LMFDB - Embedded newform 1859.4.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.732051 q^{2} +5.92820 q^{3} -7.46410 q^{4} +12.8564 q^{5} +4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} +O(q^{10})$	\(q+0.732051 q^{2} +5.92820 q^{3} -7.46410 q^{4} +12.8564 q^{5} +4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} +9.41154 q^{10} +11.0000 q^{11} -44.2487 q^{12} -12.3923 q^{14} +76.2154 q^{15} +51.4256 q^{16} -82.7846 q^{17} +5.96152 q^{18} +67.9230 q^{19} -95.9615 q^{20} -100.354 q^{21} +8.05256 q^{22} +13.3538 q^{23} -67.1103 q^{24} +40.2872 q^{25} -111.785 q^{27} +126.354 q^{28} +168.995 q^{29} +55.7935 q^{30} +65.4974 q^{31} +128.210 q^{32} +65.2102 q^{33} -60.6025 q^{34} -217.636 q^{35} -60.7846 q^{36} -40.8564 q^{37} +49.7231 q^{38} -145.541 q^{40} -274.928 q^{41} -73.4641 q^{42} -2.28719 q^{43} -82.1051 q^{44} +104.697 q^{45} +9.77568 q^{46} -71.8461 q^{47} +304.862 q^{48} -56.4359 q^{49} +29.4923 q^{50} -490.764 q^{51} -149.005 q^{53} -81.8320 q^{54} +141.420 q^{55} +191.636 q^{56} +402.662 q^{57} +123.713 q^{58} -545.631 q^{59} -568.879 q^{60} +101.303 q^{61} +47.9474 q^{62} -137.856 q^{63} -317.549 q^{64} +47.7372 q^{66} -411.641 q^{67} +617.913 q^{68} +79.1642 q^{69} -159.321 q^{70} +470.636 q^{71} -92.1896 q^{72} -610.600 q^{73} -29.9090 q^{74} +238.831 q^{75} -506.985 q^{76} -186.210 q^{77} -978.225 q^{79} +661.149 q^{80} -882.559 q^{81} -201.261 q^{82} -26.1539 q^{83} +749.051 q^{84} -1064.31 q^{85} -1.67434 q^{86} +1001.84 q^{87} -124.526 q^{88} +352.887 q^{89} +76.6438 q^{90} -99.6743 q^{92} +388.282 q^{93} -52.5950 q^{94} +873.246 q^{95} +760.056 q^{96} -847.585 q^{97} -41.3140 q^{98} +89.5795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} + 44 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 26 * q^6 - 20 * q^7 + 12 * q^8 + 44 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} + 44 q^{9} + 50 q^{10} + 22 q^{11} - 40 q^{12} - 4 q^{14} + 194 q^{15} - 8 q^{16} - 124 q^{17} - 92 q^{18} - 72 q^{19} - 88 q^{20} - 76 q^{21} - 22 q^{22} - 98 q^{23} - 252 q^{24} + 136 q^{25} - 182 q^{27} + 128 q^{28} + 144 q^{29} - 266 q^{30} + 34 q^{31} + 104 q^{32} - 22 q^{33} + 52 q^{34} - 172 q^{35} - 80 q^{36} - 54 q^{37} + 432 q^{38} - 492 q^{40} - 536 q^{41} - 140 q^{42} - 60 q^{43} - 88 q^{44} - 428 q^{45} + 314 q^{46} + 272 q^{47} + 776 q^{48} - 390 q^{49} - 232 q^{50} - 164 q^{51} - 492 q^{53} + 110 q^{54} - 22 q^{55} + 120 q^{56} + 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} + 840 q^{61} + 134 q^{62} - 248 q^{63} + 224 q^{64} + 286 q^{66} - 754 q^{67} + 640 q^{68} + 962 q^{69} - 284 q^{70} + 678 q^{71} + 744 q^{72} + 400 q^{73} + 6 q^{74} - 520 q^{75} - 432 q^{76} - 220 q^{77} + 316 q^{79} + 1544 q^{80} - 1294 q^{81} + 512 q^{82} - 468 q^{83} + 736 q^{84} - 452 q^{85} + 156 q^{86} + 1200 q^{87} + 132 q^{88} + 1842 q^{89} + 1532 q^{90} - 40 q^{92} + 638 q^{93} - 992 q^{94} + 2952 q^{95} + 952 q^{96} - 2194 q^{97} + 870 q^{98} + 484 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 26 * q^6 - 20 * q^7 + 12 * q^8 + 44 * q^9 + 50 * q^10 + 22 * q^11 - 40 * q^12 - 4 * q^14 + 194 * q^15 - 8 * q^16 - 124 * q^17 - 92 * q^18 - 72 * q^19 - 88 * q^20 - 76 * q^21 - 22 * q^22 - 98 * q^23 - 252 * q^24 + 136 * q^25 - 182 * q^27 + 128 * q^28 + 144 * q^29 - 266 * q^30 + 34 * q^31 + 104 * q^32 - 22 * q^33 + 52 * q^34 - 172 * q^35 - 80 * q^36 - 54 * q^37 + 432 * q^38 - 492 * q^40 - 536 * q^41 - 140 * q^42 - 60 * q^43 - 88 * q^44 - 428 * q^45 + 314 * q^46 + 272 * q^47 + 776 * q^48 - 390 * q^49 - 232 * q^50 - 164 * q^51 - 492 * q^53 + 110 * q^54 - 22 * q^55 + 120 * q^56 + 1512 * q^57 + 192 * q^58 - 634 * q^59 - 632 * q^60 + 840 * q^61 + 134 * q^62 - 248 * q^63 + 224 * q^64 + 286 * q^66 - 754 * q^67 + 640 * q^68 + 962 * q^69 - 284 * q^70 + 678 * q^71 + 744 * q^72 + 400 * q^73 + 6 * q^74 - 520 * q^75 - 432 * q^76 - 220 * q^77 + 316 * q^79 + 1544 * q^80 - 1294 * q^81 + 512 * q^82 - 468 * q^83 + 736 * q^84 - 452 * q^85 + 156 * q^86 + 1200 * q^87 + 132 * q^88 + 1842 * q^89 + 1532 * q^90 - 40 * q^92 + 638 * q^93 - 992 * q^94 + 2952 * q^95 + 952 * q^96 - 2194 * q^97 + 870 * q^98 + 484 * 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 $

$2$	0.732051	0.258819	0.129410	−	0.991591i	$-0.458692\pi$
$2$	0.732051	0.258819	0.129410	+	0.991591i	$0.458692\pi$
$3$	5.92820	1.14088	0.570442	−	0.821338i	$-0.306772\pi$
$3$	5.92820	1.14088	0.570442	+	0.821338i	$0.306772\pi$
$4$	−7.46410	−0.933013
$5$	12.8564	1.14991	0.574956	−	0.818184i	$-0.305019\pi$
$5$	12.8564	1.14991	0.574956	+	0.818184i	$0.305019\pi$
$6$	4.33975	0.295282
$7$	−16.9282	−0.914037	−0.457019	−	0.889457i	$-0.651083\pi$
$7$	−16.9282	−0.914037	−0.457019	+	0.889457i	$0.651083\pi$
$8$	−11.3205	−0.500301
$9$	8.14359	0.301615
$10$	9.41154	0.297619
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−44.2487	−1.06446
$13$	0	0
$13$	0	0
$14$	−12.3923	−0.236570
$15$	76.2154	1.31192
$16$	51.4256	0.803525
$17$	−82.7846	−1.18107	−0.590536	−	0.807011i	$-0.701084\pi$
$17$	−82.7846	−1.18107	−0.590536	+	0.807011i	$0.701084\pi$
$18$	5.96152	0.0780636
$19$	67.9230	0.820138	0.410069	−	0.912055i	$-0.365505\pi$
$19$	67.9230	0.820138	0.410069	+	0.912055i	$0.365505\pi$
$20$	−95.9615	−1.07288
$21$	−100.354	−1.04281
$22$	8.05256	0.0780369
$23$	13.3538	0.121064	0.0605319	−	0.998166i	$-0.480720\pi$
$23$	13.3538	0.121064	0.0605319	+	0.998166i	$0.480720\pi$
$24$	−67.1103	−0.570784
$25$	40.2872	0.322297
$26$	0	0
$27$	−111.785	−0.796776
$28$	126.354	0.852808
$29$	168.995	1.08212	0.541061	−	0.840983i	$-0.318023\pi$
$29$	168.995	1.08212	0.541061	+	0.840983i	$0.318023\pi$
$30$	55.7935	0.339549
$31$	65.4974	0.379474	0.189737	−	0.981835i	$-0.439237\pi$
$31$	65.4974	0.379474	0.189737	+	0.981835i	$0.439237\pi$
$32$	128.210	0.708268
$33$	65.2102	0.343989
$34$	−60.6025	−0.305684
$35$	−217.636	−1.05106
$36$	−60.7846	−0.281410
$37$	−40.8564	−0.181534	−0.0907669	−	0.995872i	$-0.528932\pi$
$37$	−40.8564	−0.181534	−0.0907669	+	0.995872i	$0.528932\pi$
$38$	49.7231	0.212267
$39$	0	0
$40$	−145.541	−0.575302
$41$	−274.928	−1.04723	−0.523617	−	0.851954i	$-0.675418\pi$
$41$	−274.928	−1.04723	−0.523617	+	0.851954i	$0.675418\pi$
$42$	−73.4641	−0.269899
$43$	−2.28719	−0.00811146	−0.00405573	−	0.999992i	$-0.501291\pi$
$43$	−2.28719	−0.00811146	−0.00405573	+	0.999992i	$0.501291\pi$
$44$	−82.1051	−0.281314
$45$	104.697	0.346830
$46$	9.77568	0.0313336
$47$	−71.8461	−0.222975	−0.111488	−	0.993766i	$-0.535562\pi$
$47$	−71.8461	−0.222975	−0.111488	+	0.993766i	$0.535562\pi$
$48$	304.862	0.916729
$49$	−56.4359	−0.164536
$50$	29.4923	0.0834167
$51$	−490.764	−1.34746
$52$	0	0
$53$	−149.005	−0.386178	−0.193089	−	0.981181i	$-0.561851\pi$
$53$	−149.005	−0.386178	−0.193089	+	0.981181i	$0.561851\pi$
$54$	−81.8320	−0.206221
$55$	141.420	0.346711
$56$	191.636	0.457293
$57$	402.662	0.935681
$58$	123.713	0.280074
$59$	−545.631	−1.20398	−0.601992	−	0.798502i	$-0.705626\pi$
$59$	−545.631	−1.20398	−0.601992	+	0.798502i	$0.705626\pi$
$60$	−568.879	−1.22403
$61$	101.303	0.212631	0.106315	−	0.994332i	$-0.466095\pi$
$61$	101.303	0.212631	0.106315	+	0.994332i	$0.466095\pi$
$62$	47.9474	0.0982150
$63$	−137.856	−0.275687
$64$	−317.549	−0.620212
$65$	0	0
$66$	47.7372	0.0890310
$67$	−411.641	−0.750596	−0.375298	−	0.926904i	$-0.622460\pi$
$67$	−411.641	−0.750596	−0.375298	+	0.926904i	$0.622460\pi$
$68$	617.913	1.10195
$69$	79.1642	0.138120
$70$	−159.321	−0.272035
$71$	470.636	0.786679	0.393339	−	0.919393i	$-0.371320\pi$
$71$	470.636	0.786679	0.393339	+	0.919393i	$0.371320\pi$
$72$	−92.1896	−0.150898
$73$	−610.600	−0.978977	−0.489488	−	0.872010i	$-0.662816\pi$
$73$	−610.600	−0.978977	−0.489488	+	0.872010i	$0.662816\pi$
$74$	−29.9090	−0.0469844
$75$	238.831	0.367704
$76$	−506.985	−0.765199
$77$	−186.210	−0.275593
$78$	0	0
$79$	−978.225	−1.39315	−0.696576	−	0.717483i	$-0.745294\pi$
$79$	−978.225	−1.39315	−0.696576	+	0.717483i	$0.745294\pi$
$80$	661.149	0.923983
$81$	−882.559	−1.21064
$82$	−201.261	−0.271044
$83$	−26.1539	−0.0345875	−0.0172938	−	0.999850i	$-0.505505\pi$
$83$	−26.1539	−0.0345875	−0.0172938	+	0.999850i	$0.505505\pi$
$84$	749.051	0.972955
$85$	−1064.31	−1.35813
$86$	−1.67434	−0.00209940
$87$	1001.84	1.23458
$88$	−124.526	−0.150846
$89$	352.887	0.420292	0.210146	−	0.977670i	$-0.432606\pi$
$89$	352.887	0.420292	0.210146	+	0.977670i	$0.432606\pi$
$90$	76.6438	0.0897663
$91$	0	0
$92$	−99.6743	−0.112954
$93$	388.282	0.432935
$94$	−52.5950	−0.0577102
$95$	873.246	0.943086
$96$	760.056	0.808051
$97$	−847.585	−0.887208	−0.443604	−	0.896223i	$-0.646300\pi$
$97$	−847.585	−0.887208	−0.443604	+	0.896223i	$0.646300\pi$
$98$	−41.3140	−0.0425851
$99$	89.5795	0.0909402
$100$	−300.708	−0.300708
$101$	1293.46	1.27430	0.637150	−	0.770740i	$-0.280113\pi$
$101$	1293.46	1.27430	0.637150	+	0.770740i	$0.280113\pi$
$102$	−359.264	−0.348750
$103$	−1725.24	−1.65042	−0.825209	−	0.564828i	$-0.808943\pi$
$103$	−1725.24	−1.65042	−0.825209	+	0.564828i	$0.808943\pi$
$104$	0	0
$105$	−1290.19	−1.19914
$106$	−109.079	−0.0999502
$107$	−484.179	−0.437452	−0.218726	−	0.975786i	$-0.570190\pi$
$107$	−484.179	−0.437452	−0.218726	+	0.975786i	$0.570190\pi$
$108$	834.372	0.743402
$109$	64.2563	0.0564645	0.0282323	−	0.999601i	$-0.491012\pi$
$109$	64.2563	0.0564645	0.0282323	+	0.999601i	$0.491012\pi$
$110$	103.527	0.0897355
$111$	−242.205	−0.207109
$112$	−870.543	−0.734452
$113$	−2005.08	−1.66922	−0.834612	−	0.550839i	$-0.814308\pi$
$113$	−2005.08	−1.66922	−0.834612	+	0.550839i	$0.814308\pi$
$114$	294.769	0.242172
$115$	171.682	0.139213
$116$	−1261.39	−1.00963
$117$	0	0
$118$	−399.429	−0.311614
$119$	1401.39	1.07954
$120$	−862.797	−0.656352
$121$	121.000	0.0909091
$122$	74.1587	0.0550329
$123$	−1629.83	−1.19477
$124$	−488.879	−0.354054
$125$	−1089.10	−0.779298
$126$	−100.918	−0.0713530
$127$	109.605	0.0765816	0.0382908	−	0.999267i	$-0.487809\pi$
$127$	109.605	0.0765816	0.0382908	+	0.999267i	$0.487809\pi$
$128$	−1258.14	−0.868791
$129$	−13.5589	−0.00925423
$130$	0	0
$131$	1156.71	0.771469	0.385734	−	0.922610i	$-0.373948\pi$
$131$	1156.71	0.771469	0.385734	+	0.922610i	$0.373948\pi$
$132$	−486.736	−0.320946
$133$	−1149.82	−0.749636
$134$	−301.342	−0.194269
$135$	−1437.15	−0.916223
$136$	937.164	0.590891
$137$	−198.323	−0.123678	−0.0618391	−	0.998086i	$-0.519697\pi$
$137$	−198.323	−0.123678	−0.0618391	+	0.998086i	$0.519697\pi$
$138$	57.9522	0.0357480
$139$	−2900.14	−1.76969	−0.884844	−	0.465888i	$-0.845735\pi$
$139$	−2900.14	−1.76969	−0.884844	+	0.465888i	$0.845735\pi$
$140$	1624.46	0.980654
$141$	−425.918	−0.254389
$142$	344.529	0.203607
$143$	0	0
$144$	418.789	0.242355
$145$	2172.67	1.24435
$146$	−446.990	−0.253378
$147$	−334.564	−0.187717
$148$	304.956	0.169373
$149$	−3488.34	−1.91796	−0.958980	−	0.283472i	$-0.908514\pi$
$149$	−3488.34	−1.91796	−0.958980	+	0.283472i	$0.908514\pi$
$150$	174.836	0.0951687
$151$	1163.32	0.626953	0.313477	−	0.949596i	$-0.398506\pi$
$151$	1163.32	0.626953	0.313477	+	0.949596i	$0.398506\pi$
$152$	−768.923	−0.410315
$153$	−674.164	−0.356228
$154$	−136.315	−0.0713286
$155$	842.061	0.436361
$156$	0	0
$157$	342.057	0.173880	0.0869398	−	0.996214i	$-0.472291\pi$
$157$	342.057	0.173880	0.0869398	+	0.996214i	$0.472291\pi$
$158$	−716.111	−0.360574
$159$	−883.333	−0.440584
$160$	1648.32	0.814446
$161$	−226.056	−0.110657
$162$	−646.078	−0.313338
$163$	1394.89	0.670285	0.335142	−	0.942167i	$-0.391216\pi$
$163$	1394.89	0.670285	0.335142	+	0.942167i	$0.391216\pi$
$164$	2052.09	0.977082
$165$	838.369	0.395557
$166$	−19.1460	−0.00895191
$167$	−478.703	−0.221815	−0.110908	−	0.993831i	$-0.535376\pi$
$167$	−478.703	−0.221815	−0.110908	+	0.993831i	$0.535376\pi$
$168$	1136.06	0.521718
$169$	0	0
$170$	−779.131	−0.351509
$171$	553.138	0.247365
$172$	17.0718	0.00756809
$173$	1808.58	0.794822	0.397411	−	0.917641i	$-0.369909\pi$
$173$	1808.58	0.794822	0.397411	+	0.917641i	$0.369909\pi$
$174$	733.395	0.319532
$175$	−681.990	−0.294592
$176$	565.682	0.242272
$177$	−3234.61	−1.37361
$178$	258.331	0.108780
$179$	−4429.85	−1.84973	−0.924867	−	0.380292i	$-0.875824\pi$
$179$	−4429.85	−1.84973	−0.924867	+	0.380292i	$0.875824\pi$
$180$	−781.472	−0.323597
$181$	3409.17	1.40001	0.700005	−	0.714138i	$-0.253181\pi$
$181$	3409.17	1.40001	0.700005	+	0.714138i	$0.253181\pi$
$182$	0	0
$183$	600.543	0.242587
$184$	−151.172	−0.0605682
$185$	−525.267	−0.208748
$186$	284.242	0.112052
$187$	−910.631	−0.356106
$188$	536.267	0.208039
$189$	1892.31	0.728283
$190$	639.261	0.244089
$191$	2923.75	1.10762	0.553810	−	0.832643i	$-0.313173\pi$
$191$	2923.75	1.10762	0.553810	+	0.832643i	$0.313173\pi$
$192$	−1882.49	−0.707590
$193$	2484.18	0.926505	0.463253	−	0.886226i	$-0.346682\pi$
$193$	2484.18	0.926505	0.463253	+	0.886226i	$0.346682\pi$
$194$	−620.475	−0.229626
$195$	0	0
$196$	421.244	0.153514
$197$	5125.67	1.85375	0.926876	−	0.375369i	$-0.122484\pi$
$197$	5125.67	1.85375	0.926876	+	0.375369i	$0.122484\pi$
$198$	65.5768	0.0235371
$199$	−7.69219	−0.00274013	−0.00137006	−	0.999999i	$-0.500436\pi$
$199$	−7.69219	−0.00274013	−0.00137006	+	0.999999i	$0.500436\pi$
$200$	−456.071	−0.161246
$201$	−2440.29	−0.856343
$202$	946.879	0.329813
$203$	−2860.78	−0.989100
$204$	3663.11	1.25720
$205$	−3534.59	−1.20423
$206$	−1262.96	−0.427160
$207$	108.748	0.0365146
$208$	0	0
$209$	747.154	0.247281
$210$	−944.484	−0.310360
$211$	3107.34	1.01383	0.506915	−	0.861996i	$-0.330786\pi$
$211$	3107.34	1.01383	0.506915	+	0.861996i	$0.330786\pi$
$212$	1112.19	0.360309
$213$	2790.03	0.897509
$214$	−354.444	−0.113221
$215$	−29.4050	−0.00932746
$216$	1265.46	0.398628
$217$	−1108.75	−0.346853
$218$	47.0388	0.0146141
$219$	−3619.76	−1.11690
$220$	−1055.58	−0.323486
$221$	0	0
$222$	−177.306	−0.0536037
$223$	12.3185	0.00369913	0.00184957	−	0.999998i	$-0.499411\pi$
$223$	12.3185	0.00369913	0.00184957	+	0.999998i	$0.499411\pi$
$224$	−2170.37	−0.647383
$225$	328.082	0.0972096
$226$	−1467.82	−0.432027
$227$	−4615.90	−1.34964	−0.674820	−	0.737983i	$-0.735779\pi$
$227$	−4615.90	−1.34964	−0.674820	+	0.737983i	$0.735779\pi$
$228$	−3005.51	−0.873003
$229$	−5074.63	−1.46437	−0.732186	−	0.681105i	$-0.761500\pi$
$229$	−5074.63	−1.46437	−0.732186	+	0.681105i	$0.761500\pi$
$230$	125.680	0.0360309
$231$	−1103.89	−0.314419
$232$	−1913.11	−0.541386
$233$	211.683	0.0595184	0.0297592	−	0.999557i	$-0.490526\pi$
$233$	211.683	0.0595184	0.0297592	+	0.999557i	$0.490526\pi$
$234$	0	0
$235$	−923.683	−0.256402
$236$	4072.64	1.12333
$237$	−5799.12	−1.58942
$238$	1025.89	0.279406
$239$	−4312.49	−1.16716	−0.583581	−	0.812055i	$-0.698349\pi$
$239$	−4312.49	−1.16716	−0.583581	+	0.812055i	$0.698349\pi$
$240$	3919.42	1.05416
$241$	996.584	0.266372	0.133186	−	0.991091i	$-0.457479\pi$
$241$	996.584	0.266372	0.133186	+	0.991091i	$0.457479\pi$
$242$	88.5781	0.0235290
$243$	−2213.80	−0.584426
$244$	−756.133	−0.198387
$245$	−725.563	−0.189202
$246$	−1193.12	−0.309230
$247$	0	0
$248$	−741.464	−0.189851
$249$	−155.046	−0.0394603
$250$	−797.278	−0.201697
$251$	−276.892	−0.0696306	−0.0348153	−	0.999394i	$-0.511084\pi$
$251$	−276.892	−0.0696306	−0.0348153	+	0.999394i	$0.511084\pi$
$252$	1028.97	0.257219
$253$	146.892	0.0365021
$254$	80.2364	0.0198208
$255$	−6309.46	−1.54947
$256$	1619.36	0.395352
$257$	−3235.18	−0.785233	−0.392617	−	0.919702i	$-0.628430\pi$
$257$	−3235.18	−0.785233	−0.392617	+	0.919702i	$0.628430\pi$
$258$	−9.92581	−0.00239517
$259$	691.626	0.165929
$260$	0	0
$261$	1376.23	0.326384
$262$	846.772	0.199671
$263$	207.944	0.0487544	0.0243772	−	0.999703i	$-0.492240\pi$
$263$	207.944	0.0487544	0.0243772	+	0.999703i	$0.492240\pi$
$264$	−738.213	−0.172098
$265$	−1915.67	−0.444071
$266$	−841.723	−0.194020
$267$	2091.99	0.479504
$268$	3072.53	0.700316
$269$	5033.04	1.14078	0.570390	−	0.821374i	$-0.306792\pi$
$269$	5033.04	1.14078	0.570390	+	0.821374i	$0.306792\pi$
$270$	−1052.07	−0.237136
$271$	−1487.01	−0.333319	−0.166660	−	0.986015i	$-0.553298\pi$
$271$	−1487.01	−0.333319	−0.166660	+	0.986015i	$0.553298\pi$
$272$	−4257.25	−0.949021
$273$	0	0
$274$	−145.183	−0.0320102
$275$	443.159	0.0971764
$276$	−590.890	−0.128867
$277$	−235.836	−0.0511552	−0.0255776	−	0.999673i	$-0.508142\pi$
$277$	−235.836	−0.0511552	−0.0255776	+	0.999673i	$0.508142\pi$
$278$	−2123.05	−0.458029
$279$	533.384	0.114455
$280$	2463.75	0.525847
$281$	4915.01	1.04343	0.521717	−	0.853118i	$-0.325292\pi$
$281$	4915.01	1.04343	0.521717	+	0.853118i	$0.325292\pi$
$282$	−311.794	−0.0658406
$283$	−5199.56	−1.09216	−0.546081	−	0.837733i	$-0.683881\pi$
$283$	−5199.56	−1.09216	−0.546081	+	0.837733i	$0.683881\pi$
$284$	−3512.87	−0.733981
$285$	5176.78	1.07595
$286$	0	0
$287$	4654.04	0.957210
$288$	1044.09	0.213624
$289$	1940.29	0.394930
$290$	1590.50	0.322060
$291$	−5024.65	−1.01220
$292$	4557.58	0.913398
$293$	8880.92	1.77075	0.885373	−	0.464881i	$-0.153903\pi$
$293$	8880.92	1.77075	0.885373	+	0.464881i	$0.153903\pi$
$294$	−244.918	−0.0485846
$295$	−7014.85	−1.38448
$296$	462.515	0.0908215
$297$	−1229.63	−0.240237
$298$	−2553.64	−0.496405
$299$	0	0
$300$	−1782.66	−0.343072
$301$	38.7180	0.00741417
$302$	851.612	0.162267
$303$	7667.90	1.45383
$304$	3492.99	0.659001
$305$	1302.39	0.244507
$306$	−493.522	−0.0921987
$307$	1497.93	0.278474	0.139237	−	0.990259i	$-0.455535\pi$
$307$	1497.93	0.278474	0.139237	+	0.990259i	$0.455535\pi$
$308$	1389.89	0.257131
$309$	−10227.6	−1.88293
$310$	616.432	0.112939
$311$	−7484.71	−1.36469	−0.682345	−	0.731030i	$-0.739040\pi$
$311$	−7484.71	−1.36469	−0.682345	+	0.731030i	$0.739040\pi$
$312$	0	0
$313$	−658.363	−0.118891	−0.0594455	−	0.998232i	$-0.518933\pi$
$313$	−658.363	−0.118891	−0.0594455	+	0.998232i	$0.518933\pi$
$314$	250.403	0.0450034
$315$	−1772.34	−0.317016
$316$	7301.57	1.29983
$317$	−233.708	−0.0414080	−0.0207040	−	0.999786i	$-0.506591\pi$
$317$	−233.708	−0.0414080	−0.0207040	+	0.999786i	$0.506591\pi$
$318$	−646.645	−0.114032
$319$	1858.94	0.326272
$320$	−4082.53	−0.713189
$321$	−2870.31	−0.499082
$322$	−165.485	−0.0286401
$323$	−5622.98	−0.968641
$324$	6587.51	1.12955
$325$	0	0
$326$	1021.13	0.173482
$327$	380.924	0.0644194
$328$	3112.33	0.523931
$329$	1216.23	0.203808
$330$	613.729	0.102378
$331$	−8532.95	−1.41696	−0.708480	−	0.705731i	$-0.750619\pi$
$331$	−8532.95	−1.41696	−0.708480	+	0.705731i	$0.750619\pi$
$332$	195.215	0.0322706
$333$	−332.718	−0.0547533
$334$	−350.435	−0.0574100
$335$	−5292.22	−0.863120
$336$	−5160.76	−0.837924
$337$	11691.2	1.88979	0.944895	−	0.327373i	$-0.106163\pi$
$337$	11691.2	1.88979	0.944895	+	0.327373i	$0.106163\pi$
$338$	0	0
$339$	−11886.5	−1.90439
$340$	7944.14	1.26715
$341$	720.472	0.114416
$342$	404.925	0.0640229
$343$	6761.73	1.06443
$344$	25.8921	0.00405817
$345$	1017.77	0.158825
$346$	1323.98	0.205715
$347$	4598.79	0.711459	0.355729	−	0.934589i	$-0.384232\pi$
$347$	4598.79	0.711459	0.355729	+	0.934589i	$0.384232\pi$
$348$	−7477.80	−1.15187
$349$	−6720.27	−1.03074	−0.515369	−	0.856968i	$-0.672345\pi$
$349$	−6720.27	−1.03074	−0.515369	+	0.856968i	$0.672345\pi$
$350$	−499.251	−0.0762460
$351$	0	0
$352$	1410.31	0.213551
$353$	−5738.70	−0.865270	−0.432635	−	0.901569i	$-0.642416\pi$
$353$	−5738.70	−0.865270	−0.432635	+	0.901569i	$0.642416\pi$
$354$	−2367.90	−0.355515
$355$	6050.69	0.904611
$356$	−2633.99	−0.392138
$357$	8307.75	1.23163
$358$	−3242.87	−0.478746
$359$	4115.27	0.605001	0.302501	−	0.953149i	$-0.402179\pi$
$359$	4115.27	0.605001	0.302501	+	0.953149i	$0.402179\pi$
$360$	−1185.23	−0.173519
$361$	−2245.46	−0.327374
$362$	2495.69	0.362349
$363$	717.313	0.103717
$364$	0	0
$365$	−7850.12	−1.12574
$366$	439.628	0.0627861
$367$	9662.99	1.37440	0.687199	−	0.726469i	$-0.258840\pi$
$367$	9662.99	1.37440	0.687199	+	0.726469i	$0.258840\pi$
$368$	686.729	0.0972778
$369$	−2238.90	−0.315861
$370$	−384.522	−0.0540279
$371$	2522.39	0.352981
$372$	−2898.18	−0.403934
$373$	−141.780	−0.0196812	−0.00984062	−	0.999952i	$-0.503132\pi$
$373$	−141.780	−0.0196812	−0.00984062	+	0.999952i	$0.503132\pi$
$374$	−666.628	−0.0921671
$375$	−6456.42	−0.889088
$376$	813.334	0.111555
$377$	0	0
$378$	1385.27	0.188494
$379$	2819.73	0.382163	0.191082	−	0.981574i	$-0.438800\pi$
$379$	2819.73	0.382163	0.191082	+	0.981574i	$0.438800\pi$
$380$	−6518.00	−0.879911
$381$	649.760	0.0873707
$382$	2140.34	0.286673
$383$	6337.84	0.845557	0.422778	−	0.906233i	$-0.361055\pi$
$383$	6337.84	0.845557	0.422778	+	0.906233i	$0.361055\pi$
$384$	−7458.53	−0.991189
$385$	−2393.99	−0.316907
$386$	1818.55	0.239797
$387$	−18.6259	−0.00244653
$388$	6326.46	0.827776
$389$	−8805.25	−1.14767	−0.573836	−	0.818970i	$-0.694545\pi$
$389$	−8805.25	−1.14767	−0.573836	+	0.818970i	$0.694545\pi$
$390$	0	0
$391$	−1105.49	−0.142985
$392$	638.883	0.0823176
$393$	6857.23	0.880156
$394$	3752.25	0.479786
$395$	−12576.5	−1.60200
$396$	−668.631	−0.0848484
$397$	−4315.26	−0.545534	−0.272767	−	0.962080i	$-0.587939\pi$
$397$	−4315.26	−0.545534	−0.272767	+	0.962080i	$0.587939\pi$
$398$	−5.63108	−0.000709197 0
$399$	−6816.34	−0.855247
$400$	2071.79	0.258974
$401$	−361.681	−0.0450411	−0.0225206	−	0.999746i	$-0.507169\pi$
$401$	−361.681	−0.0450411	−0.0225206	+	0.999746i	$0.507169\pi$
$402$	−1786.42	−0.221638
$403$	0	0
$404$	−9654.53	−1.18894
$405$	−11346.5	−1.39213
$406$	−2094.24	−0.255998
$407$	−449.420	−0.0547345
$408$	5555.70	0.674137
$409$	−9220.50	−1.11473	−0.557365	−	0.830268i	$-0.688188\pi$
$409$	−9220.50	−1.11473	−0.557365	+	0.830268i	$0.688188\pi$
$410$	−2587.50	−0.311677
$411$	−1175.70	−0.141102
$412$	12877.4	1.53986
$413$	9236.55	1.10049
$414$	79.6092	0.00945067
$415$	−336.245	−0.0397726
$416$	0	0
$417$	−17192.6	−2.01901
$418$	546.954	0.0640010
$419$	−14912.9	−1.73876	−0.869380	−	0.494144i	$-0.835481\pi$
$419$	−14912.9	−1.73876	−0.869380	+	0.494144i	$0.835481\pi$
$420$	9630.11	1.11881
$421$	13486.0	1.56121	0.780603	−	0.625027i	$-0.214912\pi$
$421$	13486.0	1.56121	0.780603	+	0.625027i	$0.214912\pi$
$422$	2274.73	0.262399
$423$	−585.085	−0.0672525
$424$	1686.81	0.193205
$425$	−3335.16	−0.380656
$426$	2042.44	0.232292
$427$	−1714.87	−0.194352
$428$	3613.96	0.408148
$429$	0	0
$430$	−21.5260	−0.00241413
$431$	−406.334	−0.0454116	−0.0227058	−	0.999742i	$-0.507228\pi$
$431$	−406.334	−0.0454116	−0.0227058	+	0.999742i	$0.507228\pi$
$432$	−5748.59	−0.640230
$433$	−1766.69	−0.196078	−0.0980391	−	0.995183i	$-0.531257\pi$
$433$	−1766.69	−0.196078	−0.0980391	+	0.995183i	$0.531257\pi$
$434$	−811.664	−0.0897722
$435$	12880.0	1.41965
$436$	−479.615	−0.0526821
$437$	907.033	0.0992889
$438$	−2649.85	−0.289075
$439$	7824.19	0.850634	0.425317	−	0.905044i	$-0.360163\pi$
$439$	7824.19	0.850634	0.425317	+	0.905044i	$0.360163\pi$
$440$	−1600.95	−0.173460
$441$	−459.591	−0.0496265
$442$	0	0
$443$	11667.9	1.25137	0.625686	−	0.780075i	$-0.284819\pi$
$443$	11667.9	1.25137	0.625686	+	0.780075i	$0.284819\pi$
$444$	1807.84	0.193235
$445$	4536.86	0.483299
$446$	9.01776	0.000957406 0
$447$	−20679.6	−2.18817
$448$	5375.53	0.566897
$449$	−16975.3	−1.78421	−0.892107	−	0.451825i	$-0.850773\pi$
$449$	−16975.3	−1.78421	−0.892107	+	0.451825i	$0.850773\pi$
$450$	240.173	0.0251597
$451$	−3024.21	−0.315753
$452$	14966.1	1.55741
$453$	6896.42	0.715280
$454$	−3379.07	−0.349312
$455$	0	0
$456$	−4558.33	−0.468122
$457$	16192.9	1.65748	0.828741	−	0.559632i	$-0.189057\pi$
$457$	16192.9	1.65748	0.828741	+	0.559632i	$0.189057\pi$
$458$	−3714.89	−0.379007
$459$	9254.05	0.941050
$460$	−1281.45	−0.129887
$461$	−8586.04	−0.867444	−0.433722	−	0.901047i	$-0.642800\pi$
$461$	−8586.04	−0.867444	−0.433722	+	0.901047i	$0.642800\pi$
$462$	−808.105	−0.0813776
$463$	7917.20	0.794694	0.397347	−	0.917668i	$-0.369931\pi$
$463$	7917.20	0.794694	0.397347	+	0.917668i	$0.369931\pi$
$464$	8690.67	0.869513
$465$	4991.91	0.497837
$466$	154.962	0.0154045
$467$	−15155.0	−1.50169	−0.750844	−	0.660480i	$-0.770353\pi$
$467$	−15155.0	−1.50169	−0.750844	+	0.660480i	$0.770353\pi$
$468$	0	0
$469$	6968.34	0.686073
$470$	−676.183	−0.0663617
$471$	2027.78	0.198376
$472$	6176.82	0.602354
$473$	−25.1591	−0.00244570
$474$	−4245.25	−0.411373
$475$	2736.43	0.264328
$476$	−10460.2	−1.00723
$477$	−1213.44	−0.116477
$478$	−3156.96	−0.302084
$479$	−10001.1	−0.953993	−0.476996	−	0.878905i	$-0.658275\pi$
$479$	−10001.1	−0.953993	−0.476996	+	0.878905i	$0.658275\pi$
$480$	9771.59	0.929188
$481$	0	0
$482$	729.550	0.0689421
$483$	−1340.11	−0.126246
$484$	−903.156	−0.0848193
$485$	−10896.9	−1.02021
$486$	−1620.62	−0.151261
$487$	−7044.54	−0.655480	−0.327740	−	0.944768i	$-0.606287\pi$
$487$	−7044.54	−0.655480	−0.327740	+	0.944768i	$0.606287\pi$
$488$	−1146.80	−0.106379
$489$	8269.21	0.764717
$490$	−531.149	−0.0489691
$491$	−13326.4	−1.22487	−0.612437	−	0.790520i	$-0.709811\pi$
$491$	−13326.4	−1.22487	−0.612437	+	0.790520i	$0.709811\pi$
$492$	12165.2	1.11474
$493$	−13990.2	−1.27806
$494$	0	0
$495$	1151.67	0.104573
$496$	3368.25	0.304917
$497$	−7967.02	−0.719054
$498$	−113.501	−0.0102131
$499$	20069.1	1.80044	0.900218	−	0.435440i	$-0.143407\pi$
$499$	20069.1	1.80044	0.900218	+	0.435440i	$0.143407\pi$
$500$	8129.17	0.727095
$501$	−2837.85	−0.253065
$502$	−202.699	−0.0180217
$503$	7782.35	0.689856	0.344928	−	0.938629i	$-0.387903\pi$
$503$	7782.35	0.689856	0.344928	+	0.938629i	$0.387903\pi$
$504$	1560.60	0.137926
$505$	16629.3	1.46533
$506$	107.532	0.00944744
$507$	0	0
$508$	−818.102	−0.0714516
$509$	1475.93	0.128526	0.0642628	−	0.997933i	$-0.479530\pi$
$509$	1475.93	0.128526	0.0642628	+	0.997933i	$0.479530\pi$
$510$	−4618.85	−0.401031
$511$	10336.4	0.894821
$512$	11250.6	0.971116
$513$	−7592.75	−0.653466
$514$	−2368.32	−0.203233
$515$	−22180.4	−1.89784
$516$	101.205	0.00863431
$517$	−790.307	−0.0672295
$518$	506.305	0.0429455
$519$	10721.7	0.906799
$520$	0	0
$521$	7609.43	0.639875	0.319938	−	0.947439i	$-0.396338\pi$
$521$	7609.43	0.639875	0.319938	+	0.947439i	$0.396338\pi$
$522$	1007.47	0.0844744
$523$	12452.9	1.04116	0.520581	−	0.853812i	$-0.325715\pi$
$523$	12452.9	1.04116	0.520581	+	0.853812i	$0.325715\pi$
$524$	−8633.82	−0.719790
$525$	−4042.97	−0.336095
$526$	152.226	0.0126186
$527$	−5422.18	−0.448186
$528$	3353.48	0.276404
$529$	−11988.7	−0.985344
$530$	−1402.37	−0.114934
$531$	−4443.39	−0.363139
$532$	8582.34	0.699420
$533$	0	0
$534$	1531.44	0.124105
$535$	−6224.81	−0.503031
$536$	4659.99	0.375524
$537$	−26261.0	−2.11033
$538$	3684.44	0.295255
$539$	−620.795	−0.0496095
$540$	10727.0	0.854847
$541$	−9312.17	−0.740039	−0.370020	−	0.929024i	$-0.620649\pi$
$541$	−9312.17	−0.740039	−0.370020	+	0.929024i	$0.620649\pi$
$542$	−1088.57	−0.0862693
$543$	20210.3	1.59725
$544$	−10613.8	−0.836515
$545$	826.105	0.0649292
$546$	0	0
$547$	−11018.6	−0.861278	−0.430639	−	0.902524i	$-0.641712\pi$
$547$	−11018.6	−0.861278	−0.430639	+	0.902524i	$0.641712\pi$
$548$	1480.31	0.115393
$549$	824.968	0.0641325
$550$	324.415	0.0251511
$551$	11478.6	0.887490
$552$	−896.179	−0.0691013
$553$	16559.6	1.27339
$554$	−172.644	−0.0132399
$555$	−3113.89	−0.238157
$556$	21646.9	1.65114
$557$	12018.4	0.914250	0.457125	−	0.889403i	$-0.348879\pi$
$557$	12018.4	0.914250	0.457125	+	0.889403i	$0.348879\pi$
$558$	390.464	0.0296231
$559$	0	0
$560$	−11192.1	−0.844555
$561$	−5398.40	−0.406276
$562$	3598.04	0.270061
$563$	−8763.89	−0.656046	−0.328023	−	0.944670i	$-0.606382\pi$
$563$	−8763.89	−0.656046	−0.328023	+	0.944670i	$0.606382\pi$
$564$	3179.10	0.237348
$565$	−25778.1	−1.91946
$566$	−3806.34	−0.282672
$567$	14940.1	1.10657
$568$	−5327.84	−0.393576
$569$	−10273.2	−0.756895	−0.378447	−	0.925623i	$-0.623542\pi$
$569$	−10273.2	−0.756895	−0.378447	+	0.925623i	$0.623542\pi$
$570$	3789.67	0.278477
$571$	2602.62	0.190747	0.0953734	−	0.995442i	$-0.469596\pi$
$571$	2602.62	0.190747	0.0953734	+	0.995442i	$0.469596\pi$
$572$	0	0
$573$	17332.6	1.26366
$574$	3406.99	0.247744
$575$	537.988	0.0390185
$576$	−2585.99	−0.187065
$577$	19727.0	1.42331	0.711653	−	0.702532i	$-0.247947\pi$
$577$	19727.0	1.42331	0.711653	+	0.702532i	$0.247947\pi$
$578$	1420.39	0.102215
$579$	14726.7	1.05703
$580$	−16217.0	−1.16099
$581$	442.739	0.0316143
$582$	−3678.30	−0.261977
$583$	−1639.06	−0.116437
$584$	6912.30	0.489783
$585$	0	0
$586$	6501.28	0.458303
$587$	10116.2	0.711309	0.355654	−	0.934618i	$-0.384258\pi$
$587$	10116.2	0.711309	0.355654	+	0.934618i	$0.384258\pi$
$588$	2497.22	0.175142
$589$	4448.78	0.311221
$590$	−5135.23	−0.358329
$591$	30386.0	2.11491
$592$	−2101.07	−0.145867
$593$	−3130.32	−0.216774	−0.108387	−	0.994109i	$-0.534569\pi$
$593$	−3130.32	−0.216774	−0.108387	+	0.994109i	$0.534569\pi$
$594$	−900.152	−0.0621779
$595$	18016.9	1.24138
$596$	26037.3	1.78948
$597$	−45.6009	−0.00312616
$598$	0	0
$599$	10080.1	0.687581	0.343790	−	0.939046i	$-0.388289\pi$
$599$	10080.1	0.687581	0.343790	+	0.939046i	$0.388289\pi$
$600$	−2703.68	−0.183962
$601$	4777.02	0.324224	0.162112	−	0.986772i	$-0.448169\pi$
$601$	4777.02	0.324224	0.162112	+	0.986772i	$0.448169\pi$
$602$	28.3435	0.00191893
$603$	−3352.24	−0.226391
$604$	−8683.16	−0.584955
$605$	1555.63	0.104537
$606$	5613.29	0.376278
$607$	−2571.35	−0.171941	−0.0859703	−	0.996298i	$-0.527399\pi$
$607$	−2571.35	−0.171941	−0.0859703	+	0.996298i	$0.527399\pi$
$608$	8708.43	0.580877
$609$	−16959.3	−1.12845
$610$	953.414	0.0632830
$611$	0	0
$612$	5032.03	0.332366
$613$	−12711.9	−0.837564	−0.418782	−	0.908087i	$-0.637543\pi$
$613$	−12711.9	−0.837564	−0.418782	+	0.908087i	$0.637543\pi$
$614$	1096.56	0.0720744
$615$	−20953.8	−1.37388
$616$	2107.99	0.137879
$617$	−16236.1	−1.05939	−0.529693	−	0.848189i	$-0.677693\pi$
$617$	−16236.1	−1.05939	−0.529693	+	0.848189i	$0.677693\pi$
$618$	−7487.11	−0.487339
$619$	−12657.3	−0.821874	−0.410937	−	0.911664i	$-0.634798\pi$
$619$	−12657.3	−0.821874	−0.410937	+	0.911664i	$0.634798\pi$
$620$	−6285.23	−0.407131
$621$	−1492.75	−0.0964607
$622$	−5479.19	−0.353208
$623$	−5973.75	−0.384162
$624$	0	0
$625$	−19037.8	−1.21842
$626$	−481.955	−0.0307713
$627$	4429.28	0.282119
$628$	−2553.15	−0.162232
$629$	3382.28	0.214404
$630$	−1297.44	−0.0820497
$631$	3949.97	0.249201	0.124600	−	0.992207i	$-0.460235\pi$
$631$	3949.97	0.249201	0.124600	+	0.992207i	$0.460235\pi$
$632$	11074.0	0.696994
$633$	18421.0	1.15666
$634$	−171.086	−0.0107172
$635$	1409.13	0.0880621
$636$	6593.29	0.411070
$637$	0	0
$638$	1360.84	0.0844455
$639$	3832.67	0.237274
$640$	−16175.2	−0.999033
$641$	−7398.27	−0.455872	−0.227936	−	0.973676i	$-0.573198\pi$
$641$	−7398.27	−0.455872	−0.227936	+	0.973676i	$0.573198\pi$
$642$	−2101.22	−0.129172
$643$	12491.7	0.766134	0.383067	−	0.923721i	$-0.374868\pi$
$643$	12491.7	0.766134	0.383067	+	0.923721i	$0.374868\pi$
$644$	1687.31	0.103244
$645$	−174.319	−0.0106415
$646$	−4116.31	−0.250703
$647$	−10472.0	−0.636315	−0.318158	−	0.948038i	$-0.603064\pi$
$647$	−10472.0	−0.636315	−0.318158	+	0.948038i	$0.603064\pi$
$648$	9991.02	0.605685
$649$	−6001.94	−0.363015
$650$	0	0
$651$	−6572.92	−0.395719
$652$	−10411.6	−0.625384
$653$	6337.94	0.379820	0.189910	−	0.981801i	$-0.439180\pi$
$653$	6337.94	0.379820	0.189910	+	0.981801i	$0.439180\pi$
$654$	278.856	0.0166730
$655$	14871.2	0.887121
$656$	−14138.4	−0.841479
$657$	−4972.48	−0.295274
$658$	890.339	0.0527493
$659$	15196.7	0.898302	0.449151	−	0.893456i	$-0.351726\pi$
$659$	15196.7	0.898302	0.449151	+	0.893456i	$0.351726\pi$
$660$	−6257.67	−0.369060
$661$	−2298.17	−0.135232	−0.0676161	−	0.997711i	$-0.521539\pi$
$661$	−2298.17	−0.135232	−0.0676161	+	0.997711i	$0.521539\pi$
$662$	−6246.55	−0.366736
$663$	0	0
$664$	296.075	0.0173042
$665$	−14782.5	−0.862016
$666$	−243.566	−0.0141712
$667$	2256.73	0.131006
$668$	3573.09	0.206956
$669$	73.0265	0.00422028
$670$	−3874.18	−0.223392
$671$	1114.33	0.0641106
$672$	−12866.4	−0.738589
$673$	23199.6	1.32880	0.664398	−	0.747379i	$-0.268688\pi$
$673$	23199.6	1.32880	0.664398	+	0.747379i	$0.268688\pi$
$674$	8558.54	0.489114
$675$	−4503.49	−0.256799
$676$	0	0
$677$	−2145.38	−0.121793	−0.0608963	−	0.998144i	$-0.519396\pi$
$677$	−2145.38	−0.121793	−0.0608963	+	0.998144i	$0.519396\pi$
$678$	−8701.55	−0.492892
$679$	14348.1	0.810941
$680$	12048.6	0.679472
$681$	−27364.0	−1.53978
$682$	527.422	0.0296129
$683$	29544.6	1.65519	0.827593	−	0.561329i	$-0.189710\pi$
$683$	29544.6	1.65519	0.827593	+	0.561329i	$0.189710\pi$
$684$	−4128.68	−0.230795
$685$	−2549.72	−0.142219
$686$	4949.93	0.275495
$687$	−30083.4	−1.67068
$688$	−117.620	−0.00651776
$689$	0	0
$690$	745.057	0.0411070
$691$	−27803.1	−1.53065	−0.765325	−	0.643644i	$-0.777422\pi$
$691$	−27803.1	−1.53065	−0.765325	+	0.643644i	$0.777422\pi$
$692$	−13499.5	−0.741579
$693$	−1516.42	−0.0831227
$694$	3366.55	0.184139
$695$	−37285.4	−2.03498
$696$	−11341.3	−0.617659
$697$	22759.8	1.23686
$698$	−4919.58	−0.266775
$699$	1254.90	0.0679036
$700$	5090.44	0.274858
$701$	−19697.8	−1.06130	−0.530652	−	0.847590i	$-0.678053\pi$
$701$	−19697.8	−1.06130	−0.530652	+	0.847590i	$0.678053\pi$
$702$	0	0
$703$	−2775.09	−0.148883
$704$	−3493.03	−0.187001
$705$	−5475.78	−0.292524
$706$	−4201.02	−0.223948
$707$	−21896.0	−1.16476
$708$	24143.5	1.28159
$709$	−19122.5	−1.01292	−0.506460	−	0.862263i	$-0.669046\pi$
$709$	−19122.5	−1.01292	−0.506460	+	0.862263i	$0.669046\pi$
$710$	4429.41	0.234131
$711$	−7966.27	−0.420195
$712$	−3994.86	−0.210272
$713$	874.641	0.0459405
$714$	6081.70	0.318770
$715$	0	0
$716$	33064.8	1.72582
$717$	−25565.3	−1.33160
$718$	3012.59	0.156586
$719$	1837.44	0.0953060	0.0476530	−	0.998864i	$-0.484826\pi$
$719$	1837.44	0.0953060	0.0476530	+	0.998864i	$0.484826\pi$
$720$	5384.13	0.278687
$721$	29205.2	1.50854
$722$	−1643.79	−0.0847307
$723$	5907.95	0.303899
$724$	−25446.4	−1.30623
$725$	6808.33	0.348765
$726$	525.109	0.0268438
$727$	−7555.46	−0.385442	−0.192721	−	0.981254i	$-0.561731\pi$
$727$	−7555.46	−0.385442	−0.192721	+	0.981254i	$0.561731\pi$
$728$	0	0
$729$	10705.2	0.543881
$730$	−5746.69	−0.291362
$731$	189.344	0.00958021
$732$	−4482.51	−0.226337
$733$	−11984.6	−0.603905	−0.301952	−	0.953323i	$-0.597638\pi$
$733$	−11984.6	−0.603905	−0.301952	+	0.953323i	$0.597638\pi$
$734$	7073.80	0.355720
$735$	−4301.29	−0.215858
$736$	1712.10	0.0857456
$737$	−4528.05	−0.226313
$738$	−1638.99	−0.0817508
$739$	27142.5	1.35109	0.675543	−	0.737321i	$-0.263909\pi$
$739$	27142.5	1.35109	0.675543	+	0.737321i	$0.263909\pi$
$740$	3920.64	0.194764
$741$	0	0
$742$	1846.52	0.0913582
$743$	29222.6	1.44290	0.721450	−	0.692467i	$-0.243476\pi$
$743$	29222.6	1.44290	0.721450	+	0.692467i	$0.243476\pi$
$744$	−4395.55	−0.216598
$745$	−44847.6	−2.20549
$746$	−103.790	−0.00509388
$747$	−212.987	−0.0104321
$748$	6797.04	0.332252
$749$	8196.29	0.399847
$750$	−4726.43	−0.230113
$751$	−8859.39	−0.430471	−0.215236	−	0.976562i	$-0.569052\pi$
$751$	−8859.39	−0.430471	−0.215236	+	0.976562i	$0.569052\pi$
$752$	−3694.73	−0.179166
$753$	−1641.47	−0.0794404
$754$	0	0
$755$	14956.2	0.720941
$756$	−14124.4	−0.679497
$757$	35734.4	1.71571	0.857853	−	0.513896i	$-0.171798\pi$
$757$	35734.4	1.71571	0.857853	+	0.513896i	$0.171798\pi$
$758$	2064.19	0.0989112
$759$	870.806	0.0416446
$760$	−9885.59	−0.471826
$761$	−34394.7	−1.63838	−0.819189	−	0.573524i	$-0.805576\pi$
$761$	−34394.7	−1.63838	−0.819189	+	0.573524i	$0.805576\pi$
$762$	475.658	0.0226132
$763$	−1087.74	−0.0516107
$764$	−21823.2	−1.03342
$765$	−8667.33	−0.409631
$766$	4639.62	0.218846
$767$	0	0
$768$	9599.92	0.451051
$769$	11602.7	0.544091	0.272045	−	0.962284i	$-0.412300\pi$
$769$	11602.7	0.544091	0.272045	+	0.962284i	$0.412300\pi$
$770$	−1752.53	−0.0820216
$771$	−19178.8	−0.895859
$772$	−18542.2	−0.864441
$773$	12680.6	0.590026	0.295013	−	0.955493i	$-0.404676\pi$
$773$	12680.6	0.590026	0.295013	+	0.955493i	$0.404676\pi$
$774$	−13.6351	−0.000633210 0
$775$	2638.71	0.122303
$776$	9595.09	0.443871
$777$	4100.10	0.189305
$778$	−6445.89	−0.297039
$779$	−18674.0	−0.858876
$780$	0	0
$781$	5176.99	0.237193
$782$	−809.276	−0.0370072
$783$	−18891.0	−0.862210
$784$	−2902.25	−0.132209
$785$	4397.62	0.199946
$786$	5019.84	0.227801
$787$	4417.61	0.200090	0.100045	−	0.994983i	$-0.468101\pi$
$787$	4417.61	0.200090	0.100045	+	0.994983i	$0.468101\pi$
$788$	−38258.5	−1.72957
$789$	1232.74	0.0556231
$790$	−9206.61	−0.414628
$791$	33942.4	1.52573
$792$	−1014.09	−0.0454974
$793$	0	0
$794$	−3158.99	−0.141194
$795$	−11356.5	−0.506633
$796$	57.4153	0.00255657
$797$	−27030.1	−1.20132	−0.600661	−	0.799504i	$-0.705096\pi$
$797$	−27030.1	−1.20132	−0.600661	+	0.799504i	$0.705096\pi$
$798$	−4989.91	−0.221354
$799$	5947.75	0.263350
$800$	5165.23	0.228273
$801$	2873.77	0.126766
$802$	−264.769	−0.0116575
$803$	−6716.60	−0.295173
$804$	18214.6	0.798979
$805$	−2906.27	−0.127246
$806$	0	0
$807$	29836.9	1.30150
$808$	−14642.6	−0.637533
$809$	23647.0	1.02767	0.513835	−	0.857889i	$-0.328224\pi$
$809$	23647.0	1.02767	0.513835	+	0.857889i	$0.328224\pi$
$810$	−8306.24	−0.360311
$811$	−33486.1	−1.44988	−0.724941	−	0.688811i	$-0.758133\pi$
$811$	−33486.1	−1.44988	−0.724941	+	0.688811i	$0.758133\pi$
$812$	21353.1	0.922843
$813$	−8815.30	−0.380278
$814$	−328.999	−0.0141663
$815$	17933.3	0.770768
$816$	−25237.8	−1.08272
$817$	−155.353	−0.00665251
$818$	−6749.88	−0.288513
$819$	0	0
$820$	26382.5	1.12356
$821$	−2605.69	−0.110766	−0.0553832	−	0.998465i	$-0.517638\pi$
$821$	−2605.69	−0.110766	−0.0553832	+	0.998465i	$0.517638\pi$
$822$	−860.673	−0.0365200
$823$	31976.2	1.35434	0.677169	−	0.735828i	$-0.263207\pi$
$823$	31976.2	1.35434	0.677169	+	0.735828i	$0.263207\pi$
$824$	19530.6	0.825705
$825$	2627.14	0.110867
$826$	6761.62	0.284827
$827$	37759.0	1.58768	0.793839	−	0.608128i	$-0.208079\pi$
$827$	37759.0	1.58768	0.793839	+	0.608128i	$0.208079\pi$
$828$	−811.707	−0.0340686
$829$	−1137.55	−0.0476584	−0.0238292	−	0.999716i	$-0.507586\pi$
$829$	−1137.55	−0.0476584	−0.0238292	+	0.999716i	$0.507586\pi$
$830$	−246.149	−0.0102939
$831$	−1398.08	−0.0583621
$832$	0	0
$833$	4672.03	0.194329
$834$	−12585.9	−0.522557
$835$	−6154.40	−0.255068
$836$	−5576.83	−0.230716
$837$	−7321.60	−0.302356
$838$	−10917.0	−0.450024
$839$	37372.2	1.53782	0.768911	−	0.639356i	$-0.220799\pi$
$839$	37372.2	1.53782	0.768911	+	0.639356i	$0.220799\pi$
$840$	14605.6	0.599930
$841$	4170.26	0.170989
$842$	9872.44	0.404070
$843$	29137.2	1.19044
$844$	−23193.5	−0.945917
$845$	0	0
$846$	−428.312	−0.0174062
$847$	−2048.31	−0.0830943
$848$	−7662.68	−0.310304
$849$	−30824.0	−1.24603
$850$	−2441.51	−0.0985211
$851$	−545.589	−0.0219772
$852$	−20825.0	−0.837387
$853$	22490.8	0.902780	0.451390	−	0.892327i	$-0.350928\pi$
$853$	22490.8	0.902780	0.451390	+	0.892327i	$0.350928\pi$
$854$	−1255.37	−0.0503021
$855$	7111.36	0.284449
$856$	5481.16	0.218858
$857$	43409.5	1.73027	0.865135	−	0.501539i	$-0.167233\pi$
$857$	43409.5	1.73027	0.865135	+	0.501539i	$0.167233\pi$
$858$	0	0
$859$	29533.2	1.17306	0.586532	−	0.809926i	$-0.300493\pi$
$859$	29533.2	1.17306	0.586532	+	0.809926i	$0.300493\pi$
$860$	219.482	0.00870264
$861$	27590.1	1.09207
$862$	−297.457	−0.0117534
$863$	−14351.6	−0.566090	−0.283045	−	0.959107i	$-0.591345\pi$
$863$	−14351.6	−0.566090	−0.283045	+	0.959107i	$0.591345\pi$
$864$	−14331.9	−0.564331
$865$	23251.9	0.913975
$866$	−1293.31	−0.0507488
$867$	11502.4	0.450569
$868$	8275.85	0.323618
$869$	−10760.5	−0.420051
$870$	9428.82	0.367433
$871$	0	0
$872$	−727.413	−0.0282492
$873$	−6902.39	−0.267595
$874$	663.994	0.0256979
$875$	18436.5	0.712307
$876$	27018.3	1.04208
$877$	43248.7	1.66523	0.832614	−	0.553854i	$-0.186844\pi$
$877$	43248.7	1.66523	0.832614	+	0.553854i	$0.186844\pi$
$878$	5727.71	0.220160
$879$	52647.9	2.02021
$880$	7272.64	0.278591
$881$	3816.13	0.145935	0.0729675	−	0.997334i	$-0.476753\pi$
$881$	3816.13	0.145935	0.0729675	+	0.997334i	$0.476753\pi$
$882$	−336.444	−0.0128443
$883$	48787.6	1.85938	0.929690	−	0.368343i	$-0.120075\pi$
$883$	48787.6	1.85938	0.929690	+	0.368343i	$0.120075\pi$
$884$	0	0
$885$	−41585.5	−1.57953
$886$	8541.49	0.323879
$887$	41495.1	1.57077	0.785384	−	0.619009i	$-0.212466\pi$
$887$	41495.1	1.57077	0.785384	+	0.619009i	$0.212466\pi$
$888$	2741.88	0.103617
$889$	−1855.41	−0.0699984
$890$	3321.21	0.125087
$891$	−9708.15	−0.365023
$892$	−91.9464	−0.00345134
$893$	−4880.01	−0.182870
$894$	−15138.5	−0.566340
$895$	−56951.9	−2.12703
$896$	21298.1	0.794107
$897$	0	0
$898$	−12426.7	−0.461788
$899$	11068.7	0.410637
$900$	−2448.84	−0.0906978
$901$	12335.3	0.456104
$902$	−2213.88	−0.0817228
$903$	229.528	0.00845871
$904$	22698.5	0.835113
$905$	43829.7	1.60989
$906$	5048.53	0.185128
$907$	21615.3	0.791316	0.395658	−	0.918398i	$-0.370517\pi$
$907$	21615.3	0.791316	0.395658	+	0.918398i	$0.370517\pi$
$908$	34453.6	1.25923
$909$	10533.4	0.384347
$910$	0	0
$911$	3646.35	0.132611	0.0663057	−	0.997799i	$-0.478879\pi$
$911$	3646.35	0.132611	0.0663057	+	0.997799i	$0.478879\pi$
$912$	20707.1	0.751844
$913$	−287.693	−0.0104285
$914$	11854.0	0.428988
$915$	7720.82	0.278954
$916$	37877.6	1.36628
$917$	−19581.1	−0.705151
$918$	6774.43	0.243562
$919$	31280.0	1.12278	0.561388	−	0.827553i	$-0.310267\pi$
$919$	31280.0	1.12278	0.561388	+	0.827553i	$0.310267\pi$
$920$	−1943.53	−0.0696482
$921$	8880.05	0.317707
$922$	−6285.42	−0.224511
$923$	0	0
$924$	8239.56	0.293357
$925$	−1645.99	−0.0585079
$926$	5795.79	0.205682
$927$	−14049.7	−0.497790
$928$	21666.9	0.766433
$929$	−6557.92	−0.231602	−0.115801	−	0.993272i	$-0.536944\pi$
$929$	−6557.92	−0.231602	−0.115801	+	0.993272i	$0.536944\pi$
$930$	3654.33	0.128850
$931$	−3833.30	−0.134942
$932$	−1580.02	−0.0555314
$933$	−44370.9	−1.55695
$934$	−11094.2	−0.388665
$935$	−11707.4	−0.409491
$936$	0	0
$937$	−24473.3	−0.853265	−0.426632	−	0.904425i	$-0.640300\pi$
$937$	−24473.3	−0.853265	−0.426632	+	0.904425i	$0.640300\pi$
$938$	5101.18	0.177569
$939$	−3902.91	−0.135641
$940$	6894.46	0.239226
$941$	−15420.8	−0.534224	−0.267112	−	0.963665i	$-0.586069\pi$
$941$	−15420.8	−0.534224	−0.267112	+	0.963665i	$0.586069\pi$
$942$	1484.44	0.0513436
$943$	−3671.34	−0.126782
$944$	−28059.4	−0.967432
$945$	24328.3	0.837461
$946$	−18.4177	−0.000632993 0
$947$	33141.2	1.13722	0.568608	−	0.822609i	$-0.307482\pi$
$947$	33141.2	1.13722	0.568608	+	0.822609i	$0.307482\pi$
$948$	43285.2	1.48295
$949$	0	0
$950$	2003.20	0.0684132
$951$	−1385.47	−0.0472417
$952$	−15864.5	−0.540096
$953$	−20735.4	−0.704813	−0.352406	−	0.935847i	$-0.614637\pi$
$953$	−20735.4	−0.704813	−0.352406	+	0.935847i	$0.614637\pi$
$954$	−888.298	−0.0301464
$955$	37589.0	1.27367
$956$	32188.9	1.08898
$957$	11020.2	0.372239
$958$	−7321.32	−0.246911
$959$	3357.26	0.113046
$960$	−24202.1	−0.813666
$961$	−25501.1	−0.856000
$962$	0	0
$963$	−3942.96	−0.131942
$964$	−7438.60	−0.248528
$965$	31937.7	1.06540
$966$	−981.027	−0.0326750
$967$	8178.87	0.271990	0.135995	−	0.990710i	$-0.456577\pi$
$967$	8178.87	0.271990	0.135995	+	0.990710i	$0.456577\pi$
$968$	−1369.78	−0.0454819
$969$	−33334.2	−1.10511
$970$	−7977.08	−0.264050
$971$	−20576.1	−0.680039	−0.340020	−	0.940418i	$-0.610434\pi$
$971$	−20576.1	−0.680039	−0.340020	+	0.940418i	$0.610434\pi$
$972$	16524.1	0.545277
$973$	49094.1	1.61756
$974$	−5156.96	−0.169651
$975$	0	0
$976$	5209.55	0.170854
$977$	−14541.9	−0.476188	−0.238094	−	0.971242i	$-0.576523\pi$
$977$	−14541.9	−0.476188	−0.238094	+	0.971242i	$0.576523\pi$
$978$	6053.48	0.197923
$979$	3881.76	0.126723
$980$	5415.68	0.176528
$981$	523.277	0.0170305
$982$	−9755.62	−0.317021
$983$	29285.7	0.950223	0.475111	−	0.879926i	$-0.342408\pi$
$983$	29285.7	0.950223	0.475111	+	0.879926i	$0.342408\pi$
$984$	18450.5	0.597745
$985$	65897.7	2.13165
$986$	−10241.5	−0.330787
$987$	7210.03	0.232521
$988$	0	0
$989$	−30.5427	−0.000982004 0
$990$	843.082	0.0270655
$991$	−38085.9	−1.22083	−0.610413	−	0.792083i	$-0.708997\pi$
$991$	−38085.9	−1.22083	−0.610413	+	0.792083i	$0.708997\pi$
$992$	8397.44	0.268769
$993$	−50585.1	−1.61658
$994$	−5832.26	−0.186105
$995$	−98.8940	−0.00315090
$996$	1157.28	0.0368170
$997$	−26803.6	−0.851434	−0.425717	−	0.904856i	$-0.639978\pi$
$997$	−26803.6	−0.851434	−0.425717	+	0.904856i	$0.639978\pi$
$998$	14691.6	0.465987
$999$	4567.12	0.144642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.a.1.2		2
13.12	even	2		11.4.a.a.1.1	✓	2
39.38	odd	2		99.4.a.c.1.2		2
52.51	odd	2		176.4.a.i.1.1		2
65.12	odd	4		275.4.b.c.199.2		4
65.38	odd	4		275.4.b.c.199.3		4
65.64	even	2		275.4.a.b.1.2		2
91.90	odd	2		539.4.a.e.1.1		2
104.51	odd	2		704.4.a.n.1.2		2
104.77	even	2		704.4.a.p.1.1		2
143.25	even	10		121.4.c.c.9.1		8
143.38	even	10		121.4.c.c.3.2		8
143.51	odd	10		121.4.c.f.27.2		8
143.64	even	10		121.4.c.c.81.2		8
143.90	odd	10		121.4.c.f.81.1		8
143.103	even	10		121.4.c.c.27.1		8
143.116	odd	10		121.4.c.f.3.1		8
143.129	odd	10		121.4.c.f.9.2		8
143.142	odd	2		121.4.a.c.1.2		2
156.155	even	2		1584.4.a.bc.1.2		2
195.194	odd	2		2475.4.a.q.1.1		2
429.428	even	2		1089.4.a.v.1.1		2
572.571	even	2		1936.4.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.a.a.1.1	✓	2	13.12	even	2
99.4.a.c.1.2		2	39.38	odd	2
121.4.a.c.1.2		2	143.142	odd	2
121.4.c.c.3.2		8	143.38	even	10
121.4.c.c.9.1		8	143.25	even	10
121.4.c.c.27.1		8	143.103	even	10
121.4.c.c.81.2		8	143.64	even	10
121.4.c.f.3.1		8	143.116	odd	10
121.4.c.f.9.2		8	143.129	odd	10
121.4.c.f.27.2		8	143.51	odd	10
121.4.c.f.81.1		8	143.90	odd	10
176.4.a.i.1.1		2	52.51	odd	2
275.4.a.b.1.2		2	65.64	even	2
275.4.b.c.199.2		4	65.12	odd	4
275.4.b.c.199.3		4	65.38	odd	4
539.4.a.e.1.1		2	91.90	odd	2
704.4.a.n.1.2		2	104.51	odd	2
704.4.a.p.1.1		2	104.77	even	2
1089.4.a.v.1.1		2	429.428	even	2
1584.4.a.bc.1.2		2	156.155	even	2
1859.4.a.a.1.2		2	1.1	even	1	trivial
1936.4.a.w.1.1		2	572.571	even	2
2475.4.a.q.1.1		2	195.194	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+0.732051 q^{2} +5.92820 q^{3} -7.46410 q^{4} +12.8564 q^{5} +4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} +O(q^{10})\)	\(q+0.732051 q^{2} +5.92820 q^{3} -7.46410 q^{4} +12.8564 q^{5} +4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} +9.41154 q^{10} +11.0000 q^{11} -44.2487 q^{12} -12.3923 q^{14} +76.2154 q^{15} +51.4256 q^{16} -82.7846 q^{17} +5.96152 q^{18} +67.9230 q^{19} -95.9615 q^{20} -100.354 q^{21} +8.05256 q^{22} +13.3538 q^{23} -67.1103 q^{24} +40.2872 q^{25} -111.785 q^{27} +126.354 q^{28} +168.995 q^{29} +55.7935 q^{30} +65.4974 q^{31} +128.210 q^{32} +65.2102 q^{33} -60.6025 q^{34} -217.636 q^{35} -60.7846 q^{36} -40.8564 q^{37} +49.7231 q^{38} -145.541 q^{40} -274.928 q^{41} -73.4641 q^{42} -2.28719 q^{43} -82.1051 q^{44} +104.697 q^{45} +9.77568 q^{46} -71.8461 q^{47} +304.862 q^{48} -56.4359 q^{49} +29.4923 q^{50} -490.764 q^{51} -149.005 q^{53} -81.8320 q^{54} +141.420 q^{55} +191.636 q^{56} +402.662 q^{57} +123.713 q^{58} -545.631 q^{59} -568.879 q^{60} +101.303 q^{61} +47.9474 q^{62} -137.856 q^{63} -317.549 q^{64} +47.7372 q^{66} -411.641 q^{67} +617.913 q^{68} +79.1642 q^{69} -159.321 q^{70} +470.636 q^{71} -92.1896 q^{72} -610.600 q^{73} -29.9090 q^{74} +238.831 q^{75} -506.985 q^{76} -186.210 q^{77} -978.225 q^{79} +661.149 q^{80} -882.559 q^{81} -201.261 q^{82} -26.1539 q^{83} +749.051 q^{84} -1064.31 q^{85} -1.67434 q^{86} +1001.84 q^{87} -124.526 q^{88} +352.887 q^{89} +76.6438 q^{90} -99.6743 q^{92} +388.282 q^{93} -52.5950 q^{94} +873.246 q^{95} +760.056 q^{96} -847.585 q^{97} -41.3140 q^{98} +89.5795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} + 44 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 26 * q^6 - 20 * q^7 + 12 * q^8 + 44 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} + 44 q^{9} + 50 q^{10} + 22 q^{11} - 40 q^{12} - 4 q^{14} + 194 q^{15} - 8 q^{16} - 124 q^{17} - 92 q^{18} - 72 q^{19} - 88 q^{20} - 76 q^{21} - 22 q^{22} - 98 q^{23} - 252 q^{24} + 136 q^{25} - 182 q^{27} + 128 q^{28} + 144 q^{29} - 266 q^{30} + 34 q^{31} + 104 q^{32} - 22 q^{33} + 52 q^{34} - 172 q^{35} - 80 q^{36} - 54 q^{37} + 432 q^{38} - 492 q^{40} - 536 q^{41} - 140 q^{42} - 60 q^{43} - 88 q^{44} - 428 q^{45} + 314 q^{46} + 272 q^{47} + 776 q^{48} - 390 q^{49} - 232 q^{50} - 164 q^{51} - 492 q^{53} + 110 q^{54} - 22 q^{55} + 120 q^{56} + 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} + 840 q^{61} + 134 q^{62} - 248 q^{63} + 224 q^{64} + 286 q^{66} - 754 q^{67} + 640 q^{68} + 962 q^{69} - 284 q^{70} + 678 q^{71} + 744 q^{72} + 400 q^{73} + 6 q^{74} - 520 q^{75} - 432 q^{76} - 220 q^{77} + 316 q^{79} + 1544 q^{80} - 1294 q^{81} + 512 q^{82} - 468 q^{83} + 736 q^{84} - 452 q^{85} + 156 q^{86} + 1200 q^{87} + 132 q^{88} + 1842 q^{89} + 1532 q^{90} - 40 q^{92} + 638 q^{93} - 992 q^{94} + 2952 q^{95} + 952 q^{96} - 2194 q^{97} + 870 q^{98} + 484 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 + 26 * q^6 - 20 * q^7 + 12 * q^8 + 44 * q^9 + 50 * q^10 + 22 * q^11 - 40 * q^12 - 4 * q^14 + 194 * q^15 - 8 * q^16 - 124 * q^17 - 92 * q^18 - 72 * q^19 - 88 * q^20 - 76 * q^21 - 22 * q^22 - 98 * q^23 - 252 * q^24 + 136 * q^25 - 182 * q^27 + 128 * q^28 + 144 * q^29 - 266 * q^30 + 34 * q^31 + 104 * q^32 - 22 * q^33 + 52 * q^34 - 172 * q^35 - 80 * q^36 - 54 * q^37 + 432 * q^38 - 492 * q^40 - 536 * q^41 - 140 * q^42 - 60 * q^43 - 88 * q^44 - 428 * q^45 + 314 * q^46 + 272 * q^47 + 776 * q^48 - 390 * q^49 - 232 * q^50 - 164 * q^51 - 492 * q^53 + 110 * q^54 - 22 * q^55 + 120 * q^56 + 1512 * q^57 + 192 * q^58 - 634 * q^59 - 632 * q^60 + 840 * q^61 + 134 * q^62 - 248 * q^63 + 224 * q^64 + 286 * q^66 - 754 * q^67 + 640 * q^68 + 962 * q^69 - 284 * q^70 + 678 * q^71 + 744 * q^72 + 400 * q^73 + 6 * q^74 - 520 * q^75 - 432 * q^76 - 220 * q^77 + 316 * q^79 + 1544 * q^80 - 1294 * q^81 + 512 * q^82 - 468 * q^83 + 736 * q^84 - 452 * q^85 + 156 * q^86 + 1200 * q^87 + 132 * q^88 + 1842 * q^89 + 1532 * q^90 - 40 * q^92 + 638 * q^93 - 992 * q^94 + 2952 * q^95 + 952 * q^96 - 2194 * q^97 + 870 * q^98 + 484 * q^99

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