LMFDB - Embedded newform 294.5.g.c.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,5,Mod(19,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.19"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	294.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,18,-16,66,0,0,0,54,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.3907691467$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.31
Dual form			294.5.g.c.19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 2.44949i) q^{2} +(4.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(12.2574 - 7.07679i) q^{5} -14.6969i q^{6} +22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +(-34.6690 - 20.0162i) q^{10} +(-32.0147 + 55.4511i) q^{11} +(-36.0000 + 20.7846i) q^{12} -228.919i q^{13} +73.5442 q^{15} +(-32.0000 - 55.4256i) q^{16} +(195.250 + 112.728i) q^{17} +(38.1838 - 66.1362i) q^{18} +(255.250 - 147.369i) q^{19} +113.229i q^{20} +181.103 q^{22} +(-354.749 - 614.444i) q^{23} +(101.823 + 58.7878i) q^{24} +(-212.338 + 367.780i) q^{25} +(-560.735 + 323.741i) q^{26} +140.296i q^{27} +740.397 q^{29} +(-104.007 - 180.146i) q^{30} +(577.390 + 333.356i) q^{31} +(-90.5097 + 156.767i) q^{32} +(-288.132 + 166.353i) q^{33} -637.683i q^{34} -216.000 q^{36} +(416.882 + 722.061i) q^{37} +(-721.955 - 416.821i) q^{38} +(594.749 - 1030.14i) q^{39} +(277.352 - 160.129i) q^{40} -2817.60i q^{41} +3066.41 q^{43} +(-256.118 - 443.609i) q^{44} +(330.949 + 191.073i) q^{45} +(-1003.38 + 1737.91i) q^{46} +(531.502 - 306.863i) q^{47} -332.554i q^{48} +1201.17 q^{50} +(585.749 + 1014.55i) q^{51} +(1586.00 + 915.677i) q^{52} +(576.300 - 998.181i) q^{53} +(343.654 - 198.409i) q^{54} +906.246i q^{55} +1531.50 q^{57} +(-1047.08 - 1813.59i) q^{58} +(3024.67 + 1746.30i) q^{59} +(-294.177 + 509.529i) q^{60} +(-1967.79 + 1136.11i) q^{61} -1885.75i q^{62} +512.000 q^{64} +(-1620.01 - 2805.94i) q^{65} +(814.962 + 470.518i) q^{66} +(4337.31 - 7512.44i) q^{67} +(-1562.00 + 901.820i) q^{68} -3686.66i q^{69} -353.591 q^{71} +(305.470 + 529.090i) q^{72} +(-3524.68 - 2034.97i) q^{73} +(1179.12 - 2042.30i) q^{74} +(-1911.04 + 1103.34i) q^{75} +2357.90i q^{76} -3364.41 q^{78} +(-3236.41 - 5605.63i) q^{79} +(-784.471 - 452.915i) q^{80} +(-364.500 + 631.333i) q^{81} +(-6901.69 + 3984.69i) q^{82} -8225.83i q^{83} +3191.00 q^{85} +(-4336.55 - 7511.13i) q^{86} +(3331.79 + 1923.61i) q^{87} +(-724.410 + 1254.72i) q^{88} +(13456.5 - 7769.13i) q^{89} -1080.87i q^{90} +5675.99 q^{92} +(1732.17 + 3000.21i) q^{93} +(-1503.32 - 867.939i) q^{94} +(2085.79 - 3612.70i) q^{95} +(-814.587 + 470.302i) q^{96} +1558.61i q^{97} -1728.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} - 16 q^{4} + 66 q^{5} + 54 q^{9} + 48 q^{10} - 162 q^{11} - 144 q^{12} + 396 q^{15} - 128 q^{16} + 204 q^{17} + 444 q^{19} - 192 q^{22} + 312 q^{23} - 476 q^{25} - 1632 q^{26} + 2724 q^{29}+ \cdots - 8748 q^{99}+O(q^{100}) $ 4 * q + 18 * q^3 - 16 * q^4 + 66 * q^5 + 54 * q^9 + 48 * q^10 - 162 * q^11 - 144 * q^12 + 396 * q^15 - 128 * q^16 + 204 * q^17 + 444 * q^19 - 192 * q^22 + 312 * q^23 - 476 * q^25 - 1632 * q^26 + 2724 * q^29 + 144 * q^30 + 3786 * q^31 - 1458 * q^33 - 864 * q^36 + 1396 * q^37 - 1632 * q^38 + 648 * q^39 - 384 * q^40 - 632 * q^43 - 1296 * q^44 + 1782 * q^45 - 4896 * q^46 + 7896 * q^47 + 2112 * q^50 + 612 * q^51 + 1728 * q^52 - 1038 * q^53 + 2664 * q^57 - 336 * q^58 + 966 * q^59 - 1584 * q^60 - 5088 * q^61 + 2048 * q^64 - 744 * q^65 - 864 * q^66 + 14600 * q^67 - 1632 * q^68 - 9696 * q^71 - 22584 * q^73 + 768 * q^74 - 4284 * q^75 - 9792 * q^78 + 3974 * q^79 - 4224 * q^80 - 1458 * q^81 - 18816 * q^82 + 1224 * q^85 - 18240 * q^86 + 12258 * q^87 + 768 * q^88 + 33156 * q^89 - 4992 * q^92 + 11358 * q^93 + 16320 * q^94 + 3252 * q^95 - 8748 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.41421	−	2.44949i	−0.353553	−	0.612372i
$2$	−1.41421	−	2.44949i	−0.353553	−	0.612372i
$3$	4.50000	+	2.59808i	0.500000	+	0.288675i
$3$	4.50000	+	2.59808i	0.500000	+	0.288675i
$4$	−4.00000	+	6.92820i	−0.250000	+	0.433013i
$5$	12.2574	−	7.07679i	0.490294	−	0.283072i	−0.234402	−	0.972140i	$-0.575313\pi$
$5$	12.2574	−	7.07679i	0.490294	−	0.283072i	0.724697	+	0.689068i	$0.241980\pi$
$6$		−	14.6969i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	22.6274			0.353553
$9$	13.5000	+	23.3827i	0.166667	+	0.288675i
$10$	−34.6690	−	20.0162i	−0.346690	−	0.200162i
$11$	−32.0147	+	55.4511i	−0.264584	+	0.458274i	−0.967455	−	0.253044i	$-0.918568\pi$
$11$	−32.0147	+	55.4511i	−0.264584	+	0.458274i	0.702870	+	0.711318i	$0.251901\pi$
$12$	−36.0000	+	20.7846i	−0.250000	+	0.144338i
$13$		−	228.919i		−	1.35455i	−0.735729	−	0.677276i	$-0.763161\pi$
$13$		−	228.919i		−	1.35455i	0.735729	−	0.677276i	$-0.236839\pi$
$14$		0			0
$15$	73.5442			0.326863
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	195.250	+	112.728i	0.675605	+	0.390061i	0.798197	−	0.602397i	$-0.205787\pi$
$17$	195.250	+	112.728i	0.675605	+	0.390061i	−0.122592	+	0.992457i	$0.539121\pi$
$18$	38.1838	−	66.1362i	0.117851	−	0.204124i
$19$	255.250	−	147.369i	0.707063	−	0.408223i	−0.102910	−	0.994691i	$-0.532815\pi$
$19$	255.250	−	147.369i	0.707063	−	0.408223i	0.809973	+	0.586468i	$0.199482\pi$
$20$			113.229i			0.283072i
$21$		0			0
$22$	181.103			0.374179
$23$	−354.749	−	614.444i	−0.670604	−	1.16152i	−0.977733	−	0.209852i	$-0.932702\pi$
$23$	−354.749	−	614.444i	−0.670604	−	1.16152i	0.307129	−	0.951668i	$-0.400632\pi$
$24$	101.823	+	58.7878i	0.176777	+	0.102062i
$25$	−212.338	+	367.780i	−0.339741	+	0.588449i
$26$	−560.735	+	323.741i	−0.829490	+	0.478906i
$27$			140.296i			0.192450i
$28$		0			0
$29$	740.397			0.880377			0.440188	−	0.897905i	$-0.354912\pi$
$29$	740.397			0.880377			0.440188	+	0.897905i	$0.354912\pi$
$30$	−104.007	−	180.146i	−0.115563	−	0.200162i
$31$	577.390	+	333.356i	0.600822	+	0.346885i	0.769365	−	0.638809i	$-0.220573\pi$
$31$	577.390	+	333.356i	0.600822	+	0.346885i	−0.168543	+	0.985694i	$0.553906\pi$
$32$	−90.5097	+	156.767i	−0.0883883	+	0.153093i
$33$	−288.132	+	166.353i	−0.264584	+	0.152758i
$34$		−	637.683i		−	0.551629i
$35$		0			0
$36$	−216.000			−0.166667
$37$	416.882	+	722.061i	0.304516	+	0.527437i	0.977153	−	0.212535i	$-0.0681720\pi$
$37$	416.882	+	722.061i	0.304516	+	0.527437i	−0.672638	+	0.739972i	$0.734839\pi$
$38$	−721.955	−	416.821i	−0.499969	−	0.288657i
$39$	594.749	−	1030.14i	0.391025	−	0.677276i
$40$	277.352	−	160.129i	0.173345	−	0.100081i
$41$		−	2817.60i		−	1.67615i	−0.545558	−	0.838073i	$-0.683682\pi$
$41$		−	2817.60i		−	1.67615i	0.545558	−	0.838073i	$-0.316318\pi$
$42$		0			0
$43$	3066.41			1.65841			0.829207	−	0.558942i	$-0.188793\pi$
$43$	3066.41			1.65841			0.829207	+	0.558942i	$0.188793\pi$
$44$	−256.118	−	443.609i	−0.132292	−	0.229137i
$45$	330.949	+	191.073i	0.163431	+	0.0943572i
$46$	−1003.38	+	1737.91i	−0.474188	+	0.821318i
$47$	531.502	−	306.863i	0.240608	−	0.138915i	−0.374848	−	0.927086i	$-0.622305\pi$
$47$	531.502	−	306.863i	0.240608	−	0.138915i	0.615456	+	0.788171i	$0.288972\pi$
$48$		−	332.554i		−	0.144338i
$49$		0			0
$50$	1201.17			0.480466
$51$	585.749	+	1014.55i	0.225202	+	0.390061i
$52$	1586.00	+	915.677i	0.586538	+	0.338638i
$53$	576.300	−	998.181i	0.205162	−	0.355351i	−0.745022	−	0.667040i	$-0.767561\pi$
$53$	576.300	−	998.181i	0.205162	−	0.355351i	0.950184	+	0.311688i	$0.100895\pi$
$54$	343.654	−	198.409i	0.117851	−	0.0680414i
$55$			906.246i			0.299585i
$56$		0			0
$57$	1531.50			0.471375
$58$	−1047.08	−	1813.59i	−0.311260	−	0.539119i
$59$	3024.67	+	1746.30i	0.868909	+	0.501665i	0.866986	−	0.498333i	$-0.166054\pi$
$59$	3024.67	+	1746.30i	0.868909	+	0.501665i	0.00192348	+	0.999998i	$0.499388\pi$
$60$	−294.177	+	509.529i	−0.0817157	+	0.141536i
$61$	−1967.79	+	1136.11i	−0.528834	+	0.305323i	−0.740542	−	0.672010i	$-0.765431\pi$
$61$	−1967.79	+	1136.11i	−0.528834	+	0.305323i	0.211707	+	0.977333i	$0.432098\pi$
$62$		−	1885.75i		−	0.490569i
$63$		0			0
$64$	512.000			0.125000
$65$	−1620.01	−	2805.94i	−0.383435	−	0.664129i
$66$	814.962	+	470.518i	0.187089	+	0.108016i
$67$	4337.31	−	7512.44i	0.966208	−	1.67352i	0.259874	−	0.965642i	$-0.416319\pi$
$67$	4337.31	−	7512.44i	0.966208	−	1.67352i	0.706334	−	0.707879i	$-0.250348\pi$
$68$	−1562.00	+	901.820i	−0.337802	+	0.195030i
$69$		−	3686.66i		−	0.774346i
$70$		0			0
$71$	−353.591			−0.0701431			−0.0350715	−	0.999385i	$-0.511166\pi$
$71$	−353.591			−0.0701431			−0.0350715	+	0.999385i	$0.511166\pi$
$72$	305.470	+	529.090i	0.0589256	+	0.102062i
$73$	−3524.68	−	2034.97i	−0.661415	−	0.381868i	0.131401	−	0.991329i	$-0.458052\pi$
$73$	−3524.68	−	2034.97i	−0.661415	−	0.381868i	−0.792816	+	0.609461i	$0.791386\pi$
$74$	1179.12	−	2042.30i	0.215325	−	0.372954i
$75$	−1911.04	+	1103.34i	−0.339741	+	0.196150i
$76$			2357.90i			0.408223i
$77$		0			0
$78$	−3364.41			−0.552993
$79$	−3236.41	−	5605.63i	−0.518573	−	0.898194i	−0.999767	−	0.0215805i	$-0.993130\pi$
$79$	−3236.41	−	5605.63i	−0.518573	−	0.898194i	0.481194	−	0.876614i	$-0.340203\pi$
$80$	−784.471	−	452.915i	−0.122574	−	0.0707679i
$81$	−364.500	+	631.333i	−0.0555556	+	0.0962250i
$82$	−6901.69	+	3984.69i	−1.02643	+	0.592607i
$83$		−	8225.83i		−	1.19405i	−0.802222	−	0.597026i	$-0.796349\pi$
$83$		−	8225.83i		−	1.19405i	0.802222	−	0.597026i	$-0.203651\pi$
$84$		0			0
$85$	3191.00			0.441660
$86$	−4336.55	−	7511.13i	−0.586338	−	1.01557i
$87$	3331.79	+	1923.61i	0.440188	+	0.254143i
$88$	−724.410	+	1254.72i	−0.0935447	+	0.162024i
$89$	13456.5	−	7769.13i	1.69884	−	0.980828i	0.751983	−	0.659183i	$-0.229098\pi$
$89$	13456.5	−	7769.13i	1.69884	−	0.980828i	0.946860	−	0.321645i	$-0.104236\pi$
$90$		−	1080.87i		−	0.133441i
$91$		0			0
$92$	5675.99			0.670604
$93$	1732.17	+	3000.21i	0.200274	+	0.346885i
$94$	−1503.32	−	867.939i	−0.170135	−	0.0982276i
$95$	2085.79	−	3612.70i	0.231113	−	0.400299i
$96$	−814.587	+	470.302i	−0.0883883	+	0.0510310i
$97$			1558.61i			0.165651i	0.996564	+	0.0828254i	$0.0263944\pi$
$97$			1558.61i			0.165651i	−0.996564	+	0.0828254i	$0.973606\pi$
$98$		0			0
$99$	−1728.79			−0.176390
$100$	−1698.70	−	2942.24i	−0.169870	−	0.294224i
$101$	−13627.2	−	7867.66i	−1.33587	−	0.771264i	−0.349676	−	0.936871i	$-0.613708\pi$
$101$	−13627.2	−	7867.66i	−1.33587	−	0.771264i	−0.986192	+	0.165607i	$0.947042\pi$
$102$	1656.75	−	2869.57i	0.159242	−	0.275814i
$103$	−29.2099	+	16.8644i	−0.00275332	+	0.00158963i	−0.501376	−	0.865229i	$-0.667173\pi$
$103$	−29.2099	+	16.8644i	−0.00275332	+	0.00158963i	0.498623	+	0.866819i	$0.333839\pi$
$104$		−	5179.85i		−	0.478906i
$105$		0			0
$106$	−3260.05			−0.290143
$107$	2723.23	+	4716.78i	0.237858	+	0.411981i	0.960099	−	0.279659i	$-0.0902215\pi$
$107$	2723.23	+	4716.78i	0.237858	+	0.411981i	−0.722242	+	0.691641i	$0.756888\pi$
$108$	−972.000	−	561.184i	−0.0833333	−	0.0481125i
$109$	−8348.89	+	14460.7i	−0.702709	+	1.21713i	0.264803	+	0.964303i	$0.414693\pi$
$109$	−8348.89	+	14460.7i	−0.702709	+	1.21713i	−0.967512	+	0.252825i	$0.918640\pi$
$110$	2219.84	−	1281.62i	0.183458	−	0.105919i
$111$			4332.37i			0.351625i
$112$		0			0
$113$	9455.64			0.740515			0.370258	−	0.928929i	$-0.379269\pi$
$113$	9455.64			0.740515			0.370258	+	0.928929i	$0.379269\pi$
$114$	−2165.87	−	3751.39i	−0.166656	−	0.288657i
$115$	−8696.58	−	5020.97i	−0.657586	−	0.379658i
$116$	−2961.59	+	5129.62i	−0.220094	+	0.381214i
$117$	5352.74	−	3090.41i	0.391025	−	0.225759i
$118$		−	9878.54i		−	0.709461i
$119$		0			0
$120$	1664.11			0.115563
$121$	5270.62	+	9128.97i	0.359990	+	0.623521i
$122$	5565.76	+	3213.39i	0.373942	+	0.215896i
$123$	7320.35	−	12679.2i	0.483862	−	0.838073i
$124$	−4619.12	+	2666.85i	−0.300411	+	0.173442i
$125$			14856.7i			0.950827i
$126$		0			0
$127$	−2380.07			−0.147564			−0.0737822	−	0.997274i	$-0.523507\pi$
$127$	−2380.07			−0.147564			−0.0737822	+	0.997274i	$0.523507\pi$
$128$	−724.077	−	1254.14i	−0.0441942	−	0.0765466i
$129$	13798.8	+	7966.76i	0.829207	+	0.478743i
$130$	−4582.09	+	7936.41i	−0.271129	+	0.469610i
$131$	3758.37	−	2169.90i	0.219006	−	0.126443i	−0.386484	−	0.922296i	$-0.626310\pi$
$131$	3758.37	−	2169.90i	0.219006	−	0.126443i	0.605490	+	0.795853i	$0.292977\pi$
$132$		−	2661.65i		−	0.152758i
$133$		0			0
$134$	−24535.5			−1.36642
$135$	992.846	+	1719.66i	0.0544772	+	0.0943572i
$136$	4418.00	+	2550.73i	0.238862	+	0.137907i
$137$	15379.6	−	26638.2i	0.819414	−	1.41927i	−0.0867001	−	0.996234i	$-0.527632\pi$
$137$	15379.6	−	26638.2i	0.819414	−	1.41927i	0.906114	−	0.423033i	$-0.139034\pi$
$138$	−9030.44	+	5213.73i	−0.474188	+	0.273773i
$139$			27186.6i			1.40710i	0.710644	+	0.703551i	$0.248404\pi$
$139$			27186.6i			1.40710i	−0.710644	+	0.703551i	$0.751596\pi$
$140$		0			0
$141$	3189.01			0.160405
$142$	500.054	+	866.118i	0.0247993	+	0.0429537i
$143$	12693.8	+	7328.78i	0.620755	+	0.358393i
$144$	864.000	−	1496.49i	0.0416667	−	0.0721688i
$145$	9075.31	−	5239.63i	0.431644	−	0.249210i
$146$			11511.6i			0.540043i
$147$		0			0
$148$	−6670.12			−0.304516
$149$	2913.46	+	5046.26i	0.131231	+	0.227299i	0.924151	−	0.382027i	$-0.124774\pi$
$149$	2913.46	+	5046.26i	0.131231	+	0.227299i	−0.792920	+	0.609325i	$0.791440\pi$
$150$	5405.25	+	3120.72i	0.240233	+	0.138699i
$151$	−12593.4	+	21812.4i	−0.552317	+	0.956642i	0.445789	+	0.895138i	$0.352923\pi$
$151$	−12593.4	+	21812.4i	−0.552317	+	0.956642i	−0.998107	+	0.0615039i	$0.980410\pi$
$152$	5775.64	−	3334.57i	0.249985	−	0.144329i
$153$			6087.29i			0.260040i
$154$		0			0
$155$	9436.37			0.392773
$156$	4757.99	+	8241.09i	0.195513	+	0.338638i
$157$	−20694.6	−	11948.0i	−0.839571	−	0.484726i	0.0175475	−	0.999846i	$-0.494414\pi$
$157$	−20694.6	−	11948.0i	−0.839571	−	0.484726i	−0.857118	+	0.515120i	$0.827747\pi$
$158$	−9153.96	+	15855.1i	−0.366686	+	0.635119i
$159$	5186.70	−	2994.54i	0.205162	−	0.118450i
$160$			2562.07i			0.100081i
$161$		0			0
$162$	2061.92			0.0785674
$163$	21293.0	+	36880.5i	0.801422	+	1.38810i	0.918680	+	0.395001i	$0.129256\pi$
$163$	21293.0	+	36880.5i	0.801422	+	1.38810i	−0.117259	+	0.993101i	$0.537411\pi$
$164$	19520.9	+	11270.4i	0.725793	+	0.419037i
$165$	−2354.50	+	4078.11i	−0.0864828	+	0.149793i
$166$	−20149.1	+	11633.1i	−0.731205	+	0.422161i
$167$		−	26356.3i		−	0.945043i	−0.881319	−	0.472521i	$-0.843344\pi$
$167$		−	26356.3i		−	0.945043i	0.881319	−	0.472521i	$-0.156656\pi$
$168$		0			0
$169$	−23843.0			−0.834809
$170$	−4512.75	−	7816.31i	−0.156150	−	0.270461i
$171$	6891.74	+	3978.95i	0.235688	+	0.136074i
$172$	−12265.6	+	21244.7i	−0.414603	+	0.718114i
$173$	−24265.3	+	14009.6i	−0.810763	+	0.468094i	−0.847221	−	0.531241i	$-0.821726\pi$
$173$	−24265.3	+	14009.6i	−0.810763	+	0.468094i	0.0364578	+	0.999335i	$0.488393\pi$
$174$		−	10881.6i		−	0.359412i
$175$		0			0
$176$	4097.88			0.132292
$177$	9074.02	+	15716.7i	0.289636	+	0.501665i
$178$	−38060.8	−	21974.4i	−1.20126	−	0.693550i
$179$	−12699.2	+	21995.7i	−0.396343	+	0.686487i	−0.993272	−	0.115808i	$-0.963054\pi$
$179$	−12699.2	+	21995.7i	−0.396343	+	0.686487i	0.596928	+	0.802295i	$0.296388\pi$
$180$	−2647.59	+	1528.59i	−0.0817157	+	0.0471786i
$181$			44097.2i			1.34603i	0.739630	+	0.673014i	$0.235001\pi$
$181$			44097.2i			1.34603i	−0.739630	+	0.673014i	$0.764999\pi$
$182$		0			0
$183$	−11806.8			−0.352556
$184$	−8027.06	−	13903.3i	−0.237094	−	0.410659i
$185$	10219.8	+	5900.38i	0.298605	+	0.172400i
$186$	4899.32	−	8485.87i	0.141615	−	0.245285i
$187$	−12501.7	+	7217.88i	−0.357509	+	0.206408i
$188$			4909.81i			0.138915i
$189$		0			0
$190$	−11799.0			−0.326843
$191$	32279.6	+	55909.8i	0.884832	+	1.53257i	0.845906	+	0.533332i	$0.179060\pi$
$191$	32279.6	+	55909.8i	0.884832	+	1.53257i	0.0389256	+	0.999242i	$0.487606\pi$
$192$	2304.00	+	1330.22i	0.0625000	+	0.0360844i
$193$	−18337.3	+	31761.1i	−0.492290	+	0.852670i	−0.999961	−	0.00888055i	$-0.997173\pi$
$193$	−18337.3	+	31761.1i	−0.492290	+	0.852670i	0.507671	+	0.861551i	$0.330507\pi$
$194$	3817.80	−	2204.20i	0.101440	−	0.0585664i
$195$		−	16835.7i		−	0.442753i
$196$		0			0
$197$	−73147.0			−1.88480			−0.942398	−	0.334494i	$-0.891434\pi$
$197$	−73147.0			−1.88480			−0.942398	+	0.334494i	$0.891434\pi$
$198$	2444.89	+	4234.67i	0.0623632	+	0.108016i
$199$	1213.33	+	700.514i	0.0306387	+	0.0176893i	0.515241	−	0.857045i	$-0.327702\pi$
$199$	1213.33	+	700.514i	0.0306387	+	0.0176893i	−0.484602	+	0.874735i	$0.661036\pi$
$200$	−4804.66	+	8321.92i	−0.120117	+	0.208048i
$201$	39035.8	−	22537.3i	0.966208	−	0.557840i
$202$			44506.2i			1.09073i
$203$		0			0
$204$	−9371.99			−0.225202
$205$	−19939.6	−	34536.4i	−0.474469	−	0.821805i
$206$	82.6182	+	47.6996i	0.00194689	+	0.00112404i
$207$	9578.23	−	16590.0i	0.223535	−	0.387173i
$208$	−12688.0	+	7325.41i	−0.293269	+	0.169319i
$209$			18871.8i			0.432038i
$210$		0			0
$211$	58231.7			1.30796			0.653980	−	0.756512i	$-0.273098\pi$
$211$	58231.7			1.30796			0.653980	+	0.756512i	$0.273098\pi$
$212$	4610.40	+	7985.45i	0.102581	+	0.177676i
$213$	−1591.16	−	918.657i	−0.0350715	−	0.0202486i
$214$	7702.46	−	13341.1i	0.168191	−	0.291315i
$215$	37586.1	−	21700.3i	0.813111	−	0.469450i
$216$			3174.54i			0.0680414i
$217$		0			0
$218$	47228.4			0.993781
$219$	−10574.0	−	18314.8i	−0.220472	−	0.381868i
$220$	−6278.65	−	3624.98i	−0.129724	−	0.0748963i
$221$	25805.5	−	44696.4i	0.528357	−	0.915141i
$222$	10612.1	−	6126.89i	0.215325	−	0.124318i
$223$			61050.9i			1.22767i	0.789434	+	0.613836i	$0.210374\pi$
$223$			61050.9i			1.22767i	−0.789434	+	0.613836i	$0.789626\pi$
$224$		0			0
$225$	−11466.3			−0.226494
$226$	−13372.3	−	23161.5i	−0.261812	−	0.453471i
$227$	−21645.2	−	12496.8i	−0.420058	−	0.242520i	0.275044	−	0.961432i	$-0.411307\pi$
$227$	−21645.2	−	12496.8i	−0.420058	−	0.242520i	−0.695102	+	0.718911i	$0.744641\pi$
$228$	−6125.99	+	10610.5i	−0.117844	+	0.204112i
$229$	16392.9	−	9464.44i	0.312597	−	0.180478i	−0.335491	−	0.942043i	$-0.608902\pi$
$229$	16392.9	−	9464.44i	0.312597	−	0.180478i	0.648088	+	0.761565i	$0.275569\pi$
$230$			28402.9i			0.536917i
$231$		0			0
$232$	16753.3			0.311260
$233$	−3342.37	−	5789.15i	−0.0615662	−	0.106636i	0.833599	−	0.552369i	$-0.186276\pi$
$233$	−3342.37	−	5789.15i	−0.0615662	−	0.106636i	−0.895166	+	0.445734i	$0.852943\pi$
$234$	−15139.8	−	8740.99i	−0.276497	−	0.159635i
$235$	4343.21	−	7522.66i	0.0786457	−	0.136218i
$236$	−24197.4	+	13970.4i	−0.434455	+	0.250832i
$237$		−	33633.8i		−	0.598796i
$238$		0			0
$239$	−96461.0			−1.68871			−0.844356	−	0.535782i	$-0.820017\pi$
$239$	−96461.0			−1.68871			−0.844356	+	0.535782i	$0.820017\pi$
$240$	−2353.41	−	4076.23i	−0.0408579	−	0.0707679i
$241$	−47371.8	−	27350.1i	−0.815616	−	0.470896i	0.0332863	−	0.999446i	$-0.489403\pi$
$241$	−47371.8	−	27350.1i	−0.815616	−	0.470896i	−0.848902	+	0.528550i	$0.822736\pi$
$242$	14907.6	−	25820.6i	0.254551	−	0.440896i
$243$	−3280.50	+	1894.00i	−0.0555556	+	0.0320750i
$244$		−	18177.7i		−	0.305323i
$245$		0			0
$246$	−41410.1			−0.684284
$247$	−33735.5	−	58431.6i	−0.552959	−	0.957753i
$248$	13064.9	+	7542.99i	0.212423	+	0.122642i
$249$	21371.3	−	37016.2i	0.344693	−	0.597026i
$250$	36391.3	−	21010.5i	0.582260	−	0.336168i
$251$		−	108137.i		−	1.71643i	−0.513286	−	0.858217i	$-0.671572\pi$
$251$		−	108137.i		−	1.71643i	0.513286	−	0.858217i	$-0.328428\pi$
$252$		0			0
$253$	45428.8			0.709725
$254$	3365.92	+	5829.95i	0.0521719	+	0.0903643i
$255$	14359.5	+	8290.45i	0.220830	+	0.127496i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−31078.3	+	17943.0i	−0.470533	+	0.271663i	−0.716463	−	0.697625i	$-0.754240\pi$
$257$	−31078.3	+	17943.0i	−0.470533	+	0.271663i	0.245930	+	0.969288i	$0.420907\pi$
$258$		−	45066.8i		−	0.677045i
$259$		0			0
$260$	25920.2			0.383435
$261$	9995.36	+	17312.5i	0.146729	+	0.254143i
$262$	−10630.3	−	6137.39i	−0.154861	−	0.0894090i
$263$	32715.8	−	56665.4i	0.472984	−	0.819232i	−0.526538	−	0.850151i	$-0.676510\pi$
$263$	32715.8	−	56665.4i	0.472984	−	0.819232i	0.999522	+	0.0309199i	$0.00984367\pi$
$264$	−6519.69	+	3764.15i	−0.0935447	+	0.0540081i
$265$		−	16313.4i		−	0.232302i
$266$		0			0
$267$	80739.2			1.13256
$268$	34698.5	+	60099.5i	0.483104	+	0.836761i
$269$	59938.7	+	34605.6i	0.828329	+	0.478236i	0.853280	−	0.521453i	$-0.174610\pi$
$269$	59938.7	+	34605.6i	0.828329	+	0.478236i	−0.0249511	+	0.999689i	$0.507943\pi$
$270$	2808.19	−	4863.93i	0.0385212	−	0.0667206i
$271$	−5672.94	+	3275.27i	−0.0772449	+	0.0445973i	−0.538125	−	0.842865i	$-0.680867\pi$
$271$	−5672.94	+	3275.27i	−0.0772449	+	0.0445973i	0.460880	+	0.887462i	$0.347534\pi$
$272$		−	14429.1i		−	0.195030i
$273$		0			0
$274$	−87000.1			−1.15883
$275$	−13595.9	−	23548.8i	−0.179780	−	0.311389i
$276$	25542.0	+	14746.7i	0.335302	+	0.193587i
$277$	−39551.6	+	68505.4i	−0.515471	+	0.892823i	0.484367	+	0.874865i	$0.339050\pi$
$277$	−39551.6	+	68505.4i	−0.515471	+	0.892823i	−0.999839	+	0.0179578i	$0.994284\pi$
$278$	66593.4	−	38447.7i	0.861671	−	0.497486i
$279$			18001.2i			0.231257i
$280$		0			0
$281$	34363.1			0.435191			0.217596	−	0.976039i	$-0.430179\pi$
$281$	34363.1			0.435191			0.217596	+	0.976039i	$0.430179\pi$
$282$	−4509.95	−	7811.45i	−0.0567118	−	0.0982276i
$283$	−79598.4	−	45956.1i	−0.993874	−	0.573813i	−0.0874439	−	0.996169i	$-0.527870\pi$
$283$	−79598.4	−	45956.1i	−0.993874	−	0.573813i	−0.906430	+	0.422356i	$0.861203\pi$
$284$	1414.37	−	2449.75i	0.0175358	−	0.0303729i
$285$	18772.1	−	10838.1i	0.231113	−	0.133433i
$286$		−	41457.8i		−	0.506844i
$287$		0			0
$288$	−4887.52			−0.0589256
$289$	−16345.5	−	28311.3i	−0.195705	−	0.338972i
$290$	−25668.9	−	14819.9i	−0.305218	−	0.176218i
$291$	−4049.38	+	7013.74i	−0.0478193	+	0.0828254i
$292$	28197.4	−	16279.8i	0.330707	−	0.190934i
$293$			23218.2i			0.270453i	0.990815	+	0.135227i	$0.0431763\pi$
$293$			23218.2i			0.270453i	−0.990815	+	0.135227i	$0.956824\pi$
$294$		0			0
$295$	49432.7			0.568028
$296$	9432.97	+	16338.4i	0.107663	+	0.186477i
$297$	−7779.58	−	4491.54i	−0.0881948	−	0.0509193i
$298$	8240.51	−	14273.0i	0.0927943	−	0.160724i
$299$	−140658.	+	81208.9i	−1.57334	+	0.908367i
$300$		−	17653.5i		−	0.196150i
$301$		0			0
$302$	71239.0			0.781095
$303$	−40881.6	−	70808.9i	−0.445289	−	0.771264i
$304$	−16336.0	−	9431.59i	−0.176766	−	0.102056i
$305$	−16080.0	+	27851.3i	−0.172856	+	0.299396i
$306$	14910.7	−	8608.72i	0.159242	−	0.0919382i
$307$		−	66385.9i		−	0.704367i	−0.935931	−	0.352183i	$-0.885439\pi$
$307$		−	66385.9i		−	0.704367i	0.935931	−	0.352183i	$-0.114561\pi$
$308$		0			0
$309$	−175.260			−0.00183555
$310$	−13345.0	−	23114.3i	−0.138866	−	0.240523i
$311$	82879.0	+	47850.2i	0.856888	+	0.494724i	0.862969	−	0.505257i	$-0.168602\pi$
$311$	82879.0	+	47850.2i	0.856888	+	0.494724i	−0.00608108	+	0.999982i	$0.501936\pi$
$312$	13457.6	−	23309.3i	0.138248	−	0.239453i
$313$	−41486.1	+	23952.0i	−0.423461	+	0.244486i	−0.696557	−	0.717501i	$-0.745286\pi$
$313$	−41486.1	+	23952.0i	−0.423461	+	0.244486i	0.273096	+	0.961987i	$0.411952\pi$
$314$			67588.2i			0.685507i
$315$		0			0
$316$	51782.6			0.518573
$317$	17064.1	+	29555.9i	0.169811	+	0.294121i	0.938353	−	0.345678i	$-0.112351\pi$
$317$	17064.1	+	29555.9i	0.169811	+	0.294121i	−0.768543	+	0.639799i	$0.779018\pi$
$318$	−14670.2	−	8469.85i	−0.145071	−	0.0837571i
$319$	−23703.6	+	41055.8i	−0.232934	+	0.403454i
$320$	6275.77	−	3623.32i	0.0612868	−	0.0353839i
$321$			28300.7i			0.274654i
$322$		0			0
$323$	66450.0			0.636927
$324$	−2916.00	−	5050.66i	−0.0277778	−	0.0481125i
$325$	84192.0	+	48608.3i	0.797084	+	0.460196i
$326$	60225.6	−	104314.i	0.566691	−	0.981537i
$327$	−75140.0	+	43382.1i	−0.702709	+	0.405709i
$328$		−	63755.1i		−	0.592607i
$329$		0			0
$330$	13319.0			0.122305
$331$	−66642.6	−	115428.i	−0.608270	−	1.05355i	−0.991526	−	0.129912i	$-0.958531\pi$
$331$	−66642.6	−	115428.i	−0.608270	−	1.05355i	0.383256	−	0.923642i	$-0.374803\pi$
$332$	56990.2	+	32903.3i	0.517040	+	0.298513i
$333$	−11255.8	+	19495.7i	−0.101505	+	0.175812i
$334$	−64559.5	+	37273.4i	−0.578718	+	0.334123i
$335$		−	122777.i		−	1.09402i
$336$		0			0
$337$	−49734.4			−0.437922			−0.218961	−	0.975734i	$-0.570267\pi$
$337$	−49734.4			−0.437922			−0.218961	+	0.975734i	$0.570267\pi$
$338$	33719.0	+	58403.1i	0.295149	+	0.511214i
$339$	42550.4	+	24566.5i	0.370258	+	0.213768i
$340$	−12764.0	+	22107.9i	−0.110415	+	0.191245i
$341$	−36970.0	+	21344.6i	−0.317936	+	0.183561i
$342$		−	22508.3i		−	0.192438i
$343$		0			0
$344$	69384.9			0.586338
$345$	−26089.7	−	45188.8i	−0.219195	−	0.379658i
$346$	68632.7	+	39625.1i	0.573296	+	0.330993i
$347$	−9384.77	+	16254.9i	−0.0779408	+	0.134997i	−0.902361	−	0.430980i	$-0.858168\pi$
$347$	−9384.77	+	16254.9i	−0.0779408	+	0.134997i	0.824421	+	0.565978i	$0.191501\pi$
$348$	−26654.3	+	15388.9i	−0.220094	+	0.127071i
$349$		−	4574.17i		−	0.0375545i	−0.999824	−	0.0187772i	$-0.994023\pi$
$349$		−	4574.17i		−	0.0375545i	0.999824	−	0.0187772i	$-0.00597733\pi$
$350$		0			0
$351$	32116.5			0.260683
$352$	−5795.28	−	10037.7i	−0.0467724	−	0.0810121i
$353$	−52734.9	−	30446.5i	−0.423203	−	0.244336i	0.273244	−	0.961945i	$-0.411903\pi$
$353$	−52734.9	−	30446.5i	−0.423203	−	0.244336i	−0.696447	+	0.717608i	$0.745237\pi$
$354$	25665.2	−	44453.4i	0.204804	−	0.354731i
$355$	−4334.10	+	2502.29i	−0.0343908	+	0.0198555i
$356$			124306.i			0.980828i
$357$		0			0
$358$	71837.7			0.560514
$359$	−116059.	−	201020.i	−0.900513	−	1.55973i	−0.826830	−	0.562452i	$-0.809858\pi$
$359$	−116059.	−	201020.i	−0.900513	−	1.55973i	−0.0736826	−	0.997282i	$-0.523475\pi$
$360$	7488.51	+	4323.50i	0.0577817	+	0.0333603i
$361$	−21725.5	+	37629.7i	−0.166708	+	0.288746i
$362$	108016.	−	62362.9i	0.824271	−	0.475893i
$363$			54773.8i			0.415681i
$364$		0			0
$365$	−57604.4			−0.432384
$366$	16697.3	+	28920.5i	0.124647	+	0.215896i
$367$	125329.	+	72358.9i	0.930509	+	0.537229i	0.886972	−	0.461822i	$-0.152804\pi$
$367$	125329.	+	72358.9i	0.930509	+	0.537229i	0.0435362	+	0.999052i	$0.486138\pi$
$368$	−22704.0	+	39324.4i	−0.167651	+	0.290380i
$369$	65883.1	−	38037.6i	0.483862	−	0.279358i
$370$		−	33377.6i		−	0.243810i
$371$		0			0
$372$	−27714.7			−0.200274
$373$	74441.6	+	128937.i	0.535054	+	0.926741i	0.999161	+	0.0409616i	$0.0130421\pi$
$373$	74441.6	+	128937.i	0.535054	+	0.926741i	−0.464107	+	0.885779i	$0.653625\pi$
$374$	35360.2	+	20415.2i	0.252797	+	0.145952i
$375$	−38598.8	+	66855.0i	−0.274480	+	0.475414i
$376$	12026.5	−	6943.52i	0.0850676	−	0.0491138i
$377$		−	169491.i		−	1.19252i
$378$		0			0
$379$	140667.			0.979299			0.489649	−	0.871919i	$-0.337125\pi$
$379$	140667.			0.979299			0.489649	+	0.871919i	$0.337125\pi$
$380$	16686.3	+	28901.6i	0.115556	+	0.200149i
$381$	−10710.3	−	6183.59i	−0.0737822	−	0.0425982i
$382$	91300.4	−	158137.i	0.625671	−	1.08369i
$383$	−25393.9	+	14661.2i	−0.173114	+	0.0999473i	−0.584053	−	0.811715i	$-0.698534\pi$
$383$	−25393.9	+	14661.2i	−0.173114	+	0.0999473i	0.410939	+	0.911663i	$0.365201\pi$
$384$		−	7524.83i		−	0.0510310i
$385$		0			0
$386$	103731.			0.696202
$387$	41396.5	+	71700.8i	0.276402	+	0.478743i
$388$	−10798.4	−	6234.43i	−0.0717289	−	0.0414127i
$389$	−66209.9	+	114679.i	−0.437546	+	0.757852i	−0.997500	−	0.0706723i	$-0.977486\pi$
$389$	−66209.9	+	114679.i	−0.437546	+	0.757852i	0.559954	+	0.828524i	$0.310819\pi$
$390$	−41238.8	+	23809.2i	−0.271129	+	0.156537i
$391$		−	159960.i		−	1.04630i
$392$		0			0
$393$	22550.2			0.146004
$394$	103446.	+	179173.i	0.666376	+	1.15420i
$395$	−79339.7	−	45806.8i	−0.508507	−	0.293586i
$396$	6915.18	−	11977.4i	0.0440974	−	0.0763790i
$397$	−29642.0	+	17113.8i	−0.188073	+	0.108584i	−0.591080	−	0.806613i	$-0.701298\pi$
$397$	−29642.0	+	17113.8i	−0.188073	+	0.108584i	0.403007	+	0.915197i	$0.367965\pi$
$398$		−	3962.70i		−	0.0250164i
$399$		0			0
$400$	27179.3			0.169870
$401$	89540.6	+	155089.i	0.556841	+	0.964477i	0.997758	+	0.0669288i	$0.0213200\pi$
$401$	89540.6	+	155089.i	0.556841	+	0.964477i	−0.440917	+	0.897548i	$0.645347\pi$
$402$	−110410.	−	63745.1i	−0.683212	−	0.394453i
$403$	76311.7	−	132176.i	0.469873	−	0.813845i
$404$	109018.	−	62941.3i	0.667934	−	0.385632i
$405$			10318.0i			0.0629048i
$406$		0			0
$407$	−53385.5			−0.322281
$408$	13254.0	+	22956.6i	0.0796208	+	0.137907i
$409$	−43099.3	−	24883.4i	−0.257646	−	0.148752i	0.365614	−	0.930767i	$-0.380859\pi$
$409$	−43099.3	−	24883.4i	−0.257646	−	0.148752i	−0.623260	+	0.782014i	$0.714192\pi$
$410$	−56397.6	+	97683.6i	−0.335501	+	0.581104i
$411$	138416.	−	79914.7i	0.819414	−	0.473089i
$412$		−	269.830i		−	0.00158963i
$413$		0			0
$414$	−54182.7			−0.316126
$415$	−58212.4	−	100827.i	−0.338002	−	0.585437i
$416$	35887.0	+	20719.4i	0.207372	+	0.119727i
$417$	−70633.0	+	122340.i	−0.406196	+	0.703551i
$418$	46226.4	−	26688.8i	0.264568	−	0.152748i
$419$		−	43951.2i		−	0.250347i	−0.992135	−	0.125174i	$-0.960051\pi$
$419$		−	43951.2i		−	0.250347i	0.992135	−	0.125174i	$-0.0399488\pi$
$420$		0			0
$421$	−218257.			−1.23141			−0.615707	−	0.787975i	$-0.711129\pi$
$421$	−218257.			−1.23141			−0.615707	+	0.787975i	$0.711129\pi$
$422$	−82352.0	−	142638.i	−0.462433	−	0.800958i
$423$	14350.6	+	8285.30i	0.0802025	+	0.0463050i
$424$	13040.2	−	22586.3i	0.0725357	−	0.125636i
$425$	−82917.9	+	47872.7i	−0.459061	+	0.265039i
$426$			5196.71i			0.0286358i
$427$		0			0
$428$	−43571.7			−0.237858
$429$	38081.5	+	65959.0i	0.206918	+	0.358393i
$430$	−106309.	−	61377.8i	−0.574956	−	0.331951i
$431$	38369.8	−	66458.5i	0.206555	−	0.357763i	−0.744072	−	0.668099i	$-0.767108\pi$
$431$	38369.8	−	66458.5i	0.206555	−	0.357763i	0.950627	+	0.310336i	$0.100442\pi$
$432$	7776.00	−	4489.48i	0.0416667	−	0.0240563i
$433$			216713.i			1.15587i	0.816083	+	0.577935i	$0.196141\pi$
$433$			216713.i			1.15587i	−0.816083	+	0.577935i	$0.803859\pi$
$434$		0			0
$435$	54451.9			0.287763
$436$	−66791.1	−	115686.i	−0.351354	−	0.608564i
$437$	−181099.	−	104558.i	−0.948318	−	0.547512i
$438$	−29907.9	+	51802.0i	−0.155897	+	0.270021i
$439$	−20578.6	+	11881.0i	−0.106779	+	0.0616489i	−0.552438	−	0.833554i	$-0.686303\pi$
$439$	−20578.6	+	11881.0i	−0.106779	+	0.0616489i	0.445659	+	0.895203i	$0.352969\pi$
$440$			20506.0i			0.105919i
$441$		0			0
$442$	−145978.			−0.747210
$443$	−87432.4	−	151437.i	−0.445517	−	0.771659i	0.552571	−	0.833466i	$-0.313647\pi$
$443$	−87432.4	−	151437.i	−0.445517	−	0.771659i	−0.998088	+	0.0618072i	$0.980314\pi$
$444$	−30015.5	−	17329.5i	−0.152258	−	0.0879062i
$445$	109961.	−	190458.i	0.555289	−	0.961788i
$446$	149544.	−	86339.0i	0.751793	−	0.434048i
$447$			30277.6i			0.151532i
$448$		0			0
$449$	−195154.			−0.968023			−0.484011	−	0.875062i	$-0.660821\pi$
$449$	−195154.			−0.968023			−0.484011	+	0.875062i	$0.660821\pi$
$450$	16215.7	+	28086.5i	0.0800777	+	0.138699i
$451$	156239.	+	90204.7i	0.768134	+	0.443482i
$452$	−37822.6	+	65510.6i	−0.185129	+	0.320653i
$453$	−113340.	+	65437.2i	−0.552317	+	0.318881i
$454$			70692.8i			0.342976i
$455$		0			0
$456$	34653.9			0.166656
$457$	−29236.1	−	50638.5i	−0.139987	−	0.242464i	0.787505	−	0.616309i	$-0.211373\pi$
$457$	−29236.1	−	50638.5i	−0.139987	−	0.242464i	−0.927491	+	0.373844i	$0.878039\pi$
$458$	−46366.1	−	26769.5i	−0.221039	−	0.127617i
$459$	−15815.2	+	27392.8i	−0.0750672	+	0.130020i
$460$	69572.6	−	40167.8i	0.328793	−	0.189829i
$461$			307243.i			1.44571i	0.691002	+	0.722853i	$0.257169\pi$
$461$			307243.i			1.44571i	−0.691002	+	0.722853i	$0.742831\pi$
$462$		0			0
$463$	−17772.2			−0.0829049			−0.0414524	−	0.999140i	$-0.513199\pi$
$463$	−17772.2			−0.0829049			−0.0414524	+	0.999140i	$0.513199\pi$
$464$	−23692.7	−	41037.0i	−0.110047	−	0.190607i
$465$	42463.7	+	24516.4i	0.196387	+	0.113384i
$466$	−9453.65	+	16374.2i	−0.0435339	+	0.0754029i
$467$	−56261.4	+	32482.5i	−0.257974	+	0.148942i	−0.623410	−	0.781895i	$-0.714253\pi$
$467$	−56261.4	+	32482.5i	−0.257974	+	0.148942i	0.365436	+	0.930837i	$0.380920\pi$
$468$			49446.5i			0.225759i
$469$		0			0
$470$	−24568.9			−0.111222
$471$	−62083.7	−	107532.i	−0.279857	−	0.484726i
$472$	68440.5	+	39514.2i	0.307206	+	0.177365i
$473$	−98170.2	+	170036.i	−0.438790	+	0.760007i
$474$	−82385.6	+	47565.4i	−0.366686	+	0.211706i
$475$			125168.i			0.554760i
$476$		0			0
$477$	31120.2			0.136775
$478$	136416.	+	236280.i	0.597050	+	1.03412i
$479$	−182677.	−	105468.i	−0.796181	−	0.459675i	0.0459530	−	0.998944i	$-0.485368\pi$
$479$	−182677.	−	105468.i	−0.796181	−	0.459675i	−0.842134	+	0.539268i	$0.818701\pi$
$480$	−6656.46	+	11529.3i	−0.0288909	+	0.0500405i
$481$	165294.	−	95432.3i	0.714440	−	0.412482i
$482$			154716.i			0.665948i
$483$		0			0
$484$	−84329.8			−0.359990
$485$	11029.9	+	19104.4i	0.0468910	+	0.0812177i
$486$	9278.66	+	5357.03i	0.0392837	+	0.0226805i
$487$	114444.	−	198223.i	0.482542	−	0.835787i	−0.517257	−	0.855830i	$-0.673047\pi$
$487$	114444.	−	198223.i	0.482542	−	0.835787i	0.999799	+	0.0200431i	$0.00638033\pi$
$488$	−44526.1	+	25707.1i	−0.186971	+	0.107948i
$489$			221283.i			0.925402i
$490$		0			0
$491$	140350.			0.582169			0.291085	−	0.956697i	$-0.405984\pi$
$491$	140350.			0.582169			0.291085	+	0.956697i	$0.405984\pi$
$492$	58562.8	+	101434.i	0.241931	+	0.419037i
$493$	144562.	+	83463.1i	0.594787	+	0.343400i
$494$	−95418.3	+	165269.i	−0.391001	+	0.677234i
$495$	−21190.5	+	12234.3i	−0.0864828	+	0.0499309i
$496$		−	42669.6i		−	0.173442i
$497$		0			0
$498$	−120894.			−0.487470
$499$	172663.	+	299062.i	0.693424	+	1.20105i	0.970709	+	0.240258i	$0.0772322\pi$
$499$	172663.	+	299062.i	0.693424	+	1.20105i	−0.277285	+	0.960788i	$0.589434\pi$
$500$	−102930.	−	59426.7i	−0.411720	−	0.237707i
$501$	68475.7	−	118603.i	0.272810	−	0.472521i
$502$	−264881.	+	152929.i	−1.05110	+	0.606851i
$503$		−	58979.0i		−	0.233110i	−0.993184	−	0.116555i	$-0.962815\pi$
$503$		−	58979.0i		−	0.233110i	0.993184	−	0.116555i	$-0.0371851\pi$
$504$		0			0
$505$	−222711.			−0.873291
$506$	−64246.0	−	111277.i	−0.250926	−	0.434616i
$507$	−107293.	−	61945.9i	−0.417404	−	0.240988i
$508$	9520.26	−	16489.6i	0.0368911	−	0.0638972i
$509$	−20653.6	+	11924.3i	−0.0797186	+	0.0460255i	−0.539329	−	0.842095i	$-0.681322\pi$
$509$	−20653.6	+	11924.3i	−0.0797186	+	0.0460255i	0.459611	+	0.888120i	$0.347989\pi$
$510$		−	46897.9i		−	0.180307i
$511$		0			0
$512$	11585.2			0.0441942
$513$	20675.2	+	35810.6i	0.0785626	+	0.136074i
$514$	87902.6	+	50750.6i	0.332717	+	0.192094i
$515$	−238.691	+	413.425i	−0.000899957	+	0.00155877i
$516$	−110391.	+	63734.1i	−0.414603	+	0.239371i
$517$			39296.5i			0.147019i
$518$		0			0
$519$	−145592.			−0.540509
$520$	−36656.7	−	63491.3i	−0.135565	−	0.234805i
$521$	−417171.	−	240854.i	−1.53688	−	0.887315i	−0.999019	−	0.0442788i	$-0.985901\pi$
$521$	−417171.	−	240854.i	−1.53688	−	0.887315i	−0.537856	−	0.843037i	$-0.680766\pi$
$522$	28271.1	−	48967.1i	0.103753	−	0.179706i
$523$	399593.	−	230705.i	1.46088	−	0.843438i	0.461826	−	0.886970i	$-0.347194\pi$
$523$	399593.	−	230705.i	1.46088	−	0.843438i	0.999052	+	0.0435320i	$0.0138610\pi$
$524$			34718.3i			0.126443i
$525$		0			0
$526$	−185068.			−0.668900
$527$	75156.9	+	130176.i	0.270612	+	0.468714i
$528$	18440.5	+	10646.6i	0.0661461	+	0.0381895i
$529$	−111774.	+	193598.i	−0.399419	+	0.691813i
$530$	−39959.6	+	23070.7i	−0.142255	+	0.0821312i
$531$			94299.9i			0.334443i
$532$		0			0
$533$	−645003.			−2.27043
$534$	−114182.	−	197770.i	−0.400421	−	0.693550i
$535$	66759.3	+	38543.5i	0.233240	+	0.134661i
$536$	98142.1	−	169987.i	0.341606	−	0.591679i
$537$	−114293.	+	65987.2i	−0.396343	+	0.228829i
$538$		−	195759.i		−	0.676328i
$539$		0			0
$540$	−15885.5			−0.0544772
$541$	254098.	+	440111.i	0.868174	+	1.50372i	0.863861	+	0.503731i	$0.168040\pi$
$541$	254098.	+	440111.i	0.868174	+	1.50372i	0.00431302	+	0.999991i	$0.498627\pi$
$542$	16045.5	+	9263.87i	0.0546204	+	0.0315351i
$543$	−114568.	+	198438.i	−0.388565	+	0.673014i
$544$	−35344.0	+	20405.9i	−0.119431	+	0.0689536i
$545$			236333.i			0.795668i
$546$		0			0
$547$	40170.8			0.134257			0.0671283	−	0.997744i	$-0.478616\pi$
$547$	40170.8			0.134257			0.0671283	+	0.997744i	$0.478616\pi$
$548$	123037.	+	213106.i	0.409707	+	0.709634i
$549$	−53130.4	−	30674.9i	−0.176278	−	0.101774i
$550$	−38455.0	+	66606.0i	−0.127124	+	0.220185i
$551$	188986.	−	109111.i	0.622482	−	0.359390i
$552$		−	83419.7i		−	0.273773i
$553$		0			0
$554$	223738.			0.728987
$555$	30659.3	+	53103.4i	0.0995350	+	0.172400i
$556$	−188355.	−	108747.i	−0.609293	−	0.351776i
$557$	39230.2	−	67948.7i	0.126447	−	0.219013i	−0.795850	−	0.605493i	$-0.792976\pi$
$557$	39230.2	−	67948.7i	0.126447	−	0.219013i	0.922298	+	0.386480i	$0.126309\pi$
$558$	44093.9	−	25457.6i	0.141615	−	0.0817616i
$559$		−	701959.i		−	2.24641i
$560$		0			0
$561$	−75010.4			−0.238339
$562$	−48596.8	−	84172.2i	−0.153863	−	0.266499i
$563$	355612.	+	205312.i	1.12191	+	0.647737i	0.941889	−	0.335926i	$-0.109049\pi$
$563$	355612.	+	205312.i	1.12191	+	0.647737i	0.180024	+	0.983662i	$0.442382\pi$
$564$	−12756.1	+	22094.1i	−0.0401013	+	0.0694574i
$565$	115901.	−	66915.6i	0.363071	−	0.209619i
$566$			259967.i			0.811495i
$567$		0			0
$568$	−8000.86			−0.0247993
$569$	74404.3	+	128872.i	0.229812	+	0.398047i	0.957752	−	0.287594i	$-0.0928554\pi$
$569$	74404.3	+	128872.i	0.229812	+	0.398047i	−0.727940	+	0.685641i	$0.759522\pi$
$570$	−53095.6	−	30654.8i	−0.163421	−	0.0943514i
$571$	−36146.3	+	62607.3i	−0.110864	+	0.192023i	−0.916119	−	0.400906i	$-0.868695\pi$
$571$	−36146.3	+	62607.3i	−0.110864	+	0.192023i	0.805255	+	0.592929i	$0.202029\pi$
$572$	−101551.	+	58630.3i	−0.310378	+	0.179197i
$573$			335459.i			1.02172i
$574$		0			0
$575$	301307.			0.911326
$576$	6912.00	+	11971.9i	0.0208333	+	0.0360844i
$577$	482666.	+	278667.i	1.44976	+	0.837018i	0.998466	−	0.0553596i	$-0.0176305\pi$
$577$	482666.	+	278667.i	1.44976	+	0.837018i	0.451290	+	0.892377i	$0.350964\pi$
$578$	−46232.1	+	80076.3i	−0.138385	+	0.239689i
$579$	−165036.	+	95283.4i	−0.492290	+	0.284223i
$580$			83834.1i			0.249210i
$581$		0			0
$582$	22906.8			0.0676267
$583$	36900.2	+	63913.0i	0.108565	+	0.188041i
$584$	−79754.4	−	46046.2i	−0.233845	−	0.135011i
$585$	43740.3	−	75760.5i	0.127812	−	0.221376i
$586$	56872.6	−	32835.4i	0.165618	−	0.0956197i
$587$		−	308119.i		−	0.894217i	−0.894480	−	0.447109i	$-0.852454\pi$
$587$		−	308119.i		−	0.894217i	0.894480	−	0.447109i	$-0.147546\pi$
$588$		0			0
$589$	196505.			0.566426
$590$	−69908.3	−	121085.i	−0.200828	−	0.347845i
$591$	−329162.	−	190042.i	−0.942398	−	0.544094i
$592$	26680.5	−	46211.9i	0.0761290	−	0.131859i
$593$	200805.	−	115935.i	0.571038	−	0.329689i	−0.186526	−	0.982450i	$-0.559723\pi$
$593$	200805.	−	115935.i	0.571038	−	0.329689i	0.757564	+	0.652761i	$0.226389\pi$
$594$			25408.0i			0.0720108i
$595$		0			0
$596$	−46615.3			−0.131231
$597$	3639.98	+	6304.62i	0.0102129	+	0.0176893i
$598$	397841.	+	229693.i	1.11252	+	0.642312i
$599$	167042.	−	289325.i	0.465555	−	0.806365i	−0.533671	−	0.845692i	$-0.679188\pi$
$599$	167042.	−	289325.i	0.465555	−	0.806365i	0.999226	+	0.0393269i	$0.0125214\pi$
$600$	−43242.0	+	24965.8i	−0.120117	+	0.0693493i
$601$			645072.i			1.78591i	0.450147	+	0.892955i	$0.351372\pi$
$601$			645072.i			1.78591i	−0.450147	+	0.892955i	$0.648628\pi$
$602$		0			0
$603$	234215.			0.644139
$604$	−100747.	−	174499.i	−0.276159	−	0.478321i
$605$	129208.	+	74598.1i	0.353002	+	0.203806i
$606$	−115631.	+	200278.i	−0.314867	+	0.545366i
$607$	−120643.	+	69653.0i	−0.327433	+	0.189044i	−0.654701	−	0.755888i	$-0.727205\pi$
$607$	−120643.	+	69653.0i	−0.327433	+	0.189044i	0.327268	+	0.944932i	$0.393872\pi$
$608$			53353.1i			0.144329i
$609$		0			0
$610$	90962.0			0.244456
$611$	−70246.8	−	121671.i	−0.188167	−	0.325915i
$612$	−42174.0	−	24349.1i	−0.112601	−	0.0650101i
$613$	203665.	−	352759.i	0.541997	−	0.938765i	−0.456793	−	0.889573i	$-0.651002\pi$
$613$	203665.	−	352759.i	0.541997	−	0.938765i	0.998789	−	0.0491924i	$-0.0156647\pi$
$614$	−162611.	+	93883.8i	−0.431335	+	0.249031i
$615$		−	207218.i		−	0.547870i
$616$		0			0
$617$	276504.			0.726325			0.363163	−	0.931726i	$-0.381697\pi$
$617$	276504.			0.726325			0.363163	+	0.931726i	$0.381697\pi$
$618$	247.855	+	429.297i	0.000648963	+	0.00112404i
$619$	−193904.	−	111950.i	−0.506064	−	0.292176i	0.225150	−	0.974324i	$-0.427713\pi$
$619$	−193904.	−	111950.i	−0.506064	−	0.292176i	−0.731214	+	0.682148i	$0.761046\pi$
$620$	−37745.5	+	65377.1i	−0.0981933	+	0.170076i
$621$	86204.1	−	49770.0i	0.223535	−	0.129058i
$622$		−	270682.i		−	0.699646i
$623$		0			0
$624$	−76127.9			−0.195513
$625$	−27573.7	−	47759.1i	−0.0705888	−	0.122263i
$626$	117340.	+	67746.5i	0.299432	+	0.172877i
$627$	−49030.5	+	84923.3i	−0.124719	+	0.216019i
$628$	165557.	−	95584.2i	0.419785	−	0.242363i
$629$			187976.i			0.475119i
$630$		0			0
$631$	299528.			0.752278			0.376139	−	0.926563i	$-0.377251\pi$
$631$	299528.			0.752278			0.376139	+	0.926563i	$0.377251\pi$
$632$	−73231.7	−	126841.i	−0.183343	−	0.317560i
$633$	262042.	+	151290.i	0.653980	+	0.377575i
$634$	48264.6	−	83596.7i	0.120074	−	0.207975i
$635$	−29173.3	+	16843.2i	−0.0723500	+	0.0417713i
$636$			47912.7i			0.118450i
$637$		0			0
$638$	134088.			0.329418
$639$	−4773.48	−	8267.92i	−0.0116905	−	0.0202486i
$640$	−17750.6	−	10248.3i	−0.0433363	−	0.0250202i
$641$	−288942.	+	500462.i	−0.703226	+	1.21802i	0.264102	+	0.964495i	$0.414924\pi$
$641$	−288942.	+	500462.i	−0.703226	+	1.21802i	−0.967328	+	0.253528i	$0.918409\pi$
$642$	69322.2	−	40023.2i	0.168191	−	0.0971050i
$643$		−	135320.i		−	0.327295i	−0.986519	−	0.163647i	$-0.947674\pi$
$643$		−	135320.i		−	0.327295i	0.986519	−	0.163647i	$-0.0523259\pi$
$644$		0			0
$645$	225516.			0.542074
$646$	−93974.4	−	162768.i	−0.225188	−	0.390037i
$647$	−188880.	−	109050.i	−0.451209	−	0.260506i	0.257132	−	0.966376i	$-0.417223\pi$
$647$	−188880.	−	109050.i	−0.451209	−	0.260506i	−0.708341	+	0.705871i	$0.750556\pi$
$648$	−8247.69	+	14285.4i	−0.0196419	+	0.0340207i
$649$	−193668.	+	111814.i	−0.459800	+	0.265465i
$650$		−	274970.i		−	0.650816i
$651$		0			0
$652$	−340688.			−0.801422
$653$	−72127.2	−	124928.i	−0.169150	−	0.292977i	0.768971	−	0.639284i	$-0.220769\pi$
$653$	−72127.2	−	124928.i	−0.169150	−	0.292977i	−0.938121	+	0.346307i	$0.887436\pi$
$654$	212528.	+	122703.i	0.496890	+	0.286880i
$655$	30711.8	−	53194.4i	0.0715851	−	0.123989i
$656$	−156167.	+	90163.3i	−0.362896	+	0.209518i
$657$		−	109889.i		−	0.254579i
$658$		0			0
$659$	−159392.			−0.367024			−0.183512	−	0.983017i	$-0.558747\pi$
$659$	−159392.			−0.367024			−0.183512	+	0.983017i	$0.558747\pi$
$660$	−18836.0	−	32624.8i	−0.0432414	−	0.0748963i
$661$	−305674.	−	176481.i	−0.699609	−	0.403919i	0.107593	−	0.994195i	$-0.465686\pi$
$661$	−305674.	−	176481.i	−0.699609	−	0.403919i	−0.807202	+	0.590276i	$0.799019\pi$
$662$	−188494.	+	326481.i	−0.430112	+	0.744975i
$663$	232249.	−	134089.i	0.528357	−	0.305047i
$664$		−	186129.i		−	0.422161i
$665$		0			0
$666$	63672.5			0.143550
$667$	−262655.	−	454932.i	−0.590384	−	1.02258i
$668$	182602.	+	105425.i	0.409216	+	0.236261i
$669$	−158615.	+	274729.i	−0.354398	+	0.613836i
$670$	−300741.	+	173633.i	−0.669950	+	0.386796i
$671$		−	145488.i		−	0.323135i
$672$		0			0
$673$	504858.			1.11465			0.557326	−	0.830294i	$-0.311827\pi$
$673$	504858.			1.11465			0.557326	+	0.830294i	$0.311827\pi$
$674$	70335.1	+	121824.i	0.154829	+	0.268172i
$675$	−51598.2	−	29790.2i	−0.113247	−	0.0653832i
$676$	95371.9	−	165189.i	0.208702	−	0.361483i
$677$	169486.	−	97853.0i	0.369792	−	0.213500i	−0.303576	−	0.952807i	$-0.598180\pi$
$677$	169486.	−	97853.0i	0.369792	−	0.213500i	0.673368	+	0.739308i	$0.264847\pi$
$678$		−	138969.i		−	0.302314i
$679$		0			0
$680$	72204.0			0.156150
$681$	−64935.5	−	112472.i	−0.140019	−	0.242520i
$682$	104567.	+	60371.7i	0.224815	+	0.129797i
$683$	117221.	−	203032.i	0.251283	−	0.435235i	−0.712596	−	0.701574i	$-0.752481\pi$
$683$	117221.	−	203032.i	0.251283	−	0.435235i	0.963879	+	0.266340i	$0.0858142\pi$
$684$	−55134.0	+	31831.6i	−0.117844	+	0.0680372i
$685$		−	435352.i		−	0.927812i
$686$		0			0
$687$	98357.4			0.208398
$688$	−98125.0	−	169958.i	−0.207302	−	0.359057i
$689$	−228503.	−	131926.i	−0.481341	−	0.277902i
$690$	−73792.9	+	127813.i	−0.154995	+	0.268459i
$691$	77344.0	−	44654.6i	0.161983	−	0.0935212i	−0.416817	−	0.908990i	$-0.636854\pi$
$691$	77344.0	−	44654.6i	0.161983	−	0.0935212i	0.578800	+	0.815469i	$0.303521\pi$
$692$		−	224153.i		−	0.468094i
$693$		0			0
$694$	53088.3			0.110225
$695$	192394.	+	333236.i	0.398311	+	0.689895i
$696$	75389.7	+	43526.3i	0.155630	+	0.0898531i
$697$	317621.	−	550136.i	0.653799	−	1.13241i
$698$	−11204.4	+	6468.85i	−0.0229973	+	0.0132775i
$699$		−	34734.9i		−	0.0710905i
$700$		0			0
$701$	122213.			0.248704			0.124352	−	0.992238i	$-0.460315\pi$
$701$	122213.			0.248704			0.124352	+	0.992238i	$0.460315\pi$
$702$	−45419.5	−	78669.0i	−0.0921655	−	0.159635i
$703$	212818.	+	122871.i	0.430624	+	0.248621i
$704$	−16391.5	+	28391.0i	−0.0330731	+	0.0572842i
$705$	39088.9	−	22568.0i	0.0786457	−	0.0454061i
$706$			172231.i			0.345544i
$707$		0			0
$708$	−145184.			−0.289636
$709$	−42009.9	−	72763.3i	−0.0835717	−	0.144750i	0.821210	−	0.570626i	$-0.193299\pi$
$709$	−42009.9	−	72763.3i	−0.0835717	−	0.144750i	−0.904782	+	0.425876i	$0.859966\pi$
$710$	12258.7	+	7077.55i	0.0243179	+	0.0140400i
$711$	87383.1	−	151352.i	0.172858	−	0.299398i
$712$	304487.	−	175795.i	0.600632	−	0.346775i
$713$		−	473032.i		−	0.930489i
$714$		0			0
$715$	207457.			0.405804
$716$	−101594.	−	175966.i	−0.198172	−	0.343243i
$717$	−434074.	−	250613.i	−0.844356	−	0.487489i
$718$	−328264.	+	568570.i	−0.636759	+	1.10290i
$719$	−657416.	+	379560.i	−1.27169	+	0.734213i	−0.975307	−	0.220855i	$-0.929115\pi$
$719$	−657416.	+	379560.i	−1.27169	+	0.734213i	−0.296388	+	0.955068i	$0.595782\pi$
$720$		−	24457.4i		−	0.0471786i
$721$		0			0
$722$	122898.			0.235760
$723$	−142115.	−	246151.i	−0.271872	−	0.470896i
$724$	−305515.	−	176389.i	−0.582847	−	0.336507i
$725$	−157214.	+	272303.i	−0.299100	+	0.518057i
$726$	134168.	−	77461.9i	0.254551	−	0.146965i
$727$			92384.1i			0.174795i	0.996174	+	0.0873974i	$0.0278550\pi$
$727$			92384.1i			0.174795i	−0.996174	+	0.0873974i	$0.972145\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$	81464.9	+	141101.i	0.152871	+	0.264780i
$731$	598715.	+	345668.i	1.12043	+	0.646882i
$732$	47227.0	−	81799.6i	0.0881391	−	0.152661i
$733$	−2903.50	+	1676.34i	−0.00540399	+	0.00312000i	−0.502700	−	0.864461i	$-0.667660\pi$
$733$	−2903.50	+	1676.34i	−0.00540399	+	0.00312000i	0.497296	+	0.867581i	$0.334326\pi$
$734$		−	409324.i		−	0.759757i
$735$		0			0
$736$	128433.			0.237094
$737$	277715.	+	481017.i	0.511287	+	0.885575i
$738$	−186346.	−	107587.i	−0.342142	−	0.197536i
$739$	13592.8	−	23543.4i	0.0248897	−	0.0431103i	−0.853312	−	0.521400i	$-0.825410\pi$
$739$	13592.8	−	23543.4i	0.0248897	−	0.0431103i	0.878202	+	0.478290i	$0.158743\pi$
$740$	−81758.0	+	47203.0i	−0.149302	+	0.0861998i
$741$		−	350589.i		−	0.638502i
$742$		0			0
$743$	773801.			1.40169			0.700845	−	0.713314i	$-0.252807\pi$
$743$	773801.			1.40169			0.700845	+	0.713314i	$0.252807\pi$
$744$	39194.6	+	67887.0i	0.0708076	+	0.122642i
$745$	71422.6	+	41235.9i	0.128684	+	0.0742955i
$746$	210553.	−	364688.i	0.378340	−	0.655305i
$747$	192342.	−	111049.i	0.344693	−	0.199009i
$748$		−	115486.i		−	0.206408i
$749$		0			0
$750$	218348.			0.388174
$751$	−98922.2	−	171338.i	−0.175394	−	0.303791i	0.764904	−	0.644145i	$-0.222786\pi$
$751$	−98922.2	−	171338.i	−0.175394	−	0.303791i	−0.940297	+	0.340354i	$0.889453\pi$
$752$	−34016.1	−	19639.2i	−0.0601519	−	0.0347287i
$753$	280948.	−	486617.i	0.495492	−	0.858217i
$754$	−415167.	+	239697.i	−0.730264	+	0.421618i
$755$			356483.i			0.625381i
$756$		0			0
$757$	−770706.			−1.34492			−0.672461	−	0.740132i	$-0.734763\pi$
$757$	−770706.			−1.34492			−0.672461	+	0.740132i	$0.734763\pi$
$758$	−198934.	−	344564.i	−0.346234	−	0.599696i
$759$	204430.	+	118027.i	0.354863	+	0.204880i
$760$	47196.1	−	81746.0i	0.0817107	−	0.141527i
$761$	131757.	−	76069.9i	0.227512	−	0.131354i	−0.381912	−	0.924199i	$-0.624734\pi$
$761$	131757.	−	76069.9i	0.227512	−	0.131354i	0.609424	+	0.792845i	$0.291401\pi$
$762$			34979.7i			0.0602429i
$763$		0			0
$764$	−516473.			−0.884832
$765$	43078.4	+	74614.0i	0.0736100	+	0.127496i
$766$	71824.8	+	41468.0i	0.122410	+	0.0706734i
$767$	399760.	−	692405.i	0.679531	−	1.17698i
$768$	−18432.0	+	10641.7i	−0.0312500	+	0.0180422i
$769$		−	961897.i		−	1.62658i	−0.581857	−	0.813291i	$-0.697674\pi$
$769$		−	961897.i		−	1.62658i	0.581857	−	0.813291i	$-0.302326\pi$
$770$		0			0
$771$	−186470.			−0.313689
$772$	−146698.	−	254089.i	−0.246145	−	0.426335i
$773$	130829.	+	75534.4i	0.218951	+	0.126411i	0.605464	−	0.795872i	$-0.292987\pi$
$773$	130829.	+	75534.4i	0.218951	+	0.126411i	−0.386514	+	0.922284i	$0.626321\pi$
$774$	117087.	−	202801.i	0.195446	−	0.338522i
$775$	−245204.	+	141569.i	−0.408248	+	0.235702i
$776$			35267.3i			0.0585664i
$777$		0			0
$778$	374540.			0.618783
$779$	−415226.	−	719192.i	−0.684242	−	1.18514i
$780$	116641.	+	67342.7i	0.191717	+	0.110688i
$781$	11320.1	−	19607.0i	0.0185588	−	0.0321447i
$782$	−391821.	+	226218.i	−0.640728	+	0.369924i
$783$			103875.i			0.169429i
$784$		0			0
$785$	−338215.			−0.548849
$786$	−31890.8	−	55236.5i	−0.0516203	−	0.0894090i
$787$	172244.	+	99445.4i	0.278097	+	0.160559i	0.632561	−	0.774510i	$-0.282004\pi$
$787$	172244.	+	99445.4i	0.278097	+	0.160559i	−0.354465	+	0.935069i	$0.615337\pi$
$788$	292588.	−	506777.i	0.471199	−	0.816140i
$789$	294442.	−	169996.i	0.472984	−	0.273077i
$790$			259123.i			0.415194i
$791$		0			0
$792$	−39118.2			−0.0623632
$793$	260076.	+	450465.i	0.413575	+	0.716333i
$794$	83840.2	+	48405.1i	0.132988	+	0.0767804i
$795$	42383.5	−	73410.4i	0.0670599	−	0.116151i
$796$	−9706.60	+	5604.11i	−0.0153194	+	0.00884465i
$797$			990756.i			1.55973i	0.625947	+	0.779866i	$0.284713\pi$
$797$			990756.i			1.55973i	−0.625947	+	0.779866i	$0.715287\pi$
$798$		0			0
$799$	138368.			0.216741
$800$	−38437.3	−	66575.4i	−0.0600583	−	0.104024i
$801$	363326.	+	209767.i	0.566281	+	0.326943i
$802$	253259.	−	438657.i	0.393746	−	0.681988i
$803$	225683.	−	130298.i	0.350000	−	0.202073i
$804$			360597.i			0.557840i
$805$		0			0
$806$	−431684.			−0.664501
$807$	179816.	+	311451.i	0.276110	+	0.478236i
$808$	−308348.	−	178025.i	−0.472301	−	0.272683i
$809$	46144.3	−	79924.3i	0.0705052	−	0.122119i	−0.828618	−	0.559815i	$-0.810872\pi$
$809$	46144.3	−	79924.3i	0.0705052	−	0.122119i	0.899123	+	0.437696i	$0.144206\pi$
$810$	25273.7	−	14591.8i	0.0385212	−	0.0222402i
$811$			617125.i			0.938277i	0.883125	+	0.469139i	$0.155436\pi$
$811$			617125.i			0.938277i	−0.883125	+	0.469139i	$0.844564\pi$
$812$		0			0
$813$	−34037.6			−0.0514966
$814$	75498.5	+	130767.i	0.113943	+	0.197356i
$815$	521991.	+	301372.i	0.785865	+	0.453719i
$816$	37488.0	−	64931.0i	0.0563004	−	0.0975152i
$817$	782700.	−	451892.i	1.17260	−	0.677003i
$818$			140762.i			0.210367i
$819$		0			0
$820$	319033.			0.474469
$821$	−153533.	−	265927.i	−0.227780	−	0.394526i	0.729370	−	0.684119i	$-0.239813\pi$
$821$	−153533.	−	265927.i	−0.227780	−	0.394526i	−0.957150	+	0.289593i	$0.906480\pi$
$822$	−391500.	−	226033.i	−0.579413	−	0.334524i
$823$	−423429.	+	733401.i	−0.625146	+	1.08278i	0.363367	+	0.931646i	$0.381627\pi$
$823$	−423429.	+	733401.i	−0.625146	+	1.08278i	−0.988513	+	0.151138i	$0.951706\pi$
$824$	−660.946	+	381.597i	−0.000973445	+	0.000562019i
$825$		−	141293.i		−	0.207592i
$826$		0			0
$827$	294059.			0.429956			0.214978	−	0.976619i	$-0.431032\pi$
$827$	294059.			0.429956			0.214978	+	0.976619i	$0.431032\pi$
$828$	76625.9	+	132720.i	0.111767	+	0.193587i
$829$	−895803.	−	517192.i	−1.30348	−	0.752563i	−0.322479	−	0.946577i	$-0.604516\pi$
$829$	−895803.	−	517192.i	−1.30348	−	0.752563i	−0.980999	+	0.194013i	$0.937849\pi$
$830$	−164650.	+	285182.i	−0.239004	+	0.413967i
$831$	−355964.	+	205516.i	−0.515471	+	0.297608i
$832$		−	117207.i		−	0.169319i
$833$		0			0
$834$	399560.			0.574447
$835$	−186518.	−	323059.i	−0.267515	−	0.463349i
$836$	−130748.	−	75487.4i	−0.187078	−	0.108009i
$837$	−46768.6	+	81005.6i	−0.0667580	+	0.115628i
$838$	−107658.	+	62156.4i	−0.153306	+	0.0885111i
$839$		−	307258.i		−	0.436495i	−0.975893	−	0.218248i	$-0.929966\pi$
$839$		−	307258.i		−	0.436495i	0.975893	−	0.218248i	$-0.0700340\pi$
$840$		0			0
$841$	−159093.			−0.224937
$842$	308662.	+	534618.i	0.435370	+	0.754084i
$843$	154634.	+	89278.1i	0.217596	+	0.125629i
$844$	−232927.	+	403441.i	−0.326990	+	0.566363i
$845$	−292252.	+	168732.i	−0.409302	+	0.236311i
$846$		−	46868.7i		−	0.0654851i
$847$		0			0
$848$	−73766.4			−0.102581
$849$	−238795.	−	413605.i	−0.331291	−	0.573813i
$850$	234527.	+	135404.i	0.324605	+	0.187411i
$851$	295777.	−	512302.i	0.408419	−	0.707402i
$852$	12729.3	−	7349.26i	0.0175358	−	0.0101243i
$853$		−	70737.4i		−	0.0972190i	−0.998818	−	0.0486095i	$-0.984521\pi$
$853$		−	70737.4i		−	0.0972190i	0.998818	−	0.0486095i	$-0.0154790\pi$
$854$		0			0
$855$	112633.			0.154075
$856$	61619.7	+	106728.i	0.0840954	+	0.145657i
$857$	−285670.	−	164932.i	−0.388958	−	0.224565i	0.292751	−	0.956189i	$-0.405429\pi$
$857$	−285670.	−	164932.i	−0.388958	−	0.224565i	−0.681709	+	0.731624i	$0.738763\pi$
$858$	107711.	−	186560.i	0.146313	−	0.253422i
$859$	60589.3	−	34981.2i	0.0821125	−	0.0474077i	−0.458382	−	0.888756i	$-0.651571\pi$
$859$	60589.3	−	34981.2i	0.0821125	−	0.0474077i	0.540494	+	0.841348i	$0.318237\pi$
$860$			347205.i			0.469450i
$861$		0			0
$862$	−217052.			−0.292113
$863$	386112.	+	668765.i	0.518431	+	0.897949i	0.999771	+	0.0214151i	$0.00681715\pi$
$863$	386112.	+	668765.i	0.518431	+	0.897949i	−0.481339	+	0.876534i	$0.659850\pi$
$864$	−21993.8	−	12698.2i	−0.0294628	−	0.0170103i
$865$	−198286.	+	343441.i	−0.265008	+	0.459008i
$866$	530836.	−	306478.i	0.707823	−	0.408662i
$867$		−	169868.i		−	0.225981i
$868$		0			0
$869$	414451.			0.548825
$870$	−77006.6	−	133379.i	−0.101739	−	0.176218i
$871$	−1.71974e6	−	992893.i	−2.26687	−	1.30878i
$872$	−188914.	+	327208.i	−0.248445	+	0.430320i
$873$	−36444.4	+	21041.2i	−0.0478193	+	0.0276085i
$874$			591468.i			0.774299i
$875$		0			0
$876$	169185.			0.220472
$877$	−121260.	−	210028.i	−0.157659	−	0.273073i	0.776365	−	0.630283i	$-0.217061\pi$
$877$	−121260.	−	210028.i	−0.157659	−	0.273073i	−0.934024	+	0.357211i	$0.883728\pi$
$878$	58204.9	+	33604.6i	0.0755042	+	0.0435923i
$879$	−60322.5	+	104482.i	−0.0780732	+	0.135227i
$880$	50229.2	−	28999.9i	0.0648621	−	0.0374482i
$881$		−	646528.i		−	0.832982i	−0.909140	−	0.416491i	$-0.863260\pi$
$881$		−	646528.i		−	0.832982i	0.909140	−	0.416491i	$-0.136740\pi$
$882$		0			0
$883$	−461877.			−0.592387			−0.296193	−	0.955128i	$-0.595717\pi$
$883$	−461877.			−0.592387			−0.296193	+	0.955128i	$0.595717\pi$
$884$	206444.	+	357571.i	0.264179	+	0.457571i
$885$	222447.	+	128430.i	0.284014	+	0.163976i
$886$	−247296.	+	428329.i	−0.315028	+	0.545645i
$887$	186391.	−	107613.i	0.236907	−	0.136778i	−0.376847	−	0.926275i	$-0.622992\pi$
$887$	186391.	−	107613.i	0.236907	−	0.136778i	0.613754	+	0.789497i	$0.289658\pi$
$888$			98030.3i			0.124318i
$889$		0			0
$890$	−622034.			−0.785297
$891$	−23338.7	−	40423.9i	−0.0293983	−	0.0509193i
$892$	−422973.	−	244204.i	−0.531598	−	0.306918i
$893$	90443.9	−	156653.i	0.113417	−	0.196443i
$894$	74164.6	−	42818.9i	0.0927943	−	0.0535748i
$895$			359479.i			0.448774i
$896$		0			0
$897$	−843948.			−1.04889
$898$	275990.	+	478029.i	0.342248	+	0.592791i
$899$	427498.	+	246816.i	0.528950	+	0.305389i
$900$	45865.0	−	79440.6i	0.0566235	−	0.0980748i
$901$	225045.	−	129930.i	0.277217	−	0.160051i
$902$		−	510275.i		−	0.627179i
$903$		0			0
$904$	213957.			0.261812
$905$	312067.	+	540516.i	0.381022	+	0.659950i
$906$	320575.	+	185084.i	0.390547	+	0.225483i
$907$	−549134.	+	951128.i	−0.667519	+	1.15618i	0.311076	+	0.950385i	$0.399311\pi$
$907$	−549134.	+	951128.i	−0.667519	+	1.15618i	−0.978596	+	0.205793i	$0.934023\pi$
$908$	173161.	−	99974.7i	0.210029	−	0.121260i
$909$		−	424854.i		−	0.514176i
$910$		0			0
$911$	−1.32312e6			−1.59427			−0.797133	−	0.603803i	$-0.793651\pi$
$911$	−1.32312e6			−1.59427			−0.797133	+	0.603803i	$0.793651\pi$
$912$	−49008.0	−	84884.3i	−0.0589219	−	0.102056i
$913$	456131.	+	263348.i	0.547203	+	0.315928i
$914$	−82692.2	+	143227.i	−0.0989857	+	0.171448i
$915$	−144720.	+	83553.9i	−0.172856	+	0.0997987i
$916$			151431.i			0.180478i
$917$		0			0
$918$	89464.5			0.106161
$919$	−258264.	−	447326.i	−0.305797	−	0.529656i	0.671642	−	0.740876i	$-0.265589\pi$
$919$	−258264.	−	447326.i	−0.305797	−	0.529656i	−0.977438	+	0.211221i	$0.932256\pi$
$920$	−196781.	−	113612.i	−0.232492	−	0.134229i
$921$	172476.	−	298736.i	0.203333	−	0.352183i
$922$	752588.	−	434507.i	0.885310	−	0.511134i
$923$			80943.8i			0.0950124i
$924$		0			0
$925$	−354080.			−0.413826
$926$	25133.7	+	43532.9i	0.0293113	+	0.0507687i
$927$	−788.669	−	455.338i	−0.000917773	−	0.000529876i
$928$	−67013.1	+	116070.i	−0.0778151	+	0.134780i
$929$	−1.07335e6	+	619697.i	−1.24368	+	0.718039i	−0.969841	−	0.243737i	$-0.921627\pi$
$929$	−1.07335e6	+	619697.i	−1.24368	+	0.718039i	−0.273838	+	0.961776i	$0.588293\pi$
$930$		−	138686.i		−	0.160349i
$931$		0			0
$932$	53477.9			0.0615662
$933$	248637.	+	430652.i	0.285629	+	0.494724i
$934$	159131.	+	91874.5i	0.182415	+	0.105318i
$935$	−102159.	+	176944.i	−0.116856	+	0.202401i
$936$	121119.	−	69928.0i	0.138248	−	0.0798177i
$937$			1.15260e6i			1.31281i	0.754411	+	0.656403i	$0.227923\pi$
$937$			1.15260e6i			1.31281i	−0.754411	+	0.656403i	$0.772077\pi$
$938$		0			0
$939$	−248917.			−0.282308
$940$	34745.7	+	60181.3i	0.0393228	+	0.0681092i
$941$	−93104.2	−	53753.7i	−0.105145	−	0.0607057i	0.446505	−	0.894781i	$-0.352668\pi$
$941$	−93104.2	−	53753.7i	−0.105145	−	0.0607057i	−0.551650	+	0.834075i	$0.686002\pi$
$942$	−175599.	+	304147.i	−0.197889	+	0.342753i
$943$	−1.73126e6	+	999543.i	−1.94688	+	1.12403i
$944$		−	223526.i		−	0.250832i
$945$		0			0
$946$	555334.			0.620543
$947$	206307.	+	357335.i	0.230046	+	0.398451i	0.957821	−	0.287364i	$-0.0927790\pi$
$947$	206307.	+	357335.i	0.230046	+	0.398451i	−0.727775	+	0.685815i	$0.759446\pi$
$948$	233022.	+	134535.i	0.259286	+	0.149699i
$949$	−465845.	+	806867.i	−0.517260	+	0.895920i
$950$	306597.	−	177014.i	0.339720	−	0.196137i
$951$			177335.i			0.196080i
$952$		0			0
$953$	1.43052e6			1.57510			0.787550	−	0.616251i	$-0.211349\pi$
$953$	1.43052e6			1.57510			0.787550	+	0.616251i	$0.211349\pi$
$954$	−44010.6	−	76228.6i	−0.0483572	−	0.0837571i
$955$	791324.	+	456871.i	0.867656	+	0.500942i
$956$	385844.	−	668301.i	0.422178	−	0.731234i
$957$	−213332.	+	123168.i	−0.232934	+	0.134485i
$958$			596619.i			0.650079i
$959$		0			0
$960$	37654.6			0.0408579
$961$	−239507.	−	414839.i	−0.259342	−	0.449193i
$962$	−467521.	−	269923.i	−0.505186	−	0.291669i
$963$	−73527.3	+	127353.i	−0.0792859	+	0.137327i
$964$	378974.	−	218801.i	0.407808	−	0.235448i
$965$			519077.i			0.557413i
$966$		0			0
$967$	−344533.			−0.368449			−0.184225	−	0.982884i	$-0.558977\pi$
$967$	−344533.			−0.368449			−0.184225	+	0.982884i	$0.558977\pi$
$968$	119260.	+	206565.i	0.127276	+	0.220448i
$969$	299025.	+	172642.i	0.318463	+	0.183865i
$970$	31197.4	−	54035.5i	0.0331570	−	0.0574296i
$971$	1.25848e6	−	726581.i	1.33477	−	0.770630i	0.348744	−	0.937218i	$-0.386608\pi$
$971$	1.25848e6	−	726581.i	1.33477	−	0.770630i	0.986027	+	0.166588i	$0.0532751\pi$
$972$		−	30304.0i		−	0.0320750i
$973$		0			0
$974$	−647393.			−0.682417
$975$	252576.	+	437474.i	0.265695	+	0.460196i
$976$	125939.	+	72710.8i	0.132209	+	0.0763307i
$977$	−772853.	+	1.33862e6i	−0.809669	+	1.40239i	0.103424	+	0.994637i	$0.467020\pi$
$977$	−772853.	+	1.33862e6i	−0.809669	+	1.40239i	−0.913093	+	0.407751i	$0.866313\pi$
$978$	542031.	−	312941.i	0.566691	−	0.327179i
$979$			994907.i			1.03805i
$980$		0			0
$981$	−450840.			−0.468473
$982$	−198485.	−	343786.i	−0.205828	−	0.356504i
$983$	−116280.	−	67134.0i	−0.120336	−	0.0694761i	0.438624	−	0.898671i	$-0.355466\pi$
$983$	−116280.	−	67134.0i	−0.120336	−	0.0694761i	−0.558960	+	0.829195i	$0.688799\pi$
$984$	165641.	−	286898.i	0.171071	−	0.296304i
$985$	−896589.	+	517646.i	−0.924105	+	0.533532i
$986$		−	472139.i		−	0.485641i
$987$		0			0
$988$	539768.			0.552959
$989$	−1.08781e6	−	1.88414e6i	−1.11214	−	1.92628i
$990$	59935.7	+	34603.9i	0.0611526	+	0.0353065i
$991$	395596.	−	685192.i	0.402814	−	0.697694i	−0.591251	−	0.806488i	$-0.701366\pi$
$991$	395596.	−	685192.i	0.402814	−	0.697694i	0.994064	+	0.108794i	$0.0346990\pi$
$992$	−104519.	+	60344.0i	−0.106211	+	0.0613212i
$993$		−	692571.i		−	0.702369i
$994$		0			0
$995$	19829.5			0.0200293
$996$	170971.	+	296130.i	0.172347	+	0.298513i
$997$	−582624.	−	336378.i	−0.586136	−	0.338406i	0.177432	−	0.984133i	$-0.443221\pi$
$997$	−582624.	−	336378.i	−0.586136	−	0.338406i	−0.763568	+	0.645727i	$0.776554\pi$
$998$	488366.	−	845874.i	0.490325	−	0.849268i
$999$	−101302.	+	58487.0i	−0.101505	+	0.0586041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.5.g.c.31.1		4
7.2	even	3		42.5.g.a.19.1	✓	4
7.3	odd	6		294.5.c.a.97.4		4
7.4	even	3		294.5.c.a.97.3		4
7.5	odd	6	inner	294.5.g.c.19.1		4
7.6	odd	2		42.5.g.a.31.1	yes	4
21.2	odd	6		126.5.n.b.19.2		4
21.11	odd	6		882.5.c.a.685.1		4
21.17	even	6		882.5.c.a.685.2		4
21.20	even	2		126.5.n.b.73.2		4
28.23	odd	6		336.5.bh.d.145.2		4
28.27	even	2		336.5.bh.d.241.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.g.a.19.1	✓	4	7.2	even	3
42.5.g.a.31.1	yes	4	7.6	odd	2
126.5.n.b.19.2		4	21.2	odd	6
126.5.n.b.73.2		4	21.20	even	2
294.5.c.a.97.3		4	7.4	even	3
294.5.c.a.97.4		4	7.3	odd	6
294.5.g.c.19.1		4	7.5	odd	6	inner
294.5.g.c.31.1		4	1.1	even	1	trivial
336.5.bh.d.145.2		4	28.23	odd	6
336.5.bh.d.241.2		4	28.27	even	2
882.5.c.a.685.1		4	21.11	odd	6
882.5.c.a.685.2		4	21.17	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	294.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 2.44949i) q^{2} +(4.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(12.2574 - 7.07679i) q^{5} -14.6969i q^{6} +22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +(-34.6690 - 20.0162i) q^{10} +(-32.0147 + 55.4511i) q^{11} +(-36.0000 + 20.7846i) q^{12} -228.919i q^{13} +73.5442 q^{15} +(-32.0000 - 55.4256i) q^{16} +(195.250 + 112.728i) q^{17} +(38.1838 - 66.1362i) q^{18} +(255.250 - 147.369i) q^{19} +113.229i q^{20} +181.103 q^{22} +(-354.749 - 614.444i) q^{23} +(101.823 + 58.7878i) q^{24} +(-212.338 + 367.780i) q^{25} +(-560.735 + 323.741i) q^{26} +140.296i q^{27} +740.397 q^{29} +(-104.007 - 180.146i) q^{30} +(577.390 + 333.356i) q^{31} +(-90.5097 + 156.767i) q^{32} +(-288.132 + 166.353i) q^{33} -637.683i q^{34} -216.000 q^{36} +(416.882 + 722.061i) q^{37} +(-721.955 - 416.821i) q^{38} +(594.749 - 1030.14i) q^{39} +(277.352 - 160.129i) q^{40} -2817.60i q^{41} +3066.41 q^{43} +(-256.118 - 443.609i) q^{44} +(330.949 + 191.073i) q^{45} +(-1003.38 + 1737.91i) q^{46} +(531.502 - 306.863i) q^{47} -332.554i q^{48} +1201.17 q^{50} +(585.749 + 1014.55i) q^{51} +(1586.00 + 915.677i) q^{52} +(576.300 - 998.181i) q^{53} +(343.654 - 198.409i) q^{54} +906.246i q^{55} +1531.50 q^{57} +(-1047.08 - 1813.59i) q^{58} +(3024.67 + 1746.30i) q^{59} +(-294.177 + 509.529i) q^{60} +(-1967.79 + 1136.11i) q^{61} -1885.75i q^{62} +512.000 q^{64} +(-1620.01 - 2805.94i) q^{65} +(814.962 + 470.518i) q^{66} +(4337.31 - 7512.44i) q^{67} +(-1562.00 + 901.820i) q^{68} -3686.66i q^{69} -353.591 q^{71} +(305.470 + 529.090i) q^{72} +(-3524.68 - 2034.97i) q^{73} +(1179.12 - 2042.30i) q^{74} +(-1911.04 + 1103.34i) q^{75} +2357.90i q^{76} -3364.41 q^{78} +(-3236.41 - 5605.63i) q^{79} +(-784.471 - 452.915i) q^{80} +(-364.500 + 631.333i) q^{81} +(-6901.69 + 3984.69i) q^{82} -8225.83i q^{83} +3191.00 q^{85} +(-4336.55 - 7511.13i) q^{86} +(3331.79 + 1923.61i) q^{87} +(-724.410 + 1254.72i) q^{88} +(13456.5 - 7769.13i) q^{89} -1080.87i q^{90} +5675.99 q^{92} +(1732.17 + 3000.21i) q^{93} +(-1503.32 - 867.939i) q^{94} +(2085.79 - 3612.70i) q^{95} +(-814.587 + 470.302i) q^{96} +1558.61i q^{97} -1728.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} - 16 q^{4} + 66 q^{5} + 54 q^{9} + 48 q^{10} - 162 q^{11} - 144 q^{12} + 396 q^{15} - 128 q^{16} + 204 q^{17} + 444 q^{19} - 192 q^{22} + 312 q^{23} - 476 q^{25} - 1632 q^{26} + 2724 q^{29}+ \cdots - 8748 q^{99}+O(q^{100}) \) 4 * q + 18 * q^3 - 16 * q^4 + 66 * q^5 + 54 * q^9 + 48 * q^10 - 162 * q^11 - 144 * q^12 + 396 * q^15 - 128 * q^16 + 204 * q^17 + 444 * q^19 - 192 * q^22 + 312 * q^23 - 476 * q^25 - 1632 * q^26 + 2724 * q^29 + 144 * q^30 + 3786 * q^31 - 1458 * q^33 - 864 * q^36 + 1396 * q^37 - 1632 * q^38 + 648 * q^39 - 384 * q^40 - 632 * q^43 - 1296 * q^44 + 1782 * q^45 - 4896 * q^46 + 7896 * q^47 + 2112 * q^50 + 612 * q^51 + 1728 * q^52 - 1038 * q^53 + 2664 * q^57 - 336 * q^58 + 966 * q^59 - 1584 * q^60 - 5088 * q^61 + 2048 * q^64 - 744 * q^65 - 864 * q^66 + 14600 * q^67 - 1632 * q^68 - 9696 * q^71 - 22584 * q^73 + 768 * q^74 - 4284 * q^75 - 9792 * q^78 + 3974 * q^79 - 4224 * q^80 - 1458 * q^81 - 18816 * q^82 + 1224 * q^85 - 18240 * q^86 + 12258 * q^87 + 768 * q^88 + 33156 * q^89 - 4992 * q^92 + 11358 * q^93 + 16320 * q^94 + 3252 * q^95 - 8748 * q^99

Introduction

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