LMFDB - Embedded newform 48.4.j.a.13.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [48,4,Mod(13,48)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(48, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 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("48.13"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.12
Character	$\chi$	$=$	48.13
Dual form			48.4.j.a.37.12

$q$-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} +(-2.12132 - 2.12132i) q^{3} +(6.61320 + 4.50173i) q^{4} +(11.7911 - 11.7911i) q^{5} +(-3.96764 - 7.50052i) q^{6} +12.5754i q^{7} +(14.1273 + 17.6754i) q^{8} +9.00000i q^{9} +(41.6906 - 22.0536i) q^{10} +(-17.0042 + 17.0042i) q^{11} +(-4.47910 - 23.5783i) q^{12} +(-49.2384 - 49.2384i) q^{13} +(-10.4716 + 33.9921i) q^{14} -50.0252 q^{15} +(23.4688 + 59.5417i) q^{16} -51.8247 q^{17} +(-7.49436 + 24.3277i) q^{18} +(-11.6655 - 11.6655i) q^{19} +(131.057 - 24.8964i) q^{20} +(26.6763 - 26.6763i) q^{21} +(-60.1231 + 31.8041i) q^{22} +74.5524i q^{23} +(7.52650 - 67.4637i) q^{24} -153.058i q^{25} +(-92.0939 - 174.096i) q^{26} +(19.0919 - 19.0919i) q^{27} +(-56.6109 + 83.1633i) q^{28} +(211.183 + 211.183i) q^{29} +(-135.222 - 41.6564i) q^{30} -326.094 q^{31} +(13.8571 + 180.488i) q^{32} +72.1427 q^{33} +(-140.086 - 43.1547i) q^{34} +(148.277 + 148.277i) q^{35} +(-40.5156 + 59.5188i) q^{36} +(110.757 - 110.757i) q^{37} +(-21.8187 - 41.2465i) q^{38} +208.901i q^{39} +(374.988 + 41.8350i) q^{40} -348.225i q^{41} +(94.3217 - 49.8945i) q^{42} +(205.838 - 205.838i) q^{43} +(-189.000 + 35.9038i) q^{44} +(106.120 + 106.120i) q^{45} +(-62.0803 + 201.521i) q^{46} +254.983 q^{47} +(76.5222 - 176.092i) q^{48} +184.861 q^{49} +(127.453 - 413.728i) q^{50} +(109.937 + 109.937i) q^{51} +(-103.965 - 547.282i) q^{52} +(-225.602 + 225.602i) q^{53} +(67.5047 - 35.7088i) q^{54} +400.995i q^{55} +(-222.274 + 177.656i) q^{56} +49.4924i q^{57} +(394.989 + 746.696i) q^{58} +(285.442 - 285.442i) q^{59} +(-330.827 - 225.200i) q^{60} +(286.952 + 286.952i) q^{61} +(-881.456 - 271.541i) q^{62} -113.178 q^{63} +(-112.837 + 499.411i) q^{64} -1161.15 q^{65} +(195.007 + 60.0737i) q^{66} +(-627.335 - 627.335i) q^{67} +(-342.727 - 233.301i) q^{68} +(158.150 - 158.150i) q^{69} +(277.332 + 524.274i) q^{70} -274.784i q^{71} +(-159.078 + 127.146i) q^{72} -298.190i q^{73} +(391.612 - 207.156i) q^{74} +(-324.686 + 324.686i) q^{75} +(-24.6312 - 129.661i) q^{76} +(-213.834 - 213.834i) q^{77} +(-173.953 + 564.674i) q^{78} -175.664 q^{79} +(978.782 + 425.338i) q^{80} -81.0000 q^{81} +(289.969 - 941.276i) q^{82} +(125.254 + 125.254i) q^{83} +(296.506 - 56.3262i) q^{84} +(-611.068 + 611.068i) q^{85} +(727.796 - 384.991i) q^{86} -895.973i q^{87} +(-540.779 - 60.3313i) q^{88} +900.271i q^{89} +(198.482 + 375.215i) q^{90} +(619.190 - 619.190i) q^{91} +(-335.615 + 493.030i) q^{92} +(691.750 + 691.750i) q^{93} +(689.237 + 212.326i) q^{94} -275.096 q^{95} +(353.478 - 412.269i) q^{96} +5.27858 q^{97} +(499.691 + 153.935i) q^{98} +(-153.038 - 153.038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29}+ \cdots - 360 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	2.70307	+	0.832707i	0.955680	+	0.294406i
$2$	2.70307	+	0.832707i	0.955680	+	0.294406i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$4$	6.61320	+	4.50173i	0.826650	+	0.562717i
$5$	11.7911	−	11.7911i	1.05462	−	1.05462i	0.0562056	−	0.998419i	$-0.482100\pi$
$5$	11.7911	−	11.7911i	1.05462	−	1.05462i	0.998419	−	0.0562056i	$-0.0179002\pi$
$6$	−3.96764	−	7.50052i	−0.269964	−	0.510346i
$7$			12.5754i			0.679005i	0.940605	+	0.339503i	$0.110259\pi$
$7$			12.5754i			0.679005i	−0.940605	+	0.339503i	$0.889741\pi$
$8$	14.1273	+	17.6754i	0.624346	+	0.781148i
$9$			9.00000i			0.333333i
$10$	41.6906	−	22.0536i	1.31837	−	0.697396i
$11$	−17.0042	+	17.0042i	−0.466087	+	0.466087i	−0.900644	−	0.434557i	$-0.856905\pi$
$11$	−17.0042	+	17.0042i	−0.466087	+	0.466087i	0.434557	+	0.900644i	$0.356905\pi$
$12$	−4.47910	−	23.5783i	−0.107750	−	0.567206i
$13$	−49.2384	−	49.2384i	−1.05048	−	1.05048i	−0.998656	−	0.0518270i	$-0.983496\pi$
$13$	−49.2384	−	49.2384i	−1.05048	−	1.05048i	−0.0518270	−	0.998656i	$-0.516504\pi$
$14$	−10.4716	+	33.9921i	−0.199903	+	0.648912i
$15$	−50.0252			−0.861098
$16$	23.4688	+	59.5417i	0.366700	+	0.930339i
$17$	−51.8247			−0.739372			−0.369686	−	0.929157i	$-0.620535\pi$
$17$	−51.8247			−0.739372			−0.369686	+	0.929157i	$0.620535\pi$
$18$	−7.49436	+	24.3277i	−0.0981354	+	0.318560i
$19$	−11.6655	−	11.6655i	−0.140855	−	0.140855i	0.633163	−	0.774018i	$-0.281756\pi$
$19$	−11.6655	−	11.6655i	−0.140855	−	0.140855i	−0.774018	+	0.633163i	$0.781756\pi$
$20$	131.057	−	24.8964i	1.46526	−	0.278351i
$21$	26.6763	−	26.6763i	0.277203	−	0.277203i
$22$	−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	$0.890270\pi$
$24$	7.52650	−	67.4637i	0.0640142	−	0.573790i
$25$		−	153.058i		−	1.22447i
$26$	−92.0939	−	174.096i	−0.694657	−	1.31319i
$27$	19.0919	−	19.0919i	0.136083	−	0.136083i
$28$	−56.6109	+	83.1633i	−0.382087	+	0.561300i
$29$	211.183	+	211.183i	1.35227	+	1.35227i	0.883122	+	0.469143i	$0.155437\pi$
$29$	211.183	+	211.183i	1.35227	+	1.35227i	0.469143	+	0.883122i	$0.344563\pi$
$30$	−135.222	−	41.6564i	−0.822934	−	0.253512i
$31$	−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
$33$	72.1427			0.380558
$34$	−140.086	−	43.1547i	−0.706604	−	0.217676i
$35$	148.277	+	148.277i	0.716096	+	0.716096i
$36$	−40.5156	+	59.5188i	−0.187572	+	0.275550i
$37$	110.757	−	110.757i	0.492117	−	0.492117i	−0.416855	−	0.908973i	$-0.636868\pi$
$37$	110.757	−	110.757i	0.492117	−	0.492117i	0.908973	+	0.416855i	$0.136868\pi$
$38$	−21.8187	−	41.2465i	−0.0931436	−	0.176081i
$39$			208.901i			0.857716i
$40$	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	$-0.230808\pi$
$42$	94.3217	−	49.8945i	0.346527	−	0.183307i
$43$	205.838	−	205.838i	0.729998	−	0.729998i	−0.240621	−	0.970619i	$-0.577351\pi$
$43$	205.838	−	205.838i	0.729998	−	0.729998i	0.970619	+	0.240621i	$0.0773511\pi$
$44$	−189.000	+	35.9038i	−0.647566	+	0.123016i
$45$	106.120	+	106.120i	0.351542	+	0.351542i
$46$	−62.0803	+	201.521i	−0.198984	+	0.645926i
$47$	254.983			0.791342			0.395671	−	0.918392i	$-0.370512\pi$
$47$	254.983			0.791342			0.395671	+	0.918392i	$0.370512\pi$
$48$	76.5222	−	176.092i	0.230105	−	0.529514i
$49$	184.861			0.538952
$50$	127.453	−	413.728i	0.360491	−	1.17020i
$51$	109.937	+	109.937i	0.301848	+	0.301848i
$52$	−103.965	−	547.282i	−0.277258	−	1.45951i
$53$	−225.602	+	225.602i	−0.584694	+	0.584694i	−0.936189	−	0.351496i	$-0.885673\pi$
$53$	−225.602	+	225.602i	−0.584694	+	0.584694i	0.351496	+	0.936189i	$0.385673\pi$
$54$	67.5047	−	35.7088i	0.170115	−	0.0899880i
$55$			400.995i			0.983094i
$56$	−222.274	+	177.656i	−0.530404	+	0.423934i
$57$			49.4924i			0.115007i
$58$	394.989	+	746.696i	0.894218	+	1.69045i
$59$	285.442	−	285.442i	0.629854	−	0.629854i	−0.318177	−	0.948031i	$-0.603071\pi$
$59$	285.442	−	285.442i	0.629854	−	0.629854i	0.948031	+	0.318177i	$0.103071\pi$
$60$	−330.827	−	225.200i	−0.711826	−	0.484554i
$61$	286.952	+	286.952i	0.602301	+	0.602301i	0.940923	−	0.338621i	$-0.109961\pi$
$61$	286.952	+	286.952i	0.602301	+	0.602301i	−0.338621	+	0.940923i	$0.609961\pi$
$62$	−881.456	−	271.541i	−1.80556	−	0.556221i
$63$	−113.178			−0.226335
$64$	−112.837	+	499.411i	−0.220385	+	0.975413i
$65$	−1161.15			−2.21573
$66$	195.007	+	60.0737i	0.363692	+	0.112039i
$67$	−627.335	−	627.335i	−1.14390	−	1.14390i	−0.987731	−	0.156168i	$-0.950086\pi$
$67$	−627.335	−	627.335i	−1.14390	−	1.14390i	−0.156168	−	0.987731i	$-0.549914\pi$
$68$	−342.727	−	233.301i	−0.611202	−	0.416057i
$69$	158.150	−	158.150i	0.275927	−	0.275927i
$70$	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	$-0.0737595\pi$
$72$	−159.078	+	127.146i	−0.260383	+	0.208115i
$73$		−	298.190i		−	0.478089i	−0.971009	−	0.239044i	$-0.923166\pi$
$73$		−	298.190i		−	0.478089i	0.971009	−	0.239044i	$-0.0768341\pi$
$74$	391.612	−	207.156i	0.615189	−	0.325424i
$75$	−324.686	+	324.686i	−0.499887	+	0.499887i
$76$	−24.6312	−	129.661i	−0.0371763	−	0.195699i
$77$	−213.834	−	213.834i	−0.316475	−	0.316475i
$78$	−173.953	+	564.674i	−0.252517	+	0.819702i
$79$	−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
$81$	−81.0000			−0.111111
$82$	289.969	−	941.276i	0.390509	−	1.26764i
$83$	125.254	+	125.254i	0.165644	+	0.165644i	0.785062	−	0.619418i	$-0.212631\pi$
$83$	125.254	+	125.254i	0.165644	+	0.165644i	−0.619418	+	0.785062i	$0.712631\pi$
$84$	296.506	−	56.3262i	0.385136	−	0.0731631i
$85$	−611.068	+	611.068i	−0.779760	+	0.779760i
$86$	727.796	−	384.991i	0.912561	−	0.482729i
$87$		−	895.973i		−	1.10412i
$88$	−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	$0.819891\pi$
$90$	198.482	+	375.215i	0.232465	+	0.439457i
$91$	619.190	−	619.190i	0.713283	−	0.713283i
$92$	−335.615	+	493.030i	−0.380329	+	0.558717i
$93$	691.750	+	691.750i	0.771302	+	0.771302i
$94$	689.237	+	212.326i	0.756270	+	0.232976i
$95$	−275.096			−0.297098
$96$	353.478	−	412.269i	0.375799	−	0.438302i
$97$	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
$99$	−153.038	−	153.038i	−0.155362	−	0.155362i
$100$	689.028	−	1012.21i	0.689028	−	1.01221i
$101$	−459.109	+	459.109i	−0.452307	+	0.452307i	−0.896120	−	0.443812i	$-0.853626\pi$
$101$	−459.109	+	459.109i	−0.452307	+	0.452307i	0.443812	+	0.896120i	$0.353626\pi$
$102$	205.622	+	388.712i	0.199604	+	0.377336i
$103$			791.173i			0.756860i	0.925630	+	0.378430i	$0.123536\pi$
$103$			791.173i			0.756860i	−0.925630	+	0.378430i	$0.876464\pi$
$104$	174.699	−	1565.91i	0.164718	−	1.47645i
$105$		−	629.085i		−	0.584690i
$106$	−797.678	+	421.958i	−0.730918	+	0.386643i
$107$	1525.81	−	1525.81i	1.37855	−	1.37855i	0.531487	−	0.847067i	$-0.321634\pi$
$107$	1525.81	−	1525.81i	1.37855	−	1.37855i	0.847067	−	0.531487i	$-0.178366\pi$
$108$	212.205	−	40.3119i	0.189069	−	0.0359168i
$109$	−413.307	−	413.307i	−0.363189	−	0.363189i	0.501796	−	0.864986i	$-0.332673\pi$
$109$	−413.307	−	413.307i	−0.363189	−	0.363189i	−0.864986	+	0.501796i	$0.832673\pi$
$110$	−333.911	+	1083.92i	−0.289429	+	0.939523i
$111$	−469.902			−0.401812
$112$	−748.758	+	295.129i	−0.631705	+	0.248991i
$113$	210.248			0.175031			0.0875154	−	0.996163i	$-0.472107\pi$
$113$	210.248			0.175031			0.0875154	+	0.996163i	$0.472107\pi$
$114$	−41.2126	+	133.781i	−0.0338589	+	0.109910i
$115$	879.053	+	879.053i	0.712801	+	0.712801i
$116$	445.906	+	2347.28i	0.356908	+	1.87879i
$117$	443.146	−	443.146i	0.350161	−	0.350161i
$118$	1009.26	−	533.881i	0.787372	−	0.416506i
$119$		−	651.714i		−	0.502038i
$120$	−706.723	−	884.214i	−0.537623	−	0.672645i
$121$			752.715i			0.565526i
$122$	536.704	+	1014.60i	0.398286	+	0.752929i
$123$	−738.696	+	738.696i	−0.541512	+	0.541512i
$124$	−2156.52	−	1467.99i	−1.56179	−	1.06314i
$125$	−330.838	−	330.838i	−0.236729	−	0.236729i
$126$	−305.929	−	94.2442i	−0.216304	−	0.0666345i
$127$	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
$129$	−873.295			−0.596041
$130$	−3138.66	−	966.895i	−2.11753	−	0.652325i
$131$	938.828	+	938.828i	0.626151	+	0.626151i	0.947097	−	0.320946i	$-0.104001\pi$
$131$	938.828	+	938.828i	0.626151	+	0.626151i	−0.320946	+	0.947097i	$0.604001\pi$
$132$	477.094	+	324.767i	0.314589	+	0.214146i
$133$	146.697	−	146.697i	0.0956411	−	0.0956411i
$134$	−1173.35	−	2218.12i	−0.756430	−	1.42997i
$135$		−	450.227i		−	0.287033i
$136$	−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	$0.969440\pi$
$138$	559.182	−	295.798i	0.344933	−	0.182464i
$139$	−1253.43	+	1253.43i	−0.764852	+	0.764852i	−0.977195	−	0.212343i	$-0.931891\pi$
$139$	−1253.43	+	1253.43i	−0.764852	+	0.764852i	0.212343	+	0.977195i	$0.431891\pi$
$140$	313.082	+	1648.09i	0.189002	+	0.994919i
$141$	−540.901	−	540.901i	−0.323064	−	0.323064i
$142$	228.815	−	742.761i	0.135223	−	0.438952i
$143$	1674.52			0.979233
$144$	−535.875	+	211.219i	−0.310113	+	0.122233i
$145$	4980.14			2.85226
$146$	248.305	−	806.028i	0.140752	−	0.456900i
$147$	−392.148	−	392.148i	−0.220026	−	0.220026i
$148$	1231.06	−	233.860i	0.683731	−	0.129886i
$149$	1686.80	−	1686.80i	0.927436	−	0.927436i	−0.0701033	−	0.997540i	$-0.522333\pi$
$149$	1686.80	−	1686.80i	0.927436	−	0.927436i	0.997540	+	0.0701033i	$0.0223329\pi$
$150$	−1148.02	+	607.281i	−0.624902	+	0.330562i
$151$			1682.23i			0.906611i	0.891355	+	0.453306i	$0.149755\pi$
$151$			1682.23i			0.906611i	−0.891355	+	0.453306i	$0.850245\pi$
$152$	41.3894	−	370.993i	0.0220863	−	0.197971i
$153$		−	466.422i		−	0.246457i
$154$	−399.947	−	756.069i	−0.209277	−	0.395622i
$155$	−3844.99	+	3844.99i	−1.99250	+	1.99250i
$156$	−940.416	+	1381.50i	−0.482651	+	0.709031i
$157$	−1066.81	−	1066.81i	−0.542300	−	0.542300i	0.381903	−	0.924202i	$-0.375269\pi$
$157$	−1066.81	−	1066.81i	−0.542300	−	0.542300i	−0.924202	+	0.381903i	$0.875269\pi$
$158$	−474.833	−	146.277i	−0.239087	−	0.0736529i
$159$	957.147			0.477400
$160$	2291.54	+	1964.76i	1.13226	+	0.970798i
$161$	−937.523			−0.458927
$162$	−218.949	−	67.4492i	−0.106187	−	0.0327118i
$163$	−2379.54	−	2379.54i	−1.14343	−	1.14343i	−0.987817	−	0.155618i	$-0.950263\pi$
$163$	−2379.54	−	2379.54i	−1.14343	−	1.14343i	−0.155618	−	0.987817i	$-0.549737\pi$
$164$	1567.61	−	2302.88i	0.746403	−	1.09649i
$165$	850.639	−	850.639i	0.401346	−	0.401346i
$166$	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	$-0.0623448\pi$
$168$	848.380	+	94.6484i	0.389607	+	0.0434660i
$169$			2651.84i			1.20703i
$170$	−2160.60	+	1142.92i	−0.974768	+	0.515635i
$171$	104.989	−	104.989i	0.0469516	−	0.0469516i
$172$	2287.87	−	434.619i	1.01424	−	0.192671i
$173$	−450.278	−	450.278i	−0.197885	−	0.197885i	0.601208	−	0.799093i	$-0.294686\pi$
$173$	−450.278	−	450.278i	−0.197885	−	0.197885i	−0.799093	+	0.601208i	$0.794686\pi$
$174$	746.083	−	2421.88i	0.325060	−	1.05519i
$175$	1924.76			0.831419
$176$	−1411.53	−	613.390i	−0.604533	−	0.262705i
$177$	−1211.03			−0.514274
$178$	−749.662	+	2433.50i	−0.315672	+	1.02471i
$179$	−647.759	−	647.759i	−0.270479	−	0.270479i	0.558814	−	0.829293i	$-0.311257\pi$
$179$	−647.759	−	647.759i	−0.270479	−	0.270479i	−0.829293	+	0.558814i	$0.811257\pi$
$180$	224.068	+	1179.51i	0.0927836	+	0.488420i
$181$	−755.750	+	755.750i	−0.310356	+	0.310356i	−0.845047	−	0.534691i	$-0.820428\pi$
$181$	−755.750	+	755.750i	−0.310356	+	0.310356i	0.534691	+	0.845047i	$0.320428\pi$
$182$	2189.32	−	1158.11i	0.891666	−	0.471676i
$183$		−	1217.43i		−	0.491777i
$184$	−1317.74	+	1053.23i	−0.527963	+	0.421983i
$185$		−	2611.89i		−	1.03800i
$186$	1293.82	+	2445.87i	0.510042	+	0.964195i
$187$	881.237	−	881.237i	0.344612	−	0.344612i
$188$	1686.25	+	1147.86i	0.654163	+	0.445301i
$189$	240.087	+	240.087i	0.0924009	+	0.0924009i
$190$	−743.605	−	229.075i	−0.283931	−	0.0874675i
$191$	760.485			0.288098			0.144049	−	0.989571i	$-0.453988\pi$
$191$	760.485			0.288098			0.144049	+	0.989571i	$0.453988\pi$
$192$	1298.77	−	820.049i	0.488182	−	0.308239i
$193$	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
$195$	2463.16	+	2463.16i	0.904568	+	0.904568i
$196$	1222.52	+	832.193i	0.445525	+	0.303277i
$197$	83.4121	−	83.4121i	0.0301668	−	0.0301668i	−0.691862	−	0.722029i	$-0.743210\pi$
$197$	83.4121	−	83.4121i	0.0301668	−	0.0301668i	0.722029	+	0.691862i	$0.243210\pi$
$198$	−286.236	−	541.108i	−0.102737	−	0.194216i
$199$			1734.18i			0.617754i	0.951102	+	0.308877i	$0.0999531\pi$
$199$			1734.18i			0.617754i	−0.951102	+	0.308877i	$0.900047\pi$
$200$	2705.36	−	2162.31i	0.956490	−	0.764491i
$201$			2661.56i			0.933989i
$202$	−1623.31	+	858.701i	−0.565423	+	0.299099i
$203$	−2655.70	+	2655.70i	−0.918195	+	0.918195i
$204$	232.128	+	1221.94i	0.0796676	+	0.419377i
$205$	−4105.94	−	4105.94i	−1.39888	−	1.39888i
$206$	−658.815	+	2138.60i	−0.222824	+	0.723316i
$207$	−670.972			−0.225294
$208$	1776.17	−	4087.31i	0.592093	−	1.36252i
$209$	396.723			0.131301
$210$	523.843	−	1700.46i	0.172136	−	0.558776i
$211$	−365.900	−	365.900i	−0.119382	−	0.119382i	0.644892	−	0.764274i	$-0.276902\pi$
$211$	−365.900	−	365.900i	−0.119382	−	0.119382i	−0.764274	+	0.644892i	$0.776902\pi$
$212$	−2507.55	+	476.350i	−0.812354	+	0.154320i
$213$	−582.905	+	582.905i	−0.187512	+	0.187512i
$214$	5394.91	−	2853.81i	1.72331	−	0.911602i
$215$		−	4854.09i		−	1.53975i
$216$	607.173	+	67.7385i	0.191263	+	0.0213381i
$217$		−	4100.75i		−	1.28284i
$218$	−773.035	−	1461.36i	−0.240168	−	0.454018i
$219$	−632.556	+	632.556i	−0.195179	+	0.195179i
$220$	−1805.17	+	2651.86i	−0.553203	+	0.812674i
$221$	2551.77	+	2551.77i	0.776698	+	0.776698i
$222$	−1270.18	−	391.291i	−0.384004	−	0.118296i
$223$	−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
$225$	1377.53			0.408156
$226$	568.316	+	175.075i	0.167274	+	0.0515302i
$227$	−1502.81	−	1502.81i	−0.439407	−	0.439407i	0.452406	−	0.891812i	$-0.350566\pi$
$227$	−1502.81	−	1502.81i	−0.439407	−	0.439407i	−0.891812	+	0.452406i	$0.850566\pi$
$228$	−222.801	+	327.303i	−0.0647166	+	0.0950709i
$229$	−3443.65	+	3443.65i	−0.993723	+	0.993723i	−0.999980	−	0.00625772i	$-0.998008\pi$
$229$	−3443.65	+	3443.65i	−0.993723	+	0.993723i	0.00625772	+	0.999980i	$0.498008\pi$
$230$	1644.15	+	3108.14i	0.471357	+	0.891063i
$231$			907.219i			0.258401i
$232$	−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	$0.948810\pi$
$234$	1566.87	−	828.845i	0.437732	−	0.231552i
$235$	3006.52	−	3006.52i	0.834569	−	0.834569i
$236$	3172.67	−	602.702i	0.875098	−	0.166240i
$237$	372.640	+	372.640i	0.102133	+	0.102133i
$238$	542.686	−	1761.63i	0.147803	−	0.479788i
$239$	−4603.80			−1.24600			−0.623002	−	0.782220i	$-0.714087\pi$
$239$	−4603.80			−1.24600			−0.623002	+	0.782220i	$0.714087\pi$
$240$	−1174.03	−	2978.59i	−0.315765	−	0.801113i
$241$	−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
$243$	171.827	+	171.827i	0.0453609	+	0.0453609i
$244$	605.889	+	3189.45i	0.158967	+	0.836817i
$245$	2179.70	−	2179.70i	0.568392	−	0.568392i
$246$	−2611.86	+	1381.63i	−0.676937	+	0.358088i
$247$			1148.78i			0.295931i
$248$	−4606.84	−	5763.83i	−1.17957	−	1.47582i
$249$		−	531.408i		−	0.135248i
$250$	−618.788	−	1169.77i	−0.156542	−	0.295931i
$251$	−476.440	+	476.440i	−0.119811	+	0.119811i	−0.764470	−	0.644659i	$-0.776999\pi$
$251$	−476.440	+	476.440i	−0.119811	+	0.119811i	0.644659	+	0.764470i	$0.276999\pi$
$252$	−748.470	−	509.498i	−0.187100	−	0.127362i
$253$	−1267.70	−	1267.70i	−0.315019	−	0.315019i
$254$	479.436	+	147.695i	0.118435	+	0.0364850i
$255$	2592.54			0.636672
$256$	−2994.43	+	2794.75i	−0.731062	+	0.682311i
$257$	925.326			0.224592			0.112296	−	0.993675i	$-0.464179\pi$
$257$	925.326			0.224592			0.112296	+	0.993675i	$0.464179\pi$
$258$	−2360.58	−	727.198i	−0.569625	−	0.175478i
$259$	1392.81	+	1392.81i	0.334150	+	0.334150i
$260$	−7678.89	−	5227.17i	−1.83163	−	1.24683i
$261$	−1900.65	+	1900.65i	−0.450755	+	0.450755i
$262$	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	$0.866337\pi$
$264$	1019.18	+	1275.15i	0.237600	+	0.297272i
$265$			5320.17i			1.23327i
$266$	518.689	−	274.378i	0.119560	−	0.0632450i
$267$	1909.76	−	1909.76i	0.437737	−	0.437737i
$268$	−1324.60	−	6972.79i	−0.301913	−	1.58929i
$269$	3773.37	+	3773.37i	0.855266	+	0.855266i	0.990776	−	0.135510i	$-0.0432673\pi$
$269$	3773.37	+	3773.37i	0.855266	+	0.855266i	−0.135510	+	0.990776i	$0.543267\pi$
$270$	374.907	−	1217.00i	0.0845042	−	0.274311i
$271$	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
$273$	−2627.00			−0.582394
$274$	−255.998	+	831.002i	−0.0564431	+	0.183221i
$275$	2602.63	+	2602.63i	0.570708	+	0.570708i
$276$	1757.82	−	333.928i	0.383364	−	0.0728264i
$277$	4550.73	−	4550.73i	0.987101	−	0.987101i	−0.0128173	−	0.999918i	$-0.504080\pi$
$277$	4550.73	−	4550.73i	0.987101	−	0.987101i	0.999918	+	0.0128173i	$0.00407998\pi$
$278$	−4431.85	+	2344.37i	−0.956131	+	0.505777i
$279$		−	2934.85i		−	0.629766i
$280$	−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	$0.884891\pi$
$282$	−1011.68	−	1912.50i	−0.213634	−	0.403858i
$283$	6242.23	−	6242.23i	1.31117	−	1.31117i	0.390621	−	0.920552i	$-0.372260\pi$
$283$	6242.23	−	6242.23i	1.31117	−	1.31117i	0.920552	−	0.390621i	$-0.127740\pi$
$284$	1237.00	−	1817.20i	0.258460	−	0.379687i
$285$	583.568	+	583.568i	0.121290	+	0.121290i
$286$	4526.35	+	1394.38i	0.935834	+	0.288292i
$287$	4379.05			0.900651
$288$	−1624.39	+	124.714i	−0.332355	+	0.0255169i
$289$	−2227.20			−0.453329
$290$	13461.7	+	4147.00i	2.72585	+	0.839725i
$291$	−11.1976	−	11.1976i	−0.00225571	−	0.00225571i
$292$	1342.37	−	1971.99i	0.269028	−	0.395212i
$293$	−2458.24	+	2458.24i	−0.490143	+	0.490143i	−0.908351	−	0.418208i	$-0.862658\pi$
$293$	−2458.24	+	2458.24i	−0.490143	+	0.490143i	0.418208	+	0.908351i	$0.362658\pi$
$294$	−733.461	−	1386.55i	−0.145498	−	0.275052i
$295$		−	6731.33i		−	1.32852i
$296$	3522.37	+	392.969i	0.691668	+	0.0771651i
$297$			649.284i			0.126853i
$298$	5964.15	−	3154.93i	1.15938	−	0.613290i
$299$	3670.84	−	3670.84i	0.710001	−	0.710001i
$300$	−3608.86	+	685.564i	−0.694526	+	0.131937i
$301$	2588.48	+	2588.48i	0.495673	+	0.495673i
$302$	−1400.81	+	4547.20i	−0.266912	+	0.866431i
$303$	1947.83			0.369307
$304$	420.807	−	968.356i	0.0793912	−	0.182694i
$305$	6766.93			1.27040
$306$	388.393	−	1260.77i	0.0725586	−	0.235535i
$307$	−3008.49	−	3008.49i	−0.559295	−	0.559295i	0.369812	−	0.929107i	$-0.379422\pi$
$307$	−3008.49	−	3008.49i	−0.559295	−	0.559295i	−0.929107	+	0.369812i	$0.879422\pi$
$308$	−451.503	−	2376.75i	−0.0835284	−	0.439700i
$309$	1678.33	−	1678.33i	0.308987	−	0.308987i
$310$	−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	$0.865218\pi$
$312$	−3692.40	+	2951.21i	−0.670003	+	0.535511i
$313$		−	5237.61i		−	0.945837i	−0.881106	−	0.472919i	$-0.843200\pi$
$313$		−	5237.61i		−	0.945837i	0.881106	−	0.472919i	$-0.156800\pi$
$314$	−1995.33	−	3772.02i	−0.358609	−	0.677922i
$315$	−1334.49	+	1334.49i	−0.238699	+	0.238699i
$316$	−1161.70	−	790.794i	−0.206807	−	0.140777i
$317$	−989.530	−	989.530i	−0.175323	−	0.175323i	0.613990	−	0.789314i	$-0.289563\pi$
$317$	−989.530	−	989.530i	−0.175323	−	0.175323i	−0.789314	+	0.613990i	$0.789563\pi$
$318$	2587.24	+	797.022i	0.456242	+	0.140550i
$319$	−7181.99			−1.26055
$320$	4558.13	+	7219.06i	0.796272	+	1.26112i
$321$	−6473.45			−1.12558
$322$	−2534.19	−	780.682i	−0.438587	−	0.135111i
$323$	604.559	+	604.559i	0.104144	+	0.104144i
$324$	−535.669	−	364.640i	−0.0918500	−	0.0625241i
$325$	−7536.35	+	7536.35i	−1.28628	+	1.28628i
$326$	−4450.61	−	8413.52i	−0.756124	−	1.42939i
$327$			1753.51i			0.296543i
$328$	6154.99	−	4919.48i	1.03614	−	0.828150i
$329$			3206.50i			0.537325i
$330$	3007.67	−	1591.01i	0.501718	−	0.265400i
$331$	−5652.55	+	5652.55i	−0.938647	+	0.938647i	−0.998224	−	0.0595765i	$-0.981025\pi$
$331$	−5652.55	+	5652.55i	−0.938647	+	0.938647i	0.0595765	+	0.998224i	$0.481025\pi$
$332$	264.470	+	1392.19i	0.0437189	+	0.230140i
$333$	996.813	+	996.813i	0.164039	+	0.164039i
$334$	699.466	−	2270.56i	0.114590	−	0.371974i
$335$	−14793.9			−2.41277
$336$	2214.42	+	962.293i	0.359543	+	0.156242i
$337$	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
$339$	−446.004	−	446.004i	−0.0714560	−	0.0714560i
$340$	−6791.98	+	1290.25i	−1.08337	+	0.205805i
$341$	5544.96	−	5544.96i	0.880577	−	0.880577i
$342$	371.218	−	196.368i	0.0586936	−	0.0310479i
$343$			6638.03i			1.04496i
$344$	6546.19	+	730.317i	1.02601	+	0.114465i
$345$		−	3729.50i		−	0.581999i
$346$	−842.185	−	1592.08i	−0.130856	−	0.247373i
$347$	6530.87	−	6530.87i	1.01036	−	1.01036i	0.0104158	−	0.999946i	$-0.496684\pi$
$347$	6530.87	−	6530.87i	1.01036	−	1.01036i	0.999946	−	0.0104158i	$-0.00331552\pi$
$348$	4033.43	−	5925.25i	0.621307	−	0.912721i
$349$	7267.79	+	7267.79i	1.11472	+	1.11472i	0.992504	+	0.122213i	$0.0389990\pi$
$349$	7267.79	+	7267.79i	1.11472	+	1.11472i	0.122213	+	0.992504i	$0.461001\pi$
$350$	5202.77	+	1602.76i	0.794571	+	0.244775i
$351$	−1880.11			−0.285905
$352$	−3304.68	−	2833.43i	−0.500399	−	0.429040i
$353$	−8253.63			−1.24447			−0.622233	−	0.782832i	$-0.713774\pi$
$353$	−8253.63			−1.24447			−0.622233	+	0.782832i	$0.713774\pi$
$354$	−3273.50	−	1008.43i	−0.491481	−	0.151405i
$355$	−3240.00	−	3240.00i	−0.484398	−	0.484398i
$356$	−4052.78	+	5953.67i	−0.603362	+	0.886360i
$357$	−1382.49	+	1382.49i	−0.204956	+	0.204956i
$358$	−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	$0.884525\pi$
$360$	−376.515	+	3374.89i	−0.0551225	+	0.494090i
$361$		−	6586.83i		−	0.960320i
$362$	−2672.16	+	1413.53i	−0.387972	+	0.205230i
$363$	1596.75	−	1596.75i	0.230875	−	0.230875i
$364$	6882.26	−	1307.40i	0.991012	−	0.188259i
$365$	−3515.97	−	3515.97i	−0.504204	−	0.504204i
$366$	1013.76	−	3290.81i	0.144782	−	0.469982i
$367$	−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
$369$	3134.02			0.442143
$370$	2174.93	−	7060.12i	0.305593	−	0.991995i
$371$	−2837.02	−	2837.02i	−0.397010	−	0.397010i
$372$	1460.61	+	7688.75i	0.203572	+	1.07162i
$373$	1141.57	−	1141.57i	0.158468	−	0.158468i	−0.623420	−	0.781887i	$-0.714257\pi$
$373$	1141.57	−	1141.57i	0.158468	−	0.158468i	0.781887	+	0.623420i	$0.214257\pi$
$374$	3115.86	−	1648.23i	0.430795	−	0.227883i
$375$			1403.63i			0.193288i
$376$	3602.23	+	4506.92i	0.494071	+	0.618155i
$377$		−	20796.6i		−	2.84106i
$378$	449.051	+	848.895i	0.0611023	+	0.115509i
$379$	−2602.11	+	2602.11i	−0.352668	+	0.352668i	−0.861101	−	0.508433i	$-0.830225\pi$
$379$	−2602.11	+	2602.11i	−0.352668	+	0.352668i	0.508433	+	0.861101i	$0.330225\pi$
$380$	−1819.27	−	1238.41i	−0.245596	−	0.167182i
$381$	−376.252	−	376.252i	−0.0505931	−	0.0505931i
$382$	2055.65	+	633.261i	0.275330	+	0.0848179i
$383$	−370.858			−0.0494777			−0.0247388	−	0.999694i	$-0.507875\pi$
$383$	−370.858			−0.0494777			−0.0247388	+	0.999694i	$0.507875\pi$
$384$	4193.54	−	1135.15i	0.557294	−	0.150854i
$385$	−5042.65			−0.667526
$386$	5906.17	+	1819.45i	0.778799	+	0.239916i
$387$	1852.54	+	1852.54i	0.243333	+	0.243333i
$388$	34.9083	+	23.7627i	0.00456752	+	0.00310920i
$389$	−6457.55	+	6457.55i	−0.841673	+	0.841673i	−0.989077	−	0.147403i	$-0.952909\pi$
$389$	−6457.55	+	6457.55i	−0.841673	+	0.841673i	0.147403	+	0.989077i	$0.452909\pi$
$390$	4607.02	+	8709.20i	0.598168	+	1.13079i
$391$		−	3863.66i		−	0.499728i
$392$	2611.59	+	3267.48i	0.336492	+	0.421001i
$393$		−	3983.11i		−	0.511250i
$394$	294.927	−	156.011i	0.0377112	−	0.0199486i
$395$	−2071.27	+	2071.27i	−0.263840	+	0.263840i
$396$	−323.134	−	1701.00i	−0.0410053	−	0.215855i
$397$	−232.353	−	232.353i	−0.0293739	−	0.0293739i	0.692267	−	0.721641i	$-0.256612\pi$
$397$	−232.353	−	232.353i	−0.0293739	−	0.0293739i	−0.721641	+	0.692267i	$0.756612\pi$
$398$	−1444.07	+	4687.62i	−0.181871	+	0.590375i
$399$	−622.384			−0.0780906
$400$	9113.36	−	3592.10i	1.13917	−	0.449012i
$401$	−119.615			−0.0148960			−0.00744801	−	0.999972i	$-0.502371\pi$
$401$	−119.615			−0.0148960			−0.00744801	+	0.999972i	$0.502371\pi$
$402$	−2216.30	+	7194.38i	−0.274972	+	0.892595i
$403$	16056.4	+	16056.4i	1.98467	+	1.98467i
$404$	−5102.96	+	969.393i	−0.628421	+	0.119379i
$405$	−955.076	+	955.076i	−0.117181	+	0.117181i
$406$	−9389.97	+	4967.13i	−1.14782	+	0.607179i
$407$			3766.67i			0.458739i
$408$	−390.059	+	3496.28i	−0.0473303	+	0.424245i
$409$		−	626.952i		−	0.0757965i	−0.999282	−	0.0378983i	$-0.987934\pi$
$409$		−	626.952i		−	0.0757965i	0.999282	−	0.0378983i	$-0.0120663\pi$
$410$	−7679.60	−	14517.7i	−0.925045	−	1.74873i
$411$	652.155	−	652.155i	0.0782687	−	0.0782687i
$412$	−3561.65	+	5232.18i	−0.425897	+	0.625658i
$413$	3589.54	+	3589.54i	0.427674	+	0.427674i
$414$	−1813.69	−	558.723i	−0.215309	−	0.0663278i
$415$	2953.76			0.349384
$416$	8204.65	−	9569.26i	0.966986	−	1.12782i
$417$	5317.85			0.624499
$418$	1072.37	+	330.354i	0.125482	+	0.0386559i
$419$	−4981.58	−	4981.58i	−0.580826	−	0.580826i	0.354304	−	0.935130i	$-0.384718\pi$
$419$	−4981.58	−	4981.58i	−0.580826	−	0.580826i	−0.935130	+	0.354304i	$0.884718\pi$
$420$	2831.97	−	4160.27i	0.329015	−	0.483334i
$421$	10770.4	−	10770.4i	1.24683	−	1.24683i	0.289723	−	0.957110i	$-0.406437\pi$
$421$	10770.4	−	10770.4i	1.24683	−	1.24683i	0.957110	−	0.289723i	$-0.0935632\pi$
$422$	−684.366	−	1293.74i	−0.0789442	−	0.149238i
$423$			2294.85i			0.263781i
$424$	−7174.74	−	800.441i	−0.821783	−	0.0916813i
$425$			7932.20i			0.905337i
$426$	−2061.02	+	1090.25i	−0.234406	+	0.123997i
$427$	−3608.52	+	3608.52i	−0.408966	+	0.408966i
$428$	16959.2	−	3221.69i	1.91532	−	0.363846i
$429$	−3552.19	−	3552.19i	−0.399770	−	0.399770i
$430$	4042.03	−	13120.9i	0.453312	−	1.47151i
$431$	7546.94			0.843442			0.421721	−	0.906726i	$-0.361426\pi$
$431$	7546.94			0.843442			0.421721	+	0.906726i	$0.361426\pi$
$432$	1584.83	+	688.699i	0.176505	+	0.0767015i
$433$	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
$435$	−10564.5	−	10564.5i	−1.16443	−	1.16443i
$436$	−872.684	−	4593.88i	−0.0958578	−	0.504603i
$437$	869.689	−	869.689i	0.0952010	−	0.0952010i
$438$	−2236.58	+	1183.11i	−0.243990	+	0.129067i
$439$			7198.92i			0.782656i	0.920251	+	0.391328i	$0.127984\pi$
$439$			7198.92i			0.782656i	−0.920251	+	0.391328i	$0.872016\pi$
$440$	−7087.73	+	5664.99i	−0.767942	+	0.613790i
$441$			1663.74i			0.179651i
$442$	4772.73	+	9022.48i	0.513610	+	0.970940i
$443$	−5582.95	+	5582.95i	−0.598767	+	0.598767i	−0.939984	−	0.341217i	$-0.889161\pi$
$443$	−5582.95	+	5582.95i	−0.598767	+	0.598767i	0.341217	+	0.939984i	$0.389161\pi$
$444$	−3107.56	−	2115.37i	−0.332158	−	0.226106i
$445$	10615.2	+	10615.2i	1.13080	+	1.13080i
$446$	−10912.8	−	3361.78i	−1.15860	−	0.356917i
$447$	−7156.49			−0.757249
$448$	−6280.28	−	1418.96i	−0.662311	−	0.149642i
$449$	1224.53			0.128706			0.0643530	−	0.997927i	$-0.479502\pi$
$449$	1224.53			0.128706			0.0643530	+	0.997927i	$0.479502\pi$
$450$	3723.55	+	1147.07i	0.390066	+	0.120164i
$451$	5921.28	+	5921.28i	0.618231	+	0.618231i
$452$	1390.41	+	946.481i	0.144689	+	0.0984927i
$453$	3568.56	−	3568.56i	0.370123	−	0.370123i
$454$	−2810.81	−	5313.62i	−0.290568	−	0.549297i
$455$		−	14601.8i		−	1.50449i
$456$	−874.795	+	699.195i	−0.0898378	+	0.0718044i
$457$			11182.3i			1.14461i	0.820040	+	0.572307i	$0.193951\pi$
$457$			11182.3i			1.14461i	−0.820040	+	0.572307i	$0.806049\pi$
$458$	−12176.0	+	6440.88i	−1.24224	+	0.657123i
$459$	−989.431	+	989.431i	−0.100616	+	0.100616i
$460$	1856.09	+	9770.61i	0.188132	+	0.990341i
$461$	−11334.9	−	11334.9i	−1.14516	−	1.14516i	−0.987492	−	0.157670i	$-0.949602\pi$
$461$	−11334.9	−	11334.9i	−1.14516	−	1.14516i	−0.157670	−	0.987492i	$-0.550398\pi$
$462$	−755.448	+	2452.28i	−0.0760749	+	0.246949i
$463$	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
$465$	16312.9			1.62687
$466$	−948.453	+	3078.80i	−0.0942837	+	0.306057i
$467$	−843.917	−	843.917i	−0.0836228	−	0.0836228i	0.664058	−	0.747681i	$-0.268833\pi$
$467$	−843.917	−	843.917i	−0.0836228	−	0.0836228i	−0.747681	+	0.664058i	$0.768833\pi$
$468$	4925.54	−	935.688i	0.486502	−	0.0924192i
$469$	7888.96	−	7888.96i	0.776713	−	0.776713i
$470$	10630.4	−	5623.29i	1.04328	−	0.551879i
$471$			4526.11i			0.442786i
$472$	9077.83	+	1012.76i	0.885256	+	0.0987625i
$473$			7000.20i			0.680485i
$474$	696.974	+	1317.57i	0.0675381	+	0.127675i
$475$	−1785.50	+	1785.50i	−0.172472	+	0.172472i
$476$	2933.84	−	4309.91i	0.282505	−	0.415009i
$477$	−2030.41	−	2030.41i	−0.194898	−	0.194898i
$478$	−12444.4	−	3833.62i	−1.19078	−	0.366832i
$479$	10569.4			1.00821			0.504103	−	0.863644i	$-0.331823\pi$
$479$	10569.4			1.00821			0.504103	+	0.863644i	$0.331823\pi$
$480$	−693.206	−	9028.97i	−0.0659175	−	0.858571i
$481$	−10907.0			−1.03392
$482$	−12654.7	−	3898.39i	−1.19586	−	0.368395i
$483$	1988.79	+	1988.79i	0.187356	+	0.187356i
$484$	−3388.52	+	4977.85i	−0.318231	+	0.467492i
$485$	62.2400	−	62.2400i	0.00582716	−	0.00582716i
$486$	321.379	+	607.542i	0.0299960	+	0.0567051i
$487$		−	1579.10i		−	0.146932i	−0.997298	−	0.0734661i	$-0.976594\pi$
$487$		−	1579.10i		−	0.146932i	0.997298	−	0.0734661i	$-0.0234061\pi$
$488$	−1018.11	+	9125.83i	−0.0944422	+	0.846531i
$489$			10095.5i			0.933611i
$490$	7706.95	−	4076.84i	0.710539	−	0.375863i
$491$	8650.50	−	8650.50i	0.795095	−	0.795095i	−0.187222	−	0.982318i	$-0.559948\pi$
$491$	8650.50	−	8650.50i	0.795095	−	0.795095i	0.982318	+	0.187222i	$0.0599485\pi$
$492$	−8210.55	+	1559.73i	−0.752358	+	0.142923i
$493$	−10944.5	−	10944.5i	−0.999828	−	0.999828i
$494$	−956.595	+	3105.23i	−0.0871240	+	0.282816i
$495$	−3608.95			−0.327698
$496$	−7653.04	−	19416.2i	−0.692806	−	1.75769i
$497$	3455.51			0.311873
$498$	442.507	−	1436.44i	0.0398177	−	0.129253i
$499$	−11942.3	−	11942.3i	−1.07137	−	1.07137i	−0.997250	−	0.0741168i	$-0.976386\pi$
$499$	−11942.3	−	11942.3i	−1.07137	−	1.07137i	−0.0741168	−	0.997250i	$-0.523614\pi$
$500$	−698.554	−	3677.24i	−0.0624806	−	0.328903i
$501$	−1781.89	+	1781.89i	−0.158900	+	0.158900i
$502$	−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	$0.953417\pi$
$504$	−1598.91	−	2000.47i	−0.141311	−	0.176801i
$505$			10826.8i			0.954029i
$506$	−2371.07	−	4482.32i	−0.208314	−	0.393801i
$507$	5625.41	−	5625.41i	0.492768	−	0.492768i
$508$	1172.96	+	798.458i	0.102445	+	0.0697360i
$509$	1392.67	+	1392.67i	0.121275	+	0.121275i	0.765140	−	0.643864i	$-0.222670\pi$
$509$	1392.67	+	1392.67i	0.121275	+	0.121275i	−0.643864	+	0.765140i	$0.722670\pi$
$510$	7007.83	+	2158.83i	0.608455	+	0.187440i
$511$	3749.84			0.324625
$512$	−10421.4	+	5060.92i	−0.899538	+	0.436842i
$513$	−445.431			−0.0383358
$514$	2501.22	+	770.525i	0.214639	+	0.0661214i
$515$	9328.77	+	9328.77i	0.798203	+	0.798203i
$516$	−5775.27	−	3931.34i	−0.492717	−	0.335402i
$517$	−4335.78	+	4335.78i	−0.368834	+	0.368834i
$518$	2605.06	+	4924.66i	0.220965	+	0.417717i
$519$			1910.37i			0.161572i
$520$	−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	$-0.0157414\pi$
$522$	−6720.27	+	3554.90i	−0.563483	+	0.298073i
$523$	−9451.05	+	9451.05i	−0.790183	+	0.790183i	−0.981524	−	0.191341i	$-0.938716\pi$
$523$	−9451.05	+	9451.05i	−0.790183	+	0.790183i	0.191341	+	0.981524i	$0.438716\pi$
$524$	1982.30	+	10435.0i	0.165262	+	0.869953i
$525$	−4083.04	−	4083.04i	−0.339426	−	0.339426i
$526$	−2895.86	+	9400.34i	−0.240049	+	0.779228i
$527$	16899.7			1.39689
$528$	1693.10	+	4295.50i	0.139551	+	0.354048i
$529$	6608.93			0.543185
$530$	−4430.14	+	14380.8i	−0.363081	+	1.17861i
$531$	2568.98	+	2568.98i	0.209951	+	0.209951i
$532$	1630.53	−	309.747i	0.132881	−	0.0252429i
$533$	−17146.0	+	17146.0i	−1.39339	+	1.39339i
$534$	6752.50	−	3571.96i	0.547209	−	0.289464i
$535$		−	35981.7i		−	2.90771i
$536$	2225.80	−	19951.0i	0.179366	−	1.60774i
$537$			2748.21i			0.220845i
$538$	7057.58	+	13341.8i	0.565565	+	1.06916i
$539$	−3143.40	+	3143.40i	−0.251198	+	0.251198i
$540$	2026.80	−	2977.44i	0.161518	−	0.237275i
$541$	2893.97	+	2893.97i	0.229984	+	0.229984i	0.812686	−	0.582702i	$-0.198004\pi$
$541$	2893.97	+	2893.97i	0.229984	+	0.229984i	−0.582702	+	0.812686i	$0.698004\pi$
$542$	21643.7	+	6667.56i	1.71527	+	0.528406i
$543$	3206.38			0.253405
$544$	−718.141	−	9353.74i	−0.0565994	−	0.737203i
$545$	−9746.66			−0.766057
$546$	−7100.98	−	2187.52i	−0.556582	−	0.171460i
$547$	−956.857	−	956.857i	−0.0747939	−	0.0747939i	0.668720	−	0.743514i	$-0.266842\pi$
$547$	−956.857	−	956.857i	−0.0747939	−	0.0747939i	−0.743514	+	0.668720i	$0.766842\pi$
$548$	−1383.96	+	2033.09i	−0.107883	+	0.158484i
$549$	−2582.56	+	2582.56i	−0.200767	+	0.200767i
$550$	4867.88	+	9202.34i	0.377394	+	0.713435i
$551$		−	4927.09i		−	0.380946i
$552$	5029.58	+	561.119i	0.387814	+	0.0432660i
$553$		−	2209.04i		−	0.169870i
$554$	16090.4	−	8511.53i	1.23396	−	0.652744i
$555$	−5540.65	+	5540.65i	−0.423761	+	0.423761i
$556$	−13931.8	+	2646.57i	−1.06266	+	0.201870i
$557$	−8482.07	−	8482.07i	−0.645236	−	0.645236i	0.306602	−	0.951838i	$-0.400808\pi$
$557$	−8482.07	−	8482.07i	−0.645236	−	0.645236i	−0.951838	+	0.306602i	$0.900808\pi$
$558$	2443.87	−	7933.10i	0.185407	−	0.601855i
$559$	−20270.2			−1.53370
$560$	−5348.77	+	12308.5i	−0.403619	+	0.928804i
$561$	−3738.77			−0.281374
$562$	−2775.46	+	9009.48i	−0.208319	+	0.676232i
$563$	9461.78	+	9461.78i	0.708289	+	0.708289i	0.966175	−	0.257886i	$-0.0830260\pi$
$563$	9461.78	+	9461.78i	0.708289	+	0.708289i	−0.257886	+	0.966175i	$0.583026\pi$
$564$	−1142.09	−	6012.07i	−0.0852674	−	0.448854i
$565$	2479.05	−	2479.05i	0.184592	−	0.184592i
$566$	22071.1	−	11675.2i	1.63908	−	0.867044i
$567$		−	1018.60i		−	0.0754450i
$568$	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	$0.914579\pi$
$570$	1091.48	+	2063.37i	0.0802057	+	0.151623i
$571$	990.936	−	990.936i	0.0726259	−	0.0726259i	−0.669861	−	0.742487i	$-0.733646\pi$
$571$	990.936	−	990.936i	0.0726259	−	0.0726259i	0.742487	+	0.669861i	$0.233646\pi$
$572$	11073.9	+	7538.24i	0.809483	+	0.551031i
$573$	−1613.23	−	1613.23i	−0.117616	−	0.117616i
$574$	11836.9	+	3646.46i	0.860735	+	0.265157i
$575$	11410.9			0.827594
$576$	−4494.70	−	1015.53i	−0.325138	−	0.0734615i
$577$	−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
$579$	−4635.05	−	4635.05i	−0.332688	−	0.332688i
$580$	32934.7	+	22419.3i	2.35782	+	1.60502i
$581$	−1575.11	+	1575.11i	−0.112473	+	0.112473i
$582$	−20.9435	−	39.5921i	−0.00149164	−	0.00281983i
$583$		−	7672.35i		−	0.545036i
$584$	5270.61	−	4212.63i	0.373458	−	0.298493i
$585$		−	10450.3i		−	0.738577i
$586$	−8691.80	+	4597.81i	−0.612721	+	0.324119i
$587$	4038.29	−	4038.29i	0.283949	−	0.283949i	−0.550733	−	0.834682i	$-0.685652\pi$
$587$	4038.29	−	4038.29i	0.283949	−	0.283949i	0.834682	+	0.550733i	$0.185652\pi$
$588$	−828.009	−	4358.70i	−0.0580723	−	0.305697i
$589$	3804.04	+	3804.04i	0.266116	+	0.266116i
$590$	5605.23	−	18195.3i	0.391125	−	1.26964i
$591$	−353.888			−0.0246311
$592$	9194.00	+	3995.33i	0.638296	+	0.277376i
$593$	11081.1			0.767361			0.383681	−	0.923466i	$-0.374656\pi$
$593$	11081.1			0.767361			0.383681	+	0.923466i	$0.374656\pi$
$594$	−540.663	+	1755.06i	−0.0373463	+	0.121231i
$595$	−7684.40	−	7684.40i	−0.529461	−	0.529461i
$596$	18748.7	−	3561.62i	1.28855	−	0.244781i
$597$	3678.76	−	3678.76i	0.252197	−	0.252197i
$598$	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	$0.922857\pi$
$600$	−10325.9	−	1151.99i	−0.702588	−	0.0783833i
$601$		−	24290.7i		−	1.64865i	−0.566117	−	0.824325i	$-0.691555\pi$
$601$		−	24290.7i		−	1.64865i	0.566117	−	0.824325i	$-0.308445\pi$
$602$	4841.40	+	9152.29i	0.327775	+	0.619634i
$603$	5646.02	−	5646.02i	0.381299	−	0.381299i
$604$	−7572.97	+	11125.0i	−0.510165	+	0.749450i
$605$	8875.31	+	8875.31i	0.596418	+	0.596418i
$606$	5265.14	+	1621.97i	0.352940	+	0.108726i
$607$	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
$609$	11267.2			0.749703
$610$	18291.5	+	5634.87i	1.21410	+	0.374015i
$611$	−12555.0	−	12555.0i	−0.831292	−	0.831292i
$612$	2099.71	−	3084.54i	0.138686	−	0.203734i
$613$	−2217.95	+	2217.95i	−0.146137	+	0.146137i	−0.776390	−	0.630253i	$-0.782951\pi$
$613$	−2217.95	+	2217.95i	−0.146137	+	0.146137i	0.630253	+	0.776390i	$0.282951\pi$
$614$	−5626.97	−	10637.4i	−0.369847	−	0.699167i
$615$			17420.0i			1.14218i
$616$	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	$0.672269\pi$
$618$	5934.21	−	3139.09i	0.386260	−	0.204325i
$619$	−11171.8	+	11171.8i	−0.725417	+	0.725417i	−0.969703	−	0.244287i	$-0.921446\pi$
$619$	−11171.8	+	11171.8i	−0.725417	+	0.725417i	0.244287	+	0.969703i	$0.421446\pi$
$620$	−42736.9	+	8118.58i	−2.76831	+	0.525887i
$621$	1423.35	+	1423.35i	0.0919757	+	0.0919757i
$622$	−3753.08	+	12183.0i	−0.241937	+	0.785358i
$623$	−11321.2			−0.728050
$624$	−12438.3	+	4902.66i	−0.797967	+	0.314525i
$625$	11330.4			0.725148
$626$	4361.39	−	14157.6i	0.278460	−	0.903918i
$627$	−841.578	−	841.578i	−0.0536035	−	0.0536035i
$628$	−2252.54	−	11857.6i	−0.143131	−	0.753453i
$629$	−5739.95	+	5739.95i	−0.363858	+	0.363858i
$630$	−4718.47	+	2495.99i	−0.298394	+	0.157845i
$631$		−	17415.1i		−	1.09871i	−0.835590	−	0.549354i	$-0.814874\pi$
$631$		−	17415.1i		−	1.09871i	0.835590	−	0.549354i	$-0.185126\pi$
$632$	−2481.67	−	3104.93i	−0.156195	−	0.195423i
$633$			1552.38i			0.0974749i
$634$	−1850.78	−	3498.76i	−0.115937	−	0.219169i
$635$	2091.34	−	2091.34i	0.130697	−	0.130697i
$636$	6329.80	+	4308.82i	0.394643	+	0.268641i
$637$	−9102.24	−	9102.24i	−0.566160	−	0.566160i
$638$	−19413.4	−	5980.49i	−1.20468	−	0.371113i
$639$	2473.06			0.153103
$640$	6309.59	+	23309.2i	0.389700	+	1.43965i
$641$	−2727.28			−0.168051			−0.0840257	−	0.996464i	$-0.526778\pi$
$641$	−2727.28			−0.168051			−0.0840257	+	0.996464i	$0.526778\pi$
$642$	−17498.2	−	5390.48i	−1.07570	−	0.331379i
$643$	11681.7	+	11681.7i	0.716458	+	0.716458i	0.967878	−	0.251420i	$-0.0808975\pi$
$643$	11681.7	+	11681.7i	0.716458	+	0.716458i	−0.251420	+	0.967878i	$0.580897\pi$
$644$	−6200.03	−	4220.48i	−0.379372	−	0.258246i
$645$	−10297.1	+	10297.1i	−0.628600	+	0.628600i
$646$	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	$0.957324\pi$
$648$	−1144.31	−	1431.70i	−0.0693718	−	0.0867942i
$649$			9707.43i			0.587134i
$650$	−26646.9	+	14095.7i	−1.60796	+	0.850585i
$651$	−8699.00	+	8699.00i	−0.523718	+	0.523718i
$652$	−5024.32	−	26448.4i	−0.301791	−	1.58865i
$653$	−22924.8	−	22924.8i	−1.37384	−	1.37384i	−0.854673	−	0.519167i	$-0.826242\pi$
$653$	−22924.8	−	22924.8i	−1.37384	−	1.37384i	−0.519167	−	0.854673i	$-0.673758\pi$
$654$	−1460.16	+	4739.87i	−0.0873041	+	0.283400i
$655$	22139.6			1.32071
$656$	20733.9	−	8172.42i	1.23403	−	0.486401i
$657$	2683.71			0.159363
$658$	−2670.07	+	8667.40i	−0.158192	+	0.513511i
$659$	−11508.4	−	11508.4i	−0.680276	−	0.680276i	0.279786	−	0.960062i	$-0.409736\pi$
$659$	−11508.4	−	11508.4i	−0.680276	−	0.680276i	−0.960062	+	0.279786i	$0.909736\pi$
$660$	9454.79	−	1796.10i	0.557617	−	0.105929i
$661$	10207.0	−	10207.0i	0.600615	−	0.600615i	−0.339861	−	0.940476i	$-0.610380\pi$
$661$	10207.0	−	10207.0i	0.600615	−	0.600615i	0.940476	+	0.339861i	$0.110380\pi$
$662$	−19986.2	+	10572.3i	−1.17339	+	0.620703i
$663$		−	10826.2i		−	0.634171i
$664$	−444.405	+	3983.42i	−0.0259733	+	0.232811i
$665$		−	3459.43i		−	0.201731i
$666$	1864.41	+	3524.51i	0.108475	+	0.205063i
$667$	−15744.2	+	15744.2i	−0.913970	+	0.913970i
$668$	3781.42	−	5555.03i	0.219023	−	0.321752i
$669$	8564.13	+	8564.13i	0.494930	+	0.494930i
$670$	−39989.0	−	12319.0i	−2.30583	−	0.710334i
$671$	−9758.76			−0.561450
$672$	5184.42	+	4445.11i	0.297609	+	0.255169i
$673$	−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
$675$	−2922.17	−	2922.17i	−0.166629	−	0.166629i
$676$	−11937.9	+	17537.2i	−0.679215	+	0.997791i
$677$	10411.1	−	10411.1i	0.591035	−	0.591035i	−0.346876	−	0.937911i	$-0.612758\pi$
$677$	10411.1	−	10411.1i	0.591035	−	0.591035i	0.937911	+	0.346876i	$0.112758\pi$
$678$	−834.190	−	1576.97i	−0.0472520	−	0.0893262i
$679$			66.3800i			0.00375174i
$680$	−19433.6	−	2168.09i	−1.09595	−	0.122268i
$681$			6375.90i			0.358774i
$682$	19605.8	−	10371.1i	1.10080	−	0.582303i
$683$	11126.8	−	11126.8i	0.623358	−	0.623358i	−0.323030	−	0.946389i	$-0.604702\pi$
$683$	11126.8	−	11126.8i	0.623358	−	0.623358i	0.946389	+	0.323030i	$0.104702\pi$
$684$	1166.95	−	221.681i	0.0652330	−	0.0123921i
$685$	3624.91	+	3624.91i	0.202191	+	0.202191i
$686$	−5527.53	+	17943.1i	−0.307642	+	0.998644i
$687$	14610.2			0.811371
$688$	17086.7	+	7425.15i	0.946836	+	0.411455i
$689$	22216.5			1.22842
$690$	3105.58	−	10081.1i	0.171344	−	0.556205i
$691$	2722.85	+	2722.85i	0.149901	+	0.149901i	0.778074	−	0.628173i	$-0.216197\pi$
$691$	2722.85	+	2722.85i	0.149901	+	0.149901i	−0.628173	+	0.778074i	$0.716197\pi$
$692$	−950.748	−	5004.81i	−0.0522283	−	0.274934i
$693$	1924.50	−	1924.50i	0.105492	−	0.105492i
$694$	23091.7	−	12215.1i	1.26304	−	0.668126i
$695$			29558.5i			1.61326i
$696$	15836.7	−	12657.7i	0.862481	−	0.689353i
$697$			18046.6i			0.980724i
$698$	13593.4	+	25697.3i	0.737133	+	1.39349i
$699$	2416.18	−	2416.18i	0.130742	−	0.130742i
$700$	12728.8	+	8664.77i	0.687293	+	0.467853i
$701$	2736.38	+	2736.38i	0.147435	+	0.147435i	0.776971	−	0.629536i	$-0.216755\pi$
$701$	2736.38	+	2736.38i	0.147435	+	0.147435i	−0.629536	+	0.776971i	$0.716755\pi$
$702$	−5082.07	−	1565.58i	−0.273234	−	0.0841723i
$703$	−2584.06			−0.138634
$704$	−6573.39	−	10410.8i	−0.351909	−	0.557346i
$705$	−12755.6			−0.681423
$706$	−22310.1	−	6872.85i	−1.18931	−	0.366378i
$707$	−5773.45	−	5773.45i	−0.307119	−	0.307119i
$708$	−8008.77	−	5451.73i	−0.425124	−	0.289390i
$709$	−783.090	+	783.090i	−0.0414803	+	0.0414803i	−0.727543	−	0.686062i	$-0.759338\pi$
$709$	−783.090	+	783.090i	−0.0414803	+	0.0414803i	0.686062	+	0.727543i	$0.259338\pi$
$710$	−6059.98	−	11455.9i	−0.320320	−	0.605539i
$711$		−	1580.98i		−	0.0833915i
$712$	−15912.6	+	12718.4i	−0.837571	+	0.669443i
$713$		−	24311.1i		−	1.27694i
$714$	−4888.19	+	2585.77i	−0.256213	+	0.135532i
$715$	19744.4	−	19744.4i	1.03272	−	1.03272i
$716$	−1367.72	−	7199.79i	−0.0713885	−	0.375795i
$717$	9766.14	+	9766.14i	0.508679	+	0.508679i
$718$	−4020.06	+	13049.6i	−0.208951	+	0.678283i
$719$	−11021.5			−0.571671			−0.285835	−	0.958279i	$-0.592271\pi$
$719$	−11021.5			−0.571671			−0.285835	+	0.958279i	$0.592271\pi$
$720$	−3828.04	+	8809.04i	−0.198143	+	0.455963i
$721$	−9949.27			−0.513912
$722$	5484.90	−	17804.7i	0.282724	−	0.917759i
$723$	9931.14	+	9931.14i	0.510848	+	0.510848i
$724$	−8400.11	+	1595.74i	−0.431198	+	0.0819133i
$725$	32323.3	−	32323.3i	1.65580	−	1.65580i
$726$	5645.75	−	2986.51i	0.288614	−	0.152672i
$727$			21740.4i			1.10909i	0.832154	+	0.554544i	$0.187107\pi$
$727$			21740.4i			1.10909i	−0.832154	+	0.554544i	$0.812893\pi$
$728$	19691.9	+	2196.91i	1.00252	+	0.111844i
$729$		−	729.000i		−	0.0370370i
$730$	−6576.16	−	12431.7i	−0.333417	−	0.630299i
$731$	−10667.5	+	10667.5i	−0.539741	+	0.539741i
$732$	5480.55	−	8051.12i	0.276731	−	0.406527i
$733$	13194.8	+	13194.8i	0.664886	+	0.664886i	0.956528	−	0.291642i	$-0.0942015\pi$
$733$	13194.8	+	13194.8i	0.664886	+	0.664886i	−0.291642	+	0.956528i	$0.594202\pi$
$734$	−6910.04	−	2128.70i	−0.347485	−	0.107046i
$735$	−9247.69			−0.464090
$736$	−13455.8	+	1033.08i	−0.673898	+	0.0517391i
$737$	21334.7			1.06631
$738$	8471.48	+	2609.72i	0.422547	+	0.130170i
$739$	21786.6	+	21786.6i	1.08448	+	1.08448i	0.996085	+	0.0883973i	$0.0281745\pi$
$739$	21786.6	+	21786.6i	1.08448	+	1.08448i	0.0883973	+	0.996085i	$0.471825\pi$
$740$	11758.0	−	17272.9i	0.584099	−	0.858061i
$741$	2436.93	−	2436.93i	0.120813	−	0.120813i
$742$	−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	$-0.0586268\pi$
$744$	−2454.35	+	21999.5i	−0.120942	+	1.08406i
$745$		−	39778.3i		−	1.95619i
$746$	4036.35	−	2135.16i	0.198098	−	0.104790i
$747$	−1127.29	+	1127.29i	−0.0552146	+	0.0552146i
$748$	9794.89	−	1860.70i	0.478792	−	0.0909546i
$749$	19187.5	+	19187.5i	0.936045	+	0.936045i
$750$	−1168.81	+	3794.11i	−0.0569052	+	0.184722i
$751$	−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
$753$	2021.36			0.0978255
$754$	17317.5	−	56214.8i	0.836427	−	2.71515i
$755$	19835.3	+	19835.3i	0.956135	+	0.956135i
$756$	506.936	+	2668.55i	0.0243877	+	0.128379i
$757$	2105.29	−	2105.29i	0.101081	−	0.101081i	−0.654758	−	0.755839i	$-0.727229\pi$
$757$	2105.29	−	2105.29i	0.101081	−	0.101081i	0.755839	+	0.654758i	$0.227229\pi$
$758$	−9200.47	+	4866.89i	−0.440866	+	0.233210i
$759$			5378.41i			0.257212i
$760$	−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	$-0.100292\pi$
$762$	−703.729	−	1330.34i	−0.0334559	−	0.0632458i
$763$	5197.48	−	5197.48i	0.246607	−	0.246607i
$764$	5029.24	+	3423.50i	0.238156	+	0.162118i
$765$	−5499.61	−	5499.61i	−0.259920	−	0.259920i
$766$	−1002.46	−	308.816i	−0.0472849	−	0.0145665i
$767$	−28109.4			−1.32330
$768$	12280.7	+	423.592i	0.577007	+	0.0199024i
$769$	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
$771$	−1962.91	−	1962.91i	−0.0916895	−	0.0916895i
$772$	14449.7	+	9836.22i	0.673650	+	0.458566i
$773$	−21614.3	+	21614.3i	−1.00571	+	1.00571i	−0.00572318	+	0.999984i	$0.501822\pi$
$773$	−21614.3	+	21614.3i	−1.00571	+	1.00571i	−0.999984	+	0.00572318i	$0.998178\pi$
$774$	3464.92	+	6550.16i	0.160910	+	0.304187i
$775$			49911.4i			2.31338i
$776$	74.5722	+	93.3007i	0.00344972	+	0.00431611i
$777$		−	5909.19i		−	0.272833i
$778$	−22832.5	+	12078.0i	−1.05216	+	0.556577i
$779$	−4062.20	+	4062.20i	−0.186834	+	0.186834i
$780$	5200.89	+	27377.9i	0.238746	+	1.25678i
$781$	4672.48	+	4672.48i	0.214077	+	0.214077i
$782$	3217.29	−	10443.7i	0.147123	−	0.477580i
$783$	8063.76			0.368040
$784$	4338.46	+	11006.9i	0.197634	+	0.501408i
$785$	−25157.8			−1.14385
$786$	3316.76	−	10766.6i	0.150515	−	0.488592i
$787$	−20949.4	−	20949.4i	−0.948874	−	0.948874i	0.0498808	−	0.998755i	$-0.484116\pi$
$787$	−20949.4	−	20949.4i	−0.948874	−	0.948874i	−0.998755	+	0.0498808i	$0.984116\pi$
$788$	927.120	−	176.122i	0.0419128	−	0.00796204i
$789$	7377.21	−	7377.21i	0.332871	−	0.332871i
$790$	−7323.55	+	3874.03i	−0.329823	+	0.174471i
$791$			2643.94i			0.118847i
$792$	542.982	−	4867.01i	0.0243611	−	0.218361i
$793$		−	28258.1i		−	1.26541i
$794$	−434.584	−	821.548i	−0.0194242	−	0.0367199i
$795$	11285.8	−	11285.8i	0.503478	−	0.503478i
$796$	−7806.83	+	11468.5i	−0.347620	+	0.510666i
$797$	1576.38	+	1576.38i	0.0700603	+	0.0700603i	0.741269	−	0.671208i	$-0.234224\pi$
$797$	1576.38	+	1576.38i	0.0700603	+	0.0700603i	−0.671208	+	0.741269i	$0.734224\pi$
$798$	−1682.35	−	518.263i	−0.0746297	−	0.0229904i
$799$	−13214.4			−0.585097
$800$	27625.2	−	2120.95i	1.22087	−	0.0937336i
$801$	−8102.44			−0.357410
$802$	−323.329	−	99.6044i	−0.0142358	−	0.00438548i
$803$	5070.48	+	5070.48i	0.222831	+	0.222831i
$804$	−11981.6	+	17601.4i	−0.525571	+	0.772082i
$805$	−11054.4	+	11054.4i	−0.483995	+	0.483995i
$806$	30031.2	+	56771.7i	1.31241	+	2.48101i
$807$		−	16009.1i		−	0.698322i
$808$	−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	$-0.0563388\pi$
$810$	−3376.94	+	1786.34i	−0.146486	+	0.0774885i
$811$	20649.6	−	20649.6i	0.894090	−	0.894090i	−0.100816	−	0.994905i	$-0.532145\pi$
$811$	20649.6	−	20649.6i	0.894090	−	0.894090i	0.994905	+	0.100816i	$0.0321452\pi$
$812$	−29517.9	+	5607.42i	−1.27571	+	0.242342i
$813$	−16985.6	−	16985.6i	−0.732732	−	0.732732i
$814$	−3136.53	+	10181.6i	−0.135056	+	0.438408i
$815$	−56114.6			−2.41179
$816$	−3965.74	+	9125.91i	−0.170133	+	0.391508i
$817$	−4802.38			−0.205647
$818$	522.067	−	1694.70i	0.0223150	−	0.0724373i
$819$	5572.71	+	5572.71i	0.237761	+	0.237761i
$820$	−8669.55	−	45637.2i	−0.369212	−	1.94356i
$821$	13405.1	−	13405.1i	0.569844	−	0.569844i	−0.362240	−	0.932085i	$-0.617988\pi$
$821$	13405.1	−	13405.1i	0.569844	−	0.569844i	0.932085	+	0.362240i	$0.117988\pi$
$822$	2305.88	−	1219.77i	0.0978426	−	0.0517571i
$823$		−	17203.4i		−	0.728643i	−0.931273	−	0.364321i	$-0.881301\pi$
$823$		−	17203.4i		−	0.728643i	0.931273	−	0.364321i	$-0.118699\pi$
$824$	−13984.3	+	11177.2i	−0.591219	+	0.472542i
$825$		−	11042.0i		−	0.465981i
$826$	6713.74	+	12691.8i	0.282810	+	0.534630i
$827$	−11127.2	+	11127.2i	−0.467872	+	0.467872i	−0.901224	−	0.433353i	$-0.857330\pi$
$827$	−11127.2	+	11127.2i	−0.467872	+	0.467872i	0.433353	+	0.901224i	$0.357330\pi$
$828$	−4437.27	−	3020.54i	−0.186239	−	0.126776i
$829$	−5752.09	−	5752.09i	−0.240987	−	0.240987i	0.576271	−	0.817259i	$-0.304507\pi$
$829$	−5752.09	−	5752.09i	−0.240987	−	0.240987i	−0.817259	+	0.576271i	$0.804507\pi$
$830$	7984.23	+	2459.61i	0.333899	+	0.102861i
$831$	−19307.1			−0.805964
$832$	30146.1	−	19034.3i	1.25617	−	0.793145i
$833$	−9580.34			−0.398486
$834$	14374.5	+	4428.21i	0.596821	+	0.183856i
$835$	−9904.39	−	9904.39i	−0.410486	−	0.410486i
$836$	2623.61	+	1785.94i	0.108540	+	0.0738853i
$837$	−6225.75	+	6225.75i	−0.257101	+	0.257101i
$838$	−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	$-0.392844\pi$
$840$	11119.3	−	8887.30i	0.456729	−	0.365049i
$841$			64807.5i			2.65724i
$842$	38081.7	−	20144.6i	1.55865	−	0.824499i
$843$	7070.47	−	7070.47i	0.288873	−	0.288873i
$844$	−772.585	−	4066.95i	−0.0315089	−	0.165865i
$845$	31268.1	+	31268.1i	1.27296	+	1.27296i
$846$	−1910.93	+	6203.14i	−0.0776587	+	0.252090i
$847$	−9465.66			−0.383995
$848$	−18727.3	−	8138.10i	−0.758371	−	0.329556i
$849$	−26483.5			−1.07057
$850$	−6605.20	+	21441.3i	−0.266537	+	0.865213i
$851$	8257.21	+	8257.21i	0.332613	+	0.332613i
$852$	−6478.95	+	1230.78i	−0.260522	+	0.0494906i
$853$	−27266.2	+	27266.2i	−1.09446	+	1.09446i	−0.0994157	+	0.995046i	$0.531697\pi$
$853$	−27266.2	+	27266.2i	−1.09446	+	1.09446i	−0.995046	+	0.0994157i	$0.968303\pi$
$854$	−12758.9	+	6749.24i	−0.511243	+	0.270438i
$855$		−	2475.87i		−	0.0990326i
$856$	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	$-0.195840\pi$
$858$	−6643.90	−	12559.8i	−0.264358	−	0.499747i
$859$	17255.5	−	17255.5i	0.685388	−	0.685388i	−0.275821	−	0.961209i	$-0.588950\pi$
$859$	17255.5	−	17255.5i	0.685388	−	0.685388i	0.961209	+	0.275821i	$0.0889496\pi$
$860$	21851.8	−	32101.0i	0.866442	−	1.27283i
$861$	−9289.36	−	9289.36i	−0.367689	−	0.367689i
$862$	20399.9	+	6284.39i	0.806061	+	0.248314i
$863$	39885.9			1.57327			0.786635	−	0.617418i	$-0.211821\pi$
$863$	39885.9			1.57327			0.786635	+	0.617418i	$0.211821\pi$
$864$	3710.42	+	3181.30i	0.146101	+	0.125266i
$865$	−10618.5			−0.417388
$866$	15175.5	+	4674.95i	0.595478	+	0.183443i
$867$	4724.61	+	4724.61i	0.185071	+	0.185071i
$868$	18460.5	−	27119.1i	0.721877	−	1.06046i
$869$	2987.03	−	2987.03i	0.116603	−	0.116603i
$870$	−19759.4	−	37353.7i	−0.770009	−	1.45564i
$871$			61778.0i			2.40329i
$872$	1466.43	−	13144.3i	0.0569489	−	0.510460i
$873$			47.5072i			0.00184178i
$874$	3075.03	−	1626.64i	0.119010	−	0.0629540i
$875$	4160.41	−	4160.41i	0.160740	−	0.160740i
$876$	−7030.82	+	1335.62i	−0.271175	+	0.0515142i
$877$	8855.51	+	8855.51i	0.340968	+	0.340968i	0.856731	−	0.515763i	$-0.172491\pi$
$877$	8855.51	+	8855.51i	0.340968	+	0.340968i	−0.515763	+	0.856731i	$0.672491\pi$
$878$	−5994.59	+	19459.2i	−0.230419	+	0.747969i
$879$	10429.4			0.400200
$880$	−23875.9	+	9410.88i	−0.914611	+	0.360501i
$881$	−43343.8			−1.65753			−0.828767	−	0.559593i	$-0.810957\pi$
$881$	−43343.8			−1.65753			−0.828767	+	0.559593i	$0.810957\pi$
$882$	−1385.41	+	4497.22i	−0.0528903	+	0.171689i
$883$	11229.3	+	11229.3i	0.427968	+	0.427968i	0.887936	−	0.459968i	$-0.152139\pi$
$883$	11229.3	+	11229.3i	0.427968	+	0.427968i	−0.459968	+	0.887936i	$0.652139\pi$
$884$	5387.97	+	28362.7i	0.204997	+	1.07912i
$885$	−14279.3	+	14279.3i	−0.542366	+	0.542366i
$886$	−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	$0.753782\pi$
$888$	−6638.47	−	8305.69i	−0.250870	−	0.313875i
$889$			2230.45i			0.0841473i
$890$	19854.2	+	37532.8i	0.747770	+	1.41360i
$891$	1377.34	−	1377.34i	0.0517874	−	0.0517874i
$892$	−26698.6	−	18174.3i	−1.00217	−	0.682197i
$893$	−2974.49	−	2974.49i	−0.111464	−	0.111464i
$894$	−19344.5	−	5959.25i	−0.723688	−	0.222939i
$895$	−15275.5			−0.570508
$896$	−15794.5	−	9065.19i	−0.588902	−	0.337998i
$897$	−15574.1			−0.579714
$898$	3309.98	+	1019.67i	0.123002	+	0.0378918i
$899$	−68865.5	−	68865.5i	−2.55483	−	2.55483i
$900$	9109.85	+	6201.25i	0.337402	+	0.229676i
$901$	11691.7	−	11691.7i	0.432306	−	0.432306i
$902$	11075.0	+	20936.3i	0.408820	+	0.772842i
$903$		−	10982.0i		−	0.404715i
$904$	2970.25	+	3716.21i	0.109280	+	0.136725i
$905$			17822.2i			0.654618i
$906$	12617.6	−	6674.51i	0.462685	−	0.244752i
$907$	14588.0	−	14588.0i	0.534053	−	0.534053i	−0.387723	−	0.921776i	$-0.626738\pi$
$907$	14588.0	−	14588.0i	0.534053	−	0.534053i	0.921776	+	0.387723i	$0.126738\pi$
$908$	−3173.14	−	16703.7i	−0.115974	−	0.610497i
$909$	−4131.98	−	4131.98i	−0.150769	−	0.150769i
$910$	12159.0	−	39469.8i	0.442932	−	1.43781i
$911$	50418.8			1.83365			0.916823	−	0.399295i	$-0.130745\pi$
$911$	50418.8			1.83365			0.916823	+	0.399295i	$0.130745\pi$
$912$	−2946.86	+	1161.53i	−0.106996	+	0.0421733i
$913$	−4259.69			−0.154409
$914$	−9311.61	+	30226.7i	−0.336981	+	1.09388i
$915$	−14354.8	−	14354.8i	−0.518640	−	0.518640i
$916$	−38275.9	+	7271.14i	−1.38064	+	0.262277i
$917$	−11806.1	+	11806.1i	−0.425160	+	0.425160i
$918$	−3498.41	+	1850.60i	−0.125779	+	0.0665346i
$919$		−	53290.4i		−	1.91283i	−0.292018	−	0.956413i	$-0.594327\pi$
$919$		−	53290.4i		−	1.91283i	0.292018	−	0.956413i	$-0.405673\pi$
$920$	−3118.90	+	27956.2i	−0.111769	+	1.00184i
$921$			12763.9i			0.456662i
$922$	−21200.4	−	40077.8i	−0.757266	−	1.43155i
$923$	−13529.9	+	13529.9i	−0.482495	+	0.482495i
$924$	−4084.06	+	5999.62i	−0.145407	+	0.213607i
$925$	−16952.3	−	16952.3i	−0.602581	−	0.602581i
$926$	8145.35	+	2509.25i	0.289064	+	0.0890488i
$927$	−7120.55			−0.252287
$928$	−35189.6	+	41042.4i	−1.24478	+	1.45181i
$929$	44859.2			1.58427			0.792133	−	0.610349i	$-0.208971\pi$
$929$	44859.2			1.58427			0.792133	+	0.610349i	$0.208971\pi$
$930$	44095.0	+	13583.9i	1.55477	+	0.478960i
$931$	−2156.48	−	2156.48i	−0.0759140	−	0.0759140i
$932$	−5127.47	+	7532.43i	−0.180210	+	0.264735i
$933$	9560.97	−	9560.97i	0.335490	−	0.335490i
$934$	−1578.43	−	2983.91i	−0.0552976	−	0.104536i
$935$		−	20781.4i		−	0.726872i
$936$	14093.2	+	1572.29i	0.492149	+	0.0549060i
$937$			22463.9i			0.783204i	0.920135	+	0.391602i	$0.128079\pi$
$937$			22463.9i			0.783204i	−0.920135	+	0.391602i	$0.871921\pi$
$938$	27893.6	−	14755.2i	0.970958	−	0.513620i
$939$	−11110.6	+	11110.6i	−0.386136	+	0.386136i
$940$	33417.3	−	6348.17i	1.15952	−	0.220271i
$941$	20653.7	+	20653.7i	0.715507	+	0.715507i	0.967682	−	0.252175i	$-0.0811458\pi$
$941$	20653.7	+	20653.7i	0.715507	+	0.715507i	−0.252175	+	0.967682i	$0.581146\pi$
$942$	−3768.92	+	12234.4i	−0.130359	+	0.423162i
$943$	25961.0			0.896507
$944$	23694.7	+	10296.7i	0.816946	+	0.355010i
$945$	5661.77			0.194897
$946$	−5829.11	+	18922.0i	−0.200339	+	0.650326i
$947$	33123.2	+	33123.2i	1.13660	+	1.13660i	0.989055	+	0.147544i	$0.0471368\pi$
$947$	33123.2	+	33123.2i	1.13660	+	1.13660i	0.147544	+	0.989055i	$0.452863\pi$
$948$	786.818	+	4141.87i	0.0269564	+	0.141901i
$949$	−14682.4	+	14682.4i	−0.502224	+	0.502224i
$950$	−6313.12	+	3339.53i	−0.215605	+	0.114051i
$951$			4198.22i			0.143151i
$952$	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	$-0.0591546\pi$
$954$	−3797.62	−	7179.10i	−0.128881	−	0.243639i
$955$	8966.93	−	8966.93i	0.303836	−	0.303836i
$956$	−30445.9	−	20725.1i	−1.03001	−	0.701147i
$957$	15235.3	+	15235.3i	0.514616	+	0.514616i
$958$	28570.0	+	8801.25i	0.963522	+	0.296822i
$959$	−3866.02			−0.130178
$960$	5644.69	−	24983.2i	0.189773	−	0.839926i
$961$	76546.3			2.56944
$962$	−29482.4	−	9082.33i	−0.988099	−	0.304393i
$963$	13732.3	+	13732.3i	0.459518	+	0.459518i
$964$	−30960.2	−	21075.2i	−1.03440	−	0.704137i
$965$	25763.3	−	25763.3i	0.859430	−	0.859430i
$966$	3719.76	+	7031.91i	0.123894	+	0.234211i
$967$		−	6501.58i		−	0.216212i	−0.994139	−	0.108106i	$-0.965521\pi$
$967$		−	6501.58i		−	0.216212i	0.994139	−	0.108106i	$-0.0344786\pi$
$968$	−13304.5	+	10633.9i	−0.441759	+	0.353084i
$969$		−	2564.93i		−	0.0850333i
$970$	220.067	−	116.412i	0.00728446	−	0.00385335i
$971$	−16761.7	+	16761.7i	−0.553975	+	0.553975i	−0.927586	−	0.373611i	$-0.878120\pi$
$971$	−16761.7	+	16761.7i	−0.553975	+	0.553975i	0.373611	+	0.927586i	$0.378120\pi$
$972$	362.807	+	1909.84i	0.0119723	+	0.0630229i
$973$	−15762.3	−	15762.3i	−0.519338	−	0.519338i
$974$	1314.93	−	4268.43i	0.0432578	−	0.140420i
$975$	31974.0			1.05024
$976$	−10351.2	+	23820.0i	−0.339480	+	0.781208i
$977$	−7407.34			−0.242561			−0.121280	−	0.992618i	$-0.538700\pi$
$977$	−7407.34			−0.242561			−0.121280	+	0.992618i	$0.538700\pi$
$978$	−8406.61	+	27288.9i	−0.274861	+	0.892233i
$979$	−15308.4	−	15308.4i	−0.499753	−	0.499753i
$980$	24227.2	−	4602.37i	0.789705	−	0.150018i
$981$	3719.76	−	3719.76i	0.121063	−	0.121063i
$982$	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	$-0.196591\pi$
$984$	−23492.5	−	2620.91i	−0.761092	−	0.0849102i
$985$		−	1967.04i		−	0.0636294i
$986$	−20470.2	−	38697.3i	−0.661160	−	1.24987i
$987$	6802.01	−	6802.01i	0.219362	−	0.219362i
$988$	−5171.49	+	7597.10i	−0.166525	+	0.244631i
$989$	15345.7	+	15345.7i	0.493392	+	0.493392i
$990$	−9755.27	−	3005.20i	−0.313174	−	0.0964763i
$991$	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
$993$	23981.7			0.766402
$994$	9340.48	+	2877.42i	0.298050	+	0.0918172i
$995$	20447.9	+	20447.9i	0.651498	+	0.651498i
$996$	2392.26	−	3514.31i	0.0761060	−	0.111802i
$997$	−22390.7	+	22390.7i	−0.711255	+	0.711255i	−0.966798	−	0.255543i	$-0.917746\pi$
$997$	−22390.7	+	22390.7i	−0.711255	+	0.711255i	0.255543	+	0.966798i	$0.417746\pi$
$998$	−22336.5	−	42225.4i	−0.708467	−	1.33930i
$999$		−	4229.12i		−	0.133937i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.12	✓	24	1.1	even	1	trivial
48.4.j.a.37.12	yes	24	16.5	even	4	inner
144.4.k.b.37.1		24	48.5	odd	4
144.4.k.b.109.1		24	3.2	odd	2
192.4.j.a.49.12		24	16.11	odd	4
192.4.j.a.145.12		24	4.3	odd	2
384.4.j.a.97.6		24	16.3	odd	4
384.4.j.a.289.6		24	8.3	odd	2
384.4.j.b.97.7		24	16.13	even	4
384.4.j.b.289.7		24	8.5	even	2
576.4.k.b.145.2		24	12.11	even	2
576.4.k.b.433.2		24	48.11	even	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.70307 + 0.832707i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(6.61320 + 4.50173i) q^{4} +(11.7911 - 11.7911i) q^{5} +(-3.96764 - 7.50052i) q^{6} +12.5754i q^{7} +(14.1273 + 17.6754i) q^{8} +9.00000i q^{9} +(41.6906 - 22.0536i) q^{10} +(-17.0042 + 17.0042i) q^{11} +(-4.47910 - 23.5783i) q^{12} +(-49.2384 - 49.2384i) q^{13} +(-10.4716 + 33.9921i) q^{14} -50.0252 q^{15} +(23.4688 + 59.5417i) q^{16} -51.8247 q^{17} +(-7.49436 + 24.3277i) q^{18} +(-11.6655 - 11.6655i) q^{19} +(131.057 - 24.8964i) q^{20} +(26.6763 - 26.6763i) q^{21} +(-60.1231 + 31.8041i) q^{22} +74.5524i q^{23} +(7.52650 - 67.4637i) q^{24} -153.058i q^{25} +(-92.0939 - 174.096i) q^{26} +(19.0919 - 19.0919i) q^{27} +(-56.6109 + 83.1633i) q^{28} +(211.183 + 211.183i) q^{29} +(-135.222 - 41.6564i) q^{30} -326.094 q^{31} +(13.8571 + 180.488i) q^{32} +72.1427 q^{33} +(-140.086 - 43.1547i) q^{34} +(148.277 + 148.277i) q^{35} +(-40.5156 + 59.5188i) q^{36} +(110.757 - 110.757i) q^{37} +(-21.8187 - 41.2465i) q^{38} +208.901i q^{39} +(374.988 + 41.8350i) q^{40} -348.225i q^{41} +(94.3217 - 49.8945i) q^{42} +(205.838 - 205.838i) q^{43} +(-189.000 + 35.9038i) q^{44} +(106.120 + 106.120i) q^{45} +(-62.0803 + 201.521i) q^{46} +254.983 q^{47} +(76.5222 - 176.092i) q^{48} +184.861 q^{49} +(127.453 - 413.728i) q^{50} +(109.937 + 109.937i) q^{51} +(-103.965 - 547.282i) q^{52} +(-225.602 + 225.602i) q^{53} +(67.5047 - 35.7088i) q^{54} +400.995i q^{55} +(-222.274 + 177.656i) q^{56} +49.4924i q^{57} +(394.989 + 746.696i) q^{58} +(285.442 - 285.442i) q^{59} +(-330.827 - 225.200i) q^{60} +(286.952 + 286.952i) q^{61} +(-881.456 - 271.541i) q^{62} -113.178 q^{63} +(-112.837 + 499.411i) q^{64} -1161.15 q^{65} +(195.007 + 60.0737i) q^{66} +(-627.335 - 627.335i) q^{67} +(-342.727 - 233.301i) q^{68} +(158.150 - 158.150i) q^{69} +(277.332 + 524.274i) q^{70} -274.784i q^{71} +(-159.078 + 127.146i) q^{72} -298.190i q^{73} +(391.612 - 207.156i) q^{74} +(-324.686 + 324.686i) q^{75} +(-24.6312 - 129.661i) q^{76} +(-213.834 - 213.834i) q^{77} +(-173.953 + 564.674i) q^{78} -175.664 q^{79} +(978.782 + 425.338i) q^{80} -81.0000 q^{81} +(289.969 - 941.276i) q^{82} +(125.254 + 125.254i) q^{83} +(296.506 - 56.3262i) q^{84} +(-611.068 + 611.068i) q^{85} +(727.796 - 384.991i) q^{86} -895.973i q^{87} +(-540.779 - 60.3313i) q^{88} +900.271i q^{89} +(198.482 + 375.215i) q^{90} +(619.190 - 619.190i) q^{91} +(-335.615 + 493.030i) q^{92} +(691.750 + 691.750i) q^{93} +(689.237 + 212.326i) q^{94} -275.096 q^{95} +(353.478 - 412.269i) q^{96} +5.27858 q^{97} +(499.691 + 153.935i) q^{98} +(-153.038 - 153.038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29}+ \cdots - 360 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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