LMFDB - Embedded newform 48.4.j.a.13.2

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			13.2
Character	$\chi$	$=$	48.13
Dual form			48.4.j.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24080 + 1.72593i) q^{2} +(2.12132 + 2.12132i) q^{3} +(2.04234 - 7.73491i) q^{4} +(14.6111 - 14.6111i) q^{5} +(-8.41470 - 1.09220i) q^{6} +26.8889i q^{7} +(8.77342 + 20.8573i) q^{8} +9.00000i q^{9} +O(q^{10})$	\(q+(-2.24080 + 1.72593i) q^{2} +(2.12132 + 2.12132i) q^{3} +(2.04234 - 7.73491i) q^{4} +(14.6111 - 14.6111i) q^{5} +(-8.41470 - 1.09220i) q^{6} +26.8889i q^{7} +(8.77342 + 20.8573i) q^{8} +9.00000i q^{9} +(-7.52282 + 57.9584i) q^{10} +(23.1955 - 23.1955i) q^{11} +(20.7407 - 12.0758i) q^{12} +(13.0684 + 13.0684i) q^{13} +(-46.4082 - 60.2525i) q^{14} +61.9898 q^{15} +(-55.6577 - 31.5947i) q^{16} -5.45837 q^{17} +(-15.5334 - 20.1672i) q^{18} +(4.68315 + 4.68315i) q^{19} +(-83.1749 - 142.857i) q^{20} +(-57.0399 + 57.0399i) q^{21} +(-11.9426 + 92.0101i) q^{22} +34.0741i q^{23} +(-25.6338 + 62.8563i) q^{24} -301.971i q^{25} +(-51.8388 - 6.72852i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(207.983 + 54.9163i) q^{28} +(-143.499 - 143.499i) q^{29} +(-138.907 + 106.990i) q^{30} -97.8482 q^{31} +(179.248 - 25.2639i) q^{32} +98.4101 q^{33} +(12.2311 - 9.42076i) q^{34} +(392.877 + 392.877i) q^{35} +(69.6142 + 18.3811i) q^{36} +(-268.672 + 268.672i) q^{37} +(-18.5768 - 2.41121i) q^{38} +55.4446i q^{39} +(432.939 + 176.559i) q^{40} -115.423i q^{41} +(29.3681 - 226.261i) q^{42} +(73.4743 - 73.4743i) q^{43} +(-132.042 - 226.788i) q^{44} +(131.500 + 131.500i) q^{45} +(-58.8094 - 76.3531i) q^{46} -583.126 q^{47} +(-51.0453 - 185.090i) q^{48} -380.010 q^{49} +(521.180 + 676.656i) q^{50} +(-11.5790 - 11.5790i) q^{51} +(127.773 - 74.3928i) q^{52} +(163.300 - 163.300i) q^{53} +(9.82982 - 75.7323i) q^{54} -677.825i q^{55} +(-560.829 + 235.907i) q^{56} +19.8689i q^{57} +(569.220 + 73.8830i) q^{58} +(-45.5102 + 45.5102i) q^{59} +(126.605 - 479.486i) q^{60} +(187.762 + 187.762i) q^{61} +(219.258 - 168.879i) q^{62} -242.000 q^{63} +(-358.054 + 365.980i) q^{64} +381.889 q^{65} +(-220.517 + 169.849i) q^{66} +(-223.276 - 223.276i) q^{67} +(-11.1479 + 42.2200i) q^{68} +(-72.2821 + 72.2821i) q^{69} +(-1558.43 - 202.280i) q^{70} +779.124i q^{71} +(-187.716 + 78.9608i) q^{72} +34.8164i q^{73} +(138.331 - 1065.75i) q^{74} +(640.577 - 640.577i) q^{75} +(45.7883 - 26.6591i) q^{76} +(623.700 + 623.700i) q^{77} +(-95.6934 - 124.240i) q^{78} +234.796 q^{79} +(-1274.86 + 351.588i) q^{80} -81.0000 q^{81} +(199.212 + 258.640i) q^{82} +(34.3162 + 34.3162i) q^{83} +(324.703 + 557.693i) q^{84} +(-79.7531 + 79.7531i) q^{85} +(-37.8296 + 291.452i) q^{86} -608.813i q^{87} +(687.299 + 280.292i) q^{88} -1126.75i q^{89} +(-521.625 - 67.7054i) q^{90} +(-351.395 + 351.395i) q^{91} +(263.560 + 69.5910i) q^{92} +(-207.567 - 207.567i) q^{93} +(1306.67 - 1006.43i) q^{94} +136.852 q^{95} +(433.835 + 326.649i) q^{96} +1339.63 q^{97} +(851.526 - 655.871i) q^{98} +(208.759 + 208.759i) 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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.24080	+	1.72593i	−0.792241	+	0.610208i
$2$	−2.24080	+	1.72593i	−0.792241	+	0.610208i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$4$	2.04234	−	7.73491i	0.255293	−	0.966864i
$5$	14.6111	−	14.6111i	1.30686	−	1.30686i	0.383191	−	0.923669i	$-0.374825\pi$
$5$	14.6111	−	14.6111i	1.30686	−	1.30686i	0.923669	−	0.383191i	$-0.125175\pi$
$6$	−8.41470	−	1.09220i	−0.572547	−	0.0743149i
$7$			26.8889i			1.45186i	0.687768	+	0.725931i	$0.258591\pi$
$7$			26.8889i			1.45186i	−0.687768	+	0.725931i	$0.741409\pi$
$8$	8.77342	+	20.8573i	0.387734	+	0.921771i
$9$			9.00000i			0.333333i
$10$	−7.52282	+	57.9584i	−0.237893	+	1.83281i
$11$	23.1955	−	23.1955i	0.635791	−	0.635791i	−0.313723	−	0.949514i	$-0.601576\pi$
$11$	23.1955	−	23.1955i	0.635791	−	0.635791i	0.949514	+	0.313723i	$0.101576\pi$
$12$	20.7407	−	12.0758i	0.498943	−	0.290498i
$13$	13.0684	+	13.0684i	0.278810	+	0.278810i	0.832634	−	0.553824i	$-0.186832\pi$
$13$	13.0684	+	13.0684i	0.278810	+	0.278810i	−0.553824	+	0.832634i	$0.686832\pi$
$14$	−46.4082	−	60.2525i	−0.885937	−	1.15022i
$15$	61.9898			1.06705
$16$	−55.6577	−	31.5947i	−0.869651	−	0.493667i
$17$	−5.45837			−0.0778735			−0.0389368	−	0.999242i	$-0.512397\pi$
$17$	−5.45837			−0.0778735			−0.0389368	+	0.999242i	$0.512397\pi$
$18$	−15.5334	−	20.1672i	−0.203403	−	0.264080i
$19$	4.68315	+	4.68315i	0.0565467	+	0.0565467i	0.734815	−	0.678268i	$-0.237269\pi$
$19$	4.68315	+	4.68315i	0.0565467	+	0.0565467i	−0.678268	+	0.734815i	$0.737269\pi$
$20$	−83.1749	−	142.857i	−0.929924	−	1.59719i
$21$	−57.0399	+	57.0399i	−0.592720	+	0.592720i
$22$	−11.9426	+	92.0101i	−0.115735	+	0.891665i
$23$			34.0741i			0.308910i	0.988000	+	0.154455i	$0.0493622\pi$
$23$			34.0741i			0.308910i	−0.988000	+	0.154455i	$0.950638\pi$
$24$	−25.6338	+	62.8563i	−0.218020	+	0.534603i
$25$		−	301.971i		−	2.41577i
$26$	−51.8388	−	6.72852i	−0.391017	−	0.0507528i
$27$	−19.0919	+	19.0919i	−0.136083	+	0.136083i
$28$	207.983	+	54.9163i	1.40375	+	0.370650i
$29$	−143.499	−	143.499i	−0.918863	−	0.918863i	0.0780836	−	0.996947i	$-0.475120\pi$
$29$	−143.499	−	143.499i	−0.918863	−	0.918863i	−0.996947	+	0.0780836i	$0.975120\pi$
$30$	−138.907	+	106.990i	−0.845359	+	0.651120i
$31$	−97.8482			−0.566905			−0.283452	−	0.958986i	$-0.591480\pi$
$31$	−97.8482			−0.566905			−0.283452	+	0.958986i	$0.591480\pi$
$32$	179.248	−	25.2639i	0.990213	−	0.139564i
$33$	98.4101			0.519121
$34$	12.2311	−	9.42076i	0.0616946	−	0.0475190i
$35$	392.877	+	392.877i	1.89738	+	1.89738i
$36$	69.6142	+	18.3811i	0.322288	+	0.0850976i
$37$	−268.672	+	268.672i	−1.19377	+	1.19377i	−0.217765	+	0.976001i	$0.569877\pi$
$37$	−268.672	+	268.672i	−1.19377	+	1.19377i	−0.976001	+	0.217765i	$0.930123\pi$
$38$	−18.5768	−	2.41121i	−0.0793039	−	0.0102934i
$39$			55.4446i			0.227647i
$40$	432.939	+	176.559i	1.71134	+	0.697912i
$41$		−	115.423i		−	0.439661i	−0.975538	−	0.219830i	$-0.929450\pi$
$41$		−	115.423i		−	0.439661i	0.975538	−	0.219830i	$-0.0705504\pi$
$42$	29.3681	−	226.261i	0.107895	−	0.831260i
$43$	73.4743	−	73.4743i	0.260575	−	0.260575i	−0.564713	−	0.825288i	$-0.691013\pi$
$43$	73.4743	−	73.4743i	0.260575	−	0.260575i	0.825288	+	0.564713i	$0.191013\pi$
$44$	−132.042	−	226.788i	−0.452410	−	0.777036i
$45$	131.500	+	131.500i	0.435620	+	0.435620i
$46$	−58.8094	−	76.3531i	−0.188500	−	0.244732i
$47$	−583.126			−1.80974			−0.904869	−	0.425690i	$-0.860031\pi$
$47$	−583.126			−1.80974			−0.904869	+	0.425690i	$0.860031\pi$
$48$	−51.0453	−	185.090i	−0.153495	−	0.556572i
$49$	−380.010			−1.10790
$50$	521.180	+	676.656i	1.47412	+	1.91387i
$51$	−11.5790	−	11.5790i	−0.0317917	−	0.0317917i
$52$	127.773	−	74.3928i	0.340749	−	0.198393i
$53$	163.300	−	163.300i	0.423225	−	0.423225i	−0.463087	−	0.886313i	$-0.653258\pi$
$53$	163.300	−	163.300i	0.423225	−	0.423225i	0.886313	+	0.463087i	$0.153258\pi$
$54$	9.82982	−	75.7323i	0.0247716	−	0.190849i
$55$		−	677.825i		−	1.66178i
$56$	−560.829	+	235.907i	−1.33828	+	0.562936i
$57$			19.8689i			0.0461702i
$58$	569.220	+	73.8830i	1.28866	+	0.167264i
$59$	−45.5102	+	45.5102i	−0.100422	+	0.100422i	−0.755533	−	0.655111i	$-0.772622\pi$
$59$	−45.5102	+	45.5102i	−0.100422	+	0.100422i	0.655111	+	0.755533i	$0.272622\pi$
$60$	126.605	−	479.486i	0.272410	−	1.03169i
$61$	187.762	+	187.762i	0.394106	+	0.394106i	0.876148	−	0.482042i	$-0.160105\pi$
$61$	187.762	+	187.762i	0.394106	+	0.394106i	−0.482042	+	0.876148i	$0.660105\pi$
$62$	219.258	−	168.879i	0.449126	−	0.345930i
$63$	−242.000			−0.483954
$64$	−358.054	+	365.980i	−0.699324	+	0.714804i
$65$	381.889			0.728731
$66$	−220.517	+	169.849i	−0.411269	+	0.316772i
$67$	−223.276	−	223.276i	−0.407128	−	0.407128i	0.473608	−	0.880736i	$-0.342951\pi$
$67$	−223.276	−	223.276i	−0.407128	−	0.407128i	−0.880736	+	0.473608i	$0.842951\pi$
$68$	−11.1479	+	42.2200i	−0.0198806	+	0.0752931i
$69$	−72.2821	+	72.2821i	−0.126112	+	0.126112i
$70$	−1558.43	−	202.280i	−2.66098	−	0.345387i
$71$			779.124i			1.30232i	0.758939	+	0.651162i	$0.225718\pi$
$71$			779.124i			1.30232i	−0.758939	+	0.651162i	$0.774282\pi$
$72$	−187.716	+	78.9608i	−0.307257	+	0.129245i
$73$			34.8164i			0.0558212i	0.999610	+	0.0279106i	$0.00888538\pi$
$73$			34.8164i			0.0558212i	−0.999610	+	0.0279106i	$0.991115\pi$
$74$	138.331	−	1065.75i	0.217306	−	1.67420i
$75$	640.577	−	640.577i	0.986233	−	0.986233i
$76$	45.7883	−	26.6591i	0.0691090	−	0.0402370i
$77$	623.700	+	623.700i	0.923081	+	0.923081i
$78$	−95.6934	−	124.240i	−0.138912	−	0.180352i
$79$	234.796			0.334388			0.167194	−	0.985924i	$-0.446529\pi$
$79$	234.796			0.334388			0.167194	+	0.985924i	$0.446529\pi$
$80$	−1274.86	+	351.588i	−1.78167	+	0.491359i
$81$	−81.0000			−0.111111
$82$	199.212	+	258.640i	0.268284	+	0.348317i
$83$	34.3162	+	34.3162i	0.0453819	+	0.0453819i	0.729434	−	0.684052i	$-0.239784\pi$
$83$	34.3162	+	34.3162i	0.0453819	+	0.0453819i	−0.684052	+	0.729434i	$0.739784\pi$
$84$	324.703	+	557.693i	0.421762	+	0.724397i
$85$	−79.7531	+	79.7531i	−0.101770	+	0.101770i
$86$	−37.8296	+	291.452i	−0.0474334	+	0.365443i
$87$		−	608.813i		−	0.750249i
$88$	687.299	+	280.292i	0.832572	+	0.339536i
$89$		−	1126.75i		−	1.34196i	−0.741474	−	0.670982i	$-0.765873\pi$
$89$		−	1126.75i		−	1.34196i	0.741474	−	0.670982i	$-0.234127\pi$
$90$	−521.625	−	67.7054i	−0.610935	−	0.0792975i
$91$	−351.395	+	351.395i	−0.404793	+	0.404793i
$92$	263.560	+	69.5910i	0.298674	+	0.0788627i
$93$	−207.567	−	207.567i	−0.231438	−	0.231438i
$94$	1306.67	−	1006.43i	1.43375	−	1.10432i
$95$	136.852			0.147797
$96$	433.835	+	326.649i	0.461230	+	0.347276i
$97$	1339.63			1.40225			0.701127	−	0.713037i	$-0.252681\pi$
$97$	1339.63			1.40225			0.701127	+	0.713037i	$0.252681\pi$
$98$	851.526	−	655.871i	0.877726	−	0.676050i
$99$	208.759	+	208.759i	0.211930	+	0.211930i
$100$	−2335.72	−	616.728i	−2.33572	−	0.616728i
$101$	−678.522	+	678.522i	−0.668470	+	0.668470i	−0.957362	−	0.288892i	$-0.906713\pi$
$101$	−678.522	+	678.522i	−0.668470	+	0.668470i	0.288892	+	0.957362i	$0.406713\pi$
$102$	45.9306	+	5.96165i	0.0445863	+	0.00578717i
$103$		−	878.610i		−	0.840505i	−0.907407	−	0.420253i	$-0.861941\pi$
$103$		−	878.610i		−	0.840505i	0.907407	−	0.420253i	$-0.138059\pi$
$104$	−157.917	+	387.227i	−0.148895	+	0.365103i
$105$			1666.84i			1.54920i
$106$	−84.0780	+	647.765i	−0.0770413	+	0.593552i
$107$	174.580	−	174.580i	0.157731	−	0.157731i	−0.623829	−	0.781561i	$-0.714424\pi$
$107$	174.580	−	174.580i	0.157731	−	0.157731i	0.781561	+	0.623829i	$0.214424\pi$
$108$	108.682	+	186.666i	0.0968325	+	0.166314i
$109$	1435.56	+	1435.56i	1.26148	+	1.26148i	0.950374	+	0.311110i	$0.100701\pi$
$109$	1435.56	+	1435.56i	1.26148	+	1.26148i	0.311110	+	0.950374i	$0.399299\pi$
$110$	1169.88	+	1518.87i	1.01403	+	1.31653i
$111$	−1139.88			−0.974706
$112$	849.545	−	1496.57i	0.716736	−	1.26261i
$113$	421.516			0.350911			0.175455	−	0.984487i	$-0.443860\pi$
$113$	421.516			0.350911			0.175455	+	0.984487i	$0.443860\pi$
$114$	−34.2923	−	44.5222i	−0.0281734	−	0.0365780i
$115$	497.861	+	497.861i	0.403703	+	0.403703i
$116$	−1403.02	+	816.876i	−1.12299	+	0.653836i
$117$	−117.616	+	117.616i	−0.0929366	+	0.0929366i
$118$	23.4318	−	180.526i	0.0182803	−	0.140837i
$119$		−	146.769i		−	0.113062i
$120$	543.863	+	1292.94i	0.413731	+	0.983573i
$121$			254.939i			0.191539i
$122$	−744.801	−	96.6729i	−0.552714	−	0.0717406i
$123$	244.850	−	244.850i	0.179491	−	0.179491i
$124$	−199.840	+	756.847i	−0.144727	+	0.548120i
$125$	−2585.75	−	2585.75i	−1.85021	−	1.85021i
$126$	542.272	−	417.674i	0.383408	−	0.295312i
$127$	353.404			0.246925			0.123463	−	0.992349i	$-0.460600\pi$
$127$	353.404			0.246925			0.123463	+	0.992349i	$0.460600\pi$
$128$	170.672	−	1438.06i	0.117855	−	0.993031i
$129$	311.725			0.212759
$130$	−855.736	+	659.113i	−0.577331	+	0.444677i
$131$	−1471.55	−	1471.55i	−0.981450	−	0.981450i	0.0183815	−	0.999831i	$-0.494149\pi$
$131$	−1471.55	−	1471.55i	−0.981450	−	0.981450i	−0.999831	+	0.0183815i	$0.994149\pi$
$132$	200.987	−	761.193i	0.132528	−	0.501920i
$133$	−125.924	+	125.924i	−0.0820980	+	0.0820980i
$134$	885.676	+	114.958i	0.570976	+	0.0741110i
$135$			557.908i			0.355682i
$136$	−47.8886	−	113.847i	−0.0301942	−	0.0717816i
$137$		−	348.474i		−	0.217315i	−0.994079	−	0.108657i	$-0.965345\pi$
$137$		−	348.474i		−	0.217315i	0.994079	−	0.108657i	$-0.0346552\pi$
$138$	37.2158	−	286.723i	0.0229567	−	0.176866i
$139$	−1085.54	+	1085.54i	−0.662404	+	0.662404i	−0.955946	−	0.293542i	$-0.905166\pi$
$139$	−1085.54	+	1085.54i	−0.662404	+	0.662404i	0.293542	+	0.955946i	$0.405166\pi$
$140$	3841.26	−	2236.48i	2.31890	−	1.35012i
$141$	−1237.00	−	1237.00i	−0.738823	−	0.738823i
$142$	−1344.71	−	1745.86i	−0.794688	−	1.03175i
$143$	606.257			0.354530
$144$	284.352	−	500.919i	0.164556	−	0.289884i
$145$	−4193.36			−2.40165
$146$	−60.0906	−	78.0165i	−0.0340626	−	0.0442239i
$147$	−806.124	−	806.124i	−0.452299	−	0.452299i
$148$	1529.43	+	2626.87i	0.849449	+	1.45897i
$149$	2136.62	−	2136.62i	1.17476	−	1.17476i	0.193694	−	0.981062i	$-0.437953\pi$
$149$	2136.62	−	2136.62i	1.17476	−	1.17476i	0.981062	−	0.193694i	$-0.0620468\pi$
$150$	−329.813	+	2540.99i	−0.179528	+	1.38314i
$151$			2622.36i			1.41328i	0.707575	+	0.706639i	$0.249789\pi$
$151$			2622.36i			1.41328i	−0.707575	+	0.706639i	$0.750211\pi$
$152$	−56.5906	+	138.765i	−0.0301981	+	0.0740483i
$153$		−	49.1254i		−	0.0259578i
$154$	−2474.05	−	321.124i	−1.29457	−	0.168032i
$155$	−1429.67	+	1429.67i	−0.740866	+	0.740866i
$156$	428.859	+	113.237i	0.220104	+	0.0581167i
$157$	1174.74	+	1174.74i	0.597162	+	0.597162i	0.939556	−	0.342394i	$-0.111238\pi$
$157$	1174.74	+	1174.74i	0.597162	+	0.597162i	−0.342394	+	0.939556i	$0.611238\pi$
$158$	−526.131	+	405.242i	−0.264916	+	0.204046i
$159$	692.822			0.345562
$160$	2249.88	−	2988.15i	1.11168	−	1.47646i
$161$	−916.213			−0.448495
$162$	181.505	−	139.800i	0.0880268	−	0.0678009i
$163$	−1355.60	−	1355.60i	−0.651403	−	0.651403i	0.301928	−	0.953331i	$-0.402370\pi$
$163$	−1355.60	−	1355.60i	−0.651403	−	0.651403i	−0.953331	+	0.301928i	$0.902370\pi$
$164$	−892.788	−	235.734i	−0.425092	−	0.112242i
$165$	1437.88	−	1437.88i	0.678419	−	0.678419i
$166$	−136.123	−	17.6684i	−0.0636458	−	0.00826103i
$167$			2044.59i			0.947398i	0.880687	+	0.473699i	$0.157081\pi$
$167$			2044.59i			0.947398i	−0.880687	+	0.473699i	$0.842919\pi$
$168$	−1690.13	−	689.263i	−0.776170	−	0.316534i
$169$		−	1855.43i		−	0.844530i
$170$	41.0624	−	316.359i	0.0185255	−	0.142727i
$171$	−42.1483	+	42.1483i	−0.0188489	+	0.0188489i
$172$	−418.257	−	718.377i	−0.185418	−	0.318464i
$173$	−408.164	−	408.164i	−0.179376	−	0.179376i	0.611708	−	0.791084i	$-0.290483\pi$
$173$	−408.164	−	408.164i	−0.179376	−	0.179376i	−0.791084	+	0.611708i	$0.790483\pi$
$174$	1050.77	+	1364.23i	0.457808	+	0.594378i
$175$	8119.65			3.50736
$176$	−2023.86	+	558.153i	−0.866786	+	0.239047i
$177$	−193.083			−0.0819946
$178$	1944.68	+	2524.81i	0.818876	+	1.06316i
$179$	1927.19	+	1927.19i	0.804719	+	0.804719i	0.983829	−	0.179110i	$-0.0573217\pi$
$179$	1927.19	+	1927.19i	0.804719	+	0.804719i	−0.179110	+	0.983829i	$0.557322\pi$
$180$	1285.71	−	748.574i	0.532396	−	0.309975i
$181$	−205.719	+	205.719i	−0.0844804	+	0.0844804i	−0.748084	−	0.663604i	$-0.769026\pi$
$181$	−205.719	+	205.719i	−0.0844804	+	0.0844804i	0.663604	+	0.748084i	$0.269026\pi$
$182$	180.922	−	1393.89i	0.0736860	−	0.567702i
$183$			796.607i			0.321786i
$184$	−710.694	+	298.946i	−0.284745	+	0.119775i
$185$			7851.20i			3.12017i
$186$	823.363	+	106.870i	0.324580	+	0.0421295i
$187$	−126.610	+	126.610i	−0.0495113	+	0.0495113i
$188$	−1190.94	+	4510.43i	−0.462013	+	1.74977i
$189$	−513.359	−	513.359i	−0.197573	−	0.197573i
$190$	−306.658	+	236.197i	−0.117091	+	0.0901871i
$191$	−1536.67			−0.582143			−0.291071	−	0.956701i	$-0.594012\pi$
$191$	−1536.67			−0.582143			−0.291071	+	0.956701i	$0.594012\pi$
$192$	−1535.91	+	16.8129i	−0.577316	+	0.00631963i
$193$	127.730			0.0476385			0.0238192	−	0.999716i	$-0.492417\pi$
$193$	127.730			0.0476385			0.0238192	+	0.999716i	$0.492417\pi$
$194$	−3001.83	+	2312.10i	−1.11092	+	0.855666i
$195$	810.109	+	810.109i	0.297503	+	0.297503i
$196$	−776.112	+	2939.35i	−0.282840	+	1.07119i
$197$	2282.46	−	2282.46i	0.825475	−	0.825475i	−0.161412	−	0.986887i	$-0.551605\pi$
$197$	2282.46	−	2282.46i	0.825475	−	0.825475i	0.986887	+	0.161412i	$0.0516049\pi$
$198$	−828.091	−	107.484i	−0.297222	−	0.0385785i
$199$		−	4155.43i		−	1.48026i	−0.672466	−	0.740128i	$-0.734765\pi$
$199$		−	4155.43i		−	1.48026i	0.672466	−	0.740128i	$-0.265235\pi$
$200$	6298.30	−	2649.32i	2.22678	−	0.936675i
$201$		−	947.282i		−	0.332418i
$202$	349.350	−	2691.51i	0.121684	−	0.937495i
$203$	3858.51	−	3858.51i	1.33406	−	1.33406i
$204$	−113.210	+	65.9140i	−0.0388545	+	0.0226221i
$205$	−1686.47	−	1686.47i	−0.574575	−	0.574575i
$206$	1516.42	+	1968.79i	0.512883	+	0.665883i
$207$	−306.667			−0.102970
$208$	−314.465	−	1140.25i	−0.104828	−	0.380106i
$209$	217.256			0.0719038
$210$	−2876.84	−	3735.04i	−0.945337	−	1.22734i
$211$	673.956	+	673.956i	0.219891	+	0.219891i	0.808453	−	0.588561i	$-0.200305\pi$
$211$	673.956	+	673.956i	0.219891	+	0.219891i	−0.588561	+	0.808453i	$0.700305\pi$
$212$	−929.595	−	1596.62i	−0.301155	−	0.517248i
$213$	−1652.77	+	1652.77i	−0.531671	+	0.531671i
$214$	−89.8856	+	692.509i	−0.0287124	+	0.221210i
$215$		−	2147.09i		−	0.681070i
$216$	−565.706	−	230.704i	−0.178201	−	0.0726732i
$217$		−	2631.03i		−	0.823068i
$218$	−5694.47	−	739.125i	−1.76917	−	0.229633i
$219$	−73.8567	+	73.8567i	−0.0227889	+	0.0227889i
$220$	−5242.92	−	1384.35i	−1.60672	−	0.424241i
$221$	−71.3323	−	71.3323i	−0.0217119	−	0.0217119i
$222$	2554.23	−	1967.35i	0.772202	−	0.594773i
$223$	−2979.58			−0.894741			−0.447371	−	0.894349i	$-0.647639\pi$
$223$	−2979.58			−0.894741			−0.447371	+	0.894349i	$0.647639\pi$
$224$	679.316	+	4819.76i	0.202628	+	1.43765i
$225$	2717.74			0.805256
$226$	−944.533	+	727.507i	−0.278006	+	0.214129i
$227$	1929.35	+	1929.35i	0.564120	+	0.564120i	0.930475	−	0.366355i	$-0.119394\pi$
$227$	1929.35	+	1929.35i	0.564120	+	0.564120i	−0.366355	+	0.930475i	$0.619394\pi$
$228$	153.684	+	40.5792i	0.0446403	+	0.0117869i
$229$	3209.50	−	3209.50i	0.926156	−	0.926156i	−0.0712994	−	0.997455i	$-0.522715\pi$
$229$	3209.50	−	3209.50i	0.926156	−	0.926156i	0.997455	+	0.0712994i	$0.0227146\pi$
$230$	−1974.88	−	256.333i	−0.566173	−	0.0734875i
$231$			2646.14i			0.753692i
$232$	1734.02	−	4251.97i	0.490707	−	1.20326i
$233$			294.276i			0.0827412i	0.999144	+	0.0413706i	$0.0131724\pi$
$233$			294.276i			0.0827412i	−0.999144	+	0.0413706i	$0.986828\pi$
$234$	60.5567	−	466.549i	0.0169176	−	0.130339i
$235$	−8520.14	+	8520.14i	−2.36507	+	2.36507i
$236$	259.070	+	444.965i	0.0714577	+	0.122732i
$237$	498.079	+	498.079i	0.136513	+	0.136513i
$238$	253.313	+	328.880i	0.0689911	+	0.0895721i
$239$	−1922.58			−0.520339			−0.260170	−	0.965563i	$-0.583778\pi$
$239$	−1922.58			−0.520339			−0.260170	+	0.965563i	$0.583778\pi$
$240$	−3450.21	−	1958.55i	−0.927958	−	0.526766i
$241$	3843.86			1.02741			0.513703	−	0.857968i	$-0.328273\pi$
$241$	3843.86			1.02741			0.513703	+	0.857968i	$0.328273\pi$
$242$	−440.006	−	571.266i	−0.116879	−	0.151745i
$243$	−171.827	−	171.827i	−0.0453609	−	0.0453609i
$244$	1835.80	−	1068.85i	0.481659	−	0.280434i
$245$	−5552.38	+	5552.38i	−1.44787	+	1.44787i
$246$	−126.065	+	971.251i	−0.0326733	+	0.251727i
$247$			122.403i			0.0315316i
$248$	−858.464	−	2040.85i	−0.219808	−	0.522557i
$249$			145.591i			0.0370542i
$250$	10256.9	+	1331.32i	2.59483	+	0.336800i
$251$	2843.24	−	2843.24i	0.714995	−	0.714995i	−0.252580	−	0.967576i	$-0.581279\pi$
$251$	2843.24	−	2843.24i	0.714995	−	0.714995i	0.967576	+	0.252580i	$0.0812792\pi$
$252$	−494.246	+	1871.85i	−0.123550	+	0.467917i
$253$	790.365	+	790.365i	0.196403	+	0.196403i
$254$	−791.906	+	609.949i	−0.195624	+	0.150676i
$255$	−338.364			−0.0830947
$256$	2099.55	+	3516.97i	0.512586	+	0.858636i
$257$	−666.774			−0.161837			−0.0809187	−	0.996721i	$-0.525785\pi$
$257$	−666.774			−0.161837			−0.0809187	+	0.996721i	$0.525785\pi$
$258$	−698.513	+	538.015i	−0.168556	+	0.129827i
$259$	−7224.27	−	7224.27i	−1.73318	−	1.73318i
$260$	779.949	−	2953.88i	0.186040	−	0.704583i
$261$	1291.49	−	1291.49i	0.306288	−	0.306288i
$262$	5837.23	+	757.655i	1.37643	+	0.178657i
$263$		−	2105.93i		−	0.493753i	−0.969047	−	0.246876i	$-0.920596\pi$
$263$		−	2105.93i		−	0.493753i	0.969047	−	0.246876i	$-0.0794042\pi$
$264$	863.394	+	2052.57i	0.201281	+	0.478511i
$265$		−	4771.99i		−	1.10619i
$266$	64.8346	−	499.508i	0.0149446	−	0.115138i
$267$	2390.19	−	2390.19i	0.547854	−	0.547854i
$268$	−2183.03	+	1271.02i	−0.497574	+	0.289700i
$269$	4501.90	+	4501.90i	1.02039	+	1.02039i	0.999788	+	0.0206059i	$0.00655952\pi$
$269$	4501.90	+	4501.90i	1.02039	+	1.02039i	0.0206059	+	0.999788i	$0.493440\pi$
$270$	−962.910	−	1250.16i	−0.217040	−	0.281786i
$271$	−1153.92			−0.258656			−0.129328	−	0.991602i	$-0.541282\pi$
$271$	−1153.92			−0.258656			−0.129328	+	0.991602i	$0.541282\pi$
$272$	303.800	+	172.456i	0.0677228	+	0.0384436i
$273$	−1490.84			−0.330512
$274$	601.441	+	780.859i	0.132607	+	0.172166i
$275$	−7004.36	−	7004.36i	−1.53592	−	1.53592i
$276$	411.471	+	706.720i	0.0897377	+	0.154129i
$277$	−5285.17	+	5285.17i	−1.14641	+	1.14641i	−0.159156	+	0.987253i	$0.550877\pi$
$277$	−5285.17	+	5285.17i	−1.14641	+	1.14641i	−0.987253	+	0.159156i	$0.949123\pi$
$278$	558.910	−	4306.03i	0.120580	−	0.928987i
$279$		−	880.634i		−	0.188968i
$280$	−4747.48	+	11641.2i	−1.01327	+	2.48463i
$281$			5520.01i			1.17187i	0.810357	+	0.585936i	$0.199273\pi$
$281$			5520.01i			1.17187i	−0.810357	+	0.585936i	$0.800727\pi$
$282$	4906.83	+	636.892i	1.03616	+	0.134491i
$283$	4233.41	−	4233.41i	0.889223	−	0.889223i	−0.105226	−	0.994448i	$-0.533556\pi$
$283$	4233.41	−	4233.41i	0.889223	−	0.889223i	0.994448	+	0.105226i	$0.0335565\pi$
$284$	6026.45	+	1591.24i	1.25917	+	0.332474i
$285$	290.308	+	290.308i	0.0603380	+	0.0603380i
$286$	−1358.50	+	1046.36i	−0.280873	+	0.216337i
$287$	3103.60			0.638326
$288$	227.375	+	1613.23i	0.0465215	+	0.330071i
$289$	−4883.21			−0.993936
$290$	9396.47	−	7237.44i	1.90269	−	1.46551i
$291$	2841.78	+	2841.78i	0.572468	+	0.572468i
$292$	269.302	+	71.1070i	0.0539715	+	0.0142508i
$293$	−1434.65	+	1434.65i	−0.286052	+	0.286052i	−0.835517	−	0.549465i	$-0.814832\pi$
$293$	−1434.65	+	1434.65i	−0.286052	+	0.286052i	0.549465	+	0.835517i	$0.314832\pi$
$294$	3197.67	+	415.048i	0.634326	+	0.0823336i
$295$			1329.91i			0.262476i
$296$	−7960.93	−	3246.60i	−1.56324	−	0.637515i
$297$			885.691i			0.173040i
$298$	−1100.08	+	8475.38i	−0.213845	+	1.64754i
$299$	−445.295	+	445.295i	−0.0861273	+	0.0861273i
$300$	−3646.53	−	6263.08i	−0.701775	−	1.20533i
$301$	1975.64	+	1975.64i	0.378319	+	0.378319i
$302$	−4526.01	−	5876.18i	−0.862393	−	1.11966i
$303$	−2878.73			−0.545803
$304$	−112.691	−	408.616i	−0.0212607	−	0.0770912i
$305$	5486.84			1.03008
$306$	84.7869	+	110.080i	0.0158397	+	0.0205649i
$307$	6589.97	+	6589.97i	1.22511	+	1.22511i	0.965791	+	0.259321i	$0.0834987\pi$
$307$	6589.97	+	6589.97i	1.22511	+	1.22511i	0.259321	+	0.965791i	$0.416501\pi$
$308$	6098.07	−	3550.45i	1.12815	−	0.656837i
$309$	1863.81	−	1863.81i	0.343135	−	0.343135i
$310$	736.095	−	5671.12i	0.134862	−	1.03903i
$311$		−	1906.34i		−	0.347585i	−0.984782	−	0.173792i	$-0.944398\pi$
$311$		−	1906.34i		−	0.347585i	0.984782	−	0.173792i	$-0.0556022\pi$
$312$	−1156.42	+	486.439i	−0.209839	+	0.0882666i
$313$			5657.11i			1.02159i	0.859702	+	0.510797i	$0.170649\pi$
$313$			5657.11i			1.02159i	−0.859702	+	0.510797i	$0.829351\pi$
$314$	−4659.87	−	604.837i	−0.837490	−	0.108704i
$315$	−3535.89	+	3535.89i	−0.632460	+	0.632460i
$316$	479.535	−	1816.13i	0.0853669	−	0.323308i
$317$	587.024	+	587.024i	0.104008	+	0.104008i	0.757196	−	0.653188i	$-0.226569\pi$
$317$	587.024	+	587.024i	0.104008	+	0.104008i	−0.653188	+	0.757196i	$0.726569\pi$
$318$	−1552.47	+	1195.76i	−0.273769	+	0.210865i
$319$	−6657.04			−1.16841
$320$	115.803	+	10579.0i	0.0202300	+	1.84807i
$321$	740.678			0.128787
$322$	2053.05	−	1581.32i	0.355316	−	0.273675i
$323$	−25.5624	−	25.5624i	−0.00440349	−	0.00440349i
$324$	−165.430	+	626.528i	−0.0283659	+	0.107429i
$325$	3946.28	−	3946.28i	0.673540	−	0.673540i
$326$	5377.29	+	697.955i	0.913559	+	0.118577i
$327$			6090.57i			1.03000i
$328$	2407.42	−	1012.66i	0.405266	−	0.170471i
$329$		−	15679.6i		−	2.62749i
$330$	−740.322	+	5703.69i	−0.123495	+	0.951448i
$331$	7738.24	−	7738.24i	1.28499	−	1.28499i	0.347200	−	0.937791i	$-0.387133\pi$
$331$	7738.24	−	7738.24i	1.28499	−	1.28499i	0.937791	−	0.347200i	$-0.112867\pi$
$332$	335.519	−	195.347i	0.0554638	−	0.0322924i
$333$	−2418.04	−	2418.04i	−0.397922	−	0.397922i
$334$	−3528.82	−	4581.52i	−0.578109	−	0.750568i
$335$	−6524.65			−1.06412
$336$	4976.86	−	1372.55i	0.808066	−	0.222853i
$337$	−5948.81			−0.961579			−0.480789	−	0.876836i	$-0.659650\pi$
$337$	−5948.81			−0.961579			−0.480789	+	0.876836i	$0.659650\pi$
$338$	3202.34	+	4157.65i	0.515339	+	0.669072i
$339$	894.171	+	894.171i	0.143259	+	0.143259i
$340$	454.000	+	779.766i	0.0724164	+	0.124379i
$341$	−2269.64	+	2269.64i	−0.360433	+	0.360433i
$342$	21.7009	−	167.191i	0.00343114	−	0.0264346i
$343$		−	995.165i		−	0.156658i
$344$	2177.10	+	887.855i	0.341224	+	0.139157i
$345$			2112.25i			0.329622i
$346$	1619.07	+	210.151i	0.251566	+	0.0326525i
$347$	−4649.48	+	4649.48i	−0.719300	+	0.719300i	−0.968462	−	0.249162i	$-0.919845\pi$
$347$	−4649.48	+	4649.48i	−0.719300	+	0.719300i	0.249162	+	0.968462i	$0.419845\pi$
$348$	−4709.12	−	1243.41i	−0.725388	−	0.191533i
$349$	−2080.00	−	2080.00i	−0.319025	−	0.319025i	0.529367	−	0.848393i	$-0.322429\pi$
$349$	−2080.00	−	2080.00i	−0.319025	−	0.319025i	−0.848393	+	0.529367i	$0.822429\pi$
$350$	−18194.5	+	14013.9i	−2.77868	+	2.14022i
$351$	−499.001			−0.0758824
$352$	3571.73	−	4743.75i	0.540835	−	0.718302i
$353$	3582.84			0.540213			0.270106	−	0.962830i	$-0.412941\pi$
$353$	3582.84			0.540213			0.270106	+	0.962830i	$0.412941\pi$
$354$	432.661	−	333.248i	0.0649595	−	0.0500337i
$355$	11383.9	+	11383.9i	1.70195	+	1.70195i
$356$	−8715.27	−	2301.20i	−1.29750	−	0.342594i
$357$	311.345	−	311.345i	0.0461572	−	0.0461572i
$358$	−7644.63	−	992.249i	−1.12858	−	0.146486i
$359$		−	7283.18i		−	1.07073i	−0.844621	−	0.535364i	$-0.820174\pi$
$359$		−	7283.18i		−	1.07073i	0.844621	−	0.535364i	$-0.179826\pi$
$360$	−1589.03	+	3896.45i	−0.232637	+	0.570447i
$361$		−	6815.14i		−	0.993605i
$362$	105.918	−	816.030i	0.0153783	−	0.118480i
$363$	−540.806	+	540.806i	−0.0781955	+	0.0781955i
$364$	2000.34	+	3435.68i	0.288039	+	0.494721i
$365$	508.707	+	508.707i	0.0729506	+	0.0729506i
$366$	−1374.89	−	1785.03i	−0.196356	−	0.254932i
$367$	−4603.82			−0.654816			−0.327408	−	0.944883i	$-0.606175\pi$
$367$	−4603.82			−0.654816			−0.327408	+	0.944883i	$0.606175\pi$
$368$	1076.56	−	1896.48i	0.152499	−	0.268644i
$369$	1038.81			0.146554
$370$	−13550.6	−	17592.9i	−1.90395	−	2.47193i
$371$	4390.94	+	4390.94i	0.614465	+	0.614465i
$372$	−2029.44	+	1181.59i	−0.282853	+	0.164685i
$373$	−7197.92	+	7197.92i	−0.999180	+	0.999180i	−1.00000		0.000819708i	$-0.999739\pi$
$373$	−7197.92	+	7197.92i	−0.999180	+	0.999180i	0.000819708		1.00000i	$0.499739\pi$
$374$	65.1874	−	502.226i	0.00901273	−	0.0694371i
$375$		−	10970.4i		−	1.51069i
$376$	−5116.01	−	12162.4i	−0.701697	−	1.66816i
$377$		−	3750.60i		−	0.512376i
$378$	2036.35	+	264.312i	0.277087	+	0.0359650i
$379$	2684.91	−	2684.91i	0.363891	−	0.363891i	−0.501352	−	0.865243i	$-0.667164\pi$
$379$	2684.91	−	2684.91i	0.363891	−	0.363891i	0.865243	+	0.501352i	$0.167164\pi$
$380$	279.499	−	1058.54i	0.0377316	−	0.142900i
$381$	749.682	+	749.682i	0.100807	+	0.100807i
$382$	3443.36	−	2652.17i	0.461197	−	0.355228i
$383$	12844.4			1.71363			0.856814	−	0.515625i	$-0.172440\pi$
$383$	12844.4			1.71363			0.856814	+	0.515625i	$0.172440\pi$
$384$	3412.64	−	2688.54i	0.453517	−	0.357289i
$385$	18225.9			2.41268
$386$	−286.218	+	220.453i	−0.0377412	+	0.0290694i
$387$	661.269	+	661.269i	0.0868584	+	0.0868584i
$388$	2735.98	−	10361.9i	0.357985	−	1.35579i
$389$	−1921.42	+	1921.42i	−0.250437	+	0.250437i	−0.821150	−	0.570713i	$-0.806667\pi$
$389$	−1921.42	+	1921.42i	−0.250437	+	0.250437i	0.570713	+	0.821150i	$0.306667\pi$
$390$	−3213.48	−	417.100i	−0.417233	−	0.0541556i
$391$		−	185.989i		−	0.0240560i
$392$	−3333.99	−	7925.99i	−0.429571	−	1.02123i
$393$		−	6243.26i		−	0.801350i
$394$	−1175.17	+	9053.89i	−0.150264	+	1.15769i
$395$	3430.64	−	3430.64i	0.436999	−	0.436999i
$396$	2041.09	−	1188.38i	0.259012	−	0.150803i
$397$	6960.80	+	6960.80i	0.879982	+	0.879982i	0.993532	−	0.113551i	$-0.0362224\pi$
$397$	6960.80	+	6960.80i	0.879982	+	0.879982i	−0.113551	+	0.993532i	$0.536222\pi$
$398$	7171.98	+	9311.48i	0.903263	+	1.17272i
$399$	−534.252			−0.0670328
$400$	−9540.68	+	16807.0i	−1.19258	+	2.10087i
$401$	−13711.0			−1.70747			−0.853737	−	0.520705i	$-0.825669\pi$
$401$	−13711.0			−1.70747			−0.853737	+	0.520705i	$0.825669\pi$
$402$	1634.94	+	2122.67i	0.202844	+	0.263356i
$403$	−1278.72	−	1278.72i	−0.158059	−	0.158059i
$404$	3862.53	+	6634.08i	0.475664	+	0.816975i
$405$	−1183.50	+	1183.50i	−0.145207	+	0.145207i
$406$	−1986.63	+	15305.7i	−0.242844	+	1.87095i
$407$			12463.9i			1.51797i
$408$	139.919	−	343.093i	0.0169780	−	0.0416315i
$409$			1491.35i			0.180299i	0.995928	+	0.0901496i	$0.0287345\pi$
$409$			1491.35i			0.180299i	−0.995928	+	0.0901496i	$0.971265\pi$
$410$	6689.74	+	868.309i	0.805812	+	0.104592i
$411$	739.225	−	739.225i	0.0887184	−	0.0887184i
$412$	−6795.97	−	1794.42i	−0.812654	−	0.214575i
$413$	−1223.72	−	1223.72i	−0.145799	−	0.145799i
$414$	687.178	−	529.285i	0.0815772	−	0.0628332i
$415$	1002.80			0.118616
$416$	2672.64	+	2012.33i	0.314993	+	0.237169i
$417$	−4605.55			−0.540850
$418$	−486.826	+	374.968i	−0.0569652	+	0.0438763i
$419$	7971.51	+	7971.51i	0.929436	+	0.929436i	0.997669	−	0.0682334i	$-0.0217363\pi$
$419$	7971.51	+	7971.51i	0.929436	+	0.929436i	−0.0682334	+	0.997669i	$0.521736\pi$
$420$	12892.8	+	3404.25i	1.49787	+	0.395501i
$421$	6869.92	−	6869.92i	0.795296	−	0.795296i	−0.187054	−	0.982350i	$-0.559894\pi$
$421$	6869.92	−	6869.92i	0.795296	−	0.795296i	0.982350	+	0.187054i	$0.0598939\pi$
$422$	−2673.40	−	346.999i	−0.308386	−	0.0400276i
$423$		−	5248.14i		−	0.603246i
$424$	4838.69	+	1973.29i	0.554216	+	0.226018i
$425$			1648.27i			0.188124i
$426$	850.960	−	6556.09i	0.0967821	−	0.745642i
$427$	−5048.71	+	5048.71i	−0.572187	+	0.572187i
$428$	−993.806	−	1706.91i	−0.112237	−	0.192772i
$429$	1286.06	+	1286.06i	0.144736	+	0.144736i
$430$	3705.72	+	4811.19i	0.415594	+	0.539572i
$431$	−7332.75			−0.819504			−0.409752	−	0.912197i	$-0.634385\pi$
$431$	−7332.75			−0.819504			−0.409752	+	0.912197i	$0.634385\pi$
$432$	1665.81	−	459.408i	0.185524	−	0.0511649i
$433$	−1171.84			−0.130058			−0.0650288	−	0.997883i	$-0.520714\pi$
$433$	−1171.84			−0.130058			−0.0650288	+	0.997883i	$0.520714\pi$
$434$	4540.96	+	5895.59i	0.502242	+	0.652068i
$435$	−8895.46	−	8895.46i	−0.980470	−	0.980470i
$436$	14035.8	−	8172.02i	1.54173	−	0.897635i
$437$	−159.574	+	159.574i	−0.0174679	+	0.0174679i
$438$	38.0265	−	292.969i	0.00414835	−	0.0319603i
$439$			14740.0i			1.60251i	0.598326	+	0.801253i	$0.295833\pi$
$439$			14740.0i			1.60251i	−0.598326	+	0.801253i	$0.704167\pi$
$440$	14137.6	−	5946.85i	1.53178	−	0.644329i
$441$		−	3420.09i		−	0.369301i
$442$	282.956	+	36.7268i	0.0304498	+	0.00395230i
$443$	−5856.74	+	5856.74i	−0.628131	+	0.628131i	−0.947598	−	0.319466i	$-0.896496\pi$
$443$	−5856.74	+	5856.74i	−0.628131	+	0.628131i	0.319466	+	0.947598i	$0.396496\pi$
$444$	−2328.02	+	8816.85i	−0.248836	+	0.942408i
$445$	−16463.0	−	16463.0i	−1.75376	−	1.75376i
$446$	6676.63	−	5142.54i	0.708851	−	0.545978i
$447$	9064.90			0.959184
$448$	−9840.78	−	9627.66i	−1.03780	−	1.01532i
$449$	1619.32			0.170201			0.0851005	−	0.996372i	$-0.472879\pi$
$449$	1619.32			0.170201			0.0851005	+	0.996372i	$0.472879\pi$
$450$	−6089.90	+	4690.62i	−0.637957	+	0.491373i
$451$	−2677.30	−	2677.30i	−0.279532	−	0.279532i
$452$	860.881	−	3260.39i	0.0895851	−	0.339283i
$453$	−5562.87	+	5562.87i	−0.576968	+	0.576968i
$454$	−7653.19	−	993.361i	−0.791150	−	0.102689i
$455$			10268.6i			1.05802i
$456$	−414.412	+	174.318i	−0.0425584	+	0.0179018i
$457$			14520.4i			1.48629i	0.669131	+	0.743145i	$0.266667\pi$
$457$			14520.4i			1.48629i	−0.669131	+	0.743145i	$0.733333\pi$
$458$	−1652.47	+	12731.2i	−0.168591	+	1.29889i
$459$	104.211	−	104.211i	0.0105972	−	0.0105972i
$460$	4867.72	−	2834.11i	0.493388	−	0.287263i
$461$	−2585.41	−	2585.41i	−0.261203	−	0.261203i	0.564339	−	0.825543i	$-0.309131\pi$
$461$	−2585.41	−	2585.41i	−0.261203	−	0.261203i	−0.825543	+	0.564339i	$0.809131\pi$
$462$	−4567.04	−	5929.45i	−0.459909	−	0.597106i
$463$	6446.14			0.647036			0.323518	−	0.946222i	$-0.395134\pi$
$463$	6446.14			0.647036			0.323518	+	0.946222i	$0.395134\pi$
$464$	3453.01	+	12520.6i	0.345478	+	1.25270i
$465$	−6065.59			−0.604914
$466$	−507.900	−	659.414i	−0.0504893	−	0.0655510i
$467$	−2471.47	−	2471.47i	−0.244895	−	0.244895i	0.573977	−	0.818871i	$-0.305400\pi$
$467$	−2471.47	−	2471.47i	−0.244895	−	0.244895i	−0.818871	+	0.573977i	$0.805400\pi$
$468$	669.536	+	1149.96i	0.0661310	+	0.113583i
$469$	6003.65	−	6003.65i	0.591093	−	0.591093i
$470$	4386.75	−	33797.1i	0.430523	−	3.31690i
$471$			4984.00i			0.487581i
$472$	−1348.50	−	549.940i	−0.131504	−	0.0536293i
$473$		−	3408.55i		−	0.331343i
$474$	−1975.74	−	256.445i	−0.191453	−	0.0248500i
$475$	1414.17	−	1414.17i	0.136604	−	0.136604i
$476$	−1135.25	−	299.754i	−0.109315	−	0.0288638i
$477$	1469.70	+	1469.70i	0.141075	+	0.141075i
$478$	4308.10	−	3318.23i	0.412234	−	0.317515i
$479$	−4936.05			−0.470843			−0.235422	−	0.971893i	$-0.575647\pi$
$479$	−4936.05			−0.470843			−0.235422	+	0.971893i	$0.575647\pi$
$480$	11111.5	−	1566.10i	1.05660	−	0.148922i
$481$	−7022.23			−0.665667
$482$	−8613.31	+	6634.23i	−0.813954	+	0.626931i
$483$	−1943.58	−	1943.58i	−0.183097	−	0.183097i
$484$	1971.93	+	520.672i	0.185192	+	0.0488986i
$485$	19573.5	−	19573.5i	1.83255	−	1.83255i
$486$	681.590	+	88.4684i	0.0636164	+	0.00825721i
$487$		−	2236.98i		−	0.208146i	−0.994570	−	0.104073i	$-0.966812\pi$
$487$		−	2236.98i		−	0.208146i	0.994570	−	0.104073i	$-0.0331876\pi$
$488$	−2268.89	+	5563.53i	−0.210467	+	0.516084i
$489$		−	5751.32i		−	0.531868i
$490$	2858.75	−	22024.8i	0.263562	−	2.03057i
$491$	−339.268	+	339.268i	−0.0311832	+	0.0311832i	−0.722526	−	0.691343i	$-0.757019\pi$
$491$	−339.268	+	339.268i	−0.0311832	+	0.0311832i	0.691343	+	0.722526i	$0.257019\pi$
$492$	−1393.82	−	2393.96i	−0.127720	−	0.219366i
$493$	783.269	+	783.269i	0.0715551	+	0.0715551i
$494$	−211.258	−	274.280i	−0.0192408	−	0.0249806i
$495$	6100.43			0.553927
$496$	5446.00	+	3091.48i	0.493010	+	0.279862i
$497$	−20949.7			−1.89079
$498$	−251.280	−	326.241i	−0.0226107	−	0.0293558i
$499$	−11481.3	−	11481.3i	−1.03001	−	1.03001i	−0.999536	−	0.0304745i	$-0.990298\pi$
$499$	−11481.3	−	11481.3i	−1.03001	−	1.03001i	−0.0304745	−	0.999536i	$-0.509702\pi$
$500$	−25281.5	+	14719.5i	−2.26125	+	1.31656i
$501$	−4337.24	+	4337.24i	−0.386774	+	0.386774i
$502$	−1463.90	+	11278.4i	−0.130153	+	1.00274i
$503$		−	14599.0i		−	1.29411i	−0.762444	−	0.647054i	$-0.776001\pi$
$503$		−	14599.0i		−	1.29411i	0.762444	−	0.647054i	$-0.223999\pi$
$504$	−2123.17	−	5047.46i	−0.187645	−	0.446095i
$505$			19828.0i			1.74719i
$506$	−3135.16	−	406.935i	−0.275445	−	0.0357519i
$507$	3935.97	−	3935.97i	0.344778	−	0.344778i
$508$	721.771	−	2733.54i	0.0630383	−	0.238743i
$509$	−9776.63	−	9776.63i	−0.851359	−	0.851359i	0.138942	−	0.990301i	$-0.455630\pi$
$509$	−9776.63	−	9776.63i	−0.851359	−	0.851359i	−0.990301	+	0.138942i	$0.955630\pi$
$510$	758.204	−	583.991i	0.0658311	−	0.0507050i
$511$	−936.173			−0.0810447
$512$	−10774.7	−	4257.15i	−0.930038	−	0.367463i
$513$	−178.820			−0.0153901
$514$	1494.11	−	1150.80i	0.128214	−	0.0987544i
$515$	−12837.5	−	12837.5i	−1.09842	−	1.09842i
$516$	636.650	−	2411.17i	0.0543158	−	0.205709i
$517$	−13525.9	+	13525.9i	−1.15062	+	1.15062i
$518$	28656.7	+	3719.55i	2.43070	+	0.315498i
$519$		−	1731.69i		−	0.146460i
$520$	3350.47	+	7965.17i	0.282554	+	0.671723i
$521$			7529.46i			0.633151i	0.948567	+	0.316575i	$0.102533\pi$
$521$			7529.46i			0.633151i	−0.948567	+	0.316575i	$0.897467\pi$
$522$	−664.947	+	5122.98i	−0.0557547	+	0.429553i
$523$	6097.66	−	6097.66i	0.509813	−	0.509813i	−0.404656	−	0.914469i	$-0.632609\pi$
$523$	6097.66	−	6097.66i	0.509813	−	0.509813i	0.914469	+	0.404656i	$0.132609\pi$
$524$	−14387.7	+	8376.89i	−1.19949	+	0.698371i
$525$	17224.4	+	17224.4i	1.43187	+	1.43187i
$526$	3634.68	+	4718.95i	0.301292	+	0.391171i
$527$	534.092			0.0441469
$528$	−5477.28	−	3109.24i	−0.451454	−	0.256273i
$529$	11006.0			0.904574
$530$	8236.12	+	10693.1i	0.675008	+	0.876372i
$531$	−409.592	−	409.592i	−0.0334741	−	0.0334741i
$532$	716.834	+	1231.20i	0.0584186	+	0.100337i
$533$	1508.40	−	1508.40i	0.122582	−	0.122582i
$534$	−1230.63	+	9481.22i	−0.0997279	+	0.768338i
$535$		−	5101.61i		−	0.412265i
$536$	2698.05	−	6615.84i	0.217421	−	0.533136i
$537$			8176.37i			0.657051i
$538$	−17857.8	−	2317.89i	−1.43105	−	0.185746i
$539$	−8814.52	+	8814.52i	−0.704394	+	0.704394i
$540$	4315.37	+	1139.44i	0.343896	+	0.0908032i
$541$	−4747.68	−	4747.68i	−0.377299	−	0.377299i	0.492828	−	0.870127i	$-0.335963\pi$
$541$	−4747.68	−	4747.68i	−0.377299	−	0.377299i	−0.870127	+	0.492828i	$0.835963\pi$
$542$	2585.71	−	1991.59i	0.204918	−	0.157834i
$543$	−872.791			−0.0689780
$544$	−978.401	+	137.900i	−0.0771114	+	0.0108684i
$545$	41950.4			3.29717
$546$	3340.67	−	2573.09i	0.261845	−	0.201681i
$547$	−6489.70	−	6489.70i	−0.507275	−	0.507275i	0.406414	−	0.913689i	$-0.366779\pi$
$547$	−6489.70	−	6489.70i	−0.507275	−	0.507275i	−0.913689	+	0.406414i	$0.866779\pi$
$548$	−2695.41	−	711.703i	−0.210114	−	0.0554790i
$549$	−1689.86	+	1689.86i	−0.131369	+	0.131369i
$550$	27784.4	+	3606.33i	2.15405	+	0.279590i
$551$		−	1344.05i		−	0.103917i
$552$	−2141.77	−	873.448i	−0.165145	−	0.0673486i
$553$			6313.41i			0.485485i
$554$	2721.17	−	20964.8i	0.208685	−	1.60778i
$555$	−16654.9	+	16654.9i	−1.27380	+	1.27380i
$556$	6179.50	+	10613.6i	0.471347	+	0.809561i
$557$	13178.1	+	13178.1i	1.00247	+	1.00247i	0.999997	+	0.00247058i	$0.000786410\pi$
$557$	13178.1	+	13178.1i	1.00247	+	1.00247i	0.00247058	+	0.999997i	$0.499214\pi$
$558$	1519.91	+	1973.32i	0.115310	+	0.149709i
$559$	1920.39			0.145302
$560$	−9453.79	−	34279.4i	−0.713385	−	2.58673i
$561$	−537.159			−0.0404258
$562$	−9527.14	−	12369.2i	−0.715086	−	0.928406i
$563$	13912.9	+	13912.9i	1.04149	+	1.04149i	0.999101	+	0.0423880i	$0.0134966\pi$
$563$	13912.9	+	13912.9i	1.04149	+	1.04149i	0.0423880	+	0.999101i	$0.486503\pi$
$564$	−12094.4	+	7041.69i	−0.902957	+	0.525725i
$565$	6158.84	−	6158.84i	0.458591	−	0.458591i
$566$	−2179.65	+	16792.8i	−0.161868	+	1.24709i
$567$		−	2178.00i		−	0.161318i
$568$	−16250.4	+	6835.58i	−1.20044	+	0.504955i
$569$		−	8207.75i		−	0.604722i	−0.953193	−	0.302361i	$-0.902225\pi$
$569$		−	8207.75i		−	0.604722i	0.953193	−	0.302361i	$-0.0977749\pi$
$570$	−1151.57	−	149.470i	−0.0846210	−	0.0109835i
$571$	17905.9	−	17905.9i	1.31233	−	1.31233i	0.392632	−	0.919695i	$-0.371564\pi$
$571$	17905.9	−	17905.9i	1.31233	−	1.31233i	0.919695	−	0.392632i	$-0.128436\pi$
$572$	1238.18	−	4689.34i	0.0905089	−	0.342782i
$573$	−3259.76	−	3259.76i	−0.237659	−	0.237659i
$574$	−6954.53	+	5356.59i	−0.505708	+	0.389512i
$575$	10289.4			0.746256
$576$	−3293.82	−	3222.49i	−0.238268	−	0.233108i
$577$	19888.0			1.43492			0.717458	−	0.696602i	$-0.245305\pi$
$577$	19888.0			1.43492			0.717458	+	0.696602i	$0.245305\pi$
$578$	10942.3	−	8428.06i	0.787437	−	0.606507i
$579$	270.957	+	270.957i	0.0194483	+	0.0194483i
$580$	−8564.28	+	32435.3i	−0.613125	+	2.32207i
$581$	−922.724	+	922.724i	−0.0658882	+	0.0658882i
$582$	−11272.6	−	1463.14i	−0.802857	−	0.104208i
$583$		−	7575.64i		−	0.538166i
$584$	−726.176	+	305.459i	−0.0514544	+	0.0216438i
$585$			3437.00i			0.242910i
$586$	738.659	−	5690.88i	0.0520712	−	0.401174i
$587$	−12662.0	+	12662.0i	−0.890315	+	0.890315i	−0.994552	−	0.104237i	$-0.966760\pi$
$587$	−12662.0	+	12662.0i	−0.890315	+	0.890315i	0.104237	+	0.994552i	$0.466760\pi$
$588$	−7881.67	+	4588.91i	−0.552780	+	0.321843i
$589$	−458.238	−	458.238i	−0.0320566	−	0.0320566i
$590$	−2295.33	−	2980.06i	−0.160165	−	0.207944i
$591$	9683.66			0.673997
$592$	23442.2	−	6465.04i	1.62748	−	0.448837i
$593$	−13327.0			−0.922889			−0.461445	−	0.887169i	$-0.652669\pi$
$593$	−13327.0			−0.922889			−0.461445	+	0.887169i	$0.652669\pi$
$594$	−1528.64	−	1984.65i	−0.105591	−	0.137090i
$595$	−2144.47	−	2144.47i	−0.147756	−	0.147756i
$596$	−12162.8	−	20890.3i	−0.835922	−	1.43574i
$597$	8815.01	−	8815.01i	0.604312	−	0.604312i
$598$	229.268	−	1766.36i	0.0156781	−	0.120789i
$599$			16403.3i			1.11890i	0.828863	+	0.559451i	$0.188988\pi$
$599$			16403.3i			1.11890i	−0.828863	+	0.559451i	$0.811012\pi$
$600$	18980.8	+	7740.66i	1.29148	+	0.526685i
$601$			7619.35i			0.517137i	0.965993	+	0.258569i	$0.0832508\pi$
$601$			7619.35i			0.517137i	−0.965993	+	0.258569i	$0.916749\pi$
$602$	−7836.82	−	1017.20i	−0.530573	−	0.0688668i
$603$	2009.49	−	2009.49i	0.135709	−	0.135709i
$604$	20283.7	+	5355.77i	1.36645	+	0.360800i
$605$	3724.94	+	3724.94i	0.250315	+	0.250315i
$606$	6450.64	−	4968.47i	0.432408	−	0.333053i
$607$	−9012.16			−0.602623			−0.301312	−	0.953526i	$-0.597424\pi$
$607$	−9012.16			−0.602623			−0.301312	+	0.953526i	$0.597424\pi$
$608$	957.758	+	721.129i	0.0638852	+	0.0481014i
$609$	16370.3			1.08926
$610$	−12294.9	+	9469.89i	−0.816074	+	0.628565i
$611$	−7620.54	−	7620.54i	−0.504573	−	0.504573i
$612$	−379.980	−	100.331i	−0.0250977	−	0.00662686i
$613$	4092.45	−	4092.45i	0.269645	−	0.269645i	−0.559312	−	0.828957i	$-0.688935\pi$
$613$	4092.45	−	4092.45i	0.269645	−	0.269645i	0.828957	+	0.559312i	$0.188935\pi$
$614$	−26140.6	−	3392.97i	−1.71816	−	0.223012i
$615$		−	7155.07i		−	0.469138i
$616$	−7536.72	+	18480.7i	−0.492959	+	1.20878i
$617$		−	1667.40i		−	0.108796i	−0.998519	−	0.0543978i	$-0.982676\pi$
$617$		−	1667.40i		−	0.108796i	0.998519	−	0.0543978i	$-0.0173239\pi$
$618$	−959.620	+	7393.24i	−0.0624621	+	0.481229i
$619$	−7367.45	+	7367.45i	−0.478389	+	0.478389i	−0.904616	−	0.426227i	$-0.859842\pi$
$619$	−7367.45	+	7367.45i	−0.478389	+	0.478389i	0.426227	+	0.904616i	$0.359842\pi$
$620$	8138.51	+	13978.3i	0.527178	+	0.905454i
$621$	−650.539	−	650.539i	−0.0420374	−	0.0420374i
$622$	3290.21	+	4271.73i	0.212099	+	0.275371i
$623$	30296.9			1.94834
$624$	1751.75	−	3085.92i	0.112382	−	0.197974i
$625$	−37815.1			−2.42016
$626$	−9763.76	−	12676.4i	−0.623384	−	0.809348i
$627$	460.869	+	460.869i	0.0293546	+	0.0293546i
$628$	11485.7	−	6687.29i	0.729826	−	0.424923i
$629$	1466.51	−	1466.51i	0.0929628	−	0.0929628i
$630$	1820.52	−	14025.9i	0.115129	−	0.886993i
$631$		−	10707.1i		−	0.675502i	−0.941236	−	0.337751i	$-0.890334\pi$
$631$		−	10707.1i		−	0.675502i	0.941236	−	0.337751i	$-0.109666\pi$
$632$	2059.97	+	4897.22i	0.129654	+	0.308229i
$633$			2859.35i			0.179540i
$634$	−2328.56	−	302.240i	−0.145866	−	0.0189330i
$635$	5163.63	−	5163.63i	0.322697	−	0.322697i
$636$	1414.98	−	5358.92i	0.0882196	−	0.334111i
$637$	−4966.13	−	4966.13i	−0.308894	−	0.308894i
$638$	14917.1	−	11489.6i	0.925663	−	0.712973i
$639$	−7012.11			−0.434108
$640$	−18518.0	−	23505.4i	−1.14373	−	1.45177i
$641$	−17229.7			−1.06167			−0.530837	−	0.847474i	$-0.678122\pi$
$641$	−17229.7			−1.06167			−0.530837	+	0.847474i	$0.678122\pi$
$642$	−1659.71	+	1278.36i	−0.102030	+	0.0785868i
$643$	15204.3	+	15204.3i	0.932505	+	0.932505i	0.997862	−	0.0653574i	$-0.0208187\pi$
$643$	15204.3	+	15204.3i	0.932505	+	0.932505i	−0.0653574	+	0.997862i	$0.520819\pi$
$644$	−1871.22	+	7086.83i	−0.114498	+	0.433634i
$645$	4554.66	−	4554.66i	0.278046	−	0.278046i
$646$	101.399	+	13.1613i	0.00617568	+	0.000801584i
$647$		−	15349.4i		−	0.932687i	−0.884604	−	0.466343i	$-0.845571\pi$
$647$		−	15349.4i		−	0.932687i	0.884604	−	0.466343i	$-0.154429\pi$
$648$	−710.647	−	1689.44i	−0.0430816	−	0.102419i
$649$			2111.26i			0.127695i
$650$	−2031.82	+	15653.8i	−0.122607	+	0.944605i
$651$	5581.25	−	5581.25i	0.336016	−	0.336016i
$652$	−13254.0	+	7716.83i	−0.796116	+	0.463519i
$653$	−1800.83	−	1800.83i	−0.107920	−	0.107920i	0.651085	−	0.759005i	$-0.274314\pi$
$653$	−1800.83	−	1800.83i	−0.107920	−	0.107920i	−0.759005	+	0.651085i	$0.774314\pi$
$654$	−10511.9	−	13647.7i	−0.628512	−	0.816007i
$655$	−43002.0			−2.56523
$656$	−3646.76	+	6424.19i	−0.217046	+	0.382351i
$657$	−313.348			−0.0186071
$658$	27061.9	+	35134.8i	1.60331	+	2.08161i
$659$	−8640.80	−	8640.80i	−0.510771	−	0.510771i	0.403992	−	0.914763i	$-0.367622\pi$
$659$	−8640.80	−	8640.80i	−0.510771	−	0.510771i	−0.914763	+	0.403992i	$0.867622\pi$
$660$	−8185.25	−	14058.6i	−0.482743	−	0.829134i
$661$	10455.9	−	10455.9i	0.615258	−	0.615258i	−0.329053	−	0.944311i	$-0.606729\pi$
$661$	10455.9	−	10455.9i	0.615258	−	0.615258i	0.944311	+	0.329053i	$0.106729\pi$
$662$	−3984.18	+	30695.5i	−0.233912	+	1.80213i
$663$		−	302.637i		−	0.0177277i
$664$	−414.673	+	1016.82i	−0.0242356	+	0.0594278i
$665$			3679.80i			0.214581i
$666$	9591.72	+	1244.98i	0.558065	+	0.0724352i
$667$	4889.59	−	4889.59i	0.283846	−	0.283846i
$668$	15814.8	+	4175.76i	0.916005	+	0.241864i
$669$	−6320.64	−	6320.64i	−0.365277	−	0.365277i
$670$	14620.4	−	11261.1i	0.843039	−	0.649333i
$671$	8710.47			0.501138
$672$	−8783.22	+	11665.3i	−0.504196	+	0.669642i
$673$	−13498.3			−0.773139			−0.386569	−	0.922260i	$-0.626340\pi$
$673$	−13498.3			−0.773139			−0.386569	+	0.922260i	$0.626340\pi$
$674$	13330.1	−	10267.2i	0.761803	−	0.586763i
$675$	5765.19	+	5765.19i	0.328744	+	0.328744i
$676$	−14351.6	−	3789.43i	−0.816546	−	0.215603i
$677$	1664.87	−	1664.87i	0.0945141	−	0.0945141i	−0.658269	−	0.752783i	$-0.728711\pi$
$677$	1664.87	−	1664.87i	0.0945141	−	0.0945141i	0.752783	+	0.658269i	$0.228711\pi$
$678$	−3546.93	−	460.381i	−0.200913	−	0.0260779i
$679$			36021.1i			2.03588i
$680$	−2363.14	−	963.727i	−0.133268	−	0.0543489i
$681$			8185.52i			0.460602i
$682$	1168.57	−	9003.03i	0.0656110	−	0.505489i
$683$	1119.87	−	1119.87i	0.0627388	−	0.0627388i	−0.675041	−	0.737780i	$-0.735874\pi$
$683$	1119.87	−	1119.87i	0.0627388	−	0.0627388i	0.737780	+	0.675041i	$0.235874\pi$
$684$	239.932	+	412.095i	0.0134123	+	0.0230363i
$685$	−5091.60	−	5091.60i	−0.284000	−	0.284000i
$686$	1717.58	+	2229.96i	0.0955942	+	0.124111i
$687$	13616.7			0.756203
$688$	−6410.81	+	1768.01i	−0.355247	+	0.0979721i
$689$	4268.14			0.235999
$690$	−3645.59	−	4733.12i	−0.201138	−	0.261140i
$691$	−6727.79	−	6727.79i	−0.370387	−	0.370387i	0.497231	−	0.867618i	$-0.334350\pi$
$691$	−6727.79	−	6727.79i	−0.370387	−	0.370387i	−0.867618	+	0.497231i	$0.834350\pi$
$692$	−3990.72	+	2323.50i	−0.219226	+	0.127639i
$693$	−5613.30	+	5613.30i	−0.307694	+	0.307694i
$694$	2393.87	−	18443.2i	0.130937	−	1.00878i
$695$			31721.9i			1.73134i
$696$	12698.2	−	5341.38i	0.691558	−	0.290897i
$697$			630.023i			0.0342379i
$698$	8250.78	+	1070.93i	0.447417	+	0.0580733i
$699$	−624.255	+	624.255i	−0.0337789	+	0.0337789i
$700$	16583.1	−	62804.8i	0.895404	−	3.39114i
$701$	4997.17	+	4997.17i	0.269244	+	0.269244i	0.828796	−	0.559551i	$-0.189027\pi$
$701$	4997.17	+	4997.17i	0.269244	+	0.269244i	−0.559551	+	0.828796i	$0.689027\pi$
$702$	1118.16	−	861.241i	0.0601172	−	0.0463040i
$703$	−2516.46			−0.135007
$704$	183.840	+	16794.3i	0.00984196	+	0.899091i
$705$	−36147.9			−1.93108
$706$	−8028.41	+	6183.72i	−0.427979	+	0.329642i
$707$	−18244.7	−	18244.7i	−0.970526	−	0.970526i
$708$	−394.343	+	1493.48i	−0.0209326	+	0.0792776i
$709$	13706.1	−	13706.1i	0.726014	−	0.726014i	−0.243809	−	0.969823i	$-0.578397\pi$
$709$	13706.1	−	13706.1i	0.726014	−	0.726014i	0.969823	+	0.243809i	$0.0783970\pi$
$710$	−45156.7	−	5861.21i	−2.38690	−	0.309813i
$711$			2113.17i			0.111463i
$712$	23500.9	−	9885.41i	1.23698	−	0.520325i
$713$		−	3334.09i		−	0.175123i
$714$	−160.302	+	1235.02i	−0.00840216	+	0.0647331i
$715$	8858.10	−	8858.10i	0.463321	−	0.463321i
$716$	18842.6	−	10970.6i	0.983493	−	0.572615i
$717$	−4078.40	−	4078.40i	−0.212428	−	0.212428i
$718$	12570.2	+	16320.1i	0.653367	+	0.848276i
$719$	−15019.2			−0.779029			−0.389515	−	0.921020i	$-0.627357\pi$
$719$	−15019.2			−0.779029			−0.389515	+	0.921020i	$0.627357\pi$
$720$	−3164.29	−	11473.7i	−0.163786	−	0.593889i
$721$	23624.8			1.22030
$722$	11762.4	+	15271.3i	0.606305	+	0.787175i
$723$	8154.06	+	8154.06i	0.419437	+	0.419437i
$724$	1171.07	+	2011.36i	0.0601138	+	0.103248i
$725$	−43332.4	+	43332.4i	−2.21976	+	2.21976i
$726$	278.444	−	2145.23i	0.0142342	−	0.109665i
$727$		−	11712.1i		−	0.597494i	−0.954332	−	0.298747i	$-0.903431\pi$
$727$		−	11712.1i		−	0.597494i	0.954332	−	0.298747i	$-0.0965687\pi$
$728$	−10412.1	−	4246.21i	−0.530079	−	0.216175i
$729$		−	729.000i		−	0.0370370i
$730$	−2017.90	−	261.918i	−0.102309	−	0.0132795i
$731$	−401.050	+	401.050i	−0.0202919	+	0.0202919i
$732$	6161.68	+	1626.95i	0.311123	+	0.0821498i
$733$	−18107.1	−	18107.1i	−0.912418	−	0.912418i	0.0840439	−	0.996462i	$-0.473216\pi$
$733$	−18107.1	−	18107.1i	−0.912418	−	0.912418i	−0.996462	+	0.0840439i	$0.973216\pi$
$734$	10316.2	−	7945.86i	0.518772	−	0.399574i
$735$	−23556.8			−1.18218
$736$	860.843	+	6107.70i	0.0431129	+	0.305887i
$737$	−10358.0			−0.517697
$738$	−2327.76	+	1792.91i	−0.116106	+	0.0894281i
$739$	5930.06	+	5930.06i	0.295184	+	0.295184i	0.839124	−	0.543940i	$-0.183068\pi$
$739$	5930.06	+	5930.06i	0.295184	+	0.295184i	−0.543940	+	0.839124i	$0.683068\pi$
$740$	60728.3	+	16034.8i	3.01678	+	0.796558i
$741$	−259.655	+	259.655i	−0.0128727	+	0.0128727i
$742$	−17417.7	−	2260.76i	−0.861756	−	0.111853i
$743$		−	37209.5i		−	1.83726i	−0.395118	−	0.918630i	$-0.629296\pi$
$743$		−	37209.5i		−	1.83726i	0.395118	−	0.918630i	$-0.370704\pi$
$744$	2508.22	−	6150.37i	0.123596	−	0.303069i
$745$		−	62436.9i		−	3.07048i
$746$	3705.98	−	28552.2i	0.181884	−	1.40130i
$747$	−308.846	+	308.846i	−0.0151273	+	0.0151273i
$748$	720.734	+	1237.89i	0.0352308	+	0.0605106i
$749$	4694.24	+	4694.24i	0.229004	+	0.229004i
$750$	18934.1	+	24582.4i	0.921835	+	1.19683i
$751$	38763.9			1.88351			0.941753	−	0.336304i	$-0.109177\pi$
$751$	38763.9			1.88351			0.941753	+	0.336304i	$0.109177\pi$
$752$	32455.4	+	18423.7i	1.57384	+	0.893408i
$753$	12062.9			0.583791
$754$	6473.27	+	8404.34i	0.312656	+	0.405926i
$755$	38315.7	+	38315.7i	1.84696	+	1.84696i
$756$	−5019.24	+	2922.33i	−0.241466	+	0.140587i
$757$	−20356.8	+	20356.8i	−0.977384	+	0.977384i	−0.999750	−	0.0223658i	$-0.992880\pi$
$757$	−20356.8	+	20356.8i	−0.977384	+	0.977384i	0.0223658	+	0.999750i	$0.492880\pi$
$758$	−1382.38	+	10650.3i	−0.0662404	+	0.510339i
$759$			3353.24i			0.160362i
$760$	1200.66	+	2854.37i	0.0573061	+	0.136235i
$761$		−	21557.8i		−	1.02690i	−0.858121	−	0.513448i	$-0.828368\pi$
$761$		−	21557.8i		−	1.02690i	0.858121	−	0.513448i	$-0.171632\pi$
$762$	−2973.78	−	385.988i	−0.141376	−	0.0183502i
$763$	−38600.6	+	38600.6i	−1.83150	+	1.83150i
$764$	−3138.40	+	11886.0i	−0.148617	+	0.562853i
$765$	−717.778	−	717.778i	−0.0339233	−	0.0339233i
$766$	−28781.8	+	22168.6i	−1.35761	+	1.04567i
$767$	−1189.49			−0.0559975
$768$	−3006.81	+	11914.4i	−0.141274	+	0.559799i
$769$	22834.1			1.07076			0.535382	−	0.844610i	$-0.320168\pi$
$769$	22834.1			1.07076			0.535382	+	0.844610i	$0.320168\pi$
$770$	−40840.6	+	31456.7i	−1.91142	+	1.47223i
$771$	−1414.44	−	1414.44i	−0.0660698	−	0.0660698i
$772$	260.869	−	987.982i	0.0121618	−	0.0460599i
$773$	−2123.96	+	2123.96i	−0.0988275	+	0.0988275i	−0.754792	−	0.655964i	$-0.772262\pi$
$773$	−2123.96	+	2123.96i	−0.0988275	+	0.0988275i	0.655964	+	0.754792i	$0.272262\pi$
$774$	−2623.07	−	340.467i	−0.121814	−	0.0158111i
$775$			29547.3i			1.36951i
$776$	11753.1	+	27941.0i	0.543702	+	1.29256i
$777$		−	30650.0i		−	1.41514i
$778$	989.279	−	7621.74i	0.0455879	−	0.351225i
$779$	540.544	−	540.544i	0.0248614	−	0.0248614i
$780$	7920.64	−	4611.60i	0.363595	−	0.211695i
$781$	18072.2	+	18072.2i	0.828006	+	0.828006i
$782$	321.004	+	416.764i	0.0146791	+	0.0190581i
$783$	5479.32			0.250083
$784$	21150.5	+	12006.3i	0.963488	+	0.546935i
$785$	34328.6			1.56082
$786$	10775.4	+	13989.9i	0.488990	+	0.634863i
$787$	17766.3	+	17766.3i	0.804703	+	0.804703i	0.983827	−	0.179124i	$-0.0573263\pi$
$787$	17766.3	+	17766.3i	0.804703	+	0.804703i	−0.179124	+	0.983827i	$0.557326\pi$
$788$	−12993.1	−	22316.2i	−0.587384	−	1.00886i
$789$	4467.34	−	4467.34i	0.201574	−	0.201574i
$790$	−1766.33	+	13608.4i	−0.0795485	+	0.612868i
$791$			11334.1i			0.509474i
$792$	−2522.62	+	6185.69i	−0.113179	+	0.277524i
$793$			4907.51i			0.219761i
$794$	−27611.6	−	3583.90i	−1.23413	−	0.160186i
$795$	10122.9	−	10122.9i	0.451601	−	0.451601i
$796$	−32141.9	−	8486.82i	−1.43121	−	0.377899i
$797$	11229.8	+	11229.8i	0.499097	+	0.499097i	0.911157	−	0.412059i	$-0.135190\pi$
$797$	11229.8	+	11229.8i	0.499097	+	0.499097i	−0.412059	+	0.911157i	$0.635190\pi$
$798$	1197.15	−	922.081i	0.0531061	−	0.0409039i
$799$	3182.92			0.140931
$800$	−7628.95	−	54127.6i	−0.337155	−	2.39212i
$801$	10140.7			0.447321
$802$	30723.7	−	23664.3i	1.35273	−	1.04191i
$803$	807.583	+	807.583i	0.0354907	+	0.0354907i
$804$	−7327.14	−	1934.67i	−0.321403	−	0.0848641i
$805$	−13386.9	+	13386.9i	−0.586121	+	0.586121i
$806$	5072.34	+	658.374i	0.221669	+	0.0287720i
$807$			19100.0i			0.833148i
$808$	−20105.1	−	8199.18i	−0.875365	−	0.356988i
$809$			1902.91i			0.0826981i	0.999145	+	0.0413491i	$0.0131656\pi$
$809$			1902.91i			0.0826981i	−0.999145	+	0.0413491i	$0.986834\pi$
$810$	609.349	−	4694.63i	0.0264325	−	0.203645i
$811$	25145.5	−	25145.5i	1.08875	−	1.08875i	0.0930971	−	0.995657i	$-0.470323\pi$
$811$	25145.5	−	25145.5i	1.08875	−	1.08875i	0.995657	−	0.0930971i	$-0.0296767\pi$
$812$	−21964.8	−	37725.7i	−0.949280	−	1.63043i
$813$	−2447.84	−	2447.84i	−0.105596	−	0.105596i
$814$	−21511.9	−	27929.2i	−0.926278	−	1.20260i
$815$	−39613.7			−1.70258
$816$	278.624	+	1010.29i	0.0119532	+	0.0433423i
$817$	688.182			0.0294693
$818$	−2573.96	−	3341.81i	−0.110020	−	0.142841i
$819$	−3162.55	−	3162.55i	−0.134931	−	0.134931i
$820$	−16489.0	+	9600.32i	−0.702221	+	0.408851i
$821$	1370.67	−	1370.67i	0.0582662	−	0.0582662i	−0.677373	−	0.735639i	$-0.736882\pi$
$821$	1370.67	−	1370.67i	0.0582662	−	0.0582662i	0.735639	+	0.677373i	$0.236882\pi$
$822$	−380.604	+	2932.30i	−0.0161497	+	0.124423i
$823$		−	42263.7i		−	1.79006i	−0.446003	−	0.895031i	$-0.647153\pi$
$823$		−	42263.7i		−	1.79006i	0.446003	−	0.895031i	$-0.352847\pi$
$824$	18325.4	−	7708.42i	0.774754	−	0.325893i
$825$		−	29717.0i		−	1.25408i
$826$	4854.15	+	630.054i	0.204476	+	0.0265404i
$827$	17377.6	−	17377.6i	0.730686	−	0.730686i	−0.240070	−	0.970756i	$-0.577170\pi$
$827$	17377.6	−	17377.6i	0.730686	−	0.730686i	0.970756	+	0.240070i	$0.0771703\pi$
$828$	−626.319	+	2372.04i	−0.0262876	+	0.0995581i
$829$	17427.0	+	17427.0i	0.730113	+	0.730113i	0.970642	−	0.240529i	$-0.0773209\pi$
$829$	17427.0	+	17427.0i	0.730113	+	0.730113i	−0.240529	+	0.970642i	$0.577321\pi$
$830$	−2247.07	+	1730.76i	−0.0939722	+	0.0723801i
$831$	−22423.1			−0.936039
$832$	−9461.98	+	103.576i	−0.394273	+	0.00431594i
$833$	2074.24			0.0862762
$834$	10320.1	−	7948.84i	0.428484	−	0.330031i
$835$	29873.9	+	29873.9i	1.23812	+	1.23812i
$836$	443.711	−	1680.45i	0.0183565	−	0.0695212i
$837$	1868.11	−	1868.11i	0.0771460	−	0.0771460i
$838$	−31620.8	−	4104.28i	−1.30349	−	0.169189i
$839$		−	31608.4i		−	1.30065i	−0.759658	−	0.650323i	$-0.774634\pi$
$839$		−	31608.4i		−	1.30065i	0.759658	−	0.650323i	$-0.225366\pi$
$840$	−34765.7	+	14623.8i	−1.42801	+	0.600679i
$841$			16794.7i			0.688619i
$842$	−3537.11	+	27251.1i	−0.144771	+	1.11536i
$843$	−11709.7	+	11709.7i	−0.478415	+	0.478415i
$844$	6589.44	−	3836.54i	0.268741	−	0.156468i
$845$	−27110.0	−	27110.0i	−1.10368	−	1.10368i
$846$	9057.91	+	11760.0i	0.368105	+	0.477917i
$847$	−6855.01			−0.278088
$848$	−14248.3	+	3929.48i	−0.576991	+	0.159126i
$849$	17960.8			0.726047
$850$	−2844.80	−	3693.44i	−0.114795	−	0.149040i
$851$	−9154.74	−	9154.74i	−0.368767	−	0.368767i
$852$	9408.51	+	16159.6i	0.378322	+	0.649786i
$853$	−12042.1	+	12042.1i	−0.483367	+	0.483367i	−0.906205	−	0.422838i	$-0.861034\pi$
$853$	−12042.1	+	12042.1i	−0.483367	+	0.483367i	0.422838	+	0.906205i	$0.361034\pi$
$854$	2599.42	−	20026.8i	0.104157	−	0.802464i
$855$			1231.67i			0.0492658i
$856$	5172.92	+	2109.60i	0.206550	+	0.0842343i
$857$			30191.5i			1.20341i	0.798718	+	0.601705i	$0.205512\pi$
$857$			30191.5i			1.20341i	−0.798718	+	0.601705i	$0.794488\pi$
$858$	−5101.47	−	662.155i	−0.202985	−	0.0263468i
$859$	−12486.8	+	12486.8i	−0.495978	+	0.495978i	−0.910183	−	0.414206i	$-0.864059\pi$
$859$	−12486.8	+	12486.8i	−0.495978	+	0.495978i	0.414206	+	0.910183i	$0.364059\pi$
$860$	−16607.5	−	4385.09i	−0.658502	−	0.173872i
$861$	6583.73	+	6583.73i	0.260596	+	0.260596i
$862$	16431.2	−	12655.8i	0.649245	−	0.500068i
$863$	−21201.2			−0.836267			−0.418133	−	0.908386i	$-0.637316\pi$
$863$	−21201.2			−0.836267			−0.418133	+	0.908386i	$0.637316\pi$
$864$	−2939.84	+	3904.51i	−0.115759	+	0.153743i
$865$	−11927.5			−0.468840
$866$	2625.85	−	2022.51i	0.103037	−	0.0793621i
$867$	−10358.8	−	10358.8i	−0.405773	−	0.405773i
$868$	−20350.7	−	5373.46i	−0.795794	−	0.210123i
$869$	5446.22	−	5446.22i	0.212601	−	0.212601i
$870$	35285.8	+	4579.99i	1.37506	+	0.178479i
$871$		−	5835.74i		−	0.227022i
$872$	−17347.1	+	42536.7i	−0.673679	+	1.65192i
$873$			12056.6i			0.467418i
$874$	82.1597	−	632.986i	0.00317974	−	0.0244978i
$875$	69527.8	−	69527.8i	2.68625	−	2.68625i
$876$	420.434	+	722.116i	0.0162159	+	0.0278516i
$877$	−5223.37	−	5223.37i	−0.201118	−	0.201118i	0.599361	−	0.800479i	$-0.295421\pi$
$877$	−5223.37	−	5223.37i	−0.201118	−	0.201118i	−0.800479	+	0.599361i	$0.795421\pi$
$878$	−25440.1	−	33029.3i	−0.977861	−	1.26957i
$879$	−6086.72			−0.233561
$880$	−21415.7	+	37726.2i	−0.820366	+	1.44517i
$881$	−40623.3			−1.55350			−0.776749	−	0.629810i	$-0.783133\pi$
$881$	−40623.3			−1.55350			−0.776749	+	0.629810i	$0.783133\pi$
$882$	5902.83	+	7663.73i	0.225350	+	0.292575i
$883$	−30217.0	−	30217.0i	−1.15162	−	1.15162i	−0.986227	−	0.165398i	$-0.947109\pi$
$883$	−30217.0	−	30217.0i	−1.15162	−	1.15162i	−0.165398	−	0.986227i	$-0.552891\pi$
$884$	−697.434	+	406.064i	−0.0265353	+	0.0154496i
$885$	−2821.17	+	2821.17i	−0.107155	+	0.107155i
$886$	3015.45	−	23232.1i	0.114341	−	0.880922i
$887$		−	26591.6i		−	1.00660i	−0.864111	−	0.503302i	$-0.832118\pi$
$887$		−	26591.6i		−	1.00660i	0.864111	−	0.503302i	$-0.167882\pi$
$888$	−10000.6	−	23774.8i	−0.377927	−	0.898456i
$889$			9502.62i			0.358501i
$890$	65304.3	+	8476.30i	2.45956	+	0.319243i
$891$	−1878.83	+	1878.83i	−0.0706435	+	0.0706435i
$892$	−6085.32	+	23046.8i	−0.228421	+	0.865093i
$893$	−2730.87	−	2730.87i	−0.102335	−	0.102335i
$894$	−20312.6	+	15645.4i	−0.759905	+	0.585302i
$895$	56316.8			2.10331
$896$	38667.8	+	4589.17i	1.44174	+	0.171109i
$897$	−1889.22			−0.0703226
$898$	−3628.56	+	2794.82i	−0.134840	+	0.103858i
$899$	14041.1	+	14041.1i	0.520908	+	0.520908i
$900$	5550.56	−	21021.5i	0.205576	−	0.778573i
$901$	−891.351	+	891.351i	−0.0329581	+	0.0329581i
$902$	10620.1	+	1378.46i	0.392030	+	0.0508843i
$903$			8381.93i			0.308896i
$904$	3698.14	+	8791.69i	0.136060	+	0.323460i
$905$			6011.57i			0.220808i
$906$	2864.15	−	22066.4i	0.105028	−	0.809168i
$907$	−17765.7	+	17765.7i	−0.650387	+	0.650387i	−0.953086	−	0.302699i	$-0.902112\pi$
$907$	−17765.7	+	17765.7i	−0.650387	+	0.650387i	0.302699	+	0.953086i	$0.402112\pi$
$908$	18863.7	−	10982.9i	0.689443	−	0.401411i
$909$	−6106.70	−	6106.70i	−0.222823	−	0.222823i
$910$	−17722.8	−	23009.8i	−0.645610	−	0.838204i
$911$	−32406.1			−1.17855			−0.589277	−	0.807931i	$-0.700587\pi$
$911$	−32406.1			−1.17855			−0.589277	+	0.807931i	$0.700587\pi$
$912$	627.752	−	1105.86i	0.0227927	−	0.0401520i
$913$	1591.96			0.0577068
$914$	−25061.1	−	32537.2i	−0.906945	−	1.17750i
$915$	11639.3	+	11639.3i	0.420530	+	0.420530i
$916$	−18270.3	−	31380.1i	−0.659025	−	1.13191i
$917$	39568.3	−	39568.3i	1.42493	−	1.42493i
$918$	−53.6548	+	413.375i	−0.00192906	+	0.0148621i
$919$			28632.2i			1.02774i	0.857870	+	0.513868i	$0.171788\pi$
$919$			28632.2i			1.02774i	−0.857870	+	0.513868i	$0.828212\pi$
$920$	−6016.10	+	14752.0i	−0.215592	+	0.528651i
$921$			27958.9i			1.00030i
$922$	10255.6	+	1331.15i	0.366324	+	0.0475478i
$923$	−10181.9	+	10181.9i	−0.363100	+	0.363100i
$924$	20467.6	+	5404.32i	0.728718	+	0.192412i
$925$	81131.0	+	81131.0i	2.88386	+	2.88386i
$926$	−14444.5	+	11125.6i	−0.512609	+	0.394826i
$927$	7907.49			0.280168
$928$	−29347.1	−	22096.5i	−1.03811	−	0.781630i
$929$	−5285.59			−0.186668			−0.0933340	−	0.995635i	$-0.529752\pi$
$929$	−5285.59			−0.186668			−0.0933340	+	0.995635i	$0.529752\pi$
$930$	13591.8	−	10468.8i	0.479238	−	0.369123i
$931$	−1779.64	−	1779.64i	−0.0626482	−	0.0626482i
$932$	2276.20	+	601.014i	0.0799994	+	0.0211232i
$933$	4043.97	−	4043.97i	0.141901	−	0.141901i
$934$	9803.62	+	1272.48i	0.343452	+	0.0445791i
$935$			3699.82i			0.129409i
$936$	−3485.04	−	1421.25i	−0.121701	−	0.0496316i
$937$		−	41589.1i		−	1.45001i	−0.688746	−	0.725003i	$-0.741838\pi$
$937$		−	41589.1i		−	1.45001i	0.688746	−	0.725003i	$-0.258162\pi$
$938$	−3091.09	+	23814.8i	−0.107599	+	0.828978i
$939$	−12000.5	+	12000.5i	−0.417064	+	0.417064i
$940$	48501.5	+	83303.6i	1.68292	+	2.89049i
$941$	13190.1	+	13190.1i	0.456945	+	0.456945i	0.897651	−	0.440707i	$-0.145272\pi$
$941$	13190.1	+	13190.1i	0.456945	+	0.456945i	−0.440707	+	0.897651i	$0.645272\pi$
$942$	−8602.03	−	11168.1i	−0.297526	−	0.386282i
$943$	3932.94			0.135816
$944$	3970.87	−	1095.11i	0.136908	−	0.0377572i
$945$	−15001.5			−0.516401
$946$	5882.91	+	7637.86i	0.202188	+	0.262503i
$947$	−8427.73	−	8427.73i	−0.289192	−	0.289192i	0.547569	−	0.836761i	$-0.315553\pi$
$947$	−8427.73	−	8427.73i	−0.289192	−	0.289192i	−0.836761	+	0.547569i	$0.815553\pi$
$948$	4869.84	−	2835.35i	0.166841	−	0.0971390i
$949$	−454.995	+	454.995i	−0.0155635	+	0.0155635i
$950$	−728.115	+	5609.64i	−0.0248665	+	0.191580i
$951$			2490.53i			0.0849222i
$952$	3061.21	−	1287.67i	0.104217	−	0.0438378i
$953$			49459.8i			1.68118i	0.541675	+	0.840588i	$0.317790\pi$
$953$			49459.8i			1.68118i	−0.541675	+	0.840588i	$0.682210\pi$
$954$	−5829.89	−	756.702i	−0.197851	−	0.0256804i
$955$	−22452.4	+	22452.4i	−0.760779	+	0.760779i
$956$	−3926.56	+	14871.0i	−0.132839	+	0.503097i
$957$	−14121.7	−	14121.7i	−0.477002	−	0.477002i
$958$	11060.7	−	8519.27i	0.373021	−	0.287312i
$959$	9370.06			0.315511
$960$	−22195.7	+	22687.0i	−0.746212	+	0.762730i
$961$	−20216.7			−0.678619
$962$	15735.4	−	12119.9i	0.527369	−	0.406195i
$963$	1571.22	+	1571.22i	0.0525771	+	0.0525771i
$964$	7850.48	−	29731.9i	0.262289	−	0.993362i
$965$	1866.29	−	1866.29i	0.0622568	−	0.0622568i
$966$	7709.66	+	1000.69i	0.256785	+	0.0333299i
$967$			32986.2i			1.09696i	0.836163	+	0.548482i	$0.184794\pi$
$967$			32986.2i			1.09696i	−0.836163	+	0.548482i	$0.815206\pi$
$968$	−5317.33	+	2236.68i	−0.176555	+	0.0742663i
$969$		−	108.452i		−	0.00359544i
$970$	−10077.8	+	77642.7i	−0.333586	+	2.57006i
$971$	−29353.0	+	29353.0i	−0.970117	+	0.970117i	−0.999566	−	0.0294494i	$-0.990625\pi$
$971$	−29353.0	+	29353.0i	−0.970117	+	0.970117i	0.0294494	+	0.999566i	$0.490625\pi$
$972$	−1680.00	+	978.136i	−0.0554382	+	0.0322775i
$973$	−29188.9	−	29188.9i	−0.961718	−	0.961718i
$974$	3860.86	+	5012.61i	0.127012	+	0.164902i
$975$	16742.7			0.549943
$976$	−4518.11	−	16382.7i	−0.148178	−	0.537292i
$977$	44894.0			1.47010			0.735050	−	0.678013i	$-0.237159\pi$
$977$	44894.0			1.47010			0.735050	+	0.678013i	$0.237159\pi$
$978$	9926.36	+	12887.5i	0.324550	+	0.421368i
$979$	−26135.4	−	26135.4i	−0.853208	−	0.853208i
$980$	31607.3	+	54287.1i	1.03026	+	1.76953i
$981$	−12920.0	+	12920.0i	−0.420495	+	0.420495i
$982$	174.678	−	1345.78i	0.00567639	−	0.0437328i
$983$		−	2200.38i		−	0.0713949i	−0.999363	−	0.0356974i	$-0.988635\pi$
$983$		−	2200.38i		−	0.0713949i	0.999363	−	0.0356974i	$-0.0113653\pi$
$984$	7255.07	+	2958.73i	0.235044	+	0.0958547i
$985$		−	66698.7i		−	2.15756i
$986$	−3107.01	−	403.281i	−0.100352	−	0.0130254i
$987$	33261.4	−	33261.4i	1.07267	−	1.07267i
$988$	946.774	+	249.988i	0.0304867	+	0.00804979i
$989$	2503.57	+	2503.57i	0.0804944	+	0.0804944i
$990$	−13669.8	+	10528.9i	−0.438844	+	0.338010i
$991$	−40976.5			−1.31348			−0.656741	−	0.754116i	$-0.728065\pi$
$991$	−40976.5			−1.31348			−0.656741	+	0.754116i	$0.728065\pi$
$992$	−17539.1	+	2472.02i	−0.561357	+	0.0791197i
$993$	32830.6			1.04919
$994$	46944.1	−	36157.7i	1.49796	−	1.15378i
$995$	−60715.6	−	60715.6i	−1.93449	−	1.93449i
$996$	1126.14	+	297.348i	0.0358263	+	0.00945967i
$997$	22095.1	−	22095.1i	0.701864	−	0.701864i	−0.262946	−	0.964810i	$-0.584694\pi$
$997$	22095.1	−	22095.1i	0.701864	−	0.701864i	0.964810	+	0.262946i	$0.0846942\pi$
$998$	45543.3	+	5911.38i	1.44454	+	0.187496i
$999$		−	10258.9i		−	0.324902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.13.2	✓	24
3.2	odd	2		144.4.k.b.109.11		24
4.3	odd	2		192.4.j.a.145.6		24
8.3	odd	2		384.4.j.a.289.12		24
8.5	even	2		384.4.j.b.289.1		24
12.11	even	2		576.4.k.b.145.1		24
16.3	odd	4		384.4.j.a.97.12		24
16.5	even	4	inner	48.4.j.a.37.2	yes	24
16.11	odd	4		192.4.j.a.49.6		24
16.13	even	4		384.4.j.b.97.1		24
48.5	odd	4		144.4.k.b.37.11		24
48.11	even	4		576.4.k.b.433.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.2	✓	24	1.1	even	1	trivial
48.4.j.a.37.2	yes	24	16.5	even	4	inner
144.4.k.b.37.11		24	48.5	odd	4
144.4.k.b.109.11		24	3.2	odd	2
192.4.j.a.49.6		24	16.11	odd	4
192.4.j.a.145.6		24	4.3	odd	2
384.4.j.a.97.12		24	16.3	odd	4
384.4.j.a.289.12		24	8.3	odd	2
384.4.j.b.97.1		24	16.13	even	4
384.4.j.b.289.1		24	8.5	even	2
576.4.k.b.145.1		24	12.11	even	2
576.4.k.b.433.1		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.24080 + 1.72593i) q^{2} +(2.12132 + 2.12132i) q^{3} +(2.04234 - 7.73491i) q^{4} +(14.6111 - 14.6111i) q^{5} +(-8.41470 - 1.09220i) q^{6} +26.8889i q^{7} +(8.77342 + 20.8573i) q^{8} +9.00000i q^{9} +O(q^{10})\)	\(q+(-2.24080 + 1.72593i) q^{2} +(2.12132 + 2.12132i) q^{3} +(2.04234 - 7.73491i) q^{4} +(14.6111 - 14.6111i) q^{5} +(-8.41470 - 1.09220i) q^{6} +26.8889i q^{7} +(8.77342 + 20.8573i) q^{8} +9.00000i q^{9} +(-7.52282 + 57.9584i) q^{10} +(23.1955 - 23.1955i) q^{11} +(20.7407 - 12.0758i) q^{12} +(13.0684 + 13.0684i) q^{13} +(-46.4082 - 60.2525i) q^{14} +61.9898 q^{15} +(-55.6577 - 31.5947i) q^{16} -5.45837 q^{17} +(-15.5334 - 20.1672i) q^{18} +(4.68315 + 4.68315i) q^{19} +(-83.1749 - 142.857i) q^{20} +(-57.0399 + 57.0399i) q^{21} +(-11.9426 + 92.0101i) q^{22} +34.0741i q^{23} +(-25.6338 + 62.8563i) q^{24} -301.971i q^{25} +(-51.8388 - 6.72852i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(207.983 + 54.9163i) q^{28} +(-143.499 - 143.499i) q^{29} +(-138.907 + 106.990i) q^{30} -97.8482 q^{31} +(179.248 - 25.2639i) q^{32} +98.4101 q^{33} +(12.2311 - 9.42076i) q^{34} +(392.877 + 392.877i) q^{35} +(69.6142 + 18.3811i) q^{36} +(-268.672 + 268.672i) q^{37} +(-18.5768 - 2.41121i) q^{38} +55.4446i q^{39} +(432.939 + 176.559i) q^{40} -115.423i q^{41} +(29.3681 - 226.261i) q^{42} +(73.4743 - 73.4743i) q^{43} +(-132.042 - 226.788i) q^{44} +(131.500 + 131.500i) q^{45} +(-58.8094 - 76.3531i) q^{46} -583.126 q^{47} +(-51.0453 - 185.090i) q^{48} -380.010 q^{49} +(521.180 + 676.656i) q^{50} +(-11.5790 - 11.5790i) q^{51} +(127.773 - 74.3928i) q^{52} +(163.300 - 163.300i) q^{53} +(9.82982 - 75.7323i) q^{54} -677.825i q^{55} +(-560.829 + 235.907i) q^{56} +19.8689i q^{57} +(569.220 + 73.8830i) q^{58} +(-45.5102 + 45.5102i) q^{59} +(126.605 - 479.486i) q^{60} +(187.762 + 187.762i) q^{61} +(219.258 - 168.879i) q^{62} -242.000 q^{63} +(-358.054 + 365.980i) q^{64} +381.889 q^{65} +(-220.517 + 169.849i) q^{66} +(-223.276 - 223.276i) q^{67} +(-11.1479 + 42.2200i) q^{68} +(-72.2821 + 72.2821i) q^{69} +(-1558.43 - 202.280i) q^{70} +779.124i q^{71} +(-187.716 + 78.9608i) q^{72} +34.8164i q^{73} +(138.331 - 1065.75i) q^{74} +(640.577 - 640.577i) q^{75} +(45.7883 - 26.6591i) q^{76} +(623.700 + 623.700i) q^{77} +(-95.6934 - 124.240i) q^{78} +234.796 q^{79} +(-1274.86 + 351.588i) q^{80} -81.0000 q^{81} +(199.212 + 258.640i) q^{82} +(34.3162 + 34.3162i) q^{83} +(324.703 + 557.693i) q^{84} +(-79.7531 + 79.7531i) q^{85} +(-37.8296 + 291.452i) q^{86} -608.813i q^{87} +(687.299 + 280.292i) q^{88} -1126.75i q^{89} +(-521.625 - 67.7054i) q^{90} +(-351.395 + 351.395i) q^{91} +(263.560 + 69.5910i) q^{92} +(-207.567 - 207.567i) q^{93} +(1306.67 - 1006.43i) q^{94} +136.852 q^{95} +(433.835 + 326.649i) q^{96} +1339.63 q^{97} +(851.526 - 655.871i) q^{98} +(208.759 + 208.759i) 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

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