LMFDB - Embedded newform 48.4.j.a.13.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(48, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("48.13"); S:= CuspForms(chi, 4); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	48.13
Dual form			48.4.j.a.37.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.987020 + 2.65062i) q^{2} +(2.12132 + 2.12132i) q^{3} +(-6.05158 - 5.23243i) q^{4} +(-11.8955 + 11.8955i) q^{5} +(-7.71660 + 3.52903i) q^{6} +0.485059i q^{7} +(19.8422 - 10.8759i) q^{8} +9.00000i q^{9} +(-19.7893 - 43.2714i) q^{10} +(-30.9469 + 30.9469i) q^{11} +(-1.73767 - 23.9370i) q^{12} +(-18.4511 - 18.4511i) q^{13} +(-1.28571 - 0.478764i) q^{14} -50.4682 q^{15} +(9.24327 + 63.3290i) q^{16} +135.964 q^{17} +(-23.8556 - 8.88318i) q^{18} +(65.8832 + 65.8832i) q^{19} +(134.229 - 9.74414i) q^{20} +(-1.02897 + 1.02897i) q^{21} +(-51.4834 - 112.574i) q^{22} +128.108i q^{23} +(65.1631 + 19.0204i) q^{24} -158.004i q^{25} +(67.1184 - 30.6952i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(2.53804 - 2.93538i) q^{28} +(6.64817 + 6.64817i) q^{29} +(49.8131 - 133.772i) q^{30} -15.1323 q^{31} +(-176.984 - 38.0066i) q^{32} -131.297 q^{33} +(-134.199 + 360.389i) q^{34} +(-5.77001 - 5.77001i) q^{35} +(47.0919 - 54.4642i) q^{36} +(51.4363 - 51.4363i) q^{37} +(-239.660 + 109.603i) q^{38} -78.2813i q^{39} +(-106.658 + 365.407i) q^{40} -410.253i q^{41} +(-1.71179 - 3.74301i) q^{42} +(69.9911 - 69.9911i) q^{43} +(349.206 - 25.3501i) q^{44} +(-107.059 - 107.059i) q^{45} +(-339.567 - 126.446i) q^{46} -487.269 q^{47} +(-114.733 + 153.949i) q^{48} +342.765 q^{49} +(418.809 + 155.953i) q^{50} +(288.423 + 288.423i) q^{51} +(15.1142 + 208.202i) q^{52} +(-217.138 + 217.138i) q^{53} +(-31.7613 - 69.4494i) q^{54} -736.257i q^{55} +(5.27547 + 9.62466i) q^{56} +279.519i q^{57} +(-24.1837 + 11.0599i) q^{58} +(-293.944 + 293.944i) q^{59} +(305.412 + 264.071i) q^{60} +(207.076 + 207.076i) q^{61} +(14.9359 - 40.1099i) q^{62} -4.36553 q^{63} +(275.428 - 431.605i) q^{64} +438.968 q^{65} +(129.593 - 348.018i) q^{66} +(284.693 + 284.693i) q^{67} +(-822.798 - 711.423i) q^{68} +(-271.759 + 271.759i) q^{69} +(20.9892 - 9.59899i) q^{70} -614.701i q^{71} +(97.8834 + 178.580i) q^{72} -486.171i q^{73} +(85.5694 + 187.107i) q^{74} +(335.178 - 335.178i) q^{75} +(-53.9681 - 743.427i) q^{76} +(-15.0111 - 15.0111i) q^{77} +(207.494 + 77.2652i) q^{78} +960.347 q^{79} +(-863.281 - 643.375i) q^{80} -81.0000 q^{81} +(1087.42 + 404.928i) q^{82} +(463.472 + 463.472i) q^{83} +(11.6109 - 0.842875i) q^{84} +(-1617.36 + 1617.36i) q^{85} +(116.437 + 254.603i) q^{86} +28.2058i q^{87} +(-277.480 + 950.633i) q^{88} +1278.38i q^{89} +(389.443 - 178.104i) q^{90} +(8.94987 - 8.94987i) q^{91} +(670.318 - 775.258i) q^{92} +(-32.1004 - 32.1004i) q^{93} +(480.945 - 1291.57i) q^{94} -1567.42 q^{95} +(-294.817 - 456.065i) q^{96} -994.918 q^{97} +(-338.316 + 908.539i) q^{98} +(-278.523 - 278.523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29}+ \cdots - 360 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−0.987020	+	2.65062i	−0.348964	+	0.937136i
$2$	−0.987020	+	2.65062i	−0.348964	+	0.937136i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$4$	−6.05158	−	5.23243i	−0.756448	−	0.654054i
$5$	−11.8955	+	11.8955i	−1.06396	+	1.06396i	−0.0661534	+	0.997809i	$0.521073\pi$
$5$	−11.8955	+	11.8955i	−1.06396	+	1.06396i	−0.997809	+	0.0661534i	$0.978927\pi$
$6$	−7.71660	+	3.52903i	−0.525048	+	0.240120i
$7$			0.485059i			0.0261907i	0.999914	+	0.0130954i	$0.00416851\pi$
$7$			0.485059i			0.0261907i	−0.999914	+	0.0130954i	$0.995831\pi$
$8$	19.8422	−	10.8759i	0.876911	−	0.480653i
$9$			9.00000i			0.333333i
$10$	−19.7893	−	43.2714i	−0.625793	−	1.36836i
$11$	−30.9469	+	30.9469i	−0.848260	+	0.848260i	−0.989916	−	0.141656i	$-0.954757\pi$
$11$	−30.9469	+	30.9469i	−0.848260	+	0.848260i	0.141656	+	0.989916i	$0.454757\pi$
$12$	−1.73767	−	23.9370i	−0.0418019	−	0.575835i
$13$	−18.4511	−	18.4511i	−0.393647	−	0.393647i	0.482338	−	0.875985i	$-0.339788\pi$
$13$	−18.4511	−	18.4511i	−0.393647	−	0.393647i	−0.875985	+	0.482338i	$0.839788\pi$
$14$	−1.28571	−	0.478764i	−0.0245443	−	0.00913964i
$15$	−50.4682			−0.868722
$16$	9.24327	+	63.3290i	0.144426	+	0.989516i
$17$	135.964			1.93977			0.969886	−	0.243558i	$-0.0783148\pi$
$17$	135.964			1.93977			0.969886	+	0.243558i	$0.0783148\pi$
$18$	−23.8556	−	8.88318i	−0.312379	−	0.116321i
$19$	65.8832	+	65.8832i	0.795508	+	0.795508i	0.982384	−	0.186876i	$-0.0598362\pi$
$19$	65.8832	+	65.8832i	0.795508	+	0.795508i	−0.186876	+	0.982384i	$0.559836\pi$
$20$	134.229	−	9.74414i	1.50072	−	0.108943i
$21$	−1.02897	+	1.02897i	−0.0106923	+	0.0106923i
$22$	−51.4834	−	112.574i	−0.498922	−	1.09095i
$23$			128.108i			1.16141i	0.814114	+	0.580705i	$0.197223\pi$
$23$			128.108i			1.16141i	−0.814114	+	0.580705i	$0.802777\pi$
$24$	65.1631	+	19.0204i	0.554223	+	0.161772i
$25$		−	158.004i		−	1.26403i
$26$	67.1184	−	30.6952i	0.506269	−	0.231532i
$27$	−19.0919	+	19.0919i	−0.136083	+	0.136083i
$28$	2.53804	−	2.93538i	0.0171302	−	0.0198119i
$29$	6.64817	+	6.64817i	0.0425702	+	0.0425702i	0.728071	−	0.685501i	$-0.240417\pi$
$29$	6.64817	+	6.64817i	0.0425702	+	0.0425702i	−0.685501	+	0.728071i	$0.740417\pi$
$30$	49.8131	−	133.772i	0.303153	−	0.814111i
$31$	−15.1323			−0.0876722			−0.0438361	−	0.999039i	$-0.513958\pi$
$31$	−15.1323			−0.0876722			−0.0438361	+	0.999039i	$0.513958\pi$
$32$	−176.984	−	38.0066i	−0.977710	−	0.209959i
$33$	−131.297			−0.692601
$34$	−134.199	+	360.389i	−0.676912	+	1.81783i
$35$	−5.77001	−	5.77001i	−0.0278660	−	0.0278660i
$36$	47.0919	−	54.4642i	0.218018	−	0.252149i
$37$	51.4363	−	51.4363i	0.228542	−	0.228542i	−0.583541	−	0.812084i	$-0.698333\pi$
$37$	51.4363	−	51.4363i	0.228542	−	0.228542i	0.812084	+	0.583541i	$0.198333\pi$
$38$	−239.660	+	109.603i	−1.02310	+	0.467895i
$39$		−	78.2813i		−	0.321411i
$40$	−106.658	+	365.407i	−0.421604	+	1.44440i
$41$		−	410.253i		−	1.56270i	−0.624092	−	0.781350i	$-0.714531\pi$
$41$		−	410.253i		−	1.56270i	0.624092	−	0.781350i	$-0.285469\pi$
$42$	−1.71179	−	3.74301i	−0.00628892	−	0.0137514i
$43$	69.9911	−	69.9911i	0.248222	−	0.248222i	−0.572019	−	0.820241i	$-0.693839\pi$
$43$	69.9911	−	69.9911i	0.248222	−	0.248222i	0.820241	+	0.572019i	$0.193839\pi$
$44$	349.206	−	25.3501i	1.19647	−	0.0868562i
$45$	−107.059	−	107.059i	−0.354654	−	0.354654i
$46$	−339.567	−	126.446i	−1.08840	−	0.405291i
$47$	−487.269			−1.51225			−0.756123	−	0.654430i	$-0.772909\pi$
$47$	−487.269			−1.51225			−0.756123	+	0.654430i	$0.772909\pi$
$48$	−114.733	+	153.949i	−0.345006	+	0.462930i
$49$	342.765			0.999314
$50$	418.809	+	155.953i	1.18457	+	0.441103i
$51$	288.423	+	288.423i	0.791909	+	0.791909i
$52$	15.1142	+	208.202i	0.0403068	+	0.555239i
$53$	−217.138	+	217.138i	−0.562757	+	0.562757i	−0.930090	−	0.367333i	$-0.880271\pi$
$53$	−217.138	+	217.138i	−0.562757	+	0.562757i	0.367333	+	0.930090i	$0.380271\pi$
$54$	−31.7613	−	69.4494i	−0.0800400	−	0.175016i
$55$		−	736.257i		−	1.80503i
$56$	5.27547	+	9.62466i	0.0125887	+	0.0229670i
$57$			279.519i			0.649529i
$58$	−24.1837	+	11.0599i	−0.0547495	+	0.0250386i
$59$	−293.944	+	293.944i	−0.648613	+	0.648613i	−0.952658	−	0.304044i	$-0.901663\pi$
$59$	−293.944	+	293.944i	−0.648613	+	0.648613i	0.304044	+	0.952658i	$0.401663\pi$
$60$	305.412	+	264.071i	0.657143	+	0.568191i
$61$	207.076	+	207.076i	0.434646	+	0.434646i	0.890205	−	0.455559i	$-0.150561\pi$
$61$	207.076	+	207.076i	0.434646	+	0.434646i	−0.455559	+	0.890205i	$0.650561\pi$
$62$	14.9359	−	40.1099i	0.0305945	−	0.0821608i
$63$	−4.36553			−0.00873025
$64$	275.428	−	431.605i	0.537946	−	0.842979i
$65$	438.968			0.837651
$66$	129.593	−	348.018i	0.241693	−	0.649061i
$67$	284.693	+	284.693i	0.519115	+	0.519115i	0.917304	−	0.398188i	$-0.130361\pi$
$67$	284.693	+	284.693i	0.519115	+	0.519115i	−0.398188	+	0.917304i	$0.630361\pi$
$68$	−822.798	−	711.423i	−1.46734	−	1.26872i
$69$	−271.759	+	271.759i	−0.474144	+	0.474144i
$70$	20.9892	−	9.59899i	0.0358384	−	0.0163900i
$71$		−	614.701i		−	1.02749i	−0.857944	−	0.513744i	$-0.828258\pi$
$71$		−	614.701i		−	1.02749i	0.857944	−	0.513744i	$-0.171742\pi$
$72$	97.8834	+	178.580i	0.160218	+	0.292304i
$73$		−	486.171i		−	0.779479i	−0.920925	−	0.389740i	$-0.872565\pi$
$73$		−	486.171i		−	0.779479i	0.920925	−	0.389740i	$-0.127435\pi$
$74$	85.5694	+	187.107i	0.134422	+	0.293928i
$75$	335.178	−	335.178i	0.516040	−	0.516040i
$76$	−53.9681	−	743.427i	−0.0814548	−	1.12207i
$77$	−15.0111	−	15.0111i	−0.0222166	−	0.0222166i
$78$	207.494	+	77.2652i	0.301206	+	0.112161i
$79$	960.347			1.36769			0.683845	−	0.729628i	$-0.260307\pi$
$79$	960.347			1.36769			0.683845	+	0.729628i	$0.260307\pi$
$80$	−863.281	−	643.375i	−1.20647	−	0.899144i
$81$	−81.0000			−0.111111
$82$	1087.42	+	404.928i	1.46446	+	0.545327i
$83$	463.472	+	463.472i	0.612923	+	0.612923i	0.943707	−	0.330784i	$-0.107313\pi$
$83$	463.472	+	463.472i	0.612923	+	0.612923i	−0.330784	+	0.943707i	$0.607313\pi$
$84$	11.6109	−	0.842875i	0.0150815	−	0.00109482i
$85$	−1617.36	+	1617.36i	−2.06385	+	2.06385i
$86$	116.437	+	254.603i	0.145997	+	0.319238i
$87$			28.2058i			0.0347584i
$88$	−277.480	+	950.633i	−0.336130	+	1.15157i
$89$			1278.38i			1.52257i	0.648420	+	0.761283i	$0.275430\pi$
$89$			1278.38i			1.52257i	−0.648420	+	0.761283i	$0.724570\pi$
$90$	389.443	−	178.104i	0.456121	−	0.208598i
$91$	8.94987	−	8.94987i	0.0103099	−	0.0103099i
$92$	670.318	−	775.258i	0.759625	−	0.878546i
$93$	−32.1004	−	32.1004i	−0.0357920	−	0.0357920i
$94$	480.945	−	1291.57i	0.527720	−	1.41718i
$95$	−1567.42			−1.69278
$96$	−294.817	−	456.065i	−0.313433	−	0.484864i
$97$	−994.918			−1.04143			−0.520714	−	0.853731i	$-0.674334\pi$
$97$	−994.918			−1.04143			−0.520714	+	0.853731i	$0.674334\pi$
$98$	−338.316	+	908.539i	−0.348725	+	0.936493i
$99$	−278.523	−	278.523i	−0.282753	−	0.282753i
$100$	−826.747	+	956.175i	−0.826747	+	0.956175i
$101$	1317.80	−	1317.80i	1.29828	−	1.29828i	0.368750	−	0.929529i	$-0.379786\pi$
$101$	1317.80	−	1317.80i	1.29828	−	1.29828i	0.929529	−	0.368750i	$-0.120214\pi$
$102$	−1049.18	+	479.821i	−1.01847	+	0.465778i
$103$			1345.19i			1.28685i	0.765511	+	0.643423i	$0.222486\pi$
$103$			1345.19i			1.28685i	−0.765511	+	0.643423i	$0.777514\pi$
$104$	−566.783	−	165.438i	−0.534401	−	0.155986i
$105$		−	24.4801i		−	0.0227525i
$106$	−361.230	−	789.868i	−0.330998	−	0.723762i
$107$	437.734	−	437.734i	0.395489	−	0.395489i	−0.481149	−	0.876639i	$-0.659781\pi$
$107$	437.734	−	437.734i	0.395489	−	0.395489i	0.876639	+	0.481149i	$0.159781\pi$
$108$	215.433	−	15.6391i	0.191945	−	0.0139340i
$109$	173.959	+	173.959i	0.152864	+	0.152864i	0.779396	−	0.626532i	$-0.215526\pi$
$109$	173.959	+	173.959i	0.152864	+	0.152864i	−0.626532	+	0.779396i	$0.715526\pi$
$110$	1951.54	+	726.700i	1.69156	+	0.629892i
$111$	218.226			0.186604
$112$	−30.7183	+	4.48354i	−0.0259162	+	0.00378263i
$113$	312.932			0.260514			0.130257	−	0.991480i	$-0.458420\pi$
$113$	312.932			0.260514			0.130257	+	0.991480i	$0.458420\pi$
$114$	−740.899	−	275.891i	−0.608697	−	0.226663i
$115$	−1523.91	−	1523.91i	−1.23570	−	1.23570i
$116$	−5.44583	−	75.0181i	−0.00435891	−	0.0600453i
$117$	166.060	−	166.060i	0.131216	−	0.131216i
$118$	−489.005	−	1069.26i	−0.381496	−	0.834182i
$119$			65.9507i			0.0508041i
$120$	−1001.40	+	548.888i	−0.761792	+	0.417554i
$121$		−	584.427i		−	0.439089i
$122$	−753.269	+	344.492i	−0.558998	+	0.255646i
$123$	870.278	−	870.278i	0.637970	−	0.637970i
$124$	91.5743	+	79.1787i	0.0663194	+	0.0573424i
$125$	392.601	+	392.601i	0.280922	+	0.280922i
$126$	4.30887	−	11.5714i	0.00304655	−	0.00818143i
$127$	1457.94			1.01867			0.509335	−	0.860569i	$-0.329892\pi$
$127$	1457.94			1.01867			0.509335	+	0.860569i	$0.329892\pi$
$128$	872.169	+	1156.06i	0.602262	+	0.798298i
$129$	296.947			0.202672
$130$	−433.271	+	1163.54i	−0.292310	+	0.784993i
$131$	−203.507	−	203.507i	−0.135729	−	0.135729i	0.635978	−	0.771707i	$-0.280597\pi$
$131$	−203.507	−	203.507i	−0.135729	−	0.135729i	−0.771707	+	0.635978i	$0.780597\pi$
$132$	794.553	+	687.002i	0.523916	+	0.452999i
$133$	−31.9573	+	31.9573i	−0.0208349	+	0.0208349i
$134$	−1035.61	+	473.615i	−0.667634	+	0.305329i
$135$		−	454.214i		−	0.289574i
$136$	2697.83	−	1478.74i	1.70101	−	0.932357i
$137$		−	432.979i		−	0.270014i	−0.990845	−	0.135007i	$-0.956894\pi$
$137$		−	432.979i		−	0.270014i	0.990845	−	0.135007i	$-0.0431056\pi$
$138$	−452.098	−	988.561i	−0.278878	−	0.609797i
$139$	−1058.62	+	1058.62i	−0.645975	+	0.645975i	−0.952018	−	0.306043i	$-0.900995\pi$
$139$	−1058.62	+	1058.62i	−0.645975	+	0.645975i	0.306043	+	0.952018i	$0.400995\pi$
$140$	4.72649	+	65.1089i	0.00285329	+	0.0393050i
$141$	−1033.65	−	1033.65i	−0.617372	−	0.617372i
$142$	1629.34	+	606.723i	0.962895	+	0.358557i
$143$	1142.01			0.667829
$144$	−569.961	+	83.1895i	−0.329839	+	0.0481421i
$145$	−158.166			−0.0905861
$146$	1288.65	+	479.860i	0.730478	+	0.272010i
$147$	727.114	+	727.114i	0.407968	+	0.407968i
$148$	−580.407	+	42.1339i	−0.322359	+	0.0234012i
$149$	1703.13	−	1703.13i	0.936414	−	0.936414i	−0.0616815	−	0.998096i	$-0.519646\pi$
$149$	1703.13	−	1703.13i	0.936414	−	0.936414i	0.998096	+	0.0616815i	$0.0196463\pi$
$150$	557.602	+	1219.26i	0.303520	+	0.663679i
$151$		−	541.560i		−	0.291864i	−0.989295	−	0.145932i	$-0.953382\pi$
$151$		−	541.560i		−	0.291864i	0.989295	−	0.145932i	$-0.0466182\pi$
$152$	2023.81	+	590.729i	1.07995	+	0.315227i
$153$			1223.68i			0.646591i
$154$	54.6050	−	24.9725i	0.0285727	−	0.0130671i
$155$	180.006	−	180.006i	0.0932800	−	0.0932800i
$156$	−409.602	+	473.726i	−0.210220	+	0.243131i
$157$	−8.94805	−	8.94805i	−0.00454861	−	0.00454861i	0.704829	−	0.709377i	$-0.251024\pi$
$157$	−8.94805	−	8.94805i	−0.00454861	−	0.00454861i	−0.709377	+	0.704829i	$0.751024\pi$
$158$	−947.882	+	2545.52i	−0.477275	+	1.28171i
$159$	−921.236			−0.459489
$160$	2557.42	−	1653.21i	1.26364	−	0.816859i
$161$	−62.1402			−0.0304182
$162$	79.9487	−	214.700i	0.0387738	−	0.104126i
$163$	−1308.41	−	1308.41i	−0.628727	−	0.628727i	0.319021	−	0.947748i	$-0.396646\pi$
$163$	−1308.41	−	1308.41i	−0.628727	−	0.628727i	−0.947748	+	0.319021i	$0.896646\pi$
$164$	−2146.62	+	2482.68i	−1.02209	+	1.18210i
$165$	1561.84	−	1561.84i	0.736902	−	0.736902i
$166$	−1685.94	+	771.031i	−0.788281	+	0.360504i
$167$			2374.12i			1.10009i	0.835135	+	0.550045i	$0.185390\pi$
$167$			2374.12i			1.10009i	−0.835135	+	0.550045i	$0.814610\pi$
$168$	−9.22603	+	31.6080i	−0.00423692	+	0.0145155i
$169$		−	1516.12i		−	0.690084i
$170$	−2690.63	−	5883.36i	−1.21390	−	2.65431i
$171$	−592.949	+	592.949i	−0.265169	+	0.265169i
$172$	−789.781	+	57.3331i	−0.350118	+	0.0254163i
$173$	−1310.49	−	1310.49i	−0.575922	−	0.575922i	0.357855	−	0.933777i	$-0.383508\pi$
$173$	−1310.49	−	1310.49i	−0.575922	−	0.575922i	−0.933777	+	0.357855i	$0.883508\pi$
$174$	−74.7629	−	27.8397i	−0.0325733	−	0.0121294i
$175$	76.6414			0.0331060
$176$	−2245.89	−	1673.79i	−0.961877	−	0.716855i
$177$	−1247.10			−0.529591
$178$	−3388.51	−	1261.79i	−1.42685	−	0.531321i
$179$	248.652	+	248.652i	0.103828	+	0.103828i	0.757112	−	0.653285i	$-0.226610\pi$
$179$	248.652	+	248.652i	0.103828	+	0.103828i	−0.653285	+	0.757112i	$0.726610\pi$
$180$	87.6973	+	1208.06i	0.0363143	+	0.500241i
$181$	1152.86	−	1152.86i	0.473434	−	0.473434i	−0.429590	−	0.903024i	$-0.641342\pi$
$181$	1152.86	−	1152.86i	0.473434	−	0.473434i	0.903024	+	0.429590i	$0.141342\pi$
$182$	14.8890	+	32.5564i	0.00606399	+	0.0132596i
$183$			878.550i			0.354887i
$184$	1393.30	+	2541.96i	0.558235	+	1.01845i
$185$			1223.72i			0.486321i
$186$	116.770	−	53.4023i	0.0460321	−	0.0210519i
$187$	−4207.67	+	4207.67i	−1.64543	+	1.64543i
$188$	2948.75	+	2549.60i	1.14393	+	0.989090i
$189$	−9.26070	−	9.26070i	−0.00356411	−	0.00356411i
$190$	1547.08	−	4154.65i	0.590721	−	1.58637i
$191$	−457.697			−0.173392			−0.0866959	−	0.996235i	$-0.527631\pi$
$191$	−457.697			−0.173392			−0.0866959	+	0.996235i	$0.527631\pi$
$192$	1499.85	−	331.302i	0.563760	−	0.124529i
$193$	−61.7567			−0.0230329			−0.0115164	−	0.999934i	$-0.503666\pi$
$193$	−61.7567			−0.0230329			−0.0115164	+	0.999934i	$0.503666\pi$
$194$	982.004	−	2637.15i	0.363422	−	0.975960i
$195$	931.192	+	931.192i	0.341970	+	0.341970i
$196$	−2074.27	−	1793.49i	−0.755929	−	0.653606i
$197$	−613.568	+	613.568i	−0.221903	+	0.221903i	−0.809299	−	0.587396i	$-0.800153\pi$
$197$	−613.568	+	613.568i	−0.221903	+	0.221903i	0.587396	+	0.809299i	$0.300153\pi$
$198$	1013.16	−	463.350i	0.363649	−	0.166307i
$199$			3343.30i			1.19095i	0.803372	+	0.595477i	$0.203037\pi$
$199$			3343.30i			1.19095i	−0.803372	+	0.595477i	$0.796963\pi$
$200$	−1718.44	−	3135.16i	−0.607561	−	1.10845i
$201$			1207.85i			0.423856i
$202$	2192.29	+	4793.69i	0.763610	+	1.66972i
$203$	−3.22476	+	3.22476i	−0.00111494	+	0.00111494i
$204$	−236.261	−	3254.57i	−0.0810863	−	1.11699i
$205$	4880.15	+	4880.15i	1.66266	+	1.66266i
$206$	−3565.58	−	1327.73i	−1.20595	−	0.449063i
$207$	−1152.98			−0.387137
$208$	997.940	−	1339.04i	0.332667	−	0.446372i
$209$	−4077.77			−1.34959
$210$	64.8874	+	24.1623i	0.0213222	+	0.00793981i
$211$	−445.986	−	445.986i	−0.145512	−	0.145512i	0.630598	−	0.776110i	$-0.282810\pi$
$211$	−445.986	−	445.986i	−0.145512	−	0.145512i	−0.776110	+	0.630598i	$0.782810\pi$
$212$	2450.18	−	177.868i	0.793770	−	0.0576226i
$213$	1303.98	−	1303.98i	0.419470	−	0.419470i
$214$	728.215	+	1592.32i	0.232616	+	0.508639i
$215$			1665.15i			0.528198i
$216$	−171.184	+	586.468i	−0.0539239	+	0.184741i
$217$		−	7.34006i		−	0.00229620i
$218$	−632.799	+	289.398i	−0.196599	+	0.0899104i
$219$	1031.32	−	1031.32i	0.318221	−	0.318221i
$220$	−3852.41	+	4455.52i	−1.18059	+	1.36541i
$221$	−2508.68	−	2508.68i	−0.763585	−	0.763585i
$222$	−215.393	+	578.433i	−0.0651182	+	0.174873i
$223$	6100.84			1.83203			0.916014	−	0.401146i	$-0.131388\pi$
$223$	6100.84			1.83203			0.916014	+	0.401146i	$0.131388\pi$
$224$	18.4355	−	85.8480i	0.00549898	−	0.0256070i
$225$	1422.04			0.421345
$226$	−308.870	+	829.463i	−0.0909103	+	0.244137i
$227$	−3652.90	−	3652.90i	−1.06807	−	1.06807i	−0.997507	−	0.0705613i	$-0.977521\pi$
$227$	−3652.90	−	3652.90i	−1.06807	−	1.06807i	−0.0705613	−	0.997507i	$-0.522479\pi$
$228$	1462.56	−	1691.53i	0.424827	−	0.491335i
$229$	1707.86	−	1707.86i	0.492832	−	0.492832i	−0.416365	−	0.909197i	$-0.636696\pi$
$229$	1707.86	−	1707.86i	0.492832	−	0.492832i	0.909197	+	0.416365i	$0.136696\pi$
$230$	5543.43	−	2535.17i	1.58923	−	0.726802i
$231$		−	63.6867i		−	0.0181397i
$232$	204.220	+	59.6095i	0.0577917	+	0.0168688i
$233$			3019.27i			0.848924i	0.905446	+	0.424462i	$0.139537\pi$
$233$			3019.27i			0.848924i	−0.905446	+	0.424462i	$0.860463\pi$
$234$	276.257	+	604.066i	0.0771773	+	0.168756i
$235$	5796.29	−	5796.29i	1.60897	−	1.60897i
$236$	3316.86	−	240.783i	0.914870	−	0.0664138i
$237$	2037.20	+	2037.20i	0.558357	+	0.558357i
$238$	−174.810	−	65.0946i	−0.0476103	−	0.0177288i
$239$	2964.22			0.802256			0.401128	−	0.916022i	$-0.368618\pi$
$239$	2964.22			0.802256			0.401128	+	0.916022i	$0.368618\pi$
$240$	−466.491	−	3196.10i	−0.125466	−	0.859614i
$241$	−2606.84			−0.696769			−0.348384	−	0.937352i	$-0.613270\pi$
$241$	−2606.84			−0.696769			−0.348384	+	0.937352i	$0.613270\pi$
$242$	1549.09	+	576.841i	0.411486	+	0.153226i
$243$	−171.827	−	171.827i	−0.0453609	−	0.0453609i
$244$	−169.626	−	2336.65i	−0.0445049	−	0.613069i
$245$	−4077.35	+	4077.35i	−1.06323	+	1.06323i
$246$	1447.79	+	3165.76i	0.375236	+	0.820493i
$247$		−	2431.23i		−	0.626298i
$248$	−300.258	+	164.578i	−0.0768807	+	0.0421399i
$249$			1966.34i			0.500450i
$250$	−1428.14	+	653.131i	−0.361294	+	0.165230i
$251$	3018.73	−	3018.73i	0.759126	−	0.759126i	−0.217037	−	0.976163i	$-0.569639\pi$
$251$	3018.73	−	3018.73i	0.759126	−	0.759126i	0.976163	+	0.217037i	$0.0696394\pi$
$252$	26.4184	+	22.8424i	0.00660398	+	0.00571006i
$253$	−3964.56	−	3964.56i	−0.985177	−	0.985177i
$254$	−1439.01	+	3864.44i	−0.355479	+	0.954632i
$255$	−6861.86			−1.68512
$256$	−3925.12	+	1170.73i	−0.958282	+	0.285824i
$257$	1988.50			0.482644			0.241322	−	0.970445i	$-0.422419\pi$
$257$	1988.50			0.482644			0.241322	+	0.970445i	$0.422419\pi$
$258$	−293.093	+	787.095i	−0.0707255	+	0.189932i
$259$	24.9496	+	24.9496i	0.00598570	+	0.00598570i
$260$	−2656.45	−	2296.87i	−0.633639	−	0.547869i
$261$	−59.8336	+	59.8336i	−0.0141901	+	0.0141901i
$262$	740.284	−	338.554i	0.174561	−	0.0798318i
$263$		−	6049.85i		−	1.41844i	−0.704987	−	0.709220i	$-0.749047\pi$
$263$		−	6049.85i		−	1.41844i	0.704987	−	0.709220i	$-0.250953\pi$
$264$	−2605.22	+	1427.97i	−0.607350	+	0.332901i
$265$		−	5165.90i		−	1.19751i
$266$	−53.1641	−	116.249i	−0.0122545	−	0.0267958i
$267$	−2711.86	+	2711.86i	−0.621585	+	0.621585i
$268$	−233.205	−	3212.47i	−0.0531540	−	0.732213i
$269$	3883.56	+	3883.56i	0.880242	+	0.880242i	0.993559	−	0.113317i	$-0.0361475\pi$
$269$	3883.56	+	3883.56i	0.880242	+	0.880242i	−0.113317	+	0.993559i	$0.536148\pi$
$270$	1203.95	+	448.318i	0.271370	+	0.101051i
$271$	−3321.60			−0.744549			−0.372275	−	0.928123i	$-0.621422\pi$
$271$	−3321.60			−0.744549			−0.372275	+	0.928123i	$0.621422\pi$
$272$	1256.75	+	8610.47i	0.280154	+	1.91944i
$273$	37.9711			0.00841800
$274$	1147.66	+	427.359i	0.253039	+	0.0942251i
$275$	4889.75	+	4889.75i	1.07223	+	1.07223i
$276$	3066.53	−	222.611i	0.668781	−	0.0485492i
$277$	−3603.29	+	3603.29i	−0.781591	+	0.781591i	−0.980099	−	0.198508i	$-0.936390\pi$
$277$	−3603.29	+	3603.29i	−0.781591	+	0.781591i	0.198508	+	0.980099i	$0.436390\pi$
$278$	−1761.11	−	3850.86i	−0.379944	−	0.830789i
$279$		−	136.191i		−	0.0292241i
$280$	−177.244	−	51.7356i	−0.0378298	−	0.0110421i
$281$			823.661i			0.174859i	0.996171	+	0.0874297i	$0.0278653\pi$
$281$			823.661i			0.174859i	−0.996171	+	0.0874297i	$0.972135\pi$
$282$	3760.06	−	1719.59i	0.794002	−	0.363120i
$283$	−2003.74	+	2003.74i	−0.420883	+	0.420883i	−0.885508	−	0.464624i	$-0.846189\pi$
$283$	−2003.74	+	2003.74i	−0.420883	+	0.420883i	0.464624	+	0.885508i	$0.346189\pi$
$284$	−3216.38	+	3719.91i	−0.672032	+	0.777240i
$285$	−3325.01	−	3325.01i	−0.691075	−	0.691075i
$286$	−1127.19	+	3027.03i	−0.233049	+	0.625847i
$287$	198.997			0.0409283
$288$	342.059	−	1592.86i	0.0699863	−	0.325903i
$289$	13573.2			2.76272
$290$	156.113	−	419.239i	0.0316113	−	0.0848915i
$291$	−2110.54	−	2110.54i	−0.425162	−	0.425162i
$292$	−2543.86	+	2942.10i	−0.509822	+	0.589635i
$293$	−1900.08	+	1900.08i	−0.378852	+	0.378852i	−0.870688	−	0.491836i	$-0.836326\pi$
$293$	−1900.08	+	1900.08i	−0.378852	+	0.378852i	0.491836	+	0.870688i	$0.336326\pi$
$294$	−2644.98	+	1209.63i	−0.524688	+	0.239955i
$295$		−	6993.19i		−	1.38020i
$296$	461.193	−	1580.03i	0.0905618	−	0.310261i
$297$		−	1181.67i		−	0.230867i
$298$	2833.33	+	6195.37i	0.550772	+	1.20432i
$299$	2363.74	−	2363.74i	0.457185	−	0.457185i
$300$	−3782.15	+	274.560i	−0.727875	+	0.0528391i
$301$	33.9499	+	33.9499i	0.00650112	+	0.00650112i
$302$	1435.47	+	534.531i	0.273517	+	0.101850i
$303$	5590.96			1.06004
$304$	−3563.34	+	4781.30i	−0.672275	+	0.902060i
$305$	−4926.54			−0.924894
$306$	−3243.50	−	1207.79i	−0.605944	−	0.225637i
$307$	−3489.52	−	3489.52i	−0.648721	−	0.648721i	0.303963	−	0.952684i	$-0.401690\pi$
$307$	−3489.52	−	3489.52i	−0.648721	−	0.648721i	−0.952684	+	0.303963i	$0.901690\pi$
$308$	12.2963	+	169.386i	0.00227483	+	0.0313365i
$309$	−2853.57	+	2853.57i	−0.525352	+	0.525352i
$310$	299.457	+	654.796i	0.0548646	+	0.119967i
$311$		−	1471.68i		−	0.268332i	−0.990959	−	0.134166i	$-0.957164\pi$
$311$		−	1471.68i		−	0.268332i	0.990959	−	0.134166i	$-0.0428356\pi$
$312$	−851.382	−	1553.28i	−0.154487	−	0.281849i
$313$		−	1258.85i		−	0.227331i	−0.993519	−	0.113665i	$-0.963741\pi$
$313$		−	1258.85i		−	0.227331i	0.993519	−	0.113665i	$-0.0362592\pi$
$314$	32.5498	−	14.8860i	0.00584997	−	0.00267537i
$315$	51.9301	−	51.9301i	0.00928866	−	0.00928866i
$316$	−5811.62	−	5024.95i	−1.03459	−	0.894543i
$317$	−5902.41	−	5902.41i	−1.04578	−	1.04578i	−0.998901	−	0.0468795i	$-0.985072\pi$
$317$	−5902.41	−	5902.41i	−1.04578	−	1.04578i	−0.0468795	−	0.998901i	$-0.514928\pi$
$318$	909.279	−	2441.85i	0.160345	−	0.430604i
$319$	−411.481			−0.0722211
$320$	1857.80	+	8410.50i	0.324544	+	1.46925i
$321$	1857.15			0.322916
$322$	61.3336	−	164.710i	0.0106149	−	0.0285060i
$323$	8957.75	+	8957.75i	1.54310	+	1.54310i
$324$	490.178	+	423.827i	0.0840497	+	0.0726727i
$325$	−2915.35	+	2915.35i	−0.497583	+	0.497583i
$326$	4759.52	−	2176.67i	0.808606	−	0.369799i
$327$			738.044i			0.124813i
$328$	−4461.88	−	8140.33i	−0.751116	−	1.37035i
$329$		−	236.355i		−	0.0396068i
$330$	2598.27	+	5681.40i	0.433425	+	0.947730i
$331$	−3256.70	+	3256.70i	−0.540798	+	0.540798i	−0.923763	−	0.382965i	$-0.874903\pi$
$331$	−3256.70	+	3256.70i	−0.540798	+	0.540798i	0.382965	+	0.923763i	$0.374903\pi$
$332$	−379.652	−	5229.82i	−0.0627593	−	0.864529i
$333$	462.926	+	462.926i	0.0761808	+	0.0761808i
$334$	−6292.90	−	2343.31i	−1.03093	−	0.383893i
$335$	−6773.10			−1.10464
$336$	−74.6744	−	55.6524i	−0.0121245	−	0.00903597i
$337$	−4882.53			−0.789224			−0.394612	−	0.918848i	$-0.629121\pi$
$337$	−4882.53			−0.789224			−0.394612	+	0.918848i	$0.629121\pi$
$338$	4018.65	+	1496.44i	0.646703	+	0.240815i
$339$	663.828	+	663.828i	0.106355	+	0.106355i
$340$	18250.3	−	1324.85i	2.91106	−	0.211324i
$341$	468.298	−	468.298i	0.0743688	−	0.0743688i
$342$	−986.430	−	2156.94i	−0.155965	−	0.341034i
$343$			332.637i			0.0523635i
$344$	627.562	−	2150.00i	0.0983601	−	0.336977i
$345$		−	6465.40i		−	1.00894i
$346$	4767.09	−	2180.13i	0.740694	−	0.338741i
$347$	1744.70	−	1744.70i	0.269914	−	0.269914i	−0.559151	−	0.829066i	$-0.688873\pi$
$347$	1744.70	−	1744.70i	0.269914	−	0.269914i	0.829066	+	0.559151i	$0.188873\pi$
$348$	147.585	−	170.690i	0.0227339	−	0.0262929i
$349$	6212.48	+	6212.48i	0.952855	+	0.952855i	0.998938	−	0.0460825i	$-0.0146737\pi$
$349$	6212.48	+	6212.48i	0.952855	+	0.952855i	−0.0460825	+	0.998938i	$0.514674\pi$
$350$	−75.6467	+	203.147i	−0.0115528	+	0.0310248i
$351$	704.532			0.107137
$352$	6653.32	−	4300.94i	1.00745	−	0.651253i
$353$	683.045			0.102988			0.0514941	−	0.998673i	$-0.483602\pi$
$353$	683.045			0.102988			0.0514941	+	0.998673i	$0.483602\pi$
$354$	1230.91	−	3305.58i	0.184808	−	0.496298i
$355$	7312.16	+	7312.16i	1.09321	+	1.09321i
$356$	6689.06	−	7736.24i	0.995841	−	1.15174i
$357$	−139.902	+	139.902i	−0.0207407	+	0.0207407i
$358$	−904.508	+	413.658i	−0.133533	+	0.0610684i
$359$		−	4019.67i		−	0.590947i	−0.955351	−	0.295473i	$-0.904523\pi$
$359$		−	4019.67i		−	0.590947i	0.955351	−	0.295473i	$-0.0954773\pi$
$360$	−3288.66	−	959.925i	−0.481466	−	0.140535i
$361$			1822.20i			0.265665i
$362$	1917.90	+	4193.70i	0.278460	+	0.608884i
$363$	1239.76	−	1239.76i	0.179257	−	0.179257i
$364$	−100.990	+	7.33126i	−0.0145421	+	0.00105567i
$365$	5783.23	+	5783.23i	0.829337	+	0.829337i
$366$	−2328.70	−	867.147i	−0.332577	−	0.123843i
$367$	−8041.99			−1.14384			−0.571919	−	0.820310i	$-0.693801\pi$
$367$	−8041.99			−1.14384			−0.571919	+	0.820310i	$0.693801\pi$
$368$	−8112.97	+	1184.14i	−1.14923	+	0.167738i
$369$	3692.28			0.520900
$370$	−3243.61	−	1207.83i	−0.455749	−	0.169709i
$371$	−105.325	−	105.325i	−0.0147390	−	0.0147390i
$372$	26.2950	+	362.222i	0.00366487	+	0.0504847i
$373$	805.266	−	805.266i	0.111783	−	0.111783i	−0.649003	−	0.760786i	$-0.724814\pi$
$373$	805.266	−	805.266i	0.111783	−	0.111783i	0.760786	+	0.649003i	$0.224814\pi$
$374$	−6999.89	−	15306.0i	−0.967795	−	2.11619i
$375$			1665.66i			0.229372i
$376$	−9668.51	+	5299.51i	−1.32610	+	0.726865i
$377$		−	245.332i		−	0.0335152i
$378$	33.6871	−	15.4061i	0.00458380	−	0.00209631i
$379$	519.461	−	519.461i	0.0704034	−	0.0704034i	−0.671028	−	0.741432i	$-0.734147\pi$
$379$	519.461	−	519.461i	0.0704034	−	0.0704034i	0.741432	+	0.671028i	$0.234147\pi$
$380$	9485.39	+	8201.44i	1.28050	+	1.10717i
$381$	3092.75	+	3092.75i	0.415870	+	0.415870i
$382$	451.757	−	1213.18i	0.0605075	−	0.162492i
$383$	2907.38			0.387886			0.193943	−	0.981013i	$-0.437872\pi$
$383$	2907.38			0.387886			0.193943	+	0.981013i	$0.437872\pi$
$384$	−602.223	+	4302.52i	−0.0800314	+	0.571776i
$385$	357.128			0.0472752
$386$	60.9552	−	163.694i	0.00803766	−	0.0215849i
$387$	629.920	+	629.920i	0.0827407	+	0.0827407i
$388$	6020.83	+	5205.84i	0.787786	+	0.681151i
$389$	6046.78	−	6046.78i	0.788133	−	0.788133i	−0.193055	−	0.981188i	$-0.561840\pi$
$389$	6046.78	−	6046.78i	0.788133	−	0.788133i	0.981188	+	0.193055i	$0.0618396\pi$
$390$	−3387.34	+	1549.13i	−0.439807	+	0.201137i
$391$			17418.1i			2.25287i
$392$	6801.22	−	3727.88i	0.876310	−	0.480323i
$393$		−	863.406i		−	0.110822i
$394$	−1020.73	−	2231.94i	−0.130517	−	0.285390i
$395$	−11423.8	+	11423.8i	−1.45517	+	1.45517i
$396$	228.151	+	3142.85i	0.0289521	+	0.398824i
$397$	−4121.17	−	4121.17i	−0.520996	−	0.520996i	0.396876	−	0.917872i	$-0.370094\pi$
$397$	−4121.17	−	4121.17i	−0.520996	−	0.520996i	−0.917872	+	0.396876i	$0.870094\pi$
$398$	−8861.81	−	3299.90i	−1.11609	−	0.415601i
$399$	−135.583			−0.0170117
$400$	10006.2	−	1460.48i	1.25078	−	0.182560i
$401$	3991.60			0.497084			0.248542	−	0.968621i	$-0.420049\pi$
$401$	3991.60			0.497084			0.248542	+	0.968621i	$0.420049\pi$
$402$	−3201.55	−	1192.17i	−0.397211	−	0.147911i
$403$	279.207	+	279.207i	0.0345119	+	0.0345119i
$404$	−14870.1	+	1079.47i	−1.83122	+	0.132935i
$405$	963.533	−	963.533i	0.118218	−	0.118218i
$406$	−5.36471	−	11.7305i	−0.000655779	−	0.00143393i
$407$			3183.59i			0.387727i
$408$	8859.84	+	2586.09i	1.07507	+	0.313801i
$409$			7470.32i			0.903138i	0.892236	+	0.451569i	$0.149136\pi$
$409$			7470.32i			0.903138i	−0.892236	+	0.451569i	$0.850864\pi$
$410$	−17752.2	+	8118.62i	−2.13834	+	0.977927i
$411$	918.486	−	918.486i	0.110233	−	0.110233i
$412$	7038.59	−	8140.50i	0.841667	−	0.973431i
$413$	−142.580	−	142.580i	−0.0169877	−	0.0169877i
$414$	1138.01	−	3056.10i	0.135097	−	0.362800i
$415$	−11026.4			−1.30425
$416$	2564.29	+	3966.82i	0.302223	+	0.467522i
$417$	−4491.32			−0.527437
$418$	4024.84	−	10808.6i	0.470960	−	1.26475i
$419$	−11052.5	−	11052.5i	−1.28866	−	1.28866i	−0.935601	−	0.353059i	$-0.885142\pi$
$419$	−11052.5	−	11052.5i	−1.28866	−	1.28866i	−0.353059	−	0.935601i	$-0.614858\pi$
$420$	−128.090	+	148.143i	−0.0148814	+	0.0172111i
$421$	2747.59	−	2747.59i	0.318075	−	0.318075i	−0.529952	−	0.848027i	$-0.677790\pi$
$421$	2747.59	−	2747.59i	0.318075	−	0.318075i	0.848027	+	0.529952i	$0.177790\pi$
$422$	1622.34	−	741.943i	0.187143	−	0.0855858i
$423$		−	4385.42i		−	0.504082i
$424$	−1946.92	+	6670.06i	−0.222997	+	0.763979i
$425$		−	21482.9i		−	2.45194i
$426$	2169.30	+	4743.40i	0.246720	+	0.539480i
$427$	−100.444	+	100.444i	−0.0113837	+	0.0113837i
$428$	−4939.40	+	358.569i	−0.557838	+	0.0404955i
$429$	2422.57	+	2422.57i	0.272640	+	0.272640i
$430$	−4413.69	−	1643.54i	−0.494993	−	0.184322i
$431$	11.7027			0.00130789			0.000653945	−	1.00000i	$-0.499792\pi$
$431$	11.7027			0.00130789			0.000653945		1.00000i	$0.499792\pi$
$432$	−1385.54	−	1032.60i	−0.154310	−	0.115002i
$433$	−8291.16			−0.920202			−0.460101	−	0.887866i	$-0.652187\pi$
$433$	−8291.16			−0.920202			−0.460101	+	0.887866i	$0.652187\pi$
$434$	19.4557	+	7.24479i	0.00215185	+	0.000801292i
$435$	−335.521	−	335.521i	−0.0369816	−	0.0369816i
$436$	−142.498	−	1962.95i	−0.0156523	−	0.215615i
$437$	−8440.19	+	8440.19i	−0.923911	+	0.923911i
$438$	1715.71	+	3751.59i	0.187169	+	0.409264i
$439$		−	14287.6i		−	1.55332i	−0.629918	−	0.776661i	$-0.716912\pi$
$439$		−	14287.6i		−	1.55332i	0.629918	−	0.776661i	$-0.283088\pi$
$440$	−8007.48	−	14609.0i	−0.867594	−	1.58285i
$441$			3084.88i			0.333105i
$442$	9125.69	−	4173.45i	0.982047	−	0.449119i
$443$	−5070.34	+	5070.34i	−0.543790	+	0.543790i	−0.924638	−	0.380847i	$-0.875632\pi$
$443$	−5070.34	+	5070.34i	−0.543790	+	0.543790i	0.380847	+	0.924638i	$0.375632\pi$
$444$	−1320.61	−	1141.85i	−0.141156	−	0.122049i
$445$	−15207.0	−	15207.0i	−1.61995	−	1.61995i
$446$	−6021.65	+	16171.0i	−0.639313	+	1.71686i
$447$	7225.76			0.764579
$448$	209.354	+	133.599i	0.0220783	+	0.0140892i
$449$	16521.3			1.73650			0.868249	−	0.496128i	$-0.165245\pi$
$449$	16521.3			1.73650			0.868249	+	0.496128i	$0.165245\pi$
$450$	−1403.58	+	3769.28i	−0.147034	+	0.394857i
$451$	12696.1	+	12696.1i	1.32558	+	1.32558i
$452$	−1893.73	−	1637.39i	−0.197066	−	0.170391i
$453$	1148.82	−	1148.82i	0.119153	−	0.119153i
$454$	13287.9	−	6076.97i	1.37364	−	0.628208i
$455$			212.926i			0.0219387i
$456$	3040.03	+	5546.28i	0.312198	+	0.569580i
$457$		−	3323.22i		−	0.340161i	−0.985430	−	0.170080i	$-0.945597\pi$
$457$		−	3323.22i		−	0.340161i	0.985430	−	0.170080i	$-0.0544028\pi$
$458$	2841.20	+	6212.58i	0.289870	+	0.633832i
$459$	−2595.81	+	2595.81i	−0.263970	+	0.263970i
$460$	1248.31	+	17195.8i	0.126527	+	1.74295i
$461$	−1193.80	−	1193.80i	−0.120609	−	0.120609i	0.644226	−	0.764835i	$-0.277180\pi$
$461$	−1193.80	−	1193.80i	−0.120609	−	0.120609i	−0.764835	+	0.644226i	$0.777180\pi$
$462$	168.809	+	62.8601i	0.0169994	+	0.00633012i
$463$	6199.48			0.622277			0.311139	−	0.950365i	$-0.399290\pi$
$463$	6199.48			0.622277			0.311139	+	0.950365i	$0.399290\pi$
$464$	−359.571	+	482.473i	−0.0359756	+	0.0482721i
$465$	763.699			0.0761628
$466$	−8002.95	−	2980.09i	−0.795557	−	0.296244i
$467$	−2566.04	−	2566.04i	−0.254265	−	0.254265i	0.568451	−	0.822717i	$-0.307543\pi$
$467$	−2566.04	−	2566.04i	−0.254265	−	0.254265i	−0.822717	+	0.568451i	$0.807543\pi$
$468$	−1873.82	+	136.027i	−0.185080	+	0.0134356i
$469$	−138.093	+	138.093i	−0.0135960	+	0.0135960i
$470$	9642.72	+	21084.8i	0.946352	+	2.06930i
$471$		−	37.9634i		−	0.00371393i
$472$	−2635.59	+	9029.40i	−0.257018	+	0.880534i
$473$			4332.02i			0.421113i
$474$	−7410.62	+	3389.09i	−0.718103	+	0.328410i
$475$	10409.8	−	10409.8i	1.00555	−	1.00555i
$476$	345.082	−	399.106i	0.0332286	−	0.0384306i
$477$	−1954.24	−	1954.24i	−0.187586	−	0.187586i
$478$	−2925.74	+	7857.02i	−0.279959	+	0.751823i
$479$	4563.85			0.435339			0.217670	−	0.976023i	$-0.430154\pi$
$479$	4563.85			0.435339			0.217670	+	0.976023i	$0.430154\pi$
$480$	8932.08	+	1918.12i	0.849358	+	0.182396i
$481$	−1898.11			−0.179930
$482$	2573.00	−	6909.74i	0.243147	−	0.652967i
$483$	−131.819	−	131.819i	−0.0124182	−	0.0124182i
$484$	−3057.98	+	3536.71i	−0.287188	+	0.332148i
$485$	11835.0	−	11835.0i	1.10804	−	1.10804i
$486$	625.045	−	285.851i	0.0583387	−	0.0266800i
$487$		−	1099.80i		−	0.102334i	−0.998690	−	0.0511672i	$-0.983706\pi$
$487$		−	1099.80i		−	0.102334i	0.998690	−	0.0511672i	$-0.0162941\pi$
$488$	6361.00	+	1856.71i	0.590060	+	0.172232i
$489$		−	5551.11i		−	0.513353i
$490$	−6783.07	−	14831.9i	−0.625363	−	1.36742i
$491$	11017.7	−	11017.7i	1.01267	−	1.01267i	0.0127523	−	0.999919i	$-0.495941\pi$
$491$	11017.7	−	11017.7i	1.01267	−	1.01267i	0.999919	−	0.0127523i	$-0.00405929\pi$
$492$	−9820.23	+	712.886i	−0.899858	+	0.0653239i
$493$	903.913	+	903.913i	0.0825764	+	0.0825764i
$494$	6444.28	+	2399.68i	0.586927	+	0.218556i
$495$	6626.31			0.601678
$496$	−139.872	−	958.312i	−0.0126622	−	0.0867530i
$497$	298.167			0.0269107
$498$	−5212.03	−	1940.82i	−0.468989	−	0.174639i
$499$	−3603.08	−	3603.08i	−0.323238	−	0.323238i	0.526770	−	0.850008i	$-0.323403\pi$
$499$	−3603.08	−	3603.08i	−0.323238	−	0.323238i	−0.850008	+	0.526770i	$0.823403\pi$
$500$	−321.598	−	4430.11i	−0.0287646	−	0.396241i
$501$	−5036.28	+	5036.28i	−0.449110	+	0.449110i
$502$	5021.96	+	10981.1i	0.446496	+	0.976312i
$503$			17947.0i			1.59089i	0.606028	+	0.795443i	$0.292762\pi$
$503$			17947.0i			1.59089i	−0.606028	+	0.795443i	$0.707238\pi$
$504$	−86.6220	+	47.4792i	−0.00765565	+	0.00419622i
$505$			31351.7i			2.76264i
$506$	14421.7	−	6595.45i	1.26704	−	0.579453i
$507$	3216.17	−	3216.17i	0.281726	−	0.281726i
$508$	−8822.82	−	7628.56i	−0.770570	−	0.666265i
$509$	1844.54	+	1844.54i	0.160625	+	0.160625i	0.782843	−	0.622219i	$-0.213769\pi$
$509$	1844.54	+	1844.54i	0.160625	+	0.160625i	−0.622219	+	0.782843i	$0.713769\pi$
$510$	6772.80	−	18188.2i	0.588048	−	1.57919i
$511$	235.822			0.0204151
$512$	771.004	−	11559.6i	0.0665506	−	0.997783i
$513$	−2515.67			−0.216510
$514$	−1962.69	+	5270.77i	−0.168426	+	0.452303i
$515$	−16001.6	−	16001.6i	−1.36916	−	1.36916i
$516$	−1797.00	−	1553.76i	−0.153311	−	0.132559i
$517$	15079.5	−	15079.5i	1.28278	−	1.28278i
$518$	−90.7578	+	41.5062i	−0.00769821	+	0.00352062i
$519$		−	5559.93i		−	0.470239i
$520$	8710.11	−	4774.19i	0.734545	−	0.402619i
$521$		−	5221.57i		−	0.439081i	−0.975603	−	0.219541i	$-0.929544\pi$
$521$		−	5221.57i		−	0.439081i	0.975603	−	0.219541i	$-0.0704558\pi$
$522$	−99.5391	−	217.653i	−0.00834619	−	0.0182498i
$523$	−581.412	+	581.412i	−0.0486106	+	0.0486106i	−0.730994	−	0.682384i	$-0.760943\pi$
$523$	−581.412	+	581.412i	−0.0486106	+	0.0486106i	0.682384	+	0.730994i	$0.260943\pi$
$524$	166.702	+	2296.37i	0.0138977	+	0.191446i
$525$	162.581	+	162.581i	0.0135155	+	0.0135155i
$526$	16035.9	+	5971.33i	1.32927	+	0.494985i
$527$	−2057.45			−0.170064
$528$	−1213.61	−	8314.89i	−0.100030	−	0.685340i
$529$	−4244.75			−0.348874
$530$	13692.9	+	5098.85i	1.12223	+	0.417887i
$531$	−2645.49	−	2645.49i	−0.216204	−	0.216204i
$532$	360.606	−	26.1777i	0.0293877	−	0.00213336i
$533$	−7569.61	+	7569.61i	−0.615152	+	0.615152i
$534$	−4511.45	−	9864.78i	−0.365599	−	0.799421i
$535$			10414.1i			0.841572i
$536$	8745.23	+	2552.64i	0.704732	+	0.205704i
$537$			1054.94i			0.0847749i
$538$	−14127.0	+	6460.70i	−1.13208	+	0.517733i
$539$	−10607.5	+	10607.5i	−0.847678	+	0.847678i
$540$	−2376.64	+	2748.71i	−0.189397	+	0.219048i
$541$	4813.94	+	4813.94i	0.382564	+	0.382564i	0.872025	−	0.489461i	$-0.162806\pi$
$541$	4813.94	+	4813.94i	0.382564	+	0.382564i	−0.489461	+	0.872025i	$0.662806\pi$
$542$	3278.49	−	8804.30i	0.259821	−	0.697744i
$543$	4891.18			0.386557
$544$	−24063.5	−	5167.53i	−1.89654	−	0.407272i
$545$	−4138.64			−0.325284
$546$	−37.4782	+	100.647i	−0.00293758	+	0.00788881i
$547$	−10287.7	−	10287.7i	−0.804154	−	0.804154i	0.179588	−	0.983742i	$-0.442524\pi$
$547$	−10287.7	−	10287.7i	−0.804154	−	0.804154i	−0.983742	+	0.179588i	$0.942524\pi$
$548$	−2265.53	+	2620.21i	−0.176604	+	0.204251i
$549$	−1863.69	+	1863.69i	−0.144882	+	0.144882i
$550$	−17787.1	+	8134.59i	−1.37899	+	0.630654i
$551$			876.006i			0.0677298i
$552$	−2436.67	+	8347.93i	−0.187883	+	0.643680i
$553$			465.825i			0.0358208i
$554$	−5994.44	−	13107.5i	−0.459710	−	1.00520i
$555$	−2595.89	+	2595.89i	−0.198540	+	0.198540i
$556$	11945.4	−	867.162i	0.911149	−	0.0661436i
$557$	16473.4	+	16473.4i	1.25315	+	1.25315i	0.954302	+	0.298843i	$0.0966006\pi$
$557$	16473.4	+	16473.4i	1.25315	+	1.25315i	0.298843	+	0.954302i	$0.403399\pi$
$558$	360.990	+	134.423i	0.0273869	+	0.0101982i
$559$	−2582.82			−0.195424
$560$	312.075	−	418.743i	0.0235492	−	0.0315984i
$561$	−17851.6			−1.34349
$562$	−2183.21	−	812.970i	−0.163867	−	0.0610197i
$563$	−3846.62	−	3846.62i	−0.287950	−	0.287950i	0.548319	−	0.836269i	$-0.315268\pi$
$563$	−3846.62	−	3846.62i	−0.287950	−	0.287950i	−0.836269	+	0.548319i	$0.815268\pi$
$564$	846.715	+	11663.8i	0.0632148	+	0.870804i
$565$	−3722.47	+	3722.47i	−0.277178	+	0.277178i
$566$	−3333.42	−	7288.89i	−0.247552	−	0.541298i
$567$		−	39.2898i		−	0.00291008i
$568$	−6685.45	−	12197.0i	−0.493865	−	0.901015i
$569$			16206.0i			1.19401i	0.802239	+	0.597003i	$0.203642\pi$
$569$			16206.0i			1.19401i	−0.802239	+	0.597003i	$0.796358\pi$
$570$	12095.2	−	5531.48i	0.888792	−	0.406471i
$571$	15842.4	−	15842.4i	1.16109	−	1.16109i	0.176858	−	0.984236i	$-0.443407\pi$
$571$	15842.4	−	15842.4i	1.16109	−	1.16109i	0.984236	−	0.176858i	$-0.0565933\pi$
$572$	−6910.96	−	5975.49i	−0.505178	−	0.436797i
$573$	−970.923	−	970.923i	−0.0707869	−	0.0707869i
$574$	−196.414	+	527.466i	−0.0142825	+	0.0383554i
$575$	20241.7			1.46806
$576$	3884.45	+	2478.86i	0.280993	+	0.179315i
$577$	−18218.5			−1.31446			−0.657231	−	0.753689i	$-0.728272\pi$
$577$	−18218.5			−1.31446			−0.657231	+	0.753689i	$0.728272\pi$
$578$	−13397.1	+	35977.5i	−0.964090	+	2.58904i
$579$	−131.006	−	131.006i	−0.00940314	−	0.00940314i
$580$	957.156	+	827.594i	0.0685237	+	0.0592482i
$581$	−224.811	+	224.811i	−0.0160529	+	0.0160529i
$582$	7677.38	−	3511.09i	0.546800	−	0.250068i
$583$		−	13439.5i		−	0.954728i
$584$	−5287.56	−	9646.71i	−0.374659	−	0.683534i
$585$			3950.71i			0.279217i
$586$	−3160.97	−	6911.79i	−0.222830	−	0.487241i
$587$	3225.64	−	3225.64i	0.226808	−	0.226808i	−0.584550	−	0.811358i	$-0.698729\pi$
$587$	3225.64	−	3225.64i	0.226808	−	0.226808i	0.811358	+	0.584550i	$0.198729\pi$
$588$	−595.613	−	8204.76i	−0.0417733	−	0.575440i
$589$	−996.964	−	996.964i	−0.0697439	−	0.0697439i
$590$	18536.3	+	6902.42i	1.29344	+	0.481641i
$591$	−2603.15			−0.181183
$592$	3732.85	+	2781.97i	0.259154	+	0.193139i
$593$	−15436.7			−1.06898			−0.534492	−	0.845174i	$-0.679497\pi$
$593$	−15436.7			−1.06898			−0.534492	+	0.845174i	$0.679497\pi$
$594$	3132.16	+	1166.33i	0.216354	+	0.0805644i
$595$	−784.514	−	784.514i	−0.0540537	−	0.0540537i
$596$	−19218.1	+	1395.11i	−1.32081	+	0.0958827i
$597$	−7092.20	+	7092.20i	−0.486205	+	0.486205i
$598$	3932.31	+	8598.43i	0.268903	+	0.587986i
$599$			13650.7i			0.931142i	0.885010	+	0.465571i	$0.154151\pi$
$599$			13650.7i			0.931142i	−0.885010	+	0.465571i	$0.845849\pi$
$600$	3005.30	−	10296.0i	0.204485	−	0.700557i
$601$			27042.7i			1.83543i	0.397236	+	0.917716i	$0.369969\pi$
$601$			27042.7i			1.83543i	−0.397236	+	0.917716i	$0.630031\pi$
$602$	−123.497	+	56.4790i	−0.00836109	+	0.00382377i
$603$	−2562.23	+	2562.23i	−0.173038	+	0.173038i
$604$	−2833.68	+	3277.30i	−0.190895	+	0.220780i
$605$	6952.03	+	6952.03i	0.467174	+	0.467174i
$606$	−5518.39	+	14819.5i	−0.369916	+	0.993402i
$607$	−3562.32			−0.238205			−0.119102	−	0.992882i	$-0.538002\pi$
$607$	−3562.32			−0.238205			−0.119102	+	0.992882i	$0.538002\pi$
$608$	−9156.31	−	14164.3i	−0.610752	−	0.944800i
$609$	−13.6815			−0.000910348
$610$	4862.59	−	13058.4i	0.322755	−	0.866752i
$611$	8990.64	+	8990.64i	0.595290	+	0.595290i
$612$	6402.81	−	7405.18i	0.422905	−	0.489112i
$613$	11418.0	−	11418.0i	0.752315	−	0.752315i	−0.222595	−	0.974911i	$-0.571453\pi$
$613$	11418.0	−	11418.0i	0.752315	−	0.752315i	0.974911	+	0.222595i	$0.0714529\pi$
$614$	12693.6	−	5805.17i	0.834321	−	0.381559i
$615$			20704.7i			1.35755i
$616$	−461.114	−	134.594i	−0.0301604	−	0.00880350i
$617$			3981.62i			0.259796i	0.991527	+	0.129898i	$0.0414649\pi$
$617$			3981.62i			0.259796i	−0.991527	+	0.129898i	$0.958535\pi$
$618$	−4747.20	−	10380.3i	−0.308997	−	0.675656i
$619$	6160.23	−	6160.23i	0.400001	−	0.400001i	−0.478232	−	0.878233i	$-0.658722\pi$
$619$	6160.23	−	6160.23i	0.400001	−	0.400001i	0.878233	+	0.478232i	$0.158722\pi$
$620$	−2031.19	+	147.451i	−0.131572	+	0.00955126i
$621$	−2445.83	−	2445.83i	−0.158048	−	0.158048i
$622$	3900.87	+	1452.58i	0.251464	+	0.0936384i
$623$	−620.092			−0.0398771
$624$	4957.48	−	723.575i	0.318041	−	0.0464202i
$625$	10410.2			0.666252
$626$	3336.74	+	1242.51i	0.213040	+	0.0793304i
$627$	−8650.26	−	8650.26i	−0.550970	−	0.550970i
$628$	7.32978	+	100.970i	0.000465748	+	0.00641583i
$629$	6993.48	−	6993.48i	0.443320	−	0.443320i
$630$	86.3909	+	188.903i	0.00546333	+	0.0119461i
$631$		−	670.100i		−	0.0422761i	−0.999777	−	0.0211381i	$-0.993271\pi$
$631$		−	670.100i		−	0.0422761i	0.999777	−	0.0211381i	$-0.00672896\pi$
$632$	19055.4	−	10444.7i	1.19934	−	0.657384i
$633$		−	1892.16i		−	0.118810i
$634$	21470.8	−	9819.25i	1.34498	−	0.615098i
$635$	−17342.8	+	17342.8i	−1.08383	+	1.08383i
$636$	5574.94	+	4820.31i	0.347580	+	0.300531i
$637$	−6324.38	−	6324.38i	−0.393377	−	0.393377i
$638$	406.140	−	1090.68i	0.0252026	−	0.0676810i
$639$	5532.31			0.342496
$640$	−24126.7	−	3377.01i	−1.49014	−	0.208575i
$641$	−3038.11			−0.187204			−0.0936022	−	0.995610i	$-0.529838\pi$
$641$	−3038.11			−0.187204			−0.0936022	+	0.995610i	$0.529838\pi$
$642$	−1833.04	+	4922.60i	−0.112686	+	0.302616i
$643$	11363.4	+	11363.4i	0.696934	+	0.696934i	0.963748	−	0.266814i	$-0.0859710\pi$
$643$	11363.4	+	11363.4i	0.696934	+	0.696934i	−0.266814	+	0.963748i	$0.585971\pi$
$644$	376.046	+	325.144i	0.0230098	+	0.0198952i
$645$	−3532.33	+	3532.33i	−0.215636	+	0.215636i
$646$	−32585.1	+	14902.1i	−1.98459	+	0.907610i
$647$		−	25695.9i		−	1.56137i	−0.624923	−	0.780687i	$-0.714869\pi$
$647$		−	25695.9i		−	1.56137i	0.624923	−	0.780687i	$-0.285131\pi$
$648$	−1607.22	+	880.950i	−0.0974346	+	0.0534059i
$649$		−	18193.3i		−	1.10039i
$650$	−4849.97	−	10605.0i	−0.292664	−	0.639941i
$651$	15.5706	−	15.5706i	0.000937420	−	0.000937420i
$652$	1071.78	+	14764.1i	0.0643775	+	0.886821i
$653$	−20933.8	−	20933.8i	−1.25452	−	1.25452i	−0.953673	−	0.300847i	$-0.902731\pi$
$653$	−20933.8	−	20933.8i	−1.25452	−	1.25452i	−0.300847	−	0.953673i	$-0.597269\pi$
$654$	−1956.27	−	728.464i	−0.116967	−	0.0435554i
$655$	4841.61			0.288821
$656$	25980.9	−	3792.08i	1.54632	−	0.225695i
$657$	4375.54			0.259826
$658$	626.486	+	233.287i	0.0371170	+	0.0138214i
$659$	5253.27	+	5253.27i	0.310529	+	0.310529i	0.845114	−	0.534586i	$-0.179532\pi$
$659$	5253.27	+	5253.27i	0.310529	+	0.310529i	−0.534586	+	0.845114i	$0.679532\pi$
$660$	−17623.8	+	1279.37i	−1.03940	+	0.0754539i
$661$	3182.14	−	3182.14i	0.187248	−	0.187248i	−0.607257	−	0.794505i	$-0.707730\pi$
$661$	3182.14	−	3182.14i	0.187248	−	0.187248i	0.794505	+	0.607257i	$0.207730\pi$
$662$	−5417.84	−	11846.7i	−0.318082	−	0.695521i
$663$		−	10643.4i		−	0.623465i
$664$	14237.0	+	4155.63i	0.832082	+	0.242876i
$665$		−	760.293i		−	0.0443352i
$666$	−1683.96	+	770.124i	−0.0979761	+	0.0448074i
$667$	−851.686	+	851.686i	−0.0494414	+	0.0494414i
$668$	12422.4	−	14367.2i	0.719519	−	0.832161i
$669$	12941.8	+	12941.8i	0.747922	+	0.747922i
$670$	6685.19	−	17952.9i	0.385480	−	1.03520i
$671$	−12816.8			−0.737385
$672$	221.219	−	143.004i	0.0126989	−	0.00820905i
$673$	27736.4			1.58865			0.794325	−	0.607493i	$-0.207825\pi$
$673$	27736.4			1.58865			0.794325	+	0.607493i	$0.207825\pi$
$674$	4819.16	−	12941.7i	0.275411	−	0.739610i
$675$	3016.60	+	3016.60i	0.172013	+	0.172013i
$676$	−7932.97	+	9174.90i	−0.451353	+	0.522013i
$677$	6076.45	−	6076.45i	0.344959	−	0.344959i	−0.513269	−	0.858228i	$-0.671566\pi$
$677$	6076.45	−	6076.45i	0.344959	−	0.344959i	0.858228	+	0.513269i	$0.171566\pi$
$678$	−2414.77	+	1104.35i	−0.136783	+	0.0625547i
$679$		−	482.594i		−	0.0272758i
$680$	−14501.7	+	49682.2i	−0.817816	+	2.80180i
$681$		−	15498.0i		−	0.872075i
$682$	779.061	+	1703.50i	0.0437416	+	0.0956457i
$683$	−2360.09	+	2360.09i	−0.132220	+	0.132220i	−0.770120	−	0.637900i	$-0.779803\pi$
$683$	−2360.09	+	2360.09i	−0.132220	+	0.132220i	0.637900	+	0.770120i	$0.279803\pi$
$684$	6690.85	−	485.713i	0.374022	−	0.0271516i
$685$	5150.48	+	5150.48i	0.287284	+	0.287284i
$686$	−881.694	−	328.319i	−0.0490717	−	0.0182730i
$687$	7245.84			0.402396
$688$	5079.42	+	3785.52i	0.281469	+	0.209770i
$689$	8012.84			0.443055
$690$	17137.3	+	6381.48i	0.945517	+	0.352085i
$691$	10248.5	+	10248.5i	0.564211	+	0.564211i	0.930501	−	0.366290i	$-0.119372\pi$
$691$	10248.5	+	10248.5i	0.564211	+	0.564211i	−0.366290	+	0.930501i	$0.619372\pi$
$692$	1073.48	+	14787.6i	0.0589707	+	0.812340i
$693$	135.100	−	135.100i	0.00740552	−	0.00740552i
$694$	2902.48	+	6346.58i	0.158756	+	0.347137i
$695$		−	25185.4i		−	1.37459i
$696$	306.764	+	559.666i	0.0167067	+	0.0304800i
$697$		−	55779.7i		−	3.03128i
$698$	−22598.8	+	10335.1i	−1.22547	+	0.560442i
$699$	−6404.85	+	6404.85i	−0.346572	+	0.346572i
$700$	−463.802	−	401.021i	−0.0250429	−	0.0216531i
$701$	−5637.61	−	5637.61i	−0.303751	−	0.303751i	0.538728	−	0.842480i	$-0.318905\pi$
$701$	−5637.61	−	5637.61i	−0.303751	−	0.303751i	−0.842480	+	0.538728i	$0.818905\pi$
$702$	−695.387	+	1867.45i	−0.0373870	+	0.100402i
$703$	6777.57			0.363614
$704$	4833.20	+	21880.5i	0.258747	+	1.17138i
$705$	24591.6			1.31372
$706$	−674.179	+	1810.49i	−0.0359392	+	0.0965139i
$707$	639.212	+	639.212i	0.0340029	+	0.0340029i
$708$	7546.91	+	6525.35i	0.400608	+	0.346381i
$709$	−1798.00	+	1798.00i	−0.0952402	+	0.0952402i	−0.753122	−	0.657881i	$-0.771453\pi$
$709$	−1798.00	+	1798.00i	−0.0952402	+	0.0952402i	0.657881	+	0.753122i	$0.271453\pi$
$710$	−26599.0	+	12164.5i	−1.40598	+	0.642994i
$711$			8643.12i			0.455897i
$712$	13903.6	+	25366.0i	0.731826	+	1.33516i
$713$		−	1938.57i		−	0.101823i
$714$	−232.742	−	508.915i	−0.0121991	−	0.0266746i
$715$	−13584.7	+	13584.7i	−0.710545	+	0.710545i
$716$	−203.683	−	2805.80i	−0.0106313	−	0.146449i
$717$	6288.05	+	6288.05i	0.327520	+	0.327520i
$718$	10654.6	+	3967.49i	0.553797	+	0.206219i
$719$	−35035.3			−1.81724			−0.908622	−	0.417620i	$-0.862864\pi$
$719$	−35035.3			−1.81724			−0.908622	+	0.417620i	$0.862864\pi$
$720$	5790.37	−	7769.53i	0.299715	−	0.402157i
$721$	−652.495			−0.0337034
$722$	−4829.96	−	1798.55i	−0.248965	−	0.0927078i
$723$	−5529.94	−	5529.94i	−0.284455	−	0.284455i
$724$	−13008.9	+	944.364i	−0.667780	+	0.0484765i
$725$	1050.44	−	1050.44i	0.0538101	−	0.0538101i
$726$	2062.46	+	4509.79i	0.105434	+	0.230543i
$727$			24515.4i			1.25066i	0.780362	+	0.625328i	$0.215035\pi$
$727$			24515.4i			1.25066i	−0.780362	+	0.625328i	$0.784965\pi$
$728$	80.2472	−	274.923i	0.00408539	−	0.0139963i
$729$		−	729.000i		−	0.0370370i
$730$	−21037.3	+	9620.98i	−1.06661	+	0.487792i
$731$	9516.28	−	9516.28i	0.481494	−	0.481494i
$732$	4596.96	−	5316.62i	0.232115	−	0.268453i
$733$	−23583.9	−	23583.9i	−1.18839	−	1.18839i	−0.977512	−	0.210878i	$-0.932368\pi$
$733$	−23583.9	−	23583.9i	−1.18839	−	1.18839i	−0.210878	−	0.977512i	$-0.567632\pi$
$734$	7937.60	−	21316.3i	0.399159	−	1.07193i
$735$	−17298.7			−0.868126
$736$	4868.96	−	22673.2i	0.243848	−	1.13552i
$737$	−17620.7			−0.880689
$738$	−3644.35	+	9786.82i	−0.181776	+	0.488154i
$739$	−17246.2	−	17246.2i	−0.858472	−	0.858472i	0.132686	−	0.991158i	$-0.457640\pi$
$739$	−17246.2	−	17246.2i	−0.858472	−	0.858472i	−0.991158	+	0.132686i	$0.957640\pi$
$740$	6403.01	−	7405.42i	0.318080	−	0.367877i
$741$	5157.42	−	5157.42i	0.255685	−	0.255685i
$742$	383.133	−	175.218i	0.0189559	−	0.00866908i
$743$			14249.5i			0.703587i	0.936078	+	0.351793i	$0.114428\pi$
$743$			14249.5i			0.703587i	−0.936078	+	0.351793i	$0.885572\pi$
$744$	−986.066	−	287.822i	−0.0485900	−	0.0141829i
$745$			40519.0i			1.99262i
$746$	1339.64	+	2929.27i	0.0657477	+	0.143764i
$747$	−4171.24	+	4171.24i	−0.204308	+	0.204308i
$748$	47479.4	−	3446.71i	2.32088	−	0.168481i
$749$	212.327	+	212.327i	0.0103582	+	0.0103582i
$750$	−4415.04	−	1644.04i	−0.214953	−	0.0800427i
$751$	10260.0			0.498524			0.249262	−	0.968436i	$-0.419812\pi$
$751$	10260.0			0.498524			0.249262	+	0.968436i	$0.419812\pi$
$752$	−4503.96	−	30858.3i	−0.218408	−	1.49639i
$753$	12807.4			0.619824
$754$	650.282	+	242.148i	0.0314083	+	0.0116956i
$755$	6442.11	+	6442.11i	0.310533	+	0.310533i
$756$	7.58588	+	104.498i	0.000364941	+	0.00502718i
$757$	−18953.4	+	18953.4i	−0.910005	+	0.910005i	−0.996272	−	0.0862671i	$-0.972506\pi$
$757$	−18953.4	+	18953.4i	−0.910005	+	0.910005i	0.0862671	+	0.996272i	$0.472506\pi$
$758$	864.175	+	1889.61i	0.0414093	+	0.0905459i
$759$		−	16820.2i		−	0.804394i
$760$	−31101.2	+	17047.2i	−1.48442	+	0.813640i
$761$		−	24434.3i		−	1.16392i	−0.813218	−	0.581960i	$-0.802286\pi$
$761$		−	24434.3i		−	1.16392i	0.813218	−	0.581960i	$-0.197714\pi$
$762$	−11250.3	+	5145.10i	−0.534851	+	0.244603i
$763$	−84.3802	+	84.3802i	−0.00400363	+	0.00400363i
$764$	2769.79	+	2394.87i	0.131162	+	0.113408i
$765$	−14556.2	−	14556.2i	−0.687949	−	0.687949i
$766$	−2869.65	+	7706.37i	−0.135358	+	0.363502i
$767$	10847.1			0.510649
$768$	−10809.9	−	5842.94i	−0.507904	−	0.274530i
$769$	−6752.03			−0.316625			−0.158312	−	0.987389i	$-0.550605\pi$
$769$	−6752.03			−0.316625			−0.158312	+	0.987389i	$0.550605\pi$
$770$	−352.493	+	946.612i	−0.0164974	+	0.0443033i
$771$	4218.26	+	4218.26i	0.197039	+	0.197039i
$772$	373.726	+	323.138i	0.0174232	+	0.0150648i
$773$	−18608.6	+	18608.6i	−0.865854	+	0.865854i	−0.992010	−	0.126157i	$-0.959736\pi$
$773$	−18608.6	+	18608.6i	−0.865854	+	0.865854i	0.126157	+	0.992010i	$0.459736\pi$
$774$	−2291.42	+	1047.94i	−0.106413	+	0.0486657i
$775$			2390.96i			0.110821i
$776$	−19741.4	+	10820.7i	−0.913240	+	0.500566i
$777$			105.852i			0.00488730i
$778$	10059.4	+	21996.0i	0.463557	+	1.01362i
$779$	27028.8	−	27028.8i	1.24314	−	1.24314i
$780$	−762.784	−	10507.6i	−0.0350154	−	0.482349i
$781$	19023.1	+	19023.1i	0.871576	+	0.871576i
$782$	−46168.9	−	17192.1i	−2.11125	−	0.786172i
$783$	−253.852			−0.0115861
$784$	3168.27	+	21706.9i	0.144327	+	0.988837i
$785$	212.883			0.00967911
$786$	2288.56	+	852.199i	0.103855	+	0.0386729i
$787$	23406.2	+	23406.2i	1.06016	+	1.06016i	0.998071	+	0.0620850i	$0.0197750\pi$
$787$	23406.2	+	23406.2i	1.06016	+	1.06016i	0.0620850	+	0.998071i	$0.480225\pi$
$788$	6923.51	−	502.603i	0.312995	−	0.0227214i
$789$	12833.7	−	12833.7i	0.579076	−	0.579076i
$790$	−19004.6	−	41555.6i	−0.855890	−	1.87150i
$791$			151.790i			0.00682307i
$792$	−8555.70	−	2497.32i	−0.383855	−	0.112043i
$793$		−	7641.56i		−	0.342194i
$794$	14991.3	−	6855.98i	0.670054	−	0.306435i
$795$	10958.5	−	10958.5i	0.488880	−	0.488880i
$796$	17493.6	−	20232.2i	0.778949	−	0.900895i
$797$	1487.10	+	1487.10i	0.0660925	+	0.0660925i	0.739380	−	0.673288i	$-0.235119\pi$
$797$	1487.10	+	1487.10i	0.0660925	+	0.0660925i	−0.673288	+	0.739380i	$0.735119\pi$
$798$	133.823	−	359.380i	0.00593646	−	0.0159422i
$799$	−66251.1			−2.93341
$800$	−6005.20	+	27964.3i	−0.265395	+	1.23586i
$801$	−11505.5			−0.507522
$802$	−3939.79	+	10580.2i	−0.173465	+	0.465835i
$803$	15045.5	+	15045.5i	0.661201	+	0.661201i
$804$	6319.99	−	7309.39i	0.277225	−	0.320625i
$805$	739.186	−	739.186i	0.0323638	−	0.0323638i
$806$	−1015.65	+	464.489i	−0.0443857	+	0.0202989i
$807$			16476.6i			0.718715i
$808$	11815.8	−	40480.4i	0.514454	−	1.76250i
$809$		−	10505.2i		−	0.456542i	−0.973598	−	0.228271i	$-0.926693\pi$
$809$		−	10505.2i		−	0.456542i	0.973598	−	0.228271i	$-0.0733072\pi$
$810$	1602.93	+	3504.99i	0.0695325	+	0.152040i
$811$	−27073.1	+	27073.1i	−1.17221	+	1.17221i	−0.190531	+	0.981681i	$0.561021\pi$
$811$	−27073.1	+	27073.1i	−1.17221	+	1.17221i	−0.981681	+	0.190531i	$0.938979\pi$
$812$	36.3882	−	2.64155i	0.00157263	−	0.000114163i
$813$	−7046.18	−	7046.18i	−0.303961	−	0.303961i
$814$	−8438.49	−	3142.27i	−0.363352	−	0.135303i
$815$	31128.3			1.33788
$816$	−15599.6	+	20931.5i	−0.669234	+	0.897978i
$817$	9222.48			0.394925
$818$	−19801.0	−	7373.36i	−0.846363	−	0.315163i
$819$	80.5488	+	80.5488i	0.00343663	+	0.00343663i
$820$	−3997.56	−	55067.7i	−0.170245	−	2.34518i
$821$	−9907.96	+	9907.96i	−0.421182	+	0.421182i	−0.885610	−	0.464429i	$-0.846260\pi$
$821$	−9907.96	+	9907.96i	−0.421182	+	0.421182i	0.464429	+	0.885610i	$0.346260\pi$
$822$	1527.99	+	3341.12i	0.0648357	+	0.141770i
$823$		−	17501.8i		−	0.741281i	−0.928776	−	0.370640i	$-0.879138\pi$
$823$		−	17501.8i		−	0.741281i	0.928776	−	0.370640i	$-0.120862\pi$
$824$	14630.1	+	26691.5i	0.618526	+	1.12845i
$825$			20745.4i			0.875471i
$826$	518.655	−	237.196i	0.0218478	−	0.00999166i
$827$	7074.02	−	7074.02i	0.297446	−	0.297446i	−0.542567	−	0.840013i	$-0.682547\pi$
$827$	7074.02	−	7074.02i	0.297446	−	0.297446i	0.840013	+	0.542567i	$0.182547\pi$
$828$	6977.32	+	6032.87i	0.292849	+	0.253208i
$829$	21066.1	+	21066.1i	0.882576	+	0.882576i	0.993796	−	0.111220i	$-0.0354758\pi$
$829$	21066.1	+	21066.1i	0.882576	+	0.882576i	−0.111220	+	0.993796i	$0.535476\pi$
$830$	10883.3	−	29226.9i	0.455138	−	1.22226i
$831$	−15287.5			−0.638167
$832$	−13045.5	+	2881.63i	−0.543597	+	0.120075i
$833$	46603.7			1.93844
$834$	4433.03	−	11904.8i	0.184057	−	0.494280i
$835$	−28241.3	−	28241.3i	−1.17046	−	1.17046i
$836$	24677.0	+	21336.7i	1.02090	+	0.882708i
$837$	288.904	−	288.904i	0.0119307	−	0.0119307i
$838$	40204.9	−	18386.9i	1.65735	−	0.757953i
$839$			30444.6i			1.25276i	0.779519	+	0.626379i	$0.215464\pi$
$839$			30444.6i			1.25276i	−0.779519	+	0.626379i	$0.784536\pi$
$840$	−266.243	−	485.739i	−0.0109360	−	0.0199519i
$841$		−	24300.6i		−	0.996376i
$842$	4570.90	+	9994.76i	0.187083	+	0.409076i
$843$	−1747.25	+	1747.25i	−0.0713861	+	0.0713861i
$844$	365.329	+	5032.52i	0.0148994	+	0.205244i
$845$	18034.9	+	18034.9i	0.734224	+	0.734224i
$846$	11624.1	+	4328.50i	0.472393	+	0.175907i
$847$	283.482			0.0115001
$848$	−15758.2	−	11744.0i	−0.638134	−	0.475580i
$849$	−8501.15			−0.343650
$850$	56943.0	+	21204.1i	2.29780	+	0.855639i
$851$	6589.41	+	6589.41i	0.265431	+	0.265431i
$852$	−14714.1	+	1068.15i	−0.591663	+	0.0429510i
$853$	−882.218	+	882.218i	−0.0354122	+	0.0354122i	−0.724591	−	0.689179i	$-0.757971\pi$
$853$	−882.218	+	882.218i	−0.0354122	+	0.0354122i	0.689179	+	0.724591i	$0.257971\pi$
$854$	−167.099	−	365.380i	−0.00669557	−	0.0146406i
$855$		−	14106.8i		−	0.564261i
$856$	3924.86	−	13446.4i	0.156716	−	0.536902i
$857$			8006.81i			0.319145i	0.987186	+	0.159572i	$0.0510116\pi$
$857$			8006.81i			0.319145i	−0.987186	+	0.159572i	$0.948988\pi$
$858$	−8812.43	+	4030.18i	−0.350643	+	0.160359i
$859$	−20266.0	+	20266.0i	−0.804967	+	0.804967i	−0.983867	−	0.178900i	$-0.942746\pi$
$859$	−20266.0	+	20266.0i	−0.804967	+	0.804967i	0.178900	+	0.983867i	$0.442746\pi$
$860$	8712.81	−	10076.8i	0.345470	−	0.399554i
$861$	422.136	+	422.136i	0.0167089	+	0.0167089i
$862$	−11.5508	+	31.0195i	−0.000456407	+	0.00122567i
$863$	41478.0			1.63607			0.818034	−	0.575169i	$-0.195064\pi$
$863$	41478.0			1.63607			0.818034	+	0.575169i	$0.195064\pi$
$864$	4104.58	−	2653.35i	0.161621	−	0.104478i
$865$	31177.7			1.22552
$866$	8183.54	−	21976.7i	0.321118	−	0.862355i
$867$	28793.2	+	28793.2i	1.12787	+	1.12787i
$868$	−38.4064	+	44.4190i	−0.00150184	+	0.00173696i
$869$	−29719.8	+	29719.8i	−1.16016	+	1.16016i
$870$	1220.51	−	558.173i	0.0475621	−	0.0217515i
$871$		−	10505.8i		−	0.408696i
$872$	5343.69	+	1559.77i	0.207523	+	0.0605738i
$873$		−	8954.26i		−	0.347143i
$874$	−14041.1	−	30702.4i	−0.543418	−	1.18824i
$875$	−190.435	+	190.435i	−0.00735756	+	0.00735756i
$876$	−11637.5	+	844.806i	−0.448851	+	0.0325837i
$877$	6027.15	+	6027.15i	0.232067	+	0.232067i	0.813555	−	0.581488i	$-0.197529\pi$
$877$	6027.15	+	6027.15i	0.232067	+	0.232067i	−0.581488	+	0.813555i	$0.697529\pi$
$878$	37870.9	+	14102.1i	1.45567	+	0.542054i
$879$	−8061.34			−0.309331
$880$	46626.4	−	6805.42i	1.78611	−	0.260694i
$881$	−40154.3			−1.53556			−0.767782	−	0.640712i	$-0.778639\pi$
$881$	−40154.3			−1.53556			−0.767782	+	0.640712i	$0.778639\pi$
$882$	−8176.85	−	3044.84i	−0.312164	−	0.116242i
$883$	4435.93	+	4435.93i	0.169061	+	0.169061i	0.786567	−	0.617505i	$-0.211857\pi$
$883$	4435.93	+	4435.93i	0.169061	+	0.169061i	−0.617505	+	0.786567i	$0.711857\pi$
$884$	2054.98	+	28308.0i	0.0781861	+	1.07704i
$885$	14834.8	−	14834.8i	0.563465	−	0.563465i
$886$	−8435.02	−	18444.1i	−0.319842	−	0.699369i
$887$		−	3275.31i		−	0.123984i	−0.998077	−	0.0619921i	$-0.980255\pi$
$887$		−	3275.31i		−	0.123984i	0.998077	−	0.0619921i	$-0.0197454\pi$
$888$	4330.08	−	2373.41i	0.163635	−	0.0896917i
$889$			707.186i			0.0266797i
$890$	55317.5	−	25298.3i	2.08342	−	0.952811i
$891$	2506.70	−	2506.70i	0.0942511	−	0.0942511i
$892$	−36919.7	−	31922.2i	−1.38583	−	1.19825i
$893$	−32102.9	−	32102.9i	−1.20300	−	1.20300i
$894$	−7131.98	+	19152.8i	−0.266811	+	0.716515i
$895$	−5915.67			−0.220937
$896$	−560.758	+	423.054i	−0.0209080	+	0.0157737i
$897$	10028.5			0.373290
$898$	−16306.8	+	43791.7i	−0.605976	+	1.62734i
$899$	−100.602	−	100.602i	−0.00373222	−	0.00373222i
$900$	−8605.58	−	7440.72i	−0.318725	−	0.275582i
$901$	−29522.9	+	29522.9i	−1.09162	+	1.09162i
$902$	−46183.8	+	21121.2i	−1.70482	+	0.779666i
$903$			144.037i			0.00530814i
$904$	6209.26	−	3403.42i	0.228448	−	0.125217i
$905$			27427.7i			1.00743i
$906$	1911.18	+	4179.00i	0.0700825	+	0.153243i
$907$	18595.8	−	18595.8i	0.680775	−	0.680775i	−0.279400	−	0.960175i	$-0.590135\pi$
$907$	18595.8	−	18595.8i	0.680775	−	0.680775i	0.960175	+	0.279400i	$0.0901354\pi$
$908$	2992.27	+	41219.4i	0.109363	+	1.50651i
$909$	11860.2	+	11860.2i	0.432759	+	0.432759i
$910$	−564.385	−	210.162i	−0.0205596	−	0.00765583i
$911$	−25144.8			−0.914472			−0.457236	−	0.889345i	$-0.651161\pi$
$911$	−25144.8			−0.914472			−0.457236	+	0.889345i	$0.651161\pi$
$912$	−17701.6	+	2583.67i	−0.642719	+	0.0938090i
$913$	−28686.1			−1.03984
$914$	8808.59	+	3280.08i	0.318777	+	0.118704i
$915$	−10450.8	−	10450.8i	−0.377586	−	0.377586i
$916$	−19271.5	+	1398.99i	−0.695141	+	0.0504628i
$917$	98.7128	−	98.7128i	0.00355484	−	0.00355484i
$918$	−4318.39	−	9442.63i	−0.155259	−	0.339491i
$919$		−	18292.8i		−	0.656608i	−0.944572	−	0.328304i	$-0.893523\pi$
$919$		−	18292.8i		−	0.656608i	0.944572	−	0.328304i	$-0.106477\pi$
$920$	−46811.7	−	13663.8i	−1.67754	−	0.489655i
$921$		−	14804.8i		−	0.529679i
$922$	4342.61	−	1986.00i	0.155115	−	0.0709387i
$923$	−11341.9	+	11341.9i	−0.404467	+	0.404467i
$924$	−333.237	+	385.405i	−0.0118644	+	0.0137218i
$925$	−8127.14	−	8127.14i	−0.288885	−	0.288885i
$926$	−6119.02	+	16432.5i	−0.217153	+	0.583158i
$927$	−12106.7			−0.428948
$928$	−923.949	−	1429.30i	−0.0326833	−	0.0505593i
$929$	16680.0			0.589078			0.294539	−	0.955640i	$-0.404834\pi$
$929$	16680.0			0.589078			0.294539	+	0.955640i	$0.404834\pi$
$930$	−753.787	+	2024.28i	−0.0265781	+	0.0713749i
$931$	22582.4	+	22582.4i	0.794962	+	0.794962i
$932$	15798.2	−	18271.4i	0.555242	−	0.642167i
$933$	3121.91	−	3121.91i	0.109546	−	0.109546i
$934$	9334.32	−	4268.86i	0.327011	−	0.149552i
$935$		−	100104.i		−	3.50135i
$936$	1488.94	−	5101.05i	0.0519953	−	0.178134i
$937$		−	2053.17i		−	0.0715839i	−0.999359	−	0.0357920i	$-0.988605\pi$
$937$		−	2053.17i		−	0.0715839i	0.999359	−	0.0357920i	$-0.0113954\pi$
$938$	−229.731	−	502.332i	−0.00799679	−	0.0174858i
$939$	2670.43	−	2670.43i	0.0928074	−	0.0928074i
$940$	−65405.5	+	4748.02i	−2.26946	+	0.164748i
$941$	−17468.5	−	17468.5i	−0.605160	−	0.605160i	0.336517	−	0.941677i	$-0.390751\pi$
$941$	−17468.5	−	17468.5i	−0.605160	−	0.605160i	−0.941677	+	0.336517i	$0.890751\pi$
$942$	100.627	+	37.4706i	0.00348046	+	0.00129603i
$943$	52556.8			1.81494
$944$	−21332.1	−	15898.1i	−0.735490	−	0.548136i
$945$	220.321			0.00758416
$946$	−11482.6	−	4275.80i	−0.394641	−	0.146954i
$947$	22999.8	+	22999.8i	0.789223	+	0.789223i	0.981367	−	0.192144i	$-0.0615441\pi$
$947$	22999.8	+	22999.8i	0.789223	+	0.789223i	−0.192144	+	0.981367i	$0.561544\pi$
$948$	−1668.77	−	22987.8i	−0.0571721	−	0.787563i
$949$	−8970.37	+	8970.37i	−0.306839	+	0.306839i
$950$	17317.8	+	37867.2i	0.591435	+	1.29324i
$951$		−	25041.8i		−	0.853876i
$952$	717.275	+	1308.61i	0.0244191	+	0.0445507i
$953$			29341.4i			0.997336i	0.866793	+	0.498668i	$0.166177\pi$
$953$			29341.4i			0.997336i	−0.866793	+	0.498668i	$0.833823\pi$
$954$	7108.81	−	3251.07i	0.241254	−	0.110333i
$955$	5444.52	−	5444.52i	0.184482	−	0.184482i
$956$	−17938.2	−	15510.1i	−0.606865	−	0.524719i
$957$	−872.884	−	872.884i	−0.0294841	−	0.0294841i
$958$	−4504.61	+	12097.0i	−0.151918	+	0.407972i
$959$	210.020			0.00707186
$960$	−13900.4	+	21782.3i	−0.467326	+	0.732315i
$961$	−29562.0			−0.992314
$962$	1873.47	−	5031.17i	0.0627891	−	0.168619i
$963$	3939.61	+	3939.61i	0.131830	+	0.131830i
$964$	15775.5	+	13640.1i	0.527069	+	0.455724i
$965$	734.625	−	734.625i	0.0245061	−	0.0245061i
$966$	479.511	−	219.294i	0.0159710	−	0.00730402i
$967$			8861.99i			0.294708i	0.989084	+	0.147354i	$0.0470756\pi$
$967$			8861.99i			0.294708i	−0.989084	+	0.147354i	$0.952924\pi$
$968$	−6356.19	−	11596.3i	−0.211049	−	0.385042i
$969$			38004.5i			1.25994i
$970$	19688.7	+	43051.5i	0.651718	+	1.42505i
$971$	38037.4	−	38037.4i	1.25714	−	1.25714i	0.304681	−	0.952454i	$-0.401450\pi$
$971$	38037.4	−	38037.4i	1.25714	−	1.25714i	0.952454	−	0.304681i	$-0.0985500\pi$
$972$	140.752	+	1938.90i	0.00464466	+	0.0639817i
$973$	−513.491	−	513.491i	−0.0169186	−	0.0169186i
$974$	2915.16	+	1085.53i	0.0959013	+	0.0357111i
$975$	−12368.8			−0.406275
$976$	−11199.9	+	15028.0i	−0.367315	+	0.492863i
$977$	26081.9			0.854078			0.427039	−	0.904233i	$-0.359557\pi$
$977$	26081.9			0.854078			0.427039	+	0.904233i	$0.359557\pi$
$978$	14713.9	+	5479.06i	0.481082	+	0.179142i
$979$	−39562.1	−	39562.1i	−1.29153	−	1.29153i
$980$	46008.8	−	3339.95i	1.49969	−	0.108868i
$981$	−1565.63	+	1565.63i	−0.0509548	+	0.0509548i
$982$	18329.0	+	40078.4i	0.595624	+	1.30240i
$983$			28987.6i			0.940552i	0.882520	+	0.470276i	$0.155846\pi$
$983$			28987.6i			0.940552i	−0.882520	+	0.470276i	$0.844154\pi$
$984$	7803.18	−	26733.3i	0.252801	−	0.866085i
$985$		−	14597.3i		−	0.472193i
$986$	−3288.11	+	1503.75i	−0.106202	+	0.0485691i
$987$	501.384	−	501.384i	0.0161694	−	0.0161694i
$988$	−12721.3	+	14712.8i	−0.409633	+	0.473762i
$989$	8966.45	+	8966.45i	0.288288	+	0.288288i
$990$	−6540.30	+	17563.8i	−0.209964	+	0.563854i
$991$	33373.6			1.06977			0.534887	−	0.844923i	$-0.320354\pi$
$991$	33373.6			1.06977			0.534887	+	0.844923i	$0.320354\pi$
$992$	2678.18	+	575.127i	0.0857180	+	0.0184076i
$993$	−13817.0			−0.441560
$994$	−294.297	+	790.327i	−0.00939086	+	0.0252189i
$995$	−39770.1	−	39770.1i	−1.26713	−	1.26713i
$996$	10288.8	−	11899.5i	0.327321	−	0.378564i
$997$	−5283.79	+	5283.79i	−0.167843	+	0.167843i	−0.786031	−	0.618188i	$-0.787867\pi$
$997$	−5283.79	+	5283.79i	−0.167843	+	0.167843i	0.618188	+	0.786031i	$0.287867\pi$
$998$	13106.7	−	5994.08i	0.415717	−	0.190120i
$999$			1964.03i			0.0622014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.13.5	✓	24
3.2	odd	2		144.4.k.b.109.8		24
4.3	odd	2		192.4.j.a.145.1		24
8.3	odd	2		384.4.j.a.289.7		24
8.5	even	2		384.4.j.b.289.6		24
12.11	even	2		576.4.k.b.145.12		24
16.3	odd	4		384.4.j.a.97.7		24
16.5	even	4	inner	48.4.j.a.37.5	yes	24
16.11	odd	4		192.4.j.a.49.1		24
16.13	even	4		384.4.j.b.97.6		24
48.5	odd	4		144.4.k.b.37.8		24
48.11	even	4		576.4.k.b.433.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.5	✓	24	1.1	even	1	trivial
48.4.j.a.37.5	yes	24	16.5	even	4	inner
144.4.k.b.37.8		24	48.5	odd	4
144.4.k.b.109.8		24	3.2	odd	2
192.4.j.a.49.1		24	16.11	odd	4
192.4.j.a.145.1		24	4.3	odd	2
384.4.j.a.97.7		24	16.3	odd	4
384.4.j.a.289.7		24	8.3	odd	2
384.4.j.b.97.6		24	16.13	even	4
384.4.j.b.289.6		24	8.5	even	2
576.4.k.b.145.12		24	12.11	even	2
576.4.k.b.433.12		24	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.987020 + 2.65062i) q^{2} +(2.12132 + 2.12132i) q^{3} +(-6.05158 - 5.23243i) q^{4} +(-11.8955 + 11.8955i) q^{5} +(-7.71660 + 3.52903i) q^{6} +0.485059i q^{7} +(19.8422 - 10.8759i) q^{8} +9.00000i q^{9} +(-19.7893 - 43.2714i) q^{10} +(-30.9469 + 30.9469i) q^{11} +(-1.73767 - 23.9370i) q^{12} +(-18.4511 - 18.4511i) q^{13} +(-1.28571 - 0.478764i) q^{14} -50.4682 q^{15} +(9.24327 + 63.3290i) q^{16} +135.964 q^{17} +(-23.8556 - 8.88318i) q^{18} +(65.8832 + 65.8832i) q^{19} +(134.229 - 9.74414i) q^{20} +(-1.02897 + 1.02897i) q^{21} +(-51.4834 - 112.574i) q^{22} +128.108i q^{23} +(65.1631 + 19.0204i) q^{24} -158.004i q^{25} +(67.1184 - 30.6952i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(2.53804 - 2.93538i) q^{28} +(6.64817 + 6.64817i) q^{29} +(49.8131 - 133.772i) q^{30} -15.1323 q^{31} +(-176.984 - 38.0066i) q^{32} -131.297 q^{33} +(-134.199 + 360.389i) q^{34} +(-5.77001 - 5.77001i) q^{35} +(47.0919 - 54.4642i) q^{36} +(51.4363 - 51.4363i) q^{37} +(-239.660 + 109.603i) q^{38} -78.2813i q^{39} +(-106.658 + 365.407i) q^{40} -410.253i q^{41} +(-1.71179 - 3.74301i) q^{42} +(69.9911 - 69.9911i) q^{43} +(349.206 - 25.3501i) q^{44} +(-107.059 - 107.059i) q^{45} +(-339.567 - 126.446i) q^{46} -487.269 q^{47} +(-114.733 + 153.949i) q^{48} +342.765 q^{49} +(418.809 + 155.953i) q^{50} +(288.423 + 288.423i) q^{51} +(15.1142 + 208.202i) q^{52} +(-217.138 + 217.138i) q^{53} +(-31.7613 - 69.4494i) q^{54} -736.257i q^{55} +(5.27547 + 9.62466i) q^{56} +279.519i q^{57} +(-24.1837 + 11.0599i) q^{58} +(-293.944 + 293.944i) q^{59} +(305.412 + 264.071i) q^{60} +(207.076 + 207.076i) q^{61} +(14.9359 - 40.1099i) q^{62} -4.36553 q^{63} +(275.428 - 431.605i) q^{64} +438.968 q^{65} +(129.593 - 348.018i) q^{66} +(284.693 + 284.693i) q^{67} +(-822.798 - 711.423i) q^{68} +(-271.759 + 271.759i) q^{69} +(20.9892 - 9.59899i) q^{70} -614.701i q^{71} +(97.8834 + 178.580i) q^{72} -486.171i q^{73} +(85.5694 + 187.107i) q^{74} +(335.178 - 335.178i) q^{75} +(-53.9681 - 743.427i) q^{76} +(-15.0111 - 15.0111i) q^{77} +(207.494 + 77.2652i) q^{78} +960.347 q^{79} +(-863.281 - 643.375i) q^{80} -81.0000 q^{81} +(1087.42 + 404.928i) q^{82} +(463.472 + 463.472i) q^{83} +(11.6109 - 0.842875i) q^{84} +(-1617.36 + 1617.36i) q^{85} +(116.437 + 254.603i) q^{86} +28.2058i q^{87} +(-277.480 + 950.633i) q^{88} +1278.38i q^{89} +(389.443 - 178.104i) q^{90} +(8.94987 - 8.94987i) q^{91} +(670.318 - 775.258i) q^{92} +(-32.1004 - 32.1004i) q^{93} +(480.945 - 1291.57i) q^{94} -1567.42 q^{95} +(-294.817 - 456.065i) q^{96} -994.918 q^{97} +(-338.316 + 908.539i) q^{98} +(-278.523 - 278.523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29}+ \cdots - 360 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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