LMFDB - Embedded newform 171.4.u.b.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(28,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("171.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.u (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:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.2
Character	$\chi$	$=$	171.100
Dual form			171.4.u.b.118.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.579114 + 0.210780i) q^{2} +(-5.83741 + 4.89817i) q^{4} +(-9.88078 - 8.29096i) q^{5} +(6.05695 + 10.4909i) q^{7} +(4.81321 - 8.33672i) q^{8} +O(q^{10})$	\(q+(-0.579114 + 0.210780i) q^{2} +(-5.83741 + 4.89817i) q^{4} +(-9.88078 - 8.29096i) q^{5} +(6.05695 + 10.4909i) q^{7} +(4.81321 - 8.33672i) q^{8} +(7.46967 + 2.71874i) q^{10} +(-1.51059 + 2.61642i) q^{11} +(-2.02601 - 11.4901i) q^{13} +(-5.71895 - 4.79877i) q^{14} +(9.55569 - 54.1930i) q^{16} +(104.502 - 38.0357i) q^{17} +(82.6622 - 5.09509i) q^{19} +98.2887 q^{20} +(0.323315 - 1.83361i) q^{22} +(0.581304 - 0.487772i) q^{23} +(7.18382 + 40.7415i) q^{25} +(3.59517 + 6.22702i) q^{26} +(-86.7433 - 31.5720i) q^{28} +(96.6410 + 35.1745i) q^{29} +(-59.9698 - 103.871i) q^{31} +(19.2619 + 109.239i) q^{32} +(-52.5015 + 44.0540i) q^{34} +(27.1326 - 153.877i) q^{35} +336.206 q^{37} +(-46.7969 + 20.3742i) q^{38} +(-116.678 + 42.4672i) q^{40} +(17.2295 - 97.7133i) q^{41} +(88.1148 + 73.9371i) q^{43} +(-3.99773 - 22.6722i) q^{44} +(-0.233828 + 0.405003i) q^{46} +(-298.069 - 108.488i) q^{47} +(98.1267 - 169.960i) q^{49} +(-12.7477 - 22.0797i) q^{50} +(68.1070 + 57.1486i) q^{52} +(244.521 - 205.177i) q^{53} +(36.6185 - 13.3280i) q^{55} +116.613 q^{56} -63.3802 q^{58} +(-225.451 + 82.0576i) q^{59} +(-166.128 + 139.398i) q^{61} +(56.6232 + 47.5125i) q^{62} +(185.936 + 322.050i) q^{64} +(-75.2452 + 130.329i) q^{65} +(-510.695 - 185.878i) q^{67} +(-423.717 + 733.899i) q^{68} +(16.7213 + 94.8312i) q^{70} +(-166.135 - 139.403i) q^{71} +(-99.2537 + 562.895i) q^{73} +(-194.702 + 70.8657i) q^{74} +(-457.577 + 434.636i) q^{76} -36.5983 q^{77} +(185.717 - 1053.25i) q^{79} +(-543.730 + 456.244i) q^{80} +(10.6182 + 60.2188i) q^{82} +(315.557 + 546.561i) q^{83} +(-1347.92 - 490.601i) q^{85} +(-66.6130 - 24.2451i) q^{86} +(14.5416 + 25.1868i) q^{88} +(23.4357 + 132.910i) q^{89} +(108.270 - 90.8496i) q^{91} +(-1.00412 + 5.69465i) q^{92} +195.483 q^{94} +(-859.011 - 635.006i) q^{95} +(859.388 - 312.792i) q^{97} +(-21.0022 + 119.110i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) $ 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8	$ 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8} + 75 q^{10} - 39 q^{11} - 156 q^{13} - 93 q^{14} + 504 q^{16} - 12 q^{17} + 546 q^{19} + 198 q^{20} - 6 q^{22} - 6 q^{23} - 498 q^{25} + 639 q^{26} - 1368 q^{28} + 630 q^{29} - 591 q^{31} - 147 q^{32} - 408 q^{34} - 2001 q^{35} - 72 q^{37} - 2934 q^{38} + 2886 q^{40} + 477 q^{41} + 588 q^{43} + 3423 q^{44} - 1728 q^{46} + 1242 q^{47} - 639 q^{49} + 1788 q^{50} + 2733 q^{52} + 300 q^{53} + 315 q^{55} - 4638 q^{56} - 2820 q^{58} - 2097 q^{59} - 2316 q^{61} + 1320 q^{62} - 1785 q^{64} + 2433 q^{65} + 57 q^{67} + 438 q^{68} - 213 q^{70} + 792 q^{71} + 4068 q^{73} - 4287 q^{74} + 5538 q^{76} - 3786 q^{77} + 1824 q^{79} + 2739 q^{80} + 2205 q^{82} - 1071 q^{83} - 2394 q^{85} + 5256 q^{86} + 1101 q^{88} + 3006 q^{89} - 3285 q^{91} + 1452 q^{92} - 1086 q^{94} + 3078 q^{95} - 2535 q^{97} + 2403 q^{98}+O(q^{100}) $ 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8 + 75 * q^10 - 39 * q^11 - 156 * q^13 - 93 * q^14 + 504 * q^16 - 12 * q^17 + 546 * q^19 + 198 * q^20 - 6 * q^22 - 6 * q^23 - 498 * q^25 + 639 * q^26 - 1368 * q^28 + 630 * q^29 - 591 * q^31 - 147 * q^32 - 408 * q^34 - 2001 * q^35 - 72 * q^37 - 2934 * q^38 + 2886 * q^40 + 477 * q^41 + 588 * q^43 + 3423 * q^44 - 1728 * q^46 + 1242 * q^47 - 639 * q^49 + 1788 * q^50 + 2733 * q^52 + 300 * q^53 + 315 * q^55 - 4638 * q^56 - 2820 * q^58 - 2097 * q^59 - 2316 * q^61 + 1320 * q^62 - 1785 * q^64 + 2433 * q^65 + 57 * q^67 + 438 * q^68 - 213 * q^70 + 792 * q^71 + 4068 * q^73 - 4287 * q^74 + 5538 * q^76 - 3786 * q^77 + 1824 * q^79 + 2739 * q^80 + 2205 * q^82 - 1071 * q^83 - 2394 * q^85 + 5256 * q^86 + 1101 * q^88 + 3006 * q^89 - 3285 * q^91 + 1452 * q^92 - 1086 * q^94 + 3078 * q^95 - 2535 * q^97 + 2403 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.579114	+	0.210780i	−0.204748	+	0.0745221i	−0.442358	−	0.896838i	$-0.645858\pi$
$2$	−0.579114	+	0.210780i	−0.204748	+	0.0745221i	0.237611	+	0.971361i	$0.423636\pi$
$3$		0			0
$3$		0			0
$4$	−5.83741	+	4.89817i	−0.729676	+	0.612271i
$5$	−9.88078	−	8.29096i	−0.883764	−	0.741566i	0.0831853	−	0.996534i	$-0.473491\pi$
$5$	−9.88078	−	8.29096i	−0.883764	−	0.741566i	−0.966950	+	0.254968i	$0.917935\pi$
$6$		0			0
$7$	6.05695	+	10.4909i	0.327045	+	0.566458i	0.981924	−	0.189276i	$-0.0606140\pi$
$7$	6.05695	+	10.4909i	0.327045	+	0.566458i	−0.654879	+	0.755733i	$0.727281\pi$
$8$	4.81321	−	8.33672i	0.212716	−	0.368435i
$9$		0			0
$10$	7.46967	+	2.71874i	0.236212	+	0.0859740i
$11$	−1.51059	+	2.61642i	−0.0414055	+	0.0717164i	−0.885985	−	0.463713i	$-0.846517\pi$
$11$	−1.51059	+	2.61642i	−0.0414055	+	0.0717164i	0.844580	+	0.535429i	$0.179850\pi$
$12$		0			0
$13$	−2.02601	−	11.4901i	−0.0432242	−	0.245136i	0.955539	−	0.294866i	$-0.0952751\pi$
$13$	−2.02601	−	11.4901i	−0.0432242	−	0.245136i	−0.998763	+	0.0497298i	$0.984164\pi$
$14$	−5.71895	−	4.79877i	−0.109175	−	0.0916089i
$15$		0			0
$16$	9.55569	−	54.1930i	0.149308	−	0.846766i
$17$	104.502	−	38.0357i	1.49091	−	0.542647i	0.537222	−	0.843441i	$-0.319474\pi$
$17$	104.502	−	38.0357i	1.49091	−	0.542647i	0.953689	+	0.300794i	$0.0972516\pi$
$18$		0			0
$19$	82.6622	−	5.09509i	0.998106	−	0.0615208i
$19$	82.6622	−	5.09509i	0.998106	−	0.0615208i
$20$	98.2887			1.09890
$21$		0			0
$22$	0.323315	−	1.83361i	0.00313322	−	0.0177694i
$23$	0.581304	−	0.487772i	0.00527001	−	0.00442206i	−0.640149	−	0.768251i	$-0.721127\pi$
$23$	0.581304	−	0.487772i	0.00527001	−	0.00442206i	0.645419	+	0.763829i	$0.276683\pi$
$24$		0			0
$25$	7.18382	+	40.7415i	0.0574706	+	0.325932i
$26$	3.59517	+	6.22702i	0.0271181	+	0.0469700i
$27$		0			0
$28$	−86.7433	−	31.5720i	−0.585462	−	0.213091i
$29$	96.6410	+	35.1745i	0.618820	+	0.225232i	0.632358	−	0.774676i	$-0.282087\pi$
$29$	96.6410	+	35.1745i	0.618820	+	0.225232i	−0.0135379	+	0.999908i	$0.504309\pi$
$30$		0			0
$31$	−59.9698	−	103.871i	−0.347448	−	0.601798i	0.638347	−	0.769748i	$-0.279618\pi$
$31$	−59.9698	−	103.871i	−0.347448	−	0.601798i	−0.985795	+	0.167951i	$0.946285\pi$
$32$	19.2619	+	109.239i	0.106408	+	0.603468i
$33$		0			0
$34$	−52.5015	+	44.0540i	−0.264821	+	0.222212i
$35$	27.1326	−	153.877i	0.131036	−	0.743140i
$36$		0			0
$37$	336.206			1.49384			0.746919	−	0.664915i	$-0.231532\pi$
$37$	336.206			1.49384			0.746919	+	0.664915i	$0.231532\pi$
$38$	−46.7969	+	20.3742i	−0.199775	+	0.0869771i
$39$		0			0
$40$	−116.678	+	42.4672i	−0.461209	+	0.167866i
$41$	17.2295	−	97.7133i	0.0656291	−	0.372201i	−0.934249	−	0.356620i	$-0.883929\pi$
$41$	17.2295	−	97.7133i	0.0656291	−	0.372201i	0.999879	−	0.0155811i	$-0.00495983\pi$
$42$		0			0
$43$	88.1148	+	73.9371i	0.312497	+	0.262216i	0.785523	−	0.618832i	$-0.212394\pi$
$43$	88.1148	+	73.9371i	0.312497	+	0.262216i	−0.473026	+	0.881048i	$0.656838\pi$
$44$	−3.99773	−	22.6722i	−0.0136973	−	0.0776811i
$45$		0			0
$46$	−0.233828	+	0.405003i	−0.000749481	+	0.00129814i
$47$	−298.069	−	108.488i	−0.925059	−	0.336694i	−0.164810	−	0.986325i	$-0.552701\pi$
$47$	−298.069	−	108.488i	−0.925059	−	0.336694i	−0.760249	+	0.649631i	$0.774923\pi$
$48$		0			0
$49$	98.1267	−	169.960i	0.286084	−	0.495512i
$50$	−12.7477	−	22.0797i	−0.0360561	−	0.0624509i
$51$		0			0
$52$	68.1070	+	57.1486i	0.181630	+	0.152405i
$53$	244.521	−	205.177i	0.633727	−	0.531760i	−0.268358	−	0.963319i	$-0.586481\pi$
$53$	244.521	−	205.177i	0.633727	−	0.531760i	0.902084	+	0.431559i	$0.142037\pi$
$54$		0			0
$55$	36.6185	−	13.3280i	0.0897751	−	0.0326755i
$56$	116.613			0.278270
$57$		0			0
$58$	−63.3802			−0.143487
$59$	−225.451	+	82.0576i	−0.497479	+	0.181068i	−0.578560	−	0.815640i	$-0.696385\pi$
$59$	−225.451	+	82.0576i	−0.497479	+	0.181068i	0.0810806	+	0.996708i	$0.474163\pi$
$60$		0			0
$61$	−166.128	+	139.398i	−0.348697	+	0.292592i	−0.800267	−	0.599644i	$-0.795309\pi$
$61$	−166.128	+	139.398i	−0.348697	+	0.292592i	0.451570	+	0.892236i	$0.350864\pi$
$62$	56.6232	+	47.5125i	0.115986	+	0.0973241i
$63$		0			0
$64$	185.936	+	322.050i	0.363156	+	0.629004i
$65$	−75.2452	+	130.329i	−0.143585	+	0.248696i
$66$		0			0
$67$	−510.695	−	185.878i	−0.931213	−	0.338934i	−0.168523	−	0.985698i	$-0.553900\pi$
$67$	−510.695	−	185.878i	−0.931213	−	0.338934i	−0.762690	+	0.646764i	$0.776122\pi$
$68$	−423.717	+	733.899i	−0.755635	+	1.30880i
$69$		0			0
$70$	16.7213	+	94.8312i	0.0285511	+	0.161921i
$71$	−166.135	−	139.403i	−0.277698	−	0.233016i	0.493292	−	0.869864i	$-0.335794\pi$
$71$	−166.135	−	139.403i	−0.277698	−	0.233016i	−0.770990	+	0.636848i	$0.780238\pi$
$72$		0			0
$73$	−99.2537	+	562.895i	−0.159134	+	0.902492i	0.795775	+	0.605592i	$0.207064\pi$
$73$	−99.2537	+	562.895i	−0.159134	+	0.902492i	−0.954909	+	0.296900i	$0.904047\pi$
$74$	−194.702	+	70.8657i	−0.305860	+	0.111324i
$75$		0			0
$76$	−457.577	+	434.636i	−0.690627	+	0.656002i
$77$	−36.5983			−0.0541657
$78$		0			0
$79$	185.717	−	1053.25i	0.264491	−	1.50000i	−0.505989	−	0.862540i	$-0.668872\pi$
$79$	185.717	−	1053.25i	0.264491	−	1.50000i	0.770480	−	0.637464i	$-0.220017\pi$
$80$	−543.730	+	456.244i	−0.759886	+	0.637620i
$81$		0			0
$82$	10.6182	+	60.2188i	0.0142998	+	0.0810982i
$83$	315.557	+	546.561i	0.417312	+	0.722806i	0.995668	−	0.0929786i	$-0.0296388\pi$
$83$	315.557	+	546.561i	0.417312	+	0.722806i	−0.578356	+	0.815785i	$0.696305\pi$
$84$		0			0
$85$	−1347.92	−	490.601i	−1.72002	−	0.626037i
$86$	−66.6130	−	24.2451i	−0.0835240	−	0.0304002i
$87$		0			0
$88$	14.5416	+	25.1868i	0.0176152	+	0.0305104i
$89$	23.4357	+	132.910i	0.0279121	+	0.158297i	0.995578	−	0.0939377i	$-0.0299455\pi$
$89$	23.4357	+	132.910i	0.0279121	+	0.158297i	−0.967666	+	0.252235i	$0.918834\pi$
$90$		0			0
$91$	108.270	−	90.8496i	0.124723	−	0.104655i
$92$	−1.00412	+	5.69465i	−0.00113790	+	0.00645335i
$93$		0			0
$94$	195.483			0.214495
$95$	−859.011	−	635.006i	−0.927712	−	0.685792i
$96$		0			0
$97$	859.388	−	312.792i	0.899563	−	0.327414i	0.149485	−	0.988764i	$-0.452238\pi$
$97$	859.388	−	312.792i	0.899563	−	0.327414i	0.750078	+	0.661350i	$0.230016\pi$
$98$	−21.0022	+	119.110i	−0.0216484	+	0.122774i
$99$		0			0
$100$	−241.493	−	202.637i	−0.241493	−	0.202637i
$101$	−160.308	−	909.149i	−0.157933	−	0.895680i	−0.956056	−	0.293186i	$-0.905285\pi$
$101$	−160.308	−	909.149i	−0.157933	−	0.895680i	0.798123	−	0.602495i	$-0.205827\pi$
$102$		0			0
$103$	−277.844	+	481.240i	−0.265794	+	0.460368i	−0.967771	−	0.251831i	$-0.918967\pi$
$103$	−277.844	+	481.240i	−0.265794	+	0.460368i	0.701977	+	0.712199i	$0.252301\pi$
$104$	−105.541	−	38.4139i	−0.0995112	−	0.0362191i
$105$		0			0
$106$	−98.3581	+	170.361i	−0.0901262	+	0.156103i
$107$	−395.739	−	685.440i	−0.357547	−	0.619290i	0.630003	−	0.776592i	$-0.283053\pi$
$107$	−395.739	−	685.440i	−0.357547	−	0.619290i	−0.987550	+	0.157303i	$0.949720\pi$
$108$		0			0
$109$	118.707	+	99.6071i	0.104313	+	0.0875287i	0.693452	−	0.720502i	$-0.256089\pi$
$109$	118.707	+	99.6071i	0.104313	+	0.0875287i	−0.589140	+	0.808031i	$0.700533\pi$
$110$	−18.3970	+	15.4369i	−0.0159462	+	0.0133805i
$111$		0			0
$112$	626.414	−	227.996i	0.528487	−	0.192354i
$113$	2112.80			1.75890			0.879448	−	0.475995i	$-0.157912\pi$
$113$	2112.80			1.75890			0.879448	+	0.475995i	$0.157912\pi$
$114$		0			0
$115$	−9.78783			−0.00793670
$116$	−736.424	+	268.036i	−0.589442	+	0.214539i
$117$		0			0
$118$	113.266	−	95.0414i	0.0883642	−	0.0741464i
$119$	1031.99	+	865.946i	0.794981	+	0.667068i
$120$		0			0
$121$	660.936	+	1144.78i	0.496571	+	0.860087i
$122$	66.8247	−	115.744i	0.0495904	−	0.0858931i
$123$		0			0
$124$	858.844	+	312.594i	0.621988	+	0.226385i
$125$	−539.349	+	934.180i	−0.385927	+	0.668444i
$126$		0			0
$127$	157.503	+	893.242i	0.110048	+	0.624114i	0.989083	+	0.147357i	$0.0470766\pi$
$127$	157.503	+	893.242i	0.110048	+	0.624114i	−0.879035	+	0.476757i	$0.841812\pi$
$128$	−855.345	−	717.720i	−0.590645	−	0.495610i
$129$		0			0
$130$	16.1049	−	91.3353i	0.0108653	−	0.0616203i
$131$	1094.67	−	398.429i	0.730092	−	0.265732i	0.0498884	−	0.998755i	$-0.484113\pi$
$131$	1094.67	−	398.429i	0.730092	−	0.265732i	0.680204	+	0.733023i	$0.261891\pi$
$132$		0			0
$133$	554.133	+	836.344i	0.361274	+	0.545265i
$134$	334.930			0.215922
$135$		0			0
$136$	185.898	−	1054.28i	0.117210	−	0.664733i
$137$	1494.23	−	1253.81i	0.931831	−	0.781899i	−0.0443144	−	0.999018i	$-0.514110\pi$
$137$	1494.23	−	1253.81i	0.931831	−	0.781899i	0.976145	+	0.217119i	$0.0696659\pi$
$138$		0			0
$139$	−115.018	−	652.298i	−0.0701847	−	0.398037i	−0.999581	−	0.0289534i	$-0.990783\pi$
$139$	−115.018	−	652.298i	−0.0701847	−	0.398037i	0.929396	−	0.369084i	$-0.120329\pi$
$140$	595.330	+	1031.14i	0.359390	+	0.622481i
$141$		0			0
$142$	125.594	+	45.7126i	0.0742228	+	0.0270149i
$143$	33.1233	+	12.0559i	0.0193700	+	0.00705011i
$144$		0			0
$145$	−663.259	−	1148.80i	−0.379867	−	0.657948i
$146$	−61.1681	−	346.901i	−0.0346733	−	0.196642i
$147$		0			0
$148$	−1962.57	+	1646.80i	−1.09002	+	0.914634i
$149$	489.098	−	2773.81i	0.268916	−	1.52510i	−0.488732	−	0.872434i	$-0.662541\pi$
$149$	489.098	−	2773.81i	0.268916	−	1.52510i	0.757648	−	0.652663i	$-0.226348\pi$
$150$		0			0
$151$	2643.70			1.42478			0.712389	−	0.701784i	$-0.247613\pi$
$151$	2643.70			1.42478			0.712389	+	0.701784i	$0.247613\pi$
$152$	355.394	−	713.656i	0.189647	−	0.380823i
$153$		0			0
$154$	21.1946	−	7.71420i	0.0110903	−	0.00403654i
$155$	−268.640	+	1523.53i	−0.139211	+	0.789503i
$156$		0			0
$157$	−2485.07	−	2085.22i	−1.26325	−	1.05999i	−0.995328	−	0.0965521i	$-0.969219\pi$
$157$	−2485.07	−	2085.22i	−1.26325	−	1.05999i	−0.267922	−	0.963441i	$-0.586337\pi$
$158$	114.454	+	649.099i	0.0576294	+	0.326833i
$159$		0			0
$160$	715.378	−	1239.07i	0.353472	−	0.612232i
$161$	8.63811	+	3.14402i	0.00422844	+	0.00153903i
$162$		0			0
$163$	896.372	−	1552.56i	0.430732	−	0.746049i	−0.566205	−	0.824265i	$-0.691589\pi$
$163$	896.372	−	1552.56i	0.430732	−	0.746049i	0.996936	+	0.0782155i	$0.0249222\pi$
$164$	378.041	+	654.786i	0.180000	+	0.311769i
$165$		0			0
$166$	−297.948	−	250.008i	−0.139309	−	0.116894i
$167$	763.089	−	640.307i	0.353590	−	0.296697i	−0.448640	−	0.893713i	$-0.648091\pi$
$167$	763.089	−	640.307i	0.353590	−	0.296697i	0.802230	+	0.597015i	$0.203647\pi$
$168$		0			0
$169$	1936.59	−	704.860i	0.881469	−	0.320829i
$170$	884.005			0.398824
$171$		0			0
$172$	−876.519			−0.388569
$173$	681.837	−	248.168i	0.299648	−	0.109063i	−0.187821	−	0.982203i	$-0.560142\pi$
$173$	681.837	−	248.168i	0.299648	−	0.109063i	0.487469	+	0.873140i	$0.337920\pi$
$174$		0			0
$175$	−383.904	+	322.134i	−0.165831	+	0.139149i
$176$	127.357	+	106.865i	0.0545448	+	0.0457685i
$177$		0			0
$178$	−41.5868	−	72.0305i	−0.0175116	−	0.0303310i
$179$	−2046.77	+	3545.10i	−0.854651	+	1.48030i	0.0223170	+	0.999751i	$0.492896\pi$
$179$	−2046.77	+	3545.10i	−0.854651	+	1.48030i	−0.876968	+	0.480548i	$0.840438\pi$
$180$		0			0
$181$	−1495.86	−	544.450i	−0.614291	−	0.223584i	0.0160889	−	0.999871i	$-0.494879\pi$
$181$	−1495.86	−	544.450i	−0.614291	−	0.223584i	−0.630380	+	0.776287i	$0.717101\pi$
$182$	−43.5515	+	75.4335i	−0.0177377	+	0.0307225i
$183$		0			0
$184$	−1.26848	−	7.19391i	−0.000508227	−	0.00288230i
$185$	−3321.98	−	2787.47i	−1.32020	−	1.10778i
$186$		0			0
$187$	−58.3427	+	330.878i	−0.0228152	+	0.129391i
$188$	2271.34	−	826.701i	0.881142	−	0.320710i
$189$		0			0
$190$	631.312	+	186.678i	0.241053	+	0.0712793i
$191$	1987.88			0.753078			0.376539	−	0.926401i	$-0.377114\pi$
$191$	1987.88			0.753078			0.376539	+	0.926401i	$0.377114\pi$
$192$		0			0
$193$	−532.104	+	3017.71i	−0.198454	+	1.12549i	0.708959	+	0.705250i	$0.249165\pi$
$193$	−532.104	+	3017.71i	−0.198454	+	1.12549i	−0.907413	+	0.420240i	$0.861946\pi$
$194$	−431.753	+	362.284i	−0.159784	+	0.134075i
$195$		0			0
$196$	259.689	+	1472.77i	0.0946389	+	0.536724i
$197$	−380.723	−	659.432i	−0.137692	−	0.238490i	0.788930	−	0.614483i	$-0.210635\pi$
$197$	−380.723	−	659.432i	−0.137692	−	0.238490i	−0.926623	+	0.375992i	$0.877302\pi$
$198$		0			0
$199$	738.250	+	268.701i	0.262981	+	0.0957171i	0.470146	−	0.882589i	$-0.344201\pi$
$199$	738.250	+	268.701i	0.262981	+	0.0957171i	−0.207165	+	0.978306i	$0.566424\pi$
$200$	374.228	+	136.208i	0.132309	+	0.0481567i
$201$		0			0
$202$	284.467	+	492.711i	0.0990843	+	0.171619i
$203$	216.337	+	1226.91i	0.0747973	+	0.424196i
$204$		0			0
$205$	−980.378	+	822.635i	−0.334013	+	0.280270i
$206$	59.4674	−	337.257i	0.0201131	−	0.114067i
$207$		0			0
$208$	−642.042			−0.214027
$209$	−111.538	+	223.976i	−0.0369150	+	0.0741278i
$210$		0			0
$211$	465.105	−	169.284i	0.151749	−	0.0552323i	−0.265029	−	0.964241i	$-0.585381\pi$
$211$	465.105	−	169.284i	0.151749	−	0.0552323i	0.416778	+	0.909008i	$0.363159\pi$
$212$	−422.375	+	2395.41i	−0.136834	+	0.776025i
$213$		0			0
$214$	373.655	+	313.534i	0.119358	+	0.100153i
$215$	−257.634	−	1461.11i	−0.0817231	−	0.463475i
$216$		0			0
$217$	726.468	−	1258.28i	0.227262	−	0.393629i
$218$	−89.7402	−	32.6628i	−0.0278806	−	0.0101477i
$219$		0			0
$220$	−148.474	+	257.165i	−0.0455005	+	0.0788093i
$221$	−648.755	−	1123.68i	−0.197466	−	0.342021i
$222$		0			0
$223$	1606.74	+	1348.21i	0.482489	+	0.404856i	0.851325	−	0.524638i	$-0.175799\pi$
$223$	1606.74	+	1348.21i	0.482489	+	0.404856i	−0.368836	+	0.929494i	$0.620244\pi$
$224$	−1029.36	+	863.733i	−0.307039	+	0.257637i
$225$		0			0
$226$	−1223.55	+	445.336i	−0.360130	+	0.131077i
$227$	−4345.02			−1.27044			−0.635219	−	0.772332i	$-0.719090\pi$
$227$	−4345.02			−1.27044			−0.635219	+	0.772332i	$0.719090\pi$
$228$		0			0
$229$	−3217.61			−0.928495			−0.464248	−	0.885705i	$-0.653675\pi$
$229$	−3217.61			−0.928495			−0.464248	+	0.885705i	$0.653675\pi$
$230$	5.66827	−	2.06308i	0.00162502	−	0.000591459i
$231$		0			0
$232$	758.393	−	636.367i	0.214616	−	0.180084i
$233$	−2086.28	−	1750.60i	−0.586595	−	0.492212i	0.300510	−	0.953779i	$-0.402843\pi$
$233$	−2086.28	−	1750.60i	−0.586595	−	0.492212i	−0.887106	+	0.461567i	$0.847288\pi$
$234$		0			0
$235$	2045.68	+	3543.22i	0.567853	+	0.983551i
$236$	914.121	−	1583.30i	0.252136	−	0.436713i
$237$		0			0
$238$	−780.166	−	283.957i	−0.212482	−	0.0773371i
$239$	−2941.67	+	5095.12i	−0.796154	+	1.37898i	0.125950	+	0.992037i	$0.459802\pi$
$239$	−2941.67	+	5095.12i	−0.796154	+	1.37898i	−0.922104	+	0.386943i	$0.873531\pi$
$240$		0			0
$241$	−372.838	−	2114.47i	−0.0996538	−	0.565165i	−0.993222	−	0.116237i	$-0.962917\pi$
$241$	−372.838	−	2114.47i	−0.0996538	−	0.565165i	0.893568	−	0.448928i	$-0.148194\pi$
$242$	−624.053	−	523.643i	−0.165767	−	0.139095i
$243$		0			0
$244$	286.963	−	1627.45i	0.0752906	−	0.426994i
$245$	−2378.71	+	865.778i	−0.620285	+	0.225765i
$246$		0			0
$247$	−226.018	−	939.472i	−0.0582233	−	0.242013i
$248$	−1154.59			−0.295631
$249$		0			0
$250$	115.438	−	654.680i	0.0292037	−	0.165623i
$251$	3850.15	−	3230.66i	0.968204	−	0.812419i	−0.0140644	−	0.999901i	$-0.504477\pi$
$251$	3850.15	−	3230.66i	0.968204	−	0.812419i	0.982268	+	0.187482i	$0.0600325\pi$
$252$		0			0
$253$	0.398104	+	2.25776i	9.89271e−5	+	0.000561044i
$254$	−279.490	−	484.090i	−0.0690423	−	0.119585i
$255$		0			0
$256$	−2148.94	−	782.149i	−0.524642	−	0.190954i
$257$	2254.87	+	820.706i	0.547296	+	0.199199i	0.600845	−	0.799366i	$-0.294831\pi$
$257$	2254.87	+	820.706i	0.547296	+	0.199199i	−0.0535487	+	0.998565i	$0.517053\pi$
$258$		0			0
$259$	2036.39	+	3527.12i	0.488551	+	0.846196i
$260$	−199.134	−	1129.35i	−0.0474991	−	0.269381i
$261$		0			0
$262$	−549.960	+	461.471i	−0.129682	+	0.108816i
$263$	−854.310	+	4845.03i	−0.200300	+	1.13596i	0.704365	+	0.709838i	$0.251232\pi$
$263$	−854.310	+	4845.03i	−0.200300	+	1.13596i	−0.904666	+	0.426122i	$0.859879\pi$
$264$		0			0
$265$	−4117.17			−0.954400
$266$	−497.191	−	367.538i	−0.114604	−	0.0847188i
$267$		0			0
$268$	3891.59	−	1416.42i	0.887004	−	0.322843i
$269$	−1082.41	+	6138.65i	−0.245337	+	1.39138i	0.574371	+	0.818595i	$0.305247\pi$
$269$	−1082.41	+	6138.65i	−0.245337	+	1.39138i	−0.819708	+	0.572781i	$0.805864\pi$
$270$		0			0
$271$	−2943.86	−	2470.19i	−0.659878	−	0.553703i	0.250173	−	0.968201i	$-0.419513\pi$
$271$	−2943.86	−	2470.19i	−0.659878	−	0.553703i	−0.910050	+	0.414498i	$0.863957\pi$
$272$	−1062.68	−	6026.74i	−0.236891	−	1.34347i
$273$		0			0
$274$	−601.052	+	1041.05i	−0.132521	+	0.229534i
$275$	−117.449	−	42.7478i	−0.0257542	−	0.00937378i
$276$		0			0
$277$	773.809	−	1340.28i	0.167847	−	0.290720i	−0.769816	−	0.638266i	$-0.779652\pi$
$277$	773.809	−	1340.28i	0.167847	−	0.290720i	0.937663	+	0.347547i	$0.112985\pi$
$278$	204.100	+	353.511i	0.0440327	+	0.0762669i
$279$		0			0
$280$	−1152.23	−	966.838i	−0.245925	−	0.206356i
$281$	−4264.26	+	3578.14i	−0.905283	+	0.759623i	−0.971216	−	0.238202i	$-0.923442\pi$
$281$	−4264.26	+	3578.14i	−0.905283	+	0.759623i	0.0659329	+	0.997824i	$0.478998\pi$
$282$		0			0
$283$	−7490.27	+	2726.23i	−1.57332	+	0.572642i	−0.973738	−	0.227670i	$-0.926889\pi$
$283$	−7490.27	+	2726.23i	−1.57332	+	0.572642i	−0.599584	+	0.800312i	$0.704667\pi$
$284$	1652.62			0.345299
$285$		0			0
$286$	−21.7233			−0.00449136
$287$	1129.46	−	411.091i	0.232300	−	0.0845503i
$288$		0			0
$289$	5710.41	−	4791.60i	1.16231	−	0.975290i
$290$	626.246	+	525.483i	0.126808	+	0.106405i
$291$		0			0
$292$	−2177.77	−	3772.01i	−0.436454	−	0.755960i
$293$	−1247.82	+	2161.28i	−0.248800	+	0.430934i	−0.963193	−	0.268811i	$-0.913369\pi$
$293$	−1247.82	+	2161.28i	−0.248800	+	0.430934i	0.714393	+	0.699744i	$0.246703\pi$
$294$		0			0
$295$	2907.97	+	1058.42i	0.573928	+	0.208893i
$296$	1618.23	−	2802.86i	0.317763	−	0.550381i
$297$		0			0
$298$	301.421	+	1709.44i	0.0585935	+	0.332300i
$299$	−6.78226	−	5.69099i	−0.00131180	−	0.00110073i
$300$		0			0
$301$	−241.963	+	1372.24i	−0.0463339	+	0.262773i
$302$	−1531.01	+	557.241i	−0.291720	+	0.106177i
$303$		0			0
$304$	513.776	−	4528.40i	0.0969311	−	0.854347i
$305$	2797.22			0.525142
$306$		0			0
$307$	−1332.30	+	7555.86i	−0.247682	+	1.40468i	0.566497	+	0.824063i	$0.308298\pi$
$307$	−1332.30	+	7555.86i	−0.247682	+	1.40468i	−0.814180	+	0.580613i	$0.802813\pi$
$308$	213.639	−	179.265i	0.0395235	−	0.0331641i
$309$		0			0
$310$	−165.557	−	938.922i	−0.0303323	−	0.172023i
$311$	4917.39	+	8517.17i	0.896590	+	1.55294i	0.831824	+	0.555040i	$0.187297\pi$
$311$	4917.39	+	8517.17i	0.896590	+	1.55294i	0.0647666	+	0.997900i	$0.479370\pi$
$312$		0			0
$313$	−730.057	−	265.719i	−0.131838	−	0.0479850i	0.275259	−	0.961370i	$-0.411237\pi$
$313$	−730.057	−	265.719i	−0.131838	−	0.0479850i	−0.407096	+	0.913385i	$0.633459\pi$
$314$	1878.66	+	683.777i	0.337640	+	0.122891i
$315$		0			0
$316$	4074.91	+	7057.95i	0.725416	+	1.25646i
$317$	−1023.66	−	5805.47i	−0.181371	−	1.02860i	−0.930530	−	0.366215i	$-0.880653\pi$
$317$	−1023.66	−	5805.47i	−0.181371	−	1.02860i	0.749160	−	0.662390i	$-0.230458\pi$
$318$		0			0
$319$	−238.016	+	199.719i	−0.0417754	+	0.0350537i
$320$	832.915	−	4723.69i	0.145504	−	0.825195i
$321$		0			0
$322$	−5.66515			−0.000980454
$323$	8444.58	−	3676.56i	1.45470	−	0.633341i
$324$		0			0
$325$	453.568	−	165.085i	0.0774136	−	0.0281763i
$326$	−191.852	+	1088.05i	−0.0325942	+	0.184851i
$327$		0			0
$328$	−731.679	−	613.952i	−0.123171	−	0.103353i
$329$	−667.244	−	3784.13i	−0.111813	−	0.634121i
$330$		0			0
$331$	−1444.06	+	2501.19i	−0.239797	+	0.415341i	−0.960656	−	0.277741i	$-0.910414\pi$
$331$	−1444.06	+	2501.19i	−0.239797	+	0.415341i	0.720859	+	0.693082i	$0.243748\pi$
$332$	−4519.19	−	1644.85i	−0.747056	−	0.271906i
$333$		0			0
$334$	−306.951	+	531.655i	−0.0502863	+	0.0870984i
$335$	3504.96	+	6070.77i	0.571631	+	0.990094i
$336$		0			0
$337$	−3977.42	−	3337.46i	−0.642920	−	0.539474i	0.261993	−	0.965070i	$-0.415620\pi$
$337$	−3977.42	−	3337.46i	−0.642920	−	0.539474i	−0.904913	+	0.425596i	$0.860065\pi$
$338$	−972.934	+	816.389i	−0.156570	+	0.131378i
$339$		0			0
$340$	10271.4	−	3738.48i	1.63836	−	0.596316i
$341$	362.359			0.0575450
$342$		0			0
$343$	6532.46			1.02834
$344$	1040.51	−	378.714i	0.163083	−	0.0593572i
$345$		0			0
$346$	−342.552	+	287.435i	−0.0532246	+	0.0446607i
$347$	−7258.64	−	6090.72i	−1.12295	−	0.942268i	−0.124201	−	0.992257i	$-0.539637\pi$
$347$	−7258.64	−	6090.72i	−1.12295	−	0.942268i	−0.998750	+	0.0499890i	$0.984081\pi$
$348$		0			0
$349$	1785.30	+	3092.23i	0.273825	+	0.474279i	0.969838	−	0.243751i	$-0.0783778\pi$
$349$	1785.30	+	3092.23i	0.273825	+	0.474279i	−0.696013	+	0.718029i	$0.745044\pi$
$350$	154.425	−	267.472i	0.0235839	−	0.0408485i
$351$		0			0
$352$	−314.913	−	114.619i	−0.0476844	−	0.0173557i
$353$	3912.18	−	6776.09i	0.589870	−	1.02168i	−0.404379	−	0.914592i	$-0.632512\pi$
$353$	3912.18	−	6776.09i	0.589870	−	1.02168i	0.994249	−	0.107093i	$-0.0341543\pi$
$354$		0			0
$355$	485.751	+	2754.83i	0.0726225	+	0.411863i
$356$	−787.821	−	661.060i	−0.117288	−	0.0984161i
$357$		0			0
$358$	438.073	−	2484.44i	0.0646729	−	0.366778i
$359$	−1397.43	+	508.623i	−0.205441	+	0.0747746i	−0.442691	−	0.896674i	$-0.645976\pi$
$359$	−1397.43	+	508.623i	−0.205441	+	0.0747746i	0.237250	+	0.971449i	$0.423754\pi$
$360$		0			0
$361$	6807.08	−	842.343i	0.992430	−	0.122808i
$362$	981.034			0.142437
$363$		0			0
$364$	−187.022	+	1060.65i	−0.0269302	+	0.152729i
$365$	5647.65	−	4738.94i	0.809894	−	0.679582i
$366$		0			0
$367$	−1562.97	−	8864.06i	−0.222307	−	1.26076i	−0.867767	−	0.496970i	$-0.834446\pi$
$367$	−1562.97	−	8864.06i	−0.222307	−	1.26076i	0.645461	−	0.763793i	$-0.276665\pi$
$368$	−20.8791	−	36.1636i	−0.00295760	−	0.00512271i
$369$		0			0
$370$	2511.35	+	914.057i	0.352862	+	0.128431i
$371$	3633.55	+	1322.51i	0.508476	+	0.185070i
$372$		0			0
$373$	−4721.91	−	8178.58i	−0.655472	−	1.13531i	−0.981775	−	0.190046i	$-0.939136\pi$
$373$	−4721.91	−	8178.58i	−0.655472	−	1.13531i	0.326303	−	0.945265i	$-0.394197\pi$
$374$	−35.9554	−	203.913i	−0.00497115	−	0.0281928i
$375$		0			0
$376$	−2339.10	+	1962.74i	−0.320825	+	0.269204i
$377$	208.361	−	1181.68i	0.0284646	−	0.161431i
$378$		0			0
$379$	−3992.70			−0.541138			−0.270569	−	0.962701i	$-0.587212\pi$
$379$	−3992.70			−0.541138			−0.270569	+	0.962701i	$0.587212\pi$
$380$	8124.76	−	500.790i	1.09682	−	0.0676053i
$381$		0			0
$382$	−1151.21	+	419.006i	−0.154191	+	0.0561209i
$383$	−189.066	+	1072.24i	−0.0252240	+	0.143053i	−0.994819	−	0.101663i	$-0.967584\pi$
$383$	−189.066	+	1072.24i	−0.0252240	+	0.143053i	0.969595	+	0.244716i	$0.0786947\pi$
$384$		0			0
$385$	361.620	+	303.435i	0.0478697	+	0.0401675i
$386$	−327.925	−	1859.75i	−0.0432408	−	0.245231i
$387$		0			0
$388$	−3484.49	+	6035.32i	−0.455924	+	0.789683i
$389$	−6028.38	−	2194.15i	−0.785735	−	0.285984i	−0.0821729	−	0.996618i	$-0.526186\pi$
$389$	−6028.38	−	2194.15i	−0.785735	−	0.285984i	−0.703562	+	0.710634i	$0.748408\pi$
$390$		0			0
$391$	42.1947	−	73.0834i	0.00545749	−	0.00945266i
$392$	−944.609	−	1636.11i	−0.121709	−	0.210806i
$393$		0			0
$394$	359.477	+	301.637i	0.0459650	+	0.0385692i
$395$	−10567.5	+	8867.20i	−1.34610	+	1.12951i
$396$		0			0
$397$	−2745.37	+	999.233i	−0.347069	+	0.126323i	−0.509672	−	0.860369i	$-0.670233\pi$
$397$	−2745.37	+	999.233i	−0.347069	+	0.126323i	0.162603	+	0.986692i	$0.448011\pi$
$398$	−484.168			−0.0609777
$399$		0			0
$400$	2276.55			0.284569
$401$	466.586	−	169.823i	0.0581052	−	0.0211486i	−0.312804	−	0.949818i	$-0.601268\pi$
$401$	466.586	−	169.823i	0.0581052	−	0.0211486i	0.370909	+	0.928669i	$0.379046\pi$
$402$		0			0
$403$	−1071.98	+	899.500i	−0.132504	+	0.111184i
$404$	5388.95	+	4521.86i	0.663639	+	0.556859i
$405$		0			0
$406$	−383.891	−	664.919i	−0.0469266	−	0.0812792i
$407$	−507.870	+	879.657i	−0.0618531	+	0.107133i
$408$		0			0
$409$	10516.9	+	3827.84i	1.27146	+	0.462774i	0.887599	−	0.460616i	$-0.152371\pi$
$409$	10516.9	+	3827.84i	1.27146	+	0.462774i	0.383862	+	0.923390i	$0.374594\pi$
$410$	394.355	−	683.044i	0.0475020	−	0.0822759i
$411$		0			0
$412$	−735.305	−	4170.12i	−0.0879268	−	0.498658i
$413$	−2226.41	−	1868.18i	−0.265265	−	0.222584i
$414$		0			0
$415$	1413.57	−	8016.73i	0.167203	−	0.948255i
$416$	1216.14	−	442.641i	0.143333	−	0.0521688i
$417$		0			0
$418$	17.3835	−	153.217i	0.00203410	−	0.0179285i
$419$	14324.4			1.67015			0.835073	−	0.550138i	$-0.185425\pi$
$419$	14324.4			1.67015			0.835073	+	0.550138i	$0.185425\pi$
$420$		0			0
$421$	−1354.78	+	7683.35i	−0.156836	+	0.889462i	0.800252	+	0.599664i	$0.204699\pi$
$421$	−1354.78	+	7683.35i	−0.156836	+	0.889462i	−0.957088	+	0.289798i	$0.906412\pi$
$422$	−233.667	+	196.070i	−0.0269543	+	0.0226174i
$423$		0			0
$424$	−533.577	−	3026.06i	−0.0611150	−	0.346601i
$425$	2300.35	+	3984.33i	0.262549	+	0.454749i
$426$		0			0
$427$	−2468.65	−	898.514i	−0.279780	−	0.101832i
$428$	5667.49	+	2062.80i	0.640067	+	0.232965i
$429$		0			0
$430$	457.173	+	791.847i	0.0512717	+	0.0888052i
$431$	1816.52	+	10302.0i	0.203013	+	1.15134i	0.900536	+	0.434781i	$0.143174\pi$
$431$	1816.52	+	10302.0i	0.203013	+	1.15134i	−0.697523	+	0.716562i	$0.745715\pi$
$432$		0			0
$433$	3628.33	−	3044.53i	0.402694	−	0.337900i	−0.418840	−	0.908060i	$-0.637563\pi$
$433$	3628.33	−	3044.53i	0.402694	−	0.337900i	0.821534	+	0.570160i	$0.193119\pi$
$434$	−155.487	+	881.812i	−0.0171973	+	0.0975307i
$435$		0			0
$436$	−1180.83			−0.129706
$437$	45.5666	−	43.2821i	0.00498798	−	0.00473790i
$438$		0			0
$439$	−13231.8	+	4816.00i	−1.43855	+	0.523588i	−0.939368	−	0.342912i	$-0.888587\pi$
$439$	−13231.8	+	4816.00i	−1.43855	+	0.523588i	−0.499178	+	0.866500i	$0.666365\pi$
$440$	65.1402	−	369.429i	0.00705781	−	0.0400269i
$441$		0			0
$442$	612.552	+	513.992i	0.0659188	+	0.0553125i
$443$	−74.2865	−	421.300i	−0.00796717	−	0.0451841i	0.980565	−	0.196195i	$-0.0628584\pi$
$443$	−74.2865	−	421.300i	−0.00796717	−	0.0451841i	−0.988532	+	0.151010i	$0.951747\pi$
$444$		0			0
$445$	870.392	−	1507.56i	0.0927203	−	0.160596i
$446$	−1214.66	−	442.100i	−0.128959	−	0.0469373i
$447$		0			0
$448$	−2252.41	+	3901.28i	−0.237536	+	0.411425i
$449$	3540.96	+	6133.12i	0.372178	+	0.644632i	0.989900	−	0.141765i	$-0.0452776\pi$
$449$	3540.96	+	6133.12i	0.372178	+	0.644632i	−0.617722	+	0.786397i	$0.711944\pi$
$450$		0			0
$451$	229.632	+	192.684i	0.0239755	+	0.0201179i
$452$	−12333.3	+	10348.8i	−1.28342	+	1.07692i
$453$		0			0
$454$	2516.26	−	915.845i	0.260119	−	0.0946757i
$455$	−1823.03			−0.187835
$456$		0			0
$457$	5134.15			0.525526			0.262763	−	0.964860i	$-0.415366\pi$
$457$	5134.15			0.525526			0.262763	+	0.964860i	$0.415366\pi$
$458$	1863.36	−	678.208i	0.190107	−	0.0691934i
$459$		0			0
$460$	57.1356	−	47.9425i	0.00579122	−	0.00485941i
$461$	−14275.7	−	11978.8i	−1.44227	−	1.21021i	−0.937985	−	0.346675i	$-0.887311\pi$
$461$	−14275.7	−	11978.8i	−1.44227	−	1.21021i	−0.504288	−	0.863536i	$-0.668245\pi$
$462$		0			0
$463$	2075.02	+	3594.05i	0.208282	+	0.360755i	0.951173	−	0.308657i	$-0.0998795\pi$
$463$	2075.02	+	3594.05i	0.208282	+	0.360755i	−0.742891	+	0.669412i	$0.766546\pi$
$464$	2829.68	−	4901.15i	0.283113	−	0.490367i
$465$		0			0
$466$	1577.18	+	574.048i	0.156785	+	0.0570650i
$467$	4173.89	−	7229.38i	0.413585	−	0.716351i	−0.581693	−	0.813408i	$-0.697610\pi$
$467$	4173.89	−	7229.38i	0.413585	−	0.716351i	0.995279	+	0.0970572i	$0.0309430\pi$
$468$		0			0
$469$	−1143.22	−	6483.52i	−0.112556	−	0.638339i
$470$	−1931.52	−	1620.74i	−0.189563	−	0.159062i
$471$		0			0
$472$	−401.053	+	2274.49i	−0.0391101	+	0.221805i
$473$	−326.556	+	118.857i	−0.0317443	+	0.0115540i
$474$		0			0
$475$	801.412	+	3331.18i	0.0774133	+	0.321779i
$476$	−10265.7			−0.988505
$477$		0			0
$478$	629.611	−	3570.70i	0.0602463	−	0.341674i
$479$	1016.94	−	853.312i	0.0970043	−	0.0813963i	−0.592996	−	0.805206i	$-0.702055\pi$
$479$	1016.94	−	853.312i	0.0970043	−	0.0813963i	0.690000	+	0.723809i	$0.257610\pi$
$480$		0			0
$481$	−681.158	−	3863.04i	−0.0645699	−	0.366194i
$482$	661.603	+	1145.93i	0.0625212	+	0.108290i
$483$		0			0
$484$	−9465.46	−	3445.15i	−0.888942	−	0.323549i
$485$	−11084.8	−	4034.53i	−1.03780	−	0.377729i
$486$		0			0
$487$	−2868.50	−	4968.38i	−0.266907	−	0.462297i	0.701154	−	0.713010i	$-0.252668\pi$
$487$	−2868.50	−	4968.38i	−0.266907	−	0.462297i	−0.968062	+	0.250712i	$0.919335\pi$
$488$	362.513	+	2055.92i	0.0336275	+	0.190711i
$489$		0			0
$490$	1195.05	−	1002.77i	0.110177	−	0.0924499i
$491$	−969.723	+	5499.57i	−0.0891303	+	0.505483i	0.907258	+	0.420574i	$0.138171\pi$
$491$	−969.723	+	5499.57i	−0.0891303	+	0.505483i	−0.996389	+	0.0849094i	$0.972940\pi$
$492$		0			0
$493$	11437.1			1.04483
$494$	328.912	+	496.421i	0.0299564	+	0.0452127i
$495$		0			0
$496$	−6202.12	+	2257.39i	−0.561458	+	0.204354i
$497$	456.205	−	2587.27i	0.0411742	−	0.233511i
$498$		0			0
$499$	11516.4	+	9663.44i	1.03316	+	0.866924i	0.991224	−	0.132196i	$-0.0422030\pi$
$499$	11516.4	+	9663.44i	1.03316	+	0.866924i	0.0419361	+	0.999120i	$0.486647\pi$
$500$	−1427.37	−	8095.01i	−0.127668	−	0.724040i
$501$		0			0
$502$	−1548.72	+	2682.45i	−0.137694	+	0.238494i
$503$	−16736.4	−	6091.54i	−1.48358	−	0.539977i	−0.531826	−	0.846854i	$-0.678494\pi$
$503$	−16736.4	−	6091.54i	−1.48358	−	0.539977i	−0.951749	+	0.306877i	$0.900716\pi$
$504$		0			0
$505$	−5953.76	+	10312.2i	−0.524631	+	0.908688i
$506$	−0.706438	−	1.22359i	−6.20652e−5	−	0.000107500i
$507$		0			0
$508$	−5294.66	−	4442.75i	−0.462426	−	0.388022i
$509$	−11901.9	+	9986.84i	−1.03643	+	0.869664i	−0.991601	−	0.129331i	$-0.958717\pi$
$509$	−11901.9	+	9986.84i	−1.03643	+	0.869664i	−0.0448237	+	0.998995i	$0.514273\pi$
$510$		0			0
$511$	−6506.48	+	2368.16i	−0.563267	+	0.205013i
$512$	10341.9			0.892682
$513$		0			0
$514$	−1478.82			−0.126902
$515$	6735.26	−	2451.43i	0.576293	−	0.209753i
$516$		0			0
$517$	734.110	−	615.992i	0.0624490	−	0.0524009i
$518$	−1922.75	−	1613.38i	−0.163090	−	0.136849i
$519$		0			0
$520$	724.342	+	1254.60i	0.0610856	+	0.105803i
$521$	−8352.57	+	14467.1i	−0.702366	+	1.21653i	0.265267	+	0.964175i	$0.414540\pi$
$521$	−8352.57	+	14467.1i	−0.702366	+	1.21653i	−0.967634	+	0.252359i	$0.918793\pi$
$522$		0			0
$523$	−13397.9	−	4876.42i	−1.12017	−	0.407707i	−0.285454	−	0.958393i	$-0.592144\pi$
$523$	−13397.9	−	4876.42i	−1.12017	−	0.407707i	−0.834713	+	0.550685i	$0.814366\pi$
$524$	−4438.49	+	7687.69i	−0.370031	+	0.640913i
$525$		0			0
$526$	−526.494	−	2985.90i	−0.0436430	−	0.247512i
$527$	−10217.8	−	8573.72i	−0.844578	−	0.708685i
$528$		0			0
$529$	−2112.68	+	11981.6i	−0.173640	+	0.984761i
$530$	2384.31	−	867.819i	0.195411	−	0.0711239i
$531$		0			0
$532$	−7331.26	−	2167.84i	−0.597463	−	0.176669i
$533$	−1157.64			−0.0940769
$534$		0			0
$535$	−1772.75	+	10053.7i	−0.143257	+	0.812451i
$536$	−4007.69	+	3362.85i	−0.322959	+	0.270995i
$537$		0			0
$538$	−667.068	−	3783.13i	−0.0534560	−	0.303164i
$539$	296.459	+	513.481i	0.0236909	+	0.0410338i
$540$		0			0
$541$	6774.12	+	2465.58i	0.538341	+	0.195940i	0.596859	−	0.802346i	$-0.296415\pi$
$541$	6774.12	+	2465.58i	0.538341	+	0.195940i	−0.0585180	+	0.998286i	$0.518638\pi$
$542$	2225.50	+	810.015i	0.176371	+	0.0641940i
$543$		0			0
$544$	6167.90	+	10683.1i	0.486115	+	0.841976i
$545$	−347.081	−	1968.39i	−0.0272795	−	0.154710i
$546$		0			0
$547$	−8186.46	+	6869.25i	−0.639904	+	0.536943i	−0.903989	−	0.427556i	$-0.859375\pi$
$547$	−8186.46	+	6869.25i	−0.639904	+	0.536943i	0.264085	+	0.964500i	$0.414930\pi$
$548$	−2581.07	+	14638.0i	−0.201201	+	1.14107i
$549$		0			0
$550$	77.0265			0.00597167
$551$	8167.78	+	2415.20i	0.631504	+	0.186735i
$552$		0			0
$553$	12174.5	−	4431.16i	0.936189	−	0.340745i
$554$	−165.620	+	939.276i	−0.0127013	+	0.0720325i
$555$		0			0
$556$	3866.47	+	3244.36i	0.294919	+	0.247466i
$557$	−2230.14	−	12647.7i	−0.169648	−	0.962121i	−0.944142	−	0.329540i	$-0.893106\pi$
$557$	−2230.14	−	12647.7i	−0.169648	−	0.962121i	0.774494	−	0.632581i	$-0.218005\pi$
$558$		0			0
$559$	671.021	−	1162.24i	0.0507713	−	0.0879385i
$560$	−8079.77	−	2940.80i	−0.609701	−	0.221913i
$561$		0			0
$562$	1715.29	−	2970.97i	0.128746	−	0.222995i
$563$	1629.61	+	2822.57i	0.121989	+	0.211291i	0.920552	−	0.390620i	$-0.127739\pi$
$563$	1629.61	+	2822.57i	0.121989	+	0.211291i	−0.798563	+	0.601911i	$0.794406\pi$
$564$		0			0
$565$	−20876.1	−	17517.1i	−1.55445	−	1.30434i
$566$	3763.08	−	3157.60i	0.279460	−	0.234494i
$567$		0			0
$568$	−1961.81	+	714.040i	−0.144922	+	0.0527473i
$569$	16891.2			1.24449			0.622246	−	0.782822i	$-0.286220\pi$
$569$	16891.2			1.24449			0.622246	+	0.782822i	$0.286220\pi$
$570$		0			0
$571$	15460.8			1.13312			0.566561	−	0.824020i	$-0.308274\pi$
$571$	15460.8			1.13312			0.566561	+	0.824020i	$0.308274\pi$
$572$	−252.406	+	91.8684i	−0.0184504	+	0.00671541i
$573$		0			0
$574$	−567.438	+	476.137i	−0.0412620	+	0.0346229i
$575$	24.0485	+	20.1791i	0.00174416	+	0.00146352i
$576$		0			0
$577$	2533.17	+	4387.58i	0.182768	+	0.316564i	0.942822	−	0.333296i	$-0.108161\pi$
$577$	2533.17	+	4387.58i	0.182768	+	0.316564i	−0.760054	+	0.649860i	$0.774828\pi$
$578$	−2297.00	+	3978.52i	−0.165299	+	0.286306i
$579$		0			0
$580$	9498.72	+	3457.25i	0.680022	+	0.247508i
$581$	−3822.63	+	6620.99i	−0.272959	+	0.472779i
$582$		0			0
$583$	167.459	+	949.708i	0.0118961	+	0.0674664i
$584$	4214.97	+	3536.78i	0.298659	+	0.250605i
$585$		0			0
$586$	267.073	−	1514.64i	0.0188271	−	0.106774i
$587$	8754.32	−	3186.31i	0.615553	−	0.224043i	−0.0153783	−	0.999882i	$-0.504895\pi$
$587$	8754.32	−	3186.31i	0.615553	−	0.224043i	0.630931	+	0.775839i	$0.282673\pi$
$588$		0			0
$589$	−5486.46	−	8280.63i	−0.383813	−	0.579282i
$590$	−1907.14			−0.133078
$591$		0			0
$592$	3212.68	−	18220.0i	0.223041	−	1.26493i
$593$	14921.0	−	12520.2i	1.03328	−	0.867023i	0.0420405	−	0.999116i	$-0.486614\pi$
$593$	14921.0	−	12520.2i	1.03328	−	0.867023i	0.991237	+	0.132093i	$0.0421697\pi$
$594$		0			0
$595$	−3017.39	−	17112.4i	−0.207900	−	1.17906i
$596$	10731.5	+	18587.6i	0.737552	+	1.27748i
$597$		0			0
$598$	5.12725	+	1.86617i	0.000350617	+	0.000127614i
$599$	17719.7	+	6449.44i	1.20869	+	0.439928i	0.866250	−	0.499611i	$-0.166524\pi$
$599$	17719.7	+	6449.44i	1.20869	+	0.439928i	0.342442	+	0.939539i	$0.388746\pi$
$600$		0			0
$601$	−11107.6	−	19239.0i	−0.753893	−	1.30578i	−0.945923	−	0.324392i	$-0.894840\pi$
$601$	−11107.6	−	19239.0i	−0.753893	−	1.30578i	0.192030	−	0.981389i	$-0.438493\pi$
$602$	−149.117	−	845.685i	−0.0100956	−	0.0572550i
$603$		0			0
$604$	−15432.4	+	12949.3i	−1.03963	+	0.872351i
$605$	2960.72	−	16791.1i	0.198959	−	1.12835i
$606$		0			0
$607$	19595.4			1.31030			0.655152	−	0.755498i	$-0.272605\pi$
$607$	19595.4			1.31030			0.655152	+	0.755498i	$0.272605\pi$
$608$	2148.81	+	8931.83i	0.143332	+	0.595779i
$609$		0			0
$610$	−1619.91	+	589.599i	−0.107522	+	0.0391347i
$611$	−642.647	+	3644.63i	−0.0425511	+	0.241319i
$612$		0			0
$613$	2574.00	+	2159.84i	0.169597	+	0.142309i	0.723636	−	0.690182i	$-0.242470\pi$
$613$	2574.00	+	2159.84i	0.169597	+	0.142309i	−0.554039	+	0.832491i	$0.686914\pi$
$614$	−821.071	−	4656.53i	−0.0539670	−	0.306062i
$615$		0			0
$616$	−176.155	+	305.110i	−0.0115219	+	0.0199565i
$617$	−1847.15	−	672.308i	−0.120524	−	0.0438673i	0.281054	−	0.959692i	$-0.409316\pi$
$617$	−1847.15	−	672.308i	−0.120524	−	0.0438673i	−0.401578	+	0.915825i	$0.631538\pi$
$618$		0			0
$619$	−5645.08	+	9777.57i	−0.366551	+	0.634885i	−0.989024	−	0.147756i	$-0.952795\pi$
$619$	−5645.08	+	9777.57i	−0.366551	+	0.634885i	0.622473	+	0.782641i	$0.286128\pi$
$620$	−5894.35	−	10209.3i	−0.381811	−	0.661316i
$621$		0			0
$622$	−4642.98	−	3895.92i	−0.299303	−	0.251145i
$623$	−1252.41	+	1050.89i	−0.0805403	+	0.0675813i
$624$		0			0
$625$	17933.8	−	6527.38i	1.14776	−	0.417752i
$626$	478.794			0.0305694
$627$		0			0
$628$	24720.2			1.57077
$629$	35134.3	−	12787.8i	2.22718	−	0.810627i
$630$		0			0
$631$	15372.7	−	12899.3i	0.969856	−	0.813805i	−0.0126725	−	0.999920i	$-0.504034\pi$
$631$	15372.7	−	12899.3i	0.969856	−	0.813805i	0.982528	+	0.186114i	$0.0595895\pi$
$632$	−7886.79	−	6617.80i	−0.496392	−	0.416522i
$633$		0			0
$634$	1816.49	+	3146.26i	0.113789	+	0.197088i
$635$	5849.59	−	10131.8i	0.365565	−	0.633177i
$636$		0			0
$637$	−2151.66	−	783.142i	−0.133834	−	0.0487115i
$638$	95.7416	−	165.829i	0.00594114	−	0.0102904i
$639$		0			0
$640$	2500.89	+	14183.3i	0.154463	+	0.876005i
$641$	−8476.56	−	7112.68i	−0.522315	−	0.438274i	0.343123	−	0.939290i	$-0.388515\pi$
$641$	−8476.56	−	7112.68i	−0.522315	−	0.438274i	−0.865438	+	0.501016i	$0.832960\pi$
$642$		0			0
$643$	48.8915	−	277.278i	0.00299859	−	0.0170059i	−0.983272	−	0.182145i	$-0.941696\pi$
$643$	48.8915	−	277.278i	0.00299859	−	0.0170059i	0.986270	+	0.165139i	$0.0528072\pi$
$644$	−65.8241	+	23.9580i	−0.00402769	+	0.00146596i
$645$		0			0
$646$	−4115.43	+	3909.10i	−0.250649	+	0.238083i
$647$	−7004.52			−0.425620			−0.212810	−	0.977094i	$-0.568262\pi$
$647$	−7004.52			−0.425620			−0.212810	+	0.977094i	$0.568262\pi$
$648$		0			0
$649$	125.868	−	713.831i	0.00761285	−	0.0431746i
$650$	−227.871	+	191.206i	−0.0137505	+	0.0115380i
$651$		0			0
$652$	2372.22	+	13453.5i	0.142490	+	0.808099i
$653$	6500.76	+	11259.6i	0.389578	+	0.674769i	0.992393	−	0.123112i	$-0.0392875\pi$
$653$	6500.76	+	11259.6i	0.389578	+	0.674769i	−0.602815	+	0.797881i	$0.705954\pi$
$654$		0			0
$655$	−14119.6	−	5139.11i	−0.842287	−	0.306568i
$656$	−5130.74	−	1867.44i	−0.305368	−	0.111145i
$657$		0			0
$658$	1184.03	+	2050.80i	0.0701494	+	0.121502i
$659$	3328.33	+	18875.9i	0.196743	+	1.11578i	0.909915	+	0.414794i	$0.136146\pi$
$659$	3328.33	+	18875.9i	0.196743	+	1.11578i	−0.713173	+	0.700988i	$0.752742\pi$
$660$		0			0
$661$	5904.72	−	4954.65i	0.347454	−	0.291548i	−0.452313	−	0.891859i	$-0.649401\pi$
$661$	5904.72	−	4954.65i	0.347454	−	0.291548i	0.799767	+	0.600311i	$0.204957\pi$
$662$	309.075	−	1752.85i	0.0181458	−	0.102910i
$663$		0			0
$664$	6075.37			0.355076
$665$	1458.83	−	12858.0i	0.0850689	−	0.749794i
$666$		0			0
$667$	73.3349	−	26.6917i	0.00425718	−	0.00154949i
$668$	−1318.13	+	7475.47i	−0.0763471	+	0.432986i
$669$		0			0
$670$	−3309.37	−	2776.89i	−0.190824	−	0.160120i
$671$	−113.772	−	645.234i	−0.00654564	−	0.0371222i
$672$		0			0
$673$	−8919.11	+	15448.4i	−0.510856	+	0.884829i	0.489064	+	0.872248i	$0.337338\pi$
$673$	−8919.11	+	15448.4i	−0.510856	+	0.884829i	−0.999921	+	0.0125817i	$0.995995\pi$
$674$	3006.85	+	1094.40i	0.171839	+	0.0625443i
$675$		0			0
$676$	−7852.13	+	13600.3i	−0.446753	+	0.773799i
$677$	−14375.0	−	24898.3i	−0.816068	−	1.41347i	−0.908559	−	0.417758i	$-0.862816\pi$
$677$	−14375.0	−	24898.3i	−0.816068	−	1.41347i	0.0924905	−	0.995714i	$-0.470517\pi$
$678$		0			0
$679$	8486.75	+	7121.23i	0.479664	+	0.402485i
$680$	−10577.8	+	8875.83i	−0.596530	+	0.500548i
$681$		0			0
$682$	−209.847	+	76.3781i	−0.0117822	+	0.00428837i
$683$	10050.8			0.563082			0.281541	−	0.959549i	$-0.409154\pi$
$683$	10050.8			0.563082			0.281541	+	0.959549i	$0.409154\pi$
$684$		0			0
$685$	−25159.5			−1.40335
$686$	−3783.04	+	1376.91i	−0.210550	+	0.0766338i
$687$		0			0
$688$	4848.87	−	4068.69i	0.268694	−	0.225461i
$689$	−2852.90	−	2393.87i	−0.157746	−	0.132365i
$690$		0			0
$691$	−804.246	−	1392.99i	−0.0442763	−	0.0766889i	0.843038	−	0.537854i	$-0.180765\pi$
$691$	−804.246	−	1392.99i	−0.0442763	−	0.0766889i	−0.887314	+	0.461165i	$0.847432\pi$
$692$	−2764.59	+	4788.41i	−0.151870	+	0.263046i
$693$		0			0
$694$	5487.38	+	1997.24i	0.300141	+	0.109243i
$695$	−4271.71	+	7398.82i	−0.233144	+	0.403818i
$696$		0			0
$697$	−1916.07	−	10866.6i	−0.104127	−	0.590532i
$698$	−1685.67	−	1414.45i	−0.0914092	−	0.0767014i
$699$		0			0
$700$	663.141	−	3760.86i	0.0358062	−	0.203067i
$701$	7962.00	−	2897.93i	0.428988	−	0.156139i	−0.118497	−	0.992954i	$-0.537808\pi$
$701$	7962.00	−	2897.93i	0.428988	−	0.156139i	0.547485	+	0.836816i	$0.315585\pi$
$702$		0			0
$703$	27791.6	−	1713.00i	1.49101	−	0.0919020i
$704$	−1123.49			−0.0601466
$705$		0			0
$706$	−837.330	+	4748.74i	−0.0446365	+	0.253146i
$707$	8566.86	−	7188.45i	0.455714	−	0.382389i
$708$		0			0
$709$	2084.94	+	11824.3i	0.110439	+	0.626334i	0.988908	+	0.148532i	$0.0474549\pi$
$709$	2084.94	+	11824.3i	0.110439	+	0.626334i	−0.878468	+	0.477801i	$0.841434\pi$
$710$	−861.969	−	1492.97i	−0.0455621	−	0.0789159i
$711$		0			0
$712$	1220.84	+	444.349i	0.0642596	+	0.0233886i
$713$	−85.5258	−	31.1289i	−0.00449224	−	0.00163504i
$714$		0			0
$715$	−227.329	−	393.746i	−0.0118904	−	0.0205948i
$716$	−5416.70	−	30719.6i	−0.282726	−	1.60342i
$717$		0			0
$718$	702.063	−	589.101i	0.0364913	−	0.0306198i
$719$	1451.70	−	8232.99i	0.0752979	−	0.427036i	−0.923734	−	0.383036i	$-0.874879\pi$
$719$	1451.70	−	8232.99i	0.0752979	−	0.427036i	0.999032	−	0.0440002i	$-0.0140102\pi$
$720$		0			0
$721$	−6731.54			−0.347706
$722$	−3764.53	+	1922.61i	−0.194046	+	0.0991027i
$723$		0			0
$724$	11398.8	−	4148.81i	0.585127	−	0.212969i
$725$	−738.807	+	4189.98i	−0.0378464	+	0.214637i
$726$		0			0
$727$	−6692.93	−	5616.04i	−0.341440	−	0.286503i	0.455902	−	0.890030i	$-0.349317\pi$
$727$	−6692.93	−	5616.04i	−0.341440	−	0.286503i	−0.797342	+	0.603528i	$0.793761\pi$
$728$	−236.260	−	1339.90i	−0.0120280	−	0.0682142i
$729$		0			0
$730$	−2271.76	+	3934.80i	−0.115180	+	0.199498i
$731$	12020.4	+	4375.08i	0.608196	+	0.221365i
$732$		0			0
$733$	7562.34	−	13098.4i	0.381066	−	0.660026i	−0.610149	−	0.792287i	$-0.708890\pi$
$733$	7562.34	−	13098.4i	0.381066	−	0.660026i	0.991215	+	0.132261i	$0.0422237\pi$
$734$	2773.51	+	4803.86i	0.139472	+	0.241572i
$735$		0			0
$736$	64.4809	+	54.1059i	0.00322934	+	0.00270974i
$737$	1257.78	−	1055.41i	0.0628644	−	0.0527495i
$738$		0			0
$739$	11061.1	−	4025.92i	0.550595	−	0.200400i	−0.0517157	−	0.998662i	$-0.516469\pi$
$739$	11061.1	−	4025.92i	0.550595	−	0.200400i	0.602311	+	0.798262i	$0.294247\pi$
$740$	33045.3			1.64158
$741$		0			0
$742$	−2383.00			−0.117901
$743$	−19928.4	+	7253.34i	−0.983986	+	0.358141i	−0.783389	−	0.621532i	$-0.786510\pi$
$743$	−19928.4	+	7253.34i	−0.983986	+	0.358141i	−0.200597	+	0.979674i	$0.564288\pi$
$744$		0			0
$745$	−27830.2	+	23352.3i	−1.36862	+	1.14841i
$746$	4458.40	+	3741.05i	0.218812	+	0.183605i
$747$		0			0
$748$	−1280.13	−	2217.24i	−0.0625749	−	0.108383i
$749$	4793.94	−	8303.35i	0.233868	−	0.405071i
$750$		0			0
$751$	8646.44	+	3147.05i	0.420124	+	0.152913i	0.543427	−	0.839456i	$-0.317126\pi$
$751$	8646.44	+	3147.05i	0.420124	+	0.152913i	−0.123303	+	0.992369i	$0.539349\pi$
$752$	−8727.55	+	15116.6i	−0.423219	+	0.733038i
$753$		0			0
$754$	128.409	+	728.244i	0.00620210	+	0.0351738i
$755$	−26121.9	−	21918.9i	−1.25917	−	1.05657i
$756$		0			0
$757$	3520.89	−	19968.0i	0.169048	−	0.958716i	−0.775745	−	0.631047i	$-0.782626\pi$
$757$	3520.89	−	19968.0i	0.169048	−	0.958716i	0.944792	−	0.327669i	$-0.106263\pi$
$758$	2312.23	−	841.583i	0.110797	−	0.0403267i
$759$		0			0
$760$	−9428.47	+	4104.92i	−0.450008	+	0.195922i
$761$	28177.3			1.34222			0.671109	−	0.741359i	$-0.265818\pi$
$761$	28177.3			1.34222			0.671109	+	0.741359i	$0.265818\pi$
$762$		0			0
$763$	−325.970	+	1848.67i	−0.0154664	+	0.0877145i
$764$	−11604.1	+	9736.97i	−0.549503	+	0.461088i
$765$		0			0
$766$	−116.517	−	660.803i	−0.00549601	−	0.0311694i
$767$	1399.62	+	2424.20i	0.0658894	+	0.114124i
$768$		0			0
$769$	−2435.90	−	886.596i	−0.114227	−	0.0415754i	0.284274	−	0.958743i	$-0.408247\pi$
$769$	−2435.90	−	886.596i	−0.114227	−	0.0415754i	−0.398502	+	0.917168i	$0.630470\pi$
$770$	−273.377	−	99.5011i	−0.0127946	−	0.00465685i
$771$		0			0
$772$	−11675.1	−	20221.9i	−0.544297	−	0.942751i
$773$	6173.55	+	35011.9i	0.287254	+	1.62910i	0.697122	+	0.716953i	$0.254464\pi$
$773$	6173.55	+	35011.9i	0.287254	+	1.62910i	−0.409868	+	0.912145i	$0.634425\pi$
$774$		0			0
$775$	3801.03	−	3189.44i	0.176177	−	0.147830i
$776$	1528.76	−	8670.01i	0.0707206	−	0.401076i
$777$		0			0
$778$	3953.60			0.182189
$779$	926.369	−	8164.98i	0.0426067	−	0.375534i
$780$		0			0
$781$	615.699	−	224.096i	0.0282093	−	0.0102673i
$782$	−9.03102	+	51.2175i	−0.000412978	+	0.00234211i
$783$		0			0
$784$	−8273.00	−	6941.87i	−0.376868	−	0.316230i
$785$	7265.95	+	41207.3i	0.330360	+	1.87357i
$786$		0			0
$787$	8614.36	−	14920.5i	0.390176	−	0.675805i	−0.602296	−	0.798273i	$-0.705747\pi$
$787$	8614.36	−	14920.5i	0.390176	−	0.675805i	0.992473	+	0.122468i	$0.0390808\pi$
$788$	5452.45	+	1984.53i	0.246492	+	0.0897156i
$789$		0			0
$790$	4250.77	−	7362.54i	0.191437	−	0.331579i
$791$	12797.1	+	22165.2i	0.575237	+	0.996340i
$792$		0			0
$793$	1938.27	+	1626.40i	0.0867970	+	0.0728313i
$794$	1379.26	−	1157.34i	0.0616477	−	0.0517285i
$795$		0			0
$796$	−5625.61	+	2047.56i	−0.250496	+	0.0911729i
$797$	−37056.2			−1.64692			−0.823462	−	0.567372i	$-0.807960\pi$
$797$	−37056.2			−1.64692			−0.823462	+	0.567372i	$0.807960\pi$
$798$		0			0
$799$	−35275.2			−1.56189
$800$	−4312.20	+	1569.51i	−0.190574	+	0.0693633i
$801$		0			0
$802$	−234.411	+	196.694i	−0.0103209	+	0.00866024i
$803$	−1322.84	−	1109.99i	−0.0581345	−	0.0487806i
$804$		0			0
$805$	−59.2844	−	102.684i	−0.00259565	−	0.00449580i
$806$	431.203	−	746.866i	0.0188443	−	0.0326392i
$807$		0			0
$808$	−8350.92	−	3039.49i	−0.363594	−	0.132338i
$809$	−4629.34	+	8018.25i	−0.201185	+	0.348463i	−0.948911	−	0.315545i	$-0.897813\pi$
$809$	−4629.34	+	8018.25i	−0.201185	+	0.348463i	0.747725	+	0.664008i	$0.231146\pi$
$810$		0			0
$811$	4355.71	+	24702.4i	0.188594	+	1.06957i	0.921251	+	0.388970i	$0.127169\pi$
$811$	4355.71	+	24702.4i	0.188594	+	1.06957i	−0.732657	+	0.680598i	$0.761720\pi$
$812$	−7272.44	−	6102.30i	−0.314301	−	0.263730i
$813$		0			0
$814$	108.700	−	616.471i	0.00468053	−	0.0265446i
$815$	−21729.1	+	7908.74i	−0.933910	+	0.339915i
$816$		0			0
$817$	7660.48	+	5662.85i	0.328037	+	0.242495i
$818$	−6897.32			−0.294816
$819$		0			0
$820$	1693.46	−	9604.12i	0.0721199	−	0.409013i
$821$	−2608.44	+	2188.74i	−0.110883	+	0.0930421i	−0.696544	−	0.717515i	$-0.745280\pi$
$821$	−2608.44	+	2188.74i	−0.110883	+	0.0930421i	0.585660	+	0.810557i	$0.300835\pi$
$822$		0			0
$823$	−1245.99	−	7066.38i	−0.0527735	−	0.299293i	0.946985	−	0.321278i	$-0.104113\pi$
$823$	−1245.99	−	7066.38i	−0.0527735	−	0.299293i	−0.999758	+	0.0219849i	$0.993001\pi$
$824$	2674.64	+	4632.61i	0.113077	+	0.195855i
$825$		0			0
$826$	1683.12	+	612.606i	0.0708998	+	0.0258054i
$827$	−25419.9	−	9252.10i	−1.06885	−	0.389029i	−0.253103	−	0.967439i	$-0.581451\pi$
$827$	−25419.9	−	9252.10i	−1.06885	−	0.389029i	−0.815746	+	0.578410i	$0.803673\pi$
$828$		0			0
$829$	21727.6	+	37633.3i	0.910290	+	1.57667i	0.813655	+	0.581348i	$0.197475\pi$
$829$	21727.6	+	37633.3i	0.910290	+	1.57667i	0.0966351	+	0.995320i	$0.469192\pi$
$830$	871.152	+	4940.55i	0.0364315	+	0.206613i
$831$		0			0
$832$	3323.67	−	2788.89i	0.138495	−	0.116211i
$833$	3789.89	−	21493.5i	0.157637	−	0.894006i
$834$		0			0
$835$	−12848.7			−0.532511
$836$	−445.978	−	1853.77i	−0.0184503	−	0.0766913i
$837$		0			0
$838$	−8295.45	+	3019.30i	−0.341959	+	0.124463i
$839$	−498.954	+	2829.71i	−0.0205314	+	0.116439i	−0.993351	−	0.115125i	$-0.963273\pi$
$839$	−498.954	+	2829.71i	−0.0205314	+	0.116439i	0.972820	+	0.231564i	$0.0743843\pi$
$840$		0			0
$841$	−10580.8	−	8878.36i	−0.433836	−	0.364031i
$842$	−834.925	−	4735.10i	−0.0341727	−	0.193803i
$843$		0			0
$844$	−1885.82	+	3266.34i	−0.0769108	+	0.133213i
$845$	−24979.0	−	9091.60i	−1.01693	−	0.370131i
$846$		0			0
$847$	−8006.51	+	13867.7i	−0.324802	+	0.562573i
$848$	−8782.61	−	15211.9i	−0.355656	−	0.616014i
$849$		0			0
$850$	−2171.98	−	1822.51i	−0.0876452	−	0.0735431i
$851$	195.438	−	163.992i	0.00787254	−	0.00660584i
$852$		0			0
$853$	−27332.6	+	9948.26i	−1.09713	+	0.399322i	−0.826257	−	0.563293i	$-0.809534\pi$
$853$	−27332.6	+	9948.26i	−1.09713	+	0.399322i	−0.270872	+	0.962615i	$0.587312\pi$
$854$	1619.02			0.0648731
$855$		0			0
$856$	−7619.10			−0.304224
$857$	726.682	−	264.491i	0.0289650	−	0.0105424i	−0.327497	−	0.944852i	$-0.606205\pi$
$857$	726.682	−	264.491i	0.0289650	−	0.0105424i	0.356462	+	0.934310i	$0.383983\pi$
$858$		0			0
$859$	−4509.12	+	3783.60i	−0.179103	+	0.150285i	−0.727932	−	0.685650i	$-0.759518\pi$
$859$	−4509.12	+	3783.60i	−0.179103	+	0.150285i	0.548829	+	0.835935i	$0.315074\pi$
$860$	8660.69	+	7267.18i	0.343404	+	0.288150i
$861$		0			0
$862$	−3223.42	−	5583.13i	−0.127367	−	0.220606i
$863$	−21404.1	+	37073.1i	−0.844270	+	1.46232i	0.0419828	+	0.999118i	$0.486633\pi$
$863$	−21404.1	+	37073.1i	−0.844270	+	1.46232i	−0.886253	+	0.463201i	$0.846701\pi$
$864$		0			0
$865$	−8794.63	−	3200.98i	−0.345695	−	0.125823i
$866$	−1459.49	+	2527.91i	−0.0572696	+	0.0991938i
$867$		0			0
$868$	1922.57	+	10903.5i	0.0751802	+	0.426368i
$869$	2475.21	+	2076.95i	0.0966235	+	0.0810767i
$870$		0			0
$871$	−1101.08	+	6244.51i	−0.0428341	+	0.242924i
$872$	1401.76	−	510.199i	0.0544376	−	0.0198137i
$873$		0			0
$874$	−17.2652	+	34.6698i	−0.000668199	+	0.00134179i
$875$	−13067.2			−0.504861
$876$		0			0
$877$	−5151.11	+	29213.4i	−0.198336	+	1.12482i	0.709251	+	0.704956i	$0.249033\pi$
$877$	−5151.11	+	29213.4i	−0.198336	+	1.12482i	−0.907587	+	0.419864i	$0.862078\pi$
$878$	6647.63	−	5578.02i	0.255520	−	0.214407i
$879$		0			0
$880$	−372.371	−	2111.82i	−0.0142644	−	0.0808972i
$881$	−7051.37	−	12213.3i	−0.269656	−	0.467057i	0.699117	−	0.715007i	$-0.253577\pi$
$881$	−7051.37	−	12213.3i	−0.269656	−	0.467057i	−0.968773	+	0.247950i	$0.920243\pi$
$882$		0			0
$883$	27450.7	+	9991.24i	1.04619	+	0.380784i	0.807225	−	0.590244i	$-0.200968\pi$
$883$	27450.7	+	9991.24i	1.04619	+	0.380784i	0.238969	+	0.971027i	$0.423191\pi$
$884$	9291.01	+	3381.65i	0.353496	+	0.128662i
$885$		0			0
$886$	131.822	+	228.322i	0.00499847	+	0.00865760i
$887$	−4168.15	−	23638.8i	−0.157782	−	0.894828i	−0.956198	−	0.292721i	$-0.905439\pi$
$887$	−4168.15	−	23638.8i	−0.157782	−	0.894828i	0.798416	−	0.602107i	$-0.205672\pi$
$888$		0			0
$889$	−8416.97	+	7062.67i	−0.317543	+	0.266450i
$890$	−186.292	+	1056.51i	−0.00701630	+	0.0397914i
$891$		0			0
$892$	−15983.0			−0.599943
$893$	−25191.8	−	7449.18i	−0.944021	−	0.279146i
$894$		0			0
$895$	49616.0	−	18058.7i	1.85305	−	0.674455i
$896$	2348.78	−	13320.6i	0.0875749	−	0.496662i
$897$		0			0
$898$	−3343.36	−	2805.41i	−0.124242	−	0.104251i
$899$	−2141.94	−	12147.6i	−0.0794637	−	0.450661i
$900$		0			0
$901$	17748.9	−	30742.0i	0.656272	−	1.13670i
$902$	−173.597	−	63.1843i	−0.00640816	−	0.00233238i
$903$		0			0
$904$	10169.3	−	17613.8i	0.374145	−	0.648038i
$905$	10266.3	+	17781.7i	0.377086	+	0.653132i
$906$		0			0
$907$	14893.2	+	12496.9i	0.545227	+	0.457500i	0.873321	−	0.487145i	$-0.161962\pi$
$907$	14893.2	+	12496.9i	0.545227	+	0.457500i	−0.328094	+	0.944645i	$0.606406\pi$
$908$	25363.7	−	21282.7i	0.927009	−	0.777853i
$909$		0			0
$910$	1055.74	−	384.258i	0.0384587	−	0.0139978i
$911$	−29980.8			−1.09035			−0.545174	−	0.838323i	$-0.683536\pi$
$911$	−29980.8			−1.09035			−0.545174	+	0.838323i	$0.683536\pi$
$912$		0			0
$913$	−1906.71			−0.0691160
$914$	−2973.26	+	1082.18i	−0.107600	+	0.0391633i
$915$		0			0
$916$	18782.5	−	15760.4i	0.677501	−	0.568491i
$917$	10810.3	+	9070.90i	0.389299	+	0.326660i
$918$		0			0
$919$	3660.45	+	6340.09i	0.131390	+	0.227574i	0.924212	−	0.381879i	$-0.124723\pi$
$919$	3660.45	+	6340.09i	0.131390	+	0.227574i	−0.792823	+	0.609452i	$0.791389\pi$
$920$	−47.1109	+	81.5985i	−0.00168826	+	0.00292415i
$921$		0			0
$922$	10792.2	+	3928.03i	0.385489	+	0.140307i
$923$	−1265.17	+	2191.33i	−0.0451175	+	0.0781458i
$924$		0			0
$925$	2415.25	+	13697.5i	0.0858517	+	0.486889i
$926$	−1959.23	−	1643.99i	−0.0695295	−	0.0583421i
$927$		0			0
$928$	−1980.95	+	11234.5i	−0.0700732	+	0.397405i
$929$	−21706.8	+	7900.65i	−0.766608	+	0.279022i	−0.695577	−	0.718452i	$-0.744851\pi$
$929$	−21706.8	+	7900.65i	−0.766608	+	0.279022i	−0.0710309	+	0.997474i	$0.522629\pi$
$930$		0			0
$931$	7245.41	−	14549.3i	0.255058	−	0.512173i
$932$	20753.2			0.729392
$933$		0			0
$934$	−893.344	+	5066.41i	−0.0312967	+	0.177492i
$935$	3319.77	−	2785.61i	0.116115	−	0.0974325i
$936$		0			0
$937$	−80.7138	−	457.751i	−0.00281409	−	0.0159595i	0.983368	−	0.181622i	$-0.0581348\pi$
$937$	−80.7138	−	457.751i	−0.00281409	−	0.0159595i	−0.986182	+	0.165663i	$0.947024\pi$
$938$	2028.65	+	3513.73i	0.0706160	+	0.122311i
$939$		0			0
$940$	−29296.8	−	10663.2i	−1.01655	−	0.369994i
$941$	44422.4	+	16168.4i	1.53893	+	0.560123i	0.965787	−	0.259335i	$-0.0835033\pi$
$941$	44422.4	+	16168.4i	1.53893	+	0.560123i	0.573139	+	0.819458i	$0.305726\pi$
$942$		0			0
$943$	−37.6462	−	65.2051i	−0.00130003	−	0.00225172i
$944$	2292.61	+	13002.0i	0.0790444	+	0.448283i
$945$		0			0
$946$	164.060	−	137.663i	0.00563855	−	0.00473130i
$947$	2430.48	−	13783.9i	0.0834002	−	0.472986i	−0.914290	−	0.405060i	$-0.867251\pi$
$947$	2430.48	−	13783.9i	0.0834002	−	0.472986i	0.997690	−	0.0679260i	$-0.0216382\pi$
$948$		0			0
$949$	6668.80			0.228112
$950$	−1166.25	−	1760.21i	−0.0398298	−	0.0601144i
$951$		0			0
$952$	12186.4	−	4435.47i	0.414876	−	0.151003i
$953$	−9809.88	+	55634.6i	−0.333445	+	1.89106i	0.108629	+	0.994082i	$0.465354\pi$
$953$	−9809.88	+	55634.6i	−0.333445	+	1.89106i	−0.442074	+	0.896979i	$0.645757\pi$
$954$		0			0
$955$	−19641.8	−	16481.4i	−0.665544	−	0.558457i
$956$	−7785.03	−	44151.1i	−0.263374	−	1.49367i
$957$		0			0
$958$	−409.062	+	708.515i	−0.0137956	+	0.0238947i
$959$	22204.1	+	8081.64i	0.747663	+	0.272127i
$960$		0			0
$961$	7702.75	−	13341.6i	0.258560	−	0.447839i
$962$	1208.72	+	2093.56i	0.0405101	+	0.0701655i
$963$		0			0
$964$	12533.4	+	10516.8i	0.418749	+	0.351372i
$965$	30277.3	−	25405.7i	1.01001	−	0.847500i
$966$		0			0
$967$	−48700.3	+	17725.5i	−1.61954	+	0.589464i	−0.983294	−	0.182022i	$-0.941736\pi$
$967$	−48700.3	+	17725.5i	−1.61954	+	0.589464i	−0.636246	+	0.771486i	$0.719514\pi$
$968$	12724.9			0.422514
$969$		0			0
$970$	7269.74			0.240636
$971$	−8713.88	+	3171.59i	−0.287994	+	0.104821i	−0.481977	−	0.876184i	$-0.660081\pi$
$971$	−8713.88	+	3171.59i	−0.287994	+	0.104821i	0.193984	+	0.981005i	$0.437859\pi$
$972$		0			0
$973$	6146.57	−	5157.58i	0.202518	−	0.169933i
$974$	2708.42	+	2272.64i	0.0891000	+	0.0747638i
$975$		0			0
$976$	5966.93	+	10335.0i	0.195693	+	0.338951i
$977$	13524.1	−	23424.5i	0.442860	−	0.767057i	−0.555040	−	0.831824i	$-0.687297\pi$
$977$	13524.1	−	23424.5i	0.442860	−	0.767057i	0.997900	+	0.0647668i	$0.0206304\pi$
$978$		0			0
$979$	−383.151	−	139.456i	−0.0125082	−	0.00455262i
$980$	9644.75	−	16705.2i	0.314378	−	0.544518i
$981$		0			0
$982$	−597.621	−	3389.28i	−0.0194204	−	0.110139i
$983$	24968.0	+	20950.6i	0.810127	+	0.679777i	0.950638	−	0.310302i	$-0.100430\pi$
$983$	24968.0	+	20950.6i	0.810127	+	0.679777i	−0.140511	+	0.990079i	$0.544875\pi$
$984$		0			0
$985$	−1705.48	+	9672.27i	−0.0551687	+	0.312877i
$986$	−6623.37	+	2410.71i	−0.213926	+	0.0778627i
$987$		0			0
$988$	5921.05	+	4377.01i	0.190662	+	0.140943i
$989$	87.2859			0.00280640
$990$		0			0
$991$	8237.76	−	46718.7i	0.264058	−	1.49755i	−0.507648	−	0.861565i	$-0.669485\pi$
$991$	8237.76	−	46718.7i	0.264058	−	1.49755i	0.771705	−	0.635980i	$-0.219404\pi$
$992$	10191.6	−	8551.81i	0.326195	−	0.273710i
$993$		0			0
$994$	281.150	+	1594.48i	0.00897137	+	0.0508792i
$995$	−5066.70	−	8775.78i	−0.161432	−	0.279609i
$996$		0			0
$997$	1302.66	+	474.129i	0.0413797	+	0.0150610i	0.362627	−	0.931934i	$-0.381880\pi$
$997$	1302.66	+	474.129i	0.0413797	+	0.0150610i	−0.321247	+	0.946995i	$0.604102\pi$
$998$	−8706.19	−	3168.80i	−0.276142	−	0.100507i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.u.b.100.2		24
3.2	odd	2		19.4.e.a.5.3	yes	24
19.4	even	9	inner	171.4.u.b.118.2		24
57.2	even	18		361.4.a.m.1.7		12
57.17	odd	18		361.4.a.n.1.6		12
57.23	odd	18		19.4.e.a.4.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.e.a.4.3	✓	24	57.23	odd	18
19.4.e.a.5.3	yes	24	3.2	odd	2
171.4.u.b.100.2		24	1.1	even	1	trivial
171.4.u.b.118.2		24	19.4	even	9	inner
361.4.a.m.1.7		12	57.2	even	18
361.4.a.n.1.6		12	57.17	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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.579114 + 0.210780i) q^{2} +(-5.83741 + 4.89817i) q^{4} +(-9.88078 - 8.29096i) q^{5} +(6.05695 + 10.4909i) q^{7} +(4.81321 - 8.33672i) q^{8} +O(q^{10})\)	\(q+(-0.579114 + 0.210780i) q^{2} +(-5.83741 + 4.89817i) q^{4} +(-9.88078 - 8.29096i) q^{5} +(6.05695 + 10.4909i) q^{7} +(4.81321 - 8.33672i) q^{8} +(7.46967 + 2.71874i) q^{10} +(-1.51059 + 2.61642i) q^{11} +(-2.02601 - 11.4901i) q^{13} +(-5.71895 - 4.79877i) q^{14} +(9.55569 - 54.1930i) q^{16} +(104.502 - 38.0357i) q^{17} +(82.6622 - 5.09509i) q^{19} +98.2887 q^{20} +(0.323315 - 1.83361i) q^{22} +(0.581304 - 0.487772i) q^{23} +(7.18382 + 40.7415i) q^{25} +(3.59517 + 6.22702i) q^{26} +(-86.7433 - 31.5720i) q^{28} +(96.6410 + 35.1745i) q^{29} +(-59.9698 - 103.871i) q^{31} +(19.2619 + 109.239i) q^{32} +(-52.5015 + 44.0540i) q^{34} +(27.1326 - 153.877i) q^{35} +336.206 q^{37} +(-46.7969 + 20.3742i) q^{38} +(-116.678 + 42.4672i) q^{40} +(17.2295 - 97.7133i) q^{41} +(88.1148 + 73.9371i) q^{43} +(-3.99773 - 22.6722i) q^{44} +(-0.233828 + 0.405003i) q^{46} +(-298.069 - 108.488i) q^{47} +(98.1267 - 169.960i) q^{49} +(-12.7477 - 22.0797i) q^{50} +(68.1070 + 57.1486i) q^{52} +(244.521 - 205.177i) q^{53} +(36.6185 - 13.3280i) q^{55} +116.613 q^{56} -63.3802 q^{58} +(-225.451 + 82.0576i) q^{59} +(-166.128 + 139.398i) q^{61} +(56.6232 + 47.5125i) q^{62} +(185.936 + 322.050i) q^{64} +(-75.2452 + 130.329i) q^{65} +(-510.695 - 185.878i) q^{67} +(-423.717 + 733.899i) q^{68} +(16.7213 + 94.8312i) q^{70} +(-166.135 - 139.403i) q^{71} +(-99.2537 + 562.895i) q^{73} +(-194.702 + 70.8657i) q^{74} +(-457.577 + 434.636i) q^{76} -36.5983 q^{77} +(185.717 - 1053.25i) q^{79} +(-543.730 + 456.244i) q^{80} +(10.6182 + 60.2188i) q^{82} +(315.557 + 546.561i) q^{83} +(-1347.92 - 490.601i) q^{85} +(-66.6130 - 24.2451i) q^{86} +(14.5416 + 25.1868i) q^{88} +(23.4357 + 132.910i) q^{89} +(108.270 - 90.8496i) q^{91} +(-1.00412 + 5.69465i) q^{92} +195.483 q^{94} +(-859.011 - 635.006i) q^{95} +(859.388 - 312.792i) q^{97} +(-21.0022 + 119.110i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) \) 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8} + 75 q^{10} - 39 q^{11} - 156 q^{13} - 93 q^{14} + 504 q^{16} - 12 q^{17} + 546 q^{19} + 198 q^{20} - 6 q^{22} - 6 q^{23} - 498 q^{25} + 639 q^{26} - 1368 q^{28} + 630 q^{29} - 591 q^{31} - 147 q^{32} - 408 q^{34} - 2001 q^{35} - 72 q^{37} - 2934 q^{38} + 2886 q^{40} + 477 q^{41} + 588 q^{43} + 3423 q^{44} - 1728 q^{46} + 1242 q^{47} - 639 q^{49} + 1788 q^{50} + 2733 q^{52} + 300 q^{53} + 315 q^{55} - 4638 q^{56} - 2820 q^{58} - 2097 q^{59} - 2316 q^{61} + 1320 q^{62} - 1785 q^{64} + 2433 q^{65} + 57 q^{67} + 438 q^{68} - 213 q^{70} + 792 q^{71} + 4068 q^{73} - 4287 q^{74} + 5538 q^{76} - 3786 q^{77} + 1824 q^{79} + 2739 q^{80} + 2205 q^{82} - 1071 q^{83} - 2394 q^{85} + 5256 q^{86} + 1101 q^{88} + 3006 q^{89} - 3285 q^{91} + 1452 q^{92} - 1086 q^{94} + 3078 q^{95} - 2535 q^{97} + 2403 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8 + 75 * q^10 - 39 * q^11 - 156 * q^13 - 93 * q^14 + 504 * q^16 - 12 * q^17 + 546 * q^19 + 198 * q^20 - 6 * q^22 - 6 * q^23 - 498 * q^25 + 639 * q^26 - 1368 * q^28 + 630 * q^29 - 591 * q^31 - 147 * q^32 - 408 * q^34 - 2001 * q^35 - 72 * q^37 - 2934 * q^38 + 2886 * q^40 + 477 * q^41 + 588 * q^43 + 3423 * q^44 - 1728 * q^46 + 1242 * q^47 - 639 * q^49 + 1788 * q^50 + 2733 * q^52 + 300 * q^53 + 315 * q^55 - 4638 * q^56 - 2820 * q^58 - 2097 * q^59 - 2316 * q^61 + 1320 * q^62 - 1785 * q^64 + 2433 * q^65 + 57 * q^67 + 438 * q^68 - 213 * q^70 + 792 * q^71 + 4068 * q^73 - 4287 * q^74 + 5538 * q^76 - 3786 * q^77 + 1824 * q^79 + 2739 * q^80 + 2205 * q^82 - 1071 * q^83 - 2394 * q^85 + 5256 * q^86 + 1101 * q^88 + 3006 * q^89 - 3285 * q^91 + 1452 * q^92 - 1086 * q^94 + 3078 * q^95 - 2535 * q^97 + 2403 * q^98

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