LMFDB - Embedded newform 48.7.i.a.5.13

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			5.13
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.38773 + 5.91374i) q^{2} +(9.03029 + 25.4451i) q^{3} +(-5.94475 - 63.7233i) q^{4} +(65.5814 - 65.5814i) q^{5} +(-199.129 - 83.6886i) q^{6} +515.866i q^{7} +(408.872 + 308.168i) q^{8} +(-565.908 + 459.554i) q^{9} +O(q^{10})$	\(q+(-5.38773 + 5.91374i) q^{2} +(9.03029 + 25.4451i) q^{3} +(-5.94475 - 63.7233i) q^{4} +(65.5814 - 65.5814i) q^{5} +(-199.129 - 83.6886i) 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} +(1567.76 - 726.705i) 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} +(331.275 - 5822.58i) q^{18} +(-7422.29 + 7422.29i) q^{19} +(-4568.93 - 3789.20i) q^{20} +(-13126.3 + 4658.42i) q^{21} +(-467.531 - 10044.9i) q^{22} +4013.78 q^{23} +(-4149.14 + 13186.6i) q^{24} +7023.17i q^{25} +(263.128 + 5653.33i) q^{26} +(-16803.7 - 10249.7i) q^{27} +(32872.7 - 3066.69i) q^{28} +(-10151.7 - 10151.7i) q^{29} +(-18547.5 + 7570.72i) 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} +(32648.5 + 33329.6i) 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} +(43172.1 - 102724. i) q^{42} +(3710.24 + 3710.24i) q^{43} +(61922.2 + 51354.6i) q^{44} +(-6974.85 + 67251.2i) q^{45} +(-21625.1 + 23736.4i) q^{46} +157041. i q^{47} +(-55628.0 - 95583.0i) q^{48} -148469. q^{49} +(-41533.2 - 37838.9i) q^{50} +(184769. - 65573.4i) q^{51} +(-34850.0 - 28902.6i) q^{52} +(-110634. + 110634. i) q^{53} +(151148. - 44150.3i) 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} +(55157.8 - 150474. 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} +(251373. - 102605. i) q^{66} +(228444. - 228444. i) q^{67} +(-462726. + 43167.7i) q^{68} +(36245.6 + 102131. i) q^{69} +(-382343. + 17795.7i) q^{70} +118484. q^{71} +(-373004. + 13503.8i) q^{72} +693029. i q^{73} +(-364932. + 16985.4i) q^{74} +(-178705. + 63421.2i) q^{75} +(517097. + 428850. i) q^{76} +(-458511. - 458511. i) q^{77} +(-141474. + 57746.6i) 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} +(374883. + 808757. 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} +(-360128. - 403578. i) q^{90} +(258052. + 258052. i) q^{91} +(-23860.9 - 255771. i) q^{92} +(-358809. - 1.01103e6i) q^{93} +(-928702. - 846096. i) q^{94} +973529. i q^{95} +(864962. + 186006. i) q^{96} +1.32256e6 q^{97} +(799911. - 878008. i) q^{98} +(94529.4 - 911448. i) 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
$3$	9.03029	+	25.4451i	0.334455	+	0.942412i
$3$	9.03029	+	25.4451i	0.334455	+	0.942412i
$4$	−5.94475	−	63.7233i	−0.0928866	−	0.995677i
$5$	65.5814	−	65.5814i	0.524651	−	0.524651i	−0.394322	−	0.918973i	$-0.629020\pi$
$5$	65.5814	−	65.5814i	0.524651	−	0.524651i	0.918973	+	0.394322i	$0.129020\pi$
$6$	−199.129	−	83.6886i	−0.921892	−	0.387447i
$7$			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	−0.957202	−	0.289420i	$-0.906537\pi$
$11$	−888.817	+	888.817i	−0.667782	+	0.667782i	0.289420	+	0.957202i	$0.406537\pi$
$12$	1567.76	−	726.705i	0.907271	−	0.420547i
$13$	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	$-0.735295\pi$
$17$		−	7261.49i		−	1.47802i	0.673697	−	0.739008i	$-0.264705\pi$
$18$	331.275	−	5822.58i	0.0568030	−	0.998385i
$19$	−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
$21$	−13126.3	+	4658.42i	−1.41737	+	0.503015i
$22$	−467.531	−	10044.9i	−0.0439079	−	0.943365i
$23$	4013.78			0.329890			0.164945	−	0.986303i	$-0.447255\pi$
$23$	4013.78			0.329890			0.164945	+	0.986303i	$0.447255\pi$
$24$	−4149.14	+	13186.6i	−0.300141	+	0.953895i
$25$			7023.17i			0.449483i
$26$	263.128	+	5653.33i	0.0149709	+	0.321651i
$27$	−16803.7	−	10249.7i	−0.853717	−	0.520738i
$28$	32872.7	−	3066.69i	1.49748	−	0.139700i
$29$	−10151.7	−	10151.7i	−0.416240	−	0.416240i	0.467665	−	0.883906i	$-0.345095\pi$
$29$	−10151.7	−	10151.7i	−0.416240	−	0.416240i	−0.883906	+	0.467665i	$0.845095\pi$
$30$	−18547.5	+	7570.72i	−0.686946	+	0.280397i
$31$	−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
$36$	32648.5	+	33329.6i	0.699770	+	0.714369i
$37$	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	$-0.365175\pi$
$41$	56655.0			0.822029			0.411014	+	0.911629i	$0.365175\pi$
$42$	43172.1	−	102724.i	0.582714	−	1.38651i
$43$	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
$45$	−6974.85	+	67251.2i	−0.0765415	+	0.738010i
$46$	−21625.1	+	23736.4i	−0.222170	+	0.243861i
$47$			157041.i			1.51259i	0.654233	+	0.756293i	$0.272992\pi$
$47$			157041.i			1.51259i	−0.654233	+	0.756293i	$0.727008\pi$
$48$	−55628.0	−	95583.0i	−0.503002	−	0.864285i
$49$	−148469.			−1.26197
$50$	−41533.2	−	37838.9i	−0.332266	−	0.302711i
$51$	184769.	−	65573.4i	1.39290	−	0.494330i
$52$	−34850.0	−	28902.6i	−0.247852	−	0.205554i
$53$	−110634.	+	110634.i	−0.743124	+	0.743124i	−0.973178	−	0.230054i	$-0.926110\pi$
$53$	−110634.	+	110634.i	−0.743124	+	0.743124i	0.230054	+	0.973178i	$0.426110\pi$
$54$	151148.	−	44150.3i	0.959888	−	0.280383i
$55$			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	−0.132782	−	0.991145i	$-0.542391\pi$
$59$	176290.	−	176290.i	0.858363	−	0.858363i	0.991145	+	0.132782i	$0.0423911\pi$
$60$	55157.8	−	150474.i	0.255360	−	0.696641i
$61$	−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
$66$	251373.	−	102605.i	0.874353	−	0.356893i
$67$	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
$69$	36245.6	+	102131.i	0.110334	+	0.310893i
$70$	−382343.	+	17795.7i	−1.11470	+	0.0518826i
$71$	118484.			0.331042			0.165521	−	0.986206i	$-0.447069\pi$
$71$	118484.			0.331042			0.165521	+	0.986206i	$0.447069\pi$
$72$	−373004.	+	13503.8i	−0.999345	+	0.0361793i
$73$			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
$75$	−178705.	+	63421.2i	−0.423598	+	0.150332i
$76$	517097.	+	428850.i	1.17796	+	0.976932i
$77$	−458511.	−	458511.i	−1.00433	−	1.00433i
$78$	−141474.	+	57746.6i	−0.298120	+	0.121687i
$79$	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	0.991853	−	0.127389i	$-0.0406597\pi$
$83$	494289.	+	494289.i	0.864464	+	0.864464i	−0.127389	+	0.991853i	$0.540660\pi$
$84$	374883.	+	808757.i	0.632495	+	1.36452i
$85$	−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	$-0.478309\pi$
$89$	96004.8			0.136183			0.0680915	+	0.997679i	$0.478309\pi$
$90$	−360128.	−	403578.i	−0.494002	−	0.553606i
$91$	258052.	+	258052.i	0.342439	+	0.342439i
$92$	−23860.9	−	255771.i	−0.0306424	−	0.328464i
$93$	−358809.	−	1.01103e6i	−0.446082	−	1.25695i
$94$	−928702.	−	846096.i	−1.11813	−	1.01868i
$95$			973529.i			1.13548i
$96$	864962.	+	186006.i	0.977650	+	0.210239i
$97$	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
$99$	94529.4	−	911448.i	0.0974229	−	0.939347i
$100$	447539.	−	41750.9i	0.447539	−	0.0417509i
$101$	−54030.7	+	54030.7i	−0.0524417	+	0.0524417i	−0.732841	−	0.680400i	$-0.761806\pi$
$101$	−54030.7	+	54030.7i	−0.0524417	+	0.0524417i	0.680400	+	0.732841i	$0.261806\pi$
$102$	−607704.	+	1.44597e6i	−0.572653	+	1.36257i
$103$		−	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	−0.335381	−	0.942083i	$-0.608865\pi$
$107$	743236.	−	743236.i	0.606702	−	0.606702i	0.942083	+	0.335381i	$0.108865\pi$
$108$	−553250.	+	1.13172e6i	−0.439188	+	0.898395i
$109$	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	$0.0155106\pi$
$113$			140563.i			0.0974173i	−0.998813	+	0.0487087i	$0.984489\pi$
$114$	2.09915e6	−	856831.i	1.41687	−	0.578336i
$115$	263229.	−	263229.i	0.173077	−	0.173077i
$116$	−586550.	+	707248.i	−0.375778	+	0.453104i
$117$	−53201.5	+	512966.i	−0.0332174	+	0.320281i
$118$	92731.1	+	1.99233e6i	0.0564390	+	1.21260i
$119$	3.74596e6			2.22291
$120$	592692.	+	1.13690e6i	0.342993	+	0.657931i
$121$			191568.i			0.108135i
$122$	−15249.9	−	327646.i	−0.00839825	−	0.180437i
$123$	511611.	+	1.44159e6i	0.274932	+	0.774689i
$124$	236208.	+	2.53198e6i	0.123888	+	1.32799i
$125$	1.48530e6	+	1.48530e6i	0.760473	+	0.760473i
$126$	3.00368e6	+	170894.i	1.50156	+	0.0854308i
$127$	−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	0.150013	−	0.988684i	$-0.452068\pi$
$131$	−1.88541e6	−	1.88541e6i	−0.838670	−	0.838670i	−0.988684	+	0.150013i	$0.952068\pi$
$132$	−747548.	+	2.03936e6i	−0.325025	+	0.886692i
$133$	−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	$-0.384289\pi$
$137$	1.82855e6			0.711125			0.355562	+	0.934653i	$0.384289\pi$
$138$	−799258.	−	335907.i	−0.304123	−	0.127815i
$139$	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
$141$	−3.99593e6	+	1.41813e6i	−1.42548	+	0.505892i
$142$	−638358.	+	700682.i	−0.222946	+	0.244712i
$143$			889226.i			0.304091i
$144$	1.92978e6	−	2.27860e6i	0.646281	−	0.763100i
$145$	−1.33152e6			−0.436762
$146$	−4.09840e6	−	3.73385e6i	−1.31691	−	1.19977i
$147$	−1.34072e6	−	3.77781e6i	−0.422071	−	1.18929i
$148$	1.86571e6	−	2.24963e6i	0.575518	−	0.693946i
$149$	−510450.	+	510450.i	−0.154310	+	0.154310i	−0.780040	−	0.625730i	$-0.784801\pi$
$149$	−510450.	+	510450.i	−0.154310	+	0.154310i	0.625730	+	0.780040i	$0.284801\pi$
$150$	587759.	−	1.39851e6i	0.174151	−	0.414375i
$151$			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
$156$	420723.	−	1.14776e6i	0.110821	−	0.302328i
$157$	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
$162$	2.48832e6	+	3.44728e6i	0.585276	+	0.810834i
$163$	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
$165$	−2.96638e6	+	1.05275e6i	−0.660352	+	0.234354i
$166$	−5.58620e6	+	260004.i	−1.22121	+	0.0568401i
$167$	−7.92672e6			−1.70194			−0.850970	−	0.525214i	$-0.823985\pi$
$167$	−7.92672e6			−1.70194			−0.850970	+	0.525214i	$0.823985\pi$
$168$	−6.80255e6	−	2.14040e6i	−1.43464	−	0.451406i
$169$			4.32635e6i			0.896317i
$170$	5.38197e6	−	250498.i	1.09546	−	0.0509868i
$171$	789392.	−	7.61128e6i	0.157872	−	1.52219i
$172$	214372.	−	258485.i	0.0421292	−	0.0507984i
$173$	4.57413e6	+	4.57413e6i	0.883425	+	0.883425i	0.993881	−	0.110456i	$-0.0352310\pi$
$173$	4.57413e6	+	4.57413e6i	0.883425	+	0.883425i	−0.110456	+	0.993881i	$0.535231\pi$
$174$	1.17191e6	+	2.87107e6i	0.222458	+	0.545000i
$175$	−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	0.857603	−	0.514313i	$-0.171953\pi$
$179$	1.96888e6	+	1.96888e6i	0.343289	+	0.343289i	−0.514313	+	0.857603i	$0.671953\pi$
$180$	4.32693e6	+	44669.4i	0.741929	+	0.00765936i
$181$	−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
$186$	7.91216e6	+	3.32527e6i	1.22958	+	0.516760i
$187$	6.45414e6	+	6.45414e6i	0.986992	+	0.986992i
$188$	1.00072e7	−	933570.i	1.50605	−	0.140499i
$189$	5.28747e6	−	8.66847e6i	0.783181	−	1.28398i
$190$	−5.75720e6	−	5.24511e6i	−0.839364	−	0.764705i
$191$			520548.i			0.0747069i	0.999302	+	0.0373535i	$0.0118927\pi$
$191$			520548.i			0.0747069i	−0.999302	+	0.0373535i	$0.988107\pi$
$192$	−5.76017e6	+	4.11302e6i	−0.813827	+	0.581108i
$193$	−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
$195$	1.66949e6	−	592491.i	0.225155	−	0.0799057i
$196$	882611.	+	9.46094e6i	0.117220	+	1.25651i
$197$	1.62515e6	−	1.62515e6i	0.212566	−	0.212566i	−0.592790	−	0.805357i	$-0.701974\pi$
$197$	1.62515e6	−	1.62515e6i	0.212566	−	0.212566i	0.805357	+	0.592790i	$0.201974\pi$
$198$	4.88077e6	+	5.46966e6i	0.628772	+	0.704636i
$199$			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
$204$	−5.27696e6	−	1.13843e7i	−0.621575	−	1.34096i
$205$	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
$210$	−3.90548e6	−	9.56805e6i	−0.421713	−	1.03316i
$211$	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
$213$	1.06994e6	+	3.01483e6i	0.110719	+	0.311978i
$214$	390953.	+	8.39966e6i	0.0398918	+	0.857078i
$215$	486645.			0.0489662
$216$	−3.71194e6	−	9.36918e6i	−0.368332	−	0.929694i
$217$		−	2.04974e7i		−	2.00595i
$218$	269656.	+	5.79359e6i	0.0260280	+	0.559214i
$219$	−1.76342e7	+	6.25825e6i	−1.67889	+	0.595828i
$220$	7.42885e6	−	693037.i	0.697675	−	0.0650861i
$221$	−3.63241e6	−	3.63241e6i	−0.336526	−	0.336526i
$222$	−3.72764e6	−	9.13236e6i	−0.340702	−	0.834688i
$223$	−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	$-0.937996\pi$
$227$	−1.37400e7	−	1.37400e7i	−1.17465	−	1.17465i	−0.193563	−	0.981088i	$-0.562004\pi$
$228$	−6.24259e6	+	1.70302e7i	−0.526696	+	1.43686i
$229$	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	$-0.555211\pi$
$233$	−4.36612e6			−0.345166			−0.172583	+	0.984995i	$0.555211\pi$
$234$	−2.74692e6	−	3.07834e6i	−0.214387	−	0.240253i
$235$	1.02990e7	+	1.02990e7i	0.793580	+	0.793580i
$236$	−1.22818e7	−	1.01858e7i	−0.934382	−	0.774922i
$237$	4.12863e6	+	1.16335e7i	0.310142	+	0.873904i
$238$	−2.01822e7	+	2.21526e7i	−1.49706	+	1.64322i
$239$			4.85229e6i			0.355429i	0.984082	+	0.177715i	$0.0568704\pi$
$239$			4.85229e6i			0.355429i	−0.984082	+	0.177715i	$0.943130\pi$
$240$	−9.91663e6	−	2.62031e6i	−0.717349	−	0.189548i
$241$	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
$243$	1.42196e7	−	1.92183e6i	0.990990	−	0.133936i
$244$	2.01978e6	+	1.67508e6i	0.139038	+	0.115310i
$245$	−9.73681e6	+	9.73681e6i	−0.662092	+	0.662092i
$246$	−1.12816e7	−	4.74138e6i	−0.757822	−	0.318493i
$247$			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	−0.257276	−	0.966338i	$-0.582825\pi$
$251$	1.12126e7	−	1.12126e7i	0.709062	−	0.709062i	0.966338	+	0.257276i	$0.0828250\pi$
$252$	−1.71936e7	+	1.68422e7i	−1.07440	+	1.05244i
$253$	−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	$0.0789634\pi$
$257$			8.33569e6i			0.491069i	−0.969388	+	0.245534i	$0.921037\pi$
$258$	−428310.	−	1.04932e6i	−0.0249401	−	0.0611010i
$259$	−1.66577e7	+	1.66577e7i	−0.958772	+	0.958772i
$260$	−4.18098e6	+	390044.i	−0.237880	+	0.0221918i
$261$	1.04102e7	+	1.07967e6i	0.585512	+	0.0607255i
$262$	2.13079e7	−	991753.i	1.18478	−	0.0551442i
$263$	−1.13641e7			−0.624692			−0.312346	−	0.949968i	$-0.601115\pi$
$263$	−1.13641e7			−0.624692			−0.312346	+	0.949968i	$0.601115\pi$
$264$	−8.03269e6	−	1.54084e7i	−0.436565	−	0.837422i
$265$			1.45111e7i			0.779762i
$266$	4.32724e7	−	2.01407e6i	2.29914	−	0.107011i
$267$	866951.	+	2.44285e6i	0.0455471	+	0.128340i
$268$	−1.59153e7	−	1.31992e7i	−0.826817	−	0.685713i
$269$	−1.34161e7	−	1.34161e7i	−0.689238	−	0.689238i	0.272826	−	0.962064i	$-0.412042\pi$
$269$	−1.34161e7	−	1.34161e7i	−0.689238	−	0.689238i	−0.962064	+	0.272826i	$0.912042\pi$
$270$	7.01704e6	−	1.28079e7i	0.356503	−	0.650710i
$271$	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
$276$	6.29265e6	−	2.91683e6i	0.299300	−	0.138734i
$277$	−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	$-0.696510\pi$
$281$	−2.56885e7			−1.15776			−0.578881	+	0.815412i	$0.696510\pi$
$282$	1.31426e7	−	3.12714e7i	0.586047	−	1.39444i
$283$	−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
$285$	−2.47715e7	+	8.79125e6i	−1.07009	+	0.379766i
$286$	−5.25866e6	−	4.79091e6i	−0.224790	−	0.204795i
$287$			2.92264e7i			1.23632i
$288$	3.07792e6	+	2.36887e7i	0.128849	+	0.991664i
$289$	−2.85917e7			−1.18453
$290$	7.17388e6	−	7.87429e6i	0.294144	−	0.322862i
$291$	1.19431e7	+	3.36528e7i	0.484663	+	1.36566i
$292$	4.41621e7	−	4.11988e6i	1.77379	−	0.165476i
$293$	8.93615e6	−	8.93615e6i	0.355261	−	0.355261i	−0.506802	−	0.862063i	$-0.669172\pi$
$293$	8.93615e6	−	8.93615e6i	0.355261	−	0.355261i	0.862063	+	0.506802i	$0.169172\pi$
$294$	2.95645e7	+	1.24252e7i	1.16340	+	0.488945i
$295$		−	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
$300$	5.10377e6	+	1.10107e7i	0.189028	+	0.407803i
$301$	−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
$306$	−4.22806e7	−	2.40555e6i	−1.47563	−	0.0839557i
$307$	−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
$309$	8.69767e6	−	3.08674e6i	0.294800	−	0.104622i
$310$	−1.37069e6	−	2.94494e7i	−0.0460103	−	0.988535i
$311$	2.09314e7			0.695851			0.347926	−	0.937522i	$-0.386886\pi$
$311$	2.09314e7			0.695851			0.347926	+	0.937522i	$0.386886\pi$
$312$	4.52083e6	+	8.67188e6i	0.148852	+	0.285528i
$313$		−	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
$315$	−3.46926e7	−	3.59809e6i	−1.10995	−	0.115117i
$316$	−2.71793e6	−	2.91342e7i	−0.0861343	−	0.923297i
$317$	9.99334e6	+	9.99334e6i	0.313713	+	0.313713i	0.846346	−	0.532633i	$-0.178797\pi$
$317$	9.99334e6	+	9.99334e6i	0.313713	+	0.313713i	−0.532633	+	0.846346i	$0.678797\pi$
$318$	3.12892e7	−	1.27716e7i	0.973002	−	0.397159i
$319$	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
$324$	−3.37927e7	−	3.85775e6i	−0.993547	−	0.113423i
$325$	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
$330$	9.75639e6	−	2.32144e7i	0.271486	−	0.645974i
$331$	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
$333$	−3.31128e7	−	3.43425e6i	−0.896734	−	0.0930034i
$334$	4.27070e7	−	4.68766e7i	1.14620	−	1.25810i
$335$		−	2.99634e7i		−	0.796996i
$336$	4.93081e7	−	2.86966e7i	1.29987	−	0.756507i
$337$	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
$339$	−3.57664e6	+	1.26933e6i	−0.0918072	+	0.0325817i
$340$	−2.75152e7	+	3.31772e7i	−0.700062	+	0.844118i
$341$	3.53162e7	−	3.53162e7i	0.890658	−	0.890658i
$342$	4.07581e7	+	4.56758e7i	1.01891	+	1.14185i
$343$		−	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	−0.746843	−	0.665001i	$-0.768431\pi$
$347$	−3.41950e6	+	3.41950e6i	−0.0818417	+	0.0818417i	0.665001	+	0.746843i	$0.268431\pi$
$348$	−2.32927e7	−	8.53817e6i	−0.552691	−	0.202594i
$349$	−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	$-0.867042\pi$
$353$		−	3.56875e7i		−	0.811321i	0.914024	−	0.405660i	$-0.132958\pi$
$354$	−4.98578e7	+	2.03509e7i	−1.12389	+	0.458748i
$355$	7.77032e6	−	7.77032e6i	0.173682	−	0.173682i
$356$	−570724.	−	6.11774e6i	−0.0126496	−	0.135594i
$357$	3.38271e7	+	9.53164e7i	0.743464	+	2.09490i
$358$	−2.22513e7	+	1.03566e6i	−0.484960	+	0.0225719i
$359$	−3.27114e7			−0.706994			−0.353497	−	0.935436i	$-0.615008\pi$
$359$	−3.27114e7			−0.706994			−0.353497	+	0.935436i	$0.615008\pi$
$360$	−2.35765e7	+	2.53477e7i	−0.505326	+	0.543289i
$361$		−	6.31350e7i		−	1.34199i
$362$	4.95675e7	−	2.30707e6i	1.04489	−	0.0486334i
$363$	−4.87447e6	+	1.72991e6i	−0.101908	+	0.0361664i
$364$	1.49099e7	−	1.79780e7i	0.309150	−	0.372766i
$365$	4.54498e7	+	4.54498e7i	0.934659	+	0.934659i
$366$	8.19928e6	−	3.34678e6i	0.167237	−	0.0682627i
$367$	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
$372$	−6.22934e7	+	2.88748e7i	−1.21008	+	0.560907i
$373$	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
$378$	2.27757e7	+	7.79721e7i	0.421692	+	1.44366i
$379$	−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
$381$	−2.80310e7	−	7.89843e7i	−0.506831	−	1.42812i
$382$	−3.07839e6	−	2.80457e6i	−0.0552247	−	0.0503126i
$383$			5.87882e7i			1.04639i	0.852213	+	0.523195i	$0.175260\pi$
$383$			5.87882e7i			1.04639i	−0.852213	+	0.523195i	$0.824740\pi$
$384$	6.71093e6	−	5.62240e7i	0.118519	−	0.992952i
$385$	−6.01396e7			−1.05385
$386$	5.46189e6	−	5.99514e6i	0.0949688	−	0.104241i
$387$	−3.80470e6	−	394599.i	−0.0656429	−	0.00680805i
$388$	−7.86231e6	−	8.42781e7i	−0.134603	−	1.44285i
$389$	1.59328e7	−	1.59328e7i	0.270671	−	0.270671i	−0.558699	−	0.829370i	$-0.688699\pi$
$389$	1.59328e7	−	1.59328e7i	0.270671	−	0.270671i	0.829370	+	0.558699i	$0.188699\pi$
$390$	−5.49093e6	+	1.30651e7i	−0.0925662	+	0.220252i
$391$		−	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
$396$	−5.86424e7	−	605400.i	−0.944336	−	0.00974892i
$397$	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	$-0.799309\pi$
$401$		−	7.60286e7i		−	1.17908i	0.807739	−	0.589541i	$-0.200691\pi$
$402$	−6.46080e7	+	2.63716e7i	−0.994507	+	0.405937i
$403$	−1.98761e7	+	1.98761e7i	−0.303680	+	0.303680i
$404$	3.76422e6	+	3.12182e6i	0.0570861	+	0.0473439i
$405$	−2.69584e7	−	4.12633e7i	−0.405816	−	0.621153i
$406$	2.75469e6	+	5.91848e7i	0.0411619	+	0.884367i
$407$	−5.74011e7			−0.851406
$408$	9.57547e7	+	3.01290e7i	1.40987	+	0.443612i
$409$		−	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
$411$	1.65124e7	+	4.65277e7i	0.237839	+	0.670172i
$412$	−2.17819e7	+	2.03204e6i	−0.311462	+	0.0290563i
$413$	9.09419e7	+	9.09419e7i	1.29096	+	1.29096i
$414$	1.32966e6	−	2.33705e7i	0.0187388	−	0.329358i
$415$	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	0.930728	−	0.365711i	$-0.119174\pi$
$419$	4.15627e7	+	4.15627e7i	0.565017	+	0.565017i	−0.365711	+	0.930728i	$0.619174\pi$
$420$	7.76247e7	+	2.84541e7i	1.04774	+	0.384058i
$421$	−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
$426$	−2.35935e7	−	9.91573e6i	−0.305185	−	0.128261i
$427$	−1.49557e7	−	1.49557e7i	−0.192098	−	0.192098i
$428$	−5.17798e7	−	4.29431e7i	−0.660433	−	0.547724i
$429$	−2.26265e7	+	8.02997e6i	−0.286579	+	0.101705i
$430$	−2.62191e6	+	2.87789e6i	−0.0329771	+	0.0361967i
$431$		−	1.09069e8i		−	1.36229i	−0.732148	−	0.681146i	$-0.761482\pi$
$431$		−	1.09069e8i		−	1.36229i	0.732148	−	0.681146i	$-0.238518\pi$
$432$	7.54058e7	+	2.85271e7i	0.935306	+	0.353840i
$433$	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
$435$	−1.20240e7	−	3.38807e7i	−0.146077	−	0.411609i
$436$	−3.57146e7	−	2.96196e7i	−0.430910	−	0.357371i
$437$	−2.97914e7	+	2.97914e7i	−0.356983	+	0.356983i
$438$	5.79986e7	−	1.38002e8i	0.690232	−	1.64234i
$439$			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	−0.552739	−	0.833354i	$-0.686417\pi$
$443$	2.43962e7	−	2.43962e7i	0.280616	−	0.280616i	0.833354	+	0.552739i	$0.186417\pi$
$444$	7.40900e7	+	2.71584e7i	0.846468	+	0.310281i
$445$	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	$0.240240\pi$
$449$			1.24028e8i			1.37019i	−0.728452	+	0.685097i	$0.759760\pi$
$450$	4.08930e7	+	2.32660e6i	0.448757	+	0.0255320i
$451$	−5.03560e7	+	5.03560e7i	−0.548936	+	0.548936i
$452$	8.95715e6	−	835612.i	0.0969961	−	0.00904877i
$453$	−7.21981e7	+	2.56226e7i	−0.776660	+	0.275631i
$454$	1.55282e8	−	7.22744e6i	1.65941	−	0.0772355i
$455$	3.38468e7			0.359321
$456$	−6.70790e7	−	1.28671e8i	−0.707444	−	1.35702i
$457$			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
$459$	−7.44280e7	+	1.22020e8i	−0.769659	+	1.26181i
$460$	−1.83386e7	−	1.52090e7i	−0.188406	−	0.156252i
$461$	1.03800e8	+	1.03800e8i	1.05948	+	1.05948i	0.998115	+	0.0613648i	$0.0195453\pi$
$461$	1.03800e8	+	1.03800e8i	1.05948	+	1.05948i	0.0613648	+	0.998115i	$0.480455\pi$
$462$	5.29306e7	+	1.29675e8i	0.536761	+	1.31501i
$463$	−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	0.495615	−	0.868542i	$-0.334943\pi$
$467$	−3.79817e7	−	3.79817e7i	−0.372927	−	0.372927i	−0.868542	+	0.495615i	$0.834943\pi$
$468$	3.30042e7	+	340721.i	0.321982	+	0.00332400i
$469$	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
$474$	−9.10412e7	−	3.82622e7i	−0.854876	−	0.359282i
$475$	−5.21280e7	−	5.21280e7i	−0.486396	−	0.486396i
$476$	−2.22688e7	−	2.38705e8i	−0.206479	−	2.21330i
$477$	1.17664e7	−	1.13451e8i	0.108415	−	1.04533i
$478$	−2.86952e7	−	2.61428e7i	−0.262740	−	0.239370i
$479$			2.06066e8i			1.87500i	0.347989	+	0.937499i	$0.386865\pi$
$479$			2.06066e8i			1.87500i	−0.347989	+	0.937499i	$0.613135\pi$
$480$	6.89239e7	−	4.45269e7i	0.623227	−	0.402623i
$481$	3.23055e7			0.290296
$482$	−4.92075e7	+	5.40118e7i	−0.439431	+	0.482333i
$483$	−5.26859e7	+	1.86979e7i	−0.467577	+	0.165940i
$484$	1.22073e7	−	1.13882e6i	0.107668	−	0.0100443i
$485$	8.67356e7	−	8.67356e7i	0.760277	−	0.760277i
$486$	−6.52463e7	+	9.44455e7i	−0.568391	+	0.822759i
$487$		−	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	−0.384778	−	0.923009i	$-0.625722\pi$
$491$	6.37109e7	−	6.37109e7i	0.538232	−	0.538232i	0.923009	+	0.384778i	$0.125722\pi$
$492$	8.88217e7	−	4.11715e7i	0.745803	−	0.345701i
$493$	−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
$498$	−5.70608e7	−	1.39793e8i	−0.462008	−	1.13188i
$499$	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
$501$	−7.15806e7	−	2.01696e8i	−0.569223	−	1.60393i
$502$	5.89798e6	+	1.26719e8i	0.0466222	+	1.00168i
$503$	−1.31189e8			−1.03084			−0.515422	−	0.856936i	$-0.672365\pi$
$503$	−1.31189e8			−1.03084			−0.515422	+	0.856936i	$0.672365\pi$
$504$	−6.96618e6	−	1.92420e8i	−0.0544130	−	1.50300i
$505$			7.08682e6i			0.0550272i
$506$	−1.87657e6	−	4.03182e7i	−0.0144848	−	0.311207i
$507$	−1.10084e8	+	3.90682e7i	−0.844699	+	0.299778i
$508$	1.84531e7	+	1.97804e8i	0.140760	+	1.50884i
$509$	−2.69973e7	−	2.69973e7i	−0.204723	−	0.204723i	0.597297	−	0.802020i	$-0.296241\pi$
$509$	−2.69973e7	−	2.69973e7i	−0.204723	−	0.204723i	−0.802020	+	0.597297i	$0.796241\pi$
$510$	5.49747e7	+	1.34683e8i	0.414431	+	1.01532i
$511$	−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
$516$	8.51302e6	+	3.12053e6i	0.0619633	+	0.0227132i
$517$	−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	$-0.729916\pi$
$521$	−1.86991e8			−1.32223			−0.661115	+	0.750285i	$0.729916\pi$
$522$	−6.24720e7	+	5.57460e7i	−0.439212	+	0.391925i
$523$	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
$525$	−3.27169e7	−	9.21881e7i	−0.226097	−	0.637084i
$526$	6.12264e7	−	6.72041e7i	0.420709	−	0.461784i
$527$			2.88527e8i			1.97131i
$528$	1.34399e8	+	3.55127e7i	0.913049	+	0.241258i
$529$	−1.31925e8			−0.891172
$530$	−8.58148e7	−	7.81817e7i	−0.576414	−	0.525143i
$531$	−1.87491e7	+	1.80778e8i	−0.125227	+	1.20743i
$532$	−2.21229e8	+	2.66753e8i	−1.46929	+	1.77163i
$533$	2.83405e7	−	2.83405e7i	0.187166	−	0.187166i
$534$	−1.91173e7	−	8.03450e6i	−0.125546	−	0.0527637i
$535$		−	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
$540$	3.79368e7	+	1.10503e8i	0.240924	+	0.701764i
$541$	−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
$546$	−2.97895e7	−	7.29815e7i	−0.183015	−	0.448368i
$547$	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
$549$	3.08336e6	−	2.97296e7i	0.0186341	−	0.179669i
$550$	7.05473e7	−	3.28355e6i	0.424026	−	0.0197358i
$551$	1.50698e8			0.900848
$552$	−1.66537e7	+	5.29282e7i	−0.0990135	+	0.314681i
$553$			2.35853e8i			1.39465i
$554$	2.73348e8	−	1.27227e7i	1.60763	−	0.0748255i
$555$	3.82463e7	+	1.07769e8i	0.223723	+	0.630396i
$556$	5.08214e7	−	6.12793e7i	0.295680	−	0.356524i
$557$	−1.35137e8	−	1.35137e8i	−0.782004	−	0.782004i	0.198165	−	0.980169i	$-0.436502\pi$
$557$	−1.35137e8	−	1.35137e8i	−0.782004	−	0.782004i	−0.980169	+	0.198165i	$0.936502\pi$
$558$	−1.31629e7	+	2.31354e8i	−0.0757613	+	1.33160i
$559$	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	0.136488	−	0.990642i	$-0.456418\pi$
$563$	−1.52427e8	−	1.52427e8i	−0.854154	−	0.854154i	−0.990642	+	0.136488i	$0.956418\pi$
$564$	1.14123e8	+	2.46204e8i	0.636113	+	1.37233i
$565$	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	$-0.290983\pi$
$569$	2.24920e8			1.22093			0.610465	+	0.792044i	$0.290983\pi$
$570$	8.14732e7	−	1.93857e8i	0.439937	−	1.04679i
$571$	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
$573$	−1.32454e7	+	4.70070e6i	−0.0704047	+	0.0249861i
$574$	−1.72838e8	−	1.57464e8i	−0.913908	−	0.832618i
$575$			2.81894e7i			0.148280i
$576$	−1.56672e8	−	1.09427e8i	−0.819831	−	0.572605i
$577$	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
$579$	−9.15459e6	−	2.57953e7i	−0.0471632	−	0.132894i
$580$	7.91556e6	+	8.48490e7i	0.0405693	+	0.434873i
$581$	−2.54987e8	+	2.54987e8i	−1.30014	+	1.30014i
$582$	−2.63360e8	−	1.10683e8i	−1.33592	−	0.561453i
$583$		−	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	−0.232463	−	0.972605i	$-0.574679\pi$
$587$	1.49703e8	−	1.49703e8i	0.740142	−	0.740142i	0.972605	+	0.232463i	$0.0746786\pi$
$588$	−2.32765e8	+	1.07893e8i	−1.14495	+	0.530716i
$589$	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	$-0.751811\pi$
$593$		−	2.93220e8i		−	1.40614i	0.711119	−	0.703071i	$-0.248189\pi$
$594$	−9.51013e7	+	1.73584e8i	−0.453761	+	0.828231i
$595$	2.45665e8	−	2.45665e8i	1.16625	−	1.16625i
$596$	3.55620e7	+	2.94931e7i	0.167976	+	0.139310i
$597$	−3.95656e8	+	1.40416e8i	−1.85950	+	0.659922i
$598$	1.05614e6	+	2.26912e7i	0.00493875	+	0.106109i
$599$	1.19287e8			0.555023			0.277511	−	0.960722i	$-0.410490\pi$
$599$	1.19287e8			0.555023			0.277511	+	0.960722i	$0.410490\pi$
$600$	−9.26120e7	−	2.91401e7i	−0.428759	−	0.134908i
$601$			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
$603$	−2.42960e7	+	2.34261e8i	−0.110811	+	1.06843i
$604$	1.80809e8	−	1.68676e7i	0.820557	−	0.0765497i
$605$	1.25633e7	+	1.25633e7i	0.0567332	+	0.0567332i
$606$	1.52808e7	−	6.23732e6i	0.0686640	−	0.0280272i
$607$	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
$612$	2.42022e8	−	2.37076e8i	1.05585	−	1.03427i
$613$	−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	$-0.670344\pi$
$617$	−2.39570e8			−1.01994			−0.509972	+	0.860191i	$0.670344\pi$
$618$	−2.86065e7	+	6.80663e7i	−0.121199	+	0.288381i
$619$	−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
$621$	−6.74463e7	−	4.11399e7i	−0.281633	−	0.171786i
$622$	−1.12773e8	+	1.23783e8i	−0.468632	+	0.514386i
$623$			4.95256e7i			0.204817i
$624$	−7.56403e7	−	1.99867e7i	−0.311314	−	0.0822598i
$625$	8.50788e7			0.348483
$626$	1.58674e8	+	1.44560e8i	0.646817	+	0.589284i
$627$	3.35726e8	−	1.19147e8i	1.36202	−	0.483370i
$628$	−2.13687e8	−	1.77219e8i	−0.862777	−	0.715537i
$629$	2.34479e8	−	2.34479e8i	0.942217	−	0.942217i
$630$	2.08193e8	−	1.85778e8i	0.832614	−	0.742971i
$631$		−	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
$636$	−9.30499e7	+	2.53847e8i	−0.361697	+	0.986733i
$637$	−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	$-0.781713\pi$
$641$		−	3.33574e8i		−	1.26654i	0.773933	−	0.633268i	$-0.218287\pi$
$642$	−2.10200e8	+	8.57992e7i	−0.794378	+	0.324249i
$643$	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
$645$	4.39454e6	+	1.23827e7i	0.0163770	+	0.0461463i
$646$	−6.09115e8	+	2.83506e7i	−2.25944	+	0.105163i
$647$	−3.29562e8			−1.21682			−0.608408	−	0.793625i	$-0.708191\pi$
$647$	−3.29562e8			−1.21682			−0.608408	+	0.793625i	$0.708191\pi$
$648$	2.04880e8	−	1.79057e8i	0.752964	−	0.658062i
$649$			3.13379e8i			1.14640i
$650$	−3.97043e7	+	1.84800e6i	−0.144576	+	0.00672916i
$651$	5.21558e8	−	1.85097e8i	1.89043	−	0.670899i
$652$	−2.32620e7	−	1.92921e7i	−0.0839273	−	0.0696044i
$653$	1.67012e8	+	1.67012e8i	0.599801	+	0.599801i	0.940260	−	0.340458i	$-0.110582\pi$
$653$	1.67012e8	+	1.67012e8i	0.599801	+	0.599801i	−0.340458	+	0.940260i	$0.610582\pi$
$654$	−1.44983e8	+	5.91792e7i	−0.518305	+	0.211561i
$655$	−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	0.649583	−	0.760291i	$-0.274943\pi$
$659$	−3.16835e7	−	3.16835e7i	−0.110707	−	0.110707i	−0.760291	+	0.649583i	$0.774943\pi$
$660$	8.47190e7	+	1.82770e8i	0.294679	+	0.635729i
$661$	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
$666$	1.98712e8	−	1.77318e8i	0.672670	−	0.600248i
$667$	−4.07466e7	−	4.07466e7i	−0.137314	−	0.137314i
$668$	4.71223e7	+	5.05117e8i	0.158087	+	1.69458i
$669$	−7.69185e7	−	2.16737e8i	−0.256893	−	0.723861i
$670$	1.77196e8	+	1.61435e8i	0.589154	+	0.536750i
$671$		−	5.15362e7i		−	0.170587i
$672$	−9.59542e7	+	4.46205e8i	−0.316196	+	1.47037i
$673$	−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
$675$	7.19852e7	−	1.18015e8i	0.234063	−	0.383731i
$676$	2.75689e8	−	2.57190e7i	0.892442	−	0.0832558i
$677$	−2.73177e8	+	2.73177e8i	−0.880395	+	0.880395i	−0.993575	−	0.113179i	$-0.963897\pi$
$677$	−2.73177e8	+	2.73177e8i	−0.880395	+	0.880395i	0.113179	+	0.993575i	$0.463897\pi$
$678$	1.17635e7	−	2.79901e7i	0.0377440	−	0.0898082i
$679$			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	−0.575481	−	0.817815i	$-0.695185\pi$
$683$	7.72107e7	−	7.72107e7i	0.242335	−	0.242335i	0.817815	+	0.575481i	$0.195185\pi$
$684$	−4.89708e8	−	5.05554e6i	−1.53027	−	0.0157979i
$685$	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
$690$	−7.44457e7	+	3.03872e7i	−0.226617	+	0.0925003i
$691$	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
$693$	4.70185e8	+	4.87645e7i	1.41276	+	0.146523i
$694$	−1.79871e6	−	3.86454e7i	−0.00538125	−	0.115616i
$695$	1.15369e8			0.343666
$696$	1.75987e8	−	9.17459e7i	0.521980	−	0.272119i
$697$		−	4.11400e8i		−	1.21497i
$698$	−1.22309e7	−	2.62781e8i	−0.0359659	−	0.772730i
$699$	−3.94273e7	−	1.11096e8i	−0.115443	−	0.325289i
$700$	2.15379e7	+	2.30871e8i	0.0627927	+	0.673092i
$701$	−3.38616e8	−	3.38616e8i	−0.982999	−	0.982999i	0.0168585	−	0.999858i	$-0.494634\pi$
$701$	−3.38616e8	−	3.38616e8i	−0.982999	−	0.982999i	−0.999858	+	0.0168585i	$0.994634\pi$
$702$	5.35234e7	−	9.76939e7i	0.154715	−	0.282395i
$703$	−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
$708$	1.48270e8	−	4.04491e8i	0.417786	−	1.13975i
$709$	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
$714$	−7.45928e8	−	3.13494e8i	−2.04928	−	0.861260i
$715$	5.83167e7	+	5.83167e7i	0.159542	+	0.159542i
$716$	1.13759e8	−	1.37168e8i	0.309918	−	0.373692i
$717$	−1.23467e8	+	4.38176e7i	−0.334961	+	0.118875i
$718$	1.76240e8	−	1.93447e8i	0.476137	−	0.522623i
$719$		−	2.06254e8i		−	0.554902i	−0.960740	−	0.277451i	$-0.910510\pi$
$719$		−	2.06254e8i		−	0.554902i	0.960740	−	0.277451i	$-0.0894895\pi$
$720$	−2.28760e7	−	2.75992e8i	−0.0612891	−	0.739433i
$721$	1.76334e8			0.470468
$722$	3.73365e8	+	3.40155e8i	0.992022	+	0.903784i
$723$	8.24760e7	+	2.32397e8i	0.218229	+	0.614915i
$724$	−2.53413e8	+	3.05560e8i	−0.667749	+	0.805156i
$725$	7.12970e7	−	7.12970e7i	0.187093	−	0.187093i
$726$	1.60320e7	−	3.81467e7i	0.0418966	−	0.0996889i
$727$		−	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
$732$	−2.43835e7	+	6.65200e7i	−0.0621675	+	0.169597i
$733$	−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
$738$	1.87684e7	−	3.29879e8i	0.0466937	−	0.820701i
$739$	−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
$741$	−1.88948e8	+	6.70563e7i	−0.464395	+	0.164811i
$742$	6.45002e8	−	3.00210e7i	1.57888	−	0.0734874i
$743$	−3.41867e8			−0.833471			−0.416736	−	0.909028i	$-0.636826\pi$
$743$	−3.41867e8			−0.833471			−0.416736	+	0.909028i	$0.636826\pi$
$744$	1.64862e8	−	5.23957e8i	0.400314	−	1.27226i
$745$			6.69520e7i			0.161918i
$746$	−7.31394e8	+	3.40419e7i	−1.76171	+	0.0819970i
$747$	−5.06874e8	−	5.25697e7i	−1.21601	−	0.126117i
$748$	3.72911e8	−	4.49647e8i	0.891046	−	1.07440i
$749$	3.83410e8	+	3.83410e8i	0.912470	+	0.912470i
$750$	−1.71463e8	−	4.20068e8i	−0.406431	−	0.995716i
$751$	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
$756$	−5.83816e8	−	2.85403e8i	−1.35117	−	0.660531i
$757$	−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	$-0.263702\pi$
$761$	5.95862e8			1.35205			0.676023	+	0.736880i	$0.263702\pi$
$762$	6.18117e8	+	2.59778e8i	1.39703	+	0.587135i
$763$	2.64454e8	+	2.64454e8i	0.595355	+	0.595355i
$764$	3.31711e7	−	3.09453e6i	0.0743839	−	0.00693928i
$765$	4.88344e8	+	5.06478e7i	1.09079	+	0.113130i
$766$	−3.47658e8	−	3.16735e8i	−0.773511	−	0.704708i
$767$		−	1.76371e8i		−	0.390877i
$768$	2.96338e8	+	3.42606e8i	0.654189	+	0.756331i
$769$	−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
$771$	−2.12103e8	+	7.52737e7i	−0.462789	+	0.164240i
$772$	6.02657e6	+	6.46004e7i	0.0130984	+	0.140405i
$773$	2.76113e8	−	2.76113e8i	0.597790	−	0.597790i	−0.341934	−	0.939724i	$-0.611082\pi$
$773$	2.76113e8	−	2.76113e8i	0.597790	−	0.597790i	0.939724	+	0.341934i	$0.111082\pi$
$774$	2.28323e7	−	2.03740e7i	0.0492409	−	0.0439394i
$775$		−	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
$780$	−4.76802e7	−	1.02863e8i	−0.100474	−	0.216759i
$781$	−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
$786$	2.17652e8	+	5.33226e8i	0.448223	+	1.09810i
$787$	−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
$789$	−1.02621e8	−	2.89160e8i	−0.208932	−	0.588717i
$790$	1.57719e7	+	3.38860e8i	0.0319891	+	0.687288i
$791$	−7.25118e7			−0.146514
$792$	3.19530e8	−	3.43535e8i	0.643185	−	0.691504i
$793$			2.90048e7i			0.0581634i
$794$	1.99549e7	+	4.28733e8i	0.0398647	+	0.856496i
$795$	−3.69236e8	+	1.31039e8i	−0.734857	+	0.260795i
$796$	9.90860e8	−	9.24373e7i	1.96459	−	0.183277i
$797$	2.24392e8	+	2.24392e8i	0.443233	+	0.443233i	0.893097	−	0.449864i	$-0.148528\pi$
$797$	2.24392e8	+	2.24392e8i	0.443233	+	0.443233i	−0.449864	+	0.893097i	$0.648528\pi$
$798$	4.42010e8	+	1.08288e9i	0.869808	+	2.13095i
$799$	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
$804$	1.92135e8	−	5.24158e8i	0.369691	−	1.00854i
$805$	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	$-0.252441\pi$
$809$	7.43028e8			1.40333			0.701665	+	0.712507i	$0.252441\pi$
$810$	3.89265e8	+	6.28903e7i	0.732471	+	0.118339i
$811$	−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
$813$	2.50972e8	+	7.07178e8i	0.467040	+	1.31600i
$814$	3.09261e8	−	3.39455e8i	0.573393	−	0.629375i
$815$		−	4.37948e7i		−	0.0809003i
$816$	−6.94075e8	+	4.03942e8i	−1.27743	+	0.743445i
$817$	−5.50769e7			−0.100996
$818$	1.98259e7	+	1.80624e7i	0.0362220	+	0.0330001i
$819$	−2.64622e8	−	2.74449e7i	−0.481697	−	0.0499585i
$820$	−2.58853e8	−	2.14677e8i	−0.469474	−	0.389354i
$821$	5.25314e7	−	5.25314e7i	0.0949270	−	0.0949270i	−0.658049	−	0.752976i	$-0.728618\pi$
$821$	5.25314e7	−	5.25314e7i	0.0949270	−	0.0949270i	0.752976	+	0.658049i	$0.228618\pi$
$822$	−3.64117e8	−	1.53029e8i	−0.655580	−	0.275523i
$823$			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	$-0.457053\pi$
$827$	6.36551e8	−	6.36551e8i	1.12543	−	1.12543i	0.990912	−	0.134513i	$-0.0429471\pi$
$828$	1.31044e8	+	1.33777e8i	0.230847	+	0.235663i
$829$	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
$834$	−1.01540e8	−	2.48763e8i	−0.175040	−	0.428832i
$835$	−5.19845e8	+	5.19845e8i	−0.892924	+	0.892924i
$836$	−8.40774e8	+	7.84358e7i	−1.43900	+	0.134244i
$837$	6.67677e8	+	4.07260e8i	1.13865	+	0.694537i
$838$	−4.69719e8	+	2.18626e7i	−0.798190	+	0.0371509i
$839$	8.43273e8			1.42785			0.713925	−	0.700223i	$-0.246916\pi$
$839$	8.43273e8			1.42785			0.713925	+	0.700223i	$0.246916\pi$
$840$	−5.86491e8	+	3.05750e8i	−0.989517	+	0.515856i
$841$		−	3.88710e8i		−	0.653488i
$842$	2.33114e8	−	1.08500e7i	0.390509	−	0.0181758i
$843$	−2.31974e8	−	6.53646e8i	−0.387220	−	1.09109i
$844$	−7.74107e8	−	6.41998e8i	−1.28758	−	1.06784i
$845$	2.83728e8	+	2.83728e8i	0.470253	+	0.470253i
$846$	9.14386e8	+	5.20238e7i	1.51014	+	0.0859194i
$847$	−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
$852$	1.85754e8	−	8.61027e7i	0.300345	−	0.139219i
$853$	−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	$-0.523072\pi$
$857$	−9.11632e7			−0.144836			−0.0724181	+	0.997374i	$0.523072\pi$
$858$	7.44180e7	−	1.77070e8i	0.117819	−	0.280339i
$859$	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
$861$	−7.43670e8	+	2.63923e8i	−1.16512	+	0.413493i
$862$	6.45007e8	+	5.87635e8i	1.00703	+	0.917458i
$863$		−	1.65009e8i		−	0.256729i	−0.991727	−	0.128364i	$-0.959027\pi$
$863$		−	1.65009e8i		−	0.256729i	0.991727	−	0.128364i	$-0.0409727\pi$
$864$	−5.74968e8	+	2.92234e8i	−0.891462	+	0.453096i
$865$	5.99955e8			0.926980
$866$	−5.53067e8	+	6.07064e8i	−0.851577	+	0.934718i
$867$	−2.58191e8	−	7.27518e8i	−0.396172	−	1.11631i
$868$	−1.30616e9	+	1.21852e8i	−1.99727	+	0.186326i
$869$	−4.06366e8	+	4.06366e8i	−0.619238	+	0.619238i
$870$	2.65144e8	+	1.11433e8i	0.402647	+	0.169222i
$871$		−	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
$876$	5.03627e8	+	1.08651e9i	0.749199	+	1.61629i
$877$	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	$0.101878\pi$
$881$			4.30277e8i			0.629246i	−0.949217	+	0.314623i	$0.898122\pi$
$882$	−4.91841e7	+	8.64474e8i	−0.0716835	+	1.25993i
$883$	−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
$885$	5.88358e8	−	2.08804e8i	0.848813	−	0.301238i
$886$	1.28328e7	+	2.75713e8i	0.0184510	+	0.396421i
$887$	−1.01476e9			−1.45409			−0.727045	−	0.686589i	$-0.759107\pi$
$887$	−1.01476e9			−1.45409			−0.727045	+	0.686589i	$0.759107\pi$
$888$	−5.59784e8	+	2.91827e8i	−0.799433	+	0.416761i
$889$		−	1.60130e9i		−	2.27913i
$890$	3.31186e6	+	7.11555e7i	0.00469788	+	0.100934i
$891$	3.65364e8	+	5.59237e8i	0.516527	+	0.790610i
$892$	5.06363e7	+	5.42784e8i	0.0713457	+	0.764773i
$893$	−1.16561e9	−	1.16561e9i	−1.63681	−	1.63681i
$894$	1.44364e8	−	5.89264e7i	0.202044	−	0.0824702i
$895$	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
$900$	−2.34079e8	+	2.29296e8i	−0.321096	+	0.314534i
$901$	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
$906$	2.37458e8	−	5.65008e8i	0.319303	−	0.759749i
$907$	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
$909$	5.74639e6	−	5.54064e7i	0.00765074	−	0.0737681i
$910$	−1.82357e8	+	2.00161e8i	−0.241991	+	0.265617i
$911$		−	3.20339e8i		−	0.423696i	−0.977303	−	0.211848i	$-0.932052\pi$
$911$		−	3.20339e8i		−	0.423696i	0.977303	−	0.211848i	$-0.0679482\pi$
$912$	1.12233e9	+	2.96558e8i	1.47958	+	0.390954i
$913$	−8.78666e8			−1.15455
$914$	−5.20118e8	−	4.73854e8i	−0.681182	−	0.620592i
$915$	−9.67576e7	+	3.43386e7i	−0.126305	+	0.0448249i
$916$	4.90801e8	−	5.91797e8i	0.638586	−	0.769992i
$917$	9.72618e8	−	9.72618e8i	1.26135	−	1.26135i
$918$	−3.20597e8	−	1.09756e9i	−0.414411	−	1.41873i
$919$			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
$924$	−1.05204e9	−	3.85635e8i	−1.33357	−	0.488833i
$925$	−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	$-0.883983\pi$
$929$		−	5.71597e8i		−	0.712923i	0.934310	−	0.356461i	$-0.116017\pi$
$930$	7.36966e8	−	3.00814e8i	0.916218	−	0.373981i
$931$	1.10198e9	−	1.10198e9i	1.36561	−	1.36561i
$932$	2.59555e7	+	2.78224e8i	0.0320613	+	0.343674i
$933$	1.89016e8	+	5.32601e8i	0.232731	+	0.655778i
$934$	4.29249e8	−	1.99789e7i	0.526828	−	0.0245206i
$935$	8.46543e8			1.03565
$936$	−1.79833e8	+	1.93343e8i	−0.219301	+	0.235776i
$937$		−	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
$939$	6.82726e8	−	2.42295e8i	0.824612	−	0.292649i
$940$	5.95060e8	−	7.17510e8i	0.716436	−	0.863862i
$941$	−7.13084e7	−	7.13084e7i	−0.0855799	−	0.0855799i	0.663021	−	0.748601i	$-0.269274\pi$
$941$	−7.13084e7	−	7.13084e7i	−0.0855799	−	0.0855799i	−0.748601	+	0.663021i	$0.769274\pi$
$942$	−8.67461e8	+	3.54079e8i	−1.03776	+	0.423592i
$943$	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	$0.0293888\pi$
$947$	9.23961e8	+	9.23961e8i	1.08794	+	1.08794i	0.0921964	+	0.995741i	$0.470611\pi$
$948$	7.16779e8	−	3.32248e8i	0.841318	−	0.389975i
$949$	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	$-0.219686\pi$
$953$	1.33488e9			1.54228			0.771141	+	0.636664i	$0.219686\pi$
$954$	6.07526e8	+	6.80827e8i	0.699713	+	0.784136i
$955$	3.41383e7	+	3.41383e7i	0.0391951	+	0.0391951i
$956$	3.09204e8	−	2.88456e7i	0.353893	−	0.0330146i
$957$	1.62961e8	+	4.59182e8i	0.185929	+	0.523901i
$958$	−1.21862e9	−	1.11023e9i	−1.38603	−	1.26275i
$959$			9.43289e8i			1.06952i
$960$	−1.08023e8	+	6.47497e8i	−0.122096	+	0.731854i
$961$	6.91280e8			0.778904
$962$	−1.74053e8	+	1.91047e8i	−0.195505	+	0.214592i
$963$	−7.90462e7	+	7.62159e8i	−0.0885120	+	0.853428i
$964$	−5.42949e7	−	5.82001e8i	−0.0606077	−	0.649670i
$965$	−6.64840e7	+	6.64840e7i	−0.0739836	+	0.0739836i
$966$	1.73283e8	−	4.12310e8i	0.192232	−	0.457396i
$967$			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	−0.938421	−	0.345495i	$-0.887711\pi$
$971$	−5.42822e8	+	5.42822e8i	−0.592925	+	0.592925i	0.345495	+	0.938421i	$0.387711\pi$
$972$	−2.06997e8	−	8.94697e8i	−0.225406	−	0.974265i
$973$	−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	$-0.953705\pi$
$977$		−	2.70311e8i		−	0.289855i	0.989442	−	0.144927i	$-0.0462948\pi$
$978$	−9.44318e7	+	3.85451e7i	−0.100949	+	0.0412053i
$979$	−8.53307e7	+	8.53307e7i	−0.0909405	+	0.0909405i
$980$	6.78345e8	+	5.62579e8i	0.720729	+	0.597730i
$981$	−5.45214e7	+	5.25693e8i	−0.0577510	+	0.556833i
$982$	3.35129e7	+	7.20027e8i	0.0353897	+	0.760351i
$983$	1.54724e8			0.162891			0.0814454	−	0.996678i	$-0.474046\pi$
$983$	1.54724e8			0.162891			0.0814454	+	0.996678i	$0.474046\pi$
$984$	−2.35070e8	+	7.47090e8i	−0.246724	+	0.784129i
$985$		−	2.13159e8i		−	0.223046i
$986$	−3.87759e7	−	8.33103e8i	−0.0404512	−	0.869097i
$987$	−7.31565e8	−	2.06137e9i	−0.760854	−	2.14390i
$988$	4.73191e8	−	4.41439e7i	0.490643	−	0.0457720i
$989$	1.48921e7	+	1.48921e7i	0.0153945	+	0.0153945i
$990$	6.78795e8	+	3.86200e7i	0.699573	+	0.0398021i
$991$	−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
$996$	1.13413e9	+	4.15727e8i	1.14785	+	0.420755i
$997$	−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.5.13	✓	92
3.2	odd	2	inner	48.7.i.a.5.34	yes	92
4.3	odd	2		192.7.i.a.113.19		92
12.11	even	2		192.7.i.a.113.43		92
16.3	odd	4		192.7.i.a.17.43		92
16.13	even	4	inner	48.7.i.a.29.34	yes	92
48.29	odd	4	inner	48.7.i.a.29.13	yes	92
48.35	even	4		192.7.i.a.17.19		92

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

\(f(q)\)	\(=\)	\(q+(-5.38773 + 5.91374i) q^{2} +(9.03029 + 25.4451i) q^{3} +(-5.94475 - 63.7233i) q^{4} +(65.5814 - 65.5814i) q^{5} +(-199.129 - 83.6886i) q^{6} +515.866i q^{7} +(408.872 + 308.168i) q^{8} +(-565.908 + 459.554i) q^{9} +O(q^{10})\)	\(q+(-5.38773 + 5.91374i) q^{2} +(9.03029 + 25.4451i) q^{3} +(-5.94475 - 63.7233i) q^{4} +(65.5814 - 65.5814i) q^{5} +(-199.129 - 83.6886i) 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} +(1567.76 - 726.705i) 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} +(331.275 - 5822.58i) q^{18} +(-7422.29 + 7422.29i) q^{19} +(-4568.93 - 3789.20i) q^{20} +(-13126.3 + 4658.42i) q^{21} +(-467.531 - 10044.9i) q^{22} +4013.78 q^{23} +(-4149.14 + 13186.6i) q^{24} +7023.17i q^{25} +(263.128 + 5653.33i) q^{26} +(-16803.7 - 10249.7i) q^{27} +(32872.7 - 3066.69i) q^{28} +(-10151.7 - 10151.7i) q^{29} +(-18547.5 + 7570.72i) 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} +(32648.5 + 33329.6i) 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} +(43172.1 - 102724. i) q^{42} +(3710.24 + 3710.24i) q^{43} +(61922.2 + 51354.6i) q^{44} +(-6974.85 + 67251.2i) q^{45} +(-21625.1 + 23736.4i) q^{46} +157041. i q^{47} +(-55628.0 - 95583.0i) q^{48} -148469. q^{49} +(-41533.2 - 37838.9i) q^{50} +(184769. - 65573.4i) q^{51} +(-34850.0 - 28902.6i) q^{52} +(-110634. + 110634. i) q^{53} +(151148. - 44150.3i) 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} +(55157.8 - 150474. 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} +(251373. - 102605. i) q^{66} +(228444. - 228444. i) q^{67} +(-462726. + 43167.7i) q^{68} +(36245.6 + 102131. i) q^{69} +(-382343. + 17795.7i) q^{70} +118484. q^{71} +(-373004. + 13503.8i) q^{72} +693029. i q^{73} +(-364932. + 16985.4i) q^{74} +(-178705. + 63421.2i) q^{75} +(517097. + 428850. i) q^{76} +(-458511. - 458511. i) q^{77} +(-141474. + 57746.6i) 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} +(374883. + 808757. 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} +(-360128. - 403578. i) q^{90} +(258052. + 258052. i) q^{91} +(-23860.9 - 255771. i) q^{92} +(-358809. - 1.01103e6i) q^{93} +(-928702. - 846096. i) q^{94} +973529. i q^{95} +(864962. + 186006. i) q^{96} +1.32256e6 q^{97} +(799911. - 878008. i) q^{98} +(94529.4 - 911448. i) 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

L-functions

Modular forms

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