LMFDB - Embedded newform 98.7.d.c.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,7,Mod(19,98)] 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("98.19"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-128,336,0,0,0,756] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$22.5453001947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 285x^{6} + 282x^{5} + 62091x^{4} + 29260x^{3} + 4838750x^{2} + 2401000x + 294122500 $ x^8 - 2x^7 + 285x^6 + 282x^5 + 62091x^4 + 29260x^3 + 4838750x^2 + 2401000*x + 294122500
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-4.86132 + 8.42006i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.7.d.c.31.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.82843 + 4.89898i) q^{2} +(-27.6101 + 15.9407i) q^{3} +(-16.0000 - 27.7128i) q^{4} +(-111.836 - 64.5687i) q^{5} -180.349i q^{6} +181.019 q^{8} +(143.713 - 248.917i) q^{9} +(632.642 - 365.256i) q^{10} +(-1189.23 - 2059.81i) q^{11} +(883.524 + 510.103i) q^{12} -820.701i q^{13} +4117.09 q^{15} +(-512.000 + 886.810i) q^{16} +(2284.02 - 1318.68i) q^{17} +(812.961 + 1408.09i) q^{18} +(4814.93 + 2779.90i) q^{19} +4132.40i q^{20} +13454.6 q^{22} +(-5696.37 + 9866.40i) q^{23} +(-4997.97 + 2885.58i) q^{24} +(525.743 + 910.614i) q^{25} +(4020.60 + 2321.29i) q^{26} -14078.0i q^{27} -32822.6 q^{29} +(-11644.9 + 20169.5i) q^{30} +(-40622.4 + 23453.4i) q^{31} +(-2896.31 - 5016.55i) q^{32} +(65669.6 + 37914.4i) q^{33} +14919.2i q^{34} -9197.60 q^{36} +(-10862.8 + 18814.9i) q^{37} +(-27237.3 + 15725.5i) q^{38} +(13082.5 + 22659.6i) q^{39} +(-20244.5 - 11688.2i) q^{40} +85846.0i q^{41} +113977. q^{43} +(-38055.4 + 65913.9i) q^{44} +(-32144.6 + 18558.7i) q^{45} +(-32223.5 - 55812.8i) q^{46} +(-33367.3 - 19264.6i) q^{47} -32646.6i q^{48} -5948.11 q^{50} +(-42041.4 + 72817.9i) q^{51} +(-22743.9 + 13131.2i) q^{52} +(-16620.4 - 28787.3i) q^{53} +(68968.0 + 39818.7i) q^{54} +307149. i q^{55} -177254. q^{57} +(92836.2 - 160797. i) q^{58} +(289901. - 167374. i) q^{59} +(-65873.4 - 114096. i) q^{60} +(145845. + 84203.9i) q^{61} -265344. i q^{62} +32768.0 q^{64} +(-52991.6 + 91784.1i) q^{65} +(-371483. + 214476. i) q^{66} +(161261. + 279312. i) q^{67} +(-73088.7 - 42197.8i) q^{68} -363217. i q^{69} +325510. q^{71} +(26014.7 - 45058.9i) q^{72} +(-93404.3 + 53927.0i) q^{73} +(-61449.1 - 106433. i) q^{74} +(-29031.7 - 16761.4i) q^{75} -177914. i q^{76} -148012. q^{78} +(169525. - 293625. i) q^{79} +(114520. - 66118.4i) q^{80} +(329180. + 570157. i) q^{81} +(-420558. - 242809. i) q^{82} +224674. i q^{83} -340582. q^{85} +(-322376. + 558372. i) q^{86} +(906235. - 523215. i) q^{87} +(-215274. - 372865. i) q^{88} +(-331888. - 191615. i) q^{89} -209967. i q^{90} +364567. q^{92} +(747726. - 1.29510e6i) q^{93} +(188754. - 108977. i) q^{94} +(-358989. - 621787. i) q^{95} +(159935. + 92338.5i) q^{96} -32664.1i q^{97} -683629. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 128 q^{4} + 336 q^{5} + 756 q^{9} + 2016 q^{10} - 1356 q^{11} + 27144 q^{15} - 4096 q^{16} + 17304 q^{17} - 6816 q^{18} + 32004 q^{19} + 25248 q^{22} - 4128 q^{23} - 10752 q^{24} + 4664 q^{25} + 4704 q^{26}+ \cdots - 4625928 q^{99}+O(q^{100}) $ 8 * q - 128 * q^4 + 336 * q^5 + 756 * q^9 + 2016 * q^10 - 1356 * q^11 + 27144 * q^15 - 4096 * q^16 + 17304 * q^17 - 6816 * q^18 + 32004 * q^19 + 25248 * q^22 - 4128 * q^23 - 10752 * q^24 + 4664 * q^25 + 4704 * q^26 - 30312 * q^29 + 9648 * q^30 + 3108 * q^31 - 3276 * q^33 - 48384 * q^36 - 6124 * q^37 - 155568 * q^38 + 100764 * q^39 - 64512 * q^40 - 297376 * q^43 - 43392 * q^44 + 172116 * q^45 - 194064 * q^46 - 313908 * q^47 + 38784 * q^50 + 253692 * q^51 - 255360 * q^52 + 278484 * q^53 - 386064 * q^54 - 81288 * q^57 - 169824 * q^58 + 835464 * q^59 - 434304 * q^60 + 995316 * q^61 + 262144 * q^64 + 8316 * q^65 - 1673280 * q^66 + 648808 * q^67 - 553728 * q^68 + 190128 * q^71 - 218112 * q^72 + 1617084 * q^73 - 1158144 * q^74 + 2042208 * q^75 + 1122432 * q^78 + 70096 * q^79 - 344064 * q^80 + 1177920 * q^81 - 66528 * q^82 + 2190984 * q^85 - 573024 * q^86 + 2057076 * q^87 - 403968 * q^88 - 739116 * q^89 + 264192 * q^92 - 23364 * q^93 - 3795120 * q^94 + 725640 * q^95 + 344064 * q^96 - 4625928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.82843	+	4.89898i	−0.353553	+	0.612372i
$2$	−2.82843	+	4.89898i	−0.353553	+	0.612372i
$3$	−27.6101	+	15.9407i	−1.02260	+	0.590397i	−0.914855	−	0.403782i	$-0.867695\pi$
$3$	−27.6101	+	15.9407i	−1.02260	+	0.590397i	−0.107742	+	0.994179i	$0.534362\pi$
$4$	−16.0000	−	27.7128i	−0.250000	−	0.433013i
$5$	−111.836	−	64.5687i	−0.894691	−	0.516550i	−0.0192168	−	0.999815i	$-0.506117\pi$
$5$	−111.836	−	64.5687i	−0.894691	−	0.516550i	−0.875474	+	0.483265i	$0.839451\pi$
$6$		−	180.349i		−	0.834947i
$7$		0			0
$7$		0			0
$8$	181.019			0.353553
$9$	143.713	−	248.917i	0.197136	−	0.341450i
$10$	632.642	−	365.256i	0.632642	−	0.365256i
$11$	−1189.23	−	2059.81i	−0.893487	−	1.54756i	−0.835666	−	0.549237i	$-0.814918\pi$
$11$	−1189.23	−	2059.81i	−0.893487	−	1.54756i	−0.0578204	−	0.998327i	$-0.518415\pi$
$12$	883.524	+	510.103i	0.511299	+	0.295198i
$13$		−	820.701i		−	0.373555i	−0.982402	−	0.186778i	$-0.940196\pi$
$13$		−	820.701i		−	0.373555i	0.982402	−	0.186778i	$-0.0598044\pi$
$14$		0			0
$15$	4117.09			1.21988
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	2284.02	−	1318.68i	0.464894	−	0.268406i	−0.249206	−	0.968450i	$-0.580170\pi$
$17$	2284.02	−	1318.68i	0.464894	−	0.268406i	0.714100	+	0.700044i	$0.246836\pi$
$18$	812.961	+	1408.09i	0.139397	+	0.241442i
$19$	4814.93	+	2779.90i	0.701987	+	0.405292i	0.808087	−	0.589063i	$-0.200503\pi$
$19$	4814.93	+	2779.90i	0.701987	+	0.405292i	−0.106100	+	0.994355i	$0.533836\pi$
$20$			4132.40i			0.516550i
$21$		0			0
$22$	13454.6			1.26358
$23$	−5696.37	+	9866.40i	−0.468182	+	0.810914i	−0.999339	−	0.0363589i	$-0.988424\pi$
$23$	−5696.37	+	9866.40i	−0.468182	+	0.810914i	0.531157	+	0.847273i	$0.321757\pi$
$24$	−4997.97	+	2885.58i	−0.361543	+	0.208737i
$25$	525.743	+	910.614i	0.0336476	+	0.0582793i
$26$	4020.60	+	2321.29i	0.228755	+	0.132072i
$27$		−	14078.0i		−	0.715238i
$28$		0			0
$29$	−32822.6			−1.34579			−0.672897	−	0.739736i	$-0.734950\pi$
$29$	−32822.6			−1.34579			−0.672897	+	0.739736i	$0.734950\pi$
$30$	−11644.9	+	20169.5i	−0.431292	+	0.747019i
$31$	−40622.4	+	23453.4i	−1.36358	+	0.787263i	−0.990098	−	0.140375i	$-0.955169\pi$
$31$	−40622.4	+	23453.4i	−1.36358	+	0.787263i	−0.373481	+	0.927638i	$0.621836\pi$
$32$	−2896.31	−	5016.55i	−0.0883883	−	0.153093i
$33$	65669.6	+	37914.4i	1.82735	+	1.05502i
$34$			14919.2i			0.379584i
$35$		0			0
$36$	−9197.60			−0.197136
$37$	−10862.8	+	18814.9i	−0.214454	+	0.371446i	−0.953104	−	0.302644i	$-0.902131\pi$
$37$	−10862.8	+	18814.9i	−0.214454	+	0.371446i	0.738649	+	0.674090i	$0.235464\pi$
$38$	−27237.3	+	15725.5i	−0.496380	+	0.286585i
$39$	13082.5	+	22659.6i	0.220546	+	0.381996i
$40$	−20244.5	−	11688.2i	−0.316321	−	0.182628i
$41$			85846.0i			1.24557i	0.782392	+	0.622786i	$0.213999\pi$
$41$			85846.0i			1.24557i	−0.782392	+	0.622786i	$0.786001\pi$
$42$		0			0
$43$	113977.			1.43355			0.716774	−	0.697305i	$-0.245618\pi$
$43$	113977.			1.43355			0.716774	+	0.697305i	$0.245618\pi$
$44$	−38055.4	+	65913.9i	−0.446743	+	0.773782i
$45$	−32144.6	+	18558.7i	−0.352752	+	0.203662i
$46$	−32223.5	−	55812.8i	−0.331054	−	0.573403i
$47$	−33367.3	−	19264.6i	−0.321387	−	0.185553i	0.330624	−	0.943763i	$-0.392741\pi$
$47$	−33367.3	−	19264.6i	−0.321387	−	0.185553i	−0.652011	+	0.758210i	$0.726074\pi$
$48$		−	32646.6i		−	0.295198i
$49$		0			0
$50$	−5948.11			−0.0475849
$51$	−42041.4	+	72817.9i	−0.316932	+	0.548943i
$52$	−22743.9	+	13131.2i	−0.161754	+	0.0933888i
$53$	−16620.4	−	28787.3i	−0.111638	−	0.193363i	0.804793	−	0.593556i	$-0.202276\pi$
$53$	−16620.4	−	28787.3i	−0.111638	−	0.193363i	−0.916431	+	0.400193i	$0.868943\pi$
$54$	68968.0	+	39818.7i	0.437992	+	0.252875i
$55$			307149.i			1.84612i
$56$		0			0
$57$	−177254.			−0.957133
$58$	92836.2	−	160797.i	0.475810	−	0.824127i
$59$	289901.	−	167374.i	1.41154	−	0.814953i	0.416007	−	0.909361i	$-0.363429\pi$
$59$	289901.	−	167374.i	1.41154	−	0.814953i	0.995534	+	0.0944082i	$0.0300959\pi$
$60$	−65873.4	−	114096.i	−0.304969	−	0.528222i
$61$	145845.	+	84203.9i	0.642544	+	0.370973i	0.785594	−	0.618742i	$-0.212358\pi$
$61$	145845.	+	84203.9i	0.642544	+	0.370973i	−0.143050	+	0.989716i	$0.545691\pi$
$62$		−	265344.i		−	1.11336i
$63$		0			0
$64$	32768.0			0.125000
$65$	−52991.6	+	91784.1i	−0.192960	+	0.334216i
$66$	−371483.	+	214476.i	−1.29213	+	0.746014i
$67$	161261.	+	279312.i	0.536173	+	0.928679i	0.999106	+	0.0422855i	$0.0134639\pi$
$67$	161261.	+	279312.i	0.536173	+	0.928679i	−0.462932	+	0.886394i	$0.653203\pi$
$68$	−73088.7	−	42197.8i	−0.232447	−	0.134203i
$69$		−	363217.i		−	1.10565i
$70$		0			0
$71$	325510.			0.909473			0.454737	−	0.890626i	$-0.349733\pi$
$71$	325510.			0.909473			0.454737	+	0.890626i	$0.349733\pi$
$72$	26014.7	−	45058.9i	0.0696983	−	0.120721i
$73$	−93404.3	+	53927.0i	−0.240103	+	0.138624i	−0.615224	−	0.788352i	$-0.710935\pi$
$73$	−93404.3	+	53927.0i	−0.240103	+	0.138624i	0.375121	+	0.926976i	$0.377601\pi$
$74$	−61449.1	−	106433.i	−0.151642	−	0.262652i
$75$	−29031.7	−	16761.4i	−0.0688158	−	0.0397308i
$76$		−	177914.i		−	0.405292i
$77$		0			0
$78$	−148012.			−0.311899
$79$	169525.	−	293625.i	0.343836	−	0.595542i	−0.641305	−	0.767286i	$-0.721607\pi$
$79$	169525.	−	293625.i	0.343836	−	0.595542i	0.985142	+	0.171744i	$0.0549402\pi$
$80$	114520.	−	66118.4i	0.223673	−	0.129137i
$81$	329180.	+	570157.i	0.619411	+	1.07285i
$82$	−420558.	−	242809.i	−0.762754	−	0.440376i
$83$			224674.i			0.392934i	0.980510	+	0.196467i	$0.0629468\pi$
$83$			224674.i			0.392934i	−0.980510	+	0.196467i	$0.937053\pi$
$84$		0			0
$85$	−340582.			−0.554581
$86$	−322376.	+	558372.i	−0.506836	+	0.877866i
$87$	906235.	−	523215.i	1.37620	−	0.794552i
$88$	−215274.	−	372865.i	−0.315895	−	0.547147i
$89$	−331888.	−	191615.i	−0.470783	−	0.271807i	0.245784	−	0.969325i	$-0.420955\pi$
$89$	−331888.	−	191615.i	−0.470783	−	0.271807i	−0.716568	+	0.697518i	$0.754288\pi$
$90$		−	209967.i		−	0.288021i
$91$		0			0
$92$	364567.			0.468182
$93$	747726.	−	1.29510e6i	0.929595	−	1.61011i
$94$	188754.	−	108977.i	0.227255	−	0.131206i
$95$	−358989.	−	621787.i	−0.418707	−	0.725222i
$96$	159935.	+	92338.5i	0.180771	+	0.104368i
$97$		−	32664.1i		−	0.0357895i	−0.999840	−	0.0178948i	$-0.994304\pi$
$97$		−	32664.1i		−	0.0357895i	0.999840	−	0.0178948i	$-0.00569638\pi$
$98$		0			0
$99$	−683629.			−0.704555
$100$	16823.8	−	29139.7i	0.0168238	−	0.0291397i
$101$	433003.	−	249994.i	0.420268	−	0.242642i	−0.274924	−	0.961466i	$-0.588653\pi$
$101$	433003.	−	249994.i	0.420268	−	0.242642i	0.695192	+	0.718824i	$0.255319\pi$
$102$	−237822.	−	411920.i	−0.224105	−	0.388161i
$103$	−386249.	−	223001.i	−0.353472	−	0.204077i	0.312741	−	0.949838i	$-0.398753\pi$
$103$	−386249.	−	223001.i	−0.353472	−	0.204077i	−0.666214	+	0.745761i	$0.732086\pi$
$104$		−	148563.i		−	0.132072i
$105$		0			0
$106$	188038.			0.157880
$107$	944735.	−	1.63633e6i	0.771186	−	1.33573i	−0.165728	−	0.986171i	$-0.552997\pi$
$107$	944735.	−	1.63633e6i	0.771186	−	1.33573i	0.936914	−	0.349561i	$-0.113669\pi$
$108$	−390142.	+	225249.i	−0.309707	+	0.178810i
$109$	960930.	+	1.66438e6i	0.742014	+	1.28521i	0.951577	+	0.307411i	$0.0994626\pi$
$109$	960930.	+	1.66438e6i	0.742014	+	1.28521i	−0.209563	+	0.977795i	$0.567204\pi$
$110$	−1.50471e6	−	868747.i	−1.13051	−	0.652703i
$111$		−	692640.i		−	0.506453i
$112$		0			0
$113$	−472481.			−0.327453			−0.163726	−	0.986506i	$-0.552351\pi$
$113$	−472481.			−0.327453			−0.163726	+	0.986506i	$0.552351\pi$
$114$	501351.	−	868365.i	0.338398	−	0.586122i
$115$	1.27412e6	−	735614.i	0.837756	−	0.483678i
$116$	525161.	+	909605.i	0.336448	+	0.582746i
$117$	−204287.	−	117945.i	−0.127551	−	0.0736413i
$118$			1.89362e6i			1.15252i
$119$		0			0
$120$	745272.			0.431292
$121$	−1.94276e6	+	3.36496e6i	−1.09664	+	1.89943i
$122$	−825026.	+	476329.i	−0.454347	+	0.262318i
$123$	−1.36845e6	−	2.37022e6i	−0.735381	−	1.27372i
$124$	1.29992e6	+	750507.i	0.681790	+	0.393631i
$125$			1.88199e6i			0.963577i
$126$		0			0
$127$	−632211.			−0.308639			−0.154319	−	0.988021i	$-0.549319\pi$
$127$	−632211.			−0.308639			−0.154319	+	0.988021i	$0.549319\pi$
$128$	−92681.9	+	160530.i	−0.0441942	+	0.0765466i
$129$	−3.14692e6	+	1.81688e6i	−1.46594	+	0.846362i
$130$	−299766.	−	519209.i	−0.136443	−	0.236327i
$131$	−111928.	−	64621.5i	−0.0497879	−	0.0287451i	0.474899	−	0.880040i	$-0.342484\pi$
$131$	−111928.	−	64621.5i	−0.0497879	−	0.0287451i	−0.524687	+	0.851295i	$0.675818\pi$
$132$		−	2.42652e6i		−	1.05502i
$133$		0			0
$134$	−1.82446e6			−0.758263
$135$	−909001.	+	1.57444e6i	−0.369456	+	0.639917i
$136$	413452.	−	238707.i	0.164365	−	0.0948960i
$137$	798004.	+	1.38218e6i	0.310344	+	0.537532i	0.978437	−	0.206546i	$-0.0662224\pi$
$137$	798004.	+	1.38218e6i	0.310344	+	0.537532i	−0.668093	+	0.744078i	$0.732889\pi$
$138$	1.77939e6	+	1.02733e6i	0.677071	+	0.390907i
$139$			688428.i			0.256339i	0.991752	+	0.128169i	$0.0409101\pi$
$139$			688428.i			0.256339i	−0.991752	+	0.128169i	$0.959090\pi$
$140$		0			0
$141$	1.22837e6			0.438199
$142$	−920683.	+	1.59467e6i	−0.321547	+	0.556936i
$143$	−1.69049e6	+	976002.i	−0.578101	+	0.333767i
$144$	147162.	+	254891.i	0.0492841	+	0.0853626i
$145$	3.67075e6	+	2.11931e6i	1.20407	+	0.695170i
$146$		−	610114.i		−	0.196044i
$147$		0			0
$148$	695217.			0.214454
$149$	−316745.	+	548619.i	−0.0957527	+	0.165849i	−0.909923	−	0.414778i	$-0.863859\pi$
$149$	−316745.	+	548619.i	−0.0957527	+	0.165849i	0.814170	+	0.580627i	$0.197192\pi$
$150$	164228.	−	94817.1i	0.0486601	−	0.0280939i
$151$	1.24696e6	+	2.15980e6i	0.362178	+	0.627311i	0.988319	−	0.152399i	$-0.0486999\pi$
$151$	1.24696e6	+	2.15980e6i	0.362178	+	0.627311i	−0.626141	+	0.779710i	$0.715367\pi$
$152$	871595.	+	503216.i	0.248190	+	0.143292i
$153$		−	758044.i		−	0.211651i
$154$		0			0
$155$	6.05741e6			1.62664
$156$	418642.	−	725109.i	0.110273	−	0.190998i
$157$	−2.23038e6	+	1.28771e6i	−0.576342	+	0.332751i	−0.759678	−	0.650299i	$-0.774644\pi$
$157$	−2.23038e6	+	1.28771e6i	−0.576342	+	0.332751i	0.183336	+	0.983050i	$0.441310\pi$
$158$	958976.	+	1.66100e6i	0.243129	+	0.421112i
$159$	917781.	+	529881.i	0.228322	+	0.131822i
$160$			748044.i			0.182628i
$161$		0			0
$162$	−3.72425e6			−0.875979
$163$	437858.	−	758391.i	0.101104	−	0.175118i	−0.811036	−	0.584997i	$-0.801096\pi$
$163$	437858.	−	758391.i	0.101104	−	0.175118i	0.912140	+	0.409879i	$0.134429\pi$
$164$	2.37904e6	−	1.37354e6i	0.539348	−	0.311393i
$165$	−4.89617e6	−	8.48041e6i	−1.08994	−	1.88784i
$166$	−1.10068e6	−	635475.i	−0.240622	−	0.138923i
$167$		−	4.20699e6i		−	0.903280i	−0.892200	−	0.451640i	$-0.850839\pi$
$167$		−	4.20699e6i		−	0.903280i	0.892200	−	0.451640i	$-0.149161\pi$
$168$		0			0
$169$	4.15326e6			0.860457
$170$	963312.	−	1.66851e6i	0.196074	−	0.339610i
$171$	1.38393e6	−	799013.i	0.276774	−	0.159796i
$172$	−1.82363e6	−	3.15863e6i	−0.358387	−	0.620745i
$173$	3.28647e6	+	1.89744e6i	0.634732	+	0.366463i	0.782583	−	0.622547i	$-0.213902\pi$
$173$	3.28647e6	+	1.89744e6i	0.634732	+	0.366463i	−0.147850	+	0.989010i	$0.547235\pi$
$174$			5.91950e6i			1.12367i
$175$		0			0
$176$	2.43554e6			0.446743
$177$	−5.33613e6	+	9.24245e6i	−0.962291	+	1.66674i
$178$	1.87744e6	−	1.08394e6i	0.332894	−	0.192196i
$179$	−662601.	−	1.14766e6i	−0.115530	−	0.200103i	0.802462	−	0.596704i	$-0.203523\pi$
$179$	−662601.	−	1.14766e6i	−0.115530	−	0.200103i	−0.917991	+	0.396600i	$0.870190\pi$
$180$	1.02863e6	+	593877.i	0.176376	+	0.101831i
$181$			4.90685e6i			0.827499i	0.910391	+	0.413749i	$0.135781\pi$
$181$			4.90685e6i			0.827499i	−0.910391	+	0.413749i	$0.864219\pi$
$182$		0			0
$183$	−5.36908e6			−0.876085
$184$	−1.03115e6	+	1.78601e6i	−0.165527	+	0.286702i
$185$	2.42970e6	−	1.40279e6i	0.383741	−	0.221553i
$186$	4.22978e6	+	7.32619e6i	0.657323	+	1.13852i
$187$	−5.43246e6	−	3.13643e6i	−0.830752	−	0.479635i
$188$			1.23294e6i			0.185553i
$189$		0			0
$190$	4.06150e6			0.592142
$191$	3.15391e6	−	5.46273e6i	0.452636	−	0.783989i	−0.545913	−	0.837842i	$-0.683817\pi$
$191$	3.15391e6	−	5.46273e6i	0.452636	−	0.783989i	0.998549	+	0.0538534i	$0.0171504\pi$
$192$	−904728.	+	522345.i	−0.127825	+	0.0737996i
$193$	−437455.	−	757694.i	−0.0608501	−	0.105395i	0.833996	−	0.551771i	$-0.186048\pi$
$193$	−437455.	−	757694.i	−0.0608501	−	0.105395i	−0.894846	+	0.446376i	$0.852714\pi$
$194$	160021.	+	92388.1i	0.0219165	+	0.0126535i
$195$		−	3.37889e6i		−	0.455691i
$196$		0			0
$197$	−6.85421e6			−0.896518			−0.448259	−	0.893904i	$-0.647956\pi$
$197$	−6.85421e6			−0.896518			−0.448259	+	0.893904i	$0.647956\pi$
$198$	1.93360e6	−	3.34909e6i	0.249098	−	0.431450i
$199$	−8.24491e6	+	4.76020e6i	−1.04623	+	0.604040i	−0.921591	−	0.388162i	$-0.873110\pi$
$199$	−8.24491e6	+	4.76020e6i	−1.04623	+	0.604040i	−0.124637	+	0.992202i	$0.539777\pi$
$200$	95169.7	+	164839.i	0.0118962	+	0.0206048i
$201$	−8.90487e6	−	5.14123e6i	−1.09658	−	0.633110i
$202$			2.82836e6i			0.343148i
$203$		0			0
$204$	2.69065e6			0.316932
$205$	5.54297e6	−	9.60071e6i	0.643400	−	1.11440i
$206$	2.18495e6	−	1.26148e6i	0.249943	−	0.144305i
$207$	1.63728e6	+	2.83585e6i	0.184591	+	0.319722i
$208$	727805.	+	420199.i	0.0808770	+	0.0466944i
$209$		−	1.32238e7i		−	1.44849i
$210$		0			0
$211$	−1.02482e7			−1.09094			−0.545469	−	0.838131i	$-0.683649\pi$
$211$	−1.02482e7			−1.09094			−0.545469	+	0.838131i	$0.683649\pi$
$212$	−531852.	+	921195.i	−0.0558191	+	0.0966816i
$213$	−8.98738e6	+	5.18887e6i	−0.930025	+	0.536950i
$214$	5.34423e6	+	9.25648e6i	0.545311	+	0.944506i
$215$	−1.27468e7	−	7.35936e6i	−1.28258	−	0.740499i
$216$		−	2.54840e6i		−	0.252875i
$217$		0			0
$218$	−1.08717e7			−1.04937
$219$	1.71927e6	−	2.97786e6i	0.163686	−	0.283512i
$220$	8.51195e6	−	4.91438e6i	0.799394	−	0.461530i
$221$	−1.08224e6	−	1.87450e6i	−0.100265	−	0.173663i
$222$	3.39323e6	+	1.95908e6i	0.310138	+	0.179058i
$223$		−	1.75966e6i		−	0.158677i	−0.996848	−	0.0793385i	$-0.974719\pi$
$223$		−	1.75966e6i		−	0.158677i	0.996848	−	0.0793385i	$-0.0252808\pi$
$224$		0			0
$225$	302224.			0.0265327
$226$	1.33638e6	−	2.31467e6i	0.115772	−	0.200523i
$227$	8.44566e6	−	4.87610e6i	0.722031	−	0.416865i	−0.0934685	−	0.995622i	$-0.529795\pi$
$227$	8.44566e6	−	4.87610e6i	0.722031	−	0.416865i	0.815500	+	0.578757i	$0.196462\pi$
$228$	2.83607e6	+	4.91221e6i	0.239283	+	0.414451i
$229$	1.75825e7	+	1.01513e7i	1.46411	+	0.845306i	0.999198	−	0.0400494i	$-0.0127515\pi$
$229$	1.75825e7	+	1.01513e7i	1.46411	+	0.845306i	0.464915	+	0.885355i	$0.346085\pi$
$230$			8.32253e6i			0.684025i
$231$		0			0
$232$	−5.94152e6			−0.475810
$233$	2.71453e6	−	4.70171e6i	0.214599	−	0.371696i	−0.738550	−	0.674199i	$-0.764489\pi$
$233$	2.71453e6	−	4.70171e6i	0.214599	−	0.371696i	0.953148	+	0.302503i	$0.0978223\pi$
$234$	1.15562e6	−	667197.i	0.0901919	−	0.0520723i
$235$	2.48779e6	+	4.30897e6i	0.191694	+	0.332025i
$236$	−9.27682e6	−	5.35598e6i	−0.705770	−	0.407477i
$237$			1.08094e7i			0.811999i
$238$		0			0
$239$	−920423.			−0.0674208			−0.0337104	−	0.999432i	$-0.510732\pi$
$239$	−920423.			−0.0674208			−0.0337104	+	0.999432i	$0.510732\pi$
$240$	−2.10795e6	+	3.65107e6i	−0.152485	+	0.264111i
$241$	2.15894e7	−	1.24646e7i	1.54237	−	0.890488i	0.543681	−	0.839292i	$-0.317030\pi$
$241$	2.15894e7	−	1.24646e7i	1.54237	−	0.890488i	0.998689	−	0.0511961i	$-0.0163034\pi$
$242$	−1.09899e7	−	1.90351e7i	−0.775440	−	1.34310i
$243$	−9.28949e6	−	5.36329e6i	−0.647401	−	0.373777i
$244$		−	5.38905e6i		−	0.370973i
$245$		0			0
$246$	1.54822e7			1.03999
$247$	2.28146e6	−	3.95161e6i	0.151399	−	0.262231i
$248$	−7.35344e6	+	4.24551e6i	−0.482098	+	0.278339i
$249$	−3.58147e6	−	6.20329e6i	−0.231987	−	0.401813i
$250$	−9.21981e6	−	5.32306e6i	−0.590068	−	0.340676i
$251$		−	9.00977e6i		−	0.569761i	−0.958563	−	0.284880i	$-0.908046\pi$
$251$		−	9.00977e6i		−	0.569761i	0.958563	−	0.284880i	$-0.0919539\pi$
$252$		0			0
$253$	2.70972e7			1.67326
$254$	1.78816e6	−	3.09719e6i	0.109120	−	0.189002i
$255$	9.40351e6	−	5.42912e6i	0.567113	−	0.327423i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−1.52035e7	−	8.77772e6i	−0.895659	−	0.517109i	−0.0198699	−	0.999803i	$-0.506325\pi$
$257$	−1.52035e7	−	8.77772e6i	−0.895659	−	0.517109i	−0.875789	+	0.482693i	$0.839659\pi$
$258$		−	2.05556e7i		−	1.19694i
$259$		0			0
$260$	3.39146e6			0.192960
$261$	−4.71701e6	+	8.17011e6i	−0.265305	+	0.459522i
$262$	633159.	−	365555.i	0.0352054	−	0.0203258i
$263$	4.02078e6	+	6.96420e6i	0.221026	+	0.382828i	0.955120	−	0.296220i	$-0.0957261\pi$
$263$	4.02078e6	+	6.96420e6i	0.221026	+	0.382828i	−0.734094	+	0.679048i	$0.762393\pi$
$264$	1.18875e7	+	6.86323e6i	0.646067	+	0.373007i
$265$			4.29263e6i			0.230667i
$266$		0			0
$267$	1.22179e7			0.641895
$268$	5.16035e6	−	8.93799e6i	0.268087	−	0.464340i
$269$	−1.41178e7	+	8.15090e6i	−0.725286	+	0.418744i	−0.816695	−	0.577069i	$-0.804196\pi$
$269$	−1.41178e7	+	8.15090e6i	−0.725286	+	0.418744i	0.0914090	+	0.995813i	$0.470863\pi$
$270$	−5.14209e6	−	8.90636e6i	−0.261245	−	0.452490i
$271$	2.67932e7	+	1.54691e7i	1.34622	+	0.777243i	0.987712	−	0.156283i	$-0.0499511\pi$
$271$	2.67932e7	+	1.54691e7i	1.34622	+	0.777243i	0.358511	+	0.933525i	$0.383284\pi$
$272$			2.70066e6i			0.134203i
$273$		0			0
$274$	−9.02839e6			−0.438893
$275$	1.25046e6	−	2.16586e6i	0.0601273	−	0.104144i
$276$	−1.00658e7	+	5.81146e6i	−0.478761	+	0.276413i
$277$	6.70800e6	+	1.16186e7i	0.315612	+	0.546656i	0.979567	−	0.201116i	$-0.0644568\pi$
$277$	6.70800e6	+	1.16186e7i	0.315612	+	0.546656i	−0.663955	+	0.747772i	$0.731123\pi$
$278$	−3.37260e6	−	1.94717e6i	−0.156975	−	0.0906295i
$279$			1.34822e7i			0.620793i
$280$		0			0
$281$	−1.17351e6			−0.0528895			−0.0264447	−	0.999650i	$-0.508419\pi$
$281$	−1.17351e6			−0.0528895			−0.0264447	+	0.999650i	$0.508419\pi$
$282$	−3.47435e6	+	6.01775e6i	−0.154927	+	0.268341i
$283$	2.44869e7	−	1.41375e7i	1.08038	−	0.623756i	0.149379	−	0.988780i	$-0.452273\pi$
$283$	2.44869e7	−	1.41375e7i	1.08038	−	0.623756i	0.930998	+	0.365024i	$0.118939\pi$
$284$	−5.20817e6	−	9.02081e6i	−0.227368	−	0.393813i
$285$	1.98235e7	+	1.14451e7i	0.856338	+	0.494407i
$286$		−	1.10422e7i		−	0.472017i
$287$		0			0
$288$	−1.66494e6			−0.0696983
$289$	−8.59095e6	+	1.48800e7i	−0.355916	+	0.616465i
$290$	−2.07649e7	+	1.19886e7i	−0.851405	+	0.491559i
$291$	520689.	+	901860.i	0.0211300	+	0.0365982i
$292$	2.98894e6	+	1.72566e6i	0.120052	+	0.0693119i
$293$		−	5.58159e6i		−	0.221899i	−0.993826	−	0.110949i	$-0.964611\pi$
$293$		−	5.58159e6i		−	0.221899i	0.993826	−	0.110949i	$-0.0353892\pi$
$294$		0			0
$295$	−4.32286e7			−1.68386
$296$	−1.96637e6	+	3.40585e6i	−0.0758211	+	0.131326i
$297$	−2.89981e7	+	1.67420e7i	−1.10688	+	0.639056i
$298$	−1.79178e6	−	3.10346e6i	−0.0677074	−	0.117273i
$299$	8.09736e6	+	4.67501e6i	0.302921	+	0.174892i
$300$			1.07273e6i			0.0397308i
$301$		0			0
$302$	−1.41078e7			−0.512197
$303$	−7.97017e6	+	1.38047e7i	−0.286510	+	0.496250i
$304$	−4.93049e6	+	2.84662e6i	−0.175497	+	0.101323i
$305$	−1.08739e7	−	1.88341e7i	−0.383252	−	0.663812i
$306$	3.71364e6	+	2.14407e6i	0.129609	+	0.0748299i
$307$			4.40807e7i			1.52347i	0.647891	+	0.761733i	$0.275651\pi$
$307$			4.40807e7i			1.52347i	−0.647891	+	0.761733i	$0.724349\pi$
$308$		0			0
$309$	1.42192e7			0.481946
$310$	−1.71330e7	+	2.96751e7i	−0.575105	+	0.996111i
$311$	−2.44238e7	+	1.41011e7i	−0.811956	+	0.468783i	−0.847635	−	0.530580i	$-0.821974\pi$
$311$	−2.44238e7	+	1.41011e7i	−0.811956	+	0.468783i	0.0356786	+	0.999363i	$0.488641\pi$
$312$	2.36819e6	+	4.10183e6i	0.0779747	+	0.135056i
$313$	5.13461e6	+	2.96447e6i	0.167446	+	0.0966750i	0.581381	−	0.813631i	$-0.302513\pi$
$313$	5.13461e6	+	2.96447e6i	0.167446	+	0.0966750i	−0.413935	+	0.910306i	$0.635846\pi$
$314$		−	1.45688e7i		−	0.470581i
$315$		0			0
$316$	−1.08496e7			−0.343836
$317$	−2.26491e7	+	3.92294e7i	−0.711007	+	1.23150i	0.253473	+	0.967342i	$0.418427\pi$
$317$	−2.26491e7	+	3.92294e7i	−0.711007	+	1.23150i	−0.964480	+	0.264157i	$0.914906\pi$
$318$	−5.19175e6	+	2.99746e6i	−0.161448	+	0.0932121i
$319$	3.90336e7	+	6.76082e7i	1.20245	+	2.08270i
$320$	−3.66465e6	−	2.11579e6i	−0.111836	−	0.0645687i
$321$			6.02390e7i			1.82122i
$322$		0			0
$323$	1.46632e7			0.435132
$324$	1.05338e7	−	1.82450e7i	0.309705	−	0.536426i
$325$	747342.	−	431478.i	0.0217705	−	0.0125692i
$326$	2.47690e6	+	4.29011e6i	0.0714916	+	0.123827i
$327$	−5.30628e7	−	3.06358e7i	−1.51756	−	0.876165i
$328$			1.55398e7i			0.440376i
$329$		0			0
$330$	5.53938e7			1.54141
$331$	3.34507e7	−	5.79383e7i	0.922404	−	1.59765i	0.126719	−	0.991939i	$-0.459555\pi$
$331$	3.34507e7	−	5.79383e7i	0.922404	−	1.59765i	0.795685	−	0.605711i	$-0.207111\pi$
$332$	6.22636e6	−	3.59479e6i	0.170145	−	0.0982334i
$333$	3.12223e6	+	5.40786e6i	0.0845536	+	0.146451i
$334$	2.06100e7	+	1.18992e7i	0.553144	+	0.319358i
$335$		−	4.16497e7i		−	1.10784i
$336$		0			0
$337$	−3.67215e7			−0.959469			−0.479735	−	0.877414i	$-0.659267\pi$
$337$	−3.67215e7			−0.959469			−0.479735	+	0.877414i	$0.659267\pi$
$338$	−1.17472e7	+	2.03467e7i	−0.304217	+	0.526920i
$339$	1.30452e7	−	7.53168e6i	0.334852	−	0.193327i
$340$	5.44931e6	+	9.43849e6i	0.138645	+	0.240141i
$341$	9.66188e7	+	5.57829e7i	2.43668	+	1.40682i
$342$			9.03980e6i			0.225985i
$343$		0			0
$344$	2.06321e7			0.506836
$345$	−2.34524e7	+	4.06208e7i	−0.571124	+	0.989216i
$346$	−1.85911e7	+	1.07336e7i	−0.448824	+	0.259128i
$347$	−3.31773e7	−	5.74648e7i	−0.794059	−	1.37535i	−0.923435	−	0.383756i	$-0.874630\pi$
$347$	−3.31773e7	−	5.74648e7i	−0.794059	−	1.37535i	0.129375	−	0.991596i	$-0.458703\pi$
$348$	−2.89995e7	−	1.67429e7i	−0.688102	−	0.397276i
$349$			9.44163e6i			0.222111i	0.993814	+	0.111056i	$0.0354232\pi$
$349$			9.44163e6i			0.222111i	−0.993814	+	0.111056i	$0.964577\pi$
$350$		0			0
$351$	−1.15539e7			−0.267181
$352$	−6.88876e6	+	1.19317e7i	−0.157948	+	0.273573i
$353$	−9.53150e6	+	5.50301e6i	−0.216689	+	0.125105i	−0.604416	−	0.796669i	$-0.706594\pi$
$353$	−9.53150e6	+	5.50301e6i	−0.216689	+	0.125105i	0.387727	+	0.921774i	$0.373260\pi$
$354$	−3.01857e7	−	5.22832e7i	−0.680443	−	1.17856i
$355$	−3.64039e7	−	2.10178e7i	−0.813697	−	0.469788i
$356$			1.22634e7i			0.271807i
$357$		0			0
$358$	7.49648e6			0.163384
$359$	2.73638e7	−	4.73954e7i	0.591415	−	1.02436i	−0.402627	−	0.915364i	$-0.631903\pi$
$359$	2.73638e7	−	4.73954e7i	0.591415	−	1.02436i	0.994042	−	0.108997i	$-0.0347638\pi$
$360$	−5.81879e6	+	3.35948e6i	−0.124717	+	0.0720053i
$361$	−8.06726e6	−	1.39729e7i	−0.171476	−	0.297006i
$362$	−2.40386e7	−	1.38787e7i	−0.506737	−	0.292565i
$363$		−	1.23876e8i		−	2.58980i
$364$		0			0
$365$	1.39280e7			0.286424
$366$	1.51860e7	−	2.63030e7i	0.309743	−	0.536490i
$367$	8.26059e7	−	4.76926e7i	1.67114	−	0.964834i	0.704140	−	0.710061i	$-0.251333\pi$
$367$	8.26059e7	−	4.76926e7i	1.67114	−	0.964834i	0.967001	−	0.254773i	$-0.0820007\pi$
$368$	−5.83308e6	−	1.01032e7i	−0.117045	−	0.202729i
$369$	2.13686e7	+	1.23371e7i	0.425301	+	0.245548i
$370$			1.58708e7i			0.313323i
$371$		0			0
$372$	−4.78545e7			−0.929595
$373$	2.11254e7	−	3.65902e7i	0.407078	−	0.705081i	−0.587483	−	0.809237i	$-0.699881\pi$
$373$	2.11254e7	−	3.65902e7i	0.407078	−	0.705081i	0.994561	+	0.104156i	$0.0332142\pi$
$374$	3.07306e7	−	1.77423e7i	0.587431	−	0.339153i
$375$	−3.00002e7	−	5.19619e7i	−0.568893	−	0.985351i
$376$	−6.04013e6	−	3.48727e6i	−0.113627	−	0.0656028i
$377$			2.69375e7i			0.502728i
$378$		0			0
$379$	2.92437e7			0.537173			0.268587	−	0.963256i	$-0.413443\pi$
$379$	2.92437e7			0.537173			0.268587	+	0.963256i	$0.413443\pi$
$380$	−1.14877e7	+	1.98972e7i	−0.209354	+	0.362611i
$381$	1.74554e7	−	1.00779e7i	0.315613	−	0.182219i
$382$	1.78412e7	+	3.09019e7i	0.320062	+	0.554364i
$383$	−2.53968e7	−	1.46629e7i	−0.452047	−	0.260989i	0.256647	−	0.966505i	$-0.417382\pi$
$383$	−2.53968e7	−	1.46629e7i	−0.452047	−	0.260989i	−0.708694	+	0.705516i	$0.750715\pi$
$384$		−	5.90966e6i		−	0.104368i
$385$		0			0
$386$	4.94924e6			0.0860550
$387$	1.63799e7	−	2.83709e7i	0.282605	−	0.489486i
$388$	−905215.	+	522626.i	−0.0154973	+	0.00894738i
$389$	5.20331e7	+	9.01241e7i	0.883957	+	1.53106i	0.846904	+	0.531746i	$0.178464\pi$
$389$	5.20331e7	+	9.01241e7i	0.883957	+	1.53106i	0.0370533	+	0.999313i	$0.488203\pi$
$390$	1.65531e7	+	9.55696e6i	0.279053	+	0.161111i
$391$			3.00468e7i			0.502652i
$392$		0			0
$393$	4.12045e6			0.0678840
$394$	1.93866e7	−	3.35786e7i	0.316967	−	0.549003i
$395$	−3.79180e7	+	2.18920e7i	−0.615254	+	0.355217i
$396$	1.09381e7	+	1.89453e7i	0.176139	+	0.305081i
$397$	−6.06717e7	−	3.50288e7i	−0.969649	−	0.559827i	−0.0705197	−	0.997510i	$-0.522466\pi$
$397$	−6.06717e7	−	3.50288e7i	−0.969649	−	0.559827i	−0.899129	+	0.437683i	$0.855799\pi$
$398$		−	5.38555e7i		−	0.854242i
$399$		0			0
$400$	−1.07672e6			−0.0168238
$401$	−3.84740e7	+	6.66389e7i	−0.596670	+	1.03346i	0.396639	+	0.917975i	$0.370177\pi$
$401$	−3.84740e7	+	6.66389e7i	−0.596670	+	1.03346i	−0.993309	+	0.115488i	$0.963157\pi$
$402$	5.03736e7	−	2.90832e7i	0.775398	−	0.447676i
$403$	1.92482e7	+	3.33388e7i	0.294086	+	0.509372i
$404$	−1.38561e7	−	7.99982e6i	−0.210134	−	0.121321i
$405$		−	8.50190e7i		−	1.27983i
$406$		0			0
$407$	5.16733e7			0.766449
$408$	−7.61031e6	+	1.31814e7i	−0.112053	+	0.194081i
$409$	−3.50627e7	+	2.02435e7i	−0.512479	+	0.295880i	−0.733852	−	0.679309i	$-0.762279\pi$
$409$	−3.50627e7	+	2.02435e7i	−0.512479	+	0.295880i	0.221373	+	0.975189i	$0.428946\pi$
$410$	3.13558e7	+	5.43098e7i	0.454952	+	0.788001i
$411$	−4.40660e7	−	2.54415e7i	−0.634714	−	0.366452i
$412$			1.42721e7i			0.204077i
$413$		0			0
$414$	−1.85237e7			−0.261052
$415$	1.45069e7	−	2.51268e7i	0.202970	−	0.351554i
$416$	−4.11709e6	+	2.37700e6i	−0.0571887	+	0.0330179i
$417$	−1.09740e7	−	1.90076e7i	−0.151342	−	0.262131i
$418$	6.47830e7	+	3.74025e7i	0.887017	+	0.512120i
$419$			5.02960e7i			0.683741i	0.939747	+	0.341870i	$0.111060\pi$
$419$			5.02960e7i			0.683741i	−0.939747	+	0.341870i	$0.888940\pi$
$420$		0			0
$421$	1.61043e6			0.0215822			0.0107911	−	0.999942i	$-0.496565\pi$
$421$	1.61043e6			0.0215822			0.0107911	+	0.999942i	$0.496565\pi$
$422$	2.89863e7	−	5.02057e7i	0.385705	−	0.668061i
$423$	−9.59061e6	+	5.53714e6i	−0.126714	+	0.0731584i
$424$	−3.00861e6	−	5.21106e6i	−0.0394701	−	0.0683642i
$425$	2.40162e6	+	1.38658e6i	0.0312851	+	0.0180624i
$426$		−	5.87053e7i		−	0.759362i
$427$		0			0
$428$	−6.04631e7			−0.771186
$429$	3.11163e7	−	5.38951e7i	0.394109	−	0.682617i
$430$	7.21067e7	−	4.16308e7i	0.906923	−	0.523612i
$431$	−3.45151e7	−	5.97819e7i	−0.431099	−	0.746686i	0.565869	−	0.824495i	$-0.308541\pi$
$431$	−3.45151e7	−	5.97819e7i	−0.431099	−	0.746686i	−0.996968	+	0.0778092i	$0.975207\pi$
$432$	1.24845e7	+	7.20796e6i	0.154854	+	0.0894048i
$433$			7.91462e7i			0.974915i	0.873147	+	0.487457i	$0.162076\pi$
$433$			7.91462e7i			0.974915i	−0.873147	+	0.487457i	$0.837924\pi$
$434$		0			0
$435$	−1.35133e8			−1.64170
$436$	3.07497e7	−	5.32601e7i	0.371007	−	0.642603i
$437$	−5.48552e7	+	3.16707e7i	−0.657315	+	0.379501i
$438$	9.72565e6	+	1.68453e7i	0.115743	+	0.200474i
$439$	−2.09035e7	−	1.20687e7i	−0.247073	−	0.142648i	0.371350	−	0.928493i	$-0.378895\pi$
$439$	−2.09035e7	−	1.20687e7i	−0.247073	−	0.142648i	−0.618423	+	0.785845i	$0.712228\pi$
$440$			5.55998e7i			0.652703i
$441$		0			0
$442$	1.22442e7			0.141796
$443$	−2.35504e7	+	4.07904e7i	−0.270886	+	0.469188i	−0.969089	−	0.246712i	$-0.920650\pi$
$443$	−2.35504e7	+	4.07904e7i	−0.270886	+	0.469188i	0.698203	+	0.715900i	$0.253983\pi$
$444$	−1.91950e7	+	1.10822e7i	−0.219300	+	0.126613i
$445$	2.47447e7	+	4.28591e7i	0.280804	+	0.486366i
$446$	8.62053e6	+	4.97707e6i	0.0971694	+	0.0561008i
$447$		−	2.01966e7i		−	0.226128i
$448$		0			0
$449$	−4.69720e6			−0.0518920			−0.0259460	−	0.999663i	$-0.508260\pi$
$449$	−4.69720e6			−0.0518920			−0.0259460	+	0.999663i	$0.508260\pi$
$450$	−854817.	+	1.48059e6i	−0.00938071	+	0.0162479i
$451$	1.76826e8	−	1.02091e8i	1.92760	−	1.11290i
$452$	7.55969e6	+	1.30938e7i	0.0818632	+	0.141791i
$453$	−6.88575e7	−	3.97549e7i	−0.740724	−	0.427657i
$454$			5.51668e7i			0.589536i
$455$		0			0
$456$	−3.20865e7			−0.338398
$457$	−5.91484e7	+	1.02448e8i	−0.619718	+	1.07338i	0.369819	+	0.929104i	$0.379420\pi$
$457$	−5.91484e7	+	1.02448e8i	−0.619718	+	1.07338i	−0.989537	+	0.144280i	$0.953914\pi$
$458$	−9.94617e7	+	5.74243e7i	−1.03528	+	0.597722i
$459$	−1.85644e7	−	3.21545e7i	−0.191975	−	0.332510i
$460$	−4.07719e7	−	2.35397e7i	−0.418878	−	0.241839i
$461$		−	1.71817e8i		−	1.75373i	−0.480733	−	0.876867i	$-0.659629\pi$
$461$		−	1.71817e8i		−	1.75373i	0.480733	−	0.876867i	$-0.340371\pi$
$462$		0			0
$463$	4.58717e7			0.462170			0.231085	−	0.972934i	$-0.425772\pi$
$463$	4.58717e7			0.462170			0.231085	+	0.972934i	$0.425772\pi$
$464$	1.68052e7	−	2.91074e7i	0.168224	−	0.291373i
$465$	−1.67246e8	+	9.65595e7i	−1.66340	+	0.960364i
$466$	1.53557e7	+	2.65969e7i	0.151744	+	0.262829i
$467$	−1.12372e7	−	6.48779e6i	−0.110333	−	0.0637010i	0.443818	−	0.896117i	$-0.353624\pi$
$467$	−1.12372e7	−	6.48779e6i	−0.110333	−	0.0637010i	−0.554151	+	0.832416i	$0.686957\pi$
$468$			7.54848e6i			0.0736413i
$469$		0			0
$470$	−2.81461e7			−0.271097
$471$	4.10541e7	−	7.11077e7i	0.392910	−	0.680541i
$472$	5.24776e7	−	3.02980e7i	0.499055	−	0.288129i
$473$	−1.35545e8	−	2.34771e8i	−1.28086	−	2.21851i
$474$	−5.29549e7	−	3.05735e7i	−0.497246	−	0.287085i
$475$			5.84605e6i			0.0545484i
$476$		0			0
$477$	−9.55422e6			−0.0880319
$478$	2.60335e6	−	4.50914e6i	0.0238369	−	0.0412866i
$479$	2.00019e7	−	1.15481e7i	0.181997	−	0.105076i	−0.406233	−	0.913769i	$-0.633158\pi$
$479$	2.00019e7	−	1.15481e7i	0.181997	−	0.105076i	0.588231	+	0.808693i	$0.299825\pi$
$480$	−1.19244e7	−	2.06536e7i	−0.107823	−	0.186755i
$481$	1.54414e7	+	8.91507e6i	0.138756	+	0.0801105i
$482$			1.41021e8i			1.25934i
$483$		0			0
$484$	1.24337e8			1.09664
$485$	−2.10908e6	+	3.65304e6i	−0.0184871	+	0.0320205i
$486$	5.25493e7	−	3.03394e7i	0.457782	−	0.264300i
$487$	1.67086e7	+	2.89401e7i	0.144661	+	0.250561i	0.929246	−	0.369460i	$-0.120457\pi$
$487$	1.67086e7	+	2.89401e7i	0.144661	+	0.250561i	−0.784585	+	0.620021i	$0.787124\pi$
$488$	2.64008e7	+	1.52425e7i	0.227174	+	0.131159i
$489$			2.79190e7i			0.238767i
$490$		0			0
$491$	1.96184e8			1.65737			0.828686	−	0.559714i	$-0.189089\pi$
$491$	1.96184e8			1.65737			0.828686	+	0.559714i	$0.189089\pi$
$492$	−4.37903e7	+	7.58470e7i	−0.367691	+	0.636859i
$493$	−7.49674e7	+	4.32825e7i	−0.625651	+	0.361220i
$494$	1.29059e7	+	2.23537e7i	0.107055	+	0.185425i
$495$	7.64546e7	+	4.41411e7i	0.630359	+	0.363938i
$496$		−	4.80325e7i		−	0.393631i
$497$		0			0
$498$	4.05197e7			0.328079
$499$	−4.63697e7	+	8.03147e7i	−0.373192	+	0.646388i	−0.990055	−	0.140683i	$-0.955070\pi$
$499$	−4.63697e7	+	8.03147e7i	−0.373192	+	0.646388i	0.616862	+	0.787071i	$0.288403\pi$
$500$	5.21551e7	−	3.01118e7i	0.417241	−	0.240894i
$501$	6.70625e7	+	1.16156e8i	0.533294	+	0.923692i
$502$	4.41387e7	+	2.54835e7i	0.348906	+	0.201441i
$503$			1.26998e8i			0.997914i	0.866627	+	0.498957i	$0.166283\pi$
$503$			1.26998e8i			0.997914i	−0.866627	+	0.498957i	$0.833717\pi$
$504$		0			0
$505$	−6.45673e7			−0.501347
$506$	−7.66424e7	+	1.32749e8i	−0.591586	+	1.02466i
$507$	−1.14672e8	+	6.62059e7i	−0.879900	+	0.508011i
$508$	1.01154e7	+	1.75203e7i	0.0771597	+	0.133645i
$509$	1.24437e8	+	7.18438e7i	0.943619	+	0.544799i	0.891093	−	0.453821i	$-0.149939\pi$
$509$	1.24437e8	+	7.18438e7i	0.943619	+	0.544799i	0.0525259	+	0.998620i	$0.483273\pi$
$510$			6.14235e7i			0.463046i
$511$		0			0
$512$	5.93164e6			0.0441942
$513$	3.91355e7	−	6.77847e7i	0.289881	−	0.502088i
$514$	8.60037e7	−	4.96543e7i	0.633327	−	0.365651i
$515$	2.87978e7	+	4.98792e7i	0.210832	+	0.365172i
$516$	1.00702e8	+	5.81401e7i	0.732971	+	0.423181i
$517$			9.16404e7i			0.663156i
$518$		0			0
$519$	−1.20986e8			−0.865434
$520$	−9.59250e6	+	1.66147e7i	−0.0682216	+	0.118163i
$521$	1.12128e8	−	6.47370e7i	0.792866	−	0.457761i	−0.0481045	−	0.998842i	$-0.515318\pi$
$521$	1.12128e8	−	6.47370e7i	0.792866	−	0.457761i	0.840971	+	0.541081i	$0.181985\pi$
$522$	−2.66835e7	−	4.62171e7i	−0.187599	−	0.324931i
$523$	2.11656e8	+	1.22200e8i	1.47954	+	0.854210i	0.999732	−	0.0231657i	$-0.00737454\pi$
$523$	2.11656e8	+	1.22200e8i	1.47954	+	0.854210i	0.479804	+	0.877376i	$0.340708\pi$
$524$			4.13578e6i			0.0287451i
$525$		0			0
$526$	−4.54900e7			−0.312578
$527$	−6.18550e7	+	1.07136e8i	−0.422613	+	0.731987i
$528$	−6.72457e7	+	3.88243e7i	−0.456838	+	0.263756i
$529$	9.12076e6	+	1.57976e7i	0.0616118	+	0.106715i
$530$	−2.10295e7	−	1.21414e7i	−0.141254	−	0.0815531i
$531$		−	9.62151e7i		−	0.642628i
$532$		0			0
$533$	7.04539e7			0.465290
$534$	−3.45576e7	+	5.98554e7i	−0.226944	+	0.393079i
$535$	−2.11311e8	+	1.22001e8i	−1.37995	+	0.796712i
$536$	2.91914e7	+	5.05609e7i	0.189566	+	0.328338i
$537$	3.65890e7	+	2.11247e7i	0.236280	+	0.136417i
$538$		−	9.22169e7i		−	0.592194i
$539$		0			0
$540$	5.81761e7			0.369456
$541$	2.21709e6	−	3.84011e6i	0.0140020	−	0.0242522i	−0.858939	−	0.512077i	$-0.828876\pi$
$541$	2.21709e6	−	3.84011e6i	0.0140020	−	0.0242522i	0.872942	+	0.487825i	$0.162210\pi$
$542$	−1.51565e8	+	8.75063e7i	−0.951924	+	0.549594i
$543$	−7.82187e7	−	1.35479e8i	−0.488553	−	0.846198i
$544$	−1.32305e7	−	7.63861e6i	−0.0821823	−	0.0474480i
$545$		−	2.48184e8i		−	1.53315i
$546$		0			0
$547$	−7.96292e7			−0.486531			−0.243265	−	0.969960i	$-0.578219\pi$
$547$	−7.96292e7			−0.486531			−0.243265	+	0.969960i	$0.578219\pi$
$548$	2.55361e7	−	4.42299e7i	0.155172	−	0.268766i
$549$	4.19196e7	−	2.42023e7i	0.253338	−	0.146265i
$550$	7.07367e6	+	1.22520e7i	0.0425164	+	0.0736406i
$551$	−1.58038e8	−	9.12434e7i	−0.944729	−	0.545440i
$552$		−	6.57492e7i		−	0.390907i
$553$		0			0
$554$	−7.58924e7			−0.446343
$555$	−4.47229e7	+	7.74624e7i	−0.261608	+	0.453119i
$556$	1.90783e7	−	1.10149e7i	0.110998	−	0.0640847i
$557$	−1.46346e7	−	2.53478e7i	−0.0846865	−	0.146681i	0.820571	−	0.571544i	$-0.193656\pi$
$557$	−1.46346e7	−	2.53478e7i	−0.0846865	−	0.146681i	−0.905258	+	0.424863i	$0.860322\pi$
$558$	−6.60488e7	−	3.81333e7i	−0.380157	−	0.219483i
$559$		−	9.35411e7i		−	0.535509i
$560$		0			0
$561$	1.99988e8			1.13270
$562$	3.31920e6	−	5.74902e6i	0.0186992	−	0.0323880i
$563$	−1.62041e8	+	9.35545e7i	−0.908030	+	0.524251i	−0.879797	−	0.475350i	$-0.842321\pi$
$563$	−1.62041e8	+	9.35545e7i	−0.908030	+	0.524251i	−0.0282330	+	0.999601i	$0.508988\pi$
$564$	−1.96539e7	−	3.40415e7i	−0.109550	−	0.189746i
$565$	5.28405e7	+	3.05075e7i	0.292969	+	0.169146i
$566$			1.59948e8i			0.882124i
$567$		0			0
$568$	5.89237e7			0.321547
$569$	−3.18400e7	+	5.51485e7i	−0.172837	+	0.299362i	−0.939410	−	0.342794i	$-0.888627\pi$
$569$	−3.18400e7	+	5.51485e7i	−0.172837	+	0.299362i	0.766574	+	0.642156i	$0.221960\pi$
$570$	−1.12138e8	+	6.47432e7i	−0.605522	+	0.349598i
$571$	7.74210e7	+	1.34097e8i	0.415863	+	0.720296i	0.995519	−	0.0945655i	$-0.0301462\pi$
$571$	7.74210e7	+	1.34097e8i	0.415863	+	0.720296i	−0.579655	+	0.814862i	$0.696813\pi$
$572$	5.40955e7	+	3.12321e7i	0.289050	+	0.166883i
$573$			2.01102e8i			1.06894i
$574$		0			0
$575$	−1.19793e7			−0.0630127
$576$	4.70917e6	−	8.15652e6i	0.0246421	−	0.0426813i
$577$	2.73237e8	−	1.57754e8i	1.42237	−	0.821205i	0.425868	−	0.904785i	$-0.359969\pi$
$577$	2.73237e8	−	1.57754e8i	1.42237	−	0.821205i	0.996501	+	0.0835798i	$0.0266354\pi$
$578$	−4.85977e7	−	8.41737e7i	−0.251671	−	0.435906i
$579$	2.41564e7	+	1.39467e7i	0.124450	+	0.0718514i
$580$		−	1.35636e8i		−	0.695170i
$581$		0			0
$582$	−5.89093e6			−0.0298823
$583$	−3.95309e7	+	6.84696e7i	−0.199495	+	0.345535i
$584$	−1.69080e7	+	9.76183e6i	−0.0848894	+	0.0490109i
$585$	1.52311e7	+	2.63811e7i	0.0760789	+	0.131772i
$586$	2.73441e7	+	1.57871e7i	0.135885	+	0.0784531i
$587$			5.57952e7i			0.275856i	0.990442	+	0.137928i	$0.0440443\pi$
$587$			5.57952e7i			0.275856i	−0.990442	+	0.137928i	$0.955956\pi$
$588$		0			0
$589$	−2.60792e8			−1.27629
$590$	1.22269e8	−	2.11776e8i	0.595333	−	1.03115i
$591$	1.89246e8	−	1.09261e8i	0.916776	−	0.529301i
$592$	−1.11235e7	−	1.92664e7i	−0.0536136	−	0.0928615i
$593$	−2.39874e8	−	1.38491e8i	−1.15032	−	0.664137i	−0.201354	−	0.979518i	$-0.564534\pi$
$593$	−2.39874e8	−	1.38491e8i	−1.15032	−	0.664137i	−0.948965	+	0.315381i	$0.897868\pi$
$594$		−	1.89415e8i		−	0.903762i
$595$		0			0
$596$	2.02717e7			0.0957527
$597$	1.51762e8	−	2.62859e8i	0.713247	−	1.23538i
$598$	−4.58056e7	+	2.64459e7i	−0.214198	+	0.123667i
$599$	9.32594e7	+	1.61530e8i	0.433923	+	0.751576i	0.997207	−	0.0746871i	$-0.0237958\pi$
$599$	9.32594e7	+	1.61530e8i	0.433923	+	0.751576i	−0.563284	+	0.826263i	$0.690462\pi$
$600$	−5.25529e6	−	3.03415e6i	−0.0243301	−	0.0140470i
$601$			2.43621e8i			1.12226i	0.827729	+	0.561128i	$0.189632\pi$
$601$			2.43621e8i			1.12226i	−0.827729	+	0.561128i	$0.810368\pi$
$602$		0			0
$603$	9.27009e7			0.422797
$604$	3.99028e7	−	6.91136e7i	0.181089	−	0.313655i
$605$	4.34542e8	−	2.50883e8i	1.96230	−	1.13294i
$606$	−4.50861e7	−	7.80914e7i	−0.202593	−	0.350902i
$607$	−9.01650e7	−	5.20568e7i	−0.403155	−	0.232762i	0.284689	−	0.958620i	$-0.408110\pi$
$607$	−9.01650e7	−	5.20568e7i	−0.403155	−	0.232762i	−0.687844	+	0.725858i	$0.741443\pi$
$608$		−	3.22058e7i		−	0.143292i
$609$		0			0
$610$	1.23024e8			0.542001
$611$	−1.58105e7	+	2.73846e7i	−0.0693142	+	0.120056i
$612$	−2.10075e7	+	1.21287e7i	−0.0916475	+	0.0529127i
$613$	−1.42147e8	−	2.46207e8i	−0.617103	−	1.06885i	−0.990012	−	0.140986i	$-0.954973\pi$
$613$	−1.42147e8	−	2.46207e8i	−0.617103	−	1.06885i	0.372909	−	0.927868i	$-0.378361\pi$
$614$	−2.15950e8	−	1.24679e8i	−0.932929	−	0.538627i
$615$			3.53436e8i			1.51944i
$616$		0			0
$617$	−1.78930e8			−0.761776			−0.380888	−	0.924621i	$-0.624382\pi$
$617$	−1.78930e8			−0.761776			−0.380888	+	0.924621i	$0.624382\pi$
$618$	−4.02179e7	+	6.96594e7i	−0.170394	+	0.295131i
$619$	−2.04695e8	+	1.18181e8i	−0.863048	+	0.498281i	−0.865032	−	0.501717i	$-0.832702\pi$
$619$	−2.04695e8	+	1.18181e8i	−0.863048	+	0.498281i	0.00198390	+	0.999998i	$0.499369\pi$
$620$	−9.69186e7	−	1.67868e8i	−0.406661	−	0.704357i
$621$	1.38900e8	+	8.01937e7i	0.579997	+	0.334862i
$622$		−	1.59536e8i		−	0.662959i
$623$		0			0
$624$	−2.67931e7			−0.110273
$625$	1.29732e8	−	2.24703e8i	0.531383	−	0.920383i
$626$	−2.90458e7	+	1.67696e7i	−0.118402	+	0.0683595i
$627$	2.10796e8	+	3.65110e8i	0.855185	+	1.48122i
$628$	7.13722e7	+	4.12068e7i	0.288171	+	0.166376i
$629$			5.72980e7i			0.230244i
$630$		0			0
$631$	1.51341e8			0.602378			0.301189	−	0.953564i	$-0.402616\pi$
$631$	1.51341e8			0.602378			0.301189	+	0.953564i	$0.402616\pi$
$632$	3.06872e7	−	5.31519e7i	0.121564	−	0.210556i
$633$	2.82954e8	−	1.63364e8i	1.11559	−	0.644087i
$634$	−1.28123e8	−	2.21915e8i	−0.502758	−	0.870802i
$635$	7.07041e7	+	4.08211e7i	0.276136	+	0.159427i
$636$		−	3.39124e7i		−	0.131822i
$637$		0			0
$638$	−4.41615e8			−1.70052
$639$	4.67799e7	−	8.10252e7i	0.179290	−	0.310540i
$640$	2.07304e7	−	1.19687e7i	0.0790802	−	0.0456570i
$641$	1.15332e8	+	1.99760e8i	0.437899	+	0.758463i	0.997527	−	0.0702803i	$-0.0223894\pi$
$641$	1.15332e8	+	1.99760e8i	0.437899	+	0.758463i	−0.559628	+	0.828744i	$0.689056\pi$
$642$	−2.95110e8	−	1.70382e8i	−1.11527	−	0.643899i
$643$		−	1.68539e8i		−	0.633967i	−0.948431	−	0.316983i	$-0.897330\pi$
$643$		−	1.68539e8i		−	0.633967i	0.948431	−	0.316983i	$-0.102670\pi$
$644$		0			0
$645$	4.69254e8			1.74875
$646$	−4.14738e7	+	7.18347e7i	−0.153842	+	0.266463i
$647$	1.43881e8	−	8.30696e7i	0.531239	−	0.306711i	−0.210282	−	0.977641i	$-0.567438\pi$
$647$	1.43881e8	−	8.30696e7i	0.531239	−	0.306711i	0.741521	+	0.670930i	$0.234105\pi$
$648$	5.95880e7	+	1.03209e8i	0.218995	+	0.379310i
$649$	−6.89518e8	−	3.98093e8i	−2.52239	−	1.45630i
$650$			4.88161e6i			0.0177756i
$651$		0			0
$652$	−2.80229e7			−0.101104
$653$	1.18804e8	−	2.05775e8i	0.426670	−	0.739014i	−0.569905	−	0.821711i	$-0.693020\pi$
$653$	1.18804e8	−	2.05775e8i	0.426670	−	0.739014i	0.996575	+	0.0826970i	$0.0263534\pi$
$654$	3.00168e8	−	1.73302e8i	1.07308	−	0.619542i
$655$	8.34506e6	+	1.44541e7i	0.0296965	+	0.0514359i
$656$	−7.61291e7	−	4.39532e7i	−0.269674	−	0.155696i
$657$			3.09999e7i			0.109311i
$658$		0			0
$659$	−3.19568e8			−1.11662			−0.558312	−	0.829631i	$-0.688551\pi$
$659$	−3.19568e8			−1.11662			−0.558312	+	0.829631i	$0.688551\pi$
$660$	−1.56677e8	+	2.71373e8i	−0.544972	+	0.943919i
$661$	−3.66423e8	+	2.11554e8i	−1.26876	+	0.732517i	−0.974753	−	0.223287i	$-0.928321\pi$
$661$	−3.66423e8	+	2.11554e8i	−1.26876	+	0.732517i	−0.294004	+	0.955804i	$0.594988\pi$
$662$	1.89226e8	+	3.27748e8i	0.652238	+	1.12971i
$663$	5.97617e7	+	3.45034e7i	0.205061	+	0.118392i
$664$			4.06704e7i			0.138923i
$665$		0			0
$666$	−3.53240e7			−0.119577
$667$	1.86969e8	−	3.23840e8i	0.630076	−	1.09132i
$668$	−1.16588e8	+	6.73119e7i	−0.391132	+	0.225820i
$669$	2.80502e7	+	4.85844e7i	0.0936824	+	0.162263i
$670$	2.04041e8	+	1.17803e8i	0.678411	+	0.391681i
$671$		−	4.00551e8i		−	1.32584i
$672$		0			0
$673$	−2.60395e8			−0.854256			−0.427128	−	0.904191i	$-0.640475\pi$
$673$	−2.60395e8			−0.854256			−0.427128	+	0.904191i	$0.640475\pi$
$674$	1.03864e8	−	1.79898e8i	0.339224	−	0.587553i
$675$	1.28197e7	−	7.40144e6i	0.0416836	−	0.0240660i
$676$	−6.64522e7	−	1.15099e8i	−0.215114	−	0.372589i
$677$	2.43309e8	+	1.40475e8i	0.784139	+	0.452723i	0.837895	−	0.545831i	$-0.183786\pi$
$677$	2.43309e8	+	1.40475e8i	0.784139	+	0.452723i	−0.0537564	+	0.998554i	$0.517119\pi$
$678$			8.52112e7i			0.273406i
$679$		0			0
$680$	−6.16520e7			−0.196074
$681$	−1.55457e8	+	2.69260e8i	−0.492231	+	0.852570i
$682$	−5.46559e8	+	3.15556e8i	−1.72299	+	0.994771i
$683$	−1.08581e8	−	1.88068e8i	−0.340794	−	0.590272i	0.643787	−	0.765205i	$-0.277362\pi$
$683$	−1.08581e8	−	1.88068e8i	−0.340794	−	0.590272i	−0.984580	+	0.174933i	$0.944029\pi$
$684$	−4.42858e7	−	2.55684e7i	−0.138387	−	0.0798979i
$685$		−	2.06105e8i		−	0.641233i
$686$		0			0
$687$	−6.47274e8			−1.99626
$688$	−5.83563e7	+	1.01076e8i	−0.179194	+	0.310372i
$689$	−2.36258e7	+	1.36403e7i	−0.0722318	+	0.0417031i
$690$	−1.32667e8	−	2.29786e8i	−0.403846	−	0.699481i
$691$	4.52106e8	+	2.61024e8i	1.37027	+	0.791126i	0.990962	−	0.134144i	$-0.0428285\pi$
$691$	4.52106e8	+	2.61024e8i	1.37027	+	0.791126i	0.379309	+	0.925270i	$0.376162\pi$
$692$		−	1.21436e8i		−	0.366463i
$693$		0			0
$694$	3.75359e8			1.12297
$695$	4.44509e7	−	7.69913e7i	0.132412	−	0.229344i
$696$	1.64046e8	−	9.47120e7i	0.486562	−	0.280917i
$697$	1.13204e8	+	1.96074e8i	0.334319	+	0.579058i
$698$	−4.62543e7	−	2.67050e7i	−0.136015	−	0.0785282i
$699$			1.73086e8i			0.506794i
$700$		0			0
$701$	3.81338e8			1.10702			0.553511	−	0.832842i	$-0.313288\pi$
$701$	3.81338e8			1.10702			0.553511	+	0.832842i	$0.313288\pi$
$702$	3.26792e7	−	5.66021e7i	0.0944627	−	0.163614i
$703$	−1.04607e8	+	6.03948e7i	−0.301088	+	0.173833i
$704$	−3.89687e7	−	6.74958e7i	−0.111686	−	0.193446i
$705$	−1.37376e8	−	7.93142e7i	−0.392052	−	0.226352i
$706$		−	6.22595e7i		−	0.176926i
$707$		0			0
$708$	3.41512e8			0.962291
$709$	−1.19766e8	+	2.07441e8i	−0.336043	+	0.582043i	−0.983685	−	0.179902i	$-0.942422\pi$
$709$	−1.19766e8	+	2.07441e8i	−0.336043	+	0.582043i	0.647642	+	0.761945i	$0.275755\pi$
$710$	2.05932e8	−	1.18895e8i	0.575371	−	0.332190i
$711$	−4.87256e7	−	8.43953e7i	−0.135565	−	0.234806i
$712$	−6.00781e7	−	3.46861e7i	−0.166447	−	0.0960982i
$713$		−	5.34396e8i		−	1.47433i
$714$		0			0
$715$	2.52077e8			0.689628
$716$	−2.12032e7	+	3.67251e7i	−0.0577648	+	0.100052i
$717$	2.54130e7	−	1.46722e7i	0.0689443	−	0.0398050i
$718$	1.54793e8	+	2.68109e8i	0.418194	+	0.724333i
$719$	4.18017e8	+	2.41342e8i	1.12462	+	0.649302i	0.942577	−	0.333988i	$-0.108394\pi$
$719$	4.18017e8	+	2.41342e8i	1.12462	+	0.649302i	0.182047	+	0.983290i	$0.441728\pi$
$720$		−	3.80082e7i		−	0.101831i
$721$		0			0
$722$	9.12706e7			0.242504
$723$	−3.97390e8	+	6.88299e8i	−1.05148	+	1.82122i
$724$	1.35983e8	−	7.85097e7i	0.358318	−	0.206875i
$725$	−1.72562e7	−	2.98887e7i	−0.0452827	−	0.0784319i
$726$	6.06865e8	+	3.50374e8i	1.58592	+	0.915634i
$727$			5.49464e8i			1.43000i	0.699124	+	0.715000i	$0.253574\pi$
$727$			5.49464e8i			1.43000i	−0.699124	+	0.715000i	$0.746426\pi$
$728$		0			0
$729$	−1.37966e8			−0.356115
$730$	−3.93943e7	+	6.82329e7i	−0.101266	+	0.175398i
$731$	2.60326e8	−	1.50299e8i	0.666447	−	0.384774i
$732$	8.59052e7	+	1.48792e8i	0.219021	+	0.379356i
$733$	−5.09314e8	−	2.94053e8i	−1.29322	−	0.746643i	−0.313999	−	0.949423i	$-0.601669\pi$
$733$	−5.09314e8	−	2.94053e8i	−1.29322	−	0.746643i	−0.979224	+	0.202780i	$0.935002\pi$
$734$			5.39580e8i			1.36448i
$735$		0			0
$736$	6.59938e7			0.165527
$737$	3.83553e8	−	6.64334e8i	0.958127	−	1.65952i
$738$	−1.20879e8	+	6.97895e7i	−0.300733	+	0.173628i
$739$	−3.92818e8	−	6.80381e8i	−0.973325	−	1.68585i	−0.685354	−	0.728210i	$-0.740352\pi$
$739$	−3.92818e8	−	6.80381e8i	−0.973325	−	1.68585i	−0.287972	−	0.957639i	$-0.592981\pi$
$740$	−7.77505e7	−	4.48893e7i	−0.191870	−	0.110776i
$741$			1.45473e8i			0.357542i
$742$		0			0
$743$	5.34716e8			1.30364			0.651819	−	0.758375i	$-0.274006\pi$
$743$	5.34716e8			1.30364			0.651819	+	0.758375i	$0.274006\pi$
$744$	1.35353e8	−	2.34438e8i	0.328661	−	0.569258i
$745$	7.08472e7	−	4.09037e7i	0.171338	−	0.0989221i
$746$	1.19503e8	+	2.06986e8i	0.287848	+	0.498567i
$747$	5.59253e7	+	3.22885e7i	0.134167	+	0.0774616i
$748$			2.00732e8i			0.479635i
$749$		0			0
$750$	3.39414e8			0.804536
$751$	−3.36530e8	+	5.82887e8i	−0.794518	+	1.37615i	0.128626	+	0.991693i	$0.458943\pi$
$751$	−3.36530e8	+	5.82887e8i	−0.794518	+	1.37615i	−0.923145	+	0.384453i	$0.874390\pi$
$752$	3.41682e7	−	1.97270e7i	0.0803467	−	0.0463882i
$753$	1.43622e8	+	2.48761e8i	0.336385	+	0.582636i
$754$	−1.31966e8	−	7.61907e7i	−0.307857	−	0.177741i
$755$		−	3.22059e8i		−	0.748332i
$756$		0			0
$757$	−4.17395e8			−0.962188			−0.481094	−	0.876669i	$-0.659760\pi$
$757$	−4.17395e8			−0.962188			−0.481094	+	0.876669i	$0.659760\pi$
$758$	−8.27136e7	+	1.43264e8i	−0.189919	+	0.328950i
$759$	−7.48156e8	+	4.31948e8i	−1.71107	+	0.987885i
$760$	−6.49840e7	−	1.12556e8i	−0.148035	−	0.256405i
$761$	3.96918e8	+	2.29161e8i	0.900631	+	0.519980i	0.877405	−	0.479751i	$-0.159273\pi$
$761$	3.96918e8	+	2.29161e8i	0.900631	+	0.519980i	0.0232261	+	0.999730i	$0.492606\pi$
$762$			1.14018e8i			0.257697i
$763$		0			0
$764$	−2.01850e8			−0.452636
$765$	−4.89459e7	+	8.47768e7i	−0.109328	+	0.189362i
$766$	1.43666e8	−	8.29457e7i	0.319645	−	0.184547i
$767$	−1.37364e8	−	2.37922e8i	−0.304430	−	0.527288i
$768$	2.89513e7	+	1.67150e7i	0.0639123	+	0.0368998i
$769$		−	4.67013e8i		−	1.02695i	−0.858104	−	0.513475i	$-0.828358\pi$
$769$		−	4.67013e8i		−	1.02695i	0.858104	−	0.513475i	$-0.171642\pi$
$770$		0			0
$771$	5.59692e8			1.22120
$772$	−1.39986e7	+	2.42462e7i	−0.0304250	+	0.0526977i
$773$	4.73930e7	−	2.73624e7i	0.102607	−	0.0592400i	−0.447819	−	0.894124i	$-0.647799\pi$
$773$	4.73930e7	−	2.73624e7i	0.102607	−	0.0592400i	0.550425	+	0.834884i	$0.314466\pi$
$774$	9.26589e7	+	1.60490e8i	0.199832	+	0.346119i
$775$	−4.27139e7	−	2.46609e7i	−0.0917623	−	0.0529790i
$776$		−	5.91284e6i		−	0.0126535i
$777$		0			0
$778$	−5.88688e8			−1.25010
$779$	−2.38643e8	+	4.13342e8i	−0.504820	+	0.874375i
$780$	−9.36387e7	+	5.40623e7i	−0.197320	+	0.113923i
$781$	−3.87107e8	−	6.70489e8i	−0.812602	−	1.40747i
$782$	−1.47198e8	−	8.49851e7i	−0.307810	−	0.177714i
$783$			4.62077e8i			0.962563i
$784$		0			0
$785$	3.32584e8			0.687530
$786$	−1.16544e7	+	2.01860e7i	−0.0240006	+	0.0415703i
$787$	−3.05483e8	+	1.76371e8i	−0.626704	+	0.361828i	−0.779475	−	0.626434i	$-0.784514\pi$
$787$	−3.05483e8	+	1.76371e8i	−0.626704	+	0.361828i	0.152770	+	0.988262i	$0.451181\pi$
$788$	1.09667e8	+	1.89949e8i	0.224129	+	0.388204i
$789$	−2.22029e8	−	1.28188e8i	−0.452041	−	0.260986i
$790$		−	2.47680e8i		−	0.502353i
$791$		0			0
$792$	−1.23750e8			−0.249098
$793$	6.91062e7	−	1.19695e8i	0.138579	−	0.240026i
$794$	3.43211e8	−	1.98153e8i	0.685645	−	0.395858i
$795$	−6.84275e7	−	1.18520e8i	−0.136185	−	0.235879i
$796$	2.63837e8	+	1.52326e8i	0.523114	+	0.302020i
$797$			6.57525e8i			1.29879i	0.760453	+	0.649393i	$0.224977\pi$
$797$			6.57525e8i			1.29879i	−0.760453	+	0.649393i	$0.775023\pi$
$798$		0			0
$799$	−1.01616e8			−0.199214
$800$	3.04543e6	−	5.27484e6i	0.00594811	−	0.0103024i
$801$	−9.53928e7	+	5.50751e7i	−0.185617	+	0.107166i
$802$	−2.17642e8	−	3.76967e8i	−0.421909	−	0.730769i
$803$	2.22159e8	+	1.28263e8i	0.429058	+	0.247717i
$804$			3.29039e8i			0.633110i
$805$		0			0
$806$	−2.17768e8			−0.415901
$807$	2.59862e8	−	4.50095e8i	0.494450	−	0.856413i
$808$	7.83819e7	−	4.52538e7i	0.148587	−	0.0857869i
$809$	3.44264e8	+	5.96282e8i	0.650198	+	1.12618i	0.983075	+	0.183206i	$0.0586475\pi$
$809$	3.44264e8	+	5.96282e8i	0.650198	+	1.12618i	−0.332876	+	0.942971i	$0.608019\pi$
$810$	4.16507e8	+	2.40470e8i	0.783730	+	0.452487i
$811$		−	4.12718e8i		−	0.773732i	−0.922136	−	0.386866i	$-0.873558\pi$
$811$		−	4.12718e8i		−	0.773732i	0.922136	−	0.386866i	$-0.126442\pi$
$812$		0			0
$813$	−9.86353e8			−1.83553
$814$	−1.46154e8	+	2.53147e8i	−0.270981	+	0.469352i
$815$	−9.79368e7	+	5.65438e7i	−0.180914	+	0.104451i
$816$	−4.30504e7	−	7.45655e7i	−0.0792331	−	0.137236i
$817$	5.48792e8	+	3.16845e8i	1.00633	+	0.581006i
$818$		−	2.29029e8i		−	0.418437i
$819$		0			0
$820$	−3.54750e8			−0.643400
$821$	1.98839e8	−	3.44399e8i	0.359312	−	0.622347i	−0.628534	−	0.777782i	$-0.716345\pi$
$821$	1.98839e8	−	3.44399e8i	0.359312	−	0.622347i	0.987846	+	0.155435i	$0.0496780\pi$
$822$	2.49275e8	−	1.43919e8i	0.448811	−	0.259121i
$823$	1.08211e8	+	1.87427e8i	0.194121	+	0.336228i	0.946612	−	0.322375i	$-0.104481\pi$
$823$	1.08211e8	+	1.87427e8i	0.194121	+	0.336228i	−0.752491	+	0.658603i	$0.771148\pi$
$824$	−6.99185e7	−	4.03675e7i	−0.124971	−	0.0721523i
$825$			7.97329e7i			0.141996i
$826$		0			0
$827$	4.58785e8			0.811134			0.405567	−	0.914065i	$-0.367074\pi$
$827$	4.58785e8			0.811134			0.405567	+	0.914065i	$0.367074\pi$
$828$	5.23929e7	−	9.07472e7i	0.0922957	−	0.159861i
$829$	−6.95641e8	+	4.01628e8i	−1.22102	+	0.704954i	−0.965135	−	0.261754i	$-0.915699\pi$
$829$	−6.95641e8	+	4.01628e8i	−1.22102	+	0.704954i	−0.255881	+	0.966708i	$0.582366\pi$
$830$	8.20636e7	+	1.42138e8i	0.143521	+	0.248586i
$831$	−3.70417e8	−	2.13861e8i	−0.645488	−	0.372673i
$832$		−	2.68927e7i		−	0.0466944i
$833$		0			0
$834$	1.24157e8			0.214029
$835$	−2.71640e8	+	4.70495e8i	−0.466589	+	0.808156i
$836$	−3.66468e8	+	2.11580e8i	−0.627216	+	0.362123i
$837$	3.30177e8	+	5.71884e8i	0.563081	+	0.975284i
$838$	−2.46399e8	−	1.42259e8i	−0.418704	−	0.241739i
$839$			1.09867e9i			1.86030i	0.367185	+	0.930148i	$0.380322\pi$
$839$			1.09867e9i			1.86030i	−0.367185	+	0.930148i	$0.619678\pi$
$840$		0			0
$841$	4.82497e8			0.811160
$842$	−4.55499e6	+	7.88947e6i	−0.00763046	+	0.0132163i
$843$	3.24009e7	−	1.87066e7i	0.0540846	−	0.0312258i
$844$	1.63971e8	+	2.84007e8i	0.272735	+	0.472390i
$845$	−4.64485e8	−	2.68171e8i	−0.769842	−	0.444469i
$846$		−	6.26456e7i		−	0.103462i
$847$		0			0
$848$	3.40385e7			0.0558191
$849$	−4.50725e8	+	7.80679e8i	−0.736527	+	1.27570i
$850$	−1.35856e7	+	7.84365e6i	−0.0221219	+	0.0127721i
$851$	−1.23757e8	−	2.14353e8i	−0.200807	−	0.347808i
$852$	2.87596e8	+	1.66044e8i	0.465012	+	0.268475i
$853$		−	8.99416e8i		−	1.44915i	−0.689196	−	0.724575i	$-0.742036\pi$
$853$		−	8.99416e8i		−	1.44915i	0.689196	−	0.724575i	$-0.257964\pi$
$854$		0			0
$855$	−2.06365e8			−0.330170
$856$	1.71015e8	−	2.96207e8i	0.272655	−	0.472253i
$857$	−8.09008e8	+	4.67081e8i	−1.28532	+	0.742078i	−0.977815	−	0.209470i	$-0.932826\pi$
$857$	−8.09008e8	+	4.67081e8i	−1.28532	+	0.742078i	−0.307501	+	0.951548i	$0.599493\pi$
$858$	1.76021e8	+	3.04877e8i	0.278677	+	0.482683i
$859$	−3.89837e8	−	2.25073e8i	−0.615041	−	0.355094i	0.159895	−	0.987134i	$-0.448884\pi$
$859$	−3.89837e8	−	2.25073e8i	−0.615041	−	0.355094i	−0.774936	+	0.632040i	$0.782218\pi$
$860$			4.70999e8i			0.740499i
$861$		0			0
$862$	3.90494e8			0.609667
$863$	−2.32956e8	+	4.03492e8i	−0.362445	+	0.627773i	−0.988363	−	0.152116i	$-0.951391\pi$
$863$	−2.32956e8	+	4.03492e8i	−0.362445	+	0.627773i	0.625918	+	0.779889i	$0.284725\pi$
$864$	−7.06233e7	+	4.07744e7i	−0.109498	+	0.0632187i
$865$	−2.45031e8	−	4.24406e8i	−0.378593	−	0.655742i
$866$	−3.87736e8	−	2.23859e8i	−0.597011	−	0.344684i
$867$		−	5.47783e8i		−	0.840527i
$868$		0			0
$869$	−8.06416e8			−1.22885
$870$	3.82215e8	−	6.62015e8i	0.580430	−	1.00533i
$871$	2.29232e8	−	1.32347e8i	0.346913	−	0.200290i
$872$	1.73947e8	+	3.01285e8i	0.262342	+	0.454389i
$873$	−8.13067e6	−	4.69424e6i	−0.0122203	−	0.00705542i
$874$		−	3.58313e8i		−	0.536695i
$875$		0			0
$876$	−1.10033e8			−0.163686
$877$	−1.87763e8	+	3.25216e8i	−0.278363	+	0.482140i	−0.970978	−	0.239168i	$-0.923125\pi$
$877$	−1.87763e8	+	3.25216e8i	−0.278363	+	0.482140i	0.692615	+	0.721308i	$0.256459\pi$
$878$	1.18248e8	−	6.82706e7i	0.174707	−	0.100867i
$879$	8.89745e7	+	1.54108e8i	0.131008	+	0.226913i
$880$	−2.72382e8	−	1.57260e8i	−0.399697	−	0.230765i
$881$		−	6.74362e8i		−	0.986201i	−0.869972	−	0.493101i	$-0.835863\pi$
$881$		−	6.74362e8i		−	0.986201i	0.869972	−	0.493101i	$-0.164137\pi$
$882$		0			0
$883$	1.23657e9			1.79612			0.898061	−	0.439871i	$-0.144976\pi$
$883$	1.23657e9			1.79612			0.898061	+	0.439871i	$0.144976\pi$
$884$	−3.46317e7	+	5.99839e7i	−0.0501323	+	0.0868317i
$885$	1.19355e9	−	6.89094e8i	1.72191	−	0.994143i
$886$	−1.33221e8	−	2.30746e8i	−0.191545	−	0.331766i
$887$	−4.15490e8	−	2.39883e8i	−0.595374	−	0.343739i	0.171846	−	0.985124i	$-0.445027\pi$
$887$	−4.15490e8	−	2.39883e8i	−0.595374	−	0.343739i	−0.767219	+	0.641385i	$0.778360\pi$
$888$		−	1.25381e8i		−	0.179058i
$889$		0			0
$890$	−2.79955e8			−0.397116
$891$	7.82943e8	−	1.35610e9i	1.10687	−	1.91716i
$892$	−4.87651e7	+	2.81545e7i	−0.0687091	+	0.0396692i
$893$	−1.07108e8	−	1.85516e8i	−0.150406	−	0.260511i
$894$	9.89426e7	+	5.71245e7i	0.138475	+	0.0799485i
$895$			1.71133e8i			0.238707i
$896$		0			0
$897$	−2.98092e8			−0.413022
$898$	1.32857e7	−	2.30115e7i	0.0183466	−	0.0317772i
$899$	1.33333e9	−	7.69799e8i	1.83510	−	1.05949i
$900$	−4.83558e6	−	8.37547e6i	−0.00663316	−	0.0114890i
$901$	−7.59226e7	−	4.38339e7i	−0.103800	−	0.0599289i
$902$			1.15503e9i			1.57388i
$903$		0			0
$904$	−8.55281e7			−0.115772
$905$	3.16829e8	−	5.48765e8i	0.427444	−	0.740355i
$906$	3.89517e8	−	2.24888e8i	0.523771	−	0.302399i
$907$	2.16162e6	+	3.74403e6i	0.00289705	+	0.00501784i	0.867470	−	0.497489i	$-0.165745\pi$
$907$	2.16162e6	+	3.74403e6i	0.00289705	+	0.00501784i	−0.864573	+	0.502507i	$0.832411\pi$
$908$	−2.70261e8	−	1.56035e8i	−0.361016	−	0.208432i
$909$		−	1.43709e8i		−	0.191334i
$910$		0			0
$911$	−4.54738e8			−0.601459			−0.300730	−	0.953709i	$-0.597230\pi$
$911$	−4.54738e8			−0.601459			−0.300730	+	0.953709i	$0.597230\pi$
$912$	9.07542e7	−	1.57191e8i	0.119642	−	0.207225i
$913$	4.62786e8	−	2.67190e8i	0.608090	−	0.351081i
$914$	−3.34594e8	−	5.79533e8i	−0.438207	−	0.758997i
$915$	6.00458e8	+	3.46675e8i	0.783825	+	0.452542i
$916$		−	6.49681e8i		−	0.845306i
$917$		0			0
$918$	2.10033e8			0.271493
$919$	3.08907e8	−	5.35042e8i	0.397998	−	0.689353i	−0.595481	−	0.803369i	$-0.703038\pi$
$919$	3.08907e8	−	5.35042e8i	0.397998	−	0.689353i	0.993479	+	0.114017i	$0.0363718\pi$
$920$	2.30641e8	−	1.33160e8i	0.296191	−	0.171006i
$921$	−7.02677e8	−	1.21707e9i	−0.899450	−	1.55789i
$922$	8.41729e8	+	4.85972e8i	1.07394	+	0.620039i
$923$		−	2.67147e8i		−	0.339738i
$924$		0			0
$925$	−2.28441e7			−0.0288635
$926$	−1.29745e8	+	2.24724e8i	−0.163402	+	0.283020i
$927$	−1.11018e8	+	6.40960e7i	−0.139365	+	0.0804622i
$928$	9.50643e7	+	1.64656e8i	0.118952	+	0.206032i
$929$	6.08765e8	+	3.51471e8i	0.759282	+	0.438371i	0.829038	−	0.559193i	$-0.188889\pi$
$929$	6.08765e8	+	3.51471e8i	0.759282	+	0.438371i	−0.0697562	+	0.997564i	$0.522222\pi$
$930$		−	1.09245e9i		−	1.35816i
$931$		0			0
$932$	−1.73730e8			−0.214599
$933$	4.49563e8	−	7.78666e8i	0.553536	−	0.958752i
$934$	6.35671e7	−	3.67005e7i	0.0780174	−	0.0450434i
$935$	4.05031e8	+	7.01534e8i	0.495511	+	0.858250i
$936$	−3.69798e7	−	2.13503e7i	−0.0450959	−	0.0260361i
$937$			2.35920e8i			0.286779i	0.989666	+	0.143389i	$0.0458001\pi$
$937$			2.35920e8i			0.286779i	−0.989666	+	0.143389i	$0.954200\pi$
$938$		0			0
$939$	−1.89023e8			−0.228306
$940$	7.96092e7	−	1.37887e8i	0.0958472	−	0.166012i
$941$	3.18894e8	−	1.84114e8i	0.382717	−	0.220962i	−0.296283	−	0.955100i	$-0.595747\pi$
$941$	3.18894e8	−	1.84114e8i	0.382717	−	0.220962i	0.679000	+	0.734139i	$0.262414\pi$
$942$	2.32237e8	+	4.02246e8i	0.277830	+	0.481215i
$943$	−8.46991e8	−	4.89010e8i	−1.01005	−	0.583154i
$944$			3.42783e8i			0.407477i
$945$		0			0
$946$	1.53352e9			1.81140
$947$	−3.01831e8	+	5.22786e8i	−0.355397	+	0.615566i	−0.987186	−	0.159575i	$-0.948988\pi$
$947$	−3.01831e8	+	5.22786e8i	−0.355397	+	0.615566i	0.631789	+	0.775141i	$0.282321\pi$
$948$	2.99558e8	−	1.72950e8i	0.351606	−	0.203000i
$949$	4.42579e7	+	7.66569e7i	0.0517836	+	0.0896918i
$950$	−2.86397e7	−	1.65351e7i	−0.0334039	−	0.0192858i
$951$		−	1.44417e9i		−	1.67910i
$952$		0			0
$953$	2.87119e8			0.331729			0.165864	−	0.986149i	$-0.446959\pi$
$953$	2.87119e8			0.331729			0.165864	+	0.986149i	$0.446959\pi$
$954$	2.70234e7	−	4.68059e7i	0.0311240	−	0.0539083i
$955$	−7.05443e8	+	4.07288e8i	−0.809938	+	0.467618i
$956$	1.47268e7	+	2.55075e7i	0.0168552	+	0.0291941i
$957$	−2.15544e9	−	1.24445e9i	−2.45924	−	1.41984i
$958$			1.30652e8i			0.148600i
$959$		0			0
$960$	1.34909e8			0.152485
$961$	6.56367e8	−	1.13686e9i	0.739566	−	1.28097i
$962$	−8.73495e7	+	5.04313e7i	−0.0981150	+	0.0566467i
$963$	−2.71541e8	−	4.70322e8i	−0.304058	−	0.526643i
$964$	−6.90859e8	−	3.98868e8i	−0.771185	−	0.445244i
$965$			1.12984e8i			0.125728i
$966$		0			0
$967$	−7.68357e8			−0.849735			−0.424868	−	0.905256i	$-0.639679\pi$
$967$	−7.68357e8			−0.849735			−0.424868	+	0.905256i	$0.639679\pi$
$968$	−3.51677e8	+	6.09123e8i	−0.387720	+	0.671550i
$969$	−4.04853e8	+	2.33742e8i	−0.444965	+	0.256901i
$970$	−1.19308e7	−	2.06647e7i	−0.0130723	−	0.0226419i
$971$	7.15458e8	+	4.13070e8i	0.781496	+	0.451197i	0.836960	−	0.547264i	$-0.184331\pi$
$971$	7.15458e8	+	4.13070e8i	0.781496	+	0.451197i	−0.0554643	+	0.998461i	$0.517664\pi$
$972$			3.43251e8i			0.373777i
$973$		0			0
$974$	−1.89036e8			−0.204582
$975$	−1.37561e7	+	2.38263e7i	−0.0148417	+	0.0257065i
$976$	−1.49346e8	+	8.62248e7i	−0.160636	+	0.0927433i
$977$	4.17857e8	+	7.23750e8i	0.448068	+	0.776077i	0.998260	−	0.0589610i	$-0.0187788\pi$
$977$	4.17857e8	+	7.23750e8i	0.448068	+	0.776077i	−0.550192	+	0.835038i	$0.685445\pi$
$978$	−1.36775e8	−	7.89670e7i	−0.146214	−	0.0844168i
$979$			9.11500e8i			0.971423i
$980$		0			0
$981$	5.52390e8			0.585112
$982$	−5.54893e8	+	9.61103e8i	−0.585969	+	1.01493i
$983$	−1.91250e8	+	1.10418e8i	−0.201345	+	0.116247i	−0.597283	−	0.802031i	$-0.703753\pi$
$983$	−1.91250e8	+	1.10418e8i	−0.201345	+	0.116247i	0.395938	+	0.918277i	$0.370420\pi$
$984$	−2.47715e8	−	4.29056e8i	−0.259997	−	0.450327i
$985$	7.66550e8	+	4.42568e8i	0.802106	+	0.463096i
$986$		−	4.89685e8i		−	0.510842i
$987$		0			0
$988$	−1.46014e8			−0.151399
$989$	−6.49256e8	+	1.12454e9i	−0.671161	+	1.16249i
$990$	−4.32493e8	+	2.49700e8i	−0.445731	+	0.257343i
$991$	3.64147e8	+	6.30721e8i	0.374158	+	0.648061i	0.990201	−	0.139652i	$-0.0445983\pi$
$991$	3.64147e8	+	6.30721e8i	0.374158	+	0.648061i	−0.616042	+	0.787713i	$0.711265\pi$
$992$	2.35310e8	+	1.35856e8i	0.241049	+	0.139170i
$993$			2.13291e9i			2.17834i
$994$		0			0
$995$	1.22944e9			1.24807
$996$	−1.14607e8	+	1.98505e8i	−0.115993	+	0.200906i
$997$	1.47059e8	−	8.49047e7i	0.148391	−	0.0856735i	−0.423966	−	0.905678i	$-0.639362\pi$
$997$	1.47059e8	−	8.49047e7i	0.148391	−	0.0856735i	0.572357	+	0.820005i	$0.306029\pi$
$998$	−2.62307e8	−	4.54328e8i	−0.263887	−	0.457065i
$999$	2.64876e8	+	1.52926e8i	0.265672	+	0.153386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.7.d.c.19.1		8
7.2	even	3		98.7.b.c.97.5		8
7.3	odd	6	inner	98.7.d.c.31.1		8
7.4	even	3		14.7.d.a.3.2	✓	8
7.5	odd	6		98.7.b.c.97.8		8
7.6	odd	2		14.7.d.a.5.2	yes	8
21.11	odd	6		126.7.n.c.73.3		8
21.20	even	2		126.7.n.c.19.3		8
28.11	odd	6		112.7.s.c.17.1		8
28.27	even	2		112.7.s.c.33.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.d.a.3.2	✓	8	7.4	even	3
14.7.d.a.5.2	yes	8	7.6	odd	2
98.7.b.c.97.5		8	7.2	even	3
98.7.b.c.97.8		8	7.5	odd	6
98.7.d.c.19.1		8	1.1	even	1	trivial
98.7.d.c.31.1		8	7.3	odd	6	inner
112.7.s.c.17.1		8	28.11	odd	6
112.7.s.c.33.1		8	28.27	even	2
126.7.n.c.19.3		8	21.20	even	2
126.7.n.c.73.3		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.82843 + 4.89898i) q^{2} +(-27.6101 + 15.9407i) q^{3} +(-16.0000 - 27.7128i) q^{4} +(-111.836 - 64.5687i) q^{5} -180.349i q^{6} +181.019 q^{8} +(143.713 - 248.917i) q^{9} +(632.642 - 365.256i) q^{10} +(-1189.23 - 2059.81i) q^{11} +(883.524 + 510.103i) q^{12} -820.701i q^{13} +4117.09 q^{15} +(-512.000 + 886.810i) q^{16} +(2284.02 - 1318.68i) q^{17} +(812.961 + 1408.09i) q^{18} +(4814.93 + 2779.90i) q^{19} +4132.40i q^{20} +13454.6 q^{22} +(-5696.37 + 9866.40i) q^{23} +(-4997.97 + 2885.58i) q^{24} +(525.743 + 910.614i) q^{25} +(4020.60 + 2321.29i) q^{26} -14078.0i q^{27} -32822.6 q^{29} +(-11644.9 + 20169.5i) q^{30} +(-40622.4 + 23453.4i) q^{31} +(-2896.31 - 5016.55i) q^{32} +(65669.6 + 37914.4i) q^{33} +14919.2i q^{34} -9197.60 q^{36} +(-10862.8 + 18814.9i) q^{37} +(-27237.3 + 15725.5i) q^{38} +(13082.5 + 22659.6i) q^{39} +(-20244.5 - 11688.2i) q^{40} +85846.0i q^{41} +113977. q^{43} +(-38055.4 + 65913.9i) q^{44} +(-32144.6 + 18558.7i) q^{45} +(-32223.5 - 55812.8i) q^{46} +(-33367.3 - 19264.6i) q^{47} -32646.6i q^{48} -5948.11 q^{50} +(-42041.4 + 72817.9i) q^{51} +(-22743.9 + 13131.2i) q^{52} +(-16620.4 - 28787.3i) q^{53} +(68968.0 + 39818.7i) q^{54} +307149. i q^{55} -177254. q^{57} +(92836.2 - 160797. i) q^{58} +(289901. - 167374. i) q^{59} +(-65873.4 - 114096. i) q^{60} +(145845. + 84203.9i) q^{61} -265344. i q^{62} +32768.0 q^{64} +(-52991.6 + 91784.1i) q^{65} +(-371483. + 214476. i) q^{66} +(161261. + 279312. i) q^{67} +(-73088.7 - 42197.8i) q^{68} -363217. i q^{69} +325510. q^{71} +(26014.7 - 45058.9i) q^{72} +(-93404.3 + 53927.0i) q^{73} +(-61449.1 - 106433. i) q^{74} +(-29031.7 - 16761.4i) q^{75} -177914. i q^{76} -148012. q^{78} +(169525. - 293625. i) q^{79} +(114520. - 66118.4i) q^{80} +(329180. + 570157. i) q^{81} +(-420558. - 242809. i) q^{82} +224674. i q^{83} -340582. q^{85} +(-322376. + 558372. i) q^{86} +(906235. - 523215. i) q^{87} +(-215274. - 372865. i) q^{88} +(-331888. - 191615. i) q^{89} -209967. i q^{90} +364567. q^{92} +(747726. - 1.29510e6i) q^{93} +(188754. - 108977. i) q^{94} +(-358989. - 621787. i) q^{95} +(159935. + 92338.5i) q^{96} -32664.1i q^{97} -683629. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 128 q^{4} + 336 q^{5} + 756 q^{9} + 2016 q^{10} - 1356 q^{11} + 27144 q^{15} - 4096 q^{16} + 17304 q^{17} - 6816 q^{18} + 32004 q^{19} + 25248 q^{22} - 4128 q^{23} - 10752 q^{24} + 4664 q^{25} + 4704 q^{26}+ \cdots - 4625928 q^{99}+O(q^{100}) \) 8 * q - 128 * q^4 + 336 * q^5 + 756 * q^9 + 2016 * q^10 - 1356 * q^11 + 27144 * q^15 - 4096 * q^16 + 17304 * q^17 - 6816 * q^18 + 32004 * q^19 + 25248 * q^22 - 4128 * q^23 - 10752 * q^24 + 4664 * q^25 + 4704 * q^26 - 30312 * q^29 + 9648 * q^30 + 3108 * q^31 - 3276 * q^33 - 48384 * q^36 - 6124 * q^37 - 155568 * q^38 + 100764 * q^39 - 64512 * q^40 - 297376 * q^43 - 43392 * q^44 + 172116 * q^45 - 194064 * q^46 - 313908 * q^47 + 38784 * q^50 + 253692 * q^51 - 255360 * q^52 + 278484 * q^53 - 386064 * q^54 - 81288 * q^57 - 169824 * q^58 + 835464 * q^59 - 434304 * q^60 + 995316 * q^61 + 262144 * q^64 + 8316 * q^65 - 1673280 * q^66 + 648808 * q^67 - 553728 * q^68 + 190128 * q^71 - 218112 * q^72 + 1617084 * q^73 - 1158144 * q^74 + 2042208 * q^75 + 1122432 * q^78 + 70096 * q^79 - 344064 * q^80 + 1177920 * q^81 - 66528 * q^82 + 2190984 * q^85 - 573024 * q^86 + 2057076 * q^87 - 403968 * q^88 - 739116 * q^89 + 264192 * q^92 - 23364 * q^93 - 3795120 * q^94 + 725640 * q^95 + 344064 * q^96 - 4625928 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more