LMFDB - Embedded newform 48.4.j.a.37.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(13,48)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			37.12
Character	$\chi$	$=$	48.37
Dual form			48.4.j.a.13.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.70307 - 0.832707i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(6.61320 - 4.50173i) q^{4} +(11.7911 + 11.7911i) q^{5} +(-3.96764 + 7.50052i) q^{6} -12.5754i q^{7} +(14.1273 - 17.6754i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 24 * q - 20 * q^4 + 84 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.998419	+	0.0562056i	$0.0179002\pi$
$5$	11.7911	+	11.7911i	1.05462	+	1.05462i	0.0562056	+	0.998419i	$0.482100\pi$
$6$	−3.96764	+	7.50052i	−0.269964	+	0.510346i
$7$		−	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
$9$		−	9.00000i		−	0.333333i
$10$	41.6906	+	22.0536i	1.31837	+	0.697396i
$11$	−17.0042	−	17.0042i	−0.466087	−	0.466087i	0.434557	−	0.900644i	$-0.356905\pi$
$11$	−17.0042	−	17.0042i	−0.466087	−	0.466087i	−0.900644	+	0.434557i	$0.856905\pi$
$12$	−4.47910	+	23.5783i	−0.107750	+	0.567206i
$13$	−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
$15$	−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	−0.774018	−	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
$21$	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	$-0.890270\pi$
$23$		−	74.5524i		−	0.675881i	0.941168	−	0.337940i	$-0.109730\pi$
$24$	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	0.469143	−	0.883122i	$-0.344563\pi$
$29$	211.183	−	211.183i	1.35227	−	1.35227i	0.883122	−	0.469143i	$-0.155437\pi$
$30$	−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	0.908973	−	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
$39$		−	208.901i		−	0.857716i
$40$	374.988	−	41.8350i	1.48227	−	0.165367i
$41$			348.225i			1.32643i	0.748430	+	0.663214i	$0.230808\pi$
$41$			348.225i			1.32643i	−0.748430	+	0.663214i	$0.769192\pi$
$42$	94.3217	+	49.8945i	0.346527	+	0.183307i
$43$	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
$45$	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	0.351496	−	0.936189i	$-0.385673\pi$
$53$	−225.602	−	225.602i	−0.584694	−	0.584694i	−0.936189	+	0.351496i	$0.885673\pi$
$54$	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	0.948031	−	0.318177i	$-0.103071\pi$
$59$	285.442	+	285.442i	0.629854	+	0.629854i	−0.318177	+	0.948031i	$0.603071\pi$
$60$	−330.827	+	225.200i	−0.711826	+	0.484554i
$61$	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
$63$	−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	−0.156168	+	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
$69$	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	$0.0737595\pi$
$71$			274.784i			0.459308i	−0.973272	+	0.229654i	$0.926241\pi$
$72$	−159.078	−	127.146i	−0.260383	−	0.208115i
$73$			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
$75$	−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	−0.619418	−	0.785062i	$-0.712631\pi$
$83$	125.254	−	125.254i	0.165644	−	0.165644i	0.785062	+	0.619418i	$0.212631\pi$
$84$	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	$-0.819891\pi$
$89$		−	900.271i		−	1.07223i	0.844145	−	0.536116i	$-0.180109\pi$
$90$	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	0.443812	−	0.896120i	$-0.353626\pi$
$101$	−459.109	−	459.109i	−0.452307	−	0.452307i	−0.896120	+	0.443812i	$0.853626\pi$
$102$	205.622	−	388.712i	0.199604	−	0.377336i
$103$		−	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
$105$			629.085i			0.584690i
$106$	−797.678	−	421.958i	−0.730918	−	0.386643i
$107$	1525.81	+	1525.81i	1.37855	+	1.37855i	0.847067	+	0.531487i	$0.178366\pi$
$107$	1525.81	+	1525.81i	1.37855	+	1.37855i	0.531487	+	0.847067i	$0.321634\pi$
$108$	212.205	+	40.3119i	0.189069	+	0.0359168i
$109$	−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
$111$	−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	−0.320946	−	0.947097i	$-0.604001\pi$
$131$	938.828	−	938.828i	0.626151	−	0.626151i	0.947097	+	0.320946i	$0.104001\pi$
$132$	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	$-0.969440\pi$
$137$		−	307.429i		−	0.191718i	0.995395	−	0.0958592i	$-0.0305598\pi$
$138$	559.182	+	295.798i	0.344933	+	0.182464i
$139$	−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
$141$	−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	0.997540	−	0.0701033i	$-0.0223329\pi$
$149$	1686.80	+	1686.80i	0.927436	+	0.927436i	−0.0701033	+	0.997540i	$0.522333\pi$
$150$	−1148.02	−	607.281i	−0.624902	−	0.330562i
$151$		−	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
$153$			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	−0.924202	−	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
$159$	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	−0.155618	+	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
$165$	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	$0.0623448\pi$
$167$			839.991i			0.389224i	−0.980880	+	0.194612i	$0.937655\pi$
$168$	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	−0.799093	−	0.601208i	$-0.794686\pi$
$173$	−450.278	+	450.278i	−0.197885	+	0.197885i	0.601208	+	0.799093i	$0.294686\pi$
$174$	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	−0.829293	−	0.558814i	$-0.811257\pi$
$179$	−647.759	+	647.759i	−0.270479	+	0.270479i	0.558814	+	0.829293i	$0.311257\pi$
$180$	224.068	−	1179.51i	0.0927836	−	0.488420i
$181$	−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
$183$			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	0.722029	−	0.691862i	$-0.243210\pi$
$197$	83.4121	+	83.4121i	0.0301668	+	0.0301668i	−0.691862	+	0.722029i	$0.743210\pi$
$198$	−286.236	+	541.108i	−0.102737	+	0.194216i
$199$		−	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
$201$		−	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	−0.764274	−	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
$213$	−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	−0.891812	−	0.452406i	$-0.850566\pi$
$227$	−1502.81	+	1502.81i	−0.439407	+	0.439407i	0.452406	+	0.891812i	$0.350566\pi$
$228$	−222.801	−	327.303i	−0.0647166	−	0.0950709i
$229$	−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
$231$		−	907.219i		−	0.258401i
$232$	−749.283	−	6716.19i	−0.212038	−	1.90060i
$233$		−	1139.00i		−	0.320250i	−0.987097	−	0.160125i	$-0.948810\pi$
$233$		−	1139.00i		−	0.320250i	0.987097	−	0.160125i	$-0.0511898\pi$
$234$	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	0.644659	−	0.764470i	$-0.276999\pi$
$251$	−476.440	−	476.440i	−0.119811	−	0.119811i	−0.764470	+	0.644659i	$0.776999\pi$
$252$	−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	$-0.866337\pi$
$263$		−	3477.65i		−	0.815365i	0.913124	−	0.407683i	$-0.133663\pi$
$264$	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	−0.135510	−	0.990776i	$-0.543267\pi$
$269$	3773.37	−	3773.37i	0.855266	−	0.855266i	0.990776	+	0.135510i	$0.0432673\pi$
$270$	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	0.999918	−	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
$279$			2934.85i			0.629766i
$280$	−526.090	−	4715.60i	−0.112285	−	1.00647i
$281$		−	3333.05i		−	0.707592i	−0.935323	−	0.353796i	$-0.884891\pi$
$281$		−	3333.05i		−	0.707592i	0.935323	−	0.353796i	$-0.115109\pi$
$282$	−1011.68	+	1912.50i	−0.213634	+	0.403858i
$283$	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
$285$	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	0.418208	−	0.908351i	$-0.362658\pi$
$293$	−2458.24	−	2458.24i	−0.490143	−	0.490143i	−0.908351	+	0.418208i	$0.862658\pi$
$294$	−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	−0.929107	−	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
$309$	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	$-0.865218\pi$
$311$		−	4507.09i		−	0.821779i	0.911685	−	0.410890i	$-0.134782\pi$
$312$	−3692.40	−	2951.21i	−0.670003	−	0.535511i
$313$			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
$315$	−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	−0.789314	−	0.613990i	$-0.789563\pi$
$317$	−989.530	+	989.530i	−0.175323	+	0.175323i	0.613990	+	0.789314i	$0.289563\pi$
$318$	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	0.0595765	−	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
$333$	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	0.999946	+	0.0104158i	$0.00331552\pi$
$347$	6530.87	+	6530.87i	1.01036	+	1.01036i	0.0104158	+	0.999946i	$0.496684\pi$
$348$	4033.43	+	5925.25i	0.621307	+	0.912721i
$349$	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
$351$	−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	$-0.884525\pi$
$359$		−	4827.70i		−	0.709738i	0.934916	−	0.354869i	$-0.115475\pi$
$360$	−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	0.781887	−	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
$375$		−	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	0.508433	−	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
$381$	−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	0.147403	−	0.989077i	$-0.452909\pi$
$389$	−6457.55	−	6457.55i	−0.841673	−	0.841673i	−0.989077	+	0.147403i	$0.952909\pi$
$390$	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	−0.721641	−	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
$399$	−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	$0.0120663\pi$
$409$			626.952i			0.0757965i	−0.999282	+	0.0378983i	$0.987934\pi$
$410$	−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	−0.935130	−	0.354304i	$-0.884718\pi$
$419$	−4981.58	+	4981.58i	−0.580826	+	0.580826i	0.354304	+	0.935130i	$0.384718\pi$
$420$	2831.97	+	4160.27i	0.329015	+	0.483334i
$421$	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
$423$		−	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	$-0.872016\pi$
$439$		−	7198.92i		−	0.782656i	0.920251	−	0.391328i	$-0.127984\pi$
$440$	−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	0.341217	−	0.939984i	$-0.389161\pi$
$443$	−5582.95	−	5582.95i	−0.598767	−	0.598767i	−0.939984	+	0.341217i	$0.889161\pi$
$444$	−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	$-0.806049\pi$
$457$		−	11182.3i		−	1.14461i	0.820040	−	0.572307i	$-0.193951\pi$
$458$	−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	−0.157670	+	0.987492i	$0.550398\pi$
$461$	−11334.9	+	11334.9i	−1.14516	+	1.14516i	−0.987492	+	0.157670i	$0.949602\pi$
$462$	−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	−0.747681	−	0.664058i	$-0.768833\pi$
$467$	−843.917	+	843.917i	−0.0836228	+	0.0836228i	0.664058	+	0.747681i	$0.268833\pi$
$468$	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	$0.0234061\pi$
$487$			1579.10i			0.146932i	−0.997298	+	0.0734661i	$0.976594\pi$
$488$	−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	0.982318	−	0.187222i	$-0.0599485\pi$
$491$	8650.50	+	8650.50i	0.795095	+	0.795095i	−0.187222	+	0.982318i	$0.559948\pi$
$492$	−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	−0.0741168	+	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
$501$	−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	$-0.953417\pi$
$503$		−	3290.09i		−	0.291646i	0.989311	−	0.145823i	$-0.0465830\pi$
$504$	−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	−0.643864	−	0.765140i	$-0.722670\pi$
$509$	1392.67	−	1392.67i	0.121275	−	0.121275i	0.765140	+	0.643864i	$0.222670\pi$
$510$	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	$0.0157414\pi$
$521$			1175.72i			0.0988661i	−0.998777	+	0.0494331i	$0.984259\pi$
$522$	−6720.27	−	3554.90i	−0.563483	−	0.298073i
$523$	−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
$525$	−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	−0.582702	−	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
$543$	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	−0.743514	−	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
$549$	−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	−0.951838	−	0.306602i	$-0.900808\pi$
$557$	−8482.07	+	8482.07i	−0.645236	+	0.645236i	0.306602	+	0.951838i	$0.400808\pi$
$558$	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	−0.257886	−	0.966175i	$-0.583026\pi$
$563$	9461.78	−	9461.78i	0.708289	−	0.708289i	0.966175	+	0.257886i	$0.0830260\pi$
$564$	−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	$-0.914579\pi$
$569$		−	7197.61i		−	0.530298i	0.964207	−	0.265149i	$-0.0854211\pi$
$570$	1091.48	−	2063.37i	0.0802057	−	0.151623i
$571$	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
$573$	−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	0.834682	−	0.550733i	$-0.185652\pi$
$587$	4038.29	+	4038.29i	0.283949	+	0.283949i	−0.550733	+	0.834682i	$0.685652\pi$
$588$	−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	$-0.922857\pi$
$599$		−	7036.50i		−	0.479973i	0.970776	−	0.239986i	$-0.0771430\pi$
$600$	−10325.9	+	1151.99i	−0.702588	+	0.0783833i
$601$			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
$603$	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	0.630253	−	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
$615$		−	17420.0i		−	1.14218i
$616$	758.688	+	6800.49i	0.0496240	+	0.444804i
$617$		−	26271.5i		−	1.71418i	−0.515164	−	0.857092i	$-0.672269\pi$
$617$		−	26271.5i		−	1.71418i	0.515164	−	0.857092i	$-0.327731\pi$
$618$	5934.21	+	3139.09i	0.386260	+	0.204325i
$619$	−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
$621$	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	$0.185126\pi$
$631$			17415.1i			1.09871i	−0.835590	+	0.549354i	$0.814874\pi$
$632$	−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	−0.251420	−	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
$645$	−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	$-0.957324\pi$
$647$		−	4399.67i		−	0.267340i	0.991026	−	0.133670i	$-0.0426762\pi$
$648$	−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	−0.519167	+	0.854673i	$0.673758\pi$
$653$	−22924.8	+	22924.8i	−1.37384	+	1.37384i	−0.854673	+	0.519167i	$0.826242\pi$
$654$	−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	−0.960062	−	0.279786i	$-0.909736\pi$
$659$	−11508.4	+	11508.4i	−0.680276	+	0.680276i	0.279786	+	0.960062i	$0.409736\pi$
$660$	9454.79	+	1796.10i	0.557617	+	0.105929i
$661$	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
$663$			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	0.937911	−	0.346876i	$-0.112758\pi$
$677$	10411.1	+	10411.1i	0.591035	+	0.591035i	−0.346876	+	0.937911i	$0.612758\pi$
$678$	−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	0.946389	−	0.323030i	$-0.104702\pi$
$683$	11126.8	+	11126.8i	0.623358	+	0.623358i	−0.323030	+	0.946389i	$0.604702\pi$
$684$	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	−0.628173	−	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
$693$	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	−0.629536	−	0.776971i	$-0.716755\pi$
$701$	2736.38	−	2736.38i	0.147435	−	0.147435i	0.776971	+	0.629536i	$0.216755\pi$
$702$	−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	0.686062	−	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
$711$			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	$-0.812893\pi$
$727$		−	21740.4i		−	1.10909i	0.832154	−	0.554544i	$-0.187107\pi$
$728$	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	−0.291642	−	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
$735$	−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	0.0883973	−	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
$741$	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	$0.0586268\pi$
$743$			7418.24i			0.366284i	−0.983086	+	0.183142i	$0.941373\pi$
$744$	−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	0.755839	−	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
$759$		−	5378.41i		−	0.257212i
$760$	−3886.38	+	4862.43i	−0.185492	+	0.232077i
$761$			13011.0i			0.619776i	0.950773	+	0.309888i	$0.100292\pi$
$761$			13011.0i			0.619776i	−0.950773	+	0.309888i	$0.899708\pi$
$762$	−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	−0.999984	−	0.00572318i	$-0.998178\pi$
$773$	−21614.3	−	21614.3i	−1.00571	−	1.00571i	−0.00572318	−	0.999984i	$-0.501822\pi$
$774$	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	−0.998755	−	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
$789$	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	−0.671208	−	0.741269i	$-0.734224\pi$
$797$	1576.38	−	1576.38i	0.0700603	−	0.0700603i	0.741269	+	0.671208i	$0.234224\pi$
$798$	−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	$0.0563388\pi$
$809$			8102.89i			0.352142i	−0.984378	+	0.176071i	$0.943661\pi$
$810$	−3376.94	−	1786.34i	−0.146486	−	0.0774885i
$811$	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
$813$	−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	0.932085	−	0.362240i	$-0.117988\pi$
$821$	13405.1	+	13405.1i	0.569844	+	0.569844i	−0.362240	+	0.932085i	$0.617988\pi$
$822$	2305.88	+	1219.77i	0.0978426	+	0.0517571i
$823$			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
$825$			11042.0i			0.465981i
$826$	6713.74	−	12691.8i	0.282810	−	0.534630i
$827$	−11127.2	−	11127.2i	−0.467872	−	0.467872i	0.433353	−	0.901224i	$-0.357330\pi$
$827$	−11127.2	−	11127.2i	−0.467872	−	0.467872i	−0.901224	+	0.433353i	$0.857330\pi$
$828$	−4437.27	+	3020.54i	−0.186239	+	0.126776i
$829$	−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
$831$	−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	$0.392844\pi$
$839$			45875.9i			1.88774i	−0.330318	+	0.943870i	$0.607156\pi$
$840$	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	−0.995046	−	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
$855$			2475.87i			0.0990326i
$856$	48524.7	−	5413.60i	1.93755	−	0.216160i
$857$			28960.0i			1.15432i	0.816629	+	0.577162i	$0.195840\pi$
$857$			28960.0i			1.15432i	−0.816629	+	0.577162i	$0.804160\pi$
$858$	−6643.90	+	12559.8i	−0.264358	+	0.499747i
$859$	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
$861$	−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	−0.515763	−	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
$879$	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	−0.459968	−	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
$885$	−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	$-0.753782\pi$
$887$		−	36912.9i		−	1.39731i	0.715459	−	0.698655i	$-0.246218\pi$
$888$	−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	0.921776	−	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
$909$	−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	$0.405673\pi$
$919$			53290.4i			1.91283i	−0.292018	+	0.956413i	$0.594327\pi$
$920$	−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	$-0.871921\pi$
$937$		−	22463.9i		−	0.783204i	0.920135	−	0.391602i	$-0.128079\pi$
$938$	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	−0.252175	−	0.967682i	$-0.581146\pi$
$941$	20653.7	−	20653.7i	0.715507	−	0.715507i	0.967682	+	0.252175i	$0.0811458\pi$
$942$	−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	0.147544	−	0.989055i	$-0.452863\pi$
$947$	33123.2	−	33123.2i	1.13660	−	1.13660i	0.989055	−	0.147544i	$-0.0471368\pi$
$948$	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	$0.0591546\pi$
$953$			10871.9i			0.369544i	−0.982781	+	0.184772i	$0.940845\pi$
$954$	−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	$0.0344786\pi$
$967$			6501.58i			0.216212i	−0.994139	+	0.108106i	$0.965521\pi$
$968$	−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	0.373611	−	0.927586i	$-0.378120\pi$
$971$	−16761.7	−	16761.7i	−0.553975	−	0.553975i	−0.927586	+	0.373611i	$0.878120\pi$
$972$	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	$0.196591\pi$
$983$			35694.8i			1.15818i	−0.815265	+	0.579088i	$0.803409\pi$
$984$	−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	0.255543	−	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
$999$			4229.12i			0.133937i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.12	✓	24	16.13	even	4	inner
48.4.j.a.37.12	yes	24	1.1	even	1	trivial
144.4.k.b.37.1		24	3.2	odd	2
144.4.k.b.109.1		24	48.29	odd	4
192.4.j.a.49.12		24	4.3	odd	2
192.4.j.a.145.12		24	16.3	odd	4
384.4.j.a.97.6		24	8.3	odd	2
384.4.j.a.289.6		24	16.11	odd	4
384.4.j.b.97.7		24	8.5	even	2
384.4.j.b.289.7		24	16.5	even	4
576.4.k.b.145.2		24	48.35	even	4
576.4.k.b.433.2		24	12.11	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.70307 - 0.832707i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(6.61320 - 4.50173i) q^{4} +(11.7911 + 11.7911i) q^{5} +(-3.96764 + 7.50052i) q^{6} -12.5754i q^{7} +(14.1273 - 17.6754i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) \) 24 * q - 20 * q^4 + 84 * q^8	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) \) 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

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