LMFDB - Embedded newform 6015.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12459 q^{2} -1.00000 q^{3} +2.51388 q^{4} +1.00000 q^{5} +2.12459 q^{6} +3.70349 q^{7} -1.09177 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.12459 q^{2} -1.00000 q^{3} +2.51388 q^{4} +1.00000 q^{5} +2.12459 q^{6} +3.70349 q^{7} -1.09177 q^{8} +1.00000 q^{9} -2.12459 q^{10} -4.40799 q^{11} -2.51388 q^{12} -1.01097 q^{13} -7.86839 q^{14} -1.00000 q^{15} -2.70818 q^{16} +7.95531 q^{17} -2.12459 q^{18} -7.36741 q^{19} +2.51388 q^{20} -3.70349 q^{21} +9.36516 q^{22} -3.13914 q^{23} +1.09177 q^{24} +1.00000 q^{25} +2.14789 q^{26} -1.00000 q^{27} +9.31011 q^{28} -6.96532 q^{29} +2.12459 q^{30} -1.01603 q^{31} +7.93732 q^{32} +4.40799 q^{33} -16.9018 q^{34} +3.70349 q^{35} +2.51388 q^{36} -11.0735 q^{37} +15.6527 q^{38} +1.01097 q^{39} -1.09177 q^{40} +3.72554 q^{41} +7.86839 q^{42} -12.4670 q^{43} -11.0811 q^{44} +1.00000 q^{45} +6.66939 q^{46} -10.1539 q^{47} +2.70818 q^{48} +6.71583 q^{49} -2.12459 q^{50} -7.95531 q^{51} -2.54145 q^{52} +11.5205 q^{53} +2.12459 q^{54} -4.40799 q^{55} -4.04338 q^{56} +7.36741 q^{57} +14.7984 q^{58} -6.99377 q^{59} -2.51388 q^{60} +11.3368 q^{61} +2.15865 q^{62} +3.70349 q^{63} -11.4472 q^{64} -1.01097 q^{65} -9.36516 q^{66} -6.72134 q^{67} +19.9987 q^{68} +3.13914 q^{69} -7.86839 q^{70} +14.4261 q^{71} -1.09177 q^{72} +5.52316 q^{73} +23.5267 q^{74} -1.00000 q^{75} -18.5208 q^{76} -16.3249 q^{77} -2.14789 q^{78} -0.0462182 q^{79} -2.70818 q^{80} +1.00000 q^{81} -7.91524 q^{82} +12.4234 q^{83} -9.31011 q^{84} +7.95531 q^{85} +26.4872 q^{86} +6.96532 q^{87} +4.81253 q^{88} +11.8647 q^{89} -2.12459 q^{90} -3.74411 q^{91} -7.89142 q^{92} +1.01603 q^{93} +21.5728 q^{94} -7.36741 q^{95} -7.93732 q^{96} +4.04374 q^{97} -14.2684 q^{98} -4.40799 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * 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 $

$2$	−2.12459	−1.50231	−0.751155	−	0.660125i	$-0.770503\pi$
$2$	−2.12459	−1.50231	−0.751155	+	0.660125i	$0.770503\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.51388	1.25694
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.12459	0.867360
$7$	3.70349	1.39979	0.699894	−	0.714247i	$-0.253231\pi$
$7$	3.70349	1.39979	0.699894	+	0.714247i	$0.253231\pi$
$8$	−1.09177	−0.386001
$9$	1.00000	0.333333
$10$	−2.12459	−0.671854
$11$	−4.40799	−1.32906	−0.664529	−	0.747262i	$-0.731368\pi$
$11$	−4.40799	−1.32906	−0.664529	+	0.747262i	$0.731368\pi$
$12$	−2.51388	−0.725693
$13$	−1.01097	−0.280392	−0.140196	−	0.990124i	$-0.544773\pi$
$13$	−1.01097	−0.280392	−0.140196	+	0.990124i	$0.544773\pi$
$14$	−7.86839	−2.10292
$15$	−1.00000	−0.258199
$16$	−2.70818	−0.677045
$17$	7.95531	1.92945	0.964723	−	0.263268i	$-0.0848003\pi$
$17$	7.95531	1.92945	0.964723	+	0.263268i	$0.0848003\pi$
$18$	−2.12459	−0.500770
$19$	−7.36741	−1.69020	−0.845100	−	0.534608i	$-0.820459\pi$
$19$	−7.36741	−1.69020	−0.845100	+	0.534608i	$0.820459\pi$
$20$	2.51388	0.562120
$21$	−3.70349	−0.808168
$22$	9.36516	1.99666
$23$	−3.13914	−0.654557	−0.327278	−	0.944928i	$-0.606131\pi$
$23$	−3.13914	−0.654557	−0.327278	+	0.944928i	$0.606131\pi$
$24$	1.09177	0.222858
$25$	1.00000	0.200000
$26$	2.14789	0.421236
$27$	−1.00000	−0.192450
$28$	9.31011	1.75945
$29$	−6.96532	−1.29343	−0.646714	−	0.762733i	$-0.723857\pi$
$29$	−6.96532	−1.29343	−0.646714	+	0.762733i	$0.723857\pi$
$30$	2.12459	0.387895
$31$	−1.01603	−0.182484	−0.0912422	−	0.995829i	$-0.529084\pi$
$31$	−1.01603	−0.182484	−0.0912422	+	0.995829i	$0.529084\pi$
$32$	7.93732	1.40313
$33$	4.40799	0.767332
$34$	−16.9018	−2.89863
$35$	3.70349	0.626004
$36$	2.51388	0.418979
$37$	−11.0735	−1.82048	−0.910240	−	0.414081i	$-0.864103\pi$
$37$	−11.0735	−1.82048	−0.910240	+	0.414081i	$0.864103\pi$
$38$	15.6527	2.53921
$39$	1.01097	0.161885
$40$	−1.09177	−0.172625
$41$	3.72554	0.581832	0.290916	−	0.956749i	$-0.406040\pi$
$41$	3.72554	0.581832	0.290916	+	0.956749i	$0.406040\pi$
$42$	7.86839	1.21412
$43$	−12.4670	−1.90120	−0.950598	−	0.310424i	$-0.899529\pi$
$43$	−12.4670	−1.90120	−0.950598	+	0.310424i	$0.899529\pi$
$44$	−11.0811	−1.67054
$45$	1.00000	0.149071
$46$	6.66939	0.983347
$47$	−10.1539	−1.48109	−0.740547	−	0.672004i	$-0.765434\pi$
$47$	−10.1539	−1.48109	−0.740547	+	0.672004i	$0.765434\pi$
$48$	2.70818	0.390892
$49$	6.71583	0.959404
$50$	−2.12459	−0.300462
$51$	−7.95531	−1.11397
$52$	−2.54145	−0.352436
$53$	11.5205	1.58246	0.791228	−	0.611521i	$-0.209442\pi$
$53$	11.5205	1.58246	0.791228	+	0.611521i	$0.209442\pi$
$54$	2.12459	0.289120
$55$	−4.40799	−0.594373
$56$	−4.04338	−0.540319
$57$	7.36741	0.975838
$58$	14.7984	1.94313
$59$	−6.99377	−0.910511	−0.455255	−	0.890361i	$-0.650452\pi$
$59$	−6.99377	−0.910511	−0.455255	+	0.890361i	$0.650452\pi$
$60$	−2.51388	−0.324540
$61$	11.3368	1.45153	0.725764	−	0.687944i	$-0.241487\pi$
$61$	11.3368	1.45153	0.725764	+	0.687944i	$0.241487\pi$
$62$	2.15865	0.274148
$63$	3.70349	0.466596
$64$	−11.4472	−1.43090
$65$	−1.01097	−0.125395
$66$	−9.36516	−1.15277
$67$	−6.72134	−0.821143	−0.410571	−	0.911828i	$-0.634671\pi$
$67$	−6.72134	−0.821143	−0.410571	+	0.911828i	$0.634671\pi$
$68$	19.9987	2.42519
$69$	3.13914	0.377908
$70$	−7.86839	−0.940452
$71$	14.4261	1.71207	0.856033	−	0.516922i	$-0.172922\pi$
$71$	14.4261	1.71207	0.856033	+	0.516922i	$0.172922\pi$
$72$	−1.09177	−0.128667
$73$	5.52316	0.646437	0.323219	−	0.946324i	$-0.395235\pi$
$73$	5.52316	0.646437	0.323219	+	0.946324i	$0.395235\pi$
$74$	23.5267	2.73493
$75$	−1.00000	−0.115470
$76$	−18.5208	−2.12448
$77$	−16.3249	−1.86040
$78$	−2.14789	−0.243201
$79$	−0.0462182	−0.00519995	−0.00259998	−	0.999997i	$-0.500828\pi$
$79$	−0.0462182	−0.00519995	−0.00259998	+	0.999997i	$0.500828\pi$
$80$	−2.70818	−0.302784
$81$	1.00000	0.111111
$82$	−7.91524	−0.874092
$83$	12.4234	1.36364	0.681821	−	0.731519i	$-0.261188\pi$
$83$	12.4234	1.36364	0.681821	+	0.731519i	$0.261188\pi$
$84$	−9.31011	−1.01582
$85$	7.95531	0.862874
$86$	26.4872	2.85619
$87$	6.96532	0.746761
$88$	4.81253	0.513017
$89$	11.8647	1.25766	0.628828	−	0.777544i	$-0.283535\pi$
$89$	11.8647	1.25766	0.628828	+	0.777544i	$0.283535\pi$
$90$	−2.12459	−0.223951
$91$	−3.74411	−0.392489
$92$	−7.89142	−0.822737
$93$	1.01603	0.105357
$94$	21.5728	2.22506
$95$	−7.36741	−0.755881
$96$	−7.93732	−0.810099
$97$	4.04374	0.410580	0.205290	−	0.978701i	$-0.434186\pi$
$97$	4.04374	0.410580	0.205290	+	0.978701i	$0.434186\pi$
$98$	−14.2684	−1.44132
$99$	−4.40799	−0.443019
$100$	2.51388	0.251388
$101$	3.19062	0.317479	0.158739	−	0.987321i	$-0.449257\pi$
$101$	3.19062	0.317479	0.158739	+	0.987321i	$0.449257\pi$
$102$	16.9018	1.67352
$103$	3.21407	0.316692	0.158346	−	0.987384i	$-0.449384\pi$
$103$	3.21407	0.316692	0.158346	+	0.987384i	$0.449384\pi$
$104$	1.10375	0.108232
$105$	−3.70349	−0.361424
$106$	−24.4762	−2.37734
$107$	−1.71870	−0.166153	−0.0830766	−	0.996543i	$-0.526475\pi$
$107$	−1.71870	−0.166153	−0.0830766	+	0.996543i	$0.526475\pi$
$108$	−2.51388	−0.241898
$109$	10.2510	0.981865	0.490932	−	0.871198i	$-0.336656\pi$
$109$	10.2510	0.981865	0.490932	+	0.871198i	$0.336656\pi$
$110$	9.36516	0.892933
$111$	11.0735	1.05105
$112$	−10.0297	−0.947719
$113$	19.5474	1.83886	0.919430	−	0.393254i	$-0.128651\pi$
$113$	19.5474	1.83886	0.919430	+	0.393254i	$0.128651\pi$
$114$	−15.6527	−1.46601
$115$	−3.13914	−0.292727
$116$	−17.5100	−1.62576
$117$	−1.01097	−0.0934641
$118$	14.8589	1.36787
$119$	29.4624	2.70081
$120$	1.09177	0.0996649
$121$	8.43035	0.766395
$122$	−24.0860	−2.18064
$123$	−3.72554	−0.335921
$124$	−2.55417	−0.229372
$125$	1.00000	0.0894427
$126$	−7.86839	−0.700972
$127$	12.4857	1.10793	0.553965	−	0.832540i	$-0.313114\pi$
$127$	12.4857	1.10793	0.553965	+	0.832540i	$0.313114\pi$
$128$	8.44589	0.746519
$129$	12.4670	1.09766
$130$	2.14789	0.188383
$131$	19.6296	1.71505	0.857523	−	0.514446i	$-0.172002\pi$
$131$	19.6296	1.71505	0.857523	+	0.514446i	$0.172002\pi$
$132$	11.0811	0.964489
$133$	−27.2851	−2.36592
$134$	14.2801	1.23361
$135$	−1.00000	−0.0860663
$136$	−8.68540	−0.744767
$137$	11.0991	0.948263	0.474131	−	0.880454i	$-0.342762\pi$
$137$	11.0991	0.948263	0.474131	+	0.880454i	$0.342762\pi$
$138$	−6.66939	−0.567736
$139$	−0.787115	−0.0667622	−0.0333811	−	0.999443i	$-0.510628\pi$
$139$	−0.787115	−0.0667622	−0.0333811	+	0.999443i	$0.510628\pi$
$140$	9.31011	0.786848
$141$	10.1539	0.855111
$142$	−30.6496	−2.57205
$143$	4.45634	0.372658
$144$	−2.70818	−0.225682
$145$	−6.96532	−0.578438
$146$	−11.7344	−0.971150
$147$	−6.71583	−0.553912
$148$	−27.8375	−2.28823
$149$	14.3108	1.17238	0.586191	−	0.810173i	$-0.300627\pi$
$149$	14.3108	1.17238	0.586191	+	0.810173i	$0.300627\pi$
$150$	2.12459	0.173472
$151$	−14.2968	−1.16346	−0.581730	−	0.813382i	$-0.697624\pi$
$151$	−14.2968	−1.16346	−0.581730	+	0.813382i	$0.697624\pi$
$152$	8.04355	0.652418
$153$	7.95531	0.643149
$154$	34.6838	2.79490
$155$	−1.01603	−0.0816095
$156$	2.54145	0.203479
$157$	15.0071	1.19770	0.598850	−	0.800861i	$-0.295625\pi$
$157$	15.0071	1.19770	0.598850	+	0.800861i	$0.295625\pi$
$158$	0.0981946	0.00781194
$159$	−11.5205	−0.913631
$160$	7.93732	0.627500
$161$	−11.6258	−0.916240
$162$	−2.12459	−0.166923
$163$	16.0762	1.25918	0.629591	−	0.776926i	$-0.283222\pi$
$163$	16.0762	1.25918	0.629591	+	0.776926i	$0.283222\pi$
$164$	9.36555	0.731326
$165$	4.40799	0.343161
$166$	−26.3946	−2.04862
$167$	−12.4663	−0.964670	−0.482335	−	0.875987i	$-0.660211\pi$
$167$	−12.4663	−0.964670	−0.482335	+	0.875987i	$0.660211\pi$
$168$	4.04338	0.311953
$169$	−11.9779	−0.921380
$170$	−16.9018	−1.29631
$171$	−7.36741	−0.563400
$172$	−31.3404	−2.38969
$173$	−16.9376	−1.28774	−0.643870	−	0.765135i	$-0.722672\pi$
$173$	−16.9376	−1.28774	−0.643870	+	0.765135i	$0.722672\pi$
$174$	−14.7984	−1.12187
$175$	3.70349	0.279957
$176$	11.9376	0.899832
$177$	6.99377	0.525684
$178$	−25.2076	−1.88939
$179$	4.04509	0.302344	0.151172	−	0.988507i	$-0.451695\pi$
$179$	4.04509	0.302344	0.151172	+	0.988507i	$0.451695\pi$
$180$	2.51388	0.187373
$181$	24.3205	1.80773	0.903863	−	0.427822i	$-0.140719\pi$
$181$	24.3205	1.80773	0.903863	+	0.427822i	$0.140719\pi$
$182$	7.95469	0.589641
$183$	−11.3368	−0.838040
$184$	3.42724	0.252659
$185$	−11.0735	−0.814144
$186$	−2.15865	−0.158280
$187$	−35.0669	−2.56435
$188$	−25.5256	−1.86164
$189$	−3.70349	−0.269389
$190$	15.6527	1.13557
$191$	−5.25089	−0.379941	−0.189971	−	0.981790i	$-0.560839\pi$
$191$	−5.25089	−0.379941	−0.189971	+	0.981790i	$0.560839\pi$
$192$	11.4472	0.826128
$193$	−9.03726	−0.650516	−0.325258	−	0.945625i	$-0.605451\pi$
$193$	−9.03726	−0.650516	−0.325258	+	0.945625i	$0.605451\pi$
$194$	−8.59129	−0.616819
$195$	1.01097	0.0723970
$196$	16.8828	1.20591
$197$	−2.12844	−0.151645	−0.0758225	−	0.997121i	$-0.524158\pi$
$197$	−2.12844	−0.151645	−0.0758225	+	0.997121i	$0.524158\pi$
$198$	9.36516	0.665553
$199$	−17.5925	−1.24710	−0.623549	−	0.781785i	$-0.714310\pi$
$199$	−17.5925	−1.24710	−0.623549	+	0.781785i	$0.714310\pi$
$200$	−1.09177	−0.0772001
$201$	6.72134	0.474087
$202$	−6.77876	−0.476952
$203$	−25.7960	−1.81052
$204$	−19.9987	−1.40019
$205$	3.72554	0.260203
$206$	−6.82859	−0.475770
$207$	−3.13914	−0.218186
$208$	2.73788	0.189838
$209$	32.4755	2.24637
$210$	7.86839	0.542970
$211$	17.9496	1.23570	0.617851	−	0.786295i	$-0.288004\pi$
$211$	17.9496	1.23570	0.617851	+	0.786295i	$0.288004\pi$
$212$	28.9610	1.98905
$213$	−14.4261	−0.988461
$214$	3.65153	0.249614
$215$	−12.4670	−0.850241
$216$	1.09177	0.0742859
$217$	−3.76286	−0.255439
$218$	−21.7791	−1.47507
$219$	−5.52316	−0.373221
$220$	−11.0811	−0.747090
$221$	−8.04257	−0.541002
$222$	−23.5267	−1.57901
$223$	23.0434	1.54310	0.771550	−	0.636169i	$-0.219482\pi$
$223$	23.0434	1.54310	0.771550	+	0.636169i	$0.219482\pi$
$224$	29.3958	1.96409
$225$	1.00000	0.0666667
$226$	−41.5301	−2.76254
$227$	−4.31868	−0.286641	−0.143320	−	0.989676i	$-0.545778\pi$
$227$	−4.31868	−0.286641	−0.143320	+	0.989676i	$0.545778\pi$
$228$	18.5208	1.22657
$229$	−25.9886	−1.71738	−0.858688	−	0.512498i	$-0.828720\pi$
$229$	−25.9886	−1.71738	−0.858688	+	0.512498i	$0.828720\pi$
$230$	6.66939	0.439766
$231$	16.3249	1.07410
$232$	7.60456	0.499264
$233$	−22.1277	−1.44963	−0.724816	−	0.688942i	$-0.758075\pi$
$233$	−22.1277	−1.44963	−0.724816	+	0.688942i	$0.758075\pi$
$234$	2.14789	0.140412
$235$	−10.1539	−0.662366
$236$	−17.5815	−1.14446
$237$	0.0462182	0.00300219
$238$	−62.5955	−4.05746
$239$	14.8671	0.961673	0.480837	−	0.876810i	$-0.340333\pi$
$239$	14.8671	0.961673	0.480837	+	0.876810i	$0.340333\pi$
$240$	2.70818	0.174812
$241$	17.7091	1.14074	0.570372	−	0.821386i	$-0.306799\pi$
$241$	17.7091	1.14074	0.570372	+	0.821386i	$0.306799\pi$
$242$	−17.9110	−1.15136
$243$	−1.00000	−0.0641500
$244$	28.4993	1.82448
$245$	6.71583	0.429059
$246$	7.91524	0.504657
$247$	7.44822	0.473919
$248$	1.10928	0.0704391
$249$	−12.4234	−0.787299
$250$	−2.12459	−0.134371
$251$	3.71568	0.234531	0.117266	−	0.993101i	$-0.462587\pi$
$251$	3.71568	0.234531	0.117266	+	0.993101i	$0.462587\pi$
$252$	9.31011	0.586482
$253$	13.8373	0.869944
$254$	−26.5271	−1.66446
$255$	−7.95531	−0.498181
$256$	4.95029	0.309393
$257$	−13.5708	−0.846525	−0.423263	−	0.906007i	$-0.639115\pi$
$257$	−13.5708	−0.846525	−0.423263	+	0.906007i	$0.639115\pi$
$258$	−26.4872	−1.64902
$259$	−41.0108	−2.54828
$260$	−2.54145	−0.157614
$261$	−6.96532	−0.431142
$262$	−41.7048	−2.57653
$263$	−0.584079	−0.0360159	−0.0180079	−	0.999838i	$-0.505732\pi$
$263$	−0.584079	−0.0360159	−0.0180079	+	0.999838i	$0.505732\pi$
$264$	−4.81253	−0.296191
$265$	11.5205	0.707696
$266$	57.9697	3.55435
$267$	−11.8647	−0.726108
$268$	−16.8966	−1.03213
$269$	9.29786	0.566900	0.283450	−	0.958987i	$-0.408521\pi$
$269$	9.29786	0.566900	0.283450	+	0.958987i	$0.408521\pi$
$270$	2.12459	0.129298
$271$	−8.88500	−0.539726	−0.269863	−	0.962899i	$-0.586978\pi$
$271$	−8.88500	−0.539726	−0.269863	+	0.962899i	$0.586978\pi$
$272$	−21.5444	−1.30632
$273$	3.74411	0.226604
$274$	−23.5811	−1.42459
$275$	−4.40799	−0.265812
$276$	7.89142	0.475007
$277$	6.58343	0.395560	0.197780	−	0.980246i	$-0.436627\pi$
$277$	6.58343	0.395560	0.197780	+	0.980246i	$0.436627\pi$
$278$	1.67229	0.100298
$279$	−1.01603	−0.0608281
$280$	−4.04338	−0.241638
$281$	21.7917	1.29998	0.649992	−	0.759941i	$-0.274772\pi$
$281$	21.7917	1.29998	0.649992	+	0.759941i	$0.274772\pi$
$282$	−21.5728	−1.28464
$283$	−6.08952	−0.361985	−0.180992	−	0.983485i	$-0.557931\pi$
$283$	−6.08952	−0.361985	−0.180992	+	0.983485i	$0.557931\pi$
$284$	36.2655	2.15196
$285$	7.36741	0.436408
$286$	−9.46788	−0.559847
$287$	13.7975	0.814441
$288$	7.93732	0.467711
$289$	46.2869	2.72276
$290$	14.7984	0.868994
$291$	−4.04374	−0.237048
$292$	13.8845	0.812531
$293$	15.8758	0.927477	0.463738	−	0.885972i	$-0.346508\pi$
$293$	15.8758	0.927477	0.463738	+	0.885972i	$0.346508\pi$
$294$	14.2684	0.832148
$295$	−6.99377	−0.407193
$296$	12.0898	0.702707
$297$	4.40799	0.255777
$298$	−30.4045	−1.76128
$299$	3.17357	0.183533
$300$	−2.51388	−0.145139
$301$	−46.1713	−2.66127
$302$	30.3749	1.74788
$303$	−3.19062	−0.183296
$304$	19.9523	1.14434
$305$	11.3368	0.649143
$306$	−16.9018	−0.966209
$307$	28.8051	1.64399	0.821997	−	0.569492i	$-0.192860\pi$
$307$	28.8051	1.64399	0.821997	+	0.569492i	$0.192860\pi$
$308$	−41.0388	−2.33841
$309$	−3.21407	−0.182842
$310$	2.15865	0.122603
$311$	9.08148	0.514963	0.257482	−	0.966283i	$-0.417107\pi$
$311$	9.08148	0.514963	0.257482	+	0.966283i	$0.417107\pi$
$312$	−1.10375	−0.0624875
$313$	9.45082	0.534192	0.267096	−	0.963670i	$-0.413936\pi$
$313$	9.45082	0.534192	0.267096	+	0.963670i	$0.413936\pi$
$314$	−31.8840	−1.79932
$315$	3.70349	0.208668
$316$	−0.116187	−0.00653602
$317$	4.63846	0.260522	0.130261	−	0.991480i	$-0.458418\pi$
$317$	4.63846	0.260522	0.130261	+	0.991480i	$0.458418\pi$
$318$	24.4762	1.37256
$319$	30.7030	1.71904
$320$	−11.4472	−0.639916
$321$	1.71870	0.0959286
$322$	24.7000	1.37648
$323$	−58.6100	−3.26115
$324$	2.51388	0.139660
$325$	−1.01097	−0.0560784
$326$	−34.1552	−1.89168
$327$	−10.2510	−0.566880
$328$	−4.06745	−0.224587
$329$	−37.6048	−2.07322
$330$	−9.36516	−0.515535
$331$	26.1170	1.43552	0.717761	−	0.696289i	$-0.245167\pi$
$331$	26.1170	1.43552	0.717761	+	0.696289i	$0.245167\pi$
$332$	31.2308	1.71401
$333$	−11.0735	−0.606827
$334$	26.4857	1.44923
$335$	−6.72134	−0.367226
$336$	10.0297	0.547166
$337$	2.13360	0.116225	0.0581123	−	0.998310i	$-0.481492\pi$
$337$	2.13360	0.116225	0.0581123	+	0.998310i	$0.481492\pi$
$338$	25.4482	1.38420
$339$	−19.5474	−1.06167
$340$	19.9987	1.08458
$341$	4.47865	0.242532
$342$	15.6527	0.846402
$343$	−1.05242	−0.0568255
$344$	13.6111	0.733863
$345$	3.13914	0.169006
$346$	35.9854	1.93459
$347$	7.06462	0.379248	0.189624	−	0.981857i	$-0.439273\pi$
$347$	7.06462	0.379248	0.189624	+	0.981857i	$0.439273\pi$
$348$	17.5100	0.938632
$349$	−26.8539	−1.43746	−0.718729	−	0.695290i	$-0.755276\pi$
$349$	−26.8539	−1.43746	−0.718729	+	0.695290i	$0.755276\pi$
$350$	−7.86839	−0.420583
$351$	1.01097	0.0539615
$352$	−34.9876	−1.86484
$353$	−11.0711	−0.589255	−0.294628	−	0.955612i	$-0.595196\pi$
$353$	−11.0711	−0.589255	−0.294628	+	0.955612i	$0.595196\pi$
$354$	−14.8589	−0.789740
$355$	14.4261	0.765659
$356$	29.8264	1.58080
$357$	−29.4624	−1.55932
$358$	−8.59415	−0.454215
$359$	3.22429	0.170172	0.0850858	−	0.996374i	$-0.472884\pi$
$359$	3.22429	0.170172	0.0850858	+	0.996374i	$0.472884\pi$
$360$	−1.09177	−0.0575416
$361$	35.2788	1.85678
$362$	−51.6710	−2.71577
$363$	−8.43035	−0.442479
$364$	−9.41223	−0.493335
$365$	5.52316	0.289096
$366$	24.0860	1.25900
$367$	11.0033	0.574366	0.287183	−	0.957876i	$-0.407281\pi$
$367$	11.0033	0.574366	0.287183	+	0.957876i	$0.407281\pi$
$368$	8.50136	0.443164
$369$	3.72554	0.193944
$370$	23.5267	1.22310
$371$	42.6659	2.21510
$372$	2.55417	0.132428
$373$	−5.13216	−0.265733	−0.132867	−	0.991134i	$-0.542418\pi$
$373$	−5.13216	−0.265733	−0.132867	+	0.991134i	$0.542418\pi$
$374$	74.5027	3.85244
$375$	−1.00000	−0.0516398
$376$	11.0857	0.571704
$377$	7.04172	0.362667
$378$	7.86839	0.404706
$379$	25.8528	1.32797	0.663985	−	0.747746i	$-0.268864\pi$
$379$	25.8528	1.32797	0.663985	+	0.747746i	$0.268864\pi$
$380$	−18.5208	−0.950095
$381$	−12.4857	−0.639664
$382$	11.1560	0.570790
$383$	5.23835	0.267667	0.133834	−	0.991004i	$-0.457271\pi$
$383$	5.23835	0.267667	0.133834	+	0.991004i	$0.457271\pi$
$384$	−8.44589	−0.431003
$385$	−16.3249	−0.831996
$386$	19.2005	0.977277
$387$	−12.4670	−0.633732
$388$	10.1655	0.516074
$389$	−9.80769	−0.497270	−0.248635	−	0.968597i	$-0.579982\pi$
$389$	−9.80769	−0.497270	−0.248635	+	0.968597i	$0.579982\pi$
$390$	−2.14789	−0.108763
$391$	−24.9729	−1.26293
$392$	−7.33217	−0.370331
$393$	−19.6296	−0.990182
$394$	4.52206	0.227818
$395$	−0.0462182	−0.00232549
$396$	−11.0811	−0.556848
$397$	−30.1416	−1.51276	−0.756382	−	0.654130i	$-0.773035\pi$
$397$	−30.1416	−1.51276	−0.756382	+	0.654130i	$0.773035\pi$
$398$	37.3768	1.87353
$399$	27.2851	1.36597
$400$	−2.70818	−0.135409
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−14.2801	−0.712226
$403$	1.02717	0.0511672
$404$	8.02083	0.399051
$405$	1.00000	0.0496904
$406$	54.8059	2.71997
$407$	48.8121	2.41952
$408$	8.68540	0.429992
$409$	−4.65898	−0.230372	−0.115186	−	0.993344i	$-0.536746\pi$
$409$	−4.65898	−0.230372	−0.115186	+	0.993344i	$0.536746\pi$
$410$	−7.91524	−0.390906
$411$	−11.0991	−0.547480
$412$	8.07979	0.398062
$413$	−25.9013	−1.27452
$414$	6.66939	0.327782
$415$	12.4234	0.609840
$416$	−8.02438	−0.393427
$417$	0.787115	0.0385452
$418$	−68.9970	−3.37475
$419$	−21.1774	−1.03458	−0.517291	−	0.855810i	$-0.673059\pi$
$419$	−21.1774	−1.03458	−0.517291	+	0.855810i	$0.673059\pi$
$420$	−9.31011	−0.454287
$421$	−8.65752	−0.421942	−0.210971	−	0.977492i	$-0.567663\pi$
$421$	−8.65752	−0.421942	−0.210971	+	0.977492i	$0.567663\pi$
$422$	−38.1355	−1.85641
$423$	−10.1539	−0.493698
$424$	−12.5777	−0.610829
$425$	7.95531	0.385889
$426$	30.6496	1.48498
$427$	41.9857	2.03183
$428$	−4.32060	−0.208844
$429$	−4.45634	−0.215154
$430$	26.4872	1.27733
$431$	12.4447	0.599440	0.299720	−	0.954027i	$-0.403107\pi$
$431$	12.4447	0.599440	0.299720	+	0.954027i	$0.403107\pi$
$432$	2.70818	0.130297
$433$	−5.56777	−0.267570	−0.133785	−	0.991010i	$-0.542713\pi$
$433$	−5.56777	−0.267570	−0.133785	+	0.991010i	$0.542713\pi$
$434$	7.99452	0.383749
$435$	6.96532	0.333962
$436$	25.7697	1.23414
$437$	23.1274	1.10633
$438$	11.7344	0.560693
$439$	−6.65749	−0.317745	−0.158872	−	0.987299i	$-0.550786\pi$
$439$	−6.65749	−0.317745	−0.158872	+	0.987299i	$0.550786\pi$
$440$	4.81253	0.229428
$441$	6.71583	0.319801
$442$	17.0871	0.812752
$443$	40.7392	1.93558	0.967789	−	0.251761i	$-0.0810096\pi$
$443$	40.7392	1.93558	0.967789	+	0.251761i	$0.0810096\pi$
$444$	27.8375	1.32111
$445$	11.8647	0.562441
$446$	−48.9577	−2.31822
$447$	−14.3108	−0.676875
$448$	−42.3945	−2.00295
$449$	0.0851195	0.00401704	0.00200852	−	0.999998i	$-0.499361\pi$
$449$	0.0851195	0.00401704	0.00200852	+	0.999998i	$0.499361\pi$
$450$	−2.12459	−0.100154
$451$	−16.4221	−0.773288
$452$	49.1396	2.31133
$453$	14.2968	0.671724
$454$	9.17542	0.430624
$455$	−3.74411	−0.175527
$456$	−8.04355	−0.376674
$457$	−18.2475	−0.853581	−0.426791	−	0.904350i	$-0.640356\pi$
$457$	−18.2475	−0.853581	−0.426791	+	0.904350i	$0.640356\pi$
$458$	55.2151	2.58003
$459$	−7.95531	−0.371322
$460$	−7.89142	−0.367939
$461$	35.5103	1.65388	0.826940	−	0.562290i	$-0.190080\pi$
$461$	35.5103	1.65388	0.826940	+	0.562290i	$0.190080\pi$
$462$	−34.6838	−1.61363
$463$	−6.84512	−0.318120	−0.159060	−	0.987269i	$-0.550846\pi$
$463$	−6.84512	−0.318120	−0.159060	+	0.987269i	$0.550846\pi$
$464$	18.8633	0.875709
$465$	1.01603	0.0471173
$466$	47.0122	2.17780
$467$	−5.25269	−0.243066	−0.121533	−	0.992587i	$-0.538781\pi$
$467$	−5.25269	−0.243066	−0.121533	+	0.992587i	$0.538781\pi$
$468$	−2.54145	−0.117479
$469$	−24.8924	−1.14942
$470$	21.5728	0.995079
$471$	−15.0071	−0.691492
$472$	7.63562	0.351458
$473$	54.9543	2.52680
$474$	−0.0981946	−0.00451023
$475$	−7.36741	−0.338040
$476$	74.0648	3.39475
$477$	11.5205	0.527485
$478$	−31.5865	−1.44473
$479$	−8.99312	−0.410906	−0.205453	−	0.978667i	$-0.565867\pi$
$479$	−8.99312	−0.410906	−0.205453	+	0.978667i	$0.565867\pi$
$480$	−7.93732	−0.362287
$481$	11.1950	0.510448
$482$	−37.6246	−1.71375
$483$	11.6258	0.528991
$484$	21.1929	0.963312
$485$	4.04374	0.183617
$486$	2.12459	0.0963733
$487$	19.2951	0.874342	0.437171	−	0.899378i	$-0.355980\pi$
$487$	19.2951	0.874342	0.437171	+	0.899378i	$0.355980\pi$
$488$	−12.3772	−0.560290
$489$	−16.0762	−0.726990
$490$	−14.2684	−0.644579
$491$	−7.59531	−0.342772	−0.171386	−	0.985204i	$-0.554824\pi$
$491$	−7.59531	−0.342772	−0.171386	+	0.985204i	$0.554824\pi$
$492$	−9.36555	−0.422231
$493$	−55.4113	−2.49560
$494$	−15.8244	−0.711974
$495$	−4.40799	−0.198124
$496$	2.75159	0.123550
$497$	53.4270	2.39653
$498$	26.3946	1.18277
$499$	−6.47896	−0.290038	−0.145019	−	0.989429i	$-0.546324\pi$
$499$	−6.47896	−0.290038	−0.145019	+	0.989429i	$0.546324\pi$
$500$	2.51388	0.112424
$501$	12.4663	0.556952
$502$	−7.89429	−0.352339
$503$	17.5674	0.783290	0.391645	−	0.920116i	$-0.371906\pi$
$503$	17.5674	0.783290	0.391645	+	0.920116i	$0.371906\pi$
$504$	−4.04338	−0.180106
$505$	3.19062	0.141981
$506$	−29.3986	−1.30693
$507$	11.9779	0.531959
$508$	31.3876	1.39260
$509$	−6.98536	−0.309621	−0.154810	−	0.987944i	$-0.549477\pi$
$509$	−6.98536	−0.309621	−0.154810	+	0.987944i	$0.549477\pi$
$510$	16.9018	0.748422
$511$	20.4550	0.904875
$512$	−27.4091	−1.21132
$513$	7.36741	0.325279
$514$	28.8324	1.27174
$515$	3.21407	0.141629
$516$	31.3404	1.37969
$517$	44.7581	1.96846
$518$	87.1310	3.82832
$519$	16.9376	0.743477
$520$	1.10375	0.0484026
$521$	18.0966	0.792827	0.396413	−	0.918072i	$-0.370255\pi$
$521$	18.0966	0.792827	0.396413	+	0.918072i	$0.370255\pi$
$522$	14.7984	0.647710
$523$	5.93579	0.259554	0.129777	−	0.991543i	$-0.458574\pi$
$523$	5.93579	0.259554	0.129777	+	0.991543i	$0.458574\pi$
$524$	49.3464	2.15571
$525$	−3.70349	−0.161634
$526$	1.24093	0.0541070
$527$	−8.08283	−0.352094
$528$	−11.9376	−0.519518
$529$	−13.1458	−0.571556
$530$	−24.4762	−1.06318
$531$	−6.99377	−0.303504
$532$	−68.5914	−2.97382
$533$	−3.76640	−0.163141
$534$	25.2076	1.09084
$535$	−1.71870	−0.0743059
$536$	7.33819	0.316962
$537$	−4.04509	−0.174559
$538$	−19.7541	−0.851660
$539$	−29.6033	−1.27510
$540$	−2.51388	−0.108180
$541$	−32.8550	−1.41255	−0.706273	−	0.707940i	$-0.749625\pi$
$541$	−32.8550	−1.41255	−0.706273	+	0.707940i	$0.749625\pi$
$542$	18.8770	0.810836
$543$	−24.3205	−1.04369
$544$	63.1438	2.70727
$545$	10.2510	0.439103
$546$	−7.95469	−0.340429
$547$	−17.7990	−0.761031	−0.380515	−	0.924775i	$-0.624253\pi$
$547$	−17.7990	−0.761031	−0.380515	+	0.924775i	$0.624253\pi$
$548$	27.9018	1.19191
$549$	11.3368	0.483842
$550$	9.36516	0.399332
$551$	51.3164	2.18615
$552$	−3.42724	−0.145873
$553$	−0.171168	−0.00727882
$554$	−13.9871	−0.594254
$555$	11.0735	0.470046
$556$	−1.97871	−0.0839159
$557$	14.1851	0.601044	0.300522	−	0.953775i	$-0.402839\pi$
$557$	14.1851	0.601044	0.300522	+	0.953775i	$0.402839\pi$
$558$	2.15865	0.0913828
$559$	12.6037	0.533081
$560$	−10.0297	−0.423833
$561$	35.0669	1.48053
$562$	−46.2984	−1.95298
$563$	3.21626	0.135549	0.0677746	−	0.997701i	$-0.478410\pi$
$563$	3.21626	0.135549	0.0677746	+	0.997701i	$0.478410\pi$
$564$	25.5256	1.07482
$565$	19.5474	0.822363
$566$	12.9377	0.543813
$567$	3.70349	0.155532
$568$	−15.7501	−0.660858
$569$	20.9566	0.878547	0.439274	−	0.898353i	$-0.355236\pi$
$569$	20.9566	0.878547	0.439274	+	0.898353i	$0.355236\pi$
$570$	−15.6527	−0.655620
$571$	−18.6948	−0.782351	−0.391176	−	0.920316i	$-0.627931\pi$
$571$	−18.6948	−0.782351	−0.391176	+	0.920316i	$0.627931\pi$
$572$	11.2027	0.468407
$573$	5.25089	0.219359
$574$	−29.3140	−1.22354
$575$	−3.13914	−0.130911
$576$	−11.4472	−0.476965
$577$	35.6601	1.48455	0.742274	−	0.670096i	$-0.233747\pi$
$577$	35.6601	1.48455	0.742274	+	0.670096i	$0.233747\pi$
$578$	−98.3407	−4.09043
$579$	9.03726	0.375576
$580$	−17.5100	−0.727061
$581$	46.0098	1.90881
$582$	8.59129	0.356121
$583$	−50.7820	−2.10318
$584$	−6.03005	−0.249525
$585$	−1.01097	−0.0417984
$586$	−33.7296	−1.39336
$587$	−41.4732	−1.71178	−0.855890	−	0.517157i	$-0.826990\pi$
$587$	−41.4732	−1.71178	−0.855890	+	0.517157i	$0.826990\pi$
$588$	−16.8828	−0.696233
$589$	7.48551	0.308435
$590$	14.8589	0.611730
$591$	2.12844	0.0875523
$592$	29.9892	1.23255
$593$	−38.9160	−1.59809	−0.799044	−	0.601272i	$-0.794661\pi$
$593$	−38.9160	−1.59809	−0.799044	+	0.601272i	$0.794661\pi$
$594$	−9.36516	−0.384257
$595$	29.4624	1.20784
$596$	35.9755	1.47361
$597$	17.5925	0.720012
$598$	−6.74254	−0.275723
$599$	25.3317	1.03503	0.517513	−	0.855675i	$-0.326858\pi$
$599$	25.3317	1.03503	0.517513	+	0.855675i	$0.326858\pi$
$600$	1.09177	0.0445715
$601$	13.7605	0.561301	0.280650	−	0.959810i	$-0.409450\pi$
$601$	13.7605	0.561301	0.280650	+	0.959810i	$0.409450\pi$
$602$	98.0950	3.99806
$603$	−6.72134	−0.273714
$604$	−35.9405	−1.46240
$605$	8.43035	0.342742
$606$	6.77876	0.275368
$607$	−12.5263	−0.508429	−0.254214	−	0.967148i	$-0.581817\pi$
$607$	−12.5263	−0.508429	−0.254214	+	0.967148i	$0.581817\pi$
$608$	−58.4775	−2.37158
$609$	25.7960	1.04531
$610$	−24.0860	−0.975214
$611$	10.2652	0.415287
$612$	19.9987	0.808398
$613$	−17.4589	−0.705157	−0.352578	−	0.935782i	$-0.614695\pi$
$613$	−17.4589	−0.705157	−0.352578	+	0.935782i	$0.614695\pi$
$614$	−61.1990	−2.46979
$615$	−3.72554	−0.150228
$616$	17.8231	0.718115
$617$	−8.19777	−0.330030	−0.165015	−	0.986291i	$-0.552767\pi$
$617$	−8.19777	−0.330030	−0.165015	+	0.986291i	$0.552767\pi$
$618$	6.82859	0.274686
$619$	−1.24931	−0.0502139	−0.0251070	−	0.999685i	$-0.507993\pi$
$619$	−1.24931	−0.0502139	−0.0251070	+	0.999685i	$0.507993\pi$
$620$	−2.55417	−0.102578
$621$	3.13914	0.125969
$622$	−19.2944	−0.773635
$623$	43.9408	1.76045
$624$	−2.73788	−0.109603
$625$	1.00000	0.0400000
$626$	−20.0791	−0.802522
$627$	−32.4755	−1.29694
$628$	37.7261	1.50543
$629$	−88.0935	−3.51252
$630$	−7.86839	−0.313484
$631$	−31.8322	−1.26722	−0.633610	−	0.773653i	$-0.718428\pi$
$631$	−31.8322	−1.26722	−0.633610	+	0.773653i	$0.718428\pi$
$632$	0.0504598	0.00200718
$633$	−17.9496	−0.713433
$634$	−9.85483	−0.391385
$635$	12.4857	0.495482
$636$	−28.9610	−1.14838
$637$	−6.78949	−0.269009
$638$	−65.2313	−2.58253
$639$	14.4261	0.570688
$640$	8.44589	0.333853
$641$	5.33212	0.210606	0.105303	−	0.994440i	$-0.466419\pi$
$641$	5.33212	0.210606	0.105303	+	0.994440i	$0.466419\pi$
$642$	−3.65153	−0.144115
$643$	29.8019	1.17527	0.587636	−	0.809125i	$-0.300059\pi$
$643$	29.8019	1.17527	0.587636	+	0.809125i	$0.300059\pi$
$644$	−29.2258	−1.15166
$645$	12.4670	0.490887
$646$	124.522	4.89926
$647$	−3.19259	−0.125514	−0.0627569	−	0.998029i	$-0.519989\pi$
$647$	−3.19259	−0.125514	−0.0627569	+	0.998029i	$0.519989\pi$
$648$	−1.09177	−0.0428890
$649$	30.8284	1.21012
$650$	2.14789	0.0842473
$651$	3.76286	0.147478
$652$	40.4135	1.58271
$653$	30.9005	1.20923	0.604615	−	0.796518i	$-0.293327\pi$
$653$	30.9005	1.20923	0.604615	+	0.796518i	$0.293327\pi$
$654$	21.7791	0.851630
$655$	19.6296	0.766992
$656$	−10.0894	−0.393926
$657$	5.52316	0.215479
$658$	79.8946	3.11462
$659$	14.6351	0.570102	0.285051	−	0.958512i	$-0.407989\pi$
$659$	14.6351	0.570102	0.285051	+	0.958512i	$0.407989\pi$
$660$	11.0811	0.431332
$661$	−16.3098	−0.634379	−0.317190	−	0.948362i	$-0.602739\pi$
$661$	−16.3098	−0.634379	−0.317190	+	0.948362i	$0.602739\pi$
$662$	−55.4880	−2.15660
$663$	8.04257	0.312347
$664$	−13.5635	−0.526367
$665$	−27.2851	−1.05807
$666$	23.5267	0.911642
$667$	21.8651	0.846621
$668$	−31.3387	−1.21253
$669$	−23.0434	−0.890909
$670$	14.2801	0.551688
$671$	−49.9724	−1.92916
$672$	−29.3958	−1.13397
$673$	−9.58673	−0.369541	−0.184771	−	0.982782i	$-0.559154\pi$
$673$	−9.58673	−0.369541	−0.184771	+	0.982782i	$0.559154\pi$
$674$	−4.53302	−0.174606
$675$	−1.00000	−0.0384900
$676$	−30.1111	−1.15812
$677$	45.2587	1.73943	0.869716	−	0.493553i	$-0.164302\pi$
$677$	45.2587	1.73943	0.869716	+	0.493553i	$0.164302\pi$
$678$	41.5301	1.59495
$679$	14.9760	0.574725
$680$	−8.68540	−0.333070
$681$	4.31868	0.165492
$682$	−9.51528	−0.364359
$683$	7.16086	0.274003	0.137001	−	0.990571i	$-0.456254\pi$
$683$	7.16086	0.274003	0.137001	+	0.990571i	$0.456254\pi$
$684$	−18.5208	−0.708159
$685$	11.0991	0.424076
$686$	2.23596	0.0853695
$687$	25.9886	0.991528
$688$	33.7628	1.28720
$689$	−11.6468	−0.443708
$690$	−6.66939	−0.253899
$691$	−14.2387	−0.541667	−0.270834	−	0.962626i	$-0.587299\pi$
$691$	−14.2387	−0.541667	−0.270834	+	0.962626i	$0.587299\pi$
$692$	−42.5790	−1.61861
$693$	−16.3249	−0.620133
$694$	−15.0094	−0.569749
$695$	−0.787115	−0.0298570
$696$	−7.60456	−0.288250
$697$	29.6378	1.12261
$698$	57.0536	2.15951
$699$	22.1277	0.836946
$700$	9.31011	0.351889
$701$	−11.2652	−0.425480	−0.212740	−	0.977109i	$-0.568239\pi$
$701$	−11.2652	−0.425480	−0.212740	+	0.977109i	$0.568239\pi$
$702$	−2.14789	−0.0810670
$703$	81.5834	3.07698
$704$	50.4590	1.90174
$705$	10.1539	0.382417
$706$	23.5215	0.885244
$707$	11.8164	0.444403
$708$	17.5815	0.660752
$709$	−8.39189	−0.315164	−0.157582	−	0.987506i	$-0.550370\pi$
$709$	−8.39189	−0.315164	−0.157582	+	0.987506i	$0.550370\pi$
$710$	−30.6496	−1.15026
$711$	−0.0462182	−0.00173332
$712$	−12.9536	−0.485456
$713$	3.18946	0.119446
$714$	62.5955	2.34258
$715$	4.45634	0.166658
$716$	10.1689	0.380028
$717$	−14.8671	−0.555222
$718$	−6.85030	−0.255651
$719$	9.73900	0.363203	0.181602	−	0.983372i	$-0.441872\pi$
$719$	9.73900	0.363203	0.181602	+	0.983372i	$0.441872\pi$
$720$	−2.70818	−0.100928
$721$	11.9033	0.443302
$722$	−74.9529	−2.78946
$723$	−17.7091	−0.658609
$724$	61.1386	2.27220
$725$	−6.96532	−0.258685
$726$	17.9110	0.664740
$727$	15.8787	0.588908	0.294454	−	0.955666i	$-0.404862\pi$
$727$	15.8787	0.588908	0.294454	+	0.955666i	$0.404862\pi$
$728$	4.08773	0.151501
$729$	1.00000	0.0370370
$730$	−11.7344	−0.434311
$731$	−99.1787	−3.66826
$732$	−28.4993	−1.05336
$733$	−32.3658	−1.19546	−0.597729	−	0.801698i	$-0.703930\pi$
$733$	−32.3658	−1.19546	−0.597729	+	0.801698i	$0.703930\pi$
$734$	−23.3774	−0.862877
$735$	−6.71583	−0.247717
$736$	−24.9164	−0.918430
$737$	29.6276	1.09135
$738$	−7.91524	−0.291364
$739$	8.34649	0.307030	0.153515	−	0.988146i	$-0.450941\pi$
$739$	8.34649	0.307030	0.153515	+	0.988146i	$0.450941\pi$
$740$	−27.8375	−1.02333
$741$	−7.44822	−0.273617
$742$	−90.6474	−3.32777
$743$	−4.79831	−0.176033	−0.0880165	−	0.996119i	$-0.528053\pi$
$743$	−4.79831	−0.176033	−0.0880165	+	0.996119i	$0.528053\pi$
$744$	−1.10928	−0.0406680
$745$	14.3108	0.524305
$746$	10.9037	0.399214
$747$	12.4234	0.454548
$748$	−88.1538	−3.22322
$749$	−6.36519	−0.232579
$750$	2.12459	0.0775790
$751$	−2.89659	−0.105698	−0.0528490	−	0.998603i	$-0.516830\pi$
$751$	−2.89659	−0.105698	−0.0528490	+	0.998603i	$0.516830\pi$
$752$	27.4985	1.00277
$753$	−3.71568	−0.135407
$754$	−14.9608	−0.544839
$755$	−14.2968	−0.520315
$756$	−9.31011	−0.338605
$757$	43.3959	1.57725	0.788625	−	0.614874i	$-0.210793\pi$
$757$	43.3959	1.57725	0.788625	+	0.614874i	$0.210793\pi$
$758$	−54.9266	−1.99502
$759$	−13.8373	−0.502262
$760$	8.04355	0.291770
$761$	−44.8306	−1.62511	−0.812554	−	0.582886i	$-0.801924\pi$
$761$	−44.8306	−1.62511	−0.812554	+	0.582886i	$0.801924\pi$
$762$	26.5271	0.960975
$763$	37.9643	1.37440
$764$	−13.2001	−0.477563
$765$	7.95531	0.287625
$766$	−11.1293	−0.402120
$767$	7.07048	0.255300
$768$	−4.95029	−0.178628
$769$	9.31220	0.335807	0.167903	−	0.985803i	$-0.446300\pi$
$769$	9.31220	0.335807	0.167903	+	0.985803i	$0.446300\pi$
$770$	34.6838	1.24992
$771$	13.5708	0.488741
$772$	−22.7185	−0.817658
$773$	23.4708	0.844188	0.422094	−	0.906552i	$-0.361295\pi$
$773$	23.4708	0.844188	0.422094	+	0.906552i	$0.361295\pi$
$774$	26.4872	0.952063
$775$	−1.01603	−0.0364969
$776$	−4.41486	−0.158484
$777$	41.0108	1.47125
$778$	20.8373	0.747053
$779$	−27.4476	−0.983412
$780$	2.54145	0.0909985
$781$	−63.5901	−2.27543
$782$	53.0570	1.89732
$783$	6.96532	0.248920
$784$	−18.1877	−0.649560
$785$	15.0071	0.535628
$786$	41.7048	1.48756
$787$	−9.00226	−0.320896	−0.160448	−	0.987044i	$-0.551294\pi$
$787$	−9.00226	−0.320896	−0.160448	+	0.987044i	$0.551294\pi$
$788$	−5.35063	−0.190608
$789$	0.584079	0.0207938
$790$	0.0981946	0.00349361
$791$	72.3934	2.57401
$792$	4.81253	0.171006
$793$	−11.4611	−0.406997
$794$	64.0385	2.27264
$795$	−11.5205	−0.408588
$796$	−44.2253	−1.56752
$797$	−42.7188	−1.51318	−0.756589	−	0.653891i	$-0.773135\pi$
$797$	−42.7188	−1.51318	−0.756589	+	0.653891i	$0.773135\pi$
$798$	−57.9697	−2.05210
$799$	−80.7772	−2.85769
$800$	7.93732	0.280627
$801$	11.8647	0.419219
$802$	2.12459	0.0750218
$803$	−24.3460	−0.859153
$804$	16.8966	0.595898
$805$	−11.6258	−0.409755
$806$	−2.18232	−0.0768690
$807$	−9.29786	−0.327300
$808$	−3.48344	−0.122547
$809$	30.9347	1.08761	0.543803	−	0.839213i	$-0.316984\pi$
$809$	30.9347	1.08761	0.543803	+	0.839213i	$0.316984\pi$
$810$	−2.12459	−0.0746504
$811$	6.87484	0.241408	0.120704	−	0.992689i	$-0.461485\pi$
$811$	6.87484	0.241408	0.120704	+	0.992689i	$0.461485\pi$
$812$	−64.8479	−2.27572
$813$	8.88500	0.311611
$814$	−103.706	−3.63488
$815$	16.0762	0.563124
$816$	21.5444	0.754205
$817$	91.8494	3.21340
$818$	9.89841	0.346090
$819$	−3.74411	−0.130830
$820$	9.36555	0.327059
$821$	10.5784	0.369189	0.184595	−	0.982815i	$-0.440903\pi$
$821$	10.5784	0.369189	0.184595	+	0.982815i	$0.440903\pi$
$822$	23.5811	0.822485
$823$	19.4601	0.678336	0.339168	−	0.940726i	$-0.389855\pi$
$823$	19.4601	0.678336	0.339168	+	0.940726i	$0.389855\pi$
$824$	−3.50905	−0.122243
$825$	4.40799	0.153466
$826$	55.0297	1.91473
$827$	−35.6149	−1.23845	−0.619226	−	0.785213i	$-0.712554\pi$
$827$	−35.6149	−1.23845	−0.619226	+	0.785213i	$0.712554\pi$
$828$	−7.89142	−0.274246
$829$	−53.7867	−1.86809	−0.934044	−	0.357158i	$-0.883746\pi$
$829$	−53.7867	−1.86809	−0.934044	+	0.357158i	$0.883746\pi$
$830$	−26.3946	−0.916169
$831$	−6.58343	−0.228377
$832$	11.5727	0.401212
$833$	53.4265	1.85112
$834$	−1.67229	−0.0579068
$835$	−12.4663	−0.431413
$836$	81.6393	2.82355
$837$	1.01603	0.0351191
$838$	44.9932	1.55426
$839$	−28.3632	−0.979206	−0.489603	−	0.871946i	$-0.662858\pi$
$839$	−28.3632	−0.979206	−0.489603	+	0.871946i	$0.662858\pi$
$840$	4.04338	0.139510
$841$	19.5157	0.672955
$842$	18.3937	0.633888
$843$	−21.7917	−0.750547
$844$	45.1231	1.55320
$845$	−11.9779	−0.412054
$846$	21.5728	0.741688
$847$	31.2217	1.07279
$848$	−31.1995	−1.07139
$849$	6.08952	0.208992
$850$	−16.9018	−0.579725
$851$	34.7615	1.19161
$852$	−36.2655	−1.24243
$853$	3.59687	0.123155	0.0615773	−	0.998102i	$-0.480387\pi$
$853$	3.59687	0.123155	0.0615773	+	0.998102i	$0.480387\pi$
$854$	−89.2023	−3.05244
$855$	−7.36741	−0.251960
$856$	1.87643	0.0641352
$857$	−48.5995	−1.66013	−0.830064	−	0.557668i	$-0.811696\pi$
$857$	−48.5995	−1.66013	−0.830064	+	0.557668i	$0.811696\pi$
$858$	9.46788	0.323228
$859$	35.1683	1.19993	0.599964	−	0.800027i	$-0.295182\pi$
$859$	35.1683	1.19993	0.599964	+	0.800027i	$0.295182\pi$
$860$	−31.3404	−1.06870
$861$	−13.7975	−0.470217
$862$	−26.4399	−0.900545
$863$	−48.7804	−1.66050	−0.830252	−	0.557388i	$-0.811804\pi$
$863$	−48.7804	−1.66050	−0.830252	+	0.557388i	$0.811804\pi$
$864$	−7.93732	−0.270033
$865$	−16.9376	−0.575895
$866$	11.8292	0.401973
$867$	−46.2869	−1.57199
$868$	−9.45935	−0.321071
$869$	0.203729	0.00691104
$870$	−14.7984	−0.501714
$871$	6.79507	0.230242
$872$	−11.1917	−0.379000
$873$	4.04374	0.136860
$874$	−49.1361	−1.66205
$875$	3.70349	0.125201
$876$	−13.8845	−0.469115
$877$	−12.5311	−0.423144	−0.211572	−	0.977362i	$-0.567858\pi$
$877$	−12.5311	−0.423144	−0.211572	+	0.977362i	$0.567858\pi$
$878$	14.1444	0.477351
$879$	−15.8758	−0.535479
$880$	11.9376	0.402417
$881$	10.8317	0.364930	0.182465	−	0.983212i	$-0.441592\pi$
$881$	10.8317	0.364930	0.182465	+	0.983212i	$0.441592\pi$
$882$	−14.2684	−0.480441
$883$	−10.2723	−0.345689	−0.172844	−	0.984949i	$-0.555296\pi$
$883$	−10.2723	−0.345689	−0.172844	+	0.984949i	$0.555296\pi$
$884$	−20.2180	−0.680005
$885$	6.99377	0.235093
$886$	−86.5541	−2.90784
$887$	−47.1262	−1.58234	−0.791171	−	0.611594i	$-0.790528\pi$
$887$	−47.1262	−1.58234	−0.791171	+	0.611594i	$0.790528\pi$
$888$	−12.0898	−0.405708
$889$	46.2408	1.55087
$890$	−25.2076	−0.844961
$891$	−4.40799	−0.147673
$892$	57.9282	1.93958
$893$	74.8078	2.50335
$894$	30.4045	1.01688
$895$	4.04509	0.135212
$896$	31.2793	1.04497
$897$	−3.17357	−0.105963
$898$	−0.180844	−0.00603484
$899$	7.07697	0.236030
$900$	2.51388	0.0837959
$901$	91.6488	3.05326
$902$	34.8903	1.16172
$903$	46.1713	1.53649
$904$	−21.3413	−0.709801
$905$	24.3205	0.808440
$906$	−30.3749	−1.00914
$907$	39.0198	1.29563	0.647816	−	0.761797i	$-0.275683\pi$
$907$	39.0198	1.29563	0.647816	+	0.761797i	$0.275683\pi$
$908$	−10.8566	−0.360290
$909$	3.19062	0.105826
$910$	7.95469	0.263696
$911$	−10.9389	−0.362423	−0.181211	−	0.983444i	$-0.558002\pi$
$911$	−10.9389	−0.362423	−0.181211	+	0.983444i	$0.558002\pi$
$912$	−19.9523	−0.660686
$913$	−54.7621	−1.81236
$914$	38.7684	1.28234
$915$	−11.3368	−0.374783
$916$	−65.3322	−2.15864
$917$	72.6980	2.40070
$918$	16.9018	0.557841
$919$	28.7381	0.947983	0.473992	−	0.880529i	$-0.342813\pi$
$919$	28.7381	0.947983	0.473992	+	0.880529i	$0.342813\pi$
$920$	3.42724	0.112993
$921$	−28.8051	−0.949160
$922$	−75.4448	−2.48464
$923$	−14.5843	−0.480050
$924$	41.0388	1.35008
$925$	−11.0735	−0.364096
$926$	14.5431	0.477915
$927$	3.21407	0.105564
$928$	−55.2860	−1.81485
$929$	−13.4986	−0.442875	−0.221437	−	0.975175i	$-0.571075\pi$
$929$	−13.4986	−0.442875	−0.221437	+	0.975175i	$0.571075\pi$
$930$	−2.15865	−0.0707848
$931$	−49.4783	−1.62159
$932$	−55.6262	−1.82210
$933$	−9.08148	−0.297314
$934$	11.1598	0.365160
$935$	−35.0669	−1.14681
$936$	1.10375	0.0360772
$937$	−31.3474	−1.02407	−0.512037	−	0.858963i	$-0.671109\pi$
$937$	−31.3474	−1.02407	−0.512037	+	0.858963i	$0.671109\pi$
$938$	52.8861	1.72679
$939$	−9.45082	−0.308416
$940$	−25.5256	−0.832553
$941$	39.7680	1.29640	0.648199	−	0.761471i	$-0.275522\pi$
$941$	39.7680	1.29640	0.648199	+	0.761471i	$0.275522\pi$
$942$	31.8840	1.03884
$943$	−11.6950	−0.380842
$944$	18.9404	0.616457
$945$	−3.70349	−0.120475
$946$	−116.755	−3.79604
$947$	0.0131603	0.000427653 0	0.000213827	−	1.00000i	$-0.499932\pi$
$947$	0.0131603	0.000427653 0	0.000213827		1.00000i	$0.499932\pi$
$948$	0.116187	0.00377357
$949$	−5.58374	−0.181256
$950$	15.6527	0.507841
$951$	−4.63846	−0.150412
$952$	−32.1663	−1.04252
$953$	30.3489	0.983097	0.491548	−	0.870850i	$-0.336431\pi$
$953$	30.3489	0.983097	0.491548	+	0.870850i	$0.336431\pi$
$954$	−24.4762	−0.792447
$955$	−5.25089	−0.169915
$956$	37.3741	1.20876
$957$	−30.7030	−0.992488
$958$	19.1067	0.617309
$959$	41.1055	1.32737
$960$	11.4472	0.369456
$961$	−29.9677	−0.966699
$962$	−23.7848	−0.766852
$963$	−1.71870	−0.0553844
$964$	44.5185	1.43385
$965$	−9.03726	−0.290920
$966$	−24.7000	−0.794709
$967$	16.5609	0.532563	0.266282	−	0.963895i	$-0.414205\pi$
$967$	16.5609	0.532563	0.266282	+	0.963895i	$0.414205\pi$
$968$	−9.20404	−0.295829
$969$	58.6100	1.88283
$970$	−8.59129	−0.275850
$971$	33.5152	1.07556	0.537778	−	0.843087i	$-0.319264\pi$
$971$	33.5152	1.07556	0.537778	+	0.843087i	$0.319264\pi$
$972$	−2.51388	−0.0806326
$973$	−2.91507	−0.0934529
$974$	−40.9940	−1.31353
$975$	1.01097	0.0323769
$976$	−30.7021	−0.982749
$977$	19.3364	0.618625	0.309313	−	0.950960i	$-0.399901\pi$
$977$	19.3364	0.618625	0.309313	+	0.950960i	$0.399901\pi$
$978$	34.1552	1.09216
$979$	−52.2995	−1.67150
$980$	16.8828	0.539300
$981$	10.2510	0.327288
$982$	16.1369	0.514950
$983$	8.45776	0.269761	0.134880	−	0.990862i	$-0.456935\pi$
$983$	8.45776	0.269761	0.134880	+	0.990862i	$0.456935\pi$
$984$	4.06745	0.129666
$985$	−2.12844	−0.0678177
$986$	117.726	3.74916
$987$	37.6048	1.19697
$988$	18.7239	0.595687
$989$	39.1356	1.24444
$990$	9.36516	0.297644
$991$	4.65123	0.147751	0.0738756	−	0.997267i	$-0.476463\pi$
$991$	4.65123	0.147751	0.0738756	+	0.997267i	$0.476463\pi$
$992$	−8.06455	−0.256050
$993$	−26.1170	−0.828799
$994$	−113.510	−3.60033
$995$	−17.5925	−0.557719
$996$	−31.2308	−0.989587
$997$	2.88570	0.0913910	0.0456955	−	0.998955i	$-0.485450\pi$
$997$	2.88570	0.0913910	0.0456955	+	0.998955i	$0.485450\pi$
$998$	13.7651	0.435728
$999$	11.0735	0.350352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.g.1.6	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.g.1.6	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12459 q^{2} -1.00000 q^{3} +2.51388 q^{4} +1.00000 q^{5} +2.12459 q^{6} +3.70349 q^{7} -1.09177 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.12459 q^{2} -1.00000 q^{3} +2.51388 q^{4} +1.00000 q^{5} +2.12459 q^{6} +3.70349 q^{7} -1.09177 q^{8} +1.00000 q^{9} -2.12459 q^{10} -4.40799 q^{11} -2.51388 q^{12} -1.01097 q^{13} -7.86839 q^{14} -1.00000 q^{15} -2.70818 q^{16} +7.95531 q^{17} -2.12459 q^{18} -7.36741 q^{19} +2.51388 q^{20} -3.70349 q^{21} +9.36516 q^{22} -3.13914 q^{23} +1.09177 q^{24} +1.00000 q^{25} +2.14789 q^{26} -1.00000 q^{27} +9.31011 q^{28} -6.96532 q^{29} +2.12459 q^{30} -1.01603 q^{31} +7.93732 q^{32} +4.40799 q^{33} -16.9018 q^{34} +3.70349 q^{35} +2.51388 q^{36} -11.0735 q^{37} +15.6527 q^{38} +1.01097 q^{39} -1.09177 q^{40} +3.72554 q^{41} +7.86839 q^{42} -12.4670 q^{43} -11.0811 q^{44} +1.00000 q^{45} +6.66939 q^{46} -10.1539 q^{47} +2.70818 q^{48} +6.71583 q^{49} -2.12459 q^{50} -7.95531 q^{51} -2.54145 q^{52} +11.5205 q^{53} +2.12459 q^{54} -4.40799 q^{55} -4.04338 q^{56} +7.36741 q^{57} +14.7984 q^{58} -6.99377 q^{59} -2.51388 q^{60} +11.3368 q^{61} +2.15865 q^{62} +3.70349 q^{63} -11.4472 q^{64} -1.01097 q^{65} -9.36516 q^{66} -6.72134 q^{67} +19.9987 q^{68} +3.13914 q^{69} -7.86839 q^{70} +14.4261 q^{71} -1.09177 q^{72} +5.52316 q^{73} +23.5267 q^{74} -1.00000 q^{75} -18.5208 q^{76} -16.3249 q^{77} -2.14789 q^{78} -0.0462182 q^{79} -2.70818 q^{80} +1.00000 q^{81} -7.91524 q^{82} +12.4234 q^{83} -9.31011 q^{84} +7.95531 q^{85} +26.4872 q^{86} +6.96532 q^{87} +4.81253 q^{88} +11.8647 q^{89} -2.12459 q^{90} -3.74411 q^{91} -7.89142 q^{92} +1.01603 q^{93} +21.5728 q^{94} -7.36741 q^{95} -7.93732 q^{96} +4.04374 q^{97} -14.2684 q^{98} -4.40799 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * q^99

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