LMFDB - Embedded newform 1849.4.a.l.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.96613 q^{2} -5.58493 q^{3} +7.73016 q^{4} -7.81764 q^{5} +22.1506 q^{6} +27.2797 q^{7} +1.07022 q^{8} +4.19148 q^{9} +O(q^{10})$	\(q-3.96613 q^{2} -5.58493 q^{3} +7.73016 q^{4} -7.81764 q^{5} +22.1506 q^{6} +27.2797 q^{7} +1.07022 q^{8} +4.19148 q^{9} +31.0057 q^{10} +35.5775 q^{11} -43.1724 q^{12} -11.2420 q^{13} -108.195 q^{14} +43.6610 q^{15} -66.0859 q^{16} -99.0441 q^{17} -16.6239 q^{18} +6.44168 q^{19} -60.4316 q^{20} -152.355 q^{21} -141.105 q^{22} +61.8133 q^{23} -5.97710 q^{24} -63.8845 q^{25} +44.5871 q^{26} +127.384 q^{27} +210.876 q^{28} +254.467 q^{29} -173.165 q^{30} +40.5146 q^{31} +253.543 q^{32} -198.698 q^{33} +392.821 q^{34} -213.263 q^{35} +32.4008 q^{36} +294.894 q^{37} -25.5485 q^{38} +62.7857 q^{39} -8.36659 q^{40} +215.393 q^{41} +604.260 q^{42} +275.019 q^{44} -32.7675 q^{45} -245.159 q^{46} +342.251 q^{47} +369.085 q^{48} +401.182 q^{49} +253.374 q^{50} +553.155 q^{51} -86.9024 q^{52} -362.672 q^{53} -505.221 q^{54} -278.132 q^{55} +29.1953 q^{56} -35.9763 q^{57} -1009.25 q^{58} +368.277 q^{59} +337.506 q^{60} +784.986 q^{61} -160.686 q^{62} +114.342 q^{63} -476.898 q^{64} +87.8858 q^{65} +788.060 q^{66} +373.379 q^{67} -765.627 q^{68} -345.223 q^{69} +845.828 q^{70} -651.097 q^{71} +4.48580 q^{72} -1054.17 q^{73} -1169.59 q^{74} +356.791 q^{75} +49.7952 q^{76} +970.542 q^{77} -249.016 q^{78} -862.639 q^{79} +516.636 q^{80} -824.601 q^{81} -854.275 q^{82} -531.306 q^{83} -1177.73 q^{84} +774.291 q^{85} -1421.18 q^{87} +38.0757 q^{88} -1082.31 q^{89} +129.960 q^{90} -306.678 q^{91} +477.827 q^{92} -226.272 q^{93} -1357.41 q^{94} -50.3587 q^{95} -1416.02 q^{96} +541.385 q^{97} -1591.14 q^{98} +149.122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9}+O(q^{10}) $ 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9	\( 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} + 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} + 625 q^{18} + 610 q^{19} + 345 q^{20} + 611 q^{21} + 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} + 1071 q^{26} + 1609 q^{27} + 46 q^{28} + 773 q^{29} + 375 q^{30} - 97 q^{31} + 1967 q^{32} + 500 q^{33} + 217 q^{34} + 247 q^{35} + 175 q^{36} + 228 q^{37} + 1253 q^{38} + 1493 q^{39} + 2220 q^{40} - 951 q^{41} + 2643 q^{42} - 1378 q^{44} + 1086 q^{45} - 565 q^{46} - 2 q^{47} + 2303 q^{48} + 1264 q^{49} + 3273 q^{50} + 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} + 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} + 2999 q^{61} + 5569 q^{62} + 2377 q^{63} + 2082 q^{64} + 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} + 1817 q^{69} + 2738 q^{70} + 8003 q^{71} + 1412 q^{72} - 1011 q^{73} - 1413 q^{74} + 7457 q^{75} + 5516 q^{76} + 4052 q^{77} + 1091 q^{78} - 4422 q^{79} + 1610 q^{80} + 2108 q^{81} + 4676 q^{82} - 297 q^{83} - 54 q^{84} + 4333 q^{85} + 1377 q^{87} + 3652 q^{88} + 2480 q^{89} - 1414 q^{90} + 4551 q^{91} - 3286 q^{92} + 4 q^{93} + 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} + 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 + 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 + 625 * q^18 + 610 * q^19 + 345 * q^20 + 611 * q^21 + 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 + 1071 * q^26 + 1609 * q^27 + 46 * q^28 + 773 * q^29 + 375 * q^30 - 97 * q^31 + 1967 * q^32 + 500 * q^33 + 217 * q^34 + 247 * q^35 + 175 * q^36 + 228 * q^37 + 1253 * q^38 + 1493 * q^39 + 2220 * q^40 - 951 * q^41 + 2643 * q^42 - 1378 * q^44 + 1086 * q^45 - 565 * q^46 - 2 * q^47 + 2303 * q^48 + 1264 * q^49 + 3273 * q^50 + 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 + 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 + 2999 * q^61 + 5569 * q^62 + 2377 * q^63 + 2082 * q^64 + 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 + 1817 * q^69 + 2738 * q^70 + 8003 * q^71 + 1412 * q^72 - 1011 * q^73 - 1413 * q^74 + 7457 * q^75 + 5516 * q^76 + 4052 * q^77 + 1091 * q^78 - 4422 * q^79 + 1610 * q^80 + 2108 * q^81 + 4676 * q^82 - 297 * q^83 - 54 * q^84 + 4333 * q^85 + 1377 * q^87 + 3652 * q^88 + 2480 * q^89 - 1414 * q^90 + 4551 * q^91 - 3286 * q^92 + 4 * q^93 + 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 + 753 * q^98 + 5072 * 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 $

$2$	−3.96613	−1.40224	−0.701119	−	0.713045i	$-0.747316\pi$
$2$	−3.96613	−1.40224	−0.701119	+	0.713045i	$0.747316\pi$
$3$	−5.58493	−1.07482	−0.537410	−	0.843321i	$-0.680597\pi$
$3$	−5.58493	−1.07482	−0.537410	+	0.843321i	$0.680597\pi$
$4$	7.73016	0.966270
$5$	−7.81764	−0.699231	−0.349615	−	0.936893i	$-0.613688\pi$
$5$	−7.81764	−0.699231	−0.349615	+	0.936893i	$0.613688\pi$
$6$	22.1506	1.50715
$7$	27.2797	1.47297	0.736483	−	0.676456i	$-0.236485\pi$
$7$	27.2797	1.47297	0.736483	+	0.676456i	$0.236485\pi$
$8$	1.07022	0.0472975
$9$	4.19148	0.155240
$10$	31.0057	0.980488
$11$	35.5775	0.975182	0.487591	−	0.873072i	$-0.337876\pi$
$11$	35.5775	0.975182	0.487591	+	0.873072i	$0.337876\pi$
$12$	−43.1724	−1.03857
$13$	−11.2420	−0.239844	−0.119922	−	0.992783i	$-0.538264\pi$
$13$	−11.2420	−0.239844	−0.119922	+	0.992783i	$0.538264\pi$
$14$	−108.195	−2.06545
$15$	43.6610	0.751548
$16$	−66.0859	−1.03259
$17$	−99.0441	−1.41304	−0.706521	−	0.707692i	$-0.749737\pi$
$17$	−99.0441	−1.41304	−0.706521	+	0.707692i	$0.749737\pi$
$18$	−16.6239	−0.217683
$19$	6.44168	0.0777801	0.0388901	−	0.999243i	$-0.487618\pi$
$19$	6.44168	0.0777801	0.0388901	+	0.999243i	$0.487618\pi$
$20$	−60.4316	−0.675646
$21$	−152.355	−1.58317
$22$	−141.105	−1.36744
$23$	61.8133	0.560390	0.280195	−	0.959943i	$-0.409601\pi$
$23$	61.8133	0.560390	0.280195	+	0.959943i	$0.409601\pi$
$24$	−5.97710	−0.0508363
$25$	−63.8845	−0.511076
$26$	44.5871	0.336318
$27$	127.384	0.907966
$28$	210.876	1.42328
$29$	254.467	1.62943	0.814713	−	0.579864i	$-0.196894\pi$
$29$	254.467	1.62943	0.814713	+	0.579864i	$0.196894\pi$
$30$	−173.165	−1.05385
$31$	40.5146	0.234731	0.117365	−	0.993089i	$-0.462555\pi$
$31$	40.5146	0.234731	0.117365	+	0.993089i	$0.462555\pi$
$32$	253.543	1.40064
$33$	−198.698	−1.04815
$34$	392.821	1.98142
$35$	−213.263	−1.02994
$36$	32.4008	0.150004
$37$	294.894	1.31028	0.655138	−	0.755509i	$-0.272610\pi$
$37$	294.894	1.31028	0.655138	+	0.755509i	$0.272610\pi$
$38$	−25.5485	−0.109066
$39$	62.7857	0.257789
$40$	−8.36659	−0.0330718
$41$	215.393	0.820456	0.410228	−	0.911983i	$-0.365449\pi$
$41$	215.393	0.820456	0.410228	+	0.911983i	$0.365449\pi$
$42$	604.260	2.21999
$43$	0	0
$43$	0	0
$44$	275.019	0.942289
$45$	−32.7675	−0.108549
$46$	−245.159	−0.785799
$47$	342.251	1.06218	0.531090	−	0.847315i	$-0.321782\pi$
$47$	342.251	1.06218	0.531090	+	0.847315i	$0.321782\pi$
$48$	369.085	1.10985
$49$	401.182	1.16963
$50$	253.374	0.716650
$51$	553.155	1.51877
$52$	−86.9024	−0.231754
$53$	−362.672	−0.939941	−0.469970	−	0.882682i	$-0.655735\pi$
$53$	−362.672	−0.939941	−0.469970	+	0.882682i	$0.655735\pi$
$54$	−505.221	−1.27318
$55$	−278.132	−0.681878
$56$	29.1953	0.0696675
$57$	−35.9763	−0.0835997
$58$	−1009.25	−2.28484
$59$	368.277	0.812637	0.406319	−	0.913731i	$-0.366812\pi$
$59$	368.277	0.812637	0.406319	+	0.913731i	$0.366812\pi$
$60$	337.506	0.726198
$61$	784.986	1.64766	0.823829	−	0.566838i	$-0.191834\pi$
$61$	784.986	1.64766	0.823829	+	0.566838i	$0.191834\pi$
$62$	−160.686	−0.329148
$63$	114.342	0.228663
$64$	−476.898	−0.931441
$65$	87.8858	0.167706
$66$	788.060	1.46975
$67$	373.379	0.680829	0.340414	−	0.940275i	$-0.389433\pi$
$67$	373.379	0.680829	0.340414	+	0.940275i	$0.389433\pi$
$68$	−765.627	−1.36538
$69$	−345.223	−0.602318
$70$	845.828	1.44422
$71$	−651.097	−1.08832	−0.544162	−	0.838980i	$-0.683152\pi$
$71$	−651.097	−1.08832	−0.544162	+	0.838980i	$0.683152\pi$
$72$	4.48580	0.00734245
$73$	−1054.17	−1.69015	−0.845073	−	0.534650i	$-0.820443\pi$
$73$	−1054.17	−1.69015	−0.845073	+	0.534650i	$0.820443\pi$
$74$	−1169.59	−1.83732
$75$	356.791	0.549315
$76$	49.7952	0.0751566
$77$	970.542	1.43641
$78$	−249.016	−0.361481
$79$	−862.639	−1.22854	−0.614269	−	0.789097i	$-0.710549\pi$
$79$	−862.639	−1.22854	−0.614269	+	0.789097i	$0.710549\pi$
$80$	516.636	0.722021
$81$	−824.601	−1.13114
$82$	−854.275	−1.15047
$83$	−531.306	−0.702631	−0.351316	−	0.936257i	$-0.614266\pi$
$83$	−531.306	−0.702631	−0.351316	+	0.936257i	$0.614266\pi$
$84$	−1177.73	−1.52977
$85$	774.291	0.988043
$86$	0	0
$87$	−1421.18	−1.75134
$88$	38.0757	0.0461236
$89$	−1082.31	−1.28904	−0.644518	−	0.764589i	$-0.722942\pi$
$89$	−1082.31	−1.28904	−0.644518	+	0.764589i	$0.722942\pi$
$90$	129.960	0.152211
$91$	−306.678	−0.353281
$92$	477.827	0.541488
$93$	−226.272	−0.252293
$94$	−1357.41	−1.48943
$95$	−50.3587	−0.0543863
$96$	−1416.02	−1.50544
$97$	541.385	0.566694	0.283347	−	0.959017i	$-0.408555\pi$
$97$	541.385	0.566694	0.283347	+	0.959017i	$0.408555\pi$
$98$	−1591.14	−1.64010
$99$	149.122	0.151387
$100$	−493.837	−0.493837
$101$	1491.02	1.46893	0.734464	−	0.678647i	$-0.237433\pi$
$101$	1491.02	1.46893	0.734464	+	0.678647i	$0.237433\pi$
$102$	−2193.88	−2.12967
$103$	1344.08	1.28579	0.642896	−	0.765953i	$-0.277733\pi$
$103$	1344.08	1.28579	0.642896	+	0.765953i	$0.277733\pi$
$104$	−12.0314	−0.0113440
$105$	1191.06	1.10700
$106$	1438.40	1.31802
$107$	−627.186	−0.566657	−0.283329	−	0.959023i	$-0.591439\pi$
$107$	−627.186	−0.566657	−0.283329	+	0.959023i	$0.591439\pi$
$108$	984.699	0.877340
$109$	−1968.69	−1.72996	−0.864982	−	0.501803i	$-0.832670\pi$
$109$	−1968.69	−1.72996	−0.864982	+	0.501803i	$0.832670\pi$
$110$	1103.11	0.956154
$111$	−1646.96	−1.40831
$112$	−1802.80	−1.52097
$113$	878.996	0.731761	0.365881	−	0.930662i	$-0.380768\pi$
$113$	878.996	0.731761	0.365881	+	0.930662i	$0.380768\pi$
$114$	142.687	0.117227
$115$	−483.234	−0.391842
$116$	1967.07	1.57447
$117$	−47.1205	−0.0372333
$118$	−1460.63	−1.13951
$119$	−2701.89	−2.08136
$120$	46.7268	0.0355463
$121$	−65.2450	−0.0490195
$122$	−3113.35	−2.31041
$123$	−1202.95	−0.881843
$124$	313.185	0.226813
$125$	1476.63	1.05659
$126$	−453.496	−0.320640
$127$	60.1325	0.0420149	0.0210075	−	0.999779i	$-0.493313\pi$
$127$	60.1325	0.0420149	0.0210075	+	0.999779i	$0.493313\pi$
$128$	−136.910	−0.0945411
$129$	0	0
$130$	−348.566	−0.235164
$131$	1662.99	1.10913	0.554564	−	0.832141i	$-0.312885\pi$
$131$	1662.99	1.10913	0.554564	+	0.832141i	$0.312885\pi$
$132$	−1535.96	−1.01279
$133$	175.727	0.114567
$134$	−1480.87	−0.954684
$135$	−995.843	−0.634878
$136$	−105.999	−0.0668333
$137$	1501.64	0.936450	0.468225	−	0.883609i	$-0.344894\pi$
$137$	1501.64	0.936450	0.468225	+	0.883609i	$0.344894\pi$
$138$	1369.20	0.844593
$139$	952.583	0.581274	0.290637	−	0.956833i	$-0.406133\pi$
$139$	952.583	0.581274	0.290637	+	0.956833i	$0.406133\pi$
$140$	−1648.56	−0.995203
$141$	−1911.45	−1.14165
$142$	2582.33	1.52609
$143$	−399.961	−0.233891
$144$	−276.998	−0.160300
$145$	−1989.33	−1.13935
$146$	4180.95	2.36999
$147$	−2240.58	−1.25714
$148$	2279.58	1.26608
$149$	3486.69	1.91705	0.958527	−	0.285002i	$-0.0919943\pi$
$149$	3486.69	1.91705	0.958527	+	0.285002i	$0.0919943\pi$
$150$	−1415.08	−0.770270
$151$	1443.17	0.777770	0.388885	−	0.921286i	$-0.372860\pi$
$151$	1443.17	0.777770	0.388885	+	0.921286i	$0.372860\pi$
$152$	6.89401	0.00367880
$153$	−415.141	−0.219361
$154$	−3849.29	−2.01419
$155$	−316.729	−0.164131
$156$	485.344	0.249094
$157$	99.6804	0.0506711	0.0253355	−	0.999679i	$-0.491935\pi$
$157$	99.6804	0.0506711	0.0253355	+	0.999679i	$0.491935\pi$
$158$	3421.33	1.72270
$159$	2025.50	1.01027
$160$	−1982.11	−0.979372
$161$	1686.25	0.825434
$162$	3270.47	1.58613
$163$	−700.263	−0.336496	−0.168248	−	0.985745i	$-0.553811\pi$
$163$	−700.263	−0.336496	−0.168248	+	0.985745i	$0.553811\pi$
$164$	1665.02	0.792782
$165$	1553.35	0.732896
$166$	2107.23	0.985256
$167$	−1492.50	−0.691577	−0.345788	−	0.938313i	$-0.612388\pi$
$167$	−1492.50	−0.691577	−0.345788	+	0.938313i	$0.612388\pi$
$168$	−163.054	−0.0748801
$169$	−2070.62	−0.942475
$170$	−3070.94	−1.38547
$171$	27.0002	0.0120746
$172$	0	0
$173$	455.479	0.200170	0.100085	−	0.994979i	$-0.468088\pi$
$173$	455.479	0.200170	0.100085	+	0.994979i	$0.468088\pi$
$174$	5636.59	2.45580
$175$	−1742.75	−0.752797
$176$	−2351.17	−1.00697
$177$	−2056.80	−0.873440
$178$	4292.56	1.80753
$179$	−3800.19	−1.58681	−0.793407	−	0.608691i	$-0.791695\pi$
$179$	−3800.19	−1.58681	−0.793407	+	0.608691i	$0.791695\pi$
$180$	−253.298	−0.104887
$181$	−2650.05	−1.08827	−0.544135	−	0.838998i	$-0.683142\pi$
$181$	−2650.05	−1.08827	−0.544135	+	0.838998i	$0.683142\pi$
$182$	1216.32	0.495384
$183$	−4384.09	−1.77094
$184$	66.1538	0.0265050
$185$	−2305.37	−0.916186
$186$	897.422	0.353775
$187$	−3523.74	−1.37797
$188$	2645.66	1.02635
$189$	3475.00	1.33740
$190$	199.729	0.0762625
$191$	2758.28	1.04493	0.522467	−	0.852660i	$-0.325012\pi$
$191$	2758.28	1.04493	0.522467	+	0.852660i	$0.325012\pi$
$192$	2663.44	1.00113
$193$	1052.85	0.392673	0.196336	−	0.980537i	$-0.437096\pi$
$193$	1052.85	0.392673	0.196336	+	0.980537i	$0.437096\pi$
$194$	−2147.20	−0.794640
$195$	−490.836	−0.180254
$196$	3101.20	1.13018
$197$	−783.967	−0.283529	−0.141765	−	0.989900i	$-0.545278\pi$
$197$	−783.967	−0.283529	−0.141765	+	0.989900i	$0.545278\pi$
$198$	−591.437	−0.212281
$199$	−3845.91	−1.37000	−0.684999	−	0.728544i	$-0.740197\pi$
$199$	−3845.91	−1.37000	−0.684999	+	0.728544i	$0.740197\pi$
$200$	−68.3704	−0.0241726
$201$	−2085.30	−0.731769
$202$	−5913.57	−2.05979
$203$	6941.79	2.40009
$204$	4275.97	1.46754
$205$	−1683.86	−0.573688
$206$	−5330.81	−1.80299
$207$	259.089	0.0869948
$208$	742.937	0.247661
$209$	229.178	0.0758498
$210$	−4723.89	−1.55228
$211$	−2145.95	−0.700157	−0.350078	−	0.936720i	$-0.613845\pi$
$211$	−2145.95	−0.700157	−0.350078	+	0.936720i	$0.613845\pi$
$212$	−2803.51	−0.908236
$213$	3636.33	1.16975
$214$	2487.50	0.794588
$215$	0	0
$216$	136.329	0.0429445
$217$	1105.23	0.345750
$218$	7808.06	2.42582
$219$	5887.44	1.81660
$220$	−2150.00	−0.658878
$221$	1113.45	0.338909
$222$	6532.06	1.97479
$223$	−3797.08	−1.14023	−0.570116	−	0.821565i	$-0.693102\pi$
$223$	−3797.08	−1.14023	−0.570116	+	0.821565i	$0.693102\pi$
$224$	6916.59	2.06310
$225$	−267.771	−0.0793394
$226$	−3486.21	−1.02610
$227$	−3625.01	−1.05991	−0.529957	−	0.848025i	$-0.677792\pi$
$227$	−3625.01	−1.05991	−0.529957	+	0.848025i	$0.677792\pi$
$228$	−278.103	−0.0807799
$229$	−3024.26	−0.872702	−0.436351	−	0.899777i	$-0.643729\pi$
$229$	−3024.26	−0.872702	−0.436351	+	0.899777i	$0.643729\pi$
$230$	1916.57	0.549455
$231$	−5420.41	−1.54388
$232$	272.336	0.0770677
$233$	2130.63	0.599065	0.299532	−	0.954086i	$-0.403169\pi$
$233$	2130.63	0.599065	0.299532	+	0.954086i	$0.403169\pi$
$234$	186.886	0.0522099
$235$	−2675.60	−0.742710
$236$	2846.84	0.785227
$237$	4817.78	1.32046
$238$	10716.1	2.91857
$239$	108.870	0.0294652	0.0147326	−	0.999891i	$-0.495310\pi$
$239$	108.870	0.0294652	0.0147326	+	0.999891i	$0.495310\pi$
$240$	−2885.38	−0.776043
$241$	965.411	0.258040	0.129020	−	0.991642i	$-0.458817\pi$
$241$	965.411	0.258040	0.129020	+	0.991642i	$0.458817\pi$
$242$	258.770	0.0687370
$243$	1165.97	0.307808
$244$	6068.07	1.59208
$245$	−3136.30	−0.817840
$246$	4771.07	1.23655
$247$	−72.4173	−0.0186551
$248$	43.3596	0.0111022
$249$	2967.31	0.755203
$250$	−5856.51	−1.48159
$251$	3762.28	0.946107	0.473054	−	0.881034i	$-0.343152\pi$
$251$	3762.28	0.946107	0.473054	+	0.881034i	$0.343152\pi$
$252$	883.884	0.220950
$253$	2199.16	0.546482
$254$	−238.493	−0.0589149
$255$	−4324.36	−1.06197
$256$	4358.18	1.06401
$257$	−431.776	−0.104799	−0.0523997	−	0.998626i	$-0.516687\pi$
$257$	−431.776	−0.104799	−0.0523997	+	0.998626i	$0.516687\pi$
$258$	0	0
$259$	8044.61	1.92999
$260$	679.371	0.162049
$261$	1066.59	0.252952
$262$	−6595.61	−1.55526
$263$	−3261.15	−0.764605	−0.382303	−	0.924037i	$-0.624869\pi$
$263$	−3261.15	−0.764605	−0.382303	+	0.924037i	$0.624869\pi$
$264$	−212.650	−0.0495746
$265$	2835.24	0.657236
$266$	−696.956	−0.160651
$267$	6044.61	1.38548
$268$	2886.28	0.657865
$269$	5317.03	1.20515	0.602574	−	0.798063i	$-0.294142\pi$
$269$	5317.03	1.20515	0.602574	+	0.798063i	$0.294142\pi$
$270$	3949.64	0.890249
$271$	248.730	0.0557538	0.0278769	−	0.999611i	$-0.491125\pi$
$271$	248.730	0.0557538	0.0278769	+	0.999611i	$0.491125\pi$
$272$	6545.42	1.45910
$273$	1712.78	0.379714
$274$	−5955.69	−1.31313
$275$	−2272.85	−0.498392
$276$	−2668.63	−0.582002
$277$	−1965.56	−0.426350	−0.213175	−	0.977014i	$-0.568380\pi$
$277$	−1965.56	−0.426350	−0.213175	+	0.977014i	$0.568380\pi$
$278$	−3778.07	−0.815084
$279$	169.816	0.0364395
$280$	−228.238	−0.0487137
$281$	−19.9773	−0.00424109	−0.00212054	−	0.999998i	$-0.500675\pi$
$281$	−19.9773	−0.00424109	−0.00212054	+	0.999998i	$0.500675\pi$
$282$	7581.06	1.60087
$283$	−1458.77	−0.306412	−0.153206	−	0.988194i	$-0.548960\pi$
$283$	−1458.77	−0.306412	−0.153206	+	0.988194i	$0.548960\pi$
$284$	−5033.08	−1.05161
$285$	281.250	0.0584555
$286$	1586.30	0.327971
$287$	5875.85	1.20850
$288$	1062.72	0.217436
$289$	4896.73	0.996689
$290$	7889.95	1.59763
$291$	−3023.60	−0.609095
$292$	−8148.87	−1.63314
$293$	−869.642	−0.173396	−0.0866980	−	0.996235i	$-0.527632\pi$
$293$	−869.642	−0.173396	−0.0866980	+	0.996235i	$0.527632\pi$
$294$	8886.41	1.76281
$295$	−2879.06	−0.568221
$296$	315.601	0.0619727
$297$	4532.00	0.885432
$298$	−13828.7	−2.68816
$299$	−694.904	−0.134406
$300$	2758.05	0.530787
$301$	0	0
$302$	−5723.78	−1.09062
$303$	−8327.24	−1.57884
$304$	−425.704	−0.0803151
$305$	−6136.74	−1.15209
$306$	1646.50	0.307596
$307$	−2613.03	−0.485778	−0.242889	−	0.970054i	$-0.578095\pi$
$307$	−2613.03	−0.485778	−0.242889	+	0.970054i	$0.578095\pi$
$308$	7502.45	1.38796
$309$	−7506.62	−1.38200
$310$	1256.19	0.230150
$311$	544.423	0.0992649	0.0496325	−	0.998768i	$-0.484195\pi$
$311$	544.423	0.0992649	0.0496325	+	0.998768i	$0.484195\pi$
$312$	67.1945	0.0121928
$313$	1758.88	0.317629	0.158815	−	0.987308i	$-0.449233\pi$
$313$	1758.88	0.317629	0.158815	+	0.987308i	$0.449233\pi$
$314$	−395.345	−0.0710529
$315$	−893.887	−0.159888
$316$	−6668.34	−1.18710
$317$	3882.56	0.687906	0.343953	−	0.938987i	$-0.388234\pi$
$317$	3882.56	0.687906	0.343953	+	0.938987i	$0.388234\pi$
$318$	−8033.39	−1.41664
$319$	9053.30	1.58899
$320$	3728.21	0.651292
$321$	3502.79	0.609055
$322$	−6687.87	−1.15746
$323$	−638.010	−0.109907
$324$	−6374.30	−1.09299
$325$	718.189	0.122578
$326$	2777.33	0.471847
$327$	10995.0	1.85940
$328$	230.517	0.0388055
$329$	9336.52	1.56456
$330$	−6160.77	−1.02769
$331$	931.843	0.154739	0.0773697	−	0.997002i	$-0.475348\pi$
$331$	931.843	0.154739	0.0773697	+	0.997002i	$0.475348\pi$
$332$	−4107.08	−0.678931
$333$	1236.04	0.203407
$334$	5919.45	0.969755
$335$	−2918.94	−0.476057
$336$	10068.5	1.63477
$337$	1231.26	0.199024	0.0995122	−	0.995036i	$-0.468272\pi$
$337$	1231.26	0.199024	0.0995122	+	0.995036i	$0.468272\pi$
$338$	8212.33	1.32157
$339$	−4909.13	−0.786512
$340$	5985.39	0.954716
$341$	1441.41	0.228905
$342$	−107.086	−0.0169314
$343$	1587.19	0.249855
$344$	0	0
$345$	2698.83	0.421160
$346$	−1806.49	−0.280686
$347$	−2637.45	−0.408028	−0.204014	−	0.978968i	$-0.565399\pi$
$347$	−2637.45	−0.408028	−0.204014	+	0.978968i	$0.565399\pi$
$348$	−10986.0	−1.69227
$349$	−1739.81	−0.266848	−0.133424	−	0.991059i	$-0.542597\pi$
$349$	−1739.81	−0.266848	−0.133424	+	0.991059i	$0.542597\pi$
$350$	6911.97	1.05560
$351$	−1432.05	−0.217770
$352$	9020.42	1.36588
$353$	−954.531	−0.143922	−0.0719611	−	0.997407i	$-0.522926\pi$
$353$	−954.531	−0.143922	−0.0719611	+	0.997407i	$0.522926\pi$
$354$	8157.54	1.22477
$355$	5090.04	0.760990
$356$	−8366.40	−1.24556
$357$	15089.9	2.23709
$358$	15072.1	2.22509
$359$	−4025.31	−0.591776	−0.295888	−	0.955223i	$-0.595615\pi$
$359$	−4025.31	−0.591776	−0.295888	+	0.955223i	$0.595615\pi$
$360$	−35.0684	−0.00513407
$361$	−6817.50	−0.993950
$362$	10510.4	1.52601
$363$	364.389	0.0526872
$364$	−2370.67	−0.341365
$365$	8241.08	1.18180
$366$	17387.9	2.48327
$367$	−10167.0	−1.44608	−0.723040	−	0.690806i	$-0.757256\pi$
$367$	−10167.0	−1.44608	−0.723040	+	0.690806i	$0.757256\pi$
$368$	−4084.99	−0.578654
$369$	902.814	0.127367
$370$	9143.40	1.28471
$371$	−9893.59	−1.38450
$372$	−1749.12	−0.243783
$373$	9489.37	1.31727	0.658634	−	0.752464i	$-0.271135\pi$
$373$	9489.37	1.31727	0.658634	+	0.752464i	$0.271135\pi$
$374$	13975.6	1.93225
$375$	−8246.89	−1.13565
$376$	366.284	0.0502384
$377$	−2860.72	−0.390808
$378$	−13782.3	−1.87536
$379$	−7715.74	−1.04573	−0.522864	−	0.852416i	$-0.675136\pi$
$379$	−7715.74	−1.04573	−0.522864	+	0.852416i	$0.675136\pi$
$380$	−389.281	−0.0525518
$381$	−335.836	−0.0451585
$382$	−10939.7	−1.46525
$383$	−2278.33	−0.303962	−0.151981	−	0.988383i	$-0.548565\pi$
$383$	−2278.33	−0.303962	−0.151981	+	0.988383i	$0.548565\pi$
$384$	764.634	0.101615
$385$	−7587.35	−1.00438
$386$	−4175.74	−0.550621
$387$	0	0
$388$	4185.00	0.547580
$389$	12112.4	1.57872	0.789359	−	0.613932i	$-0.210413\pi$
$389$	12112.4	1.57872	0.789359	+	0.613932i	$0.210413\pi$
$390$	1946.72	0.252759
$391$	−6122.24	−0.791854
$392$	429.353	0.0553204
$393$	−9287.67	−1.19211
$394$	3109.31	0.397576
$395$	6743.80	0.859031
$396$	1152.74	0.146281
$397$	−11184.0	−1.41387	−0.706936	−	0.707278i	$-0.749923\pi$
$397$	−11184.0	−1.41387	−0.706936	+	0.707278i	$0.749923\pi$
$398$	15253.4	1.92106
$399$	−981.424	−0.123139
$400$	4221.87	0.527733
$401$	13723.6	1.70904	0.854521	−	0.519417i	$-0.173851\pi$
$401$	13723.6	1.70904	0.854521	+	0.519417i	$0.173851\pi$
$402$	8270.56	1.02611
$403$	−455.465	−0.0562986
$404$	11525.8	1.41938
$405$	6446.44	0.790928
$406$	−27532.0	−3.36550
$407$	10491.6	1.27776
$408$	591.997	0.0718338
$409$	5223.83	0.631545	0.315773	−	0.948835i	$-0.397736\pi$
$409$	5223.83	0.631545	0.315773	+	0.948835i	$0.397736\pi$
$410$	6678.41	0.804447
$411$	−8386.55	−1.00652
$412$	10390.0	1.24242
$413$	10046.5	1.19699
$414$	−1027.58	−0.121987
$415$	4153.56	0.491301
$416$	−2850.33	−0.335935
$417$	−5320.11	−0.624765
$418$	−908.951	−0.106359
$419$	−16180.6	−1.88658	−0.943288	−	0.331975i	$-0.892285\pi$
$419$	−16180.6	−1.88658	−0.943288	+	0.331975i	$0.892285\pi$
$420$	9207.08	1.06967
$421$	−718.855	−0.0832181	−0.0416091	−	0.999134i	$-0.513248\pi$
$421$	−718.855	−0.0832181	−0.0416091	+	0.999134i	$0.513248\pi$
$422$	8511.10	0.981786
$423$	1434.54	0.164893
$424$	−388.139	−0.0444568
$425$	6327.38	0.722172
$426$	−14422.2	−1.64027
$427$	21414.2	2.42694
$428$	−4848.25	−0.547544
$429$	2233.76	0.251391
$430$	0	0
$431$	3806.82	0.425448	0.212724	−	0.977112i	$-0.431767\pi$
$431$	3806.82	0.425448	0.212724	+	0.977112i	$0.431767\pi$
$432$	−8418.29	−0.937558
$433$	3641.99	0.404210	0.202105	−	0.979364i	$-0.435222\pi$
$433$	3641.99	0.404210	0.202105	+	0.979364i	$0.435222\pi$
$434$	−4383.47	−0.484824
$435$	11110.3	1.22459
$436$	−15218.3	−1.67161
$437$	398.181	0.0435872
$438$	−23350.3	−2.54731
$439$	16629.0	1.80788	0.903940	−	0.427659i	$-0.140662\pi$
$439$	16629.0	1.80788	0.903940	+	0.427659i	$0.140662\pi$
$440$	−297.662	−0.0322511
$441$	1681.55	0.181573
$442$	−4416.09	−0.475231
$443$	7341.32	0.787351	0.393675	−	0.919249i	$-0.371203\pi$
$443$	7341.32	0.787351	0.393675	+	0.919249i	$0.371203\pi$
$444$	−12731.3	−1.36081
$445$	8461.08	0.901334
$446$	15059.7	1.59887
$447$	−19472.9	−2.06049
$448$	−13009.6	−1.37198
$449$	9291.04	0.976551	0.488276	−	0.872690i	$-0.337626\pi$
$449$	9291.04	0.976551	0.488276	+	0.872690i	$0.337626\pi$
$450$	1062.01	0.111253
$451$	7663.12	0.800094
$452$	6794.78	0.707079
$453$	−8059.99	−0.835963
$454$	14377.3	1.48625
$455$	2397.50	0.247025
$456$	−38.5026	−0.00395405
$457$	17851.2	1.82723	0.913614	−	0.406583i	$-0.133280\pi$
$457$	17851.2	1.82723	0.913614	+	0.406583i	$0.133280\pi$
$458$	11994.6	1.22374
$459$	−12616.6	−1.28299
$460$	−3735.48	−0.378625
$461$	7060.59	0.713329	0.356664	−	0.934233i	$-0.383914\pi$
$461$	7060.59	0.713329	0.356664	+	0.934233i	$0.383914\pi$
$462$	21498.0	2.16489
$463$	−9465.08	−0.950064	−0.475032	−	0.879969i	$-0.657563\pi$
$463$	−9465.08	−0.950064	−0.475032	+	0.879969i	$0.657563\pi$
$464$	−16816.7	−1.68253
$465$	1768.91	0.176411
$466$	−8450.34	−0.840031
$467$	8411.42	0.833478	0.416739	−	0.909026i	$-0.363173\pi$
$467$	8411.42	0.833478	0.416739	+	0.909026i	$0.363173\pi$
$468$	−364.249	−0.0359774
$469$	10185.7	1.00284
$470$	10611.8	1.04146
$471$	−556.708	−0.0544623
$472$	394.137	0.0384357
$473$	0	0
$474$	−19107.9	−1.85160
$475$	−411.523	−0.0397516
$476$	−20886.1	−2.01116
$477$	−1520.13	−0.145916
$478$	−431.790	−0.0413172
$479$	10345.8	0.986874	0.493437	−	0.869781i	$-0.335740\pi$
$479$	10345.8	0.986874	0.493437	+	0.869781i	$0.335740\pi$
$480$	11070.0	1.05265
$481$	−3315.19	−0.314261
$482$	−3828.94	−0.361833
$483$	−9417.58	−0.887194
$484$	−504.354	−0.0473661
$485$	−4232.36	−0.396250
$486$	−4624.40	−0.431619
$487$	11630.8	1.08222	0.541111	−	0.840951i	$-0.318004\pi$
$487$	11630.8	1.08222	0.541111	+	0.840951i	$0.318004\pi$
$488$	840.107	0.0779300
$489$	3910.92	0.361673
$490$	12439.0	1.14681
$491$	−1893.42	−0.174031	−0.0870153	−	0.996207i	$-0.527733\pi$
$491$	−1893.42	−0.174031	−0.0870153	+	0.996207i	$0.527733\pi$
$492$	−9299.02	−0.852098
$493$	−25203.5	−2.30245
$494$	287.216	0.0261588
$495$	−1165.78	−0.105855
$496$	−2677.45	−0.242381
$497$	−17761.7	−1.60306
$498$	−11768.7	−1.05897
$499$	−3854.79	−0.345820	−0.172910	−	0.984938i	$-0.555317\pi$
$499$	−3854.79	−0.345820	−0.172910	+	0.984938i	$0.555317\pi$
$500$	11414.6	1.02095
$501$	8335.52	0.743321
$502$	−14921.7	−1.32667
$503$	18467.0	1.63698	0.818491	−	0.574519i	$-0.194811\pi$
$503$	18467.0	1.63698	0.818491	+	0.574519i	$0.194811\pi$
$504$	122.371	0.0108152
$505$	−11656.2	−1.02712
$506$	−8722.14	−0.766297
$507$	11564.3	1.01299
$508$	464.834	0.0405978
$509$	−2185.83	−0.190344	−0.0951722	−	0.995461i	$-0.530340\pi$
$509$	−2185.83	−0.190344	−0.0951722	+	0.995461i	$0.530340\pi$
$510$	17151.0	1.48913
$511$	−28757.3	−2.48953
$512$	−16189.8	−1.39745
$513$	820.567	0.0706217
$514$	1712.48	0.146954
$515$	−10507.6	−0.899066
$516$	0	0
$517$	12176.4	1.03582
$518$	−31905.9	−2.70631
$519$	−2543.82	−0.215147
$520$	94.0571	0.00793207
$521$	−4477.45	−0.376508	−0.188254	−	0.982120i	$-0.560283\pi$
$521$	−4477.45	−0.376508	−0.188254	+	0.982120i	$0.560283\pi$
$522$	−4230.25	−0.354699
$523$	6309.76	0.527546	0.263773	−	0.964585i	$-0.415033\pi$
$523$	6309.76	0.527546	0.263773	+	0.964585i	$0.415033\pi$
$524$	12855.1	1.07172
$525$	9733.14	0.809122
$526$	12934.1	1.07216
$527$	−4012.74	−0.331684
$528$	13131.1	1.08231
$529$	−8346.12	−0.685964
$530$	−11244.9	−0.921600
$531$	1543.63	0.126154
$532$	1358.40	0.110703
$533$	−2421.44	−0.196781
$534$	−23973.7	−1.94278
$535$	4903.11	0.396224
$536$	399.598	0.0322015
$537$	21223.8	1.70554
$538$	−21088.0	−1.68990
$539$	14273.0	1.14060
$540$	−7698.02	−0.613463
$541$	−5712.26	−0.453955	−0.226977	−	0.973900i	$-0.572884\pi$
$541$	−5712.26	−0.453955	−0.226977	+	0.973900i	$0.572884\pi$
$542$	−986.495	−0.0781800
$543$	14800.4	1.16969
$544$	−25112.0	−1.97917
$545$	15390.5	1.20964
$546$	−6793.09	−0.532449
$547$	−18692.8	−1.46114	−0.730572	−	0.682836i	$-0.760746\pi$
$547$	−18692.8	−1.46114	−0.730572	+	0.682836i	$0.760746\pi$
$548$	11607.9	0.904864
$549$	3290.25	0.255782
$550$	9014.40	0.698864
$551$	1639.20	0.126737
$552$	−369.464	−0.0284881
$553$	−23532.5	−1.80959
$554$	7795.65	0.597844
$555$	12875.4	0.984736
$556$	7363.62	0.561667
$557$	4570.87	0.347709	0.173854	−	0.984771i	$-0.444378\pi$
$557$	4570.87	0.347709	0.173854	+	0.984771i	$0.444378\pi$
$558$	−673.513	−0.0510969
$559$	0	0
$560$	14093.7	1.06351
$561$	19679.8	1.48108
$562$	79.2325	0.00594701
$563$	18759.2	1.40427	0.702136	−	0.712043i	$-0.252230\pi$
$563$	18759.2	1.40427	0.702136	+	0.712043i	$0.252230\pi$
$564$	−14775.8	−1.10315
$565$	−6871.67	−0.511670
$566$	5785.65	0.429662
$567$	−22494.9	−1.66613
$568$	−696.816	−0.0514749
$569$	24853.6	1.83113	0.915567	−	0.402165i	$-0.131742\pi$
$569$	24853.6	1.83113	0.915567	+	0.402165i	$0.131742\pi$
$570$	−1115.47	−0.0819685
$571$	15792.2	1.15741	0.578707	−	0.815535i	$-0.303557\pi$
$571$	15792.2	1.15741	0.578707	+	0.815535i	$0.303557\pi$
$572$	−3091.76	−0.226002
$573$	−15404.8	−1.12312
$574$	−23304.4	−1.69461
$575$	−3948.91	−0.286402
$576$	−1998.91	−0.144597
$577$	25427.2	1.83457	0.917286	−	0.398228i	$-0.130375\pi$
$577$	25427.2	1.83457	0.917286	+	0.398228i	$0.130375\pi$
$578$	−19421.1	−1.39760
$579$	−5880.10	−0.422053
$580$	−15377.9	−1.10092
$581$	−14493.9	−1.03495
$582$	11992.0	0.854096
$583$	−12903.0	−0.916613
$584$	−1128.19	−0.0799396
$585$	368.371	0.0260347
$586$	3449.11	0.243142
$587$	7793.55	0.547997	0.273999	−	0.961730i	$-0.411654\pi$
$587$	7793.55	0.547997	0.273999	+	0.961730i	$0.411654\pi$
$588$	−17320.0	−1.21474
$589$	260.982	0.0182574
$590$	11418.7	0.796781
$591$	4378.40	0.304743
$592$	−19488.3	−1.35298
$593$	1888.61	0.130785	0.0653927	−	0.997860i	$-0.479170\pi$
$593$	1888.61	0.130785	0.0653927	+	0.997860i	$0.479170\pi$
$594$	−17974.5	−1.24159
$595$	21122.4	1.45535
$596$	26952.7	1.85239
$597$	21479.2	1.47250
$598$	2756.08	0.188469
$599$	12091.9	0.824811	0.412406	−	0.911000i	$-0.364689\pi$
$599$	12091.9	0.824811	0.412406	+	0.911000i	$0.364689\pi$
$600$	381.844	0.0259812
$601$	18724.4	1.27086	0.635429	−	0.772160i	$-0.280823\pi$
$601$	18724.4	1.27086	0.635429	+	0.772160i	$0.280823\pi$
$602$	0	0
$603$	1565.01	0.105692
$604$	11155.9	0.751535
$605$	510.062	0.0342760
$606$	33026.9	2.21390
$607$	12721.9	0.850686	0.425343	−	0.905032i	$-0.360153\pi$
$607$	12721.9	0.850686	0.425343	+	0.905032i	$0.360153\pi$
$608$	1633.24	0.108942
$609$	−38769.4	−2.57967
$610$	24339.1	1.61551
$611$	−3847.59	−0.254757
$612$	−3209.11	−0.211962
$613$	−9912.18	−0.653098	−0.326549	−	0.945180i	$-0.605886\pi$
$613$	−9912.18	−0.653098	−0.326549	+	0.945180i	$0.605886\pi$
$614$	10363.6	0.681176
$615$	9404.26	0.616612
$616$	1038.69	0.0679385
$617$	−1431.04	−0.0933733	−0.0466866	−	0.998910i	$-0.514866\pi$
$617$	−1431.04	−0.0933733	−0.0466866	+	0.998910i	$0.514866\pi$
$618$	29772.2	1.93789
$619$	12355.3	0.802266	0.401133	−	0.916020i	$-0.368616\pi$
$619$	12355.3	0.802266	0.401133	+	0.916020i	$0.368616\pi$
$620$	−2448.37	−0.158595
$621$	7874.03	0.508815
$622$	−2159.25	−0.139193
$623$	−29525.0	−1.89871
$624$	−4149.25	−0.266191
$625$	−3558.21	−0.227725
$626$	−6975.95	−0.445391
$627$	−1279.95	−0.0815249
$628$	770.545	0.0489620
$629$	−29207.5	−1.85148
$630$	3545.27	0.224201
$631$	27696.1	1.74733	0.873663	−	0.486531i	$-0.161738\pi$
$631$	27696.1	1.74733	0.873663	+	0.486531i	$0.161738\pi$
$632$	−923.213	−0.0581067
$633$	11985.0	0.752543
$634$	−15398.7	−0.964608
$635$	−470.094	−0.0293781
$636$	15657.4	0.976192
$637$	−4510.09	−0.280528
$638$	−35906.5	−2.22814
$639$	−2729.06	−0.168951
$640$	1070.31	0.0661061
$641$	−2850.67	−0.175655	−0.0878273	−	0.996136i	$-0.527992\pi$
$641$	−2850.67	−0.175655	−0.0878273	+	0.996136i	$0.527992\pi$
$642$	−13892.5	−0.854040
$643$	−4146.82	−0.254331	−0.127165	−	0.991882i	$-0.540588\pi$
$643$	−4146.82	−0.254331	−0.127165	+	0.991882i	$0.540588\pi$
$644$	13035.0	0.797593
$645$	0	0
$646$	2530.43	0.154115
$647$	5274.29	0.320485	0.160242	−	0.987078i	$-0.448772\pi$
$647$	5274.29	0.320485	0.160242	+	0.987078i	$0.448772\pi$
$648$	−882.504	−0.0535001
$649$	13102.4	0.792469
$650$	−2848.43	−0.171884
$651$	−6172.62	−0.371619
$652$	−5413.15	−0.325146
$653$	−27052.5	−1.62120	−0.810602	−	0.585598i	$-0.800860\pi$
$653$	−27052.5	−1.62120	−0.810602	+	0.585598i	$0.800860\pi$
$654$	−43607.5	−2.60732
$655$	−13000.6	−0.775537
$656$	−14234.4	−0.847196
$657$	−4418.51	−0.262378
$658$	−37029.8	−2.19388
$659$	−26393.3	−1.56015	−0.780075	−	0.625686i	$-0.784819\pi$
$659$	−26393.3	−1.56015	−0.780075	+	0.625686i	$0.784819\pi$
$660$	12007.6	0.708176
$661$	−6330.81	−0.372526	−0.186263	−	0.982500i	$-0.559638\pi$
$661$	−6330.81	−0.372526	−0.186263	+	0.982500i	$0.559638\pi$
$662$	−3695.81	−0.216981
$663$	−6218.56	−0.364267
$664$	−568.614	−0.0332327
$665$	−1373.77	−0.0801091
$666$	−4902.29	−0.285225
$667$	15729.5	0.913114
$668$	−11537.3	−0.668250
$669$	21206.5	1.22554
$670$	11576.9	0.667544
$671$	27927.8	1.60677
$672$	−38628.7	−2.21746
$673$	−1876.81	−0.107497	−0.0537486	−	0.998555i	$-0.517117\pi$
$673$	−1876.81	−0.107497	−0.0537486	+	0.998555i	$0.517117\pi$
$674$	−4883.35	−0.279080
$675$	−8137.87	−0.464040
$676$	−16006.2	−0.910685
$677$	−14082.8	−0.799475	−0.399737	−	0.916630i	$-0.630899\pi$
$677$	−14082.8	−0.799475	−0.399737	+	0.916630i	$0.630899\pi$
$678$	19470.2	1.10288
$679$	14768.8	0.834721
$680$	828.661	0.0467319
$681$	20245.4	1.13922
$682$	−5716.81	−0.320979
$683$	16468.0	0.922592	0.461296	−	0.887246i	$-0.347385\pi$
$683$	16468.0	0.922592	0.461296	+	0.887246i	$0.347385\pi$
$684$	208.715	0.0116673
$685$	−11739.3	−0.654795
$686$	−6295.01	−0.350357
$687$	16890.3	0.937998
$688$	0	0
$689$	4077.16	0.225439
$690$	−10703.9	−0.590566
$691$	28801.9	1.58564	0.792818	−	0.609458i	$-0.208613\pi$
$691$	28801.9	1.58564	0.792818	+	0.609458i	$0.208613\pi$
$692$	3520.93	0.193419
$693$	4068.01	0.222988
$694$	10460.5	0.572153
$695$	−7446.95	−0.406445
$696$	−1520.98	−0.0828340
$697$	−21333.4	−1.15934
$698$	6900.30	0.374184
$699$	−11899.4	−0.643887
$700$	−13471.7	−0.727406
$701$	−9176.55	−0.494427	−0.247214	−	0.968961i	$-0.579515\pi$
$701$	−9176.55	−0.494427	−0.247214	+	0.968961i	$0.579515\pi$
$702$	5679.69	0.305365
$703$	1899.61	0.101913
$704$	−16966.8	−0.908324
$705$	14943.0	0.798280
$706$	3785.79	0.201813
$707$	40674.5	2.16368
$708$	−15899.4	−0.843978
$709$	2072.72	0.109792	0.0548960	−	0.998492i	$-0.482517\pi$
$709$	2072.72	0.109792	0.0548960	+	0.998492i	$0.482517\pi$
$710$	−20187.7	−1.06709
$711$	−3615.73	−0.190718
$712$	−1158.30	−0.0609681
$713$	2504.34	0.131541
$714$	−59848.4	−3.13693
$715$	3126.75	0.163544
$716$	−29376.1	−1.53329
$717$	−608.029	−0.0316698
$718$	15964.9	0.829810
$719$	6681.80	0.346577	0.173289	−	0.984871i	$-0.444561\pi$
$719$	6681.80	0.346577	0.173289	+	0.984871i	$0.444561\pi$
$720$	2165.47	0.112086
$721$	36666.2	1.89393
$722$	27039.1	1.39375
$723$	−5391.76	−0.277347
$724$	−20485.3	−1.05156
$725$	−16256.5	−0.832761
$726$	−1445.21	−0.0738800
$727$	−24018.9	−1.22532	−0.612662	−	0.790345i	$-0.709901\pi$
$727$	−24018.9	−1.22532	−0.612662	+	0.790345i	$0.709901\pi$
$728$	−328.213	−0.0167093
$729$	15752.4	0.800302
$730$	−32685.2	−1.65717
$731$	0	0
$732$	−33889.7	−1.71120
$733$	−570.639	−0.0287545	−0.0143772	−	0.999897i	$-0.504577\pi$
$733$	−570.639	−0.0287545	−0.0143772	+	0.999897i	$0.504577\pi$
$734$	40323.5	2.02775
$735$	17516.0	0.879031
$736$	15672.3	0.784905
$737$	13283.9	0.663932
$738$	−3580.67	−0.178599
$739$	39621.9	1.97228	0.986140	−	0.165917i	$-0.0530584\pi$
$739$	39621.9	1.97228	0.986140	+	0.165917i	$0.0530584\pi$
$740$	−17820.9	−0.885283
$741$	404.446	0.0200508
$742$	39239.2	1.94140
$743$	−4473.03	−0.220861	−0.110430	−	0.993884i	$-0.535223\pi$
$743$	−4473.03	−0.220861	−0.110430	+	0.993884i	$0.535223\pi$
$744$	−242.160	−0.0119328
$745$	−27257.7	−1.34046
$746$	−37636.0	−1.84712
$747$	−2226.96	−0.109076
$748$	−27239.0	−1.33150
$749$	−17109.4	−0.834667
$750$	32708.2	1.59245
$751$	−5045.05	−0.245135	−0.122568	−	0.992460i	$-0.539113\pi$
$751$	−5045.05	−0.245135	−0.122568	+	0.992460i	$0.539113\pi$
$752$	−22618.0	−1.09680
$753$	−21012.1	−1.01690
$754$	11346.0	0.548005
$755$	−11282.2	−0.543841
$756$	26862.3	1.29229
$757$	−36002.5	−1.72858	−0.864288	−	0.502997i	$-0.832231\pi$
$757$	−36002.5	−1.72858	−0.864288	+	0.502997i	$0.832231\pi$
$758$	30601.6	1.46636
$759$	−12282.2	−0.587370
$760$	−53.8949	−0.00257233
$761$	−2731.51	−0.130114	−0.0650572	−	0.997882i	$-0.520723\pi$
$761$	−2731.51	−0.130114	−0.0650572	+	0.997882i	$0.520723\pi$
$762$	1331.97	0.0633230
$763$	−53705.2	−2.54818
$764$	21322.0	1.00969
$765$	3245.42	0.153384
$766$	9036.16	0.426227
$767$	−4140.17	−0.194906
$768$	−24340.2	−1.14362
$769$	29177.5	1.36823	0.684113	−	0.729376i	$-0.260189\pi$
$769$	29177.5	1.36823	0.684113	+	0.729376i	$0.260189\pi$
$770$	30092.4	1.40838
$771$	2411.44	0.112641
$772$	8138.70	0.379428
$773$	−19267.3	−0.896505	−0.448252	−	0.893907i	$-0.647953\pi$
$773$	−19267.3	−0.896505	−0.448252	+	0.893907i	$0.647953\pi$
$774$	0	0
$775$	−2588.26	−0.119965
$776$	579.401	0.0268032
$777$	−44928.6	−2.07440
$778$	−48039.2	−2.21374
$779$	1387.49	0.0638151
$780$	−3794.24	−0.174174
$781$	−23164.4	−1.06131
$782$	24281.6	1.11037
$783$	32415.1	1.47946
$784$	−26512.5	−1.20775
$785$	−779.265	−0.0354308
$786$	36836.1	1.67163
$787$	−3926.89	−0.177863	−0.0889317	−	0.996038i	$-0.528345\pi$
$787$	−3926.89	−0.177863	−0.0889317	+	0.996038i	$0.528345\pi$
$788$	−6060.19	−0.273966
$789$	18213.3	0.821814
$790$	−26746.8	−1.20457
$791$	23978.8	1.07786
$792$	159.593	0.00716023
$793$	−8824.80	−0.395180
$794$	44357.0	1.98258
$795$	−15834.6	−0.706411
$796$	−29729.5	−1.32379
$797$	−15429.5	−0.685746	−0.342873	−	0.939382i	$-0.611400\pi$
$797$	−15429.5	−0.685746	−0.342873	+	0.939382i	$0.611400\pi$
$798$	3892.45	0.172671
$799$	−33898.0	−1.50091
$800$	−16197.5	−0.715835
$801$	−4536.46	−0.200110
$802$	−54429.7	−2.39648
$803$	−37504.5	−1.64820
$804$	−16119.7	−0.707087
$805$	−13182.5	−0.577169
$806$	1806.43	0.0789440
$807$	−29695.3	−1.29532
$808$	1595.72	0.0694766
$809$	−3814.09	−0.165756	−0.0828778	−	0.996560i	$-0.526411\pi$
$809$	−3814.09	−0.165756	−0.0828778	+	0.996560i	$0.526411\pi$
$810$	−25567.4	−1.10907
$811$	−22218.1	−0.962000	−0.481000	−	0.876721i	$-0.659726\pi$
$811$	−22218.1	−0.962000	−0.481000	+	0.876721i	$0.659726\pi$
$812$	53661.2	2.31913
$813$	−1389.14	−0.0599253
$814$	−41610.9	−1.79172
$815$	5474.40	0.235288
$816$	−36555.7	−1.56827
$817$	0	0
$818$	−20718.4	−0.885576
$819$	−1285.43	−0.0548434
$820$	−13016.5	−0.554338
$821$	−12983.5	−0.551921	−0.275961	−	0.961169i	$-0.588996\pi$
$821$	−12983.5	−0.551921	−0.275961	+	0.961169i	$0.588996\pi$
$822$	33262.1	1.41137
$823$	26269.5	1.11263	0.556316	−	0.830971i	$-0.312214\pi$
$823$	26269.5	1.11263	0.556316	+	0.830971i	$0.312214\pi$
$824$	1438.47	0.0608147
$825$	12693.7	0.535682
$826$	−39845.7	−1.67846
$827$	−16392.4	−0.689262	−0.344631	−	0.938738i	$-0.611996\pi$
$827$	−16392.4	−0.689262	−0.344631	+	0.938738i	$0.611996\pi$
$828$	2002.80	0.0840605
$829$	−19801.1	−0.829577	−0.414788	−	0.909918i	$-0.636144\pi$
$829$	−19801.1	−0.829577	−0.414788	+	0.909918i	$0.636144\pi$
$830$	−16473.5	−0.688921
$831$	10977.5	0.458250
$832$	5361.28	0.223400
$833$	−39734.7	−1.65273
$834$	21100.2	0.876069
$835$	11667.8	0.483572
$836$	1771.59	0.0732914
$837$	5160.92	0.213127
$838$	64174.4	2.64543
$839$	20936.1	0.861493	0.430747	−	0.902473i	$-0.358250\pi$
$839$	20936.1	0.861493	0.430747	+	0.902473i	$0.358250\pi$
$840$	1274.69	0.0523585
$841$	40364.6	1.65503
$842$	2851.07	0.116692
$843$	111.572	0.00455841
$844$	−16588.5	−0.676541
$845$	16187.3	0.659008
$846$	−5689.56	−0.231219
$847$	−1779.86	−0.0722041
$848$	23967.5	0.970575
$849$	8147.11	0.329338
$850$	−25095.2	−1.01266
$851$	18228.3	0.734265
$852$	28109.4	1.13030
$853$	15928.2	0.639358	0.319679	−	0.947526i	$-0.396425\pi$
$853$	15928.2	0.639358	0.319679	+	0.947526i	$0.396425\pi$
$854$	−84931.4	−3.40315
$855$	−211.077	−0.00844292
$856$	−671.226	−0.0268014
$857$	8854.62	0.352938	0.176469	−	0.984306i	$-0.443532\pi$
$857$	8854.62	0.352938	0.176469	+	0.984306i	$0.443532\pi$
$858$	−8859.36	−0.352510
$859$	24147.0	0.959120	0.479560	−	0.877509i	$-0.340796\pi$
$859$	24147.0	0.959120	0.479560	+	0.877509i	$0.340796\pi$
$860$	0	0
$861$	−32816.2	−1.29892
$862$	−15098.3	−0.596579
$863$	−9043.80	−0.356726	−0.178363	−	0.983965i	$-0.557080\pi$
$863$	−9043.80	−0.356726	−0.178363	+	0.983965i	$0.557080\pi$
$864$	32297.4	1.27174
$865$	−3560.77	−0.139965
$866$	−14444.6	−0.566798
$867$	−27347.9	−1.07126
$868$	8543.59	0.334088
$869$	−30690.5	−1.19805
$870$	−44064.8	−1.71717
$871$	−4197.52	−0.163292
$872$	−2106.93	−0.0818229
$873$	2269.20	0.0879736
$874$	−1579.24	−0.0611196
$875$	40282.1	1.55632
$876$	45510.9	1.75533
$877$	−15398.1	−0.592880	−0.296440	−	0.955051i	$-0.595800\pi$
$877$	−15398.1	−0.592880	−0.296440	+	0.955051i	$0.595800\pi$
$878$	−65952.8	−2.53508
$879$	4856.89	0.186370
$880$	18380.6	0.704102
$881$	19785.4	0.756625	0.378313	−	0.925678i	$-0.376504\pi$
$881$	19785.4	0.756625	0.378313	+	0.925678i	$0.376504\pi$
$882$	−6669.23	−0.254608
$883$	−42827.1	−1.63222	−0.816108	−	0.577899i	$-0.803873\pi$
$883$	−42827.1	−1.63222	−0.816108	+	0.577899i	$0.803873\pi$
$884$	8607.17	0.327478
$885$	16079.3	0.610736
$886$	−29116.6	−1.10405
$887$	−7435.69	−0.281473	−0.140736	−	0.990047i	$-0.544947\pi$
$887$	−7435.69	−0.281473	−0.140736	+	0.990047i	$0.544947\pi$
$888$	−1762.61	−0.0666096
$889$	1640.40	0.0618865
$890$	−33557.7	−1.26388
$891$	−29337.2	−1.10307
$892$	−29352.1	−1.10177
$893$	2204.67	0.0826165
$894$	77232.2	2.88930
$895$	29708.6	1.10955
$896$	−3734.87	−0.139256
$897$	3880.99	0.144462
$898$	−36849.5	−1.36936
$899$	10309.7	0.382476
$900$	−2069.91	−0.0766633
$901$	35920.5	1.32818
$902$	−30392.9	−1.12192
$903$	0	0
$904$	940.718	0.0346104
$905$	20717.1	0.760952
$906$	31966.9	1.17222
$907$	24000.9	0.878652	0.439326	−	0.898328i	$-0.355217\pi$
$907$	24000.9	0.878652	0.439326	+	0.898328i	$0.355217\pi$
$908$	−28021.9	−1.02416
$909$	6249.57	0.228036
$910$	−9508.78	−0.346388
$911$	48941.7	1.77992	0.889962	−	0.456034i	$-0.150730\pi$
$911$	48941.7	1.77992	0.889962	+	0.456034i	$0.150730\pi$
$912$	2377.53	0.0863244
$913$	−18902.5	−0.685193
$914$	−70800.1	−2.56221
$915$	34273.3	1.23829
$916$	−23378.0	−0.843266
$917$	45365.8	1.63371
$918$	50039.2	1.79906
$919$	−39649.2	−1.42318	−0.711591	−	0.702593i	$-0.752025\pi$
$919$	−39649.2	−1.42318	−0.711591	+	0.702593i	$0.752025\pi$
$920$	−517.166	−0.0185331
$921$	14593.6	0.522124
$922$	−28003.2	−1.00026
$923$	7319.62	0.261027
$924$	−41900.7	−1.49181
$925$	−18839.1	−0.669651
$926$	37539.7	1.33222
$927$	5633.70	0.199606
$928$	64518.5	2.28224
$929$	42712.0	1.50843	0.754216	−	0.656626i	$-0.228017\pi$
$929$	42712.0	1.50843	0.754216	+	0.656626i	$0.228017\pi$
$930$	−7015.72	−0.247370
$931$	2584.29	0.0909738
$932$	16470.1	0.578858
$933$	−3040.57	−0.106692
$934$	−33360.8	−1.16873
$935$	27547.3	0.963522
$936$	−50.4293	−0.00176104
$937$	−30586.9	−1.06642	−0.533208	−	0.845984i	$-0.679014\pi$
$937$	−30586.9	−1.06642	−0.533208	+	0.845984i	$0.679014\pi$
$938$	−40397.7	−1.40622
$939$	−9823.24	−0.341394
$940$	−20682.8	−0.717658
$941$	30224.1	1.04705	0.523527	−	0.852009i	$-0.324616\pi$
$941$	30224.1	1.04705	0.523527	+	0.852009i	$0.324616\pi$
$942$	2207.98	0.0763691
$943$	13314.1	0.459775
$944$	−24337.9	−0.839123
$945$	−27166.3	−0.935153
$946$	0	0
$947$	14870.2	0.510259	0.255129	−	0.966907i	$-0.417882\pi$
$947$	14870.2	0.510259	0.255129	+	0.966907i	$0.417882\pi$
$948$	37242.2	1.27592
$949$	11850.9	0.405371
$950$	1632.15	0.0557411
$951$	−21683.8	−0.739376
$952$	−2891.62	−0.0984432
$953$	−20245.1	−0.688145	−0.344073	−	0.938943i	$-0.611807\pi$
$953$	−20245.1	−0.688145	−0.344073	+	0.938943i	$0.611807\pi$
$954$	6029.04	0.204609
$955$	−21563.3	−0.730650
$956$	841.579	0.0284714
$957$	−50562.1	−1.70788
$958$	−41032.9	−1.38383
$959$	40964.3	1.37936
$960$	−20821.8	−0.700022
$961$	−28149.6	−0.944902
$962$	13148.5	0.440669
$963$	−2628.84	−0.0879678
$964$	7462.78	0.249336
$965$	−8230.81	−0.274569
$966$	37351.3	1.24406
$967$	−23602.8	−0.784917	−0.392459	−	0.919770i	$-0.628375\pi$
$967$	−23602.8	−0.784917	−0.392459	+	0.919770i	$0.628375\pi$
$968$	−69.8265	−0.00231850
$969$	3563.24	0.118130
$970$	16786.1	0.555637
$971$	26609.1	0.879429	0.439714	−	0.898138i	$-0.355080\pi$
$971$	26609.1	0.879429	0.439714	+	0.898138i	$0.355080\pi$
$972$	9013.17	0.297425
$973$	25986.2	0.856196
$974$	−46129.2	−1.51753
$975$	−4011.04	−0.131750
$976$	−51876.5	−1.70136
$977$	−30637.4	−1.00325	−0.501625	−	0.865085i	$-0.667264\pi$
$977$	−30637.4	−1.00325	−0.501625	+	0.865085i	$0.667264\pi$
$978$	−15511.2	−0.507151
$979$	−38505.7	−1.25705
$980$	−24244.1	−0.790254
$981$	−8251.71	−0.268559
$982$	7509.56	0.244032
$983$	39147.1	1.27019	0.635097	−	0.772433i	$-0.280960\pi$
$983$	39147.1	1.27019	0.635097	+	0.772433i	$0.280960\pi$
$984$	−1287.42	−0.0417089
$985$	6128.77	0.198253
$986$	99960.2	3.22858
$987$	−52143.8	−1.68162
$988$	−559.797	−0.0180258
$989$	0	0
$990$	4623.64	0.148433
$991$	14977.7	0.480104	0.240052	−	0.970760i	$-0.422835\pi$
$991$	14977.7	0.480104	0.240052	+	0.970760i	$0.422835\pi$
$992$	10272.2	0.328773
$993$	−5204.28	−0.166317
$994$	70445.3	2.24788
$995$	30066.0	0.957945
$996$	22937.8	0.729730
$997$	28720.0	0.912307	0.456153	−	0.889901i	$-0.349227\pi$
$997$	28720.0	0.912307	0.456153	+	0.889901i	$0.349227\pi$
$998$	15288.6	0.484922
$999$	37564.8	1.18969

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.l.1.10		60
43.15	even	21		43.4.g.a.10.9	✓	120
43.23	even	21		43.4.g.a.13.9	yes	120
43.42	odd	2		1849.4.a.k.1.51		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.g.a.10.9	✓	120	43.15	even	21
43.4.g.a.13.9	yes	120	43.23	even	21
1849.4.a.k.1.51		60	43.42	odd	2
1849.4.a.l.1.10		60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-3.96613 q^{2} -5.58493 q^{3} +7.73016 q^{4} -7.81764 q^{5} +22.1506 q^{6} +27.2797 q^{7} +1.07022 q^{8} +4.19148 q^{9} +O(q^{10})\)	\(q-3.96613 q^{2} -5.58493 q^{3} +7.73016 q^{4} -7.81764 q^{5} +22.1506 q^{6} +27.2797 q^{7} +1.07022 q^{8} +4.19148 q^{9} +31.0057 q^{10} +35.5775 q^{11} -43.1724 q^{12} -11.2420 q^{13} -108.195 q^{14} +43.6610 q^{15} -66.0859 q^{16} -99.0441 q^{17} -16.6239 q^{18} +6.44168 q^{19} -60.4316 q^{20} -152.355 q^{21} -141.105 q^{22} +61.8133 q^{23} -5.97710 q^{24} -63.8845 q^{25} +44.5871 q^{26} +127.384 q^{27} +210.876 q^{28} +254.467 q^{29} -173.165 q^{30} +40.5146 q^{31} +253.543 q^{32} -198.698 q^{33} +392.821 q^{34} -213.263 q^{35} +32.4008 q^{36} +294.894 q^{37} -25.5485 q^{38} +62.7857 q^{39} -8.36659 q^{40} +215.393 q^{41} +604.260 q^{42} +275.019 q^{44} -32.7675 q^{45} -245.159 q^{46} +342.251 q^{47} +369.085 q^{48} +401.182 q^{49} +253.374 q^{50} +553.155 q^{51} -86.9024 q^{52} -362.672 q^{53} -505.221 q^{54} -278.132 q^{55} +29.1953 q^{56} -35.9763 q^{57} -1009.25 q^{58} +368.277 q^{59} +337.506 q^{60} +784.986 q^{61} -160.686 q^{62} +114.342 q^{63} -476.898 q^{64} +87.8858 q^{65} +788.060 q^{66} +373.379 q^{67} -765.627 q^{68} -345.223 q^{69} +845.828 q^{70} -651.097 q^{71} +4.48580 q^{72} -1054.17 q^{73} -1169.59 q^{74} +356.791 q^{75} +49.7952 q^{76} +970.542 q^{77} -249.016 q^{78} -862.639 q^{79} +516.636 q^{80} -824.601 q^{81} -854.275 q^{82} -531.306 q^{83} -1177.73 q^{84} +774.291 q^{85} -1421.18 q^{87} +38.0757 q^{88} -1082.31 q^{89} +129.960 q^{90} -306.678 q^{91} +477.827 q^{92} -226.272 q^{93} -1357.41 q^{94} -50.3587 q^{95} -1416.02 q^{96} +541.385 q^{97} -1591.14 q^{98} +149.122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9}+O(q^{10}) \) 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9	\( 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} + 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} + 625 q^{18} + 610 q^{19} + 345 q^{20} + 611 q^{21} + 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} + 1071 q^{26} + 1609 q^{27} + 46 q^{28} + 773 q^{29} + 375 q^{30} - 97 q^{31} + 1967 q^{32} + 500 q^{33} + 217 q^{34} + 247 q^{35} + 175 q^{36} + 228 q^{37} + 1253 q^{38} + 1493 q^{39} + 2220 q^{40} - 951 q^{41} + 2643 q^{42} - 1378 q^{44} + 1086 q^{45} - 565 q^{46} - 2 q^{47} + 2303 q^{48} + 1264 q^{49} + 3273 q^{50} + 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} + 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} + 2999 q^{61} + 5569 q^{62} + 2377 q^{63} + 2082 q^{64} + 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} + 1817 q^{69} + 2738 q^{70} + 8003 q^{71} + 1412 q^{72} - 1011 q^{73} - 1413 q^{74} + 7457 q^{75} + 5516 q^{76} + 4052 q^{77} + 1091 q^{78} - 4422 q^{79} + 1610 q^{80} + 2108 q^{81} + 4676 q^{82} - 297 q^{83} - 54 q^{84} + 4333 q^{85} + 1377 q^{87} + 3652 q^{88} + 2480 q^{89} - 1414 q^{90} + 4551 q^{91} - 3286 q^{92} + 4 q^{93} + 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} + 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 + 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 + 625 * q^18 + 610 * q^19 + 345 * q^20 + 611 * q^21 + 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 + 1071 * q^26 + 1609 * q^27 + 46 * q^28 + 773 * q^29 + 375 * q^30 - 97 * q^31 + 1967 * q^32 + 500 * q^33 + 217 * q^34 + 247 * q^35 + 175 * q^36 + 228 * q^37 + 1253 * q^38 + 1493 * q^39 + 2220 * q^40 - 951 * q^41 + 2643 * q^42 - 1378 * q^44 + 1086 * q^45 - 565 * q^46 - 2 * q^47 + 2303 * q^48 + 1264 * q^49 + 3273 * q^50 + 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 + 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 + 2999 * q^61 + 5569 * q^62 + 2377 * q^63 + 2082 * q^64 + 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 + 1817 * q^69 + 2738 * q^70 + 8003 * q^71 + 1412 * q^72 - 1011 * q^73 - 1413 * q^74 + 7457 * q^75 + 5516 * q^76 + 4052 * q^77 + 1091 * q^78 - 4422 * q^79 + 1610 * q^80 + 2108 * q^81 + 4676 * q^82 - 297 * q^83 - 54 * q^84 + 4333 * q^85 + 1377 * q^87 + 3652 * q^88 + 2480 * q^89 - 1414 * q^90 + 4551 * q^91 - 3286 * q^92 + 4 * q^93 + 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 + 753 * q^98 + 5072 * q^99

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