LMFDB - Embedded newform 48.7.i.a.5.6

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			5.6
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.60798 - 2.47360i) q^{2} +(14.3156 - 22.8925i) q^{3} +(51.7626 + 37.6382i) q^{4} +(4.45378 - 4.45378i) q^{5} +(-165.539 + 138.754i) q^{6} +601.125i q^{7} +(-300.707 - 414.390i) q^{8} +(-319.129 - 655.437i) q^{9} +O(q^{10})$	\(q+(-7.60798 - 2.47360i) q^{2} +(14.3156 - 22.8925i) q^{3} +(51.7626 + 37.6382i) q^{4} +(4.45378 - 4.45378i) q^{5} +(-165.539 + 138.754i) q^{6} +601.125i q^{7} +(-300.707 - 414.390i) q^{8} +(-319.129 - 655.437i) q^{9} +(-44.9011 + 22.8674i) q^{10} +(-1076.06 + 1076.06i) q^{11} +(1602.64 - 646.162i) q^{12} +(2.96399 - 2.96399i) q^{13} +(1486.94 - 4573.35i) q^{14} +(-38.1996 - 165.716i) q^{15} +(1262.74 + 3896.50i) q^{16} +7878.09i q^{17} +(806.637 + 5775.95i) q^{18} +(293.047 - 293.047i) q^{19} +(398.171 - 62.9072i) q^{20} +(13761.2 + 8605.45i) q^{21} +(10848.4 - 5524.91i) q^{22} +20786.8 q^{23} +(-13791.2 + 951.691i) q^{24} +15585.3i q^{25} +(-29.8817 + 15.2182i) q^{26} +(-19573.1 - 2077.31i) q^{27} +(-22625.2 + 31115.8i) q^{28} +(-5760.80 - 5760.80i) q^{29} +(-119.294 + 1355.26i) q^{30} +6416.37 q^{31} +(31.5023 - 32768.0i) q^{32} +(9229.27 + 40038.2i) q^{33} +(19487.2 - 59936.3i) q^{34} +(2677.28 + 2677.28i) q^{35} +(8150.50 - 45938.6i) q^{36} +(-46003.9 - 46003.9i) q^{37} +(-2954.37 + 1504.61i) q^{38} +(-25.4218 - 110.284i) q^{39} +(-3184.89 - 506.320i) q^{40} +84654.6 q^{41} +(-83408.7 - 99509.8i) q^{42} +(14962.0 + 14962.0i) q^{43} +(-96200.9 + 15198.8i) q^{44} +(-4340.50 - 1497.84i) q^{45} +(-158145. - 51418.2i) q^{46} +67746.2i q^{47} +(107277. + 26873.5i) q^{48} -243703. q^{49} +(38551.8 - 118573. i) q^{50} +(180349. + 112779. i) q^{51} +(264.983 - 41.8647i) q^{52} +(-80765.3 + 80765.3i) q^{53} +(143773. + 64220.1i) q^{54} +9585.10i q^{55} +(249100. - 180763. i) q^{56} +(-2513.43 - 10903.7i) q^{57} +(29578.1 + 58078.0i) q^{58} +(-126259. + 126259. i) q^{59} +(4259.95 - 10015.7i) q^{60} +(-142023. + 142023. i) q^{61} +(-48815.6 - 15871.5i) q^{62} +(394000. - 191836. i) q^{63} +(-81294.5 + 249220. i) q^{64} -26.4019i q^{65} +(28822.3 - 327439. i) q^{66} +(186144. - 186144. i) q^{67} +(-296517. + 407790. i) q^{68} +(297575. - 475861. i) q^{69} +(-13746.2 - 26991.2i) q^{70} -54066.9 q^{71} +(-175642. + 329338. i) q^{72} +216110. i q^{73} +(236201. + 463791. i) q^{74} +(356786. + 223113. i) q^{75} +(26198.6 - 4139.13i) q^{76} +(-646849. - 646849. i) q^{77} +(-79.3904 + 901.923i) q^{78} +416580. q^{79} +(22978.1 + 11730.2i) q^{80} +(-327754. + 418338. i) q^{81} +(-644050. - 209402. i) q^{82} +(-451651. - 451651. i) q^{83} +(388424. + 963388. i) q^{84} +(35087.3 + 35087.3i) q^{85} +(-76820.7 - 150841. i) q^{86} +(-214348. + 49409.7i) q^{87} +(769490. + 122330. i) q^{88} -528727. q^{89} +(29317.4 + 22132.2i) q^{90} +(1781.73 + 1781.73i) q^{91} +(1.07598e6 + 782376. i) q^{92} +(91853.9 - 146886. i) q^{93} +(167577. - 515412. i) q^{94} -2610.33i q^{95} +(-749689. - 469814. i) q^{96} -454607. q^{97} +(1.85408e6 + 602822. i) q^{98} +(1.04869e6 + 361889. 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 $

$2$	−7.60798	−	2.47360i	−0.950997	−	0.309200i
$2$	−7.60798	−	2.47360i	−0.950997	−	0.309200i
$3$	14.3156	−	22.8925i	0.530206	−	0.847869i
$3$	14.3156	−	22.8925i	0.530206	−	0.847869i
$4$	51.7626	+	37.6382i	0.808791	+	0.588096i
$5$	4.45378	−	4.45378i	0.0356302	−	0.0356302i	−0.689067	−	0.724697i	$-0.741980\pi$
$5$	4.45378	−	4.45378i	0.0356302	−	0.0356302i	0.724697	+	0.689067i	$0.241980\pi$
$6$	−165.539	+	138.754i	−0.766386	+	0.642381i
$7$			601.125i			1.75255i	0.481810	+	0.876276i	$0.339980\pi$
$7$			601.125i			1.75255i	−0.481810	+	0.876276i	$0.660020\pi$
$8$	−300.707	−	414.390i	−0.587318	−	0.809356i
$9$	−319.129	−	655.437i	−0.437763	−	0.899091i
$10$	−44.9011	+	22.8674i	−0.0449011	+	0.0228674i
$11$	−1076.06	+	1076.06i	−0.808462	+	0.808462i	−0.984401	−	0.175939i	$-0.943704\pi$
$11$	−1076.06	+	1076.06i	−0.808462	+	0.808462i	0.175939	+	0.984401i	$0.443704\pi$
$12$	1602.64	−	646.162i	0.927454	−	0.373936i
$13$	2.96399	−	2.96399i	0.00134911	−	0.00134911i	−0.706432	−	0.707781i	$-0.749696\pi$
$13$	2.96399	−	2.96399i	0.00134911	−	0.00134911i	0.707781	+	0.706432i	$0.249696\pi$
$14$	1486.94	−	4573.35i	0.541889	−	1.66667i
$15$	−38.1996	−	165.716i	−0.0113184	−	0.0491011i
$16$	1262.74	+	3896.50i	0.308285	+	0.951294i
$17$			7878.09i			1.60352i	0.597647	+	0.801759i	$0.296102\pi$
$17$			7878.09i			1.60352i	−0.597647	+	0.801759i	$0.703898\pi$
$18$	806.637	+	5775.95i	0.138312	+	0.990389i
$19$	293.047	−	293.047i	0.0427244	−	0.0427244i	−0.685422	−	0.728146i	$-0.740382\pi$
$19$	293.047	−	293.047i	0.0427244	−	0.0427244i	0.728146	+	0.685422i	$0.240382\pi$
$20$	398.171	−	62.9072i	0.0497714	−	0.00786340i
$21$	13761.2	+	8605.45i	1.48593	+	0.929214i
$22$	10848.4	−	5524.91i	1.01882	−	0.518869i
$23$	20786.8			1.70846			0.854228	−	0.519898i	$-0.174030\pi$
$23$	20786.8			1.70846			0.854228	+	0.519898i	$0.174030\pi$
$24$	−13791.2	+	951.691i	−0.997627	+	0.0688434i
$25$			15585.3i			0.997461i
$26$	−29.8817	+	15.2182i	−0.00170014	+	0.000865854i
$27$	−19573.1	−	2077.31i	−0.994415	−	0.105538i
$28$	−22625.2	+	31115.8i	−1.03067	+	1.41745i
$29$	−5760.80	−	5760.80i	−0.236205	−	0.236205i	0.579072	−	0.815277i	$-0.303415\pi$
$29$	−5760.80	−	5760.80i	−0.236205	−	0.236205i	−0.815277	+	0.579072i	$0.803415\pi$
$30$	−119.294	+	1355.26i	−0.00441831	+	0.0501947i
$31$	6416.37			0.215379			0.107690	−	0.994185i	$-0.465655\pi$
$31$	6416.37			0.215379			0.107690	+	0.994185i	$0.465655\pi$
$32$	31.5023	−	32768.0i	0.000961373	−	1.00000i
$33$	9229.27	+	40038.2i	0.256818	+	1.11412i
$34$	19487.2	−	59936.3i	0.495808	−	1.52494i
$35$	2677.28	+	2677.28i	0.0624438	+	0.0624438i
$36$	8150.50	−	45938.6i	0.174693	−	0.984623i
$37$	−46003.9	−	46003.9i	−0.908216	−	0.908216i	0.0879122	−	0.996128i	$-0.471980\pi$
$37$	−46003.9	−	46003.9i	−0.908216	−	0.908216i	−0.996128	+	0.0879122i	$0.971980\pi$
$38$	−2954.37	+	1504.61i	−0.0538412	+	0.0274204i
$39$	−25.4218	−	110.284i	−0.000428561	−	0.00185917i
$40$	−3184.89	−	506.320i	−0.0497638	−	0.00791125i
$41$	84654.6			1.22828			0.614142	−	0.789195i	$-0.289502\pi$
$41$	84654.6			1.22828			0.614142	+	0.789195i	$0.289502\pi$
$42$	−83408.7	−	99509.8i	−1.12581	−	1.34313i
$43$	14962.0	+	14962.0i	0.188185	+	0.188185i	0.794911	−	0.606726i	$-0.207517\pi$
$43$	14962.0	+	14962.0i	0.188185	+	0.188185i	−0.606726	+	0.794911i	$0.707517\pi$
$44$	−96200.9	+	15198.8i	−1.12933	+	0.178423i
$45$	−4340.50	−	1497.84i	−0.0476324	−	0.0164372i
$46$	−158145.	−	51418.2i	−1.62474	−	0.528254i
$47$			67746.2i			0.652516i	0.945281	+	0.326258i	$0.105788\pi$
$47$			67746.2i			0.652516i	−0.945281	+	0.326258i	$0.894212\pi$
$48$	107277.	+	26873.5i	0.970027	+	0.242996i
$49$	−243703.			−2.07144
$50$	38551.8	−	118573.i	0.308415	−	0.948582i
$51$	180349.	+	112779.i	1.35957	+	0.850196i
$52$	264.983	−	41.8647i	0.00188455	−	0.000297741i
$53$	−80765.3	+	80765.3i	−0.542497	+	0.542497i	−0.924260	−	0.381763i	$-0.875317\pi$
$53$	−80765.3	+	80765.3i	−0.542497	+	0.542497i	0.381763	+	0.924260i	$0.375317\pi$
$54$	143773.	+	64220.1i	0.913054	+	0.407840i
$55$			9585.10i			0.0576114i
$56$	249100.	−	180763.i	1.41844	−	1.02931i
$57$	−2513.43	−	10903.7i	−0.0135719	−	0.0588774i
$58$	29578.1	+	58078.0i	0.151596	+	0.297665i
$59$	−126259.	+	126259.i	−0.614762	+	0.614762i	−0.944183	−	0.329421i	$-0.893146\pi$
$59$	−126259.	+	126259.i	−0.614762	+	0.614762i	0.329421	+	0.944183i	$0.393146\pi$
$60$	4259.95	−	10015.7i	0.0197220	−	0.0463689i
$61$	−142023.	+	142023.i	−0.625703	+	0.625703i	−0.946984	−	0.321281i	$-0.895887\pi$
$61$	−142023.	+	142023.i	−0.625703	+	0.625703i	0.321281	+	0.946984i	$0.395887\pi$
$62$	−48815.6	−	15871.5i	−0.204825	−	0.0665953i
$63$	394000.	−	191836.i	1.57570	−	0.767202i
$64$	−81294.5	+	249220.i	−0.310114	+	0.950699i
$65$		−	26.4019i		−	9.61381e-5i
$66$	28822.3	−	327439.i	0.100253	−	1.13893i
$67$	186144.	−	186144.i	0.618907	−	0.618907i	−0.326344	−	0.945251i	$-0.605817\pi$
$67$	186144.	−	186144.i	0.618907	−	0.618907i	0.945251	+	0.326344i	$0.105817\pi$
$68$	−296517.	+	407790.i	−0.943024	+	1.29691i
$69$	297575.	−	475861.i	0.905834	−	1.44855i
$70$	−13746.2	−	26991.2i	−0.0400763	−	0.0786915i
$71$	−54066.9			−0.151062			−0.0755312	−	0.997143i	$-0.524065\pi$
$71$	−54066.9			−0.151062			−0.0755312	+	0.997143i	$0.524065\pi$
$72$	−175642.	+	329338.i	−0.470578	+	0.882358i
$73$			216110.i			0.555529i	0.960649	+	0.277764i	$0.0895935\pi$
$73$			216110.i			0.555529i	−0.960649	+	0.277764i	$0.910407\pi$
$74$	236201.	+	463791.i	0.582890	+	1.14453i
$75$	356786.	+	223113.i	0.845716	+	0.528860i
$76$	26198.6	−	4139.13i	0.0596812	−	0.00942905i
$77$	−646849.	−	646849.i	−1.41687	−	1.41687i
$78$	−79.3904	+	901.923i	−0.000167296	+	0.00190058i
$79$	416580.			0.844922			0.422461	−	0.906381i	$-0.361166\pi$
$79$	416580.			0.844922			0.422461	+	0.906381i	$0.361166\pi$
$80$	22978.1	+	11730.2i	0.0448791	+	0.0229105i
$81$	−327754.	+	418338.i	−0.616728	+	0.787176i
$82$	−644050.	−	209402.i	−1.16810	−	0.379786i
$83$	−451651.	−	451651.i	−0.789894	−	0.789894i	0.191582	−	0.981477i	$-0.438638\pi$
$83$	−451651.	−	451651.i	−0.789894	−	0.789894i	−0.981477	+	0.191582i	$0.938638\pi$
$84$	388424.	+	963388.i	0.655342	+	1.62541i
$85$	35087.3	+	35087.3i	0.0571338	+	0.0571338i
$86$	−76820.7	−	150841.i	−0.120777	−	0.237150i
$87$	−214348.	+	49409.7i	−0.325508	+	0.0750334i
$88$	769490.	+	122330.i	1.12916	+	0.179509i
$89$	−528727.			−0.750000			−0.375000	−	0.927025i	$-0.622357\pi$
$89$	−528727.			−0.750000			−0.375000	+	0.927025i	$0.622357\pi$
$90$	29317.4	+	22132.2i	0.0402159	+	0.0303597i
$91$	1781.73	+	1781.73i	0.00236438	+	0.00236438i
$92$	1.07598e6	+	782376.i	1.38178	+	1.00474i
$93$	91853.9	−	146886.i	0.114195	−	0.182613i
$94$	167577.	−	515412.i	0.201758	−	0.620541i
$95$		−	2610.33i		−	0.00304456i
$96$	−749689.	−	469814.i	−0.847359	−	0.531021i
$97$	−454607.			−0.498105			−0.249053	−	0.968490i	$-0.580119\pi$
$97$	−454607.			−0.498105			−0.249053	+	0.968490i	$0.580119\pi$
$98$	1.85408e6	+	602822.i	1.96993	+	0.640488i
$99$	1.04869e6	+	361889.i	1.08080	+	0.372966i
$100$	−586603.	+	806737.i	−0.586603	+	0.806737i
$101$	407284.	−	407284.i	0.395306	−	0.395306i	−0.481268	−	0.876574i	$-0.659823\pi$
$101$	407284.	−	407284.i	0.395306	−	0.395306i	0.876574	+	0.481268i	$0.159823\pi$
$102$	−1.09312e6	−	1.30413e6i	−1.03007	−	1.22891i
$103$		−	1.39686e6i		−	1.27833i	−0.769071	−	0.639163i	$-0.779281\pi$
$103$		−	1.39686e6i		−	1.27833i	0.769071	−	0.639163i	$-0.220719\pi$
$104$	−2119.54	−	336.956i	−0.00188426	−	0.000299552i
$105$	99616.3	−	22962.7i	0.0860523	−	0.0198361i
$106$	814241.	−	414680.i	0.683653	−	0.348173i
$107$	1.19686e6	−	1.19686e6i	0.976994	−	0.976994i	−0.0227476	−	0.999741i	$-0.507241\pi$
$107$	1.19686e6	−	1.19686e6i	0.976994	−	0.976994i	0.999741	+	0.0227476i	$0.00724140\pi$
$108$	−934967.	−	844222.i	−0.742207	−	0.670170i
$109$	−831406.	+	831406.i	−0.641998	+	0.641998i	−0.951046	−	0.309048i	$-0.899990\pi$
$109$	−831406.	+	831406.i	−0.641998	+	0.641998i	0.309048	+	0.951046i	$0.399990\pi$
$110$	23709.7	−	72923.2i	0.0178134	−	0.0547883i
$111$	−1.71171e6	+	394570.i	−1.25159	+	0.288506i
$112$	−2.34228e6	+	759063.i	−1.66719	+	0.540286i
$113$			233006.i			0.161485i	0.996735	+	0.0807425i	$0.0257291\pi$
$113$			233006.i			0.161485i	−0.996735	+	0.0807425i	$0.974271\pi$
$114$	−7849.25	+	89172.2i	−0.00529802	+	0.0601887i
$115$	92579.8	−	92579.8i	0.0608727	−	0.0608727i
$116$	−81368.2	−	515020.i	−0.0521291	−	0.329952i
$117$	−2888.60	−	996.814i	−0.00180356	−	0.000622381i
$118$	1.27289e6	−	648263.i	0.774721	−	0.394553i
$119$	−4.73572e6			−2.81025
$120$	−57184.4	+	65661.6i	−0.0330928	+	0.0379986i
$121$		−	544262.i		−	0.307222i
$122$	1.43181e6	−	729199.i	0.788509	−	0.401575i
$123$	1.21188e6	−	1.93795e6i	0.651244	−	1.04142i
$124$	332128.	+	241500.i	0.174197	+	0.126664i
$125$	139004.	+	139004.i	0.0711700	+	0.0711700i
$126$	−3.47207e6	+	484890.i	−1.73571	+	0.242399i
$127$	1.98543e6			0.969268			0.484634	−	0.874717i	$-0.338953\pi$
$127$	1.98543e6			0.969268			0.484634	+	0.874717i	$0.338953\pi$
$128$	1.23496e6	−	1.69497e6i	0.588874	−	0.808225i
$129$	556708.	−	128328.i	0.259333	−	0.0597793i
$130$	−65.3078	+	200.865i	−2.97259e−5	+	9.14270e-5i
$131$	2.94956e6	+	2.94956e6i	1.31203	+	1.31203i	0.919919	+	0.392109i	$0.128254\pi$
$131$	2.94956e6	+	2.94956e6i	1.31203	+	1.31203i	0.392109	+	0.919919i	$0.371746\pi$
$132$	−1.02923e6	+	2.41985e6i	−0.447499	+	1.05212i
$133$	176158.	+	176158.i	0.0748767	+	0.0748767i
$134$	−1.87663e6	+	955735.i	−0.779945	+	0.397213i
$135$	−96426.1	+	77922.3i	−0.0391916	+	0.0316709i
$136$	3.26460e6	−	2.36900e6i	1.29782	−	0.941776i
$137$	−3.14062e6			−1.22139			−0.610693	−	0.791867i	$-0.709109\pi$
$137$	−3.14062e6			−1.22139			−0.610693	+	0.791867i	$0.709109\pi$
$138$	−3.44103e6	+	2.88426e6i	−1.30934	+	1.09748i
$139$	2.32106e6	+	2.32106e6i	0.864253	+	0.864253i	0.991829	−	0.127575i	$-0.0407195\pi$
$139$	2.32106e6	+	2.32106e6i	0.864253	+	0.864253i	−0.127575	+	0.991829i	$0.540720\pi$
$140$	37815.1	+	239351.i	0.0137810	+	0.0872270i
$141$	1.55088e6	+	969826.i	0.553248	+	0.345968i
$142$	411340.	+	133740.i	0.143660	+	0.0467085i
$143$			6378.88i			0.00218140i
$144$	2.15093e6	−	2.07113e6i	0.720344	−	0.693617i
$145$	−51314.7			−0.0168321
$146$	534570.	−	1.64416e6i	0.171769	−	0.528306i
$147$	−3.48874e6	+	5.57895e6i	−1.09829	+	1.75631i
$148$	−649779.	−	4.11278e6i	−0.200438	−	1.26868i
$149$	3.36894e6	−	3.36894e6i	1.01844	−	1.01844i	0.0186113	−	0.999827i	$-0.494075\pi$
$149$	3.36894e6	−	3.36894e6i	1.01844	−	1.01844i	0.999827	−	0.0186113i	$-0.00592451\pi$
$150$	−2.16253e6	−	2.57998e6i	−0.640750	−	0.764440i
$151$			476882.i			0.138510i	0.997599	+	0.0692549i	$0.0220622\pi$
$151$			476882.i			0.138510i	−0.997599	+	0.0692549i	$0.977938\pi$
$152$	−209557.	−	33314.5i	−0.0596721	−	0.00948642i
$153$	5.16359e6	−	2.51413e6i	1.44171	−	0.701961i
$154$	3.32116e6	+	6.52125e6i	0.909344	+	1.78554i
$155$	28577.1	−	28577.1i	0.00767402	−	0.00767402i
$156$	2835.00	−	6665.43i	0.000746756	−	0.00175572i
$157$	2.13915e6	−	2.13915e6i	0.552768	−	0.552768i	−0.374471	−	0.927239i	$-0.622176\pi$
$157$	2.13915e6	−	2.13915e6i	0.552768	−	0.552768i	0.927239	+	0.374471i	$0.122176\pi$
$158$	−3.16933e6	−	1.03045e6i	−0.803519	−	0.261250i
$159$	692715.	+	3.00512e6i	0.172331	+	0.747601i
$160$	−145801.	−	146082.i	−0.0355960	−	0.0356645i
$161$			1.24955e7i			2.99416i
$162$	3.52835e6	−	2.37197e6i	0.829901	−	0.557910i
$163$	1.89269e6	−	1.89269e6i	0.437036	−	0.437036i	−0.453977	−	0.891013i	$-0.649995\pi$
$163$	1.89269e6	−	1.89269e6i	0.437036	−	0.437036i	0.891013	+	0.453977i	$0.149995\pi$
$164$	4.38195e6	+	3.18624e6i	0.993426	+	0.722350i
$165$	219426.	+	137216.i	0.0488469	+	0.0305459i
$166$	2.31895e6	+	4.55336e6i	0.506952	+	0.995423i
$167$	−3.05826e6			−0.656637			−0.328319	−	0.944567i	$-0.606482\pi$
$167$	−3.05826e6			−0.656637			−0.328319	+	0.944567i	$0.606482\pi$
$168$	−572085.	−	8.29024e6i	−0.120652	−	1.74839i
$169$			4.82679e6i			0.999996i
$170$	−180151.	−	353735.i	−0.0366683	−	0.0719998i
$171$	−285593.	−	98554.0i	−0.0571163	−	0.0197100i
$172$	211331.	+	1.33762e6i	0.0415314	+	0.262873i
$173$	−5.42576e6	−	5.42576e6i	−1.04791	−	1.04791i	−0.998793	−	0.0491121i	$-0.984361\pi$
$173$	−5.42576e6	−	5.42576e6i	−1.04791	−	1.04791i	−0.0491121	−	0.998793i	$-0.515639\pi$
$174$	1.75297e6	+	154303.i	0.332758	+	0.0292905i
$175$	−9.36873e6			−1.74810
$176$	−5.55166e6	−	2.83409e6i	−1.01832	−	0.519848i
$177$	1.08291e6	+	4.69786e6i	0.195287	+	0.847188i
$178$	4.02254e6	+	1.30786e6i	0.713248	+	0.231900i
$179$	80546.0	+	80546.0i	0.0140438	+	0.0140438i	0.714094	−	0.700050i	$-0.246839\pi$
$179$	80546.0	+	80546.0i	0.0140438	+	0.0140438i	−0.700050	+	0.714094i	$0.746839\pi$
$180$	−168300.	−	240901.i	−0.0288580	−	0.0413067i
$181$	5.44863e6	+	5.44863e6i	0.918865	+	0.918865i	0.996947	−	0.0780821i	$-0.0248796\pi$
$181$	5.44863e6	+	5.44863e6i	0.918865	+	0.918865i	−0.0780821	+	0.996947i	$0.524880\pi$
$182$	−9148.07	−	17962.6i	−0.00151745	−	0.00297959i
$183$	1.21811e6	+	5.28439e6i	0.198762	+	0.862266i
$184$	−6.25073e6	−	8.61384e6i	−1.00341	−	1.38275i
$185$	−409782.			−0.0647199
$186$	−1.06216e6	+	890298.i	−0.165064	+	0.138356i
$187$	−8.47732e6	−	8.47732e6i	−1.29638	−	1.29638i
$188$	−2.54984e6	+	3.50672e6i	−0.383742	+	0.527749i
$189$	1.24872e6	−	1.17659e7i	0.184961	−	1.74276i
$190$	−6456.91	+	19859.3i	−0.000941378	+	0.00289537i
$191$		−	5.86433e6i		−	0.841624i	−0.907148	−	0.420812i	$-0.861745\pi$
$191$		−	5.86433e6i		−	0.841624i	0.907148	−	0.420812i	$-0.138255\pi$
$192$	4.54148e6	+	5.42876e6i	0.641644	+	0.767003i
$193$	546624.			0.0760356			0.0380178	−	0.999277i	$-0.487896\pi$
$193$	546624.			0.0760356			0.0380178	+	0.999277i	$0.487896\pi$
$194$	3.45864e6	+	1.12452e6i	0.473696	+	0.154014i
$195$	−604.405	−	377.958i	−8.15125e−5	−	5.09730e-5i
$196$	−1.26147e7	−	9.17251e6i	−1.67536	−	1.21820i
$197$	4.88632e6	−	4.88632e6i	0.639121	−	0.639121i	−0.311218	−	0.950339i	$-0.600737\pi$
$197$	4.88632e6	−	4.88632e6i	0.639121	−	0.639121i	0.950339	+	0.311218i	$0.100737\pi$
$198$	−7.08327e6	−	5.34729e6i	−0.912512	−	0.688871i
$199$		−	1.00060e7i		−	1.26971i	−0.772633	−	0.634853i	$-0.781061\pi$
$199$		−	1.00060e7i		−	1.26971i	0.772633	−	0.634853i	$-0.218939\pi$
$200$	6.45841e6	−	4.68662e6i	0.807301	−	0.585827i
$201$	−1.59654e6	−	6.92606e6i	−0.196603	−	0.852900i
$202$	−4.10607e6	+	2.09115e6i	−0.498164	+	0.253706i
$203$	3.46296e6	−	3.46296e6i	0.413961	−	0.413961i
$204$	5.09052e6	+	1.26257e7i	0.599614	+	1.48719i
$205$	377033.	−	377033.i	0.0437641	−	0.0437641i
$206$	−3.45528e6	+	1.06273e7i	−0.395258	+	1.21569i
$207$	−6.63366e6	−	1.36244e7i	−0.747898	−	1.53606i
$208$	15291.9	+	7806.45i	0.00169931	+	0.000867488i
$209$			630674.i			0.0690821i
$210$	−814679.	−	71710.9i	−0.0879688	−	0.00774332i
$211$	−8.30664e6	+	8.30664e6i	−0.884256	+	0.884256i	−0.993964	−	0.109708i	$-0.965008\pi$
$211$	−8.30664e6	+	8.30664e6i	−0.884256	+	0.884256i	0.109708	+	0.993964i	$0.465008\pi$
$212$	−7.22048e6	+	1.14077e6i	−0.757807	+	0.119726i
$213$	−773998.	+	1.23772e6i	−0.0800942	+	0.128081i
$214$	−1.20662e7	+	6.14513e6i	−1.23120	+	0.627032i
$215$	133275.			0.0134102
$216$	5.02494e6	+	8.73555e6i	0.498620	+	0.866820i
$217$			3.85704e6i			0.377463i
$218$	8.38189e6	−	4.26876e6i	0.809044	−	0.412033i
$219$	4.94729e6	+	3.09374e6i	0.471016	+	0.294545i
$220$	−360765.	+	496150.i	−0.0338811	+	0.0465956i
$221$	23350.6	+	23350.6i	0.00216332	+	0.00216332i
$222$	1.39987e7	+	1.23221e6i	1.27946	+	0.112623i
$223$	1.53330e7			1.38265			0.691325	−	0.722544i	$-0.257027\pi$
$223$	1.53330e7			1.38265			0.691325	+	0.722544i	$0.257027\pi$
$224$	1.96977e7	+	18936.8i	1.75255	+	0.00168486i
$225$	1.02152e7	−	4.97373e6i	0.896808	−	0.436651i
$226$	576364.	−	1.77271e6i	0.0499311	−	0.153572i
$227$	−1.47785e6	−	1.47785e6i	−0.126343	−	0.126343i	0.641108	−	0.767451i	$-0.278475\pi$
$227$	−1.47785e6	−	1.47785e6i	−0.126343	−	0.126343i	−0.767451	+	0.641108i	$0.778475\pi$
$228$	280293.	−	659004.i	0.0236487	−	0.0556011i
$229$	−3.21086e6	−	3.21086e6i	−0.267372	−	0.267372i	0.560669	−	0.828040i	$-0.310544\pi$
$229$	−3.21086e6	−	3.21086e6i	−0.267372	−	0.267372i	−0.828040	+	0.560669i	$0.810544\pi$
$230$	−933350.	+	475340.i	−0.0767116	+	0.0390679i
$231$	−2.40680e7	+	5.54795e6i	−1.95256	+	0.450087i
$232$	−654906.	+	4.11953e6i	−0.0524463	+	0.329901i
$233$	7.56423e6			0.597994			0.298997	−	0.954254i	$-0.403348\pi$
$233$	7.56423e6			0.597994			0.298997	+	0.954254i	$0.403348\pi$
$234$	19510.7	+	14729.0i	0.00152274	+	0.00114954i
$235$	301727.	+	301727.i	0.0232493	+	0.0232493i
$236$	−1.12877e7	+	1.78334e6i	−0.858753	+	0.135675i
$237$	5.96358e6	−	9.53653e6i	0.447983	−	0.716383i
$238$	3.60292e7	+	1.17143e7i	2.67254	+	0.868929i
$239$			8.28415e6i			0.606812i	0.952861	+	0.303406i	$0.0981238\pi$
$239$			8.28415e6i			0.606812i	−0.952861	+	0.303406i	$0.901876\pi$
$240$	597478.	−	358101.i	0.0432203	−	0.0259043i
$241$	−9.73879e6			−0.695751			−0.347876	−	0.937541i	$-0.613097\pi$
$241$	−9.73879e6			−0.695751			−0.347876	+	0.937541i	$0.613097\pi$
$242$	−1.34629e6	+	4.14073e6i	−0.0949929	+	0.292167i
$243$	4.88479e6	+	1.34918e7i	0.340429	+	0.940270i
$244$	−1.26969e7	+	2.00599e6i	−0.874037	+	0.138089i
$245$	−1.08540e6	+	1.08540e6i	−0.0738058	+	0.0738058i
$246$	−1.40137e7	+	1.17462e7i	−0.941340	+	0.789027i
$247$		−	1737.18i		−	0.000115280i
$248$	−1.92945e6	−	2.65888e6i	−0.126496	−	0.174319i
$249$	−1.68051e7	+	3.87376e6i	−1.08853	+	0.250920i
$250$	−713699.	−	1.40138e6i	−0.0456767	−	0.0896882i
$251$	2.80806e6	−	2.80806e6i	0.177576	−	0.177576i	−0.612722	−	0.790298i	$-0.709925\pi$
$251$	2.80806e6	−	2.80806e6i	0.177576	−	0.177576i	0.790298	+	0.612722i	$0.209925\pi$
$252$	2.76148e7	+	4.89947e6i	1.72560	+	0.306159i
$253$	−2.23679e7	+	2.23679e7i	−1.38122	+	1.38122i
$254$	−1.51051e7	−	4.91116e6i	−0.921771	−	0.299698i
$255$	1.30553e6	−	300939.i	0.0787346	−	0.0181492i
$256$	−1.35882e7	+	9.84051e6i	−0.809920	+	0.586540i
$257$		−	1.01247e7i		−	0.596461i	−0.954494	−	0.298231i	$-0.903604\pi$
$257$		−	1.01247e7i		−	0.596461i	0.954494	−	0.298231i	$-0.0963965\pi$
$258$	−4.55285e6	−	400758.i	−0.265109	−	0.0233358i
$259$	2.76541e7	−	2.76541e7i	1.59170	−	1.59170i
$260$	993.720	−	1366.63i	5.65384e−5	−	7.77556e-5i
$261$	−1.93740e6	+	5.61428e6i	−0.108968	+	0.315771i
$262$	−1.51441e7	−	2.97362e7i	−0.842056	−	1.65341i
$263$	2.53059e7			1.39109			0.695545	−	0.718482i	$-0.255163\pi$
$263$	2.53059e7			1.39109			0.695545	+	0.718482i	$0.255163\pi$
$264$	1.38161e7	−	1.58643e7i	0.750887	−	0.862201i
$265$			719422.i			0.0386586i
$266$	−904461.	−	1.77595e6i	−0.0480557	−	0.0943594i
$267$	−7.56903e6	+	1.21039e7i	−0.397655	+	0.635902i
$268$	1.66414e7	−	2.62919e6i	0.864543	−	0.136589i
$269$	8.49825e6	+	8.49825e6i	0.436589	+	0.436589i	0.890862	−	0.454273i	$-0.150101\pi$
$269$	8.49825e6	+	8.49825e6i	0.436589	+	0.436589i	−0.454273	+	0.890862i	$0.650101\pi$
$270$	926356.	−	354312.i	0.0470637	−	0.0180009i
$271$	9.20022e6			0.462265			0.231132	−	0.972922i	$-0.425757\pi$
$271$	9.20022e6			0.462265			0.231132	+	0.972922i	$0.425757\pi$
$272$	−3.06970e7	+	9.94795e6i	−1.52542	+	0.494342i
$273$	66294.6	−	15281.7i	0.00325829	−	0.000751075i
$274$	2.38937e7	+	7.76862e6i	1.16153	+	0.377652i
$275$	−1.67708e7	−	1.67708e7i	−0.806409	−	0.806409i
$276$	3.33138e7	−	1.34316e7i	1.58452	−	0.638853i
$277$	−5.90657e6	−	5.90657e6i	−0.277905	−	0.277905i	0.554367	−	0.832272i	$-0.312960\pi$
$277$	−5.90657e6	−	5.90657e6i	−0.277905	−	0.277905i	−0.832272	+	0.554367i	$0.812960\pi$
$278$	−1.19172e7	−	2.33999e7i	−0.554675	−	1.08913i
$279$	−2.04765e6	−	4.20552e6i	−0.0942850	−	0.193646i
$280$	304362.	−	1.91452e6i	0.0138649	−	0.0872137i
$281$	2.94813e6			0.132870			0.0664351	−	0.997791i	$-0.478837\pi$
$281$	2.94813e6			0.132870			0.0664351	+	0.997791i	$0.478837\pi$
$282$	−9.40008e6	−	1.12147e7i	−0.419164	−	0.500079i
$283$	2.38483e7	+	2.38483e7i	1.05220	+	1.05220i	0.998560	+	0.0536384i	$0.0170818\pi$
$283$	2.38483e7	+	2.38483e7i	1.05220	+	1.05220i	0.0536384	+	0.998560i	$0.482918\pi$
$284$	−2.79864e6	−	2.03498e6i	−0.122178	−	0.0888393i
$285$	−59756.9	−	37368.4i	−0.00258139	−	0.00161425i
$286$	15778.8	−	48530.4i	0.000674490	−	0.00207451i
$287$			5.08880e7i			2.15263i
$288$	−2.14874e7	+	1.04366e7i	−0.899511	+	0.436898i
$289$	−3.79267e7			−1.57127
$290$	390401.	+	126932.i	0.0160073	+	0.00520448i
$291$	−6.50796e6	+	1.04071e7i	−0.264098	+	0.422328i
$292$	−8.13399e6	+	1.11864e7i	−0.326704	+	0.449307i
$293$	5.01057e6	−	5.01057e6i	0.199198	−	0.199198i	−0.600458	−	0.799656i	$-0.705015\pi$
$293$	5.01057e6	−	5.01057e6i	0.199198	−	0.199198i	0.799656	+	0.600458i	$0.205015\pi$
$294$	4.03423e7	−	3.38148e7i	1.58752	−	1.33065i
$295$			1.12466e6i			0.0438082i
$296$	−5.22986e6	+	3.28972e7i	−0.201658	+	1.26848i
$297$	2.32972e7	−	1.88265e7i	0.889271	−	0.718623i
$298$	−3.39642e7	+	1.72974e7i	−1.28343	+	0.653631i
$299$	61611.8	−	61611.8i	0.00230489	−	0.00230489i
$300$	1.00706e7	+	2.49777e7i	0.372987	+	0.925100i
$301$	−8.99406e6	+	8.99406e6i	−0.329804	+	0.329804i
$302$	1.17962e6	−	3.62811e6i	0.0428272	−	0.131722i
$303$	−3.49323e6	−	1.51542e7i	−0.125574	−	0.544762i
$304$	1.51190e6	+	771816.i	0.0538148	+	0.0274722i
$305$			1.26508e6i			0.0445879i
$306$	−4.55034e7	+	6.35476e6i	−1.58811	+	0.221786i
$307$	1.21708e7	−	1.21708e7i	0.420635	−	0.420635i	−0.464787	−	0.885422i	$-0.653869\pi$
$307$	1.21708e7	−	1.21708e7i	0.420635	−	0.420635i	0.885422	+	0.464787i	$0.153869\pi$
$308$	−9.13638e6	−	5.78288e7i	−0.312696	−	1.97921i
$309$	−3.19776e7	−	1.99969e7i	−1.08385	−	0.677777i
$310$	−288102.	+	146726.i	−0.00967077	+	0.00492516i
$311$	4.58067e7			1.52282			0.761408	−	0.648273i	$-0.224508\pi$
$311$	4.58067e7			1.52282			0.761408	+	0.648273i	$0.224508\pi$
$312$	−38056.2	+	43697.8i	−0.00125303	+	0.00143878i
$313$			1.54611e7i			0.504206i	0.967700	+	0.252103i	$0.0811222\pi$
$313$			1.54611e7i			0.504206i	−0.967700	+	0.252103i	$0.918878\pi$
$314$	−2.15660e7	+	1.09832e7i	−0.696597	+	0.354765i
$315$	900391.	−	2.60919e6i	0.0288071	−	0.0834782i
$316$	2.15633e7	+	1.56793e7i	0.683365	+	0.496896i
$317$	3.85304e7	+	3.85304e7i	1.20955	+	1.20955i	0.971171	+	0.238384i	$0.0766176\pi$
$317$	3.85304e7	+	3.85304e7i	1.20955	+	1.20955i	0.238384	+	0.971171i	$0.423382\pi$
$318$	2.16330e6	−	2.45764e7i	0.0672721	−	0.764251i
$319$	1.23980e7			0.381925
$320$	747904.	+	1.47204e6i	0.0228242	+	0.0449231i
$321$	−1.02653e7	−	4.45328e7i	−0.310354	−	1.34637i
$322$	3.09088e7	−	9.50652e7i	0.925793	−	2.84744i
$323$	2.30865e6	+	2.30865e6i	0.0685094	+	0.0685094i
$324$	−3.27109e7	+	9.31819e6i	−0.961739	+	0.273966i
$325$	46194.7	+	46194.7i	0.00134568	+	0.00134568i
$326$	−1.90813e7	+	9.71779e6i	−0.550751	+	0.280488i
$327$	7.13088e6	+	3.09350e7i	0.203939	+	0.884722i
$328$	−2.54562e7	−	3.50801e7i	−0.721394	−	0.994120i
$329$	−4.07240e7			−1.14357
$330$	−1.32997e6	−	1.58671e6i	−0.0370085	−	0.0441525i
$331$	−3.82270e7	−	3.82270e7i	−1.05411	−	1.05411i	−0.998450	−	0.0556616i	$-0.982273\pi$
$331$	−3.82270e7	−	3.82270e7i	−1.05411	−	1.05411i	−0.0556616	−	0.998450i	$-0.517727\pi$
$332$	−6.37933e6	−	4.03780e7i	−0.174325	−	1.10339i
$333$	−1.54715e7	+	4.48338e7i	−0.418985	+	1.21415i
$334$	2.32672e7	+	7.56492e6i	0.624460	+	0.203032i
$335$		−	1.65809e6i		−	0.0441036i
$336$	−1.61543e7	+	6.44871e7i	−0.425864	+	1.70002i
$337$	6.97588e7			1.82267			0.911337	−	0.411661i	$-0.135051\pi$
$337$	6.97588e7			1.82267			0.911337	+	0.411661i	$0.135051\pi$
$338$	1.19395e7	−	3.67221e7i	0.309199	−	0.950994i
$339$	5.33408e6	+	3.33562e6i	0.136918	+	0.0856204i
$340$	495589.	+	3.13683e6i	0.0126091	+	0.0798094i
$341$	−6.90441e6	+	6.90441e6i	−0.174126	+	0.174126i
$342$	1.92900e6	+	1.45624e6i	0.0482231	+	0.0364045i
$343$		−	7.57739e7i		−	1.87775i
$344$	1.70093e6	−	1.06993e7i	0.0417841	−	0.262833i
$345$	−794046.	−	3.44471e6i	−0.0193370	−	0.0838872i
$346$	2.78579e7	+	5.47002e7i	0.672543	+	1.32057i
$347$	−2.86932e7	+	2.86932e7i	−0.686738	+	0.686738i	−0.961509	−	0.274772i	$-0.911398\pi$
$347$	−2.86932e7	+	2.86932e7i	−0.686738	+	0.686738i	0.274772	+	0.961509i	$0.411398\pi$
$348$	−1.29549e7	−	5.51009e6i	−0.307395	−	0.130744i
$349$	−4.37493e6	+	4.37493e6i	−0.102919	+	0.102919i	−0.756691	−	0.653772i	$-0.773185\pi$
$349$	−4.37493e6	+	4.37493e6i	−0.102919	+	0.102919i	0.653772	+	0.756691i	$0.273185\pi$
$350$	7.12771e7	+	2.31745e7i	1.66244	+	0.540513i
$351$	−64171.5	+	51857.3i	−0.00148396	+	0.00119919i
$352$	3.52265e7	+	3.52943e7i	0.807684	+	0.809239i
$353$		−	2.48090e7i		−	0.564007i	−0.959413	−	0.282004i	$-0.909001\pi$
$353$		−	2.48090e7i		−	0.564007i	0.959413	−	0.282004i	$-0.0909990\pi$
$354$	3.38185e6	−	3.84199e7i	0.0762333	−	0.866056i
$355$	−240802.	+	240802.i	−0.00538239	+	0.00538239i
$356$	−2.73683e7	−	1.99003e7i	−0.606593	−	0.441072i
$357$	−6.77945e7	+	1.08412e8i	−1.49001	+	2.38272i
$358$	−413554.	−	812031.i	−0.00901328	−	0.0176980i
$359$	−3.41044e6			−0.0737101			−0.0368551	−	0.999321i	$-0.511734\pi$
$359$	−3.41044e6			−0.0737101			−0.0368551	+	0.999321i	$0.511734\pi$
$360$	684529.	+	2.24907e6i	0.0146718	+	0.0482055i
$361$			4.68741e7i			0.996349i
$362$	−2.79753e7	−	5.49308e7i	−0.589725	−	1.15795i
$363$	−1.24595e7	−	7.79142e6i	−0.260484	−	0.162891i
$364$	25165.9	+	159288.i	0.000521806	+	0.00330277i
$365$	962507.	+	962507.i	0.0197936	+	0.0197936i
$366$	3.80408e6	−	4.32166e7i	0.0775901	−	0.881470i
$367$	−8.47907e6			−0.171534			−0.0857669	−	0.996315i	$-0.527334\pi$
$367$	−8.47907e6			−0.171534			−0.0857669	+	0.996315i	$0.527334\pi$
$368$	2.62482e7	+	8.09957e7i	0.526692	+	1.62524i
$369$	−2.70157e7	−	5.54858e7i	−0.537697	−	1.10434i
$370$	3.11761e6	+	1.01364e6i	0.0615484	+	0.0200114i
$371$	−4.85501e7	−	4.85501e7i	−0.950754	−	0.950754i
$372$	1.02831e7	−	4.14601e6i	0.199755	−	0.0805381i
$373$	1.73526e7	+	1.73526e7i	0.334379	+	0.334379i	0.854247	−	0.519868i	$-0.174019\pi$
$373$	1.73526e7	+	1.73526e7i	0.334379	+	0.334379i	−0.519868	+	0.854247i	$0.674019\pi$
$374$	4.35258e7	+	8.54647e7i	0.832016	+	1.63370i
$375$	5.17206e6	−	1.19222e6i	0.0980776	−	0.0226080i
$376$	2.80734e7	−	2.03718e7i	0.528118	−	0.383235i
$377$	−34149.9			−0.000637332
$378$	−3.86043e7	+	8.64256e7i	−0.714760	+	1.60017i
$379$	4.59451e7	+	4.59451e7i	0.843959	+	0.843959i	0.989371	−	0.145412i	$-0.0464508\pi$
$379$	4.59451e7	+	4.59451e7i	0.843959	+	0.843959i	−0.145412	+	0.989371i	$0.546451\pi$
$380$	98248.1	−	135118.i	0.00179050	−	0.00246241i
$381$	2.84226e7	−	4.54514e7i	0.513912	−	0.821812i
$382$	−1.45060e7	+	4.46157e7i	−0.260230	+	0.800382i
$383$		−	5.49300e7i		−	0.977716i	−0.872363	−	0.488858i	$-0.837414\pi$
$383$		−	5.49300e7i		−	0.977716i	0.872363	−	0.488858i	$-0.162586\pi$
$384$	−2.11229e7	−	5.25357e7i	−0.373044	−	0.927814i
$385$	−5.76184e6			−0.100967
$386$	−4.15871e6	−	1.35213e6i	−0.0723097	−	0.0235102i
$387$	5.03185e6	−	1.45815e7i	0.0868151	−	0.251576i
$388$	−2.35316e7	−	1.71106e7i	−0.402863	−	0.292934i
$389$	5.07529e7	−	5.07529e7i	0.862208	−	0.862208i	−0.129387	−	0.991594i	$-0.541301\pi$
$389$	5.07529e7	−	5.07529e7i	0.862208	−	0.862208i	0.991594	+	0.129387i	$0.0413009\pi$
$390$	3663.38	+	4370.55i	6.17573e−5	+	7.36788e-5i
$391$			1.63760e8i			2.73954i
$392$	7.32831e7	+	1.00988e8i	1.21659	+	1.67653i
$393$	1.09747e8	−	2.52980e7i	1.80807	−	0.416782i
$394$	−4.92618e7	+	2.50882e7i	−0.805418	+	0.410186i
$395$	1.85535e6	−	1.85535e6i	0.0301048	−	0.0301048i
$396$	4.06623e7	+	5.82032e7i	0.654797	+	0.937263i
$397$	4.72496e7	−	4.72496e7i	0.755138	−	0.755138i	−0.220295	−	0.975433i	$-0.570702\pi$
$397$	4.72496e7	−	4.72496e7i	0.755138	−	0.755138i	0.975433	+	0.220295i	$0.0707020\pi$
$398$	−2.47509e7	+	7.61257e7i	−0.392593	+	1.20749i
$399$	6.55448e6	−	1.51088e6i	0.103186	−	0.0237855i
$400$	−6.07282e7	+	1.96802e7i	−0.948879	+	0.307503i
$401$		−	2.27090e6i		−	0.0352181i	−0.999845	−	0.0176090i	$-0.994395\pi$
$401$		−	2.27090e6i		−	0.0352181i	0.999845	−	0.0176090i	$-0.00560542\pi$
$402$	−4.98587e6	+	5.66425e7i	−0.0767473	+	0.871895i
$403$	19018.0	−	19018.0i	0.000290570	−	0.000290570i
$404$	3.64115e7	−	5.75267e6i	0.552198	−	0.0872419i
$405$	403438.	+	3.32293e6i	0.00607313	+	0.0500215i
$406$	−3.49121e7	+	1.77802e7i	−0.521673	+	0.265679i
$407$	9.90061e7			1.46852
$408$	−7.49750e6	−	1.08648e8i	−0.110392	−	1.59971i
$409$		−	8.25133e7i		−	1.20602i	−0.797734	−	0.603009i	$-0.793968\pi$
$409$		−	8.25133e7i		−	1.20602i	0.797734	−	0.603009i	$-0.206032\pi$
$410$	−3.80109e6	+	1.93583e6i	−0.0551514	+	0.0280877i
$411$	−4.49597e7	+	7.18964e7i	−0.647587	+	1.03558i
$412$	5.25753e7	−	7.23053e7i	0.751779	−	1.03390i
$413$	−7.58976e7	−	7.58976e7i	−1.07740	−	1.07740i
$414$	1.67674e7	+	1.20063e8i	0.236300	+	1.69204i
$415$	−4.02311e6			−0.0562883
$416$	−97030.6	−	97217.3i	−0.00134781	−	0.00135040i
$417$	8.63619e7	−	1.99074e7i	1.19101	−	0.274541i
$418$	1.56003e6	−	4.79815e6i	0.0213602	−	0.0656969i
$419$	−9.45349e7	−	9.45349e7i	−1.28514	−	1.28514i	−0.937704	−	0.347436i	$-0.887053\pi$
$419$	−9.45349e7	−	9.45349e7i	−1.28514	−	1.28514i	−0.347436	−	0.937704i	$-0.612947\pi$
$420$	6.02067e6	+	2.56076e6i	0.0812638	+	0.0345638i
$421$	−6.55188e7	−	6.55188e7i	−0.878051	−	0.878051i	0.115282	−	0.993333i	$-0.463223\pi$
$421$	−6.55188e7	−	6.55188e7i	−0.878051	−	0.878051i	−0.993333	+	0.115282i	$0.963223\pi$
$422$	8.37440e7	−	4.26494e7i	1.11434	−	0.567513i
$423$	4.44034e7	−	2.16198e7i	0.586671	−	0.285647i
$424$	5.77550e7	+	9.18165e6i	0.757691	+	0.120455i
$425$	−1.22783e8			−1.59945
$426$	8.95020e6	−	7.50201e6i	0.115772	−	0.0970396i
$427$	−8.53735e7	−	8.53735e7i	−1.09658	−	1.09658i
$428$	1.07000e8	−	1.69050e7i	1.36475	−	0.215617i
$429$	146028.	+	91317.3i	0.00184954	+	0.00115659i
$430$	−1.01395e6	−	329669.i	−0.0127530	−	0.00414642i
$431$			3.28502e7i			0.410304i	0.978730	+	0.205152i	$0.0657689\pi$
$431$			3.28502e7i			0.410304i	−0.978730	+	0.205152i	$0.934231\pi$
$432$	−1.66214e7	−	7.88896e7i	−0.206166	−	0.978517i
$433$	−7.44391e6			−0.0916933			−0.0458467	−	0.998948i	$-0.514599\pi$
$433$	−7.44391e6			−0.0916933			−0.0458467	+	0.998948i	$0.514599\pi$
$434$	9.54077e6	−	2.93443e7i	0.116712	−	0.358967i
$435$	−734599.	+	1.17472e6i	−0.00892447	+	0.0142714i
$436$	−7.43284e7	+	1.17432e7i	−0.896799	+	0.141686i
$437$	6.09150e6	−	6.09150e6i	0.0729928	−	0.0729928i
$438$	−2.99862e7	−	3.57747e7i	−0.356861	−	0.425749i
$439$		−	4.49932e7i		−	0.531806i	−0.964000	−	0.265903i	$-0.914330\pi$
$439$		−	4.49932e7i		−	0.531806i	0.964000	−	0.265903i	$-0.0856701\pi$
$440$	3.97197e6	−	2.88231e6i	0.0466281	−	0.0338362i
$441$	7.77725e7	+	1.59732e8i	0.906798	+	1.86241i
$442$	−119891.	−	235411.i	−0.00138841	−	0.00272621i
$443$	−8.94679e7	+	8.94679e7i	−1.02910	+	1.02910i	−0.0295320	+	0.999564i	$0.509402\pi$
$443$	−8.94679e7	+	8.94679e7i	−1.02910	+	1.02910i	−0.999564	+	0.0295320i	$0.990598\pi$
$444$	−1.03454e8	−	4.40018e7i	−1.18194	−	0.502714i
$445$	−2.35483e6	+	2.35483e6i	−0.0267227	+	0.0267227i
$446$	−1.16653e8	−	3.79277e7i	−1.31490	−	0.427515i
$447$	−2.88950e7	−	1.25352e8i	−0.323519	−	1.40348i
$448$	−1.49813e8	−	4.88682e7i	−1.66615	−	0.543491i
$449$			1.33460e8i			1.47439i	0.675678	+	0.737196i	$0.263851\pi$
$449$			1.33460e8i			1.47439i	−0.675678	+	0.737196i	$0.736149\pi$
$450$	−9.00200e7	+	1.25717e7i	−0.987874	+	0.137961i
$451$	−9.10937e7	+	9.10937e7i	−0.993022	+	0.993022i
$452$	−8.76993e6	+	1.20610e7i	−0.0949687	+	0.130608i
$453$	1.09170e7	+	6.82684e6i	0.117438	+	0.0734388i
$454$	7.58783e6	+	1.48990e7i	0.0810867	+	0.159217i
$455$	15870.9			0.000168487
$456$	−3.76258e6	+	4.32036e6i	−0.0396818	+	0.0455643i
$457$		−	9.73186e7i		−	1.01964i	−0.860281	−	0.509821i	$-0.829712\pi$
$457$		−	9.73186e7i		−	1.01964i	0.860281	−	0.509821i	$-0.170288\pi$
$458$	1.64858e7	+	3.23706e7i	0.171598	+	0.336941i
$459$	1.63652e7	−	1.54198e8i	0.169233	−	1.59456i
$460$	8.27671e6	−	1.30764e6i	0.0850323	−	0.0134343i
$461$	3.56601e7	+	3.56601e7i	0.363981	+	0.363981i	0.865276	−	0.501295i	$-0.167143\pi$
$461$	3.56601e7	+	3.56601e7i	0.363981	+	0.363981i	−0.501295	+	0.865276i	$0.667143\pi$
$462$	1.96832e8	+	1.73258e7i	1.99604	+	0.175699i
$463$	−9.25741e7			−0.932710			−0.466355	−	0.884598i	$-0.654433\pi$
$463$	−9.25741e7			−0.932710			−0.466355	+	0.884598i	$0.654433\pi$
$464$	1.51726e7	−	2.97213e7i	0.151882	−	0.297519i
$465$	−245102.	−	1.06330e6i	−0.00243775	−	0.0105754i
$466$	−5.75485e7	−	1.87109e7i	−0.568691	−	0.184900i
$467$	−5.39368e7	−	5.39368e7i	−0.529583	−	0.529583i	0.390865	−	0.920448i	$-0.372176\pi$
$467$	−5.39368e7	−	5.39368e7i	−0.529583	−	0.529583i	−0.920448	+	0.390865i	$0.872176\pi$
$468$	−112003.	−	160319.i	−0.00109268	−	0.00156404i
$469$	1.11896e8	+	1.11896e8i	1.08467	+	1.08467i
$470$	−1.54918e6	−	3.04188e6i	−0.0149213	−	0.0292987i
$471$	−1.83473e7	−	7.95937e7i	−0.175594	−	0.761756i
$472$	9.02876e7	+	1.43535e7i	0.858622	+	0.136500i
$473$	−3.22002e7			−0.304281
$474$	−6.89603e7	+	5.78022e7i	−0.647536	+	0.542762i
$475$	4.56723e6	+	4.56723e6i	0.0426159	+	0.0426159i
$476$	−2.45133e8	−	1.78244e8i	−2.27290	−	1.65270i
$477$	7.87111e7	+	2.71620e7i	0.725239	+	0.250269i
$478$	2.04917e7	−	6.30256e7i	0.187626	−	0.577076i
$479$			1.49481e8i			1.36013i	0.733154	+	0.680063i	$0.238048\pi$
$479$			1.49481e8i			1.36013i	−0.733154	+	0.680063i	$0.761952\pi$
$480$	−5.43139e6	+	1.24650e6i	−0.0491120	+	0.0112712i
$481$	−272710.			−0.00245056
$482$	7.40925e7	+	2.40899e7i	0.661658	+	0.215126i
$483$	2.86052e8	+	1.78880e8i	2.53865	+	1.58752i
$484$	2.04850e7	−	2.81724e7i	0.180676	−	0.248478i
$485$	−2.02472e6	+	2.02472e6i	−0.0177476	+	0.0177476i
$486$	−3.78993e6	−	1.14729e8i	−0.0330159	−	0.999455i
$487$			6.06965e7i			0.525504i	0.964863	+	0.262752i	$0.0846302\pi$
$487$			6.06965e7i			0.525504i	−0.964863	+	0.262752i	$0.915370\pi$
$488$	1.01560e8	+	1.61456e7i	0.873904	+	0.138930i
$489$	−1.62334e7	−	7.04233e7i	−0.138830	−	0.602268i
$490$	1.09425e7	−	5.57284e6i	0.0930099	−	0.0473684i
$491$	5.78165e7	−	5.78165e7i	0.488436	−	0.488436i	−0.419376	−	0.907812i	$-0.637751\pi$
$491$	5.78165e7	−	5.78165e7i	0.488436	−	0.488436i	0.907812	+	0.419376i	$0.137751\pi$
$492$	1.35671e8	−	5.47006e7i	1.13918	−	0.459300i
$493$	4.53841e7	−	4.53841e7i	0.378759	−	0.378759i
$494$	−4297.07	+	13216.4i	−3.56445e−5	+	0.000109631i
$495$	6.28243e6	−	3.05888e6i	0.0517979	−	0.0252201i
$496$	8.10218e6	+	2.50014e7i	0.0663983	+	0.204889i
$497$		−	3.25010e7i		−	0.264745i
$498$	1.37435e8	+	1.20975e7i	1.11278	+	0.0979505i
$499$	−1.09098e8	+	1.09098e8i	−0.878043	+	0.878043i	−0.993332	−	0.115289i	$-0.963220\pi$
$499$	−1.09098e8	+	1.09098e8i	−0.878043	+	0.878043i	0.115289	+	0.993332i	$0.463220\pi$
$500$	1.96335e6	+	1.24271e7i	0.0157068	+	0.0994165i
$501$	−4.37808e7	+	7.00111e7i	−0.348153	+	0.556742i
$502$	−2.83097e7	+	1.44176e7i	−0.223781	+	0.113968i
$503$	−9.85462e7			−0.774348			−0.387174	−	0.922007i	$-0.626549\pi$
$503$	−9.85462e7			−0.774348			−0.387174	+	0.922007i	$0.626549\pi$
$504$	−1.97974e8	−	1.05583e8i	−1.54638	−	0.824713i
$505$		−	3.62791e6i		−	0.0281697i
$506$	2.25504e8	−	1.14845e8i	1.74061	−	0.886464i
$507$	1.10497e8	+	6.90983e7i	0.847866	+	0.530204i
$508$	1.02771e8	+	7.47281e7i	0.783936	+	0.570023i
$509$	1.21445e8	+	1.21445e8i	0.920929	+	0.920929i	0.997095	−	0.0761657i	$-0.0242678\pi$
$509$	1.21445e8	+	1.21445e8i	0.920929	+	0.920929i	−0.0761657	+	0.997095i	$0.524268\pi$
$510$	−1.06768e7	−	939812.i	−0.0804881	−	0.00708485i
$511$	−1.29909e8			−0.973593
$512$	1.27720e8	−	4.12546e7i	0.951590	−	0.307371i
$513$	−6.34458e6	+	5.12708e6i	−0.0469949	+	0.0379767i
$514$	−2.50444e7	+	7.70284e7i	−0.184426	+	0.567233i
$515$	−6.22132e6	−	6.22132e6i	−0.0455471	−	0.0455471i
$516$	3.36467e7	+	1.43109e7i	0.244902	+	0.104164i
$517$	−7.28992e7	−	7.28992e7i	−0.527535	−	0.527535i
$518$	−2.78797e8	+	1.41987e8i	−2.00585	+	1.02155i
$519$	−2.01882e8	+	4.65361e7i	−1.44409	+	0.332880i
$520$	−10940.7	+	7939.24i	−7.78099e−5	+	5.64637e-5i
$521$	6.15534e7			0.435250			0.217625	−	0.976032i	$-0.430169\pi$
$521$	6.15534e7			0.435250			0.217625	+	0.976032i	$0.430169\pi$
$522$	2.86272e7	−	3.79210e7i	0.201265	−	0.266605i
$523$	6.14692e7	+	6.14692e7i	0.429687	+	0.429687i	0.888522	−	0.458834i	$-0.151733\pi$
$523$	6.14692e7	+	6.14692e7i	0.429687	+	0.429687i	−0.458834	+	0.888522i	$0.651733\pi$
$524$	4.16609e7	+	2.63693e8i	0.289557	+	1.83275i
$525$	−1.34119e8	+	2.14473e8i	−0.926855	+	1.48216i
$526$	−1.92527e8	−	6.25968e7i	−1.32292	−	0.430125i
$527$			5.05487e7i			0.345365i
$528$	−1.44355e8	+	8.65195e7i	−0.980684	+	0.587777i
$529$	2.84055e8			1.91882
$530$	1.77956e6	−	5.47334e6i	0.0119532	−	0.0367642i
$531$	1.23048e8	+	4.24620e7i	0.821847	+	0.283607i
$532$	2.48813e6	+	1.57486e7i	0.0165249	+	0.104594i
$533$	250915.	−	250915.i	0.00165709	−	0.00165709i
$534$	8.75250e7	−	7.33631e7i	0.574789	−	0.481786i
$535$		−	1.06611e7i		−	0.0696210i
$536$	−1.33111e8	−	2.11615e7i	−0.864412	−	0.137421i
$537$	2.99696e6	−	690834.i	0.0193534	−	0.00446119i
$538$	−4.36332e7	−	8.56757e7i	−0.280202	−	0.550188i
$539$	2.62239e8	−	2.62239e8i	1.67468	−	1.67468i
$540$	−7.92412e6	+	404162.i	−0.0503234	+	0.00256669i
$541$	6.51711e7	−	6.51711e7i	0.411588	−	0.411588i	−0.470703	−	0.882292i	$-0.656000\pi$
$541$	6.51711e7	−	6.51711e7i	0.411588	−	0.411588i	0.882292	+	0.470703i	$0.156000\pi$
$542$	−6.99951e7	−	2.27577e7i	−0.439612	−	0.142932i
$543$	2.02733e8	−	4.67323e7i	1.26626	−	0.291889i
$544$	2.58149e8	+	248178.i	1.60352	+	0.00154158i
$545$			7.40580e6i			0.0457491i
$546$	−542169.	−	47723.6i	−0.00333086	−	0.000293194i
$547$	9.47553e7	−	9.47553e7i	0.578951	−	0.578951i	−0.355664	−	0.934614i	$-0.615745\pi$
$547$	9.47553e7	−	9.47553e7i	0.578951	−	0.578951i	0.934614	+	0.355664i	$0.115745\pi$
$548$	−1.62566e8	−	1.18207e8i	−0.987846	−	0.718293i
$549$	1.38411e8	+	4.77634e7i	0.836473	+	0.288654i
$550$	8.61076e7	+	1.69076e8i	0.517551	+	1.01623i
$551$	−3.37637e6			−0.0201834
$552$	−2.86675e8	+	1.97826e7i	−1.70440	+	0.117616i
$553$			2.50417e8i			1.48077i
$554$	3.03266e7	+	5.95475e7i	0.178359	+	0.350215i
$555$	−5.86627e6	+	9.38092e6i	−0.0343149	+	0.0548740i
$556$	3.27836e7	+	2.07504e8i	0.190736	+	1.20726i
$557$	−1.94486e8	−	1.94486e8i	−1.12544	−	1.12544i	−0.990909	−	0.134533i	$-0.957047\pi$
$557$	−1.94486e8	−	1.94486e8i	−1.12544	−	1.12544i	−0.134533	−	0.990909i	$-0.542953\pi$
$558$	5.17568e6	+	3.70606e7i	0.0297896	+	0.213309i
$559$	88694.6			0.000507764
$560$	−7.05132e6	+	1.38127e7i	−0.0401519	+	0.0786530i
$561$	−3.15424e8	+	7.27090e7i	−1.78651	+	0.411812i
$562$	−2.24293e7	−	7.29249e6i	−0.126359	−	0.0410835i
$563$	2.41830e7	+	2.41830e7i	0.135514	+	0.135514i	0.771610	−	0.636096i	$-0.219452\pi$
$563$	2.41830e7	+	2.41830e7i	0.135514	+	0.135514i	−0.636096	+	0.771610i	$0.719452\pi$
$564$	4.37750e7	+	1.08573e8i	0.243999	+	0.605179i
$565$	1.03776e6	+	1.03776e6i	0.00575375	+	0.00575375i
$566$	−1.22446e8	−	2.40428e8i	−0.675298	−	1.32598i
$567$	−2.51473e8	−	1.97021e8i	−1.37957	−	1.08085i
$568$	1.62583e7	+	2.24048e7i	0.0887218	+	0.122263i
$569$	−2.03358e8			−1.10388			−0.551942	−	0.833882i	$-0.686113\pi$
$569$	−2.03358e8			−1.10388			−0.551942	+	0.833882i	$0.686113\pi$
$570$	362195.	+	432112.i	0.00195577	+	0.00233331i
$571$	9.71255e7	+	9.71255e7i	0.521705	+	0.521705i	0.918086	−	0.396381i	$-0.129734\pi$
$571$	9.71255e7	+	9.71255e7i	0.521705	+	0.521705i	−0.396381	+	0.918086i	$0.629734\pi$
$572$	−240089.	+	330187.i	−0.00128288	+	0.00176430i
$573$	−1.34249e8	−	8.39512e7i	−0.713586	−	0.446234i
$574$	1.25877e8	−	3.87155e8i	0.665594	−	2.04715i
$575$			3.23969e8i			1.70412i
$576$	1.89292e8	−	2.62499e7i	0.990521	−	0.137360i
$577$	−2.64669e8			−1.37777			−0.688884	−	0.724872i	$-0.741899\pi$
$577$	−2.64669e8			−1.37777			−0.688884	+	0.724872i	$0.741899\pi$
$578$	2.88545e8	+	9.38154e7i	1.49428	+	0.485837i
$579$	7.82524e6	−	1.25136e7i	0.0403146	−	0.0644682i
$580$	−2.65618e6	−	1.93139e6i	−0.0136136	−	0.00989888i
$581$	2.71499e8	−	2.71499e8i	1.38433	−	1.38433i
$582$	7.52553e7	−	6.30787e7i	0.381740	−	0.319973i
$583$		−	1.73817e8i		−	0.877176i
$584$	8.95539e7	−	6.49859e7i	0.449621	−	0.326272i
$585$	−17304.8	+	8425.62i	−8.64368e−5	+	4.20856e-5i
$586$	−5.05144e7	+	2.57261e7i	−0.251028	+	0.127844i
$587$	−1.14037e8	+	1.14037e8i	−0.563808	+	0.563808i	−0.930387	−	0.366579i	$-0.880529\pi$
$587$	−1.14037e8	+	1.14037e8i	−0.563808	+	0.563808i	0.366579	+	0.930387i	$0.380529\pi$
$588$	−3.90568e8	+	1.57471e8i	−1.92116	+	0.774585i
$589$	1.88030e6	−	1.88030e6i	0.00920196	−	0.00920196i
$590$	2.78196e6	−	8.55640e6i	0.0135455	−	0.0416615i
$591$	−4.19094e7	−	1.81810e8i	−0.203025	−	0.880756i
$592$	1.21163e8	−	2.37345e8i	0.583991	−	1.14397i
$593$			3.78808e8i			1.81658i	0.418341	+	0.908290i	$0.362612\pi$
$593$			3.78808e8i			1.81658i	−0.418341	+	0.908290i	$0.637388\pi$
$594$	−2.23814e8	+	8.56040e7i	−1.06789	+	0.408446i
$595$	−2.10918e7	+	2.10918e7i	−0.100130	+	0.100130i
$596$	3.01186e8	−	4.75845e7i	1.42264	−	0.224764i
$597$	−2.29063e8	−	1.43242e8i	−1.07654	−	0.673206i
$598$	−621144.	+	316338.i	−0.00290462	+	0.00147927i
$599$	1.64595e8			0.765839			0.382919	−	0.923782i	$-0.374919\pi$
$599$	1.64595e8			0.765839			0.382919	+	0.923782i	$0.374919\pi$
$600$	−1.48324e7	−	2.14940e8i	−0.0686686	−	0.995094i
$601$		−	4.09819e8i		−	1.88785i	−0.330154	−	0.943927i	$-0.607101\pi$
$601$		−	4.09819e8i		−	1.88785i	0.330154	−	0.943927i	$-0.392899\pi$
$602$	9.06743e7	−	4.61789e7i	0.415618	−	0.211667i
$603$	−1.81410e8	−	6.26019e7i	−0.827388	−	0.285519i
$604$	−1.79490e7	+	2.46847e7i	−0.0814571	+	0.112025i
$605$	−2.42402e6	−	2.42402e6i	−0.0109464	−	0.0109464i
$606$	−1.09091e7	+	1.23934e8i	−0.0490198	+	0.556894i
$607$	4.23031e8			1.89150			0.945749	−	0.324898i	$-0.105330\pi$
$607$	4.23031e8			1.89150			0.945749	+	0.324898i	$0.105330\pi$
$608$	−9.59332e6	−	9.61178e6i	−0.0426833	−	0.0427655i
$609$	−2.97014e7	−	1.28850e8i	−0.131500	−	0.570470i
$610$	3.12929e6	−	9.62467e6i	0.0137866	−	0.0424030i
$611$	200799.	+	200799.i	0.000880315	+	0.000880315i
$612$	3.61908e8	+	6.42103e7i	1.57886	+	0.280124i
$613$	−1.59960e8	−	1.59960e8i	−0.694432	−	0.694432i	0.268772	−	0.963204i	$-0.413382\pi$
$613$	−1.59960e8	−	1.59960e8i	−0.694432	−	0.694432i	−0.963204	+	0.268772i	$0.913382\pi$
$614$	−1.22701e8	+	6.24897e7i	−0.530083	+	0.269962i
$615$	−3.23377e6	−	1.40287e7i	−0.0139022	−	0.0603102i
$616$	−7.35358e7	+	4.62560e8i	−0.314598	+	1.97891i
$617$	1.61821e7			0.0688937			0.0344468	−	0.999407i	$-0.489033\pi$
$617$	1.61821e7			0.0688937			0.0344468	+	0.999407i	$0.489033\pi$
$618$	1.93821e8	+	2.31236e8i	0.821173	+	0.979691i
$619$	1.35105e8	+	1.35105e8i	0.569639	+	0.569639i	0.932027	−	0.362388i	$-0.118038\pi$
$619$	1.35105e8	+	1.35105e8i	0.569639	+	0.569639i	−0.362388	+	0.932027i	$0.618038\pi$
$620$	2.55481e6	−	403636.i	0.0107197	−	0.00169361i
$621$	−4.06861e8	−	4.31806e7i	−1.69891	−	0.180308i
$622$	−3.48496e8	−	1.13307e8i	−1.44819	−	0.470854i
$623$		−	3.17831e8i		−	1.31441i
$624$	397621.	−	238316.i	0.00163650	−	0.000980843i
$625$	−2.42283e8			−0.992389
$626$	3.82446e7	−	1.17628e8i	0.155901	−	0.479499i
$627$	1.44377e7	+	9.02845e6i	0.0585726	+	0.0366278i
$628$	1.91242e8	−	3.02144e7i	0.772155	−	0.121993i
$629$	3.62422e8	−	3.62422e8i	1.45634	−	1.45634i
$630$	−1.33042e7	+	1.76234e7i	−0.0532069	+	0.0704804i
$631$			4.28199e8i			1.70435i	0.523261	+	0.852173i	$0.324715\pi$
$631$			4.28199e8i			1.70435i	−0.523261	+	0.852173i	$0.675285\pi$
$632$	−1.25268e8	−	1.72627e8i	−0.496238	−	0.683843i
$633$	7.12451e7	+	3.09074e8i	0.280895	+	1.21857i
$634$	−1.97830e8	−	3.88447e8i	−0.776289	−	1.52428i
$635$	8.84268e6	−	8.84268e6i	0.0345353	−	0.0345353i
$636$	−7.72504e7	+	1.81625e8i	−0.300282	+	0.706000i
$637$	−722332.	+	722332.i	−0.00279459	+	0.00279459i
$638$	−9.43235e7	−	3.06676e7i	−0.363210	−	0.118091i
$639$	1.72543e7	+	3.54375e7i	0.0661295	+	0.135819i
$640$	−2.04880e6	−	1.30493e7i	−0.00781555	−	0.0497790i
$641$			1.89899e8i			0.721024i	0.932755	+	0.360512i	$0.117398\pi$
$641$			1.89899e8i			0.721024i	−0.932755	+	0.360512i	$0.882602\pi$
$642$	−3.20579e7	+	3.64197e8i	−0.121152	+	1.37636i
$643$	1.96842e8	−	1.96842e8i	0.740431	−	0.740431i	−0.232230	−	0.972661i	$-0.574602\pi$
$643$	1.96842e8	−	1.96842e8i	0.740431	−	0.740431i	0.972661	+	0.232230i	$0.0746022\pi$
$644$	−4.70306e8	+	6.46798e8i	−1.76085	+	2.42165i
$645$	1.90791e6	−	3.05100e6i	0.00711015	−	0.0113701i
$646$	−1.18535e7	−	2.32748e7i	−0.0439691	−	0.0863353i
$647$	−3.62501e8			−1.33843			−0.669217	−	0.743067i	$-0.733370\pi$
$647$	−3.62501e8			−1.33843			−0.669217	+	0.743067i	$0.733370\pi$
$648$	2.71913e8	+	1.00211e7i	0.999322	+	0.0368290i
$649$		−	2.71726e8i		−	0.994024i
$650$	−237181.	−	465716.i	−0.000863655	−	0.00169582i
$651$	8.82971e7	+	5.52157e7i	0.320039	+	0.200133i
$652$	1.69208e8	−	2.67332e7i	0.610490	−	0.0964514i
$653$	−1.56936e8	−	1.56936e8i	−0.563617	−	0.563617i	0.366716	−	0.930333i	$-0.380482\pi$
$653$	−1.56936e8	−	1.56936e8i	−0.563617	−	0.563617i	−0.930333	+	0.366716i	$0.880482\pi$
$654$	2.22692e7	−	2.52992e8i	0.0796107	−	0.904426i
$655$	2.62734e7			0.0934957
$656$	1.06897e8	+	3.29857e8i	0.378662	+	1.16846i
$657$	1.41647e8	−	6.89670e7i	0.499471	−	0.243190i
$658$	3.09827e8	+	1.00735e8i	1.08753	+	0.353591i
$659$	1.53399e8	+	1.53399e8i	0.536001	+	0.536001i	0.922352	−	0.386351i	$-0.126265\pi$
$659$	1.53399e8	+	1.53399e8i	0.536001	+	0.536001i	−0.386351	+	0.922352i	$0.626265\pi$
$660$	6.19352e6	+	1.53615e7i	0.0215430	+	0.0534319i
$661$	3.15310e8	+	3.15310e8i	1.09178	+	1.09178i	0.995339	+	0.0964363i	$0.0307444\pi$
$661$	3.15310e8	+	3.15310e8i	1.09178	+	1.09178i	0.0964363	+	0.995339i	$0.469256\pi$
$662$	1.96272e8	+	3.85389e8i	0.676526	+	1.32839i
$663$	868829.	−	200275.i	0.00298122	−	0.000687205i
$664$	−5.13452e7	+	3.22975e8i	−0.175386	+	1.10323i
$665$	1.56914e6			0.00533575
$666$	2.28607e8	−	3.02824e8i	0.773869	−	1.02510i
$667$	−1.19749e8	−	1.19749e8i	−0.403546	−	0.403546i
$668$	−1.58304e8	−	1.15107e8i	−0.531082	−	0.386166i
$669$	2.19501e8	−	3.51010e8i	0.733090	−	1.17231i
$670$	−4.10145e6	+	1.26147e7i	−0.0136368	+	0.0419424i
$671$		−	3.05651e8i		−	1.01171i
$672$	2.82417e8	−	4.50657e8i	0.930642	−	1.48504i
$673$	−2.15942e8			−0.708421			−0.354211	−	0.935166i	$-0.615250\pi$
$673$	−2.15942e8			−0.708421			−0.354211	+	0.935166i	$0.615250\pi$
$674$	−5.30723e8	−	1.72555e8i	−1.73336	−	0.563571i
$675$	3.23756e7	−	3.05053e8i	0.105270	−	0.991890i
$676$	−1.81672e8	+	2.49847e8i	−0.588094	+	0.808788i
$677$	−9.46602e7	+	9.46602e7i	−0.305071	+	0.305071i	−0.842994	−	0.537923i	$-0.819209\pi$
$677$	−9.46602e7	+	9.46602e7i	−0.305071	+	0.305071i	0.537923	+	0.842994i	$0.319209\pi$
$678$	−3.23306e7	−	3.85717e7i	−0.103735	−	0.123760i
$679$		−	2.73276e8i		−	0.872955i
$680$	3.98883e6	−	2.50908e7i	0.0126858	−	0.0797973i
$681$	−5.49878e7	+	1.26753e7i	−0.174110	+	0.0401345i
$682$	6.96074e7	−	3.54499e7i	0.219433	−	0.111754i
$683$	1.28855e8	−	1.28855e8i	0.404426	−	0.404426i	−0.475364	−	0.879789i	$-0.657683\pi$
$683$	1.28855e8	−	1.28855e8i	0.404426	−	0.404426i	0.879789	+	0.475364i	$0.157683\pi$
$684$	−1.10737e7	−	1.58506e7i	−0.0346038	−	0.0495311i
$685$	−1.39876e7	+	1.39876e7i	−0.0435183	+	0.0435183i
$686$	−1.87434e8	+	5.76486e8i	−0.580600	+	1.78573i
$687$	−1.19470e8	+	2.75392e7i	−0.368458	+	0.0849339i
$688$	−3.94064e7	+	7.71927e7i	−0.121005	+	0.237034i
$689$			478775.i			0.00146377i
$690$	−2.47975e6	+	2.81714e7i	−0.00754849	+	0.0857554i
$691$	−2.46130e8	+	2.46130e8i	−0.745986	+	0.745986i	−0.973723	−	0.227736i	$-0.926868\pi$
$691$	−2.46130e8	+	2.46130e8i	−0.745986	+	0.745986i	0.227736	+	0.973723i	$0.426868\pi$
$692$	−7.66359e7	−	4.85067e8i	−0.231267	−	1.46381i
$693$	−2.17540e8	+	6.30397e8i	−0.653643	+	1.89415i
$694$	2.89273e8	−	1.47322e8i	0.865425	−	0.440746i
$695$	2.06749e7			0.0615871
$696$	8.49309e7	+	7.39659e7i	0.251906	+	0.219383i
$697$			6.66917e8i			1.96958i
$698$	4.41062e7	−	2.24626e7i	0.129698	−	0.0660531i
$699$	1.08286e8	−	1.73164e8i	0.317060	−	0.507021i
$700$	−4.84950e8	−	3.52622e8i	−1.41385	−	1.02805i
$701$	−1.28744e8	−	1.28744e8i	−0.373744	−	0.373744i	0.495095	−	0.868839i	$-0.335133\pi$
$701$	−1.28744e8	−	1.28744e8i	−0.373744	−	0.373744i	−0.868839	+	0.495095i	$0.835133\pi$
$702$	616489.	−	235794.i	0.00178203	−	0.000681588i
$703$	−2.69626e7			−0.0776060
$704$	−1.80699e8	−	3.55655e8i	−0.517889	−	1.01932i
$705$	1.12267e7	−	2.58788e6i	0.0320393	−	0.00738543i
$706$	−6.13675e7	+	1.88746e8i	−0.174391	+	0.536369i
$707$	2.44829e8	+	2.44829e8i	0.692795	+	0.692795i
$708$	−1.20764e8	+	2.83932e8i	−0.340282	+	0.800046i
$709$	−1.62657e8	−	1.62657e8i	−0.456389	−	0.456389i	0.441079	−	0.897468i	$-0.354596\pi$
$709$	−1.62657e8	−	1.62657e8i	−0.456389	−	0.456389i	−0.897468	+	0.441079i	$0.854596\pi$
$710$	2.42766e6	−	1.23637e6i	0.00678287	−	0.00345440i
$711$	−1.32943e8	−	2.73042e8i	−0.369875	−	0.759662i
$712$	1.58992e8	+	2.19099e8i	0.440489	+	0.607017i
$713$	1.33376e8			0.367966
$714$	7.83947e8	−	6.57101e8i	2.15373	−	1.80525i
$715$	28410.1	+	28410.1i	7.77240e−5	+	7.77240e-5i
$716$	1.13767e6	+	7.20088e6i	0.00309939	+	0.0196176i
$717$	1.89644e8	+	1.18592e8i	0.514497	+	0.321735i
$718$	2.59466e7	+	8.43606e6i	0.0700981	+	0.0227912i
$719$			3.94701e8i			1.06190i	0.847404	+	0.530948i	$0.178164\pi$
$719$			3.94701e8i			1.06190i	−0.847404	+	0.530948i	$0.821836\pi$
$720$	355429.	−	1.88041e7i	0.000952259	−	0.0503798i
$721$	8.39689e8			2.24033
$722$	1.15948e8	−	3.56617e8i	0.308071	−	0.947525i
$723$	−1.39416e8	+	2.22945e8i	−0.368892	+	0.589906i
$724$	7.69589e7	+	4.87112e8i	0.202789	+	1.28355i
$725$	8.97840e7	−	8.97840e7i	0.235605	−	0.235605i
$726$	7.55187e7	+	9.00968e7i	0.197353	+	0.235450i
$727$		−	8.71631e7i		−	0.226845i	−0.993547	−	0.113423i	$-0.963819\pi$
$727$		−	8.71631e7i		−	0.226845i	0.993547	−	0.113423i	$-0.0361814\pi$
$728$	202553.	−	1.27411e6i	0.000524981	−	0.00330227i
$729$	3.78790e8	+	8.13187e7i	0.977723	+	0.209898i
$730$	−4.94188e6	−	9.70359e6i	−0.0127035	−	0.0249439i
$731$	−1.17872e8	+	1.17872e8i	−0.301758	+	0.301758i
$732$	−1.35842e8	+	3.19381e8i	−0.346338	+	0.814284i
$733$	−2.02104e7	+	2.02104e7i	−0.0513172	+	0.0513172i	−0.732300	−	0.680982i	$-0.761553\pi$
$733$	−2.02104e7	+	2.02104e7i	−0.0513172	+	0.0513172i	0.680982	+	0.732300i	$0.261553\pi$
$734$	6.45086e7	+	2.09738e7i	0.163128	+	0.0530383i
$735$	9.30933e6	+	4.03855e7i	0.0234453	+	0.101710i
$736$	654831.	−	6.81141e8i	0.00164246	−	1.70846i
$737$			4.00606e8i			1.00073i
$738$	6.82856e7	+	4.88961e8i	0.169887	+	1.21648i
$739$	−2.02467e8	+	2.02467e8i	−0.501674	+	0.501674i	−0.911958	−	0.410284i	$-0.865430\pi$
$739$	−2.02467e8	+	2.02467e8i	−0.501674	+	0.501674i	0.410284	+	0.911958i	$0.365430\pi$
$740$	−2.12114e7	−	1.54235e7i	−0.0523449	−	0.0380615i
$741$	−39768.2	−	24868.7i	−9.77420e−5	−	6.11220e-5i
$742$	2.49274e8	+	4.89461e8i	0.610191	+	1.19814i
$743$	5.24437e8			1.27858			0.639289	−	0.768967i	$-0.279229\pi$
$743$	5.24437e8			1.27858			0.639289	+	0.768967i	$0.279229\pi$
$744$	−8.84894e7	+	6.10639e6i	−0.214868	+	0.0148274i
$745$		−	3.00090e7i		−	0.0725744i
$746$	−8.90950e7	−	1.74942e8i	−0.214603	−	0.421383i
$747$	−1.51894e8	+	4.40164e8i	−0.364400	+	1.05597i
$748$	−1.19737e8	−	7.57879e8i	−0.286105	−	1.81090i
$749$	7.19462e8	+	7.19462e8i	1.71223	+	1.71223i
$750$	−4.22980e7	−	3.72322e6i	−0.100262	−	0.00882541i
$751$	−4.72553e8			−1.11566			−0.557829	−	0.829956i	$-0.688365\pi$
$751$	−4.72553e8			−1.11566			−0.557829	+	0.829956i	$0.688365\pi$
$752$	−2.63973e8	+	8.55457e7i	−0.620735	+	0.201161i
$753$	−2.40844e7	−	1.04482e8i	−0.0564093	−	0.244714i
$754$	259812.	+	84473.2i	0.000606101	+	0.000197063i
$755$	2.12393e6	+	2.12393e6i	0.00493514	+	0.00493514i
$756$	5.07483e8	−	5.62032e8i	1.17451	−	1.30076i
$757$	−6.24181e7	−	6.24181e7i	−0.143887	−	0.143887i	0.631494	−	0.775381i	$-0.282442\pi$
$757$	−6.24181e7	−	6.24181e7i	−0.143887	−	0.143887i	−0.775381	+	0.631494i	$0.782442\pi$
$758$	−2.35899e8	−	4.63199e8i	−0.541651	−	1.06355i
$759$	1.91847e8	+	8.32265e8i	0.438762	+	1.90343i
$760$	−1.08170e6	+	784945.i	−0.00246413	+	0.00178813i
$761$	−1.81677e8			−0.412237			−0.206118	−	0.978527i	$-0.566083\pi$
$761$	−1.81677e8			−0.412237			−0.206118	+	0.978527i	$0.566083\pi$
$762$	−3.28667e8	+	2.75487e8i	−0.742833	+	0.622640i
$763$	−4.99779e8	−	4.99779e8i	−1.12514	−	1.12514i
$764$	2.20722e8	−	3.03553e8i	0.494956	−	0.680698i
$765$	1.18001e7	−	3.41949e7i	0.0263574	−	0.0763795i
$766$	−1.35875e8	+	4.17906e8i	−0.302310	+	0.929805i
$767$			748462.i			0.00165876i
$768$	3.07505e7	+	4.51940e8i	0.0678842	+	0.997693i
$769$	−3.69719e8			−0.813004			−0.406502	−	0.913650i	$-0.633252\pi$
$769$	−3.69719e8			−0.813004			−0.406502	+	0.913650i	$0.633252\pi$
$770$	4.38360e7	+	1.42525e7i	0.0960193	+	0.0312190i
$771$	−2.31779e8	−	1.44941e8i	−0.505721	−	0.316248i
$772$	2.82947e7	+	2.05739e7i	0.0614969	+	0.0447163i
$773$	−2.97469e8	+	2.97469e8i	−0.644026	+	0.644026i	−0.951543	−	0.307516i	$-0.900502\pi$
$773$	−2.97469e8	+	2.97469e8i	−0.644026	+	0.644026i	0.307516	+	0.951543i	$0.400502\pi$
$774$	−7.43510e7	+	9.84889e7i	−0.160348	+	0.212405i
$775$			1.00001e8i			0.214832i
$776$	1.36704e8	+	1.88385e8i	0.292546	+	0.403144i
$777$	−2.37186e8	−	1.02895e9i	−0.505622	−	2.19348i
$778$	−5.11669e8	+	2.60584e8i	−1.08655	+	0.553362i
$779$	2.48078e7	−	2.48078e7i	0.0524778	−	0.0524778i
$780$	−17059.9	−	42312.8i	−3.59495e−5	−	8.91637e-5i
$781$	5.81794e7	−	5.81794e7i	0.122128	−	0.122128i
$782$	4.05077e8	−	1.24588e9i	0.847066	−	2.60530i
$783$	1.00790e8	+	1.24724e8i	0.209957	+	0.259814i
$784$	−3.07732e8	−	9.49587e8i	−0.638594	−	1.97055i
$785$		−	1.90546e7i		−	0.0393905i
$786$	−8.97531e8	−	7.90039e7i	−1.84834	−	0.162697i
$787$	1.05679e8	−	1.05679e8i	0.216802	−	0.216802i	−0.590347	−	0.807149i	$-0.701009\pi$
$787$	1.05679e8	−	1.05679e8i	0.216802	−	0.216802i	0.807149	+	0.590347i	$0.201009\pi$
$788$	4.36840e8	−	6.90165e7i	0.892779	−	0.141050i
$789$	3.62269e8	−	5.79315e8i	0.737565	−	1.17946i
$790$	−1.87049e7	+	9.52609e6i	−0.0379380	+	0.0193212i
$791$	−1.40066e8			−0.283011
$792$	−1.65387e8	−	5.43391e8i	−0.332909	−	1.09380i
$793$			841908.i			0.00168828i
$794$	−4.76350e8	+	2.42597e8i	−0.951623	+	0.484646i
$795$	1.64693e7	+	1.02989e7i	0.0327774	+	0.0204970i
$796$	3.76609e8	−	5.17939e8i	0.746709	−	1.02693i
$797$	−6.47482e7	−	6.47482e7i	−0.127895	−	0.127895i	0.640262	−	0.768157i	$-0.278826\pi$
$797$	−6.47482e7	−	6.47482e7i	−0.127895	−	0.127895i	−0.768157	+	0.640262i	$0.778826\pi$
$798$	−5.36037e7	−	4.71838e6i	−0.105484	−	0.00928506i
$799$	−5.33711e8			−1.04632
$800$	5.10700e8	+	490973.i	0.997461	+	0.000958932i
$801$	1.68732e8	+	3.46547e8i	0.328322	+	0.674318i
$802$	−5.61730e6	+	1.72770e7i	−0.0108894	+	0.0334923i
$803$	−2.32548e8	−	2.32548e8i	−0.449124	−	0.449124i
$804$	1.78043e8	−	4.18602e8i	0.342576	−	0.805440i
$805$	5.56520e7	+	5.56520e7i	0.106683	+	0.106683i
$806$	−191732.	+	97645.8i	−0.000366175	+	0.000186487i
$807$	3.16203e8	−	7.28885e7i	0.601652	−	0.138688i
$808$	−2.91248e8	−	4.63014e7i	−0.552114	−	0.0877728i
$809$	4.69344e8			0.886433			0.443216	−	0.896415i	$-0.353837\pi$
$809$	4.69344e8			0.886433			0.443216	+	0.896415i	$0.353837\pi$
$810$	5.15025e6	−	2.62787e7i	0.00969110	−	0.0494481i
$811$	7.80082e7	+	7.80082e7i	0.146244	+	0.146244i	0.776438	−	0.630194i	$-0.217025\pi$
$811$	7.80082e7	+	7.80082e7i	0.146244	+	0.146244i	−0.630194	+	0.776438i	$0.717025\pi$
$812$	3.09592e8	−	4.89125e7i	0.578257	−	0.0913590i
$813$	1.31706e8	−	2.10616e8i	0.245096	−	0.391940i
$814$	−7.53236e8	−	2.44901e8i	−1.39655	−	0.454065i
$815$		−	1.68593e7i		−	0.0311434i
$816$	−2.11711e8	+	8.45140e8i	−0.389649	+	1.55546i
$817$	8.76915e6			0.0160802
$818$	−2.04105e8	+	6.27759e8i	−0.372901	+	1.14692i
$819$	599210.	−	1.73641e6i	0.00109076	−	0.00316083i
$820$	3.37071e7	−	5.32539e6i	0.0611335	−	0.00965850i
$821$	−2.03286e8	+	2.03286e8i	−0.367348	+	0.367348i	−0.866509	−	0.499161i	$-0.833641\pi$
$821$	−2.03286e8	+	2.03286e8i	−0.367348	+	0.367348i	0.499161	+	0.866509i	$0.333641\pi$
$822$	5.19895e8	−	4.35774e8i	0.936053	−	0.784595i
$823$		−	2.41849e8i		−	0.433856i	−0.976188	−	0.216928i	$-0.930396\pi$
$823$		−	2.41849e8i		−	0.433856i	0.976188	−	0.216928i	$-0.0696036\pi$
$824$	−5.78846e8	+	4.20046e8i	−1.03462	+	0.750785i
$825$	−6.24008e8	+	1.43841e8i	−1.11129	+	0.256166i
$826$	3.89687e8	+	7.65167e8i	0.691474	+	1.35774i
$827$	−1.94116e8	+	1.94116e8i	−0.343198	+	0.343198i	−0.857568	−	0.514370i	$-0.828026\pi$
$827$	−1.94116e8	+	1.94116e8i	−0.343198	+	0.343198i	0.514370	+	0.857568i	$0.328026\pi$
$828$	1.69423e8	−	9.54915e8i	0.298456	−	1.68219i
$829$	−1.48583e8	+	1.48583e8i	−0.260798	+	0.260798i	−0.825378	−	0.564580i	$-0.809038\pi$
$829$	−1.48583e8	+	1.48583e8i	−0.260798	+	0.260798i	0.564580	+	0.825378i	$0.309038\pi$
$830$	3.06077e7	+	9.95157e6i	0.0535300	+	0.0174043i
$831$	−2.19772e8	+	5.06600e7i	−0.382974	+	0.0882799i
$832$	497730.	+	979642.i	0.000864219	+	0.00170097i
$833$		−	1.91991e9i		−	3.32159i
$834$	−7.06282e8	−	6.21694e7i	−1.21753	−	0.107171i
$835$	−1.36208e7	+	1.36208e7i	−0.0233961	+	0.0233961i
$836$	−2.37374e7	+	3.26453e7i	−0.0406269	+	0.0558730i
$837$	−1.25588e8	−	1.33288e7i	−0.214176	−	0.0227308i
$838$	4.85378e8	+	9.53061e8i	0.824799	+	1.61953i
$839$	7.04435e8			1.19277			0.596383	−	0.802700i	$-0.296604\pi$
$839$	7.04435e8			1.19277			0.596383	+	0.802700i	$0.296604\pi$
$840$	−3.94708e7	−	3.43750e7i	−0.0665945	−	0.0579968i
$841$		−	5.28450e8i		−	0.888414i
$842$	3.36398e8	+	6.60533e8i	0.563530	+	1.10652i
$843$	4.22042e7	−	6.74899e7i	0.0704486	−	0.112657i
$844$	−7.42620e8	+	1.17327e8i	−1.23521	+	0.195150i
$845$	2.14975e7	+	2.14975e7i	0.0356301	+	0.0356301i
$846$	−3.91298e8	+	5.46466e7i	−0.646245	+	0.0902510i
$847$	3.27170e8			0.538422
$848$	−4.16687e8	−	2.12717e8i	−0.683318	−	0.348830i
$849$	8.87348e8	−	2.04544e8i	1.45001	−	0.334244i
$850$	9.34127e8	+	3.03715e8i	1.52107	+	0.494549i
$851$	−9.56273e8	−	9.56273e8i	−1.55165	−	1.55165i
$852$	−8.66498e7	+	3.49360e7i	−0.140104	+	0.0564877i
$853$	4.92845e8	+	4.92845e8i	0.794078	+	0.794078i	0.982154	−	0.188077i	$-0.0602254\pi$
$853$	4.92845e8	+	4.92845e8i	0.794078	+	0.794078i	−0.188077	+	0.982154i	$0.560225\pi$
$854$	4.38340e8	+	8.60699e8i	0.703780	+	1.38190i
$855$	−1.71091e6	+	833032.i	−0.00273734	+	0.00133280i
$856$	−8.55871e8	−	1.36063e8i	−1.36454	−	0.216929i
$857$	−1.50823e8			−0.239622			−0.119811	−	0.992797i	$-0.538229\pi$
$857$	−1.50823e8			−0.239622			−0.119811	+	0.992797i	$0.538229\pi$
$858$	−885097.	−	1.05595e6i	−0.00140129	−	0.00167180i
$859$	3.63184e8	+	3.63184e8i	0.572990	+	0.572990i	0.932963	−	0.359973i	$-0.117214\pi$
$859$	3.63184e8	+	3.63184e8i	0.572990	+	0.572990i	−0.359973	+	0.932963i	$0.617214\pi$
$860$	6.89868e6	+	5.01624e6i	0.0108460	+	0.00788647i
$861$	1.16495e9	+	7.28491e8i	1.82515	+	1.14134i
$862$	8.12582e7	−	2.49923e8i	0.126866	−	0.390198i
$863$		−	1.31944e8i		−	0.205285i	−0.994718	−	0.102642i	$-0.967270\pi$
$863$		−	1.31944e8i		−	0.205285i	0.994718	−	0.102642i	$-0.0327297\pi$
$864$	−6.86859e7	+	6.41305e8i	−0.106494	+	0.994313i
$865$	−4.83303e7			−0.0746742
$866$	5.66331e7	+	1.84133e7i	0.0872001	+	0.0283516i
$867$	−5.42942e8	+	8.68235e8i	−0.833099	+	1.33223i
$868$	−1.45172e8	+	1.99650e8i	−0.221985	+	0.305289i
$869$	−4.48266e8	+	4.48266e8i	−0.683088	+	0.683088i
$870$	8.49460e6	−	7.12013e6i	0.0128999	−	0.0108126i
$871$		−	1.10346e6i		−	0.00166994i
$872$	5.94537e8	+	9.45169e7i	0.896663	+	0.142548i
$873$	1.45078e8	+	2.97966e8i	0.218052	+	0.447842i
$874$	−6.14119e7	+	3.12761e7i	−0.0919853	+	0.0468466i
$875$	−8.35588e7	+	8.35588e7i	−0.124729	+	0.124729i
$876$	1.39642e8	+	3.46347e8i	0.207732	+	0.515228i
$877$	−5.38226e8	+	5.38226e8i	−0.797931	+	0.797931i	−0.982769	−	0.184838i	$-0.940824\pi$
$877$	−5.38226e8	+	5.38226e8i	−0.797931	+	0.797931i	0.184838	+	0.982769i	$0.440824\pi$
$878$	−1.11295e8	+	3.42307e8i	−0.164434	+	0.505746i
$879$	−4.29751e7	−	1.86433e8i	−0.0632776	−	0.274509i
$880$	−3.73483e7	+	1.21035e7i	−0.0548054	+	0.0177608i
$881$		−	3.06797e8i		−	0.448667i	−0.974512	−	0.224333i	$-0.927980\pi$
$881$		−	3.06797e8i		−	0.448667i	0.974512	−	0.224333i	$-0.0720204\pi$
$882$	−1.96579e8	−	1.40761e9i	−0.286505	−	2.05153i
$883$	9.48731e8	−	9.48731e8i	1.37804	−	1.37804i	0.530106	−	0.847931i	$-0.322152\pi$
$883$	9.48731e8	−	9.48731e8i	1.37804	−	1.37804i	0.847931	−	0.530106i	$-0.177848\pi$
$884$	329814.	+	2.08756e6i	0.000477433	+	0.00302191i
$885$	2.57463e7	+	1.61002e7i	0.0371436	+	0.0232274i
$886$	9.01977e8	−	4.59362e8i	1.29686	−	0.660471i
$887$	−9.51949e8			−1.36409			−0.682044	−	0.731311i	$-0.738909\pi$
$887$	−9.51949e8			−1.36409			−0.682044	+	0.731311i	$0.738909\pi$
$888$	6.78230e8	+	5.90667e8i	0.968586	+	0.843537i
$889$			1.19349e9i			1.69869i
$890$	2.37404e7	−	1.20906e7i	0.0336758	−	0.0171505i
$891$	−9.74734e7	−	8.02842e8i	−0.137801	−	1.13500i
$892$	7.93676e8	+	5.77106e8i	1.11828	+	0.813132i
$893$	1.98528e7	+	1.98528e7i	0.0278784	+	0.0278784i
$894$	−9.02371e7	+	1.02515e9i	−0.126291	+	1.43474i
$895$	717469.			0.00100077
$896$	1.01889e9	+	7.42364e8i	1.41646	+	1.03203i
$897$	−528437.	−	2.29245e6i	−0.000732177	−	0.00317631i
$898$	3.30127e8	−	1.01536e9i	0.455882	−	1.40214i
$899$	−3.69634e7	−	3.69634e7i	−0.0508737	−	0.0508737i
$900$	7.15968e8	+	1.27028e8i	0.982123	+	0.174250i
$901$	−6.36276e8	−	6.36276e8i	−0.869904	−	0.869904i
$902$	9.18368e8	−	4.67710e8i	1.25140	−	0.637319i
$903$	7.71410e7	+	3.34651e8i	0.104766	+	0.454495i
$904$	9.65555e7	−	7.00666e7i	0.130699	−	0.0948431i
$905$	4.85340e7			0.0654788
$906$	−6.61695e7	−	7.89428e7i	−0.0889760	−	0.106152i
$907$	7.31080e7	+	7.31080e7i	0.0979813	+	0.0979813i	0.754398	−	0.656417i	$-0.227929\pi$
$907$	7.31080e7	+	7.31080e7i	0.0979813	+	0.0979813i	−0.656417	+	0.754398i	$0.727929\pi$
$908$	−2.08738e7	−	1.32121e8i	−0.0278833	−	0.176487i
$909$	−3.96925e8	−	1.36973e8i	−0.528466	−	0.182366i
$910$	−120745.	−	39258.1i	−0.000160231	−	5.20961e-5i
$911$			5.68170e8i			0.751490i	0.926723	+	0.375745i	$0.122613\pi$
$911$			5.68170e8i			0.751490i	−0.926723	+	0.375745i	$0.877387\pi$
$912$	3.93124e7	−	2.35621e7i	0.0518257	−	0.0310620i
$913$	9.72011e8			1.27720
$914$	−2.40727e8	+	7.40398e8i	−0.315273	+	0.969676i
$915$	2.89607e7	+	1.81103e7i	0.0378047	+	0.0236408i
$916$	−4.53517e7	−	2.87054e8i	−0.0590075	−	0.373488i
$917$	−1.77305e9	+	1.77305e9i	−2.29940	+	2.29940i
$918$	−5.05931e8	+	1.13266e9i	−0.653979	+	1.46410i
$919$			8.00486e7i			0.103135i	0.998670	+	0.0515676i	$0.0164218\pi$
$919$			8.00486e7i			0.103135i	−0.998670	+	0.0515676i	$0.983578\pi$
$920$	−6.62036e7	−	1.05248e7i	−0.0850194	−	0.0135160i
$921$	−1.04388e8	−	4.52853e8i	−0.133620	−	0.579667i
$922$	−1.83092e8	−	3.59509e8i	−0.233602	−	0.458688i
$923$	−160254.	+	160254.i	−0.000203799	+	0.000203799i
$924$	−1.45463e9	−	6.18698e8i	−1.84390	−	0.784264i
$925$	7.16985e8	−	7.16985e8i	0.905910	−	0.905910i
$926$	7.04302e8	+	2.28991e8i	0.887004	+	0.288394i
$927$	−9.15555e8	+	4.45779e8i	−1.14933	+	0.559604i
$928$	−1.88951e8	+	1.88588e8i	−0.236432	+	0.235978i
$929$		−	1.27627e9i		−	1.59183i	−0.605411	−	0.795913i	$-0.706991\pi$
$929$		−	1.27627e9i		−	1.59183i	0.605411	−	0.795913i	$-0.293009\pi$
$930$	−765437.	+	8.69582e6i	−0.000951613	+	0.0108109i
$931$	−7.14162e7	+	7.14162e7i	−0.0885009	+	0.0885009i
$932$	3.91544e8	+	2.84704e8i	0.483652	+	0.351678i
$933$	6.55748e8	−	1.04863e9i	0.807407	−	1.29115i
$934$	2.76932e8	+	5.43767e8i	0.339885	+	0.667379i
$935$	−7.55122e7			−0.0923810
$936$	455554.	+	1.49676e6i	0.000555536	+	0.00182526i
$937$		−	8.34332e7i		−	0.101419i	−0.998713	−	0.0507096i	$-0.983852\pi$
$937$		−	8.34332e7i		−	0.101419i	0.998713	−	0.0507096i	$-0.0161483\pi$
$938$	−5.74517e8	−	1.12809e9i	−0.696136	−	1.36689i
$939$	3.53943e8	+	2.21335e8i	0.427501	+	0.267333i
$940$	4.26173e6	+	2.69746e7i	0.00513100	+	0.0324767i
$941$	−3.02783e8	−	3.02783e8i	−0.363381	−	0.363381i	0.501675	−	0.865056i	$-0.332717\pi$
$941$	−3.02783e8	−	3.02783e8i	−0.363381	−	0.363381i	−0.865056	+	0.501675i	$0.832717\pi$
$942$	−5.72972e7	+	6.50930e8i	−0.0685458	+	0.778721i
$943$	1.75970e9			2.09847
$944$	−6.51401e8	−	3.32537e8i	−0.774342	−	0.395297i
$945$	−4.68411e7	−	5.79641e7i	−0.0555049	−	0.0686853i
$946$	2.44978e8	+	7.96503e7i	0.289370	+	0.0940837i
$947$	2.28860e8	+	2.28860e8i	0.269475	+	0.269475i	0.828889	−	0.559413i	$-0.188974\pi$
$947$	2.28860e8	+	2.28860e8i	0.269475	+	0.269475i	−0.559413	+	0.828889i	$0.688974\pi$
$948$	6.67628e8	−	2.69178e8i	0.783627	−	0.315947i
$949$	640548.	+	640548.i	0.000749468	+	0.000749468i
$950$	−2.34499e7	−	4.60449e7i	−0.0273508	−	0.0537045i
$951$	1.43364e9	−	3.30471e8i	1.66686	−	0.384230i
$952$	1.42406e9	+	1.96243e9i	1.65051	+	2.27449i
$953$	−1.51596e7			−0.0175150			−0.00875750	−	0.999962i	$-0.502788\pi$
$953$	−1.51596e7			−0.0175150			−0.00875750	+	0.999962i	$0.502788\pi$
$954$	−5.31644e8	−	4.01348e8i	−0.612317	−	0.462249i
$955$	−2.61184e7	−	2.61184e7i	−0.0299873	−	0.0299873i
$956$	−3.11800e8	+	4.28809e8i	−0.356864	+	0.490784i
$957$	1.77484e8	−	2.83820e8i	0.202499	−	0.323823i
$958$	3.69756e8	−	1.13725e9i	0.420551	−	1.29348i
$959$		−	1.88790e9i		−	2.14054i
$960$	4.44053e7	+	3.95173e6i	0.0501904	+	0.00446657i
$961$	−8.46334e8			−0.953612
$962$	2.07477e6	+	674575.i	0.00233048	+	0.000757714i
$963$	−1.16642e9	−	4.02513e8i	−1.30610	−	0.450715i
$964$	−5.04106e8	−	3.66550e8i	−0.562717	−	0.409169i
$965$	2.43455e6	−	2.43455e6i	0.00270917	−	0.00270917i
$966$	−1.73380e9	−	2.06849e9i	−1.92339	−	2.29468i
$967$		−	6.12218e8i		−	0.677060i	−0.940956	−	0.338530i	$-0.890070\pi$
$967$		−	6.12218e8i		−	0.677060i	0.940956	−	0.338530i	$-0.109930\pi$
$968$	−2.25537e8	+	1.63663e8i	−0.248652	+	0.180437i
$969$	8.59002e7	−	1.98010e7i	0.0944111	−	0.0217629i
$970$	2.04124e7	−	1.03957e7i	0.0223655	−	0.0113904i
$971$	−8.25481e8	+	8.25481e8i	−0.901674	+	0.901674i	−0.995581	−	0.0939071i	$-0.970064\pi$
$971$	−8.25481e8	+	8.25481e8i	−0.901674	+	0.901674i	0.0939071	+	0.995581i	$0.470064\pi$
$972$	−2.54959e8	+	8.82228e8i	−0.277633	+	0.960687i
$973$	−1.39524e9	+	1.39524e9i	−1.51465	+	1.51465i
$974$	1.50139e8	−	4.61777e8i	0.162486	−	0.499753i
$975$	1.71882e6	−	396207.i	0.00185445	−	0.000427473i
$976$	−7.32729e8	−	3.74054e8i	−0.788123	−	0.402333i
$977$			1.52786e8i			0.163832i	0.996639	+	0.0819161i	$0.0261039\pi$
$977$			1.52786e8i			0.163832i	−0.996639	+	0.0819161i	$0.973896\pi$
$978$	−5.06957e7	+	5.75934e8i	−0.0541944	+	0.615681i
$979$	5.68943e8	−	5.68943e8i	0.606347	−	0.606347i
$980$	−9.70354e7	+	1.53306e7i	−0.103098	+	0.0162885i
$981$	8.10260e8	+	2.79609e8i	0.858258	+	0.296172i
$982$	−5.82882e8	+	2.96852e8i	−0.615526	+	0.313477i
$983$	2.50707e8			0.263941			0.131970	−	0.991254i	$-0.457870\pi$
$983$	2.50707e8			0.263941			0.131970	+	0.991254i	$0.457870\pi$
$984$	−1.16749e9	+	8.05650e7i	−1.22537	+	0.0845593i
$985$		−	4.35252e7i		−	0.0455440i
$986$	−4.57543e8	+	2.33019e8i	−0.477311	+	0.243086i
$987$	−5.82987e8	+	9.32271e8i	−0.606327	+	0.969596i
$988$	65384.1	−	89920.7i	6.77955e−5	−	9.32371e-5i
$989$	3.11013e8	+	3.11013e8i	0.321506	+	0.321506i
$990$	−5.53630e7	+	7.73169e6i	−0.0570577	+	0.00796836i
$991$	2.52035e7			0.0258964			0.0129482	−	0.999916i	$-0.495878\pi$
$991$	2.52035e7			0.0258964			0.0129482	+	0.999916i	$0.495878\pi$
$992$	202130.	−	2.10251e8i	0.000207060	−	0.215379i
$993$	−1.42235e9	+	3.27869e8i	−1.45264	+	0.334852i
$994$	−8.03944e7	+	2.47267e8i	−0.0818590	+	0.251771i
$995$	−4.45647e7	−	4.45647e7i	−0.0452399	−	0.0452399i
$996$	−1.01567e9	−	4.31995e8i	−1.02796	−	0.437221i
$997$	4.28044e8	+	4.28044e8i	0.431920	+	0.431920i	0.889281	−	0.457361i	$-0.151205\pi$
$997$	4.28044e8	+	4.28044e8i	0.431920	+	0.431920i	−0.457361	+	0.889281i	$0.651205\pi$
$998$	1.09988e9	−	5.60151e8i	1.10651	−	0.563525i
$999$	8.04873e8	+	9.96001e8i	0.807292	+	0.998995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.i.a.5.6	✓	92
3.2	odd	2	inner	48.7.i.a.5.41	yes	92
4.3	odd	2		192.7.i.a.113.16		92
12.11	even	2		192.7.i.a.113.8		92
16.3	odd	4		192.7.i.a.17.8		92
16.13	even	4	inner	48.7.i.a.29.41	yes	92
48.29	odd	4	inner	48.7.i.a.29.6	yes	92
48.35	even	4		192.7.i.a.17.16		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.6	✓	92	1.1	even	1	trivial
48.7.i.a.5.41	yes	92	3.2	odd	2	inner
48.7.i.a.29.6	yes	92	48.29	odd	4	inner
48.7.i.a.29.41	yes	92	16.13	even	4	inner
192.7.i.a.17.8		92	16.3	odd	4
192.7.i.a.17.16		92	48.35	even	4
192.7.i.a.113.8		92	12.11	even	2
192.7.i.a.113.16		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)

\(f(q)\)	\(=\)	\(q+(-7.60798 - 2.47360i) q^{2} +(14.3156 - 22.8925i) q^{3} +(51.7626 + 37.6382i) q^{4} +(4.45378 - 4.45378i) q^{5} +(-165.539 + 138.754i) q^{6} +601.125i q^{7} +(-300.707 - 414.390i) q^{8} +(-319.129 - 655.437i) q^{9} +O(q^{10})\)	\(q+(-7.60798 - 2.47360i) q^{2} +(14.3156 - 22.8925i) q^{3} +(51.7626 + 37.6382i) q^{4} +(4.45378 - 4.45378i) q^{5} +(-165.539 + 138.754i) q^{6} +601.125i q^{7} +(-300.707 - 414.390i) q^{8} +(-319.129 - 655.437i) q^{9} +(-44.9011 + 22.8674i) q^{10} +(-1076.06 + 1076.06i) q^{11} +(1602.64 - 646.162i) q^{12} +(2.96399 - 2.96399i) q^{13} +(1486.94 - 4573.35i) q^{14} +(-38.1996 - 165.716i) q^{15} +(1262.74 + 3896.50i) q^{16} +7878.09i q^{17} +(806.637 + 5775.95i) q^{18} +(293.047 - 293.047i) q^{19} +(398.171 - 62.9072i) q^{20} +(13761.2 + 8605.45i) q^{21} +(10848.4 - 5524.91i) q^{22} +20786.8 q^{23} +(-13791.2 + 951.691i) q^{24} +15585.3i q^{25} +(-29.8817 + 15.2182i) q^{26} +(-19573.1 - 2077.31i) q^{27} +(-22625.2 + 31115.8i) q^{28} +(-5760.80 - 5760.80i) q^{29} +(-119.294 + 1355.26i) q^{30} +6416.37 q^{31} +(31.5023 - 32768.0i) q^{32} +(9229.27 + 40038.2i) q^{33} +(19487.2 - 59936.3i) q^{34} +(2677.28 + 2677.28i) q^{35} +(8150.50 - 45938.6i) q^{36} +(-46003.9 - 46003.9i) q^{37} +(-2954.37 + 1504.61i) q^{38} +(-25.4218 - 110.284i) q^{39} +(-3184.89 - 506.320i) q^{40} +84654.6 q^{41} +(-83408.7 - 99509.8i) q^{42} +(14962.0 + 14962.0i) q^{43} +(-96200.9 + 15198.8i) q^{44} +(-4340.50 - 1497.84i) q^{45} +(-158145. - 51418.2i) q^{46} +67746.2i q^{47} +(107277. + 26873.5i) q^{48} -243703. q^{49} +(38551.8 - 118573. i) q^{50} +(180349. + 112779. i) q^{51} +(264.983 - 41.8647i) q^{52} +(-80765.3 + 80765.3i) q^{53} +(143773. + 64220.1i) q^{54} +9585.10i q^{55} +(249100. - 180763. i) q^{56} +(-2513.43 - 10903.7i) q^{57} +(29578.1 + 58078.0i) q^{58} +(-126259. + 126259. i) q^{59} +(4259.95 - 10015.7i) q^{60} +(-142023. + 142023. i) q^{61} +(-48815.6 - 15871.5i) q^{62} +(394000. - 191836. i) q^{63} +(-81294.5 + 249220. i) q^{64} -26.4019i q^{65} +(28822.3 - 327439. i) q^{66} +(186144. - 186144. i) q^{67} +(-296517. + 407790. i) q^{68} +(297575. - 475861. i) q^{69} +(-13746.2 - 26991.2i) q^{70} -54066.9 q^{71} +(-175642. + 329338. i) q^{72} +216110. i q^{73} +(236201. + 463791. i) q^{74} +(356786. + 223113. i) q^{75} +(26198.6 - 4139.13i) q^{76} +(-646849. - 646849. i) q^{77} +(-79.3904 + 901.923i) q^{78} +416580. q^{79} +(22978.1 + 11730.2i) q^{80} +(-327754. + 418338. i) q^{81} +(-644050. - 209402. i) q^{82} +(-451651. - 451651. i) q^{83} +(388424. + 963388. i) q^{84} +(35087.3 + 35087.3i) q^{85} +(-76820.7 - 150841. i) q^{86} +(-214348. + 49409.7i) q^{87} +(769490. + 122330. i) q^{88} -528727. q^{89} +(29317.4 + 22132.2i) q^{90} +(1781.73 + 1781.73i) q^{91} +(1.07598e6 + 782376. i) q^{92} +(91853.9 - 146886. i) q^{93} +(167577. - 515412. i) q^{94} -2610.33i q^{95} +(-749689. - 469814. i) q^{96} -454607. q^{97} +(1.85408e6 + 602822. i) q^{98} +(1.04869e6 + 361889. 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

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