LMFDB - Embedded newform 6043.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66509 q^{2} +0.277531 q^{3} +5.10272 q^{4} +0.539093 q^{5} -0.739647 q^{6} +3.78634 q^{7} -8.26903 q^{8} -2.92298 q^{9} +O(q^{10})$	\(q-2.66509 q^{2} +0.277531 q^{3} +5.10272 q^{4} +0.539093 q^{5} -0.739647 q^{6} +3.78634 q^{7} -8.26903 q^{8} -2.92298 q^{9} -1.43673 q^{10} +3.60856 q^{11} +1.41616 q^{12} +4.26828 q^{13} -10.0909 q^{14} +0.149615 q^{15} +11.8323 q^{16} +1.85574 q^{17} +7.79000 q^{18} -3.20887 q^{19} +2.75084 q^{20} +1.05083 q^{21} -9.61714 q^{22} +9.08496 q^{23} -2.29492 q^{24} -4.70938 q^{25} -11.3754 q^{26} -1.64381 q^{27} +19.3206 q^{28} +10.2688 q^{29} -0.398738 q^{30} +1.42156 q^{31} -14.9961 q^{32} +1.00149 q^{33} -4.94572 q^{34} +2.04119 q^{35} -14.9151 q^{36} +4.81209 q^{37} +8.55193 q^{38} +1.18458 q^{39} -4.45778 q^{40} +7.06529 q^{41} -2.80055 q^{42} -8.08222 q^{43} +18.4135 q^{44} -1.57576 q^{45} -24.2123 q^{46} -1.60750 q^{47} +3.28383 q^{48} +7.33634 q^{49} +12.5509 q^{50} +0.515027 q^{51} +21.7798 q^{52} -0.318129 q^{53} +4.38091 q^{54} +1.94535 q^{55} -31.3093 q^{56} -0.890562 q^{57} -27.3673 q^{58} +5.46257 q^{59} +0.763444 q^{60} +8.50376 q^{61} -3.78859 q^{62} -11.0674 q^{63} +16.3014 q^{64} +2.30100 q^{65} -2.66906 q^{66} -11.2592 q^{67} +9.46933 q^{68} +2.52136 q^{69} -5.43995 q^{70} +4.26327 q^{71} +24.1702 q^{72} -1.97900 q^{73} -12.8247 q^{74} -1.30700 q^{75} -16.3740 q^{76} +13.6632 q^{77} -3.15702 q^{78} -5.93095 q^{79} +6.37871 q^{80} +8.31272 q^{81} -18.8296 q^{82} -3.56966 q^{83} +5.36208 q^{84} +1.00042 q^{85} +21.5399 q^{86} +2.84991 q^{87} -29.8393 q^{88} -6.50396 q^{89} +4.19953 q^{90} +16.1611 q^{91} +46.3580 q^{92} +0.394527 q^{93} +4.28413 q^{94} -1.72988 q^{95} -4.16189 q^{96} -1.55539 q^{97} -19.5520 q^{98} -10.5477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.66509	−1.88451	−0.942253	−	0.334903i	$-0.891296\pi$
$2$	−2.66509	−1.88451	−0.942253	+	0.334903i	$0.891296\pi$
$3$	0.277531	0.160233	0.0801164	−	0.996786i	$-0.474471\pi$
$3$	0.277531	0.160233	0.0801164	+	0.996786i	$0.474471\pi$
$4$	5.10272	2.55136
$5$	0.539093	0.241090	0.120545	−	0.992708i	$-0.461536\pi$
$5$	0.539093	0.241090	0.120545	+	0.992708i	$0.461536\pi$
$6$	−0.739647	−0.301960
$7$	3.78634	1.43110	0.715550	−	0.698561i	$-0.246176\pi$
$7$	3.78634	1.43110	0.715550	+	0.698561i	$0.246176\pi$
$8$	−8.26903	−2.92354
$9$	−2.92298	−0.974325
$10$	−1.43673	−0.454335
$11$	3.60856	1.08802	0.544011	−	0.839078i	$-0.316905\pi$
$11$	3.60856	1.08802	0.544011	+	0.839078i	$0.316905\pi$
$12$	1.41616	0.408812
$13$	4.26828	1.18381	0.591904	−	0.806008i	$-0.298376\pi$
$13$	4.26828	1.18381	0.591904	+	0.806008i	$0.298376\pi$
$14$	−10.0909	−2.69692
$15$	0.149615	0.0386305
$16$	11.8323	2.95807
$17$	1.85574	0.450084	0.225042	−	0.974349i	$-0.427748\pi$
$17$	1.85574	0.450084	0.225042	+	0.974349i	$0.427748\pi$
$18$	7.79000	1.83612
$19$	−3.20887	−0.736165	−0.368082	−	0.929793i	$-0.619986\pi$
$19$	−3.20887	−0.736165	−0.368082	+	0.929793i	$0.619986\pi$
$20$	2.75084	0.615106
$21$	1.05083	0.229309
$22$	−9.61714	−2.05038
$23$	9.08496	1.89435	0.947173	−	0.320724i	$-0.103926\pi$
$23$	9.08496	1.89435	0.947173	+	0.320724i	$0.103926\pi$
$24$	−2.29492	−0.468448
$25$	−4.70938	−0.941876
$26$	−11.3754	−2.23089
$27$	−1.64381	−0.316352
$28$	19.3206	3.65125
$29$	10.2688	1.90687	0.953433	−	0.301605i	$-0.0975224\pi$
$29$	10.2688	1.90687	0.953433	+	0.301605i	$0.0975224\pi$
$30$	−0.398738	−0.0727993
$31$	1.42156	0.255320	0.127660	−	0.991818i	$-0.459253\pi$
$31$	1.42156	0.255320	0.127660	+	0.991818i	$0.459253\pi$
$32$	−14.9961	−2.65096
$33$	1.00149	0.174337
$34$	−4.94572	−0.848185
$35$	2.04119	0.345024
$36$	−14.9151	−2.48585
$37$	4.81209	0.791103	0.395551	−	0.918444i	$-0.370553\pi$
$37$	4.81209	0.791103	0.395551	+	0.918444i	$0.370553\pi$
$38$	8.55193	1.38731
$39$	1.18458	0.189685
$40$	−4.45778	−0.704836
$41$	7.06529	1.10341	0.551706	−	0.834038i	$-0.313977\pi$
$41$	7.06529	1.10341	0.551706	+	0.834038i	$0.313977\pi$
$42$	−2.80055	−0.432135
$43$	−8.08222	−1.23253	−0.616263	−	0.787540i	$-0.711354\pi$
$43$	−8.08222	−1.23253	−0.616263	+	0.787540i	$0.711354\pi$
$44$	18.4135	2.77593
$45$	−1.57576	−0.234900
$46$	−24.2123	−3.56990
$47$	−1.60750	−0.234477	−0.117239	−	0.993104i	$-0.537404\pi$
$47$	−1.60750	−0.234477	−0.117239	+	0.993104i	$0.537404\pi$
$48$	3.28383	0.473981
$49$	7.33634	1.04805
$50$	12.5509	1.77497
$51$	0.515027	0.0721182
$52$	21.7798	3.02032
$53$	−0.318129	−0.0436984	−0.0218492	−	0.999761i	$-0.506955\pi$
$53$	−0.318129	−0.0436984	−0.0218492	+	0.999761i	$0.506955\pi$
$54$	4.38091	0.596167
$55$	1.94535	0.262311
$56$	−31.3093	−4.18389
$57$	−0.890562	−0.117958
$58$	−27.3673	−3.59350
$59$	5.46257	0.711166	0.355583	−	0.934645i	$-0.384282\pi$
$59$	5.46257	0.711166	0.355583	+	0.934645i	$0.384282\pi$
$60$	0.763444	0.0985602
$61$	8.50376	1.08880	0.544398	−	0.838827i	$-0.316758\pi$
$61$	8.50376	1.08880	0.544398	+	0.838827i	$0.316758\pi$
$62$	−3.78859	−0.481151
$63$	−11.0674	−1.39436
$64$	16.3014	2.03768
$65$	2.30100	0.285404
$66$	−2.66906	−0.328539
$67$	−11.2592	−1.37553	−0.687766	−	0.725932i	$-0.741409\pi$
$67$	−11.2592	−1.37553	−0.687766	+	0.725932i	$0.741409\pi$
$68$	9.46933	1.14832
$69$	2.52136	0.303536
$70$	−5.43995	−0.650199
$71$	4.26327	0.505957	0.252978	−	0.967472i	$-0.418590\pi$
$71$	4.26327	0.505957	0.252978	+	0.967472i	$0.418590\pi$
$72$	24.1702	2.84848
$73$	−1.97900	−0.231624	−0.115812	−	0.993271i	$-0.536947\pi$
$73$	−1.97900	−0.231624	−0.115812	+	0.993271i	$0.536947\pi$
$74$	−12.8247	−1.49084
$75$	−1.30700	−0.150919
$76$	−16.3740	−1.87822
$77$	13.6632	1.55707
$78$	−3.15702	−0.357462
$79$	−5.93095	−0.667284	−0.333642	−	0.942700i	$-0.608278\pi$
$79$	−5.93095	−0.667284	−0.333642	+	0.942700i	$0.608278\pi$
$80$	6.37871	0.713161
$81$	8.31272	0.923635
$82$	−18.8296	−2.07939
$83$	−3.56966	−0.391821	−0.195911	−	0.980622i	$-0.562766\pi$
$83$	−3.56966	−0.391821	−0.195911	+	0.980622i	$0.562766\pi$
$84$	5.36208	0.585050
$85$	1.00042	0.108510
$86$	21.5399	2.32270
$87$	2.84991	0.305543
$88$	−29.8393	−3.18088
$89$	−6.50396	−0.689419	−0.344709	−	0.938709i	$-0.612023\pi$
$89$	−6.50396	−0.689419	−0.344709	+	0.938709i	$0.612023\pi$
$90$	4.19953	0.442670
$91$	16.1611	1.69415
$92$	46.3580	4.83316
$93$	0.394527	0.0409106
$94$	4.28413	0.441874
$95$	−1.72988	−0.177482
$96$	−4.16189	−0.424771
$97$	−1.55539	−0.157926	−0.0789630	−	0.996878i	$-0.525161\pi$
$97$	−1.55539	−0.157926	−0.0789630	+	0.996878i	$0.525161\pi$
$98$	−19.5520	−1.97505
$99$	−10.5477	−1.06009
$100$	−24.0306	−2.40306
$101$	−2.24622	−0.223508	−0.111754	−	0.993736i	$-0.535647\pi$
$101$	−2.24622	−0.223508	−0.111754	+	0.993736i	$0.535647\pi$
$102$	−1.37259	−0.135907
$103$	12.8463	1.26579	0.632893	−	0.774239i	$-0.281867\pi$
$103$	12.8463	1.26579	0.632893	+	0.774239i	$0.281867\pi$
$104$	−35.2945	−3.46091
$105$	0.566494	0.0552841
$106$	0.847844	0.0823499
$107$	−3.84567	−0.371775	−0.185887	−	0.982571i	$-0.559516\pi$
$107$	−3.84567	−0.371775	−0.185887	+	0.982571i	$0.559516\pi$
$108$	−8.38791	−0.807127
$109$	−0.114484	−0.0109655	−0.00548277	−	0.999985i	$-0.501745\pi$
$109$	−0.114484	−0.0109655	−0.00548277	+	0.999985i	$0.501745\pi$
$110$	−5.18453	−0.494326
$111$	1.33551	0.126761
$112$	44.8011	4.23330
$113$	−3.30438	−0.310850	−0.155425	−	0.987848i	$-0.549675\pi$
$113$	−3.30438	−0.310850	−0.155425	+	0.987848i	$0.549675\pi$
$114$	2.37343	0.222292
$115$	4.89764	0.456707
$116$	52.3987	4.86510
$117$	−12.4761	−1.15341
$118$	−14.5582	−1.34020
$119$	7.02646	0.644115
$120$	−1.23717	−0.112938
$121$	2.02170	0.183791
$122$	−22.6633	−2.05184
$123$	1.96084	0.176803
$124$	7.25382	0.651412
$125$	−5.23426	−0.468166
$126$	29.4956	2.62767
$127$	−2.49127	−0.221065	−0.110532	−	0.993873i	$-0.535256\pi$
$127$	−2.49127	−0.221065	−0.110532	+	0.993873i	$0.535256\pi$
$128$	−13.4526	−1.18905
$129$	−2.24307	−0.197491
$130$	−6.13238	−0.537845
$131$	−1.44080	−0.125884	−0.0629418	−	0.998017i	$-0.520048\pi$
$131$	−1.44080	−0.125884	−0.0629418	+	0.998017i	$0.520048\pi$
$132$	5.11031	0.444796
$133$	−12.1499	−1.05353
$134$	30.0069	2.59220
$135$	−0.886167	−0.0762691
$136$	−15.3452	−1.31584
$137$	17.3033	1.47832	0.739162	−	0.673528i	$-0.235222\pi$
$137$	17.3033	1.47832	0.739162	+	0.673528i	$0.235222\pi$
$138$	−6.71966	−0.572016
$139$	7.83682	0.664710	0.332355	−	0.943154i	$-0.392157\pi$
$139$	7.83682	0.664710	0.332355	+	0.943154i	$0.392157\pi$
$140$	10.4156	0.880279
$141$	−0.446131	−0.0375710
$142$	−11.3620	−0.953478
$143$	15.4023	1.28801
$144$	−34.5855	−2.88213
$145$	5.53583	0.459726
$146$	5.27421	0.436497
$147$	2.03607	0.167932
$148$	24.5547	2.01839
$149$	0.0658682	0.00539613	0.00269807	−	0.999996i	$-0.499141\pi$
$149$	0.0658682	0.00539613	0.00269807	+	0.999996i	$0.499141\pi$
$150$	3.48328	0.284408
$151$	−18.8330	−1.53261	−0.766306	−	0.642476i	$-0.777907\pi$
$151$	−18.8330	−1.53261	−0.766306	+	0.642476i	$0.777907\pi$
$152$	26.5342	2.15221
$153$	−5.42429	−0.438528
$154$	−36.4137	−2.93430
$155$	0.766353	0.0615549
$156$	6.04459	0.483954
$157$	−0.767293	−0.0612367	−0.0306183	−	0.999531i	$-0.509748\pi$
$157$	−0.767293	−0.0612367	−0.0306183	+	0.999531i	$0.509748\pi$
$158$	15.8065	1.25750
$159$	−0.0882908	−0.00700192
$160$	−8.08429	−0.639120
$161$	34.3987	2.71100
$162$	−22.1542	−1.74060
$163$	14.1193	1.10591	0.552954	−	0.833212i	$-0.313501\pi$
$163$	14.1193	1.10591	0.552954	+	0.833212i	$0.313501\pi$
$164$	36.0522	2.81520
$165$	0.539895	0.0420308
$166$	9.51347	0.738389
$167$	−7.56279	−0.585226	−0.292613	−	0.956231i	$-0.594525\pi$
$167$	−7.56279	−0.585226	−0.292613	+	0.956231i	$0.594525\pi$
$168$	−8.68932	−0.670396
$169$	5.21822	0.401401
$170$	−2.66620	−0.204489
$171$	9.37945	0.717264
$172$	−41.2413	−3.14462
$173$	9.67182	0.735335	0.367668	−	0.929957i	$-0.380156\pi$
$173$	9.67182	0.735335	0.367668	+	0.929957i	$0.380156\pi$
$174$	−7.59528	−0.575796
$175$	−17.8313	−1.34792
$176$	42.6975	3.21845
$177$	1.51603	0.113952
$178$	17.3337	1.29921
$179$	9.27403	0.693174	0.346587	−	0.938018i	$-0.387341\pi$
$179$	9.27403	0.693174	0.346587	+	0.938018i	$0.387341\pi$
$180$	−8.04064	−0.599314
$181$	−17.9696	−1.33567	−0.667833	−	0.744311i	$-0.732778\pi$
$181$	−17.9696	−1.33567	−0.667833	+	0.744311i	$0.732778\pi$
$182$	−43.0709	−3.19263
$183$	2.36006	0.174461
$184$	−75.1238	−5.53820
$185$	2.59416	0.190727
$186$	−1.05145	−0.0770962
$187$	6.69655	0.489701
$188$	−8.20260	−0.598236
$189$	−6.22403	−0.452731
$190$	4.61028	0.334465
$191$	22.9500	1.66060	0.830302	−	0.557313i	$-0.188168\pi$
$191$	22.9500	1.66060	0.830302	+	0.557313i	$0.188168\pi$
$192$	4.52415	0.326503
$193$	−2.05832	−0.148161	−0.0740807	−	0.997252i	$-0.523602\pi$
$193$	−2.05832	−0.148161	−0.0740807	+	0.997252i	$0.523602\pi$
$194$	4.14526	0.297612
$195$	0.638600	0.0457311
$196$	37.4353	2.67395
$197$	11.3754	0.810464	0.405232	−	0.914214i	$-0.367191\pi$
$197$	11.3754	0.810464	0.405232	+	0.914214i	$0.367191\pi$
$198$	28.1107	1.99774
$199$	−21.2172	−1.50405	−0.752023	−	0.659136i	$-0.770922\pi$
$199$	−21.2172	−1.50405	−0.752023	+	0.659136i	$0.770922\pi$
$200$	38.9420	2.75362
$201$	−3.12479	−0.220406
$202$	5.98639	0.421201
$203$	38.8811	2.72892
$204$	2.62804	0.183999
$205$	3.80885	0.266021
$206$	−34.2367	−2.38538
$207$	−26.5551	−1.84571
$208$	50.5036	3.50179
$209$	−11.5794	−0.800963
$210$	−1.50976	−0.104183
$211$	−9.28354	−0.639105	−0.319553	−	0.947569i	$-0.603533\pi$
$211$	−9.28354	−0.639105	−0.319553	+	0.947569i	$0.603533\pi$
$212$	−1.62332	−0.111490
$213$	1.18319	0.0810709
$214$	10.2491	0.700612
$215$	−4.35707	−0.297149
$216$	13.5927	0.924868
$217$	5.38250	0.365388
$218$	0.305109	0.0206646
$219$	−0.549234	−0.0371138
$220$	9.92657	0.669249
$221$	7.92083	0.532812
$222$	−3.55925	−0.238881
$223$	23.8528	1.59730	0.798651	−	0.601795i	$-0.205548\pi$
$223$	23.8528	1.59730	0.798651	+	0.601795i	$0.205548\pi$
$224$	−56.7803	−3.79379
$225$	13.7654	0.917694
$226$	8.80648	0.585798
$227$	−21.1867	−1.40621	−0.703107	−	0.711084i	$-0.748204\pi$
$227$	−21.1867	−1.40621	−0.703107	+	0.711084i	$0.748204\pi$
$228$	−4.54429	−0.300953
$229$	7.70719	0.509306	0.254653	−	0.967033i	$-0.418039\pi$
$229$	7.70719	0.509306	0.254653	+	0.967033i	$0.418039\pi$
$230$	−13.0527	−0.860667
$231$	3.79197	0.249493
$232$	−84.9129	−5.57481
$233$	−13.0931	−0.857761	−0.428880	−	0.903361i	$-0.641092\pi$
$233$	−13.0931	−0.857761	−0.428880	+	0.903361i	$0.641092\pi$
$234$	33.2499	2.17361
$235$	−0.866590	−0.0565301
$236$	27.8739	1.81444
$237$	−1.64602	−0.106921
$238$	−18.7262	−1.21384
$239$	11.9953	0.775914	0.387957	−	0.921678i	$-0.373181\pi$
$239$	11.9953	0.775914	0.387957	+	0.921678i	$0.373181\pi$
$240$	1.77029	0.114272
$241$	21.4804	1.38368	0.691838	−	0.722053i	$-0.256801\pi$
$241$	21.4804	1.38368	0.691838	+	0.722053i	$0.256801\pi$
$242$	−5.38802	−0.346355
$243$	7.23848	0.464349
$244$	43.3923	2.77791
$245$	3.95497	0.252674
$246$	−5.22582	−0.333186
$247$	−13.6963	−0.871478
$248$	−11.7549	−0.746438
$249$	−0.990693	−0.0627826
$250$	13.9498	0.882262
$251$	−15.5893	−0.983985	−0.491992	−	0.870599i	$-0.663731\pi$
$251$	−15.5893	−0.983985	−0.491992	+	0.870599i	$0.663731\pi$
$252$	−56.4737	−3.55751
$253$	32.7836	2.06109
$254$	6.63948	0.416598
$255$	0.277647	0.0173869
$256$	3.24951	0.203094
$257$	−19.0827	−1.19035	−0.595175	−	0.803596i	$-0.702917\pi$
$257$	−19.0827	−1.19035	−0.595175	+	0.803596i	$0.702917\pi$
$258$	5.97799	0.372173
$259$	18.2202	1.13215
$260$	11.7414	0.728168
$261$	−30.0154	−1.85791
$262$	3.83987	0.237228
$263$	−25.9580	−1.60064	−0.800321	−	0.599572i	$-0.795338\pi$
$263$	−25.9580	−1.60064	−0.800321	+	0.599572i	$0.795338\pi$
$264$	−8.28134	−0.509681
$265$	−0.171501	−0.0105352
$266$	32.3805	1.98537
$267$	−1.80505	−0.110468
$268$	−57.4526	−3.50948
$269$	−15.6189	−0.952303	−0.476152	−	0.879363i	$-0.657969\pi$
$269$	−15.6189	−0.952303	−0.476152	+	0.879363i	$0.657969\pi$
$270$	2.36172	0.143730
$271$	−9.20458	−0.559138	−0.279569	−	0.960126i	$-0.590192\pi$
$271$	−9.20458	−0.559138	−0.279569	+	0.960126i	$0.590192\pi$
$272$	21.9577	1.33138
$273$	4.48523	0.271458
$274$	−46.1150	−2.78591
$275$	−16.9941	−1.02478
$276$	12.8658	0.774430
$277$	−8.91287	−0.535523	−0.267761	−	0.963485i	$-0.586284\pi$
$277$	−8.91287	−0.535523	−0.267761	+	0.963485i	$0.586284\pi$
$278$	−20.8858	−1.25265
$279$	−4.15519	−0.248764
$280$	−16.8786	−1.00869
$281$	−24.9772	−1.49002	−0.745009	−	0.667055i	$-0.767555\pi$
$281$	−24.9772	−1.49002	−0.745009	+	0.667055i	$0.767555\pi$
$282$	1.18898	0.0708027
$283$	15.1851	0.902660	0.451330	−	0.892357i	$-0.350950\pi$
$283$	15.1851	0.902660	0.451330	+	0.892357i	$0.350950\pi$
$284$	21.7542	1.29088
$285$	−0.480095	−0.0284384
$286$	−41.0487	−2.42726
$287$	26.7516	1.57909
$288$	43.8333	2.58290
$289$	−13.5562	−0.797425
$290$	−14.7535	−0.866355
$291$	−0.431670	−0.0253049
$292$	−10.0983	−0.590956
$293$	30.1664	1.76234	0.881171	−	0.472798i	$-0.156756\pi$
$293$	30.1664	1.76234	0.881171	+	0.472798i	$0.156756\pi$
$294$	−5.42630	−0.316468
$295$	2.94483	0.171455
$296$	−39.7913	−2.31282
$297$	−5.93179	−0.344198
$298$	−0.175545	−0.0101690
$299$	38.7772	2.24254
$300$	−6.66926	−0.385050
$301$	−30.6020	−1.76387
$302$	50.1918	2.88821
$303$	−0.623398	−0.0358133
$304$	−37.9683	−2.17763
$305$	4.58432	0.262497
$306$	14.4562	0.826408
$307$	−31.4660	−1.79586	−0.897930	−	0.440138i	$-0.854929\pi$
$307$	−31.4660	−1.79586	−0.897930	+	0.440138i	$0.854929\pi$
$308$	69.7196	3.97264
$309$	3.56526	0.202821
$310$	−2.04240	−0.116001
$311$	0.662989	0.0375946	0.0187973	−	0.999823i	$-0.494016\pi$
$311$	0.662989	0.0375946	0.0187973	+	0.999823i	$0.494016\pi$
$312$	−9.79535	−0.554552
$313$	−18.1950	−1.02844	−0.514221	−	0.857658i	$-0.671919\pi$
$313$	−18.1950	−1.02844	−0.514221	+	0.857658i	$0.671919\pi$
$314$	2.04491	0.115401
$315$	−5.96634	−0.336165
$316$	−30.2640	−1.70248
$317$	−8.39700	−0.471622	−0.235811	−	0.971799i	$-0.575775\pi$
$317$	−8.39700	−0.471622	−0.235811	+	0.971799i	$0.575775\pi$
$318$	0.235303	0.0131952
$319$	37.0555	2.07471
$320$	8.78798	0.491263
$321$	−1.06729	−0.0595705
$322$	−91.6758	−5.10889
$323$	−5.95483	−0.331336
$324$	42.4175	2.35653
$325$	−20.1009	−1.11500
$326$	−37.6292	−2.08409
$327$	−0.0317728	−0.00175704
$328$	−58.4231	−3.22588
$329$	−6.08652	−0.335561
$330$	−1.43887	−0.0792072
$331$	3.56817	0.196125	0.0980623	−	0.995180i	$-0.468736\pi$
$331$	3.56817	0.196125	0.0980623	+	0.995180i	$0.468736\pi$
$332$	−18.2150	−0.999676
$333$	−14.0656	−0.770792
$334$	20.1555	1.10286
$335$	−6.06977	−0.331627
$336$	12.4337	0.678314
$337$	22.7989	1.24194	0.620968	−	0.783836i	$-0.286740\pi$
$337$	22.7989	1.24194	0.620968	+	0.783836i	$0.286740\pi$
$338$	−13.9070	−0.756443
$339$	−0.917069	−0.0498084
$340$	5.10485	0.276849
$341$	5.12978	0.277793
$342$	−24.9971	−1.35169
$343$	1.27351	0.0687629
$344$	66.8321	3.60335
$345$	1.35925	0.0731795
$346$	−25.7763	−1.38574
$347$	4.37956	0.235107	0.117553	−	0.993067i	$-0.462495\pi$
$347$	4.37956	0.235107	0.117553	+	0.993067i	$0.462495\pi$
$348$	14.5423	0.779549
$349$	−29.7177	−1.59075	−0.795376	−	0.606117i	$-0.792726\pi$
$349$	−29.7177	−1.59075	−0.795376	+	0.606117i	$0.792726\pi$
$350$	47.5220	2.54016
$351$	−7.01625	−0.374500
$352$	−54.1143	−2.88430
$353$	−30.6569	−1.63170	−0.815851	−	0.578263i	$-0.803731\pi$
$353$	−30.6569	−1.63170	−0.815851	+	0.578263i	$0.803731\pi$
$354$	−4.04037	−0.214743
$355$	2.29830	0.121981
$356$	−33.1879	−1.75896
$357$	1.95006	0.103208
$358$	−24.7162	−1.30629
$359$	−11.2354	−0.592982	−0.296491	−	0.955036i	$-0.595816\pi$
$359$	−11.2354	−0.592982	−0.296491	+	0.955036i	$0.595816\pi$
$360$	13.0300	0.686740
$361$	−8.70317	−0.458061
$362$	47.8905	2.51707
$363$	0.561085	0.0294493
$364$	82.4658	4.32238
$365$	−1.06686	−0.0558422
$366$	−6.28978	−0.328772
$367$	−8.73982	−0.456215	−0.228107	−	0.973636i	$-0.573254\pi$
$367$	−8.73982	−0.456215	−0.228107	+	0.973636i	$0.573254\pi$
$368$	107.496	5.60361
$369$	−20.6517	−1.07508
$370$	−6.91369	−0.359426
$371$	−1.20454	−0.0625368
$372$	2.01316	0.104378
$373$	−36.8820	−1.90968	−0.954838	−	0.297127i	$-0.903971\pi$
$373$	−36.8820	−1.90968	−0.954838	+	0.297127i	$0.903971\pi$
$374$	−17.8469	−0.922843
$375$	−1.45267	−0.0750156
$376$	13.2924	0.685505
$377$	43.8301	2.25736
$378$	16.5876	0.853174
$379$	10.1345	0.520575	0.260288	−	0.965531i	$-0.416183\pi$
$379$	10.1345	0.520575	0.260288	+	0.965531i	$0.416183\pi$
$380$	−8.82708	−0.452820
$381$	−0.691407	−0.0354218
$382$	−61.1639	−3.12942
$383$	27.0818	1.38381	0.691907	−	0.721987i	$-0.256771\pi$
$383$	27.0818	1.38381	0.691907	+	0.721987i	$0.256771\pi$
$384$	−3.73351	−0.190525
$385$	7.36574	0.375393
$386$	5.48562	0.279211
$387$	23.6241	1.20088
$388$	−7.93672	−0.402926
$389$	10.8321	0.549208	0.274604	−	0.961557i	$-0.411453\pi$
$389$	10.8321	0.549208	0.274604	+	0.961557i	$0.411453\pi$
$390$	−1.70193	−0.0861804
$391$	16.8593	0.852614
$392$	−60.6645	−3.06402
$393$	−0.399868	−0.0201707
$394$	−30.3165	−1.52732
$395$	−3.19733	−0.160875
$396$	−53.8221	−2.70466
$397$	13.4332	0.674192	0.337096	−	0.941470i	$-0.390555\pi$
$397$	13.4332	0.674192	0.337096	+	0.941470i	$0.390555\pi$
$398$	56.5458	2.83438
$399$	−3.37197	−0.168809
$400$	−55.7228	−2.78614
$401$	15.5964	0.778845	0.389423	−	0.921059i	$-0.372675\pi$
$401$	15.5964	0.778845	0.389423	+	0.921059i	$0.372675\pi$
$402$	8.32785	0.415355
$403$	6.06762	0.302249
$404$	−11.4618	−0.570248
$405$	4.48133	0.222679
$406$	−103.622	−5.14266
$407$	17.3647	0.860737
$408$	−4.25877	−0.210841
$409$	34.8043	1.72096	0.860480	−	0.509483i	$-0.170163\pi$
$409$	34.8043	1.72096	0.860480	+	0.509483i	$0.170163\pi$
$410$	−10.1509	−0.501319
$411$	4.80222	0.236876
$412$	65.5512	3.22948
$413$	20.6831	1.01775
$414$	70.7719	3.47825
$415$	−1.92438	−0.0944640
$416$	−64.0076	−3.13823
$417$	2.17496	0.106508
$418$	30.8601	1.50942
$419$	−6.36922	−0.311157	−0.155578	−	0.987824i	$-0.549724\pi$
$419$	−6.36922	−0.311157	−0.155578	+	0.987824i	$0.549724\pi$
$420$	2.89066	0.141050
$421$	−20.5358	−1.00085	−0.500427	−	0.865779i	$-0.666824\pi$
$421$	−20.5358	−1.00085	−0.500427	+	0.865779i	$0.666824\pi$
$422$	24.7415	1.20440
$423$	4.69867	0.228457
$424$	2.63062	0.127754
$425$	−8.73939	−0.423923
$426$	−3.15331	−0.152778
$427$	32.1981	1.55818
$428$	−19.6234	−0.948531
$429$	4.27463	0.206381
$430$	11.6120	0.559980
$431$	−15.0923	−0.726968	−0.363484	−	0.931600i	$-0.618413\pi$
$431$	−15.0923	−0.726968	−0.363484	+	0.931600i	$0.618413\pi$
$432$	−19.4501	−0.935792
$433$	14.6441	0.703751	0.351876	−	0.936047i	$-0.385544\pi$
$433$	14.6441	0.703751	0.351876	+	0.936047i	$0.385544\pi$
$434$	−14.3449	−0.688576
$435$	1.53637	0.0736632
$436$	−0.584178	−0.0279770
$437$	−29.1524	−1.39455
$438$	1.46376	0.0699411
$439$	2.18159	0.104121	0.0520607	−	0.998644i	$-0.483421\pi$
$439$	2.18159	0.104121	0.0520607	+	0.998644i	$0.483421\pi$
$440$	−16.0861	−0.766877
$441$	−21.4440	−1.02114
$442$	−21.1097	−1.00409
$443$	22.1513	1.05244	0.526220	−	0.850349i	$-0.323609\pi$
$443$	22.1513	1.05244	0.526220	+	0.850349i	$0.323609\pi$
$444$	6.81471	0.323412
$445$	−3.50624	−0.166212
$446$	−63.5699	−3.01012
$447$	0.0182805	0.000864638 0
$448$	61.7226	2.91612
$449$	−9.10743	−0.429806	−0.214903	−	0.976635i	$-0.568944\pi$
$449$	−9.10743	−0.429806	−0.214903	+	0.976635i	$0.568944\pi$
$450$	−36.6861	−1.72940
$451$	25.4955	1.20054
$452$	−16.8613	−0.793090
$453$	−5.22676	−0.245575
$454$	56.4646	2.65002
$455$	8.71236	0.408442
$456$	7.36408	0.344855
$457$	−26.7750	−1.25248	−0.626242	−	0.779629i	$-0.715408\pi$
$457$	−26.7750	−1.25248	−0.626242	+	0.779629i	$0.715408\pi$
$458$	−20.5404	−0.959789
$459$	−3.05049	−0.142385
$460$	24.9913	1.16522
$461$	−25.2017	−1.17376	−0.586881	−	0.809673i	$-0.699644\pi$
$461$	−25.2017	−1.17376	−0.586881	+	0.809673i	$0.699644\pi$
$462$	−10.1060	−0.470172
$463$	27.4127	1.27397	0.636987	−	0.770875i	$-0.280180\pi$
$463$	27.4127	1.27397	0.636987	+	0.770875i	$0.280180\pi$
$464$	121.503	5.64065
$465$	0.212687	0.00986312
$466$	34.8944	1.61645
$467$	−17.5658	−0.812847	−0.406424	−	0.913685i	$-0.633224\pi$
$467$	−17.5658	−0.812847	−0.406424	+	0.913685i	$0.633224\pi$
$468$	−63.6619	−2.94277
$469$	−42.6312	−1.96853
$470$	2.30954	0.106531
$471$	−0.212948	−0.00981213
$472$	−45.1701	−2.07912
$473$	−29.1652	−1.34102
$474$	4.38681	0.201493
$475$	15.1118	0.693376
$476$	35.8541	1.64337
$477$	0.929884	0.0425765
$478$	−31.9687	−1.46221
$479$	−31.5509	−1.44160	−0.720799	−	0.693144i	$-0.756225\pi$
$479$	−31.5509	−1.44160	−0.720799	+	0.693144i	$0.756225\pi$
$480$	−2.24365	−0.102408
$481$	20.5394	0.936514
$482$	−57.2473	−2.60754
$483$	9.54673	0.434391
$484$	10.3162	0.468916
$485$	−0.838500	−0.0380743
$486$	−19.2912	−0.875067
$487$	−3.06159	−0.138734	−0.0693669	−	0.997591i	$-0.522098\pi$
$487$	−3.06159	−0.138734	−0.0693669	+	0.997591i	$0.522098\pi$
$488$	−70.3179	−3.18314
$489$	3.91855	0.177203
$490$	−10.5404	−0.476165
$491$	−4.04279	−0.182449	−0.0912243	−	0.995830i	$-0.529078\pi$
$491$	−4.04279	−0.182449	−0.0912243	+	0.995830i	$0.529078\pi$
$492$	10.0056	0.451088
$493$	19.0562	0.858249
$494$	36.5020	1.64230
$495$	−5.68621	−0.255576
$496$	16.8203	0.755255
$497$	16.1422	0.724075
$498$	2.64029	0.118314
$499$	26.9602	1.20691	0.603453	−	0.797399i	$-0.293791\pi$
$499$	26.9602	1.20691	0.603453	+	0.797399i	$0.293791\pi$
$500$	−26.7089	−1.19446
$501$	−2.09891	−0.0937725
$502$	41.5468	1.85432
$503$	27.4293	1.22301	0.611506	−	0.791240i	$-0.290564\pi$
$503$	27.4293	1.22301	0.611506	+	0.791240i	$0.290564\pi$
$504$	91.5164	4.07647
$505$	−1.21092	−0.0538854
$506$	−87.3714	−3.88413
$507$	1.44822	0.0643177
$508$	−12.7123	−0.564016
$509$	−26.3734	−1.16898	−0.584491	−	0.811400i	$-0.698706\pi$
$509$	−26.3734	−1.16898	−0.584491	+	0.811400i	$0.698706\pi$
$510$	−0.739956	−0.0327658
$511$	−7.49315	−0.331477
$512$	18.2449	0.806318
$513$	5.27478	0.232887
$514$	50.8573	2.24322
$515$	6.92537	0.305168
$516$	−11.4457	−0.503871
$517$	−5.80074	−0.255116
$518$	−48.5585	−2.13354
$519$	2.68423	0.117825
$520$	−19.0270	−0.834391
$521$	24.0382	1.05313	0.526567	−	0.850134i	$-0.323479\pi$
$521$	24.0382	1.05313	0.526567	+	0.850134i	$0.323479\pi$
$522$	79.9939	3.50124
$523$	29.6643	1.29713	0.648564	−	0.761160i	$-0.275370\pi$
$523$	29.6643	1.29713	0.648564	+	0.761160i	$0.275370\pi$
$524$	−7.35201	−0.321174
$525$	−4.94874	−0.215981
$526$	69.1806	3.01642
$527$	2.63805	0.114915
$528$	11.8499	0.515701
$529$	59.5365	2.58854
$530$	0.457067	0.0198537
$531$	−15.9670	−0.692907
$532$	−61.9973	−2.68792
$533$	30.1566	1.30623
$534$	4.81064	0.208177
$535$	−2.07317	−0.0896311
$536$	93.1029	4.02143
$537$	2.57384	0.111069
$538$	41.6259	1.79462
$539$	26.4736	1.14030
$540$	−4.52186	−0.194590
$541$	−7.64223	−0.328565	−0.164283	−	0.986413i	$-0.552531\pi$
$541$	−7.64223	−0.328565	−0.164283	+	0.986413i	$0.552531\pi$
$542$	24.5311	1.05370
$543$	−4.98712	−0.214018
$544$	−27.8289	−1.19315
$545$	−0.0617173	−0.00264368
$546$	−11.9535	−0.511564
$547$	−1.33931	−0.0572648	−0.0286324	−	0.999590i	$-0.509115\pi$
$547$	−1.33931	−0.0572648	−0.0286324	+	0.999590i	$0.509115\pi$
$548$	88.2941	3.77174
$549$	−24.8563	−1.06084
$550$	45.2908	1.93121
$551$	−32.9512	−1.40377
$552$	−20.8492	−0.887402
$553$	−22.4566	−0.954950
$554$	23.7536	1.00919
$555$	0.719962	0.0305607
$556$	39.9891	1.69591
$557$	14.7044	0.623045	0.311522	−	0.950239i	$-0.399161\pi$
$557$	14.7044	0.623045	0.311522	+	0.950239i	$0.399161\pi$
$558$	11.0740	0.468798
$559$	−34.4972	−1.45907
$560$	24.1519	1.02061
$561$	1.85850	0.0784661
$562$	66.5667	2.80795
$563$	24.6264	1.03788	0.518939	−	0.854811i	$-0.326327\pi$
$563$	24.6264	1.03788	0.518939	+	0.854811i	$0.326327\pi$
$564$	−2.27648	−0.0958571
$565$	−1.78137	−0.0749427
$566$	−40.4697	−1.70107
$567$	31.4748	1.32182
$568$	−35.2531	−1.47919
$569$	34.3217	1.43884	0.719420	−	0.694575i	$-0.244408\pi$
$569$	34.3217	1.43884	0.719420	+	0.694575i	$0.244408\pi$
$570$	1.27950	0.0535923
$571$	38.4107	1.60744	0.803718	−	0.595011i	$-0.202852\pi$
$571$	38.4107	1.60744	0.803718	+	0.595011i	$0.202852\pi$
$572$	78.5938	3.28617
$573$	6.36935	0.266083
$574$	−71.2954	−2.97581
$575$	−42.7845	−1.78424
$576$	−47.6486	−1.98536
$577$	−4.83005	−0.201078	−0.100539	−	0.994933i	$-0.532057\pi$
$577$	−4.83005	−0.201078	−0.100539	+	0.994933i	$0.532057\pi$
$578$	36.1286	1.50275
$579$	−0.571249	−0.0237403
$580$	28.2478	1.17293
$581$	−13.5159	−0.560735
$582$	1.15044	0.0476873
$583$	−1.14799	−0.0475448
$584$	16.3644	0.677163
$585$	−6.72577	−0.278076
$586$	−80.3963	−3.32114
$587$	−43.2931	−1.78690	−0.893449	−	0.449165i	$-0.851722\pi$
$587$	−43.2931	−1.78690	−0.893449	+	0.449165i	$0.851722\pi$
$588$	10.3895	0.428455
$589$	−4.56160	−0.187957
$590$	−7.84825	−0.323107
$591$	3.15703	0.129863
$592$	56.9381	2.34014
$593$	−14.3723	−0.590198	−0.295099	−	0.955467i	$-0.595353\pi$
$593$	−14.3723	−0.590198	−0.295099	+	0.955467i	$0.595353\pi$
$594$	15.8088	0.648642
$595$	3.78792	0.155289
$596$	0.336107	0.0137675
$597$	−5.88844	−0.240998
$598$	−103.345	−4.22608
$599$	−14.9520	−0.610924	−0.305462	−	0.952204i	$-0.598811\pi$
$599$	−14.9520	−0.610924	−0.305462	+	0.952204i	$0.598811\pi$
$600$	10.8076	0.441220
$601$	18.0045	0.734418	0.367209	−	0.930139i	$-0.380313\pi$
$601$	18.0045	0.734418	0.367209	+	0.930139i	$0.380313\pi$
$602$	81.5571	3.32402
$603$	32.9104	1.34022
$604$	−96.0997	−3.91024
$605$	1.08988	0.0443101
$606$	1.66141	0.0674903
$607$	26.8145	1.08837	0.544184	−	0.838966i	$-0.316839\pi$
$607$	26.8145	1.08837	0.544184	+	0.838966i	$0.316839\pi$
$608$	48.1205	1.95155
$609$	10.7907	0.437262
$610$	−12.2176	−0.494678
$611$	−6.86124	−0.277576
$612$	−27.6786	−1.11884
$613$	9.73767	0.393301	0.196650	−	0.980474i	$-0.436994\pi$
$613$	9.73767	0.393301	0.196650	+	0.980474i	$0.436994\pi$
$614$	83.8598	3.38431
$615$	1.05707	0.0426254
$616$	−112.982	−4.55216
$617$	11.0946	0.446650	0.223325	−	0.974744i	$-0.428309\pi$
$617$	11.0946	0.446650	0.223325	+	0.974744i	$0.428309\pi$
$618$	−9.50175	−0.382217
$619$	−23.4171	−0.941211	−0.470605	−	0.882344i	$-0.655964\pi$
$619$	−23.4171	−0.941211	−0.470605	+	0.882344i	$0.655964\pi$
$620$	3.91048	0.157049
$621$	−14.9340	−0.599280
$622$	−1.76693	−0.0708473
$623$	−24.6262	−0.986628
$624$	14.0163	0.561102
$625$	20.7251	0.829006
$626$	48.4913	1.93810
$627$	−3.21364	−0.128341
$628$	−3.91528	−0.156237
$629$	8.93000	0.356062
$630$	15.9009	0.633505
$631$	0.738808	0.0294115	0.0147057	−	0.999892i	$-0.495319\pi$
$631$	0.738808	0.0294115	0.0147057	+	0.999892i	$0.495319\pi$
$632$	49.0432	1.95083
$633$	−2.57647	−0.102406
$634$	22.3788	0.888774
$635$	−1.34303	−0.0532964
$636$	−0.450523	−0.0178644
$637$	31.3136	1.24069
$638$	−98.7564	−3.90980
$639$	−12.4614	−0.492966
$640$	−7.25218	−0.286668
$641$	−23.0989	−0.912351	−0.456175	−	0.889890i	$-0.650781\pi$
$641$	−23.0989	−0.912351	−0.456175	+	0.889890i	$0.650781\pi$
$642$	2.84444	0.112261
$643$	40.9212	1.61378	0.806888	−	0.590705i	$-0.201150\pi$
$643$	40.9212	1.61378	0.806888	+	0.590705i	$0.201150\pi$
$644$	175.527	6.91673
$645$	−1.20922	−0.0476131
$646$	15.8702	0.624404
$647$	−15.3263	−0.602539	−0.301270	−	0.953539i	$-0.597410\pi$
$647$	−15.3263	−0.602539	−0.301270	+	0.953539i	$0.597410\pi$
$648$	−68.7381	−2.70029
$649$	19.7120	0.773764
$650$	53.5709	2.10122
$651$	1.49381	0.0585472
$652$	72.0467	2.82157
$653$	27.0951	1.06031	0.530157	−	0.847899i	$-0.322133\pi$
$653$	27.0951	1.06031	0.530157	+	0.847899i	$0.322133\pi$
$654$	0.0846775	0.00331115
$655$	−0.776727	−0.0303492
$656$	83.5986	3.26398
$657$	5.78456	0.225677
$658$	16.2211	0.632366
$659$	35.8521	1.39660	0.698300	−	0.715806i	$-0.253940\pi$
$659$	35.8521	1.39660	0.698300	+	0.715806i	$0.253940\pi$
$660$	2.75493	0.107236
$661$	41.0631	1.59717	0.798585	−	0.601882i	$-0.205582\pi$
$661$	41.0631	1.59717	0.798585	+	0.601882i	$0.205582\pi$
$662$	−9.50951	−0.369598
$663$	2.19828	0.0853741
$664$	29.5176	1.14551
$665$	−6.54990	−0.253994
$666$	37.4862	1.45256
$667$	93.2915	3.61226
$668$	−38.5908	−1.49312
$669$	6.61990	0.255940
$670$	16.1765	0.624952
$671$	30.6863	1.18463
$672$	−15.7583	−0.607890
$673$	−13.4533	−0.518587	−0.259293	−	0.965799i	$-0.583490\pi$
$673$	−13.4533	−0.518587	−0.259293	+	0.965799i	$0.583490\pi$
$674$	−60.7612	−2.34044
$675$	7.74133	0.297964
$676$	26.6271	1.02412
$677$	34.1746	1.31343	0.656717	−	0.754137i	$-0.271944\pi$
$677$	34.1746	1.31343	0.656717	+	0.754137i	$0.271944\pi$
$678$	2.44407	0.0938641
$679$	−5.88923	−0.226008
$680$	−8.27248	−0.317235
$681$	−5.87999	−0.225322
$682$	−13.6713	−0.523503
$683$	0.267230	0.0102253	0.00511264	−	0.999987i	$-0.498373\pi$
$683$	0.267230	0.0102253	0.00511264	+	0.999987i	$0.498373\pi$
$684$	47.8607	1.83000
$685$	9.32811	0.356409
$686$	−3.39402	−0.129584
$687$	2.13899	0.0816075
$688$	−95.6312	−3.64591
$689$	−1.35786	−0.0517305
$690$	−3.62252	−0.137907
$691$	−27.5191	−1.04688	−0.523439	−	0.852063i	$-0.675351\pi$
$691$	−27.5191	−1.04688	−0.523439	+	0.852063i	$0.675351\pi$
$692$	49.3526	1.87610
$693$	−39.9373	−1.51709
$694$	−11.6719	−0.443060
$695$	4.22477	0.160255
$696$	−23.5660	−0.893267
$697$	13.1114	0.496628
$698$	79.2004	2.99778
$699$	−3.63376	−0.137441
$700$	−90.9881	−3.43903
$701$	22.4593	0.848277	0.424138	−	0.905597i	$-0.360577\pi$
$701$	22.4593	0.848277	0.424138	+	0.905597i	$0.360577\pi$
$702$	18.6990	0.705747
$703$	−15.4414	−0.582382
$704$	58.8246	2.21704
$705$	−0.240506	−0.00905797
$706$	81.7034	3.07495
$707$	−8.50496	−0.319862
$708$	7.73589	0.290733
$709$	−19.5708	−0.734997	−0.367499	−	0.930024i	$-0.619786\pi$
$709$	−19.5708	−0.734997	−0.367499	+	0.930024i	$0.619786\pi$
$710$	−6.12517	−0.229874
$711$	17.3360	0.650151
$712$	53.7815	2.01555
$713$	12.9148	0.483664
$714$	−5.19710	−0.194497
$715$	8.30329	0.310526
$716$	47.3228	1.76854
$717$	3.32908	0.124327
$718$	29.9434	1.11748
$719$	−27.6875	−1.03257	−0.516284	−	0.856417i	$-0.672685\pi$
$719$	−27.6875	−1.03257	−0.516284	+	0.856417i	$0.672685\pi$
$720$	−18.6448	−0.694851
$721$	48.6405	1.81147
$722$	23.1947	0.863219
$723$	5.96149	0.221710
$724$	−91.6936	−3.40777
$725$	−48.3596	−1.79603
$726$	−1.49534	−0.0554974
$727$	9.93001	0.368284	0.184142	−	0.982900i	$-0.441049\pi$
$727$	9.93001	0.368284	0.184142	+	0.982900i	$0.441049\pi$
$728$	−133.637	−4.95292
$729$	−22.9293	−0.849232
$730$	2.84329	0.105235
$731$	−14.9985	−0.554740
$732$	12.0427	0.445112
$733$	21.5503	0.795978	0.397989	−	0.917390i	$-0.369708\pi$
$733$	21.5503	0.795978	0.397989	+	0.917390i	$0.369708\pi$
$734$	23.2924	0.859739
$735$	1.09763	0.0404866
$736$	−136.239	−5.02184
$737$	−40.6296	−1.49661
$738$	55.0386	2.02600
$739$	17.2452	0.634374	0.317187	−	0.948363i	$-0.397262\pi$
$739$	17.2452	0.634374	0.317187	+	0.948363i	$0.397262\pi$
$740$	13.2373	0.486612
$741$	−3.80117	−0.139639
$742$	3.21022	0.117851
$743$	−1.63643	−0.0600347	−0.0300174	−	0.999549i	$-0.509556\pi$
$743$	−1.63643	−0.0600347	−0.0300174	+	0.999549i	$0.509556\pi$
$744$	−3.26236	−0.119604
$745$	0.0355091	0.00130095
$746$	98.2939	3.59879
$747$	10.4340	0.381761
$748$	34.1706	1.24940
$749$	−14.5610	−0.532047
$750$	3.87150	0.141367
$751$	−38.4848	−1.40433	−0.702165	−	0.712014i	$-0.747783\pi$
$751$	−38.4848	−1.40433	−0.702165	+	0.712014i	$0.747783\pi$
$752$	−19.0204	−0.693602
$753$	−4.32651	−0.157667
$754$	−116.811	−4.25401
$755$	−10.1528	−0.369497
$756$	−31.7594	−1.15508
$757$	11.6104	0.421987	0.210993	−	0.977487i	$-0.432330\pi$
$757$	11.6104	0.421987	0.210993	+	0.977487i	$0.432330\pi$
$758$	−27.0094	−0.981026
$759$	9.09849	0.330254
$760$	14.3044	0.518876
$761$	−20.5186	−0.743797	−0.371898	−	0.928273i	$-0.621293\pi$
$761$	−20.5186	−0.743797	−0.371898	+	0.928273i	$0.621293\pi$
$762$	1.84266	0.0667526
$763$	−0.433473	−0.0156928
$764$	117.107	4.23680
$765$	−2.92420	−0.105725
$766$	−72.1754	−2.60780
$767$	23.3158	0.841884
$768$	0.901840	0.0325424
$769$	31.0079	1.11817	0.559087	−	0.829109i	$-0.311152\pi$
$769$	31.0079	1.11817	0.559087	+	0.829109i	$0.311152\pi$
$770$	−19.6304	−0.707430
$771$	−5.29606	−0.190733
$772$	−10.5030	−0.378013
$773$	−16.5808	−0.596370	−0.298185	−	0.954508i	$-0.596381\pi$
$773$	−16.5808	−0.596370	−0.298185	+	0.954508i	$0.596381\pi$
$774$	−62.9605	−2.26307
$775$	−6.69466	−0.240479
$776$	12.8616	0.461704
$777$	5.05668	0.181407
$778$	−28.8685	−1.03499
$779$	−22.6716	−0.812294
$780$	3.25859	0.116676
$781$	15.3842	0.550492
$782$	−44.9317	−1.60675
$783$	−16.8800	−0.603240
$784$	86.8058	3.10021
$785$	−0.413642	−0.0147635
$786$	1.06569	0.0380118
$787$	−2.32871	−0.0830096	−0.0415048	−	0.999138i	$-0.513215\pi$
$787$	−2.32871	−0.0830096	−0.0415048	+	0.999138i	$0.513215\pi$
$788$	58.0455	2.06778
$789$	−7.20417	−0.256475
$790$	8.52118	0.303170
$791$	−12.5115	−0.444857
$792$	87.2195	3.09921
$793$	36.2964	1.28892
$794$	−35.8007	−1.27052
$795$	−0.0475970	−0.00168809
$796$	−108.265	−3.83736
$797$	43.2483	1.53193	0.765967	−	0.642880i	$-0.222261\pi$
$797$	43.2483	1.53193	0.765967	+	0.642880i	$0.222261\pi$
$798$	8.98660	0.318122
$799$	−2.98310	−0.105534
$800$	70.6223	2.49688
$801$	19.0109	0.671718
$802$	−41.5658	−1.46774
$803$	−7.14133	−0.252012
$804$	−15.9449	−0.562334
$805$	18.5441	0.653594
$806$	−16.1708	−0.569591
$807$	−4.33475	−0.152590
$808$	18.5741	0.653434
$809$	4.48700	0.157754	0.0788772	−	0.996884i	$-0.474866\pi$
$809$	4.48700	0.157754	0.0788772	+	0.996884i	$0.474866\pi$
$810$	−11.9432	−0.419640
$811$	−33.1843	−1.16526	−0.582628	−	0.812739i	$-0.697976\pi$
$811$	−33.1843	−1.16526	−0.582628	+	0.812739i	$0.697976\pi$
$812$	198.399	6.96245
$813$	−2.55456	−0.0895923
$814$	−46.2786	−1.62206
$815$	7.61161	0.266623
$816$	6.09395	0.213331
$817$	25.9348	0.907343
$818$	−92.7566	−3.24316
$819$	−47.2386	−1.65065
$820$	19.4355	0.678716
$821$	−15.3407	−0.535395	−0.267697	−	0.963503i	$-0.586263\pi$
$821$	−15.3407	−0.535395	−0.267697	+	0.963503i	$0.586263\pi$
$822$	−12.7984	−0.446394
$823$	42.1844	1.47046	0.735228	−	0.677820i	$-0.237075\pi$
$823$	42.1844	1.47046	0.735228	+	0.677820i	$0.237075\pi$
$824$	−106.227	−3.70058
$825$	−4.71639	−0.164204
$826$	−55.1224	−1.91795
$827$	−23.2453	−0.808318	−0.404159	−	0.914689i	$-0.632436\pi$
$827$	−23.2453	−0.808318	−0.404159	+	0.914689i	$0.632436\pi$
$828$	−135.503	−4.70907
$829$	−37.5596	−1.30450	−0.652250	−	0.758004i	$-0.726175\pi$
$829$	−37.5596	−1.30450	−0.652250	+	0.758004i	$0.726175\pi$
$830$	5.12865	0.178018
$831$	−2.47360	−0.0858083
$832$	69.5790	2.41222
$833$	13.6144	0.471710
$834$	−5.79648	−0.200716
$835$	−4.07705	−0.141092
$836$	−59.0864	−2.04354
$837$	−2.33678	−0.0807708
$838$	16.9746	0.586377
$839$	26.1352	0.902286	0.451143	−	0.892452i	$-0.351016\pi$
$839$	26.1352	0.902286	0.451143	+	0.892452i	$0.351016\pi$
$840$	−4.68435	−0.161626
$841$	76.4480	2.63614
$842$	54.7299	1.88612
$843$	−6.93197	−0.238750
$844$	−47.3713	−1.63059
$845$	2.81310	0.0967737
$846$	−12.5224	−0.430529
$847$	7.65483	0.263023
$848$	−3.76420	−0.129263
$849$	4.21434	0.144636
$850$	23.2913	0.798885
$851$	43.7177	1.49862
$852$	6.03749	0.206841
$853$	−20.5071	−0.702148	−0.351074	−	0.936348i	$-0.614184\pi$
$853$	−20.5071	−0.702148	−0.351074	+	0.936348i	$0.614184\pi$
$854$	−85.8109	−2.93639
$855$	5.05639	0.172925
$856$	31.8000	1.08690
$857$	50.2486	1.71646	0.858230	−	0.513266i	$-0.171564\pi$
$857$	50.2486	1.71646	0.858230	+	0.513266i	$0.171564\pi$
$858$	−11.3923	−0.388927
$859$	−56.3936	−1.92413	−0.962063	−	0.272827i	$-0.912041\pi$
$859$	−56.3936	−1.92413	−0.962063	+	0.272827i	$0.912041\pi$
$860$	−22.2329	−0.758135
$861$	7.42440	0.253023
$862$	40.2222	1.36998
$863$	−15.8985	−0.541192	−0.270596	−	0.962693i	$-0.587221\pi$
$863$	−15.8985	−0.541192	−0.270596	+	0.962693i	$0.587221\pi$
$864$	24.6508	0.838637
$865$	5.21401	0.177282
$866$	−39.0279	−1.32622
$867$	−3.76228	−0.127774
$868$	27.4654	0.932236
$869$	−21.4022	−0.726019
$870$	−4.09456	−0.138819
$871$	−48.0575	−1.62837
$872$	0.946669	0.0320582
$873$	4.54637	0.153871
$874$	77.6940	2.62804
$875$	−19.8187	−0.669993
$876$	−2.80259	−0.0946906
$877$	−50.9073	−1.71902	−0.859508	−	0.511122i	$-0.829230\pi$
$877$	−50.9073	−1.71902	−0.859508	+	0.511122i	$0.829230\pi$
$878$	−5.81413	−0.196217
$879$	8.37213	0.282385
$880$	23.0179	0.775935
$881$	32.3649	1.09040	0.545200	−	0.838306i	$-0.316454\pi$
$881$	32.3649	1.09040	0.545200	+	0.838306i	$0.316454\pi$
$882$	57.1501	1.92434
$883$	−25.9743	−0.874105	−0.437053	−	0.899436i	$-0.643978\pi$
$883$	−25.9743	−0.874105	−0.437053	+	0.899436i	$0.643978\pi$
$884$	40.4177	1.35940
$885$	0.817283	0.0274727
$886$	−59.0352	−1.98333
$887$	6.34635	0.213090	0.106545	−	0.994308i	$-0.466021\pi$
$887$	6.34635	0.213090	0.106545	+	0.994308i	$0.466021\pi$
$888$	−11.0433	−0.370590
$889$	−9.43280	−0.316366
$890$	9.34446	0.313227
$891$	29.9969	1.00494
$892$	121.714	4.07529
$893$	5.15824	0.172614
$894$	−0.0487192	−0.00162941
$895$	4.99956	0.167117
$896$	−50.9359	−1.70165
$897$	10.7619	0.359329
$898$	24.2721	0.809972
$899$	14.5977	0.486860
$900$	70.2410	2.34137
$901$	−0.590366	−0.0196679
$902$	−67.9479	−2.26242
$903$	−8.49301	−0.282630
$904$	27.3240	0.908783
$905$	−9.68726	−0.322015
$906$	13.9298	0.462787
$907$	46.6831	1.55009	0.775043	−	0.631908i	$-0.217728\pi$
$907$	46.6831	1.55009	0.775043	+	0.631908i	$0.217728\pi$
$908$	−108.110	−3.58776
$909$	6.56566	0.217769
$910$	−23.2192	−0.769710
$911$	4.18927	0.138797	0.0693983	−	0.997589i	$-0.477892\pi$
$911$	4.18927	0.138797	0.0693983	+	0.997589i	$0.477892\pi$
$912$	−10.5374	−0.348928
$913$	−12.8813	−0.426310
$914$	71.3579	2.36031
$915$	1.27229	0.0420607
$916$	39.3276	1.29942
$917$	−5.45537	−0.180152
$918$	8.12984	0.268325
$919$	−44.0975	−1.45464	−0.727321	−	0.686297i	$-0.759235\pi$
$919$	−44.0975	−1.45464	−0.727321	+	0.686297i	$0.759235\pi$
$920$	−40.4987	−1.33520
$921$	−8.73281	−0.287756
$922$	67.1650	2.21196
$923$	18.1968	0.598955
$924$	19.3494	0.636547
$925$	−22.6620	−0.745121
$926$	−73.0573	−2.40081
$927$	−37.5495	−1.23329
$928$	−153.992	−5.05503
$929$	−26.7743	−0.878438	−0.439219	−	0.898380i	$-0.644745\pi$
$929$	−26.7743	−0.878438	−0.439219	+	0.898380i	$0.644745\pi$
$930$	−0.566830	−0.0185871
$931$	−23.5414	−0.771537
$932$	−66.8106	−2.18846
$933$	0.184000	0.00602390
$934$	46.8144	1.53181
$935$	3.61006	0.118062
$936$	103.165	3.37206
$937$	38.6056	1.26119	0.630594	−	0.776113i	$-0.282811\pi$
$937$	38.6056	1.26119	0.630594	+	0.776113i	$0.282811\pi$
$938$	113.616	3.70970
$939$	−5.04968	−0.164790
$940$	−4.42196	−0.144229
$941$	−6.09443	−0.198673	−0.0993363	−	0.995054i	$-0.531672\pi$
$941$	−6.09443	−0.198673	−0.0993363	+	0.995054i	$0.531672\pi$
$942$	0.567526	0.0184910
$943$	64.1879	2.09025
$944$	64.6347	2.10368
$945$	−3.35533	−0.109149
$946$	77.7278	2.52715
$947$	22.3276	0.725551	0.362775	−	0.931877i	$-0.381829\pi$
$947$	22.3276	0.725551	0.362775	+	0.931877i	$0.381829\pi$
$948$	−8.39920	−0.272793
$949$	−8.44692	−0.274199
$950$	−40.2743	−1.30667
$951$	−2.33043	−0.0755694
$952$	−58.1020	−1.88310
$953$	44.7462	1.44947	0.724735	−	0.689027i	$-0.241962\pi$
$953$	44.7462	1.44947	0.724735	+	0.689027i	$0.241962\pi$
$954$	−2.47823	−0.0802356
$955$	12.3722	0.400355
$956$	61.2088	1.97963
$957$	10.2841	0.332437
$958$	84.0862	2.71670
$959$	65.5163	2.11563
$960$	2.43894	0.0787164
$961$	−28.9792	−0.934812
$962$	−54.7393	−1.76487
$963$	11.2408	0.362230
$964$	109.609	3.53025
$965$	−1.10963	−0.0357202
$966$	−25.4429	−0.818612
$967$	41.1933	1.32469	0.662344	−	0.749200i	$-0.269562\pi$
$967$	41.1933	1.32469	0.662344	+	0.749200i	$0.269562\pi$
$968$	−16.7175	−0.537321
$969$	−1.65265	−0.0530909
$970$	2.23468	0.0717513
$971$	3.85651	0.123761	0.0618806	−	0.998084i	$-0.480290\pi$
$971$	3.85651	0.123761	0.0618806	+	0.998084i	$0.480290\pi$
$972$	36.9359	1.18472
$973$	29.6728	0.951267
$974$	8.15942	0.261445
$975$	−5.57865	−0.178660
$976$	100.619	3.22074
$977$	8.11448	0.259605	0.129803	−	0.991540i	$-0.458566\pi$
$977$	8.11448	0.259605	0.129803	+	0.991540i	$0.458566\pi$
$978$	−10.4433	−0.333939
$979$	−23.4699	−0.750103
$980$	20.1811	0.644662
$981$	0.334633	0.0106840
$982$	10.7744	0.343825
$983$	29.2813	0.933929	0.466964	−	0.884276i	$-0.345348\pi$
$983$	29.2813	0.933929	0.466964	+	0.884276i	$0.345348\pi$
$984$	−16.2142	−0.516891
$985$	6.13240	0.195394
$986$	−50.7866	−1.61737
$987$	−1.68920	−0.0537678
$988$	−69.8886	−2.22345
$989$	−73.4266	−2.33483
$990$	15.1543	0.481634
$991$	−13.7949	−0.438211	−0.219105	−	0.975701i	$-0.570314\pi$
$991$	−13.7949	−0.438211	−0.219105	+	0.975701i	$0.570314\pi$
$992$	−21.3179	−0.676843
$993$	0.990280	0.0314256
$994$	−43.0203	−1.36452
$995$	−11.4380	−0.362610
$996$	−5.05523	−0.160181
$997$	−18.4890	−0.585554	−0.292777	−	0.956181i	$-0.594579\pi$
$997$	−18.4890	−0.585554	−0.292777	+	0.956181i	$0.594579\pi$
$998$	−71.8515	−2.27442
$999$	−7.91017	−0.250267

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.5	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.5	✓	259	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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66509 q^{2} +0.277531 q^{3} +5.10272 q^{4} +0.539093 q^{5} -0.739647 q^{6} +3.78634 q^{7} -8.26903 q^{8} -2.92298 q^{9} +O(q^{10})\)	\(q-2.66509 q^{2} +0.277531 q^{3} +5.10272 q^{4} +0.539093 q^{5} -0.739647 q^{6} +3.78634 q^{7} -8.26903 q^{8} -2.92298 q^{9} -1.43673 q^{10} +3.60856 q^{11} +1.41616 q^{12} +4.26828 q^{13} -10.0909 q^{14} +0.149615 q^{15} +11.8323 q^{16} +1.85574 q^{17} +7.79000 q^{18} -3.20887 q^{19} +2.75084 q^{20} +1.05083 q^{21} -9.61714 q^{22} +9.08496 q^{23} -2.29492 q^{24} -4.70938 q^{25} -11.3754 q^{26} -1.64381 q^{27} +19.3206 q^{28} +10.2688 q^{29} -0.398738 q^{30} +1.42156 q^{31} -14.9961 q^{32} +1.00149 q^{33} -4.94572 q^{34} +2.04119 q^{35} -14.9151 q^{36} +4.81209 q^{37} +8.55193 q^{38} +1.18458 q^{39} -4.45778 q^{40} +7.06529 q^{41} -2.80055 q^{42} -8.08222 q^{43} +18.4135 q^{44} -1.57576 q^{45} -24.2123 q^{46} -1.60750 q^{47} +3.28383 q^{48} +7.33634 q^{49} +12.5509 q^{50} +0.515027 q^{51} +21.7798 q^{52} -0.318129 q^{53} +4.38091 q^{54} +1.94535 q^{55} -31.3093 q^{56} -0.890562 q^{57} -27.3673 q^{58} +5.46257 q^{59} +0.763444 q^{60} +8.50376 q^{61} -3.78859 q^{62} -11.0674 q^{63} +16.3014 q^{64} +2.30100 q^{65} -2.66906 q^{66} -11.2592 q^{67} +9.46933 q^{68} +2.52136 q^{69} -5.43995 q^{70} +4.26327 q^{71} +24.1702 q^{72} -1.97900 q^{73} -12.8247 q^{74} -1.30700 q^{75} -16.3740 q^{76} +13.6632 q^{77} -3.15702 q^{78} -5.93095 q^{79} +6.37871 q^{80} +8.31272 q^{81} -18.8296 q^{82} -3.56966 q^{83} +5.36208 q^{84} +1.00042 q^{85} +21.5399 q^{86} +2.84991 q^{87} -29.8393 q^{88} -6.50396 q^{89} +4.19953 q^{90} +16.1611 q^{91} +46.3580 q^{92} +0.394527 q^{93} +4.28413 q^{94} -1.72988 q^{95} -4.16189 q^{96} -1.55539 q^{97} -19.5520 q^{98} -10.5477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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