LMFDB - Embedded newform 1859.4.a.f.1.14

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + \cdots + 2596992 $ x^17 - 4x^16 - 99x^15 + 375x^14 + 3949x^13 - 13998x^12 - 81750x^11 + 267574x^10 + 941923x^9 - 2799440x^8 - 6021311x^7 + 15765187x^6 + 20197463x^5 - 42560950x^4 - 32766128x^3 + 37775816x^2 + 27375104x + 2596992
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-3.21160$ 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)

$f(q)$	$=$	$q+3.21160 q^{2} -6.73941 q^{3} +2.31437 q^{4} -9.24473 q^{5} -21.6443 q^{6} -8.56428 q^{7} -18.2600 q^{8} +18.4196 q^{9} +O(q^{10})$	\(q+3.21160 q^{2} -6.73941 q^{3} +2.31437 q^{4} -9.24473 q^{5} -21.6443 q^{6} -8.56428 q^{7} -18.2600 q^{8} +18.4196 q^{9} -29.6904 q^{10} +11.0000 q^{11} -15.5975 q^{12} -27.5051 q^{14} +62.3040 q^{15} -77.1587 q^{16} +1.99463 q^{17} +59.1564 q^{18} +77.2727 q^{19} -21.3958 q^{20} +57.7182 q^{21} +35.3276 q^{22} +145.746 q^{23} +123.061 q^{24} -39.5350 q^{25} +57.8267 q^{27} -19.8210 q^{28} +131.935 q^{29} +200.096 q^{30} +116.933 q^{31} -101.723 q^{32} -74.1335 q^{33} +6.40596 q^{34} +79.1745 q^{35} +42.6299 q^{36} +312.226 q^{37} +248.169 q^{38} +168.808 q^{40} -266.525 q^{41} +185.368 q^{42} -27.4479 q^{43} +25.4581 q^{44} -170.284 q^{45} +468.079 q^{46} -429.212 q^{47} +520.004 q^{48} -269.653 q^{49} -126.970 q^{50} -13.4426 q^{51} +394.864 q^{53} +185.716 q^{54} -101.692 q^{55} +156.383 q^{56} -520.772 q^{57} +423.721 q^{58} -602.657 q^{59} +144.195 q^{60} +123.518 q^{61} +375.543 q^{62} -157.751 q^{63} +290.575 q^{64} -238.087 q^{66} -795.530 q^{67} +4.61633 q^{68} -982.244 q^{69} +254.277 q^{70} +717.265 q^{71} -336.341 q^{72} -333.884 q^{73} +1002.75 q^{74} +266.442 q^{75} +178.838 q^{76} -94.2071 q^{77} -153.521 q^{79} +713.311 q^{80} -887.047 q^{81} -855.972 q^{82} +481.440 q^{83} +133.582 q^{84} -18.4398 q^{85} -88.1518 q^{86} -889.161 q^{87} -200.859 q^{88} +574.872 q^{89} -546.885 q^{90} +337.312 q^{92} -788.062 q^{93} -1378.46 q^{94} -714.365 q^{95} +685.554 q^{96} +1130.45 q^{97} -866.018 q^{98} +202.616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 95 q^{12} - 60 q^{14} + 28 q^{15} + 350 q^{16} + 118 q^{17} - 478 q^{18} - 403 q^{19} - 98 q^{20} - 220 q^{21} - 44 q^{22} - 215 q^{23} - 26 q^{24} + 319 q^{25} - 384 q^{27} + 396 q^{28} - 7 q^{29} - 1269 q^{30} - 682 q^{31} - 813 q^{32} - 66 q^{33} - 738 q^{34} + 10 q^{35} + 560 q^{36} - 1084 q^{37} + 410 q^{38} + 95 q^{40} - 240 q^{41} + 393 q^{42} - 435 q^{43} + 858 q^{44} - 1242 q^{45} - 1671 q^{46} - 549 q^{47} + 894 q^{48} + 403 q^{49} + 651 q^{50} + 1552 q^{51} - 566 q^{53} - 311 q^{54} - 176 q^{55} - 1925 q^{56} + 534 q^{57} - 618 q^{58} - 2010 q^{59} + 411 q^{60} + 460 q^{61} - 823 q^{62} - 820 q^{63} + 3171 q^{64} - 154 q^{66} + 232 q^{67} + 1795 q^{68} - 1608 q^{69} - 207 q^{70} - 489 q^{71} - 2556 q^{72} - 290 q^{73} + 2653 q^{74} - 2852 q^{75} - 2421 q^{76} + 66 q^{77} - 732 q^{79} - 4915 q^{80} + 2393 q^{81} - 1772 q^{82} + 117 q^{83} - 4161 q^{84} - 4858 q^{85} - 1034 q^{86} + 3032 q^{87} - 693 q^{88} - 4113 q^{89} + 15145 q^{90} - 3554 q^{92} - 802 q^{93} + 2325 q^{94} - 3924 q^{95} - 2601 q^{96} - 2793 q^{97} - 533 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 95 * q^12 - 60 * q^14 + 28 * q^15 + 350 * q^16 + 118 * q^17 - 478 * q^18 - 403 * q^19 - 98 * q^20 - 220 * q^21 - 44 * q^22 - 215 * q^23 - 26 * q^24 + 319 * q^25 - 384 * q^27 + 396 * q^28 - 7 * q^29 - 1269 * q^30 - 682 * q^31 - 813 * q^32 - 66 * q^33 - 738 * q^34 + 10 * q^35 + 560 * q^36 - 1084 * q^37 + 410 * q^38 + 95 * q^40 - 240 * q^41 + 393 * q^42 - 435 * q^43 + 858 * q^44 - 1242 * q^45 - 1671 * q^46 - 549 * q^47 + 894 * q^48 + 403 * q^49 + 651 * q^50 + 1552 * q^51 - 566 * q^53 - 311 * q^54 - 176 * q^55 - 1925 * q^56 + 534 * q^57 - 618 * q^58 - 2010 * q^59 + 411 * q^60 + 460 * q^61 - 823 * q^62 - 820 * q^63 + 3171 * q^64 - 154 * q^66 + 232 * q^67 + 1795 * q^68 - 1608 * q^69 - 207 * q^70 - 489 * q^71 - 2556 * q^72 - 290 * q^73 + 2653 * q^74 - 2852 * q^75 - 2421 * q^76 + 66 * q^77 - 732 * q^79 - 4915 * q^80 + 2393 * q^81 - 1772 * q^82 + 117 * q^83 - 4161 * q^84 - 4858 * q^85 - 1034 * q^86 + 3032 * q^87 - 693 * q^88 - 4113 * q^89 + 15145 * q^90 - 3554 * q^92 - 802 * q^93 + 2325 * q^94 - 3924 * q^95 - 2601 * q^96 - 2793 * q^97 - 533 * q^98 + 1485 * 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 $

$2$	3.21160	1.13547	0.567736	−	0.823211i	$-0.307819\pi$
$2$	3.21160	1.13547	0.567736	+	0.823211i	$0.307819\pi$
$3$	−6.73941	−1.29700	−0.648500	−	0.761215i	$-0.724603\pi$
$3$	−6.73941	−1.29700	−0.648500	+	0.761215i	$0.724603\pi$
$4$	2.31437	0.289297
$5$	−9.24473	−0.826874	−0.413437	−	0.910533i	$-0.635672\pi$
$5$	−9.24473	−0.826874	−0.413437	+	0.910533i	$0.635672\pi$
$6$	−21.6443	−1.47271
$7$	−8.56428	−0.462428	−0.231214	−	0.972903i	$-0.574270\pi$
$7$	−8.56428	−0.462428	−0.231214	+	0.972903i	$0.574270\pi$
$8$	−18.2600	−0.806984
$9$	18.4196	0.682208
$10$	−29.6904	−0.938892
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−15.5975	−0.375218
$13$	0	0
$13$	0	0
$14$	−27.5051	−0.525074
$15$	62.3040	1.07246
$16$	−77.1587	−1.20560
$17$	1.99463	0.0284570	0.0142285	−	0.999899i	$-0.495471\pi$
$17$	1.99463	0.0284570	0.0142285	+	0.999899i	$0.495471\pi$
$18$	59.1564	0.774628
$19$	77.2727	0.933030	0.466515	−	0.884513i	$-0.345509\pi$
$19$	77.2727	0.933030	0.466515	+	0.884513i	$0.345509\pi$
$20$	−21.3958	−0.239212
$21$	57.7182	0.599769
$22$	35.3276	0.342358
$23$	145.746	1.32131	0.660657	−	0.750688i	$-0.270278\pi$
$23$	145.746	1.32131	0.660657	+	0.750688i	$0.270278\pi$
$24$	123.061	1.04666
$25$	−39.5350	−0.316280
$26$	0	0
$27$	57.8267	0.412176
$28$	−19.8210	−0.133779
$29$	131.935	0.844815	0.422407	−	0.906406i	$-0.361185\pi$
$29$	131.935	0.844815	0.422407	+	0.906406i	$0.361185\pi$
$30$	200.096	1.21774
$31$	116.933	0.677480	0.338740	−	0.940880i	$-0.389999\pi$
$31$	116.933	0.677480	0.338740	+	0.940880i	$0.389999\pi$
$32$	−101.723	−0.561946
$33$	−74.1335	−0.391060
$34$	6.40596	0.0323122
$35$	79.1745	0.382369
$36$	42.6299	0.197361
$37$	312.226	1.38729	0.693645	−	0.720317i	$-0.256004\pi$
$37$	312.226	1.38729	0.693645	+	0.720317i	$0.256004\pi$
$38$	248.169	1.05943
$39$	0	0
$40$	168.808	0.667274
$41$	−266.525	−1.01522	−0.507612	−	0.861586i	$-0.669472\pi$
$41$	−266.525	−1.01522	−0.507612	+	0.861586i	$0.669472\pi$
$42$	185.368	0.681021
$43$	−27.4479	−0.0973435	−0.0486718	−	0.998815i	$-0.515499\pi$
$43$	−27.4479	−0.0973435	−0.0486718	+	0.998815i	$0.515499\pi$
$44$	25.4581	0.0872263
$45$	−170.284	−0.564100
$46$	468.079	1.50031
$47$	−429.212	−1.33207	−0.666033	−	0.745923i	$-0.732009\pi$
$47$	−429.212	−1.33207	−0.666033	+	0.745923i	$0.732009\pi$
$48$	520.004	1.56367
$49$	−269.653	−0.786160
$50$	−126.970	−0.359127
$51$	−13.4426	−0.0369087
$52$	0	0
$53$	394.864	1.02337	0.511686	−	0.859173i	$-0.329021\pi$
$53$	394.864	1.02337	0.511686	+	0.859173i	$0.329021\pi$
$54$	185.716	0.468014
$55$	−101.692	−0.249312
$56$	156.383	0.373172
$57$	−520.772	−1.21014
$58$	423.721	0.959264
$59$	−602.657	−1.32982	−0.664908	−	0.746925i	$-0.731529\pi$
$59$	−602.657	−1.32982	−0.664908	+	0.746925i	$0.731529\pi$
$60$	144.195	0.310258
$61$	123.518	0.259260	0.129630	−	0.991562i	$-0.458621\pi$
$61$	123.518	0.259260	0.129630	+	0.991562i	$0.458621\pi$
$62$	375.543	0.769259
$63$	−157.751	−0.315472
$64$	290.575	0.567530
$65$	0	0
$66$	−238.087	−0.444038
$67$	−795.530	−1.45059	−0.725295	−	0.688438i	$-0.758297\pi$
$67$	−795.530	−1.45059	−0.725295	+	0.688438i	$0.758297\pi$
$68$	4.61633	0.00823253
$69$	−982.244	−1.71374
$70$	254.277	0.434170
$71$	717.265	1.19892	0.599462	−	0.800403i	$-0.295381\pi$
$71$	717.265	1.19892	0.599462	+	0.800403i	$0.295381\pi$
$72$	−336.341	−0.550531
$73$	−333.884	−0.535317	−0.267659	−	0.963514i	$-0.586250\pi$
$73$	−333.884	−0.535317	−0.267659	+	0.963514i	$0.586250\pi$
$74$	1002.75	1.57523
$75$	266.442	0.410215
$76$	178.838	0.269923
$77$	−94.2071	−0.139427
$78$	0	0
$79$	−153.521	−0.218639	−0.109320	−	0.994007i	$-0.534867\pi$
$79$	−153.521	−0.218639	−0.109320	+	0.994007i	$0.534867\pi$
$80$	713.311	0.996883
$81$	−887.047	−1.21680
$82$	−855.972	−1.15276
$83$	481.440	0.636686	0.318343	−	0.947976i	$-0.396874\pi$
$83$	481.440	0.636686	0.318343	+	0.947976i	$0.396874\pi$
$84$	133.582	0.173511
$85$	−18.4398	−0.0235304
$86$	−88.1518	−0.110531
$87$	−889.161	−1.09572
$88$	−200.859	−0.243315
$89$	574.872	0.684678	0.342339	−	0.939576i	$-0.388781\pi$
$89$	574.872	0.684678	0.342339	+	0.939576i	$0.388781\pi$
$90$	−546.885	−0.640520
$91$	0	0
$92$	337.312	0.382252
$93$	−788.062	−0.878691
$94$	−1378.46	−1.51252
$95$	−714.365	−0.771498
$96$	685.554	0.728844
$97$	1130.45	1.18330	0.591648	−	0.806197i	$-0.298478\pi$
$97$	1130.45	1.18330	0.591648	+	0.806197i	$0.298478\pi$
$98$	−866.018	−0.892663
$99$	202.616	0.205693
$100$	−91.4987	−0.0914987
$101$	461.040	0.454210	0.227105	−	0.973870i	$-0.427074\pi$
$101$	461.040	0.454210	0.227105	+	0.973870i	$0.427074\pi$
$102$	−43.1724	−0.0419088
$103$	−580.574	−0.555395	−0.277697	−	0.960669i	$-0.589571\pi$
$103$	−580.574	−0.555395	−0.277697	+	0.960669i	$0.589571\pi$
$104$	0	0
$105$	−533.589	−0.495933
$106$	1268.14	1.16201
$107$	−683.349	−0.617400	−0.308700	−	0.951159i	$-0.599894\pi$
$107$	−683.349	−0.617400	−0.308700	+	0.951159i	$0.599894\pi$
$108$	133.833	0.119241
$109$	1291.27	1.13469	0.567343	−	0.823481i	$-0.307971\pi$
$109$	1291.27	1.13469	0.567343	+	0.823481i	$0.307971\pi$
$110$	−326.594	−0.283087
$111$	−2104.22	−1.79931
$112$	660.809	0.557505
$113$	1253.84	1.04382	0.521911	−	0.853000i	$-0.325219\pi$
$113$	1253.84	1.04382	0.521911	+	0.853000i	$0.325219\pi$
$114$	−1672.51	−1.37408
$115$	−1347.39	−1.09256
$116$	305.346	0.244402
$117$	0	0
$118$	−1935.49	−1.50997
$119$	−17.0826	−0.0131593
$120$	−1137.67	−0.865454
$121$	121.000	0.0909091
$122$	396.691	0.294383
$123$	1796.22	1.31675
$124$	270.628	0.195993
$125$	1521.08	1.08840
$126$	−506.633	−0.358210
$127$	388.885	0.271716	0.135858	−	0.990728i	$-0.456621\pi$
$127$	388.885	0.271716	0.135858	+	0.990728i	$0.456621\pi$
$128$	1747.00	1.20636
$129$	184.983	0.126255
$130$	0	0
$131$	−1576.22	−1.05126	−0.525630	−	0.850713i	$-0.676170\pi$
$131$	−1576.22	−1.05126	−0.525630	+	0.850713i	$0.676170\pi$
$132$	−171.573	−0.113132
$133$	−661.785	−0.431459
$134$	−2554.93	−1.64710
$135$	−534.592	−0.340818
$136$	−36.4219	−0.0229643
$137$	−1922.54	−1.19894	−0.599468	−	0.800399i	$-0.704621\pi$
$137$	−1922.54	−1.19894	−0.599468	+	0.800399i	$0.704621\pi$
$138$	−3154.57	−1.94591
$139$	−1258.35	−0.767855	−0.383928	−	0.923363i	$-0.625429\pi$
$139$	−1258.35	−0.767855	−0.383928	+	0.923363i	$0.625429\pi$
$140$	183.239	0.110618
$141$	2892.64	1.72769
$142$	2303.57	1.36135
$143$	0	0
$144$	−1421.23	−0.822473
$145$	−1219.70	−0.698555
$146$	−1072.30	−0.607838
$147$	1817.30	1.01965
$148$	722.609	0.401339
$149$	−2798.52	−1.53868	−0.769341	−	0.638838i	$-0.779415\pi$
$149$	−2798.52	−1.53868	−0.769341	+	0.638838i	$0.779415\pi$
$150$	855.706	0.465787
$151$	975.206	0.525570	0.262785	−	0.964854i	$-0.415359\pi$
$151$	975.206	0.525570	0.262785	+	0.964854i	$0.415359\pi$
$152$	−1411.00	−0.752940
$153$	36.7404	0.0194136
$154$	−302.556	−0.158316
$155$	−1081.02	−0.560190
$156$	0	0
$157$	−1106.70	−0.562574	−0.281287	−	0.959624i	$-0.590761\pi$
$157$	−1106.70	−0.562574	−0.281287	+	0.959624i	$0.590761\pi$
$158$	−493.049	−0.248259
$159$	−2661.15	−1.32731
$160$	940.403	0.464659
$161$	−1248.21	−0.611012
$162$	−2848.84	−1.38164
$163$	1971.65	0.947435	0.473718	−	0.880677i	$-0.342912\pi$
$163$	1971.65	0.947435	0.473718	+	0.880677i	$0.342912\pi$
$164$	−616.839	−0.293701
$165$	685.344	0.323357
$166$	1546.19	0.722939
$167$	−2383.32	−1.10435	−0.552176	−	0.833727i	$-0.686202\pi$
$167$	−2383.32	−1.10435	−0.552176	+	0.833727i	$0.686202\pi$
$168$	−1053.93	−0.484004
$169$	0	0
$170$	−59.2214	−0.0267181
$171$	1423.33	0.636520
$172$	−63.5248	−0.0281612
$173$	−139.292	−0.0612150	−0.0306075	−	0.999531i	$-0.509744\pi$
$173$	−139.292	−0.0612150	−0.0306075	+	0.999531i	$0.509744\pi$
$174$	−2855.63	−1.24416
$175$	338.589	0.146257
$176$	−848.745	−0.363503
$177$	4061.55	1.72477
$178$	1846.26	0.777433
$179$	−1339.42	−0.559288	−0.279644	−	0.960104i	$-0.590216\pi$
$179$	−1339.42	−0.559288	−0.279644	+	0.960104i	$0.590216\pi$
$180$	−394.102	−0.163192
$181$	406.144	0.166787	0.0833934	−	0.996517i	$-0.473424\pi$
$181$	406.144	0.166787	0.0833934	+	0.996517i	$0.473424\pi$
$182$	0	0
$183$	−832.439	−0.336260
$184$	−2661.32	−1.06628
$185$	−2886.45	−1.14711
$186$	−2530.94	−0.997729
$187$	21.9410	0.00858011
$188$	−993.359	−0.385362
$189$	−495.244	−0.190602
$190$	−2294.25	−0.876014
$191$	−3639.43	−1.37874	−0.689372	−	0.724407i	$-0.742113\pi$
$191$	−3639.43	−1.37874	−0.689372	+	0.724407i	$0.742113\pi$
$192$	−1958.31	−0.736086
$193$	−3788.87	−1.41310	−0.706551	−	0.707662i	$-0.749750\pi$
$193$	−3788.87	−1.41310	−0.706551	+	0.707662i	$0.749750\pi$
$194$	3630.55	1.34360
$195$	0	0
$196$	−624.078	−0.227434
$197$	−1540.65	−0.557191	−0.278596	−	0.960408i	$-0.589869\pi$
$197$	−1540.65	−0.557191	−0.278596	+	0.960408i	$0.589869\pi$
$198$	650.721	0.233559
$199$	2444.24	0.870693	0.435346	−	0.900263i	$-0.356626\pi$
$199$	2444.24	0.870693	0.435346	+	0.900263i	$0.356626\pi$
$200$	721.907	0.255233
$201$	5361.40	1.88141
$202$	1480.68	0.515743
$203$	−1129.93	−0.390666
$204$	−31.1113	−0.0106776
$205$	2463.95	0.839463
$206$	−1864.57	−0.630635
$207$	2684.59	0.901410
$208$	0	0
$209$	849.999	0.281319
$210$	−1713.68	−0.563118
$211$	−4611.86	−1.50471	−0.752354	−	0.658759i	$-0.771081\pi$
$211$	−4611.86	−1.50471	−0.752354	+	0.658759i	$0.771081\pi$
$212$	913.863	0.296058
$213$	−4833.94	−1.55501
$214$	−2194.64	−0.701041
$215$	253.749	0.0804908
$216$	−1055.91	−0.332619
$217$	−1001.45	−0.313285
$218$	4147.03	1.28840
$219$	2250.18	0.694306
$220$	−235.353	−0.0721251
$221$	0	0
$222$	−6757.92	−2.04307
$223$	−5600.05	−1.68164	−0.840822	−	0.541311i	$-0.817928\pi$
$223$	−5600.05	−1.68164	−0.840822	+	0.541311i	$0.817928\pi$
$224$	871.186	0.259860
$225$	−728.219	−0.215769
$226$	4026.85	1.18523
$227$	−701.211	−0.205026	−0.102513	−	0.994732i	$-0.532688\pi$
$227$	−701.211	−0.205026	−0.102513	+	0.994732i	$0.532688\pi$
$228$	−1205.26	−0.350090
$229$	−3026.57	−0.873369	−0.436684	−	0.899615i	$-0.643847\pi$
$229$	−3026.57	−0.873369	−0.436684	+	0.899615i	$0.643847\pi$
$230$	−4327.26	−1.24057
$231$	634.900	0.180837
$232$	−2409.12	−0.681752
$233$	3061.71	0.860855	0.430427	−	0.902625i	$-0.358363\pi$
$233$	3061.71	0.860855	0.430427	+	0.902625i	$0.358363\pi$
$234$	0	0
$235$	3967.95	1.10145
$236$	−1394.77	−0.384712
$237$	1034.64	0.283575
$238$	−54.8625	−0.0149420
$239$	5192.19	1.40525	0.702625	−	0.711560i	$-0.252011\pi$
$239$	5192.19	1.40525	0.702625	+	0.711560i	$0.252011\pi$
$240$	−4807.29	−1.29296
$241$	4479.41	1.19728	0.598639	−	0.801019i	$-0.295708\pi$
$241$	4479.41	1.19728	0.598639	+	0.801019i	$0.295708\pi$
$242$	388.604	0.103225
$243$	4416.85	1.16601
$244$	285.867	0.0750032
$245$	2492.87	0.650056
$246$	5768.74	1.49513
$247$	0	0
$248$	−2135.20	−0.546715
$249$	−3244.62	−0.825781
$250$	4885.10	1.23584
$251$	4328.58	1.08852	0.544258	−	0.838918i	$-0.316811\pi$
$251$	4328.58	1.08852	0.544258	+	0.838918i	$0.316811\pi$
$252$	−365.095	−0.0912651
$253$	1603.21	0.398391
$254$	1248.94	0.308526
$255$	124.274	0.0305189
$256$	3286.05	0.802259
$257$	−5438.32	−1.31997	−0.659987	−	0.751277i	$-0.729438\pi$
$257$	−5438.32	−1.31997	−0.659987	+	0.751277i	$0.729438\pi$
$258$	594.091	0.143358
$259$	−2674.00	−0.641521
$260$	0	0
$261$	2430.18	0.576340
$262$	−5062.19	−1.19368
$263$	−1546.93	−0.362691	−0.181346	−	0.983419i	$-0.558045\pi$
$263$	−1546.93	−0.362691	−0.181346	+	0.983419i	$0.558045\pi$
$264$	1353.67	0.315579
$265$	−3650.41	−0.846199
$266$	−2125.39	−0.489910
$267$	−3874.30	−0.888027
$268$	−1841.16	−0.419651
$269$	8395.89	1.90300	0.951499	−	0.307653i	$-0.0995436\pi$
$269$	8395.89	1.90300	0.951499	+	0.307653i	$0.0995436\pi$
$270$	−1716.90	−0.386989
$271$	438.196	0.0982233	0.0491117	−	0.998793i	$-0.484361\pi$
$271$	438.196	0.0982233	0.0491117	+	0.998793i	$0.484361\pi$
$272$	−153.903	−0.0343079
$273$	0	0
$274$	−6174.45	−1.36136
$275$	−434.885	−0.0953619
$276$	−2273.28	−0.495780
$277$	7314.57	1.58661	0.793303	−	0.608828i	$-0.208360\pi$
$277$	7314.57	1.58661	0.793303	+	0.608828i	$0.208360\pi$
$278$	−4041.32	−0.871878
$279$	2153.87	0.462182
$280$	−1445.72	−0.308566
$281$	−6581.82	−1.39729	−0.698645	−	0.715468i	$-0.746213\pi$
$281$	−6581.82	−1.39729	−0.698645	+	0.715468i	$0.746213\pi$
$282$	9290.00	1.96174
$283$	−2890.91	−0.607233	−0.303617	−	0.952794i	$-0.598194\pi$
$283$	−2890.91	−0.607233	−0.303617	+	0.952794i	$0.598194\pi$
$284$	1660.02	0.346845
$285$	4814.40	1.00063
$286$	0	0
$287$	2282.60	0.469468
$288$	−1873.70	−0.383364
$289$	−4909.02	−0.999190
$290$	−3917.19	−0.793190
$291$	−7618.55	−1.53473
$292$	−772.732	−0.154866
$293$	1325.21	0.264231	0.132116	−	0.991234i	$-0.457823\pi$
$293$	1325.21	0.264231	0.132116	+	0.991234i	$0.457823\pi$
$294$	5836.45	1.15778
$295$	5571.40	1.09959
$296$	−5701.24	−1.11952
$297$	636.094	0.124276
$298$	−8987.73	−1.74713
$299$	0	0
$300$	616.647	0.118674
$301$	235.072	0.0450144
$302$	3131.97	0.596770
$303$	−3107.14	−0.589111
$304$	−5962.26	−1.12486
$305$	−1141.89	−0.214375
$306$	117.995	0.0220436
$307$	8918.33	1.65797	0.828983	−	0.559273i	$-0.188920\pi$
$307$	8918.33	1.65797	0.828983	+	0.559273i	$0.188920\pi$
$308$	−218.031	−0.0403359
$309$	3912.72	0.720347
$310$	−3471.80	−0.636080
$311$	4670.84	0.851637	0.425819	−	0.904809i	$-0.359986\pi$
$311$	4670.84	0.851637	0.425819	+	0.904809i	$0.359986\pi$
$312$	0	0
$313$	−647.440	−0.116918	−0.0584592	−	0.998290i	$-0.518619\pi$
$313$	−647.440	−0.116918	−0.0584592	+	0.998290i	$0.518619\pi$
$314$	−3554.27	−0.638788
$315$	1458.36	0.260856
$316$	−355.306	−0.0632517
$317$	−4557.80	−0.807544	−0.403772	−	0.914860i	$-0.632301\pi$
$317$	−4557.80	−0.807544	−0.403772	+	0.914860i	$0.632301\pi$
$318$	−8546.54	−1.50713
$319$	1451.28	0.254721
$320$	−2686.29	−0.469276
$321$	4605.37	0.800768
$322$	−4008.76	−0.693787
$323$	154.131	0.0265513
$324$	−2052.96	−0.352016
$325$	0	0
$326$	6332.17	1.07579
$327$	−8702.37	−1.47169
$328$	4866.73	0.819269
$329$	3675.90	0.615984
$330$	2201.05	0.367163
$331$	−5474.03	−0.909004	−0.454502	−	0.890746i	$-0.650183\pi$
$331$	−5474.03	−0.909004	−0.454502	+	0.890746i	$0.650183\pi$
$332$	1114.23	0.184191
$333$	5751.09	0.946420
$334$	−7654.27	−1.25396
$335$	7354.46	1.19945
$336$	−4453.46	−0.723084
$337$	3545.64	0.573126	0.286563	−	0.958061i	$-0.407487\pi$
$337$	3545.64	0.573126	0.286563	+	0.958061i	$0.407487\pi$
$338$	0	0
$339$	−8450.17	−1.35384
$340$	−42.6767	−0.00680726
$341$	1286.27	0.204268
$342$	4571.18	0.722751
$343$	5246.93	0.825970
$344$	501.198	0.0785546
$345$	9080.58	1.41705
$346$	−447.351	−0.0695080
$347$	3053.35	0.472370	0.236185	−	0.971708i	$-0.424103\pi$
$347$	3053.35	0.472370	0.236185	+	0.971708i	$0.424103\pi$
$348$	−2057.85	−0.316990
$349$	2662.74	0.408405	0.204202	−	0.978929i	$-0.434540\pi$
$349$	2662.74	0.408405	0.204202	+	0.978929i	$0.434540\pi$
$350$	1087.41	0.166070
$351$	0	0
$352$	−1118.95	−0.169433
$353$	−6213.06	−0.936793	−0.468396	−	0.883518i	$-0.655168\pi$
$353$	−6213.06	−0.936793	−0.468396	+	0.883518i	$0.655168\pi$
$354$	13044.1	1.95843
$355$	−6630.92	−0.991360
$356$	1330.47	0.198075
$357$	115.127	0.0170676
$358$	−4301.67	−0.635056
$359$	9377.86	1.37868	0.689338	−	0.724440i	$-0.257902\pi$
$359$	9377.86	1.37868	0.689338	+	0.724440i	$0.257902\pi$
$360$	3109.38	0.455219
$361$	−887.933	−0.129455
$362$	1304.37	0.189382
$363$	−815.468	−0.117909
$364$	0	0
$365$	3086.67	0.442640
$366$	−2673.46	−0.381814
$367$	−363.670	−0.0517259	−0.0258630	−	0.999665i	$-0.508233\pi$
$367$	−363.670	−0.0517259	−0.0258630	+	0.999665i	$0.508233\pi$
$368$	−11245.6	−1.59298
$369$	−4909.29	−0.692594
$370$	−9270.12	−1.30252
$371$	−3381.73	−0.473236
$372$	−1823.87	−0.254202
$373$	−12088.5	−1.67806	−0.839032	−	0.544082i	$-0.816878\pi$
$373$	−12088.5	−1.67806	−0.839032	+	0.544082i	$0.816878\pi$
$374$	70.4656	0.00974248
$375$	−10251.2	−1.41165
$376$	7837.40	1.07495
$377$	0	0
$378$	−1590.53	−0.216423
$379$	1150.70	0.155956	0.0779779	−	0.996955i	$-0.475154\pi$
$379$	1150.70	0.155956	0.0779779	+	0.996955i	$0.475154\pi$
$380$	−1653.31	−0.223192
$381$	−2620.85	−0.352416
$382$	−11688.4	−1.56553
$383$	−846.632	−0.112953	−0.0564763	−	0.998404i	$-0.517987\pi$
$383$	−846.632	−0.112953	−0.0564763	+	0.998404i	$0.517987\pi$
$384$	−11773.7	−1.56465
$385$	870.919	0.115289
$386$	−12168.3	−1.60454
$387$	−505.580	−0.0664085
$388$	2616.28	0.342324
$389$	13178.1	1.71763	0.858815	−	0.512287i	$-0.171201\pi$
$389$	13178.1	1.71763	0.858815	+	0.512287i	$0.171201\pi$
$390$	0	0
$391$	290.710	0.0376006
$392$	4923.85	0.634419
$393$	10622.8	1.36348
$394$	−4947.95	−0.632675
$395$	1419.26	0.180787
$396$	468.929	0.0595065
$397$	7696.35	0.972969	0.486485	−	0.873689i	$-0.338279\pi$
$397$	7696.35	0.972969	0.486485	+	0.873689i	$0.338279\pi$
$398$	7849.93	0.988647
$399$	4460.04	0.559602
$400$	3050.47	0.381308
$401$	−14669.0	−1.82677	−0.913385	−	0.407096i	$-0.866541\pi$
$401$	−14669.0	−1.82677	−0.913385	+	0.407096i	$0.866541\pi$
$402$	17218.7	2.13629
$403$	0	0
$404$	1067.02	0.131402
$405$	8200.51	1.00614
$406$	−3628.87	−0.443590
$407$	3434.49	0.418284
$408$	245.462	0.0297848
$409$	−11158.9	−1.34907	−0.674536	−	0.738242i	$-0.735656\pi$
$409$	−11158.9	−1.34907	−0.674536	+	0.738242i	$0.735656\pi$
$410$	7913.23	0.953186
$411$	12956.8	1.55502
$412$	−1343.67	−0.160674
$413$	5161.32	0.614944
$414$	8621.83	1.02353
$415$	−4450.78	−0.526459
$416$	0	0
$417$	8480.53	0.995908
$418$	2729.86	0.319430
$419$	−10288.0	−1.19952	−0.599761	−	0.800179i	$-0.704738\pi$
$419$	−10288.0	−1.19952	−0.599761	+	0.800179i	$0.704738\pi$
$420$	−1234.93	−0.143472
$421$	1337.37	0.154821	0.0774105	−	0.996999i	$-0.475335\pi$
$421$	1337.37	0.154821	0.0774105	+	0.996999i	$0.475335\pi$
$422$	−14811.4	−1.70855
$423$	−7905.93	−0.908746
$424$	−7210.19	−0.825844
$425$	−78.8577	−0.00900038
$426$	−15524.7	−1.76566
$427$	−1057.84	−0.119889
$428$	−1581.53	−0.178612
$429$	0	0
$430$	814.940	0.0913951
$431$	10370.3	1.15898	0.579489	−	0.814980i	$-0.303252\pi$
$431$	10370.3	1.15898	0.579489	+	0.814980i	$0.303252\pi$
$432$	−4461.83	−0.496921
$433$	−2694.83	−0.299089	−0.149544	−	0.988755i	$-0.547781\pi$
$433$	−2694.83	−0.299089	−0.149544	+	0.988755i	$0.547781\pi$
$434$	−3216.26	−0.355727
$435$	8220.05	0.906026
$436$	2988.47	0.328261
$437$	11262.2	1.23282
$438$	7226.68	0.788365
$439$	4828.74	0.524973	0.262486	−	0.964936i	$-0.415458\pi$
$439$	4828.74	0.524973	0.262486	+	0.964936i	$0.415458\pi$
$440$	1856.89	0.201191
$441$	−4966.91	−0.536325
$442$	0	0
$443$	−7476.20	−0.801817	−0.400909	−	0.916118i	$-0.631305\pi$
$443$	−7476.20	−0.801817	−0.400909	+	0.916118i	$0.631305\pi$
$444$	−4869.96	−0.520536
$445$	−5314.54	−0.566142
$446$	−17985.1	−1.90946
$447$	18860.4	1.99567
$448$	−2488.57	−0.262442
$449$	−5959.28	−0.626360	−0.313180	−	0.949694i	$-0.601394\pi$
$449$	−5959.28	−0.626360	−0.313180	+	0.949694i	$0.601394\pi$
$450$	−2338.75	−0.244999
$451$	−2931.77	−0.306102
$452$	2901.87	0.301974
$453$	−6572.31	−0.681664
$454$	−2252.01	−0.232802
$455$	0	0
$456$	9509.27	0.976563
$457$	9440.50	0.966320	0.483160	−	0.875532i	$-0.339489\pi$
$457$	9440.50	0.966320	0.483160	+	0.875532i	$0.339489\pi$
$458$	−9720.13	−0.991686
$459$	115.343	0.0117293
$460$	−3118.35	−0.316074
$461$	−7591.85	−0.767002	−0.383501	−	0.923541i	$-0.625282\pi$
$461$	−7591.85	−0.767002	−0.383501	+	0.923541i	$0.625282\pi$
$462$	2039.05	0.205335
$463$	−16829.6	−1.68928	−0.844639	−	0.535336i	$-0.820185\pi$
$463$	−16829.6	−1.68928	−0.844639	+	0.535336i	$0.820185\pi$
$464$	−10179.9	−1.01851
$465$	7285.42	0.726566
$466$	9832.98	0.977476
$467$	−8679.62	−0.860054	−0.430027	−	0.902816i	$-0.641496\pi$
$467$	−8679.62	−0.860054	−0.430027	+	0.902816i	$0.641496\pi$
$468$	0	0
$469$	6813.15	0.670793
$470$	12743.5	1.25067
$471$	7458.50	0.729659
$472$	11004.5	1.07314
$473$	−301.927	−0.0293502
$474$	3322.86	0.321992
$475$	−3054.97	−0.295098
$476$	−39.5355	−0.00380695
$477$	7273.24	0.698152
$478$	16675.2	1.59562
$479$	−12084.5	−1.15272	−0.576362	−	0.817194i	$-0.695528\pi$
$479$	−12084.5	−1.15272	−0.576362	+	0.817194i	$0.695528\pi$
$480$	−6337.76	−0.602662
$481$	0	0
$482$	14386.1	1.35948
$483$	8412.21	0.792482
$484$	280.039	0.0262997
$485$	−10450.7	−0.978436
$486$	14185.2	1.32398
$487$	7072.90	0.658118	0.329059	−	0.944309i	$-0.393268\pi$
$487$	7072.90	0.658118	0.329059	+	0.944309i	$0.393268\pi$
$488$	−2255.44	−0.209219
$489$	−13287.8	−1.22882
$490$	8006.10	0.738120
$491$	19698.9	1.81059	0.905294	−	0.424786i	$-0.139651\pi$
$491$	19698.9	1.81059	0.905294	+	0.424786i	$0.139651\pi$
$492$	4157.13	0.380930
$493$	263.161	0.0240409
$494$	0	0
$495$	−1873.13	−0.170083
$496$	−9022.43	−0.816772
$497$	−6142.86	−0.554416
$498$	−10420.4	−0.937651
$499$	−5489.94	−0.492512	−0.246256	−	0.969205i	$-0.579200\pi$
$499$	−5489.94	−0.492512	−0.246256	+	0.969205i	$0.579200\pi$
$500$	3520.35	0.314870
$501$	16062.2	1.43234
$502$	13901.7	1.23598
$503$	−2065.66	−0.183108	−0.0915541	−	0.995800i	$-0.529183\pi$
$503$	−2065.66	−0.183108	−0.0915541	+	0.995800i	$0.529183\pi$
$504$	2880.52	0.254581
$505$	−4262.19	−0.375575
$506$	5148.87	0.452362
$507$	0	0
$508$	900.025	0.0786066
$509$	−5021.58	−0.437284	−0.218642	−	0.975805i	$-0.570163\pi$
$509$	−5021.58	−0.437284	−0.218642	+	0.975805i	$0.570163\pi$
$510$	399.117	0.0346533
$511$	2859.48	0.247546
$512$	−3422.49	−0.295418
$513$	4468.42	0.384573
$514$	−17465.7	−1.49879
$515$	5367.25	0.459241
$516$	428.120	0.0365250
$517$	−4721.34	−0.401633
$518$	−8587.81	−0.728430
$519$	938.748	0.0793959
$520$	0	0
$521$	−19464.0	−1.63672	−0.818361	−	0.574704i	$-0.805117\pi$
$521$	−19464.0	−1.63672	−0.818361	+	0.574704i	$0.805117\pi$
$522$	7804.78	0.654417
$523$	5167.23	0.432021	0.216011	−	0.976391i	$-0.430695\pi$
$523$	5167.23	0.432021	0.216011	+	0.976391i	$0.430695\pi$
$524$	−3647.96	−0.304126
$525$	−2281.89	−0.189695
$526$	−4968.12	−0.411826
$527$	233.239	0.0192791
$528$	5720.04	0.471464
$529$	9074.98	0.745869
$530$	−11723.7	−0.960836
$531$	−11100.7	−0.907212
$532$	−1531.62	−0.124820
$533$	0	0
$534$	−12442.7	−1.00833
$535$	6317.38	0.510512
$536$	14526.3	1.17060
$537$	9026.87	0.725397
$538$	26964.2	2.16080
$539$	−2966.18	−0.237036
$540$	−1237.25	−0.0985975
$541$	−22414.4	−1.78128	−0.890638	−	0.454714i	$-0.849742\pi$
$541$	−22414.4	−1.78128	−0.890638	+	0.454714i	$0.849742\pi$
$542$	1407.31	0.111530
$543$	−2737.17	−0.216322
$544$	−202.900	−0.0159913
$545$	−11937.4	−0.938242
$546$	0	0
$547$	21652.9	1.69252	0.846262	−	0.532766i	$-0.178848\pi$
$547$	21652.9	1.69252	0.846262	+	0.532766i	$0.178848\pi$
$548$	−4449.49	−0.346848
$549$	2275.16	0.176869
$550$	−1396.68	−0.108281
$551$	10194.9	0.788238
$552$	17935.7	1.38296
$553$	1314.80	0.101105
$554$	23491.5	1.80155
$555$	19453.0	1.48781
$556$	−2912.29	−0.222138
$557$	−11649.3	−0.886169	−0.443084	−	0.896480i	$-0.646116\pi$
$557$	−11649.3	−0.886169	−0.443084	+	0.896480i	$0.646116\pi$
$558$	6917.37	0.524795
$559$	0	0
$560$	−6109.00	−0.460986
$561$	−147.869	−0.0111284
$562$	−21138.2	−1.58658
$563$	3186.65	0.238546	0.119273	−	0.992861i	$-0.461944\pi$
$563$	3186.65	0.238546	0.119273	+	0.992861i	$0.461944\pi$
$564$	6694.65	0.499815
$565$	−11591.5	−0.863108
$566$	−9284.46	−0.689496
$567$	7596.93	0.562682
$568$	−13097.2	−0.967513
$569$	9842.04	0.725131	0.362566	−	0.931958i	$-0.381901\pi$
$569$	9842.04	0.725131	0.362566	+	0.931958i	$0.381901\pi$
$570$	15461.9	1.13619
$571$	26032.4	1.90792	0.953959	−	0.299937i	$-0.0969656\pi$
$571$	26032.4	1.90792	0.953959	+	0.299937i	$0.0969656\pi$
$572$	0	0
$573$	24527.6	1.78823
$574$	7330.78	0.533068
$575$	−5762.07	−0.417905
$576$	5352.28	0.387173
$577$	−15843.7	−1.14312	−0.571561	−	0.820560i	$-0.693662\pi$
$577$	−15843.7	−1.14312	−0.571561	+	0.820560i	$0.693662\pi$
$578$	−15765.8	−1.13455
$579$	25534.7	1.83279
$580$	−2822.84	−0.202090
$581$	−4123.19	−0.294421
$582$	−24467.7	−1.74265
$583$	4343.50	0.308558
$584$	6096.70	0.431992
$585$	0	0
$586$	4256.06	0.300027
$587$	20397.0	1.43420	0.717098	−	0.696973i	$-0.245470\pi$
$587$	20397.0	1.43420	0.717098	+	0.696973i	$0.245470\pi$
$588$	4205.92	0.294981
$589$	9035.76	0.632109
$590$	17893.1	1.24855
$591$	10383.1	0.722677
$592$	−24091.0	−1.67252
$593$	−1609.52	−0.111459	−0.0557294	−	0.998446i	$-0.517748\pi$
$593$	−1609.52	−0.111459	−0.0557294	+	0.998446i	$0.517748\pi$
$594$	2042.88	0.141112
$595$	157.924	0.0108811
$596$	−6476.82	−0.445136
$597$	−16472.8	−1.12929
$598$	0	0
$599$	2421.96	0.165206	0.0826032	−	0.996583i	$-0.473677\pi$
$599$	2421.96	0.165206	0.0826032	+	0.996583i	$0.473677\pi$
$600$	−4865.22	−0.331036
$601$	−25228.7	−1.71231	−0.856157	−	0.516716i	$-0.827154\pi$
$601$	−25228.7	−1.71231	−0.856157	+	0.516716i	$0.827154\pi$
$602$	754.957	0.0511125
$603$	−14653.4	−0.989604
$604$	2256.99	0.152046
$605$	−1118.61	−0.0751703
$606$	−9978.89	−0.668919
$607$	−5341.93	−0.357203	−0.178602	−	0.983921i	$-0.557157\pi$
$607$	−5341.93	−0.357203	−0.178602	+	0.983921i	$0.557157\pi$
$608$	−7860.42	−0.524313
$609$	7615.03	0.506694
$610$	−3667.30	−0.243417
$611$	0	0
$612$	85.0310	0.00561630
$613$	−3071.27	−0.202361	−0.101181	−	0.994868i	$-0.532262\pi$
$613$	−3071.27	−0.202361	−0.101181	+	0.994868i	$0.532262\pi$
$614$	28642.1	1.88258
$615$	−16605.6	−1.08878
$616$	1720.22	0.112515
$617$	−6926.69	−0.451958	−0.225979	−	0.974132i	$-0.572558\pi$
$617$	−6926.69	−0.451958	−0.225979	+	0.974132i	$0.572558\pi$
$618$	12566.1	0.817933
$619$	−6035.13	−0.391878	−0.195939	−	0.980616i	$-0.562775\pi$
$619$	−6035.13	−0.391878	−0.195939	+	0.980616i	$0.562775\pi$
$620$	−2501.88	−0.162061
$621$	8428.03	0.544614
$622$	15000.9	0.967010
$623$	−4923.37	−0.316614
$624$	0	0
$625$	−9120.12	−0.583687
$626$	−2079.32	−0.132758
$627$	−5728.49	−0.364871
$628$	−2561.32	−0.162751
$629$	622.777	0.0394781
$630$	4683.68	0.296194
$631$	29016.2	1.83061	0.915306	−	0.402759i	$-0.131949\pi$
$631$	29016.2	1.83061	0.915306	+	0.402759i	$0.131949\pi$
$632$	2803.29	0.176438
$633$	31081.2	1.95160
$634$	−14637.8	−0.916943
$635$	−3595.14	−0.224675
$636$	−6158.89	−0.383987
$637$	0	0
$638$	4660.93	0.289229
$639$	13211.7	0.817916
$640$	−16150.5	−0.997508
$641$	19644.8	1.21049	0.605245	−	0.796039i	$-0.293075\pi$
$641$	19644.8	1.21049	0.605245	+	0.796039i	$0.293075\pi$
$642$	14790.6	0.909250
$643$	1085.35	0.0665660	0.0332830	−	0.999446i	$-0.489404\pi$
$643$	1085.35	0.0665660	0.0332830	+	0.999446i	$0.489404\pi$
$644$	−2888.83	−0.176764
$645$	−1710.12	−0.104397
$646$	495.006	0.0301482
$647$	28797.9	1.74986	0.874931	−	0.484248i	$-0.160907\pi$
$647$	28797.9	1.74986	0.874931	+	0.484248i	$0.160907\pi$
$648$	16197.4	0.981938
$649$	−6629.22	−0.400955
$650$	0	0
$651$	6749.19	0.406331
$652$	4563.15	0.274090
$653$	11107.0	0.665622	0.332811	−	0.942994i	$-0.392003\pi$
$653$	11107.0	0.665622	0.332811	+	0.942994i	$0.392003\pi$
$654$	−27948.5	−1.67106
$655$	14571.7	0.869259
$656$	20564.7	1.22396
$657$	−6150.01	−0.365198
$658$	11805.5	0.699433
$659$	−26209.3	−1.54927	−0.774636	−	0.632407i	$-0.782067\pi$
$659$	−26209.3	−1.54927	−0.774636	+	0.632407i	$0.782067\pi$
$660$	1586.14	0.0935463
$661$	−13826.3	−0.813585	−0.406792	−	0.913521i	$-0.633353\pi$
$661$	−13826.3	−0.813585	−0.406792	+	0.913521i	$0.633353\pi$
$662$	−17580.4	−1.03215
$663$	0	0
$664$	−8791.07	−0.513795
$665$	6118.03	0.356762
$666$	18470.2	1.07463
$667$	19229.0	1.11627
$668$	−5515.90	−0.319486
$669$	37741.0	2.18109
$670$	23619.6	1.36195
$671$	1358.70	0.0781699
$672$	−5871.28	−0.337038
$673$	−20899.8	−1.19707	−0.598535	−	0.801097i	$-0.704250\pi$
$673$	−20899.8	−1.19707	−0.598535	+	0.801097i	$0.704250\pi$
$674$	11387.2	0.650769
$675$	−2286.18	−0.130363
$676$	0	0
$677$	−795.174	−0.0451418	−0.0225709	−	0.999745i	$-0.507185\pi$
$677$	−795.174	−0.0451418	−0.0225709	+	0.999745i	$0.507185\pi$
$678$	−27138.6	−1.53724
$679$	−9681.48	−0.547189
$680$	336.711	0.0189886
$681$	4725.75	0.265919
$682$	4130.98	0.231940
$683$	11629.9	0.651543	0.325772	−	0.945448i	$-0.394376\pi$
$683$	11629.9	0.651543	0.325772	+	0.945448i	$0.394376\pi$
$684$	3294.13	0.184143
$685$	17773.4	0.991368
$686$	16851.1	0.937866
$687$	20397.3	1.13276
$688$	2117.85	0.117358
$689$	0	0
$690$	29163.2	1.60902
$691$	−14865.5	−0.818394	−0.409197	−	0.912446i	$-0.634191\pi$
$691$	−14865.5	−0.818394	−0.409197	+	0.912446i	$0.634191\pi$
$692$	−322.375	−0.0177093
$693$	−1735.26	−0.0951184
$694$	9806.13	0.536362
$695$	11633.1	0.634919
$696$	16236.0	0.884232
$697$	−531.619	−0.0288903
$698$	8551.66	0.463732
$699$	−20634.1	−1.11653
$700$	783.621	0.0423116
$701$	14716.2	0.792901	0.396450	−	0.918056i	$-0.370242\pi$
$701$	14716.2	0.792901	0.396450	+	0.918056i	$0.370242\pi$
$702$	0	0
$703$	24126.6	1.29438
$704$	3196.33	0.171117
$705$	−26741.7	−1.42858
$706$	−19953.9	−1.06370
$707$	−3948.48	−0.210040
$708$	9399.94	0.498971
$709$	−21772.0	−1.15326	−0.576632	−	0.817004i	$-0.695633\pi$
$709$	−21772.0	−1.15326	−0.576632	+	0.817004i	$0.695633\pi$
$710$	−21295.9	−1.12566
$711$	−2827.81	−0.149158
$712$	−10497.1	−0.552524
$713$	17042.6	0.895163
$714$	369.741	0.0193798
$715$	0	0
$716$	−3099.91	−0.161800
$717$	−34992.3	−1.82261
$718$	30117.9	1.56545
$719$	−5885.75	−0.305287	−0.152644	−	0.988281i	$-0.548779\pi$
$719$	−5885.75	−0.305287	−0.152644	+	0.988281i	$0.548779\pi$
$720$	13138.9	0.680081
$721$	4972.20	0.256830
$722$	−2851.69	−0.146993
$723$	−30188.5	−1.55287
$724$	939.968	0.0482509
$725$	−5216.03	−0.267198
$726$	−2618.96	−0.133882
$727$	−23746.6	−1.21143	−0.605717	−	0.795680i	$-0.707113\pi$
$727$	−23746.6	−1.21143	−0.605717	+	0.795680i	$0.707113\pi$
$728$	0	0
$729$	−5816.69	−0.295519
$730$	9913.14	0.502605
$731$	−54.7485	−0.00277011
$732$	−1926.58	−0.0972791
$733$	−11449.1	−0.576918	−0.288459	−	0.957492i	$-0.593143\pi$
$733$	−11449.1	−0.576918	−0.288459	+	0.957492i	$0.593143\pi$
$734$	−1167.96	−0.0587334
$735$	−16800.5	−0.843122
$736$	−14825.8	−0.742507
$737$	−8750.83	−0.437369
$738$	−15766.7	−0.786421
$739$	−19534.4	−0.972376	−0.486188	−	0.873854i	$-0.661613\pi$
$739$	−19534.4	−0.972376	−0.486188	+	0.873854i	$0.661613\pi$
$740$	−6680.33	−0.331856
$741$	0	0
$742$	−10860.7	−0.537346
$743$	23126.9	1.14192	0.570958	−	0.820979i	$-0.306572\pi$
$743$	23126.9	1.14192	0.570958	+	0.820979i	$0.306572\pi$
$744$	14390.0	0.709089
$745$	25871.6	1.27230
$746$	−38823.4	−1.90539
$747$	8867.94	0.434352
$748$	50.7796	0.00248220
$749$	5852.39	0.285503
$750$	−32922.7	−1.60289
$751$	25162.1	1.22261	0.611303	−	0.791397i	$-0.290646\pi$
$751$	25162.1	1.22261	0.611303	+	0.791397i	$0.290646\pi$
$752$	33117.5	1.60594
$753$	−29172.0	−1.41180
$754$	0	0
$755$	−9015.51	−0.434580
$756$	−1146.18	−0.0551405
$757$	21691.0	1.04144	0.520722	−	0.853726i	$-0.325663\pi$
$757$	21691.0	1.04144	0.520722	+	0.853726i	$0.325663\pi$
$758$	3695.57	0.177083
$759$	−10804.7	−0.516713
$760$	13044.3	0.622586
$761$	−19703.3	−0.938562	−0.469281	−	0.883049i	$-0.655487\pi$
$761$	−19703.3	−0.938562	−0.469281	+	0.883049i	$0.655487\pi$
$762$	−8417.13	−0.400158
$763$	−11058.8	−0.524711
$764$	−8423.01	−0.398866
$765$	−339.655	−0.0160526
$766$	−2719.04	−0.128255
$767$	0	0
$768$	−22146.0	−1.04053
$769$	−29598.8	−1.38799	−0.693993	−	0.719981i	$-0.744150\pi$
$769$	−29598.8	−1.38799	−0.693993	+	0.719981i	$0.744150\pi$
$770$	2797.04	0.130907
$771$	36651.1	1.71200
$772$	−8768.86	−0.408806
$773$	−3230.81	−0.150329	−0.0751645	−	0.997171i	$-0.523948\pi$
$773$	−3230.81	−0.150329	−0.0751645	+	0.997171i	$0.523948\pi$
$774$	−1623.72	−0.0754050
$775$	−4622.96	−0.214273
$776$	−20641.9	−0.954900
$777$	18021.1	0.832053
$778$	42322.9	1.95032
$779$	−20595.1	−0.947235
$780$	0	0
$781$	7889.91	0.361489
$782$	933.645	0.0426945
$783$	7629.34	0.348213
$784$	20806.1	0.947798
$785$	10231.1	0.465178
$786$	34116.2	1.54820
$787$	−30136.2	−1.36498	−0.682489	−	0.730896i	$-0.739103\pi$
$787$	−30136.2	−1.36498	−0.682489	+	0.730896i	$0.739103\pi$
$788$	−3565.64	−0.161194
$789$	10425.4	0.470411
$790$	4558.11	0.205279
$791$	−10738.3	−0.482692
$792$	−3699.75	−0.165991
$793$	0	0
$794$	24717.6	1.10478
$795$	24601.6	1.09752
$796$	5656.90	0.251889
$797$	12168.3	0.540808	0.270404	−	0.962747i	$-0.412843\pi$
$797$	12168.3	0.540808	0.270404	+	0.962747i	$0.412843\pi$
$798$	14323.9	0.635413
$799$	−856.121	−0.0379066
$800$	4021.62	0.177732
$801$	10588.9	0.467093
$802$	−47111.0	−2.07425
$803$	−3672.72	−0.161404
$804$	12408.3	0.544287
$805$	11539.4	0.505230
$806$	0	0
$807$	−56583.3	−2.46819
$808$	−8418.58	−0.366540
$809$	−39265.2	−1.70642	−0.853209	−	0.521569i	$-0.825347\pi$
$809$	−39265.2	−1.70642	−0.853209	+	0.521569i	$0.825347\pi$
$810$	26336.8	1.14244
$811$	−43307.1	−1.87512	−0.937558	−	0.347828i	$-0.886919\pi$
$811$	−43307.1	−1.87512	−0.937558	+	0.347828i	$0.886919\pi$
$812$	−2615.07	−0.113018
$813$	−2953.18	−0.127396
$814$	11030.2	0.474949
$815$	−18227.4	−0.783409
$816$	1037.22	0.0444973
$817$	−2120.98	−0.0908244
$818$	−35837.8	−1.53183
$819$	0	0
$820$	5702.51	0.242854
$821$	10683.4	0.454143	0.227072	−	0.973878i	$-0.427085\pi$
$821$	10683.4	0.454143	0.227072	+	0.973878i	$0.427085\pi$
$822$	41612.1	1.76568
$823$	−20923.3	−0.886197	−0.443098	−	0.896473i	$-0.646121\pi$
$823$	−20923.3	−0.886197	−0.443098	+	0.896473i	$0.646121\pi$
$824$	10601.3	0.448194
$825$	2930.86	0.123684
$826$	16576.1	0.698252
$827$	−11604.4	−0.487938	−0.243969	−	0.969783i	$-0.578449\pi$
$827$	−11604.4	−0.487938	−0.243969	+	0.969783i	$0.578449\pi$
$828$	6213.15	0.260775
$829$	−10914.1	−0.457251	−0.228626	−	0.973514i	$-0.573423\pi$
$829$	−10914.1	−0.457251	−0.228626	+	0.973514i	$0.573423\pi$
$830$	−14294.1	−0.597779
$831$	−49295.8	−2.05783
$832$	0	0
$833$	−537.859	−0.0223718
$834$	27236.1	1.13083
$835$	22033.2	0.913160
$836$	1967.22	0.0813847
$837$	6761.88	0.279241
$838$	−33040.8	−1.36202
$839$	−24920.3	−1.02544	−0.512721	−	0.858555i	$-0.671362\pi$
$839$	−24920.3	−1.02544	−0.512721	+	0.858555i	$0.671362\pi$
$840$	9743.31	0.400210
$841$	−6982.27	−0.286288
$842$	4295.11	0.175795
$843$	44357.6	1.81229
$844$	−10673.6	−0.435307
$845$	0	0
$846$	−25390.7	−1.03186
$847$	−1036.28	−0.0420389
$848$	−30467.2	−1.23378
$849$	19483.0	0.787581
$850$	−253.259	−0.0102197
$851$	45505.9	1.83304
$852$	−11187.5	−0.449858
$853$	−28838.3	−1.15757	−0.578783	−	0.815481i	$-0.696472\pi$
$853$	−28838.3	−1.15757	−0.578783	+	0.815481i	$0.696472\pi$
$854$	−3397.37	−0.136131
$855$	−13158.3	−0.526322
$856$	12477.9	0.498232
$857$	27001.6	1.07626	0.538131	−	0.842861i	$-0.319131\pi$
$857$	27001.6	1.07626	0.538131	+	0.842861i	$0.319131\pi$
$858$	0	0
$859$	−7994.62	−0.317547	−0.158773	−	0.987315i	$-0.550754\pi$
$859$	−7994.62	−0.317547	−0.158773	+	0.987315i	$0.550754\pi$
$860$	587.270	0.0232857
$861$	−15383.3	−0.608900
$862$	33305.3	1.31599
$863$	−32708.0	−1.29014	−0.645072	−	0.764121i	$-0.723173\pi$
$863$	−32708.0	−1.29014	−0.645072	+	0.764121i	$0.723173\pi$
$864$	−5882.32	−0.231621
$865$	1287.72	0.0506171
$866$	−8654.72	−0.339607
$867$	33083.9	1.29595
$868$	−2317.73	−0.0906325
$869$	−1688.74	−0.0659222
$870$	26399.5	1.02877
$871$	0	0
$872$	−23578.5	−0.915673
$873$	20822.4	0.807254
$874$	36169.7	1.39984
$875$	−13027.0	−0.503305
$876$	5207.76	0.200861
$877$	23507.6	0.905124	0.452562	−	0.891733i	$-0.350510\pi$
$877$	23507.6	0.905124	0.452562	+	0.891733i	$0.350510\pi$
$878$	15508.0	0.596092
$879$	−8931.16	−0.342708
$880$	7846.42	0.300571
$881$	−14451.3	−0.552641	−0.276321	−	0.961065i	$-0.589115\pi$
$881$	−14451.3	−0.552641	−0.276321	+	0.961065i	$0.589115\pi$
$882$	−15951.7	−0.608982
$883$	3014.49	0.114887	0.0574437	−	0.998349i	$-0.481705\pi$
$883$	3014.49	0.114887	0.0574437	+	0.998349i	$0.481705\pi$
$884$	0	0
$885$	−37547.9	−1.42617
$886$	−24010.6	−0.910441
$887$	19662.7	0.744316	0.372158	−	0.928169i	$-0.378618\pi$
$887$	19662.7	0.744316	0.372158	+	0.928169i	$0.378618\pi$
$888$	38423.0	1.45202
$889$	−3330.52	−0.125649
$890$	−17068.2	−0.642839
$891$	−9757.52	−0.366879
$892$	−12960.6	−0.486495
$893$	−33166.4	−1.24286
$894$	60572.0	2.26603
$895$	12382.5	0.462461
$896$	−14961.8	−0.557855
$897$	0	0
$898$	−19138.8	−0.711214
$899$	15427.6	0.572345
$900$	−1685.37	−0.0624212
$901$	787.608	0.0291221
$902$	−9415.69	−0.347570
$903$	−1584.25	−0.0583836
$904$	−22895.1	−0.842347
$905$	−3754.69	−0.137912
$906$	−21107.6	−0.774011
$907$	−30398.4	−1.11286	−0.556429	−	0.830895i	$-0.687829\pi$
$907$	−30398.4	−1.11286	−0.556429	+	0.830895i	$0.687829\pi$
$908$	−1622.86	−0.0593135
$909$	8492.19	0.309866
$910$	0	0
$911$	28057.5	1.02040	0.510201	−	0.860055i	$-0.329571\pi$
$911$	28057.5	1.02040	0.510201	+	0.860055i	$0.329571\pi$
$912$	40182.1	1.45895
$913$	5295.84	0.191968
$914$	30319.1	1.09723
$915$	7695.67	0.278045
$916$	−7004.62	−0.252663
$917$	13499.2	0.486132
$918$	370.436	0.0133183
$919$	−16880.7	−0.605924	−0.302962	−	0.953003i	$-0.597976\pi$
$919$	−16880.7	−0.605924	−0.302962	+	0.953003i	$0.597976\pi$
$920$	24603.2	0.881677
$921$	−60104.2	−2.15038
$922$	−24382.0	−0.870909
$923$	0	0
$924$	1469.40	0.0523156
$925$	−12343.9	−0.438772
$926$	−54049.8	−1.91813
$927$	−10693.9	−0.378895
$928$	−13420.8	−0.474741
$929$	−41748.6	−1.47441	−0.737206	−	0.675669i	$-0.763855\pi$
$929$	−41748.6	−1.47441	−0.737206	+	0.675669i	$0.763855\pi$
$930$	23397.9	0.824996
$931$	−20836.8	−0.733511
$932$	7085.94	0.249043
$933$	−31478.7	−1.10457
$934$	−27875.5	−0.976567
$935$	−202.838	−0.00709467
$936$	0	0
$937$	−24848.4	−0.866343	−0.433171	−	0.901312i	$-0.642605\pi$
$937$	−24848.4	−0.866343	−0.433171	+	0.901312i	$0.642605\pi$
$938$	21881.1	0.761667
$939$	4363.36	0.151643
$940$	9183.33	0.318646
$941$	−39305.5	−1.36166	−0.680831	−	0.732441i	$-0.738381\pi$
$941$	−39305.5	−1.36166	−0.680831	+	0.732441i	$0.738381\pi$
$942$	23953.7	0.828507
$943$	−38845.0	−1.34143
$944$	46500.2	1.60323
$945$	4578.40	0.157604
$946$	−969.670	−0.0333263
$947$	−36951.9	−1.26798	−0.633989	−	0.773342i	$-0.718583\pi$
$947$	−36951.9	−1.26798	−0.633989	+	0.773342i	$0.718583\pi$
$948$	2394.55	0.0820374
$949$	0	0
$950$	−9811.35	−0.335076
$951$	30716.8	1.04738
$952$	311.927	0.0106194
$953$	−47773.6	−1.62386	−0.811930	−	0.583754i	$-0.801583\pi$
$953$	−47773.6	−1.62386	−0.811930	+	0.583754i	$0.801583\pi$
$954$	23358.7	0.792733
$955$	33645.6	1.14005
$956$	12016.7	0.406534
$957$	−9780.77	−0.330373
$958$	−38810.6	−1.30889
$959$	16465.2	0.554421
$960$	18104.0	0.608650
$961$	−16117.6	−0.541021
$962$	0	0
$963$	−12587.0	−0.421195
$964$	10367.0	0.346369
$965$	35027.0	1.16846
$966$	27016.7	0.899842
$967$	23468.8	0.780462	0.390231	−	0.920717i	$-0.372395\pi$
$967$	23468.8	0.780462	0.390231	+	0.920717i	$0.372395\pi$
$968$	−2209.45	−0.0733621
$969$	−1038.75	−0.0344370
$970$	−33563.4	−1.11099
$971$	32799.3	1.08402	0.542009	−	0.840373i	$-0.317664\pi$
$971$	32799.3	1.08402	0.542009	+	0.840373i	$0.317664\pi$
$972$	10222.3	0.337324
$973$	10776.9	0.355078
$974$	22715.3	0.747275
$975$	0	0
$976$	−9530.49	−0.312565
$977$	5246.67	0.171808	0.0859038	−	0.996303i	$-0.472622\pi$
$977$	5246.67	0.171808	0.0859038	+	0.996303i	$0.472622\pi$
$978$	−42675.1	−1.39529
$979$	6323.60	0.206438
$980$	5769.43	0.188059
$981$	23784.6	0.774092
$982$	63265.0	2.05587
$983$	−32963.0	−1.06954	−0.534769	−	0.844998i	$-0.679601\pi$
$983$	−32963.0	−1.06954	−0.534769	+	0.844998i	$0.679601\pi$
$984$	−32798.9	−1.06259
$985$	14242.9	0.460727
$986$	845.168	0.0272978
$987$	−24773.4	−0.798931
$988$	0	0
$989$	−4000.44	−0.128621
$990$	−6015.74	−0.193124
$991$	48862.0	1.56625	0.783124	−	0.621866i	$-0.213625\pi$
$991$	48862.0	1.56625	0.783124	+	0.621866i	$0.213625\pi$
$992$	−11894.8	−0.380707
$993$	36891.8	1.17898
$994$	−19728.4	−0.629524
$995$	−22596.4	−0.719953
$996$	−7509.27	−0.238896
$997$	52631.8	1.67188	0.835941	−	0.548819i	$-0.184922\pi$
$997$	52631.8	1.67188	0.835941	+	0.548819i	$0.184922\pi$
$998$	−17631.5	−0.559234
$999$	18055.0	0.571808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.f.1.14		17
13.4	even	6		143.4.e.a.133.14	yes	34
13.10	even	6		143.4.e.a.100.14	✓	34
13.12	even	2		1859.4.a.i.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.14	✓	34	13.10	even	6
143.4.e.a.133.14	yes	34	13.4	even	6
1859.4.a.f.1.14		17	1.1	even	1	trivial
1859.4.a.i.1.4		17	13.12	even	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)

\(f(q)\)	\(=\)	\(q+3.21160 q^{2} -6.73941 q^{3} +2.31437 q^{4} -9.24473 q^{5} -21.6443 q^{6} -8.56428 q^{7} -18.2600 q^{8} +18.4196 q^{9} +O(q^{10})\)	\(q+3.21160 q^{2} -6.73941 q^{3} +2.31437 q^{4} -9.24473 q^{5} -21.6443 q^{6} -8.56428 q^{7} -18.2600 q^{8} +18.4196 q^{9} -29.6904 q^{10} +11.0000 q^{11} -15.5975 q^{12} -27.5051 q^{14} +62.3040 q^{15} -77.1587 q^{16} +1.99463 q^{17} +59.1564 q^{18} +77.2727 q^{19} -21.3958 q^{20} +57.7182 q^{21} +35.3276 q^{22} +145.746 q^{23} +123.061 q^{24} -39.5350 q^{25} +57.8267 q^{27} -19.8210 q^{28} +131.935 q^{29} +200.096 q^{30} +116.933 q^{31} -101.723 q^{32} -74.1335 q^{33} +6.40596 q^{34} +79.1745 q^{35} +42.6299 q^{36} +312.226 q^{37} +248.169 q^{38} +168.808 q^{40} -266.525 q^{41} +185.368 q^{42} -27.4479 q^{43} +25.4581 q^{44} -170.284 q^{45} +468.079 q^{46} -429.212 q^{47} +520.004 q^{48} -269.653 q^{49} -126.970 q^{50} -13.4426 q^{51} +394.864 q^{53} +185.716 q^{54} -101.692 q^{55} +156.383 q^{56} -520.772 q^{57} +423.721 q^{58} -602.657 q^{59} +144.195 q^{60} +123.518 q^{61} +375.543 q^{62} -157.751 q^{63} +290.575 q^{64} -238.087 q^{66} -795.530 q^{67} +4.61633 q^{68} -982.244 q^{69} +254.277 q^{70} +717.265 q^{71} -336.341 q^{72} -333.884 q^{73} +1002.75 q^{74} +266.442 q^{75} +178.838 q^{76} -94.2071 q^{77} -153.521 q^{79} +713.311 q^{80} -887.047 q^{81} -855.972 q^{82} +481.440 q^{83} +133.582 q^{84} -18.4398 q^{85} -88.1518 q^{86} -889.161 q^{87} -200.859 q^{88} +574.872 q^{89} -546.885 q^{90} +337.312 q^{92} -788.062 q^{93} -1378.46 q^{94} -714.365 q^{95} +685.554 q^{96} +1130.45 q^{97} -866.018 q^{98} +202.616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 95 q^{12} - 60 q^{14} + 28 q^{15} + 350 q^{16} + 118 q^{17} - 478 q^{18} - 403 q^{19} - 98 q^{20} - 220 q^{21} - 44 q^{22} - 215 q^{23} - 26 q^{24} + 319 q^{25} - 384 q^{27} + 396 q^{28} - 7 q^{29} - 1269 q^{30} - 682 q^{31} - 813 q^{32} - 66 q^{33} - 738 q^{34} + 10 q^{35} + 560 q^{36} - 1084 q^{37} + 410 q^{38} + 95 q^{40} - 240 q^{41} + 393 q^{42} - 435 q^{43} + 858 q^{44} - 1242 q^{45} - 1671 q^{46} - 549 q^{47} + 894 q^{48} + 403 q^{49} + 651 q^{50} + 1552 q^{51} - 566 q^{53} - 311 q^{54} - 176 q^{55} - 1925 q^{56} + 534 q^{57} - 618 q^{58} - 2010 q^{59} + 411 q^{60} + 460 q^{61} - 823 q^{62} - 820 q^{63} + 3171 q^{64} - 154 q^{66} + 232 q^{67} + 1795 q^{68} - 1608 q^{69} - 207 q^{70} - 489 q^{71} - 2556 q^{72} - 290 q^{73} + 2653 q^{74} - 2852 q^{75} - 2421 q^{76} + 66 q^{77} - 732 q^{79} - 4915 q^{80} + 2393 q^{81} - 1772 q^{82} + 117 q^{83} - 4161 q^{84} - 4858 q^{85} - 1034 q^{86} + 3032 q^{87} - 693 q^{88} - 4113 q^{89} + 15145 q^{90} - 3554 q^{92} - 802 q^{93} + 2325 q^{94} - 3924 q^{95} - 2601 q^{96} - 2793 q^{97} - 533 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 95 * q^12 - 60 * q^14 + 28 * q^15 + 350 * q^16 + 118 * q^17 - 478 * q^18 - 403 * q^19 - 98 * q^20 - 220 * q^21 - 44 * q^22 - 215 * q^23 - 26 * q^24 + 319 * q^25 - 384 * q^27 + 396 * q^28 - 7 * q^29 - 1269 * q^30 - 682 * q^31 - 813 * q^32 - 66 * q^33 - 738 * q^34 + 10 * q^35 + 560 * q^36 - 1084 * q^37 + 410 * q^38 + 95 * q^40 - 240 * q^41 + 393 * q^42 - 435 * q^43 + 858 * q^44 - 1242 * q^45 - 1671 * q^46 - 549 * q^47 + 894 * q^48 + 403 * q^49 + 651 * q^50 + 1552 * q^51 - 566 * q^53 - 311 * q^54 - 176 * q^55 - 1925 * q^56 + 534 * q^57 - 618 * q^58 - 2010 * q^59 + 411 * q^60 + 460 * q^61 - 823 * q^62 - 820 * q^63 + 3171 * q^64 - 154 * q^66 + 232 * q^67 + 1795 * q^68 - 1608 * q^69 - 207 * q^70 - 489 * q^71 - 2556 * q^72 - 290 * q^73 + 2653 * q^74 - 2852 * q^75 - 2421 * q^76 + 66 * q^77 - 732 * q^79 - 4915 * q^80 + 2393 * q^81 - 1772 * q^82 + 117 * q^83 - 4161 * q^84 - 4858 * q^85 - 1034 * q^86 + 3032 * q^87 - 693 * q^88 - 4113 * q^89 + 15145 * q^90 - 3554 * q^92 - 802 * q^93 + 2325 * q^94 - 3924 * q^95 - 2601 * q^96 - 2793 * q^97 - 533 * q^98 + 1485 * q^99

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