LMFDB - Embedded newform 6047.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, 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("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$0$
Dimension:	$287$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59707 q^{2} -2.63415 q^{3} +4.74475 q^{4} -0.775653 q^{5} +6.84106 q^{6} +2.06715 q^{7} -7.12830 q^{8} +3.93875 q^{9} +O(q^{10})$	\(q-2.59707 q^{2} -2.63415 q^{3} +4.74475 q^{4} -0.775653 q^{5} +6.84106 q^{6} +2.06715 q^{7} -7.12830 q^{8} +3.93875 q^{9} +2.01442 q^{10} +0.868468 q^{11} -12.4984 q^{12} +5.42552 q^{13} -5.36854 q^{14} +2.04319 q^{15} +9.02317 q^{16} -8.03282 q^{17} -10.2292 q^{18} -1.76967 q^{19} -3.68028 q^{20} -5.44520 q^{21} -2.25547 q^{22} -7.03750 q^{23} +18.7770 q^{24} -4.39836 q^{25} -14.0904 q^{26} -2.47280 q^{27} +9.80814 q^{28} -5.89931 q^{29} -5.30629 q^{30} -8.89929 q^{31} -9.17716 q^{32} -2.28767 q^{33} +20.8618 q^{34} -1.60339 q^{35} +18.6884 q^{36} +7.16902 q^{37} +4.59595 q^{38} -14.2916 q^{39} +5.52909 q^{40} -7.11737 q^{41} +14.1415 q^{42} -11.7338 q^{43} +4.12066 q^{44} -3.05510 q^{45} +18.2769 q^{46} +6.17520 q^{47} -23.7684 q^{48} -2.72687 q^{49} +11.4228 q^{50} +21.1596 q^{51} +25.7427 q^{52} -0.447451 q^{53} +6.42203 q^{54} -0.673630 q^{55} -14.7353 q^{56} +4.66158 q^{57} +15.3209 q^{58} -15.0907 q^{59} +9.69442 q^{60} +8.00322 q^{61} +23.1120 q^{62} +8.14200 q^{63} +5.78736 q^{64} -4.20832 q^{65} +5.94124 q^{66} +3.38923 q^{67} -38.1137 q^{68} +18.5378 q^{69} +4.16412 q^{70} -11.7111 q^{71} -28.0766 q^{72} +7.38827 q^{73} -18.6184 q^{74} +11.5859 q^{75} -8.39665 q^{76} +1.79526 q^{77} +37.1163 q^{78} +1.72862 q^{79} -6.99885 q^{80} -5.30251 q^{81} +18.4843 q^{82} +10.6809 q^{83} -25.8361 q^{84} +6.23068 q^{85} +30.4733 q^{86} +15.5397 q^{87} -6.19070 q^{88} -7.32614 q^{89} +7.93430 q^{90} +11.2154 q^{91} -33.3912 q^{92} +23.4421 q^{93} -16.0374 q^{94} +1.37265 q^{95} +24.1740 q^{96} -2.48725 q^{97} +7.08187 q^{98} +3.42068 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) $ 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * 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 $

$2$	−2.59707	−1.83640	−0.918202	−	0.396114i	$-0.870359\pi$
$2$	−2.59707	−1.83640	−0.918202	+	0.396114i	$0.870359\pi$
$3$	−2.63415	−1.52083	−0.760414	−	0.649439i	$-0.775004\pi$
$3$	−2.63415	−1.52083	−0.760414	+	0.649439i	$0.775004\pi$
$4$	4.74475	2.37238
$5$	−0.775653	−0.346883	−0.173441	−	0.984844i	$-0.555489\pi$
$5$	−0.775653	−0.346883	−0.173441	+	0.984844i	$0.555489\pi$
$6$	6.84106	2.79285
$7$	2.06715	0.781311	0.390655	−	0.920537i	$-0.372248\pi$
$7$	2.06715	0.781311	0.390655	+	0.920537i	$0.372248\pi$
$8$	−7.12830	−2.52024
$9$	3.93875	1.31292
$10$	2.01442	0.637016
$11$	0.868468	0.261853	0.130926	−	0.991392i	$-0.458205\pi$
$11$	0.868468	0.261853	0.130926	+	0.991392i	$0.458205\pi$
$12$	−12.4984	−3.60797
$13$	5.42552	1.50477	0.752384	−	0.658725i	$-0.228904\pi$
$13$	5.42552	1.50477	0.752384	+	0.658725i	$0.228904\pi$
$14$	−5.36854	−1.43480
$15$	2.04319	0.527549
$16$	9.02317	2.25579
$17$	−8.03282	−1.94824	−0.974122	−	0.226022i	$-0.927428\pi$
$17$	−8.03282	−1.94824	−0.974122	+	0.226022i	$0.927428\pi$
$18$	−10.2292	−2.41104
$19$	−1.76967	−0.405990	−0.202995	−	0.979180i	$-0.565068\pi$
$19$	−1.76967	−0.405990	−0.202995	+	0.979180i	$0.565068\pi$
$20$	−3.68028	−0.822936
$21$	−5.44520	−1.18824
$22$	−2.25547	−0.480867
$23$	−7.03750	−1.46742	−0.733710	−	0.679463i	$-0.762213\pi$
$23$	−7.03750	−1.46742	−0.733710	+	0.679463i	$0.762213\pi$
$24$	18.7770	3.83284
$25$	−4.39836	−0.879672
$26$	−14.0904	−2.76336
$27$	−2.47280	−0.475891
$28$	9.80814	1.85356
$29$	−5.89931	−1.09548	−0.547738	−	0.836650i	$-0.684511\pi$
$29$	−5.89931	−1.09548	−0.547738	+	0.836650i	$0.684511\pi$
$30$	−5.30629	−0.968792
$31$	−8.89929	−1.59836	−0.799180	−	0.601092i	$-0.794732\pi$
$31$	−8.89929	−1.59836	−0.799180	+	0.601092i	$0.794732\pi$
$32$	−9.17716	−1.62231
$33$	−2.28767	−0.398233
$34$	20.8618	3.57776
$35$	−1.60339	−0.271023
$36$	18.6884	3.11473
$37$	7.16902	1.17858	0.589290	−	0.807922i	$-0.299408\pi$
$37$	7.16902	1.17858	0.589290	+	0.807922i	$0.299408\pi$
$38$	4.59595	0.745562
$39$	−14.2916	−2.28849
$40$	5.52909	0.874226
$41$	−7.11737	−1.11155	−0.555773	−	0.831334i	$-0.687578\pi$
$41$	−7.11737	−1.11155	−0.555773	+	0.831334i	$0.687578\pi$
$42$	14.1415	2.18209
$43$	−11.7338	−1.78938	−0.894691	−	0.446686i	$-0.852604\pi$
$43$	−11.7338	−1.78938	−0.894691	+	0.446686i	$0.852604\pi$
$44$	4.12066	0.621214
$45$	−3.05510	−0.455428
$46$	18.2769	2.69477
$47$	6.17520	0.900746	0.450373	−	0.892840i	$-0.351291\pi$
$47$	6.17520	0.900746	0.450373	+	0.892840i	$0.351291\pi$
$48$	−23.7684	−3.43067
$49$	−2.72687	−0.389553
$50$	11.4228	1.61543
$51$	21.1596	2.96294
$52$	25.7427	3.56988
$53$	−0.447451	−0.0614622	−0.0307311	−	0.999528i	$-0.509784\pi$
$53$	−0.447451	−0.0614622	−0.0307311	+	0.999528i	$0.509784\pi$
$54$	6.42203	0.873928
$55$	−0.673630	−0.0908322
$56$	−14.7353	−1.96909
$57$	4.66158	0.617441
$58$	15.3209	2.01173
$59$	−15.0907	−1.96465	−0.982323	−	0.187193i	$-0.940061\pi$
$59$	−15.0907	−1.96465	−0.982323	+	0.187193i	$0.940061\pi$
$60$	9.69442	1.25154
$61$	8.00322	1.02471	0.512354	−	0.858774i	$-0.328774\pi$
$61$	8.00322	1.02471	0.512354	+	0.858774i	$0.328774\pi$
$62$	23.1120	2.93523
$63$	8.14200	1.02580
$64$	5.78736	0.723419
$65$	−4.20832	−0.521978
$66$	5.94124	0.731316
$67$	3.38923	0.414061	0.207030	−	0.978335i	$-0.433620\pi$
$67$	3.38923	0.414061	0.207030	+	0.978335i	$0.433620\pi$
$68$	−38.1137	−4.62197
$69$	18.5378	2.23169
$70$	4.16412	0.497708
$71$	−11.7111	−1.38985	−0.694925	−	0.719082i	$-0.744563\pi$
$71$	−11.7111	−1.38985	−0.694925	+	0.719082i	$0.744563\pi$
$72$	−28.0766	−3.30886
$73$	7.38827	0.864732	0.432366	−	0.901698i	$-0.357679\pi$
$73$	7.38827	0.864732	0.432366	+	0.901698i	$0.357679\pi$
$74$	−18.6184	−2.16435
$75$	11.5859	1.33783
$76$	−8.39665	−0.963162
$77$	1.79526	0.204589
$78$	37.1163	4.20260
$79$	1.72862	0.194485	0.0972427	−	0.995261i	$-0.468998\pi$
$79$	1.72862	0.194485	0.0972427	+	0.995261i	$0.468998\pi$
$80$	−6.99885	−0.782495
$81$	−5.30251	−0.589168
$82$	18.4843	2.04125
$83$	10.6809	1.17238	0.586189	−	0.810174i	$-0.300627\pi$
$83$	10.6809	1.17238	0.586189	+	0.810174i	$0.300627\pi$
$84$	−25.8361	−2.81895
$85$	6.23068	0.675812
$86$	30.4733	3.28603
$87$	15.5397	1.66603
$88$	−6.19070	−0.659931
$89$	−7.32614	−0.776570	−0.388285	−	0.921539i	$-0.626932\pi$
$89$	−7.32614	−0.776570	−0.388285	+	0.921539i	$0.626932\pi$
$90$	7.93430	0.836349
$91$	11.2154	1.17569
$92$	−33.3912	−3.48127
$93$	23.4421	2.43083
$94$	−16.0374	−1.65413
$95$	1.37265	0.140831
$96$	24.1740	2.46725
$97$	−2.48725	−0.252542	−0.126271	−	0.991996i	$-0.540301\pi$
$97$	−2.48725	−0.252542	−0.126271	+	0.991996i	$0.540301\pi$
$98$	7.08187	0.715377
$99$	3.42068	0.343791
$100$	−20.8691	−2.08691
$101$	12.0326	1.19729	0.598646	−	0.801013i	$-0.295705\pi$
$101$	12.0326	1.19729	0.598646	+	0.801013i	$0.295705\pi$
$102$	−54.9530	−5.44116
$103$	−7.15520	−0.705023	−0.352512	−	0.935807i	$-0.614672\pi$
$103$	−7.15520	−0.705023	−0.352512	+	0.935807i	$0.614672\pi$
$104$	−38.6747	−3.79237
$105$	4.22358	0.412179
$106$	1.16206	0.112869
$107$	−3.39159	−0.327878	−0.163939	−	0.986470i	$-0.552420\pi$
$107$	−3.39159	−0.327878	−0.163939	+	0.986470i	$0.552420\pi$
$108$	−11.7328	−1.12899
$109$	−8.33494	−0.798342	−0.399171	−	0.916876i	$-0.630702\pi$
$109$	−8.33494	−0.798342	−0.399171	+	0.916876i	$0.630702\pi$
$110$	1.74946	0.166805
$111$	−18.8843	−1.79242
$112$	18.6523	1.76248
$113$	20.1472	1.89529	0.947645	−	0.319327i	$-0.103457\pi$
$113$	20.1472	1.89529	0.947645	+	0.319327i	$0.103457\pi$
$114$	−12.1064	−1.13387
$115$	5.45866	0.509023
$116$	−27.9908	−2.59888
$117$	21.3698	1.97563
$118$	39.1916	3.60788
$119$	−16.6051	−1.52218
$120$	−14.5645	−1.32955
$121$	−10.2458	−0.931433
$122$	−20.7849	−1.88178
$123$	18.7482	1.69047
$124$	−42.2249	−3.79191
$125$	7.28987	0.652026
$126$	−21.1453	−1.88377
$127$	−3.45422	−0.306512	−0.153256	−	0.988186i	$-0.548976\pi$
$127$	−3.45422	−0.306512	−0.153256	+	0.988186i	$0.548976\pi$
$128$	3.32418	0.293819
$129$	30.9085	2.72134
$130$	10.9293	0.958562
$131$	16.4086	1.43363	0.716815	−	0.697264i	$-0.245599\pi$
$131$	16.4086	1.43363	0.716815	+	0.697264i	$0.245599\pi$
$132$	−10.8544	−0.944759
$133$	−3.65818	−0.317205
$134$	−8.80206	−0.760382
$135$	1.91804	0.165078
$136$	57.2604	4.91003
$137$	10.0916	0.862187	0.431094	−	0.902307i	$-0.358128\pi$
$137$	10.0916	0.862187	0.431094	+	0.902307i	$0.358128\pi$
$138$	−48.1440	−4.09829
$139$	−8.65731	−0.734304	−0.367152	−	0.930161i	$-0.619667\pi$
$139$	−8.65731	−0.734304	−0.367152	+	0.930161i	$0.619667\pi$
$140$	−7.60771	−0.642969
$141$	−16.2664	−1.36988
$142$	30.4145	2.55233
$143$	4.71189	0.394028
$144$	35.5400	2.96167
$145$	4.57582	0.380001
$146$	−19.1878	−1.58800
$147$	7.18299	0.592443
$148$	34.0152	2.79603
$149$	−12.9998	−1.06499	−0.532493	−	0.846435i	$-0.678745\pi$
$149$	−12.9998	−1.06499	−0.532493	+	0.846435i	$0.678745\pi$
$150$	−30.0895	−2.45679
$151$	5.44358	0.442992	0.221496	−	0.975161i	$-0.428906\pi$
$151$	5.44358	0.442992	0.221496	+	0.975161i	$0.428906\pi$
$152$	12.6148	1.02319
$153$	−31.6392	−2.55788
$154$	−4.66240	−0.375707
$155$	6.90276	0.554443
$156$	−67.8103	−5.42917
$157$	−3.96128	−0.316144	−0.158072	−	0.987428i	$-0.550528\pi$
$157$	−3.96128	−0.316144	−0.158072	+	0.987428i	$0.550528\pi$
$158$	−4.48935	−0.357153
$159$	1.17865	0.0934734
$160$	7.11829	0.562751
$161$	−14.5476	−1.14651
$162$	13.7710	1.08195
$163$	−3.96285	−0.310395	−0.155197	−	0.987883i	$-0.549601\pi$
$163$	−3.96285	−0.310395	−0.155197	+	0.987883i	$0.549601\pi$
$164$	−33.7702	−2.63701
$165$	1.77444	0.138140
$166$	−27.7389	−2.15296
$167$	2.82871	0.218892	0.109446	−	0.993993i	$-0.465092\pi$
$167$	2.82871	0.218892	0.109446	+	0.993993i	$0.465092\pi$
$168$	38.8150	2.99464
$169$	16.4363	1.26433
$170$	−16.1815	−1.24106
$171$	−6.97029	−0.533031
$172$	−55.6738	−4.24509
$173$	−0.987860	−0.0751056	−0.0375528	−	0.999295i	$-0.511956\pi$
$173$	−0.987860	−0.0751056	−0.0375528	+	0.999295i	$0.511956\pi$
$174$	−40.3576	−3.05950
$175$	−9.09209	−0.687298
$176$	7.83633	0.590686
$177$	39.7513	2.98789
$178$	19.0265	1.42610
$179$	14.9924	1.12058	0.560292	−	0.828295i	$-0.310689\pi$
$179$	14.9924	1.12058	0.560292	+	0.828295i	$0.310689\pi$
$180$	−14.4957	−1.08045
$181$	5.09987	0.379070	0.189535	−	0.981874i	$-0.439302\pi$
$181$	5.09987	0.379070	0.189535	+	0.981874i	$0.439302\pi$
$182$	−29.1271	−2.15904
$183$	−21.0817	−1.55840
$184$	50.1654	3.69824
$185$	−5.56067	−0.408829
$186$	−60.8806	−4.46398
$187$	−6.97624	−0.510153
$188$	29.2998	2.13691
$189$	−5.11167	−0.371819
$190$	−3.56487	−0.258623
$191$	24.5268	1.77470	0.887348	−	0.461101i	$-0.152545\pi$
$191$	24.5268	1.77470	0.887348	+	0.461101i	$0.152545\pi$
$192$	−15.2448	−1.10020
$193$	−0.556743	−0.0400752	−0.0200376	−	0.999799i	$-0.506379\pi$
$193$	−0.556743	−0.0400752	−0.0200376	+	0.999799i	$0.506379\pi$
$194$	6.45956	0.463769
$195$	11.0854	0.793839
$196$	−12.9383	−0.924167
$197$	−17.1379	−1.22103	−0.610513	−	0.792006i	$-0.709037\pi$
$197$	−17.1379	−1.22103	−0.610513	+	0.792006i	$0.709037\pi$
$198$	−8.88372	−0.631339
$199$	−21.0085	−1.48926	−0.744628	−	0.667480i	$-0.767373\pi$
$199$	−21.0085	−1.48926	−0.744628	+	0.667480i	$0.767373\pi$
$200$	31.3529	2.21698
$201$	−8.92775	−0.629715
$202$	−31.2496	−2.19871
$203$	−12.1948	−0.855907
$204$	100.397	7.02922
$205$	5.52061	0.385576
$206$	18.5825	1.29471
$207$	−27.7189	−1.92660
$208$	48.9554	3.39445
$209$	−1.53690	−0.106310
$210$	−10.9689	−0.756928
$211$	16.1330	1.11064	0.555320	−	0.831637i	$-0.312596\pi$
$211$	16.1330	1.11064	0.555320	+	0.831637i	$0.312596\pi$
$212$	−2.12305	−0.145811
$213$	30.8488	2.11372
$214$	8.80820	0.602116
$215$	9.10133	0.620705
$216$	17.6269	1.19936
$217$	−18.3962	−1.24882
$218$	21.6464	1.46608
$219$	−19.4618	−1.31511
$220$	−3.19621	−0.215488
$221$	−43.5822	−2.93166
$222$	49.0437	3.29160
$223$	12.3540	0.827288	0.413644	−	0.910439i	$-0.364256\pi$
$223$	12.3540	0.827288	0.413644	+	0.910439i	$0.364256\pi$
$224$	−18.9706	−1.26753
$225$	−17.3240	−1.15494
$226$	−52.3236	−3.48052
$227$	23.0699	1.53120	0.765602	−	0.643315i	$-0.222441\pi$
$227$	23.0699	1.53120	0.765602	+	0.643315i	$0.222441\pi$
$228$	22.1180	1.46480
$229$	−2.39061	−0.157976	−0.0789881	−	0.996876i	$-0.525169\pi$
$229$	−2.39061	−0.157976	−0.0789881	+	0.996876i	$0.525169\pi$
$230$	−14.1765	−0.934771
$231$	−4.72898	−0.311144
$232$	42.0521	2.76086
$233$	7.97759	0.522629	0.261315	−	0.965254i	$-0.415844\pi$
$233$	7.97759	0.522629	0.261315	+	0.965254i	$0.415844\pi$
$234$	−55.4987	−3.62806
$235$	−4.78982	−0.312453
$236$	−71.6018	−4.66088
$237$	−4.55345	−0.295779
$238$	43.1245	2.79534
$239$	−14.8415	−0.960015	−0.480008	−	0.877264i	$-0.659366\pi$
$239$	−14.8415	−0.960015	−0.480008	+	0.877264i	$0.659366\pi$
$240$	18.4360	1.19004
$241$	−7.06041	−0.454801	−0.227400	−	0.973801i	$-0.573023\pi$
$241$	−7.06041	−0.454801	−0.227400	+	0.973801i	$0.573023\pi$
$242$	26.6089	1.71049
$243$	21.3860	1.37191
$244$	37.9733	2.43099
$245$	2.11511	0.135129
$246$	−48.6904	−3.10439
$247$	−9.60139	−0.610922
$248$	63.4368	4.02824
$249$	−28.1350	−1.78299
$250$	−18.9323	−1.19738
$251$	−6.33342	−0.399762	−0.199881	−	0.979820i	$-0.564056\pi$
$251$	−6.33342	−0.399762	−0.199881	+	0.979820i	$0.564056\pi$
$252$	38.6318	2.43357
$253$	−6.11184	−0.384248
$254$	8.97083	0.562880
$255$	−16.4125	−1.02779
$256$	−20.2078	−1.26299
$257$	−29.6788	−1.85131	−0.925657	−	0.378364i	$-0.876487\pi$
$257$	−29.6788	−1.85131	−0.925657	+	0.378364i	$0.876487\pi$
$258$	−80.2714	−4.99748
$259$	14.8195	0.920837
$260$	−19.9674	−1.23833
$261$	−23.2359	−1.43827
$262$	−42.6143	−2.63272
$263$	−1.71453	−0.105722	−0.0528611	−	0.998602i	$-0.516834\pi$
$263$	−1.71453	−0.105722	−0.0528611	+	0.998602i	$0.516834\pi$
$264$	16.3072	1.00364
$265$	0.347067	0.0213202
$266$	9.50055	0.582516
$267$	19.2982	1.18103
$268$	16.0811	0.982308
$269$	7.46245	0.454994	0.227497	−	0.973779i	$-0.426946\pi$
$269$	7.46245	0.454994	0.227497	+	0.973779i	$0.426946\pi$
$270$	−4.98127	−0.303150
$271$	17.1361	1.04094	0.520471	−	0.853880i	$-0.325757\pi$
$271$	17.1361	1.04094	0.520471	+	0.853880i	$0.325757\pi$
$272$	−72.4815	−4.39483
$273$	−29.5430	−1.78802
$274$	−26.2087	−1.58332
$275$	−3.81984	−0.230345
$276$	87.9574	5.29441
$277$	10.3103	0.619485	0.309743	−	0.950820i	$-0.399757\pi$
$277$	10.3103	0.619485	0.309743	+	0.950820i	$0.399757\pi$
$278$	22.4836	1.34848
$279$	−35.0520	−2.09851
$280$	11.4295	0.683042
$281$	−9.91913	−0.591726	−0.295863	−	0.955230i	$-0.595607\pi$
$281$	−9.91913	−0.591726	−0.295863	+	0.955230i	$0.595607\pi$
$282$	42.2450	2.51565
$283$	4.21158	0.250352	0.125176	−	0.992135i	$-0.460050\pi$
$283$	4.21158	0.250352	0.125176	+	0.992135i	$0.460050\pi$
$284$	−55.5662	−3.29725
$285$	−3.61577	−0.214180
$286$	−12.2371	−0.723594
$287$	−14.7127	−0.868463
$288$	−36.1465	−2.12995
$289$	47.5261	2.79566
$290$	−11.8837	−0.697836
$291$	6.55179	0.384073
$292$	35.0555	2.05147
$293$	0.0522114	0.00305022	0.00152511	−	0.999999i	$-0.499515\pi$
$293$	0.0522114	0.00305022	0.00152511	+	0.999999i	$0.499515\pi$
$294$	−18.6547	−1.08796
$295$	11.7052	0.681502
$296$	−51.1029	−2.97030
$297$	−2.14755	−0.124613
$298$	33.7614	1.95574
$299$	−38.1821	−2.20813
$300$	54.9724	3.17384
$301$	−24.2555	−1.39806
$302$	−14.1373	−0.813512
$303$	−31.6958	−1.82088
$304$	−15.9680	−0.915830
$305$	−6.20773	−0.355453
$306$	82.1692	4.69730
$307$	−14.4567	−0.825088	−0.412544	−	0.910938i	$-0.635360\pi$
$307$	−14.4567	−0.825088	−0.412544	+	0.910938i	$0.635360\pi$
$308$	8.51805	0.485361
$309$	18.8479	1.07222
$310$	−17.9269	−1.01818
$311$	−12.5497	−0.711629	−0.355815	−	0.934557i	$-0.615797\pi$
$311$	−12.5497	−0.711629	−0.355815	+	0.934557i	$0.615797\pi$
$312$	101.875	5.76754
$313$	−25.6393	−1.44922	−0.724609	−	0.689161i	$-0.757979\pi$
$313$	−25.6393	−1.44922	−0.724609	+	0.689161i	$0.757979\pi$
$314$	10.2877	0.580568
$315$	−6.31537	−0.355831
$316$	8.20189	0.461392
$317$	13.0472	0.732804	0.366402	−	0.930457i	$-0.380589\pi$
$317$	13.0472	0.732804	0.366402	+	0.930457i	$0.380589\pi$
$318$	−3.06104	−0.171655
$319$	−5.12336	−0.286853
$320$	−4.48898	−0.250942
$321$	8.93397	0.498646
$322$	37.7811	2.10546
$323$	14.2154	0.790969
$324$	−25.1591	−1.39773
$325$	−23.8634	−1.32370
$326$	10.2918	0.570010
$327$	21.9555	1.21414
$328$	50.7348	2.80136
$329$	12.7651	0.703763
$330$	−4.60834	−0.253681
$331$	4.19227	0.230428	0.115214	−	0.993341i	$-0.463245\pi$
$331$	4.19227	0.230428	0.115214	+	0.993341i	$0.463245\pi$
$332$	50.6781	2.78132
$333$	28.2370	1.54738
$334$	−7.34635	−0.401974
$335$	−2.62887	−0.143630
$336$	−49.1329	−2.68042
$337$	10.9409	0.595988	0.297994	−	0.954568i	$-0.403682\pi$
$337$	10.9409	0.595988	0.297994	+	0.954568i	$0.403682\pi$
$338$	−42.6861	−2.32182
$339$	−53.0708	−2.88241
$340$	29.5630	1.60328
$341$	−7.72874	−0.418535
$342$	18.1023	0.978860
$343$	−20.1069	−1.08567
$344$	83.6418	4.50966
$345$	−14.3789	−0.774135
$346$	2.56554	0.137924
$347$	−16.7739	−0.900469	−0.450234	−	0.892910i	$-0.648660\pi$
$347$	−16.7739	−0.900469	−0.450234	+	0.892910i	$0.648660\pi$
$348$	73.7319	3.95245
$349$	10.7883	0.577485	0.288743	−	0.957407i	$-0.406763\pi$
$349$	10.7883	0.577485	0.288743	+	0.957407i	$0.406763\pi$
$350$	23.6128	1.26216
$351$	−13.4162	−0.716106
$352$	−7.97007	−0.424806
$353$	−2.37670	−0.126499	−0.0632495	−	0.997998i	$-0.520146\pi$
$353$	−2.37670	−0.126499	−0.0632495	+	0.997998i	$0.520146\pi$
$354$	−103.237	−5.48697
$355$	9.08374	0.482115
$356$	−34.7607	−1.84232
$357$	43.7403	2.31498
$358$	−38.9362	−2.05784
$359$	36.3997	1.92110	0.960551	−	0.278105i	$-0.0897064\pi$
$359$	36.3997	1.92110	0.960551	+	0.278105i	$0.0897064\pi$
$360$	21.7777	1.14779
$361$	−15.8683	−0.835172
$362$	−13.2447	−0.696126
$363$	26.9889	1.41655
$364$	53.2142	2.78918
$365$	−5.73074	−0.299960
$366$	54.7506	2.86186
$367$	−3.07255	−0.160386	−0.0801929	−	0.996779i	$-0.525554\pi$
$367$	−3.07255	−0.160386	−0.0801929	+	0.996779i	$0.525554\pi$
$368$	−63.5005	−3.31019
$369$	−28.0335	−1.45937
$370$	14.4414	0.750774
$371$	−0.924951	−0.0480211
$372$	111.227	5.76684
$373$	4.38016	0.226796	0.113398	−	0.993550i	$-0.463826\pi$
$373$	4.38016	0.226796	0.113398	+	0.993550i	$0.463826\pi$
$374$	18.1178	0.936847
$375$	−19.2026	−0.991619
$376$	−44.0187	−2.27009
$377$	−32.0068	−1.64844
$378$	13.2753	0.682810
$379$	−34.3109	−1.76243	−0.881216	−	0.472714i	$-0.843274\pi$
$379$	−34.3109	−1.76243	−0.881216	+	0.472714i	$0.843274\pi$
$380$	6.51289	0.334104
$381$	9.09893	0.466152
$382$	−63.6977	−3.25906
$383$	−13.8511	−0.707757	−0.353878	−	0.935291i	$-0.615137\pi$
$383$	−13.8511	−0.707757	−0.353878	+	0.935291i	$0.615137\pi$
$384$	−8.75638	−0.446847
$385$	−1.39250	−0.0709682
$386$	1.44590	0.0735943
$387$	−46.2163	−2.34931
$388$	−11.8014	−0.599125
$389$	22.4250	1.13699	0.568495	−	0.822687i	$-0.307526\pi$
$389$	22.4250	1.13699	0.568495	+	0.822687i	$0.307526\pi$
$390$	−28.7894	−1.45781
$391$	56.5309	2.85889
$392$	19.4380	0.981766
$393$	−43.2228	−2.18030
$394$	44.5083	2.24230
$395$	−1.34081	−0.0674636
$396$	16.2303	0.815601
$397$	19.8719	0.997340	0.498670	−	0.866792i	$-0.333822\pi$
$397$	19.8719	0.997340	0.498670	+	0.866792i	$0.333822\pi$
$398$	54.5606	2.73487
$399$	9.63621	0.482414
$400$	−39.6872	−1.98436
$401$	17.3821	0.868019	0.434010	−	0.900908i	$-0.357098\pi$
$401$	17.3821	0.868019	0.434010	+	0.900908i	$0.357098\pi$
$402$	23.1860	1.15641
$403$	−48.2833	−2.40516
$404$	57.0919	2.84043
$405$	4.11291	0.204372
$406$	31.6707	1.57179
$407$	6.22606	0.308614
$408$	−150.832	−7.46732
$409$	−12.2067	−0.603581	−0.301790	−	0.953374i	$-0.597584\pi$
$409$	−12.2067	−0.603581	−0.301790	+	0.953374i	$0.597584\pi$
$410$	−14.3374	−0.708073
$411$	−26.5829	−1.31124
$412$	−33.9497	−1.67258
$413$	−31.1949	−1.53500
$414$	71.9879	3.53801
$415$	−8.28466	−0.406678
$416$	−49.7909	−2.44120
$417$	22.8047	1.11675
$418$	3.99144	0.195228
$419$	16.0838	0.785745	0.392872	−	0.919593i	$-0.371481\pi$
$419$	16.0838	0.785745	0.392872	+	0.919593i	$0.371481\pi$
$420$	20.0399	0.977845
$421$	17.4473	0.850331	0.425166	−	0.905116i	$-0.360216\pi$
$421$	17.4473	0.850331	0.425166	+	0.905116i	$0.360216\pi$
$422$	−41.8984	−2.03958
$423$	24.3226	1.18260
$424$	3.18957	0.154899
$425$	35.3312	1.71382
$426$	−80.1163	−3.88165
$427$	16.5439	0.800615
$428$	−16.0923	−0.777850
$429$	−12.4118	−0.599249
$430$	−23.6367	−1.13987
$431$	−0.628459	−0.0302718	−0.0151359	−	0.999885i	$-0.504818\pi$
$431$	−0.628459	−0.0302718	−0.0151359	+	0.999885i	$0.504818\pi$
$432$	−22.3125	−1.07351
$433$	17.2854	0.830684	0.415342	−	0.909665i	$-0.363662\pi$
$433$	17.2854	0.830684	0.415342	+	0.909665i	$0.363662\pi$
$434$	47.7761	2.29333
$435$	−12.0534	−0.577916
$436$	−39.5472	−1.89397
$437$	12.4541	0.595759
$438$	50.5436	2.41507
$439$	32.8972	1.57010	0.785049	−	0.619433i	$-0.212638\pi$
$439$	32.8972	1.57010	0.785049	+	0.619433i	$0.212638\pi$
$440$	4.80184	0.228919
$441$	−10.7405	−0.511451
$442$	113.186	5.38370
$443$	−35.0305	−1.66435	−0.832175	−	0.554514i	$-0.812904\pi$
$443$	−35.0305	−1.66435	−0.832175	+	0.554514i	$0.812904\pi$
$444$	−89.6012	−4.25229
$445$	5.68255	0.269379
$446$	−32.0843	−1.51923
$447$	34.2434	1.61966
$448$	11.9634	0.565216
$449$	14.5810	0.688122	0.344061	−	0.938947i	$-0.388197\pi$
$449$	14.5810	0.688122	0.344061	+	0.938947i	$0.388197\pi$
$450$	44.9917	2.12093
$451$	−6.18121	−0.291062
$452$	95.5935	4.49634
$453$	−14.3392	−0.673714
$454$	−59.9141	−2.81191
$455$	−8.69925	−0.407827
$456$	−33.2292	−1.55610
$457$	14.5808	0.682059	0.341030	−	0.940053i	$-0.389224\pi$
$457$	14.5808	0.682059	0.341030	+	0.940053i	$0.389224\pi$
$458$	6.20858	0.290108
$459$	19.8636	0.927152
$460$	25.9000	1.20759
$461$	−23.0210	−1.07220	−0.536099	−	0.844155i	$-0.680102\pi$
$461$	−23.0210	−1.07220	−0.536099	+	0.844155i	$0.680102\pi$
$462$	12.2815	0.571385
$463$	13.9624	0.648887	0.324443	−	0.945905i	$-0.394823\pi$
$463$	13.9624	0.648887	0.324443	+	0.945905i	$0.394823\pi$
$464$	−53.2305	−2.47116
$465$	−18.1829	−0.843212
$466$	−20.7183	−0.959758
$467$	−4.86555	−0.225151	−0.112575	−	0.993643i	$-0.535910\pi$
$467$	−4.86555	−0.225151	−0.112575	+	0.993643i	$0.535910\pi$
$468$	101.394	4.68695
$469$	7.00607	0.323510
$470$	12.4395	0.573790
$471$	10.4346	0.480801
$472$	107.571	4.95137
$473$	−10.1904	−0.468555
$474$	11.8256	0.543169
$475$	7.78366	0.357139
$476$	−78.7870	−3.61119
$477$	−1.76240	−0.0806947
$478$	38.5443	1.76298
$479$	21.4660	0.980805	0.490402	−	0.871496i	$-0.336850\pi$
$479$	21.4660	0.980805	0.490402	+	0.871496i	$0.336850\pi$
$480$	−18.7507	−0.855846
$481$	38.8957	1.77349
$482$	18.3363	0.835197
$483$	38.3206	1.74365
$484$	−48.6136	−2.20971
$485$	1.92924	0.0876025
$486$	−55.5409	−2.51939
$487$	−40.4414	−1.83258	−0.916288	−	0.400520i	$-0.868829\pi$
$487$	−40.4414	−1.83258	−0.916288	+	0.400520i	$0.868829\pi$
$488$	−57.0494	−2.58251
$489$	10.4388	0.472057
$490$	−5.49307	−0.248152
$491$	−33.0060	−1.48954	−0.744769	−	0.667322i	$-0.767440\pi$
$491$	−33.0060	−1.48954	−0.744769	+	0.667322i	$0.767440\pi$
$492$	88.9557	4.01043
$493$	47.3881	2.13425
$494$	24.9354	1.12190
$495$	−2.65326	−0.119255
$496$	−80.2998	−3.60557
$497$	−24.2086	−1.08591
$498$	73.0686	3.27428
$499$	−9.56933	−0.428382	−0.214191	−	0.976792i	$-0.568711\pi$
$499$	−9.56933	−0.428382	−0.214191	+	0.976792i	$0.568711\pi$
$500$	34.5886	1.54685
$501$	−7.45125	−0.332897
$502$	16.4483	0.734124
$503$	9.32185	0.415641	0.207820	−	0.978167i	$-0.433363\pi$
$503$	9.32185	0.415641	0.207820	+	0.978167i	$0.433363\pi$
$504$	−58.0386	−2.58525
$505$	−9.33316	−0.415320
$506$	15.8729	0.705635
$507$	−43.2956	−1.92282
$508$	−16.3894	−0.727162
$509$	34.1837	1.51516	0.757582	−	0.652740i	$-0.226381\pi$
$509$	34.1837	1.51516	0.757582	+	0.652740i	$0.226381\pi$
$510$	42.6245	1.88744
$511$	15.2727	0.675624
$512$	45.8327	2.02554
$513$	4.37605	0.193207
$514$	77.0779	3.39976
$515$	5.54996	0.244560
$516$	146.653	6.45604
$517$	5.36297	0.235863
$518$	−38.4871	−1.69103
$519$	2.60217	0.114223
$520$	29.9982	1.31551
$521$	17.5370	0.768310	0.384155	−	0.923269i	$-0.374493\pi$
$521$	17.5370	0.768310	0.384155	+	0.923269i	$0.374493\pi$
$522$	60.3452	2.64124
$523$	36.2892	1.58681	0.793407	−	0.608691i	$-0.208305\pi$
$523$	36.2892	1.58681	0.793407	+	0.608691i	$0.208305\pi$
$524$	77.8549	3.40111
$525$	23.9499	1.04526
$526$	4.45274	0.194149
$527$	71.4863	3.11399
$528$	−20.6421	−0.898331
$529$	26.5264	1.15332
$530$	−0.901356	−0.0391524
$531$	−59.4386	−2.57942
$532$	−17.3572	−0.752529
$533$	−38.6154	−1.67262
$534$	−50.1186	−2.16884
$535$	2.63070	0.113735
$536$	−24.1595	−1.04353
$537$	−39.4922	−1.70421
$538$	−19.3805	−0.835552
$539$	−2.36820	−0.102006
$540$	9.10061	0.391628
$541$	19.3552	0.832144	0.416072	−	0.909332i	$-0.363406\pi$
$541$	19.3552	0.832144	0.416072	+	0.909332i	$0.363406\pi$
$542$	−44.5035	−1.91159
$543$	−13.4338	−0.576501
$544$	73.7185	3.16065
$545$	6.46502	0.276931
$546$	76.7252	3.28353
$547$	26.3522	1.12674	0.563368	−	0.826206i	$-0.309505\pi$
$547$	26.3522	1.12674	0.563368	+	0.826206i	$0.309505\pi$
$548$	47.8823	2.04543
$549$	31.5227	1.34536
$550$	9.92037	0.423006
$551$	10.4398	0.444752
$552$	−132.143	−5.62439
$553$	3.57333	0.151954
$554$	−26.7765	−1.13762
$555$	14.6476	0.621758
$556$	−41.0768	−1.74204
$557$	37.8246	1.60268	0.801341	−	0.598208i	$-0.204121\pi$
$557$	37.8246	1.60268	0.801341	+	0.598208i	$0.204121\pi$
$558$	91.0325	3.85371
$559$	−63.6617	−2.69260
$560$	−14.4677	−0.611372
$561$	18.3765	0.775855
$562$	25.7606	1.08665
$563$	1.37711	0.0580382	0.0290191	−	0.999579i	$-0.490762\pi$
$563$	1.37711	0.0580382	0.0290191	+	0.999579i	$0.490762\pi$
$564$	−77.1801	−3.24987
$565$	−15.6272	−0.657443
$566$	−10.9377	−0.459747
$567$	−10.9611	−0.460323
$568$	83.4802	3.50275
$569$	25.4686	1.06770	0.533849	−	0.845580i	$-0.320745\pi$
$569$	25.4686	1.06770	0.533849	+	0.845580i	$0.320745\pi$
$570$	9.39039	0.393320
$571$	−29.3389	−1.22779	−0.613897	−	0.789386i	$-0.710399\pi$
$571$	−29.3389	−1.22779	−0.613897	+	0.789386i	$0.710399\pi$
$572$	22.3567	0.934783
$573$	−64.6072	−2.69901
$574$	38.2099	1.59485
$575$	30.9535	1.29085
$576$	22.7949	0.949789
$577$	−15.5966	−0.649296	−0.324648	−	0.945835i	$-0.605246\pi$
$577$	−15.5966	−0.649296	−0.324648	+	0.945835i	$0.605246\pi$
$578$	−123.429	−5.13395
$579$	1.46654	0.0609475
$580$	21.7111	0.901506
$581$	22.0790	0.915992
$582$	−17.0154	−0.705313
$583$	−0.388597	−0.0160940
$584$	−52.6658	−2.17933
$585$	−16.5755	−0.685313
$586$	−0.135596	−0.00560144
$587$	−40.5404	−1.67328	−0.836641	−	0.547752i	$-0.815484\pi$
$587$	−40.5404	−1.67328	−0.836641	+	0.547752i	$0.815484\pi$
$588$	34.0815	1.40550
$589$	15.7488	0.648919
$590$	−30.3991	−1.25151
$591$	45.1438	1.85697
$592$	64.6873	2.65863
$593$	−28.1266	−1.15502	−0.577510	−	0.816383i	$-0.695976\pi$
$593$	−28.1266	−1.15502	−0.577510	+	0.816383i	$0.695976\pi$
$594$	5.57733	0.228841
$595$	12.8798	0.528019
$596$	−61.6809	−2.52655
$597$	55.3396	2.26490
$598$	99.1614	4.05501
$599$	−10.7550	−0.439438	−0.219719	−	0.975563i	$-0.570514\pi$
$599$	−10.7550	−0.439438	−0.219719	+	0.975563i	$0.570514\pi$
$600$	−82.5881	−3.37165
$601$	−48.2605	−1.96859	−0.984293	−	0.176544i	$-0.943508\pi$
$601$	−48.2605	−1.96859	−0.984293	+	0.176544i	$0.943508\pi$
$602$	62.9931	2.56741
$603$	13.3493	0.543627
$604$	25.8284	1.05094
$605$	7.94716	0.323098
$606$	82.3161	3.34386
$607$	43.9992	1.78587	0.892936	−	0.450183i	$-0.148641\pi$
$607$	43.9992	1.78587	0.892936	+	0.450183i	$0.148641\pi$
$608$	16.2406	0.658642
$609$	32.1229	1.30169
$610$	16.1219	0.652756
$611$	33.5037	1.35541
$612$	−150.120	−6.06826
$613$	29.6653	1.19817	0.599085	−	0.800685i	$-0.295531\pi$
$613$	29.6653	1.19817	0.599085	+	0.800685i	$0.295531\pi$
$614$	37.5450	1.51519
$615$	−14.5421	−0.586395
$616$	−12.7971	−0.515611
$617$	25.0075	1.00677	0.503383	−	0.864064i	$-0.332089\pi$
$617$	25.0075	1.00677	0.503383	+	0.864064i	$0.332089\pi$
$618$	−48.9492	−1.96903
$619$	13.1365	0.528002	0.264001	−	0.964522i	$-0.414958\pi$
$619$	13.1365	0.528002	0.264001	+	0.964522i	$0.414958\pi$
$620$	32.7519	1.31535
$621$	17.4024	0.698332
$622$	32.5924	1.30684
$623$	−15.1443	−0.606742
$624$	−128.956	−5.16237
$625$	16.3374	0.653496
$626$	66.5869	2.66135
$627$	4.04843	0.161679
$628$	−18.7953	−0.750013
$629$	−57.5874	−2.29616
$630$	16.4014	0.653449
$631$	−16.5689	−0.659597	−0.329799	−	0.944051i	$-0.606981\pi$
$631$	−16.5689	−0.659597	−0.329799	+	0.944051i	$0.606981\pi$
$632$	−12.3222	−0.490149
$633$	−42.4967	−1.68909
$634$	−33.8845	−1.34572
$635$	2.67928	0.106324
$636$	5.59242	0.221754
$637$	−14.7947	−0.586187
$638$	13.3057	0.526778
$639$	−46.1270	−1.82476
$640$	−2.57841	−0.101921
$641$	0.672540	0.0265637	0.0132819	−	0.999912i	$-0.495772\pi$
$641$	0.672540	0.0265637	0.0132819	+	0.999912i	$0.495772\pi$
$642$	−23.2021	−0.915714
$643$	26.2009	1.03326	0.516632	−	0.856208i	$-0.327186\pi$
$643$	26.2009	1.03326	0.516632	+	0.856208i	$0.327186\pi$
$644$	−69.0247	−2.71996
$645$	−23.9743	−0.943986
$646$	−36.9185	−1.45254
$647$	2.85373	0.112192	0.0560958	−	0.998425i	$-0.482135\pi$
$647$	2.85373	0.112192	0.0560958	+	0.998425i	$0.482135\pi$
$648$	37.7979	1.48484
$649$	−13.1058	−0.514448
$650$	61.9748	2.43085
$651$	48.4584	1.89923
$652$	−18.8028	−0.736373
$653$	9.57456	0.374682	0.187341	−	0.982295i	$-0.440013\pi$
$653$	9.57456	0.374682	0.187341	+	0.982295i	$0.440013\pi$
$654$	−57.0198	−2.22965
$655$	−12.7274	−0.497301
$656$	−64.2212	−2.50742
$657$	29.1005	1.13532
$658$	−33.1518	−1.29239
$659$	−20.9439	−0.815860	−0.407930	−	0.913013i	$-0.633749\pi$
$659$	−20.9439	−0.815860	−0.407930	+	0.913013i	$0.633749\pi$
$660$	8.41929	0.327720
$661$	47.0866	1.83146	0.915729	−	0.401797i	$-0.131614\pi$
$661$	47.0866	1.83146	0.915729	+	0.401797i	$0.131614\pi$
$662$	−10.8876	−0.423158
$663$	114.802	4.45854
$664$	−76.1365	−2.95467
$665$	2.83748	0.110033
$666$	−73.3333	−2.84161
$667$	41.5164	1.60752
$668$	13.4215	0.519295
$669$	−32.5424	−1.25816
$670$	6.82735	0.263763
$671$	6.95054	0.268323
$672$	49.9714	1.92769
$673$	38.9569	1.50168	0.750838	−	0.660486i	$-0.229650\pi$
$673$	38.9569	1.50168	0.750838	+	0.660486i	$0.229650\pi$
$674$	−28.4142	−1.09447
$675$	10.8763	0.418628
$676$	77.9860	2.99946
$677$	15.6802	0.602638	0.301319	−	0.953523i	$-0.402573\pi$
$677$	15.6802	0.602638	0.301319	+	0.953523i	$0.402573\pi$
$678$	137.828	5.29326
$679$	−5.14153	−0.197314
$680$	−44.4142	−1.70321
$681$	−60.7696	−2.32870
$682$	20.0721	0.768599
$683$	6.83330	0.261469	0.130734	−	0.991417i	$-0.458266\pi$
$683$	6.83330	0.261469	0.130734	+	0.991417i	$0.458266\pi$
$684$	−33.0723	−1.26455
$685$	−7.82761	−0.299078
$686$	52.2191	1.99373
$687$	6.29724	0.240255
$688$	−105.876	−4.03647
$689$	−2.42766	−0.0924863
$690$	37.3430	1.42162
$691$	−19.8985	−0.756974	−0.378487	−	0.925607i	$-0.623556\pi$
$691$	−19.8985	−0.756974	−0.378487	+	0.925607i	$0.623556\pi$
$692$	−4.68715	−0.178179
$693$	7.07106	0.268608
$694$	43.5628	1.65362
$695$	6.71507	0.254717
$696$	−110.772	−4.19878
$697$	57.1725	2.16556
$698$	−28.0180	−1.06050
$699$	−21.0142	−0.794829
$700$	−43.1397	−1.63053
$701$	45.7263	1.72706	0.863529	−	0.504299i	$-0.168249\pi$
$701$	45.7263	1.72706	0.863529	+	0.504299i	$0.168249\pi$
$702$	34.8429	1.31506
$703$	−12.6868	−0.478492
$704$	5.02613	0.189429
$705$	12.6171	0.475187
$706$	6.17244	0.232303
$707$	24.8733	0.935458
$708$	188.610	7.08839
$709$	−19.2019	−0.721143	−0.360571	−	0.932732i	$-0.617418\pi$
$709$	−19.2019	−0.721143	−0.360571	+	0.932732i	$0.617418\pi$
$710$	−23.5911	−0.885357
$711$	6.80861	0.255343
$712$	52.2230	1.95714
$713$	62.6287	2.34546
$714$	−113.596	−4.25124
$715$	−3.65479	−0.136681
$716$	71.1352	2.65845
$717$	39.0947	1.46002
$718$	−94.5324	−3.52792
$719$	26.5642	0.990677	0.495339	−	0.868700i	$-0.335044\pi$
$719$	26.5642	0.990677	0.495339	+	0.868700i	$0.335044\pi$
$720$	−27.5667	−1.02735
$721$	−14.7909	−0.550842
$722$	41.2109	1.53371
$723$	18.5982	0.691673
$724$	24.1976	0.899298
$725$	25.9473	0.963659
$726$	−70.0919	−2.60135
$727$	−28.2304	−1.04701	−0.523503	−	0.852024i	$-0.675375\pi$
$727$	−28.2304	−1.04701	−0.523503	+	0.852024i	$0.675375\pi$
$728$	−79.9467	−2.96302
$729$	−40.4265	−1.49728
$730$	14.8831	0.550848
$731$	94.2551	3.48615
$732$	−100.027	−3.69712
$733$	−42.7246	−1.57807	−0.789035	−	0.614348i	$-0.789419\pi$
$733$	−42.7246	−1.57807	−0.789035	+	0.614348i	$0.789419\pi$
$734$	7.97961	0.294533
$735$	−5.57151	−0.205508
$736$	64.5843	2.38061
$737$	2.94344	0.108423
$738$	72.8049	2.67999
$739$	−36.7423	−1.35159	−0.675794	−	0.737091i	$-0.736199\pi$
$739$	−36.7423	−1.35159	−0.675794	+	0.737091i	$0.736199\pi$
$740$	−26.3840	−0.969896
$741$	25.2915	0.929106
$742$	2.40216	0.0881860
$743$	−22.1036	−0.810904	−0.405452	−	0.914116i	$-0.632886\pi$
$743$	−22.1036	−0.810904	−0.405452	+	0.914116i	$0.632886\pi$
$744$	−167.102	−6.12626
$745$	10.0833	0.369425
$746$	−11.3756	−0.416489
$747$	42.0693	1.53923
$748$	−33.1005	−1.21028
$749$	−7.01095	−0.256175
$750$	49.8705	1.82101
$751$	31.7198	1.15747	0.578735	−	0.815515i	$-0.303546\pi$
$751$	31.7198	1.15747	0.578735	+	0.815515i	$0.303546\pi$
$752$	55.7199	2.03190
$753$	16.6832	0.607969
$754$	83.1239	3.02719
$755$	−4.22233	−0.153666
$756$	−24.2536	−0.882094
$757$	28.3298	1.02966	0.514831	−	0.857292i	$-0.327855\pi$
$757$	28.3298	1.02966	0.514831	+	0.857292i	$0.327855\pi$
$758$	89.1076	3.23654
$759$	16.0995	0.584375
$760$	−9.78467	−0.354927
$761$	18.6435	0.675826	0.337913	−	0.941177i	$-0.390279\pi$
$761$	18.6435	0.675826	0.337913	+	0.941177i	$0.390279\pi$
$762$	−23.6305	−0.856044
$763$	−17.2296	−0.623753
$764$	116.374	4.21025
$765$	24.5411	0.887285
$766$	35.9721	1.29973
$767$	−81.8751	−2.95634
$768$	53.2304	1.92079
$769$	35.4371	1.27789	0.638947	−	0.769251i	$-0.279370\pi$
$769$	35.4371	1.27789	0.638947	+	0.769251i	$0.279370\pi$
$770$	3.61641	0.130326
$771$	78.1785	2.81553
$772$	−2.64161	−0.0950735
$773$	19.2193	0.691271	0.345636	−	0.938369i	$-0.387663\pi$
$773$	19.2193	0.691271	0.345636	+	0.938369i	$0.387663\pi$
$774$	120.027	4.31428
$775$	39.1423	1.40603
$776$	17.7299	0.636466
$777$	−39.0367	−1.40043
$778$	−58.2391	−2.08797
$779$	12.5954	0.451277
$780$	52.5972	1.88328
$781$	−10.1707	−0.363936
$782$	−146.815	−5.25008
$783$	14.5878	0.521327
$784$	−24.6050	−0.878751
$785$	3.07258	0.109665
$786$	112.253	4.00392
$787$	−32.6004	−1.16208	−0.581039	−	0.813875i	$-0.697354\pi$
$787$	−32.6004	−1.16208	−0.581039	+	0.813875i	$0.697354\pi$
$788$	−81.3151	−2.89673
$789$	4.51632	0.160785
$790$	3.48218	0.123890
$791$	41.6474	1.48081
$792$	−24.3836	−0.866434
$793$	43.4217	1.54195
$794$	−51.6085	−1.83152
$795$	−0.914227	−0.0324243
$796$	−99.6803	−3.53307
$797$	−18.0298	−0.638648	−0.319324	−	0.947646i	$-0.603456\pi$
$797$	−18.0298	−0.638648	−0.319324	+	0.947646i	$0.603456\pi$
$798$	−25.0259	−0.885906
$799$	−49.6043	−1.75487
$800$	40.3645	1.42710
$801$	−28.8558	−1.01957
$802$	−45.1424	−1.59403
$803$	6.41648	0.226433
$804$	−42.3600	−1.49392
$805$	11.2839	0.397705
$806$	125.395	4.41684
$807$	−19.6572	−0.691967
$808$	−85.7723	−3.01746
$809$	20.0714	0.705674	0.352837	−	0.935685i	$-0.385217\pi$
$809$	20.0714	0.705674	0.352837	+	0.935685i	$0.385217\pi$
$810$	−10.6815	−0.375309
$811$	−46.3628	−1.62802	−0.814008	−	0.580853i	$-0.802719\pi$
$811$	−46.3628	−1.62802	−0.814008	+	0.580853i	$0.802719\pi$
$812$	−57.8613	−2.03053
$813$	−45.1389	−1.58309
$814$	−16.1695	−0.566741
$815$	3.07380	0.107671
$816$	190.927	6.68378
$817$	20.7649	0.726472
$818$	31.7015	1.10842
$819$	44.1746	1.54358
$820$	26.1939	0.914732
$821$	−20.2018	−0.705046	−0.352523	−	0.935803i	$-0.614676\pi$
$821$	−20.2018	−0.705046	−0.352523	+	0.935803i	$0.614676\pi$
$822$	69.0376	2.40796
$823$	−10.9908	−0.383115	−0.191557	−	0.981481i	$-0.561354\pi$
$823$	−10.9908	−0.383115	−0.191557	+	0.981481i	$0.561354\pi$
$824$	51.0045	1.77682
$825$	10.0620	0.350315
$826$	81.0152	2.81888
$827$	−33.0782	−1.15024	−0.575120	−	0.818069i	$-0.695045\pi$
$827$	−33.0782	−1.15024	−0.575120	+	0.818069i	$0.695045\pi$
$828$	−131.519	−4.57062
$829$	18.0310	0.626242	0.313121	−	0.949713i	$-0.398625\pi$
$829$	18.0310	0.626242	0.313121	+	0.949713i	$0.398625\pi$
$830$	21.5158	0.746824
$831$	−27.1589	−0.942130
$832$	31.3994	1.08858
$833$	21.9045	0.758945
$834$	−59.2252	−2.05080
$835$	−2.19410	−0.0759299
$836$	−7.29222	−0.252207
$837$	22.0062	0.760645
$838$	−41.7707	−1.44294
$839$	−38.7196	−1.33675	−0.668375	−	0.743824i	$-0.733010\pi$
$839$	−38.7196	−1.33675	−0.668375	+	0.743824i	$0.733010\pi$
$840$	−30.1070	−1.03879
$841$	5.80191	0.200066
$842$	−45.3119	−1.56155
$843$	26.1285	0.899913
$844$	76.5470	2.63486
$845$	−12.7488	−0.438573
$846$	−63.1673	−2.17174
$847$	−21.1796	−0.727739
$848$	−4.03743	−0.138646
$849$	−11.0939	−0.380742
$850$	−91.7576	−3.14726
$851$	−50.4520	−1.72947
$852$	146.370	5.01455
$853$	−47.7349	−1.63441	−0.817206	−	0.576346i	$-0.804478\pi$
$853$	−47.7349	−1.63441	−0.817206	+	0.576346i	$0.804478\pi$
$854$	−42.9656	−1.47025
$855$	5.40653	0.184899
$856$	24.1763	0.826329
$857$	−45.8957	−1.56777	−0.783883	−	0.620908i	$-0.786764\pi$
$857$	−45.8957	−1.56777	−0.783883	+	0.620908i	$0.786764\pi$
$858$	32.2343	1.10046
$859$	−52.9776	−1.80757	−0.903786	−	0.427984i	$-0.859224\pi$
$859$	−52.9776	−1.80757	−0.903786	+	0.427984i	$0.859224\pi$
$860$	43.1835	1.47255
$861$	38.7555	1.32078
$862$	1.63215	0.0555912
$863$	18.3387	0.624256	0.312128	−	0.950040i	$-0.398958\pi$
$863$	18.3387	0.624256	0.312128	+	0.950040i	$0.398958\pi$
$864$	22.6933	0.772042
$865$	0.766237	0.0260528
$866$	−44.8914	−1.52547
$867$	−125.191	−4.25171
$868$	−87.2854	−2.96266
$869$	1.50125	0.0509265
$870$	31.3035	1.06129
$871$	18.3884	0.623066
$872$	59.4139	2.01201
$873$	−9.79666	−0.331567
$874$	−32.3440	−1.09405
$875$	15.0693	0.509435
$876$	−92.3415	−3.11993
$877$	−40.6678	−1.37325	−0.686627	−	0.727010i	$-0.740909\pi$
$877$	−40.6678	−1.37325	−0.686627	+	0.727010i	$0.740909\pi$
$878$	−85.4362	−2.88333
$879$	−0.137533	−0.00463886
$880$	−6.07828	−0.204899
$881$	−7.35756	−0.247882	−0.123941	−	0.992290i	$-0.539553\pi$
$881$	−7.35756	−0.247882	−0.123941	+	0.992290i	$0.539553\pi$
$882$	27.8937	0.939230
$883$	−7.83441	−0.263649	−0.131824	−	0.991273i	$-0.542083\pi$
$883$	−7.83441	−0.263649	−0.131824	+	0.991273i	$0.542083\pi$
$884$	−206.787	−6.95499
$885$	−30.8332	−1.03645
$886$	90.9765	3.05642
$887$	−1.00061	−0.0335971	−0.0167986	−	0.999859i	$-0.505347\pi$
$887$	−1.00061	−0.0335971	−0.0167986	+	0.999859i	$0.505347\pi$
$888$	134.613	4.51731
$889$	−7.14040	−0.239481
$890$	−14.7580	−0.494688
$891$	−4.60506	−0.154275
$892$	58.6169	1.96264
$893$	−10.9281	−0.365694
$894$	−88.9325	−2.97435
$895$	−11.6289	−0.388711
$896$	6.87159	0.229564
$897$	100.577	3.35818
$898$	−37.8679	−1.26367
$899$	52.4997	1.75096
$900$	−82.1983	−2.73994
$901$	3.59430	0.119743
$902$	16.0530	0.534507
$903$	63.8926	2.12621
$904$	−143.615	−4.77658
$905$	−3.95573	−0.131493
$906$	37.2398	1.23721
$907$	−25.3787	−0.842686	−0.421343	−	0.906901i	$-0.638441\pi$
$907$	−25.3787	−0.842686	−0.421343	+	0.906901i	$0.638441\pi$
$908$	109.461	3.63259
$909$	47.3936	1.57195
$910$	22.5925	0.748935
$911$	−0.435314	−0.0144226	−0.00721130	−	0.999974i	$-0.502295\pi$
$911$	−0.435314	−0.0144226	−0.00721130	+	0.999974i	$0.502295\pi$
$912$	42.0622	1.39282
$913$	9.27600	0.306991
$914$	−37.8672	−1.25254
$915$	16.3521	0.540583
$916$	−11.3429	−0.374779
$917$	33.9192	1.12011
$918$	−51.5870	−1.70263
$919$	−21.1827	−0.698752	−0.349376	−	0.936983i	$-0.613606\pi$
$919$	−21.1827	−0.698752	−0.349376	+	0.936983i	$0.613606\pi$
$920$	−38.9110	−1.28286
$921$	38.0811	1.25482
$922$	59.7872	1.96899
$923$	−63.5387	−2.09140
$924$	−22.4378	−0.738150
$925$	−31.5319	−1.03676
$926$	−36.2612	−1.19162
$927$	−28.1825	−0.925636
$928$	54.1390	1.77720
$929$	−30.1240	−0.988336	−0.494168	−	0.869366i	$-0.664527\pi$
$929$	−30.1240	−0.988336	−0.494168	+	0.869366i	$0.664527\pi$
$930$	47.2222	1.54848
$931$	4.82567	0.158155
$932$	37.8517	1.23987
$933$	33.0578	1.08227
$934$	12.6362	0.413468
$935$	5.41114	0.176963
$936$	−152.330	−4.97906
$937$	−10.0826	−0.329385	−0.164693	−	0.986345i	$-0.552663\pi$
$937$	−10.0826	−0.329385	−0.164693	+	0.986345i	$0.552663\pi$
$938$	−18.1952	−0.594095
$939$	67.5377	2.20401
$940$	−22.7265	−0.741257
$941$	0.380700	0.0124105	0.00620523	−	0.999981i	$-0.498025\pi$
$941$	0.380700	0.0124105	0.00620523	+	0.999981i	$0.498025\pi$
$942$	−27.0993	−0.882944
$943$	50.0885	1.63111
$944$	−136.166	−4.43183
$945$	3.96488	0.128978
$946$	26.4651	0.860455
$947$	45.5143	1.47902	0.739509	−	0.673147i	$-0.235058\pi$
$947$	45.5143	1.47902	0.739509	+	0.673147i	$0.235058\pi$
$948$	−21.6050	−0.701698
$949$	40.0852	1.30122
$950$	−20.2147	−0.655850
$951$	−34.3683	−1.11447
$952$	118.366	3.83626
$953$	53.0969	1.71998	0.859989	−	0.510313i	$-0.170471\pi$
$953$	53.0969	1.71998	0.859989	+	0.510313i	$0.170471\pi$
$954$	4.57707	0.148188
$955$	−19.0243	−0.615611
$956$	−70.4191	−2.27752
$957$	13.4957	0.436254
$958$	−55.7485	−1.80115
$959$	20.8610	0.673636
$960$	11.8247	0.381639
$961$	48.1973	1.55475
$962$	−101.015	−3.25684
$963$	−13.3586	−0.430476
$964$	−33.4999	−1.07896
$965$	0.431839	0.0139014
$966$	−99.5210	−3.20204
$967$	−23.3007	−0.749298	−0.374649	−	0.927167i	$-0.622237\pi$
$967$	−23.3007	−0.749298	−0.374649	+	0.927167i	$0.622237\pi$
$968$	73.0349	2.34743
$969$	−37.4456	−1.20293
$970$	−5.01038	−0.160873
$971$	32.2438	1.03475	0.517376	−	0.855758i	$-0.326909\pi$
$971$	32.2438	1.03475	0.517376	+	0.855758i	$0.326909\pi$
$972$	101.471	3.25469
$973$	−17.8960	−0.573720
$974$	105.029	3.36535
$975$	62.8598	2.01312
$976$	72.2144	2.31153
$977$	−9.10069	−0.291157	−0.145578	−	0.989347i	$-0.546504\pi$
$977$	−9.10069	−0.291157	−0.145578	+	0.989347i	$0.546504\pi$
$978$	−27.1101	−0.866886
$979$	−6.36252	−0.203347
$980$	10.0357	0.320577
$981$	−32.8292	−1.04816
$982$	85.7187	2.73539
$983$	−41.6334	−1.32790	−0.663949	−	0.747778i	$-0.731121\pi$
$983$	−41.6334	−1.32790	−0.663949	+	0.747778i	$0.731121\pi$
$984$	−133.643	−4.26038
$985$	13.2931	0.423553
$986$	−123.070	−3.91935
$987$	−33.6252	−1.07030
$988$	−45.5562	−1.44934
$989$	82.5763	2.62577
$990$	6.89069	0.219000
$991$	−25.4059	−0.807044	−0.403522	−	0.914970i	$-0.632214\pi$
$991$	−25.4059	−0.807044	−0.403522	+	0.914970i	$0.632214\pi$
$992$	81.6702	2.59303
$993$	−11.0431	−0.350441
$994$	62.8714	1.99416
$995$	16.2953	0.516597
$996$	−133.494	−4.22991
$997$	−1.99317	−0.0631243	−0.0315621	−	0.999502i	$-0.510048\pi$
$997$	−1.99317	−0.0631243	−0.0315621	+	0.999502i	$0.510048\pi$
$998$	24.8522	0.786682
$999$	−17.7276	−0.560876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.14	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.14	✓	287	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59707 q^{2} -2.63415 q^{3} +4.74475 q^{4} -0.775653 q^{5} +6.84106 q^{6} +2.06715 q^{7} -7.12830 q^{8} +3.93875 q^{9} +O(q^{10})\)	\(q-2.59707 q^{2} -2.63415 q^{3} +4.74475 q^{4} -0.775653 q^{5} +6.84106 q^{6} +2.06715 q^{7} -7.12830 q^{8} +3.93875 q^{9} +2.01442 q^{10} +0.868468 q^{11} -12.4984 q^{12} +5.42552 q^{13} -5.36854 q^{14} +2.04319 q^{15} +9.02317 q^{16} -8.03282 q^{17} -10.2292 q^{18} -1.76967 q^{19} -3.68028 q^{20} -5.44520 q^{21} -2.25547 q^{22} -7.03750 q^{23} +18.7770 q^{24} -4.39836 q^{25} -14.0904 q^{26} -2.47280 q^{27} +9.80814 q^{28} -5.89931 q^{29} -5.30629 q^{30} -8.89929 q^{31} -9.17716 q^{32} -2.28767 q^{33} +20.8618 q^{34} -1.60339 q^{35} +18.6884 q^{36} +7.16902 q^{37} +4.59595 q^{38} -14.2916 q^{39} +5.52909 q^{40} -7.11737 q^{41} +14.1415 q^{42} -11.7338 q^{43} +4.12066 q^{44} -3.05510 q^{45} +18.2769 q^{46} +6.17520 q^{47} -23.7684 q^{48} -2.72687 q^{49} +11.4228 q^{50} +21.1596 q^{51} +25.7427 q^{52} -0.447451 q^{53} +6.42203 q^{54} -0.673630 q^{55} -14.7353 q^{56} +4.66158 q^{57} +15.3209 q^{58} -15.0907 q^{59} +9.69442 q^{60} +8.00322 q^{61} +23.1120 q^{62} +8.14200 q^{63} +5.78736 q^{64} -4.20832 q^{65} +5.94124 q^{66} +3.38923 q^{67} -38.1137 q^{68} +18.5378 q^{69} +4.16412 q^{70} -11.7111 q^{71} -28.0766 q^{72} +7.38827 q^{73} -18.6184 q^{74} +11.5859 q^{75} -8.39665 q^{76} +1.79526 q^{77} +37.1163 q^{78} +1.72862 q^{79} -6.99885 q^{80} -5.30251 q^{81} +18.4843 q^{82} +10.6809 q^{83} -25.8361 q^{84} +6.23068 q^{85} +30.4733 q^{86} +15.5397 q^{87} -6.19070 q^{88} -7.32614 q^{89} +7.93430 q^{90} +11.2154 q^{91} -33.3912 q^{92} +23.4421 q^{93} -16.0374 q^{94} +1.37265 q^{95} +24.1740 q^{96} -2.48725 q^{97} +7.08187 q^{98} +3.42068 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * q^99

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