LMFDB - Embedded newform 99.6.f.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,6,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, 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:	$15.8779981615$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 86 x^{14} - 146 x^{13} + 7205 x^{12} - 23732 x^{11} + 774165 x^{10} + \cdots + 393784336 $ x^16 - 5x^15 + 86x^14 - 146x^13 + 7205x^12 - 23732x^11 + 774165x^10 - 1228996x^9 + 44649817x^8 - 92720004x^7 + 943915592x^6 - 1892495035x^5 + 8611100939x^4 - 17760110698x^3 + 18348896492x^2 - 4224271656*x + 393784336
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$-7.26917 + 5.28136i$ of defining polynomial
Character	$\chi$	$=$	99.64
Dual form			99.6.f.a.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.46756 + 7.59437i) q^{2} +(-25.6970 - 18.6700i) q^{4} +(2.24156 + 6.89880i) q^{5} +(136.674 + 99.2995i) q^{7} +(-1.52919 + 1.11102i) q^{8} +O(q^{10})$	\(q+(-2.46756 + 7.59437i) q^{2} +(-25.6970 - 18.6700i) q^{4} +(2.24156 + 6.89880i) q^{5} +(136.674 + 99.2995i) q^{7} +(-1.52919 + 1.11102i) q^{8} -57.9232 q^{10} +(328.761 + 230.146i) q^{11} +(-82.1221 + 252.746i) q^{13} +(-1091.37 + 792.926i) q^{14} +(-318.757 - 981.033i) q^{16} +(212.954 + 655.405i) q^{17} +(-2189.10 + 1590.47i) q^{19} +(71.1992 - 219.129i) q^{20} +(-2559.05 + 1928.84i) q^{22} -1409.32 q^{23} +(2485.61 - 1805.90i) q^{25} +(-1716.80 - 1247.33i) q^{26} +(-1658.20 - 5103.41i) q^{28} +(-2168.11 - 1575.22i) q^{29} +(1335.02 - 4108.76i) q^{31} +8176.39 q^{32} -5502.86 q^{34} +(-378.685 + 1165.47i) q^{35} +(636.281 + 462.285i) q^{37} +(-6676.90 - 20549.4i) q^{38} +(-11.0925 - 8.05916i) q^{40} +(-10431.5 + 7578.95i) q^{41} -20070.0 q^{43} +(-4151.37 - 12052.0i) q^{44} +(3477.58 - 10702.9i) q^{46} +(15223.4 - 11060.4i) q^{47} +(3625.75 + 11158.9i) q^{49} +(7581.29 + 23332.8i) q^{50} +(6829.06 - 4961.60i) q^{52} +(-9207.82 + 28338.8i) q^{53} +(-850.793 + 2783.94i) q^{55} -319.325 q^{56} +(17312.7 - 12578.4i) q^{58} +(-16651.4 - 12097.9i) q^{59} +(9605.36 + 29562.3i) q^{61} +(27909.2 + 20277.2i) q^{62} +(-9975.51 + 30701.5i) q^{64} -1927.72 q^{65} -764.687 q^{67} +(6764.11 - 20817.8i) q^{68} +(-7916.60 - 5751.75i) q^{70} +(16135.3 + 49659.4i) q^{71} +(57261.6 + 41603.0i) q^{73} +(-5080.83 + 3691.44i) q^{74} +85947.4 q^{76} +(22079.8 + 64100.8i) q^{77} +(-1168.98 + 3597.74i) q^{79} +(6053.44 - 4398.08i) q^{80} +(-31816.9 - 97922.4i) q^{82} +(1810.96 + 5573.57i) q^{83} +(-4044.16 + 2938.25i) q^{85} +(49524.0 - 152419. i) q^{86} +(-758.435 + 13.3242i) q^{88} -62319.7 q^{89} +(-36321.5 + 26389.1i) q^{91} +(36215.3 + 26312.0i) q^{92} +(46432.4 + 142904. i) q^{94} +(-15879.3 - 11537.0i) q^{95} +(30837.4 - 94907.9i) q^{97} -93691.8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 73 q^{4} + 10 q^{5} + 196 q^{7} - 527 q^{8}+O(q^{10}) $ 16 * q + q^2 - 73 * q^4 + 10 * q^5 + 196 * q^7 - 527 * q^8	$ 16 q + q^{2} - 73 q^{4} + 10 q^{5} + 196 q^{7} - 527 q^{8} - 672 q^{10} + 692 q^{11} + 1162 q^{13} - 560 q^{14} + 6399 q^{16} + 22 q^{17} - 3236 q^{19} + 5514 q^{20} - 13059 q^{22} + 10848 q^{23} + 15686 q^{25} - 16216 q^{26} + 8838 q^{28} - 13070 q^{29} - 14764 q^{31} + 58812 q^{32} - 26966 q^{34} - 43368 q^{35} + 4638 q^{37} - 68144 q^{38} + 52284 q^{40} + 14806 q^{41} - 24376 q^{43} + 104960 q^{44} + 50452 q^{46} - 40364 q^{47} + 32246 q^{49} - 10839 q^{50} - 80654 q^{52} + 11654 q^{53} + 7052 q^{55} - 70632 q^{56} + 10276 q^{58} - 70804 q^{59} - 31446 q^{61} + 153388 q^{62} + 17695 q^{64} + 41284 q^{65} - 64200 q^{67} + 94114 q^{68} - 103768 q^{70} + 184380 q^{71} - 1750 q^{73} - 306048 q^{74} + 174806 q^{76} - 384646 q^{77} + 24324 q^{79} + 386444 q^{80} - 316255 q^{82} + 46028 q^{83} + 63914 q^{85} - 22931 q^{86} + 211871 q^{88} - 148364 q^{89} - 258448 q^{91} + 58658 q^{92} - 55370 q^{94} + 4716 q^{95} + 484296 q^{97} - 743692 q^{98}+O(q^{100}) $ 16 * q + q^2 - 73 * q^4 + 10 * q^5 + 196 * q^7 - 527 * q^8 - 672 * q^10 + 692 * q^11 + 1162 * q^13 - 560 * q^14 + 6399 * q^16 + 22 * q^17 - 3236 * q^19 + 5514 * q^20 - 13059 * q^22 + 10848 * q^23 + 15686 * q^25 - 16216 * q^26 + 8838 * q^28 - 13070 * q^29 - 14764 * q^31 + 58812 * q^32 - 26966 * q^34 - 43368 * q^35 + 4638 * q^37 - 68144 * q^38 + 52284 * q^40 + 14806 * q^41 - 24376 * q^43 + 104960 * q^44 + 50452 * q^46 - 40364 * q^47 + 32246 * q^49 - 10839 * q^50 - 80654 * q^52 + 11654 * q^53 + 7052 * q^55 - 70632 * q^56 + 10276 * q^58 - 70804 * q^59 - 31446 * q^61 + 153388 * q^62 + 17695 * q^64 + 41284 * q^65 - 64200 * q^67 + 94114 * q^68 - 103768 * q^70 + 184380 * q^71 - 1750 * q^73 - 306048 * q^74 + 174806 * q^76 - 384646 * q^77 + 24324 * q^79 + 386444 * q^80 - 316255 * q^82 + 46028 * q^83 + 63914 * q^85 - 22931 * q^86 + 211871 * q^88 - 148364 * q^89 - 258448 * q^91 + 58658 * q^92 - 55370 * q^94 + 4716 * q^95 + 484296 * q^97 - 743692 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−2.46756	+	7.59437i	−0.436207	+	1.34251i	0.455637	+	0.890165i	$0.349411\pi$
$2$	−2.46756	+	7.59437i	−0.436207	+	1.34251i	−0.891845	+	0.452342i	$0.850589\pi$
$3$		0			0
$3$		0			0
$4$	−25.6970	−	18.6700i	−0.803033	−	0.583437i
$5$	2.24156	+	6.89880i	0.0400982	+	0.123410i	0.969102	−	0.246661i	$-0.0793335\pi$
$5$	2.24156	+	6.89880i	0.0400982	+	0.123410i	−0.929004	+	0.370071i	$0.879333\pi$
$6$		0			0
$7$	136.674	+	99.2995i	1.05424	+	0.765953i	0.973015	−	0.230743i	$-0.0741156\pi$
$7$	136.674	+	99.2995i	1.05424	+	0.765953i	0.0812288	+	0.996695i	$0.474116\pi$
$8$	−1.52919	+	1.11102i	−0.00844766	+	0.00613759i
$9$		0			0
$10$	−57.9232			−0.183169
$11$	328.761	+	230.146i	0.819217	+	0.573484i
$11$	328.761	+	230.146i	0.819217	+	0.573484i
$12$		0			0
$13$	−82.1221	+	252.746i	−0.134773	+	0.414787i	−0.995555	−	0.0941865i	$-0.969975\pi$
$13$	−82.1221	+	252.746i	−0.134773	+	0.414787i	0.860782	+	0.508974i	$0.169975\pi$
$14$	−1091.37	+	792.926i	−1.48817	+	1.08122i
$15$		0			0
$16$	−318.757	−	981.033i	−0.311286	−	0.958040i
$17$	212.954	+	655.405i	0.178716	+	0.550031i	0.999784	−	0.0207998i	$-0.00662125\pi$
$17$	212.954	+	655.405i	0.178716	+	0.550031i	−0.821068	+	0.570831i	$0.806621\pi$
$18$		0			0
$19$	−2189.10	+	1590.47i	−1.39117	+	1.01075i	−0.395436	+	0.918493i	$0.629407\pi$
$19$	−2189.10	+	1590.47i	−1.39117	+	1.01075i	−0.995736	+	0.0922522i	$0.970593\pi$
$20$	71.1992	−	219.129i	0.0398016	−	0.122497i
$21$		0			0
$22$	−2559.05	+	1928.84i	−1.12725	+	0.849647i
$23$	−1409.32			−0.555507			−0.277754	−	0.960652i	$-0.589590\pi$
$23$	−1409.32			−0.555507			−0.277754	+	0.960652i	$0.589590\pi$
$24$		0			0
$25$	2485.61	−	1805.90i	0.795395	−	0.577888i
$26$	−1716.80	−	1247.33i	−0.498066	−	0.361866i
$27$		0			0
$28$	−1658.20	−	5103.41i	−0.399706	−	1.23017i
$29$	−2168.11	−	1575.22i	−0.478724	−	0.347814i	0.322107	−	0.946703i	$-0.395609\pi$
$29$	−2168.11	−	1575.22i	−0.478724	−	0.347814i	−0.800832	+	0.598890i	$0.795609\pi$
$30$		0			0
$31$	1335.02	−	4108.76i	0.249507	−	0.767903i	−0.745356	−	0.666667i	$-0.767720\pi$
$31$	1335.02	−	4108.76i	0.249507	−	0.767903i	0.994862	−	0.101236i	$-0.0322797\pi$
$32$	8176.39			1.41152
$33$		0			0
$34$	−5502.86			−0.816378
$35$	−378.685	+	1165.47i	−0.0522526	+	0.160817i
$36$		0			0
$37$	636.281	+	462.285i	0.0764090	+	0.0555144i	0.625334	−	0.780357i	$-0.284963\pi$
$37$	636.281	+	462.285i	0.0764090	+	0.0555144i	−0.548925	+	0.835872i	$0.684963\pi$
$38$	−6676.90	−	20549.4i	−0.750094	−	2.30855i
$39$		0			0
$40$	−11.0925	−	8.05916i	−0.00109617	−	0.000796416i
$41$	−10431.5	+	7578.95i	−0.969144	+	0.704125i	−0.955256	−	0.295779i	$-0.904421\pi$
$41$	−10431.5	+	7578.95i	−0.969144	+	0.704125i	−0.0138879	+	0.999904i	$0.504421\pi$
$42$		0			0
$43$	−20070.0			−1.65530			−0.827650	−	0.561245i	$-0.810323\pi$
$43$	−20070.0			−1.65530			−0.827650	+	0.561245i	$0.810323\pi$
$44$	−4151.37	−	12052.0i	−0.323266	−	0.938488i
$45$		0			0
$46$	3477.58	−	10702.9i	0.242316	−	0.745772i
$47$	15223.4	−	11060.4i	1.00523	−	0.730344i	0.0420282	−	0.999116i	$-0.486618\pi$
$47$	15223.4	−	11060.4i	1.00523	−	0.730344i	0.963204	+	0.268773i	$0.0866181\pi$
$48$		0			0
$49$	3625.75	+	11158.9i	0.215729	+	0.663945i
$50$	7581.29	+	23332.8i	0.428862	+	1.31990i
$51$		0			0
$52$	6829.06	−	4961.60i	0.350229	−	0.254456i
$53$	−9207.82	+	28338.8i	−0.450264	+	1.38577i	0.426342	+	0.904562i	$0.359802\pi$
$53$	−9207.82	+	28338.8i	−0.450264	+	1.38577i	−0.876606	+	0.481209i	$0.840198\pi$
$54$		0			0
$55$	−850.793	+	2783.94i	−0.0379243	+	0.124095i
$56$	−319.325			−0.0136070
$57$		0			0
$58$	17312.7	−	12578.4i	0.675765	−	0.490972i
$59$	−16651.4	−	12097.9i	−0.622760	−	0.452461i	0.231125	−	0.972924i	$-0.425759\pi$
$59$	−16651.4	−	12097.9i	−0.622760	−	0.452461i	−0.853884	+	0.520463i	$0.825759\pi$
$60$		0			0
$61$	9605.36	+	29562.3i	0.330513	+	1.01722i	0.968890	+	0.247491i	$0.0796062\pi$
$61$	9605.36	+	29562.3i	0.330513	+	1.01722i	−0.638377	+	0.769724i	$0.720394\pi$
$62$	27909.2	+	20277.2i	0.922079	+	0.669929i
$63$		0			0
$64$	−9975.51	+	30701.5i	−0.304428	+	0.936935i
$65$	−1927.72			−0.0565928
$66$		0			0
$67$	−764.687			−0.0208112			−0.0104056	−	0.999946i	$-0.503312\pi$
$67$	−764.687			−0.0208112			−0.0104056	+	0.999946i	$0.503312\pi$
$68$	6764.11	−	20817.8i	0.177394	−	0.545962i
$69$		0			0
$70$	−7916.60	−	5751.75i	−0.193105	−	0.140299i
$71$	16135.3	+	49659.4i	0.379867	+	1.16911i	0.940136	+	0.340799i	$0.110698\pi$
$71$	16135.3	+	49659.4i	0.379867	+	1.16911i	−0.560269	+	0.828311i	$0.689302\pi$
$72$		0			0
$73$	57261.6	+	41603.0i	1.25764	+	0.913728i	0.998639	−	0.0521489i	$-0.0166071\pi$
$73$	57261.6	+	41603.0i	1.25764	+	0.913728i	0.259000	+	0.965877i	$0.416607\pi$
$74$	−5080.83	+	3691.44i	−0.107859	+	0.0783639i
$75$		0			0
$76$	85947.4			1.70686
$77$	22079.8	+	64100.8i	0.424392	+	1.23207i
$78$		0			0
$79$	−1168.98	+	3597.74i	−0.0210736	+	0.0648578i	−0.961040	−	0.276408i	$-0.910856\pi$
$79$	−1168.98	+	3597.74i	−0.0210736	+	0.0648578i	0.939967	+	0.341266i	$0.110856\pi$
$80$	6053.44	−	4398.08i	0.105749	−	0.0768313i
$81$		0			0
$82$	−31816.9	−	97922.4i	−0.522545	−	1.60823i
$83$	1810.96	+	5573.57i	0.0288546	+	0.0888052i	0.964447	−	0.264277i	$-0.0851335\pi$
$83$	1810.96	+	5573.57i	0.0288546	+	0.0888052i	−0.935592	+	0.353083i	$0.885133\pi$
$84$		0			0
$85$	−4044.16	+	2938.25i	−0.0607129	+	0.0441105i
$86$	49524.0	−	152419.i	0.722053	−	2.22225i
$87$		0			0
$88$	−758.435	+	13.3242i	−0.0104403	+	0.000183415i
$89$	−62319.7			−0.833969			−0.416985	−	0.908914i	$-0.636913\pi$
$89$	−62319.7			−0.833969			−0.416985	+	0.908914i	$0.636913\pi$
$90$		0			0
$91$	−36321.5	+	26389.1i	−0.459791	+	0.334057i
$92$	36215.3	+	26312.0i	0.446090	+	0.324104i
$93$		0			0
$94$	46432.4	+	142904.i	0.542003	+	1.66811i
$95$	−15879.3	−	11537.0i	−0.180519	−	0.131155i
$96$		0			0
$97$	30837.4	−	94907.9i	0.332774	−	1.02417i	−0.635035	−	0.772484i	$-0.719014\pi$
$97$	30837.4	−	94907.9i	0.332774	−	1.02417i	0.967808	−	0.251688i	$-0.0809858\pi$
$98$	−93691.8			−0.985454
$99$		0			0
$100$	−97589.0			−0.975890
$101$	38832.0	−	119513.i	0.378780	−	1.16576i	−0.562113	−	0.827060i	$-0.690012\pi$
$101$	38832.0	−	119513.i	0.378780	−	1.16576i	0.940893	−	0.338704i	$-0.109988\pi$
$102$		0			0
$103$	75842.4	+	55102.8i	0.704400	+	0.511776i	0.881362	−	0.472441i	$-0.156627\pi$
$103$	75842.4	+	55102.8i	0.704400	+	0.511776i	−0.176962	+	0.984218i	$0.556627\pi$
$104$	−155.226	−	477.736i	−0.00140728	−	0.00433116i
$105$		0			0
$106$	−192494.	−	139855.i	−1.66400	−	1.20897i
$107$	147.214	−	106.957i	0.00124305	−	0.000903131i	−0.587164	−	0.809468i	$-0.699755\pi$
$107$	147.214	−	106.957i	0.00124305	−	0.000903131i	0.588407	+	0.808565i	$0.299755\pi$
$108$		0			0
$109$	−16703.4			−0.134660			−0.0673300	−	0.997731i	$-0.521448\pi$
$109$	−16703.4			−0.134660			−0.0673300	+	0.997731i	$0.521448\pi$
$110$	−19042.9	−	13330.8i	−0.150055	−	0.105045i
$111$		0			0
$112$	53850.3	−	165734.i	0.405642	−	1.24844i
$113$	120149.	−	87293.3i	0.885164	−	0.643109i	−0.0494489	−	0.998777i	$-0.515746\pi$
$113$	120149.	−	87293.3i	0.885164	−	0.643109i	0.934612	+	0.355668i	$0.115746\pi$
$114$		0			0
$115$	−3159.07	−	9722.61i	−0.0222748	−	0.0685549i
$116$	26304.5	+	80957.1i	0.181504	+	0.558611i
$117$		0			0
$118$	132965.	−	96604.4i	0.879085	−	0.638693i
$119$	−35976.1	+	110723.i	−0.232888	+	0.716755i
$120$		0			0
$121$	55116.9	+	151326.i	0.342232	+	0.939615i
$122$	−248208.			−1.50979
$123$		0			0
$124$	−111016.	+	80658.2i	−0.648385	+	0.471079i
$125$	36369.2	+	26423.7i	0.208189	+	0.151258i
$126$		0			0
$127$	12095.7	+	37226.7i	0.0665458	+	0.204807i	0.978800	−	0.204817i	$-0.0656599\pi$
$127$	12095.7	+	37226.7i	0.0665458	+	0.204807i	−0.912254	+	0.409624i	$0.865660\pi$
$128$	3131.70	+	2275.31i	0.0168949	+	0.0122748i
$129$		0			0
$130$	4756.78	−	14639.9i	0.0246862	−	0.0759763i
$131$	92680.8			0.471858			0.235929	−	0.971770i	$-0.424187\pi$
$131$	92680.8			0.471858			0.235929	+	0.971770i	$0.424187\pi$
$132$		0			0
$133$	−457126.			−2.24082
$134$	1886.91	−	5807.31i	0.00907798	−	0.0279391i
$135$		0			0
$136$	−1053.82	−	765.642i	−0.00488559	−	0.00354959i
$137$	−14565.3	−	44827.4i	−0.0663008	−	0.204053i	0.912418	−	0.409260i	$-0.134213\pi$
$137$	−14565.3	−	44827.4i	−0.0663008	−	0.204053i	−0.978719	+	0.205207i	$0.934213\pi$
$138$		0			0
$139$	241726.	+	175625.i	1.06118	+	0.770989i	0.974305	−	0.225231i	$-0.0723135\pi$
$139$	241726.	+	175625.i	1.06118	+	0.770989i	0.0868700	+	0.996220i	$0.472314\pi$
$140$	31490.5	−	22879.2i	0.135787	−	0.0986552i
$141$		0			0
$142$	−416946.			−1.73524
$143$	−85166.9	+	64193.0i	−0.348282	+	0.262511i
$144$		0			0
$145$	6007.21	−	18488.3i	0.0237275	−	0.0730259i
$146$	−457245.	+	332208.i	−1.77528	+	1.28982i
$147$		0			0
$148$	−7719.68	−	23758.7i	−0.0289698	−	0.0891598i
$149$	94859.2	+	291947.i	0.350037	+	1.07730i	0.958832	+	0.283975i	$0.0916534\pi$
$149$	94859.2	+	291947.i	0.350037	+	1.07730i	−0.608795	+	0.793328i	$0.708347\pi$
$150$		0			0
$151$	224817.	−	163339.i	0.802393	−	0.582973i	−0.109222	−	0.994017i	$-0.534836\pi$
$151$	224817.	−	163339.i	0.802393	−	0.582973i	0.911615	+	0.411045i	$0.134836\pi$
$152$	1580.50	−	4864.27i	0.00554861	−	0.0170769i
$153$		0			0
$154$	−541288.	+	9509.35i	−1.83919	+	0.0323109i
$155$	31338.0			0.104771
$156$		0			0
$157$	203429.	−	147800.i	0.658664	−	0.478548i	−0.207547	−	0.978225i	$-0.566548\pi$
$157$	203429.	−	147800.i	0.658664	−	0.478548i	0.866212	+	0.499677i	$0.166548\pi$
$158$	−24438.1	−	17755.3i	−0.0778796	−	0.0565829i
$159$		0			0
$160$	18327.8	+	56407.3i	0.0565993	+	0.174195i
$161$	−192617.	−	139945.i	−0.585640	−	0.425492i
$162$		0			0
$163$	−19904.5	+	61259.6i	−0.0586788	+	0.180595i	−0.976100	−	0.217324i	$-0.930267\pi$
$163$	−19904.5	+	61259.6i	−0.0586788	+	0.180595i	0.917421	+	0.397918i	$0.130267\pi$
$164$	409558.			1.18907
$165$		0			0
$166$	−46796.4			−0.131808
$167$	120662.	−	371358.i	0.334794	−	1.03039i	−0.632029	−	0.774945i	$-0.717778\pi$
$167$	120662.	−	371358.i	0.334794	−	1.03039i	0.966823	−	0.255446i	$-0.0822223\pi$
$168$		0			0
$169$	243246.	+	176729.i	0.655132	+	0.475981i
$170$	−12335.0	−	37963.1i	−0.0327353	−	0.100749i
$171$		0			0
$172$	515740.	+	374707.i	1.32926	+	0.965764i
$173$	469783.	−	341317.i	1.19339	−	0.867048i	0.199771	−	0.979843i	$-0.435980\pi$
$173$	469783.	−	341317.i	1.19339	−	0.867048i	0.993618	+	0.112794i	$0.0359801\pi$
$174$		0			0
$175$	519043.			1.28118
$176$	120986.	−	395886.i	0.294410	−	0.963360i
$177$		0			0
$178$	153777.	−	473278.i	0.363783	−	1.11961i
$179$	−228369.	+	165920.i	−0.532728	+	0.387049i	−0.821377	−	0.570386i	$-0.806794\pi$
$179$	−228369.	+	165920.i	−0.532728	+	0.387049i	0.288649	+	0.957435i	$0.406794\pi$
$180$		0			0
$181$	−140053.	−	431038.i	−0.317757	−	0.977956i	−0.974605	−	0.223933i	$-0.928110\pi$
$181$	−140053.	−	431038.i	−0.317757	−	0.977956i	0.656847	−	0.754024i	$-0.271890\pi$
$182$	−110783.	−	340955.i	−0.247911	−	0.762991i
$183$		0			0
$184$	2155.12	−	1565.78i	0.00469274	−	0.00340947i
$185$	−1762.95	+	5425.82i	−0.00378714	+	0.0116556i
$186$		0			0
$187$	−80827.6	+	264482.i	−0.169027	+	0.553085i
$188$	−597694.			−1.23334
$189$		0			0
$190$	126800.	−	92125.2i	0.254820	−	0.185138i
$191$	497534.	+	361480.i	0.986824	+	0.716969i	0.959223	−	0.282650i	$-0.0912134\pi$
$191$	497534.	+	361480.i	0.986824	+	0.716969i	0.0276005	+	0.999619i	$0.491213\pi$
$192$		0			0
$193$	10430.4	+	32101.3i	0.0201561	+	0.0620340i	0.960629	−	0.277836i	$-0.0896171\pi$
$193$	10430.4	+	32101.3i	0.0201561	+	0.0620340i	−0.940473	+	0.339870i	$0.889617\pi$
$194$	644672.	+	468382.i	1.22980	+	0.893502i
$195$		0			0
$196$	115166.	−	354444.i	0.214133	−	0.659034i
$197$	411926.			0.756230			0.378115	−	0.925759i	$-0.376572\pi$
$197$	411926.			0.756230			0.378115	+	0.925759i	$0.376572\pi$
$198$		0			0
$199$	−766254.			−1.37164			−0.685820	−	0.727772i	$-0.740556\pi$
$199$	−766254.			−1.37164			−0.685820	+	0.727772i	$0.740556\pi$
$200$	−1794.57	+	5523.13i	−0.00317239	+	0.00976361i
$201$		0			0
$202$	811803.	+	589809.i	1.39982	+	1.01703i
$203$	−139905.	−	430584.i	−0.238283	−	0.733361i
$204$		0			0
$205$	−75668.6	−	54976.4i	−0.125757	−	0.0913675i
$206$	−605616.	+	440006.i	−0.994328	+	0.722421i
$207$		0			0
$208$	274129.			0.439336
$209$	−1.08573e6	+	19074.1i	−1.71932	+	0.0302050i
$210$		0			0
$211$	−131979.	+	406190.i	−0.204079	+	0.628091i	0.795671	+	0.605729i	$0.207119\pi$
$211$	−131979.	+	406190.i	−0.204079	+	0.628091i	−0.999750	+	0.0223619i	$0.992881\pi$
$212$	765698.	−	556313.i	1.17009	−	0.850118i
$213$		0			0
$214$	449.013	+	1381.92i	0.000670231	+	0.00206276i
$215$	−44988.1	−	138459.i	−0.0663745	−	0.204280i
$216$		0			0
$217$	590460.	−	428994.i	0.851218	−	0.618446i
$218$	41216.7	−	126852.i	0.0587397	−	0.180782i
$219$		0			0
$220$	73839.1	−	55654.8i	0.102856	−	0.0775257i
$221$	−183139.			−0.252232
$222$		0			0
$223$	−813854.	+	591300.i	−1.09593	+	0.796243i	−0.980391	−	0.197060i	$-0.936861\pi$
$223$	−813854.	+	591300.i	−1.09593	+	0.796243i	−0.115542	+	0.993303i	$0.536861\pi$
$224$	1.11750e6	+	811911.i	1.48808	+	1.08116i
$225$		0			0
$226$	366463.	+	1.12786e6i	0.477264	+	1.46887i
$227$	399952.	+	290582.i	0.515161	+	0.374286i	0.814778	−	0.579773i	$-0.196859\pi$
$227$	399952.	+	290582.i	0.515161	+	0.374286i	−0.299617	+	0.954060i	$0.596859\pi$
$228$		0			0
$229$	−31308.9	+	96358.8i	−0.0394529	+	0.121423i	−0.968843	−	0.247675i	$-0.920333\pi$
$229$	−31308.9	+	96358.8i	−0.0394529	+	0.121423i	0.929390	+	0.369098i	$0.120333\pi$
$230$	81632.3			0.101752
$231$		0			0
$232$	5065.55			0.00617884
$233$	−162695.	+	500723.i	−0.196329	+	0.604238i	0.803630	+	0.595130i	$0.202899\pi$
$233$	−162695.	+	500723.i	−0.196329	+	0.604238i	−0.999959	+	0.00910832i	$0.997101\pi$
$234$		0			0
$235$	110428.	+	80230.5i	0.130439	+	0.0947697i
$236$	202023.	+	621763.i	0.236113	+	0.726682i
$237$		0			0
$238$	−752098.	−	546431.i	−0.860661	−	0.625307i
$239$	−334566.	+	243076.i	−0.378867	+	0.275263i	−0.760878	−	0.648895i	$-0.775232\pi$
$239$	−334566.	+	243076.i	−0.378867	+	0.275263i	0.382011	+	0.924158i	$0.375232\pi$
$240$		0			0
$241$	679718.			0.753852			0.376926	−	0.926243i	$-0.376981\pi$
$241$	679718.			0.753852			0.376926	+	0.926243i	$0.376981\pi$
$242$	−1.28523e6	+	45171.8i	−1.41072	+	0.0495825i
$243$		0			0
$244$	305098.	−	938995.i	0.328068	−	1.00969i
$245$	−68855.9	+	50026.7i	−0.0732868	+	0.0532460i
$246$		0			0
$247$	−222212.	−	683898.i	−0.231753	−	0.713261i
$248$	2523.43	+	7766.30i	0.00260532	+	0.00801835i
$249$		0			0
$250$	−290415.	+	210999.i	−0.293879	+	0.213516i
$251$	−245400.	+	755262.i	−0.245861	+	0.756682i	0.749633	+	0.661854i	$0.230230\pi$
$251$	−245400.	+	755262.i	−0.245861	+	0.756682i	−0.995494	+	0.0948281i	$0.969770\pi$
$252$		0			0
$253$	−463329.	−	324349.i	−0.455081	−	0.318574i
$254$	−312560.			−0.303983
$255$		0			0
$256$	−860727.	+	625354.i	−0.820853	+	0.596384i
$257$	−499851.	−	363163.i	−0.472071	−	0.342980i	0.326177	−	0.945309i	$-0.394240\pi$
$257$	−499851.	−	363163.i	−0.472071	−	0.342980i	−0.798248	+	0.602329i	$0.794240\pi$
$258$		0			0
$259$	41058.4	+	126365.i	0.0380323	+	0.117051i
$260$	49536.8	+	35990.6i	0.0454459	+	0.0330184i
$261$		0			0
$262$	−228695.	+	703852.i	−0.205828	+	0.633473i
$263$	66349.1			0.0591488			0.0295744	−	0.999563i	$-0.490585\pi$
$263$	66349.1			0.0591488			0.0295744	+	0.999563i	$0.490585\pi$
$264$		0			0
$265$	−216143.			−0.189072
$266$	1.12798e6	−	3.47158e6i	0.977460	−	3.00831i
$267$		0			0
$268$	19650.2	+	14276.7i	0.0167120	+	0.0121420i
$269$	526779.	+	1.62126e6i	0.443862	+	1.36607i	0.883727	+	0.468003i	$0.155026\pi$
$269$	526779.	+	1.62126e6i	0.443862	+	1.36607i	−0.439865	+	0.898064i	$0.644974\pi$
$270$		0			0
$271$	−182580.	−	132652.i	−0.151018	−	0.109721i	0.509710	−	0.860346i	$-0.329753\pi$
$271$	−182580.	−	132652.i	−0.151018	−	0.109721i	−0.660729	+	0.750625i	$0.729753\pi$
$272$	575093.	−	417829.i	0.471320	−	0.342434i
$273$		0			0
$274$	376377.			0.302863
$275$	1.23279e6	−	21657.7i	0.983011	−	0.0172695i
$276$		0			0
$277$	260659.	−	802225.i	0.204114	−	0.628198i	−0.795635	−	0.605777i	$-0.792862\pi$
$277$	260659.	−	802225.i	0.204114	−	0.628198i	0.999749	−	0.0224214i	$-0.00713756\pi$
$278$	−1.93023e6	+	1.40240e6i	−1.49795	+	1.08833i
$279$		0			0
$280$	−715.784	−	2202.96i	−0.000545616	−	0.00167923i
$281$	−505507.	−	1.55579e6i	−0.381910	−	1.17540i	−0.938697	−	0.344743i	$-0.887966\pi$
$281$	−505507.	−	1.55579e6i	−0.381910	−	1.17540i	0.556787	−	0.830655i	$-0.312034\pi$
$282$		0			0
$283$	−726846.	+	528084.i	−0.539481	+	0.391956i	−0.823892	−	0.566746i	$-0.808202\pi$
$283$	−726846.	+	528084.i	−0.539481	+	0.391956i	0.284411	+	0.958702i	$0.408202\pi$
$284$	512511.	−	1.57735e6i	0.377057	−	1.16046i
$285$		0			0
$286$	−277350.	−	805189.i	−0.200500	−	0.582080i
$287$	−2.17831e6			−1.56104
$288$		0			0
$289$	764483.	−	555429.i	0.538422	−	0.391187i
$290$	125584.	+	91241.9i	0.0876876	+	0.0637088i
$291$		0			0
$292$	−694726.	−	2.13815e6i	−0.476822	−	1.46751i
$293$	−1.33284e6	−	968363.i	−0.907002	−	0.658975i	0.0332530	−	0.999447i	$-0.489413\pi$
$293$	−1.33284e6	−	968363.i	−0.907002	−	0.658975i	−0.940255	+	0.340472i	$0.889413\pi$
$294$		0			0
$295$	46136.3	−	141993.i	0.0308665	−	0.0949974i
$296$	−1486.60			−0.000986202
$297$		0			0
$298$	−2.45122e6			−1.59898
$299$	115736.	−	356199.i	0.0748671	−	0.230417i
$300$		0			0
$301$	−2.74305e6	−	1.99294e6i	−1.74509	−	1.26788i
$302$	685709.	+	2.11039e6i	0.432636	+	1.33152i
$303$		0			0
$304$	2.25809e6	+	1.64060e6i	1.40139	+	1.01817i
$305$	−182413.	+	132531.i	−0.112281	+	0.0815770i
$306$		0			0
$307$	−1.28570e6			−0.778561			−0.389281	−	0.921119i	$-0.627276\pi$
$307$	−1.28570e6			−0.778561			−0.389281	+	0.921119i	$0.627276\pi$
$308$	629376.	−	2.05943e6i	0.378036	−	1.23700i
$309$		0			0
$310$	−77328.5	+	237993.i	−0.0457020	+	0.140656i
$311$	171861.	−	124864.i	0.100757	−	0.0732043i	−0.536266	−	0.844049i	$-0.680166\pi$
$311$	171861.	−	124864.i	0.100757	−	0.0732043i	0.637023	+	0.770845i	$0.280166\pi$
$312$		0			0
$313$	902319.	+	2.77705e6i	0.520594	+	1.60222i	0.772867	+	0.634568i	$0.218822\pi$
$313$	902319.	+	2.77705e6i	0.520594	+	1.60222i	−0.252273	+	0.967656i	$0.581178\pi$
$314$	620474.	+	1.90962e6i	0.355140	+	1.09301i
$315$		0			0
$316$	97209.1	−	70626.5i	0.0547632	−	0.0397878i
$317$	379659.	−	1.16847e6i	0.212200	−	0.653084i	−0.787141	−	0.616774i	$-0.788439\pi$
$317$	379659.	−	1.16847e6i	0.212200	−	0.653084i	0.999341	−	0.0363107i	$-0.0115606\pi$
$318$		0			0
$319$	−350259.	−	1.01685e6i	−0.192714	−	0.559476i
$320$	−234164.			−0.127834
$321$		0			0
$322$	1.53809e6	−	1.11748e6i	0.826687	−	0.600623i
$323$	−1.50858e6	−	1.09605e6i	−0.804566	−	0.584551i
$324$		0			0
$325$	252310.	+	776531.i	0.132503	+	0.407803i
$326$	−416113.	−	302324.i	−0.216854	−	0.157554i
$327$		0			0
$328$	7531.42	−	23179.3i	0.00386538	−	0.0118964i
$329$	3.17894e6			1.61917
$330$		0			0
$331$	2.85151e6			1.43055			0.715277	−	0.698841i	$-0.246300\pi$
$331$	2.85151e6			1.43055			0.715277	+	0.698841i	$0.246300\pi$
$332$	57522.2	−	177035.i	0.0286411	−	0.0881483i
$333$		0			0
$334$	2.52249e6	+	1.83270e6i	1.23727	+	0.898927i
$335$	−1714.09	−	5275.42i	−0.000834490	−	0.00256830i
$336$		0			0
$337$	−2.53938e6	−	1.84497e6i	−1.21801	−	0.884940i	−0.222081	−	0.975028i	$-0.571285\pi$
$337$	−2.53938e6	−	1.84497e6i	−1.21801	−	0.884940i	−0.995934	+	0.0900885i	$0.971285\pi$
$338$	−1.94237e6	+	1.41121e6i	−0.924782	+	0.671893i
$339$		0			0
$340$	158780.			0.0744901
$341$	1.38451e6	−	1.04355e6i	0.644780	−	0.485991i
$342$		0			0
$343$	264878.	−	815209.i	0.121565	−	0.374140i
$344$	30690.9	−	22298.2i	0.0139834	−	0.0101595i
$345$		0			0
$346$	1.43287e6	+	4.40993e6i	0.643454	+	1.98035i
$347$	587833.	+	1.80916e6i	0.262078	+	0.806593i	0.992352	+	0.123439i	$0.0393923\pi$
$347$	587833.	+	1.80916e6i	0.262078	+	0.806593i	−0.730274	+	0.683154i	$0.760608\pi$
$348$		0			0
$349$	−1.74204e6	+	1.26567e6i	−0.765586	+	0.556231i	−0.900619	−	0.434610i	$-0.856886\pi$
$349$	−1.74204e6	+	1.26567e6i	−0.765586	+	0.556231i	0.135032	+	0.990841i	$0.456886\pi$
$350$	−1.28077e6	+	3.94181e6i	−0.558858	+	1.71999i
$351$		0			0
$352$	2.68808e6	+	1.88176e6i	1.15634	+	0.809483i
$353$	−588980.			−0.251573			−0.125786	−	0.992057i	$-0.540145\pi$
$353$	−588980.			−0.251573			−0.125786	+	0.992057i	$0.540145\pi$
$354$		0			0
$355$	−306422.	+	222629.i	−0.129047	+	0.0937584i
$356$	1.60143e6	+	1.16351e6i	0.669704	+	0.486569i
$357$		0			0
$358$	−696543.	−	2.14374e6i	−0.287237	−	0.884025i
$359$	1.29065e6	+	937713.i	0.528534	+	0.384002i	0.819809	−	0.572637i	$-0.194080\pi$
$359$	1.29065e6	+	937713.i	0.528534	+	0.384002i	−0.291275	+	0.956639i	$0.594080\pi$
$360$		0			0
$361$	1.49739e6	−	4.60848e6i	0.604736	−	1.86119i
$362$	3.61905e6			1.45152
$363$		0			0
$364$	1.42604e6			0.564128
$365$	−158656.	+	488292.i	−0.0623337	+	0.191844i
$366$		0			0
$367$	1.80750e6	+	1.31323e6i	0.700509	+	0.508949i	0.880098	−	0.474792i	$-0.157477\pi$
$367$	1.80750e6	+	1.31323e6i	0.700509	+	0.508949i	−0.179589	+	0.983742i	$0.557477\pi$
$368$	449230.	+	1.38259e6i	0.172922	+	0.532198i
$369$		0			0
$370$	−36855.5	−	26777.1i	−0.0139958	−	0.0101685i
$371$	−4.07250e6	+	2.95884e6i	−1.53612	+	1.11606i
$372$		0			0
$373$	1.30323e6			0.485008			0.242504	−	0.970150i	$-0.422031\pi$
$373$	1.30323e6			0.485008			0.242504	+	0.970150i	$0.422031\pi$
$374$	−1.80913e6	−	1.26646e6i	−0.668790	−	0.468180i
$375$		0			0
$376$	−10991.1	+	33827.0i	−0.00400931	+	0.0123394i
$377$	576180.	−	418619.i	0.208788	−	0.151693i
$378$		0			0
$379$	922182.	+	2.83818e6i	0.329776	+	1.01495i	0.969239	+	0.246123i	$0.0791568\pi$
$379$	922182.	+	2.83818e6i	0.329776	+	1.01495i	−0.639463	+	0.768822i	$0.720843\pi$
$380$	192656.	+	592934.i	0.0684421	+	0.210643i
$381$		0			0
$382$	−3.97291e6	+	2.88649e6i	−1.39300	+	1.01207i
$383$	1.06290e6	−	3.27127e6i	0.370250	−	1.13951i	−0.576378	−	0.817183i	$-0.695534\pi$
$383$	1.06290e6	−	3.27127e6i	0.370250	−	1.13951i	0.946628	−	0.322329i	$-0.104466\pi$
$384$		0			0
$385$	−392726.	+	296009.i	−0.135032	+	0.101778i
$386$	−269527.			−0.0920733
$387$		0			0
$388$	−2.56436e6	+	1.86312e6i	−0.864768	+	0.628291i
$389$	942956.	+	685098.i	0.315949	+	0.229551i	0.734445	−	0.678668i	$-0.237442\pi$
$389$	942956.	+	685098.i	0.315949	+	0.229551i	−0.418496	+	0.908219i	$0.637442\pi$
$390$		0			0
$391$	−300120.	−	923674.i	−0.0992779	−	0.305546i
$392$	−17942.3	−	13035.8i	−0.00589742	−	0.00428473i
$393$		0			0
$394$	−1.01645e6	+	3.12832e6i	−0.329873	+	1.01524i
$395$	−27440.4			−0.00884908
$396$		0			0
$397$	996554.			0.317340			0.158670	−	0.987332i	$-0.449279\pi$
$397$	996554.			0.317340			0.158670	+	0.987332i	$0.449279\pi$
$398$	1.89078e6	−	5.81921e6i	0.598319	−	1.84144i
$399$		0			0
$400$	−2.56395e6	−	1.86282e6i	−0.801235	−	0.582131i
$401$	71241.6	+	219259.i	0.0221245	+	0.0680921i	0.961509	−	0.274773i	$-0.0886027\pi$
$401$	71241.6	+	219259.i	0.0221245	+	0.0680921i	−0.939385	+	0.342865i	$0.888603\pi$
$402$		0			0
$403$	928837.	+	674839.i	0.284890	+	0.206985i
$404$	−3.22917e6	+	2.34613e6i	−0.984322	+	0.715152i
$405$		0			0
$406$	3.61524e6			1.08848
$407$	102792.	+	298419.i	0.0307589	+	0.0892977i
$408$		0			0
$409$	138946.	−	427633.i	0.0410714	−	0.126405i	−0.928418	−	0.371536i	$-0.878831\pi$
$409$	138946.	−	427633.i	0.0410714	−	0.126405i	0.969490	+	0.245132i	$0.0788312\pi$
$410$	604228.	−	438997.i	0.177518	−	0.128974i
$411$		0			0
$412$	−920158.	−	2.83196e6i	−0.267066	−	0.821946i
$413$	−1.07449e6	−	3.30695e6i	−0.309976	−	0.954009i
$414$		0			0
$415$	−34391.6	+	24987.0i	−0.00980239	+	0.00712186i
$416$	−671462.	+	2.06655e6i	−0.190234	+	0.585480i
$417$		0			0
$418$	2.53425e6	−	8.29250e6i	0.709428	−	2.32137i
$419$	2.53917e6			0.706573			0.353287	−	0.935515i	$-0.385064\pi$
$419$	2.53917e6			0.706573			0.353287	+	0.935515i	$0.385064\pi$
$420$		0			0
$421$	5.53835e6	−	4.02385e6i	1.52291	−	1.10646i	0.562893	−	0.826530i	$-0.309688\pi$
$421$	5.53835e6	−	4.02385e6i	1.52291	−	1.10646i	0.960020	−	0.279931i	$-0.0903117\pi$
$422$	−2.75909e6	−	2.00460e6i	−0.754197	−	0.547956i
$423$		0			0
$424$	−17404.5	−	53565.5i	−0.00470161	−	0.0144701i
$425$	1.71292e6	+	1.24451e6i	0.460006	+	0.334214i
$426$		0			0
$427$	−1.62271e6	+	4.99420e6i	−0.430697	+	1.32555i
$428$	−5779.85			−0.00152513
$429$		0			0
$430$	1.16252e6			0.303200
$431$	1.01973e6	−	3.13840e6i	0.264418	−	0.813795i	−0.727409	−	0.686204i	$-0.759276\pi$
$431$	1.01973e6	−	3.13840e6i	0.264418	−	0.813795i	0.991827	−	0.127590i	$-0.0407243\pi$
$432$		0			0
$433$	−4.09511e6	−	2.97527e6i	−1.04965	−	0.762618i	−0.0775066	−	0.996992i	$-0.524696\pi$
$433$	−4.09511e6	−	2.97527e6i	−1.04965	−	0.762618i	−0.972146	+	0.234374i	$0.924696\pi$
$434$	1.80094e6	+	5.54274e6i	0.458961	+	1.41254i
$435$		0			0
$436$	429228.	+	311852.i	0.108136	+	0.0785657i
$437$	3.08513e6	−	2.24148e6i	0.772806	−	0.561476i
$438$		0			0
$439$	2.33340e6			0.577868			0.288934	−	0.957349i	$-0.406699\pi$
$439$	2.33340e6			0.577868			0.288934	+	0.957349i	$0.406699\pi$
$440$	−1792.00	−	5202.43i	−0.000441271	−	0.00128107i
$441$		0			0
$442$	451906.	−	1.39082e6i	0.110025	−	0.338623i
$443$	922966.	−	670574.i	0.223448	−	0.162345i	−0.470429	−	0.882438i	$-0.655901\pi$
$443$	922966.	−	670574.i	0.223448	−	0.162345i	0.693877	+	0.720093i	$0.255901\pi$
$444$		0			0
$445$	−139693.	−	429931.i	−0.0334407	−	0.102920i
$446$	−2.48231e6	−	7.63977e6i	−0.590907	−	1.81863i
$447$		0			0
$448$	−4.41203e6	+	3.20553e6i	−1.03859	+	0.754579i
$449$	1.62339e6	−	4.99629e6i	0.380021	−	1.16958i	−0.560007	−	0.828488i	$-0.689202\pi$
$449$	1.62339e6	−	4.99629e6i	0.380021	−	1.16958i	0.940028	−	0.341097i	$-0.110798\pi$
$450$		0			0
$451$	−5.17375e6	+	90892.4i	−1.19774	+	0.0210420i
$452$	−4.71723e6			−1.08603
$453$		0			0
$454$	−3.19369e6	+	2.32035e6i	−0.727199	+	0.528341i
$455$	−263470.	−	191422.i	−0.0596626	−	0.0433474i
$456$		0			0
$457$	−676752.	−	2.08283e6i	−0.151579	−	0.466512i	0.846219	−	0.532835i	$-0.178873\pi$
$457$	−676752.	−	2.08283e6i	−0.151579	−	0.466512i	−0.997798	+	0.0663227i	$0.978873\pi$
$458$	−654527.	−	475542.i	−0.145802	−	0.105932i
$459$		0			0
$460$	−100342.	+	308822.i	−0.0221101	+	0.0680478i
$461$	−5.62999e6			−1.23383			−0.616915	−	0.787030i	$-0.711618\pi$
$461$	−5.62999e6			−1.23383			−0.616915	+	0.787030i	$0.711618\pi$
$462$		0			0
$463$	3.63260e6			0.787526			0.393763	−	0.919212i	$-0.371173\pi$
$463$	3.63260e6			0.787526			0.393763	+	0.919212i	$0.371173\pi$
$464$	−854245.	+	2.62910e6i	−0.184199	+	0.566906i
$465$		0			0
$466$	−3.40122e6	−	2.47113e6i	−0.725554	−	0.527146i
$467$	1.29395e6	+	3.98237e6i	0.274552	+	0.844985i	0.989337	+	0.145641i	$0.0465245\pi$
$467$	1.29395e6	+	3.98237e6i	0.274552	+	0.844985i	−0.714785	+	0.699344i	$0.753476\pi$
$468$		0			0
$469$	−104513.	−	75933.0i	−0.0219400	−	0.0159404i
$470$	−881787.	+	640656.i	−0.184128	+	0.133777i
$471$		0			0
$472$	38904.2			0.00803788
$473$	−6.59824e6	−	4.61903e6i	−1.35605	−	0.949288i
$474$		0			0
$475$	−2.56900e6	+	7.90658e6i	−0.522433	+	1.60788i
$476$	2.99168e6	−	2.17358e6i	0.605198	−	0.439702i
$477$		0			0
$478$	−1.02045e6	−	3.14062e6i	−0.204278	−	0.628703i
$479$	1.62449e6	+	4.99968e6i	0.323504	+	0.995642i	0.972111	+	0.234519i	$0.0753516\pi$
$479$	1.62449e6	+	4.99968e6i	0.323504	+	0.995642i	−0.648608	+	0.761123i	$0.724648\pi$
$480$		0			0
$481$	−169093.	+	122854.i	−0.0333245	+	0.0242117i
$482$	−1.67725e6	+	5.16203e6i	−0.328836	+	1.01205i
$483$		0			0
$484$	1.40892e6	−	4.91766e6i	0.273383	−	0.954213i
$485$	723875.			0.139736
$486$		0			0
$487$	−5.02953e6	+	3.65417e6i	−0.960959	+	0.698178i	−0.953373	−	0.301794i	$-0.902415\pi$
$487$	−5.02953e6	+	3.65417e6i	−0.960959	+	0.698178i	−0.00758565	+	0.999971i	$0.502415\pi$
$488$	−47532.7	−	34534.6i	−0.00903531	−	0.00656454i
$489$		0			0
$490$	−210015.	−	646361.i	−0.0395149	−	0.121614i
$491$	4.06908e6	+	2.95636e6i	0.761715	+	0.553418i	0.899436	−	0.437053i	$-0.143978\pi$
$491$	4.06908e6	+	2.95636e6i	0.761715	+	0.553418i	−0.137721	+	0.990471i	$0.543978\pi$
$492$		0			0
$493$	570701.	−	1.75644e6i	0.105753	−	0.325473i
$494$	5.74209e6			1.05865
$495$		0			0
$496$	−4.45637e6			−0.813349
$497$	−2.72587e6	+	8.38938e6i	−0.495011	+	1.52349i
$498$		0			0
$499$	−1.11941e6	−	813298.i	−0.201251	−	0.146217i	0.482596	−	0.875843i	$-0.339694\pi$
$499$	−1.11941e6	−	813298.i	−0.201251	−	0.146217i	−0.683846	+	0.729626i	$0.739694\pi$
$500$	−441249.	−	1.35802e6i	−0.0789330	−	0.242931i
$501$		0			0
$502$	−5.13020e6	−	3.72731e6i	−0.908605	−	0.660140i
$503$	−5.01570e6	+	3.64412e6i	−0.883917	+	0.642203i	−0.934285	−	0.356527i	$-0.883961\pi$
$503$	−5.01570e6	+	3.64412e6i	−0.883917	+	0.642203i	0.0503677	+	0.998731i	$0.483961\pi$
$504$		0			0
$505$	911539.			0.159055
$506$	3.60652e6	−	2.71834e6i	0.626198	−	0.471985i
$507$		0			0
$508$	384199.	−	1.18244e6i	0.0660536	−	0.203292i
$509$	−7.12004e6	+	5.17301e6i	−1.21811	+	0.885012i	−0.995942	−	0.0899958i	$-0.971315\pi$
$509$	−7.12004e6	+	5.17301e6i	−1.21811	+	0.885012i	−0.222172	+	0.975007i	$0.571315\pi$
$510$		0			0
$511$	3.69502e6	+	1.13721e7i	0.625985	+	1.92658i
$512$	−2.58700e6	−	7.96197e6i	−0.436135	−	1.34229i
$513$		0			0
$514$	3.99141e6	−	2.89993e6i	0.666374	−	0.484149i
$515$	−210138.	+	646738.i	−0.0349129	+	0.107451i
$516$		0			0
$517$	7.55037e6	−	132645.i	1.24234	−	0.0218255i
$518$	−1.06097e6			−0.173732
$519$		0			0
$520$	2947.86	−	2141.74i	0.000478077	−	0.000347343i
$521$	7.30101e6	+	5.30450e6i	1.17839	+	0.856150i	0.991989	−	0.126324i	$-0.0403178\pi$
$521$	7.30101e6	+	5.30450e6i	1.17839	+	0.856150i	0.186401	+	0.982474i	$0.440318\pi$
$522$		0			0
$523$	−811202.	−	2.49662e6i	−0.129681	−	0.399116i	0.865044	−	0.501696i	$-0.167290\pi$
$523$	−811202.	−	2.49662e6i	−0.129681	−	0.399116i	−0.994725	+	0.102580i	$0.967290\pi$
$524$	−2.38162e6	−	1.73035e6i	−0.378918	−	0.275300i
$525$		0			0
$526$	−163721.	+	503880.i	−0.0258011	+	0.0794077i
$527$	2.97720e6			0.466961
$528$		0			0
$529$	−4.45016e6			−0.691412
$530$	533347.	−	1.64147e6i	0.0824746	−	0.253831i
$531$		0			0
$532$	1.17468e7	+	8.53453e6i	1.79945	+	1.30738i
$533$	−1.05889e6	−	3.25892e6i	−0.161448	−	0.496885i
$534$		0			0
$535$	1067.87	+	775.849i	0.000161299	+	0.000117191i
$536$	1169.35	−	849.583i	0.000175806	−	0.000127730i
$537$		0			0
$538$	−1.36123e7			−2.02757
$539$	−1.37617e6	+	4.50307e6i	−0.204033	+	0.667632i
$540$		0			0
$541$	167587.	−	515779.i	0.0246177	−	0.0757654i	−0.937993	−	0.346654i	$-0.887318\pi$
$541$	167587.	−	515779.i	0.0246177	−	0.0757654i	0.962611	+	0.270889i	$0.0873177\pi$
$542$	1.45793e6	−	1.05925e6i	0.213177	−	0.154882i
$543$		0			0
$544$	1.74119e6	+	5.35884e6i	0.252261	+	0.776379i
$545$	−37441.6	−	115234.i	−0.00539962	−	0.0166183i
$546$		0			0
$547$	1.46612e6	−	1.06520e6i	0.209509	−	0.152217i	−0.478083	−	0.878315i	$-0.658668\pi$
$547$	1.46612e6	−	1.06520e6i	0.209509	−	0.152217i	0.687591	+	0.726098i	$0.258668\pi$
$548$	−462642.	+	1.42387e6i	−0.0658103	+	0.202543i
$549$		0			0
$550$	−2.87751e6	+	9.41572e6i	−0.405612	+	1.32723i
$551$	7.25154e6			1.01754
$552$		0			0
$553$	−517023.	+	375639.i	−0.0718947	+	0.0522346i
$554$	5.44920e6	+	3.95908e6i	0.754325	+	0.548049i
$555$		0			0
$556$	−2.93275e6	−	9.02606e6i	−0.402335	−	1.23826i
$557$	−8.16487e6	−	5.93213e6i	−1.11509	−	0.810163i	−0.131636	−	0.991298i	$-0.542023\pi$
$557$	−8.16487e6	−	5.93213e6i	−1.11509	−	0.810163i	−0.983458	+	0.181135i	$0.942023\pi$
$558$		0			0
$559$	1.64819e6	−	5.07261e6i	0.223089	−	0.686597i
$560$	1.26408e6			0.170335
$561$		0			0
$562$	1.30626e7			1.74457
$563$	473005.	−	1.45576e6i	0.0628919	−	0.193561i	−0.914673	−	0.404194i	$-0.867552\pi$
$563$	473005.	−	1.45576e6i	0.0628919	−	0.193561i	0.977565	+	0.210632i	$0.0675522\pi$
$564$		0			0
$565$	871539.	+	633210.i	0.114859	+	0.0834501i
$566$	−2.21693e6	−	6.82302e6i	−0.290878	−	0.895231i
$567$		0			0
$568$	−79846.6	−	58012.0i	−0.0103845	−	0.00754478i
$569$	5.61083e6	−	4.07651e6i	0.726518	−	0.527846i	−0.161942	−	0.986800i	$-0.551776\pi$
$569$	5.61083e6	−	4.07651e6i	0.726518	−	0.527846i	0.888460	+	0.458954i	$0.151776\pi$
$570$		0			0
$571$	1.50802e7			1.93560			0.967800	−	0.251720i	$-0.0809962\pi$
$571$	1.50802e7			1.93560			0.967800	+	0.251720i	$0.0809962\pi$
$572$	3.38702e6	−	59503.2i	0.432840	−	0.00760414i
$573$		0			0
$574$	5.37510e6	−	1.65429e7i	0.680937	−	2.09571i
$575$	−3.50302e6	+	2.54509e6i	−0.441847	+	0.321021i
$576$		0			0
$577$	−2.48909e6	−	7.66064e6i	−0.311244	−	0.957911i	−0.977273	−	0.211985i	$-0.932007\pi$
$577$	−2.48909e6	−	7.66064e6i	−0.311244	−	0.957911i	0.666029	−	0.745926i	$-0.267993\pi$
$578$	2.33173e6	+	7.17632e6i	0.290307	+	0.893474i
$579$		0			0
$580$	−499544.	+	362940.i	−0.0616600	+	0.0447986i
$581$	−305941.	+	941591.i	−0.0376009	+	0.115724i
$582$		0			0
$583$	−9.54922e6	+	7.19755e6i	−1.16358	+	0.877027i
$584$	−133786.			−0.0162322
$585$		0			0
$586$	1.06430e7	−	7.73257e6i	1.28032	−	0.930207i
$587$	−1.23705e7	−	8.98773e6i	−1.48181	−	1.07660i	−0.976967	−	0.213392i	$-0.931549\pi$
$587$	−1.23705e7	−	8.98773e6i	−1.48181	−	1.07660i	−0.504847	−	0.863209i	$-0.668451\pi$
$588$		0			0
$589$	3.61238e6	+	1.11178e7i	0.429048	+	1.32047i
$590$	964502.	+	700752.i	0.114070	+	0.0828771i
$591$		0			0
$592$	250698.	−	771569.i	0.0293999	−	0.0904837i
$593$	1.17854e7			1.37628			0.688141	−	0.725577i	$-0.258427\pi$
$593$	1.17854e7			1.37628			0.688141	+	0.725577i	$0.258427\pi$
$594$		0			0
$595$	−844499.			−0.0977927
$596$	3.01304e6	−	9.27319e6i	0.347448	−	1.06933i
$597$		0			0
$598$	2.41952e6	+	1.75789e6i	0.276679	+	0.201019i
$599$	1.86854e6	+	5.75077e6i	0.212782	+	0.654876i	0.999304	+	0.0373132i	$0.0118799\pi$
$599$	1.86854e6	+	5.75077e6i	0.212782	+	0.654876i	−0.786521	+	0.617563i	$0.788120\pi$
$600$		0			0
$601$	6.29384e6	+	4.57274e6i	0.710771	+	0.516405i	0.883422	−	0.468578i	$-0.155233\pi$
$601$	6.29384e6	+	4.57274e6i	0.710771	+	0.516405i	−0.172651	+	0.984983i	$0.555233\pi$
$602$	2.19038e7	−	1.59140e7i	2.46336	−	1.78974i
$603$		0			0
$604$	−8.82668e6			−0.984476
$605$	−920421.	+	719446.i	−0.102235	+	0.0799116i
$606$		0			0
$607$	−4.63872e6	+	1.42765e7i	−0.511007	+	1.57272i	0.279426	+	0.960167i	$0.409856\pi$
$607$	−4.63872e6	+	1.42765e7i	−0.511007	+	1.57272i	−0.790432	+	0.612549i	$0.790144\pi$
$608$	−1.78989e7	+	1.30043e7i	−1.96367	+	1.42669i
$609$		0			0
$610$	−556373.	−	1.71234e6i	−0.0605399	−	0.186323i
$611$	1.54530e6	+	4.75595e6i	0.167460	+	0.515388i
$612$		0			0
$613$	−259502.	+	188540.i	−0.0278927	+	0.0202652i	−0.601644	−	0.798764i	$-0.705487\pi$
$613$	−259502.	+	188540.i	−0.0278927	+	0.0202652i	0.573752	+	0.819029i	$0.305487\pi$
$614$	3.17253e6	−	9.76406e6i	0.339614	−	1.04522i
$615$		0			0
$616$	−104982.	−	73491.2i	−0.0111471	−	0.00780339i
$617$	4.56312e6			0.482558			0.241279	−	0.970456i	$-0.422433\pi$
$617$	4.56312e6			0.482558			0.241279	+	0.970456i	$0.422433\pi$
$618$		0			0
$619$	−4.24334e6	+	3.08296e6i	−0.445124	+	0.323401i	−0.787668	−	0.616100i	$-0.788712\pi$
$619$	−4.24334e6	+	3.08296e6i	−0.445124	+	0.323401i	0.342544	+	0.939502i	$0.388712\pi$
$620$	−805295.	−	585081.i	−0.0841348	−	0.0611275i
$621$		0			0
$622$	524188.	+	1.61328e6i	0.0543264	+	0.167199i
$623$	−8.51748e6	−	6.18831e6i	−0.879207	−	0.638781i
$624$		0			0
$625$	2.86616e6	−	8.82114e6i	0.293495	−	0.903285i
$626$	−2.33165e7			−2.37808
$627$		0			0
$628$	−7.98695e6			−0.808131
$629$	−167485.	+	515467.i	−0.0168791	+	0.0519486i
$630$		0			0
$631$	548006.	+	398150.i	0.0547914	+	0.0398083i	0.614844	−	0.788649i	$-0.289219\pi$
$631$	548006.	+	398150.i	0.0547914	+	0.0398083i	−0.560052	+	0.828457i	$0.689219\pi$
$632$	−2209.58	−	6800.39i	−0.000220048	−	0.000677238i
$633$		0			0
$634$	7.93696e6	+	5.76654e6i	0.784207	+	0.569760i
$635$	−229706.	+	166891.i	−0.0226068	+	0.0164248i
$636$		0			0
$637$	−3.11813e6			−0.304470
$638$	8.58663e6	−	150850.i	0.835163	−	0.0146721i
$639$		0			0
$640$	−8677.04	+	26705.2i	−0.000837378	+	0.00257719i
$641$	3.26531e6	−	2.37239e6i	0.313892	−	0.228056i	−0.419673	−	0.907675i	$-0.637855\pi$
$641$	3.26531e6	−	2.37239e6i	0.313892	−	0.228056i	0.733565	+	0.679620i	$0.237855\pi$
$642$		0			0
$643$	−3.28174e6	−	1.01001e7i	−0.313023	−	0.963386i	−0.976561	−	0.215243i	$-0.930946\pi$
$643$	−3.28174e6	−	1.01001e7i	−0.313023	−	0.963386i	0.663537	−	0.748143i	$-0.269054\pi$
$644$	2.33693e6	+	7.19233e6i	0.222040	+	0.683368i
$645$		0			0
$646$	1.20463e7	−	8.75214e6i	1.13572	−	0.825150i
$647$	−1.27543e6	+	3.92537e6i	−0.119783	+	0.368655i	−0.992915	−	0.118830i	$-0.962086\pi$
$647$	−1.27543e6	+	3.92537e6i	−0.119783	+	0.368655i	0.873131	+	0.487485i	$0.162086\pi$
$648$		0			0
$649$	−2.69004e6	−	7.80958e6i	−0.250696	−	0.727807i
$650$	−6.51986e6			−0.605278
$651$		0			0
$652$	1.65520e6	−	1.20258e6i	0.152487	−	0.110788i
$653$	1.13459e7	+	8.24328e6i	1.04125	+	0.756514i	0.970530	−	0.240982i	$-0.0774694\pi$
$653$	1.13459e7	+	8.24328e6i	1.04125	+	0.756514i	0.0707229	+	0.997496i	$0.477469\pi$
$654$		0			0
$655$	207749.	+	639387.i	0.0189207	+	0.0582318i
$656$	1.07603e7	+	7.81783e6i	0.976260	+	0.709295i
$657$		0			0
$658$	−7.84421e6	+	2.41420e7i	−0.706293	+	2.17375i
$659$	5.47205e6			0.490836			0.245418	−	0.969417i	$-0.421075\pi$
$659$	5.47205e6			0.490836			0.245418	+	0.969417i	$0.421075\pi$
$660$		0			0
$661$	−7.43446e6			−0.661829			−0.330914	−	0.943661i	$-0.607357\pi$
$661$	−7.43446e6			−0.661829			−0.330914	+	0.943661i	$0.607357\pi$
$662$	−7.03627e6	+	2.16554e7i	−0.624018	+	1.92053i
$663$		0			0
$664$	−8961.67	−	6511.03i	−0.000788803	−	0.000573099i
$665$	−1.02467e6	−	3.15362e6i	−0.0898527	−	0.276538i
$666$		0			0
$667$	3.05555e6	+	2.21999e6i	0.265935	+	0.193213i
$668$	−1.00339e7	+	7.29006e6i	−0.870019	+	0.632106i
$669$		0			0
$670$	44293.1			0.00381197
$671$	−3.64576e6	+	1.19296e7i	−0.312595	+	1.02286i
$672$		0			0
$673$	−638734.	+	1.96582e6i	−0.0543604	+	0.167304i	−0.974551	−	0.224167i	$-0.928034\pi$
$673$	−638734.	+	1.96582e6i	−0.0543604	+	0.167304i	0.920190	+	0.391471i	$0.128034\pi$
$674$	2.02774e7	−	1.47324e7i	1.71934	−	1.24918i
$675$		0			0
$676$	−2.95118e6	−	9.08280e6i	−0.248387	−	0.764457i
$677$	−1.41950e6	−	4.36878e6i	−0.119032	−	0.366343i	0.873735	−	0.486403i	$-0.161691\pi$
$677$	−1.41950e6	−	4.36878e6i	−0.119032	−	0.366343i	−0.992767	+	0.120060i	$0.961691\pi$
$678$		0			0
$679$	1.36390e7	−	9.90930e6i	1.13529	−	0.824838i
$680$	2919.82	−	8986.30i	0.000242150	−	0.000745261i
$681$		0			0
$682$	4.50874e6	+	1.30895e7i	0.371189	+	1.07761i
$683$	−1.18636e7			−0.973120			−0.486560	−	0.873647i	$-0.661748\pi$
$683$	−1.18636e7			−0.973120			−0.486560	+	0.873647i	$0.661748\pi$
$684$		0			0
$685$	276607.	−	200967.i	0.0225235	−	0.0163643i
$686$	5.53740e6	+	4.02316e6i	0.449258	+	0.326405i
$687$		0			0
$688$	6.39746e6	+	1.96893e7i	0.515272	+	1.58584i
$689$	−6.40634e6	−	4.65448e6i	−0.514117	−	0.373528i
$690$		0			0
$691$	4.58540e6	−	1.41124e7i	0.365327	−	1.12436i	−0.584449	−	0.811431i	$-0.698689\pi$
$691$	4.58540e6	−	1.41124e7i	0.365327	−	1.12436i	0.949776	−	0.312931i	$-0.101311\pi$
$692$	−1.84444e7			−1.46420
$693$		0			0
$694$	−1.51900e7			−1.19718
$695$	−669756.	+	2.06130e6i	−0.0525962	+	0.161874i
$696$		0			0
$697$	−7.18871e6	−	5.22291e6i	−0.560492	−	0.407221i
$698$	−5.31334e6	−	1.63528e7i	−0.412790	−	1.27044i
$699$		0			0
$700$	−1.33379e7	−	9.69054e6i	−1.02883	−	0.747485i
$701$	2.99523e6	−	2.17616e6i	0.230216	−	0.167262i	−0.466697	−	0.884417i	$-0.654556\pi$
$701$	2.99523e6	−	2.17616e6i	0.230216	−	0.167262i	0.696913	+	0.717155i	$0.254556\pi$
$702$		0			0
$703$	−2.12813e6			−0.162409
$704$	−1.03454e7	+	7.79763e6i	−0.786710	+	0.592968i
$705$		0			0
$706$	1.45334e6	−	4.47293e6i	0.109738	−	0.337739i
$707$	1.71749e7	−	1.24783e7i	1.29225	−	0.938872i
$708$		0			0
$709$	1.18006e6	+	3.63184e6i	0.0881631	+	0.271338i	0.985412	−	0.170188i	$-0.0544374\pi$
$709$	1.18006e6	+	3.63184e6i	0.0881631	+	0.271338i	−0.897249	+	0.441526i	$0.854437\pi$
$710$	−934609.	−	2.87643e6i	−0.0695800	−	0.214145i
$711$		0			0
$712$	95298.6	−	69238.5i	0.00704509	−	0.00511856i
$713$	−1.88146e6	+	5.79055e6i	−0.138603	+	0.426575i
$714$		0			0
$715$	−633761.	−	443658.i	−0.0463618	−	0.0324551i
$716$	8.96614e6			0.653617
$717$		0			0
$718$	−1.03061e7	+	7.48782e6i	−0.746076	+	0.542056i
$719$	−1.77013e7	−	1.28608e7i	−1.27698	−	0.927780i	−0.277522	−	0.960719i	$-0.589513\pi$
$719$	−1.77013e7	−	1.28608e7i	−1.27698	−	0.927780i	−0.999457	+	0.0329393i	$0.989513\pi$
$720$		0			0
$721$	4.89402e6	+	1.50622e7i	0.350612	+	1.07907i
$722$	3.13036e7	+	2.27434e7i	2.23487	+	1.62372i
$723$		0			0
$724$	−4.44854e6	+	1.36912e7i	−0.315407	+	0.970722i
$725$	−8.23376e6			−0.581772
$726$		0			0
$727$	−4.10803e6			−0.288268			−0.144134	−	0.989558i	$-0.546040\pi$
$727$	−4.10803e6			−0.288268			−0.144134	+	0.989558i	$0.546040\pi$
$728$	26223.6	−	80707.9i	0.00183385	−	0.00564401i
$729$		0			0
$730$	−3.31677e6	−	2.40978e6i	−0.230361	−	0.167367i
$731$	−4.27399e6	−	1.31540e7i	−0.295828	−	0.910466i
$732$		0			0
$733$	−1.93504e7	−	1.40589e7i	−1.33024	−	0.966475i	−0.999743	−	0.0226678i	$-0.992784\pi$
$733$	−1.93504e7	−	1.40589e7i	−1.33024	−	0.966475i	−0.330496	−	0.943807i	$-0.607216\pi$
$734$	−1.44332e7	+	1.04864e7i	−0.988835	+	0.718431i
$735$		0			0
$736$	−1.15231e7			−0.784109
$737$	−251399.	−	175989.i	−0.0170489	−	0.0119349i
$738$		0			0
$739$	804837.	−	2.47703e6i	0.0542122	−	0.166848i	−0.920284	−	0.391250i	$-0.872043\pi$
$739$	804837.	−	2.47703e6i	0.0542122	−	0.166848i	0.974497	+	0.224402i	$0.0720428\pi$
$740$	146603.	−	106513.i	0.00984153	−	0.00715029i
$741$		0			0
$742$	−1.24214e7	−	3.82292e7i	−0.828249	−	2.54909i
$743$	3.13315e6	+	9.64283e6i	0.208213	+	0.640815i	0.999566	+	0.0294549i	$0.00937716\pi$
$743$	3.13315e6	+	9.64283e6i	0.208213	+	0.640815i	−0.791353	+	0.611360i	$0.790623\pi$
$744$		0			0
$745$	−1.80145e6	+	1.30883e6i	−0.118914	+	0.0863958i
$746$	−3.21580e6	+	9.89720e6i	−0.211564	+	0.651126i
$747$		0			0
$748$	7.01491e6	−	5.28735e6i	0.458425	−	0.345529i
$749$	30741.1			0.00200224
$750$		0			0
$751$	−1.50306e7	+	1.09204e7i	−0.972474	+	0.706543i	−0.956014	−	0.293321i	$-0.905239\pi$
$751$	−1.50306e7	+	1.09204e7i	−0.972474	+	0.706543i	−0.0164596	+	0.999865i	$0.505239\pi$
$752$	−1.57032e7	−	1.14090e7i	−1.01261	−	0.735706i
$753$		0			0
$754$	1.75739e6	+	5.40869e6i	0.112574	+	0.346469i
$755$	1.63079e6	+	1.18484e6i	0.104119	+	0.0756468i
$756$		0			0
$757$	8.49345e6	−	2.61402e7i	0.538697	−	1.65794i	−0.196825	−	0.980439i	$-0.563063\pi$
$757$	8.49345e6	−	2.61402e7i	0.538697	−	1.65794i	0.735522	−	0.677500i	$-0.236937\pi$
$758$	−2.38298e7			−1.50642
$759$		0			0
$760$	37100.4			0.00232994
$761$	1.70700e6	−	5.25360e6i	0.106849	−	0.328848i	−0.883311	−	0.468788i	$-0.844691\pi$
$761$	1.70700e6	−	5.25360e6i	0.106849	−	0.328848i	0.990160	+	0.139940i	$0.0446909\pi$
$762$		0			0
$763$	−2.28292e6	−	1.65864e6i	−0.141964	−	0.103143i
$764$	−6.03633e6	−	1.85779e7i	−0.374145	−	1.15150i
$765$		0			0
$766$	2.22204e7	+	1.61441e7i	1.36830	+	0.994126i
$767$	4.42515e6	−	3.21506e6i	0.271606	−	0.197333i
$768$		0			0
$769$	1.46025e7			0.890455			0.445227	−	0.895417i	$-0.353123\pi$
$769$	1.46025e7			0.890455			0.445227	+	0.895417i	$0.353123\pi$
$770$	−1.27893e6	−	3.71292e6i	−0.0777357	−	0.225678i
$771$		0			0
$772$	331302.	−	1.01964e6i	0.0200070	−	0.0615751i
$773$	1.90721e7	−	1.38567e7i	1.14802	−	0.834087i	0.159805	−	0.987149i	$-0.448913\pi$
$773$	1.90721e7	−	1.38567e7i	1.14802	−	0.834087i	0.988217	+	0.153062i	$0.0489134\pi$
$774$		0			0
$775$	−4.10168e6	−	1.26237e7i	−0.245306	−	0.754973i
$776$	58288.4	+	179393.i	0.00347478	+	0.0106943i
$777$		0			0
$778$	−7.52969e6	+	5.47064e6i	−0.445993	+	0.324033i
$779$	1.07815e7	−	3.31821e7i	0.636556	−	1.95912i
$780$		0			0
$781$	−6.12423e6	+	2.00396e7i	−0.359273	+	1.17560i
$782$	7.75528e6			0.453504
$783$		0			0
$784$	9.79153e6	−	7.11397e6i	0.568932	−	0.413354i
$785$	1.47564e6	+	1.07212e6i	0.0854686	+	0.0620966i
$786$		0			0
$787$	−2.24806e6	−	6.91881e6i	−0.129381	−	0.398194i	0.865293	−	0.501267i	$-0.167132\pi$
$787$	−2.24806e6	−	6.91881e6i	−0.129381	−	0.398194i	−0.994674	+	0.103073i	$0.967132\pi$
$788$	−1.05853e7	−	7.69066e6i	−0.607277	−	0.441213i
$789$		0			0
$790$	67710.9	−	208393.i	0.00386003	−	0.0118800i
$791$	2.50894e7			1.42577
$792$		0			0
$793$	−8.26055e6			−0.466472
$794$	−2.45906e6	+	7.56820e6i	−0.138426	+	0.426031i
$795$		0			0
$796$	1.96905e7	+	1.43060e7i	1.10147	+	0.800265i
$797$	−1.21750e6	−	3.74707e6i	−0.0678925	−	0.208952i	0.911354	−	0.411623i	$-0.135038\pi$
$797$	−1.21750e6	−	3.74707e6i	−0.0678925	−	0.208952i	−0.979247	+	0.202671i	$0.935038\pi$
$798$		0			0
$799$	1.04909e7	+	7.62211e6i	0.581363	+	0.422385i
$800$	2.03233e7	−	1.47657e7i	1.12271	−	0.815700i
$801$		0			0
$802$	−1.84093e6			−0.101065
$803$	9.25064e6	+	2.68559e7i	0.506271	+	1.46978i
$804$		0			0
$805$	533688.	−	1.64252e6i	0.0290267	−	0.0893350i
$806$	−7.41694e6	+	5.38872e6i	−0.402149	+	0.292178i
$807$		0			0
$808$	73399.6	+	225901.i	0.00395517	+	0.0121728i
$809$	−3.38270e6	−	1.04109e7i	−0.181716	−	0.559264i	0.818161	−	0.574990i	$-0.194994\pi$
$809$	−3.38270e6	−	1.04109e7i	−0.181716	−	0.559264i	−0.999876	+	0.0157262i	$0.994994\pi$
$810$		0			0
$811$	4.39609e6	−	3.19395e6i	0.234701	−	0.170520i	−0.464218	−	0.885721i	$-0.653665\pi$
$811$	4.39609e6	−	3.19395e6i	0.234701	−	0.170520i	0.698919	+	0.715201i	$0.253665\pi$
$812$	−4.44385e6	+	1.36768e7i	−0.236521	+	0.727936i
$813$		0			0
$814$	−2.51995e6	+	44270.4i	−0.133300	+	0.00234182i
$815$	−467235.			−0.0246400
$816$		0			0
$817$	4.39352e7	−	3.19208e7i	2.30281	−	1.67309i
$818$	2.90474e6	+	2.11042e6i	0.151784	+	0.110277i
$819$		0			0
$820$	918049.	+	2.82546e6i	0.0476794	+	0.146742i
$821$	−1.47312e7	−	1.07029e7i	−0.762747	−	0.554168i	0.137004	−	0.990570i	$-0.456253\pi$
$821$	−1.47312e7	−	1.07029e7i	−0.762747	−	0.554168i	−0.899752	+	0.436402i	$0.856253\pi$
$822$		0			0
$823$	−5.25451e6	+	1.61717e7i	−0.270416	+	0.832255i	0.719980	+	0.693995i	$0.244151\pi$
$823$	−5.25451e6	+	1.61717e7i	−0.270416	+	0.832255i	−0.990396	+	0.138260i	$0.955849\pi$
$824$	−177198.			−0.00909160
$825$		0			0
$826$	2.77656e7			1.41598
$827$	1.08664e6	−	3.34434e6i	0.0552488	−	0.170038i	−0.919624	−	0.392799i	$-0.871507\pi$
$827$	1.08664e6	−	3.34434e6i	0.0552488	−	0.170038i	0.974873	+	0.222761i	$0.0715068\pi$
$828$		0			0
$829$	−1.35797e7	−	9.86622e6i	−0.686283	−	0.498614i	0.189153	−	0.981948i	$-0.439426\pi$
$829$	−1.35797e7	−	9.86622e6i	−0.686283	−	0.498614i	−0.875436	+	0.483334i	$0.839426\pi$
$830$	−104897.	−	322839.i	−0.00528527	−	0.0162664i
$831$		0			0
$832$	−6.94046e6	−	5.04254e6i	−0.347600	−	0.252546i
$833$	−6.54149e6	+	4.75267e6i	−0.326636	+	0.237315i
$834$		0			0
$835$	2.83240e6			0.140585
$836$	2.82562e7	+	1.97804e7i	1.39829	+	0.978859i
$837$		0			0
$838$	−6.26556e6	+	1.92834e7i	−0.308212	+	0.948580i
$839$	−2.39641e7	+	1.74109e7i	−1.17532	+	0.853920i	−0.991636	−	0.129066i	$-0.958802\pi$
$839$	−2.39641e7	+	1.74109e7i	−1.17532	+	0.853920i	−0.183683	+	0.982985i	$0.558802\pi$
$840$		0			0
$841$	−4.11893e6	−	1.26768e7i	−0.200814	−	0.618043i
$842$	1.68924e7	+	5.19894e7i	0.821127	+	2.52717i
$843$		0			0
$844$	1.09750e7	−	7.97383e6i	0.530334	−	0.385310i
$845$	−673966.	+	2.07425e6i	−0.0324710	+	0.0999355i
$846$		0			0
$847$	−7.49355e6	+	2.61554e7i	−0.358905	+	1.25272i
$848$	3.07363e7			1.46778
$849$		0			0
$850$	−1.36780e7	+	9.93762e6i	−0.649343	+	0.471775i
$851$	−896723.	−	651507.i	−0.0424458	−	0.0308386i
$852$		0			0
$853$	−62571.3	−	192575.i	−0.00294444	−	0.00906205i	0.949574	−	0.313545i	$-0.101516\pi$
$853$	−62571.3	−	192575.i	−0.00294444	−	0.00906205i	−0.952518	+	0.304482i	$0.901516\pi$
$854$	−3.39237e7	−	2.46470e7i	−1.59169	−	1.15643i
$855$		0			0
$856$	−106.286	+	327.116i	−4.95785e−6	+	1.52587e-5i
$857$	−2.29630e7			−1.06801			−0.534006	−	0.845481i	$-0.679314\pi$
$857$	−2.29630e7			−1.06801			−0.534006	+	0.845481i	$0.679314\pi$
$858$		0			0
$859$	−1.69282e7			−0.782760			−0.391380	−	0.920229i	$-0.628002\pi$
$859$	−1.69282e7			−0.782760			−0.391380	+	0.920229i	$0.628002\pi$
$860$	−1.42897e6	+	4.39792e6i	−0.0658835	+	0.202769i
$861$		0			0
$862$	2.13179e7	+	1.54884e7i	0.977184	+	0.709966i
$863$	−939944.	−	2.89285e6i	−0.0429610	−	0.132221i	0.927275	−	0.374380i	$-0.122144\pi$
$863$	−939944.	−	2.89285e6i	−0.0429610	−	0.132221i	−0.970237	+	0.242159i	$0.922144\pi$
$864$		0			0
$865$	3.40773e6	+	2.47586e6i	0.154855	+	0.112509i
$866$	3.27002e7	−	2.37581e7i	1.48169	−	1.07651i
$867$		0			0
$868$	−2.31824e7			−1.04438
$869$	−1.21232e6	+	913763.i	−0.0544587	+	0.0410472i
$870$		0			0
$871$	62797.6	−	193271.i	0.00280477	−	0.00863221i
$872$	25542.7	−	18557.8i	0.00113756	−	0.000826488i
$873$		0			0
$874$	9.40988e6	+	2.89606e7i	0.416683	+	1.28242i
$875$	2.34686e6	+	7.22288e6i	0.103625	+	0.318926i
$876$		0			0
$877$	−236071.	+	171515.i	−0.0103644	+	0.00753016i	−0.592955	−	0.805235i	$-0.702039\pi$
$877$	−236071.	+	171515.i	−0.0103644	+	0.00753016i	0.582591	+	0.812765i	$0.302039\pi$
$878$	−5.75782e6	+	1.77207e7i	−0.252070	+	0.775792i
$879$		0			0
$880$	3.00234e6	−	52745.0i	0.130693	−	0.00229602i
$881$	−1.98246e7			−0.860529			−0.430264	−	0.902703i	$-0.641580\pi$
$881$	−1.98246e7			−0.860529			−0.430264	+	0.902703i	$0.641580\pi$
$882$		0			0
$883$	7.79723e6	−	5.66502e6i	0.336541	−	0.244512i	−0.406660	−	0.913580i	$-0.633307\pi$
$883$	7.79723e6	−	5.66502e6i	0.336541	−	0.244512i	0.743201	+	0.669068i	$0.233307\pi$
$884$	4.70613e6	+	3.41920e6i	0.202550	+	0.147161i
$885$		0			0
$886$	2.81511e6	+	8.66403e6i	0.120479	+	0.370796i
$887$	3.08789e7	+	2.24348e7i	1.31781	+	0.957444i	0.999957	+	0.00930377i	$0.00296152\pi$
$887$	3.08789e7	+	2.24348e7i	1.31781	+	0.957444i	0.317852	+	0.948140i	$0.397038\pi$
$888$		0			0
$889$	−2.04342e6	+	6.28902e6i	−0.0867170	+	0.266887i
$890$	3.60976e6			0.152758
$891$		0			0
$892$	3.19532e7			1.34463
$893$	−1.57341e7	+	4.84247e7i	−0.660259	+	2.03207i
$894$		0			0
$895$	−1.65655e6	−	1.20356e6i	−0.0691270	−	0.0502237i
$896$	202084.	+	621952.i	0.00840935	+	0.0258813i
$897$		0			0
$898$	3.39378e7	+	2.46573e7i	1.40441	+	1.02036i
$899$	−9.36666e6	+	6.80528e6i	−0.386532	+	0.280832i
$900$		0			0
$901$	−2.05342e7			−0.842686
$902$	1.20763e7	−	3.95156e7i	0.494215	−	1.61716i
$903$		0			0
$904$	−86745.8	+	266976.i	−0.00353043	+	0.0108655i
$905$	2.65971e6	−	1.93239e6i	0.107948	−	0.0784286i
$906$		0			0
$907$	1.07505e7	+	3.30867e7i	0.433922	+	1.33547i	0.894188	+	0.447692i	$0.147754\pi$
$907$	1.07505e7	+	3.30867e7i	0.433922	+	1.33547i	−0.460266	+	0.887781i	$0.652246\pi$
$908$	−4.85241e6	−	1.49342e7i	−0.195318	−	0.601128i
$909$		0			0
$910$	2.10386e6	−	1.52854e6i	0.0842195	−	0.0611891i
$911$	4.61761e6	−	1.42116e7i	0.184341	−	0.567343i	−0.815595	−	0.578623i	$-0.803590\pi$
$911$	4.61761e6	−	1.42116e7i	0.184341	−	0.567343i	0.999936	+	0.0112796i	$0.00359047\pi$
$912$		0			0
$913$	−687360.	+	2.24916e6i	−0.0272902	+	0.0892983i
$914$	1.74877e7			0.692416
$915$		0			0
$916$	2.60356e6	−	1.89160e6i	0.102525	−	0.0744887i
$917$	1.26671e7	+	9.20316e6i	0.497454	+	0.361421i
$918$		0			0
$919$	−1.03543e7	−	3.18672e7i	−0.404419	−	1.24467i	−0.921380	−	0.388664i	$-0.872937\pi$
$919$	−1.03543e7	−	3.18672e7i	−0.404419	−	1.24467i	0.516961	−	0.856009i	$-0.327063\pi$
$920$	15632.8	+	11357.9i	0.000608932	+	0.000442415i
$921$		0			0
$922$	1.38923e7	−	4.27562e7i	0.538205	−	1.65643i
$923$	−1.38763e7			−0.536128
$924$		0			0
$925$	2.41639e6			0.0928565
$926$	−8.96365e6	+	2.75873e7i	−0.343524	+	1.05726i
$927$		0			0
$928$	−1.77273e7	−	1.28796e7i	−0.675728	−	0.490945i
$929$	−5.80487e6	−	1.78656e7i	−0.220675	−	0.679168i	−0.998702	−	0.0509372i	$-0.983779\pi$
$929$	−5.80487e6	−	1.78656e7i	−0.220675	−	0.679168i	0.778027	−	0.628231i	$-0.216221\pi$
$930$		0			0
$931$	−2.56851e7	−	1.86613e7i	−0.971195	−	0.705615i
$932$	1.35293e7	−	9.82960e6i	0.510193	−	0.370677i
$933$		0			0
$934$	−3.34365e7			−1.25416
$935$	−2.00579e6	+	35237.7i	−0.0750337	+	0.00131819i
$936$		0			0
$937$	−5.98166e6	+	1.84096e7i	−0.222573	+	0.685009i	0.775956	+	0.630787i	$0.217268\pi$
$937$	−5.98166e6	+	1.84096e7i	−0.222573	+	0.685009i	−0.998529	+	0.0542222i	$0.982732\pi$
$938$	834555.	−	606340.i	0.0309705	−	0.0225014i
$939$		0			0
$940$	−1.33976e6	−	4.12337e6i	−0.0494548	−	0.152206i
$941$	4.73500e6	+	1.45728e7i	0.174320	+	0.536501i	0.999602	−	0.0282201i	$-0.00898393\pi$
$941$	4.73500e6	+	1.45728e7i	0.174320	+	0.536501i	−0.825282	+	0.564721i	$0.808984\pi$
$942$		0			0
$943$	1.47014e7	−	1.06812e7i	0.538367	−	0.391146i
$944$	−6.56073e6	+	2.01919e7i	−0.239620	+	0.737473i
$945$		0			0
$946$	5.13602e7	−	3.87118e7i	1.86594	−	1.40642i
$947$	8.60741e6			0.311887			0.155944	−	0.987766i	$-0.450158\pi$
$947$	8.60741e6			0.311887			0.155944	+	0.987766i	$0.450158\pi$
$948$		0			0
$949$	−1.52174e7	+	1.10561e7i	−0.548498	+	0.398507i
$950$	−5.37063e7	−	3.90199e7i	−1.93071	−	1.40274i
$951$		0			0
$952$	−68001.4	−	209287.i	−0.00243179	−	0.00748427i
$953$	−8.75294e6	−	6.35938e6i	−0.312192	−	0.226821i	0.420645	−	0.907226i	$-0.361804\pi$
$953$	−8.75294e6	−	6.35938e6i	−0.312192	−	0.226821i	−0.732836	+	0.680405i	$0.761804\pi$
$954$		0			0
$955$	−1.37853e6	+	4.24267e6i	−0.0489110	+	0.150533i
$956$	1.31356e7			0.464841
$957$		0			0
$958$	−4.19779e7			−1.47777
$959$	2.46064e6	−	7.57308e6i	0.0863976	−	0.265905i
$960$		0			0
$961$	8.06185e6	+	5.85727e6i	0.281596	+	0.204591i
$962$	−515747.	−	1.58731e6i	−0.0179680	−	0.0552997i
$963$		0			0
$964$	−1.74667e7	−	1.26903e7i	−0.605368	−	0.439825i
$965$	−198080.	+	143914.i	−0.00684736	+	0.00497490i
$966$		0			0
$967$	2.85326e7			0.981241			0.490621	−	0.871373i	$-0.336770\pi$
$967$	2.85326e7			0.981241			0.490621	+	0.871373i	$0.336770\pi$
$968$	−252411.	−	170170.i	−0.00865803	−	0.00583707i
$969$		0			0
$970$	−1.78620e6	+	5.49737e6i	−0.0609539	+	0.187597i
$971$	−1.59878e7	+	1.16158e7i	−0.544177	+	0.395368i	−0.825634	−	0.564206i	$-0.809182\pi$
$971$	−1.59878e7	+	1.16158e7i	−0.544177	+	0.395368i	0.281457	+	0.959574i	$0.409182\pi$
$972$		0			0
$973$	1.55983e7	+	4.80066e7i	0.528196	+	1.62562i
$974$	−1.53404e7	−	4.72130e7i	−0.518131	−	1.59464i
$975$		0			0
$976$	2.59398e7	−	1.88463e7i	0.871649	−	0.633290i
$977$	1.12663e7	−	3.46742e7i	0.377613	−	1.16217i	−0.564087	−	0.825716i	$-0.690772\pi$
$977$	1.12663e7	−	3.46742e7i	0.377613	−	1.16217i	0.941699	−	0.336456i	$-0.109228\pi$
$978$		0			0
$979$	−2.04883e7	−	1.43426e7i	−0.683202	−	0.478268i
$980$	2.70339e6			0.0899174
$981$		0			0
$982$	−3.24924e7	+	2.36071e7i	−1.07523	+	0.781203i
$983$	1.79973e7	+	1.30758e7i	0.594050	+	0.431602i	0.843762	−	0.536718i	$-0.180336\pi$
$983$	1.79973e7	+	1.30758e7i	0.594050	+	0.431602i	−0.249712	+	0.968320i	$0.580336\pi$
$984$		0			0
$985$	923356.	+	2.84180e6i	0.0303234	+	0.0933260i
$986$	1.19308e7	+	8.66822e6i	0.390820	+	0.283947i
$987$		0			0
$988$	−7.05818e6	+	2.17228e7i	−0.230038	+	0.707985i
$989$	2.82850e7			0.919531
$990$		0			0
$991$	5.60917e7			1.81432			0.907161	−	0.420784i	$-0.138245\pi$
$991$	5.60917e7			1.81432			0.907161	+	0.420784i	$0.138245\pi$
$992$	1.09156e7	−	3.35948e7i	0.352183	−	1.08391i
$993$		0			0
$994$	−5.69858e7	−	4.14026e7i	−1.82937	−	1.32911i
$995$	−1.71760e6	−	5.28623e6i	−0.0550002	−	0.169273i
$996$		0			0
$997$	−2.88706e7	−	2.09757e7i	−0.919853	−	0.668312i	0.0236346	−	0.999721i	$-0.492476\pi$
$997$	−2.88706e7	−	2.09757e7i	−0.919853	−	0.668312i	−0.943487	+	0.331409i	$0.892476\pi$
$998$	8.93869e6	−	6.49434e6i	0.284085	−	0.206400i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.6.f.a.64.1		16
3.2	odd	2		11.6.c.a.9.4	yes	16
11.4	even	5		1089.6.a.bg.1.1		8
11.5	even	5	inner	99.6.f.a.82.1		16
11.7	odd	10		1089.6.a.bb.1.8		8
33.5	odd	10		11.6.c.a.5.4	✓	16
33.26	odd	10		121.6.a.g.1.8		8
33.29	even	10		121.6.a.i.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.6.c.a.5.4	✓	16	33.5	odd	10
11.6.c.a.9.4	yes	16	3.2	odd	2
99.6.f.a.64.1		16	1.1	even	1	trivial
99.6.f.a.82.1		16	11.5	even	5	inner
121.6.a.g.1.8		8	33.26	odd	10
121.6.a.i.1.1		8	33.29	even	10
1089.6.a.bb.1.8		8	11.7	odd	10
1089.6.a.bg.1.1		8	11.4	even	5

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.46756 + 7.59437i) q^{2} +(-25.6970 - 18.6700i) q^{4} +(2.24156 + 6.89880i) q^{5} +(136.674 + 99.2995i) q^{7} +(-1.52919 + 1.11102i) q^{8} +O(q^{10})\)	\(q+(-2.46756 + 7.59437i) q^{2} +(-25.6970 - 18.6700i) q^{4} +(2.24156 + 6.89880i) q^{5} +(136.674 + 99.2995i) q^{7} +(-1.52919 + 1.11102i) q^{8} -57.9232 q^{10} +(328.761 + 230.146i) q^{11} +(-82.1221 + 252.746i) q^{13} +(-1091.37 + 792.926i) q^{14} +(-318.757 - 981.033i) q^{16} +(212.954 + 655.405i) q^{17} +(-2189.10 + 1590.47i) q^{19} +(71.1992 - 219.129i) q^{20} +(-2559.05 + 1928.84i) q^{22} -1409.32 q^{23} +(2485.61 - 1805.90i) q^{25} +(-1716.80 - 1247.33i) q^{26} +(-1658.20 - 5103.41i) q^{28} +(-2168.11 - 1575.22i) q^{29} +(1335.02 - 4108.76i) q^{31} +8176.39 q^{32} -5502.86 q^{34} +(-378.685 + 1165.47i) q^{35} +(636.281 + 462.285i) q^{37} +(-6676.90 - 20549.4i) q^{38} +(-11.0925 - 8.05916i) q^{40} +(-10431.5 + 7578.95i) q^{41} -20070.0 q^{43} +(-4151.37 - 12052.0i) q^{44} +(3477.58 - 10702.9i) q^{46} +(15223.4 - 11060.4i) q^{47} +(3625.75 + 11158.9i) q^{49} +(7581.29 + 23332.8i) q^{50} +(6829.06 - 4961.60i) q^{52} +(-9207.82 + 28338.8i) q^{53} +(-850.793 + 2783.94i) q^{55} -319.325 q^{56} +(17312.7 - 12578.4i) q^{58} +(-16651.4 - 12097.9i) q^{59} +(9605.36 + 29562.3i) q^{61} +(27909.2 + 20277.2i) q^{62} +(-9975.51 + 30701.5i) q^{64} -1927.72 q^{65} -764.687 q^{67} +(6764.11 - 20817.8i) q^{68} +(-7916.60 - 5751.75i) q^{70} +(16135.3 + 49659.4i) q^{71} +(57261.6 + 41603.0i) q^{73} +(-5080.83 + 3691.44i) q^{74} +85947.4 q^{76} +(22079.8 + 64100.8i) q^{77} +(-1168.98 + 3597.74i) q^{79} +(6053.44 - 4398.08i) q^{80} +(-31816.9 - 97922.4i) q^{82} +(1810.96 + 5573.57i) q^{83} +(-4044.16 + 2938.25i) q^{85} +(49524.0 - 152419. i) q^{86} +(-758.435 + 13.3242i) q^{88} -62319.7 q^{89} +(-36321.5 + 26389.1i) q^{91} +(36215.3 + 26312.0i) q^{92} +(46432.4 + 142904. i) q^{94} +(-15879.3 - 11537.0i) q^{95} +(30837.4 - 94907.9i) q^{97} -93691.8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 73 q^{4} + 10 q^{5} + 196 q^{7} - 527 q^{8}+O(q^{10}) \) 16 * q + q^2 - 73 * q^4 + 10 * q^5 + 196 * q^7 - 527 * q^8	\( 16 q + q^{2} - 73 q^{4} + 10 q^{5} + 196 q^{7} - 527 q^{8} - 672 q^{10} + 692 q^{11} + 1162 q^{13} - 560 q^{14} + 6399 q^{16} + 22 q^{17} - 3236 q^{19} + 5514 q^{20} - 13059 q^{22} + 10848 q^{23} + 15686 q^{25} - 16216 q^{26} + 8838 q^{28} - 13070 q^{29} - 14764 q^{31} + 58812 q^{32} - 26966 q^{34} - 43368 q^{35} + 4638 q^{37} - 68144 q^{38} + 52284 q^{40} + 14806 q^{41} - 24376 q^{43} + 104960 q^{44} + 50452 q^{46} - 40364 q^{47} + 32246 q^{49} - 10839 q^{50} - 80654 q^{52} + 11654 q^{53} + 7052 q^{55} - 70632 q^{56} + 10276 q^{58} - 70804 q^{59} - 31446 q^{61} + 153388 q^{62} + 17695 q^{64} + 41284 q^{65} - 64200 q^{67} + 94114 q^{68} - 103768 q^{70} + 184380 q^{71} - 1750 q^{73} - 306048 q^{74} + 174806 q^{76} - 384646 q^{77} + 24324 q^{79} + 386444 q^{80} - 316255 q^{82} + 46028 q^{83} + 63914 q^{85} - 22931 q^{86} + 211871 q^{88} - 148364 q^{89} - 258448 q^{91} + 58658 q^{92} - 55370 q^{94} + 4716 q^{95} + 484296 q^{97} - 743692 q^{98}+O(q^{100}) \) 16 * q + q^2 - 73 * q^4 + 10 * q^5 + 196 * q^7 - 527 * q^8 - 672 * q^10 + 692 * q^11 + 1162 * q^13 - 560 * q^14 + 6399 * q^16 + 22 * q^17 - 3236 * q^19 + 5514 * q^20 - 13059 * q^22 + 10848 * q^23 + 15686 * q^25 - 16216 * q^26 + 8838 * q^28 - 13070 * q^29 - 14764 * q^31 + 58812 * q^32 - 26966 * q^34 - 43368 * q^35 + 4638 * q^37 - 68144 * q^38 + 52284 * q^40 + 14806 * q^41 - 24376 * q^43 + 104960 * q^44 + 50452 * q^46 - 40364 * q^47 + 32246 * q^49 - 10839 * q^50 - 80654 * q^52 + 11654 * q^53 + 7052 * q^55 - 70632 * q^56 + 10276 * q^58 - 70804 * q^59 - 31446 * q^61 + 153388 * q^62 + 17695 * q^64 + 41284 * q^65 - 64200 * q^67 + 94114 * q^68 - 103768 * q^70 + 184380 * q^71 - 1750 * q^73 - 306048 * q^74 + 174806 * q^76 - 384646 * q^77 + 24324 * q^79 + 386444 * q^80 - 316255 * q^82 + 46028 * q^83 + 63914 * q^85 - 22931 * q^86 + 211871 * q^88 - 148364 * q^89 - 258448 * q^91 + 58658 * q^92 - 55370 * q^94 + 4716 * q^95 + 484296 * q^97 - 743692 * q^98

Introduction

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