LMFDB - Embedded newform 48.7.i.a.5.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(5,48)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.34
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.38773 - 5.91374i) q^{2} +(-25.4451 - 9.03029i) q^{3} +(-5.94475 - 63.7233i) q^{4} +(-65.5814 + 65.5814i) q^{5} +(-190.494 + 101.823i) q^{6} +515.866i q^{7} +(-408.872 - 308.168i) q^{8} +(565.908 + 459.554i) q^{9} +O(q^{10})$	\(q+(5.38773 - 5.91374i) q^{2} +(-25.4451 - 9.03029i) q^{3} +(-5.94475 - 63.7233i) q^{4} +(-65.5814 + 65.5814i) q^{5} +(-190.494 + 101.823i) q^{6} +515.866i q^{7} +(-408.872 - 308.168i) q^{8} +(565.908 + 459.554i) q^{9} +(34.4968 + 741.166i) q^{10} +(888.817 - 888.817i) q^{11} +(-424.175 + 1675.13i) q^{12} +(500.230 - 500.230i) q^{13} +(3050.70 + 2779.35i) q^{14} +(2260.94 - 1076.51i) q^{15} +(-4025.32 + 757.638i) q^{16} +7261.49i q^{17} +(5766.64 - 870.683i) q^{18} +(-7422.29 + 7422.29i) q^{19} +(4568.93 + 3789.20i) q^{20} +(4658.42 - 13126.3i) q^{21} +(-467.531 - 10044.9i) q^{22} -4013.78 q^{23} +(7620.95 + 11533.6i) q^{24} +7023.17i q^{25} +(-263.128 - 5653.33i) q^{26} +(-10249.7 - 16803.7i) q^{27} +(32872.7 - 3066.69i) q^{28} +(10151.7 + 10151.7i) q^{29} +(5815.17 - 19170.6i) q^{30} -39733.9 q^{31} +(-17206.9 + 27886.7i) q^{32} +(-30642.3 + 14589.8i) q^{33} +(42942.6 + 39122.9i) q^{34} +(-33831.2 - 33831.2i) q^{35} +(25920.1 - 38793.4i) q^{36} +(32290.7 + 32290.7i) q^{37} +(3904.24 + 83882.9i) q^{38} +(-17245.6 + 8211.18i) q^{39} +(47024.5 - 6604.29i) q^{40} -56655.0 q^{41} +(-52527.1 - 98269.6i) q^{42} +(3710.24 + 3710.24i) q^{43} +(-61922.2 - 51354.6i) q^{44} +(-67251.2 + 6974.85i) q^{45} +(-21625.1 + 23736.4i) q^{46} -157041. i q^{47} +(109266. + 17071.6i) q^{48} -148469. q^{49} +(41533.2 + 37838.9i) q^{50} +(65573.4 - 184769. i) q^{51} +(-34850.0 - 28902.6i) q^{52} +(110634. - 110634. i) q^{53} +(-154595. - 29919.8i) q^{54} +116580. i q^{55} +(158974. - 210923. i) q^{56} +(255887. - 121836. i) q^{57} +(114729. - 5339.94i) q^{58} +(-176290. + 176290. i) q^{59} +(-82039.3 - 137675. i) q^{60} +(-28991.5 + 28991.5i) q^{61} +(-214076. + 234976. i) q^{62} +(-237068. + 291933. i) q^{63} +(72208.7 + 252003. i) q^{64} +65611.5i q^{65} +(-78812.4 + 259817. i) q^{66} +(228444. - 228444. i) q^{67} +(462726. - 43167.7i) q^{68} +(102131. + 36245.6i) q^{69} +(-382343. + 17795.7i) q^{70} -118484. q^{71} +(-89764.0 - 362293. i) q^{72} +693029. i q^{73} +(364932. - 16985.4i) q^{74} +(63421.2 - 178705. i) q^{75} +(517097. + 428850. i) q^{76} +(458511. + 458511. i) q^{77} +(-44355.9 + 146226. i) q^{78} +457198. q^{79} +(214299. - 313673. i) q^{80} +(109062. + 520130. i) q^{81} +(-305242. + 335043. i) q^{82} +(-494289. - 494289. i) q^{83} +(-864143. - 218818. i) q^{84} +(-476219. - 476219. i) q^{85} +(41931.1 - 1951.64i) q^{86} +(-166638. - 349983. i) q^{87} +(-637318. + 89507.3i) q^{88} -96004.8 q^{89} +(-321084. + 435285. i) q^{90} +(258052. + 258052. i) q^{91} +(23860.9 + 255771. i) q^{92} +(1.01103e6 + 358809. i) q^{93} +(-928702. - 846096. i) q^{94} -973529. i q^{95} +(689655. - 554196. i) q^{96} +1.32256e6 q^{97} +(-799911. + 878008. i) q^{98} +(911448. - 94529.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	5.38773	−	5.91374i	0.673466	−	0.739218i
$2$	5.38773	−	5.91374i	0.673466	−	0.739218i
$3$	−25.4451	−	9.03029i	−0.942412	−	0.334455i
$3$	−25.4451	−	9.03029i	−0.942412	−	0.334455i
$4$	−5.94475	−	63.7233i	−0.0928866	−	0.995677i
$5$	−65.5814	+	65.5814i	−0.524651	+	0.524651i	−0.918973	−	0.394322i	$-0.870980\pi$
$5$	−65.5814	+	65.5814i	−0.524651	+	0.524651i	0.394322	+	0.918973i	$0.370980\pi$
$6$	−190.494	+	101.823i	−0.881918	+	0.471403i
$7$			515.866i			1.50398i	0.659172	+	0.751992i	$0.270907\pi$
$7$			515.866i			1.50398i	−0.659172	+	0.751992i	$0.729093\pi$
$8$	−408.872	−	308.168i	−0.798578	−	0.601891i
$9$	565.908	+	459.554i	0.776279	+	0.630389i
$10$	34.4968	+	741.166i	0.0344968	+	0.741166i
$11$	888.817	−	888.817i	0.667782	−	0.667782i	−0.289420	−	0.957202i	$-0.593463\pi$
$11$	888.817	−	888.817i	0.667782	−	0.667782i	0.957202	+	0.289420i	$0.0934625\pi$
$12$	−424.175	+	1675.13i	−0.245472	+	0.969404i
$13$	500.230	−	500.230i	0.227688	−	0.227688i	−0.584038	−	0.811726i	$-0.698528\pi$
$13$	500.230	−	500.230i	0.227688	−	0.227688i	0.811726	+	0.584038i	$0.198528\pi$
$14$	3050.70	+	2779.35i	1.11177	+	1.01288i
$15$	2260.94	−	1076.51i	0.669909	−	0.318965i
$16$	−4025.32	+	757.638i	−0.982744	+	0.184970i
$17$			7261.49i			1.47802i	0.673697	+	0.739008i	$0.264705\pi$
$17$			7261.49i			1.47802i	−0.673697	+	0.739008i	$0.735295\pi$
$18$	5766.64	−	870.683i	0.988793	−	0.149294i
$19$	−7422.29	+	7422.29i	−1.08212	+	1.08212i	−0.0858137	+	0.996311i	$0.527349\pi$
$19$	−7422.29	+	7422.29i	−1.08212	+	1.08212i	−0.996311	+	0.0858137i	$0.972651\pi$
$20$	4568.93	+	3789.20i	0.571116	+	0.473650i
$21$	4658.42	−	13126.3i	0.503015	−	1.41737i
$22$	−467.531	−	10044.9i	−0.0439079	−	0.943365i
$23$	−4013.78			−0.329890			−0.164945	−	0.986303i	$-0.552745\pi$
$23$	−4013.78			−0.329890			−0.164945	+	0.986303i	$0.552745\pi$
$24$	7620.95	+	11533.6i	0.551284	+	0.834318i
$25$			7023.17i			0.449483i
$26$	−263.128	−	5653.33i	−0.0149709	−	0.321651i
$27$	−10249.7	−	16803.7i	−0.520738	−	0.853717i
$28$	32872.7	−	3066.69i	1.49748	−	0.139700i
$29$	10151.7	+	10151.7i	0.416240	+	0.416240i	0.883906	−	0.467665i	$-0.154905\pi$
$29$	10151.7	+	10151.7i	0.416240	+	0.416240i	−0.467665	+	0.883906i	$0.654905\pi$
$30$	5815.17	−	19170.6i	0.215377	−	0.710021i
$31$	−39733.9			−1.33376			−0.666878	−	0.745167i	$-0.732370\pi$
$31$	−39733.9			−1.33376			−0.666878	+	0.745167i	$0.732370\pi$
$32$	−17206.9	+	27886.7i	−0.525112	+	0.851033i
$33$	−30642.3	+	14589.8i	−0.852668	+	0.405982i
$34$	42942.6	+	39122.9i	1.09258	+	0.995393i
$35$	−33831.2	−	33831.2i	−0.789066	−	0.789066i
$36$	25920.1	−	38793.4i	0.555558	−	0.831478i
$37$	32290.7	+	32290.7i	0.637488	+	0.637488i	0.949935	−	0.312447i	$-0.101149\pi$
$37$	32290.7	+	32290.7i	0.637488	+	0.637488i	−0.312447	+	0.949935i	$0.601149\pi$
$38$	3904.24	+	83882.9i	0.0711518	+	1.52870i
$39$	−17245.6	+	8211.18i	−0.290727	+	0.138424i
$40$	47024.5	−	6604.29i	0.734758	−	0.103192i
$41$	−56655.0			−0.822029			−0.411014	−	0.911629i	$-0.634825\pi$
$41$	−56655.0			−0.822029			−0.411014	+	0.911629i	$0.634825\pi$
$42$	−52527.1	−	98269.6i	−0.708983	−	1.32639i
$43$	3710.24	+	3710.24i	0.0466655	+	0.0466655i	0.730054	−	0.683389i	$-0.239495\pi$
$43$	3710.24	+	3710.24i	0.0466655	+	0.0466655i	−0.683389	+	0.730054i	$0.739495\pi$
$44$	−61922.2	−	51354.6i	−0.726923	−	0.602867i
$45$	−67251.2	+	6974.85i	−0.738010	+	0.0765415i
$46$	−21625.1	+	23736.4i	−0.222170	+	0.243861i
$47$		−	157041.i		−	1.51259i	−0.654233	−	0.756293i	$-0.727008\pi$
$47$		−	157041.i		−	1.51259i	0.654233	−	0.756293i	$-0.272992\pi$
$48$	109266.	+	17071.6i	0.988014	+	0.154366i
$49$	−148469.			−1.26197
$50$	41533.2	+	37838.9i	0.332266	+	0.302711i
$51$	65573.4	−	184769.i	0.494330	−	1.39290i
$52$	−34850.0	−	28902.6i	−0.247852	−	0.205554i
$53$	110634.	−	110634.i	0.743124	−	0.743124i	−0.230054	−	0.973178i	$-0.573890\pi$
$53$	110634.	−	110634.i	0.743124	−	0.743124i	0.973178	+	0.230054i	$0.0738902\pi$
$54$	−154595.	−	29919.8i	−0.981782	−	0.190010i
$55$			116580.i			0.700705i
$56$	158974.	−	210923.i	0.905234	−	1.20105i
$57$	255887.	−	121836.i	1.38173	−	0.657885i
$58$	114729.	−	5339.94i	0.588016	−	0.0273686i
$59$	−176290.	+	176290.i	−0.858363	+	0.858363i	−0.991145	−	0.132782i	$-0.957609\pi$
$59$	−176290.	+	176290.i	−0.858363	+	0.858363i	0.132782	+	0.991145i	$0.457609\pi$
$60$	−82039.3	−	137675.i	−0.379812	−	0.637386i
$61$	−28991.5	+	28991.5i	−0.127726	+	0.127726i	−0.768080	−	0.640354i	$-0.778788\pi$
$61$	−28991.5	+	28991.5i	−0.127726	+	0.127726i	0.640354	+	0.768080i	$0.278788\pi$
$62$	−214076.	+	234976.i	−0.898239	+	0.985936i
$63$	−237068.	+	291933.i	−0.948095	+	1.16751i
$64$	72208.7	+	252003.i	0.275454	+	0.961314i
$65$			65611.5i			0.238913i
$66$	−78812.4	+	259817.i	−0.274134	+	0.903723i
$67$	228444.	−	228444.i	0.759549	−	0.759549i	−0.216691	−	0.976240i	$-0.569526\pi$
$67$	228444.	−	228444.i	0.759549	−	0.759549i	0.976240	+	0.216691i	$0.0695264\pi$
$68$	462726.	−	43167.7i	1.47163	−	0.137288i
$69$	102131.	+	36245.6i	0.310893	+	0.110334i
$70$	−382343.	+	17795.7i	−1.11470	+	0.0518826i
$71$	−118484.			−0.331042			−0.165521	−	0.986206i	$-0.552931\pi$
$71$	−118484.			−0.331042			−0.165521	+	0.986206i	$0.552931\pi$
$72$	−89764.0	−	362293.i	−0.240494	−	0.970651i
$73$			693029.i			1.78149i	0.454506	+	0.890744i	$0.349816\pi$
$73$			693029.i			1.78149i	−0.454506	+	0.890744i	$0.650184\pi$
$74$	364932.	−	16985.4i	0.900569	−	0.0419160i
$75$	63421.2	−	178705.i	0.150332	−	0.423598i
$76$	517097.	+	428850.i	1.17796	+	0.976932i
$77$	458511.	+	458511.i	1.00433	+	1.00433i
$78$	−44355.9	+	146226.i	−0.0934690	+	0.308135i
$79$	457198.			0.927306			0.463653	−	0.886017i	$-0.346538\pi$
$79$	457198.			0.927306			0.463653	+	0.886017i	$0.346538\pi$
$80$	214299.	−	313673.i	0.418553	−	0.612642i
$81$	109062.	+	520130.i	0.205219	+	0.978716i
$82$	−305242.	+	335043.i	−0.553608	+	0.607658i
$83$	−494289.	−	494289.i	−0.864464	−	0.864464i	0.127389	−	0.991853i	$-0.459340\pi$
$83$	−494289.	−	494289.i	−0.864464	−	0.864464i	−0.991853	+	0.127389i	$0.959340\pi$
$84$	−864143.	−	218818.i	−1.45797	−	0.369186i
$85$	−476219.	−	476219.i	−0.775442	−	0.775442i
$86$	41931.1	−	1951.64i	0.0659236	−	0.00306835i
$87$	−166638.	−	349983.i	−0.253056	−	0.531483i
$88$	−637318.	+	89507.3i	−0.935208	+	0.131344i
$89$	−96004.8			−0.136183			−0.0680915	−	0.997679i	$-0.521691\pi$
$89$	−96004.8			−0.136183			−0.0680915	+	0.997679i	$0.521691\pi$
$90$	−321084.	+	435285.i	−0.440444	+	0.597098i
$91$	258052.	+	258052.i	0.342439	+	0.342439i
$92$	23860.9	+	255771.i	0.0306424	+	0.328464i
$93$	1.01103e6	+	358809.i	1.25695	+	0.446082i
$94$	−928702.	−	846096.i	−1.11813	−	1.01868i
$95$		−	973529.i		−	1.13548i
$96$	689655.	−	554196.i	0.779504	−	0.626397i
$97$	1.32256e6			1.44911			0.724555	−	0.689217i	$-0.242045\pi$
$97$	1.32256e6			1.44911			0.724555	+	0.689217i	$0.242045\pi$
$98$	−799911.	+	878008.i	−0.849892	+	0.932869i
$99$	911448.	−	94529.4i	0.939347	−	0.0974229i
$100$	447539.	−	41750.9i	0.447539	−	0.0417509i
$101$	54030.7	−	54030.7i	0.0524417	−	0.0524417i	−0.680400	−	0.732841i	$-0.738194\pi$
$101$	54030.7	−	54030.7i	0.0524417	−	0.0524417i	0.732841	+	0.680400i	$0.238194\pi$
$102$	−739388.	−	1.38327e6i	−0.696742	−	1.30349i
$103$		−	341821.i		−	0.312814i	−0.987693	−	0.156407i	$-0.950009\pi$
$103$		−	341821.i		−	0.312814i	0.987693	−	0.156407i	$-0.0499912\pi$
$104$	−358685.	+	50375.0i	−0.318870	+	0.0447832i
$105$	555334.	+	1.16635e6i	0.479718	+	1.00753i
$106$	−58195.2	−	1.25033e6i	−0.0488618	−	1.04980i
$107$	−743236.	+	743236.i	−0.606702	+	0.606702i	−0.942083	−	0.335381i	$-0.891135\pi$
$107$	−743236.	+	743236.i	−0.606702	+	0.606702i	0.335381	+	0.942083i	$0.391135\pi$
$108$	−1.00986e6	+	753037.i	−0.801656	+	0.597785i
$109$	512640.	−	512640.i	0.395852	−	0.395852i	−0.480915	−	0.876767i	$-0.659695\pi$
$109$	512640.	−	512640.i	0.395852	−	0.395852i	0.876767	+	0.480915i	$0.159695\pi$
$110$	689423.	+	628100.i	0.517974	+	0.471901i
$111$	−530046.	−	1.11323e6i	−0.387565	−	0.813988i
$112$	−390840.	−	2.07653e6i	−0.278192	−	1.47803i
$113$		−	140563.i		−	0.0974173i	−0.998813	−	0.0487087i	$-0.984489\pi$
$113$		−	140563.i		−	0.0974173i	0.998813	−	0.0487087i	$-0.0155106\pi$
$114$	658143.	−	2.16967e6i	0.444228	−	1.46446i
$115$	263229.	−	263229.i	0.173077	−	0.173077i
$116$	586550.	−	707248.i	0.375778	−	0.453104i
$117$	512966.	−	53201.5i	0.320281	−	0.0332174i
$118$	92731.1	+	1.99233e6i	0.0564390	+	1.21260i
$119$	−3.74596e6			−2.22291
$120$	−1.25618e6	−	256598.i	−0.726957	−	0.148494i
$121$			191568.i			0.108135i
$122$	15249.9	+	327646.i	0.00839825	+	0.180437i
$123$	1.44159e6	+	511611.i	0.774689	+	0.274932i
$124$	236208.	+	2.53198e6i	0.123888	+	1.32799i
$125$	−1.48530e6	−	1.48530e6i	−0.760473	−	0.760473i
$126$	449156.	+	2.97482e6i	0.224536	+	1.48713i
$127$	−3.10411e6			−1.51539			−0.757697	−	0.652607i	$-0.773675\pi$
$127$	−3.10411e6			−1.51539			−0.757697	+	0.652607i	$0.773675\pi$
$128$	1.87932e6	+	930699.i	0.896130	+	0.443792i
$129$	−60902.9	−	127912.i	−0.0283706	−	0.0595856i
$130$	388010.	+	353497.i	0.176609	+	0.160900i
$131$	1.88541e6	+	1.88541e6i	0.838670	+	0.838670i	0.988684	−	0.150013i	$-0.0479317\pi$
$131$	1.88541e6	+	1.88541e6i	0.838670	+	0.838670i	−0.150013	+	0.988684i	$0.547932\pi$
$132$	1.11187e6	+	1.86590e6i	0.483429	+	0.811272i
$133$	−3.82891e6	−	3.82891e6i	−1.62750	−	1.62750i
$134$	−120165.	−	2.58176e6i	−0.0499418	−	1.07300i
$135$	1.77420e6	+	429822.i	0.721109	+	0.174698i
$136$	2.23776e6	−	2.96902e6i	0.889604	−	1.18031i
$137$	−1.82855e6			−0.711125			−0.355562	−	0.934653i	$-0.615711\pi$
$137$	−1.82855e6			−0.711125			−0.355562	+	0.934653i	$0.615711\pi$
$138$	764601.	−	408695.i	0.290936	−	0.155511i
$139$	879589.	+	879589.i	0.327518	+	0.327518i	0.851642	−	0.524124i	$-0.175607\pi$
$139$	879589.	+	879589.i	0.327518	+	0.327518i	−0.524124	+	0.851642i	$0.675607\pi$
$140$	−1.95472e6	+	2.35696e6i	−0.712361	+	0.858949i
$141$	−1.41813e6	+	3.99593e6i	−0.505892	+	1.42548i
$142$	−638358.	+	700682.i	−0.222946	+	0.244712i
$143$		−	889226.i		−	0.304091i
$144$	−2.62613e6	−	1.42110e6i	−0.879487	−	0.475923i
$145$	−1.33152e6			−0.436762
$146$	4.09840e6	+	3.73385e6i	1.31691	+	1.19977i
$147$	3.77781e6	+	1.34072e6i	1.18929	+	0.422071i
$148$	1.86571e6	−	2.24963e6i	0.575518	−	0.693946i
$149$	510450.	−	510450.i	0.154310	−	0.154310i	−0.625730	−	0.780040i	$-0.715199\pi$
$149$	510450.	−	510450.i	0.154310	−	0.154310i	0.780040	+	0.625730i	$0.215199\pi$
$150$	−715121.	−	1.33787e6i	−0.211888	−	0.396407i
$151$			2.83740e6i			0.824120i	0.911157	+	0.412060i	$0.135191\pi$
$151$			2.83740e6i			0.824120i	−0.911157	+	0.412060i	$0.864809\pi$
$152$	5.32208e6	−	747453.i	1.51548	−	0.212840i
$153$	−3.33704e6	+	4.10933e6i	−0.931725	+	1.14735i
$154$	5.18185e6	−	241184.i	1.41881	−	0.0660368i
$155$	2.60580e6	−	2.60580e6i	0.699756	−	0.699756i
$156$	625765.	+	1.05013e6i	0.164830	+	0.276612i
$157$	3.06721e6	−	3.06721e6i	0.792584	−	0.792584i	−0.189330	−	0.981914i	$-0.560632\pi$
$157$	3.06721e6	−	3.06721e6i	0.792584	−	0.792584i	0.981914	+	0.189330i	$0.0606316\pi$
$158$	2.46326e6	−	2.70375e6i	0.624509	−	0.685481i
$159$	−3.81416e6	+	1.81604e6i	−0.948871	+	0.451787i
$160$	−700396.	−	2.95729e6i	−0.170995	−	0.721996i
$161$		−	2.07057e6i		−	0.496150i
$162$	3.66351e6	+	2.15735e6i	0.861693	+	0.507430i
$163$	333897.	−	333897.i	0.0770992	−	0.0770992i	−0.667506	−	0.744605i	$-0.732638\pi$
$163$	333897.	−	333897.i	0.0770992	−	0.0770992i	0.744605	+	0.667506i	$0.232638\pi$
$164$	336800.	+	3.61025e6i	0.0763555	+	0.818475i
$165$	1.05275e6	−	2.96638e6i	0.234354	−	0.660352i
$166$	−5.58620e6	+	260004.i	−1.22121	+	0.0568401i
$167$	7.92672e6			1.70194			0.850970	−	0.525214i	$-0.176015\pi$
$167$	7.92672e6			1.70194			0.850970	+	0.525214i	$0.176015\pi$
$168$	−5.94980e6	+	3.93139e6i	−1.25480	+	0.829122i
$169$			4.32635e6i			0.896317i
$170$	−5.38197e6	+	250498.i	−1.09546	+	0.0509868i
$171$	−7.61128e6	+	789392.i	−1.52219	+	0.157872i
$172$	214372.	−	258485.i	0.0421292	−	0.0507984i
$173$	−4.57413e6	−	4.57413e6i	−0.883425	−	0.883425i	0.110456	−	0.993881i	$-0.464769\pi$
$173$	−4.57413e6	−	4.57413e6i	−0.883425	−	0.883425i	−0.993881	+	0.110456i	$0.964769\pi$
$174$	−2.96751e6	−	900161.i	−0.563307	−	0.170873i
$175$	−3.62302e6			−0.676015
$176$	−2.90437e6	+	4.25118e6i	−0.532739	+	0.779778i
$177$	6.07766e6	−	2.89376e6i	1.09602	−	0.521847i
$178$	−517248.	+	567748.i	−0.0917146	+	0.100669i
$179$	−1.96888e6	−	1.96888e6i	−0.343289	−	0.343289i	0.514313	−	0.857603i	$-0.328047\pi$
$179$	−1.96888e6	−	1.96888e6i	−0.343289	−	0.343289i	−0.857603	+	0.514313i	$0.828047\pi$
$180$	844251.	+	4.24400e6i	0.144762	+	0.727710i
$181$	−4.38594e6	−	4.38594e6i	−0.739650	−	0.739650i	0.232860	−	0.972510i	$-0.425192\pi$
$181$	−4.38594e6	−	4.38594e6i	−0.739650	−	0.739650i	−0.972510	+	0.232860i	$0.925192\pi$
$182$	2.91637e6	−	135739.i	0.483758	−	0.0225160i
$183$	999492.	−	475890.i	0.163090	−	0.0776521i
$184$	1.64112e6	+	1.23692e6i	0.263443	+	0.198558i
$185$	−4.23534e6			−0.668918
$186$	7.56908e6	−	4.04583e6i	1.17626	−	0.628737i
$187$	6.45414e6	+	6.45414e6i	0.986992	+	0.986992i
$188$	−1.00072e7	+	933570.i	−1.50605	+	0.140499i
$189$	8.66847e6	−	5.28747e6i	1.28398	−	0.783181i
$190$	−5.75720e6	−	5.24511e6i	−0.839364	−	0.764705i
$191$		−	520548.i		−	0.0747069i	−0.999302	−	0.0373535i	$-0.988107\pi$
$191$		−	520548.i		−	0.0747069i	0.999302	−	0.0373535i	$-0.0118927\pi$
$192$	438300.	−	7.06430e6i	0.0619252	−	0.998081i
$193$	−1.01376e6			−0.141015			−0.0705075	−	0.997511i	$-0.522462\pi$
$193$	−1.01376e6			−0.141015			−0.0705075	+	0.997511i	$0.522462\pi$
$194$	7.12562e6	−	7.82130e6i	0.975927	−	1.07121i
$195$	592491.	−	1.66949e6i	0.0799057	−	0.225155i
$196$	882611.	+	9.46094e6i	0.117220	+	1.25651i
$197$	−1.62515e6	+	1.62515e6i	−0.212566	+	0.212566i	−0.805357	−	0.592790i	$-0.798026\pi$
$197$	−1.62515e6	+	1.62515e6i	−0.212566	+	0.212566i	0.592790	+	0.805357i	$0.298026\pi$
$198$	4.35161e6	−	5.89937e6i	0.560602	−	0.759994i
$199$			1.55494e7i			1.97312i	0.163385	+	0.986562i	$0.447759\pi$
$199$			1.55494e7i			1.97312i	−0.163385	+	0.986562i	$0.552241\pi$
$200$	2.16432e6	−	2.87158e6i	0.270540	−	0.358947i
$201$	−7.87571e6	+	3.74987e6i	−0.969843	+	0.461773i
$202$	−28421.0	−	610627.i	−0.00344814	−	0.0740836i
$203$	−5.23691e6	+	5.23691e6i	−0.626019	+	0.626019i
$204$	−1.21639e7	−	3.08014e6i	−1.43279	−	0.362811i
$205$	3.71551e6	−	3.71551e6i	0.431278	−	0.431278i
$206$	−2.02144e6	−	1.84164e6i	−0.231238	−	0.210670i
$207$	−2.27143e6	−	1.84455e6i	−0.256087	−	0.207959i
$208$	−1.63459e6	+	2.39258e6i	−0.181643	+	0.265874i
$209$			1.31941e7i			1.44525i
$210$	9.88945e6	+	2.99985e6i	1.06786	+	0.323923i
$211$	1.11114e7	−	1.11114e7i	1.18282	−	1.18282i	0.203813	−	0.979010i	$-0.434667\pi$
$211$	1.11114e7	−	1.11114e7i	1.18282	−	1.18282i	0.979010	−	0.203813i	$-0.0653335\pi$
$212$	−7.70766e6	−	6.39228e6i	−0.808938	−	0.670885i
$213$	3.01483e6	+	1.06994e6i	0.311978	+	0.110719i
$214$	390953.	+	8.39966e6i	0.0398918	+	0.857078i
$215$	−486645.			−0.0489662
$216$	−987559.	+	1.00292e7i	−0.0979945	+	0.995187i
$217$		−	2.04974e7i		−	2.00595i
$218$	−269656.	−	5.79359e6i	−0.0260280	−	0.559214i
$219$	6.25825e6	−	1.76342e7i	0.595828	−	1.67889i
$220$	7.42885e6	−	693037.i	0.697675	−	0.0650861i
$221$	3.63241e6	+	3.63241e6i	0.336526	+	0.336526i
$222$	−9.43913e6	−	2.86325e6i	−0.862726	−	0.261698i
$223$	−8.51783e6			−0.768094			−0.384047	−	0.923314i	$-0.625470\pi$
$223$	−8.51783e6			−0.768094			−0.384047	+	0.923314i	$0.625470\pi$
$224$	−1.43858e7	−	8.87644e6i	−1.27994	−	0.789759i
$225$	−3.22752e6	+	3.97446e6i	−0.283349	+	0.348924i
$226$	−831254.	−	757316.i	−0.0720126	−	0.0656073i
$227$	1.37400e7	+	1.37400e7i	1.17465	+	1.17465i	0.981088	+	0.193563i	$0.0620044\pi$
$227$	1.37400e7	+	1.37400e7i	1.17465	+	1.17465i	0.193563	+	0.981088i	$0.437996\pi$
$228$	−9.28495e6	−	1.55817e7i	−0.783385	−	1.31465i
$229$	8.49453e6	+	8.49453e6i	0.707347	+	0.707347i	0.965977	−	0.258629i	$-0.0832708\pi$
$229$	8.49453e6	+	8.49453e6i	0.707347	+	0.707347i	−0.258629	+	0.965977i	$0.583271\pi$
$230$	−138462.	−	2.97487e6i	−0.0113802	−	0.244504i
$231$	−7.52638e6	−	1.58074e7i	−0.610591	−	1.28240i
$232$	−1.02231e6	−	7.27917e6i	−0.0818691	−	0.582932i
$233$	4.36612e6			0.345166			0.172583	−	0.984995i	$-0.444789\pi$
$233$	4.36612e6			0.345166			0.172583	+	0.984995i	$0.444789\pi$
$234$	2.44910e6	−	3.32019e6i	0.191144	−	0.259128i
$235$	1.02990e7	+	1.02990e7i	0.793580	+	0.793580i
$236$	1.22818e7	+	1.01858e7i	0.934382	+	0.774922i
$237$	−1.16335e7	−	4.12863e6i	−0.873904	−	0.310142i
$238$	−2.01822e7	+	2.21526e7i	−1.49706	+	1.64322i
$239$		−	4.85229e6i		−	0.355429i	−0.984082	−	0.177715i	$-0.943130\pi$
$239$		−	4.85229e6i		−	0.355429i	0.984082	−	0.177715i	$-0.0568704\pi$
$240$	−8.28542e6	+	6.04626e6i	−0.599351	+	0.437374i
$241$	9.13326e6			0.652491			0.326246	−	0.945285i	$-0.394216\pi$
$241$	9.13326e6			0.652491			0.326246	+	0.945285i	$0.394216\pi$
$242$	1.13288e6	+	1.03212e6i	0.0799355	+	0.0728254i
$243$	1.92183e6	−	1.42196e7i	0.133936	−	0.990990i
$244$	2.01978e6	+	1.67508e6i	0.139038	+	0.115310i
$245$	9.73681e6	−	9.73681e6i	0.662092	−	0.662092i
$246$	1.07925e7	−	5.76879e6i	0.724962	−	0.387507i
$247$			7.42571e6i			0.492773i
$248$	1.62461e7	+	1.22447e7i	1.06511	+	0.802776i
$249$	8.11367e6	+	1.70408e7i	0.525556	+	1.10381i
$250$	−1.67861e7	+	781289.i	−1.07431	+	0.0500025i
$251$	−1.12126e7	+	1.12126e7i	−0.709062	+	0.709062i	−0.966338	−	0.257276i	$-0.917175\pi$
$251$	−1.12126e7	+	1.12126e7i	−0.709062	+	0.709062i	0.257276	+	0.966338i	$0.417175\pi$
$252$	2.00122e7	+	1.33713e7i	1.25053	+	0.835550i
$253$	−3.56751e6	+	3.56751e6i	−0.220295	+	0.220295i
$254$	−1.67241e7	+	1.83569e7i	−1.02057	+	1.12021i
$255$	7.81704e6	+	1.64178e7i	0.471435	+	0.990137i
$256$	1.56292e7	−	6.09947e6i	0.931572	−	0.363557i
$257$		−	8.33569e6i		−	0.491069i	−0.969388	−	0.245534i	$-0.921037\pi$
$257$		−	8.33569e6i		−	0.491069i	0.969388	−	0.245534i	$-0.0789634\pi$
$258$	−1.08457e6	−	328991.i	−0.0631534	−	0.0191569i
$259$	−1.66577e7	+	1.66577e7i	−0.958772	+	0.958772i
$260$	4.18098e6	−	390044.i	0.237880	−	0.0221918i
$261$	1.07967e6	+	1.04102e7i	0.0607255	+	0.585512i
$262$	2.13079e7	−	991753.i	1.18478	−	0.0551442i
$263$	1.13641e7			0.624692			0.312346	−	0.949968i	$-0.398885\pi$
$263$	1.13641e7			0.624692			0.312346	+	0.949968i	$0.398885\pi$
$264$	1.70249e7	+	3.47764e6i	0.925279	+	0.189005i
$265$			1.45111e7i			0.779762i
$266$	−4.32724e7	+	2.01407e6i	−2.29914	+	0.107011i
$267$	2.44285e6	+	866951.i	0.128340	+	0.0455471i
$268$	−1.59153e7	−	1.31992e7i	−0.826817	−	0.685713i
$269$	1.34161e7	+	1.34161e7i	0.689238	+	0.689238i	0.962064	−	0.272826i	$-0.0879582\pi$
$269$	1.34161e7	+	1.34161e7i	0.689238	+	0.689238i	−0.272826	+	0.962064i	$0.587958\pi$
$270$	1.21008e7	−	8.17639e6i	0.614782	−	0.415404i
$271$	2.77923e7			1.39642			0.698211	−	0.715892i	$-0.253980\pi$
$271$	2.77923e7			1.39642			0.698211	+	0.715892i	$0.253980\pi$
$272$	−5.50158e6	−	2.92298e7i	−0.273389	−	1.45251i
$273$	−4.23587e6	−	8.89644e6i	−0.208188	−	0.437248i
$274$	−9.85175e6	+	1.08136e7i	−0.478919	+	0.525676i
$275$	6.24231e6	+	6.24231e6i	0.300156	+	0.300156i
$276$	1.70254e6	−	6.72359e6i	0.0809788	−	0.319797i
$277$	−2.41869e7	−	2.41869e7i	−1.13800	−	1.13800i	−0.988809	−	0.149190i	$-0.952333\pi$
$277$	−2.41869e7	−	2.41869e7i	−1.13800	−	1.13800i	−0.149190	−	0.988809i	$-0.547667\pi$
$278$	9.94065e6	−	462677.i	0.462680	−	0.0215349i
$279$	−2.24857e7	−	1.82599e7i	−1.03537	−	0.840785i
$280$	3.40693e6	+	2.42584e7i	0.155199	+	1.10506i
$281$	2.56885e7			1.15776			0.578881	−	0.815412i	$-0.303490\pi$
$281$	2.56885e7			1.15776			0.578881	+	0.815412i	$0.303490\pi$
$282$	1.59904e7	+	2.99155e7i	0.713038	+	1.33398i
$283$	−1.53487e7	−	1.53487e7i	−0.677194	−	0.677194i	0.282171	−	0.959364i	$-0.408946\pi$
$283$	−1.53487e7	−	1.53487e7i	−0.677194	−	0.677194i	−0.959364	+	0.282171i	$0.908946\pi$
$284$	704355.	+	7.55017e6i	0.0307494	+	0.329611i
$285$	−8.79125e6	+	2.47715e7i	−0.379766	+	1.07009i
$286$	−5.25866e6	−	4.79091e6i	−0.224790	−	0.204795i
$287$		−	2.92264e7i		−	1.23632i
$288$	−2.25529e7	+	7.87380e6i	−0.944115	+	0.329615i
$289$	−2.85917e7			−1.18453
$290$	−7.17388e6	+	7.87429e6i	−0.294144	+	0.322862i
$291$	−3.36528e7	−	1.19431e7i	−1.36566	−	0.484663i
$292$	4.41621e7	−	4.11988e6i	1.77379	−	0.165476i
$293$	−8.93615e6	+	8.93615e6i	−0.355261	+	0.355261i	−0.862063	−	0.506802i	$-0.830828\pi$
$293$	−8.93615e6	+	8.93615e6i	−0.355261	+	0.355261i	0.506802	+	0.862063i	$0.330828\pi$
$294$	2.82825e7	−	1.51176e7i	1.11295	−	0.594895i
$295$		−	2.31226e7i		−	0.900682i
$296$	−3.25180e6	−	2.31537e7i	−0.125386	−	0.892783i
$297$	−2.40455e7	−	5.82533e6i	−0.917836	−	0.222357i
$298$	−268504.	−	5.76883e6i	−0.0101462	−	0.217991i
$299$	−2.00781e6	+	2.00781e6i	−0.0751120	+	0.0751120i
$300$	−1.17647e7	−	2.97905e6i	−0.435730	−	0.110335i
$301$	−1.91399e6	+	1.91399e6i	−0.0701842	+	0.0701842i
$302$	1.67797e7	+	1.52872e7i	0.609204	+	0.555017i
$303$	−1.86273e6	+	886905.i	−0.0669611	+	0.0318823i
$304$	2.42537e7	−	3.55005e7i	0.863291	−	1.26361i
$305$		−	3.80260e6i		−	0.134024i
$306$	6.32246e6	+	4.18744e7i	0.220659	+	1.46145i
$307$	−2.68971e7	+	2.68971e7i	−0.929589	+	0.929589i	−0.997679	−	0.0680902i	$-0.978309\pi$
$307$	−2.68971e7	+	2.68971e7i	−0.929589	+	0.929589i	0.0680902	+	0.997679i	$0.478309\pi$
$308$	2.64921e7	−	3.19436e7i	0.906702	−	1.09328i
$309$	−3.08674e6	+	8.69767e6i	−0.104622	+	0.294800i
$310$	−1.37069e6	−	2.94494e7i	−0.0460103	−	0.988535i
$311$	−2.09314e7			−0.695851			−0.347926	−	0.937522i	$-0.613114\pi$
$311$	−2.09314e7			−0.695851			−0.347926	+	0.937522i	$0.613114\pi$
$312$	9.58168e6	+	1.95723e6i	0.315484	+	0.0644434i
$313$		−	2.68313e7i		−	0.875002i	−0.899218	−	0.437501i	$-0.855864\pi$
$313$		−	2.68313e7i		−	0.875002i	0.899218	−	0.437501i	$-0.144136\pi$
$314$	−1.61340e6	−	3.46640e7i	−0.0521139	−	1.11967i
$315$	−3.59809e6	−	3.46926e7i	−0.115117	−	1.10995i
$316$	−2.71793e6	−	2.91342e7i	−0.0861343	−	0.923297i
$317$	−9.99334e6	−	9.99334e6i	−0.313713	−	0.313713i	0.532633	−	0.846346i	$-0.321203\pi$
$317$	−9.99334e6	−	9.99334e6i	−0.313713	−	0.313713i	−0.846346	+	0.532633i	$0.821203\pi$
$318$	−9.81005e6	+	3.23403e7i	−0.305063	+	1.00569i
$319$	1.80460e7			0.555915
$320$	−2.12622e7	−	1.17911e7i	−0.648872	−	0.359837i
$321$	2.56234e7	−	1.22001e7i	0.774677	−	0.368848i
$322$	−1.22448e7	−	1.11557e7i	−0.366763	−	0.334140i
$323$	−5.38969e7	−	5.38969e7i	−1.59940	−	1.59940i
$324$	3.24960e7	−	1.00418e7i	0.955423	−	0.295242i
$325$	3.51320e6	+	3.51320e6i	0.102342	+	0.102342i
$326$	−175635.	−	3.77353e6i	−0.00506942	−	0.108917i
$327$	−1.76735e7	+	8.41490e6i	−0.505451	+	0.240661i
$328$	2.31647e7	+	1.74593e7i	0.656454	+	0.494772i
$329$	8.10123e7			2.27491
$330$	−1.18705e7	−	2.22078e7i	−0.330315	−	0.617964i
$331$	9.99546e6	+	9.99546e6i	0.275625	+	0.275625i	0.831360	−	0.555735i	$-0.187563\pi$
$331$	9.99546e6	+	9.99546e6i	0.275625	+	0.275625i	−0.555735	+	0.831360i	$0.687563\pi$
$332$	−2.85593e7	+	3.44362e7i	−0.780429	+	0.941024i
$333$	3.43425e6	+	3.31128e7i	0.0930034	+	0.896734i
$334$	4.27070e7	−	4.68766e7i	1.14620	−	1.25810i
$335$			2.99634e7i			0.796996i
$336$	−8.80668e6	+	5.63669e7i	−0.232164	+	1.48596i
$337$	9.34427e6			0.244149			0.122075	−	0.992521i	$-0.461045\pi$
$337$	9.34427e6			0.244149			0.122075	+	0.992521i	$0.461045\pi$
$338$	2.55849e7	+	2.33092e7i	0.662573	+	0.603639i
$339$	−1.26933e6	+	3.57664e6i	−0.0325817	+	0.0918072i
$340$	−2.75152e7	+	3.31772e7i	−0.700062	+	0.844118i
$341$	−3.53162e7	+	3.53162e7i	−0.890658	+	0.890658i
$342$	−3.63392e7	+	4.92642e7i	−0.908443	+	1.23155i
$343$		−	1.58991e7i		−	0.393994i
$344$	−373635.	−	2.66039e6i	−0.00917851	−	0.0653536i
$345$	−9.07492e6	+	4.32086e6i	−0.220997	+	0.105223i
$346$	−5.16944e7	+	2.40606e6i	−1.24800	+	0.0580869i
$347$	3.41950e6	−	3.41950e6i	0.0818417	−	0.0818417i	−0.665001	−	0.746843i	$-0.731569\pi$
$347$	3.41950e6	−	3.41950e6i	0.0818417	−	0.0818417i	0.746843	+	0.665001i	$0.231569\pi$
$348$	−2.13115e7	+	1.26993e7i	−0.505680	+	0.301330i
$349$	−2.32519e7	+	2.32519e7i	−0.546994	+	0.546994i	−0.925570	−	0.378576i	$-0.876414\pi$
$349$	−2.32519e7	+	2.32519e7i	−0.546994	+	0.546994i	0.378576	+	0.925570i	$0.376414\pi$
$350$	−1.95198e7	+	2.14256e7i	−0.455273	+	0.499722i
$351$	−1.35329e7	−	3.27852e6i	−0.312946	−	0.0758152i
$352$	9.49239e6	+	4.00799e7i	0.217645	+	0.918964i
$353$			3.56875e7i			0.811321i	0.914024	+	0.405660i	$0.132958\pi$
$353$			3.56875e7i			0.811321i	−0.914024	+	0.405660i	$0.867042\pi$
$354$	1.56318e7	−	5.15325e7i	0.352370	−	1.16164i
$355$	7.77032e6	−	7.77032e6i	0.173682	−	0.173682i
$356$	570724.	+	6.11774e6i	0.0126496	+	0.135594i
$357$	9.53164e7	+	3.38271e7i	2.09490	+	0.743464i
$358$	−2.22513e7	+	1.03566e6i	−0.484960	+	0.0225719i
$359$	3.27114e7			0.706994			0.353497	−	0.935436i	$-0.384992\pi$
$359$	3.27114e7			0.706994			0.353497	+	0.935436i	$0.384992\pi$
$360$	2.96465e7	+	1.78728e7i	0.635428	+	0.383077i
$361$		−	6.31350e7i		−	1.34199i
$362$	−4.95675e7	+	2.30707e6i	−1.04489	+	0.0486334i
$363$	1.72991e6	−	4.87447e6i	0.0361664	−	0.101908i
$364$	1.49099e7	−	1.79780e7i	0.309150	−	0.372766i
$365$	−4.54498e7	−	4.54498e7i	−0.934659	−	0.934659i
$366$	2.57070e6	−	8.47471e6i	0.0524335	−	0.172855i
$367$	2.97470e7			0.601789			0.300895	−	0.953657i	$-0.402715\pi$
$367$	2.97470e7			0.601789			0.300895	+	0.953657i	$0.402715\pi$
$368$	1.61567e7	−	3.04099e6i	0.324198	−	0.0610199i
$369$	−3.20615e7	−	2.60360e7i	−0.638124	−	0.518198i
$370$	−2.28188e7	+	2.50467e7i	−0.450493	+	0.494476i
$371$	5.70724e7	+	5.70724e7i	1.11765	+	1.11765i
$372$	1.68541e7	−	6.65595e7i	0.327399	−	1.29295i
$373$	6.47167e7	+	6.47167e7i	1.24707	+	1.24707i	0.957009	+	0.290057i	$0.0936743\pi$
$373$	6.47167e7	+	6.47167e7i	1.24707	+	1.24707i	0.290057	+	0.957009i	$0.406326\pi$
$374$	7.29413e7	−	3.39497e6i	1.39431	−	0.0648966i
$375$	2.43809e7	+	5.12062e7i	0.462334	+	0.971022i
$376$	−4.83951e7	+	6.42098e7i	−0.910412	+	1.20792i
$377$	1.01564e7			0.189546
$378$	1.54346e7	−	7.97505e7i	0.285773	−	1.47658i
$379$	−2.46123e7	−	2.46123e7i	−0.452100	−	0.452100i	0.443951	−	0.896051i	$-0.353576\pi$
$379$	−2.46123e7	−	2.46123e7i	−0.452100	−	0.452100i	−0.896051	+	0.443951i	$0.853576\pi$
$380$	−6.20365e7	+	5.78738e6i	−1.13057	+	0.105471i
$381$	7.89843e7	+	2.80310e7i	1.42812	+	0.506831i
$382$	−3.07839e6	−	2.80457e6i	−0.0552247	−	0.0503126i
$383$		−	5.87882e7i		−	1.04639i	−0.852213	−	0.523195i	$-0.824740\pi$
$383$		−	5.87882e7i		−	1.04639i	0.852213	−	0.523195i	$-0.175260\pi$
$384$	−3.94150e7	−	4.06526e7i	−0.696095	−	0.717950i
$385$	−6.01396e7			−1.05385
$386$	−5.46189e6	+	5.99514e6i	−0.0949688	+	0.104241i
$387$	394599.	+	3.80470e6i	0.00680805	+	0.0656429i
$388$	−7.86231e6	−	8.42781e7i	−0.134603	−	1.44285i
$389$	−1.59328e7	+	1.59328e7i	−0.270671	+	0.270671i	−0.829370	−	0.558699i	$-0.811301\pi$
$389$	−1.59328e7	+	1.59328e7i	−0.270671	+	0.270671i	0.558699	+	0.829370i	$0.311301\pi$
$390$	−6.68077e6	−	1.24986e7i	−0.112624	−	0.210702i
$391$		−	2.91460e7i		−	0.487583i
$392$	6.07049e7	+	4.57535e7i	1.00778	+	0.759567i
$393$	−3.09486e7	−	6.50002e7i	−0.509875	−	1.07087i
$394$	854853.	+	1.83666e7i	0.0139766	+	0.300289i
$395$	−2.99837e7	+	2.99837e7i	−0.486512	+	0.486512i
$396$	−1.14421e7	−	5.75185e7i	−0.184255	−	0.926237i
$397$	3.79360e7	−	3.79360e7i	0.606289	−	0.606289i	−0.335685	−	0.941974i	$-0.608968\pi$
$397$	3.79360e7	−	3.79360e7i	0.606289	−	0.606289i	0.941974	+	0.335685i	$0.108968\pi$
$398$	9.19552e7	+	8.37760e7i	1.45857	+	1.32883i
$399$	6.28509e7	+	1.32003e8i	0.989448	+	2.07810i
$400$	−5.32102e6	−	2.82705e7i	−0.0831409	−	0.441727i
$401$			7.60286e7i			1.17908i	0.807739	+	0.589541i	$0.200691\pi$
$401$			7.60286e7i			1.17908i	−0.807739	+	0.589541i	$0.799309\pi$
$402$	−2.02564e7	+	6.67782e7i	−0.311806	+	1.02791i
$403$	−1.98761e7	+	1.98761e7i	−0.303680	+	0.303680i
$404$	−3.76422e6	−	3.12182e6i	−0.0570861	−	0.0473439i
$405$	−4.12633e7	−	2.69584e7i	−0.621153	−	0.405816i
$406$	2.75469e6	+	5.91848e7i	0.0411619	+	0.884367i
$407$	5.74011e7			0.851406
$408$	−8.37512e7	+	5.53394e7i	−1.23313	+	0.814806i
$409$		−	3.35250e6i		−	0.0490004i	−0.999700	−	0.0245002i	$-0.992201\pi$
$409$		−	3.35250e6i		−	0.0490004i	0.999700	−	0.0245002i	$-0.00779943\pi$
$410$	−1.95442e6	−	4.19908e7i	−0.0283573	−	0.609260i
$411$	4.65277e7	+	1.65124e7i	0.670172	+	0.237839i
$412$	−2.17819e7	+	2.03204e6i	−0.311462	+	0.0290563i
$413$	−9.09419e7	−	9.09419e7i	−1.29096	−	1.29096i
$414$	−2.31460e7	+	3.49473e6i	−0.326193	+	0.0492507i
$415$	6.48323e7			0.907084
$416$	5.34236e6	+	2.25571e7i	0.0742084	+	0.313331i
$417$	−1.44383e7	−	3.03242e7i	−0.199117	−	0.418197i
$418$	7.80267e7	+	7.10864e7i	1.06835	+	0.973325i
$419$	−4.15627e7	−	4.15627e7i	−0.565017	−	0.565017i	0.365711	−	0.930728i	$-0.380826\pi$
$419$	−4.15627e7	−	4.15627e7i	−0.565017	−	0.565017i	−0.930728	+	0.365711i	$0.880826\pi$
$420$	7.10221e7	−	4.23213e7i	0.958618	−	0.571230i
$421$	−2.06268e7	−	2.06268e7i	−0.276431	−	0.276431i	0.555252	−	0.831682i	$-0.312622\pi$
$421$	−2.06268e7	−	2.06268e7i	−0.276431	−	0.276431i	−0.831682	+	0.555252i	$0.812622\pi$
$422$	−5.84474e6	−	1.25575e8i	−0.0777728	−	1.67096i
$423$	7.21689e7	−	8.88709e7i	0.953518	−	1.17419i
$424$	−7.93291e7	+	1.11413e7i	−1.04072	+	0.146163i
$425$	−5.09987e7			−0.664342
$426$	2.25705e7	−	1.20644e7i	0.291952	−	0.156054i
$427$	−1.49557e7	−	1.49557e7i	−0.192098	−	0.192098i
$428$	5.17798e7	+	4.29431e7i	0.660433	+	0.547724i
$429$	−8.02997e6	+	2.26265e7i	−0.101705	+	0.286579i
$430$	−2.62191e6	+	2.87789e6i	−0.0329771	+	0.0361967i
$431$			1.09069e8i			1.36229i	0.732148	+	0.681146i	$0.238518\pi$
$431$			1.09069e8i			1.36229i	−0.732148	+	0.681146i	$0.761482\pi$
$432$	5.39894e7	+	5.98747e7i	0.669664	+	0.742664i
$433$	1.02653e8			1.26447			0.632234	−	0.774777i	$-0.282138\pi$
$433$	1.02653e8			1.26447			0.632234	+	0.774777i	$0.282138\pi$
$434$	−1.21216e8	−	1.10434e8i	−1.48283	−	1.35094i
$435$	3.38807e7	+	1.20240e7i	0.411609	+	0.146077i
$436$	−3.57146e7	−	2.96196e7i	−0.430910	−	0.357371i
$437$	2.97914e7	−	2.97914e7i	0.356983	−	0.356983i
$438$	−7.05664e7	−	1.32018e8i	−0.839799	−	1.57113i
$439$			1.36074e8i			1.60836i	0.594386	+	0.804180i	$0.297395\pi$
$439$			1.36074e8i			1.60836i	−0.594386	+	0.804180i	$0.702605\pi$
$440$	3.59262e7	−	4.76662e7i	0.421748	−	0.559567i
$441$	−8.40198e7	−	6.82295e7i	−0.979639	−	0.795530i
$442$	4.10516e7	−	1.91070e6i	0.475405	−	0.0221272i
$443$	−2.43962e7	+	2.43962e7i	−0.280616	+	0.280616i	−0.833354	−	0.552739i	$-0.813583\pi$
$443$	−2.43962e7	+	2.43962e7i	−0.280616	+	0.280616i	0.552739	+	0.833354i	$0.313583\pi$
$444$	−6.77880e7	+	4.03942e7i	−0.774469	+	0.461498i
$445$	6.29613e6	−	6.29613e6i	0.0714485	−	0.0714485i
$446$	−4.58918e7	+	5.03723e7i	−0.517285	+	0.567789i
$447$	−1.75980e7	+	8.37894e6i	−0.197033	+	0.0938138i
$448$	−1.30000e8	+	3.72500e7i	−1.44580	+	0.414279i
$449$		−	1.24028e8i		−	1.37019i	−0.728452	−	0.685097i	$-0.759760\pi$
$449$		−	1.24028e8i		−	1.37019i	0.728452	−	0.685097i	$-0.240240\pi$
$450$	6.11495e6	+	4.05001e7i	0.0671051	+	0.444445i
$451$	−5.03560e7	+	5.03560e7i	−0.548936	+	0.548936i
$452$	−8.95715e6	+	835612.i	−0.0969961	+	0.00904877i
$453$	2.56226e7	−	7.21981e7i	0.275631	−	0.776660i
$454$	1.55282e8	−	7.22744e6i	1.65941	−	0.0772355i
$455$	−3.38468e7			−0.359321
$456$	−1.42171e8	−	2.90409e7i	−1.49939	−	0.306278i
$457$			8.79507e7i			0.921490i	0.887533	+	0.460745i	$0.152418\pi$
$457$			8.79507e7i			0.921490i	−0.887533	+	0.460745i	$0.847582\pi$
$458$	9.60007e7	−	4.46825e6i	0.999258	−	0.0465094i
$459$	1.22020e8	−	7.44280e7i	1.26181	−	0.769659i
$460$	−1.83386e7	−	1.52090e7i	−0.188406	−	0.156252i
$461$	−1.03800e8	−	1.03800e8i	−1.05948	−	1.05948i	−0.998115	−	0.0613648i	$-0.980455\pi$
$461$	−1.03800e8	−	1.03800e8i	−1.05948	−	1.05948i	−0.0613648	−	0.998115i	$-0.519545\pi$
$462$	−1.34031e8	−	4.06567e7i	−1.35918	−	0.412293i
$463$	−1.36101e7			−0.137125			−0.0685626	−	0.997647i	$-0.521841\pi$
$463$	−1.36101e7			−0.137125			−0.0685626	+	0.997647i	$0.521841\pi$
$464$	−4.85551e7	−	3.31725e7i	−0.486050	−	0.332066i
$465$	−8.98362e7	+	4.27738e7i	−0.893496	+	0.425421i
$466$	2.35235e7	−	2.58201e7i	0.232458	−	0.255153i
$467$	3.79817e7	+	3.79817e7i	0.372927	+	0.372927i	0.868542	−	0.495615i	$-0.165057\pi$
$467$	3.79817e7	+	3.79817e7i	0.372927	+	0.372927i	−0.495615	+	0.868542i	$0.665057\pi$
$468$	−6.43963e6	−	3.23716e7i	−0.0628237	−	0.315811i
$469$	1.17847e8	+	1.17847e8i	1.14235	+	1.14235i
$470$	1.16394e8	−	5.41742e6i	1.12108	−	0.0521794i
$471$	−1.05743e8	+	5.03478e7i	−1.01202	+	0.481856i
$472$	1.26407e8	−	1.77530e7i	1.20211	−	0.168829i
$473$	6.59544e6			0.0623248
$474$	−8.70936e7	+	4.65533e7i	−0.817807	+	0.437135i
$475$	−5.21280e7	−	5.21280e7i	−0.486396	−	0.486396i
$476$	2.22688e7	+	2.38705e8i	0.206479	+	2.21330i
$477$	1.13451e8	−	1.17664e7i	1.04533	−	0.108415i
$478$	−2.86952e7	−	2.61428e7i	−0.262740	−	0.239370i
$479$		−	2.06066e8i		−	1.87500i	−0.347989	−	0.937499i	$-0.613135\pi$
$479$		−	2.06066e8i		−	1.87500i	0.347989	−	0.937499i	$-0.386865\pi$
$480$	−8.88358e6	+	8.15735e7i	−0.0803275	+	0.737607i
$481$	3.23055e7			0.290296
$482$	4.92075e7	−	5.40118e7i	0.439431	−	0.482333i
$483$	−1.86979e7	+	5.26859e7i	−0.165940	+	0.467577i
$484$	1.22073e7	−	1.13882e6i	0.107668	−	0.0100443i
$485$	−8.67356e7	+	8.67356e7i	−0.760277	+	0.760277i
$486$	−7.37369e7	−	8.79767e7i	−0.642357	−	0.766406i
$487$		−	1.07643e8i		−	0.931964i	−0.884794	−	0.465982i	$-0.845701\pi$
$487$		−	1.07643e8i		−	0.931964i	0.884794	−	0.465982i	$-0.154299\pi$
$488$	2.07880e7	−	2.91955e6i	0.178877	−	0.0251221i
$489$	−1.15112e7	+	5.48086e6i	−0.0984454	+	0.0468729i
$490$	−5.12171e6	−	1.10040e8i	−0.0435338	−	0.935327i
$491$	−6.37109e7	+	6.37109e7i	−0.538232	+	0.538232i	−0.923009	−	0.384778i	$-0.874278\pi$
$491$	−6.37109e7	+	6.37109e7i	−0.538232	+	0.538232i	0.384778	+	0.923009i	$0.374278\pi$
$492$	2.40317e7	−	9.49045e7i	0.201785	−	0.796878i
$493$	−7.37164e7	+	7.37164e7i	−0.615210	+	0.615210i
$494$	4.39137e7	+	4.00077e7i	0.364267	+	0.331866i
$495$	−5.35746e7	+	6.59734e7i	−0.441717	+	0.543943i
$496$	1.59942e8	−	3.01039e7i	1.31074	−	0.246705i
$497$		−	6.11217e7i		−	0.497882i
$498$	1.44489e8	+	4.38292e7i	1.16990	+	0.354875i
$499$	8.69398e7	−	8.69398e7i	0.699709	−	0.699709i	−0.264639	−	0.964348i	$-0.585253\pi$
$499$	8.69398e7	−	8.69398e7i	0.699709	−	0.699709i	0.964348	+	0.264639i	$0.0852528\pi$
$500$	−8.58184e7	+	1.03478e8i	−0.686547	+	0.827823i
$501$	−2.01696e8	−	7.15806e7i	−1.60393	−	0.569223i
$502$	5.89798e6	+	1.26719e8i	0.0466222	+	1.00168i
$503$	1.31189e8			1.03084			0.515422	−	0.856936i	$-0.327635\pi$
$503$	1.31189e8			1.03084			0.515422	+	0.856936i	$0.327635\pi$
$504$	1.86895e8	−	4.63062e7i	1.45984	−	0.361699i
$505$			7.08682e6i			0.0550272i
$506$	1.87657e6	+	4.03182e7i	0.0144848	+	0.311207i
$507$	3.90682e7	−	1.10084e8i	0.299778	−	0.844699i
$508$	1.84531e7	+	1.97804e8i	0.140760	+	1.50884i
$509$	2.69973e7	+	2.69973e7i	0.204723	+	0.204723i	0.802020	−	0.597297i	$-0.203759\pi$
$509$	2.69973e7	+	2.69973e7i	0.204723	+	0.204723i	−0.597297	+	0.802020i	$0.703759\pi$
$510$	1.39207e8	+	4.22268e7i	1.04942	+	0.318330i
$511$	−3.57510e8			−2.67933
$512$	4.81351e7	−	1.25289e8i	0.358635	−	0.933478i
$513$	2.00798e8	+	4.86459e7i	1.48733	+	0.360325i
$514$	−4.92951e7	−	4.49104e7i	−0.363007	−	0.330718i
$515$	2.24171e7	+	2.24171e7i	0.164118	+	0.164118i
$516$	−7.78891e6	+	4.64133e6i	−0.0566928	+	0.0337827i
$517$	−1.39581e8	−	1.39581e8i	−1.01008	−	1.01008i
$518$	8.76219e6	+	1.88256e8i	0.0630411	+	1.35444i
$519$	7.50835e7	+	1.57695e8i	0.537084	+	1.12802i
$520$	2.02194e7	−	2.68267e7i	0.143800	−	0.190791i
$521$	1.86991e8			1.32223			0.661115	−	0.750285i	$-0.270084\pi$
$521$	1.86991e8			1.32223			0.661115	+	0.750285i	$0.270084\pi$
$522$	6.73800e7	+	4.97022e7i	0.473718	+	0.349433i
$523$	8.85010e7	+	8.85010e7i	0.618647	+	0.618647i	0.945184	−	0.326537i	$-0.105882\pi$
$523$	8.85010e7	+	8.85010e7i	0.618647	+	0.618647i	−0.326537	+	0.945184i	$0.605882\pi$
$524$	1.08936e8	−	1.31353e8i	0.757143	−	0.912946i
$525$	9.21881e7	+	3.27169e7i	0.637084	+	0.226097i
$526$	6.12264e7	−	6.72041e7i	0.420709	−	0.461784i
$527$		−	2.88527e8i		−	1.97131i
$528$	1.12291e8	−	8.19443e7i	0.762860	−	0.556695i
$529$	−1.31925e8			−0.891172
$530$	8.58148e7	+	7.81817e7i	0.576414	+	0.525143i
$531$	−1.80778e8	+	1.87491e7i	−1.20743	+	0.125227i
$532$	−2.21229e8	+	2.66753e8i	−1.46929	+	1.77163i
$533$	−2.83405e7	+	2.83405e7i	−0.187166	+	0.187166i
$534$	1.82884e7	−	9.77551e6i	0.120102	−	0.0641971i
$535$		−	9.74848e7i		−	0.636613i
$536$	−1.63804e8	+	2.30052e7i	−1.06373	+	0.149394i
$537$	3.23188e7	+	6.78780e7i	0.208705	+	0.438335i
$538$	1.51622e8	−	7.05707e6i	0.973675	−	0.0453187i
$539$	−1.31962e8	+	1.31962e8i	−0.842718	+	0.842718i
$540$	1.68425e7	−	1.15613e8i	0.106961	−	0.734218i
$541$	−1.44255e8	+	1.44255e8i	−0.911041	+	0.911041i	−0.996354	−	0.0853133i	$-0.972811\pi$
$541$	−1.44255e8	+	1.44255e8i	−0.911041	+	0.911041i	0.0853133	+	0.996354i	$0.472811\pi$
$542$	1.49737e8	−	1.64356e8i	0.940442	−	1.03226i
$543$	7.19944e7	+	1.51207e8i	0.449675	+	0.944435i
$544$	−2.02499e8	−	1.24947e8i	−1.25784	−	0.776123i
$545$			6.72393e7i			0.415369i
$546$	−7.54330e7	−	2.28817e7i	−0.463429	−	0.140576i
$547$	7.70967e7	−	7.70967e7i	0.471057	−	0.471057i	−0.431199	−	0.902257i	$-0.641909\pi$
$547$	7.70967e7	−	7.70967e7i	0.471057	−	0.471057i	0.902257	+	0.431199i	$0.141909\pi$
$548$	1.08703e7	+	1.16521e8i	0.0660540	+	0.708051i
$549$	−2.97296e7	+	3.08336e6i	−0.179669	+	0.0186341i
$550$	7.05473e7	−	3.28355e6i	0.424026	−	0.0197358i
$551$	−1.50698e8			−0.900848
$552$	−3.05888e7	−	4.62933e7i	−0.181863	−	0.275233i
$553$			2.35853e8i			1.39465i
$554$	−2.73348e8	+	1.27227e7i	−1.60763	+	0.0748255i
$555$	1.07769e8	+	3.82463e7i	0.630396	+	0.223723i
$556$	5.08214e7	−	6.12793e7i	0.295680	−	0.356524i
$557$	1.35137e8	+	1.35137e8i	0.782004	+	0.782004i	0.980169	−	0.198165i	$-0.0634981\pi$
$557$	1.35137e8	+	1.35137e8i	0.782004	+	0.782004i	−0.198165	+	0.980169i	$0.563498\pi$
$558$	−2.29131e8	+	3.45956e7i	−1.31881	+	0.199122i
$559$	3.71194e6			0.0212503
$560$	1.61813e8	+	1.10550e8i	0.921404	+	0.629497i
$561$	−1.05944e8	−	2.22509e8i	−0.600048	−	1.26026i
$562$	1.38403e8	−	1.51915e8i	0.779714	−	0.855839i
$563$	1.52427e8	+	1.52427e8i	0.854154	+	0.854154i	0.990642	−	0.136488i	$-0.0435816\pi$
$563$	1.52427e8	+	1.52427e8i	0.854154	+	0.854154i	−0.136488	+	0.990642i	$0.543582\pi$
$564$	2.63064e8	+	6.66130e7i	1.46631	+	0.371297i
$565$	9.21832e6	+	9.21832e6i	0.0511101	+	0.0511101i
$566$	−1.73463e8	+	8.07366e6i	−0.956661	+	0.0445268i
$567$	−2.68317e8	+	5.62614e7i	−1.47197	+	0.308647i
$568$	4.84447e7	+	3.65129e7i	0.264363	+	0.199251i
$569$	−2.24920e8			−1.22093			−0.610465	−	0.792044i	$-0.709017\pi$
$569$	−2.24920e8			−1.22093			−0.610465	+	0.792044i	$0.709017\pi$
$570$	9.91277e7	+	1.85452e8i	0.535267	+	1.00140i
$571$	2.21896e7	+	2.21896e7i	0.119190	+	0.119190i	0.764186	−	0.644996i	$-0.223141\pi$
$571$	2.21896e7	+	2.21896e7i	0.119190	+	0.119190i	−0.644996	+	0.764186i	$0.723141\pi$
$572$	−5.66644e7	+	5.28622e6i	−0.302777	+	0.0282460i
$573$	−4.70070e6	+	1.32454e7i	−0.0249861	+	0.0704047i
$574$	−1.72838e8	−	1.57464e8i	−0.913908	−	0.832618i
$575$		−	2.81894e7i		−	0.148280i
$576$	−7.49453e7	+	1.75794e8i	−0.392172	+	0.919892i
$577$	1.70762e8			0.888920			0.444460	−	0.895799i	$-0.353396\pi$
$577$	1.70762e8			0.888920			0.444460	+	0.895799i	$0.353396\pi$
$578$	−1.54044e8	+	1.69084e8i	−0.797741	+	0.875626i
$579$	2.57953e7	+	9.15459e6i	0.132894	+	0.0471632i
$580$	7.91556e6	+	8.48490e7i	0.0405693	+	0.434873i
$581$	2.54987e8	−	2.54987e8i	1.30014	−	1.30014i
$582$	−2.51941e8	+	1.34668e8i	−1.27800	+	0.683116i
$583$		−	1.96667e8i		−	0.992490i
$584$	2.13570e8	−	2.83360e8i	1.07226	−	1.42266i
$585$	−3.01520e7	+	3.71301e7i	−0.150608	+	0.185463i
$586$	4.70055e6	+	1.00992e8i	0.0233591	+	0.501872i
$587$	−1.49703e8	+	1.49703e8i	−0.740142	+	0.740142i	−0.972605	−	0.232463i	$-0.925321\pi$
$587$	−1.49703e8	+	1.49703e8i	−0.740142	+	0.740142i	0.232463	+	0.972605i	$0.425321\pi$
$588$	6.29769e7	−	2.48705e8i	0.309777	−	1.22336i
$589$	2.94917e8	−	2.94917e8i	1.44329	−	1.44329i
$590$	−1.36741e8	−	1.24579e8i	−0.665800	−	0.606579i
$591$	5.60277e7	−	2.66765e7i	0.271419	−	0.129231i
$592$	−1.54445e8	−	1.05516e8i	−0.744404	−	0.508571i
$593$			2.93220e8i			1.40614i	0.711119	+	0.703071i	$0.248189\pi$
$593$			2.93220e8i			1.40614i	−0.711119	+	0.703071i	$0.751811\pi$
$594$	−1.64000e8	+	1.10814e8i	−0.782502	+	0.528731i
$595$	2.45665e8	−	2.45665e8i	1.16625	−	1.16625i
$596$	−3.55620e7	−	2.94931e7i	−0.167976	−	0.139310i
$597$	1.40416e8	−	3.95656e8i	0.659922	−	1.85950i
$598$	1.05614e6	+	2.26912e7i	0.00493875	+	0.106109i
$599$	−1.19287e8			−0.555023			−0.277511	−	0.960722i	$-0.589510\pi$
$599$	−1.19287e8			−0.555023			−0.277511	+	0.960722i	$0.589510\pi$
$600$	−8.10025e7	+	5.35232e7i	−0.375011	+	0.247793i
$601$			1.48680e8i			0.684904i	0.939535	+	0.342452i	$0.111257\pi$
$601$			1.48680e8i			0.684904i	−0.939535	+	0.342452i	$0.888743\pi$
$602$	1.00679e6	+	2.16309e7i	0.00461474	+	0.0991481i
$603$	2.34261e8	−	2.42960e7i	1.06843	−	0.110811i
$604$	1.80809e8	−	1.68676e7i	0.820557	−	0.0765497i
$605$	−1.25633e7	−	1.25633e7i	−0.0567332	−	0.0567332i
$606$	−4.79097e6	+	1.57941e7i	−0.0215281	+	0.0709705i
$607$	2.11651e8			0.946357			0.473179	−	0.880967i	$-0.343107\pi$
$607$	2.11651e8			0.946357			0.473179	+	0.880967i	$0.343107\pi$
$608$	−7.92686e7	−	3.34697e8i	−0.352688	−	1.48916i
$609$	1.80545e8	−	8.59630e7i	0.799342	−	0.380592i
$610$	−2.24876e7	−	2.04874e7i	−0.0990726	−	0.0902603i
$611$	−7.85567e7	−	7.85567e7i	−0.344397	−	0.344397i
$612$	2.81698e8	+	1.88219e8i	1.22894	+	0.821123i
$613$	−5.63189e7	−	5.63189e7i	−0.244496	−	0.244496i	0.574211	−	0.818707i	$-0.305309\pi$
$613$	−5.63189e7	−	5.63189e7i	−0.244496	−	0.244496i	−0.818707	+	0.574211i	$0.805309\pi$
$614$	1.41483e7	+	3.03977e8i	0.0611222	+	1.31322i
$615$	−1.28094e8	+	6.09895e7i	−0.550685	+	0.262198i
$616$	−4.61738e7	−	3.28771e8i	−0.197539	−	1.40654i
$617$	2.39570e8			1.01994			0.509972	−	0.860191i	$-0.329656\pi$
$617$	2.39570e8			1.01994			0.509972	+	0.860191i	$0.329656\pi$
$618$	3.48053e7	+	6.51149e7i	0.147462	+	0.275877i
$619$	−1.66908e8	−	1.66908e8i	−0.703727	−	0.703727i	0.261481	−	0.965209i	$-0.415789\pi$
$619$	−1.66908e8	−	1.66908e8i	−0.703727	−	0.703727i	−0.965209	+	0.261481i	$0.915789\pi$
$620$	−1.81541e8	−	1.50560e8i	−0.761729	−	0.631733i
$621$	4.11399e7	+	6.74463e7i	0.171786	+	0.281633i
$622$	−1.12773e8	+	1.23783e8i	−0.468632	+	0.514386i
$623$		−	4.95256e7i		−	0.204817i
$624$	6.31981e7	−	4.61186e7i	0.260106	−	0.189811i
$625$	8.50788e7			0.348483
$626$	−1.58674e8	−	1.44560e8i	−0.646817	−	0.589284i
$627$	1.19147e8	−	3.35726e8i	0.483370	−	1.36202i
$628$	−2.13687e8	−	1.77219e8i	−0.862777	−	0.715537i
$629$	−2.34479e8	+	2.34479e8i	−0.942217	+	0.942217i
$630$	−2.24549e8	−	1.65636e8i	−0.898026	−	0.662420i
$631$		−	1.25603e8i		−	0.499932i	−0.968255	−	0.249966i	$-0.919580\pi$
$631$		−	1.25603e8i		−	0.499932i	0.968255	−	0.249966i	$-0.0804195\pi$
$632$	−1.86935e8	−	1.40894e8i	−0.740526	−	0.558137i
$633$	−3.83069e8	+	1.82391e8i	−1.51031	+	0.719105i
$634$	−1.12939e8	+	5.25665e6i	−0.443178	+	0.0206272i
$635$	2.03572e8	−	2.03572e8i	0.795053	−	0.795053i
$636$	1.38398e8	+	2.32255e8i	0.537971	+	0.902804i
$637$	−7.42687e7	+	7.42687e7i	−0.287334	+	0.287334i
$638$	9.72269e7	−	1.06719e8i	0.374390	−	0.410943i
$639$	−6.70508e7	−	5.44496e7i	−0.256981	−	0.208685i
$640$	−1.84285e8	+	6.22119e7i	−0.702991	+	0.237320i
$641$			3.33574e8i			1.26654i	0.773933	+	0.633268i	$0.218287\pi$
$641$			3.33574e8i			1.26654i	−0.773933	+	0.633268i	$0.781713\pi$
$642$	6.59035e7	−	2.17261e8i	0.249060	−	0.821062i
$643$	9.00686e7	−	9.00686e7i	0.338798	−	0.338798i	−0.517117	−	0.855915i	$-0.672995\pi$
$643$	9.00686e7	−	9.00686e7i	0.338798	−	0.338798i	0.855915	+	0.517117i	$0.172995\pi$
$644$	−1.31944e8	+	1.23090e7i	−0.494005	+	0.0460857i
$645$	1.23827e7	+	4.39454e6i	0.0461463	+	0.0163770i
$646$	−6.09115e8	+	2.83506e7i	−2.25944	+	0.105163i
$647$	3.29562e8			1.21682			0.608408	−	0.793625i	$-0.291809\pi$
$647$	3.29562e8			1.21682			0.608408	+	0.793625i	$0.291809\pi$
$648$	1.15695e8	−	2.46276e8i	0.425197	−	0.905101i
$649$			3.13379e8i			1.14640i
$650$	3.97043e7	−	1.84800e6i	0.144576	−	0.00672916i
$651$	−1.85097e8	+	5.21558e8i	−0.670899	+	1.89043i
$652$	−2.32620e7	−	1.92921e7i	−0.0839273	−	0.0696044i
$653$	−1.67012e8	−	1.67012e8i	−0.599801	−	0.599801i	0.340458	−	0.940260i	$-0.389418\pi$
$653$	−1.67012e8	−	1.67012e8i	−0.599801	−	0.599801i	−0.940260	+	0.340458i	$0.889418\pi$
$654$	−4.54564e7	+	1.49854e8i	−0.162503	+	0.535715i
$655$	−2.47295e8			−0.880019
$656$	2.28055e8	−	4.29240e7i	0.807844	−	0.152051i
$657$	−3.18484e8	+	3.92190e8i	−1.12303	+	1.38293i
$658$	4.36472e8	−	4.79086e8i	1.53207	−	1.68165i
$659$	3.16835e7	+	3.16835e7i	0.110707	+	0.110707i	0.760291	−	0.649583i	$-0.225057\pi$
$659$	3.16835e7	+	3.16835e7i	0.110707	+	0.110707i	−0.649583	+	0.760291i	$0.725057\pi$
$660$	−1.95286e8	−	4.94502e7i	−0.679266	−	0.172003i
$661$	3.46917e7	+	3.46917e7i	0.120122	+	0.120122i	0.764612	−	0.644491i	$-0.222931\pi$
$661$	3.46917e7	+	3.46917e7i	0.120122	+	0.120122i	−0.644491	+	0.764612i	$0.722931\pi$
$662$	1.12963e8	−	5.25776e6i	0.389371	−	0.0181229i
$663$	−5.96254e7	−	1.25229e8i	−0.204593	−	0.429699i
$664$	4.97768e7	+	3.54425e8i	0.170029	+	1.21065i
$665$	5.02211e8			1.70774
$666$	2.14324e8	+	1.58094e8i	0.725517	+	0.535171i
$667$	−4.07466e7	−	4.07466e7i	−0.137314	−	0.137314i
$668$	−4.71223e7	−	5.05117e8i	−0.158087	−	1.69458i
$669$	2.16737e8	+	7.69185e7i	0.723861	+	0.256893i
$670$	1.77196e8	+	1.61435e8i	0.589154	+	0.536750i
$671$			5.15362e7i			0.170587i
$672$	2.85891e8	+	3.55770e8i	0.942091	+	1.17236i
$673$	−4.11121e7			−0.134873			−0.0674364	−	0.997724i	$-0.521482\pi$
$673$	−4.11121e7			−0.134873			−0.0674364	+	0.997724i	$0.521482\pi$
$674$	5.03444e7	−	5.52596e7i	0.164426	−	0.180480i
$675$	1.18015e8	−	7.19852e7i	0.383731	−	0.234063i
$676$	2.75689e8	−	2.57190e7i	0.892442	−	0.0832558i
$677$	2.73177e8	−	2.73177e8i	0.880395	−	0.880395i	−0.113179	−	0.993575i	$-0.536103\pi$
$677$	2.73177e8	−	2.73177e8i	0.880395	−	0.880395i	0.993575	+	0.113179i	$0.0361035\pi$
$678$	1.43126e7	+	2.67765e7i	0.0459228	+	0.0859140i
$679$			6.82266e8i			2.17944i
$680$	4.79570e7	+	3.41468e8i	0.152520	+	1.08598i
$681$	−2.25539e8	−	4.73692e8i	−0.714137	−	1.49987i
$682$	1.85769e7	+	3.99125e8i	0.0585624	+	1.25822i
$683$	−7.72107e7	+	7.72107e7i	−0.242335	+	0.242335i	−0.817815	−	0.575481i	$-0.804815\pi$
$683$	−7.72107e7	+	7.72107e7i	−0.242335	+	0.242335i	0.575481	+	0.817815i	$0.304815\pi$
$684$	9.55497e7	+	4.80323e8i	0.298580	+	1.50095i
$685$	1.19919e8	−	1.19919e8i	0.373092	−	0.373092i
$686$	−9.40230e7	−	8.56599e7i	−0.291247	−	0.265341i
$687$	−1.39436e8	−	2.92852e8i	−0.430036	−	0.903188i
$688$	−1.77459e7	−	1.21239e7i	−0.0544920	−	0.0372285i
$689$		−	1.10685e8i		−	0.338400i
$690$	−2.33408e7	+	7.69464e7i	−0.0710507	+	0.234229i
$691$	3.83688e7	−	3.83688e7i	0.116291	−	0.116291i	−0.646567	−	0.762857i	$-0.723796\pi$
$691$	3.83688e7	−	3.83688e7i	0.116291	−	0.116291i	0.762857	+	0.646567i	$0.223796\pi$
$692$	−2.64286e8	+	3.18670e8i	−0.797548	+	0.961664i
$693$	4.87645e7	+	4.70185e8i	0.146523	+	1.41276i
$694$	−1.79871e6	−	3.86454e7i	−0.00538125	−	0.115616i
$695$	−1.15369e8			−0.343666
$696$	−3.97201e7	+	1.94451e8i	−0.117810	+	0.576743i
$697$		−	4.11400e8i		−	1.21497i
$698$	1.22309e7	+	2.62781e8i	0.0359659	+	0.772730i
$699$	−1.11096e8	−	3.94273e7i	−0.325289	−	0.115443i
$700$	2.15379e7	+	2.30871e8i	0.0627927	+	0.673092i
$701$	3.38616e8	+	3.38616e8i	0.982999	+	0.982999i	0.999858	−	0.0168585i	$-0.00536648\pi$
$701$	3.38616e8	+	3.38616e8i	0.982999	+	0.982999i	−0.0168585	+	0.999858i	$0.505366\pi$
$702$	−9.23000e7	+	6.23664e7i	−0.266803	+	0.180277i
$703$	−4.79342e8			−1.37968
$704$	2.88165e8	+	1.59804e8i	0.825891	+	0.458005i
$705$	−1.69056e8	−	3.55062e8i	−0.482462	−	1.01330i
$706$	2.11047e8	+	1.92275e8i	0.599743	+	0.546397i
$707$	2.78726e7	+	2.78726e7i	0.0788715	+	0.0788715i
$708$	−2.20530e8	−	3.70086e8i	−0.621396	−	1.04280i
$709$	1.33164e8	+	1.33164e8i	0.373635	+	0.373635i	0.868799	−	0.495164i	$-0.164892\pi$
$709$	1.33164e8	+	1.33164e8i	0.373635	+	0.373635i	−0.495164	+	0.868799i	$0.664892\pi$
$710$	−4.08731e6	−	8.78161e7i	−0.0114199	−	0.245357i
$711$	2.58732e8	+	2.10107e8i	0.719848	+	0.584563i
$712$	3.92537e7	+	2.95856e7i	0.108753	+	0.0819673i
$713$	1.59483e8			0.439993
$714$	7.13584e8	−	3.81425e8i	1.96042	−	1.04789i
$715$	5.83167e7	+	5.83167e7i	0.159542	+	0.159542i
$716$	−1.13759e8	+	1.37168e8i	−0.309918	+	0.373692i
$717$	−4.38176e7	+	1.23467e8i	−0.118875	+	0.334961i
$718$	1.76240e8	−	1.93447e8i	0.476137	−	0.522623i
$719$			2.06254e8i			0.554902i	0.960740	+	0.277451i	$0.0894895\pi$
$719$			2.06254e8i			0.554902i	−0.960740	+	0.277451i	$0.910510\pi$
$720$	2.65423e8	−	7.90280e7i	0.711117	−	0.211731i
$721$	1.76334e8			0.470468
$722$	−3.73365e8	−	3.40155e8i	−0.992022	−	0.903784i
$723$	−2.32397e8	−	8.24760e7i	−0.614915	−	0.218229i
$724$	−2.53413e8	+	3.05560e8i	−0.667749	+	0.805156i
$725$	−7.12970e7	+	7.12970e7i	−0.187093	+	0.187093i
$726$	−1.95061e7	−	3.64926e7i	−0.0509753	−	0.0953663i
$727$		−	1.76665e7i		−	0.0459777i	−0.999736	−	0.0229888i	$-0.992682\pi$
$727$		−	1.76665e7i		−	0.0459777i	0.999736	−	0.0229888i	$-0.00731822\pi$
$728$	−2.59868e7	−	1.85034e8i	−0.0673533	−	0.479575i
$729$	−1.77308e8	+	3.44465e8i	−0.457664	+	0.889125i
$730$	−5.13650e8	+	2.39073e7i	−1.32038	+	0.0614556i
$731$	−2.69418e7	+	2.69418e7i	−0.0689724	+	0.0689724i
$732$	−3.62670e7	−	6.08619e7i	−0.0924652	−	0.155172i
$733$	−2.06167e8	+	2.06167e8i	−0.523489	+	0.523489i	−0.918623	−	0.395134i	$-0.870698\pi$
$733$	−2.06167e8	+	2.06167e8i	−0.523489	+	0.523489i	0.395134	+	0.918623i	$0.370698\pi$
$734$	1.60269e8	−	1.75916e8i	0.405285	−	0.444853i
$735$	−3.35680e8	+	1.59828e8i	−0.845403	+	0.402523i
$736$	6.90645e7	−	1.11931e8i	0.173229	−	0.280748i
$737$		−	4.06091e8i		−	1.01443i
$738$	−3.26709e8	+	4.93286e7i	−0.812816	+	0.122724i
$739$	−1.93345e8	+	1.93345e8i	−0.479071	+	0.479071i	−0.904835	−	0.425763i	$-0.860006\pi$
$739$	−1.93345e8	+	1.93345e8i	−0.479071	+	0.479071i	0.425763	+	0.904835i	$0.360006\pi$
$740$	2.51780e7	+	2.69890e8i	0.0621335	+	0.666026i
$741$	6.70563e7	−	1.88948e8i	0.164811	−	0.464395i
$742$	6.45002e8	−	3.00210e7i	1.57888	−	0.0734874i
$743$	3.41867e8			0.833471			0.416736	−	0.909028i	$-0.363174\pi$
$743$	3.41867e8			0.833471			0.416736	+	0.909028i	$0.363174\pi$
$744$	−3.02810e8	−	4.58275e8i	−0.735278	−	1.11278i
$745$			6.69520e7i			0.161918i
$746$	7.31394e8	−	3.40419e7i	1.76171	−	0.0819970i
$747$	−5.25697e7	−	5.06874e8i	−0.126117	−	1.21601i
$748$	3.72911e8	−	4.49647e8i	0.891046	−	1.07440i
$749$	−3.83410e8	−	3.83410e8i	−0.912470	−	0.912470i
$750$	4.34178e8	+	1.31703e8i	1.02916	+	0.312185i
$751$	3.57308e8			0.843573			0.421787	−	0.906695i	$-0.361403\pi$
$751$	3.57308e8			0.843573			0.421787	+	0.906695i	$0.361403\pi$
$752$	1.18980e8	+	6.32141e8i	0.279783	+	1.48649i
$753$	3.86558e8	−	1.84052e8i	0.905378	−	0.431079i
$754$	5.47197e7	−	6.00621e7i	0.127653	−	0.140116i
$755$	−1.86081e8	−	1.86081e8i	−0.432375	−	0.432375i
$756$	−3.88467e8	−	5.20951e8i	−0.899059	−	1.20568i
$757$	−4.22889e8	−	4.22889e8i	−0.974852	−	0.974852i	0.0248395	−	0.999691i	$-0.492093\pi$
$757$	−4.22889e8	−	4.22889e8i	−0.974852	−	0.974852i	−0.999691	+	0.0248395i	$0.992093\pi$
$758$	−2.78155e8	+	1.29464e7i	−0.638675	+	0.0297264i
$759$	1.22991e8	−	5.85601e7i	0.281287	−	0.133930i
$760$	−3.00011e8	+	3.98049e8i	−0.683433	+	0.906766i
$761$	−5.95862e8			−1.35205			−0.676023	−	0.736880i	$-0.736298\pi$
$761$	−5.95862e8			−1.35205			−0.676023	+	0.736880i	$0.736298\pi$
$762$	5.91314e8	−	3.16070e8i	1.33645	−	0.714362i
$763$	2.64454e8	+	2.64454e8i	0.595355	+	0.595355i
$764$	−3.31711e7	+	3.09453e6i	−0.0743839	+	0.00693928i
$765$	−5.06478e7	−	4.88344e8i	−0.113130	−	1.09079i
$766$	−3.47658e8	−	3.16735e8i	−0.773511	−	0.704708i
$767$			1.76371e8i			0.390877i
$768$	−4.52766e8	+	1.40656e7i	−0.999518	+	0.0310509i
$769$	−5.36098e8			−1.17887			−0.589435	−	0.807816i	$-0.700649\pi$
$769$	−5.36098e8			−1.17887			−0.589435	+	0.807816i	$0.700649\pi$
$770$	−3.24016e8	+	3.55650e8i	−0.709731	+	0.779024i
$771$	−7.52737e7	+	2.12103e8i	−0.164240	+	0.462789i
$772$	6.02657e6	+	6.46004e7i	0.0130984	+	0.140405i
$773$	−2.76113e8	+	2.76113e8i	−0.597790	+	0.597790i	−0.939724	−	0.341934i	$-0.888918\pi$
$773$	−2.76113e8	+	2.76113e8i	−0.597790	+	0.597790i	0.341934	+	0.939724i	$0.388918\pi$
$774$	2.46260e7	+	1.81652e7i	0.0531094	+	0.0391756i
$775$		−	2.79058e8i		−	0.599500i
$776$	−5.40759e8	−	4.07572e8i	−1.15723	−	0.872207i
$777$	5.74280e8	−	2.73433e8i	1.22422	−	0.582891i
$778$	8.38087e6	+	1.80064e8i	0.0177971	+	0.382373i
$779$	4.20510e8	−	4.20510e8i	0.889538	−	0.889538i
$780$	−1.09908e8	−	2.78308e7i	−0.231603	−	0.0586464i
$781$	−1.05310e8	+	1.05310e8i	−0.221064	+	0.221064i
$782$	−1.72362e8	−	1.57031e8i	−0.360430	−	0.328371i
$783$	6.65344e7	−	2.74637e8i	0.138599	−	0.572103i
$784$	5.97636e8	−	1.12486e8i	1.24019	−	0.233426i
$785$			4.02304e8i			0.831659i
$786$	−5.51137e8	−	1.67181e8i	−1.13499	−	0.344286i
$787$	−5.54908e8	+	5.54908e8i	−1.13841	+	1.13841i	−0.149669	+	0.988736i	$0.547821\pi$
$787$	−5.54908e8	+	5.54908e8i	−1.13841	+	1.13841i	−0.988736	+	0.149669i	$0.952179\pi$
$788$	1.13221e8	+	9.38988e7i	0.231392	+	0.191903i
$789$	−2.89160e8	−	1.02621e8i	−0.588717	−	0.208932i
$790$	1.57719e7	+	3.38860e8i	0.0319891	+	0.687288i
$791$	7.25118e7			0.146514
$792$	−4.01797e8	−	2.42229e8i	−0.808780	−	0.487585i
$793$			2.90048e7i			0.0581634i
$794$	−1.99549e7	−	4.28733e8i	−0.0398647	−	0.856496i
$795$	1.31039e8	−	3.69236e8i	0.260795	−	0.734857i
$796$	9.90860e8	−	9.24373e7i	1.96459	−	0.183277i
$797$	−2.24392e8	−	2.24392e8i	−0.443233	−	0.443233i	0.449864	−	0.893097i	$-0.351472\pi$
$797$	−2.24392e8	−	2.24392e8i	−0.443233	−	0.443233i	−0.893097	+	0.449864i	$0.851472\pi$
$798$	1.11926e9	+	3.39514e8i	2.20253	+	0.668111i
$799$	1.14035e9			2.23563
$800$	−1.95853e8	−	1.20847e8i	−0.382525	−	0.236029i
$801$	−5.43299e7	−	4.41193e7i	−0.105716	−	0.0858483i
$802$	4.49614e8	+	4.09621e8i	0.871598	+	0.794071i
$803$	6.15976e8	+	6.15976e8i	1.18964	+	1.18964i
$804$	2.85773e8	+	4.79574e8i	0.549862	+	0.922758i
$805$	1.35791e8	+	1.35791e8i	0.260305	+	0.260305i
$806$	1.04551e7	+	2.24629e8i	0.0199675	+	0.429004i
$807$	−2.20223e8	−	4.62525e8i	−0.419027	−	0.880065i
$808$	−3.87422e7	+	5.44110e6i	−0.0734430	+	0.0103146i
$809$	−7.43028e8			−1.40333			−0.701665	−	0.712507i	$-0.747559\pi$
$809$	−7.43028e8			−1.40333			−0.701665	+	0.712507i	$0.747559\pi$
$810$	−3.81740e8	+	9.87759e7i	−0.718312	+	0.185864i
$811$	−8.01430e7	−	8.01430e7i	−0.150246	−	0.150246i	0.627982	−	0.778228i	$-0.283881\pi$
$811$	−8.01430e7	−	8.01430e7i	−0.150246	−	0.150246i	−0.778228	+	0.627982i	$0.783881\pi$
$812$	3.64846e8	+	3.02581e8i	0.681461	+	0.565163i
$813$	−7.07178e8	−	2.50972e8i	−1.31600	−	0.467040i
$814$	3.09261e8	−	3.39455e8i	0.573393	−	0.629375i
$815$			4.37948e7i			0.0809003i
$816$	−1.23966e8	+	7.93437e8i	−0.228155	+	1.46030i
$817$	−5.50769e7			−0.100996
$818$	−1.98259e7	−	1.80624e7i	−0.0362220	−	0.0330001i
$819$	2.74449e7	+	2.64622e8i	0.0499585	+	0.481697i
$820$	−2.58853e8	−	2.14677e8i	−0.469474	−	0.389354i
$821$	−5.25314e7	+	5.25314e7i	−0.0949270	+	0.0949270i	−0.752976	−	0.658049i	$-0.771382\pi$
$821$	−5.25314e7	+	5.25314e7i	−0.0949270	+	0.0949270i	0.658049	+	0.752976i	$0.271382\pi$
$822$	3.48329e8	−	1.86189e8i	0.627154	−	0.335227i
$823$			1.88995e8i			0.339041i	0.985527	+	0.169520i	$0.0542218\pi$
$823$			1.88995e8i			0.339041i	−0.985527	+	0.169520i	$0.945778\pi$
$824$	−1.05338e8	+	1.39761e8i	−0.188280	+	0.249807i
$825$	−1.02466e8	−	2.15206e8i	−0.182482	−	0.383260i
$826$	−1.02778e9	+	4.78368e7i	−1.82372	+	0.0848833i
$827$	−6.36551e8	+	6.36551e8i	−1.12543	+	1.12543i	−0.134513	+	0.990912i	$0.542947\pi$
$827$	−6.36551e8	+	6.36551e8i	−1.12543	+	1.12543i	−0.990912	+	0.134513i	$0.957053\pi$
$828$	−1.04037e8	+	1.55708e8i	−0.183273	+	0.274297i
$829$	5.15919e7	−	5.15919e7i	0.0905561	−	0.0905561i	−0.660378	−	0.750934i	$-0.729604\pi$
$829$	5.15919e7	−	5.15919e7i	0.0905561	−	0.0905561i	0.750934	+	0.660378i	$0.229604\pi$
$830$	3.49299e8	−	3.83402e8i	0.610890	−	0.670533i
$831$	3.97024e8	+	8.33855e8i	0.691853	+	1.45307i
$832$	1.62180e8	+	8.99384e7i	0.281597	+	0.156162i
$833$		−	1.07811e9i		−	1.86521i
$834$	−2.57119e8	−	7.79941e7i	−0.443237	−	0.134451i
$835$	−5.19845e8	+	5.19845e8i	−0.892924	+	0.892924i
$836$	8.40774e8	−	7.84358e7i	1.43900	−	0.134244i
$837$	4.07260e8	+	6.67677e8i	0.694537	+	1.13865i
$838$	−4.69719e8	+	2.18626e7i	−0.798190	+	0.0371509i
$839$	−8.43273e8			−1.42785			−0.713925	−	0.700223i	$-0.753084\pi$
$839$	−8.43273e8			−1.42785			−0.713925	+	0.700223i	$0.753084\pi$
$840$	1.32370e8	−	6.48022e8i	0.223333	−	1.09333i
$841$		−	3.88710e8i		−	0.653488i
$842$	−2.33114e8	+	1.08500e7i	−0.390509	+	0.0181758i
$843$	−6.53646e8	−	2.31974e8i	−1.09109	−	0.387220i
$844$	−7.74107e8	−	6.41998e8i	−1.28758	−	1.06784i
$845$	−2.83728e8	−	2.83728e8i	−0.470253	−	0.470253i
$846$	−1.36733e8	−	9.05600e8i	−0.225820	−	1.49563i
$847$	−9.88235e7			−0.162633
$848$	−3.61517e8	+	5.29158e8i	−0.592845	+	0.867757i
$849$	2.51947e8	+	5.29153e8i	0.411704	+	0.864686i
$850$	−2.74767e8	+	3.01593e8i	−0.447412	+	0.491094i
$851$	−1.29608e8	−	1.29608e8i	−0.210301	−	0.210301i
$852$	5.02579e7	−	1.98476e8i	0.0812616	−	0.320914i
$853$	−2.28072e8	−	2.28072e8i	−0.367473	−	0.367473i	0.499082	−	0.866555i	$-0.333671\pi$
$853$	−2.28072e8	−	2.28072e8i	−0.367473	−	0.367473i	−0.866555	+	0.499082i	$0.833671\pi$
$854$	−1.69022e8	+	7.86693e6i	−0.271374	+	0.0126308i
$855$	4.47389e8	−	5.50927e8i	0.715791	−	0.881446i
$856$	5.32930e8	−	7.48467e7i	0.849667	−	0.119330i
$857$	9.11632e7			0.144836			0.0724181	−	0.997374i	$-0.476928\pi$
$857$	9.11632e7			0.144836			0.0724181	+	0.997374i	$0.476928\pi$
$858$	9.05438e7	+	1.69392e8i	0.143350	+	0.268184i
$859$	1.79156e8	+	1.79156e8i	0.282652	+	0.282652i	0.834166	−	0.551514i	$-0.185950\pi$
$859$	1.79156e8	+	1.79156e8i	0.282652	+	0.282652i	−0.551514	+	0.834166i	$0.685950\pi$
$860$	2.89298e6	+	3.10106e7i	0.00454831	+	0.0487545i
$861$	−2.63923e8	+	7.43670e8i	−0.413493	+	1.16512i
$862$	6.45007e8	+	5.87635e8i	1.00703	+	0.917458i
$863$			1.65009e8i			0.256729i	0.991727	+	0.128364i	$0.0409727\pi$
$863$			1.65009e8i			0.256729i	−0.991727	+	0.128364i	$0.959027\pi$
$864$	6.44964e8	+	3.30954e6i	0.999987	+	0.00513128i
$865$	5.99955e8			0.926980
$866$	5.53067e8	−	6.07064e8i	0.851577	−	0.934718i
$867$	7.27518e8	+	2.58191e8i	1.11631	+	0.396172i
$868$	−1.30616e9	+	1.21852e8i	−1.99727	+	0.186326i
$869$	4.06366e8	−	4.06366e8i	0.619238	−	0.619238i
$870$	2.53647e8	−	1.35580e8i	0.385188	−	0.205891i
$871$		−	2.28549e8i		−	0.345880i
$872$	−3.67584e8	+	5.16248e7i	−0.554379	+	0.0778590i
$873$	7.48449e8	+	6.07789e8i	1.12491	+	0.913503i
$874$	−1.56707e7	−	3.36687e8i	−0.0234723	−	0.504304i
$875$	7.66215e8	−	7.66215e8i	1.14374	−	1.14374i
$876$	−1.16091e9	−	2.93966e8i	−1.72698	−	0.437305i
$877$	6.87607e8	−	6.87607e8i	1.01939	−	1.01939i	0.0195843	−	0.999808i	$-0.493766\pi$
$877$	6.87607e8	−	6.87607e8i	1.01939	−	1.01939i	0.999808	−	0.0195843i	$-0.00623429\pi$
$878$	8.04710e8	+	7.33132e8i	1.18893	+	1.08318i
$879$	3.08077e8	−	1.46685e8i	0.453621	−	0.215983i
$880$	−8.83252e7	−	4.69271e8i	−0.129609	−	0.688613i
$881$		−	4.30277e8i		−	0.629246i	−0.949217	−	0.314623i	$-0.898122\pi$
$881$		−	4.30277e8i		−	0.629246i	0.949217	−	0.314623i	$-0.101878\pi$
$882$	−8.56168e8	+	1.29270e8i	−1.24782	+	0.188404i
$883$	−5.50659e8	+	5.50659e8i	−0.799835	+	0.799835i	−0.983069	−	0.183234i	$-0.941343\pi$
$883$	−5.50659e8	+	5.50659e8i	−0.799835	+	0.799835i	0.183234	+	0.983069i	$0.441343\pi$
$884$	2.09876e8	−	2.53063e8i	0.303812	−	0.366330i
$885$	−2.08804e8	+	5.88358e8i	−0.301238	+	0.848813i
$886$	1.28328e7	+	2.75713e8i	0.0184510	+	0.396421i
$887$	1.01476e9			1.45409			0.727045	−	0.686589i	$-0.240893\pi$
$887$	1.01476e9			1.45409			0.727045	+	0.686589i	$0.240893\pi$
$888$	−1.26343e8	+	6.18514e8i	−0.180431	+	0.883305i
$889$		−	1.60130e9i		−	2.27913i
$890$	−3.31186e6	−	7.11555e7i	−0.00469788	−	0.100934i
$891$	5.59237e8	+	3.65364e8i	0.790610	+	0.516527i
$892$	5.06363e7	+	5.42784e8i	0.0713457	+	0.764773i
$893$	1.16561e9	+	1.16561e9i	1.63681	+	1.63681i
$894$	−4.52621e7	+	1.49213e8i	−0.0633465	+	0.208831i
$895$	2.58244e8			0.360214
$896$	−4.80116e8	+	9.69478e8i	−0.667456	+	1.34776i
$897$	6.92201e7	−	3.29579e7i	0.0959080	−	0.0456648i
$898$	−7.33472e8	−	6.68232e8i	−1.01287	−	0.922780i
$899$	−4.03366e8	−	4.03366e8i	−0.555163	−	0.555163i
$900$	2.72453e8	+	1.82041e8i	0.373735	+	0.249714i
$901$	8.03369e8	+	8.03369e8i	1.09835	+	1.09835i
$902$	2.64880e7	+	5.69097e8i	0.0360936	+	0.775473i
$903$	6.59854e7	−	3.14177e7i	0.0896158	−	0.0426689i
$904$	−4.33171e7	+	5.74723e7i	−0.0586346	+	0.0777953i
$905$	5.75271e8			0.776117
$906$	−2.88913e8	−	5.40509e8i	−0.388493	−	0.726806i
$907$	1.29272e8	+	1.29272e8i	0.173254	+	0.173254i	0.788407	−	0.615154i	$-0.210906\pi$
$907$	1.29272e8	+	1.29272e8i	0.173254	+	0.173254i	−0.615154	+	0.788407i	$0.710906\pi$
$908$	7.93877e8	−	9.57238e8i	1.06046	−	1.27868i
$909$	5.54064e7	−	5.74639e6i	0.0737681	−	0.00765074i
$910$	−1.82357e8	+	2.00161e8i	−0.241991	+	0.265617i
$911$			3.20339e8i			0.423696i	0.977303	+	0.211848i	$0.0679482\pi$
$911$			3.20339e8i			0.423696i	−0.977303	+	0.211848i	$0.932052\pi$
$912$	−9.37718e8	+	6.84297e8i	−1.23620	+	0.902111i
$913$	−8.78666e8			−1.15455
$914$	5.20118e8	+	4.73854e8i	0.681182	+	0.620592i
$915$	−3.43386e7	+	9.67576e7i	−0.0448249	+	0.126305i
$916$	4.90801e8	−	5.91797e8i	0.638586	−	0.769992i
$917$	−9.72618e8	+	9.72618e8i	−1.26135	+	1.26135i
$918$	2.17262e8	−	1.12259e9i	0.280838	−	1.45109i
$919$			4.14157e8i			0.533604i	0.963751	+	0.266802i	$0.0859669\pi$
$919$			4.14157e8i			0.533604i	−0.963751	+	0.266802i	$0.914033\pi$
$920$	−1.88746e8	+	2.65082e7i	−0.242389	+	0.0340421i
$921$	9.27290e8	−	4.41512e8i	1.18696	−	0.565150i
$922$	−1.17309e9	+	5.46001e7i	−1.49671	+	0.0696628i
$923$	−5.92691e7	+	5.92691e7i	−0.0753743	+	0.0753743i
$924$	−9.62555e8	+	5.73576e8i	−1.22014	+	0.727069i
$925$	−2.26783e8	+	2.26783e8i	−0.286540	+	0.286540i
$926$	−7.33273e7	+	8.04864e7i	−0.0923491	+	0.101365i
$927$	1.57085e8	−	1.93439e8i	0.197195	−	0.242831i
$928$	−4.57775e8	+	1.08418e8i	−0.572807	+	0.135662i
$929$			5.71597e8i			0.712923i	0.934310	+	0.356461i	$0.116017\pi$
$929$			5.71597e8i			0.712923i	−0.934310	+	0.356461i	$0.883983\pi$
$930$	−2.31060e8	+	7.61722e8i	−0.287260	+	0.946995i
$931$	1.10198e9	−	1.10198e9i	1.36561	−	1.36561i
$932$	−2.59555e7	−	2.78224e8i	−0.0320613	−	0.343674i
$933$	5.32601e8	+	1.89016e8i	0.655778	+	0.232731i
$934$	4.29249e8	−	1.99789e7i	0.526828	−	0.0245206i
$935$	−8.46543e8			−1.03565
$936$	−2.26133e8	−	1.36327e8i	−0.275763	−	0.166248i
$937$		−	1.07263e9i		−	1.30386i	−0.758277	−	0.651932i	$-0.773959\pi$
$937$		−	1.07263e9i		−	1.30386i	0.758277	−	0.651932i	$-0.226041\pi$
$938$	1.33184e9	−	6.19892e7i	1.61378	−	0.0751116i
$939$	−2.42295e8	+	6.82726e8i	−0.292649	+	0.824612i
$940$	5.95060e8	−	7.17510e8i	0.716436	−	0.863862i
$941$	7.13084e7	+	7.13084e7i	0.0855799	+	0.0855799i	0.748601	−	0.663021i	$-0.230726\pi$
$941$	7.13084e7	+	7.13084e7i	0.0855799	+	0.0855799i	−0.663021	+	0.748601i	$0.730726\pi$
$942$	−2.71973e8	+	8.96600e8i	−0.325367	+	1.07262i
$943$	2.27401e8			0.271179
$944$	5.76059e8	−	8.43186e8i	0.684780	−	1.00232i
$945$	−2.21731e8	+	9.15249e8i	−0.262742	+	1.08454i
$946$	3.55345e7	−	3.90038e7i	0.0419736	−	0.0460716i
$947$	−9.23961e8	−	9.23961e8i	−1.08794	−	1.08794i	−0.995741	−	0.0921964i	$-0.970611\pi$
$947$	−9.23961e8	−	9.23961e8i	−1.08794	−	1.08794i	−0.0921964	−	0.995741i	$-0.529389\pi$
$948$	−1.93932e8	+	7.65866e8i	−0.227627	+	0.898934i
$949$	3.46674e8	+	3.46674e8i	0.405623	+	0.405623i
$950$	−5.89123e8	+	2.74201e7i	−0.687125	+	0.0319815i
$951$	1.64039e8	+	3.44524e8i	0.190724	+	0.400570i
$952$	1.53162e9	+	1.15439e9i	1.77517	+	1.33795i
$953$	−1.33488e9			−1.54228			−0.771141	−	0.636664i	$-0.780314\pi$
$953$	−1.33488e9			−1.54228			−0.771141	+	0.636664i	$0.780314\pi$
$954$	5.41660e8	−	7.34314e8i	0.623852	−	0.845740i
$955$	3.41383e7	+	3.41383e7i	0.0391951	+	0.0391951i
$956$	−3.09204e8	+	2.88456e7i	−0.353893	+	0.0330146i
$957$	−4.59182e8	−	1.62961e8i	−0.523901	−	0.185929i
$958$	−1.21862e9	−	1.11023e9i	−1.38603	−	1.26275i
$959$		−	9.43289e8i		−	1.06952i
$960$	4.34542e8	+	4.92031e8i	0.491155	+	0.556133i
$961$	6.91280e8			0.778904
$962$	1.74053e8	−	1.91047e8i	0.195505	−	0.214592i
$963$	−7.62159e8	+	7.90462e7i	−0.853428	+	0.0885120i
$964$	−5.42949e7	−	5.82001e8i	−0.0606077	−	0.649670i
$965$	6.64840e7	−	6.64840e7i	0.0739836	−	0.0739836i
$966$	2.10832e8	+	3.94432e8i	0.233887	+	0.437563i
$967$			3.64378e8i			0.402970i	0.979492	+	0.201485i	$0.0645767\pi$
$967$			3.64378e8i			0.402970i	−0.979492	+	0.201485i	$0.935423\pi$
$968$	5.90352e7	−	7.83268e7i	0.0650856	−	0.0863544i
$969$	8.84708e8	+	1.85812e9i	0.972364	+	2.04222i
$970$	4.56242e7	+	9.80240e8i	0.0499897	+	1.07403i
$971$	5.42822e8	−	5.42822e8i	0.592925	−	0.592925i	−0.345495	−	0.938421i	$-0.612289\pi$
$971$	5.42822e8	−	5.42822e8i	0.592925	−	0.592925i	0.938421	+	0.345495i	$0.112289\pi$
$972$	−9.17546e8	−	3.79332e7i	−0.999147	−	0.0413067i
$973$	−4.53751e8	+	4.53751e8i	−0.492582	+	0.492582i
$974$	−6.36573e8	−	5.79952e8i	−0.688925	−	0.627646i
$975$	−5.76685e7	−	1.21119e8i	−0.0622193	−	0.130677i
$976$	9.47349e7	−	1.38665e8i	0.101897	−	0.149148i
$977$			2.70311e8i			0.289855i	0.989442	+	0.144927i	$0.0462948\pi$
$977$			2.70311e8i			0.289855i	−0.989442	+	0.144927i	$0.953705\pi$
$978$	−2.96070e7	+	9.76039e7i	−0.0316503	+	0.104340i
$979$	−8.53307e7	+	8.53307e7i	−0.0909405	+	0.0909405i
$980$	−6.78345e8	−	5.62579e8i	−0.720729	−	0.597730i
$981$	5.25693e8	−	5.45214e7i	0.556833	−	0.0577510i
$982$	3.35129e7	+	7.20027e8i	0.0353897	+	0.760351i
$983$	−1.54724e8			−0.162891			−0.0814454	−	0.996678i	$-0.525954\pi$
$983$	−1.54724e8			−0.162891			−0.0814454	+	0.996678i	$0.525954\pi$
$984$	−4.31765e8	−	6.53437e8i	−0.453171	−	0.685833i
$985$		−	2.13159e8i		−	0.223046i
$986$	3.87759e7	+	8.33103e8i	0.0404512	+	0.869097i
$987$	−2.06137e9	−	7.31565e8i	−2.14390	−	0.760854i
$988$	4.73191e8	−	4.41439e7i	0.490643	−	0.0457720i
$989$	−1.48921e7	−	1.48921e7i	−0.0153945	−	0.0153945i
$990$	1.01504e8	+	6.72273e8i	0.104611	+	0.692852i
$991$	−5.86968e8			−0.603105			−0.301553	−	0.953449i	$-0.597505\pi$
$991$	−5.86968e8			−0.603105			−0.301553	+	0.953449i	$0.597505\pi$
$992$	6.83696e8	−	1.10805e9i	0.700371	−	1.13507i
$993$	−1.64074e8	−	3.44598e8i	−0.167568	−	0.351937i
$994$	−3.61458e8	−	3.29307e8i	−0.368044	−	0.335307i
$995$	−1.01975e9	−	1.01975e9i	−1.03520	−	1.03520i
$996$	1.03766e9	−	6.18333e8i	1.05022	−	0.625813i
$997$	−5.27372e8	−	5.27372e8i	−0.532147	−	0.532147i	0.389064	−	0.921211i	$-0.372798\pi$
$997$	−5.27372e8	−	5.27372e8i	−0.532147	−	0.532147i	−0.921211	+	0.389064i	$0.872798\pi$
$998$	−4.57317e7	−	9.82548e8i	−0.0460072	−	0.988467i
$999$	2.11634e8	−	8.73573e8i	0.212270	−	0.876198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.i.a.5.34	yes	92
3.2	odd	2	inner	48.7.i.a.5.13	✓	92
4.3	odd	2		192.7.i.a.113.43		92
12.11	even	2		192.7.i.a.113.19		92
16.3	odd	4		192.7.i.a.17.19		92
16.13	even	4	inner	48.7.i.a.29.13	yes	92
48.29	odd	4	inner	48.7.i.a.29.34	yes	92
48.35	even	4		192.7.i.a.17.43		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.13	✓	92	3.2	odd	2	inner
48.7.i.a.5.34	yes	92	1.1	even	1	trivial
48.7.i.a.29.13	yes	92	16.13	even	4	inner
48.7.i.a.29.34	yes	92	48.29	odd	4	inner
192.7.i.a.17.19		92	16.3	odd	4
192.7.i.a.17.43		92	48.35	even	4
192.7.i.a.113.19		92	12.11	even	2
192.7.i.a.113.43		92	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.38773 - 5.91374i) q^{2} +(-25.4451 - 9.03029i) q^{3} +(-5.94475 - 63.7233i) q^{4} +(-65.5814 + 65.5814i) q^{5} +(-190.494 + 101.823i) q^{6} +515.866i q^{7} +(-408.872 - 308.168i) q^{8} +(565.908 + 459.554i) q^{9} +O(q^{10})\)	\(q+(5.38773 - 5.91374i) q^{2} +(-25.4451 - 9.03029i) q^{3} +(-5.94475 - 63.7233i) q^{4} +(-65.5814 + 65.5814i) q^{5} +(-190.494 + 101.823i) q^{6} +515.866i q^{7} +(-408.872 - 308.168i) q^{8} +(565.908 + 459.554i) q^{9} +(34.4968 + 741.166i) q^{10} +(888.817 - 888.817i) q^{11} +(-424.175 + 1675.13i) q^{12} +(500.230 - 500.230i) q^{13} +(3050.70 + 2779.35i) q^{14} +(2260.94 - 1076.51i) q^{15} +(-4025.32 + 757.638i) q^{16} +7261.49i q^{17} +(5766.64 - 870.683i) q^{18} +(-7422.29 + 7422.29i) q^{19} +(4568.93 + 3789.20i) q^{20} +(4658.42 - 13126.3i) q^{21} +(-467.531 - 10044.9i) q^{22} -4013.78 q^{23} +(7620.95 + 11533.6i) q^{24} +7023.17i q^{25} +(-263.128 - 5653.33i) q^{26} +(-10249.7 - 16803.7i) q^{27} +(32872.7 - 3066.69i) q^{28} +(10151.7 + 10151.7i) q^{29} +(5815.17 - 19170.6i) q^{30} -39733.9 q^{31} +(-17206.9 + 27886.7i) q^{32} +(-30642.3 + 14589.8i) q^{33} +(42942.6 + 39122.9i) q^{34} +(-33831.2 - 33831.2i) q^{35} +(25920.1 - 38793.4i) q^{36} +(32290.7 + 32290.7i) q^{37} +(3904.24 + 83882.9i) q^{38} +(-17245.6 + 8211.18i) q^{39} +(47024.5 - 6604.29i) q^{40} -56655.0 q^{41} +(-52527.1 - 98269.6i) q^{42} +(3710.24 + 3710.24i) q^{43} +(-61922.2 - 51354.6i) q^{44} +(-67251.2 + 6974.85i) q^{45} +(-21625.1 + 23736.4i) q^{46} -157041. i q^{47} +(109266. + 17071.6i) q^{48} -148469. q^{49} +(41533.2 + 37838.9i) q^{50} +(65573.4 - 184769. i) q^{51} +(-34850.0 - 28902.6i) q^{52} +(110634. - 110634. i) q^{53} +(-154595. - 29919.8i) q^{54} +116580. i q^{55} +(158974. - 210923. i) q^{56} +(255887. - 121836. i) q^{57} +(114729. - 5339.94i) q^{58} +(-176290. + 176290. i) q^{59} +(-82039.3 - 137675. i) q^{60} +(-28991.5 + 28991.5i) q^{61} +(-214076. + 234976. i) q^{62} +(-237068. + 291933. i) q^{63} +(72208.7 + 252003. i) q^{64} +65611.5i q^{65} +(-78812.4 + 259817. i) q^{66} +(228444. - 228444. i) q^{67} +(462726. - 43167.7i) q^{68} +(102131. + 36245.6i) q^{69} +(-382343. + 17795.7i) q^{70} -118484. q^{71} +(-89764.0 - 362293. i) q^{72} +693029. i q^{73} +(364932. - 16985.4i) q^{74} +(63421.2 - 178705. i) q^{75} +(517097. + 428850. i) q^{76} +(458511. + 458511. i) q^{77} +(-44355.9 + 146226. i) q^{78} +457198. q^{79} +(214299. - 313673. i) q^{80} +(109062. + 520130. i) q^{81} +(-305242. + 335043. i) q^{82} +(-494289. - 494289. i) q^{83} +(-864143. - 218818. i) q^{84} +(-476219. - 476219. i) q^{85} +(41931.1 - 1951.64i) q^{86} +(-166638. - 349983. i) q^{87} +(-637318. + 89507.3i) q^{88} -96004.8 q^{89} +(-321084. + 435285. i) q^{90} +(258052. + 258052. i) q^{91} +(23860.9 + 255771. i) q^{92} +(1.01103e6 + 358809. i) q^{93} +(-928702. - 846096. i) q^{94} -973529. i q^{95} +(689655. - 554196. i) q^{96} +1.32256e6 q^{97} +(-799911. + 878008. i) q^{98} +(911448. - 94529.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Introduction

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