LMFDB - Embedded newform 48.7.i.a.5.11

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			5.11
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.62988 - 5.68370i) q^{2} +(26.3911 - 5.70179i) q^{3} +(-0.608985 + 63.9971i) q^{4} +(-89.3741 + 89.3741i) q^{5} +(-180.986 - 117.899i) q^{6} -331.991i q^{7} +(367.169 - 356.834i) q^{8} +(663.979 - 300.953i) q^{9} +O(q^{10})$	\(q+(-5.62988 - 5.68370i) q^{2} +(26.3911 - 5.70179i) q^{3} +(-0.608985 + 63.9971i) q^{4} +(-89.3741 + 89.3741i) q^{5} +(-180.986 - 117.899i) q^{6} -331.991i q^{7} +(367.169 - 356.834i) q^{8} +(663.979 - 300.953i) q^{9} +(1011.14 + 4.81082i) q^{10} +(-300.455 + 300.455i) q^{11} +(348.827 + 1692.43i) q^{12} +(2557.18 - 2557.18i) q^{13} +(-1886.94 + 1869.07i) q^{14} +(-1849.09 + 2868.27i) q^{15} +(-4095.26 - 77.9466i) q^{16} -6127.72i q^{17} +(-5448.65 - 2079.53i) q^{18} +(5539.28 - 5539.28i) q^{19} +(-5665.26 - 5774.11i) q^{20} +(-1892.95 - 8761.61i) q^{21} +(3399.23 + 16.1729i) q^{22} -5696.38 q^{23} +(7655.40 - 11510.8i) q^{24} -350.476i q^{25} +(-28930.9 - 137.648i) q^{26} +(15807.2 - 11728.4i) q^{27} +(21246.5 + 202.178i) q^{28} +(-13917.5 - 13917.5i) q^{29} +(26712.6 - 5638.36i) q^{30} -35368.3 q^{31} +(22612.8 + 23715.1i) q^{32} +(-6216.21 + 9642.48i) q^{33} +(-34828.2 + 34498.3i) q^{34} +(29671.4 + 29671.4i) q^{35} +(18855.8 + 42676.0i) q^{36} +(22170.7 + 22170.7i) q^{37} +(-62669.1 - 298.167i) q^{38} +(52906.3 - 82067.4i) q^{39} +(-923.649 + 64707.2i) q^{40} +112504. q^{41} +(-39141.4 + 60085.7i) q^{42} +(20479.5 + 20479.5i) q^{43} +(-19045.3 - 19411.2i) q^{44} +(-32445.1 + 86240.0i) q^{45} +(32069.9 + 32376.5i) q^{46} -45992.4i q^{47} +(-108523. + 21293.2i) q^{48} +7430.75 q^{49} +(-1992.00 + 1973.13i) q^{50} +(-34939.0 - 161717. i) q^{51} +(162095. + 165210. i) q^{52} +(94308.3 - 94308.3i) q^{53} +(-155653. - 23814.0i) q^{54} -53705.9i q^{55} +(-118466. - 121897. i) q^{56} +(114604. - 177771. i) q^{57} +(-749.151 + 157457. i) q^{58} +(-65410.2 + 65410.2i) q^{59} +(-182435. - 120083. i) q^{60} +(-299720. + 299720. i) q^{61} +(199119. + 201023. i) q^{62} +(-99913.8 - 220435. i) q^{63} +(7482.31 - 262037. i) q^{64} +457092. i q^{65} +(89801.5 - 18954.9i) q^{66} +(279791. - 279791. i) q^{67} +(392156. + 3731.69i) q^{68} +(-150334. + 32479.6i) q^{69} +(1597.15 - 335690. i) q^{70} -581529. q^{71} +(136402. - 347431. i) q^{72} +421050. i q^{73} +(1193.40 - 250830. i) q^{74} +(-1998.34 - 9249.44i) q^{75} +(351124. + 357871. i) q^{76} +(99748.6 + 99748.6i) q^{77} +(-764303. + 161325. i) q^{78} +634651. q^{79} +(372977. - 359044. i) q^{80} +(350295. - 399653. i) q^{81} +(-633381. - 639437. i) q^{82} +(-52444.2 - 52444.2i) q^{83} +(561871. - 115807. i) q^{84} +(547660. + 547660. i) q^{85} +(1102.37 - 231696. i) q^{86} +(-446654. - 287944. i) q^{87} +(-3105.10 + 217531. i) q^{88} -499550. q^{89} +(672825. - 301112. i) q^{90} +(-848963. - 848963. i) q^{91} +(3469.01 - 364552. i) q^{92} +(-933408. + 201663. i) q^{93} +(-261407. + 258931. i) q^{94} +990136. i q^{95} +(731994. + 496933. i) q^{96} -389343. q^{97} +(-41834.2 - 42234.2i) q^{98} +(-109073. + 289919. 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 $

$2$	−5.62988	−	5.68370i	−0.703735	−	0.710463i
$2$	−5.62988	−	5.68370i	−0.703735	−	0.710463i
$3$	26.3911	−	5.70179i	0.977448	−	0.211178i
$3$	26.3911	−	5.70179i	0.977448	−	0.211178i
$4$	−0.608985	+	63.9971i	−0.00951540	+	0.999955i
$5$	−89.3741	+	89.3741i	−0.714993	+	0.714993i	−0.967575	−	0.252582i	$-0.918720\pi$
$5$	−89.3741	+	89.3741i	−0.714993	+	0.714993i	0.252582	+	0.967575i	$0.418720\pi$
$6$	−180.986	−	117.899i	−0.837898	−	0.545828i
$7$		−	331.991i		−	0.967905i	−0.875094	−	0.483952i	$-0.839201\pi$
$7$		−	331.991i		−	0.967905i	0.875094	−	0.483952i	$-0.160799\pi$
$8$	367.169	−	356.834i	0.717127	−	0.696942i
$9$	663.979	−	300.953i	0.910808	−	0.412830i
$10$	1011.14	+	4.81082i	1.01114	+	0.00481082i
$11$	−300.455	+	300.455i	−0.225737	+	0.225737i	−0.810909	−	0.585172i	$-0.801027\pi$
$11$	−300.455	+	300.455i	−0.225737	+	0.225737i	0.585172	+	0.810909i	$0.301027\pi$
$12$	348.827	+	1692.43i	0.201867	+	0.979413i
$13$	2557.18	−	2557.18i	1.16394	−	1.16394i	0.180338	−	0.983605i	$-0.442281\pi$
$13$	2557.18	−	2557.18i	1.16394	−	1.16394i	0.983605	−	0.180338i	$-0.0577193\pi$
$14$	−1886.94	+	1869.07i	−0.687661	+	0.681148i
$15$	−1849.09	+	2868.27i	−0.547878	+	0.849859i
$16$	−4095.26	−	77.9466i	−0.999819	−	0.0190299i
$17$		−	6127.72i		−	1.24725i	−0.781725	−	0.623623i	$-0.785660\pi$
$17$		−	6127.72i		−	1.24725i	0.781725	−	0.623623i	$-0.214340\pi$
$18$	−5448.65	−	2079.53i	−0.934268	−	0.356573i
$19$	5539.28	−	5539.28i	0.807593	−	0.807593i	−0.176676	−	0.984269i	$-0.556535\pi$
$19$	5539.28	−	5539.28i	0.807593	−	0.807593i	0.984269	+	0.176676i	$0.0565346\pi$
$20$	−5665.26	−	5774.11i	−0.708157	−	0.721764i
$21$	−1892.95	−	8761.61i	−0.204400	−	0.946076i
$22$	3399.23	+	16.1729i	0.319236	+	0.00151886i
$23$	−5696.38			−0.468183			−0.234091	−	0.972215i	$-0.575211\pi$
$23$	−5696.38			−0.468183			−0.234091	+	0.972215i	$0.575211\pi$
$24$	7655.40	−	11510.8i	0.553776	−	0.832666i
$25$		−	350.476i		−	0.0224304i
$26$	−28930.9	−	137.648i	−1.64605	−	0.00783157i
$27$	15807.2	−	11728.4i	0.803087	−	0.595862i
$28$	21246.5	+	202.178i	0.967861	+	0.00921000i
$29$	−13917.5	−	13917.5i	−0.570648	−	0.570648i	0.361661	−	0.932310i	$-0.382210\pi$
$29$	−13917.5	−	13917.5i	−0.570648	−	0.570648i	−0.932310	+	0.361661i	$0.882210\pi$
$30$	26712.6	−	5638.36i	0.989354	−	0.208828i
$31$	−35368.3			−1.18721			−0.593607	−	0.804755i	$-0.702297\pi$
$31$	−35368.3			−1.18721			−0.593607	+	0.804755i	$0.702297\pi$
$32$	22612.8	+	23715.1i	0.690087	+	0.723726i
$33$	−6216.21	+	9642.48i	−0.172975	+	0.268316i
$34$	−34828.2	+	34498.3i	−0.886123	+	0.877731i
$35$	29671.4	+	29671.4i	0.692045	+	0.692045i
$36$	18855.8	+	42676.0i	0.404145	+	0.914695i
$37$	22170.7	+	22170.7i	0.437697	+	0.437697i	0.891236	−	0.453539i	$-0.149839\pi$
$37$	22170.7	+	22170.7i	0.437697	+	0.437697i	−0.453539	+	0.891236i	$0.649839\pi$
$38$	−62669.1	−	298.167i	−1.14210	−	0.00543387i
$39$	52906.3	−	82067.4i	0.891895	−	1.38349i
$40$	−923.649	+	64707.2i	−0.0144320	+	1.01105i
$41$	112504.			1.63236			0.816178	−	0.577801i	$-0.196089\pi$
$41$	112504.			1.63236			0.816178	+	0.577801i	$0.196089\pi$
$42$	−39141.4	+	60085.7i	−0.528309	+	0.811005i
$43$	20479.5	+	20479.5i	0.257581	+	0.257581i	0.824070	−	0.566489i	$-0.191699\pi$
$43$	20479.5	+	20479.5i	0.257581	+	0.257581i	−0.566489	+	0.824070i	$0.691699\pi$
$44$	−19045.3	−	19411.2i	−0.223578	−	0.227874i
$45$	−32445.1	+	86240.0i	−0.356051	+	0.946392i
$46$	32069.9	+	32376.5i	0.329476	+	0.332626i
$47$		−	45992.4i		−	0.442988i	−0.975162	−	0.221494i	$-0.928907\pi$
$47$		−	45992.4i		−	0.442988i	0.975162	−	0.221494i	$-0.0710934\pi$
$48$	−108523.	+	21293.2i	−0.981289	+	0.192539i
$49$	7430.75			0.0631603
$50$	−1992.00	+	1973.13i	−0.0159360	+	0.0157851i
$51$	−34939.0	−	161717.i	−0.263390	−	1.21912i
$52$	162095.	+	165210.i	1.15281	+	1.17497i
$53$	94308.3	−	94308.3i	0.633465	−	0.633465i	−0.315471	−	0.948935i	$-0.602162\pi$
$53$	94308.3	−	94308.3i	0.633465	−	0.633465i	0.948935	+	0.315471i	$0.102162\pi$
$54$	−155653.	−	23814.0i	−0.988498	−	0.151235i
$55$		−	53705.9i		−	0.322800i
$56$	−118466.	−	121897.i	−0.674574	−	0.694111i
$57$	114604.	−	177771.i	0.618834	−	0.959925i
$58$	−749.151	+	157457.i	−0.00383959	+	0.807009i
$59$	−65410.2	+	65410.2i	−0.318485	+	0.318485i	−0.848185	−	0.529700i	$-0.822305\pi$
$59$	−65410.2	+	65410.2i	−0.318485	+	0.318485i	0.529700	+	0.848185i	$0.322305\pi$
$60$	−182435.	−	120083.i	−0.844607	−	0.555940i
$61$	−299720.	+	299720.i	−1.32046	+	1.32046i	−0.407066	+	0.913399i	$0.633448\pi$
$61$	−299720.	+	299720.i	−1.32046	+	1.32046i	−0.913399	+	0.407066i	$0.866552\pi$
$62$	199119.	+	201023.i	0.835484	+	0.843472i
$63$	−99913.8	−	220435.i	−0.399580	−	0.881575i
$64$	7482.31	−	262037.i	0.0285427	−	0.999593i
$65$			457092.i			1.66442i
$66$	89801.5	−	18954.9i	0.312357	−	0.0659309i
$67$	279791.	−	279791.i	0.930272	−	0.930272i	−0.0674506	−	0.997723i	$-0.521487\pi$
$67$	279791.	−	279791.i	0.930272	−	0.930272i	0.997723	+	0.0674506i	$0.0214865\pi$
$68$	392156.	+	3731.69i	1.24719	+	0.0118680i
$69$	−150334.	+	32479.6i	−0.457624	+	0.0988696i
$70$	1597.15	−	335690.i	0.00465641	−	0.978689i
$71$	−581529.			−1.62479			−0.812393	−	0.583110i	$-0.801835\pi$
$71$	−581529.			−1.62479			−0.812393	+	0.583110i	$0.801835\pi$
$72$	136402.	−	347431.i	0.365446	−	0.930832i
$73$			421050.i			1.08234i	0.840912	+	0.541172i	$0.182019\pi$
$73$			421050.i			1.08234i	−0.840912	+	0.541172i	$0.817981\pi$
$74$	1193.40	−	250830.i	0.00294504	−	0.618991i
$75$	−1998.34	−	9249.44i	−0.00473681	−	0.0219246i
$76$	351124.	+	357871.i	0.799871	+	0.815241i
$77$	99748.6	+	99748.6i	0.218492	+	0.218492i
$78$	−764303.	+	161325.i	−1.61058	+	0.339953i
$79$	634651.			1.28722			0.643611	−	0.765353i	$-0.277435\pi$
$79$	634651.			1.28722			0.643611	+	0.765353i	$0.277435\pi$
$80$	372977.	−	359044.i	0.728470	−	0.701257i
$81$	350295.	−	399653.i	0.659143	−	0.752018i
$82$	−633381.	−	639437.i	−1.14875	−	1.15973i
$83$	−52444.2	−	52444.2i	−0.0917199	−	0.0917199i	0.659758	−	0.751478i	$-0.270659\pi$
$83$	−52444.2	−	52444.2i	−0.0917199	−	0.0917199i	−0.751478	+	0.659758i	$0.770659\pi$
$84$	561871.	−	115807.i	0.947978	−	0.195388i
$85$	547660.	+	547660.i	0.891773	+	0.891773i
$86$	1102.37	−	231696.i	0.00173313	−	0.364270i
$87$	−446654.	−	287944.i	−0.678287	−	0.437271i
$88$	−3105.10	+	217531.i	−0.00455645	+	0.319207i
$89$	−499550.			−0.708613			−0.354306	−	0.935129i	$-0.615283\pi$
$89$	−499550.			−0.708613			−0.354306	+	0.935129i	$0.615283\pi$
$90$	672825.	−	301112.i	0.922942	−	0.413048i
$91$	−848963.	−	848963.i	−1.12659	−	1.12659i
$92$	3469.01	−	364552.i	0.00445494	−	0.468161i
$93$	−933408.	+	201663.i	−1.16044	+	0.250713i
$94$	−261407.	+	258931.i	−0.314727	+	0.311746i
$95$			990136.i			1.15485i
$96$	731994.	+	496933.i	0.827359	+	0.561674i
$97$	−389343.			−0.426596			−0.213298	−	0.976987i	$-0.568421\pi$
$97$	−389343.			−0.426596			−0.213298	+	0.976987i	$0.568421\pi$
$98$	−41834.2	−	42234.2i	−0.0444481	−	0.0448731i
$99$	−109073.	+	289919.i	−0.112412	+	0.298794i
$100$	22429.4	+	213.435i	0.0224294	+	0.000213435i
$101$	−268382.	+	268382.i	−0.260489	+	0.260489i	−0.825253	−	0.564764i	$-0.808967\pi$
$101$	−268382.	+	268382.i	−0.260489	+	0.260489i	0.564764	+	0.825253i	$0.308967\pi$
$102$	−722451.	+	1.10903e6i	−0.680782	+	1.04506i
$103$			861510.i			0.788404i	0.919024	+	0.394202i	$0.128979\pi$
$103$			861510.i			0.788404i	−0.919024	+	0.394202i	$0.871021\pi$
$104$	26427.5	−	1.85141e6i	0.0234940	−	1.64590i
$105$	952242.	+	613881.i	0.822583	+	0.530294i
$106$	−1.06696e6	−	5076.41i	−0.895844	−	0.00426225i
$107$	325805.	−	325805.i	0.265954	−	0.265954i	−0.561514	−	0.827468i	$-0.689781\pi$
$107$	325805.	−	325805.i	0.265954	−	0.265954i	0.827468	+	0.561514i	$0.189781\pi$
$108$	740954.	+	1.01875e6i	0.588193	+	0.808720i
$109$	437591.	−	437591.i	0.337901	−	0.337901i	−0.517676	−	0.855577i	$-0.673203\pi$
$109$	437591.	−	437591.i	0.337901	−	0.337901i	0.855577	+	0.517676i	$0.173203\pi$
$110$	−305248.	+	302358.i	−0.229338	+	0.227166i
$111$	711521.	+	458696.i	0.520258	+	0.335394i
$112$	−25877.6	+	1.35959e6i	−0.0184192	+	0.967730i
$113$			2.44787e6i			1.69650i	0.529597	+	0.848249i	$0.322343\pi$
$113$			2.44787e6i			1.69650i	−0.529597	+	0.848249i	$0.677657\pi$
$114$	−1.65560e6	+	349457.i	−1.11749	+	0.235874i
$115$	509109.	−	509109.i	0.334747	−	0.334747i
$116$	899158.	−	882207.i	0.576052	−	0.565192i
$117$	928324.	−	2.46751e6i	0.579618	−	1.54064i
$118$	740024.	+	3520.89i	0.450401	+	0.00214292i
$119$	−2.03435e6			−1.20722
$120$	344571.	+	1.71296e6i	0.199405	+	0.991296i
$121$			1.59101e6i			0.898086i
$122$	3.39091e6	+	16133.3i	1.86740	+	0.00888472i
$123$	2.96909e6	−	641472.i	1.59554	−	0.344717i
$124$	21538.8	−	2.26347e6i	0.0112968	−	1.18716i
$125$	−1.36515e6	−	1.36515e6i	−0.698956	−	0.698956i
$126$	−690387.	+	1.80890e6i	−0.345128	+	0.904282i
$127$	−400020.			−0.195286			−0.0976428	−	0.995222i	$-0.531130\pi$
$127$	−400020.			−0.195286			−0.0976428	+	0.995222i	$0.531130\pi$
$128$	−1.53147e6	+	1.43271e6i	−0.730260	+	0.683169i
$129$	657246.	+	423706.i	0.306167	+	0.197377i
$130$	2.59798e6	−	2.57337e6i	1.18251	−	1.17131i
$131$	463991.	+	463991.i	0.206393	+	0.206393i	0.802732	−	0.596339i	$-0.203379\pi$
$131$	463991.	+	463991.i	0.206393	+	0.206393i	−0.596339	+	0.802732i	$0.703379\pi$
$132$	−613305.	−	403692.i	−0.266658	−	0.175521i
$133$	−1.83899e6	−	1.83899e6i	−0.781673	−	0.781673i
$134$	−3.16544e6	−	15060.6i	−1.31559	−	0.00625931i
$135$	−364540.	+	2.46096e6i	−0.148164	+	1.00024i
$136$	−2.18658e6	−	2.24991e6i	−0.869259	−	0.894434i
$137$	2.87001e6			1.11615			0.558074	−	0.829791i	$-0.311541\pi$
$137$	2.87001e6			1.11615			0.558074	+	0.829791i	$0.311541\pi$
$138$	1.03096e6	+	671596.i	0.392289	+	0.255547i
$139$	−3.68867e6	−	3.68867e6i	−1.37349	−	1.37349i	−0.855212	−	0.518278i	$-0.826573\pi$
$139$	−3.68867e6	−	3.68867e6i	−1.37349	−	1.37349i	−0.518278	−	0.855212i	$-0.673427\pi$
$140$	−1.91696e6	+	1.88082e6i	−0.698599	+	0.685429i
$141$	−262239.	−	1.21379e6i	−0.0935492	−	0.432998i
$142$	3.27393e6	+	3.30524e6i	1.14342	+	1.15435i
$143$			1.53664e6i			0.525489i
$144$	−2.74262e6	+	1.18073e6i	−0.918499	+	0.395423i
$145$	2.48774e6			0.816019
$146$	2.39313e6	−	2.37046e6i	0.768966	−	0.761683i
$147$	196106.	−	42368.6i	0.0617359	−	0.0133380i
$148$	−1.43236e6	+	1.40536e6i	−0.441842	+	0.433513i
$149$	−476071.	+	476071.i	−0.143917	+	0.143917i	−0.775394	−	0.631477i	$-0.782449\pi$
$149$	−476071.	+	476071.i	−0.143917	+	0.143917i	0.631477	+	0.775394i	$0.282449\pi$
$150$	−41320.6	+	63431.2i	−0.0122432	+	0.0187944i
$151$		−	1.34355e6i		−	0.390232i	−0.980780	−	0.195116i	$-0.937492\pi$
$151$		−	1.34355e6i		−	0.390232i	0.980780	−	0.195116i	$-0.0625084\pi$
$152$	57246.4	−	4.01046e6i	0.0163011	−	1.14199i
$153$	−1.84416e6	−	4.06868e6i	−0.514901	−	1.13600i
$154$	5369.25	−	1.12851e6i	0.00147012	−	0.308990i
$155$	3.16101e6	−	3.16101e6i	0.848850	−	0.848850i
$156$	5.21985e6	+	3.43583e6i	1.37494	+	0.905019i
$157$	−1.16602e6	+	1.16602e6i	−0.301304	+	0.301304i	−0.841524	−	0.540220i	$-0.818341\pi$
$157$	−1.16602e6	+	1.16602e6i	−0.301304	+	0.301304i	0.540220	+	0.841524i	$0.318341\pi$
$158$	−3.57301e6	−	3.60717e6i	−0.905863	−	0.914524i
$159$	1.95117e6	−	3.02663e6i	0.485405	−	0.752952i
$160$	−4.14051e6	−	98516.6i	−1.01087	−	0.0240519i
$161$			1.89115e6i			0.453156i
$162$	−4.24363e6	+	259022.i	−0.998142	+	0.0609244i
$163$	−77624.3	+	77624.3i	−0.0179240	+	0.0179240i	−0.716012	−	0.698088i	$-0.754034\pi$
$163$	−77624.3	+	77624.3i	−0.0179240	+	0.0179240i	0.698088	+	0.716012i	$0.254034\pi$
$164$	−68513.1	+	7.19991e6i	−0.0155325	+	1.63228i
$165$	−306220.	−	1.41736e6i	−0.0681682	−	0.315520i
$166$	−2822.96	+	593332.i	−0.000617135	+	0.129710i
$167$	2.32195e6			0.498545			0.249272	−	0.968433i	$-0.419809\pi$
$167$	2.32195e6			0.498545			0.249272	+	0.968433i	$0.419809\pi$
$168$	−3.82148e6	−	2.54153e6i	−0.805941	−	0.536002i
$169$		−	8.25156e6i		−	1.70953i
$170$	29479.3	−	6.19600e6i	0.00600027	−	1.26114i
$171$	2.01090e6	−	5.34503e6i	0.402163	−	1.06896i
$172$	−1.32310e6	+	1.29816e6i	−0.260020	+	0.255118i
$173$	−1.93188e6	−	1.93188e6i	−0.373114	−	0.373114i	0.495496	−	0.868610i	$-0.334986\pi$
$173$	−1.93188e6	−	1.93188e6i	−0.373114	−	0.373114i	−0.868610	+	0.495496i	$0.834986\pi$
$174$	878018.	+	4.15974e6i	0.166669	+	0.789620i
$175$	−116355.			−0.0217105
$176$	1.25386e6	−	1.20702e6i	0.229991	−	0.221400i
$177$	−1.35329e6	+	2.09920e6i	−0.244046	+	0.378560i
$178$	2.81240e6	+	2.83929e6i	0.498675	+	0.503443i
$179$	4.24932e6	+	4.24932e6i	0.740901	+	0.740901i	0.972751	−	0.231850i	$-0.0744779\pi$
$179$	4.24932e6	+	4.24932e6i	0.740901	+	0.740901i	−0.231850	+	0.972751i	$0.574478\pi$
$180$	−5.49935e6	−	2.12891e6i	−0.942961	−	0.365040i
$181$	2.84268e6	+	2.84268e6i	0.479394	+	0.479394i	0.904938	−	0.425544i	$-0.139917\pi$
$181$	2.84268e6	+	2.84268e6i	0.479394	+	0.479394i	−0.425544	+	0.904938i	$0.639917\pi$
$182$	−45697.8	+	9.60481e6i	−0.00758021	+	1.59322i
$183$	−6.20100e6	+	9.61889e6i	−1.01183	+	1.56954i
$184$	−2.09153e6	+	2.03266e6i	−0.335746	+	0.326296i
$185$	−3.96297e6			−0.625901
$186$	6.40116e6	+	4.16988e6i	0.994764	+	0.648014i
$187$	1.84111e6	+	1.84111e6i	0.281549	+	0.281549i
$188$	2.94338e6	+	28008.7i	0.442968	+	0.00421521i
$189$	−3.89371e6	−	5.24784e6i	−0.576738	−	0.777312i
$190$	5.62764e6	−	5.57435e6i	0.820476	−	0.812705i
$191$			7.21585e6i			1.03559i	0.855505	+	0.517794i	$0.173247\pi$
$191$			7.21585e6i			1.03559i	−0.855505	+	0.517794i	$0.826753\pi$
$192$	−1.29662e6	−	6.95811e6i	−0.183192	−	0.983077i
$193$	1.27711e7			1.77646			0.888231	−	0.459398i	$-0.151935\pi$
$193$	1.27711e7			1.77646			0.888231	+	0.459398i	$0.151935\pi$
$194$	2.19195e6	+	2.21291e6i	0.300210	+	0.303081i
$195$	2.60624e6	+	1.20632e7i	0.351489	+	1.62689i
$196$	−4525.22	+	475547.i	−0.000600996	+	0.0631575i
$197$	6.40039e6	−	6.40039e6i	0.837159	−	0.837159i	−0.151325	−	0.988484i	$-0.548354\pi$
$197$	6.40039e6	−	6.40039e6i	0.837159	−	0.837159i	0.988484	+	0.151325i	$0.0483541\pi$
$198$	2.26188e6	−	1.01227e6i	0.291390	−	0.130407i
$199$			7.34066e6i			0.931485i	0.884920	+	0.465743i	$0.154213\pi$
$199$			7.34066e6i			0.931485i	−0.884920	+	0.465743i	$0.845787\pi$
$200$	−125062.	−	128684.i	−0.0156327	−	0.0160855i
$201$	5.78869e6	−	8.97931e6i	0.712840	−	1.10574i
$202$	3.03636e6	+	14446.4i	0.368382	+	0.00175269i
$203$	−4.62050e6	+	4.62050e6i	−0.552333	+	0.552333i
$204$	1.03707e7	−	2.13751e6i	1.22157	−	0.251778i
$205$	−1.00549e7	+	1.00549e7i	−1.16712	+	1.16712i
$206$	4.89657e6	−	4.85019e6i	0.560132	−	0.554827i
$207$	−3.78227e6	+	1.71434e6i	−0.426424	+	0.193280i
$208$	−1.06716e7	+	1.02730e7i	−1.18588	+	1.14158i
$209$			3.32861e6i			0.364606i
$210$	−1.87189e6	−	8.86834e6i	−0.202126	−	0.957600i
$211$	−994369.	+	994369.i	−0.105852	+	0.105852i	−0.758049	−	0.652197i	$-0.773847\pi$
$211$	−994369.	+	994369.i	−0.105852	+	0.105852i	0.652197	+	0.758049i	$0.273847\pi$
$212$	5.97803e6	+	6.09289e6i	0.627408	+	0.639464i
$213$	−1.53472e7	+	3.31576e6i	−1.58814	+	0.343118i
$214$	−3.68602e6	−	17537.4i	−0.376111	−	0.00178947i
$215$	−3.66067e6			−0.368337
$216$	1.61882e6	−	9.94683e6i	0.160634	−	0.987014i
$217$			1.17420e7i			1.14911i
$218$	−4.95072e6	−	23554.6i	−0.477858	−	0.00227356i
$219$	2.40074e6	+	1.11120e7i	0.228567	+	1.05793i
$220$	3.43702e6	+	32706.1i	0.322786	+	0.00307157i
$221$	−1.56697e7	−	1.56697e7i	−1.45172	−	1.45172i
$222$	−1.39868e6	−	6.62648e6i	−0.127838	−	0.605653i
$223$	−1.43957e7			−1.29813			−0.649063	−	0.760735i	$-0.724839\pi$
$223$	−1.43957e7			−1.29813			−0.649063	+	0.760735i	$0.724839\pi$
$224$	7.87320e6	−	7.50724e6i	0.700498	−	0.667939i
$225$	−105477.	−	232709.i	−0.00925996	−	0.0204298i
$226$	1.39130e7	−	1.37812e7i	1.20530	−	1.19388i
$227$	−1.06621e7	−	1.06621e7i	−0.911515	−	0.911515i	0.0848765	−	0.996391i	$-0.472950\pi$
$227$	−1.06621e7	−	1.06621e7i	−0.911515	−	0.911515i	−0.996391	+	0.0848765i	$0.972950\pi$
$228$	1.13071e7	+	7.44257e6i	0.953993	+	0.627940i
$229$	7.60293e6	+	7.60293e6i	0.633103	+	0.633103i	0.948845	−	0.315742i	$-0.102253\pi$
$229$	7.60293e6	+	7.60293e6i	0.633103	+	0.633103i	−0.315742	+	0.948845i	$0.602253\pi$
$230$	−5.75984e6	−	27404.2i	−0.473399	−	0.00225234i
$231$	3.20122e6	+	2.06373e6i	0.259705	+	0.167424i
$232$	−1.00763e7	−	143833.i	−0.806936	−	0.0115184i
$233$	−2.57281e6			−0.203395			−0.101697	−	0.994815i	$-0.532427\pi$
$233$	−2.57281e6			−0.203395			−0.101697	+	0.994815i	$0.532427\pi$
$234$	−1.92509e7	+	8.61545e6i	−1.50246	+	0.672404i
$235$	4.11053e6	+	4.11053e6i	0.316734	+	0.316734i
$236$	−4.14623e6	−	4.22590e6i	−0.315440	−	0.321501i
$237$	1.67491e7	−	3.61865e6i	1.25819	−	0.271832i
$238$	1.14531e7	+	1.15626e7i	0.849560	+	0.857682i
$239$		−	6.78615e6i		−	0.497084i	−0.968621	−	0.248542i	$-0.920049\pi$
$239$		−	6.78615e6i		−	0.497084i	0.968621	−	0.248542i	$-0.0799514\pi$
$240$	7.79607e6	−	1.16022e7i	0.563951	−	0.839279i
$241$	2.22899e6			0.159241			0.0796207	−	0.996825i	$-0.474629\pi$
$241$	2.22899e6			0.159241			0.0796207	+	0.996825i	$0.474629\pi$
$242$	9.04285e6	−	8.95721e6i	0.638057	−	0.632014i
$243$	6.96594e6	−	1.25446e7i	0.485468	−	0.874254i
$244$	−1.89987e7	−	1.93638e7i	−1.30784	−	1.33297i
$245$	−664117.	+	664117.i	−0.0451592	+	0.0451592i
$246$	−2.03616e7	−	1.32640e7i	−1.36775	−	0.890985i
$247$		−	2.83299e7i		−	1.87998i
$248$	−1.29861e7	+	1.26206e7i	−0.851384	+	0.827420i
$249$	−1.68309e6	−	1.08503e6i	−0.109021	−	0.0702822i
$250$	−73482.9	+	1.54447e7i	−0.00470291	+	0.988461i
$251$	1.72104e7	−	1.72104e7i	1.08836	−	1.08836i	0.0926572	−	0.995698i	$-0.470464\pi$
$251$	1.72104e7	−	1.72104e7i	1.08836	−	1.08836i	0.995698	−	0.0926572i	$-0.0295361\pi$
$252$	1.41681e7	−	6.25995e6i	0.885338	−	0.391174i
$253$	1.71151e6	−	1.71151e6i	0.105686	−	0.105686i
$254$	2.25206e6	+	2.27359e6i	0.137429	+	0.138743i
$255$	1.75760e7	+	1.13307e7i	1.05998	+	0.683339i
$256$	1.67651e7	+	638423.i	0.999276	+	0.0380530i
$257$			2.43272e7i			1.43315i	0.697509	+	0.716576i	$0.254292\pi$
$257$			2.43272e7i			1.43315i	−0.697509	+	0.716576i	$0.745708\pi$
$258$	−1.29199e6	−	6.12100e6i	−0.0752317	−	0.356421i
$259$	7.36048e6	−	7.36048e6i	0.423649	−	0.423649i
$260$	−2.92526e7	−	278362.i	−1.66435	−	0.0158376i
$261$	−1.34295e7	−	5.05243e6i	−0.755332	−	0.284170i
$262$	24975.6	−	5.24939e6i	0.00138871	−	0.291881i
$263$	−1.49111e6			−0.0819677			−0.0409838	−	0.999160i	$-0.513049\pi$
$263$	−1.49111e6			−0.0819677			−0.0409838	+	0.999160i	$0.513049\pi$
$264$	1.15837e6	+	5.75858e6i	0.0629557	+	0.312971i
$265$			1.68575e7i			0.905846i
$266$	−98989.0	+	2.08056e7i	−0.00525947	+	1.10544i
$267$	−1.31837e7	+	2.84833e6i	−0.692632	+	0.149643i
$268$	1.77354e7	+	1.80762e7i	0.921378	+	0.939082i
$269$	1.72617e7	+	1.72617e7i	0.886801	+	0.886801i	0.994214	−	0.107414i	$-0.0342570\pi$
$269$	1.72617e7	+	1.72617e7i	0.886801	+	0.886801i	−0.107414	+	0.994214i	$0.534257\pi$
$270$	1.60397e7	−	1.17830e7i	0.814901	−	0.598637i
$271$	1.80060e7			0.904712			0.452356	−	0.891837i	$-0.350584\pi$
$271$	1.80060e7			0.904712			0.452356	+	0.891837i	$0.350584\pi$
$272$	−477635.	+	2.50946e7i	−0.0237350	+	1.24702i
$273$	−2.72457e7	−	1.75644e7i	−1.33909	−	0.863269i
$274$	−1.61578e7	−	1.63123e7i	−0.785471	−	0.792981i
$275$	105302.	+	105302.i	0.00506337	+	0.00506337i
$276$	−1.98705e6	−	9.64069e6i	−0.0945107	−	0.458544i
$277$	4.81021e6	+	4.81021e6i	0.226321	+	0.226321i	0.811154	−	0.584833i	$-0.198840\pi$
$277$	4.81021e6	+	4.81021e6i	0.226321	+	0.226321i	−0.584833	+	0.811154i	$0.698840\pi$
$278$	−198553.	+	4.17321e7i	−0.00924150	+	1.94239i
$279$	−2.34838e7	+	1.06442e7i	−1.08132	+	0.490118i
$280$	2.14822e7	+	306643.i	0.978600	+	0.0139688i
$281$	1.48446e7			0.669037			0.334518	−	0.942389i	$-0.391426\pi$
$281$	1.48446e7			0.669037			0.334518	+	0.942389i	$0.391426\pi$
$282$	−5.42244e6	+	8.32397e6i	−0.241795	+	0.371179i
$283$	−2.86352e7	−	2.86352e7i	−1.26340	−	1.26340i	−0.949434	−	0.313967i	$-0.898342\pi$
$283$	−2.86352e7	−	2.86352e7i	−1.26340	−	1.26340i	−0.313967	−	0.949434i	$-0.601658\pi$
$284$	354143.	−	3.72162e7i	0.0154605	−	1.62471i
$285$	5.64555e6	+	2.61308e7i	0.243878	+	1.12880i
$286$	8.73380e6	−	8.65109e6i	0.373341	−	0.369805i
$287$		−	3.73502e7i		−	1.57997i
$288$	2.21515e7	+	8.94092e6i	0.927313	+	0.374287i
$289$	−1.34114e7			−0.555624
$290$	−1.40056e7	−	1.41396e7i	−0.574261	−	0.579751i
$291$	−1.02752e7	+	2.21995e6i	−0.416975	+	0.0900875i
$292$	−2.69460e7	−	256414.i	−1.08230	−	0.0102989i
$293$	2.68096e7	−	2.68096e7i	1.06583	−	1.06583i	0.0681542	−	0.997675i	$-0.478289\pi$
$293$	2.68096e7	−	2.68096e7i	1.06583	−	1.06583i	0.997675	−	0.0681542i	$-0.0217110\pi$
$294$	−1.34486e6	−	876076.i	−0.0529219	−	0.0344747i
$295$		−	1.16920e7i		−	0.455430i
$296$	1.60517e7	+	229126.i	0.618934	+	0.00883484i
$297$	−1.22550e6	+	8.27319e6i	−0.0467782	+	0.315794i
$298$	5.38607e6	+	25625.9i	0.203528	+	0.000968345i
$299$	−1.45667e7	+	1.45667e7i	−0.544938	+	0.544938i
$300$	593154.	−	122255.i	0.0219687	−	0.00452797i
$301$	6.79901e6	−	6.79901e6i	0.249314	−	0.249314i
$302$	−7.63635e6	+	7.56402e6i	−0.277246	+	0.274620i
$303$	−5.55263e6	+	8.61314e6i	−0.199605	+	0.309623i
$304$	−2.31165e7	+	2.22530e7i	−0.822815	+	0.792078i
$305$		−	5.35745e7i		−	1.88825i
$306$	−1.27428e7	+	3.33878e7i	−0.444734	+	1.16526i
$307$	−4.78911e6	+	4.78911e6i	−0.165516	+	0.165516i	−0.785005	−	0.619489i	$-0.787340\pi$
$307$	−4.78911e6	+	4.78911e6i	−0.165516	+	0.165516i	0.619489	+	0.785005i	$0.287340\pi$
$308$	−6.44437e6	+	6.32288e6i	−0.220561	+	0.216403i
$309$	4.91215e6	+	2.27362e7i	0.166493	+	0.770623i
$310$	−3.57624e7	−	170150.i	−1.20044	−	0.00571147i
$311$	5.19833e7			1.72815			0.864077	−	0.503360i	$-0.167903\pi$
$311$	5.19833e7			1.72815			0.864077	+	0.503360i	$0.167903\pi$
$312$	−9.85890e6	−	4.90114e7i	−0.324612	−	1.61374i
$313$			3.39737e7i			1.10792i	0.832543	+	0.553961i	$0.186884\pi$
$313$			3.39737e7i			1.10792i	−0.832543	+	0.553961i	$0.813116\pi$
$314$	1.31918e7	+	62764.1i	0.426104	+	0.00202732i
$315$	2.86309e7	+	1.07715e7i	0.916018	+	0.344623i
$316$	−386493.	+	4.06158e7i	−0.0122484	+	1.28716i
$317$	3.15579e7	+	3.15579e7i	0.990673	+	0.990673i	0.999957	−	0.00928396i	$-0.00295522\pi$
$317$	3.15579e7	+	3.15579e7i	0.990673	+	0.990673i	−0.00928396	+	0.999957i	$0.502955\pi$
$318$	−2.81873e7	+	5.94964e6i	−0.876541	+	0.185016i
$319$	8.36320e6			0.257632
$320$	2.27506e7	+	2.40881e7i	0.694294	+	0.735110i
$321$	6.74068e6	−	1.04560e7i	0.203793	−	0.316120i
$322$	1.07487e7	−	1.06469e7i	0.321951	−	0.318902i
$323$	−3.39432e7	−	3.39432e7i	−1.00727	−	1.00727i
$324$	2.53633e7	+	2.26613e7i	0.745712	+	0.666269i
$325$	−896230.	−	896230.i	−0.0261078	−	0.0261078i
$326$	878208.	+	4178.35i	0.0253481	+	0.000120601i
$327$	9.05345e6	−	1.40436e7i	0.258923	−	0.401637i
$328$	4.13079e7	−	4.01452e7i	1.17061	−	1.13766i
$329$	−1.52691e7			−0.428771
$330$	−6.33186e6	+	9.72001e6i	−0.176193	+	0.270474i
$331$	−1.49197e7	−	1.49197e7i	−0.411412	−	0.411412i	0.470818	−	0.882230i	$-0.343959\pi$
$331$	−1.49197e7	−	1.49197e7i	−0.411412	−	0.411412i	−0.882230	+	0.470818i	$0.843959\pi$
$332$	3.38822e6	−	3.32434e6i	0.0925885	−	0.0908430i
$333$	2.13932e7	+	8.04853e6i	0.579353	+	0.217964i
$334$	−1.30723e7	−	1.31973e7i	−0.350843	−	0.354197i
$335$			5.00122e7i			1.33028i
$336$	7.06917e6	+	3.60286e7i	0.186359	+	0.949795i
$337$	−4.50002e7			−1.17578			−0.587888	−	0.808942i	$-0.700041\pi$
$337$	−4.50002e7			−1.17578			−0.587888	+	0.808942i	$0.700041\pi$
$338$	−4.68994e7	+	4.64553e7i	−1.21456	+	1.20305i
$339$	1.39573e7	+	6.46020e7i	0.358262	+	1.65824i
$340$	−3.53822e7	+	3.47151e7i	−0.900218	+	0.883247i
$341$	1.06266e7	−	1.06266e7i	0.267998	−	0.267998i
$342$	−4.17007e7	+	1.86625e7i	−1.04247	+	0.466542i
$343$		−	4.15254e7i		−	1.02904i
$344$	1.48272e7	+	211648.i	0.364237	+	0.00519923i
$345$	1.05331e7	−	1.63388e7i	0.256507	−	0.397889i
$346$	−103989.	+	2.18565e7i	−0.00251049	+	0.527657i
$347$	−4.57321e7	+	4.57321e7i	−1.09454	+	1.09454i	−0.0995047	+	0.995037i	$0.531726\pi$
$347$	−4.57321e7	+	4.57321e7i	−1.09454	+	1.09454i	−0.995037	+	0.0995047i	$0.968274\pi$
$348$	1.86996e7	−	2.84092e7i	0.443705	−	0.674095i
$349$	7.11183e6	−	7.11183e6i	0.167304	−	0.167304i	−0.618489	−	0.785793i	$-0.712255\pi$
$349$	7.11183e6	−	7.11183e6i	0.167304	−	0.167304i	0.785793	+	0.618489i	$0.212255\pi$
$350$	655064.	+	661327.i	0.0152785	+	0.0154245i
$351$	1.04303e7	−	7.04133e7i	0.241198	−	1.62830i
$352$	−1.39194e7	−	331190.i	−0.319149	−	0.00759363i
$353$			1.56708e7i			0.356260i	0.984007	+	0.178130i	$0.0570047\pi$
$353$			1.56708e7i			0.356260i	−0.984007	+	0.178130i	$0.942995\pi$
$354$	1.95501e7	−	4.12654e6i	0.440696	−	0.0930200i
$355$	5.19736e7	−	5.19736e7i	1.16171	−	1.16171i
$356$	304219.	−	3.19697e7i	0.00674273	−	0.708581i
$357$	−5.36887e7	+	1.15994e7i	−1.17999	+	0.254937i
$358$	228732.	−	4.80750e7i	0.00498514	−	1.04778i
$359$	7.73058e7			1.67082			0.835408	−	0.549630i	$-0.185231\pi$
$359$	7.73058e7			1.67082			0.835408	+	0.549630i	$0.185231\pi$
$360$	1.88605e7	+	4.32422e7i	0.404247	+	0.926831i
$361$		−	1.43213e7i		−	0.304412i
$362$	153015.	−	3.21609e7i	0.00322559	−	0.677958i
$363$	9.07163e6	+	4.19886e7i	0.189656	+	0.877832i
$364$	5.48481e7	−	5.38141e7i	1.13725	−	1.11582i
$365$	−3.76310e7	−	3.76310e7i	−0.773869	−	0.773869i
$366$	8.95818e7	−	1.89085e7i	1.82716	−	0.385668i
$367$	−5.40651e7			−1.09375			−0.546876	−	0.837214i	$-0.684183\pi$
$367$	−5.40651e7			−1.09375			−0.546876	+	0.837214i	$0.684183\pi$
$368$	2.33281e7	+	444013.i	0.468098	+	0.00890948i
$369$	7.47000e7	−	3.38583e7i	1.48676	−	0.673886i
$370$	2.23110e7	+	2.25244e7i	0.440468	+	0.444680i
$371$	−3.13096e7	−	3.13096e7i	−0.613134	−	0.613134i
$372$	−1.23374e7	−	5.98582e7i	−0.239660	−	1.16277i
$373$	2.68623e7	+	2.68623e7i	0.517627	+	0.517627i	0.916853	−	0.399226i	$-0.130721\pi$
$373$	2.68623e7	+	2.68623e7i	0.517627	+	0.517627i	−0.399226	+	0.916853i	$0.630721\pi$
$374$	99102.8	−	2.08295e7i	0.00189440	−	0.398166i
$375$	−4.38115e7	−	2.82439e7i	−0.830796	−	0.535589i
$376$	−1.64117e7	−	1.68870e7i	−0.308737	−	0.317679i
$377$	−7.11794e7			−1.32840
$378$	−7.90605e6	+	5.16754e7i	−0.146381	+	0.956772i
$379$	4.19678e7	+	4.19678e7i	0.770900	+	0.770900i	0.978264	−	0.207364i	$-0.0664884\pi$
$379$	4.19678e7	+	4.19678e7i	0.770900	+	0.770900i	−0.207364	+	0.978264i	$0.566488\pi$
$380$	−6.33659e7	−	602979.i	−1.15479	−	0.0109888i
$381$	−1.05570e7	+	2.28083e6i	−0.190882	+	0.0412400i
$382$	4.10127e7	−	4.06243e7i	0.735747	−	0.728780i
$383$		−	4.63827e6i		−	0.0825581i	−0.999148	−	0.0412791i	$-0.986857\pi$
$383$		−	4.63827e6i		−	0.0825581i	0.999148	−	0.0412791i	$-0.0131433\pi$
$384$	−3.22480e7	+	4.65429e7i	−0.569521	+	0.821977i
$385$	−1.78299e7			−0.312440
$386$	−7.18996e7	−	7.25870e7i	−1.25016	−	1.26211i
$387$	1.97613e7	+	7.43458e6i	0.340944	+	0.128270i
$388$	237104.	−	2.49168e7i	0.00405923	−	0.426577i
$389$	−1.97398e7	+	1.97398e7i	−0.335346	+	0.335346i	−0.854613	−	0.519266i	$-0.826205\pi$
$389$	−1.97398e7	+	1.97398e7i	−0.335346	+	0.335346i	0.519266	+	0.854613i	$0.326205\pi$
$390$	5.38906e7	−	8.27272e7i	0.908488	−	1.39462i
$391$			3.49058e7i			0.583939i
$392$	2.72834e6	−	2.65155e6i	0.0452940	−	0.0440191i
$393$	1.48908e7	+	9.59964e6i	0.245324	+	0.158153i
$394$	−7.24113e7	−	344519.i	−1.18391	−	0.00563280i
$395$	−5.67214e7	+	5.67214e7i	−0.920355	+	0.920355i
$396$	−1.84876e7	−	7.15692e6i	−0.297710	−	0.115250i
$397$	3.52424e7	−	3.52424e7i	0.563240	−	0.563240i	−0.366986	−	0.930226i	$-0.619610\pi$
$397$	3.52424e7	−	3.52424e7i	0.563240	−	0.563240i	0.930226	+	0.366986i	$0.119610\pi$
$398$	4.17221e7	−	4.13270e7i	0.661786	−	0.655518i
$399$	−5.90186e7	−	3.80474e7i	−0.929116	−	0.598972i
$400$	−27318.4	+	1.43529e6i	−0.000426850	+	0.0224264i
$401$			4.26844e7i			0.661966i	0.943637	+	0.330983i	$0.107380\pi$
$401$			4.26844e7i			0.661966i	−0.943637	+	0.330983i	$0.892620\pi$
$402$	−8.36253e7	+	1.76512e7i	−1.28724	+	0.271705i
$403$	−9.04432e7	+	9.04432e7i	−1.38185	+	1.38185i
$404$	−1.70122e7	−	1.73391e7i	−0.257998	−	0.262955i
$405$	4.41130e6	+	6.70260e7i	0.0664051	+	1.00897i
$406$	5.22744e7	+	248712.i	0.781108	+	0.00371636i
$407$	−1.33226e7			−0.197609
$408$	−7.05348e7	−	4.69101e7i	−1.03854	−	0.690695i
$409$		−	3.23908e7i		−	0.473426i	−0.971580	−	0.236713i	$-0.923930\pi$
$409$		−	3.23908e7i		−	0.473426i	0.971580	−	0.236713i	$-0.0760701\pi$
$410$	1.13757e8	+	541234.i	1.65054	+	0.00785296i
$411$	7.57427e7	−	1.63642e7i	1.09098	−	0.235705i
$412$	−5.51341e7	−	524647.i	−0.788368	−	0.00750197i
$413$	2.17156e7	+	2.17156e7i	0.308263	+	0.308263i
$414$	3.10376e7	+	1.18458e7i	0.437408	+	0.166941i
$415$	9.37432e6			0.131158
$416$	1.18469e8	+	2.81877e6i	1.64560	+	0.0391543i
$417$	−1.18380e8	−	7.63160e7i	−1.63257	−	1.05246i
$418$	1.89188e7	−	1.87397e7i	0.259039	−	0.256586i
$419$	−7.12008e7	−	7.12008e7i	−0.967927	−	0.967927i	0.0315743	−	0.999501i	$-0.489948\pi$
$419$	−7.12008e7	−	7.12008e7i	−0.967927	−	0.967927i	−0.999501	+	0.0315743i	$0.989948\pi$
$420$	−3.98665e7	+	6.05669e7i	−0.538097	+	0.817499i
$421$	4.31863e6	+	4.31863e6i	0.0578761	+	0.0578761i	0.735452	−	0.677576i	$-0.236970\pi$
$421$	4.31863e6	+	4.31863e6i	0.0578761	+	0.0578761i	−0.677576	+	0.735452i	$0.736970\pi$
$422$	1.12499e7	+	53524.7i	0.149696	+	0.000712225i
$423$	−1.38416e7	−	3.05380e7i	−0.182879	−	0.403477i
$424$	974642.	−	6.82796e7i	0.0127864	−	0.895763i
$425$	−2.14762e6			−0.0279763
$426$	1.05248e8	+	6.85615e7i	1.36140	+	0.886853i
$427$	9.95046e7	+	9.95046e7i	1.27808	+	1.27808i
$428$	2.06522e7	+	2.10490e7i	0.263411	+	0.268473i
$429$	8.76160e6	+	4.05536e7i	0.110971	+	0.513638i
$430$	2.06091e7	+	2.08062e7i	0.259212	+	0.261690i
$431$			9.18944e7i			1.14778i	0.818934	+	0.573888i	$0.194566\pi$
$431$			9.18944e7i			1.14778i	−0.818934	+	0.573888i	$0.805434\pi$
$432$	−6.56486e7	+	4.67985e7i	−0.814281	+	0.580471i
$433$	2.34100e7			0.288362			0.144181	−	0.989551i	$-0.453945\pi$
$433$	2.34100e7			0.288362			0.144181	+	0.989551i	$0.453945\pi$
$434$	6.67379e7	−	6.61058e7i	0.816400	−	0.808669i
$435$	6.56541e7	−	1.41846e7i	0.797616	−	0.172325i
$436$	2.77381e7	+	2.82711e7i	0.334670	+	0.341101i
$437$	−3.15538e7	+	3.15538e7i	−0.378101	+	0.378101i
$438$	4.96413e7	−	7.62042e7i	0.590773	−	0.906894i
$439$			1.01083e8i			1.19477i	0.801956	+	0.597384i	$0.203793\pi$
$439$			1.01083e8i			1.19477i	−0.801956	+	0.597384i	$0.796207\pi$
$440$	−1.91641e7	−	1.97191e7i	−0.224973	−	0.231489i
$441$	4.93386e6	−	2.23631e6i	0.0575270	−	0.0260745i
$442$	−843466.	+	1.77280e8i	−0.00976789	+	2.05302i
$443$	−1.39763e7	+	1.39763e7i	−0.160762	+	0.160762i	−0.782904	−	0.622142i	$-0.786262\pi$
$443$	−1.39763e7	+	1.39763e7i	−0.160762	+	0.160762i	0.622142	+	0.782904i	$0.286262\pi$
$444$	−2.97885e7	+	4.52560e7i	−0.340330	+	0.517043i
$445$	4.46468e7	−	4.46468e7i	0.506653	−	0.506653i
$446$	8.10458e7	+	8.18207e7i	0.913536	+	0.922271i
$447$	−9.84958e6	+	1.52785e7i	−0.110280	+	0.171064i
$448$	−8.69941e7	−	2.48406e6i	−0.967510	−	0.0276267i
$449$			4.04035e7i			0.446354i	0.974778	+	0.223177i	$0.0716428\pi$
$449$			4.04035e7i			0.446354i	−0.974778	+	0.223177i	$0.928357\pi$
$450$	−728825.	+	1.90962e6i	−0.00799808	+	0.0209560i
$451$	−3.38023e7	+	3.38023e7i	−0.368482	+	0.368482i
$452$	−1.56657e8	−	1.49072e6i	−1.69642	−	0.0161429i
$453$	−7.66065e6	−	3.54578e7i	−0.0824083	−	0.381432i
$454$	−573916.	+	1.20626e8i	−0.00613311	+	1.28906i
$455$	1.51751e8			1.61100
$456$	−2.13560e7	−	1.06167e8i	−0.225230	−	1.11968i
$457$		−	6.21220e7i		−	0.650874i	−0.945564	−	0.325437i	$-0.894489\pi$
$457$		−	6.21220e7i		−	0.650874i	0.945564	−	0.325437i	$-0.105511\pi$
$458$	409249.	−	8.60164e7i	0.00425982	−	0.895333i
$459$	−7.18681e7	−	9.68619e7i	−0.743187	−	1.00165i
$460$	3.22714e7	+	3.28915e7i	0.331547	+	0.337917i
$461$	4.70095e6	+	4.70095e6i	0.0479825	+	0.0479825i	0.730691	−	0.682708i	$-0.239198\pi$
$461$	4.70095e6	+	4.70095e6i	0.0479825	+	0.0479825i	−0.682708	+	0.730691i	$0.739198\pi$
$462$	−6.29285e6	−	2.98133e7i	−0.0638148	−	0.302332i
$463$	−3.11521e7			−0.313866			−0.156933	−	0.987609i	$-0.550161\pi$
$463$	−3.11521e7			−0.313866			−0.156933	+	0.987609i	$0.550161\pi$
$464$	5.59111e7	+	5.80807e7i	0.559686	+	0.581404i
$465$	6.53991e7	−	1.01446e8i	0.650449	−	1.00896i
$466$	1.44846e7	+	1.46231e7i	0.143136	+	0.144505i
$467$	1.38128e8	+	1.38128e8i	1.35623	+	1.35623i	0.878519	+	0.477707i	$0.158532\pi$
$467$	1.38128e8	+	1.38128e8i	1.35623	+	1.35623i	0.477707	+	0.878519i	$0.341468\pi$
$468$	1.57348e8	+	6.09127e7i	1.53505	+	0.594252i
$469$	−9.28883e7	−	9.28883e7i	−0.900415	−	0.900415i
$470$	221261.	−	4.65048e7i	0.00213114	−	0.447924i
$471$	−2.41240e7	+	3.74208e7i	−0.230881	+	0.358138i
$472$	−675990.	+	4.73572e7i	−0.00642857	+	0.450360i
$473$	−1.23063e7			−0.116291
$474$	−1.14863e8	−	7.48245e7i	−1.07856	−	0.702601i
$475$	−1.94138e6	−	1.94138e6i	−0.0181147	−	0.0181147i
$476$	1.23889e6	−	1.30193e8i	0.0114871	−	1.20716i
$477$	3.42364e7	−	9.10011e7i	0.315452	−	0.838478i
$478$	−3.85705e7	+	3.82052e7i	−0.353160	+	0.349815i
$479$		−	1.15436e8i		−	1.05035i	−0.850993	−	0.525177i	$-0.823999\pi$
$479$		−	1.15436e8i		−	1.05035i	0.850993	−	0.525177i	$-0.176001\pi$
$480$	−1.09834e8	+	2.10084e7i	−0.993149	+	0.189963i
$481$	1.13389e8			1.01891
$482$	−1.25489e7	−	1.26689e7i	−0.112064	−	0.113135i
$483$	1.07829e7	+	4.99094e7i	0.0956964	+	0.442936i
$484$	−1.01820e8	−	968904.i	−0.898045	−	0.00854565i
$485$	3.47972e7	−	3.47972e7i	0.305013	−	0.305013i
$486$	−1.10517e8	+	3.10322e7i	−0.962766	+	0.270336i
$487$			8.10002e6i			0.0701292i	0.999385	+	0.0350646i	$0.0111637\pi$
$487$			8.10002e6i			0.0701292i	−0.999385	+	0.0350646i	$0.988836\pi$
$488$	−3.09750e6	+	2.16999e8i	−0.0266533	+	1.86723i
$489$	−1.60599e6	+	2.49119e6i	−0.0137346	+	0.0213049i
$490$	7.51354e6	+	35748.0i	0.0638641	+	0.000303853i
$491$	4.38254e7	−	4.38254e7i	0.370238	−	0.370238i	−0.497326	−	0.867564i	$-0.665685\pi$
$491$	4.38254e7	−	4.38254e7i	0.370238	−	0.370238i	0.867564	+	0.497326i	$0.165685\pi$
$492$	3.92442e7	+	1.90404e8i	0.329519	+	1.59875i
$493$	−8.52828e7	+	8.52828e7i	−0.711739	+	0.711739i
$494$	−1.61019e8	+	1.59494e8i	−1.33566	+	1.32301i
$495$	−1.61630e7	−	3.56596e7i	−0.133262	−	0.294009i
$496$	1.44842e8	+	2.75684e6i	1.18700	+	0.0225926i
$497$			1.93062e8i			1.57264i
$498$	3.30856e6	+	1.56748e7i	0.0267886	+	0.126915i
$499$	2.74470e7	−	2.74470e7i	0.220899	−	0.220899i	−0.587978	−	0.808877i	$-0.700076\pi$
$499$	2.74470e7	−	2.74470e7i	0.220899	−	0.220899i	0.808877	+	0.587978i	$0.200076\pi$
$500$	8.81968e7	−	8.65341e7i	0.705575	−	0.692273i
$501$	6.12789e7	−	1.32393e7i	0.487301	−	0.105281i
$502$	−1.94712e8	−	926400.i	−1.53915	−	0.00732298i
$503$	5.71922e7			0.449400			0.224700	−	0.974428i	$-0.427860\pi$
$503$	5.71922e7			0.449400			0.224700	+	0.974428i	$0.427860\pi$
$504$	−1.15344e8	−	4.52843e7i	−0.900957	−	0.353717i
$505$		−	4.79728e7i		−	0.372495i
$506$	−1.93633e7	−	92126.7i	−0.149461	−	0.000711105i
$507$	−4.70487e7	−	2.17768e8i	−0.361014	−	1.67097i
$508$	243606.	−	2.56001e7i	0.00185822	−	0.195277i
$509$	−1.28803e8	−	1.28803e8i	−0.976727	−	0.976727i	0.0230080	−	0.999735i	$-0.492676\pi$
$509$	−1.28803e8	−	1.28803e8i	−0.976727	−	0.976727i	−0.999735	+	0.0230080i	$0.992676\pi$
$510$	−3.45503e7	−	1.63687e8i	−0.260460	−	1.23397i
$511$	1.39785e8			1.04761
$512$	−9.07566e7	−	9.88819e7i	−0.676190	−	0.736728i
$513$	2.25936e7	−	1.52527e8i	0.167353	−	1.12978i
$514$	1.38268e8	−	1.36959e8i	1.01820	−	1.00856i
$515$	−7.69967e7	−	7.69967e7i	−0.563703	−	0.563703i
$516$	−2.75162e7	+	4.18038e7i	−0.200281	+	0.304275i
$517$	1.38187e7	+	1.38187e7i	0.0999987	+	0.0999987i
$518$	−8.32733e7	−	396198.i	−0.599124	−	0.00285052i
$519$	−6.19995e7	−	3.99692e7i	−0.443492	−	0.285906i
$520$	1.63106e8	+	1.67830e8i	1.16001	+	1.19360i
$521$	−1.57334e8			−1.11253			−0.556263	−	0.831006i	$-0.687765\pi$
$521$	−1.57334e8			−1.11253			−0.556263	+	0.831006i	$0.687765\pi$
$522$	4.68898e7	+	1.04774e8i	0.329661	+	0.736616i
$523$	−1.16907e8	−	1.16907e8i	−0.817210	−	0.817210i	0.168493	−	0.985703i	$-0.446110\pi$
$523$	−1.16907e8	−	1.16907e8i	−0.817210	−	0.817210i	−0.985703	+	0.168493i	$0.946110\pi$
$524$	−2.99766e7	+	2.94115e7i	−0.208348	+	0.204420i
$525$	−3.07073e6	+	663432.i	−0.0212209	+	0.00458478i
$526$	8.39477e6	+	8.47503e6i	0.0576835	+	0.0582350i
$527$			2.16727e8i			1.48075i
$528$	2.62086e7	−	3.90039e7i	0.178050	−	0.264976i
$529$	−1.15587e8			−0.780805
$530$	9.58128e7	−	9.49054e7i	0.643570	−	0.637475i
$531$	−2.37456e7	+	6.31164e7i	−0.158599	+	0.421559i
$532$	1.18810e8	−	1.16570e8i	0.789075	−	0.774199i
$533$	2.87692e8	−	2.87692e8i	1.89997	−	1.89997i
$534$	9.04115e7	+	5.88963e7i	0.593745	+	0.386780i
$535$			5.82371e7i			0.380310i
$536$	2.89154e6	−	2.02570e8i	0.0187774	−	1.31547i
$537$	1.36373e8	+	8.79154e7i	0.880654	+	0.567731i
$538$	929158.	−	1.95291e8i	0.00596682	−	1.25411i
$539$	−2.23261e6	+	2.23261e6i	−0.0142576	+	0.0142576i
$540$	−1.57272e8	−	2.48282e7i	−0.998784	−	0.157675i
$541$	6.65694e7	−	6.65694e7i	0.420419	−	0.420419i	−0.464929	−	0.885348i	$-0.653920\pi$
$541$	6.65694e7	−	6.65694e7i	0.420419	−	0.420419i	0.885348	+	0.464929i	$0.153920\pi$
$542$	−1.01372e8	−	1.02341e8i	−0.636677	−	0.642765i
$543$	9.12299e7	+	5.88131e7i	0.569820	+	0.367345i
$544$	1.45319e8	−	1.38565e8i	0.902665	−	0.860709i
$545$			7.82187e7i			0.483193i
$546$	5.35586e7	+	2.53742e8i	0.329042	+	1.55889i
$547$	−6.73910e7	+	6.73910e7i	−0.411756	+	0.411756i	−0.882350	−	0.470594i	$-0.844040\pi$
$547$	−6.73910e7	+	6.73910e7i	−0.411756	+	0.411756i	0.470594	+	0.882350i	$0.344040\pi$
$548$	−1.74779e6	+	1.83672e8i	−0.0106206	+	1.11610i
$549$	−1.08806e8	+	2.89210e8i	−0.657562	+	1.74782i
$550$	5668.20	−	1.19135e6i	3.40688e−5	−	0.00716061i
$551$	−1.54186e8			−0.921703
$552$	−4.36080e7	+	6.55697e7i	−0.259268	+	0.389840i
$553$		−	2.10699e8i		−	1.24591i
$554$	258923.	−	5.44207e7i	0.00152280	−	0.320063i
$555$	−1.04587e8	+	2.25960e7i	−0.611786	+	0.132176i
$556$	2.38311e8	−	2.33818e8i	1.38650	−	1.36036i
$557$	2.85544e7	+	2.85544e7i	0.165237	+	0.165237i	0.784882	−	0.619645i	$-0.212723\pi$
$557$	2.85544e7	+	2.85544e7i	0.165237	+	0.165237i	−0.619645	+	0.784882i	$0.712723\pi$
$558$	1.92709e8	+	7.35495e7i	1.10918	+	0.423328i
$559$	1.04740e8			0.599619
$560$	−1.19199e8	−	1.23825e8i	−0.678750	−	0.705090i
$561$	5.90864e7	+	3.80912e7i	0.334656	+	0.215743i
$562$	−8.35733e7	−	8.43724e7i	−0.470824	−	0.475326i
$563$	−1.34526e8	−	1.34526e8i	−0.753842	−	0.753842i	0.221352	−	0.975194i	$-0.428953\pi$
$563$	−1.34526e8	−	1.34526e8i	−0.753842	−	0.753842i	−0.975194	+	0.221352i	$0.928953\pi$
$564$	7.78387e7	−	1.60434e7i	0.433869	−	0.0894248i
$565$	−2.18776e8	−	2.18776e8i	−1.21298	−	1.21298i
$566$	−1.54137e6	+	3.23967e8i	−0.00850077	+	1.78670i
$567$	−1.32681e8	−	1.16295e8i	−0.727882	−	0.637987i
$568$	−2.13519e8	+	2.07509e8i	−1.16518	+	1.13238i
$569$	2.21669e8			1.20328			0.601642	−	0.798766i	$-0.294513\pi$
$569$	2.21669e8			1.20328			0.601642	+	0.798766i	$0.294513\pi$
$570$	1.16736e8	−	1.79201e8i	0.630347	−	0.967643i
$571$	1.25808e8	+	1.25808e8i	0.675771	+	0.675771i	0.959040	−	0.283269i	$-0.0914190\pi$
$571$	1.25808e8	+	1.25808e8i	0.675771	+	0.675771i	−0.283269	+	0.959040i	$0.591419\pi$
$572$	−9.83404e7	−	935791.i	−0.525465	−	0.00500024i
$573$	4.11433e7	+	1.90434e8i	0.218693	+	1.01223i
$574$	−2.12288e8	+	2.10277e8i	−1.12251	+	1.11188i
$575$			1.99644e6i			0.0105015i
$576$	−7.38928e7	−	1.76239e8i	−0.386665	−	0.922220i
$577$	−4.11443e7			−0.214182			−0.107091	−	0.994249i	$-0.534154\pi$
$577$	−4.11443e7			−0.214182			−0.107091	+	0.994249i	$0.534154\pi$
$578$	7.55046e7	+	7.62265e7i	0.391012	+	0.394750i
$579$	3.37043e8	−	7.28181e7i	1.73640	−	0.375149i
$580$	−1.51500e6	+	1.59208e8i	−0.00776475	+	0.815982i
$581$	−1.74110e7	+	1.74110e7i	−0.0887761	+	0.0887761i
$582$	7.04655e7	+	4.59030e7i	0.357444	+	0.232848i
$583$			5.66709e7i			0.285992i
$584$	1.50245e8	+	1.54597e8i	0.754332	+	0.776178i
$585$	1.37563e8	+	3.03500e8i	0.687124	+	1.51597i
$586$	−3.03313e8	−	1.44310e6i	−1.50729	−	0.00717141i
$587$	1.79476e8	−	1.79476e8i	0.887345	−	0.887345i	−0.106922	−	0.994267i	$-0.534100\pi$
$587$	1.79476e8	−	1.79476e8i	0.887345	−	0.887345i	0.994267	+	0.106922i	$0.0340996\pi$
$588$	2.59204e6	+	1.25760e7i	0.0127500	+	0.0618601i
$589$	−1.95915e8	+	1.95915e8i	−0.958785	+	0.958785i
$590$	−6.64536e7	+	6.58243e7i	−0.323566	+	0.320502i
$591$	1.32420e8	−	2.05407e8i	0.641490	−	0.995068i
$592$	−8.90665e7	−	9.25228e7i	−0.429289	−	0.445947i
$593$			3.25563e8i			1.56124i	0.625004	+	0.780622i	$0.285097\pi$
$593$			3.25563e8i			1.56124i	−0.625004	+	0.780622i	$0.714903\pi$
$594$	5.39218e7	−	3.96117e7i	0.257279	−	0.189001i
$595$	1.81818e8	−	1.81818e8i	0.863151	−	0.863151i
$596$	−3.01773e7	−	3.07571e7i	−0.142541	−	0.145280i
$597$	4.18549e7	+	1.93728e8i	0.196709	+	0.910478i
$598$	1.64801e8	+	784093.i	0.770650	+	0.00366660i
$599$	−3.52178e8			−1.63863			−0.819316	−	0.573342i	$-0.805647\pi$
$599$	−3.52178e8			−1.63863			−0.819316	+	0.573342i	$0.805647\pi$
$600$	−4.03425e6	−	2.68303e6i	−0.0186771	−	0.0124214i
$601$			3.72233e8i			1.71471i	0.514725	+	0.857355i	$0.327894\pi$
$601$			3.72233e8i			1.71471i	−0.514725	+	0.857355i	$0.672106\pi$
$602$	−7.69212e7	−	365976.i	−0.352579	−	0.00167750i
$603$	1.01572e8	−	2.69980e8i	0.463255	−	1.23134i
$604$	8.59834e7	+	818203.i	0.390215	+	0.00371322i
$605$	−1.42196e8	−	1.42196e8i	−0.642125	−	0.642125i
$606$	8.02152e7	−	1.69314e7i	0.360445	−	0.0760809i
$607$	−7.03812e7			−0.314695			−0.157348	−	0.987543i	$-0.550294\pi$
$607$	−7.03812e7			−0.314695			−0.157348	+	0.987543i	$0.550294\pi$
$608$	2.56623e8	+	6.10591e6i	1.14179	+	0.0271669i
$609$	−9.55949e7	+	1.48285e8i	−0.423236	+	0.656517i
$610$	−3.04502e8	+	3.01618e8i	−1.34153	+	1.32882i
$611$	−1.17611e8	−	1.17611e8i	−0.515613	−	0.515613i
$612$	2.61507e8	−	1.15543e8i	1.14085	−	0.504068i
$613$	−1.35278e7	−	1.35278e7i	−0.0587280	−	0.0587280i	0.677133	−	0.735861i	$-0.263222\pi$
$613$	−1.35278e7	−	1.35278e7i	−0.0587280	−	0.0587280i	−0.735861	+	0.677133i	$0.763222\pi$
$614$	5.41820e7	+	257787.i	0.234072	+	0.00111367i
$615$	−2.08029e8	+	3.22691e8i	−0.894332	+	1.38727i
$616$	7.22183e7	+	1.03086e6i	0.308962	+	0.00441021i
$617$	−9.28818e7			−0.395435			−0.197718	−	0.980259i	$-0.563353\pi$
$617$	−9.28818e7			−0.395435			−0.197718	+	0.980259i	$0.563353\pi$
$618$	1.01571e8	−	1.55921e8i	0.430332	−	0.660601i
$619$	−1.04915e8	−	1.04915e8i	−0.442350	−	0.442350i	0.450451	−	0.892801i	$-0.351263\pi$
$619$	−1.04915e8	−	1.04915e8i	−0.442350	−	0.442350i	−0.892801	+	0.450451i	$0.851263\pi$
$620$	2.00371e8	+	2.04221e8i	0.840735	+	0.856889i
$621$	−9.00435e7	+	6.68091e7i	−0.375991	+	0.278972i
$622$	−2.92659e8	−	2.95458e8i	−1.21616	−	1.22779i
$623$			1.65846e8i			0.685870i
$624$	−2.23062e8	+	3.31963e8i	−0.918061	+	1.36627i
$625$	2.49494e8			1.02193
$626$	1.93096e8	−	1.91267e8i	0.787138	−	0.779683i
$627$	1.89791e7	+	8.78457e7i	0.0769967	+	0.356384i
$628$	−7.39116e7	−	7.53317e7i	−0.298424	−	0.304158i
$629$	1.35856e8	−	1.35856e8i	0.545917	−	0.545917i
$630$	−9.99665e7	−	2.23372e8i	−0.399791	−	0.893320i
$631$		−	1.24021e8i		−	0.493636i	−0.969062	−	0.246818i	$-0.920615\pi$
$631$		−	1.24021e8i		−	0.493636i	0.969062	−	0.246818i	$-0.0793850\pi$
$632$	2.33024e8	−	2.26465e8i	0.923102	−	0.897120i
$633$	−2.05728e7	+	3.19122e7i	−0.0811114	+	0.125819i
$634$	1.69869e6	−	3.57033e8i	0.00666572	−	1.40101i
$635$	3.57514e7	−	3.57514e7i	0.139628	−	0.139628i
$636$	1.92507e8	+	1.26713e8i	0.748299	+	0.492548i
$637$	1.90018e7	−	1.90018e7i	0.0735150	−	0.0735150i
$638$	−4.70838e7	−	4.75340e7i	−0.181305	−	0.183038i
$639$	−3.86123e8	+	1.75013e8i	−1.47987	+	0.670760i
$640$	8.82629e6	−	2.64921e8i	0.0336696	−	1.01059i
$641$			5.37536e7i			0.204095i	0.994780	+	0.102048i	$0.0325394\pi$
$641$			5.37536e7i			0.204095i	−0.994780	+	0.102048i	$0.967461\pi$
$642$	−9.73781e7	+	2.05541e7i	−0.368007	+	0.0776772i
$643$	1.12471e8	−	1.12471e8i	0.423065	−	0.423065i	−0.463193	−	0.886258i	$-0.653296\pi$
$643$	1.12471e8	−	1.12471e8i	0.423065	−	0.423065i	0.886258	+	0.463193i	$0.153296\pi$
$644$	−1.21028e8	−	1.15168e6i	−0.453136	−	0.00431196i
$645$	−9.66091e7	+	2.08724e7i	−0.360030	+	0.0777845i
$646$	−1.82709e6	+	3.84019e8i	−0.00677737	+	1.42447i
$647$	1.73764e8			0.641574			0.320787	−	0.947151i	$-0.396053\pi$
$647$	1.73764e8			0.641574			0.320787	+	0.947151i	$0.396053\pi$
$648$	−1.39923e7	−	2.71738e8i	−0.0514240	−	0.998677i
$649$		−	3.93057e7i		−	0.143788i
$650$	−48242.1	+	1.01396e7i	−0.000175666	+	0.0369215i
$651$	6.69503e7	+	3.09883e8i	0.242666	+	1.12320i
$652$	−4.92046e6	−	5.01500e6i	−0.0177526	−	0.0180937i
$653$	−1.58065e8	−	1.58065e8i	−0.567670	−	0.567670i	0.363805	−	0.931475i	$-0.381477\pi$
$653$	−1.58065e8	−	1.58065e8i	−0.567670	−	0.567670i	−0.931475	+	0.363805i	$0.881477\pi$
$654$	−1.30789e8	+	2.76064e7i	−0.467562	+	0.0986907i
$655$	−8.29375e7			−0.295139
$656$	−4.60731e8	−	8.76927e6i	−1.63206	−	0.0310636i
$657$	1.26716e8	+	2.79569e8i	0.446824	+	0.985808i
$658$	8.59630e7	+	8.67849e7i	0.301741	+	0.304626i
$659$	−2.43463e6	−	2.43463e6i	−0.00850701	−	0.00850701i	0.702840	−	0.711347i	$-0.251915\pi$
$659$	−2.43463e6	−	2.43463e6i	−0.00850701	−	0.00850701i	−0.711347	+	0.702840i	$0.751915\pi$
$660$	9.08932e7	−	1.87340e7i	0.316155	−	0.0651628i
$661$	2.42659e8	+	2.42659e8i	0.840218	+	0.840218i	0.988887	−	0.148669i	$-0.0474989\pi$
$661$	2.42659e8	+	2.42659e8i	0.840218	+	0.840218i	−0.148669	+	0.988887i	$0.547499\pi$
$662$	−803096.	+	1.68795e8i	−0.00276818	+	0.581817i
$663$	−5.02886e8	−	3.24195e8i	−1.72556	−	1.11241i
$664$	−3.79698e7	−	541992.i	−0.129698	−	0.00185135i
$665$	3.28717e8			1.11778
$666$	−7.46956e7	−	1.66905e8i	−0.252856	−	0.564997i
$667$	7.92795e7	+	7.92795e7i	0.267168	+	0.267168i
$668$	−1.41404e6	+	1.48598e8i	−0.00474385	+	0.498522i
$669$	−3.79917e8	+	8.20811e7i	−1.26885	+	0.274135i
$670$	2.84255e8	−	2.81563e8i	0.945112	−	0.936161i
$671$		−	1.80105e8i		−	0.596154i
$672$	1.64977e8	−	2.43016e8i	0.543647	−	0.800805i
$673$	−1.07458e8			−0.352527			−0.176264	−	0.984343i	$-0.556401\pi$
$673$	−1.07458e8			−0.352527			−0.176264	+	0.984343i	$0.556401\pi$
$674$	2.53346e8	+	2.55768e8i	0.827435	+	0.835346i
$675$	−4.11050e6	−	5.54003e6i	−0.0133655	−	0.0180136i
$676$	5.28076e8	+	5.02508e6i	1.70945	+	0.0162668i
$677$	−3.91926e7	+	3.91926e7i	−0.126310	+	0.126310i	−0.767436	−	0.641126i	$-0.778468\pi$
$677$	−3.91926e7	+	3.91926e7i	−0.126310	+	0.126310i	0.641126	+	0.767436i	$0.278468\pi$
$678$	2.88601e8	−	4.43030e8i	0.925995	−	1.42149i
$679$			1.29258e8i			0.412904i
$680$	3.96508e8	+	5.65986e6i	1.26103	+	0.0180003i
$681$	−3.42176e8	−	2.20591e8i	−1.08345	−	0.698467i
$682$	−1.20225e8	−	572007.i	−0.379002	−	0.00180322i
$683$	−3.11806e8	+	3.11806e8i	−0.978637	+	0.978637i	−0.999777	−	0.0211392i	$-0.993271\pi$
$683$	−3.11806e8	+	3.11806e8i	−0.978637	+	0.978637i	0.0211392	+	0.999777i	$0.493271\pi$
$684$	3.40842e8	+	1.31947e8i	1.06509	+	0.412317i
$685$	−2.56505e8	+	2.56505e8i	−0.798038	+	0.798038i
$686$	−2.36018e8	+	2.33783e8i	−0.731093	+	0.724170i
$687$	2.44000e8	+	1.57299e8i	0.752523	+	0.485128i
$688$	−8.22725e7	−	8.54651e7i	−0.252632	−	0.262436i
$689$		−	4.82327e8i		−	1.47463i
$690$	−1.52165e8	+	3.21182e7i	−0.463198	+	0.0977697i
$691$	−9.67120e7	+	9.67120e7i	−0.293121	+	0.293121i	−0.838312	−	0.545191i	$-0.816457\pi$
$691$	−9.67120e7	+	9.67120e7i	−0.293121	+	0.293121i	0.545191	+	0.838312i	$0.316457\pi$
$692$	1.24811e8	−	1.22458e8i	0.376647	−	0.369547i
$693$	9.62506e7	+	3.62113e7i	0.289204	+	0.108804i
$694$	5.17393e8	+	2.46166e6i	1.54790	+	0.00736460i
$695$	6.59344e8			1.96407
$696$	−2.66746e8	+	5.36574e7i	−0.791170	+	0.159148i
$697$		−	6.89391e8i		−	2.03595i
$698$	−8.04603e7	−	382815.i	−0.236600	−	0.00112570i
$699$	−6.78993e7	+	1.46696e7i	−0.198808	+	0.0429525i
$700$	70858.4	−	7.44638e6i	0.000206584	−	0.0217096i
$701$	7.83295e7	+	7.83295e7i	0.227390	+	0.227390i	0.811602	−	0.584211i	$-0.198596\pi$
$701$	7.83295e7	+	7.83295e7i	0.227390	+	0.227390i	−0.584211	+	0.811602i	$0.698596\pi$
$702$	−4.58930e8	+	3.37136e8i	−1.32658	+	0.974526i
$703$	2.45619e8			0.706962
$704$	7.64824e7	+	8.09786e7i	0.219201	+	0.232088i
$705$	1.31919e8	+	8.50440e7i	0.376478	+	0.242704i
$706$	8.90681e7	−	8.82246e7i	0.253109	−	0.250712i
$707$	8.91004e7	+	8.91004e7i	0.252128	+	0.252128i
$708$	−1.33519e8	−	8.78851e7i	−0.376220	−	0.247637i
$709$	−8.10613e7	−	8.10613e7i	−0.227444	−	0.227444i	0.584180	−	0.811624i	$-0.301416\pi$
$709$	−8.10613e7	−	8.10613e7i	−0.227444	−	0.227444i	−0.811624	+	0.584180i	$0.801416\pi$
$710$	−5.88008e8	−	2.79763e6i	−1.64289	−	0.00781655i
$711$	4.21395e8	−	1.91000e8i	1.17241	−	0.531404i
$712$	−1.83419e8	+	1.78257e8i	−0.508165	+	0.493862i
$713$	2.01471e8			0.555833
$714$	3.68189e8	+	2.39847e8i	1.01152	+	0.658932i
$715$	−1.37336e8	−	1.37336e8i	−0.375721	−	0.375721i
$716$	−2.74532e8	+	2.69356e8i	−0.747918	+	0.733818i
$717$	−3.86932e7	−	1.79094e8i	−0.104973	−	0.485874i
$718$	−4.35222e8	−	4.39383e8i	−1.17581	−	1.18705i
$719$		−	5.07101e8i		−	1.36429i	−0.731216	−	0.682146i	$-0.761047\pi$
$719$		−	5.07101e8i		−	1.36429i	0.731216	−	0.682146i	$-0.238953\pi$
$720$	1.39593e8	−	3.50646e8i	0.373996	−	0.939445i
$721$	2.86014e8			0.763100
$722$	−8.13981e7	+	8.06272e7i	−0.216273	+	0.214225i
$723$	5.88253e7	−	1.27092e7i	0.155650	−	0.0336282i
$724$	−1.83655e8	+	1.80192e8i	−0.483934	+	0.474811i
$725$	−4.87776e6	+	4.87776e6i	−0.0127999	+	0.0127999i
$726$	1.87579e8	−	2.87951e8i	0.490200	−	0.752504i
$727$			2.81037e8i			0.731408i	0.930731	+	0.365704i	$0.119172\pi$
$727$			2.81037e8i			0.731408i	−0.930731	+	0.365704i	$0.880828\pi$
$728$	−6.14652e8	−	8.77371e6i	−1.59307	−	0.0227399i
$729$	1.12312e8	−	3.70784e8i	0.289897	−	0.957058i
$730$	−2.02560e6	+	4.25741e8i	−0.00520696	+	1.09440i
$731$	1.25493e8	−	1.25493e8i	0.321267	−	0.321267i
$732$	−6.11805e8	−	4.02704e8i	−1.55984	−	1.02672i
$733$	3.35731e8	−	3.35731e8i	0.852471	−	0.852471i	−0.137966	−	0.990437i	$-0.544057\pi$
$733$	3.35731e8	−	3.35731e8i	0.852471	−	0.852471i	0.990437	+	0.137966i	$0.0440566\pi$
$734$	3.04380e8	+	3.07290e8i	0.769711	+	0.777070i
$735$	−1.37401e7	+	2.13134e7i	−0.0346042	+	0.0536774i
$736$	−1.28811e8	−	1.35090e8i	−0.323087	−	0.338836i
$737$			1.68130e8i			0.419993i
$738$	−6.12993e8	−	2.33955e8i	−1.52506	−	0.582054i
$739$	−2.91895e8	+	2.91895e8i	−0.723259	+	0.723259i	−0.969268	−	0.246009i	$-0.920881\pi$
$739$	−2.91895e8	+	2.91895e8i	−0.723259	+	0.723259i	0.246009	+	0.969268i	$0.420881\pi$
$740$	2.41339e6	−	2.53619e8i	0.00595570	−	0.625873i
$741$	−1.61531e8	−	7.47657e8i	−0.397010	−	1.83759i
$742$	−1.68533e6	+	3.54223e8i	−0.00412546	+	0.867092i
$743$	−5.52908e8			−1.34799			−0.673994	−	0.738737i	$-0.735423\pi$
$743$	−5.52908e8			−1.34799			−0.673994	+	0.738737i	$0.735423\pi$
$744$	−2.70758e8	+	4.07116e8i	−0.657450	+	0.988553i
$745$		−	8.50969e7i		−	0.205800i
$746$	1.44594e6	−	3.03909e8i	0.00348284	−	0.732027i
$747$	−5.06051e7	−	1.90386e7i	−0.121404	−	0.0456745i
$748$	−1.18947e8	+	1.16704e8i	−0.284216	+	0.278857i
$749$	−1.08164e8	−	1.08164e8i	−0.257418	−	0.257418i
$750$	8.61232e7	+	4.08022e8i	0.204144	+	0.967162i
$751$	−1.79734e8			−0.424336			−0.212168	−	0.977233i	$-0.568052\pi$
$751$	−1.79734e8			−0.424336			−0.212168	+	0.977233i	$0.568052\pi$
$752$	−3.58495e6	+	1.88351e8i	−0.00843004	+	0.442908i
$753$	3.56072e8	−	5.52332e8i	0.833974	−	1.29365i
$754$	4.00731e8	+	4.04563e8i	0.934844	+	0.943782i
$755$	1.20079e8	+	1.20079e8i	0.279013	+	0.279013i
$756$	3.38218e8	−	2.45990e8i	0.782764	−	0.569315i
$757$	2.02216e8	+	2.02216e8i	0.466152	+	0.466152i	0.900665	−	0.434513i	$-0.143080\pi$
$757$	2.02216e8	+	2.02216e8i	0.466152	+	0.466152i	−0.434513	+	0.900665i	$0.643080\pi$
$758$	2.25903e6	−	4.74806e8i	0.00518698	−	1.09021i
$759$	3.54099e7	−	5.49272e7i	0.0809840	−	0.125621i
$760$	3.53315e8	+	3.63547e8i	0.804861	+	0.828172i
$761$	−4.93826e8			−1.12052			−0.560261	−	0.828316i	$-0.689299\pi$
$761$	−4.93826e8			−1.12052			−0.560261	+	0.828316i	$0.689299\pi$
$762$	7.23979e7	+	4.71618e7i	0.163629	+	0.106592i
$763$	−1.45276e8	−	1.45276e8i	−0.327056	−	0.327056i
$764$	−4.61793e8	−	4.39435e6i	−1.03554	−	0.00985404i
$765$	5.28455e8	+	1.98815e8i	1.18038	+	0.444083i
$766$	−2.63626e7	+	2.61129e7i	−0.0586545	+	0.0580990i
$767$			3.34532e8i			0.741398i
$768$	4.46088e8	−	7.87423e7i	0.984776	−	0.173830i
$769$	−8.61277e8			−1.89393			−0.946965	−	0.321336i	$-0.895868\pi$
$769$	−8.61277e8			−1.89393			−0.946965	+	0.321336i	$0.895868\pi$
$770$	1.00380e8	+	1.01340e8i	0.219875	+	0.221977i
$771$	1.38708e8	+	6.42020e8i	0.302649	+	1.40083i
$772$	−7.77740e6	+	8.17312e8i	−0.0169037	+	1.77638i
$773$	3.05444e7	−	3.05444e7i	0.0661291	−	0.0661291i	−0.673269	−	0.739398i	$-0.735110\pi$
$773$	3.05444e7	−	3.05444e7i	0.0661291	−	0.0661291i	0.739398	+	0.673269i	$0.235110\pi$
$774$	−6.89978e7	−	1.54173e8i	−0.148803	−	0.332496i
$775$			1.23957e7i			0.0266297i
$776$	−1.42955e8	+	1.38931e8i	−0.305924	+	0.297313i
$777$	1.52283e8	−	2.36219e8i	0.324630	−	0.503560i
$778$	2.23328e8	+	1.06255e6i	0.474246	+	0.00225637i
$779$	6.23189e8	−	6.23189e8i	1.31828	−	1.31828i
$780$	−7.73594e8	+	1.59446e8i	−1.63016	+	0.335992i
$781$	1.74723e8	−	1.74723e8i	0.366774	−	0.366774i
$782$	1.98394e8	−	1.96515e8i	0.414867	−	0.410938i
$783$	−3.83227e8	−	5.67669e7i	−0.798308	−	0.118252i
$784$	−3.04308e7	−	579202.i	−0.0631489	−	0.00120194i
$785$		−	2.08423e8i		−	0.430861i
$786$	−2.92718e7	−	1.38680e8i	−0.0602813	−	0.285591i
$787$	3.83336e8	−	3.83336e8i	0.786421	−	0.786421i	−0.194485	−	0.980906i	$-0.562303\pi$
$787$	3.83336e8	−	3.83336e8i	0.786421	−	0.786421i	0.980906	+	0.194485i	$0.0623034\pi$
$788$	4.05709e8	+	4.13504e8i	0.829155	+	0.845087i
$789$	−3.93520e7	+	8.50201e6i	−0.0801191	+	0.0173097i
$790$	6.41722e8	+	3.05319e6i	1.30156	+	0.00619259i
$791$	8.12672e8			1.64205
$792$	6.34048e7	+	1.45370e8i	0.127628	+	0.292618i
$793$			1.53288e9i			3.07389i
$794$	−3.98717e8	−	1.89702e6i	−0.796533	−	0.00378975i
$795$	9.61177e7	+	4.44887e8i	0.191294	+	0.885417i
$796$	−4.69781e8	−	4.47036e6i	−0.931443	−	0.00886345i
$797$	2.03224e8	+	2.03224e8i	0.401421	+	0.401421i	0.878733	−	0.477313i	$-0.158389\pi$
$797$	2.03224e8	+	2.03224e8i	0.401421	+	0.401421i	−0.477313	+	0.878733i	$0.658389\pi$
$798$	1.16017e8	+	5.49646e8i	0.228303	+	1.08162i
$799$	−2.81829e8			−0.552516
$800$	8.31155e6	−	7.92523e6i	0.0162335	−	0.0154790i
$801$	−3.31691e8	+	1.50341e8i	−0.645410	+	0.292537i
$802$	2.42605e8	−	2.40308e8i	0.470303	−	0.465849i
$803$	−1.26507e8	−	1.26507e8i	−0.244325	−	0.244325i
$804$	5.71125e8	+	3.75927e8i	1.09891	+	0.723329i
$805$	−1.69020e8	−	1.69020e8i	−0.324004	−	0.324004i
$806$	1.02324e9	+	4.86836e6i	1.95421	+	0.00929775i
$807$	5.53977e8	+	3.57132e8i	1.05407	+	0.679529i
$808$	−2.77363e6	+	1.94309e8i	−0.00525792	+	0.368349i
$809$	−3.64283e8			−0.688008			−0.344004	−	0.938968i	$-0.611783\pi$
$809$	−3.64283e8			−0.688008			−0.344004	+	0.938968i	$0.611783\pi$
$810$	3.56121e8	−	4.02421e8i	0.670104	−	0.757226i
$811$	1.00560e8	+	1.00560e8i	0.188523	+	0.188523i	0.795057	−	0.606534i	$-0.207441\pi$
$811$	1.00560e8	+	1.00560e8i	0.188523	+	0.188523i	−0.606534	+	0.795057i	$0.707441\pi$
$812$	−2.92885e8	−	2.98513e8i	−0.547052	−	0.557564i
$813$	4.75199e8	−	1.02667e8i	0.884309	−	0.191055i
$814$	7.50046e7	+	7.57217e7i	0.139064	+	0.140394i
$815$		−	1.38752e7i		−	0.0256311i
$816$	1.30479e8	+	6.64997e8i	0.240143	+	1.22391i
$817$	2.26883e8			0.416041
$818$	−1.84100e8	+	1.82356e8i	−0.336352	+	0.333166i
$819$	−8.19191e8	−	3.08195e8i	−1.49119	−	0.561015i
$820$	−6.37362e8	−	6.49609e8i	−1.15596	−	1.17818i
$821$	−4.20661e8	+	4.20661e8i	−0.760155	+	0.760155i	−0.976350	−	0.216195i	$-0.930635\pi$
$821$	−4.20661e8	+	4.20661e8i	−0.760155	+	0.760155i	0.216195	+	0.976350i	$0.430635\pi$
$822$	−5.19431e8	−	3.38370e8i	−0.935217	−	0.609224i
$823$			2.63518e8i			0.472727i	0.971665	+	0.236363i	$0.0759556\pi$
$823$			2.63518e8i			0.472727i	−0.971665	+	0.236363i	$0.924044\pi$
$824$	3.07416e8	+	3.16320e8i	0.549472	+	0.565386i
$825$	3.37946e6	+	2.17863e6i	0.00601845	+	0.00387991i
$826$	1.16890e6	−	2.45681e8i	0.00207414	−	0.435945i
$827$	−3.67513e8	+	3.67513e8i	−0.649765	+	0.649765i	−0.952936	−	0.303171i	$-0.901955\pi$
$827$	−3.67513e8	+	3.67513e8i	−0.649765	+	0.649765i	0.303171	+	0.952936i	$0.401955\pi$
$828$	−1.07410e8	−	2.43099e8i	−0.189213	−	0.428244i
$829$	4.29670e8	−	4.29670e8i	0.754173	−	0.754173i	−0.221082	−	0.975255i	$-0.570959\pi$
$829$	4.29670e8	−	4.29670e8i	0.754173	−	0.754173i	0.975255	+	0.221082i	$0.0709588\pi$
$830$	−5.27762e7	−	5.32808e7i	−0.0923005	−	0.0931830i
$831$	1.54374e8	+	9.95198e7i	0.269011	+	0.173423i
$832$	−6.50943e8	−	6.89211e8i	−1.13025	−	1.19669i
$833$		−	4.55336e7i		−	0.0787765i
$834$	2.32708e8	+	1.10249e9i	0.401155	+	1.90053i
$835$	−2.07523e8	+	2.07523e8i	−0.356456	+	0.356456i
$836$	−2.13022e8	−	2.02708e6i	−0.364590	−	0.00346937i
$837$	−5.59072e8	+	4.14812e8i	−0.953436	+	0.707416i
$838$	−3.83258e6	+	8.05536e8i	−0.00651268	+	1.36884i
$839$	−2.59415e8			−0.439248			−0.219624	−	0.975585i	$-0.570483\pi$
$839$	−2.59415e8			−0.439248			−0.219624	+	0.975585i	$0.570483\pi$
$840$	5.68688e8	−	1.14395e8i	0.959480	−	0.193005i
$841$		−	2.07427e8i		−	0.348721i
$842$	232462.	−	4.88591e7i	0.000389418	−	0.0818483i
$843$	3.91766e8	−	8.46409e7i	0.653948	−	0.141286i
$844$	−6.30312e7	−	6.42423e7i	−0.104840	−	0.106855i
$845$	7.37476e8	+	7.37476e8i	1.22230	+	1.22230i
$846$	−9.56426e7	+	2.50596e8i	−0.157958	+	0.413870i
$847$	5.28203e8			0.869262
$848$	−3.93568e8	+	3.78866e8i	−0.645405	+	0.621295i
$849$	−9.18987e8	−	5.92443e8i	−1.50171	−	0.968107i
$850$	1.20908e7	+	1.22064e7i	0.0196879	+	0.0198761i
$851$	−1.26293e8	−	1.26293e8i	−0.204922	−	0.204922i
$852$	−2.02853e8	−	9.84194e8i	−0.327991	−	1.59134i
$853$	4.61316e8	+	4.61316e8i	0.743279	+	0.743279i	0.973207	−	0.229929i	$-0.0738493\pi$
$853$	4.61316e8	+	4.61316e8i	0.743279	+	0.743279i	−0.229929	+	0.973207i	$0.573849\pi$
$854$	5.35611e6	−	1.12575e9i	0.00859956	−	1.80746i
$855$	2.97985e8	+	6.57430e8i	0.476755	+	1.05184i
$856$	3.36707e6	−	2.35884e8i	0.00536823	−	0.376077i
$857$	−2.28609e8			−0.363205			−0.181602	−	0.983372i	$-0.558128\pi$
$857$	−2.28609e8			−0.363205			−0.181602	+	0.983372i	$0.558128\pi$
$858$	1.81168e8	−	2.78110e8i	0.286826	−	0.440306i
$859$	1.71702e8	+	1.71702e8i	0.270891	+	0.270891i	0.829459	−	0.558568i	$-0.188649\pi$
$859$	1.71702e8	+	1.71702e8i	0.270891	+	0.270891i	−0.558568	+	0.829459i	$0.688649\pi$
$860$	2.22930e6	−	2.34272e8i	0.00350487	−	0.368320i
$861$	−2.12963e8	−	9.85713e8i	−0.333653	−	1.54433i
$862$	5.22301e8	−	5.17354e8i	0.815452	−	0.807730i
$863$			2.55084e8i			0.396873i	0.980114	+	0.198437i	$0.0635864\pi$
$863$			2.55084e8i			0.396873i	−0.980114	+	0.198437i	$0.936414\pi$
$864$	6.35582e8	+	1.09657e8i	0.985441	+	0.170018i
$865$	3.45320e8			0.533548
$866$	−1.31795e8	−	1.33055e8i	−0.202930	−	0.204870i
$867$	−3.53942e8	+	7.64691e7i	−0.543093	+	0.117335i
$868$	−7.51452e8	−	7.15069e6i	−1.14906	−	0.0109342i
$869$	−1.90684e8	+	1.90684e8i	−0.290573	+	0.290573i
$870$	−4.50245e8	−	2.93301e8i	−0.683740	−	0.445406i
$871$		−	1.43096e9i		−	2.16557i
$872$	4.52234e6	−	3.16818e8i	0.00682047	−	0.477815i
$873$	−2.58515e8	+	1.17174e8i	−0.388547	+	0.176112i
$874$	3.56987e8	+	1.69847e6i	0.534709	+	0.00254404i
$875$	−4.53217e8	+	4.53217e8i	−0.676522	+	0.676522i
$876$	−7.12596e8	+	1.46874e8i	−1.06006	+	0.218490i
$877$	1.59310e8	−	1.59310e8i	0.236181	−	0.236181i	−0.579086	−	0.815267i	$-0.696590\pi$
$877$	1.59310e8	−	1.59310e8i	0.236181	−	0.236181i	0.815267	+	0.579086i	$0.196590\pi$
$878$	5.74524e8	−	5.69083e8i	0.848838	−	0.840799i
$879$	5.54672e8	−	8.60397e8i	0.816713	−	1.26687i
$880$	−4.18619e6	+	2.19939e8i	−0.00614287	+	0.322742i
$881$		−	7.75555e8i		−	1.13419i	−0.823653	−	0.567094i	$-0.808068\pi$
$881$		−	7.75555e8i		−	1.13419i	0.823653	−	0.567094i	$-0.191932\pi$
$882$	−4.04876e7	−	1.54525e7i	−0.0590087	−	0.0225213i
$883$	−4.41343e8	+	4.41343e8i	−0.641054	+	0.641054i	−0.950815	−	0.309761i	$-0.899751\pi$
$883$	−4.41343e8	+	4.41343e8i	−0.641054	+	0.641054i	0.309761	+	0.950815i	$0.399751\pi$
$884$	1.01236e9	−	9.93273e8i	1.46547	−	1.43784i
$885$	−6.66652e7	−	3.08564e8i	−0.0961765	−	0.445159i
$886$	1.58122e8	+	752316.i	0.227349	+	0.00108168i
$887$	−5.58813e8			−0.800747			−0.400374	−	0.916352i	$-0.631120\pi$
$887$	−5.58813e8			−0.800747			−0.400374	+	0.916352i	$0.631120\pi$
$888$	4.24927e8	−	8.54763e7i	0.606842	−	0.122069i
$889$			1.32803e8i			0.189018i
$890$	−5.05116e8	−	2.40324e6i	−0.716508	−	0.00340901i
$891$	1.48298e7	+	2.25326e8i	0.0209653	+	0.318551i
$892$	8.76675e6	−	9.21280e8i	0.0123522	−	1.29807i
$893$	−2.54765e8	−	2.54765e8i	−0.357754	−	0.357754i
$894$	1.42290e8	−	3.00340e7i	0.199142	−	0.0420339i
$895$	−7.59559e8			−1.05948
$896$	4.75647e8	+	5.08434e8i	0.661243	+	0.706822i
$897$	−3.01374e8	+	4.67487e8i	−0.417570	+	0.647727i
$898$	2.29641e8	−	2.27466e8i	0.317118	−	0.314115i
$899$	4.92240e8	+	4.92240e8i	0.677482	+	0.677482i
$900$	1.49569e7	−	6.60849e6i	0.0205170	−	0.00906514i
$901$	−5.77895e8	−	5.77895e8i	−0.790087	−	0.790087i
$902$	3.82425e8	+	1.81951e6i	0.521107	+	0.00247933i
$903$	1.40667e8	−	2.18200e8i	0.191042	−	0.296341i
$904$	8.73485e8	+	8.98783e8i	1.18236	+	1.21660i
$905$	−5.08125e8			−0.685527
$906$	−1.58403e8	+	2.43164e8i	−0.213000	+	0.326975i
$907$	1.21432e8	+	1.21432e8i	0.162746	+	0.162746i	0.783782	−	0.621036i	$-0.213288\pi$
$907$	1.21432e8	+	1.21432e8i	0.162746	+	0.162746i	−0.621036	+	0.783782i	$0.713288\pi$
$908$	6.88834e8	−	6.75848e8i	0.920147	−	0.902800i
$909$	−9.74295e7	+	2.58970e8i	−0.129718	+	0.344793i
$910$	−8.54337e8	−	8.62506e8i	−1.13372	−	1.14456i
$911$			4.87382e8i			0.644635i	0.946632	+	0.322318i	$0.104462\pi$
$911$			4.87382e8i			0.644635i	−0.946632	+	0.322318i	$0.895538\pi$
$912$	−4.83189e8	+	7.19087e8i	−0.636989	+	0.947975i
$913$	3.15143e7			0.0414091
$914$	−3.53083e8	+	3.49739e8i	−0.462422	+	0.458043i
$915$	−3.05471e8	−	1.41389e9i	−0.398755	−	1.84566i
$916$	−4.91196e8	+	4.81936e8i	−0.639099	+	0.627051i
$917$	1.54041e8	−	1.54041e8i	0.199769	−	0.199769i
$918$	−1.45926e8	+	9.53797e8i	−0.188627	+	1.23290i
$919$		−	6.65645e8i		−	0.857623i	−0.903394	−	0.428811i	$-0.858932\pi$
$919$		−	6.65645e8i		−	0.857623i	0.903394	−	0.428811i	$-0.141068\pi$
$920$	5.26145e6	−	3.68597e8i	0.00675682	−	0.473356i
$921$	−9.90833e7	+	1.53696e8i	−0.126830	+	0.196736i
$922$	253042.	−	5.31846e7i	0.000322849	−	0.0678567i
$923$	−1.48708e9	+	1.48708e9i	−1.89116	+	1.89116i
$924$	−1.34022e8	+	2.03612e8i	−0.169887	+	0.258100i
$925$	7.77029e6	−	7.77029e6i	0.00981775	−	0.00981775i
$926$	1.75383e8	+	1.77060e8i	0.220879	+	0.222991i
$927$	2.59274e8	+	5.72025e8i	0.325477	+	0.718084i
$928$	1.53412e7	−	6.44770e8i	0.0191962	−	0.806790i
$929$			7.45580e7i			0.0929924i	0.998918	+	0.0464962i	$0.0148055\pi$
$929$			7.45580e7i			0.0929924i	−0.998918	+	0.0464962i	$0.985194\pi$
$930$	−9.44778e8	+	1.99419e8i	−1.17458	+	0.247924i
$931$	4.11610e7	−	4.11610e7i	0.0510078	−	0.0510078i
$932$	1.56680e6	−	1.64652e8i	0.00193538	−	0.203386i
$933$	1.37190e9	−	2.96398e8i	1.68918	−	0.364947i
$934$	7.43515e6	−	1.56273e9i	0.00912534	−	1.91797i
$935$	−3.29095e8			−0.402612
$936$	−5.39640e8	−	1.23725e9i	−0.658077	−	1.50879i
$937$		−	5.54973e8i		−	0.674610i	−0.941395	−	0.337305i	$-0.890485\pi$
$937$		−	5.54973e8i		−	0.674610i	0.941395	−	0.337305i	$-0.109515\pi$
$938$	−4.99998e6	+	1.05090e9i	−0.00605842	+	1.27336i
$939$	1.93711e8	+	8.96602e8i	0.233968	+	1.08294i
$940$	−2.65565e8	+	2.60559e8i	−0.319733	+	0.313705i
$941$	3.51592e8	+	3.51592e8i	0.421959	+	0.421959i	0.885878	−	0.463919i	$-0.153557\pi$
$941$	3.51592e8	+	3.51592e8i	0.421959	+	0.421959i	−0.463919	+	0.885878i	$0.653557\pi$
$942$	3.48504e8	−	7.35606e7i	0.416923	−	0.0880020i
$943$	−6.40863e8			−0.764241
$944$	2.72970e8	−	2.62773e8i	0.324488	−	0.312367i
$945$	8.17018e8	+	1.21024e8i	0.968136	+	0.143409i
$946$	6.92832e7	+	6.99456e7i	0.0818379	+	0.0826204i
$947$	9.34733e8	+	9.34733e8i	1.10062	+	1.10062i	0.994336	+	0.106285i	$0.0338955\pi$
$947$	9.34733e8	+	9.34733e8i	1.10062	+	1.10062i	0.106285	+	0.994336i	$0.466105\pi$
$948$	2.21383e8	+	1.07410e9i	0.259848	+	1.26072i
$949$	1.07670e9	+	1.07670e9i	1.25979	+	1.25979i
$950$	−104500.	+	2.19640e7i	−0.000121884	+	0.0256177i
$951$	1.01278e9	+	6.52911e8i	1.17754	+	0.759123i
$952$	−7.46951e8	+	7.25927e8i	−0.865727	+	0.841360i
$953$	9.64651e8			1.11453			0.557265	−	0.830335i	$-0.311851\pi$
$953$	9.64651e8			1.11453			0.557265	+	0.830335i	$0.311851\pi$
$954$	−7.09970e8	+	3.17736e8i	−0.817702	+	0.365949i
$955$	−6.44910e8	−	6.44910e8i	−0.740439	−	0.740439i
$956$	4.34294e8	+	4.13267e6i	0.497061	+	0.00472995i
$957$	2.20714e8	−	4.76852e7i	0.251822	−	0.0544062i
$958$	−6.56105e8	+	6.49892e8i	−0.746237	+	0.739170i
$959$		−	9.52818e8i		−	1.08032i
$960$	7.37759e8	+	5.05991e8i	0.833875	+	0.571912i
$961$	3.63413e8			0.409478
$962$	−6.38366e8	−	6.44469e8i	−0.717042	−	0.723898i
$963$	1.18276e8	−	3.14380e8i	0.132439	−	0.352027i
$964$	−1.35742e6	+	1.42649e8i	−0.00151525	+	0.159234i
$965$	−1.14140e9	+	1.14140e9i	−1.27016	+	1.27016i
$966$	2.22964e8	−	3.42271e8i	0.247345	−	0.379698i
$967$		−	3.92147e8i		−	0.433680i	−0.976207	−	0.216840i	$-0.930425\pi$
$967$		−	3.92147e8i		−	0.433680i	0.976207	−	0.216840i	$-0.0695750\pi$
$968$	5.67729e8	+	5.84171e8i	0.625914	+	0.644042i
$969$	−1.08933e9	−	7.02260e8i	−1.19726	−	0.771839i
$970$	−3.93680e8	−	1.87306e6i	−0.431349	−	0.00205227i
$971$	7.44775e8	−	7.44775e8i	0.813518	−	0.813518i	−0.171641	−	0.985160i	$-0.554907\pi$
$971$	7.44775e8	−	7.44775e8i	0.813518	−	0.813518i	0.985160	+	0.171641i	$0.0549070\pi$
$972$	7.98575e8	+	4.53439e8i	0.869595	+	0.493765i
$973$	−1.22461e9	+	1.22461e9i	−1.32941	+	1.32941i
$974$	4.60381e7	−	4.56021e7i	0.0498242	−	0.0493524i
$975$	−2.87626e7	−	1.85424e7i	−0.0310323	−	0.0200056i
$976$	1.25079e9	−	1.20407e9i	1.34535	−	1.29510i
$977$		−	9.69389e8i		−	1.03948i	−0.854326	−	0.519738i	$-0.826030\pi$
$977$		−	9.69389e8i		−	1.03948i	0.854326	−	0.519738i	$-0.173970\pi$
$978$	2.32007e7	−	4.89709e6i	0.0248019	−	0.00523506i
$979$	1.50092e8	−	1.50092e8i	0.159960	−	0.159960i
$980$	−4.20971e7	−	4.29060e7i	−0.0447275	−	0.0455869i
$981$	1.58857e8	−	4.22246e8i	0.168267	−	0.447258i
$982$	−4.95822e8	−	2.35903e6i	−0.523590	−	0.00249114i
$983$	7.50910e8			0.790547			0.395273	−	0.918564i	$-0.370650\pi$
$983$	7.50910e8			0.790547			0.395273	+	0.918564i	$0.370650\pi$
$984$	8.61260e8	−	1.29500e9i	0.903959	−	1.35921i
$985$			1.14406e9i			1.19713i
$986$	9.64854e8	+	4.59059e6i	1.00654	+	0.00478892i
$987$	−4.02967e8	+	8.70611e7i	−0.419101	+	0.0905467i
$988$	1.81303e9	+	1.72525e7i	1.87990	+	0.0178888i
$989$	−1.16659e8	−	1.16659e8i	−0.120595	−	0.120595i
$990$	−1.11683e8	+	2.92625e8i	−0.115102	+	0.301582i
$991$	1.01118e8			0.103898			0.0519490	−	0.998650i	$-0.483457\pi$
$991$	1.01118e8			0.103898			0.0519490	+	0.998650i	$0.483457\pi$
$992$	−7.99775e8	−	8.38762e8i	−0.819281	−	0.859218i
$993$	−4.78817e8	−	3.08678e8i	−0.489014	−	0.315253i
$994$	1.09731e9	−	1.08692e9i	1.11730	−	1.10672i
$995$	−6.56065e8	−	6.56065e8i	−0.666006	−	0.666006i
$996$	7.04640e7	−	1.07052e8i	0.0713164	−	0.108347i
$997$	3.54461e8	+	3.54461e8i	0.357670	+	0.357670i	0.862953	−	0.505283i	$-0.168612\pi$
$997$	3.54461e8	+	3.54461e8i	0.357670	+	0.357670i	−0.505283	+	0.862953i	$0.668612\pi$
$998$	−3.10524e8	−	1.47741e6i	−0.312394	−	0.00148631i
$999$	6.10481e8	+	9.04299e7i	0.612316	+	0.0907018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.i.a.5.11	✓	92
3.2	odd	2	inner	48.7.i.a.5.36	yes	92
4.3	odd	2		192.7.i.a.113.5		92
12.11	even	2		192.7.i.a.113.20		92
16.3	odd	4		192.7.i.a.17.20		92
16.13	even	4	inner	48.7.i.a.29.36	yes	92
48.29	odd	4	inner	48.7.i.a.29.11	yes	92
48.35	even	4		192.7.i.a.17.5		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.11	✓	92	1.1	even	1	trivial
48.7.i.a.5.36	yes	92	3.2	odd	2	inner
48.7.i.a.29.11	yes	92	48.29	odd	4	inner
48.7.i.a.29.36	yes	92	16.13	even	4	inner
192.7.i.a.17.5		92	48.35	even	4
192.7.i.a.17.20		92	16.3	odd	4
192.7.i.a.113.5		92	4.3	odd	2
192.7.i.a.113.20		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)

\(f(q)\)	\(=\)	\(q+(-5.62988 - 5.68370i) q^{2} +(26.3911 - 5.70179i) q^{3} +(-0.608985 + 63.9971i) q^{4} +(-89.3741 + 89.3741i) q^{5} +(-180.986 - 117.899i) q^{6} -331.991i q^{7} +(367.169 - 356.834i) q^{8} +(663.979 - 300.953i) q^{9} +O(q^{10})\)	\(q+(-5.62988 - 5.68370i) q^{2} +(26.3911 - 5.70179i) q^{3} +(-0.608985 + 63.9971i) q^{4} +(-89.3741 + 89.3741i) q^{5} +(-180.986 - 117.899i) q^{6} -331.991i q^{7} +(367.169 - 356.834i) q^{8} +(663.979 - 300.953i) q^{9} +(1011.14 + 4.81082i) q^{10} +(-300.455 + 300.455i) q^{11} +(348.827 + 1692.43i) q^{12} +(2557.18 - 2557.18i) q^{13} +(-1886.94 + 1869.07i) q^{14} +(-1849.09 + 2868.27i) q^{15} +(-4095.26 - 77.9466i) q^{16} -6127.72i q^{17} +(-5448.65 - 2079.53i) q^{18} +(5539.28 - 5539.28i) q^{19} +(-5665.26 - 5774.11i) q^{20} +(-1892.95 - 8761.61i) q^{21} +(3399.23 + 16.1729i) q^{22} -5696.38 q^{23} +(7655.40 - 11510.8i) q^{24} -350.476i q^{25} +(-28930.9 - 137.648i) q^{26} +(15807.2 - 11728.4i) q^{27} +(21246.5 + 202.178i) q^{28} +(-13917.5 - 13917.5i) q^{29} +(26712.6 - 5638.36i) q^{30} -35368.3 q^{31} +(22612.8 + 23715.1i) q^{32} +(-6216.21 + 9642.48i) q^{33} +(-34828.2 + 34498.3i) q^{34} +(29671.4 + 29671.4i) q^{35} +(18855.8 + 42676.0i) q^{36} +(22170.7 + 22170.7i) q^{37} +(-62669.1 - 298.167i) q^{38} +(52906.3 - 82067.4i) q^{39} +(-923.649 + 64707.2i) q^{40} +112504. q^{41} +(-39141.4 + 60085.7i) q^{42} +(20479.5 + 20479.5i) q^{43} +(-19045.3 - 19411.2i) q^{44} +(-32445.1 + 86240.0i) q^{45} +(32069.9 + 32376.5i) q^{46} -45992.4i q^{47} +(-108523. + 21293.2i) q^{48} +7430.75 q^{49} +(-1992.00 + 1973.13i) q^{50} +(-34939.0 - 161717. i) q^{51} +(162095. + 165210. i) q^{52} +(94308.3 - 94308.3i) q^{53} +(-155653. - 23814.0i) q^{54} -53705.9i q^{55} +(-118466. - 121897. i) q^{56} +(114604. - 177771. i) q^{57} +(-749.151 + 157457. i) q^{58} +(-65410.2 + 65410.2i) q^{59} +(-182435. - 120083. i) q^{60} +(-299720. + 299720. i) q^{61} +(199119. + 201023. i) q^{62} +(-99913.8 - 220435. i) q^{63} +(7482.31 - 262037. i) q^{64} +457092. i q^{65} +(89801.5 - 18954.9i) q^{66} +(279791. - 279791. i) q^{67} +(392156. + 3731.69i) q^{68} +(-150334. + 32479.6i) q^{69} +(1597.15 - 335690. i) q^{70} -581529. q^{71} +(136402. - 347431. i) q^{72} +421050. i q^{73} +(1193.40 - 250830. i) q^{74} +(-1998.34 - 9249.44i) q^{75} +(351124. + 357871. i) q^{76} +(99748.6 + 99748.6i) q^{77} +(-764303. + 161325. i) q^{78} +634651. q^{79} +(372977. - 359044. i) q^{80} +(350295. - 399653. i) q^{81} +(-633381. - 639437. i) q^{82} +(-52444.2 - 52444.2i) q^{83} +(561871. - 115807. i) q^{84} +(547660. + 547660. i) q^{85} +(1102.37 - 231696. i) q^{86} +(-446654. - 287944. i) q^{87} +(-3105.10 + 217531. i) q^{88} -499550. q^{89} +(672825. - 301112. i) q^{90} +(-848963. - 848963. i) q^{91} +(3469.01 - 364552. i) q^{92} +(-933408. + 201663. i) q^{93} +(-261407. + 258931. i) q^{94} +990136. i q^{95} +(731994. + 496933. i) q^{96} -389343. q^{97} +(-41834.2 - 42234.2i) q^{98} +(-109073. + 289919. 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more