LMFDB - Embedded newform 6017.2.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30378 q^{2} +2.53807 q^{3} +3.30742 q^{4} +3.98214 q^{5} -5.84717 q^{6} -4.26603 q^{7} -3.01201 q^{8} +3.44182 q^{9} +O(q^{10})$	\(q-2.30378 q^{2} +2.53807 q^{3} +3.30742 q^{4} +3.98214 q^{5} -5.84717 q^{6} -4.26603 q^{7} -3.01201 q^{8} +3.44182 q^{9} -9.17400 q^{10} -1.00000 q^{11} +8.39448 q^{12} +0.239607 q^{13} +9.82801 q^{14} +10.1070 q^{15} +0.324190 q^{16} +1.10862 q^{17} -7.92921 q^{18} +1.67372 q^{19} +13.1706 q^{20} -10.8275 q^{21} +2.30378 q^{22} -3.87775 q^{23} -7.64472 q^{24} +10.8575 q^{25} -0.552003 q^{26} +1.12137 q^{27} -14.1096 q^{28} -2.02650 q^{29} -23.2843 q^{30} +9.78699 q^{31} +5.27717 q^{32} -2.53807 q^{33} -2.55403 q^{34} -16.9879 q^{35} +11.3835 q^{36} -9.41514 q^{37} -3.85589 q^{38} +0.608140 q^{39} -11.9943 q^{40} +7.37283 q^{41} +24.9442 q^{42} +9.44813 q^{43} -3.30742 q^{44} +13.7058 q^{45} +8.93351 q^{46} +10.3308 q^{47} +0.822818 q^{48} +11.1990 q^{49} -25.0133 q^{50} +2.81377 q^{51} +0.792481 q^{52} +12.0331 q^{53} -2.58340 q^{54} -3.98214 q^{55} +12.8493 q^{56} +4.24802 q^{57} +4.66862 q^{58} +4.50186 q^{59} +33.4280 q^{60} -2.69193 q^{61} -22.5471 q^{62} -14.6829 q^{63} -12.8058 q^{64} +0.954149 q^{65} +5.84717 q^{66} -6.26446 q^{67} +3.66668 q^{68} -9.84203 q^{69} +39.1365 q^{70} +8.56057 q^{71} -10.3668 q^{72} -7.48196 q^{73} +21.6905 q^{74} +27.5571 q^{75} +5.53569 q^{76} +4.26603 q^{77} -1.40102 q^{78} -16.5502 q^{79} +1.29097 q^{80} -7.47934 q^{81} -16.9854 q^{82} -0.664294 q^{83} -35.8111 q^{84} +4.41470 q^{85} -21.7664 q^{86} -5.14341 q^{87} +3.01201 q^{88} -9.23046 q^{89} -31.5753 q^{90} -1.02217 q^{91} -12.8254 q^{92} +24.8401 q^{93} -23.7999 q^{94} +6.66499 q^{95} +13.3938 q^{96} -15.9767 q^{97} -25.8001 q^{98} -3.44182 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * 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 $

$2$	−2.30378	−1.62902	−0.814511	−	0.580149i	$-0.802994\pi$
$2$	−2.30378	−1.62902	−0.814511	+	0.580149i	$0.802994\pi$
$3$	2.53807	1.46536	0.732679	−	0.680575i	$-0.238270\pi$
$3$	2.53807	1.46536	0.732679	+	0.680575i	$0.238270\pi$
$4$	3.30742	1.65371
$5$	3.98214	1.78087	0.890434	−	0.455111i	$-0.150401\pi$
$5$	3.98214	1.78087	0.890434	+	0.455111i	$0.150401\pi$
$6$	−5.84717	−2.38710
$7$	−4.26603	−1.61241	−0.806204	−	0.591638i	$-0.798481\pi$
$7$	−4.26603	−1.61241	−0.806204	+	0.591638i	$0.798481\pi$
$8$	−3.01201	−1.06491
$9$	3.44182	1.14727
$10$	−9.17400	−2.90107
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	8.39448	2.42328
$13$	0.239607	0.0664550	0.0332275	−	0.999448i	$-0.489421\pi$
$13$	0.239607	0.0664550	0.0332275	+	0.999448i	$0.489421\pi$
$14$	9.82801	2.62665
$15$	10.1070	2.60961
$16$	0.324190	0.0810475
$17$	1.10862	0.268881	0.134440	−	0.990922i	$-0.457076\pi$
$17$	1.10862	0.268881	0.134440	+	0.990922i	$0.457076\pi$
$18$	−7.92921	−1.86893
$19$	1.67372	0.383978	0.191989	−	0.981397i	$-0.438506\pi$
$19$	1.67372	0.383978	0.191989	+	0.981397i	$0.438506\pi$
$20$	13.1706	2.94504
$21$	−10.8275	−2.36275
$22$	2.30378	0.491168
$23$	−3.87775	−0.808568	−0.404284	−	0.914634i	$-0.632479\pi$
$23$	−3.87775	−0.808568	−0.404284	+	0.914634i	$0.632479\pi$
$24$	−7.64472	−1.56047
$25$	10.8575	2.17149
$26$	−0.552003	−0.108257
$27$	1.12137	0.215808
$28$	−14.1096	−2.66645
$29$	−2.02650	−0.376312	−0.188156	−	0.982139i	$-0.560251\pi$
$29$	−2.02650	−0.376312	−0.188156	+	0.982139i	$0.560251\pi$
$30$	−23.2843	−4.25111
$31$	9.78699	1.75780	0.878898	−	0.477010i	$-0.158279\pi$
$31$	9.78699	1.75780	0.878898	+	0.477010i	$0.158279\pi$
$32$	5.27717	0.932880
$33$	−2.53807	−0.441822
$34$	−2.55403	−0.438012
$35$	−16.9879	−2.87149
$36$	11.3835	1.89726
$37$	−9.41514	−1.54784	−0.773920	−	0.633283i	$-0.781707\pi$
$37$	−9.41514	−1.54784	−0.773920	+	0.633283i	$0.781707\pi$
$38$	−3.85589	−0.625508
$39$	0.608140	0.0973803
$40$	−11.9943	−1.89646
$41$	7.37283	1.15144	0.575721	−	0.817646i	$-0.304721\pi$
$41$	7.37283	1.15144	0.575721	+	0.817646i	$0.304721\pi$
$42$	24.9442	3.84898
$43$	9.44813	1.44083	0.720413	−	0.693545i	$-0.243952\pi$
$43$	9.44813	1.44083	0.720413	+	0.693545i	$0.243952\pi$
$44$	−3.30742	−0.498612
$45$	13.7058	2.04314
$46$	8.93351	1.31717
$47$	10.3308	1.50690	0.753452	−	0.657503i	$-0.228387\pi$
$47$	10.3308	1.50690	0.753452	+	0.657503i	$0.228387\pi$
$48$	0.822818	0.118764
$49$	11.1990	1.59986
$50$	−25.0133	−3.53741
$51$	2.81377	0.394006
$52$	0.792481	0.109897
$53$	12.0331	1.65288	0.826438	−	0.563027i	$-0.190363\pi$
$53$	12.0331	1.65288	0.826438	+	0.563027i	$0.190363\pi$
$54$	−2.58340	−0.351556
$55$	−3.98214	−0.536952
$56$	12.8493	1.71707
$57$	4.24802	0.562665
$58$	4.66862	0.613020
$59$	4.50186	0.586092	0.293046	−	0.956098i	$-0.405331\pi$
$59$	4.50186	0.586092	0.293046	+	0.956098i	$0.405331\pi$
$60$	33.4280	4.31554
$61$	−2.69193	−0.344666	−0.172333	−	0.985039i	$-0.555131\pi$
$61$	−2.69193	−0.344666	−0.172333	+	0.985039i	$0.555131\pi$
$62$	−22.5471	−2.86349
$63$	−14.6829	−1.84987
$64$	−12.8058	−1.60073
$65$	0.954149	0.118348
$66$	5.84717	0.719737
$67$	−6.26446	−0.765326	−0.382663	−	0.923888i	$-0.624993\pi$
$67$	−6.26446	−0.765326	−0.382663	+	0.923888i	$0.624993\pi$
$68$	3.66668	0.444651
$69$	−9.84203	−1.18484
$70$	39.1365	4.67771
$71$	8.56057	1.01595	0.507976	−	0.861371i	$-0.330394\pi$
$71$	8.56057	1.01595	0.507976	+	0.861371i	$0.330394\pi$
$72$	−10.3668	−1.22174
$73$	−7.48196	−0.875697	−0.437849	−	0.899049i	$-0.644259\pi$
$73$	−7.48196	−0.875697	−0.437849	+	0.899049i	$0.644259\pi$
$74$	21.6905	2.52146
$75$	27.5571	3.18202
$76$	5.53569	0.634988
$77$	4.26603	0.486159
$78$	−1.40102	−0.158635
$79$	−16.5502	−1.86204	−0.931021	−	0.364965i	$-0.881081\pi$
$79$	−16.5502	−1.86204	−0.931021	+	0.364965i	$0.881081\pi$
$80$	1.29097	0.144335
$81$	−7.47934	−0.831037
$82$	−16.9854	−1.87572
$83$	−0.664294	−0.0729157	−0.0364578	−	0.999335i	$-0.511607\pi$
$83$	−0.664294	−0.0729157	−0.0364578	+	0.999335i	$0.511607\pi$
$84$	−35.8111	−3.90731
$85$	4.41470	0.478841
$86$	−21.7664	−2.34714
$87$	−5.14341	−0.551432
$88$	3.01201	0.321082
$89$	−9.23046	−0.978427	−0.489213	−	0.872164i	$-0.662716\pi$
$89$	−9.23046	−0.978427	−0.489213	+	0.872164i	$0.662716\pi$
$90$	−31.5753	−3.32832
$91$	−1.02217	−0.107153
$92$	−12.8254	−1.33714
$93$	24.8401	2.57580
$94$	−23.7999	−2.45478
$95$	6.66499	0.683814
$96$	13.3938	1.36700
$97$	−15.9767	−1.62219	−0.811096	−	0.584913i	$-0.801128\pi$
$97$	−15.9767	−1.62219	−0.811096	+	0.584913i	$0.801128\pi$
$98$	−25.8001	−2.60620
$99$	−3.44182	−0.345916
$100$	35.9102	3.59102
$101$	−16.5539	−1.64718	−0.823589	−	0.567187i	$-0.808032\pi$
$101$	−16.5539	−1.64718	−0.823589	+	0.567187i	$0.808032\pi$
$102$	−6.48231	−0.641845
$103$	13.2353	1.30411	0.652056	−	0.758171i	$-0.273907\pi$
$103$	13.2353	1.30411	0.652056	+	0.758171i	$0.273907\pi$
$104$	−0.721700	−0.0707685
$105$	−43.1167	−4.20775
$106$	−27.7217	−2.69257
$107$	14.5438	1.40600	0.703001	−	0.711189i	$-0.251843\pi$
$107$	14.5438	1.40600	0.703001	+	0.711189i	$0.251843\pi$
$108$	3.70885	0.356884
$109$	13.4304	1.28640	0.643202	−	0.765697i	$-0.277606\pi$
$109$	13.4304	1.28640	0.643202	+	0.765697i	$0.277606\pi$
$110$	9.17400	0.874707
$111$	−23.8963	−2.26814
$112$	−1.38300	−0.130682
$113$	19.8752	1.86970	0.934852	−	0.355038i	$-0.115532\pi$
$113$	19.8752	1.86970	0.934852	+	0.355038i	$0.115532\pi$
$114$	−9.78653	−0.916593
$115$	−15.4418	−1.43995
$116$	−6.70249	−0.622311
$117$	0.824684	0.0762420
$118$	−10.3713	−0.954757
$119$	−4.72942	−0.433545
$120$	−30.4424	−2.77899
$121$	1.00000	0.0909091
$122$	6.20162	0.561469
$123$	18.7128	1.68727
$124$	32.3697	2.90689
$125$	23.3253	2.08628
$126$	33.8262	3.01348
$127$	15.4483	1.37082	0.685408	−	0.728160i	$-0.259624\pi$
$127$	15.4483	1.37082	0.685408	+	0.728160i	$0.259624\pi$
$128$	18.9475	1.67474
$129$	23.9800	2.11133
$130$	−2.19815	−0.192791
$131$	14.2948	1.24894	0.624471	−	0.781048i	$-0.285315\pi$
$131$	14.2948	1.24894	0.624471	+	0.781048i	$0.285315\pi$
$132$	−8.39448	−0.730646
$133$	−7.14014	−0.619128
$134$	14.4320	1.24673
$135$	4.46546	0.384326
$136$	−3.33919	−0.286333
$137$	−10.8970	−0.930993	−0.465496	−	0.885050i	$-0.654124\pi$
$137$	−10.8970	−0.930993	−0.465496	+	0.885050i	$0.654124\pi$
$138$	22.6739	1.93013
$139$	−5.23250	−0.443815	−0.221907	−	0.975068i	$-0.571228\pi$
$139$	−5.23250	−0.443815	−0.221907	+	0.975068i	$0.571228\pi$
$140$	−56.1863	−4.74861
$141$	26.2204	2.20815
$142$	−19.7217	−1.65501
$143$	−0.239607	−0.0200369
$144$	1.11580	0.0929836
$145$	−8.06982	−0.670162
$146$	17.2368	1.42653
$147$	28.4239	2.34436
$148$	−31.1398	−2.55968
$149$	3.87854	0.317742	0.158871	−	0.987299i	$-0.449215\pi$
$149$	3.87854	0.317742	0.158871	+	0.987299i	$0.449215\pi$
$150$	−63.4855	−5.18357
$151$	−9.03658	−0.735386	−0.367693	−	0.929947i	$-0.619852\pi$
$151$	−9.03658	−0.735386	−0.367693	+	0.929947i	$0.619852\pi$
$152$	−5.04127	−0.408901
$153$	3.81568	0.308480
$154$	−9.82801	−0.791963
$155$	38.9732	3.13040
$156$	2.01138	0.161039
$157$	15.2715	1.21880	0.609398	−	0.792865i	$-0.291411\pi$
$157$	15.2715	1.21880	0.609398	+	0.792865i	$0.291411\pi$
$158$	38.1281	3.03331
$159$	30.5410	2.42206
$160$	21.0144	1.66134
$161$	16.5426	1.30374
$162$	17.2308	1.35378
$163$	21.7300	1.70202	0.851012	−	0.525147i	$-0.175990\pi$
$163$	21.7300	1.70202	0.851012	+	0.525147i	$0.175990\pi$
$164$	24.3850	1.90415
$165$	−10.1070	−0.786827
$166$	1.53039	0.118781
$167$	11.8949	0.920453	0.460226	−	0.887802i	$-0.347768\pi$
$167$	11.8949	0.920453	0.460226	+	0.887802i	$0.347768\pi$
$168$	32.6126	2.51612
$169$	−12.9426	−0.995584
$170$	−10.1705	−0.780043
$171$	5.76064	0.440527
$172$	31.2489	2.38271
$173$	8.79578	0.668731	0.334366	−	0.942443i	$-0.391478\pi$
$173$	8.79578	0.668731	0.334366	+	0.942443i	$0.391478\pi$
$174$	11.8493	0.898294
$175$	−46.3183	−3.50133
$176$	−0.324190	−0.0244367
$177$	11.4261	0.858835
$178$	21.2650	1.59388
$179$	−19.2364	−1.43780	−0.718899	−	0.695114i	$-0.755354\pi$
$179$	−19.2364	−1.43780	−0.718899	+	0.695114i	$0.755354\pi$
$180$	45.3309	3.37877
$181$	−9.55691	−0.710359	−0.355180	−	0.934798i	$-0.615580\pi$
$181$	−9.55691	−0.710359	−0.355180	+	0.934798i	$0.615580\pi$
$182$	2.35486	0.174554
$183$	−6.83232	−0.505059
$184$	11.6799	0.861050
$185$	−37.4925	−2.75650
$186$	−57.2263	−4.19603
$187$	−1.10862	−0.0810706
$188$	34.1683	2.49198
$189$	−4.78380	−0.347970
$190$	−15.3547	−1.11395
$191$	−2.32991	−0.168586	−0.0842931	−	0.996441i	$-0.526863\pi$
$191$	−2.32991	−0.168586	−0.0842931	+	0.996441i	$0.526863\pi$
$192$	−32.5021	−2.34564
$193$	5.77583	0.415753	0.207877	−	0.978155i	$-0.433345\pi$
$193$	5.77583	0.415753	0.207877	+	0.978155i	$0.433345\pi$
$194$	36.8069	2.64258
$195$	2.42170	0.173422
$196$	37.0398	2.64570
$197$	−19.4656	−1.38686	−0.693432	−	0.720522i	$-0.743902\pi$
$197$	−19.4656	−1.38686	−0.693432	+	0.720522i	$0.743902\pi$
$198$	7.92921	0.563504
$199$	−17.5635	−1.24505	−0.622523	−	0.782601i	$-0.713892\pi$
$199$	−17.5635	−1.24505	−0.622523	+	0.782601i	$0.713892\pi$
$200$	−32.7029	−2.31244
$201$	−15.8997	−1.12148
$202$	38.1367	2.68329
$203$	8.64512	0.606768
$204$	9.30631	0.651572
$205$	29.3597	2.05057
$206$	−30.4913	−2.12443
$207$	−13.3465	−0.927648
$208$	0.0776781	0.00538601
$209$	−1.67372	−0.115774
$210$	99.3315	6.85452
$211$	−4.06736	−0.280009	−0.140004	−	0.990151i	$-0.544712\pi$
$211$	−4.06736	−0.280009	−0.140004	+	0.990151i	$0.544712\pi$
$212$	39.7986	2.73338
$213$	21.7274	1.48873
$214$	−33.5058	−2.29041
$215$	37.6238	2.56592
$216$	−3.37759	−0.229816
$217$	−41.7516	−2.83428
$218$	−30.9409	−2.09558
$219$	−18.9898	−1.28321
$220$	−13.1706	−0.887963
$221$	0.265634	0.0178685
$222$	55.0520	3.69485
$223$	25.8060	1.72810	0.864049	−	0.503408i	$-0.167921\pi$
$223$	25.8060	1.72810	0.864049	+	0.503408i	$0.167921\pi$
$224$	−22.5125	−1.50418
$225$	37.3695	2.49130
$226$	−45.7882	−3.04579
$227$	−1.95544	−0.129787	−0.0648936	−	0.997892i	$-0.520671\pi$
$227$	−1.95544	−0.129787	−0.0648936	+	0.997892i	$0.520671\pi$
$228$	14.0500	0.930484
$229$	19.8009	1.30848	0.654241	−	0.756286i	$-0.272988\pi$
$229$	19.8009	1.30848	0.654241	+	0.756286i	$0.272988\pi$
$230$	35.5745	2.34571
$231$	10.8275	0.712397
$232$	6.10385	0.400738
$233$	16.9713	1.11183	0.555915	−	0.831239i	$-0.312368\pi$
$233$	16.9713	1.11183	0.555915	+	0.831239i	$0.312368\pi$
$234$	−1.89989	−0.124200
$235$	41.1388	2.68360
$236$	14.8896	0.969227
$237$	−42.0056	−2.72856
$238$	10.8956	0.706254
$239$	11.9663	0.774035	0.387017	−	0.922072i	$-0.373505\pi$
$239$	11.9663	0.774035	0.387017	+	0.922072i	$0.373505\pi$
$240$	3.27658	0.211502
$241$	20.5162	1.32156	0.660781	−	0.750579i	$-0.270225\pi$
$241$	20.5162	1.32156	0.660781	+	0.750579i	$0.270225\pi$
$242$	−2.30378	−0.148093
$243$	−22.3472	−1.43357
$244$	−8.90334	−0.569978
$245$	44.5960	2.84914
$246$	−43.1102	−2.74861
$247$	0.401035	0.0255172
$248$	−29.4786	−1.87189
$249$	−1.68603	−0.106848
$250$	−53.7364	−3.39859
$251$	17.6380	1.11330	0.556649	−	0.830748i	$-0.312087\pi$
$251$	17.6380	1.11330	0.556649	+	0.830748i	$0.312087\pi$
$252$	−48.5625	−3.05915
$253$	3.87775	0.243792
$254$	−35.5896	−2.23309
$255$	11.2048	0.701674
$256$	−18.0394	−1.12746
$257$	1.88561	0.117621	0.0588107	−	0.998269i	$-0.481269\pi$
$257$	1.88561	0.117621	0.0588107	+	0.998269i	$0.481269\pi$
$258$	−55.2448	−3.43939
$259$	40.1653	2.49575
$260$	3.15577	0.195713
$261$	−6.97485	−0.431733
$262$	−32.9321	−2.03455
$263$	14.5005	0.894141	0.447071	−	0.894499i	$-0.352467\pi$
$263$	14.5005	0.894141	0.447071	+	0.894499i	$0.352467\pi$
$264$	7.64472	0.470500
$265$	47.9176	2.94356
$266$	16.4493	1.00857
$267$	−23.4276	−1.43375
$268$	−20.7192	−1.26563
$269$	25.1358	1.53256	0.766278	−	0.642509i	$-0.222107\pi$
$269$	25.1358	1.53256	0.766278	+	0.642509i	$0.222107\pi$
$270$	−10.2875	−0.626075
$271$	18.0695	1.09764	0.548821	−	0.835940i	$-0.315077\pi$
$271$	18.0695	1.09764	0.548821	+	0.835940i	$0.315077\pi$
$272$	0.359405	0.0217921
$273$	−2.59434	−0.157017
$274$	25.1043	1.51661
$275$	−10.8575	−0.654730
$276$	−32.5517	−1.95938
$277$	−7.02113	−0.421859	−0.210929	−	0.977501i	$-0.567649\pi$
$277$	−7.02113	−0.421859	−0.210929	+	0.977501i	$0.567649\pi$
$278$	12.0545	0.722984
$279$	33.6851	2.01667
$280$	51.1679	3.05787
$281$	−13.0086	−0.776025	−0.388013	−	0.921654i	$-0.626838\pi$
$281$	−13.0086	−0.776025	−0.388013	+	0.921654i	$0.626838\pi$
$282$	−60.4060	−3.59713
$283$	14.3409	0.852477	0.426239	−	0.904611i	$-0.359838\pi$
$283$	14.3409	0.852477	0.426239	+	0.904611i	$0.359838\pi$
$284$	28.3134	1.68009
$285$	16.9162	1.00203
$286$	0.552003	0.0326406
$287$	−31.4527	−1.85659
$288$	18.1631	1.07027
$289$	−15.7710	−0.927703
$290$	18.5911	1.09171
$291$	−40.5501	−2.37709
$292$	−24.7460	−1.44815
$293$	6.30326	0.368240	0.184120	−	0.982904i	$-0.441056\pi$
$293$	6.30326	0.368240	0.184120	+	0.982904i	$0.441056\pi$
$294$	−65.4825	−3.81902
$295$	17.9271	1.04375
$296$	28.3586	1.64831
$297$	−1.12137	−0.0650686
$298$	−8.93531	−0.517609
$299$	−0.929137	−0.0537334
$300$	91.1428	5.26213
$301$	−40.3060	−2.32320
$302$	20.8183	1.19796
$303$	−42.0151	−2.41370
$304$	0.542603	0.0311204
$305$	−10.7197	−0.613805
$306$	−8.79051	−0.502520
$307$	−3.30017	−0.188350	−0.0941752	−	0.995556i	$-0.530021\pi$
$307$	−3.30017	−0.188350	−0.0941752	+	0.995556i	$0.530021\pi$
$308$	14.1096	0.803966
$309$	33.5922	1.91099
$310$	−89.7859	−5.09950
$311$	−13.7765	−0.781195	−0.390597	−	0.920562i	$-0.627732\pi$
$311$	−13.7765	−0.781195	−0.390597	+	0.920562i	$0.627732\pi$
$312$	−1.83173	−0.103701
$313$	−12.8179	−0.724513	−0.362256	−	0.932079i	$-0.617994\pi$
$313$	−12.8179	−0.724513	−0.362256	+	0.932079i	$0.617994\pi$
$314$	−35.1822	−1.98544
$315$	−58.4694	−3.29438
$316$	−54.7384	−3.07928
$317$	−17.3093	−0.972188	−0.486094	−	0.873906i	$-0.661579\pi$
$317$	−17.3093	−0.972188	−0.486094	+	0.873906i	$0.661579\pi$
$318$	−70.3598	−3.94558
$319$	2.02650	0.113462
$320$	−50.9947	−2.85069
$321$	36.9132	2.06030
$322$	−38.1106	−2.12382
$323$	1.85552	0.103244
$324$	−24.7373	−1.37429
$325$	2.60153	0.144307
$326$	−50.0612	−2.77263
$327$	34.0875	1.88504
$328$	−22.2071	−1.22618
$329$	−44.0715	−2.42974
$330$	23.2843	1.28176
$331$	1.17681	0.0646833	0.0323416	−	0.999477i	$-0.489704\pi$
$331$	1.17681	0.0646833	0.0323416	+	0.999477i	$0.489704\pi$
$332$	−2.19710	−0.120581
$333$	−32.4052	−1.77580
$334$	−27.4032	−1.49944
$335$	−24.9460	−1.36295
$336$	−3.51017	−0.191495
$337$	23.7231	1.29228	0.646139	−	0.763220i	$-0.276383\pi$
$337$	23.7231	1.29228	0.646139	+	0.763220i	$0.276383\pi$
$338$	29.8169	1.62183
$339$	50.4448	2.73978
$340$	14.6013	0.791865
$341$	−9.78699	−0.529995
$342$	−13.2713	−0.717628
$343$	−17.9131	−0.967214
$344$	−28.4579	−1.53435
$345$	−39.1924	−2.11005
$346$	−20.2636	−1.08938
$347$	−27.9352	−1.49964	−0.749819	−	0.661642i	$-0.769860\pi$
$347$	−27.9352	−1.49964	−0.749819	+	0.661642i	$0.769860\pi$
$348$	−17.0114	−0.911908
$349$	19.8487	1.06248	0.531239	−	0.847222i	$-0.321726\pi$
$349$	19.8487	1.06248	0.531239	+	0.847222i	$0.321726\pi$
$350$	106.707	5.70375
$351$	0.268688	0.0143415
$352$	−5.27717	−0.281274
$353$	0.222781	0.0118574	0.00592872	−	0.999982i	$-0.498113\pi$
$353$	0.222781	0.0118574	0.00592872	+	0.999982i	$0.498113\pi$
$354$	−26.3232	−1.39906
$355$	34.0894	1.80928
$356$	−30.5290	−1.61803
$357$	−12.0036	−0.635299
$358$	44.3166	2.34220
$359$	−9.35655	−0.493820	−0.246910	−	0.969038i	$-0.579415\pi$
$359$	−9.35655	−0.493820	−0.246910	+	0.969038i	$0.579415\pi$
$360$	−41.2821	−2.17576
$361$	−16.1987	−0.852561
$362$	22.0171	1.15719
$363$	2.53807	0.133214
$364$	−3.38075	−0.177199
$365$	−29.7942	−1.55950
$366$	15.7402	0.822752
$367$	8.82606	0.460717	0.230358	−	0.973106i	$-0.426010\pi$
$367$	8.82606	0.460717	0.230358	+	0.973106i	$0.426010\pi$
$368$	−1.25713	−0.0655324
$369$	25.3759	1.32102
$370$	86.3745	4.49040
$371$	−51.3337	−2.66511
$372$	82.1567	4.25963
$373$	13.7180	0.710293	0.355147	−	0.934811i	$-0.384431\pi$
$373$	13.7180	0.710293	0.355147	+	0.934811i	$0.384431\pi$
$374$	2.55403	0.132066
$375$	59.2013	3.05714
$376$	−31.1165	−1.60471
$377$	−0.485564	−0.0250078
$378$	11.0208	0.566851
$379$	−28.4038	−1.45901	−0.729503	−	0.683978i	$-0.760248\pi$
$379$	−28.4038	−1.45901	−0.729503	+	0.683978i	$0.760248\pi$
$380$	22.0439	1.13083
$381$	39.2089	2.00873
$382$	5.36760	0.274630
$383$	7.06772	0.361143	0.180572	−	0.983562i	$-0.442205\pi$
$383$	7.06772	0.361143	0.180572	+	0.983562i	$0.442205\pi$
$384$	48.0902	2.45410
$385$	16.9879	0.865786
$386$	−13.3063	−0.677271
$387$	32.5188	1.65302
$388$	−52.8418	−2.68263
$389$	23.4828	1.19063	0.595313	−	0.803494i	$-0.297028\pi$
$389$	23.4828	1.19063	0.595313	+	0.803494i	$0.297028\pi$
$390$	−5.57908	−0.282508
$391$	−4.29897	−0.217408
$392$	−33.7316	−1.70370
$393$	36.2812	1.83015
$394$	44.8445	2.25923
$395$	−65.9053	−3.31605
$396$	−11.3835	−0.572045
$397$	1.47453	0.0740047	0.0370024	−	0.999315i	$-0.488219\pi$
$397$	1.47453	0.0740047	0.0370024	+	0.999315i	$0.488219\pi$
$398$	40.4626	2.02821
$399$	−18.1222	−0.907244
$400$	3.51988	0.175994
$401$	−14.5488	−0.726531	−0.363265	−	0.931686i	$-0.618338\pi$
$401$	−14.5488	−0.726531	−0.363265	+	0.931686i	$0.618338\pi$
$402$	36.6294	1.82691
$403$	2.34503	0.116814
$404$	−54.7508	−2.72396
$405$	−29.7838	−1.47997
$406$	−19.9165	−0.988438
$407$	9.41514	0.466691
$408$	−8.47511	−0.419581
$409$	−19.0056	−0.939766	−0.469883	−	0.882729i	$-0.655704\pi$
$409$	−19.0056	−0.939766	−0.469883	+	0.882729i	$0.655704\pi$
$410$	−67.6383	−3.34042
$411$	−27.6574	−1.36424
$412$	43.7747	2.15662
$413$	−19.2051	−0.945020
$414$	30.7475	1.51116
$415$	−2.64531	−0.129853
$416$	1.26445	0.0619945
$417$	−13.2805	−0.650347
$418$	3.85589	0.188598
$419$	−30.1199	−1.47146	−0.735728	−	0.677277i	$-0.763160\pi$
$419$	−30.1199	−1.47146	−0.735728	+	0.677277i	$0.763160\pi$
$420$	−142.605	−6.95841
$421$	−14.8792	−0.725169	−0.362585	−	0.931951i	$-0.618106\pi$
$421$	−14.8792	−0.725169	−0.362585	+	0.931951i	$0.618106\pi$
$422$	9.37033	0.456140
$423$	35.5568	1.72883
$424$	−36.2439	−1.76016
$425$	12.0368	0.583873
$426$	−50.0551	−2.42518
$427$	11.4838	0.555742
$428$	48.1025	2.32512
$429$	−0.608140	−0.0293613
$430$	−86.6771	−4.17994
$431$	16.7160	0.805182	0.402591	−	0.915380i	$-0.368110\pi$
$431$	16.7160	0.805182	0.402591	+	0.915380i	$0.368110\pi$
$432$	0.363537	0.0174907
$433$	−21.0529	−1.01174	−0.505869	−	0.862610i	$-0.668828\pi$
$433$	−21.0529	−1.01174	−0.505869	+	0.862610i	$0.668828\pi$
$434$	96.1867	4.61711
$435$	−20.4818	−0.982027
$436$	44.4201	2.12734
$437$	−6.49027	−0.310472
$438$	43.7483	2.09038
$439$	18.1058	0.864141	0.432071	−	0.901840i	$-0.357783\pi$
$439$	18.1058	0.864141	0.432071	+	0.901840i	$0.357783\pi$
$440$	11.9943	0.571805
$441$	38.5449	1.83547
$442$	−0.611963	−0.0291081
$443$	−2.68647	−0.127638	−0.0638191	−	0.997961i	$-0.520328\pi$
$443$	−2.68647	−0.127638	−0.0638191	+	0.997961i	$0.520328\pi$
$444$	−79.0352	−3.75085
$445$	−36.7570	−1.74245
$446$	−59.4514	−2.81511
$447$	9.84402	0.465606
$448$	54.6300	2.58103
$449$	12.7497	0.601697	0.300848	−	0.953672i	$-0.402730\pi$
$449$	12.7497	0.601697	0.300848	+	0.953672i	$0.402730\pi$
$450$	−86.0912	−4.05838
$451$	−7.37283	−0.347173
$452$	65.7357	3.09195
$453$	−22.9355	−1.07760
$454$	4.50491	0.211426
$455$	−4.07043	−0.190825
$456$	−12.7951	−0.599186
$457$	26.6427	1.24629	0.623147	−	0.782105i	$-0.285854\pi$
$457$	26.6427	1.24629	0.623147	+	0.782105i	$0.285854\pi$
$458$	−45.6171	−2.13155
$459$	1.24318	0.0580266
$460$	−51.0724	−2.38127
$461$	−38.1924	−1.77880	−0.889400	−	0.457131i	$-0.848877\pi$
$461$	−38.1924	−1.77880	−0.889400	+	0.457131i	$0.848877\pi$
$462$	−24.9442	−1.16051
$463$	10.6895	0.496784	0.248392	−	0.968660i	$-0.420098\pi$
$463$	10.6895	0.496784	0.248392	+	0.968660i	$0.420098\pi$
$464$	−0.656971	−0.0304991
$465$	98.9169	4.58716
$466$	−39.0983	−1.81119
$467$	−7.36289	−0.340714	−0.170357	−	0.985382i	$-0.554492\pi$
$467$	−7.36289	−0.340714	−0.170357	+	0.985382i	$0.554492\pi$
$468$	2.72758	0.126082
$469$	26.7244	1.23402
$470$	−94.7748	−4.37164
$471$	38.7601	1.78597
$472$	−13.5597	−0.624135
$473$	−9.44813	−0.434425
$474$	96.7719	4.44488
$475$	18.1724	0.833805
$476$	−15.6422	−0.716958
$477$	41.4158	1.89630
$478$	−27.5677	−1.26092
$479$	32.8567	1.50126	0.750631	−	0.660722i	$-0.229750\pi$
$479$	32.8567	1.50126	0.750631	+	0.660722i	$0.229750\pi$
$480$	53.3362	2.43445
$481$	−2.25593	−0.102862
$482$	−47.2648	−2.15285
$483$	41.9864	1.91045
$484$	3.30742	0.150337
$485$	−63.6217	−2.88891
$486$	51.4832	2.33532
$487$	2.62659	0.119022	0.0595112	−	0.998228i	$-0.481046\pi$
$487$	2.62659	0.119022	0.0595112	+	0.998228i	$0.481046\pi$
$488$	8.10813	0.367038
$489$	55.1523	2.49407
$490$	−102.740	−4.64130
$491$	13.8747	0.626158	0.313079	−	0.949727i	$-0.398640\pi$
$491$	13.8747	0.626158	0.313079	+	0.949727i	$0.398640\pi$
$492$	61.8910	2.79026
$493$	−2.24663	−0.101183
$494$	−0.923898	−0.0415681
$495$	−13.7058	−0.616031
$496$	3.17284	0.142465
$497$	−36.5196	−1.63813
$498$	3.88424	0.174057
$499$	5.30974	0.237697	0.118848	−	0.992912i	$-0.462080\pi$
$499$	5.30974	0.237697	0.118848	+	0.992912i	$0.462080\pi$
$500$	77.1466	3.45010
$501$	30.1901	1.34879
$502$	−40.6340	−1.81359
$503$	−18.1124	−0.807593	−0.403797	−	0.914849i	$-0.632310\pi$
$503$	−18.1124	−0.807593	−0.403797	+	0.914849i	$0.632310\pi$
$504$	44.2251	1.96994
$505$	−65.9201	−2.93341
$506$	−8.93351	−0.397143
$507$	−32.8492	−1.45889
$508$	51.0940	2.26693
$509$	−14.9004	−0.660449	−0.330225	−	0.943902i	$-0.607125\pi$
$509$	−14.9004	−0.660449	−0.330225	+	0.943902i	$0.607125\pi$
$510$	−25.8135	−1.14304
$511$	31.9183	1.41198
$512$	3.66373	0.161916
$513$	1.87686	0.0828655
$514$	−4.34405	−0.191608
$515$	52.7049	2.32245
$516$	79.3121	3.49152
$517$	−10.3308	−0.454348
$518$	−92.5321	−4.06563
$519$	22.3244	0.979930
$520$	−2.87391	−0.126029
$521$	4.83008	0.211610	0.105805	−	0.994387i	$-0.466258\pi$
$521$	4.83008	0.211610	0.105805	+	0.994387i	$0.466258\pi$
$522$	16.0686	0.703302
$523$	−21.5141	−0.940747	−0.470373	−	0.882467i	$-0.655881\pi$
$523$	−21.5141	−0.940747	−0.470373	+	0.882467i	$0.655881\pi$
$524$	47.2789	2.06539
$525$	−117.559	−5.13071
$526$	−33.4061	−1.45658
$527$	10.8501	0.472637
$528$	−0.822818	−0.0358086
$529$	−7.96302	−0.346218
$530$	−110.392	−4.79512
$531$	15.4946	0.672408
$532$	−23.6154	−1.02386
$533$	1.76658	0.0765191
$534$	53.9721	2.33560
$535$	57.9155	2.50391
$536$	18.8687	0.815002
$537$	−48.8235	−2.10689
$538$	−57.9074	−2.49657
$539$	−11.1990	−0.482375
$540$	14.7692	0.635564
$541$	−1.61904	−0.0696081	−0.0348040	−	0.999394i	$-0.511081\pi$
$541$	−1.61904	−0.0696081	−0.0348040	+	0.999394i	$0.511081\pi$
$542$	−41.6281	−1.78808
$543$	−24.2561	−1.04093
$544$	5.85039	0.250833
$545$	53.4820	2.29092
$546$	5.97681	0.255784
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−36.0409	−1.53959
$549$	−9.26514	−0.395426
$550$	25.0133	1.06657
$551$	−3.39180	−0.144495
$552$	29.6443	1.26175
$553$	70.6036	3.00237
$554$	16.1752	0.687217
$555$	−95.1587	−4.03926
$556$	−17.3061	−0.733941
$557$	−15.9533	−0.675962	−0.337981	−	0.941153i	$-0.609744\pi$
$557$	−15.9533	−0.675962	−0.337981	+	0.941153i	$0.609744\pi$
$558$	−77.6031	−3.28520
$559$	2.26384	0.0957501
$560$	−5.50732	−0.232727
$561$	−2.81377	−0.118797
$562$	29.9689	1.26416
$563$	−5.52511	−0.232856	−0.116428	−	0.993199i	$-0.537144\pi$
$563$	−5.52511	−0.232856	−0.116428	+	0.993199i	$0.537144\pi$
$564$	86.7217	3.65164
$565$	79.1460	3.32970
$566$	−33.0383	−1.38870
$567$	31.9071	1.33997
$568$	−25.7846	−1.08190
$569$	30.1646	1.26456	0.632282	−	0.774738i	$-0.282118\pi$
$569$	30.1646	1.26456	0.632282	+	0.774738i	$0.282118\pi$
$570$	−38.9714	−1.63233
$571$	−39.3044	−1.64484	−0.822418	−	0.568884i	$-0.807376\pi$
$571$	−39.3044	−1.64484	−0.822418	+	0.568884i	$0.807376\pi$
$572$	−0.792481	−0.0331353
$573$	−5.91347	−0.247039
$574$	72.4602	3.02443
$575$	−42.1026	−1.75580
$576$	−44.0754	−1.83647
$577$	20.9956	0.874058	0.437029	−	0.899447i	$-0.356031\pi$
$577$	20.9956	0.874058	0.437029	+	0.899447i	$0.356031\pi$
$578$	36.3329	1.51125
$579$	14.6595	0.609228
$580$	−26.6903	−1.10825
$581$	2.83390	0.117570
$582$	93.4187	3.87233
$583$	−12.0331	−0.498361
$584$	22.5358	0.932537
$585$	3.28401	0.135777
$586$	−14.5214	−0.599872
$587$	0.0321604	0.00132740	0.000663701	−	1.00000i	$-0.499789\pi$
$587$	0.0321604	0.00132740	0.000663701		1.00000i	$0.499789\pi$
$588$	94.0098	3.87690
$589$	16.3807	0.674954
$590$	−41.3001	−1.70030
$591$	−49.4050	−2.03225
$592$	−3.05229	−0.125449
$593$	−12.0995	−0.496865	−0.248433	−	0.968649i	$-0.579915\pi$
$593$	−12.0995	−0.496865	−0.248433	+	0.968649i	$0.579915\pi$
$594$	2.58340	0.105998
$595$	−18.8332	−0.772087
$596$	12.8280	0.525453
$597$	−44.5776	−1.82444
$598$	2.14053	0.0875328
$599$	5.95315	0.243239	0.121620	−	0.992577i	$-0.461191\pi$
$599$	5.95315	0.243239	0.121620	+	0.992577i	$0.461191\pi$
$600$	−83.0023	−3.38855
$601$	−24.9138	−1.01626	−0.508128	−	0.861281i	$-0.669662\pi$
$601$	−24.9138	−1.01626	−0.508128	+	0.861281i	$0.669662\pi$
$602$	92.8563	3.78454
$603$	−21.5612	−0.878038
$604$	−29.8878	−1.21612
$605$	3.98214	0.161897
$606$	96.7937	3.93198
$607$	−44.4229	−1.80307	−0.901535	−	0.432706i	$-0.857559\pi$
$607$	−44.4229	−1.80307	−0.901535	+	0.432706i	$0.857559\pi$
$608$	8.83250	0.358205
$609$	21.9419	0.889132
$610$	24.6958	0.999902
$611$	2.47533	0.100141
$612$	12.6201	0.510136
$613$	−35.1906	−1.42133	−0.710667	−	0.703529i	$-0.751607\pi$
$613$	−35.1906	−1.42133	−0.710667	+	0.703529i	$0.751607\pi$
$614$	7.60287	0.306827
$615$	74.5170	3.00481
$616$	−12.8493	−0.517715
$617$	−19.4229	−0.781936	−0.390968	−	0.920404i	$-0.627860\pi$
$617$	−19.4229	−0.781936	−0.390968	+	0.920404i	$0.627860\pi$
$618$	−77.3891	−3.11305
$619$	−38.8990	−1.56348	−0.781741	−	0.623603i	$-0.785668\pi$
$619$	−38.8990	−1.56348	−0.781741	+	0.623603i	$0.785668\pi$
$620$	128.901	5.17678
$621$	−4.34840	−0.174495
$622$	31.7381	1.27258
$623$	39.3774	1.57762
$624$	0.197153	0.00789243
$625$	38.5973	1.54389
$626$	29.5298	1.18025
$627$	−4.24802	−0.169650
$628$	50.5092	2.01554
$629$	−10.4378	−0.416184
$630$	134.701	5.36661
$631$	20.4180	0.812829	0.406414	−	0.913689i	$-0.366779\pi$
$631$	20.4180	0.812829	0.406414	+	0.913689i	$0.366779\pi$
$632$	49.8494	1.98290
$633$	−10.3233	−0.410313
$634$	39.8769	1.58372
$635$	61.5174	2.44124
$636$	101.012	4.00538
$637$	2.68336	0.106319
$638$	−4.66862	−0.184833
$639$	29.4639	1.16558
$640$	75.4518	2.98249
$641$	30.2787	1.19594	0.597969	−	0.801519i	$-0.295974\pi$
$641$	30.2787	1.19594	0.597969	+	0.801519i	$0.295974\pi$
$642$	−85.0401	−3.35627
$643$	27.9713	1.10308	0.551540	−	0.834148i	$-0.314040\pi$
$643$	27.9713	1.10308	0.551540	+	0.834148i	$0.314040\pi$
$644$	54.7134	2.15601
$645$	95.4920	3.75999
$646$	−4.27473	−0.168187
$647$	−24.2473	−0.953261	−0.476630	−	0.879104i	$-0.658142\pi$
$647$	−24.2473	−0.953261	−0.476630	+	0.879104i	$0.658142\pi$
$648$	22.5279	0.884978
$649$	−4.50186	−0.176714
$650$	−5.99335	−0.235079
$651$	−105.969	−4.15324
$652$	71.8702	2.81465
$653$	−25.5506	−0.999871	−0.499935	−	0.866063i	$-0.666643\pi$
$653$	−25.5506	−0.999871	−0.499935	+	0.866063i	$0.666643\pi$
$654$	−78.5302	−3.07077
$655$	56.9239	2.22420
$656$	2.39020	0.0933215
$657$	−25.7516	−1.00466
$658$	101.531	3.95810
$659$	−13.0434	−0.508097	−0.254049	−	0.967191i	$-0.581762\pi$
$659$	−13.0434	−0.508097	−0.254049	+	0.967191i	$0.581762\pi$
$660$	−33.4280	−1.30118
$661$	13.0702	0.508373	0.254186	−	0.967155i	$-0.418192\pi$
$661$	13.0702	0.508373	0.254186	+	0.967155i	$0.418192\pi$
$662$	−2.71111	−0.105370
$663$	0.674198	0.0261837
$664$	2.00086	0.0776485
$665$	−28.4331	−1.10259
$666$	74.6547	2.89281
$667$	7.85828	0.304274
$668$	39.3413	1.52216
$669$	65.4975	2.53228
$670$	57.4702	2.22027
$671$	2.69193	0.103921
$672$	−57.1385	−2.20417
$673$	0.853595	0.0329037	0.0164518	−	0.999865i	$-0.494763\pi$
$673$	0.853595	0.0329037	0.0164518	+	0.999865i	$0.494763\pi$
$674$	−54.6528	−2.10515
$675$	12.1753	0.468626
$676$	−42.8066	−1.64641
$677$	−30.8462	−1.18552	−0.592759	−	0.805380i	$-0.701961\pi$
$677$	−30.8462	−1.18552	−0.592759	+	0.805380i	$0.701961\pi$
$678$	−116.214	−4.46317
$679$	68.1572	2.61563
$680$	−13.2971	−0.509922
$681$	−4.96305	−0.190185
$682$	22.5471	0.863374
$683$	−0.692076	−0.0264815	−0.0132408	−	0.999912i	$-0.504215\pi$
$683$	−0.692076	−0.0264815	−0.0132408	+	0.999912i	$0.504215\pi$
$684$	19.0529	0.728504
$685$	−43.3934	−1.65798
$686$	41.2678	1.57561
$687$	50.2562	1.91739
$688$	3.06299	0.116775
$689$	2.88322	0.109842
$690$	90.2908	3.43731
$691$	40.9031	1.55603	0.778014	−	0.628247i	$-0.216227\pi$
$691$	40.9031	1.55603	0.778014	+	0.628247i	$0.216227\pi$
$692$	29.0914	1.10589
$693$	14.6829	0.557757
$694$	64.3566	2.44294
$695$	−20.8366	−0.790376
$696$	15.4920	0.587224
$697$	8.17369	0.309600
$698$	−45.7272	−1.73080
$699$	43.0745	1.62923
$700$	−153.194	−5.79019
$701$	23.4308	0.884969	0.442485	−	0.896776i	$-0.354097\pi$
$701$	23.4308	0.884969	0.442485	+	0.896776i	$0.354097\pi$
$702$	−0.619000	−0.0233626
$703$	−15.7583	−0.594336
$704$	12.8058	0.482638
$705$	104.413	3.93243
$706$	−0.513239	−0.0193160
$707$	70.6196	2.65592
$708$	37.7908	1.42026
$709$	4.87997	0.183271	0.0916356	−	0.995793i	$-0.470791\pi$
$709$	4.87997	0.183271	0.0916356	+	0.995793i	$0.470791\pi$
$710$	−78.5346	−2.94735
$711$	−56.9628	−2.13627
$712$	27.8023	1.04193
$713$	−37.9516	−1.42130
$714$	27.6537	1.03492
$715$	−0.954149	−0.0356832
$716$	−63.6230	−2.37770
$717$	30.3713	1.13424
$718$	21.5555	0.804443
$719$	−51.5845	−1.92378	−0.961889	−	0.273442i	$-0.911838\pi$
$719$	−51.5845	−1.92378	−0.961889	+	0.273442i	$0.911838\pi$
$720$	4.44329	0.165592
$721$	−56.4622	−2.10276
$722$	37.3182	1.38884
$723$	52.0715	1.93656
$724$	−31.6087	−1.17473
$725$	−22.0027	−0.817159
$726$	−5.84717	−0.217009
$727$	29.3422	1.08824	0.544120	−	0.839007i	$-0.316863\pi$
$727$	29.3422	1.08824	0.544120	+	0.839007i	$0.316863\pi$
$728$	3.07879	0.114108
$729$	−34.2809	−1.26966
$730$	68.6395	2.54046
$731$	10.4744	0.387410
$732$	−22.5973	−0.835222
$733$	23.5474	0.869742	0.434871	−	0.900493i	$-0.356794\pi$
$733$	23.5474	0.869742	0.434871	+	0.900493i	$0.356794\pi$
$734$	−20.3333	−0.750517
$735$	113.188	4.17500
$736$	−20.4636	−0.754297
$737$	6.26446	0.230754
$738$	−58.4607	−2.15197
$739$	−8.33389	−0.306567	−0.153284	−	0.988182i	$-0.548985\pi$
$739$	−8.33389	−0.306567	−0.153284	+	0.988182i	$0.548985\pi$
$740$	−124.003	−4.55845
$741$	1.01786	0.0373919
$742$	118.262	4.34152
$743$	−24.2424	−0.889369	−0.444684	−	0.895687i	$-0.646684\pi$
$743$	−24.2424	−0.889369	−0.444684	+	0.895687i	$0.646684\pi$
$744$	−74.8188	−2.74299
$745$	15.4449	0.565857
$746$	−31.6034	−1.15708
$747$	−2.28638	−0.0836542
$748$	−3.66668	−0.134067
$749$	−62.0443	−2.26705
$750$	−136.387	−4.98015
$751$	8.55298	0.312103	0.156051	−	0.987749i	$-0.450123\pi$
$751$	8.55298	0.312103	0.156051	+	0.987749i	$0.450123\pi$
$752$	3.34914	0.122131
$753$	44.7664	1.63138
$754$	1.11863	0.0407383
$755$	−35.9850	−1.30963
$756$	−15.8220	−0.575442
$757$	−25.0608	−0.910852	−0.455426	−	0.890274i	$-0.650513\pi$
$757$	−25.0608	−0.910852	−0.455426	+	0.890274i	$0.650513\pi$
$758$	65.4362	2.37675
$759$	9.84203	0.357243
$760$	−20.0751	−0.728199
$761$	8.47099	0.307073	0.153537	−	0.988143i	$-0.450934\pi$
$761$	8.47099	0.307073	0.153537	+	0.988143i	$0.450934\pi$
$762$	−90.3289	−3.27227
$763$	−57.2947	−2.07421
$764$	−7.70598	−0.278793
$765$	15.1946	0.549362
$766$	−16.2825	−0.588310
$767$	1.07868	0.0389488
$768$	−45.7852	−1.65213
$769$	−40.0278	−1.44344	−0.721720	−	0.692185i	$-0.756648\pi$
$769$	−40.0278	−1.44344	−0.721720	+	0.692185i	$0.756648\pi$
$770$	−39.1365	−1.41038
$771$	4.78583	0.172357
$772$	19.1031	0.687536
$773$	−50.1623	−1.80421	−0.902106	−	0.431514i	$-0.857980\pi$
$773$	−50.1623	−1.80421	−0.902106	+	0.431514i	$0.857980\pi$
$774$	−74.9162	−2.69281
$775$	106.262	3.81704
$776$	48.1222	1.72748
$777$	101.942	3.65717
$778$	−54.0993	−1.93955
$779$	12.3400	0.442128
$780$	8.00959	0.286789
$781$	−8.56057	−0.306321
$782$	9.90390	0.354163
$783$	−2.27246	−0.0812111
$784$	3.63060	0.129664
$785$	60.8132	2.17052
$786$	−83.5841	−2.98135
$787$	52.3215	1.86506	0.932530	−	0.361092i	$-0.117596\pi$
$787$	52.3215	1.86506	0.932530	+	0.361092i	$0.117596\pi$
$788$	−64.3808	−2.29347
$789$	36.8034	1.31024
$790$	151.831	5.40192
$791$	−84.7883	−3.01472
$792$	10.3668	0.368369
$793$	−0.645005	−0.0229048
$794$	−3.39701	−0.120555
$795$	121.619	4.31336
$796$	−58.0900	−2.05895
$797$	−26.2201	−0.928762	−0.464381	−	0.885635i	$-0.653723\pi$
$797$	−26.2201	−0.928762	−0.464381	+	0.885635i	$0.653723\pi$
$798$	41.7496	1.47792
$799$	11.4530	0.405177
$800$	57.2967	2.02574
$801$	−31.7696	−1.12252
$802$	33.5172	1.18353
$803$	7.48196	0.264033
$804$	−52.5869	−1.85460
$805$	65.8751	2.32179
$806$	−5.40245	−0.190293
$807$	63.7965	2.24574
$808$	49.8607	1.75409
$809$	−14.7187	−0.517483	−0.258742	−	0.965947i	$-0.583308\pi$
$809$	−14.7187	−0.517483	−0.258742	+	0.965947i	$0.583308\pi$
$810$	68.6154	2.41090
$811$	−4.44788	−0.156186	−0.0780931	−	0.996946i	$-0.524883\pi$
$811$	−4.44788	−0.156186	−0.0780931	+	0.996946i	$0.524883\pi$
$812$	28.5930	1.00342
$813$	45.8616	1.60844
$814$	−21.6905	−0.760250
$815$	86.5319	3.03108
$816$	0.912195	0.0319332
$817$	15.8135	0.553245
$818$	43.7848	1.53090
$819$	−3.51812	−0.122933
$820$	97.1047	3.39104
$821$	−30.8260	−1.07583	−0.537917	−	0.842998i	$-0.680789\pi$
$821$	−30.8260	−1.07583	−0.537917	+	0.842998i	$0.680789\pi$
$822$	63.7166	2.22237
$823$	−10.3276	−0.359999	−0.179999	−	0.983667i	$-0.557610\pi$
$823$	−10.3276	−0.359999	−0.179999	+	0.983667i	$0.557610\pi$
$824$	−39.8649	−1.38876
$825$	−27.5571	−0.959414
$826$	44.2443	1.53946
$827$	13.6156	0.473460	0.236730	−	0.971576i	$-0.423924\pi$
$827$	13.6156	0.473460	0.236730	+	0.971576i	$0.423924\pi$
$828$	−44.1426	−1.53406
$829$	35.6558	1.23838	0.619189	−	0.785242i	$-0.287462\pi$
$829$	35.6558	1.23838	0.619189	+	0.785242i	$0.287462\pi$
$830$	6.09423	0.211534
$831$	−17.8201	−0.618174
$832$	−3.06837	−0.106376
$833$	12.4155	0.430171
$834$	30.5953	1.05943
$835$	47.3671	1.63921
$836$	−5.53569	−0.191456
$837$	10.9749	0.379347
$838$	69.3898	2.39703
$839$	16.5368	0.570914	0.285457	−	0.958392i	$-0.407855\pi$
$839$	16.5368	0.570914	0.285457	+	0.958392i	$0.407855\pi$
$840$	129.868	4.48087
$841$	−24.8933	−0.858389
$842$	34.2785	1.18132
$843$	−33.0167	−1.13715
$844$	−13.4525	−0.463053
$845$	−51.5393	−1.77300
$846$	−81.9151	−2.81630
$847$	−4.26603	−0.146582
$848$	3.90102	0.133961
$849$	36.3982	1.24918
$850$	−27.7303	−0.951141
$851$	36.5096	1.25153
$852$	71.8615	2.46193
$853$	54.0237	1.84974	0.924868	−	0.380289i	$-0.124176\pi$
$853$	54.0237	1.84974	0.924868	+	0.380289i	$0.124176\pi$
$854$	−26.4563	−0.905316
$855$	22.9397	0.784521
$856$	−43.8061	−1.49726
$857$	−20.3714	−0.695873	−0.347936	−	0.937518i	$-0.613118\pi$
$857$	−20.3714	−0.695873	−0.347936	+	0.937518i	$0.613118\pi$
$858$	1.40102	0.0478301
$859$	20.8255	0.710558	0.355279	−	0.934760i	$-0.384386\pi$
$859$	20.8255	0.710558	0.355279	+	0.934760i	$0.384386\pi$
$860$	124.438	4.24329
$861$	−79.8292	−2.72057
$862$	−38.5101	−1.31166
$863$	4.32385	0.147186	0.0735928	−	0.997288i	$-0.476553\pi$
$863$	4.32385	0.147186	0.0735928	+	0.997288i	$0.476553\pi$
$864$	5.91766	0.201323
$865$	35.0261	1.19092
$866$	48.5013	1.64814
$867$	−40.0278	−1.35942
$868$	−138.090	−4.68708
$869$	16.5502	0.561427
$870$	47.1857	1.59974
$871$	−1.50101	−0.0508597
$872$	−40.4527	−1.36990
$873$	−54.9890	−1.86110
$874$	14.9522	0.505765
$875$	−99.5064	−3.36393
$876$	−62.8071	−2.12206
$877$	3.44140	0.116208	0.0581038	−	0.998311i	$-0.481495\pi$
$877$	3.44140	0.116208	0.0581038	+	0.998311i	$0.481495\pi$
$878$	−41.7118	−1.40770
$879$	15.9981	0.539604
$880$	−1.29097	−0.0435186
$881$	−28.9444	−0.975162	−0.487581	−	0.873078i	$-0.662121\pi$
$881$	−28.9444	−0.975162	−0.487581	+	0.873078i	$0.662121\pi$
$882$	−88.7992	−2.99003
$883$	−32.6872	−1.10001	−0.550006	−	0.835161i	$-0.685375\pi$
$883$	−32.6872	−1.10001	−0.550006	+	0.835161i	$0.685375\pi$
$884$	0.878563	0.0295493
$885$	45.5002	1.52947
$886$	6.18905	0.207925
$887$	40.4964	1.35974	0.679868	−	0.733334i	$-0.262037\pi$
$887$	40.4964	1.35974	0.679868	+	0.733334i	$0.262037\pi$
$888$	71.9761	2.41536
$889$	−65.9029	−2.21031
$890$	84.6802	2.83849
$891$	7.47934	0.250567
$892$	85.3513	2.85777
$893$	17.2909	0.578617
$894$	−22.6785	−0.758482
$895$	−76.6022	−2.56053
$896$	−80.8307	−2.70036
$897$	−2.35822	−0.0787386
$898$	−29.3726	−0.980177
$899$	−19.8334	−0.661480
$900$	123.597	4.11988
$901$	13.3402	0.444427
$902$	16.9854	0.565552
$903$	−102.300	−3.40432
$904$	−59.8645	−1.99106
$905$	−38.0570	−1.26506
$906$	52.8385	1.75544
$907$	−0.0280674	−0.000931963 0	−0.000465982	−	1.00000i	$-0.500148\pi$
$907$	−0.0280674	−0.000931963 0	−0.000465982		1.00000i	$0.500148\pi$
$908$	−6.46746	−0.214630
$909$	−56.9757	−1.88976
$910$	9.37739	0.310857
$911$	−30.2306	−1.00158	−0.500792	−	0.865568i	$-0.666958\pi$
$911$	−30.2306	−1.00158	−0.500792	+	0.865568i	$0.666958\pi$
$912$	1.37717	0.0456025
$913$	0.664294	0.0219849
$914$	−61.3791	−2.03024
$915$	−27.2073	−0.899445
$916$	65.4900	2.16385
$917$	−60.9820	−2.01380
$918$	−2.86402	−0.0945266
$919$	41.4350	1.36682	0.683408	−	0.730037i	$-0.260497\pi$
$919$	41.4350	1.36682	0.683408	+	0.730037i	$0.260497\pi$
$920$	46.5109	1.53342
$921$	−8.37606	−0.276001
$922$	87.9871	2.89770
$923$	2.05117	0.0675151
$924$	35.8111	1.17810
$925$	−102.225	−3.36113
$926$	−24.6264	−0.809272
$927$	45.5535	1.49617
$928$	−10.6942	−0.351054
$929$	−30.6298	−1.00493	−0.502466	−	0.864597i	$-0.667574\pi$
$929$	−30.6298	−1.00493	−0.502466	+	0.864597i	$0.667574\pi$
$930$	−227.883	−7.47259
$931$	18.7440	0.614309
$932$	56.1314	1.83864
$933$	−34.9658	−1.14473
$934$	16.9625	0.555030
$935$	−4.41470	−0.144376
$936$	−2.48396	−0.0811908
$937$	−7.37277	−0.240858	−0.120429	−	0.992722i	$-0.538427\pi$
$937$	−7.37277	−0.240858	−0.120429	+	0.992722i	$0.538427\pi$
$938$	−61.5672	−2.01024
$939$	−32.5329	−1.06167
$940$	136.063	4.43789
$941$	9.42733	0.307322	0.153661	−	0.988124i	$-0.450894\pi$
$941$	9.42733	0.307322	0.153661	+	0.988124i	$0.450894\pi$
$942$	−89.2949	−2.90939
$943$	−28.5900	−0.931019
$944$	1.45946	0.0475013
$945$	−19.0498	−0.619690
$946$	21.7664	0.707688
$947$	−18.0487	−0.586505	−0.293253	−	0.956035i	$-0.594738\pi$
$947$	−18.0487	−0.586505	−0.293253	+	0.956035i	$0.594738\pi$
$948$	−138.930	−4.51224
$949$	−1.79273	−0.0581944
$950$	−41.8652	−1.35829
$951$	−43.9323	−1.42460
$952$	14.2451	0.461686
$953$	−19.6596	−0.636838	−0.318419	−	0.947950i	$-0.603152\pi$
$953$	−19.6596	−0.636838	−0.318419	+	0.947950i	$0.603152\pi$
$954$	−95.4132	−3.08912
$955$	−9.27802	−0.300230
$956$	39.5776	1.28003
$957$	5.14341	0.166263
$958$	−75.6947	−2.44559
$959$	46.4869	1.50114
$960$	−129.428	−4.17728
$961$	64.7853	2.08985
$962$	5.19718	0.167564
$963$	50.0571	1.61307
$964$	67.8555	2.18548
$965$	23.0002	0.740402
$966$	−96.7275	−3.11216
$967$	−28.4547	−0.915041	−0.457520	−	0.889199i	$-0.651262\pi$
$967$	−28.4547	−0.915041	−0.457520	+	0.889199i	$0.651262\pi$
$968$	−3.01201	−0.0968098
$969$	4.70946	0.151290
$970$	146.571	4.70610
$971$	53.1850	1.70679	0.853394	−	0.521267i	$-0.174540\pi$
$971$	53.1850	1.70679	0.853394	+	0.521267i	$0.174540\pi$
$972$	−73.9117	−2.37072
$973$	22.3220	0.715610
$974$	−6.05111	−0.193890
$975$	6.60286	0.211461
$976$	−0.872696	−0.0279343
$977$	16.5598	0.529794	0.264897	−	0.964277i	$-0.414662\pi$
$977$	16.5598	0.529794	0.264897	+	0.964277i	$0.414662\pi$
$978$	−127.059	−4.06290
$979$	9.23046	0.295007
$980$	147.498	4.71165
$981$	46.2252	1.47586
$982$	−31.9644	−1.02002
$983$	26.1604	0.834386	0.417193	−	0.908818i	$-0.363014\pi$
$983$	26.1604	0.834386	0.417193	+	0.908818i	$0.363014\pi$
$984$	−56.3632	−1.79679
$985$	−77.5147	−2.46982
$986$	5.17574	0.164829
$987$	−111.857	−3.56044
$988$	1.32639	0.0421981
$989$	−36.6375	−1.16501
$990$	31.5753	1.00353
$991$	32.8391	1.04317	0.521584	−	0.853200i	$-0.325341\pi$
$991$	32.8391	1.04317	0.521584	+	0.853200i	$0.325341\pi$
$992$	51.6476	1.63981
$993$	2.98683	0.0947841
$994$	84.1333	2.66855
$995$	−69.9406	−2.21727
$996$	−5.57640	−0.176695
$997$	−35.0668	−1.11058	−0.555289	−	0.831657i	$-0.687392\pi$
$997$	−35.0668	−1.11058	−0.555289	+	0.831657i	$0.687392\pi$
$998$	−12.2325	−0.387213
$999$	−10.5579	−0.334036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.14	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.14	✓	121	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30378 q^{2} +2.53807 q^{3} +3.30742 q^{4} +3.98214 q^{5} -5.84717 q^{6} -4.26603 q^{7} -3.01201 q^{8} +3.44182 q^{9} +O(q^{10})\)	\(q-2.30378 q^{2} +2.53807 q^{3} +3.30742 q^{4} +3.98214 q^{5} -5.84717 q^{6} -4.26603 q^{7} -3.01201 q^{8} +3.44182 q^{9} -9.17400 q^{10} -1.00000 q^{11} +8.39448 q^{12} +0.239607 q^{13} +9.82801 q^{14} +10.1070 q^{15} +0.324190 q^{16} +1.10862 q^{17} -7.92921 q^{18} +1.67372 q^{19} +13.1706 q^{20} -10.8275 q^{21} +2.30378 q^{22} -3.87775 q^{23} -7.64472 q^{24} +10.8575 q^{25} -0.552003 q^{26} +1.12137 q^{27} -14.1096 q^{28} -2.02650 q^{29} -23.2843 q^{30} +9.78699 q^{31} +5.27717 q^{32} -2.53807 q^{33} -2.55403 q^{34} -16.9879 q^{35} +11.3835 q^{36} -9.41514 q^{37} -3.85589 q^{38} +0.608140 q^{39} -11.9943 q^{40} +7.37283 q^{41} +24.9442 q^{42} +9.44813 q^{43} -3.30742 q^{44} +13.7058 q^{45} +8.93351 q^{46} +10.3308 q^{47} +0.822818 q^{48} +11.1990 q^{49} -25.0133 q^{50} +2.81377 q^{51} +0.792481 q^{52} +12.0331 q^{53} -2.58340 q^{54} -3.98214 q^{55} +12.8493 q^{56} +4.24802 q^{57} +4.66862 q^{58} +4.50186 q^{59} +33.4280 q^{60} -2.69193 q^{61} -22.5471 q^{62} -14.6829 q^{63} -12.8058 q^{64} +0.954149 q^{65} +5.84717 q^{66} -6.26446 q^{67} +3.66668 q^{68} -9.84203 q^{69} +39.1365 q^{70} +8.56057 q^{71} -10.3668 q^{72} -7.48196 q^{73} +21.6905 q^{74} +27.5571 q^{75} +5.53569 q^{76} +4.26603 q^{77} -1.40102 q^{78} -16.5502 q^{79} +1.29097 q^{80} -7.47934 q^{81} -16.9854 q^{82} -0.664294 q^{83} -35.8111 q^{84} +4.41470 q^{85} -21.7664 q^{86} -5.14341 q^{87} +3.01201 q^{88} -9.23046 q^{89} -31.5753 q^{90} -1.02217 q^{91} -12.8254 q^{92} +24.8401 q^{93} -23.7999 q^{94} +6.66499 q^{95} +13.3938 q^{96} -15.9767 q^{97} -25.8001 q^{98} -3.44182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

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