LMFDB - Embedded newform 6041.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58676 q^{2} -0.792673 q^{3} +4.69133 q^{4} +0.0189688 q^{5} +2.05046 q^{6} +1.00000 q^{7} -6.96183 q^{8} -2.37167 q^{9} +O(q^{10})$	\(q-2.58676 q^{2} -0.792673 q^{3} +4.69133 q^{4} +0.0189688 q^{5} +2.05046 q^{6} +1.00000 q^{7} -6.96183 q^{8} -2.37167 q^{9} -0.0490676 q^{10} +1.90691 q^{11} -3.71869 q^{12} +1.13142 q^{13} -2.58676 q^{14} -0.0150360 q^{15} +8.62593 q^{16} +4.67946 q^{17} +6.13494 q^{18} +6.17467 q^{19} +0.0889887 q^{20} -0.792673 q^{21} -4.93272 q^{22} -0.672030 q^{23} +5.51846 q^{24} -4.99964 q^{25} -2.92672 q^{26} +4.25798 q^{27} +4.69133 q^{28} +0.916635 q^{29} +0.0388946 q^{30} -9.79033 q^{31} -8.38956 q^{32} -1.51156 q^{33} -12.1046 q^{34} +0.0189688 q^{35} -11.1263 q^{36} -8.85609 q^{37} -15.9724 q^{38} -0.896849 q^{39} -0.132057 q^{40} -3.12450 q^{41} +2.05046 q^{42} +3.27588 q^{43} +8.94595 q^{44} -0.0449876 q^{45} +1.73838 q^{46} +2.88149 q^{47} -6.83755 q^{48} +1.00000 q^{49} +12.9329 q^{50} -3.70928 q^{51} +5.30788 q^{52} -7.10418 q^{53} -11.0144 q^{54} +0.0361717 q^{55} -6.96183 q^{56} -4.89450 q^{57} -2.37112 q^{58} -1.02691 q^{59} -0.0705390 q^{60} -6.18790 q^{61} +25.3252 q^{62} -2.37167 q^{63} +4.44991 q^{64} +0.0214617 q^{65} +3.91004 q^{66} +10.7732 q^{67} +21.9529 q^{68} +0.532700 q^{69} -0.0490676 q^{70} +15.3073 q^{71} +16.5112 q^{72} -14.0770 q^{73} +22.9086 q^{74} +3.96308 q^{75} +28.9674 q^{76} +1.90691 q^{77} +2.31993 q^{78} -9.04102 q^{79} +0.163623 q^{80} +3.73982 q^{81} +8.08235 q^{82} -1.75149 q^{83} -3.71869 q^{84} +0.0887635 q^{85} -8.47391 q^{86} -0.726592 q^{87} -13.2756 q^{88} +2.29165 q^{89} +0.116372 q^{90} +1.13142 q^{91} -3.15272 q^{92} +7.76053 q^{93} -7.45373 q^{94} +0.117126 q^{95} +6.65018 q^{96} -6.20466 q^{97} -2.58676 q^{98} -4.52256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * 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 $

$2$	−2.58676	−1.82912	−0.914558	−	0.404455i	$-0.867461\pi$
$2$	−2.58676	−1.82912	−0.914558	+	0.404455i	$0.867461\pi$
$3$	−0.792673	−0.457650	−0.228825	−	0.973468i	$-0.573488\pi$
$3$	−0.792673	−0.457650	−0.228825	+	0.973468i	$0.573488\pi$
$4$	4.69133	2.34567
$5$	0.0189688	0.00848308	0.00424154	−	0.999991i	$-0.498650\pi$
$5$	0.0189688	0.00848308	0.00424154	+	0.999991i	$0.498650\pi$
$6$	2.05046	0.837095
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−6.96183	−2.46138
$9$	−2.37167	−0.790556
$10$	−0.0490676	−0.0155165
$11$	1.90691	0.574955	0.287478	−	0.957787i	$-0.407183\pi$
$11$	1.90691	0.574955	0.287478	+	0.957787i	$0.407183\pi$
$12$	−3.71869	−1.07349
$13$	1.13142	0.313800	0.156900	−	0.987614i	$-0.449850\pi$
$13$	1.13142	0.313800	0.156900	+	0.987614i	$0.449850\pi$
$14$	−2.58676	−0.691341
$15$	−0.0150360	−0.00388229
$16$	8.62593	2.15648
$17$	4.67946	1.13494	0.567468	−	0.823396i	$-0.307923\pi$
$17$	4.67946	1.13494	0.567468	+	0.823396i	$0.307923\pi$
$18$	6.13494	1.44602
$19$	6.17467	1.41657	0.708283	−	0.705928i	$-0.249470\pi$
$19$	6.17467	1.41657	0.708283	+	0.705928i	$0.249470\pi$
$20$	0.0889887	0.0198985
$21$	−0.792673	−0.172976
$22$	−4.93272	−1.05166
$23$	−0.672030	−0.140128	−0.0700640	−	0.997543i	$-0.522320\pi$
$23$	−0.672030	−0.140128	−0.0700640	+	0.997543i	$0.522320\pi$
$24$	5.51846	1.12645
$25$	−4.99964	−0.999928
$26$	−2.92672	−0.573977
$27$	4.25798	0.819449
$28$	4.69133	0.886578
$29$	0.916635	0.170215	0.0851074	−	0.996372i	$-0.472877\pi$
$29$	0.916635	0.170215	0.0851074	+	0.996372i	$0.472877\pi$
$30$	0.0388946	0.00710115
$31$	−9.79033	−1.75839	−0.879197	−	0.476458i	$-0.841920\pi$
$31$	−9.79033	−1.75839	−0.879197	+	0.476458i	$0.841920\pi$
$32$	−8.38956	−1.48308
$33$	−1.51156	−0.263129
$34$	−12.1046	−2.07593
$35$	0.0189688	0.00320630
$36$	−11.1263	−1.85438
$37$	−8.85609	−1.45593	−0.727966	−	0.685613i	$-0.759534\pi$
$37$	−8.85609	−1.45593	−0.727966	+	0.685613i	$0.759534\pi$
$38$	−15.9724	−2.59106
$39$	−0.896849	−0.143611
$40$	−0.132057	−0.0208801
$41$	−3.12450	−0.487966	−0.243983	−	0.969780i	$-0.578454\pi$
$41$	−3.12450	−0.487966	−0.243983	+	0.969780i	$0.578454\pi$
$42$	2.05046	0.316392
$43$	3.27588	0.499567	0.249783	−	0.968302i	$-0.419641\pi$
$43$	3.27588	0.499567	0.249783	+	0.968302i	$0.419641\pi$
$44$	8.94595	1.34865
$45$	−0.0449876	−0.00670636
$46$	1.73838	0.256310
$47$	2.88149	0.420309	0.210154	−	0.977668i	$-0.432603\pi$
$47$	2.88149	0.420309	0.210154	+	0.977668i	$0.432603\pi$
$48$	−6.83755	−0.986915
$49$	1.00000	0.142857
$50$	12.9329	1.82898
$51$	−3.70928	−0.519403
$52$	5.30788	0.736070
$53$	−7.10418	−0.975834	−0.487917	−	0.872890i	$-0.662243\pi$
$53$	−7.10418	−0.975834	−0.487917	+	0.872890i	$0.662243\pi$
$54$	−11.0144	−1.49887
$55$	0.0361717	0.00487740
$56$	−6.96183	−0.930314
$57$	−4.89450	−0.648292
$58$	−2.37112	−0.311343
$59$	−1.02691	−0.133693	−0.0668463	−	0.997763i	$-0.521294\pi$
$59$	−1.02691	−0.133693	−0.0668463	+	0.997763i	$0.521294\pi$
$60$	−0.0705390	−0.00910654
$61$	−6.18790	−0.792279	−0.396140	−	0.918190i	$-0.629650\pi$
$61$	−6.18790	−0.792279	−0.396140	+	0.918190i	$0.629650\pi$
$62$	25.3252	3.21631
$63$	−2.37167	−0.298802
$64$	4.44991	0.556239
$65$	0.0214617	0.00266199
$66$	3.91004	0.481293
$67$	10.7732	1.31615	0.658077	−	0.752951i	$-0.271370\pi$
$67$	10.7732	1.31615	0.658077	+	0.752951i	$0.271370\pi$
$68$	21.9529	2.66218
$69$	0.532700	0.0641296
$70$	−0.0490676	−0.00586470
$71$	15.3073	1.81664	0.908322	−	0.418271i	$-0.137364\pi$
$71$	15.3073	1.81664	0.908322	+	0.418271i	$0.137364\pi$
$72$	16.5112	1.94586
$73$	−14.0770	−1.64759	−0.823797	−	0.566885i	$-0.808148\pi$
$73$	−14.0770	−1.64759	−0.823797	+	0.566885i	$0.808148\pi$
$74$	22.9086	2.66307
$75$	3.96308	0.457617
$76$	28.9674	3.32279
$77$	1.90691	0.217313
$78$	2.31993	0.262681
$79$	−9.04102	−1.01719	−0.508597	−	0.861005i	$-0.669836\pi$
$79$	−9.04102	−1.01719	−0.508597	+	0.861005i	$0.669836\pi$
$80$	0.163623	0.0182936
$81$	3.73982	0.415535
$82$	8.08235	0.892546
$83$	−1.75149	−0.192251	−0.0961255	−	0.995369i	$-0.530645\pi$
$83$	−1.75149	−0.192251	−0.0961255	+	0.995369i	$0.530645\pi$
$84$	−3.71869	−0.405743
$85$	0.0887635	0.00962775
$86$	−8.47391	−0.913765
$87$	−0.726592	−0.0778989
$88$	−13.2756	−1.41518
$89$	2.29165	0.242914	0.121457	−	0.992597i	$-0.461243\pi$
$89$	2.29165	0.242914	0.121457	+	0.992597i	$0.461243\pi$
$90$	0.116372	0.0122667
$91$	1.13142	0.118605
$92$	−3.15272	−0.328693
$93$	7.76053	0.804730
$94$	−7.45373	−0.768793
$95$	0.117126	0.0120169
$96$	6.65018	0.678731
$97$	−6.20466	−0.629988	−0.314994	−	0.949094i	$-0.602002\pi$
$97$	−6.20466	−0.629988	−0.314994	+	0.949094i	$0.602002\pi$
$98$	−2.58676	−0.261302
$99$	−4.52256	−0.454535
$100$	−23.4550	−2.34550
$101$	1.25137	0.124516	0.0622579	−	0.998060i	$-0.480170\pi$
$101$	1.25137	0.124516	0.0622579	+	0.998060i	$0.480170\pi$
$102$	9.59503	0.950049
$103$	−2.90342	−0.286082	−0.143041	−	0.989717i	$-0.545688\pi$
$103$	−2.90342	−0.286082	−0.143041	+	0.989717i	$0.545688\pi$
$104$	−7.87677	−0.772381
$105$	−0.0150360	−0.00146737
$106$	18.3768	1.78491
$107$	−17.2346	−1.66613	−0.833067	−	0.553171i	$-0.813417\pi$
$107$	−17.2346	−1.66613	−0.833067	+	0.553171i	$0.813417\pi$
$108$	19.9756	1.92215
$109$	−12.7363	−1.21991	−0.609957	−	0.792435i	$-0.708813\pi$
$109$	−12.7363	−1.21991	−0.609957	+	0.792435i	$0.708813\pi$
$110$	−0.0935676	−0.00892132
$111$	7.01999	0.666308
$112$	8.62593	0.815074
$113$	16.5837	1.56006	0.780030	−	0.625743i	$-0.215204\pi$
$113$	16.5837	1.56006	0.780030	+	0.625743i	$0.215204\pi$
$114$	12.6609	1.18580
$115$	−0.0127476	−0.00118872
$116$	4.30024	0.399267
$117$	−2.68336	−0.248077
$118$	2.65638	0.244539
$119$	4.67946	0.428965
$120$	0.104678	0.00955578
$121$	−7.36369	−0.669426
$122$	16.0066	1.44917
$123$	2.47671	0.223318
$124$	−45.9297	−4.12461
$125$	−0.189681	−0.0169656
$126$	6.13494	0.546544
$127$	4.04878	0.359271	0.179636	−	0.983733i	$-0.442508\pi$
$127$	4.04878	0.359271	0.179636	+	0.983733i	$0.442508\pi$
$128$	5.26825	0.465652
$129$	−2.59670	−0.228627
$130$	−0.0555162	−0.00486910
$131$	−11.2173	−0.980063	−0.490031	−	0.871705i	$-0.663015\pi$
$131$	−11.2173	−0.980063	−0.490031	+	0.871705i	$0.663015\pi$
$132$	−7.09122	−0.617212
$133$	6.17467	0.535412
$134$	−27.8677	−2.40740
$135$	0.0807686	0.00695145
$136$	−32.5776	−2.79351
$137$	3.94322	0.336892	0.168446	−	0.985711i	$-0.446125\pi$
$137$	3.94322	0.336892	0.168446	+	0.985711i	$0.446125\pi$
$138$	−1.37797	−0.117300
$139$	1.28385	0.108894	0.0544472	−	0.998517i	$-0.482660\pi$
$139$	1.28385	0.108894	0.0544472	+	0.998517i	$0.482660\pi$
$140$	0.0889887	0.00752092
$141$	−2.28408	−0.192354
$142$	−39.5964	−3.32285
$143$	2.15752	0.180421
$144$	−20.4579	−1.70482
$145$	0.0173874	0.00144395
$146$	36.4139	3.01364
$147$	−0.792673	−0.0653786
$148$	−41.5469	−3.41513
$149$	−11.0158	−0.902453	−0.451226	−	0.892410i	$-0.649013\pi$
$149$	−11.0158	−0.902453	−0.451226	+	0.892410i	$0.649013\pi$
$150$	−10.2515	−0.837035
$151$	16.3621	1.33153	0.665764	−	0.746162i	$-0.268106\pi$
$151$	16.3621	1.33153	0.665764	+	0.746162i	$0.268106\pi$
$152$	−42.9870	−3.48671
$153$	−11.0981	−0.897230
$154$	−4.93272	−0.397490
$155$	−0.185710	−0.0149166
$156$	−4.20742	−0.336863
$157$	3.73501	0.298086	0.149043	−	0.988831i	$-0.452381\pi$
$157$	3.73501	0.298086	0.149043	+	0.988831i	$0.452381\pi$
$158$	23.3870	1.86057
$159$	5.63130	0.446591
$160$	−0.159139	−0.0125811
$161$	−0.672030	−0.0529634
$162$	−9.67402	−0.760063
$163$	−14.3704	−1.12558	−0.562789	−	0.826600i	$-0.690272\pi$
$163$	−14.3704	−1.12558	−0.562789	+	0.826600i	$0.690272\pi$
$164$	−14.6581	−1.14460
$165$	−0.0286724	−0.00223214
$166$	4.53068	0.351649
$167$	−20.1833	−1.56183	−0.780915	−	0.624637i	$-0.785247\pi$
$167$	−20.1833	−1.56183	−0.780915	+	0.624637i	$0.785247\pi$
$168$	5.51846	0.425758
$169$	−11.7199	−0.901529
$170$	−0.229610	−0.0176103
$171$	−14.6443	−1.11988
$172$	15.3682	1.17182
$173$	1.96647	0.149508	0.0747538	−	0.997202i	$-0.476183\pi$
$173$	1.96647	0.149508	0.0747538	+	0.997202i	$0.476183\pi$
$174$	1.87952	0.142486
$175$	−4.99964	−0.377937
$176$	16.4489	1.23988
$177$	0.814006	0.0611844
$178$	−5.92795	−0.444319
$179$	13.5492	1.01271	0.506357	−	0.862324i	$-0.330992\pi$
$179$	13.5492	1.01271	0.506357	+	0.862324i	$0.330992\pi$
$180$	−0.211052	−0.0157309
$181$	−7.85174	−0.583615	−0.291807	−	0.956477i	$-0.594257\pi$
$181$	−7.85174	−0.583615	−0.291807	+	0.956477i	$0.594257\pi$
$182$	−2.92672	−0.216943
$183$	4.90498	0.362587
$184$	4.67856	0.344908
$185$	−0.167989	−0.0123508
$186$	−20.0746	−1.47194
$187$	8.92331	0.652537
$188$	13.5180	0.985904
$189$	4.25798	0.309722
$190$	−0.302976	−0.0219802
$191$	16.3122	1.18031	0.590155	−	0.807290i	$-0.299067\pi$
$191$	16.3122	1.18031	0.590155	+	0.807290i	$0.299067\pi$
$192$	−3.52733	−0.254563
$193$	12.4237	0.894277	0.447138	−	0.894465i	$-0.352443\pi$
$193$	12.4237	0.894277	0.447138	+	0.894465i	$0.352443\pi$
$194$	16.0500	1.15232
$195$	−0.0170121	−0.00121826
$196$	4.69133	0.335095
$197$	9.24777	0.658877	0.329438	−	0.944177i	$-0.393141\pi$
$197$	9.24777	0.658877	0.329438	+	0.944177i	$0.393141\pi$
$198$	11.6988	0.831397
$199$	−2.07509	−0.147099	−0.0735497	−	0.997292i	$-0.523433\pi$
$199$	−2.07509	−0.147099	−0.0735497	+	0.997292i	$0.523433\pi$
$200$	34.8067	2.46120
$201$	−8.53962	−0.602338
$202$	−3.23699	−0.227754
$203$	0.916635	0.0643352
$204$	−17.4015	−1.21835
$205$	−0.0592680	−0.00413945
$206$	7.51044	0.523277
$207$	1.59383	0.110779
$208$	9.75957	0.676705
$209$	11.7745	0.814463
$210$	0.0388946	0.00268398
$211$	18.7053	1.28772	0.643861	−	0.765142i	$-0.277331\pi$
$211$	18.7053	1.28772	0.643861	+	0.765142i	$0.277331\pi$
$212$	−33.3281	−2.28898
$213$	−12.1337	−0.831388
$214$	44.5819	3.04755
$215$	0.0621393	0.00423787
$216$	−29.6433	−2.01697
$217$	−9.79033	−0.664611
$218$	32.9457	2.23136
$219$	11.1585	0.754021
$220$	0.169694	0.0114407
$221$	5.29445	0.356143
$222$	−18.1590	−1.21875
$223$	15.0535	1.00806	0.504030	−	0.863686i	$-0.331850\pi$
$223$	15.0535	1.00806	0.504030	+	0.863686i	$0.331850\pi$
$224$	−8.38956	−0.560551
$225$	11.8575	0.790499
$226$	−42.8980	−2.85353
$227$	13.2169	0.877235	0.438617	−	0.898674i	$-0.355468\pi$
$227$	13.2169	0.877235	0.438617	+	0.898674i	$0.355468\pi$
$228$	−22.9617	−1.52068
$229$	−12.5968	−0.832421	−0.416210	−	0.909268i	$-0.636642\pi$
$229$	−12.5968	−0.832421	−0.416210	+	0.909268i	$0.636642\pi$
$230$	0.0329749	0.00217430
$231$	−1.51156	−0.0994532
$232$	−6.38146	−0.418963
$233$	9.50070	0.622411	0.311206	−	0.950343i	$-0.399267\pi$
$233$	9.50070	0.622411	0.311206	+	0.950343i	$0.399267\pi$
$234$	6.94121	0.453761
$235$	0.0546583	0.00356551
$236$	−4.81759	−0.313598
$237$	7.16658	0.465519
$238$	−12.1046	−0.784627
$239$	−10.3980	−0.672589	−0.336295	−	0.941757i	$-0.609174\pi$
$239$	−10.3980	−0.672589	−0.336295	+	0.941757i	$0.609174\pi$
$240$	−0.129700	−0.00837208
$241$	−15.8193	−1.01901	−0.509506	−	0.860467i	$-0.670172\pi$
$241$	−15.8193	−1.01901	−0.509506	+	0.860467i	$0.670172\pi$
$242$	19.0481	1.22446
$243$	−15.7384	−1.00962
$244$	−29.0295	−1.85842
$245$	0.0189688	0.00121187
$246$	−6.40666	−0.408474
$247$	6.98616	0.444519
$248$	68.1586	4.32808
$249$	1.38836	0.0879837
$250$	0.490659	0.0310320
$251$	0.738483	0.0466126	0.0233063	−	0.999728i	$-0.492581\pi$
$251$	0.738483	0.0466126	0.0233063	+	0.999728i	$0.492581\pi$
$252$	−11.1263	−0.700890
$253$	−1.28150	−0.0805673
$254$	−10.4732	−0.657148
$255$	−0.0703605	−0.00440614
$256$	−22.5275	−1.40797
$257$	17.8495	1.11342	0.556711	−	0.830706i	$-0.312063\pi$
$257$	17.8495	1.11342	0.556711	+	0.830706i	$0.312063\pi$
$258$	6.71704	0.418185
$259$	−8.85609	−0.550291
$260$	0.100684	0.00624415
$261$	−2.17395	−0.134564
$262$	29.0166	1.79265
$263$	−24.9073	−1.53585	−0.767925	−	0.640540i	$-0.778711\pi$
$263$	−24.9073	−1.53585	−0.767925	+	0.640540i	$0.778711\pi$
$264$	10.5232	0.647659
$265$	−0.134757	−0.00827809
$266$	−15.9724	−0.979330
$267$	−1.81653	−0.111170
$268$	50.5406	3.08726
$269$	−10.4041	−0.634352	−0.317176	−	0.948367i	$-0.602735\pi$
$269$	−10.4041	−0.634352	−0.317176	+	0.948367i	$0.602735\pi$
$270$	−0.208929	−0.0127150
$271$	−7.16442	−0.435207	−0.217604	−	0.976037i	$-0.569824\pi$
$271$	−7.16442	−0.435207	−0.217604	+	0.976037i	$0.569824\pi$
$272$	40.3647	2.44747
$273$	−0.896849	−0.0542798
$274$	−10.2002	−0.616215
$275$	−9.53387	−0.574914
$276$	2.49907	0.150427
$277$	9.87134	0.593111	0.296556	−	0.955016i	$-0.404162\pi$
$277$	9.87134	0.593111	0.296556	+	0.955016i	$0.404162\pi$
$278$	−3.32101	−0.199181
$279$	23.2194	1.39011
$280$	−0.132057	−0.00789193
$281$	−19.2057	−1.14572	−0.572859	−	0.819654i	$-0.694166\pi$
$281$	−19.2057	−1.14572	−0.572859	+	0.819654i	$0.694166\pi$
$282$	5.90837	0.351838
$283$	14.2398	0.846470	0.423235	−	0.906020i	$-0.360894\pi$
$283$	14.2398	0.846470	0.423235	+	0.906020i	$0.360894\pi$
$284$	71.8117	4.26124
$285$	−0.0928425	−0.00549952
$286$	−5.58100	−0.330011
$287$	−3.12450	−0.184434
$288$	19.8972	1.17246
$289$	4.89733	0.288078
$290$	−0.0449771	−0.00264115
$291$	4.91827	0.288314
$292$	−66.0401	−3.86470
$293$	13.5106	0.789295	0.394648	−	0.918833i	$-0.370867\pi$
$293$	13.5106	0.789295	0.394648	+	0.918833i	$0.370867\pi$
$294$	2.05046	0.119585
$295$	−0.0194792	−0.00113413
$296$	61.6546	3.58360
$297$	8.11959	0.471146
$298$	28.4953	1.65069
$299$	−0.760350	−0.0439722
$300$	18.5921	1.07342
$301$	3.27588	0.188818
$302$	−42.3248	−2.43552
$303$	−0.991927	−0.0569847
$304$	53.2623	3.05480
$305$	−0.117377	−0.00672097
$306$	28.7082	1.64114
$307$	13.1301	0.749376	0.374688	−	0.927151i	$-0.377750\pi$
$307$	13.1301	0.749376	0.374688	+	0.927151i	$0.377750\pi$
$308$	8.94595	0.509743
$309$	2.30146	0.130926
$310$	0.480388	0.0272842
$311$	−20.8713	−1.18350	−0.591752	−	0.806120i	$-0.701563\pi$
$311$	−20.8713	−1.18350	−0.591752	+	0.806120i	$0.701563\pi$
$312$	6.24371	0.353480
$313$	−5.06907	−0.286521	−0.143260	−	0.989685i	$-0.545759\pi$
$313$	−5.06907	−0.286521	−0.143260	+	0.989685i	$0.545759\pi$
$314$	−9.66158	−0.545234
$315$	−0.0449876	−0.00253476
$316$	−42.4144	−2.38600
$317$	32.3402	1.81641	0.908203	−	0.418529i	$-0.137454\pi$
$317$	32.3402	1.81641	0.908203	+	0.418529i	$0.137454\pi$
$318$	−14.5668	−0.816867
$319$	1.74794	0.0978660
$320$	0.0844093	0.00471862
$321$	13.6614	0.762507
$322$	1.73838	0.0968762
$323$	28.8941	1.60771
$324$	17.5447	0.974707
$325$	−5.65671	−0.313778
$326$	37.1728	2.05881
$327$	10.0957	0.558294
$328$	21.7523	1.20107
$329$	2.88149	0.158862
$330$	0.0741686	0.00408285
$331$	−7.18883	−0.395134	−0.197567	−	0.980289i	$-0.563304\pi$
$331$	−7.18883	−0.395134	−0.197567	+	0.980289i	$0.563304\pi$
$332$	−8.21682	−0.450957
$333$	21.0037	1.15100
$334$	52.2094	2.85677
$335$	0.204354	0.0111650
$336$	−6.83755	−0.373019
$337$	−5.62157	−0.306226	−0.153113	−	0.988209i	$-0.548930\pi$
$337$	−5.62157	−0.306226	−0.153113	+	0.988209i	$0.548930\pi$
$338$	30.3165	1.64900
$339$	−13.1454	−0.713961
$340$	0.416419	0.0225835
$341$	−18.6693	−1.01100
$342$	37.8812	2.04838
$343$	1.00000	0.0539949
$344$	−22.8061	−1.22962
$345$	0.0101047	0.000544017 0
$346$	−5.08678	−0.273467
$347$	1.04308	0.0559956	0.0279978	−	0.999608i	$-0.491087\pi$
$347$	1.04308	0.0559956	0.0279978	+	0.999608i	$0.491087\pi$
$348$	−3.40869	−0.182725
$349$	−14.3777	−0.769623	−0.384812	−	0.922995i	$-0.625734\pi$
$349$	−14.3777	−0.769623	−0.384812	+	0.922995i	$0.625734\pi$
$350$	12.9329	0.691291
$351$	4.81757	0.257143
$352$	−15.9981	−0.852704
$353$	9.49393	0.505311	0.252655	−	0.967556i	$-0.418696\pi$
$353$	9.49393	0.505311	0.252655	+	0.967556i	$0.418696\pi$
$354$	−2.10564	−0.111913
$355$	0.290361	0.0154107
$356$	10.7509	0.569796
$357$	−3.70928	−0.196316
$358$	−35.0485	−1.85237
$359$	−10.4318	−0.550572	−0.275286	−	0.961362i	$-0.588772\pi$
$359$	−10.4318	−0.550572	−0.275286	+	0.961362i	$0.588772\pi$
$360$	0.313196	0.0165069
$361$	19.1266	1.00666
$362$	20.3106	1.06750
$363$	5.83700	0.306363
$364$	5.30788	0.278208
$365$	−0.267024	−0.0139767
$366$	−12.6880	−0.663214
$367$	−8.25600	−0.430959	−0.215480	−	0.976508i	$-0.569132\pi$
$367$	−8.25600	−0.430959	−0.215480	+	0.976508i	$0.569132\pi$
$368$	−5.79688	−0.302183
$369$	7.41029	0.385764
$370$	0.434547	0.0225910
$371$	−7.10418	−0.368831
$372$	36.4072	1.88763
$373$	−19.8452	−1.02755	−0.513773	−	0.857926i	$-0.671753\pi$
$373$	−19.8452	−1.02755	−0.513773	+	0.857926i	$0.671753\pi$
$374$	−23.0825	−1.19357
$375$	0.150355	0.00776429
$376$	−20.0605	−1.03454
$377$	1.03710	0.0534135
$378$	−11.0144	−0.566518
$379$	−4.79807	−0.246460	−0.123230	−	0.992378i	$-0.539325\pi$
$379$	−4.79807	−0.246460	−0.123230	+	0.992378i	$0.539325\pi$
$380$	0.549476	0.0281875
$381$	−3.20936	−0.164420
$382$	−42.1958	−2.15892
$383$	−7.59972	−0.388327	−0.194164	−	0.980969i	$-0.562199\pi$
$383$	−7.59972	−0.388327	−0.194164	+	0.980969i	$0.562199\pi$
$384$	−4.17600	−0.213106
$385$	0.0361717	0.00184348
$386$	−32.1371	−1.63574
$387$	−7.76930	−0.394936
$388$	−29.1081	−1.47774
$389$	−1.20136	−0.0609115	−0.0304558	−	0.999536i	$-0.509696\pi$
$389$	−1.20136	−0.0609115	−0.0304558	+	0.999536i	$0.509696\pi$
$390$	0.0440062	0.00222834
$391$	−3.14474	−0.159036
$392$	−6.96183	−0.351626
$393$	8.89168	0.448526
$394$	−23.9218	−1.20516
$395$	−0.171497	−0.00862894
$396$	−21.2168	−1.06619
$397$	−14.9130	−0.748461	−0.374231	−	0.927336i	$-0.622093\pi$
$397$	−14.9130	−0.748461	−0.374231	+	0.927336i	$0.622093\pi$
$398$	5.36777	0.269062
$399$	−4.89450	−0.245031
$400$	−43.1265	−2.15633
$401$	9.76431	0.487606	0.243803	−	0.969825i	$-0.421605\pi$
$401$	9.76431	0.487606	0.243803	+	0.969825i	$0.421605\pi$
$402$	22.0900	1.10175
$403$	−11.0770	−0.551785
$404$	5.87059	0.292073
$405$	0.0709397	0.00352502
$406$	−2.37112	−0.117677
$407$	−16.8878	−0.837096
$408$	25.8234	1.27845
$409$	−1.76206	−0.0871283	−0.0435641	−	0.999051i	$-0.513871\pi$
$409$	−1.76206	−0.0871283	−0.0435641	+	0.999051i	$0.513871\pi$
$410$	0.153312	0.00757154
$411$	−3.12569	−0.154179
$412$	−13.6209	−0.671053
$413$	−1.02691	−0.0505310
$414$	−4.12286	−0.202628
$415$	−0.0332236	−0.00163088
$416$	−9.49213	−0.465390
$417$	−1.01767	−0.0498356
$418$	−30.4579	−1.48975
$419$	−28.0207	−1.36890	−0.684451	−	0.729059i	$-0.739958\pi$
$419$	−28.0207	−1.36890	−0.684451	+	0.729059i	$0.739958\pi$
$420$	−0.0705390	−0.00344195
$421$	−27.9338	−1.36141	−0.680704	−	0.732558i	$-0.738326\pi$
$421$	−27.9338	−1.36141	−0.680704	+	0.732558i	$0.738326\pi$
$422$	−48.3860	−2.35539
$423$	−6.83394	−0.332278
$424$	49.4581	2.40190
$425$	−23.3956	−1.13485
$426$	31.3870	1.52070
$427$	−6.18790	−0.299453
$428$	−80.8534	−3.90820
$429$	−1.71021	−0.0825698
$430$	−0.160740	−0.00775155
$431$	10.4442	0.503079	0.251539	−	0.967847i	$-0.419063\pi$
$431$	10.4442	0.503079	0.251539	+	0.967847i	$0.419063\pi$
$432$	36.7290	1.76713
$433$	30.3749	1.45972	0.729862	−	0.683595i	$-0.239584\pi$
$433$	30.3749	1.45972	0.729862	+	0.683595i	$0.239584\pi$
$434$	25.3252	1.21565
$435$	−0.0137826	−0.000660823 0
$436$	−59.7501	−2.86151
$437$	−4.14956	−0.198501
$438$	−28.8644	−1.37919
$439$	19.4570	0.928633	0.464317	−	0.885669i	$-0.346300\pi$
$439$	19.4570	0.928633	0.464317	+	0.885669i	$0.346300\pi$
$440$	−0.251822	−0.0120051
$441$	−2.37167	−0.112937
$442$	−13.6955	−0.651427
$443$	−8.55586	−0.406501	−0.203251	−	0.979127i	$-0.565151\pi$
$443$	−8.55586	−0.406501	−0.203251	+	0.979127i	$0.565151\pi$
$444$	32.9331	1.56294
$445$	0.0434698	0.00206066
$446$	−38.9399	−1.84386
$447$	8.73196	0.413008
$448$	4.44991	0.210239
$449$	6.81714	0.321721	0.160860	−	0.986977i	$-0.448573\pi$
$449$	6.81714	0.321721	0.160860	+	0.986977i	$0.448573\pi$
$450$	−30.6725	−1.44592
$451$	−5.95815	−0.280559
$452$	77.7994	3.65938
$453$	−12.9698	−0.609374
$454$	−34.1889	−1.60456
$455$	0.0214617	0.00100614
$456$	34.0747	1.59569
$457$	12.1665	0.569126	0.284563	−	0.958657i	$-0.408151\pi$
$457$	12.1665	0.569126	0.284563	+	0.958657i	$0.408151\pi$
$458$	32.5849	1.52259
$459$	19.9250	0.930021
$460$	−0.0598031	−0.00278833
$461$	−4.94025	−0.230090	−0.115045	−	0.993360i	$-0.536701\pi$
$461$	−4.94025	−0.230090	−0.115045	+	0.993360i	$0.536701\pi$
$462$	3.91004	0.181912
$463$	−8.63800	−0.401442	−0.200721	−	0.979648i	$-0.564328\pi$
$463$	−8.63800	−0.401442	−0.200721	+	0.979648i	$0.564328\pi$
$464$	7.90683	0.367065
$465$	0.147208	0.00682659
$466$	−24.5760	−1.13846
$467$	5.03008	0.232764	0.116382	−	0.993205i	$-0.462870\pi$
$467$	5.03008	0.232764	0.116382	+	0.993205i	$0.462870\pi$
$468$	−12.5885	−0.581905
$469$	10.7732	0.497460
$470$	−0.141388	−0.00652174
$471$	−2.96064	−0.136419
$472$	7.14919	0.329068
$473$	6.24681	0.287229
$474$	−18.5382	−0.851489
$475$	−30.8711	−1.41646
$476$	21.9529	1.00621
$477$	16.8488	0.771452
$478$	26.8971	1.23024
$479$	−8.89326	−0.406343	−0.203172	−	0.979143i	$-0.565125\pi$
$479$	−8.89326	−0.406343	−0.203172	+	0.979143i	$0.565125\pi$
$480$	0.126146	0.00575773
$481$	−10.0200	−0.456872
$482$	40.9208	1.86389
$483$	0.532700	0.0242387
$484$	−34.5455	−1.57025
$485$	−0.117695	−0.00534424
$486$	40.7115	1.84671
$487$	−1.37604	−0.0623544	−0.0311772	−	0.999514i	$-0.509926\pi$
$487$	−1.37604	−0.0623544	−0.0311772	+	0.999514i	$0.509926\pi$
$488$	43.0791	1.95010
$489$	11.3911	0.515121
$490$	−0.0490676	−0.00221665
$491$	10.5083	0.474233	0.237117	−	0.971481i	$-0.423798\pi$
$491$	10.5083	0.474233	0.237117	+	0.971481i	$0.423798\pi$
$492$	11.6191	0.523829
$493$	4.28936	0.193183
$494$	−18.0715	−0.813077
$495$	−0.0857874	−0.00385586
$496$	−84.4507	−3.79195
$497$	15.3073	0.686627
$498$	−3.59135	−0.160932
$499$	−8.52836	−0.381782	−0.190891	−	0.981611i	$-0.561138\pi$
$499$	−8.52836	−0.381782	−0.190891	+	0.981611i	$0.561138\pi$
$500$	−0.889855	−0.0397955
$501$	15.9988	0.714772
$502$	−1.91028	−0.0852599
$503$	−29.8662	−1.33167	−0.665835	−	0.746099i	$-0.731924\pi$
$503$	−29.8662	−1.33167	−0.665835	+	0.746099i	$0.731924\pi$
$504$	16.5112	0.735465
$505$	0.0237369	0.00105628
$506$	3.31494	0.147367
$507$	9.29004	0.412585
$508$	18.9942	0.842730
$509$	−32.6973	−1.44928	−0.724640	−	0.689127i	$-0.757994\pi$
$509$	−32.6973	−1.44928	−0.724640	+	0.689127i	$0.757994\pi$
$510$	0.182006	0.00805935
$511$	−14.0770	−0.622732
$512$	47.7368	2.10969
$513$	26.2916	1.16080
$514$	−46.1724	−2.03658
$515$	−0.0550742	−0.00242686
$516$	−12.1820	−0.536282
$517$	5.49475	0.241659
$518$	22.9086	1.00655
$519$	−1.55877	−0.0684222
$520$	−0.149413	−0.00655218
$521$	16.7663	0.734543	0.367271	−	0.930114i	$-0.380292\pi$
$521$	16.7663	0.734543	0.367271	+	0.930114i	$0.380292\pi$
$522$	5.62350	0.246134
$523$	5.43094	0.237479	0.118739	−	0.992925i	$-0.462115\pi$
$523$	5.43094	0.237479	0.118739	+	0.992925i	$0.462115\pi$
$524$	−52.6242	−2.29890
$525$	3.96308	0.172963
$526$	64.4292	2.80925
$527$	−45.8134	−1.99566
$528$	−13.0386	−0.567432
$529$	−22.5484	−0.980364
$530$	0.348585	0.0151416
$531$	2.43550	0.105692
$532$	28.9674	1.25590
$533$	−3.53514	−0.153124
$534$	4.69893	0.203343
$535$	−0.326919	−0.0141340
$536$	−75.0011	−3.23955
$537$	−10.7401	−0.463468
$538$	26.9130	1.16030
$539$	1.90691	0.0821365
$540$	0.378912	0.0163058
$541$	−6.98282	−0.300215	−0.150108	−	0.988670i	$-0.547962\pi$
$541$	−6.98282	−0.300215	−0.150108	+	0.988670i	$0.547962\pi$
$542$	18.5326	0.796045
$543$	6.22386	0.267091
$544$	−39.2586	−1.68320
$545$	−0.241591	−0.0103486
$546$	2.31993	0.0992840
$547$	−8.68229	−0.371228	−0.185614	−	0.982623i	$-0.559427\pi$
$547$	−8.68229	−0.371228	−0.185614	+	0.982623i	$0.559427\pi$
$548$	18.4990	0.790236
$549$	14.6757	0.626342
$550$	24.6618	1.05158
$551$	5.65992	0.241121
$552$	−3.70857	−0.157847
$553$	−9.04102	−0.384463
$554$	−25.5348	−1.08487
$555$	0.133160	0.00565235
$556$	6.02295	0.255430
$557$	−20.0476	−0.849443	−0.424721	−	0.905324i	$-0.639628\pi$
$557$	−20.0476	−0.849443	−0.424721	+	0.905324i	$0.639628\pi$
$558$	−60.0631	−2.54267
$559$	3.70640	0.156764
$560$	0.163623	0.00691434
$561$	−7.07327	−0.298634
$562$	49.6807	2.09565
$563$	24.7558	1.04333	0.521666	−	0.853150i	$-0.325311\pi$
$563$	24.7558	1.04333	0.521666	+	0.853150i	$0.325311\pi$
$564$	−10.7154	−0.451199
$565$	0.314571	0.0132341
$566$	−36.8350	−1.54829
$567$	3.73982	0.157058
$568$	−106.567	−4.47145
$569$	−11.9304	−0.500147	−0.250073	−	0.968227i	$-0.580455\pi$
$569$	−11.9304	−0.500147	−0.250073	+	0.968227i	$0.580455\pi$
$570$	0.240161	0.0100593
$571$	−27.2239	−1.13929	−0.569643	−	0.821892i	$-0.692919\pi$
$571$	−27.2239	−1.13929	−0.569643	+	0.821892i	$0.692919\pi$
$572$	10.1217	0.423208
$573$	−12.9303	−0.540169
$574$	8.08235	0.337351
$575$	3.35991	0.140118
$576$	−10.5537	−0.439738
$577$	31.1968	1.29874	0.649369	−	0.760473i	$-0.275033\pi$
$577$	31.1968	1.29874	0.649369	+	0.760473i	$0.275033\pi$
$578$	−12.6682	−0.526929
$579$	−9.84793	−0.409266
$580$	0.0815702	0.00338702
$581$	−1.75149	−0.0726640
$582$	−12.7224	−0.527360
$583$	−13.5470	−0.561061
$584$	98.0020	4.05535
$585$	−0.0509000	−0.00210446
$586$	−34.9486	−1.44371
$587$	13.3690	0.551798	0.275899	−	0.961187i	$-0.411025\pi$
$587$	13.3690	0.551798	0.275899	+	0.961187i	$0.411025\pi$
$588$	−3.71869	−0.153356
$589$	−60.4520	−2.49088
$590$	0.0503881	0.00207445
$591$	−7.33046	−0.301535
$592$	−76.3920	−3.13969
$593$	−23.8709	−0.980260	−0.490130	−	0.871649i	$-0.663051\pi$
$593$	−23.8709	−0.980260	−0.490130	+	0.871649i	$0.663051\pi$
$594$	−21.0034	−0.861781
$595$	0.0887635	0.00363895
$596$	−51.6790	−2.11685
$597$	1.64487	0.0673200
$598$	1.96684	0.0804302
$599$	−9.38888	−0.383619	−0.191810	−	0.981432i	$-0.561436\pi$
$599$	−9.38888	−0.383619	−0.191810	+	0.981432i	$0.561436\pi$
$600$	−27.5903	−1.12637
$601$	−5.81265	−0.237103	−0.118551	−	0.992948i	$-0.537825\pi$
$601$	−5.81265	−0.237103	−0.118551	+	0.992948i	$0.537825\pi$
$602$	−8.47391	−0.345371
$603$	−25.5504	−1.04049
$604$	76.7600	3.12332
$605$	−0.139680	−0.00567880
$606$	2.56588	0.104232
$607$	30.7014	1.24613	0.623066	−	0.782169i	$-0.285887\pi$
$607$	30.7014	1.24613	0.623066	+	0.782169i	$0.285887\pi$
$608$	−51.8027	−2.10088
$609$	−0.726592	−0.0294430
$610$	0.303626	0.0122934
$611$	3.26018	0.131893
$612$	−52.0650	−2.10460
$613$	−21.3891	−0.863899	−0.431950	−	0.901898i	$-0.642174\pi$
$613$	−21.3891	−0.863899	−0.431950	+	0.901898i	$0.642174\pi$
$614$	−33.9645	−1.37070
$615$	0.0469801	0.00189442
$616$	−13.2756	−0.534889
$617$	21.5380	0.867087	0.433543	−	0.901133i	$-0.357263\pi$
$617$	21.5380	0.867087	0.433543	+	0.901133i	$0.357263\pi$
$618$	−5.95333	−0.239478
$619$	−13.6459	−0.548477	−0.274238	−	0.961662i	$-0.588426\pi$
$619$	−13.6459	−0.548477	−0.274238	+	0.961662i	$0.588426\pi$
$620$	−0.871229	−0.0349894
$621$	−2.86149	−0.114828
$622$	53.9891	2.16477
$623$	2.29165	0.0918130
$624$	−7.73616	−0.309694
$625$	24.9946	0.999784
$626$	13.1125	0.524079
$627$	−9.33337	−0.372739
$628$	17.5222	0.699211
$629$	−41.4417	−1.65239
$630$	0.116372	0.00463638
$631$	1.62588	0.0647252	0.0323626	−	0.999476i	$-0.489697\pi$
$631$	1.62588	0.0647252	0.0323626	+	0.999476i	$0.489697\pi$
$632$	62.9421	2.50370
$633$	−14.8272	−0.589327
$634$	−83.6564	−3.32242
$635$	0.0768003	0.00304773
$636$	26.4183	1.04755
$637$	1.13142	0.0448286
$638$	−4.52151	−0.179008
$639$	−36.3039	−1.43616
$640$	0.0999321	0.00395016
$641$	−16.5408	−0.653321	−0.326660	−	0.945142i	$-0.605923\pi$
$641$	−16.5408	−0.653321	−0.326660	+	0.945142i	$0.605923\pi$
$642$	−35.3389	−1.39471
$643$	30.5274	1.20388	0.601941	−	0.798541i	$-0.294394\pi$
$643$	30.5274	1.20388	0.601941	+	0.798541i	$0.294394\pi$
$644$	−3.15272	−0.124234
$645$	−0.0492562	−0.00193946
$646$	−74.7422	−2.94069
$647$	26.6253	1.04675	0.523374	−	0.852103i	$-0.324673\pi$
$647$	26.6253	1.04675	0.523374	+	0.852103i	$0.324673\pi$
$648$	−26.0360	−1.02279
$649$	−1.95823	−0.0768673
$650$	14.6325	0.573936
$651$	7.76053	0.304159
$652$	−67.4164	−2.64023
$653$	−26.3698	−1.03193	−0.515966	−	0.856609i	$-0.672567\pi$
$653$	−26.3698	−1.03193	−0.515966	+	0.856609i	$0.672567\pi$
$654$	−26.1152	−1.02118
$655$	−0.212779	−0.00831396
$656$	−26.9518	−1.05229
$657$	33.3861	1.30252
$658$	−7.45373	−0.290577
$659$	−33.6328	−1.31015	−0.655074	−	0.755565i	$-0.727363\pi$
$659$	−33.6328	−1.31015	−0.655074	+	0.755565i	$0.727363\pi$
$660$	−0.134512	−0.00523586
$661$	−2.68415	−0.104401	−0.0522006	−	0.998637i	$-0.516624\pi$
$661$	−2.68415	−0.104401	−0.0522006	+	0.998637i	$0.516624\pi$
$662$	18.5958	0.722746
$663$	−4.19677	−0.162989
$664$	12.1936	0.473203
$665$	0.117126	0.00454194
$666$	−54.3316	−2.10531
$667$	−0.616006	−0.0238519
$668$	−94.6866	−3.66353
$669$	−11.9325	−0.461339
$670$	−0.528615	−0.0204222
$671$	−11.7998	−0.455525
$672$	6.65018	0.256536
$673$	10.3389	0.398537	0.199268	−	0.979945i	$-0.436143\pi$
$673$	10.3389	0.398537	0.199268	+	0.979945i	$0.436143\pi$
$674$	14.5416	0.560123
$675$	−21.2884	−0.819390
$676$	−54.9819	−2.11469
$677$	17.2251	0.662016	0.331008	−	0.943628i	$-0.392611\pi$
$677$	17.2251	0.662016	0.331008	+	0.943628i	$0.392611\pi$
$678$	34.0041	1.30592
$679$	−6.20466	−0.238113
$680$	−0.617957	−0.0236976
$681$	−10.4767	−0.401467
$682$	48.2930	1.84923
$683$	3.31850	0.126979	0.0634894	−	0.997983i	$-0.479777\pi$
$683$	3.31850	0.126979	0.0634894	+	0.997983i	$0.479777\pi$
$684$	−68.7011	−2.62685
$685$	0.0747980	0.00285788
$686$	−2.58676	−0.0987630
$687$	9.98516	0.380957
$688$	28.2575	1.07731
$689$	−8.03783	−0.306217
$690$	−0.0261383	−0.000995070 0
$691$	−24.0621	−0.915366	−0.457683	−	0.889116i	$-0.651320\pi$
$691$	−24.0621	−0.915366	−0.457683	+	0.889116i	$0.651320\pi$
$692$	9.22534	0.350695
$693$	−4.52256	−0.171798
$694$	−2.69821	−0.102422
$695$	0.0243530	0.000923761 0
$696$	5.05841	0.191739
$697$	−14.6210	−0.553810
$698$	37.1918	1.40773
$699$	−7.53095	−0.284847
$700$	−23.4550	−0.886515
$701$	27.2280	1.02839	0.514193	−	0.857674i	$-0.328091\pi$
$701$	27.2280	1.02839	0.514193	+	0.857674i	$0.328091\pi$
$702$	−12.4619	−0.470345
$703$	−54.6834	−2.06243
$704$	8.48559	0.319813
$705$	−0.0433262	−0.00163176
$706$	−24.5585	−0.924272
$707$	1.25137	0.0470626
$708$	3.81877	0.143518
$709$	16.9287	0.635770	0.317885	−	0.948129i	$-0.397027\pi$
$709$	16.9287	0.635770	0.317885	+	0.948129i	$0.397027\pi$
$710$	−0.751094	−0.0281880
$711$	21.4423	0.804149
$712$	−15.9541	−0.597905
$713$	6.57939	0.246400
$714$	9.59503	0.359085
$715$	0.0409255	0.00153053
$716$	63.5637	2.37549
$717$	8.24220	0.307811
$718$	26.9847	1.00706
$719$	−0.575436	−0.0214601	−0.0107301	−	0.999942i	$-0.503416\pi$
$719$	−0.575436	−0.0214601	−0.0107301	+	0.999942i	$0.503416\pi$
$720$	−0.388060	−0.0144621
$721$	−2.90342	−0.108129
$722$	−49.4758	−1.84130
$723$	12.5395	0.466351
$724$	−36.8351	−1.36897
$725$	−4.58285	−0.170203
$726$	−15.0989	−0.560374
$727$	−53.0606	−1.96791	−0.983955	−	0.178417i	$-0.942902\pi$
$727$	−53.0606	−1.96791	−0.983955	+	0.178417i	$0.942902\pi$
$728$	−7.87677	−0.291933
$729$	1.25595	0.0465166
$730$	0.690727	0.0255650
$731$	15.3293	0.566976
$732$	23.0109	0.850508
$733$	−15.2958	−0.564964	−0.282482	−	0.959273i	$-0.591158\pi$
$733$	−15.2958	−0.564964	−0.282482	+	0.959273i	$0.591158\pi$
$734$	21.3563	0.788275
$735$	−0.0150360	−0.000554612 0
$736$	5.63803	0.207821
$737$	20.5435	0.756730
$738$	−19.1686	−0.705608
$739$	37.7786	1.38971	0.694854	−	0.719151i	$-0.255469\pi$
$739$	37.7786	1.38971	0.694854	+	0.719151i	$0.255469\pi$
$740$	−0.788092	−0.0289708
$741$	−5.53775	−0.203434
$742$	18.3768	0.674634
$743$	−7.00105	−0.256844	−0.128422	−	0.991720i	$-0.540991\pi$
$743$	−7.00105	−0.256844	−0.128422	+	0.991720i	$0.540991\pi$
$744$	−54.0275	−1.98075
$745$	−0.208957	−0.00765558
$746$	51.3348	1.87950
$747$	4.15395	0.151985
$748$	41.8622	1.53063
$749$	−17.2346	−0.629740
$750$	−0.388932	−0.0142018
$751$	−6.34039	−0.231364	−0.115682	−	0.993286i	$-0.536905\pi$
$751$	−6.34039	−0.231364	−0.115682	+	0.993286i	$0.536905\pi$
$752$	24.8555	0.906388
$753$	−0.585376	−0.0213323
$754$	−2.68273	−0.0976994
$755$	0.310368	0.0112955
$756$	19.9756	0.726505
$757$	−43.8195	−1.59265	−0.796324	−	0.604871i	$-0.793225\pi$
$757$	−43.8195	−1.59265	−0.796324	+	0.604871i	$0.793225\pi$
$758$	12.4114	0.450804
$759$	1.01581	0.0368717
$760$	−0.815410	−0.0295780
$761$	−46.7825	−1.69586	−0.847932	−	0.530105i	$-0.822152\pi$
$761$	−46.7825	−1.69586	−0.847932	+	0.530105i	$0.822152\pi$
$762$	8.30185	0.300744
$763$	−12.7363	−0.461084
$764$	76.5260	2.76861
$765$	−0.210518	−0.00761128
$766$	19.6587	0.710296
$767$	−1.16187	−0.0419528
$768$	17.8570	0.644358
$769$	11.9295	0.430190	0.215095	−	0.976593i	$-0.430994\pi$
$769$	11.9295	0.430190	0.215095	+	0.976593i	$0.430994\pi$
$770$	−0.0935676	−0.00337194
$771$	−14.1488	−0.509558
$772$	58.2836	2.09767
$773$	−48.4504	−1.74264	−0.871320	−	0.490716i	$-0.836735\pi$
$773$	−48.4504	−1.74264	−0.871320	+	0.490716i	$0.836735\pi$
$774$	20.0973	0.722383
$775$	48.9481	1.75827
$776$	43.1958	1.55064
$777$	7.01999	0.251841
$778$	3.10764	0.111414
$779$	−19.2928	−0.691236
$780$	−0.0798094	−0.00285764
$781$	29.1897	1.04449
$782$	8.13468	0.290896
$783$	3.90301	0.139482
$784$	8.62593	0.308069
$785$	0.0708485	0.00252869
$786$	−23.0007	−0.820406
$787$	−14.5187	−0.517537	−0.258769	−	0.965939i	$-0.583317\pi$
$787$	−14.5187	−0.517537	−0.258769	+	0.965939i	$0.583317\pi$
$788$	43.3844	1.54550
$789$	19.7434	0.702882
$790$	0.443621	0.0157833
$791$	16.5837	0.589647
$792$	31.4853	1.11878
$793$	−7.00113	−0.248617
$794$	38.5763	1.36902
$795$	0.106819	0.00378847
$796$	−9.73494	−0.345046
$797$	2.06282	0.0730688	0.0365344	−	0.999332i	$-0.488368\pi$
$797$	2.06282	0.0730688	0.0365344	+	0.999332i	$0.488368\pi$
$798$	12.6609	0.448191
$799$	13.4838	0.477023
$800$	41.9448	1.48297
$801$	−5.43504	−0.192038
$802$	−25.2579	−0.891889
$803$	−26.8437	−0.947293
$804$	−40.0622	−1.41288
$805$	−0.0127476	−0.000449293 0
$806$	28.6535	1.00928
$807$	8.24708	0.290311
$808$	−8.71182	−0.306481
$809$	−51.4318	−1.80824	−0.904122	−	0.427273i	$-0.859474\pi$
$809$	−51.4318	−1.80824	−0.904122	+	0.427273i	$0.859474\pi$
$810$	−0.183504	−0.00644768
$811$	−33.4479	−1.17452	−0.587258	−	0.809400i	$-0.699793\pi$
$811$	−33.4479	−1.17452	−0.587258	+	0.809400i	$0.699793\pi$
$812$	4.30024	0.150909
$813$	5.67904	0.199173
$814$	43.6847	1.53115
$815$	−0.272589	−0.00954838
$816$	−31.9960	−1.12008
$817$	20.2275	0.707669
$818$	4.55803	0.159368
$819$	−2.68336	−0.0937642
$820$	−0.278046	−0.00970978
$821$	−4.64530	−0.162122	−0.0810610	−	0.996709i	$-0.525831\pi$
$821$	−4.64530	−0.162122	−0.0810610	+	0.996709i	$0.525831\pi$
$822$	8.08540	0.282011
$823$	−1.07528	−0.0374818	−0.0187409	−	0.999824i	$-0.505966\pi$
$823$	−1.07528	−0.0374818	−0.0187409	+	0.999824i	$0.505966\pi$
$824$	20.2131	0.704157
$825$	7.55725	0.263110
$826$	2.65638	0.0924272
$827$	6.23050	0.216656	0.108328	−	0.994115i	$-0.465450\pi$
$827$	6.23050	0.216656	0.108328	+	0.994115i	$0.465450\pi$
$828$	7.47720	0.259851
$829$	−41.3028	−1.43451	−0.717254	−	0.696812i	$-0.754601\pi$
$829$	−41.3028	−1.43451	−0.717254	+	0.696812i	$0.754601\pi$
$830$	0.0859414	0.00298307
$831$	−7.82475	−0.271438
$832$	5.03473	0.174548
$833$	4.67946	0.162134
$834$	2.63247	0.0911551
$835$	−0.382852	−0.0132491
$836$	55.2383	1.91046
$837$	−41.6870	−1.44091
$838$	72.4829	2.50388
$839$	26.3294	0.908991	0.454495	−	0.890749i	$-0.349820\pi$
$839$	26.3294	0.908991	0.454495	+	0.890749i	$0.349820\pi$
$840$	0.104678	0.00361174
$841$	−28.1598	−0.971027
$842$	72.2580	2.49018
$843$	15.2239	0.524338
$844$	87.7525	3.02057
$845$	−0.222312	−0.00764775
$846$	17.6778	0.607774
$847$	−7.36369	−0.253019
$848$	−61.2802	−2.10437
$849$	−11.2875	−0.387387
$850$	60.5188	2.07578
$851$	5.95156	0.204017
$852$	−56.9232	−1.95016
$853$	−56.3409	−1.92908	−0.964538	−	0.263943i	$-0.914977\pi$
$853$	−56.3409	−1.92908	−0.964538	+	0.263943i	$0.914977\pi$
$854$	16.0066	0.547735
$855$	−0.277784	−0.00950000
$856$	119.985	4.10099
$857$	−9.52023	−0.325205	−0.162603	−	0.986692i	$-0.551989\pi$
$857$	−9.52023	−0.325205	−0.162603	+	0.986692i	$0.551989\pi$
$858$	4.42391	0.151030
$859$	7.51995	0.256577	0.128289	−	0.991737i	$-0.459052\pi$
$859$	7.51995	0.256577	0.128289	+	0.991737i	$0.459052\pi$
$860$	0.291516	0.00994062
$861$	2.47671	0.0844061
$862$	−27.0166	−0.920189
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−35.7226	−1.21531
$865$	0.0373014	0.00126829
$866$	−78.5726	−2.67000
$867$	−3.88199	−0.131839
$868$	−45.9297	−1.55895
$869$	−17.2404	−0.584841
$870$	0.0356522	0.00120872
$871$	12.1890	0.413009
$872$	88.6678	3.00267
$873$	14.7154	0.498041
$874$	10.7339	0.363081
$875$	−0.189681	−0.00641238
$876$	52.3482	1.76868
$877$	−48.3535	−1.63278	−0.816390	−	0.577500i	$-0.804028\pi$
$877$	−48.3535	−1.63278	−0.816390	+	0.577500i	$0.804028\pi$
$878$	−50.3307	−1.69858
$879$	−10.7095	−0.361221
$880$	0.312015	0.0105180
$881$	51.0138	1.71870	0.859350	−	0.511388i	$-0.170868\pi$
$881$	51.0138	1.71870	0.859350	+	0.511388i	$0.170868\pi$
$882$	6.13494	0.206574
$883$	−47.5952	−1.60171	−0.800853	−	0.598862i	$-0.795620\pi$
$883$	−47.5952	−1.60171	−0.800853	+	0.598862i	$0.795620\pi$
$884$	24.8380	0.835392
$885$	0.0154407	0.000519033 0
$886$	22.1320	0.743538
$887$	39.6437	1.33110	0.665552	−	0.746351i	$-0.268196\pi$
$887$	39.6437	1.33110	0.665552	+	0.746351i	$0.268196\pi$
$888$	−48.8720	−1.64004
$889$	4.04878	0.135792
$890$	−0.112446	−0.00376919
$891$	7.13150	0.238914
$892$	70.6212	2.36457
$893$	17.7923	0.595395
$894$	−22.5875	−0.755439
$895$	0.257011	0.00859093
$896$	5.26825	0.176000
$897$	0.602709	0.0201239
$898$	−17.6343	−0.588465
$899$	−8.97416	−0.299305
$900$	55.6274	1.85425
$901$	−33.2437	−1.10751
$902$	15.4123	0.513174
$903$	−2.59670	−0.0864128
$904$	−115.453	−3.83990
$905$	−0.148938	−0.00495085
$906$	33.5498	1.11462
$907$	−14.4439	−0.479603	−0.239802	−	0.970822i	$-0.577082\pi$
$907$	−14.4439	−0.479603	−0.239802	+	0.970822i	$0.577082\pi$
$908$	62.0047	2.05770
$909$	−2.96783	−0.0984368
$910$	−0.0555162	−0.00184035
$911$	−29.3306	−0.971767	−0.485883	−	0.874024i	$-0.661502\pi$
$911$	−29.3306	−0.971767	−0.485883	+	0.874024i	$0.661502\pi$
$912$	−42.2196	−1.39803
$913$	−3.33994	−0.110536
$914$	−31.4719	−1.04100
$915$	0.0930414	0.00307586
$916$	−59.0958	−1.95258
$917$	−11.2173	−0.370429
$918$	−51.5413	−1.70112
$919$	−30.5542	−1.00789	−0.503944	−	0.863736i	$-0.668118\pi$
$919$	−30.5542	−1.00789	−0.503944	+	0.863736i	$0.668118\pi$
$920$	0.0887464	0.00292588
$921$	−10.4079	−0.342952
$922$	12.7793	0.420862
$923$	17.3190	0.570063
$924$	−7.09122	−0.233284
$925$	44.2773	1.45583
$926$	22.3444	0.734284
$927$	6.88594	0.226164
$928$	−7.69016	−0.252442
$929$	−57.9647	−1.90176	−0.950879	−	0.309562i	$-0.899818\pi$
$929$	−57.9647	−1.90176	−0.950879	+	0.309562i	$0.899818\pi$
$930$	−0.380791	−0.0124866
$931$	6.17467	0.202367
$932$	44.5709	1.45997
$933$	16.5441	0.541631
$934$	−13.0116	−0.425753
$935$	0.169264	0.00553553
$936$	18.6811	0.610611
$937$	−19.6364	−0.641494	−0.320747	−	0.947165i	$-0.603934\pi$
$937$	−19.6364	−0.641494	−0.320747	+	0.947165i	$0.603934\pi$
$938$	−27.8677	−0.909911
$939$	4.01811	0.131126
$940$	0.256420	0.00836350
$941$	−0.204269	−0.00665897	−0.00332948	−	0.999994i	$-0.501060\pi$
$941$	−0.204269	−0.00665897	−0.00332948	+	0.999994i	$0.501060\pi$
$942$	7.65848	0.249527
$943$	2.09976	0.0683776
$944$	−8.85807	−0.288306
$945$	0.0807686	0.00262740
$946$	−16.1590	−0.525374
$947$	−14.2366	−0.462627	−0.231313	−	0.972879i	$-0.574302\pi$
$947$	−14.2366	−0.462627	−0.231313	+	0.972879i	$0.574302\pi$
$948$	33.6208	1.09195
$949$	−15.9271	−0.517015
$950$	79.8562	2.59088
$951$	−25.6352	−0.831279
$952$	−32.5776	−1.05585
$953$	50.9899	1.65173	0.825863	−	0.563871i	$-0.190688\pi$
$953$	50.9899	1.65173	0.825863	+	0.563871i	$0.190688\pi$
$954$	−43.5837	−1.41108
$955$	0.309422	0.0100127
$956$	−48.7804	−1.57767
$957$	−1.38555	−0.0447884
$958$	23.0047	0.743249
$959$	3.94322	0.127333
$960$	−0.0669090	−0.00215948
$961$	64.8505	2.09195
$962$	25.9193	0.835672
$963$	40.8748	1.31717
$964$	−74.2136	−2.39026
$965$	0.235662	0.00758622
$966$	−1.37797	−0.0443354
$967$	−42.7924	−1.37611	−0.688055	−	0.725658i	$-0.741535\pi$
$967$	−42.7924	−1.37611	−0.688055	+	0.725658i	$0.741535\pi$
$968$	51.2648	1.64771
$969$	−22.9036	−0.735770
$970$	0.304448	0.00977524
$971$	−59.1908	−1.89952	−0.949762	−	0.312974i	$-0.898675\pi$
$971$	−59.1908	−1.89952	−0.949762	+	0.312974i	$0.898675\pi$
$972$	−73.8340	−2.36823
$973$	1.28385	0.0411583
$974$	3.55949	0.114053
$975$	4.48392	0.143600
$976$	−53.3764	−1.70854
$977$	14.5742	0.466271	0.233135	−	0.972444i	$-0.425101\pi$
$977$	14.5742	0.466271	0.233135	+	0.972444i	$0.425101\pi$
$978$	−29.4659	−0.942216
$979$	4.36998	0.139665
$980$	0.0889887	0.00284264
$981$	30.2062	0.964410
$982$	−27.1825	−0.867428
$983$	−3.76412	−0.120057	−0.0600284	−	0.998197i	$-0.519119\pi$
$983$	−3.76412	−0.120057	−0.0600284	+	0.998197i	$0.519119\pi$
$984$	−17.2425	−0.549669
$985$	0.175419	0.00558930
$986$	−11.0955	−0.353354
$987$	−2.28408	−0.0727031
$988$	32.7744	1.04269
$989$	−2.20149	−0.0700032
$990$	0.221911	0.00705281
$991$	−29.9492	−0.951367	−0.475683	−	0.879617i	$-0.657799\pi$
$991$	−29.9492	−0.951367	−0.475683	+	0.879617i	$0.657799\pi$
$992$	82.1365	2.60784
$993$	5.69840	0.180833
$994$	−39.5964	−1.25592
$995$	−0.0393619	−0.00124786
$996$	6.51325	0.206380
$997$	43.4488	1.37604	0.688018	−	0.725694i	$-0.258481\pi$
$997$	43.4488	1.37604	0.688018	+	0.725694i	$0.258481\pi$
$998$	22.0608	0.698323
$999$	−37.7091	−1.19306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.2	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.2	✓	83	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58676 q^{2} -0.792673 q^{3} +4.69133 q^{4} +0.0189688 q^{5} +2.05046 q^{6} +1.00000 q^{7} -6.96183 q^{8} -2.37167 q^{9} +O(q^{10})\)	\(q-2.58676 q^{2} -0.792673 q^{3} +4.69133 q^{4} +0.0189688 q^{5} +2.05046 q^{6} +1.00000 q^{7} -6.96183 q^{8} -2.37167 q^{9} -0.0490676 q^{10} +1.90691 q^{11} -3.71869 q^{12} +1.13142 q^{13} -2.58676 q^{14} -0.0150360 q^{15} +8.62593 q^{16} +4.67946 q^{17} +6.13494 q^{18} +6.17467 q^{19} +0.0889887 q^{20} -0.792673 q^{21} -4.93272 q^{22} -0.672030 q^{23} +5.51846 q^{24} -4.99964 q^{25} -2.92672 q^{26} +4.25798 q^{27} +4.69133 q^{28} +0.916635 q^{29} +0.0388946 q^{30} -9.79033 q^{31} -8.38956 q^{32} -1.51156 q^{33} -12.1046 q^{34} +0.0189688 q^{35} -11.1263 q^{36} -8.85609 q^{37} -15.9724 q^{38} -0.896849 q^{39} -0.132057 q^{40} -3.12450 q^{41} +2.05046 q^{42} +3.27588 q^{43} +8.94595 q^{44} -0.0449876 q^{45} +1.73838 q^{46} +2.88149 q^{47} -6.83755 q^{48} +1.00000 q^{49} +12.9329 q^{50} -3.70928 q^{51} +5.30788 q^{52} -7.10418 q^{53} -11.0144 q^{54} +0.0361717 q^{55} -6.96183 q^{56} -4.89450 q^{57} -2.37112 q^{58} -1.02691 q^{59} -0.0705390 q^{60} -6.18790 q^{61} +25.3252 q^{62} -2.37167 q^{63} +4.44991 q^{64} +0.0214617 q^{65} +3.91004 q^{66} +10.7732 q^{67} +21.9529 q^{68} +0.532700 q^{69} -0.0490676 q^{70} +15.3073 q^{71} +16.5112 q^{72} -14.0770 q^{73} +22.9086 q^{74} +3.96308 q^{75} +28.9674 q^{76} +1.90691 q^{77} +2.31993 q^{78} -9.04102 q^{79} +0.163623 q^{80} +3.73982 q^{81} +8.08235 q^{82} -1.75149 q^{83} -3.71869 q^{84} +0.0887635 q^{85} -8.47391 q^{86} -0.726592 q^{87} -13.2756 q^{88} +2.29165 q^{89} +0.116372 q^{90} +1.13142 q^{91} -3.15272 q^{92} +7.76053 q^{93} -7.45373 q^{94} +0.117126 q^{95} +6.65018 q^{96} -6.20466 q^{97} -2.58676 q^{98} -4.52256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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