LMFDB - Embedded newform 126.7.n.c.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,7,Mod(19,126)] 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("126.19"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-128,336] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$28.9868145361$
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:	$\Z[a_1, \ldots, a_{13}]$
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			19.3
Root			$-4.86132 + 8.42006i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.7.n.c.73.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.82843 - 4.89898i) q^{2} +(-16.0000 - 27.7128i) q^{4} +(-111.836 - 64.5687i) q^{5} +(298.743 + 168.528i) q^{7} -181.019 q^{8} +(-632.642 + 365.256i) q^{10} +(1189.23 + 2059.81i) q^{11} +820.701i q^{13} +(1670.59 - 986.866i) q^{14} +(-512.000 + 886.810i) q^{16} +(2284.02 - 1318.68i) q^{17} +(-4814.93 - 2779.90i) q^{19} +4132.40i q^{20} +13454.6 q^{22} +(5696.37 - 9866.40i) q^{23} +(525.743 + 910.614i) q^{25} +(4020.60 + 2321.29i) q^{26} +(-109.502 - 10975.5i) q^{28} +32822.6 q^{29} +(40622.4 - 23453.4i) q^{31} +(2896.31 + 5016.55i) q^{32} -14919.2i q^{34} +(-22528.7 - 38137.0i) q^{35} +(-10862.8 + 18814.9i) q^{37} +(-27237.3 + 15725.5i) q^{38} +(20244.5 + 11688.2i) q^{40} +85846.0i q^{41} +113977. q^{43} +(38055.4 - 65913.9i) q^{44} +(-32223.5 - 55812.8i) q^{46} +(-33367.3 - 19264.6i) q^{47} +(60845.6 + 100693. i) q^{49} +5948.11 q^{50} +(22743.9 - 13131.2i) q^{52} +(16620.4 + 28787.3i) q^{53} -307149. i q^{55} +(-54078.2 - 30506.8i) q^{56} +(92836.2 - 160797. i) q^{58} +(289901. - 167374. i) q^{59} +(-145845. - 84203.9i) q^{61} -265344. i q^{62} +32768.0 q^{64} +(52991.6 - 91784.1i) q^{65} +(161261. + 279312. i) q^{67} +(-73088.7 - 42197.8i) q^{68} +(-250553. + 2499.76i) q^{70} -325510. q^{71} +(93404.3 - 53927.0i) q^{73} +(61449.1 + 106433. i) q^{74} +177914. i q^{76} +(8138.93 + 815772. i) q^{77} +(169525. - 293625. i) q^{79} +(114520. - 66118.4i) q^{80} +(420558. + 242809. i) q^{82} +224674. i q^{83} -340582. q^{85} +(322376. - 558372. i) q^{86} +(-215274. - 372865. i) q^{88} +(-331888. - 191615. i) q^{89} +(-138311. + 245178. i) q^{91} -364567. q^{92} +(-188754. + 108977. i) q^{94} +(358989. + 621787. i) q^{95} +32664.1i q^{97} +(665391. - 13278.5i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 128 q^{4} + 336 q^{5} + 652 q^{7} - 2016 q^{10} + 1356 q^{11} - 2064 q^{14} - 4096 q^{16} + 17304 q^{17} - 32004 q^{19} + 25248 q^{22} + 4128 q^{23} + 4664 q^{25} + 4704 q^{26} - 7552 q^{28} + 30312 q^{29}+ \cdots + 3532320 q^{98}+O(q^{100}) $ 8 * q - 128 * q^4 + 336 * q^5 + 652 * q^7 - 2016 * q^10 + 1356 * q^11 - 2064 * q^14 - 4096 * q^16 + 17304 * q^17 - 32004 * q^19 + 25248 * q^22 + 4128 * q^23 + 4664 * q^25 + 4704 * q^26 - 7552 * q^28 + 30312 * q^29 - 3108 * q^31 - 98028 * q^35 - 6124 * q^37 - 155568 * q^38 + 64512 * q^40 - 297376 * q^43 + 43392 * q^44 - 194064 * q^46 - 313908 * q^47 + 32432 * q^49 - 38784 * q^50 + 255360 * q^52 - 278484 * q^53 + 125952 * q^56 - 169824 * q^58 + 835464 * q^59 - 995316 * q^61 + 262144 * q^64 - 8316 * q^65 + 648808 * q^67 - 553728 * q^68 - 1572816 * q^70 - 190128 * q^71 - 1617084 * q^73 + 1158144 * q^74 - 1456224 * q^77 + 70096 * q^79 - 344064 * q^80 + 66528 * q^82 + 2190984 * q^85 + 573024 * q^86 - 403968 * q^88 - 739116 * q^89 + 2233752 * q^91 - 264192 * q^92 + 3795120 * q^94 - 725640 * q^95 + 3532320 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$		0			0
$3$		0			0
$4$	−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	$0.839451\pi$
$6$		0			0
$7$	298.743	+	168.528i	0.870971	+	0.491335i
$7$	298.743	+	168.528i	0.870971	+	0.491335i
$8$	−181.019			−0.353553
$9$		0			0
$10$	−632.642	+	365.256i	−0.632642	+	0.365256i
$11$	1189.23	+	2059.81i	0.893487	+	1.54756i	0.835666	+	0.549237i	$0.185082\pi$
$11$	1189.23	+	2059.81i	0.893487	+	1.54756i	0.0578204	+	0.998327i	$0.481585\pi$
$12$		0			0
$13$			820.701i			0.373555i	0.982402	+	0.186778i	$0.0598044\pi$
$13$			820.701i			0.373555i	−0.982402	+	0.186778i	$0.940196\pi$
$14$	1670.59	−	986.866i	0.608815	−	0.359645i
$15$		0			0
$16$	−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	$0.246836\pi$
$18$		0			0
$19$	−4814.93	−	2779.90i	−0.701987	−	0.405292i	0.106100	−	0.994355i	$-0.466164\pi$
$19$	−4814.93	−	2779.90i	−0.701987	−	0.405292i	−0.808087	+	0.589063i	$0.799497\pi$
$20$			4132.40i			0.516550i
$21$		0			0
$22$	13454.6			1.26358
$23$	5696.37	−	9866.40i	0.468182	−	0.810914i	−0.531157	−	0.847273i	$-0.678243\pi$
$23$	5696.37	−	9866.40i	0.468182	−	0.810914i	0.999339	+	0.0363589i	$0.0115759\pi$
$24$		0			0
$25$	525.743	+	910.614i	0.0336476	+	0.0582793i
$26$	4020.60	+	2321.29i	0.228755	+	0.132072i
$27$		0			0
$28$	−109.502	−	10975.5i	−0.00498823	−	0.499975i
$29$	32822.6			1.34579			0.672897	−	0.739736i	$-0.265050\pi$
$29$	32822.6			1.34579			0.672897	+	0.739736i	$0.265050\pi$
$30$		0			0
$31$	40622.4	−	23453.4i	1.36358	−	0.787263i	0.373481	−	0.927638i	$-0.378164\pi$
$31$	40622.4	−	23453.4i	1.36358	−	0.787263i	0.990098	+	0.140375i	$0.0448308\pi$
$32$	2896.31	+	5016.55i	0.0883883	+	0.153093i
$33$		0			0
$34$		−	14919.2i		−	0.379584i
$35$	−22528.7	−	38137.0i	−0.525450	−	0.889493i
$36$		0			0
$37$	−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
$39$		0			0
$40$	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
$45$		0			0
$46$	−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	$0.726074\pi$
$48$		0			0
$49$	60845.6	+	100693.i	0.517179	+	0.855877i
$50$	5948.11			0.0475849
$51$		0			0
$52$	22743.9	−	13131.2i	0.161754	−	0.0933888i
$53$	16620.4	+	28787.3i	0.111638	+	0.193363i	0.916431	−	0.400193i	$-0.131057\pi$
$53$	16620.4	+	28787.3i	0.111638	+	0.193363i	−0.804793	+	0.593556i	$0.797724\pi$
$54$		0			0
$55$		−	307149.i		−	1.84612i
$56$	−54078.2	−	30506.8i	−0.307935	−	0.173713i
$57$		0			0
$58$	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	$0.0300959\pi$
$60$		0			0
$61$	−145845.	−	84203.9i	−0.642544	−	0.370973i	0.143050	−	0.989716i	$-0.454309\pi$
$61$	−145845.	−	84203.9i	−0.642544	−	0.370973i	−0.785594	+	0.618742i	$0.787642\pi$
$62$		−	265344.i		−	1.11336i
$63$		0			0
$64$	32768.0			0.125000
$65$	52991.6	−	91784.1i	0.192960	−	0.334216i
$66$		0			0
$67$	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
$69$		0			0
$70$	−250553.	+	2499.76i	−0.730476	+	0.00728793i
$71$	−325510.			−0.909473			−0.454737	−	0.890626i	$-0.650267\pi$
$71$	−325510.			−0.909473			−0.454737	+	0.890626i	$0.650267\pi$
$72$		0			0
$73$	93404.3	−	53927.0i	0.240103	−	0.138624i	−0.375121	−	0.926976i	$-0.622399\pi$
$73$	93404.3	−	53927.0i	0.240103	−	0.138624i	0.615224	+	0.788352i	$0.289065\pi$
$74$	61449.1	+	106433.i	0.151642	+	0.262652i
$75$		0			0
$76$			177914.i			0.405292i
$77$	8138.93	+	815772.i	0.0178277	+	1.78688i
$78$		0			0
$79$	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
$81$		0			0
$82$	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
$87$		0			0
$88$	−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	$0.754288\pi$
$90$		0			0
$91$	−138311.	+	245178.i	−0.183541	+	0.325355i
$92$	−364567.			−0.468182
$93$		0			0
$94$	−188754.	+	108977.i	−0.227255	+	0.131206i
$95$	358989.	+	621787.i	0.418707	+	0.725222i
$96$		0			0
$97$			32664.1i			0.0357895i	0.999840	+	0.0178948i	$0.00569638\pi$
$97$			32664.1i			0.0357895i	−0.999840	+	0.0178948i	$0.994304\pi$
$98$	665391.	−	13278.5i	0.706966	−	0.0141082i
$99$		0			0
$100$	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	$0.255319\pi$
$102$		0			0
$103$	386249.	+	223001.i	0.353472	+	0.204077i	0.666214	−	0.745761i	$-0.267914\pi$
$103$	386249.	+	223001.i	0.353472	+	0.204077i	−0.312741	+	0.949838i	$0.601247\pi$
$104$		−	148563.i		−	0.132072i
$105$		0			0
$106$	188038.			0.157880
$107$	−944735.	+	1.63633e6i	−0.771186	+	1.33573i	0.165728	+	0.986171i	$0.447003\pi$
$107$	−944735.	+	1.63633e6i	−0.771186	+	1.33573i	−0.936914	+	0.349561i	$0.886331\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−302409.	+	178642.i	−0.215249	+	0.127154i
$113$	472481.			0.327453			0.163726	−	0.986506i	$-0.447649\pi$
$113$	472481.			0.327453			0.163726	+	0.986506i	$0.447649\pi$
$114$		0			0
$115$	−1.27412e6	+	735614.i	−0.837756	+	0.483678i
$116$	−525161.	−	909605.i	−0.336448	−	0.582746i
$117$		0			0
$118$		−	1.89362e6i		−	1.15252i
$119$	904570.	−	9024.86i	0.536786	−	0.00535550i
$120$		0			0
$121$	−1.94276e6	+	3.36496e6i	−1.09664	+	1.89943i
$122$	−825026.	+	476329.i	−0.454347	+	0.262318i
$123$		0			0
$124$	−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
$129$		0			0
$130$	−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	$0.675818\pi$
$132$		0			0
$133$	−969934.	−	1.64193e6i	−0.412275	−	0.697908i
$134$	1.82446e6			0.758263
$135$		0			0
$136$	−413452.	+	238707.i	−0.164365	+	0.0948960i
$137$	−798004.	−	1.38218e6i	−0.310344	−	0.537532i	0.668093	−	0.744078i	$-0.267111\pi$
$137$	−798004.	−	1.38218e6i	−0.310344	−	0.537532i	−0.978437	+	0.206546i	$0.933778\pi$
$138$		0			0
$139$		−	688428.i		−	0.256339i	−0.991752	−	0.128169i	$-0.959090\pi$
$139$		−	688428.i		−	0.256339i	0.991752	−	0.128169i	$-0.0409101\pi$
$140$	−696425.	+	1.23452e6i	−0.253799	+	0.449900i
$141$		0			0
$142$	−920683.	+	1.59467e6i	−0.321547	+	0.556936i
$143$	−1.69049e6	+	976002.i	−0.578101	+	0.333767i
$144$		0			0
$145$	−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	−0.814170	−	0.580627i	$-0.802808\pi$
$149$	316745.	−	548619.i	0.0957527	−	0.165849i	0.909923	+	0.414778i	$0.136141\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	4.01947e6	+	2.26748e6i	1.10054	+	0.620842i
$155$	−6.05741e6			−1.62664
$156$		0			0
$157$	2.23038e6	−	1.28771e6i	0.576342	−	0.332751i	−0.183336	−	0.983050i	$-0.558690\pi$
$157$	2.23038e6	−	1.28771e6i	0.576342	−	0.332751i	0.759678	+	0.650299i	$0.225356\pi$
$158$	−958976.	−	1.66100e6i	−0.243129	−	0.421112i
$159$		0			0
$160$		−	748044.i		−	0.182628i
$161$	3.36451e6	−	1.98752e6i	0.806203	−	0.476248i
$162$		0			0
$163$	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
$165$		0			0
$166$	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
$171$		0			0
$172$	−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	$0.547235\pi$
$174$		0			0
$175$	3598.11	+	360642.i	0.000671368	+	0.0672918i
$176$	−2.43554e6			−0.446743
$177$		0			0
$178$	−1.87744e6	+	1.08394e6i	−0.332894	+	0.192196i
$179$	662601.	+	1.14766e6i	0.115530	+	0.200103i	0.917991	−	0.396600i	$-0.129810\pi$
$179$	662601.	+	1.14766e6i	0.115530	+	0.200103i	−0.802462	+	0.596704i	$0.796477\pi$
$180$		0			0
$181$		−	4.90685e6i		−	0.827499i	−0.910391	−	0.413749i	$-0.864219\pi$
$181$		−	4.90685e6i		−	0.827499i	0.910391	−	0.413749i	$-0.135781\pi$
$182$	809922.	+	1.37105e6i	0.134347	+	0.227426i
$183$		0			0
$184$	−1.03115e6	+	1.78601e6i	−0.165527	+	0.286702i
$185$	2.42970e6	−	1.40279e6i	0.383741	−	0.221553i
$186$		0			0
$187$	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	−0.998549	−	0.0538534i	$-0.982850\pi$
$191$	−3.15391e6	+	5.46273e6i	−0.452636	+	0.783989i	0.545913	+	0.837842i	$0.316183\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	1.81696e6	−	3.29729e6i	0.241311	−	0.437914i
$197$	6.85421e6			0.896518			0.448259	−	0.893904i	$-0.352044\pi$
$197$	6.85421e6			0.896518			0.448259	+	0.893904i	$0.352044\pi$
$198$		0			0
$199$	8.24491e6	−	4.76020e6i	1.04623	−	0.604040i	0.124637	−	0.992202i	$-0.460223\pi$
$199$	8.24491e6	−	4.76020e6i	1.04623	−	0.604040i	0.921591	+	0.388162i	$0.126890\pi$
$200$	−95169.7	−	164839.i	−0.0118962	−	0.0206048i
$201$		0			0
$202$		−	2.82836e6i		−	0.343148i
$203$	9.80551e6	+	5.53152e6i	1.17215	+	0.661236i
$204$		0			0
$205$	5.54297e6	−	9.60071e6i	0.643400	−	1.11440i
$206$	2.18495e6	−	1.26148e6i	0.249943	−	0.144305i
$207$		0			0
$208$	−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
$213$		0			0
$214$	5.34423e6	+	9.25648e6i	0.545311	+	0.944506i
$215$	−1.27468e7	−	7.35936e6i	−1.28258	−	0.740499i
$216$		0			0
$217$	1.60882e7	−	160511.i	1.57445	−	0.0157082i
$218$	1.08717e7			1.04937
$219$		0			0
$220$	−8.51195e6	+	4.91438e6i	−0.799394	+	0.461530i
$221$	1.08224e6	+	1.87450e6i	0.100265	+	0.173663i
$222$		0			0
$223$			1.75966e6i			0.158677i	0.996848	+	0.0793385i	$0.0252808\pi$
$223$			1.75966e6i			0.158677i	−0.996848	+	0.0793385i	$0.974719\pi$
$224$	19821.9	+	1.98677e6i	0.00176361	+	0.176768i
$225$		0			0
$226$	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	$0.196462\pi$
$228$		0			0
$229$	−1.75825e7	−	1.01513e7i	−1.46411	−	0.845306i	−0.464915	−	0.885355i	$-0.653915\pi$
$229$	−1.75825e7	−	1.01513e7i	−1.46411	−	0.845306i	−0.999198	+	0.0400494i	$0.987248\pi$
$230$			8.32253e6i			0.684025i
$231$		0			0
$232$	−5.94152e6			−0.475810
$233$	−2.71453e6	+	4.70171e6i	−0.214599	+	0.371696i	−0.953148	−	0.302503i	$-0.902178\pi$
$233$	−2.71453e6	+	4.70171e6i	−0.214599	+	0.371696i	0.738550	+	0.674199i	$0.235511\pi$
$234$		0			0
$235$	2.48779e6	+	4.30897e6i	0.191694	+	0.332025i
$236$	−9.27682e6	−	5.35598e6i	−0.705770	−	0.407477i
$237$		0			0
$238$	2.51430e6	−	4.45700e6i	0.186503	−	0.330606i
$239$	920423.			0.0674208			0.0337104	−	0.999432i	$-0.489268\pi$
$239$	920423.			0.0674208			0.0337104	+	0.999432i	$0.489268\pi$
$240$		0			0
$241$	−2.15894e7	+	1.24646e7i	−1.54237	+	0.890488i	−0.543681	+	0.839292i	$0.682970\pi$
$241$	−2.15894e7	+	1.24646e7i	−1.54237	+	0.890488i	−0.998689	+	0.0511961i	$0.983697\pi$
$242$	1.09899e7	+	1.90351e7i	0.775440	+	1.34310i
$243$		0			0
$244$			5.38905e6i			0.370973i
$245$	−303128.	−	1.51899e7i	−0.0206124	−	1.03289i
$246$		0			0
$247$	2.28146e6	−	3.95161e6i	0.151399	−	0.262231i
$248$	−7.35344e6	+	4.24551e6i	−0.482098	+	0.278339i
$249$		0			0
$250$	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
$255$		0			0
$256$	−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	$0.839659\pi$
$258$		0			0
$259$	−6.41600e6	+	3.79012e6i	−0.369288	+	0.218149i
$260$	−3.39146e6			−0.192960
$261$		0			0
$262$	−633159.	+	365555.i	−0.0352054	+	0.0203258i
$263$	−4.02078e6	−	6.96420e6i	−0.221026	−	0.382828i	0.734094	−	0.679048i	$-0.237607\pi$
$263$	−4.02078e6	−	6.96420e6i	−0.221026	−	0.382828i	−0.955120	+	0.296220i	$0.904274\pi$
$264$		0			0
$265$		−	4.29263e6i		−	0.230667i
$266$	−1.07871e7	+	107623.i	−0.573141	+	0.00571821i
$267$		0			0
$268$	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	$0.470863\pi$
$270$		0			0
$271$	−2.67932e7	−	1.54691e7i	−1.34622	−	0.777243i	−0.358511	−	0.933525i	$-0.616716\pi$
$271$	−2.67932e7	−	1.54691e7i	−1.34622	−	0.777243i	−0.987712	+	0.156283i	$0.950049\pi$
$272$			2.70066e6i			0.134203i
$273$		0			0
$274$	−9.02839e6			−0.438893
$275$	−1.25046e6	+	2.16586e6i	−0.0601273	+	0.104144i
$276$		0			0
$277$	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
$279$		0			0
$280$	4.07812e6	+	6.90353e6i	0.185775	+	0.314483i
$281$	1.17351e6			0.0528895			0.0264447	−	0.999650i	$-0.491581\pi$
$281$	1.17351e6			0.0528895			0.0264447	+	0.999650i	$0.491581\pi$
$282$		0			0
$283$	−2.44869e7	+	1.41375e7i	−1.08038	+	0.623756i	−0.930998	−	0.365024i	$-0.881061\pi$
$283$	−2.44869e7	+	1.41375e7i	−1.08038	+	0.623756i	−0.149379	+	0.988780i	$0.547727\pi$
$284$	5.20817e6	+	9.02081e6i	0.227368	+	0.393813i
$285$		0			0
$286$			1.10422e7i			0.472017i
$287$	−1.44675e7	+	2.56459e7i	−0.611993	+	1.08486i
$288$		0			0
$289$	−8.59095e6	+	1.48800e7i	−0.355916	+	0.616465i
$290$	−2.07649e7	+	1.19886e7i	−0.851405	+	0.491559i
$291$		0			0
$292$	−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
$297$		0			0
$298$	−1.79178e6	−	3.10346e6i	−0.0677074	−	0.117273i
$299$	8.09736e6	+	4.67501e6i	0.302921	+	0.174892i
$300$		0			0
$301$	3.40499e7	+	1.92083e7i	1.24858	+	0.704353i
$302$	1.41078e7			0.512197
$303$		0			0
$304$	4.93049e6	−	2.84662e6i	0.175497	−	0.101323i
$305$	1.08739e7	+	1.88341e7i	0.383252	+	0.663812i
$306$		0			0
$307$		−	4.40807e7i		−	1.52347i	−0.647891	−	0.761733i	$-0.724349\pi$
$307$		−	4.40807e7i		−	1.52347i	0.647891	−	0.761733i	$-0.275651\pi$
$308$	2.24771e7	−	1.32779e7i	0.769287	−	0.454441i
$309$		0			0
$310$	−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	$0.488641\pi$
$312$		0			0
$313$	−5.13461e6	−	2.96447e6i	−0.167446	−	0.0966750i	0.413935	−	0.910306i	$-0.364154\pi$
$313$	−5.13461e6	−	2.96447e6i	−0.167446	−	0.0966750i	−0.581381	+	0.813631i	$0.697487\pi$
$314$		−	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	$-0.581573\pi$
$317$	2.26491e7	−	3.92294e7i	0.711007	−	1.23150i	0.964480	−	0.264157i	$-0.0850937\pi$
$318$		0			0
$319$	3.90336e7	+	6.76082e7i	1.20245	+	2.08270i
$320$	−3.66465e6	−	2.11579e6i	−0.111836	−	0.0645687i
$321$		0			0
$322$	−220533.	−	2.21042e7i	−0.00660551	−	0.662076i
$323$	−1.46632e7			−0.435132
$324$		0			0
$325$	−747342.	+	431478.i	−0.0217705	+	0.0125692i
$326$	−2.47690e6	−	4.29011e6i	−0.0714916	−	0.123827i
$327$		0			0
$328$		−	1.55398e7i		−	0.440376i
$329$	−6.72162e6	−	1.13785e7i	−0.188750	−	0.319520i
$330$		0			0
$331$	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
$333$		0			0
$334$	−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
$339$		0			0
$340$	5.44931e6	+	9.43849e6i	0.138645	+	0.240141i
$341$	9.66188e7	+	5.57829e7i	2.43668	+	1.40682i
$342$		0			0
$343$	1.20760e6	+	4.03355e7i	0.0299254	+	0.999552i
$344$	−2.06321e7			−0.506836
$345$		0			0
$346$	1.85911e7	−	1.07336e7i	0.448824	−	0.259128i
$347$	3.31773e7	+	5.74648e7i	0.794059	+	1.37535i	0.923435	+	0.383756i	$0.125370\pi$
$347$	3.31773e7	+	5.74648e7i	0.794059	+	1.37535i	−0.129375	+	0.991596i	$0.541297\pi$
$348$		0			0
$349$		−	9.44163e6i		−	0.222111i	−0.993814	−	0.111056i	$-0.964577\pi$
$349$		−	9.44163e6i		−	0.222111i	0.993814	−	0.111056i	$-0.0354232\pi$
$350$	1.77695e6	+	1.00242e6i	0.0414450	+	0.0233801i
$351$		0			0
$352$	−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	$0.373260\pi$
$354$		0			0
$355$	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	$0.368097\pi$
$359$	−2.73638e7	+	4.73954e7i	−0.591415	+	1.02436i	−0.994042	+	0.108997i	$0.965236\pi$
$360$		0			0
$361$	−8.06726e6	−	1.39729e7i	−0.171476	−	0.297006i
$362$	−2.40386e7	−	1.38787e7i	−0.506737	−	0.292565i
$363$		0			0
$364$	9.00756e6	−	89868.1i	0.186768	−	0.00186338i
$365$	−1.39280e7			−0.286424
$366$		0			0
$367$	−8.26059e7	+	4.76926e7i	−1.67114	+	0.964834i	−0.704140	+	0.710061i	$0.748667\pi$
$367$	−8.26059e7	+	4.76926e7i	−1.67114	+	0.964834i	−0.967001	+	0.254773i	$0.917999\pi$
$368$	5.83308e6	+	1.01032e7i	0.117045	+	0.202729i
$369$		0			0
$370$		−	1.58708e7i		−	0.313323i
$371$	113747.	+	1.14010e7i	0.00222751	+	0.223265i
$372$		0			0
$373$	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
$375$		0			0
$376$	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
$381$		0			0
$382$	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	$0.750715\pi$
$384$		0			0
$385$	5.17631e7	−	9.17584e7i	0.907065	−	1.60792i
$386$	−4.94924e6			−0.0860550
$387$		0			0
$388$	905215.	−	522626.i	0.0154973	−	0.00894738i
$389$	−5.20331e7	−	9.01241e7i	−0.883957	−	1.53106i	−0.846904	−	0.531746i	$-0.821536\pi$
$389$	−5.20331e7	−	9.01241e7i	−0.883957	−	1.53106i	−0.0370533	−	0.999313i	$-0.511797\pi$
$390$		0			0
$391$		−	3.00468e7i		−	0.502652i
$392$	−1.10142e7	−	1.82274e7i	−0.182851	−	0.302598i
$393$		0			0
$394$	1.93866e7	−	3.35786e7i	0.316967	−	0.549003i
$395$	−3.79180e7	+	2.18920e7i	−0.615254	+	0.355217i
$396$		0			0
$397$	6.06717e7	+	3.50288e7i	0.969649	+	0.559827i	0.899129	−	0.437683i	$-0.144201\pi$
$397$	6.06717e7	+	3.50288e7i	0.969649	+	0.559827i	0.0705197	+	0.997510i	$0.477534\pi$
$398$		−	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	$-0.629823\pi$
$401$	3.84740e7	−	6.66389e7i	0.596670	−	1.03346i	0.993309	−	0.115488i	$-0.0368432\pi$
$402$		0			0
$403$	1.92482e7	+	3.33388e7i	0.294086	+	0.509372i
$404$	−1.38561e7	−	7.99982e6i	−0.210134	−	0.121321i
$405$		0			0
$406$	5.48330e7	−	3.23915e7i	0.819339	−	0.484008i
$407$	−5.16733e7			−0.766449
$408$		0			0
$409$	3.50627e7	−	2.02435e7i	0.512479	−	0.295880i	−0.221373	−	0.975189i	$-0.571054\pi$
$409$	3.50627e7	−	2.02435e7i	0.512479	−	0.295880i	0.733852	+	0.679309i	$0.237721\pi$
$410$	−3.13558e7	−	5.43098e7i	−0.454952	−	0.788001i
$411$		0			0
$412$		−	1.42721e7i		−	0.204077i
$413$	1.14813e8	−	1.14549e6i	1.62983	−	0.0162607i
$414$		0			0
$415$	1.45069e7	−	2.51268e7i	0.202970	−	0.351554i
$416$	−4.11709e6	+	2.37700e6i	−0.0571887	+	0.0330179i
$417$		0			0
$418$	−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
$423$		0			0
$424$	−3.00861e6	−	5.21106e6i	−0.0394701	−	0.0683642i
$425$	2.40162e6	+	1.38658e6i	0.0312851	+	0.0180624i
$426$		0			0
$427$	−2.93796e7	−	4.97343e7i	−0.377365	−	0.638811i
$428$	6.04631e7			0.771186
$429$		0			0
$430$	−7.21067e7	+	4.16308e7i	−0.906923	+	0.523612i
$431$	3.45151e7	+	5.97819e7i	0.431099	+	0.746686i	0.996968	−	0.0778092i	$-0.0247925\pi$
$431$	3.45151e7	+	5.97819e7i	0.431099	+	0.746686i	−0.565869	+	0.824495i	$0.691459\pi$
$432$		0			0
$433$		−	7.91462e7i		−	0.974915i	−0.873147	−	0.487457i	$-0.837924\pi$
$433$		−	7.91462e7i		−	0.974915i	0.873147	−	0.487457i	$-0.162076\pi$
$434$	4.47180e7	−	7.92697e7i	0.547032	−	0.969702i
$435$		0			0
$436$	3.07497e7	−	5.32601e7i	0.371007	−	0.642603i
$437$	−5.48552e7	+	3.16707e7i	−0.657315	+	0.379501i
$438$		0			0
$439$	2.09035e7	+	1.20687e7i	0.247073	+	0.142648i	0.618423	−	0.785845i	$-0.287772\pi$
$439$	2.09035e7	+	1.20687e7i	0.247073	+	0.142648i	−0.371350	+	0.928493i	$0.621105\pi$
$440$			5.55998e7i			0.652703i
$441$		0			0
$442$	1.22442e7			0.141796
$443$	2.35504e7	−	4.07904e7i	0.270886	−	0.469188i	−0.698203	−	0.715900i	$-0.746017\pi$
$443$	2.35504e7	−	4.07904e7i	0.270886	−	0.469188i	0.969089	+	0.246712i	$0.0793500\pi$
$444$		0			0
$445$	2.47447e7	+	4.28591e7i	0.280804	+	0.486366i
$446$	8.62053e6	+	4.97707e6i	0.0971694	+	0.0561008i
$447$		0			0
$448$	9.78921e6	+	5.52233e6i	0.108871	+	0.0614169i
$449$	4.69720e6			0.0518920			0.0259460	−	0.999663i	$-0.491740\pi$
$449$	4.69720e6			0.0518920			0.0259460	+	0.999663i	$0.491740\pi$
$450$		0			0
$451$	−1.76826e8	+	1.02091e8i	−1.92760	+	1.11290i
$452$	−7.55969e6	−	1.30938e7i	−0.0818632	−	0.141791i
$453$		0			0
$454$		−	5.51668e7i		−	0.589536i
$455$	3.12991e7	−	1.84893e7i	0.332275	−	0.196285i
$456$		0			0
$457$	−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
$459$		0			0
$460$	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
$465$		0			0
$466$	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	$0.686957\pi$
$468$		0			0
$469$	1.10365e6	+	1.10620e8i	0.0106982	+	1.07229i
$470$	2.81461e7			0.271097
$471$		0			0
$472$	−5.24776e7	+	3.02980e7i	−0.499055	+	0.288129i
$473$	1.35545e8	+	2.34771e8i	1.28086	+	2.21851i
$474$		0			0
$475$		−	5.84605e6i		−	0.0545484i
$476$	−1.47232e7	−	2.49238e7i	−0.136516	−	0.231096i
$477$		0			0
$478$	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	$0.299825\pi$
$480$		0			0
$481$	−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
$486$		0			0
$487$	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
$489$		0			0
$490$	−7.52722e7	−	4.14784e7i	−0.639803	−	0.352561i
$491$	−1.96184e8			−1.65737			−0.828686	−	0.559714i	$-0.810911\pi$
$491$	−1.96184e8			−1.65737			−0.828686	+	0.559714i	$0.810911\pi$
$492$		0			0
$493$	7.49674e7	−	4.32825e7i	0.625651	−	0.361220i
$494$	−1.29059e7	−	2.23537e7i	−0.107055	−	0.185425i
$495$		0			0
$496$			4.80325e7i			0.393631i
$497$	−9.72439e7	−	5.48576e7i	−0.792124	−	0.446856i
$498$		0			0
$499$	−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
$501$		0			0
$502$	−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
$507$		0			0
$508$	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	$0.483273\pi$
$510$		0			0
$511$	3.69921e7	−	369069.i	0.277234	−	0.00276595i
$512$	−5.93164e6			−0.0441942
$513$		0			0
$514$	−8.60037e7	+	4.96543e7i	−0.633327	+	0.365651i
$515$	−2.87978e7	−	4.98792e7i	−0.210832	−	0.365172i
$516$		0			0
$517$		−	9.16404e7i		−	0.663156i
$518$	420549.	+	4.21520e7i	0.00302571	+	0.303269i
$519$		0			0
$520$	−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	$0.181985\pi$
$522$		0			0
$523$	−2.11656e8	−	1.22200e8i	−1.47954	−	0.854210i	−0.479804	−	0.877376i	$-0.659292\pi$
$523$	−2.11656e8	−	1.22200e8i	−1.47954	−	0.854210i	−0.999732	+	0.0231657i	$0.992625\pi$
$524$			4.13578e6i			0.0287451i
$525$		0			0
$526$	−4.54900e7			−0.312578
$527$	6.18550e7	−	1.07136e8i	0.422613	−	0.731987i
$528$		0			0
$529$	9.12076e6	+	1.57976e7i	0.0616118	+	0.106715i
$530$	−2.10295e7	−	1.21414e7i	−0.141254	−	0.0815531i
$531$		0			0
$532$	−2.99834e7	+	5.31504e7i	−0.199134	+	0.352998i
$533$	−7.04539e7			−0.465290
$534$		0			0
$535$	2.11311e8	−	1.22001e8i	1.37995	−	0.796712i
$536$	−2.91914e7	−	5.05609e7i	−0.189566	−	0.328338i
$537$		0			0
$538$			9.22169e7i			0.592194i
$539$	−1.35049e8	+	2.45078e8i	−0.862432	+	1.56508i
$540$		0			0
$541$	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
$543$		0			0
$544$	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
$549$		0			0
$550$	7.07367e6	+	1.22520e7i	0.0425164	+	0.0736406i
$551$	−1.58038e8	−	9.12434e7i	−0.944729	−	0.545440i
$552$		0			0
$553$	1.00128e8	−	5.91488e7i	0.592082	−	0.349761i
$554$	7.58924e7			0.446343
$555$		0			0
$556$	−1.90783e7	+	1.10149e7i	−0.110998	+	0.0640847i
$557$	1.46346e7	+	2.53478e7i	0.0846865	+	0.146681i	0.905258	−	0.424863i	$-0.139678\pi$
$557$	1.46346e7	+	2.53478e7i	0.0846865	+	0.146681i	−0.820571	+	0.571544i	$0.806344\pi$
$558$		0			0
$559$			9.35411e7i			0.535509i
$560$	4.53550e7	−	452505.i	0.258262	−	0.00257667i
$561$		0			0
$562$	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	$0.508988\pi$
$564$		0			0
$565$	−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	−0.766574	−	0.642156i	$-0.778040\pi$
$569$	3.18400e7	−	5.51485e7i	0.172837	−	0.299362i	0.939410	+	0.342794i	$0.111373\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	8.47185e7	+	1.43413e8i	0.447964	+	0.758322i
$575$	1.19793e7			0.0630127
$576$		0			0
$577$	−2.73237e8	+	1.57754e8i	−1.42237	+	0.821205i	−0.996501	−	0.0835798i	$-0.973365\pi$
$577$	−2.73237e8	+	1.57754e8i	−1.42237	+	0.821205i	−0.425868	+	0.904785i	$0.640031\pi$
$578$	4.85977e7	+	8.41737e7i	0.251671	+	0.435906i
$579$		0			0
$580$			1.35636e8i			0.695170i
$581$	−3.78639e7	+	6.71199e7i	−0.193062	+	0.342234i
$582$		0			0
$583$	−3.95309e7	+	6.84696e7i	−0.199495	+	0.345535i
$584$	−1.69080e7	+	9.76183e6i	−0.0848894	+	0.0490109i
$585$		0			0
$586$	−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
$591$		0			0
$592$	−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	$0.897868\pi$
$594$		0			0
$595$	−1.01747e8	−	5.73976e7i	−0.483024	−	0.272485i
$596$	−2.02717e7			−0.0957527
$597$		0			0
$598$	4.58056e7	−	2.64459e7i	0.214198	−	0.123667i
$599$	−9.32594e7	−	1.61530e8i	−0.433923	−	0.751576i	0.563284	−	0.826263i	$-0.309538\pi$
$599$	−9.32594e7	−	1.61530e8i	−0.433923	−	0.751576i	−0.997207	+	0.0746871i	$0.976204\pi$
$600$		0			0
$601$		−	2.43621e8i		−	1.12226i	−0.827729	−	0.561128i	$-0.810368\pi$
$601$		−	2.43621e8i		−	1.12226i	0.827729	−	0.561128i	$-0.189632\pi$
$602$	1.90409e8	−	1.12480e8i	0.872765	−	0.515569i
$603$		0			0
$604$	3.99028e7	−	6.91136e7i	0.181089	−	0.313655i
$605$	4.34542e8	−	2.50883e8i	1.96230	−	1.13294i
$606$		0			0
$607$	9.01650e7	+	5.20568e7i	0.403155	+	0.232762i	0.687844	−	0.725858i	$-0.258557\pi$
$607$	9.01650e7	+	5.20568e7i	0.403155	+	0.232762i	−0.284689	+	0.958620i	$0.591890\pi$
$608$		−	3.22058e7i		−	0.143292i
$609$		0			0
$610$	1.23024e8			0.542001
$611$	1.58105e7	−	2.73846e7i	0.0693142	−	0.120056i
$612$		0			0
$613$	−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
$615$		0			0
$616$	−1.47330e6	−	1.47670e8i	−0.00630304	−	0.631759i
$617$	1.78930e8			0.761776			0.380888	−	0.924621i	$-0.375618\pi$
$617$	1.78930e8			0.761776			0.380888	+	0.924621i	$0.375618\pi$
$618$		0			0
$619$	2.04695e8	−	1.18181e8i	0.863048	−	0.498281i	−0.00198390	−	0.999998i	$-0.500631\pi$
$619$	2.04695e8	−	1.18181e8i	0.863048	−	0.498281i	0.865032	+	0.501717i	$0.167298\pi$
$620$	9.69186e7	+	1.67868e8i	0.406661	+	0.704357i
$621$		0			0
$622$			1.59536e8i			0.662959i
$623$	−6.68565e7	−	1.13176e8i	−0.276490	−	0.468048i
$624$		0			0
$625$	1.29732e8	−	2.24703e8i	0.531383	−	0.920383i
$626$	−2.90458e7	+	1.67696e7i	−0.118402	+	0.0683595i
$627$		0			0
$628$	−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
$633$		0			0
$634$	−1.28123e8	−	2.21915e8i	−0.502758	−	0.870802i
$635$	7.07041e7	+	4.08211e7i	0.276136	+	0.159427i
$636$		0			0
$637$	−8.26389e7	+	4.99360e7i	−0.319717	+	0.193195i
$638$	4.41615e8			1.70052
$639$		0			0
$640$	−2.07304e7	+	1.19687e7i	−0.0790802	+	0.0456570i
$641$	−1.15332e8	−	1.99760e8i	−0.437899	−	0.758463i	0.559628	−	0.828744i	$-0.310944\pi$
$641$	−1.15332e8	−	1.99760e8i	−0.437899	−	0.758463i	−0.997527	+	0.0702803i	$0.977611\pi$
$642$		0			0
$643$			1.68539e8i			0.633967i	0.948431	+	0.316983i	$0.102670\pi$
$643$			1.68539e8i			0.633967i	−0.948431	+	0.316983i	$0.897330\pi$
$644$	−1.08912e8	−	6.14398e7i	−0.407772	−	0.230034i
$645$		0			0
$646$	−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	$0.234105\pi$
$648$		0			0
$649$	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	−0.996575	−	0.0826970i	$-0.973647\pi$
$653$	−1.18804e8	+	2.05775e8i	−0.426670	+	0.739014i	0.569905	+	0.821711i	$0.306980\pi$
$654$		0			0
$655$	8.34506e6	+	1.44541e7i	0.0296965	+	0.0514359i
$656$	−7.61291e7	−	4.39532e7i	−0.269674	−	0.155696i
$657$		0			0
$658$	−7.47547e7	+	745825.i	−0.262398	+	0.00261794i
$659$	3.19568e8			1.11662			0.558312	−	0.829631i	$-0.311449\pi$
$659$	3.19568e8			1.11662			0.558312	+	0.829631i	$0.311449\pi$
$660$		0			0
$661$	3.66423e8	−	2.11554e8i	1.26876	−	0.732517i	0.294004	−	0.955804i	$-0.405012\pi$
$661$	3.66423e8	−	2.11554e8i	1.26876	−	0.732517i	0.974753	+	0.223287i	$0.0716787\pi$
$662$	−1.89226e8	−	3.27748e8i	−0.652238	−	1.12971i
$663$		0			0
$664$		−	4.06704e7i		−	0.138923i
$665$	2.45687e6	+	2.46254e8i	0.00835444	+	0.837373i
$666$		0			0
$667$	1.86969e8	−	3.23840e8i	0.630076	−	1.09132i
$668$	−1.16588e8	+	6.73119e7i	−0.391132	+	0.225820i
$669$		0			0
$670$	−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
$675$		0			0
$676$	−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	$0.517119\pi$
$678$		0			0
$679$	−5.50482e6	+	9.75817e6i	−0.0175846	+	0.0311716i
$680$	6.16520e7			0.196074
$681$		0			0
$682$	5.46559e8	−	3.15556e8i	1.72299	−	0.994771i
$683$	1.08581e8	+	1.88068e8i	0.340794	+	0.590272i	0.984580	−	0.174933i	$-0.0559709\pi$
$683$	1.08581e8	+	1.88068e8i	0.340794	+	0.590272i	−0.643787	+	0.765205i	$0.722638\pi$
$684$		0			0
$685$			2.06105e8i			0.641233i
$686$	2.01019e8	+	1.08170e8i	0.622678	+	0.335070i
$687$		0			0
$688$	−5.83563e7	+	1.01076e8i	−0.179194	+	0.310372i
$689$	−2.36258e7	+	1.36403e7i	−0.0722318	+	0.0417031i
$690$		0			0
$691$	−4.52106e8	−	2.61024e8i	−1.37027	−	0.791126i	−0.379309	−	0.925270i	$-0.623838\pi$
$691$	−4.52106e8	−	2.61024e8i	−1.37027	−	0.791126i	−0.990962	+	0.134144i	$0.957171\pi$
$692$		−	1.21436e8i		−	0.366463i
$693$		0			0
$694$	3.75359e8			1.12297
$695$	−4.44509e7	+	7.69913e7i	−0.132412	+	0.229344i
$696$		0			0
$697$	1.13204e8	+	1.96074e8i	0.334319	+	0.579058i
$698$	−4.62543e7	−	2.67050e7i	−0.136015	−	0.0785282i
$699$		0			0
$700$	9.93683e6	−	5.86999e6i	0.0289704	−	0.0171137i
$701$	−3.81338e8			−1.10702			−0.553511	−	0.832842i	$-0.686712\pi$
$701$	−3.81338e8			−1.10702			−0.553511	+	0.832842i	$0.686712\pi$
$702$		0			0
$703$	1.04607e8	−	6.03948e7i	0.301088	−	0.173833i
$704$	3.89687e7	+	6.74958e7i	0.111686	+	0.193446i
$705$		0			0
$706$			6.22595e7i			0.176926i
$707$	1.71488e8	−	1.71093e6i	0.485260	−	0.00484142i
$708$		0			0
$709$	−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
$711$		0			0
$712$	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
$717$		0			0
$718$	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	$0.441728\pi$
$720$		0			0
$721$	7.78072e7	+	1.31714e8i	0.207594	+	0.351419i
$722$	−9.12706e7			−0.242504
$723$		0			0
$724$	−1.35983e8	+	7.85097e7i	−0.358318	+	0.206875i
$725$	1.72562e7	+	2.98887e7i	0.0452827	+	0.0784319i
$726$		0			0
$727$		−	5.49464e8i		−	1.43000i	−0.699124	−	0.715000i	$-0.746426\pi$
$727$		−	5.49464e8i		−	1.43000i	0.699124	−	0.715000i	$-0.253574\pi$
$728$	2.50370e7	−	4.43820e7i	0.0648915	−	0.115031i
$729$		0			0
$730$	−3.93943e7	+	6.82329e7i	−0.101266	+	0.175398i
$731$	2.60326e8	−	1.50299e8i	0.666447	−	0.384774i
$732$		0			0
$733$	5.09314e8	+	2.94053e8i	1.29322	+	0.746643i	0.979224	−	0.202780i	$-0.0649977\pi$
$733$	5.09314e8	+	2.94053e8i	1.29322	+	0.746643i	0.313999	+	0.949423i	$0.398331\pi$
$734$			5.39580e8i			1.36448i
$735$		0			0
$736$	6.59938e7			0.165527
$737$	−3.83553e8	+	6.64334e8i	−0.958127	+	1.65952i
$738$		0			0
$739$	−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
$741$		0			0
$742$	5.61750e7	+	3.16897e7i	0.137509	+	0.0775722i
$743$	−5.34716e8			−1.30364			−0.651819	−	0.758375i	$-0.725994\pi$
$743$	−5.34716e8			−1.30364			−0.651819	+	0.758375i	$0.725994\pi$
$744$		0			0
$745$	−7.08472e7	+	4.09037e7i	−0.171338	+	0.0989221i
$746$	−1.19503e8	−	2.06986e8i	−0.287848	−	0.498567i
$747$		0			0
$748$		−	2.00732e8i		−	0.479635i
$749$	−5.58000e8	+	3.29628e8i	−1.32797	+	0.784473i
$750$		0			0
$751$	−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
$753$		0			0
$754$	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
$759$		0			0
$760$	−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	$0.492606\pi$
$762$		0			0
$763$	6.57647e6	+	6.59165e8i	0.0148054	+	1.48395i
$764$	2.01850e8			0.452636
$765$		0			0
$766$	−1.43666e8	+	8.29457e7i	−0.319645	+	0.184547i
$767$	1.37364e8	+	2.37922e8i	0.304430	+	0.527288i
$768$		0			0
$769$			4.67013e8i			1.02695i	0.858104	+	0.513475i	$0.171642\pi$
$769$			4.67013e8i			1.02695i	−0.858104	+	0.513475i	$0.828358\pi$
$770$	−3.03115e8	−	5.13119e8i	−0.663949	−	1.12395i
$771$		0			0
$772$	−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	$0.314466\pi$
$774$		0			0
$775$	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
$780$		0			0
$781$	−3.87107e8	−	6.70489e8i	−0.812602	−	1.40747i
$782$	−1.47198e8	−	8.49851e7i	−0.307810	−	0.177714i
$783$		0			0
$784$	−1.20449e8	+	2.40366e6i	−0.249950	+	0.00498799i
$785$	−3.32584e8			−0.687530
$786$		0			0
$787$	3.05483e8	−	1.76371e8i	0.626704	−	0.361828i	−0.152770	−	0.988262i	$-0.548819\pi$
$787$	3.05483e8	−	1.76371e8i	0.626704	−	0.361828i	0.779475	+	0.626434i	$0.215486\pi$
$788$	−1.09667e8	−	1.89949e8i	−0.224129	−	0.388204i
$789$		0			0
$790$			2.47680e8i			0.502353i
$791$	1.41150e8	+	7.96262e7i	0.285202	+	0.160889i
$792$		0			0
$793$	6.91062e7	−	1.19695e8i	0.138579	−	0.240026i
$794$	3.43211e8	−	1.98153e8i	0.685645	−	0.395858i
$795$		0			0
$796$	−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
$801$		0			0
$802$	−2.17642e8	−	3.76967e8i	−0.421909	−	0.730769i
$803$	2.22159e8	+	1.28263e8i	0.429058	+	0.247717i
$804$		0			0
$805$	−5.04606e8	+	5.03444e6i	−0.967309	+	0.00965081i
$806$	2.17768e8			0.415901
$807$		0			0
$808$	−7.83819e7	+	4.52538e7i	−0.148587	+	0.0857869i
$809$	−3.44264e8	−	5.96282e8i	−0.650198	−	1.12618i	−0.983075	−	0.183206i	$-0.941352\pi$
$809$	−3.44264e8	−	5.96282e8i	−0.650198	−	1.12618i	0.332876	−	0.942971i	$-0.391981\pi$
$810$		0			0
$811$			4.12718e8i			0.773732i	0.922136	+	0.386866i	$0.126442\pi$
$811$			4.12718e8i			0.773732i	−0.922136	+	0.386866i	$0.873558\pi$
$812$	−3.59413e6	−	3.60242e8i	−0.00671313	−	0.672863i
$813$		0			0
$814$	−1.46154e8	+	2.53147e8i	−0.270981	+	0.469352i
$815$	−9.79368e7	+	5.65438e7i	−0.180914	+	0.104451i
$816$		0			0
$817$	−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	−0.987846	−	0.155435i	$-0.950322\pi$
$821$	−1.98839e8	+	3.44399e8i	−0.359312	+	0.622347i	0.628534	+	0.777782i	$0.283655\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	3.19129e8	−	5.65707e8i	0.566273	−	1.00381i
$827$	−4.58785e8			−0.811134			−0.405567	−	0.914065i	$-0.632926\pi$
$827$	−4.58785e8			−0.811134			−0.405567	+	0.914065i	$0.632926\pi$
$828$		0			0
$829$	6.95641e8	−	4.01628e8i	1.22102	−	0.704954i	0.255881	−	0.966708i	$-0.417634\pi$
$829$	6.95641e8	−	4.01628e8i	1.22102	−	0.704954i	0.965135	+	0.261754i	$0.0843010\pi$
$830$	−8.20636e7	−	1.42138e8i	−0.143521	−	0.248586i
$831$		0			0
$832$			2.68927e7i			0.0466944i
$833$	2.71755e8	+	1.49749e8i	0.470156	+	0.259077i
$834$		0			0
$835$	−2.71640e8	+	4.70495e8i	−0.466589	+	0.808156i
$836$	−3.66468e8	+	2.11580e8i	−0.627216	+	0.362123i
$837$		0			0
$838$	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
$843$		0			0
$844$	1.63971e8	+	2.84007e8i	0.272735	+	0.472390i
$845$	−4.64485e8	−	2.68171e8i	−0.769842	−	0.444469i
$846$		0			0
$847$	−1.14748e9	+	6.77848e8i	−1.88840	+	1.11553i
$848$	−3.40385e7			−0.0558191
$849$		0			0
$850$	1.35856e7	−	7.84365e6i	0.0221219	−	0.0127721i
$851$	1.23757e8	+	2.14353e8i	0.200807	+	0.347808i
$852$		0			0
$853$			8.99416e8i			1.44915i	0.689196	+	0.724575i	$0.257964\pi$
$853$			8.99416e8i			1.44915i	−0.689196	+	0.724575i	$0.742036\pi$
$854$	−3.26745e8	+	3.25993e6i	−0.524609	+	0.00523401i
$855$		0			0
$856$	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	$0.599493\pi$
$858$		0			0
$859$	3.89837e8	+	2.25073e8i	0.615041	+	0.355094i	0.774936	−	0.632040i	$-0.217782\pi$
$859$	3.89837e8	+	2.25073e8i	0.615041	+	0.355094i	−0.159895	+	0.987134i	$0.551116\pi$
$860$			4.70999e8i			0.740499i
$861$		0			0
$862$	3.90494e8			0.609667
$863$	2.32956e8	−	4.03492e8i	0.362445	−	0.627773i	−0.625918	−	0.779889i	$-0.715275\pi$
$863$	2.32956e8	−	4.03492e8i	0.362445	−	0.627773i	0.988363	+	0.152116i	$0.0486087\pi$
$864$		0			0
$865$	−2.45031e8	−	4.24406e8i	−0.378593	−	0.655742i
$866$	−3.87736e8	−	2.23859e8i	−0.597011	−	0.344684i
$867$		0			0
$868$	−2.61859e8	−	4.43281e8i	−0.400414	−	0.677829i
$869$	8.06416e8			1.22885
$870$		0			0
$871$	−2.29232e8	+	1.32347e8i	−0.346913	+	0.200290i
$872$	−1.73947e8	−	3.01285e8i	−0.262342	−	0.454389i
$873$		0			0
$874$			3.58313e8i			0.536695i
$875$	−3.17167e8	+	5.62230e8i	−0.473439	+	0.839247i
$876$		0			0
$877$	−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
$879$		0			0
$880$	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
$885$		0			0
$886$	−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	$0.778360\pi$
$888$		0			0
$889$	−1.88868e8	−	1.06545e8i	−0.268815	−	0.151645i
$890$	2.79955e8			0.397116
$891$		0			0
$892$	4.87651e7	−	2.81545e7i	0.0687091	−	0.0396692i
$893$	1.07108e8	+	1.85516e8i	0.150406	+	0.260511i
$894$		0			0
$895$		−	1.71133e8i		−	0.238707i
$896$	5.47418e7	−	3.23376e7i	0.0761018	−	0.0449556i
$897$		0			0
$898$	1.32857e7	−	2.30115e7i	0.0183466	−	0.0317772i
$899$	1.33333e9	−	7.69799e8i	1.83510	−	1.05949i
$900$		0			0
$901$	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
$906$		0			0
$907$	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
$909$		0			0
$910$	−2.05155e6	−	2.05629e8i	−0.00272244	−	0.272873i
$911$	4.54738e8			0.601459			0.300730	−	0.953709i	$-0.402770\pi$
$911$	4.54738e8			0.601459			0.300730	+	0.953709i	$0.402770\pi$
$912$		0			0
$913$	−4.62786e8	+	2.67190e8i	−0.608090	+	0.351081i
$914$	3.34594e8	+	5.79533e8i	0.438207	+	0.758997i
$915$		0			0
$916$			6.49681e8i			0.845306i
$917$	−2.25471e7	−	3.81682e7i	−0.0292403	−	0.0494987i
$918$		0			0
$919$	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
$921$		0			0
$922$	−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
$927$		0			0
$928$	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	$0.522222\pi$
$930$		0			0
$931$	−1.30507e7	−	6.53975e8i	−0.0161727	−	0.810423i
$932$	1.73730e8			0.214599
$933$		0			0
$934$	−6.35671e7	+	3.67005e7i	−0.0780174	+	0.0450434i
$935$	−4.05031e8	−	7.01534e8i	−0.495511	−	0.858250i
$936$		0			0
$937$		−	2.35920e8i		−	0.286779i	−0.989666	−	0.143389i	$-0.954200\pi$
$937$		−	2.35920e8i		−	0.286779i	0.989666	−	0.143389i	$-0.0458001\pi$
$938$	5.45045e8	+	3.07473e8i	0.660425	+	0.372561i
$939$		0			0
$940$	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	$0.262414\pi$
$942$		0			0
$943$	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	−0.631789	−	0.775141i	$-0.717679\pi$
$947$	3.01831e8	−	5.22786e8i	0.355397	−	0.615566i	0.987186	+	0.159575i	$0.0510123\pi$
$948$		0			0
$949$	4.42579e7	+	7.66569e7i	0.0517836	+	0.0896918i
$950$	−2.86397e7	−	1.65351e7i	−0.0334039	−	0.0192858i
$951$		0			0
$952$	−1.63745e8	+	1.63367e6i	−0.189783	+	0.00189345i
$953$	−2.87119e8			−0.331729			−0.165864	−	0.986149i	$-0.553041\pi$
$953$	−2.87119e8			−0.331729			−0.165864	+	0.986149i	$0.553041\pi$
$954$		0			0
$955$	7.05443e8	−	4.07288e8i	0.809938	−	0.467618i
$956$	−1.47268e7	−	2.55075e7i	−0.0168552	−	0.0291941i
$957$		0			0
$958$		−	1.30652e8i		−	0.148600i
$959$	−5.46143e6	−	5.47404e8i	−0.00619228	−	0.620657i
$960$		0			0
$961$	6.56367e8	−	1.13686e9i	0.739566	−	1.28097i
$962$	−8.73495e7	+	5.04313e7i	−0.0981150	+	0.0566467i
$963$		0			0
$964$	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
$969$		0			0
$970$	−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	$0.517664\pi$
$972$		0			0
$973$	1.16019e8	−	2.05663e8i	0.125948	−	0.223264i
$974$	1.89036e8			0.204582
$975$		0			0
$976$	1.49346e8	−	8.62248e7i	0.160636	−	0.0927433i
$977$	−4.17857e8	−	7.23750e8i	−0.448068	−	0.776077i	0.550192	−	0.835038i	$-0.314555\pi$
$977$	−4.17857e8	−	7.23750e8i	−0.448068	−	0.776077i	−0.998260	+	0.0589610i	$0.981221\pi$
$978$		0			0
$979$		−	9.11500e8i		−	0.971423i
$980$	−4.16104e8	+	2.51438e8i	−0.442103	+	0.267149i
$981$		0			0
$982$	−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	$0.370420\pi$
$984$		0			0
$985$	−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
$990$		0			0
$991$	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
$993$		0			0
$994$	−5.43794e8	+	3.21235e8i	−0.553701	+	0.327088i
$995$	−1.22944e9			−1.24807
$996$		0			0
$997$	−1.47059e8	+	8.49047e7i	−0.148391	+	0.0856735i	−0.572357	−	0.820005i	$-0.693971\pi$
$997$	−1.47059e8	+	8.49047e7i	−0.148391	+	0.0856735i	0.423966	+	0.905678i	$0.360638\pi$
$998$	2.62307e8	+	4.54328e8i	0.263887	+	0.457065i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.7.n.c.19.3		8
3.2	odd	2		14.7.d.a.5.2	yes	8
7.3	odd	6	inner	126.7.n.c.73.3		8
12.11	even	2		112.7.s.c.33.1		8
21.2	odd	6		98.7.b.c.97.8		8
21.5	even	6		98.7.b.c.97.5		8
21.11	odd	6		98.7.d.c.31.1		8
21.17	even	6		14.7.d.a.3.2	✓	8
21.20	even	2		98.7.d.c.19.1		8
84.59	odd	6		112.7.s.c.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.d.a.3.2	✓	8	21.17	even	6
14.7.d.a.5.2	yes	8	3.2	odd	2
98.7.b.c.97.5		8	21.5	even	6
98.7.b.c.97.8		8	21.2	odd	6
98.7.d.c.19.1		8	21.20	even	2
98.7.d.c.31.1		8	21.11	odd	6
112.7.s.c.17.1		8	84.59	odd	6
112.7.s.c.33.1		8	12.11	even	2
126.7.n.c.19.3		8	1.1	even	1	trivial
126.7.n.c.73.3		8	7.3	odd	6	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.82843 - 4.89898i) q^{2} +(-16.0000 - 27.7128i) q^{4} +(-111.836 - 64.5687i) q^{5} +(298.743 + 168.528i) q^{7} -181.019 q^{8} +(-632.642 + 365.256i) q^{10} +(1189.23 + 2059.81i) q^{11} +820.701i q^{13} +(1670.59 - 986.866i) q^{14} +(-512.000 + 886.810i) q^{16} +(2284.02 - 1318.68i) q^{17} +(-4814.93 - 2779.90i) q^{19} +4132.40i q^{20} +13454.6 q^{22} +(5696.37 - 9866.40i) q^{23} +(525.743 + 910.614i) q^{25} +(4020.60 + 2321.29i) q^{26} +(-109.502 - 10975.5i) q^{28} +32822.6 q^{29} +(40622.4 - 23453.4i) q^{31} +(2896.31 + 5016.55i) q^{32} -14919.2i q^{34} +(-22528.7 - 38137.0i) q^{35} +(-10862.8 + 18814.9i) q^{37} +(-27237.3 + 15725.5i) q^{38} +(20244.5 + 11688.2i) q^{40} +85846.0i q^{41} +113977. q^{43} +(38055.4 - 65913.9i) q^{44} +(-32223.5 - 55812.8i) q^{46} +(-33367.3 - 19264.6i) q^{47} +(60845.6 + 100693. i) q^{49} +5948.11 q^{50} +(22743.9 - 13131.2i) q^{52} +(16620.4 + 28787.3i) q^{53} -307149. i q^{55} +(-54078.2 - 30506.8i) q^{56} +(92836.2 - 160797. i) q^{58} +(289901. - 167374. i) q^{59} +(-145845. - 84203.9i) q^{61} -265344. i q^{62} +32768.0 q^{64} +(52991.6 - 91784.1i) q^{65} +(161261. + 279312. i) q^{67} +(-73088.7 - 42197.8i) q^{68} +(-250553. + 2499.76i) q^{70} -325510. q^{71} +(93404.3 - 53927.0i) q^{73} +(61449.1 + 106433. i) q^{74} +177914. i q^{76} +(8138.93 + 815772. i) q^{77} +(169525. - 293625. i) q^{79} +(114520. - 66118.4i) q^{80} +(420558. + 242809. i) q^{82} +224674. i q^{83} -340582. q^{85} +(322376. - 558372. i) q^{86} +(-215274. - 372865. i) q^{88} +(-331888. - 191615. i) q^{89} +(-138311. + 245178. i) q^{91} -364567. q^{92} +(-188754. + 108977. i) q^{94} +(358989. + 621787. i) q^{95} +32664.1i q^{97} +(665391. - 13278.5i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 128 q^{4} + 336 q^{5} + 652 q^{7} - 2016 q^{10} + 1356 q^{11} - 2064 q^{14} - 4096 q^{16} + 17304 q^{17} - 32004 q^{19} + 25248 q^{22} + 4128 q^{23} + 4664 q^{25} + 4704 q^{26} - 7552 q^{28} + 30312 q^{29}+ \cdots + 3532320 q^{98}+O(q^{100}) \) 8 * q - 128 * q^4 + 336 * q^5 + 652 * q^7 - 2016 * q^10 + 1356 * q^11 - 2064 * q^14 - 4096 * q^16 + 17304 * q^17 - 32004 * q^19 + 25248 * q^22 + 4128 * q^23 + 4664 * q^25 + 4704 * q^26 - 7552 * q^28 + 30312 * q^29 - 3108 * q^31 - 98028 * q^35 - 6124 * q^37 - 155568 * q^38 + 64512 * q^40 - 297376 * q^43 + 43392 * q^44 - 194064 * q^46 - 313908 * q^47 + 32432 * q^49 - 38784 * q^50 + 255360 * q^52 - 278484 * q^53 + 125952 * q^56 - 169824 * q^58 + 835464 * q^59 - 995316 * q^61 + 262144 * q^64 - 8316 * q^65 + 648808 * q^67 - 553728 * q^68 - 1572816 * q^70 - 190128 * q^71 - 1617084 * q^73 + 1158144 * q^74 - 1456224 * q^77 + 70096 * q^79 - 344064 * q^80 + 66528 * q^82 + 2190984 * q^85 + 573024 * q^86 - 403968 * q^88 - 739116 * q^89 + 2233752 * q^91 - 264192 * q^92 + 3795120 * q^94 - 725640 * q^95 + 3532320 * q^98

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