32727.8i		−	0.0744542i
$664$			92483.8i			0.209763i
$665$	−105819.	+	330644.i	−0.239287	+	0.747682i
$666$	−360208.			−0.812092
$667$	370354.			0.832464
$668$		−	432948.i		−	0.970249i
$669$	−294976.			−0.659075
$670$			804103.i			1.79127i
$671$		−	779510.i		−	1.73132i
$672$	200542.	+	64181.1i	0.444085	+	0.142124i
$673$	−853196.			−1.88373			−0.941865	−	0.335990i	$-0.890929\pi$
$673$	−853196.			−1.88373			−0.941865	+	0.335990i	$0.890929\pi$
$674$	−866429.			−1.90727
$675$			36601.5i			0.0803326i
$676$	561005.			1.22765
$677$		−	556621.i		−	1.21446i	−0.794527	−	0.607229i	$-0.792281\pi$
$677$		−	556621.i		−	1.21446i	0.794527	−	0.607229i	$-0.207719\pi$
$678$		−	64568.2i		−	0.140462i
$679$	−695956.	−	222733.i	−1.50953	−	0.483109i
$680$	−137198.			−0.296709
$681$	−324280.			−0.699240
$682$			175311.i			0.376913i
$683$	403219.			0.864370			0.432185	−	0.901785i	$-0.357743\pi$
$683$	403219.			0.864370			0.432185	+	0.901785i	$0.357743\pi$
$684$			403628.i			0.862718i
$685$			390378.i			0.831962i
$686$	−621046.	+	463925.i	−1.31970	+	0.985824i
$687$	−87552.9			−0.185506
$688$	14618.8			0.0308841
$689$			205776.i			0.433467i
$690$	−817204.			−1.71645
$691$			771714.i			1.61622i	0.589032	+	0.808110i	$0.299509\pi$
$691$			771714.i			1.61622i	−0.589032	+	0.808110i	$0.700491\pi$
$692$		−	400057.i		−	0.835428i
$693$	129224.	−	403777.i	0.269078	−	0.840766i
$694$	−856237.			−1.77777
$695$	700185.			1.44958
$696$			157363.i			0.324851i
$697$	−100327.			−0.206515
$698$		−	684293.i		−	1.40453i
$699$		−	127254.i		−	0.260445i
$700$	−21383.3	+	66814.8i	−0.0436394	+	0.136357i
$701$	−504883.			−1.02744			−0.513718	−	0.857959i	$-0.671732\pi$
$701$	−504883.			−1.02744			−0.513718	+	0.857959i	$0.671732\pi$
$702$	−415573.			−0.843282
$703$		−	275226.i		−	0.556903i
$704$	−1.01887e6			−2.05577
$705$			271318.i			0.545885i
$706$		−	448999.i		−	0.900815i
$707$	−424015.	−	135701.i	−0.848286	−	0.271484i
$708$	727256.			1.45084
$709$	−516087.			−1.02667			−0.513335	−	0.858188i	$-0.671590\pi$
$709$	−516087.			−1.02667			−0.513335	+	0.858188i	$0.671590\pi$
$710$			729629.i			1.44739i
$711$	−600946.			−1.18877
$712$			411955.i			0.812625i
$713$		−	152745.i		−	0.300461i
$714$	35791.4	−	111835.i	0.0702073	−	0.219371i
$715$	374675.			0.732896
$716$	889389.			1.73486
$717$			169198.i			0.329122i
$718$	1.52464e6			2.95745
$719$			127596.i			0.246819i	0.992356	+	0.123410i	$0.0393829\pi$
$719$			127596.i			0.246819i	−0.992356	+	0.123410i	$0.960617\pi$
$720$			80151.2i			0.154613i
$721$	799474.	+	255863.i	1.53792	+	0.492194i
$722$	370298.			0.710358
$723$	372683.			0.712957
$724$			689560.i			1.31551i
$725$	21056.7			0.0400604
$726$		−	374612.i		−	0.710737i
$727$			195688.i			0.370249i	0.982715	+	0.185125i	$0.0592689\pi$
$727$			195688.i			0.370249i	−0.982715	+	0.185125i	$0.940731\pi$
$728$	−315875.	−	101092.i	−0.596008	−	0.190746i
$729$	−254356.			−0.478615
$730$	1.50880e6			2.83129
$731$			17991.0i			0.0336683i
$732$	−693058.			−1.29344
$733$		−	409372.i		−	0.761922i	−0.924591	−	0.380961i	$-0.875593\pi$
$733$		−	409372.i		−	0.761922i	0.924591	−	0.380961i	$-0.124407\pi$
$734$		−	1.51985e6i		−	2.82103i
$735$	−263961.	−	188235.i	−0.488612	−	0.348438i
$736$	760690.			1.40427
$737$	750290.			1.38132
$738$			510011.i			0.936411i
$739$	943818.			1.72822			0.864111	−	0.503301i	$-0.167881\pi$
$739$	943818.			1.72822			0.864111	+	0.503301i	$0.167881\pi$
$740$		−	721234.i		−	1.31708i
$741$		−	127121.i		−	0.231515i
$742$	−225038.	+	703160.i	−0.408742	+	1.27716i
$743$	899503.			1.62939			0.814695	−	0.579890i	$-0.196905\pi$
$743$	899503.			1.62939			0.814695	+	0.579890i	$0.196905\pi$
$744$	64901.1			0.117248
$745$		−	582434.i		−	1.04938i
$746$	−338175.			−0.607665
$747$			66492.2i			0.119160i
$748$			307448.i			0.549501i
$749$	−389.500	+	1217.04i	−0.000694295	+	0.00216941i
$750$	509604.			0.905962
$751$	−632810.			−1.12200			−0.561001	−	0.827815i	$-0.689583\pi$
$751$	−632810.			−1.12200			−0.561001	+	0.827815i	$0.689583\pi$
$752$			114442.i			0.202371i
$753$	−116886.			−0.206145
$754$			239078.i			0.420529i
$755$			107725.i			0.188982i
$756$	−896720.	−	286985.i	−1.56896	−	0.502129i
$757$	619820.			1.08162			0.540808	−	0.841146i	$-0.318118\pi$
$757$	619820.			1.08162			0.540808	+	0.841146i	$0.318118\pi$
$758$	1.68433e6			2.93149
$759$			762515.i			1.32362i
$760$	−532903.			−0.922616
$761$		−	768144.i		−	1.32640i	−0.748444	−	0.663198i	$-0.769199\pi$
$761$		−	768144.i		−	1.32640i	0.748444	−	0.663198i	$-0.230801\pi$
$762$		−	1.03757e6i		−	1.78692i
$763$	65576.4	−	204901.i	0.112642	−	0.351962i
$764$	−154112.			−0.264027
$765$	−98640.2			−0.168551
$766$		−	634928.i		−	1.08210i
$767$	460064.			0.782037
$768$			452845.i			0.767763i
$769$		−	1.17178e6i		−	1.98150i	−0.135693	−	0.990751i	$-0.543326\pi$
$769$		−	1.17178e6i		−	1.98150i	0.135693	−	0.990751i	$-0.456674\pi$
$770$	1.28031e6	+	409748.i	2.15940	+	0.691091i
$771$	489048.			0.822702
$772$	−369957.			−0.620750
$773$			596498.i			0.998275i	0.866523	+	0.499138i	$0.166350\pi$
$773$			596498.i			0.998275i	−0.866523	+	0.499138i	$0.833650\pi$
$774$	91457.5			0.152664
$775$		−	8684.42i		−	0.0144590i
$776$		−	1.12168e6i		−	1.86271i
$777$	244792.	+	78343.1i	0.405467	+	0.129765i
$778$	51025.3			0.0842998
$779$	−389687.			−0.642157
$780$		−	333121.i		−	0.547536i
$781$	680801.			1.11614
$782$		−	424208.i		−	0.693690i
$783$			282602.i			0.460948i
$784$	−111338.	−	79397.2i	−0.181139	−	0.129173i
$785$	192419.			0.312254
$786$	506602.			0.820015
$787$			177090.i			0.285920i	0.989728	+	0.142960i	$0.0456621\pi$
$787$			177090.i			0.285920i	−0.989728	+	0.142960i	$0.954338\pi$
$788$	1.65022e6			2.65759
$789$			200299.i			0.321755i
$790$		−	1.90550e6i		−	3.05319i
$791$	28207.3	−	88137.3i	0.0450826	−	0.140866i
$792$	650773.			1.03748
$793$	−438430.			−0.697194
$794$			61663.4i			0.0978108i
$795$	−308771.			−0.488542
$796$			1.30166e6i			2.05434i
$797$			1.11542e6i			1.75599i	0.478666	+	0.877997i	$0.341120\pi$
$797$			1.11542e6i			1.75599i	−0.478666	+	0.877997i	$0.658880\pi$
$798$	139020.	−	434386.i	0.218309	−	0.682134i
$799$	−140841.			−0.220615
$800$	43249.5			0.0675774
$801$			296180.i			0.461626i
$802$	2.06601e6			3.21206
$803$		−	1.40782e6i		−	2.18332i
$804$		−	667079.i		−	1.03196i
$805$	−1.11550e6	−	357004.i	−1.72139	−	0.550911i
$806$	98602.6			0.151781
$807$	−615056.			−0.944425
$808$		−	683391.i		−	1.04676i
$809$	−76077.2			−0.116241			−0.0581203	−	0.998310i	$-0.518511\pi$
$809$	−76077.2			−0.116241			−0.0581203	+	0.998310i	$0.518511\pi$
$810$			127507.i			0.194341i
$811$			1.25940e6i			1.91480i	0.288764	+	0.957400i	$0.406756\pi$
$811$			1.25940e6i			1.91480i	−0.288764	+	0.957400i	$0.593244\pi$
$812$	−165101.	+	515880.i	−0.250403	+	0.782414i
$813$	529187.			0.800623
$814$	−1.06572e6			−1.60840
$815$		−	46432.1i		−	0.0699042i
$816$	20713.9			0.0311087
$817$			69880.5i			0.104692i
$818$			186585.i			0.278849i
$819$	−227102.	−	72681.3i	−0.338573	−	0.108357i
$820$	−1.02118e6			−1.51871
$821$	−1.15542e6			−1.71417			−0.857087	−	0.515171i	$-0.827728\pi$
$821$	−1.15542e6			−1.71417			−0.857087	+	0.515171i	$0.827728\pi$
$822$		−	512861.i		−	0.759026i
$823$	−388695.			−0.573864			−0.286932	−	0.957951i	$-0.592635\pi$
$823$	−388695.			−0.573864			−0.286932	+	0.957951i	$0.592635\pi$
$824$			1.28852e6i			1.89775i
$825$			43353.3i			0.0636963i
$826$	1.57209e6	+	503130.i	2.30419	+	0.737429i
$827$	685878.			1.00285			0.501425	−	0.865201i	$-0.332809\pi$
$827$	685878.			1.00285			0.501425	+	0.865201i	$0.332809\pi$
$828$	−1.36173e6			−1.98624
$829$			559594.i			0.814262i	0.913370	+	0.407131i	$0.133471\pi$
$829$			559594.i			0.814262i	−0.913370	+	0.407131i	$0.866529\pi$
$830$	−210835.			−0.306046
$831$		−	202034.i		−	0.292565i
$832$			573057.i			0.827850i
$833$	97712.3	−	137021.i	0.140818	−	0.197468i
$834$	−919873.			−1.32250
$835$	410968.			0.589434
$836$			1.19418e6i			1.70867i
$837$	116553.			0.166370
$838$			1.45076e6i			2.06589i
$839$			1.25364e6i			1.78094i	0.455046	+	0.890468i	$0.349623\pi$
$839$			1.25364e6i			1.78094i	−0.455046	+	0.890468i	$0.650377\pi$
$840$	151691.	−	473976.i	0.214981	−	0.671735i
$841$	−544701.			−0.770134
$842$	1.16102e6			1.63763
$843$		−	274558.i		−	0.386348i
$844$	−1.40871e6			−1.97759
$845$			532524.i			0.745806i
$846$			715963.i			1.00035i
$847$	163654.	−	511355.i	0.228117	−	0.712781i
$848$	−130239.			−0.181113
$849$	620828.			0.861303
$850$		−	24118.6i		−	0.0333822i
$851$	928541.			1.28216
$852$		−	605296.i		−	0.833851i
$853$			928155.i			1.27562i	0.770193	+	0.637811i	$0.220160\pi$
$853$			928155.i			1.27562i	−0.770193	+	0.637811i	$0.779840\pi$
$854$	−1.49817e6	−	479471.i	−2.05421	−	0.657425i
$855$	−383137.			−0.524109
$856$	−1961.52			−0.00267698
$857$		−	500430.i		−	0.681368i	−0.940178	−	0.340684i	$-0.889341\pi$
$857$		−	500430.i		−	0.681368i	0.940178	−	0.340684i	$-0.110659\pi$
$858$	−492232.			−0.668644
$859$		−	937091.i		−	1.26998i	−0.772522	−	0.634988i	$-0.781005\pi$
$859$		−	937091.i		−	1.26998i	0.772522	−	0.634988i	$-0.218995\pi$
$860$			183123.i			0.247597i
$861$	110924.	−	346596.i	0.149631	−	0.467539i
$862$	1.17663e6			1.58353
$863$	−290438.			−0.389970			−0.194985	−	0.980806i	$-0.562466\pi$
$863$	−290438.			−0.389970			−0.194985	+	0.980806i	$0.562466\pi$
$864$			580451.i			0.777567i
$865$	379746.			0.507530
$866$			418449.i			0.557965i
$867$			25492.1i			0.0339131i
$868$	212764.	+	68092.7i	0.282396	+	0.0903776i
$869$	−1.77798e6			−2.35443
$870$	−358740.			−0.473960
$871$		−	421996.i		−	0.556252i
$872$	330243.			0.434310
$873$		−	806446.i		−	1.05815i
$874$		−	1.64770e6i		−	2.15703i
$875$	695622.	+	222626.i	0.908567	+	0.290777i
$876$	−1.25169e6			−1.63113
$877$	−54446.7			−0.0707901			−0.0353950	−	0.999373i	$-0.511269\pi$
$877$	−54446.7			−0.0707901			−0.0353950	+	0.999373i	$0.511269\pi$
$878$			845933.i			1.09735i
$879$	−138239.			−0.178918
$880$			237138.i			0.306221i
$881$		−	713208.i		−	0.918892i	−0.888206	−	0.459446i	$-0.848048\pi$
$881$		−	713208.i		−	0.918892i	0.888206	−	0.459446i	$-0.151952\pi$
$882$	−696547.	−	496721.i	−0.895392	−	0.638521i
$883$	−828642.			−1.06279			−0.531393	−	0.847126i	$-0.678331\pi$
$883$	−828642.			−1.06279			−0.531393	+	0.847126i	$0.678331\pi$
$884$	172922.			0.221282
$885$			690334.i			0.881400i
$886$	−72135.0			−0.0918922
$887$			262680.i			0.333872i	0.985968	+	0.166936i	$0.0533873\pi$
$887$			262680.i			0.333872i	−0.985968	+	0.166936i	$0.946613\pi$
$888$			394536.i			0.500334i
$889$	453272.	−	1.41630e6i	0.573529	−	1.79206i
$890$	−939134.			−1.18563
$891$	118974.			0.149864
$892$		−	1.55855e6i		−	1.95880i
$893$	−547050.			−0.686000
$894$			765177.i			0.957386i
$895$			844236.i			1.05394i
$896$	−428790.	+	1.33981e6i	−0.534108	+	1.66889i
$897$	428871.			0.533018
$898$	−12210.2			−0.0151416
$899$		−	67052.7i		−	0.0829654i
$900$	−77422.3			−0.0955830
$901$		−	160282.i		−	0.197440i
$902$			1.50893e6i			1.85463i
$903$	−62153.2	−	19891.4i	−0.0762234	−	0.0243944i
$904$	142052.			0.173824
$905$	−654552.			−0.799185
$906$		−	141524.i		−	0.172414i
$907$	−830192.			−1.00917			−0.504585	−	0.863362i	$-0.668354\pi$
$907$	−830192.			−1.00917			−0.504585	+	0.863362i	$0.668354\pi$
$908$		−	1.71338e6i		−	2.07818i
$909$		−	491331.i		−	0.594630i
$910$	230460.	−	720100.i	0.278299	−	0.869580i
$911$	−706572.			−0.851372			−0.425686	−	0.904871i	$-0.639967\pi$
$911$	−706572.			−0.851372			−0.425686	+	0.904871i	$0.639967\pi$
$912$	80456.7			0.0967325
$913$			196726.i			0.236004i
$914$	−223155.			−0.267124
$915$		−	657872.i		−	0.785777i
$916$		−	462599.i		−	0.551332i
$917$	691525.	+	221315.i	0.822373	+	0.263191i
$918$	323695.			0.384106
$919$	370685.			0.438909			0.219454	−	0.975623i	$-0.429572\pi$
$919$	370685.			0.438909			0.219454	+	0.975623i	$0.429572\pi$
$920$		−	1.79787e6i		−	2.12414i
$921$	−261475.			−0.308255
$922$			2.08428e6i			2.45185i
$923$		−	382912.i		−	0.449464i
$924$	−1.06213e6	−	339924.i	−1.24404	−	0.398142i
$925$	52792.8			0.0617009
$926$	273610.			0.319087
$927$			926398.i			1.07805i
$928$	333931.			0.387758
$929$			1.53465e6i			1.77819i	0.457726	+	0.889093i	$0.348664\pi$
$929$			1.53465e6i			1.77819i	−0.457726	+	0.889093i	$0.651336\pi$
$930$			147955.i			0.171066i
$931$	379532.	−	532215.i	0.437874	−	0.614027i
$932$	672363.			0.774055
$933$	−365700.			−0.420108
$934$			1.13193e6i			1.29756i
$935$	−291840.			−0.333827
$936$		−	366023.i		−	0.417789i
$937$			282152.i			0.321369i	0.987006	+	0.160685i	$0.0513702\pi$
$937$			282152.i			0.321369i	−0.987006	+	0.160685i	$0.948630\pi$
$938$	461498.	−	1.44201e6i	0.524523	−	1.63893i
$939$	614352.			0.696765
$940$	−1.43355e6			−1.62240
$941$			676437.i			0.763921i	0.924179	+	0.381960i	$0.124751\pi$
$941$			676437.i			0.763921i	−0.924179	+	0.381960i	$0.875249\pi$
$942$	−252791.			−0.284879
$943$		−	1.31470e6i		−	1.47844i
$944$			291182.i			0.326753i
$945$	272415.	−	851195.i	0.305048	−	0.953159i
$946$	270589.			0.302362
$947$	−169249.			−0.188723			−0.0943616	−	0.995538i	$-0.530081\pi$
$947$	−169249.			−0.188723			−0.0943616	+	0.995538i	$0.530081\pi$
$948$			1.58079e6i			1.75896i
$949$	−791822.			−0.879215
$950$		−	93681.1i		−	0.103802i
$951$			733222.i			0.810726i
$952$	246039.	+	78742.1i	0.271476	+	0.0868827i
$953$	−62012.3			−0.0682798			−0.0341399	−	0.999417i	$-0.510869\pi$
$953$	−62012.3			−0.0682798			−0.0341399	+	0.999417i	$0.510869\pi$
$954$	−814793.			−0.895263
$955$		−	146288.i		−	0.160399i
$956$	−893983.			−0.978168
$957$			334733.i			0.365489i
$958$		−	1.10674e6i		−	1.20590i
$959$	224049.	−	700069.i	0.243616	−	0.761208i
$960$	−859883.			−0.933033
$961$	895866.			0.970055
$962$			599408.i			0.647697i
$963$	−1410.26			−0.00152071
$964$			1.96913e6i			2.11895i
$965$		−	351175.i		−	0.377111i
$966$	1.46550e6	+	469017.i	1.57048	+	0.502614i
$967$	885946.			0.947446			0.473723	−	0.880674i	$-0.342910\pi$
$967$	885946.			0.947446			0.473723	+	0.880674i	$0.342910\pi$
$968$	824159.			0.879549
$969$			99016.1i			0.105453i
$970$	2.55710e6			2.71771
$971$			17300.0i			0.0183489i	0.999958	+	0.00917443i	$0.00292035\pi$
$971$			17300.0i			0.0183489i	−0.999958	+	0.00917443i	$0.997080\pi$
$972$		−	1.66218e6i		−	1.75932i
$973$	−1.25565e6	−	401857.i	−1.32630	−	0.424468i
$974$	1.37153e6			1.44573
$975$	24383.8			0.0256502
$976$		−	277489.i		−	0.291304i
$977$	990621.			1.03781			0.518906	−	0.854832i	$-0.326340\pi$
$977$	990621.			1.03781			0.518906	+	0.854832i	$0.326340\pi$
$978$			61000.6i			0.0637758i
$979$			876285.i			0.914282i
$980$	994569.	−	1.39468e6i	1.03558	−	1.45218i
$981$	237432.			0.246718
$982$	−2.66385e6			−2.76240
$983$		−	150923.i		−	0.156189i	−0.996946	−	0.0780943i	$-0.975116\pi$
$983$		−	150923.i		−	0.156189i	0.996946	−	0.0780943i	$-0.0248835\pi$
$984$	558614.			0.576928
$985$			1.56644e6i			1.61451i
$986$		−	186221.i		−	0.191547i
$987$	155718.	−	486559.i	0.159847	−	0.499460i
$988$	671661.			0.688076
$989$	−235758.			−0.241032
$990$			1.48357e6i			1.51369i
$991$	−149168.			−0.151890			−0.0759448	−	0.997112i	$-0.524197\pi$
$991$	−149168.			−0.151890			−0.0759448	+	0.997112i	$0.524197\pi$
$992$		−	137723.i		−	0.139953i
$993$			638582.i			0.647617i
$994$	418756.	−	1.30845e6i	0.423826	−	1.32430i
$995$	−1.23558e6			−1.24803
$996$	174908.			0.176315
$997$			288865.i			0.290606i	0.989387	+	0.145303i	$0.0464158\pi$
$997$			288865.i			0.290606i	−0.989387	+	0.145303i	$0.953584\pi$
$998$	2.52580e6			2.53594
$999$			708531.i			0.709950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.5.c.a.69.39	✓	44
7.6	odd	2	inner	119.5.c.a.69.40	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.5.c.a.69.39	✓	44	1.1	even	1	trivial
119.5.c.a.69.40	yes	44	7.6	odd	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	119.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.58903 q^{2} -5.18871i q^{3} +27.4153 q^{4} +26.0235i q^{5} -34.1886i q^{6} +(14.9357 - 46.6683i) q^{7} +75.2159 q^{8} +54.0773 q^{9} +171.470i q^{10} +159.995 q^{11} -142.250i q^{12} -89.9878i q^{13} +(98.4115 - 307.499i) q^{14} +135.028 q^{15} +56.9547 q^{16} +70.0928i q^{17} +356.317 q^{18} +272.253i q^{19} +713.443i q^{20} +(-242.148 - 77.4968i) q^{21} +1054.21 q^{22} -918.510 q^{23} -390.273i q^{24} -52.2225 q^{25} -592.932i q^{26} -700.877i q^{27} +(409.466 - 1279.43i) q^{28} -403.212 q^{29} +889.706 q^{30} +166.296i q^{31} -828.178 q^{32} -830.165i q^{33} +461.844i q^{34} +(1214.47 + 388.678i) q^{35} +1482.55 q^{36} -1010.92 q^{37} +1793.88i q^{38} -466.921 q^{39} +1957.38i q^{40} +1431.34i q^{41} +(-1595.52 - 510.628i) q^{42} +256.675 q^{43} +4386.30 q^{44} +1407.28i q^{45} -6052.09 q^{46} +2009.34i q^{47} -295.521i q^{48} +(-1954.85 - 1394.04i) q^{49} -344.096 q^{50} +363.691 q^{51} -2467.04i q^{52} -2286.71 q^{53} -4618.10i q^{54} +4163.62i q^{55} +(1123.40 - 3510.20i) q^{56} +1412.64 q^{57} -2656.78 q^{58} +5112.51i q^{59} +3701.85 q^{60} -4872.10i q^{61} +1095.73i q^{62} +(807.679 - 2523.69i) q^{63} -6368.17 q^{64} +2341.80 q^{65} -5469.98i q^{66} +4689.48 q^{67} +1921.62i q^{68} +4765.88i q^{69} +(8002.19 + 2561.01i) q^{70} +4255.15 q^{71} +4067.47 q^{72} -8799.21i q^{73} -6660.99 q^{74} +270.967i q^{75} +7463.91i q^{76} +(2389.62 - 7466.66i) q^{77} -3076.55 q^{78} -11112.7 q^{79} +1482.16i q^{80} +743.614 q^{81} +9431.15i q^{82} +1229.58i q^{83} +(-6638.57 - 2124.60i) q^{84} -1824.06 q^{85} +1691.24 q^{86} +2092.15i q^{87} +12034.1 q^{88} +5476.97i q^{89} +9272.61i q^{90} +(-4199.57 - 1344.03i) q^{91} -25181.2 q^{92} +862.864 q^{93} +13239.6i q^{94} -7084.98 q^{95} +4297.18i q^{96} -14912.8i q^{97} +(-12880.6 - 9185.38i) q^{98} +8652.07 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{2} + 378 q^{4} - 130 q^{7} - 6 q^{8} - 1232 q^{9} + 192 q^{11} - 294 q^{14} - 128 q^{15} + 3178 q^{16} + 682 q^{18} + 312 q^{21} + 336 q^{22} + 876 q^{23} - 3800 q^{25} - 2426 q^{28} - 3372 q^{29}+ \cdots - 19620 q^{99}+O(q^{100}) \) 44 * q - 6 * q^2 + 378 * q^4 - 130 * q^7 - 6 * q^8 - 1232 * q^9 + 192 * q^11 - 294 * q^14 - 128 * q^15 + 3178 * q^16 + 682 * q^18 + 312 * q^21 + 336 * q^22 + 876 * q^23 - 3800 * q^25 - 2426 * q^28 - 3372 * q^29 + 2866 * q^30 + 2808 * q^32 - 2904 * q^35 - 6288 * q^36 - 488 * q^37 - 1156 * q^39 + 2494 * q^42 + 2676 * q^43 - 8376 * q^44 + 2492 * q^46 - 3216 * q^49 + 3660 * q^50 + 7668 * q^53 + 3126 * q^56 - 8940 * q^57 + 6420 * q^58 - 7530 * q^60 + 13934 * q^63 + 22394 * q^64 + 16440 * q^65 - 25844 * q^67 - 1216 * q^70 - 11364 * q^71 + 5620 * q^72 + 15600 * q^74 - 276 * q^77 + 38692 * q^78 + 2168 * q^79 + 37180 * q^81 + 13384 * q^84 - 61026 * q^86 - 23564 * q^88 - 14604 * q^91 + 7068 * q^92 - 60464 * q^93 + 16164 * q^95 - 16710 * q^98 - 19620 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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