LMFDB - Embedded newform 144.4.k.b.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,4,Mod(37,144)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("144.37"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	144.37
Dual form			144.4.k.b.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.70307 + 0.832707i) q^{2} +(6.61320 - 4.50173i) q^{4} +(-11.7911 - 11.7911i) q^{5} -12.5754i q^{7} +(-14.1273 + 17.6754i) q^{8} +(41.6906 + 22.0536i) q^{10} +(17.0042 + 17.0042i) q^{11} +(-49.2384 + 49.2384i) q^{13} +(10.4716 + 33.9921i) q^{14} +(23.4688 - 59.5417i) q^{16} +51.8247 q^{17} +(-11.6655 + 11.6655i) q^{19} +(-131.057 - 24.8964i) q^{20} +(-60.1231 - 31.8041i) q^{22} +74.5524i q^{23} +153.058i q^{25} +(92.0939 - 174.096i) q^{26} +(-56.6109 - 83.1633i) q^{28} +(-211.183 + 211.183i) q^{29} -326.094 q^{31} +(-13.8571 + 180.488i) q^{32} +(-140.086 + 43.1547i) q^{34} +(-148.277 + 148.277i) q^{35} +(110.757 + 110.757i) q^{37} +(21.8187 - 41.2465i) q^{38} +(374.988 - 41.8350i) q^{40} -348.225i q^{41} +(205.838 + 205.838i) q^{43} +(189.000 + 35.9038i) q^{44} +(-62.0803 - 201.521i) q^{46} -254.983 q^{47} +184.861 q^{49} +(-127.453 - 413.728i) q^{50} +(-103.965 + 547.282i) q^{52} +(225.602 + 225.602i) q^{53} -400.995i q^{55} +(222.274 + 177.656i) q^{56} +(394.989 - 746.696i) q^{58} +(-285.442 - 285.442i) q^{59} +(286.952 - 286.952i) q^{61} +(881.456 - 271.541i) q^{62} +(-112.837 - 499.411i) q^{64} +1161.15 q^{65} +(-627.335 + 627.335i) q^{67} +(342.727 - 233.301i) q^{68} +(277.332 - 524.274i) q^{70} -274.784i q^{71} +298.190i q^{73} +(-391.612 - 207.156i) q^{74} +(-24.6312 + 129.661i) q^{76} +(213.834 - 213.834i) q^{77} -175.664 q^{79} +(-978.782 + 425.338i) q^{80} +(289.969 + 941.276i) q^{82} +(-125.254 + 125.254i) q^{83} +(-611.068 - 611.068i) q^{85} +(-727.796 - 384.991i) q^{86} +(-540.779 + 60.3313i) q^{88} +900.271i q^{89} +(619.190 + 619.190i) q^{91} +(335.615 + 493.030i) q^{92} +(689.237 - 212.326i) q^{94} +275.096 q^{95} +5.27858 q^{97} +(-499.691 + 153.935i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} - 84 q^{8} + 72 q^{10} + 40 q^{11} + 348 q^{14} - 192 q^{16} + 24 q^{19} - 80 q^{20} + 704 q^{22} + 20 q^{26} - 344 q^{28} - 400 q^{29} - 744 q^{31} + 960 q^{32} - 704 q^{34} + 456 q^{35}+ \cdots - 6760 q^{98}+O(q^{100}) $ 24 * q - 20 * q^4 - 84 * q^8 + 72 * q^10 + 40 * q^11 + 348 * q^14 - 192 * q^16 + 24 * q^19 - 80 * q^20 + 704 * q^22 + 20 * q^26 - 344 * q^28 - 400 * q^29 - 744 * q^31 + 960 * q^32 - 704 * q^34 + 456 * q^35 + 16 * q^37 - 1256 * q^38 + 1744 * q^40 + 1240 * q^43 + 200 * q^44 - 1432 * q^46 - 1176 * q^49 - 708 * q^50 + 1008 * q^52 - 752 * q^53 - 1344 * q^56 + 1936 * q^58 + 1376 * q^59 - 912 * q^61 + 996 * q^62 - 56 * q^64 - 976 * q^65 - 2256 * q^67 + 1568 * q^68 - 1760 * q^70 + 2740 * q^74 - 1880 * q^76 - 1904 * q^77 + 5992 * q^79 - 712 * q^80 - 40 * q^82 - 2680 * q^83 - 240 * q^85 + 1712 * q^86 - 3936 * q^88 - 3496 * q^91 - 5296 * q^92 + 5272 * q^94 + 7728 * q^95 - 6760 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.70307	+	0.832707i	−0.955680	+	0.294406i
$2$	−2.70307	+	0.832707i	−0.955680	+	0.294406i
$3$		0			0
$3$		0			0
$4$	6.61320	−	4.50173i	0.826650	−	0.562717i
$5$	−11.7911	−	11.7911i	−1.05462	−	1.05462i	−0.998419	−	0.0562056i	$-0.982100\pi$
$5$	−11.7911	−	11.7911i	−1.05462	−	1.05462i	−0.0562056	−	0.998419i	$-0.517900\pi$
$6$		0			0
$7$		−	12.5754i		−	0.679005i	−0.940605	−	0.339503i	$-0.889741\pi$
$7$		−	12.5754i		−	0.679005i	0.940605	−	0.339503i	$-0.110259\pi$
$8$	−14.1273	+	17.6754i	−0.624346	+	0.781148i
$9$		0			0
$10$	41.6906	+	22.0536i	1.31837	+	0.697396i
$11$	17.0042	+	17.0042i	0.466087	+	0.466087i	0.900644	−	0.434557i	$-0.143095\pi$
$11$	17.0042	+	17.0042i	0.466087	+	0.466087i	−0.434557	+	0.900644i	$0.643095\pi$
$12$		0			0
$13$	−49.2384	+	49.2384i	−1.05048	+	1.05048i	−0.0518270	+	0.998656i	$0.516504\pi$
$13$	−49.2384	+	49.2384i	−1.05048	+	1.05048i	−0.998656	+	0.0518270i	$0.983496\pi$
$14$	10.4716	+	33.9921i	0.199903	+	0.648912i
$15$		0			0
$16$	23.4688	−	59.5417i	0.366700	−	0.930339i
$17$	51.8247			0.739372			0.369686	−	0.929157i	$-0.379465\pi$
$17$	51.8247			0.739372			0.369686	+	0.929157i	$0.379465\pi$
$18$		0			0
$19$	−11.6655	+	11.6655i	−0.140855	+	0.140855i	−0.774018	−	0.633163i	$-0.781756\pi$
$19$	−11.6655	+	11.6655i	−0.140855	+	0.140855i	0.633163	+	0.774018i	$0.281756\pi$
$20$	−131.057	−	24.8964i	−1.46526	−	0.278351i
$21$		0			0
$22$	−60.1231	−	31.8041i	−0.582649	−	0.308211i
$23$			74.5524i			0.675881i	0.941168	+	0.337940i	$0.109730\pi$
$23$			74.5524i			0.675881i	−0.941168	+	0.337940i	$0.890270\pi$
$24$		0			0
$25$			153.058i			1.22447i
$26$	92.0939	−	174.096i	0.694657	−	1.31319i
$27$		0			0
$28$	−56.6109	−	83.1633i	−0.382087	−	0.561300i
$29$	−211.183	+	211.183i	−1.35227	+	1.35227i	−0.469143	+	0.883122i	$0.655437\pi$
$29$	−211.183	+	211.183i	−1.35227	+	1.35227i	−0.883122	+	0.469143i	$0.844563\pi$
$30$		0			0
$31$	−326.094			−1.88930			−0.944648	−	0.328084i	$-0.893597\pi$
$31$	−326.094			−1.88930			−0.944648	+	0.328084i	$0.893597\pi$
$32$	−13.8571	+	180.488i	−0.0765506	+	0.997066i
$33$		0			0
$34$	−140.086	+	43.1547i	−0.706604	+	0.217676i
$35$	−148.277	+	148.277i	−0.716096	+	0.716096i
$36$		0			0
$37$	110.757	+	110.757i	0.492117	+	0.492117i	0.908973	−	0.416855i	$-0.136868\pi$
$37$	110.757	+	110.757i	0.492117	+	0.492117i	−0.416855	+	0.908973i	$0.636868\pi$
$38$	21.8187	−	41.2465i	0.0931436	−	0.176081i
$39$		0			0
$40$	374.988	−	41.8350i	1.48227	−	0.165367i
$41$		−	348.225i		−	1.32643i	−0.748430	−	0.663214i	$-0.769192\pi$
$41$		−	348.225i		−	1.32643i	0.748430	−	0.663214i	$-0.230808\pi$
$42$		0			0
$43$	205.838	+	205.838i	0.729998	+	0.729998i	0.970619	−	0.240621i	$-0.0773511\pi$
$43$	205.838	+	205.838i	0.729998	+	0.729998i	−0.240621	+	0.970619i	$0.577351\pi$
$44$	189.000	+	35.9038i	0.647566	+	0.123016i
$45$		0			0
$46$	−62.0803	−	201.521i	−0.198984	−	0.645926i
$47$	−254.983			−0.791342			−0.395671	−	0.918392i	$-0.629488\pi$
$47$	−254.983			−0.791342			−0.395671	+	0.918392i	$0.629488\pi$
$48$		0			0
$49$	184.861			0.538952
$50$	−127.453	−	413.728i	−0.360491	−	1.17020i
$51$		0			0
$52$	−103.965	+	547.282i	−0.277258	+	1.45951i
$53$	225.602	+	225.602i	0.584694	+	0.584694i	0.936189	−	0.351496i	$-0.114327\pi$
$53$	225.602	+	225.602i	0.584694	+	0.584694i	−0.351496	+	0.936189i	$0.614327\pi$
$54$		0			0
$55$		−	400.995i		−	0.983094i
$56$	222.274	+	177.656i	0.530404	+	0.423934i
$57$		0			0
$58$	394.989	−	746.696i	0.894218	−	1.69045i
$59$	−285.442	−	285.442i	−0.629854	−	0.629854i	0.318177	−	0.948031i	$-0.396929\pi$
$59$	−285.442	−	285.442i	−0.629854	−	0.629854i	−0.948031	+	0.318177i	$0.896929\pi$
$60$		0			0
$61$	286.952	−	286.952i	0.602301	−	0.602301i	−0.338621	−	0.940923i	$-0.609961\pi$
$61$	286.952	−	286.952i	0.602301	−	0.602301i	0.940923	+	0.338621i	$0.109961\pi$
$62$	881.456	−	271.541i	1.80556	−	0.556221i
$63$		0			0
$64$	−112.837	−	499.411i	−0.220385	−	0.975413i
$65$	1161.15			2.21573
$66$		0			0
$67$	−627.335	+	627.335i	−1.14390	+	1.14390i	−0.156168	+	0.987731i	$0.549914\pi$
$67$	−627.335	+	627.335i	−1.14390	+	1.14390i	−0.987731	+	0.156168i	$0.950086\pi$
$68$	342.727	−	233.301i	0.611202	−	0.416057i
$69$		0			0
$70$	277.332	−	524.274i	0.473536	−	0.895182i
$71$		−	274.784i		−	0.459308i	−0.973272	−	0.229654i	$-0.926241\pi$
$71$		−	274.784i		−	0.459308i	0.973272	−	0.229654i	$-0.0737595\pi$
$72$		0			0
$73$			298.190i			0.478089i	0.971009	+	0.239044i	$0.0768341\pi$
$73$			298.190i			0.478089i	−0.971009	+	0.239044i	$0.923166\pi$
$74$	−391.612	−	207.156i	−0.615189	−	0.325424i
$75$		0			0
$76$	−24.6312	+	129.661i	−0.0371763	+	0.195699i
$77$	213.834	−	213.834i	0.316475	−	0.316475i
$78$		0			0
$79$	−175.664			−0.250174			−0.125087	−	0.992146i	$-0.539921\pi$
$79$	−175.664			−0.250174			−0.125087	+	0.992146i	$0.539921\pi$
$80$	−978.782	+	425.338i	−1.36789	+	0.594428i
$81$		0			0
$82$	289.969	+	941.276i	0.390509	+	1.26764i
$83$	−125.254	+	125.254i	−0.165644	+	0.165644i	−0.785062	−	0.619418i	$-0.787369\pi$
$83$	−125.254	+	125.254i	−0.165644	+	0.165644i	0.619418	+	0.785062i	$0.287369\pi$
$84$		0			0
$85$	−611.068	−	611.068i	−0.779760	−	0.779760i
$86$	−727.796	−	384.991i	−0.912561	−	0.482729i
$87$		0			0
$88$	−540.779	+	60.3313i	−0.655082	+	0.0730834i
$89$			900.271i			1.07223i	0.844145	+	0.536116i	$0.180109\pi$
$89$			900.271i			1.07223i	−0.844145	+	0.536116i	$0.819891\pi$
$90$		0			0
$91$	619.190	+	619.190i	0.713283	+	0.713283i
$92$	335.615	+	493.030i	0.380329	+	0.558717i
$93$		0			0
$94$	689.237	−	212.326i	0.756270	−	0.232976i
$95$	275.096			0.297098
$96$		0			0
$97$	5.27858			0.00552534			0.00276267	−	0.999996i	$-0.499121\pi$
$97$	5.27858			0.00552534			0.00276267	+	0.999996i	$0.499121\pi$
$98$	−499.691	+	153.935i	−0.515066	+	0.158671i
$99$		0			0
$100$	689.028	+	1012.21i	0.689028	+	1.01221i
$101$	459.109	+	459.109i	0.452307	+	0.452307i	0.896120	−	0.443812i	$-0.146374\pi$
$101$	459.109	+	459.109i	0.452307	+	0.452307i	−0.443812	+	0.896120i	$0.646374\pi$
$102$		0			0
$103$		−	791.173i		−	0.756860i	−0.925630	−	0.378430i	$-0.876464\pi$
$103$		−	791.173i		−	0.756860i	0.925630	−	0.378430i	$-0.123536\pi$
$104$	−174.699	−	1565.91i	−0.164718	−	1.47645i
$105$		0			0
$106$	−797.678	−	421.958i	−0.730918	−	0.386643i
$107$	−1525.81	−	1525.81i	−1.37855	−	1.37855i	−0.847067	−	0.531487i	$-0.821634\pi$
$107$	−1525.81	−	1525.81i	−1.37855	−	1.37855i	−0.531487	−	0.847067i	$-0.678366\pi$
$108$		0			0
$109$	−413.307	+	413.307i	−0.363189	+	0.363189i	−0.864986	−	0.501796i	$-0.832673\pi$
$109$	−413.307	+	413.307i	−0.363189	+	0.363189i	0.501796	+	0.864986i	$0.332673\pi$
$110$	333.911	+	1083.92i	0.289429	+	0.939523i
$111$		0			0
$112$	−748.758	−	295.129i	−0.631705	−	0.248991i
$113$	−210.248			−0.175031			−0.0875154	−	0.996163i	$-0.527893\pi$
$113$	−210.248			−0.175031			−0.0875154	+	0.996163i	$0.527893\pi$
$114$		0			0
$115$	879.053	−	879.053i	0.712801	−	0.712801i
$116$	−445.906	+	2347.28i	−0.356908	+	1.87879i
$117$		0			0
$118$	1009.26	+	533.881i	0.787372	+	0.416506i
$119$		−	651.714i		−	0.502038i
$120$		0			0
$121$		−	752.715i		−	0.565526i
$122$	−536.704	+	1014.60i	−0.398286	+	0.752929i
$123$		0			0
$124$	−2156.52	+	1467.99i	−1.56179	+	1.06314i
$125$	330.838	−	330.838i	0.236729	−	0.236729i
$126$		0			0
$127$	177.367			0.123927			0.0619637	−	0.998078i	$-0.480264\pi$
$127$	177.367			0.123927			0.0619637	+	0.998078i	$0.480264\pi$
$128$	720.869	+	1255.99i	0.497785	+	0.867301i
$129$		0			0
$130$	−3138.66	+	966.895i	−2.11753	+	0.652325i
$131$	−938.828	+	938.828i	−0.626151	+	0.626151i	−0.947097	−	0.320946i	$-0.895999\pi$
$131$	−938.828	+	938.828i	−0.626151	+	0.626151i	0.320946	+	0.947097i	$0.395999\pi$
$132$		0			0
$133$	146.697	+	146.697i	0.0956411	+	0.0956411i
$134$	1173.35	−	2218.12i	0.756430	−	1.42997i
$135$		0			0
$136$	−732.145	+	916.020i	−0.461624	+	0.577559i
$137$			307.429i			0.191718i	0.995395	+	0.0958592i	$0.0305598\pi$
$137$			307.429i			0.191718i	−0.995395	+	0.0958592i	$0.969440\pi$
$138$		0			0
$139$	−1253.43	−	1253.43i	−0.764852	−	0.764852i	0.212343	−	0.977195i	$-0.431891\pi$
$139$	−1253.43	−	1253.43i	−0.764852	−	0.764852i	−0.977195	+	0.212343i	$0.931891\pi$
$140$	−313.082	+	1648.09i	−0.189002	+	0.994919i
$141$		0			0
$142$	228.815	+	742.761i	0.135223	+	0.438952i
$143$	−1674.52			−0.979233
$144$		0			0
$145$	4980.14			2.85226
$146$	−248.305	−	806.028i	−0.140752	−	0.456900i
$147$		0			0
$148$	1231.06	+	233.860i	0.683731	+	0.129886i
$149$	−1686.80	−	1686.80i	−0.927436	−	0.927436i	0.0701033	−	0.997540i	$-0.477667\pi$
$149$	−1686.80	−	1686.80i	−0.927436	−	0.927436i	−0.997540	+	0.0701033i	$0.977667\pi$
$150$		0			0
$151$		−	1682.23i		−	0.906611i	−0.891355	−	0.453306i	$-0.850245\pi$
$151$		−	1682.23i		−	0.906611i	0.891355	−	0.453306i	$-0.149755\pi$
$152$	−41.3894	−	370.993i	−0.0220863	−	0.197971i
$153$		0			0
$154$	−399.947	+	756.069i	−0.209277	+	0.395622i
$155$	3844.99	+	3844.99i	1.99250	+	1.99250i
$156$		0			0
$157$	−1066.81	+	1066.81i	−0.542300	+	0.542300i	−0.924202	−	0.381903i	$-0.875269\pi$
$157$	−1066.81	+	1066.81i	−0.542300	+	0.542300i	0.381903	+	0.924202i	$0.375269\pi$
$158$	474.833	−	146.277i	0.239087	−	0.0736529i
$159$		0			0
$160$	2291.54	−	1964.76i	1.13226	−	0.970798i
$161$	937.523			0.458927
$162$		0			0
$163$	−2379.54	+	2379.54i	−1.14343	+	1.14343i	−0.155618	+	0.987817i	$0.549737\pi$
$163$	−2379.54	+	2379.54i	−1.14343	+	1.14343i	−0.987817	+	0.155618i	$0.950263\pi$
$164$	−1567.61	−	2302.88i	−0.746403	−	1.09649i
$165$		0			0
$166$	234.271	−	442.871i	0.109536	−	0.207069i
$167$		−	839.991i		−	0.389224i	−0.980880	−	0.194612i	$-0.937655\pi$
$167$		−	839.991i		−	0.389224i	0.980880	−	0.194612i	$-0.0623448\pi$
$168$		0			0
$169$		−	2651.84i		−	1.20703i
$170$	2160.60	+	1142.92i	0.974768	+	0.515635i
$171$		0			0
$172$	2287.87	+	434.619i	1.01424	+	0.192671i
$173$	450.278	−	450.278i	0.197885	−	0.197885i	−0.601208	−	0.799093i	$-0.705314\pi$
$173$	450.278	−	450.278i	0.197885	−	0.197885i	0.799093	+	0.601208i	$0.205314\pi$
$174$		0			0
$175$	1924.76			0.831419
$176$	1411.53	−	613.390i	0.604533	−	0.262705i
$177$		0			0
$178$	−749.662	−	2433.50i	−0.315672	−	1.02471i
$179$	647.759	−	647.759i	0.270479	−	0.270479i	−0.558814	−	0.829293i	$-0.688743\pi$
$179$	647.759	−	647.759i	0.270479	−	0.270479i	0.829293	+	0.558814i	$0.188743\pi$
$180$		0			0
$181$	−755.750	−	755.750i	−0.310356	−	0.310356i	0.534691	−	0.845047i	$-0.320428\pi$
$181$	−755.750	−	755.750i	−0.310356	−	0.310356i	−0.845047	+	0.534691i	$0.820428\pi$
$182$	−2189.32	−	1158.11i	−0.891666	−	0.471676i
$183$		0			0
$184$	−1317.74	−	1053.23i	−0.527963	−	0.421983i
$185$		−	2611.89i		−	1.03800i
$186$		0			0
$187$	881.237	+	881.237i	0.344612	+	0.344612i
$188$	−1686.25	+	1147.86i	−0.654163	+	0.445301i
$189$		0			0
$190$	−743.605	+	229.075i	−0.283931	+	0.0874675i
$191$	−760.485			−0.288098			−0.144049	−	0.989571i	$-0.546012\pi$
$191$	−760.485			−0.288098			−0.144049	+	0.989571i	$0.546012\pi$
$192$		0			0
$193$	2184.99			0.814915			0.407458	−	0.913224i	$-0.366415\pi$
$193$	2184.99			0.814915			0.407458	+	0.913224i	$0.366415\pi$
$194$	−14.2684	+	4.39551i	−0.00528046	+	0.00162670i
$195$		0			0
$196$	1222.52	−	832.193i	0.445525	−	0.303277i
$197$	−83.4121	−	83.4121i	−0.0301668	−	0.0301668i	0.691862	−	0.722029i	$-0.256790\pi$
$197$	−83.4121	−	83.4121i	−0.0301668	−	0.0301668i	−0.722029	+	0.691862i	$0.756790\pi$
$198$		0			0
$199$		−	1734.18i		−	0.617754i	−0.951102	−	0.308877i	$-0.900047\pi$
$199$		−	1734.18i		−	0.617754i	0.951102	−	0.308877i	$-0.0999531\pi$
$200$	−2705.36	−	2162.31i	−0.956490	−	0.764491i
$201$		0			0
$202$	−1623.31	−	858.701i	−0.565423	−	0.299099i
$203$	2655.70	+	2655.70i	0.918195	+	0.918195i
$204$		0			0
$205$	−4105.94	+	4105.94i	−1.39888	+	1.39888i
$206$	658.815	+	2138.60i	0.222824	+	0.723316i
$207$		0			0
$208$	1776.17	+	4087.31i	0.592093	+	1.36252i
$209$	−396.723			−0.131301
$210$		0			0
$211$	−365.900	+	365.900i	−0.119382	+	0.119382i	−0.764274	−	0.644892i	$-0.776902\pi$
$211$	−365.900	+	365.900i	−0.119382	+	0.119382i	0.644892	+	0.764274i	$0.276902\pi$
$212$	2507.55	+	476.350i	0.812354	+	0.154320i
$213$		0			0
$214$	5394.91	+	2853.81i	1.72331	+	0.911602i
$215$		−	4854.09i		−	1.53975i
$216$		0			0
$217$			4100.75i			1.28284i
$218$	773.035	−	1461.36i	0.240168	−	0.454018i
$219$		0			0
$220$	−1805.17	−	2651.86i	−0.553203	−	0.812674i
$221$	−2551.77	+	2551.77i	−0.776698	+	0.776698i
$222$		0			0
$223$	−4037.17			−1.21233			−0.606164	−	0.795340i	$-0.707292\pi$
$223$	−4037.17			−1.21233			−0.606164	+	0.795340i	$0.707292\pi$
$224$	2269.70	+	174.258i	0.677013	+	0.0519782i
$225$		0			0
$226$	568.316	−	175.075i	0.167274	−	0.0515302i
$227$	1502.81	−	1502.81i	0.439407	−	0.439407i	−0.452406	−	0.891812i	$-0.649434\pi$
$227$	1502.81	−	1502.81i	0.439407	−	0.439407i	0.891812	+	0.452406i	$0.149434\pi$
$228$		0			0
$229$	−3443.65	−	3443.65i	−0.993723	−	0.993723i	0.00625772	−	0.999980i	$-0.498008\pi$
$229$	−3443.65	−	3443.65i	−0.993723	−	0.993723i	−0.999980	+	0.00625772i	$0.998008\pi$
$230$	−1644.15	+	3108.14i	−0.471357	+	0.891063i
$231$		0			0
$232$	−749.283	−	6716.19i	−0.212038	−	1.90060i
$233$			1139.00i			0.320250i	0.987097	+	0.160125i	$0.0511898\pi$
$233$			1139.00i			0.320250i	−0.987097	+	0.160125i	$0.948810\pi$
$234$		0			0
$235$	3006.52	+	3006.52i	0.834569	+	0.834569i
$236$	−3172.67	−	602.702i	−0.875098	−	0.166240i
$237$		0			0
$238$	542.686	+	1761.63i	0.147803	+	0.479788i
$239$	4603.80			1.24600			0.623002	−	0.782220i	$-0.285913\pi$
$239$	4603.80			1.24600			0.623002	+	0.782220i	$0.285913\pi$
$240$		0			0
$241$	−4681.58			−1.25132			−0.625658	−	0.780097i	$-0.715170\pi$
$241$	−4681.58			−1.25132			−0.625658	+	0.780097i	$0.715170\pi$
$242$	626.791	+	2034.64i	0.166494	+	0.540462i
$243$		0			0
$244$	605.889	−	3189.45i	0.158967	−	0.836817i
$245$	−2179.70	−	2179.70i	−0.568392	−	0.568392i
$246$		0			0
$247$		−	1148.78i		−	0.295931i
$248$	4606.84	−	5763.83i	1.17957	−	1.47582i
$249$		0			0
$250$	−618.788	+	1169.77i	−0.156542	+	0.295931i
$251$	476.440	+	476.440i	0.119811	+	0.119811i	0.764470	−	0.644659i	$-0.223001\pi$
$251$	476.440	+	476.440i	0.119811	+	0.119811i	−0.644659	+	0.764470i	$0.723001\pi$
$252$		0			0
$253$	−1267.70	+	1267.70i	−0.315019	+	0.315019i
$254$	−479.436	+	147.695i	−0.118435	+	0.0364850i
$255$		0			0
$256$	−2994.43	−	2794.75i	−0.731062	−	0.682311i
$257$	−925.326			−0.224592			−0.112296	−	0.993675i	$-0.535821\pi$
$257$	−925.326			−0.224592			−0.112296	+	0.993675i	$0.535821\pi$
$258$		0			0
$259$	1392.81	−	1392.81i	0.334150	−	0.334150i
$260$	7678.89	−	5227.17i	1.83163	−	1.24683i
$261$		0			0
$262$	1755.95	−	3319.49i	0.414058	−	0.782743i
$263$			3477.65i			0.815365i	0.913124	+	0.407683i	$0.133663\pi$
$263$			3477.65i			0.815365i	−0.913124	+	0.407683i	$0.866337\pi$
$264$		0			0
$265$		−	5320.17i		−	1.23327i
$266$	−518.689	−	274.378i	−0.119560	−	0.0632450i
$267$		0			0
$268$	−1324.60	+	6972.79i	−0.301913	+	1.58929i
$269$	−3773.37	+	3773.37i	−0.855266	+	0.855266i	−0.990776	−	0.135510i	$-0.956733\pi$
$269$	−3773.37	+	3773.37i	−0.855266	+	0.855266i	0.135510	+	0.990776i	$0.456733\pi$
$270$		0			0
$271$	8007.09			1.79482			0.897410	−	0.441198i	$-0.145446\pi$
$271$	8007.09			1.79482			0.897410	+	0.441198i	$0.145446\pi$
$272$	1216.26	−	3085.73i	0.271128	−	0.687867i
$273$		0			0
$274$	−255.998	−	831.002i	−0.0564431	−	0.183221i
$275$	−2602.63	+	2602.63i	−0.570708	+	0.570708i
$276$		0			0
$277$	4550.73	+	4550.73i	0.987101	+	0.987101i	0.999918	−	0.0128173i	$-0.00407998\pi$
$277$	4550.73	+	4550.73i	0.987101	+	0.987101i	−0.0128173	+	0.999918i	$0.504080\pi$
$278$	4431.85	+	2344.37i	0.956131	+	0.505777i
$279$		0			0
$280$	−526.090	−	4715.60i	−0.112285	−	1.00647i
$281$			3333.05i			0.707592i	0.935323	+	0.353796i	$0.115109\pi$
$281$			3333.05i			0.707592i	−0.935323	+	0.353796i	$0.884891\pi$
$282$		0			0
$283$	6242.23	+	6242.23i	1.31117	+	1.31117i	0.920552	+	0.390621i	$0.127740\pi$
$283$	6242.23	+	6242.23i	1.31117	+	1.31117i	0.390621	+	0.920552i	$0.372260\pi$
$284$	−1237.00	−	1817.20i	−0.258460	−	0.379687i
$285$		0			0
$286$	4526.35	−	1394.38i	0.935834	−	0.288292i
$287$	−4379.05			−0.900651
$288$		0			0
$289$	−2227.20			−0.453329
$290$	−13461.7	+	4147.00i	−2.72585	+	0.839725i
$291$		0			0
$292$	1342.37	+	1971.99i	0.269028	+	0.395212i
$293$	2458.24	+	2458.24i	0.490143	+	0.490143i	0.908351	−	0.418208i	$-0.137342\pi$
$293$	2458.24	+	2458.24i	0.490143	+	0.490143i	−0.418208	+	0.908351i	$0.637342\pi$
$294$		0			0
$295$			6731.33i			1.32852i
$296$	−3522.37	+	392.969i	−0.691668	+	0.0771651i
$297$		0			0
$298$	5964.15	+	3154.93i	1.15938	+	0.613290i
$299$	−3670.84	−	3670.84i	−0.710001	−	0.710001i
$300$		0			0
$301$	2588.48	−	2588.48i	0.495673	−	0.495673i
$302$	1400.81	+	4547.20i	0.266912	+	0.866431i
$303$		0			0
$304$	420.807	+	968.356i	0.0793912	+	0.182694i
$305$	−6766.93			−1.27040
$306$		0			0
$307$	−3008.49	+	3008.49i	−0.559295	+	0.559295i	−0.929107	−	0.369812i	$-0.879422\pi$
$307$	−3008.49	+	3008.49i	−0.559295	+	0.559295i	0.369812	+	0.929107i	$0.379422\pi$
$308$	451.503	−	2376.75i	0.0835284	−	0.439700i
$309$		0			0
$310$	−13595.1	−	7191.55i	−2.49080	−	1.31759i
$311$			4507.09i			0.821779i	0.911685	+	0.410890i	$0.134782\pi$
$311$			4507.09i			0.821779i	−0.911685	+	0.410890i	$0.865218\pi$
$312$		0			0
$313$			5237.61i			0.945837i	0.881106	+	0.472919i	$0.156800\pi$
$313$			5237.61i			0.945837i	−0.881106	+	0.472919i	$0.843200\pi$
$314$	1995.33	−	3772.02i	0.358609	−	0.677922i
$315$		0			0
$316$	−1161.70	+	790.794i	−0.206807	+	0.140777i
$317$	989.530	−	989.530i	0.175323	−	0.175323i	−0.613990	−	0.789314i	$-0.710437\pi$
$317$	989.530	−	989.530i	0.175323	−	0.175323i	0.789314	+	0.613990i	$0.210437\pi$
$318$		0			0
$319$	−7181.99			−1.26055
$320$	−4558.13	+	7219.06i	−0.796272	+	1.26112i
$321$		0			0
$322$	−2534.19	+	780.682i	−0.438587	+	0.135111i
$323$	−604.559	+	604.559i	−0.104144	+	0.104144i
$324$		0			0
$325$	−7536.35	−	7536.35i	−1.28628	−	1.28628i
$326$	4450.61	−	8413.52i	0.756124	−	1.42939i
$327$		0			0
$328$	6154.99	+	4919.48i	1.03614	+	0.828150i
$329$			3206.50i			0.537325i
$330$		0			0
$331$	−5652.55	−	5652.55i	−0.938647	−	0.938647i	0.0595765	−	0.998224i	$-0.481025\pi$
$331$	−5652.55	−	5652.55i	−0.938647	−	0.938647i	−0.998224	+	0.0595765i	$0.981025\pi$
$332$	−264.470	+	1392.19i	−0.0437189	+	0.230140i
$333$		0			0
$334$	699.466	+	2270.56i	0.114590	+	0.371974i
$335$	14793.9			2.41277
$336$		0			0
$337$	291.315			0.0470888			0.0235444	−	0.999723i	$-0.492505\pi$
$337$	291.315			0.0470888			0.0235444	+	0.999723i	$0.492505\pi$
$338$	2208.21	+	7168.13i	0.355357	+	1.15353i
$339$		0			0
$340$	−6791.98	−	1290.25i	−1.08337	−	0.205805i
$341$	−5544.96	−	5544.96i	−0.880577	−	0.880577i
$342$		0			0
$343$		−	6638.03i		−	1.04496i
$344$	−6546.19	+	730.317i	−1.02601	+	0.114465i
$345$		0			0
$346$	−842.185	+	1592.08i	−0.130856	+	0.247373i
$347$	−6530.87	−	6530.87i	−1.01036	−	1.01036i	−0.999946	−	0.0104158i	$-0.996684\pi$
$347$	−6530.87	−	6530.87i	−1.01036	−	1.01036i	−0.0104158	−	0.999946i	$-0.503316\pi$
$348$		0			0
$349$	7267.79	−	7267.79i	1.11472	−	1.11472i	0.122213	−	0.992504i	$-0.461001\pi$
$349$	7267.79	−	7267.79i	1.11472	−	1.11472i	0.992504	−	0.122213i	$-0.0389990\pi$
$350$	−5202.77	+	1602.76i	−0.794571	+	0.244775i
$351$		0			0
$352$	−3304.68	+	2833.43i	−0.500399	+	0.429040i
$353$	8253.63			1.24447			0.622233	−	0.782832i	$-0.286226\pi$
$353$	8253.63			1.24447			0.622233	+	0.782832i	$0.286226\pi$
$354$		0			0
$355$	−3240.00	+	3240.00i	−0.484398	+	0.484398i
$356$	4052.78	+	5953.67i	0.603362	+	0.886360i
$357$		0			0
$358$	−1211.55	+	2290.33i	−0.178861	+	0.338122i
$359$			4827.70i			0.709738i	0.934916	+	0.354869i	$0.115475\pi$
$359$			4827.70i			0.709738i	−0.934916	+	0.354869i	$0.884525\pi$
$360$		0			0
$361$			6586.83i			0.960320i
$362$	2672.16	+	1413.53i	0.387972	+	0.205230i
$363$		0			0
$364$	6882.26	+	1307.40i	0.991012	+	0.188259i
$365$	3515.97	−	3515.97i	0.504204	−	0.504204i
$366$		0			0
$367$	−2556.37			−0.363600			−0.181800	−	0.983336i	$-0.558192\pi$
$367$	−2556.37			−0.363600			−0.181800	+	0.983336i	$0.558192\pi$
$368$	4438.98	+	1749.66i	0.628798	+	0.247846i
$369$		0			0
$370$	2174.93	+	7060.12i	0.305593	+	0.991995i
$371$	2837.02	−	2837.02i	0.397010	−	0.397010i
$372$		0			0
$373$	1141.57	+	1141.57i	0.158468	+	0.158468i	0.781887	−	0.623420i	$-0.214257\pi$
$373$	1141.57	+	1141.57i	0.158468	+	0.158468i	−0.623420	+	0.781887i	$0.714257\pi$
$374$	−3115.86	−	1648.23i	−0.430795	−	0.227883i
$375$		0			0
$376$	3602.23	−	4506.92i	0.494071	−	0.618155i
$377$		−	20796.6i		−	2.84106i
$378$		0			0
$379$	−2602.11	−	2602.11i	−0.352668	−	0.352668i	0.508433	−	0.861101i	$-0.330225\pi$
$379$	−2602.11	−	2602.11i	−0.352668	−	0.352668i	−0.861101	+	0.508433i	$0.830225\pi$
$380$	1819.27	−	1238.41i	0.245596	−	0.167182i
$381$		0			0
$382$	2055.65	−	633.261i	0.275330	−	0.0848179i
$383$	370.858			0.0494777			0.0247388	−	0.999694i	$-0.492125\pi$
$383$	370.858			0.0494777			0.0247388	+	0.999694i	$0.492125\pi$
$384$		0			0
$385$	−5042.65			−0.667526
$386$	−5906.17	+	1819.45i	−0.778799	+	0.239916i
$387$		0			0
$388$	34.9083	−	23.7627i	0.00456752	−	0.00310920i
$389$	6457.55	+	6457.55i	0.841673	+	0.841673i	0.989077	−	0.147403i	$-0.0470914\pi$
$389$	6457.55	+	6457.55i	0.841673	+	0.841673i	−0.147403	+	0.989077i	$0.547091\pi$
$390$		0			0
$391$			3863.66i			0.499728i
$392$	−2611.59	+	3267.48i	−0.336492	+	0.421001i
$393$		0			0
$394$	294.927	+	156.011i	0.0377112	+	0.0199486i
$395$	2071.27	+	2071.27i	0.263840	+	0.263840i
$396$		0			0
$397$	−232.353	+	232.353i	−0.0293739	+	0.0293739i	−0.721641	−	0.692267i	$-0.756612\pi$
$397$	−232.353	+	232.353i	−0.0293739	+	0.0293739i	0.692267	+	0.721641i	$0.256612\pi$
$398$	1444.07	+	4687.62i	0.181871	+	0.590375i
$399$		0			0
$400$	9113.36	+	3592.10i	1.13917	+	0.449012i
$401$	119.615			0.0148960			0.00744801	−	0.999972i	$-0.497629\pi$
$401$	119.615			0.0148960			0.00744801	+	0.999972i	$0.497629\pi$
$402$		0			0
$403$	16056.4	−	16056.4i	1.98467	−	1.98467i
$404$	5102.96	+	969.393i	0.628421	+	0.119379i
$405$		0			0
$406$	−9389.97	−	4967.13i	−1.14782	−	0.607179i
$407$			3766.67i			0.458739i
$408$		0			0
$409$			626.952i			0.0757965i	0.999282	+	0.0378983i	$0.0120663\pi$
$409$			626.952i			0.0757965i	−0.999282	+	0.0378983i	$0.987934\pi$
$410$	7679.60	−	14517.7i	0.925045	−	1.74873i
$411$		0			0
$412$	−3561.65	−	5232.18i	−0.425897	−	0.625658i
$413$	−3589.54	+	3589.54i	−0.427674	+	0.427674i
$414$		0			0
$415$	2953.76			0.349384
$416$	−8204.65	−	9569.26i	−0.966986	−	1.12782i
$417$		0			0
$418$	1072.37	−	330.354i	0.125482	−	0.0386559i
$419$	4981.58	−	4981.58i	0.580826	−	0.580826i	−0.354304	−	0.935130i	$-0.615282\pi$
$419$	4981.58	−	4981.58i	0.580826	−	0.580826i	0.935130	+	0.354304i	$0.115282\pi$
$420$		0			0
$421$	10770.4	+	10770.4i	1.24683	+	1.24683i	0.957110	+	0.289723i	$0.0935632\pi$
$421$	10770.4	+	10770.4i	1.24683	+	1.24683i	0.289723	+	0.957110i	$0.406437\pi$
$422$	684.366	−	1293.74i	0.0789442	−	0.149238i
$423$		0			0
$424$	−7174.74	+	800.441i	−0.821783	+	0.0916813i
$425$			7932.20i			0.905337i
$426$		0			0
$427$	−3608.52	−	3608.52i	−0.408966	−	0.408966i
$428$	−16959.2	−	3221.69i	−1.91532	−	0.363846i
$429$		0			0
$430$	4042.03	+	13120.9i	0.453312	+	1.47151i
$431$	−7546.94			−0.843442			−0.421721	−	0.906726i	$-0.638574\pi$
$431$	−7546.94			−0.843442			−0.421721	+	0.906726i	$0.638574\pi$
$432$		0			0
$433$	5614.17			0.623094			0.311547	−	0.950231i	$-0.399153\pi$
$433$	5614.17			0.623094			0.311547	+	0.950231i	$0.399153\pi$
$434$	−3414.72	−	11084.6i	−0.377677	−	1.22599i
$435$		0			0
$436$	−872.684	+	4593.88i	−0.0958578	+	0.504603i
$437$	−869.689	−	869.689i	−0.0952010	−	0.0952010i
$438$		0			0
$439$		−	7198.92i		−	0.782656i	−0.920251	−	0.391328i	$-0.872016\pi$
$439$		−	7198.92i		−	0.782656i	0.920251	−	0.391328i	$-0.127984\pi$
$440$	7087.73	+	5664.99i	0.767942	+	0.613790i
$441$		0			0
$442$	4772.73	−	9022.48i	0.513610	−	0.970940i
$443$	5582.95	+	5582.95i	0.598767	+	0.598767i	0.939984	−	0.341217i	$-0.110839\pi$
$443$	5582.95	+	5582.95i	0.598767	+	0.598767i	−0.341217	+	0.939984i	$0.610839\pi$
$444$		0			0
$445$	10615.2	−	10615.2i	1.13080	−	1.13080i
$446$	10912.8	−	3361.78i	1.15860	−	0.356917i
$447$		0			0
$448$	−6280.28	+	1418.96i	−0.662311	+	0.149642i
$449$	−1224.53			−0.128706			−0.0643530	−	0.997927i	$-0.520498\pi$
$449$	−1224.53			−0.128706			−0.0643530	+	0.997927i	$0.520498\pi$
$450$		0			0
$451$	5921.28	−	5921.28i	0.618231	−	0.618231i
$452$	−1390.41	+	946.481i	−0.144689	+	0.0984927i
$453$		0			0
$454$	−2810.81	+	5313.62i	−0.290568	+	0.549297i
$455$		−	14601.8i		−	1.50449i
$456$		0			0
$457$		−	11182.3i		−	1.14461i	−0.820040	−	0.572307i	$-0.806049\pi$
$457$		−	11182.3i		−	1.14461i	0.820040	−	0.572307i	$-0.193951\pi$
$458$	12176.0	+	6440.88i	1.24224	+	0.657123i
$459$		0			0
$460$	1856.09	−	9770.61i	0.188132	−	0.990341i
$461$	11334.9	−	11334.9i	1.14516	−	1.14516i	0.157670	−	0.987492i	$-0.449602\pi$
$461$	11334.9	−	11334.9i	1.14516	−	1.14516i	0.987492	−	0.157670i	$-0.0503982\pi$
$462$		0			0
$463$	3013.37			0.302469			0.151234	−	0.988498i	$-0.451675\pi$
$463$	3013.37			0.302469			0.151234	+	0.988498i	$0.451675\pi$
$464$	7617.98	+	17530.4i	0.762189	+	1.75394i
$465$		0			0
$466$	−948.453	−	3078.80i	−0.0942837	−	0.306057i
$467$	843.917	−	843.917i	0.0836228	−	0.0836228i	−0.664058	−	0.747681i	$-0.731167\pi$
$467$	843.917	−	843.917i	0.0836228	−	0.0836228i	0.747681	+	0.664058i	$0.231167\pi$
$468$		0			0
$469$	7888.96	+	7888.96i	0.776713	+	0.776713i
$470$	−10630.4	−	5623.29i	−1.04328	−	0.551879i
$471$		0			0
$472$	9077.83	−	1012.76i	0.885256	−	0.0987625i
$473$			7000.20i			0.680485i
$474$		0			0
$475$	−1785.50	−	1785.50i	−0.172472	−	0.172472i
$476$	−2933.84	−	4309.91i	−0.282505	−	0.415009i
$477$		0			0
$478$	−12444.4	+	3833.62i	−1.19078	+	0.366832i
$479$	−10569.4			−1.00821			−0.504103	−	0.863644i	$-0.668177\pi$
$479$	−10569.4			−1.00821			−0.504103	+	0.863644i	$0.668177\pi$
$480$		0			0
$481$	−10907.0			−1.03392
$482$	12654.7	−	3898.39i	1.19586	−	0.368395i
$483$		0			0
$484$	−3388.52	−	4977.85i	−0.318231	−	0.467492i
$485$	−62.2400	−	62.2400i	−0.00582716	−	0.00582716i
$486$		0			0
$487$			1579.10i			0.146932i	0.997298	+	0.0734661i	$0.0234061\pi$
$487$			1579.10i			0.146932i	−0.997298	+	0.0734661i	$0.976594\pi$
$488$	1018.11	+	9125.83i	0.0944422	+	0.846531i
$489$		0			0
$490$	7706.95	+	4076.84i	0.710539	+	0.375863i
$491$	−8650.50	−	8650.50i	−0.795095	−	0.795095i	0.187222	−	0.982318i	$-0.440052\pi$
$491$	−8650.50	−	8650.50i	−0.795095	−	0.795095i	−0.982318	+	0.187222i	$0.940052\pi$
$492$		0			0
$493$	−10944.5	+	10944.5i	−0.999828	+	0.999828i
$494$	956.595	+	3105.23i	0.0871240	+	0.282816i
$495$		0			0
$496$	−7653.04	+	19416.2i	−0.692806	+	1.75769i
$497$	−3455.51			−0.311873
$498$		0			0
$499$	−11942.3	+	11942.3i	−1.07137	+	1.07137i	−0.0741168	+	0.997250i	$0.523614\pi$
$499$	−11942.3	+	11942.3i	−1.07137	+	1.07137i	−0.997250	+	0.0741168i	$0.976386\pi$
$500$	698.554	−	3677.24i	0.0624806	−	0.328903i
$501$		0			0
$502$	−1684.59	−	891.117i	−0.149775	−	0.0792281i
$503$			3290.09i			0.291646i	0.989311	+	0.145823i	$0.0465830\pi$
$503$			3290.09i			0.291646i	−0.989311	+	0.145823i	$0.953417\pi$
$504$		0			0
$505$		−	10826.8i		−	0.954029i
$506$	2371.07	−	4482.32i	0.208314	−	0.393801i
$507$		0			0
$508$	1172.96	−	798.458i	0.102445	−	0.0697360i
$509$	−1392.67	+	1392.67i	−0.121275	+	0.121275i	−0.765140	−	0.643864i	$-0.777330\pi$
$509$	−1392.67	+	1392.67i	−0.121275	+	0.121275i	0.643864	+	0.765140i	$0.277330\pi$
$510$		0			0
$511$	3749.84			0.324625
$512$	10421.4	+	5060.92i	0.899538	+	0.436842i
$513$		0			0
$514$	2501.22	−	770.525i	0.214639	−	0.0661214i
$515$	−9328.77	+	9328.77i	−0.798203	+	0.798203i
$516$		0			0
$517$	−4335.78	−	4335.78i	−0.368834	−	0.368834i
$518$	−2605.06	+	4924.66i	−0.220965	+	0.417717i
$519$		0			0
$520$	−16403.9	+	20523.7i	−1.38338	+	1.73081i
$521$		−	1175.72i		−	0.0988661i	−0.998777	−	0.0494331i	$-0.984259\pi$
$521$		−	1175.72i		−	0.0988661i	0.998777	−	0.0494331i	$-0.0157414\pi$
$522$		0			0
$523$	−9451.05	−	9451.05i	−0.790183	−	0.790183i	0.191341	−	0.981524i	$-0.438716\pi$
$523$	−9451.05	−	9451.05i	−0.790183	−	0.790183i	−0.981524	+	0.191341i	$0.938716\pi$
$524$	−1982.30	+	10435.0i	−0.165262	+	0.869953i
$525$		0			0
$526$	−2895.86	−	9400.34i	−0.240049	−	0.779228i
$527$	−16899.7			−1.39689
$528$		0			0
$529$	6608.93			0.543185
$530$	4430.14	+	14380.8i	0.363081	+	1.17861i
$531$		0			0
$532$	1630.53	+	309.747i	0.132881	+	0.0252429i
$533$	17146.0	+	17146.0i	1.39339	+	1.39339i
$534$		0			0
$535$			35981.7i			2.90771i
$536$	−2225.80	−	19951.0i	−0.179366	−	1.60774i
$537$		0			0
$538$	7057.58	−	13341.8i	0.565565	−	1.06916i
$539$	3143.40	+	3143.40i	0.251198	+	0.251198i
$540$		0			0
$541$	2893.97	−	2893.97i	0.229984	−	0.229984i	−0.582702	−	0.812686i	$-0.698004\pi$
$541$	2893.97	−	2893.97i	0.229984	−	0.229984i	0.812686	+	0.582702i	$0.198004\pi$
$542$	−21643.7	+	6667.56i	−1.71527	+	0.528406i
$543$		0			0
$544$	−718.141	+	9353.74i	−0.0565994	+	0.737203i
$545$	9746.66			0.766057
$546$		0			0
$547$	−956.857	+	956.857i	−0.0747939	+	0.0747939i	−0.743514	−	0.668720i	$-0.766842\pi$
$547$	−956.857	+	956.857i	−0.0747939	+	0.0747939i	0.668720	+	0.743514i	$0.266842\pi$
$548$	1383.96	+	2033.09i	0.107883	+	0.158484i
$549$		0			0
$550$	4867.88	−	9202.34i	0.377394	−	0.713435i
$551$		−	4927.09i		−	0.380946i
$552$		0			0
$553$			2209.04i			0.169870i
$554$	−16090.4	−	8511.53i	−1.23396	−	0.652744i
$555$		0			0
$556$	−13931.8	−	2646.57i	−1.06266	−	0.201870i
$557$	8482.07	−	8482.07i	0.645236	−	0.645236i	−0.306602	−	0.951838i	$-0.599192\pi$
$557$	8482.07	−	8482.07i	0.645236	−	0.645236i	0.951838	+	0.306602i	$0.0991919\pi$
$558$		0			0
$559$	−20270.2			−1.53370
$560$	5348.77	+	12308.5i	0.403619	+	0.928804i
$561$		0			0
$562$	−2775.46	−	9009.48i	−0.208319	−	0.676232i
$563$	−9461.78	+	9461.78i	−0.708289	+	0.708289i	−0.966175	−	0.257886i	$-0.916974\pi$
$563$	−9461.78	+	9461.78i	−0.708289	+	0.708289i	0.257886	+	0.966175i	$0.416974\pi$
$564$		0			0
$565$	2479.05	+	2479.05i	0.184592	+	0.184592i
$566$	−22071.1	−	11675.2i	−1.63908	−	0.867044i
$567$		0			0
$568$	4856.91	+	3881.97i	0.358788	+	0.286767i
$569$			7197.61i			0.530298i	0.964207	+	0.265149i	$0.0854211\pi$
$569$			7197.61i			0.530298i	−0.964207	+	0.265149i	$0.914579\pi$
$570$		0			0
$571$	990.936	+	990.936i	0.0726259	+	0.0726259i	0.742487	−	0.669861i	$-0.233646\pi$
$571$	990.936	+	990.936i	0.0726259	+	0.0726259i	−0.669861	+	0.742487i	$0.733646\pi$
$572$	−11073.9	+	7538.24i	−0.809483	+	0.551031i
$573$		0			0
$574$	11836.9	−	3646.46i	0.860735	−	0.265157i
$575$	−11410.9			−0.827594
$576$		0			0
$577$	−14836.1			−1.07043			−0.535214	−	0.844717i	$-0.679769\pi$
$577$	−14836.1			−1.07043			−0.535214	+	0.844717i	$0.679769\pi$
$578$	6020.29	−	1854.61i	0.433237	−	0.133463i
$579$		0			0
$580$	32934.7	−	22419.3i	2.35782	−	1.60502i
$581$	1575.11	+	1575.11i	0.112473	+	0.112473i
$582$		0			0
$583$			7672.35i			0.545036i
$584$	−5270.61	−	4212.63i	−0.373458	−	0.298493i
$585$		0			0
$586$	−8691.80	−	4597.81i	−0.612721	−	0.324119i
$587$	−4038.29	−	4038.29i	−0.283949	−	0.283949i	0.550733	−	0.834682i	$-0.314348\pi$
$587$	−4038.29	−	4038.29i	−0.283949	−	0.283949i	−0.834682	+	0.550733i	$0.814348\pi$
$588$		0			0
$589$	3804.04	−	3804.04i	0.266116	−	0.266116i
$590$	−5605.23	−	18195.3i	−0.391125	−	1.26964i
$591$		0			0
$592$	9194.00	−	3995.33i	0.638296	−	0.277376i
$593$	−11081.1			−0.767361			−0.383681	−	0.923466i	$-0.625344\pi$
$593$	−11081.1			−0.767361			−0.383681	+	0.923466i	$0.625344\pi$
$594$		0			0
$595$	−7684.40	+	7684.40i	−0.529461	+	0.529461i
$596$	−18748.7	−	3561.62i	−1.28855	−	0.244781i
$597$		0			0
$598$	12979.3	+	6865.82i	0.887563	+	0.469506i
$599$			7036.50i			0.479973i	0.970776	+	0.239986i	$0.0771430\pi$
$599$			7036.50i			0.479973i	−0.970776	+	0.239986i	$0.922857\pi$
$600$		0			0
$601$			24290.7i			1.64865i	0.566117	+	0.824325i	$0.308445\pi$
$601$			24290.7i			1.64865i	−0.566117	+	0.824325i	$0.691555\pi$
$602$	−4841.40	+	9152.29i	−0.327775	+	0.619634i
$603$		0			0
$604$	−7572.97	−	11125.0i	−0.510165	−	0.749450i
$605$	−8875.31	+	8875.31i	−0.596418	+	0.596418i
$606$		0			0
$607$	10931.5			0.730967			0.365484	−	0.930818i	$-0.380904\pi$
$607$	10931.5			0.730967			0.365484	+	0.930818i	$0.380904\pi$
$608$	−1943.83	−	2267.13i	−0.129659	−	0.151224i
$609$		0			0
$610$	18291.5	−	5634.87i	1.21410	−	0.374015i
$611$	12555.0	−	12555.0i	0.831292	−	0.831292i
$612$		0			0
$613$	−2217.95	−	2217.95i	−0.146137	−	0.146137i	0.630253	−	0.776390i	$-0.282951\pi$
$613$	−2217.95	−	2217.95i	−0.146137	−	0.146137i	−0.776390	+	0.630253i	$0.782951\pi$
$614$	5626.97	−	10637.4i	0.369847	−	0.699167i
$615$		0			0
$616$	758.688	+	6800.49i	0.0496240	+	0.444804i
$617$			26271.5i			1.71418i	0.515164	+	0.857092i	$0.327731\pi$
$617$			26271.5i			1.71418i	−0.515164	+	0.857092i	$0.672269\pi$
$618$		0			0
$619$	−11171.8	−	11171.8i	−0.725417	−	0.725417i	0.244287	−	0.969703i	$-0.421446\pi$
$619$	−11171.8	−	11171.8i	−0.725417	−	0.725417i	−0.969703	+	0.244287i	$0.921446\pi$
$620$	42736.9	+	8118.58i	2.76831	+	0.525887i
$621$		0			0
$622$	−3753.08	−	12183.0i	−0.241937	−	0.785358i
$623$	11321.2			0.728050
$624$		0			0
$625$	11330.4			0.725148
$626$	−4361.39	−	14157.6i	−0.278460	−	0.903918i
$627$		0			0
$628$	−2252.54	+	11857.6i	−0.143131	+	0.753453i
$629$	5739.95	+	5739.95i	0.363858	+	0.363858i
$630$		0			0
$631$			17415.1i			1.09871i	0.835590	+	0.549354i	$0.185126\pi$
$631$			17415.1i			1.09871i	−0.835590	+	0.549354i	$0.814874\pi$
$632$	2481.67	−	3104.93i	0.156195	−	0.195423i
$633$		0			0
$634$	−1850.78	+	3498.76i	−0.115937	+	0.219169i
$635$	−2091.34	−	2091.34i	−0.130697	−	0.130697i
$636$		0			0
$637$	−9102.24	+	9102.24i	−0.566160	+	0.566160i
$638$	19413.4	−	5980.49i	1.20468	−	0.371113i
$639$		0			0
$640$	6309.59	−	23309.2i	0.389700	−	1.43965i
$641$	2727.28			0.168051			0.0840257	−	0.996464i	$-0.473222\pi$
$641$	2727.28			0.168051			0.0840257	+	0.996464i	$0.473222\pi$
$642$		0			0
$643$	11681.7	−	11681.7i	0.716458	−	0.716458i	−0.251420	−	0.967878i	$-0.580897\pi$
$643$	11681.7	−	11681.7i	0.716458	−	0.716458i	0.967878	+	0.251420i	$0.0808975\pi$
$644$	6200.03	−	4220.48i	0.379372	−	0.258246i
$645$		0			0
$646$	1130.75	−	2137.59i	0.0688678	−	0.130189i
$647$			4399.67i			0.267340i	0.991026	+	0.133670i	$0.0426762\pi$
$647$			4399.67i			0.267340i	−0.991026	+	0.133670i	$0.957324\pi$
$648$		0			0
$649$		−	9707.43i		−	0.587134i
$650$	26646.9	+	14095.7i	1.60796	+	0.850585i
$651$		0			0
$652$	−5024.32	+	26448.4i	−0.301791	+	1.58865i
$653$	22924.8	−	22924.8i	1.37384	−	1.37384i	0.519167	−	0.854673i	$-0.326242\pi$
$653$	22924.8	−	22924.8i	1.37384	−	1.37384i	0.854673	−	0.519167i	$-0.173758\pi$
$654$		0			0
$655$	22139.6			1.32071
$656$	−20733.9	−	8172.42i	−1.23403	−	0.486401i
$657$		0			0
$658$	−2670.07	−	8667.40i	−0.158192	−	0.513511i
$659$	11508.4	−	11508.4i	0.680276	−	0.680276i	−0.279786	−	0.960062i	$-0.590264\pi$
$659$	11508.4	−	11508.4i	0.680276	−	0.680276i	0.960062	+	0.279786i	$0.0902636\pi$
$660$		0			0
$661$	10207.0	+	10207.0i	0.600615	+	0.600615i	0.940476	−	0.339861i	$-0.110380\pi$
$661$	10207.0	+	10207.0i	0.600615	+	0.600615i	−0.339861	+	0.940476i	$0.610380\pi$
$662$	19986.2	+	10572.3i	1.17339	+	0.620703i
$663$		0			0
$664$	−444.405	−	3983.42i	−0.0259733	−	0.232811i
$665$		−	3459.43i		−	0.201731i
$666$		0			0
$667$	−15744.2	−	15744.2i	−0.913970	−	0.913970i
$668$	−3781.42	−	5555.03i	−0.219023	−	0.321752i
$669$		0			0
$670$	−39989.0	+	12319.0i	−2.30583	+	0.710334i
$671$	9758.76			0.561450
$672$		0			0
$673$	−23908.4			−1.36939			−0.684695	−	0.728830i	$-0.740065\pi$
$673$	−23908.4			−1.36939			−0.684695	+	0.728830i	$0.740065\pi$
$674$	−787.445	+	242.580i	−0.0450019	+	0.0138632i
$675$		0			0
$676$	−11937.9	−	17537.2i	−0.679215	−	0.997791i
$677$	−10411.1	−	10411.1i	−0.591035	−	0.591035i	0.346876	−	0.937911i	$-0.387242\pi$
$677$	−10411.1	−	10411.1i	−0.591035	−	0.591035i	−0.937911	+	0.346876i	$0.887242\pi$
$678$		0			0
$679$		−	66.3800i		−	0.00375174i
$680$	19433.6	−	2168.09i	1.09595	−	0.122268i
$681$		0			0
$682$	19605.8	+	10371.1i	1.10080	+	0.582303i
$683$	−11126.8	−	11126.8i	−0.623358	−	0.623358i	0.323030	−	0.946389i	$-0.395298\pi$
$683$	−11126.8	−	11126.8i	−0.623358	−	0.623358i	−0.946389	+	0.323030i	$0.895298\pi$
$684$		0			0
$685$	3624.91	−	3624.91i	0.202191	−	0.202191i
$686$	5527.53	+	17943.1i	0.307642	+	0.998644i
$687$		0			0
$688$	17086.7	−	7425.15i	0.946836	−	0.411455i
$689$	−22216.5			−1.22842
$690$		0			0
$691$	2722.85	−	2722.85i	0.149901	−	0.149901i	−0.628173	−	0.778074i	$-0.716197\pi$
$691$	2722.85	−	2722.85i	0.149901	−	0.149901i	0.778074	+	0.628173i	$0.216197\pi$
$692$	950.748	−	5004.81i	0.0522283	−	0.274934i
$693$		0			0
$694$	23091.7	+	12215.1i	1.26304	+	0.668126i
$695$			29558.5i			1.61326i
$696$		0			0
$697$		−	18046.6i		−	0.980724i
$698$	−13593.4	+	25697.3i	−0.737133	+	1.39349i
$699$		0			0
$700$	12728.8	−	8664.77i	0.687293	−	0.467853i
$701$	−2736.38	+	2736.38i	−0.147435	+	0.147435i	−0.776971	−	0.629536i	$-0.783245\pi$
$701$	−2736.38	+	2736.38i	−0.147435	+	0.147435i	0.629536	+	0.776971i	$0.283245\pi$
$702$		0			0
$703$	−2584.06			−0.138634
$704$	6573.39	−	10410.8i	0.351909	−	0.557346i
$705$		0			0
$706$	−22310.1	+	6872.85i	−1.18931	+	0.366378i
$707$	5773.45	−	5773.45i	0.307119	−	0.307119i
$708$		0			0
$709$	−783.090	−	783.090i	−0.0414803	−	0.0414803i	0.686062	−	0.727543i	$-0.259338\pi$
$709$	−783.090	−	783.090i	−0.0414803	−	0.0414803i	−0.727543	+	0.686062i	$0.759338\pi$
$710$	6059.98	−	11455.9i	0.320320	−	0.605539i
$711$		0			0
$712$	−15912.6	−	12718.4i	−0.837571	−	0.669443i
$713$		−	24311.1i		−	1.27694i
$714$		0			0
$715$	19744.4	+	19744.4i	1.03272	+	1.03272i
$716$	1367.72	−	7199.79i	0.0713885	−	0.375795i
$717$		0			0
$718$	−4020.06	−	13049.6i	−0.208951	−	0.678283i
$719$	11021.5			0.571671			0.285835	−	0.958279i	$-0.407729\pi$
$719$	11021.5			0.571671			0.285835	+	0.958279i	$0.407729\pi$
$720$		0			0
$721$	−9949.27			−0.513912
$722$	−5484.90	−	17804.7i	−0.282724	−	0.917759i
$723$		0			0
$724$	−8400.11	−	1595.74i	−0.431198	−	0.0819133i
$725$	−32323.3	−	32323.3i	−1.65580	−	1.65580i
$726$		0			0
$727$		−	21740.4i		−	1.10909i	−0.832154	−	0.554544i	$-0.812893\pi$
$727$		−	21740.4i		−	1.10909i	0.832154	−	0.554544i	$-0.187107\pi$
$728$	−19691.9	+	2196.91i	−1.00252	+	0.111844i
$729$		0			0
$730$	−6576.16	+	12431.7i	−0.333417	+	0.630299i
$731$	10667.5	+	10667.5i	0.539741	+	0.539741i
$732$		0			0
$733$	13194.8	−	13194.8i	0.664886	−	0.664886i	−0.291642	−	0.956528i	$-0.594202\pi$
$733$	13194.8	−	13194.8i	0.664886	−	0.664886i	0.956528	+	0.291642i	$0.0942015\pi$
$734$	6910.04	−	2128.70i	0.347485	−	0.107046i
$735$		0			0
$736$	−13455.8	−	1033.08i	−0.673898	−	0.0517391i
$737$	−21334.7			−1.06631
$738$		0			0
$739$	21786.6	−	21786.6i	1.08448	−	1.08448i	0.0883973	−	0.996085i	$-0.471825\pi$
$739$	21786.6	−	21786.6i	1.08448	−	1.08448i	0.996085	−	0.0883973i	$-0.0281745\pi$
$740$	−11758.0	−	17272.9i	−0.584099	−	0.858061i
$741$		0			0
$742$	−5306.26	+	10031.1i	−0.262532	+	0.496297i
$743$		−	7418.24i		−	0.366284i	−0.983086	−	0.183142i	$-0.941373\pi$
$743$		−	7418.24i		−	0.366284i	0.983086	−	0.183142i	$-0.0586268\pi$
$744$		0			0
$745$			39778.3i			1.95619i
$746$	−4036.35	−	2135.16i	−0.198098	−	0.104790i
$747$		0			0
$748$	9794.89	+	1860.70i	0.478792	+	0.0909546i
$749$	−19187.5	+	19187.5i	−0.936045	+	0.936045i
$750$		0			0
$751$	−9320.68			−0.452885			−0.226442	−	0.974025i	$-0.572709\pi$
$751$	−9320.68			−0.452885			−0.226442	+	0.974025i	$0.572709\pi$
$752$	−5984.15	+	15182.1i	−0.290185	+	0.736217i
$753$		0			0
$754$	17317.5	+	56214.8i	0.836427	+	2.71515i
$755$	−19835.3	+	19835.3i	−0.956135	+	0.956135i
$756$		0			0
$757$	2105.29	+	2105.29i	0.101081	+	0.101081i	0.755839	−	0.654758i	$-0.227229\pi$
$757$	2105.29	+	2105.29i	0.101081	+	0.101081i	−0.654758	+	0.755839i	$0.727229\pi$
$758$	9200.47	+	4866.89i	0.440866	+	0.233210i
$759$		0			0
$760$	−3886.38	+	4862.43i	−0.185492	+	0.232077i
$761$		−	13011.0i		−	0.619776i	−0.950773	−	0.309888i	$-0.899708\pi$
$761$		−	13011.0i		−	0.619776i	0.950773	−	0.309888i	$-0.100292\pi$
$762$		0			0
$763$	5197.48	+	5197.48i	0.246607	+	0.246607i
$764$	−5029.24	+	3423.50i	−0.238156	+	0.162118i
$765$		0			0
$766$	−1002.46	+	308.816i	−0.0472849	+	0.0145665i
$767$	28109.4			1.32330
$768$		0			0
$769$	26438.9			1.23981			0.619904	−	0.784677i	$-0.287171\pi$
$769$	26438.9			1.23981			0.619904	+	0.784677i	$0.287171\pi$
$770$	13630.7	−	4199.05i	0.637941	−	0.196524i
$771$		0			0
$772$	14449.7	−	9836.22i	0.673650	−	0.458566i
$773$	21614.3	+	21614.3i	1.00571	+	1.00571i	0.999984	+	0.00572318i	$0.00182175\pi$
$773$	21614.3	+	21614.3i	1.00571	+	1.00571i	0.00572318	+	0.999984i	$0.498178\pi$
$774$		0			0
$775$		−	49911.4i		−	2.31338i
$776$	−74.5722	+	93.3007i	−0.00344972	+	0.00431611i
$777$		0			0
$778$	−22832.5	−	12078.0i	−1.05216	−	0.556577i
$779$	4062.20	+	4062.20i	0.186834	+	0.186834i
$780$		0			0
$781$	4672.48	−	4672.48i	0.214077	−	0.214077i
$782$	−3217.29	−	10443.7i	−0.147123	−	0.477580i
$783$		0			0
$784$	4338.46	−	11006.9i	0.197634	−	0.501408i
$785$	25157.8			1.14385
$786$		0			0
$787$	−20949.4	+	20949.4i	−0.948874	+	0.948874i	−0.998755	−	0.0498808i	$-0.984116\pi$
$787$	−20949.4	+	20949.4i	−0.948874	+	0.948874i	0.0498808	+	0.998755i	$0.484116\pi$
$788$	−927.120	−	176.122i	−0.0419128	−	0.00796204i
$789$		0			0
$790$	−7323.55	−	3874.03i	−0.329823	−	0.174471i
$791$			2643.94i			0.118847i
$792$		0			0
$793$			28258.1i			1.26541i
$794$	434.584	−	821.548i	0.0194242	−	0.0367199i
$795$		0			0
$796$	−7806.83	−	11468.5i	−0.347620	−	0.510666i
$797$	−1576.38	+	1576.38i	−0.0700603	+	0.0700603i	−0.741269	−	0.671208i	$-0.765776\pi$
$797$	−1576.38	+	1576.38i	−0.0700603	+	0.0700603i	0.671208	+	0.741269i	$0.265776\pi$
$798$		0			0
$799$	−13214.4			−0.585097
$800$	−27625.2	−	2120.95i	−1.22087	−	0.0937336i
$801$		0			0
$802$	−323.329	+	99.6044i	−0.0142358	+	0.00438548i
$803$	−5070.48	+	5070.48i	−0.222831	+	0.222831i
$804$		0			0
$805$	−11054.4	−	11054.4i	−0.483995	−	0.483995i
$806$	−30031.2	+	56771.7i	−1.31241	+	2.48101i
$807$		0			0
$808$	−14600.9	+	1628.93i	−0.635715	+	0.0709228i
$809$		−	8102.89i		−	0.352142i	−0.984378	−	0.176071i	$-0.943661\pi$
$809$		−	8102.89i		−	0.352142i	0.984378	−	0.176071i	$-0.0563388\pi$
$810$		0			0
$811$	20649.6	+	20649.6i	0.894090	+	0.894090i	0.994905	−	0.100816i	$-0.0321452\pi$
$811$	20649.6	+	20649.6i	0.894090	+	0.894090i	−0.100816	+	0.994905i	$0.532145\pi$
$812$	29517.9	+	5607.42i	1.27571	+	0.242342i
$813$		0			0
$814$	−3136.53	−	10181.6i	−0.135056	−	0.438408i
$815$	56114.6			2.41179
$816$		0			0
$817$	−4802.38			−0.205647
$818$	−522.067	−	1694.70i	−0.0223150	−	0.0724373i
$819$		0			0
$820$	−8669.55	+	45637.2i	−0.369212	+	1.94356i
$821$	−13405.1	−	13405.1i	−0.569844	−	0.569844i	0.362240	−	0.932085i	$-0.382012\pi$
$821$	−13405.1	−	13405.1i	−0.569844	−	0.569844i	−0.932085	+	0.362240i	$0.882012\pi$
$822$		0			0
$823$			17203.4i			0.728643i	0.931273	+	0.364321i	$0.118699\pi$
$823$			17203.4i			0.728643i	−0.931273	+	0.364321i	$0.881301\pi$
$824$	13984.3	+	11177.2i	0.591219	+	0.472542i
$825$		0			0
$826$	6713.74	−	12691.8i	0.282810	−	0.534630i
$827$	11127.2	+	11127.2i	0.467872	+	0.467872i	0.901224	−	0.433353i	$-0.142670\pi$
$827$	11127.2	+	11127.2i	0.467872	+	0.467872i	−0.433353	+	0.901224i	$0.642670\pi$
$828$		0			0
$829$	−5752.09	+	5752.09i	−0.240987	+	0.240987i	−0.817259	−	0.576271i	$-0.804507\pi$
$829$	−5752.09	+	5752.09i	−0.240987	+	0.240987i	0.576271	+	0.817259i	$0.304507\pi$
$830$	−7984.23	+	2459.61i	−0.333899	+	0.102861i
$831$		0			0
$832$	30146.1	+	19034.3i	1.25617	+	0.793145i
$833$	9580.34			0.398486
$834$		0			0
$835$	−9904.39	+	9904.39i	−0.410486	+	0.410486i
$836$	−2623.61	+	1785.94i	−0.108540	+	0.0738853i
$837$		0			0
$838$	−9317.38	+	17613.8i	−0.384086	+	0.726083i
$839$		−	45875.9i		−	1.88774i	−0.330318	−	0.943870i	$-0.607156\pi$
$839$		−	45875.9i		−	1.88774i	0.330318	−	0.943870i	$-0.392844\pi$
$840$		0			0
$841$		−	64807.5i		−	2.65724i
$842$	−38081.7	−	20144.6i	−1.55865	−	0.824499i
$843$		0			0
$844$	−772.585	+	4066.95i	−0.0315089	+	0.165865i
$845$	−31268.1	+	31268.1i	−1.27296	+	1.27296i
$846$		0			0
$847$	−9465.66			−0.383995
$848$	18727.3	−	8138.10i	0.758371	−	0.329556i
$849$		0			0
$850$	−6605.20	−	21441.3i	−0.266537	−	0.865213i
$851$	−8257.21	+	8257.21i	−0.332613	+	0.332613i
$852$		0			0
$853$	−27266.2	−	27266.2i	−1.09446	−	1.09446i	−0.995046	−	0.0994157i	$-0.968303\pi$
$853$	−27266.2	−	27266.2i	−1.09446	−	1.09446i	−0.0994157	−	0.995046i	$-0.531697\pi$
$854$	12758.9	+	6749.24i	0.511243	+	0.270438i
$855$		0			0
$856$	48524.7	−	5413.60i	1.93755	−	0.216160i
$857$		−	28960.0i		−	1.15432i	−0.816629	−	0.577162i	$-0.804160\pi$
$857$		−	28960.0i		−	1.15432i	0.816629	−	0.577162i	$-0.195840\pi$
$858$		0			0
$859$	17255.5	+	17255.5i	0.685388	+	0.685388i	0.961209	−	0.275821i	$-0.0889496\pi$
$859$	17255.5	+	17255.5i	0.685388	+	0.685388i	−0.275821	+	0.961209i	$0.588950\pi$
$860$	−21851.8	−	32101.0i	−0.866442	−	1.27283i
$861$		0			0
$862$	20399.9	−	6284.39i	0.806061	−	0.248314i
$863$	−39885.9			−1.57327			−0.786635	−	0.617418i	$-0.788179\pi$
$863$	−39885.9			−1.57327			−0.786635	+	0.617418i	$0.788179\pi$
$864$		0			0
$865$	−10618.5			−0.417388
$866$	−15175.5	+	4674.95i	−0.595478	+	0.183443i
$867$		0			0
$868$	18460.5	+	27119.1i	0.721877	+	1.06046i
$869$	−2987.03	−	2987.03i	−0.116603	−	0.116603i
$870$		0			0
$871$		−	61778.0i		−	2.40329i
$872$	−1466.43	−	13144.3i	−0.0569489	−	0.510460i
$873$		0			0
$874$	3075.03	+	1626.64i	0.119010	+	0.0629540i
$875$	−4160.41	−	4160.41i	−0.160740	−	0.160740i
$876$		0			0
$877$	8855.51	−	8855.51i	0.340968	−	0.340968i	−0.515763	−	0.856731i	$-0.672491\pi$
$877$	8855.51	−	8855.51i	0.340968	−	0.340968i	0.856731	+	0.515763i	$0.172491\pi$
$878$	5994.59	+	19459.2i	0.230419	+	0.747969i
$879$		0			0
$880$	−23875.9	−	9410.88i	−0.914611	−	0.360501i
$881$	43343.8			1.65753			0.828767	−	0.559593i	$-0.189043\pi$
$881$	43343.8			1.65753			0.828767	+	0.559593i	$0.189043\pi$
$882$		0			0
$883$	11229.3	−	11229.3i	0.427968	−	0.427968i	−0.459968	−	0.887936i	$-0.652139\pi$
$883$	11229.3	−	11229.3i	0.427968	−	0.427968i	0.887936	+	0.459968i	$0.152139\pi$
$884$	−5387.97	+	28362.7i	−0.204997	+	1.07912i
$885$		0			0
$886$	−19740.1	−	10442.2i	−0.748511	−	0.395949i
$887$			36912.9i			1.39731i	0.715459	+	0.698655i	$0.246218\pi$
$887$			36912.9i			1.39731i	−0.715459	+	0.698655i	$0.753782\pi$
$888$		0			0
$889$		−	2230.45i		−	0.0841473i
$890$	−19854.2	+	37532.8i	−0.747770	+	1.41360i
$891$		0			0
$892$	−26698.6	+	18174.3i	−1.00217	+	0.682197i
$893$	2974.49	−	2974.49i	0.111464	−	0.111464i
$894$		0			0
$895$	−15275.5			−0.570508
$896$	15794.5	−	9065.19i	0.588902	−	0.337998i
$897$		0			0
$898$	3309.98	−	1019.67i	0.123002	−	0.0378918i
$899$	68865.5	−	68865.5i	2.55483	−	2.55483i
$900$		0			0
$901$	11691.7	+	11691.7i	0.432306	+	0.432306i
$902$	−11075.0	+	20936.3i	−0.408820	+	0.772842i
$903$		0			0
$904$	2970.25	−	3716.21i	0.109280	−	0.136725i
$905$			17822.2i			0.654618i
$906$		0			0
$907$	14588.0	+	14588.0i	0.534053	+	0.534053i	0.921776	−	0.387723i	$-0.126738\pi$
$907$	14588.0	+	14588.0i	0.534053	+	0.534053i	−0.387723	+	0.921776i	$0.626738\pi$
$908$	3173.14	−	16703.7i	0.115974	−	0.610497i
$909$		0			0
$910$	12159.0	+	39469.8i	0.442932	+	1.43781i
$911$	−50418.8			−1.83365			−0.916823	−	0.399295i	$-0.869255\pi$
$911$	−50418.8			−1.83365			−0.916823	+	0.399295i	$0.869255\pi$
$912$		0			0
$913$	−4259.69			−0.154409
$914$	9311.61	+	30226.7i	0.336981	+	1.09388i
$915$		0			0
$916$	−38275.9	−	7271.14i	−1.38064	−	0.262277i
$917$	11806.1	+	11806.1i	0.425160	+	0.425160i
$918$		0			0
$919$			53290.4i			1.91283i	0.292018	+	0.956413i	$0.405673\pi$
$919$			53290.4i			1.91283i	−0.292018	+	0.956413i	$0.594327\pi$
$920$	3118.90	+	27956.2i	0.111769	+	1.00184i
$921$		0			0
$922$	−21200.4	+	40077.8i	−0.757266	+	1.43155i
$923$	13529.9	+	13529.9i	0.482495	+	0.482495i
$924$		0			0
$925$	−16952.3	+	16952.3i	−0.602581	+	0.602581i
$926$	−8145.35	+	2509.25i	−0.289064	+	0.0890488i
$927$		0			0
$928$	−35189.6	−	41042.4i	−1.24478	−	1.45181i
$929$	−44859.2			−1.58427			−0.792133	−	0.610349i	$-0.791029\pi$
$929$	−44859.2			−1.58427			−0.792133	+	0.610349i	$0.791029\pi$
$930$		0			0
$931$	−2156.48	+	2156.48i	−0.0759140	+	0.0759140i
$932$	5127.47	+	7532.43i	0.180210	+	0.264735i
$933$		0			0
$934$	−1578.43	+	2983.91i	−0.0552976	+	0.104536i
$935$		−	20781.4i		−	0.726872i
$936$		0			0
$937$		−	22463.9i		−	0.783204i	−0.920135	−	0.391602i	$-0.871921\pi$
$937$		−	22463.9i		−	0.783204i	0.920135	−	0.391602i	$-0.128079\pi$
$938$	−27893.6	−	14755.2i	−0.970958	−	0.513620i
$939$		0			0
$940$	33417.3	+	6348.17i	1.15952	+	0.220271i
$941$	−20653.7	+	20653.7i	−0.715507	+	0.715507i	−0.967682	−	0.252175i	$-0.918854\pi$
$941$	−20653.7	+	20653.7i	−0.715507	+	0.715507i	0.252175	+	0.967682i	$0.418854\pi$
$942$		0			0
$943$	25961.0			0.896507
$944$	−23694.7	+	10296.7i	−0.816946	+	0.355010i
$945$		0			0
$946$	−5829.11	−	18922.0i	−0.200339	−	0.650326i
$947$	−33123.2	+	33123.2i	−1.13660	+	1.13660i	−0.147544	+	0.989055i	$0.547137\pi$
$947$	−33123.2	+	33123.2i	−1.13660	+	1.13660i	−0.989055	+	0.147544i	$0.952863\pi$
$948$		0			0
$949$	−14682.4	−	14682.4i	−0.502224	−	0.502224i
$950$	6313.12	+	3339.53i	0.215605	+	0.114051i
$951$		0			0
$952$	11519.3	+	9206.97i	0.392166	+	0.313445i
$953$		−	10871.9i		−	0.369544i	−0.982781	−	0.184772i	$-0.940845\pi$
$953$		−	10871.9i		−	0.369544i	0.982781	−	0.184772i	$-0.0591546\pi$
$954$		0			0
$955$	8966.93	+	8966.93i	0.303836	+	0.303836i
$956$	30445.9	−	20725.1i	1.03001	−	0.701147i
$957$		0			0
$958$	28570.0	−	8801.25i	0.963522	−	0.296822i
$959$	3866.02			0.130178
$960$		0			0
$961$	76546.3			2.56944
$962$	29482.4	−	9082.33i	0.988099	−	0.304393i
$963$		0			0
$964$	−30960.2	+	21075.2i	−1.03440	+	0.704137i
$965$	−25763.3	−	25763.3i	−0.859430	−	0.859430i
$966$		0			0
$967$			6501.58i			0.216212i	0.994139	+	0.108106i	$0.0344786\pi$
$967$			6501.58i			0.216212i	−0.994139	+	0.108106i	$0.965521\pi$
$968$	13304.5	+	10633.9i	0.441759	+	0.353084i
$969$		0			0
$970$	220.067	+	116.412i	0.00728446	+	0.00385335i
$971$	16761.7	+	16761.7i	0.553975	+	0.553975i	0.927586	−	0.373611i	$-0.121880\pi$
$971$	16761.7	+	16761.7i	0.553975	+	0.553975i	−0.373611	+	0.927586i	$0.621880\pi$
$972$		0			0
$973$	−15762.3	+	15762.3i	−0.519338	+	0.519338i
$974$	−1314.93	−	4268.43i	−0.0432578	−	0.140420i
$975$		0			0
$976$	−10351.2	−	23820.0i	−0.339480	−	0.781208i
$977$	7407.34			0.242561			0.121280	−	0.992618i	$-0.461300\pi$
$977$	7407.34			0.242561			0.121280	+	0.992618i	$0.461300\pi$
$978$		0			0
$979$	−15308.4	+	15308.4i	−0.499753	+	0.499753i
$980$	−24227.2	−	4602.37i	−0.789705	−	0.150018i
$981$		0			0
$982$	30586.3	+	16179.6i	0.993938	+	0.525776i
$983$		−	35694.8i		−	1.15818i	−0.815265	−	0.579088i	$-0.803409\pi$
$983$		−	35694.8i		−	1.15818i	0.815265	−	0.579088i	$-0.196591\pi$
$984$		0			0
$985$			1967.04i			0.0636294i
$986$	20470.2	−	38697.3i	0.661160	−	1.24987i
$987$		0			0
$988$	−5171.49	−	7597.10i	−0.166525	−	0.244631i
$989$	−15345.7	+	15345.7i	−0.493392	+	0.493392i
$990$		0			0
$991$	46662.2			1.49573			0.747867	−	0.663849i	$-0.231078\pi$
$991$	46662.2			1.49573			0.747867	+	0.663849i	$0.231078\pi$
$992$	4518.73	−	58856.1i	0.144627	−	1.88375i
$993$		0			0
$994$	9340.48	−	2877.42i	0.298050	−	0.0918172i
$995$	−20447.9	+	20447.9i	−0.651498	+	0.651498i
$996$		0			0
$997$	−22390.7	−	22390.7i	−0.711255	−	0.711255i	0.255543	−	0.966798i	$-0.417746\pi$
$997$	−22390.7	−	22390.7i	−0.711255	−	0.711255i	−0.966798	+	0.255543i	$0.917746\pi$
$998$	22336.5	−	42225.4i	0.708467	−	1.33930i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.k.b.37.1		24
3.2	odd	2		48.4.j.a.37.12	yes	24
4.3	odd	2		576.4.k.b.433.2		24
12.11	even	2		192.4.j.a.49.12		24
16.3	odd	4		576.4.k.b.145.2		24
16.13	even	4	inner	144.4.k.b.109.1		24
24.5	odd	2		384.4.j.b.97.7		24
24.11	even	2		384.4.j.a.97.6		24
48.5	odd	4		384.4.j.b.289.7		24
48.11	even	4		384.4.j.a.289.6		24
48.29	odd	4		48.4.j.a.13.12	✓	24
48.35	even	4		192.4.j.a.145.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.12	✓	24	48.29	odd	4
48.4.j.a.37.12	yes	24	3.2	odd	2
144.4.k.b.37.1		24	1.1	even	1	trivial
144.4.k.b.109.1		24	16.13	even	4	inner
192.4.j.a.49.12		24	12.11	even	2
192.4.j.a.145.12		24	48.35	even	4
384.4.j.a.97.6		24	24.11	even	2
384.4.j.a.289.6		24	48.11	even	4
384.4.j.b.97.7		24	24.5	odd	2
384.4.j.b.289.7		24	48.5	odd	4
576.4.k.b.145.2		24	16.3	odd	4
576.4.k.b.433.2		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70307 + 0.832707i) q^{2} +(6.61320 - 4.50173i) q^{4} +(-11.7911 - 11.7911i) q^{5} -12.5754i q^{7} +(-14.1273 + 17.6754i) q^{8} +(41.6906 + 22.0536i) q^{10} +(17.0042 + 17.0042i) q^{11} +(-49.2384 + 49.2384i) q^{13} +(10.4716 + 33.9921i) q^{14} +(23.4688 - 59.5417i) q^{16} +51.8247 q^{17} +(-11.6655 + 11.6655i) q^{19} +(-131.057 - 24.8964i) q^{20} +(-60.1231 - 31.8041i) q^{22} +74.5524i q^{23} +153.058i q^{25} +(92.0939 - 174.096i) q^{26} +(-56.6109 - 83.1633i) q^{28} +(-211.183 + 211.183i) q^{29} -326.094 q^{31} +(-13.8571 + 180.488i) q^{32} +(-140.086 + 43.1547i) q^{34} +(-148.277 + 148.277i) q^{35} +(110.757 + 110.757i) q^{37} +(21.8187 - 41.2465i) q^{38} +(374.988 - 41.8350i) q^{40} -348.225i q^{41} +(205.838 + 205.838i) q^{43} +(189.000 + 35.9038i) q^{44} +(-62.0803 - 201.521i) q^{46} -254.983 q^{47} +184.861 q^{49} +(-127.453 - 413.728i) q^{50} +(-103.965 + 547.282i) q^{52} +(225.602 + 225.602i) q^{53} -400.995i q^{55} +(222.274 + 177.656i) q^{56} +(394.989 - 746.696i) q^{58} +(-285.442 - 285.442i) q^{59} +(286.952 - 286.952i) q^{61} +(881.456 - 271.541i) q^{62} +(-112.837 - 499.411i) q^{64} +1161.15 q^{65} +(-627.335 + 627.335i) q^{67} +(342.727 - 233.301i) q^{68} +(277.332 - 524.274i) q^{70} -274.784i q^{71} +298.190i q^{73} +(-391.612 - 207.156i) q^{74} +(-24.6312 + 129.661i) q^{76} +(213.834 - 213.834i) q^{77} -175.664 q^{79} +(-978.782 + 425.338i) q^{80} +(289.969 + 941.276i) q^{82} +(-125.254 + 125.254i) q^{83} +(-611.068 - 611.068i) q^{85} +(-727.796 - 384.991i) q^{86} +(-540.779 + 60.3313i) q^{88} +900.271i q^{89} +(619.190 + 619.190i) q^{91} +(335.615 + 493.030i) q^{92} +(689.237 - 212.326i) q^{94} +275.096 q^{95} +5.27858 q^{97} +(-499.691 + 153.935i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} - 84 q^{8} + 72 q^{10} + 40 q^{11} + 348 q^{14} - 192 q^{16} + 24 q^{19} - 80 q^{20} + 704 q^{22} + 20 q^{26} - 344 q^{28} - 400 q^{29} - 744 q^{31} + 960 q^{32} - 704 q^{34} + 456 q^{35}+ \cdots - 6760 q^{98}+O(q^{100}) \) 24 * q - 20 * q^4 - 84 * q^8 + 72 * q^10 + 40 * q^11 + 348 * q^14 - 192 * q^16 + 24 * q^19 - 80 * q^20 + 704 * q^22 + 20 * q^26 - 344 * q^28 - 400 * q^29 - 744 * q^31 + 960 * q^32 - 704 * q^34 + 456 * q^35 + 16 * q^37 - 1256 * q^38 + 1744 * q^40 + 1240 * q^43 + 200 * q^44 - 1432 * q^46 - 1176 * q^49 - 708 * q^50 + 1008 * q^52 - 752 * q^53 - 1344 * q^56 + 1936 * q^58 + 1376 * q^59 - 912 * q^61 + 996 * q^62 - 56 * q^64 - 976 * q^65 - 2256 * q^67 + 1568 * q^68 - 1760 * q^70 + 2740 * q^74 - 1880 * q^76 - 1904 * q^77 + 5992 * q^79 - 712 * q^80 - 40 * q^82 - 2680 * q^83 - 240 * q^85 + 1712 * q^86 - 3936 * q^88 - 3496 * q^91 - 5296 * q^92 + 5272 * q^94 + 7728 * q^95 - 6760 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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