LMFDB - Embedded newform 6018.2.a.ba.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 31 x^{10} + 111 x^{9} + 381 x^{8} - 1101 x^{7} - 2301 x^{6} + 4690 x^{5} + \cdots + 5653 $ x^12 - 4x^11 - 31x^10 + 111x^9 + 381x^8 - 1101x^7 - 2301x^6 + 4690x^5 + 6915x^4 - 8325x^3 - 10082x^2 + 5149*x + 5653
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.37577$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.375767 q^{5} +1.00000 q^{6} +4.48414 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.375767 q^{5} +1.00000 q^{6} +4.48414 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.375767 q^{10} +1.75649 q^{11} +1.00000 q^{12} -1.25881 q^{13} +4.48414 q^{14} -0.375767 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +0.881605 q^{19} -0.375767 q^{20} +4.48414 q^{21} +1.75649 q^{22} +3.19356 q^{23} +1.00000 q^{24} -4.85880 q^{25} -1.25881 q^{26} +1.00000 q^{27} +4.48414 q^{28} -0.444823 q^{29} -0.375767 q^{30} +0.957058 q^{31} +1.00000 q^{32} +1.75649 q^{33} -1.00000 q^{34} -1.68499 q^{35} +1.00000 q^{36} +4.28193 q^{37} +0.881605 q^{38} -1.25881 q^{39} -0.375767 q^{40} -0.330075 q^{41} +4.48414 q^{42} -6.12752 q^{43} +1.75649 q^{44} -0.375767 q^{45} +3.19356 q^{46} +8.85366 q^{47} +1.00000 q^{48} +13.1075 q^{49} -4.85880 q^{50} -1.00000 q^{51} -1.25881 q^{52} +7.93586 q^{53} +1.00000 q^{54} -0.660030 q^{55} +4.48414 q^{56} +0.881605 q^{57} -0.444823 q^{58} +1.00000 q^{59} -0.375767 q^{60} +4.32180 q^{61} +0.957058 q^{62} +4.48414 q^{63} +1.00000 q^{64} +0.473019 q^{65} +1.75649 q^{66} +7.80965 q^{67} -1.00000 q^{68} +3.19356 q^{69} -1.68499 q^{70} +7.05567 q^{71} +1.00000 q^{72} -4.66139 q^{73} +4.28193 q^{74} -4.85880 q^{75} +0.881605 q^{76} +7.87633 q^{77} -1.25881 q^{78} -7.46981 q^{79} -0.375767 q^{80} +1.00000 q^{81} -0.330075 q^{82} -12.1261 q^{83} +4.48414 q^{84} +0.375767 q^{85} -6.12752 q^{86} -0.444823 q^{87} +1.75649 q^{88} +1.72277 q^{89} -0.375767 q^{90} -5.64466 q^{91} +3.19356 q^{92} +0.957058 q^{93} +8.85366 q^{94} -0.331278 q^{95} +1.00000 q^{96} -18.1585 q^{97} +13.1075 q^{98} +1.75649 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.375767	−0.168048	−0.0840241	−	0.996464i	$-0.526777\pi$
$5$	−0.375767	−0.168048	−0.0840241	+	0.996464i	$0.526777\pi$
$6$	1.00000	0.408248
$7$	4.48414	1.69484	0.847422	−	0.530919i	$-0.178153\pi$
$7$	4.48414	1.69484	0.847422	+	0.530919i	$0.178153\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.375767	−0.118828
$11$	1.75649	0.529601	0.264800	−	0.964303i	$-0.414694\pi$
$11$	1.75649	0.529601	0.264800	+	0.964303i	$0.414694\pi$
$12$	1.00000	0.288675
$13$	−1.25881	−0.349130	−0.174565	−	0.984646i	$-0.555852\pi$
$13$	−1.25881	−0.349130	−0.174565	+	0.984646i	$0.555852\pi$
$14$	4.48414	1.19844
$15$	−0.375767	−0.0970227
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	0.881605	0.202254	0.101127	−	0.994874i	$-0.467755\pi$
$19$	0.881605	0.202254	0.101127	+	0.994874i	$0.467755\pi$
$20$	−0.375767	−0.0840241
$21$	4.48414	0.978519
$22$	1.75649	0.374484
$23$	3.19356	0.665902	0.332951	−	0.942944i	$-0.391956\pi$
$23$	3.19356	0.665902	0.332951	+	0.942944i	$0.391956\pi$
$24$	1.00000	0.204124
$25$	−4.85880	−0.971760
$26$	−1.25881	−0.246872
$27$	1.00000	0.192450
$28$	4.48414	0.847422
$29$	−0.444823	−0.0826016	−0.0413008	−	0.999147i	$-0.513150\pi$
$29$	−0.444823	−0.0826016	−0.0413008	+	0.999147i	$0.513150\pi$
$30$	−0.375767	−0.0686054
$31$	0.957058	0.171893	0.0859464	−	0.996300i	$-0.472609\pi$
$31$	0.957058	0.171893	0.0859464	+	0.996300i	$0.472609\pi$
$32$	1.00000	0.176777
$33$	1.75649	0.305765
$34$	−1.00000	−0.171499
$35$	−1.68499	−0.284816
$36$	1.00000	0.166667
$37$	4.28193	0.703944	0.351972	−	0.936010i	$-0.385511\pi$
$37$	4.28193	0.703944	0.351972	+	0.936010i	$0.385511\pi$
$38$	0.881605	0.143015
$39$	−1.25881	−0.201570
$40$	−0.375767	−0.0594140
$41$	−0.330075	−0.0515491	−0.0257746	−	0.999668i	$-0.508205\pi$
$41$	−0.330075	−0.0515491	−0.0257746	+	0.999668i	$0.508205\pi$
$42$	4.48414	0.691917
$43$	−6.12752	−0.934438	−0.467219	−	0.884142i	$-0.654744\pi$
$43$	−6.12752	−0.934438	−0.467219	+	0.884142i	$0.654744\pi$
$44$	1.75649	0.264800
$45$	−0.375767	−0.0560161
$46$	3.19356	0.470864
$47$	8.85366	1.29144	0.645720	−	0.763575i	$-0.276557\pi$
$47$	8.85366	1.29144	0.645720	+	0.763575i	$0.276557\pi$
$48$	1.00000	0.144338
$49$	13.1075	1.87250
$50$	−4.85880	−0.687138
$51$	−1.00000	−0.140028
$52$	−1.25881	−0.174565
$53$	7.93586	1.09007	0.545037	−	0.838412i	$-0.316516\pi$
$53$	7.93586	1.09007	0.545037	+	0.838412i	$0.316516\pi$
$54$	1.00000	0.136083
$55$	−0.660030	−0.0889984
$56$	4.48414	0.599218
$57$	0.881605	0.116771
$58$	−0.444823	−0.0584081
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.375767	−0.0485114
$61$	4.32180	0.553350	0.276675	−	0.960964i	$-0.410767\pi$
$61$	4.32180	0.553350	0.276675	+	0.960964i	$0.410767\pi$
$62$	0.957058	0.121547
$63$	4.48414	0.564948
$64$	1.00000	0.125000
$65$	0.473019	0.0586707
$66$	1.75649	0.216209
$67$	7.80965	0.954100	0.477050	−	0.878876i	$-0.341706\pi$
$67$	7.80965	0.954100	0.477050	+	0.878876i	$0.341706\pi$
$68$	−1.00000	−0.121268
$69$	3.19356	0.384459
$70$	−1.68499	−0.201395
$71$	7.05567	0.837354	0.418677	−	0.908135i	$-0.362494\pi$
$71$	7.05567	0.837354	0.418677	+	0.908135i	$0.362494\pi$
$72$	1.00000	0.117851
$73$	−4.66139	−0.545574	−0.272787	−	0.962074i	$-0.587945\pi$
$73$	−4.66139	−0.545574	−0.272787	+	0.962074i	$0.587945\pi$
$74$	4.28193	0.497764
$75$	−4.85880	−0.561046
$76$	0.881605	0.101127
$77$	7.87633	0.897591
$78$	−1.25881	−0.142532
$79$	−7.46981	−0.840420	−0.420210	−	0.907427i	$-0.638044\pi$
$79$	−7.46981	−0.840420	−0.420210	+	0.907427i	$0.638044\pi$
$80$	−0.375767	−0.0420121
$81$	1.00000	0.111111
$82$	−0.330075	−0.0364507
$83$	−12.1261	−1.33102	−0.665508	−	0.746391i	$-0.731785\pi$
$83$	−12.1261	−1.33102	−0.665508	+	0.746391i	$0.731785\pi$
$84$	4.48414	0.489260
$85$	0.375767	0.0407577
$86$	−6.12752	−0.660747
$87$	−0.444823	−0.0476900
$88$	1.75649	0.187242
$89$	1.72277	0.182613	0.0913065	−	0.995823i	$-0.470896\pi$
$89$	1.72277	0.182613	0.0913065	+	0.995823i	$0.470896\pi$
$90$	−0.375767	−0.0396094
$91$	−5.64466	−0.591722
$92$	3.19356	0.332951
$93$	0.957058	0.0992423
$94$	8.85366	0.913186
$95$	−0.331278	−0.0339884
$96$	1.00000	0.102062
$97$	−18.1585	−1.84372	−0.921860	−	0.387524i	$-0.873331\pi$
$97$	−18.1585	−1.84372	−0.921860	+	0.387524i	$0.873331\pi$
$98$	13.1075	1.32406
$99$	1.75649	0.176534
$100$	−4.85880	−0.485880
$101$	−12.4054	−1.23439	−0.617193	−	0.786812i	$-0.711730\pi$
$101$	−12.4054	−1.23439	−0.617193	+	0.786812i	$0.711730\pi$
$102$	−1.00000	−0.0990148
$103$	8.77028	0.864161	0.432080	−	0.901835i	$-0.357780\pi$
$103$	8.77028	0.864161	0.432080	+	0.901835i	$0.357780\pi$
$104$	−1.25881	−0.123436
$105$	−1.68499	−0.164438
$106$	7.93586	0.770799
$107$	3.02792	0.292720	0.146360	−	0.989231i	$-0.453244\pi$
$107$	3.02792	0.292720	0.146360	+	0.989231i	$0.453244\pi$
$108$	1.00000	0.0962250
$109$	−10.6820	−1.02315	−0.511577	−	0.859238i	$-0.670938\pi$
$109$	−10.6820	−1.02315	−0.511577	+	0.859238i	$0.670938\pi$
$110$	−0.660030	−0.0629314
$111$	4.28193	0.406422
$112$	4.48414	0.423711
$113$	−2.60402	−0.244966	−0.122483	−	0.992471i	$-0.539086\pi$
$113$	−2.60402	−0.244966	−0.122483	+	0.992471i	$0.539086\pi$
$114$	0.881605	0.0825698
$115$	−1.20003	−0.111904
$116$	−0.444823	−0.0413008
$117$	−1.25881	−0.116377
$118$	1.00000	0.0920575
$119$	−4.48414	−0.411060
$120$	−0.375767	−0.0343027
$121$	−7.91476	−0.719523
$122$	4.32180	0.391277
$123$	−0.330075	−0.0297619
$124$	0.957058	0.0859464
$125$	3.70461	0.331351
$126$	4.48414	0.399479
$127$	7.90115	0.701114	0.350557	−	0.936541i	$-0.385992\pi$
$127$	7.90115	0.701114	0.350557	+	0.936541i	$0.385992\pi$
$128$	1.00000	0.0883883
$129$	−6.12752	−0.539498
$130$	0.473019	0.0414865
$131$	7.05421	0.616329	0.308164	−	0.951333i	$-0.400285\pi$
$131$	7.05421	0.616329	0.308164	+	0.951333i	$0.400285\pi$
$132$	1.75649	0.152882
$133$	3.95324	0.342789
$134$	7.80965	0.674651
$135$	−0.375767	−0.0323409
$136$	−1.00000	−0.0857493
$137$	−11.2264	−0.959132	−0.479566	−	0.877506i	$-0.659206\pi$
$137$	−11.2264	−0.959132	−0.479566	+	0.877506i	$0.659206\pi$
$138$	3.19356	0.271854
$139$	−1.57689	−0.133750	−0.0668750	−	0.997761i	$-0.521303\pi$
$139$	−1.57689	−0.133750	−0.0668750	+	0.997761i	$0.521303\pi$
$140$	−1.68499	−0.142408
$141$	8.85366	0.745613
$142$	7.05567	0.592098
$143$	−2.21108	−0.184900
$144$	1.00000	0.0833333
$145$	0.167150	0.0138810
$146$	−4.66139	−0.385779
$147$	13.1075	1.08109
$148$	4.28193	0.351972
$149$	−5.08529	−0.416603	−0.208302	−	0.978065i	$-0.566794\pi$
$149$	−5.08529	−0.416603	−0.208302	+	0.978065i	$0.566794\pi$
$150$	−4.85880	−0.396719
$151$	21.9231	1.78408	0.892039	−	0.451958i	$-0.149274\pi$
$151$	21.9231	1.78408	0.892039	+	0.451958i	$0.149274\pi$
$152$	0.881605	0.0715076
$153$	−1.00000	−0.0808452
$154$	7.87633	0.634692
$155$	−0.359631	−0.0288863
$156$	−1.25881	−0.100785
$157$	−9.76469	−0.779307	−0.389654	−	0.920962i	$-0.627405\pi$
$157$	−9.76469	−0.779307	−0.389654	+	0.920962i	$0.627405\pi$
$158$	−7.46981	−0.594266
$159$	7.93586	0.629355
$160$	−0.375767	−0.0297070
$161$	14.3203	1.12860
$162$	1.00000	0.0785674
$163$	−3.85974	−0.302318	−0.151159	−	0.988509i	$-0.548301\pi$
$163$	−3.85974	−0.302318	−0.151159	+	0.988509i	$0.548301\pi$
$164$	−0.330075	−0.0257746
$165$	−0.660030	−0.0513833
$166$	−12.1261	−0.941171
$167$	3.01146	0.233034	0.116517	−	0.993189i	$-0.462827\pi$
$167$	3.01146	0.233034	0.116517	+	0.993189i	$0.462827\pi$
$168$	4.48414	0.345959
$169$	−11.4154	−0.878108
$170$	0.375767	0.0288200
$171$	0.881605	0.0674180
$172$	−6.12752	−0.467219
$173$	5.58993	0.424995	0.212497	−	0.977162i	$-0.431840\pi$
$173$	5.58993	0.424995	0.212497	+	0.977162i	$0.431840\pi$
$174$	−0.444823	−0.0337219
$175$	−21.7875	−1.64698
$176$	1.75649	0.132400
$177$	1.00000	0.0751646
$178$	1.72277	0.129127
$179$	18.6864	1.39668	0.698342	−	0.715764i	$-0.253921\pi$
$179$	18.6864	1.39668	0.698342	+	0.715764i	$0.253921\pi$
$180$	−0.375767	−0.0280080
$181$	11.3684	0.845005	0.422503	−	0.906362i	$-0.361152\pi$
$181$	11.3684	0.845005	0.422503	+	0.906362i	$0.361152\pi$
$182$	−5.64466	−0.418410
$183$	4.32180	0.319477
$184$	3.19356	0.235432
$185$	−1.60901	−0.118297
$186$	0.957058	0.0701749
$187$	−1.75649	−0.128447
$188$	8.85366	0.645720
$189$	4.48414	0.326173
$190$	−0.331278	−0.0240334
$191$	7.12113	0.515267	0.257633	−	0.966243i	$-0.417057\pi$
$191$	7.12113	0.515267	0.257633	+	0.966243i	$0.417057\pi$
$192$	1.00000	0.0721688
$193$	−17.8384	−1.28404	−0.642018	−	0.766690i	$-0.721902\pi$
$193$	−17.8384	−1.28404	−0.642018	+	0.766690i	$0.721902\pi$
$194$	−18.1585	−1.30371
$195$	0.473019	0.0338736
$196$	13.1075	0.936249
$197$	10.3524	0.737577	0.368789	−	0.929513i	$-0.379773\pi$
$197$	10.3524	0.737577	0.368789	+	0.929513i	$0.379773\pi$
$198$	1.75649	0.124828
$199$	−21.0395	−1.49145	−0.745726	−	0.666253i	$-0.767897\pi$
$199$	−21.0395	−1.49145	−0.745726	+	0.666253i	$0.767897\pi$
$200$	−4.85880	−0.343569
$201$	7.80965	0.550850
$202$	−12.4054	−0.872843
$203$	−1.99465	−0.139997
$204$	−1.00000	−0.0700140
$205$	0.124032	0.00866274
$206$	8.77028	0.611054
$207$	3.19356	0.221967
$208$	−1.25881	−0.0872826
$209$	1.54853	0.107114
$210$	−1.68499	−0.116276
$211$	8.97686	0.617993	0.308996	−	0.951063i	$-0.400007\pi$
$211$	8.97686	0.617993	0.308996	+	0.951063i	$0.400007\pi$
$212$	7.93586	0.545037
$213$	7.05567	0.483446
$214$	3.02792	0.206984
$215$	2.30252	0.157031
$216$	1.00000	0.0680414
$217$	4.29158	0.291332
$218$	−10.6820	−0.723479
$219$	−4.66139	−0.314987
$220$	−0.660030	−0.0444992
$221$	1.25881	0.0846765
$222$	4.28193	0.287384
$223$	8.49521	0.568881	0.284441	−	0.958694i	$-0.408192\pi$
$223$	8.49521	0.568881	0.284441	+	0.958694i	$0.408192\pi$
$224$	4.48414	0.299609
$225$	−4.85880	−0.323920
$226$	−2.60402	−0.173217
$227$	9.96003	0.661070	0.330535	−	0.943794i	$-0.392771\pi$
$227$	9.96003	0.661070	0.330535	+	0.943794i	$0.392771\pi$
$228$	0.881605	0.0583857
$229$	−23.1617	−1.53057	−0.765286	−	0.643691i	$-0.777402\pi$
$229$	−23.1617	−1.53057	−0.765286	+	0.643691i	$0.777402\pi$
$230$	−1.20003	−0.0791279
$231$	7.87633	0.518224
$232$	−0.444823	−0.0292041
$233$	−16.6643	−1.09172	−0.545858	−	0.837878i	$-0.683796\pi$
$233$	−16.6643	−1.09172	−0.545858	+	0.837878i	$0.683796\pi$
$234$	−1.25881	−0.0822908
$235$	−3.32692	−0.217024
$236$	1.00000	0.0650945
$237$	−7.46981	−0.485217
$238$	−4.48414	−0.290663
$239$	16.6754	1.07864	0.539320	−	0.842101i	$-0.318681\pi$
$239$	16.6754	1.07864	0.539320	+	0.842101i	$0.318681\pi$
$240$	−0.375767	−0.0242557
$241$	−21.0667	−1.35702	−0.678512	−	0.734590i	$-0.737375\pi$
$241$	−21.0667	−1.35702	−0.678512	+	0.734590i	$0.737375\pi$
$242$	−7.91476	−0.508780
$243$	1.00000	0.0641500
$244$	4.32180	0.276675
$245$	−4.92537	−0.314670
$246$	−0.330075	−0.0210448
$247$	−1.10977	−0.0706130
$248$	0.957058	0.0607733
$249$	−12.1261	−0.768463
$250$	3.70461	0.234300
$251$	22.0904	1.39433	0.697167	−	0.716909i	$-0.254444\pi$
$251$	22.0904	1.39433	0.697167	+	0.716909i	$0.254444\pi$
$252$	4.48414	0.282474
$253$	5.60944	0.352662
$254$	7.90115	0.495762
$255$	0.375767	0.0235315
$256$	1.00000	0.0625000
$257$	−0.352041	−0.0219597	−0.0109798	−	0.999940i	$-0.503495\pi$
$257$	−0.352041	−0.0219597	−0.0109798	+	0.999940i	$0.503495\pi$
$258$	−6.12752	−0.381483
$259$	19.2007	1.19308
$260$	0.473019	0.0293354
$261$	−0.444823	−0.0275339
$262$	7.05421	0.435810
$263$	−4.96317	−0.306042	−0.153021	−	0.988223i	$-0.548900\pi$
$263$	−4.96317	−0.306042	−0.153021	+	0.988223i	$0.548900\pi$
$264$	1.75649	0.108104
$265$	−2.98204	−0.183185
$266$	3.95324	0.242388
$267$	1.72277	0.105432
$268$	7.80965	0.477050
$269$	−24.1925	−1.47504	−0.737522	−	0.675323i	$-0.764004\pi$
$269$	−24.1925	−1.47504	−0.737522	+	0.675323i	$0.764004\pi$
$270$	−0.375767	−0.0228685
$271$	−4.02447	−0.244469	−0.122234	−	0.992501i	$-0.539006\pi$
$271$	−4.02447	−0.244469	−0.122234	+	0.992501i	$0.539006\pi$
$272$	−1.00000	−0.0606339
$273$	−5.64466	−0.341631
$274$	−11.2264	−0.678209
$275$	−8.53441	−0.514644
$276$	3.19356	0.192229
$277$	8.49671	0.510518	0.255259	−	0.966873i	$-0.417839\pi$
$277$	8.49671	0.510518	0.255259	+	0.966873i	$0.417839\pi$
$278$	−1.57689	−0.0945755
$279$	0.957058	0.0572976
$280$	−1.68499	−0.100698
$281$	−1.16600	−0.0695579	−0.0347790	−	0.999395i	$-0.511073\pi$
$281$	−1.16600	−0.0695579	−0.0347790	+	0.999395i	$0.511073\pi$
$282$	8.85366	0.527228
$283$	13.6809	0.813245	0.406622	−	0.913596i	$-0.366707\pi$
$283$	13.6809	0.813245	0.406622	+	0.913596i	$0.366707\pi$
$284$	7.05567	0.418677
$285$	−0.331278	−0.0196232
$286$	−2.21108	−0.130744
$287$	−1.48010	−0.0873677
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	0.167150	0.00981538
$291$	−18.1585	−1.06447
$292$	−4.66139	−0.272787
$293$	14.8482	0.867439	0.433719	−	0.901048i	$-0.357201\pi$
$293$	14.8482	0.867439	0.433719	+	0.901048i	$0.357201\pi$
$294$	13.1075	0.764444
$295$	−0.375767	−0.0218780
$296$	4.28193	0.248882
$297$	1.75649	0.101922
$298$	−5.08529	−0.294583
$299$	−4.02007	−0.232487
$300$	−4.85880	−0.280523
$301$	−27.4766	−1.58373
$302$	21.9231	1.26153
$303$	−12.4054	−0.712673
$304$	0.881605	0.0505635
$305$	−1.62399	−0.0929895
$306$	−1.00000	−0.0571662
$307$	16.5014	0.941785	0.470892	−	0.882191i	$-0.343932\pi$
$307$	16.5014	0.941785	0.470892	+	0.882191i	$0.343932\pi$
$308$	7.87633	0.448795
$309$	8.77028	0.498924
$310$	−0.359631	−0.0204257
$311$	16.0296	0.908957	0.454479	−	0.890758i	$-0.349826\pi$
$311$	16.0296	0.908957	0.454479	+	0.890758i	$0.349826\pi$
$312$	−1.25881	−0.0712659
$313$	6.05074	0.342008	0.171004	−	0.985270i	$-0.445299\pi$
$313$	6.05074	0.342008	0.171004	+	0.985270i	$0.445299\pi$
$314$	−9.76469	−0.551053
$315$	−1.68499	−0.0949386
$316$	−7.46981	−0.420210
$317$	9.36349	0.525906	0.262953	−	0.964809i	$-0.415304\pi$
$317$	9.36349	0.525906	0.262953	+	0.964809i	$0.415304\pi$
$318$	7.93586	0.445021
$319$	−0.781325	−0.0437458
$320$	−0.375767	−0.0210060
$321$	3.02792	0.169002
$322$	14.3203	0.798042
$323$	−0.881605	−0.0490538
$324$	1.00000	0.0555556
$325$	6.11629	0.339271
$326$	−3.85974	−0.213771
$327$	−10.6820	−0.590718
$328$	−0.330075	−0.0182254
$329$	39.7010	2.18879
$330$	−0.660030	−0.0363335
$331$	−26.5728	−1.46057	−0.730286	−	0.683141i	$-0.760613\pi$
$331$	−26.5728	−1.46057	−0.730286	+	0.683141i	$0.760613\pi$
$332$	−12.1261	−0.665508
$333$	4.28193	0.234648
$334$	3.01146	0.164780
$335$	−2.93461	−0.160335
$336$	4.48414	0.244630
$337$	5.38585	0.293386	0.146693	−	0.989182i	$-0.453137\pi$
$337$	5.38585	0.293386	0.146693	+	0.989182i	$0.453137\pi$
$338$	−11.4154	−0.620916
$339$	−2.60402	−0.141431
$340$	0.375767	0.0203788
$341$	1.68106	0.0910345
$342$	0.881605	0.0476717
$343$	27.3868	1.47875
$344$	−6.12752	−0.330374
$345$	−1.20003	−0.0646077
$346$	5.58993	0.300517
$347$	−10.6408	−0.571229	−0.285615	−	0.958345i	$-0.592198\pi$
$347$	−10.6408	−0.571229	−0.285615	+	0.958345i	$0.592198\pi$
$348$	−0.444823	−0.0238450
$349$	21.8848	1.17147	0.585733	−	0.810504i	$-0.300807\pi$
$349$	21.8848	1.17147	0.585733	+	0.810504i	$0.300807\pi$
$350$	−21.7875	−1.16459
$351$	−1.25881	−0.0671902
$352$	1.75649	0.0936210
$353$	−9.57095	−0.509410	−0.254705	−	0.967019i	$-0.581978\pi$
$353$	−9.57095	−0.509410	−0.254705	+	0.967019i	$0.581978\pi$
$354$	1.00000	0.0531494
$355$	−2.65129	−0.140716
$356$	1.72277	0.0913065
$357$	−4.48414	−0.237326
$358$	18.6864	0.987605
$359$	−8.00405	−0.422437	−0.211219	−	0.977439i	$-0.567743\pi$
$359$	−8.00405	−0.422437	−0.211219	+	0.977439i	$0.567743\pi$
$360$	−0.375767	−0.0198047
$361$	−18.2228	−0.959093
$362$	11.3684	0.597509
$363$	−7.91476	−0.415417
$364$	−5.64466	−0.295861
$365$	1.75160	0.0916828
$366$	4.32180	0.225904
$367$	−26.1688	−1.36600	−0.683000	−	0.730418i	$-0.739325\pi$
$367$	−26.1688	−1.36600	−0.683000	+	0.730418i	$0.739325\pi$
$368$	3.19356	0.166476
$369$	−0.330075	−0.0171830
$370$	−1.60901	−0.0836483
$371$	35.5855	1.84751
$372$	0.957058	0.0496212
$373$	−31.8142	−1.64728	−0.823639	−	0.567115i	$-0.808059\pi$
$373$	−31.8142	−1.64728	−0.823639	+	0.567115i	$0.808059\pi$
$374$	−1.75649	−0.0908257
$375$	3.70461	0.191305
$376$	8.85366	0.456593
$377$	0.559946	0.0288387
$378$	4.48414	0.230639
$379$	−0.262412	−0.0134792	−0.00673960	−	0.999977i	$-0.502145\pi$
$379$	−0.262412	−0.0134792	−0.00673960	+	0.999977i	$0.502145\pi$
$380$	−0.331278	−0.0169942
$381$	7.90115	0.404788
$382$	7.12113	0.364349
$383$	7.35604	0.375876	0.187938	−	0.982181i	$-0.439820\pi$
$383$	7.35604	0.375876	0.187938	+	0.982181i	$0.439820\pi$
$384$	1.00000	0.0510310
$385$	−2.95967	−0.150839
$386$	−17.8384	−0.907950
$387$	−6.12752	−0.311479
$388$	−18.1585	−0.921860
$389$	36.9661	1.87426	0.937129	−	0.348983i	$-0.113473\pi$
$389$	36.9661	1.87426	0.937129	+	0.348983i	$0.113473\pi$
$390$	0.473019	0.0239522
$391$	−3.19356	−0.161505
$392$	13.1075	0.662028
$393$	7.05421	0.355838
$394$	10.3524	0.521546
$395$	2.80691	0.141231
$396$	1.75649	0.0882668
$397$	−27.6840	−1.38942	−0.694710	−	0.719290i	$-0.744467\pi$
$397$	−27.6840	−1.38942	−0.694710	+	0.719290i	$0.744467\pi$
$398$	−21.0395	−1.05462
$399$	3.95324	0.197909
$400$	−4.85880	−0.242940
$401$	13.9219	0.695227	0.347613	−	0.937638i	$-0.386992\pi$
$401$	13.9219	0.695227	0.347613	+	0.937638i	$0.386992\pi$
$402$	7.80965	0.389510
$403$	−1.20475	−0.0600130
$404$	−12.4054	−0.617193
$405$	−0.375767	−0.0186720
$406$	−1.99465	−0.0989927
$407$	7.52114	0.372809
$408$	−1.00000	−0.0495074
$409$	35.3750	1.74918	0.874590	−	0.484863i	$-0.161131\pi$
$409$	35.3750	1.74918	0.874590	+	0.484863i	$0.161131\pi$
$410$	0.124032	0.00612548
$411$	−11.2264	−0.553755
$412$	8.77028	0.432080
$413$	4.48414	0.220650
$414$	3.19356	0.156955
$415$	4.55661	0.223675
$416$	−1.25881	−0.0617181
$417$	−1.57689	−0.0772206
$418$	1.54853	0.0757409
$419$	−0.295111	−0.0144171	−0.00720856	−	0.999974i	$-0.502295\pi$
$419$	−0.295111	−0.0144171	−0.00720856	+	0.999974i	$0.502295\pi$
$420$	−1.68499	−0.0822192
$421$	−6.85349	−0.334019	−0.167009	−	0.985955i	$-0.553411\pi$
$421$	−6.85349	−0.334019	−0.167009	+	0.985955i	$0.553411\pi$
$422$	8.97686	0.436987
$423$	8.85366	0.430480
$424$	7.93586	0.385400
$425$	4.85880	0.235686
$426$	7.05567	0.341848
$427$	19.3795	0.937842
$428$	3.02792	0.146360
$429$	−2.21108	−0.106752
$430$	2.30252	0.111037
$431$	9.19028	0.442680	0.221340	−	0.975197i	$-0.428957\pi$
$431$	9.19028	0.442680	0.221340	+	0.975197i	$0.428957\pi$
$432$	1.00000	0.0481125
$433$	−19.8252	−0.952736	−0.476368	−	0.879246i	$-0.658047\pi$
$433$	−19.8252	−0.952736	−0.476368	+	0.879246i	$0.658047\pi$
$434$	4.29158	0.206002
$435$	0.167150	0.00801423
$436$	−10.6820	−0.511577
$437$	2.81545	0.134681
$438$	−4.66139	−0.222730
$439$	−34.8092	−1.66135	−0.830675	−	0.556757i	$-0.812045\pi$
$439$	−34.8092	−1.66135	−0.830675	+	0.556757i	$0.812045\pi$
$440$	−0.660030	−0.0314657
$441$	13.1075	0.624166
$442$	1.25881	0.0598754
$443$	−3.31373	−0.157440	−0.0787200	−	0.996897i	$-0.525083\pi$
$443$	−3.31373	−0.157440	−0.0787200	+	0.996897i	$0.525083\pi$
$444$	4.28193	0.203211
$445$	−0.647360	−0.0306878
$446$	8.49521	0.402260
$447$	−5.08529	−0.240526
$448$	4.48414	0.211856
$449$	−11.8111	−0.557399	−0.278699	−	0.960378i	$-0.589903\pi$
$449$	−11.8111	−0.557399	−0.278699	+	0.960378i	$0.589903\pi$
$450$	−4.85880	−0.229046
$451$	−0.579773	−0.0273004
$452$	−2.60402	−0.122483
$453$	21.9231	1.03004
$454$	9.96003	0.467447
$455$	2.12108	0.0994378
$456$	0.881605	0.0412849
$457$	42.6410	1.99466	0.997330	−	0.0730294i	$-0.0232667\pi$
$457$	42.6410	1.99466	0.997330	+	0.0730294i	$0.0232667\pi$
$458$	−23.1617	−1.08228
$459$	−1.00000	−0.0466760
$460$	−1.20003	−0.0559519
$461$	−12.2429	−0.570210	−0.285105	−	0.958496i	$-0.592028\pi$
$461$	−12.2429	−0.570210	−0.285105	+	0.958496i	$0.592028\pi$
$462$	7.87633	0.366440
$463$	14.2517	0.662331	0.331165	−	0.943573i	$-0.392558\pi$
$463$	14.2517	0.662331	0.331165	+	0.943573i	$0.392558\pi$
$464$	−0.444823	−0.0206504
$465$	−0.359631	−0.0166775
$466$	−16.6643	−0.771960
$467$	−31.7838	−1.47078	−0.735390	−	0.677644i	$-0.763001\pi$
$467$	−31.7838	−1.47078	−0.735390	+	0.677644i	$0.763001\pi$
$468$	−1.25881	−0.0581884
$469$	35.0195	1.61705
$470$	−3.32692	−0.153459
$471$	−9.76469	−0.449933
$472$	1.00000	0.0460287
$473$	−10.7629	−0.494879
$474$	−7.46981	−0.343100
$475$	−4.28354	−0.196542
$476$	−4.48414	−0.205530
$477$	7.93586	0.363358
$478$	16.6754	0.762714
$479$	−28.2541	−1.29096	−0.645481	−	0.763777i	$-0.723343\pi$
$479$	−28.2541	−1.29096	−0.645481	+	0.763777i	$0.723343\pi$
$480$	−0.375767	−0.0171514
$481$	−5.39012	−0.245768
$482$	−21.0667	−0.959561
$483$	14.3203	0.651598
$484$	−7.91476	−0.359762
$485$	6.82338	0.309834
$486$	1.00000	0.0453609
$487$	8.97343	0.406625	0.203312	−	0.979114i	$-0.434829\pi$
$487$	8.97343	0.406625	0.203312	+	0.979114i	$0.434829\pi$
$488$	4.32180	0.195639
$489$	−3.85974	−0.174543
$490$	−4.92537	−0.222505
$491$	10.7617	0.485668	0.242834	−	0.970068i	$-0.421923\pi$
$491$	10.7617	0.485668	0.242834	+	0.970068i	$0.421923\pi$
$492$	−0.330075	−0.0148809
$493$	0.444823	0.0200338
$494$	−1.10977	−0.0499309
$495$	−0.660030	−0.0296661
$496$	0.957058	0.0429732
$497$	31.6386	1.41918
$498$	−12.1261	−0.543385
$499$	−8.16995	−0.365737	−0.182869	−	0.983137i	$-0.558538\pi$
$499$	−8.16995	−0.365737	−0.182869	+	0.983137i	$0.558538\pi$
$500$	3.70461	0.165675
$501$	3.01146	0.134542
$502$	22.0904	0.985943
$503$	3.01227	0.134311	0.0671553	−	0.997743i	$-0.478608\pi$
$503$	3.01227	0.134311	0.0671553	+	0.997743i	$0.478608\pi$
$504$	4.48414	0.199739
$505$	4.66155	0.207436
$506$	5.60944	0.249370
$507$	−11.4154	−0.506976
$508$	7.90115	0.350557
$509$	−29.8559	−1.32334	−0.661669	−	0.749796i	$-0.730152\pi$
$509$	−29.8559	−1.32334	−0.661669	+	0.749796i	$0.730152\pi$
$510$	0.375767	0.0166393
$511$	−20.9023	−0.924663
$512$	1.00000	0.0441942
$513$	0.881605	0.0389238
$514$	−0.352041	−0.0155278
$515$	−3.29558	−0.145221
$516$	−6.12752	−0.269749
$517$	15.5513	0.683947
$518$	19.2007	0.843632
$519$	5.58993	0.245371
$520$	0.473019	0.0207432
$521$	−24.6882	−1.08161	−0.540804	−	0.841148i	$-0.681880\pi$
$521$	−24.6882	−1.08161	−0.540804	+	0.841148i	$0.681880\pi$
$522$	−0.444823	−0.0194694
$523$	−21.1372	−0.924263	−0.462132	−	0.886811i	$-0.652915\pi$
$523$	−21.1372	−0.924263	−0.462132	+	0.886811i	$0.652915\pi$
$524$	7.05421	0.308164
$525$	−21.7875	−0.950885
$526$	−4.96317	−0.216405
$527$	−0.957058	−0.0416901
$528$	1.75649	0.0764412
$529$	−12.8012	−0.556574
$530$	−2.98204	−0.129531
$531$	1.00000	0.0433963
$532$	3.95324	0.171395
$533$	0.415501	0.0179974
$534$	1.72277	0.0745515
$535$	−1.13779	−0.0491911
$536$	7.80965	0.337325
$537$	18.6864	0.806376
$538$	−24.1925	−1.04301
$539$	23.0231	0.991676
$540$	−0.375767	−0.0161705
$541$	10.3180	0.443607	0.221804	−	0.975091i	$-0.428806\pi$
$541$	10.3180	0.443607	0.221804	+	0.975091i	$0.428806\pi$
$542$	−4.02447	−0.172866
$543$	11.3684	0.487864
$544$	−1.00000	−0.0428746
$545$	4.01396	0.171939
$546$	−5.64466	−0.241569
$547$	−19.4354	−0.830998	−0.415499	−	0.909594i	$-0.636393\pi$
$547$	−19.4354	−0.830998	−0.415499	+	0.909594i	$0.636393\pi$
$548$	−11.2264	−0.479566
$549$	4.32180	0.184450
$550$	−8.53441	−0.363909
$551$	−0.392158	−0.0167065
$552$	3.19356	0.135927
$553$	−33.4957	−1.42438
$554$	8.49671	0.360991
$555$	−1.60901	−0.0682986
$556$	−1.57689	−0.0668750
$557$	−26.5926	−1.12676	−0.563382	−	0.826197i	$-0.690500\pi$
$557$	−26.5926	−1.12676	−0.563382	+	0.826197i	$0.690500\pi$
$558$	0.957058	0.0405155
$559$	7.71336	0.326241
$560$	−1.68499	−0.0712039
$561$	−1.75649	−0.0741589
$562$	−1.16600	−0.0491849
$563$	46.1081	1.94322	0.971611	−	0.236582i	$-0.0760273\pi$
$563$	46.1081	1.94322	0.971611	+	0.236582i	$0.0760273\pi$
$564$	8.85366	0.372806
$565$	0.978506	0.0411660
$566$	13.6809	0.575051
$567$	4.48414	0.188316
$568$	7.05567	0.296049
$569$	−4.48354	−0.187960	−0.0939799	−	0.995574i	$-0.529959\pi$
$569$	−4.48354	−0.187960	−0.0939799	+	0.995574i	$0.529959\pi$
$570$	−0.331278	−0.0138757
$571$	6.78052	0.283756	0.141878	−	0.989884i	$-0.454686\pi$
$571$	6.78052	0.283756	0.141878	+	0.989884i	$0.454686\pi$
$572$	−2.21108	−0.0924498
$573$	7.12113	0.297489
$574$	−1.48010	−0.0617783
$575$	−15.5168	−0.647097
$576$	1.00000	0.0416667
$577$	−30.9532	−1.28860	−0.644299	−	0.764774i	$-0.722851\pi$
$577$	−30.9532	−1.28860	−0.644299	+	0.764774i	$0.722851\pi$
$578$	1.00000	0.0415945
$579$	−17.8384	−0.741338
$580$	0.167150	0.00694052
$581$	−54.3753	−2.25587
$582$	−18.1585	−0.752695
$583$	13.9392	0.577304
$584$	−4.66139	−0.192890
$585$	0.473019	0.0195569
$586$	14.8482	0.613372
$587$	20.1771	0.832798	0.416399	−	0.909182i	$-0.363292\pi$
$587$	20.1771	0.832798	0.416399	+	0.909182i	$0.363292\pi$
$588$	13.1075	0.540544
$589$	0.843747	0.0347660
$590$	−0.375767	−0.0154701
$591$	10.3524	0.425840
$592$	4.28193	0.175986
$593$	−14.6190	−0.600332	−0.300166	−	0.953887i	$-0.597042\pi$
$593$	−14.6190	−0.600332	−0.300166	+	0.953887i	$0.597042\pi$
$594$	1.75649	0.0720695
$595$	1.68499	0.0690780
$596$	−5.08529	−0.208302
$597$	−21.0395	−0.861090
$598$	−4.02007	−0.164393
$599$	−10.5306	−0.430270	−0.215135	−	0.976584i	$-0.569019\pi$
$599$	−10.5306	−0.430270	−0.215135	+	0.976584i	$0.569019\pi$
$600$	−4.85880	−0.198360
$601$	40.2045	1.63998	0.819989	−	0.572380i	$-0.193980\pi$
$601$	40.2045	1.63998	0.819989	+	0.572380i	$0.193980\pi$
$602$	−27.4766	−1.11986
$603$	7.80965	0.318033
$604$	21.9231	0.892039
$605$	2.97411	0.120915
$606$	−12.4054	−0.503936
$607$	26.8400	1.08940	0.544701	−	0.838631i	$-0.316643\pi$
$607$	26.8400	1.08940	0.544701	+	0.838631i	$0.316643\pi$
$608$	0.881605	0.0357538
$609$	−1.99465	−0.0808272
$610$	−1.62399	−0.0657535
$611$	−11.1451	−0.450881
$612$	−1.00000	−0.0404226
$613$	−25.6124	−1.03448	−0.517238	−	0.855842i	$-0.673040\pi$
$613$	−25.6124	−1.03448	−0.517238	+	0.855842i	$0.673040\pi$
$614$	16.5014	0.665942
$615$	0.124032	0.00500143
$616$	7.87633	0.317346
$617$	−20.9726	−0.844327	−0.422163	−	0.906520i	$-0.638729\pi$
$617$	−20.9726	−0.844327	−0.422163	+	0.906520i	$0.638729\pi$
$618$	8.77028	0.352792
$619$	23.8475	0.958511	0.479256	−	0.877675i	$-0.340907\pi$
$619$	23.8475	0.958511	0.479256	+	0.877675i	$0.340907\pi$
$620$	−0.359631	−0.0144431
$621$	3.19356	0.128153
$622$	16.0296	0.642730
$623$	7.72513	0.309501
$624$	−1.25881	−0.0503926
$625$	22.9019	0.916077
$626$	6.05074	0.241836
$627$	1.54853	0.0618422
$628$	−9.76469	−0.389654
$629$	−4.28193	−0.170732
$630$	−1.68499	−0.0671317
$631$	−28.4476	−1.13248	−0.566240	−	0.824241i	$-0.691602\pi$
$631$	−28.4476	−1.13248	−0.566240	+	0.824241i	$0.691602\pi$
$632$	−7.46981	−0.297133
$633$	8.97686	0.356798
$634$	9.36349	0.371872
$635$	−2.96899	−0.117821
$636$	7.93586	0.314677
$637$	−16.4998	−0.653746
$638$	−0.781325	−0.0309330
$639$	7.05567	0.279118
$640$	−0.375767	−0.0148535
$641$	−22.5077	−0.889000	−0.444500	−	0.895779i	$-0.646619\pi$
$641$	−22.5077	−0.889000	−0.444500	+	0.895779i	$0.646619\pi$
$642$	3.02792	0.119502
$643$	−32.3237	−1.27472	−0.637361	−	0.770565i	$-0.719974\pi$
$643$	−32.3237	−1.27472	−0.637361	+	0.770565i	$0.719974\pi$
$644$	14.3203	0.564301
$645$	2.30252	0.0906617
$646$	−0.881605	−0.0346863
$647$	28.3080	1.11290	0.556451	−	0.830880i	$-0.312163\pi$
$647$	28.3080	1.11290	0.556451	+	0.830880i	$0.312163\pi$
$648$	1.00000	0.0392837
$649$	1.75649	0.0689481
$650$	6.11629	0.239901
$651$	4.29158	0.168200
$652$	−3.85974	−0.151159
$653$	−4.40444	−0.172359	−0.0861795	−	0.996280i	$-0.527466\pi$
$653$	−4.40444	−0.172359	−0.0861795	+	0.996280i	$0.527466\pi$
$654$	−10.6820	−0.417701
$655$	−2.65074	−0.103573
$656$	−0.330075	−0.0128873
$657$	−4.66139	−0.181858
$658$	39.7010	1.54771
$659$	0.730750	0.0284660	0.0142330	−	0.999899i	$-0.495469\pi$
$659$	0.730750	0.0284660	0.0142330	+	0.999899i	$0.495469\pi$
$660$	−0.660030	−0.0256916
$661$	−13.1332	−0.510824	−0.255412	−	0.966832i	$-0.582211\pi$
$661$	−13.1332	−0.510824	−0.255412	+	0.966832i	$0.582211\pi$
$662$	−26.5728	−1.03278
$663$	1.25881	0.0488880
$664$	−12.1261	−0.470585
$665$	−1.48550	−0.0576051
$666$	4.28193	0.165921
$667$	−1.42057	−0.0550046
$668$	3.01146	0.116517
$669$	8.49521	0.328444
$670$	−2.93461	−0.113374
$671$	7.59118	0.293054
$672$	4.48414	0.172979
$673$	−21.6295	−0.833758	−0.416879	−	0.908962i	$-0.636876\pi$
$673$	−21.6295	−0.833758	−0.416879	+	0.908962i	$0.636876\pi$
$674$	5.38585	0.207455
$675$	−4.85880	−0.187015
$676$	−11.4154	−0.439054
$677$	18.6124	0.715334	0.357667	−	0.933849i	$-0.383572\pi$
$677$	18.6124	0.715334	0.357667	+	0.933849i	$0.383572\pi$
$678$	−2.60402	−0.100007
$679$	−81.4254	−3.12482
$680$	0.375767	0.0144100
$681$	9.96003	0.381669
$682$	1.68106	0.0643711
$683$	−8.65063	−0.331007	−0.165504	−	0.986209i	$-0.552925\pi$
$683$	−8.65063	−0.331007	−0.165504	+	0.986209i	$0.552925\pi$
$684$	0.881605	0.0337090
$685$	4.21850	0.161180
$686$	27.3868	1.04563
$687$	−23.1617	−0.883676
$688$	−6.12752	−0.233609
$689$	−9.98972	−0.380578
$690$	−1.20003	−0.0456845
$691$	29.5156	1.12283	0.561414	−	0.827535i	$-0.310258\pi$
$691$	29.5156	1.12283	0.561414	+	0.827535i	$0.310258\pi$
$692$	5.58993	0.212497
$693$	7.87633	0.299197
$694$	−10.6408	−0.403920
$695$	0.592543	0.0224765
$696$	−0.444823	−0.0168610
$697$	0.330075	0.0125025
$698$	21.8848	0.828351
$699$	−16.6643	−0.630303
$700$	−21.7875	−0.823491
$701$	−14.2547	−0.538391	−0.269196	−	0.963086i	$-0.586758\pi$
$701$	−14.2547	−0.538391	−0.269196	+	0.963086i	$0.586758\pi$
$702$	−1.25881	−0.0475106
$703$	3.77496	0.142375
$704$	1.75649	0.0662001
$705$	−3.32692	−0.125299
$706$	−9.57095	−0.360207
$707$	−55.6276	−2.09209
$708$	1.00000	0.0375823
$709$	19.0260	0.714536	0.357268	−	0.934002i	$-0.383708\pi$
$709$	19.0260	0.714536	0.357268	+	0.934002i	$0.383708\pi$
$710$	−2.65129	−0.0995011
$711$	−7.46981	−0.280140
$712$	1.72277	0.0645635
$713$	3.05642	0.114464
$714$	−4.48414	−0.167815
$715$	0.830851	0.0310721
$716$	18.6864	0.698342
$717$	16.6754	0.622753
$718$	−8.00405	−0.298708
$719$	−29.8493	−1.11319	−0.556596	−	0.830783i	$-0.687893\pi$
$719$	−29.8493	−1.11319	−0.556596	+	0.830783i	$0.687893\pi$
$720$	−0.375767	−0.0140040
$721$	39.3271	1.46462
$722$	−18.2228	−0.678181
$723$	−21.0667	−0.783478
$724$	11.3684	0.422503
$725$	2.16131	0.0802689
$726$	−7.91476	−0.293744
$727$	−1.68385	−0.0624504	−0.0312252	−	0.999512i	$-0.509941\pi$
$727$	−1.68385	−0.0624504	−0.0312252	+	0.999512i	$0.509941\pi$
$728$	−5.64466	−0.209205
$729$	1.00000	0.0370370
$730$	1.75160	0.0648295
$731$	6.12752	0.226634
$732$	4.32180	0.159738
$733$	−3.06441	−0.113187	−0.0565933	−	0.998397i	$-0.518024\pi$
$733$	−3.06441	−0.113187	−0.0565933	+	0.998397i	$0.518024\pi$
$734$	−26.1688	−0.965908
$735$	−4.92537	−0.181675
$736$	3.19356	0.117716
$737$	13.7175	0.505292
$738$	−0.330075	−0.0121502
$739$	−19.7827	−0.727718	−0.363859	−	0.931454i	$-0.618541\pi$
$739$	−19.7827	−0.727718	−0.363859	+	0.931454i	$0.618541\pi$
$740$	−1.60901	−0.0591483
$741$	−1.10977	−0.0407684
$742$	35.5855	1.30638
$743$	−5.16844	−0.189612	−0.0948059	−	0.995496i	$-0.530223\pi$
$743$	−5.16844	−0.189612	−0.0948059	+	0.995496i	$0.530223\pi$
$744$	0.957058	0.0350875
$745$	1.91089	0.0700094
$746$	−31.8142	−1.16480
$747$	−12.1261	−0.443672
$748$	−1.75649	−0.0642235
$749$	13.5776	0.496115
$750$	3.70461	0.135273
$751$	26.5411	0.968500	0.484250	−	0.874930i	$-0.339093\pi$
$751$	26.5411	0.968500	0.484250	+	0.874930i	$0.339093\pi$
$752$	8.85366	0.322860
$753$	22.0904	0.805019
$754$	0.559946	0.0203920
$755$	−8.23799	−0.299811
$756$	4.48414	0.163087
$757$	−11.1200	−0.404165	−0.202082	−	0.979369i	$-0.564771\pi$
$757$	−11.1200	−0.404165	−0.202082	+	0.979369i	$0.564771\pi$
$758$	−0.262412	−0.00953123
$759$	5.60944	0.203610
$760$	−0.331278	−0.0120167
$761$	−42.8737	−1.55417	−0.777086	−	0.629395i	$-0.783303\pi$
$761$	−42.8737	−1.55417	−0.777086	+	0.629395i	$0.783303\pi$
$762$	7.90115	0.286228
$763$	−47.8997	−1.73409
$764$	7.12113	0.257633
$765$	0.375767	0.0135859
$766$	7.35604	0.265785
$767$	−1.25881	−0.0454529
$768$	1.00000	0.0360844
$769$	11.0106	0.397052	0.198526	−	0.980096i	$-0.436385\pi$
$769$	11.0106	0.397052	0.198526	+	0.980096i	$0.436385\pi$
$770$	−2.95967	−0.106659
$771$	−0.352041	−0.0126784
$772$	−17.8384	−0.642018
$773$	−19.4039	−0.697910	−0.348955	−	0.937140i	$-0.613463\pi$
$773$	−19.4039	−0.697910	−0.348955	+	0.937140i	$0.613463\pi$
$774$	−6.12752	−0.220249
$775$	−4.65015	−0.167038
$776$	−18.1585	−0.651853
$777$	19.2007	0.688823
$778$	36.9661	1.32530
$779$	−0.290996	−0.0104260
$780$	0.473019	0.0169368
$781$	12.3932	0.443463
$782$	−3.19356	−0.114201
$783$	−0.444823	−0.0158967
$784$	13.1075	0.468125
$785$	3.66925	0.130961
$786$	7.05421	0.251615
$787$	−39.5371	−1.40935	−0.704673	−	0.709532i	$-0.748906\pi$
$787$	−39.5371	−1.40935	−0.704673	+	0.709532i	$0.748906\pi$
$788$	10.3524	0.368789
$789$	−4.96317	−0.176694
$790$	2.80691	0.0998654
$791$	−11.6768	−0.415179
$792$	1.75649	0.0624140
$793$	−5.44031	−0.193191
$794$	−27.6840	−0.982468
$795$	−2.98204	−0.105762
$796$	−21.0395	−0.745726
$797$	−19.6389	−0.695644	−0.347822	−	0.937561i	$-0.613079\pi$
$797$	−19.6389	−0.695644	−0.347822	+	0.937561i	$0.613079\pi$
$798$	3.95324	0.139943
$799$	−8.85366	−0.313220
$800$	−4.85880	−0.171784
$801$	1.72277	0.0608710
$802$	13.9219	0.491600
$803$	−8.18766	−0.288936
$804$	7.80965	0.275425
$805$	−5.38112	−0.189659
$806$	−1.20475	−0.0424356
$807$	−24.1925	−0.851617
$808$	−12.4054	−0.436421
$809$	−40.9856	−1.44098	−0.720489	−	0.693466i	$-0.756083\pi$
$809$	−40.9856	−1.44098	−0.720489	+	0.693466i	$0.756083\pi$
$810$	−0.375767	−0.0132031
$811$	41.0226	1.44050	0.720249	−	0.693716i	$-0.244028\pi$
$811$	41.0226	1.44050	0.720249	+	0.693716i	$0.244028\pi$
$812$	−1.99465	−0.0699984
$813$	−4.02447	−0.141144
$814$	7.52114	0.263616
$815$	1.45036	0.0508040
$816$	−1.00000	−0.0350070
$817$	−5.40205	−0.188994
$818$	35.3750	1.23686
$819$	−5.64466	−0.197241
$820$	0.124032	0.00433137
$821$	33.2456	1.16028	0.580140	−	0.814517i	$-0.302998\pi$
$821$	33.2456	1.16028	0.580140	+	0.814517i	$0.302998\pi$
$822$	−11.2264	−0.391564
$823$	−42.2412	−1.47244	−0.736218	−	0.676745i	$-0.763390\pi$
$823$	−42.2412	−1.47244	−0.736218	+	0.676745i	$0.763390\pi$
$824$	8.77028	0.305527
$825$	−8.53441	−0.297130
$826$	4.48414	0.156023
$827$	24.0193	0.835235	0.417617	−	0.908623i	$-0.362865\pi$
$827$	24.0193	0.835235	0.417617	+	0.908623i	$0.362865\pi$
$828$	3.19356	0.110984
$829$	−15.1761	−0.527089	−0.263544	−	0.964647i	$-0.584892\pi$
$829$	−15.1761	−0.527089	−0.263544	+	0.964647i	$0.584892\pi$
$830$	4.55661	0.158162
$831$	8.49671	0.294748
$832$	−1.25881	−0.0436413
$833$	−13.1075	−0.454148
$834$	−1.57689	−0.0546032
$835$	−1.13161	−0.0391609
$836$	1.54853	0.0535569
$837$	0.957058	0.0330808
$838$	−0.295111	−0.0101944
$839$	−25.0681	−0.865445	−0.432723	−	0.901527i	$-0.642447\pi$
$839$	−25.0681	−0.865445	−0.432723	+	0.901527i	$0.642447\pi$
$840$	−1.68499	−0.0581378
$841$	−28.8021	−0.993177
$842$	−6.85349	−0.236187
$843$	−1.16600	−0.0401593
$844$	8.97686	0.308996
$845$	4.28954	0.147565
$846$	8.85366	0.304395
$847$	−35.4909	−1.21948
$848$	7.93586	0.272519
$849$	13.6809	0.469527
$850$	4.85880	0.166655
$851$	13.6746	0.468758
$852$	7.05567	0.241723
$853$	23.5679	0.806951	0.403475	−	0.914991i	$-0.367802\pi$
$853$	23.5679	0.806951	0.403475	+	0.914991i	$0.367802\pi$
$854$	19.3795	0.663154
$855$	−0.331278	−0.0113295
$856$	3.02792	0.103492
$857$	−21.5583	−0.736419	−0.368209	−	0.929743i	$-0.620029\pi$
$857$	−21.5583	−0.736419	−0.368209	+	0.929743i	$0.620029\pi$
$858$	−2.21108	−0.0754849
$859$	−12.9336	−0.441290	−0.220645	−	0.975354i	$-0.570816\pi$
$859$	−12.9336	−0.441290	−0.220645	+	0.975354i	$0.570816\pi$
$860$	2.30252	0.0785153
$861$	−1.48010	−0.0504418
$862$	9.19028	0.313022
$863$	−7.99219	−0.272057	−0.136029	−	0.990705i	$-0.543434\pi$
$863$	−7.99219	−0.272057	−0.136029	+	0.990705i	$0.543434\pi$
$864$	1.00000	0.0340207
$865$	−2.10051	−0.0714196
$866$	−19.8252	−0.673686
$867$	1.00000	0.0339618
$868$	4.29158	0.145666
$869$	−13.1206	−0.445087
$870$	0.167150	0.00566691
$871$	−9.83084	−0.333105
$872$	−10.6820	−0.361739
$873$	−18.1585	−0.614573
$874$	2.81545	0.0952341
$875$	16.6120	0.561588
$876$	−4.66139	−0.157494
$877$	−0.731862	−0.0247132	−0.0123566	−	0.999924i	$-0.503933\pi$
$877$	−0.731862	−0.0247132	−0.0123566	+	0.999924i	$0.503933\pi$
$878$	−34.8092	−1.17475
$879$	14.8482	0.500816
$880$	−0.660030	−0.0222496
$881$	11.0598	0.372614	0.186307	−	0.982492i	$-0.440348\pi$
$881$	11.0598	0.372614	0.186307	+	0.982492i	$0.440348\pi$
$882$	13.1075	0.441352
$883$	56.3300	1.89566	0.947828	−	0.318782i	$-0.103274\pi$
$883$	56.3300	1.89566	0.947828	+	0.318782i	$0.103274\pi$
$884$	1.25881	0.0423383
$885$	−0.375767	−0.0126313
$886$	−3.31373	−0.111327
$887$	19.9609	0.670220	0.335110	−	0.942179i	$-0.391227\pi$
$887$	19.9609	0.670220	0.335110	+	0.942179i	$0.391227\pi$
$888$	4.28193	0.143692
$889$	35.4298	1.18828
$890$	−0.647360	−0.0216996
$891$	1.75649	0.0588445
$892$	8.49521	0.284441
$893$	7.80543	0.261199
$894$	−5.08529	−0.170078
$895$	−7.02172	−0.234710
$896$	4.48414	0.149805
$897$	−4.02007	−0.134226
$898$	−11.8111	−0.394140
$899$	−0.425722	−0.0141986
$900$	−4.85880	−0.161960
$901$	−7.93586	−0.264382
$902$	−0.579773	−0.0193043
$903$	−27.4766	−0.914365
$904$	−2.60402	−0.0866084
$905$	−4.27187	−0.142002
$906$	21.9231	0.728347
$907$	16.6065	0.551409	0.275705	−	0.961242i	$-0.411089\pi$
$907$	16.6065	0.551409	0.275705	+	0.961242i	$0.411089\pi$
$908$	9.96003	0.330535
$909$	−12.4054	−0.411462
$910$	2.12108	0.0703131
$911$	33.1857	1.09949	0.549746	−	0.835332i	$-0.314725\pi$
$911$	33.1857	1.09949	0.549746	+	0.835332i	$0.314725\pi$
$912$	0.881605	0.0291928
$913$	−21.2994	−0.704907
$914$	42.6410	1.41044
$915$	−1.62399	−0.0536875
$916$	−23.1617	−0.765286
$917$	31.6320	1.04458
$918$	−1.00000	−0.0330049
$919$	27.1930	0.897014	0.448507	−	0.893779i	$-0.351956\pi$
$919$	27.1930	0.897014	0.448507	+	0.893779i	$0.351956\pi$
$920$	−1.20003	−0.0395640
$921$	16.5014	0.543740
$922$	−12.2429	−0.403199
$923$	−8.88172	−0.292345
$924$	7.87633	0.259112
$925$	−20.8050	−0.684065
$926$	14.2517	0.468339
$927$	8.77028	0.288054
$928$	−0.444823	−0.0146020
$929$	25.7725	0.845567	0.422784	−	0.906231i	$-0.361053\pi$
$929$	25.7725	0.845567	0.422784	+	0.906231i	$0.361053\pi$
$930$	−0.359631	−0.0117928
$931$	11.5556	0.378720
$932$	−16.6643	−0.545858
$933$	16.0296	0.524787
$934$	−31.7838	−1.04000
$935$	0.660030	0.0215853
$936$	−1.25881	−0.0411454
$937$	−54.0290	−1.76505	−0.882526	−	0.470264i	$-0.844159\pi$
$937$	−54.0290	−1.76505	−0.882526	+	0.470264i	$0.844159\pi$
$938$	35.0195	1.14343
$939$	6.05074	0.197458
$940$	−3.32692	−0.108512
$941$	27.7766	0.905493	0.452746	−	0.891639i	$-0.350444\pi$
$941$	27.7766	0.905493	0.452746	+	0.891639i	$0.350444\pi$
$942$	−9.76469	−0.318151
$943$	−1.05411	−0.0343267
$944$	1.00000	0.0325472
$945$	−1.68499	−0.0548128
$946$	−10.7629	−0.349932
$947$	48.3797	1.57213	0.786065	−	0.618144i	$-0.212115\pi$
$947$	48.3797	1.57213	0.786065	+	0.618144i	$0.212115\pi$
$948$	−7.46981	−0.242608
$949$	5.86779	0.190476
$950$	−4.28354	−0.138976
$951$	9.36349	0.303632
$952$	−4.48414	−0.145332
$953$	−6.68119	−0.216425	−0.108212	−	0.994128i	$-0.534513\pi$
$953$	−6.68119	−0.216425	−0.108212	+	0.994128i	$0.534513\pi$
$954$	7.93586	0.256933
$955$	−2.67589	−0.0865897
$956$	16.6754	0.539320
$957$	−0.781325	−0.0252567
$958$	−28.2541	−0.912848
$959$	−50.3405	−1.62558
$960$	−0.375767	−0.0121278
$961$	−30.0840	−0.970453
$962$	−5.39012	−0.173784
$963$	3.02792	0.0975733
$964$	−21.0667	−0.678512
$965$	6.70308	0.215780
$966$	14.3203	0.460750
$967$	−15.6164	−0.502189	−0.251094	−	0.967963i	$-0.580790\pi$
$967$	−15.6164	−0.502189	−0.251094	+	0.967963i	$0.580790\pi$
$968$	−7.91476	−0.254390
$969$	−0.881605	−0.0283212
$970$	6.82338	0.219086
$971$	−51.7926	−1.66210	−0.831052	−	0.556195i	$-0.812261\pi$
$971$	−51.7926	−1.66210	−0.831052	+	0.556195i	$0.812261\pi$
$972$	1.00000	0.0320750
$973$	−7.07099	−0.226685
$974$	8.97343	0.287527
$975$	6.11629	0.195878
$976$	4.32180	0.138337
$977$	22.0555	0.705618	0.352809	−	0.935695i	$-0.385227\pi$
$977$	22.0555	0.705618	0.352809	+	0.935695i	$0.385227\pi$
$978$	−3.85974	−0.123421
$979$	3.02602	0.0967120
$980$	−4.92537	−0.157335
$981$	−10.6820	−0.341051
$982$	10.7617	0.343419
$983$	−50.6197	−1.61452	−0.807259	−	0.590198i	$-0.799050\pi$
$983$	−50.6197	−1.61452	−0.807259	+	0.590198i	$0.799050\pi$
$984$	−0.330075	−0.0105224
$985$	−3.89009	−0.123949
$986$	0.444823	0.0141661
$987$	39.7010	1.26370
$988$	−1.10977	−0.0353065
$989$	−19.5686	−0.622244
$990$	−0.660030	−0.0209771
$991$	−59.1066	−1.87758	−0.938792	−	0.344484i	$-0.888054\pi$
$991$	−59.1066	−1.87758	−0.938792	+	0.344484i	$0.888054\pi$
$992$	0.957058	0.0303866
$993$	−26.5728	−0.843262
$994$	31.6386	1.00351
$995$	7.90596	0.250636
$996$	−12.1261	−0.384231
$997$	24.8521	0.787075	0.393538	−	0.919309i	$-0.371251\pi$
$997$	24.8521	0.787075	0.393538	+	0.919309i	$0.371251\pi$
$998$	−8.16995	−0.258615
$999$	4.28193	0.135474

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.5	✓	12	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.375767 q^{5} +1.00000 q^{6} +4.48414 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.375767 q^{5} +1.00000 q^{6} +4.48414 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.375767 q^{10} +1.75649 q^{11} +1.00000 q^{12} -1.25881 q^{13} +4.48414 q^{14} -0.375767 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +0.881605 q^{19} -0.375767 q^{20} +4.48414 q^{21} +1.75649 q^{22} +3.19356 q^{23} +1.00000 q^{24} -4.85880 q^{25} -1.25881 q^{26} +1.00000 q^{27} +4.48414 q^{28} -0.444823 q^{29} -0.375767 q^{30} +0.957058 q^{31} +1.00000 q^{32} +1.75649 q^{33} -1.00000 q^{34} -1.68499 q^{35} +1.00000 q^{36} +4.28193 q^{37} +0.881605 q^{38} -1.25881 q^{39} -0.375767 q^{40} -0.330075 q^{41} +4.48414 q^{42} -6.12752 q^{43} +1.75649 q^{44} -0.375767 q^{45} +3.19356 q^{46} +8.85366 q^{47} +1.00000 q^{48} +13.1075 q^{49} -4.85880 q^{50} -1.00000 q^{51} -1.25881 q^{52} +7.93586 q^{53} +1.00000 q^{54} -0.660030 q^{55} +4.48414 q^{56} +0.881605 q^{57} -0.444823 q^{58} +1.00000 q^{59} -0.375767 q^{60} +4.32180 q^{61} +0.957058 q^{62} +4.48414 q^{63} +1.00000 q^{64} +0.473019 q^{65} +1.75649 q^{66} +7.80965 q^{67} -1.00000 q^{68} +3.19356 q^{69} -1.68499 q^{70} +7.05567 q^{71} +1.00000 q^{72} -4.66139 q^{73} +4.28193 q^{74} -4.85880 q^{75} +0.881605 q^{76} +7.87633 q^{77} -1.25881 q^{78} -7.46981 q^{79} -0.375767 q^{80} +1.00000 q^{81} -0.330075 q^{82} -12.1261 q^{83} +4.48414 q^{84} +0.375767 q^{85} -6.12752 q^{86} -0.444823 q^{87} +1.75649 q^{88} +1.72277 q^{89} -0.375767 q^{90} -5.64466 q^{91} +3.19356 q^{92} +0.957058 q^{93} +8.85366 q^{94} -0.331278 q^{95} +1.00000 q^{96} -18.1585 q^{97} +13.1075 q^{98} +1.75649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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