LMFDB - Embedded newform 171.4.u.b.82.2

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			82.2
Character	$\chi$	$=$	171.82
Dual form			171.4.u.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38101 + 1.15881i) q^{2} +(-0.824823 + 4.67780i) q^{4} +(3.13553 + 17.7825i) q^{5} +(-14.1277 + 24.4699i) q^{7} +(-11.4927 - 19.9060i) q^{8} +O(q^{10})$	\(q+(-1.38101 + 1.15881i) q^{2} +(-0.824823 + 4.67780i) q^{4} +(3.13553 + 17.7825i) q^{5} +(-14.1277 + 24.4699i) q^{7} +(-11.4927 - 19.9060i) q^{8} +(-24.9367 - 20.9244i) q^{10} +(1.89653 + 3.28489i) q^{11} +(44.0524 - 16.0338i) q^{13} +(-8.84538 - 50.1646i) q^{14} +(3.23077 + 1.17590i) q^{16} +(-14.5268 + 12.1895i) q^{17} +(75.4905 - 34.0614i) q^{19} -85.7692 q^{20} +(-6.42569 - 2.33876i) q^{22} +(2.85514 - 16.1923i) q^{23} +(-188.924 + 68.7626i) q^{25} +(-42.2569 + 73.1911i) q^{26} +(-102.813 - 86.2701i) q^{28} +(-108.300 - 90.8743i) q^{29} +(-89.1238 + 154.367i) q^{31} +(166.970 - 60.7720i) q^{32} +(5.93652 - 33.6677i) q^{34} +(-479.434 - 174.500i) q^{35} -29.5834 q^{37} +(-64.7828 + 134.518i) q^{38} +(317.942 - 266.785i) q^{40} +(328.747 + 119.654i) q^{41} +(-13.5956 - 77.1044i) q^{43} +(-16.9303 + 6.16214i) q^{44} +(14.8208 + 25.6704i) q^{46} +(-158.409 - 132.921i) q^{47} +(-227.685 - 394.363i) q^{49} +(181.224 - 313.888i) q^{50} +(38.6673 + 219.293i) q^{52} +(-67.7541 + 384.253i) q^{53} +(-52.4668 + 44.0249i) q^{55} +649.464 q^{56} +254.869 q^{58} +(-26.7893 + 22.4789i) q^{59} +(-117.777 + 667.946i) q^{61} +(-55.8005 - 316.460i) q^{62} +(-173.917 + 301.233i) q^{64} +(423.248 + 733.087i) q^{65} +(-579.933 - 486.622i) q^{67} +(-45.0379 - 78.0079i) q^{68} +(864.317 - 314.586i) q^{70} +(-18.2055 - 103.248i) q^{71} +(803.809 + 292.563i) q^{73} +(40.8551 - 34.2815i) q^{74} +(97.0663 + 381.224i) q^{76} -107.175 q^{77} +(591.826 + 215.407i) q^{79} +(-10.7803 + 61.1382i) q^{80} +(-592.661 + 215.711i) q^{82} +(-385.876 + 668.357i) q^{83} +(-262.308 - 220.103i) q^{85} +(108.125 + 90.7276i) q^{86} +(43.5926 - 75.5046i) q^{88} +(972.442 - 353.940i) q^{89} +(-230.015 + 1304.48i) q^{91} +(73.3894 + 26.7116i) q^{92} +372.795 q^{94} +(842.400 + 1235.61i) q^{95} +(561.010 - 470.743i) q^{97} +(771.427 + 280.776i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.38101	+	1.15881i	−0.488262	+	0.409701i	−0.853403	−	0.521252i	$-0.825465\pi$
$2$	−1.38101	+	1.15881i	−0.488262	+	0.409701i	0.365141	+	0.930952i	$0.381021\pi$
$3$		0			0
$3$		0			0
$4$	−0.824823	+	4.67780i	−0.103103	+	0.584725i
$5$	3.13553	+	17.7825i	0.280451	+	1.59051i	0.721098	+	0.692833i	$0.243638\pi$
$5$	3.13553	+	17.7825i	0.280451	+	1.59051i	−0.440647	+	0.897680i	$0.645251\pi$
$6$		0			0
$7$	−14.1277	+	24.4699i	−0.762826	+	1.32125i	0.178563	+	0.983928i	$0.442855\pi$
$7$	−14.1277	+	24.4699i	−0.762826	+	1.32125i	−0.941389	+	0.337324i	$0.890478\pi$
$8$	−11.4927	−	19.9060i	−0.507911	−	0.879729i
$9$		0			0
$10$	−24.9367	−	20.9244i	−0.788568	−	0.661687i
$11$	1.89653	+	3.28489i	0.0519841	+	0.0900391i	0.890847	−	0.454304i	$-0.150112\pi$
$11$	1.89653	+	3.28489i	0.0519841	+	0.0900391i	−0.838862	+	0.544344i	$0.816779\pi$
$12$		0			0
$13$	44.0524	−	16.0338i	0.939841	−	0.342074i	0.173738	−	0.984792i	$-0.444415\pi$
$13$	44.0524	−	16.0338i	0.939841	−	0.342074i	0.766103	+	0.642718i	$0.222193\pi$
$14$	−8.84538	−	50.1646i	−0.168859	−	0.957648i
$15$		0			0
$16$	3.23077	+	1.17590i	0.0504808	+	0.0183735i
$17$	−14.5268	+	12.1895i	−0.207252	+	0.173905i	−0.740505	−	0.672051i	$-0.765414\pi$
$17$	−14.5268	+	12.1895i	−0.207252	+	0.173905i	0.533253	+	0.845956i	$0.320969\pi$
$18$		0			0
$19$	75.4905	−	34.0614i	0.911511	−	0.411275i
$19$	75.4905	−	34.0614i	0.911511	−	0.411275i
$20$	−85.7692			−0.958929
$21$		0			0
$22$	−6.42569	−	2.33876i	−0.0622709	−	0.0226648i
$23$	2.85514	−	16.1923i	0.0258843	−	0.146797i	−0.969127	−	0.246564i	$-0.920699\pi$
$23$	2.85514	−	16.1923i	0.0258843	−	0.146797i	0.995011	+	0.0997667i	$0.0318097\pi$
$24$		0			0
$25$	−188.924	+	68.7626i	−1.51139	+	0.550101i
$26$	−42.2569	+	73.1911i	−0.318741	+	0.552075i
$27$		0			0
$28$	−102.813	−	86.2701i	−0.693920	−	0.582268i
$29$	−108.300	−	90.8743i	−0.693475	−	0.581894i	0.226434	−	0.974026i	$-0.427293\pi$
$29$	−108.300	−	90.8743i	−0.693475	−	0.581894i	−0.919909	+	0.392132i	$0.871738\pi$
$30$		0			0
$31$	−89.1238	+	154.367i	−0.516358	+	0.894359i	0.483461	+	0.875366i	$0.339379\pi$
$31$	−89.1238	+	154.367i	−0.516358	+	0.894359i	−0.999820	+	0.0189932i	$0.993954\pi$
$32$	166.970	−	60.7720i	0.922386	−	0.335721i
$33$		0			0
$34$	5.93652	−	33.6677i	0.0299442	−	0.169822i
$35$	−479.434	−	174.500i	−2.31541	−	0.842739i
$36$		0			0
$37$	−29.5834			−0.131446			−0.0657228	−	0.997838i	$-0.520935\pi$
$37$	−29.5834			−0.131446			−0.0657228	+	0.997838i	$0.520935\pi$
$38$	−64.7828	+	134.518i	−0.276557	+	0.574257i
$39$		0			0
$40$	317.942	−	266.785i	1.25678	−	1.05456i
$41$	328.747	+	119.654i	1.25224	+	0.455777i	0.881157	−	0.472824i	$-0.156765\pi$
$41$	328.747	+	119.654i	1.25224	+	0.455777i	0.371080	+	0.928601i	$0.378987\pi$
$42$		0			0
$43$	−13.5956	−	77.1044i	−0.0482165	−	0.273449i	0.951162	−	0.308691i	$-0.0998909\pi$
$43$	−13.5956	−	77.1044i	−0.0482165	−	0.273449i	−0.999379	+	0.0352419i	$0.988780\pi$
$44$	−16.9303	+	6.16214i	−0.0580079	+	0.0211131i
$45$		0			0
$46$	14.8208	+	25.6704i	0.0475045	+	0.0822802i
$47$	−158.409	−	132.921i	−0.491624	−	0.412521i	0.362984	−	0.931795i	$-0.381758\pi$
$47$	−158.409	−	132.921i	−0.491624	−	0.412521i	−0.854608	+	0.519274i	$0.826202\pi$
$48$		0			0
$49$	−227.685	−	394.363i	−0.663806	−	1.14975i
$50$	181.224	−	313.888i	0.512578	−	0.887810i
$51$		0			0
$52$	38.6673	+	219.293i	0.103119	+	0.584818i
$53$	−67.7541	+	384.253i	−0.175599	+	0.995871i	0.761851	+	0.647752i	$0.224291\pi$
$53$	−67.7541	+	384.253i	−0.175599	+	0.995871i	−0.937450	+	0.348119i	$0.886820\pi$
$54$		0			0
$55$	−52.4668	+	44.0249i	−0.128630	+	0.107933i
$56$	649.464			1.54979
$57$		0			0
$58$	254.869			0.577000
$59$	−26.7893	+	22.4789i	−0.0591131	+	0.0496018i	−0.671866	−	0.740673i	$-0.734507\pi$
$59$	−26.7893	+	22.4789i	−0.0591131	+	0.0496018i	0.612752	+	0.790275i	$0.290062\pi$
$60$		0			0
$61$	−117.777	+	667.946i	−0.247210	+	1.40200i	0.568095	+	0.822963i	$0.307681\pi$
$61$	−117.777	+	667.946i	−0.247210	+	1.40200i	−0.815305	+	0.579032i	$0.803431\pi$
$62$	−55.8005	−	316.460i	−0.114301	−	0.648234i
$63$		0			0
$64$	−173.917	+	301.233i	−0.339681	+	0.588345i
$65$	423.248	+	733.087i	0.807653	+	1.39890i
$66$		0			0
$67$	−579.933	−	486.622i	−1.05746	−	0.887318i	−0.0636054	−	0.997975i	$-0.520260\pi$
$67$	−579.933	−	486.622i	−1.05746	−	0.887318i	−0.993859	+	0.110657i	$0.964704\pi$
$68$	−45.0379	−	78.0079i	−0.0803183	−	0.139115i
$69$		0			0
$70$	864.317	−	314.586i	1.47580	−	0.537146i
$71$	−18.2055	−	103.248i	−0.0304309	−	0.172582i	0.965805	−	0.259271i	$-0.0834824\pi$
$71$	−18.2055	−	103.248i	−0.0304309	−	0.172582i	−0.996235	+	0.0866892i	$0.972371\pi$
$72$		0			0
$73$	803.809	+	292.563i	1.28875	+	0.469066i	0.893316	−	0.449428i	$-0.148372\pi$
$73$	803.809	+	292.563i	1.28875	+	0.469066i	0.395433	+	0.918495i	$0.370595\pi$
$74$	40.8551	−	34.2815i	0.0641799	−	0.0538533i
$75$		0			0
$76$	97.0663	+	381.224i	0.146503	+	0.575387i
$77$	−107.175			−0.158619
$78$		0			0
$79$	591.826	+	215.407i	0.842856	+	0.306774i	0.727124	−	0.686506i	$-0.240856\pi$
$79$	591.826	+	215.407i	0.842856	+	0.306774i	0.115732	+	0.993281i	$0.463079\pi$
$80$	−10.7803	+	61.1382i	−0.0150660	+	0.0854433i
$81$		0			0
$82$	−592.661	+	215.711i	−0.798152	+	0.290504i
$83$	−385.876	+	668.357i	−0.510306	+	0.883875i	0.489623	+	0.871934i	$0.337134\pi$
$83$	−385.876	+	668.357i	−0.510306	+	0.883875i	−0.999929	+	0.0119412i	$0.996199\pi$
$84$		0			0
$85$	−262.308	−	220.103i	−0.334722	−	0.280865i
$86$	108.125	+	90.7276i	0.135575	+	0.113761i
$87$		0			0
$88$	43.5926	−	75.5046i	0.0528067	−	0.0914638i
$89$	972.442	−	353.940i	1.15819	−	0.421545i	0.309737	−	0.950822i	$-0.399759\pi$
$89$	972.442	−	353.940i	1.15819	−	0.421545i	0.848449	+	0.529277i	$0.177537\pi$
$90$		0			0
$91$	−230.015	+	1304.48i	−0.264968	+	1.50271i
$92$	73.3894	+	26.7116i	0.0831672	+	0.0302704i
$93$		0			0
$94$	372.795			0.409051
$95$	842.400	+	1235.61i	0.909772	+	1.33443i
$96$		0			0
$97$	561.010	−	470.743i	0.587236	−	0.492750i	−0.300078	−	0.953915i	$-0.597013\pi$
$97$	561.010	−	470.743i	0.587236	−	0.492750i	0.887314	+	0.461165i	$0.152568\pi$
$98$	771.427	+	280.776i	0.795162	+	0.289415i
$99$		0			0
$100$	−165.829	−	940.465i	−0.165829	−	0.940465i
$101$	72.9983	−	26.5692i	0.0719169	−	0.0261756i	−0.305811	−	0.952092i	$-0.598928\pi$
$101$	72.9983	−	26.5692i	0.0719169	−	0.0261756i	0.377728	+	0.925917i	$0.376705\pi$
$102$		0			0
$103$	17.0377	+	29.5102i	0.0162988	+	0.0282304i	0.874060	−	0.485818i	$-0.161478\pi$
$103$	17.0377	+	29.5102i	0.0162988	+	0.0282304i	−0.857761	+	0.514049i	$0.828145\pi$
$104$	−825.450	−	692.635i	−0.778289	−	0.653062i
$105$		0			0
$106$	−351.706	−	609.172i	−0.322271	−	0.558189i
$107$	381.411	−	660.622i	0.344601	−	0.596867i	−0.640680	−	0.767808i	$-0.721347\pi$
$107$	381.411	−	660.622i	0.344601	−	0.596867i	0.985281	+	0.170941i	$0.0546808\pi$
$108$		0			0
$109$	−55.9552	−	317.338i	−0.0491700	−	0.278857i	0.950303	−	0.311328i	$-0.100774\pi$
$109$	−55.9552	−	317.338i	−0.0491700	−	0.278857i	−0.999473	+	0.0324705i	$0.989663\pi$
$110$	21.4410	−	121.598i	0.0185847	−	0.105399i
$111$		0			0
$112$	−74.4178	+	62.4439i	−0.0627841	+	0.0526821i
$113$	−2249.24			−1.87248			−0.936241	−	0.351358i	$-0.885720\pi$
$113$	−2249.24			−1.87248			−0.936241	+	0.351358i	$0.885720\pi$
$114$		0			0
$115$	296.892			0.240742
$116$	514.420	−	431.650i	0.411748	−	0.345497i
$117$		0			0
$118$	10.9477	−	62.0873i	0.00854081	−	0.0484373i
$119$	−93.0443	−	527.681i	−0.0716753	−	0.406491i
$120$		0			0
$121$	658.306	−	1140.22i	0.494595	−	0.856664i
$122$	−611.370	−	1058.92i	−0.453695	−	0.785823i
$123$		0			0
$124$	−648.587	−	544.229i	−0.469716	−	0.394139i
$125$	−686.596	−	1189.22i	−0.491288	−	0.850935i
$126$		0			0
$127$	−1310.41	+	476.951i	−0.915593	+	0.333249i	−0.756484	−	0.654012i	$-0.773084\pi$
$127$	−1310.41	+	476.951i	−0.915593	+	0.333249i	−0.159109	+	0.987261i	$0.550862\pi$
$128$	137.949	+	782.345i	0.0952582	+	0.540236i
$129$		0			0
$130$	−1434.02	−	521.940i	−0.967475	−	0.352132i
$131$	−1411.30	+	1184.22i	−0.941265	+	0.789815i	−0.977805	−	0.209517i	$-0.932811\pi$
$131$	−1411.30	+	1184.22i	−0.941265	+	0.789815i	0.0365401	+	0.999332i	$0.488366\pi$
$132$		0			0
$133$	−233.029	+	2328.46i	−0.151926	+	1.51807i
$134$	1364.80			0.879854
$135$		0			0
$136$	409.596	+	149.081i	0.258254	+	0.0939969i
$137$	−233.604	+	1324.83i	−0.145680	+	0.826191i	0.821139	+	0.570728i	$0.193339\pi$
$137$	−233.604	+	1324.83i	−0.145680	+	0.826191i	−0.966819	+	0.255463i	$0.917772\pi$
$138$		0			0
$139$	−1698.47	+	618.192i	−1.03642	+	0.377225i	−0.803521	−	0.595276i	$-0.797043\pi$
$139$	−1698.47	+	618.192i	−1.03642	+	0.377225i	−0.232897	+	0.972501i	$0.574820\pi$
$140$	1211.72	−	2098.77i	0.731495	−	1.26699i
$141$		0			0
$142$	144.787	+	121.491i	0.0855653	+	0.0717978i
$143$	136.216	+	114.299i	0.0796569	+	0.0668401i
$144$		0			0
$145$	1276.39	−	2210.78i	0.731026	−	1.26617i
$146$	−1449.09	+	527.427i	−0.821424	+	0.298974i
$147$		0			0
$148$	24.4011	−	138.385i	0.0135524	−	0.0768595i
$149$	1757.57	+	639.702i	0.966345	+	0.351721i	0.776517	−	0.630097i	$-0.216985\pi$
$149$	1757.57	+	639.702i	0.966345	+	0.351721i	0.189828	+	0.981817i	$0.439207\pi$
$150$		0			0
$151$	−1143.34			−0.616182			−0.308091	−	0.951357i	$-0.599690\pi$
$151$	−1143.34			−0.616182			−0.308091	+	0.951357i	$0.599690\pi$
$152$	−1545.62	−	1111.25i	−0.824777	−	0.592991i
$153$		0			0
$154$	148.010	−	124.195i	0.0774478	−	0.0649864i
$155$	−3024.48	−	1100.82i	−1.56730	−	0.570452i
$156$		0			0
$157$	−28.1749	−	159.788i	−0.0143223	−	0.0812259i	0.976809	−	0.214113i	$-0.0686862\pi$
$157$	−28.1749	−	159.788i	−0.0143223	−	0.0812259i	−0.991131	+	0.132888i	$0.957575\pi$
$158$	−1066.93	+	388.333i	−0.537220	+	0.195532i
$159$		0			0
$160$	1604.22	+	2778.58i	0.792653	+	1.37291i
$161$	355.888	+	298.626i	0.174211	+	0.146180i
$162$		0			0
$163$	192.718	+	333.797i	0.0926063	+	0.160399i	0.908607	−	0.417652i	$-0.137147\pi$
$163$	192.718	+	333.797i	0.0926063	+	0.160399i	−0.816001	+	0.578051i	$0.803814\pi$
$164$	−830.878	+	1439.12i	−0.395614	+	0.685223i
$165$		0			0
$166$	−241.597	−	1370.17i	−0.112961	−	0.640635i
$167$	−197.258	+	1118.71i	−0.0914030	+	0.518372i	0.904387	+	0.426712i	$0.140328\pi$
$167$	−197.258	+	1118.71i	−0.0914030	+	0.518372i	−0.995790	+	0.0916598i	$0.970783\pi$
$168$		0			0
$169$	0.532926	−	0.447178i	0.000242570	−	0.000203540i
$170$	617.309			0.278502
$171$		0			0
$172$	371.893			0.164864
$173$	461.513	−	387.255i	0.202822	−	0.170188i	−0.535719	−	0.844396i	$-0.679959\pi$
$173$	461.513	−	387.255i	0.202822	−	0.170188i	0.738541	+	0.674208i	$0.235515\pi$
$174$		0			0
$175$	986.445	−	5594.41i	0.426104	−	2.41656i
$176$	2.26454	+	12.8429i	0.000969865	+	0.00550038i
$177$		0			0
$178$	−932.807	+	1615.67i	−0.392791	+	0.680334i
$179$	−1001.83	−	1735.22i	−0.418327	−	0.724563i	0.577445	−	0.816430i	$-0.304050\pi$
$179$	−1001.83	−	1735.22i	−0.418327	−	0.724563i	−0.995771	+	0.0918669i	$0.970717\pi$
$180$		0			0
$181$	3533.60	+	2965.04i	1.45111	+	1.21762i	0.931769	+	0.363052i	$0.118265\pi$
$181$	3533.60	+	2965.04i	1.45111	+	1.21762i	0.519337	+	0.854570i	$0.326179\pi$
$182$	−1193.99	−	2068.05i	−0.486287	−	0.842274i
$183$		0			0
$184$	−355.137	+	129.259i	−0.142288	+	0.0517887i
$185$	−92.7598	−	526.067i	−0.0368640	−	0.209066i
$186$		0			0
$187$	−67.5916	−	24.6013i	−0.0264320	−	0.00962047i
$188$	752.437	−	631.369i	0.291899	−	0.244933i
$189$		0			0
$190$	−2595.20	−	730.213i	−0.990924	−	0.278817i
$191$	1417.19			0.536883			0.268441	−	0.963296i	$-0.413491\pi$
$191$	1417.19			0.536883			0.268441	+	0.963296i	$0.413491\pi$
$192$		0			0
$193$	−4428.30	−	1611.77i	−1.65158	−	0.601128i	−0.662577	−	0.748994i	$-0.730537\pi$
$193$	−4428.30	−	1611.77i	−1.65158	−	0.601128i	−0.989007	+	0.147866i	$0.952759\pi$
$194$	−229.261	+	1300.20i	−0.0848453	+	0.481182i
$195$		0			0
$196$	2032.55	−	739.788i	0.740725	−	0.269602i
$197$	−554.421	+	960.285i	−0.200512	+	0.347297i	−0.948693	−	0.316197i	$-0.897594\pi$
$197$	−554.421	+	960.285i	−0.200512	+	0.347297i	0.748182	+	0.663494i	$0.230927\pi$
$198$		0			0
$199$	3180.09	+	2668.41i	1.13282	+	0.950547i	0.999180	−	0.0404838i	$-0.0128899\pi$
$199$	3180.09	+	2668.41i	1.13282	+	0.950547i	0.133637	+	0.991030i	$0.457334\pi$
$200$	3540.04	+	2970.44i	1.25159	+	1.05021i
$201$		0			0
$202$	−70.0230	+	121.283i	−0.0243901	+	0.0422449i
$203$	3753.72	−	1366.24i	1.29783	−	0.472371i
$204$		0			0
$205$	−1096.95	+	6221.13i	−0.373729	+	2.11952i
$206$	−57.7260	−	21.0105i	−0.0195241	−	0.00710619i
$207$		0			0
$208$	161.177			0.0537290
$209$	255.058	+	183.379i	0.0844149	+	0.0606919i
$210$		0			0
$211$	−1491.77	+	1251.75i	−0.486720	+	0.408406i	−0.852849	−	0.522158i	$-0.825127\pi$
$211$	−1491.77	+	1251.75i	−0.486720	+	0.408406i	0.366129	+	0.930564i	$0.380683\pi$
$212$	−1741.57	−	633.881i	−0.564206	−	0.205354i
$213$		0			0
$214$	238.801	+	1354.31i	0.0762810	+	0.432611i
$215$	1328.48	−	483.527i	0.421403	−	0.153378i
$216$		0			0
$217$	−2518.23	−	4361.71i	−0.787783	−	1.36448i
$218$	445.008	+	373.406i	0.138256	+	0.116010i
$219$		0			0
$220$	−162.664	−	281.742i	−0.0498491	−	0.0863411i
$221$	−444.499	+	769.895i	−0.135295	+	0.234338i
$222$		0			0
$223$	228.777	+	1297.46i	0.0686999	+	0.389616i	0.999698	+	0.0245913i	$0.00782844\pi$
$223$	228.777	+	1297.46i	0.0686999	+	0.389616i	−0.930998	+	0.365025i	$0.881060\pi$
$224$	−871.815	+	4944.31i	−0.260047	+	1.47480i
$225$		0			0
$226$	3106.23	−	2606.44i	0.914262	−	0.767157i
$227$	−2912.98			−0.851724			−0.425862	−	0.904788i	$-0.640029\pi$
$227$	−2912.98			−0.851724			−0.425862	+	0.904788i	$0.640029\pi$
$228$		0			0
$229$	333.495			0.0962356			0.0481178	−	0.998842i	$-0.484678\pi$
$229$	333.495			0.0962356			0.0481178	+	0.998842i	$0.484678\pi$
$230$	−410.012	+	344.041i	−0.117545	+	0.0986321i
$231$		0			0
$232$	−564.283	+	3200.21i	−0.159685	+	0.905620i
$233$	122.604	+	695.323i	0.0344724	+	0.195503i	0.997181	−	0.0750393i	$-0.0239082\pi$
$233$	122.604	+	695.323i	0.0344724	+	0.195503i	−0.962708	+	0.270542i	$0.912797\pi$
$234$		0			0
$235$	1866.97	−	3233.68i	0.518245	−	0.897626i
$236$	−83.0554	−	143.856i	−0.0229087	−	0.0396790i
$237$		0			0
$238$	739.976	+	620.914i	0.201536	+	0.169109i
$239$	−789.615	−	1367.65i	−0.213707	−	0.370151i	0.739165	−	0.673525i	$-0.235220\pi$
$239$	−789.615	−	1367.65i	−0.213707	−	0.370151i	−0.952872	+	0.303373i	$0.901887\pi$
$240$		0			0
$241$	3598.71	−	1309.82i	0.961882	−	0.350096i	0.187111	−	0.982339i	$-0.440087\pi$
$241$	3598.71	−	1309.82i	0.961882	−	0.350096i	0.774771	+	0.632242i	$0.217865\pi$
$242$	412.166	+	2337.51i	0.109484	+	0.620913i
$243$		0			0
$244$	−3027.37	−	1101.87i	−0.794294	−	0.289099i
$245$	6298.83	−	5285.35i	1.64252	−	1.37824i
$246$		0			0
$247$	2779.41	−	2710.88i	0.715989	−	0.698338i
$248$	4097.10			1.04906
$249$		0			0
$250$	2326.27	+	846.694i	0.588506	+	0.214199i
$251$	739.191	−	4192.16i	0.185886	−	1.05421i	−0.738926	−	0.673786i	$-0.764667\pi$
$251$	739.191	−	4192.16i	0.185886	−	1.05421i	0.924812	−	0.380424i	$-0.124222\pi$
$252$		0			0
$253$	58.6048	−	21.3304i	0.0145630	−	0.00530051i
$254$	1257.00	−	2177.19i	0.310517	−	0.537831i
$255$		0			0
$256$	−3228.74	−	2709.24i	−0.788268	−	0.661435i
$257$	4992.24	+	4188.99i	1.21170	+	1.01674i	0.999217	+	0.0395748i	$0.0126003\pi$
$257$	4992.24	+	4188.99i	1.21170	+	1.01674i	0.212486	+	0.977164i	$0.431844\pi$
$258$		0			0
$259$	417.947	−	723.905i	0.100270	−	0.173673i
$260$	−3778.34	+	1375.20i	−0.901241	+	0.328025i
$261$		0			0
$262$	576.739	−	3270.85i	0.135996	−	0.771273i
$263$	−573.601	−	208.774i	−0.134486	−	0.0489488i	0.273901	−	0.961758i	$-0.411686\pi$
$263$	−573.601	−	208.774i	−0.134486	−	0.0489488i	−0.408386	+	0.912809i	$0.633908\pi$
$264$		0			0
$265$	−7045.41			−1.63319
$266$	−2376.42	−	3485.67i	−0.547773	−	0.803459i
$267$		0			0
$268$	2754.66	−	2311.44i	0.627865	−	0.526841i
$269$	4050.24	+	1474.17i	0.918020	+	0.334132i	0.757450	−	0.652893i	$-0.226445\pi$
$269$	4050.24	+	1474.17i	0.918020	+	0.334132i	0.160569	+	0.987025i	$0.448667\pi$
$270$		0			0
$271$	638.438	+	3620.76i	0.143108	+	0.811607i	0.968867	+	0.247583i	$0.0796363\pi$
$271$	638.438	+	3620.76i	0.143108	+	0.811607i	−0.825758	+	0.564024i	$0.809253\pi$
$272$	−61.2666	+	22.2992i	−0.0136575	+	0.00497091i
$273$		0			0
$274$	−1212.62	−	2100.31i	−0.267361	−	0.463083i
$275$	−584.177	−	490.182i	−0.128099	−	0.107488i
$276$		0			0
$277$	692.274	+	1199.05i	0.150161	+	0.260087i	0.931287	−	0.364287i	$-0.118687\pi$
$277$	692.274	+	1199.05i	0.150161	+	0.260087i	−0.781125	+	0.624374i	$0.785354\pi$
$278$	1629.24	−	2821.93i	0.351494	−	0.608806i
$279$		0			0
$280$	2036.42	+	11549.1i	0.434640	+	2.46496i
$281$	−604.675	+	3429.28i	−0.128370	+	0.728021i	0.850879	+	0.525361i	$0.176070\pi$
$281$	−604.675	+	3429.28i	−0.128370	+	0.728021i	−0.979249	+	0.202660i	$0.935041\pi$
$282$		0			0
$283$	6213.33	−	5213.60i	1.30510	−	1.09511i	0.315864	−	0.948804i	$-0.397706\pi$
$283$	6213.33	−	5213.60i	1.30510	−	1.09511i	0.989239	−	0.146307i	$-0.0467388\pi$
$284$	497.992			0.104051
$285$		0			0
$286$	−320.566			−0.0662779
$287$	−7572.39	+	6353.99i	−1.55744	+	1.30684i
$288$		0			0
$289$	−790.687	+	4484.21i	−0.160938	+	0.912724i
$290$	799.151	+	4532.21i	0.161820	+	0.917726i
$291$		0			0
$292$	−2031.55	+	3518.75i	−0.407149	+	0.705202i
$293$	1178.82	+	2041.78i	0.235042	+	0.407105i	0.959285	−	0.282440i	$-0.0911437\pi$
$293$	1178.82	+	2041.78i	0.235042	+	0.407105i	−0.724243	+	0.689545i	$0.757810\pi$
$294$		0			0
$295$	−483.730	−	405.897i	−0.0954706	−	0.0801093i
$296$	339.994	+	588.887i	0.0667627	+	0.115636i
$297$		0			0
$298$	−3168.51	+	1153.24i	−0.615930	+	0.224180i
$299$	−133.848	−	759.089i	−0.0258884	−	0.146820i
$300$		0			0
$301$	2078.82	+	756.627i	0.398076	+	0.144888i
$302$	1578.96	−	1324.91i	0.300858	−	0.252450i
$303$		0			0
$304$	283.946	−	21.2750i	0.0535704	−	0.00401383i
$305$	−12247.0			−2.29922
$306$		0			0
$307$	−4449.75	−	1619.58i	−0.827234	−	0.301089i	−0.106511	−	0.994312i	$-0.533968\pi$
$307$	−4449.75	−	1619.58i	−0.827234	−	0.301089i	−0.720723	+	0.693223i	$0.756190\pi$
$308$	88.4001	−	501.342i	0.0163541	−	0.0927487i
$309$		0			0
$310$	5452.49	−	1984.54i	0.998969	−	0.363595i
$311$	−250.927	+	434.618i	−0.0457516	+	0.0792441i	−0.887994	−	0.459854i	$-0.847902\pi$
$311$	−250.927	+	434.618i	−0.0457516	+	0.0792441i	0.842243	+	0.539098i	$0.181235\pi$
$312$		0			0
$313$	2222.05	+	1864.52i	0.401271	+	0.336706i	0.820985	−	0.570950i	$-0.193425\pi$
$313$	2222.05	+	1864.52i	0.401271	+	0.336706i	−0.419714	+	0.907656i	$0.637870\pi$
$314$	224.073	+	188.020i	0.0402713	+	0.0337917i
$315$		0			0
$316$	−1495.78	+	2590.77i	−0.266280	+	0.461210i
$317$	5743.21	−	2090.36i	1.01757	−	0.370366i	0.221236	−	0.975220i	$-0.428991\pi$
$317$	5743.21	−	2090.36i	1.01757	−	0.370366i	0.796336	+	0.604854i	$0.206769\pi$
$318$		0			0
$319$	93.1180	−	528.098i	0.0163436	−	0.0926891i
$320$	−5901.99	−	2148.15i	−1.03103	−	0.375266i
$321$		0			0
$322$	−837.536			−0.144951
$323$	−681.449	+	1414.99i	−0.117390	+	0.243754i
$324$		0			0
$325$	−7220.02	+	6058.32i	−1.23229	+	1.03401i
$326$	−652.953	−	237.655i	−0.110932	−	0.0403758i
$327$		0			0
$328$	−1396.37	−	7919.20i	−0.235066	−	1.33312i
$329$	5490.52	−	1998.39i	0.920068	−	0.334877i
$330$		0			0
$331$	−2642.46	−	4576.87i	−0.438799	−	0.760023i	0.558798	−	0.829304i	$-0.311263\pi$
$331$	−2642.46	−	4576.87i	−0.438799	−	0.760023i	−0.997597	+	0.0692810i	$0.977929\pi$
$332$	−2808.16	−	2356.33i	−0.464210	−	0.389519i
$333$		0			0
$334$	−1023.95	−	1773.53i	−0.167749	−	0.290549i
$335$	6834.94	−	11838.5i	1.11472	−	1.93076i
$336$		0			0
$337$	262.672	+	1489.69i	0.0424589	+	0.240796i	0.998650	−	0.0519474i	$-0.0165428\pi$
$337$	262.672	+	1489.69i	0.0424589	+	0.240796i	−0.956191	+	0.292744i	$0.905432\pi$
$338$	−0.217785	+	1.23512i	−3.50471e−5	+	0.000198762i
$339$		0			0
$340$	1245.96	−	1045.48i	0.198740	−	0.166762i
$341$	−676.104			−0.107370
$342$		0			0
$343$	3175.08			0.499820
$344$	−1378.59	+	1156.77i	−0.216071	+	0.181305i
$345$		0			0
$346$	−188.601	+	1069.61i	−0.0293042	+	0.166192i
$347$	−2114.64	−	11992.7i	−0.327146	−	1.85534i	−0.494144	−	0.869380i	$-0.664518\pi$
$347$	−2114.64	−	11992.7i	−0.327146	−	1.85534i	0.166998	−	0.985957i	$-0.446593\pi$
$348$		0			0
$349$	2256.58	−	3908.52i	0.346109	−	0.599479i	−0.639445	−	0.768836i	$-0.720836\pi$
$349$	2256.58	−	3908.52i	0.346109	−	0.599479i	0.985555	+	0.169358i	$0.0541693\pi$
$350$	5120.55	+	8869.06i	0.782015	+	1.35449i
$351$		0			0
$352$	516.292	+	433.220i	0.0781774	+	0.0655987i
$353$	−153.600	−	266.043i	−0.0231595	−	0.0401134i	0.854213	−	0.519923i	$-0.174039\pi$
$353$	−153.600	−	266.043i	−0.0231595	−	0.0401134i	−0.877373	+	0.479809i	$0.840706\pi$
$354$		0			0
$355$	1778.93	−	647.478i	0.265960	−	0.0968015i
$356$	853.568	+	4840.83i	0.127076	+	0.720684i
$357$		0			0
$358$	3394.34	+	1235.44i	0.501107	+	0.182388i
$359$	5687.78	−	4772.62i	0.836183	−	0.701641i	−0.120519	−	0.992711i	$-0.538456\pi$
$359$	5687.78	−	4772.62i	0.836183	−	0.701641i	0.956702	+	0.291070i	$0.0940113\pi$
$360$		0			0
$361$	4538.64	−	5142.63i	0.661706	−	0.749764i
$362$	−8315.85			−1.20738
$363$		0			0
$364$	−5912.38	−	2151.93i	−0.851354	−	0.309868i
$365$	−2682.12	+	15211.1i	−0.384626	+	2.18132i
$366$		0			0
$367$	−6630.10	+	2413.16i	−0.943020	+	0.343231i	−0.767358	−	0.641219i	$-0.778429\pi$
$367$	−6630.10	+	2413.16i	−0.943020	+	0.343231i	−0.175662	+	0.984450i	$0.556207\pi$
$368$	28.2649	−	48.9563i	0.00400383	−	0.00693484i
$369$		0			0
$370$	737.713	+	619.015i	0.103654	+	0.0869758i
$371$	−8445.43	−	7086.56i	−1.18185	−	0.991687i
$372$		0			0
$373$	990.373	−	1715.38i	0.137479	−	0.238120i	−0.789063	−	0.614312i	$-0.789433\pi$
$373$	990.373	−	1715.38i	0.137479	−	0.238120i	0.926542	+	0.376192i	$0.122767\pi$
$374$	121.853	−	44.3509i	0.0168473	−	0.00613190i
$375$		0			0
$376$	−825.370	+	4680.91i	−0.113205	+	0.642020i
$377$	−6227.92	−	2266.78i	−0.850807	−	0.309669i
$378$		0			0
$379$	−5986.20			−0.811321			−0.405660	−	0.914024i	$-0.632958\pi$
$379$	−5986.20			−0.811321			−0.405660	+	0.914024i	$0.632958\pi$
$380$	−6474.76	+	2921.42i	−0.874075	+	0.394384i
$381$		0			0
$382$	−1957.16	+	1642.26i	−0.262139	+	0.219961i
$383$	−3995.44	−	1454.22i	−0.533048	−	0.194014i	0.0614507	−	0.998110i	$-0.480427\pi$
$383$	−3995.44	−	1454.22i	−0.533048	−	0.194014i	−0.594499	+	0.804096i	$0.702650\pi$
$384$		0			0
$385$	−336.049	−	1905.83i	−0.0444848	−	0.252286i
$386$	7983.27	−	2905.67i	1.05269	−	0.383147i
$387$		0			0
$388$	1739.31	+	3012.57i	0.227577	+	0.394176i
$389$	−1982.65	−	1663.64i	−0.258418	−	0.216838i	0.504369	−	0.863488i	$-0.331725\pi$
$389$	−1982.65	−	1663.64i	−0.258418	−	0.216838i	−0.762787	+	0.646650i	$0.776170\pi$
$390$		0			0
$391$	155.899	+	270.026i	0.0201641	+	0.0349253i
$392$	−5233.45	+	9064.60i	−0.674309	+	1.16794i
$393$		0			0
$394$	−347.123	−	1968.63i	−0.0443853	−	0.251722i
$395$	−1974.78	+	11199.6i	−0.251550	+	1.42661i
$396$		0			0
$397$	4146.90	−	3479.66i	0.524249	−	0.439897i	−0.341861	−	0.939750i	$-0.611057\pi$
$397$	4146.90	−	3479.66i	0.524249	−	0.439897i	0.866110	+	0.499854i	$0.166613\pi$
$398$	−7483.93			−0.942551
$399$		0			0
$400$	−691.227			−0.0864034
$401$	889.929	−	746.739i	0.110825	−	0.0929935i	−0.585691	−	0.810534i	$-0.699177\pi$
$401$	889.929	−	746.739i	0.110825	−	0.0929935i	0.696516	+	0.717541i	$0.254732\pi$
$402$		0			0
$403$	−1451.03	+	8229.23i	−0.179358	+	1.01719i
$404$	64.0748	+	363.386i	0.00789070	+	0.0447504i
$405$		0			0
$406$	−3600.73	+	6236.64i	−0.440150	+	0.762363i
$407$	−56.1058	−	97.1782i	−0.00683308	−	0.0118352i
$408$		0			0
$409$	2085.66	+	1750.08i	0.252150	+	0.211579i	0.760097	−	0.649809i	$-0.225151\pi$
$409$	2085.66	+	1750.08i	0.252150	+	0.211579i	−0.507948	+	0.861388i	$0.669596\pi$
$410$	−5694.19	−	9862.62i	−0.685892	−	1.18800i
$411$		0			0
$412$	−152.096	+	55.3584i	−0.0181875	+	0.00661969i
$413$	−171.585	−	973.109i	−0.0204435	−	0.115941i
$414$		0			0
$415$	−13095.0	−	4766.18i	−1.54893	−	0.563765i
$416$	6381.01	−	5354.30i	0.752055	−	0.631049i
$417$		0			0
$418$	−564.740	+	42.3139i	−0.0660821	+	0.00495129i
$419$	10546.9			1.22971			0.614856	−	0.788639i	$-0.289214\pi$
$419$	10546.9			1.22971			0.614856	+	0.788639i	$0.289214\pi$
$420$		0			0
$421$	7454.34	+	2713.16i	0.862951	+	0.314089i	0.735309	−	0.677732i	$-0.237037\pi$
$421$	7454.34	+	2713.16i	0.862951	+	0.314089i	0.127642	+	0.991820i	$0.459259\pi$
$422$	609.625	−	3457.36i	0.0703225	−	0.398819i
$423$		0			0
$424$	8427.61	−	3067.40i	0.965285	−	0.351335i
$425$	1906.29	−	3301.78i	0.217573	−	0.376847i
$426$		0			0
$427$	−14680.7	−	12318.6i	−1.66381	−	1.39610i
$428$	2775.66	+	2329.06i	0.313474	+	0.263036i
$429$		0			0
$430$	−1274.33	+	2207.21i	−0.142916	+	0.247537i
$431$	15137.3	−	5509.51i	1.69173	−	0.615740i	0.696889	−	0.717179i	$-0.254567\pi$
$431$	15137.3	−	5509.51i	1.69173	−	0.615740i	0.994842	+	0.101439i	$0.0323448\pi$
$432$		0			0
$433$	1270.06	−	7202.89i	0.140959	−	0.799420i	−0.829564	−	0.558412i	$-0.811411\pi$
$433$	1270.06	−	7202.89i	0.140959	−	0.799420i	0.970523	−	0.241008i	$-0.0774781\pi$
$434$	8532.10	+	3105.43i	0.943673	+	0.343469i
$435$		0			0
$436$	1530.60			0.168124
$437$	−335.997	−	1319.62i	−0.0367801	−	0.144453i
$438$		0			0
$439$	6792.31	−	5699.42i	0.738449	−	0.619632i	−0.193972	−	0.981007i	$-0.562137\pi$
$439$	6792.31	−	5699.42i	0.738449	−	0.619632i	0.932421	+	0.361375i	$0.117693\pi$
$440$	1479.35	+	538.438i	0.160284	+	0.0583386i
$441$		0			0
$442$	−278.301	−	1578.33i	−0.0299490	−	0.169849i
$443$	−8943.71	+	3255.24i	−0.959206	+	0.349123i	−0.773722	−	0.633525i	$-0.781608\pi$
$443$	−8943.71	+	3255.24i	−0.959206	+	0.349123i	−0.185484	+	0.982647i	$0.559385\pi$
$444$		0			0
$445$	9343.05	+	16182.6i	0.995288	+	1.72389i
$446$	−1819.45	−	1526.70i	−0.193170	−	0.162088i
$447$		0			0
$448$	−4914.10	−	8511.47i	−0.518235	−	0.897609i
$449$	5289.97	−	9162.49i	0.556011	−	0.963040i	−0.441813	−	0.897107i	$-0.645664\pi$
$449$	5289.97	−	9162.49i	0.556011	−	0.963040i	0.997824	−	0.0659325i	$-0.0210022\pi$
$450$		0			0
$451$	230.429	+	1306.83i	0.0240587	+	0.136444i
$452$	1855.22	−	10521.5i	0.193058	−	1.09489i
$453$		0			0
$454$	4022.87	−	3375.59i	0.415865	−	0.348952i
$455$	−23918.1			−2.46439
$456$		0			0
$457$	−4177.34			−0.427588			−0.213794	−	0.976879i	$-0.568582\pi$
$457$	−4177.34			−0.427588			−0.213794	+	0.976879i	$0.568582\pi$
$458$	−460.561	+	386.456i	−0.0469882	+	0.0394278i
$459$		0			0
$460$	−244.883	+	1388.80i	−0.0248212	+	0.140768i
$461$	2761.61	+	15661.8i	0.279004	+	1.58231i	0.725949	+	0.687748i	$0.241401\pi$
$461$	2761.61	+	15661.8i	0.279004	+	1.58231i	−0.446945	+	0.894561i	$0.647488\pi$
$462$		0			0
$463$	2187.46	−	3788.80i	0.219568	−	0.380303i	−0.735108	−	0.677950i	$-0.762869\pi$
$463$	2187.46	−	3788.80i	0.219568	−	0.380303i	0.954676	+	0.297647i	$0.0962019\pi$
$464$	−243.032	−	420.944i	−0.0243157	−	0.0421161i
$465$		0			0
$466$	−975.064	−	818.176i	−0.0969291	−	0.0813332i
$467$	−2670.63	−	4625.67i	−0.264630	−	0.458352i	0.702837	−	0.711351i	$-0.251916\pi$
$467$	−2670.63	−	4625.67i	−0.264630	−	0.458352i	−0.967467	+	0.252999i	$0.918583\pi$
$468$		0			0
$469$	20100.7	−	7316.07i	1.97903	−	0.720308i
$470$	1168.91	+	6629.21i	0.114719	+	0.650602i
$471$		0			0
$472$	755.347	+	274.924i	0.0736603	+	0.0268102i
$473$	227.495	−	190.891i	0.0221146	−	0.0185564i
$474$		0			0
$475$	−11919.8	+	11625.9i	−1.15141	+	1.12302i
$476$	2545.13			0.245075
$477$		0			0
$478$	2675.32	+	973.736i	0.255996	+	0.0931750i
$479$	−2307.48	+	13086.4i	−0.220107	+	1.24829i	0.651714	+	0.758465i	$0.274050\pi$
$479$	−2307.48	+	13086.4i	−0.220107	+	1.24829i	−0.871821	+	0.489825i	$0.837061\pi$
$480$		0			0
$481$	−1303.22	+	474.334i	−0.123538	+	0.0449641i
$482$	−3452.04	+	5979.11i	−0.326216	+	0.565022i
$483$		0			0
$484$	4790.74	+	4019.91i	0.449919	+	0.377527i
$485$	10130.0	+	8500.12i	0.948416	+	0.795815i
$486$		0			0
$487$	9026.56	−	15634.5i	0.839902	−	1.45475i	−0.0500737	−	0.998746i	$-0.515946\pi$
$487$	9026.56	−	15634.5i	0.839902	−	1.45475i	0.889976	−	0.456008i	$-0.150721\pi$
$488$	14649.7	−	5332.05i	1.35894	−	0.494612i
$489$		0			0
$490$	−2574.07	+	14598.3i	−0.237316	+	1.34588i
$491$	19219.0	+	6995.16i	1.76648	+	0.642947i	1.00000		0.000681822i	$0.000217031\pi$
$491$	19219.0	+	6995.16i	1.76648	+	0.642947i	0.766483	+	0.642265i	$0.222005\pi$
$492$		0			0
$493$	2680.96			0.244918
$494$	−697.003	+	6964.57i	−0.0634811	+	0.634313i
$495$		0			0
$496$	−469.459	+	393.923i	−0.0424987	+	0.0356606i
$497$	2783.69	+	1013.18i	0.251238	+	0.0914432i
$498$		0			0
$499$	1864.96	+	10576.7i	0.167309	+	0.948856i	0.946652	+	0.322258i	$0.104442\pi$
$499$	1864.96	+	10576.7i	0.167309	+	0.948856i	−0.779343	+	0.626598i	$0.784447\pi$
$500$	6129.25	−	2230.86i	0.548217	−	0.199535i
$501$		0			0
$502$	3837.08	+	6646.01i	0.341150	+	0.590888i
$503$	−3466.42	−	2908.67i	−0.307276	−	0.257835i	0.476089	−	0.879397i	$-0.342054\pi$
$503$	−3466.42	−	2908.67i	−0.307276	−	0.257835i	−0.783365	+	0.621562i	$0.786498\pi$
$504$		0			0
$505$	701.355	+	1214.78i	0.0618018	+	0.107044i
$506$	−56.2161	+	97.3692i	−0.00493896	+	0.00855452i
$507$		0			0
$508$	−1150.22	−	6523.25i	−0.100459	−	0.569729i
$509$	1133.83	−	6430.24i	0.0987346	−	0.559952i	−0.894804	−	0.446459i	$-0.852685\pi$
$509$	1133.83	−	6430.24i	0.0987346	−	0.559952i	0.993539	−	0.113493i	$-0.0362040\pi$
$510$		0			0
$511$	−18515.0	+	15535.9i	−1.60285	+	1.34495i
$512$	1243.12			0.107302
$513$		0			0
$514$	−11748.6			−1.00819
$515$	−471.343	+	395.503i	−0.0403298	+	0.0338407i
$516$		0			0
$517$	136.203	−	772.443i	0.0115864	−	0.0657099i
$518$	261.677	+	1484.04i	0.0221958	+	0.125878i
$519$		0			0
$520$	9728.54	−	16850.3i	0.820432	−	1.42103i
$521$	7213.85	+	12494.8i	0.606611	+	1.05068i	0.991795	+	0.127842i	$0.0408049\pi$
$521$	7213.85	+	12494.8i	0.606611	+	1.05068i	−0.385183	+	0.922840i	$0.625862\pi$
$522$		0			0
$523$	5978.50	+	5016.56i	0.499850	+	0.419424i	0.857541	−	0.514416i	$-0.171991\pi$
$523$	5978.50	+	5016.56i	0.499850	+	0.419424i	−0.357691	+	0.933840i	$0.616436\pi$
$524$	−4375.48	−	7578.55i	−0.364778	−	0.631814i
$525$		0			0
$526$	1034.08	−	376.374i	0.0857186	−	0.0311990i
$527$	−586.964	−	3328.84i	−0.0485172	−	0.275155i
$528$		0			0
$529$	11179.2	+	4068.90i	0.918813	+	0.334421i
$530$	9729.81	−	8164.28i	0.797427	−	0.669120i
$531$		0			0
$532$	−10699.9	−	3010.63i	−0.871989	−	0.245352i
$533$	16400.6			1.33281
$534$		0			0
$535$	12943.4	+	4711.02i	1.04597	+	0.380702i
$536$	−3021.67	+	17136.7i	−0.243501	+	1.38096i
$537$		0			0
$538$	−7301.71	+	2657.60i	−0.585128	+	0.212969i
$539$	863.624	−	1495.84i	0.0690147	−	0.119537i
$540$		0			0
$541$	10973.0	+	9207.44i	0.872026	+	0.731717i	0.964524	−	0.263996i	$-0.0850407\pi$
$541$	10973.0	+	9207.44i	0.872026	+	0.731717i	−0.0924978	+	0.995713i	$0.529485\pi$
$542$	−5077.46	−	4260.49i	−0.402390	−	0.337645i
$543$		0			0
$544$	−1684.76	+	2918.10i	−0.132782	+	0.229986i
$545$	5467.60	−	1990.04i	0.429736	−	0.156411i
$546$		0			0
$547$	−3443.46	+	19528.8i	−0.269162	+	1.52649i	0.487754	+	0.872981i	$0.337816\pi$
$547$	−3443.46	+	19528.8i	−0.269162	+	1.52649i	−0.756916	+	0.653512i	$0.773295\pi$
$548$	−6004.62	−	2185.50i	−0.468075	−	0.170365i
$549$		0			0
$550$	1374.78			0.106584
$551$	−11270.9	−	3171.31i	−0.871429	−	0.245195i
$552$		0			0
$553$	−13632.2	+	11438.7i	−1.04828	+	0.879610i
$554$	−2345.51	−	853.697i	−0.179876	−	0.0654695i
$555$		0			0
$556$	−1490.84	−	8454.99i	−0.113716	−	0.644913i
$557$	−21505.2	+	7827.25i	−1.63592	+	0.595424i	−0.986318	−	0.164854i	$-0.947285\pi$
$557$	−21505.2	+	7827.25i	−1.63592	+	0.595424i	−0.649597	+	0.760279i	$0.725062\pi$
$558$		0			0
$559$	−1835.19	−	3178.65i	−0.138856	−	0.240505i
$560$	−1343.75	−	1127.54i	−0.101399	−	0.0850842i
$561$		0			0
$562$	−3138.82	−	5436.59i	−0.235593	−	0.408058i
$563$	−2993.41	+	5184.74i	−0.224080	+	0.388119i	−0.956043	−	0.293226i	$-0.905271\pi$
$563$	−2993.41	+	5184.74i	−0.224080	+	0.388119i	0.731963	+	0.681345i	$0.238605\pi$
$564$		0			0
$565$	−7052.56	−	39997.0i	−0.525139	−	2.97821i
$566$	−2539.13	+	14400.1i	−0.188565	+	1.06940i
$567$		0			0
$568$	−1846.03	+	1549.00i	−0.136369	+	0.114427i
$569$	5945.95			0.438079			0.219040	−	0.975716i	$-0.429708\pi$
$569$	5945.95			0.438079			0.219040	+	0.975716i	$0.429708\pi$
$570$		0			0
$571$	18946.7			1.38861			0.694305	−	0.719681i	$-0.255712\pi$
$571$	18946.7			1.38861			0.694305	+	0.719681i	$0.255712\pi$
$572$	−647.020	+	542.914i	−0.0472959	+	0.0396860i
$573$		0			0
$574$	3094.52	−	17549.9i	0.225022	−	1.27616i
$575$	574.021	+	3255.44i	0.0416319	+	0.236106i
$576$		0			0
$577$	−6629.84	+	11483.2i	−0.478343	+	0.828514i	−0.999692	−	0.0248299i	$-0.992096\pi$
$577$	−6629.84	+	11483.2i	−0.478343	+	0.828514i	0.521349	+	0.853343i	$0.325429\pi$
$578$	−4104.39	−	7109.01i	−0.295364	−	0.511585i
$579$		0			0
$580$	9288.79	+	7794.22i	0.664993	+	0.557995i
$581$	−10903.1	−	18884.7i	−0.778548	−	1.34849i
$582$		0			0
$583$	−1390.72	+	506.182i	−0.0987957	+	0.0359587i
$584$	−3414.21	−	19362.9i	−0.241920	−	1.37199i
$585$		0			0
$586$	−3994.00	−	1453.70i	−0.281554	−	0.102477i
$587$	−6997.02	+	5871.19i	−0.491989	+	0.412828i	−0.854739	−	0.519059i	$-0.826283\pi$
$587$	−6997.02	+	5871.19i	−0.491989	+	0.412828i	0.362749	+	0.931887i	$0.381838\pi$
$588$		0			0
$589$	−1470.05	+	14688.9i	−0.102839	+	1.02758i
$590$	1138.39			0.0794355
$591$		0			0
$592$	−95.5773	−	34.7873i	−0.00663547	−	0.00241512i
$593$	2497.34	−	14163.1i	0.172940	−	0.980791i	−0.767555	−	0.640983i	$-0.778527\pi$
$593$	2497.34	−	14163.1i	0.172940	−	0.980791i	0.940495	−	0.339808i	$-0.110362\pi$
$594$		0			0
$595$	9091.73	−	3309.12i	0.626428	−	0.228001i
$596$	−4442.08	+	7693.90i	−0.305293	+	0.528783i
$597$		0			0
$598$	1064.48	+	893.208i	0.0727926	+	0.0610803i
$599$	17568.2	+	14741.4i	1.19836	+	1.00554i	0.999675	+	0.0254774i	$0.00811058\pi$
$599$	17568.2	+	14741.4i	1.19836	+	1.00554i	0.198682	+	0.980064i	$0.436334\pi$
$600$		0			0
$601$	−3255.11	+	5638.02i	−0.220930	+	0.382662i	−0.955091	−	0.296314i	$-0.904243\pi$
$601$	−3255.11	+	5638.02i	−0.220930	+	0.382662i	0.734161	+	0.678976i	$0.237576\pi$
$602$	−3747.66	+	1364.04i	−0.253726	+	0.0923488i
$603$		0			0
$604$	943.050	−	5348.30i	0.0635301	−	0.360297i
$605$	22340.1	+	8131.13i	1.50125	+	0.546409i
$606$		0			0
$607$	−5716.61			−0.382257			−0.191129	−	0.981565i	$-0.561215\pi$
$607$	−5716.61			−0.382257			−0.191129	+	0.981565i	$0.561215\pi$
$608$	10534.6	−	10274.9i	0.702691	−	0.685368i
$609$		0			0
$610$	16913.3	−	14192.0i	1.12262	−	0.941993i
$611$	−9109.51	−	3315.59i	−0.603161	−	0.219533i
$612$		0			0
$613$	−1438.04	−	8155.54i	−0.0947504	−	0.537356i	−0.994824	−	0.101617i	$-0.967598\pi$
$613$	−1438.04	−	8155.54i	−0.0947504	−	0.537356i	0.900073	−	0.435739i	$-0.143513\pi$
$614$	8021.95	−	2919.75i	0.527263	−	0.191908i
$615$		0			0
$616$	1231.73	+	2133.42i	0.0805645	+	0.139542i
$617$	−13497.7	−	11325.9i	−0.880710	−	0.739003i	0.0856149	−	0.996328i	$-0.472715\pi$
$617$	−13497.7	−	11325.9i	−0.880710	−	0.739003i	−0.966325	+	0.257325i	$0.917159\pi$
$618$		0			0
$619$	−14790.0	−	25617.0i	−0.960354	−	1.66338i	−0.721610	−	0.692300i	$-0.756597\pi$
$619$	−14790.0	−	25617.0i	−0.960354	−	1.66338i	−0.238745	−	0.971082i	$-0.576736\pi$
$620$	7644.08	−	13239.9i	0.495151	−	0.857627i
$621$		0			0
$622$	−157.105	−	890.989i	−0.0101276	−	0.0574363i
$623$	−5077.50	+	28796.0i	−0.326526	+	1.85182i
$624$		0			0
$625$	−257.082	+	215.717i	−0.0164532	+	0.0138059i
$626$	−5229.30			−0.333874
$627$		0			0
$628$	770.695			0.0489715
$629$	429.754	−	360.606i	0.0272423	−	0.0228590i
$630$		0			0
$631$	−914.694	+	5187.49i	−0.0577075	+	0.327275i	−0.999971	−	0.00759657i	$-0.997582\pi$
$631$	−914.694	+	5187.49i	−0.0577075	+	0.327275i	0.942264	+	0.334872i	$0.108693\pi$
$632$	−2513.80	−	14256.5i	−0.158218	−	0.897299i
$633$		0			0
$634$	−5509.13	+	9542.08i	−0.345103	+	0.597736i
$635$	−12590.2	−	21806.9i	−0.786815	−	1.36280i
$636$		0			0
$637$	−16353.2	−	13722.0i	−1.01717	−	0.853507i
$638$	483.367	+	837.217i	0.0299948	+	0.0519526i
$639$		0			0
$640$	−13479.5	+	4906.14i	−0.832537	+	0.303019i
$641$	2518.62	+	14283.8i	0.155194	+	0.880150i	0.958608	+	0.284729i	$0.0919035\pi$
$641$	2518.62	+	14283.8i	0.155194	+	0.880150i	−0.803414	+	0.595421i	$0.796985\pi$
$642$		0			0
$643$	10965.0	+	3990.94i	0.672501	+	0.244770i	0.655624	−	0.755087i	$-0.272406\pi$
$643$	10965.0	+	3990.94i	0.672501	+	0.244770i	0.0168766	+	0.999858i	$0.494628\pi$
$644$	−1690.46	+	1418.46i	−0.103437	+	0.0867938i
$645$		0			0
$646$	−698.617	−	2743.79i	−0.0425491	−	0.167110i
$647$	−28681.4			−1.74278			−0.871391	−	0.490589i	$-0.836782\pi$
$647$	−28681.4			−1.74278			−0.871391	+	0.490589i	$0.836782\pi$
$648$		0			0
$649$	−124.647	−	45.3679i	−0.00753904	−	0.00274399i
$650$	2950.52	−	16733.2i	0.178045	−	1.00974i
$651$		0			0
$652$	−1720.40	+	626.173i	−0.103337	+	0.0376117i
$653$	12630.0	−	21875.8i	0.756891	−	1.31097i	−0.187538	−	0.982257i	$-0.560051\pi$
$653$	12630.0	−	21875.8i	0.756891	−	1.31097i	0.944429	−	0.328716i	$-0.106616\pi$
$654$		0			0
$655$	−25483.5	−	21383.2i	−1.52019	−	1.27559i
$656$	921.406	+	773.151i	0.0548397	+	0.0460160i
$657$		0			0
$658$	−5266.74	+	9122.26i	−0.312035	+	0.540460i
$659$	−19634.6	+	7146.40i	−1.16063	+	0.422434i	−0.849322	−	0.527875i	$-0.822989\pi$
$659$	−19634.6	+	7146.40i	−1.16063	+	0.422434i	−0.311307	+	0.950309i	$0.600767\pi$
$660$		0			0
$661$	2650.82	−	15033.6i	0.155984	−	0.884626i	−0.801898	−	0.597461i	$-0.796176\pi$
$661$	2650.82	−	15033.6i	0.155984	−	0.884626i	0.957881	−	0.287165i	$-0.0927128\pi$
$662$	8952.99	+	3258.62i	0.525631	+	0.191314i
$663$		0			0
$664$	17739.1			1.03676
$665$	−42136.5	+	3157.13i	−2.45712	+	0.184103i
$666$		0			0
$667$	−1780.68	+	1494.16i	−0.103370	+	0.0867381i
$668$	−5070.39	−	1845.47i	−0.293681	−	0.106891i
$669$		0			0
$670$	4279.36	+	24269.5i	0.246756	+	1.39942i
$671$	−2417.49	+	879.896i	−0.139085	+	0.0506229i
$672$		0			0
$673$	−3486.67	−	6039.08i	−0.199704	−	0.345898i	0.748728	−	0.662877i	$-0.230665\pi$
$673$	−3486.67	−	6039.08i	−0.199704	−	0.345898i	−0.948433	+	0.316979i	$0.897332\pi$
$674$	−2089.01	−	1752.89i	−0.119385	−	0.100176i
$675$		0			0
$676$	1.65224	+	2.86177i	9.40055e−5	+	0.000162822i
$677$	−7993.27	+	13844.8i	−0.453776	+	0.785963i	−0.998617	−	0.0525762i	$-0.983257\pi$
$677$	−7993.27	+	13844.8i	−0.453776	+	0.785963i	0.544841	+	0.838540i	$0.316590\pi$
$678$		0			0
$679$	3593.26	+	20378.4i	0.203088	+	1.15177i
$680$	−1366.73	+	7751.09i	−0.0770758	+	0.437119i
$681$		0			0
$682$	933.709	−	783.475i	0.0524246	−	0.0439894i
$683$	30854.4			1.72857			0.864284	−	0.503005i	$-0.167772\pi$
$683$	30854.4			1.72857			0.864284	+	0.503005i	$0.167772\pi$
$684$		0			0
$685$	−24291.3			−1.35492
$686$	−4384.83	+	3679.31i	−0.244043	+	0.204777i
$687$		0			0
$688$	46.7432	−	265.094i	0.00259022	−	0.0146898i
$689$	3176.29	+	18013.6i	0.175627	+	0.996029i
$690$		0			0
$691$	8251.58	−	14292.2i	0.454277	−	0.786830i	−0.544370	−	0.838845i	$-0.683231\pi$
$691$	8251.58	−	14292.2i	0.454277	−	0.786830i	0.998646	+	0.0520154i	$0.0165645\pi$
$692$	1430.84	+	2478.28i	0.0786015	+	0.136142i
$693$		0			0
$694$	16817.6	+	14111.6i	0.919866	+	0.771859i
$695$	−16318.6	−	28264.6i	−0.890646	−	1.54264i
$696$		0			0
$697$	−6234.19	+	2269.06i	−0.338790	+	0.123309i
$698$	1412.85	+	8012.66i	0.0766147	+	0.434504i
$699$		0			0
$700$	25355.9	+	9228.79i	1.36909	+	0.498308i
$701$	−7744.83	+	6498.69i	−0.417287	+	0.350145i	−0.827130	−	0.562011i	$-0.810028\pi$
$701$	−7744.83	+	6498.69i	−0.417287	+	0.350145i	0.409843	+	0.912156i	$0.365584\pi$
$702$		0			0
$703$	−2233.27	+	1007.65i	−0.119814	+	0.0540603i
$704$	−1319.35			−0.0706321
$705$		0			0
$706$	520.417	+	189.416i	0.0277424	+	0.0100974i
$707$	−381.153	+	2161.63i	−0.0202754	+	0.114988i
$708$		0			0
$709$	−22553.1	+	8208.65i	−1.19464	+	0.434813i	−0.861350	−	0.508012i	$-0.830381\pi$
$709$	−22553.1	+	8208.65i	−1.19464	+	0.434813i	−0.333289	+	0.942825i	$0.608158\pi$
$710$	−1706.42	+	2955.61i	−0.0901986	+	0.156228i
$711$		0			0
$712$	−18221.5	−	15289.7i	−0.959102	−	0.804782i
$713$	2245.10	+	1883.86i	0.117924	+	0.0989497i
$714$		0			0
$715$	−1605.40	+	2780.64i	−0.0839702	+	0.145441i
$716$	8943.37	−	3255.12i	0.466801	−	0.169902i
$717$		0			0
$718$	−2324.36	+	13182.1i	−0.120814	+	0.685169i
$719$	−14145.8	−	5148.66i	−0.733728	−	0.267055i	−0.0519858	−	0.998648i	$-0.516555\pi$
$719$	−14145.8	−	5148.66i	−0.733728	−	0.267055i	−0.681742	+	0.731593i	$0.738777\pi$
$720$		0			0
$721$	−962.817			−0.0497326
$722$	−308.603	+	12361.5i	−0.0159072	+	0.637182i
$723$		0			0
$724$	−16784.5	+	14083.8i	−0.861587	+	0.722958i
$725$	26709.2	+	9721.34i	1.36821	+	0.497988i
$726$		0			0
$727$	1735.94	+	9845.02i	0.0885592	+	0.502244i	0.996532	+	0.0832143i	$0.0265186\pi$
$727$	1735.94	+	9845.02i	0.0885592	+	0.502244i	−0.907972	+	0.419030i	$0.862370\pi$
$728$	28610.5	−	10413.4i	1.45656	−	0.530144i
$729$		0			0
$730$	−13922.7	−	24114.7i	−0.705891	−	1.22264i
$731$	1137.36	+	954.361i	0.0575471	+	0.0482877i
$732$		0			0
$733$	−4411.67	−	7641.24i	−0.222304	−	0.385042i	0.733203	−	0.680010i	$-0.238024\pi$
$733$	−4411.67	−	7641.24i	−0.222304	−	0.385042i	−0.955507	+	0.294968i	$0.904691\pi$
$734$	6359.87	−	11015.6i	0.319819	−	0.553943i
$735$		0			0
$736$	−507.317	−	2877.14i	−0.0254075	−	0.144093i
$737$	498.636	−	2827.91i	0.0249220	−	0.141340i
$738$		0			0
$739$	8193.05	−	6874.79i	0.407830	−	0.342210i	−0.415681	−	0.909511i	$-0.636457\pi$
$739$	8193.05	−	6874.79i	0.407830	−	0.342210i	0.823511	+	0.567301i	$0.192012\pi$
$740$	2537.35			0.126047
$741$		0			0
$742$	19875.2			0.983345
$743$	−2123.19	+	1781.57i	−0.104835	+	0.0879669i	−0.693698	−	0.720266i	$-0.744020\pi$
$743$	−2123.19	+	1781.57i	−0.104835	+	0.0879669i	0.588864	+	0.808232i	$0.299576\pi$
$744$		0			0
$745$	−5864.58	+	33259.7i	−0.288405	+	1.63563i
$746$	620.073	+	3516.61i	0.0304323	+	0.172590i
$747$		0			0
$748$	170.831	−	295.888i	0.00835055	−	0.0144636i
$749$	10776.9	+	18666.2i	0.525741	+	0.910611i
$750$		0			0
$751$	−1510.12	−	1267.14i	−0.0733758	−	0.0615696i	0.605362	−	0.795950i	$-0.293028\pi$
$751$	−1510.12	−	1267.14i	−0.0733758	−	0.0615696i	−0.678738	+	0.734381i	$0.737473\pi$
$752$	−355.481	−	615.710i	−0.0172381	−	0.0298572i
$753$		0			0
$754$	11227.6	−	4086.52i	0.542288	−	0.197377i
$755$	−3584.97	−	20331.4i	−0.172808	−	0.980046i
$756$		0			0
$757$	30387.9	+	11060.3i	1.45901	+	0.531035i	0.945091	−	0.326807i	$-0.105973\pi$
$757$	30387.9	+	11060.3i	1.45901	+	0.531035i	0.513914	+	0.857841i	$0.328195\pi$
$758$	8267.03	−	6936.86i	0.396137	−	0.332398i
$759$		0			0
$760$	14914.5	−	30969.3i	0.711851	−	1.47812i
$761$	−10342.9			−0.492679			−0.246340	−	0.969184i	$-0.579228\pi$
$761$	−10342.9			−0.492679			−0.246340	+	0.969184i	$0.579228\pi$
$762$		0			0
$763$	8555.75	+	3114.04i	0.405949	+	0.147753i
$764$	−1168.93	+	6629.35i	−0.0553541	+	0.313929i
$765$		0			0
$766$	7202.92	−	2621.65i	0.339755	−	0.123661i
$767$	−819.712	+	1419.78i	−0.0385894	+	0.0668389i
$768$		0			0
$769$	12734.5	+	10685.5i	0.597162	+	0.501078i	0.890532	−	0.454921i	$-0.150332\pi$
$769$	12734.5	+	10685.5i	0.597162	+	0.501078i	−0.293370	+	0.955999i	$0.594777\pi$
$770$	2672.58	+	2242.56i	0.125082	+	0.104956i
$771$		0			0
$772$	11192.1	−	19385.3i	0.521778	−	0.903745i
$773$	−10522.7	+	3829.95i	−0.489619	+	0.178207i	−0.575019	−	0.818140i	$-0.695005\pi$
$773$	−10522.7	+	3829.95i	−0.489619	+	0.178207i	0.0854002	+	0.996347i	$0.472783\pi$
$774$		0			0
$775$	6222.93	−	35292.0i	0.288431	−	1.63577i
$776$	−15818.1	−	5757.33i	−0.731750	−	0.266335i
$777$		0			0
$778$	4665.91			0.215014
$779$	28892.9	−	2164.84i	1.32888	−	0.0995679i
$780$		0			0
$781$	304.632	−	255.617i	0.0139572	−	0.0117115i
$782$	−528.207	−	192.252i	−0.0241543	−	0.00879144i
$783$		0			0
$784$	−271.866	−	1541.83i	−0.0123846	−	0.0702365i
$785$	2753.08	−	1002.04i	0.125174	−	0.0455597i
$786$		0			0
$787$	11148.2	+	19309.3i	0.504944	+	0.874589i	0.999984	+	0.00571864i	$0.00182031\pi$
$787$	11148.2	+	19309.3i	0.504944	+	0.874589i	−0.495039	+	0.868871i	$0.664846\pi$
$788$	−4034.72	−	3385.53i	−0.182400	−	0.153052i
$789$		0			0
$790$	−10250.9	−	17755.1i	−0.461660	−	0.799619i
$791$	31776.6	−	55038.7i	1.42838	−	2.47402i
$792$		0			0
$793$	5521.33	+	31313.0i	0.247249	+	1.40222i
$794$	−1694.66	+	9610.91i	−0.0757448	+	0.429570i
$795$		0			0
$796$	−15105.3	+	12674.9i	−0.672605	+	0.564383i
$797$	−14805.2			−0.658000			−0.329000	−	0.944330i	$-0.606712\pi$
$797$	−14805.2			−0.658000			−0.329000	+	0.944330i	$0.606712\pi$
$798$		0			0
$799$	3921.42			0.173629
$800$	−27365.7	+	22962.5i	−1.20940	+	1.01481i
$801$		0			0
$802$	−363.677	+	2062.51i	−0.0160123	+	0.0908104i
$803$	563.413	+	3195.27i	0.0247602	+	0.140422i
$804$		0			0
$805$	−4194.41	+	7264.93i	−0.183644	+	0.318081i
$806$	−7532.20	−	13046.1i	−0.329169	−	0.570138i
$807$		0			0
$808$	−1367.84	−	1147.75i	−0.0595548	−	0.0499724i
$809$	17258.6	+	29892.7i	0.750035	+	1.29910i	0.947805	+	0.318850i	$0.103297\pi$
$809$	17258.6	+	29892.7i	0.750035	+	1.29910i	−0.197770	+	0.980248i	$0.563370\pi$
$810$		0			0
$811$	19063.6	−	6938.59i	0.825418	−	0.300428i	0.105441	−	0.994426i	$-0.466375\pi$
$811$	19063.6	−	6938.59i	0.825418	−	0.300428i	0.719977	+	0.693998i	$0.244152\pi$
$812$	3294.86	+	18686.1i	0.142398	+	0.807577i
$813$		0			0
$814$	190.094	+	69.1885i	0.00818524	+	0.00297918i
$815$	−5331.47	+	4473.63i	−0.229145	+	0.192276i
$816$		0			0
$817$	−3652.63	−	5357.57i	−0.156413	−	0.229422i
$818$	−4908.33			−0.209799
$819$		0			0
$820$	−28196.4	−	10262.7i	−1.20081	−	0.437058i
$821$	1787.28	−	10136.2i	0.0759762	−	0.430882i	−0.922965	−	0.384883i	$-0.874242\pi$
$821$	1787.28	−	10136.2i	0.0759762	−	0.430882i	0.998941	−	0.0459992i	$-0.0146472\pi$
$822$		0			0
$823$	28457.2	−	10357.6i	1.20529	−	0.438690i	0.340224	−	0.940345i	$-0.389497\pi$
$823$	28457.2	−	10357.6i	1.20529	−	0.438690i	0.865068	+	0.501654i	$0.167275\pi$
$824$	391.620	−	678.305i	0.0165567	−	0.0286771i
$825$		0			0
$826$	1364.61	+	1145.04i	0.0574828	+	0.0482338i
$827$	30743.2	+	25796.6i	1.29268	+	1.08469i	0.991361	+	0.131163i	$0.0418711\pi$
$827$	30743.2	+	25796.6i	1.29268	+	1.08469i	0.301318	+	0.953524i	$0.402573\pi$
$828$		0			0
$829$	−6182.23	+	10707.9i	−0.259008	+	0.448615i	−0.965976	−	0.258630i	$-0.916729\pi$
$829$	−6182.23	+	10707.9i	−0.259008	+	0.448615i	0.706968	+	0.707245i	$0.250062\pi$
$830$	23607.4	−	8592.40i	0.987259	−	0.359333i
$831$		0			0
$832$	−2831.56	+	16058.6i	−0.117989	+	0.669147i
$833$	8114.62	+	2953.48i	0.337521	+	0.122848i
$834$		0			0
$835$	−20511.9			−0.850112
$836$	−1068.19	+	1041.86i	−0.0441915	+	0.0431020i
$837$		0			0
$838$	−14565.4	+	12221.8i	−0.600422	+	0.503814i
$839$	−24369.3	−	8869.71i	−1.00277	−	0.364978i	−0.212117	−	0.977244i	$-0.568036\pi$
$839$	−24369.3	−	8869.71i	−1.00277	−	0.364978i	−0.790652	+	0.612266i	$0.790258\pi$
$840$		0			0
$841$	−764.401	−	4335.13i	−0.0313420	−	0.177750i
$842$	−13438.6	+	4891.24i	−0.550029	+	0.200194i
$843$		0			0
$844$	−4624.97	−	8010.68i	−0.188623	−	0.326705i
$845$	9.62294	+	8.07461i	0.000391763	+	0.000328728i
$846$		0			0
$847$	18600.7	+	32217.4i	0.754580	+	1.30697i
$848$	−670.743	+	1161.76i	−0.0271620	+	0.0470460i
$849$		0			0
$850$	1193.53	+	6768.83i	0.0481619	+	0.273140i
$851$	−84.4648	+	479.024i	−0.00340237	+	0.0192958i
$852$		0			0
$853$	−5251.13	+	4406.22i	−0.210780	+	0.176865i	−0.742065	−	0.670328i	$-0.766154\pi$
$853$	−5251.13	+	4406.22i	−0.210780	+	0.176865i	0.531286	+	0.847193i	$0.321709\pi$
$854$	34549.1			1.38436
$855$		0			0
$856$	−17533.8			−0.700108
$857$	−7879.11	+	6611.36i	−0.314055	+	0.263524i	−0.786166	−	0.618016i	$-0.787937\pi$
$857$	−7879.11	+	6611.36i	−0.314055	+	0.263524i	0.472110	+	0.881539i	$0.343492\pi$
$858$		0			0
$859$	−2877.09	+	16316.8i	−0.114278	+	0.648104i	0.872827	+	0.488030i	$0.162284\pi$
$859$	−2877.09	+	16316.8i	−0.114278	+	0.648104i	−0.987105	+	0.160074i	$0.948827\pi$
$860$	1166.08	+	6613.19i	0.0462362	+	0.262218i
$861$		0			0
$862$	−14520.3	+	25149.9i	−0.573739	+	0.993745i
$863$	22188.2	+	38431.2i	0.875199	+	1.51589i	0.856551	+	0.516063i	$0.172603\pi$
$863$	22188.2	+	38431.2i	0.875199	+	1.51589i	0.0186479	+	0.999826i	$0.494064\pi$
$864$		0			0
$865$	8333.45	+	6992.59i	0.327567	+	0.274862i
$866$	6592.80	+	11419.1i	0.258698	+	0.448078i
$867$		0			0
$868$	22480.3	−	8182.16i	0.879069	−	0.319955i
$869$	414.828	+	2352.61i	0.0161934	+	0.0918374i
$870$		0			0
$871$	−33349.8	−	12138.3i	−1.29738	−	0.472207i
$872$	−5673.84	+	4760.92i	−0.220344	+	0.184891i
$873$		0			0
$874$	1993.20	+	1433.05i	0.0771407	+	0.0554619i
$875$	38800.1			1.49907
$876$		0			0
$877$	−15200.5	−	5532.52i	−0.585272	−	0.213021i	0.0323769	−	0.999476i	$-0.489692\pi$
$877$	−15200.5	−	5532.52i	−0.585272	−	0.213021i	−0.617648	+	0.786454i	$0.711915\pi$
$878$	−2775.73	+	15742.0i	−0.106693	+	0.605086i
$879$		0			0
$880$	−221.277	+	80.5383i	−0.00847643	+	0.00308517i
$881$	16626.3	−	28797.7i	0.635818	−	1.10127i	−0.350523	−	0.936554i	$-0.613996\pi$
$881$	16626.3	−	28797.7i	0.635818	−	1.10127i	0.986341	−	0.164715i	$-0.0526705\pi$
$882$		0			0
$883$	−10732.3	−	9005.49i	−0.409028	−	0.343215i	0.414943	−	0.909847i	$-0.363802\pi$
$883$	−10732.3	−	9005.49i	−0.409028	−	0.343215i	−0.823971	+	0.566632i	$0.808246\pi$
$884$	−3234.79	−	2714.31i	−0.123074	−	0.103272i
$885$		0			0
$886$	8579.18	−	14859.6i	0.325308	−	0.563451i
$887$	26317.5	−	9578.79i	0.996230	−	0.362598i	0.208100	−	0.978108i	$-0.433272\pi$
$887$	26317.5	−	9578.79i	0.996230	−	0.362598i	0.788129	+	0.615510i	$0.211050\pi$
$888$		0			0
$889$	6842.18	−	38803.9i	0.258132	−	1.46394i
$890$	−31655.5	−	11521.6i	−1.19224	−	0.433940i
$891$		0			0
$892$	−6257.97			−0.234902
$893$	−16485.8	−	4638.63i	−0.617780	−	0.173825i
$894$		0			0
$895$	27715.3	−	23255.9i	1.03511	−	0.868558i
$896$	−21092.8	−	7677.17i	−0.786453	−	0.286246i
$897$		0			0
$898$	3312.05	+	18783.6i	0.123079	+	0.698014i
$899$	23680.1	−	8618.85i	0.878504	−	0.319749i
$900$		0			0
$901$	−3699.58	−	6407.87i	−0.136794	−	0.236933i
$902$	−1832.59	−	1537.72i	−0.0676479	−	0.0567633i
$903$		0			0
$904$	25849.9	+	44773.3i	0.951055	+	1.64728i
$905$	−41646.1	+	72133.1i	−1.52968	+	2.64949i
$906$		0			0
$907$	−1106.20	−	6273.57i	−0.0404970	−	0.229670i	0.957841	−	0.287298i	$-0.0927572\pi$
$907$	−1106.20	−	6273.57i	−0.0404970	−	0.229670i	−0.998338	+	0.0576287i	$0.981646\pi$
$908$	2402.69	−	13626.4i	0.0878152	−	0.498025i
$909$		0			0
$910$	33031.3	−	27716.5i	1.20327	−	1.00966i
$911$	12817.6			0.466154			0.233077	−	0.972458i	$-0.425121\pi$
$911$	12817.6			0.466154			0.233077	+	0.972458i	$0.425121\pi$
$912$		0			0
$913$	−2927.30			−0.106111
$914$	5768.96	−	4840.73i	0.208775	−	0.175183i
$915$		0			0
$916$	−275.074	+	1560.02i	−0.00992216	+	0.0562714i
$917$	−9039.35	−	51264.7i	−0.325524	−	1.84614i
$918$		0			0
$919$	15038.7	−	26047.7i	0.539804	−	0.934968i	−0.459110	−	0.888379i	$-0.651832\pi$
$919$	15038.7	−	26047.7i	0.539804	−	0.934968i	0.998914	−	0.0465887i	$-0.0148350\pi$
$920$	−3412.10	−	5909.93i	−0.122276	−	0.211787i
$921$		0			0
$922$	−21962.9	−	18429.1i	−0.784500	−	0.658274i
$923$	−2457.46	−	4256.44i	−0.0876362	−	0.151790i
$924$		0			0
$925$	5589.01	−	2034.23i	0.198665	−	0.0723083i
$926$	1369.57	+	7767.23i	0.0486036	+	0.275645i
$927$		0			0
$928$	−23605.4	−	8591.66i	−0.835006	−	0.303917i
$929$	20645.8	−	17323.9i	0.729134	−	0.611816i	−0.200761	−	0.979640i	$-0.564342\pi$
$929$	20645.8	−	17323.9i	0.729134	−	0.611816i	0.929895	+	0.367824i	$0.119897\pi$
$930$		0			0
$931$	−30620.6	−	22015.4i	−1.07793	−	0.774999i
$932$	−3353.71			−0.117870
$933$		0			0
$934$	9048.45	+	3293.36i	0.316996	+	0.115377i
$935$	225.537	−	1279.09i	0.00788862	−	0.0447386i
$936$		0			0
$937$	31790.0	−	11570.6i	1.10836	−	0.403411i	0.277969	−	0.960590i	$-0.410339\pi$
$937$	31790.0	−	11570.6i	1.10836	−	0.403411i	0.830392	+	0.557179i	$0.188116\pi$
$938$	−19281.5	+	33396.5i	−0.671175	+	1.16251i
$939$		0			0
$940$	13586.6	+	11400.5i	0.471432	+	0.395579i
$941$	−33321.0	−	27959.6i	−1.15434	−	0.968606i	−0.154527	−	0.987989i	$-0.549385\pi$
$941$	−33321.0	−	27959.6i	−1.15434	−	0.968606i	−0.999812	+	0.0193826i	$0.993830\pi$
$942$		0			0
$943$	2876.10	−	4981.55i	0.0993199	−	0.172027i
$944$	−112.983	+	41.1225i	−0.00389543	+	0.00141782i
$945$		0			0
$946$	−92.9677	+	527.246i	−0.00319518	+	0.0181208i
$947$	−2373.02	−	863.710i	−0.0814286	−	0.0296376i	0.300985	−	0.953629i	$-0.402685\pi$
$947$	−2373.02	−	863.710i	−0.0814286	−	0.0296376i	−0.382413	+	0.923991i	$0.624907\pi$
$948$		0			0
$949$	40100.6			1.37168
$950$	2989.18	−	29868.3i	0.102086	−	1.02006i
$951$		0			0
$952$	−9434.67	+	7916.63i	−0.321197	+	0.269516i
$953$	25325.5	+	9217.72i	0.860832	+	0.313317i	0.734449	−	0.678664i	$-0.237441\pi$
$953$	25325.5	+	9217.72i	0.860832	+	0.313317i	0.126383	+	0.991981i	$0.459663\pi$
$954$		0			0
$955$	4443.66	+	25201.2i	0.150569	+	0.853919i
$956$	7048.91	−	2565.59i	0.238471	−	0.0867962i
$957$		0			0
$958$	−11977.9	−	20746.4i	−0.403955	−	0.699671i
$959$	−29118.3	−	24433.1i	−0.980478	−	0.822719i
$960$		0			0
$961$	−990.613	−	1715.79i	−0.0332521	−	0.0575943i
$962$	1250.10	−	2165.24i	0.0418971	−	0.0725679i
$963$		0			0
$964$	3158.80	+	17914.4i	0.105537	+	0.598533i
$965$	14776.2	−	83799.9i	0.492914	−	2.79545i
$966$		0			0
$967$	−20185.5	+	16937.7i	−0.671275	+	0.563267i	−0.913442	−	0.406968i	$-0.866586\pi$
$967$	−20185.5	+	16937.7i	−0.671275	+	0.563267i	0.242168	+	0.970234i	$0.422142\pi$
$968$	−30262.9			−1.00484
$969$		0			0
$970$	−23839.7			−0.789121
$971$	26155.6	−	21947.1i	0.864441	−	0.725352i	−0.0984788	−	0.995139i	$-0.531398\pi$
$971$	26155.6	−	21947.1i	0.864441	−	0.725352i	0.962920	+	0.269787i	$0.0869532\pi$
$972$		0			0
$973$	8868.37	−	50295.0i	0.292196	−	1.65713i
$974$	5651.53	+	32051.4i	0.185921	+	1.05441i
$975$		0			0
$976$	−1165.95	+	2019.49i	−0.0382389	+	0.0662317i
$977$	−6848.44	−	11861.8i	−0.224259	−	0.388428i	0.731838	−	0.681479i	$-0.238663\pi$
$977$	−6848.44	−	11861.8i	−0.224259	−	0.388428i	−0.956097	+	0.293051i	$0.905329\pi$
$978$		0			0
$979$	3006.92	+	2523.10i	0.0981629	+	0.0823684i
$980$	19528.4	+	33824.2i	0.636542	+	1.10252i
$981$		0			0
$982$	−34647.8	+	12610.8i	−1.12592	+	0.409802i
$983$	−1035.24	−	5871.16i	−0.0335902	−	0.190499i	0.963396	−	0.268084i	$-0.0863904\pi$
$983$	−1035.24	−	5871.16i	−0.0335902	−	0.190499i	−0.996986	+	0.0775844i	$0.975279\pi$
$984$		0			0
$985$	−18814.7	−	6847.97i	−0.608614	−	0.221517i
$986$	−3702.45	+	3106.72i	−0.119584	+	0.100343i
$987$		0			0
$988$	10388.5	+	15237.5i	0.334515	+	0.490658i
$989$	−1287.32			−0.0413896
$990$		0			0
$991$	−41880.8	−	15243.4i	−1.34247	−	0.488619i	−0.431881	−	0.901931i	$-0.642150\pi$
$991$	−41880.8	−	15243.4i	−1.34247	−	0.488619i	−0.910590	+	0.413312i	$0.864372\pi$
$992$	−5499.79	+	31190.8i	−0.176027	+	0.998297i
$993$		0			0
$994$	−5018.39	+	1826.54i	−0.160134	+	0.0582842i
$995$	−37479.7	+	64916.8i	−1.19416	+	2.06834i
$996$		0			0
$997$	1857.95	+	1559.00i	0.0590188	+	0.0495227i	0.671820	−	0.740715i	$-0.265513\pi$
$997$	1857.95	+	1559.00i	0.0590188	+	0.0495227i	−0.612801	+	0.790237i	$0.709957\pi$
$998$	−14831.9	−	12445.5i	−0.470437	−	0.394744i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.u.b.82.2		24
3.2	odd	2		19.4.e.a.6.3	✓	24
19.16	even	9	inner	171.4.u.b.73.2		24
57.23	odd	18		361.4.a.n.1.7		12
57.35	odd	18		19.4.e.a.16.3	yes	24
57.53	even	18		361.4.a.m.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.e.a.6.3	✓	24	3.2	odd	2
19.4.e.a.16.3	yes	24	57.35	odd	18
171.4.u.b.73.2		24	19.16	even	9	inner
171.4.u.b.82.2		24	1.1	even	1	trivial
361.4.a.m.1.6		12	57.53	even	18
361.4.a.n.1.7		12	57.23	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)

\(f(q)\)	\(=\)	\(q+(-1.38101 + 1.15881i) q^{2} +(-0.824823 + 4.67780i) q^{4} +(3.13553 + 17.7825i) q^{5} +(-14.1277 + 24.4699i) q^{7} +(-11.4927 - 19.9060i) q^{8} +O(q^{10})\)	\(q+(-1.38101 + 1.15881i) q^{2} +(-0.824823 + 4.67780i) q^{4} +(3.13553 + 17.7825i) q^{5} +(-14.1277 + 24.4699i) q^{7} +(-11.4927 - 19.9060i) q^{8} +(-24.9367 - 20.9244i) q^{10} +(1.89653 + 3.28489i) q^{11} +(44.0524 - 16.0338i) q^{13} +(-8.84538 - 50.1646i) q^{14} +(3.23077 + 1.17590i) q^{16} +(-14.5268 + 12.1895i) q^{17} +(75.4905 - 34.0614i) q^{19} -85.7692 q^{20} +(-6.42569 - 2.33876i) q^{22} +(2.85514 - 16.1923i) q^{23} +(-188.924 + 68.7626i) q^{25} +(-42.2569 + 73.1911i) q^{26} +(-102.813 - 86.2701i) q^{28} +(-108.300 - 90.8743i) q^{29} +(-89.1238 + 154.367i) q^{31} +(166.970 - 60.7720i) q^{32} +(5.93652 - 33.6677i) q^{34} +(-479.434 - 174.500i) q^{35} -29.5834 q^{37} +(-64.7828 + 134.518i) q^{38} +(317.942 - 266.785i) q^{40} +(328.747 + 119.654i) q^{41} +(-13.5956 - 77.1044i) q^{43} +(-16.9303 + 6.16214i) q^{44} +(14.8208 + 25.6704i) q^{46} +(-158.409 - 132.921i) q^{47} +(-227.685 - 394.363i) q^{49} +(181.224 - 313.888i) q^{50} +(38.6673 + 219.293i) q^{52} +(-67.7541 + 384.253i) q^{53} +(-52.4668 + 44.0249i) q^{55} +649.464 q^{56} +254.869 q^{58} +(-26.7893 + 22.4789i) q^{59} +(-117.777 + 667.946i) q^{61} +(-55.8005 - 316.460i) q^{62} +(-173.917 + 301.233i) q^{64} +(423.248 + 733.087i) q^{65} +(-579.933 - 486.622i) q^{67} +(-45.0379 - 78.0079i) q^{68} +(864.317 - 314.586i) q^{70} +(-18.2055 - 103.248i) q^{71} +(803.809 + 292.563i) q^{73} +(40.8551 - 34.2815i) q^{74} +(97.0663 + 381.224i) q^{76} -107.175 q^{77} +(591.826 + 215.407i) q^{79} +(-10.7803 + 61.1382i) q^{80} +(-592.661 + 215.711i) q^{82} +(-385.876 + 668.357i) q^{83} +(-262.308 - 220.103i) q^{85} +(108.125 + 90.7276i) q^{86} +(43.5926 - 75.5046i) q^{88} +(972.442 - 353.940i) q^{89} +(-230.015 + 1304.48i) q^{91} +(73.3894 + 26.7116i) q^{92} +372.795 q^{94} +(842.400 + 1235.61i) q^{95} +(561.010 - 470.743i) q^{97} +(771.427 + 280.776i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) \) 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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