LMFDB - Embedded newform 38.6.e.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, 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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	38.25
Dual form			38.6.e.a.35.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.06418 + 2.57115i) q^{2} +(12.9479 + 4.71264i) q^{3} +(2.77837 - 15.7569i) q^{4} +(-13.1062 - 74.3288i) q^{5} +(-51.7915 + 18.8506i) q^{6} +(39.5277 - 68.4640i) q^{7} +(32.0000 + 55.4256i) q^{8} +(-40.7104 - 34.1601i) q^{9} +O(q^{10})$	\(q+(-3.06418 + 2.57115i) q^{2} +(12.9479 + 4.71264i) q^{3} +(2.77837 - 15.7569i) q^{4} +(-13.1062 - 74.3288i) q^{5} +(-51.7915 + 18.8506i) q^{6} +(39.5277 - 68.4640i) q^{7} +(32.0000 + 55.4256i) q^{8} +(-40.7104 - 34.1601i) q^{9} +(231.270 + 194.059i) q^{10} +(-20.5737 - 35.6348i) q^{11} +(110.231 - 190.925i) q^{12} +(1071.56 - 390.014i) q^{13} +(54.9113 + 311.417i) q^{14} +(180.588 - 1024.16i) q^{15} +(-240.561 - 87.5572i) q^{16} +(851.216 - 714.255i) q^{17} +212.575 q^{18} +(-1150.39 + 1073.64i) q^{19} -1207.61 q^{20} +(834.445 - 700.183i) q^{21} +(154.664 + 56.2931i) q^{22} +(-479.761 + 2720.86i) q^{23} +(153.131 + 868.448i) q^{24} +(-2416.46 + 879.520i) q^{25} +(-2280.65 + 3950.20i) q^{26} +(-2040.26 - 3533.83i) q^{27} +(-968.959 - 813.053i) q^{28} +(-3063.83 - 2570.86i) q^{29} +(2079.93 + 3602.54i) q^{30} +(-832.075 + 1441.20i) q^{31} +(962.245 - 350.229i) q^{32} +(-98.4523 - 558.351i) q^{33} +(-771.820 + 4377.21i) q^{34} +(-5606.90 - 2040.75i) q^{35} +(-651.366 + 546.561i) q^{36} +11620.4 q^{37} +(764.504 - 6247.65i) q^{38} +15712.4 q^{39} +(3700.32 - 3104.94i) q^{40} +(-7502.02 - 2730.51i) q^{41} +(-756.614 + 4290.97i) q^{42} +(1213.71 + 6883.31i) q^{43} +(-618.656 + 225.172i) q^{44} +(-2005.52 + 3473.66i) q^{45} +(-5525.66 - 9570.73i) q^{46} +(-7979.51 - 6695.61i) q^{47} +(-2702.13 - 2267.36i) q^{48} +(5278.62 + 9142.84i) q^{49} +(5143.09 - 8908.09i) q^{50} +(14387.5 - 5236.61i) q^{51} +(-3168.25 - 17968.0i) q^{52} +(-2096.46 + 11889.6i) q^{53} +(15337.7 + 5582.47i) q^{54} +(-2379.05 + 1996.26i) q^{55} +5059.54 q^{56} +(-19954.8 + 8479.99i) q^{57} +15998.2 q^{58} +(19693.4 - 16524.7i) q^{59} +(-15635.9 - 5691.02i) q^{60} +(-2287.20 + 12971.4i) q^{61} +(-1155.91 - 6555.47i) q^{62} +(-3947.92 + 1436.93i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-43033.3 - 74535.9i) q^{65} +(1737.28 + 1457.75i) q^{66} +(42479.3 + 35644.3i) q^{67} +(-8889.47 - 15397.0i) q^{68} +(-19034.3 + 32968.4i) q^{69} +(22427.6 - 8162.98i) q^{70} +(12538.2 + 71107.6i) q^{71} +(590.611 - 3349.52i) q^{72} +(6298.26 + 2292.38i) q^{73} +(-35606.9 + 29877.7i) q^{74} -35432.9 q^{75} +(13721.1 + 21109.6i) q^{76} -3252.93 q^{77} +(-48145.5 + 40398.8i) q^{78} +(57445.8 + 20908.6i) q^{79} +(-3355.18 + 19028.2i) q^{80} +(-7520.85 - 42652.9i) q^{81} +(30008.1 - 10922.0i) q^{82} +(-22100.1 + 38278.5i) q^{83} +(-8714.33 - 15093.7i) q^{84} +(-64245.9 - 53908.7i) q^{85} +(-21417.1 - 17971.0i) q^{86} +(-27554.5 - 47725.8i) q^{87} +(1316.72 - 2280.63i) q^{88} +(-98716.5 + 35929.9i) q^{89} +(-2786.04 - 15800.4i) q^{90} +(15654.2 - 88779.3i) q^{91} +(41539.4 + 15119.1i) q^{92} +(-17565.4 + 14739.1i) q^{93} +41666.1 q^{94} +(94879.6 + 71435.7i) q^{95} +14109.5 q^{96} +(124717. - 104650. i) q^{97} +(-39682.3 - 14443.2i) q^{98} +(-379.721 + 2153.51i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9}+O(q^{10}) $ 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9	\( 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9} + 600 q^{11} - 1662 q^{13} - 1776 q^{14} - 1206 q^{15} + 4194 q^{17} - 4368 q^{18} + 9570 q^{19} - 1344 q^{20} + 2430 q^{21} - 5160 q^{22} - 1170 q^{23} - 1152 q^{24} + 5940 q^{25} - 1776 q^{26} - 5130 q^{27} + 768 q^{28} - 7554 q^{29} + 294 q^{31} - 45912 q^{33} + 1584 q^{34} + 22116 q^{35} + 6048 q^{36} + 28608 q^{37} - 9528 q^{38} - 38868 q^{39} + 37278 q^{41} - 9720 q^{42} + 13212 q^{43} + 20640 q^{44} - 34344 q^{45} - 29856 q^{46} - 3054 q^{47} - 9216 q^{48} + 1422 q^{49} + 16584 q^{50} + 2352 q^{51} - 1824 q^{52} + 73806 q^{53} + 136944 q^{54} - 41598 q^{55} + 56064 q^{56} + 178248 q^{57} - 52848 q^{58} + 123528 q^{59} + 46944 q^{60} - 149172 q^{61} + 58344 q^{62} - 170124 q^{63} - 49152 q^{64} - 202674 q^{65} - 84840 q^{66} - 313212 q^{67} + 35520 q^{68} - 19938 q^{69} - 88464 q^{70} + 75810 q^{71} + 48384 q^{72} + 172872 q^{73} + 4872 q^{74} + 174960 q^{75} + 31008 q^{76} - 115056 q^{77} + 101304 q^{78} + 158058 q^{79} - 47250 q^{81} - 149112 q^{82} - 148440 q^{83} - 176736 q^{84} - 226752 q^{85} - 57528 q^{86} + 182874 q^{87} - 38400 q^{88} - 322464 q^{89} + 48816 q^{90} - 27264 q^{91} + 88992 q^{92} + 779424 q^{93} + 143712 q^{94} + 634752 q^{95} - 108552 q^{97} - 173544 q^{98} + 656436 q^{99}+O(q^{100}) \) 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9 + 600 * q^11 - 1662 * q^13 - 1776 * q^14 - 1206 * q^15 + 4194 * q^17 - 4368 * q^18 + 9570 * q^19 - 1344 * q^20 + 2430 * q^21 - 5160 * q^22 - 1170 * q^23 - 1152 * q^24 + 5940 * q^25 - 1776 * q^26 - 5130 * q^27 + 768 * q^28 - 7554 * q^29 + 294 * q^31 - 45912 * q^33 + 1584 * q^34 + 22116 * q^35 + 6048 * q^36 + 28608 * q^37 - 9528 * q^38 - 38868 * q^39 + 37278 * q^41 - 9720 * q^42 + 13212 * q^43 + 20640 * q^44 - 34344 * q^45 - 29856 * q^46 - 3054 * q^47 - 9216 * q^48 + 1422 * q^49 + 16584 * q^50 + 2352 * q^51 - 1824 * q^52 + 73806 * q^53 + 136944 * q^54 - 41598 * q^55 + 56064 * q^56 + 178248 * q^57 - 52848 * q^58 + 123528 * q^59 + 46944 * q^60 - 149172 * q^61 + 58344 * q^62 - 170124 * q^63 - 49152 * q^64 - 202674 * q^65 - 84840 * q^66 - 313212 * q^67 + 35520 * q^68 - 19938 * q^69 - 88464 * q^70 + 75810 * q^71 + 48384 * q^72 + 172872 * q^73 + 4872 * q^74 + 174960 * q^75 + 31008 * q^76 - 115056 * q^77 + 101304 * q^78 + 158058 * q^79 - 47250 * q^81 - 149112 * q^82 - 148440 * q^83 - 176736 * q^84 - 226752 * q^85 - 57528 * q^86 + 182874 * q^87 - 38400 * q^88 - 322464 * q^89 + 48816 * q^90 - 27264 * q^91 + 88992 * q^92 + 779424 * q^93 + 143712 * q^94 + 634752 * q^95 - 108552 * q^97 - 173544 * q^98 + 656436 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−3.06418	+	2.57115i	−0.541675	+	0.454519i
$2$	−3.06418	+	2.57115i	−0.541675	+	0.454519i
$3$	12.9479	+	4.71264i	0.830606	+	0.302316i	0.722108	−	0.691781i	$-0.243173\pi$
$3$	12.9479	+	4.71264i	0.830606	+	0.302316i	0.108499	+	0.994097i	$0.465396\pi$
$4$	2.77837	−	15.7569i	0.0868241	−	0.492404i
$5$	−13.1062	−	74.3288i	−0.234450	−	1.32963i	−0.843768	−	0.536708i	$-0.819668\pi$
$5$	−13.1062	−	74.3288i	−0.234450	−	1.32963i	0.609318	−	0.792926i	$-0.291443\pi$
$6$	−51.7915	+	18.8506i	−0.587327	+	0.213770i
$7$	39.5277	−	68.4640i	0.304899	−	0.528101i	−0.672340	−	0.740243i	$-0.734711\pi$
$7$	39.5277	−	68.4640i	0.304899	−	0.528101i	0.977239	+	0.212142i	$0.0680439\pi$
$8$	32.0000	+	55.4256i	0.176777	+	0.306186i
$9$	−40.7104	−	34.1601i	−0.167533	−	0.140576i
$10$	231.270	+	194.059i	0.731341	+	0.613668i
$11$	−20.5737	−	35.6348i	−0.0512663	−	0.0887958i	0.839253	−	0.543740i	$-0.182992\pi$
$11$	−20.5737	−	35.6348i	−0.0512663	−	0.0887958i	−0.890520	+	0.454945i	$0.849659\pi$
$12$	110.231	−	190.925i	0.220978	−	0.382745i
$13$	1071.56	−	390.014i	1.75856	−	0.640062i	0.758622	−	0.651531i	$-0.225873\pi$
$13$	1071.56	−	390.014i	1.75856	−	0.640062i	0.999934	+	0.0114683i	$0.00365056\pi$
$14$	54.9113	+	311.417i	0.0748758	+	0.424642i
$15$	180.588	−	1024.16i	0.207234	−	1.17528i
$16$	−240.561	−	87.5572i	−0.234923	−	0.0855050i
$17$	851.216	−	714.255i	0.714360	−	0.599420i	−0.211459	−	0.977387i	$-0.567821\pi$
$17$	851.216	−	714.255i	0.714360	−	0.599420i	0.925819	+	0.377967i	$0.123377\pi$
$18$	212.575			0.154643
$19$	−1150.39	+	1073.64i	−0.731073	+	0.682299i
$19$	−1150.39	+	1073.64i	−0.731073	+	0.682299i
$20$	−1207.61			−0.675073
$21$	834.445	−	700.183i	0.412905	−	0.346468i
$22$	154.664	+	56.2931i	0.0681291	+	0.0247970i
$23$	−479.761	+	2720.86i	−0.189106	+	1.07247i	0.731460	+	0.681885i	$0.238839\pi$
$23$	−479.761	+	2720.86i	−0.189106	+	1.07247i	−0.920566	+	0.390588i	$0.872272\pi$
$24$	153.131	+	868.448i	0.0542669	+	0.307763i
$25$	−2416.46	+	879.520i	−0.773268	+	0.281446i
$26$	−2280.65	+	3950.20i	−0.661646	+	1.14600i
$27$	−2040.26	−	3533.83i	−0.538611	−	0.932902i
$28$	−968.959	−	813.053i	−0.233566	−	0.195985i
$29$	−3063.83	−	2570.86i	−0.676502	−	0.567653i	0.238480	−	0.971147i	$-0.423351\pi$
$29$	−3063.83	−	2570.86i	−0.676502	−	0.567653i	−0.914982	+	0.403495i	$0.867795\pi$
$30$	2079.93	+	3602.54i	0.421935	+	0.730812i
$31$	−832.075	+	1441.20i	−0.155510	+	0.269351i	−0.933245	−	0.359242i	$-0.883035\pi$
$31$	−832.075	+	1441.20i	−0.155510	+	0.269351i	0.777735	+	0.628593i	$0.216369\pi$
$32$	962.245	−	350.229i	0.166116	−	0.0604612i
$33$	−98.4523	−	558.351i	−0.0157377	−	0.0892529i
$34$	−771.820	+	4377.21i	−0.114503	+	0.649381i
$35$	−5606.90	−	2040.75i	−0.773665	−	0.281591i
$36$	−651.366	+	546.561i	−0.0837663	+	0.0702882i
$37$	11620.4			1.39546			0.697728	−	0.716363i	$-0.254195\pi$
$37$	11620.4			1.39546			0.697728	+	0.716363i	$0.254195\pi$
$38$	764.504	−	6247.65i	0.0858857	−	0.701872i
$39$	15712.4			1.65417
$40$	3700.32	−	3104.94i	0.365670	−	0.306834i
$41$	−7502.02	−	2730.51i	−0.696977	−	0.253679i	−0.0308573	−	0.999524i	$-0.509824\pi$
$41$	−7502.02	−	2730.51i	−0.696977	−	0.253679i	−0.666120	+	0.745845i	$0.732046\pi$
$42$	−756.614	+	4290.97i	−0.0661837	+	0.375346i
$43$	1213.71	+	6883.31i	0.100102	+	0.567709i	0.993064	+	0.117576i	$0.0375124\pi$
$43$	1213.71	+	6883.31i	0.100102	+	0.567709i	−0.892961	+	0.450133i	$0.851376\pi$
$44$	−618.656	+	225.172i	−0.0481745	+	0.0175341i
$45$	−2005.52	+	3473.66i	−0.147637	+	0.255715i
$46$	−5525.66	−	9570.73i	−0.385026	−	0.666884i
$47$	−7979.51	−	6695.61i	−0.526904	−	0.442125i	0.340126	−	0.940380i	$-0.389530\pi$
$47$	−7979.51	−	6695.61i	−0.526904	−	0.442125i	−0.867031	+	0.498254i	$0.833975\pi$
$48$	−2702.13	−	2267.36i	−0.169279	−	0.142042i
$49$	5278.62	+	9142.84i	0.314073	+	0.543990i
$50$	5143.09	−	8908.09i	0.290937	−	0.503918i
$51$	14387.5	−	5236.61i	0.774566	−	0.281919i
$52$	−3168.25	−	17968.0i	−0.162484	−	0.921493i
$53$	−2096.46	+	11889.6i	−0.102517	+	0.581403i	0.889666	+	0.456612i	$0.150937\pi$
$53$	−2096.46	+	11889.6i	−0.102517	+	0.581403i	−0.992183	+	0.124791i	$0.960174\pi$
$54$	15337.7	+	5582.47i	0.715775	+	0.260521i
$55$	−2379.05	+	1996.26i	−0.106046	+	0.0889836i
$56$	5059.54			0.215596
$57$	−19954.8	+	8479.99i	−0.813504	+	0.345707i
$58$	15998.2			0.624454
$59$	19693.4	−	16524.7i	0.736530	−	0.618022i	−0.195373	−	0.980729i	$-0.562592\pi$
$59$	19693.4	−	16524.7i	0.736530	−	0.618022i	0.931903	+	0.362707i	$0.118147\pi$
$60$	−15635.9	−	5691.02i	−0.560720	−	0.204085i
$61$	−2287.20	+	12971.4i	−0.0787009	+	0.446335i	0.919838	+	0.392298i	$0.128320\pi$
$61$	−2287.20	+	12971.4i	−0.0787009	+	0.446335i	−0.998539	+	0.0540365i	$0.982791\pi$
$62$	−1155.91	−	6555.47i	−0.0381894	−	0.216583i
$63$	−3947.92	+	1436.93i	−0.125319	+	0.0456124i
$64$	−2048.00	+	3547.24i	−0.0625000	+	0.108253i
$65$	−43033.3	−	74535.9i	−1.26334	−	2.18817i
$66$	1737.28	+	1457.75i	0.0490919	+	0.0411930i
$67$	42479.3	+	35644.3i	1.15609	+	0.970071i	0.999844	−	0.0176476i	$-0.00561771\pi$
$67$	42479.3	+	35644.3i	1.15609	+	0.970071i	0.156242	+	0.987719i	$0.450062\pi$
$68$	−8889.47	−	15397.0i	−0.233133	−	0.403798i
$69$	−19034.3	+	32968.4i	−0.481298	+	0.833633i
$70$	22427.6	−	8162.98i	0.547064	−	0.199115i
$71$	12538.2	+	71107.6i	0.295181	+	1.67406i	0.666465	+	0.745536i	$0.267807\pi$
$71$	12538.2	+	71107.6i	0.295181	+	1.67406i	−0.371284	+	0.928519i	$0.621082\pi$
$72$	590.611	−	3349.52i	0.0134267	−	0.0761468i
$73$	6298.26	+	2292.38i	0.138329	+	0.0503477i	0.410257	−	0.911970i	$-0.365439\pi$
$73$	6298.26	+	2292.38i	0.138329	+	0.0503477i	−0.271928	+	0.962318i	$0.587661\pi$
$74$	−35606.9	+	29877.7i	−0.755884	+	0.634262i
$75$	−35432.9			−0.727367
$76$	13721.1	+	21109.6i	0.272492	+	0.419223i
$77$	−3252.93			−0.0625242
$78$	−48145.5	+	40398.8i	−0.896023	+	0.751852i
$79$	57445.8	+	20908.6i	1.03560	+	0.376926i	0.803209	−	0.595697i	$-0.203124\pi$
$79$	57445.8	+	20908.6i	1.03560	+	0.376926i	0.232387	+	0.972623i	$0.425346\pi$
$80$	−3355.18	+	19028.2i	−0.0586126	+	0.332409i
$81$	−7520.85	−	42652.9i	−0.127366	−	0.722330i
$82$	30008.1	−	10922.0i	0.492837	−	0.179378i
$83$	−22100.1	+	38278.5i	−0.352127	+	0.609901i	−0.986622	−	0.163025i	$-0.947875\pi$
$83$	−22100.1	+	38278.5i	−0.352127	+	0.609901i	0.634495	+	0.772927i	$0.281208\pi$
$84$	−8714.33	−	15093.7i	−0.134752	−	0.233398i
$85$	−64245.9	−	53908.7i	−0.964491	−	0.809304i
$86$	−21417.1	−	17971.0i	−0.312258	−	0.262016i
$87$	−27554.5	−	47725.8i	−0.390296	−	0.676013i
$88$	1316.72	−	2280.63i	0.0181254	−	0.0313940i
$89$	−98716.5	+	35929.9i	−1.32104	+	0.480818i	−0.903790	−	0.427976i	$-0.859227\pi$
$89$	−98716.5	+	35929.9i	−1.32104	+	0.480818i	−0.417246	+	0.908794i	$0.637005\pi$
$90$	−2786.04	−	15800.4i	−0.0362561	−	0.205619i
$91$	15654.2	−	88779.3i	0.198165	−	1.12385i
$92$	41539.4	+	15119.1i	0.511671	+	0.186233i
$93$	−17565.4	+	14739.1i	−0.210597	+	0.176712i
$94$	41666.1			0.486366
$95$	94879.6	+	71435.7i	1.07861	+	0.812094i
$96$	14109.5			0.156255
$97$	124717.	−	104650.i	1.34585	−	1.12930i	0.365768	−	0.930706i	$-0.380806\pi$
$97$	124717.	−	104650.i	1.34585	−	1.12930i	0.980081	−	0.198596i	$-0.0636382\pi$
$98$	−39682.3	−	14443.2i	−0.417380	−	0.151914i
$99$	−379.721	+	2153.51i	−0.00389383	+	0.0220830i
$100$	7144.70	+	40519.6i	0.0714470	+	0.405196i
$101$	82748.2	−	30117.9i	0.807152	−	0.293779i	0.0947050	−	0.995505i	$-0.469809\pi$
$101$	82748.2	−	30117.9i	0.807152	−	0.293779i	0.712447	+	0.701726i	$0.247587\pi$
$102$	−30621.6	+	53038.2i	−0.291426	+	0.504764i
$103$	5230.42	+	9059.35i	0.0485784	+	0.0841402i	0.889292	−	0.457340i	$-0.151198\pi$
$103$	5230.42	+	9059.35i	0.0485784	+	0.0841402i	−0.840714	+	0.541480i	$0.817864\pi$
$104$	55906.6	+	46911.2i	0.506850	+	0.425298i
$105$	−62980.1	−	52846.6i	−0.557481	−	0.467782i
$106$	−24146.0	−	41822.1i	−0.208728	−	0.361528i
$107$	72529.3	−	125624.i	0.612426	−	1.06075i	−0.378404	−	0.925641i	$-0.623527\pi$
$107$	72529.3	−	125624.i	0.612426	−	1.06075i	0.990830	−	0.135113i	$-0.0431397\pi$
$108$	−61350.9	+	22329.9i	−0.506129	+	0.184216i
$109$	17701.1	+	100388.i	0.142704	+	0.809312i	0.969182	+	0.246344i	$0.0792294\pi$
$109$	17701.1	+	100388.i	0.142704	+	0.809312i	−0.826479	+	0.562968i	$0.809660\pi$
$110$	2157.14	−	12233.8i	0.0169980	−	0.0964004i
$111$	150459.	+	54762.7i	1.15907	+	0.421868i
$112$	−15503.3	+	13008.8i	−0.116783	+	0.0979927i
$113$	−158263.			−1.16596			−0.582980	−	0.812487i	$-0.698113\pi$
$113$	−158263.			−1.16596			−0.582980	+	0.812487i	$0.698113\pi$
$114$	39341.6	−	77290.9i	0.283524	−	0.557014i
$115$	208526.			1.47033
$116$	−49021.2	+	41133.7i	−0.338251	+	0.283826i
$117$	−56946.4	−	20726.8i	−0.384593	−	0.139980i
$118$	−17856.5	+	101269.i	−0.118057	+	0.669534i
$119$	−15254.1	−	86510.4i	−0.0987461	−	0.560017i
$120$	62543.8	−	22764.1i	0.396489	−	0.144310i
$121$	79678.9	−	138008.i	0.494744	−	0.856921i
$122$	−26342.9	−	45627.3i	−0.160238	−	0.277540i
$123$	−84267.2	−	70708.6i	−0.502222	−	0.421414i
$124$	20397.0	+	17115.1i	0.119128	+	0.0999598i
$125$	−20886.2	−	36175.9i	−0.119559	−	0.207083i
$126$	8402.58	−	14553.7i	0.0471505	−	0.0816671i
$127$	−229074.	+	83376.1i	−1.26028	+	0.458704i	−0.883862	−	0.467747i	$-0.845066\pi$
$127$	−229074.	+	83376.1i	−1.26028	+	0.458704i	−0.376416	+	0.926451i	$0.622844\pi$
$128$	−2845.05	−	16135.1i	−0.0153485	−	0.0870455i
$129$	−16723.6	+	94844.0i	−0.0884819	+	0.501806i
$130$	323505.	+	117746.i	1.67889	+	0.611066i
$131$	203201.	−	170506.i	1.03454	−	0.868084i	0.0431574	−	0.999068i	$-0.486258\pi$
$131$	203201.	−	170506.i	1.03454	−	0.868084i	0.991384	+	0.130985i	$0.0418139\pi$
$132$	−9071.43			−0.0453149
$133$	28033.5	+	121199.i	0.137419	+	0.594113i
$134$	−221811.			−1.06714
$135$	−235925.	+	197965.i	−1.11414	+	0.934876i
$136$	66826.9	+	24323.0i	0.309816	+	0.112764i
$137$	−50422.5	+	285960.i	−0.229521	+	1.30168i	0.624330	+	0.781161i	$0.285372\pi$
$137$	−50422.5	+	285960.i	−0.229521	+	1.30168i	−0.853851	+	0.520518i	$0.825739\pi$
$138$	−26442.2	−	149961.i	−0.118195	−	0.670318i
$139$	−320914.	+	116803.i	−1.40881	+	0.512765i	−0.930780	−	0.365579i	$-0.880871\pi$
$139$	−320914.	+	116803.i	−1.40881	+	0.512765i	−0.478029	+	0.878344i	$0.658649\pi$
$140$	−47733.9	+	82677.6i	−0.205829	+	0.356507i
$141$	−71763.7	−	124298.i	−0.303989	−	0.526524i
$142$	−221247.	−	185649.i	−0.920783	−	0.772629i
$143$	−35944.0	−	30160.6i	−0.146989	−	0.123339i
$144$	6802.39	+	11782.1i	0.0273373	+	0.0473495i
$145$	−150934.	+	261425.i	−0.596164	+	1.03259i
$146$	−25193.0	+	9169.52i	−0.0978134	+	0.0356012i
$147$	25260.0	+	143257.i	0.0964140	+	0.546791i
$148$	32285.7	−	183101.i	0.121159	−	0.687128i
$149$	136095.	+	49534.6i	0.502200	+	0.182786i	0.580683	−	0.814130i	$-0.302785\pi$
$149$	136095.	+	49534.6i	0.502200	+	0.182786i	−0.0784831	+	0.996915i	$0.525008\pi$
$150$	108573.	−	91103.3i	0.393997	−	0.330602i
$151$	12034.6			0.0429527			0.0214764	−	0.999769i	$-0.493163\pi$
$151$	12034.6			0.0429527			0.0214764	+	0.999769i	$0.493163\pi$
$152$	−96319.7	−	29404.5i	−0.338147	−	0.103230i
$153$	−59052.3			−0.203943
$154$	9967.56	−	8363.77i	0.0338678	−	0.0284185i
$155$	118028.	+	42958.6i	0.394598	+	0.143622i
$156$	43654.8	−	247578.i	0.143622	−	0.814519i
$157$	−22532.5	−	127788.i	−0.0729560	−	0.413754i	−0.999311	−	0.0371034i	$-0.988187\pi$
$157$	−22532.5	−	127788.i	−0.0729560	−	0.413754i	0.926355	−	0.376650i	$-0.122924\pi$
$158$	−229783.	+	83634.3i	−0.732277	+	0.266527i
$159$	−83176.0	+	144065.i	−0.260919	+	0.451924i
$160$	−38643.4	−	66932.4i	−0.119337	−	0.206698i
$161$	167317.	+	140396.i	0.508716	+	0.426863i
$162$	132712.	+	111359.i	0.397304	+	0.333378i
$163$	200318.	+	346960.i	0.590541	+	1.02285i	0.994160	+	0.107920i	$0.0344189\pi$
$163$	200318.	+	346960.i	0.590541	+	1.02285i	−0.403619	+	0.914927i	$0.632248\pi$
$164$	−63867.8	+	110622.i	−0.185427	+	0.321169i
$165$	−40211.2	+	14635.7i	−0.114984	+	0.0418508i
$166$	−30701.1	−	174115.i	−0.0864737	−	0.490417i
$167$	10007.2	−	56753.7i	0.0277665	−	0.157472i	−0.967772	−	0.251828i	$-0.918968\pi$
$167$	10007.2	−	56753.7i	0.0277665	−	0.157472i	0.995538	+	0.0943564i	$0.0300793\pi$
$168$	65510.3	+	23843.8i	0.179076	+	0.0651782i
$169$	711693.	−	597182.i	1.91680	−	1.60838i
$170$	335468.			0.890285
$171$	83508.5	−	4410.96i	0.218394	−	0.0115357i
$172$	111832.			0.288234
$173$	−106546.	+	89402.4i	−0.270658	+	0.227109i	−0.768007	−	0.640442i	$-0.778751\pi$
$173$	−106546.	+	89402.4i	−0.270658	+	0.227109i	0.497349	+	0.867550i	$0.334307\pi$
$174$	207142.	+	75393.6i	0.518675	+	0.188782i
$175$	−35301.7	+	200206.i	−0.0871366	+	0.494176i
$176$	1829.17	+	10373.7i	0.00445115	+	0.0252437i
$177$	332862.	−	121152.i	0.798604	−	0.290668i
$178$	210104.	−	363910.i	0.497031	−	0.860884i
$179$	−204606.	−	354388.i	−0.477293	−	0.826696i	0.522368	−	0.852720i	$-0.325049\pi$
$179$	−204606.	−	354388.i	−0.477293	−	0.826696i	−0.999661	+	0.0260238i	$0.991715\pi$
$180$	49162.2	+	41252.0i	0.113097	+	0.0948994i
$181$	−473818.	−	397580.i	−1.07502	−	0.902045i	−0.0795184	−	0.996833i	$-0.525338\pi$
$181$	−473818.	−	397580.i	−1.07502	−	0.902045i	−0.995497	+	0.0947880i	$0.969783\pi$
$182$	180298.	+	312285.i	0.403471	+	0.698832i
$183$	−90743.7	+	157173.i	−0.200304	+	0.346936i
$184$	−166158.	+	60476.4i	−0.361806	+	0.131687i
$185$	−152299.	−	863729.i	−0.327165	−	1.85545i
$186$	15927.0	−	90326.7i	0.0337561	−	0.191441i
$187$	−42965.0	−	15638.0i	−0.0898485	−	0.0327022i
$188$	−127672.	+	107130.i	−0.263452	+	0.221063i
$189$	−322587.			−0.656889
$190$	−474400.	+	25058.1i	−0.953368	+	0.0503575i
$191$	676517.			1.34182			0.670911	−	0.741538i	$-0.265903\pi$
$191$	676517.			1.34182			0.670911	+	0.741538i	$0.265903\pi$
$192$	−43234.1	+	36277.7i	−0.0846396	+	0.0710210i
$193$	740599.	+	269556.i	1.43117	+	0.520902i	0.937265	−	0.348616i	$-0.113348\pi$
$193$	740599.	+	269556.i	1.43117	+	0.520902i	0.493901	+	0.869518i	$0.335571\pi$
$194$	−113084.	+	641333.i	−0.215724	+	1.22343i
$195$	−205929.	−	1.16788e6i	−0.387821	−	2.19944i
$196$	158729.	−	57772.7i	0.295132	−	0.107419i
$197$	−322803.	+	559111.i	−0.592614	+	1.02644i	0.401265	+	0.915962i	$0.368571\pi$
$197$	−322803.	+	559111.i	−0.592614	+	1.02644i	−0.993879	+	0.110475i	$0.964763\pi$
$198$	−4373.46	−	7575.05i	−0.00792797	−	0.0137316i
$199$	−418799.	−	351414.i	−0.749675	−	0.629052i	0.185742	−	0.982599i	$-0.440531\pi$
$199$	−418799.	−	351414.i	−0.749675	−	0.629052i	−0.935417	+	0.353547i	$0.884976\pi$
$200$	−126075.	−	105789.i	−0.222871	−	0.187011i
$201$	382037.	+	661708.i	0.666984	+	1.15525i
$202$	−176118.	+	305045.i	−0.303686	+	0.525999i
$203$	−297117.	+	108142.i	−0.506043	+	0.184185i
$204$	−42539.1	−	241251.i	−0.0715670	−	0.405877i
$205$	−104633.	+	593403.i	−0.173894	+	0.986199i
$206$	−39319.9	−	14311.3i	−0.0645571	−	0.0234969i
$207$	112476.	−	94378.6i	0.182446	−	0.153090i
$208$	−291923.			−0.467854
$209$	61926.7	+	18905.0i	0.0980647	+	0.0299372i
$210$	328859.			0.514590
$211$	−270587.	+	227049.i	−0.418409	+	0.351087i	−0.827557	−	0.561381i	$-0.810270\pi$
$211$	−270587.	+	227049.i	−0.418409	+	0.351087i	0.409149	+	0.912468i	$0.365826\pi$
$212$	181519.	+	66067.4i	0.277384	+	0.100960i
$213$	−172762.	+	979780.i	−0.260914	+	1.47972i
$214$	100757.	+	571419.i	0.150397	+	0.852944i
$215$	495721.	−	180428.i	0.731377	−	0.266199i
$216$	130576.	−	226165.i	0.190428	−	0.329831i
$217$	65780.0	+	113934.i	0.0948297	+	0.164250i
$218$	−312352.	−	262095.i	−0.445147	−	0.373523i
$219$	70745.9	+	59362.9i	0.0996761	+	0.0836382i
$220$	24845.0	+	43032.8i	0.0346085	+	0.0599436i
$221$	633555.	−	1.09735e6i	0.872577	−	1.51135i
$222$	−601837.	+	219051.i	−0.819589	+	0.298306i
$223$	−189462.	−	1.07450e6i	−0.255130	−	1.44691i	−0.795739	−	0.605639i	$-0.792918\pi$
$223$	−189462.	−	1.07450e6i	−0.255130	−	1.44691i	0.540610	−	0.841273i	$-0.318194\pi$
$224$	14057.3	−	79722.9i	0.0187190	−	0.106160i
$225$	128420.	+	46740.9i	0.169112	+	0.0615518i
$226$	484946.	−	406918.i	0.631572	−	0.529951i
$227$	−148065.			−0.190717			−0.0953584	−	0.995443i	$-0.530400\pi$
$227$	−148065.			−0.190717			−0.0953584	+	0.995443i	$0.530400\pi$
$228$	78176.9	+	337986.i	0.0995958	+	0.430588i
$229$	−1.05341e6			−1.32742			−0.663708	−	0.747992i	$-0.731018\pi$
$229$	−1.05341e6			−1.32742			−0.663708	+	0.747992i	$0.731018\pi$
$230$	−638961.	+	536152.i	−0.796443	+	0.668295i
$231$	−42118.5	−	15329.9i	−0.0519330	−	0.0189021i
$232$	44448.8	−	252082.i	0.0542176	−	0.307483i
$233$	−108550.	−	615618.i	−0.130991	−	0.742885i	−0.977568	−	0.210620i	$-0.932452\pi$
$233$	−108550.	−	615618.i	−0.130991	−	0.742885i	0.846577	−	0.532266i	$-0.178659\pi$
$234$	227786.	−	82907.2i	0.271948	−	0.0989811i
$235$	−393096.	+	680862.i	−0.464332	+	0.804247i
$236$	−205663.	−	356219.i	−0.240368	−	0.416329i
$237$	645266.	+	541443.i	0.746222	+	0.626155i
$238$	269173.	+	225863.i	0.308027	+	0.258465i
$239$	41812.2	+	72420.9i	0.0473487	+	0.0820104i	0.888728	−	0.458434i	$-0.151589\pi$
$239$	41812.2	+	72420.9i	0.0473487	+	0.0820104i	−0.841380	+	0.540444i	$0.818256\pi$
$240$	−133115.	+	230563.i	−0.149176	+	0.258381i
$241$	−625929.	+	227820.i	−0.694197	+	0.252667i	−0.664931	−	0.746905i	$-0.731539\pi$
$241$	−625929.	+	227820.i	−0.694197	+	0.252667i	−0.0292656	+	0.999572i	$0.509317\pi$
$242$	110689.	+	627748.i	0.121497	+	0.689043i
$243$	−68554.9	+	388794.i	−0.0744772	+	0.422381i
$244$	198034.	+	72078.5i	0.212944	+	0.0775052i
$245$	610394.	−	512182.i	0.649674	−	0.545141i
$246$	440012.			0.463582
$247$	−813970.	+	1.59913e6i	−0.848919	+	1.66779i
$248$	−106506.			−0.109962
$249$	−466542.	+	391475.i	−0.476862	+	0.400134i
$250$	157013.	+	57147.9i	0.158886	+	0.0578296i
$251$	77838.2	−	441443.i	0.0779846	−	0.442272i	−0.920667	−	0.390350i	$-0.872354\pi$
$251$	77838.2	−	441443.i	0.0779846	−	0.442272i	0.998651	−	0.0519225i	$-0.0165349\pi$
$252$	11672.7	+	66199.4i	0.0115790	+	0.0656679i
$253$	106828.	−	38882.1i	0.104926	−	0.0381899i
$254$	487551.	−	844463.i	0.474172	−	0.821289i
$255$	−577795.	−	1.00077e6i	−0.556447	−	0.963794i
$256$	50203.5	+	42125.7i	0.0478778	+	0.0401742i
$257$	277210.	+	232606.i	0.261804	+	0.219679i	0.764235	−	0.644938i	$-0.223117\pi$
$257$	277210.	+	232606.i	0.261804	+	0.219679i	−0.502432	+	0.864617i	$0.667561\pi$
$258$	−192614.	−	333618.i	−0.180152	−	0.312032i
$259$	459327.	−	795577.i	0.425473	−	0.736941i
$260$	−1.29402e6	+	470984.i	−1.18715	+	0.432089i
$261$	36909.0	+	209321.i	0.0335375	+	0.190201i
$262$	−184248.	+	1.04492e6i	−0.165825	+	0.940439i
$263$	606386.	+	220706.i	0.540580	+	0.196755i	0.597856	−	0.801603i	$-0.296019\pi$
$263$	606386.	+	220706.i	0.540580	+	0.196755i	−0.0572764	+	0.998358i	$0.518242\pi$
$264$	27796.5	−	23324.0i	0.0245460	−	0.0205965i
$265$	911216.			0.797088
$266$	−397520.	−	299296.i	−0.344473	−	0.259356i
$267$	−1.44749e6			−1.24262
$268$	679668.	−	570310.i	0.578043	−	0.485036i
$269$	1.41305e6	+	514307.i	1.19063	+	0.433353i	0.859943	−	0.510389i	$-0.170499\pi$
$269$	1.41305e6	+	514307.i	1.19063	+	0.433353i	0.330683	+	0.943742i	$0.392721\pi$
$270$	213920.	−	1.21320e6i	0.178584	−	1.01280i
$271$	−180841.	−	1.02560e6i	−0.149580	−	0.848311i	−0.963575	−	0.267439i	$-0.913823\pi$
$271$	−180841.	−	1.02560e6i	−0.149580	−	0.848311i	0.813995	−	0.580872i	$-0.197288\pi$
$272$	−267308.	+	97292.0i	−0.219073	+	0.0797361i
$273$	621073.	−	1.07573e6i	0.504355	−	0.873568i
$274$	−580743.	−	1.00588e6i	−0.467312	−	0.809409i
$275$	81057.1	+	68015.0i	0.0646338	+	0.0542342i
$276$	466596.	+	391520.i	0.368696	+	0.309372i
$277$	249104.	+	431461.i	0.195066	+	0.337864i	0.946922	−	0.321463i	$-0.104175\pi$
$277$	249104.	+	431461.i	0.195066	+	0.337864i	−0.751856	+	0.659327i	$0.770841\pi$
$278$	683020.	−	1.18303e6i	0.530056	−	0.918083i
$279$	83105.5	−	30247.9i	0.0639174	−	0.0232640i
$280$	−66311.3	−	376070.i	−0.0505466	−	0.286664i
$281$	362443.	−	2.05552e6i	0.273825	−	1.55294i	−0.468843	−	0.883282i	$-0.655329\pi$
$281$	362443.	−	2.05552e6i	0.273825	−	1.55294i	0.742668	−	0.669659i	$-0.233560\pi$
$282$	539487.	+	196357.i	0.403978	+	0.147036i
$283$	−1.56545e6	+	1.31357e6i	−1.16191	+	0.974957i	−0.999930	−	0.0118369i	$-0.996232\pi$
$283$	−1.56545e6	+	1.31357e6i	−1.16191	+	0.974957i	−0.161979	+	0.986794i	$0.551788\pi$
$284$	1.15527e6			0.849940
$285$	891839.	+	1.37207e6i	0.650390	+	1.00061i
$286$	187686.			0.135680
$287$	−483479.	+	405687.i	−0.346476	+	0.290728i
$288$	−51137.2	−	18612.4i	−0.0363292	−	0.0132228i
$289$	−32147.3	+	182316.i	−0.0226412	+	0.128405i
$290$	−209675.	−	1.18912e6i	−0.146403	−	0.830295i
$291$	2.10800e6	−	767249.i	1.45928	−	0.531134i
$292$	53619.7	−	92872.1i	0.0368017	−	0.0637424i
$293$	607697.	+	1.05256e6i	0.413541	+	0.716273i	0.995274	−	0.0971061i	$-0.0309586\pi$
$293$	607697.	+	1.05256e6i	0.413541	+	0.716273i	−0.581733	+	0.813380i	$0.697625\pi$
$294$	−445735.	−	374016.i	−0.300752	−	0.252361i
$295$	−1.48637e6	−	1.24721e6i	−0.994423	−	0.834420i
$296$	371852.	+	644067.i	0.246684	+	0.427269i
$297$	−83951.5	+	145408.i	−0.0552252	+	0.0956528i
$298$	−544380.	+	198138.i	−0.355109	+	0.129249i
$299$	547083.	+	3.10266e6i	0.353896	+	2.00704i
$300$	−98445.7	+	558313.i	−0.0631530	+	0.358158i
$301$	519234.	+	188986.i	0.330329	+	0.120230i
$302$	−36876.3	+	30942.9i	−0.0232664	+	0.0195228i
$303$	1.21335e6			0.759240
$304$	370744.	−	157552.i	0.230086	−	0.0977775i
$305$	994122.			0.611913
$306$	180947.	−	151832.i	0.110471	−	0.0926960i
$307$	−1.38601e6	−	504468.i	−0.839309	−	0.305483i	−0.113635	−	0.993523i	$-0.536249\pi$
$307$	−1.38601e6	−	504468.i	−0.839309	−	0.305483i	−0.725673	+	0.688039i	$0.758472\pi$
$308$	−9037.85	+	51256.2i	−0.00542860	+	0.0307871i
$309$	25029.3	+	141948.i	0.0149126	+	0.0845734i
$310$	−472111.	+	171834.i	−0.279023	+	0.101556i
$311$	−530739.	+	919268.i	−0.311158	+	0.538941i	−0.978613	−	0.205709i	$-0.934050\pi$
$311$	−530739.	+	919268.i	−0.311158	+	0.538941i	0.667456	+	0.744650i	$0.267383\pi$
$312$	502796.	+	870867.i	0.292419	+	0.506484i
$313$	−2.46167e6	−	2.06559e6i	−1.42026	−	1.19174i	−0.951199	−	0.308578i	$-0.900147\pi$
$313$	−2.46167e6	−	2.06559e6i	−1.42026	−	1.19174i	−0.469064	−	0.883164i	$-0.655409\pi$
$314$	397607.	+	333632.i	0.227578	+	0.190960i
$315$	158547.	+	274612.i	0.0900290	+	0.155935i
$316$	489060.	−	847078.i	0.275515	−	0.477206i
$317$	−3.11425e6	+	1.13349e6i	−1.74062	+	0.633536i	−0.999293	−	0.0376032i	$-0.988028\pi$
$317$	−3.11425e6	+	1.13349e6i	−1.74062	+	0.633536i	−0.741332	+	0.671139i	$0.765805\pi$
$318$	−115547.	−	655299.i	−0.0640753	−	0.363389i
$319$	−28577.5	+	162071.i	−0.0157234	+	0.0891719i
$320$	290504.	+	105735.i	0.158590	+	0.0577221i
$321$	1.53112e6	−	1.28476e6i	0.829368	−	0.695922i
$322$	−873667.			−0.469576
$323$	−212376.	+	1.73557e6i	−0.113266	+	0.925627i
$324$	−692973.			−0.366736
$325$	−2.24635e6	+	1.88491e6i	−1.17969	+	0.989879i
$326$	−1.50590e6	−	548101.i	−0.784785	−	0.285638i
$327$	−243901.	+	1.38323e6i	−0.126137	+	0.715361i
$328$	−88724.3	−	503180.i	−0.0455363	−	0.258249i
$329$	−773820.	+	281647.i	−0.394140	+	0.143455i
$330$	85583.8	−	148235.i	0.0432620	−	0.0749320i
$331$	144880.	+	250939.i	0.0726838	+	0.125892i	0.900077	−	0.435732i	$-0.143510\pi$
$331$	144880.	+	250939.i	0.0726838	+	0.125892i	−0.827393	+	0.561624i	$0.810177\pi$
$332$	541749.	+	454581.i	0.269745	+	0.226343i
$333$	−473070.	−	396953.i	−0.233784	−	0.196168i
$334$	115258.	+	199633.i	0.0565336	+	0.0979190i
$335$	2.09266e6	−	3.62460e6i	1.01880	−	1.76460i
$336$	−262041.	+	95375.2i	−0.126626	+	0.0460880i
$337$	−304799.	−	1.72860e6i	−0.146197	−	0.829126i	−0.966398	−	0.257050i	$-0.917249\pi$
$337$	−304799.	−	1.72860e6i	−0.146197	−	0.829126i	0.820201	−	0.572076i	$-0.193862\pi$
$338$	−645311.	+	3.65974e6i	−0.307240	+	1.74244i
$339$	−2.04917e6	−	745837.i	−0.968454	−	0.352488i
$340$	−1.02793e6	+	862539.i	−0.482245	+	0.404652i
$341$	68475.6			0.0318896
$342$	−244544.	+	228229.i	−0.113055	+	0.105513i
$343$	2.16329e6			0.992841
$344$	−342673.	+	287537.i	−0.156129	+	0.131008i
$345$	2.69997e6	+	982708.i	1.22127	+	0.444505i
$346$	96607.7	−	547889.i	0.0433832	−	0.246038i
$347$	174805.	+	991371.i	0.0779347	+	0.441990i	0.998659	+	0.0517755i	$0.0164880\pi$
$347$	174805.	+	991371.i	0.0779347	+	0.441990i	−0.920724	+	0.390214i	$0.872401\pi$
$348$	−828569.	+	301574.i	−0.366759	+	0.133489i
$349$	−1.80966e6	+	3.13442e6i	−0.795304	+	1.37751i	0.127341	+	0.991859i	$0.459356\pi$
$349$	−1.80966e6	+	3.13442e6i	−0.795304	+	1.37751i	−0.922646	+	0.385649i	$0.873978\pi$
$350$	−406589.	−	704232.i	−0.177413	−	0.307288i
$351$	−3.56449e6	−	2.99097e6i	−1.54429	−	1.29582i
$352$	−32277.3	−	27083.9i	−0.0138848	−	0.0116508i
$353$	−1.03153e6	−	1.78667e6i	−0.440602	−	0.763145i	0.557132	−	0.830424i	$-0.311902\pi$
$353$	−1.03153e6	−	1.78667e6i	−0.440602	−	0.763145i	−0.997734	+	0.0672786i	$0.978568\pi$
$354$	−708450.	+	1.22707e6i	−0.300470	+	0.520429i
$355$	5.12101e6	−	1.86390e6i	2.15668	−	0.784966i
$356$	291873.	+	1.65529e6i	0.122059	+	0.692230i
$357$	210184.	−	1.19201e6i	0.0872829	−	0.495006i
$358$	1.53813e6	+	559835.i	0.634288	+	0.230862i
$359$	−1.78651e6	+	1.49906e6i	−0.731593	+	0.613879i	−0.930565	−	0.366126i	$-0.880684\pi$
$359$	−1.78651e6	+	1.49906e6i	−0.731593	+	0.613879i	0.198973	+	0.980005i	$0.436240\pi$
$360$	−256707.			−0.104395
$361$	170690.	−	2.47021e6i	0.0689352	−	0.997621i
$362$	2.47410e6			0.992307
$363$	1.68205e6	−	1.41141e6i	0.669998	−	0.562195i
$364$	−1.35540e6	−	493324.i	−0.536183	−	0.195154i
$365$	87843.7	−	498187.i	0.0345127	−	0.195731i
$366$	−126060.	−	714921.i	−0.0491897	−	0.278968i
$367$	3.17804e6	−	1.15671e6i	1.23167	−	0.448291i	0.357501	−	0.933913i	$-0.383629\pi$
$367$	3.17804e6	−	1.15671e6i	1.23167	−	0.448291i	0.874169	+	0.485622i	$0.161407\pi$
$368$	353642.	−	612527.i	0.136127	−	0.235779i
$369$	212136.	+	367430.i	0.0811050	+	0.140478i
$370$	2.68745e6	+	2.25504e6i	1.02055	+	0.856346i
$371$	731140.	+	613500.i	0.275782	+	0.231409i
$372$	183440.	+	317728.i	0.0687286	+	0.119041i
$373$	−1.68176e6	+	2.91289e6i	−0.625881	+	1.08406i	0.362489	+	0.931988i	$0.381927\pi$
$373$	−1.68176e6	+	2.91289e6i	−0.625881	+	1.08406i	−0.988370	+	0.152069i	$0.951406\pi$
$374$	171860.	−	62551.9i	0.0635325	−	0.0231239i
$375$	−99947.4	−	566830.i	−0.0367023	−	0.208149i
$376$	115764.	−	656529.i	0.0422282	−	0.239488i
$377$	−4.28573e6	−	1.55988e6i	−1.55300	−	0.565246i
$378$	988463.	−	829419.i	0.355820	−	0.298569i
$379$	1.58463e6			0.566671			0.283335	−	0.959021i	$-0.408559\pi$
$379$	1.58463e6			0.566671			0.283335	+	0.959021i	$0.408559\pi$
$380$	1.38922e6	−	1.29654e6i	0.493528	−	0.460602i
$381$	−3.35894e6			−1.18547
$382$	−2.07297e6	+	1.73943e6i	−0.726832	+	0.609884i
$383$	3.74876e6	+	1.36444e6i	1.30584	+	0.475287i	0.898895	−	0.438165i	$-0.144371\pi$
$383$	3.74876e6	+	1.36444e6i	1.30584	+	0.475287i	0.406946	+	0.913452i	$0.366594\pi$
$384$	39201.5	−	222323.i	0.0135667	−	0.0769407i
$385$	42633.5	+	241786.i	0.0146588	+	0.0831343i
$386$	−2.96240e6	+	1.07822e6i	−1.01199	+	0.368333i
$387$	185724.	−	321683.i	0.0630362	−	0.109182i
$388$	−1.30245e6	−	2.25591e6i	−0.439221	−	0.760752i
$389$	540053.	+	453159.i	0.180952	+	0.151836i	0.728764	−	0.684764i	$-0.240095\pi$
$389$	540053.	+	453159.i	0.180952	+	0.151836i	−0.547813	+	0.836601i	$0.684539\pi$
$390$	3.63380e6	+	3.04912e6i	1.20976	+	1.01511i
$391$	1.53501e6	+	2.65871e6i	0.507771	+	0.879486i
$392$	−337832.	+	585142.i	−0.111042	+	0.192330i
$393$	3.43456e6	−	1.25008e6i	1.12173	−	0.408277i
$394$	−448433.	−	2.54319e6i	−0.145531	−	0.825350i
$395$	801214.	−	4.54391e6i	0.258378	−	1.46534i
$396$	32877.6	+	11966.5i	0.0105357	+	0.00383467i
$397$	2.62396e6	−	2.20176e6i	0.835566	−	0.701123i	−0.120996	−	0.992653i	$-0.538609\pi$
$397$	2.62396e6	−	2.20176e6i	0.835566	−	0.701123i	0.956562	+	0.291530i	$0.0941644\pi$
$398$	2.18681e6			0.691996
$399$	−208192.	+	1.70138e6i	−0.0654684	+	0.535018i
$400$	658315.			0.205724
$401$	3.70542e6	−	3.10922e6i	1.15074	−	0.965585i	0.151003	−	0.988533i	$-0.451750\pi$
$401$	3.70542e6	−	3.10922e6i	1.15074	−	0.965585i	0.999737	+	0.0229484i	$0.00730534\pi$
$402$	−2.87198e6	−	1.04532e6i	−0.886373	−	0.322613i
$403$	−329527.	+	1.86884e6i	−0.101072	+	0.573205i
$404$	−244660.	−	1.38754e6i	−0.0745778	−	0.422952i
$405$	−3.07177e6	+	1.11803e6i	−0.930573	+	0.338701i
$406$	632370.	−	1.09530e6i	0.190395	−	0.329775i
$407$	−239075.	−	414089.i	−0.0715398	−	0.123911i
$408$	750641.	+	629862.i	0.223245	+	0.187325i
$409$	−229856.	−	192872.i	−0.0679436	−	0.0570114i	0.608183	−	0.793797i	$-0.291899\pi$
$409$	−229856.	−	192872.i	−0.0679436	−	0.0570114i	−0.676127	+	0.736785i	$0.736343\pi$
$410$	−1.20511e6	−	2.08732e6i	−0.354053	−	0.613238i
$411$	−2.00049e6	+	3.46495e6i	−0.584160	+	1.01179i
$412$	157279.	−	57245.0i	0.0456488	−	0.0166148i
$413$	−352913.	−	2.00147e6i	−0.101811	−	0.577397i
$414$	−101985.	+	578385.i	−0.0292439	+	0.165850i
$415$	3.13484e6	+	1.14099e6i	0.893502	+	0.325208i
$416$	894505.	−	750579.i	0.253425	−	0.212649i
$417$	−4.70561e6			−1.32518
$418$	−238362.	+	101295.i	−0.0667263	+	0.0283560i
$419$	4.26792e6			1.18763			0.593815	−	0.804601i	$-0.297621\pi$
$419$	4.26792e6			1.18763			0.593815	+	0.804601i	$0.297621\pi$
$420$	−1.00768e6	+	845546.i	−0.278741	+	0.233891i
$421$	−2.56412e6	−	933264.i	−0.705072	−	0.256625i	−0.0354972	−	0.999370i	$-0.511301\pi$
$421$	−2.56412e6	−	933264.i	−0.705072	−	0.256625i	−0.669575	+	0.742745i	$0.733524\pi$
$422$	245348.	−	1.39144e6i	0.0670660	−	0.380350i
$423$	96126.7	+	545162.i	0.0261212	+	0.148141i
$424$	−726075.	+	264270.i	−0.196140	+	0.0713892i
$425$	−1.42873e6	+	2.47463e6i	−0.383687	+	0.664566i
$426$	−1.98979e6	−	3.44641e6i	−0.531230	−	0.920118i
$427$	797663.	+	669318.i	0.211714	+	0.177649i
$428$	−1.77794e6	−	1.49187e6i	−0.469146	−	0.393660i
$429$	−323262.	−	559906.i	−0.0848031	−	0.146883i
$430$	−1.05507e6	+	1.82744e6i	−0.275176	+	0.476619i
$431$	−3.62726e6	+	1.32022e6i	−0.940559	+	0.342335i	−0.766386	−	0.642380i	$-0.777947\pi$
$431$	−3.62726e6	+	1.32022e6i	−0.940559	+	0.342335i	−0.174172	+	0.984715i	$0.555725\pi$
$432$	181395.	+	1.02874e6i	0.0467644	+	0.265214i
$433$	224757.	−	1.27466e6i	0.0576093	−	0.326719i	−0.942360	−	0.334602i	$-0.891398\pi$
$433$	224757.	−	1.27466e6i	0.0576093	−	0.326719i	0.999969	+	0.00788304i	$0.00250928\pi$
$434$	−494504.	−	179985.i	−0.126022	−	0.0458681i
$435$	−3.18627e6	+	2.67360e6i	−0.807345	+	0.677443i
$436$	1.63099e6			0.410898
$437$	−2.36931e6	−	3.64514e6i	−0.593497	−	0.913083i
$438$	−369409.			−0.0920072
$439$	2.35631e6	−	1.97718e6i	0.583541	−	0.489649i	−0.302567	−	0.953128i	$-0.597843\pi$
$439$	2.35631e6	−	1.97718e6i	0.583541	−	0.489649i	0.886108	+	0.463479i	$0.153399\pi$
$440$	−186773.	−	67979.9i	−0.0459921	−	0.0167398i
$441$	97425.4	−	552527.i	0.0238548	−	0.135287i
$442$	880126.	+	4.99144e6i	0.214284	+	1.21526i
$443$	−4.63706e6	+	1.68775e6i	−1.12262	+	0.408601i	−0.835608	−	0.549326i	$-0.814885\pi$
$443$	−4.63706e6	+	1.68775e6i	−1.12262	+	0.408601i	−0.287013	+	0.957927i	$0.592662\pi$
$444$	1.28092e6	−	2.21862e6i	0.308365	−	0.534104i
$445$	3.96442e6	+	6.86657e6i	0.949029	+	1.64377i
$446$	3.34324e6	+	2.80531e6i	0.795847	+	0.667795i
$447$	1.52870e6	+	1.28273e6i	0.361872	+	0.303646i
$448$	161905.	+	280428.i	0.0381124	+	0.0660126i
$449$	−2.36258e6	+	4.09210e6i	−0.553057	+	0.957923i	0.444995	+	0.895533i	$0.353206\pi$
$449$	−2.36258e6	+	4.09210e6i	−0.553057	+	0.957923i	−0.998052	+	0.0623898i	$0.980128\pi$
$450$	−513678.	+	186964.i	−0.119580	+	0.0435237i
$451$	57043.4	+	323509.i	0.0132058	+	0.0748938i
$452$	−439714.	+	2.49374e6i	−0.101233	+	0.574123i
$453$	155823.	+	56714.9i	0.0356768	+	0.0129853i
$454$	453699.	−	380698.i	0.103307	−	0.0866845i
$455$	−6.80403e6			−1.54077
$456$	−1.10856e6	−	834646.i	−0.249659	−	0.187971i
$457$	−2.01587e6			−0.451515			−0.225758	−	0.974184i	$-0.572486\pi$
$457$	−2.01587e6			−0.451515			−0.225758	+	0.974184i	$0.572486\pi$
$458$	3.22782e6	−	2.70847e6i	0.719029	−	0.603337i
$459$	−4.26075e6	−	1.55079e6i	−0.943963	−	0.343574i
$460$	579362.	−	3.28573e6i	0.127660	−	0.723997i
$461$	1.29449e6	+	7.34143e6i	0.283692	+	1.60890i	0.709920	+	0.704282i	$0.248731\pi$
$461$	1.29449e6	+	7.34143e6i	0.283692	+	1.60890i	−0.426228	+	0.904616i	$0.640158\pi$
$462$	168474.	−	61319.5i	0.0367222	−	0.0133658i
$463$	−966410.	+	1.67387e6i	−0.209512	+	0.362885i	−0.951561	−	0.307460i	$-0.900521\pi$
$463$	−966410.	+	1.67387e6i	−0.209512	+	0.362885i	0.742049	+	0.670346i	$0.233854\pi$
$464$	511941.	+	886708.i	0.110389	+	0.191199i
$465$	1.32576e6	+	1.11244e6i	0.284336	+	0.238586i
$466$	1.91546e6	+	1.60727e6i	0.408610	+	0.342865i
$467$	−594278.	−	1.02932e6i	−0.126095	−	0.218403i	0.796066	−	0.605210i	$-0.206911\pi$
$467$	−594278.	−	1.02932e6i	−0.126095	−	0.218403i	−0.922160	+	0.386808i	$0.873578\pi$
$468$	−484809.	+	839713.i	−0.102319	+	0.177221i
$469$	4.11946e6	−	1.49936e6i	0.864785	−	0.314756i
$470$	−546083.	−	3.09699e6i	−0.114029	−	0.646688i
$471$	310472.	−	1.76077e6i	0.0644867	−	0.365722i
$472$	1.54608e6	+	562728.i	0.319431	+	0.116263i
$473$	220314.	−	184866.i	0.0452783	−	0.0379930i
$474$	−3.36934e6			−0.688810
$475$	1.83558e6	−	3.60620e6i	0.373284	−	0.733358i
$476$	−1.40552e6			−0.284328
$477$	491497.	−	412415.i	0.0989065	−	0.0829924i
$478$	−314325.	−	114405.i	−0.0629230	−	0.0229021i
$479$	−1.17476e6	+	6.66240e6i	−0.233943	+	1.32676i	0.610885	+	0.791720i	$0.290814\pi$
$479$	−1.17476e6	+	6.66240e6i	−0.233943	+	1.32676i	−0.844828	+	0.535038i	$0.820297\pi$
$480$	−184922.	−	1.04874e6i	−0.0366341	−	0.207762i
$481$	1.24519e7	−	4.53211e6i	2.45399	−	0.893178i
$482$	1.33220e6	−	2.30744e6i	0.261187	−	0.452389i
$483$	1.50476e6	+	2.60633e6i	0.293495	+	0.508348i
$484$	−1.95320e6	−	1.63893e6i	−0.378996	−	0.318015i
$485$	−9.41308e6	−	7.89851e6i	−1.81709	−	1.52472i
$486$	−789584.	−	1.36760e6i	−0.151638	−	0.262645i
$487$	2.60757e6	−	4.51644e6i	0.498210	−	0.862926i	−0.501787	−	0.864991i	$-0.667324\pi$
$487$	2.60757e6	−	4.51644e6i	0.498210	−	0.862926i	0.999998	+	0.00206520i	$0.000657373\pi$
$488$	−792136.	+	288314.i	−0.150574	+	0.0548045i
$489$	958587.	+	5.43642e6i	0.181284	+	1.02811i
$490$	−553461.	+	3.13883e6i	−0.104135	+	0.590579i
$491$	−5.25822e6	−	1.91384e6i	−0.984318	−	0.358262i	−0.200800	−	0.979632i	$-0.564354\pi$
$491$	−5.25822e6	−	1.91384e6i	−0.984318	−	0.358262i	−0.783517	+	0.621370i	$0.786576\pi$
$492$	−1.34828e6	+	1.13134e6i	−0.251111	+	0.210707i
$493$	−4.44422e6			−0.823528
$494$	−1.61746e6	−	6.99287e6i	−0.298207	−	1.28925i
$495$	165044.			0.0302752
$496$	326352.	−	273842.i	0.0595638	−	0.0499799i
$497$	5.36391e6	+	1.95230e6i	0.974071	+	0.354533i
$498$	423026.	−	2.39910e6i	0.0764352	−	0.433486i
$499$	716983.	+	4.06621e6i	0.128901	+	0.731036i	0.978914	+	0.204273i	$0.0654831\pi$
$499$	716983.	+	4.06621e6i	0.128901	+	0.731036i	−0.850013	+	0.526762i	$0.823406\pi$
$500$	−628050.	+	228592.i	−0.112349	+	0.0408917i
$501$	397032.	−	687679.i	0.0706693	−	0.122403i
$502$	896505.	+	1.55279e6i	0.158779	+	0.275014i
$503$	5.28500e6	+	4.43464e6i	0.931375	+	0.781517i	0.976064	−	0.217484i	$-0.0697851\pi$
$503$	5.28500e6	+	4.43464e6i	0.931375	+	0.781517i	−0.0446885	+	0.999001i	$0.514230\pi$
$504$	−205976.	−	172834.i	−0.0361194	−	0.0303078i
$505$	−3.32314e6	−	5.75585e6i	−0.579856	−	1.00434i
$506$	−227367.	+	393811.i	−0.0394777	+	0.0683773i
$507$	1.20292e7	−	4.37828e6i	2.07834	−	0.756455i
$508$	677299.	+	3.84115e6i	0.116445	+	0.660392i
$509$	−111582.	+	632811.i	−0.0190897	+	0.108263i	−0.992864	−	0.119254i	$-0.961950\pi$
$509$	−111582.	+	632811.i	−0.0190897	+	0.108263i	0.973774	+	0.227517i	$0.0730608\pi$
$510$	4.34360e6	+	1.58094e6i	0.739476	+	0.269147i
$511$	405901.	−	340591.i	0.0687651	−	0.0577007i
$512$	−262144.			−0.0441942
$513$	6.14115e6	+	1.87478e6i	1.03028	+	0.314525i
$514$	−1.44749e6			−0.241661
$515$	604820.	−	507504.i	0.100487	−	0.0843182i
$516$	1.44798e6	+	527023.i	0.239409	+	0.0871376i
$517$	−74427.9	+	422102.i	−0.0122464	+	0.0694530i
$518$	638090.	+	3.61879e6i	0.104486	+	0.592569i
$519$	−1.80086e6	+	655459.i	−0.293468	+	0.106814i
$520$	2.75413e6	−	4.77030e6i	0.446659	−	0.773636i
$521$	−186222.	−	322546.i	−0.0300563	−	0.0520591i	0.850606	−	0.525804i	$-0.176235\pi$
$521$	−186222.	−	322546.i	−0.0300563	−	0.0520591i	−0.880662	+	0.473745i	$0.842902\pi$
$522$	−651292.	−	546499.i	−0.104616	−	0.0877835i
$523$	−4.87107e6	−	4.08731e6i	−0.778699	−	0.653406i	0.164221	−	0.986424i	$-0.447489\pi$
$523$	−4.87107e6	−	4.08731e6i	−0.778699	−	0.653406i	−0.942921	+	0.333017i	$0.891933\pi$
$524$	−2.12208e6	−	3.67556e6i	−0.337625	−	0.584783i
$525$	−1.40058e6	+	2.42588e6i	−0.221774	+	0.384123i
$526$	−2.42554e6	+	882826.i	−0.382248	+	0.139127i
$527$	321106.	+	1.82108e6i	0.0503642	+	0.285629i
$528$	−25203.8	+	142938.i	−0.00393442	+	0.0223132i
$529$	−1.12471e6	−	409362.i	−0.174744	−	0.0636016i
$530$	−2.79213e6	+	2.34287e6i	−0.431763	+	0.362292i
$531$	−1.36621e6			−0.210272
$532$	1.98761e6	−	104986.i	0.304475	−	0.0160825i
$533$	−9.10377e6			−1.38804
$534$	4.43537e6	−	3.72172e6i	0.673096	−	0.564795i
$535$	−1.02881e7	−	3.74456e6i	−1.55400	−	0.565609i
$536$	−616273.	+	3.49506e6i	−0.0926534	+	0.525464i
$537$	−979108.	−	5.55280e6i	−0.146519	−	0.830953i
$538$	−5.65218e6	+	2.05723e6i	−0.841900	+	0.306427i
$539$	217202.	−	376205.i	0.0322027	−	0.0557767i
$540$	2.46383e6	+	4.26748e6i	0.363602	+	0.629777i
$541$	4.25200e6	+	3.56785e6i	0.624598	+	0.524100i	0.899245	−	0.437445i	$-0.144117\pi$
$541$	4.25200e6	+	3.56785e6i	0.624598	+	0.524100i	−0.274647	+	0.961545i	$0.588561\pi$
$542$	3.19110e6	+	2.67765e6i	0.466598	+	0.391522i
$543$	−4.26128e6	−	7.38075e6i	−0.620212	−	1.07424i
$544$	568926.	−	985408.i	0.0824249	−	0.142764i
$545$	7.22973e6	−	2.63141e6i	1.04263	−	0.379487i
$546$	862786.	+	4.89310e6i	0.123857	+	0.702429i
$547$	1.58383e6	−	8.98235e6i	0.226329	−	1.28358i	−0.633799	−	0.773498i	$-0.718505\pi$
$547$	1.58383e6	−	8.98235e6i	0.226329	−	1.28358i	0.860128	−	0.510078i	$-0.170383\pi$
$548$	4.36576e6	+	1.58901e6i	0.621024	+	0.226034i
$549$	536215.	−	449938.i	0.0759291	−	0.0637121i
$550$	−423250.			−0.0596610
$551$	6.28477e6	−	331965.i	0.881881	−	0.0465815i
$552$	−2.43639e6			−0.340329
$553$	3.70218e6	−	3.10650e6i	0.514808	−	0.431975i
$554$	−1.87265e6	−	681589.i	−0.259228	−	0.0943514i
$555$	2.09850e6	−	1.19012e7i	0.289185	−	1.64005i
$556$	948842.	+	5.38115e6i	0.130169	+	0.738224i
$557$	−2.20679e6	+	803205.i	−0.301385	+	0.109695i	−0.488286	−	0.872683i	$-0.662378\pi$
$557$	−2.20679e6	+	803205.i	−0.301385	+	0.109695i	0.186901	+	0.982379i	$0.440156\pi$
$558$	−176878.	+	306362.i	−0.0240485	+	0.0416533i
$559$	3.98515e6	+	6.90248e6i	0.539405	+	0.934277i
$560$	1.17012e6	+	981849.i	0.157674	+	0.132304i
$561$	−482609.	−	404957.i	−0.0647423	−	0.0543253i
$562$	4.17445e6	+	7.23036e6i	0.557517	+	0.965649i
$563$	1.66918e6	−	2.89111e6i	0.221939	−	0.384409i	−0.733458	−	0.679735i	$-0.762095\pi$
$563$	1.66918e6	−	2.89111e6i	0.221939	−	0.384409i	0.955397	+	0.295326i	$0.0954282\pi$
$564$	−2.15795e6	+	785429.i	−0.285656	+	0.103970i
$565$	2.07422e6	+	1.17635e7i	0.273360	+	1.55030i
$566$	1.41943e6	−	8.05000e6i	0.186240	−	1.05622i
$567$	−3.21747e6	−	1.17106e6i	−0.420297	−	0.152976i
$568$	−3.53996e6	+	2.97038e6i	−0.460392	+	0.386314i
$569$	2.07907e6			0.269208			0.134604	−	0.990899i	$-0.457024\pi$
$569$	2.07907e6			0.269208			0.134604	+	0.990899i	$0.457024\pi$
$570$	−6.26056e6	−	1.91123e6i	−0.807098	−	0.246391i
$571$	−3.13896e6			−0.402898			−0.201449	−	0.979499i	$-0.564565\pi$
$571$	−3.13896e6			−0.402898			−0.201449	+	0.979499i	$0.564565\pi$
$572$	−575104.	+	482569.i	−0.0734947	+	0.0616694i
$573$	8.75945e6	+	3.18818e6i	1.11453	+	0.405654i
$574$	438383.	−	2.48619e6i	0.0555359	−	0.314960i
$575$	−1.23373e6	−	6.99681e6i	−0.155614	−	0.882532i
$576$	204549.	−	74449.7i	0.0256886	−	0.00934990i
$577$	2.05889e6	−	3.56611e6i	0.257451	−	0.445918i	−0.708108	−	0.706105i	$-0.750451\pi$
$577$	2.05889e6	−	3.56611e6i	0.257451	−	0.445918i	0.965558	+	0.260187i	$0.0837842\pi$
$578$	−370258.	−	641305.i	−0.0460983	−	0.0798445i
$579$	8.31886e6	+	6.98036e6i	1.03126	+	0.865329i
$580$	3.69990e6	+	3.10458e6i	0.456688	+	0.383207i
$581$	1.74713e6	+	3.02612e6i	0.214726	+	0.371917i
$582$	−4.48657e6	+	7.77097e6i	−0.549044	+	0.950972i
$583$	466815.	−	169907.i	0.0568818	−	0.0207033i
$584$	74487.8	+	422441.i	0.00903759	+	0.0512547i
$585$	−794248.	+	4.50441e6i	−0.0959548	+	0.544187i
$586$	−4.56839e6	−	1.66276e6i	−0.549565	−	0.200025i
$587$	−1.00272e7	+	8.41380e6i	−1.20111	+	1.00785i	−0.201513	+	0.979486i	$0.564586\pi$
$587$	−1.00272e7	+	8.41380e6i	−1.20111	+	1.00785i	−0.999598	+	0.0283660i	$0.990970\pi$
$588$	2.32747e6			0.277613
$589$	−590117.	−	2.55128e6i	−0.0700890	−	0.303020i
$590$	7.76126e6			0.917914
$591$	−6.81450e6	+	5.71804e6i	−0.802537	+	0.673409i
$592$	−2.79541e6	−	1.01745e6i	−0.327825	−	0.119318i
$593$	−98205.8	+	556953.i	−0.0114683	+	0.0650402i	−0.990005	−	0.141033i	$-0.954958\pi$
$593$	−98205.8	+	556953.i	−0.0114683	+	0.0650402i	0.978537	+	0.206074i	$0.0660686\pi$
$594$	−116624.	−	661408.i	−0.0135620	−	0.0769137i
$595$	−6.23030e6	+	2.26764e6i	−0.721467	+	0.262592i
$596$	1.15864e6	−	2.00681e6i	0.133608	−	0.231415i
$597$	−3.76647e6	−	6.52371e6i	−0.432512	−	0.749133i
$598$	−9.65378e6	−	8.10048e6i	−1.10394	−	0.926313i
$599$	3.98483e6	+	3.34367e6i	0.453777	+	0.380764i	0.840835	−	0.541291i	$-0.182064\pi$
$599$	3.98483e6	+	3.34367e6i	0.453777	+	0.380764i	−0.387058	+	0.922055i	$0.626509\pi$
$600$	−1.13385e6	−	1.96389e6i	−0.128581	−	0.222710i
$601$	−2.12538e6	+	3.68126e6i	−0.240021	+	0.415729i	−0.960720	−	0.277519i	$-0.910488\pi$
$601$	−2.12538e6	+	3.68126e6i	−0.240021	+	0.415729i	0.720699	+	0.693248i	$0.243821\pi$
$602$	−2.07694e6	+	755943.i	−0.233578	+	0.0850154i
$603$	−511735.	−	2.90219e6i	−0.0573128	−	0.325037i
$604$	33436.7	−	189629.i	0.00372933	−	0.0211501i
$605$	−1.13023e7	−	4.11368e6i	−1.25538	−	0.456923i
$606$	−3.71791e6	+	3.11970e6i	−0.411261	+	0.345089i
$607$	−2.91329e6			−0.320931			−0.160466	−	0.987041i	$-0.551300\pi$
$607$	−2.91329e6			−0.320931			−0.160466	+	0.987041i	$0.551300\pi$
$608$	−730937.	+	1.43600e6i	−0.0801901	+	0.157542i
$609$	−4.35666e6			−0.476004
$610$	−3.04617e6	+	2.55604e6i	−0.331458	+	0.278127i
$611$	−1.11619e7	−	4.06259e6i	−1.20958	−	0.440251i
$612$	−164069.	+	930483.i	−0.0177072	+	0.100422i
$613$	841144.	+	4.77036e6i	0.0904105	+	0.512743i	0.996057	+	0.0887108i	$0.0282747\pi$
$613$	841144.	+	4.77036e6i	0.0904105	+	0.512743i	−0.905647	+	0.424033i	$0.860614\pi$
$614$	5.54406e6	−	2.01787e6i	0.593481	−	0.216009i
$615$	−4.15127e6	+	7.19020e6i	−0.442581	+	0.766573i
$616$	−104094.	−	180296.i	−0.0110528	−	0.0191440i
$617$	−1.24023e6	−	1.04068e6i	−0.131157	−	0.110054i	0.574850	−	0.818259i	$-0.305061\pi$
$617$	−1.24023e6	−	1.04068e6i	−0.131157	−	0.110054i	−0.706006	+	0.708206i	$0.749505\pi$
$618$	−441665.	−	370601.i	−0.0465181	−	0.0390333i
$619$	−3.15444e6	−	5.46366e6i	−0.330900	−	0.573135i	0.651789	−	0.758400i	$-0.274019\pi$
$619$	−3.15444e6	−	5.46366e6i	−0.330900	−	0.573135i	−0.982689	+	0.185265i	$0.940685\pi$
$620$	1.00482e6	−	1.74040e6i	0.104981	−	0.181832i
$621$	1.05939e7	−	3.85586e6i	1.10237	−	0.401229i
$622$	−737295.	−	4.18141e6i	−0.0764127	−	0.433358i
$623$	−1.44213e6	+	8.17874e6i	−0.148862	+	0.844241i
$624$	−3.77979e6	−	1.37573e6i	−0.388603	−	0.141440i
$625$	−8.57116e6	+	7.19206e6i	−0.877687	+	0.736467i
$626$	1.28539e7			1.31099
$627$	712727.	+	536618.i	0.0724026	+	0.0545126i
$628$	−2.07615e6			−0.210068
$629$	9.89145e6	−	8.29991e6i	0.996858	−	0.836463i
$630$	−1.19189e6	−	433811.i	−0.119642	−	0.0435461i
$631$	−1.34993e6	+	7.65585e6i	−0.134970	+	0.765455i	0.839910	+	0.542726i	$0.182608\pi$
$631$	−1.34993e6	+	7.65585e6i	−0.134970	+	0.765455i	−0.974880	+	0.222730i	$0.928503\pi$
$632$	679396.	+	3.85304e6i	0.0676597	+	0.383717i
$633$	−4.57353e6	+	1.66463e6i	−0.453672	+	0.165123i
$634$	6.62823e6	−	1.14804e7i	0.654899	−	1.13432i
$635$	9.19953e6	+	1.59341e7i	0.905381	+	1.56817i
$636$	2.03893e6	+	1.71086e6i	0.199875	+	0.167715i
$637$	9.22218e6	+	7.73833e6i	0.900503	+	0.755611i
$638$	−329142.	−	570091.i	−0.0320134	−	0.0554488i
$639$	1.91861e6	−	3.32312e6i	0.185880	−	0.321954i
$640$	−1.16201e6	+	422939.i	−0.112140	+	0.0408157i
$641$	−594830.	−	3.37345e6i	−0.0571805	−	0.324287i	0.942778	−	0.333422i	$-0.108203\pi$
$641$	−594830.	−	3.37345e6i	−0.0571805	−	0.324287i	−0.999958	+	0.00913514i	$0.997092\pi$
$642$	−1.38831e6	+	7.87349e6i	−0.132938	+	0.753928i
$643$	−7.89026e6	−	2.87182e6i	−0.752599	−	0.273924i	−0.0629002	−	0.998020i	$-0.520035\pi$
$643$	−7.89026e6	−	2.87182e6i	−0.752599	−	0.273924i	−0.689699	+	0.724096i	$0.742257\pi$
$644$	2.67707e6	−	2.24633e6i	0.254358	−	0.213432i
$645$	7.26882e6			0.687962
$646$	−3.81166e6	−	5.86415e6i	−0.359362	−	0.552871i
$647$	1.10774e7			1.04034			0.520172	−	0.854062i	$-0.325868\pi$
$647$	1.10774e7			1.04034			0.520172	+	0.854062i	$0.325868\pi$
$648$	2.12339e6	−	1.78174e6i	0.198652	−	0.166689i
$649$	−994021.	−	361794.i	−0.0926369	−	0.0337171i
$650$	2.03682e6	−	1.15514e7i	0.189091	−	1.07239i
$651$	314780.	+	1.78520e6i	0.0291108	+	0.165096i
$652$	6.02358e6	−	2.19240e6i	0.554927	−	0.201977i
$653$	−5.14838e6	+	8.91726e6i	−0.472485	+	0.818368i	−0.999504	−	0.0314856i	$-0.989976\pi$
$653$	−5.14838e6	+	8.91726e6i	−0.472485	+	0.818368i	0.527019	+	0.849853i	$0.323310\pi$
$654$	−2.80914e6	−	4.86557e6i	−0.256820	−	0.444825i
$655$	−1.53367e7	−	1.28690e7i	−1.39678	−	1.17204i
$656$	1.56562e6	+	1.31371e6i	0.142045	+	0.119190i
$657$	−178097.	−	308473.i	−0.0160969	−	0.0278807i
$658$	1.64696e6	−	2.85262e6i	0.148292	−	0.256850i
$659$	5.04131e6	−	1.83489e6i	0.452199	−	0.164587i	−0.105873	−	0.994380i	$-0.533764\pi$
$659$	5.04131e6	−	1.83489e6i	0.452199	−	0.164587i	0.558072	+	0.829793i	$0.311541\pi$
$660$	118892.	+	674269.i	0.0106241	+	0.0602522i
$661$	−2.48844e6	+	1.41127e7i	−0.221526	+	1.25633i	0.647691	+	0.761903i	$0.275735\pi$
$661$	−2.48844e6	+	1.41127e7i	−0.221526	+	1.25633i	−0.869217	+	0.494431i	$0.835376\pi$
$662$	−1.08914e6	−	396414.i	−0.0965914	−	0.0351564i
$663$	1.33746e7	−	1.12226e7i	1.18167	−	0.991541i
$664$	−2.82881e6			−0.248991
$665$	8.64115e6	−	3.67215e6i	0.757735	−	0.322007i
$666$	2.47020e6			0.215797
$667$	8.46484e6	−	7.10284e6i	0.736722	−	0.618184i
$668$	−866460.	−	315366.i	−0.0751290	−	0.0273447i
$669$	2.61057e6	−	1.48053e7i	0.225512	−	1.27894i
$670$	2.90709e6	+	1.64870e7i	0.250191	+	1.41890i
$671$	509287.	−	185365.i	0.0436673	−	0.0158936i
$672$	557717.	−	965994.i	0.0476421	−	0.0825185i
$673$	−1.79089e6	−	3.10192e6i	−0.152417	−	0.263993i	0.779699	−	0.626155i	$-0.215372\pi$
$673$	−1.79089e6	−	3.10192e6i	−0.152417	−	0.263993i	−0.932115	+	0.362162i	$0.882039\pi$
$674$	5.37846e6	+	4.51306e6i	0.456045	+	0.382667i
$675$	8.03828e6	+	6.74492e6i	0.679053	+	0.569793i
$676$	−7.43240e6	−	1.28733e7i	−0.625550	−	1.08348i
$677$	8.76702e6	−	1.51849e7i	0.735157	−	1.27333i	−0.219497	−	0.975613i	$-0.570442\pi$
$677$	8.76702e6	−	1.51849e7i	0.735157	−	1.27333i	0.954654	−	0.297717i	$-0.0962251\pi$
$678$	8.19668e6	−	2.98335e6i	0.684800	−	0.249247i
$679$	−2.23498e6	−	1.26752e7i	−0.186037	−	1.05507i
$680$	932055.	−	5.28595e6i	0.0772982	−	0.438380i
$681$	−1.91713e6	−	697779.i	−0.158411	−	0.0576567i
$682$	−209821.	+	176061.i	−0.0172738	+	0.0144945i
$683$	−2.59797e6			−0.213100			−0.106550	−	0.994307i	$-0.533980\pi$
$683$	−2.59797e6			−0.213100			−0.106550	+	0.994307i	$0.533980\pi$
$684$	162514.	−	1.32809e6i	0.0132816	−	0.108540i
$685$	2.19159e7			1.78457
$686$	−6.62871e6	+	5.56215e6i	−0.537797	+	0.451265i
$687$	−1.36394e7	−	4.96432e6i	−1.10256	−	0.401299i
$688$	310710.	−	1.76213e6i	0.0250256	−	0.141927i
$689$	2.39064e6	+	1.35580e7i	0.191852	+	1.08805i
$690$	−1.07999e7	+	3.93083e6i	−0.863566	+	0.314312i
$691$	−3.70544e6	+	6.41801e6i	−0.295219	+	0.511335i	−0.975036	−	0.222047i	$-0.928726\pi$
$691$	−3.70544e6	+	6.41801e6i	−0.295219	+	0.511335i	0.679817	+	0.733382i	$0.262059\pi$
$692$	1.11268e6	+	1.92722e6i	0.0883296	+	0.152991i
$693$	132428.	+	111120.i	0.0104748	+	0.00878943i
$694$	−3.08460e6	−	2.58828e6i	−0.243108	−	0.203992i
$695$	1.28878e7	+	2.23223e7i	1.01209	+	1.75298i
$696$	1.76349e6	−	3.05445e6i	0.137991	−	0.239007i
$697$	−8.33612e6	+	3.03410e6i	−0.649953	+	0.236563i
$698$	−2.51395e6	−	1.42573e7i	−0.195307	−	1.10764i
$699$	1.49569e6	−	8.48250e6i	0.115784	−	0.656646i
$700$	3.05655e6	+	1.11249e6i	0.235769	+	0.0858128i
$701$	−1.74497e6	+	1.46420e6i	−0.134120	+	0.112540i	−0.707380	−	0.706834i	$-0.750123\pi$
$701$	−1.74497e6	+	1.46420e6i	−0.134120	+	0.112540i	0.573260	+	0.819374i	$0.305679\pi$
$702$	1.86125e7			1.42548
$703$	−1.33680e7	+	1.24761e7i	−1.02018	+	0.952118i
$704$	168540.			0.0128166
$705$	−8.29841e6	+	6.96319e6i	−0.628814	+	0.527637i
$706$	7.75460e6	+	2.82244e6i	0.585528	+	0.213115i
$707$	1.20886e6	−	6.85576e6i	0.0909549	−	0.515831i
$708$	−984168.	−	5.58149e6i	−0.0737881	−	0.418473i
$709$	5.35669e6	−	1.94968e6i	0.400204	−	0.145662i	−0.134074	−	0.990971i	$-0.542806\pi$
$709$	5.35669e6	−	1.94968e6i	0.400204	−	0.145662i	0.534278	+	0.845309i	$0.320584\pi$
$710$	−1.08993e7	+	1.88782e7i	−0.811436	+	1.40545i
$711$	−1.62440e6	−	2.81355e6i	−0.120509	−	0.208728i
$712$	−5.15036e6	−	4.32167e6i	−0.380748	−	0.319486i
$713$	−3.52209e6	−	2.95539e6i	−0.259464	−	0.217716i
$714$	2.42080e6	+	4.19296e6i	0.177711	+	0.307804i
$715$	−1.77071e6	+	3.06696e6i	−0.129534	+	0.224359i
$716$	−6.15253e6	+	2.23934e6i	−0.448509	+	0.163244i
$717$	200086.	+	1.13474e6i	0.0145351	+	0.0824326i
$718$	1.61988e6	−	9.18677e6i	0.117266	−	0.665046i
$719$	−7.83966e6	−	2.85340e6i	−0.565555	−	0.205845i	0.0433891	−	0.999058i	$-0.486184\pi$
$719$	−7.83966e6	−	2.85340e6i	−0.565555	−	0.205845i	−0.608944	+	0.793213i	$0.708407\pi$
$720$	786595.	−	660032.i	0.0565483	−	0.0474497i
$721$	826985.			0.0592461
$722$	5.82825e6	+	8.00803e6i	0.416098	+	0.571719i
$723$	−9.17808e6			−0.652989
$724$	−7.58108e6	+	6.36128e6i	−0.537508	+	0.451023i
$725$	9.66474e6	+	3.51768e6i	0.682881	+	0.248548i
$726$	−1.52516e6	+	8.64963e6i	−0.107393	+	0.609054i
$727$	−3.33151e6	−	1.88940e7i	−0.233779	−	1.32583i	−0.845170	−	0.534498i	$-0.820501\pi$
$727$	−3.33151e6	−	1.88940e7i	−0.233779	−	1.32583i	0.611391	−	0.791329i	$-0.290610\pi$
$728$	5.42158e6	−	1.97329e6i	0.379138	−	0.137995i
$729$	−7.98216e6	+	1.38255e7i	−0.556290	+	0.963523i
$730$	1.01174e6	+	1.75239e6i	0.0702689	+	0.121709i
$731$	5.94957e6	+	4.99228e6i	0.411805	+	0.345546i
$732$	2.22444e6	+	1.86653e6i	0.153441	+	0.128753i
$733$	−233943.	−	405201.i	−0.0160824	−	0.0278555i	0.857872	−	0.513863i	$-0.171786\pi$
$733$	−233943.	−	405201.i	−0.0160824	−	0.0278555i	−0.873955	+	0.486008i	$0.838453\pi$
$734$	−6.76400e6	+	1.17156e7i	−0.463408	+	0.802646i
$735$	1.03170e7	−	3.75509e6i	0.704428	−	0.256391i
$736$	491275.	+	2.78616e6i	0.0334295	+	0.189588i
$737$	396220.	−	2.24708e6i	0.0268700	−	0.152387i
$738$	−1.59474e6	−	580437.i	−0.107783	−	0.0392297i
$739$	−1.03363e7	+	8.67316e6i	−0.696230	+	0.584207i	−0.920698	−	0.390275i	$-0.872380\pi$
$739$	−1.03363e7	+	8.67316e6i	−0.696230	+	0.584207i	0.224468	+	0.974481i	$0.427936\pi$
$740$	−1.40329e7			−0.942034
$741$	−1.80753e7	+	1.68694e7i	−1.20932	+	1.12864i
$742$	−3.81774e6			−0.254564
$743$	−5.75143e6	+	4.82602e6i	−0.382211	+	0.320713i	−0.813570	−	0.581467i	$-0.802479\pi$
$743$	−5.75143e6	+	4.82602e6i	−0.382211	+	0.320713i	0.431359	+	0.902181i	$0.358034\pi$
$744$	−1.37902e6	−	501922.i	−0.0913352	−	0.0332433i
$745$	1.89816e6	−	1.07650e7i	0.125297	−	0.710597i
$746$	−2.33627e6	−	1.32497e7i	−0.153701	−	0.871682i
$747$	2.20730e6	−	803392.i	0.144730	−	0.0526776i
$748$	−365779.	+	633548.i	−0.0239037	+	0.0414024i
$749$	−5.73383e6	−	9.93128e6i	−0.373457	−	0.646846i
$750$	1.76366e6	+	1.47989e6i	0.114489	+	0.0960673i
$751$	−7.33005e6	−	6.15064e6i	−0.474250	−	0.397943i	0.374092	−	0.927392i	$-0.377954\pi$
$751$	−7.33005e6	−	6.15064e6i	−0.474250	−	0.397943i	−0.848342	+	0.529449i	$0.822399\pi$
$752$	1.33331e6	+	2.30937e6i	0.0859781	+	0.148918i
$753$	3.08820e6	−	5.34892e6i	0.198481	−	0.343778i
$754$	1.71429e7	−	6.23951e6i	1.09814	−	0.399689i
$755$	−157728.	−	894520.i	−0.0100703	−	0.0571114i
$756$	−896265.	+	5.08297e6i	−0.0570338	+	0.323455i
$757$	−1.90737e7	−	6.94226e6i	−1.20975	−	0.440313i	−0.343133	−	0.939287i	$-0.611488\pi$
$757$	−1.90737e7	−	6.94226e6i	−1.20975	−	0.440313i	−0.866617	+	0.498974i	$0.833710\pi$
$758$	−4.85560e6	+	4.07433e6i	−0.306952	+	0.257563i
$759$	1.56643e6			0.0986974
$760$	−923221.	+	7.54471e6i	−0.0579791	+	0.473815i
$761$	−2.98766e6			−0.187012			−0.0935061	−	0.995619i	$-0.529807\pi$
$761$	−2.98766e6			−0.187012			−0.0935061	+	0.995619i	$0.529807\pi$
$762$	1.02924e7	−	8.63634e6i	0.642139	−	0.538819i
$763$	7.57265e6	+	2.75622e6i	0.470909	+	0.171397i
$764$	1.87961e6	−	1.06598e7i	0.116503	−	0.660719i
$765$	773950.	+	4.38929e6i	0.0478145	+	0.271169i
$766$	−1.49950e7	+	5.45774e6i	−0.923369	+	0.336079i
$767$	1.46577e7	−	2.53879e7i	0.899657	−	1.55825i
$768$	451505.	+	782029.i	0.0276223	+	0.0478432i
$769$	−2.43866e6	−	2.04628e6i	−0.148708	−	0.124781i	0.565398	−	0.824818i	$-0.308722\pi$
$769$	−2.43866e6	−	2.04628e6i	−0.148708	−	0.124781i	−0.714107	+	0.700037i	$0.753167\pi$
$770$	−752306.	−	631260.i	−0.0457265	−	0.0383691i
$771$	2.49308e6	+	4.31815e6i	0.151043	+	0.261614i
$772$	6.30504e6	−	1.09206e7i	0.380754	−	0.659485i
$773$	−1.67254e7	+	6.08755e6i	−1.00676	+	0.366432i	−0.792189	−	0.610275i	$-0.791059\pi$
$773$	−1.67254e7	+	6.08755e6i	−1.00676	+	0.366432i	−0.214575	+	0.976708i	$0.568837\pi$
$774$	258005.	+	1.46322e6i	0.0154801	+	0.0877923i
$775$	743116.	−	4.21442e6i	0.0444429	−	0.252048i
$776$	9.79124e6	+	3.56372e6i	0.583692	+	0.212446i
$777$	9.69657e6	−	8.13639e6i	0.576190	−	0.483481i
$778$	−2.81996e6			−0.167030
$779$	1.15618e7	−	4.91332e6i	0.682626	−	0.290089i
$780$	−1.89744e7			−1.11669
$781$	2.27594e6	−	1.90974e6i	0.133516	−	0.112033i
$782$	−1.15395e7	−	4.20002e6i	−0.674791	−	0.245604i
$783$	−2.83397e6	+	1.60722e7i	−0.165193	+	0.936855i
$784$	−469311.	−	2.66160e6i	−0.0272691	−	0.154651i
$785$	−9.20304e6	+	3.34963e6i	−0.533037	+	0.194010i
$786$	−7.30996e6	+	1.26612e7i	−0.422045	+	0.731003i
$787$	7.25847e6	+	1.25720e7i	0.417742	+	0.723551i	0.995712	−	0.0925075i	$-0.0294882\pi$
$787$	7.25847e6	+	1.25720e7i	0.417742	+	0.723551i	−0.577970	+	0.816058i	$0.696155\pi$
$788$	7.91300e6	+	6.63980e6i	0.453968	+	0.380925i
$789$	6.81130e6	+	5.71536e6i	0.389527	+	0.326852i
$790$	9.22802e6	+	1.59834e7i	0.526066	+	0.911174i
$791$	−6.25577e6	+	1.08353e7i	−0.355500	+	0.615744i
$792$	−131511.	+	47865.9i	−0.00744985	+	0.00271152i
$793$	2.60815e6	+	1.47916e7i	0.147282	+	0.835278i
$794$	−2.37921e6	+	1.34932e7i	−0.133931	+	0.759562i
$795$	1.17983e7	+	4.29423e6i	0.662067	+	0.240973i
$796$	−6.70078e6	+	5.62262e6i	−0.374837	+	0.314526i
$797$	2.16675e7			1.20827			0.604133	−	0.796884i	$-0.293520\pi$
$797$	2.16675e7			1.20827			0.604133	+	0.796884i	$0.293520\pi$
$798$	−3.73656e6	−	5.74861e6i	−0.207713	−	0.319563i
$799$	−1.15747e7			−0.641418
$800$	−2.01720e6	+	1.69263e6i	−0.111435	+	0.0935054i
$801$	5.24615e6	+	1.90944e6i	0.288908	+	0.105154i
$802$	−3.35981e6	+	1.90544e7i	−0.184450	+	1.04607i
$803$	−47890.4	−	271600.i	−0.00262095	−	0.0148642i
$804$	1.14879e7	−	4.18126e6i	0.626760	−	0.228122i
$805$	8.24255e6	−	1.42765e7i	0.448303	−	0.776484i
$806$	−3.79534e6	−	6.57373e6i	−0.205785	−	0.356430i
$807$	1.58722e7	+	1.33184e7i	0.857932	+	0.719891i
$808$	4.31725e6	+	3.62260e6i	0.232637	+	0.195205i
$809$	−5.19860e6	−	9.00423e6i	−0.279264	−	0.483699i	0.691938	−	0.721957i	$-0.256757\pi$
$809$	−5.19860e6	−	9.00423e6i	−0.279264	−	0.483699i	−0.971202	+	0.238258i	$0.923424\pi$
$810$	6.53781e6	−	1.13238e7i	0.350122	−	0.606430i
$811$	−2.63470e7	+	9.58952e6i	−1.40663	+	0.511970i	−0.930138	−	0.367210i	$-0.880313\pi$
$811$	−2.63470e7	+	9.58952e6i	−1.40663	+	0.511970i	−0.476489	+	0.879180i	$0.658091\pi$
$812$	878480.	+	4.98211e6i	0.0467565	+	0.265169i
$813$	2.49178e6	−	1.41316e7i	0.132216	−	0.749833i
$814$	1.79725e6	+	654147.i	0.0950711	+	0.0346030i
$815$	2.31637e7	−	1.94367e7i	1.22156	−	1.02501i
$816$	−3.91957e6			−0.206069
$817$	−8.78644e6	−	6.61539e6i	−0.460530	−	0.346737i
$818$	1.20023e6			0.0627162
$819$	−3.67000e6	+	3.07949e6i	−0.191186	+	0.160424i
$820$	9.05949e6	+	3.29738e6i	0.470510	+	0.171252i
$821$	3.35173e6	−	1.90086e7i	0.173544	−	0.984220i	−0.766266	−	0.642524i	$-0.777887\pi$
$821$	3.35173e6	−	1.90086e7i	0.173544	−	0.984220i	0.939810	−	0.341696i	$-0.111001\pi$
$822$	−2.77905e6	−	1.57608e7i	−0.143455	−	0.813576i
$823$	2.98320e7	−	1.08579e7i	1.53526	−	0.558789i	0.570358	−	0.821396i	$-0.306805\pi$
$823$	2.98320e7	−	1.08579e7i	1.53526	−	0.558789i	0.964903	+	0.262607i	$0.0845824\pi$
$824$	−334747.	+	579798.i	−0.0171751	+	0.0297481i
$825$	728987.	+	1.26264e6i	0.0372894	+	0.0645871i
$826$	6.22747e6	+	5.22547e6i	0.317586	+	0.266487i
$827$	−2.45225e7	−	2.05768e7i	−1.24681	−	1.04620i	−0.996960	−	0.0779137i	$-0.975174\pi$
$827$	−2.45225e7	−	2.05768e7i	−1.24681	−	1.04620i	−0.249850	−	0.968284i	$-0.580381\pi$
$828$	−1.17462e6	−	2.03449e6i	−0.0595415	−	0.103129i
$829$	6.03320e6	−	1.04498e7i	0.304903	−	0.528107i	−0.672337	−	0.740245i	$-0.734709\pi$
$829$	6.03320e6	−	1.04498e7i	0.304903	−	0.528107i	0.977240	+	0.212138i	$0.0680427\pi$
$830$	−1.25394e7	+	4.56396e6i	−0.631801	+	0.229957i
$831$	1.19205e6	+	6.76044e6i	0.0598813	+	0.339604i
$832$	−811071.	+	4.59981e6i	−0.0406210	+	0.230373i
$833$	1.10236e7	+	4.01225e6i	0.550440	+	0.200344i
$834$	1.44188e7	−	1.20988e7i	0.717819	−	0.602322i
$835$	−4.34959e6			−0.215890
$836$	469941.	−	923250.i	0.0232556	−	0.0456881i
$837$	6.79059e6			0.335038
$838$	−1.30777e7	+	1.09735e7i	−0.643310	+	0.539801i
$839$	2.56977e7	+	9.35320e6i	1.26035	+	0.458728i	0.883885	−	0.467704i	$-0.154919\pi$
$839$	2.56977e7	+	9.35320e6i	1.26035	+	0.458728i	0.376461	+	0.926433i	$0.377141\pi$
$840$	913692.	−	5.18181e6i	0.0446788	−	0.253386i
$841$	−783990.	−	4.44623e6i	−0.0382226	−	0.216771i
$842$	1.02565e7	−	3.73306e6i	0.498561	−	0.181461i
$843$	1.43798e7	−	2.49065e7i	0.696920	−	1.20710i
$844$	2.82581e6	+	4.89445e6i	0.136548	+	0.236509i
$845$	−5.37154e7	−	4.50726e7i	−2.58796	−	2.17155i
$846$	−1.69624e6	−	1.42332e6i	−0.0814821	−	0.0683716i
$847$	−6.29905e6	−	1.09103e7i	−0.301694	−	0.522549i
$848$	1.54534e6	−	2.67662e6i	0.0737965	−	0.127819i
$849$	−2.64596e7	+	9.63049e6i	−1.25983	+	0.458542i
$850$	−1.98477e6	−	1.12562e7i	−0.0942242	−	0.534372i
$851$	−5.57500e6	+	3.16174e7i	−0.263889	+	1.49659i
$852$	1.49583e7	+	5.44438e6i	0.705966	+	0.256951i
$853$	131487.	−	110330.i	0.00618741	−	0.00519186i	−0.639689	−	0.768634i	$-0.720937\pi$
$853$	131487.	−	110330.i	0.00618741	−	0.00519186i	0.645876	+	0.763442i	$0.276492\pi$
$854$	−4.16510e6			−0.195425
$855$	−1.42234e6	−	6.14927e6i	−0.0665407	−	0.287679i
$856$	9.28375e6			0.433051
$857$	−52703.3	+	44223.3i	−0.00245124	+	0.00205683i	−0.644012	−	0.765015i	$-0.722731\pi$
$857$	−52703.3	+	44223.3i	−0.00245124	+	0.00205683i	0.641561	+	0.767072i	$0.278287\pi$
$858$	2.43014e6	+	884497.i	0.112697	+	0.0410184i
$859$	−4.44494e6	+	2.52085e7i	−0.205534	+	1.16564i	0.691064	+	0.722793i	$0.257142\pi$
$859$	−4.44494e6	+	2.52085e7i	−0.205534	+	1.16564i	−0.896598	+	0.442845i	$0.853969\pi$
$860$	−1.46569e6	−	8.31233e6i	−0.0675765	−	0.383245i
$861$	−8.17188e6	+	2.97432e6i	−0.375677	+	0.136735i
$862$	7.72011e6	−	1.33716e7i	0.353879	−	0.612937i
$863$	−1.26875e7	−	2.19754e7i	−0.579894	−	1.00441i	−0.995491	−	0.0948564i	$-0.969761\pi$
$863$	−1.26875e7	−	2.19754e7i	−0.579894	−	1.00441i	0.415597	−	0.909549i	$-0.363573\pi$
$864$	−3.20088e6	−	2.68585e6i	−0.145876	−	0.122405i
$865$	8.04158e6	+	6.74768e6i	0.365427	+	0.306630i
$866$	2.58864e6	+	4.48366e6i	0.117295	+	0.203160i
$867$	−1.27543e6	+	2.20911e6i	−0.0576247	+	0.0998090i
$868$	1.97801e6	−	719938.i	0.0891108	−	0.0324337i
$869$	−436803.	−	2.47724e6i	−0.0196217	−	0.111280i
$870$	2.88907e6	−	1.63848e7i	0.129408	−	0.733908i
$871$	5.94207e7	+	2.16274e7i	2.65395	+	0.965958i
$872$	−4.99764e6	+	4.19351e6i	−0.222574	+	0.186761i
$873$	−8.65214e6			−0.384227
$874$	1.66322e7	+	5.07748e6i	0.736497	+	0.224838i
$875$	−3.30233e6			−0.145814
$876$	1.13193e6	−	949806.i	0.0498380	−	0.0418191i
$877$	8.72358e6	+	3.17512e6i	0.382997	+	0.139400i	0.526342	−	0.850273i	$-0.323563\pi$
$877$	8.72358e6	+	3.17512e6i	0.382997	+	0.139400i	−0.143344	+	0.989673i	$0.545786\pi$
$878$	−2.13653e6	+	1.21169e7i	−0.0935347	+	0.530462i
$879$	2.90804e6	+	1.64923e7i	0.126949	+	0.719961i
$880$	747093.	−	271920.i	0.0325213	−	0.0118368i
$881$	6.59127e6	−	1.14164e7i	0.286108	−	0.495553i	−0.686770	−	0.726875i	$-0.740972\pi$
$881$	6.59127e6	−	1.14164e7i	0.286108	−	0.495553i	0.972877	+	0.231322i	$0.0743052\pi$
$882$	1.12210e6	+	1.94354e6i	0.0485692	+	0.0841243i
$883$	2.84826e7	+	2.38997e7i	1.22936	+	1.03155i	0.998281	+	0.0586171i	$0.0186691\pi$
$883$	2.84826e7	+	2.38997e7i	1.22936	+	1.03155i	0.231076	+	0.972936i	$0.425775\pi$
$884$	−1.55306e7	−	1.30317e7i	−0.668433	−	0.560882i
$885$	−1.33676e7	−	2.31534e7i	−0.573716	−	0.993704i
$886$	9.86931e6	−	1.70941e7i	0.422379	−	0.731582i
$887$	−1.36124e7	+	4.95452e6i	−0.580933	+	0.211442i	−0.615737	−	0.787952i	$-0.711142\pi$
$887$	−1.36124e7	+	4.95452e6i	−0.580933	+	0.211442i	0.0348036	+	0.999394i	$0.488919\pi$
$888$	1.77944e6	+	1.00917e7i	0.0757270	+	0.429469i
$889$	−3.34651e6	+	1.89790e7i	−0.142016	+	0.805413i
$890$	−2.98027e7	−	1.08473e7i	−1.26119	−	0.459035i
$891$	−1.36519e6	+	1.14553e6i	−0.0576102	+	0.0483407i
$892$	−1.74571e7			−0.734617
$893$	1.63682e7	−	864579.i	0.686867	−	0.0362807i
$894$	−7.98232e6			−0.334030
$895$	−2.36596e7	+	1.98528e7i	−0.987302	+	0.828445i
$896$	−1.21713e6	−	442999.i	−0.0506486	−	0.0184346i
$897$	−7.53817e6	+	4.27511e7i	−0.312813	+	1.77405i
$898$	−3.28206e6	−	1.86135e7i	−0.135817	−	0.770258i
$899$	6.25444e6	−	2.27643e6i	0.258101	−	0.0939409i
$900$	1.09329e6	−	1.89363e6i	0.0449914	−	0.0779273i
$901$	6.70766e6	+	1.16180e7i	0.275270	+	0.476782i
$902$	−1.00658e6	−	844623.i	−0.0411939	−	0.0345658i
$903$	5.83235e6	+	4.89392e6i	0.238026	+	0.199727i
$904$	−5.06442e6	−	8.77183e6i	−0.206115	−	0.357001i
$905$	−2.33417e7	+	4.04291e7i	−0.947353	+	1.64086i
$906$	−623292.	+	226860.i	−0.0252273	+	0.00918199i
$907$	−6.56474e6	−	3.72305e7i	−0.264971	−	1.50273i	−0.769117	−	0.639109i	$-0.779303\pi$
$907$	−6.56474e6	−	3.72305e7i	−0.264971	−	1.50273i	0.504145	−	0.863619i	$-0.331808\pi$
$908$	−411381.	+	2.33306e6i	−0.0165588	+	0.0939097i
$909$	−4.39754e6	−	1.60057e6i	−0.176523	−	0.0642490i
$910$	2.08488e7	−	1.74942e7i	0.834596	−	0.700310i
$911$	−3.56582e6			−0.142352			−0.0711760	−	0.997464i	$-0.522675\pi$
$911$	−3.56582e6			−0.142352			−0.0711760	+	0.997464i	$0.522675\pi$
$912$	5.54283e6	−	292775.i	0.220671	−	0.0116559i
$913$	1.81873e6			0.0722089
$914$	6.17699e6	−	5.18311e6i	0.244575	−	0.205222i
$915$	1.28718e7	+	4.68494e6i	0.508259	+	0.184991i
$916$	−2.92675e6	+	1.65984e7i	−0.115252	+	0.653625i
$917$	−3.64145e6	−	2.06517e7i	−0.143005	−	0.811021i
$918$	1.70430e7	−	6.20315e6i	0.667482	−	0.242944i
$919$	5.55477e6	−	9.62114e6i	0.216959	−	0.375783i	−0.736918	−	0.675982i	$-0.763720\pi$
$919$	5.55477e6	−	9.62114e6i	0.216959	−	0.375783i	0.953877	+	0.300199i	$0.0970530\pi$
$920$	6.67283e6	+	1.15577e7i	0.259920	+	0.450195i
$921$	−1.55686e7	−	1.30636e7i	−0.604782	−	0.507473i
$922$	−2.28425e7	−	1.91671e7i	−0.884945	−	0.742557i
$923$	4.11683e7	+	7.13056e7i	1.59059	+	2.75499i
$924$	−358573.	+	621066.i	−0.0138165	+	0.0239308i
$925$	−2.80802e7	+	1.02204e7i	−1.07906	+	0.392746i
$926$	−1.34252e6	−	7.61382e6i	−0.0514510	−	0.291793i
$927$	96535.7	−	547481.i	0.00368968	−	0.0209252i
$928$	−3.84854e6	−	1.40075e6i	−0.146699	−	0.0533939i
$929$	−1.45753e7	+	1.22301e7i	−0.554088	+	0.464935i	−0.876323	−	0.481725i	$-0.840010\pi$
$929$	−1.45753e7	+	1.22301e7i	−0.554088	+	0.464935i	0.322234	+	0.946660i	$0.395566\pi$
$930$	−6.92262e6			−0.262460
$931$	−1.58886e7	−	4.85048e6i	−0.600774	−	0.183405i
$932$	−1.00018e7			−0.377173
$933$	−1.12041e7	+	9.40137e6i	−0.421380	+	0.353580i
$934$	4.46751e6	+	1.62604e6i	0.167571	+	0.0609908i
$935$	−599246.	+	3.39849e6i	−0.0224169	+	0.127133i
$936$	−673489.	−	3.81955e6i	−0.0251270	−	0.142502i
$937$	−6.54993e6	+	2.38398e6i	−0.243718	+	0.0887062i	−0.460991	−	0.887405i	$-0.652506\pi$
$937$	−6.54993e6	+	2.38398e6i	−0.243718	+	0.0887062i	0.217273	+	0.976111i	$0.430284\pi$
$938$	−8.76768e6	+	1.51861e7i	−0.325370	+	0.563557i
$939$	−2.21390e7	−	3.83459e7i	−0.819397	−	1.41924i
$940$	9.63612e6	+	8.08566e6i	0.355699	+	0.298467i
$941$	6.96299e6	+	5.84264e6i	0.256343	+	0.215097i	0.761898	−	0.647697i	$-0.224268\pi$
$941$	6.96299e6	+	5.84264e6i	0.256343	+	0.215097i	−0.505555	+	0.862794i	$0.668712\pi$
$942$	3.57587e6	+	6.19360e6i	0.131297	+	0.227413i
$943$	1.10285e7	−	1.91019e7i	0.403866	−	0.699517i
$944$	−6.18432e6	+	2.25091e6i	−0.225872	+	0.0822107i
$945$	4.22788e6	+	2.39775e7i	0.154008	+	0.873422i
$946$	−199765.	+	1.13292e6i	−0.00725757	+	0.0411597i
$947$	4.00423e7	+	1.45742e7i	1.45092	+	0.528093i	0.942849	−	0.333221i	$-0.108135\pi$
$947$	4.00423e7	+	1.45742e7i	1.45092	+	0.528093i	0.508074	+	0.861314i	$0.330358\pi$
$948$	1.03243e7	−	8.66309e6i	0.373111	−	0.313077i
$949$	7.64300e6			0.275485
$950$	3.64754e6	+	1.57696e7i	0.131127	+	0.566907i
$951$	−4.56646e7			−1.63730
$952$	4.30676e6	−	3.61380e6i	0.154013	−	0.129233i
$953$	−9.70100e6	−	3.53088e6i	−0.346007	−	0.125936i	0.163171	−	0.986598i	$-0.447828\pi$
$953$	−9.70100e6	−	3.53088e6i	−0.346007	−	0.125936i	−0.509177	+	0.860662i	$0.670050\pi$
$954$	−445653.	+	2.52743e6i	−0.0158535	+	0.0899099i
$955$	−8.86655e6	−	5.02847e7i	−0.314591	−	1.78413i
$956$	1.25730e6	−	457620.i	0.0444933	−	0.0161942i
$957$	−1.13380e6	+	1.96380e6i	−0.0400181	+	0.0693133i
$958$	−1.35304e7	−	2.34353e7i	−0.476316	−	0.825004i
$959$	1.75849e7	+	1.47555e7i	0.617437	+	0.518091i
$960$	3.26311e6	+	2.73808e6i	0.114276	+	0.0958887i
$961$	1.29299e7	+	2.23952e7i	0.451633	+	0.782252i
$962$	−2.65020e7	+	4.59029e7i	−0.923297	+	1.59920i
$963$	−7.24404e6	+	2.63661e6i	−0.251718	+	0.0916180i
$964$	1.85067e6	+	1.04957e7i	0.0641412	+	0.363763i
$965$	1.03294e7	−	5.85807e7i	0.357072	−	2.02505i
$966$	−1.13121e7	−	4.11728e6i	−0.390033	−	0.141960i
$967$	7.18021e6	−	6.02491e6i	0.246928	−	0.207197i	−0.510920	−	0.859628i	$-0.670695\pi$
$967$	7.18021e6	−	6.02491e6i	0.246928	−	0.207197i	0.757848	+	0.652431i	$0.226251\pi$
$968$	1.01989e7			0.349837
$969$	−1.09289e7	+	2.14711e7i	−0.373911	+	0.734590i
$970$	4.91516e7			1.67729
$971$	7.62448e6	−	6.39769e6i	0.259515	−	0.217759i	−0.503742	−	0.863854i	$-0.668044\pi$
$971$	7.62448e6	−	6.39769e6i	0.259515	−	0.217759i	0.763257	+	0.646096i	$0.223599\pi$
$972$	5.93573e6	+	2.16043e6i	0.201516	+	0.0733457i
$973$	−4.68819e6	+	2.65880e7i	−0.158753	+	0.900335i
$974$	3.62239e6	+	2.05436e7i	0.122348	+	0.693872i
$975$	−3.79683e7	+	1.38193e7i	−1.27912	+	0.465560i
$976$	1.68595e6	−	2.92014e6i	0.0566525	−	0.0981250i
$977$	−1.83218e7	−	3.17342e7i	−0.614088	−	1.06363i	−0.990544	−	0.137197i	$-0.956191\pi$
$977$	−1.83218e7	−	3.17342e7i	−0.614088	−	1.06363i	0.376456	−	0.926435i	$-0.377143\pi$
$978$	−1.69151e7	−	1.41935e7i	−0.565494	−	0.474506i
$979$	3.31132e6	+	2.77853e6i	0.110419	+	0.0926526i
$980$	−6.37450e6	−	1.10410e7i	−0.212022	−	0.367233i
$981$	2.70865e6	−	4.69151e6i	0.0898627	−	0.155647i
$982$	2.10329e7	−	7.65535e6i	0.696018	−	0.253330i
$983$	−4.38928e6	−	2.48929e7i	−0.144881	−	0.821658i	−0.967463	−	0.253012i	$-0.918579\pi$
$983$	−4.38928e6	−	2.48929e7i	−0.144881	−	0.821658i	0.822583	−	0.568646i	$-0.192532\pi$
$984$	1.22252e6	−	6.93324e6i	0.0402501	−	0.228270i
$985$	4.57888e7	+	1.66657e7i	1.50372	+	0.547311i
$986$	1.36179e7	−	1.14268e7i	0.446085	−	0.374310i
$987$	−1.13466e7			−0.370744
$988$	2.29359e7	+	1.72687e7i	0.747522	+	0.562816i
$989$	−1.93108e7			−0.627783
$990$	−505725.	+	424354.i	−0.0163993	+	0.0137607i
$991$	−2.66118e7	−	9.68592e6i	−0.860777	−	0.313297i	−0.126351	−	0.991986i	$-0.540326\pi$
$991$	−2.66118e7	−	9.68592e6i	−0.860777	−	0.313297i	−0.734426	+	0.678688i	$0.762549\pi$
$992$	−295912.	+	1.67820e6i	−0.00954736	+	0.0541458i
$993$	693299.	+	3.93189e6i	0.0223124	+	0.126540i
$994$	−2.14556e7	+	7.80922e6i	−0.688772	+	0.250693i
$995$	−2.06313e7	+	3.57345e7i	−0.660647	+	1.14427i
$996$	4.87222e6	+	8.43893e6i	0.155625	+	0.269550i
$997$	3.03971e6	+	2.55062e6i	0.0968487	+	0.0812657i	0.689926	−	0.723880i	$-0.257643\pi$
$997$	3.03971e6	+	2.55062e6i	0.0968487	+	0.0812657i	−0.593078	+	0.805145i	$0.702087\pi$
$998$	−1.26518e7	−	1.06161e7i	−0.402093	−	0.337396i
$999$	−2.37086e7	−	4.10644e7i	−0.751608	−	1.30182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.a.25.3	✓	24
19.4	even	9		722.6.a.o.1.4		12
19.15	odd	18		722.6.a.p.1.9		12
19.16	even	9	inner	38.6.e.a.35.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.a.25.3	✓	24	1.1	even	1	trivial
38.6.e.a.35.3	yes	24	19.16	even	9	inner
722.6.a.o.1.4		12	19.4	even	9
722.6.a.p.1.9		12	19.15	odd	18

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.06418 + 2.57115i) q^{2} +(12.9479 + 4.71264i) q^{3} +(2.77837 - 15.7569i) q^{4} +(-13.1062 - 74.3288i) q^{5} +(-51.7915 + 18.8506i) q^{6} +(39.5277 - 68.4640i) q^{7} +(32.0000 + 55.4256i) q^{8} +(-40.7104 - 34.1601i) q^{9} +O(q^{10})\)	\(q+(-3.06418 + 2.57115i) q^{2} +(12.9479 + 4.71264i) q^{3} +(2.77837 - 15.7569i) q^{4} +(-13.1062 - 74.3288i) q^{5} +(-51.7915 + 18.8506i) q^{6} +(39.5277 - 68.4640i) q^{7} +(32.0000 + 55.4256i) q^{8} +(-40.7104 - 34.1601i) q^{9} +(231.270 + 194.059i) q^{10} +(-20.5737 - 35.6348i) q^{11} +(110.231 - 190.925i) q^{12} +(1071.56 - 390.014i) q^{13} +(54.9113 + 311.417i) q^{14} +(180.588 - 1024.16i) q^{15} +(-240.561 - 87.5572i) q^{16} +(851.216 - 714.255i) q^{17} +212.575 q^{18} +(-1150.39 + 1073.64i) q^{19} -1207.61 q^{20} +(834.445 - 700.183i) q^{21} +(154.664 + 56.2931i) q^{22} +(-479.761 + 2720.86i) q^{23} +(153.131 + 868.448i) q^{24} +(-2416.46 + 879.520i) q^{25} +(-2280.65 + 3950.20i) q^{26} +(-2040.26 - 3533.83i) q^{27} +(-968.959 - 813.053i) q^{28} +(-3063.83 - 2570.86i) q^{29} +(2079.93 + 3602.54i) q^{30} +(-832.075 + 1441.20i) q^{31} +(962.245 - 350.229i) q^{32} +(-98.4523 - 558.351i) q^{33} +(-771.820 + 4377.21i) q^{34} +(-5606.90 - 2040.75i) q^{35} +(-651.366 + 546.561i) q^{36} +11620.4 q^{37} +(764.504 - 6247.65i) q^{38} +15712.4 q^{39} +(3700.32 - 3104.94i) q^{40} +(-7502.02 - 2730.51i) q^{41} +(-756.614 + 4290.97i) q^{42} +(1213.71 + 6883.31i) q^{43} +(-618.656 + 225.172i) q^{44} +(-2005.52 + 3473.66i) q^{45} +(-5525.66 - 9570.73i) q^{46} +(-7979.51 - 6695.61i) q^{47} +(-2702.13 - 2267.36i) q^{48} +(5278.62 + 9142.84i) q^{49} +(5143.09 - 8908.09i) q^{50} +(14387.5 - 5236.61i) q^{51} +(-3168.25 - 17968.0i) q^{52} +(-2096.46 + 11889.6i) q^{53} +(15337.7 + 5582.47i) q^{54} +(-2379.05 + 1996.26i) q^{55} +5059.54 q^{56} +(-19954.8 + 8479.99i) q^{57} +15998.2 q^{58} +(19693.4 - 16524.7i) q^{59} +(-15635.9 - 5691.02i) q^{60} +(-2287.20 + 12971.4i) q^{61} +(-1155.91 - 6555.47i) q^{62} +(-3947.92 + 1436.93i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-43033.3 - 74535.9i) q^{65} +(1737.28 + 1457.75i) q^{66} +(42479.3 + 35644.3i) q^{67} +(-8889.47 - 15397.0i) q^{68} +(-19034.3 + 32968.4i) q^{69} +(22427.6 - 8162.98i) q^{70} +(12538.2 + 71107.6i) q^{71} +(590.611 - 3349.52i) q^{72} +(6298.26 + 2292.38i) q^{73} +(-35606.9 + 29877.7i) q^{74} -35432.9 q^{75} +(13721.1 + 21109.6i) q^{76} -3252.93 q^{77} +(-48145.5 + 40398.8i) q^{78} +(57445.8 + 20908.6i) q^{79} +(-3355.18 + 19028.2i) q^{80} +(-7520.85 - 42652.9i) q^{81} +(30008.1 - 10922.0i) q^{82} +(-22100.1 + 38278.5i) q^{83} +(-8714.33 - 15093.7i) q^{84} +(-64245.9 - 53908.7i) q^{85} +(-21417.1 - 17971.0i) q^{86} +(-27554.5 - 47725.8i) q^{87} +(1316.72 - 2280.63i) q^{88} +(-98716.5 + 35929.9i) q^{89} +(-2786.04 - 15800.4i) q^{90} +(15654.2 - 88779.3i) q^{91} +(41539.4 + 15119.1i) q^{92} +(-17565.4 + 14739.1i) q^{93} +41666.1 q^{94} +(94879.6 + 71435.7i) q^{95} +14109.5 q^{96} +(124717. - 104650. i) q^{97} +(-39682.3 - 14443.2i) q^{98} +(-379.721 + 2153.51i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9}+O(q^{10}) \) 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9	\( 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9} + 600 q^{11} - 1662 q^{13} - 1776 q^{14} - 1206 q^{15} + 4194 q^{17} - 4368 q^{18} + 9570 q^{19} - 1344 q^{20} + 2430 q^{21} - 5160 q^{22} - 1170 q^{23} - 1152 q^{24} + 5940 q^{25} - 1776 q^{26} - 5130 q^{27} + 768 q^{28} - 7554 q^{29} + 294 q^{31} - 45912 q^{33} + 1584 q^{34} + 22116 q^{35} + 6048 q^{36} + 28608 q^{37} - 9528 q^{38} - 38868 q^{39} + 37278 q^{41} - 9720 q^{42} + 13212 q^{43} + 20640 q^{44} - 34344 q^{45} - 29856 q^{46} - 3054 q^{47} - 9216 q^{48} + 1422 q^{49} + 16584 q^{50} + 2352 q^{51} - 1824 q^{52} + 73806 q^{53} + 136944 q^{54} - 41598 q^{55} + 56064 q^{56} + 178248 q^{57} - 52848 q^{58} + 123528 q^{59} + 46944 q^{60} - 149172 q^{61} + 58344 q^{62} - 170124 q^{63} - 49152 q^{64} - 202674 q^{65} - 84840 q^{66} - 313212 q^{67} + 35520 q^{68} - 19938 q^{69} - 88464 q^{70} + 75810 q^{71} + 48384 q^{72} + 172872 q^{73} + 4872 q^{74} + 174960 q^{75} + 31008 q^{76} - 115056 q^{77} + 101304 q^{78} + 158058 q^{79} - 47250 q^{81} - 149112 q^{82} - 148440 q^{83} - 176736 q^{84} - 226752 q^{85} - 57528 q^{86} + 182874 q^{87} - 38400 q^{88} - 322464 q^{89} + 48816 q^{90} - 27264 q^{91} + 88992 q^{92} + 779424 q^{93} + 143712 q^{94} + 634752 q^{95} - 108552 q^{97} - 173544 q^{98} + 656436 q^{99}+O(q^{100}) \) 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9 + 600 * q^11 - 1662 * q^13 - 1776 * q^14 - 1206 * q^15 + 4194 * q^17 - 4368 * q^18 + 9570 * q^19 - 1344 * q^20 + 2430 * q^21 - 5160 * q^22 - 1170 * q^23 - 1152 * q^24 + 5940 * q^25 - 1776 * q^26 - 5130 * q^27 + 768 * q^28 - 7554 * q^29 + 294 * q^31 - 45912 * q^33 + 1584 * q^34 + 22116 * q^35 + 6048 * q^36 + 28608 * q^37 - 9528 * q^38 - 38868 * q^39 + 37278 * q^41 - 9720 * q^42 + 13212 * q^43 + 20640 * q^44 - 34344 * q^45 - 29856 * q^46 - 3054 * q^47 - 9216 * q^48 + 1422 * q^49 + 16584 * q^50 + 2352 * q^51 - 1824 * q^52 + 73806 * q^53 + 136944 * q^54 - 41598 * q^55 + 56064 * q^56 + 178248 * q^57 - 52848 * q^58 + 123528 * q^59 + 46944 * q^60 - 149172 * q^61 + 58344 * q^62 - 170124 * q^63 - 49152 * q^64 - 202674 * q^65 - 84840 * q^66 - 313212 * q^67 + 35520 * q^68 - 19938 * q^69 - 88464 * q^70 + 75810 * q^71 + 48384 * q^72 + 172872 * q^73 + 4872 * q^74 + 174960 * q^75 + 31008 * q^76 - 115056 * q^77 + 101304 * q^78 + 158058 * q^79 - 47250 * q^81 - 149112 * q^82 - 148440 * q^83 - 176736 * q^84 - 226752 * q^85 - 57528 * q^86 + 182874 * q^87 - 38400 * q^88 - 322464 * q^89 + 48816 * q^90 - 27264 * q^91 + 88992 * q^92 + 779424 * q^93 + 143712 * q^94 + 634752 * q^95 - 108552 * q^97 - 173544 * q^98 + 656436 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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