LMFDB - Embedded newform 2166.4.a.bn.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,4,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, 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("2166.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2166.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:	$127.798137072$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 1070 x^{10} + 7482 x^{9} + 417010 x^{8} - 4200618 x^{7} - 64345712 x^{6} + \cdots + 565410754316 $ x^12 - 4x^11 - 1070x^10 + 7482x^9 + 417010x^8 - 4200618x^7 - 64345712x^6 + 936334106x^5 + 1344230809x^4 - 69705492578x^3 + 369902885942x^2 - 765810305188*x + 565410754316
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 19^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-15.3418$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -16.8015 q^{5} +6.00000 q^{6} -12.5352 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -16.8015 q^{5} +6.00000 q^{6} -12.5352 q^{7} -8.00000 q^{8} +9.00000 q^{9} +33.6030 q^{10} -59.1305 q^{11} -12.0000 q^{12} +54.0762 q^{13} +25.0704 q^{14} +50.4044 q^{15} +16.0000 q^{16} +23.0736 q^{17} -18.0000 q^{18} -67.2059 q^{20} +37.6056 q^{21} +118.261 q^{22} +1.43998 q^{23} +24.0000 q^{24} +157.290 q^{25} -108.152 q^{26} -27.0000 q^{27} -50.1408 q^{28} +10.8499 q^{29} -100.809 q^{30} -246.879 q^{31} -32.0000 q^{32} +177.391 q^{33} -46.1472 q^{34} +210.610 q^{35} +36.0000 q^{36} +150.309 q^{37} -162.229 q^{39} +134.412 q^{40} -164.816 q^{41} -75.2112 q^{42} -545.530 q^{43} -236.522 q^{44} -151.213 q^{45} -2.87996 q^{46} -552.413 q^{47} -48.0000 q^{48} -185.869 q^{49} -314.580 q^{50} -69.2208 q^{51} +216.305 q^{52} -349.500 q^{53} +54.0000 q^{54} +993.480 q^{55} +100.282 q^{56} -21.6998 q^{58} -403.618 q^{59} +201.618 q^{60} +116.064 q^{61} +493.758 q^{62} -112.817 q^{63} +64.0000 q^{64} -908.560 q^{65} -354.783 q^{66} +41.6388 q^{67} +92.2944 q^{68} -4.31994 q^{69} -421.220 q^{70} -515.922 q^{71} -72.0000 q^{72} +610.890 q^{73} -300.619 q^{74} -471.869 q^{75} +741.212 q^{77} +324.457 q^{78} -1274.94 q^{79} -268.824 q^{80} +81.0000 q^{81} +329.633 q^{82} +207.705 q^{83} +150.422 q^{84} -387.671 q^{85} +1091.06 q^{86} -32.5497 q^{87} +473.044 q^{88} -1414.47 q^{89} +302.427 q^{90} -677.855 q^{91} +5.75992 q^{92} +740.637 q^{93} +1104.83 q^{94} +96.0000 q^{96} -179.981 q^{97} +371.738 q^{98} -532.174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} - 36 q^{3} + 48 q^{4} + 10 q^{5} + 72 q^{6} + 56 q^{7} - 96 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q - 24 * q^2 - 36 * q^3 + 48 * q^4 + 10 * q^5 + 72 * q^6 + 56 * q^7 - 96 * q^8 + 108 * q^9	\( 12 q - 24 q^{2} - 36 q^{3} + 48 q^{4} + 10 q^{5} + 72 q^{6} + 56 q^{7} - 96 q^{8} + 108 q^{9} - 20 q^{10} + 78 q^{11} - 144 q^{12} - 44 q^{13} - 112 q^{14} - 30 q^{15} + 192 q^{16} + 200 q^{17} - 216 q^{18} + 40 q^{20} - 168 q^{21} - 156 q^{22} + 330 q^{23} + 288 q^{24} + 738 q^{25} + 88 q^{26} - 324 q^{27} + 224 q^{28} - 282 q^{29} + 60 q^{30} - 304 q^{31} - 384 q^{32} - 234 q^{33} - 400 q^{34} + 486 q^{35} + 432 q^{36} + 280 q^{37} + 132 q^{39} - 80 q^{40} - 338 q^{41} + 336 q^{42} + 792 q^{43} + 312 q^{44} + 90 q^{45} - 660 q^{46} + 1088 q^{47} - 576 q^{48} + 928 q^{49} - 1476 q^{50} - 600 q^{51} - 176 q^{52} - 312 q^{53} + 648 q^{54} + 1058 q^{55} - 448 q^{56} + 564 q^{58} - 694 q^{59} - 120 q^{60} + 1438 q^{61} + 608 q^{62} + 504 q^{63} + 768 q^{64} + 1040 q^{65} + 468 q^{66} - 1248 q^{67} + 800 q^{68} - 990 q^{69} - 972 q^{70} - 1314 q^{71} - 864 q^{72} + 2860 q^{73} - 560 q^{74} - 2214 q^{75} + 4028 q^{77} - 264 q^{78} + 16 q^{79} + 160 q^{80} + 972 q^{81} + 676 q^{82} + 1258 q^{83} - 672 q^{84} + 1926 q^{85} - 1584 q^{86} + 846 q^{87} - 624 q^{88} - 4776 q^{89} - 180 q^{90} + 1484 q^{91} + 1320 q^{92} + 912 q^{93} - 2176 q^{94} + 1152 q^{96} - 4088 q^{97} - 1856 q^{98} + 702 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 - 36 * q^3 + 48 * q^4 + 10 * q^5 + 72 * q^6 + 56 * q^7 - 96 * q^8 + 108 * q^9 - 20 * q^10 + 78 * q^11 - 144 * q^12 - 44 * q^13 - 112 * q^14 - 30 * q^15 + 192 * q^16 + 200 * q^17 - 216 * q^18 + 40 * q^20 - 168 * q^21 - 156 * q^22 + 330 * q^23 + 288 * q^24 + 738 * q^25 + 88 * q^26 - 324 * q^27 + 224 * q^28 - 282 * q^29 + 60 * q^30 - 304 * q^31 - 384 * q^32 - 234 * q^33 - 400 * q^34 + 486 * q^35 + 432 * q^36 + 280 * q^37 + 132 * q^39 - 80 * q^40 - 338 * q^41 + 336 * q^42 + 792 * q^43 + 312 * q^44 + 90 * q^45 - 660 * q^46 + 1088 * q^47 - 576 * q^48 + 928 * q^49 - 1476 * q^50 - 600 * q^51 - 176 * q^52 - 312 * q^53 + 648 * q^54 + 1058 * q^55 - 448 * q^56 + 564 * q^58 - 694 * q^59 - 120 * q^60 + 1438 * q^61 + 608 * q^62 + 504 * q^63 + 768 * q^64 + 1040 * q^65 + 468 * q^66 - 1248 * q^67 + 800 * q^68 - 990 * q^69 - 972 * q^70 - 1314 * q^71 - 864 * q^72 + 2860 * q^73 - 560 * q^74 - 2214 * q^75 + 4028 * q^77 - 264 * q^78 + 16 * q^79 + 160 * q^80 + 972 * q^81 + 676 * q^82 + 1258 * q^83 - 672 * q^84 + 1926 * q^85 - 1584 * q^86 + 846 * q^87 - 624 * q^88 - 4776 * q^89 - 180 * q^90 + 1484 * q^91 + 1320 * q^92 + 912 * q^93 - 2176 * q^94 + 1152 * q^96 - 4088 * q^97 - 1856 * q^98 + 702 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−16.8015	−1.50277	−0.751385	−	0.659864i	$-0.770614\pi$
$5$	−16.8015	−1.50277	−0.751385	+	0.659864i	$0.770614\pi$
$6$	6.00000	0.408248
$7$	−12.5352	−0.676837	−0.338419	−	0.940996i	$-0.609892\pi$
$7$	−12.5352	−0.676837	−0.338419	+	0.940996i	$0.609892\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	33.6030	1.06262
$11$	−59.1305	−1.62077	−0.810387	−	0.585895i	$-0.800743\pi$
$11$	−59.1305	−1.62077	−0.810387	+	0.585895i	$0.800743\pi$
$12$	−12.0000	−0.288675
$13$	54.0762	1.15369	0.576847	−	0.816852i	$-0.304283\pi$
$13$	54.0762	1.15369	0.576847	+	0.816852i	$0.304283\pi$
$14$	25.0704	0.478596
$15$	50.4044	0.867625
$16$	16.0000	0.250000
$17$	23.0736	0.329187	0.164593	−	0.986362i	$-0.447369\pi$
$17$	23.0736	0.329187	0.164593	+	0.986362i	$0.447369\pi$
$18$	−18.0000	−0.235702
$19$	0	0
$19$	0	0
$20$	−67.2059	−0.751385
$21$	37.6056	0.390772
$22$	118.261	1.14606
$23$	1.43998	0.0130546	0.00652732	−	0.999979i	$-0.497922\pi$
$23$	1.43998	0.0130546	0.00652732	+	0.999979i	$0.497922\pi$
$24$	24.0000	0.204124
$25$	157.290	1.25832
$26$	−108.152	−0.815785
$27$	−27.0000	−0.192450
$28$	−50.1408	−0.338419
$29$	10.8499	0.0694749	0.0347375	−	0.999396i	$-0.488940\pi$
$29$	10.8499	0.0694749	0.0347375	+	0.999396i	$0.488940\pi$
$30$	−100.809	−0.613503
$31$	−246.879	−1.43035	−0.715174	−	0.698946i	$-0.753653\pi$
$31$	−246.879	−1.43035	−0.715174	+	0.698946i	$0.753653\pi$
$32$	−32.0000	−0.176777
$33$	177.391	0.935754
$34$	−46.1472	−0.232770
$35$	210.610	1.01713
$36$	36.0000	0.166667
$37$	150.309	0.667857	0.333928	−	0.942598i	$-0.391626\pi$
$37$	150.309	0.667857	0.333928	+	0.942598i	$0.391626\pi$
$38$	0	0
$39$	−162.229	−0.666086
$40$	134.412	0.531309
$41$	−164.816	−0.627805	−0.313902	−	0.949455i	$-0.601636\pi$
$41$	−164.816	−0.627805	−0.313902	+	0.949455i	$0.601636\pi$
$42$	−75.2112	−0.276318
$43$	−545.530	−1.93471	−0.967355	−	0.253427i	$-0.918442\pi$
$43$	−545.530	−1.93471	−0.967355	+	0.253427i	$0.918442\pi$
$44$	−236.522	−0.810387
$45$	−151.213	−0.500923
$46$	−2.87996	−0.00923103
$47$	−552.413	−1.71442	−0.857210	−	0.514967i	$-0.827804\pi$
$47$	−552.413	−1.71442	−0.857210	+	0.514967i	$0.827804\pi$
$48$	−48.0000	−0.144338
$49$	−185.869	−0.541892
$50$	−314.580	−0.889765
$51$	−69.2208	−0.190056
$52$	216.305	0.576847
$53$	−349.500	−0.905802	−0.452901	−	0.891561i	$-0.649611\pi$
$53$	−349.500	−0.905802	−0.452901	+	0.891561i	$0.649611\pi$
$54$	54.0000	0.136083
$55$	993.480	2.43565
$56$	100.282	0.239298
$57$	0	0
$58$	−21.6998	−0.0491262
$59$	−403.618	−0.890620	−0.445310	−	0.895376i	$-0.646907\pi$
$59$	−403.618	−0.890620	−0.445310	+	0.895376i	$0.646907\pi$
$60$	201.618	0.433812
$61$	116.064	0.243614	0.121807	−	0.992554i	$-0.461131\pi$
$61$	116.064	0.243614	0.121807	+	0.992554i	$0.461131\pi$
$62$	493.758	1.01141
$63$	−112.817	−0.225612
$64$	64.0000	0.125000
$65$	−908.560	−1.73374
$66$	−354.783	−0.661678
$67$	41.6388	0.0759251	0.0379626	−	0.999279i	$-0.487913\pi$
$67$	41.6388	0.0759251	0.0379626	+	0.999279i	$0.487913\pi$
$68$	92.2944	0.164593
$69$	−4.31994	−0.00753710
$70$	−421.220	−0.719220
$71$	−515.922	−0.862377	−0.431188	−	0.902262i	$-0.641906\pi$
$71$	−515.922	−0.862377	−0.431188	+	0.902262i	$0.641906\pi$
$72$	−72.0000	−0.117851
$73$	610.890	0.979442	0.489721	−	0.871879i	$-0.337099\pi$
$73$	610.890	0.979442	0.489721	+	0.871879i	$0.337099\pi$
$74$	−300.619	−0.472246
$75$	−471.869	−0.726490
$76$	0	0
$77$	741.212	1.09700
$78$	324.457	0.470994
$79$	−1274.94	−1.81572	−0.907859	−	0.419276i	$-0.862284\pi$
$79$	−1274.94	−1.81572	−0.907859	+	0.419276i	$0.862284\pi$
$80$	−268.824	−0.375693
$81$	81.0000	0.111111
$82$	329.633	0.443925
$83$	207.705	0.274682	0.137341	−	0.990524i	$-0.456144\pi$
$83$	207.705	0.274682	0.137341	+	0.990524i	$0.456144\pi$
$84$	150.422	0.195386
$85$	−387.671	−0.494692
$86$	1091.06	1.36805
$87$	−32.5497	−0.0401114
$88$	473.044	0.573030
$89$	−1414.47	−1.68465	−0.842325	−	0.538970i	$-0.818813\pi$
$89$	−1414.47	−1.68465	−0.842325	+	0.538970i	$0.818813\pi$
$90$	302.427	0.354206
$91$	−677.855	−0.780863
$92$	5.75992	0.00652732
$93$	740.637	0.825812
$94$	1104.83	1.21228
$95$	0	0
$96$	96.0000	0.102062
$97$	−179.981	−0.188395	−0.0941975	−	0.995554i	$-0.530029\pi$
$97$	−179.981	−0.188395	−0.0941975	+	0.995554i	$0.530029\pi$
$98$	371.738	0.383175
$99$	−532.174	−0.540258
$100$	629.159	0.629159
$101$	−1680.54	−1.65565	−0.827824	−	0.560989i	$-0.810421\pi$
$101$	−1680.54	−1.65565	−0.827824	+	0.560989i	$0.810421\pi$
$102$	138.442	0.134390
$103$	148.991	0.142529	0.0712644	−	0.997457i	$-0.477297\pi$
$103$	148.991	0.142529	0.0712644	+	0.997457i	$0.477297\pi$
$104$	−432.609	−0.407893
$105$	−631.830	−0.587241
$106$	698.999	0.640498
$107$	−1692.85	−1.52948	−0.764740	−	0.644339i	$-0.777133\pi$
$107$	−1692.85	−1.52948	−0.764740	+	0.644339i	$0.777133\pi$
$108$	−108.000	−0.0962250
$109$	1834.85	1.61236	0.806178	−	0.591673i	$-0.201532\pi$
$109$	1834.85	1.61236	0.806178	+	0.591673i	$0.201532\pi$
$110$	−1986.96	−1.72227
$111$	−450.928	−0.385587
$112$	−200.563	−0.169209
$113$	9.49991	0.00790864	0.00395432	−	0.999992i	$-0.498741\pi$
$113$	9.49991	0.00790864	0.00395432	+	0.999992i	$0.498741\pi$
$114$	0	0
$115$	−24.1938	−0.0196181
$116$	43.3995	0.0347375
$117$	486.686	0.384565
$118$	807.236	0.629764
$119$	−289.232	−0.222806
$120$	−403.236	−0.306752
$121$	2165.41	1.62691
$122$	−232.128	−0.172261
$123$	494.449	0.362463
$124$	−987.516	−0.715174
$125$	−542.516	−0.388193
$126$	225.634	0.159532
$127$	−946.769	−0.661513	−0.330756	−	0.943716i	$-0.607304\pi$
$127$	−946.769	−0.661513	−0.330756	+	0.943716i	$0.607304\pi$
$128$	−128.000	−0.0883883
$129$	1636.59	1.11700
$130$	1817.12	1.22594
$131$	−1923.13	−1.28263	−0.641315	−	0.767278i	$-0.721611\pi$
$131$	−1923.13	−1.28263	−0.641315	+	0.767278i	$0.721611\pi$
$132$	709.566	0.467877
$133$	0	0
$134$	−83.2775	−0.0536872
$135$	453.640	0.289208
$136$	−184.589	−0.116385
$137$	2793.82	1.74228	0.871139	−	0.491037i	$-0.163382\pi$
$137$	2793.82	1.74228	0.871139	+	0.491037i	$0.163382\pi$
$138$	8.63989	0.00532954
$139$	1746.07	1.06547	0.532733	−	0.846283i	$-0.321165\pi$
$139$	1746.07	1.06547	0.532733	+	0.846283i	$0.321165\pi$
$140$	842.439	0.508565
$141$	1657.24	0.989821
$142$	1031.84	0.609792
$143$	−3197.55	−1.86988
$144$	144.000	0.0833333
$145$	−182.294	−0.104405
$146$	−1221.78	−0.692570
$147$	557.607	0.312861
$148$	601.237	0.333928
$149$	2780.80	1.52894	0.764471	−	0.644659i	$-0.223000\pi$
$149$	2780.80	1.52894	0.764471	+	0.644659i	$0.223000\pi$
$150$	943.739	0.513706
$151$	−1977.06	−1.06550	−0.532751	−	0.846272i	$-0.678842\pi$
$151$	−1977.06	−1.06550	−0.532751	+	0.846272i	$0.678842\pi$
$152$	0	0
$153$	207.663	0.109729
$154$	−1482.42	−0.775696
$155$	4147.93	2.14948
$156$	−648.914	−0.333043
$157$	−3177.71	−1.61534	−0.807671	−	0.589634i	$-0.799272\pi$
$157$	−3177.71	−1.61534	−0.807671	+	0.589634i	$0.799272\pi$
$158$	2549.88	1.28391
$159$	1048.50	0.522965
$160$	537.647	0.265655
$161$	−18.0504	−0.00883587
$162$	−162.000	−0.0785674
$163$	−2274.88	−1.09314	−0.546571	−	0.837413i	$-0.684067\pi$
$163$	−2274.88	−1.09314	−0.546571	+	0.837413i	$0.684067\pi$
$164$	−659.265	−0.313902
$165$	−2980.44	−1.40622
$166$	−415.410	−0.194229
$167$	3743.92	1.73481	0.867406	−	0.497602i	$-0.165786\pi$
$167$	3743.92	1.73481	0.867406	+	0.497602i	$0.165786\pi$
$168$	−300.845	−0.138159
$169$	727.232	0.331011
$170$	775.342	0.349800
$171$	0	0
$172$	−2182.12	−0.967355
$173$	91.5803	0.0402469	0.0201235	−	0.999798i	$-0.493594\pi$
$173$	91.5803	0.0402469	0.0201235	+	0.999798i	$0.493594\pi$
$174$	65.0993	0.0283630
$175$	−1971.66	−0.851676
$176$	−946.088	−0.405193
$177$	1210.85	0.514200
$178$	2828.95	1.19123
$179$	−4002.91	−1.67146	−0.835730	−	0.549140i	$-0.814955\pi$
$179$	−4002.91	−1.67146	−0.835730	+	0.549140i	$0.814955\pi$
$180$	−604.853	−0.250462
$181$	−3935.80	−1.61628	−0.808138	−	0.588994i	$-0.799524\pi$
$181$	−3935.80	−1.61628	−0.808138	+	0.588994i	$0.799524\pi$
$182$	1355.71	0.552154
$183$	−348.192	−0.140651
$184$	−11.5198	−0.00461551
$185$	−2525.42	−1.00364
$186$	−1481.27	−0.583937
$187$	−1364.35	−0.533537
$188$	−2209.65	−0.857210
$189$	338.450	0.130257
$190$	0	0
$191$	822.648	0.311648	0.155824	−	0.987785i	$-0.450197\pi$
$191$	822.648	0.311648	0.155824	+	0.987785i	$0.450197\pi$
$192$	−192.000	−0.0721688
$193$	4696.08	1.75146	0.875729	−	0.482803i	$-0.160381\pi$
$193$	4696.08	1.75146	0.875729	+	0.482803i	$0.160381\pi$
$194$	359.962	0.133215
$195$	2725.68	1.00097
$196$	−743.475	−0.270946
$197$	−4587.25	−1.65903	−0.829513	−	0.558488i	$-0.811382\pi$
$197$	−4587.25	−1.65903	−0.829513	+	0.558488i	$0.811382\pi$
$198$	1064.35	0.382020
$199$	−2392.40	−0.852225	−0.426113	−	0.904670i	$-0.640117\pi$
$199$	−2392.40	−0.852225	−0.426113	+	0.904670i	$0.640117\pi$
$200$	−1258.32	−0.444883
$201$	−124.916	−0.0438354
$202$	3361.09	1.17072
$203$	−136.005	−0.0470232
$204$	−276.883	−0.0950280
$205$	2769.16	0.943446
$206$	−297.981	−0.100783
$207$	12.9598	0.00435155
$208$	865.219	0.288424
$209$	0	0
$210$	1263.66	0.415242
$211$	1800.77	0.587537	0.293769	−	0.955877i	$-0.405091\pi$
$211$	1800.77	0.587537	0.293769	+	0.955877i	$0.405091\pi$
$212$	−1398.00	−0.452901
$213$	1547.77	0.497893
$214$	3385.71	1.08151
$215$	9165.71	2.90742
$216$	216.000	0.0680414
$217$	3094.68	0.968113
$218$	−3669.70	−1.14011
$219$	−1832.67	−0.565481
$220$	3973.92	1.21783
$221$	1247.73	0.379781
$222$	901.856	0.272651
$223$	−2316.94	−0.695757	−0.347879	−	0.937540i	$-0.613098\pi$
$223$	−2316.94	−0.695757	−0.347879	+	0.937540i	$0.613098\pi$
$224$	401.126	0.119649
$225$	1415.61	0.419439
$226$	−18.9998	−0.00559225
$227$	−1912.33	−0.559145	−0.279572	−	0.960125i	$-0.590193\pi$
$227$	−1912.33	−0.559145	−0.279572	+	0.960125i	$0.590193\pi$
$228$	0	0
$229$	−137.988	−0.0398187	−0.0199093	−	0.999802i	$-0.506338\pi$
$229$	−137.988	−0.0398187	−0.0199093	+	0.999802i	$0.506338\pi$
$230$	48.3876	0.0138721
$231$	−2223.64	−0.633353
$232$	−86.7991	−0.0245631
$233$	−2507.25	−0.704958	−0.352479	−	0.935820i	$-0.614661\pi$
$233$	−2507.25	−0.704958	−0.352479	+	0.935820i	$0.614661\pi$
$234$	−973.371	−0.271928
$235$	9281.36	2.57638
$236$	−1614.47	−0.445310
$237$	3824.81	1.04831
$238$	578.465	0.157547
$239$	2538.31	0.686986	0.343493	−	0.939155i	$-0.388390\pi$
$239$	2538.31	0.686986	0.343493	+	0.939155i	$0.388390\pi$
$240$	806.471	0.216906
$241$	−3265.55	−0.872833	−0.436416	−	0.899745i	$-0.643752\pi$
$241$	−3265.55	−0.872833	−0.436416	+	0.899745i	$0.643752\pi$
$242$	−4330.83	−1.15040
$243$	−243.000	−0.0641500
$244$	464.256	0.121807
$245$	3122.87	0.814339
$246$	−988.898	−0.256300
$247$	0	0
$248$	1975.03	0.505704
$249$	−623.115	−0.158588
$250$	1085.03	0.274494
$251$	6579.61	1.65459	0.827294	−	0.561770i	$-0.189879\pi$
$251$	6579.61	1.65459	0.827294	+	0.561770i	$0.189879\pi$
$252$	−451.267	−0.112806
$253$	−85.1468	−0.0211586
$254$	1893.54	0.467760
$255$	1163.01	0.285610
$256$	256.000	0.0625000
$257$	−1994.67	−0.484140	−0.242070	−	0.970259i	$-0.577826\pi$
$257$	−1994.67	−0.484140	−0.242070	+	0.970259i	$0.577826\pi$
$258$	−3273.18	−0.789842
$259$	−1884.16	−0.452030
$260$	−3634.24	−0.866869
$261$	97.6490	0.0231583
$262$	3846.26	0.906956
$263$	−5607.83	−1.31481	−0.657403	−	0.753540i	$-0.728345\pi$
$263$	−5607.83	−1.31481	−0.657403	+	0.753540i	$0.728345\pi$
$264$	−1419.13	−0.330839
$265$	5872.11	1.36121
$266$	0	0
$267$	4243.42	0.972633
$268$	166.555	0.0379626
$269$	2433.53	0.551580	0.275790	−	0.961218i	$-0.411061\pi$
$269$	2433.53	0.551580	0.275790	+	0.961218i	$0.411061\pi$
$270$	−907.280	−0.204501
$271$	−1611.42	−0.361206	−0.180603	−	0.983556i	$-0.557805\pi$
$271$	−1611.42	−0.361206	−0.180603	+	0.983556i	$0.557805\pi$
$272$	369.178	0.0822967
$273$	2033.57	0.450832
$274$	−5587.64	−1.23198
$275$	−9300.62	−2.03945
$276$	−17.2798	−0.00376855
$277$	1302.14	0.282447	0.141223	−	0.989978i	$-0.454896\pi$
$277$	1302.14	0.282447	0.141223	+	0.989978i	$0.454896\pi$
$278$	−3492.14	−0.753398
$279$	−2221.91	−0.476783
$280$	−1684.88	−0.359610
$281$	−2495.54	−0.529791	−0.264895	−	0.964277i	$-0.585337\pi$
$281$	−2495.54	−0.529791	−0.264895	+	0.964277i	$0.585337\pi$
$282$	−3314.48	−0.699909
$283$	−3601.12	−0.756411	−0.378205	−	0.925722i	$-0.623459\pi$
$283$	−3601.12	−0.756411	−0.378205	+	0.925722i	$0.623459\pi$
$284$	−2063.69	−0.431188
$285$	0	0
$286$	6395.10	1.32220
$287$	2066.01	0.424921
$288$	−288.000	−0.0589256
$289$	−4380.61	−0.891636
$290$	364.588	0.0738254
$291$	539.944	0.108770
$292$	2443.56	0.489721
$293$	−6213.16	−1.23883	−0.619414	−	0.785065i	$-0.712630\pi$
$293$	−6213.16	−1.23883	−0.619414	+	0.785065i	$0.712630\pi$
$294$	−1115.21	−0.221226
$295$	6781.38	1.33840
$296$	−1202.47	−0.236123
$297$	1596.52	0.311918
$298$	−5561.61	−1.08112
$299$	77.8687	0.0150611
$300$	−1887.48	−0.363245
$301$	6838.32	1.30948
$302$	3954.12	0.753423
$303$	5041.63	0.955888
$304$	0	0
$305$	−1950.05	−0.366096
$306$	−415.325	−0.0775900
$307$	9070.88	1.68633	0.843163	−	0.537657i	$-0.180691\pi$
$307$	9070.88	1.68633	0.843163	+	0.537657i	$0.180691\pi$
$308$	2964.85	0.548500
$309$	−446.972	−0.0822891
$310$	−8295.87	−1.51992
$311$	1929.33	0.351775	0.175888	−	0.984410i	$-0.443720\pi$
$311$	1929.33	0.351775	0.175888	+	0.984410i	$0.443720\pi$
$312$	1297.83	0.235497
$313$	−4099.72	−0.740351	−0.370175	−	0.928962i	$-0.620702\pi$
$313$	−4099.72	−0.740351	−0.370175	+	0.928962i	$0.620702\pi$
$314$	6355.41	1.14222
$315$	1895.49	0.339043
$316$	−5099.75	−0.907859
$317$	−1342.18	−0.237805	−0.118903	−	0.992906i	$-0.537938\pi$
$317$	−1342.18	−0.237805	−0.118903	+	0.992906i	$0.537938\pi$
$318$	−2097.00	−0.369792
$319$	−641.559	−0.112603
$320$	−1075.29	−0.187846
$321$	5078.56	0.883046
$322$	36.1009	0.00624790
$323$	0	0
$324$	324.000	0.0555556
$325$	8505.63	1.45171
$326$	4549.76	0.772968
$327$	−5504.55	−0.930895
$328$	1318.53	0.221962
$329$	6924.61	1.16038
$330$	5960.88	0.994350
$331$	−2603.95	−0.432406	−0.216203	−	0.976348i	$-0.569367\pi$
$331$	−2603.95	−0.432406	−0.216203	+	0.976348i	$0.569367\pi$
$332$	830.821	0.137341
$333$	1352.78	0.222619
$334$	−7487.85	−1.22670
$335$	−699.593	−0.114098
$336$	601.689	0.0976930
$337$	2160.45	0.349220	0.174610	−	0.984638i	$-0.444133\pi$
$337$	2160.45	0.349220	0.174610	+	0.984638i	$0.444133\pi$
$338$	−1454.46	−0.234060
$339$	−28.4997	−0.00456606
$340$	−1550.68	−0.247346
$341$	14598.1	2.31827
$342$	0	0
$343$	6629.48	1.04361
$344$	4364.24	0.684023
$345$	72.5814	0.0113265
$346$	−183.161	−0.0284589
$347$	1214.28	0.187856	0.0939281	−	0.995579i	$-0.470058\pi$
$347$	1214.28	0.187856	0.0939281	+	0.995579i	$0.470058\pi$
$348$	−130.199	−0.0200557
$349$	7338.17	1.12551	0.562756	−	0.826623i	$-0.309741\pi$
$349$	7338.17	1.12551	0.562756	+	0.826623i	$0.309741\pi$
$350$	3943.32	0.602226
$351$	−1460.06	−0.222029
$352$	1892.18	0.286515
$353$	1114.59	0.168056	0.0840280	−	0.996463i	$-0.473221\pi$
$353$	1114.59	0.168056	0.0840280	+	0.996463i	$0.473221\pi$
$354$	−2421.71	−0.363594
$355$	8668.26	1.29595
$356$	−5657.89	−0.842325
$357$	867.697	0.128637
$358$	8005.82	1.18190
$359$	7534.65	1.10770	0.553849	−	0.832617i	$-0.313158\pi$
$359$	7534.65	1.10770	0.553849	+	0.832617i	$0.313158\pi$
$360$	1209.71	0.177103
$361$	0	0
$362$	7871.60	1.14288
$363$	−6496.24	−0.939296
$364$	−2711.42	−0.390432
$365$	−10263.9	−1.47188
$366$	696.383	0.0994550
$367$	10871.7	1.54632	0.773158	−	0.634214i	$-0.218676\pi$
$367$	10871.7	1.54632	0.773158	+	0.634214i	$0.218676\pi$
$368$	23.0397	0.00326366
$369$	−1483.35	−0.209268
$370$	5050.84	0.709677
$371$	4381.05	0.613080
$372$	2962.55	0.412906
$373$	−1819.04	−0.252511	−0.126255	−	0.991998i	$-0.540296\pi$
$373$	−1819.04	−0.252511	−0.126255	+	0.991998i	$0.540296\pi$
$374$	2728.71	0.377268
$375$	1627.55	0.224123
$376$	4419.31	0.606139
$377$	586.720	0.0801529
$378$	−676.901	−0.0921059
$379$	−295.425	−0.0400395	−0.0200198	−	0.999800i	$-0.506373\pi$
$379$	−295.425	−0.0400395	−0.0200198	+	0.999800i	$0.506373\pi$
$380$	0	0
$381$	2840.31	0.381925
$382$	−1645.30	−0.220368
$383$	−1472.82	−0.196495	−0.0982473	−	0.995162i	$-0.531324\pi$
$383$	−1472.82	−0.196495	−0.0982473	+	0.995162i	$0.531324\pi$
$384$	384.000	0.0510310
$385$	−12453.5	−1.64854
$386$	−9392.16	−1.23847
$387$	−4909.77	−0.644903
$388$	−719.925	−0.0941975
$389$	−10415.5	−1.35755	−0.678776	−	0.734345i	$-0.737489\pi$
$389$	−10415.5	−1.35755	−0.678776	+	0.734345i	$0.737489\pi$
$390$	−5451.36	−0.707796
$391$	33.2256	0.00429741
$392$	1486.95	0.191588
$393$	5769.38	0.740526
$394$	9174.50	1.17311
$395$	21420.8	2.72861
$396$	−2128.70	−0.270129
$397$	1126.85	0.142456	0.0712282	−	0.997460i	$-0.477308\pi$
$397$	1126.85	0.142456	0.0712282	+	0.997460i	$0.477308\pi$
$398$	4784.80	0.602614
$399$	0	0
$400$	2516.64	0.314580
$401$	−3100.90	−0.386163	−0.193082	−	0.981183i	$-0.561848\pi$
$401$	−3100.90	−0.386163	−0.193082	+	0.981183i	$0.561848\pi$
$402$	249.833	0.0309963
$403$	−13350.3	−1.65019
$404$	−6722.18	−0.827824
$405$	−1360.92	−0.166974
$406$	272.011	0.0332504
$407$	−8887.86	−1.08244
$408$	553.767	0.0671949
$409$	−2970.41	−0.359113	−0.179557	−	0.983748i	$-0.557466\pi$
$409$	−2970.41	−0.359113	−0.179557	+	0.983748i	$0.557466\pi$
$410$	−5538.32	−0.667117
$411$	−8381.46	−1.00590
$412$	595.962	0.0712644
$413$	5059.43	0.602805
$414$	−25.9197	−0.00307701
$415$	−3489.75	−0.412784
$416$	−1730.44	−0.203946
$417$	−5238.21	−0.615147
$418$	0	0
$419$	−813.697	−0.0948728	−0.0474364	−	0.998874i	$-0.515105\pi$
$419$	−813.697	−0.0948728	−0.0474364	+	0.998874i	$0.515105\pi$
$420$	−2527.32	−0.293620
$421$	10724.5	1.24152	0.620760	−	0.784001i	$-0.286824\pi$
$421$	10724.5	1.24152	0.620760	+	0.784001i	$0.286824\pi$
$422$	−3601.55	−0.415451
$423$	−4971.72	−0.571474
$424$	2796.00	0.320249
$425$	3629.24	0.414222
$426$	−3095.53	−0.352064
$427$	−1454.88	−0.164887
$428$	−6771.42	−0.764740
$429$	9592.65	1.07957
$430$	−18331.4	−2.05586
$431$	−906.410	−0.101300	−0.0506499	−	0.998716i	$-0.516129\pi$
$431$	−906.410	−0.101300	−0.0506499	+	0.998716i	$0.516129\pi$
$432$	−432.000	−0.0481125
$433$	−5946.86	−0.660019	−0.330009	−	0.943978i	$-0.607052\pi$
$433$	−5946.86	−0.660019	−0.330009	+	0.943978i	$0.607052\pi$
$434$	−6189.36	−0.684559
$435$	546.882	0.0602782
$436$	7339.41	0.806178
$437$	0	0
$438$	3665.34	0.399856
$439$	9885.86	1.07478	0.537388	−	0.843335i	$-0.319411\pi$
$439$	9885.86	1.07478	0.537388	+	0.843335i	$0.319411\pi$
$440$	−7947.84	−0.861133
$441$	−1672.82	−0.180631
$442$	−2495.47	−0.268546
$443$	−5552.10	−0.595458	−0.297729	−	0.954650i	$-0.596229\pi$
$443$	−5552.10	−0.595458	−0.297729	+	0.954650i	$0.596229\pi$
$444$	−1803.71	−0.192794
$445$	23765.2	2.53164
$446$	4633.88	0.491975
$447$	−8342.41	−0.882735
$448$	−802.253	−0.0846046
$449$	−12804.9	−1.34588	−0.672939	−	0.739698i	$-0.734969\pi$
$449$	−12804.9	−1.34588	−0.672939	+	0.739698i	$0.734969\pi$
$450$	−2831.22	−0.296588
$451$	9745.67	1.01753
$452$	37.9996	0.00395432
$453$	5931.17	0.615167
$454$	3824.66	0.395375
$455$	11389.0	1.17346
$456$	0	0
$457$	−5454.01	−0.558267	−0.279133	−	0.960252i	$-0.590047\pi$
$457$	−5454.01	−0.558267	−0.279133	+	0.960252i	$0.590047\pi$
$458$	275.975	0.0281561
$459$	−622.988	−0.0633520
$460$	−96.7752	−0.00980906
$461$	4367.34	0.441231	0.220615	−	0.975361i	$-0.429193\pi$
$461$	4367.34	0.441231	0.220615	+	0.975361i	$0.429193\pi$
$462$	4447.27	0.447848
$463$	−17084.7	−1.71489	−0.857443	−	0.514578i	$-0.827949\pi$
$463$	−17084.7	−1.71489	−0.857443	+	0.514578i	$0.827949\pi$
$464$	173.598	0.0173687
$465$	−12443.8	−1.24101
$466$	5014.50	0.498481
$467$	11953.8	1.18449	0.592244	−	0.805759i	$-0.298242\pi$
$467$	11953.8	1.18449	0.592244	+	0.805759i	$0.298242\pi$
$468$	1946.74	0.192282
$469$	−521.950	−0.0513889
$470$	−18562.7	−1.82178
$471$	9533.12	0.932618
$472$	3228.94	0.314882
$473$	32257.4	3.13573
$474$	−7649.63	−0.741264
$475$	0	0
$476$	−1156.93	−0.111403
$477$	−3145.50	−0.301934
$478$	−5076.62	−0.485772
$479$	−2510.92	−0.239514	−0.119757	−	0.992803i	$-0.538211\pi$
$479$	−2510.92	−0.239514	−0.119757	+	0.992803i	$0.538211\pi$
$480$	−1612.94	−0.153376
$481$	8128.15	0.770503
$482$	6531.10	0.617186
$483$	54.1513	0.00510139
$484$	8661.66	0.813454
$485$	3023.95	0.283115
$486$	486.000	0.0453609
$487$	7167.83	0.666951	0.333476	−	0.942759i	$-0.391779\pi$
$487$	7167.83	0.666951	0.333476	+	0.942759i	$0.391779\pi$
$488$	−928.511	−0.0861306
$489$	6824.63	0.631126
$490$	−6245.74	−0.575824
$491$	−1568.68	−0.144183	−0.0720913	−	0.997398i	$-0.522967\pi$
$491$	−1568.68	−0.144183	−0.0720913	+	0.997398i	$0.522967\pi$
$492$	1977.80	0.181232
$493$	250.346	0.0228702
$494$	0	0
$495$	8941.32	0.811884
$496$	−3950.07	−0.357587
$497$	6467.19	0.583688
$498$	1246.23	0.112138
$499$	1302.04	0.116808	0.0584039	−	0.998293i	$-0.481399\pi$
$499$	1302.04	0.116808	0.0584039	+	0.998293i	$0.481399\pi$
$500$	−2170.06	−0.194096
$501$	−11231.8	−1.00159
$502$	−13159.2	−1.16997
$503$	−3406.03	−0.301923	−0.150962	−	0.988540i	$-0.548237\pi$
$503$	−3406.03	−0.301923	−0.150962	+	0.988540i	$0.548237\pi$
$504$	902.534	0.0797660
$505$	28235.6	2.48806
$506$	170.294	0.0149614
$507$	−2181.70	−0.191109
$508$	−3787.07	−0.330756
$509$	−4759.33	−0.414447	−0.207223	−	0.978294i	$-0.566443\pi$
$509$	−4759.33	−0.414447	−0.207223	+	0.978294i	$0.566443\pi$
$510$	−2326.03	−0.201957
$511$	−7657.63	−0.662923
$512$	−512.000	−0.0441942
$513$	0	0
$514$	3989.33	0.342339
$515$	−2503.26	−0.214188
$516$	6546.36	0.558502
$517$	32664.5	2.77869
$518$	3768.31	0.319634
$519$	−274.741	−0.0232366
$520$	7268.48	0.612969
$521$	11521.7	0.968853	0.484427	−	0.874832i	$-0.339028\pi$
$521$	11521.7	0.968853	0.484427	+	0.874832i	$0.339028\pi$
$522$	−195.298	−0.0163754
$523$	−4477.15	−0.374326	−0.187163	−	0.982329i	$-0.559929\pi$
$523$	−4477.15	−0.374326	−0.187163	+	0.982329i	$0.559929\pi$
$524$	−7692.51	−0.641315
$525$	5914.97	0.491716
$526$	11215.7	0.929708
$527$	−5696.39	−0.470852
$528$	2838.26	0.233939
$529$	−12164.9	−0.999830
$530$	−11744.2	−0.962522
$531$	−3632.56	−0.296873
$532$	0	0
$533$	−8912.64	−0.724295
$534$	−8486.84	−0.687755
$535$	28442.5	2.29846
$536$	−333.110	−0.0268436
$537$	12008.7	0.965018
$538$	−4867.06	−0.390026
$539$	10990.5	0.878284
$540$	1814.56	0.144604
$541$	22878.4	1.81815	0.909075	−	0.416634i	$-0.136790\pi$
$541$	22878.4	1.81815	0.909075	+	0.416634i	$0.136790\pi$
$542$	3222.84	0.255411
$543$	11807.4	0.933157
$544$	−738.356	−0.0581925
$545$	−30828.2	−2.42300
$546$	−4067.13	−0.318786
$547$	12020.8	0.939623	0.469812	−	0.882767i	$-0.344322\pi$
$547$	12020.8	0.939623	0.469812	+	0.882767i	$0.344322\pi$
$548$	11175.3	0.871139
$549$	1044.57	0.0812047
$550$	18601.2	1.44211
$551$	0	0
$552$	34.5595	0.00266477
$553$	15981.6	1.22894
$554$	−2604.27	−0.199720
$555$	7576.26	0.579449
$556$	6984.28	0.532733
$557$	−11352.3	−0.863580	−0.431790	−	0.901974i	$-0.642118\pi$
$557$	−11352.3	−0.863580	−0.431790	+	0.901974i	$0.642118\pi$
$558$	4443.82	0.337136
$559$	−29500.2	−2.23206
$560$	3369.76	0.254283
$561$	4093.06	0.308038
$562$	4991.07	0.374619
$563$	17565.3	1.31490	0.657452	−	0.753496i	$-0.271634\pi$
$563$	17565.3	1.31490	0.657452	+	0.753496i	$0.271634\pi$
$564$	6628.96	0.494911
$565$	−159.613	−0.0118849
$566$	7202.23	0.534863
$567$	−1015.35	−0.0752041
$568$	4127.38	0.304896
$569$	−5658.12	−0.416873	−0.208436	−	0.978036i	$-0.566837\pi$
$569$	−5658.12	−0.416873	−0.208436	+	0.978036i	$0.566837\pi$
$570$	0	0
$571$	12125.3	0.888665	0.444333	−	0.895862i	$-0.353441\pi$
$571$	12125.3	0.888665	0.444333	+	0.895862i	$0.353441\pi$
$572$	−12790.2	−0.934939
$573$	−2467.94	−0.179930
$574$	−4132.01	−0.300465
$575$	226.494	0.0164269
$576$	576.000	0.0416667
$577$	12127.3	0.874986	0.437493	−	0.899222i	$-0.355867\pi$
$577$	12127.3	0.874986	0.437493	+	0.899222i	$0.355867\pi$
$578$	8761.22	0.630482
$579$	−14088.2	−1.01120
$580$	−729.177	−0.0522024
$581$	−2603.62	−0.185915
$582$	−1079.89	−0.0769120
$583$	20666.1	1.46810
$584$	−4887.12	−0.346285
$585$	−8177.04	−0.577913
$586$	12426.3	0.875983
$587$	−3207.76	−0.225551	−0.112775	−	0.993620i	$-0.535974\pi$
$587$	−3207.76	−0.225551	−0.112775	+	0.993620i	$0.535974\pi$
$588$	2230.43	0.156431
$589$	0	0
$590$	−13562.8	−0.946390
$591$	13761.7	0.957839
$592$	2404.95	0.166964
$593$	16976.2	1.17560	0.587800	−	0.809006i	$-0.299994\pi$
$593$	16976.2	1.17560	0.587800	+	0.809006i	$0.299994\pi$
$594$	−3193.05	−0.220559
$595$	4859.53	0.334826
$596$	11123.2	0.764471
$597$	7177.20	0.492032
$598$	−155.737	−0.0106498
$599$	13457.7	0.917974	0.458987	−	0.888443i	$-0.348212\pi$
$599$	13457.7	0.917974	0.458987	+	0.888443i	$0.348212\pi$
$600$	3774.95	0.256853
$601$	−15392.4	−1.04471	−0.522355	−	0.852728i	$-0.674946\pi$
$601$	−15392.4	−1.04471	−0.522355	+	0.852728i	$0.674946\pi$
$602$	−13676.6	−0.925944
$603$	374.749	0.0253084
$604$	−7908.23	−0.532751
$605$	−36382.2	−2.44487
$606$	−10083.3	−0.675915
$607$	−6717.90	−0.449211	−0.224606	−	0.974450i	$-0.572109\pi$
$607$	−6717.90	−0.449211	−0.224606	+	0.974450i	$0.572109\pi$
$608$	0	0
$609$	408.016	0.0271489
$610$	3900.09	0.258869
$611$	−29872.4	−1.97792
$612$	830.650	0.0548644
$613$	−9639.40	−0.635125	−0.317563	−	0.948237i	$-0.602864\pi$
$613$	−9639.40	−0.635125	−0.317563	+	0.948237i	$0.602864\pi$
$614$	−18141.8	−1.19241
$615$	−8307.48	−0.544699
$616$	−5929.70	−0.387848
$617$	26266.3	1.71384	0.856922	−	0.515447i	$-0.172374\pi$
$617$	26266.3	1.71384	0.856922	+	0.515447i	$0.172374\pi$
$618$	893.943	0.0581872
$619$	290.860	0.0188864	0.00944319	−	0.999955i	$-0.496994\pi$
$619$	290.860	0.0188864	0.00944319	+	0.999955i	$0.496994\pi$
$620$	16591.7	1.07474
$621$	−38.8795	−0.00251237
$622$	−3858.65	−0.248743
$623$	17730.7	1.14023
$624$	−2595.66	−0.166521
$625$	−10546.2	−0.674954
$626$	8199.44	0.523507
$627$	0	0
$628$	−12710.8	−0.807671
$629$	3468.18	0.219849
$630$	−3790.98	−0.239740
$631$	2885.75	0.182060	0.0910301	−	0.995848i	$-0.470984\pi$
$631$	2885.75	0.182060	0.0910301	+	0.995848i	$0.470984\pi$
$632$	10199.5	0.641953
$633$	−5402.32	−0.339215
$634$	2684.36	0.168154
$635$	15907.1	0.994102
$636$	4194.00	0.261482
$637$	−10051.1	−0.625178
$638$	1283.12	0.0796225
$639$	−4643.30	−0.287459
$640$	2150.59	0.132827
$641$	−16814.1	−1.03606	−0.518030	−	0.855362i	$-0.673335\pi$
$641$	−16814.1	−1.03606	−0.518030	+	0.855362i	$0.673335\pi$
$642$	−10157.1	−0.624408
$643$	24108.2	1.47859	0.739297	−	0.673379i	$-0.235158\pi$
$643$	24108.2	1.47859	0.739297	+	0.673379i	$0.235158\pi$
$644$	−72.2018	−0.00441793
$645$	−27497.1	−1.67860
$646$	0	0
$647$	−3286.55	−0.199703	−0.0998513	−	0.995002i	$-0.531837\pi$
$647$	−3286.55	−0.199703	−0.0998513	+	0.995002i	$0.531837\pi$
$648$	−648.000	−0.0392837
$649$	23866.1	1.44349
$650$	−17011.3	−1.02652
$651$	−9284.03	−0.558940
$652$	−9099.51	−0.546571
$653$	−23923.2	−1.43367	−0.716835	−	0.697243i	$-0.754410\pi$
$653$	−23923.2	−1.43367	−0.716835	+	0.697243i	$0.754410\pi$
$654$	11009.1	0.658242
$655$	32311.4	1.92750
$656$	−2637.06	−0.156951
$657$	5498.01	0.326481
$658$	−13849.2	−0.820515
$659$	14015.8	0.828495	0.414248	−	0.910164i	$-0.364045\pi$
$659$	14015.8	0.828495	0.414248	+	0.910164i	$0.364045\pi$
$660$	−11921.8	−0.703112
$661$	−17198.3	−1.01201	−0.506004	−	0.862531i	$-0.668878\pi$
$661$	−17198.3	−1.01201	−0.506004	+	0.862531i	$0.668878\pi$
$662$	5207.91	0.305757
$663$	−3743.20	−0.219267
$664$	−1661.64	−0.0971147
$665$	0	0
$666$	−2705.57	−0.157415
$667$	15.6236	0.000906971 0
$668$	14975.7	0.867406
$669$	6950.82	0.401696
$670$	1399.19	0.0806795
$671$	−6862.91	−0.394843
$672$	−1203.38	−0.0690794
$673$	−28092.0	−1.60902	−0.804508	−	0.593942i	$-0.797571\pi$
$673$	−28092.0	−1.60902	−0.804508	+	0.593942i	$0.797571\pi$
$674$	−4320.90	−0.246936
$675$	−4246.82	−0.242163
$676$	2908.93	0.165506
$677$	24300.9	1.37955	0.689777	−	0.724022i	$-0.257709\pi$
$677$	24300.9	1.37955	0.689777	+	0.724022i	$0.257709\pi$
$678$	56.9995	0.00322869
$679$	2256.10	0.127513
$680$	3101.37	0.174900
$681$	5736.99	0.322822
$682$	−29196.2	−1.63927
$683$	2603.54	0.145859	0.0729294	−	0.997337i	$-0.476765\pi$
$683$	2603.54	0.145859	0.0729294	+	0.997337i	$0.476765\pi$
$684$	0	0
$685$	−46940.3	−2.61824
$686$	−13259.0	−0.737943
$687$	413.963	0.0229893
$688$	−8728.47	−0.483677
$689$	−18899.6	−1.04502
$690$	−145.163	−0.00800907
$691$	6787.35	0.373666	0.186833	−	0.982392i	$-0.440178\pi$
$691$	6787.35	0.373666	0.186833	+	0.982392i	$0.440178\pi$
$692$	366.321	0.0201235
$693$	6670.91	0.365667
$694$	−2428.56	−0.132834
$695$	−29336.6	−1.60115
$696$	260.397	0.0141815
$697$	−3802.91	−0.206665
$698$	−14676.3	−0.795857
$699$	7521.74	0.407008
$700$	−7886.63	−0.425838
$701$	20396.4	1.09895	0.549474	−	0.835511i	$-0.314828\pi$
$701$	20396.4	1.09895	0.549474	+	0.835511i	$0.314828\pi$
$702$	2920.11	0.156998
$703$	0	0
$704$	−3784.35	−0.202597
$705$	−27844.1	−1.48747
$706$	−2229.18	−0.118834
$707$	21065.9	1.12060
$708$	4843.42	0.257100
$709$	19180.8	1.01601	0.508004	−	0.861355i	$-0.330384\pi$
$709$	19180.8	1.01601	0.508004	+	0.861355i	$0.330384\pi$
$710$	−17336.5	−0.916378
$711$	−11474.4	−0.605239
$712$	11315.8	0.595613
$713$	−355.501	−0.0186727
$714$	−1735.39	−0.0909600
$715$	53723.6	2.81000
$716$	−16011.6	−0.835730
$717$	−7614.93	−0.396632
$718$	−15069.3	−0.783261
$719$	−14558.4	−0.755130	−0.377565	−	0.925983i	$-0.623238\pi$
$719$	−14558.4	−0.755130	−0.377565	+	0.925983i	$0.623238\pi$
$720$	−2419.41	−0.125231
$721$	−1867.63	−0.0964688
$722$	0	0
$723$	9796.65	0.503930
$724$	−15743.2	−0.808138
$725$	1706.58	0.0874216
$726$	12992.5	0.664182
$727$	13567.5	0.692149	0.346075	−	0.938207i	$-0.387514\pi$
$727$	13567.5	0.692149	0.346075	+	0.938207i	$0.387514\pi$
$728$	5422.84	0.276077
$729$	729.000	0.0370370
$730$	20527.7	1.04077
$731$	−12587.3	−0.636880
$732$	−1392.77	−0.0703253
$733$	−20454.9	−1.03072	−0.515361	−	0.856973i	$-0.672342\pi$
$733$	−20454.9	−1.03072	−0.515361	+	0.856973i	$0.672342\pi$
$734$	−21743.4	−1.09341
$735$	−9368.62	−0.470159
$736$	−46.0794	−0.00230776
$737$	−2462.12	−0.123057
$738$	2966.69	0.147975
$739$	18916.4	0.941610	0.470805	−	0.882237i	$-0.343963\pi$
$739$	18916.4	0.941610	0.470805	+	0.882237i	$0.343963\pi$
$740$	−10101.7	−0.501818
$741$	0	0
$742$	−8762.10	−0.433513
$743$	−2199.42	−0.108599	−0.0542995	−	0.998525i	$-0.517293\pi$
$743$	−2199.42	−0.108599	−0.0542995	+	0.998525i	$0.517293\pi$
$744$	−5925.10	−0.291969
$745$	−46721.6	−2.29765
$746$	3638.09	0.178552
$747$	1869.35	0.0915606
$748$	−5457.42	−0.266769
$749$	21220.3	1.03521
$750$	−3255.09	−0.158479
$751$	−24098.7	−1.17094	−0.585470	−	0.810694i	$-0.699090\pi$
$751$	−24098.7	−1.17094	−0.585470	+	0.810694i	$0.699090\pi$
$752$	−8838.61	−0.428605
$753$	−19738.8	−0.955277
$754$	−1173.44	−0.0566766
$755$	33217.5	1.60120
$756$	1353.80	0.0651287
$757$	7908.77	0.379721	0.189861	−	0.981811i	$-0.439196\pi$
$757$	7908.77	0.379721	0.189861	+	0.981811i	$0.439196\pi$
$758$	590.851	0.0283122
$759$	255.440	0.0122159
$760$	0	0
$761$	90.7992	0.00432519	0.00216260	−	0.999998i	$-0.499312\pi$
$761$	90.7992	0.00432519	0.00216260	+	0.999998i	$0.499312\pi$
$762$	−5680.61	−0.270062
$763$	−23000.2	−1.09130
$764$	3290.59	0.155824
$765$	−3489.04	−0.164897
$766$	2945.63	0.138943
$767$	−21826.1	−1.02750
$768$	−768.000	−0.0360844
$769$	−10956.7	−0.513797	−0.256899	−	0.966438i	$-0.582701\pi$
$769$	−10956.7	−0.513797	−0.256899	+	0.966438i	$0.582701\pi$
$770$	24906.9	1.16569
$771$	5984.00	0.279518
$772$	18784.3	0.875729
$773$	−2074.98	−0.0965483	−0.0482741	−	0.998834i	$-0.515372\pi$
$773$	−2074.98	−0.0965483	−0.0482741	+	0.998834i	$0.515372\pi$
$774$	9819.53	0.456015
$775$	−38831.6	−1.79983
$776$	1439.85	0.0666077
$777$	5652.47	0.260980
$778$	20831.0	0.959935
$779$	0	0
$780$	10902.7	0.500487
$781$	30506.7	1.39772
$782$	−66.4511	−0.00303873
$783$	−292.947	−0.0133705
$784$	−2973.90	−0.135473
$785$	53390.2	2.42749
$786$	−11538.8	−0.523631
$787$	−11297.7	−0.511714	−0.255857	−	0.966715i	$-0.582358\pi$
$787$	−11297.7	−0.511714	−0.255857	+	0.966715i	$0.582358\pi$
$788$	−18349.0	−0.829513
$789$	16823.5	0.759103
$790$	−42841.7	−1.92942
$791$	−119.083	−0.00535286
$792$	4257.40	0.191010
$793$	6276.29	0.281056
$794$	−2253.71	−0.100732
$795$	−17616.3	−0.785896
$796$	−9569.60	−0.426113
$797$	−38236.4	−1.69938	−0.849688	−	0.527286i	$-0.823210\pi$
$797$	−38236.4	−1.69938	−0.849688	+	0.527286i	$0.823210\pi$
$798$	0	0
$799$	−12746.2	−0.564364
$800$	−5033.27	−0.222441
$801$	−12730.3	−0.561550
$802$	6201.79	0.273059
$803$	−36122.2	−1.58745
$804$	−499.665	−0.0219177
$805$	303.274	0.0132783
$806$	26700.6	1.16686
$807$	−7300.60	−0.318455
$808$	13444.4	0.585360
$809$	19079.6	0.829174	0.414587	−	0.910010i	$-0.363926\pi$
$809$	19079.6	0.829174	0.414587	+	0.910010i	$0.363926\pi$
$810$	2721.84	0.118069
$811$	27629.4	1.19630	0.598150	−	0.801384i	$-0.295903\pi$
$811$	27629.4	1.19630	0.598150	+	0.801384i	$0.295903\pi$
$812$	−544.022	−0.0235116
$813$	4834.26	0.208542
$814$	17775.7	0.765404
$815$	38221.3	1.64274
$816$	−1107.53	−0.0475140
$817$	0	0
$818$	5940.82	0.253931
$819$	−6100.70	−0.260288
$820$	11076.6	0.471723
$821$	11651.5	0.495300	0.247650	−	0.968850i	$-0.420342\pi$
$821$	11651.5	0.495300	0.247650	+	0.968850i	$0.420342\pi$
$822$	16762.9	0.711282
$823$	−35092.4	−1.48632	−0.743161	−	0.669113i	$-0.766674\pi$
$823$	−35092.4	−1.48632	−0.743161	+	0.669113i	$0.766674\pi$
$824$	−1191.92	−0.0503916
$825$	27901.9	1.17748
$826$	−10118.9	−0.426247
$827$	−39467.0	−1.65950	−0.829748	−	0.558138i	$-0.811516\pi$
$827$	−39467.0	−1.65950	−0.829748	+	0.558138i	$0.811516\pi$
$828$	51.8393	0.00217577
$829$	−43662.2	−1.82925	−0.914626	−	0.404301i	$-0.867515\pi$
$829$	−43662.2	−1.82925	−0.914626	+	0.404301i	$0.867515\pi$
$830$	6979.51	0.291882
$831$	−3906.41	−0.163071
$832$	3460.87	0.144212
$833$	−4288.67	−0.178383
$834$	10476.4	0.434975
$835$	−62903.4	−2.60702
$836$	0	0
$837$	6665.74	0.275271
$838$	1627.39	0.0670852
$839$	−17125.1	−0.704679	−0.352339	−	0.935872i	$-0.614614\pi$
$839$	−17125.1	−0.704679	−0.352339	+	0.935872i	$0.614614\pi$
$840$	5054.64	0.207621
$841$	−24271.3	−0.995173
$842$	−21449.0	−0.877887
$843$	7486.61	0.305875
$844$	7203.09	0.293769
$845$	−12218.6	−0.497434
$846$	9943.44	0.404093
$847$	−27143.9	−1.10115
$848$	−5592.00	−0.226450
$849$	10803.4	0.436714
$850$	−7258.49	−0.292899
$851$	216.443	0.00871863
$852$	6191.07	0.248947
$853$	−36007.4	−1.44533	−0.722667	−	0.691197i	$-0.757084\pi$
$853$	−36007.4	−1.44533	−0.722667	+	0.691197i	$0.757084\pi$
$854$	2909.77	0.116593
$855$	0	0
$856$	13542.8	0.540753
$857$	−19461.2	−0.775708	−0.387854	−	0.921721i	$-0.626784\pi$
$857$	−19461.2	−0.775708	−0.387854	+	0.921721i	$0.626784\pi$
$858$	−19185.3	−0.763375
$859$	−30272.8	−1.20244	−0.601218	−	0.799085i	$-0.705318\pi$
$859$	−30272.8	−1.20244	−0.601218	+	0.799085i	$0.705318\pi$
$860$	36662.8	1.45371
$861$	−6198.02	−0.245328
$862$	1812.82	0.0716298
$863$	−19703.4	−0.777187	−0.388594	−	0.921409i	$-0.627039\pi$
$863$	−19703.4	−0.777187	−0.388594	+	0.921409i	$0.627039\pi$
$864$	864.000	0.0340207
$865$	−1538.68	−0.0604819
$866$	11893.7	0.466704
$867$	13141.8	0.514786
$868$	12378.7	0.484056
$869$	75387.7	2.94287
$870$	−1093.76	−0.0426231
$871$	2251.66	0.0875944
$872$	−14678.8	−0.570054
$873$	−1619.83	−0.0627984
$874$	0	0
$875$	6800.54	0.262743
$876$	−7330.68	−0.282741
$877$	−27981.0	−1.07737	−0.538684	−	0.842508i	$-0.681078\pi$
$877$	−27981.0	−1.07737	−0.538684	+	0.842508i	$0.681078\pi$
$878$	−19771.7	−0.759981
$879$	18639.5	0.715237
$880$	15895.7	0.608913
$881$	−37529.4	−1.43519	−0.717593	−	0.696463i	$-0.754756\pi$
$881$	−37529.4	−1.43519	−0.717593	+	0.696463i	$0.754756\pi$
$882$	3345.64	0.127725
$883$	18436.1	0.702632	0.351316	−	0.936257i	$-0.385734\pi$
$883$	18436.1	0.702632	0.351316	+	0.936257i	$0.385734\pi$
$884$	4990.93	0.189890
$885$	−20344.1	−0.772724
$886$	11104.2	0.421053
$887$	18530.2	0.701447	0.350723	−	0.936479i	$-0.385936\pi$
$887$	18530.2	0.701447	0.350723	+	0.936479i	$0.385936\pi$
$888$	3607.42	0.136326
$889$	11867.9	0.447736
$890$	−47530.5	−1.79014
$891$	−4789.57	−0.180086
$892$	−9267.76	−0.347879
$893$	0	0
$894$	16684.8	0.624188
$895$	67254.8	2.51182
$896$	1604.51	0.0598245
$897$	−233.606	−0.00869551
$898$	25609.8	0.951680
$899$	−2678.61	−0.0993734
$900$	5662.43	0.209720
$901$	−8064.22	−0.298178
$902$	−19491.3	−0.719502
$903$	−20515.0	−0.756030
$904$	−75.9993	−0.00279613
$905$	66127.3	2.42889
$906$	−11862.3	−0.434989
$907$	45566.7	1.66815	0.834077	−	0.551648i	$-0.186001\pi$
$907$	45566.7	1.66815	0.834077	+	0.551648i	$0.186001\pi$
$908$	−7649.33	−0.279572
$909$	−15124.9	−0.551882
$910$	−22777.9	−0.829760
$911$	−13113.3	−0.476909	−0.238454	−	0.971154i	$-0.576641\pi$
$911$	−13113.3	−0.476909	−0.238454	+	0.971154i	$0.576641\pi$
$912$	0	0
$913$	−12281.7	−0.445197
$914$	10908.0	0.394754
$915$	5850.14	0.211366
$916$	−551.950	−0.0199093
$917$	24106.8	0.868131
$918$	1245.98	0.0447966
$919$	−41086.7	−1.47478	−0.737391	−	0.675466i	$-0.763942\pi$
$919$	−41086.7	−1.47478	−0.737391	+	0.675466i	$0.763942\pi$
$920$	193.550	0.00693606
$921$	−27212.6	−0.973601
$922$	−8734.68	−0.311997
$923$	−27899.1	−0.994919
$924$	−8894.55	−0.316677
$925$	23642.1	0.840376
$926$	34169.4	1.21261
$927$	1340.91	0.0475096
$928$	−347.196	−0.0122816
$929$	−36186.2	−1.27797	−0.638984	−	0.769220i	$-0.720645\pi$
$929$	−36186.2	−1.27797	−0.638984	+	0.769220i	$0.720645\pi$
$930$	24887.6	0.877523
$931$	0	0
$932$	−10029.0	−0.352479
$933$	−5787.98	−0.203097
$934$	−23907.6	−0.837560
$935$	22923.2	0.801784
$936$	−3893.48	−0.135964
$937$	−31836.5	−1.10998	−0.554991	−	0.831856i	$-0.687278\pi$
$937$	−31836.5	−1.10998	−0.554991	+	0.831856i	$0.687278\pi$
$938$	1043.90	0.0363375
$939$	12299.2	0.427442
$940$	37125.4	1.28819
$941$	41207.7	1.42756	0.713779	−	0.700371i	$-0.246982\pi$
$941$	41207.7	1.42756	0.713779	+	0.700371i	$0.246982\pi$
$942$	−19066.2	−0.659460
$943$	−237.332	−0.00819576
$944$	−6457.89	−0.222655
$945$	−5686.47	−0.195747
$946$	−64514.9	−2.21729
$947$	25572.4	0.877500	0.438750	−	0.898609i	$-0.355421\pi$
$947$	25572.4	0.877500	0.438750	+	0.898609i	$0.355421\pi$
$948$	15299.3	0.524153
$949$	33034.6	1.12998
$950$	0	0
$951$	4026.53	0.137297
$952$	2313.86	0.0787737
$953$	−56330.0	−1.91470	−0.957350	−	0.288930i	$-0.906700\pi$
$953$	−56330.0	−1.91470	−0.957350	+	0.288930i	$0.906700\pi$
$954$	6291.00	0.213499
$955$	−13821.7	−0.468335
$956$	10153.2	0.343493
$957$	1924.68	0.0650115
$958$	5021.84	0.169362
$959$	−35021.1	−1.17924
$960$	3225.88	0.108453
$961$	31158.3	1.04590
$962$	−16256.3	−0.544828
$963$	−15235.7	−0.509827
$964$	−13062.2	−0.436416
$965$	−78901.1	−2.63204
$966$	−108.303	−0.00360723
$967$	−22394.0	−0.744717	−0.372358	−	0.928089i	$-0.621451\pi$
$967$	−22394.0	−0.744717	−0.372358	+	0.928089i	$0.621451\pi$
$968$	−17323.3	−0.575199
$969$	0	0
$970$	−6047.90	−0.200192
$971$	44875.7	1.48314	0.741571	−	0.670874i	$-0.234081\pi$
$971$	44875.7	1.48314	0.741571	+	0.670874i	$0.234081\pi$
$972$	−972.000	−0.0320750
$973$	−21887.3	−0.721147
$974$	−14335.7	−0.471606
$975$	−25516.9	−0.838148
$976$	1857.02	0.0609035
$977$	−27161.8	−0.889439	−0.444719	−	0.895670i	$-0.646697\pi$
$977$	−27161.8	−0.889439	−0.444719	+	0.895670i	$0.646697\pi$
$978$	−13649.3	−0.446274
$979$	83638.4	2.73044
$980$	12491.5	0.407169
$981$	16513.7	0.537452
$982$	3137.36	0.101952
$983$	−28968.6	−0.939933	−0.469966	−	0.882684i	$-0.655734\pi$
$983$	−28968.6	−0.939933	−0.469966	+	0.882684i	$0.655734\pi$
$984$	−3955.59	−0.128150
$985$	77072.6	2.49313
$986$	−500.692	−0.0161717
$987$	−20773.8	−0.669948
$988$	0	0
$989$	−785.552	−0.0252569
$990$	−17882.6	−0.574088
$991$	−11215.3	−0.359501	−0.179750	−	0.983712i	$-0.557529\pi$
$991$	−11215.3	−0.359501	−0.179750	+	0.983712i	$0.557529\pi$
$992$	7900.13	0.252852
$993$	7811.86	0.249650
$994$	−12934.4	−0.412730
$995$	40195.9	1.28070
$996$	−2492.46	−0.0792938
$997$	−5829.73	−0.185185	−0.0925924	−	0.995704i	$-0.529515\pi$
$997$	−5829.73	−0.185185	−0.0925924	+	0.995704i	$0.529515\pi$
$998$	−2604.07	−0.0825956
$999$	−4058.35	−0.128529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.bn.1.3	✓	12
19.18	odd	2		2166.4.a.bo.1.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.4.a.bn.1.3	✓	12	1.1	even	1	trivial
2166.4.a.bo.1.3	yes	12	19.18	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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -16.8015 q^{5} +6.00000 q^{6} -12.5352 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -16.8015 q^{5} +6.00000 q^{6} -12.5352 q^{7} -8.00000 q^{8} +9.00000 q^{9} +33.6030 q^{10} -59.1305 q^{11} -12.0000 q^{12} +54.0762 q^{13} +25.0704 q^{14} +50.4044 q^{15} +16.0000 q^{16} +23.0736 q^{17} -18.0000 q^{18} -67.2059 q^{20} +37.6056 q^{21} +118.261 q^{22} +1.43998 q^{23} +24.0000 q^{24} +157.290 q^{25} -108.152 q^{26} -27.0000 q^{27} -50.1408 q^{28} +10.8499 q^{29} -100.809 q^{30} -246.879 q^{31} -32.0000 q^{32} +177.391 q^{33} -46.1472 q^{34} +210.610 q^{35} +36.0000 q^{36} +150.309 q^{37} -162.229 q^{39} +134.412 q^{40} -164.816 q^{41} -75.2112 q^{42} -545.530 q^{43} -236.522 q^{44} -151.213 q^{45} -2.87996 q^{46} -552.413 q^{47} -48.0000 q^{48} -185.869 q^{49} -314.580 q^{50} -69.2208 q^{51} +216.305 q^{52} -349.500 q^{53} +54.0000 q^{54} +993.480 q^{55} +100.282 q^{56} -21.6998 q^{58} -403.618 q^{59} +201.618 q^{60} +116.064 q^{61} +493.758 q^{62} -112.817 q^{63} +64.0000 q^{64} -908.560 q^{65} -354.783 q^{66} +41.6388 q^{67} +92.2944 q^{68} -4.31994 q^{69} -421.220 q^{70} -515.922 q^{71} -72.0000 q^{72} +610.890 q^{73} -300.619 q^{74} -471.869 q^{75} +741.212 q^{77} +324.457 q^{78} -1274.94 q^{79} -268.824 q^{80} +81.0000 q^{81} +329.633 q^{82} +207.705 q^{83} +150.422 q^{84} -387.671 q^{85} +1091.06 q^{86} -32.5497 q^{87} +473.044 q^{88} -1414.47 q^{89} +302.427 q^{90} -677.855 q^{91} +5.75992 q^{92} +740.637 q^{93} +1104.83 q^{94} +96.0000 q^{96} -179.981 q^{97} +371.738 q^{98} -532.174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} - 36 q^{3} + 48 q^{4} + 10 q^{5} + 72 q^{6} + 56 q^{7} - 96 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q - 24 * q^2 - 36 * q^3 + 48 * q^4 + 10 * q^5 + 72 * q^6 + 56 * q^7 - 96 * q^8 + 108 * q^9	\( 12 q - 24 q^{2} - 36 q^{3} + 48 q^{4} + 10 q^{5} + 72 q^{6} + 56 q^{7} - 96 q^{8} + 108 q^{9} - 20 q^{10} + 78 q^{11} - 144 q^{12} - 44 q^{13} - 112 q^{14} - 30 q^{15} + 192 q^{16} + 200 q^{17} - 216 q^{18} + 40 q^{20} - 168 q^{21} - 156 q^{22} + 330 q^{23} + 288 q^{24} + 738 q^{25} + 88 q^{26} - 324 q^{27} + 224 q^{28} - 282 q^{29} + 60 q^{30} - 304 q^{31} - 384 q^{32} - 234 q^{33} - 400 q^{34} + 486 q^{35} + 432 q^{36} + 280 q^{37} + 132 q^{39} - 80 q^{40} - 338 q^{41} + 336 q^{42} + 792 q^{43} + 312 q^{44} + 90 q^{45} - 660 q^{46} + 1088 q^{47} - 576 q^{48} + 928 q^{49} - 1476 q^{50} - 600 q^{51} - 176 q^{52} - 312 q^{53} + 648 q^{54} + 1058 q^{55} - 448 q^{56} + 564 q^{58} - 694 q^{59} - 120 q^{60} + 1438 q^{61} + 608 q^{62} + 504 q^{63} + 768 q^{64} + 1040 q^{65} + 468 q^{66} - 1248 q^{67} + 800 q^{68} - 990 q^{69} - 972 q^{70} - 1314 q^{71} - 864 q^{72} + 2860 q^{73} - 560 q^{74} - 2214 q^{75} + 4028 q^{77} - 264 q^{78} + 16 q^{79} + 160 q^{80} + 972 q^{81} + 676 q^{82} + 1258 q^{83} - 672 q^{84} + 1926 q^{85} - 1584 q^{86} + 846 q^{87} - 624 q^{88} - 4776 q^{89} - 180 q^{90} + 1484 q^{91} + 1320 q^{92} + 912 q^{93} - 2176 q^{94} + 1152 q^{96} - 4088 q^{97} - 1856 q^{98} + 702 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 - 36 * q^3 + 48 * q^4 + 10 * q^5 + 72 * q^6 + 56 * q^7 - 96 * q^8 + 108 * q^9 - 20 * q^10 + 78 * q^11 - 144 * q^12 - 44 * q^13 - 112 * q^14 - 30 * q^15 + 192 * q^16 + 200 * q^17 - 216 * q^18 + 40 * q^20 - 168 * q^21 - 156 * q^22 + 330 * q^23 + 288 * q^24 + 738 * q^25 + 88 * q^26 - 324 * q^27 + 224 * q^28 - 282 * q^29 + 60 * q^30 - 304 * q^31 - 384 * q^32 - 234 * q^33 - 400 * q^34 + 486 * q^35 + 432 * q^36 + 280 * q^37 + 132 * q^39 - 80 * q^40 - 338 * q^41 + 336 * q^42 + 792 * q^43 + 312 * q^44 + 90 * q^45 - 660 * q^46 + 1088 * q^47 - 576 * q^48 + 928 * q^49 - 1476 * q^50 - 600 * q^51 - 176 * q^52 - 312 * q^53 + 648 * q^54 + 1058 * q^55 - 448 * q^56 + 564 * q^58 - 694 * q^59 - 120 * q^60 + 1438 * q^61 + 608 * q^62 + 504 * q^63 + 768 * q^64 + 1040 * q^65 + 468 * q^66 - 1248 * q^67 + 800 * q^68 - 990 * q^69 - 972 * q^70 - 1314 * q^71 - 864 * q^72 + 2860 * q^73 - 560 * q^74 - 2214 * q^75 + 4028 * q^77 - 264 * q^78 + 16 * q^79 + 160 * q^80 + 972 * q^81 + 676 * q^82 + 1258 * q^83 - 672 * q^84 + 1926 * q^85 - 1584 * q^86 + 846 * q^87 - 624 * q^88 - 4776 * q^89 - 180 * q^90 + 1484 * q^91 + 1320 * q^92 + 912 * q^93 - 2176 * q^94 + 1152 * q^96 - 4088 * q^97 - 1856 * q^98 + 702 * q^99

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