LMFDB - Embedded newform 350.4.j.h.249.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,4,Mod(149,350)] 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("350.149"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,24,0,24,0,0,112,0,52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 134x^{10} + 13467x^{8} - 530084x^{6} + 15364507x^{4} - 160351569x^{2} + 1275989841 $ x^12 - 134x^10 + 13467x^8 - 530084x^6 + 15364507x^4 - 160351569*x^2 + 1275989841
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.4
Root			$-8.08868 + 4.67000i$ of defining polynomial
Character	$\chi$	$=$	350.249
Dual form			350.4.j.h.149.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(-7.22265 - 4.17000i) q^{3} +(2.00000 - 3.46410i) q^{4} -16.6800 q^{6} +(-8.19644 + 16.6078i) q^{7} -8.00000i q^{8} +(21.2778 + 36.8542i) q^{9} +(13.1344 - 22.7495i) q^{11} +(-28.8906 + 16.6800i) q^{12} +38.1623i q^{13} +(2.41113 + 36.9620i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-2.07266 - 1.19665i) q^{17} +(73.7084 + 42.5556i) q^{18} +(49.8966 + 86.4235i) q^{19} +(128.454 - 85.7730i) q^{21} -52.5377i q^{22} +(-88.1421 + 50.8889i) q^{23} +(-33.3600 + 57.7812i) q^{24} +(38.1623 + 66.0990i) q^{26} -129.733i q^{27} +(41.1382 + 61.6089i) q^{28} +223.936 q^{29} +(133.663 - 231.512i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-189.731 + 109.541i) q^{33} -4.78661 q^{34} +170.222 q^{36} +(314.616 - 181.643i) q^{37} +(172.847 + 99.7933i) q^{38} +(159.137 - 275.633i) q^{39} -94.9155 q^{41} +(136.717 - 277.018i) q^{42} -406.093i q^{43} +(-52.5377 - 90.9980i) q^{44} +(-101.778 + 176.284i) q^{46} +(-296.331 + 171.087i) q^{47} +133.440i q^{48} +(-208.637 - 272.249i) q^{49} +(9.98008 + 17.2860i) q^{51} +(132.198 + 76.3245i) q^{52} +(470.817 + 271.827i) q^{53} +(-129.733 - 224.705i) q^{54} +(132.862 + 65.5715i) q^{56} -832.276i q^{57} +(387.868 - 223.936i) q^{58} +(-196.579 + 340.485i) q^{59} +(252.154 + 436.744i) q^{61} -534.653i q^{62} +(-786.468 + 51.3034i) q^{63} -64.0000 q^{64} +(-219.082 + 379.462i) q^{66} +(-47.5851 - 27.4733i) q^{67} +(-8.29066 + 4.78661i) q^{68} +848.826 q^{69} +889.302 q^{71} +(294.834 - 170.222i) q^{72} +(442.281 + 255.351i) q^{73} +(363.287 - 629.231i) q^{74} +399.173 q^{76} +(270.163 + 404.599i) q^{77} -636.546i q^{78} +(136.878 + 237.079i) q^{79} +(33.5123 - 58.0450i) q^{81} +(-164.399 + 94.9155i) q^{82} +525.188i q^{83} +(-40.2176 - 616.525i) q^{84} +(-406.093 - 703.374i) q^{86} +(-1617.41 - 933.811i) q^{87} +(-181.996 - 105.075i) q^{88} +(827.936 + 1434.03i) q^{89} +(-633.790 - 312.795i) q^{91} +407.111i q^{92} +(-1930.81 + 1114.75i) q^{93} +(-342.173 + 592.661i) q^{94} +(133.440 + 231.125i) q^{96} -5.76230i q^{97} +(-633.619 - 262.913i) q^{98} +1117.89 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{4} + 24 q^{6} + 112 q^{9} + 52 q^{11} + 16 q^{14} - 96 q^{16} - 36 q^{19} + 370 q^{21} + 48 q^{24} + 320 q^{26} + 1616 q^{29} + 1230 q^{31} + 240 q^{34} + 896 q^{36} - 180 q^{39} - 404 q^{41}+ \cdots + 228 q^{99}+O(q^{100}) $ 12 * q + 24 * q^4 + 24 * q^6 + 112 * q^9 + 52 * q^11 + 16 * q^14 - 96 * q^16 - 36 * q^19 + 370 * q^21 + 48 * q^24 + 320 * q^26 + 1616 * q^29 + 1230 * q^31 + 240 * q^34 + 896 * q^36 - 180 * q^39 - 404 * q^41 - 208 * q^44 + 212 * q^46 + 432 * q^49 + 678 * q^51 - 1296 * q^54 + 896 * q^56 - 182 * q^59 + 1294 * q^61 - 768 * q^64 - 1256 * q^66 + 6192 * q^69 + 2132 * q^71 + 1704 * q^74 - 288 * q^76 + 2842 * q^79 + 2786 * q^81 + 608 * q^84 + 996 * q^86 - 388 * q^89 - 7710 * q^91 - 1608 * q^94 - 192 * q^96 + 228 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	−7.22265	−	4.17000i	−1.39000	−	0.802517i	−0.396685	−	0.917955i	$-0.629839\pi$
$3$	−7.22265	−	4.17000i	−1.39000	−	0.802517i	−0.993315	+	0.115438i	$0.963173\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−16.6800			−1.13493
$7$	−8.19644	+	16.6078i	−0.442566	+	0.896736i
$7$	−8.19644	+	16.6078i	−0.442566	+	0.896736i
$8$		−	8.00000i		−	0.353553i
$9$	21.2778	+	36.8542i	0.788066	+	1.36497i
$10$		0			0
$11$	13.1344	−	22.7495i	0.360016	−	0.623567i	−0.627947	−	0.778256i	$-0.716104\pi$
$11$	13.1344	−	22.7495i	0.360016	−	0.623567i	0.987963	+	0.154690i	$0.0494377\pi$
$12$	−28.8906	+	16.6800i	−0.695000	+	0.401258i
$13$			38.1623i			0.814177i	0.913389	+	0.407089i	$0.133456\pi$
$13$			38.1623i			0.814177i	−0.913389	+	0.407089i	$0.866544\pi$
$14$	2.41113	+	36.9620i	0.0460286	+	0.705607i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−2.07266	−	1.19665i	−0.0295703	−	0.0170724i	0.485142	−	0.874435i	$-0.338768\pi$
$17$	−2.07266	−	1.19665i	−0.0295703	−	0.0170724i	−0.514712	+	0.857363i	$0.672101\pi$
$18$	73.7084	+	42.5556i	0.965180	+	0.557247i
$19$	49.8966	+	86.4235i	0.602478	+	1.04352i	0.992445	+	0.122693i	$0.0391531\pi$
$19$	49.8966	+	86.4235i	0.602478	+	1.04352i	−0.389967	+	0.920829i	$0.627514\pi$
$20$		0			0
$21$	128.454	−	85.7730i	1.33481	−	0.891296i
$22$		−	52.5377i		−	0.509140i
$23$	−88.1421	+	50.8889i	−0.799083	+	0.461351i	−0.843150	−	0.537678i	$-0.819302\pi$
$23$	−88.1421	+	50.8889i	−0.799083	+	0.461351i	0.0440674	+	0.999029i	$0.485968\pi$
$24$	−33.3600	+	57.7812i	−0.283732	+	0.491439i
$25$		0			0
$26$	38.1623	+	66.0990i	0.287855	+	0.498580i
$27$		−	129.733i		−	0.924711i
$28$	41.1382	+	61.6089i	0.277656	+	0.415821i
$29$	223.936			1.43392			0.716962	−	0.697112i	$-0.245532\pi$
$29$	223.936			1.43392			0.716962	+	0.697112i	$0.245532\pi$
$30$		0			0
$31$	133.663	−	231.512i	0.774408	−	1.34131i	−0.160719	−	0.987000i	$-0.551381\pi$
$31$	133.663	−	231.512i	0.774408	−	1.34131i	0.935127	−	0.354314i	$-0.115285\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−189.731	+	109.541i	−1.00085	+	0.577838i
$34$	−4.78661			−0.0241440
$35$		0			0
$36$	170.222			0.788066
$37$	314.616	−	181.643i	1.39790	−	0.807081i	0.403732	−	0.914877i	$-0.367713\pi$
$37$	314.616	−	181.643i	1.39790	−	0.807081i	0.994173	+	0.107797i	$0.0343796\pi$
$38$	172.847	+	99.7933i	0.737881	+	0.426016i
$39$	159.137	−	275.633i	0.653391	−	1.13171i
$40$		0			0
$41$	−94.9155			−0.361544			−0.180772	−	0.983525i	$-0.557860\pi$
$41$	−94.9155			−0.361544			−0.180772	+	0.983525i	$0.557860\pi$
$42$	136.717	−	277.018i	0.502282	−	1.01773i
$43$		−	406.093i		−	1.44020i	−0.693870	−	0.720101i	$-0.744096\pi$
$43$		−	406.093i		−	1.44020i	0.693870	−	0.720101i	$-0.255904\pi$
$44$	−52.5377	−	90.9980i	−0.180008	−	0.311783i
$45$		0			0
$46$	−101.778	+	176.284i	−0.326224	+	0.565037i
$47$	−296.331	+	171.087i	−0.919665	+	0.530969i	−0.883528	−	0.468378i	$-0.844839\pi$
$47$	−296.331	+	171.087i	−0.919665	+	0.530969i	−0.0361369	+	0.999347i	$0.511505\pi$
$48$			133.440i			0.401258i
$49$	−208.637	−	272.249i	−0.608270	−	0.793730i
$50$		0			0
$51$	9.98008	+	17.2860i	0.0274018	+	0.0474613i
$52$	132.198	+	76.3245i	0.352549	+	0.203544i
$53$	470.817	+	271.827i	1.22022	+	0.704495i	0.964965	−	0.262378i	$-0.0845068\pi$
$53$	470.817	+	271.827i	1.22022	+	0.704495i	0.255256	+	0.966873i	$0.417840\pi$
$54$	−129.733	−	224.705i	−0.326935	−	0.566267i
$55$		0			0
$56$	132.862	+	65.5715i	0.317044	+	0.156471i
$57$		−	832.276i		−	1.93399i
$58$	387.868	−	223.936i	0.878095	−	0.506969i
$59$	−196.579	+	340.485i	−0.433770	+	0.751311i	−0.997194	−	0.0748565i	$-0.976150\pi$
$59$	−196.579	+	340.485i	−0.433770	+	0.751311i	0.563425	+	0.826167i	$0.309483\pi$
$60$		0			0
$61$	252.154	+	436.744i	0.529263	+	0.916711i	0.999418	+	0.0341268i	$0.0108650\pi$
$61$	252.154	+	436.744i	0.529263	+	0.916711i	−0.470154	+	0.882584i	$0.655802\pi$
$62$		−	534.653i		−	1.09518i
$63$	−786.468	+	51.3034i	−1.57279	+	0.102597i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−219.082	+	379.462i	−0.408593	+	0.707705i
$67$	−47.5851	−	27.4733i	−0.0867678	−	0.0500954i	0.455988	−	0.889986i	$-0.349286\pi$
$67$	−47.5851	−	27.4733i	−0.0867678	−	0.0500954i	−0.542756	+	0.839890i	$0.682619\pi$
$68$	−8.29066	+	4.78661i	−0.0147851	+	0.00853621i
$69$	848.826			1.48097
$70$		0			0
$71$	889.302			1.48649			0.743245	−	0.669020i	$-0.233286\pi$
$71$	889.302			1.48649			0.743245	+	0.669020i	$0.233286\pi$
$72$	294.834	−	170.222i	0.482590	−	0.278623i
$73$	442.281	+	255.351i	0.709111	+	0.409405i	0.810732	−	0.585418i	$-0.199070\pi$
$73$	442.281	+	255.351i	0.709111	+	0.409405i	−0.101621	+	0.994823i	$0.532403\pi$
$74$	363.287	−	629.231i	0.570692	−	0.988468i
$75$		0			0
$76$	399.173			0.602478
$77$	270.163	+	404.599i	0.399844	+	0.598809i
$78$		−	636.546i		−	0.924034i
$79$	136.878	+	237.079i	0.194936	+	0.337640i	0.946880	−	0.321588i	$-0.104217\pi$
$79$	136.878	+	237.079i	0.194936	+	0.337640i	−0.751943	+	0.659228i	$0.770883\pi$
$80$		0			0
$81$	33.5123	−	58.0450i	0.0459702	−	0.0796228i
$82$	−164.399	+	94.9155i	−0.221400	+	0.127825i
$83$			525.188i			0.694541i	0.937765	+	0.347271i	$0.112891\pi$
$83$			525.188i			0.694541i	−0.937765	+	0.347271i	$0.887109\pi$
$84$	−40.2176	−	616.525i	−0.0522393	−	0.800815i
$85$		0			0
$86$	−406.093	−	703.374i	−0.509188	−	0.881939i
$87$	−1617.41	−	933.811i	−1.99315	−	1.15075i
$88$	−181.996	−	105.075i	−0.220464	−	0.127285i
$89$	827.936	+	1434.03i	0.986079	+	1.70794i	0.637042	+	0.770829i	$0.280158\pi$
$89$	827.936	+	1434.03i	0.986079	+	1.70794i	0.349036	+	0.937109i	$0.386509\pi$
$90$		0			0
$91$	−633.790	−	312.795i	−0.730102	−	0.360327i
$92$			407.111i			0.461351i
$93$	−1930.81	+	1114.75i	−2.15285	+	1.24295i
$94$	−342.173	+	592.661i	−0.375452	+	0.650301i
$95$		0			0
$96$	133.440	+	231.125i	0.141866	+	0.245720i
$97$		−	5.76230i		−	0.00603168i	−0.999995	−	0.00301584i	$-0.999040\pi$
$97$		−	5.76230i		−	0.00603168i	0.999995	−	0.00301584i	$-0.000959973\pi$
$98$	−633.619	−	262.913i	−0.653114	−	0.271002i
$99$	1117.89			1.13487
$100$		0			0
$101$	−577.490	+	1000.24i	−0.568934	+	0.985423i	0.427737	+	0.903903i	$0.359311\pi$
$101$	−577.490	+	1000.24i	−0.568934	+	0.985423i	−0.996672	+	0.0815203i	$0.974022\pi$
$102$	34.5720	+	19.9602i	0.0335602	+	0.0193760i
$103$	1416.65	−	817.906i	1.35521	−	0.782433i	0.366240	−	0.930520i	$-0.380645\pi$
$103$	1416.65	−	817.906i	1.35521	−	0.782433i	0.988974	+	0.148087i	$0.0473116\pi$
$104$	305.298			0.287855
$105$		0			0
$106$	1087.31			0.996307
$107$	−574.917	+	331.929i	−0.519433	+	0.299895i	−0.736703	−	0.676217i	$-0.763618\pi$
$107$	−574.917	+	331.929i	−0.519433	+	0.299895i	0.217269	+	0.976112i	$0.430285\pi$
$108$	−449.409	−	259.467i	−0.400411	−	0.231178i
$109$	−903.003	+	1564.05i	−0.793505	+	1.37439i	0.130280	+	0.991477i	$0.458412\pi$
$109$	−903.003	+	1564.05i	−0.793505	+	1.37439i	−0.923784	+	0.382913i	$0.874921\pi$
$110$		0			0
$111$	−3029.81			−2.59078
$112$	295.696	−	19.2890i	0.249470	−	0.0162736i
$113$		−	448.406i		−	0.373297i	−0.982427	−	0.186648i	$-0.940238\pi$
$113$		−	448.406i		−	0.373297i	0.982427	−	0.186648i	$-0.0597625\pi$
$114$	−832.276	−	1441.54i	−0.683770	−	1.18432i
$115$		0			0
$116$	447.871	−	775.735i	0.358481	−	0.620907i
$117$	−1406.44	+	812.008i	−1.11133	+	0.641625i
$118$			786.316i			0.613443i
$119$	36.8622	−	24.6140i	0.0283963	−	0.0189611i
$120$		0			0
$121$	320.473	+	555.076i	0.240776	+	0.417037i
$122$	873.489	+	504.309i	0.648213	+	0.374246i
$123$	685.542	+	395.798i	0.502546	+	0.290145i
$124$	−534.653	−	926.047i	−0.387204	−	0.670657i
$125$		0			0
$126$	−1310.90	+	875.329i	−0.926859	+	0.618893i
$127$			1780.09i			1.24376i	0.783112	+	0.621881i	$0.213631\pi$
$127$			1780.09i			1.24376i	−0.783112	+	0.621881i	$0.786369\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−1693.41	+	2933.07i	−1.15579	+	2.00188i
$130$		0			0
$131$	−1470.44	−	2546.88i	−0.980709	−	1.69864i	−0.659640	−	0.751581i	$-0.729291\pi$
$131$	−1470.44	−	2546.88i	−0.980709	−	1.69864i	−0.321068	−	0.947056i	$-0.604042\pi$
$132$			876.329i			0.577838i
$133$	−1844.28	+	120.307i	−1.20240	+	0.0784357i
$134$	−109.893			−0.0708456
$135$		0			0
$136$	−9.57322	+	16.5813i	−0.00603601	+	0.0104547i
$137$	1432.71	+	827.177i	0.893467	+	0.515843i	0.875075	−	0.483988i	$-0.160812\pi$
$137$	1432.71	+	827.177i	0.893467	+	0.515843i	0.0183918	+	0.999831i	$0.494145\pi$
$138$	1470.21	−	848.826i	0.906903	−	0.523601i
$139$	−409.882			−0.250113			−0.125057	−	0.992150i	$-0.539911\pi$
$139$	−409.882			−0.250113			−0.125057	+	0.992150i	$0.539911\pi$
$140$		0			0
$141$	2853.72			1.70445
$142$	1540.32	−	889.302i	0.910285	−	0.525553i
$143$	868.172	+	501.240i	0.507694	+	0.293117i
$144$	340.444	−	589.667i	0.197016	−	0.341243i
$145$		0			0
$146$	1021.40			0.578986
$147$	371.630	+	2836.38i	0.208514	+	1.59143i
$148$		−	1453.15i		−	0.807081i
$149$	−1489.59	−	2580.05i	−0.819008	−	1.41856i	−0.906414	−	0.422390i	$-0.861191\pi$
$149$	−1489.59	−	2580.05i	−0.819008	−	1.41856i	0.0874065	−	0.996173i	$-0.472142\pi$
$150$		0			0
$151$	987.312	−	1710.07i	0.532095	−	0.921615i	−0.467203	−	0.884150i	$-0.654738\pi$
$151$	987.312	−	1710.07i	0.532095	−	0.921615i	0.999298	−	0.0374653i	$-0.0119284\pi$
$152$	691.388	−	399.173i	0.368941	−	0.213008i
$153$		−	101.848i		−	0.0538167i
$154$	872.535	+	430.622i	0.456564	+	0.225328i
$155$		0			0
$156$	−636.546	−	1102.53i	−0.326695	−	0.565853i
$157$	607.342	+	350.649i	0.308734	+	0.178247i	0.646360	−	0.763033i	$-0.276291\pi$
$157$	607.342	+	350.649i	0.308734	+	0.178247i	−0.337626	+	0.941280i	$0.609624\pi$
$158$	474.159	+	273.756i	0.238747	+	0.137841i
$159$	−2267.03	−	3926.62i	−1.13074	−	1.95850i
$160$		0			0
$161$	−122.700	−	1880.95i	−0.0600626	−	0.920745i
$162$		−	134.049i		−	0.0650117i
$163$	774.335	−	447.062i	0.372089	−	0.214826i	−0.302281	−	0.953219i	$-0.597748\pi$
$163$	774.335	−	447.062i	0.372089	−	0.214826i	0.674371	+	0.738393i	$0.264415\pi$
$164$	−189.831	+	328.797i	−0.0903861	+	0.156553i
$165$		0			0
$166$	525.188	+	909.653i	0.245557	+	0.425318i
$167$			1037.45i			0.480719i	0.970684	+	0.240359i	$0.0772653\pi$
$167$			1037.45i			0.480719i	−0.970684	+	0.240359i	$0.922735\pi$
$168$	−686.184	−	1027.64i	−0.315121	−	0.471927i
$169$	740.643			0.337115
$170$		0			0
$171$	−2123.38	+	3677.80i	−0.949584	+	1.64473i
$172$	−1406.75	−	812.187i	−0.623625	−	0.360050i
$173$	1590.96	−	918.538i	0.699180	−	0.403672i	−0.107862	−	0.994166i	$-0.534401\pi$
$173$	1590.96	−	918.538i	0.699180	−	0.403672i	0.807042	+	0.590494i	$0.201067\pi$
$174$	−3735.24			−1.62740
$175$		0			0
$176$	−420.302			−0.180008
$177$	2839.64	−	1639.47i	1.20588	−	0.696214i
$178$	2868.05	+	1655.87i	1.20769	+	0.697263i
$179$	24.8972	−	43.1233i	0.0103961	−	0.0180066i	−0.860781	−	0.508976i	$-0.830024\pi$
$179$	24.8972	−	43.1233i	0.0103961	−	0.0180066i	0.871177	+	0.490970i	$0.163357\pi$
$180$		0			0
$181$	1000.59			0.410903			0.205452	−	0.978667i	$-0.434134\pi$
$181$	1000.59			0.410903			0.205452	+	0.978667i	$0.434134\pi$
$182$	−1410.55	+	92.0140i	−0.574489	+	0.0374755i
$183$		−	4205.93i		−	1.69897i
$184$	407.111	+	705.137i	0.163112	+	0.282518i
$185$		0			0
$186$	−2229.50	+	3861.61i	−0.878899	+	1.52230i
$187$	−54.4465	+	31.4347i	−0.0212916	+	0.0122927i
$188$			1368.69i			0.530969i
$189$	2154.58	+	1063.35i	0.829221	+	0.409246i
$190$		0			0
$191$	498.904	+	864.126i	0.189002	+	0.327361i	0.944918	−	0.327308i	$-0.106141\pi$
$191$	498.904	+	864.126i	0.189002	+	0.327361i	−0.755916	+	0.654669i	$0.772808\pi$
$192$	462.250	+	266.880i	0.173750	+	0.100315i
$193$	2219.67	+	1281.53i	0.827853	+	0.477961i	0.853117	−	0.521720i	$-0.174709\pi$
$193$	2219.67	+	1281.53i	0.827853	+	0.477961i	−0.0252640	+	0.999681i	$0.508043\pi$
$194$	−5.76230	−	9.98060i	−0.00213252	−	0.00369363i
$195$		0			0
$196$	−1360.37	+	178.240i	−0.495763	+	0.0649562i
$197$			821.223i			0.297004i	0.988912	+	0.148502i	$0.0474451\pi$
$197$			821.223i			0.297004i	−0.988912	+	0.148502i	$0.952555\pi$
$198$	1936.24	−	1117.89i	0.694961	−	0.401236i
$199$	−1618.13	+	2802.69i	−0.576413	+	0.998377i	0.419473	+	0.907768i	$0.362215\pi$
$199$	−1618.13	+	2802.69i	−0.576413	+	0.998377i	−0.995886	+	0.0906096i	$0.971118\pi$
$200$		0			0
$201$	229.127	+	396.860i	0.0804048	+	0.139265i
$202$			2309.96i			0.804595i
$203$	−1835.47	+	3719.07i	−0.634606	+	1.28585i
$204$	79.8407			0.0274018
$205$		0			0
$206$	1635.81	−	2833.31i	0.553264	−	0.958281i
$207$	−3750.94	−	2165.61i	−1.25946	−	0.727150i
$208$	528.792	−	305.298i	0.176275	−	0.101772i
$209$	2621.46			0.867607
$210$		0			0
$211$	−3164.93			−1.03262			−0.516309	−	0.856402i	$-0.672695\pi$
$211$	−3164.93			−1.03262			−0.516309	+	0.856402i	$0.672695\pi$
$212$	1883.27	−	1087.31i	0.610111	−	0.352248i
$213$	−6423.12	−	3708.39i	−2.06622	−	1.19293i
$214$	−663.857	+	1149.83i	−0.212058	+	0.367295i
$215$		0			0
$216$	−1037.87			−0.326935
$217$	2749.33	+	4117.42i	0.860077	+	1.28806i
$218$			3612.01i			1.12218i
$219$	−2129.63	−	3688.62i	−0.657109	−	1.13815i
$220$		0			0
$221$	45.6670	−	79.0975i	0.0139000	−	0.0240755i
$222$	−5247.79	+	3029.81i	−1.58652	+	0.915980i
$223$		−	4697.63i		−	1.41066i	−0.708880	−	0.705329i	$-0.750799\pi$
$223$		−	4697.63i		−	1.41066i	0.708880	−	0.705329i	$-0.249201\pi$
$224$	492.871	−	329.105i	0.147015	−	0.0981664i
$225$		0			0
$226$	−448.406	−	776.662i	−0.131980	−	0.228597i
$227$	644.273	+	371.971i	0.188378	+	0.108760i	0.591223	−	0.806508i	$-0.298645\pi$
$227$	644.273	+	371.971i	0.188378	+	0.108760i	−0.402845	+	0.915268i	$0.631979\pi$
$228$	−2883.09	−	1664.55i	−0.837444	−	0.483498i
$229$	−478.567	−	828.903i	−0.138099	−	0.239194i	0.788678	−	0.614806i	$-0.210766\pi$
$229$	−478.567	−	828.903i	−0.138099	−	0.239194i	−0.926777	+	0.375612i	$0.877432\pi$
$230$		0			0
$231$	−264.118	−	4048.86i	−0.0752280	−	1.15323i
$232$		−	1791.48i		−	0.506969i
$233$	−742.980	+	428.960i	−0.208902	+	0.120610i	−0.600801	−	0.799399i	$-0.705152\pi$
$233$	−742.980	+	428.960i	−0.208902	+	0.120610i	0.391899	+	0.920008i	$0.371818\pi$
$234$	−1624.02	+	2812.88i	−0.453698	+	0.785827i
$235$		0			0
$236$	786.316	+	1361.94i	0.216885	+	0.375655i
$237$		−	2283.12i		−	0.625758i
$238$	39.2332	−	79.4950i	0.0106853	−	0.0216508i
$239$	1814.74			0.491154			0.245577	−	0.969377i	$-0.421023\pi$
$239$	1814.74			0.491154			0.245577	+	0.969377i	$0.421023\pi$
$240$		0			0
$241$	1840.55	−	3187.92i	0.491951	−	0.852084i	−0.508006	−	0.861353i	$-0.669617\pi$
$241$	1840.55	−	3187.92i	0.491951	−	0.852084i	0.999957	+	0.00926972i	$0.00295069\pi$
$242$	1110.15	+	640.947i	0.294890	+	0.170255i
$243$	−3517.61	+	2030.89i	−0.928620	+	0.536139i
$244$	2017.24			0.529263
$245$		0			0
$246$	1583.19			0.410327
$247$	−3298.12	+	1904.17i	−0.849612	+	0.490524i
$248$	−1852.09	−	1069.31i	−0.474226	−	0.273795i
$249$	2190.03	−	3793.25i	0.557381	−	0.965412i
$250$		0			0
$251$	−2588.41			−0.650913			−0.325457	−	0.945557i	$-0.605518\pi$
$251$	−2588.41			−0.650913			−0.325457	+	0.945557i	$0.605518\pi$
$252$	−1395.22	+	2827.01i	−0.348771	+	0.706687i
$253$			2673.59i			0.664375i
$254$	1780.09	+	3083.21i	0.439736	+	0.761645i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−962.625	+	555.772i	−0.233645	+	0.134895i	−0.612253	−	0.790662i	$-0.709736\pi$
$257$	−962.625	+	555.772i	−0.233645	+	0.134895i	0.378607	+	0.925557i	$0.376403\pi$
$258$			6773.63i			1.63453i
$259$	437.965	+	6713.89i	0.105073	+	1.61074i
$260$		0			0
$261$	4764.85	+	8252.96i	1.13003	+	1.95726i
$262$	−5093.75	−	2940.88i	−1.20112	−	0.693466i
$263$	−2375.43	−	1371.45i	−0.556939	−	0.321549i	0.194977	−	0.980808i	$-0.437537\pi$
$263$	−2375.43	−	1371.45i	−0.556939	−	0.321549i	−0.751916	+	0.659259i	$0.770870\pi$
$264$	876.329	+	1517.85i	0.204297	+	0.353852i
$265$		0			0
$266$	−3074.08	+	2052.66i	−0.708585	+	0.473144i
$267$		−	13810.0i		−	3.16538i
$268$	−190.340	+	109.893i	−0.0433839	+	0.0250477i
$269$	−962.573	+	1667.23i	−0.218175	+	0.377891i	−0.954250	−	0.299010i	$-0.903344\pi$
$269$	−962.573	+	1667.23i	−0.218175	+	0.377891i	0.736075	+	0.676900i	$0.236677\pi$
$270$		0			0
$271$	143.298	+	248.199i	0.0321207	+	0.0556347i	0.881639	−	0.471925i	$-0.156441\pi$
$271$	143.298	+	248.199i	0.0321207	+	0.0556347i	−0.849518	+	0.527559i	$0.823107\pi$
$272$			38.2929i			0.00853621i
$273$	3273.29	+	4902.11i	0.725673	+	1.08677i
$274$	3308.71			0.729512
$275$		0			0
$276$	1697.65	−	2940.42i	0.370242	−	0.641277i
$277$	1246.10	+	719.437i	0.270292	+	0.156053i	0.629020	−	0.777389i	$-0.283456\pi$
$277$	1246.10	+	719.437i	0.270292	+	0.156053i	−0.358728	+	0.933442i	$0.616789\pi$
$278$	−709.937	+	409.882i	−0.153163	+	0.0884285i
$279$	11376.2			2.44114
$280$		0			0
$281$	−2659.15			−0.564525			−0.282262	−	0.959337i	$-0.591085\pi$
$281$	−2659.15			−0.564525			−0.282262	+	0.959337i	$0.591085\pi$
$282$	4942.79	−	2853.72i	1.04376	−	0.602612i
$283$	−288.512	−	166.573i	−0.0606017	−	0.0349884i	0.469393	−	0.882989i	$-0.344473\pi$
$283$	−288.512	−	166.573i	−0.0606017	−	0.0349884i	−0.529995	+	0.848001i	$0.677806\pi$
$284$	1778.60	−	3080.63i	0.371622	−	0.643669i
$285$		0			0
$286$	2004.96			0.414530
$287$	777.970	−	1576.34i	0.160007	−	0.324210i
$288$		−	1361.78i		−	0.278623i
$289$	−2453.64	−	4249.82i	−0.499417	−	0.865016i
$290$		0			0
$291$	−24.0288	+	41.6191i	−0.00484052	+	0.00838403i
$292$	1769.12	−	1021.40i	0.354555	−	0.204703i
$293$			7675.26i			1.53035i	0.643821	+	0.765176i	$0.277348\pi$
$293$			7675.26i			1.53035i	−0.643821	+	0.765176i	$0.722652\pi$
$294$	3480.06	+	4541.12i	0.690344	+	0.900828i
$295$		0			0
$296$	−1453.15	−	2516.92i	−0.285346	−	0.494234i
$297$	−2951.37	−	1703.97i	−0.576619	−	0.332911i
$298$	−5160.10	−	2979.18i	−1.00308	−	0.579126i
$299$	−1942.03	−	3363.70i	−0.375621	−	0.650595i
$300$		0			0
$301$	6744.31	+	3328.52i	1.29148	+	0.637384i
$302$		−	3949.25i		−	0.752496i
$303$	8342.01	−	4816.26i	1.58164	−	0.913159i
$304$	798.346	−	1382.78i	0.150619	−	0.260880i
$305$		0			0
$306$	−101.848	−	176.407i	−0.0190271	−	0.0329559i
$307$		−	3833.02i		−	0.712580i	−0.934375	−	0.356290i	$-0.884041\pi$
$307$		−	3833.02i		−	0.712580i	0.934375	−	0.356290i	$-0.115959\pi$
$308$	1941.90	−	126.675i	0.359253	−	0.0234350i
$309$	−13642.7			−2.51166
$310$		0			0
$311$	−220.933	+	382.667i	−0.0402828	+	0.0697719i	−0.885464	−	0.464708i	$-0.846159\pi$
$311$	−220.933	+	382.667i	−0.0402828	+	0.0697719i	0.845181	+	0.534480i	$0.179493\pi$
$312$	−2205.06	−	1273.09i	−0.400118	−	0.231009i
$313$	7210.56	−	4163.02i	1.30212	−	0.751781i	0.321356	−	0.946959i	$-0.395862\pi$
$313$	7210.56	−	4163.02i	1.30212	−	0.751781i	0.980768	+	0.195177i	$0.0625282\pi$
$314$	1402.60			0.252080
$315$		0			0
$316$	1095.02			0.194936
$317$	−3003.47	+	1734.05i	−0.532151	+	0.307237i	−0.741892	−	0.670520i	$-0.766071\pi$
$317$	−3003.47	+	1734.05i	−0.532151	+	0.307237i	0.209741	+	0.977757i	$0.432738\pi$
$318$	−7853.23	−	4534.07i	−1.38487	−	0.799553i
$319$	2941.27	−	5094.42i	0.516236	−	0.894147i
$320$		0			0
$321$	5536.57			0.962683
$322$	−2093.48	−	3135.21i	−0.362313	−	0.542603i
$323$		−	238.836i		−	0.0411430i
$324$	−134.049	−	232.180i	−0.0229851	−	0.0398114i
$325$		0			0
$326$	894.125	−	1548.67i	0.151905	−	0.263107i
$327$	13044.1	−	7531.04i	2.20594	−	1.27360i
$328$			759.324i			0.127825i
$329$	−412.511	−	6323.69i	−0.0691261	−	1.05969i
$330$		0			0
$331$	5484.37	+	9499.21i	0.910720	+	1.57741i	0.813050	+	0.582194i	$0.197806\pi$
$331$	5484.37	+	9499.21i	0.910720	+	1.57741i	0.0976697	+	0.995219i	$0.468861\pi$
$332$	1819.31	+	1050.38i	0.300745	+	0.173635i
$333$	13388.6	+	7729.93i	2.20328	+	1.27207i
$334$	1037.45	+	1796.91i	0.169960	+	0.294379i
$335$		0			0
$336$	−2216.14	−	1093.73i	−0.359823	−	0.177583i
$337$		−	4317.34i		−	0.697865i	−0.937148	−	0.348932i	$-0.886544\pi$
$337$		−	4317.34i		−	0.697865i	0.937148	−	0.348932i	$-0.113456\pi$
$338$	1282.83	−	740.643i	0.206440	−	0.119188i
$339$	−1869.85	+	3238.68i	−0.299577	+	0.518882i
$340$		0			0
$341$	−3511.18	−	6081.55i	−0.557599	−	0.965790i
$342$			8493.52i			1.34291i
$343$	6231.54	−	1233.52i	0.980966	−	0.194180i
$344$	−3248.75			−0.509188
$345$		0			0
$346$	1837.08	−	3181.91i	0.285439	−	0.494395i
$347$	7281.05	+	4203.72i	1.12642	+	0.650338i	0.943032	−	0.332703i	$-0.107961\pi$
$347$	7281.05	+	4203.72i	1.12642	+	0.650338i	0.183387	+	0.983041i	$0.441294\pi$
$348$	−6469.63	+	3735.24i	−0.996577	+	0.575374i
$349$	6083.47			0.933068			0.466534	−	0.884503i	$-0.345503\pi$
$349$	6083.47			0.933068			0.466534	+	0.884503i	$0.345503\pi$
$350$		0			0
$351$	4950.91			0.752878
$352$	−727.984	+	420.302i	−0.110232	+	0.0636425i
$353$	−10076.4	−	5817.60i	−1.51930	−	0.877166i	−0.999742	−	0.0227283i	$-0.992765\pi$
$353$	−10076.4	−	5817.60i	−1.51930	−	0.877166i	−0.519554	−	0.854438i	$-0.673902\pi$
$354$	3278.94	−	5679.28i	0.492298	−	0.852685i
$355$		0			0
$356$	6623.48			0.986079
$357$	−368.883	+	24.0632i	−0.0546873	+	0.00356740i
$358$		−	99.5889i		−	0.0147023i
$359$	−839.170	−	1453.48i	−0.123370	−	0.213682i	0.797725	−	0.603022i	$-0.206037\pi$
$359$	−839.170	−	1453.48i	−0.123370	−	0.213682i	−0.921094	+	0.389339i	$0.872703\pi$
$360$		0			0
$361$	−1549.85	+	2684.42i	−0.225959	+	0.391372i
$362$	1733.08	−	1000.59i	0.251626	−	0.145276i
$363$		−	5345.49i		−	0.772908i
$364$	−2351.13	+	1569.92i	−0.338552	+	0.226062i
$365$		0			0
$366$	−4205.93	−	7284.89i	−0.600677	−	1.04040i
$367$	−5904.34	−	3408.87i	−0.839793	−	0.484854i	0.0174011	−	0.999849i	$-0.494461\pi$
$367$	−5904.34	−	3408.87i	−0.839793	−	0.484854i	−0.857194	+	0.514994i	$0.827794\pi$
$368$	1410.27	+	814.222i	0.199771	+	0.115338i
$369$	−2019.59	−	3498.04i	−0.284921	−	0.493497i
$370$		0			0
$371$	−8373.46	+	5591.22i	−1.17177	+	0.782430i
$372$			8918.02i			1.24295i
$373$	11499.0	−	6638.96i	1.59624	−	0.921588i	0.604034	−	0.796959i	$-0.293559\pi$
$373$	11499.0	−	6638.96i	1.59624	−	0.921588i	0.992203	−	0.124629i	$-0.0397742\pi$
$374$	−62.8694	+	108.893i	−0.00869225	+	0.0150554i
$375$		0			0
$376$	1368.69	+	2370.64i	0.187726	+	0.325151i
$377$			8545.88i			1.16747i
$378$	4795.20	−	312.803i	0.652482	−	0.0425632i
$379$	−11844.1			−1.60525			−0.802623	−	0.596487i	$-0.796563\pi$
$379$	−11844.1			−1.60525			−0.802623	+	0.596487i	$0.796563\pi$
$380$		0			0
$381$	7422.99	−	12857.0i	0.998140	−	1.72883i
$382$	1728.25	+	997.807i	0.231479	+	0.133645i
$383$	−5961.27	+	3441.74i	−0.795318	+	0.459177i	−0.841831	−	0.539741i	$-0.818522\pi$
$383$	−5961.27	+	3441.74i	−0.795318	+	0.459177i	0.0465135	+	0.998918i	$0.485189\pi$
$384$	1067.52			0.141866
$385$		0			0
$386$	5126.12			0.675939
$387$	14966.2	−	8640.76i	1.96583	−	1.13497i
$388$	−19.9612	−	11.5246i	−0.00261179	−	0.00150792i
$389$	−2088.51	+	3617.41i	−0.272215	+	0.471491i	−0.969429	−	0.245373i	$-0.921090\pi$
$389$	−2088.51	+	3617.41i	−0.272215	+	0.471491i	0.697213	+	0.716864i	$0.254423\pi$
$390$		0			0
$391$	243.585			0.0315055
$392$	−2178.00	+	1669.09i	−0.280626	+	0.215056i
$393$			24526.9i			3.14814i
$394$	821.223	+	1422.40i	0.105007	+	0.181877i
$395$		0			0
$396$	2235.77	−	3872.47i	0.283717	−	0.491412i
$397$	−5095.94	+	2942.14i	−0.644227	+	0.371944i	−0.786241	−	0.617920i	$-0.787975\pi$
$397$	−5095.94	+	2942.14i	−0.644227	+	0.371944i	0.142014	+	0.989865i	$0.454642\pi$
$398$			6472.52i			0.815172i
$399$	13822.3	+	6821.70i	1.73428	+	0.855920i
$400$		0			0
$401$	4698.92	+	8138.77i	0.585169	+	1.01354i	0.994854	+	0.101316i	$0.0323052\pi$
$401$	4698.92	+	8138.77i	0.585169	+	1.01354i	−0.409685	+	0.912227i	$0.634361\pi$
$402$	793.719	+	458.254i	0.0984754	+	0.0568548i
$403$	8835.01	+	5100.89i	1.09207	+	0.630505i
$404$	2309.96	+	4000.97i	0.284467	+	0.492712i
$405$		0			0
$406$	539.937	+	8277.10i	0.0660015	+	1.01179i
$407$		−	9543.13i		−	1.16225i
$408$	138.288	−	79.8407i	0.0167801	−	0.00968800i
$409$	−4162.07	+	7208.91i	−0.503181	+	0.871535i	0.496812	+	0.867858i	$0.334504\pi$
$409$	−4162.07	+	7208.91i	−0.503181	+	0.871535i	−0.999993	+	0.00367699i	$0.998830\pi$
$410$		0			0
$411$	−6898.66	−	11948.8i	−0.827945	−	1.43404i
$412$		−	6543.24i		−	0.782433i
$413$	−4043.45	−	6055.50i	−0.481756	−	0.721481i
$414$	−8662.42			−1.02834
$415$		0			0
$416$	610.596	−	1057.58i	0.0719638	−	0.124645i
$417$	2960.44	+	1709.21i	0.347658	+	0.200720i
$418$	4540.50	−	2621.46i	0.531299	−	0.306746i
$419$	7948.44			0.926746			0.463373	−	0.886163i	$-0.346639\pi$
$419$	7948.44			0.926746			0.463373	+	0.886163i	$0.346639\pi$
$420$		0			0
$421$	−7628.47			−0.883109			−0.441554	−	0.897235i	$-0.645573\pi$
$421$	−7628.47			−0.883109			−0.441554	+	0.897235i	$0.645573\pi$
$422$	−5481.81	+	3164.93i	−0.632347	+	0.365086i
$423$	−12610.5	−	7280.68i	−1.44951	−	0.836877i
$424$	2174.61	−	3766.54i	0.249077	−	0.431413i
$425$		0			0
$426$	−14833.6			−1.68706
$427$	−9320.12	+	607.976i	−1.05628	+	0.0689041i
$428$			2655.43i			0.299895i
$429$	−4180.34	−	7240.56i	−0.470463	−	0.814866i
$430$		0			0
$431$	−3496.19	+	6055.59i	−0.390733	+	0.676769i	−0.992546	−	0.121868i	$-0.961112\pi$
$431$	−3496.19	+	6055.59i	−0.390733	+	0.676769i	0.601814	+	0.798636i	$0.294445\pi$
$432$	−1797.64	+	1037.87i	−0.200206	+	0.115589i
$433$		−	10000.3i		−	1.10989i	−0.831886	−	0.554947i	$-0.812739\pi$
$433$		−	10000.3i		−	1.10989i	0.831886	−	0.554947i	$-0.187261\pi$
$434$	8879.40	+	4382.25i	0.982085	+	0.484689i
$435$		0			0
$436$	3612.01	+	6256.19i	0.396752	+	0.687195i
$437$	−8795.99	−	5078.37i	−0.962859	−	0.555907i
$438$	−7377.24	−	4259.25i	−0.804791	−	0.464646i
$439$	3365.41	+	5829.07i	0.365882	+	0.633727i	0.988917	−	0.148467i	$-0.0474339\pi$
$439$	3365.41	+	5829.07i	0.365882	+	0.633727i	−0.623035	+	0.782194i	$0.714101\pi$
$440$		0			0
$441$	5594.21	−	13482.0i	0.604061	−	1.45578i
$442$		−	182.668i		−	0.0196575i
$443$	−6067.47	+	3503.05i	−0.650731	+	0.375700i	−0.788736	−	0.614732i	$-0.789264\pi$
$443$	−6067.47	+	3503.05i	−0.650731	+	0.375700i	0.138005	+	0.990432i	$0.455931\pi$
$444$	−6059.62	+	10495.6i	−0.647696	+	1.12184i
$445$		0			0
$446$	−4697.63	−	8136.54i	−0.498743	−	0.863848i
$447$			24846.4i			2.62907i
$448$	524.572	−	1062.90i	0.0553208	−	0.112092i
$449$	−5307.59			−0.557863			−0.278932	−	0.960311i	$-0.589980\pi$
$449$	−5307.59			−0.557863			−0.278932	+	0.960311i	$0.589980\pi$
$450$		0			0
$451$	−1246.66	+	2159.28i	−0.130162	+	0.225447i
$452$	−1553.32	−	896.813i	−0.161642	−	0.0933241i
$453$	−14262.0	+	8234.18i	−1.47922	+	0.854030i
$454$	1487.88			0.153810
$455$		0			0
$456$	−6658.21			−0.683770
$457$	−10357.5	+	5979.89i	−1.06018	+	0.612095i	−0.925482	−	0.378792i	$-0.876340\pi$
$457$	−10357.5	+	5979.89i	−1.06018	+	0.612095i	−0.134697	+	0.990887i	$0.543006\pi$
$458$	−1657.81	−	957.135i	−0.169136	−	0.0976506i
$459$	−155.246	+	268.894i	−0.0157870	+	0.0273440i
$460$		0			0
$461$	−3761.36			−0.380009			−0.190004	−	0.981783i	$-0.560850\pi$
$461$	−3761.36			−0.380009			−0.190004	+	0.981783i	$0.560850\pi$
$462$	−4506.32	−	6748.71i	−0.453794	−	0.679607i
$463$		−	17527.2i		−	1.75930i	−0.475617	−	0.879652i	$-0.657775\pi$
$463$		−	17527.2i		−	1.75930i	0.475617	−	0.879652i	$-0.342225\pi$
$464$	−1791.48	−	3102.94i	−0.179240	−	0.310454i
$465$		0			0
$466$	−857.919	+	1485.96i	−0.0852840	+	0.147716i
$467$	8830.23	−	5098.13i	0.874977	−	0.505168i	0.00597804	−	0.999982i	$-0.498097\pi$
$467$	8830.23	−	5098.13i	0.874977	−	0.505168i	0.868999	+	0.494814i	$0.164764\pi$
$468$			6496.06i			0.641625i
$469$	846.298	−	565.100i	0.0833229	−	0.0556373i
$470$		0			0
$471$	−2924.41	−	5065.23i	−0.286093	−	0.495528i
$472$	2723.88	+	1572.63i	0.265628	+	0.153361i
$473$	−9238.42	−	5333.81i	−0.898062	−	0.518496i
$474$	−2283.12	−	3954.48i	−0.221239	−	0.383197i
$475$		0			0
$476$	−11.5411	−	176.923i	−0.00111132	−	0.0170362i
$477$			23135.5i			2.22075i
$478$	3143.22	−	1814.74i	0.300769	−	0.173649i
$479$	8849.51	−	15327.8i	0.844143	−	1.46210i	−0.0422211	−	0.999108i	$-0.513443\pi$
$479$	8849.51	−	15327.8i	0.844143	−	1.46210i	0.886364	−	0.462990i	$-0.153223\pi$
$480$		0			0
$481$	6931.92	+	12006.4i	0.657107	+	1.13814i
$482$		−	7362.19i		−	0.695723i
$483$	−6957.36	+	14097.1i	−0.655426	+	1.32804i
$484$	2563.79			0.240776
$485$		0			0
$486$	−4061.78	+	7035.22i	−0.379108	+	0.656634i
$487$	8556.16	+	4939.90i	0.796133	+	0.459647i	0.842117	−	0.539295i	$-0.181309\pi$
$487$	8556.16	+	4939.90i	0.796133	+	0.459647i	−0.0459844	+	0.998942i	$0.514642\pi$
$488$	3493.95	−	2017.24i	0.324106	−	0.187123i
$489$	−7457.00			−0.689606
$490$		0			0
$491$	−13584.5			−1.24860			−0.624299	−	0.781185i	$-0.714615\pi$
$491$	−13584.5			−1.24860			−0.624299	+	0.781185i	$0.714615\pi$
$492$	2742.17	−	1583.19i	0.251273	−	0.145073i
$493$	−464.143	−	267.973i	−0.0424015	−	0.0244805i
$494$	−3808.34	+	6596.23i	−0.346853	+	0.600766i
$495$		0			0
$496$	−4277.23			−0.387204
$497$	−7289.11	+	14769.3i	−0.657870	+	1.33299i
$498$		−	8760.14i		−	0.788255i
$499$	5824.16	+	10087.7i	0.522495	+	0.904988i	0.999657	+	0.0261729i	$0.00833205\pi$
$499$	5824.16	+	10087.7i	0.522495	+	0.904988i	−0.477162	+	0.878815i	$0.658335\pi$
$500$		0			0
$501$	4326.15	−	7493.11i	0.385785	−	0.668199i
$502$	−4483.27	+	2588.41i	−0.398601	+	0.230133i
$503$		−	14501.5i		−	1.28547i	−0.766091	−	0.642733i	$-0.777801\pi$
$503$		−	14501.5i		−	1.28547i	0.766091	−	0.642733i	$-0.222199\pi$
$504$	410.427	+	6291.75i	0.0362736	+	0.556065i
$505$		0			0
$506$	2673.59	+	4630.79i	0.234892	+	0.406845i
$507$	−5349.40	−	3088.48i	−0.468590	−	0.270541i
$508$	6166.42	+	3560.19i	0.538565	+	0.310940i
$509$	−1185.26	−	2052.93i	−0.103214	−	0.178771i	0.809793	−	0.586715i	$-0.199579\pi$
$509$	−1185.26	−	2052.93i	−0.103214	−	0.178771i	−0.913007	+	0.407944i	$0.866246\pi$
$510$		0			0
$511$	−7865.94	+	5252.33i	−0.680957	+	0.454696i
$512$			512.000i			0.0441942i
$513$	11212.0	−	6473.26i	0.964956	−	0.557117i
$514$	−1111.54	+	1925.25i	−0.0953853	+	0.165212i
$515$		0			0
$516$	6773.63	+	11732.3i	0.577893	+	1.00094i
$517$			8988.50i			0.764630i
$518$	7472.47	+	11190.8i	0.633825	+	0.949223i
$519$	−15321.2			−1.29581
$520$		0			0
$521$	3037.18	−	5260.55i	0.255396	−	0.442359i	−0.709607	−	0.704598i	$-0.751127\pi$
$521$	3037.18	−	5260.55i	0.255396	−	0.442359i	0.965003	+	0.262239i	$0.0844608\pi$
$522$	16505.9	+	9529.70i	1.38399	+	0.799049i
$523$	1427.91	−	824.403i	0.119384	−	0.0689266i	−0.439119	−	0.898429i	$-0.644709\pi$
$523$	1427.91	−	824.403i	0.119384	−	0.0689266i	0.558503	+	0.829502i	$0.311376\pi$
$524$	−11763.5			−0.980709
$525$		0			0
$526$	−5485.81			−0.454739
$527$	−554.078	+	319.897i	−0.0457989	+	0.0264420i
$528$	3035.69	+	1752.66i	0.250211	+	0.144460i
$529$	−904.141	+	1566.02i	−0.0743110	+	0.128710i
$530$		0			0
$531$	−16731.1			−1.36736
$532$	−3271.80	+	6629.38i	−0.266636	+	0.540263i
$533$		−	3622.19i		−	0.294361i
$534$	−13810.0	−	23919.6i	−1.11913	−	1.93839i
$535$		0			0
$536$	−219.786	+	380.681i	−0.0177114	+	0.0306771i
$537$	−359.648	+	207.643i	−0.0289012	+	0.0166861i
$538$			3850.29i			0.308546i
$539$	−8933.86	+	1170.54i	−0.713931	+	0.0935413i
$540$		0			0
$541$	−6879.27	−	11915.3i	−0.546697	−	0.946907i	−0.998498	−	0.0547883i	$-0.982552\pi$
$541$	−6879.27	−	11915.3i	−0.546697	−	0.946907i	0.451801	−	0.892119i	$-0.350782\pi$
$542$	496.397	+	286.595i	0.0393397	+	0.0227128i
$543$	−7226.93	−	4172.47i	−0.571155	−	0.329757i
$544$	38.2929	+	66.3252i	0.00301800	+	0.00522734i
$545$		0			0
$546$	10571.6	+	5217.41i	0.828614	+	0.408946i
$547$			4368.90i			0.341501i	0.985314	+	0.170750i	$0.0546192\pi$
$547$			4368.90i			0.341501i	−0.985314	+	0.170750i	$0.945381\pi$
$548$	5730.85	−	3308.71i	0.446733	−	0.257922i
$549$	−10730.6	+	18585.9i	−0.834189	+	1.44486i
$550$		0			0
$551$	11173.6	+	19353.3i	0.863907	+	1.49633i
$552$		−	6790.61i		−	0.523601i
$553$	−5059.27	+	330.030i	−0.389046	+	0.0253785i
$554$	2877.75			0.220693
$555$		0			0
$556$	−819.765	+	1419.87i	−0.0625284	+	0.108302i
$557$	−8917.62	−	5148.59i	−0.678369	−	0.391657i	0.120871	−	0.992668i	$-0.461431\pi$
$557$	−8917.62	−	5148.59i	−0.678369	−	0.391657i	−0.799240	+	0.601012i	$0.794765\pi$
$558$	19704.2	−	11376.2i	1.49489	−	0.863072i
$559$	15497.4			1.17258
$560$		0			0
$561$	524.331			0.0394604
$562$	−4605.78	+	2659.15i	−0.345699	+	0.199590i
$563$	12270.6	+	7084.45i	0.918553	+	0.530327i	0.883173	−	0.469047i	$-0.155403\pi$
$563$	12270.6	+	7084.45i	0.918553	+	0.530327i	0.0353796	+	0.999374i	$0.488736\pi$
$564$	5707.45	−	9885.59i	0.426111	−	0.738047i
$565$		0			0
$566$	−666.290			−0.0494811
$567$	689.317	+	1032.33i	0.0510557	+	0.0764615i
$568$		−	7114.42i		−	0.525553i
$569$	−11983.6	−	20756.1i	−0.882912	−	1.52925i	−0.848088	−	0.529856i	$-0.822246\pi$
$569$	−11983.6	−	20756.1i	−0.882912	−	1.52925i	−0.0348246	−	0.999393i	$-0.511087\pi$
$570$		0			0
$571$	−10352.6	+	17931.3i	−0.758745	+	1.31418i	0.184746	+	0.982786i	$0.440854\pi$
$571$	−10352.6	+	17931.3i	−0.758745	+	1.31418i	−0.943491	+	0.331398i	$0.892480\pi$
$572$	3472.69	−	2004.96i	0.253847	−	0.146559i
$573$		−	8321.71i		−	0.606709i
$574$	−228.853	−	3508.26i	−0.0166414	−	0.255108i
$575$		0			0
$576$	−1361.78	−	2358.67i	−0.0985082	−	0.170621i
$577$	1312.22	+	757.610i	0.0946766	+	0.0546616i	0.546591	−	0.837400i	$-0.315925\pi$
$577$	1312.22	+	757.610i	0.0946766	+	0.0546616i	−0.451914	+	0.892061i	$0.649259\pi$
$578$	−8499.64	−	4907.27i	−0.611658	−	0.353141i
$579$	−10688.0	−	18512.1i	−0.767144	−	1.32873i
$580$		0			0
$581$	−8722.21	−	4304.68i	−0.622820	−	0.307380i
$582$			96.1151i			0.00684553i
$583$	12367.8	−	7140.58i	0.878600	−	0.507260i
$584$	2042.81	−	3538.25i	0.144747	−	0.250708i
$585$		0			0
$586$	7675.26	+	13293.9i	0.541061	+	0.937146i
$587$		−	25148.2i		−	1.76828i	−0.467226	−	0.884138i	$-0.654746\pi$
$587$		−	25148.2i		−	1.76828i	0.467226	−	0.884138i	$-0.345254\pi$
$588$	10568.8	+	4385.39i	0.741238	+	0.307569i
$589$	26677.4			1.86625
$590$		0			0
$591$	3424.50	−	5931.40i	0.238350	−	0.412835i
$592$	−5033.85	−	2906.29i	−0.349476	−	0.201770i
$593$	−13605.1	+	7854.88i	−0.942146	+	0.543948i	−0.890633	−	0.454724i	$-0.849738\pi$
$593$	−13605.1	+	7854.88i	−0.942146	+	0.543948i	−0.0515139	+	0.998672i	$0.516405\pi$
$594$	−6815.89			−0.470807
$595$		0			0
$596$	−11916.7			−0.819008
$597$	23374.4	−	13495.2i	1.60243	−	0.925163i
$598$	−6727.41	−	3884.07i	−0.460040	−	0.265604i
$599$	−5243.91	+	9082.71i	−0.357696	+	0.619548i	−0.987576	−	0.157145i	$-0.949771\pi$
$599$	−5243.91	+	9082.71i	−0.357696	+	0.619548i	0.629879	+	0.776693i	$0.283104\pi$
$600$		0			0
$601$	19266.8			1.30767			0.653835	−	0.756637i	$-0.273159\pi$
$601$	19266.8			1.30767			0.653835	+	0.756637i	$0.273159\pi$
$602$	15010.0	−	979.142i	1.01622	−	0.0662905i
$603$		−	2338.28i		−	0.157914i
$604$	−3949.25	−	6840.30i	−0.266047	−	0.460808i
$605$		0			0
$606$	9632.53	−	16684.0i	0.645701	−	1.11839i
$607$	6046.38	−	3490.88i	0.404308	−	0.233427i	−0.284033	−	0.958814i	$-0.591673\pi$
$607$	6046.38	−	3490.88i	0.404308	−	0.233427i	0.688341	+	0.725387i	$0.258339\pi$
$608$		−	3193.38i		−	0.213008i
$609$	28765.5	−	19207.6i	1.91402	−	1.27805i
$610$		0			0
$611$	−6529.05	−	11308.6i	−0.432303	−	0.748770i
$612$	−352.813	−	203.697i	−0.0233033	−	0.0134542i
$613$	574.820	+	331.873i	0.0378740	+	0.0218666i	0.518817	−	0.854885i	$-0.326372\pi$
$613$	574.820	+	331.873i	0.0378740	+	0.0218666i	−0.480943	+	0.876752i	$0.659706\pi$
$614$	−3833.02	−	6638.99i	−0.251935	−	0.436365i
$615$		0			0
$616$	3236.79	−	2161.31i	0.211711	−	0.141366i
$617$			7749.41i			0.505640i	0.967513	+	0.252820i	$0.0813580\pi$
$617$			7749.41i			0.505640i	−0.967513	+	0.252820i	$0.918642\pi$
$618$	−23629.8	+	13642.7i	−1.53807	+	0.888007i
$619$	−8215.93	+	14230.4i	−0.533483	+	0.924020i	0.465752	+	0.884915i	$0.345784\pi$
$619$	−8215.93	+	14230.4i	−0.533483	+	0.924020i	−0.999235	+	0.0391048i	$0.987549\pi$
$620$		0			0
$621$	6601.98	+	11435.0i	0.426616	+	0.738920i
$622$			883.732i			0.0569685i
$623$	−30602.1	+	1996.26i	−1.96797	+	0.128376i
$624$	−5092.37			−0.326695
$625$		0			0
$626$	8326.03	−	14421.1i	0.531590	−	0.920740i
$627$	−18933.9	−	10931.5i	−1.20597	−	0.696269i
$628$	2429.37	−	1402.60i	0.154367	−	0.0891237i
$629$	−869.456			−0.0551153
$630$		0			0
$631$	14436.7			0.910804			0.455402	−	0.890286i	$-0.349496\pi$
$631$	14436.7			0.910804			0.455402	+	0.890286i	$0.349496\pi$
$632$	1896.64	−	1095.02i	0.119374	−	0.0689204i
$633$	22859.2	+	13197.7i	1.43534	+	0.828694i
$634$	−3468.11	+	6006.94i	−0.217250	+	0.376287i
$635$		0			0
$636$	−18136.3			−1.13074
$637$	10389.6	−	7962.05i	0.646237	−	0.495240i
$638$		−	11765.1i		−	0.730068i
$639$	18922.4	+	32774.5i	1.17145	+	2.02901i
$640$		0			0
$641$	−7444.58	+	12894.4i	−0.458726	+	0.794537i	−0.998894	−	0.0470206i	$-0.985027\pi$
$641$	−7444.58	+	12894.4i	−0.458726	+	0.794537i	0.540168	+	0.841557i	$0.318361\pi$
$642$	9589.62	−	5536.57i	0.589520	−	0.340360i
$643$			26252.6i			1.61011i	0.593198	+	0.805057i	$0.297865\pi$
$643$			26252.6i			1.61011i	−0.593198	+	0.805057i	$0.702135\pi$
$644$	−6761.21	−	3336.86i	−0.413710	−	0.204178i
$645$		0			0
$646$	−238.836	−	413.676i	−0.0145462	−	0.0251948i
$647$	−6113.60	−	3529.69i	−0.371485	−	0.214477i	0.302622	−	0.953111i	$-0.402138\pi$
$647$	−6113.60	−	3529.69i	−0.371485	−	0.214477i	−0.674107	+	0.738634i	$0.735471\pi$
$648$	−464.360	−	268.098i	−0.0281509	−	0.0162529i
$649$	5163.91	+	8944.15i	0.312328	+	0.540969i
$650$		0			0
$651$	−2687.81	−	41203.4i	−0.161818	−	2.48063i
$652$		−	3576.50i		−	0.214826i
$653$	9284.04	−	5360.14i	0.556374	−	0.321223i	−0.195315	−	0.980741i	$-0.562573\pi$
$653$	9284.04	−	5360.14i	0.556374	−	0.321223i	0.751689	+	0.659518i	$0.229239\pi$
$654$	15062.1	−	26088.3i	0.900572	−	1.55984i
$655$		0			0
$656$	759.324	+	1315.19i	0.0451930	+	0.0782766i
$657$			21733.2i			1.29055i
$658$	−7038.18	−	10540.4i	−0.416986	−	0.624482i
$659$	−5021.59			−0.296834			−0.148417	−	0.988925i	$-0.547418\pi$
$659$	−5021.59			−0.296834			−0.148417	+	0.988925i	$0.547418\pi$
$660$		0			0
$661$	3169.37	−	5489.51i	0.186497	−	0.323022i	−0.757583	−	0.652739i	$-0.773620\pi$
$661$	3169.37	−	5489.51i	0.186497	−	0.323022i	0.944080	+	0.329717i	$0.106953\pi$
$662$	18998.4	+	10968.7i	1.11540	+	0.643976i
$663$	−659.673	+	380.862i	−0.0386419	+	0.0223099i
$664$	4201.51			0.245557
$665$		0			0
$666$	30919.7			1.79897
$667$	−19738.2	+	11395.8i	−1.14582	+	0.661542i
$668$	3593.82	+	2074.89i	0.208157	+	0.120180i
$669$	−19589.1	+	33929.3i	−1.13208	+	1.96081i
$670$		0			0
$671$	13247.6			0.762174
$672$	−4932.20	+	321.741i	−0.283131	+	0.0184694i
$673$			6498.81i			0.372230i	0.982528	+	0.186115i	$0.0595897\pi$
$673$			6498.81i			0.372230i	−0.982528	+	0.186115i	$0.940410\pi$
$674$	−4317.34	−	7477.85i	−0.246732	−	0.427353i
$675$		0			0
$676$	1481.29	−	2565.66i	0.0842789	−	0.145975i
$677$	773.013	−	446.299i	0.0438838	−	0.0253363i	−0.477898	−	0.878416i	$-0.658601\pi$
$677$	773.013	−	446.299i	0.0438838	−	0.0253363i	0.521781	+	0.853079i	$0.325268\pi$
$678$			7479.41i			0.423665i
$679$	95.6990	+	47.2303i	0.00540882	+	0.00266942i
$680$		0			0
$681$	−3102.24	−	5373.23i	−0.174564	−	0.302354i
$682$	−12163.1	−	7022.37i	−0.682917	−	0.394282i
$683$	17901.9	+	10335.7i	1.00292	+	0.579038i	0.909112	−	0.416552i	$-0.136762\pi$
$683$	17901.9	+	10335.7i	1.00292	+	0.579038i	0.0938111	+	0.995590i	$0.470095\pi$
$684$	8493.52	+	14711.2i	0.474792	+	0.822364i
$685$		0			0
$686$	9559.82	−	8368.05i	0.532064	−	0.465734i
$687$			7982.50i			0.443306i
$688$	−5626.99	+	3248.75i	−0.311813	+	0.180025i
$689$	−10373.5	+	17967.4i	−0.573584	+	0.993477i
$690$		0			0
$691$	−5751.92	−	9962.61i	−0.316662	−	0.548474i	0.663128	−	0.748506i	$-0.269229\pi$
$691$	−5751.92	−	9962.61i	−0.316662	−	0.548474i	−0.979789	+	0.200032i	$0.935895\pi$
$692$		−	7348.31i		−	0.403672i
$693$	−9162.69	+	18565.6i	−0.502254	+	1.01768i
$694$	16814.9			0.919717
$695$		0			0
$696$	−7470.49	+	12939.3i	−0.406851	+	0.704686i
$697$	196.728	+	113.581i	0.0106910	+	0.00617243i
$698$	10536.9	−	6083.47i	0.571385	−	0.329889i
$699$	7155.05			0.387165
$700$		0			0
$701$	9731.33			0.524318			0.262159	−	0.965025i	$-0.415565\pi$
$701$	9731.33			0.524318			0.262159	+	0.965025i	$0.415565\pi$
$702$	8575.24	−	4950.91i	0.461042	−	0.266183i
$703$	31396.5	+	18126.8i	1.68441	+	0.972496i
$704$	−840.604	+	1455.97i	−0.0450021	+	0.0779458i
$705$		0			0
$706$	−23270.4			−1.24050
$707$	−11878.4	−	17789.2i	−0.631873	−	0.946299i
$708$		−	13115.7i		−	0.696214i
$709$	2181.10	+	3777.78i	0.115533	+	0.200110i	0.917993	−	0.396597i	$-0.129809\pi$
$709$	2181.10	+	3777.78i	0.115533	+	0.200110i	−0.802460	+	0.596707i	$0.796476\pi$
$710$		0			0
$711$	−5824.91	+	10089.0i	−0.307245	+	0.532164i
$712$	11472.2	−	6623.48i	0.603847	−	0.348631i
$713$			27207.9i			1.42909i
$714$	−614.862	+	410.562i	−0.0322278	+	0.0215195i
$715$		0			0
$716$	−99.5889	−	172.493i	−0.00519806	−	0.00900331i
$717$	−13107.2	−	7567.47i	−0.682704	−	0.394160i
$718$	−2906.97	−	1678.34i	−0.151096	−	0.0872355i
$719$	12574.0	+	21778.9i	0.652201	+	1.12965i	0.982588	+	0.185799i	$0.0594875\pi$
$719$	12574.0	+	21778.9i	0.652201	+	1.12965i	−0.330387	+	0.943846i	$0.607179\pi$
$720$		0			0
$721$	1972.07	+	30231.4i	0.101864	+	1.56155i
$722$			6199.40i			0.319554i
$723$	−26587.3	+	15350.2i	−1.36762	+	0.789597i
$724$	2001.19	−	3466.15i	0.102726	−	0.177926i
$725$		0			0
$726$	−5345.49	−	9258.66i	−0.273264	−	0.473308i
$727$			12965.7i			0.661446i	0.943728	+	0.330723i	$0.107293\pi$
$727$			12965.7i			0.661446i	−0.943728	+	0.330723i	$0.892707\pi$
$728$	−2502.36	+	5070.32i	−0.127395	+	0.258130i
$729$	32065.6			1.62910
$730$		0			0
$731$	−485.953	+	841.695i	−0.0245877	+	0.0425872i
$732$	−14569.8	−	8411.87i	−0.735676	−	0.424743i
$733$	−7886.94	+	4553.53i	−0.397423	+	0.229452i	−0.685371	−	0.728194i	$-0.740360\pi$
$733$	−7886.94	+	4553.53i	−0.397423	+	0.229452i	0.287949	+	0.957646i	$0.407027\pi$
$734$	−13635.5			−0.685688
$735$		0			0
$736$	3256.89			0.163112
$737$	−1250.01	+	721.692i	−0.0624757	+	0.0360704i
$738$	−6996.07	−	4039.18i	−0.348955	−	0.201469i
$739$	−3263.50	+	5652.54i	−0.162449	+	0.281370i	−0.935746	−	0.352674i	$-0.885273\pi$
$739$	−3263.50	+	5652.54i	−0.162449	+	0.281370i	0.773298	+	0.634043i	$0.218606\pi$
$740$		0			0
$741$	31761.5			1.57461
$742$	−8912.04	+	18057.7i	−0.440932	+	0.893424i
$743$		−	35778.0i		−	1.76658i	−0.468827	−	0.883290i	$-0.655323\pi$
$743$		−	35778.0i		−	1.76658i	0.468827	−	0.883290i	$-0.344677\pi$
$744$	8918.02	+	15446.5i	0.439449	+	0.761149i
$745$		0			0
$746$	13277.9	−	22998.0i	0.651661	−	1.12871i
$747$	−19355.4	+	11174.8i	−0.948028	+	0.547344i
$748$			251.478i			0.0122927i
$749$	−800.322	−	12268.7i	−0.0390429	−	0.598518i
$750$		0			0
$751$	−14794.2	−	25624.3i	−0.718838	−	1.24506i	−0.961460	−	0.274943i	$-0.911341\pi$
$751$	−14794.2	−	25624.3i	−0.718838	−	1.24506i	0.242622	−	0.970121i	$-0.421992\pi$
$752$	4741.29	+	2737.38i	0.229916	+	0.132742i
$753$	18695.2	+	10793.7i	0.904769	+	0.522369i
$754$	8545.88	+	14801.9i	0.412762	+	0.714925i
$755$		0			0
$756$	7992.72	−	5336.99i	0.384514	−	0.256752i
$757$			7623.03i			0.366002i	0.983113	+	0.183001i	$0.0585812\pi$
$757$			7623.03i			0.366002i	−0.983113	+	0.183001i	$0.941419\pi$
$758$	−20514.5	+	11844.1i	−0.983008	+	0.567540i
$759$	11148.9	−	19310.4i	0.533172	−	0.923482i
$760$		0			0
$761$	−12592.8	−	21811.3i	−0.599853	−	1.03898i	−0.992842	−	0.119433i	$-0.961892\pi$
$761$	−12592.8	−	21811.3i	−0.599853	−	1.03898i	0.392989	−	0.919543i	$-0.371441\pi$
$762$		−	29691.9i		−	1.41158i
$763$	−18573.9	−	27816.5i	−0.881287	−	1.31982i
$764$	3991.23			0.189002
$765$		0			0
$766$	−6883.48	+	11922.5i	−0.324687	+	0.562375i
$767$	−12993.7	−	7501.90i	−0.611700	−	0.353165i
$768$	1849.00	−	1067.52i	0.0868750	−	0.0501573i
$769$	7545.46			0.353831			0.176916	−	0.984226i	$-0.443388\pi$
$769$	7545.46			0.353831			0.176916	+	0.984226i	$0.443388\pi$
$770$		0			0
$771$	9270.27			0.433023
$772$	8878.70	−	5126.12i	0.413927	−	0.238981i
$773$	−20960.7	−	12101.7i	−0.975298	−	0.563089i	−0.0744507	−	0.997225i	$-0.523720\pi$
$773$	−20960.7	−	12101.7i	−0.975298	−	0.563089i	−0.900847	+	0.434136i	$0.857054\pi$
$774$	17281.5	−	29932.5i	0.802547	−	1.39005i
$775$		0			0
$776$	−46.0984			−0.00213252
$777$	24833.7	−	50318.4i	1.14659	−	2.32325i
$778$			8354.05i			0.384971i
$779$	−4735.97	−	8202.94i	−0.217822	−	0.377279i
$780$		0			0
$781$	11680.5	−	20231.2i	0.535160	−	0.926925i
$782$	421.902	−	243.585i	0.0192931	−	0.0111389i
$783$		−	29051.9i		−	1.32596i
$784$	−2103.30	+	5068.95i	−0.0958138	+	0.230911i
$785$		0			0
$786$	24526.9	+	42481.9i	1.11304	+	1.92783i
$787$	5423.80	+	3131.43i	0.245664	+	0.141834i	0.617777	−	0.786353i	$-0.288033\pi$
$787$	5423.80	+	3131.43i	0.245664	+	0.141834i	−0.372113	+	0.928187i	$0.621367\pi$
$788$	2844.80	+	1642.45i	0.128606	+	0.0742509i
$789$	11437.9	+	19811.1i	0.516097	+	0.893906i
$790$		0			0
$791$	7447.03	+	3675.34i	0.334748	+	0.165208i
$792$		−	8943.09i		−	0.401236i
$793$	−16667.1	+	9622.78i	−0.746365	+	0.430914i
$794$	−5884.29	+	10191.9i	−0.263004	+	0.455537i
$795$		0			0
$796$	6472.52	+	11210.7i	0.288207	+	0.499189i
$797$		−	41906.4i		−	1.86248i	−0.364402	−	0.931242i	$-0.618726\pi$
$797$		−	41906.4i		−	1.86248i	0.364402	−	0.931242i	$-0.381274\pi$
$798$	30762.5	−	2006.72i	1.36464	−	0.0890190i
$799$	818.925			0.0362597
$800$		0			0
$801$	−35233.3	+	61025.8i	−1.55419	+	2.69194i
$802$	16277.5	+	9397.84i	0.716683	+	0.413777i
$803$	11618.2	−	6707.78i	0.510583	−	0.294785i
$804$	1833.02			0.0804048
$805$		0			0
$806$	20403.6			0.891669
$807$	13904.7	−	8027.86i	0.606527	−	0.350179i
$808$	8001.93	+	4619.92i	0.348400	+	0.201149i
$809$	17243.3	−	29866.2i	0.749371	−	1.29795i	−0.198753	−	0.980050i	$-0.563689\pi$
$809$	17243.3	−	29866.2i	0.749371	−	1.29795i	0.948125	−	0.317899i	$-0.102977\pi$
$810$		0			0
$811$	15173.9			0.657002			0.328501	−	0.944504i	$-0.393457\pi$
$811$	15173.9			0.657002			0.328501	+	0.944504i	$0.393457\pi$
$812$	9212.29	+	13796.4i	0.398138	+	0.596255i
$813$		−	2390.20i		−	0.103110i
$814$	−9543.13	−	16529.2i	−0.410917	−	0.711729i
$815$		0			0
$816$	159.681	−	276.576i	0.00685045	−	0.0118653i
$817$	35096.0	−	20262.7i	1.50288	−	0.867689i
$818$			16648.3i			0.711605i
$819$	−1957.85	−	30013.4i	−0.0835323	−	1.28053i
$820$		0			0
$821$	7607.33	+	13176.3i	0.323383	+	0.560117i	0.981184	−	0.193076i	$-0.0618463\pi$
$821$	7607.33	+	13176.3i	0.323383	+	0.560117i	−0.657800	+	0.753192i	$0.728513\pi$
$822$	−23897.6	−	13797.3i	−1.01402	−	0.585446i
$823$	19493.9	+	11254.8i	0.825657	+	0.476693i	0.852363	−	0.522950i	$-0.175169\pi$
$823$	19493.9	+	11254.8i	0.825657	+	0.476693i	−0.0267063	+	0.999643i	$0.508502\pi$
$824$	−6543.24	−	11333.2i	−0.276632	−	0.479141i
$825$		0			0
$826$	−13059.0	−	6444.99i	−0.550096	−	0.271489i
$827$		−	32024.2i		−	1.34654i	−0.739395	−	0.673272i	$-0.764888\pi$
$827$		−	32024.2i		−	1.34654i	0.739395	−	0.673272i	$-0.235112\pi$
$828$	−15003.8	+	8662.42i	−0.629730	+	0.363575i
$829$	−9541.87	+	16527.0i	−0.399762	+	0.692408i	−0.993696	−	0.112105i	$-0.964241\pi$
$829$	−9541.87	+	16527.0i	−0.399762	+	0.692408i	0.593934	+	0.804514i	$0.297574\pi$
$830$		0			0
$831$	−6000.10	−	10392.5i	−0.250471	−	0.433828i
$832$		−	2442.38i		−	0.101772i
$833$	106.646	+	813.947i	0.00443584	+	0.0338555i
$834$	6836.84			0.283861
$835$		0			0
$836$	5242.91	−	9080.99i	0.216902	−	0.375685i
$837$	−30034.8	−	17340.6i	−1.24033	−	0.716103i
$838$	13767.1	−	7948.44i	0.567514	−	0.327654i
$839$	−23198.0			−0.954568			−0.477284	−	0.878749i	$-0.658379\pi$
$839$	−23198.0			−0.954568			−0.477284	+	0.878749i	$0.658379\pi$
$840$		0			0
$841$	25758.1			1.05614
$842$	−13212.9	+	7628.47i	−0.540791	+	0.312226i
$843$	19206.1	+	11088.6i	0.784689	+	0.453040i
$844$	−6329.85	+	10963.6i	−0.258155	+	0.447137i
$845$		0			0
$846$	−29122.7			−1.18352
$847$	−11845.3	+	772.702i	−0.480531	+	0.0313463i
$848$		−	8698.45i		−	0.352248i
$849$	1389.22	+	2406.19i	0.0561575	+	0.0972677i
$850$		0			0
$851$	−18487.3	+	32020.9i	−0.744695	+	1.28985i
$852$	−25692.5	+	14833.6i	−1.03311	+	0.596466i
$853$		−	26109.1i		−	1.04802i	−0.851713	−	0.524009i	$-0.824436\pi$
$853$		−	26109.1i		−	1.04802i	0.851713	−	0.524009i	$-0.175564\pi$
$854$	−15534.9	+	10373.2i	−0.622477	+	0.415647i
$855$		0			0
$856$	2655.43	+	4599.34i	0.106029	+	0.183647i
$857$	18156.7	+	10482.8i	0.723713	+	0.417836i	0.816118	−	0.577885i	$-0.196122\pi$
$857$	18156.7	+	10482.8i	0.723713	+	0.417836i	−0.0924046	+	0.995722i	$0.529455\pi$
$858$	−14481.1	−	8360.67i	−0.576197	−	0.332667i
$859$	−15673.2	−	27146.7i	−0.622540	−	1.07827i	−0.989011	−	0.147841i	$-0.952768\pi$
$859$	−15673.2	−	27146.7i	−0.622540	−	1.07827i	0.366472	−	0.930429i	$-0.380566\pi$
$860$		0			0
$861$	−12192.3	+	8141.19i	−0.482594	+	0.322243i
$862$			13984.8i			0.552579i
$863$	12564.3	−	7254.00i	0.495589	−	0.286129i	−0.231301	−	0.972882i	$-0.574298\pi$
$863$	12564.3	−	7254.00i	0.495589	−	0.286129i	0.726890	+	0.686754i	$0.240965\pi$
$864$	−2075.73	+	3595.27i	−0.0817336	+	0.141567i
$865$		0			0
$866$	−10000.3	−	17321.0i	−0.392407	−	0.679669i
$867$			40926.6i			1.60316i
$868$	19761.8	−	1289.12i	0.772765	−	0.0504095i
$869$	7191.25			0.280721
$870$		0			0
$871$	1048.44	−	1815.95i	0.0407866	−	0.0706444i
$872$	12512.4	+	7224.02i	0.485920	+	0.280546i
$873$	212.365	−	122.609i	0.00823306	−	0.00475336i
$874$	−20313.5			−0.786171
$875$		0			0
$876$	−17037.0			−0.657109
$877$	91.5298	−	52.8448i	0.00352422	−	0.00203471i	−0.498237	−	0.867041i	$-0.666019\pi$
$877$	91.5298	−	52.8448i	0.00352422	−	0.00203471i	0.501761	+	0.865006i	$0.332686\pi$
$878$	11658.1	+	6730.83i	0.448113	+	0.258718i
$879$	32005.8	−	55435.7i	1.22813	−	2.12719i
$880$		0			0
$881$	22941.4			0.877316			0.438658	−	0.898654i	$-0.355454\pi$
$881$	22941.4			0.877316			0.438658	+	0.898654i	$0.355454\pi$
$882$	−3792.55	−	28945.7i	−0.144787	−	1.10505i
$883$			25169.9i			0.959267i	0.877469	+	0.479634i	$0.159230\pi$
$883$			25169.9i			0.959267i	−0.877469	+	0.479634i	$0.840770\pi$
$884$	−182.668	−	316.390i	−0.00694998	−	0.0120377i
$885$		0			0
$886$	−7006.11	+	12134.9i	−0.265660	+	0.460137i
$887$	−18411.9	+	10630.1i	−0.696969	+	0.402395i	−0.806217	−	0.591619i	$-0.798489\pi$
$887$	−18411.9	+	10630.1i	−0.696969	+	0.402395i	0.109249	+	0.994014i	$0.465156\pi$
$888$			24238.5i			0.915980i
$889$	−29563.4	−	14590.4i	−1.11533	−	0.550447i
$890$		0			0
$891$	−880.330	−	1524.78i	−0.0331001	−	0.0573310i
$892$	−16273.1	−	9395.26i	−0.610833	−	0.352664i
$893$	−29571.8	−	17073.3i	−1.10816	−	0.639794i
$894$	24846.4	+	43035.2i	0.929516	+	1.60997i
$895$		0			0
$896$	−154.312	−	2365.57i	−0.00575358	−	0.0882009i
$897$			32393.1i			1.20577i
$898$	−9193.01	+	5307.59i	−0.341620	+	0.197234i
$899$	29932.0	−	51843.7i	1.11044	−	1.92334i
$900$		0			0
$901$	−650.564	−	1126.81i	−0.0240549	−	0.0416642i
$902$			4986.65i			0.184077i
$903$	−34831.9	−	52164.5i	−1.28365	−	1.92240i
$904$	−3587.25			−0.131980
$905$		0			0
$906$	−16468.4	+	28524.0i	−0.603890	+	1.04597i
$907$	46233.4	+	26692.9i	1.69256	+	0.977202i	0.952438	+	0.304732i	$0.0985667\pi$
$907$	46233.4	+	26692.9i	1.69256	+	0.977202i	0.740124	+	0.672470i	$0.234767\pi$
$908$	2577.09	−	1487.88i	0.0941892	−	0.0543802i
$909$	−49150.8			−1.79343
$910$		0			0
$911$	−3333.00			−0.121215			−0.0606076	−	0.998162i	$-0.519304\pi$
$911$	−3333.00			−0.121215			−0.0606076	+	0.998162i	$0.519304\pi$
$912$	−11532.4	+	6658.21i	−0.418722	+	0.241749i
$913$	11947.8	+	6898.05i	0.433093	+	0.250046i
$914$	−11959.8	+	20714.9i	−0.432816	+	0.749660i
$915$		0			0
$916$	−3828.54			−0.138099
$917$	54350.3	−	3545.41i	1.95726	−	0.127677i
$918$			620.983i			0.0223262i
$919$	−3111.62	−	5389.48i	−0.111690	−	0.193452i	0.804762	−	0.593598i	$-0.202293\pi$
$919$	−3111.62	−	5389.48i	−0.111690	−	0.193452i	−0.916452	+	0.400145i	$0.868960\pi$
$920$		0			0
$921$	−15983.7	+	27684.6i	−0.571858	+	0.990486i
$922$	−6514.87	+	3761.36i	−0.232707	+	0.134353i
$923$			33937.8i			1.21027i
$924$	−14553.9	−	7182.78i	−0.518168	−	0.255732i
$925$		0			0
$926$	−17527.2	−	30358.0i	−0.622008	−	1.07735i
$927$	60286.5	+	34806.4i	2.13600	+	1.23322i
$928$	−6205.88	−	3582.97i	−0.219524	−	0.126742i
$929$	1873.99	+	3245.84i	0.0661825	+	0.114631i	0.897218	−	0.441588i	$-0.145585\pi$
$929$	1873.99	+	3245.84i	0.0661825	+	0.114631i	−0.831035	+	0.556219i	$0.812251\pi$
$930$		0			0
$931$	13118.5	−	31615.4i	0.461805	−	1.11295i
$932$			3431.68i			0.120610i
$933$	3191.44	−	1842.58i	0.111986	−	0.0646553i
$934$	10196.3	−	17660.5i	0.357208	−	0.618702i
$935$		0			0
$936$	6496.06	+	11251.5i	0.226849	+	0.392914i
$937$		−	31970.1i		−	1.11464i	−0.830298	−	0.557320i	$-0.811830\pi$
$937$		−	31970.1i		−	1.11464i	0.830298	−	0.557320i	$-0.188170\pi$
$938$	900.732	−	1825.08i	0.0313539	−	0.0635298i
$939$	−69439.1			−2.41327
$940$		0			0
$941$	19806.0	−	34305.1i	0.686141	−	1.18843i	−0.286936	−	0.957950i	$-0.592637\pi$
$941$	19806.0	−	34305.1i	0.686141	−	1.18843i	0.973077	−	0.230481i	$-0.0740300\pi$
$942$	−10130.5	−	5848.83i	−0.350391	−	0.202298i
$943$	8366.06	−	4830.15i	0.288904	−	0.166799i
$944$	6290.53			0.216885
$945$		0			0
$946$	−21335.2			−0.733264
$947$	−28999.5	+	16742.9i	−0.995098	+	0.574520i	−0.906794	−	0.421573i	$-0.861478\pi$
$947$	−28999.5	+	16742.9i	−0.995098	+	0.574520i	−0.0883040	+	0.996094i	$0.528145\pi$
$948$	−7908.97	−	4566.24i	−0.270961	−	0.156440i
$949$	−9744.77	+	16878.4i	−0.333328	+	0.577342i
$950$		0			0
$951$	28924.0			0.986252
$952$	−196.912	−	294.898i	−0.00670375	−	0.0100396i
$953$		−	2871.26i		−	0.0975963i	−0.998809	−	0.0487981i	$-0.984461\pi$
$953$		−	2871.26i		−	0.0975963i	0.998809	−	0.0487981i	$-0.0155391\pi$
$954$	23135.5	+	40071.8i	0.785155	+	1.35993i
$955$		0			0
$956$	3629.48	−	6286.45i	0.122789	−	0.212676i
$957$	−42487.5	+	24530.2i	−1.43514	+	0.828576i
$958$		−	35398.0i		−	1.19380i
$959$	−25480.7	+	17014.3i	−0.857993	+	0.572909i
$960$		0			0
$961$	−20836.3	−	36089.5i	−0.699415	−	1.21142i
$962$	24012.9	+	13863.8i	0.804788	+	0.464645i
$963$	−24465.9	−	14125.4i	−0.818695	−	0.472674i
$964$	−7362.19	−	12751.7i	−0.245975	−	0.426042i
$965$		0			0
$966$	2046.63	+	31374.3i	0.0681669	+	1.04498i
$967$		−	39768.7i		−	1.32252i	−0.750158	−	0.661259i	$-0.770023\pi$
$967$		−	39768.7i		−	1.32252i	0.750158	−	0.661259i	$-0.229977\pi$
$968$	4440.61	−	2563.79i	0.147445	−	0.0851273i
$969$	−995.945	+	1725.03i	−0.0330179	+	0.0571887i
$970$		0			0
$971$	14076.5	+	24381.2i	0.465228	+	0.805799i	0.999212	−	0.0396960i	$-0.0126390\pi$
$971$	14076.5	+	24381.2i	0.465228	+	0.805799i	−0.533984	+	0.845495i	$0.679306\pi$
$972$			16247.1i			0.536139i
$973$	3359.58	−	6807.24i	0.110692	−	0.224286i
$974$	19759.6			0.650040
$975$		0			0
$976$	4034.47	−	6987.91i	0.132316	−	0.229178i
$977$	−19977.7	−	11534.1i	−0.654189	−	0.377696i	0.135870	−	0.990727i	$-0.456617\pi$
$977$	−19977.7	−	11534.1i	−0.654189	−	0.377696i	−0.790059	+	0.613030i	$0.789950\pi$
$978$	−12915.9	+	7457.00i	−0.422295	+	0.243812i
$979$	43497.9			1.42002
$980$		0			0
$981$	−76855.6			−2.50134
$982$	−23529.1	+	13584.5i	−0.764607	+	0.441446i
$983$	−2249.66	−	1298.84i	−0.0729938	−	0.0421430i	0.463059	−	0.886328i	$-0.346752\pi$
$983$	−2249.66	−	1298.84i	−0.0729938	−	0.0421430i	−0.536053	+	0.844185i	$0.680085\pi$
$984$	3166.38	−	5484.33i	0.102582	−	0.177677i
$985$		0			0
$986$	−1071.89			−0.0346207
$987$	−23390.4	+	47394.0i	−0.754330	+	1.52844i
$988$			15233.3i			0.490524i
$989$	20665.6	+	35793.9i	0.664438	+	1.15084i
$990$		0			0
$991$	12219.0	−	21163.9i	0.391674	−	0.678399i	−0.600997	−	0.799252i	$-0.705229\pi$
$991$	12219.0	−	21163.9i	0.391674	−	0.678399i	0.992670	+	0.120853i	$0.0385628\pi$
$992$	−7408.37	+	4277.23i	−0.237113	+	0.136897i
$993$		−	91479.3i		−	2.92347i
$994$	2144.22	+	32870.3i	0.0684210	+	1.04888i
$995$		0			0
$996$	−8760.14	−	15173.0i	−0.278690	−	0.482706i
$997$	3653.44	+	2109.31i	0.116054	+	0.0670036i	0.556903	−	0.830577i	$-0.311989\pi$
$997$	3653.44	+	2109.31i	0.116054	+	0.0670036i	−0.440850	+	0.897581i	$0.645323\pi$
$998$	20175.5	+	11648.3i	0.639923	+	0.369460i
$999$	−23565.2	−	40816.1i	−0.746316	−	1.29266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.j.h.249.4		12
5.2	odd	4		350.4.e.j.151.1	yes	6
5.3	odd	4		350.4.e.i.151.3	yes	6
5.4	even	2	inner	350.4.j.h.249.3		12
7.2	even	3	inner	350.4.j.h.149.3		12
35.2	odd	12		350.4.e.j.51.1	yes	6
35.3	even	12		2450.4.a.ch.1.3		3
35.9	even	6	inner	350.4.j.h.149.4		12
35.17	even	12		2450.4.a.cd.1.1		3
35.18	odd	12		2450.4.a.ci.1.1		3
35.23	odd	12		350.4.e.i.51.3	✓	6
35.32	odd	12		2450.4.a.cc.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.e.i.51.3	✓	6	35.23	odd	12
350.4.e.i.151.3	yes	6	5.3	odd	4
350.4.e.j.51.1	yes	6	35.2	odd	12
350.4.e.j.151.1	yes	6	5.2	odd	4
350.4.j.h.149.3		12	7.2	even	3	inner
350.4.j.h.149.4		12	35.9	even	6	inner
350.4.j.h.249.3		12	5.4	even	2	inner
350.4.j.h.249.4		12	1.1	even	1	trivial
2450.4.a.cc.1.3		3	35.32	odd	12
2450.4.a.cd.1.1		3	35.17	even	12
2450.4.a.ch.1.3		3	35.3	even	12
2450.4.a.ci.1.1		3	35.18	odd	12

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(-7.22265 - 4.17000i) q^{3} +(2.00000 - 3.46410i) q^{4} -16.6800 q^{6} +(-8.19644 + 16.6078i) q^{7} -8.00000i q^{8} +(21.2778 + 36.8542i) q^{9} +(13.1344 - 22.7495i) q^{11} +(-28.8906 + 16.6800i) q^{12} +38.1623i q^{13} +(2.41113 + 36.9620i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-2.07266 - 1.19665i) q^{17} +(73.7084 + 42.5556i) q^{18} +(49.8966 + 86.4235i) q^{19} +(128.454 - 85.7730i) q^{21} -52.5377i q^{22} +(-88.1421 + 50.8889i) q^{23} +(-33.3600 + 57.7812i) q^{24} +(38.1623 + 66.0990i) q^{26} -129.733i q^{27} +(41.1382 + 61.6089i) q^{28} +223.936 q^{29} +(133.663 - 231.512i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-189.731 + 109.541i) q^{33} -4.78661 q^{34} +170.222 q^{36} +(314.616 - 181.643i) q^{37} +(172.847 + 99.7933i) q^{38} +(159.137 - 275.633i) q^{39} -94.9155 q^{41} +(136.717 - 277.018i) q^{42} -406.093i q^{43} +(-52.5377 - 90.9980i) q^{44} +(-101.778 + 176.284i) q^{46} +(-296.331 + 171.087i) q^{47} +133.440i q^{48} +(-208.637 - 272.249i) q^{49} +(9.98008 + 17.2860i) q^{51} +(132.198 + 76.3245i) q^{52} +(470.817 + 271.827i) q^{53} +(-129.733 - 224.705i) q^{54} +(132.862 + 65.5715i) q^{56} -832.276i q^{57} +(387.868 - 223.936i) q^{58} +(-196.579 + 340.485i) q^{59} +(252.154 + 436.744i) q^{61} -534.653i q^{62} +(-786.468 + 51.3034i) q^{63} -64.0000 q^{64} +(-219.082 + 379.462i) q^{66} +(-47.5851 - 27.4733i) q^{67} +(-8.29066 + 4.78661i) q^{68} +848.826 q^{69} +889.302 q^{71} +(294.834 - 170.222i) q^{72} +(442.281 + 255.351i) q^{73} +(363.287 - 629.231i) q^{74} +399.173 q^{76} +(270.163 + 404.599i) q^{77} -636.546i q^{78} +(136.878 + 237.079i) q^{79} +(33.5123 - 58.0450i) q^{81} +(-164.399 + 94.9155i) q^{82} +525.188i q^{83} +(-40.2176 - 616.525i) q^{84} +(-406.093 - 703.374i) q^{86} +(-1617.41 - 933.811i) q^{87} +(-181.996 - 105.075i) q^{88} +(827.936 + 1434.03i) q^{89} +(-633.790 - 312.795i) q^{91} +407.111i q^{92} +(-1930.81 + 1114.75i) q^{93} +(-342.173 + 592.661i) q^{94} +(133.440 + 231.125i) q^{96} -5.76230i q^{97} +(-633.619 - 262.913i) q^{98} +1117.89 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{4} + 24 q^{6} + 112 q^{9} + 52 q^{11} + 16 q^{14} - 96 q^{16} - 36 q^{19} + 370 q^{21} + 48 q^{24} + 320 q^{26} + 1616 q^{29} + 1230 q^{31} + 240 q^{34} + 896 q^{36} - 180 q^{39} - 404 q^{41}+ \cdots + 228 q^{99}+O(q^{100}) \) 12 * q + 24 * q^4 + 24 * q^6 + 112 * q^9 + 52 * q^11 + 16 * q^14 - 96 * q^16 - 36 * q^19 + 370 * q^21 + 48 * q^24 + 320 * q^26 + 1616 * q^29 + 1230 * q^31 + 240 * q^34 + 896 * q^36 - 180 * q^39 - 404 * q^41 - 208 * q^44 + 212 * q^46 + 432 * q^49 + 678 * q^51 - 1296 * q^54 + 896 * q^56 - 182 * q^59 + 1294 * q^61 - 768 * q^64 - 1256 * q^66 + 6192 * q^69 + 2132 * q^71 + 1704 * q^74 - 288 * q^76 + 2842 * q^79 + 2786 * q^81 + 608 * q^84 + 996 * q^86 - 388 * q^89 - 7710 * q^91 - 1608 * q^94 - 192 * q^96 + 228 * q^99

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