LMFDB - Embedded newform 60.4.e.a.11.15

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			11.15
Character	$\chi$	$=$	60.11
Dual form			60.4.e.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.622346 - 2.75911i) q^{2} +(-1.95519 - 4.81427i) q^{3} +(-7.22537 - 3.43424i) q^{4} +5.00000i q^{5} +(-14.4999 + 2.39845i) q^{6} -20.3642i q^{7} +(-13.9721 + 17.7983i) q^{8} +(-19.3544 + 18.8257i) q^{9} +O(q^{10})$	\(q+(0.622346 - 2.75911i) q^{2} +(-1.95519 - 4.81427i) q^{3} +(-7.22537 - 3.43424i) q^{4} +5.00000i q^{5} +(-14.4999 + 2.39845i) q^{6} -20.3642i q^{7} +(-13.9721 + 17.7983i) q^{8} +(-19.3544 + 18.8257i) q^{9} +(13.7955 + 3.11173i) q^{10} -15.2982 q^{11} +(-2.40639 + 41.4995i) q^{12} +27.7054 q^{13} +(-56.1872 - 12.6736i) q^{14} +(24.0714 - 9.77596i) q^{15} +(40.4119 + 49.6274i) q^{16} -92.5031i q^{17} +(39.8969 + 65.1171i) q^{18} -127.926i q^{19} +(17.1712 - 36.1268i) q^{20} +(-98.0390 + 39.8160i) q^{21} +(-9.52081 + 42.2095i) q^{22} +51.1779 q^{23} +(113.004 + 32.4666i) q^{24} -25.0000 q^{25} +(17.2423 - 76.4421i) q^{26} +(128.474 + 56.3698i) q^{27} +(-69.9358 + 147.139i) q^{28} -99.2953i q^{29} +(-11.9922 - 72.4996i) q^{30} -25.8075i q^{31} +(162.078 - 80.6156i) q^{32} +(29.9110 + 73.6499i) q^{33} +(-255.226 - 57.5690i) q^{34} +101.821 q^{35} +(204.495 - 69.5545i) q^{36} +356.629 q^{37} +(-352.962 - 79.6144i) q^{38} +(-54.1693 - 133.381i) q^{39} +(-88.9915 - 69.8607i) q^{40} +292.895i q^{41} +(48.8425 + 295.280i) q^{42} +521.476i q^{43} +(110.535 + 52.5379i) q^{44} +(-94.1283 - 96.7722i) q^{45} +(31.8504 - 141.205i) q^{46} -573.546 q^{47} +(159.907 - 291.585i) q^{48} -71.7025 q^{49} +(-15.5587 + 68.9777i) q^{50} +(-445.335 + 180.861i) q^{51} +(-200.182 - 95.1470i) q^{52} -305.765i q^{53} +(235.485 - 319.391i) q^{54} -76.4912i q^{55} +(362.449 + 284.532i) q^{56} +(-615.871 + 250.120i) q^{57} +(-273.967 - 61.7961i) q^{58} +295.688 q^{59} +(-207.498 - 12.0320i) q^{60} +326.449 q^{61} +(-71.2056 - 16.0612i) q^{62} +(383.370 + 394.139i) q^{63} +(-121.559 - 497.361i) q^{64} +138.527i q^{65} +(221.823 - 36.6920i) q^{66} -299.605i q^{67} +(-317.678 + 668.369i) q^{68} +(-100.063 - 246.384i) q^{69} +(63.3681 - 280.936i) q^{70} -653.840 q^{71} +(-64.6418 - 607.511i) q^{72} +504.190 q^{73} +(221.947 - 983.979i) q^{74} +(48.8798 + 120.357i) q^{75} +(-439.330 + 924.314i) q^{76} +311.537i q^{77} +(-401.725 + 66.4498i) q^{78} +110.758i q^{79} +(-248.137 + 202.060i) q^{80} +(20.1889 - 728.720i) q^{81} +(808.129 + 182.282i) q^{82} +1479.78 q^{83} +(845.106 + 49.0044i) q^{84} +462.515 q^{85} +(1438.81 + 324.539i) q^{86} +(-478.035 + 194.141i) q^{87} +(213.749 - 272.283i) q^{88} +772.934i q^{89} +(-325.586 + 199.484i) q^{90} -564.199i q^{91} +(-369.779 - 175.757i) q^{92} +(-124.244 + 50.4585i) q^{93} +(-356.944 + 1582.48i) q^{94} +639.631 q^{95} +(-704.998 - 622.667i) q^{96} -26.1154 q^{97} +(-44.6238 + 197.835i) q^{98} +(296.089 - 288.000i) 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 $

$2$	0.622346	−	2.75911i	0.220033	−	0.975492i
$2$	0.622346	−	2.75911i	0.220033	−	0.975492i
$3$	−1.95519	−	4.81427i	−0.376277	−	0.926507i
$3$	−1.95519	−	4.81427i	−0.376277	−	0.926507i
$4$	−7.22537	−	3.43424i	−0.903171	−	0.429280i
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$	−14.4999	+	2.39845i	−0.986594	+	0.163194i
$7$		−	20.3642i		−	1.09957i	−0.835308	−	0.549783i	$-0.814710\pi$
$7$		−	20.3642i		−	1.09957i	0.835308	−	0.549783i	$-0.185290\pi$
$8$	−13.9721	+	17.7983i	−0.617487	+	0.786581i
$9$	−19.3544	+	18.8257i	−0.716831	+	0.697247i
$10$	13.7955	+	3.11173i	0.436254	+	0.0984016i
$11$	−15.2982			−0.419327			−0.209663	−	0.977774i	$-0.567237\pi$
$11$	−15.2982			−0.419327			−0.209663	+	0.977774i	$0.567237\pi$
$12$	−2.40639	+	41.4995i	−0.0578889	+	0.998323i
$13$	27.7054			0.591084			0.295542	−	0.955330i	$-0.404500\pi$
$13$	27.7054			0.591084			0.295542	+	0.955330i	$0.404500\pi$
$14$	−56.1872	−	12.6736i	−1.07262	−	0.241940i
$15$	24.0714	−	9.77596i	0.414347	−	0.168276i
$16$	40.4119	+	49.6274i	0.631437	+	0.775428i
$17$		−	92.5031i		−	1.31972i	−0.751387	−	0.659861i	$-0.770615\pi$
$17$		−	92.5031i		−	1.31972i	0.751387	−	0.659861i	$-0.229385\pi$
$18$	39.8969	+	65.1171i	0.522433	+	0.852681i
$19$		−	127.926i		−	1.54465i	−0.635230	−	0.772323i	$-0.719095\pi$
$19$		−	127.926i		−	1.54465i	0.635230	−	0.772323i	$-0.280905\pi$
$20$	17.1712	−	36.1268i	0.191980	−	0.403910i
$21$	−98.0390	+	39.8160i	−1.01876	+	0.413741i
$22$	−9.52081	+	42.2095i	−0.0922656	+	0.409050i
$23$	51.1779			0.463971			0.231985	−	0.972719i	$-0.425478\pi$
$23$	51.1779			0.463971			0.231985	+	0.972719i	$0.425478\pi$
$24$	113.004	+	32.4666i	0.961119	+	0.276134i
$25$	−25.0000			−0.200000
$26$	17.2423	−	76.4421i	0.130058	−	0.576598i
$27$	128.474	+	56.3698i	0.915731	+	0.401791i
$28$	−69.9358	+	147.139i	−0.472022	+	0.993096i
$29$		−	99.2953i		−	0.635816i	−0.948121	−	0.317908i	$-0.897020\pi$
$29$		−	99.2953i		−	0.635816i	0.948121	−	0.317908i	$-0.102980\pi$
$30$	−11.9922	−	72.4996i	−0.0729824	−	0.441218i
$31$		−	25.8075i		−	0.149521i	−0.997202	−	0.0747606i	$-0.976181\pi$
$31$		−	25.8075i		−	0.149521i	0.997202	−	0.0747606i	$-0.0238193\pi$
$32$	162.078	−	80.6156i	0.895360	−	0.445342i
$33$	29.9110	+	73.6499i	0.157783	+	0.388509i
$34$	−255.226	−	57.5690i	−1.28738	−	0.290382i
$35$	101.821			0.491741
$36$	204.495	−	69.5545i	0.946736	−	0.322012i
$37$	356.629			1.58458			0.792290	−	0.610144i	$-0.208888\pi$
$37$	356.629			1.58458			0.792290	+	0.610144i	$0.208888\pi$
$38$	−352.962	−	79.6144i	−1.50679	−	0.339873i
$39$	−54.1693	−	133.381i	−0.222411	−	0.547643i
$40$	−88.9915	−	69.8607i	−0.351770	−	0.276149i
$41$			292.895i			1.11567i	0.829952	+	0.557835i	$0.188368\pi$
$41$			292.895i			1.11567i	−0.829952	+	0.557835i	$0.811632\pi$
$42$	48.8425	+	295.280i	0.179442	+	1.08483i
$43$			521.476i			1.84940i	0.380694	+	0.924701i	$0.375685\pi$
$43$			521.476i			1.84940i	−0.380694	+	0.924701i	$0.624315\pi$
$44$	110.535	+	52.5379i	0.378724	+	0.180009i
$45$	−94.1283	−	96.7722i	−0.311818	−	0.320577i
$46$	31.8504	−	141.205i	0.102089	−	0.452600i
$47$	−573.546			−1.78001			−0.890003	−	0.455955i	$-0.849298\pi$
$47$	−573.546			−1.78001			−0.890003	+	0.455955i	$0.849298\pi$
$48$	159.907	−	291.585i	0.480844	−	0.876806i
$49$	−71.7025			−0.209045
$50$	−15.5587	+	68.9777i	−0.0440065	+	0.195098i
$51$	−445.335	+	180.861i	−1.22273	+	0.496581i
$52$	−200.182	−	95.1470i	−0.533850	−	0.253741i
$53$		−	305.765i		−	0.792454i	−0.918153	−	0.396227i	$-0.870319\pi$
$53$		−	305.765i		−	0.792454i	0.918153	−	0.396227i	$-0.129681\pi$
$54$	235.485	−	319.391i	0.593435	−	0.804882i
$55$		−	76.4912i		−	0.187529i
$56$	362.449	+	284.532i	0.864898	+	0.678968i
$57$	−615.871	+	250.120i	−1.43113	+	0.581215i
$58$	−273.967	−	61.7961i	−0.620234	−	0.139900i
$59$	295.688			0.652462			0.326231	−	0.945290i	$-0.394221\pi$
$59$	295.688			0.652462			0.326231	+	0.945290i	$0.394221\pi$
$60$	−207.498	−	12.0320i	−0.446464	−	0.0258887i
$61$	326.449			0.685204			0.342602	−	0.939481i	$-0.388692\pi$
$61$	326.449			0.685204			0.342602	+	0.939481i	$0.388692\pi$
$62$	−71.2056	−	16.0612i	−0.145857	−	0.0328995i
$63$	383.370	+	394.139i	0.766669	+	0.788203i
$64$	−121.559	−	497.361i	−0.237419	−	0.971407i
$65$			138.527i			0.264341i
$66$	221.823	−	36.6920i	0.413705	−	0.0684314i
$67$		−	299.605i		−	0.546307i	−0.961971	−	0.273153i	$-0.911933\pi$
$67$		−	299.605i		−	0.546307i	0.961971	−	0.273153i	$-0.0880666\pi$
$68$	−317.678	+	668.369i	−0.566531	+	1.19194i
$69$	−100.063	−	246.384i	−0.174581	−	0.429872i
$70$	63.3681	−	280.936i	0.108199	−	0.479689i
$71$	−653.840			−1.09291			−0.546454	−	0.837489i	$-0.684023\pi$
$71$	−653.840			−1.09291			−0.546454	+	0.837489i	$0.684023\pi$
$72$	−64.6418	−	607.511i	−0.105807	−	0.994387i
$73$	504.190			0.808369			0.404184	−	0.914677i	$-0.367555\pi$
$73$	504.190			0.808369			0.404184	+	0.914677i	$0.367555\pi$
$74$	221.947	−	983.979i	0.348660	−	1.54575i
$75$	48.8798	+	120.357i	0.0752554	+	0.185301i
$76$	−439.330	+	924.314i	−0.663086	+	1.39508i
$77$			311.537i			0.461077i
$78$	−401.725	+	66.4498i	−0.583160	+	0.0964610i
$79$			110.758i			0.157738i	0.996885	+	0.0788688i	$0.0251308\pi$
$79$			110.758i			0.157738i	−0.996885	+	0.0788688i	$0.974869\pi$
$80$	−248.137	+	202.060i	−0.346782	+	0.282387i
$81$	20.1889	−	728.720i	0.0276939	−	0.999616i
$82$	808.129	+	182.282i	1.08833	+	0.245484i
$83$	1479.78			1.95695			0.978474	−	0.206371i	$-0.0661655\pi$
$83$	1479.78			1.95695			0.978474	+	0.206371i	$0.0661655\pi$
$84$	845.106	+	49.0044i	1.09772	+	0.0636526i
$85$	462.515			0.590198
$86$	1438.81	+	324.539i	1.80408	+	0.406929i
$87$	−478.035	+	194.141i	−0.589089	+	0.239243i
$88$	213.749	−	272.283i	0.258929	−	0.329834i
$89$			772.934i			0.920572i	0.887771	+	0.460286i	$0.152253\pi$
$89$			772.934i			0.920572i	−0.887771	+	0.460286i	$0.847747\pi$
$90$	−325.586	+	199.484i	−0.381330	+	0.233639i
$91$		−	564.199i		−	0.649935i
$92$	−369.779	−	175.757i	−0.419045	−	0.199174i
$93$	−124.244	+	50.4585i	−0.138532	+	0.0562614i
$94$	−356.944	+	1582.48i	−0.391659	+	1.73638i
$95$	639.631			0.690787
$96$	−704.998	−	622.667i	−0.749516	−	0.661986i
$97$	−26.1154			−0.0273362			−0.0136681	−	0.999907i	$-0.504351\pi$
$97$	−26.1154			−0.0273362			−0.0136681	+	0.999907i	$0.504351\pi$
$98$	−44.6238	+	197.835i	−0.0459967	+	0.203922i
$99$	296.089	−	288.000i	0.300586	−	0.292374i
$100$	180.634	+	85.8561i	0.180634	+	0.0858561i
$101$		−	196.046i		−	0.193141i	−0.995326	−	0.0965706i	$-0.969213\pi$
$101$		−	196.046i		−	0.193141i	0.995326	−	0.0965706i	$-0.0307874\pi$
$102$	221.864	+	1341.29i	0.215370	+	1.30203i
$103$		−	685.393i		−	0.655668i	−0.944735	−	0.327834i	$-0.893681\pi$
$103$		−	685.393i		−	0.655668i	0.944735	−	0.327834i	$-0.106319\pi$
$104$	−387.103	+	493.108i	−0.364986	+	0.464935i
$105$	−199.080	−	490.195i	−0.185031	−	0.455601i
$106$	−843.639	−	190.292i	−0.773033	−	0.174366i
$107$	503.806			0.455185			0.227593	−	0.973756i	$-0.426915\pi$
$107$	503.806			0.455185			0.227593	+	0.973756i	$0.426915\pi$
$108$	−734.681	−	848.502i	−0.654581	−	0.755992i
$109$	−928.609			−0.816006			−0.408003	−	0.912981i	$-0.633775\pi$
$109$	−928.609			−0.816006			−0.408003	+	0.912981i	$0.633775\pi$
$110$	−211.048	−	47.6040i	−0.182933	−	0.0412624i
$111$	−697.279	−	1716.91i	−0.596241	−	1.46813i
$112$	1010.62	−	822.959i	0.852634	−	0.694306i
$113$		−	451.244i		−	0.375659i	−0.982202	−	0.187830i	$-0.939855\pi$
$113$		−	451.244i		−	0.375659i	0.982202	−	0.187830i	$-0.0601453\pi$
$114$	306.824	+	1854.92i	0.252076	+	1.52394i
$115$			255.889i			0.207494i
$116$	−341.004	+	717.445i	−0.272944	+	0.574251i
$117$	−536.222	+	521.572i	−0.423707	+	0.412131i
$118$	184.020	−	815.835i	0.143563	−	0.636472i
$119$	−1883.75			−1.45112
$120$	−162.333	+	565.020i	−0.123491	+	0.429826i
$121$	−1096.96			−0.824165
$122$	203.164	−	900.708i	0.150767	−	0.668412i
$123$	1410.08	−	572.666i	1.03368	−	0.419801i
$124$	−88.6291	+	186.468i	−0.0641865	+	0.135043i
$125$		−	125.000i		−	0.0894427i
$126$	1326.06	−	812.470i	0.937578	−	0.574449i
$127$		−	1069.78i		−	0.747463i	−0.927537	−	0.373732i	$-0.878078\pi$
$127$		−	1069.78i		−	0.747463i	0.927537	−	0.373732i	$-0.121922\pi$
$128$	−1447.92	+	25.8634i	−0.999841	+	0.0178595i
$129$	2510.53	−	1019.59i	1.71348	−	0.695888i
$130$	382.211	+	86.2117i	0.257862	+	0.0581636i
$131$	−728.141			−0.485633			−0.242817	−	0.970072i	$-0.578071\pi$
$131$	−728.141			−0.485633			−0.242817	+	0.970072i	$0.578071\pi$
$132$	36.8136	−	634.870i	0.0242743	−	0.418623i
$133$	−2605.12			−1.69844
$134$	−826.642	−	186.458i	−0.532918	−	0.120205i
$135$	−281.849	+	642.368i	−0.179687	+	0.409527i
$136$	1646.40	+	1292.47i	1.03807	+	0.814912i
$137$		−	1335.43i		−	0.832801i	−0.909181	−	0.416400i	$-0.863291\pi$
$137$		−	1335.43i		−	0.832801i	0.909181	−	0.416400i	$-0.136709\pi$
$138$	−742.075	+	122.747i	−0.457751	+	0.0757170i
$139$			2006.84i			1.22459i	0.790629	+	0.612296i	$0.209754\pi$
$139$			2006.84i			1.22459i	−0.790629	+	0.612296i	$0.790246\pi$
$140$	−735.696	−	349.679i	−0.444126	−	0.211095i
$141$	1121.39	+	2761.21i	0.669775	+	1.64919i
$142$	−406.915	+	1804.01i	−0.240476	+	1.06612i
$143$	−423.843			−0.247857
$144$	−1716.42	−	199.728i	−0.993298	−	0.115584i
$145$	496.477			0.284346
$146$	313.781	−	1391.11i	0.177868	−	0.788558i
$147$	140.192	+	345.195i	0.0786588	+	0.193682i
$148$	−2576.78	−	1224.75i	−1.43115	−	0.680230i
$149$			2021.25i			1.11132i	0.831409	+	0.555661i	$0.187535\pi$
$149$			2021.25i			1.11132i	−0.831409	+	0.555661i	$0.812465\pi$
$150$	362.498	−	59.9611i	0.197319	−	0.0326387i
$151$			264.606i			0.142605i	0.997455	+	0.0713024i	$0.0227155\pi$
$151$			264.606i			0.142605i	−0.997455	+	0.0713024i	$0.977284\pi$
$152$	2276.87	+	1787.40i	1.21499	+	0.953799i
$153$	1741.43	+	1790.35i	0.920172	+	0.946019i
$154$	859.565	+	193.884i	0.449777	+	0.101452i
$155$	129.037			0.0668679
$156$	−66.6701	+	1149.76i	−0.0342172	+	0.590092i
$157$	2339.73			1.18937			0.594684	−	0.803960i	$-0.297277\pi$
$157$	2339.73			1.18937			0.594684	+	0.803960i	$0.297277\pi$
$158$	305.594	+	68.9299i	0.153872	+	0.0347074i
$159$	−1472.04	+	597.830i	−0.734215	+	0.298182i
$160$	403.078	+	810.388i	0.199163	+	0.400417i
$161$		−	1042.20i		−	0.510166i
$162$	−1998.05	−	509.220i	−0.969025	−	0.246964i
$163$			1541.95i			0.740948i	0.928843	+	0.370474i	$0.120805\pi$
$163$			1541.95i			0.740948i	−0.928843	+	0.370474i	$0.879195\pi$
$164$	1005.87	−	2116.27i	0.478935	−	1.00764i
$165$	−368.250	+	149.555i	−0.173747	+	0.0705627i
$166$	920.934	−	4082.87i	0.430592	−	1.90899i
$167$	−151.105			−0.0700173			−0.0350086	−	0.999387i	$-0.511146\pi$
$167$	−151.105			−0.0700173			−0.0350086	+	0.999387i	$0.511146\pi$
$168$	661.157	−	2301.24i	0.303627	−	1.05681i
$169$	−1429.41			−0.650620
$170$	287.845	−	1276.13i	0.129863	−	0.575734i
$171$	2408.29	+	2475.94i	1.07700	+	1.10725i
$172$	1790.87	−	3767.85i	0.793912	−	1.67033i
$173$		−	4436.11i		−	1.94954i	−0.223206	−	0.974771i	$-0.571652\pi$
$173$		−	4436.11i		−	1.94954i	0.223206	−	0.974771i	$-0.428348\pi$
$174$	238.154	+	1439.77i	0.103761	+	0.627293i
$175$			509.106i			0.219913i
$176$	−618.232	−	759.211i	−0.264778	−	0.325157i
$177$	−578.127	−	1423.52i	−0.245507	−	0.604511i
$178$	2132.61	+	481.033i	0.898011	+	0.202556i
$179$	2609.23			1.08951			0.544757	−	0.838594i	$-0.316622\pi$
$179$	2609.23			1.08951			0.544757	+	0.838594i	$0.316622\pi$
$180$	347.773	+	1022.47i	0.144008	+	0.423393i
$181$	−1528.41			−0.627657			−0.313828	−	0.949480i	$-0.601612\pi$
$181$	−1528.41			−0.627657			−0.313828	+	0.949480i	$0.601612\pi$
$182$	−1556.69	−	351.127i	−0.634007	−	0.143007i
$183$	−638.270	−	1571.61i	−0.257827	−	0.634847i
$184$	−715.064	+	910.879i	−0.286496	+	0.364951i
$185$			1783.15i			0.708646i
$186$	61.8978	+	374.206i	0.0244009	+	0.147517i
$187$			1415.13i			0.553395i
$188$	4144.08	+	1969.70i	1.60765	+	0.764122i
$189$	1147.93	−	2616.27i	0.441796	−	1.00691i
$190$	398.072	−	1764.81i	0.151996	−	0.673857i
$191$	−832.060			−0.315213			−0.157607	−	0.987502i	$-0.550378\pi$
$191$	−832.060			−0.315213			−0.157607	+	0.987502i	$0.550378\pi$
$192$	−2156.76	+	1557.65i	−0.810680	+	0.585489i
$193$	659.353			0.245913			0.122957	−	0.992412i	$-0.460762\pi$
$193$	659.353			0.245913			0.122957	+	0.992412i	$0.460762\pi$
$194$	−16.2528	+	72.0552i	−0.00601487	+	0.0266663i
$195$	666.906	−	270.847i	0.244913	−	0.0994653i
$196$	518.077	+	246.244i	0.188803	+	0.0897390i
$197$			963.336i			0.348400i	0.984710	+	0.174200i	$0.0557340\pi$
$197$			963.336i			0.348400i	−0.984710	+	0.174200i	$0.944266\pi$
$198$	−610.352	−	996.177i	−0.219070	−	0.357552i
$199$			870.488i			0.310087i	0.987908	+	0.155043i	$0.0495517\pi$
$199$			870.488i			0.310087i	−0.987908	+	0.155043i	$0.950448\pi$
$200$	349.303	−	444.957i	0.123497	−	0.157316i
$201$	−1442.38	+	585.785i	−0.506157	+	0.205563i
$202$	−540.911	−	122.008i	−0.188408	−	0.0424974i
$203$	−2022.07			−0.699122
$204$	3838.83	+	222.599i	1.31751	+	0.0763973i
$205$	−1464.47			−0.498943
$206$	−1891.08	−	426.552i	−0.639599	−	0.144268i
$207$	−990.519	+	963.457i	−0.332589	+	0.323502i
$208$	1119.63	+	1374.94i	0.373232	+	0.458342i
$209$			1957.05i			0.647711i
$210$	−1476.40	+	244.213i	−0.485149	+	0.0802489i
$211$		−	102.524i		−	0.0334503i	−0.999860	−	0.0167252i	$-0.994676\pi$
$211$		−	102.524i		−	0.0334503i	0.999860	−	0.0167252i	$-0.00532404\pi$
$212$	−1050.07	+	2209.27i	−0.340185	+	0.715722i
$213$	1278.38	+	3147.76i	0.411236	+	1.01259i
$214$	313.542	−	1390.06i	0.100156	−	0.444030i
$215$	−2607.38			−0.827078
$216$	−2798.34	+	1499.00i	−0.881494	+	0.472196i
$217$	−525.549			−0.164408
$218$	−577.917	+	2562.14i	−0.179548	+	0.796008i
$219$	−985.788	−	2427.31i	−0.304171	−	0.748960i
$220$	−262.689	+	552.677i	−0.0805024	+	0.169370i
$221$		−	2562.83i		−	0.780067i
$222$	−5171.09	+	855.356i	−1.56334	+	0.258593i
$223$		−	1477.75i		−	0.443756i	−0.975074	−	0.221878i	$-0.928781\pi$
$223$		−	1477.75i		−	0.443756i	0.975074	−	0.221878i	$-0.0712187\pi$
$224$	−1641.67	−	3300.59i	−0.489683	−	0.984508i
$225$	483.861	−	470.642i	0.143366	−	0.139449i
$226$	−1245.03	−	280.830i	−0.366453	−	0.0826573i
$227$	−817.892			−0.239143			−0.119571	−	0.992826i	$-0.538152\pi$
$227$	−817.892			−0.239143			−0.119571	+	0.992826i	$0.538152\pi$
$228$	5308.87	+	307.841i	1.54206	+	0.0894178i
$229$	1154.61			0.333182			0.166591	−	0.986026i	$-0.446724\pi$
$229$	1154.61			0.333182			0.166591	+	0.986026i	$0.446724\pi$
$230$	706.027	+	159.252i	0.202409	+	0.0456555i
$231$	1499.82	−	609.115i	0.427191	−	0.173493i
$232$	1767.29	+	1387.37i	0.500121	+	0.392608i
$233$			3871.61i			1.08857i	0.838899	+	0.544287i	$0.183200\pi$
$233$			3871.61i			1.08857i	−0.838899	+	0.544287i	$0.816800\pi$
$234$	1105.36	+	1804.09i	0.308801	+	0.504005i
$235$		−	2867.73i		−	0.796043i
$236$	−2136.45	−	1015.46i	−0.589285	−	0.280089i
$237$	533.220	−	216.554i	0.146145	−	0.0593530i
$238$	−1172.35	+	5197.49i	−0.319294	+	1.41556i
$239$	4418.94			1.19597			0.597987	−	0.801506i	$-0.295968\pi$
$239$	4418.94			1.19597			0.597987	+	0.801506i	$0.295968\pi$
$240$	1457.93	+	799.533i	0.392120	+	0.215040i
$241$	1310.51			0.350279			0.175139	−	0.984544i	$-0.443962\pi$
$241$	1310.51			0.350279			0.175139	+	0.984544i	$0.443962\pi$
$242$	−682.691	+	3026.64i	−0.181343	+	0.803967i
$243$	−3547.73	+	1327.59i	−0.936572	+	0.350474i
$244$	−2358.71	−	1121.10i	−0.618857	−	0.294145i
$245$		−	358.512i		−	0.0934878i
$246$	−702.492	−	4246.95i	−0.182070	−	1.10071i
$247$		−	3544.24i		−	0.913015i
$248$	459.329	+	360.585i	0.117610	+	0.0923274i
$249$	−2893.25	−	7124.05i	−0.736354	−	1.81313i
$250$	−344.889	−	77.7933i	−0.0872507	−	0.0196803i
$251$	5925.09			1.48999			0.744997	−	0.667068i	$-0.232451\pi$
$251$	5925.09			1.48999			0.744997	+	0.667068i	$0.232451\pi$
$252$	−1416.42	−	4164.38i	−0.354073	−	1.04100i
$253$	−782.932			−0.194555
$254$	−2951.65	−	665.775i	−0.729145	−	0.164466i
$255$	−904.307	−	2226.67i	−0.222078	−	0.546823i
$256$	−829.750	+	4011.08i	−0.202576	+	0.979267i
$257$			4401.57i			1.06834i	0.845378	+	0.534168i	$0.179375\pi$
$257$			4401.57i			1.06834i	−0.845378	+	0.534168i	$0.820625\pi$
$258$	−1250.73	−	7561.35i	−0.301811	−	1.82461i
$259$		−	7262.49i		−	1.74235i
$260$	475.735	−	1000.91i	0.113476	−	0.238745i
$261$	1869.30	+	1921.81i	0.443321	+	0.455773i
$262$	−453.156	+	2009.02i	−0.106855	+	0.473732i
$263$	−4384.53			−1.02799			−0.513996	−	0.857793i	$-0.671835\pi$
$263$	−4384.53			−1.02799			−0.513996	+	0.857793i	$0.671835\pi$
$264$	−1728.76	−	496.682i	−0.403023	−	0.115790i
$265$	1528.83			0.354396
$266$	−1621.29	+	7187.81i	−0.373712	+	1.65682i
$267$	3721.12	−	1511.24i	0.852916	−	0.346390i
$268$	−1028.92	+	2164.75i	−0.234519	+	0.493408i
$269$			3387.40i			0.767783i	0.923378	+	0.383892i	$0.125416\pi$
$269$			3387.40i			0.767783i	−0.923378	+	0.383892i	$0.874584\pi$
$270$	1596.96	+	1177.43i	0.359954	+	0.265392i
$271$			4088.66i			0.916489i	0.888826	+	0.458244i	$0.151522\pi$
$271$			4088.66i			0.916489i	−0.888826	+	0.458244i	$0.848478\pi$
$272$	4590.68	−	3738.23i	1.02335	−	0.833321i
$273$	−2716.21	+	1103.12i	−0.602170	+	0.244556i
$274$	−3684.60	−	831.102i	−0.812391	−	0.183243i
$275$	382.456			0.0838653
$276$	−123.154	+	2123.86i	−0.0268587	+	0.463193i
$277$	−3485.20			−0.755977			−0.377988	−	0.925810i	$-0.623384\pi$
$277$	−3485.20			−0.755977			−0.377988	+	0.925810i	$0.623384\pi$
$278$	5537.10	+	1248.95i	1.19458	+	0.269450i
$279$	485.842	+	499.489i	0.104253	+	0.107181i
$280$	−1422.66	+	1812.24i	−0.303644	+	0.386794i
$281$		−	4399.79i		−	0.934056i	−0.884243	−	0.467028i	$-0.845325\pi$
$281$		−	4399.79i		−	0.934056i	0.884243	−	0.467028i	$-0.154675\pi$
$282$	8316.37	−	1375.62i	1.75614	−	0.290485i
$283$			505.577i			0.106196i	0.998589	+	0.0530980i	$0.0169096\pi$
$283$			505.577i			0.106196i	−0.998589	+	0.0530980i	$0.983090\pi$
$284$	4724.23	+	2245.44i	0.987083	+	0.469164i
$285$	−1250.60	−	3079.36i	−0.259927	−	0.640019i
$286$	−263.777	+	1169.43i	−0.0545367	+	0.241783i
$287$	5964.58			1.22675
$288$	−1619.28	+	4611.49i	−0.331309	+	0.943522i
$289$	−3643.82			−0.741668
$290$	308.980	−	1369.83i	0.0625654	−	0.277377i
$291$	51.0606	+	125.727i	0.0102860	+	0.0253272i
$292$	−3642.96	−	1731.51i	−0.730096	−	0.347017i
$293$		−	6365.91i		−	1.26928i	−0.772806	−	0.634642i	$-0.781147\pi$
$293$		−	6365.91i		−	1.26928i	0.772806	−	0.634642i	$-0.218853\pi$
$294$	1039.68	−	171.974i	0.206243	−	0.0341148i
$295$			1478.44i			0.291790i
$296$	−4982.87	+	6347.39i	−0.978458	+	1.24640i
$297$	−1965.42	−	862.358i	−0.383991	−	0.168482i
$298$	5576.84	+	1257.92i	1.08409	+	0.244527i
$299$	1417.90			0.274245
$300$	60.1599	−	1037.49i	0.0115778	−	0.199665i
$301$	10619.5			2.03354
$302$	730.077	+	164.677i	0.139110	+	0.0313777i
$303$	−943.817	+	383.307i	−0.178947	+	0.0726746i
$304$	6348.64	−	5169.74i	1.19776	−	0.975346i
$305$			1632.24i			0.306433i
$306$	6023.53	−	3690.58i	1.12530	−	0.689466i
$307$			7389.54i			1.37376i	0.726772	+	0.686879i	$0.241020\pi$
$307$			7389.54i			1.37376i	−0.726772	+	0.686879i	$0.758980\pi$
$308$	1069.89	−	2250.97i	0.197931	−	0.416432i
$309$	−3299.67	+	1340.08i	−0.607481	+	0.246713i
$310$	80.3059	−	356.028i	0.0147131	−	0.0652291i
$311$	1630.49			0.297288			0.148644	−	0.988891i	$-0.452509\pi$
$311$	1630.49			0.297288			0.148644	+	0.988891i	$0.452509\pi$
$312$	3130.82	+	899.498i	0.568102	+	0.163218i
$313$	5922.15			1.06946			0.534728	−	0.845024i	$-0.320414\pi$
$313$	5922.15			1.06946			0.534728	+	0.845024i	$0.320414\pi$
$314$	1456.12	−	6455.57i	0.261700	−	1.16022i
$315$	−1970.69	+	1916.85i	−0.352495	+	0.342865i
$316$	380.370	−	800.269i	0.0677136	−	0.142464i
$317$		−	7808.36i		−	1.38347i	−0.722149	−	0.691737i	$-0.756846\pi$
$317$		−	7808.36i		−	1.38347i	0.722149	−	0.691737i	$-0.243154\pi$
$318$	733.361	+	4433.57i	0.129323	+	0.781831i
$319$			1519.04i			0.266615i
$320$	2486.80	−	607.794i	0.434427	−	0.106177i
$321$	−985.039	−	2425.46i	−0.171276	−	0.421732i
$322$	−2875.54	−	648.609i	−0.497663	−	0.112253i
$323$	−11833.6			−2.03850
$324$	−2648.48	+	5195.94i	−0.454128	+	0.890936i
$325$	−692.634			−0.118217
$326$	4254.40	+	959.624i	0.722789	+	0.163033i
$327$	1815.61	+	4470.58i	0.307044	+	0.756035i
$328$	−5213.03	−	4092.37i	−0.877565	−	0.688912i
$329$			11679.8i			1.95723i
$330$	183.460	+	1109.12i	0.0306035	+	0.185015i
$331$			1569.05i			0.260552i	0.991478	+	0.130276i	$0.0415863\pi$
$331$			1569.05i			0.260552i	−0.991478	+	0.130276i	$0.958414\pi$
$332$	−10691.9	−	5081.92i	−1.76746	−	0.840079i
$333$	−6902.36	+	6713.78i	−1.13588	+	1.10484i
$334$	−94.0399	+	416.916i	−0.0154061	+	0.0683013i
$335$	1498.02			0.244316
$336$	−5937.91	−	3256.38i	−0.964106	−	0.528720i
$337$	6488.72			1.04885			0.524426	−	0.851456i	$-0.324280\pi$
$337$	6488.72			1.04885			0.524426	+	0.851456i	$0.324280\pi$
$338$	−889.590	+	3943.91i	−0.143158	+	0.634675i
$339$	−2172.41	+	882.269i	−0.348051	+	0.141352i
$340$	−3341.84	−	1588.39i	−0.533050	−	0.253360i
$341$			394.809i			0.0626982i
$342$	8330.18	−	5103.86i	1.31709	−	0.806974i
$343$		−	5524.77i		−	0.869707i
$344$	−9281.38	−	7286.13i	−1.45470	−	1.14198i
$345$	1231.92	−	500.313i	0.192245	−	0.0780752i
$346$	−12239.7	−	2760.79i	−1.90176	−	0.428963i
$347$	595.599			0.0921425			0.0460712	−	0.998938i	$-0.485330\pi$
$347$	595.599			0.0921425			0.0460712	+	0.998938i	$0.485330\pi$
$348$	4120.71	+	238.944i	0.634750	+	0.0368067i
$349$	9358.18			1.43534			0.717668	−	0.696386i	$-0.245210\pi$
$349$	9358.18			1.43534			0.717668	+	0.696386i	$0.245210\pi$
$350$	1404.68	+	316.840i	0.214524	+	0.0483881i
$351$	3559.41	+	1561.75i	0.541274	+	0.237492i
$352$	−2479.50	+	1233.28i	−0.375449	+	0.186744i
$353$		−	573.683i		−	0.0864988i	−0.999064	−	0.0432494i	$-0.986229\pi$
$353$		−	573.683i		−	0.0864988i	0.999064	−	0.0432494i	$-0.0137710\pi$
$354$	−4287.45	+	709.191i	−0.643715	+	0.106478i
$355$		−	3269.20i		−	0.488763i
$356$	2654.44	−	5584.74i	0.395183	−	0.831434i
$357$	3683.10	+	9068.91i	0.546024	+	1.34448i
$358$	1623.84	−	7199.15i	0.239729	−	1.06281i
$359$	−8718.72			−1.28177			−0.640886	−	0.767636i	$-0.721433\pi$
$359$	−8718.72			−1.28177			−0.640886	+	0.767636i	$0.721433\pi$
$360$	3037.55	−	323.209i	0.444703	−	0.0473184i
$361$	−9506.11			−1.38593
$362$	−951.201	+	4217.05i	−0.138105	+	0.612274i
$363$	2144.78	+	5281.08i	0.310114	+	0.763595i
$364$	−1937.60	+	4076.55i	−0.279005	+	0.587003i
$365$			2520.95i			0.361514i
$366$	−4733.48	+	782.969i	−0.676019	+	0.111821i
$367$			3926.75i			0.558515i	0.960216	+	0.279257i	$0.0900882\pi$
$367$			3926.75i			0.558515i	−0.960216	+	0.279257i	$0.909912\pi$
$368$	2068.20	+	2539.82i	0.292968	+	0.359776i
$369$	−5513.94	−	5668.81i	−0.777897	−	0.799747i
$370$	4919.90	+	1109.73i	0.691279	+	0.155925i
$371$	−6226.68			−0.871356
$372$	1071.00	+	62.1029i	0.149270	+	0.00865561i
$373$	5278.89			0.732789			0.366395	−	0.930460i	$-0.380592\pi$
$373$	5278.89			0.732789			0.366395	+	0.930460i	$0.380592\pi$
$374$	3904.51	+	880.704i	0.539833	+	0.121765i
$375$	−601.784	+	244.399i	−0.0828693	+	0.0336552i
$376$	8013.66	−	10208.1i	1.09913	−	1.40012i
$377$		−	2751.01i		−	0.375821i
$378$	−6504.16	−	4795.48i	−0.885020	−	0.652521i
$379$			1153.98i			0.156401i	0.996938	+	0.0782003i	$0.0249174\pi$
$379$			1153.98i			0.156401i	−0.996938	+	0.0782003i	$0.975083\pi$
$380$	−4621.57	−	2196.65i	−0.623899	−	0.296541i
$381$	−5150.23	+	2091.63i	−0.692530	+	0.281253i
$382$	−517.830	+	2295.75i	−0.0693573	+	0.307488i
$383$	6431.26			0.858021			0.429010	−	0.903300i	$-0.358862\pi$
$383$	6431.26			0.858021			0.429010	+	0.903300i	$0.358862\pi$
$384$	2955.48	+	6920.13i	0.392764	+	0.919639i
$385$	−1557.69			−0.206200
$386$	410.346	−	1819.23i	0.0541089	−	0.239886i
$387$	−9817.13	−	10092.9i	−1.28949	−	1.32571i
$388$	188.693	+	89.6866i	0.0246893	+	0.0117349i
$389$		−	9956.93i		−	1.29778i	−0.760882	−	0.648890i	$-0.775233\pi$
$389$		−	9956.93i		−	1.29778i	0.760882	−	0.648890i	$-0.224767\pi$
$390$	−332.249	−	2008.63i	−0.0431387	−	0.260797i
$391$		−	4734.11i		−	0.612313i
$392$	1001.84	−	1276.18i	0.129083	−	0.164431i
$393$	1423.66	+	3505.47i	0.182733	+	0.449943i
$394$	2657.95	+	599.529i	0.339862	+	0.0766595i
$395$	−553.791			−0.0705424
$396$	−3128.41	+	1064.06i	−0.396992	+	0.135028i
$397$	−11143.6			−1.40877			−0.704386	−	0.709817i	$-0.748777\pi$
$397$	−11143.6			−1.40877			−0.704386	+	0.709817i	$0.748777\pi$
$398$	2401.77	+	541.745i	0.302487	+	0.0682292i
$399$	5093.51	+	12541.8i	0.639084	+	1.57362i
$400$	−1010.30	−	1240.68i	−0.126287	−	0.155086i
$401$			4045.81i			0.503836i	0.967749	+	0.251918i	$0.0810613\pi$
$401$			4045.81i			0.503836i	−0.967749	+	0.251918i	$0.918939\pi$
$402$	718.585	+	4344.24i	0.0891537	+	0.538983i
$403$		−	715.005i		−	0.0883795i
$404$	−673.268	+	1416.50i	−0.0829117	+	0.174440i
$405$	3643.60	+	100.944i	0.447042	+	0.0123851i
$406$	−1258.43	+	5579.12i	−0.153830	+	0.681988i
$407$	−5455.80			−0.664457
$408$	3003.26	−	10453.2i	0.364420	−	1.26841i
$409$	12909.8			1.56076			0.780379	−	0.625307i	$-0.215026\pi$
$409$	12909.8			1.56076			0.780379	+	0.625307i	$0.215026\pi$
$410$	−911.410	+	4040.64i	−0.109784	+	0.486715i
$411$	−6429.14	+	2611.03i	−0.771596	+	0.313364i
$412$	−2353.81	+	4952.22i	−0.281465	+	0.592180i
$413$		−	6021.46i		−	0.717425i
$414$	2041.84	+	3332.56i	0.242393	+	0.395619i
$415$			7398.89i			0.875174i
$416$	4490.42	−	2233.48i	0.529233	−	0.263234i
$417$	9661.49	−	3923.76i	1.13459	−	0.460786i
$418$	5399.70	+	1217.96i	0.631838	+	0.142518i
$419$	−425.462			−0.0496067			−0.0248033	−	0.999692i	$-0.507896\pi$
$419$	−425.462			−0.0496067			−0.0248033	+	0.999692i	$0.507896\pi$
$420$	−245.022	+	4225.53i	−0.0284663	+	0.490916i
$421$	−6347.87			−0.734860			−0.367430	−	0.930051i	$-0.619762\pi$
$421$	−6347.87			−0.734860			−0.367430	+	0.930051i	$0.619762\pi$
$422$	−282.874	−	63.8053i	−0.0326306	−	0.00736017i
$423$	11100.7	−	10797.4i	1.27596	−	1.24110i
$424$	5442.10	+	4272.19i	0.623329	+	0.489330i
$425$			2312.58i			0.263945i
$426$	9480.62	−	1568.20i	1.07826	−	0.178356i
$427$		−	6647.88i		−	0.753427i
$428$	−3640.19	−	1730.19i	−0.411110	−	0.195402i
$429$	828.696	+	2040.50i	0.0932629	+	0.229641i
$430$	−1622.69	+	7194.04i	−0.181984	+	0.806808i
$431$	14572.3			1.62859			0.814295	−	0.580452i	$-0.197124\pi$
$431$	14572.3			1.62859			0.814295	+	0.580452i	$0.197124\pi$
$432$	2394.38	+	8653.81i	0.266666	+	0.963789i
$433$	−8416.25			−0.934086			−0.467043	−	0.884235i	$-0.654681\pi$
$433$	−8416.25			−0.934086			−0.467043	+	0.884235i	$0.654681\pi$
$434$	−327.074	+	1450.05i	−0.0361752	+	0.160379i
$435$	−970.707	−	2390.17i	−0.106993	−	0.263448i
$436$	6709.55	+	3189.07i	0.736993	+	0.350295i
$437$		−	6546.99i		−	0.716670i
$438$	−7310.71	+	1209.27i	−0.797532	+	0.131921i
$439$			10822.6i			1.17661i	0.808638	+	0.588306i	$0.200205\pi$
$439$			10822.6i			1.17661i	−0.808638	+	0.588306i	$0.799795\pi$
$440$	1361.41	+	1068.75i	0.147506	+	0.115796i
$441$	1387.76	−	1349.85i	0.149850	−	0.145756i
$442$	−7071.13	−	1594.97i	−0.760949	−	0.171640i
$443$	11962.9			1.28301			0.641507	−	0.767117i	$-0.278309\pi$
$443$	11962.9			1.28301			0.641507	+	0.767117i	$0.278309\pi$
$444$	−858.191	+	14799.9i	−0.0917296	+	1.58192i
$445$	−3864.67			−0.411692
$446$	−4077.28	−	919.674i	−0.432881	−	0.0976408i
$447$	9730.84	−	3951.93i	1.02965	−	0.418165i
$448$	−10128.4	+	2475.45i	−1.06813	+	0.261058i
$449$		−	3582.84i		−	0.376581i	−0.982113	−	0.188291i	$-0.939705\pi$
$449$		−	3582.84i		−	0.376581i	0.982113	−	0.188291i	$-0.0602947\pi$
$450$	−997.422	−	1627.93i	−0.104487	−	0.170536i
$451$		−	4480.77i		−	0.467830i
$452$	−1549.68	+	3260.41i	−0.161263	+	0.339285i
$453$	1273.89	−	517.356i	0.132124	−	0.0536589i
$454$	−509.012	+	2256.65i	−0.0526192	+	0.233282i
$455$	2820.99			0.290660
$456$	4153.33	−	14456.2i	0.426529	−	1.48459i
$457$	−9998.12			−1.02340			−0.511699	−	0.859165i	$-0.670984\pi$
$457$	−9998.12			−1.02340			−0.511699	+	0.859165i	$0.670984\pi$
$458$	718.566	−	3185.69i	0.0733109	−	0.325016i
$459$	5214.38	−	11884.2i	0.530253	−	1.20851i
$460$	878.787	−	1848.90i	0.0890731	−	0.187403i
$461$			9035.94i			0.912897i	0.889750	+	0.456449i	$0.150879\pi$
$461$			9035.94i			0.912897i	−0.889750	+	0.456449i	$0.849121\pi$
$462$	−747.205	−	4517.26i	−0.0752448	−	0.454896i
$463$		−	2608.87i		−	0.261867i	−0.991391	−	0.130933i	$-0.958203\pi$
$463$		−	2608.87i		−	0.261867i	0.991391	−	0.130933i	$-0.0417974\pi$
$464$	4927.76	−	4012.72i	0.493030	−	0.401478i
$465$	−252.293	−	621.221i	−0.0251608	−	0.0619536i
$466$	10682.2	+	2409.49i	1.06190	+	0.239522i
$467$	−9712.48			−0.962398			−0.481199	−	0.876611i	$-0.659799\pi$
$467$	−9712.48			−0.962398			−0.481199	+	0.876611i	$0.659799\pi$
$468$	5665.61	−	1927.03i	0.559600	−	0.190336i
$469$	−6101.22			−0.600700
$470$	−7912.38	−	1784.72i	−0.776534	−	0.175155i
$471$	−4574.62	−	11264.1i	−0.447531	−	1.10196i
$472$	−4131.39	+	5262.74i	−0.402887	+	0.513214i
$473$		−	7977.66i		−	0.775504i
$474$	−265.647	−	1605.98i	−0.0257417	−	0.155623i
$475$			3198.15i			0.308929i
$476$	13610.8	+	6469.27i	1.31061	+	0.622938i
$477$	5756.23	+	5917.91i	0.552536	+	0.568056i
$478$	2750.11	−	12192.3i	0.263153	−	1.16666i
$479$	3430.18			0.327200			0.163600	−	0.986527i	$-0.447689\pi$
$479$	3430.18			0.327200			0.163600	+	0.986527i	$0.447689\pi$
$480$	3113.33	−	3524.99i	0.296049	−	0.335194i
$481$	9880.55			0.936620
$482$	815.589	−	3615.83i	0.0770727	−	0.341694i
$483$	−5017.43	+	2037.70i	−0.472673	+	0.191964i
$484$	7925.97	+	3767.24i	0.744362	+	0.353798i
$485$		−	130.577i		−	0.0122251i
$486$	1455.06	+	10614.8i	0.135808	+	0.990735i
$487$		−	7275.39i		−	0.676960i	−0.940974	−	0.338480i	$-0.890087\pi$
$487$		−	7275.39i		−	0.676960i	0.940974	−	0.338480i	$-0.109913\pi$
$488$	−4561.19	+	5810.23i	−0.423105	+	0.538969i
$489$	7423.35	−	3014.80i	0.686494	−	0.278802i
$490$	−989.175	−	223.119i	−0.0911966	−	0.0205704i
$491$	−17601.4			−1.61780			−0.808902	−	0.587944i	$-0.799938\pi$
$491$	−17601.4			−1.61780			−0.808902	+	0.587944i	$0.799938\pi$
$492$	−12155.0	−	704.820i	−1.11380	−	0.0645849i
$493$	−9185.12			−0.839102
$494$	−9778.95	−	2205.75i	−0.890639	−	0.200893i
$495$	1440.00	+	1480.44i	0.130754	+	0.134426i
$496$	1280.76	−	1042.93i	0.115943	−	0.0944131i
$497$			13314.9i			1.20172i
$498$	−21456.6	+	3549.16i	−1.93071	+	0.319361i
$499$		−	17324.8i		−	1.55424i	−0.629355	−	0.777118i	$-0.716681\pi$
$499$		−	17324.8i		−	1.55424i	0.629355	−	0.777118i	$-0.283319\pi$
$500$	−429.280	+	903.171i	−0.0383960	+	0.0807821i
$501$	295.440	+	727.462i	0.0263459	+	0.0648715i
$502$	3687.46	−	16348.0i	0.327847	−	1.45348i
$503$	17802.1			1.57805			0.789023	−	0.614364i	$-0.210587\pi$
$503$	17802.1			1.57805			0.789023	+	0.614364i	$0.210587\pi$
$504$	−12371.5	+	1316.38i	−1.09339	+	0.116342i
$505$	980.228			0.0863754
$506$	−487.255	+	2160.19i	−0.0428085	+	0.189787i
$507$	2794.78	+	6881.58i	0.244813	+	0.602804i
$508$	−3673.89	+	7729.57i	−0.320871	+	0.675087i
$509$			14138.0i			1.23115i	0.788078	+	0.615576i	$0.211076\pi$
$509$			14138.0i			1.23115i	−0.788078	+	0.615576i	$0.788924\pi$
$510$	−6706.43	+	1109.32i	−0.582286	+	0.0963165i
$511$		−	10267.4i		−	0.888855i
$512$	10550.6	+	4785.65i	0.910694	+	0.413082i
$513$	7211.17	−	16435.1i	0.620625	−	1.41448i
$514$	12144.4	+	2739.30i	1.04215	+	0.235069i
$515$	3426.97			0.293224
$516$	−21641.0	−	1254.88i	−1.84630	−	0.107060i
$517$	8774.25			0.746404
$518$	−20038.0	−	4519.78i	−1.69965	−	0.383374i
$519$	−21356.6	+	8673.44i	−1.80627	+	0.733568i
$520$	−2465.54	−	1935.52i	−0.207925	−	0.163227i
$521$			3032.05i			0.254965i	0.991841	+	0.127482i	$0.0406896\pi$
$521$			3032.05i			0.254965i	−0.991841	+	0.127482i	$0.959310\pi$
$522$	6465.82	−	3961.57i	0.542148	−	0.332171i
$523$			12845.0i			1.07394i	0.843601	+	0.536971i	$0.180432\pi$
$523$			12845.0i			1.07394i	−0.843601	+	0.536971i	$0.819568\pi$
$524$	5261.09	+	2500.61i	0.438610	+	0.208473i
$525$	2450.98	−	995.401i	0.203751	−	0.0827483i
$526$	−2728.70	+	12097.4i	−0.226192	+	1.00280i
$527$	−2387.27			−0.197326
$528$	−2446.29	+	4460.74i	−0.201631	+	0.367668i
$529$	−9547.82			−0.784731
$530$	951.459	−	4218.20i	0.0779788	−	0.345711i
$531$	−5722.87	+	5566.52i	−0.467705	+	0.454927i
$532$	18823.0	+	8946.62i	1.53398	+	0.729107i
$533$			8114.76i			0.659454i
$534$	−1853.84	−	11207.5i	−0.150231	−	0.908231i
$535$			2519.03i			0.203565i
$536$	5332.45	+	4186.12i	0.429714	+	0.337337i
$537$	−5101.55	−	12561.5i	−0.409959	−	1.00944i
$538$	9346.22	+	2108.14i	0.748967	+	0.168937i
$539$	1096.92			0.0876582
$540$	4242.51	−	3673.41i	0.338090	−	0.292738i
$541$	−11333.2			−0.900654			−0.450327	−	0.892864i	$-0.648693\pi$
$541$	−11333.2			−0.900654			−0.450327	+	0.892864i	$0.648693\pi$
$542$	11281.1	+	2544.56i	0.894028	+	0.201657i
$543$	2988.34	+	7358.18i	0.236173	+	0.581528i
$544$	−7457.19	−	14992.7i	−0.587728	−	1.18163i
$545$		−	4643.05i		−	0.364929i
$546$	1353.20	+	8180.83i	0.106065	+	0.641222i
$547$			7995.82i			0.625003i	0.949917	+	0.312501i	$0.101167\pi$
$547$			7995.82i			0.625003i	−0.949917	+	0.312501i	$0.898833\pi$
$548$	−4586.20	+	9648.99i	−0.357505	+	0.752162i
$549$	−6318.23	+	6145.61i	−0.491176	+	0.477757i
$550$	238.020	−	1055.24i	0.0184531	−	0.0818100i
$551$	−12702.5			−0.982111
$552$	5783.31	+	1661.57i	0.445931	+	0.128118i
$553$	2255.51			0.173443
$554$	−2169.00	+	9616.06i	−0.166340	+	0.737450i
$555$	8584.55	−	3486.40i	0.656566	−	0.266647i
$556$	6891.99	−	14500.2i	0.525693	−	1.10602i
$557$			6218.87i			0.473074i	0.971623	+	0.236537i	$0.0760124\pi$
$557$			6218.87i			0.473074i	−0.971623	+	0.236537i	$0.923988\pi$
$558$	1680.51	−	1029.64i	0.127494	−	0.0781147i
$559$			14447.7i			1.09315i
$560$	4114.79	+	5053.12i	0.310503	+	0.381309i
$561$	6812.84	−	2766.86i	0.512724	−	0.208230i
$562$	−12139.5	−	2738.20i	−0.911164	−	0.205523i
$563$	−7704.32			−0.576729			−0.288364	−	0.957521i	$-0.593111\pi$
$563$	−7704.32			−0.576729			−0.288364	+	0.957521i	$0.593111\pi$
$564$	1380.18	−	23801.9i	0.103043	−	1.77702i
$565$	2256.22			0.168000
$566$	1394.94	+	314.644i	0.103593	+	0.0233666i
$567$	−14839.8	−	411.131i	−1.09914	−	0.0304513i
$568$	9135.54	−	11637.2i	0.674857	−	0.859661i
$569$			4897.62i			0.360841i	0.983590	+	0.180421i	$0.0577459\pi$
$569$			4897.62i			0.360841i	−0.983590	+	0.180421i	$0.942254\pi$
$570$	−9274.59	+	1534.12i	−0.681526	+	0.112732i
$571$			7425.55i			0.544220i	0.962266	+	0.272110i	$0.0877215\pi$
$571$			7425.55i			0.544220i	−0.962266	+	0.272110i	$0.912279\pi$
$572$	3062.43	+	1455.58i	0.223857	+	0.106400i
$573$	1626.84	+	4005.76i	0.118608	+	0.292047i
$574$	3712.03	−	16456.9i	0.269926	−	1.19669i
$575$	−1279.45			−0.0927941
$576$	11715.8	+	7337.71i	0.847500	+	0.530795i
$577$	−13212.1			−0.953254			−0.476627	−	0.879106i	$-0.658141\pi$
$577$	−13212.1			−0.953254			−0.476627	+	0.879106i	$0.658141\pi$
$578$	−2267.72	+	10053.7i	−0.163191	+	0.723492i
$579$	−1289.16	−	3174.30i	−0.0925315	−	0.227840i
$580$	−3587.23	−	1705.02i	−0.256813	−	0.122064i
$581$		−	30134.5i		−	2.15179i
$582$	378.671	−	62.6363i	0.0269698	−	0.00446110i
$583$			4677.67i			0.332297i
$584$	−7044.61	+	8973.72i	−0.499157	+	0.635848i
$585$	−2607.86	−	2681.11i	−0.184311	−	0.189488i
$586$	−17564.2	−	3961.80i	−1.23818	−	0.279284i
$587$	7041.44			0.495113			0.247557	−	0.968873i	$-0.420372\pi$
$587$	7041.44			0.495113			0.247557	+	0.968873i	$0.420372\pi$
$588$	172.544	−	2975.62i	0.0121014	−	0.208694i
$589$	−3301.45			−0.230957
$590$	4079.18	+	920.101i	0.284639	+	0.0642033i
$591$	4637.76	−	1883.51i	0.322795	−	0.131095i
$592$	14412.1	+	17698.6i	1.00056	+	1.22873i
$593$			18675.4i			1.29326i	0.762802	+	0.646632i	$0.223823\pi$
$593$			18675.4i			1.29326i	−0.762802	+	0.646632i	$0.776177\pi$
$594$	−3602.51	+	4886.12i	−0.248843	+	0.337508i
$595$		−	9418.77i		−	0.648962i
$596$	6941.46	−	14604.3i	0.477069	−	1.00371i
$597$	4190.77	−	1701.97i	0.287298	−	0.116679i
$598$	882.426	−	3912.15i	0.0603430	−	0.267524i
$599$	8073.52			0.550709			0.275355	−	0.961343i	$-0.411205\pi$
$599$	8073.52			0.550709			0.275355	+	0.961343i	$0.411205\pi$
$600$	−2825.10	−	811.664i	−0.192224	−	0.0552268i
$601$	8290.31			0.562677			0.281338	−	0.959609i	$-0.409222\pi$
$601$	8290.31			0.562677			0.281338	+	0.959609i	$0.409222\pi$
$602$	6608.98	−	29300.2i	0.447445	−	1.98370i
$603$	5640.26	+	5798.68i	0.380910	+	0.391610i
$604$	908.722	−	1911.88i	0.0612175	−	0.128797i
$605$		−	5484.82i		−	0.368578i
$606$	470.205	+	2842.64i	0.0315194	+	0.190552i
$607$			15779.1i			1.05511i	0.849521	+	0.527556i	$0.176891\pi$
$607$			15779.1i			1.05511i	−0.849521	+	0.527556i	$0.823109\pi$
$608$	−10312.8	−	20734.0i	−0.687896	−	1.38302i
$609$	3953.54	+	9734.82i	0.263064	+	0.647742i
$610$	4503.54	+	1015.82i	0.298923	+	0.0674252i
$611$	−15890.3			−1.05213
$612$	−6434.00	−	18916.4i	−0.424966	−	1.24943i
$613$	27380.0			1.80403			0.902014	−	0.431708i	$-0.142089\pi$
$613$	27380.0			1.80403			0.902014	+	0.431708i	$0.142089\pi$
$614$	20388.6	+	4598.86i	1.34009	+	0.302272i
$615$	2863.33	+	7050.38i	0.187741	+	0.462274i
$616$	−5544.83	−	4352.84i	−0.362675	−	0.284709i
$617$		−	212.657i		−	0.0138756i	−0.999976	−	0.00693782i	$-0.997792\pi$
$617$		−	212.657i		−	0.0138756i	0.999976	−	0.00693782i	$-0.00220839\pi$
$618$	1643.88	+	9938.14i	0.107001	+	0.646878i
$619$		−	19326.6i		−	1.25493i	−0.778645	−	0.627465i	$-0.784092\pi$
$619$		−	19326.6i		−	1.25493i	0.778645	−	0.627465i	$-0.215908\pi$
$620$	−932.342	−	443.145i	−0.0603932	−	0.0287051i
$621$	6575.00	+	2884.88i	0.424872	+	0.186419i
$622$	1014.73	−	4498.70i	0.0654131	−	0.290002i
$623$	15740.2			1.01223
$624$	4430.27	−	8078.47i	0.284219	−	0.518266i
$625$	625.000			0.0400000
$626$	3685.63	−	16339.8i	0.235315	−	1.04325i
$627$	9421.75	−	3826.40i	0.600109	−	0.243719i
$628$	−16905.4	−	8035.20i	−1.07420	−	0.510572i
$629$		−	32989.3i		−	2.09121i
$630$	4062.35	+	6630.30i	0.256901	+	0.419298i
$631$			13797.7i			0.870486i	0.900313	+	0.435243i	$0.143338\pi$
$631$			13797.7i			0.870486i	−0.900313	+	0.435243i	$0.856662\pi$
$632$	−1971.31	−	1547.53i	−0.124073	−	0.0974009i
$633$	−493.577	+	200.454i	−0.0309920	+	0.0125866i
$634$	−21544.1	−	4859.51i	−1.34957	−	0.304410i
$635$	5348.91			0.334276
$636$	12689.1	+	735.792i	0.791125	+	0.0458743i
$637$	−1986.54			−0.123563
$638$	4191.21	+	945.372i	0.260081	+	0.0586640i
$639$	12654.7	−	12309.0i	0.783431	−	0.762027i
$640$	−129.317	−	7239.62i	−0.00798702	−	0.447142i
$641$			25984.0i			1.60110i	0.599264	+	0.800552i	$0.295460\pi$
$641$			25984.0i			1.60110i	−0.599264	+	0.800552i	$0.704540\pi$
$642$	−7305.15	+	1208.35i	−0.449083	+	0.0742833i
$643$			29221.5i			1.79220i	0.443853	+	0.896099i	$0.353611\pi$
$643$			29221.5i			1.79220i	−0.443853	+	0.896099i	$0.646389\pi$
$644$	−3579.16	+	7530.27i	−0.219004	+	0.460768i
$645$	5097.93	+	12552.6i	0.311210	+	0.766294i
$646$	−7364.58	+	32650.1i	−0.448538	+	1.98855i
$647$	3210.39			0.195075			0.0975375	−	0.995232i	$-0.468903\pi$
$647$	3210.39			0.195075			0.0975375	+	0.995232i	$0.468903\pi$
$648$	12687.9	+	10541.1i	0.769179	+	0.639034i
$649$	−4523.50			−0.273595
$650$	−431.058	+	1911.05i	−0.0260115	+	0.115320i
$651$	1027.55	+	2530.14i	0.0618631	+	0.152326i
$652$	5295.42	−	11141.1i	0.318074	−	0.669203i
$653$		−	1248.39i		−	0.0748136i	−0.999300	−	0.0374068i	$-0.988090\pi$
$653$		−	1248.39i		−	0.0748136i	0.999300	−	0.0374068i	$-0.0119097\pi$
$654$	13464.8	−	2227.22i	0.805067	−	0.133167i
$655$		−	3640.70i		−	0.217182i
$656$	−14535.6	+	11836.4i	−0.865121	+	0.704475i
$657$	−9758.31	+	9491.70i	−0.579464	+	0.563633i
$658$	32225.9	+	7268.90i	1.90927	+	0.430655i
$659$	−9138.61			−0.540197			−0.270098	−	0.962833i	$-0.587056\pi$
$659$	−9138.61			−0.540197			−0.270098	+	0.962833i	$0.587056\pi$
$660$	3174.35	+	184.068i	0.187214	+	0.0108558i
$661$	4756.08			0.279864			0.139932	−	0.990161i	$-0.455312\pi$
$661$	4756.08			0.279864			0.139932	+	0.990161i	$0.455312\pi$
$662$	4329.18	+	976.492i	0.254166	+	0.0573299i
$663$	−12338.2	+	5010.83i	−0.722737	+	0.293521i
$664$	−20675.6	+	26337.5i	−1.20839	+	1.53930i
$665$		−	13025.6i		−	0.759566i
$666$	14228.4	+	23222.7i	0.827837	+	1.35114i
$667$		−	5081.72i		−	0.295000i
$668$	1091.79	+	518.933i	0.0632376	+	0.0300570i
$669$	−7114.30	+	2889.29i	−0.411143	+	0.166975i
$670$	932.289	−	4133.21i	0.0537574	−	0.238328i
$671$	−4994.09			−0.287324
$672$	−12680.1	+	14356.8i	−0.727897	+	0.824143i
$673$	−23520.9			−1.34720			−0.673598	−	0.739098i	$-0.735252\pi$
$673$	−23520.9			−1.34720			−0.673598	+	0.739098i	$0.735252\pi$
$674$	4038.23	−	17903.1i	0.230782	−	1.02315i
$675$	−3211.84	−	1409.24i	−0.183146	−	0.0803583i
$676$	10328.0	+	4908.95i	0.587621	+	0.279299i
$677$			3924.98i			0.222820i	0.993775	+	0.111410i	$0.0355367\pi$
$677$			3924.98i			0.222820i	−0.993775	+	0.111410i	$0.964463\pi$
$678$	1082.28	+	6543.00i	0.0613051	+	0.370623i
$679$			531.820i			0.0300580i
$680$	−6462.33	+	8231.98i	−0.364440	+	0.464239i
$681$	1599.14	+	3937.56i	0.0899840	+	0.221568i
$682$	1089.32	+	245.708i	0.0611616	+	0.0137957i
$683$	−2097.25			−0.117495			−0.0587473	−	0.998273i	$-0.518711\pi$
$683$	−2097.25			−0.117495			−0.0587473	+	0.998273i	$0.518711\pi$
$684$	−8897.84	−	26160.3i	−0.497394	−	1.46237i
$685$	6677.16			0.372440
$686$	−15243.4	−	3438.32i	−0.848393	−	0.191364i
$687$	−2257.48	−	5558.60i	−0.125369	−	0.308695i
$688$	−25879.5	+	21073.8i	−1.43408	+	1.16778i
$689$		−	8471.34i		−	0.468407i
$690$	−613.737	−	3710.37i	−0.0338617	−	0.204712i
$691$		−	595.762i		−	0.0327987i	−0.999866	−	0.0163993i	$-0.994780\pi$
$691$		−	595.762i		−	0.0327987i	0.999866	−	0.0163993i	$-0.00522030\pi$
$692$	−15234.7	+	32052.5i	−0.836901	+	1.76077i
$693$	−5864.89	−	6029.63i	−0.321485	−	0.330515i
$694$	370.669	−	1643.32i	0.0202744	−	0.0898843i
$695$	−10034.2			−0.547654
$696$	3223.78	−	11220.8i	0.175570	−	0.611095i
$697$	27093.7			1.47238
$698$	5824.03	−	25820.3i	0.315821	−	1.40016i
$699$	18639.0	−	7569.75i	1.00857	−	0.409606i
$700$	1748.39	−	3678.48i	0.0944044	−	0.198619i
$701$		−	9077.51i		−	0.489091i	−0.969638	−	0.244545i	$-0.921361\pi$
$701$		−	9077.51i		−	0.489091i	0.969638	−	0.244545i	$-0.0786387\pi$
$702$	6524.21	−	8848.85i	0.350770	−	0.475752i
$703$		−	45622.2i		−	2.44762i
$704$	1859.64	+	7608.74i	0.0995563	+	0.407337i
$705$	−13806.0	+	5606.96i	−0.737539	+	0.299533i
$706$	−1582.85	−	357.030i	−0.0843789	−	0.0190326i
$707$	−3992.32			−0.212371
$708$	−711.542	+	12270.9i	−0.0377703	+	0.651368i
$709$	−8539.10			−0.452317			−0.226158	−	0.974091i	$-0.572617\pi$
$709$	−8539.10			−0.452317			−0.226158	+	0.974091i	$0.572617\pi$
$710$	−9020.07	−	2034.57i	−0.476785	−	0.107544i
$711$	−2085.10	−	2143.66i	−0.109982	−	0.113071i
$712$	−13756.9	−	10799.5i	−0.724104	−	0.568441i
$713$		−	1320.77i		−	0.0693734i
$714$	27314.3	−	4518.08i	1.43167	−	0.236814i
$715$		−	2119.22i		−	0.110845i
$716$	−18852.6	−	8960.73i	−0.984018	−	0.467707i
$717$	−8639.89	−	21274.0i	−0.450017	−	1.10808i
$718$	−5426.06	+	24055.9i	−0.282032	+	1.25036i
$719$	−17913.1			−0.929130			−0.464565	−	0.885539i	$-0.653789\pi$
$719$	−17913.1			−0.929130			−0.464565	+	0.885539i	$0.653789\pi$
$720$	998.642	−	8582.09i	0.0516905	−	0.444216i
$721$	−13957.5			−0.720950
$722$	−5916.09	+	26228.4i	−0.304950	+	1.35197i
$723$	−2562.29	−	6309.13i	−0.131802	−	0.324536i
$724$	11043.3	+	5248.93i	0.566881	+	0.269441i
$725$			2482.38i			0.127163i
$726$	15905.9	−	2631.01i	0.813116	−	0.134498i
$727$		−	32276.8i		−	1.64660i	−0.567605	−	0.823301i	$-0.692130\pi$
$727$		−	32276.8i		−	1.64660i	0.567605	−	0.823301i	$-0.307870\pi$
$728$	10041.8	+	7883.06i	0.511227	+	0.401327i
$729$	13327.9	+	14484.0i	0.677127	+	0.735866i
$730$	6955.57	+	1568.90i	0.352654	+	0.0795448i
$731$	48238.1			2.44070
$732$	−785.564	+	13547.5i	−0.0396657	+	0.684055i
$733$	12015.9			0.605481			0.302740	−	0.953073i	$-0.402099\pi$
$733$	12015.9			0.605481			0.302740	+	0.953073i	$0.402099\pi$
$734$	10834.3	+	2443.80i	0.544827	+	0.122891i
$735$	−1725.98	+	700.961i	−0.0866171	+	0.0351773i
$736$	8294.78	−	4125.73i	0.415421	−	0.206626i
$737$			4583.42i			0.229081i
$738$	−19072.5	+	11685.6i	−0.951310	+	0.582862i
$739$		−	18920.3i		−	0.941804i	−0.882185	−	0.470902i	$-0.843928\pi$
$739$		−	18920.3i		−	0.941804i	0.882185	−	0.470902i	$-0.156072\pi$
$740$	6123.76	−	12883.9i	0.304208	−	0.640029i
$741$	−17062.9	+	6929.68i	−0.845915	+	0.343547i
$742$	−3875.15	+	17180.1i	−0.191727	+	0.850001i
$743$	−32431.7			−1.60135			−0.800676	−	0.599097i	$-0.795526\pi$
$743$	−32431.7			−1.60135			−0.800676	+	0.599097i	$0.795526\pi$
$744$	837.880	−	2916.35i	0.0412878	−	0.143708i
$745$	−10106.2			−0.496999
$746$	3285.30	−	14565.0i	0.161238	−	0.714831i
$747$	−28640.3	+	27857.8i	−1.40280	+	1.36448i
$748$	4859.92	−	10224.9i	0.237562	−	0.499810i
$749$		−	10259.6i		−	0.500506i
$750$	299.806	+	1812.49i	0.0145965	+	0.0882437i
$751$		−	23544.8i		−	1.14402i	−0.820245	−	0.572012i	$-0.806163\pi$
$751$		−	23544.8i		−	1.14402i	0.820245	−	0.572012i	$-0.193837\pi$
$752$	−23178.1	−	28463.6i	−1.12396	−	1.38027i
$753$	−11584.7	−	28525.0i	−0.560650	−	1.38049i
$754$	−7590.35	−	1712.08i	−0.366610	−	0.0826928i
$755$	−1323.03			−0.0637748
$756$	−17279.1	+	14961.2i	−0.831263	+	0.719755i
$757$	11963.2			0.574388			0.287194	−	0.957872i	$-0.407278\pi$
$757$	11963.2			0.574388			0.287194	+	0.957872i	$0.407278\pi$
$758$	3183.95	+	718.173i	0.152568	+	0.0344132i
$759$	1530.78	+	3769.25i	0.0732067	+	0.180257i
$760$	−8937.01	+	11384.3i	−0.426552	+	0.543360i
$761$			2168.96i			0.103318i	0.998665	+	0.0516588i	$0.0164508\pi$
$761$			2168.96i			0.103318i	−0.998665	+	0.0516588i	$0.983549\pi$
$762$	2565.82	+	15511.8i	0.121981	+	0.737443i
$763$			18910.4i			0.897252i
$764$	6011.94	+	2857.50i	0.284692	+	0.135315i
$765$	−8951.73	+	8707.16i	−0.423072	+	0.411514i
$766$	4002.47	−	17744.5i	0.188793	−	0.836993i
$767$	8192.14			0.385660
$768$	20932.7	−	3847.78i	0.983522	−	0.180788i
$769$	6990.21			0.327794			0.163897	−	0.986477i	$-0.447594\pi$
$769$	6990.21			0.327794			0.163897	+	0.986477i	$0.447594\pi$
$770$	−969.420	+	4297.83i	−0.0453707	+	0.201147i
$771$	21190.4	−	8605.92i	0.989821	−	0.401990i
$772$	−4764.07	−	2264.38i	−0.222102	−	0.105566i
$773$			15944.4i			0.741887i	0.928655	+	0.370944i	$0.120966\pi$
$773$			15944.4i			0.741887i	−0.928655	+	0.370944i	$0.879034\pi$
$774$	−33957.0	+	20805.3i	−1.57695	+	0.966188i
$775$			645.186i			0.0299042i
$776$	364.888	−	464.809i	0.0168798	−	0.0215022i
$777$	−34963.6	+	14199.6i	−1.61430	+	0.655607i
$778$	−27472.3	−	6196.66i	−1.26597	−	0.285554i
$779$	37468.9			1.72332
$780$	−5748.80	−	333.350i	−0.263897	−	0.0153024i
$781$	10002.6			0.458286
$782$	−13061.9	−	2946.26i	−0.597306	−	0.134729i
$783$	5597.25	−	12756.8i	0.255466	−	0.582237i
$784$	−2897.64	−	3558.40i	−0.131999	−	0.162099i
$785$			11698.6i			0.531901i
$786$	10558.0	−	1746.41i	0.479123	−	0.0792522i
$787$		−	13904.9i		−	0.629803i	−0.949124	−	0.314901i	$-0.898029\pi$
$787$		−	13904.9i		−	0.629803i	0.949124	−	0.314901i	$-0.101971\pi$
$788$	3308.33	−	6960.46i	0.149561	−	0.314665i
$789$	8572.61	+	21108.3i	0.386810	+	0.952442i
$790$	−344.650	+	1527.97i	−0.0155216	+	0.0688136i
$791$	−9189.25			−0.413062
$792$	988.906	+	9293.85i	0.0443677	+	0.416973i
$793$	9044.38			0.405013
$794$	−6935.19	+	30746.5i	−0.309976	+	1.37425i
$795$	−2989.15	−	7360.18i	−0.133351	−	0.328351i
$796$	2989.47	−	6289.60i	0.133114	−	0.280061i
$797$		−	6202.60i		−	0.275668i	−0.990455	−	0.137834i	$-0.955986\pi$
$797$		−	6202.60i		−	0.275668i	0.990455	−	0.137834i	$-0.0440140\pi$
$798$	37774.0	−	6248.24i	1.67567	−	0.277174i
$799$			53054.8i			2.34911i
$800$	−4051.94	+	2015.39i	−0.179072	+	0.0890684i
$801$	−14551.0	−	14959.7i	−0.641866	−	0.659894i
$802$	11162.8	+	2517.90i	0.491488	+	0.110860i
$803$	−7713.22			−0.338971
$804$	12433.4	+	720.967i	0.545390	+	0.0316251i
$805$	5210.99			0.228153
$806$	−1972.78	−	444.981i	−0.0862135	−	0.0194464i
$807$	16307.9	−	6623.03i	0.711357	−	0.288899i
$808$	3489.28	+	2739.18i	0.151921	+	0.119262i
$809$		−	16847.6i		−	0.732175i	−0.930580	−	0.366088i	$-0.880697\pi$
$809$		−	16847.6i		−	0.732175i	0.930580	−	0.366088i	$-0.119303\pi$
$810$	2546.10	−	9990.27i	0.110445	−	0.433361i
$811$			33782.0i			1.46270i	0.682004	+	0.731348i	$0.261109\pi$
$811$			33782.0i			1.46270i	−0.682004	+	0.731348i	$0.738891\pi$
$812$	14610.2	+	6944.30i	0.631427	+	0.300119i
$813$	19683.9	−	7994.12i	0.849133	−	0.344854i
$814$	−3395.40	+	15053.2i	−0.146202	+	0.648173i
$815$	−7709.73			−0.331362
$816$	−26972.5	−	14791.8i	−1.15714	−	0.634581i
$817$	66710.4			2.85667
$818$	8034.39	−	35619.6i	0.343418	−	1.52251i
$819$	10621.4	+	10919.8i	0.453165	+	0.465894i
$820$	10581.4	+	5029.36i	0.450631	+	0.214186i
$821$			26588.7i			1.13027i	0.824998	+	0.565135i	$0.191176\pi$
$821$			26588.7i			1.13027i	−0.824998	+	0.565135i	$0.808824\pi$
$822$	3202.96	+	19363.7i	0.135908	+	0.821636i
$823$		−	33619.7i		−	1.42395i	−0.702205	−	0.711975i	$-0.747801\pi$
$823$		−	33619.7i		−	1.42395i	0.702205	−	0.711975i	$-0.252199\pi$
$824$	12198.8	+	9576.41i	0.515736	+	0.404867i
$825$	−747.775	−	1841.25i	−0.0315566	−	0.0777018i
$826$	−16613.9	−	3747.43i	−0.699843	−	0.157857i
$827$	27338.2			1.14951			0.574753	−	0.818327i	$-0.305098\pi$
$827$	27338.2			1.14951			0.574753	+	0.818327i	$0.305098\pi$
$828$	10465.6	−	3559.65i	0.439258	−	0.149404i
$829$	18514.6			0.775680			0.387840	−	0.921727i	$-0.373221\pi$
$829$	18514.6			0.775680			0.387840	+	0.921727i	$0.373221\pi$
$830$	20414.3	+	4604.67i	0.853725	+	0.192567i
$831$	6814.24	+	16778.7i	0.284457	+	0.700418i
$832$	−3367.83	−	13779.6i	−0.140335	−	0.574183i
$833$			6632.70i			0.275882i
$834$	−4813.30	−	29099.0i	−0.199845	−	1.20817i
$835$		−	755.527i		−	0.0313127i
$836$	6720.97	−	14140.4i	0.278050	−	0.584994i
$837$	1454.76	−	3315.57i	0.0600763	−	0.136921i
$838$	−264.785	+	1173.90i	−0.0109151	+	0.0483909i
$839$	−42265.2			−1.73916			−0.869580	−	0.493792i	$-0.835610\pi$
$839$	−42265.2			−1.73916			−0.869580	+	0.493792i	$0.835610\pi$
$840$	11506.2	+	3305.79i	0.472622	+	0.135786i
$841$	14529.4			0.595737
$842$	−3950.57	+	17514.5i	−0.161693	+	0.716851i
$843$	−21181.8	+	8602.44i	−0.865409	+	0.351464i
$844$	−352.091	+	740.772i	−0.0143596	+	0.0302114i
$845$		−	7147.06i		−	0.290966i
$846$	−22882.7	−	37347.7i	−0.929933	−	1.51778i
$847$			22338.8i			0.906224i
$848$	15174.3	−	12356.6i	0.614491	−	0.500385i
$849$	2433.99	−	988.501i	0.0983913	−	0.0399591i
$850$	6380.65	+	1439.22i	0.257476	+	0.0580764i
$851$	18251.5			0.735199
$852$	1573.40	−	27134.0i	0.0632672	−	1.09108i
$853$	−39949.7			−1.60358			−0.801789	−	0.597607i	$-0.796118\pi$
$853$	−39949.7			−1.60358			−0.801789	+	0.597607i	$0.796118\pi$
$854$	−18342.2	−	4137.28i	−0.734963	−	0.165779i
$855$	−12379.7	+	12041.5i	−0.495177	+	0.481649i
$856$	−7039.25	+	8966.89i	−0.281071	+	0.358040i
$857$		−	35527.4i		−	1.41609i	−0.706165	−	0.708047i	$-0.749576\pi$
$857$		−	35527.4i		−	1.41609i	0.706165	−	0.708047i	$-0.250424\pi$
$858$	6145.69	−	1016.57i	0.244534	−	0.0404487i
$859$			15149.2i			0.601728i	0.953667	+	0.300864i	$0.0972750\pi$
$859$			15149.2i			0.601728i	−0.953667	+	0.300864i	$0.902725\pi$
$860$	18839.3	+	8954.37i	0.746993	+	0.355048i
$861$	−11661.9	−	28715.1i	−0.461599	−	1.13660i
$862$	9069.01	−	40206.5i	0.358343	−	1.58868i
$863$	3598.72			0.141949			0.0709744	−	0.997478i	$-0.477389\pi$
$863$	3598.72			0.141949			0.0709744	+	0.997478i	$0.477389\pi$
$864$	25367.0	−	1220.69i	0.998844	−	0.0480657i
$865$	22180.5			0.871862
$866$	−5237.82	+	23221.4i	−0.205529	+	0.911194i
$867$	7124.36	+	17542.3i	0.279073	+	0.687161i
$868$	3797.29	+	1804.86i	0.148489	+	0.0705773i
$869$		−	1694.40i		−	0.0661436i
$870$	−7198.87	+	1190.77i	−0.280534	+	0.0464034i
$871$		−	8300.66i		−	0.322913i
$872$	12974.7	−	16527.7i	0.503873	−	0.641855i
$873$	505.449	−	491.640i	0.0195955	−	0.0190601i
$874$	−18063.9	−	4074.50i	−0.699107	−	0.157691i
$875$	−2545.53			−0.0983482
$876$	−1213.28	+	20923.6i	−0.0467956	+	0.807013i
$877$	−47342.6			−1.82286			−0.911428	−	0.411459i	$-0.865019\pi$
$877$	−47342.6			−1.82286			−0.911428	+	0.411459i	$0.865019\pi$
$878$	29860.6	+	6735.38i	1.14778	+	0.258893i
$879$	−30647.2	+	12446.6i	−1.17600	+	0.477603i
$880$	3796.06	−	3091.16i	0.145415	−	0.118412i
$881$			5694.16i			0.217754i	0.994055	+	0.108877i	$0.0347254\pi$
$881$			5694.16i			0.217754i	−0.994055	+	0.108877i	$0.965275\pi$
$882$	−2860.71	−	4669.06i	−0.109212	−	0.178249i
$883$		−	1161.20i		−	0.0442555i	−0.999755	−	0.0221278i	$-0.992956\pi$
$883$		−	1161.20i		−	0.0442555i	0.999755	−	0.0221278i	$-0.00704406\pi$
$884$	−8801.39	+	18517.4i	−0.334867	+	0.704534i
$885$	7117.61	−	2890.63i	0.270346	−	0.109794i
$886$	7445.08	−	33007.0i	0.282305	−	1.25157i
$887$	1024.65			0.0387874			0.0193937	−	0.999812i	$-0.493826\pi$
$887$	1024.65			0.0387874			0.0193937	+	0.999812i	$0.493826\pi$
$888$	40300.6	+	11578.5i	1.52297	+	0.437556i
$889$	−21785.3			−0.821885
$890$	−2405.16	+	10663.1i	−0.0905857	+	0.401603i
$891$	−308.854	+	11148.1i	−0.0116128	+	0.419166i
$892$	−5074.96	+	10677.3i	−0.190496	+	0.400788i
$893$			73371.5i			2.74948i
$894$	−4847.85	−	29307.9i	−0.181361	−	1.09642i
$895$			13046.1i			0.487245i
$896$	526.688	+	29485.9i	0.0196377	+	1.09939i
$897$	−2772.27	−	6826.17i	−0.103192	−	0.254090i
$898$	−9885.46	−	2229.77i	−0.367352	−	0.0828601i
$899$	−2562.56			−0.0950680
$900$	−5112.37	+	1738.86i	−0.189347	+	0.0644023i
$901$	−28284.2			−1.04582
$902$	−12362.9	−	2788.59i	−0.456365	−	0.102938i
$903$	−20763.1	−	51125.0i	−0.765174	−	1.88409i
$904$	8031.38	+	6304.85i	0.295486	+	0.231965i
$905$		−	7642.05i		−	0.280697i
$906$	−634.643	−	3836.76i	−0.0232722	−	0.140693i
$907$			6399.77i			0.234290i	0.993115	+	0.117145i	$0.0373742\pi$
$907$			6399.77i			0.234290i	−0.993115	+	0.117145i	$0.962626\pi$
$908$	5909.58	+	2808.84i	0.215987	+	0.102659i
$909$	3690.69	+	3794.35i	0.134667	+	0.138450i
$910$	1755.64	−	7783.43i	0.0639547	−	0.283537i
$911$	36922.8			1.34282			0.671410	−	0.741086i	$-0.265689\pi$
$911$	36922.8			1.34282			0.671410	+	0.741086i	$0.265689\pi$
$912$	−37301.4	−	20456.2i	−1.35436	−	0.742734i
$913$	−22638.0			−0.820600
$914$	−6222.30	+	27585.9i	−0.225181	+	0.998316i
$915$	7858.06	−	3191.35i	0.283912	−	0.115304i
$916$	−8342.47	−	3965.20i	−0.300920	−	0.143028i
$917$			14828.0i			0.533986i
$918$	−29544.6	−	21783.1i	−1.06222	−	0.783170i
$919$			3415.26i			0.122589i	0.998120	+	0.0612944i	$0.0195229\pi$
$919$			3415.26i			0.122589i	−0.998120	+	0.0612944i	$0.980477\pi$
$920$	−4554.40	−	3575.32i	−0.163211	−	0.128125i
$921$	35575.3	−	14448.0i	1.27280	−	0.516913i
$922$	24931.2	+	5623.49i	0.890525	+	0.200867i
$923$	−18114.9			−0.646000
$924$	−12928.6	−	749.681i	−0.460304	−	0.0266912i
$925$	−8915.73			−0.316916
$926$	−7198.15	−	1623.62i	−0.255449	−	0.0576192i
$927$	12903.0	+	13265.4i	0.457162	+	0.470003i
$928$	−8004.75	−	16093.5i	−0.283156	−	0.569285i
$929$		−	25200.8i		−	0.890001i	−0.895530	−	0.445001i	$-0.853203\pi$
$929$		−	25200.8i		−	0.890001i	0.895530	−	0.445001i	$-0.146797\pi$
$930$	−1871.03	+	309.489i	−0.0659715	+	0.0109124i
$931$			9172.62i			0.322901i
$932$	13296.1	−	27973.8i	0.467304	−	0.983169i
$933$	−3187.92	−	7849.62i	−0.111863	−	0.275440i
$934$	−6044.53	+	26797.8i	−0.211759	+	0.938812i
$935$	−7075.67			−0.247486
$936$	−1790.92	−	16831.3i	−0.0625408	−	0.587766i
$937$	−17484.4			−0.609595			−0.304797	−	0.952417i	$-0.598589\pi$
$937$	−17484.4			−0.609595			−0.304797	+	0.952417i	$0.598589\pi$
$938$	−3797.07	+	16833.9i	−0.132174	+	0.585978i
$939$	−11578.9	−	28510.8i	−0.402411	−	0.990858i
$940$	−9848.48	+	20720.4i	−0.341726	+	0.718963i
$941$		−	10865.5i		−	0.376412i	−0.982130	−	0.188206i	$-0.939733\pi$
$941$		−	10865.5i		−	0.376412i	0.982130	−	0.188206i	$-0.0602672\pi$
$942$	−33925.9	+	5611.71i	−1.17342	+	0.194097i
$943$			14989.7i			0.517638i
$944$	11949.3	+	14674.2i	0.411989	+	0.505937i
$945$	13081.3	+	5739.64i	0.450302	+	0.197577i
$946$	−22011.2	−	4964.87i	−0.756498	−	0.170636i
$947$	−6102.06			−0.209388			−0.104694	−	0.994504i	$-0.533386\pi$
$947$	−6102.06			−0.209388			−0.104694	+	0.994504i	$0.533386\pi$
$948$	−4596.41	−	266.528i	−0.157473	−	0.00913125i
$949$	13968.8			0.477814
$950$	8824.06	+	1990.36i	0.301358	+	0.0679745i
$951$	−37591.6	+	15266.9i	−1.28180	+	0.520570i
$952$	26320.1	−	33527.6i	0.896049	−	1.14143i
$953$		−	11131.8i		−	0.378377i	−0.981941	−	0.189189i	$-0.939414\pi$
$953$		−	11131.8i		−	0.378377i	0.981941	−	0.189189i	$-0.0605858\pi$
$954$	19910.5	−	12199.1i	0.675710	−	0.414004i
$955$		−	4160.30i		−	0.140968i
$956$	−31928.5	−	15175.7i	−1.08017	−	0.513408i
$957$	7313.09	−	2970.02i	0.247021	−	0.100321i
$958$	2134.76	−	9464.25i	0.0719948	−	0.319182i
$959$	−27195.1			−0.915719
$960$	−7788.26	−	10783.8i	−0.261839	−	0.362547i
$961$	29125.0			0.977643
$962$	6149.12	−	27261.5i	0.206087	−	0.913666i
$963$	−9750.89	+	9484.49i	−0.326291	+	0.317376i
$964$	−9468.89	−	4500.60i	−0.316361	−	0.150368i
$965$			3296.76i			0.109976i
$966$	2499.66	+	15111.8i	0.0832558	+	0.503327i
$967$			17597.4i			0.585207i	0.956234	+	0.292603i	$0.0945215\pi$
$967$			17597.4i			0.585207i	−0.956234	+	0.292603i	$0.905478\pi$
$968$	15326.9	−	19524.1i	0.508911	−	0.648273i
$969$	23136.9	+	56970.0i	0.767043	+	1.88869i
$970$	−360.276	−	81.2641i	−0.0119255	−	0.00268993i
$971$	−742.846			−0.0245510			−0.0122755	−	0.999925i	$-0.503908\pi$
$971$	−742.846			−0.0245510			−0.0122755	+	0.999925i	$0.503908\pi$
$972$	30193.0	+	2591.42i	0.996337	+	0.0855141i
$973$	40867.8			1.34652
$974$	−20073.6	−	4527.81i	−0.660369	−	0.148953i
$975$	1354.23	+	3334.53i	0.0444822	+	0.109529i
$976$	13192.4	+	16200.8i	0.432663	+	0.531326i
$977$			41139.6i			1.34716i	0.739116	+	0.673578i	$0.235244\pi$
$977$			41139.6i			1.34716i	−0.739116	+	0.673578i	$0.764756\pi$
$978$	−3698.27	−	22358.1i	−0.120918	−	0.731015i
$979$		−	11824.5i		−	0.386020i
$980$	−1231.22	+	2590.38i	−0.0401325	+	0.0844355i
$981$	17972.7	−	17481.7i	0.584939	−	0.568958i
$982$	−10954.2	+	48564.3i	−0.355970	+	1.57816i
$983$	−23649.8			−0.767356			−0.383678	−	0.923467i	$-0.625343\pi$
$983$	−23649.8			−0.767356			−0.383678	+	0.923467i	$0.625343\pi$
$984$	−9509.29	+	33098.3i	−0.308074	+	1.07229i
$985$	−4816.68			−0.155809
$986$	−5716.33	+	25342.8i	−0.184630	+	0.818537i
$987$	56229.9	−	22836.3i	1.81339	−	0.736462i
$988$	−12171.8	+	25608.5i	−0.391940	+	0.824609i
$989$			26688.0i			0.858068i
$990$	4980.89	−	3051.76i	0.159902	−	0.0979711i
$991$		−	38069.9i		−	1.22031i	−0.792280	−	0.610157i	$-0.791106\pi$
$991$		−	38069.9i		−	1.22031i	0.792280	−	0.610157i	$-0.208894\pi$
$992$	−2080.48	−	4182.81i	−0.0665881	−	0.133875i
$993$	7553.83	−	3067.79i	0.241403	−	0.0980397i
$994$	36737.4	+	8286.51i	1.17227	+	0.264419i
$995$	−4352.44			−0.138675
$996$	−3560.93	+	61410.0i	−0.113285	+	1.95367i
$997$	−2800.44			−0.0889576			−0.0444788	−	0.999010i	$-0.514163\pi$
$997$	−2800.44			−0.0889576			−0.0444788	+	0.999010i	$0.514163\pi$
$998$	−47801.0	−	10782.0i	−1.51615	−	0.341983i
$999$	45817.4	+	20103.1i	1.45105	+	0.636671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.e.a.11.15	yes	24
3.2	odd	2	inner	60.4.e.a.11.10	yes	24
4.3	odd	2	inner	60.4.e.a.11.9	✓	24
8.3	odd	2		960.4.h.d.191.9		24
8.5	even	2		960.4.h.d.191.16		24
12.11	even	2	inner	60.4.e.a.11.16	yes	24
24.5	odd	2		960.4.h.d.191.10		24
24.11	even	2		960.4.h.d.191.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.e.a.11.9	✓	24	4.3	odd	2	inner
60.4.e.a.11.10	yes	24	3.2	odd	2	inner
60.4.e.a.11.15	yes	24	1.1	even	1	trivial
60.4.e.a.11.16	yes	24	12.11	even	2	inner
960.4.h.d.191.9		24	8.3	odd	2
960.4.h.d.191.10		24	24.5	odd	2
960.4.h.d.191.15		24	24.11	even	2
960.4.h.d.191.16		24	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.622346 - 2.75911i) q^{2} +(-1.95519 - 4.81427i) q^{3} +(-7.22537 - 3.43424i) q^{4} +5.00000i q^{5} +(-14.4999 + 2.39845i) q^{6} -20.3642i q^{7} +(-13.9721 + 17.7983i) q^{8} +(-19.3544 + 18.8257i) q^{9} +O(q^{10})\)	\(q+(0.622346 - 2.75911i) q^{2} +(-1.95519 - 4.81427i) q^{3} +(-7.22537 - 3.43424i) q^{4} +5.00000i q^{5} +(-14.4999 + 2.39845i) q^{6} -20.3642i q^{7} +(-13.9721 + 17.7983i) q^{8} +(-19.3544 + 18.8257i) q^{9} +(13.7955 + 3.11173i) q^{10} -15.2982 q^{11} +(-2.40639 + 41.4995i) q^{12} +27.7054 q^{13} +(-56.1872 - 12.6736i) q^{14} +(24.0714 - 9.77596i) q^{15} +(40.4119 + 49.6274i) q^{16} -92.5031i q^{17} +(39.8969 + 65.1171i) q^{18} -127.926i q^{19} +(17.1712 - 36.1268i) q^{20} +(-98.0390 + 39.8160i) q^{21} +(-9.52081 + 42.2095i) q^{22} +51.1779 q^{23} +(113.004 + 32.4666i) q^{24} -25.0000 q^{25} +(17.2423 - 76.4421i) q^{26} +(128.474 + 56.3698i) q^{27} +(-69.9358 + 147.139i) q^{28} -99.2953i q^{29} +(-11.9922 - 72.4996i) q^{30} -25.8075i q^{31} +(162.078 - 80.6156i) q^{32} +(29.9110 + 73.6499i) q^{33} +(-255.226 - 57.5690i) q^{34} +101.821 q^{35} +(204.495 - 69.5545i) q^{36} +356.629 q^{37} +(-352.962 - 79.6144i) q^{38} +(-54.1693 - 133.381i) q^{39} +(-88.9915 - 69.8607i) q^{40} +292.895i q^{41} +(48.8425 + 295.280i) q^{42} +521.476i q^{43} +(110.535 + 52.5379i) q^{44} +(-94.1283 - 96.7722i) q^{45} +(31.8504 - 141.205i) q^{46} -573.546 q^{47} +(159.907 - 291.585i) q^{48} -71.7025 q^{49} +(-15.5587 + 68.9777i) q^{50} +(-445.335 + 180.861i) q^{51} +(-200.182 - 95.1470i) q^{52} -305.765i q^{53} +(235.485 - 319.391i) q^{54} -76.4912i q^{55} +(362.449 + 284.532i) q^{56} +(-615.871 + 250.120i) q^{57} +(-273.967 - 61.7961i) q^{58} +295.688 q^{59} +(-207.498 - 12.0320i) q^{60} +326.449 q^{61} +(-71.2056 - 16.0612i) q^{62} +(383.370 + 394.139i) q^{63} +(-121.559 - 497.361i) q^{64} +138.527i q^{65} +(221.823 - 36.6920i) q^{66} -299.605i q^{67} +(-317.678 + 668.369i) q^{68} +(-100.063 - 246.384i) q^{69} +(63.3681 - 280.936i) q^{70} -653.840 q^{71} +(-64.6418 - 607.511i) q^{72} +504.190 q^{73} +(221.947 - 983.979i) q^{74} +(48.8798 + 120.357i) q^{75} +(-439.330 + 924.314i) q^{76} +311.537i q^{77} +(-401.725 + 66.4498i) q^{78} +110.758i q^{79} +(-248.137 + 202.060i) q^{80} +(20.1889 - 728.720i) q^{81} +(808.129 + 182.282i) q^{82} +1479.78 q^{83} +(845.106 + 49.0044i) q^{84} +462.515 q^{85} +(1438.81 + 324.539i) q^{86} +(-478.035 + 194.141i) q^{87} +(213.749 - 272.283i) q^{88} +772.934i q^{89} +(-325.586 + 199.484i) q^{90} -564.199i q^{91} +(-369.779 - 175.757i) q^{92} +(-124.244 + 50.4585i) q^{93} +(-356.944 + 1582.48i) q^{94} +639.631 q^{95} +(-704.998 - 622.667i) q^{96} -26.1154 q^{97} +(-44.6238 + 197.835i) q^{98} +(296.089 - 288.000i) 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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