LMFDB - Embedded newform 6011.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$1$
Dimension:	$221$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66460 q^{2} -1.59742 q^{3} +5.10010 q^{4} +2.00952 q^{5} +4.25649 q^{6} +1.11567 q^{7} -8.26053 q^{8} -0.448248 q^{9} +O(q^{10})$	\(q-2.66460 q^{2} -1.59742 q^{3} +5.10010 q^{4} +2.00952 q^{5} +4.25649 q^{6} +1.11567 q^{7} -8.26053 q^{8} -0.448248 q^{9} -5.35457 q^{10} +2.18135 q^{11} -8.14700 q^{12} +1.21526 q^{13} -2.97281 q^{14} -3.21005 q^{15} +11.8108 q^{16} +7.63711 q^{17} +1.19440 q^{18} -0.455748 q^{19} +10.2488 q^{20} -1.78219 q^{21} -5.81243 q^{22} -8.55498 q^{23} +13.1955 q^{24} -0.961826 q^{25} -3.23819 q^{26} +5.50830 q^{27} +5.69002 q^{28} -3.18147 q^{29} +8.55350 q^{30} +1.07917 q^{31} -14.9501 q^{32} -3.48454 q^{33} -20.3499 q^{34} +2.24196 q^{35} -2.28611 q^{36} -9.70446 q^{37} +1.21439 q^{38} -1.94128 q^{39} -16.5997 q^{40} +0.700279 q^{41} +4.74883 q^{42} +6.94148 q^{43} +11.1251 q^{44} -0.900764 q^{45} +22.7956 q^{46} +3.85490 q^{47} -18.8669 q^{48} -5.75528 q^{49} +2.56288 q^{50} -12.1997 q^{51} +6.19795 q^{52} +5.66177 q^{53} -14.6774 q^{54} +4.38347 q^{55} -9.21602 q^{56} +0.728021 q^{57} +8.47734 q^{58} +2.80330 q^{59} -16.3716 q^{60} -1.68257 q^{61} -2.87555 q^{62} -0.500097 q^{63} +16.2143 q^{64} +2.44209 q^{65} +9.28490 q^{66} -13.9929 q^{67} +38.9500 q^{68} +13.6659 q^{69} -5.97393 q^{70} -14.3265 q^{71} +3.70277 q^{72} +10.3719 q^{73} +25.8585 q^{74} +1.53644 q^{75} -2.32436 q^{76} +2.43367 q^{77} +5.17274 q^{78} -1.45364 q^{79} +23.7341 q^{80} -7.45433 q^{81} -1.86596 q^{82} -10.3272 q^{83} -9.08936 q^{84} +15.3469 q^{85} -18.4963 q^{86} +5.08214 q^{87} -18.0191 q^{88} -8.48871 q^{89} +2.40018 q^{90} +1.35583 q^{91} -43.6313 q^{92} -1.72388 q^{93} -10.2718 q^{94} -0.915835 q^{95} +23.8816 q^{96} -9.35515 q^{97} +15.3355 q^{98} -0.977788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) $ 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * 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 $

$2$	−2.66460	−1.88416	−0.942079	−	0.335391i	$-0.891131\pi$
$2$	−2.66460	−1.88416	−0.942079	+	0.335391i	$0.891131\pi$
$3$	−1.59742	−0.922271	−0.461136	−	0.887330i	$-0.652558\pi$
$3$	−1.59742	−0.922271	−0.461136	+	0.887330i	$0.652558\pi$
$4$	5.10010	2.55005
$5$	2.00952	0.898685	0.449343	−	0.893360i	$-0.351658\pi$
$5$	2.00952	0.898685	0.449343	+	0.893360i	$0.351658\pi$
$6$	4.25649	1.73770
$7$	1.11567	0.421683	0.210842	−	0.977520i	$-0.432380\pi$
$7$	1.11567	0.421683	0.210842	+	0.977520i	$0.432380\pi$
$8$	−8.26053	−2.92054
$9$	−0.448248	−0.149416
$10$	−5.35457	−1.69326
$11$	2.18135	0.657702	0.328851	−	0.944382i	$-0.393339\pi$
$11$	2.18135	0.657702	0.328851	+	0.944382i	$0.393339\pi$
$12$	−8.14700	−2.35184
$13$	1.21526	0.337053	0.168526	−	0.985697i	$-0.446099\pi$
$13$	1.21526	0.337053	0.168526	+	0.985697i	$0.446099\pi$
$14$	−2.97281	−0.794517
$15$	−3.21005	−0.828831
$16$	11.8108	2.95271
$17$	7.63711	1.85227	0.926136	−	0.377190i	$-0.123110\pi$
$17$	7.63711	1.85227	0.926136	+	0.377190i	$0.123110\pi$
$18$	1.19440	0.281524
$19$	−0.455748	−0.104556	−0.0522779	−	0.998633i	$-0.516648\pi$
$19$	−0.455748	−0.104556	−0.0522779	+	0.998633i	$0.516648\pi$
$20$	10.2488	2.29169
$21$	−1.78219	−0.388906
$22$	−5.81243	−1.23922
$23$	−8.55498	−1.78384	−0.891918	−	0.452197i	$-0.850640\pi$
$23$	−8.55498	−1.78384	−0.891918	+	0.452197i	$0.850640\pi$
$24$	13.1955	2.69353
$25$	−0.961826	−0.192365
$26$	−3.23819	−0.635061
$27$	5.50830	1.06007
$28$	5.69002	1.07531
$29$	−3.18147	−0.590783	−0.295392	−	0.955376i	$-0.595450\pi$
$29$	−3.18147	−0.590783	−0.295392	+	0.955376i	$0.595450\pi$
$30$	8.55350	1.56165
$31$	1.07917	0.193824	0.0969120	−	0.995293i	$-0.469103\pi$
$31$	1.07917	0.193824	0.0969120	+	0.995293i	$0.469103\pi$
$32$	−14.9501	−2.64283
$33$	−3.48454	−0.606580
$34$	−20.3499	−3.48997
$35$	2.24196	0.378960
$36$	−2.28611	−0.381019
$37$	−9.70446	−1.59540	−0.797702	−	0.603052i	$-0.793951\pi$
$37$	−9.70446	−1.59540	−0.797702	+	0.603052i	$0.793951\pi$
$38$	1.21439	0.196999
$39$	−1.94128	−0.310854
$40$	−16.5997	−2.62464
$41$	0.700279	0.109365	0.0546826	−	0.998504i	$-0.482585\pi$
$41$	0.700279	0.109365	0.0546826	+	0.998504i	$0.482585\pi$
$42$	4.74883	0.732760
$43$	6.94148	1.05857	0.529283	−	0.848445i	$-0.322461\pi$
$43$	6.94148	1.05857	0.529283	+	0.848445i	$0.322461\pi$
$44$	11.1251	1.67717
$45$	−0.900764	−0.134278
$46$	22.7956	3.36103
$47$	3.85490	0.562295	0.281147	−	0.959665i	$-0.409285\pi$
$47$	3.85490	0.562295	0.281147	+	0.959665i	$0.409285\pi$
$48$	−18.8669	−2.72320
$49$	−5.75528	−0.822183
$50$	2.56288	0.362446
$51$	−12.1997	−1.70830
$52$	6.19795	0.859501
$53$	5.66177	0.777703	0.388852	−	0.921300i	$-0.372872\pi$
$53$	5.66177	0.777703	0.388852	+	0.921300i	$0.372872\pi$
$54$	−14.6774	−1.99735
$55$	4.38347	0.591067
$56$	−9.21602	−1.23154
$57$	0.728021	0.0964287
$58$	8.47734	1.11313
$59$	2.80330	0.364959	0.182480	−	0.983210i	$-0.441588\pi$
$59$	2.80330	0.364959	0.182480	+	0.983210i	$0.441588\pi$
$60$	−16.3716	−2.11356
$61$	−1.68257	−0.215430	−0.107715	−	0.994182i	$-0.534353\pi$
$61$	−1.68257	−0.215430	−0.107715	+	0.994182i	$0.534353\pi$
$62$	−2.87555	−0.365195
$63$	−0.500097	−0.0630062
$64$	16.2143	2.02679
$65$	2.44209	0.302904
$66$	9.28490	1.14289
$67$	−13.9929	−1.70951	−0.854754	−	0.519033i	$-0.826292\pi$
$67$	−13.9929	−1.70951	−0.854754	+	0.519033i	$0.826292\pi$
$68$	38.9500	4.72339
$69$	13.6659	1.64518
$70$	−5.97393	−0.714021
$71$	−14.3265	−1.70024	−0.850121	−	0.526587i	$-0.823471\pi$
$71$	−14.3265	−1.70024	−0.850121	+	0.526587i	$0.823471\pi$
$72$	3.70277	0.436376
$73$	10.3719	1.21394	0.606972	−	0.794723i	$-0.292384\pi$
$73$	10.3719	1.21394	0.606972	+	0.794723i	$0.292384\pi$
$74$	25.8585	3.00599
$75$	1.53644	0.177413
$76$	−2.32436	−0.266622
$77$	2.43367	0.277342
$78$	5.17274	0.585698
$79$	−1.45364	−0.163548	−0.0817739	−	0.996651i	$-0.526059\pi$
$79$	−1.45364	−0.163548	−0.0817739	+	0.996651i	$0.526059\pi$
$80$	23.7341	2.65355
$81$	−7.45433	−0.828259
$82$	−1.86596	−0.206061
$83$	−10.3272	−1.13356	−0.566780	−	0.823869i	$-0.691811\pi$
$83$	−10.3272	−1.13356	−0.566780	+	0.823869i	$0.691811\pi$
$84$	−9.08936	−0.991730
$85$	15.3469	1.66461
$86$	−18.4963	−1.99450
$87$	5.08214	0.544862
$88$	−18.0191	−1.92085
$89$	−8.48871	−0.899801	−0.449901	−	0.893079i	$-0.648541\pi$
$89$	−8.48871	−0.899801	−0.449901	+	0.893079i	$0.648541\pi$
$90$	2.40018	0.253001
$91$	1.35583	0.142129
$92$	−43.6313	−4.54887
$93$	−1.72388	−0.178758
$94$	−10.2718	−1.05945
$95$	−0.915835	−0.0939626
$96$	23.8816	2.43740
$97$	−9.35515	−0.949872	−0.474936	−	0.880020i	$-0.657529\pi$
$97$	−9.35515	−0.949872	−0.474936	+	0.880020i	$0.657529\pi$
$98$	15.3355	1.54912
$99$	−0.977788	−0.0982713
$100$	−4.90541	−0.490541
$101$	−9.57684	−0.952931	−0.476466	−	0.879193i	$-0.658082\pi$
$101$	−9.57684	−0.952931	−0.476466	+	0.879193i	$0.658082\pi$
$102$	32.5073	3.21870
$103$	2.54915	0.251175	0.125587	−	0.992083i	$-0.459918\pi$
$103$	2.54915	0.251175	0.125587	+	0.992083i	$0.459918\pi$
$104$	−10.0387	−0.984376
$105$	−3.58135	−0.349504
$106$	−15.0864	−1.46532
$107$	14.9858	1.44873	0.724364	−	0.689418i	$-0.242133\pi$
$107$	14.9858	1.44873	0.724364	+	0.689418i	$0.242133\pi$
$108$	28.0929	2.70324
$109$	−16.1956	−1.55126	−0.775629	−	0.631189i	$-0.782567\pi$
$109$	−16.1956	−1.55126	−0.775629	+	0.631189i	$0.782567\pi$
$110$	−11.6802	−1.11366
$111$	15.5021	1.47139
$112$	13.1770	1.24511
$113$	−8.37860	−0.788193	−0.394096	−	0.919069i	$-0.628942\pi$
$113$	−8.37860	−0.788193	−0.394096	+	0.919069i	$0.628942\pi$
$114$	−1.93989	−0.181687
$115$	−17.1914	−1.60311
$116$	−16.2258	−1.50653
$117$	−0.544739	−0.0503611
$118$	−7.46969	−0.687641
$119$	8.52049	0.781072
$120$	26.5167	2.42063
$121$	−6.24170	−0.567427
$122$	4.48337	0.405905
$123$	−1.11864	−0.100864
$124$	5.50386	0.494261
$125$	−11.9804	−1.07156
$126$	1.33256	0.118714
$127$	17.6084	1.56249	0.781247	−	0.624222i	$-0.214584\pi$
$127$	17.6084	1.56249	0.781247	+	0.624222i	$0.214584\pi$
$128$	−13.3046	−1.17597
$129$	−11.0885	−0.976285
$130$	−6.50720	−0.570719
$131$	3.16974	0.276942	0.138471	−	0.990367i	$-0.455781\pi$
$131$	3.16974	0.276942	0.138471	+	0.990367i	$0.455781\pi$
$132$	−17.7715	−1.54681
$133$	−0.508463	−0.0440894
$134$	37.2856	3.22098
$135$	11.0690	0.952672
$136$	−63.0866	−5.40963
$137$	−11.7439	−1.00335	−0.501676	−	0.865055i	$-0.667283\pi$
$137$	−11.7439	−1.00335	−0.501676	+	0.865055i	$0.667283\pi$
$138$	−36.4142	−3.09978
$139$	−10.8832	−0.923099	−0.461550	−	0.887114i	$-0.652706\pi$
$139$	−10.8832	−0.923099	−0.461550	+	0.887114i	$0.652706\pi$
$140$	11.4342	0.966368
$141$	−6.15789	−0.518588
$142$	38.1744	3.20352
$143$	2.65091	0.221680
$144$	−5.29418	−0.441182
$145$	−6.39322	−0.530928
$146$	−27.6371	−2.28726
$147$	9.19361	0.758276
$148$	−49.4937	−4.06836
$149$	13.7394	1.12557	0.562786	−	0.826603i	$-0.309730\pi$
$149$	13.7394	1.12557	0.562786	+	0.826603i	$0.309730\pi$
$150$	−4.09400	−0.334274
$151$	−21.1722	−1.72297	−0.861484	−	0.507784i	$-0.830465\pi$
$151$	−21.1722	−1.72297	−0.861484	+	0.507784i	$0.830465\pi$
$152$	3.76472	0.305359
$153$	−3.42332	−0.276759
$154$	−6.48475	−0.522556
$155$	2.16861	0.174187
$156$	−9.90074	−0.792693
$157$	−9.99540	−0.797720	−0.398860	−	0.917012i	$-0.630594\pi$
$157$	−9.99540	−0.797720	−0.398860	+	0.917012i	$0.630594\pi$
$158$	3.87338	0.308150
$159$	−9.04422	−0.717253
$160$	−30.0425	−2.37507
$161$	−9.54452	−0.752214
$162$	19.8628	1.56057
$163$	−17.4977	−1.37053	−0.685263	−	0.728296i	$-0.740313\pi$
$163$	−17.4977	−1.37053	−0.685263	+	0.728296i	$0.740313\pi$
$164$	3.57149	0.278887
$165$	−7.00225	−0.545124
$166$	27.5179	2.13581
$167$	−9.52848	−0.737336	−0.368668	−	0.929561i	$-0.620186\pi$
$167$	−9.52848	−0.737336	−0.368668	+	0.929561i	$0.620186\pi$
$168$	14.7219	1.13582
$169$	−11.5231	−0.886395
$170$	−40.8935	−3.13639
$171$	0.204288	0.0156223
$172$	35.4022	2.69940
$173$	11.4820	0.872959	0.436479	−	0.899714i	$-0.356225\pi$
$173$	11.4820	0.872959	0.436479	+	0.899714i	$0.356225\pi$
$174$	−13.5419	−1.02661
$175$	−1.07308	−0.0811172
$176$	25.7636	1.94200
$177$	−4.47806	−0.336591
$178$	22.6190	1.69537
$179$	10.7288	0.801906	0.400953	−	0.916099i	$-0.368679\pi$
$179$	10.7288	0.801906	0.400953	+	0.916099i	$0.368679\pi$
$180$	−4.59399	−0.342416
$181$	−22.4698	−1.67017	−0.835085	−	0.550122i	$-0.814581\pi$
$181$	−22.4698	−1.67017	−0.835085	+	0.550122i	$0.814581\pi$
$182$	−3.61274	−0.267794
$183$	2.68776	0.198685
$184$	70.6687	5.20976
$185$	−19.5013	−1.43377
$186$	4.59346	0.336809
$187$	16.6592	1.21824
$188$	19.6604	1.43388
$189$	6.14544	0.447015
$190$	2.44033	0.177040
$191$	7.79435	0.563980	0.281990	−	0.959417i	$-0.409006\pi$
$191$	7.79435	0.563980	0.281990	+	0.959417i	$0.409006\pi$
$192$	−25.9011	−1.86925
$193$	−6.86511	−0.494161	−0.247081	−	0.968995i	$-0.579471\pi$
$193$	−6.86511	−0.494161	−0.247081	+	0.968995i	$0.579471\pi$
$194$	24.9277	1.78971
$195$	−3.90105	−0.279360
$196$	−29.3525	−2.09661
$197$	17.6965	1.26082	0.630412	−	0.776261i	$-0.282886\pi$
$197$	17.6965	1.26082	0.630412	+	0.776261i	$0.282886\pi$
$198$	2.60541	0.185159
$199$	13.0971	0.928427	0.464214	−	0.885723i	$-0.346337\pi$
$199$	13.0971	0.928427	0.464214	+	0.885723i	$0.346337\pi$
$200$	7.94520	0.561810
$201$	22.3526	1.57663
$202$	25.5185	1.79547
$203$	−3.54946	−0.249123
$204$	−62.2196	−4.35624
$205$	1.40723	0.0982849
$206$	−6.79246	−0.473253
$207$	3.83475	0.266534
$208$	14.3532	0.995218
$209$	−0.994146	−0.0687665
$210$	9.54287	0.658521
$211$	12.8325	0.883428	0.441714	−	0.897156i	$-0.354371\pi$
$211$	12.8325	0.883428	0.441714	+	0.897156i	$0.354371\pi$
$212$	28.8756	1.98318
$213$	22.8854	1.56808
$214$	−39.9311	−2.72963
$215$	13.9490	0.951317
$216$	−45.5015	−3.09599
$217$	1.20399	0.0817323
$218$	43.1549	2.92282
$219$	−16.5683	−1.11959
$220$	22.3562	1.50725
$221$	9.28108	0.624313
$222$	−41.3069	−2.77234
$223$	−4.34130	−0.290715	−0.145357	−	0.989379i	$-0.546433\pi$
$223$	−4.34130	−0.290715	−0.145357	+	0.989379i	$0.546433\pi$
$224$	−16.6793	−1.11443
$225$	0.431137	0.0287425
$226$	22.3256	1.48508
$227$	9.70731	0.644297	0.322148	−	0.946689i	$-0.395595\pi$
$227$	9.70731	0.644297	0.322148	+	0.946689i	$0.395595\pi$
$228$	3.71298	0.245898
$229$	19.8544	1.31201	0.656007	−	0.754755i	$-0.272244\pi$
$229$	19.8544	1.31201	0.656007	+	0.754755i	$0.272244\pi$
$230$	45.8082	3.02051
$231$	−3.88759	−0.255785
$232$	26.2806	1.72541
$233$	26.8956	1.76199	0.880995	−	0.473126i	$-0.156874\pi$
$233$	26.8956	1.76199	0.880995	+	0.473126i	$0.156874\pi$
$234$	1.45151	0.0948883
$235$	7.74650	0.505326
$236$	14.2971	0.930664
$237$	2.32208	0.150835
$238$	−22.7037	−1.47166
$239$	−25.0912	−1.62302	−0.811508	−	0.584342i	$-0.801353\pi$
$239$	−25.0912	−1.62302	−0.811508	+	0.584342i	$0.801353\pi$
$240$	−37.9133	−2.44730
$241$	−4.05399	−0.261140	−0.130570	−	0.991439i	$-0.541681\pi$
$241$	−4.05399	−0.261140	−0.130570	+	0.991439i	$0.541681\pi$
$242$	16.6316	1.06912
$243$	−4.61721	−0.296194
$244$	−8.58125	−0.549358
$245$	−11.5654	−0.738884
$246$	2.98073	0.190044
$247$	−0.553852	−0.0352408
$248$	−8.91449	−0.566071
$249$	16.4969	1.04545
$250$	31.9230	2.01899
$251$	25.9503	1.63797	0.818986	−	0.573814i	$-0.194537\pi$
$251$	25.9503	1.63797	0.818986	+	0.573814i	$0.194537\pi$
$252$	−2.55054	−0.160669
$253$	−18.6614	−1.17323
$254$	−46.9194	−2.94399
$255$	−24.5155	−1.53522
$256$	3.02280	0.188925
$257$	−20.4198	−1.27375	−0.636875	−	0.770967i	$-0.719773\pi$
$257$	−20.4198	−1.27375	−0.636875	+	0.770967i	$0.719773\pi$
$258$	29.5463	1.83947
$259$	−10.8270	−0.672755
$260$	12.4549	0.772421
$261$	1.42609	0.0882726
$262$	−8.44610	−0.521802
$263$	15.5649	0.959773	0.479887	−	0.877331i	$-0.340678\pi$
$263$	15.5649	0.959773	0.479887	+	0.877331i	$0.340678\pi$
$264$	28.7841	1.77154
$265$	11.3774	0.698910
$266$	1.35485	0.0830713
$267$	13.5600	0.829861
$268$	−71.3653	−4.35933
$269$	−30.0734	−1.83361	−0.916805	−	0.399335i	$-0.869241\pi$
$269$	−30.0734	−1.83361	−0.916805	+	0.399335i	$0.869241\pi$
$270$	−29.4946	−1.79498
$271$	15.8657	0.963774	0.481887	−	0.876233i	$-0.339952\pi$
$271$	15.8657	0.963774	0.481887	+	0.876233i	$0.339952\pi$
$272$	90.2006	5.46921
$273$	−2.16583	−0.131082
$274$	31.2929	1.89048
$275$	−2.09808	−0.126519
$276$	69.6974	4.19529
$277$	−15.1170	−0.908291	−0.454145	−	0.890928i	$-0.650055\pi$
$277$	−15.1170	−0.908291	−0.454145	+	0.890928i	$0.650055\pi$
$278$	28.9993	1.73926
$279$	−0.483735	−0.0289604
$280$	−18.5198	−1.10677
$281$	1.39738	0.0833605	0.0416802	−	0.999131i	$-0.486729\pi$
$281$	1.39738	0.0833605	0.0416802	+	0.999131i	$0.486729\pi$
$282$	16.4083	0.977102
$283$	−4.03976	−0.240139	−0.120069	−	0.992766i	$-0.538312\pi$
$283$	−4.03976	−0.240139	−0.120069	+	0.992766i	$0.538312\pi$
$284$	−73.0666	−4.33570
$285$	1.46297	0.0866590
$286$	−7.06362	−0.417681
$287$	0.781279	0.0461175
$288$	6.70135	0.394881
$289$	41.3255	2.43091
$290$	17.0354	1.00035
$291$	14.9441	0.876039
$292$	52.8979	3.09562
$293$	2.24665	0.131250	0.0656252	−	0.997844i	$-0.479096\pi$
$293$	2.24665	0.131250	0.0656252	+	0.997844i	$0.479096\pi$
$294$	−24.4973	−1.42871
$295$	5.63330	0.327983
$296$	80.1640	4.65944
$297$	12.0155	0.697213
$298$	−36.6099	−2.12075
$299$	−10.3965	−0.601247
$300$	7.83600	0.452412
$301$	7.74439	0.446379
$302$	56.4154	3.24634
$303$	15.2982	0.878861
$304$	−5.38276	−0.308722
$305$	−3.38115	−0.193604
$306$	9.12179	0.521458
$307$	−1.63119	−0.0930971	−0.0465486	−	0.998916i	$-0.514822\pi$
$307$	−1.63119	−0.0930971	−0.0465486	+	0.998916i	$0.514822\pi$
$308$	12.4119	0.707236
$309$	−4.07206	−0.231651
$310$	−5.77848	−0.328195
$311$	3.60546	0.204447	0.102224	−	0.994761i	$-0.467404\pi$
$311$	3.60546	0.204447	0.102224	+	0.994761i	$0.467404\pi$
$312$	16.0360	0.907861
$313$	−4.97964	−0.281466	−0.140733	−	0.990048i	$-0.544946\pi$
$313$	−4.97964	−0.281466	−0.140733	+	0.990048i	$0.544946\pi$
$314$	26.6338	1.50303
$315$	−1.00495	−0.0566228
$316$	−7.41373	−0.417055
$317$	23.0987	1.29735	0.648675	−	0.761065i	$-0.275323\pi$
$317$	23.0987	1.29735	0.648675	+	0.761065i	$0.275323\pi$
$318$	24.0992	1.35142
$319$	−6.93990	−0.388560
$320$	32.5831	1.82145
$321$	−23.9386	−1.33612
$322$	25.4323	1.41729
$323$	−3.48060	−0.193666
$324$	−38.0178	−2.11210
$325$	−1.16887	−0.0648372
$326$	46.6244	2.58229
$327$	25.8712	1.43068
$328$	−5.78468	−0.319405
$329$	4.30079	0.237110
$330$	18.6582	1.02710
$331$	1.71957	0.0945161	0.0472580	−	0.998883i	$-0.484952\pi$
$331$	1.71957	0.0945161	0.0472580	+	0.998883i	$0.484952\pi$
$332$	−52.6699	−2.89064
$333$	4.35001	0.238379
$334$	25.3896	1.38926
$335$	−28.1191	−1.53631
$336$	−21.0492	−1.14833
$337$	9.94852	0.541930	0.270965	−	0.962589i	$-0.412657\pi$
$337$	9.94852	0.541930	0.270965	+	0.962589i	$0.412657\pi$
$338$	30.7046	1.67011
$339$	13.3842	0.726927
$340$	78.2709	4.24484
$341$	2.35404	0.127479
$342$	−0.544347	−0.0294349
$343$	−14.2307	−0.768384
$344$	−57.3403	−3.09158
$345$	27.4619	1.47850
$346$	−30.5949	−1.64479
$347$	20.9751	1.12600	0.563002	−	0.826456i	$-0.309647\pi$
$347$	20.9751	1.12600	0.563002	+	0.826456i	$0.309647\pi$
$348$	25.9194	1.38943
$349$	−3.15200	−0.168722	−0.0843612	−	0.996435i	$-0.526885\pi$
$349$	−3.15200	−0.168722	−0.0843612	+	0.996435i	$0.526885\pi$
$350$	2.85933	0.152838
$351$	6.69402	0.357301
$352$	−32.6114	−1.73819
$353$	−6.39270	−0.340249	−0.170125	−	0.985423i	$-0.554417\pi$
$353$	−6.39270	−0.340249	−0.170125	+	0.985423i	$0.554417\pi$
$354$	11.9322	0.634191
$355$	−28.7894	−1.52798
$356$	−43.2933	−2.29454
$357$	−13.6108	−0.720360
$358$	−28.5879	−1.51092
$359$	8.27485	0.436730	0.218365	−	0.975867i	$-0.429928\pi$
$359$	8.27485	0.436730	0.218365	+	0.975867i	$0.429928\pi$
$360$	7.44079	0.392164
$361$	−18.7923	−0.989068
$362$	59.8731	3.14686
$363$	9.97062	0.523322
$364$	6.91486	0.362437
$365$	20.8426	1.09095
$366$	−7.16182	−0.374354
$367$	21.0792	1.10033	0.550164	−	0.835057i	$-0.314565\pi$
$367$	21.0792	1.10033	0.550164	+	0.835057i	$0.314565\pi$
$368$	−101.041	−5.26714
$369$	−0.313899	−0.0163409
$370$	51.9632	2.70144
$371$	6.31666	0.327944
$372$	−8.79197	−0.455843
$373$	0.721822	0.0373745	0.0186873	−	0.999825i	$-0.494051\pi$
$373$	0.721822	0.0373745	0.0186873	+	0.999825i	$0.494051\pi$
$374$	−44.3902	−2.29536
$375$	19.1378	0.988269
$376$	−31.8435	−1.64220
$377$	−3.86631	−0.199125
$378$	−16.3751	−0.842247
$379$	−32.9456	−1.69230	−0.846151	−	0.532943i	$-0.821086\pi$
$379$	−32.9456	−1.69230	−0.846151	+	0.532943i	$0.821086\pi$
$380$	−4.67085	−0.239609
$381$	−28.1280	−1.44104
$382$	−20.7688	−1.06263
$383$	26.1128	1.33430	0.667150	−	0.744923i	$-0.267514\pi$
$383$	26.1128	1.33430	0.667150	+	0.744923i	$0.267514\pi$
$384$	21.2531	1.08457
$385$	4.89050	0.249243
$386$	18.2928	0.931078
$387$	−3.11151	−0.158167
$388$	−47.7122	−2.42222
$389$	20.0621	1.01719	0.508595	−	0.861006i	$-0.330165\pi$
$389$	20.0621	1.01719	0.508595	+	0.861006i	$0.330165\pi$
$390$	10.3947	0.526358
$391$	−65.3353	−3.30415
$392$	47.5417	2.40122
$393$	−5.06341	−0.255415
$394$	−47.1541	−2.37559
$395$	−2.92113	−0.146978
$396$	−4.98681	−0.250597
$397$	15.2183	0.763785	0.381892	−	0.924207i	$-0.375272\pi$
$397$	15.2183	0.763785	0.381892	+	0.924207i	$0.375272\pi$
$398$	−34.8985	−1.74930
$399$	0.812230	0.0406624
$400$	−11.3600	−0.567998
$401$	17.5860	0.878201	0.439100	−	0.898438i	$-0.355297\pi$
$401$	17.5860	0.878201	0.439100	+	0.898438i	$0.355297\pi$
$402$	−59.5607	−2.97062
$403$	1.31147	0.0653289
$404$	−48.8428	−2.43002
$405$	−14.9796	−0.744344
$406$	9.45790	0.469388
$407$	−21.1688	−1.04930
$408$	100.776	4.98915
$409$	−10.0361	−0.496255	−0.248127	−	0.968727i	$-0.579815\pi$
$409$	−10.0361	−0.496255	−0.248127	+	0.968727i	$0.579815\pi$
$410$	−3.74969	−0.185184
$411$	18.7600	0.925363
$412$	13.0009	0.640508
$413$	3.12756	0.153897
$414$	−10.2181	−0.502192
$415$	−20.7528	−1.01871
$416$	−18.1682	−0.890771
$417$	17.3850	0.851348
$418$	2.64900	0.129567
$419$	8.76747	0.428319	0.214160	−	0.976799i	$-0.431299\pi$
$419$	8.76747	0.428319	0.214160	+	0.976799i	$0.431299\pi$
$420$	−18.2653	−0.891253
$421$	2.53754	0.123672	0.0618361	−	0.998086i	$-0.480304\pi$
$421$	2.53754	0.123672	0.0618361	+	0.998086i	$0.480304\pi$
$422$	−34.1936	−1.66452
$423$	−1.72795	−0.0840159
$424$	−46.7692	−2.27131
$425$	−7.34557	−0.356313
$426$	−60.9806	−2.95452
$427$	−1.87719	−0.0908434
$428$	76.4289	3.69433
$429$	−4.23462	−0.204449
$430$	−37.1687	−1.79243
$431$	−1.99001	−0.0958555	−0.0479278	−	0.998851i	$-0.515262\pi$
$431$	−1.99001	−0.0958555	−0.0479278	+	0.998851i	$0.515262\pi$
$432$	65.0576	3.13008
$433$	−34.3799	−1.65219	−0.826095	−	0.563530i	$-0.809443\pi$
$433$	−34.3799	−1.65219	−0.826095	+	0.563530i	$0.809443\pi$
$434$	−3.20816	−0.153997
$435$	10.2127	0.489660
$436$	−82.5993	−3.95579
$437$	3.89891	0.186510
$438$	44.1480	2.10947
$439$	−3.65824	−0.174598	−0.0872992	−	0.996182i	$-0.527824\pi$
$439$	−3.65824	−0.174598	−0.0872992	+	0.996182i	$0.527824\pi$
$440$	−36.2098	−1.72624
$441$	2.57980	0.122847
$442$	−24.7304	−1.17630
$443$	−19.5677	−0.929690	−0.464845	−	0.885392i	$-0.653890\pi$
$443$	−19.5677	−0.929690	−0.464845	+	0.885392i	$0.653890\pi$
$444$	79.0623	3.75213
$445$	−17.0582	−0.808638
$446$	11.5678	0.547753
$447$	−21.9475	−1.03808
$448$	18.0898	0.854664
$449$	−11.7504	−0.554536	−0.277268	−	0.960793i	$-0.589429\pi$
$449$	−11.7504	−0.554536	−0.277268	+	0.960793i	$0.589429\pi$
$450$	−1.14881	−0.0541553
$451$	1.52756	0.0719298
$452$	−42.7317	−2.00993
$453$	33.8209	1.58904
$454$	−25.8661	−1.21396
$455$	2.72457	0.127730
$456$	−6.01384	−0.281624
$457$	41.4040	1.93680	0.968399	−	0.249407i	$-0.0802357\pi$
$457$	41.4040	1.93680	0.968399	+	0.249407i	$0.0802357\pi$
$458$	−52.9040	−2.47204
$459$	42.0675	1.96354
$460$	−87.6779	−4.08800
$461$	−33.5107	−1.56075	−0.780375	−	0.625312i	$-0.784972\pi$
$461$	−33.5107	−1.56075	−0.780375	+	0.625312i	$0.784972\pi$
$462$	10.3589	0.481938
$463$	1.76239	0.0819050	0.0409525	−	0.999161i	$-0.486961\pi$
$463$	1.76239	0.0819050	0.0409525	+	0.999161i	$0.486961\pi$
$464$	−37.5757	−1.74441
$465$	−3.46418	−0.160647
$466$	−71.6661	−3.31987
$467$	−1.96291	−0.0908325	−0.0454162	−	0.998968i	$-0.514461\pi$
$467$	−1.96291	−0.0908325	−0.0454162	+	0.998968i	$0.514461\pi$
$468$	−2.77822	−0.128423
$469$	−15.6115	−0.720871
$470$	−20.6413	−0.952113
$471$	15.9669	0.735714
$472$	−23.1568	−1.06588
$473$	15.1418	0.696221
$474$	−6.18742	−0.284198
$475$	0.438350	0.0201129
$476$	43.4553	1.99177
$477$	−2.53788	−0.116201
$478$	66.8581	3.05802
$479$	−37.9103	−1.73217	−0.866083	−	0.499899i	$-0.833370\pi$
$479$	−37.9103	−1.73217	−0.866083	+	0.499899i	$0.833370\pi$
$480$	47.9905	2.19046
$481$	−11.7935	−0.537735
$482$	10.8023	0.492030
$483$	15.2466	0.693745
$484$	−31.8333	−1.44697
$485$	−18.7994	−0.853635
$486$	12.3030	0.558077
$487$	30.0552	1.36193	0.680965	−	0.732316i	$-0.261561\pi$
$487$	30.0552	1.36193	0.680965	+	0.732316i	$0.261561\pi$
$488$	13.8989	0.629173
$489$	27.9512	1.26400
$490$	30.8171	1.39217
$491$	0.175799	0.00793369	0.00396684	−	0.999992i	$-0.498737\pi$
$491$	0.175799	0.00793369	0.00396684	+	0.999992i	$0.498737\pi$
$492$	−5.70518	−0.257209
$493$	−24.2972	−1.09429
$494$	1.47580	0.0663992
$495$	−1.96488	−0.0883150
$496$	12.7458	0.572305
$497$	−15.9836	−0.716963
$498$	−43.9577	−1.96979
$499$	−25.6199	−1.14690	−0.573452	−	0.819239i	$-0.694396\pi$
$499$	−25.6199	−1.14690	−0.573452	+	0.819239i	$0.694396\pi$
$500$	−61.1013	−2.73253
$501$	15.2210	0.680023
$502$	−69.1473	−3.08620
$503$	−20.3981	−0.909507	−0.454754	−	0.890617i	$-0.650273\pi$
$503$	−20.3981	−0.909507	−0.454754	+	0.890617i	$0.650273\pi$
$504$	4.13106	0.184012
$505$	−19.2449	−0.856385
$506$	49.7253	2.21056
$507$	18.4073	0.817497
$508$	89.8047	3.98444
$509$	30.7274	1.36197	0.680985	−	0.732298i	$-0.261552\pi$
$509$	30.7274	1.36197	0.680985	+	0.732298i	$0.261552\pi$
$510$	65.3241	2.89260
$511$	11.5716	0.511899
$512$	18.5547	0.820008
$513$	−2.51040	−0.110837
$514$	54.4105	2.39994
$515$	5.12256	0.225727
$516$	−56.5523	−2.48957
$517$	8.40889	0.369823
$518$	28.8495	1.26758
$519$	−18.3415	−0.805105
$520$	−20.1730	−0.884644
$521$	23.0172	1.00840	0.504200	−	0.863587i	$-0.331787\pi$
$521$	23.0172	1.00840	0.504200	+	0.863587i	$0.331787\pi$
$522$	−3.79995	−0.166319
$523$	−28.5621	−1.24893	−0.624466	−	0.781052i	$-0.714683\pi$
$523$	−28.5621	−1.24893	−0.624466	+	0.781052i	$0.714683\pi$
$524$	16.1660	0.706215
$525$	1.71416	0.0748120
$526$	−41.4743	−1.80836
$527$	8.24172	0.359015
$528$	−41.1553	−1.79105
$529$	50.1877	2.18207
$530$	−30.3163	−1.31686
$531$	−1.25658	−0.0545308
$532$	−2.59321	−0.112430
$533$	0.851022	0.0368618
$534$	−36.1321	−1.56359
$535$	30.1142	1.30195
$536$	115.589	4.99269
$537$	−17.1384	−0.739575
$538$	80.1337	3.45481
$539$	−12.5543	−0.540752
$540$	56.4533	2.42936
$541$	−41.5173	−1.78497	−0.892484	−	0.451080i	$-0.851039\pi$
$541$	−41.5173	−1.78497	−0.892484	+	0.451080i	$0.851039\pi$
$542$	−42.2758	−1.81590
$543$	35.8938	1.54035
$544$	−114.175	−4.89523
$545$	−32.5454	−1.39409
$546$	5.77107	0.246979
$547$	−27.3072	−1.16757	−0.583786	−	0.811908i	$-0.698429\pi$
$547$	−27.3072	−1.16757	−0.583786	+	0.811908i	$0.698429\pi$
$548$	−59.8953	−2.55860
$549$	0.754207	0.0321888
$550$	5.59055	0.238382
$551$	1.44995	0.0617698
$552$	−112.888	−4.80481
$553$	−1.62179	−0.0689653
$554$	40.2807	1.71136
$555$	31.1518	1.32232
$556$	−55.5053	−2.35395
$557$	1.80996	0.0766905	0.0383452	−	0.999265i	$-0.487791\pi$
$557$	1.80996	0.0766905	0.0383452	+	0.999265i	$0.487791\pi$
$558$	1.28896	0.0545660
$559$	8.43571	0.356792
$560$	26.4794	1.11896
$561$	−26.6118	−1.12355
$562$	−3.72345	−0.157064
$563$	−36.2814	−1.52908	−0.764540	−	0.644577i	$-0.777034\pi$
$563$	−36.2814	−1.52908	−0.764540	+	0.644577i	$0.777034\pi$
$564$	−31.4059	−1.32243
$565$	−16.8370	−0.708337
$566$	10.7643	0.452459
$567$	−8.31656	−0.349263
$568$	118.344	4.96562
$569$	−19.1550	−0.803020	−0.401510	−	0.915855i	$-0.631515\pi$
$569$	−19.1550	−0.803020	−0.401510	+	0.915855i	$0.631515\pi$
$570$	−3.89824	−0.163279
$571$	30.6443	1.28242	0.641212	−	0.767364i	$-0.278432\pi$
$571$	30.6443	1.28242	0.641212	+	0.767364i	$0.278432\pi$
$572$	13.5199	0.565296
$573$	−12.4509	−0.520142
$574$	−2.08180	−0.0868926
$575$	8.22840	0.343148
$576$	−7.26805	−0.302836
$577$	−3.65233	−0.152049	−0.0760243	−	0.997106i	$-0.524223\pi$
$577$	−3.65233	−0.152049	−0.0760243	+	0.997106i	$0.524223\pi$
$578$	−110.116	−4.58022
$579$	10.9665	0.455751
$580$	−32.6061	−1.35389
$581$	−11.5218	−0.478003
$582$	−39.8201	−1.65060
$583$	12.3503	0.511498
$584$	−85.6777	−3.54537
$585$	−1.09466	−0.0452588
$586$	−5.98642	−0.247297
$587$	−4.07613	−0.168240	−0.0841199	−	0.996456i	$-0.526808\pi$
$587$	−4.07613	−0.168240	−0.0841199	+	0.996456i	$0.526808\pi$
$588$	46.8883	1.93364
$589$	−0.491828	−0.0202654
$590$	−15.0105	−0.617972
$591$	−28.2688	−1.16282
$592$	−114.618	−4.71076
$593$	−42.0907	−1.72846	−0.864230	−	0.503097i	$-0.832194\pi$
$593$	−42.0907	−1.72846	−0.864230	+	0.503097i	$0.832194\pi$
$594$	−32.0166	−1.31366
$595$	17.1221	0.701937
$596$	70.0721	2.87026
$597$	−20.9215	−0.856262
$598$	27.7026	1.13284
$599$	−10.4078	−0.425251	−0.212626	−	0.977134i	$-0.568201\pi$
$599$	−10.4078	−0.425251	−0.212626	+	0.977134i	$0.568201\pi$
$600$	−12.6918	−0.518141
$601$	16.6863	0.680647	0.340323	−	0.940308i	$-0.389463\pi$
$601$	16.6863	0.680647	0.340323	+	0.940308i	$0.389463\pi$
$602$	−20.6357	−0.841049
$603$	6.27231	0.255428
$604$	−107.980	−4.39366
$605$	−12.5428	−0.509939
$606$	−40.7637	−1.65591
$607$	−24.1386	−0.979756	−0.489878	−	0.871791i	$-0.662959\pi$
$607$	−24.1386	−0.979756	−0.489878	+	0.871791i	$0.662959\pi$
$608$	6.81346	0.276322
$609$	5.66998	0.229759
$610$	9.00942	0.364781
$611$	4.68471	0.189523
$612$	−17.4593	−0.705750
$613$	−25.6917	−1.03768	−0.518840	−	0.854871i	$-0.673636\pi$
$613$	−25.6917	−1.03768	−0.518840	+	0.854871i	$0.673636\pi$
$614$	4.34648	0.175410
$615$	−2.24793	−0.0906453
$616$	−20.1034	−0.809988
$617$	2.02244	0.0814202	0.0407101	−	0.999171i	$-0.487038\pi$
$617$	2.02244	0.0814202	0.0407101	+	0.999171i	$0.487038\pi$
$618$	10.8504	0.436468
$619$	19.5508	0.785812	0.392906	−	0.919579i	$-0.371470\pi$
$619$	19.5508	0.785812	0.392906	+	0.919579i	$0.371470\pi$
$620$	11.0601	0.444185
$621$	−47.1234	−1.89100
$622$	−9.60712	−0.385211
$623$	−9.47058	−0.379431
$624$	−22.9281	−0.917861
$625$	−19.2658	−0.770630
$626$	13.2688	0.530326
$627$	1.58807	0.0634214
$628$	−50.9776	−2.03423
$629$	−74.1140	−2.95512
$630$	2.67780	0.106686
$631$	12.6117	0.502063	0.251031	−	0.967979i	$-0.419230\pi$
$631$	12.6117	0.502063	0.251031	+	0.967979i	$0.419230\pi$
$632$	12.0079	0.477648
$633$	−20.4989	−0.814760
$634$	−61.5488	−2.44441
$635$	35.3845	1.40419
$636$	−46.1264	−1.82903
$637$	−6.99417	−0.277119
$638$	18.4921	0.732108
$639$	6.42183	0.254044
$640$	−26.7359	−1.05683
$641$	−28.0899	−1.10948	−0.554742	−	0.832022i	$-0.687183\pi$
$641$	−28.0899	−1.10948	−0.554742	+	0.832022i	$0.687183\pi$
$642$	63.7867	2.51746
$643$	24.1860	0.953804	0.476902	−	0.878956i	$-0.341760\pi$
$643$	24.1860	0.953804	0.476902	+	0.878956i	$0.341760\pi$
$644$	−48.6780	−1.91818
$645$	−22.2825	−0.877372
$646$	9.27440	0.364896
$647$	30.0285	1.18054	0.590270	−	0.807206i	$-0.299021\pi$
$647$	30.0285	1.18054	0.590270	+	0.807206i	$0.299021\pi$
$648$	61.5767	2.41896
$649$	6.11500	0.240035
$650$	3.11457	0.122164
$651$	−1.92328	−0.0753794
$652$	−89.2400	−3.49491
$653$	−33.2571	−1.30145	−0.650726	−	0.759312i	$-0.725535\pi$
$653$	−33.2571	−1.30145	−0.650726	+	0.759312i	$0.725535\pi$
$654$	−68.9365	−2.69563
$655$	6.36966	0.248883
$656$	8.27087	0.322923
$657$	−4.64920	−0.181383
$658$	−11.4599	−0.446753
$659$	45.6106	1.77674	0.888369	−	0.459130i	$-0.151839\pi$
$659$	45.6106	1.77674	0.888369	+	0.459130i	$0.151839\pi$
$660$	−35.7122	−1.39009
$661$	−6.70039	−0.260615	−0.130307	−	0.991474i	$-0.541596\pi$
$661$	−6.70039	−0.260615	−0.130307	+	0.991474i	$0.541596\pi$
$662$	−4.58197	−0.178083
$663$	−14.8258	−0.575786
$664$	85.3084	3.31061
$665$	−1.02177	−0.0396225
$666$	−11.5910	−0.449144
$667$	27.2174	1.05386
$668$	−48.5962	−1.88024
$669$	6.93488	0.268118
$670$	74.9261	2.89465
$671$	−3.67027	−0.141689
$672$	26.6439	1.02781
$673$	41.2224	1.58901	0.794504	−	0.607259i	$-0.207731\pi$
$673$	41.2224	1.58901	0.794504	+	0.607259i	$0.207731\pi$
$674$	−26.5088	−1.02108
$675$	−5.29803	−0.203921
$676$	−58.7692	−2.26035
$677$	36.4769	1.40192	0.700961	−	0.713199i	$-0.252755\pi$
$677$	36.4769	1.40192	0.700961	+	0.713199i	$0.252755\pi$
$678$	−35.6634	−1.36965
$679$	−10.4372	−0.400545
$680$	−126.774	−4.86156
$681$	−15.5067	−0.594216
$682$	−6.27259	−0.240190
$683$	45.4940	1.74078	0.870389	−	0.492364i	$-0.163867\pi$
$683$	45.4940	1.74078	0.870389	+	0.492364i	$0.163867\pi$
$684$	1.04189	0.0398377
$685$	−23.5997	−0.901698
$686$	37.9191	1.44776
$687$	−31.7158	−1.21003
$688$	81.9846	3.12563
$689$	6.88052	0.262127
$690$	−73.1750	−2.78573
$691$	27.1568	1.03309	0.516546	−	0.856259i	$-0.327217\pi$
$691$	27.1568	1.03309	0.516546	+	0.856259i	$0.327217\pi$
$692$	58.5593	2.22609
$693$	−1.09089	−0.0414394
$694$	−55.8903	−2.12157
$695$	−21.8700	−0.829576
$696$	−41.9812	−1.59129
$697$	5.34811	0.202574
$698$	8.39881	0.317900
$699$	−42.9636	−1.62503
$700$	−5.47281	−0.206853
$701$	−29.0570	−1.09747	−0.548734	−	0.835997i	$-0.684890\pi$
$701$	−29.0570	−1.09747	−0.548734	+	0.835997i	$0.684890\pi$
$702$	−17.8369	−0.673211
$703$	4.42279	0.166809
$704$	35.3692	1.33303
$705$	−12.3744	−0.466047
$706$	17.0340	0.641083
$707$	−10.6846	−0.401835
$708$	−22.8385	−0.858325
$709$	−41.8698	−1.57245	−0.786227	−	0.617938i	$-0.787968\pi$
$709$	−41.8698	−1.57245	−0.786227	+	0.617938i	$0.787968\pi$
$710$	76.7122	2.87896
$711$	0.651594	0.0244367
$712$	70.1212	2.62790
$713$	−9.23225	−0.345750
$714$	36.2674	1.35727
$715$	5.32706	0.199221
$716$	54.7178	2.04490
$717$	40.0812	1.49686
$718$	−22.0492	−0.822868
$719$	−18.6215	−0.694464	−0.347232	−	0.937779i	$-0.612878\pi$
$719$	−18.6215	−0.694464	−0.347232	+	0.937779i	$0.612878\pi$
$720$	−10.6388	−0.396484
$721$	2.84400	0.105916
$722$	50.0740	1.86356
$723$	6.47592	0.240842
$724$	−114.598	−4.25902
$725$	3.06002	0.113646
$726$	−26.5677	−0.986021
$727$	−40.1350	−1.48853	−0.744263	−	0.667887i	$-0.767199\pi$
$727$	−40.1350	−1.48853	−0.744263	+	0.667887i	$0.767199\pi$
$728$	−11.1999	−0.415095
$729$	29.7386	1.10143
$730$	−55.5373	−2.05553
$731$	53.0129	1.96075
$732$	13.7079	0.506657
$733$	−23.8093	−0.879417	−0.439709	−	0.898141i	$-0.644918\pi$
$733$	−23.8093	−0.879417	−0.439709	+	0.898141i	$0.644918\pi$
$734$	−56.1678	−2.07319
$735$	18.4747	0.681451
$736$	127.898	4.71437
$737$	−30.5235	−1.12435
$738$	0.836415	0.0307889
$739$	3.67138	0.135054	0.0675270	−	0.997717i	$-0.478489\pi$
$739$	3.67138	0.135054	0.0675270	+	0.997717i	$0.478489\pi$
$740$	−99.4587	−3.65617
$741$	0.884735	0.0325016
$742$	−16.8314	−0.617899
$743$	15.9700	0.585883	0.292941	−	0.956130i	$-0.405366\pi$
$743$	15.9700	0.585883	0.292941	+	0.956130i	$0.405366\pi$
$744$	14.2402	0.522071
$745$	27.6095	1.01153
$746$	−1.92337	−0.0704195
$747$	4.62916	0.169372
$748$	84.9638	3.10658
$749$	16.7191	0.610904
$750$	−50.9945	−1.86206
$751$	−26.2066	−0.956291	−0.478145	−	0.878281i	$-0.658691\pi$
$751$	−26.2066	−0.956291	−0.478145	+	0.878281i	$0.658691\pi$
$752$	45.5295	1.66029
$753$	−41.4536	−1.51065
$754$	10.3022	0.375183
$755$	−42.5460	−1.54841
$756$	31.3424	1.13991
$757$	35.1717	1.27834	0.639169	−	0.769067i	$-0.279279\pi$
$757$	35.1717	1.27834	0.639169	+	0.769067i	$0.279279\pi$
$758$	87.7869	3.18856
$759$	29.8101	1.08204
$760$	7.56528	0.274422
$761$	11.2085	0.406309	0.203154	−	0.979147i	$-0.434881\pi$
$761$	11.2085	0.406309	0.203154	+	0.979147i	$0.434881\pi$
$762$	74.9500	2.71515
$763$	−18.0689	−0.654140
$764$	39.7520	1.43818
$765$	−6.87924	−0.248719
$766$	−69.5801	−2.51403
$767$	3.40675	0.123010
$768$	−4.82868	−0.174240
$769$	−19.3690	−0.698464	−0.349232	−	0.937036i	$-0.613557\pi$
$769$	−19.3690	−0.698464	−0.349232	+	0.937036i	$0.613557\pi$
$770$	−13.0312	−0.469613
$771$	32.6189	1.17474
$772$	−35.0127	−1.26014
$773$	−51.1801	−1.84082	−0.920410	−	0.390954i	$-0.872145\pi$
$773$	−51.1801	−1.84082	−0.920410	+	0.390954i	$0.872145\pi$
$774$	8.29092	0.298011
$775$	−1.03797	−0.0372850
$776$	77.2785	2.77414
$777$	17.2952	0.620462
$778$	−53.4575	−1.91655
$779$	−0.319151	−0.0114348
$780$	−19.8957	−0.712382
$781$	−31.2511	−1.11825
$782$	174.093	6.22554
$783$	−17.5245	−0.626274
$784$	−67.9746	−2.42767
$785$	−20.0860	−0.716899
$786$	13.4920	0.481243
$787$	23.6171	0.841857	0.420929	−	0.907094i	$-0.361704\pi$
$787$	23.6171	0.841857	0.420929	+	0.907094i	$0.361704\pi$
$788$	90.2539	3.21516
$789$	−24.8637	−0.885171
$790$	7.78364	0.276930
$791$	−9.34775	−0.332368
$792$	8.07705	0.287005
$793$	−2.04476	−0.0726114
$794$	−40.5507	−1.43909
$795$	−18.1746	−0.644585
$796$	66.7964	2.36754
$797$	36.5322	1.29404	0.647019	−	0.762474i	$-0.276016\pi$
$797$	36.5322	1.29404	0.647019	+	0.762474i	$0.276016\pi$
$798$	−2.16427	−0.0766143
$799$	29.4403	1.04152
$800$	14.3794	0.508388
$801$	3.80505	0.134445
$802$	−46.8596	−1.65467
$803$	22.6249	0.798414
$804$	114.000	4.02049
$805$	−19.1799	−0.676003
$806$	−3.49454	−0.123090
$807$	48.0399	1.69109
$808$	79.1098	2.78307
$809$	0.553328	0.0194540	0.00972698	−	0.999953i	$-0.496904\pi$
$809$	0.553328	0.0194540	0.00972698	+	0.999953i	$0.496904\pi$
$810$	39.9147	1.40246
$811$	−22.7689	−0.799524	−0.399762	−	0.916619i	$-0.630907\pi$
$811$	−22.7689	−0.799524	−0.399762	+	0.916619i	$0.630907\pi$
$812$	−18.1026	−0.635277
$813$	−25.3442	−0.888861
$814$	56.4065	1.97705
$815$	−35.1620	−1.23167
$816$	−144.088	−5.04410
$817$	−3.16356	−0.110679
$818$	26.7423	0.935023
$819$	−0.607748	−0.0212364
$820$	7.17699	0.250631
$821$	−18.1421	−0.633165	−0.316583	−	0.948565i	$-0.602535\pi$
$821$	−18.1421	−0.633165	−0.316583	+	0.948565i	$0.602535\pi$
$822$	−49.9880	−1.74353
$823$	28.3980	0.989892	0.494946	−	0.868924i	$-0.335188\pi$
$823$	28.3980	0.989892	0.494946	+	0.868924i	$0.335188\pi$
$824$	−21.0573	−0.733566
$825$	3.35152	0.116685
$826$	−8.33370	−0.289966
$827$	−0.261633	−0.00909786	−0.00454893	−	0.999990i	$-0.501448\pi$
$827$	−0.261633	−0.00909786	−0.00454893	+	0.999990i	$0.501448\pi$
$828$	19.5576	0.679675
$829$	−31.8534	−1.10632	−0.553158	−	0.833077i	$-0.686577\pi$
$829$	−31.8534	−1.10632	−0.553158	+	0.833077i	$0.686577\pi$
$830$	55.2979	1.91942
$831$	24.1482	0.837690
$832$	19.7047	0.683136
$833$	−43.9537	−1.52291
$834$	−46.3241	−1.60407
$835$	−19.1477	−0.662632
$836$	−5.07025	−0.175358
$837$	5.94438	0.205468
$838$	−23.3618	−0.807021
$839$	37.5771	1.29731	0.648653	−	0.761084i	$-0.275332\pi$
$839$	37.5771	1.29731	0.648653	+	0.761084i	$0.275332\pi$
$840$	29.5839	1.02074
$841$	−18.8783	−0.650975
$842$	−6.76154	−0.233018
$843$	−2.23220	−0.0768810
$844$	65.4472	2.25278
$845$	−23.1560	−0.796590
$846$	4.60430	0.158299
$847$	−6.96367	−0.239275
$848$	66.8701	2.29633
$849$	6.45319	0.221473
$850$	19.5730	0.671349
$851$	83.0214	2.84594
$852$	116.718	3.99869
$853$	42.8315	1.46652	0.733262	−	0.679946i	$-0.237997\pi$
$853$	42.8315	1.46652	0.733262	+	0.679946i	$0.237997\pi$
$854$	5.00195	0.171163
$855$	0.410521	0.0140395
$856$	−123.790	−4.23107
$857$	−1.07522	−0.0367289	−0.0183645	−	0.999831i	$-0.505846\pi$
$857$	−1.07522	−0.0367289	−0.0183645	+	0.999831i	$0.505846\pi$
$858$	11.2836	0.385215
$859$	−5.82651	−0.198798	−0.0993990	−	0.995048i	$-0.531692\pi$
$859$	−5.82651	−0.198798	−0.0993990	+	0.995048i	$0.531692\pi$
$860$	71.1415	2.42591
$861$	−1.24803	−0.0425328
$862$	5.30259	0.180607
$863$	−41.4276	−1.41021	−0.705107	−	0.709101i	$-0.749101\pi$
$863$	−41.4276	−1.41021	−0.705107	+	0.709101i	$0.749101\pi$
$864$	−82.3495	−2.80159
$865$	23.0733	0.784515
$866$	91.6086	3.11299
$867$	−66.0142	−2.24196
$868$	6.14048	0.208422
$869$	−3.17091	−0.107566
$870$	−27.2127	−0.922596
$871$	−17.0051	−0.576194
$872$	133.784	4.53051
$873$	4.19343	0.141926
$874$	−10.3890	−0.351415
$875$	−13.3662	−0.451859
$876$	−84.5002	−2.85500
$877$	−48.3929	−1.63411	−0.817056	−	0.576558i	$-0.804395\pi$
$877$	−48.3929	−1.63411	−0.817056	+	0.576558i	$0.804395\pi$
$878$	9.74776	0.328971
$879$	−3.58884	−0.121049
$880$	51.7724	1.74525
$881$	−16.6981	−0.562574	−0.281287	−	0.959624i	$-0.590761\pi$
$881$	−16.6981	−0.562574	−0.281287	+	0.959624i	$0.590761\pi$
$882$	−6.87413	−0.231464
$883$	−39.1439	−1.31730	−0.658648	−	0.752451i	$-0.728872\pi$
$883$	−39.1439	−1.31730	−0.658648	+	0.752451i	$0.728872\pi$
$884$	47.3345	1.59203
$885$	−8.99875	−0.302490
$886$	52.1402	1.75168
$887$	−29.0045	−0.973877	−0.486938	−	0.873436i	$-0.661886\pi$
$887$	−29.0045	−0.973877	−0.486938	+	0.873436i	$0.661886\pi$
$888$	−128.056	−4.29726
$889$	19.6452	0.658877
$890$	45.4534	1.52360
$891$	−16.2605	−0.544748
$892$	−22.1411	−0.741338
$893$	−1.75686	−0.0587911
$894$	58.4814	1.95591
$895$	21.5597	0.720661
$896$	−14.8435	−0.495888
$897$	16.6076	0.554513
$898$	31.3101	1.04483
$899$	−3.43333	−0.114508
$900$	2.19884	0.0732947
$901$	43.2395	1.44052
$902$	−4.07033	−0.135527
$903$	−12.3710	−0.411683
$904$	69.2117	2.30195
$905$	−45.1536	−1.50096
$906$	−90.1192	−2.99401
$907$	18.5967	0.617494	0.308747	−	0.951144i	$-0.400090\pi$
$907$	18.5967	0.617494	0.308747	+	0.951144i	$0.400090\pi$
$908$	49.5083	1.64299
$909$	4.29280	0.142383
$910$	−7.25988	−0.240663
$911$	−14.9959	−0.496836	−0.248418	−	0.968653i	$-0.579911\pi$
$911$	−14.9959	−0.496836	−0.248418	+	0.968653i	$0.579911\pi$
$912$	8.59853	0.284726
$913$	−22.5273	−0.745545
$914$	−110.325	−3.64923
$915$	5.40112	0.178555
$916$	101.259	3.34570
$917$	3.53638	0.116782
$918$	−112.093	−3.69963
$919$	−10.0711	−0.332215	−0.166108	−	0.986108i	$-0.553120\pi$
$919$	−10.0711	−0.332215	−0.166108	+	0.986108i	$0.553120\pi$
$920$	142.010	4.68194
$921$	2.60570	0.0858608
$922$	89.2927	2.94070
$923$	−17.4104	−0.573071
$924$	−19.8271	−0.652263
$925$	9.33400	0.306900
$926$	−4.69606	−0.154322
$927$	−1.14265	−0.0375296
$928$	47.5632	1.56134
$929$	22.3460	0.733148	0.366574	−	0.930389i	$-0.380531\pi$
$929$	22.3460	0.733148	0.366574	+	0.930389i	$0.380531\pi$
$930$	9.23065	0.302685
$931$	2.62296	0.0859640
$932$	137.170	4.49316
$933$	−5.75944	−0.188556
$934$	5.23036	0.171143
$935$	33.4771	1.09482
$936$	4.49983	0.147082
$937$	−15.8262	−0.517019	−0.258509	−	0.966009i	$-0.583231\pi$
$937$	−15.8262	−0.517019	−0.258509	+	0.966009i	$0.583231\pi$
$938$	41.5983	1.35823
$939$	7.95458	0.259588
$940$	39.5079	1.28861
$941$	−38.0620	−1.24078	−0.620392	−	0.784292i	$-0.713027\pi$
$941$	−38.0620	−1.24078	−0.620392	+	0.784292i	$0.713027\pi$
$942$	−42.5453	−1.38620
$943$	−5.99087	−0.195090
$944$	33.1093	1.07762
$945$	12.3494	0.401726
$946$	−40.3469	−1.31179
$947$	28.3042	0.919762	0.459881	−	0.887981i	$-0.347892\pi$
$947$	28.3042	0.919762	0.459881	+	0.887981i	$0.347892\pi$
$948$	11.8428	0.384638
$949$	12.6046	0.409163
$950$	−1.16803	−0.0378958
$951$	−36.8983	−1.19651
$952$	−70.3838	−2.28115
$953$	7.23029	0.234212	0.117106	−	0.993119i	$-0.462638\pi$
$953$	7.23029	0.234212	0.117106	+	0.993119i	$0.462638\pi$
$954$	6.76243	0.218942
$955$	15.6629	0.506840
$956$	−127.968	−4.13877
$957$	11.0859	0.358357
$958$	101.016	3.26368
$959$	−13.1024	−0.423097
$960$	−52.0488	−1.67987
$961$	−29.8354	−0.962432
$962$	31.4248	1.01318
$963$	−6.71734	−0.216463
$964$	−20.6757	−0.665921
$965$	−13.7956	−0.444095
$966$	−40.6261	−1.30712
$967$	8.01830	0.257851	0.128926	−	0.991654i	$-0.458847\pi$
$967$	8.01830	0.257851	0.128926	+	0.991654i	$0.458847\pi$
$968$	51.5598	1.65719
$969$	5.55998	0.178612
$970$	50.0928	1.60838
$971$	58.2186	1.86832	0.934162	−	0.356850i	$-0.116149\pi$
$971$	58.2186	1.86832	0.934162	+	0.356850i	$0.116149\pi$
$972$	−23.5482	−0.755310
$973$	−12.1420	−0.389255
$974$	−80.0850	−2.56609
$975$	1.86718	0.0597975
$976$	−19.8725	−0.636103
$977$	−21.3508	−0.683072	−0.341536	−	0.939869i	$-0.610947\pi$
$977$	−21.3508	−0.683072	−0.341536	+	0.939869i	$0.610947\pi$
$978$	−74.4788	−2.38157
$979$	−18.5169	−0.591801
$980$	−58.9845	−1.88419
$981$	7.25966	0.231783
$982$	−0.468434	−0.0149483
$983$	−54.0870	−1.72511	−0.862553	−	0.505966i	$-0.831136\pi$
$983$	−54.0870	−1.72511	−0.862553	+	0.505966i	$0.831136\pi$
$984$	9.24056	0.294578
$985$	35.5615	1.13308
$986$	64.7424	2.06182
$987$	−6.87017	−0.218680
$988$	−2.82470	−0.0898658
$989$	−59.3842	−1.88831
$990$	5.23563	0.166399
$991$	−45.2937	−1.43880	−0.719401	−	0.694595i	$-0.755584\pi$
$991$	−45.2937	−1.43880	−0.719401	+	0.694595i	$0.755584\pi$
$992$	−16.1336	−0.512243
$993$	−2.74687	−0.0871694
$994$	42.5900	1.35087
$995$	26.3189	0.834364
$996$	84.1359	2.66595
$997$	35.9119	1.13734	0.568670	−	0.822566i	$-0.307458\pi$
$997$	35.9119	1.13734	0.568670	+	0.822566i	$0.307458\pi$
$998$	68.2668	2.16095
$999$	−53.4551	−1.69124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.e.1.7	✓	221

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.e.1.7	✓	221	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66460 q^{2} -1.59742 q^{3} +5.10010 q^{4} +2.00952 q^{5} +4.25649 q^{6} +1.11567 q^{7} -8.26053 q^{8} -0.448248 q^{9} +O(q^{10})\)	\(q-2.66460 q^{2} -1.59742 q^{3} +5.10010 q^{4} +2.00952 q^{5} +4.25649 q^{6} +1.11567 q^{7} -8.26053 q^{8} -0.448248 q^{9} -5.35457 q^{10} +2.18135 q^{11} -8.14700 q^{12} +1.21526 q^{13} -2.97281 q^{14} -3.21005 q^{15} +11.8108 q^{16} +7.63711 q^{17} +1.19440 q^{18} -0.455748 q^{19} +10.2488 q^{20} -1.78219 q^{21} -5.81243 q^{22} -8.55498 q^{23} +13.1955 q^{24} -0.961826 q^{25} -3.23819 q^{26} +5.50830 q^{27} +5.69002 q^{28} -3.18147 q^{29} +8.55350 q^{30} +1.07917 q^{31} -14.9501 q^{32} -3.48454 q^{33} -20.3499 q^{34} +2.24196 q^{35} -2.28611 q^{36} -9.70446 q^{37} +1.21439 q^{38} -1.94128 q^{39} -16.5997 q^{40} +0.700279 q^{41} +4.74883 q^{42} +6.94148 q^{43} +11.1251 q^{44} -0.900764 q^{45} +22.7956 q^{46} +3.85490 q^{47} -18.8669 q^{48} -5.75528 q^{49} +2.56288 q^{50} -12.1997 q^{51} +6.19795 q^{52} +5.66177 q^{53} -14.6774 q^{54} +4.38347 q^{55} -9.21602 q^{56} +0.728021 q^{57} +8.47734 q^{58} +2.80330 q^{59} -16.3716 q^{60} -1.68257 q^{61} -2.87555 q^{62} -0.500097 q^{63} +16.2143 q^{64} +2.44209 q^{65} +9.28490 q^{66} -13.9929 q^{67} +38.9500 q^{68} +13.6659 q^{69} -5.97393 q^{70} -14.3265 q^{71} +3.70277 q^{72} +10.3719 q^{73} +25.8585 q^{74} +1.53644 q^{75} -2.32436 q^{76} +2.43367 q^{77} +5.17274 q^{78} -1.45364 q^{79} +23.7341 q^{80} -7.45433 q^{81} -1.86596 q^{82} -10.3272 q^{83} -9.08936 q^{84} +15.3469 q^{85} -18.4963 q^{86} +5.08214 q^{87} -18.0191 q^{88} -8.48871 q^{89} +2.40018 q^{90} +1.35583 q^{91} -43.6313 q^{92} -1.72388 q^{93} -10.2718 q^{94} -0.915835 q^{95} +23.8816 q^{96} -9.35515 q^{97} +15.3355 q^{98} -0.977788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

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