LMFDB - Embedded newform 6017.2.a.f.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.47328 q^{2} -1.34586 q^{3} +4.11710 q^{4} +2.94670 q^{5} +3.32869 q^{6} -2.85130 q^{7} -5.23618 q^{8} -1.18866 q^{9} +O(q^{10})$	\(q-2.47328 q^{2} -1.34586 q^{3} +4.11710 q^{4} +2.94670 q^{5} +3.32869 q^{6} -2.85130 q^{7} -5.23618 q^{8} -1.18866 q^{9} -7.28801 q^{10} -1.00000 q^{11} -5.54105 q^{12} -1.72879 q^{13} +7.05206 q^{14} -3.96585 q^{15} +4.71631 q^{16} -6.02426 q^{17} +2.93988 q^{18} -4.89251 q^{19} +12.1319 q^{20} +3.83746 q^{21} +2.47328 q^{22} +3.06664 q^{23} +7.04717 q^{24} +3.68306 q^{25} +4.27577 q^{26} +5.63735 q^{27} -11.7391 q^{28} -9.51723 q^{29} +9.80866 q^{30} -2.12362 q^{31} -1.19240 q^{32} +1.34586 q^{33} +14.8997 q^{34} -8.40194 q^{35} -4.89382 q^{36} -2.03716 q^{37} +12.1005 q^{38} +2.32671 q^{39} -15.4295 q^{40} -2.59459 q^{41} -9.49109 q^{42} -10.3932 q^{43} -4.11710 q^{44} -3.50262 q^{45} -7.58466 q^{46} -4.16877 q^{47} -6.34750 q^{48} +1.12992 q^{49} -9.10923 q^{50} +8.10782 q^{51} -7.11759 q^{52} +10.0709 q^{53} -13.9427 q^{54} -2.94670 q^{55} +14.9299 q^{56} +6.58464 q^{57} +23.5388 q^{58} +4.62139 q^{59} -16.3278 q^{60} -14.6861 q^{61} +5.25230 q^{62} +3.38922 q^{63} -6.48349 q^{64} -5.09422 q^{65} -3.32869 q^{66} -7.80053 q^{67} -24.8025 q^{68} -4.12728 q^{69} +20.7803 q^{70} -16.5584 q^{71} +6.22402 q^{72} +10.1702 q^{73} +5.03845 q^{74} -4.95689 q^{75} -20.1429 q^{76} +2.85130 q^{77} -5.75459 q^{78} +8.61927 q^{79} +13.8976 q^{80} -4.02112 q^{81} +6.41714 q^{82} -8.70178 q^{83} +15.7992 q^{84} -17.7517 q^{85} +25.7053 q^{86} +12.8089 q^{87} +5.23618 q^{88} +7.51142 q^{89} +8.66295 q^{90} +4.92929 q^{91} +12.6257 q^{92} +2.85810 q^{93} +10.3105 q^{94} -14.4168 q^{95} +1.60481 q^{96} -3.08062 q^{97} -2.79461 q^{98} +1.18866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.47328	−1.74887	−0.874436	−	0.485142i	$-0.838768\pi$
$2$	−2.47328	−1.74887	−0.874436	+	0.485142i	$0.838768\pi$
$3$	−1.34586	−0.777033	−0.388517	−	0.921442i	$-0.627012\pi$
$3$	−1.34586	−0.777033	−0.388517	+	0.921442i	$0.627012\pi$
$4$	4.11710	2.05855
$5$	2.94670	1.31781	0.658903	−	0.752228i	$-0.271021\pi$
$5$	2.94670	1.31781	0.658903	+	0.752228i	$0.271021\pi$
$6$	3.32869	1.35893
$7$	−2.85130	−1.07769	−0.538845	−	0.842405i	$-0.681139\pi$
$7$	−2.85130	−1.07769	−0.538845	+	0.842405i	$0.681139\pi$
$8$	−5.23618	−1.85127
$9$	−1.18866	−0.396219
$10$	−7.28801	−2.30467
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−5.54105	−1.59956
$13$	−1.72879	−0.479479	−0.239740	−	0.970837i	$-0.577062\pi$
$13$	−1.72879	−0.479479	−0.239740	+	0.970837i	$0.577062\pi$
$14$	7.05206	1.88474
$15$	−3.96585	−1.02398
$16$	4.71631	1.17908
$17$	−6.02426	−1.46110	−0.730549	−	0.682861i	$-0.760736\pi$
$17$	−6.02426	−1.46110	−0.730549	+	0.682861i	$0.760736\pi$
$18$	2.93988	0.692936
$19$	−4.89251	−1.12242	−0.561209	−	0.827674i	$-0.689664\pi$
$19$	−4.89251	−1.12242	−0.561209	+	0.827674i	$0.689664\pi$
$20$	12.1319	2.71277
$21$	3.83746	0.837402
$22$	2.47328	0.527304
$23$	3.06664	0.639439	0.319720	−	0.947512i	$-0.396411\pi$
$23$	3.06664	0.639439	0.319720	+	0.947512i	$0.396411\pi$
$24$	7.04717	1.43850
$25$	3.68306	0.736612
$26$	4.27577	0.838547
$27$	5.63735	1.08491
$28$	−11.7391	−2.21848
$29$	−9.51723	−1.76731	−0.883653	−	0.468143i	$-0.844923\pi$
$29$	−9.51723	−1.76731	−0.883653	+	0.468143i	$0.844923\pi$
$30$	9.80866	1.79081
$31$	−2.12362	−0.381413	−0.190707	−	0.981647i	$-0.561078\pi$
$31$	−2.12362	−0.381413	−0.190707	+	0.981647i	$0.561078\pi$
$32$	−1.19240	−0.210789
$33$	1.34586	0.234284
$34$	14.8997	2.55527
$35$	−8.40194	−1.42019
$36$	−4.89382	−0.815637
$37$	−2.03716	−0.334906	−0.167453	−	0.985880i	$-0.553554\pi$
$37$	−2.03716	−0.334906	−0.167453	+	0.985880i	$0.553554\pi$
$38$	12.1005	1.96296
$39$	2.32671	0.372571
$40$	−15.4295	−2.43961
$41$	−2.59459	−0.405207	−0.202603	−	0.979261i	$-0.564940\pi$
$41$	−2.59459	−0.405207	−0.202603	+	0.979261i	$0.564940\pi$
$42$	−9.49109	−1.46451
$43$	−10.3932	−1.58495	−0.792476	−	0.609904i	$-0.791208\pi$
$43$	−10.3932	−1.58495	−0.792476	+	0.609904i	$0.791208\pi$
$44$	−4.11710	−0.620676
$45$	−3.50262	−0.522140
$46$	−7.58466	−1.11830
$47$	−4.16877	−0.608078	−0.304039	−	0.952660i	$-0.598335\pi$
$47$	−4.16877	−0.608078	−0.304039	+	0.952660i	$0.598335\pi$
$48$	−6.34750	−0.916183
$49$	1.12992	0.161417
$50$	−9.10923	−1.28824
$51$	8.10782	1.13532
$52$	−7.11759	−0.987032
$53$	10.0709	1.38335	0.691675	−	0.722209i	$-0.256873\pi$
$53$	10.0709	1.38335	0.691675	+	0.722209i	$0.256873\pi$
$54$	−13.9427	−1.89737
$55$	−2.94670	−0.397333
$56$	14.9299	1.99509
$57$	6.58464	0.872156
$58$	23.5388	3.09079
$59$	4.62139	0.601653	0.300827	−	0.953679i	$-0.402737\pi$
$59$	4.62139	0.601653	0.300827	+	0.953679i	$0.402737\pi$
$60$	−16.3278	−2.10791
$61$	−14.6861	−1.88037	−0.940183	−	0.340670i	$-0.889346\pi$
$61$	−14.6861	−1.88037	−0.940183	+	0.340670i	$0.889346\pi$
$62$	5.25230	0.667043
$63$	3.38922	0.427002
$64$	−6.48349	−0.810436
$65$	−5.09422	−0.631861
$66$	−3.32869	−0.409733
$67$	−7.80053	−0.952987	−0.476493	−	0.879178i	$-0.658092\pi$
$67$	−7.80053	−0.952987	−0.476493	+	0.879178i	$0.658092\pi$
$68$	−24.8025	−3.00774
$69$	−4.12728	−0.496866
$70$	20.7803	2.48372
$71$	−16.5584	−1.96512	−0.982560	−	0.185946i	$-0.940465\pi$
$71$	−16.5584	−1.96512	−0.982560	+	0.185946i	$0.940465\pi$
$72$	6.22402	0.733508
$73$	10.1702	1.19033	0.595164	−	0.803605i	$-0.297087\pi$
$73$	10.1702	1.19033	0.595164	+	0.803605i	$0.297087\pi$
$74$	5.03845	0.585708
$75$	−4.95689	−0.572372
$76$	−20.1429	−2.31055
$77$	2.85130	0.324936
$78$	−5.75459	−0.651579
$79$	8.61927	0.969744	0.484872	−	0.874585i	$-0.338866\pi$
$79$	8.61927	0.969744	0.484872	+	0.874585i	$0.338866\pi$
$80$	13.8976	1.55380
$81$	−4.02112	−0.446791
$82$	6.41714	0.708655
$83$	−8.70178	−0.955144	−0.477572	−	0.878593i	$-0.658483\pi$
$83$	−8.70178	−0.955144	−0.477572	+	0.878593i	$0.658483\pi$
$84$	15.7992	1.72383
$85$	−17.7517	−1.92544
$86$	25.7053	2.77188
$87$	12.8089	1.37326
$88$	5.23618	0.558178
$89$	7.51142	0.796208	0.398104	−	0.917340i	$-0.369668\pi$
$89$	7.51142	0.796208	0.398104	+	0.917340i	$0.369668\pi$
$90$	8.66295	0.913156
$91$	4.92929	0.516730
$92$	12.6257	1.31632
$93$	2.85810	0.296371
$94$	10.3105	1.06345
$95$	−14.4168	−1.47913
$96$	1.60481	0.163790
$97$	−3.08062	−0.312790	−0.156395	−	0.987695i	$-0.549987\pi$
$97$	−3.08062	−0.312790	−0.156395	+	0.987695i	$0.549987\pi$
$98$	−2.79461	−0.282298
$99$	1.18866	0.119465
$100$	15.1635	1.51635
$101$	−9.37227	−0.932576	−0.466288	−	0.884633i	$-0.654409\pi$
$101$	−9.37227	−0.932576	−0.466288	+	0.884633i	$0.654409\pi$
$102$	−20.0529	−1.98553
$103$	4.16480	0.410370	0.205185	−	0.978723i	$-0.434220\pi$
$103$	4.16480	0.410370	0.205185	+	0.978723i	$0.434220\pi$
$104$	9.05223	0.887645
$105$	11.3078	1.10353
$106$	−24.9082	−2.41930
$107$	9.72118	0.939782	0.469891	−	0.882724i	$-0.344293\pi$
$107$	9.72118	0.939782	0.469891	+	0.882724i	$0.344293\pi$
$108$	23.2095	2.23334
$109$	−2.01684	−0.193178	−0.0965891	−	0.995324i	$-0.530793\pi$
$109$	−2.01684	−0.193178	−0.0965891	+	0.995324i	$0.530793\pi$
$110$	7.28801	0.694885
$111$	2.74173	0.260233
$112$	−13.4476	−1.27068
$113$	−0.484566	−0.0455842	−0.0227921	−	0.999740i	$-0.507256\pi$
$113$	−0.484566	−0.0455842	−0.0227921	+	0.999740i	$0.507256\pi$
$114$	−16.2856	−1.52529
$115$	9.03649	0.842657
$116$	−39.1834	−3.63809
$117$	2.05494	0.189979
$118$	−11.4300	−1.05221
$119$	17.1770	1.57461
$120$	20.7659	1.89566
$121$	1.00000	0.0909091
$122$	36.3229	3.28852
$123$	3.49196	0.314859
$124$	−8.74315	−0.785158
$125$	−3.88063	−0.347094
$126$	−8.38248	−0.746771
$127$	19.5778	1.73725	0.868624	−	0.495472i	$-0.165005\pi$
$127$	19.5778	1.73725	0.868624	+	0.495472i	$0.165005\pi$
$128$	18.4203	1.62814
$129$	13.9878	1.23156
$130$	12.5994	1.10504
$131$	16.6115	1.45135	0.725677	−	0.688036i	$-0.241527\pi$
$131$	16.6115	1.45135	0.725677	+	0.688036i	$0.241527\pi$
$132$	5.54105	0.482286
$133$	13.9500	1.20962
$134$	19.2929	1.66665
$135$	16.6116	1.42970
$136$	31.5441	2.70488
$137$	3.70035	0.316142	0.158071	−	0.987428i	$-0.449472\pi$
$137$	3.70035	0.316142	0.158071	+	0.987428i	$0.449472\pi$
$138$	10.2079	0.868954
$139$	12.1430	1.02996	0.514978	−	0.857203i	$-0.327800\pi$
$139$	12.1430	1.02996	0.514978	+	0.857203i	$0.327800\pi$
$140$	−34.5916	−2.92353
$141$	5.61059	0.472497
$142$	40.9535	3.43674
$143$	1.72879	0.144568
$144$	−5.60608	−0.467174
$145$	−28.0445	−2.32897
$146$	−25.1536	−2.08173
$147$	−1.52072	−0.125427
$148$	−8.38718	−0.689422
$149$	−9.58037	−0.784854	−0.392427	−	0.919783i	$-0.628365\pi$
$149$	−9.58037	−0.784854	−0.392427	+	0.919783i	$0.628365\pi$
$150$	12.2598	1.00101
$151$	6.00145	0.488391	0.244196	−	0.969726i	$-0.421476\pi$
$151$	6.00145	0.488391	0.244196	+	0.969726i	$0.421476\pi$
$152$	25.6180	2.07790
$153$	7.16078	0.578915
$154$	−7.05206	−0.568271
$155$	−6.25768	−0.502629
$156$	9.57929	0.766957
$157$	2.85994	0.228248	0.114124	−	0.993467i	$-0.463594\pi$
$157$	2.85994	0.228248	0.114124	+	0.993467i	$0.463594\pi$
$158$	−21.3179	−1.69596
$159$	−13.5541	−1.07491
$160$	−3.51365	−0.277779
$161$	−8.74392	−0.689118
$162$	9.94534	0.781380
$163$	4.96638	0.388997	0.194498	−	0.980903i	$-0.437692\pi$
$163$	4.96638	0.388997	0.194498	+	0.980903i	$0.437692\pi$
$164$	−10.6822	−0.834139
$165$	3.96585	0.308741
$166$	21.5219	1.67042
$167$	24.2458	1.87619	0.938097	−	0.346372i	$-0.112587\pi$
$167$	24.2458	1.87619	0.938097	+	0.346372i	$0.112587\pi$
$168$	−20.0936	−1.55025
$169$	−10.0113	−0.770100
$170$	43.9049	3.36735
$171$	5.81552	0.444724
$172$	−42.7899	−3.26270
$173$	−14.9495	−1.13659	−0.568295	−	0.822825i	$-0.692397\pi$
$173$	−14.9495	−1.13659	−0.568295	+	0.822825i	$0.692397\pi$
$174$	−31.6799	−2.40165
$175$	−10.5015	−0.793840
$176$	−4.71631	−0.355506
$177$	−6.21975	−0.467505
$178$	−18.5778	−1.39247
$179$	−19.8200	−1.48141	−0.740707	−	0.671828i	$-0.765509\pi$
$179$	−19.8200	−1.48141	−0.740707	+	0.671828i	$0.765509\pi$
$180$	−14.4206	−1.07485
$181$	−22.3787	−1.66340	−0.831698	−	0.555229i	$-0.812631\pi$
$181$	−22.3787	−1.66340	−0.831698	+	0.555229i	$0.812631\pi$
$182$	−12.1915	−0.903695
$183$	19.7655	1.46111
$184$	−16.0575	−1.18377
$185$	−6.00290	−0.441342
$186$	−7.06886	−0.518314
$187$	6.02426	0.440537
$188$	−17.1633	−1.25176
$189$	−16.0738	−1.16920
$190$	35.6567	2.58681
$191$	24.5052	1.77313	0.886567	−	0.462600i	$-0.153083\pi$
$191$	24.5052	1.77313	0.886567	+	0.462600i	$0.153083\pi$
$192$	8.72588	0.629736
$193$	−11.3225	−0.815009	−0.407504	−	0.913203i	$-0.633601\pi$
$193$	−11.3225	−0.815009	−0.407504	+	0.913203i	$0.633601\pi$
$194$	7.61923	0.547029
$195$	6.85612	0.490977
$196$	4.65200	0.332286
$197$	12.6698	0.902686	0.451343	−	0.892351i	$-0.350945\pi$
$197$	12.6698	0.902686	0.451343	+	0.892351i	$0.350945\pi$
$198$	−2.93988	−0.208928
$199$	5.92740	0.420182	0.210091	−	0.977682i	$-0.432624\pi$
$199$	5.92740	0.420182	0.210091	+	0.977682i	$0.432624\pi$
$200$	−19.2852	−1.36367
$201$	10.4984	0.740502
$202$	23.1802	1.63095
$203$	27.1365	1.90461
$204$	33.3807	2.33712
$205$	−7.64549	−0.533984
$206$	−10.3007	−0.717684
$207$	−3.64519	−0.253358
$208$	−8.15350	−0.565344
$209$	4.89251	0.338422
$210$	−27.9674	−1.92994
$211$	−2.85902	−0.196823	−0.0984116	−	0.995146i	$-0.531376\pi$
$211$	−2.85902	−0.196823	−0.0984116	+	0.995146i	$0.531376\pi$
$212$	41.4631	2.84769
$213$	22.2853	1.52696
$214$	−24.0432	−1.64356
$215$	−30.6257	−2.08866
$216$	−29.5182	−2.00846
$217$	6.05508	0.411045
$218$	4.98820	0.337844
$219$	−13.6876	−0.924924
$220$	−12.1319	−0.817931
$221$	10.4147	0.700566
$222$	−6.78106	−0.455115
$223$	−11.6398	−0.779460	−0.389730	−	0.920929i	$-0.627432\pi$
$223$	−11.6398	−0.779460	−0.389730	+	0.920929i	$0.627432\pi$
$224$	3.39990	0.227165
$225$	−4.37790	−0.291860
$226$	1.19847	0.0797208
$227$	−9.44804	−0.627088	−0.313544	−	0.949574i	$-0.601516\pi$
$227$	−9.44804	−0.627088	−0.313544	+	0.949574i	$0.601516\pi$
$228$	27.1096	1.79538
$229$	10.0854	0.666459	0.333230	−	0.942846i	$-0.391862\pi$
$229$	10.0854	0.666459	0.333230	+	0.942846i	$0.391862\pi$
$230$	−22.3497	−1.47370
$231$	−3.83746	−0.252486
$232$	49.8339	3.27176
$233$	−25.7384	−1.68618	−0.843091	−	0.537772i	$-0.819266\pi$
$233$	−25.7384	−1.68618	−0.843091	+	0.537772i	$0.819266\pi$
$234$	−5.08243	−0.332249
$235$	−12.2841	−0.801329
$236$	19.0267	1.23853
$237$	−11.6003	−0.753524
$238$	−42.4834	−2.75379
$239$	1.51678	0.0981123	0.0490561	−	0.998796i	$-0.484379\pi$
$239$	1.51678	0.0981123	0.0490561	+	0.998796i	$0.484379\pi$
$240$	−18.7042	−1.20735
$241$	11.0955	0.714723	0.357361	−	0.933966i	$-0.383676\pi$
$241$	11.0955	0.714723	0.357361	+	0.933966i	$0.383676\pi$
$242$	−2.47328	−0.158988
$243$	−11.5002	−0.737737
$244$	−60.4643	−3.87083
$245$	3.32954	0.212717
$246$	−8.63658	−0.550648
$247$	8.45810	0.538176
$248$	11.1196	0.706098
$249$	11.7114	0.742179
$250$	9.59787	0.607022
$251$	−26.1803	−1.65248	−0.826242	−	0.563316i	$-0.809525\pi$
$251$	−26.1803	−1.65248	−0.826242	+	0.563316i	$0.809525\pi$
$252$	13.9538	0.879005
$253$	−3.06664	−0.192798
$254$	−48.4213	−3.03822
$255$	23.8913	1.49613
$256$	−32.5915	−2.03697
$257$	−9.94390	−0.620284	−0.310142	−	0.950690i	$-0.600377\pi$
$257$	−9.94390	−0.620284	−0.310142	+	0.950690i	$0.600377\pi$
$258$	−34.5958	−2.15384
$259$	5.80855	0.360926
$260$	−20.9734	−1.30072
$261$	11.3127	0.700241
$262$	−41.0849	−2.53823
$263$	11.8030	0.727805	0.363903	−	0.931437i	$-0.381444\pi$
$263$	11.8030	0.727805	0.363903	+	0.931437i	$0.381444\pi$
$264$	−7.04717	−0.433723
$265$	29.6761	1.82299
$266$	−34.5023	−2.11547
$267$	−10.1093	−0.618680
$268$	−32.1156	−1.96177
$269$	−12.3852	−0.755138	−0.377569	−	0.925982i	$-0.623240\pi$
$269$	−12.3852	−0.755138	−0.377569	+	0.925982i	$0.623240\pi$
$270$	−41.0851	−2.50036
$271$	20.1293	1.22277	0.611383	−	0.791335i	$-0.290614\pi$
$271$	20.1293	1.22277	0.611383	+	0.791335i	$0.290614\pi$
$272$	−28.4123	−1.72275
$273$	−6.63414	−0.401517
$274$	−9.15199	−0.552892
$275$	−3.68306	−0.222097
$276$	−16.9924	−1.02282
$277$	−8.40085	−0.504758	−0.252379	−	0.967628i	$-0.581213\pi$
$277$	−8.40085	−0.504758	−0.252379	+	0.967628i	$0.581213\pi$
$278$	−30.0330	−1.80126
$279$	2.52426	0.151123
$280$	43.9940	2.62915
$281$	−11.0582	−0.659675	−0.329838	−	0.944038i	$-0.606994\pi$
$281$	−11.0582	−0.659675	−0.329838	+	0.944038i	$0.606994\pi$
$282$	−13.8765	−0.826336
$283$	−22.2760	−1.32417	−0.662087	−	0.749427i	$-0.730329\pi$
$283$	−22.2760	−1.32417	−0.662087	+	0.749427i	$0.730329\pi$
$284$	−68.1726	−4.04530
$285$	19.4030	1.14933
$286$	−4.27577	−0.252832
$287$	7.39796	0.436688
$288$	1.41736	0.0835186
$289$	19.2917	1.13481
$290$	69.3617	4.07306
$291$	4.14609	0.243048
$292$	41.8716	2.45035
$293$	27.4214	1.60198	0.800989	−	0.598680i	$-0.204308\pi$
$293$	27.4214	1.60198	0.800989	+	0.598680i	$0.204308\pi$
$294$	3.76115	0.219355
$295$	13.6179	0.792862
$296$	10.6669	0.620001
$297$	−5.63735	−0.327112
$298$	23.6949	1.37261
$299$	−5.30157	−0.306598
$300$	−20.4080	−1.17826
$301$	29.6342	1.70809
$302$	−14.8433	−0.854134
$303$	12.6138	0.724642
$304$	−23.0746	−1.32342
$305$	−43.2757	−2.47796
$306$	−17.7106	−1.01245
$307$	20.9564	1.19605	0.598023	−	0.801479i	$-0.295953\pi$
$307$	20.9564	1.19605	0.598023	+	0.801479i	$0.295953\pi$
$308$	11.7391	0.668897
$309$	−5.60524	−0.318871
$310$	15.4770	0.879033
$311$	−11.5550	−0.655227	−0.327613	−	0.944812i	$-0.606244\pi$
$311$	−11.5550	−0.655227	−0.327613	+	0.944812i	$0.606244\pi$
$312$	−12.1831	−0.689729
$313$	30.0546	1.69879	0.849394	−	0.527759i	$-0.176968\pi$
$313$	30.0546	1.69879	0.849394	+	0.527759i	$0.176968\pi$
$314$	−7.07342	−0.399176
$315$	9.98703	0.562705
$316$	35.4864	1.99627
$317$	−11.0222	−0.619066	−0.309533	−	0.950889i	$-0.600173\pi$
$317$	−11.0222	−0.619066	−0.309533	+	0.950889i	$0.600173\pi$
$318$	33.5230	1.87988
$319$	9.51723	0.532863
$320$	−19.1049	−1.06800
$321$	−13.0834	−0.730242
$322$	21.6261	1.20518
$323$	29.4737	1.63996
$324$	−16.5554	−0.919742
$325$	−6.36723	−0.353190
$326$	−12.2832	−0.680305
$327$	2.71439	0.150106
$328$	13.5857	0.750146
$329$	11.8864	0.655320
$330$	−9.80866	−0.539949
$331$	−31.0083	−1.70437	−0.852186	−	0.523239i	$-0.824723\pi$
$331$	−31.0083	−1.70437	−0.852186	+	0.523239i	$0.824723\pi$
$332$	−35.8261	−1.96621
$333$	2.42148	0.132696
$334$	−59.9665	−3.28122
$335$	−22.9859	−1.25585
$336$	18.0987	0.987362
$337$	19.4136	1.05753	0.528764	−	0.848769i	$-0.322656\pi$
$337$	19.4136	1.05753	0.528764	+	0.848769i	$0.322656\pi$
$338$	24.7607	1.34680
$339$	0.652159	0.0354204
$340$	−73.0855	−3.96362
$341$	2.12362	0.115000
$342$	−14.3834	−0.777764
$343$	16.7374	0.903733
$344$	54.4207	2.93417
$345$	−12.1619	−0.654772
$346$	36.9742	1.98775
$347$	23.0518	1.23749	0.618744	−	0.785593i	$-0.287642\pi$
$347$	23.0518	1.23749	0.618744	+	0.785593i	$0.287642\pi$
$348$	52.7354	2.82692
$349$	−14.5280	−0.777664	−0.388832	−	0.921309i	$-0.627121\pi$
$349$	−14.5280	−0.777664	−0.388832	+	0.921309i	$0.627121\pi$
$350$	25.9732	1.38832
$351$	−9.74578	−0.520191
$352$	1.19240	0.0635552
$353$	−17.6495	−0.939390	−0.469695	−	0.882829i	$-0.655636\pi$
$353$	−17.6495	−0.939390	−0.469695	+	0.882829i	$0.655636\pi$
$354$	15.3832	0.817606
$355$	−48.7927	−2.58965
$356$	30.9252	1.63903
$357$	−23.1178	−1.22353
$358$	49.0203	2.59080
$359$	−18.5507	−0.979068	−0.489534	−	0.871984i	$-0.662833\pi$
$359$	−18.5507	−0.979068	−0.489534	+	0.871984i	$0.662833\pi$
$360$	18.3403	0.966621
$361$	4.93663	0.259822
$362$	55.3487	2.90906
$363$	−1.34586	−0.0706394
$364$	20.2944	1.06372
$365$	29.9684	1.56862
$366$	−48.8855	−2.55529
$367$	−14.7257	−0.768677	−0.384339	−	0.923192i	$-0.625570\pi$
$367$	−14.7257	−0.768677	−0.384339	+	0.923192i	$0.625570\pi$
$368$	14.4633	0.753949
$369$	3.08408	0.160551
$370$	14.8468	0.771850
$371$	−28.7153	−1.49082
$372$	11.7671	0.610094
$373$	−6.08274	−0.314952	−0.157476	−	0.987523i	$-0.550336\pi$
$373$	−6.08274	−0.314952	−0.157476	+	0.987523i	$0.550336\pi$
$374$	−14.8997	−0.770443
$375$	5.22279	0.269703
$376$	21.8284	1.12572
$377$	16.4533	0.847387
$378$	39.7549	2.04477
$379$	16.3669	0.840710	0.420355	−	0.907360i	$-0.361906\pi$
$379$	16.3669	0.840710	0.420355	+	0.907360i	$0.361906\pi$
$380$	−59.3553	−3.04486
$381$	−26.3490	−1.34990
$382$	−60.6082	−3.10098
$383$	−13.3470	−0.681998	−0.340999	−	0.940064i	$-0.610765\pi$
$383$	−13.3470	−0.681998	−0.340999	+	0.940064i	$0.610765\pi$
$384$	−24.7911	−1.26512
$385$	8.40194	0.428203
$386$	28.0036	1.42535
$387$	12.3540	0.627988
$388$	−12.6832	−0.643893
$389$	35.5734	1.80364	0.901822	−	0.432107i	$-0.142230\pi$
$389$	35.5734	1.80364	0.901822	+	0.432107i	$0.142230\pi$
$390$	−16.9571	−0.858655
$391$	−18.4742	−0.934283
$392$	−5.91646	−0.298827
$393$	−22.3568	−1.12775
$394$	−31.3359	−1.57868
$395$	25.3984	1.27793
$396$	4.89382	0.245924
$397$	−4.96886	−0.249380	−0.124690	−	0.992196i	$-0.539794\pi$
$397$	−4.96886	−0.249380	−0.124690	+	0.992196i	$0.539794\pi$
$398$	−14.6601	−0.734844
$399$	−18.7748	−0.939915
$400$	17.3705	0.868524
$401$	−22.3891	−1.11806	−0.559029	−	0.829148i	$-0.688826\pi$
$401$	−22.3891	−1.11806	−0.559029	+	0.829148i	$0.688826\pi$
$402$	−25.9655	−1.29504
$403$	3.67128	0.182880
$404$	−38.5866	−1.91975
$405$	−11.8490	−0.588784
$406$	−67.1161	−3.33092
$407$	2.03716	0.100978
$408$	−42.4540	−2.10178
$409$	20.7219	1.02463	0.512316	−	0.858797i	$-0.328788\pi$
$409$	20.7219	1.02463	0.512316	+	0.858797i	$0.328788\pi$
$410$	18.9094	0.933869
$411$	−4.98016	−0.245653
$412$	17.1469	0.844767
$413$	−13.1770	−0.648396
$414$	9.01556	0.443091
$415$	−25.6416	−1.25869
$416$	2.06141	0.101069
$417$	−16.3428	−0.800311
$418$	−12.1005	−0.591856
$419$	−13.9473	−0.681373	−0.340686	−	0.940177i	$-0.610659\pi$
$419$	−13.9473	−0.681373	−0.340686	+	0.940177i	$0.610659\pi$
$420$	46.5555	2.27168
$421$	−25.1352	−1.22501	−0.612506	−	0.790466i	$-0.709839\pi$
$421$	−25.1352	−1.22501	−0.612506	+	0.790466i	$0.709839\pi$
$422$	7.07116	0.344219
$423$	4.95524	0.240932
$424$	−52.7332	−2.56095
$425$	−22.1877	−1.07626
$426$	−55.1177	−2.67046
$427$	41.8746	2.02645
$428$	40.0231	1.93459
$429$	−2.32671	−0.112334
$430$	75.7459	3.65279
$431$	21.1769	1.02006	0.510028	−	0.860158i	$-0.329635\pi$
$431$	21.1769	1.02006	0.510028	+	0.860158i	$0.329635\pi$
$432$	26.5875	1.27919
$433$	23.1733	1.11364	0.556819	−	0.830634i	$-0.312022\pi$
$433$	23.1733	1.11364	0.556819	+	0.830634i	$0.312022\pi$
$434$	−14.9759	−0.718866
$435$	37.7440	1.80968
$436$	−8.30353	−0.397667
$437$	−15.0036	−0.717718
$438$	33.8533	1.61757
$439$	−12.2394	−0.584152	−0.292076	−	0.956395i	$-0.594346\pi$
$439$	−12.2394	−0.584152	−0.292076	+	0.956395i	$0.594346\pi$
$440$	15.4295	0.735571
$441$	−1.34309	−0.0639566
$442$	−25.7583	−1.22520
$443$	9.69077	0.460423	0.230211	−	0.973141i	$-0.426058\pi$
$443$	9.69077	0.460423	0.230211	+	0.973141i	$0.426058\pi$
$444$	11.2880	0.535704
$445$	22.1339	1.04925
$446$	28.7885	1.36318
$447$	12.8938	0.609858
$448$	18.4864	0.873400
$449$	−21.6836	−1.02331	−0.511657	−	0.859190i	$-0.670968\pi$
$449$	−21.6836	−1.02331	−0.511657	+	0.859190i	$0.670968\pi$
$450$	10.8278	0.510425
$451$	2.59459	0.122174
$452$	−1.99501	−0.0938373
$453$	−8.07712	−0.379496
$454$	23.3676	1.09670
$455$	14.5252	0.680950
$456$	−34.4783	−1.61459
$457$	6.22311	0.291105	0.145552	−	0.989351i	$-0.453504\pi$
$457$	6.22311	0.291105	0.145552	+	0.989351i	$0.453504\pi$
$458$	−24.9439	−1.16555
$459$	−33.9609	−1.58516
$460$	37.2041	1.73465
$461$	12.0412	0.560813	0.280406	−	0.959881i	$-0.409531\pi$
$461$	12.0412	0.560813	0.280406	+	0.959881i	$0.409531\pi$
$462$	9.49109	0.441566
$463$	25.3485	1.17805	0.589023	−	0.808116i	$-0.299513\pi$
$463$	25.3485	1.17805	0.589023	+	0.808116i	$0.299513\pi$
$464$	−44.8863	−2.08379
$465$	8.42196	0.390559
$466$	63.6583	2.94891
$467$	−38.0466	−1.76059	−0.880293	−	0.474430i	$-0.842654\pi$
$467$	−38.0466	−1.76059	−0.880293	+	0.474430i	$0.842654\pi$
$468$	8.46038	0.391081
$469$	22.2417	1.02702
$470$	30.3821	1.40142
$471$	−3.84908	−0.177356
$472$	−24.1984	−1.11382
$473$	10.3932	0.477881
$474$	28.6909	1.31782
$475$	−18.0194	−0.826787
$476$	70.7193	3.24142
$477$	−11.9709	−0.548110
$478$	−3.75142	−0.171586
$479$	−19.3242	−0.882945	−0.441472	−	0.897275i	$-0.645544\pi$
$479$	−19.3242	−0.882945	−0.441472	+	0.897275i	$0.645544\pi$
$480$	4.72889	0.215843
$481$	3.52181	0.160581
$482$	−27.4422	−1.24996
$483$	11.7681	0.535467
$484$	4.11710	0.187141
$485$	−9.07768	−0.412196
$486$	28.4431	1.29021
$487$	36.9264	1.67330	0.836648	−	0.547741i	$-0.184512\pi$
$487$	36.9264	1.67330	0.836648	+	0.547741i	$0.184512\pi$
$488$	76.8992	3.48106
$489$	−6.68405	−0.302263
$490$	−8.23488	−0.372014
$491$	−1.06706	−0.0481558	−0.0240779	−	0.999710i	$-0.507665\pi$
$491$	−1.06706	−0.0481558	−0.0240779	+	0.999710i	$0.507665\pi$
$492$	14.3767	0.648153
$493$	57.3343	2.58221
$494$	−20.9192	−0.941201
$495$	3.50262	0.157431
$496$	−10.0157	−0.449716
$497$	47.2130	2.11779
$498$	−28.9655	−1.29798
$499$	21.8418	0.977775	0.488888	−	0.872347i	$-0.337403\pi$
$499$	21.8418	0.977775	0.488888	+	0.872347i	$0.337403\pi$
$500$	−15.9769	−0.714510
$501$	−32.6314	−1.45787
$502$	64.7510	2.88998
$503$	−38.3443	−1.70969	−0.854843	−	0.518887i	$-0.826347\pi$
$503$	−38.3443	−1.70969	−0.854843	+	0.518887i	$0.826347\pi$
$504$	−17.7466	−0.790495
$505$	−27.6173	−1.22895
$506$	7.58466	0.337179
$507$	13.4738	0.598393
$508$	80.6037	3.57621
$509$	−9.43955	−0.418401	−0.209200	−	0.977873i	$-0.567086\pi$
$509$	−9.43955	−0.418401	−0.209200	+	0.977873i	$0.567086\pi$
$510$	−59.0899	−2.61654
$511$	−28.9982	−1.28280
$512$	43.7672	1.93425
$513$	−27.5808	−1.21772
$514$	24.5940	1.08480
$515$	12.2724	0.540788
$516$	57.5893	2.53523
$517$	4.16877	0.183342
$518$	−14.3661	−0.631212
$519$	20.1199	0.883168
$520$	26.6742	1.16974
$521$	27.6098	1.20961	0.604803	−	0.796375i	$-0.293252\pi$
$521$	27.6098	1.20961	0.604803	+	0.796375i	$0.293252\pi$
$522$	−27.9795	−1.22463
$523$	3.62718	0.158605	0.0793027	−	0.996851i	$-0.474731\pi$
$523$	3.62718	0.158605	0.0793027	+	0.996851i	$0.474731\pi$
$524$	68.3912	2.98768
$525$	14.1336	0.616840
$526$	−29.1921	−1.27284
$527$	12.7932	0.557282
$528$	6.34750	0.276240
$529$	−13.5957	−0.591118
$530$	−73.3971	−3.18817
$531$	−5.49325	−0.238387
$532$	57.4336	2.49006
$533$	4.48549	0.194288
$534$	25.0032	1.08199
$535$	28.6454	1.23845
$536$	40.8450	1.76423
$537$	26.6749	1.15111
$538$	30.6320	1.32064
$539$	−1.12992	−0.0486691
$540$	68.3916	2.94311
$541$	0.119301	0.00512916	0.00256458	−	0.999997i	$-0.499184\pi$
$541$	0.119301	0.00512916	0.00256458	+	0.999997i	$0.499184\pi$
$542$	−49.7852	−2.13846
$543$	30.1186	1.29251
$544$	7.18333	0.307983
$545$	−5.94303	−0.254571
$546$	16.4081	0.702201
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	15.2347	0.650795
$549$	17.4568	0.745037
$550$	9.10923	0.388419
$551$	46.5631	1.98366
$552$	21.6111	0.919831
$553$	−24.5762	−1.04508
$554$	20.7776	0.882757
$555$	8.07906	0.342937
$556$	49.9940	2.12022
$557$	−17.7576	−0.752415	−0.376208	−	0.926535i	$-0.622772\pi$
$557$	−17.7576	−0.752415	−0.376208	+	0.926535i	$0.622772\pi$
$558$	−6.24318	−0.264295
$559$	17.9677	0.759951
$560$	−39.6262	−1.67451
$561$	−8.10782	−0.342312
$562$	27.3499	1.15369
$563$	10.3785	0.437402	0.218701	−	0.975792i	$-0.429818\pi$
$563$	10.3785	0.437402	0.218701	+	0.975792i	$0.429818\pi$
$564$	23.0994	0.972658
$565$	−1.42787	−0.0600711
$566$	55.0948	2.31581
$567$	11.4654	0.481503
$568$	86.7027	3.63796
$569$	−4.73917	−0.198676	−0.0993381	−	0.995054i	$-0.531673\pi$
$569$	−4.73917	−0.198676	−0.0993381	+	0.995054i	$0.531673\pi$
$570$	−47.9889	−2.01003
$571$	−4.72994	−0.197942	−0.0989709	−	0.995090i	$-0.531555\pi$
$571$	−4.72994	−0.197942	−0.0989709	+	0.995090i	$0.531555\pi$
$572$	7.11759	0.297601
$573$	−32.9806	−1.37778
$574$	−18.2972	−0.763710
$575$	11.2946	0.471019
$576$	7.70665	0.321110
$577$	−19.7444	−0.821971	−0.410986	−	0.911642i	$-0.634815\pi$
$577$	−19.7444	−0.821971	−0.410986	+	0.911642i	$0.634815\pi$
$578$	−47.7137	−1.98463
$579$	15.2385	0.633289
$580$	−115.462	−4.79429
$581$	24.8114	1.02935
$582$	−10.2544	−0.425060
$583$	−10.0709	−0.417096
$584$	−53.2527	−2.20361
$585$	6.05529	0.250355
$586$	−67.8208	−2.80165
$587$	20.7071	0.854675	0.427338	−	0.904092i	$-0.359452\pi$
$587$	20.7071	0.854675	0.427338	+	0.904092i	$0.359452\pi$
$588$	−6.26094	−0.258197
$589$	10.3898	0.428105
$590$	−33.6807	−1.38661
$591$	−17.0518	−0.701417
$592$	−9.60787	−0.394881
$593$	−13.2597	−0.544510	−0.272255	−	0.962225i	$-0.587769\pi$
$593$	−13.2597	−0.544510	−0.272255	+	0.962225i	$0.587769\pi$
$594$	13.9427	0.572077
$595$	50.6155	2.07503
$596$	−39.4433	−1.61566
$597$	−7.97745	−0.326495
$598$	13.1123	0.536200
$599$	−8.90443	−0.363825	−0.181913	−	0.983315i	$-0.558229\pi$
$599$	−8.90443	−0.363825	−0.181913	+	0.983315i	$0.558229\pi$
$600$	25.9551	1.05961
$601$	23.6532	0.964836	0.482418	−	0.875941i	$-0.339759\pi$
$601$	23.6532	0.964836	0.482418	+	0.875941i	$0.339759\pi$
$602$	−73.2936	−2.98722
$603$	9.27216	0.377592
$604$	24.7086	1.00538
$605$	2.94670	0.119801
$606$	−31.1974	−1.26731
$607$	44.2974	1.79797	0.898987	−	0.437975i	$-0.144304\pi$
$607$	44.2974	1.79797	0.898987	+	0.437975i	$0.144304\pi$
$608$	5.83383	0.236593
$609$	−36.5220	−1.47994
$610$	107.033	4.33363
$611$	7.20692	0.291561
$612$	29.4817	1.19173
$613$	−11.5228	−0.465400	−0.232700	−	0.972549i	$-0.574756\pi$
$613$	−11.5228	−0.465400	−0.232700	+	0.972549i	$0.574756\pi$
$614$	−51.8310	−2.09173
$615$	10.2898	0.414923
$616$	−14.9299	−0.601544
$617$	12.4727	0.502132	0.251066	−	0.967970i	$-0.419219\pi$
$617$	12.4727	0.502132	0.251066	+	0.967970i	$0.419219\pi$
$618$	13.8633	0.557665
$619$	12.3058	0.494614	0.247307	−	0.968937i	$-0.420454\pi$
$619$	12.3058	0.494614	0.247307	+	0.968937i	$0.420454\pi$
$620$	−25.7635	−1.03469
$621$	17.2877	0.693733
$622$	28.5788	1.14591
$623$	−21.4173	−0.858066
$624$	10.9735	0.439291
$625$	−29.8504	−1.19401
$626$	−74.3334	−2.97096
$627$	−6.58464	−0.262965
$628$	11.7746	0.469860
$629$	12.2724	0.489331
$630$	−24.7007	−0.984099
$631$	24.5884	0.978850	0.489425	−	0.872045i	$-0.337207\pi$
$631$	24.5884	0.978850	0.489425	+	0.872045i	$0.337207\pi$
$632$	−45.1320	−1.79526
$633$	3.84785	0.152938
$634$	27.2608	1.08267
$635$	57.6899	2.28936
$636$	−55.8035	−2.21275
$637$	−1.95339	−0.0773962
$638$	−23.5388	−0.931908
$639$	19.6823	0.778618
$640$	54.2791	2.14557
$641$	17.2955	0.683131	0.341566	−	0.939858i	$-0.389043\pi$
$641$	17.2955	0.683131	0.341566	+	0.939858i	$0.389043\pi$
$642$	32.3588	1.27710
$643$	13.1943	0.520334	0.260167	−	0.965564i	$-0.416222\pi$
$643$	13.1943	0.520334	0.260167	+	0.965564i	$0.416222\pi$
$644$	−35.9996	−1.41858
$645$	41.2180	1.62296
$646$	−72.8967	−2.86808
$647$	40.6351	1.59753	0.798765	−	0.601643i	$-0.205487\pi$
$647$	40.6351	1.59753	0.798765	+	0.601643i	$0.205487\pi$
$648$	21.0553	0.827130
$649$	−4.62139	−0.181405
$650$	15.7479	0.617684
$651$	−8.14929	−0.319396
$652$	20.4471	0.800769
$653$	−26.3499	−1.03115	−0.515575	−	0.856844i	$-0.672422\pi$
$653$	−26.3499	−1.03115	−0.515575	+	0.856844i	$0.672422\pi$
$654$	−6.71343	−0.262516
$655$	48.9492	1.91260
$656$	−12.2369	−0.477771
$657$	−12.0888	−0.471631
$658$	−29.3984	−1.14607
$659$	38.5793	1.50283	0.751417	−	0.659827i	$-0.229371\pi$
$659$	38.5793	1.50283	0.751417	+	0.659827i	$0.229371\pi$
$660$	16.3278	0.635559
$661$	12.3498	0.480351	0.240176	−	0.970729i	$-0.422795\pi$
$661$	12.3498	0.480351	0.240176	+	0.970729i	$0.422795\pi$
$662$	76.6922	2.98073
$663$	−14.0167	−0.544363
$664$	45.5640	1.76823
$665$	41.1066	1.59404
$666$	−5.98899	−0.232069
$667$	−29.1860	−1.13008
$668$	99.8223	3.86224
$669$	15.6656	0.605667
$670$	56.8504	2.19632
$671$	14.6861	0.566952
$672$	−4.57579	−0.176515
$673$	−41.2498	−1.59006	−0.795031	−	0.606568i	$-0.792546\pi$
$673$	−41.2498	−1.59006	−0.795031	+	0.606568i	$0.792546\pi$
$674$	−48.0153	−1.84948
$675$	20.7627	0.799157
$676$	−41.2175	−1.58529
$677$	20.4798	0.787104	0.393552	−	0.919302i	$-0.371246\pi$
$677$	20.4798	0.787104	0.393552	+	0.919302i	$0.371246\pi$
$678$	−1.61297	−0.0619457
$679$	8.78378	0.337090
$680$	92.9511	3.56451
$681$	12.7157	0.487269
$682$	−5.25230	−0.201121
$683$	−48.8368	−1.86869	−0.934344	−	0.356371i	$-0.884014\pi$
$683$	−48.8368	−1.86869	−0.934344	+	0.356371i	$0.884014\pi$
$684$	23.9431	0.915486
$685$	10.9038	0.416614
$686$	−41.3961	−1.58051
$687$	−13.5735	−0.517861
$688$	−49.0177	−1.86878
$689$	−17.4105	−0.663287
$690$	30.0796	1.14511
$691$	1.68571	0.0641275	0.0320637	−	0.999486i	$-0.489792\pi$
$691$	1.68571	0.0641275	0.0320637	+	0.999486i	$0.489792\pi$
$692$	−61.5486	−2.33973
$693$	−3.38922	−0.128746
$694$	−57.0136	−2.16421
$695$	35.7819	1.35728
$696$	−67.0695	−2.54226
$697$	15.6305	0.592047
$698$	35.9317	1.36003
$699$	34.6404	1.31022
$700$	−43.2358	−1.63416
$701$	−45.6853	−1.72551	−0.862756	−	0.505621i	$-0.831263\pi$
$701$	−45.6853	−1.72551	−0.862756	+	0.505621i	$0.831263\pi$
$702$	24.1040	0.909748
$703$	9.96680	0.375905
$704$	6.48349	0.244356
$705$	16.5327	0.622659
$706$	43.6522	1.64287
$707$	26.7232	1.00503
$708$	−25.6073	−0.962382
$709$	−30.4771	−1.14459	−0.572296	−	0.820047i	$-0.693947\pi$
$709$	−30.4771	−1.14459	−0.572296	+	0.820047i	$0.693947\pi$
$710$	120.678	4.52896
$711$	−10.2454	−0.384231
$712$	−39.3311	−1.47400
$713$	−6.51238	−0.243891
$714$	57.1768	2.13979
$715$	5.09422	0.190513
$716$	−81.6008	−3.04957
$717$	−2.04137	−0.0762365
$718$	45.8810	1.71226
$719$	−35.6273	−1.32867	−0.664337	−	0.747433i	$-0.731286\pi$
$719$	−35.6273	−1.32867	−0.664337	+	0.747433i	$0.731286\pi$
$720$	−16.5195	−0.615644
$721$	−11.8751	−0.442252
$722$	−12.2096	−0.454396
$723$	−14.9330	−0.555364
$724$	−92.1353	−3.42418
$725$	−35.0526	−1.30182
$726$	3.32869	0.123539
$727$	−14.8843	−0.552028	−0.276014	−	0.961154i	$-0.589014\pi$
$727$	−14.8843	−0.552028	−0.276014	+	0.961154i	$0.589014\pi$
$728$	−25.8106	−0.956606
$729$	27.5410	1.02004
$730$	−74.1203	−2.74331
$731$	62.6115	2.31577
$732$	81.3765	3.00776
$733$	36.0575	1.33181	0.665907	−	0.746035i	$-0.268045\pi$
$733$	36.0575	1.33181	0.665907	+	0.746035i	$0.268045\pi$
$734$	36.4208	1.34432
$735$	−4.48110	−0.165288
$736$	−3.65667	−0.134787
$737$	7.80053	0.287336
$738$	−7.62778	−0.280783
$739$	−24.3289	−0.894954	−0.447477	−	0.894295i	$-0.647677\pi$
$739$	−24.3289	−0.894954	−0.447477	+	0.894295i	$0.647677\pi$
$740$	−24.7145	−0.908524
$741$	−11.3834	−0.418181
$742$	71.0208	2.60726
$743$	−24.1041	−0.884293	−0.442146	−	0.896943i	$-0.645783\pi$
$743$	−24.1041	−0.884293	−0.442146	+	0.896943i	$0.645783\pi$
$744$	−14.9655	−0.548662
$745$	−28.2305	−1.03429
$746$	15.0443	0.550811
$747$	10.3434	0.378447
$748$	24.8025	0.906868
$749$	−27.7180	−1.01279
$750$	−12.9174	−0.471677
$751$	47.9202	1.74863	0.874317	−	0.485355i	$-0.161310\pi$
$751$	47.9202	1.74863	0.874317	+	0.485355i	$0.161310\pi$
$752$	−19.6612	−0.716972
$753$	35.2350	1.28403
$754$	−40.6935	−1.48197
$755$	17.6845	0.643605
$756$	−66.1774	−2.40685
$757$	39.8742	1.44925	0.724625	−	0.689143i	$-0.242013\pi$
$757$	39.8742	1.44925	0.724625	+	0.689143i	$0.242013\pi$
$758$	−40.4798	−1.47029
$759$	4.12728	0.149811
$760$	75.4887	2.73826
$761$	−16.5601	−0.600303	−0.300151	−	0.953892i	$-0.597037\pi$
$761$	−16.5601	−0.600303	−0.300151	+	0.953892i	$0.597037\pi$
$762$	65.1683	2.36080
$763$	5.75062	0.208186
$764$	100.890	3.65009
$765$	21.1007	0.762897
$766$	33.0107	1.19273
$767$	−7.98940	−0.288480
$768$	43.8636	1.58279
$769$	12.8474	0.463288	0.231644	−	0.972801i	$-0.425590\pi$
$769$	12.8474	0.463288	0.231644	+	0.972801i	$0.425590\pi$
$770$	−20.7803	−0.748871
$771$	13.3831	0.481981
$772$	−46.6157	−1.67774
$773$	3.37971	0.121560	0.0607798	−	0.998151i	$-0.480641\pi$
$773$	3.37971	0.121560	0.0607798	+	0.998151i	$0.480641\pi$
$774$	−30.5548	−1.09827
$775$	−7.82142	−0.280954
$776$	16.1307	0.579057
$777$	−7.81750	−0.280451
$778$	−87.9830	−3.15434
$779$	12.6940	0.454811
$780$	28.2273	1.01070
$781$	16.5584	0.592506
$782$	45.6919	1.63394
$783$	−53.6520	−1.91737
$784$	5.32906	0.190324
$785$	8.42739	0.300786
$786$	55.2945	1.97229
$787$	−46.3437	−1.65198	−0.825988	−	0.563688i	$-0.809382\pi$
$787$	−46.3437	−1.65198	−0.825988	+	0.563688i	$0.809382\pi$
$788$	52.1628	1.85822
$789$	−15.8852	−0.565529
$790$	−62.8174	−2.23494
$791$	1.38164	0.0491256
$792$	−6.22402	−0.221161
$793$	25.3892	0.901597
$794$	12.2894	0.436133
$795$	−39.9399	−1.41652
$796$	24.4037	0.864966
$797$	−31.2883	−1.10829	−0.554145	−	0.832420i	$-0.686955\pi$
$797$	−31.2883	−1.10829	−0.554145	+	0.832420i	$0.686955\pi$
$798$	46.4352	1.64379
$799$	25.1138	0.888461
$800$	−4.39169	−0.155270
$801$	−8.92850	−0.315473
$802$	55.3745	1.95534
$803$	−10.1702	−0.358897
$804$	43.2231	1.52436
$805$	−25.7657	−0.908123
$806$	−9.08011	−0.319833
$807$	16.6687	0.586767
$808$	49.0749	1.72645
$809$	−2.21503	−0.0778761	−0.0389381	−	0.999242i	$-0.512398\pi$
$809$	−2.21503	−0.0778761	−0.0389381	+	0.999242i	$0.512398\pi$
$810$	29.3060	1.02971
$811$	−21.2640	−0.746681	−0.373340	−	0.927694i	$-0.621788\pi$
$811$	−21.2640	−0.746681	−0.373340	+	0.927694i	$0.621788\pi$
$812$	111.724	3.92073
$813$	−27.0912	−0.950129
$814$	−5.03845	−0.176598
$815$	14.6344	0.512622
$816$	38.2390	1.33863
$817$	50.8489	1.77898
$818$	−51.2510	−1.79195
$819$	−5.85924	−0.204739
$820$	−31.4772	−1.09923
$821$	30.7599	1.07353	0.536764	−	0.843733i	$-0.319647\pi$
$821$	30.7599	1.07353	0.536764	+	0.843733i	$0.319647\pi$
$822$	12.3173	0.429615
$823$	18.3193	0.638570	0.319285	−	0.947659i	$-0.396557\pi$
$823$	18.3193	0.638570	0.319285	+	0.947659i	$0.396557\pi$
$824$	−21.8076	−0.759705
$825$	4.95689	0.172577
$826$	32.5903	1.13396
$827$	−20.2249	−0.703288	−0.351644	−	0.936134i	$-0.614377\pi$
$827$	−20.2249	−0.703288	−0.351644	+	0.936134i	$0.614377\pi$
$828$	−15.0076	−0.521550
$829$	12.8392	0.445923	0.222962	−	0.974827i	$-0.428428\pi$
$829$	12.8392	0.445923	0.222962	+	0.974827i	$0.428428\pi$
$830$	63.4187	2.20129
$831$	11.3064	0.392214
$832$	11.2086	0.388587
$833$	−6.80694	−0.235846
$834$	40.4203	1.39964
$835$	71.4451	2.47246
$836$	20.1429	0.696658
$837$	−11.9716	−0.413799
$838$	34.4957	1.19163
$839$	−0.367383	−0.0126835	−0.00634173	−	0.999980i	$-0.502019\pi$
$839$	−0.367383	−0.0126835	−0.00634173	+	0.999980i	$0.502019\pi$
$840$	−59.2099	−2.04293
$841$	61.5777	2.12337
$842$	62.1662	2.14239
$843$	14.8828	0.512590
$844$	−11.7709	−0.405171
$845$	−29.5003	−1.01484
$846$	−12.2557	−0.421359
$847$	−2.85130	−0.0979719
$848$	47.4977	1.63108
$849$	29.9805	1.02893
$850$	54.8764	1.88224
$851$	−6.24723	−0.214152
$852$	91.7508	3.14333
$853$	48.0920	1.64664	0.823319	−	0.567578i	$-0.192120\pi$
$853$	48.0920	1.64664	0.823319	+	0.567578i	$0.192120\pi$
$854$	−103.567	−3.54400
$855$	17.1366	0.586059
$856$	−50.9018	−1.73979
$857$	16.9505	0.579019	0.289510	−	0.957175i	$-0.406508\pi$
$857$	16.9505	0.579019	0.289510	+	0.957175i	$0.406508\pi$
$858$	5.75459	0.196459
$859$	36.1630	1.23387	0.616933	−	0.787016i	$-0.288375\pi$
$859$	36.1630	1.23387	0.616933	+	0.787016i	$0.288375\pi$
$860$	−126.089	−4.29961
$861$	−9.95662	−0.339321
$862$	−52.3764	−1.78395
$863$	−34.4936	−1.17418	−0.587089	−	0.809523i	$-0.699726\pi$
$863$	−34.4936	−1.17418	−0.587089	+	0.809523i	$0.699726\pi$
$864$	−6.72199	−0.228687
$865$	−44.0517	−1.49780
$866$	−57.3140	−1.94761
$867$	−25.9639	−0.881782
$868$	24.9294	0.846158
$869$	−8.61927	−0.292389
$870$	−93.3513	−3.16490
$871$	13.4855	0.456937
$872$	10.5605	0.357625
$873$	3.66180	0.123933
$874$	37.1080	1.25520
$875$	11.0648	0.374060
$876$	−56.3533	−1.90400
$877$	−13.7788	−0.465277	−0.232639	−	0.972563i	$-0.574736\pi$
$877$	−13.7788	−0.465277	−0.232639	+	0.972563i	$0.574736\pi$
$878$	30.2713	1.02161
$879$	−36.9054	−1.24479
$880$	−13.8976	−0.468487
$881$	48.3733	1.62974	0.814868	−	0.579646i	$-0.196809\pi$
$881$	48.3733	1.62974	0.814868	+	0.579646i	$0.196809\pi$
$882$	3.32183	0.111852
$883$	12.5634	0.422793	0.211396	−	0.977400i	$-0.432199\pi$
$883$	12.5634	0.422793	0.211396	+	0.977400i	$0.432199\pi$
$884$	42.8782	1.44215
$885$	−18.3277	−0.616081
$886$	−23.9680	−0.805220
$887$	−30.5742	−1.02658	−0.513291	−	0.858215i	$-0.671574\pi$
$887$	−30.5742	−1.02658	−0.513291	+	0.858215i	$0.671574\pi$
$888$	−14.3562	−0.481762
$889$	−55.8222	−1.87222
$890$	−54.7433	−1.83500
$891$	4.02112	0.134713
$892$	−47.9223	−1.60456
$893$	20.3957	0.682518
$894$	−31.8901	−1.06656
$895$	−58.4036	−1.95222
$896$	−52.5217	−1.75463
$897$	7.13518	0.238237
$898$	53.6296	1.78964
$899$	20.2110	0.674074
$900$	−18.0243	−0.600808
$901$	−60.6699	−2.02121
$902$	−6.41714	−0.213667
$903$	−39.8835	−1.32724
$904$	2.53727	0.0843885
$905$	−65.9434	−2.19203
$906$	19.9770	0.663690
$907$	48.3468	1.60533	0.802665	−	0.596430i	$-0.203415\pi$
$907$	48.3468	1.60533	0.802665	+	0.596430i	$0.203415\pi$
$908$	−38.8985	−1.29089
$909$	11.1404	0.369504
$910$	−35.9248	−1.19089
$911$	−28.2675	−0.936544	−0.468272	−	0.883584i	$-0.655123\pi$
$911$	−28.2675	−0.936544	−0.468272	+	0.883584i	$0.655123\pi$
$912$	31.0552	1.02834
$913$	8.70178	0.287987
$914$	−15.3915	−0.509105
$915$	58.2430	1.92546
$916$	41.5224	1.37194
$917$	−47.3644	−1.56411
$918$	83.9946	2.77224
$919$	−35.0627	−1.15661	−0.578306	−	0.815820i	$-0.696286\pi$
$919$	−35.0627	−1.15661	−0.578306	+	0.815820i	$0.696286\pi$
$920$	−47.3166	−1.55998
$921$	−28.2044	−0.929368
$922$	−29.7811	−0.980789
$923$	28.6259	0.942234
$924$	−15.7992	−0.519755
$925$	−7.50297	−0.246696
$926$	−62.6940	−2.06025
$927$	−4.95052	−0.162597
$928$	11.3484	0.372528
$929$	−10.7945	−0.354155	−0.177078	−	0.984197i	$-0.556664\pi$
$929$	−10.7945	−0.354155	−0.177078	+	0.984197i	$0.556664\pi$
$930$	−20.8298	−0.683038
$931$	−5.52815	−0.181178
$932$	−105.968	−3.47109
$933$	15.5515	0.509133
$934$	94.0998	3.07904
$935$	17.7517	0.580543
$936$	−10.7600	−0.351702
$937$	23.2088	0.758199	0.379099	−	0.925356i	$-0.376234\pi$
$937$	23.2088	0.758199	0.379099	+	0.925356i	$0.376234\pi$
$938$	−55.0098	−1.79613
$939$	−40.4494	−1.32001
$940$	−50.5750	−1.64958
$941$	−43.4382	−1.41604	−0.708022	−	0.706190i	$-0.750412\pi$
$941$	−43.4382	−1.41604	−0.708022	+	0.706190i	$0.750412\pi$
$942$	9.51984	0.310173
$943$	−7.95668	−0.259105
$944$	21.7959	0.709397
$945$	−47.3647	−1.54077
$946$	−25.7053	−0.835752
$947$	5.09549	0.165581	0.0827905	−	0.996567i	$-0.473617\pi$
$947$	5.09549	0.165581	0.0827905	+	0.996567i	$0.473617\pi$
$948$	−47.7598	−1.55117
$949$	−17.5820	−0.570737
$950$	44.5670	1.44594
$951$	14.8343	0.481035
$952$	−89.9417	−2.91503
$953$	25.1708	0.815363	0.407682	−	0.913124i	$-0.366337\pi$
$953$	25.1708	0.815363	0.407682	+	0.913124i	$0.366337\pi$
$954$	29.6073	0.958573
$955$	72.2096	2.33665
$956$	6.24473	0.201969
$957$	−12.8089	−0.414052
$958$	47.7941	1.54416
$959$	−10.5508	−0.340704
$960$	25.7126	0.829870
$961$	−26.4902	−0.854524
$962$	−8.71041	−0.280835
$963$	−11.5552	−0.372360
$964$	45.6812	1.47129
$965$	−33.3639	−1.07402
$966$	−29.1058	−0.936463
$967$	56.1142	1.80451	0.902256	−	0.431200i	$-0.141910\pi$
$967$	56.1142	1.80451	0.902256	+	0.431200i	$0.141910\pi$
$968$	−5.23618	−0.168297
$969$	−39.6675	−1.27431
$970$	22.4516	0.720878
$971$	51.7528	1.66083	0.830413	−	0.557149i	$-0.188105\pi$
$971$	51.7528	1.66083	0.830413	+	0.557149i	$0.188105\pi$
$972$	−47.3474	−1.51867
$973$	−34.6234	−1.10997
$974$	−91.3293	−2.92638
$975$	8.56941	0.274441
$976$	−69.2644	−2.21710
$977$	−22.7312	−0.727235	−0.363618	−	0.931548i	$-0.618458\pi$
$977$	−22.7312	−0.727235	−0.363618	+	0.931548i	$0.618458\pi$
$978$	16.5315	0.528620
$979$	−7.51142	−0.240066
$980$	13.7081	0.437888
$981$	2.39733	0.0765409
$982$	2.63914	0.0842184
$983$	−7.96890	−0.254169	−0.127084	−	0.991892i	$-0.540562\pi$
$983$	−7.96890	−0.254169	−0.127084	+	0.991892i	$0.540562\pi$
$984$	−18.2845	−0.582889
$985$	37.3341	1.18956
$986$	−141.804	−4.51595
$987$	−15.9975	−0.509205
$988$	34.8229	1.10786
$989$	−31.8723	−1.01348
$990$	−8.66295	−0.275327
$991$	−41.3921	−1.31486	−0.657431	−	0.753514i	$-0.728357\pi$
$991$	−41.3921	−1.31486	−0.657431	+	0.753514i	$0.728357\pi$
$992$	2.53221	0.0803976
$993$	41.7329	1.32435
$994$	−116.771	−3.70374
$995$	17.4663	0.553718
$996$	48.2170	1.52781
$997$	37.9007	1.20033	0.600163	−	0.799878i	$-0.295102\pi$
$997$	37.9007	1.20033	0.600163	+	0.799878i	$0.295102\pi$
$998$	−54.0209	−1.71000
$999$	−11.4842	−0.363343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.11	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.47328 q^{2} -1.34586 q^{3} +4.11710 q^{4} +2.94670 q^{5} +3.32869 q^{6} -2.85130 q^{7} -5.23618 q^{8} -1.18866 q^{9} +O(q^{10})\)	\(q-2.47328 q^{2} -1.34586 q^{3} +4.11710 q^{4} +2.94670 q^{5} +3.32869 q^{6} -2.85130 q^{7} -5.23618 q^{8} -1.18866 q^{9} -7.28801 q^{10} -1.00000 q^{11} -5.54105 q^{12} -1.72879 q^{13} +7.05206 q^{14} -3.96585 q^{15} +4.71631 q^{16} -6.02426 q^{17} +2.93988 q^{18} -4.89251 q^{19} +12.1319 q^{20} +3.83746 q^{21} +2.47328 q^{22} +3.06664 q^{23} +7.04717 q^{24} +3.68306 q^{25} +4.27577 q^{26} +5.63735 q^{27} -11.7391 q^{28} -9.51723 q^{29} +9.80866 q^{30} -2.12362 q^{31} -1.19240 q^{32} +1.34586 q^{33} +14.8997 q^{34} -8.40194 q^{35} -4.89382 q^{36} -2.03716 q^{37} +12.1005 q^{38} +2.32671 q^{39} -15.4295 q^{40} -2.59459 q^{41} -9.49109 q^{42} -10.3932 q^{43} -4.11710 q^{44} -3.50262 q^{45} -7.58466 q^{46} -4.16877 q^{47} -6.34750 q^{48} +1.12992 q^{49} -9.10923 q^{50} +8.10782 q^{51} -7.11759 q^{52} +10.0709 q^{53} -13.9427 q^{54} -2.94670 q^{55} +14.9299 q^{56} +6.58464 q^{57} +23.5388 q^{58} +4.62139 q^{59} -16.3278 q^{60} -14.6861 q^{61} +5.25230 q^{62} +3.38922 q^{63} -6.48349 q^{64} -5.09422 q^{65} -3.32869 q^{66} -7.80053 q^{67} -24.8025 q^{68} -4.12728 q^{69} +20.7803 q^{70} -16.5584 q^{71} +6.22402 q^{72} +10.1702 q^{73} +5.03845 q^{74} -4.95689 q^{75} -20.1429 q^{76} +2.85130 q^{77} -5.75459 q^{78} +8.61927 q^{79} +13.8976 q^{80} -4.02112 q^{81} +6.41714 q^{82} -8.70178 q^{83} +15.7992 q^{84} -17.7517 q^{85} +25.7053 q^{86} +12.8089 q^{87} +5.23618 q^{88} +7.51142 q^{89} +8.66295 q^{90} +4.92929 q^{91} +12.6257 q^{92} +2.85810 q^{93} +10.3105 q^{94} -14.4168 q^{95} +1.60481 q^{96} -3.08062 q^{97} -2.79461 q^{98} +1.18866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 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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