LMFDB - Embedded newform 6043.2.a.c.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.57414 q^{2} +1.55511 q^{3} +4.62619 q^{4} -0.336132 q^{5} -4.00307 q^{6} -3.88876 q^{7} -6.76018 q^{8} -0.581626 q^{9} +O(q^{10})$	\(q-2.57414 q^{2} +1.55511 q^{3} +4.62619 q^{4} -0.336132 q^{5} -4.00307 q^{6} -3.88876 q^{7} -6.76018 q^{8} -0.581626 q^{9} +0.865250 q^{10} -6.38555 q^{11} +7.19424 q^{12} +1.06414 q^{13} +10.0102 q^{14} -0.522723 q^{15} +8.14925 q^{16} -3.71098 q^{17} +1.49719 q^{18} -1.89029 q^{19} -1.55501 q^{20} -6.04745 q^{21} +16.4373 q^{22} -6.04187 q^{23} -10.5128 q^{24} -4.88702 q^{25} -2.73925 q^{26} -5.56983 q^{27} -17.9901 q^{28} -2.37857 q^{29} +1.34556 q^{30} -9.36502 q^{31} -7.45695 q^{32} -9.93025 q^{33} +9.55257 q^{34} +1.30713 q^{35} -2.69071 q^{36} -5.59566 q^{37} +4.86587 q^{38} +1.65486 q^{39} +2.27231 q^{40} +10.4691 q^{41} +15.5670 q^{42} -1.12211 q^{43} -29.5408 q^{44} +0.195503 q^{45} +15.5526 q^{46} +11.2574 q^{47} +12.6730 q^{48} +8.12242 q^{49} +12.5799 q^{50} -5.77099 q^{51} +4.92292 q^{52} +4.75352 q^{53} +14.3375 q^{54} +2.14639 q^{55} +26.2887 q^{56} -2.93961 q^{57} +6.12278 q^{58} +5.11038 q^{59} -2.41821 q^{60} -14.8617 q^{61} +24.1069 q^{62} +2.26180 q^{63} +2.89672 q^{64} -0.357692 q^{65} +25.5618 q^{66} -11.5331 q^{67} -17.1677 q^{68} -9.39579 q^{69} -3.36475 q^{70} -6.52399 q^{71} +3.93189 q^{72} -10.2370 q^{73} +14.4040 q^{74} -7.59986 q^{75} -8.74484 q^{76} +24.8319 q^{77} -4.25983 q^{78} -12.2776 q^{79} -2.73922 q^{80} -6.91683 q^{81} -26.9489 q^{82} +9.57441 q^{83} -27.9767 q^{84} +1.24738 q^{85} +2.88847 q^{86} -3.69895 q^{87} +43.1675 q^{88} +11.2199 q^{89} -0.503252 q^{90} -4.13818 q^{91} -27.9508 q^{92} -14.5637 q^{93} -28.9781 q^{94} +0.635386 q^{95} -11.5964 q^{96} -7.47598 q^{97} -20.9082 q^{98} +3.71400 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.57414	−1.82019	−0.910095	−	0.414399i	$-0.863992\pi$
$2$	−2.57414	−1.82019	−0.910095	+	0.414399i	$0.863992\pi$
$3$	1.55511	0.897845	0.448922	−	0.893571i	$-0.351808\pi$
$3$	1.55511	0.897845	0.448922	+	0.893571i	$0.351808\pi$
$4$	4.62619	2.31309
$5$	−0.336132	−0.150323	−0.0751614	−	0.997171i	$-0.523947\pi$
$5$	−0.336132	−0.150323	−0.0751614	+	0.997171i	$0.523947\pi$
$6$	−4.00307	−1.63425
$7$	−3.88876	−1.46981	−0.734906	−	0.678169i	$-0.762774\pi$
$7$	−3.88876	−1.46981	−0.734906	+	0.678169i	$0.762774\pi$
$8$	−6.76018	−2.39008
$9$	−0.581626	−0.193875
$10$	0.865250	0.273616
$11$	−6.38555	−1.92532	−0.962658	−	0.270719i	$-0.912738\pi$
$11$	−6.38555	−1.92532	−0.962658	+	0.270719i	$0.912738\pi$
$12$	7.19424	2.07680
$13$	1.06414	0.295139	0.147570	−	0.989052i	$-0.452855\pi$
$13$	1.06414	0.295139	0.147570	+	0.989052i	$0.452855\pi$
$14$	10.0102	2.67534
$15$	−0.522723	−0.134966
$16$	8.14925	2.03731
$17$	−3.71098	−0.900044	−0.450022	−	0.893017i	$-0.648584\pi$
$17$	−3.71098	−0.900044	−0.450022	+	0.893017i	$0.648584\pi$
$18$	1.49719	0.352890
$19$	−1.89029	−0.433662	−0.216831	−	0.976209i	$-0.569572\pi$
$19$	−1.89029	−0.433662	−0.216831	+	0.976209i	$0.569572\pi$
$20$	−1.55501	−0.347711
$21$	−6.04745	−1.31966
$22$	16.4373	3.50444
$23$	−6.04187	−1.25982	−0.629908	−	0.776669i	$-0.716908\pi$
$23$	−6.04187	−1.25982	−0.629908	+	0.776669i	$0.716908\pi$
$24$	−10.5128	−2.14592
$25$	−4.88702	−0.977403
$26$	−2.73925	−0.537210
$27$	−5.56983	−1.07191
$28$	−17.9901	−3.39981
$29$	−2.37857	−0.441690	−0.220845	−	0.975309i	$-0.570881\pi$
$29$	−2.37857	−0.441690	−0.220845	+	0.975309i	$0.570881\pi$
$30$	1.34556	0.245665
$31$	−9.36502	−1.68201	−0.841004	−	0.541029i	$-0.818035\pi$
$31$	−9.36502	−1.68201	−0.841004	+	0.541029i	$0.818035\pi$
$32$	−7.45695	−1.31821
$33$	−9.93025	−1.72864
$34$	9.55257	1.63825
$35$	1.30713	0.220946
$36$	−2.69071	−0.448452
$37$	−5.59566	−0.919920	−0.459960	−	0.887940i	$-0.652136\pi$
$37$	−5.59566	−0.919920	−0.459960	+	0.887940i	$0.652136\pi$
$38$	4.86587	0.789348
$39$	1.65486	0.264989
$40$	2.27231	0.359284
$41$	10.4691	1.63500	0.817500	−	0.575928i	$-0.195359\pi$
$41$	10.4691	1.63500	0.817500	+	0.575928i	$0.195359\pi$
$42$	15.5670	2.40204
$43$	−1.12211	−0.171120	−0.0855601	−	0.996333i	$-0.527268\pi$
$43$	−1.12211	−0.171120	−0.0855601	+	0.996333i	$0.527268\pi$
$44$	−29.5408	−4.45344
$45$	0.195503	0.0291439
$46$	15.5526	2.29311
$47$	11.2574	1.64206	0.821030	−	0.570885i	$-0.193400\pi$
$47$	11.2574	1.64206	0.821030	+	0.570885i	$0.193400\pi$
$48$	12.6730	1.82919
$49$	8.12242	1.16035
$50$	12.5799	1.77906
$51$	−5.77099	−0.808100
$52$	4.92292	0.682686
$53$	4.75352	0.652947	0.326473	−	0.945206i	$-0.394140\pi$
$53$	4.75352	0.652947	0.326473	+	0.945206i	$0.394140\pi$
$54$	14.3375	1.95109
$55$	2.14639	0.289419
$56$	26.2887	3.51297
$57$	−2.93961	−0.389361
$58$	6.12278	0.803960
$59$	5.11038	0.665314	0.332657	−	0.943048i	$-0.392055\pi$
$59$	5.11038	0.665314	0.332657	+	0.943048i	$0.392055\pi$
$60$	−2.41821	−0.312190
$61$	−14.8617	−1.90285	−0.951425	−	0.307882i	$-0.900380\pi$
$61$	−14.8617	−1.90285	−0.951425	+	0.307882i	$0.900380\pi$
$62$	24.1069	3.06158
$63$	2.26180	0.284960
$64$	2.89672	0.362089
$65$	−0.357692	−0.0443662
$66$	25.5618	3.14645
$67$	−11.5331	−1.40899	−0.704494	−	0.709710i	$-0.748826\pi$
$67$	−11.5331	−1.40899	−0.704494	+	0.709710i	$0.748826\pi$
$68$	−17.1677	−2.08189
$69$	−9.39579	−1.13112
$70$	−3.36475	−0.402164
$71$	−6.52399	−0.774255	−0.387128	−	0.922026i	$-0.626533\pi$
$71$	−6.52399	−0.774255	−0.387128	+	0.922026i	$0.626533\pi$
$72$	3.93189	0.463378
$73$	−10.2370	−1.19815	−0.599074	−	0.800694i	$-0.704464\pi$
$73$	−10.2370	−1.19815	−0.599074	+	0.800694i	$0.704464\pi$
$74$	14.4040	1.67443
$75$	−7.59986	−0.877556
$76$	−8.74484	−1.00310
$77$	24.8319	2.82985
$78$	−4.25983	−0.482331
$79$	−12.2776	−1.38134	−0.690671	−	0.723169i	$-0.742685\pi$
$79$	−12.2776	−1.38134	−0.690671	+	0.723169i	$0.742685\pi$
$80$	−2.73922	−0.306254
$81$	−6.91683	−0.768537
$82$	−26.9489	−2.97601
$83$	9.57441	1.05093	0.525464	−	0.850816i	$-0.323892\pi$
$83$	9.57441	1.05093	0.525464	+	0.850816i	$0.323892\pi$
$84$	−27.9767	−3.05250
$85$	1.24738	0.135297
$86$	2.88847	0.311471
$87$	−3.69895	−0.396569
$88$	43.1675	4.60167
$89$	11.2199	1.18931	0.594654	−	0.803981i	$-0.297289\pi$
$89$	11.2199	1.18931	0.594654	+	0.803981i	$0.297289\pi$
$90$	−0.503252	−0.0530474
$91$	−4.13818	−0.433799
$92$	−27.9508	−2.91408
$93$	−14.5637	−1.51018
$94$	−28.9781	−2.98886
$95$	0.635386	0.0651893
$96$	−11.5964	−1.18355
$97$	−7.47598	−0.759071	−0.379535	−	0.925177i	$-0.623916\pi$
$97$	−7.47598	−0.759071	−0.379535	+	0.925177i	$0.623916\pi$
$98$	−20.9082	−2.11205
$99$	3.71400	0.373271
$100$	−22.6083	−2.26083
$101$	−6.59403	−0.656130	−0.328065	−	0.944655i	$-0.606397\pi$
$101$	−6.59403	−0.656130	−0.328065	+	0.944655i	$0.606397\pi$
$102$	14.8553	1.47090
$103$	6.09935	0.600987	0.300494	−	0.953784i	$-0.402849\pi$
$103$	6.09935	0.600987	0.300494	+	0.953784i	$0.402849\pi$
$104$	−7.19378	−0.705408
$105$	2.03274	0.198375
$106$	−12.2362	−1.18849
$107$	−10.0102	−0.967720	−0.483860	−	0.875145i	$-0.660766\pi$
$107$	−10.0102	−0.967720	−0.483860	+	0.875145i	$0.660766\pi$
$108$	−25.7671	−2.47944
$109$	16.4205	1.57280	0.786400	−	0.617718i	$-0.211943\pi$
$109$	16.4205	1.57280	0.786400	+	0.617718i	$0.211943\pi$
$110$	−5.52510	−0.526798
$111$	−8.70188	−0.825946
$112$	−31.6904	−2.99447
$113$	−10.2502	−0.964261	−0.482130	−	0.876099i	$-0.660137\pi$
$113$	−10.2502	−0.964261	−0.482130	+	0.876099i	$0.660137\pi$
$114$	7.56697	0.708712
$115$	2.03086	0.189379
$116$	−11.0037	−1.02167
$117$	−0.618931	−0.0572202
$118$	−13.1548	−1.21100
$119$	14.4311	1.32290
$120$	3.53370	0.322581
$121$	29.7753	2.70684
$122$	38.2561	3.46355
$123$	16.2806	1.46798
$124$	−43.3244	−3.89064
$125$	3.32334	0.297249
$126$	−5.82219	−0.518682
$127$	11.2164	0.995293	0.497647	−	0.867380i	$-0.334198\pi$
$127$	11.2164	0.995293	0.497647	+	0.867380i	$0.334198\pi$
$128$	7.45735	0.659143
$129$	−1.74501	−0.153639
$130$	0.920748	0.0807549
$131$	−15.0843	−1.31792	−0.658962	−	0.752176i	$-0.729004\pi$
$131$	−15.0843	−1.31792	−0.658962	+	0.752176i	$0.729004\pi$
$132$	−45.9392	−3.99850
$133$	7.35087	0.637402
$134$	29.6877	2.56463
$135$	1.87220	0.161133
$136$	25.0869	2.15118
$137$	8.25139	0.704964	0.352482	−	0.935819i	$-0.385338\pi$
$137$	8.25139	0.704964	0.352482	+	0.935819i	$0.385338\pi$
$138$	24.1861	2.05885
$139$	−0.384467	−0.0326101	−0.0163051	−	0.999867i	$-0.505190\pi$
$139$	−0.384467	−0.0326101	−0.0163051	+	0.999867i	$0.505190\pi$
$140$	6.04705	0.511069
$141$	17.5065	1.47432
$142$	16.7937	1.40929
$143$	−6.79513	−0.568237
$144$	−4.73981	−0.394984
$145$	0.799514	0.0663960
$146$	26.3514	2.18086
$147$	12.6313	1.04181
$148$	−25.8866	−2.12786
$149$	−5.87688	−0.481453	−0.240726	−	0.970593i	$-0.577386\pi$
$149$	−5.87688	−0.481453	−0.240726	+	0.970593i	$0.577386\pi$
$150$	19.5631	1.59732
$151$	10.4408	0.849663	0.424831	−	0.905273i	$-0.360333\pi$
$151$	10.4408	0.849663	0.424831	+	0.905273i	$0.360333\pi$
$152$	12.7787	1.03649
$153$	2.15840	0.174496
$154$	−63.9206	−5.15087
$155$	3.14788	0.252844
$156$	7.65569	0.612946
$157$	4.28402	0.341902	0.170951	−	0.985280i	$-0.445316\pi$
$157$	4.28402	0.341902	0.170951	+	0.985280i	$0.445316\pi$
$158$	31.6043	2.51430
$159$	7.39226	0.586245
$160$	2.50652	0.198158
$161$	23.4954	1.85169
$162$	17.8049	1.39888
$163$	−14.5001	−1.13573	−0.567867	−	0.823120i	$-0.692231\pi$
$163$	−14.5001	−1.13573	−0.567867	+	0.823120i	$0.692231\pi$
$164$	48.4321	3.78191
$165$	3.33787	0.259853
$166$	−24.6459	−1.91289
$167$	7.88272	0.609983	0.304991	−	0.952355i	$-0.401346\pi$
$167$	7.88272	0.609983	0.304991	+	0.952355i	$0.401346\pi$
$168$	40.8818	3.15410
$169$	−11.8676	−0.912893
$170$	−3.21092	−0.246267
$171$	1.09944	0.0840763
$172$	−5.19109	−0.395817
$173$	3.51887	0.267535	0.133768	−	0.991013i	$-0.457292\pi$
$173$	3.51887	0.267535	0.133768	+	0.991013i	$0.457292\pi$
$174$	9.52161	0.721831
$175$	19.0044	1.43660
$176$	−52.0375	−3.92247
$177$	7.94721	0.597349
$178$	−28.8816	−2.16477
$179$	12.4598	0.931288	0.465644	−	0.884972i	$-0.345823\pi$
$179$	12.4598	0.931288	0.465644	+	0.884972i	$0.345823\pi$
$180$	0.904433	0.0674125
$181$	−4.45572	−0.331191	−0.165596	−	0.986194i	$-0.552955\pi$
$181$	−4.45572	−0.331191	−0.165596	+	0.986194i	$0.552955\pi$
$182$	10.6523	0.789598
$183$	−23.1117	−1.70846
$184$	40.8441	3.01107
$185$	1.88088	0.138285
$186$	37.4889	2.74882
$187$	23.6966	1.73287
$188$	52.0789	3.79824
$189$	21.6597	1.57551
$190$	−1.63557	−0.118657
$191$	−15.7909	−1.14259	−0.571296	−	0.820744i	$-0.693559\pi$
$191$	−15.7909	−1.14259	−0.571296	+	0.820744i	$0.693559\pi$
$192$	4.50472	0.325100
$193$	−23.0122	−1.65645	−0.828226	−	0.560394i	$-0.810650\pi$
$193$	−23.0122	−1.65645	−0.828226	+	0.560394i	$0.810650\pi$
$194$	19.2442	1.38165
$195$	−0.556251	−0.0398339
$196$	37.5759	2.68399
$197$	−2.29770	−0.163704	−0.0818522	−	0.996644i	$-0.526084\pi$
$197$	−2.29770	−0.163704	−0.0818522	+	0.996644i	$0.526084\pi$
$198$	−9.56035	−0.679425
$199$	−11.0826	−0.785625	−0.392812	−	0.919619i	$-0.628498\pi$
$199$	−11.0826	−0.785625	−0.392812	+	0.919619i	$0.628498\pi$
$200$	33.0371	2.33607
$201$	−17.9352	−1.26505
$202$	16.9739	1.19428
$203$	9.24969	0.649201
$204$	−26.6977	−1.86921
$205$	−3.51900	−0.245778
$206$	−15.7006	−1.09391
$207$	3.51411	0.244247
$208$	8.67195	0.601291
$209$	12.0705	0.834937
$210$	−5.23256	−0.361081
$211$	8.31581	0.572484	0.286242	−	0.958157i	$-0.407594\pi$
$211$	8.31581	0.572484	0.286242	+	0.958157i	$0.407594\pi$
$212$	21.9907	1.51033
$213$	−10.1455	−0.695161
$214$	25.7676	1.76144
$215$	0.377177	0.0257233
$216$	37.6530	2.56196
$217$	36.4183	2.47223
$218$	−42.2687	−2.86279
$219$	−15.9196	−1.07575
$220$	9.92960	0.669453
$221$	−3.94900	−0.265639
$222$	22.3998	1.50338
$223$	−4.02465	−0.269511	−0.134755	−	0.990879i	$-0.543025\pi$
$223$	−4.02465	−0.269511	−0.134755	+	0.990879i	$0.543025\pi$
$224$	28.9982	1.93753
$225$	2.84241	0.189494
$226$	26.3855	1.75514
$227$	22.0813	1.46559	0.732794	−	0.680450i	$-0.238216\pi$
$227$	22.0813	1.46559	0.732794	+	0.680450i	$0.238216\pi$
$228$	−13.5992	−0.900629
$229$	0.123134	0.00813692	0.00406846	−	0.999992i	$-0.498705\pi$
$229$	0.123134	0.00813692	0.00406846	+	0.999992i	$0.498705\pi$
$230$	−5.22773	−0.344706
$231$	38.6163	2.54077
$232$	16.0796	1.05568
$233$	−18.7787	−1.23023	−0.615117	−	0.788436i	$-0.710891\pi$
$233$	−18.7787	−1.23023	−0.615117	+	0.788436i	$0.710891\pi$
$234$	1.59322	0.104152
$235$	−3.78397	−0.246839
$236$	23.6416	1.53894
$237$	−19.0931	−1.24023
$238$	−37.1476	−2.40792
$239$	−4.40853	−0.285164	−0.142582	−	0.989783i	$-0.545540\pi$
$239$	−4.40853	−0.285164	−0.142582	+	0.989783i	$0.545540\pi$
$240$	−4.25980	−0.274969
$241$	21.6970	1.39763	0.698814	−	0.715303i	$-0.253711\pi$
$241$	21.6970	1.39763	0.698814	+	0.715303i	$0.253711\pi$
$242$	−76.6457	−4.92697
$243$	5.95304	0.381887
$244$	−68.7532	−4.40147
$245$	−2.73020	−0.174426
$246$	−41.9086	−2.67200
$247$	−2.01153	−0.127991
$248$	63.3092	4.02014
$249$	14.8893	0.943570
$250$	−8.55474	−0.541049
$251$	−18.3034	−1.15530	−0.577650	−	0.816285i	$-0.696030\pi$
$251$	−18.3034	−1.15530	−0.577650	+	0.816285i	$0.696030\pi$
$252$	10.4635	0.659140
$253$	38.5807	2.42555
$254$	−28.8725	−1.81162
$255$	1.93981	0.121476
$256$	−24.9897	−1.56185
$257$	−9.08899	−0.566956	−0.283478	−	0.958979i	$-0.591488\pi$
$257$	−9.08899	−0.566956	−0.283478	+	0.958979i	$0.591488\pi$
$258$	4.49189	0.279653
$259$	21.7601	1.35211
$260$	−1.65475	−0.102623
$261$	1.38344	0.0856327
$262$	38.8292	2.39887
$263$	−2.23616	−0.137887	−0.0689437	−	0.997621i	$-0.521963\pi$
$263$	−2.23616	−0.137887	−0.0689437	+	0.997621i	$0.521963\pi$
$264$	67.1302	4.13158
$265$	−1.59781	−0.0981527
$266$	−18.9222	−1.16019
$267$	17.4482	1.06781
$268$	−53.3541	−3.25912
$269$	−22.4472	−1.36863	−0.684314	−	0.729187i	$-0.739898\pi$
$269$	−22.4472	−1.36863	−0.684314	+	0.729187i	$0.739898\pi$
$270$	−4.81930	−0.293293
$271$	−7.72828	−0.469460	−0.234730	−	0.972061i	$-0.575421\pi$
$271$	−7.72828	−0.469460	−0.234730	+	0.972061i	$0.575421\pi$
$272$	−30.2417	−1.83367
$273$	−6.43534	−0.389484
$274$	−21.2402	−1.28317
$275$	31.2063	1.88181
$276$	−43.4667	−2.61639
$277$	9.40627	0.565168	0.282584	−	0.959243i	$-0.408808\pi$
$277$	9.40627	0.565168	0.282584	+	0.959243i	$0.408808\pi$
$278$	0.989673	0.0593566
$279$	5.44694	0.326100
$280$	−8.83646	−0.528079
$281$	−6.84820	−0.408529	−0.204265	−	0.978916i	$-0.565480\pi$
$281$	−6.84820	−0.408529	−0.204265	+	0.978916i	$0.565480\pi$
$282$	−45.0642	−2.68354
$283$	−0.819380	−0.0487071	−0.0243535	−	0.999703i	$-0.507753\pi$
$283$	−0.819380	−0.0487071	−0.0243535	+	0.999703i	$0.507753\pi$
$284$	−30.1812	−1.79093
$285$	0.988097	0.0585298
$286$	17.4916	1.03430
$287$	−40.7118	−2.40314
$288$	4.33715	0.255569
$289$	−3.22864	−0.189920
$290$	−2.05806	−0.120853
$291$	−11.6260	−0.681528
$292$	−47.3582	−2.77143
$293$	29.7269	1.73667	0.868333	−	0.495982i	$-0.165192\pi$
$293$	29.7269	1.73667	0.868333	+	0.495982i	$0.165192\pi$
$294$	−32.5147	−1.89629
$295$	−1.71776	−0.100012
$296$	37.8276	2.19869
$297$	35.5664	2.06377
$298$	15.1279	0.876336
$299$	−6.42940	−0.371822
$300$	−35.1584	−2.02987
$301$	4.36361	0.251514
$302$	−26.8761	−1.54655
$303$	−10.2545	−0.589103
$304$	−15.4044	−0.883505
$305$	4.99550	0.286041
$306$	−5.55602	−0.317617
$307$	−16.4476	−0.938716	−0.469358	−	0.883008i	$-0.655515\pi$
$307$	−16.4476	−0.938716	−0.469358	+	0.883008i	$0.655515\pi$
$308$	114.877	6.54572
$309$	9.48518	0.539593
$310$	−8.10309	−0.460224
$311$	3.40219	0.192921	0.0964603	−	0.995337i	$-0.469248\pi$
$311$	3.40219	0.192921	0.0964603	+	0.995337i	$0.469248\pi$
$312$	−11.1871	−0.633347
$313$	−10.7038	−0.605016	−0.302508	−	0.953147i	$-0.597824\pi$
$313$	−10.7038	−0.605016	−0.302508	+	0.953147i	$0.597824\pi$
$314$	−11.0277	−0.622327
$315$	−0.760263	−0.0428360
$316$	−56.7986	−3.19517
$317$	25.3412	1.42330	0.711651	−	0.702534i	$-0.247948\pi$
$317$	25.3412	1.42330	0.711651	+	0.702534i	$0.247948\pi$
$318$	−19.0287	−1.06708
$319$	15.1885	0.850393
$320$	−0.973678	−0.0544303
$321$	−15.5669	−0.868862
$322$	−60.4803	−3.37044
$323$	7.01482	0.390315
$324$	−31.9986	−1.77770
$325$	−5.20047	−0.288470
$326$	37.3252	2.06725
$327$	25.5357	1.41213
$328$	−70.7730	−3.90779
$329$	−43.7773	−2.41352
$330$	−8.59215	−0.472982
$331$	22.9138	1.25946	0.629729	−	0.776814i	$-0.283166\pi$
$331$	22.9138	1.25946	0.629729	+	0.776814i	$0.283166\pi$
$332$	44.2930	2.43090
$333$	3.25458	0.178350
$334$	−20.2912	−1.11029
$335$	3.87663	0.211803
$336$	−49.2822	−2.68856
$337$	22.9366	1.24944	0.624719	−	0.780850i	$-0.285214\pi$
$337$	22.9366	1.24944	0.624719	+	0.780850i	$0.285214\pi$
$338$	30.5489	1.66164
$339$	−15.9403	−0.865756
$340$	5.77061	0.312955
$341$	59.8009	3.23840
$342$	−2.83011	−0.153035
$343$	−4.36482	−0.235678
$344$	7.58566	0.408991
$345$	3.15822	0.170033
$346$	−9.05807	−0.486965
$347$	−30.2232	−1.62246	−0.811232	−	0.584724i	$-0.801203\pi$
$347$	−30.2232	−1.62246	−0.811232	+	0.584724i	$0.801203\pi$
$348$	−17.1120	−0.917302
$349$	−1.14328	−0.0611983	−0.0305991	−	0.999532i	$-0.509742\pi$
$349$	−1.14328	−0.0611983	−0.0305991	+	0.999532i	$0.509742\pi$
$350$	−48.9200	−2.61488
$351$	−5.92708	−0.316364
$352$	47.6167	2.53798
$353$	11.2980	0.601331	0.300665	−	0.953730i	$-0.402791\pi$
$353$	11.2980	0.601331	0.300665	+	0.953730i	$0.402791\pi$
$354$	−20.4572	−1.08729
$355$	2.19292	0.116388
$356$	51.9055	2.75098
$357$	22.4420	1.18775
$358$	−32.0732	−1.69512
$359$	7.12535	0.376061	0.188031	−	0.982163i	$-0.439790\pi$
$359$	7.12535	0.376061	0.188031	+	0.982163i	$0.439790\pi$
$360$	−1.32163	−0.0696562
$361$	−15.4268	−0.811937
$362$	11.4697	0.602831
$363$	46.3039	2.43033
$364$	−19.1440	−1.00342
$365$	3.44097	0.180109
$366$	59.4926	3.10973
$367$	−24.1229	−1.25921	−0.629603	−	0.776917i	$-0.716782\pi$
$367$	−24.1229	−1.25921	−0.629603	+	0.776917i	$0.716782\pi$
$368$	−49.2367	−2.56664
$369$	−6.08910	−0.316986
$370$	−4.84164	−0.251705
$371$	−18.4853	−0.959709
$372$	−67.3743	−3.49319
$373$	−3.04323	−0.157573	−0.0787864	−	0.996892i	$-0.525104\pi$
$373$	−3.04323	−0.157573	−0.0787864	+	0.996892i	$0.525104\pi$
$374$	−60.9985	−3.15416
$375$	5.16817	0.266883
$376$	−76.1020	−3.92466
$377$	−2.53114	−0.130360
$378$	−55.7551	−2.86773
$379$	−17.4467	−0.896175	−0.448087	−	0.893990i	$-0.647895\pi$
$379$	−17.4467	−0.896175	−0.448087	+	0.893990i	$0.647895\pi$
$380$	2.93942	0.150789
$381$	17.4427	0.893619
$382$	40.6481	2.07974
$383$	−20.6863	−1.05702	−0.528509	−	0.848928i	$-0.677249\pi$
$383$	−20.6863	−1.05702	−0.528509	+	0.848928i	$0.677249\pi$
$384$	11.5970	0.591808
$385$	−8.34678	−0.425391
$386$	59.2365	3.01506
$387$	0.652648	0.0331760
$388$	−34.5853	−1.75580
$389$	−22.3217	−1.13175	−0.565877	−	0.824490i	$-0.691462\pi$
$389$	−22.3217	−1.13175	−0.565877	+	0.824490i	$0.691462\pi$
$390$	1.43187	0.0725053
$391$	22.4212	1.13389
$392$	−54.9090	−2.77332
$393$	−23.4578	−1.18329
$394$	5.91460	0.297973
$395$	4.12690	0.207647
$396$	17.1817	0.863412
$397$	30.0412	1.50773	0.753863	−	0.657031i	$-0.228188\pi$
$397$	30.0412	1.50773	0.753863	+	0.657031i	$0.228188\pi$
$398$	28.5282	1.42999
$399$	11.4314	0.572288
$400$	−39.8255	−1.99128
$401$	−12.0980	−0.604144	−0.302072	−	0.953285i	$-0.597678\pi$
$401$	−12.0980	−0.604144	−0.302072	+	0.953285i	$0.597678\pi$
$402$	46.1677	2.30264
$403$	−9.96570	−0.496427
$404$	−30.5052	−1.51769
$405$	2.32497	0.115529
$406$	−23.8100	−1.18167
$407$	35.7314	1.77114
$408$	39.0129	1.93143
$409$	27.2150	1.34569	0.672847	−	0.739781i	$-0.265071\pi$
$409$	27.2150	1.34569	0.672847	+	0.739781i	$0.265071\pi$
$410$	9.05840	0.447362
$411$	12.8318	0.632948
$412$	28.2168	1.39014
$413$	−19.8730	−0.977887
$414$	−9.04580	−0.444577
$415$	−3.21826	−0.157978
$416$	−7.93524	−0.389057
$417$	−0.597890	−0.0292788
$418$	−31.0713	−1.51974
$419$	−21.3831	−1.04463	−0.522317	−	0.852752i	$-0.674932\pi$
$419$	−21.3831	−1.04463	−0.522317	+	0.852752i	$0.674932\pi$
$420$	9.40385	0.458861
$421$	−30.7832	−1.50028	−0.750140	−	0.661279i	$-0.770014\pi$
$421$	−30.7832	−1.50028	−0.750140	+	0.661279i	$0.770014\pi$
$422$	−21.4061	−1.04203
$423$	−6.54759	−0.318355
$424$	−32.1347	−1.56060
$425$	18.1356	0.879706
$426$	26.1160	1.26533
$427$	57.7936	2.79683
$428$	−46.3090	−2.23843
$429$	−10.5672	−0.510188
$430$	−0.970906	−0.0468212
$431$	−35.1304	−1.69217	−0.846086	−	0.533046i	$-0.821047\pi$
$431$	−35.1304	−1.69217	−0.846086	+	0.533046i	$0.821047\pi$
$432$	−45.3899	−2.18382
$433$	31.3508	1.50662	0.753312	−	0.657663i	$-0.228455\pi$
$433$	31.3508	1.50662	0.753312	+	0.657663i	$0.228455\pi$
$434$	−93.7457	−4.49994
$435$	1.24333	0.0596133
$436$	75.9644	3.63803
$437$	11.4209	0.546335
$438$	40.9794	1.95807
$439$	−33.9401	−1.61987	−0.809936	−	0.586519i	$-0.800498\pi$
$439$	−33.9401	−1.61987	−0.809936	+	0.586519i	$0.800498\pi$
$440$	−14.5100	−0.691735
$441$	−4.72421	−0.224962
$442$	10.1653	0.483513
$443$	7.19198	0.341701	0.170851	−	0.985297i	$-0.445348\pi$
$443$	7.19198	0.341701	0.170851	+	0.985297i	$0.445348\pi$
$444$	−40.2565	−1.91049
$445$	−3.77137	−0.178780
$446$	10.3600	0.490561
$447$	−9.13921	−0.432270
$448$	−11.2646	−0.532203
$449$	−26.9826	−1.27339	−0.636694	−	0.771117i	$-0.719698\pi$
$449$	−26.9826	−1.27339	−0.636694	+	0.771117i	$0.719698\pi$
$450$	−7.31677	−0.344916
$451$	−66.8511	−3.14789
$452$	−47.4195	−2.23043
$453$	16.2367	0.762865
$454$	−56.8404	−2.66765
$455$	1.39097	0.0652099
$456$	19.8723	0.930606
$457$	35.2028	1.64672	0.823360	−	0.567520i	$-0.192097\pi$
$457$	35.2028	1.64672	0.823360	+	0.567520i	$0.192097\pi$
$458$	−0.316964	−0.0148107
$459$	20.6695	0.964771
$460$	9.39516	0.438052
$461$	14.6878	0.684080	0.342040	−	0.939685i	$-0.388882\pi$
$461$	14.6878	0.684080	0.342040	+	0.939685i	$0.388882\pi$
$462$	−99.4038	−4.62468
$463$	−39.9303	−1.85572	−0.927859	−	0.372931i	$-0.878353\pi$
$463$	−39.9303	−1.85572	−0.927859	+	0.372931i	$0.878353\pi$
$464$	−19.3836	−0.899861
$465$	4.89531	0.227015
$466$	48.3390	2.23926
$467$	−1.98788	−0.0919881	−0.0459940	−	0.998942i	$-0.514646\pi$
$467$	−1.98788	−0.0919881	−0.0459940	+	0.998942i	$0.514646\pi$
$468$	−2.86329	−0.132356
$469$	44.8493	2.07095
$470$	9.74047	0.449294
$471$	6.66214	0.306975
$472$	−34.5470	−1.59016
$473$	7.16529	0.329461
$474$	49.1483	2.25745
$475$	9.23787	0.423863
$476$	66.7609	3.05998
$477$	−2.76477	−0.126590
$478$	11.3482	0.519052
$479$	2.62790	0.120072	0.0600360	−	0.998196i	$-0.480878\pi$
$479$	2.62790	0.120072	0.0600360	+	0.998196i	$0.480878\pi$
$480$	3.89792	0.177915
$481$	−5.95457	−0.271505
$482$	−55.8511	−2.54395
$483$	36.5379	1.66253
$484$	137.746	6.26119
$485$	2.51292	0.114106
$486$	−15.3239	−0.695108
$487$	−19.1490	−0.867726	−0.433863	−	0.900979i	$-0.642850\pi$
$487$	−19.1490	−0.867726	−0.433863	+	0.900979i	$0.642850\pi$
$488$	100.468	4.54797
$489$	−22.5493	−1.01971
$490$	7.02792	0.317489
$491$	41.0586	1.85295	0.926474	−	0.376358i	$-0.122824\pi$
$491$	41.0586	1.85295	0.926474	+	0.376358i	$0.122824\pi$
$492$	75.3173	3.39557
$493$	8.82683	0.397541
$494$	5.17797	0.232968
$495$	−1.24839	−0.0561111
$496$	−76.3179	−3.42678
$497$	25.3702	1.13801
$498$	−38.3271	−1.71748
$499$	−15.8171	−0.708069	−0.354035	−	0.935232i	$-0.615191\pi$
$499$	−15.8171	−0.708069	−0.354035	+	0.935232i	$0.615191\pi$
$500$	15.3744	0.687564
$501$	12.2585	0.547670
$502$	47.1154	2.10287
$503$	9.26474	0.413094	0.206547	−	0.978437i	$-0.433777\pi$
$503$	9.26474	0.413094	0.206547	+	0.978437i	$0.433777\pi$
$504$	−15.2902	−0.681078
$505$	2.21646	0.0986313
$506$	−99.3120	−4.41496
$507$	−18.4555	−0.819636
$508$	51.8891	2.30221
$509$	−25.9953	−1.15222	−0.576111	−	0.817371i	$-0.695430\pi$
$509$	−25.9953	−1.15222	−0.576111	+	0.817371i	$0.695430\pi$
$510$	−4.99335	−0.221109
$511$	39.8091	1.76105
$512$	49.4122	2.18373
$513$	10.5286	0.464849
$514$	23.3963	1.03197
$515$	−2.05019	−0.0903420
$516$	−8.07273	−0.355382
$517$	−71.8847	−3.16149
$518$	−56.0136	−2.46110
$519$	5.47225	0.240205
$520$	2.41806	0.106039
$521$	5.80099	0.254146	0.127073	−	0.991893i	$-0.459442\pi$
$521$	5.80099	0.254146	0.127073	+	0.991893i	$0.459442\pi$
$522$	−3.56116	−0.155868
$523$	−37.2021	−1.62674	−0.813368	−	0.581749i	$-0.802368\pi$
$523$	−37.2021	−1.62674	−0.813368	+	0.581749i	$0.802368\pi$
$524$	−69.7830	−3.04848
$525$	29.5540	1.28984
$526$	5.75618	0.250981
$527$	34.7534	1.51388
$528$	−80.9241	−3.52177
$529$	13.5042	0.587139
$530$	4.11299	0.178657
$531$	−2.97233	−0.128988
$532$	34.0065	1.47437
$533$	11.1406	0.482553
$534$	−44.9142	−1.94363
$535$	3.36474	0.145470
$536$	77.9655	3.36760
$537$	19.3764	0.836152
$538$	57.7821	2.49116
$539$	−51.8661	−2.23403
$540$	8.66114	0.372716
$541$	−15.5302	−0.667695	−0.333848	−	0.942627i	$-0.608347\pi$
$541$	−15.5302	−0.667695	−0.333848	+	0.942627i	$0.608347\pi$
$542$	19.8937	0.854507
$543$	−6.92915	−0.297358
$544$	27.6726	1.18645
$545$	−5.51945	−0.236427
$546$	16.5655	0.708936
$547$	12.7412	0.544773	0.272386	−	0.962188i	$-0.412187\pi$
$547$	12.7412	0.544773	0.272386	+	0.962188i	$0.412187\pi$
$548$	38.1725	1.63065
$549$	8.64396	0.368915
$550$	−80.3293	−3.42525
$551$	4.49619	0.191544
$552$	63.5172	2.70347
$553$	47.7447	2.03031
$554$	−24.2130	−1.02871
$555$	2.92498	0.124158
$556$	−1.77862	−0.0754303
$557$	−22.0250	−0.933231	−0.466615	−	0.884460i	$-0.654527\pi$
$557$	−22.0250	−0.933231	−0.466615	+	0.884460i	$0.654527\pi$
$558$	−14.0212	−0.593564
$559$	−1.19408	−0.0505043
$560$	10.6522	0.450136
$561$	36.8509	1.55585
$562$	17.6282	0.743601
$563$	−31.0630	−1.30915	−0.654575	−	0.755997i	$-0.727153\pi$
$563$	−31.0630	−1.30915	−0.654575	+	0.755997i	$0.727153\pi$
$564$	80.9885	3.41023
$565$	3.44543	0.144950
$566$	2.10920	0.0886562
$567$	26.8979	1.12960
$568$	44.1033	1.85053
$569$	9.45295	0.396288	0.198144	−	0.980173i	$-0.436509\pi$
$569$	9.45295	0.396288	0.198144	+	0.980173i	$0.436509\pi$
$570$	−2.54350	−0.106535
$571$	19.2516	0.805656	0.402828	−	0.915276i	$-0.368027\pi$
$571$	19.2516	0.805656	0.402828	+	0.915276i	$0.368027\pi$
$572$	−31.4355	−1.31439
$573$	−24.5567	−1.02587
$574$	104.798	4.37418
$575$	29.5267	1.23135
$576$	−1.68480	−0.0702002
$577$	4.42322	0.184141	0.0920705	−	0.995752i	$-0.470651\pi$
$577$	4.42322	0.184141	0.0920705	+	0.995752i	$0.470651\pi$
$578$	8.31097	0.345691
$579$	−35.7865	−1.48724
$580$	3.69870	0.153580
$581$	−37.2325	−1.54467
$582$	29.9269	1.24051
$583$	−30.3539	−1.25713
$584$	69.2038	2.86367
$585$	0.208043	0.00860150
$586$	−76.5212	−3.16106
$587$	−38.0287	−1.56961	−0.784806	−	0.619742i	$-0.787237\pi$
$587$	−38.0287	−1.56961	−0.784806	+	0.619742i	$0.787237\pi$
$588$	58.4347	2.40981
$589$	17.7026	0.729423
$590$	4.42175	0.182041
$591$	−3.57318	−0.146981
$592$	−45.6004	−1.87417
$593$	−37.7450	−1.55000	−0.775000	−	0.631961i	$-0.782250\pi$
$593$	−37.7450	−1.55000	−0.775000	+	0.631961i	$0.782250\pi$
$594$	−91.5530	−3.75646
$595$	−4.85075	−0.198861
$596$	−27.1876	−1.11365
$597$	−17.2347	−0.705369
$598$	16.5502	0.676787
$599$	−16.9753	−0.693591	−0.346795	−	0.937941i	$-0.612730\pi$
$599$	−16.9753	−0.693591	−0.346795	+	0.937941i	$0.612730\pi$
$600$	51.3764	2.09743
$601$	−26.9459	−1.09915	−0.549573	−	0.835446i	$-0.685210\pi$
$601$	−26.9459	−1.09915	−0.549573	+	0.835446i	$0.685210\pi$
$602$	−11.2325	−0.457804
$603$	6.70792	0.273168
$604$	48.3013	1.96535
$605$	−10.0084	−0.406900
$606$	26.3964	1.07228
$607$	−2.79180	−0.113316	−0.0566578	−	0.998394i	$-0.518044\pi$
$607$	−2.79180	−0.113316	−0.0566578	+	0.998394i	$0.518044\pi$
$608$	14.0958	0.571660
$609$	14.3843	0.582882
$610$	−12.8591	−0.520650
$611$	11.9795	0.484637
$612$	9.98517	0.403626
$613$	−27.9095	−1.12725	−0.563627	−	0.826030i	$-0.690594\pi$
$613$	−27.9095	−1.12725	−0.563627	+	0.826030i	$0.690594\pi$
$614$	42.3385	1.70864
$615$	−5.47244	−0.220670
$616$	−167.868	−6.76358
$617$	11.3026	0.455027	0.227513	−	0.973775i	$-0.426940\pi$
$617$	11.3026	0.455027	0.227513	+	0.973775i	$0.426940\pi$
$618$	−24.4162	−0.982162
$619$	13.9814	0.561961	0.280980	−	0.959714i	$-0.409340\pi$
$619$	13.9814	0.561961	0.280980	+	0.959714i	$0.409340\pi$
$620$	14.5627	0.584852
$621$	33.6522	1.35042
$622$	−8.75771	−0.351152
$623$	−43.6315	−1.74806
$624$	13.4859	0.539866
$625$	23.3180	0.932720
$626$	27.5531	1.10124
$627$	18.7711	0.749644
$628$	19.8187	0.790852
$629$	20.7654	0.827969
$630$	1.95702	0.0779696
$631$	−12.6439	−0.503346	−0.251673	−	0.967812i	$-0.580981\pi$
$631$	−12.6439	−0.503346	−0.251673	+	0.967812i	$0.580981\pi$
$632$	82.9989	3.30152
$633$	12.9320	0.514002
$634$	−65.2316	−2.59068
$635$	−3.77018	−0.149615
$636$	34.1980	1.35604
$637$	8.64340	0.342464
$638$	−39.0973	−1.54788
$639$	3.79452	0.150109
$640$	−2.50665	−0.0990841
$641$	−2.31962	−0.0916195	−0.0458097	−	0.998950i	$-0.514587\pi$
$641$	−2.31962	−0.0916195	−0.0458097	+	0.998950i	$0.514587\pi$
$642$	40.0715	1.58150
$643$	−25.0364	−0.987341	−0.493671	−	0.869649i	$-0.664345\pi$
$643$	−25.0364	−0.987341	−0.493671	+	0.869649i	$0.664345\pi$
$644$	108.694	4.28314
$645$	0.586553	0.0230955
$646$	−18.0571	−0.710448
$647$	−18.0125	−0.708143	−0.354072	−	0.935218i	$-0.615203\pi$
$647$	−18.0125	−0.708143	−0.354072	+	0.935218i	$0.615203\pi$
$648$	46.7590	1.83687
$649$	−32.6326	−1.28094
$650$	13.3867	0.525071
$651$	56.6345	2.21968
$652$	−67.0801	−2.62706
$653$	23.5851	0.922956	0.461478	−	0.887152i	$-0.347319\pi$
$653$	23.5851	0.922956	0.461478	+	0.887152i	$0.347319\pi$
$654$	−65.7325	−2.57034
$655$	5.07033	0.198114
$656$	85.3154	3.33101
$657$	5.95409	0.232291
$658$	112.689	4.39307
$659$	−9.49504	−0.369874	−0.184937	−	0.982750i	$-0.559208\pi$
$659$	−9.49504	−0.369874	−0.184937	+	0.982750i	$0.559208\pi$
$660$	15.4416	0.601065
$661$	−39.0496	−1.51885	−0.759426	−	0.650593i	$-0.774520\pi$
$661$	−39.0496	−1.51885	−0.759426	+	0.650593i	$0.774520\pi$
$662$	−58.9834	−2.29246
$663$	−6.14114	−0.238502
$664$	−64.7247	−2.51181
$665$	−2.47086	−0.0958159
$666$	−8.37773	−0.324631
$667$	14.3710	0.556449
$668$	36.4669	1.41095
$669$	−6.25879	−0.241979
$670$	−9.97898	−0.385522
$671$	94.9003	3.66359
$672$	45.0955	1.73960
$673$	22.9951	0.886395	0.443197	−	0.896424i	$-0.353844\pi$
$673$	22.9951	0.886395	0.443197	+	0.896424i	$0.353844\pi$
$674$	−59.0420	−2.27421
$675$	27.2198	1.04769
$676$	−54.9018	−2.11161
$677$	31.5462	1.21242	0.606209	−	0.795306i	$-0.292690\pi$
$677$	31.5462	1.21242	0.606209	+	0.795306i	$0.292690\pi$
$678$	41.0324	1.57584
$679$	29.0723	1.11569
$680$	−8.43249	−0.323371
$681$	34.3389	1.31587
$682$	−153.936	−5.89450
$683$	5.78843	0.221488	0.110744	−	0.993849i	$-0.464677\pi$
$683$	5.78843	0.221488	0.110744	+	0.993849i	$0.464677\pi$
$684$	5.08622	0.194477
$685$	−2.77355	−0.105972
$686$	11.2357	0.428979
$687$	0.191487	0.00730568
$688$	−9.14436	−0.348625
$689$	5.05842	0.192710
$690$	−8.12970	−0.309493
$691$	20.4004	0.776067	0.388033	−	0.921645i	$-0.373155\pi$
$691$	20.4004	0.776067	0.388033	+	0.921645i	$0.373155\pi$
$692$	16.2790	0.618834
$693$	−14.4428	−0.548638
$694$	77.7986	2.95319
$695$	0.129232	0.00490204
$696$	25.0055	0.947833
$697$	−38.8506	−1.47157
$698$	2.94296	0.111393
$699$	−29.2030	−1.10456
$700$	87.9180	3.32299
$701$	−44.5443	−1.68241	−0.841207	−	0.540712i	$-0.818155\pi$
$701$	−44.5443	−1.68241	−0.841207	+	0.540712i	$0.818155\pi$
$702$	15.2571	0.575843
$703$	10.5774	0.398935
$704$	−18.4971	−0.697137
$705$	−5.88450	−0.221623
$706$	−29.0826	−1.09454
$707$	25.6426	0.964388
$708$	36.7653	1.38172
$709$	11.4707	0.430792	0.215396	−	0.976527i	$-0.430896\pi$
$709$	11.4707	0.430792	0.215396	+	0.976527i	$0.430896\pi$
$710$	−5.64488	−0.211849
$711$	7.14099	0.267808
$712$	−75.8486	−2.84255
$713$	56.5823	2.11902
$714$	−57.7687	−2.16194
$715$	2.28406	0.0854189
$716$	57.6414	2.15416
$717$	−6.85575	−0.256033
$718$	−18.3416	−0.684504
$719$	−19.7848	−0.737850	−0.368925	−	0.929459i	$-0.620274\pi$
$719$	−19.7848	−0.737850	−0.368925	+	0.929459i	$0.620274\pi$
$720$	1.59320	0.0593751
$721$	−23.7189	−0.883338
$722$	39.7107	1.47788
$723$	33.7413	1.25485
$724$	−20.6130	−0.766077
$725$	11.6241	0.431709
$726$	−119.193	−4.42366
$727$	−25.4492	−0.943858	−0.471929	−	0.881637i	$-0.656442\pi$
$727$	−25.4492	−0.943858	−0.471929	+	0.881637i	$0.656442\pi$
$728$	27.9748	1.03682
$729$	30.0081	1.11141
$730$	−8.85754	−0.327832
$731$	4.16413	0.154016
$732$	−106.919	−3.95184
$733$	−3.13965	−0.115966	−0.0579828	−	0.998318i	$-0.518467\pi$
$733$	−3.13965	−0.115966	−0.0579828	+	0.998318i	$0.518467\pi$
$734$	62.0957	2.29199
$735$	−4.24577	−0.156608
$736$	45.0539	1.66071
$737$	73.6450	2.71275
$738$	15.6742	0.576975
$739$	22.1274	0.813968	0.406984	−	0.913435i	$-0.366580\pi$
$739$	22.1274	0.813968	0.406984	+	0.913435i	$0.366580\pi$
$740$	8.70130	0.319866
$741$	−3.12816	−0.114916
$742$	47.5837	1.74685
$743$	43.7326	1.60439	0.802197	−	0.597059i	$-0.203664\pi$
$743$	43.7326	1.60439	0.802197	+	0.597059i	$0.203664\pi$
$744$	98.4529	3.60946
$745$	1.97541	0.0723733
$746$	7.83371	0.286812
$747$	−5.56872	−0.203749
$748$	109.625	4.00829
$749$	38.9271	1.42237
$750$	−13.3036	−0.485778
$751$	34.0835	1.24372	0.621862	−	0.783127i	$-0.286377\pi$
$751$	34.0835	1.24372	0.621862	+	0.783127i	$0.286377\pi$
$752$	91.7394	3.34539
$753$	−28.4638	−1.03728
$754$	6.51550	0.237280
$755$	−3.50950	−0.127724
$756$	100.202	3.64431
$757$	14.4841	0.526433	0.263217	−	0.964737i	$-0.415217\pi$
$757$	14.4841	0.526433	0.263217	+	0.964737i	$0.415217\pi$
$758$	44.9101	1.63121
$759$	59.9973	2.17776
$760$	−4.29532	−0.155808
$761$	−34.1931	−1.23950	−0.619750	−	0.784799i	$-0.712766\pi$
$761$	−34.1931	−1.23950	−0.619750	+	0.784799i	$0.712766\pi$
$762$	−44.9000	−1.62656
$763$	−63.8553	−2.31172
$764$	−73.0519	−2.64292
$765$	−0.725507	−0.0262308
$766$	53.2493	1.92398
$767$	5.43816	0.196361
$768$	−38.8618	−1.40230
$769$	5.31939	0.191822	0.0959111	−	0.995390i	$-0.469424\pi$
$769$	5.31939	0.191822	0.0959111	+	0.995390i	$0.469424\pi$
$770$	21.4858	0.774293
$771$	−14.1344	−0.509038
$772$	−106.459	−3.83153
$773$	31.0930	1.11834	0.559169	−	0.829054i	$-0.311120\pi$
$773$	31.0930	1.11834	0.559169	+	0.829054i	$0.311120\pi$
$774$	−1.68001	−0.0603866
$775$	45.7670	1.64400
$776$	50.5389	1.81424
$777$	33.8395	1.21398
$778$	57.4591	2.06001
$779$	−19.7896	−0.709038
$780$	−2.57332	−0.0921396
$781$	41.6593	1.49069
$782$	−57.7154	−2.06390
$783$	13.2483	0.473454
$784$	66.1916	2.36399
$785$	−1.44000	−0.0513957
$786$	60.3837	2.15382
$787$	10.4960	0.374140	0.187070	−	0.982347i	$-0.440101\pi$
$787$	10.4960	0.374140	0.187070	+	0.982347i	$0.440101\pi$
$788$	−10.6296	−0.378664
$789$	−3.47748	−0.123801
$790$	−10.6232	−0.377957
$791$	39.8606	1.41728
$792$	−25.1073	−0.892149
$793$	−15.8150	−0.561606
$794$	−77.3303	−2.74435
$795$	−2.48478	−0.0881259
$796$	−51.2702	−1.81722
$797$	10.4685	0.370813	0.185407	−	0.982662i	$-0.440640\pi$
$797$	10.4685	0.370813	0.185407	+	0.982662i	$0.440640\pi$
$798$	−29.4261	−1.04167
$799$	−41.7760	−1.47793
$800$	36.4422	1.28843
$801$	−6.52579	−0.230578
$802$	31.1418	1.09966
$803$	65.3687	2.30681
$804$	−82.9717	−2.92618
$805$	−7.89754	−0.278352
$806$	25.6531	0.903592
$807$	−34.9079	−1.22882
$808$	44.5768	1.56821
$809$	41.0100	1.44183	0.720917	−	0.693022i	$-0.243721\pi$
$809$	41.0100	1.44183	0.720917	+	0.693022i	$0.243721\pi$
$810$	−5.98479	−0.210284
$811$	3.73031	0.130989	0.0654944	−	0.997853i	$-0.479138\pi$
$811$	3.73031	0.130989	0.0654944	+	0.997853i	$0.479138\pi$
$812$	42.7908	1.50166
$813$	−12.0184	−0.421502
$814$	−91.9775	−3.22381
$815$	4.87394	0.170727
$816$	−47.0292	−1.64635
$817$	2.12111	0.0742084
$818$	−70.0552	−2.44942
$819$	2.40687	0.0841030
$820$	−16.2796	−0.568507
$821$	30.2371	1.05528	0.527641	−	0.849468i	$-0.323077\pi$
$821$	30.2371	1.05528	0.527641	+	0.849468i	$0.323077\pi$
$822$	−33.0309	−1.15209
$823$	34.9750	1.21915	0.609577	−	0.792727i	$-0.291339\pi$
$823$	34.9750	1.21915	0.609577	+	0.792727i	$0.291339\pi$
$824$	−41.2327	−1.43641
$825$	48.5293	1.68957
$826$	51.1559	1.77994
$827$	−39.5191	−1.37421	−0.687106	−	0.726557i	$-0.741119\pi$
$827$	−39.5191	−1.37421	−0.687106	+	0.726557i	$0.741119\pi$
$828$	16.2569	0.564967
$829$	−18.4774	−0.641748	−0.320874	−	0.947122i	$-0.603977\pi$
$829$	−18.4774	−0.641748	−0.320874	+	0.947122i	$0.603977\pi$
$830$	8.28426	0.287551
$831$	14.6278	0.507433
$832$	3.08251	0.106867
$833$	−30.1421	−1.04436
$834$	1.53905	0.0532930
$835$	−2.64963	−0.0916943
$836$	55.8406	1.93129
$837$	52.1616	1.80297
$838$	55.0431	1.90143
$839$	30.9411	1.06820	0.534102	−	0.845420i	$-0.320650\pi$
$839$	30.9411	1.06820	0.534102	+	0.845420i	$0.320650\pi$
$840$	−13.7417	−0.474133
$841$	−23.3424	−0.804910
$842$	79.2402	2.73080
$843$	−10.6497	−0.366796
$844$	38.4705	1.32421
$845$	3.98908	0.137229
$846$	16.8544	0.579467
$847$	−115.789	−3.97855
$848$	38.7377	1.33026
$849$	−1.27423	−0.0437314
$850$	−46.6836	−1.60123
$851$	33.8082	1.15893
$852$	−46.9352	−1.60797
$853$	49.7020	1.70176	0.850882	−	0.525357i	$-0.176068\pi$
$853$	49.7020	1.70176	0.850882	+	0.525357i	$0.176068\pi$
$854$	−148.769	−5.09076
$855$	−0.369557	−0.0126386
$856$	67.6705	2.31293
$857$	16.6584	0.569042	0.284521	−	0.958670i	$-0.408165\pi$
$857$	16.6584	0.569042	0.284521	+	0.958670i	$0.408165\pi$
$858$	27.2014	0.928640
$859$	−28.4723	−0.971462	−0.485731	−	0.874108i	$-0.661447\pi$
$859$	−28.4723	−0.971462	−0.485731	+	0.874108i	$0.661447\pi$
$860$	1.74489	0.0595003
$861$	−63.3114	−2.15765
$862$	90.4305	3.08008
$863$	−51.2001	−1.74287	−0.871435	−	0.490511i	$-0.836810\pi$
$863$	−51.2001	−1.74287	−0.871435	+	0.490511i	$0.836810\pi$
$864$	41.5339	1.41301
$865$	−1.18281	−0.0402166
$866$	−80.7014	−2.74234
$867$	−5.02090	−0.170519
$868$	168.478	5.71851
$869$	78.3995	2.65952
$870$	−3.20052	−0.108508
$871$	−12.2728	−0.415848
$872$	−111.006	−3.75912
$873$	4.34822	0.147165
$874$	−29.3989	−0.994434
$875$	−12.9237	−0.436899
$876$	−73.6473	−2.48831
$877$	−33.9557	−1.14660	−0.573302	−	0.819344i	$-0.694338\pi$
$877$	−33.9557	−1.14660	−0.573302	+	0.819344i	$0.694338\pi$
$878$	87.3664	2.94847
$879$	46.2287	1.55926
$880$	17.4914	0.589637
$881$	5.72158	0.192765	0.0963824	−	0.995344i	$-0.469273\pi$
$881$	5.72158	0.192765	0.0963824	+	0.995344i	$0.469273\pi$
$882$	12.1608	0.409474
$883$	38.6711	1.30139	0.650693	−	0.759340i	$-0.274478\pi$
$883$	38.6711	1.30139	0.650693	+	0.759340i	$0.274478\pi$
$884$	−18.2688	−0.614447
$885$	−2.67131	−0.0897951
$886$	−18.5132	−0.621962
$887$	−30.1207	−1.01135	−0.505676	−	0.862723i	$-0.668757\pi$
$887$	−30.1207	−1.01135	−0.505676	+	0.862723i	$0.668757\pi$
$888$	58.8262	1.97408
$889$	−43.6178	−1.46289
$890$	9.70803	0.325414
$891$	44.1678	1.47968
$892$	−18.6188	−0.623404
$893$	−21.2797	−0.712100
$894$	23.5256	0.786814
$895$	−4.18813	−0.139994
$896$	−28.9998	−0.968815
$897$	−9.99844	−0.333838
$898$	69.4569	2.31781
$899$	22.2754	0.742926
$900$	13.1495	0.438318
$901$	−17.6402	−0.587681
$902$	172.084	5.72977
$903$	6.78591	0.225821
$904$	69.2934	2.30466
$905$	1.49771	0.0497856
$906$	−41.7954	−1.38856
$907$	−17.6066	−0.584619	−0.292310	−	0.956324i	$-0.594424\pi$
$907$	−17.6066	−0.584619	−0.292310	+	0.956324i	$0.594424\pi$
$908$	102.152	3.39004
$909$	3.83525	0.127207
$910$	−3.58056	−0.118694
$911$	42.2715	1.40052	0.700259	−	0.713889i	$-0.253068\pi$
$911$	42.2715	1.40052	0.700259	+	0.713889i	$0.253068\pi$
$912$	−23.9556	−0.793250
$913$	−61.1379	−2.02337
$914$	−90.6170	−2.99734
$915$	7.76856	0.256821
$916$	0.569641	0.0188215
$917$	58.6593	1.93710
$918$	−53.2062	−1.75607
$919$	−1.87292	−0.0617820	−0.0308910	−	0.999523i	$-0.509834\pi$
$919$	−1.87292	−0.0617820	−0.0308910	+	0.999523i	$0.509834\pi$
$920$	−13.7290	−0.452632
$921$	−25.5779	−0.842821
$922$	−37.8085	−1.24516
$923$	−6.94244	−0.228513
$924$	178.646	5.87704
$925$	27.3461	0.899133
$926$	102.786	3.37776
$927$	−3.54754	−0.116517
$928$	17.7369	0.582242
$929$	−36.6966	−1.20398	−0.601988	−	0.798505i	$-0.705625\pi$
$929$	−36.6966	−1.20398	−0.601988	+	0.798505i	$0.705625\pi$
$930$	−12.6012	−0.413210
$931$	−15.3537	−0.503198
$932$	−86.8738	−2.84565
$933$	5.29079	0.173213
$934$	5.11708	0.167436
$935$	−7.96520	−0.260490
$936$	4.18409	0.136761
$937$	42.2355	1.37977	0.689886	−	0.723918i	$-0.257661\pi$
$937$	42.2355	1.37977	0.689886	+	0.723918i	$0.257661\pi$
$938$	−115.448	−3.76952
$939$	−16.6456	−0.543210
$940$	−17.5054	−0.570962
$941$	−49.4819	−1.61306	−0.806531	−	0.591191i	$-0.798658\pi$
$941$	−49.4819	−1.61306	−0.806531	+	0.591191i	$0.798658\pi$
$942$	−17.1493	−0.558753
$943$	−63.2530	−2.05980
$944$	41.6457	1.35545
$945$	−7.28052	−0.236835
$946$	−18.4445	−0.599681
$947$	−8.43766	−0.274187	−0.137094	−	0.990558i	$-0.543776\pi$
$947$	−8.43766	−0.274187	−0.137094	+	0.990558i	$0.543776\pi$
$948$	−88.3283	−2.86877
$949$	−10.8936	−0.353621
$950$	−23.7796	−0.771511
$951$	39.4083	1.27790
$952$	−97.5567	−3.16183
$953$	−32.0230	−1.03733	−0.518663	−	0.854979i	$-0.673570\pi$
$953$	−32.0230	−1.03733	−0.518663	+	0.854979i	$0.673570\pi$
$954$	7.11690	0.230418
$955$	5.30784	0.171758
$956$	−20.3947	−0.659611
$957$	23.6198	0.763521
$958$	−6.76459	−0.218554
$959$	−32.0876	−1.03616
$960$	−1.51418	−0.0488699
$961$	56.7037	1.82915
$962$	15.3279	0.494191
$963$	5.82217	0.187617
$964$	100.375	3.23285
$965$	7.73513	0.249002
$966$	−94.0537	−3.02613
$967$	22.7902	0.732885	0.366442	−	0.930441i	$-0.380576\pi$
$967$	22.7902	0.732885	0.366442	+	0.930441i	$0.380576\pi$
$968$	−201.286	−6.46958
$969$	10.9088	0.350442
$970$	−6.46859	−0.207694
$971$	−3.27288	−0.105032	−0.0525158	−	0.998620i	$-0.516724\pi$
$971$	−3.27288	−0.105032	−0.0525158	+	0.998620i	$0.516724\pi$
$972$	27.5399	0.883342
$973$	1.49510	0.0479307
$974$	49.2923	1.57943
$975$	−8.08732	−0.259001
$976$	−121.112	−3.87670
$977$	15.4991	0.495859	0.247930	−	0.968778i	$-0.420250\pi$
$977$	15.4991	0.495859	0.247930	+	0.968778i	$0.420250\pi$
$978$	58.0449	1.85607
$979$	−71.6454	−2.28980
$980$	−12.6304	−0.403465
$981$	−9.55059	−0.304927
$982$	−105.691	−3.37272
$983$	58.9660	1.88072	0.940362	−	0.340176i	$-0.110487\pi$
$983$	58.9660	1.88072	0.940362	+	0.340176i	$0.110487\pi$
$984$	−110.060	−3.50858
$985$	0.772330	0.0246085
$986$	−22.7215	−0.723600
$987$	−68.0786	−2.16697
$988$	−9.30574	−0.296055
$989$	6.77964	0.215580
$990$	3.21354	0.102133
$991$	−36.6186	−1.16323	−0.581614	−	0.813465i	$-0.697578\pi$
$991$	−36.6186	−1.16323	−0.581614	+	0.813465i	$0.697578\pi$
$992$	69.8345	2.21725
$993$	35.6336	1.13080
$994$	−65.3064	−2.07139
$995$	3.72522	0.118097
$996$	68.8807	2.18257
$997$	49.5146	1.56814	0.784071	−	0.620671i	$-0.213140\pi$
$997$	49.5146	1.56814	0.784071	+	0.620671i	$0.213140\pi$
$998$	40.7153	1.28882
$999$	31.1669	0.986076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.10	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.57414 q^{2} +1.55511 q^{3} +4.62619 q^{4} -0.336132 q^{5} -4.00307 q^{6} -3.88876 q^{7} -6.76018 q^{8} -0.581626 q^{9} +O(q^{10})\)	\(q-2.57414 q^{2} +1.55511 q^{3} +4.62619 q^{4} -0.336132 q^{5} -4.00307 q^{6} -3.88876 q^{7} -6.76018 q^{8} -0.581626 q^{9} +0.865250 q^{10} -6.38555 q^{11} +7.19424 q^{12} +1.06414 q^{13} +10.0102 q^{14} -0.522723 q^{15} +8.14925 q^{16} -3.71098 q^{17} +1.49719 q^{18} -1.89029 q^{19} -1.55501 q^{20} -6.04745 q^{21} +16.4373 q^{22} -6.04187 q^{23} -10.5128 q^{24} -4.88702 q^{25} -2.73925 q^{26} -5.56983 q^{27} -17.9901 q^{28} -2.37857 q^{29} +1.34556 q^{30} -9.36502 q^{31} -7.45695 q^{32} -9.93025 q^{33} +9.55257 q^{34} +1.30713 q^{35} -2.69071 q^{36} -5.59566 q^{37} +4.86587 q^{38} +1.65486 q^{39} +2.27231 q^{40} +10.4691 q^{41} +15.5670 q^{42} -1.12211 q^{43} -29.5408 q^{44} +0.195503 q^{45} +15.5526 q^{46} +11.2574 q^{47} +12.6730 q^{48} +8.12242 q^{49} +12.5799 q^{50} -5.77099 q^{51} +4.92292 q^{52} +4.75352 q^{53} +14.3375 q^{54} +2.14639 q^{55} +26.2887 q^{56} -2.93961 q^{57} +6.12278 q^{58} +5.11038 q^{59} -2.41821 q^{60} -14.8617 q^{61} +24.1069 q^{62} +2.26180 q^{63} +2.89672 q^{64} -0.357692 q^{65} +25.5618 q^{66} -11.5331 q^{67} -17.1677 q^{68} -9.39579 q^{69} -3.36475 q^{70} -6.52399 q^{71} +3.93189 q^{72} -10.2370 q^{73} +14.4040 q^{74} -7.59986 q^{75} -8.74484 q^{76} +24.8319 q^{77} -4.25983 q^{78} -12.2776 q^{79} -2.73922 q^{80} -6.91683 q^{81} -26.9489 q^{82} +9.57441 q^{83} -27.9767 q^{84} +1.24738 q^{85} +2.88847 q^{86} -3.69895 q^{87} +43.1675 q^{88} +11.2199 q^{89} -0.503252 q^{90} -4.13818 q^{91} -27.9508 q^{92} -14.5637 q^{93} -28.9781 q^{94} +0.635386 q^{95} -11.5964 q^{96} -7.47598 q^{97} -20.9082 q^{98} +3.71400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 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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