LMFDB - Embedded newform 1849.4.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 59x^{8} + 42x^{7} + 1187x^{6} - 541x^{5} - 9389x^{4} + 2180x^{3} + 22676x^{2} - 320x - 768 $ x^10 - x^9 - 59x^8 + 42x^7 + 1187x^6 - 541x^5 - 9389x^4 + 2180x^3 + 22676x^2 - 320x - 768
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.190911$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.190911 q^{2} -1.43836 q^{3} -7.96355 q^{4} -16.3462 q^{5} -0.274600 q^{6} -6.23994 q^{7} -3.04762 q^{8} -24.9311 q^{9} +O(q^{10})$	\(q+0.190911 q^{2} -1.43836 q^{3} -7.96355 q^{4} -16.3462 q^{5} -0.274600 q^{6} -6.23994 q^{7} -3.04762 q^{8} -24.9311 q^{9} -3.12068 q^{10} -29.4459 q^{11} +11.4545 q^{12} +22.2374 q^{13} -1.19127 q^{14} +23.5118 q^{15} +63.1266 q^{16} -60.3760 q^{17} -4.75963 q^{18} +10.0377 q^{19} +130.174 q^{20} +8.97530 q^{21} -5.62155 q^{22} -40.6335 q^{23} +4.38359 q^{24} +142.200 q^{25} +4.24537 q^{26} +74.6958 q^{27} +49.6921 q^{28} +195.701 q^{29} +4.48867 q^{30} +240.848 q^{31} +36.4326 q^{32} +42.3538 q^{33} -11.5265 q^{34} +102.000 q^{35} +198.540 q^{36} -243.015 q^{37} +1.91632 q^{38} -31.9855 q^{39} +49.8172 q^{40} -172.596 q^{41} +1.71349 q^{42} +234.494 q^{44} +407.530 q^{45} -7.75740 q^{46} +583.708 q^{47} -90.7990 q^{48} -304.063 q^{49} +27.1475 q^{50} +86.8427 q^{51} -177.089 q^{52} +370.288 q^{53} +14.2603 q^{54} +481.329 q^{55} +19.0170 q^{56} -14.4379 q^{57} +37.3614 q^{58} +714.277 q^{59} -187.238 q^{60} -707.836 q^{61} +45.9807 q^{62} +155.569 q^{63} -498.057 q^{64} -363.498 q^{65} +8.08582 q^{66} -377.580 q^{67} +480.808 q^{68} +58.4458 q^{69} +19.4729 q^{70} +47.4331 q^{71} +75.9806 q^{72} +691.513 q^{73} -46.3942 q^{74} -204.535 q^{75} -79.9361 q^{76} +183.740 q^{77} -6.10639 q^{78} +288.783 q^{79} -1031.88 q^{80} +565.700 q^{81} -32.9505 q^{82} -833.823 q^{83} -71.4753 q^{84} +986.922 q^{85} -281.488 q^{87} +89.7398 q^{88} -687.209 q^{89} +77.8021 q^{90} -138.760 q^{91} +323.587 q^{92} -346.427 q^{93} +111.436 q^{94} -164.079 q^{95} -52.4032 q^{96} +1131.96 q^{97} -58.0491 q^{98} +734.118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9}+O(q^{10}) $ 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9} - 27 q^{10} + 27 q^{11} - 72 q^{12} + 15 q^{13} - 96 q^{14} - 65 q^{15} + 67 q^{16} + 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 9 q^{21} - 190 q^{22} + 61 q^{23} - 202 q^{24} + 151 q^{25} - 21 q^{26} + 97 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} - 253 q^{31} + 399 q^{32} - 424 q^{33} - 231 q^{34} + 355 q^{35} + 1092 q^{36} - 129 q^{37} + 854 q^{38} - 691 q^{39} - 1345 q^{40} + 391 q^{41} - 31 q^{42} + 377 q^{44} - 944 q^{45} - 40 q^{46} - 334 q^{47} - 2401 q^{48} + 115 q^{49} + 424 q^{50} - 795 q^{51} + 564 q^{52} - 773 q^{53} + 182 q^{54} - 1242 q^{55} + 923 q^{56} + 765 q^{57} - 1328 q^{58} - 1483 q^{59} + 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 738 q^{64} + 1063 q^{65} - 1483 q^{66} + 642 q^{67} + 1052 q^{68} - 3503 q^{69} + 85 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} + 2232 q^{74} - 82 q^{75} - 252 q^{76} + 1448 q^{77} + 2822 q^{78} + 1405 q^{79} - 3157 q^{80} - 974 q^{81} - 3304 q^{82} - 543 q^{83} + 3652 q^{84} - 973 q^{85} + 1409 q^{87} + 2686 q^{88} - 2196 q^{89} - 742 q^{90} - 3513 q^{91} - 2629 q^{92} - 983 q^{93} - 4939 q^{94} + 149 q^{95} - 3540 q^{96} - 425 q^{97} - 213 q^{98} + 3181 q^{99}+O(q^{100}) \) 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9 - 27 * q^10 + 27 * q^11 - 72 * q^12 + 15 * q^13 - 96 * q^14 - 65 * q^15 + 67 * q^16 + 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 9 * q^21 - 190 * q^22 + 61 * q^23 - 202 * q^24 + 151 * q^25 - 21 * q^26 + 97 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 - 253 * q^31 + 399 * q^32 - 424 * q^33 - 231 * q^34 + 355 * q^35 + 1092 * q^36 - 129 * q^37 + 854 * q^38 - 691 * q^39 - 1345 * q^40 + 391 * q^41 - 31 * q^42 + 377 * q^44 - 944 * q^45 - 40 * q^46 - 334 * q^47 - 2401 * q^48 + 115 * q^49 + 424 * q^50 - 795 * q^51 + 564 * q^52 - 773 * q^53 + 182 * q^54 - 1242 * q^55 + 923 * q^56 + 765 * q^57 - 1328 * q^58 - 1483 * q^59 + 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 738 * q^64 + 1063 * q^65 - 1483 * q^66 + 642 * q^67 + 1052 * q^68 - 3503 * q^69 + 85 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 + 2232 * q^74 - 82 * q^75 - 252 * q^76 + 1448 * q^77 + 2822 * q^78 + 1405 * q^79 - 3157 * q^80 - 974 * q^81 - 3304 * q^82 - 543 * q^83 + 3652 * q^84 - 973 * q^85 + 1409 * q^87 + 2686 * q^88 - 2196 * q^89 - 742 * q^90 - 3513 * q^91 - 2629 * q^92 - 983 * q^93 - 4939 * q^94 + 149 * q^95 - 3540 * q^96 - 425 * q^97 - 213 * q^98 + 3181 * 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 $

$2$	0.190911	0.0674973	0.0337487	−	0.999430i	$-0.489255\pi$
$2$	0.190911	0.0674973	0.0337487	+	0.999430i	$0.489255\pi$
$3$	−1.43836	−0.276813	−0.138407	−	0.990375i	$-0.544198\pi$
$3$	−1.43836	−0.276813	−0.138407	+	0.990375i	$0.544198\pi$
$4$	−7.96355	−0.995444
$5$	−16.3462	−1.46205	−0.731026	−	0.682349i	$-0.760958\pi$
$5$	−16.3462	−1.46205	−0.731026	+	0.682349i	$0.760958\pi$
$6$	−0.274600	−0.0186841
$7$	−6.23994	−0.336925	−0.168462	−	0.985708i	$-0.553880\pi$
$7$	−6.23994	−0.336925	−0.168462	+	0.985708i	$0.553880\pi$
$8$	−3.04762	−0.134687
$9$	−24.9311	−0.923374
$10$	−3.12068	−0.0986846
$11$	−29.4459	−0.807115	−0.403557	−	0.914954i	$-0.632226\pi$
$11$	−29.4459	−0.807115	−0.403557	+	0.914954i	$0.632226\pi$
$12$	11.4545	0.275552
$13$	22.2374	0.474427	0.237214	−	0.971458i	$-0.423766\pi$
$13$	22.2374	0.474427	0.237214	+	0.971458i	$0.423766\pi$
$14$	−1.19127	−0.0227415
$15$	23.5118	0.404715
$16$	63.1266	0.986353
$17$	−60.3760	−0.861373	−0.430687	−	0.902502i	$-0.641729\pi$
$17$	−60.3760	−0.861373	−0.430687	+	0.902502i	$0.641729\pi$
$18$	−4.75963	−0.0623253
$19$	10.0377	0.121201	0.0606004	−	0.998162i	$-0.480698\pi$
$19$	10.0377	0.121201	0.0606004	+	0.998162i	$0.480698\pi$
$20$	130.174	1.45539
$21$	8.97530	0.0932653
$22$	−5.62155	−0.0544781
$23$	−40.6335	−0.368377	−0.184189	−	0.982891i	$-0.558966\pi$
$23$	−40.6335	−0.368377	−0.184189	+	0.982891i	$0.558966\pi$
$24$	4.38359	0.0372832
$25$	142.200	1.13760
$26$	4.24537	0.0320226
$27$	74.6958	0.532415
$28$	49.6921	0.335390
$29$	195.701	1.25313	0.626563	−	0.779371i	$-0.284461\pi$
$29$	195.701	1.25313	0.626563	+	0.779371i	$0.284461\pi$
$30$	4.48867	0.0273172
$31$	240.848	1.39541	0.697704	−	0.716386i	$-0.254205\pi$
$31$	240.848	1.39541	0.697704	+	0.716386i	$0.254205\pi$
$32$	36.4326	0.201263
$33$	42.3538	0.223420
$34$	−11.5265	−0.0581404
$35$	102.000	0.492602
$36$	198.540	0.919168
$37$	−243.015	−1.07977	−0.539883	−	0.841740i	$-0.681532\pi$
$37$	−243.015	−1.07977	−0.539883	+	0.841740i	$0.681532\pi$
$38$	1.91632	0.00818073
$39$	−31.9855	−0.131328
$40$	49.8172	0.196920
$41$	−172.596	−0.657439	−0.328719	−	0.944428i	$-0.606617\pi$
$41$	−172.596	−0.657439	−0.328719	+	0.944428i	$0.606617\pi$
$42$	1.71349	0.00629515
$43$	0	0
$43$	0	0
$44$	234.494	0.803437
$45$	407.530	1.35002
$46$	−7.75740	−0.0248645
$47$	583.708	1.81154	0.905772	−	0.423766i	$-0.139292\pi$
$47$	583.708	1.81154	0.905772	+	0.423766i	$0.139292\pi$
$48$	−90.7990	−0.273036
$49$	−304.063	−0.886482
$50$	27.1475	0.0767848
$51$	86.8427	0.238439
$52$	−177.089	−0.472266
$53$	370.288	0.959679	0.479839	−	0.877356i	$-0.340695\pi$
$53$	370.288	0.959679	0.479839	+	0.877356i	$0.340695\pi$
$54$	14.2603	0.0359366
$55$	481.329	1.18004
$56$	19.0170	0.0453795
$57$	−14.4379	−0.0335500
$58$	37.3614	0.0845827
$59$	714.277	1.57612	0.788059	−	0.615599i	$-0.211086\pi$
$59$	714.277	1.57612	0.788059	+	0.615599i	$0.211086\pi$
$60$	−187.238	−0.402872
$61$	−707.836	−1.48572	−0.742862	−	0.669445i	$-0.766532\pi$
$61$	−707.836	−1.48572	−0.742862	+	0.669445i	$0.766532\pi$
$62$	45.9807	0.0941863
$63$	155.569	0.311108
$64$	−498.057	−0.972768
$65$	−363.498	−0.693637
$66$	8.08582	0.0150802
$67$	−377.580	−0.688488	−0.344244	−	0.938880i	$-0.611865\pi$
$67$	−377.580	−0.688488	−0.344244	+	0.938880i	$0.611865\pi$
$68$	480.808	0.857449
$69$	58.4458	0.101972
$70$	19.4729	0.0332493
$71$	47.4331	0.0792855	0.0396428	−	0.999214i	$-0.487378\pi$
$71$	47.4331	0.0792855	0.0396428	+	0.999214i	$0.487378\pi$
$72$	75.9806	0.124367
$73$	691.513	1.10871	0.554353	−	0.832282i	$-0.312966\pi$
$73$	691.513	1.10871	0.554353	+	0.832282i	$0.312966\pi$
$74$	−46.3942	−0.0728814
$75$	−204.535	−0.314902
$76$	−79.9361	−0.120649
$77$	183.740	0.271937
$78$	−6.10639	−0.00886426
$79$	288.783	0.411273	0.205637	−	0.978628i	$-0.434074\pi$
$79$	288.783	0.411273	0.205637	+	0.978628i	$0.434074\pi$
$80$	−1031.88	−1.44210
$81$	565.700	0.775995
$82$	−32.9505	−0.0443753
$83$	−833.823	−1.10270	−0.551349	−	0.834275i	$-0.685887\pi$
$83$	−833.823	−1.10270	−0.551349	+	0.834275i	$0.685887\pi$
$84$	−71.4753	−0.0928403
$85$	986.922	1.25937
$86$	0	0
$87$	−281.488	−0.346882
$88$	89.7398	0.108708
$89$	−687.209	−0.818472	−0.409236	−	0.912429i	$-0.634205\pi$
$89$	−687.209	−0.818472	−0.409236	+	0.912429i	$0.634205\pi$
$90$	77.8021	0.0911229
$91$	−138.760	−0.159846
$92$	323.587	0.366699
$93$	−346.427	−0.386267
$94$	111.436	0.122274
$95$	−164.079	−0.177202
$96$	−52.4032	−0.0557123
$97$	1131.96	1.18488	0.592439	−	0.805615i	$-0.298165\pi$
$97$	1131.96	1.18488	0.592439	+	0.805615i	$0.298165\pi$
$98$	−58.0491	−0.0598351
$99$	734.118	0.745269
$100$	−1132.41	−1.13241
$101$	835.261	0.822887	0.411443	−	0.911435i	$-0.365025\pi$
$101$	835.261	0.822887	0.411443	+	0.911435i	$0.365025\pi$
$102$	16.5792	0.0160940
$103$	−387.049	−0.370262	−0.185131	−	0.982714i	$-0.559271\pi$
$103$	−387.049	−0.370262	−0.185131	+	0.982714i	$0.559271\pi$
$104$	−67.7713	−0.0638992
$105$	−146.712	−0.136359
$106$	70.6922	0.0647757
$107$	−797.155	−0.720224	−0.360112	−	0.932909i	$-0.617261\pi$
$107$	−797.155	−0.720224	−0.360112	+	0.932909i	$0.617261\pi$
$108$	−594.844	−0.529990
$109$	1288.66	1.13240	0.566199	−	0.824268i	$-0.308413\pi$
$109$	1288.66	1.13240	0.566199	+	0.824268i	$0.308413\pi$
$110$	91.8912	0.0796498
$111$	349.543	0.298894
$112$	−393.906	−0.332327
$113$	−1133.47	−0.943607	−0.471804	−	0.881704i	$-0.656397\pi$
$113$	−1133.47	−0.943607	−0.471804	+	0.881704i	$0.656397\pi$
$114$	−2.75636	−0.00226454
$115$	664.206	0.538587
$116$	−1558.47	−1.24742
$117$	−554.404	−0.438074
$118$	136.364	0.106384
$119$	376.743	0.290218
$120$	−71.6552	−0.0545100
$121$	−463.942	−0.348566
$122$	−135.134	−0.100282
$123$	248.256	0.181988
$124$	−1918.01	−1.38905
$125$	−281.151	−0.201175
$126$	29.6998	0.0209989
$127$	1984.05	1.38627	0.693133	−	0.720810i	$-0.256230\pi$
$127$	1984.05	1.38627	0.693133	+	0.720810i	$0.256230\pi$
$128$	−386.545	−0.266923
$129$	0	0
$130$	−69.3959	−0.0468187
$131$	479.419	0.319748	0.159874	−	0.987137i	$-0.448891\pi$
$131$	479.419	0.319748	0.159874	+	0.987137i	$0.448891\pi$
$132$	−337.287	−0.222402
$133$	−62.6349	−0.0408356
$134$	−72.0842	−0.0464711
$135$	−1221.00	−0.778419
$136$	184.003	0.116016
$137$	−2598.71	−1.62060	−0.810302	−	0.586013i	$-0.800697\pi$
$137$	−2598.71	−1.62060	−0.810302	+	0.586013i	$0.800697\pi$
$138$	11.1580	0.00688281
$139$	−817.069	−0.498582	−0.249291	−	0.968429i	$-0.580198\pi$
$139$	−817.069	−0.498582	−0.249291	+	0.968429i	$0.580198\pi$
$140$	−812.279	−0.490358
$141$	−839.584	−0.501459
$142$	9.05551	0.00535156
$143$	−654.800	−0.382917
$144$	−1573.82	−0.910773
$145$	−3198.97	−1.83214
$146$	132.018	0.0748346
$147$	437.353	0.245390
$148$	1935.26	1.07485
$149$	−3557.21	−1.95582	−0.977911	−	0.209020i	$-0.932973\pi$
$149$	−3557.21	−1.95582	−0.977911	+	0.209020i	$0.932973\pi$
$150$	−39.0480	−0.0212550
$151$	3401.24	1.83304	0.916520	−	0.399989i	$-0.130986\pi$
$151$	3401.24	1.83304	0.916520	+	0.399989i	$0.130986\pi$
$152$	−30.5913	−0.0163242
$153$	1505.24	0.795370
$154$	35.0781	0.0183550
$155$	−3936.97	−2.04016
$156$	254.718	0.130729
$157$	913.392	0.464310	0.232155	−	0.972679i	$-0.425422\pi$
$157$	913.392	0.464310	0.232155	+	0.972679i	$0.425422\pi$
$158$	55.1318	0.0277598
$159$	−532.609	−0.265652
$160$	−595.535	−0.294258
$161$	253.551	0.124115
$162$	107.999	0.0523776
$163$	3721.79	1.78843	0.894213	−	0.447643i	$-0.147736\pi$
$163$	3721.79	1.78843	0.894213	+	0.447643i	$0.147736\pi$
$164$	1374.48	0.654443
$165$	−692.326	−0.326652
$166$	−159.186	−0.0744292
$167$	1860.33	0.862014	0.431007	−	0.902349i	$-0.358158\pi$
$167$	1860.33	0.862014	0.431007	+	0.902349i	$0.358158\pi$
$168$	−27.3533	−0.0125616
$169$	−1702.50	−0.774919
$170$	188.414	0.0850043
$171$	−250.252	−0.111914
$172$	0	0
$173$	−2169.88	−0.953601	−0.476801	−	0.879011i	$-0.658204\pi$
$173$	−2169.88	−0.953601	−0.476801	+	0.879011i	$0.658204\pi$
$174$	−53.7393	−0.0234136
$175$	−887.317	−0.383285
$176$	−1858.82	−0.796100
$177$	−1027.39	−0.436290
$178$	−131.196	−0.0552447
$179$	2024.75	0.845456	0.422728	−	0.906257i	$-0.361073\pi$
$179$	2024.75	0.845456	0.422728	+	0.906257i	$0.361073\pi$
$180$	−3245.39	−1.34387
$181$	913.028	0.374944	0.187472	−	0.982270i	$-0.439971\pi$
$181$	913.028	0.374944	0.187472	+	0.982270i	$0.439971\pi$
$182$	−26.4909	−0.0107892
$183$	1018.13	0.411268
$184$	123.836	0.0496157
$185$	3972.38	1.57868
$186$	−66.1369	−0.0260720
$187$	1777.82	0.695227
$188$	−4648.39	−1.80329
$189$	−466.097	−0.179384
$190$	−31.3246	−0.0119607
$191$	−200.169	−0.0758311	−0.0379156	−	0.999281i	$-0.512072\pi$
$191$	−200.169	−0.0758311	−0.0379156	+	0.999281i	$0.512072\pi$
$192$	716.388	0.269275
$193$	601.137	0.224201	0.112100	−	0.993697i	$-0.464242\pi$
$193$	601.137	0.224201	0.112100	+	0.993697i	$0.464242\pi$
$194$	216.104	0.0799761
$195$	522.843	0.192008
$196$	2421.42	0.882443
$197$	−487.221	−0.176209	−0.0881043	−	0.996111i	$-0.528081\pi$
$197$	−487.221	−0.176209	−0.0881043	+	0.996111i	$0.528081\pi$
$198$	140.151	0.0503037
$199$	−2852.48	−1.01612	−0.508058	−	0.861323i	$-0.669636\pi$
$199$	−2852.48	−1.01612	−0.508058	+	0.861323i	$0.669636\pi$
$200$	−433.371	−0.153220
$201$	543.097	0.190582
$202$	159.461	0.0555426
$203$	−1221.16	−0.422210
$204$	−691.576	−0.237353
$205$	2821.30	0.961210
$206$	−73.8919	−0.0249917
$207$	1013.04	0.340150
$208$	1403.77	0.467953
$209$	−295.570	−0.0978230
$210$	−28.0090	−0.00920385
$211$	−4622.59	−1.50821	−0.754104	−	0.656755i	$-0.771929\pi$
$211$	−4622.59	−1.50821	−0.754104	+	0.656755i	$0.771929\pi$
$212$	−2948.81	−0.955307
$213$	−68.2260	−0.0219473
$214$	−152.186	−0.0486132
$215$	0	0
$216$	−227.645	−0.0717095
$217$	−1502.88	−0.470148
$218$	246.020	0.0764339
$219$	−994.647	−0.306904
$220$	−3833.09	−1.17467
$221$	−1342.61	−0.408659
$222$	66.7318	0.0201745
$223$	−1600.61	−0.480648	−0.240324	−	0.970693i	$-0.577254\pi$
$223$	−1600.61	−0.480648	−0.240324	+	0.970693i	$0.577254\pi$
$224$	−227.337	−0.0678106
$225$	−3545.20	−1.05043
$226$	−216.392	−0.0636909
$227$	−3364.78	−0.983824	−0.491912	−	0.870645i	$-0.663702\pi$
$227$	−3364.78	−0.983824	−0.491912	+	0.870645i	$0.663702\pi$
$228$	114.977	0.0333972
$229$	1751.33	0.505375	0.252688	−	0.967548i	$-0.418686\pi$
$229$	1751.33	0.505375	0.252688	+	0.967548i	$0.418686\pi$
$230$	126.804	0.0363532
$231$	−264.285	−0.0752757
$232$	−596.421	−0.168780
$233$	487.131	0.136966	0.0684828	−	0.997652i	$-0.478184\pi$
$233$	487.131	0.136966	0.0684828	+	0.997652i	$0.478184\pi$
$234$	−105.842	−0.0295688
$235$	−9541.43	−2.64857
$236$	−5688.19	−1.56894
$237$	−415.374	−0.113846
$238$	71.9244	0.0195889
$239$	−1044.04	−0.282567	−0.141283	−	0.989969i	$-0.545123\pi$
$239$	−1044.04	−0.282567	−0.141283	+	0.989969i	$0.545123\pi$
$240$	1484.22	0.399192
$241$	−5568.61	−1.48841	−0.744203	−	0.667954i	$-0.767170\pi$
$241$	−5568.61	−1.48841	−0.744203	+	0.667954i	$0.767170\pi$
$242$	−88.5717	−0.0235273
$243$	−2830.47	−0.747221
$244$	5636.89	1.47896
$245$	4970.29	1.29608
$246$	47.3948	0.0122837
$247$	223.214	0.0575010
$248$	−734.015	−0.187943
$249$	1199.34	0.305241
$250$	−53.6748	−0.0135788
$251$	4323.07	1.08713	0.543566	−	0.839367i	$-0.317074\pi$
$251$	4323.07	1.08713	0.543566	+	0.839367i	$0.317074\pi$
$252$	−1238.88	−0.309691
$253$	1196.49	0.297323
$254$	378.777	0.0935692
$255$	−1419.55	−0.348611
$256$	3910.66	0.954752
$257$	−2098.48	−0.509336	−0.254668	−	0.967029i	$-0.581966\pi$
$257$	−2098.48	−0.509336	−0.254668	+	0.967029i	$0.581966\pi$
$258$	0	0
$259$	1516.40	0.363800
$260$	2894.74	0.690477
$261$	−4879.03	−1.15711
$262$	91.5265	0.0215822
$263$	−4053.69	−0.950423	−0.475211	−	0.879872i	$-0.657628\pi$
$263$	−4053.69	−0.950423	−0.475211	+	0.879872i	$0.657628\pi$
$264$	−129.078	−0.0300918
$265$	−6052.82	−1.40310
$266$	−11.9577	−0.00275629
$267$	988.456	0.226564
$268$	3006.87	0.685351
$269$	6316.81	1.43176	0.715879	−	0.698225i	$-0.246026\pi$
$269$	6316.81	1.43176	0.715879	+	0.698225i	$0.246026\pi$
$270$	−233.102	−0.0525412
$271$	2675.53	0.599730	0.299865	−	0.953982i	$-0.403058\pi$
$271$	2675.53	0.599730	0.299865	+	0.953982i	$0.403058\pi$
$272$	−3811.33	−0.849618
$273$	199.587	0.0442476
$274$	−496.123	−0.109386
$275$	−4187.19	−0.918172
$276$	−465.436	−0.101507
$277$	−1287.80	−0.279336	−0.139668	−	0.990198i	$-0.544604\pi$
$277$	−1287.80	−0.279336	−0.139668	+	0.990198i	$0.544604\pi$
$278$	−155.988	−0.0336529
$279$	−6004.62	−1.28848
$280$	−310.856	−0.0663471
$281$	−605.821	−0.128613	−0.0643065	−	0.997930i	$-0.520484\pi$
$281$	−605.821	−0.128613	−0.0643065	+	0.997930i	$0.520484\pi$
$282$	−160.286	−0.0338471
$283$	8085.19	1.69828	0.849142	−	0.528164i	$-0.177119\pi$
$283$	8085.19	1.69828	0.849142	+	0.528164i	$0.177119\pi$
$284$	−377.736	−0.0789243
$285$	236.006	0.0490519
$286$	−125.009	−0.0258459
$287$	1076.99	0.221507
$288$	−908.304	−0.185841
$289$	−1267.73	−0.258036
$290$	−610.719	−0.123664
$291$	−1628.17	−0.327990
$292$	−5506.90	−1.10365
$293$	8460.67	1.68695	0.843477	−	0.537165i	$-0.180505\pi$
$293$	8460.67	1.68695	0.843477	+	0.537165i	$0.180505\pi$
$294$	83.4957	0.0165632
$295$	−11675.8	−2.30437
$296$	740.617	0.145431
$297$	−2199.48	−0.429720
$298$	−679.110	−0.132013
$299$	−903.585	−0.174768
$300$	1628.82	0.313467
$301$	0	0
$302$	649.335	0.123725
$303$	−1201.41	−0.227786
$304$	633.649	0.119547
$305$	11570.5	2.17221
$306$	287.368	0.0536853
$307$	−6035.32	−1.12200	−0.561000	−	0.827816i	$-0.689583\pi$
$307$	−6035.32	−1.12200	−0.561000	+	0.827816i	$0.689583\pi$
$308$	−1463.23	−0.270698
$309$	556.716	0.102493
$310$	−751.611	−0.137705
$311$	730.378	0.133170	0.0665851	−	0.997781i	$-0.478790\pi$
$311$	730.378	0.133170	0.0665851	+	0.997781i	$0.478790\pi$
$312$	97.4797	0.0176881
$313$	8222.72	1.48491	0.742453	−	0.669898i	$-0.233662\pi$
$313$	8222.72	1.48491	0.742453	+	0.669898i	$0.233662\pi$
$314$	174.377	0.0313397
$315$	−2542.96	−0.454856
$316$	−2299.74	−0.409399
$317$	−810.334	−0.143574	−0.0717869	−	0.997420i	$-0.522870\pi$
$317$	−810.334	−0.143574	−0.0717869	+	0.997420i	$0.522870\pi$
$318$	−101.681	−0.0179308
$319$	−5762.57	−1.01142
$320$	8141.37	1.42224
$321$	1146.60	0.199367
$322$	48.4057	0.00837746
$323$	−606.039	−0.104399
$324$	−4504.98	−0.772460
$325$	3162.16	0.539707
$326$	710.532	0.120714
$327$	−1853.56	−0.313463
$328$	526.008	0.0885485
$329$	−3642.30	−0.610354
$330$	−132.173	−0.0220481
$331$	3825.94	0.635325	0.317662	−	0.948204i	$-0.397102\pi$
$331$	3825.94	0.635325	0.317662	+	0.948204i	$0.397102\pi$
$332$	6640.19	1.09767
$333$	6058.63	0.997029
$334$	355.157	0.0581836
$335$	6172.01	1.00661
$336$	566.580	0.0919925
$337$	10896.0	1.76125	0.880627	−	0.473811i	$-0.157122\pi$
$337$	10896.0	1.76125	0.880627	+	0.473811i	$0.157122\pi$
$338$	−325.026	−0.0523050
$339$	1630.34	0.261203
$340$	−7859.40	−1.25364
$341$	−7091.99	−1.12625
$342$	−47.7760	−0.00755388
$343$	4037.63	0.635603
$344$	0	0
$345$	−955.369	−0.149088
$346$	−414.255	−0.0643655
$347$	−10305.9	−1.59438	−0.797189	−	0.603729i	$-0.793681\pi$
$347$	−10305.9	−1.59438	−0.797189	+	0.603729i	$0.793681\pi$
$348$	2241.65	0.345302
$349$	−5783.63	−0.887079	−0.443540	−	0.896255i	$-0.646277\pi$
$349$	−5783.63	−0.887079	−0.443540	+	0.896255i	$0.646277\pi$
$350$	−169.399	−0.0258707
$351$	1661.04	0.252592
$352$	−1072.79	−0.162443
$353$	−10008.8	−1.50911	−0.754556	−	0.656236i	$-0.772148\pi$
$353$	−10008.8	−1.50911	−0.754556	+	0.656236i	$0.772148\pi$
$354$	−196.140	−0.0294484
$355$	−775.353	−0.115920
$356$	5472.63	0.814743
$357$	−541.893	−0.0803362
$358$	386.547	0.0570660
$359$	5024.84	0.738721	0.369360	−	0.929286i	$-0.379577\pi$
$359$	5024.84	0.738721	0.369360	+	0.929286i	$0.379577\pi$
$360$	−1242.00	−0.181831
$361$	−6758.24	−0.985310
$362$	174.307	0.0253077
$363$	667.317	0.0964877
$364$	1105.02	0.159118
$365$	−11303.6	−1.62099
$366$	194.372	0.0277595
$367$	8019.73	1.14067	0.570335	−	0.821412i	$-0.306813\pi$
$367$	8019.73	1.14067	0.570335	+	0.821412i	$0.306813\pi$
$368$	−2565.06	−0.363350
$369$	4303.01	0.607062
$370$	758.372	0.106556
$371$	−2310.57	−0.323340
$372$	2758.79	0.384507
$373$	10323.6	1.43308	0.716539	−	0.697547i	$-0.245725\pi$
$373$	10323.6	1.43308	0.716539	+	0.697547i	$0.245725\pi$
$374$	339.407	0.0469259
$375$	404.397	0.0556879
$376$	−1778.92	−0.243992
$377$	4351.88	0.594517
$378$	−88.9832	−0.0121079
$379$	−2810.62	−0.380928	−0.190464	−	0.981694i	$-0.560999\pi$
$379$	−2810.62	−0.380928	−0.190464	+	0.981694i	$0.560999\pi$
$380$	1306.66	0.176395
$381$	−2853.78	−0.383737
$382$	−38.2146	−0.00511840
$383$	6097.28	0.813463	0.406731	−	0.913548i	$-0.366668\pi$
$383$	6097.28	0.813463	0.406731	+	0.913548i	$0.366668\pi$
$384$	555.992	0.0738877
$385$	−3003.46	−0.397586
$386$	114.764	0.0151330
$387$	0	0
$388$	−9014.43	−1.17948
$389$	8231.65	1.07291	0.536454	−	0.843930i	$-0.319764\pi$
$389$	8231.65	1.07291	0.536454	+	0.843930i	$0.319764\pi$
$390$	99.8166	0.0129600
$391$	2453.29	0.317310
$392$	926.670	0.119398
$393$	−689.579	−0.0885105
$394$	−93.0160	−0.0118936
$395$	−4720.51	−0.601303
$396$	−5846.19	−0.741874
$397$	5185.30	0.655523	0.327761	−	0.944761i	$-0.393706\pi$
$397$	5185.30	0.655523	0.327761	+	0.944761i	$0.393706\pi$
$398$	−544.571	−0.0685851
$399$	90.0918	0.0113038
$400$	8976.58	1.12207
$401$	−6681.29	−0.832039	−0.416020	−	0.909356i	$-0.636575\pi$
$401$	−6681.29	−0.832039	−0.416020	+	0.909356i	$0.636575\pi$
$402$	103.683	0.0128638
$403$	5355.85	0.662019
$404$	−6651.64	−0.819138
$405$	−9247.08	−1.13455
$406$	−233.133	−0.0284980
$407$	7155.78	0.871495
$408$	−264.664	−0.0321147
$409$	1375.67	0.166315	0.0831573	−	0.996536i	$-0.473500\pi$
$409$	1375.67	0.166315	0.0831573	+	0.996536i	$0.473500\pi$
$410$	538.618	0.0648791
$411$	3737.89	0.448604
$412$	3082.28	0.368576
$413$	−4457.05	−0.531034
$414$	193.401	0.0229592
$415$	13629.9	1.61220
$416$	810.166	0.0954848
$417$	1175.24	0.138014
$418$	−56.4276	−0.00660279
$419$	−3509.28	−0.409164	−0.204582	−	0.978849i	$-0.565584\pi$
$419$	−3509.28	−0.409164	−0.204582	+	0.978849i	$0.565584\pi$
$420$	1168.35	0.135737
$421$	−2063.15	−0.238841	−0.119420	−	0.992844i	$-0.538104\pi$
$421$	−2063.15	−0.238841	−0.119420	+	0.992844i	$0.538104\pi$
$422$	−882.504	−0.101800
$423$	−14552.5	−1.67273
$424$	−1128.50	−0.129256
$425$	−8585.46	−0.979896
$426$	−13.0251	−0.00148138
$427$	4416.85	0.500577
$428$	6348.19	0.716942
$429$	941.840	0.105996
$430$	0	0
$431$	9348.39	1.04477	0.522385	−	0.852710i	$-0.325042\pi$
$431$	9348.39	1.04477	0.522385	+	0.852710i	$0.325042\pi$
$432$	4715.29	0.525150
$433$	8121.14	0.901333	0.450666	−	0.892692i	$-0.351186\pi$
$433$	8121.14	0.901333	0.450666	+	0.892692i	$0.351186\pi$
$434$	−286.916	−0.0317337
$435$	4601.28	0.507160
$436$	−10262.3	−1.12724
$437$	−407.869	−0.0446476
$438$	−189.889	−0.0207152
$439$	14232.3	1.54732	0.773659	−	0.633602i	$-0.218424\pi$
$439$	14232.3	1.54732	0.773659	+	0.633602i	$0.218424\pi$
$440$	−1466.91	−0.158937
$441$	7580.63	0.818554
$442$	−256.319	−0.0275834
$443$	5522.09	0.592240	0.296120	−	0.955151i	$-0.404307\pi$
$443$	5522.09	0.592240	0.296120	+	0.955151i	$0.404307\pi$
$444$	−2783.61	−0.297532
$445$	11233.3	1.19665
$446$	−305.574	−0.0324425
$447$	5116.55	0.541398
$448$	3107.85	0.327750
$449$	−11640.4	−1.22348	−0.611740	−	0.791059i	$-0.709530\pi$
$449$	−11640.4	−1.22348	−0.611740	+	0.791059i	$0.709530\pi$
$450$	−676.818	−0.0709011
$451$	5082.24	0.530628
$452$	9026.42	0.939308
$453$	−4892.22	−0.507409
$454$	−642.374	−0.0664055
$455$	2268.21	0.233704
$456$	44.0013	0.00451875
$457$	−11485.5	−1.17564	−0.587820	−	0.808992i	$-0.700013\pi$
$457$	−11485.5	−1.17564	−0.587820	+	0.808992i	$0.700013\pi$
$458$	334.348	0.0341115
$459$	−4509.84	−0.458608
$460$	−5289.44	−0.536133
$461$	−3519.04	−0.355527	−0.177764	−	0.984073i	$-0.556886\pi$
$461$	−3519.04	−0.355527	−0.177764	+	0.984073i	$0.556886\pi$
$462$	−50.4550	−0.00508091
$463$	2341.87	0.235067	0.117533	−	0.993069i	$-0.462501\pi$
$463$	2341.87	0.235067	0.117533	+	0.993069i	$0.462501\pi$
$464$	12353.9	1.23603
$465$	5662.79	0.564743
$466$	92.9987	0.00924481
$467$	2114.81	0.209554	0.104777	−	0.994496i	$-0.466587\pi$
$467$	2114.81	0.209554	0.104777	+	0.994496i	$0.466587\pi$
$468$	4415.02	0.436078
$469$	2356.07	0.231969
$470$	−1821.57	−0.178772
$471$	−1313.79	−0.128527
$472$	−2176.85	−0.212283
$473$	0	0
$474$	−79.2996	−0.00768429
$475$	1427.36	0.137878
$476$	−3000.21	−0.288896
$477$	−9231.69	−0.886143
$478$	−199.319	−0.0190725
$479$	6424.59	0.612833	0.306417	−	0.951897i	$-0.400870\pi$
$479$	6424.59	0.612833	0.306417	+	0.951897i	$0.400870\pi$
$480$	856.596	0.0814544
$481$	−5404.02	−0.512271
$482$	−1063.11	−0.100463
$483$	−364.698	−0.0343568
$484$	3694.62	0.346978
$485$	−18503.3	−1.73235
$486$	−540.368	−0.0504354
$487$	4037.94	0.375722	0.187861	−	0.982196i	$-0.439845\pi$
$487$	4037.94	0.375722	0.187861	+	0.982196i	$0.439845\pi$
$488$	2157.22	0.200108
$489$	−5353.29	−0.495060
$490$	948.884	0.0874821
$491$	−1144.72	−0.105215	−0.0526076	−	0.998615i	$-0.516753\pi$
$491$	−1144.72	−0.105215	−0.0526076	+	0.998615i	$0.516753\pi$
$492$	−1977.00	−0.181159
$493$	−11815.6	−1.07941
$494$	42.6140	0.00388116
$495$	−12000.1	−1.08962
$496$	15203.9	1.37636
$497$	−295.979	−0.0267133
$498$	228.968	0.0206030
$499$	−4755.22	−0.426599	−0.213300	−	0.976987i	$-0.568421\pi$
$499$	−4755.22	−0.426599	−0.213300	+	0.976987i	$0.568421\pi$
$500$	2238.96	0.200259
$501$	−2675.82	−0.238617
$502$	825.323	0.0733784
$503$	−15189.8	−1.34648	−0.673241	−	0.739423i	$-0.735099\pi$
$503$	−15189.8	−1.34648	−0.673241	+	0.739423i	$0.735099\pi$
$504$	−474.114	−0.0419022
$505$	−13653.4	−1.20310
$506$	228.423	0.0200685
$507$	2448.81	0.214508
$508$	−15800.1	−1.37995
$509$	−2394.00	−0.208472	−0.104236	−	0.994553i	$-0.533240\pi$
$509$	−2394.00	−0.208472	−0.104236	+	0.994553i	$0.533240\pi$
$510$	−271.008	−0.0235303
$511$	−4315.00	−0.373550
$512$	3838.95	0.331366
$513$	749.778	0.0645292
$514$	−400.623	−0.0343788
$515$	6326.79	0.541343
$516$	0	0
$517$	−17187.8	−1.46212
$518$	289.497	0.0245555
$519$	3121.08	0.263969
$520$	1107.81	0.0934240
$521$	9182.54	0.772158	0.386079	−	0.922466i	$-0.373829\pi$
$521$	9182.54	0.772158	0.386079	+	0.922466i	$0.373829\pi$
$522$	−931.462	−0.0781015
$523$	16321.6	1.36462	0.682310	−	0.731063i	$-0.260976\pi$
$523$	16321.6	1.36462	0.682310	+	0.731063i	$0.260976\pi$
$524$	−3817.88	−0.318292
$525$	1276.28	0.106098
$526$	−773.895	−0.0641510
$527$	−14541.5	−1.20197
$528$	2673.65	0.220371
$529$	−10515.9	−0.864298
$530$	−1155.55	−0.0947055
$531$	−17807.7	−1.45535
$532$	498.796	0.0406496
$533$	−3838.09	−0.311907
$534$	188.707	0.0152925
$535$	13030.5	1.05300
$536$	1150.72	0.0927304
$537$	−2912.32	−0.234033
$538$	1205.95	0.0966398
$539$	8953.40	0.715492
$540$	9723.47	0.774873
$541$	−22638.7	−1.79910	−0.899549	−	0.436821i	$-0.856104\pi$
$541$	−22638.7	−1.79910	−0.899549	+	0.436821i	$0.856104\pi$
$542$	510.789	0.0404802
$543$	−1313.27	−0.103789
$544$	−2199.65	−0.173363
$545$	−21064.8	−1.65563
$546$	38.1035	0.00298659
$547$	−23493.7	−1.83641	−0.918206	−	0.396102i	$-0.870363\pi$
$547$	−23493.7	−1.83641	−0.918206	+	0.396102i	$0.870363\pi$
$548$	20695.0	1.61322
$549$	17647.1	1.37188
$550$	−799.382	−0.0619741
$551$	1964.39	0.151880
$552$	−178.121	−0.0137343
$553$	−1801.99	−0.138568
$554$	−245.855	−0.0188545
$555$	−5713.72	−0.436998
$556$	6506.77	0.496311
$557$	−2071.07	−0.157547	−0.0787737	−	0.996893i	$-0.525100\pi$
$557$	−2071.07	−0.157547	−0.0787737	+	0.996893i	$0.525100\pi$
$558$	−1146.35	−0.0869692
$559$	0	0
$560$	6438.88	0.485879
$561$	−2557.16	−0.192448
$562$	−115.658	−0.00868103
$563$	−7675.72	−0.574588	−0.287294	−	0.957842i	$-0.592756\pi$
$563$	−7675.72	−0.574588	−0.287294	+	0.957842i	$0.592756\pi$
$564$	6686.07	0.499175
$565$	18527.9	1.37960
$566$	1543.55	0.114630
$567$	−3529.93	−0.261452
$568$	−144.558	−0.0106787
$569$	7917.36	0.583327	0.291664	−	0.956521i	$-0.405791\pi$
$569$	7917.36	0.583327	0.291664	+	0.956521i	$0.405791\pi$
$570$	45.0562	0.00331087
$571$	6374.22	0.467168	0.233584	−	0.972337i	$-0.424955\pi$
$571$	6374.22	0.467168	0.233584	+	0.972337i	$0.424955\pi$
$572$	5214.53	0.381172
$573$	287.916	0.0209911
$574$	205.609	0.0149512
$575$	−5778.08	−0.419065
$576$	12417.1	0.898229
$577$	−845.931	−0.0610339	−0.0305169	−	0.999534i	$-0.509715\pi$
$577$	−845.931	−0.0610339	−0.0305169	+	0.999534i	$0.509715\pi$
$578$	−242.025	−0.0174168
$579$	−864.653	−0.0620617
$580$	25475.2	1.82379
$581$	5203.00	0.371527
$582$	−310.836	−0.0221384
$583$	−10903.4	−0.774571
$584$	−2107.47	−0.149328
$585$	9062.42	0.640487
$586$	1615.24	0.113865
$587$	−11303.1	−0.794766	−0.397383	−	0.917653i	$-0.630082\pi$
$587$	−11303.1	−0.794766	−0.397383	+	0.917653i	$0.630082\pi$
$588$	−3482.89	−0.244272
$589$	2417.57	0.169125
$590$	−2229.03	−0.155539
$591$	700.801	0.0487768
$592$	−15340.7	−1.06503
$593$	−16273.7	−1.12695	−0.563476	−	0.826133i	$-0.690536\pi$
$593$	−16273.7	−1.12695	−0.563476	+	0.826133i	$0.690536\pi$
$594$	−419.906	−0.0290050
$595$	−6158.33	−0.424314
$596$	28328.0	1.94691
$597$	4102.90	0.281274
$598$	−172.505	−0.0117964
$599$	−20685.5	−1.41100	−0.705499	−	0.708711i	$-0.749277\pi$
$599$	−20685.5	−1.41100	−0.705499	+	0.708711i	$0.749277\pi$
$600$	623.345	0.0424132
$601$	−3962.98	−0.268974	−0.134487	−	0.990915i	$-0.542939\pi$
$601$	−3962.98	−0.268974	−0.134487	+	0.990915i	$0.542939\pi$
$602$	0	0
$603$	9413.48	0.635732
$604$	−27086.0	−1.82469
$605$	7583.70	0.509622
$606$	−229.362	−0.0153749
$607$	−8042.13	−0.537759	−0.268880	−	0.963174i	$-0.586653\pi$
$607$	−8042.13	−0.537759	−0.268880	+	0.963174i	$0.586653\pi$
$608$	365.701	0.0243933
$609$	1756.47	0.116873
$610$	2208.93	0.146618
$611$	12980.2	0.859445
$612$	−11987.1	−0.791746
$613$	2499.78	0.164707	0.0823533	−	0.996603i	$-0.473756\pi$
$613$	2499.78	0.164707	0.0823533	+	0.996603i	$0.473756\pi$
$614$	−1152.21	−0.0757320
$615$	−4058.05	−0.266076
$616$	−559.971	−0.0366264
$617$	−14266.5	−0.930874	−0.465437	−	0.885081i	$-0.654103\pi$
$617$	−14266.5	−0.930874	−0.465437	+	0.885081i	$0.654103\pi$
$618$	106.283	0.00691804
$619$	18552.6	1.20467	0.602336	−	0.798242i	$-0.294237\pi$
$619$	18552.6	1.20467	0.602336	+	0.798242i	$0.294237\pi$
$620$	31352.2	2.03086
$621$	−3035.15	−0.196130
$622$	139.437	0.00898863
$623$	4288.14	0.275764
$624$	−2019.14	−0.129535
$625$	−13179.2	−0.843469
$626$	1569.81	0.100227
$627$	425.137	0.0270787
$628$	−7273.85	−0.462194
$629$	14672.3	0.930082
$630$	−485.480	−0.0307016
$631$	5781.54	0.364754	0.182377	−	0.983229i	$-0.441621\pi$
$631$	5781.54	0.364754	0.182377	+	0.983229i	$0.441621\pi$
$632$	−880.100	−0.0553932
$633$	6648.96	0.417492
$634$	−154.702	−0.00969084
$635$	−32431.7	−2.02679
$636$	4241.46	0.264441
$637$	−6761.58	−0.420571
$638$	−1100.14	−0.0682679
$639$	−1182.56	−0.0732102
$640$	6318.56	0.390255
$641$	11652.1	0.717988	0.358994	−	0.933340i	$-0.383120\pi$
$641$	11652.1	0.717988	0.358994	+	0.933340i	$0.383120\pi$
$642$	218.899	0.0134568
$643$	16276.0	0.998232	0.499116	−	0.866535i	$-0.333658\pi$
$643$	16276.0	0.998232	0.499116	+	0.866535i	$0.333658\pi$
$644$	−2019.16	−0.123550
$645$	0	0
$646$	−115.700	−0.00704666
$647$	8989.81	0.546253	0.273127	−	0.961978i	$-0.411942\pi$
$647$	8989.81	0.546253	0.273127	+	0.961978i	$0.411942\pi$
$648$	−1724.04	−0.104517
$649$	−21032.5	−1.27211
$650$	603.691	0.0364288
$651$	2161.69	0.130143
$652$	−29638.7	−1.78028
$653$	21403.8	1.28269	0.641345	−	0.767253i	$-0.278377\pi$
$653$	21403.8	1.28269	0.641345	+	0.767253i	$0.278377\pi$
$654$	−353.866	−0.0211579
$655$	−7836.70	−0.467489
$656$	−10895.4	−0.648467
$657$	−17240.2	−1.02375
$658$	−695.356	−0.0411973
$659$	3368.05	0.199091	0.0995453	−	0.995033i	$-0.468261\pi$
$659$	3368.05	0.199091	0.0995453	+	0.995033i	$0.468261\pi$
$660$	5513.38	0.325163
$661$	−2486.31	−0.146303	−0.0731516	−	0.997321i	$-0.523306\pi$
$661$	−2486.31	−0.146303	−0.0731516	+	0.997321i	$0.523306\pi$
$662$	730.414	0.0428827
$663$	1931.16	0.113122
$664$	2541.18	0.148519
$665$	1023.85	0.0597038
$666$	1156.66	0.0672968
$667$	−7952.00	−0.461623
$668$	−14814.8	−0.858086
$669$	2302.25	0.133050
$670$	1178.31	0.0679432
$671$	20842.8	1.19915
$672$	326.993	0.0187709
$673$	1314.19	0.0752724	0.0376362	−	0.999292i	$-0.488017\pi$
$673$	1314.19	0.0752724	0.0376362	+	0.999292i	$0.488017\pi$
$674$	2080.17	0.118880
$675$	10621.7	0.605674
$676$	13557.9	0.771389
$677$	−22015.0	−1.24978	−0.624892	−	0.780711i	$-0.714857\pi$
$677$	−22015.0	−1.24978	−0.624892	+	0.780711i	$0.714857\pi$
$678$	311.250	0.0176305
$679$	−7063.36	−0.399215
$680$	−3007.76	−0.169621
$681$	4839.77	0.272335
$682$	−1353.94	−0.0760191
$683$	−1781.55	−0.0998086	−0.0499043	−	0.998754i	$-0.515892\pi$
$683$	−1781.55	−0.0998086	−0.0499043	+	0.998754i	$0.515892\pi$
$684$	1992.90	0.111404
$685$	42479.1	2.36941
$686$	770.830	0.0429015
$687$	−2519.04	−0.139895
$688$	0	0
$689$	8234.25	0.455298
$690$	−182.391	−0.0100630
$691$	17900.0	0.985455	0.492728	−	0.870184i	$-0.336000\pi$
$691$	17900.0	0.985455	0.492728	+	0.870184i	$0.336000\pi$
$692$	17280.0	0.949257
$693$	−4580.85	−0.251100
$694$	−1967.51	−0.107616
$695$	13356.0	0.728953
$696$	857.870	0.0467205
$697$	10420.7	0.566300
$698$	−1104.16	−0.0598755
$699$	−700.671	−0.0379139
$700$	7066.20	0.381539
$701$	−21853.9	−1.17748	−0.588738	−	0.808324i	$-0.700375\pi$
$701$	−21853.9	−1.17748	−0.588738	+	0.808324i	$0.700375\pi$
$702$	317.112	0.0170493
$703$	−2439.32	−0.130869
$704$	14665.7	0.785135
$705$	13724.0	0.733160
$706$	−1910.80	−0.101861
$707$	−5211.98	−0.277251
$708$	8181.68	0.434303
$709$	−6023.38	−0.319059	−0.159529	−	0.987193i	$-0.550998\pi$
$709$	−6023.38	−0.319059	−0.159529	+	0.987193i	$0.550998\pi$
$710$	−148.024	−0.00782426
$711$	−7199.67	−0.379759
$712$	2094.35	0.110238
$713$	−9786.52	−0.514036
$714$	−103.453	−0.00542248
$715$	10703.5	0.559845
$716$	−16124.2	−0.841604
$717$	1501.71	0.0782182
$718$	959.298	0.0498617
$719$	32712.1	1.69674	0.848369	−	0.529405i	$-0.177585\pi$
$719$	32712.1	1.69674	0.848369	+	0.529405i	$0.177585\pi$
$720$	25726.0	1.33160
$721$	2415.16	0.124751
$722$	−1290.22	−0.0665058
$723$	8009.69	0.412010
$724$	−7270.94	−0.373235
$725$	27828.6	1.42555
$726$	127.398	0.00651266
$727$	−1159.22	−0.0591379	−0.0295690	−	0.999563i	$-0.509413\pi$
$727$	−1159.22	−0.0591379	−0.0295690	+	0.999563i	$0.509413\pi$
$728$	422.888	0.0215292
$729$	−11202.7	−0.569154
$730$	−2157.99	−0.109412
$731$	0	0
$732$	−8107.90	−0.409394
$733$	−13950.0	−0.702938	−0.351469	−	0.936199i	$-0.614318\pi$
$733$	−13950.0	−0.702938	−0.351469	+	0.936199i	$0.614318\pi$
$734$	1531.06	0.0769922
$735$	−7149.08	−0.358773
$736$	−1480.38	−0.0741408
$737$	11118.2	0.555688
$738$	821.493	0.0409751
$739$	39671.7	1.97476	0.987381	−	0.158366i	$-0.0506224\pi$
$739$	39671.7	1.97476	0.987381	+	0.158366i	$0.0506224\pi$
$740$	−31634.2	−1.57148
$741$	−321.062	−0.0159170
$742$	−441.115	−0.0218246
$743$	−6363.81	−0.314220	−0.157110	−	0.987581i	$-0.550218\pi$
$743$	−6363.81	−0.314220	−0.157110	+	0.987581i	$0.550218\pi$
$744$	1055.78	0.0520252
$745$	58146.9	2.85952
$746$	1970.90	0.0967289
$747$	20788.1	1.01820
$748$	−14157.8	−0.692059
$749$	4974.20	0.242661
$750$	77.2039	0.00375878
$751$	28384.6	1.37919	0.689593	−	0.724197i	$-0.257789\pi$
$751$	28384.6	1.37919	0.689593	+	0.724197i	$0.257789\pi$
$752$	36847.5	1.78682
$753$	−6218.15	−0.300932
$754$	830.822	0.0401283
$755$	−55597.5	−2.68000
$756$	3711.79	0.178567
$757$	30888.5	1.48304	0.741520	−	0.670930i	$-0.234105\pi$
$757$	30888.5	1.48304	0.741520	+	0.670930i	$0.234105\pi$
$758$	−536.579	−0.0257117
$759$	−1720.99	−0.0823028
$760$	500.052	0.0238668
$761$	22824.4	1.08723	0.543615	−	0.839334i	$-0.317055\pi$
$761$	22824.4	1.08723	0.543615	+	0.839334i	$0.317055\pi$
$762$	−544.819	−0.0259012
$763$	−8041.17	−0.381533
$764$	1594.06	0.0754857
$765$	−24605.1	−1.16287
$766$	1164.04	0.0549066
$767$	15883.7	0.747753
$768$	−5624.95	−0.264288
$769$	−7291.88	−0.341940	−0.170970	−	0.985276i	$-0.554690\pi$
$769$	−7291.88	−0.341940	−0.170970	+	0.985276i	$0.554690\pi$
$770$	−573.395	−0.0268360
$771$	3018.37	0.140991
$772$	−4787.18	−0.223179
$773$	−24056.6	−1.11935	−0.559674	−	0.828713i	$-0.689074\pi$
$773$	−24056.6	−1.11935	−0.559674	+	0.828713i	$0.689074\pi$
$774$	0	0
$775$	34248.6	1.58741
$776$	−3449.79	−0.159588
$777$	−2181.13	−0.100705
$778$	1571.51	0.0724184
$779$	−1732.48	−0.0796821
$780$	−4163.69	−0.191133
$781$	−1396.71	−0.0639925
$782$	468.361	0.0214176
$783$	14618.0	0.667184
$784$	−19194.5	−0.874384
$785$	−14930.5	−0.678845
$786$	−131.648	−0.00597422
$787$	−35097.3	−1.58969	−0.794843	−	0.606815i	$-0.792447\pi$
$787$	−35097.3	−1.58969	−0.794843	+	0.606815i	$0.792447\pi$
$788$	3880.01	0.175406
$789$	5830.68	0.263090
$790$	−901.199	−0.0405863
$791$	7072.76	0.317925
$792$	−2237.31	−0.100378
$793$	−15740.5	−0.704868
$794$	989.931	0.0442460
$795$	8706.15	0.388397
$796$	22715.9	1.01149
$797$	−39237.3	−1.74386	−0.871930	−	0.489631i	$-0.837131\pi$
$797$	−39237.3	−1.74386	−0.871930	+	0.489631i	$0.837131\pi$
$798$	17.1995	0.000762978 0
$799$	−35242.0	−1.56041
$800$	5180.70	0.228957
$801$	17132.9	0.755756
$802$	−1275.53	−0.0561604
$803$	−20362.2	−0.894852
$804$	−4324.98	−0.189714
$805$	−4144.60	−0.181463
$806$	1022.49	0.0446845
$807$	−9085.87	−0.396329
$808$	−2545.56	−0.110832
$809$	21145.2	0.918945	0.459473	−	0.888192i	$-0.348038\pi$
$809$	21145.2	0.918945	0.459473	+	0.888192i	$0.348038\pi$
$810$	−1765.37	−0.0765788
$811$	−28604.0	−1.23850	−0.619250	−	0.785194i	$-0.712563\pi$
$811$	−28604.0	−1.23850	−0.619250	+	0.785194i	$0.712563\pi$
$812$	9724.76	0.420286
$813$	−3848.38	−0.166013
$814$	1366.12	0.0588236
$815$	−60837.3	−2.61477
$816$	5482.08	0.235185
$817$	0	0
$818$	262.632	0.0112258
$819$	3459.44	0.147598
$820$	−22467.6	−0.956831
$821$	1010.47	0.0429547	0.0214773	−	0.999769i	$-0.493163\pi$
$821$	1010.47	0.0429547	0.0214773	+	0.999769i	$0.493163\pi$
$822$	713.605	0.0302796
$823$	21552.4	0.912840	0.456420	−	0.889764i	$-0.349131\pi$
$823$	21552.4	0.912840	0.456420	+	0.889764i	$0.349131\pi$
$824$	1179.58	0.0498696
$825$	6022.70	0.254162
$826$	−850.900	−0.0358434
$827$	26527.8	1.11543	0.557716	−	0.830032i	$-0.311678\pi$
$827$	26527.8	1.11543	0.557716	+	0.830032i	$0.311678\pi$
$828$	−8067.39	−0.338600
$829$	43621.0	1.82753	0.913763	−	0.406248i	$-0.133163\pi$
$829$	43621.0	1.82753	0.913763	+	0.406248i	$0.133163\pi$
$830$	2602.10	0.108819
$831$	1852.32	0.0773240
$832$	−11075.5	−0.461508
$833$	18358.1	0.763591
$834$	224.367	0.00931558
$835$	−30409.3	−1.26031
$836$	2353.79	0.0973773
$837$	17990.4	0.742936
$838$	−669.962	−0.0276175
$839$	−15663.1	−0.644517	−0.322259	−	0.946652i	$-0.604442\pi$
$839$	−15663.1	−0.644517	−0.322259	+	0.946652i	$0.604442\pi$
$840$	447.124	0.0183658
$841$	13909.7	0.570326
$842$	−393.879	−0.0161211
$843$	871.390	0.0356017
$844$	36812.2	1.50134
$845$	27829.4	1.13297
$846$	−2778.23	−0.112905
$847$	2894.97	0.117441
$848$	23375.0	0.946582
$849$	−11629.4	−0.470108
$850$	−1639.06	−0.0661404
$851$	9874.54	0.397761
$852$	543.321	0.0218473
$853$	−18918.7	−0.759395	−0.379698	−	0.925111i	$-0.623972\pi$
$853$	−18918.7	−0.759395	−0.379698	+	0.925111i	$0.623972\pi$
$854$	843.227	0.0337876
$855$	4090.68	0.163624
$856$	2429.43	0.0970049
$857$	15680.6	0.625016	0.312508	−	0.949915i	$-0.398831\pi$
$857$	15680.6	0.625016	0.312508	+	0.949915i	$0.398831\pi$
$858$	179.808	0.00715448
$859$	5297.64	0.210423	0.105211	−	0.994450i	$-0.466448\pi$
$859$	5297.64	0.210423	0.105211	+	0.994450i	$0.466448\pi$
$860$	0	0
$861$	−1549.10	−0.0613162
$862$	1784.71	0.0705192
$863$	44834.6	1.76847	0.884234	−	0.467043i	$-0.154681\pi$
$863$	44834.6	1.76847	0.884234	+	0.467043i	$0.154681\pi$
$864$	2721.36	0.107156
$865$	35469.4	1.39422
$866$	1550.42	0.0608376
$867$	1823.46	0.0714279
$868$	11968.3	0.468006
$869$	−8503.45	−0.331945
$870$	878.436	0.0342319
$871$	−8396.40	−0.326637
$872$	−3927.36	−0.152520
$873$	−28221.0	−1.09409
$874$	−77.8668	−0.00301360
$875$	1754.36	0.0677809
$876$	7920.92	0.305506
$877$	4123.34	0.158763	0.0793816	−	0.996844i	$-0.474705\pi$
$877$	4123.34	0.158763	0.0793816	+	0.996844i	$0.474705\pi$
$878$	2717.11	0.104440
$879$	−12169.5	−0.466971
$880$	30384.7	1.16394
$881$	−16577.6	−0.633954	−0.316977	−	0.948433i	$-0.602668\pi$
$881$	−16577.6	−0.633954	−0.316977	+	0.948433i	$0.602668\pi$
$882$	1447.23	0.0552502
$883$	10292.1	0.392251	0.196125	−	0.980579i	$-0.437164\pi$
$883$	10292.1	0.392251	0.196125	+	0.980579i	$0.437164\pi$
$884$	10691.9	0.406797
$885$	16794.0	0.637879
$886$	1054.23	0.0399746
$887$	−36360.5	−1.37640	−0.688200	−	0.725521i	$-0.741599\pi$
$887$	−36360.5	−1.37640	−0.688200	+	0.725521i	$0.741599\pi$
$888$	−1065.28	−0.0402571
$889$	−12380.3	−0.467067
$890$	2144.56	0.0807706
$891$	−16657.5	−0.626317
$892$	12746.5	0.478458
$893$	5859.11	0.219561
$894$	976.808	0.0365429
$895$	−33097.0	−1.23610
$896$	2412.02	0.0899329
$897$	1299.68	0.0483781
$898$	−2222.28	−0.0825816
$899$	47134.1	1.74862
$900$	28232.4	1.04564
$901$	−22356.5	−0.826641
$902$	970.257	0.0358160
$903$	0	0
$904$	3454.38	0.127092
$905$	−14924.6	−0.548187
$906$	−933.980	−0.0342488
$907$	7338.83	0.268668	0.134334	−	0.990936i	$-0.457111\pi$
$907$	7338.83	0.268668	0.134334	+	0.990936i	$0.457111\pi$
$908$	26795.6	0.979342
$909$	−20824.0	−0.759833
$910$	433.026	0.0157744
$911$	30551.5	1.11111	0.555553	−	0.831481i	$-0.312507\pi$
$911$	30551.5	1.11111	0.555553	+	0.831481i	$0.312507\pi$
$912$	−911.417	−0.0330921
$913$	24552.6	0.890004
$914$	−2192.70	−0.0793525
$915$	−16642.5	−0.601295
$916$	−13946.8	−0.503073
$917$	−2991.54	−0.107731
$918$	−860.979	−0.0309548
$919$	36007.4	1.29246	0.646232	−	0.763141i	$-0.276344\pi$
$919$	36007.4	1.29246	0.646232	+	0.763141i	$0.276344\pi$
$920$	−2024.25	−0.0725407
$921$	8680.99	0.310584
$922$	−671.825	−0.0239972
$923$	1054.79	0.0376152
$924$	2104.65	0.0749328
$925$	−34556.6	−1.22834
$926$	447.090	0.0158664
$927$	9649.55	0.341891
$928$	7129.87	0.252208
$929$	32481.2	1.14712	0.573560	−	0.819163i	$-0.305562\pi$
$929$	32481.2	1.14712	0.573560	+	0.819163i	$0.305562\pi$
$930$	1081.09	0.0381186
$931$	−3052.11	−0.107442
$932$	−3879.29	−0.136342
$933$	−1050.55	−0.0368633
$934$	403.740	0.0141443
$935$	−29060.8	−1.01646
$936$	1689.61	0.0590029
$937$	−16821.4	−0.586479	−0.293239	−	0.956039i	$-0.594733\pi$
$937$	−16821.4	−0.586479	−0.293239	+	0.956039i	$0.594733\pi$
$938$	449.801	0.0156573
$939$	−11827.3	−0.411042
$940$	75983.7	2.63651
$941$	−27481.4	−0.952037	−0.476018	−	0.879435i	$-0.657920\pi$
$941$	−27481.4	−0.952037	−0.476018	+	0.879435i	$0.657920\pi$
$942$	−250.817	−0.00867523
$943$	7013.19	0.242185
$944$	45089.9	1.55461
$945$	7618.94	0.262269
$946$	0	0
$947$	108.644	0.00372806	0.00186403	−	0.999998i	$-0.499407\pi$
$947$	108.644	0.00372806	0.00186403	+	0.999998i	$0.499407\pi$
$948$	3307.86	0.113327
$949$	15377.5	0.526000
$950$	272.500	0.00930639
$951$	1165.55	0.0397431
$952$	−1148.17	−0.0390886
$953$	−28197.9	−0.958468	−0.479234	−	0.877687i	$-0.659086\pi$
$953$	−28197.9	−0.958468	−0.479234	+	0.877687i	$0.659086\pi$
$954$	−1762.43	−0.0598123
$955$	3272.02	0.110869
$956$	8314.29	0.281280
$957$	8288.67	0.279973
$958$	1226.53	0.0413646
$959$	16215.8	0.546022
$960$	−11710.2	−0.393694
$961$	28216.9	0.947163
$962$	−1031.69	−0.0345769
$963$	19874.0	0.665036
$964$	44345.9	1.48163
$965$	−9826.33	−0.327793
$966$	−69.6249	−0.00231899
$967$	29918.6	0.994950	0.497475	−	0.867478i	$-0.334261\pi$
$967$	29918.6	0.994950	0.497475	+	0.867478i	$0.334261\pi$
$968$	1413.92	0.0469474
$969$	871.705	0.0288991
$970$	−3532.49	−0.116929
$971$	−20896.6	−0.690632	−0.345316	−	0.938486i	$-0.612228\pi$
$971$	−20896.6	−0.690632	−0.345316	+	0.938486i	$0.612228\pi$
$972$	22540.6	0.743817
$973$	5098.46	0.167985
$974$	770.888	0.0253602
$975$	−4548.33	−0.149398
$976$	−44683.3	−1.46545
$977$	−35891.4	−1.17530	−0.587650	−	0.809115i	$-0.699947\pi$
$977$	−35891.4	−1.17530	−0.587650	+	0.809115i	$0.699947\pi$
$978$	−1022.00	−0.0334152
$979$	20235.5	0.660601
$980$	−39581.2	−1.29018
$981$	−32127.8	−1.04563
$982$	−218.541	−0.00710174
$983$	−3477.08	−0.112820	−0.0564098	−	0.998408i	$-0.517965\pi$
$983$	−3477.08	−0.112820	−0.0564098	+	0.998408i	$0.517965\pi$
$984$	−756.590	−0.0245114
$985$	7964.24	0.257626
$986$	−2255.74	−0.0728572
$987$	5238.95	0.168954
$988$	−1777.57	−0.0572390
$989$	0	0
$990$	−2290.95	−0.0735466
$991$	33877.8	1.08594	0.542968	−	0.839753i	$-0.317300\pi$
$991$	33877.8	1.08594	0.542968	+	0.839753i	$0.317300\pi$
$992$	8774.72	0.280844
$993$	−5503.09	−0.175866
$994$	−56.5058	−0.00180307
$995$	46627.3	1.48561
$996$	−9551.01	−0.303851
$997$	−15043.0	−0.477850	−0.238925	−	0.971038i	$-0.576795\pi$
$997$	−15043.0	−0.477850	−0.238925	+	0.971038i	$0.576795\pi$
$998$	−907.825	−0.0287943
$999$	−18152.2	−0.574884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.f.1.6		10
43.7	odd	6		43.4.c.a.6.5	✓	20
43.37	odd	6		43.4.c.a.36.5	yes	20
43.42	odd	2		1849.4.a.d.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.5	✓	20	43.7	odd	6
43.4.c.a.36.5	yes	20	43.37	odd	6
1849.4.a.d.1.5		10	43.42	odd	2
1849.4.a.f.1.6		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+0.190911 q^{2} -1.43836 q^{3} -7.96355 q^{4} -16.3462 q^{5} -0.274600 q^{6} -6.23994 q^{7} -3.04762 q^{8} -24.9311 q^{9} +O(q^{10})\)	\(q+0.190911 q^{2} -1.43836 q^{3} -7.96355 q^{4} -16.3462 q^{5} -0.274600 q^{6} -6.23994 q^{7} -3.04762 q^{8} -24.9311 q^{9} -3.12068 q^{10} -29.4459 q^{11} +11.4545 q^{12} +22.2374 q^{13} -1.19127 q^{14} +23.5118 q^{15} +63.1266 q^{16} -60.3760 q^{17} -4.75963 q^{18} +10.0377 q^{19} +130.174 q^{20} +8.97530 q^{21} -5.62155 q^{22} -40.6335 q^{23} +4.38359 q^{24} +142.200 q^{25} +4.24537 q^{26} +74.6958 q^{27} +49.6921 q^{28} +195.701 q^{29} +4.48867 q^{30} +240.848 q^{31} +36.4326 q^{32} +42.3538 q^{33} -11.5265 q^{34} +102.000 q^{35} +198.540 q^{36} -243.015 q^{37} +1.91632 q^{38} -31.9855 q^{39} +49.8172 q^{40} -172.596 q^{41} +1.71349 q^{42} +234.494 q^{44} +407.530 q^{45} -7.75740 q^{46} +583.708 q^{47} -90.7990 q^{48} -304.063 q^{49} +27.1475 q^{50} +86.8427 q^{51} -177.089 q^{52} +370.288 q^{53} +14.2603 q^{54} +481.329 q^{55} +19.0170 q^{56} -14.4379 q^{57} +37.3614 q^{58} +714.277 q^{59} -187.238 q^{60} -707.836 q^{61} +45.9807 q^{62} +155.569 q^{63} -498.057 q^{64} -363.498 q^{65} +8.08582 q^{66} -377.580 q^{67} +480.808 q^{68} +58.4458 q^{69} +19.4729 q^{70} +47.4331 q^{71} +75.9806 q^{72} +691.513 q^{73} -46.3942 q^{74} -204.535 q^{75} -79.9361 q^{76} +183.740 q^{77} -6.10639 q^{78} +288.783 q^{79} -1031.88 q^{80} +565.700 q^{81} -32.9505 q^{82} -833.823 q^{83} -71.4753 q^{84} +986.922 q^{85} -281.488 q^{87} +89.7398 q^{88} -687.209 q^{89} +77.8021 q^{90} -138.760 q^{91} +323.587 q^{92} -346.427 q^{93} +111.436 q^{94} -164.079 q^{95} -52.4032 q^{96} +1131.96 q^{97} -58.0491 q^{98} +734.118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9}+O(q^{10}) \) 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9} - 27 q^{10} + 27 q^{11} - 72 q^{12} + 15 q^{13} - 96 q^{14} - 65 q^{15} + 67 q^{16} + 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 9 q^{21} - 190 q^{22} + 61 q^{23} - 202 q^{24} + 151 q^{25} - 21 q^{26} + 97 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} - 253 q^{31} + 399 q^{32} - 424 q^{33} - 231 q^{34} + 355 q^{35} + 1092 q^{36} - 129 q^{37} + 854 q^{38} - 691 q^{39} - 1345 q^{40} + 391 q^{41} - 31 q^{42} + 377 q^{44} - 944 q^{45} - 40 q^{46} - 334 q^{47} - 2401 q^{48} + 115 q^{49} + 424 q^{50} - 795 q^{51} + 564 q^{52} - 773 q^{53} + 182 q^{54} - 1242 q^{55} + 923 q^{56} + 765 q^{57} - 1328 q^{58} - 1483 q^{59} + 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 738 q^{64} + 1063 q^{65} - 1483 q^{66} + 642 q^{67} + 1052 q^{68} - 3503 q^{69} + 85 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} + 2232 q^{74} - 82 q^{75} - 252 q^{76} + 1448 q^{77} + 2822 q^{78} + 1405 q^{79} - 3157 q^{80} - 974 q^{81} - 3304 q^{82} - 543 q^{83} + 3652 q^{84} - 973 q^{85} + 1409 q^{87} + 2686 q^{88} - 2196 q^{89} - 742 q^{90} - 3513 q^{91} - 2629 q^{92} - 983 q^{93} - 4939 q^{94} + 149 q^{95} - 3540 q^{96} - 425 q^{97} - 213 q^{98} + 3181 q^{99}+O(q^{100}) \) 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9 - 27 * q^10 + 27 * q^11 - 72 * q^12 + 15 * q^13 - 96 * q^14 - 65 * q^15 + 67 * q^16 + 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 9 * q^21 - 190 * q^22 + 61 * q^23 - 202 * q^24 + 151 * q^25 - 21 * q^26 + 97 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 - 253 * q^31 + 399 * q^32 - 424 * q^33 - 231 * q^34 + 355 * q^35 + 1092 * q^36 - 129 * q^37 + 854 * q^38 - 691 * q^39 - 1345 * q^40 + 391 * q^41 - 31 * q^42 + 377 * q^44 - 944 * q^45 - 40 * q^46 - 334 * q^47 - 2401 * q^48 + 115 * q^49 + 424 * q^50 - 795 * q^51 + 564 * q^52 - 773 * q^53 + 182 * q^54 - 1242 * q^55 + 923 * q^56 + 765 * q^57 - 1328 * q^58 - 1483 * q^59 + 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 738 * q^64 + 1063 * q^65 - 1483 * q^66 + 642 * q^67 + 1052 * q^68 - 3503 * q^69 + 85 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 + 2232 * q^74 - 82 * q^75 - 252 * q^76 + 1448 * q^77 + 2822 * q^78 + 1405 * q^79 - 3157 * q^80 - 974 * q^81 - 3304 * q^82 - 543 * q^83 + 3652 * q^84 - 973 * q^85 + 1409 * q^87 + 2686 * q^88 - 2196 * q^89 - 742 * q^90 - 3513 * q^91 - 2629 * q^92 - 983 * q^93 - 4939 * q^94 + 149 * q^95 - 3540 * q^96 - 425 * q^97 - 213 * q^98 + 3181 * q^99

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