LMFDB - Embedded newform 471.4.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,4,Mod(1,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("471.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	471.a (trivial)

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:	yes
Analytic conductor:	$27.7898996127$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 67 x^{12} + 111 x^{11} + 1707 x^{10} - 2305 x^{9} - 20677 x^{8} + 23233 x^{7} + \cdots - 2176 $ x^14 - 2x^13 - 67x^12 + 111x^11 + 1707x^10 - 2305x^9 - 20677x^8 + 23233x^7 + 120416x^6 - 120881x^5 - 291988x^4 + 288068x^3 + 157328x^2 - 128448*x - 2176
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.84344$ of defining polynomial
Character	$\chi$	$=$	471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.84344 q^{2} +3.00000 q^{3} +0.0851496 q^{4} -11.0095 q^{5} -8.53032 q^{6} +10.1709 q^{7} +22.5054 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.84344 q^{2} +3.00000 q^{3} +0.0851496 q^{4} -11.0095 q^{5} -8.53032 q^{6} +10.1709 q^{7} +22.5054 q^{8} +9.00000 q^{9} +31.3048 q^{10} -6.02237 q^{11} +0.255449 q^{12} -51.1266 q^{13} -28.9203 q^{14} -33.0284 q^{15} -64.6739 q^{16} +21.0514 q^{17} -25.5910 q^{18} +58.0164 q^{19} -0.937453 q^{20} +30.5127 q^{21} +17.1242 q^{22} +140.564 q^{23} +67.5162 q^{24} -3.79141 q^{25} +145.375 q^{26} +27.0000 q^{27} +0.866048 q^{28} +32.2667 q^{29} +93.9144 q^{30} -5.14550 q^{31} +3.85327 q^{32} -18.0671 q^{33} -59.8585 q^{34} -111.976 q^{35} +0.766347 q^{36} -117.238 q^{37} -164.966 q^{38} -153.380 q^{39} -247.773 q^{40} +228.531 q^{41} -86.7610 q^{42} -166.746 q^{43} -0.512802 q^{44} -99.0853 q^{45} -399.684 q^{46} -282.173 q^{47} -194.022 q^{48} -239.553 q^{49} +10.7807 q^{50} +63.1543 q^{51} -4.35341 q^{52} +424.570 q^{53} -76.7729 q^{54} +66.3031 q^{55} +228.900 q^{56} +174.049 q^{57} -91.7483 q^{58} -807.308 q^{59} -2.81236 q^{60} -620.972 q^{61} +14.6309 q^{62} +91.5381 q^{63} +506.435 q^{64} +562.877 q^{65} +51.3727 q^{66} +509.862 q^{67} +1.79252 q^{68} +421.691 q^{69} +318.398 q^{70} -190.631 q^{71} +202.549 q^{72} -615.270 q^{73} +333.360 q^{74} -11.3742 q^{75} +4.94008 q^{76} -61.2529 q^{77} +436.126 q^{78} -1018.00 q^{79} +712.026 q^{80} +81.0000 q^{81} -649.814 q^{82} -607.003 q^{83} +2.59814 q^{84} -231.765 q^{85} +474.131 q^{86} +96.8000 q^{87} -135.536 q^{88} +248.300 q^{89} +281.743 q^{90} -520.004 q^{91} +11.9689 q^{92} -15.4365 q^{93} +802.341 q^{94} -638.730 q^{95} +11.5598 q^{96} -1781.03 q^{97} +681.154 q^{98} -54.2013 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 42 q^{3} + 26 q^{4} - 32 q^{5} - 6 q^{6} - 60 q^{7} - 45 q^{8} + 126 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 42 * q^3 + 26 * q^4 - 32 * q^5 - 6 * q^6 - 60 * q^7 - 45 * q^8 + 126 * q^9	\( 14 q - 2 q^{2} + 42 q^{3} + 26 q^{4} - 32 q^{5} - 6 q^{6} - 60 q^{7} - 45 q^{8} + 126 q^{9} - 155 q^{10} - 61 q^{11} + 78 q^{12} - 204 q^{13} - 99 q^{14} - 96 q^{15} - 66 q^{16} - 324 q^{17} - 18 q^{18} - 400 q^{19} - 257 q^{20} - 180 q^{21} - 154 q^{22} - 105 q^{23} - 135 q^{24} - 70 q^{25} - 351 q^{26} + 378 q^{27} - 575 q^{28} - 418 q^{29} - 465 q^{30} - 663 q^{31} - 572 q^{32} - 183 q^{33} - 883 q^{34} - 386 q^{35} + 234 q^{36} - 646 q^{37} - 104 q^{38} - 612 q^{39} - 1068 q^{40} - 881 q^{41} - 297 q^{42} - 1535 q^{43} + 329 q^{44} - 288 q^{45} - 112 q^{46} - 252 q^{47} - 198 q^{48} - 1184 q^{49} + 1901 q^{50} - 972 q^{51} - 1042 q^{52} - 78 q^{53} - 54 q^{54} - 1402 q^{55} + 1092 q^{56} - 1200 q^{57} + 710 q^{58} + 110 q^{59} - 771 q^{60} - 815 q^{61} + 1186 q^{62} - 540 q^{63} - 863 q^{64} - 4 q^{65} - 462 q^{66} - 1834 q^{67} - 735 q^{68} - 315 q^{69} + 977 q^{70} - 28 q^{71} - 405 q^{72} - 2422 q^{73} + 1588 q^{74} - 210 q^{75} - 3070 q^{76} - 746 q^{77} - 1053 q^{78} - 2566 q^{79} + 1061 q^{80} + 1134 q^{81} - 3300 q^{82} + 292 q^{83} - 1725 q^{84} - 912 q^{85} + 1191 q^{86} - 1254 q^{87} - 708 q^{88} - 780 q^{89} - 1395 q^{90} - 2210 q^{91} + 1918 q^{92} - 1989 q^{93} - 1496 q^{94} + 1604 q^{95} - 1716 q^{96} - 1370 q^{97} - 13 q^{98} - 549 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 42 * q^3 + 26 * q^4 - 32 * q^5 - 6 * q^6 - 60 * q^7 - 45 * q^8 + 126 * q^9 - 155 * q^10 - 61 * q^11 + 78 * q^12 - 204 * q^13 - 99 * q^14 - 96 * q^15 - 66 * q^16 - 324 * q^17 - 18 * q^18 - 400 * q^19 - 257 * q^20 - 180 * q^21 - 154 * q^22 - 105 * q^23 - 135 * q^24 - 70 * q^25 - 351 * q^26 + 378 * q^27 - 575 * q^28 - 418 * q^29 - 465 * q^30 - 663 * q^31 - 572 * q^32 - 183 * q^33 - 883 * q^34 - 386 * q^35 + 234 * q^36 - 646 * q^37 - 104 * q^38 - 612 * q^39 - 1068 * q^40 - 881 * q^41 - 297 * q^42 - 1535 * q^43 + 329 * q^44 - 288 * q^45 - 112 * q^46 - 252 * q^47 - 198 * q^48 - 1184 * q^49 + 1901 * q^50 - 972 * q^51 - 1042 * q^52 - 78 * q^53 - 54 * q^54 - 1402 * q^55 + 1092 * q^56 - 1200 * q^57 + 710 * q^58 + 110 * q^59 - 771 * q^60 - 815 * q^61 + 1186 * q^62 - 540 * q^63 - 863 * q^64 - 4 * q^65 - 462 * q^66 - 1834 * q^67 - 735 * q^68 - 315 * q^69 + 977 * q^70 - 28 * q^71 - 405 * q^72 - 2422 * q^73 + 1588 * q^74 - 210 * q^75 - 3070 * q^76 - 746 * q^77 - 1053 * q^78 - 2566 * q^79 + 1061 * q^80 + 1134 * q^81 - 3300 * q^82 + 292 * q^83 - 1725 * q^84 - 912 * q^85 + 1191 * q^86 - 1254 * q^87 - 708 * q^88 - 780 * q^89 - 1395 * q^90 - 2210 * q^91 + 1918 * q^92 - 1989 * q^93 - 1496 * q^94 + 1604 * q^95 - 1716 * q^96 - 1370 * q^97 - 13 * q^98 - 549 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.84344	−1.00531	−0.502654	−	0.864488i	$-0.667643\pi$
$2$	−2.84344	−1.00531	−0.502654	+	0.864488i	$0.667643\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	0.0851496	0.0106437
$5$	−11.0095	−0.984718	−0.492359	−	0.870392i	$-0.663865\pi$
$5$	−11.0095	−0.984718	−0.492359	+	0.870392i	$0.663865\pi$
$6$	−8.53032	−0.580415
$7$	10.1709	0.549177	0.274588	−	0.961562i	$-0.411458\pi$
$7$	10.1709	0.549177	0.274588	+	0.961562i	$0.411458\pi$
$8$	22.5054	0.994608
$9$	9.00000	0.333333
$10$	31.3048	0.989944
$11$	−6.02237	−0.165074	−0.0825369	−	0.996588i	$-0.526302\pi$
$11$	−6.02237	−0.165074	−0.0825369	+	0.996588i	$0.526302\pi$
$12$	0.255449	0.00614514
$13$	−51.1266	−1.09077	−0.545384	−	0.838187i	$-0.683616\pi$
$13$	−51.1266	−1.09077	−0.545384	+	0.838187i	$0.683616\pi$
$14$	−28.9203	−0.552092
$15$	−33.0284	−0.568527
$16$	−64.6739	−1.01053
$17$	21.0514	0.300337	0.150168	−	0.988660i	$-0.452018\pi$
$17$	21.0514	0.300337	0.150168	+	0.988660i	$0.452018\pi$
$18$	−25.5910	−0.335103
$19$	58.0164	0.700520	0.350260	−	0.936653i	$-0.386093\pi$
$19$	58.0164	0.700520	0.350260	+	0.936653i	$0.386093\pi$
$20$	−0.937453	−0.0104810
$21$	30.5127	0.317067
$22$	17.1242	0.165950
$23$	140.564	1.27433	0.637164	−	0.770729i	$-0.280108\pi$
$23$	140.564	1.27433	0.637164	+	0.770729i	$0.280108\pi$
$24$	67.5162	0.574237
$25$	−3.79141	−0.0303313
$26$	145.375	1.09656
$27$	27.0000	0.192450
$28$	0.866048	0.00584527
$29$	32.2667	0.206613	0.103306	−	0.994650i	$-0.467058\pi$
$29$	32.2667	0.206613	0.103306	+	0.994650i	$0.467058\pi$
$30$	93.9144	0.571545
$31$	−5.14550	−0.0298116	−0.0149058	−	0.999889i	$-0.504745\pi$
$31$	−5.14550	−0.0298116	−0.0149058	+	0.999889i	$0.504745\pi$
$32$	3.85327	0.0212865
$33$	−18.0671	−0.0953054
$34$	−59.8585	−0.301931
$35$	−111.976	−0.540784
$36$	0.766347	0.00354790
$37$	−117.238	−0.520916	−0.260458	−	0.965485i	$-0.583874\pi$
$37$	−117.238	−0.520916	−0.260458	+	0.965485i	$0.583874\pi$
$38$	−164.966	−0.704238
$39$	−153.380	−0.629755
$40$	−247.773	−0.979408
$41$	228.531	0.870501	0.435250	−	0.900309i	$-0.356660\pi$
$41$	228.531	0.870501	0.435250	+	0.900309i	$0.356660\pi$
$42$	−86.7610	−0.318750
$43$	−166.746	−0.591360	−0.295680	−	0.955287i	$-0.595546\pi$
$43$	−166.746	−0.591360	−0.295680	+	0.955287i	$0.595546\pi$
$44$	−0.512802	−0.00175700
$45$	−99.0853	−0.328239
$46$	−399.684	−1.28109
$47$	−282.173	−0.875726	−0.437863	−	0.899042i	$-0.644265\pi$
$47$	−282.173	−0.875726	−0.437863	+	0.899042i	$0.644265\pi$
$48$	−194.022	−0.583430
$49$	−239.553	−0.698405
$50$	10.7807	0.0304923
$51$	63.1543	0.173400
$52$	−4.35341	−0.0116098
$53$	424.570	1.10036	0.550181	−	0.835046i	$-0.314559\pi$
$53$	424.570	1.10036	0.550181	+	0.835046i	$0.314559\pi$
$54$	−76.7729	−0.193472
$55$	66.3031	0.162551
$56$	228.900	0.546215
$57$	174.049	0.404445
$58$	−91.7483	−0.207709
$59$	−807.308	−1.78140	−0.890699	−	0.454593i	$-0.849785\pi$
$59$	−807.308	−1.78140	−0.890699	+	0.454593i	$0.849785\pi$
$60$	−2.81236	−0.00605123
$61$	−620.972	−1.30340	−0.651700	−	0.758477i	$-0.725944\pi$
$61$	−620.972	−1.30340	−0.651700	+	0.758477i	$0.725944\pi$
$62$	14.6309	0.0299698
$63$	91.5381	0.183059
$64$	506.435	0.989131
$65$	562.877	1.07410
$66$	51.3727	0.0958113
$67$	509.862	0.929694	0.464847	−	0.885391i	$-0.346109\pi$
$67$	509.862	0.929694	0.464847	+	0.885391i	$0.346109\pi$
$68$	1.79252	0.00319670
$69$	421.691	0.735733
$70$	318.398	0.543654
$71$	−190.631	−0.318644	−0.159322	−	0.987227i	$-0.550931\pi$
$71$	−190.631	−0.318644	−0.159322	+	0.987227i	$0.550931\pi$
$72$	202.549	0.331536
$73$	−615.270	−0.986465	−0.493232	−	0.869898i	$-0.664185\pi$
$73$	−615.270	−0.986465	−0.493232	+	0.869898i	$0.664185\pi$
$74$	333.360	0.523681
$75$	−11.3742	−0.0175118
$76$	4.94008	0.00745613
$77$	−61.2529	−0.0906547
$78$	436.126	0.633097
$79$	−1018.00	−1.44980	−0.724898	−	0.688857i	$-0.758113\pi$
$79$	−1018.00	−1.44980	−0.724898	+	0.688857i	$0.758113\pi$
$80$	712.026	0.995087
$81$	81.0000	0.111111
$82$	−649.814	−0.875121
$83$	−607.003	−0.802737	−0.401369	−	0.915917i	$-0.631465\pi$
$83$	−607.003	−0.802737	−0.401369	+	0.915917i	$0.631465\pi$
$84$	2.59814	0.00337477
$85$	−231.765	−0.295747
$86$	474.131	0.594498
$87$	96.8000	0.119288
$88$	−135.536	−0.164184
$89$	248.300	0.295728	0.147864	−	0.989008i	$-0.452760\pi$
$89$	248.300	0.295728	0.147864	+	0.989008i	$0.452760\pi$
$90$	281.743	0.329981
$91$	−520.004	−0.599024
$92$	11.9689	0.0135636
$93$	−15.4365	−0.0172117
$94$	802.341	0.880374
$95$	−638.730	−0.689814
$96$	11.5598	0.0122898
$97$	−1781.03	−1.86429	−0.932144	−	0.362087i	$-0.882064\pi$
$97$	−1781.03	−1.86429	−0.932144	+	0.362087i	$0.882064\pi$
$98$	681.154	0.702112
$99$	−54.2013	−0.0550246
$100$	−0.322837	−0.000322837 0
$101$	−798.052	−0.786229	−0.393115	−	0.919489i	$-0.628602\pi$
$101$	−798.052	−0.786229	−0.393115	+	0.919489i	$0.628602\pi$
$102$	−179.576	−0.174320
$103$	−624.648	−0.597557	−0.298779	−	0.954322i	$-0.596579\pi$
$103$	−624.648	−0.597557	−0.298779	+	0.954322i	$0.596579\pi$
$104$	−1150.63	−1.08489
$105$	−335.929	−0.312222
$106$	−1207.24	−1.10620
$107$	−818.101	−0.739148	−0.369574	−	0.929201i	$-0.620496\pi$
$107$	−818.101	−0.739148	−0.369574	+	0.929201i	$0.620496\pi$
$108$	2.29904	0.00204838
$109$	1426.72	1.25372	0.626859	−	0.779133i	$-0.284340\pi$
$109$	1426.72	1.25372	0.626859	+	0.779133i	$0.284340\pi$
$110$	−188.529	−0.163414
$111$	−351.715	−0.300751
$112$	−657.792	−0.554960
$113$	−539.759	−0.449348	−0.224674	−	0.974434i	$-0.572132\pi$
$113$	−539.759	−0.449348	−0.224674	+	0.974434i	$0.572132\pi$
$114$	−494.899	−0.406592
$115$	−1547.53	−1.25485
$116$	2.74749	0.00219912
$117$	−460.140	−0.363589
$118$	2295.53	1.79085
$119$	214.112	0.164938
$120$	−743.318	−0.565461
$121$	−1294.73	−0.972751
$122$	1765.70	1.31032
$123$	685.593	0.502584
$124$	−0.438138	−0.000317306 0
$125$	1417.93	1.01459
$126$	−260.283	−0.184031
$127$	−1534.58	−1.07222	−0.536109	−	0.844149i	$-0.680106\pi$
$127$	−1534.58	−1.07222	−0.536109	+	0.844149i	$0.680106\pi$
$128$	−1470.84	−1.01567
$129$	−500.237	−0.341422
$130$	−1600.51	−1.07980
$131$	2132.68	1.42239	0.711196	−	0.702994i	$-0.248154\pi$
$131$	2132.68	1.42239	0.711196	+	0.702994i	$0.248154\pi$
$132$	−1.53841	−0.00101440
$133$	590.079	0.384709
$134$	−1449.76	−0.934629
$135$	−297.256	−0.189509
$136$	473.771	0.298717
$137$	−2039.92	−1.27213	−0.636067	−	0.771634i	$-0.719440\pi$
$137$	−2039.92	−1.27213	−0.636067	+	0.771634i	$0.719440\pi$
$138$	−1199.05	−0.739638
$139$	−266.658	−0.162717	−0.0813583	−	0.996685i	$-0.525926\pi$
$139$	−266.658	−0.162717	−0.0813583	+	0.996685i	$0.525926\pi$
$140$	−9.53474	−0.00575594
$141$	−846.518	−0.505601
$142$	542.047	0.320335
$143$	307.903	0.180057
$144$	−582.066	−0.336843
$145$	−355.239	−0.203455
$146$	1749.48	0.991701
$147$	−718.659	−0.403224
$148$	−9.98281	−0.00554447
$149$	2138.72	1.17591	0.587956	−	0.808893i	$-0.299933\pi$
$149$	2138.72	1.17591	0.587956	+	0.808893i	$0.299933\pi$
$150$	32.3420	0.0176047
$151$	176.774	0.0952692	0.0476346	−	0.998865i	$-0.484832\pi$
$151$	176.774	0.0952692	0.0476346	+	0.998865i	$0.484832\pi$
$152$	1305.68	0.696743
$153$	189.463	0.100112
$154$	174.169	0.0911359
$155$	56.6493	0.0293560
$156$	−13.0602	−0.00670292
$157$	−157.000	−0.0798087
$157$	−157.000	−0.0798087
$158$	2894.62	1.45749
$159$	1273.71	0.635294
$160$	−42.4225	−0.0209612
$161$	1429.66	0.699831
$162$	−230.319	−0.111701
$163$	−1664.50	−0.799841	−0.399920	−	0.916550i	$-0.630962\pi$
$163$	−1664.50	−0.799841	−0.399920	+	0.916550i	$0.630962\pi$
$164$	19.4593	0.00926535
$165$	198.909	0.0938489
$166$	1725.98	0.806998
$167$	−370.925	−0.171875	−0.0859373	−	0.996301i	$-0.527388\pi$
$167$	−370.925	−0.171875	−0.0859373	+	0.996301i	$0.527388\pi$
$168$	686.700	0.315358
$169$	416.931	0.189773
$170$	659.011	0.297317
$171$	522.148	0.233507
$172$	−14.1983	−0.00629426
$173$	−884.595	−0.388755	−0.194377	−	0.980927i	$-0.562269\pi$
$173$	−884.595	−0.388755	−0.194377	+	0.980927i	$0.562269\pi$
$174$	−275.245	−0.119921
$175$	−38.5621	−0.0166573
$176$	389.490	0.166812
$177$	−2421.92	−1.02849
$178$	−706.027	−0.297298
$179$	611.170	0.255201	0.127601	−	0.991826i	$-0.459272\pi$
$179$	611.170	0.255201	0.127601	+	0.991826i	$0.459272\pi$
$180$	−8.43708	−0.00349368
$181$	−92.1005	−0.0378220	−0.0189110	−	0.999821i	$-0.506020\pi$
$181$	−92.1005	−0.0378220	−0.0189110	+	0.999821i	$0.506020\pi$
$182$	1478.60	0.602203
$183$	−1862.92	−0.752518
$184$	3163.44	1.26746
$185$	1290.73	0.512955
$186$	43.8928	0.0173031
$187$	−126.780	−0.0495777
$188$	−24.0269	−0.00932097
$189$	274.614	0.105689
$190$	1816.19	0.693476
$191$	2453.57	0.929498	0.464749	−	0.885442i	$-0.346145\pi$
$191$	2453.57	0.929498	0.464749	+	0.885442i	$0.346145\pi$
$192$	1519.31	0.571075
$193$	4536.01	1.69176	0.845878	−	0.533377i	$-0.179077\pi$
$193$	4536.01	1.69176	0.845878	+	0.533377i	$0.179077\pi$
$194$	5064.25	1.87418
$195$	1688.63	0.620131
$196$	−20.3978	−0.00743361
$197$	162.932	0.0589261	0.0294630	−	0.999566i	$-0.490620\pi$
$197$	162.932	0.0589261	0.0294630	+	0.999566i	$0.490620\pi$
$198$	154.118	0.0553167
$199$	−641.654	−0.228571	−0.114286	−	0.993448i	$-0.536458\pi$
$199$	−641.654	−0.228571	−0.114286	+	0.993448i	$0.536458\pi$
$200$	−85.3273	−0.0301678
$201$	1529.59	0.536759
$202$	2269.21	0.790402
$203$	328.181	0.113467
$204$	5.37757	0.00184561
$205$	−2516.01	−0.857198
$206$	1776.15	0.600729
$207$	1265.07	0.424776
$208$	3306.56	1.10225
$209$	−349.396	−0.115638
$210$	955.193	0.313879
$211$	−2045.83	−0.667493	−0.333746	−	0.942663i	$-0.608313\pi$
$211$	−2045.83	−0.667493	−0.333746	+	0.942663i	$0.608313\pi$
$212$	36.1520	0.0117119
$213$	−571.893	−0.183969
$214$	2326.22	0.743071
$215$	1835.78	0.582322
$216$	607.646	0.191412
$217$	−52.3344	−0.0163718
$218$	−4056.80	−1.26037
$219$	−1845.81	−0.569536
$220$	5.64569	0.00173015
$221$	−1076.29	−0.327597
$222$	1000.08	0.302347
$223$	−4832.90	−1.45128	−0.725638	−	0.688077i	$-0.758455\pi$
$223$	−4832.90	−1.45128	−0.725638	+	0.688077i	$0.758455\pi$
$224$	39.1912	0.0116901
$225$	−34.1227	−0.0101104
$226$	1534.77	0.451733
$227$	−3008.17	−0.879557	−0.439778	−	0.898106i	$-0.644943\pi$
$227$	−3008.17	−0.879557	−0.439778	+	0.898106i	$0.644943\pi$
$228$	14.8202	0.00430480
$229$	5873.25	1.69483	0.847414	−	0.530933i	$-0.178159\pi$
$229$	5873.25	1.69483	0.847414	+	0.530933i	$0.178159\pi$
$230$	4400.31	1.26151
$231$	−183.759	−0.0523395
$232$	726.174	0.205499
$233$	5533.42	1.55582	0.777911	−	0.628375i	$-0.216280\pi$
$233$	5533.42	1.55582	0.777911	+	0.628375i	$0.216280\pi$
$234$	1308.38	0.365519
$235$	3106.57	0.862343
$236$	−68.7420	−0.0189607
$237$	−3054.00	−0.837040
$238$	−608.815	−0.165813
$239$	−2052.40	−0.555474	−0.277737	−	0.960657i	$-0.589584\pi$
$239$	−2052.40	−0.555474	−0.277737	+	0.960657i	$0.589584\pi$
$240$	2136.08	0.574514
$241$	−2959.02	−0.790902	−0.395451	−	0.918487i	$-0.629412\pi$
$241$	−2959.02	−0.790902	−0.395451	+	0.918487i	$0.629412\pi$
$242$	3681.49	0.977914
$243$	243.000	0.0641500
$244$	−52.8756	−0.0138730
$245$	2637.35	0.687732
$246$	−1949.44	−0.505252
$247$	−2966.18	−0.764104
$248$	−115.802	−0.0296508
$249$	−1821.01	−0.463461
$250$	−4031.79	−1.01997
$251$	487.897	0.122692	0.0613462	−	0.998117i	$-0.480461\pi$
$251$	487.897	0.122692	0.0613462	+	0.998117i	$0.480461\pi$
$252$	7.79443	0.00194842
$253$	−846.525	−0.210358
$254$	4363.48	1.07791
$255$	−695.296	−0.170750
$256$	130.775	0.0319275
$257$	5287.26	1.28331	0.641654	−	0.766994i	$-0.278249\pi$
$257$	5287.26	1.28331	0.641654	+	0.766994i	$0.278249\pi$
$258$	1422.39	0.343234
$259$	−1192.42	−0.286075
$260$	47.9288	0.0114324
$261$	290.400	0.0688709
$262$	−6064.15	−1.42994
$263$	−278.969	−0.0654068	−0.0327034	−	0.999465i	$-0.510412\pi$
$263$	−278.969	−0.0654068	−0.0327034	+	0.999465i	$0.510412\pi$
$264$	−406.607	−0.0947915
$265$	−4674.29	−1.08355
$266$	−1677.85	−0.386751
$267$	744.901	0.170739
$268$	43.4145	0.00989539
$269$	−2572.03	−0.582973	−0.291486	−	0.956575i	$-0.594150\pi$
$269$	−2572.03	−0.582973	−0.291486	+	0.956575i	$0.594150\pi$
$270$	845.229	0.190515
$271$	610.483	0.136842	0.0684210	−	0.997657i	$-0.478204\pi$
$271$	610.483	0.136842	0.0684210	+	0.997657i	$0.478204\pi$
$272$	−1361.48	−0.303499
$273$	−1560.01	−0.345847
$274$	5800.40	1.27889
$275$	22.8333	0.00500691
$276$	35.9068	0.00783092
$277$	7736.18	1.67806	0.839029	−	0.544086i	$-0.183124\pi$
$277$	7736.18	1.67806	0.839029	+	0.544086i	$0.183124\pi$
$278$	758.225	0.163580
$279$	−46.3095	−0.00993720
$280$	−2520.07	−0.537868
$281$	−1828.40	−0.388160	−0.194080	−	0.980986i	$-0.562172\pi$
$281$	−1828.40	−0.388160	−0.194080	+	0.980986i	$0.562172\pi$
$282$	2407.02	0.508284
$283$	−3587.24	−0.753496	−0.376748	−	0.926316i	$-0.622958\pi$
$283$	−3587.24	−0.753496	−0.376748	+	0.926316i	$0.622958\pi$
$284$	−16.2321	−0.00339155
$285$	−1916.19	−0.398265
$286$	−875.504	−0.181013
$287$	2324.36	0.478059
$288$	34.6794	0.00709550
$289$	−4469.84	−0.909798
$290$	1010.10	0.204535
$291$	−5343.08	−1.07635
$292$	−52.3900	−0.0104996
$293$	5555.33	1.10766	0.553832	−	0.832628i	$-0.313165\pi$
$293$	5555.33	1.10766	0.553832	+	0.832628i	$0.313165\pi$
$294$	2043.46	0.405364
$295$	8888.04	1.75417
$296$	−2638.50	−0.518107
$297$	−162.604	−0.0317685
$298$	−6081.32	−1.18215
$299$	−7186.54	−1.38999
$300$	−0.968512	−0.000186390 0
$301$	−1695.95	−0.324761
$302$	−502.646	−0.0957749
$303$	−2394.16	−0.453930
$304$	−3752.15	−0.707897
$305$	6836.58	1.28348
$306$	−538.727	−0.100644
$307$	3820.14	0.710186	0.355093	−	0.934831i	$-0.384449\pi$
$307$	3820.14	0.710186	0.355093	+	0.934831i	$0.384449\pi$
$308$	−5.21566	−0.000964902 0
$309$	−1873.94	−0.345000
$310$	−161.079	−0.0295118
$311$	−5314.07	−0.968917	−0.484458	−	0.874814i	$-0.660983\pi$
$311$	−5314.07	−0.968917	−0.484458	+	0.874814i	$0.660983\pi$
$312$	−3451.88	−0.626359
$313$	698.542	0.126147	0.0630734	−	0.998009i	$-0.479910\pi$
$313$	698.542	0.126147	0.0630734	+	0.998009i	$0.479910\pi$
$314$	446.420	0.0802323
$315$	−1007.79	−0.180261
$316$	−86.6822	−0.0154312
$317$	3349.65	0.593485	0.296743	−	0.954957i	$-0.404100\pi$
$317$	3349.65	0.593485	0.296743	+	0.954957i	$0.404100\pi$
$318$	−3621.72	−0.638666
$319$	−194.322	−0.0341064
$320$	−5575.58	−0.974015
$321$	−2454.30	−0.426747
$322$	−4065.14	−0.703545
$323$	1221.33	0.210392
$324$	6.89712	0.00118263
$325$	193.842	0.0330844
$326$	4732.92	0.804086
$327$	4280.17	0.723834
$328$	5143.18	0.865807
$329$	−2869.95	−0.480928
$330$	−565.587	−0.0943470
$331$	7041.41	1.16928	0.584639	−	0.811294i	$-0.301236\pi$
$331$	7041.41	1.16928	0.584639	+	0.811294i	$0.301236\pi$
$332$	−51.6860	−0.00854410
$333$	−1055.15	−0.173639
$334$	1054.70	0.172787
$335$	−5613.31	−0.915486
$336$	−1973.38	−0.320406
$337$	−2256.12	−0.364685	−0.182342	−	0.983235i	$-0.558368\pi$
$337$	−2256.12	−0.364685	−0.182342	+	0.983235i	$0.558368\pi$
$338$	−1185.52	−0.190780
$339$	−1619.28	−0.259431
$340$	−19.7347	−0.00314784
$341$	30.9881	0.00492111
$342$	−1484.70	−0.234746
$343$	−5925.08	−0.932724
$344$	−3752.68	−0.588171
$345$	−4642.59	−0.724489
$346$	2515.29	0.390818
$347$	−7235.78	−1.11942	−0.559708	−	0.828690i	$-0.689087\pi$
$347$	−7235.78	−1.11942	−0.559708	+	0.828690i	$0.689087\pi$
$348$	8.24248	0.00126967
$349$	9749.88	1.49541	0.747706	−	0.664029i	$-0.231155\pi$
$349$	9749.88	1.49541	0.747706	+	0.664029i	$0.231155\pi$
$350$	109.649	0.0167457
$351$	−1380.42	−0.209918
$352$	−23.2058	−0.00351384
$353$	−9032.49	−1.36190	−0.680951	−	0.732329i	$-0.738433\pi$
$353$	−9032.49	−1.36190	−0.680951	+	0.732329i	$0.738433\pi$
$354$	6886.59	1.03395
$355$	2098.75	0.313774
$356$	21.1427	0.00314764
$357$	642.336	0.0952270
$358$	−1737.83	−0.256556
$359$	−913.814	−0.134343	−0.0671717	−	0.997741i	$-0.521398\pi$
$359$	−913.814	−0.134343	−0.0671717	+	0.997741i	$0.521398\pi$
$360$	−2229.95	−0.326469
$361$	−3493.09	−0.509272
$362$	261.882	0.0380227
$363$	−3884.19	−0.561618
$364$	−44.2781	−0.00637583
$365$	6773.80	0.971389
$366$	5297.09	0.756512
$367$	1373.64	0.195376	0.0976882	−	0.995217i	$-0.468855\pi$
$367$	1373.64	0.195376	0.0976882	+	0.995217i	$0.468855\pi$
$368$	−9090.80	−1.28775
$369$	2056.78	0.290167
$370$	−3670.12	−0.515677
$371$	4318.26	0.604293
$372$	−1.31441	−0.000183197 0
$373$	6804.91	0.944625	0.472312	−	0.881431i	$-0.343419\pi$
$373$	6804.91	0.944625	0.472312	+	0.881431i	$0.343419\pi$
$374$	360.490	0.0498409
$375$	4253.78	0.585771
$376$	−6350.41	−0.871004
$377$	−1649.69	−0.225366
$378$	−780.849	−0.106250
$379$	4534.98	0.614634	0.307317	−	0.951607i	$-0.400569\pi$
$379$	4534.98	0.614634	0.307317	+	0.951607i	$0.400569\pi$
$380$	−54.3877	−0.00734218
$381$	−4603.73	−0.619045
$382$	−6976.58	−0.934431
$383$	−6451.41	−0.860709	−0.430354	−	0.902660i	$-0.641611\pi$
$383$	−6451.41	−0.860709	−0.430354	+	0.902660i	$0.641611\pi$
$384$	−4412.53	−0.586396
$385$	674.362	0.0892693
$386$	−12897.9	−1.70074
$387$	−1500.71	−0.197120
$388$	−151.654	−0.0198429
$389$	−9497.93	−1.23795	−0.618977	−	0.785409i	$-0.712453\pi$
$389$	−9497.93	−1.23795	−0.618977	+	0.785409i	$0.712453\pi$
$390$	−4801.52	−0.623422
$391$	2959.07	0.382727
$392$	−5391.23	−0.694639
$393$	6398.05	0.821218
$394$	−463.288	−0.0592389
$395$	11207.6	1.42764
$396$	−4.61522	−0.000585666 0
$397$	−429.424	−0.0542876	−0.0271438	−	0.999632i	$-0.508641\pi$
$397$	−429.424	−0.0542876	−0.0271438	+	0.999632i	$0.508641\pi$
$398$	1824.51	0.229784
$399$	1770.24	0.222112
$400$	245.206	0.0306507
$401$	−12592.3	−1.56815	−0.784076	−	0.620665i	$-0.786863\pi$
$401$	−12592.3	−1.56815	−0.784076	+	0.620665i	$0.786863\pi$
$402$	−4349.28	−0.539608
$403$	263.072	0.0325175
$404$	−67.9538	−0.00836839
$405$	−891.768	−0.109413
$406$	−933.163	−0.114069
$407$	706.053	0.0859895
$408$	1421.31	0.172464
$409$	−1951.84	−0.235971	−0.117986	−	0.993015i	$-0.537644\pi$
$409$	−1951.84	−0.235971	−0.117986	+	0.993015i	$0.537644\pi$
$410$	7154.11	0.861747
$411$	−6119.77	−0.734467
$412$	−53.1886	−0.00636022
$413$	−8211.04	−0.978303
$414$	−3597.16	−0.427030
$415$	6682.78	0.790469
$416$	−197.005	−0.0232186
$417$	−799.973	−0.0939445
$418$	993.487	0.116251
$419$	4266.21	0.497418	0.248709	−	0.968578i	$-0.419994\pi$
$419$	4266.21	0.497418	0.248709	+	0.968578i	$0.419994\pi$
$420$	−28.6042	−0.00332320
$421$	−156.125	−0.0180738	−0.00903688	−	0.999959i	$-0.502877\pi$
$421$	−156.125	−0.0180738	−0.00903688	+	0.999959i	$0.502877\pi$
$422$	5817.21	0.671036
$423$	−2539.55	−0.291909
$424$	9555.11	1.09443
$425$	−79.8147	−0.00910961
$426$	1626.14	0.184946
$427$	−6315.85	−0.715797
$428$	−69.6610	−0.00786727
$429$	923.710	0.103956
$430$	−5219.94	−0.585413
$431$	−15735.3	−1.75856	−0.879282	−	0.476301i	$-0.841977\pi$
$431$	−15735.3	−1.75856	−0.879282	+	0.476301i	$0.841977\pi$
$432$	−1746.20	−0.194477
$433$	−3510.65	−0.389633	−0.194817	−	0.980840i	$-0.562411\pi$
$433$	−3510.65	−0.389633	−0.194817	+	0.980840i	$0.562411\pi$
$434$	148.810	0.0164587
$435$	−1065.72	−0.117465
$436$	121.485	0.0133442
$437$	8154.99	0.892692
$438$	5248.45	0.572559
$439$	10356.5	1.12594	0.562969	−	0.826478i	$-0.309659\pi$
$439$	10356.5	1.12594	0.562969	+	0.826478i	$0.309659\pi$
$440$	1492.18	0.161675
$441$	−2155.98	−0.232802
$442$	3060.36	0.329336
$443$	−6881.36	−0.738021	−0.369011	−	0.929425i	$-0.620303\pi$
$443$	−6881.36	−0.738021	−0.369011	+	0.929425i	$0.620303\pi$
$444$	−29.9484	−0.00320110
$445$	−2733.66	−0.291208
$446$	13742.0	1.45898
$447$	6416.16	0.678913
$448$	5150.90	0.543208
$449$	4302.84	0.452257	0.226129	−	0.974097i	$-0.427393\pi$
$449$	4302.84	0.452257	0.226129	+	0.974097i	$0.427393\pi$
$450$	97.0259	0.0101641
$451$	−1376.30	−0.143697
$452$	−45.9603	−0.00478272
$453$	530.321	0.0550037
$454$	8553.55	0.884225
$455$	5724.97	0.589869
$456$	3917.05	0.402264
$457$	−3749.39	−0.383784	−0.191892	−	0.981416i	$-0.561462\pi$
$457$	−3749.39	−0.383784	−0.191892	+	0.981416i	$0.561462\pi$
$458$	−16700.2	−1.70382
$459$	568.389	0.0577998
$460$	−131.772	−0.0133563
$461$	−1757.63	−0.177573	−0.0887865	−	0.996051i	$-0.528299\pi$
$461$	−1757.63	−0.177573	−0.0887865	+	0.996051i	$0.528299\pi$
$462$	522.507	0.0526173
$463$	−3988.06	−0.400304	−0.200152	−	0.979765i	$-0.564144\pi$
$463$	−3988.06	−0.400304	−0.200152	+	0.979765i	$0.564144\pi$
$464$	−2086.81	−0.208788
$465$	169.948	0.0169487
$466$	−15733.9	−1.56408
$467$	9949.70	0.985904	0.492952	−	0.870056i	$-0.335918\pi$
$467$	9949.70	0.985904	0.492952	+	0.870056i	$0.335918\pi$
$468$	−39.1807	−0.00386993
$469$	5185.75	0.510567
$470$	−8833.36	−0.866920
$471$	−471.000	−0.0460776
$472$	−18168.8	−1.77179
$473$	1004.20	0.0976180
$474$	8683.86	0.841483
$475$	−219.964	−0.0212477
$476$	18.2316	0.00175555
$477$	3821.13	0.366787
$478$	5835.86	0.558423
$479$	−2160.82	−0.206118	−0.103059	−	0.994675i	$-0.532863\pi$
$479$	−2160.82	−0.206118	−0.103059	+	0.994675i	$0.532863\pi$
$480$	−127.267	−0.0121020
$481$	5994.01	0.568198
$482$	8413.80	0.795100
$483$	4288.97	0.404048
$484$	−110.246	−0.0103537
$485$	19608.2	1.83580
$486$	−690.956	−0.0644905
$487$	11219.9	1.04399	0.521994	−	0.852949i	$-0.325188\pi$
$487$	11219.9	1.04399	0.521994	+	0.852949i	$0.325188\pi$
$488$	−13975.2	−1.29637
$489$	−4993.51	−0.461788
$490$	−7499.15	−0.691382
$491$	957.240	0.0879830	0.0439915	−	0.999032i	$-0.485993\pi$
$491$	957.240	0.0879830	0.0439915	+	0.999032i	$0.485993\pi$
$492$	58.3780	0.00534935
$493$	679.260	0.0620534
$494$	8434.16	0.768160
$495$	596.728	0.0541837
$496$	332.780	0.0301255
$497$	−1938.89	−0.174992
$498$	5177.93	0.465920
$499$	2214.66	0.198681	0.0993406	−	0.995053i	$-0.468327\pi$
$499$	2214.66	0.198681	0.0993406	+	0.995053i	$0.468327\pi$
$500$	120.736	0.0107989
$501$	−1112.78	−0.0992319
$502$	−1387.31	−0.123344
$503$	9593.98	0.850446	0.425223	−	0.905089i	$-0.360196\pi$
$503$	9593.98	0.850446	0.425223	+	0.905089i	$0.360196\pi$
$504$	2060.10	0.182072
$505$	8786.14	0.774214
$506$	2407.04	0.211475
$507$	1250.79	0.109566
$508$	−130.669	−0.0114124
$509$	−19111.2	−1.66422	−0.832110	−	0.554610i	$-0.812867\pi$
$509$	−19111.2	−1.66422	−0.832110	+	0.554610i	$0.812867\pi$
$510$	1977.03	0.171656
$511$	−6257.85	−0.541744
$512$	11394.9	0.983571
$513$	1566.44	0.134815
$514$	−15034.0	−1.29012
$515$	6877.05	0.588425
$516$	−42.5950	−0.00363399
$517$	1699.35	0.144559
$518$	3390.57	0.287593
$519$	−2653.79	−0.224448
$520$	12667.8	1.06831
$521$	−22375.1	−1.88151	−0.940757	−	0.339081i	$-0.889884\pi$
$521$	−22375.1	−1.88151	−0.940757	+	0.339081i	$0.889884\pi$
$522$	−825.735	−0.0692365
$523$	−10403.4	−0.869810	−0.434905	−	0.900476i	$-0.643218\pi$
$523$	−10403.4	−0.869810	−0.434905	+	0.900476i	$0.643218\pi$
$524$	181.597	0.0151395
$525$	−115.686	−0.00961707
$526$	793.233	0.0657540
$527$	−108.320	−0.00895352
$528$	1168.47	0.0963090
$529$	7591.11	0.623910
$530$	13291.1	1.08930
$531$	−7265.77	−0.593800
$532$	50.2450	0.00409473
$533$	−11684.0	−0.949514
$534$	−2118.08	−0.171645
$535$	9006.86	0.727852
$536$	11474.6	0.924681
$537$	1833.51	0.147340
$538$	7313.42	0.586067
$539$	1442.68	0.115288
$540$	−25.3112	−0.00201708
$541$	−5149.89	−0.409263	−0.204631	−	0.978839i	$-0.565600\pi$
$541$	−5149.89	−0.409263	−0.204631	+	0.978839i	$0.565600\pi$
$542$	−1735.87	−0.137568
$543$	−276.301	−0.0218365
$544$	81.1169	0.00639312
$545$	−15707.5	−1.23456
$546$	4435.80	0.347682
$547$	3547.53	0.277297	0.138649	−	0.990342i	$-0.455724\pi$
$547$	3547.53	0.277297	0.138649	+	0.990342i	$0.455724\pi$
$548$	−173.699	−0.0135402
$549$	−5588.75	−0.434466
$550$	−64.9251	−0.00503348
$551$	1872.00	0.144736
$552$	9490.32	0.731766
$553$	−10354.0	−0.796194
$554$	−21997.4	−1.68697
$555$	3872.20	0.296155
$556$	−22.7058	−0.00173191
$557$	12090.2	0.919708	0.459854	−	0.887994i	$-0.347902\pi$
$557$	12090.2	0.919708	0.459854	+	0.887994i	$0.347902\pi$
$558$	131.678	0.00998994
$559$	8525.14	0.645036
$560$	7241.95	0.546479
$561$	−380.339	−0.0286237
$562$	5198.94	0.390220
$563$	−4627.38	−0.346396	−0.173198	−	0.984887i	$-0.555410\pi$
$563$	−4627.38	−0.346396	−0.173198	+	0.984887i	$0.555410\pi$
$564$	−72.0807	−0.00538146
$565$	5942.47	0.442480
$566$	10200.1	0.757495
$567$	823.843	0.0610196
$568$	−4290.22	−0.316926
$569$	19017.9	1.40118	0.700590	−	0.713564i	$-0.252920\pi$
$569$	19017.9	1.40118	0.700590	+	0.713564i	$0.252920\pi$
$570$	5448.58	0.400378
$571$	−14356.9	−1.05222	−0.526111	−	0.850416i	$-0.676350\pi$
$571$	−14356.9	−1.05222	−0.526111	+	0.850416i	$0.676350\pi$
$572$	26.2178	0.00191647
$573$	7360.71	0.536646
$574$	−6609.19	−0.480596
$575$	−532.935	−0.0386520
$576$	4557.92	0.329710
$577$	−15920.2	−1.14865	−0.574323	−	0.818629i	$-0.694735\pi$
$577$	−15920.2	−1.14865	−0.574323	+	0.818629i	$0.694735\pi$
$578$	12709.7	0.914627
$579$	13608.0	0.976736
$580$	−30.2485	−0.00216552
$581$	−6173.76	−0.440845
$582$	15192.7	1.08206
$583$	−2556.92	−0.181641
$584$	−13846.9	−0.981145
$585$	5065.90	0.358033
$586$	−15796.2	−1.11354
$587$	7240.36	0.509100	0.254550	−	0.967060i	$-0.418073\pi$
$587$	7240.36	0.509100	0.254550	+	0.967060i	$0.418073\pi$
$588$	−61.1935	−0.00429180
$589$	−298.524	−0.0208836
$590$	−25272.6	−1.76349
$591$	488.797	0.0340210
$592$	7582.27	0.526401
$593$	−2093.93	−0.145004	−0.0725021	−	0.997368i	$-0.523098\pi$
$593$	−2093.93	−0.145004	−0.0725021	+	0.997368i	$0.523098\pi$
$594$	462.354	0.0319371
$595$	−2357.26	−0.162417
$596$	182.111	0.0125161
$597$	−1924.96	−0.131966
$598$	20434.5	1.39737
$599$	5730.79	0.390908	0.195454	−	0.980713i	$-0.437382\pi$
$599$	5730.79	0.390908	0.195454	+	0.980713i	$0.437382\pi$
$600$	−255.982	−0.0174174
$601$	−8668.24	−0.588328	−0.294164	−	0.955755i	$-0.595041\pi$
$601$	−8668.24	−0.588328	−0.294164	+	0.955755i	$0.595041\pi$
$602$	4822.34	0.326485
$603$	4588.76	0.309898
$604$	15.0522	0.00101402
$605$	14254.3	0.957885
$606$	6807.64	0.456339
$607$	−10626.6	−0.710578	−0.355289	−	0.934757i	$-0.615617\pi$
$607$	−10626.6	−0.710578	−0.355289	+	0.934757i	$0.615617\pi$
$608$	223.553	0.0149116
$609$	984.543	0.0655102
$610$	−19439.4	−1.29029
$611$	14426.5	0.955213
$612$	16.1327	0.00106557
$613$	−14962.4	−0.985849	−0.492925	−	0.870072i	$-0.664072\pi$
$613$	−14962.4	−0.985849	−0.492925	+	0.870072i	$0.664072\pi$
$614$	−10862.3	−0.713956
$615$	−7548.02	−0.494903
$616$	−1378.52	−0.0901659
$617$	−15425.9	−1.00652	−0.503261	−	0.864134i	$-0.667867\pi$
$617$	−15425.9	−1.00652	−0.503261	+	0.864134i	$0.667867\pi$
$618$	5328.45	0.346831
$619$	7010.35	0.455201	0.227601	−	0.973755i	$-0.426912\pi$
$619$	7010.35	0.455201	0.227601	+	0.973755i	$0.426912\pi$
$620$	4.82367	0.000312457 0
$621$	3795.22	0.245244
$622$	15110.2	0.974060
$623$	2525.44	0.162407
$624$	9919.68	0.636386
$625$	−15136.7	−0.968749
$626$	−1986.26	−0.126816
$627$	−1048.19	−0.0667633
$628$	−13.3685	−0.000849460 0
$629$	−2468.04	−0.156450
$630$	2865.58	0.181218
$631$	7293.47	0.460140	0.230070	−	0.973174i	$-0.426104\pi$
$631$	7293.47	0.460140	0.230070	+	0.973174i	$0.426104\pi$
$632$	−22910.5	−1.44198
$633$	−6137.50	−0.385377
$634$	−9524.52	−0.596636
$635$	16894.9	1.05583
$636$	108.456	0.00676188
$637$	12247.5	0.761797
$638$	552.542	0.0342874
$639$	−1715.68	−0.106215
$640$	16193.2	1.00015
$641$	−811.232	−0.0499871	−0.0249936	−	0.999688i	$-0.507957\pi$
$641$	−811.232	−0.0499871	−0.0249936	+	0.999688i	$0.507957\pi$
$642$	6978.66	0.429012
$643$	8842.58	0.542328	0.271164	−	0.962533i	$-0.412591\pi$
$643$	8842.58	0.542328	0.271164	+	0.962533i	$0.412591\pi$
$644$	121.735	0.00744879
$645$	5507.35	0.336204
$646$	−3472.78	−0.211509
$647$	5756.68	0.349797	0.174898	−	0.984586i	$-0.444040\pi$
$647$	5756.68	0.349797	0.174898	+	0.984586i	$0.444040\pi$
$648$	1822.94	0.110512
$649$	4861.90	0.294062
$650$	−551.179	−0.0332600
$651$	−157.003	−0.00945228
$652$	−141.732	−0.00851327
$653$	12534.3	0.751159	0.375580	−	0.926790i	$-0.377444\pi$
$653$	12534.3	0.751159	0.375580	+	0.926790i	$0.377444\pi$
$654$	−12170.4	−0.727676
$655$	−23479.7	−1.40065
$656$	−14780.0	−0.879668
$657$	−5537.43	−0.328822
$658$	8160.53	0.483481
$659$	−8447.89	−0.499367	−0.249684	−	0.968327i	$-0.580327\pi$
$659$	−8447.89	−0.499367	−0.249684	+	0.968327i	$0.580327\pi$
$660$	16.9371	0.000998900 0
$661$	4335.26	0.255102	0.127551	−	0.991832i	$-0.459288\pi$
$661$	4335.26	0.255102	0.127551	+	0.991832i	$0.459288\pi$
$662$	−20021.8	−1.17548
$663$	−3228.87	−0.189138
$664$	−13660.8	−0.798408
$665$	−6496.46	−0.378830
$666$	3000.24	0.174560
$667$	4535.52	0.263292
$668$	−31.5842	−0.00182938
$669$	−14498.7	−0.837895
$670$	15961.1	0.920346
$671$	3739.72	0.215157
$672$	117.574	0.00674926
$673$	25669.8	1.47028	0.735141	−	0.677914i	$-0.237116\pi$
$673$	25669.8	1.47028	0.735141	+	0.677914i	$0.237116\pi$
$674$	6415.14	0.366620
$675$	−102.368	−0.00583726
$676$	35.5016	0.00201989
$677$	8477.09	0.481242	0.240621	−	0.970619i	$-0.422649\pi$
$677$	8477.09	0.481242	0.240621	+	0.970619i	$0.422649\pi$
$678$	4604.32	0.260808
$679$	−18114.7	−1.02382
$680$	−5215.97	−0.294152
$681$	−9024.51	−0.507812
$682$	−88.1128	−0.00494723
$683$	6811.49	0.381602	0.190801	−	0.981629i	$-0.438891\pi$
$683$	6811.49	0.381602	0.190801	+	0.981629i	$0.438891\pi$
$684$	44.4607	0.00248538
$685$	22458.5	1.25269
$686$	16847.6	0.937675
$687$	17619.8	0.978509
$688$	10784.1	0.597587
$689$	−21706.8	−1.20024
$690$	13200.9	0.728335
$691$	−25532.6	−1.40566	−0.702828	−	0.711360i	$-0.748079\pi$
$691$	−25532.6	−1.40566	−0.702828	+	0.711360i	$0.748079\pi$
$692$	−75.3230	−0.00413779
$693$	−551.276	−0.0302182
$694$	20574.5	1.12536
$695$	2935.76	0.160230
$696$	2178.52	0.118645
$697$	4810.91	0.261443
$698$	−27723.2	−1.50335
$699$	16600.3	0.898254
$700$	−3.28355	−0.000177295 0
$701$	−26418.1	−1.42339	−0.711695	−	0.702488i	$-0.752072\pi$
$701$	−26418.1	−1.42339	−0.711695	+	0.702488i	$0.752072\pi$
$702$	3925.14	0.211032
$703$	−6801.76	−0.364912
$704$	−3049.94	−0.163280
$705$	9319.72	0.497874
$706$	25683.4	1.36913
$707$	−8116.90	−0.431779
$708$	−206.226	−0.0109470
$709$	14843.8	0.786279	0.393139	−	0.919479i	$-0.371389\pi$
$709$	14843.8	0.786279	0.393139	+	0.919479i	$0.371389\pi$
$710$	−5967.66	−0.315440
$711$	−9161.99	−0.483265
$712$	5588.10	0.294133
$713$	−723.270	−0.0379897
$714$	−1826.44	−0.0957324
$715$	−3389.85	−0.177305
$716$	52.0409	0.00271629
$717$	−6157.19	−0.320703
$718$	2598.37	0.135056
$719$	15475.1	0.802674	0.401337	−	0.915931i	$-0.368546\pi$
$719$	15475.1	0.802674	0.401337	+	0.915931i	$0.368546\pi$
$720$	6408.24	0.331696
$721$	−6353.23	−0.328165
$722$	9932.40	0.511975
$723$	−8877.06	−0.456627
$724$	−7.84232	−0.000402566 0
$725$	−122.336	−0.00626683
$726$	11044.5	0.564599
$727$	−3234.97	−0.165032	−0.0825161	−	0.996590i	$-0.526296\pi$
$727$	−3234.97	−0.165032	−0.0825161	+	0.996590i	$0.526296\pi$
$728$	−11702.9	−0.595794
$729$	729.000	0.0370370
$730$	−19260.9	−0.976545
$731$	−3510.24	−0.177607
$732$	−158.627	−0.00800958
$733$	−24043.0	−1.21153	−0.605763	−	0.795645i	$-0.707132\pi$
$733$	−24043.0	−1.21153	−0.605763	+	0.795645i	$0.707132\pi$
$734$	−3905.85	−0.196413
$735$	7912.06	0.397062
$736$	541.629	0.0271260
$737$	−3070.57	−0.153468
$738$	−5848.33	−0.291707
$739$	2068.31	0.102955	0.0514777	−	0.998674i	$-0.483607\pi$
$739$	2068.31	0.102955	0.0514777	+	0.998674i	$0.483607\pi$
$740$	109.906	0.00545974
$741$	−8898.55	−0.441156
$742$	−12278.7	−0.607500
$743$	22686.9	1.12019	0.560094	−	0.828429i	$-0.310765\pi$
$743$	22686.9	1.12019	0.560094	+	0.828429i	$0.310765\pi$
$744$	−347.405	−0.0171189
$745$	−23546.2	−1.15794
$746$	−19349.4	−0.949639
$747$	−5463.02	−0.267579
$748$	−10.7952	−0.000527691 0
$749$	−8320.82	−0.405923
$750$	−12095.4	−0.588880
$751$	31401.4	1.52577	0.762886	−	0.646533i	$-0.223782\pi$
$751$	31401.4	1.52577	0.762886	+	0.646533i	$0.223782\pi$
$752$	18249.2	0.884948
$753$	1463.69	0.0708364
$754$	4690.78	0.226563
$755$	−1946.19	−0.0938132
$756$	23.3833	0.00112492
$757$	28168.7	1.35246	0.676228	−	0.736693i	$-0.263614\pi$
$757$	28168.7	1.35246	0.676228	+	0.736693i	$0.263614\pi$
$758$	−12894.9	−0.617896
$759$	−2539.58	−0.121450
$760$	−14374.9	−0.686095
$761$	17982.7	0.856601	0.428301	−	0.903636i	$-0.359112\pi$
$761$	17982.7	0.856601	0.428301	+	0.903636i	$0.359112\pi$
$762$	13090.4	0.622331
$763$	14511.0	0.688512
$764$	208.921	0.00989330
$765$	−2085.89	−0.0985823
$766$	18344.2	0.865277
$767$	41274.9	1.94309
$768$	392.325	0.0184334
$769$	−31627.3	−1.48311	−0.741554	−	0.670894i	$-0.765911\pi$
$769$	−31627.3	−1.48311	−0.741554	+	0.670894i	$0.765911\pi$
$770$	−1917.51	−0.0897431
$771$	15861.8	0.740918
$772$	386.239	0.0180065
$773$	−18080.0	−0.841257	−0.420628	−	0.907233i	$-0.638190\pi$
$773$	−18080.0	−0.841257	−0.420628	+	0.907233i	$0.638190\pi$
$774$	4267.18	0.198166
$775$	19.5087	0.000904225 0
$776$	−40082.8	−1.85424
$777$	−3577.26	−0.165165
$778$	27006.8	1.24452
$779$	13258.5	0.609803
$780$	143.786	0.00660049
$781$	1148.05	0.0525998
$782$	−8413.92	−0.384759
$783$	871.200	0.0397626
$784$	15492.8	0.705759
$785$	1728.49	0.0785890
$786$	−18192.5	−0.825577
$787$	22252.2	1.00788	0.503941	−	0.863738i	$-0.331883\pi$
$787$	22252.2	1.00788	0.503941	+	0.863738i	$0.331883\pi$
$788$	13.8736	0.000627192 0
$789$	−836.908	−0.0377626
$790$	−31868.2	−1.43522
$791$	−5489.83	−0.246771
$792$	−1219.82	−0.0547279
$793$	31748.2	1.42171
$794$	1221.04	0.0545758
$795$	−14022.9	−0.625585
$796$	−54.6366	−0.00243284
$797$	20794.7	0.924200	0.462100	−	0.886828i	$-0.347096\pi$
$797$	20794.7	0.924200	0.462100	+	0.886828i	$0.347096\pi$
$798$	−5033.56	−0.223291
$799$	−5940.14	−0.263013
$800$	−14.6093	−0.000645648 0
$801$	2234.70	0.0985760
$802$	35805.4	1.57648
$803$	3705.38	0.162840
$804$	130.244	0.00571311
$805$	−15739.8	−0.689136
$806$	−748.030	−0.0326901
$807$	−7716.10	−0.336579
$808$	−17960.5	−0.781989
$809$	−4700.54	−0.204280	−0.102140	−	0.994770i	$-0.532569\pi$
$809$	−4700.54	−0.204280	−0.102140	+	0.994770i	$0.532569\pi$
$810$	2535.69	0.109994
$811$	21187.9	0.917394	0.458697	−	0.888593i	$-0.348316\pi$
$811$	21187.9	0.917394	0.458697	+	0.888593i	$0.348316\pi$
$812$	27.9445	0.00120771
$813$	1831.45	0.0790058
$814$	−2007.62	−0.0864460
$815$	18325.3	0.787617
$816$	−4084.44	−0.175225
$817$	−9673.98	−0.414259
$818$	5549.94	0.237224
$819$	−4680.03	−0.199675
$820$	−214.237	−0.00912376
$821$	15147.3	0.643902	0.321951	−	0.946756i	$-0.395661\pi$
$821$	15147.3	0.643902	0.321951	+	0.946756i	$0.395661\pi$
$822$	17401.2	0.738365
$823$	15595.3	0.660533	0.330266	−	0.943888i	$-0.392861\pi$
$823$	15595.3	0.660533	0.330266	+	0.943888i	$0.392861\pi$
$824$	−14058.0	−0.594335
$825$	68.4999	0.00289074
$826$	23347.6	0.983495
$827$	35450.9	1.49063	0.745313	−	0.666715i	$-0.232300\pi$
$827$	35450.9	1.49063	0.745313	+	0.666715i	$0.232300\pi$
$828$	107.720	0.00452119
$829$	−17113.5	−0.716979	−0.358490	−	0.933534i	$-0.616708\pi$
$829$	−17113.5	−0.716979	−0.358490	+	0.933534i	$0.616708\pi$
$830$	−19002.1	−0.794665
$831$	23208.6	0.968828
$832$	−25892.3	−1.07891
$833$	−5042.93	−0.209757
$834$	2274.67	0.0944431
$835$	4083.69	0.169248
$836$	−29.7510	−0.00123081
$837$	−138.929	−0.00573724
$838$	−12130.7	−0.500058
$839$	21649.8	0.890862	0.445431	−	0.895316i	$-0.353050\pi$
$839$	21649.8	0.890862	0.445431	+	0.895316i	$0.353050\pi$
$840$	−7560.21	−0.310538
$841$	−23347.9	−0.957311
$842$	443.931	0.0181697
$843$	−5485.19	−0.224104
$844$	−174.202	−0.00710460
$845$	−4590.20	−0.186873
$846$	7221.07	0.293458
$847$	−13168.6	−0.534212
$848$	−27458.6	−1.11195
$849$	−10761.7	−0.435031
$850$	226.948	0.00915796
$851$	−16479.4	−0.663817
$852$	−48.6964	−0.00195811
$853$	−13029.0	−0.522981	−0.261491	−	0.965206i	$-0.584214\pi$
$853$	−13029.0	−0.522981	−0.261491	+	0.965206i	$0.584214\pi$
$854$	17958.7	0.719596
$855$	−5748.57	−0.229938
$856$	−18411.7	−0.735162
$857$	24393.5	0.972305	0.486152	−	0.873874i	$-0.338400\pi$
$857$	24393.5	0.972305	0.486152	+	0.873874i	$0.338400\pi$
$858$	−2626.51	−0.104508
$859$	22723.2	0.902568	0.451284	−	0.892380i	$-0.350966\pi$
$859$	22723.2	0.902568	0.451284	+	0.892380i	$0.350966\pi$
$860$	156.316	0.00619807
$861$	6973.09	0.276007
$862$	44742.3	1.76790
$863$	23101.2	0.911212	0.455606	−	0.890182i	$-0.349423\pi$
$863$	23101.2	0.911212	0.455606	+	0.890182i	$0.349423\pi$
$864$	104.038	0.00409659
$865$	9738.93	0.382813
$866$	9982.33	0.391701
$867$	−13409.5	−0.525272
$868$	−4.45625	−0.000174257 0
$869$	6130.76	0.239323
$870$	3030.30	0.118088
$871$	−26067.5	−1.01408
$872$	32109.0	1.24696
$873$	−16029.3	−0.621430
$874$	−23188.2	−0.897430
$875$	14421.6	0.557187
$876$	−157.170	−0.00606197
$877$	41688.1	1.60514	0.802570	−	0.596558i	$-0.203465\pi$
$877$	41688.1	1.60514	0.802570	+	0.596558i	$0.203465\pi$
$878$	−29448.0	−1.13192
$879$	16666.0	0.639511
$880$	−4288.08	−0.164263
$881$	−1501.76	−0.0574296	−0.0287148	−	0.999588i	$-0.509141\pi$
$881$	−1501.76	−0.0574296	−0.0287148	+	0.999588i	$0.509141\pi$
$882$	6130.39	0.234037
$883$	21713.1	0.827526	0.413763	−	0.910385i	$-0.364214\pi$
$883$	21713.1	0.827526	0.413763	+	0.910385i	$0.364214\pi$
$884$	−91.6456	−0.00348685
$885$	26664.1	1.01277
$886$	19566.7	0.741939
$887$	−7016.56	−0.265606	−0.132803	−	0.991142i	$-0.542398\pi$
$887$	−7016.56	−0.265606	−0.132803	+	0.991142i	$0.542398\pi$
$888$	−7915.49	−0.299129
$889$	−15608.0	−0.588837
$890$	7772.99	0.292754
$891$	−487.812	−0.0183415
$892$	−411.519	−0.0154470
$893$	−16370.7	−0.613464
$894$	−18244.0	−0.682516
$895$	−6728.67	−0.251301
$896$	−14959.8	−0.557781
$897$	−21559.6	−0.802514
$898$	−12234.9	−0.454657
$899$	−166.028	−0.00615946
$900$	−2.90554	−0.000107612 0
$901$	8937.81	0.330479
$902$	3913.42	0.144460
$903$	−5087.86	−0.187501
$904$	−12147.5	−0.446924
$905$	1013.98	0.0372440
$906$	−1507.94	−0.0552956
$907$	−8887.41	−0.325360	−0.162680	−	0.986679i	$-0.552014\pi$
$907$	−8887.41	−0.325360	−0.162680	+	0.986679i	$0.552014\pi$
$908$	−256.145	−0.00936174
$909$	−7182.47	−0.262076
$910$	−16278.6	−0.593000
$911$	−41416.3	−1.50624	−0.753119	−	0.657885i	$-0.771451\pi$
$911$	−41416.3	−1.50624	−0.753119	+	0.657885i	$0.771451\pi$
$912$	−11256.5	−0.408704
$913$	3655.59	0.132511
$914$	10661.2	0.385821
$915$	20509.7	0.741018
$916$	500.105	0.0180392
$917$	21691.3	0.781144
$918$	−1616.18	−0.0581066
$919$	13068.8	0.469099	0.234549	−	0.972104i	$-0.424639\pi$
$919$	13068.8	0.469099	0.234549	+	0.972104i	$0.424639\pi$
$920$	−34827.8	−1.24809
$921$	11460.4	0.410026
$922$	4997.72	0.178515
$923$	9746.31	0.347566
$924$	−15.6470	−0.000557086 0
$925$	444.499	0.0158001
$926$	11339.8	0.402429
$927$	−5621.83	−0.199186
$928$	124.332	0.00439806
$929$	6759.21	0.238711	0.119355	−	0.992852i	$-0.461917\pi$
$929$	6759.21	0.238711	0.119355	+	0.992852i	$0.461917\pi$
$930$	−483.237	−0.0170387
$931$	−13898.0	−0.489247
$932$	471.169	0.0165597
$933$	−15942.2	−0.559404
$934$	−28291.4	−0.991137
$935$	1395.78	0.0488201
$936$	−10355.6	−0.361628
$937$	28656.8	0.999123	0.499561	−	0.866278i	$-0.333495\pi$
$937$	28656.8	0.999123	0.499561	+	0.866278i	$0.333495\pi$
$938$	−14745.4	−0.513277
$939$	2095.63	0.0728309
$940$	264.524	0.00917852
$941$	−30295.8	−1.04954	−0.524769	−	0.851245i	$-0.675848\pi$
$941$	−30295.8	−1.04954	−0.524769	+	0.851245i	$0.675848\pi$
$942$	1339.26	0.0463221
$943$	32123.1	1.10930
$944$	52211.8	1.80016
$945$	−3023.36	−0.104074
$946$	−2855.39	−0.0981361
$947$	32292.6	1.10810	0.554048	−	0.832484i	$-0.313082\pi$
$947$	32292.6	1.10810	0.554048	+	0.832484i	$0.313082\pi$
$948$	−260.047	−0.00890920
$949$	31456.7	1.07600
$950$	625.455	0.0213605
$951$	10048.9	0.342649
$952$	4818.68	0.164049
$953$	−8744.81	−0.297243	−0.148621	−	0.988894i	$-0.547484\pi$
$953$	−8744.81	−0.297243	−0.148621	+	0.988894i	$0.547484\pi$
$954$	−10865.1	−0.368734
$955$	−27012.5	−0.915293
$956$	−174.761	−0.00591231
$957$	−582.965	−0.0196913
$958$	6144.18	0.207212
$959$	−20747.8	−0.698627
$960$	−16726.8	−0.562348
$961$	−29764.5	−0.999111
$962$	−17043.6	−0.571214
$963$	−7362.91	−0.246383
$964$	−251.960	−0.00841812
$965$	−49939.1	−1.66590
$966$	−12195.4	−0.406192
$967$	1912.46	0.0635992	0.0317996	−	0.999494i	$-0.489876\pi$
$967$	1912.46	0.0635992	0.0317996	+	0.999494i	$0.489876\pi$
$968$	−29138.4	−0.967505
$969$	3663.99	0.121470
$970$	−55754.7	−1.84554
$971$	−34003.4	−1.12381	−0.561906	−	0.827201i	$-0.689932\pi$
$971$	−34003.4	−1.12381	−0.561906	+	0.827201i	$0.689932\pi$
$972$	20.6914	0.000682794 0
$973$	−2712.15	−0.0893602
$974$	−31903.1	−1.04953
$975$	581.527	0.0191013
$976$	40160.7	1.31712
$977$	−37936.3	−1.24226	−0.621130	−	0.783707i	$-0.713326\pi$
$977$	−37936.3	−1.24226	−0.621130	+	0.783707i	$0.713326\pi$
$978$	14198.8	0.464239
$979$	−1495.36	−0.0488169
$980$	224.570	0.00732001
$981$	12840.5	0.417906
$982$	−2721.85	−0.0884500
$983$	22986.8	0.745844	0.372922	−	0.927863i	$-0.378356\pi$
$983$	22986.8	0.745844	0.372922	+	0.927863i	$0.378356\pi$
$984$	15429.5	0.499874
$985$	−1793.80	−0.0580256
$986$	−1931.43	−0.0623828
$987$	−8609.85	−0.277664
$988$	−252.569	−0.00813290
$989$	−23438.4	−0.753586
$990$	−1696.76	−0.0544713
$991$	−21240.3	−0.680847	−0.340423	−	0.940272i	$-0.610570\pi$
$991$	−21240.3	−0.680847	−0.340423	+	0.940272i	$0.610570\pi$
$992$	−19.8270	−0.000634585 0
$993$	21124.2	0.675082
$994$	5513.11	0.175921
$995$	7064.28	0.225078
$996$	−155.058	−0.00493294
$997$	−872.926	−0.0277290	−0.0138645	−	0.999904i	$-0.504413\pi$
$997$	−872.926	−0.0277290	−0.0138645	+	0.999904i	$0.504413\pi$
$998$	−6297.26	−0.199736
$999$	−3165.44	−0.100250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.4.a.a.1.4	✓	14
3.2	odd	2		1413.4.a.a.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.4.a.a.1.4	✓	14	1.1	even	1	trivial
1413.4.a.a.1.11		14	3.2	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	471.a (trivial)

\(f(q)\)	\(=\)	\(q-2.84344 q^{2} +3.00000 q^{3} +0.0851496 q^{4} -11.0095 q^{5} -8.53032 q^{6} +10.1709 q^{7} +22.5054 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.84344 q^{2} +3.00000 q^{3} +0.0851496 q^{4} -11.0095 q^{5} -8.53032 q^{6} +10.1709 q^{7} +22.5054 q^{8} +9.00000 q^{9} +31.3048 q^{10} -6.02237 q^{11} +0.255449 q^{12} -51.1266 q^{13} -28.9203 q^{14} -33.0284 q^{15} -64.6739 q^{16} +21.0514 q^{17} -25.5910 q^{18} +58.0164 q^{19} -0.937453 q^{20} +30.5127 q^{21} +17.1242 q^{22} +140.564 q^{23} +67.5162 q^{24} -3.79141 q^{25} +145.375 q^{26} +27.0000 q^{27} +0.866048 q^{28} +32.2667 q^{29} +93.9144 q^{30} -5.14550 q^{31} +3.85327 q^{32} -18.0671 q^{33} -59.8585 q^{34} -111.976 q^{35} +0.766347 q^{36} -117.238 q^{37} -164.966 q^{38} -153.380 q^{39} -247.773 q^{40} +228.531 q^{41} -86.7610 q^{42} -166.746 q^{43} -0.512802 q^{44} -99.0853 q^{45} -399.684 q^{46} -282.173 q^{47} -194.022 q^{48} -239.553 q^{49} +10.7807 q^{50} +63.1543 q^{51} -4.35341 q^{52} +424.570 q^{53} -76.7729 q^{54} +66.3031 q^{55} +228.900 q^{56} +174.049 q^{57} -91.7483 q^{58} -807.308 q^{59} -2.81236 q^{60} -620.972 q^{61} +14.6309 q^{62} +91.5381 q^{63} +506.435 q^{64} +562.877 q^{65} +51.3727 q^{66} +509.862 q^{67} +1.79252 q^{68} +421.691 q^{69} +318.398 q^{70} -190.631 q^{71} +202.549 q^{72} -615.270 q^{73} +333.360 q^{74} -11.3742 q^{75} +4.94008 q^{76} -61.2529 q^{77} +436.126 q^{78} -1018.00 q^{79} +712.026 q^{80} +81.0000 q^{81} -649.814 q^{82} -607.003 q^{83} +2.59814 q^{84} -231.765 q^{85} +474.131 q^{86} +96.8000 q^{87} -135.536 q^{88} +248.300 q^{89} +281.743 q^{90} -520.004 q^{91} +11.9689 q^{92} -15.4365 q^{93} +802.341 q^{94} -638.730 q^{95} +11.5598 q^{96} -1781.03 q^{97} +681.154 q^{98} -54.2013 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 42 q^{3} + 26 q^{4} - 32 q^{5} - 6 q^{6} - 60 q^{7} - 45 q^{8} + 126 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 42 * q^3 + 26 * q^4 - 32 * q^5 - 6 * q^6 - 60 * q^7 - 45 * q^8 + 126 * q^9	\( 14 q - 2 q^{2} + 42 q^{3} + 26 q^{4} - 32 q^{5} - 6 q^{6} - 60 q^{7} - 45 q^{8} + 126 q^{9} - 155 q^{10} - 61 q^{11} + 78 q^{12} - 204 q^{13} - 99 q^{14} - 96 q^{15} - 66 q^{16} - 324 q^{17} - 18 q^{18} - 400 q^{19} - 257 q^{20} - 180 q^{21} - 154 q^{22} - 105 q^{23} - 135 q^{24} - 70 q^{25} - 351 q^{26} + 378 q^{27} - 575 q^{28} - 418 q^{29} - 465 q^{30} - 663 q^{31} - 572 q^{32} - 183 q^{33} - 883 q^{34} - 386 q^{35} + 234 q^{36} - 646 q^{37} - 104 q^{38} - 612 q^{39} - 1068 q^{40} - 881 q^{41} - 297 q^{42} - 1535 q^{43} + 329 q^{44} - 288 q^{45} - 112 q^{46} - 252 q^{47} - 198 q^{48} - 1184 q^{49} + 1901 q^{50} - 972 q^{51} - 1042 q^{52} - 78 q^{53} - 54 q^{54} - 1402 q^{55} + 1092 q^{56} - 1200 q^{57} + 710 q^{58} + 110 q^{59} - 771 q^{60} - 815 q^{61} + 1186 q^{62} - 540 q^{63} - 863 q^{64} - 4 q^{65} - 462 q^{66} - 1834 q^{67} - 735 q^{68} - 315 q^{69} + 977 q^{70} - 28 q^{71} - 405 q^{72} - 2422 q^{73} + 1588 q^{74} - 210 q^{75} - 3070 q^{76} - 746 q^{77} - 1053 q^{78} - 2566 q^{79} + 1061 q^{80} + 1134 q^{81} - 3300 q^{82} + 292 q^{83} - 1725 q^{84} - 912 q^{85} + 1191 q^{86} - 1254 q^{87} - 708 q^{88} - 780 q^{89} - 1395 q^{90} - 2210 q^{91} + 1918 q^{92} - 1989 q^{93} - 1496 q^{94} + 1604 q^{95} - 1716 q^{96} - 1370 q^{97} - 13 q^{98} - 549 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 42 * q^3 + 26 * q^4 - 32 * q^5 - 6 * q^6 - 60 * q^7 - 45 * q^8 + 126 * q^9 - 155 * q^10 - 61 * q^11 + 78 * q^12 - 204 * q^13 - 99 * q^14 - 96 * q^15 - 66 * q^16 - 324 * q^17 - 18 * q^18 - 400 * q^19 - 257 * q^20 - 180 * q^21 - 154 * q^22 - 105 * q^23 - 135 * q^24 - 70 * q^25 - 351 * q^26 + 378 * q^27 - 575 * q^28 - 418 * q^29 - 465 * q^30 - 663 * q^31 - 572 * q^32 - 183 * q^33 - 883 * q^34 - 386 * q^35 + 234 * q^36 - 646 * q^37 - 104 * q^38 - 612 * q^39 - 1068 * q^40 - 881 * q^41 - 297 * q^42 - 1535 * q^43 + 329 * q^44 - 288 * q^45 - 112 * q^46 - 252 * q^47 - 198 * q^48 - 1184 * q^49 + 1901 * q^50 - 972 * q^51 - 1042 * q^52 - 78 * q^53 - 54 * q^54 - 1402 * q^55 + 1092 * q^56 - 1200 * q^57 + 710 * q^58 + 110 * q^59 - 771 * q^60 - 815 * q^61 + 1186 * q^62 - 540 * q^63 - 863 * q^64 - 4 * q^65 - 462 * q^66 - 1834 * q^67 - 735 * q^68 - 315 * q^69 + 977 * q^70 - 28 * q^71 - 405 * q^72 - 2422 * q^73 + 1588 * q^74 - 210 * q^75 - 3070 * q^76 - 746 * q^77 - 1053 * q^78 - 2566 * q^79 + 1061 * q^80 + 1134 * q^81 - 3300 * q^82 + 292 * q^83 - 1725 * q^84 - 912 * q^85 + 1191 * q^86 - 1254 * q^87 - 708 * q^88 - 780 * q^89 - 1395 * q^90 - 2210 * q^91 + 1918 * q^92 - 1989 * q^93 - 1496 * q^94 + 1604 * q^95 - 1716 * q^96 - 1370 * q^97 - 13 * q^98 - 549 * q^99

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