LMFDB - Embedded newform 126.7.n.c.19.2

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			19.2
Root			$-6.30576 + 10.9219i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.7.n.c.73.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.82843 + 4.89898i) q^{2} +(-16.0000 - 27.7128i) q^{4} +(162.347 + 93.7310i) q^{5} +(141.244 + 312.569i) q^{7} +181.019 q^{8} +(-918.372 + 530.222i) q^{10} +(555.924 + 962.889i) q^{11} -706.517i q^{13} +(-1930.77 - 192.128i) q^{14} +(-512.000 + 886.810i) q^{16} +(7334.73 - 4234.71i) q^{17} +(22.0061 + 12.7052i) q^{19} -5998.78i q^{20} -6289.56 q^{22} +(-424.738 + 735.668i) q^{23} +(9758.49 + 16902.2i) q^{25} +(3461.21 + 1998.33i) q^{26} +(6402.26 - 8915.36i) q^{28} +15109.4 q^{29} +(-1205.81 + 696.173i) q^{31} +(-2896.31 - 5016.55i) q^{32} +47910.2i q^{34} +(-6366.92 + 63983.4i) q^{35} +(4646.47 - 8047.92i) q^{37} +(-124.485 + 71.8716i) q^{38} +(29387.9 + 16967.1i) q^{40} +109829. i q^{41} -45569.8 q^{43} +(17789.6 - 30812.4i) q^{44} +(-2402.68 - 4161.56i) q^{46} +(-119865. - 69204.2i) q^{47} +(-77749.5 + 88296.7i) q^{49} -110405. q^{50} +(-19579.6 + 11304.3i) q^{52} +(30937.9 + 53586.1i) q^{53} +208429. i q^{55} +(25567.8 + 56581.0i) q^{56} +(-42735.9 + 74020.8i) q^{58} +(-68015.2 + 39268.6i) q^{59} +(-151296. - 87350.5i) q^{61} -7876.29i q^{62} +32768.0 q^{64} +(66222.6 - 114701. i) q^{65} +(217974. + 377543. i) q^{67} +(-234711. - 135511. i) q^{68} +(-295445. - 212164. i) q^{70} +561559. q^{71} +(-192170. + 110949. i) q^{73} +(26284.4 + 45525.9i) q^{74} -813.135i q^{76} +(-222448. + 309766. i) q^{77} +(-333239. + 577187. i) q^{79} +(-166243. + 95980.5i) q^{80} +(-538052. - 310645. i) q^{82} +653635. i q^{83} +1.58769e6 q^{85} +(128891. - 223245. i) q^{86} +(100633. + 174301. i) q^{88} +(-114603. - 66165.9i) q^{89} +(220835. - 99791.1i) q^{91} +27183.2 q^{92} +(678060. - 391478. i) q^{94} +(2381.75 + 4125.31i) q^{95} -1.59480e6i q^{97} +(-212655. - 630634. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	162.347	+	93.7310i	1.29877	+	0.749848i	0.980192	−	0.198047i	$-0.0634600\pi$
$5$	162.347	+	93.7310i	1.29877	+	0.749848i	0.318582	+	0.947895i	$0.396793\pi$
$6$		0			0
$7$	141.244	+	312.569i	0.411789	+	0.911279i
$7$	141.244	+	312.569i	0.411789	+	0.911279i
$8$	181.019			0.353553
$9$		0			0
$10$	−918.372	+	530.222i	−0.918372	+	0.530222i
$11$	555.924	+	962.889i	0.417674	+	0.723432i	0.995705	−	0.0925823i	$-0.0295121\pi$
$11$	555.924	+	962.889i	0.417674	+	0.723432i	−0.578031	+	0.816015i	$0.696179\pi$
$12$		0			0
$13$		−	706.517i		−	0.321583i	−0.986988	−	0.160791i	$-0.948595\pi$
$13$		−	706.517i		−	0.321583i	0.986988	−	0.160791i	$-0.0514046\pi$
$14$	−1930.77	−	192.128i	−0.703632	−	0.0700176i
$15$		0			0
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	7334.73	−	4234.71i	1.49292	−	0.861939i	0.492955	−	0.870055i	$-0.335917\pi$
$17$	7334.73	−	4234.71i	1.49292	−	0.861939i	0.999967	+	0.00811595i	$0.00258342\pi$
$18$		0			0
$19$	22.0061	+	12.7052i	0.00320835	+	0.00185234i	0.501603	−	0.865098i	$-0.332744\pi$
$19$	22.0061	+	12.7052i	0.00320835	+	0.00185234i	−0.498395	+	0.866950i	$0.666077\pi$
$20$		−	5998.78i		−	0.749848i
$21$		0			0
$22$	−6289.56			−0.590680
$23$	−424.738	+	735.668i	−0.0349090	+	0.0604642i	−0.882952	−	0.469463i	$-0.844447\pi$
$23$	−424.738	+	735.668i	−0.0349090	+	0.0604642i	0.848043	+	0.529927i	$0.177781\pi$
$24$		0			0
$25$	9758.49	+	16902.2i	0.624543	+	1.08174i
$26$	3461.21	+	1998.33i	0.196928	+	0.113697i
$27$		0			0
$28$	6402.26	−	8915.36i	0.291648	−	0.406130i
$29$	15109.4			0.619518			0.309759	−	0.950815i	$-0.399752\pi$
$29$	15109.4			0.619518			0.309759	+	0.950815i	$0.399752\pi$
$30$		0			0
$31$	−1205.81	+	696.173i	−0.0404755	+	0.0233686i	−0.520101	−	0.854105i	$-0.674106\pi$
$31$	−1205.81	+	696.173i	−0.0404755	+	0.0233686i	0.479626	+	0.877473i	$0.340772\pi$
$32$	−2896.31	−	5016.55i	−0.0883883	−	0.153093i
$33$		0			0
$34$			47910.2i			1.21897i
$35$	−6366.92	+	63983.4i	−0.148500	+	1.49233i
$36$		0			0
$37$	4646.47	−	8047.92i	0.0917313	−	0.158883i	−0.816508	−	0.577334i	$-0.804093\pi$
$37$	4646.47	−	8047.92i	0.0917313	−	0.158883i	0.908240	+	0.418450i	$0.137427\pi$
$38$	−124.485	+	71.8716i	−0.00226865	+	0.00130981i
$39$		0			0
$40$	29387.9	+	16967.1i	0.459186	+	0.265111i
$41$			109829.i			1.59356i	0.604272	+	0.796778i	$0.293464\pi$
$41$			109829.i			1.59356i	−0.604272	+	0.796778i	$0.706536\pi$
$42$		0			0
$43$	−45569.8			−0.573155			−0.286577	−	0.958057i	$-0.592518\pi$
$43$	−45569.8			−0.573155			−0.286577	+	0.958057i	$0.592518\pi$
$44$	17789.6	−	30812.4i	0.208837	−	0.361716i
$45$		0			0
$46$	−2402.68	−	4161.56i	−0.0246844	−	0.0427546i
$47$	−119865.	−	69204.2i	−1.15451	−	0.666559i	−0.204531	−	0.978860i	$-0.565567\pi$
$47$	−119865.	−	69204.2i	−1.15451	−	0.666559i	−0.949983	+	0.312301i	$0.898900\pi$
$48$		0			0
$49$	−77749.5	+	88296.7i	−0.660860	+	0.750510i
$50$	−110405.			−0.883238
$51$		0			0
$52$	−19579.6	+	11304.3i	−0.139249	+	0.0803957i
$53$	30937.9	+	53586.1i	0.207809	+	0.359935i	0.951024	−	0.309117i	$-0.100034\pi$
$53$	30937.9	+	53586.1i	0.207809	+	0.359935i	−0.743215	+	0.669052i	$0.766700\pi$
$54$		0			0
$55$			208429.i			1.25277i
$56$	25567.8	+	56581.0i	0.145589	+	0.322186i
$57$		0			0
$58$	−42735.9	+	74020.8i	−0.219033	+	0.379376i
$59$	−68015.2	+	39268.6i	−0.331169	+	0.191201i	−0.656360	−	0.754448i	$-0.727905\pi$
$59$	−68015.2	+	39268.6i	−0.331169	+	0.191201i	0.325191	+	0.945648i	$0.394571\pi$
$60$		0			0
$61$	−151296.	−	87350.5i	−0.666556	−	0.384836i	0.128214	−	0.991746i	$-0.459075\pi$
$61$	−151296.	−	87350.5i	−0.666556	−	0.384836i	−0.794770	+	0.606910i	$0.792409\pi$
$62$		−	7876.29i		−	0.0330481i
$63$		0			0
$64$	32768.0			0.125000
$65$	66222.6	−	114701.i	0.241138	−	0.417664i
$66$		0			0
$67$	217974.	+	377543.i	0.724738	+	1.25528i	0.959082	+	0.283129i	$0.0913725\pi$
$67$	217974.	+	377543.i	0.724738	+	1.25528i	−0.234344	+	0.972154i	$0.575294\pi$
$68$	−234711.	−	135511.i	−0.746461	−	0.430969i
$69$		0			0
$70$	−295445.	−	212164.i	−0.861356	−	0.618554i
$71$	561559.			1.56899			0.784495	−	0.620135i	$-0.212922\pi$
$71$	561559.			1.56899			0.784495	+	0.620135i	$0.212922\pi$
$72$		0			0
$73$	−192170.	+	110949.i	−0.493988	+	0.285204i	−0.726227	−	0.687454i	$-0.758728\pi$
$73$	−192170.	+	110949.i	−0.493988	+	0.285204i	0.232239	+	0.972659i	$0.425395\pi$
$74$	26284.4	+	45525.9i	0.0648639	+	0.112347i
$75$		0			0
$76$		−	813.135i		−	0.00185234i
$77$	−222448.	+	309766.i	−0.487255	+	0.678519i
$78$		0			0
$79$	−333239.	+	577187.i	−0.675888	+	1.17067i	0.300320	+	0.953838i	$0.402906\pi$
$79$	−333239.	+	577187.i	−0.675888	+	1.17067i	−0.976208	+	0.216834i	$0.930427\pi$
$80$	−166243.	+	95980.5i	−0.324694	+	0.187462i
$81$		0			0
$82$	−538052.	−	310645.i	−0.975850	−	0.563407i
$83$			653635.i			1.14314i	0.820552	+	0.571572i	$0.193666\pi$
$83$			653635.i			1.14314i	−0.820552	+	0.571572i	$0.806334\pi$
$84$		0			0
$85$	1.58769e6			2.58529
$86$	128891.	−	223245.i	0.202641	−	0.350984i
$87$		0			0
$88$	100633.	+	174301.i	0.147670	+	0.255772i
$89$	−114603.	−	66165.9i	−0.162564	−	0.0938565i	0.416511	−	0.909131i	$-0.363253\pi$
$89$	−114603.	−	66165.9i	−0.162564	−	0.0938565i	−0.579075	+	0.815274i	$0.696586\pi$
$90$		0			0
$91$	220835.	−	99791.1i	0.293052	−	0.132424i
$92$	27183.2			0.0349090
$93$		0			0
$94$	678060.	−	391478.i	0.816365	−	0.471329i
$95$	2381.75	+	4125.31i	0.00277795	+	0.00481156i
$96$		0			0
$97$		−	1.59480e6i		−	1.74739i	−0.486470	−	0.873697i	$-0.661716\pi$
$97$		−	1.59480e6i		−	1.74739i	0.486470	−	0.873697i	$-0.338284\pi$
$98$	−212655.	−	630634.i	−0.225942	−	0.670037i
$99$		0			0
$100$	312272.	−	540870.i	0.312272	−	0.540870i
$101$	1.12882e6	−	651726.i	1.09562	−	0.632559i	0.160556	−	0.987027i	$-0.448671\pi$
$101$	1.12882e6	−	651726.i	1.09562	−	0.632559i	0.935068	+	0.354468i	$0.115338\pi$
$102$		0			0
$103$	−5747.87	−	3318.53i	−0.00526011	−	0.00303693i	0.497368	−	0.867540i	$-0.334300\pi$
$103$	−5747.87	−	3318.53i	−0.00526011	−	0.00303693i	−0.502628	+	0.864503i	$0.667633\pi$
$104$		−	127893.i		−	0.113697i
$105$		0			0
$106$	−350023.			−0.293886
$107$	655988.	−	1.13620e6i	0.535482	−	0.927481i	−0.463658	−	0.886014i	$-0.653463\pi$
$107$	655988.	−	1.13620e6i	0.535482	−	0.927481i	0.999140	−	0.0414673i	$-0.0132032\pi$
$108$		0			0
$109$	−771304.	−	1.33594e6i	−0.595589	−	1.03159i	−0.993464	−	0.114150i	$-0.963586\pi$
$109$	−771304.	−	1.33594e6i	−0.595589	−	1.03159i	0.397875	−	0.917440i	$-0.369748\pi$
$110$	−1.02109e6	−	589527.i	−0.767160	−	0.442920i
$111$		0			0
$112$	−349506.	−	34778.9i	−0.248771	−	0.0247549i
$113$	−1.02212e6			−0.708382			−0.354191	−	0.935173i	$-0.615244\pi$
$113$	−1.02212e6			−0.708382			−0.354191	+	0.935173i	$0.615244\pi$
$114$		0			0
$115$	−137910.	+	79622.2i	−0.0906779	+	0.0523529i
$116$	−241751.	−	418725.i	−0.154880	−	0.268259i
$117$		0			0
$118$		−	444274.i		−	0.270399i
$119$	2.35962e6	+	1.69448e6i	1.40024	+	1.00553i
$120$		0			0
$121$	267678.	−	463631.i	0.151097	−	0.261708i
$122$	855857.	−	494129.i	0.471326	−	0.272120i
$123$		0			0
$124$	38585.8	+	22277.5i	0.0202378	+	0.0116843i
$125$			729599.i			0.373554i
$126$		0			0
$127$	752429.			0.367329			0.183664	−	0.982989i	$-0.441204\pi$
$127$	752429.			0.367329			0.183664	+	0.982989i	$0.441204\pi$
$128$	−92681.9	+	160530.i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	374611.	+	648846.i	0.170510	+	0.295333i
$131$	−226468.	−	130752.i	−0.100738	−	0.0581611i	0.448785	−	0.893640i	$-0.351857\pi$
$131$	−226468.	−	130752.i	−0.100738	−	0.0581611i	−0.549523	+	0.835479i	$0.685190\pi$
$132$		0			0
$133$	−863.036	+	8672.95i	−0.000366838	+	0.00368648i
$134$	−2.46610e6			−1.02493
$135$		0			0
$136$	1.32773e6	−	766564.i	0.527828	−	0.304741i
$137$	−349472.	−	605303.i	−0.135910	−	0.235402i	0.790035	−	0.613062i	$-0.210062\pi$
$137$	−349472.	−	605303.i	−0.135910	−	0.235402i	−0.925945	+	0.377659i	$0.876729\pi$
$138$		0			0
$139$			1.60298e6i			0.596875i	0.954429	+	0.298438i	$0.0964655\pi$
$139$			1.60298e6i			0.596875i	−0.954429	+	0.298438i	$0.903535\pi$
$140$	1.87503e6	−	847290.i	0.683321	−	0.308779i
$141$		0			0
$142$	−1.58833e6	+	2.75106e6i	−0.554722	+	0.960806i
$143$	680297.	−	392770.i	0.232643	−	0.134317i
$144$		0			0
$145$	2.45297e6	+	1.41622e6i	0.804614	+	0.464544i
$146$		−	1.25525e6i		−	0.403340i
$147$		0			0
$148$	−297374.			−0.0917313
$149$	−2.08601e6	+	3.61308e6i	−0.630607	+	1.09224i	0.356821	+	0.934173i	$0.383861\pi$
$149$	−2.08601e6	+	3.61308e6i	−0.630607	+	1.09224i	−0.987428	+	0.158070i	$0.949473\pi$
$150$		0			0
$151$	−3.10233e6	−	5.37339e6i	−0.901067	−	1.56069i	−0.826111	−	0.563507i	$-0.809452\pi$
$151$	−3.10233e6	−	5.37339e6i	−0.901067	−	1.56069i	−0.0749560	−	0.997187i	$-0.523882\pi$
$152$	3983.53	+	2299.89i	0.00113432	+	0.000654903i
$153$		0			0
$154$	−888361.	−	1.96592e6i	−0.243236	−	0.538274i
$155$	−261012.			−0.0700914
$156$		0			0
$157$	−1.70467e6	+	984193.i	−0.440496	+	0.254320i	−0.703808	−	0.710390i	$-0.748518\pi$
$157$	−1.70467e6	+	984193.i	−0.440496	+	0.254320i	0.263312	+	0.964711i	$0.415185\pi$
$158$	−1.88509e6	−	3.26506e6i	−0.477925	−	0.827790i
$159$		0			0
$160$		−	1.08590e6i		−	0.265111i
$161$	−289938.	−	28851.4i	−0.0694749	−	0.00691337i
$162$		0			0
$163$	−609352.	+	1.05543e6i	−0.140704	+	0.243706i	−0.927762	−	0.373173i	$-0.878270\pi$
$163$	−609352.	+	1.05543e6i	−0.140704	+	0.243706i	0.787058	+	0.616879i	$0.211603\pi$
$164$	3.04368e6	−	1.75727e6i	0.690030	−	0.398389i
$165$		0			0
$166$	−3.20215e6	−	1.84876e6i	−0.700030	−	0.404163i
$167$		−	638229.i		−	0.137034i	−0.997650	−	0.0685168i	$-0.978173\pi$
$167$		−	638229.i		−	0.137034i	0.997650	−	0.0685168i	$-0.0218267\pi$
$168$		0			0
$169$	4.32764e6			0.896585
$170$	−4.49067e6	+	7.77807e6i	−0.914039	+	1.58316i
$171$		0			0
$172$	729117.	+	1.26287e6i	0.143289	+	0.248183i
$173$	−538615.	−	310969.i	−0.104026	−	0.0600592i	0.447085	−	0.894492i	$-0.352462\pi$
$173$	−538615.	−	310969.i	−0.104026	−	0.0600592i	−0.551110	+	0.834432i	$0.685796\pi$
$174$		0			0
$175$	−3.90478e6	+	5.43753e6i	−0.728588	+	1.01458i
$176$	−1.13853e6			−0.208837
$177$		0			0
$178$	648291.	−	374291.i	0.114950	−	0.0663665i
$179$	−2.76061e6	−	4.78152e6i	−0.481334	−	0.833695i	0.518436	−	0.855116i	$-0.326514\pi$
$179$	−2.76061e6	−	4.78152e6i	−0.481334	−	0.833695i	−0.999771	+	0.0214210i	$0.993181\pi$
$180$		0			0
$181$		−	3.79950e6i		−	0.640753i	−0.947290	−	0.320377i	$-0.896191\pi$
$181$		−	3.79950e6i		−	0.640753i	0.947290	−	0.320377i	$-0.103809\pi$
$182$	−135742.	+	1.36412e6i	−0.0225164	+	0.226276i
$183$		0			0
$184$	−76885.8	+	133170.i	−0.0123422	+	0.0213773i
$185$	1.50868e6	−	871036.i	0.238277	−	0.137569i
$186$		0			0
$187$	8.15510e6	+	4.70835e6i	1.24711	+	0.720019i
$188$			4.42907e6i			0.666559i
$189$		0			0
$190$	−26946.4			−0.00392862
$191$	−2.60562e6	+	4.51307e6i	−0.373948	+	0.647697i	−0.990169	−	0.139876i	$-0.955330\pi$
$191$	−2.60562e6	+	4.51307e6i	−0.373948	+	0.647697i	0.616221	+	0.787573i	$0.288663\pi$
$192$		0			0
$193$	1.81264e6	+	3.13958e6i	0.252138	+	0.436716i	0.964114	−	0.265487i	$-0.0855329\pi$
$193$	1.81264e6	+	3.13958e6i	0.252138	+	0.436716i	−0.711976	+	0.702204i	$0.752200\pi$
$194$	7.81289e6	+	4.51078e6i	1.07006	+	0.617797i
$195$		0			0
$196$	3.69094e6	+	741909.i	0.490195	+	0.0985332i
$197$	6.36761e6			0.832871			0.416435	−	0.909165i	$-0.363279\pi$
$197$	6.36761e6			0.832871			0.416435	+	0.909165i	$0.363279\pi$
$198$		0			0
$199$	3.64034e6	−	2.10175e6i	0.461937	−	0.266699i	−0.250921	−	0.968007i	$-0.580734\pi$
$199$	3.64034e6	−	2.10175e6i	0.461937	−	0.266699i	0.712858	+	0.701308i	$0.247400\pi$
$200$	1.76648e6	+	3.05963e6i	0.220809	+	0.382453i
$201$		0			0
$202$			7.37343e6i			0.894573i
$203$	2.13411e6	+	4.72274e6i	0.255111	+	0.564554i
$204$		0			0
$205$	−1.02944e7	+	1.78305e7i	−1.19492	+	2.06967i
$206$	32514.9	−	18772.5i	0.00371946	−	0.00214743i
$207$		0			0
$208$	626547.	+	361737.i	0.0696247	+	0.0401978i
$209$			28252.6i			0.00309470i
$210$		0			0
$211$	−1.33548e7			−1.42164			−0.710822	−	0.703372i	$-0.751677\pi$
$211$	−1.33548e7			−1.42164			−0.710822	+	0.703372i	$0.751677\pi$
$212$	990014.	−	1.71475e6i	0.103904	−	0.179968i
$213$		0			0
$214$	3.71083e6	+	6.42734e6i	0.378643	+	0.655828i
$215$	−7.39811e6	−	4.27130e6i	−0.744398	−	0.429779i
$216$		0			0
$217$	−387914.	−	278567.i	−0.0379627	−	0.0272616i
$218$	8.72631e6			0.842289
$219$		0			0
$220$	5.77616e6	−	3.33487e6i	0.542464	−	0.313192i
$221$	−2.99189e6	−	5.18211e6i	−0.277185	−	0.480098i
$222$		0			0
$223$			6.98597e6i			0.629959i	0.949098	+	0.314980i	$0.101998\pi$
$223$			6.98597e6i			0.629959i	−0.949098	+	0.314980i	$0.898002\pi$
$224$	1.15893e6	−	1.61385e6i	0.103113	−	0.143589i
$225$		0			0
$226$	2.89100e6	−	5.00736e6i	0.250451	−	0.433794i
$227$	416145.	−	240261.i	0.0355768	−	0.0205403i	−0.482106	−	0.876113i	$-0.660128\pi$
$227$	416145.	−	240261.i	0.0355768	−	0.0205403i	0.517683	+	0.855573i	$0.326795\pi$
$228$		0			0
$229$	−9.92126e6	−	5.72804e6i	−0.826153	−	0.476980i	0.0263807	−	0.999652i	$-0.491602\pi$
$229$	−9.92126e6	−	5.72804e6i	−0.826153	−	0.476980i	−0.852534	+	0.522672i	$0.824935\pi$
$230$		−	900822.i		−	0.0740382i
$231$		0			0
$232$	2.73510e6			0.219033
$233$	7.16013e6	−	1.24017e7i	0.566048	−	0.980424i	−0.430903	−	0.902398i	$-0.641805\pi$
$233$	7.16013e6	−	1.24017e7i	0.566048	−	0.980424i	0.996951	−	0.0780261i	$-0.0248617\pi$
$234$		0			0
$235$	−1.29732e7	−	2.24702e7i	−0.999636	−	1.73142i
$236$	2.17649e6	+	1.25660e6i	0.165585	+	0.0956004i
$237$		0			0
$238$	−1.49752e7	+	6.76702e6i	−1.11082	+	0.501957i
$239$	−9.15640e6			−0.670704			−0.335352	−	0.942093i	$-0.608855\pi$
$239$	−9.15640e6			−0.670704			−0.335352	+	0.942093i	$0.608855\pi$
$240$		0			0
$241$	2.15763e7	−	1.24571e7i	1.54144	−	0.889951i	0.542692	−	0.839932i	$-0.317405\pi$
$241$	2.15763e7	−	1.24571e7i	1.54144	−	0.889951i	0.998748	−	0.0500197i	$-0.0159284\pi$
$242$	1.51421e6	+	2.62269e6i	0.106842	+	0.185055i
$243$		0			0
$244$			5.59043e6i			0.384836i
$245$	−2.08985e7	+	7.04716e6i	−1.42108	+	0.479199i
$246$		0			0
$247$	8976.47	−	15547.7i	0.000595682	−	0.00103175i
$248$	−218274.	+	126021.i	−0.0143103	+	0.00826203i
$249$		0			0
$250$	−3.57429e6	−	2.06362e6i	−0.228754	−	0.132071i
$251$		−	2.06023e7i		−	1.30285i	−0.758714	−	0.651424i	$-0.774172\pi$
$251$		−	2.06023e7i		−	1.30285i	0.758714	−	0.651424i	$-0.225828\pi$
$252$		0			0
$253$	−944488.			−0.0583223
$254$	−2.12819e6	+	3.68614e6i	−0.129870	+	0.224942i
$255$		0			0
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−1.07717e7	−	6.21904e6i	−0.634577	−	0.366373i	0.147945	−	0.988996i	$-0.452734\pi$
$257$	−1.07717e7	−	6.21904e6i	−0.634577	−	0.366373i	−0.782523	+	0.622622i	$0.786067\pi$
$258$		0			0
$259$	3.17181e6	+	315623.i	0.182561	+	0.0181664i
$260$	−4.23824e6			−0.241138
$261$		0			0
$262$	1.28110e6	−	739642.i	0.0712325	−	0.0411261i
$263$	1.42368e7	+	2.46588e7i	0.782609	+	1.35552i	0.930417	+	0.366502i	$0.119445\pi$
$263$	1.42368e7	+	2.46588e7i	0.782609	+	1.35552i	−0.147808	+	0.989016i	$0.547222\pi$
$264$		0			0
$265$			1.15994e7i			0.623299i
$266$	−40047.6	−	28758.8i	−0.00212780	−	0.00152801i
$267$		0			0
$268$	6.97518e6	−	1.20814e7i	0.362369	−	0.627642i
$269$	1.26875e7	−	7.32511e6i	0.651805	−	0.376320i	−0.137342	−	0.990524i	$-0.543856\pi$
$269$	1.26875e7	−	7.32511e6i	0.651805	−	0.376320i	0.789148	+	0.614204i	$0.210523\pi$
$270$		0			0
$271$	1.28578e7	+	7.42345e6i	0.646039	+	0.372991i	0.786937	−	0.617033i	$-0.211666\pi$
$271$	1.28578e7	+	7.42345e6i	0.646039	+	0.372991i	−0.140898	+	0.990024i	$0.544999\pi$
$272$			8.67268e6i			0.430969i
$273$		0			0
$274$	3.95382e6			0.192205
$275$	−1.08500e7	+	1.87927e7i	−0.521711	+	0.903630i
$276$		0			0
$277$	−1.13152e7	−	1.95985e7i	−0.532381	−	0.922111i	−0.999285	−	0.0378029i	$-0.987964\pi$
$277$	−1.13152e7	−	1.95985e7i	−0.532381	−	0.922111i	0.466904	−	0.884308i	$-0.345369\pi$
$278$	−7.85296e6	−	4.53391e6i	−0.365510	−	0.211027i
$279$		0			0
$280$	−1.15254e6	+	1.15822e7i	−0.0525025	+	0.527617i
$281$	2.66513e7			1.20116			0.600579	−	0.799565i	$-0.294937\pi$
$281$	2.66513e7			1.20116			0.600579	+	0.799565i	$0.294937\pi$
$282$		0			0
$283$	2.25458e7	−	1.30169e7i	0.994735	−	0.574310i	0.0880485	−	0.996116i	$-0.471937\pi$
$283$	2.25458e7	−	1.30169e7i	0.994735	−	0.574310i	0.906686	+	0.421806i	$0.138604\pi$
$284$	−8.98494e6	−	1.55624e7i	−0.392247	−	0.679393i
$285$		0			0
$286$			4.44368e6i			0.189953i
$287$	−3.43293e7	+	1.55127e7i	−1.45217	+	0.656209i
$288$		0			0
$289$	2.37967e7	−	4.12171e7i	0.985877	−	1.70759i
$290$	−1.38761e7	+	8.01136e6i	−0.568948	+	0.328482i
$291$		0			0
$292$	6.14943e6	+	3.55038e6i	0.246994	+	0.142602i
$293$		−	2.40799e6i		−	0.0957310i	−0.998854	−	0.0478655i	$-0.984758\pi$
$293$		−	2.40799e6i		−	0.0957310i	0.998854	−	0.0478655i	$-0.0152419\pi$
$294$		0			0
$295$	−1.47227e7			−0.573486
$296$	841100.	−	1.45683e6i	0.0324319	−	0.0561737i
$297$		0			0
$298$	−1.18003e7	−	2.04387e7i	−0.445906	−	0.772332i
$299$	519762.	+	300085.i	0.0194442	+	0.0112261i
$300$		0			0
$301$	−6.43644e6	−	1.42437e7i	−0.236019	−	0.522304i
$302$	3.50989e7			1.27430
$303$		0			0
$304$	−22534.3	+	13010.2i	−0.000802089	+	0.000463086i
$305$	−1.63749e7	−	2.83622e7i	−0.577137	−	0.999631i
$306$		0			0
$307$			1.92678e7i			0.665911i	0.942942	+	0.332956i	$0.108046\pi$
$307$			1.92678e7i			0.665911i	−0.942942	+	0.332956i	$0.891954\pi$
$308$	1.21437e7	+	1.20840e6i	0.415621	+	0.0413580i
$309$		0			0
$310$	738253.	−	1.27869e6i	0.0247811	−	0.0429221i
$311$	3.26379e7	−	1.88435e7i	1.08503	−	0.626441i	0.152780	−	0.988260i	$-0.451177\pi$
$311$	3.26379e7	−	1.88435e7i	1.08503	−	0.626441i	0.932248	+	0.361819i	$0.117844\pi$
$312$		0			0
$313$	−3.47639e7	−	2.00710e7i	−1.13369	−	0.654539i	−0.188833	−	0.982009i	$-0.560470\pi$
$313$	−3.47639e7	−	2.00710e7i	−1.13369	−	0.654539i	−0.944861	+	0.327470i	$0.893804\pi$
$314$		−	1.11349e7i		−	0.359663i
$315$		0			0
$316$	2.13273e7			0.675888
$317$	2.67147e7	−	4.62713e7i	0.838636	−	1.45256i	−0.0524001	−	0.998626i	$-0.516687\pi$
$317$	2.67147e7	−	4.62713e7i	0.838636	−	1.45256i	0.891036	−	0.453933i	$-0.149980\pi$
$318$		0			0
$319$	8.39969e6	+	1.45487e7i	0.258757	+	0.448180i
$320$	5.31978e6	+	3.07138e6i	0.162347	+	0.0937310i
$321$		0			0
$322$	961412.	−	1.33880e6i	0.0287966	−	0.0401003i
$323$	215212.			0.00638643
$324$		0			0
$325$	1.19417e7	−	6.89454e6i	0.347869	−	0.200842i
$326$	−3.44702e6	−	5.97041e6i	−0.0994925	−	0.172326i
$327$		0			0
$328$			1.98813e7i			0.563407i
$329$	4.70087e6	−	4.72408e7i	0.132005	−	1.32657i
$330$		0			0
$331$	−1.04651e7	+	1.81261e7i	−0.288575	+	0.499827i	−0.973470	−	0.228815i	$-0.926515\pi$
$331$	−1.04651e7	+	1.81261e7i	−0.288575	+	0.499827i	0.684895	+	0.728642i	$0.259848\pi$
$332$	1.81141e7	−	1.04582e7i	0.494996	−	0.285786i
$333$		0			0
$334$	3.12667e6	+	1.80518e6i	0.0839156	+	0.0484487i
$335$			8.17238e7i			2.17377i
$336$		0			0
$337$	5.12346e6			0.133867			0.0669335	−	0.997757i	$-0.478678\pi$
$337$	5.12346e6			0.133867			0.0669335	+	0.997757i	$0.478678\pi$
$338$	−1.22404e7	+	2.12010e7i	−0.316990	+	0.549044i
$339$		0			0
$340$	−2.54031e7	−	4.39994e7i	−0.646323	−	1.11946i
$341$	−1.34067e6	−	774038.i	−0.0338111	−	0.0195209i
$342$		0			0
$343$	−3.85804e7	−	1.18307e7i	−0.956059	−	0.293176i
$344$	−8.24901e6			−0.202641
$345$		0			0
$346$	3.04686e6	−	1.75911e6i	0.0735571	−	0.0424682i
$347$	667759.	+	1.15659e6i	0.0159820	+	0.0276817i	0.873906	−	0.486095i	$-0.161579\pi$
$347$	667759.	+	1.15659e6i	0.0159820	+	0.0276817i	−0.857924	+	0.513777i	$0.828246\pi$
$348$		0			0
$349$			5.85989e7i			1.37852i	0.724514	+	0.689260i	$0.242064\pi$
$349$			5.85989e7i			1.37852i	−0.724514	+	0.689260i	$0.757936\pi$
$350$	−1.55940e7	−	3.45091e7i	−0.363708	−	0.804876i
$351$		0			0
$352$	3.22026e6	−	5.57765e6i	0.0738350	−	0.127886i
$353$	5.03777e7	−	2.90856e7i	1.14529	−	0.661231i	0.197552	−	0.980292i	$-0.436701\pi$
$353$	5.03777e7	−	2.90856e7i	1.14529	−	0.661231i	0.947734	+	0.319061i	$0.103367\pi$
$354$		0			0
$355$	9.11673e7	+	5.26354e7i	2.03776	+	1.17650i
$356$			4.23462e6i			0.0938565i
$357$		0			0
$358$	3.12328e7			0.680709
$359$	−2.79159e7	+	4.83518e7i	−0.603350	+	1.04503i	0.388960	+	0.921254i	$0.372834\pi$
$359$	−2.79159e7	+	4.83518e7i	−0.603350	+	1.04503i	−0.992310	+	0.123778i	$0.960499\pi$
$360$		0			0
$361$	−2.35226e7	−	4.07424e7i	−0.499993	−	0.866014i
$362$	1.86137e7	+	1.07466e7i	0.392380	+	0.226540i
$363$		0			0
$364$	−6.29886e6	−	4.52331e6i	−0.130604	−	0.0937890i
$365$	−4.15975e7			−0.855439
$366$		0			0
$367$	7.51777e6	−	4.34039e6i	0.152087	−	0.0878072i	−0.422025	−	0.906584i	$-0.638681\pi$
$367$	7.51777e6	−	4.34039e6i	0.152087	−	0.0878072i	0.574112	+	0.818777i	$0.305347\pi$
$368$	−434932.	−	753324.i	−0.00872725	−	0.0151160i
$369$		0			0
$370$			9.85465e6i			0.194552i
$371$	−1.23795e7	+	1.72389e7i	−0.242428	+	0.337589i
$372$		0			0
$373$	−3.44474e7	+	5.96646e7i	−0.663789	+	1.14972i	0.315823	+	0.948818i	$0.397719\pi$
$373$	−3.44474e7	+	5.96646e7i	−0.663789	+	1.14972i	−0.979612	+	0.200898i	$0.935614\pi$
$374$	−4.61322e7	+	2.66344e7i	−0.881839	+	0.509130i
$375$		0			0
$376$	−2.16979e7	−	1.25273e7i	−0.408183	−	0.235664i
$377$		−	1.06751e7i		−	0.199226i
$378$		0			0
$379$	2.82976e7			0.519795			0.259897	−	0.965636i	$-0.416311\pi$
$379$	2.82976e7			0.519795			0.259897	+	0.965636i	$0.416311\pi$
$380$	76215.9	−	132010.i	0.00138898	−	0.00240578i
$381$		0			0
$382$	−1.47396e7	−	2.55298e7i	−0.264421	−	0.457991i
$383$	9.34416e7	+	5.39485e7i	1.66320	+	0.960248i	0.971173	+	0.238374i	$0.0766144\pi$
$383$	9.34416e7	+	5.39485e7i	1.66320	+	0.960248i	0.692025	+	0.721874i	$0.256719\pi$
$384$		0			0
$385$	−6.51484e7	+	2.94393e7i	−1.14162	+	0.515876i
$386$	−2.05076e7			−0.356578
$387$		0			0
$388$	−4.41964e7	+	2.55168e7i	−0.756644	+	0.436849i
$389$	3.23559e7	+	5.60420e7i	0.549673	+	0.952061i	0.998297	+	0.0583403i	$0.0185808\pi$
$389$	3.23559e7	+	5.60420e7i	0.549673	+	0.952061i	−0.448624	+	0.893720i	$0.648086\pi$
$390$		0			0
$391$			7.19456e6i			0.120358i
$392$	−1.40742e7	+	1.59834e7i	−0.233649	+	0.265345i
$393$		0			0
$394$	−1.80103e7	+	3.11948e7i	−0.294464	+	0.510027i
$395$	−1.08201e8	+	6.24697e7i	−1.75565	+	1.01363i
$396$		0			0
$397$	6.55387e7	+	3.78388e7i	1.04743	+	0.604736i	0.921930	−	0.387357i	$-0.126612\pi$
$397$	6.55387e7	+	3.78388e7i	1.04743	+	0.604736i	0.125504	+	0.992093i	$0.459945\pi$
$398$			2.37786e7i			0.377170i
$399$		0			0
$400$	−1.99854e7			−0.312272
$401$	1.55716e6	−	2.69708e6i	0.0241490	−	0.0418274i	−0.853698	−	0.520768i	$-0.825646\pi$
$401$	1.55716e6	−	2.69708e6i	0.0241490	−	0.0418274i	0.877847	+	0.478941i	$0.158979\pi$
$402$		0			0
$403$	491858.	+	851923.i	0.00751492	+	0.0130162i
$404$	−3.61223e7	−	2.08552e7i	−0.547812	−	0.316279i
$405$		0			0
$406$	−2.91728e7	−	2.90295e6i	−0.435913	−	0.0433772i
$407$	1.03323e7			0.153255
$408$		0			0
$409$	1.05021e8	−	6.06337e7i	1.53499	−	0.886225i	0.535865	−	0.844304i	$-0.319986\pi$
$409$	1.05021e8	−	6.06337e7i	1.53499	−	0.886225i	0.999121	−	0.0419210i	$-0.0133478\pi$
$410$	−5.82340e7	−	1.00864e8i	−0.844939	−	1.46348i
$411$		0			0
$412$			212386.i			0.00303693i
$413$	−2.18809e7	−	1.57130e7i	−0.310609	−	0.223053i
$414$		0			0
$415$	−6.12659e7	+	1.06116e8i	−0.857184	+	1.48469i
$416$	−3.54428e6	+	2.04629e6i	−0.0492321	+	0.0284242i
$417$		0			0
$418$	−138409.	−	79910.3i	−0.00189511	−	0.00109414i
$419$		−	1.07947e7i		−	0.146746i	−0.997305	−	0.0733732i	$-0.976624\pi$
$419$		−	1.07947e7i		−	0.146746i	0.997305	−	0.0733732i	$-0.0233764\pi$
$420$		0			0
$421$	−5.16567e6			−0.0692278			−0.0346139	−	0.999401i	$-0.511020\pi$
$421$	−5.16567e6			−0.0692278			−0.0346139	+	0.999401i	$0.511020\pi$
$422$	3.77732e7	−	6.54250e7i	0.502627	−	0.870576i
$423$		0			0
$424$	5.60036e6	+	9.70011e6i	0.0734714	+	0.127256i
$425$	1.43152e8	+	8.26487e7i	1.86479	+	1.07664i
$426$		0			0
$427$	5.93351e6	−	5.96280e7i	0.0762128	−	0.765890i
$428$	−4.19832e7			−0.535482
$429$		0			0
$430$	4.18500e7	−	2.41621e7i	0.526369	−	0.303899i
$431$	−5.74292e7	−	9.94703e7i	−0.717301	−	1.24240i	−0.962066	−	0.272818i	$-0.912044\pi$
$431$	−5.74292e7	−	9.94703e7i	−0.717301	−	1.24240i	0.244765	−	0.969582i	$-0.421289\pi$
$432$		0			0
$433$			2.10551e7i			0.259355i	0.991556	+	0.129677i	$0.0413942\pi$
$433$			2.10551e7i			0.259355i	−0.991556	+	0.129677i	$0.958606\pi$
$434$	2.46188e6	−	1.11248e6i	0.0301161	−	0.0136089i
$435$		0			0
$436$	−2.46817e7	+	4.27500e7i	−0.297794	+	0.515795i
$437$	−18693.7	+	10792.8i	−0.000224001	+	0.000129327i
$438$		0			0
$439$	5.69615e6	+	3.28867e6i	0.0673268	+	0.0388711i	0.533286	−	0.845935i	$-0.320957\pi$
$439$	5.69615e6	+	3.28867e6i	0.0673268	+	0.0388711i	−0.465959	+	0.884806i	$0.654290\pi$
$440$			3.77297e7i			0.442920i
$441$		0			0
$442$	3.38494e7			0.391998
$443$	−3.89607e7	+	6.74819e7i	−0.448142	+	0.776205i	−0.998265	−	0.0588789i	$-0.981247\pi$
$443$	−3.89607e7	+	6.74819e7i	−0.448142	+	0.776205i	0.550123	+	0.835084i	$0.314581\pi$
$444$		0			0
$445$	−1.24036e7	−	2.14836e7i	−0.140756	−	0.243797i
$446$	−3.42241e7	−	1.97593e7i	−0.385770	−	0.222724i
$447$		0			0
$448$	4.62827e6	+	1.02423e7i	0.0514736	+	0.113910i
$449$	−1.49956e8			−1.65663			−0.828316	−	0.560261i	$-0.810701\pi$
$449$	−1.49956e8			−1.65663			−0.828316	+	0.560261i	$0.810701\pi$
$450$		0			0
$451$	−1.05754e8	+	6.10568e7i	−1.15283	+	0.665587i
$452$	1.63540e7	+	2.83259e7i	0.177096	+	0.306739i
$453$		0			0
$454$			2.71825e6i			0.0290483i
$455$	4.52054e7	+	4.49834e6i	0.479906	+	0.0477549i
$456$		0			0
$457$	6.34376e7	−	1.09877e8i	0.664658	−	1.15122i	−0.314719	−	0.949185i	$-0.601910\pi$
$457$	6.34376e7	−	1.09877e8i	0.664658	−	1.15122i	0.979378	−	0.202037i	$-0.0647562\pi$
$458$	5.61231e7	−	3.24027e7i	0.584178	−	0.337276i
$459$		0			0
$460$	4.41311e6	+	2.54791e6i	0.0453389	+	0.0261764i
$461$			8.34728e7i			0.852005i	0.904722	+	0.426002i	$0.140078\pi$
$461$			8.34728e7i			0.852005i	−0.904722	+	0.426002i	$0.859922\pi$
$462$		0			0
$463$	−1.31072e8			−1.32058			−0.660292	−	0.751009i	$-0.729567\pi$
$463$	−1.31072e8			−1.32058			−0.660292	+	0.751009i	$0.729567\pi$
$464$	−7.73603e6	+	1.33992e7i	−0.0774398	+	0.134130i
$465$		0			0
$466$	4.05038e7	+	7.01547e7i	0.400257	+	0.693265i
$467$	7.53418e7	+	4.34986e7i	0.739751	+	0.427095i	0.821979	−	0.569518i	$-0.192870\pi$
$467$	7.53418e7	+	4.34986e7i	0.739751	+	0.427095i	−0.0822280	+	0.996614i	$0.526204\pi$
$468$		0			0
$469$	−8.72206e7	+	1.21457e8i	−0.845474	+	1.17735i
$470$	1.46774e8			1.41370
$471$		0			0
$472$	−1.23121e7	+	7.10838e6i	−0.117086	+	0.0675997i
$473$	−2.53333e7	−	4.38786e7i	−0.239392	−	0.414639i
$474$		0			0
$475$			495936.i			0.00462748i
$476$	9.20491e6	−	9.25034e7i	0.0853490	−	0.857703i
$477$		0			0
$478$	2.58982e7	−	4.48570e7i	0.237130	−	0.410721i
$479$	1.22097e8	−	7.04928e7i	1.11096	−	0.641413i	0.171883	−	0.985117i	$-0.445015\pi$
$479$	1.22097e8	−	7.04928e7i	1.11096	−	0.641413i	0.939078	+	0.343704i	$0.111682\pi$
$480$		0			0
$481$	−5.68599e6	−	3.28281e6i	−0.0510941	−	0.0294992i
$482$			1.40936e8i			1.25858i
$483$		0			0
$484$	−1.71314e7			−0.151097
$485$	1.49482e8	−	2.58911e8i	1.31028	−	2.26947i
$486$		0			0
$487$	−7.15151e7	−	1.23868e8i	−0.619171	−	1.07244i	−0.989637	−	0.143590i	$-0.954135\pi$
$487$	−7.15151e7	−	1.23868e8i	−0.619171	−	1.07244i	0.370466	−	0.928846i	$-0.379198\pi$
$488$	−2.73874e7	−	1.58121e7i	−0.235663	−	0.136060i
$489$		0			0
$490$	2.45860e7	−	1.22314e8i	0.208978	−	1.03965i
$491$	−9.10418e7			−0.769124			−0.384562	−	0.923099i	$-0.625647\pi$
$491$	−9.10418e7			−0.769124			−0.384562	+	0.923099i	$0.625647\pi$
$492$		0			0
$493$	1.10824e8	−	6.39840e7i	0.924892	−	0.533987i
$494$	50778.6	+	87951.1i	0.000421211	+	0.000729559i
$495$		0			0
$496$		−	1.42576e6i		−	0.0116843i
$497$	7.93166e7	+	1.75526e8i	0.646093	+	1.42979i
$498$		0			0
$499$	2.83073e7	−	4.90296e7i	0.227822	−	0.394600i	−0.729340	−	0.684151i	$-0.760173\pi$
$499$	2.83073e7	−	4.90296e7i	0.227822	−	0.394600i	0.957162	+	0.289551i	$0.0935061\pi$
$500$	2.02192e7	−	1.16736e7i	0.161754	−	0.0933886i
$501$		0			0
$502$	1.00930e8	+	5.82720e7i	0.797828	+	0.460626i
$503$		−	5.77667e7i		−	0.453914i	−0.973905	−	0.226957i	$-0.927122\pi$
$503$		−	5.77667e7i		−	0.453914i	0.973905	−	0.226957i	$-0.0728777\pi$
$504$		0			0
$505$	2.44348e8			1.89729
$506$	2.67142e6	−	4.62703e6i	0.0206201	−	0.0357150i
$507$		0			0
$508$	−1.20389e7	−	2.08519e7i	−0.0918321	−	0.159058i
$509$	−1.43165e8	−	8.26565e7i	−1.08564	−	0.626793i	−0.153225	−	0.988191i	$-0.548966\pi$
$509$	−1.43165e8	−	8.26565e7i	−1.08564	−	0.626793i	−0.932411	+	0.361399i	$0.882299\pi$
$510$		0			0
$511$	−6.18220e7	−	4.43954e7i	−0.463320	−	0.332717i
$512$	5.93164e6			0.0441942
$513$		0			0
$514$	6.09339e7	−	3.51802e7i	0.448714	−	0.259065i
$515$	−622099.	−	1.07751e6i	−0.00455447	−	0.00788857i
$516$		0			0
$517$		−	1.53889e8i		−	1.11362i
$518$	−1.05175e7	+	1.46459e7i	−0.0756697	+	0.105373i
$519$		0			0
$520$	1.19876e7	−	2.07631e7i	0.0852552	−	0.147666i
$521$	−1.07568e6	+	621047.i	−0.00760627	+	0.00439148i	−0.503798	−	0.863821i	$-0.668065\pi$
$521$	−1.07568e6	+	621047.i	−0.00760627	+	0.00439148i	0.496192	+	0.868213i	$0.334731\pi$
$522$		0			0
$523$	3.51923e7	+	2.03183e7i	0.246004	+	0.142030i	0.617933	−	0.786231i	$-0.287970\pi$
$523$	3.51923e7	+	2.03183e7i	0.246004	+	0.142030i	−0.371929	+	0.928261i	$0.621304\pi$
$524$			8.36810e6i			0.0581611i
$525$		0			0
$526$	−1.61071e8			−1.10678
$527$	−5.89617e6	+	1.02125e7i	−0.0402845	+	0.0697749i
$528$		0			0
$529$	7.36571e7	+	1.27578e8i	0.497563	+	0.861804i
$530$	−5.68251e7	−	3.28080e7i	−0.381691	−	0.220370i
$531$		0			0
$532$	254161.	−	114850.i	0.00168800	−	0.000762775i
$533$	7.75964e7			0.512460
$534$		0			0
$535$	2.12995e8	−	1.22973e8i	1.39094	−	0.803060i
$536$	3.94576e7	+	6.83425e7i	0.256234	+	0.443810i
$537$		0			0
$538$			8.28742e7i			0.532197i
$539$	−1.28243e8	−	2.57778e7i	−0.818967	−	0.164619i
$540$		0			0
$541$	9.78002e7	−	1.69395e8i	0.617658	−	1.06981i	−0.372254	−	0.928131i	$-0.621415\pi$
$541$	9.78002e7	−	1.69395e8i	0.617658	−	1.06981i	0.989912	−	0.141684i	$-0.0452517\pi$
$542$	−7.27347e7	+	4.19934e7i	−0.456819	+	0.263744i
$543$		0			0
$544$	−4.24873e7	−	2.45300e7i	−0.263914	−	0.152371i
$545$		−	2.89180e8i		−	1.78640i
$546$		0			0
$547$	9.54532e7			0.583215			0.291607	−	0.956538i	$-0.405810\pi$
$547$	9.54532e7			0.583215			0.291607	+	0.956538i	$0.405810\pi$
$548$	−1.11831e7	+	1.93697e7i	−0.0679548	+	0.117701i
$549$		0			0
$550$	−6.13766e7	−	1.06307e8i	−0.368905	−	0.638963i
$551$	332500.	+	191969.i	0.00198763	+	0.00114756i
$552$		0			0
$553$	−2.27479e8	−	2.26361e7i	−1.34513	−	0.133853i
$554$	1.28017e8			0.752900
$555$		0			0
$556$	4.44231e7	−	2.56477e7i	0.258455	−	0.149219i
$557$	−6.01127e7	−	1.04118e8i	−0.347857	−	0.602506i	0.638012	−	0.770027i	$-0.279757\pi$
$557$	−6.01127e7	−	1.04118e8i	−0.347857	−	0.602506i	−0.985869	+	0.167521i	$0.946424\pi$
$558$		0			0
$559$			3.21959e7i			0.184317i
$560$	−5.34813e7	−	3.84058e7i	−0.304535	−	0.218692i
$561$		0			0
$562$	−7.53814e7	+	1.30564e8i	−0.424674	+	0.735556i
$563$	1.48035e7	−	8.54678e6i	0.0829542	−	0.0478936i	−0.457949	−	0.888978i	$-0.651416\pi$
$563$	1.48035e7	−	8.54678e6i	0.0829542	−	0.0478936i	0.540903	+	0.841085i	$0.318082\pi$
$564$		0			0
$565$	−1.65938e8	−	9.58046e7i	−0.920029	−	0.531179i
$566$			1.47269e8i			0.812197i
$567$		0			0
$568$	1.01653e8			0.554722
$569$	−4.12844e7	+	7.15067e7i	−0.224104	+	0.388159i	−0.956050	−	0.293203i	$-0.905279\pi$
$569$	−4.12844e7	+	7.15067e7i	−0.224104	+	0.388159i	0.731946	+	0.681362i	$0.238612\pi$
$570$		0			0
$571$	−1.49235e7	−	2.58483e7i	−0.0801609	−	0.138843i	0.823158	−	0.567812i	$-0.192210\pi$
$571$	−1.49235e7	−	2.58483e7i	−0.0801609	−	0.138843i	−0.903319	+	0.428970i	$0.858877\pi$
$572$	−2.17695e7	−	1.25686e7i	−0.116322	−	0.0671584i
$573$		0			0
$574$	2.11013e7	−	2.12055e8i	0.111577	−	1.12128i
$575$	−1.65792e7			−0.0872088
$576$		0			0
$577$	−2.57347e8	+	1.48579e8i	−1.33965	+	0.773448i	−0.986756	−	0.162214i	$-0.948136\pi$
$577$	−2.57347e8	+	1.48579e8i	−1.33965	+	0.773448i	−0.352896	+	0.935663i	$0.614803\pi$
$578$	1.34614e8	+	2.33159e8i	0.697121	+	1.20745i
$579$		0			0
$580$		−	9.06382e7i		−	0.464544i
$581$	−2.04306e8	+	9.23218e7i	−1.04172	+	0.470734i
$582$		0			0
$583$	−3.43983e7	+	5.95795e7i	−0.173592	+	0.300671i
$584$	−3.47865e7	+	2.00840e7i	−0.174651	+	0.100835i
$585$		0			0
$586$	1.17967e7	+	6.81084e6i	0.0586230	+	0.0338460i
$587$		−	3.09361e7i		−	0.152950i	−0.997071	−	0.0764752i	$-0.975633\pi$
$587$		−	3.09361e7i		−	0.152950i	0.997071	−	0.0764752i	$-0.0243666\pi$
$588$		0			0
$589$	−35380.1			−0.000173146
$590$	4.16422e7	−	7.21264e7i	0.202758	−	0.351187i
$591$		0			0
$592$	4.75798e6	+	8.24107e6i	0.0229328	+	0.0397208i
$593$	−1.93620e8	−	1.11786e8i	−0.928508	−	0.536075i	−0.0421688	−	0.999110i	$-0.513427\pi$
$593$	−1.93620e8	−	1.11786e8i	−0.928508	−	0.536075i	−0.886339	+	0.463036i	$0.846760\pi$
$594$		0			0
$595$	2.24251e8	+	4.96263e8i	1.06459	+	2.35592i
$596$	1.33505e8			0.630607
$597$		0			0
$598$	−2.94022e6	+	1.69754e6i	−0.0137492	+	0.00793808i
$599$	1.14788e8	+	1.98818e8i	0.534090	+	0.925071i	0.999207	+	0.0398220i	$0.0126791\pi$
$599$	1.14788e8	+	1.98818e8i	0.534090	+	0.925071i	−0.465117	+	0.885249i	$0.653988\pi$
$600$		0			0
$601$		−	2.45821e8i		−	1.13239i	−0.824272	−	0.566194i	$-0.808415\pi$
$601$		−	2.45821e8i		−	1.13239i	0.824272	−	0.566194i	$-0.191585\pi$
$602$	8.79846e7	+	8.75524e6i	0.403290	+	0.0401309i
$603$		0			0
$604$	−9.92746e7	+	1.71949e8i	−0.450534	+	0.780347i
$605$	8.69132e7	−	5.01794e7i	0.392482	−	0.226600i
$606$		0			0
$607$	−1.95506e7	−	1.12875e7i	−0.0874164	−	0.0504699i	0.455655	−	0.890157i	$-0.349405\pi$
$607$	−1.95506e7	−	1.12875e7i	−0.0874164	−	0.0504699i	−0.543071	+	0.839687i	$0.682739\pi$
$608$		−	147193.i		−	0.000654903i
$609$		0			0
$610$	1.85261e8			0.816196
$611$	−4.88940e7	+	8.46868e7i	−0.214354	+	0.371272i
$612$		0			0
$613$	−4.89992e7	−	8.48691e7i	−0.212720	−	0.368441i	0.739845	−	0.672777i	$-0.234899\pi$
$613$	−4.89992e7	−	8.48691e7i	−0.212720	−	0.368441i	−0.952565	+	0.304336i	$0.901565\pi$
$614$	−9.43924e7	−	5.44975e7i	−0.407786	−	0.235435i
$615$		0			0
$616$	−4.02674e7	+	5.60737e7i	−0.172271	+	0.239893i
$617$	−1.51949e7			−0.0646907			−0.0323454	−	0.999477i	$-0.510298\pi$
$617$	−1.51949e7			−0.0646907			−0.0323454	+	0.999477i	$0.510298\pi$
$618$		0			0
$619$	−3.56350e8	+	2.05739e8i	−1.50247	+	0.867450i	−0.502472	+	0.864593i	$0.667576\pi$
$619$	−3.56350e8	+	2.05739e8i	−1.50247	+	0.867450i	−0.999996	+	0.00285722i	$0.999091\pi$
$620$	4.17619e6	+	7.23337e6i	0.0175229	+	0.0303505i
$621$		0			0
$622$			2.13190e8i			0.885922i
$623$	4.49449e6	−	4.51667e7i	0.0185873	−	0.186790i
$624$		0			0
$625$	8.40904e7	−	1.45649e8i	0.344434	−	0.596578i
$626$	1.96655e8	−	1.13539e8i	0.801643	−	0.462829i
$627$		0			0
$628$	5.45495e7	+	3.14942e7i	0.220248	+	0.127160i
$629$		−	7.87057e7i		−	0.316267i
$630$		0			0
$631$	−3.87782e8			−1.54348			−0.771738	−	0.635941i	$-0.780612\pi$
$631$	−3.87782e8			−1.54348			−0.771738	+	0.635941i	$0.780612\pi$
$632$	−6.03227e7	+	1.04482e8i	−0.238963	+	0.413895i
$633$		0			0
$634$	1.51121e8	+	2.61750e8i	0.593005	+	1.02711i
$635$	1.22155e8	+	7.05259e7i	0.477077	+	0.275440i
$636$		0			0
$637$	6.23832e7	+	5.49313e7i	0.241351	+	0.212521i
$638$	−9.50317e7			−0.365937
$639$		0			0
$640$	−3.00932e7	+	1.73743e7i	−0.114797	+	0.0662778i
$641$	−7.01490e7	−	1.21502e8i	−0.266347	−	0.461326i	0.701569	−	0.712602i	$-0.252483\pi$
$641$	−7.01490e7	−	1.21502e8i	−0.266347	−	0.461326i	−0.967916	+	0.251276i	$0.919150\pi$
$642$		0			0
$643$			2.07832e8i			0.781772i	0.920439	+	0.390886i	$0.127831\pi$
$643$			2.07832e8i			0.781772i	−0.920439	+	0.390886i	$0.872169\pi$
$644$	3.83946e6	+	8.49663e6i	0.0143751	+	0.0318119i
$645$		0			0
$646$	−608711.	+	1.05432e6i	−0.00225794	+	0.00391087i
$647$	−6.02345e7	+	3.47764e7i	−0.222399	+	0.128402i	−0.607060	−	0.794656i	$-0.707651\pi$
$647$	−6.02345e7	+	3.47764e7i	−0.222399	+	0.128402i	0.384662	+	0.923058i	$0.374318\pi$
$648$		0			0
$649$	−7.56226e7	−	4.36607e7i	−0.276642	−	0.159719i
$650$			7.80029e7i			0.284034i
$651$		0			0
$652$	3.89985e7			0.140704
$653$	−4.98072e7	+	8.62686e7i	−0.178876	+	0.309823i	−0.941496	−	0.337024i	$-0.890580\pi$
$653$	−4.98072e7	+	8.62686e7i	−0.178876	+	0.309823i	0.762620	+	0.646847i	$0.223913\pi$
$654$		0			0
$655$	−2.45109e7	−	4.24542e7i	−0.0872240	−	0.151076i
$656$	−9.73979e7	−	5.62327e7i	−0.345015	−	0.199194i
$657$		0			0
$658$	2.18135e8	+	1.56647e8i	0.765682	+	0.549849i
$659$	−3.37346e8			−1.17874			−0.589372	−	0.807862i	$-0.700625\pi$
$659$	−3.37346e8			−1.17874			−0.589372	+	0.807862i	$0.700625\pi$
$660$		0			0
$661$	3.16534e8	−	1.82751e8i	1.09601	−	0.632784i	0.160842	−	0.986980i	$-0.448579\pi$
$661$	3.16534e8	−	1.82751e8i	1.09601	−	0.632784i	0.935171	+	0.354196i	$0.115246\pi$
$662$	−5.91995e7	−	1.02536e8i	−0.204053	−	0.353431i
$663$		0			0
$664$			1.18321e8i			0.404163i
$665$	−953036.	+	1.32713e6i	−0.00324074	+	0.00451284i
$666$		0			0
$667$	−6.41755e6	+	1.11155e7i	−0.0216268	+	0.0374587i
$668$	−1.76871e7	+	1.02117e7i	−0.0593373	+	0.0342584i
$669$		0			0
$670$	−4.00363e8	−	2.31150e8i	−1.33116	−	0.768545i
$671$		−	1.94241e8i		−	0.642944i
$672$		0			0
$673$	−4.77356e8			−1.56602			−0.783010	−	0.622008i	$-0.786317\pi$
$673$	−4.77356e8			−1.56602			−0.783010	+	0.622008i	$0.786317\pi$
$674$	−1.44913e7	+	2.50997e7i	−0.0473291	+	0.0819764i
$675$		0			0
$676$	−6.92423e7	−	1.19931e8i	−0.224146	−	0.388232i
$677$	4.89050e8	+	2.82353e8i	1.57611	+	0.909969i	0.995394	+	0.0958642i	$0.0305615\pi$
$677$	4.89050e8	+	2.82353e8i	1.57611	+	0.909969i	0.580718	+	0.814105i	$0.302772\pi$
$678$		0			0
$679$	4.98485e8	−	2.25255e8i	1.59236	−	0.719558i
$680$	2.87403e8			0.914039
$681$		0			0
$682$	7.58399e6	−	4.37862e6i	0.0239081	−	0.0138033i
$683$	2.53875e7	+	4.39724e7i	0.0796814	+	0.138012i	0.903112	−	0.429404i	$-0.141276\pi$
$683$	2.53875e7	+	4.39724e7i	0.0796814	+	0.138012i	−0.823431	+	0.567416i	$0.807943\pi$
$684$		0			0
$685$		−	1.31025e8i		−	0.407646i
$686$	1.67080e8	−	1.55542e8i	0.517551	−	0.481811i
$687$		0			0
$688$	2.33317e7	−	4.04118e7i	0.0716443	−	0.124092i
$689$	3.78595e7	−	2.18582e7i	0.115749	−	0.0668277i
$690$		0			0
$691$	1.50527e8	+	8.69068e7i	0.456226	+	0.263402i	0.710456	−	0.703741i	$-0.248489\pi$
$691$	1.50527e8	+	8.69068e7i	0.456226	+	0.263402i	−0.254230	+	0.967144i	$0.581822\pi$
$692$			1.99020e7i			0.0600592i
$693$		0			0
$694$	−7.55483e6			−0.0226020
$695$	−1.50249e8	+	2.60239e8i	−0.447566	+	0.775206i
$696$		0			0
$697$	4.65095e8	+	8.05569e8i	1.37355	+	2.37905i
$698$	−2.87075e8	−	1.65743e8i	−0.844167	−	0.487380i
$699$		0			0
$700$	2.13166e8	+	2.12119e7i	0.621474	+	0.0618422i
$701$	−1.13297e7			−0.0328899			−0.0164450	−	0.999865i	$-0.505235\pi$
$701$	−1.13297e7			−0.0328899			−0.0164450	+	0.999865i	$0.505235\pi$
$702$		0			0
$703$	204501.	−	118069.i	0.000588613	−	0.000339836i
$704$	1.82165e7	+	3.15519e7i	0.0522092	+	0.0904291i
$705$		0			0
$706$			3.29066e8i			0.935123i
$707$	3.63148e8	+	2.60782e8i	1.02760	+	0.737938i
$708$		0			0
$709$	−9.56188e7	+	1.65617e8i	−0.268290	+	0.464692i	−0.968420	−	0.249323i	$-0.919792\pi$
$709$	−9.56188e7	+	1.65617e8i	−0.268290	+	0.464692i	0.700130	+	0.714015i	$0.253125\pi$
$710$	−5.15720e8	+	2.97751e8i	−1.44092	+	0.831914i
$711$		0			0
$712$	−2.07453e7	−	1.19773e7i	−0.0574751	−	0.0331833i
$713$		−	1.18276e6i		−	0.00326309i
$714$		0			0
$715$	1.47259e8			0.402868
$716$	−8.83397e7	+	1.53009e8i	−0.240667	+	0.416848i
$717$		0			0
$718$	−1.57916e8	−	2.73519e8i	−0.426633	−	0.738949i
$719$	2.80196e8	+	1.61771e8i	0.753832	+	0.435225i	0.827077	−	0.562089i	$-0.190002\pi$
$719$	2.80196e8	+	1.61771e8i	0.753832	+	0.435225i	−0.0732447	+	0.997314i	$0.523335\pi$
$720$		0			0
$721$	225420.	−	2.26533e6i	0.000601432	−	0.00604401i
$722$	2.66128e8			0.707097
$723$		0			0
$724$	−1.05295e8	+	6.07920e7i	−0.277454	+	0.160188i
$725$	1.47445e8	+	2.55383e8i	0.386916	+	0.670158i
$726$		0			0
$727$			1.14232e8i			0.297293i	0.988890	+	0.148646i	$0.0474916\pi$
$727$			1.14232e8i			0.297293i	−0.988890	+	0.148646i	$0.952508\pi$
$728$	3.99755e7	−	1.80641e7i	0.103609	−	0.0468191i
$729$		0			0
$730$	1.17656e8	−	2.03786e8i	0.302443	−	0.523847i
$731$	−3.34242e8	+	1.92975e8i	−0.855675	+	0.494024i
$732$		0			0
$733$	−1.17409e8	−	6.77861e7i	−0.298119	−	0.172119i	0.343479	−	0.939160i	$-0.388395\pi$
$733$	−1.17409e8	−	6.77861e7i	−0.298119	−	0.172119i	−0.641597	+	0.767042i	$0.721728\pi$
$734$			4.91059e7i			0.124178i
$735$		0			0
$736$	4.92069e6			0.0123422
$737$	−2.42354e8	+	4.19770e8i	−0.605408	+	1.04860i
$738$		0			0
$739$	−3.16427e8	−	5.48068e8i	−0.784044	−	1.35800i	−0.929568	−	0.368650i	$-0.879820\pi$
$739$	−3.16427e8	−	5.48068e8i	−0.784044	−	1.35800i	0.145524	−	0.989355i	$-0.453513\pi$
$740$	−4.82777e7	−	2.78731e7i	−0.119138	−	0.0687845i
$741$		0			0
$742$	−4.94385e7	−	1.09406e8i	−0.121019	−	0.267812i
$743$	2.81712e8			0.686814			0.343407	−	0.939187i	$-0.388419\pi$
$743$	2.81712e8			0.686814			0.343407	+	0.939187i	$0.388419\pi$
$744$		0			0
$745$	−6.77316e8	+	3.91048e8i	−1.63803	+	0.945718i
$746$	−1.94864e8	−	3.37514e8i	−0.469370	−	0.812972i
$747$		0			0
$748$		−	3.01334e8i		−	0.720019i
$749$	4.47796e8	+	4.45597e7i	1.06570	+	0.106047i
$750$		0			0
$751$	−3.04177e7	+	5.26850e7i	−0.0718136	+	0.124385i	−0.899696	−	0.436517i	$-0.856212\pi$
$751$	−3.04177e7	+	5.26850e7i	−0.0718136	+	0.124385i	0.827883	+	0.560901i	$0.189545\pi$
$752$	1.22742e8	−	7.08651e7i	0.288629	−	0.166640i
$753$		0			0
$754$	5.22970e7	+	3.01937e7i	0.122001	+	0.0704372i
$755$		−	1.16314e9i		−	2.70265i
$756$		0			0
$757$	6.73226e8			1.55193			0.775967	−	0.630774i	$-0.217262\pi$
$757$	6.73226e8			1.55193			0.775967	+	0.630774i	$0.217262\pi$
$758$	−8.00377e7	+	1.38629e8i	−0.183775	+	0.318308i
$759$		0			0
$760$	431142.	+	746760.i	0.000982155	+	0.00170114i
$761$	−6.88035e8	−	3.97237e8i	−1.56119	−	0.901355i	−0.997137	−	0.0756172i	$-0.975907\pi$
$761$	−6.88035e8	−	3.97237e8i	−1.56119	−	0.901355i	−0.564055	−	0.825737i	$-0.690759\pi$
$762$		0			0
$763$	3.08631e8	−	4.29778e8i	0.694809	−	0.967545i
$764$	1.66760e8			0.373948
$765$		0			0
$766$	−5.28586e8	+	3.05179e8i	−1.17606	+	0.678998i
$767$	2.77440e7	+	4.80540e7i	0.0614869	+	0.106498i
$768$		0			0
$769$			8.61161e7i			0.189367i	0.995507	+	0.0946837i	$0.0301840\pi$
$769$			8.61161e7i			0.189367i	−0.995507	+	0.0946837i	$0.969816\pi$
$770$	4.00451e7	−	4.02428e8i	0.0877157	−	0.881487i
$771$		0			0
$772$	5.80044e7	−	1.00467e8i	0.126069	−	0.218358i
$773$	4.87520e8	−	2.81470e8i	1.05549	−	0.609387i	0.131308	−	0.991342i	$-0.458082\pi$
$773$	4.87520e8	−	2.81470e8i	1.05549	−	0.609387i	0.924181	+	0.381954i	$0.124749\pi$
$774$		0			0
$775$	−2.35337e7	−	1.35872e7i	−0.0505574	−	0.0291894i
$776$		−	2.88690e8i		−	0.617797i
$777$		0			0
$778$	−3.66065e8			−0.777354
$779$	−1.39541e6	+	2.41692e6i	−0.00295181	+	0.00511269i
$780$		0			0
$781$	3.12184e8	+	5.40718e8i	0.655326	+	1.13506i
$782$	−3.52460e7	−	2.03493e7i	−0.0737038	−	0.0425529i
$783$		0			0
$784$	−3.84947e7	−	1.14157e8i	−0.0798827	−	0.236894i
$785$	−3.68997e8			−0.762806
$786$		0			0
$787$	7.72741e8	−	4.46142e8i	1.58529	−	0.915269i	0.591225	−	0.806506i	$-0.298644\pi$
$787$	7.72741e8	−	4.46142e8i	1.58529	−	0.915269i	0.994068	−	0.108763i	$-0.0346889\pi$
$788$	−1.01882e8	−	1.76464e8i	−0.208218	−	0.360644i
$789$		0			0
$790$		−	7.06764e8i		−	1.43348i
$791$	−1.44368e8	−	3.19484e8i	−0.291704	−	0.645534i
$792$		0			0
$793$	−6.17147e7	+	1.06893e8i	−0.123757	+	0.214353i
$794$	−3.70743e8	+	2.14049e8i	−0.740647	+	0.427613i
$795$		0			0
$796$	−1.16491e8	−	6.72561e7i	−0.230969	−	0.133350i
$797$		−	9.48842e7i		−	0.187421i	−0.995599	−	0.0937106i	$-0.970127\pi$
$797$		−	9.48842e7i		−	0.187421i	0.995599	−	0.0937106i	$-0.0298729\pi$
$798$		0			0
$799$	−1.17224e9			−2.29813
$800$	5.65272e7	−	9.79080e7i	0.110405	−	0.191227i
$801$		0			0
$802$	8.80862e6	+	1.52570e7i	0.0170759	+	0.0295764i
$803$	−2.13664e8	−	1.23359e8i	−0.412652	−	0.238245i
$804$		0			0
$805$	−4.43663e7	−	3.18601e7i	−0.0850482	−	0.0610745i
$806$	−5.56474e6			−0.0106277
$807$		0			0
$808$	2.04339e8	−	1.17975e8i	0.387361	−	0.223643i
$809$	4.13738e8	+	7.16615e8i	0.781411	+	1.35344i	0.931120	+	0.364714i	$0.118833\pi$
$809$	4.13738e8	+	7.16615e8i	0.781411	+	1.35344i	−0.149709	+	0.988730i	$0.547834\pi$
$810$		0			0
$811$		−	9.28491e8i		−	1.74066i	−0.492465	−	0.870332i	$-0.663904\pi$
$811$		−	9.28491e8i		−	1.74066i	0.492465	−	0.870332i	$-0.336096\pi$
$812$	9.67345e7	−	1.34706e8i	0.180681	−	0.251605i
$813$		0			0
$814$	−2.92242e7	+	5.06179e7i	−0.0541839	+	0.0938492i
$815$	−1.97853e8	+	1.14230e8i	−0.365485	+	0.211013i
$816$		0			0
$817$	−1.00281e6	−	578975.i	−0.00183888	−	0.00106168i
$818$			6.85991e8i			1.25331i
$819$		0			0
$820$	6.58843e8			1.19492
$821$	2.77346e8	−	4.80377e8i	0.501178	−	0.868065i	−0.498821	−	0.866705i	$-0.666234\pi$
$821$	2.77346e8	−	4.80377e8i	0.501178	−	0.868065i	0.999999	−	0.00136052i	$-0.000433067\pi$
$822$		0			0
$823$	4.45911e8	+	7.72340e8i	0.799924	+	1.38551i	0.919665	+	0.392703i	$0.128460\pi$
$823$	4.45911e8	+	7.72340e8i	0.799924	+	1.38551i	−0.119741	+	0.992805i	$0.538207\pi$
$824$	−1.04048e6	−	600719.i	−0.00185973	−	0.00107372i
$825$		0			0
$826$	1.38866e8	−	6.27508e7i	0.246409	−	0.111347i
$827$	1.38059e8			0.244089			0.122044	−	0.992525i	$-0.461055\pi$
$827$	1.38059e8			0.244089			0.122044	+	0.992525i	$0.461055\pi$
$828$		0			0
$829$	−1.20818e8	+	6.97541e7i	−0.212064	+	0.122435i	−0.602270	−	0.798292i	$-0.705737\pi$
$829$	−1.20818e8	+	6.97541e7i	−0.212064	+	0.122435i	0.390206	+	0.920727i	$0.372404\pi$
$830$	−3.46572e8	−	6.00280e8i	−0.606121	−	1.04983i
$831$		0			0
$832$		−	2.31512e7i		−	0.0401978i
$833$	−1.96360e8	+	9.76878e8i	−0.339718	+	1.69007i
$834$		0			0
$835$	5.98218e7	−	1.03614e8i	0.102754	−	0.177976i
$836$	782958.	−	452041.i	0.00134005	−	0.000773676i
$837$		0			0
$838$	5.28829e7	+	3.05320e7i	0.0898635	+	0.0518827i
$839$		−	2.67389e8i		−	0.452750i	−0.974040	−	0.226375i	$-0.927313\pi$
$839$		−	2.67389e8i		−	0.452750i	0.974040	−	0.226375i	$-0.0726874\pi$
$840$		0			0
$841$	−3.66528e8			−0.616197
$842$	1.46107e7	−	2.53065e7i	0.0244757	−	0.0423932i
$843$		0			0
$844$	2.13677e8	+	3.70100e8i	0.355411	+	0.615590i
$845$	7.02579e8	+	4.05634e8i	1.16446	+	0.672302i
$846$		0			0
$847$	1.82724e8	+	1.81827e7i	0.300709	+	0.0299232i
$848$	−6.33609e7			−0.103904
$849$		0			0
$850$	−8.09788e8	+	4.67532e8i	−1.31861	+	0.761297i
$851$	3.94706e6	+	6.83651e6i	0.00640450	+	0.0110929i
$852$		0			0
$853$		−	6.69761e8i		−	1.07913i	−0.841945	−	0.539564i	$-0.818589\pi$
$853$		−	6.69761e8i		−	1.07913i	0.841945	−	0.539564i	$-0.181411\pi$
$854$	2.75334e8	+	1.97722e8i	0.442065	+	0.317454i
$855$		0			0
$856$	1.18747e8	−	2.05675e8i	0.189321	−	0.327914i
$857$	3.50523e8	−	2.02375e8i	0.556897	−	0.321524i	−0.195002	−	0.980803i	$-0.562471\pi$
$857$	3.50523e8	−	2.02375e8i	0.556897	−	0.321524i	0.751899	+	0.659278i	$0.229138\pi$
$858$		0			0
$859$	−2.97655e8	−	1.71851e8i	−0.469607	−	0.271128i	0.246468	−	0.969151i	$-0.420730\pi$
$859$	−2.97655e8	−	1.71851e8i	−0.469607	−	0.271128i	−0.716075	+	0.698023i	$0.754063\pi$
$860$			2.73363e8i			0.429779i
$861$		0			0
$862$	6.49737e8			1.01442
$863$	3.74953e8	−	6.49438e8i	0.583371	−	1.01043i	−0.411706	−	0.911317i	$-0.635067\pi$
$863$	3.74953e8	−	6.49438e8i	0.583371	−	1.01043i	0.995076	−	0.0991110i	$-0.0315999\pi$
$864$		0			0
$865$	−5.82949e7	−	1.00970e8i	−0.0900705	−	0.156007i
$866$	−1.03149e8	−	5.95529e7i	−0.158822	−	0.0916958i
$867$		0			0
$868$	−1.51326e6	+	1.52073e7i	−0.00231395	+	0.0232537i
$869$	−7.41023e8			−1.12920
$870$		0			0
$871$	2.66740e8	−	1.54003e8i	0.403677	−	0.233063i
$872$	−1.39621e8	−	2.41831e8i	−0.210572	−	0.364722i
$873$		0			0
$874$		−	122106.i		−	0.000182896i
$875$	−2.28050e8	+	1.03051e8i	−0.340412	+	0.153826i
$876$		0			0
$877$	7.44757e7	−	1.28996e8i	0.110412	−	0.191239i	−0.805524	−	0.592562i	$-0.798116\pi$
$877$	7.44757e7	−	1.28996e8i	0.110412	−	0.191239i	0.915936	+	0.401323i	$0.131450\pi$
$878$	−3.22223e7	+	1.86035e7i	−0.0476072	+	0.0274860i
$879$		0			0
$880$	−1.84837e8	−	1.06716e8i	−0.271232	−	0.156596i
$881$			1.17850e9i			1.72346i	0.507368	+	0.861729i	$0.330618\pi$
$881$			1.17850e9i			1.72346i	−0.507368	+	0.861729i	$0.669382\pi$
$882$		0			0
$883$	4.71777e8			0.685259			0.342630	−	0.939471i	$-0.388682\pi$
$883$	4.71777e8			0.685259			0.342630	+	0.939471i	$0.388682\pi$
$884$	−9.57406e7	+	1.65828e8i	−0.138592	+	0.240049i
$885$		0			0
$886$	−2.20395e8	−	3.81735e8i	−0.316884	−	0.548860i
$887$	2.67515e7	+	1.54450e7i	0.0383334	+	0.0221318i	0.519044	−	0.854747i	$-0.326288\pi$
$887$	2.67515e7	+	1.54450e7i	0.0383334	+	0.0221318i	−0.480711	+	0.876879i	$0.659621\pi$
$888$		0			0
$889$	1.06276e8	+	2.35186e8i	0.151262	+	0.334739i
$890$	1.40331e8			0.199059
$891$		0			0
$892$	1.93601e8	−	1.11776e8i	0.272780	−	0.157490i
$893$	−1.75851e6	−	3.04583e6i	−0.00246939	−	0.00427712i
$894$		0			0
$895$		−	1.03502e9i		−	1.44371i
$896$	−6.32673e7	−	6.29566e6i	−0.0879540	−	0.00875220i
$897$		0			0
$898$	4.24141e8	−	7.34633e8i	0.585708	−	1.01448i
$899$	−1.82190e7	+	1.05188e7i	−0.0250753	+	0.0144772i
$900$		0			0
$901$	4.53842e8	+	2.62026e8i	0.620484	+	0.358237i
$902$		−	6.90779e8i		−	0.941282i
$903$		0			0
$904$	−1.85024e8			−0.250451
$905$	3.56131e8	−	6.16837e8i	0.480467	−	0.832194i
$906$		0			0
$907$	3.53032e8	+	6.11470e8i	0.473143	+	0.819508i	0.999527	−	0.0307389i	$-0.00978602\pi$
$907$	3.53032e8	+	6.11470e8i	0.473143	+	0.819508i	−0.526384	+	0.850247i	$0.676453\pi$
$908$	−1.33166e7	−	7.68836e6i	−0.0177884	−	0.0102701i
$909$		0			0
$910$	−1.49897e8	+	2.08737e8i	−0.198916	+	0.276997i
$911$	−4.46529e8			−0.590602			−0.295301	−	0.955404i	$-0.595420\pi$
$911$	−4.46529e8			−0.590602			−0.295301	+	0.955404i	$0.595420\pi$
$912$		0			0
$913$	−6.29378e8	+	3.63371e8i	−0.826988	+	0.477462i
$914$	3.58858e8	+	6.21559e8i	0.469984	+	0.814037i
$915$		0			0
$916$			3.66595e8i			0.476980i
$917$	8.88163e6	−	8.92547e7i	0.0115182	−	0.115751i
$918$		0			0
$919$	3.00517e8	−	5.20511e8i	0.387188	−	0.670630i	−0.604882	−	0.796315i	$-0.706780\pi$
$919$	3.00517e8	−	5.20511e8i	0.387188	−	0.670630i	0.992070	+	0.125685i	$0.0401130\pi$
$920$	−2.49643e7	+	1.44132e7i	−0.0320595	+	0.0185095i
$921$		0			0
$922$	−4.08931e8	−	2.36097e8i	−0.521744	−	0.301229i
$923$		−	3.96751e8i		−	0.504560i
$924$		0			0
$925$	1.81370e8			0.229161
$926$	3.70727e8	−	6.42118e8i	0.466897	−	0.808689i
$927$		0			0
$928$	−4.37616e7	−	7.57973e7i	−0.0547582	−	0.0948440i
$929$	−8.46917e8	−	4.88968e8i	−1.05632	−	0.609864i	−0.131904	−	0.991262i	$-0.542109\pi$
$929$	−8.46917e8	−	4.88968e8i	−1.05632	−	0.609864i	−0.924411	+	0.381399i	$0.875443\pi$
$930$		0			0
$931$	−2.83279e6	+	955242.i	−0.00351047	+	0.00118376i
$932$	−4.58249e8			−0.566048
$933$		0			0
$934$	−4.26198e8	+	2.46065e8i	−0.523083	+	0.302002i
$935$	8.82636e8	+	1.52877e9i	1.07981	+	1.87028i
$936$		0			0
$937$		−	1.61274e8i		−	0.196041i	−0.995184	−	0.0980205i	$-0.968749\pi$
$937$		−	1.61274e8i		−	0.196041i	0.995184	−	0.0980205i	$-0.0312511\pi$
$938$	−3.48321e8	−	7.70825e8i	−0.422057	−	0.934001i
$939$		0			0
$940$	−4.15141e8	+	7.19045e8i	−0.499818	+	0.865710i
$941$	−2.13148e8	+	1.23061e8i	−0.255807	+	0.147690i	−0.622420	−	0.782683i	$-0.713851\pi$
$941$	−2.13148e8	+	1.23061e8i	−0.255807	+	0.147690i	0.366613	+	0.930373i	$0.380517\pi$
$942$		0			0
$943$	−8.07980e7	−	4.66487e7i	−0.0963530	−	0.0556294i
$944$		−	8.04221e7i		−	0.0956004i
$945$		0			0
$946$	2.86614e8			0.338551
$947$	7.08264e8	−	1.22675e9i	0.833960	−	1.44446i	−0.0609142	−	0.998143i	$-0.519402\pi$
$947$	7.08264e8	−	1.22675e9i	0.833960	−	1.44446i	0.894874	−	0.446318i	$-0.147265\pi$
$948$		0			0
$949$	7.83876e7	+	1.35771e8i	0.0917168	+	0.158858i
$950$	−2.42958e6	−	1.40272e6i	−0.00283374	−	0.00163606i
$951$		0			0
$952$	4.27137e8	+	3.06734e8i	0.495058	+	0.355509i
$953$	−7.96546e8			−0.920306			−0.460153	−	0.887840i	$-0.652205\pi$
$953$	−7.96546e8			−0.920306			−0.460153	+	0.887840i	$0.652205\pi$
$954$		0			0
$955$	−8.46029e8	+	4.88455e8i	−0.971349	+	0.560808i
$956$	1.46502e8	+	2.53750e8i	0.167676	+	0.290423i
$957$		0			0
$958$			7.97535e8i			0.907095i
$959$	1.39838e8	−	1.94729e8i	0.158551	−	0.220788i
$960$		0			0
$961$	−4.42783e8	+	7.66922e8i	−0.498908	+	0.864134i
$962$	3.21648e7	−	1.85704e7i	0.0361290	−	0.0208591i
$963$		0			0
$964$	−6.90443e8	−	3.98628e8i	−0.770720	−	0.444976i
$965$			6.79601e8i			0.756262i
$966$		0			0
$967$	−3.27333e6			−0.00362002			−0.00181001	−	0.999998i	$-0.500576\pi$
$967$	−3.27333e6			−0.00362002			−0.00181001	+	0.999998i	$0.500576\pi$
$968$	4.84548e7	−	8.39262e7i	0.0534209	−	0.0925277i
$969$		0			0
$970$	8.45599e8	+	1.46462e9i	0.926508	+	1.60476i
$971$	6.30904e8	+	3.64252e8i	0.689137	+	0.397873i	0.803289	−	0.595590i	$-0.203082\pi$
$971$	6.30904e8	+	3.64252e8i	0.689137	+	0.397873i	−0.114152	+	0.993463i	$0.536415\pi$
$972$		0			0
$973$	−5.01041e8	+	2.26411e8i	−0.543920	+	0.245787i
$974$	8.09100e8			0.875640
$975$		0			0
$976$	1.54927e8	−	8.94470e7i	0.166639	−	0.0962091i
$977$	2.38256e8	+	4.12672e8i	0.255482	+	0.442508i	0.965026	−	0.262153i	$-0.0844325\pi$
$977$	2.38256e8	+	4.12672e8i	0.255482	+	0.442508i	−0.709544	+	0.704661i	$0.751099\pi$
$978$		0			0
$979$		−	1.47133e8i		−	0.156806i
$980$	5.29673e8	+	4.66402e8i	0.562768	+	0.495544i
$981$		0			0
$982$	2.57505e8	−	4.46012e8i	0.271926	−	0.470990i
$983$	1.44830e8	−	8.36176e7i	0.152475	−	0.0880313i	−0.421822	−	0.906679i	$-0.638609\pi$
$983$	1.44830e8	−	8.36176e7i	0.152475	−	0.0880313i	0.574296	+	0.818648i	$0.305276\pi$
$984$		0			0
$985$	1.03376e9	+	5.96842e8i	1.08171	+	0.624526i
$986$			7.23896e8i			0.755171i
$987$		0			0
$988$	−574494.			−0.000595682
$989$	1.93552e7	−	3.35242e7i	0.0200083	−	0.0346553i
$990$		0			0
$991$	1.09069e8	+	1.88913e8i	0.112068	+	0.194107i	0.916604	−	0.399797i	$-0.130919\pi$
$991$	1.09069e8	+	1.88913e8i	0.112068	+	0.194107i	−0.804536	+	0.593904i	$0.797586\pi$
$992$	6.98478e6	+	4.03266e6i	0.00715513	+	0.00413102i
$993$		0			0
$994$	−1.08424e9	−	1.07891e8i	−1.10399	−	0.109857i
$995$	7.87997e8			0.799936
$996$		0			0
$997$	−1.41152e8	+	8.14940e7i	−0.142430	+	0.0822319i	−0.569521	−	0.821976i	$-0.692871\pi$
$997$	−1.41152e8	+	8.14940e7i	−0.142430	+	0.0822319i	0.427092	+	0.904208i	$0.359538\pi$
$998$	1.60130e8	+	2.77353e8i	0.161095	+	0.279024i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.7.n.c.19.2		8
3.2	odd	2		14.7.d.a.5.3	yes	8
7.3	odd	6	inner	126.7.n.c.73.2		8
12.11	even	2		112.7.s.c.33.4		8
21.2	odd	6		98.7.b.c.97.1		8
21.5	even	6		98.7.b.c.97.4		8
21.11	odd	6		98.7.d.c.31.4		8
21.17	even	6		14.7.d.a.3.3	✓	8
21.20	even	2		98.7.d.c.19.4		8
84.59	odd	6		112.7.s.c.17.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.d.a.3.3	✓	8	21.17	even	6
14.7.d.a.5.3	yes	8	3.2	odd	2
98.7.b.c.97.1		8	21.2	odd	6
98.7.b.c.97.4		8	21.5	even	6
98.7.d.c.19.4		8	21.20	even	2
98.7.d.c.31.4		8	21.11	odd	6
112.7.s.c.17.4		8	84.59	odd	6
112.7.s.c.33.4		8	12.11	even	2
126.7.n.c.19.2		8	1.1	even	1	trivial
126.7.n.c.73.2		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)

\(f(q)\)	\(=\)	\(q+(-2.82843 + 4.89898i) q^{2} +(-16.0000 - 27.7128i) q^{4} +(162.347 + 93.7310i) q^{5} +(141.244 + 312.569i) q^{7} +181.019 q^{8} +(-918.372 + 530.222i) q^{10} +(555.924 + 962.889i) q^{11} -706.517i q^{13} +(-1930.77 - 192.128i) q^{14} +(-512.000 + 886.810i) q^{16} +(7334.73 - 4234.71i) q^{17} +(22.0061 + 12.7052i) q^{19} -5998.78i q^{20} -6289.56 q^{22} +(-424.738 + 735.668i) q^{23} +(9758.49 + 16902.2i) q^{25} +(3461.21 + 1998.33i) q^{26} +(6402.26 - 8915.36i) q^{28} +15109.4 q^{29} +(-1205.81 + 696.173i) q^{31} +(-2896.31 - 5016.55i) q^{32} +47910.2i q^{34} +(-6366.92 + 63983.4i) q^{35} +(4646.47 - 8047.92i) q^{37} +(-124.485 + 71.8716i) q^{38} +(29387.9 + 16967.1i) q^{40} +109829. i q^{41} -45569.8 q^{43} +(17789.6 - 30812.4i) q^{44} +(-2402.68 - 4161.56i) q^{46} +(-119865. - 69204.2i) q^{47} +(-77749.5 + 88296.7i) q^{49} -110405. q^{50} +(-19579.6 + 11304.3i) q^{52} +(30937.9 + 53586.1i) q^{53} +208429. i q^{55} +(25567.8 + 56581.0i) q^{56} +(-42735.9 + 74020.8i) q^{58} +(-68015.2 + 39268.6i) q^{59} +(-151296. - 87350.5i) q^{61} -7876.29i q^{62} +32768.0 q^{64} +(66222.6 - 114701. i) q^{65} +(217974. + 377543. i) q^{67} +(-234711. - 135511. i) q^{68} +(-295445. - 212164. i) q^{70} +561559. q^{71} +(-192170. + 110949. i) q^{73} +(26284.4 + 45525.9i) q^{74} -813.135i q^{76} +(-222448. + 309766. i) q^{77} +(-333239. + 577187. i) q^{79} +(-166243. + 95980.5i) q^{80} +(-538052. - 310645. i) q^{82} +653635. i q^{83} +1.58769e6 q^{85} +(128891. - 223245. i) q^{86} +(100633. + 174301. i) q^{88} +(-114603. - 66165.9i) q^{89} +(220835. - 99791.1i) q^{91} +27183.2 q^{92} +(678060. - 391478. i) q^{94} +(2381.75 + 4125.31i) q^{95} -1.59480e6i q^{97} +(-212655. - 630634. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 128 q^{4} + 336 q^{5} + 652 q^{7} - 2016 q^{10} + 1356 q^{11} - 2064 q^{14} - 4096 q^{16} + 17304 q^{17} - 32004 q^{19} + 25248 q^{22} + 4128 q^{23} + 4664 q^{25} + 4704 q^{26} - 7552 q^{28} + 30312 q^{29}+ \cdots + 3532320 q^{98}+O(q^{100}) \) 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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