LMFDB - Embedded newform 1849.4.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$1$
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			1.10
Root			$5.31336$ 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)

$f(q)$	$=$	$q+5.31336 q^{2} -8.05642 q^{3} +20.2317 q^{4} -15.9193 q^{5} -42.8066 q^{6} -16.6323 q^{7} +64.9916 q^{8} +37.9059 q^{9} +O(q^{10})$	\(q+5.31336 q^{2} -8.05642 q^{3} +20.2317 q^{4} -15.9193 q^{5} -42.8066 q^{6} -16.6323 q^{7} +64.9916 q^{8} +37.9059 q^{9} -84.5852 q^{10} +31.4464 q^{11} -162.995 q^{12} +9.11045 q^{13} -88.3732 q^{14} +128.253 q^{15} +183.469 q^{16} +30.4259 q^{17} +201.407 q^{18} -7.43181 q^{19} -322.076 q^{20} +133.997 q^{21} +167.086 q^{22} +54.3032 q^{23} -523.599 q^{24} +128.426 q^{25} +48.4071 q^{26} -87.8621 q^{27} -336.500 q^{28} -264.757 q^{29} +681.453 q^{30} +314.176 q^{31} +454.906 q^{32} -253.345 q^{33} +161.664 q^{34} +264.775 q^{35} +766.901 q^{36} +206.172 q^{37} -39.4878 q^{38} -73.3976 q^{39} -1034.62 q^{40} -174.881 q^{41} +711.971 q^{42} +636.215 q^{44} -603.436 q^{45} +288.532 q^{46} -356.666 q^{47} -1478.11 q^{48} -66.3675 q^{49} +682.371 q^{50} -245.124 q^{51} +184.320 q^{52} -169.935 q^{53} -466.842 q^{54} -500.606 q^{55} -1080.96 q^{56} +59.8737 q^{57} -1406.75 q^{58} -673.320 q^{59} +2594.78 q^{60} -161.911 q^{61} +1669.33 q^{62} -630.460 q^{63} +949.319 q^{64} -145.032 q^{65} -1346.11 q^{66} +118.294 q^{67} +615.569 q^{68} -437.489 q^{69} +1406.84 q^{70} +90.1617 q^{71} +2463.56 q^{72} +98.0399 q^{73} +1095.47 q^{74} -1034.65 q^{75} -150.358 q^{76} -523.025 q^{77} -389.988 q^{78} +464.529 q^{79} -2920.71 q^{80} -315.604 q^{81} -929.203 q^{82} -149.834 q^{83} +2710.98 q^{84} -484.360 q^{85} +2132.99 q^{87} +2043.75 q^{88} -799.972 q^{89} -3206.27 q^{90} -151.528 q^{91} +1098.65 q^{92} -2531.13 q^{93} -1895.09 q^{94} +118.310 q^{95} -3664.91 q^{96} -862.058 q^{97} -352.634 q^{98} +1192.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.31336	1.87855	0.939277	−	0.343159i	$-0.111497\pi$
$2$	5.31336	1.87855	0.939277	+	0.343159i	$0.111497\pi$
$3$	−8.05642	−1.55046	−0.775229	−	0.631680i	$-0.782366\pi$
$3$	−8.05642	−1.55046	−0.775229	+	0.631680i	$0.782366\pi$
$4$	20.2317	2.52897
$5$	−15.9193	−1.42387	−0.711935	−	0.702245i	$-0.752181\pi$
$5$	−15.9193	−1.42387	−0.711935	+	0.702245i	$0.752181\pi$
$6$	−42.8066	−2.91262
$7$	−16.6323	−0.898058	−0.449029	−	0.893517i	$-0.648230\pi$
$7$	−16.6323	−0.898058	−0.449029	+	0.893517i	$0.648230\pi$
$8$	64.9916	2.87225
$9$	37.9059	1.40392
$10$	−84.5852	−2.67482
$11$	31.4464	0.861949	0.430974	−	0.902364i	$-0.358170\pi$
$11$	31.4464	0.861949	0.430974	+	0.902364i	$0.358170\pi$
$12$	−162.995	−3.92106
$13$	9.11045	0.194368	0.0971840	−	0.995266i	$-0.469016\pi$
$13$	9.11045	0.194368	0.0971840	+	0.995266i	$0.469016\pi$
$14$	−88.3732	−1.68705
$15$	128.253	2.20765
$16$	183.469	2.86671
$17$	30.4259	0.434080	0.217040	−	0.976163i	$-0.430360\pi$
$17$	30.4259	0.434080	0.217040	+	0.976163i	$0.430360\pi$
$18$	201.407	2.63734
$19$	−7.43181	−0.0897354	−0.0448677	−	0.998993i	$-0.514287\pi$
$19$	−7.43181	−0.0897354	−0.0448677	+	0.998993i	$0.514287\pi$
$20$	−322.076	−3.60092
$21$	133.997	1.39240
$22$	167.086	1.61922
$23$	54.3032	0.492304	0.246152	−	0.969231i	$-0.420834\pi$
$23$	54.3032	0.492304	0.246152	+	0.969231i	$0.420834\pi$
$24$	−523.599	−4.45330
$25$	128.426	1.02741
$26$	48.4071	0.365131
$27$	−87.8621	−0.626262
$28$	−336.500	−2.27116
$29$	−264.757	−1.69531	−0.847657	−	0.530545i	$-0.821987\pi$
$29$	−264.757	−1.69531	−0.847657	+	0.530545i	$0.821987\pi$
$30$	681.453	4.14719
$31$	314.176	1.82025	0.910124	−	0.414336i	$-0.135986\pi$
$31$	314.176	1.82025	0.910124	+	0.414336i	$0.135986\pi$
$32$	454.906	2.51302
$33$	−253.345	−1.33642
$34$	161.664	0.815443
$35$	264.775	1.27872
$36$	766.901	3.55047
$37$	206.172	0.916067	0.458033	−	0.888935i	$-0.348554\pi$
$37$	206.172	0.916067	0.458033	+	0.888935i	$0.348554\pi$
$38$	−39.4878	−0.168573
$39$	−73.3976	−0.301360
$40$	−1034.62	−4.08971
$41$	−174.881	−0.666141	−0.333070	−	0.942902i	$-0.608085\pi$
$41$	−174.881	−0.666141	−0.333070	+	0.942902i	$0.608085\pi$
$42$	711.971	2.61570
$43$	0	0
$43$	0	0
$44$	636.215	2.17984
$45$	−603.436	−1.99900
$46$	288.532	0.924820
$47$	−356.666	−1.10692	−0.553458	−	0.832877i	$-0.686692\pi$
$47$	−356.666	−1.10692	−0.553458	+	0.832877i	$0.686692\pi$
$48$	−1478.11	−4.44471
$49$	−66.3675	−0.193491
$50$	682.371	1.93004
$51$	−245.124	−0.673023
$52$	184.320	0.491551
$53$	−169.935	−0.440421	−0.220211	−	0.975452i	$-0.570674\pi$
$53$	−169.935	−0.440421	−0.220211	+	0.975452i	$0.570674\pi$
$54$	−466.842	−1.17647
$55$	−500.606	−1.22730
$56$	−1080.96	−2.57945
$57$	59.8737	0.139131
$58$	−1406.75	−3.18474
$59$	−673.320	−1.48574	−0.742871	−	0.669435i	$-0.766536\pi$
$59$	−673.320	−1.48574	−0.742871	+	0.669435i	$0.766536\pi$
$60$	2594.78	5.58308
$61$	−161.911	−0.339846	−0.169923	−	0.985457i	$-0.554352\pi$
$61$	−161.911	−0.339846	−0.169923	+	0.985457i	$0.554352\pi$
$62$	1669.33	3.41944
$63$	−630.460	−1.26080
$64$	949.319	1.85414
$65$	−145.032	−0.276755
$66$	−1346.11	−2.51053
$67$	118.294	0.215700	0.107850	−	0.994167i	$-0.465603\pi$
$67$	118.294	0.215700	0.107850	+	0.994167i	$0.465603\pi$
$68$	615.569	1.09777
$69$	−437.489	−0.763297
$70$	1406.84	2.40214
$71$	90.1617	0.150707	0.0753537	−	0.997157i	$-0.475991\pi$
$71$	90.1617	0.150707	0.0753537	+	0.997157i	$0.475991\pi$
$72$	2463.56	4.03241
$73$	98.0399	0.157188	0.0785939	−	0.996907i	$-0.474957\pi$
$73$	98.0399	0.157188	0.0785939	+	0.996907i	$0.474957\pi$
$74$	1095.47	1.72088
$75$	−1034.65	−1.59295
$76$	−150.358	−0.226938
$77$	−523.025	−0.774080
$78$	−389.988	−0.566120
$79$	464.529	0.661564	0.330782	−	0.943707i	$-0.392688\pi$
$79$	464.529	0.661564	0.330782	+	0.943707i	$0.392688\pi$
$80$	−2920.71	−4.08182
$81$	−315.604	−0.432928
$82$	−929.203	−1.25138
$83$	−149.834	−0.198150	−0.0990749	−	0.995080i	$-0.531588\pi$
$83$	−149.834	−0.198150	−0.0990749	+	0.995080i	$0.531588\pi$
$84$	2710.98	3.52134
$85$	−484.360	−0.618074
$86$	0	0
$87$	2132.99	2.62851
$88$	2043.75	2.47573
$89$	−799.972	−0.952773	−0.476387	−	0.879236i	$-0.658054\pi$
$89$	−799.972	−0.952773	−0.476387	+	0.879236i	$0.658054\pi$
$90$	−3206.27	−3.75523
$91$	−151.528	−0.174554
$92$	1098.65	1.24502
$93$	−2531.13	−2.82222
$94$	−1895.09	−2.07940
$95$	118.310	0.127772
$96$	−3664.91	−3.89634
$97$	−862.058	−0.902358	−0.451179	−	0.892433i	$-0.648996\pi$
$97$	−862.058	−0.902358	−0.451179	+	0.892433i	$0.648996\pi$
$98$	−352.634	−0.363484
$99$	1192.00	1.21011
$100$	2598.28	2.59828
$101$	−1027.99	−1.01276	−0.506380	−	0.862310i	$-0.669017\pi$
$101$	−1027.99	−1.01276	−0.506380	+	0.862310i	$0.669017\pi$
$102$	−1302.43	−1.26431
$103$	−1454.63	−1.39155	−0.695773	−	0.718262i	$-0.744938\pi$
$103$	−1454.63	−1.39155	−0.695773	+	0.718262i	$0.744938\pi$
$104$	592.103	0.558274
$105$	−2133.14	−1.98260
$106$	−902.923	−0.827355
$107$	1686.41	1.52366	0.761830	−	0.647778i	$-0.224301\pi$
$107$	1686.41	1.52366	0.761830	+	0.647778i	$0.224301\pi$
$108$	−1777.60	−1.58380
$109$	1724.21	1.51513	0.757567	−	0.652758i	$-0.226388\pi$
$109$	1724.21	1.51513	0.757567	+	0.652758i	$0.226388\pi$
$110$	−2659.90	−2.30556
$111$	−1661.01	−1.42032
$112$	−3051.51	−2.57447
$113$	−365.815	−0.304539	−0.152270	−	0.988339i	$-0.548658\pi$
$113$	−365.815	−0.304539	−0.152270	+	0.988339i	$0.548658\pi$
$114$	318.130	0.261365
$115$	−864.471	−0.700977
$116$	−5356.49	−4.28739
$117$	345.339	0.272877
$118$	−3577.59	−2.79105
$119$	−506.052	−0.389829
$120$	8335.36	6.34092
$121$	−342.125	−0.257044
$122$	−860.292	−0.638420
$123$	1408.91	1.03282
$124$	6356.33	4.60335
$125$	−54.5347	−0.0390219
$126$	−3349.86	−2.36849
$127$	−2486.96	−1.73765	−0.868827	−	0.495115i	$-0.835126\pi$
$127$	−2486.96	−1.73765	−0.868827	+	0.495115i	$0.835126\pi$
$128$	1404.83	0.970080
$129$	0	0
$130$	−770.609	−0.519899
$131$	−2385.96	−1.59131	−0.795657	−	0.605748i	$-0.792874\pi$
$131$	−2385.96	−1.59131	−0.795657	+	0.605748i	$0.792874\pi$
$132$	−5125.61	−3.37975
$133$	123.608	0.0805877
$134$	628.537	0.405204
$135$	1398.71	0.891715
$136$	1977.43	1.24679
$137$	−273.052	−0.170280	−0.0851400	−	0.996369i	$-0.527134\pi$
$137$	−273.052	−0.170280	−0.0851400	+	0.996369i	$0.527134\pi$
$138$	−2324.53	−1.43389
$139$	−96.8821	−0.0591182	−0.0295591	−	0.999563i	$-0.509410\pi$
$139$	−96.8821	−0.0591182	−0.0295591	+	0.999563i	$0.509410\pi$
$140$	5356.86	3.23384
$141$	2873.45	1.71623
$142$	479.061	0.283112
$143$	286.491	0.167535
$144$	6954.57	4.02463
$145$	4214.76	2.41391
$146$	520.921	0.295286
$147$	534.684	0.300000
$148$	4171.22	2.31670
$149$	−1045.49	−0.574833	−0.287416	−	0.957806i	$-0.592796\pi$
$149$	−1045.49	−0.574833	−0.287416	+	0.957806i	$0.592796\pi$
$150$	−5497.47	−2.99244
$151$	2794.03	1.50580	0.752898	−	0.658138i	$-0.228656\pi$
$151$	2794.03	1.50580	0.752898	+	0.658138i	$0.228656\pi$
$152$	−483.005	−0.257743
$153$	1153.32	0.609414
$154$	−2779.02	−1.45415
$155$	−5001.48	−2.59180
$156$	−1484.96	−0.762129
$157$	731.392	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$157$	731.392	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$158$	2468.21	1.24278
$159$	1369.06	0.682854
$160$	−7241.80	−3.57822
$161$	−903.185	−0.442118
$162$	−1676.92	−0.813279
$163$	833.064	0.400311	0.200155	−	0.979764i	$-0.435855\pi$
$163$	833.064	0.400311	0.200155	+	0.979764i	$0.435855\pi$
$164$	−3538.14	−1.68465
$165$	4033.09	1.90288
$166$	−796.122	−0.372235
$167$	−2486.11	−1.15198	−0.575990	−	0.817457i	$-0.695383\pi$
$167$	−2486.11	−1.15198	−0.575990	+	0.817457i	$0.695383\pi$
$168$	8708.65	3.99933
$169$	−2114.00	−0.962221
$170$	−2573.58	−1.16109
$171$	−281.709	−0.125981
$172$	0	0
$173$	−3354.66	−1.47428	−0.737139	−	0.675741i	$-0.763824\pi$
$173$	−3354.66	−1.47428	−0.737139	+	0.675741i	$0.763824\pi$
$174$	11333.3	4.93781
$175$	−2136.01	−0.922670
$176$	5769.45	2.47096
$177$	5424.54	2.30358
$178$	−4250.53	−1.78984
$179$	2570.05	1.07315	0.536576	−	0.843852i	$-0.319717\pi$
$179$	2570.05	1.07315	0.536576	+	0.843852i	$0.319717\pi$
$180$	−12208.6	−5.05541
$181$	3433.14	1.40985	0.704927	−	0.709280i	$-0.250980\pi$
$181$	3433.14	1.40985	0.704927	+	0.709280i	$0.250980\pi$
$182$	−805.120	−0.327909
$183$	1304.43	0.526917
$184$	3529.25	1.41402
$185$	−3282.12	−1.30436
$186$	−13448.8	−5.30169
$187$	956.784	0.374155
$188$	−7215.97	−2.79936
$189$	1461.35	0.562420
$190$	628.621	0.240026
$191$	−3252.00	−1.23197	−0.615986	−	0.787757i	$-0.711242\pi$
$191$	−3252.00	−1.23197	−0.615986	+	0.787757i	$0.711242\pi$
$192$	−7648.11	−2.87477
$193$	−1575.55	−0.587620	−0.293810	−	0.955864i	$-0.594923\pi$
$193$	−1575.55	−0.587620	−0.293810	+	0.955864i	$0.594923\pi$
$194$	−4580.42	−1.69513
$195$	1168.44	0.429097
$196$	−1342.73	−0.489333
$197$	619.947	0.224210	0.112105	−	0.993696i	$-0.464241\pi$
$197$	619.947	0.224210	0.112105	+	0.993696i	$0.464241\pi$
$198$	6333.53	2.27325
$199$	734.573	0.261671	0.130835	−	0.991404i	$-0.458234\pi$
$199$	734.573	0.261671	0.130835	+	0.991404i	$0.458234\pi$
$200$	8346.59	2.95096
$201$	−953.024	−0.334434
$202$	−5462.08	−1.90253
$203$	4403.51	1.52249
$204$	−4959.28	−1.70205
$205$	2783.99	0.948498
$206$	−7728.98	−2.61409
$207$	2058.41	0.691156
$208$	1671.49	0.557197
$209$	−233.703	−0.0773474
$210$	−11334.1	−3.72442
$211$	−1132.27	−0.369425	−0.184713	−	0.982793i	$-0.559135\pi$
$211$	−1132.27	−0.369425	−0.184713	+	0.982793i	$0.559135\pi$
$212$	−3438.07	−1.11381
$213$	−726.380	−0.233666
$214$	8960.50	2.86228
$215$	0	0
$216$	−5710.30	−1.79878
$217$	−5225.46	−1.63469
$218$	9161.35	2.84626
$219$	−789.850	−0.243713
$220$	−10128.1	−3.10381
$221$	277.194	0.0843713
$222$	−8825.52	−2.66815
$223$	1053.16	0.316255	0.158127	−	0.987419i	$-0.449454\pi$
$223$	1053.16	0.316255	0.158127	+	0.987419i	$0.449454\pi$
$224$	−7566.11	−2.25684
$225$	4868.09	1.44240
$226$	−1943.70	−0.572094
$227$	−3799.35	−1.11089	−0.555444	−	0.831554i	$-0.687452\pi$
$227$	−3799.35	−1.11089	−0.555444	+	0.831554i	$0.687452\pi$
$228$	1211.35	0.351858
$229$	−6324.08	−1.82492	−0.912460	−	0.409165i	$-0.865820\pi$
$229$	−6324.08	−1.82492	−0.912460	+	0.409165i	$0.865820\pi$
$230$	−4593.24	−1.31682
$231$	4213.70	1.20018
$232$	−17207.0	−4.86936
$233$	−1260.20	−0.354329	−0.177164	−	0.984181i	$-0.556692\pi$
$233$	−1260.20	−0.354329	−0.177164	+	0.984181i	$0.556692\pi$
$234$	1834.91	0.512615
$235$	5677.89	1.57610
$236$	−13622.4	−3.75739
$237$	−3742.44	−1.02573
$238$	−2688.83	−0.732316
$239$	−1489.44	−0.403111	−0.201556	−	0.979477i	$-0.564600\pi$
$239$	−1489.44	−0.403111	−0.201556	+	0.979477i	$0.564600\pi$
$240$	23530.5	6.32869
$241$	2610.20	0.697667	0.348833	−	0.937185i	$-0.386578\pi$
$241$	2610.20	0.697667	0.348833	+	0.937185i	$0.386578\pi$
$242$	−1817.83	−0.482871
$243$	4914.92	1.29750
$244$	−3275.75	−0.859460
$245$	1056.53	0.275506
$246$	7486.05	1.94022
$247$	−67.7071	−0.0174417
$248$	20418.8	5.22821
$249$	1207.13	0.307223
$250$	−289.762	−0.0733047
$251$	1203.05	0.302534	0.151267	−	0.988493i	$-0.451665\pi$
$251$	1203.05	0.302534	0.151267	+	0.988493i	$0.451665\pi$
$252$	−12755.3	−3.18853
$253$	1707.64	0.424341
$254$	−13214.1	−3.26428
$255$	3902.21	0.958297
$256$	−130.215	−0.0317909
$257$	2722.72	0.660851	0.330426	−	0.943832i	$-0.392808\pi$
$257$	2722.72	0.660851	0.330426	+	0.943832i	$0.392808\pi$
$258$	0	0
$259$	−3429.11	−0.822681
$260$	−2934.26	−0.699904
$261$	−10035.8	−2.38009
$262$	−12677.4	−2.98937
$263$	−2090.60	−0.490159	−0.245079	−	0.969503i	$-0.578814\pi$
$263$	−2090.60	−0.490159	−0.245079	+	0.969503i	$0.578814\pi$
$264$	−16465.3	−3.83852
$265$	2705.25	0.627102
$266$	656.772	0.151388
$267$	6444.90	1.47723
$268$	2393.29	0.545498
$269$	6705.95	1.51996	0.759980	−	0.649947i	$-0.225209\pi$
$269$	6705.95	1.51996	0.759980	+	0.649947i	$0.225209\pi$
$270$	7431.83	1.67514
$271$	1691.98	0.379264	0.189632	−	0.981855i	$-0.439271\pi$
$271$	1691.98	0.379264	0.189632	+	0.981855i	$0.439271\pi$
$272$	5582.22	1.24438
$273$	1220.77	0.270638
$274$	−1450.82	−0.319880
$275$	4038.52	0.885571
$276$	−8851.16	−1.93035
$277$	1523.64	0.330494	0.165247	−	0.986252i	$-0.447158\pi$
$277$	1523.64	0.330494	0.165247	+	0.986252i	$0.447158\pi$
$278$	−514.769	−0.111057
$279$	11909.1	2.55548
$280$	17208.1	3.67280
$281$	5118.39	1.08661	0.543305	−	0.839535i	$-0.317173\pi$
$281$	5118.39	1.08661	0.543305	+	0.839535i	$0.317173\pi$
$282$	15267.7	3.22403
$283$	−2730.30	−0.573497	−0.286749	−	0.958006i	$-0.592574\pi$
$283$	−2730.30	−0.573497	−0.286749	+	0.958006i	$0.592574\pi$
$284$	1824.13	0.381134
$285$	−953.151	−0.198105
$286$	1522.23	0.314724
$287$	2908.66	0.598233
$288$	17243.6	3.52808
$289$	−3987.27	−0.811574
$290$	22394.5	4.53466
$291$	6945.10	1.39907
$292$	1983.52	0.397523
$293$	−1885.86	−0.376018	−0.188009	−	0.982167i	$-0.560203\pi$
$293$	−1885.86	−0.376018	−0.188009	+	0.982167i	$0.560203\pi$
$294$	2840.97	0.563567
$295$	10718.8	2.11550
$296$	13399.4	2.63117
$297$	−2762.94	−0.539806
$298$	−5555.07	−1.07986
$299$	494.726	0.0956882
$300$	−20932.8	−4.02852
$301$	0	0
$302$	14845.7	2.82872
$303$	8281.92	1.57024
$304$	−1363.51	−0.257245
$305$	2577.52	0.483897
$306$	6128.00	1.14482
$307$	4571.21	0.849813	0.424907	−	0.905237i	$-0.360307\pi$
$307$	4571.21	0.849813	0.424907	+	0.905237i	$0.360307\pi$
$308$	−10581.7	−1.95762
$309$	11719.1	2.15753
$310$	−26574.6	−4.86883
$311$	−7395.34	−1.34840	−0.674198	−	0.738550i	$-0.735511\pi$
$311$	−7395.34	−1.34840	−0.674198	+	0.738550i	$0.735511\pi$
$312$	−4770.23	−0.865580
$313$	384.858	0.0694998	0.0347499	−	0.999396i	$-0.488937\pi$
$313$	384.858	0.0694998	0.0347499	+	0.999396i	$0.488937\pi$
$314$	3886.14	0.698432
$315$	10036.5	1.79522
$316$	9398.22	1.67307
$317$	7188.20	1.27359	0.636797	−	0.771031i	$-0.280259\pi$
$317$	7188.20	1.27359	0.636797	+	0.771031i	$0.280259\pi$
$318$	7274.32	1.28278
$319$	−8325.64	−1.46127
$320$	−15112.5	−2.64005
$321$	−13586.4	−2.36237
$322$	−4798.94	−0.830542
$323$	−226.119	−0.0389524
$324$	−6385.23	−1.09486
$325$	1170.02	0.199695
$326$	4426.37	0.752006
$327$	−13891.0	−2.34915
$328$	−11365.8	−1.91332
$329$	5932.16	0.994075
$330$	21429.2	3.57467
$331$	6318.35	1.04921	0.524604	−	0.851346i	$-0.324213\pi$
$331$	6318.35	1.04921	0.524604	+	0.851346i	$0.324213\pi$
$332$	−3031.40	−0.501114
$333$	7815.13	1.28608
$334$	−13209.6	−2.16406
$335$	−1883.16	−0.307128
$336$	24584.3	3.99161
$337$	−297.364	−0.0480667	−0.0240333	−	0.999711i	$-0.507651\pi$
$337$	−297.364	−0.0480667	−0.0240333	+	0.999711i	$0.507651\pi$
$338$	−11232.4	−1.80758
$339$	2947.16	0.472176
$340$	−9799.45	−1.56309
$341$	9879.70	1.56896
$342$	−1496.82	−0.236663
$343$	6808.71	1.07182
$344$	0	0
$345$	6964.54	1.08684
$346$	−17824.5	−2.76951
$347$	−1785.11	−0.276166	−0.138083	−	0.990421i	$-0.544094\pi$
$347$	−1785.11	−0.276166	−0.138083	+	0.990421i	$0.544094\pi$
$348$	43154.1	6.64742
$349$	1031.55	0.158216	0.0791081	−	0.996866i	$-0.474793\pi$
$349$	1031.55	0.158216	0.0791081	+	0.996866i	$0.474793\pi$
$350$	−11349.4	−1.73329
$351$	−800.463	−0.121725
$352$	14305.1	2.16610
$353$	9938.77	1.49855	0.749274	−	0.662260i	$-0.230403\pi$
$353$	9938.77	1.49855	0.749274	+	0.662260i	$0.230403\pi$
$354$	28822.5	4.32740
$355$	−1435.32	−0.214588
$356$	−16184.8	−2.40953
$357$	4076.96	0.604414
$358$	13655.6	2.01598
$359$	−10918.0	−1.60510	−0.802549	−	0.596586i	$-0.796524\pi$
$359$	−10918.0	−1.60510	−0.802549	+	0.596586i	$0.796524\pi$
$360$	−39218.3	−5.74163
$361$	−6803.77	−0.991948
$362$	18241.5	2.64849
$363$	2756.31	0.398536
$364$	−3065.67	−0.441441
$365$	−1560.73	−0.223815
$366$	6930.87	0.989843
$367$	−7088.77	−1.00826	−0.504129	−	0.863628i	$-0.668186\pi$
$367$	−7088.77	−1.00826	−0.504129	+	0.863628i	$0.668186\pi$
$368$	9962.97	1.41129
$369$	−6629.00	−0.935209
$370$	−17439.1	−2.45031
$371$	2826.40	0.395524
$372$	−51209.2	−7.13730
$373$	−14328.1	−1.98896	−0.994478	−	0.104942i	$-0.966534\pi$
$373$	−14328.1	−1.98896	−0.994478	+	0.104942i	$0.966534\pi$
$374$	5083.73	0.702871
$375$	439.354	0.0605018
$376$	−23180.3	−3.17934
$377$	−2412.05	−0.329515
$378$	7764.65	1.05654
$379$	3776.04	0.511774	0.255887	−	0.966707i	$-0.417633\pi$
$379$	3776.04	0.511774	0.255887	+	0.966707i	$0.417633\pi$
$380$	2393.61	0.323130
$381$	20036.0	2.69416
$382$	−17279.0	−2.31433
$383$	2959.22	0.394802	0.197401	−	0.980323i	$-0.436750\pi$
$383$	2959.22	0.394802	0.197401	+	0.980323i	$0.436750\pi$
$384$	−11317.9	−1.50407
$385$	8326.21	1.10219
$386$	−8371.46	−1.10388
$387$	0	0
$388$	−17440.9	−2.28203
$389$	11332.9	1.47713	0.738564	−	0.674184i	$-0.235504\pi$
$389$	11332.9	1.47713	0.738564	+	0.674184i	$0.235504\pi$
$390$	6208.35	0.806082
$391$	1652.22	0.213699
$392$	−4313.33	−0.555755
$393$	19222.3	2.46726
$394$	3294.00	0.421191
$395$	−7394.99	−0.941981
$396$	24116.3	3.06032
$397$	−5811.71	−0.734714	−0.367357	−	0.930080i	$-0.619737\pi$
$397$	−5811.71	−0.734714	−0.367357	+	0.930080i	$0.619737\pi$
$398$	3903.05	0.491563
$399$	−995.836	−0.124948
$400$	23562.2	2.94527
$401$	5842.65	0.727601	0.363800	−	0.931477i	$-0.381479\pi$
$401$	5842.65	0.727601	0.363800	+	0.931477i	$0.381479\pi$
$402$	−5063.76	−0.628252
$403$	2862.29	0.353798
$404$	−20798.0	−2.56124
$405$	5024.22	0.616433
$406$	23397.4	2.86008
$407$	6483.36	0.789603
$408$	−15931.0	−1.93309
$409$	−5605.42	−0.677677	−0.338839	−	0.940845i	$-0.610034\pi$
$409$	−5605.42	−0.677677	−0.338839	+	0.940845i	$0.610034\pi$
$410$	14792.3	1.78180
$411$	2199.82	0.264012
$412$	−29429.8	−3.51917
$413$	11198.8	1.33428
$414$	10937.0	1.29837
$415$	2385.26	0.282139
$416$	4144.40	0.488451
$417$	780.523	0.0916603
$418$	−1241.75	−0.145301
$419$	−1304.47	−0.152094	−0.0760471	−	0.997104i	$-0.524230\pi$
$419$	−1304.47	−0.152094	−0.0760471	+	0.997104i	$0.524230\pi$
$420$	−43157.1	−5.01393
$421$	−5302.77	−0.613875	−0.306937	−	0.951730i	$-0.599304\pi$
$421$	−5302.77	−0.613875	−0.306937	+	0.951730i	$0.599304\pi$
$422$	−6016.15	−0.693985
$423$	−13519.7	−1.55402
$424$	−11044.3	−1.26500
$425$	3907.47	0.445976
$426$	−3859.52	−0.438954
$427$	2692.95	0.305202
$428$	34119.0	3.85328
$429$	−2308.09	−0.259757
$430$	0	0
$431$	−6201.04	−0.693025	−0.346512	−	0.938045i	$-0.612634\pi$
$431$	−6201.04	−0.693025	−0.346512	+	0.938045i	$0.612634\pi$
$432$	−16120.0	−1.79531
$433$	−2725.05	−0.302443	−0.151221	−	0.988500i	$-0.548321\pi$
$433$	−2725.05	−0.302443	−0.151221	+	0.988500i	$0.548321\pi$
$434$	−27764.7	−3.07085
$435$	−33955.8	−3.74266
$436$	34883.8	3.83172
$437$	−403.571	−0.0441771
$438$	−4196.76	−0.457828
$439$	4535.65	0.493109	0.246554	−	0.969129i	$-0.420702\pi$
$439$	4535.65	0.493109	0.246554	+	0.969129i	$0.420702\pi$
$440$	−32535.2	−3.52512
$441$	−2515.72	−0.271646
$442$	1472.83	0.158496
$443$	−4004.86	−0.429518	−0.214759	−	0.976667i	$-0.568897\pi$
$443$	−4004.86	−0.429518	−0.214759	+	0.976667i	$0.568897\pi$
$444$	−33605.1	−3.59195
$445$	12735.0	1.35663
$446$	5595.82	0.594102
$447$	8422.93	0.891254
$448$	−15789.3	−1.66513
$449$	−1949.51	−0.204906	−0.102453	−	0.994738i	$-0.532669\pi$
$449$	−1949.51	−0.204906	−0.102453	+	0.994738i	$0.532669\pi$
$450$	25865.9	2.70962
$451$	−5499.36	−0.574179
$452$	−7401.07	−0.770170
$453$	−22509.9	−2.33467
$454$	−20187.3	−2.08686
$455$	2412.22	0.248542
$456$	3891.29	0.399619
$457$	−8398.51	−0.859662	−0.429831	−	0.902909i	$-0.641427\pi$
$457$	−8398.51	−0.859662	−0.429831	+	0.902909i	$0.641427\pi$
$458$	−33602.1	−3.42821
$459$	−2673.28	−0.271848
$460$	−17489.8	−1.77275
$461$	−4279.12	−0.432318	−0.216159	−	0.976358i	$-0.569353\pi$
$461$	−4279.12	−0.432318	−0.216159	+	0.976358i	$0.569353\pi$
$462$	22388.9	2.25460
$463$	−12361.8	−1.24082	−0.620412	−	0.784276i	$-0.713035\pi$
$463$	−12361.8	−1.24082	−0.620412	+	0.784276i	$0.713035\pi$
$464$	−48574.8	−4.85997
$465$	40294.0	4.01847
$466$	−6695.91	−0.665626
$467$	−14344.7	−1.42140	−0.710702	−	0.703493i	$-0.751623\pi$
$467$	−14344.7	−1.42140	−0.710702	+	0.703493i	$0.751623\pi$
$468$	6986.82	0.690098
$469$	−1967.49	−0.193711
$470$	30168.6	2.96080
$471$	−5892.40	−0.576449
$472$	−43760.1	−4.26742
$473$	0	0
$474$	−19884.9	−1.92688
$475$	−954.435	−0.0921947
$476$	−10238.3	−0.985866
$477$	−6441.52	−0.618316
$478$	−7913.90	−0.757267
$479$	−7487.06	−0.714181	−0.357090	−	0.934070i	$-0.616231\pi$
$479$	−7487.06	−0.714181	−0.357090	+	0.934070i	$0.616231\pi$
$480$	58343.0	5.54787
$481$	1878.32	0.178054
$482$	13868.9	1.31060
$483$	7276.43	0.685485
$484$	−6921.79	−0.650056
$485$	13723.4	1.28484
$486$	26114.7	2.43742
$487$	−6910.13	−0.642973	−0.321487	−	0.946914i	$-0.604183\pi$
$487$	−6910.13	−0.642973	−0.321487	+	0.946914i	$0.604183\pi$
$488$	−10522.9	−0.976123
$489$	−6711.51	−0.620665
$490$	5613.71	0.517554
$491$	−16290.5	−1.49731	−0.748656	−	0.662959i	$-0.769300\pi$
$491$	−16290.5	−1.49731	−0.748656	+	0.662959i	$0.769300\pi$
$492$	28504.7	2.61198
$493$	−8055.46	−0.735902
$494$	−359.752	−0.0327652
$495$	−18975.9	−1.72304
$496$	57641.7	5.21812
$497$	−1499.59	−0.135344
$498$	6413.89	0.577135
$499$	−12574.1	−1.12804	−0.564022	−	0.825760i	$-0.690747\pi$
$499$	−12574.1	−1.12804	−0.564022	+	0.825760i	$0.690747\pi$
$500$	−1103.33	−0.0986850
$501$	20029.1	1.78610
$502$	6392.24	0.568326
$503$	−6289.08	−0.557488	−0.278744	−	0.960366i	$-0.589918\pi$
$503$	−6289.08	−0.557488	−0.278744	+	0.960366i	$0.589918\pi$
$504$	−40974.6	−3.62134
$505$	16364.9	1.44204
$506$	9073.28	0.797148
$507$	17031.3	1.49188
$508$	−50315.6	−4.39447
$509$	5528.64	0.481440	0.240720	−	0.970595i	$-0.422616\pi$
$509$	5528.64	0.481440	0.240720	+	0.970595i	$0.422616\pi$
$510$	20733.8	1.80021
$511$	−1630.63	−0.141164
$512$	−11930.5	−1.02980
$513$	652.974	0.0561979
$514$	14466.8	1.24145
$515$	23156.8	1.98138
$516$	0	0
$517$	−11215.8	−0.954105
$518$	−18220.1	−1.54545
$519$	27026.5	2.28581
$520$	−9425.89	−0.794909
$521$	767.214	0.0645149	0.0322574	−	0.999480i	$-0.489730\pi$
$521$	767.214	0.0645149	0.0322574	+	0.999480i	$0.489730\pi$
$522$	−53323.9	−4.47112
$523$	12324.9	1.03046	0.515229	−	0.857052i	$-0.327707\pi$
$523$	12324.9	1.03046	0.515229	+	0.857052i	$0.327707\pi$
$524$	−48272.1	−4.02438
$525$	17208.6	1.43056
$526$	−11108.1	−0.920790
$527$	9559.09	0.790134
$528$	−46481.1	−3.83112
$529$	−9218.17	−0.757637
$530$	14373.9	1.17805
$531$	−25522.8	−2.08586
$532$	2500.80	0.203804
$533$	−1593.24	−0.129476
$534$	34244.1	2.77507
$535$	−26846.6	−2.16949
$536$	7688.10	0.619544
$537$	−20705.4	−1.66388
$538$	35631.1	2.85533
$539$	−2087.02	−0.166780
$540$	28298.3	2.25512
$541$	12669.5	1.00684	0.503422	−	0.864041i	$-0.332074\pi$
$541$	12669.5	1.00684	0.503422	+	0.864041i	$0.332074\pi$
$542$	8990.09	0.712468
$543$	−27658.8	−2.18592
$544$	13840.9	1.09085
$545$	−27448.3	−2.15735
$546$	6486.38	0.508409
$547$	3010.76	0.235340	0.117670	−	0.993053i	$-0.462458\pi$
$547$	3010.76	0.235340	0.117670	+	0.993053i	$0.462458\pi$
$548$	−5524.31	−0.430633
$549$	−6137.39	−0.477117
$550$	21458.1	1.66359
$551$	1967.62	0.152130
$552$	−28433.1	−2.19238
$553$	−7726.17	−0.594123
$554$	8095.65	0.620851
$555$	26442.2	2.02236
$556$	−1960.09	−0.149508
$557$	11347.0	0.863177	0.431589	−	0.902071i	$-0.357953\pi$
$557$	11347.0	0.863177	0.431589	+	0.902071i	$0.357953\pi$
$558$	63277.4	4.80062
$559$	0	0
$560$	48578.1	3.66571
$561$	−7708.25	−0.580112
$562$	27195.8	2.04126
$563$	23560.2	1.76366	0.881832	−	0.471565i	$-0.156311\pi$
$563$	23560.2	1.76366	0.881832	+	0.471565i	$0.156311\pi$
$564$	58134.9	4.34028
$565$	5823.53	0.433624
$566$	−14507.1	−1.07735
$567$	5249.22	0.388794
$568$	5859.75	0.432869
$569$	13831.0	1.01903	0.509513	−	0.860463i	$-0.329826\pi$
$569$	13831.0	1.01903	0.509513	+	0.860463i	$0.329826\pi$
$570$	−5064.43	−0.372150
$571$	8885.36	0.651210	0.325605	−	0.945506i	$-0.394432\pi$
$571$	8885.36	0.651210	0.325605	+	0.945506i	$0.394432\pi$
$572$	5796.21	0.423691
$573$	26199.5	1.91012
$574$	15454.8	1.12381
$575$	6973.92	0.505796
$576$	35984.8	2.60306
$577$	18749.7	1.35279	0.676396	−	0.736539i	$-0.263541\pi$
$577$	18749.7	1.35279	0.676396	+	0.736539i	$0.263541\pi$
$578$	−21185.8	−1.52459
$579$	12693.3	0.911080
$580$	85271.9	6.10469
$581$	2492.08	0.177950
$582$	36901.8	2.62823
$583$	−5343.83	−0.379620
$584$	6371.77	0.451482
$585$	−5497.58	−0.388542
$586$	−10020.3	−0.706371
$587$	−15424.9	−1.08459	−0.542296	−	0.840188i	$-0.682445\pi$
$587$	−15424.9	−1.08459	−0.542296	+	0.840188i	$0.682445\pi$
$588$	10817.6	0.758690
$589$	−2334.90	−0.163341
$590$	56952.9	3.97409
$591$	−4994.55	−0.347628
$592$	37826.3	2.62610
$593$	20825.7	1.44218	0.721088	−	0.692844i	$-0.243642\pi$
$593$	20825.7	1.44218	0.721088	+	0.692844i	$0.243642\pi$
$594$	−14680.5	−1.01405
$595$	8056.01	0.555066
$596$	−21152.1	−1.45373
$597$	−5918.02	−0.405710
$598$	2628.66	0.179755
$599$	21242.2	1.44897	0.724484	−	0.689292i	$-0.242078\pi$
$599$	21242.2	1.44897	0.724484	+	0.689292i	$0.242078\pi$
$600$	−67243.6	−4.57535
$601$	−1556.16	−0.105619	−0.0528095	−	0.998605i	$-0.516818\pi$
$601$	−1556.16	−0.105619	−0.0528095	+	0.998605i	$0.516818\pi$
$602$	0	0
$603$	4484.03	0.302825
$604$	56528.1	3.80811
$605$	5446.42	0.365997
$606$	44004.8	2.94979
$607$	11941.0	0.798470	0.399235	−	0.916849i	$-0.369276\pi$
$607$	11941.0	0.798470	0.399235	+	0.916849i	$0.369276\pi$
$608$	−3380.77	−0.225507
$609$	−35476.5	−2.36056
$610$	13695.3	0.909027
$611$	−3249.39	−0.215149
$612$	23333.7	1.54119
$613$	−5125.04	−0.337681	−0.168840	−	0.985643i	$-0.554002\pi$
$613$	−5125.04	−0.337681	−0.168840	+	0.985643i	$0.554002\pi$
$614$	24288.5	1.59642
$615$	−22429.0	−1.47061
$616$	−33992.2	−2.22335
$617$	−21253.5	−1.38676	−0.693381	−	0.720571i	$-0.743880\pi$
$617$	−21253.5	−1.38676	−0.693381	+	0.720571i	$0.743880\pi$
$618$	62267.9	4.05304
$619$	−16229.9	−1.05385	−0.526926	−	0.849911i	$-0.676656\pi$
$619$	−16229.9	−1.05385	−0.526926	+	0.849911i	$0.676656\pi$
$620$	−101189.	−6.55457
$621$	−4771.19	−0.308311
$622$	−39294.1	−2.53304
$623$	13305.3	0.855646
$624$	−13466.2	−0.863910
$625$	−15185.1	−0.971843
$626$	2044.89	0.130559
$627$	1882.81	0.119924
$628$	14797.3	0.940251
$629$	6272.97	0.397646
$630$	53327.6	3.37242
$631$	−11379.3	−0.717910	−0.358955	−	0.933355i	$-0.616867\pi$
$631$	−11379.3	−0.717910	−0.358955	+	0.933355i	$0.616867\pi$
$632$	30190.4	1.90018
$633$	9122.04	0.572778
$634$	38193.5	2.39252
$635$	39590.8	2.47419
$636$	27698.6	1.72692
$637$	−604.638	−0.0376085
$638$	−44237.1	−2.74508
$639$	3417.66	0.211581
$640$	−22363.9	−1.38127
$641$	6841.44	0.421561	0.210781	−	0.977533i	$-0.432399\pi$
$641$	6841.44	0.421561	0.210781	+	0.977533i	$0.432399\pi$
$642$	−72189.5	−4.43784
$643$	4167.38	0.255592	0.127796	−	0.991800i	$-0.459210\pi$
$643$	4167.38	0.255592	0.127796	+	0.991800i	$0.459210\pi$
$644$	−18273.0	−1.11810
$645$	0	0
$646$	−1201.45	−0.0731742
$647$	17803.0	1.08178	0.540888	−	0.841094i	$-0.318088\pi$
$647$	17803.0	1.08178	0.540888	+	0.841094i	$0.318088\pi$
$648$	−20511.6	−1.24348
$649$	−21173.5	−1.28063
$650$	6216.71	0.375138
$651$	42098.5	2.53452
$652$	16854.3	1.01237
$653$	−14735.0	−0.883037	−0.441519	−	0.897252i	$-0.645560\pi$
$653$	−14735.0	−0.883037	−0.441519	+	0.897252i	$0.645560\pi$
$654$	−73807.7	−4.41301
$655$	37982.9	2.26582
$656$	−32085.3	−1.90963
$657$	3716.29	0.220679
$658$	31519.7	1.86742
$659$	−10846.8	−0.641169	−0.320585	−	0.947220i	$-0.603879\pi$
$659$	−10846.8	−0.641169	−0.320585	+	0.947220i	$0.603879\pi$
$660$	81596.4	4.81233
$661$	8365.45	0.492251	0.246126	−	0.969238i	$-0.420842\pi$
$661$	8365.45	0.492251	0.246126	+	0.969238i	$0.420842\pi$
$662$	33571.6	1.97099
$663$	−2233.19	−0.130814
$664$	−9737.96	−0.569136
$665$	−1967.76	−0.114746
$666$	41524.5	2.41598
$667$	−14377.1	−0.834610
$668$	−50298.3	−2.91332
$669$	−8484.70	−0.490340
$670$	−10005.9	−0.576958
$671$	−5091.52	−0.292930
$672$	60955.8	3.49914
$673$	4305.90	0.246627	0.123314	−	0.992368i	$-0.460648\pi$
$673$	4305.90	0.246627	0.123314	+	0.992368i	$0.460648\pi$
$674$	−1580.00	−0.0902959
$675$	−11283.7	−0.643425
$676$	−42769.9	−2.43343
$677$	−6938.20	−0.393880	−0.196940	−	0.980416i	$-0.563100\pi$
$677$	−6938.20	−0.393880	−0.196940	+	0.980416i	$0.563100\pi$
$678$	15659.3	0.887008
$679$	14338.0	0.810370
$680$	−31479.4	−1.77526
$681$	30609.1	1.72238
$682$	52494.4	2.94738
$683$	−23567.3	−1.32032	−0.660160	−	0.751125i	$-0.729511\pi$
$683$	−23567.3	−1.32032	−0.660160	+	0.751125i	$0.729511\pi$
$684$	−5699.46	−0.318603
$685$	4346.80	0.242457
$686$	36177.1	2.01348
$687$	50949.4	2.82946
$688$	0	0
$689$	−1548.18	−0.0856038
$690$	37005.1	2.04168
$691$	−22295.2	−1.22742	−0.613710	−	0.789531i	$-0.710324\pi$
$691$	−22295.2	−1.22742	−0.613710	+	0.789531i	$0.710324\pi$
$692$	−67870.6	−3.72840
$693$	−19825.7	−1.08675
$694$	−9484.91	−0.518793
$695$	1542.30	0.0841767
$696$	138626.	7.54975
$697$	−5320.90	−0.289158
$698$	5480.98	0.297218
$699$	10152.7	0.549372
$700$	−43215.2	−2.33340
$701$	−7387.69	−0.398044	−0.199022	−	0.979995i	$-0.563777\pi$
$701$	−7387.69	−0.398044	−0.199022	+	0.979995i	$0.563777\pi$
$702$	−4253.15	−0.228668
$703$	−1532.23	−0.0822037
$704$	29852.7	1.59817
$705$	−45743.4	−2.44368
$706$	52808.2	2.81510
$707$	17097.8	0.909518
$708$	109748.	5.82568
$709$	−20824.0	−1.10305	−0.551525	−	0.834159i	$-0.685954\pi$
$709$	−20824.0	−1.10305	−0.551525	+	0.834159i	$0.685954\pi$
$710$	−7626.34	−0.403115
$711$	17608.3	0.928783
$712$	−51991.4	−2.73660
$713$	17060.8	0.896115
$714$	21662.4	1.13542
$715$	−4560.75	−0.238549
$716$	51996.5	2.71397
$717$	11999.5	0.625007
$718$	−58011.3	−3.01527
$719$	−20442.9	−1.06035	−0.530175	−	0.847888i	$-0.677874\pi$
$719$	−20442.9	−1.06035	−0.530175	+	0.847888i	$0.677874\pi$
$720$	−110712.	−5.73055
$721$	24193.8	1.24969
$722$	−36150.8	−1.86343
$723$	−21028.8	−1.08170
$724$	69458.4	3.56547
$725$	−34001.6	−1.74177
$726$	14645.2	0.748671
$727$	6810.77	0.347452	0.173726	−	0.984794i	$-0.444419\pi$
$727$	6810.77	0.347452	0.173726	+	0.984794i	$0.444419\pi$
$728$	−9848.01	−0.501362
$729$	−31075.3	−1.57879
$730$	−8292.72	−0.420448
$731$	0	0
$732$	26390.8	1.33256
$733$	18357.3	0.925025	0.462512	−	0.886613i	$-0.346948\pi$
$733$	18357.3	0.925025	0.462512	+	0.886613i	$0.346948\pi$
$734$	−37665.2	−1.89407
$735$	−8511.82	−0.427161
$736$	24702.8	1.23717
$737$	3719.91	0.185922
$738$	−35222.2	−1.75684
$739$	−18743.1	−0.932985	−0.466493	−	0.884525i	$-0.654483\pi$
$739$	−18743.1	−0.932985	−0.466493	+	0.884525i	$0.654483\pi$
$740$	−66403.1	−3.29868
$741$	545.477	0.0270426
$742$	15017.7	0.743013
$743$	4326.42	0.213622	0.106811	−	0.994279i	$-0.465936\pi$
$743$	4326.42	0.213622	0.106811	+	0.994279i	$0.465936\pi$
$744$	−164502.	−8.10612
$745$	16643.6	0.818487
$746$	−76130.3	−3.73636
$747$	−5679.59	−0.278186
$748$	19357.4	0.946226
$749$	−28048.8	−1.36833
$750$	2334.45	0.113656
$751$	−6667.40	−0.323964	−0.161982	−	0.986794i	$-0.551789\pi$
$751$	−6667.40	−0.323964	−0.161982	+	0.986794i	$0.551789\pi$
$752$	−65437.3	−3.17321
$753$	−9692.28	−0.469066
$754$	−12816.1	−0.619012
$755$	−44479.2	−2.14406
$756$	29565.6	1.42234
$757$	40354.2	1.93751	0.968757	−	0.248014i	$-0.0797778\pi$
$757$	40354.2	1.93751	0.968757	+	0.248014i	$0.0797778\pi$
$758$	20063.4	0.961395
$759$	−13757.4	−0.657923
$760$	7689.12	0.366992
$761$	−16939.6	−0.806911	−0.403455	−	0.914999i	$-0.632191\pi$
$761$	−16939.6	−0.806911	−0.403455	+	0.914999i	$0.632191\pi$
$762$	106458.	5.06113
$763$	−28677.6	−1.36068
$764$	−65793.6	−3.11562
$765$	−18360.1	−0.867726
$766$	15723.4	0.741657
$767$	−6134.25	−0.288781
$768$	1049.07	0.0492904
$769$	−41567.3	−1.94923	−0.974613	−	0.223897i	$-0.928122\pi$
$769$	−41567.3	−1.94923	−0.974613	+	0.223897i	$0.928122\pi$
$770$	44240.1	2.07052
$771$	−21935.4	−1.02462
$772$	−31876.1	−1.48607
$773$	−21859.3	−1.01711	−0.508555	−	0.861030i	$-0.669820\pi$
$773$	−21859.3	−1.01711	−0.508555	+	0.861030i	$0.669820\pi$
$774$	0	0
$775$	40348.3	1.87013
$776$	−56026.5	−2.59180
$777$	27626.3	1.27553
$778$	60215.9	2.77486
$779$	1299.68	0.0597764
$780$	23639.6	1.08517
$781$	2835.26	0.129902
$782$	8778.84	0.401446
$783$	23262.1	1.06171
$784$	−12176.4	−0.554683
$785$	−11643.3	−0.529384
$786$	102135.	4.63489
$787$	33518.2	1.51816	0.759081	−	0.650996i	$-0.225649\pi$
$787$	33518.2	1.51816	0.759081	+	0.650996i	$0.225649\pi$
$788$	12542.6	0.567020
$789$	16842.7	0.759970
$790$	−39292.2	−1.76956
$791$	6084.33	0.273494
$792$	77470.1	3.47573
$793$	−1475.09	−0.0660553
$794$	−30879.7	−1.38020
$795$	−21794.6	−0.972296
$796$	14861.7	0.661757
$797$	4177.21	0.185652	0.0928259	−	0.995682i	$-0.470410\pi$
$797$	4177.21	0.185652	0.0928259	+	0.995682i	$0.470410\pi$
$798$	−5291.23	−0.234721
$799$	−10851.9	−0.480490
$800$	58421.6	2.58189
$801$	−30323.6	−1.33762
$802$	31044.1	1.36684
$803$	3083.00	0.135488
$804$	−19281.3	−0.845772
$805$	14378.1	0.629518
$806$	15208.3	0.664629
$807$	−54026.0	−2.35663
$808$	−66810.7	−2.90890
$809$	43230.5	1.87874	0.939372	−	0.342899i	$-0.111409\pi$
$809$	43230.5	1.87874	0.939372	+	0.342899i	$0.111409\pi$
$810$	26695.4	1.15800
$811$	−2253.54	−0.0975738	−0.0487869	−	0.998809i	$-0.515536\pi$
$811$	−2253.54	−0.0975738	−0.0487869	+	0.998809i	$0.515536\pi$
$812$	89090.6	3.85033
$813$	−13631.3	−0.588032
$814$	34448.4	1.48331
$815$	−13261.8	−0.569990
$816$	−44972.7	−1.92936
$817$	0	0
$818$	−29783.6	−1.27305
$819$	−5743.78	−0.245060
$820$	56324.9	2.39872
$821$	−31030.5	−1.31909	−0.659545	−	0.751665i	$-0.729251\pi$
$821$	−31030.5	−1.31909	−0.659545	+	0.751665i	$0.729251\pi$
$822$	11688.4	0.495961
$823$	21943.1	0.929389	0.464695	−	0.885471i	$-0.346164\pi$
$823$	21943.1	0.929389	0.464695	+	0.885471i	$0.346164\pi$
$824$	−94538.9	−3.99687
$825$	−32536.0	−1.37304
$826$	59503.4	2.50652
$827$	−4293.41	−0.180528	−0.0902639	−	0.995918i	$-0.528771\pi$
$827$	−4293.41	−0.180528	−0.0902639	+	0.995918i	$0.528771\pi$
$828$	41645.2	1.74791
$829$	−27147.6	−1.13736	−0.568682	−	0.822558i	$-0.692546\pi$
$829$	−27147.6	−1.13736	−0.568682	+	0.822558i	$0.692546\pi$
$830$	12673.7	0.530014
$831$	−12275.1	−0.512417
$832$	8648.73	0.360385
$833$	−2019.29	−0.0839907
$834$	4147.19	0.172189
$835$	39577.2	1.64027
$836$	−4728.23	−0.195609
$837$	−27604.2	−1.13995
$838$	−6931.11	−0.285717
$839$	−37996.0	−1.56349	−0.781744	−	0.623599i	$-0.785670\pi$
$839$	−37996.0	−1.56349	−0.781744	+	0.623599i	$0.785670\pi$
$840$	−138636.	−5.69452
$841$	45707.2	1.87409
$842$	−28175.5	−1.15320
$843$	−41235.9	−1.68474
$844$	−22907.8	−0.934264
$845$	33653.5	1.37008
$846$	−71835.1	−2.91932
$847$	5690.32	0.230840
$848$	−31177.8	−1.26256
$849$	21996.5	0.889183
$850$	20761.8	0.837791
$851$	11195.8	0.450983
$852$	−14695.9	−0.590933
$853$	5202.98	0.208847	0.104424	−	0.994533i	$-0.466700\pi$
$853$	5202.98	0.208847	0.104424	+	0.994533i	$0.466700\pi$
$854$	14308.6	0.573338
$855$	4484.62	0.179381
$856$	109603.	4.37633
$857$	42394.2	1.68980	0.844900	−	0.534925i	$-0.179660\pi$
$857$	42394.2	1.68980	0.844900	+	0.534925i	$0.179660\pi$
$858$	−12263.7	−0.487967
$859$	39517.4	1.56964	0.784818	−	0.619727i	$-0.212757\pi$
$859$	39517.4	1.56964	0.784818	+	0.619727i	$0.212757\pi$
$860$	0	0
$861$	−23433.4	−0.927536
$862$	−32948.3	−1.30189
$863$	−13568.4	−0.535195	−0.267597	−	0.963531i	$-0.586230\pi$
$863$	−13568.4	−0.535195	−0.267597	+	0.963531i	$0.586230\pi$
$864$	−39969.0	−1.57381
$865$	53404.0	2.09918
$866$	−14479.2	−0.568155
$867$	32123.1	1.25831
$868$	−105720.	−4.13408
$869$	14607.7	0.570234
$870$	−180419.	−7.03079
$871$	1077.71	0.0419252
$872$	112059.	4.35184
$873$	−32677.0	−1.26684
$874$	−2144.31	−0.0829891
$875$	907.036	0.0350439
$876$	−15980.0	−0.616342
$877$	38668.9	1.48889	0.744444	−	0.667685i	$-0.232715\pi$
$877$	38668.9	1.48889	0.744444	+	0.667685i	$0.232715\pi$
$878$	24099.5	0.926332
$879$	15193.3	0.583000
$880$	−91845.9	−3.51832
$881$	−3206.89	−0.122637	−0.0613183	−	0.998118i	$-0.519530\pi$
$881$	−3206.89	−0.122637	−0.0613183	+	0.998118i	$0.519530\pi$
$882$	−13366.9	−0.510302
$883$	21071.4	0.803067	0.401533	−	0.915844i	$-0.368477\pi$
$883$	21071.4	0.803067	0.401533	+	0.915844i	$0.368477\pi$
$884$	5608.11	0.213372
$885$	−86355.2	−3.28000
$886$	−21279.2	−0.806873
$887$	34055.1	1.28913	0.644565	−	0.764550i	$-0.277039\pi$
$887$	34055.1	1.28913	0.644565	+	0.764550i	$0.277039\pi$
$888$	−107952.	−4.07952
$889$	41363.8	1.56052
$890$	67665.7	2.54849
$891$	−9924.61	−0.373162
$892$	21307.3	0.799799
$893$	2650.67	0.0993296
$894$	44754.0	1.67427
$895$	−40913.5	−1.52803
$896$	−23365.4	−0.871188
$897$	−3985.72	−0.148360
$898$	−10358.4	−0.384927
$899$	−83180.3	−3.08589
$900$	98489.8	3.64777
$901$	−5170.41	−0.191178
$902$	−29220.1	−1.07863
$903$	0	0
$904$	−23774.9	−0.874713
$905$	−54653.4	−2.00745
$906$	−119603.	−4.38581
$907$	2553.70	0.0934887	0.0467443	−	0.998907i	$-0.485115\pi$
$907$	2553.70	0.0934887	0.0467443	+	0.998907i	$0.485115\pi$
$908$	−76867.4	−2.80940
$909$	−38966.8	−1.42184
$910$	12817.0	0.466900
$911$	27220.5	0.989960	0.494980	−	0.868904i	$-0.335175\pi$
$911$	27220.5	0.989960	0.494980	+	0.868904i	$0.335175\pi$
$912$	10985.0	0.398848
$913$	−4711.74	−0.170795
$914$	−44624.3	−1.61492
$915$	−20765.6	−0.750262
$916$	−127947.	−4.61516
$917$	39683.9	1.42909
$918$	−14204.1	−0.510681
$919$	23260.3	0.834914	0.417457	−	0.908697i	$-0.362921\pi$
$919$	23260.3	0.834914	0.417457	+	0.908697i	$0.362921\pi$
$920$	−56183.3	−2.01338
$921$	−36827.6	−1.31760
$922$	−22736.5	−0.812132
$923$	821.414	0.0292927
$924$	85250.6	3.03521
$925$	26477.8	0.941172
$926$	−65682.6	−2.33096
$927$	−55139.1	−1.95362
$928$	−120439.	−4.26036
$929$	−24748.2	−0.874016	−0.437008	−	0.899458i	$-0.643962\pi$
$929$	−24748.2	−0.874016	−0.437008	+	0.899458i	$0.643962\pi$
$930$	214096.	7.54892
$931$	493.230	0.0173630
$932$	−25496.1	−0.896087
$933$	59580.0	2.09063
$934$	−76218.7	−2.67018
$935$	−15231.4	−0.532748
$936$	22444.2	0.783772
$937$	17033.4	0.593870	0.296935	−	0.954898i	$-0.404036\pi$
$937$	17033.4	0.593870	0.296935	+	0.954898i	$0.404036\pi$
$938$	−10454.0	−0.363897
$939$	−3100.58	−0.107757
$940$	114874.	3.98592
$941$	41401.2	1.43426	0.717131	−	0.696939i	$-0.245455\pi$
$941$	41401.2	1.43426	0.717131	+	0.696939i	$0.245455\pi$
$942$	−31308.4	−1.08289
$943$	−9496.57	−0.327944
$944$	−123534.	−4.25919
$945$	−23263.7	−0.800812
$946$	0	0
$947$	−7077.16	−0.242848	−0.121424	−	0.992601i	$-0.538746\pi$
$947$	−7077.16	−0.242848	−0.121424	+	0.992601i	$0.538746\pi$
$948$	−75716.0	−2.59403
$949$	893.188	0.0305523
$950$	−5071.25	−0.173193
$951$	−57911.1	−1.97466
$952$	−32889.1	−1.11969
$953$	−23196.5	−0.788466	−0.394233	−	0.919011i	$-0.628990\pi$
$953$	−23196.5	−0.788466	−0.394233	+	0.919011i	$0.628990\pi$
$954$	−34226.1	−1.16154
$955$	51769.7	1.75417
$956$	−30133.9	−1.01946
$957$	67074.8	2.26564
$958$	−39781.4	−1.34163
$959$	4541.47	0.152921
$960$	121753.	4.09329
$961$	68915.6	2.31330
$962$	9980.18	0.334484
$963$	63924.8	2.13910
$964$	52808.9	1.76438
$965$	25081.7	0.836694
$966$	38662.3	1.28772
$967$	−19029.4	−0.632827	−0.316413	−	0.948621i	$-0.602479\pi$
$967$	−19029.4	−0.632827	−0.316413	+	0.948621i	$0.602479\pi$
$968$	−22235.3	−0.738294
$969$	1821.71	0.0603940
$970$	72917.3	2.41364
$971$	24534.4	0.810860	0.405430	−	0.914126i	$-0.367122\pi$
$971$	24534.4	0.810860	0.405430	+	0.914126i	$0.367122\pi$
$972$	99437.3	3.28133
$973$	1611.37	0.0530916
$974$	−36716.0	−1.20786
$975$	−9426.14	−0.309618
$976$	−29705.8	−0.974241
$977$	20716.3	0.678375	0.339187	−	0.940719i	$-0.389848\pi$
$977$	20716.3	0.678375	0.339187	+	0.940719i	$0.389848\pi$
$978$	−35660.7	−1.16595
$979$	−25156.2	−0.821242
$980$	21375.4	0.696747
$981$	65357.7	2.12713
$982$	−86557.2	−2.81278
$983$	−8923.01	−0.289522	−0.144761	−	0.989467i	$-0.546241\pi$
$983$	−8923.01	−0.289522	−0.144761	+	0.989467i	$0.546241\pi$
$984$	91567.4	2.96653
$985$	−9869.15	−0.319246
$986$	−42801.5	−1.38243
$987$	−47792.0	−1.54127
$988$	−1369.83	−0.0441095
$989$	0	0
$990$	−100826.	−3.23682
$991$	15414.5	0.494104	0.247052	−	0.969002i	$-0.420538\pi$
$991$	15414.5	0.494104	0.247052	+	0.969002i	$0.420538\pi$
$992$	142920.	4.57432
$993$	−50903.3	−1.62675
$994$	−7967.88	−0.254251
$995$	−11693.9	−0.372585
$996$	24422.3	0.776957
$997$	−672.384	−0.0213587	−0.0106793	−	0.999943i	$-0.503399\pi$
$997$	−672.384	−0.0213587	−0.0106793	+	0.999943i	$0.503399\pi$
$998$	−66810.7	−2.11909
$999$	−18114.7	−0.573698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.f.1.10		10
43.7	odd	6		43.4.c.a.6.1	✓	20
43.37	odd	6		43.4.c.a.36.1	yes	20
43.42	odd	2		1849.4.a.d.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.1	✓	20	43.7	odd	6
43.4.c.a.36.1	yes	20	43.37	odd	6
1849.4.a.d.1.1		10	43.42	odd	2
1849.4.a.f.1.10		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)

\(f(q)\)	\(=\)	\(q+5.31336 q^{2} -8.05642 q^{3} +20.2317 q^{4} -15.9193 q^{5} -42.8066 q^{6} -16.6323 q^{7} +64.9916 q^{8} +37.9059 q^{9} +O(q^{10})\)	\(q+5.31336 q^{2} -8.05642 q^{3} +20.2317 q^{4} -15.9193 q^{5} -42.8066 q^{6} -16.6323 q^{7} +64.9916 q^{8} +37.9059 q^{9} -84.5852 q^{10} +31.4464 q^{11} -162.995 q^{12} +9.11045 q^{13} -88.3732 q^{14} +128.253 q^{15} +183.469 q^{16} +30.4259 q^{17} +201.407 q^{18} -7.43181 q^{19} -322.076 q^{20} +133.997 q^{21} +167.086 q^{22} +54.3032 q^{23} -523.599 q^{24} +128.426 q^{25} +48.4071 q^{26} -87.8621 q^{27} -336.500 q^{28} -264.757 q^{29} +681.453 q^{30} +314.176 q^{31} +454.906 q^{32} -253.345 q^{33} +161.664 q^{34} +264.775 q^{35} +766.901 q^{36} +206.172 q^{37} -39.4878 q^{38} -73.3976 q^{39} -1034.62 q^{40} -174.881 q^{41} +711.971 q^{42} +636.215 q^{44} -603.436 q^{45} +288.532 q^{46} -356.666 q^{47} -1478.11 q^{48} -66.3675 q^{49} +682.371 q^{50} -245.124 q^{51} +184.320 q^{52} -169.935 q^{53} -466.842 q^{54} -500.606 q^{55} -1080.96 q^{56} +59.8737 q^{57} -1406.75 q^{58} -673.320 q^{59} +2594.78 q^{60} -161.911 q^{61} +1669.33 q^{62} -630.460 q^{63} +949.319 q^{64} -145.032 q^{65} -1346.11 q^{66} +118.294 q^{67} +615.569 q^{68} -437.489 q^{69} +1406.84 q^{70} +90.1617 q^{71} +2463.56 q^{72} +98.0399 q^{73} +1095.47 q^{74} -1034.65 q^{75} -150.358 q^{76} -523.025 q^{77} -389.988 q^{78} +464.529 q^{79} -2920.71 q^{80} -315.604 q^{81} -929.203 q^{82} -149.834 q^{83} +2710.98 q^{84} -484.360 q^{85} +2132.99 q^{87} +2043.75 q^{88} -799.972 q^{89} -3206.27 q^{90} -151.528 q^{91} +1098.65 q^{92} -2531.13 q^{93} -1895.09 q^{94} +118.310 q^{95} -3664.91 q^{96} -862.058 q^{97} -352.634 q^{98} +1192.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9}+O(q^{10}) \) 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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