LMFDB - Embedded newform 60.5.f.a.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(19,60)]

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, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.f (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:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	60.19
Dual form			60.5.f.a.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59896 + 3.04063i) q^{2} -5.19615 q^{3} +(-2.49086 - 15.8049i) q^{4} +(24.9405 + 1.72355i) q^{5} +(13.5046 - 15.7996i) q^{6} -2.65040 q^{7} +(54.5305 + 33.5025i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(-2.59896 + 3.04063i) q^{2} -5.19615 q^{3} +(-2.49086 - 15.8049i) q^{4} +(24.9405 + 1.72355i) q^{5} +(13.5046 - 15.7996i) q^{6} -2.65040 q^{7} +(54.5305 + 33.5025i) q^{8} +27.0000 q^{9} +(-70.0600 + 71.3554i) q^{10} +60.4192i q^{11} +(12.9429 + 82.1248i) q^{12} +211.156i q^{13} +(6.88829 - 8.05890i) q^{14} +(-129.595 - 8.95583i) q^{15} +(-243.591 + 78.7356i) q^{16} -10.2742i q^{17} +(-70.1718 + 82.0970i) q^{18} +484.167i q^{19} +(-34.8827 - 398.476i) q^{20} +13.7719 q^{21} +(-183.712 - 157.027i) q^{22} +558.257 q^{23} +(-283.349 - 174.084i) q^{24} +(619.059 + 85.9724i) q^{25} +(-642.047 - 548.785i) q^{26} -140.296 q^{27} +(6.60178 + 41.8894i) q^{28} +948.135 q^{29} +(364.042 - 370.774i) q^{30} +1407.91i q^{31} +(393.677 - 945.301i) q^{32} -313.947i q^{33} +(31.2400 + 26.7022i) q^{34} +(-66.1025 - 4.56810i) q^{35} +(-67.2531 - 426.733i) q^{36} -2314.75i q^{37} +(-1472.17 - 1258.33i) q^{38} -1097.20i q^{39} +(1302.28 + 929.556i) q^{40} -585.519 q^{41} +(-35.7926 + 41.8753i) q^{42} -1021.57 q^{43} +(954.921 - 150.496i) q^{44} +(673.394 + 46.5358i) q^{45} +(-1450.88 + 1697.45i) q^{46} +940.273 q^{47} +(1265.74 - 409.122i) q^{48} -2393.98 q^{49} +(-1870.32 + 1658.89i) q^{50} +53.3863i q^{51} +(3337.30 - 525.959i) q^{52} +4050.71i q^{53} +(364.623 - 426.589i) q^{54} +(-104.136 + 1506.89i) q^{55} +(-144.528 - 88.7953i) q^{56} -2515.80i q^{57} +(-2464.16 + 2882.93i) q^{58} -2581.26i q^{59} +(181.256 + 2070.54i) q^{60} +174.777 q^{61} +(-4280.94 - 3659.11i) q^{62} -71.5609 q^{63} +(1851.16 + 3653.82i) q^{64} +(-363.938 + 5266.34i) q^{65} +(954.598 + 815.936i) q^{66} -42.9926 q^{67} +(-162.383 + 25.5915i) q^{68} -2900.79 q^{69} +(185.687 - 189.121i) q^{70} -4333.93i q^{71} +(1472.32 + 904.568i) q^{72} +3225.98i q^{73} +(7038.30 + 6015.93i) q^{74} +(-3216.72 - 446.726i) q^{75} +(7652.22 - 1205.99i) q^{76} -160.135i q^{77} +(3336.17 + 2851.57i) q^{78} -10889.8i q^{79} +(-6211.00 + 1543.87i) q^{80} +729.000 q^{81} +(1521.74 - 1780.35i) q^{82} +9399.28 q^{83} +(-34.3039 - 217.664i) q^{84} +(17.7081 - 256.244i) q^{85} +(2655.02 - 3106.22i) q^{86} -4926.65 q^{87} +(-2024.20 + 3294.69i) q^{88} -11508.4 q^{89} +(-1891.62 + 1926.60i) q^{90} -559.649i q^{91} +(-1390.54 - 8823.21i) q^{92} -7315.74i q^{93} +(-2443.73 + 2859.02i) q^{94} +(-834.486 + 12075.4i) q^{95} +(-2045.61 + 4911.93i) q^{96} -13754.2i q^{97} +(6221.84 - 7279.19i) q^{98} +1631.32i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9}+O(q^{10}) $ 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9	$ 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9} + 274 q^{10} - 36 q^{14} + 594 q^{16} - 12 q^{20} - 594 q^{24} + 1208 q^{25} - 2868 q^{26} - 1680 q^{29} + 468 q^{30} + 3076 q^{34} + 378 q^{36} - 7222 q^{40} - 4848 q^{41} - 3828 q^{44} - 648 q^{45} - 15280 q^{46} + 5416 q^{49} + 14472 q^{50} - 486 q^{54} + 32172 q^{56} - 7506 q^{60} + 2896 q^{61} - 18298 q^{64} - 2688 q^{65} - 15588 q^{66} + 9792 q^{69} + 27608 q^{70} + 31836 q^{74} + 50136 q^{76} - 27348 q^{80} + 17496 q^{81} - 4284 q^{84} - 15680 q^{85} - 58152 q^{86} - 38544 q^{89} + 7398 q^{90} + 4808 q^{94} + 21978 q^{96}+O(q^{100}) $ 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9 + 274 * q^10 - 36 * q^14 + 594 * q^16 - 12 * q^20 - 594 * q^24 + 1208 * q^25 - 2868 * q^26 - 1680 * q^29 + 468 * q^30 + 3076 * q^34 + 378 * q^36 - 7222 * q^40 - 4848 * q^41 - 3828 * q^44 - 648 * q^45 - 15280 * q^46 + 5416 * q^49 + 14472 * q^50 - 486 * q^54 + 32172 * q^56 - 7506 * q^60 + 2896 * q^61 - 18298 * q^64 - 2688 * q^65 - 15588 * q^66 + 9792 * q^69 + 27608 * q^70 + 31836 * q^74 + 50136 * q^76 - 27348 * q^80 + 17496 * q^81 - 4284 * q^84 - 15680 * q^85 - 58152 * q^86 - 38544 * q^89 + 7398 * q^90 + 4808 * q^94 + 21978 * q^96

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 $

$2$	−2.59896	+	3.04063i	−0.649739	+	0.760157i
$2$	−2.59896	+	3.04063i	−0.649739	+	0.760157i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	−2.49086	−	15.8049i	−0.155679	−	0.987808i
$5$	24.9405	+	1.72355i	0.997621	+	0.0689420i
$5$	24.9405	+	1.72355i	0.997621	+	0.0689420i
$6$	13.5046	−	15.7996i	0.375127	−	0.438877i
$7$	−2.65040			−0.0540899			−0.0270449	−	0.999634i	$-0.508610\pi$
$7$	−2.65040			−0.0540899			−0.0270449	+	0.999634i	$0.508610\pi$
$8$	54.5305	+	33.5025i	0.852040	+	0.523477i
$9$	27.0000			0.333333
$10$	−70.0600	+	71.3554i	−0.700600	+	0.713554i
$11$			60.4192i			0.499332i	0.968332	+	0.249666i	$0.0803209\pi$
$11$			60.4192i			0.499332i	−0.968332	+	0.249666i	$0.919679\pi$
$12$	12.9429	+	82.1248i	0.0898811	+	0.570311i
$13$			211.156i			1.24944i	0.780847	+	0.624722i	$0.214788\pi$
$13$			211.156i			1.24944i	−0.780847	+	0.624722i	$0.785212\pi$
$14$	6.88829	−	8.05890i	0.0351443	−	0.0411168i
$15$	−129.595	−	8.95583i	−0.575977	−	0.0398037i
$16$	−243.591	+	78.7356i	−0.951528	+	0.307561i
$17$		−	10.2742i		−	0.0355508i	−0.999842	−	0.0177754i	$-0.994342\pi$
$17$		−	10.2742i		−	0.0355508i	0.999842	−	0.0177754i	$-0.00565839\pi$
$18$	−70.1718	+	82.0970i	−0.216580	+	0.253386i
$19$			484.167i			1.34118i	0.741827	+	0.670591i	$0.233960\pi$
$19$			484.167i			1.34118i	−0.741827	+	0.670591i	$0.766040\pi$
$20$	−34.8827	−	398.476i	−0.0872067	−	0.996190i
$21$	13.7719			0.0312288
$22$	−183.712	−	157.027i	−0.379571	−	0.324436i
$23$	558.257			1.05531			0.527653	−	0.849460i	$-0.323072\pi$
$23$	558.257			1.05531			0.527653	+	0.849460i	$0.323072\pi$
$24$	−283.349	−	174.084i	−0.491925	−	0.302230i
$25$	619.059	+	85.9724i	0.990494	+	0.137556i
$26$	−642.047	−	548.785i	−0.949774	−	0.811812i
$27$	−140.296			−0.192450
$28$	6.60178	+	41.8894i	0.00842064	+	0.0534304i
$29$	948.135			1.12739			0.563695	−	0.825983i	$-0.309379\pi$
$29$	948.135			1.12739			0.563695	+	0.825983i	$0.309379\pi$
$30$	364.042	−	370.774i	0.404491	−	0.411971i
$31$			1407.91i			1.46505i	0.680740	+	0.732525i	$0.261659\pi$
$31$			1407.91i			1.46505i	−0.680740	+	0.732525i	$0.738341\pi$
$32$	393.677	−	945.301i	0.384450	−	0.923146i
$33$		−	313.947i		−	0.288290i
$34$	31.2400	+	26.7022i	0.0270242	+	0.0230988i
$35$	−66.1025	−	4.56810i	−0.0539612	−	0.00372906i
$36$	−67.2531	−	426.733i	−0.0518929	−	0.329269i
$37$		−	2314.75i		−	1.69083i	−0.534108	−	0.845416i	$-0.679352\pi$
$37$		−	2314.75i		−	1.69083i	0.534108	−	0.845416i	$-0.320648\pi$
$38$	−1472.17	−	1258.33i	−1.01951	−	0.871419i
$39$		−	1097.20i		−	0.721366i
$40$	1302.28	+	929.556i	0.813923	+	0.580973i
$41$	−585.519			−0.348316			−0.174158	−	0.984718i	$-0.555720\pi$
$41$	−585.519			−0.348316			−0.174158	+	0.984718i	$0.555720\pi$
$42$	−35.7926	+	41.8753i	−0.0202906	+	0.0237388i
$43$	−1021.57			−0.552500			−0.276250	−	0.961086i	$-0.589092\pi$
$43$	−1021.57			−0.552500			−0.276250	+	0.961086i	$0.589092\pi$
$44$	954.921	−	150.496i	0.493244	−	0.0777353i
$45$	673.394	+	46.5358i	0.332540	+	0.0229807i
$46$	−1450.88	+	1697.45i	−0.685673	+	0.802198i
$47$	940.273			0.425656			0.212828	−	0.977090i	$-0.431733\pi$
$47$	940.273			0.425656			0.212828	+	0.977090i	$0.431733\pi$
$48$	1265.74	−	409.122i	0.549365	−	0.177570i
$49$	−2393.98			−0.997074
$50$	−1870.32	+	1658.89i	−0.748127	+	0.663556i
$51$			53.3863i			0.0205253i
$52$	3337.30	−	525.959i	1.23421	−	0.194512i
$53$			4050.71i			1.44205i	0.692911	+	0.721023i	$0.256328\pi$
$53$			4050.71i			1.44205i	−0.692911	+	0.721023i	$0.743672\pi$
$54$	364.623	−	426.589i	0.125042	−	0.146292i
$55$	−104.136	+	1506.89i	−0.0344250	+	0.498144i
$56$	−144.528	−	88.7953i	−0.0460867	−	0.0283148i
$57$		−	2515.80i		−	0.774332i
$58$	−2464.16	+	2882.93i	−0.732509	+	0.856994i
$59$		−	2581.26i		−	0.741529i	−0.928727	−	0.370764i	$-0.879096\pi$
$59$		−	2581.26i		−	0.741529i	0.928727	−	0.370764i	$-0.120904\pi$
$60$	181.256	+	2070.54i	0.0503488	+	0.575151i
$61$	174.777			0.0469704			0.0234852	−	0.999724i	$-0.492524\pi$
$61$	174.777			0.0469704			0.0234852	+	0.999724i	$0.492524\pi$
$62$	−4280.94	−	3659.11i	−1.11367	−	0.951901i
$63$	−71.5609			−0.0180300
$64$	1851.16	+	3653.82i	0.451944	+	0.892046i
$65$	−363.938	+	5266.34i	−0.0861391	+	1.24647i
$66$	954.598	+	815.936i	0.219146	+	0.187313i
$67$	−42.9926			−0.00957731			−0.00478866	−	0.999989i	$-0.501524\pi$
$67$	−42.9926			−0.00957731			−0.00478866	+	0.999989i	$0.501524\pi$
$68$	−162.383	+	25.5915i	−0.0351174	+	0.00553450i
$69$	−2900.79			−0.609281
$70$	185.687	−	189.121i	0.0378954	−	0.0385961i
$71$		−	4333.93i		−	0.859737i	−0.902892	−	0.429868i	$-0.858560\pi$
$71$		−	4333.93i		−	0.859737i	0.902892	−	0.429868i	$-0.141440\pi$
$72$	1472.32	+	904.568i	0.284013	+	0.174492i
$73$			3225.98i			0.605364i	0.953092	+	0.302682i	$0.0978820\pi$
$73$			3225.98i			0.605364i	−0.953092	+	0.302682i	$0.902118\pi$
$74$	7038.30	+	6015.93i	1.28530	+	1.09860i
$75$	−3216.72	−	446.726i	−0.571862	−	0.0794179i
$76$	7652.22	−	1205.99i	1.32483	−	0.208793i
$77$		−	160.135i		−	0.0270088i
$78$	3336.17	+	2851.57i	0.548352	+	0.468700i
$79$		−	10889.8i		−	1.74489i	−0.488714	−	0.872444i	$-0.662534\pi$
$79$		−	10889.8i		−	1.74489i	0.488714	−	0.872444i	$-0.337466\pi$
$80$	−6211.00	+	1543.87i	−0.970468	+	0.241229i
$81$	729.000			0.111111
$82$	1521.74	−	1780.35i	0.226315	−	0.264775i
$83$	9399.28			1.36439			0.682195	−	0.731171i	$-0.261026\pi$
$83$	9399.28			1.36439			0.682195	+	0.731171i	$0.261026\pi$
$84$	−34.3039	−	217.664i	−0.00486166	−	0.0308481i
$85$	17.7081	−	256.244i	0.00245095	−	0.0354663i
$86$	2655.02	−	3106.22i	0.358981	−	0.419987i
$87$	−4926.65			−0.650899
$88$	−2024.20	+	3294.69i	−0.261389	+	0.425451i
$89$	−11508.4			−1.45290			−0.726449	−	0.687221i	$-0.758830\pi$
$89$	−11508.4			−1.45290			−0.726449	+	0.687221i	$0.758830\pi$
$90$	−1891.62	+	1926.60i	−0.233533	+	0.237851i
$91$		−	559.649i		−	0.0675823i
$92$	−1390.54	−	8823.21i	−0.164288	−	1.04244i
$93$		−	7315.74i		−	0.845848i
$94$	−2443.73	+	2859.02i	−0.276565	+	0.323565i
$95$	−834.486	+	12075.4i	−0.0924638	+	1.33799i
$96$	−2045.61	+	4911.93i	−0.221962	+	0.532978i
$97$		−	13754.2i		−	1.46181i	−0.682477	−	0.730907i	$-0.739097\pi$
$97$		−	13754.2i		−	1.46181i	0.682477	−	0.730907i	$-0.260903\pi$
$98$	6221.84	−	7279.19i	0.647838	−	0.757933i
$99$			1631.32i			0.166444i
$100$	−183.199	−	9998.32i	−0.0183199	−	0.999832i
$101$	11657.3			1.14276			0.571380	−	0.820685i	$-0.306408\pi$
$101$	11657.3			1.14276			0.571380	+	0.820685i	$0.306408\pi$
$102$	−162.328	−	138.749i	−0.0156025	−	0.0133361i
$103$	−18928.1			−1.78416			−0.892079	−	0.451879i	$-0.850754\pi$
$103$	−18928.1			−1.78416			−0.892079	+	0.451879i	$0.850754\pi$
$104$	−7074.26	+	11514.4i	−0.654055	+	1.06458i
$105$	343.478	+	23.7366i	0.0311545	+	0.00215298i
$106$	−12316.7	−	10527.6i	−1.09618	−	0.936954i
$107$	13683.7			1.19519			0.597595	−	0.801798i	$-0.296123\pi$
$107$	13683.7			1.19519			0.597595	+	0.801798i	$0.296123\pi$
$108$	349.458	+	2217.37i	0.0299604	+	0.190104i
$109$	−5285.12			−0.444838			−0.222419	−	0.974951i	$-0.571395\pi$
$109$	−5285.12			−0.444838			−0.222419	+	0.974951i	$0.571395\pi$
$110$	−4311.24	−	4232.97i	−0.356301	−	0.349832i
$111$			12027.8i			0.976203i
$112$	645.615	−	208.681i	0.0514681	−	0.0166359i
$113$		−	3269.03i		−	0.256013i	−0.991773	−	0.128007i	$-0.959142\pi$
$113$		−	3269.03i		−	0.256013i	0.991773	−	0.128007i	$-0.0408579\pi$
$114$	7649.63	+	6538.47i	0.588614	+	0.503114i
$115$	13923.2	+	962.183i	1.05279	+	0.0727549i
$116$	−2361.67	−	14985.2i	−0.175510	−	1.11364i
$117$			5701.21i			0.416481i
$118$	7848.66	+	6708.59i	0.563679	+	0.481800i
$119$			27.2308i			0.00192294i
$120$	−6766.83	−	4830.12i	−0.469919	−	0.335425i
$121$	10990.5			0.750667
$122$	−454.237	+	531.432i	−0.0305185	+	0.0357049i
$123$	3042.45			0.201100
$124$	22252.0	−	3506.91i	1.44719	−	0.228077i
$125$	15291.5	+	3211.18i	0.978654	+	0.205515i
$126$	185.984	−	217.590i	0.0117148	−	0.0137056i
$127$	−6619.39			−0.410403			−0.205201	−	0.978720i	$-0.565785\pi$
$127$	−6619.39			−0.410403			−0.205201	+	0.978720i	$0.565785\pi$
$128$	−15921.0	−	3867.43i	−0.971741	−	0.236049i
$129$	5308.25			0.318986
$130$	−15067.1	−	14793.6i	−0.891546	−	0.875360i
$131$			2116.39i			0.123326i	0.998097	+	0.0616628i	$0.0196404\pi$
$131$			2116.39i			0.123326i	−0.998097	+	0.0616628i	$0.980360\pi$
$132$	−4961.92	+	781.998i	−0.284775	+	0.0448805i
$133$		−	1283.24i		−	0.0725444i
$134$	111.736	−	130.724i	0.00622275	−	0.00728027i
$135$	−3499.06	−	241.807i	−0.191992	−	0.0132679i
$136$	344.211	−	560.257i	0.0186100	−	0.0302907i
$137$			25312.1i			1.34861i	0.738453	+	0.674305i	$0.235557\pi$
$137$			25312.1i			1.34861i	−0.738453	+	0.674305i	$0.764443\pi$
$138$	7539.02	−	8820.22i	0.395874	−	0.463149i
$139$		−	12614.4i		−	0.652887i	−0.945217	−	0.326444i	$-0.894150\pi$
$139$		−	12614.4i		−	0.652887i	0.945217	−	0.326444i	$-0.105850\pi$
$140$	92.4532	+	1056.12i	0.00471700	+	0.0538838i
$141$	−4885.80			−0.245752
$142$	13177.9	+	11263.7i	0.653535	+	0.558605i
$143$	−12757.9			−0.623888
$144$	−6576.96	+	2125.86i	−0.317176	+	0.102520i
$145$	23647.0	+	1634.16i	1.12471	+	0.0777245i
$146$	−9809.02	−	8384.19i	−0.460172	−	0.393328i
$147$	12439.5			0.575661
$148$	−36584.5	+	5765.71i	−1.67022	+	0.263226i
$149$	−12532.5			−0.564504			−0.282252	−	0.959340i	$-0.591081\pi$
$149$	−12532.5			−0.564504			−0.282252	+	0.959340i	$0.591081\pi$
$150$	9718.45	−	8619.84i	0.431931	−	0.383104i
$151$			34448.4i			1.51083i	0.655248	+	0.755414i	$0.272564\pi$
$151$			34448.4i			1.51083i	−0.655248	+	0.755414i	$0.727436\pi$
$152$	−16220.8	+	26401.9i	−0.702078	+	1.14274i
$153$		−	277.403i		−	0.0118503i
$154$	486.912	+	416.185i	0.0205310	+	0.0175487i
$155$	−2426.61	+	35114.1i	−0.101004	+	1.46157i
$156$	−17341.1	+	2732.96i	−0.712571	+	0.112301i
$157$			19365.8i			0.785661i	0.919611	+	0.392830i	$0.128504\pi$
$157$			19365.8i			0.785661i	−0.919611	+	0.392830i	$0.871496\pi$
$158$	33112.0	+	28302.2i	1.32639	+	1.13372i
$159$		−	21048.1i		−	0.832566i
$160$	11447.8	−	22897.8i	0.447179	−	0.894444i
$161$	−1479.61			−0.0570814
$162$	−1894.64	+	2216.62i	−0.0721932	+	0.0844619i
$163$	31173.2			1.17329			0.586646	−	0.809843i	$-0.300448\pi$
$163$	31173.2			1.17329			0.586646	+	0.809843i	$0.300448\pi$
$164$	1458.44	+	9254.09i	0.0542253	+	0.344069i
$165$	541.104	−	7830.01i	0.0198753	−	0.287604i
$166$	−24428.3	+	28579.7i	−0.886497	+	1.03715i
$167$	−38020.1			−1.36327			−0.681633	−	0.731695i	$-0.738730\pi$
$167$	−38020.1			−1.36327			−0.681633	+	0.731695i	$0.738730\pi$
$168$	750.990	+	461.394i	0.0266082	+	0.0163476i
$169$	−16025.8			−0.561109
$170$	733.120	+	719.810i	0.0253675	+	0.0249069i
$171$			13072.5i			0.447061i
$172$	2544.59	+	16145.9i	0.0860124	+	0.545764i
$173$		−	24872.7i		−	0.831057i	−0.909580	−	0.415529i	$-0.863597\pi$
$173$		−	24872.7i		−	0.831057i	0.909580	−	0.415529i	$-0.136403\pi$
$174$	12804.2	−	14980.1i	0.422914	−	0.494786i
$175$	−1640.76	−	227.862i	−0.0535757	−	0.00744038i
$176$	−4757.14	−	14717.6i	−0.153575	−	0.475129i
$177$			13412.6i			0.428122i
$178$	29909.8	−	34992.8i	0.944004	−	1.10443i
$179$		−	43148.8i		−	1.34667i	−0.739336	−	0.673337i	$-0.764860\pi$
$179$		−	43148.8i		−	1.34667i	0.739336	−	0.673337i	$-0.235140\pi$
$180$	−941.833	−	10758.9i	−0.0290689	−	0.332063i
$181$	−31614.8			−0.965014			−0.482507	−	0.875892i	$-0.660274\pi$
$181$	−31614.8			−0.965014			−0.482507	+	0.875892i	$0.660274\pi$
$182$	1701.68	+	1454.50i	0.0513732	+	0.0439108i
$183$	−908.167			−0.0271184
$184$	30442.0	+	18703.0i	0.899162	+	0.552428i
$185$	3989.59	−	57731.1i	0.116569	−	1.68681i
$186$	22244.4	+	19013.3i	0.642977	+	0.549580i
$187$	620.759			0.0177517
$188$	−2342.09	−	14860.9i	−0.0662655	−	0.420466i
$189$	371.842			0.0104096
$190$	−34547.9	−	33920.7i	−0.957007	−	0.939632i
$191$		−	61002.6i		−	1.67217i	−0.548597	−	0.836087i	$-0.684838\pi$
$191$		−	61002.6i		−	1.67217i	0.548597	−	0.836087i	$-0.315162\pi$
$192$	−9618.92	−	18985.8i	−0.260930	−	0.515023i
$193$			15692.0i			0.421273i	0.977564	+	0.210637i	$0.0675537\pi$
$193$			15692.0i			0.421273i	−0.977564	+	0.210637i	$0.932446\pi$
$194$	41821.5	+	35746.6i	1.11121	+	0.949798i
$195$	1891.08	−	27364.7i	0.0497324	−	0.719650i
$196$	5963.05	+	37836.6i	0.155223	+	0.984918i
$197$		−	16367.8i		−	0.421752i	−0.977513	−	0.210876i	$-0.932368\pi$
$197$		−	16367.8i		−	0.421752i	0.977513	−	0.210876i	$-0.0676317\pi$
$198$	−4960.24	−	4239.73i	−0.126524	−	0.108145i
$199$		−	19223.6i		−	0.485432i	−0.970097	−	0.242716i	$-0.921962\pi$
$199$		−	19223.6i		−	0.485432i	0.970097	−	0.242716i	$-0.0780384\pi$
$200$	30877.3	+	25428.2i	0.771933	+	0.635704i
$201$	223.396			0.00552946
$202$	−30296.8	+	35445.5i	−0.742496	+	0.868678i
$203$	−2512.94			−0.0609804
$204$	843.766	−	132.978i	0.0202750	−	0.00319535i
$205$	−14603.2	−	1009.17i	−0.347487	−	0.0240136i
$206$	49193.4	−	57553.5i	1.15924	−	1.35624i
$207$	15072.9			0.351769
$208$	−16625.5	−	51435.7i	−0.384280	−	1.18888i
$209$	−29253.0			−0.669696
$210$	−964.860	+	982.701i	−0.0218789	+	0.0222835i
$211$			26154.5i			0.587464i	0.955888	+	0.293732i	$0.0948974\pi$
$211$			26154.5i			0.587464i	−0.955888	+	0.293732i	$0.905103\pi$
$212$	64021.2	−	10089.7i	1.42447	−	0.224496i
$213$			22519.8i			0.496369i
$214$	−35563.4	+	41607.1i	−0.776561	+	0.908532i
$215$	−25478.6	−	1760.73i	−0.551186	−	0.0380905i
$216$	−7650.42	−	4700.27i	−0.163975	−	0.100743i
$217$		−	3731.54i		−	0.0792444i
$218$	13735.8	−	16070.1i	0.289028	−	0.338147i
$219$		−	16762.7i		−	0.349507i
$220$	24075.6	−	2107.58i	0.497430	−	0.0435451i
$221$	2169.46			0.0444188
$222$	−36572.1	−	31259.7i	−0.742068	−	0.634277i
$223$	28844.8			0.580040			0.290020	−	0.957021i	$-0.406338\pi$
$223$	28844.8			0.580040			0.290020	+	0.957021i	$0.406338\pi$
$224$	−1043.40	+	2505.43i	−0.0207949	+	0.0499329i
$225$	16714.6	+	2321.26i	0.330165	+	0.0458520i
$226$	9939.92	+	8496.08i	0.194610	+	0.166342i
$227$	40998.0			0.795629			0.397815	−	0.917466i	$-0.369769\pi$
$227$	40998.0			0.795629			0.397815	+	0.917466i	$0.369769\pi$
$228$	−39762.1	+	6266.51i	−0.764891	+	0.120547i
$229$	−14617.4			−0.278741			−0.139370	−	0.990240i	$-0.544508\pi$
$229$	−14617.4			−0.278741			−0.139370	+	0.990240i	$0.544508\pi$
$230$	−39111.5	+	39834.7i	−0.739347	+	0.753018i
$231$			832.088i			0.0155936i
$232$	51702.3	+	31764.9i	0.960581	+	0.590163i
$233$		−	31464.2i		−	0.579568i	−0.957092	−	0.289784i	$-0.906417\pi$
$233$		−	31464.2i		−	0.579568i	0.957092	−	0.289784i	$-0.0935834\pi$
$234$	−17335.3	−	14817.2i	−0.316591	−	0.270604i
$235$	23450.9	+	1620.61i	0.424643	+	0.0293455i
$236$	−40796.7	+	6429.56i	−0.732488	+	0.115440i
$237$			56585.3i			1.00741i
$238$	−82.7987	−	70.7716i	−0.00146174	−	0.00124941i
$239$			94111.2i			1.64758i	0.566898	+	0.823788i	$0.308143\pi$
$239$			94111.2i			1.64758i	−0.566898	+	0.823788i	$0.691857\pi$
$240$	32273.3	−	8022.16i	0.560300	−	0.139274i
$241$	44407.1			0.764573			0.382286	−	0.924044i	$-0.375137\pi$
$241$	44407.1			0.764573			0.382286	+	0.924044i	$0.375137\pi$
$242$	−28563.9	+	33418.1i	−0.487738	+	0.570625i
$243$	−3788.00			−0.0641500
$244$	−435.344	−	2762.34i	−0.00731228	−	0.0463977i
$245$	−59707.0	−	4126.14i	−0.994702	−	0.0687403i
$246$	−7907.19	+	9250.96i	−0.130663	+	0.152868i
$247$	−102235.			−1.67573
$248$	−47168.7	+	76774.3i	−0.766920	+	1.24828i
$249$	−48840.1			−0.787730
$250$	−49505.8	+	38150.0i	−0.792094	+	0.610400i
$251$		−	77178.0i		−	1.22503i	−0.790460	−	0.612514i	$-0.790158\pi$
$251$		−	77178.0i		−	1.22503i	0.790460	−	0.612514i	$-0.209842\pi$
$252$	178.248	+	1131.02i	0.00280688	+	0.0178101i
$253$			33729.4i			0.526948i
$254$	17203.5	−	20127.1i	0.266655	−	0.311971i
$255$	−92.0139	+	1331.48i	−0.00141505	+	0.0204765i
$256$	53137.4	−	38358.6i	0.810812	−	0.585306i
$257$			15226.9i			0.230540i	0.993334	+	0.115270i	$0.0367734\pi$
$257$			15226.9i			0.230540i	−0.993334	+	0.115270i	$0.963227\pi$
$258$	−13795.9	+	16140.4i	−0.207258	+	0.242480i
$259$			6135.03i			0.0914570i
$260$	84140.6	−	7365.69i	1.24468	−	0.108960i
$261$	25599.6			0.375797
$262$	−6435.16	−	5500.41i	−0.0937469	−	0.0801295i
$263$	−93637.0			−1.35374			−0.676871	−	0.736101i	$-0.736665\pi$
$263$	−93637.0			−1.35374			−0.676871	+	0.736101i	$0.736665\pi$
$264$	10518.0	−	17119.7i	0.150913	−	0.245634i
$265$	−6981.60	+	101027.i	−0.0994176	+	1.43862i
$266$	3901.85	+	3335.08i	0.0551452	+	0.0471349i
$267$	59799.4			0.838830
$268$	107.088	+	679.494i	0.00149098	+	0.00946054i
$269$	107774.			1.48939			0.744697	−	0.667403i	$-0.232594\pi$
$269$	107774.			1.48939			0.744697	+	0.667403i	$0.232594\pi$
$270$	9829.14	−	10010.9i	0.134830	−	0.137324i
$271$		−	9902.38i		−	0.134834i	−0.997725	−	0.0674172i	$-0.978524\pi$
$271$		−	9902.38i		−	0.134834i	0.997725	−	0.0674172i	$-0.0214759\pi$
$272$	808.945	+	2502.70i	0.0109341	+	0.0338276i
$273$			2908.02i			0.0390186i
$274$	−76964.6	−	65785.0i	−1.02516	−	0.876245i
$275$	−5194.39	+	37403.0i	−0.0686861	+	0.494586i
$276$	7225.45	+	45846.7i	0.0948520	+	0.601853i
$277$		−	117688.i		−	1.53382i	−0.641756	−	0.766909i	$-0.721794\pi$
$277$		−	117688.i		−	1.53382i	0.641756	−	0.766909i	$-0.278206\pi$
$278$	38355.8	+	32784.4i	0.496297	+	0.424206i
$279$			38013.7i			0.488350i
$280$	−3451.56	−	2463.70i	−0.0440250	−	0.0314248i
$281$	35905.0			0.454718			0.227359	−	0.973811i	$-0.426991\pi$
$281$	35905.0			0.454718			0.227359	+	0.973811i	$0.426991\pi$
$282$	12698.0	−	14855.9i	0.159675	−	0.186810i
$283$	109805.			1.37104			0.685519	−	0.728055i	$-0.259575\pi$
$283$	109805.			1.37104			0.685519	+	0.728055i	$0.259575\pi$
$284$	−68497.5	+	10795.2i	−0.849255	+	0.133843i
$285$	4336.11	−	62745.5i	0.0533840	−	0.772490i
$286$	33157.2	−	38792.0i	0.405364	−	0.474253i
$287$	1551.86			0.0188404
$288$	10629.3	−	25523.1i	0.128150	−	0.307715i
$289$	83415.4			0.998736
$290$	−66426.3	+	67654.6i	−0.789849	+	0.804454i
$291$			71469.0i			0.843979i
$292$	50986.4	−	8035.46i	0.597983	−	0.0942422i
$293$			55977.1i			0.652041i	0.945363	+	0.326021i	$0.105708\pi$
$293$			55977.1i			0.652041i	−0.945363	+	0.326021i	$0.894292\pi$
$294$	−32329.6	+	37823.8i	−0.374029	+	0.437593i
$295$	4448.93	−	64378.0i	0.0511225	−	0.739765i
$296$	77550.0	−	126225.i	0.885112	−	1.44066i
$297$		−	8476.58i		−	0.0960966i
$298$	32571.5	−	38106.8i	0.366780	−	0.429112i
$299$			117879.i			1.31854i
$300$	951.930	+	51952.8i	0.0105770	+	0.577253i
$301$	2707.58			0.0298847
$302$	−104745.	−	89529.8i	−1.14847	−	0.981644i
$303$	−60573.1			−0.659773
$304$	−38121.2	−	117939.i	−0.412495	−	1.27617i
$305$	4359.03	+	301.237i	0.0468586	+	0.00323823i
$306$	843.480	+	720.959i	0.00900808	+	0.00769959i
$307$	6404.55			0.0679535			0.0339767	−	0.999423i	$-0.489183\pi$
$307$	6404.55			0.0679535			0.0339767	+	0.999423i	$0.489183\pi$
$308$	−2530.93	+	398.874i	−0.0266795	+	0.00420470i
$309$	98353.5			1.03008
$310$	−100462.	−	98638.4i	−1.04539	−	1.02641i
$311$			67299.9i			0.695815i	0.937529	+	0.347908i	$0.113108\pi$
$311$			67299.9i			0.695815i	−0.937529	+	0.347908i	$0.886892\pi$
$312$	36758.9	−	59830.8i	0.377619	−	0.614633i
$313$		−	36884.5i		−	0.376492i	−0.982122	−	0.188246i	$-0.939720\pi$
$313$		−	36884.5i		−	0.376492i	0.982122	−	0.188246i	$-0.0602802\pi$
$314$	−58884.1	−	50330.7i	−0.597226	−	0.510474i
$315$	−1784.77	−	123.339i	−0.0179871	−	0.00124302i
$316$	−172113.	+	27125.0i	−1.72361	+	0.271642i
$317$		−	54907.8i		−	0.546406i	−0.961956	−	0.273203i	$-0.911917\pi$
$317$		−	54907.8i		−	0.546406i	0.961956	−	0.273203i	$-0.0880831\pi$
$318$	63999.5	+	54703.1i	0.632881	+	0.540951i
$319$			57285.6i			0.562942i
$320$	39871.4	+	94318.8i	0.389369	+	0.921082i
$321$	−71102.7			−0.690043
$322$	3845.43	−	4498.93i	0.0370880	−	0.0433908i
$323$	4974.42			0.0476802
$324$	−1815.83	−	11521.8i	−0.0172976	−	0.109756i
$325$	−18153.6	+	130718.i	−0.171868	+	1.23757i
$326$	−81017.8	+	94786.2i	−0.762334	+	0.891887i
$327$	27462.3			0.256827
$328$	−31928.7	−	19616.4i	−0.296779	−	0.182335i
$329$	−2492.10			−0.0230237
$330$	22401.9	+	21995.2i	0.205710	+	0.201976i
$331$		−	75583.2i		−	0.689873i	−0.938626	−	0.344937i	$-0.887900\pi$
$331$		−	75583.2i		−	0.689873i	0.938626	−	0.344937i	$-0.112100\pi$
$332$	−23412.3	−	148555.i	−0.212406	−	1.34775i
$333$		−	62498.3i		−	0.563611i
$334$	98812.6	−	115605.i	0.885767	−	1.03630i
$335$	−1072.26	−	74.0998i	−0.00955453	−	0.000660279i
$336$	−3354.72	+	1084.34i	−0.0297151	+	0.00960476i
$337$		−	194706.i		−	1.71443i	−0.514958	−	0.857215i	$-0.672192\pi$
$337$		−	194706.i		−	1.71443i	0.514958	−	0.857215i	$-0.327808\pi$
$338$	41650.4	−	48728.6i	0.364574	−	0.426531i
$339$			16986.4i			0.147809i
$340$	−4094.02	+	358.391i	−0.0354154	+	0.00310027i
$341$	−85065.1			−0.731547
$342$	−39748.6	−	33974.9i	−0.339837	−	0.290473i
$343$	12708.6			0.108022
$344$	−55706.9	−	34225.3i	−0.470752	−	0.289221i
$345$	−72347.1	−	4999.65i	−0.607831	−	0.0420050i
$346$	75628.7	+	64643.1i	0.631734	+	0.539970i
$347$	177898.			1.47745			0.738723	−	0.674009i	$-0.235429\pi$
$347$	177898.			1.47745			0.738723	+	0.674009i	$0.235429\pi$
$348$	12271.6	+	77865.4i	0.101331	+	0.642963i
$349$	45321.5			0.372094			0.186047	−	0.982541i	$-0.440432\pi$
$349$	45321.5			0.372094			0.186047	+	0.982541i	$0.440432\pi$
$350$	4957.10	−	4396.73i	0.0404661	−	0.0358917i
$351$		−	29624.4i		−	0.240455i
$352$	57114.4	+	23785.7i	0.460957	+	0.191968i
$353$			26069.4i			0.209210i	0.994514	+	0.104605i	$0.0333578\pi$
$353$			26069.4i			0.209210i	−0.994514	+	0.104605i	$0.966642\pi$
$354$	−40782.8	−	34858.8i	−0.325440	−	0.278168i
$355$	7469.75	−	108091.i	0.0592720	−	0.857691i
$356$	28665.8	+	181889.i	0.226185	+	1.43518i
$357$		−	141.495i		−	0.00111021i
$358$	131199.	+	112142.i	1.02368	+	0.874986i
$359$		−	122084.i		−	0.947261i	−0.880724	−	0.473630i	$-0.842943\pi$
$359$		−	122084.i		−	0.947261i	0.880724	−	0.473630i	$-0.157057\pi$
$360$	35161.5	+	25098.0i	0.271308	+	0.193658i
$361$	−104097.			−0.798771
$362$	82165.5	−	96129.0i	0.627007	−	0.733563i
$363$	−57108.4			−0.433398
$364$	−8845.21	+	1394.00i	−0.0667583	+	0.0105211i
$365$	−5560.14	+	80457.7i	−0.0417350	+	0.603923i
$366$	2360.29	−	2761.40i	0.0176199	−	0.0206142i
$367$	−246969.			−1.83362			−0.916812	−	0.399320i	$-0.869246\pi$
$367$	−246969.			−1.83362			−0.916812	+	0.399320i	$0.869246\pi$
$368$	−135986.	+	43954.7i	−1.00415	+	0.324571i
$369$	−15809.0			−0.116105
$370$	165170.	+	162171.i	1.20650	+	1.18460i
$371$		−	10736.0i		−	0.0780002i
$372$	−115625.	+	18222.4i	−0.835535	+	0.131680i
$373$			3424.66i			0.0246150i	0.999924	+	0.0123075i	$0.00391770\pi$
$373$			3424.66i			0.0246150i	−0.999924	+	0.0123075i	$0.996082\pi$
$374$	−1613.32	+	1887.50i	−0.0115340	+	0.0134941i
$375$	−79456.8	−	16685.8i	−0.565026	−	0.118654i
$376$	51273.6	+	31501.5i	0.362676	+	0.222821i
$377$			200204.i			1.40861i
$378$	−966.400	+	1130.63i	−0.00676353	+	0.00791294i
$379$			108649.i			0.756392i	0.925726	+	0.378196i	$0.123455\pi$
$379$			108649.i			0.756392i	−0.925726	+	0.378196i	$0.876545\pi$
$380$	192929.	−	16889.0i	1.33607	−	0.116960i
$381$	34395.3			0.236946
$382$	185486.	+	158543.i	1.27112	+	1.08648i
$383$	127491.			0.869127			0.434563	−	0.900641i	$-0.356903\pi$
$383$	127491.			0.869127			0.434563	+	0.900641i	$0.356903\pi$
$384$	82728.0	+	20095.7i	0.561035	+	0.136283i
$385$	276.001	−	3993.86i	0.00186204	−	0.0269446i
$386$	−47713.6	−	40782.8i	−0.320234	−	0.273718i
$387$	−27582.5			−0.184167
$388$	−217384.	+	34259.8i	−1.44399	+	0.227573i
$389$	48642.8			0.321454			0.160727	−	0.986999i	$-0.448616\pi$
$389$	48642.8			0.321454			0.160727	+	0.986999i	$0.448616\pi$
$390$	78291.1	+	76869.7i	0.514734	+	0.505389i
$391$		−	5735.64i		−	0.0375170i
$392$	−130545.	−	80204.2i	−0.849547	−	0.521945i
$393$		−	10997.1i		−	0.0712021i
$394$	49768.4	+	42539.1i	0.320598	+	0.274029i
$395$	18769.2	−	271598.i	0.120296	−	1.74074i
$396$	25782.9	−	4063.38i	0.164415	−	0.0259118i
$397$		−	84741.5i		−	0.537669i	−0.963186	−	0.268835i	$-0.913362\pi$
$397$		−	84741.5i		−	0.537669i	0.963186	−	0.268835i	$-0.0866385\pi$
$398$	58451.9	+	49961.3i	0.369005	+	0.315404i
$399$			6667.90i			0.0418835i
$400$	−157566.	+	27799.8i	−0.984790	+	0.173749i
$401$	−91175.1			−0.567006			−0.283503	−	0.958971i	$-0.591497\pi$
$401$	−91175.1			−0.567006			−0.283503	+	0.958971i	$0.591497\pi$
$402$	−580.596	+	679.264i	−0.00359271	+	0.00420326i
$403$	−297289.			−1.83050
$404$	−29036.7	−	184243.i	−0.177903	−	1.12883i
$405$	18181.6	+	1256.47i	0.110847	+	0.00766022i
$406$	6531.02	−	7640.92i	0.0396213	−	0.0463547i
$407$	139855.			0.844288
$408$	−1788.58	+	2911.18i	−0.0107445	+	0.0174884i
$409$	71290.8			0.426174			0.213087	−	0.977033i	$-0.431648\pi$
$409$	71290.8			0.426174			0.213087	+	0.977033i	$0.431648\pi$
$410$	41021.5	−	41780.0i	0.244030	−	0.248542i
$411$		−	131525.i		−	0.778621i
$412$	47147.3	+	299158.i	0.277755	+	1.76241i
$413$			6841.39i			0.0401092i
$414$	−39173.9	+	45831.2i	−0.228558	+	0.267399i
$415$	234423.	+	16200.1i	1.36114	+	0.0940637i
$416$	199606.	+	83127.3i	1.15342	+	0.480349i
$417$			65546.5i			0.376945i
$418$	76027.2	−	88947.5i	0.435127	−	0.509074i
$419$			99550.7i			0.567043i	0.958966	+	0.283522i	$0.0915028\pi$
$419$			99550.7i			0.567043i	−0.958966	+	0.283522i	$0.908497\pi$
$420$	−480.401	−	5487.78i	−0.00272336	−	0.0311098i
$421$	−207357.			−1.16992			−0.584959	−	0.811063i	$-0.698889\pi$
$421$	−207357.			−1.16992			−0.584959	+	0.811063i	$0.698889\pi$
$422$	−79526.1	−	67974.4i	−0.446565	−	0.381698i
$423$	25387.4			0.141885
$424$	−135709.	+	220887.i	−0.754878	+	1.22868i
$425$	883.297	−	6360.33i	0.00489023	−	0.0352129i
$426$	−68474.3	−	58527.9i	−0.377319	−	0.322510i
$427$	−463.229			−0.00254062
$428$	−34084.2	−	216270.i	−0.186065	−	1.18062i
$429$	66291.9			0.360202
$430$	71571.4	−	72894.8i	0.387082	−	0.394239i
$431$		−	100582.i		−	0.541458i	−0.962656	−	0.270729i	$-0.912735\pi$
$431$		−	100582.i		−	0.541458i	0.962656	−	0.270729i	$-0.0872647\pi$
$432$	34174.9	−	11046.3i	0.183122	−	0.0591901i
$433$			233144.i			1.24351i	0.783213	+	0.621754i	$0.213579\pi$
$433$			233144.i			1.24351i	−0.783213	+	0.621754i	$0.786421\pi$
$434$	11346.2	+	9698.11i	0.0602383	+	0.0514882i
$435$	−122873.	−	8491.33i	−0.649350	−	0.0448743i
$436$	13164.5	+	83530.9i	0.0692517	+	0.439414i
$437$			270289.i			1.41536i
$438$	50969.2	+	43565.5i	0.265680	+	0.227088i
$439$			116975.i			0.606965i	0.952837	+	0.303482i	$0.0981494\pi$
$439$			116975.i			0.606965i	−0.952837	+	0.303482i	$0.901851\pi$
$440$	−56163.1	+	78682.5i	−0.290099	+	0.406418i
$441$	−64637.3			−0.332358
$442$	−5638.32	+	6596.52i	−0.0288606	+	0.0337653i
$443$	190.440			0.000970400			0.000485200	−	1.00000i	$-0.499846\pi$
$443$	190.440			0.000970400			0.000485200		1.00000i	$0.499846\pi$
$444$	190098.	−	29959.5i	0.964301	−	0.151974i
$445$	−287025.	−	19835.3i	−1.44944	−	0.100166i
$446$	−74966.4	+	87706.4i	−0.376875	+	0.440922i
$447$	65121.0			0.325916
$448$	−4906.33	−	9684.11i	−0.0244456	−	0.0482507i
$449$	−87156.7			−0.432323			−0.216161	−	0.976358i	$-0.569354\pi$
$449$	−87156.7			−0.432323			−0.216161	+	0.976358i	$0.569354\pi$
$450$	−50498.6	+	44790.0i	−0.249376	+	0.221185i
$451$		−	35376.6i		−	0.173925i
$452$	−51666.8	+	8142.70i	−0.252892	+	0.0398558i
$453$		−	178999.i		−	0.872277i
$454$	−106552.	+	124660.i	−0.516951	+	0.604803i
$455$	964.582	−	13957.9i	0.00465926	−	0.0674215i
$456$	84285.8	−	137188.i	0.405345	−	0.659762i
$457$		−	285563.i		−	1.36732i	−0.729801	−	0.683659i	$-0.760387\pi$
$457$		−	285563.i		−	1.36732i	0.729801	−	0.683659i	$-0.239613\pi$
$458$	37990.1	−	44446.2i	0.181109	−	0.211887i
$459$			1441.43i			0.00684176i
$460$	−19473.5	−	222452.i	−0.0920297	−	1.05129i
$461$	144089.			0.677999			0.339000	−	0.940786i	$-0.389911\pi$
$461$	144089.			0.677999			0.339000	+	0.940786i	$0.389911\pi$
$462$	−2530.07	−	2162.56i	−0.0118536	−	0.0101317i
$463$	262762.			1.22575			0.612873	−	0.790182i	$-0.290014\pi$
$463$	262762.			1.22575			0.612873	+	0.790182i	$0.290014\pi$
$464$	−230957.	+	74652.0i	−1.07274	+	0.346741i
$465$	12609.0	−	182458.i	0.0583144	−	0.843835i
$466$	95670.8	+	81773.9i	0.440563	+	0.376568i
$467$	−188963.			−0.866451			−0.433225	−	0.901286i	$-0.642625\pi$
$467$	−188963.			−0.866451			−0.433225	+	0.901286i	$0.642625\pi$
$468$	90107.2	−	14200.9i	0.411403	−	0.0648372i
$469$	113.948			0.000518036
$470$	−65875.5	+	67093.6i	−0.298214	+	0.303728i
$471$		−	100627.i		−	0.453601i
$472$	86478.8	−	140758.i	0.388173	−	0.631812i
$473$		−	61722.6i		−	0.275881i
$474$	−172055.	−	147063.i	−0.765791	−	0.654554i
$475$	−41625.0	+	299728.i	−0.184488	+	1.32843i
$476$	430.380	−	67.8280i	0.00189950	−	0.000299361i
$477$			109369.i			0.480682i
$478$	−286157.	−	244591.i	−1.25242	−	1.07049i
$479$		−	55530.6i		−	0.242026i	−0.992651	−	0.121013i	$-0.961386\pi$
$479$		−	55530.6i		−	0.242026i	0.992651	−	0.121013i	$-0.0386142\pi$
$480$	−59484.4	+	118980.i	−0.258179	+	0.516408i
$481$	488773.			2.11260
$482$	−115412.	+	135026.i	−0.496773	+	0.581196i
$483$	7688.26			0.0329559
$484$	−27375.8	−	173704.i	−0.116863	−	0.741515i
$485$	23706.1	−	343037.i	0.100780	−	1.45834i
$486$	9844.83	−	11517.9i	0.0416808	−	0.0487641i
$487$	−48466.0			−0.204352			−0.102176	−	0.994766i	$-0.532581\pi$
$487$	−48466.0			−0.204352			−0.102176	+	0.994766i	$0.532581\pi$
$488$	9530.68	+	5855.47i	0.0400207	+	0.0245879i
$489$	−161981.			−0.677401
$490$	167722.	−	170823.i	0.698550	−	0.711467i
$491$			343043.i			1.42294i	0.702718	+	0.711469i	$0.251970\pi$
$491$			343043.i			1.42294i	−0.702718	+	0.711469i	$0.748030\pi$
$492$	−7578.30	−	48085.7i	−0.0313070	−	0.198649i
$493$		−	9741.32i		−	0.0400797i
$494$	265704.	−	310858.i	1.08879	−	1.27382i
$495$	−2811.66	+	40685.9i	−0.0114750	+	0.166048i
$496$	−110853.	−	342956.i	−0.450592	−	1.39404i
$497$			11486.7i			0.0465031i
$498$	126933.	−	148505.i	0.511819	−	0.598799i
$499$			79996.1i			0.321268i	0.987014	+	0.160634i	$0.0513539\pi$
$499$			79996.1i			0.321268i	−0.987014	+	0.160634i	$0.948646\pi$
$500$	12663.5	−	249679.i	0.0506541	−	0.998716i
$501$	197558.			0.787082
$502$	234670.	+	200582.i	0.931214	+	0.795948i
$503$	195747.			0.773677			0.386839	−	0.922147i	$-0.373567\pi$
$503$	195747.			0.773677			0.386839	+	0.922147i	$0.373567\pi$
$504$	−3902.26	−	2397.47i	−0.0153622	−	0.00943827i
$505$	290739.	+	20091.9i	1.14004	+	0.0787842i
$506$	−102559.	−	87661.3i	−0.400564	−	0.342379i
$507$	83272.7			0.323956
$508$	16487.9	+	104619.i	0.0638909	+	0.405399i
$509$	208878.			0.806228			0.403114	−	0.915150i	$-0.367928\pi$
$509$	208878.			0.806228			0.403114	+	0.915150i	$0.367928\pi$
$510$	−3809.40	−	3740.24i	−0.0146459	−	0.0143800i
$511$		−	8550.16i		−	0.0327441i
$512$	−21467.4	+	261264.i	−0.0818918	+	0.996641i
$513$		−	67926.7i		−	0.258111i
$514$	−46299.5	−	39574.2i	−0.175247	−	0.149791i
$515$	−472078.	−	32623.6i	−1.77991	−	0.123003i
$516$	−13222.1	−	83896.5i	−0.0496593	−	0.315097i
$517$			56810.6i			0.212544i
$518$	−18654.3	−	15944.7i	−0.0695217	−	0.0594232i
$519$			129242.i			0.479811i
$520$	−196281.	+	274983.i	−0.725893	+	1.01695i
$521$	52929.8			0.194996			0.0974978	−	0.995236i	$-0.468916\pi$
$521$	52929.8			0.194996			0.0974978	+	0.995236i	$0.468916\pi$
$522$	−66532.3	+	77839.0i	−0.244170	+	0.285665i
$523$	113860.			0.416262			0.208131	−	0.978101i	$-0.433262\pi$
$523$	113860.			0.416262			0.208131	+	0.978101i	$0.433262\pi$
$524$	33449.4	−	5271.63i	0.121822	−	0.0191992i
$525$	8525.62	+	1184.00i	0.0309320	+	0.00429571i
$526$	243358.	−	284715.i	0.879579	−	1.02906i
$527$	14465.2			0.0520838
$528$	24718.8	+	76474.9i	0.0886667	+	0.274316i
$529$	31809.6			0.113670
$530$	−289040.	−	283793.i	−1.02898	−	1.01030i
$531$		−	69694.1i		−	0.247176i
$532$	−20281.5	+	3196.36i	−0.0716599	+	0.0112936i
$533$		−	123636.i		−	0.435201i
$534$	−155416.	+	181828.i	−0.545021	+	0.637643i
$535$	341279.	+	23584.6i	1.19235	+	0.0823987i
$536$	−2344.41	−	1440.36i	−0.00816025	−	0.00501350i
$537$			224208.i			0.777502i
$538$	−280100.	+	327701.i	−0.967717	+	1.13217i
$539$		−	144642.i		−	0.497871i
$540$	4893.91	+	55904.6i	0.0167829	+	0.191717i
$541$	−193393.			−0.660764			−0.330382	−	0.943847i	$-0.607178\pi$
$541$	−193393.			−0.660764			−0.330382	+	0.943847i	$0.607178\pi$
$542$	30109.5	+	25735.8i	0.102495	+	0.0876072i
$543$	164275.			0.557151
$544$	−9712.21	−	4044.71i	−0.0328186	−	0.0136675i
$545$	−131814.	−	9109.16i	−0.443779	−	0.0306680i
$546$	−8842.21	−	7557.82i	−0.0296603	−	0.0253519i
$547$	−408928.			−1.36670			−0.683349	−	0.730092i	$-0.739477\pi$
$547$	−408928.			−1.36670			−0.683349	+	0.730092i	$0.739477\pi$
$548$	400055.	−	63048.7i	1.33217	−	0.209950i
$549$	4718.98			0.0156568
$550$	−100229.	−	113003.i	−0.331335	−	0.373564i
$551$			459056.i			1.51204i
$552$	−158182.	−	97183.7i	−0.519132	−	0.318945i
$553$			28862.5i			0.0943808i
$554$	357847.	+	305867.i	1.16594	+	0.996582i
$555$	−20730.5	+	299979.i	−0.0673014	+	0.973880i
$556$	−199370.	+	31420.8i	−0.644927	+	0.101641i
$557$			208237.i			0.671192i	0.942006	+	0.335596i	$0.108938\pi$
$557$			208237.i			0.671192i	−0.942006	+	0.335596i	$0.891062\pi$
$558$	−115586.	−	98795.9i	−0.371223	−	0.317300i
$559$		−	215711.i		−	0.690318i
$560$	16461.7	−	4091.87i	0.0524925	−	0.0130480i
$561$	−3225.56			−0.0102489
$562$	−93315.5	+	109174.i	−0.295448	+	0.345657i
$563$	−436386.			−1.37675			−0.688373	−	0.725357i	$-0.741675\pi$
$563$	−436386.			−1.37675			−0.688373	+	0.725357i	$0.741675\pi$
$564$	12169.8	+	77219.7i	0.0382584	+	0.242756i
$565$	5634.34	−	81531.4i	0.0176501	−	0.255404i
$566$	−285378.	+	333876.i	−0.890817	+	1.04220i
$567$	−1932.15			−0.00600999
$568$	145198.	−	236332.i	0.450052	−	0.732530i
$569$	−88780.6			−0.274216			−0.137108	−	0.990556i	$-0.543781\pi$
$569$	−88780.6			−0.274216			−0.137108	+	0.990556i	$0.543781\pi$
$570$	179516.	+	176257.i	0.552528	+	0.542497i
$571$		−	202677.i		−	0.621630i	−0.950470	−	0.310815i	$-0.899398\pi$
$571$		−	202677.i		−	0.621630i	0.950470	−	0.310815i	$-0.100602\pi$
$572$	31778.0	+	201637.i	0.0971259	+	0.616281i
$573$			316979.i			0.965430i
$574$	−4033.22	+	4718.64i	−0.0122413	+	0.0143217i
$575$	345594.	+	47994.7i	1.04527	+	0.145164i
$576$	49981.4	+	98653.2i	0.150648	+	0.297349i
$577$			438405.i			1.31681i	0.752663	+	0.658406i	$0.228769\pi$
$577$			438405.i			1.31681i	−0.752663	+	0.658406i	$0.771231\pi$
$578$	−216793.	+	253635.i	−0.648918	+	0.759197i
$579$		−	81538.1i		−	0.243222i
$580$	−33073.5	−	377809.i	−0.0983160	−	1.12309i
$581$	−24911.9			−0.0737997
$582$	−217311.	−	185745.i	−0.641557	−	0.548366i
$583$	−244741.			−0.720061
$584$	−108079.	+	175915.i	−0.316894	+	0.515794i
$585$	−9826.32	+	142191.i	−0.0287130	+	0.415490i
$586$	−170206.	−	145482.i	−0.495654	−	0.423657i
$587$	358519.			1.04049			0.520243	−	0.854018i	$-0.325841\pi$
$587$	358519.			1.04049			0.520243	+	0.854018i	$0.325841\pi$
$588$	−30984.9	−	196605.i	−0.0896181	−	0.568643i
$589$	−681665.			−1.96490
$590$	184187.	+	180843.i	0.529121	+	0.519515i
$591$			85049.5i			0.243499i
$592$	182253.	+	563853.i	0.520034	+	1.60888i
$593$		−	231043.i		−	0.657028i	−0.944499	−	0.328514i	$-0.893452\pi$
$593$		−	231043.i		−	0.657028i	0.944499	−	0.328514i	$-0.106548\pi$
$594$	25774.1	+	22030.3i	0.0730485	+	0.0624377i
$595$	−46.9336	+	679.150i	−0.000132571	+	0.00191837i
$596$	31216.8	+	198076.i	0.0878811	+	0.557621i
$597$			99888.8i			0.280264i
$598$	−358427.	−	306363.i	−1.00230	−	0.856710i
$599$		−	214270.i		−	0.597183i	−0.954381	−	0.298592i	$-0.903483\pi$
$599$		−	214270.i		−	0.597183i	0.954381	−	0.298592i	$-0.0965168\pi$
$600$	−160443.	−	132129.i	−0.445676	−	0.367024i
$601$	332989.			0.921895			0.460948	−	0.887427i	$-0.347510\pi$
$601$	332989.			0.921895			0.460948	+	0.887427i	$0.347510\pi$
$602$	−7036.89	+	8232.75i	−0.0194172	+	0.0227171i
$603$	−1160.80			−0.00319244
$604$	544454.	−	85806.0i	1.49241	−	0.235204i
$605$	274109.	+	18942.7i	0.748881	+	0.0517525i
$606$	157427.	−	184180.i	0.428680	−	0.501531i
$607$	285723.			0.775476			0.387738	−	0.921770i	$-0.373257\pi$
$607$	285723.			0.775476			0.387738	+	0.921770i	$0.373257\pi$
$608$	457684.	+	190605.i	1.23811	+	0.515618i
$609$	13057.6			0.0352071
$610$	−12244.9	+	12471.3i	−0.0329075	+	0.0335159i
$611$			198544.i			0.531833i
$612$	−4384.34	+	690.972i	−0.0117058	+	0.00184483i
$613$			458192.i			1.21935i	0.792653	+	0.609673i	$0.208699\pi$
$613$			458192.i			1.21935i	−0.792653	+	0.609673i	$0.791301\pi$
$614$	−16645.1	+	19473.9i	−0.0441520	+	0.0516553i
$615$	75880.2	+	5243.81i	0.200622	+	0.0138643i
$616$	5364.94	−	8732.27i	0.0141385	−	0.0230126i
$617$		−	479086.i		−	1.25847i	−0.777215	−	0.629235i	$-0.783368\pi$
$617$		−	479086.i		−	1.25847i	0.777215	−	0.629235i	$-0.216632\pi$
$618$	−255616.	+	299057.i	−0.669286	+	0.783026i
$619$		−	656092.i		−	1.71231i	−0.516716	−	0.856157i	$-0.672846\pi$
$619$		−	656092.i		−	1.71231i	0.516716	−	0.856157i	$-0.327154\pi$
$620$	561020.	−	49111.8i	1.45947	−	0.127762i
$621$	−78321.2			−0.203094
$622$	−204634.	−	174910.i	−0.528929	−	0.452098i
$623$	30501.9			0.0785870
$624$	86388.6	+	267268.i	0.221864	+	0.686401i
$625$	375842.	+	106444.i	0.962157	+	0.272497i
$626$	112152.	+	95861.3i	0.286193	+	0.244621i
$627$	152003.			0.386649
$628$	306074.	−	48237.3i	0.776082	−	0.122311i
$629$	−23782.2			−0.0601105
$630$	5013.56	−	5106.26i	0.0126318	−	0.0128654i
$631$		−	397661.i		−	0.998744i	−0.866388	−	0.499372i	$-0.833564\pi$
$631$		−	397661.i		−	0.998744i	0.866388	−	0.499372i	$-0.166436\pi$
$632$	364837.	−	593829.i	0.913409	−	1.48671i
$633$		−	135903.i		−	0.339173i
$634$	166954.	+	142703.i	0.415355	+	0.355021i
$635$	−165091.	−	11408.8i	−0.409426	−	0.0282940i
$636$	−332664.	+	52427.8i	−0.822415	+	0.129613i
$637$		−	505502.i		−	1.24579i
$638$	−174184.	−	148883.i	−0.427925	−	0.365766i
$639$		−	117016.i		−	0.286579i
$640$	−390412.	−	123896.i	−0.953155	−	0.302481i
$641$	−708644.			−1.72469			−0.862347	−	0.506318i	$-0.831006\pi$
$641$	−708644.			−1.72469			−0.862347	+	0.506318i	$0.831006\pi$
$642$	184793.	−	216197.i	0.448348	−	0.524541i
$643$	−280134.			−0.677553			−0.338777	−	0.940867i	$-0.610013\pi$
$643$	−280134.			−0.677553			−0.338777	+	0.940867i	$0.610013\pi$
$644$	3685.49	+	23385.1i	0.00888635	+	0.0563854i
$645$	132390.	+	9149.03i	0.318227	+	0.0219915i
$646$	−12928.3	+	15125.4i	−0.0309797	+	0.0362444i
$647$	−731125.			−1.74656			−0.873279	−	0.487220i	$-0.838011\pi$
$647$	−731125.			−1.74656			−0.873279	+	0.487220i	$0.838011\pi$
$648$	39752.8	+	24423.3i	0.0946711	+	0.0581641i
$649$	155958.			0.370269
$650$	−350284.	−	394928.i	−0.829076	−	0.934742i
$651$			19389.7i			0.0457518i
$652$	−77648.0	−	492690.i	−0.182656	−	1.15899i
$653$		−	616800.i		−	1.44650i	−0.690588	−	0.723249i	$-0.742648\pi$
$653$		−	616800.i		−	1.44650i	0.690588	−	0.723249i	$-0.257352\pi$
$654$	−71373.3	+	83502.6i	−0.166871	+	0.195229i
$655$	−3647.71	+	52783.9i	−0.00850232	+	0.123032i
$656$	142627.	−	46101.2i	0.331433	−	0.107128i
$657$			87101.6i			0.201788i
$658$	6476.87	−	7577.57i	0.0149594	−	0.0175016i
$659$		−	511326.i		−	1.17741i	−0.808349	−	0.588704i	$-0.799638\pi$
$659$		−	511326.i		−	1.17741i	0.808349	−	0.588704i	$-0.200362\pi$
$660$	−125101.	+	10951.3i	−0.287191	+	0.0251408i
$661$	−408260.			−0.934402			−0.467201	−	0.884151i	$-0.654738\pi$
$661$	−408260.			−0.934402			−0.467201	+	0.884151i	$0.654738\pi$
$662$	229820.	+	196437.i	0.524412	+	0.448237i
$663$	−11272.8			−0.0256452
$664$	512548.	+	314900.i	1.16251	+	0.714226i
$665$	2211.72	−	32004.6i	0.00500136	−	0.0723718i
$666$	190034.	+	162430.i	0.428433	+	0.366200i
$667$	529303.			1.18974
$668$	94702.6	+	600905.i	0.212231	+	1.34664i
$669$	−149882.			−0.334886
$670$	3012.06	−	3067.75i	0.00670986	−	0.00683393i
$671$			10559.9i			0.0234538i
$672$	5421.68	−	13018.6i	0.0120059	−	0.0288287i
$673$		−	582899.i		−	1.28695i	−0.765465	−	0.643477i	$-0.777491\pi$
$673$		−	582899.i		−	1.28695i	0.765465	−	0.643477i	$-0.222509\pi$
$674$	592029.	+	506033.i	1.30324	+	1.11393i
$675$	−86851.5	−	12061.6i	−0.190621	−	0.0264726i
$676$	39918.0	+	253287.i	0.0873526	+	0.554268i
$677$		−	361560.i		−	0.788865i	−0.918925	−	0.394432i	$-0.870941\pi$
$677$		−	361560.i		−	0.788865i	0.918925	−	0.394432i	$-0.129059\pi$
$678$	−51649.4	−	44146.9i	−0.112358	−	0.0960375i
$679$			36454.2i			0.0790694i
$680$	9550.44	−	13379.8i	0.0206541	−	0.0289356i
$681$	−213032.			−0.459357
$682$	221080.	−	258651.i	0.475315	−	0.556091i
$683$	−247403.			−0.530351			−0.265175	−	0.964200i	$-0.585430\pi$
$683$	−247403.			−0.530351			−0.265175	+	0.964200i	$0.585430\pi$
$684$	206610.	−	32561.7i	0.441610	−	0.0695978i
$685$	−43626.6	+	631296.i	−0.0929759	+	1.34540i
$686$	−33029.2	+	38642.2i	−0.0701858	+	0.0821134i
$687$	75954.4			0.160931
$688$	248846.	−	80434.2i	0.525720	−	0.169928i
$689$	−855331.			−1.80176
$690$	203229.	−	206987.i	0.426862	−	0.434755i
$691$			503070.i			1.05359i	0.849992	+	0.526796i	$0.176607\pi$
$691$			503070.i			1.05359i	−0.849992	+	0.526796i	$0.823393\pi$
$692$	−393111.	+	61954.4i	−0.820925	+	0.129378i
$693$		−	4323.66i		−	0.00900295i
$694$	−462349.	+	540921.i	−0.959954	+	1.12309i
$695$	21741.6	−	314611.i	0.0450113	−	0.651334i
$696$	−268653.	−	165055.i	−0.554592	−	0.340731i
$697$			6015.74i			0.0123829i
$698$	−117788.	+	137806.i	−0.241764	+	0.282850i
$699$			163493.i			0.334614i
$700$	485.551	+	26499.6i	0.000990921	+	0.0540808i
$701$	540117.			1.09914			0.549569	−	0.835449i	$-0.314792\pi$
$701$	540117.			1.09914			0.549569	+	0.835449i	$0.314792\pi$
$702$	90076.7	+	76992.4i	0.182784	+	0.156233i
$703$	1.12073e6			2.26772
$704$	−220761.	+	111846.i	−0.445428	+	0.225670i
$705$	−121854.	−	8420.92i	−0.245168	−	0.0169427i
$706$	−79267.4	−	67753.3i	−0.159032	−	0.135932i
$707$	−30896.6			−0.0618118
$708$	211986.	−	33408.9i	0.422902	−	0.0666494i
$709$	−395917.			−0.787611			−0.393805	−	0.919194i	$-0.628842\pi$
$709$	−395917.			−0.787611			−0.393805	+	0.919194i	$0.628842\pi$
$710$	309250.	+	303635.i	0.613469	+	0.602331i
$711$		−	294026.i		−	0.581629i
$712$	−627559.	−	385560.i	−1.23793	−	0.760558i
$713$			785977.i			1.54608i
$714$	430.235	+	367.740i	0.000843935	+	0.000721347i
$715$	−318188.	−	21988.8i	−0.622403	−	0.0430120i
$716$	−681963.	+	107477.i	−1.33025	+	0.209648i
$717$		−	489016.i		−	0.951228i
$718$	371212.	+	317291.i	0.720067	+	0.615472i
$719$			6357.52i			0.0122979i	0.999981	+	0.00614893i	$0.00195728\pi$
$719$			6357.52i			0.0122979i	−0.999981	+	0.00614893i	$0.998043\pi$
$720$	−167697.	+	41684.4i	−0.323489	+	0.0804096i
$721$	50167.2			0.0965050
$722$	270542.	−	316519.i	0.518992	−	0.607191i
$723$	−230746.			−0.441426
$724$	78748.0	+	499670.i	0.150232	+	0.953248i
$725$	586951.	+	81513.5i	1.11667	+	0.155079i
$726$	148422.	−	173646.i	0.281595	−	0.329451i
$727$	−683827.			−1.29383			−0.646915	−	0.762562i	$-0.723941\pi$
$727$	−683827.			−1.29383			−0.646915	+	0.762562i	$0.723941\pi$
$728$	18749.6	−	30518.0i	0.0353778	−	0.0575828i
$729$	19683.0			0.0370370
$730$	−230192.	−	226012.i	−0.431960	−	0.424118i
$731$			10495.8i			0.0196418i
$732$	2262.11	+	14353.5i	0.00422175	+	0.0267877i
$733$			162373.i			0.302209i	0.988518	+	0.151104i	$0.0482829\pi$
$733$			162373.i			0.302209i	−0.988518	+	0.151104i	$0.951717\pi$
$734$	641861.	−	750941.i	1.19138	−	1.39384i
$735$	310247.	+	21440.0i	0.574291	+	0.0396872i
$736$	219773.	−	527721.i	0.405713	−	0.974201i
$737$		−	2597.58i		−	0.00478226i
$738$	41086.9	−	48069.4i	0.0754382	−	0.0882583i
$739$			158473.i			0.290179i	0.989419	+	0.145090i	$0.0463470\pi$
$739$			158473.i			0.290179i	−0.989419	+	0.145090i	$0.953653\pi$
$740$	−922373.	+	80744.7i	−1.68439	+	0.147452i
$741$	531227.			0.967484
$742$	32644.3	+	27902.4i	0.0592924	+	0.0506797i
$743$	−200611.			−0.363394			−0.181697	−	0.983355i	$-0.558159\pi$
$743$	−200611.			−0.363394			−0.181697	+	0.983355i	$0.558159\pi$
$744$	245096.	−	398931.i	0.442782	−	0.720696i
$745$	−312568.	−	21600.5i	−0.563160	−	0.0389180i
$746$	−10413.1	−	8900.54i	−0.0187113	−	0.0159933i
$747$	253780.			0.454796
$748$	−1546.22	−	9811.05i	−0.00276356	−	0.0175353i
$749$	−36267.4			−0.0646477
$750$	257240.	−	198233.i	0.457315	−	0.352414i
$751$			339073.i			0.601192i	0.953752	+	0.300596i	$0.0971855\pi$
$751$			339073.i			0.601192i	−0.953752	+	0.300596i	$0.902814\pi$
$752$	−229042.	+	74033.0i	−0.405023	+	0.130915i
$753$			401029.i			0.707270i
$754$	−608747.	−	520322.i	−1.07077	−	0.915229i
$755$	−59373.5	+	859161.i	−0.104159	+	1.50723i
$756$	−926.204	−	5876.93i	−0.00162055	−	0.0102827i
$757$			30780.5i			0.0537136i	0.999639	+	0.0268568i	$0.00854981\pi$
$757$			30780.5i			0.0537136i	−0.999639	+	0.0268568i	$0.991450\pi$
$758$	−330361.	−	282374.i	−0.574977	−	0.491457i
$759$		−	175263.i		−	0.304234i
$760$	−450060.	+	630519.i	−0.779191	+	1.09162i
$761$	747116.			1.29009			0.645043	−	0.764146i	$-0.276839\pi$
$761$	747116.			1.29009			0.645043	+	0.764146i	$0.276839\pi$
$762$	−89392.0	+	104583.i	−0.153953	+	0.180116i
$763$	14007.7			0.0240612
$764$	−964141.	+	151949.i	−1.65179	+	0.260322i
$765$	478.118	−	6918.58i	0.000816982	−	0.0118221i
$766$	−331344.	+	387654.i	−0.564706	+	0.660673i
$767$	545049.			0.926498
$768$	−276110.	+	199317.i	−0.468123	+	0.337927i
$769$	973777.			1.64667			0.823335	−	0.567555i	$-0.192111\pi$
$769$	973777.			1.64667			0.823335	+	0.567555i	$0.192111\pi$
$770$	11426.5	+	11219.1i	0.0192723	+	0.0189224i
$771$		−	79121.5i		−	0.133102i
$772$	248011.	−	39086.5i	0.416137	−	0.0655832i
$773$			619263.i			1.03637i	0.855268	+	0.518186i	$0.173393\pi$
$773$			619263.i			1.03637i	−0.855268	+	0.518186i	$0.826607\pi$
$774$	71685.6	−	83868.1i	0.119660	−	0.139996i
$775$	−121042.	+	871581.i	−0.201526	+	1.45112i
$776$	460801.	−	750025.i	0.765226	−	1.24552i
$777$		−	31878.5i		−	0.0528027i
$778$	−126420.	+	147905.i	−0.208861	+	0.244356i
$779$		−	283489.i		−	0.467155i
$780$	−437207.	+	38273.2i	−0.718618	+	0.0629080i
$781$	261853.			0.429294
$782$	17439.9	+	14906.7i	0.0285188	+	0.0243763i
$783$	−133020.			−0.216966
$784$	583151.	−	188491.i	0.948744	−	0.306661i
$785$	−33377.8	+	482992.i	−0.0541650	+	0.783791i
$786$	33438.1	+	28581.0i	0.0541248	+	0.0462628i
$787$	135686.			0.219071			0.109536	−	0.993983i	$-0.465064\pi$
$787$	135686.			0.219071			0.109536	+	0.993983i	$0.465064\pi$
$788$	−258692.	+	40769.8i	−0.416610	+	0.0656578i
$789$	486552.			0.781584
$790$	777050.	+	762942.i	1.24507	+	1.22247i
$791$			8664.26i			0.0138477i
$792$	−54653.3	+	88956.7i	−0.0871297	+	0.141817i
$793$			36905.2i			0.0586869i
$794$	257667.	+	220239.i	0.408713	+	0.349345i
$795$	36277.4	−	524951.i	0.0573988	−	0.830585i
$796$	−303828.	+	47883.2i	−0.479514	+	0.0755714i
$797$			263583.i			0.414954i	0.978240	+	0.207477i	$0.0665253\pi$
$797$			263583.i			0.414954i	−0.978240	+	0.207477i	$0.933475\pi$
$798$	−20274.6	−	17329.6i	−0.0318381	−	0.0272134i
$799$		−	9660.55i		−	0.0151324i
$800$	324979.	−	551352.i	0.507780	−	0.861487i
$801$	−310727.			−0.484299
$802$	236960.	−	277230.i	0.368406	−	0.431014i
$803$	−194911.			−0.302278
$804$	−556.447	−	3530.75i	−0.000860819	−	0.00546205i
$805$	−36902.1	−	2550.17i	−0.0569456	−	0.00393530i
$806$	772642.	−	903947.i	1.18935	−	1.39147i
$807$	−560010.			−0.859902
$808$	635679.	+	390549.i	0.973677	+	0.598209i
$809$	−94205.5			−0.143939			−0.0719696	−	0.997407i	$-0.522928\pi$
$809$	−94205.5			−0.143939			−0.0719696	+	0.997407i	$0.522928\pi$
$810$	−51073.7	+	52018.1i	−0.0778444	+	0.0792838i
$811$			546777.i			0.831321i	0.909520	+	0.415660i	$0.136450\pi$
$811$			546777.i			0.831321i	−0.909520	+	0.415660i	$0.863550\pi$
$812$	6259.38	+	39716.8i	0.00949334	+	0.0602369i
$813$			51454.3i			0.0778467i
$814$	−363478.	+	425248.i	−0.548567	+	0.641791i
$815$	777476.	+	53728.6i	1.17050	+	0.0808891i
$816$	−4203.40	−	13004.4i	−0.00631278	−	0.0195304i
$817$		−	494612.i		−	0.741004i
$818$	−185282.	+	216769.i	−0.276902	+	0.323959i
$819$		−	15110.5i		−	0.0225274i
$820$	20424.5	+	233315.i	0.0303755	+	0.346989i
$821$	170624.			0.253135			0.126568	−	0.991958i	$-0.459604\pi$
$821$	170624.			0.253135			0.126568	+	0.991958i	$0.459604\pi$
$822$	399920.	+	341829.i	0.591874	+	0.505900i
$823$	−478412.			−0.706322			−0.353161	−	0.935563i	$-0.614893\pi$
$823$	−478412.			−0.706322			−0.353161	+	0.935563i	$0.614893\pi$
$824$	−1.03216e6	−	634141.i	−1.52017	−	0.933966i
$825$	26990.8	−	194352.i	0.0396559	−	0.285549i
$826$	−20802.1	−	17780.5i	−0.0304893	−	0.0260605i
$827$	791583.			1.15741			0.578703	−	0.815539i	$-0.303559\pi$
$827$	791583.			1.15741			0.578703	+	0.815539i	$0.303559\pi$
$828$	−37544.5	−	238227.i	−0.0547628	−	0.347480i
$829$	−424736.			−0.618030			−0.309015	−	0.951057i	$-0.599999\pi$
$829$	−424736.			−0.618030			−0.309015	+	0.951057i	$0.599999\pi$
$830$	−658513.	+	670690.i	−0.955891	+	0.973566i
$831$			611527.i			0.885551i
$832$	−771526.	+	390884.i	−1.11456	+	0.564678i
$833$			24596.2i			0.0354468i
$834$	−199303.	−	170353.i	−0.286537	−	0.244916i
$835$	−948241.	−	65529.5i	−1.36002	−	0.0939862i
$836$	72865.0	+	462341.i	0.104257	+	0.661531i
$837$		−	197525.i		−	0.281949i
$838$	−302697.	−	258728.i	−0.431042	−	0.368430i
$839$			438950.i			0.623579i	0.950151	+	0.311790i	$0.100928\pi$
$839$			438950.i			0.623579i	−0.950151	+	0.311790i	$0.899072\pi$
$840$	17934.8	+	12801.8i	0.0254179	+	0.0181431i
$841$	191679.			0.271008
$842$	538913.	−	630497.i	0.760141	−	0.889322i
$843$	−186568.			−0.262532
$844$	413370.	−	65147.1i	0.580302	−	0.0914556i
$845$	−399692.	−	27621.3i	−0.559774	−	0.0386840i
$846$	−65980.7	+	77193.6i	−0.0921883	+	0.107855i
$847$	−29129.3			−0.0406035
$848$	−318935.	−	986717.i	−0.443517	−	1.37215i
$849$	−570564.			−0.791569
$850$	17043.8	+	19216.0i	0.0235900	+	0.0265965i
$851$		−	1.29222e6i		−	1.78435i
$852$	355923.	−	56093.5i	0.490317	−	0.0772741i
$853$		−	1.32422e6i		−	1.81996i	−0.414649	−	0.909982i	$-0.636095\pi$
$853$		−	1.32422e6i		−	1.81996i	0.414649	−	0.909982i	$-0.363905\pi$
$854$	1203.91	−	1408.51i	0.00165074	−	0.00193127i
$855$	−22531.1	+	326035.i	−0.0308213	+	0.445997i
$856$	746181.	+	458439.i	1.01835	+	0.625654i
$857$		−	584716.i		−	0.796129i	−0.917357	−	0.398065i	$-0.869682\pi$
$857$		−	584716.i		−	0.796129i	0.917357	−	0.398065i	$-0.130318\pi$
$858$	−172290.	+	201569.i	−0.234037	+	0.273810i
$859$			952318.i			1.29061i	0.763924	+	0.645306i	$0.223270\pi$
$859$			952318.i			1.29061i	−0.763924	+	0.645306i	$0.776730\pi$
$860$	35635.2	+	407072.i	0.0481817	+	0.550395i
$861$	−8063.72			−0.0108775
$862$	305832.	+	261407.i	0.411593	+	0.351806i
$863$	1.36042e6			1.82663			0.913316	−	0.407251i	$-0.133513\pi$
$863$	1.36042e6			1.82663			0.913316	+	0.407251i	$0.133513\pi$
$864$	−55231.4	+	132622.i	−0.0739875	+	0.177659i
$865$	42869.3	−	620338.i	0.0572947	−	0.829080i
$866$	−708904.	−	605931.i	−0.945261	−	0.807955i
$867$	−433439.			−0.576621
$868$	−58976.7	+	9294.74i	−0.0782783	+	0.0123367i
$869$	657956.			0.871279
$870$	345161.	−	351544.i	0.456020	−	0.464452i
$871$		−	9078.13i		−	0.0119663i
$872$	−288200.	−	177065.i	−0.379020	−	0.232862i
$873$		−	371364.i		−	0.487271i
$874$	−821850.	−	702470.i	−1.07589	−	0.919613i
$875$	−40528.6	−	8510.91i	−0.0529353	−	0.0111163i
$876$	−264933.	+	41753.5i	−0.345246	+	0.0544107i
$877$			945243.i			1.22898i	0.788925	+	0.614489i	$0.210638\pi$
$877$			945243.i			1.22898i	−0.788925	+	0.614489i	$0.789362\pi$
$878$	−355677.	−	304012.i	−0.461389	−	0.394369i
$879$		−	290866.i		−	0.376456i
$880$	−93279.1	−	375264.i	−0.120453	−	0.484586i
$881$	−248183.			−0.319757			−0.159878	−	0.987137i	$-0.551110\pi$
$881$	−248183.			−0.319757			−0.159878	+	0.987137i	$0.551110\pi$
$882$	167990.	−	196538.i	0.215946	−	0.252644i
$883$	−201922.			−0.258978			−0.129489	−	0.991581i	$-0.541334\pi$
$883$	−201922.			−0.258978			−0.129489	+	0.991581i	$0.541334\pi$
$884$	−5403.81	−	34288.1i	−0.00691505	−	0.0438772i
$885$	−23117.3	+	334518.i	−0.0295156	+	0.427103i
$886$	−494.945	+	579.058i	−0.000630507	+	0.000737657i
$887$	−1.30649e6			−1.66057			−0.830287	−	0.557336i	$-0.811824\pi$
$887$	−1.30649e6			−1.66057			−0.830287	+	0.557336i	$0.811824\pi$
$888$	−402962.	+	655882.i	−0.511020	+	0.831764i
$889$	17544.1			0.0221986
$890$	806278.	−	821187.i	1.01790	−	1.03672i
$891$			44045.6i			0.0554814i
$892$	−71848.3	−	455890.i	−0.0902998	−	0.572968i
$893$			455249.i			0.570882i
$894$	−169247.	+	198009.i	−0.211760	+	0.247748i
$895$	74369.0	−	1.07615e6i	0.0928423	−	1.34347i
$896$	42197.1	+	10250.2i	0.0525614	+	0.0127679i
$897$		−	612518.i		−	0.761262i
$898$	226517.	−	265011.i	0.280897	−	0.328634i
$899$			1.33489e6i			1.65168i
$900$	−4946.37	−	269955.i	−0.00610663	−	0.333277i
$901$	41617.8			0.0512660
$902$	107567.	+	91942.3i	0.132211	+	0.113006i
$903$	−14069.0			−0.0172539
$904$	109521.	−	178262.i	0.134017	−	0.218134i
$905$	−788490.	−	54489.7i	−0.962718	−	0.0665300i
$906$	544270.	+	465211.i	0.663068	+	0.566752i
$907$	1.36506e6			1.65934			0.829672	−	0.558251i	$-0.188527\pi$
$907$	1.36506e6			1.65934			0.829672	+	0.558251i	$0.188527\pi$
$908$	−102120.	−	647970.i	−0.123862	−	0.785929i
$909$	314747.			0.380920
$910$	39934.0	+	39209.0i	0.0482236	+	0.0473481i
$911$		−	585490.i		−	0.705476i	−0.935722	−	0.352738i	$-0.885251\pi$
$911$		−	585490.i		−	0.705476i	0.935722	−	0.352738i	$-0.114749\pi$
$912$	198083.	+	612828.i	0.238154	+	0.736799i
$913$			567897.i			0.681284i
$914$	868292.	+	742166.i	1.03938	+	0.888400i
$915$	−22650.2	−	1565.27i	−0.0270539	−	0.00186959i
$916$	36409.9	+	231028.i	0.0433939	+	0.275342i
$917$		−	5609.30i		−	0.00667067i
$918$	−4382.85	−	3746.21i	−0.00520082	−	0.00444536i
$919$		−	639420.i		−	0.757103i	−0.925580	−	0.378552i	$-0.876422\pi$
$919$		−	639420.i		−	0.757103i	0.925580	−	0.378552i	$-0.123578\pi$
$920$	727005.	+	518931.i	0.858938	+	0.613104i
$921$	−33279.0			−0.0392330
$922$	−374481.	+	438122.i	−0.440523	+	0.515386i
$923$	915136.			1.07419
$924$	13151.1	−	2072.61i	0.0154034	−	0.00242758i
$925$	199005.	−	1.43297e6i	0.232584	−	1.67476i
$926$	−682906.	+	798961.i	−0.796414	+	0.931759i
$927$	−511060.			−0.594720
$928$	373259.	−	896273.i	0.433425	−	1.04075i
$929$	1.09812e6			1.27239			0.636193	−	0.771530i	$-0.280508\pi$
$929$	1.09812e6			1.27239			0.636193	+	0.771530i	$0.280508\pi$
$930$	522018.	+	512540.i	0.603558	+	0.592601i
$931$		−	1.15908e6i		−	1.33726i
$932$	−497289.	+	78372.7i	−0.572502	+	0.0902263i
$933$		−	349701.i		−	0.401729i
$934$	491108.	−	574568.i	0.562967	−	0.658639i
$935$	15482.0	+	1069.91i	0.0177095	+	0.00122384i
$936$	−191005.	+	310890.i	−0.218018	+	0.354859i
$937$			1.59851e6i			1.82069i	0.413845	+	0.910347i	$0.364185\pi$
$937$			1.59851e6i			1.82069i	−0.413845	+	0.910347i	$0.635815\pi$
$938$	−296.145	+	346.473i	−0.000336588	+	0.000393789i
$939$			191658.i			0.217368i
$940$	−32799.3	−	374676.i	−0.0371200	−	0.424034i
$941$	−1.19196e6			−1.34612			−0.673060	−	0.739588i	$-0.735020\pi$
$941$	−1.19196e6			−1.34612			−0.673060	+	0.739588i	$0.735020\pi$
$942$	305971.	+	261526.i	0.344808	+	0.294723i
$943$	−326870.			−0.367580
$944$	203237.	+	628773.i	0.228065	+	0.705586i
$945$	9273.92	+	640.887i	0.0103848	+	0.000717659i
$946$	187676.	+	160414.i	0.209713	+	0.179251i
$947$	1.07267e6			1.19609			0.598046	−	0.801462i	$-0.295944\pi$
$947$	1.07267e6			1.19609			0.598046	+	0.801462i	$0.295944\pi$
$948$	894326.	−	140946.i	0.995129	−	0.156832i
$949$	−681186.			−0.756368
$950$	−803180.	−	905545.i	−0.889950	−	1.00337i
$951$			285309.i			0.315468i
$952$	−912.300	+	1484.91i	−0.00100662	+	0.00163842i
$953$			157899.i			0.173858i	0.996215	+	0.0869290i	$0.0277053\pi$
$953$			157899.i			0.173858i	−0.996215	+	0.0869290i	$0.972295\pi$
$954$	−332551.	−	284246.i	−0.365394	−	0.312318i
$955$	105141.	−	1.52144e6i	0.115283	−	1.66819i
$956$	1.48742e6	−	234417.i	1.62749	−	0.256492i
$957$		−	297665.i		−	0.325015i
$958$	168848.	+	144322.i	0.183978	+	0.157254i
$959$		−	67087.2i		−	0.0729462i
$960$	−207178.	−	490095.i	−0.224802	−	0.531787i
$961$	−1.05870e6			−1.14637
$962$	−1.27030e6	+	1.48618e6i	−1.37264	+	1.60591i
$963$	369460.			0.398396
$964$	−110612.	−	701852.i	−0.119028	−	0.755251i
$965$	−27046.0	+	391367.i	−0.0290434	+	0.420271i
$966$	−19981.4	+	23377.2i	−0.0214128	+	0.0250517i
$967$	−1.35467e6			−1.44871			−0.724353	−	0.689429i	$-0.757862\pi$
$967$	−1.35467e6			−1.44871			−0.724353	+	0.689429i	$0.757862\pi$
$968$	599319.	+	368210.i	0.639598	+	0.392957i
$969$	−25847.9			−0.0275282
$970$	981438.	+	963620.i	1.04308	+	1.02415i
$971$			108394.i			0.114966i	0.998346	+	0.0574828i	$0.0183074\pi$
$971$			108394.i			0.114966i	−0.998346	+	0.0574828i	$0.981693\pi$
$972$	9435.35	+	59869.0i	0.00998678	+	0.0633679i
$973$			33433.4i			0.0353146i
$974$	125961.	−	147367.i	0.132776	−	0.155340i
$975$	94328.8	−	679230.i	0.0992282	−	0.714509i
$976$	−42574.1	+	13761.2i	−0.0446937	+	0.0144463i
$977$			1.55432e6i			1.62837i	0.580608	+	0.814183i	$0.302815\pi$
$977$			1.55432e6i			1.62837i	−0.580608	+	0.814183i	$0.697185\pi$
$978$	420981.	−	492523.i	0.440134	−	0.514931i
$979$		−	695328.i		−	0.725479i
$980$	83508.3	+	953942.i	0.0869516	+	0.993276i
$981$	−142698.			−0.148279
$982$	−1.04307e6	−	891554.i	−1.08166	−	0.924538i
$983$	−1.15487e6			−1.19516			−0.597580	−	0.801809i	$-0.703871\pi$
$983$	−1.15487e6			−1.19516			−0.597580	+	0.801809i	$0.703871\pi$
$984$	165906.	+	101930.i	0.171346	+	0.105271i
$985$	28210.7	−	408221.i	0.0290764	−	0.420749i
$986$	29619.8	+	25317.3i	0.0304669	+	0.0260413i
$987$	12949.4			0.0132927
$988$	254652.	+	1.61581e6i	0.260875	+	1.65530i
$989$	−570300.			−0.583057
$990$	−116403.	−	114290.i	−0.118767	−	0.116611i
$991$		−	13896.4i		−	0.0141499i	−0.999975	−	0.00707496i	$-0.997748\pi$
$991$		−	13896.4i		−	0.0141499i	0.999975	−	0.00707496i	$-0.00225205\pi$
$992$	1.33090e6	+	554263.i	1.35246	+	0.563239i
$993$			392742.i			0.398298i
$994$	−34926.7	−	29853.4i	−0.0353497	−	0.0302149i
$995$	33132.8	−	479447.i	0.0334667	−	0.484277i
$996$	121654.	+	771914.i	0.122633	+	0.778126i
$997$			763047.i			0.767646i	0.923407	+	0.383823i	$0.125393\pi$
$997$			763047.i			0.767646i	−0.923407	+	0.383823i	$0.874607\pi$
$998$	−243238.	−	207906.i	−0.244214	−	0.208740i
$999$			324750.i			0.325401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.f.a.19.8	yes	24
3.2	odd	2		180.5.f.i.19.17		24
4.3	odd	2	inner	60.5.f.a.19.18	yes	24
5.2	odd	4		300.5.c.e.151.5		24
5.3	odd	4		300.5.c.e.151.20		24
5.4	even	2	inner	60.5.f.a.19.17	yes	24
8.3	odd	2		960.5.j.d.319.8		24
8.5	even	2		960.5.j.d.319.17		24
12.11	even	2		180.5.f.i.19.7		24
15.14	odd	2		180.5.f.i.19.8		24
20.3	even	4		300.5.c.e.151.19		24
20.7	even	4		300.5.c.e.151.6		24
20.19	odd	2	inner	60.5.f.a.19.7	✓	24
40.19	odd	2		960.5.j.d.319.20		24
40.29	even	2		960.5.j.d.319.5		24
60.59	even	2		180.5.f.i.19.18		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.f.a.19.7	✓	24	20.19	odd	2	inner
60.5.f.a.19.8	yes	24	1.1	even	1	trivial
60.5.f.a.19.17	yes	24	5.4	even	2	inner
60.5.f.a.19.18	yes	24	4.3	odd	2	inner
180.5.f.i.19.7		24	12.11	even	2
180.5.f.i.19.8		24	15.14	odd	2
180.5.f.i.19.17		24	3.2	odd	2
180.5.f.i.19.18		24	60.59	even	2
300.5.c.e.151.5		24	5.2	odd	4
300.5.c.e.151.6		24	20.7	even	4
300.5.c.e.151.19		24	20.3	even	4
300.5.c.e.151.20		24	5.3	odd	4
960.5.j.d.319.5		24	40.29	even	2
960.5.j.d.319.8		24	8.3	odd	2
960.5.j.d.319.17		24	8.5	even	2
960.5.j.d.319.20		24	40.19	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59896 + 3.04063i) q^{2} -5.19615 q^{3} +(-2.49086 - 15.8049i) q^{4} +(24.9405 + 1.72355i) q^{5} +(13.5046 - 15.7996i) q^{6} -2.65040 q^{7} +(54.5305 + 33.5025i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(-2.59896 + 3.04063i) q^{2} -5.19615 q^{3} +(-2.49086 - 15.8049i) q^{4} +(24.9405 + 1.72355i) q^{5} +(13.5046 - 15.7996i) q^{6} -2.65040 q^{7} +(54.5305 + 33.5025i) q^{8} +27.0000 q^{9} +(-70.0600 + 71.3554i) q^{10} +60.4192i q^{11} +(12.9429 + 82.1248i) q^{12} +211.156i q^{13} +(6.88829 - 8.05890i) q^{14} +(-129.595 - 8.95583i) q^{15} +(-243.591 + 78.7356i) q^{16} -10.2742i q^{17} +(-70.1718 + 82.0970i) q^{18} +484.167i q^{19} +(-34.8827 - 398.476i) q^{20} +13.7719 q^{21} +(-183.712 - 157.027i) q^{22} +558.257 q^{23} +(-283.349 - 174.084i) q^{24} +(619.059 + 85.9724i) q^{25} +(-642.047 - 548.785i) q^{26} -140.296 q^{27} +(6.60178 + 41.8894i) q^{28} +948.135 q^{29} +(364.042 - 370.774i) q^{30} +1407.91i q^{31} +(393.677 - 945.301i) q^{32} -313.947i q^{33} +(31.2400 + 26.7022i) q^{34} +(-66.1025 - 4.56810i) q^{35} +(-67.2531 - 426.733i) q^{36} -2314.75i q^{37} +(-1472.17 - 1258.33i) q^{38} -1097.20i q^{39} +(1302.28 + 929.556i) q^{40} -585.519 q^{41} +(-35.7926 + 41.8753i) q^{42} -1021.57 q^{43} +(954.921 - 150.496i) q^{44} +(673.394 + 46.5358i) q^{45} +(-1450.88 + 1697.45i) q^{46} +940.273 q^{47} +(1265.74 - 409.122i) q^{48} -2393.98 q^{49} +(-1870.32 + 1658.89i) q^{50} +53.3863i q^{51} +(3337.30 - 525.959i) q^{52} +4050.71i q^{53} +(364.623 - 426.589i) q^{54} +(-104.136 + 1506.89i) q^{55} +(-144.528 - 88.7953i) q^{56} -2515.80i q^{57} +(-2464.16 + 2882.93i) q^{58} -2581.26i q^{59} +(181.256 + 2070.54i) q^{60} +174.777 q^{61} +(-4280.94 - 3659.11i) q^{62} -71.5609 q^{63} +(1851.16 + 3653.82i) q^{64} +(-363.938 + 5266.34i) q^{65} +(954.598 + 815.936i) q^{66} -42.9926 q^{67} +(-162.383 + 25.5915i) q^{68} -2900.79 q^{69} +(185.687 - 189.121i) q^{70} -4333.93i q^{71} +(1472.32 + 904.568i) q^{72} +3225.98i q^{73} +(7038.30 + 6015.93i) q^{74} +(-3216.72 - 446.726i) q^{75} +(7652.22 - 1205.99i) q^{76} -160.135i q^{77} +(3336.17 + 2851.57i) q^{78} -10889.8i q^{79} +(-6211.00 + 1543.87i) q^{80} +729.000 q^{81} +(1521.74 - 1780.35i) q^{82} +9399.28 q^{83} +(-34.3039 - 217.664i) q^{84} +(17.7081 - 256.244i) q^{85} +(2655.02 - 3106.22i) q^{86} -4926.65 q^{87} +(-2024.20 + 3294.69i) q^{88} -11508.4 q^{89} +(-1891.62 + 1926.60i) q^{90} -559.649i q^{91} +(-1390.54 - 8823.21i) q^{92} -7315.74i q^{93} +(-2443.73 + 2859.02i) q^{94} +(-834.486 + 12075.4i) q^{95} +(-2045.61 + 4911.93i) q^{96} -13754.2i q^{97} +(6221.84 - 7279.19i) q^{98} +1631.32i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9}+O(q^{10}) \) 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9	\( 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9} + 274 q^{10} - 36 q^{14} + 594 q^{16} - 12 q^{20} - 594 q^{24} + 1208 q^{25} - 2868 q^{26} - 1680 q^{29} + 468 q^{30} + 3076 q^{34} + 378 q^{36} - 7222 q^{40} - 4848 q^{41} - 3828 q^{44} - 648 q^{45} - 15280 q^{46} + 5416 q^{49} + 14472 q^{50} - 486 q^{54} + 32172 q^{56} - 7506 q^{60} + 2896 q^{61} - 18298 q^{64} - 2688 q^{65} - 15588 q^{66} + 9792 q^{69} + 27608 q^{70} + 31836 q^{74} + 50136 q^{76} - 27348 q^{80} + 17496 q^{81} - 4284 q^{84} - 15680 q^{85} - 58152 q^{86} - 38544 q^{89} + 7398 q^{90} + 4808 q^{94} + 21978 q^{96}+O(q^{100}) \) 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9 + 274 * q^10 - 36 * q^14 + 594 * q^16 - 12 * q^20 - 594 * q^24 + 1208 * q^25 - 2868 * q^26 - 1680 * q^29 + 468 * q^30 + 3076 * q^34 + 378 * q^36 - 7222 * q^40 - 4848 * q^41 - 3828 * q^44 - 648 * q^45 - 15280 * q^46 + 5416 * q^49 + 14472 * q^50 - 486 * q^54 + 32172 * q^56 - 7506 * q^60 + 2896 * q^61 - 18298 * q^64 - 2688 * q^65 - 15588 * q^66 + 9792 * q^69 + 27608 * q^70 + 31836 * q^74 + 50136 * q^76 - 27348 * q^80 + 17496 * q^81 - 4284 * q^84 - 15680 * q^85 - 58152 * q^86 - 38544 * q^89 + 7398 * q^90 + 4808 * q^94 + 21978 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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