LMFDB - Embedded newform 60.4.e.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,4,Mod(11,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("60.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	60.e (of order $2$, degree $1$, 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:	$3.54011460034$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	60.11
Dual form			60.4.e.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72356 + 0.763049i) q^{2} +(4.56698 - 2.47844i) q^{3} +(6.83551 - 4.15641i) q^{4} +5.00000i q^{5} +(-10.5473 + 10.2350i) q^{6} -20.9745i q^{7} +(-15.4454 + 16.5360i) q^{8} +(14.7146 - 22.6380i) q^{9} +O(q^{10})$	\(q+(-2.72356 + 0.763049i) q^{2} +(4.56698 - 2.47844i) q^{3} +(6.83551 - 4.15641i) q^{4} +5.00000i q^{5} +(-10.5473 + 10.2350i) q^{6} -20.9745i q^{7} +(-15.4454 + 16.5360i) q^{8} +(14.7146 - 22.6380i) q^{9} +(-3.81524 - 13.6178i) q^{10} +30.8097 q^{11} +(20.9162 - 35.9237i) q^{12} +56.7161 q^{13} +(16.0045 + 57.1251i) q^{14} +(12.3922 + 22.8349i) q^{15} +(29.4485 - 56.8224i) q^{16} -88.9672i q^{17} +(-22.8022 + 72.8839i) q^{18} +88.2358i q^{19} +(20.7821 + 34.1776i) q^{20} +(-51.9840 - 95.7899i) q^{21} +(-83.9120 + 23.5093i) q^{22} -138.240 q^{23} +(-29.5550 + 113.800i) q^{24} -25.0000 q^{25} +(-154.469 + 43.2771i) q^{26} +(11.0943 - 139.857i) q^{27} +(-87.1785 - 143.371i) q^{28} +161.030i q^{29} +(-51.1751 - 52.7363i) q^{30} +197.266i q^{31} +(-36.8464 + 177.230i) q^{32} +(140.707 - 76.3602i) q^{33} +(67.8863 + 242.307i) q^{34} +104.872 q^{35} +(6.48912 - 215.903i) q^{36} -179.128 q^{37} +(-67.3282 - 240.315i) q^{38} +(259.021 - 140.568i) q^{39} +(-82.6802 - 77.2268i) q^{40} +67.7548i q^{41} +(214.674 + 221.223i) q^{42} +41.7076i q^{43} +(210.600 - 128.058i) q^{44} +(113.190 + 73.5731i) q^{45} +(376.504 - 105.484i) q^{46} -214.016 q^{47} +(-6.34049 - 332.493i) q^{48} -96.9279 q^{49} +(68.0889 - 19.0762i) q^{50} +(-220.500 - 406.311i) q^{51} +(387.683 - 235.735i) q^{52} +263.225i q^{53} +(76.5014 + 389.373i) q^{54} +154.049i q^{55} +(346.835 + 323.958i) q^{56} +(218.688 + 402.971i) q^{57} +(-122.873 - 438.573i) q^{58} +103.646 q^{59} +(179.618 + 104.581i) q^{60} -698.376 q^{61} +(-150.524 - 537.265i) q^{62} +(-474.820 - 308.631i) q^{63} +(-34.8817 - 510.810i) q^{64} +283.580i q^{65} +(-324.958 + 315.338i) q^{66} +129.743i q^{67} +(-369.784 - 608.136i) q^{68} +(-631.338 + 342.620i) q^{69} +(-285.626 + 80.0227i) q^{70} +301.620 q^{71} +(147.071 + 592.974i) q^{72} +1115.84 q^{73} +(487.866 - 136.684i) q^{74} +(-114.175 + 61.9611i) q^{75} +(366.744 + 603.137i) q^{76} -646.217i q^{77} +(-598.199 + 580.490i) q^{78} +712.880i q^{79} +(284.112 + 147.242i) q^{80} +(-295.960 - 666.220i) q^{81} +(-51.7002 - 184.534i) q^{82} +336.355 q^{83} +(-753.480 - 438.706i) q^{84} +444.836 q^{85} +(-31.8249 - 113.593i) q^{86} +(399.103 + 735.419i) q^{87} +(-475.867 + 509.471i) q^{88} -970.209i q^{89} +(-364.419 - 114.011i) q^{90} -1189.59i q^{91} +(-944.940 + 574.581i) q^{92} +(488.913 + 900.911i) q^{93} +(582.884 - 163.304i) q^{94} -441.179 q^{95} +(270.977 + 900.726i) q^{96} -1600.81 q^{97} +(263.988 - 73.9607i) q^{98} +(453.353 - 697.471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9	$ 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9} - 30 q^{10} - 188 q^{12} + 72 q^{13} + 306 q^{16} + 256 q^{18} - 68 q^{21} - 300 q^{22} - 434 q^{24} - 600 q^{25} + 300 q^{28} - 40 q^{30} + 848 q^{33} - 468 q^{34} - 294 q^{36} + 504 q^{37} - 210 q^{40} - 228 q^{42} - 220 q^{45} + 684 q^{46} + 1212 q^{48} - 2256 q^{49} + 576 q^{52} - 1054 q^{54} + 1416 q^{57} + 3108 q^{58} + 490 q^{60} + 1992 q^{61} - 1842 q^{64} - 472 q^{66} - 1548 q^{69} + 540 q^{70} + 312 q^{72} - 2304 q^{73} - 420 q^{76} - 2792 q^{78} + 3840 q^{81} + 600 q^{82} - 176 q^{84} + 240 q^{85} - 372 q^{88} - 1170 q^{90} - 4384 q^{93} + 1044 q^{94} - 3846 q^{96} - 2448 q^{97}+O(q^{100}) $ 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9 - 30 * q^10 - 188 * q^12 + 72 * q^13 + 306 * q^16 + 256 * q^18 - 68 * q^21 - 300 * q^22 - 434 * q^24 - 600 * q^25 + 300 * q^28 - 40 * q^30 + 848 * q^33 - 468 * q^34 - 294 * q^36 + 504 * q^37 - 210 * q^40 - 228 * q^42 - 220 * q^45 + 684 * q^46 + 1212 * q^48 - 2256 * q^49 + 576 * q^52 - 1054 * q^54 + 1416 * q^57 + 3108 * q^58 + 490 * q^60 + 1992 * q^61 - 1842 * q^64 - 472 * q^66 - 1548 * q^69 + 540 * q^70 + 312 * q^72 - 2304 * q^73 - 420 * q^76 - 2792 * q^78 + 3840 * q^81 + 600 * q^82 - 176 * q^84 + 240 * q^85 - 372 * q^88 - 1170 * q^90 - 4384 * q^93 + 1044 * q^94 - 3846 * q^96 - 2448 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.72356	+	0.763049i	−0.962922	+	0.269778i
$2$	−2.72356	+	0.763049i	−0.962922	+	0.269778i
$3$	4.56698	−	2.47844i	0.878916	−	0.476977i
$3$	4.56698	−	2.47844i	0.878916	−	0.476977i
$4$	6.83551	−	4.15641i	0.854439	−	0.519551i
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$	−10.5473	+	10.2350i	−0.717650	+	0.696404i
$7$		−	20.9745i		−	1.13251i	−0.824229	−	0.566257i	$-0.808391\pi$
$7$		−	20.9745i		−	1.13251i	0.824229	−	0.566257i	$-0.191609\pi$
$8$	−15.4454	+	16.5360i	−0.682595	+	0.730797i
$9$	14.7146	−	22.6380i	0.544986	−	0.838445i
$10$	−3.81524	−	13.6178i	−0.120649	−	0.430632i
$11$	30.8097			0.844498			0.422249	−	0.906480i	$-0.361241\pi$
$11$	30.8097			0.844498			0.422249	+	0.906480i	$0.361241\pi$
$12$	20.9162	−	35.9237i	0.503166	−	0.864190i
$13$	56.7161			1.21002			0.605008	−	0.796219i	$-0.293170\pi$
$13$	56.7161			1.21002			0.605008	+	0.796219i	$0.293170\pi$
$14$	16.0045	+	57.1251i	0.305528	+	1.09052i
$15$	12.3922	+	22.8349i	0.213311	+	0.393063i
$16$	29.4485	−	56.8224i	0.460133	−	0.887850i
$17$		−	88.9672i		−	1.26928i	−0.772809	−	0.634639i	$-0.781149\pi$
$17$		−	88.9672i		−	1.26928i	0.772809	−	0.634639i	$-0.218851\pi$
$18$	−22.8022	+	72.8839i	−0.298585	+	0.954383i
$19$			88.2358i			1.06540i	0.846303	+	0.532702i	$0.178823\pi$
$19$			88.2358i			1.06540i	−0.846303	+	0.532702i	$0.821177\pi$
$20$	20.7821	+	34.1776i	0.232350	+	0.382117i
$21$	−51.9840	−	95.7899i	−0.540183	−	0.995385i
$22$	−83.9120	+	23.5093i	−0.813186	+	0.227827i
$23$	−138.240			−1.25326			−0.626630	−	0.779317i	$-0.715566\pi$
$23$	−138.240			−1.25326			−0.626630	+	0.779317i	$0.715566\pi$
$24$	−29.5550	+	113.800i	−0.251370	+	0.967891i
$25$	−25.0000			−0.200000
$26$	−154.469	+	43.2771i	−1.16515	+	0.326436i
$27$	11.0943	−	139.857i	0.0790781	−	0.996868i
$28$	−87.1785	−	143.371i	−0.588399	−	0.967665i
$29$			161.030i			1.03112i	0.856854	+	0.515560i	$0.172416\pi$
$29$			161.030i			1.03112i	−0.856854	+	0.515560i	$0.827584\pi$
$30$	−51.1751	−	52.7363i	−0.311441	−	0.320943i
$31$			197.266i			1.14290i	0.820635	+	0.571452i	$0.193620\pi$
$31$			197.266i			1.14290i	−0.820635	+	0.571452i	$0.806380\pi$
$32$	−36.8464	+	177.230i	−0.203549	+	0.979065i
$33$	140.707	−	76.3602i	0.742243	−	0.402806i
$34$	67.8863	+	242.307i	0.342424	+	1.22222i
$35$	104.872			0.506476
$36$	6.48912	−	215.903i	0.0300422	−	0.999549i
$37$	−179.128			−0.795905			−0.397953	−	0.917406i	$-0.630279\pi$
$37$	−179.128			−0.795905			−0.397953	+	0.917406i	$0.630279\pi$
$38$	−67.3282	−	240.315i	−0.287423	−	1.02590i
$39$	259.021	−	140.568i	1.06350	−	0.577150i
$40$	−82.6802	−	77.2268i	−0.326822	−	0.305266i
$41$			67.7548i			0.258086i	0.991639	+	0.129043i	$0.0411905\pi$
$41$			67.7548i			0.258086i	−0.991639	+	0.129043i	$0.958809\pi$
$42$	214.674	+	221.223i	0.788688	+	0.812749i
$43$			41.7076i			0.147915i	0.997261	+	0.0739575i	$0.0235629\pi$
$43$			41.7076i			0.147915i	−0.997261	+	0.0739575i	$0.976437\pi$
$44$	210.600	−	128.058i	0.721572	−	0.438760i
$45$	113.190	+	73.5731i	0.374964	+	0.243725i
$46$	376.504	−	105.484i	1.20679	−	0.338103i
$47$	−214.016			−0.664200			−0.332100	−	0.943244i	$-0.607757\pi$
$47$	−214.016			−0.664200			−0.332100	+	0.943244i	$0.607757\pi$
$48$	−6.34049	−	332.493i	−0.0190661	−	0.999818i
$49$	−96.9279			−0.282589
$50$	68.0889	−	19.0762i	0.192584	−	0.0539557i
$51$	−220.500	−	406.311i	−0.605416	−	1.11559i
$52$	387.683	−	235.735i	1.03389	−	0.628665i
$53$			263.225i			0.682202i	0.940027	+	0.341101i	$0.110800\pi$
$53$			263.225i			0.682202i	−0.940027	+	0.341101i	$0.889200\pi$
$54$	76.5014	+	389.373i	0.192788	+	0.981241i
$55$			154.049i			0.377671i
$56$	346.835	+	323.958i	0.827638	+	0.773048i
$57$	218.688	+	402.971i	0.508173	+	0.936401i
$58$	−122.873	−	438.573i	−0.278174	−	0.992888i
$59$	103.646			0.228704			0.114352	−	0.993440i	$-0.463521\pi$
$59$	103.646			0.228704			0.114352	+	0.993440i	$0.463521\pi$
$60$	179.618	+	104.581i	0.386477	+	0.225023i
$61$	−698.376			−1.46587			−0.732934	−	0.680300i	$-0.761849\pi$
$61$	−698.376			−1.46587			−0.732934	+	0.680300i	$0.761849\pi$
$62$	−150.524	−	537.265i	−0.308331	−	1.10053i
$63$	−474.820	−	308.631i	−0.949551	−	0.617205i
$64$	−34.8817	−	510.810i	−0.0681283	−	0.997677i
$65$			283.580i			0.541136i
$66$	−324.958	+	315.338i	−0.606054	+	0.588112i
$67$			129.743i			0.236577i	0.992979	+	0.118289i	$0.0377408\pi$
$67$			129.743i			0.236577i	−0.992979	+	0.118289i	$0.962259\pi$
$68$	−369.784	−	608.136i	−0.659455	−	1.08452i
$69$	−631.338	+	342.620i	−1.10151	+	0.597776i
$70$	−285.626	+	80.0227i	−0.487697	+	0.136636i
$71$	301.620			0.504165			0.252083	−	0.967706i	$-0.418885\pi$
$71$	301.620			0.504165			0.252083	+	0.967706i	$0.418885\pi$
$72$	147.071	+	592.974i	0.240728	+	0.970593i
$73$	1115.84			1.78903			0.894513	−	0.447041i	$-0.147522\pi$
$73$	1115.84			1.78903			0.894513	+	0.447041i	$0.147522\pi$
$74$	487.866	−	136.684i	0.766395	−	0.214718i
$75$	−114.175	+	61.9611i	−0.175783	+	0.0953954i
$76$	366.744	+	603.137i	0.553532	+	0.910323i
$77$		−	646.217i		−	0.956406i
$78$	−598.199	+	580.490i	−0.868368	+	0.842660i
$79$			712.880i			1.01526i	0.861576	+	0.507628i	$0.169478\pi$
$79$			712.880i			1.01526i	−0.861576	+	0.507628i	$0.830522\pi$
$80$	284.112	+	147.242i	0.397059	+	0.205778i
$81$	−295.960	−	666.220i	−0.405980	−	0.913882i
$82$	−51.7002	−	184.534i	−0.0696260	−	0.248517i
$83$	336.355			0.444817			0.222408	−	0.974954i	$-0.428608\pi$
$83$	336.355			0.444817			0.222408	+	0.974954i	$0.428608\pi$
$84$	−753.480	−	438.706i	−0.978707	−	0.569843i
$85$	444.836			0.567638
$86$	−31.8249	−	113.593i	−0.0399043	−	0.142431i
$87$	399.103	+	735.419i	0.491820	+	0.906267i
$88$	−475.867	+	509.471i	−0.576450	+	0.617156i
$89$		−	970.209i		−	1.15553i	−0.816204	−	0.577764i	$-0.803926\pi$
$89$		−	970.209i		−	1.15553i	0.816204	−	0.577764i	$-0.196074\pi$
$90$	−364.419	−	114.011i	−0.426813	−	0.133531i
$91$		−	1189.59i		−	1.37036i
$92$	−944.940	+	574.581i	−1.07083	+	0.651133i
$93$	488.913	+	900.911i	0.545139	+	1.00452i
$94$	582.884	−	163.304i	0.639573	−	0.179187i
$95$	−441.179			−0.476463
$96$	270.977	+	900.726i	0.288089	+	0.957604i
$97$	−1600.81			−1.67564			−0.837821	−	0.545945i	$-0.816171\pi$
$97$	−1600.81			−1.67564			−0.837821	+	0.545945i	$0.816171\pi$
$98$	263.988	−	73.9607i	0.272111	−	0.0762363i
$99$	453.353	−	697.471i	0.460240	−	0.708065i
$100$	−170.888	+	103.910i	−0.170888	+	0.103910i
$101$		−	1073.62i		−	1.05772i	−0.848710	−	0.528859i	$-0.822620\pi$
$101$		−	1073.62i		−	1.05772i	0.848710	−	0.528859i	$-0.177380\pi$
$102$	910.580	+	938.359i	0.883930	+	0.910896i
$103$			1708.82i			1.63471i	0.576134	+	0.817355i	$0.304561\pi$
$103$			1708.82i			1.63471i	−0.576134	+	0.817355i	$0.695439\pi$
$104$	−876.000	+	937.860i	−0.825951	+	0.884276i
$105$	478.950	−	259.920i	0.445150	−	0.241577i
$106$	−200.853	−	716.907i	−0.184043	−	0.656908i
$107$	787.936			0.711894			0.355947	−	0.934506i	$-0.384158\pi$
$107$	787.936			0.711894			0.355947	+	0.934506i	$0.384158\pi$
$108$	−505.467	−	1002.11i	−0.450357	−	0.892849i
$109$	1200.41			1.05485			0.527424	−	0.849602i	$-0.323158\pi$
$109$	1200.41			1.05485			0.527424	+	0.849602i	$0.323158\pi$
$110$	−117.547	−	419.560i	−0.101887	−	0.363668i
$111$	−818.075	+	443.959i	−0.699534	+	0.379628i
$112$	−1191.82	−	617.666i	−1.00550	−	0.521107i
$113$			487.048i			0.405466i	0.979234	+	0.202733i	$0.0649823\pi$
$113$			487.048i			0.405466i	−0.979234	+	0.202733i	$0.935018\pi$
$114$	−903.095	−	930.646i	−0.741952	−	0.764587i
$115$		−	691.199i		−	0.560475i
$116$	669.305	+	1100.72i	0.535719	+	0.881029i
$117$	834.556	−	1283.94i	0.659442	−	1.01453i
$118$	−282.285	+	79.0867i	−0.220224	+	0.0616993i
$119$	−1866.04			−1.43747
$120$	−569.001	−	147.775i	−0.432854	−	0.112416i
$121$	−381.762			−0.286823
$122$	1902.07	−	532.895i	1.41152	−	0.395459i
$123$	167.927	+	309.435i	0.123101	+	0.226836i
$124$	819.919	+	1348.42i	0.593798	+	0.976543i
$125$		−	125.000i		−	0.0894427i
$126$	1528.70	+	478.264i	1.08085	+	0.338152i
$127$		−	1608.28i		−	1.12372i	−0.827234	−	0.561858i	$-0.810087\pi$
$127$		−	1608.28i		−	1.12372i	0.827234	−	0.561858i	$-0.189913\pi$
$128$	484.775	+	1364.60i	0.334754	+	0.942306i
$129$	103.370	+	190.478i	0.0705520	+	0.130005i
$130$	−216.386	−	772.347i	−0.145987	−	0.521072i
$131$	1357.63			0.905468			0.452734	−	0.891646i	$-0.350449\pi$
$131$	1357.63			0.905468			0.452734	+	0.891646i	$0.350449\pi$
$132$	644.423	−	1106.80i	0.424923	−	0.729806i
$133$	1850.70			1.20659
$134$	−99.0004	−	353.363i	−0.0638234	−	0.227805i
$135$	699.284	+	55.4717i	0.445813	+	0.0353648i
$136$	1471.17	+	1374.13i	0.927584	+	0.866402i
$137$			1684.06i			1.05021i	0.851038	+	0.525105i	$0.175974\pi$
$137$			1684.06i			1.05021i	−0.851038	+	0.525105i	$0.824026\pi$
$138$	1458.05	−	1414.89i	0.899402	−	0.872776i
$139$		−	1425.55i		−	0.869885i	−0.900458	−	0.434942i	$-0.856769\pi$
$139$		−	1425.55i		−	0.869885i	0.900458	−	0.434942i	$-0.143231\pi$
$140$	716.856	−	435.892i	0.432753	−	0.263140i
$141$	−977.406	+	530.426i	−0.583776	+	0.316808i
$142$	−821.479	+	230.151i	−0.485472	+	0.136013i
$143$	1747.41			1.02186
$144$	−853.023	−	1502.78i	−0.493648	−	0.869662i
$145$	−805.148			−0.461130
$146$	−3039.05	+	851.439i	−1.72269	+	0.482641i
$147$	−442.668	+	240.230i	−0.248372	+	0.134788i
$148$	−1224.43	+	744.530i	−0.680053	+	0.413514i
$149$		−	874.024i		−	0.480556i	−0.970704	−	0.240278i	$-0.922761\pi$
$149$		−	874.024i		−	0.480556i	0.970704	−	0.240278i	$-0.0772386\pi$
$150$	263.681	−	255.875i	0.143530	−	0.139281i
$151$			1343.03i			0.723800i	0.932217	+	0.361900i	$0.117872\pi$
$151$			1343.03i			0.723800i	−0.932217	+	0.361900i	$0.882128\pi$
$152$	−1459.07	−	1362.83i	−0.778594	−	0.727240i
$153$	−2014.04	−	1309.12i	−1.06422	−	0.691738i
$154$	493.095	+	1760.01i	0.258018	+	0.920945i
$155$	−986.331			−0.511123
$156$	1186.29	−	2037.45i	0.608839	−	1.04568i
$157$	−1313.01			−0.667450			−0.333725	−	0.942670i	$-0.608306\pi$
$157$	−1313.01			−0.667450			−0.333725	+	0.942670i	$0.608306\pi$
$158$	−543.962	−	1941.57i	−0.273894	−	0.977613i
$159$	652.388	+	1202.14i	0.325395	+	0.599598i
$160$	−886.148	−	184.232i	−0.437851	−	0.0910300i
$161$			2899.50i			1.41933i
$162$	1314.42	+	1588.66i	0.637473	+	0.770473i
$163$		−	1970.74i		−	0.946995i	−0.880795	−	0.473497i	$-0.842991\pi$
$163$		−	1970.74i		−	0.946995i	0.880795	−	0.473497i	$-0.157009\pi$
$164$	281.617	+	463.139i	0.134089	+	0.220519i
$165$	381.801	+	703.537i	0.180140	+	0.331941i
$166$	−916.083	+	256.656i	−0.428324	+	0.120002i
$167$	−1196.07			−0.554221			−0.277110	−	0.960838i	$-0.589377\pi$
$167$	−1196.07			−0.554221			−0.277110	+	0.960838i	$0.589377\pi$
$168$	2386.90	+	619.900i	1.09615	+	0.284680i
$169$	1019.71			0.464139
$170$	−1211.54	+	339.431i	−0.546591	+	0.153136i
$171$	1997.48	+	1298.36i	0.893283	+	0.580631i
$172$	173.354	+	285.093i	0.0768494	+	0.126384i
$173$			3252.29i			1.42929i	0.699487	+	0.714646i	$0.253412\pi$
$173$			3252.29i			1.42929i	−0.699487	+	0.714646i	$0.746588\pi$
$174$	−1648.14	−	1698.42i	−0.718076	−	0.739982i
$175$			524.361i			0.226503i
$176$	907.300	−	1750.68i	0.388581	−	0.749788i
$177$	473.348	−	256.880i	0.201011	−	0.109086i
$178$	740.317	+	2642.42i	0.311736	+	1.11268i
$179$	−4438.90			−1.85352			−0.926758	−	0.375659i	$-0.877416\pi$
$179$	−4438.90			−1.85352			−0.926758	+	0.375659i	$0.877416\pi$
$180$	1079.51	+	32.4456i	0.447012	+	0.0134353i
$181$	−59.4849			−0.0244281			−0.0122140	−	0.999925i	$-0.503888\pi$
$181$	−59.4849			−0.0244281			−0.0122140	+	0.999925i	$0.503888\pi$
$182$	907.714	+	3239.91i	0.369694	+	1.31955i
$183$	−3189.47	+	1730.89i	−1.28837	+	0.699185i
$184$	2135.16	−	2285.94i	0.855469	−	0.915879i
$185$		−	895.641i		−	0.355940i
$186$	−2019.02	−	2080.62i	−0.795924	−	0.820205i
$187$		−	2741.05i		−	1.07190i
$188$	−1462.91	+	889.538i	−0.567519	+	0.345086i
$189$	−2933.42	−	232.698i	−1.12897	−	0.0895570i
$190$	1201.58	−	336.641i	0.458797	−	0.128540i
$191$	−1195.27			−0.452810			−0.226405	−	0.974033i	$-0.572697\pi$
$191$	−1195.27			−0.452810			−0.226405	+	0.974033i	$0.572697\pi$
$192$	−1425.32	−	2246.41i	−0.535748	−	0.844378i
$193$	−2886.55			−1.07657			−0.538286	−	0.842762i	$-0.680928\pi$
$193$	−2886.55			−1.07657			−0.538286	+	0.842762i	$0.680928\pi$
$194$	4359.89	−	1221.49i	1.61351	−	0.452052i
$195$	702.838	+	1295.11i	0.258109	+	0.475613i
$196$	−662.552	+	402.872i	−0.241455	+	0.146819i
$197$		−	520.753i		−	0.188336i	−0.995556	−	0.0941679i	$-0.969981\pi$
$197$		−	520.753i		−	0.188336i	0.995556	−	0.0941679i	$-0.0300190\pi$
$198$	−702.529	+	2245.53i	−0.252154	+	0.805974i
$199$		−	115.686i		−	0.0412098i	−0.999788	−	0.0206049i	$-0.993441\pi$
$199$		−	115.686i		−	0.0412098i	0.999788	−	0.0206049i	$-0.00655920\pi$
$200$	386.134	−	413.401i	0.136519	−	0.146159i
$201$	321.562	+	592.535i	0.112842	+	0.207931i
$202$	819.227	+	2924.07i	0.285350	+	1.01850i
$203$	3377.51			1.16776
$204$	−3196.03	−	1860.86i	−1.09690	−	0.638657i
$205$	−338.774			−0.115420
$206$	−1303.91	−	4654.07i	−0.441010	−	1.57410i
$207$	−2034.15	+	3129.47i	−0.683009	+	1.05079i
$208$	1670.20	−	3222.74i	0.556768	−	1.07431i
$209$			2718.52i			0.899732i
$210$	−1106.11	+	1073.37i	−0.363472	+	0.352712i
$211$			671.242i			0.219006i	0.993986	+	0.109503i	$0.0349259\pi$
$211$			671.242i			0.219006i	−0.993986	+	0.109503i	$0.965074\pi$
$212$	1094.07	+	1799.28i	0.354439	+	0.582900i
$213$	1377.49	−	747.549i	0.443119	−	0.240475i
$214$	−2145.99	+	601.233i	−0.685499	+	0.192054i
$215$	−208.538			−0.0661496
$216$	2141.32	+	2343.59i	0.674530	+	0.738247i
$217$	4137.55			1.29436
$218$	−3269.38	+	915.971i	−1.01574	+	0.284575i
$219$	5096.01	−	2765.54i	1.57240	−	0.853324i
$220$	640.289	+	1053.00i	0.196219	+	0.322697i
$221$		−	5045.87i		−	1.53585i
$222$	1889.31	−	1833.38i	0.571181	−	0.554272i
$223$		−	3012.48i		−	0.904622i	−0.891860	−	0.452311i	$-0.850600\pi$
$223$		−	3012.48i		−	0.904622i	0.891860	−	0.452311i	$-0.149400\pi$
$224$	3717.30	+	772.832i	1.10880	+	0.230522i
$225$	−367.866	+	565.950i	−0.108997	+	0.167689i
$226$	−371.641	−	1326.50i	−0.109386	−	0.390432i
$227$	3106.72			0.908371			0.454185	−	0.890907i	$-0.349930\pi$
$227$	3106.72			0.908371			0.454185	+	0.890907i	$0.349930\pi$
$228$	3169.76	+	1845.56i	0.920712	+	0.536076i
$229$	485.058			0.139972			0.0699858	−	0.997548i	$-0.477705\pi$
$229$	485.058			0.139972			0.0699858	+	0.997548i	$0.477705\pi$
$230$	527.418	+	1882.52i	0.151204	+	0.539694i
$231$	−1601.61	−	2951.26i	−0.456184	−	0.840600i
$232$	−2662.79	−	2487.16i	−0.753539	−	0.703837i
$233$		−	6052.81i		−	1.70186i	−0.525281	−	0.850929i	$-0.676040\pi$
$233$		−	6052.81i		−	1.70186i	0.525281	−	0.850929i	$-0.323960\pi$
$234$	−1293.25	+	4133.69i	−0.361293	+	1.15482i
$235$		−	1070.08i		−	0.297039i
$236$	708.472	−	430.794i	0.195413	−	0.118823i
$237$	1766.83	+	3255.71i	0.484254	+	0.892325i
$238$	5082.26	−	1423.88i	1.38418	−	0.387800i
$239$	4846.17			1.31160			0.655800	−	0.754934i	$-0.272331\pi$
$239$	4846.17			1.31160			0.655800	+	0.754934i	$0.272331\pi$
$240$	1662.47	−	31.7024i	0.447132	−	0.00852660i
$241$	6399.86			1.71058			0.855292	−	0.518146i	$-0.173378\pi$
$241$	6399.86			1.71058			0.855292	+	0.518146i	$0.173378\pi$
$242$	1039.75	−	291.303i	0.276189	−	0.0773787i
$243$	−3002.83	−	2309.09i	−0.792723	−	0.609582i
$244$	−4773.76	+	2902.74i	−1.25249	+	0.761593i
$245$		−	484.639i		−	0.126377i
$246$	−693.471	−	714.627i	−0.179732	−	0.185215i
$247$			5004.39i			1.28916i
$248$	−3262.00	−	3046.85i	−0.835231	−	0.780141i
$249$	1536.13	−	833.638i	0.390957	−	0.212167i
$250$	95.3811	+	340.444i	0.0241297	+	0.0861264i
$251$	39.6720			0.00997640			0.00498820	−	0.999988i	$-0.498412\pi$
$251$	39.6720			0.00997640			0.00498820	+	0.999988i	$0.498412\pi$
$252$	−4528.44	−	136.106i	−1.13200	−	0.0340233i
$253$	−4259.13			−1.05838
$254$	1227.20	+	4380.24i	0.303154	+	1.08205i
$255$	2031.56	−	1102.50i	0.498906	−	0.270750i
$256$	−2361.57	−	3346.67i	−0.576556	−	0.817058i
$257$		−	185.740i		−	0.0450823i	−0.999746	−	0.0225412i	$-0.992824\pi$
$257$		−	185.740i		−	0.0450823i	0.999746	−	0.0225412i	$-0.00717568\pi$
$258$	−426.877	−	439.900i	−0.103009	−	0.106151i
$259$			3757.12i			0.901374i
$260$	1178.68	+	1938.42i	0.281148	+	0.462367i
$261$	3645.39	+	2369.49i	0.864537	+	0.561946i
$262$	−3697.57	+	1035.93i	−0.871896	+	0.244276i
$263$	−1512.06			−0.354516			−0.177258	−	0.984164i	$-0.556723\pi$
$263$	−1512.06			−0.354516			−0.177258	+	0.984164i	$0.556723\pi$
$264$	−910.581	+	3506.15i	−0.212282	+	0.817382i
$265$	−1316.12			−0.305090
$266$	−5040.48	+	1412.17i	−1.16185	+	0.325511i
$267$	−2404.61	−	4430.93i	−0.551160	−	1.01561i
$268$	539.266	+	886.862i	0.122914	+	0.202141i
$269$		−	2951.18i		−	0.668910i	−0.942412	−	0.334455i	$-0.891448\pi$
$269$		−	2951.18i		−	0.668910i	0.942412	−	0.334455i	$-0.108552\pi$
$270$	−1946.87	+	382.507i	−0.438824	+	0.0862172i
$271$		−	903.495i		−	0.202522i	−0.994860	−	0.101261i	$-0.967712\pi$
$271$		−	903.495i		−	0.202522i	0.994860	−	0.101261i	$-0.0322877\pi$
$272$	−5055.33	−	2619.95i	−1.12693	−	0.584036i
$273$	−2948.33	−	5432.83i	−0.653630	−	1.20443i
$274$	−1285.02	−	4586.62i	−0.283324	−	1.01127i
$275$	−770.243			−0.168900
$276$	−2891.45	+	4966.08i	−0.630598	+	1.08305i
$277$	−2119.18			−0.459671			−0.229836	−	0.973229i	$-0.573819\pi$
$277$	−2119.18			−0.459671			−0.229836	+	0.973229i	$0.573819\pi$
$278$	1087.77	+	3882.58i	0.234676	+	0.837632i
$279$	4465.71	+	2902.70i	0.958263	+	0.622867i
$280$	−1619.79	+	1734.17i	−0.345718	+	0.370131i
$281$			4896.84i			1.03958i	0.854295	+	0.519788i	$0.173989\pi$
$281$			4896.84i			1.03958i	−0.854295	+	0.519788i	$0.826011\pi$
$282$	2257.28	−	2190.45i	0.476663	−	0.462552i
$283$			4875.98i			1.02419i	0.858928	+	0.512097i	$0.171131\pi$
$283$			4875.98i			1.02419i	−0.858928	+	0.512097i	$0.828869\pi$
$284$	2061.73	−	1253.66i	0.430779	−	0.261940i
$285$	−2014.86	+	1093.44i	−0.418771	+	0.227262i
$286$	−4759.16	+	1333.36i	−0.983968	+	0.275675i
$287$	1421.12			0.292286
$288$	3469.95	+	3442.00i	0.709960	+	0.704242i
$289$	−3002.16			−0.611064
$290$	2192.87	−	614.367i	0.444033	−	0.124403i
$291$	−7310.85	+	3967.51i	−1.47275	+	0.799242i
$292$	7627.32	−	4637.88i	1.52861	−	0.929491i
$293$		−	4524.68i		−	0.902166i	−0.892482	−	0.451083i	$-0.851038\pi$
$293$		−	4524.68i		−	0.902166i	0.892482	−	0.451083i	$-0.148962\pi$
$294$	1022.32	−	992.058i	0.202800	−	0.196796i
$295$			518.229i			0.102279i
$296$	2766.70	−	2962.07i	0.543281	−	0.581645i
$297$	341.814	−	4308.95i	0.0667813	−	0.841853i
$298$	666.923	+	2380.45i	0.129644	+	0.462738i
$299$	−7840.42			−1.51646
$300$	−522.906	+	898.092i	−0.100633	+	0.172838i
$301$	874.793			0.167516
$302$	−1024.79	−	3657.80i	−0.195266	−	0.696964i
$303$	−2660.92	−	4903.22i	−0.504507	−	0.929645i
$304$	5013.77	+	2598.41i	0.945920	+	0.490228i
$305$		−	3491.88i		−	0.655556i
$306$	6484.27	+	2028.65i	1.21138	+	0.378987i
$307$			6726.35i			1.25047i	0.780438	+	0.625233i	$0.214996\pi$
$307$			6726.35i			1.25047i	−0.780438	+	0.625233i	$0.785004\pi$
$308$	−2685.94	−	4417.22i	−0.496902	−	0.817191i
$309$	4235.22	+	7804.16i	0.779719	+	1.43677i
$310$	2686.33	−	752.618i	0.492171	−	0.137890i
$311$	−165.537			−0.0301824			−0.0150912	−	0.999886i	$-0.504804\pi$
$311$	−165.537			−0.0301824			−0.0150912	+	0.999886i	$0.504804\pi$
$312$	−1676.24	+	6454.30i	−0.304162	+	1.17116i
$313$	−3295.86			−0.595185			−0.297593	−	0.954693i	$-0.596184\pi$
$313$	−3295.86			−0.595185			−0.297593	+	0.954693i	$0.596184\pi$
$314$	3576.06	−	1001.89i	0.642702	−	0.180064i
$315$	1543.16	−	2374.10i	0.276022	−	0.424652i
$316$	2963.02	+	4872.90i	0.527478	+	0.867475i
$317$			164.477i			0.0291417i	0.999894	+	0.0145709i	$0.00463822\pi$
$317$			164.477i			0.0291417i	−0.999894	+	0.0145709i	$0.995362\pi$
$318$	−2694.11	−	2776.30i	−0.475088	−	0.489582i
$319$			4961.28i			0.870778i
$320$	2554.05	−	174.409i	0.446175	−	0.0304679i
$321$	3598.49	−	1952.86i	0.625695	−	0.339557i
$322$	−2212.46	−	7896.96i	−0.382906	−	1.36671i
$323$	7850.09			1.35229
$324$	−4792.12	−	3323.83i	−0.821694	−	0.569929i
$325$	−1417.90			−0.242003
$326$	1503.77	+	5367.42i	0.255479	+	0.911883i
$327$	5482.25	−	2975.15i	0.927123	−	0.503138i
$328$	−1120.40	−	1046.50i	−0.188608	−	0.176168i
$329$			4488.86i			0.752216i
$330$	−1576.69	−	1624.79i	−0.263012	−	0.271035i
$331$		−	3358.03i		−	0.557626i	−0.960345	−	0.278813i	$-0.910059\pi$
$331$		−	3358.03i		−	0.557626i	0.960345	−	0.278813i	$-0.0899410\pi$
$332$	2299.16	−	1398.03i	0.380069	−	0.231105i
$333$	−2635.80	+	4055.11i	−0.433757	+	0.667323i
$334$	3257.57	−	912.661i	0.533671	−	0.149517i
$335$	−648.716			−0.105800
$336$	−6973.87	+	132.988i	−1.13231	+	0.0215926i
$337$	3077.19			0.497404			0.248702	−	0.968580i	$-0.419996\pi$
$337$	3077.19			0.497404			0.248702	+	0.968580i	$0.419996\pi$
$338$	−2777.24	+	778.090i	−0.446930	+	0.125215i
$339$	1207.12	+	2224.34i	0.193398	+	0.356370i
$340$	3040.68	−	1848.92i	0.485012	−	0.294917i
$341$			6077.71i			0.965181i
$342$	−6430.97	−	2011.97i	−1.01680	−	0.318114i
$343$		−	5161.23i		−	0.812479i
$344$	−689.678	−	644.188i	−0.108096	−	0.100966i
$345$	−1713.10	−	3156.69i	−0.267334	−	0.492610i
$346$	−2481.66	−	8857.81i	−0.385592	−	1.37630i
$347$	−3274.08			−0.506518			−0.253259	−	0.967399i	$-0.581502\pi$
$347$	−3274.08			−0.506518			−0.253259	+	0.967399i	$0.581502\pi$
$348$	5784.78	+	3368.13i	0.891082	+	0.518824i
$349$	−2000.93			−0.306898			−0.153449	−	0.988157i	$-0.549038\pi$
$349$	−2000.93			−0.306898			−0.153449	+	0.988157i	$0.549038\pi$
$350$	−400.113	−	1428.13i	−0.0611056	−	0.218105i
$351$	629.228	−	7932.13i	0.0956857	−	1.20623i
$352$	−1135.23	+	5460.39i	−0.171897	+	0.826818i
$353$			11333.7i			1.70888i	0.519552	+	0.854439i	$0.326099\pi$
$353$			11333.7i			1.70888i	−0.519552	+	0.854439i	$0.673901\pi$
$354$	−1093.18	+	1060.82i	−0.164129	+	0.159270i
$355$			1508.10i			0.225470i
$356$	−4032.59	−	6631.88i	−0.600356	−	0.987328i
$357$	−8522.16	+	4624.87i	−1.26342	+	0.685642i
$358$	12089.6	−	3387.10i	1.78479	−	0.500039i
$359$	−4485.62			−0.659449			−0.329724	−	0.944077i	$-0.606956\pi$
$359$	−4485.62			−0.659449			−0.329724	+	0.944077i	$0.606956\pi$
$360$	−2964.87	+	735.353i	−0.434062	+	0.107657i
$361$	−926.562			−0.135087
$362$	162.010	−	45.3899i	0.0235223	−	0.00659016i
$363$	−1743.50	+	946.175i	−0.252094	+	0.136808i
$364$	−4944.42	−	8131.45i	−0.711973	−	1.17089i
$365$			5579.19i			0.800077i
$366$	7365.95	−	7147.89i	1.05198	−	1.02084i
$367$		−	11115.5i		−	1.58099i	−0.612469	−	0.790494i	$-0.709824\pi$
$367$		−	11115.5i		−	1.58099i	0.612469	−	0.790494i	$-0.290176\pi$
$368$	−4070.95	+	7855.12i	−0.576666	+	1.11271i
$369$	1533.83	+	996.986i	0.216391	+	0.140653i
$370$	683.418	+	2439.33i	0.0960248	+	0.342742i
$371$	5521.00			0.772603
$372$	7086.53	+	4126.06i	0.987686	+	0.575071i
$373$	2122.71			0.294664			0.147332	−	0.989087i	$-0.452931\pi$
$373$	2122.71			0.294664			0.147332	+	0.989087i	$0.452931\pi$
$374$	2091.56	+	7465.41i	0.289176	+	1.03216i
$375$	−309.806	−	570.873i	−0.0426621	−	0.0786126i
$376$	3305.55	−	3538.97i	0.453380	−	0.485395i
$377$			9132.97i			1.24767i
$378$	8166.89	−	1604.58i	1.11127	−	0.218335i
$379$		−	10724.8i		−	1.45355i	−0.686874	−	0.726776i	$-0.741018\pi$
$379$		−	10724.8i		−	1.45355i	0.686874	−	0.726776i	$-0.258982\pi$
$380$	−3015.69	+	1833.72i	−0.407109	+	0.247547i
$381$	−3986.03	−	7344.99i	−0.535986	−	0.987651i
$382$	3255.38	−	912.049i	0.436021	−	0.122158i
$383$	−1921.43			−0.256346			−0.128173	−	0.991752i	$-0.540911\pi$
$383$	−1921.43			−0.256346			−0.128173	+	0.991752i	$0.540911\pi$
$384$	5596.06	+	5030.63i	0.743678	+	0.668537i
$385$	3231.08			0.427718
$386$	7861.69	−	2202.58i	1.03666	−	0.290436i
$387$	944.176	+	613.711i	0.124019	+	0.0806116i
$388$	−10942.3	+	6653.61i	−1.43173	+	0.870582i
$389$		−	13145.4i		−	1.71336i	−0.515850	−	0.856679i	$-0.672524\pi$
$389$		−	13145.4i		−	1.71336i	0.515850	−	0.856679i	$-0.327476\pi$
$390$	−2902.45	−	2990.99i	−0.376849	−	0.388346i
$391$			12298.8i			1.59073i
$392$	1497.09	−	1602.80i	0.192894	−	0.206515i
$393$	6200.25	−	3364.80i	0.795831	−	0.431887i
$394$	397.360	+	1418.30i	0.0508089	+	0.181353i
$395$	−3564.40			−0.454037
$396$	199.928	−	6651.89i	0.0253706	−	0.844117i
$397$	7760.16			0.981036			0.490518	−	0.871431i	$-0.336808\pi$
$397$	7760.16			0.981036			0.490518	+	0.871431i	$0.336808\pi$
$398$	88.2739	+	315.077i	0.0111175	+	0.0396818i
$399$	8452.11	−	4586.85i	1.06049	−	0.575514i
$400$	−736.212	+	1420.56i	−0.0920265	+	0.177570i
$401$			2039.82i			0.254024i	0.991901	+	0.127012i	$0.0405387\pi$
$401$			2039.82i			0.254024i	−0.991901	+	0.127012i	$0.959461\pi$
$402$	−1327.92	−	1368.44i	−0.164753	−	0.169779i
$403$			11188.2i			1.38293i
$404$	−4462.42	−	7338.77i	−0.549539	−	0.903756i
$405$	3331.10	−	1479.80i	0.408700	−	0.181560i
$406$	−9198.84	+	2577.20i	−1.12446	+	0.315036i
$407$	−5518.89			−0.672140
$408$	10124.5	+	2629.42i	1.22852	+	0.319058i
$409$	−5909.90			−0.714489			−0.357244	−	0.934011i	$-0.616284\pi$
$409$	−5909.90			−0.714489			−0.357244	+	0.934011i	$0.616284\pi$
$410$	922.670	−	258.501i	0.111140	−	0.0311377i
$411$	4173.84	+	7691.06i	0.500926	+	0.923046i
$412$	7102.57	+	11680.7i	0.849316	+	1.39676i
$413$		−	2173.91i		−	0.259010i
$414$	3152.17	−	10075.5i	0.374205	−	1.19609i
$415$			1681.78i			0.198928i
$416$	−2089.78	+	10051.8i	−0.246298	+	1.18468i
$417$	−3533.16	−	6510.48i	−0.414915	−	0.764556i
$418$	−2074.36	−	7404.04i	−0.242728	−	0.866372i
$419$	−12975.3			−1.51285			−0.756423	−	0.654083i	$-0.773055\pi$
$419$	−12975.3			−1.51285			−0.756423	+	0.654083i	$0.773055\pi$
$420$	2193.53	−	3767.40i	0.254841	−	0.437691i
$421$	−7858.36			−0.909723			−0.454861	−	0.890562i	$-0.650311\pi$
$421$	−7858.36			−0.909723			−0.454861	+	0.890562i	$0.650311\pi$
$422$	−512.190	−	1828.16i	−0.0590830	−	0.210885i
$423$	−3149.16	+	4844.89i	−0.361980	+	0.556895i
$424$	−4352.70	−	4065.60i	−0.498551	−	0.465668i
$425$			2224.18i			0.253855i
$426$	−3181.26	+	3087.09i	−0.361814	+	0.351103i
$427$			14648.1i			1.66012i
$428$	5385.95	−	3274.99i	0.608270	−	0.369865i
$429$	7980.37	−	4330.85i	0.898125	−	0.487402i
$430$	567.964	−	159.124i	0.0636969	−	0.0178457i
$431$	8538.36			0.954242			0.477121	−	0.878838i	$-0.341680\pi$
$431$	8538.36			0.954242			0.477121	+	0.878838i	$0.341680\pi$
$432$	−7620.29	−	4748.98i	−0.848683	−	0.528901i
$433$	−6538.78			−0.725713			−0.362857	−	0.931845i	$-0.618199\pi$
$433$	−6538.78			−0.725713			−0.362857	+	0.931845i	$0.618199\pi$
$434$	−11268.8	+	3157.15i	−1.24636	+	0.349189i
$435$	−3677.10	+	1995.52i	−0.405295	+	0.219949i
$436$	8205.42	−	4989.40i	0.901304	−	0.548048i
$437$		−	12197.7i		−	1.33523i
$438$	−11769.0	+	11420.6i	−1.28389	+	1.24589i
$439$		−	12295.6i		−	1.33676i	−0.743822	−	0.668378i	$-0.766989\pi$
$439$		−	12295.6i		−	1.33676i	0.743822	−	0.668378i	$-0.233011\pi$
$440$	−2547.35	−	2379.34i	−0.276001	−	0.257796i
$441$	−1426.26	+	2194.25i	−0.154007	+	0.236935i
$442$	3850.24	+	13742.7i	0.414338	+	1.47890i
$443$	12326.2			1.32198			0.660990	−	0.750395i	$-0.270136\pi$
$443$	12326.2			1.32198			0.660990	+	0.750395i	$0.270136\pi$
$444$	−3746.69	+	6434.95i	−0.400473	+	0.687813i
$445$	4851.04			0.516768
$446$	2298.67	+	8204.66i	0.244047	+	0.871080i
$447$	−2166.22	−	3991.65i	−0.229214	−	0.422368i
$448$	−10714.0	+	731.625i	−1.12988	+	0.0771563i
$449$		−	4686.65i		−	0.492598i	−0.969194	−	0.246299i	$-0.920785\pi$
$449$		−	4686.65i		−	0.492598i	0.969194	−	0.246299i	$-0.0792146\pi$
$450$	570.055	−	1822.10i	0.0597170	−	0.190877i
$451$			2087.51i			0.217953i
$452$	2024.37	+	3329.22i	0.210660	+	0.346446i
$453$	3328.61	+	6133.57i	0.345236	+	0.636160i
$454$	−8461.32	+	2370.58i	−0.874690	+	0.245059i
$455$	5947.94			0.612844
$456$	−10041.3	−	2607.81i	−1.03120	−	0.267811i
$457$	5715.08			0.584989			0.292495	−	0.956267i	$-0.405515\pi$
$457$	5715.08			0.584989			0.292495	+	0.956267i	$0.405515\pi$
$458$	−1321.08	+	370.123i	−0.134782	+	0.0377613i
$459$	−12442.7	−	987.032i	−1.26530	−	0.100372i
$460$	−2872.91	−	4724.70i	−0.291196	−	0.478892i
$461$		−	6752.04i		−	0.682156i	−0.940035	−	0.341078i	$-0.889208\pi$
$461$		−	6752.04i		−	0.682156i	0.940035	−	0.341078i	$-0.110792\pi$
$462$	6614.04	+	6815.81i	0.666045	+	0.686364i
$463$		−	10853.9i		−	1.08946i	−0.838610	−	0.544732i	$-0.816631\pi$
$463$		−	10853.9i		−	1.08946i	0.838610	−	0.544732i	$-0.183369\pi$
$464$	9150.09	+	4742.08i	0.915479	+	0.474452i
$465$	−4504.55	+	2444.57i	−0.449234	+	0.243794i
$466$	4618.59	+	16485.2i	0.459125	+	1.63876i
$467$	−5170.48			−0.512337			−0.256169	−	0.966632i	$-0.582460\pi$
$467$	−5170.48			−0.512337			−0.256169	+	0.966632i	$0.582460\pi$
$468$	368.037	−	12245.1i	0.0363516	−	1.20947i
$469$	2721.30			0.267927
$470$	816.522	+	2914.42i	0.0801348	+	0.286026i
$471$	−5996.49	+	3254.22i	−0.586632	+	0.318358i
$472$	−1600.85	+	1713.89i	−0.156112	+	0.167136i
$473$			1285.00i			0.124914i
$474$	−7296.34	−	7518.93i	−0.707029	−	0.728599i
$475$		−	2205.90i		−	0.213081i
$476$	−12755.3	+	7756.02i	−1.22823	+	0.746842i
$477$	5958.89	+	3873.25i	0.571989	+	0.371791i
$478$	−13198.8	+	3697.86i	−1.26297	+	0.353842i
$479$	7707.91			0.735247			0.367623	−	0.929975i	$-0.380172\pi$
$479$	7707.91			0.735247			0.367623	+	0.929975i	$0.380172\pi$
$480$	−4503.63	+	1354.89i	−0.428253	+	0.128837i
$481$	−10159.4			−0.963058
$482$	−17430.4	+	4883.40i	−1.64716	+	0.461479i
$483$	7186.26	+	13242.0i	0.676990	+	1.24748i
$484$	−2609.54	+	1586.76i	−0.245073	+	0.149019i
$485$		−	8004.03i		−	0.749370i
$486$	9940.33	+	3997.64i	0.927783	+	0.373121i
$487$		−	6961.77i		−	0.647778i	−0.946095	−	0.323889i	$-0.895010\pi$
$487$		−	6961.77i		−	0.647778i	0.946095	−	0.323889i	$-0.104990\pi$
$488$	10786.7	−	11548.4i	1.00059	−	1.07125i
$489$	−4884.37	−	9000.33i	−0.451695	−	0.832329i
$490$	369.803	+	1319.94i	0.0340939	+	0.121692i
$491$	5867.71			0.539320			0.269660	−	0.962956i	$-0.413089\pi$
$491$	5867.71			0.539320			0.269660	+	0.962956i	$0.413089\pi$
$492$	2434.00	+	1417.17i	0.223035	+	0.129860i
$493$	14326.4			1.30878
$494$	−3818.59	−	13629.7i	−0.347787	−	1.24136i
$495$	3487.35	+	2266.77i	0.316656	+	0.205825i
$496$	11209.1	+	5809.19i	1.01473	+	0.525888i
$497$		−	6326.32i		−	0.570974i
$498$	−3547.63	+	3442.60i	−0.319223	+	0.309772i
$499$			5291.99i			0.474754i	0.971418	+	0.237377i	$0.0762876\pi$
$499$			5291.99i			0.474754i	−0.971418	+	0.237377i	$0.923712\pi$
$500$	−519.551	−	854.439i	−0.0464701	−	0.0764234i
$501$	−5462.44	+	2964.40i	−0.487113	+	0.264350i
$502$	−108.049	+	30.2717i	−0.00960650	+	0.00269142i
$503$	−778.873			−0.0690422			−0.0345211	−	0.999404i	$-0.510991\pi$
$503$	−778.873			−0.0690422			−0.0345211	+	0.999404i	$0.510991\pi$
$504$	12437.3	−	3084.73i	1.09921	−	0.272628i
$505$	5368.12			0.473026
$506$	11600.0	−	3249.92i	1.01913	−	0.285527i
$507$	4657.01	−	2527.30i	0.407939	−	0.221383i
$508$	−6684.68	−	10993.4i	−0.583828	−	0.960146i
$509$			7612.60i			0.662913i	0.943471	+	0.331456i	$0.107540\pi$
$509$			7612.60i			0.662913i	−0.943471	+	0.331456i	$0.892460\pi$
$510$	−4691.80	+	4552.90i	−0.407365	+	0.395305i
$511$		−	23404.1i		−	2.02610i
$512$	8985.55	+	7312.84i	0.775603	+	0.631221i
$513$	12340.4	+	978.919i	1.06207	+	0.0842501i
$514$	141.729	+	505.874i	0.0121622	+	0.0434108i
$515$	−8544.11			−0.731065
$516$	1498.29	+	872.365i	0.127827	+	0.0744258i
$517$	−6593.76			−0.560916
$518$	−2866.86	−	10232.7i	−0.243171	−	0.867953i
$519$	8060.63	+	14853.2i	0.681739	+	1.25623i
$520$	−4689.30	−	4380.00i	−0.395460	−	0.369376i
$521$		−	4248.22i		−	0.357232i	−0.983919	−	0.178616i	$-0.942838\pi$
$521$		−	4248.22i		−	0.357232i	0.983919	−	0.178616i	$-0.0571620\pi$
$522$	−11736.5	−	3671.83i	−0.984083	−	0.307877i
$523$		−	11183.4i		−	0.935022i	−0.883987	−	0.467511i	$-0.845151\pi$
$523$		−	11183.4i		−	0.935022i	0.883987	−	0.467511i	$-0.154849\pi$
$524$	9280.07	−	5642.85i	0.773668	−	0.470437i
$525$	1299.60	+	2394.75i	0.108037	+	0.199077i
$526$	4118.18	−	1153.78i	0.341371	−	0.0956408i
$527$	17550.2			1.45066
$528$	−195.349	−	10244.0i	−0.0161012	−	0.844344i
$529$	6943.23			0.570661
$530$	3584.54	−	1004.27i	0.293778	−	0.0823067i
$531$	1525.11	−	2346.33i	0.124640	−	0.191756i
$532$	12650.5	−	7692.26i	1.03095	−	0.626883i
$533$			3842.79i			0.312288i
$534$	9930.10	+	10233.0i	0.804714	+	0.829264i
$535$			3939.68i			0.318369i
$536$	−2145.44	−	2003.93i	−0.172890	−	0.161486i
$537$	−20272.4	+	11001.6i	−1.62908	+	0.884084i
$538$	2251.90	+	8037.72i	0.180458	+	0.644109i
$539$	−2986.32			−0.238645
$540$	5010.53	−	2527.33i	0.399294	−	0.201406i
$541$	15537.3			1.23475			0.617377	−	0.786667i	$-0.288195\pi$
$541$	15537.3			1.23475			0.617377	+	0.786667i	$0.288195\pi$
$542$	689.411	+	2460.72i	0.0546360	+	0.195013i
$543$	−271.666	+	147.430i	−0.0214702	+	0.0116516i
$544$	15767.6	+	3278.12i	1.24270	+	0.258360i
$545$			6002.05i			0.471742i
$546$	12175.5	+	12546.9i	0.954325	+	0.983439i
$547$		−	2188.27i		−	0.171049i	−0.996336	−	0.0855244i	$-0.972743\pi$
$547$		−	2188.27i		−	0.171049i	0.996336	−	0.0855244i	$-0.0272565\pi$
$548$	6999.64	+	11511.4i	0.545638	+	0.897340i
$549$	−10276.3	+	15809.9i	−0.798877	+	1.22905i
$550$	2097.80	−	587.733i	0.162637	−	0.0455655i
$551$	−14208.6			−1.09856
$552$	4085.67	−	15731.7i	0.315032	−	1.21302i
$553$	14952.3			1.14979
$554$	5771.69	−	1617.03i	0.442628	−	0.124009i
$555$	−2219.80	−	4090.37i	−0.169775	−	0.312841i
$556$	−5925.19	−	9744.40i	−0.451950	−	0.743264i
$557$		−	4424.18i		−	0.336550i	−0.985740	−	0.168275i	$-0.946180\pi$
$557$		−	4424.18i		−	0.336550i	0.985740	−	0.168275i	$-0.0538197\pi$
$558$	−14377.5	−	4498.10i	−1.09077	−	0.341254i
$559$			2365.49i			0.178979i
$560$	3088.33	−	5959.10i	0.233046	−	0.449675i
$561$	−6793.55	−	12518.3i	−0.511272	−	0.942111i
$562$	−3736.53	−	13336.8i	−0.280455	−	1.00103i
$563$	−24100.3			−1.80409			−0.902047	−	0.431637i	$-0.857936\pi$
$563$	−24100.3			−1.80409			−0.902047	+	0.431637i	$0.857936\pi$
$564$	−4476.40	+	7688.24i	−0.334203	+	0.573995i
$565$	−2435.24			−0.181330
$566$	−3720.61	−	13280.0i	−0.276305	−	0.986218i
$567$	−13973.6	+	6207.59i	−1.03498	+	0.459778i
$568$	−4658.63	+	4987.61i	−0.344141	+	0.368442i
$569$			5921.64i			0.436289i	0.975917	+	0.218144i	$0.0700004\pi$
$569$			5921.64i			0.436289i	−0.975917	+	0.218144i	$0.930000\pi$
$570$	4653.23	−	4515.47i	0.341934	−	0.331811i
$571$		−	4120.98i		−	0.302027i	−0.988532	−	0.151014i	$-0.951746\pi$
$571$		−	4120.98i		−	0.302027i	0.988532	−	0.151014i	$-0.0482538\pi$
$572$	11944.4	−	7262.94i	0.873114	−	0.530907i
$573$	−5458.77	+	2962.41i	−0.397982	+	0.215980i
$574$	−3870.50	+	1084.38i	−0.281449	+	0.0788524i
$575$	3455.99			0.250652
$576$	−12077.0	−	6726.73i	−0.873626	−	0.486598i
$577$	−14605.1			−1.05376			−0.526878	−	0.849941i	$-0.676637\pi$
$577$	−14605.1			−1.05376			−0.526878	+	0.849941i	$0.676637\pi$
$578$	8176.55	−	2290.79i	0.588407	−	0.164852i
$579$	−13182.8	+	7154.16i	−0.946217	+	0.513500i
$580$	−5503.60	+	3346.53i	−0.394008	+	0.239581i
$581$		−	7054.87i		−	0.503761i
$582$	16884.1	−	16384.3i	1.20252	−	1.16692i
$583$			8109.88i			0.576118i
$584$	−17234.5	+	18451.5i	−1.22118	+	1.30742i
$585$	6419.70	+	4172.78i	0.453712	+	0.294911i
$586$	3452.55	+	12323.2i	0.243385	+	0.868716i
$587$	13164.3			0.925637			0.462818	−	0.886453i	$-0.346838\pi$
$587$	13164.3			0.925637			0.462818	+	0.886453i	$0.346838\pi$
$588$	−2027.37	+	3482.01i	−0.142189	+	0.244210i
$589$	−17405.9			−1.21766
$590$	−395.434	−	1411.42i	−0.0275928	−	0.0984872i
$591$	−1290.66	−	2378.27i	−0.0898318	−	0.165531i
$592$	−5275.05	+	10178.5i	−0.366222	+	0.706645i
$593$			21694.5i			1.50233i	0.660112	+	0.751167i	$0.270509\pi$
$593$			21694.5i			1.50233i	−0.660112	+	0.751167i	$0.729491\pi$
$594$	2356.99	+	11996.5i	0.162809	+	0.828656i
$595$		−	9330.19i		−	0.642858i
$596$	−3632.80	−	5974.40i	−0.249673	−	0.410606i
$597$	−286.721	−	528.335i	−0.0196561	−	0.0362199i
$598$	21353.8	−	5982.62i	1.46024	−	0.409109i
$599$	28836.2			1.96697			0.983486	−	0.180986i	$-0.0579289\pi$
$599$	28836.2			1.96697			0.983486	+	0.180986i	$0.0579289\pi$
$600$	738.875	−	2845.01i	0.0502741	−	0.193578i
$601$	−25101.6			−1.70369			−0.851844	−	0.523795i	$-0.824516\pi$
$601$	−25101.6			−1.70369			−0.851844	+	0.523795i	$0.824516\pi$
$602$	−2382.55	+	667.510i	−0.161305	+	0.0451921i
$603$	2937.13	+	1909.12i	0.198357	+	0.128931i
$604$	5582.16	+	9180.27i	0.376051	+	0.618443i
$605$		−	1908.81i		−	0.128271i
$606$	10988.6	+	11323.8i	0.736600	+	0.759071i
$607$		−	1138.66i		−	0.0761396i	−0.999275	−	0.0380698i	$-0.987879\pi$
$607$		−	1138.66i		−	0.0761396i	0.999275	−	0.0380698i	$-0.0121209\pi$
$608$	−15638.0	−	3251.17i	−1.04310	−	0.216862i
$609$	15425.0	−	8370.97i	1.02636	−	0.556993i
$610$	2664.47	+	9510.33i	0.176855	+	0.631249i
$611$	−12138.1			−0.803693
$612$	−19208.2	−	577.319i	−1.26870	−	0.0381319i
$613$	3569.26			0.235173			0.117586	−	0.993063i	$-0.462484\pi$
$613$	3569.26			0.235173			0.117586	+	0.993063i	$0.462484\pi$
$614$	−5132.53	−	18319.6i	−0.337349	−	1.20410i
$615$	−1547.17	+	839.633i	−0.101444	+	0.0550524i
$616$	10685.9	+	9981.05i	0.698939	+	0.652838i
$617$			11344.1i			0.740190i	0.928994	+	0.370095i	$0.120675\pi$
$617$			11344.1i			0.740190i	−0.928994	+	0.370095i	$0.879325\pi$
$618$	−17489.8	−	18023.4i	−1.13842	−	1.17315i
$619$		−	2452.32i		−	0.159236i	−0.996825	−	0.0796180i	$-0.974630\pi$
$619$		−	2452.32i		−	0.159236i	0.996825	−	0.0796180i	$-0.0253701\pi$
$620$	−6742.08	+	4099.60i	−0.436723	+	0.265554i
$621$	−1533.68	+	19333.8i	−0.0991054	+	1.24934i
$622$	450.849	−	126.313i	0.0290633	−	0.00814257i
$623$	−20349.6			−1.30865
$624$	−359.608	−	18857.7i	−0.0230702	−	1.20980i
$625$	625.000			0.0400000
$626$	8976.46	−	2514.90i	0.573117	−	0.160568i
$627$	6737.70	+	12415.4i	0.429151	+	0.790789i
$628$	−8975.10	+	5457.41i	−0.570295	+	0.346775i
$629$			15936.5i			1.01022i
$630$	−2391.32	+	7643.50i	−0.151226	+	0.483372i
$631$		−	6181.89i		−	0.390011i	−0.980802	−	0.195006i	$-0.937527\pi$
$631$		−	6181.89i		−	0.390011i	0.980802	−	0.195006i	$-0.0624725\pi$
$632$	−11788.2	−	11010.7i	−0.741947	−	0.693009i
$633$	1663.64	+	3065.55i	0.104461	+	0.192488i
$634$	−125.504	−	447.962i	−0.00786181	−	0.0280612i
$635$	8041.40			0.502541
$636$	9456.00	+	5505.67i	0.589552	+	0.343261i
$637$	−5497.37			−0.341937
$638$	−3785.70	−	13512.3i	−0.234917	−	0.838492i
$639$	4438.23	−	6828.08i	0.274763	−	0.422715i
$640$	−6823.02	+	2423.88i	−0.421412	+	0.149707i
$641$		−	15093.8i		−	0.930064i	−0.885294	−	0.465032i	$-0.846043\pi$
$641$		−	15093.8i		−	0.930064i	0.885294	−	0.465032i	$-0.153957\pi$
$642$	−8310.56	+	8064.53i	−0.510890	+	0.495766i
$643$			30026.8i			1.84159i	0.390049	+	0.920794i	$0.372458\pi$
$643$			30026.8i			1.84159i	−0.390049	+	0.920794i	$0.627542\pi$
$644$	12051.5	+	19819.6i	0.737417	+	1.21274i
$645$	−952.388	+	516.849i	−0.0581399	+	0.0315518i
$646$	−21380.2	+	5990.00i	−1.30215	+	0.364820i
$647$	−11520.7			−0.700038			−0.350019	−	0.936743i	$-0.613825\pi$
$647$	−11520.7			−0.700038			−0.350019	+	0.936743i	$0.613825\pi$
$648$	15587.8	+	5396.00i	0.944982	+	0.327122i
$649$	3193.29			0.193140
$650$	3861.73	−	1081.93i	0.233030	−	0.0652872i
$651$	18896.1	−	10254.7i	1.13763	−	0.617378i
$652$	−8191.20	−	13471.0i	−0.492013	−	0.809150i
$653$		−	18334.9i		−	1.09877i	−0.835568	−	0.549386i	$-0.814862\pi$
$653$		−	18334.9i		−	1.09877i	0.835568	−	0.549386i	$-0.185138\pi$
$654$	−12661.0	+	12286.2i	−0.757011	+	0.734601i
$655$			6788.13i			0.404938i
$656$	3849.99	+	1995.28i	0.229142	+	0.118754i
$657$	16419.1	−	25260.4i	0.974995	−	1.50000i
$658$	−3425.22	−	12225.7i	−0.202932	−	0.724326i
$659$	14497.0			0.856940			0.428470	−	0.903556i	$-0.359053\pi$
$659$	14497.0			0.856940			0.428470	+	0.903556i	$0.359053\pi$
$660$	5533.99	+	3222.11i	0.326379	+	0.190031i
$661$	−9312.87			−0.548001			−0.274000	−	0.961730i	$-0.588347\pi$
$661$	−9312.87			−0.548001			−0.274000	+	0.961730i	$0.588347\pi$
$662$	2562.34	+	9145.80i	0.150436	+	0.536951i
$663$	−12505.9	−	23044.4i	−0.732563	−	1.34988i
$664$	−5195.13	+	5561.99i	−0.303630	+	0.325071i
$665$			9253.49i			0.539602i
$666$	4084.52	−	13055.6i	0.237645	−	0.759598i
$667$		−	22260.7i		−	1.29226i
$668$	−8175.77	+	4971.37i	−0.473548	+	0.287946i
$669$	−7466.27	−	13757.9i	−0.431484	−	0.795086i
$670$	1766.82	−	495.002i	0.101878	−	0.0285427i
$671$	−21516.8			−1.23792
$672$	18892.2	−	5683.60i	1.08450	−	0.326264i
$673$	17538.1			1.00453			0.502263	−	0.864715i	$-0.332501\pi$
$673$	17538.1			1.00453			0.502263	+	0.864715i	$0.332501\pi$
$674$	−8380.89	+	2348.04i	−0.478961	+	0.134189i
$675$	−277.359	+	3496.42i	−0.0158156	+	0.199374i
$676$	6970.26	−	4238.35i	0.396578	−	0.241144i
$677$			4502.20i			0.255589i	0.991801	+	0.127794i	$0.0407898\pi$
$677$			4502.20i			0.255589i	−0.991801	+	0.127794i	$0.959210\pi$
$678$	−4984.94	−	5137.02i	−0.282368	−	0.290982i
$679$			33576.0i			1.89769i
$680$	−6870.65	+	7355.83i	−0.387467	+	0.414828i
$681$	14188.3	−	7699.83i	0.798381	−	0.433272i
$682$	−4637.59	−	16553.0i	−0.260385	−	0.929394i
$683$	20582.8			1.15312			0.576558	−	0.817056i	$-0.304396\pi$
$683$	20582.8			1.15312			0.576558	+	0.817056i	$0.304396\pi$
$684$	19050.3	+	572.573i	1.06492	+	0.0320071i
$685$	−8420.29			−0.469668
$686$	3938.27	+	14056.9i	0.219189	+	0.782354i
$687$	2215.25	−	1202.19i	0.123023	−	0.0667632i
$688$	2369.92	+	1228.22i	0.131326	+	0.0680605i
$689$			14929.1i			0.825475i
$690$	7074.43	+	7290.25i	0.390317	+	0.402225i
$691$			20043.8i			1.10348i	0.834018	+	0.551738i	$0.186035\pi$
$691$			20043.8i			1.10348i	−0.834018	+	0.551738i	$0.813965\pi$
$692$	13517.9	+	22231.1i	0.742590	+	1.22124i
$693$	−14629.1	−	9508.84i	−0.801894	−	0.521228i
$694$	8917.14	−	2498.28i	0.487738	−	0.136648i
$695$	7127.77			0.389024
$696$	−18325.2	−	4759.23i	−0.998011	−	0.259193i
$697$	6027.95			0.327582
$698$	5449.65	−	1526.81i	0.295519	−	0.0827945i
$699$	−15001.6	−	27643.1i	−0.811747	−	1.49579i
$700$	2179.46	+	3584.28i	0.117680	+	0.193533i
$701$			3118.89i			0.168044i	0.996464	+	0.0840221i	$0.0267766\pi$
$701$			3118.89i			0.168044i	−0.996464	+	0.0840221i	$0.973223\pi$
$702$	4338.86	+	22083.7i	0.233276	+	1.18732i
$703$		−	15805.5i		−	0.847961i
$704$	−1074.70	−	15737.9i	−0.0575342	−	0.842536i
$705$	−2652.13	−	4887.03i	−0.141681	−	0.261073i
$706$	−8648.19	−	30868.1i	−0.461018	−	1.64552i
$707$	−22518.7			−1.19788
$708$	2167.88	−	3723.34i	0.115076	−	0.197643i
$709$	9275.46			0.491322			0.245661	−	0.969356i	$-0.420995\pi$
$709$	9275.46			0.491322			0.245661	+	0.969356i	$0.420995\pi$
$710$	−1150.75	−	4107.40i	−0.0608268	−	0.217110i
$711$	16138.2	+	10489.8i	0.851237	+	0.553301i
$712$	16043.4	+	14985.2i	0.844456	+	0.788757i
$713$		−	27270.0i		−	1.43236i
$714$	19681.6	−	19098.9i	1.03160	−	1.00106i
$715$			8737.03i			0.456988i
$716$	−30342.2	+	18449.9i	−1.58372	+	0.962997i
$717$	22132.4	−	12011.0i	1.15279	−	0.625603i
$718$	12216.8	−	3422.75i	0.634998	−	0.177905i
$719$	18100.1			0.938829			0.469415	−	0.882978i	$-0.344465\pi$
$719$	18100.1			0.938829			0.469415	+	0.882978i	$0.344465\pi$
$720$	7513.88	−	4265.12i	0.388925	−	0.220766i
$721$	35841.6			1.85133
$722$	2523.54	−	707.012i	0.130078	−	0.0364436i
$723$	29228.0	−	15861.7i	1.50346	−	0.815909i
$724$	−406.610	+	247.244i	−0.0208723	+	0.0126916i
$725$		−	4025.74i		−	0.206224i
$726$	4026.54	−	3907.34i	0.205839	−	0.199745i
$727$			30725.5i			1.56746i	0.621101	+	0.783731i	$0.286686\pi$
$727$			30725.5i			1.56746i	−0.621101	+	0.783731i	$0.713314\pi$
$728$	19671.1	+	18373.6i	1.00146	+	0.935401i
$729$	−19436.8	−	3103.24i	−0.987493	−	0.157661i
$730$	−4257.19	−	15195.2i	−0.215844	−	0.770412i
$731$	3710.60			0.187745
$732$	−14607.4	+	25088.2i	−0.737575	+	1.26679i
$733$	−20937.2			−1.05502			−0.527512	−	0.849548i	$-0.676875\pi$
$733$	−20937.2			−1.05502			−0.527512	+	0.849548i	$0.676875\pi$
$734$	8481.64	+	30273.6i	0.426517	+	1.52237i
$735$	−1201.15	−	2213.34i	−0.0602791	−	0.111075i
$736$	5093.63	−	24500.2i	0.255100	−	1.22702i
$737$			3997.35i			0.199789i
$738$	−4938.23	−	1544.96i	−0.246313	−	0.0770606i
$739$		−	22413.0i		−	1.11566i	−0.829954	−	0.557831i	$-0.811634\pi$
$739$		−	22413.0i		−	1.11566i	0.829954	−	0.557831i	$-0.188366\pi$
$740$	−3722.65	−	6122.17i	−0.184929	−	0.304129i
$741$	12403.1	+	22855.0i	0.614898	+	1.13306i
$742$	−15036.7	+	4212.79i	−0.743957	+	0.208432i
$743$	−34862.0			−1.72135			−0.860674	−	0.509156i	$-0.829958\pi$
$743$	−34862.0			−1.72135			−0.860674	+	0.509156i	$0.829958\pi$
$744$	−22448.9	−	5830.20i	−1.10621	−	0.287292i
$745$	4370.12			0.214911
$746$	−5781.32	+	1619.73i	−0.283739	+	0.0794941i
$747$	4949.34	−	7614.42i	0.242419	−	0.372955i
$748$	−11392.9	−	18736.5i	−0.556908	−	0.915875i
$749$		−	16526.5i		−	0.806230i
$750$	1279.38	+	1318.41i	0.0622883	+	0.0641885i
$751$			3994.41i			0.194085i	0.995280	+	0.0970427i	$0.0309383\pi$
$751$			3994.41i			0.194085i	−0.995280	+	0.0970427i	$0.969062\pi$
$752$	−6302.44	+	12160.9i	−0.305620	+	0.589710i
$753$	181.181	−	98.3249i	0.00876842	−	0.00475851i
$754$	−6968.90	−	24874.2i	−0.336595	−	1.20141i
$755$	−6715.13			−0.323693
$756$	−21018.6	+	10601.9i	−1.01116	+	0.510036i
$757$	2502.29			0.120142			0.0600709	−	0.998194i	$-0.480867\pi$
$757$	2502.29			0.120142			0.0600709	+	0.998194i	$0.480867\pi$
$758$	8183.55	+	29209.6i	0.392137	+	1.39966i
$759$	−19451.4	+	10556.0i	−0.930223	+	0.504821i
$760$	6814.17	−	7295.36i	0.325232	−	0.348198i
$761$			5708.61i			0.271928i	0.990714	+	0.135964i	$0.0434131\pi$
$761$			5708.61i			0.271928i	−0.990714	+	0.135964i	$0.956587\pi$
$762$	16460.8	+	16962.9i	0.782560	+	0.806434i
$763$		−	25178.0i		−	1.19463i
$764$	−8170.28	+	4968.03i	−0.386899	+	0.235258i
$765$	6545.59	−	10070.2i	0.309355	−	0.475933i
$766$	5233.12	−	1466.14i	0.246841	−	0.0691566i
$767$	5878.38			0.276735
$768$	−19079.8	−	9431.15i	−0.896462	−	0.443121i
$769$	8892.22			0.416985			0.208493	−	0.978024i	$-0.433144\pi$
$769$	8892.22			0.416985			0.208493	+	0.978024i	$0.433144\pi$
$770$	−8800.04	+	2465.47i	−0.411859	+	0.115389i
$771$	−460.347	−	848.272i	−0.0215032	−	0.0396236i
$772$	−19731.1	+	11997.7i	−0.919866	+	0.559335i
$773$		−	6494.04i		−	0.302166i	−0.988521	−	0.151083i	$-0.951724\pi$
$773$		−	6494.04i		−	0.302166i	0.988521	−	0.151083i	$-0.0482761\pi$
$774$	−3039.81	−	951.024i	−0.141168	−	0.0441652i
$775$		−	4931.65i		−	0.228581i
$776$	24725.0	−	26471.0i	1.14378	−	1.22455i
$777$	9311.80	+	17158.7i	0.429935	+	0.792232i
$778$	10030.5	+	35802.1i	0.462227	+	1.64983i
$779$	−5978.40			−0.274966
$780$	10187.3	+	5931.43i	0.467644	+	0.272281i
$781$	9292.83			0.425766
$782$	−9384.58	−	33496.5i	−0.429146	−	1.53175i
$783$	22521.1	+	1786.52i	1.02789	+	0.0815389i
$784$	−2854.38	+	5507.68i	−0.130028	+	0.250896i
$785$		−	6565.05i		−	0.298493i
$786$	−14319.2	+	13895.3i	−0.649809	+	0.630572i
$787$		−	8799.08i		−	0.398543i	−0.979944	−	0.199272i	$-0.936142\pi$
$787$		−	8799.08i		−	0.398543i	0.979944	−	0.199272i	$-0.0638576\pi$
$788$	−2164.47	−	3559.62i	−0.0978501	−	0.160921i
$789$	−6905.56	+	3747.56i	−0.311590	+	0.169096i
$790$	9707.84	−	2719.81i	0.437202	−	0.122489i
$791$	10215.6			0.459195
$792$	4531.20	+	18269.4i	0.203295	+	0.819663i
$793$	−39609.2			−1.77372
$794$	−21135.2	+	5921.38i	−0.944661	+	0.264662i
$795$	−6010.71	+	3261.94i	−0.268148	+	0.145521i
$796$	−480.838	−	790.772i	−0.0214106	−	0.0352113i
$797$			32892.0i			1.46185i	0.682459	+	0.730924i	$0.260911\pi$
$797$			32892.0i			1.46185i	−0.682459	+	0.730924i	$0.739089\pi$
$798$	−19519.8	+	18941.9i	−0.865906	+	0.840272i
$799$			19040.4i			0.843054i
$800$	921.159	−	4430.74i	0.0407099	−	0.195813i
$801$	−21963.6	−	14276.3i	−0.968846	−	0.629746i
$802$	−1556.48	−	5555.56i	−0.0685302	−	0.244605i
$803$	34378.6			1.51083
$804$	4660.86	+	2713.74i	0.204447	+	0.119038i
$805$	−14497.5			−0.634746
$806$	−8537.11	−	30471.6i	−0.373085	−	1.33166i
$807$	−7314.35	−	13478.0i	−0.319055	−	0.587916i
$808$	17753.5	+	16582.5i	0.772977	+	0.721993i
$809$		−	40905.7i		−	1.77771i	−0.458187	−	0.888856i	$-0.651501\pi$
$809$		−	40905.7i		−	1.77771i	0.458187	−	0.888856i	$-0.348499\pi$
$810$	−7943.28	+	6572.10i	−0.344566	+	0.285087i
$811$			30156.7i			1.30573i	0.757475	+	0.652865i	$0.226433\pi$
$811$			30156.7i			1.30573i	−0.757475	+	0.652865i	$0.773567\pi$
$812$	23087.0	−	14038.3i	0.997777	−	0.606710i
$813$	−2239.26	−	4126.24i	−0.0965982	−	0.178000i
$814$	15031.0	−	4211.18i	0.647219	−	0.181329i
$815$	9853.69			0.423509
$816$	−29581.0	+	564.095i	−1.26905	+	0.0242001i
$817$	−3680.10			−0.157589
$818$	16095.9	−	4509.54i	0.687997	−	0.192754i
$819$	−26929.9	−	17504.4i	−1.14897	−	0.746827i
$820$	−2315.69	+	1408.08i	−0.0986190	+	0.0599664i
$821$			10559.2i			0.448867i	0.974489	+	0.224433i	$0.0720531\pi$
$821$			10559.2i			0.448867i	−0.974489	+	0.224433i	$0.927947\pi$
$822$	−17236.3	−	17762.2i	−0.731371	−	0.753683i
$823$			31067.1i			1.31583i	0.753091	+	0.657917i	$0.228562\pi$
$823$			31067.1i			1.31583i	−0.753091	+	0.657917i	$0.771438\pi$
$824$	−28257.2	−	26393.4i	−1.19464	−	1.11585i
$825$	−3517.68	+	1909.00i	−0.148449	+	0.0805612i
$826$	1658.80	+	5920.77i	0.0698754	+	0.249407i
$827$	5421.39			0.227957			0.113978	−	0.993483i	$-0.463641\pi$
$827$	5421.39			0.227957			0.113978	+	0.993483i	$0.463641\pi$
$828$	−897.055	+	29846.3i	−0.0376507	+	1.25269i
$829$	38426.3			1.60989			0.804946	−	0.593348i	$-0.202194\pi$
$829$	38426.3			1.60989			0.804946	+	0.593348i	$0.202194\pi$
$830$	−1283.28	−	4580.41i	−0.0536665	−	0.191552i
$831$	−9678.23	+	5252.26i	−0.404012	+	0.219253i
$832$	−1978.35	−	28971.2i	−0.0824364	−	1.20720i
$833$			8623.40i			0.358683i
$834$	14590.6	+	15035.7i	0.605792	+	0.624273i
$835$		−	5980.36i		−	0.247855i
$836$	11299.3	+	18582.5i	0.467457	+	0.768766i
$837$	27589.0	+	2188.54i	1.13933	+	0.0903787i
$838$	35338.8	−	9900.75i	1.45675	−	0.408133i
$839$	14422.0			0.593448			0.296724	−	0.954963i	$-0.404106\pi$
$839$	14422.0			0.593448			0.296724	+	0.954963i	$0.404106\pi$
$840$	−3099.50	+	11934.5i	−0.127313	+	0.490213i
$841$	−1541.54			−0.0632066
$842$	21402.7	−	5996.31i	0.875992	−	0.245424i
$843$	12136.5	+	22363.8i	0.495854	+	0.913700i
$844$	2789.96	+	4588.28i	0.113785	+	0.187127i
$845$			5098.56i			0.207569i
$846$	4880.03	−	15598.3i	0.198320	−	0.633901i
$847$			8007.25i			0.324831i
$848$	14957.1	+	7751.57i	0.605693	+	0.313903i
$849$	12084.8	+	22268.5i	0.488516	+	0.900179i
$850$	−1697.16	−	6057.68i	−0.0684847	−	0.244443i
$851$	24762.6			0.997476
$852$	6308.76	−	10835.3i	0.253679	−	0.435694i
$853$	−17955.9			−0.720750			−0.360375	−	0.932807i	$-0.617351\pi$
$853$	−17955.9			−0.720750			−0.360375	+	0.932807i	$0.617351\pi$
$854$	−11177.2	−	39894.8i	−0.447863	−	1.59856i
$855$	−6491.79	+	9987.42i	−0.259666	+	0.399488i
$856$	−12170.0	+	13029.3i	−0.485935	+	0.520250i
$857$		−	26611.0i		−	1.06070i	−0.847780	−	0.530348i	$-0.822061\pi$
$857$		−	26611.0i		−	1.06070i	0.847780	−	0.530348i	$-0.177939\pi$
$858$	−18430.3	+	17884.7i	−0.733335	+	0.711625i
$859$		−	19264.8i		−	0.765201i	−0.923914	−	0.382601i	$-0.875028\pi$
$859$		−	19264.8i		−	0.765201i	0.923914	−	0.382601i	$-0.124972\pi$
$860$	−1425.46	+	866.769i	−0.0565208	+	0.0343681i
$861$	6490.23	−	3522.17i	0.256895	−	0.139414i
$862$	−23254.7	+	6515.19i	−0.918861	+	0.257434i
$863$	−47910.6			−1.88980			−0.944899	−	0.327363i	$-0.893840\pi$
$863$	−47910.6			−1.88980			−0.944899	+	0.327363i	$0.893840\pi$
$864$	24378.0	+	7119.46i	0.959902	+	0.280334i
$865$	−16261.5			−0.639198
$866$	17808.7	−	4989.41i	0.698806	−	0.195782i
$867$	−13710.8	+	7440.68i	−0.537074	+	0.291463i
$868$	28282.3	−	17197.4i	1.10595	−	0.672484i
$869$			21963.6i			0.857382i
$870$	8492.10	−	8240.70i	0.330930	−	0.321133i
$871$			7358.53i			0.286262i
$872$	−18540.8	+	19850.0i	−0.720034	+	0.770880i
$873$	−23555.3	+	36239.1i	−0.913202	+	1.40493i
$874$	9307.44	+	33221.1i	0.360216	+	1.28572i
$875$	−2621.81			−0.101295
$876$	23339.1	−	40085.0i	0.900178	−	1.54606i
$877$	−38173.3			−1.46981			−0.734904	−	0.678171i	$-0.762773\pi$
$877$	−38173.3			−1.46981			−0.734904	+	0.678171i	$0.762773\pi$
$878$	9382.12	+	33487.7i	0.360628	+	1.28719i
$879$	−11214.2	−	20664.1i	−0.430312	−	0.792928i
$880$	8753.41	+	4536.50i	0.335315	+	0.173779i
$881$			31583.6i			1.20781i	0.797057	+	0.603904i	$0.206389\pi$
$881$			31583.6i			1.20781i	−0.797057	+	0.603904i	$0.793611\pi$
$882$	2210.17	−	7064.48i	0.0843767	−	0.269698i
$883$			3771.86i			0.143752i	0.997414	+	0.0718762i	$0.0228986\pi$
$883$			3771.86i			0.143752i	−0.997414	+	0.0718762i	$0.977101\pi$
$884$	−20972.7	−	34491.1i	−0.797951	−	1.31229i
$885$	1284.40	+	2366.74i	0.0487849	+	0.0898950i
$886$	−33571.2	+	9405.52i	−1.27296	+	0.356642i
$887$	−27483.2			−1.04036			−0.520178	−	0.854058i	$-0.674134\pi$
$887$	−27483.2			−1.04036			−0.520178	+	0.854058i	$0.674134\pi$
$888$	5294.13	−	20384.8i	0.200067	−	0.770349i
$889$	−33732.8			−1.27262
$890$	−13212.1	+	3701.58i	−0.497607	+	0.139413i
$891$	−9118.43	−	20526.0i	−0.342849	−	0.771771i
$892$	−12521.1	−	20591.9i	−0.469997	−	0.772944i
$893$		−	18883.9i		−	0.707642i
$894$	8945.64	+	9218.55i	0.334661	+	0.344871i
$895$		−	22194.5i		−	0.828917i
$896$	28621.8	−	10167.9i	1.06717	−	0.379114i
$897$	−35807.0	+	19432.0i	−1.33284	+	0.723319i
$898$	3576.14	+	12764.4i	0.132892	+	0.474334i
$899$	−31765.7			−1.17847
$900$	−162.228	+	5397.56i	−0.00600845	+	0.199910i
$901$	23418.4			0.865903
$902$	−1592.87	−	5685.44i	−0.0587990	−	0.209872i
$903$	3995.16	−	2168.13i	0.147232	−	0.0799011i
$904$	−8053.85	−	7522.63i	−0.296313	−	0.276769i
$905$		−	297.425i		−	0.0109246i
$906$	−13745.9	−	14165.2i	−0.504058	−	0.519435i
$907$		−	28400.8i		−	1.03973i	−0.854249	−	0.519864i	$-0.825983\pi$
$907$		−	28400.8i		−	1.03973i	0.854249	−	0.519864i	$-0.174017\pi$
$908$	21236.0	−	12912.8i	0.776147	−	0.471945i
$909$	−24304.7	−	15798.0i	−0.886839	−	0.576442i
$910$	−16199.6	+	4538.57i	−0.590121	+	0.165332i
$911$	−35770.7			−1.30092			−0.650458	−	0.759542i	$-0.725423\pi$
$911$	−35770.7			−1.30092			−0.650458	+	0.759542i	$0.725423\pi$
$912$	29337.8	−	559.458i	1.06521	−	0.0203131i
$913$	10363.0			0.375647
$914$	−15565.3	+	4360.88i	−0.563299	+	0.157817i
$915$	−8654.43	−	15947.4i	−0.312685	−	0.576178i
$916$	3315.62	−	2016.10i	0.119597	−	0.0727225i
$917$		−	28475.5i		−	1.02546i
$918$	34641.4	−	6806.12i	1.24547	−	0.244701i
$919$			36103.6i			1.29592i	0.761675	+	0.647959i	$0.224377\pi$
$919$			36103.6i			1.29592i	−0.761675	+	0.647959i	$0.775623\pi$
$920$	11429.7	+	10675.8i	0.409593	+	0.382577i
$921$	16670.9	+	30719.1i	0.596444	+	1.09905i
$922$	5152.13	+	18389.6i	0.184031	+	0.656863i
$923$	17106.7			0.610048
$924$	−23214.5	−	13516.4i	−0.826516	−	0.481231i
$925$	4478.20			0.159181
$926$	8282.02	+	29561.1i	0.293914	+	1.04907i
$927$	38684.3	+	25144.7i	1.37062	+	0.890895i
$928$	−28539.2	−	5933.36i	−1.00953	−	0.209884i
$929$			38275.6i			1.35176i	0.737014	+	0.675878i	$0.236235\pi$
$929$			38275.6i			1.35176i	−0.737014	+	0.675878i	$0.763765\pi$
$930$	10403.1	−	10095.1i	0.366807	−	0.355948i
$931$		−	8552.51i		−	0.301071i
$932$	−25158.0	−	41374.1i	−0.884203	−	1.45413i
$933$	−756.003	+	410.274i	−0.0265278	+	0.0143963i
$934$	14082.1	−	3945.33i	0.493341	−	0.138217i
$935$	13705.3			0.479369
$936$	8341.27	+	33631.2i	0.291285	+	1.17443i
$937$	30657.8			1.06889			0.534443	−	0.845205i	$-0.320521\pi$
$937$	30657.8			1.06889			0.534443	+	0.845205i	$0.320521\pi$
$938$	−7411.60	+	2076.48i	−0.257993	+	0.0722809i
$939$	−15052.1	+	8168.61i	−0.523118	+	0.283890i
$940$	−4447.69	−	7314.54i	−0.154327	−	0.253802i
$941$			24896.8i			0.862498i	0.902233	+	0.431249i	$0.141927\pi$
$941$			24896.8i			0.862498i	−0.902233	+	0.431249i	$0.858073\pi$
$942$	13848.7	−	13438.7i	0.478995	−	0.464815i
$943$		−	9366.41i		−	0.323449i
$944$	3052.21	−	5889.40i	0.105234	−	0.203055i
$945$	1163.49	−	14667.1i	0.0400511	−	0.504890i
$946$	−980.516	−	3499.76i	−0.0336991	−	0.120282i
$947$	53361.2			1.83105			0.915526	−	0.402259i	$-0.131775\pi$
$947$	53361.2			1.83105			0.915526	+	0.402259i	$0.131775\pi$
$948$	25609.3	+	14910.8i	0.877374	+	0.510843i
$949$	63285.9			2.16475
$950$	1683.21	+	6007.88i	0.0574846	+	0.205180i
$951$	407.646	+	751.162i	0.0138999	+	0.0256131i
$952$	28821.6	−	30856.9i	0.981213	−	1.05050i
$953$			25939.5i			0.881703i	0.897580	+	0.440851i	$0.145323\pi$
$953$			25939.5i			0.881703i	−0.897580	+	0.440851i	$0.854677\pi$
$954$	−19184.8	−	6002.10i	−0.651082	−	0.203695i
$955$		−	5976.35i		−	0.202503i
$956$	33126.0	−	20142.7i	1.12068	−	0.681444i
$957$	12296.2	+	22658.1i	0.415341	+	0.765341i
$958$	−20992.9	+	5881.51i	−0.707986	+	0.198354i
$959$	35322.2			1.18938
$960$	11232.0	−	7126.60i	0.377617	−	0.239594i
$961$	−9122.93			−0.306231
$962$	27669.8	−	7752.15i	0.927350	−	0.259812i
$963$	11594.2	−	17837.3i	0.387972	−	0.596884i
$964$	43746.3	−	26600.4i	1.46159	−	0.888737i
$965$		−	14432.8i		−	0.481458i
$966$	−29676.5	−	30581.8i	−0.988431	−	1.01859i
$967$		−	24435.6i		−	0.812612i	−0.913737	−	0.406306i	$-0.866817\pi$
$967$		−	24435.6i		−	0.812612i	0.913737	−	0.406306i	$-0.133183\pi$
$968$	5896.45	−	6312.83i	0.195784	−	0.209610i
$969$	35851.2	−	19456.0i	1.18855	−	0.645013i
$970$	6107.47	+	21799.4i	0.202164	+	0.721585i
$971$	21477.2			0.709822			0.354911	−	0.934900i	$-0.384511\pi$
$971$	21477.2			0.709822			0.354911	+	0.934900i	$0.384511\pi$
$972$	−30123.4	−	3302.84i	−0.994043	−	0.108991i
$973$	−29900.2			−0.985157
$974$	5312.17	+	18960.8i	0.174757	+	0.623760i
$975$	−6475.53	+	3514.19i	−0.212700	+	0.115430i
$976$	−20566.1	+	39683.4i	−0.674493	+	1.30147i
$977$		−	33734.4i		−	1.10467i	−0.833623	−	0.552333i	$-0.813738\pi$
$977$		−	33734.4i		−	1.10467i	0.833623	−	0.552333i	$-0.186262\pi$
$978$	20170.5	+	20785.9i	0.659491	+	0.679611i
$979$		−	29891.9i		−	0.975841i
$980$	−2014.36	−	3312.76i	−0.0656596	−	0.107982i
$981$	17663.6	−	27174.9i	0.574878	−	0.884432i
$982$	−15981.0	+	4477.35i	−0.519323	+	0.145497i
$983$	9151.98			0.296951			0.148475	−	0.988916i	$-0.452563\pi$
$983$	9151.98			0.296951			0.148475	+	0.988916i	$0.452563\pi$
$984$	−7710.51	−	2002.49i	−0.249799	−	0.0648751i
$985$	2603.77			0.0842263
$986$	−39018.6	+	10931.7i	−1.26025	+	0.353079i
$987$	11125.4	+	20500.6i	0.358790	+	0.661135i
$988$	20800.3	+	34207.6i	0.669783	+	1.10151i
$989$		−	5765.64i		−	0.185376i
$990$	−11227.7	−	3512.65i	−0.360443	−	0.112767i
$991$		−	11823.3i		−	0.378990i	−0.981882	−	0.189495i	$-0.939315\pi$
$991$		−	11823.3i		−	0.378990i	0.981882	−	0.189495i	$-0.0606850\pi$
$992$	−34961.4	−	7268.54i	−1.11898	−	0.232637i
$993$	−8322.70	−	15336.1i	−0.265975	−	0.490107i
$994$	4827.29	+	17230.1i	0.154037	+	0.549804i
$995$	578.429			0.0184296
$996$	7035.28	−	12083.1i	0.223817	−	0.384406i
$997$	−10234.6			−0.325108			−0.162554	−	0.986700i	$-0.551973\pi$
$997$	−10234.6			−0.325108			−0.162554	+	0.986700i	$0.551973\pi$
$998$	−4038.05	−	14413.0i	−0.128078	−	0.457151i
$999$	−1987.31	+	25052.3i	−0.0629386	+	0.793413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.e.a.11.4	yes	24
3.2	odd	2	inner	60.4.e.a.11.21	yes	24
4.3	odd	2	inner	60.4.e.a.11.22	yes	24
8.3	odd	2		960.4.h.d.191.19		24
8.5	even	2		960.4.h.d.191.6		24
12.11	even	2	inner	60.4.e.a.11.3	✓	24
24.5	odd	2		960.4.h.d.191.20		24
24.11	even	2		960.4.h.d.191.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.e.a.11.3	✓	24	12.11	even	2	inner
60.4.e.a.11.4	yes	24	1.1	even	1	trivial
60.4.e.a.11.21	yes	24	3.2	odd	2	inner
60.4.e.a.11.22	yes	24	4.3	odd	2	inner
960.4.h.d.191.5		24	24.11	even	2
960.4.h.d.191.6		24	8.5	even	2
960.4.h.d.191.19		24	8.3	odd	2
960.4.h.d.191.20		24	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.72356 + 0.763049i) q^{2} +(4.56698 - 2.47844i) q^{3} +(6.83551 - 4.15641i) q^{4} +5.00000i q^{5} +(-10.5473 + 10.2350i) q^{6} -20.9745i q^{7} +(-15.4454 + 16.5360i) q^{8} +(14.7146 - 22.6380i) q^{9} +O(q^{10})\)	\(q+(-2.72356 + 0.763049i) q^{2} +(4.56698 - 2.47844i) q^{3} +(6.83551 - 4.15641i) q^{4} +5.00000i q^{5} +(-10.5473 + 10.2350i) q^{6} -20.9745i q^{7} +(-15.4454 + 16.5360i) q^{8} +(14.7146 - 22.6380i) q^{9} +(-3.81524 - 13.6178i) q^{10} +30.8097 q^{11} +(20.9162 - 35.9237i) q^{12} +56.7161 q^{13} +(16.0045 + 57.1251i) q^{14} +(12.3922 + 22.8349i) q^{15} +(29.4485 - 56.8224i) q^{16} -88.9672i q^{17} +(-22.8022 + 72.8839i) q^{18} +88.2358i q^{19} +(20.7821 + 34.1776i) q^{20} +(-51.9840 - 95.7899i) q^{21} +(-83.9120 + 23.5093i) q^{22} -138.240 q^{23} +(-29.5550 + 113.800i) q^{24} -25.0000 q^{25} +(-154.469 + 43.2771i) q^{26} +(11.0943 - 139.857i) q^{27} +(-87.1785 - 143.371i) q^{28} +161.030i q^{29} +(-51.1751 - 52.7363i) q^{30} +197.266i q^{31} +(-36.8464 + 177.230i) q^{32} +(140.707 - 76.3602i) q^{33} +(67.8863 + 242.307i) q^{34} +104.872 q^{35} +(6.48912 - 215.903i) q^{36} -179.128 q^{37} +(-67.3282 - 240.315i) q^{38} +(259.021 - 140.568i) q^{39} +(-82.6802 - 77.2268i) q^{40} +67.7548i q^{41} +(214.674 + 221.223i) q^{42} +41.7076i q^{43} +(210.600 - 128.058i) q^{44} +(113.190 + 73.5731i) q^{45} +(376.504 - 105.484i) q^{46} -214.016 q^{47} +(-6.34049 - 332.493i) q^{48} -96.9279 q^{49} +(68.0889 - 19.0762i) q^{50} +(-220.500 - 406.311i) q^{51} +(387.683 - 235.735i) q^{52} +263.225i q^{53} +(76.5014 + 389.373i) q^{54} +154.049i q^{55} +(346.835 + 323.958i) q^{56} +(218.688 + 402.971i) q^{57} +(-122.873 - 438.573i) q^{58} +103.646 q^{59} +(179.618 + 104.581i) q^{60} -698.376 q^{61} +(-150.524 - 537.265i) q^{62} +(-474.820 - 308.631i) q^{63} +(-34.8817 - 510.810i) q^{64} +283.580i q^{65} +(-324.958 + 315.338i) q^{66} +129.743i q^{67} +(-369.784 - 608.136i) q^{68} +(-631.338 + 342.620i) q^{69} +(-285.626 + 80.0227i) q^{70} +301.620 q^{71} +(147.071 + 592.974i) q^{72} +1115.84 q^{73} +(487.866 - 136.684i) q^{74} +(-114.175 + 61.9611i) q^{75} +(366.744 + 603.137i) q^{76} -646.217i q^{77} +(-598.199 + 580.490i) q^{78} +712.880i q^{79} +(284.112 + 147.242i) q^{80} +(-295.960 - 666.220i) q^{81} +(-51.7002 - 184.534i) q^{82} +336.355 q^{83} +(-753.480 - 438.706i) q^{84} +444.836 q^{85} +(-31.8249 - 113.593i) q^{86} +(399.103 + 735.419i) q^{87} +(-475.867 + 509.471i) q^{88} -970.209i q^{89} +(-364.419 - 114.011i) q^{90} -1189.59i q^{91} +(-944.940 + 574.581i) q^{92} +(488.913 + 900.911i) q^{93} +(582.884 - 163.304i) q^{94} -441.179 q^{95} +(270.977 + 900.726i) q^{96} -1600.81 q^{97} +(263.988 - 73.9607i) q^{98} +(453.353 - 697.471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9	\( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9} - 30 q^{10} - 188 q^{12} + 72 q^{13} + 306 q^{16} + 256 q^{18} - 68 q^{21} - 300 q^{22} - 434 q^{24} - 600 q^{25} + 300 q^{28} - 40 q^{30} + 848 q^{33} - 468 q^{34} - 294 q^{36} + 504 q^{37} - 210 q^{40} - 228 q^{42} - 220 q^{45} + 684 q^{46} + 1212 q^{48} - 2256 q^{49} + 576 q^{52} - 1054 q^{54} + 1416 q^{57} + 3108 q^{58} + 490 q^{60} + 1992 q^{61} - 1842 q^{64} - 472 q^{66} - 1548 q^{69} + 540 q^{70} + 312 q^{72} - 2304 q^{73} - 420 q^{76} - 2792 q^{78} + 3840 q^{81} + 600 q^{82} - 176 q^{84} + 240 q^{85} - 372 q^{88} - 1170 q^{90} - 4384 q^{93} + 1044 q^{94} - 3846 q^{96} - 2448 q^{97}+O(q^{100}) \) 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9 - 30 * q^10 - 188 * q^12 + 72 * q^13 + 306 * q^16 + 256 * q^18 - 68 * q^21 - 300 * q^22 - 434 * q^24 - 600 * q^25 + 300 * q^28 - 40 * q^30 + 848 * q^33 - 468 * q^34 - 294 * q^36 + 504 * q^37 - 210 * q^40 - 228 * q^42 - 220 * q^45 + 684 * q^46 + 1212 * q^48 - 2256 * q^49 + 576 * q^52 - 1054 * q^54 + 1416 * q^57 + 3108 * q^58 + 490 * q^60 + 1992 * q^61 - 1842 * q^64 - 472 * q^66 - 1548 * q^69 + 540 * q^70 + 312 * q^72 - 2304 * q^73 - 420 * q^76 - 2792 * q^78 + 3840 * q^81 + 600 * q^82 - 176 * q^84 + 240 * q^85 - 372 * q^88 - 1170 * q^90 - 4384 * q^93 + 1044 * q^94 - 3846 * q^96 - 2448 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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