LMFDB - Embedded newform 6018.2.a.ba.1.1

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			1.1
Root			$4.07242$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.07242 q^{5} +1.00000 q^{6} -1.48607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.07242 q^{5} +1.00000 q^{6} -1.48607 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.07242 q^{10} +4.90472 q^{11} +1.00000 q^{12} -3.70693 q^{13} -1.48607 q^{14} -3.07242 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +0.374290 q^{19} -3.07242 q^{20} -1.48607 q^{21} +4.90472 q^{22} -3.75854 q^{23} +1.00000 q^{24} +4.43976 q^{25} -3.70693 q^{26} +1.00000 q^{27} -1.48607 q^{28} +4.03663 q^{29} -3.07242 q^{30} +5.86726 q^{31} +1.00000 q^{32} +4.90472 q^{33} -1.00000 q^{34} +4.56582 q^{35} +1.00000 q^{36} +8.42687 q^{37} +0.374290 q^{38} -3.70693 q^{39} -3.07242 q^{40} -7.48927 q^{41} -1.48607 q^{42} +3.86423 q^{43} +4.90472 q^{44} -3.07242 q^{45} -3.75854 q^{46} +5.58129 q^{47} +1.00000 q^{48} -4.79160 q^{49} +4.43976 q^{50} -1.00000 q^{51} -3.70693 q^{52} +0.592697 q^{53} +1.00000 q^{54} -15.0693 q^{55} -1.48607 q^{56} +0.374290 q^{57} +4.03663 q^{58} +1.00000 q^{59} -3.07242 q^{60} -8.24709 q^{61} +5.86726 q^{62} -1.48607 q^{63} +1.00000 q^{64} +11.3892 q^{65} +4.90472 q^{66} +2.59730 q^{67} -1.00000 q^{68} -3.75854 q^{69} +4.56582 q^{70} +0.437051 q^{71} +1.00000 q^{72} +4.15775 q^{73} +8.42687 q^{74} +4.43976 q^{75} +0.374290 q^{76} -7.28874 q^{77} -3.70693 q^{78} +4.93005 q^{79} -3.07242 q^{80} +1.00000 q^{81} -7.48927 q^{82} +15.7023 q^{83} -1.48607 q^{84} +3.07242 q^{85} +3.86423 q^{86} +4.03663 q^{87} +4.90472 q^{88} +4.17862 q^{89} -3.07242 q^{90} +5.50874 q^{91} -3.75854 q^{92} +5.86726 q^{93} +5.58129 q^{94} -1.14997 q^{95} +1.00000 q^{96} +15.5954 q^{97} -4.79160 q^{98} +4.90472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.07242	−1.37403	−0.687014	−	0.726644i	$-0.741079\pi$
$5$	−3.07242	−1.37403	−0.687014	+	0.726644i	$0.741079\pi$
$6$	1.00000	0.408248
$7$	−1.48607	−0.561681	−0.280840	−	0.959755i	$-0.590613\pi$
$7$	−1.48607	−0.561681	−0.280840	+	0.959755i	$0.590613\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.07242	−0.971584
$11$	4.90472	1.47883	0.739414	−	0.673251i	$-0.235103\pi$
$11$	4.90472	1.47883	0.739414	+	0.673251i	$0.235103\pi$
$12$	1.00000	0.288675
$13$	−3.70693	−1.02812	−0.514059	−	0.857755i	$-0.671859\pi$
$13$	−3.70693	−1.02812	−0.514059	+	0.857755i	$0.671859\pi$
$14$	−1.48607	−0.397168
$15$	−3.07242	−0.793295
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	0.374290	0.0858679	0.0429340	−	0.999078i	$-0.486329\pi$
$19$	0.374290	0.0858679	0.0429340	+	0.999078i	$0.486329\pi$
$20$	−3.07242	−0.687014
$21$	−1.48607	−0.324286
$22$	4.90472	1.04569
$23$	−3.75854	−0.783710	−0.391855	−	0.920027i	$-0.628167\pi$
$23$	−3.75854	−0.783710	−0.391855	+	0.920027i	$0.628167\pi$
$24$	1.00000	0.204124
$25$	4.43976	0.887953
$26$	−3.70693	−0.726989
$27$	1.00000	0.192450
$28$	−1.48607	−0.280840
$29$	4.03663	0.749584	0.374792	−	0.927109i	$-0.377714\pi$
$29$	4.03663	0.749584	0.374792	+	0.927109i	$0.377714\pi$
$30$	−3.07242	−0.560945
$31$	5.86726	1.05379	0.526896	−	0.849930i	$-0.323356\pi$
$31$	5.86726	1.05379	0.526896	+	0.849930i	$0.323356\pi$
$32$	1.00000	0.176777
$33$	4.90472	0.853802
$34$	−1.00000	−0.171499
$35$	4.56582	0.771765
$36$	1.00000	0.166667
$37$	8.42687	1.38537	0.692684	−	0.721241i	$-0.256428\pi$
$37$	8.42687	1.38537	0.692684	+	0.721241i	$0.256428\pi$
$38$	0.374290	0.0607178
$39$	−3.70693	−0.593584
$40$	−3.07242	−0.485792
$41$	−7.48927	−1.16963	−0.584813	−	0.811168i	$-0.698832\pi$
$41$	−7.48927	−1.16963	−0.584813	+	0.811168i	$0.698832\pi$
$42$	−1.48607	−0.229305
$43$	3.86423	0.589290	0.294645	−	0.955607i	$-0.404799\pi$
$43$	3.86423	0.589290	0.294645	+	0.955607i	$0.404799\pi$
$44$	4.90472	0.739414
$45$	−3.07242	−0.458009
$46$	−3.75854	−0.554167
$47$	5.58129	0.814114	0.407057	−	0.913403i	$-0.366555\pi$
$47$	5.58129	0.814114	0.407057	+	0.913403i	$0.366555\pi$
$48$	1.00000	0.144338
$49$	−4.79160	−0.684515
$50$	4.43976	0.627877
$51$	−1.00000	−0.140028
$52$	−3.70693	−0.514059
$53$	0.592697	0.0814132	0.0407066	−	0.999171i	$-0.487039\pi$
$53$	0.592697	0.0814132	0.0407066	+	0.999171i	$0.487039\pi$
$54$	1.00000	0.136083
$55$	−15.0693	−2.03195
$56$	−1.48607	−0.198584
$57$	0.374290	0.0495759
$58$	4.03663	0.530036
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.07242	−0.396648
$61$	−8.24709	−1.05593	−0.527966	−	0.849265i	$-0.677045\pi$
$61$	−8.24709	−1.05593	−0.527966	+	0.849265i	$0.677045\pi$
$62$	5.86726	0.745143
$63$	−1.48607	−0.187227
$64$	1.00000	0.125000
$65$	11.3892	1.41266
$66$	4.90472	0.603729
$67$	2.59730	0.317311	0.158656	−	0.987334i	$-0.449284\pi$
$67$	2.59730	0.317311	0.158656	+	0.987334i	$0.449284\pi$
$68$	−1.00000	−0.121268
$69$	−3.75854	−0.452475
$70$	4.56582	0.545720
$71$	0.437051	0.0518684	0.0259342	−	0.999664i	$-0.491744\pi$
$71$	0.437051	0.0518684	0.0259342	+	0.999664i	$0.491744\pi$
$72$	1.00000	0.117851
$73$	4.15775	0.486628	0.243314	−	0.969948i	$-0.421765\pi$
$73$	4.15775	0.486628	0.243314	+	0.969948i	$0.421765\pi$
$74$	8.42687	0.979603
$75$	4.43976	0.512660
$76$	0.374290	0.0429340
$77$	−7.28874	−0.830629
$78$	−3.70693	−0.419727
$79$	4.93005	0.554674	0.277337	−	0.960773i	$-0.410548\pi$
$79$	4.93005	0.554674	0.277337	+	0.960773i	$0.410548\pi$
$80$	−3.07242	−0.343507
$81$	1.00000	0.111111
$82$	−7.48927	−0.827051
$83$	15.7023	1.72355	0.861777	−	0.507288i	$-0.169352\pi$
$83$	15.7023	1.72355	0.861777	+	0.507288i	$0.169352\pi$
$84$	−1.48607	−0.162143
$85$	3.07242	0.333251
$86$	3.86423	0.416691
$87$	4.03663	0.432773
$88$	4.90472	0.522845
$89$	4.17862	0.442933	0.221467	−	0.975168i	$-0.428916\pi$
$89$	4.17862	0.442933	0.221467	+	0.975168i	$0.428916\pi$
$90$	−3.07242	−0.323861
$91$	5.50874	0.577473
$92$	−3.75854	−0.391855
$93$	5.86726	0.608407
$94$	5.58129	0.575666
$95$	−1.14997	−0.117985
$96$	1.00000	0.102062
$97$	15.5954	1.58347	0.791735	−	0.610865i	$-0.209178\pi$
$97$	15.5954	1.58347	0.791735	+	0.610865i	$0.209178\pi$
$98$	−4.79160	−0.484025
$99$	4.90472	0.492943
$100$	4.43976	0.443976
$101$	5.53545	0.550798	0.275399	−	0.961330i	$-0.411190\pi$
$101$	5.53545	0.550798	0.275399	+	0.961330i	$0.411190\pi$
$102$	−1.00000	−0.0990148
$103$	7.92686	0.781057	0.390528	−	0.920591i	$-0.372292\pi$
$103$	7.92686	0.781057	0.390528	+	0.920591i	$0.372292\pi$
$104$	−3.70693	−0.363494
$105$	4.56582	0.445579
$106$	0.592697	0.0575678
$107$	10.8555	1.04944	0.524718	−	0.851276i	$-0.324171\pi$
$107$	10.8555	1.04944	0.524718	+	0.851276i	$0.324171\pi$
$108$	1.00000	0.0962250
$109$	−13.9208	−1.33337	−0.666684	−	0.745341i	$-0.732287\pi$
$109$	−13.9208	−1.33337	−0.666684	+	0.745341i	$0.732287\pi$
$110$	−15.0693	−1.43681
$111$	8.42687	0.799843
$112$	−1.48607	−0.140420
$113$	4.37971	0.412008	0.206004	−	0.978551i	$-0.433954\pi$
$113$	4.37971	0.412008	0.206004	+	0.978551i	$0.433954\pi$
$114$	0.374290	0.0350554
$115$	11.5478	1.07684
$116$	4.03663	0.374792
$117$	−3.70693	−0.342706
$118$	1.00000	0.0920575
$119$	1.48607	0.136228
$120$	−3.07242	−0.280472
$121$	13.0562	1.18693
$122$	−8.24709	−0.746657
$123$	−7.48927	−0.675284
$124$	5.86726	0.526896
$125$	1.72128	0.153956
$126$	−1.48607	−0.132389
$127$	−6.32721	−0.561449	−0.280724	−	0.959788i	$-0.590575\pi$
$127$	−6.32721	−0.561449	−0.280724	+	0.959788i	$0.590575\pi$
$128$	1.00000	0.0883883
$129$	3.86423	0.340227
$130$	11.3892	0.998903
$131$	−5.60154	−0.489409	−0.244705	−	0.969598i	$-0.578691\pi$
$131$	−5.60154	−0.489409	−0.244705	+	0.969598i	$0.578691\pi$
$132$	4.90472	0.426901
$133$	−0.556220	−0.0482303
$134$	2.59730	0.224373
$135$	−3.07242	−0.264432
$136$	−1.00000	−0.0857493
$137$	17.4376	1.48980	0.744899	−	0.667177i	$-0.232498\pi$
$137$	17.4376	1.48980	0.744899	+	0.667177i	$0.232498\pi$
$138$	−3.75854	−0.319948
$139$	14.1517	1.20033	0.600166	−	0.799876i	$-0.295101\pi$
$139$	14.1517	1.20033	0.600166	+	0.799876i	$0.295101\pi$
$140$	4.56582	0.385882
$141$	5.58129	0.470029
$142$	0.437051	0.0366765
$143$	−18.1814	−1.52041
$144$	1.00000	0.0833333
$145$	−12.4022	−1.02995
$146$	4.15775	0.344098
$147$	−4.79160	−0.395205
$148$	8.42687	0.692684
$149$	9.48677	0.777186	0.388593	−	0.921409i	$-0.372961\pi$
$149$	9.48677	0.777186	0.388593	+	0.921409i	$0.372961\pi$
$150$	4.43976	0.362505
$151$	21.9372	1.78522	0.892611	−	0.450829i	$-0.148871\pi$
$151$	21.9372	1.78522	0.892611	+	0.450829i	$0.148871\pi$
$152$	0.374290	0.0303589
$153$	−1.00000	−0.0808452
$154$	−7.28874	−0.587343
$155$	−18.0267	−1.44794
$156$	−3.70693	−0.296792
$157$	−16.7394	−1.33595	−0.667976	−	0.744183i	$-0.732839\pi$
$157$	−16.7394	−1.33595	−0.667976	+	0.744183i	$0.732839\pi$
$158$	4.93005	0.392214
$159$	0.592697	0.0470039
$160$	−3.07242	−0.242896
$161$	5.58544	0.440195
$162$	1.00000	0.0785674
$163$	−3.99279	−0.312739	−0.156370	−	0.987699i	$-0.549979\pi$
$163$	−3.99279	−0.312739	−0.156370	+	0.987699i	$0.549979\pi$
$164$	−7.48927	−0.584813
$165$	−15.0693	−1.17315
$166$	15.7023	1.21874
$167$	−4.73486	−0.366395	−0.183197	−	0.983076i	$-0.558645\pi$
$167$	−4.73486	−0.366395	−0.183197	+	0.983076i	$0.558645\pi$
$168$	−1.48607	−0.114653
$169$	0.741324	0.0570249
$170$	3.07242	0.235644
$171$	0.374290	0.0286226
$172$	3.86423	0.294645
$173$	−13.5074	−1.02695	−0.513474	−	0.858105i	$-0.671642\pi$
$173$	−13.5074	−1.02695	−0.513474	+	0.858105i	$0.671642\pi$
$174$	4.03663	0.306016
$175$	−6.59778	−0.498746
$176$	4.90472	0.369707
$177$	1.00000	0.0751646
$178$	4.17862	0.313201
$179$	−10.9797	−0.820659	−0.410329	−	0.911937i	$-0.634586\pi$
$179$	−10.9797	−0.820659	−0.410329	+	0.911937i	$0.634586\pi$
$180$	−3.07242	−0.229005
$181$	−1.47824	−0.109877	−0.0549383	−	0.998490i	$-0.517496\pi$
$181$	−1.47824	−0.109877	−0.0549383	+	0.998490i	$0.517496\pi$
$182$	5.50874	0.408335
$183$	−8.24709	−0.609643
$184$	−3.75854	−0.277083
$185$	−25.8909	−1.90353
$186$	5.86726	0.430209
$187$	−4.90472	−0.358668
$188$	5.58129	0.407057
$189$	−1.48607	−0.108095
$190$	−1.14997	−0.0834280
$191$	−14.2651	−1.03218	−0.516092	−	0.856533i	$-0.672614\pi$
$191$	−14.2651	−1.03218	−0.516092	+	0.856533i	$0.672614\pi$
$192$	1.00000	0.0721688
$193$	−5.60510	−0.403464	−0.201732	−	0.979441i	$-0.564657\pi$
$193$	−5.60510	−0.403464	−0.201732	+	0.979441i	$0.564657\pi$
$194$	15.5954	1.11968
$195$	11.3892	0.815601
$196$	−4.79160	−0.342257
$197$	3.61666	0.257677	0.128838	−	0.991666i	$-0.458875\pi$
$197$	3.61666	0.257677	0.128838	+	0.991666i	$0.458875\pi$
$198$	4.90472	0.348563
$199$	28.1123	1.99283	0.996414	−	0.0846096i	$-0.0269643\pi$
$199$	28.1123	1.99283	0.996414	+	0.0846096i	$0.0269643\pi$
$200$	4.43976	0.313939
$201$	2.59730	0.183200
$202$	5.53545	0.389473
$203$	−5.99871	−0.421027
$204$	−1.00000	−0.0700140
$205$	23.0102	1.60710
$206$	7.92686	0.552290
$207$	−3.75854	−0.261237
$208$	−3.70693	−0.257029
$209$	1.83578	0.126984
$210$	4.56582	0.315072
$211$	22.6597	1.55996	0.779978	−	0.625807i	$-0.215230\pi$
$211$	22.6597	1.55996	0.779978	+	0.625807i	$0.215230\pi$
$212$	0.592697	0.0407066
$213$	0.437051	0.0299462
$214$	10.8555	0.742064
$215$	−11.8725	−0.809701
$216$	1.00000	0.0680414
$217$	−8.71915	−0.591894
$218$	−13.9208	−0.942833
$219$	4.15775	0.280955
$220$	−15.0693	−1.01598
$221$	3.70693	0.249355
$222$	8.42687	0.565574
$223$	21.5439	1.44269	0.721344	−	0.692577i	$-0.243525\pi$
$223$	21.5439	1.44269	0.721344	+	0.692577i	$0.243525\pi$
$224$	−1.48607	−0.0992920
$225$	4.43976	0.295984
$226$	4.37971	0.291334
$227$	12.9102	0.856882	0.428441	−	0.903570i	$-0.359063\pi$
$227$	12.9102	0.856882	0.428441	+	0.903570i	$0.359063\pi$
$228$	0.374290	0.0247879
$229$	−26.5168	−1.75228	−0.876141	−	0.482056i	$-0.839890\pi$
$229$	−26.5168	−1.75228	−0.876141	+	0.482056i	$0.839890\pi$
$230$	11.5478	0.761441
$231$	−7.28874	−0.479564
$232$	4.03663	0.265018
$233$	7.54608	0.494360	0.247180	−	0.968970i	$-0.420496\pi$
$233$	7.54608	0.494360	0.247180	+	0.968970i	$0.420496\pi$
$234$	−3.70693	−0.242330
$235$	−17.1481	−1.11862
$236$	1.00000	0.0650945
$237$	4.93005	0.320241
$238$	1.48607	0.0963274
$239$	16.5904	1.07314	0.536572	−	0.843855i	$-0.319719\pi$
$239$	16.5904	1.07314	0.536572	+	0.843855i	$0.319719\pi$
$240$	−3.07242	−0.198324
$241$	−5.88902	−0.379345	−0.189673	−	0.981847i	$-0.560743\pi$
$241$	−5.88902	−0.379345	−0.189673	+	0.981847i	$0.560743\pi$
$242$	13.0562	0.839287
$243$	1.00000	0.0641500
$244$	−8.24709	−0.527966
$245$	14.7218	0.940543
$246$	−7.48927	−0.477498
$247$	−1.38747	−0.0882823
$248$	5.86726	0.372572
$249$	15.7023	0.995094
$250$	1.72128	0.108864
$251$	4.15036	0.261968	0.130984	−	0.991384i	$-0.458186\pi$
$251$	4.15036	0.261968	0.130984	+	0.991384i	$0.458186\pi$
$252$	−1.48607	−0.0936134
$253$	−18.4346	−1.15897
$254$	−6.32721	−0.397004
$255$	3.07242	0.192402
$256$	1.00000	0.0625000
$257$	2.71311	0.169239	0.0846196	−	0.996413i	$-0.473032\pi$
$257$	2.71311	0.169239	0.0846196	+	0.996413i	$0.473032\pi$
$258$	3.86423	0.240577
$259$	−12.5229	−0.778134
$260$	11.3892	0.706331
$261$	4.03663	0.249861
$262$	−5.60154	−0.346064
$263$	9.32648	0.575095	0.287548	−	0.957766i	$-0.407160\pi$
$263$	9.32648	0.575095	0.287548	+	0.957766i	$0.407160\pi$
$264$	4.90472	0.301864
$265$	−1.82101	−0.111864
$266$	−0.556220	−0.0341040
$267$	4.17862	0.255728
$268$	2.59730	0.158656
$269$	−5.67392	−0.345945	−0.172972	−	0.984927i	$-0.555337\pi$
$269$	−5.67392	−0.345945	−0.172972	+	0.984927i	$0.555337\pi$
$270$	−3.07242	−0.186982
$271$	−26.5429	−1.61236	−0.806182	−	0.591668i	$-0.798470\pi$
$271$	−26.5429	−1.61236	−0.806182	+	0.591668i	$0.798470\pi$
$272$	−1.00000	−0.0606339
$273$	5.50874	0.333404
$274$	17.4376	1.05345
$275$	21.7758	1.31313
$276$	−3.75854	−0.226238
$277$	−22.6634	−1.36171	−0.680856	−	0.732417i	$-0.738392\pi$
$277$	−22.6634	−1.36171	−0.680856	+	0.732417i	$0.738392\pi$
$278$	14.1517	0.848762
$279$	5.86726	0.351264
$280$	4.56582	0.272860
$281$	25.1519	1.50044	0.750218	−	0.661190i	$-0.229948\pi$
$281$	25.1519	1.50044	0.750218	+	0.661190i	$0.229948\pi$
$282$	5.58129	0.332361
$283$	1.87698	0.111575	0.0557875	−	0.998443i	$-0.482233\pi$
$283$	1.87698	0.111575	0.0557875	+	0.998443i	$0.482233\pi$
$284$	0.437051	0.0259342
$285$	−1.14997	−0.0681186
$286$	−18.1814	−1.07509
$287$	11.1296	0.656957
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−12.4022	−0.728284
$291$	15.5954	0.914217
$292$	4.15775	0.243314
$293$	−13.3308	−0.778791	−0.389396	−	0.921071i	$-0.627316\pi$
$293$	−13.3308	−0.778791	−0.389396	+	0.921071i	$0.627316\pi$
$294$	−4.79160	−0.279452
$295$	−3.07242	−0.178883
$296$	8.42687	0.489802
$297$	4.90472	0.284601
$298$	9.48677	0.549554
$299$	13.9326	0.805746
$300$	4.43976	0.256330
$301$	−5.74251	−0.330993
$302$	21.9372	1.26234
$303$	5.53545	0.318003
$304$	0.374290	0.0214670
$305$	25.3385	1.45088
$306$	−1.00000	−0.0571662
$307$	−5.72146	−0.326541	−0.163270	−	0.986581i	$-0.552204\pi$
$307$	−5.72146	−0.326541	−0.163270	+	0.986581i	$0.552204\pi$
$308$	−7.28874	−0.415314
$309$	7.92686	0.450943
$310$	−18.0267	−1.02385
$311$	24.6873	1.39989	0.699944	−	0.714198i	$-0.253208\pi$
$311$	24.6873	1.39989	0.699944	+	0.714198i	$0.253208\pi$
$312$	−3.70693	−0.209864
$313$	−10.0874	−0.570173	−0.285086	−	0.958502i	$-0.592022\pi$
$313$	−10.0874	−0.570173	−0.285086	+	0.958502i	$0.592022\pi$
$314$	−16.7394	−0.944661
$315$	4.56582	0.257255
$316$	4.93005	0.277337
$317$	−12.7798	−0.717785	−0.358893	−	0.933379i	$-0.616846\pi$
$317$	−12.7798	−0.717785	−0.358893	+	0.933379i	$0.616846\pi$
$318$	0.592697	0.0332368
$319$	19.7986	1.10851
$320$	−3.07242	−0.171753
$321$	10.8555	0.605893
$322$	5.58544	0.311265
$323$	−0.374290	−0.0208260
$324$	1.00000	0.0555556
$325$	−16.4579	−0.912919
$326$	−3.99279	−0.221140
$327$	−13.9208	−0.769820
$328$	−7.48927	−0.413526
$329$	−8.29416	−0.457272
$330$	−15.0693	−0.829540
$331$	4.29789	0.236233	0.118117	−	0.993000i	$-0.462314\pi$
$331$	4.29789	0.236233	0.118117	+	0.993000i	$0.462314\pi$
$332$	15.7023	0.861777
$333$	8.42687	0.461789
$334$	−4.73486	−0.259080
$335$	−7.98000	−0.435994
$336$	−1.48607	−0.0810716
$337$	16.8587	0.918351	0.459176	−	0.888345i	$-0.348145\pi$
$337$	16.8587	0.918351	0.459176	+	0.888345i	$0.348145\pi$
$338$	0.741324	0.0403227
$339$	4.37971	0.237873
$340$	3.07242	0.166625
$341$	28.7773	1.55838
$342$	0.374290	0.0202393
$343$	17.5231	0.946159
$344$	3.86423	0.208345
$345$	11.5478	0.621714
$346$	−13.5074	−0.726162
$347$	32.4580	1.74244	0.871218	−	0.490897i	$-0.163331\pi$
$347$	32.4580	1.74244	0.871218	+	0.490897i	$0.163331\pi$
$348$	4.03663	0.216386
$349$	−27.5200	−1.47311	−0.736556	−	0.676376i	$-0.763549\pi$
$349$	−27.5200	−1.47311	−0.736556	+	0.676376i	$0.763549\pi$
$350$	−6.59778	−0.352666
$351$	−3.70693	−0.197861
$352$	4.90472	0.261422
$353$	−12.1060	−0.644338	−0.322169	−	0.946682i	$-0.604412\pi$
$353$	−12.1060	−0.644338	−0.322169	+	0.946682i	$0.604412\pi$
$354$	1.00000	0.0531494
$355$	−1.34280	−0.0712686
$356$	4.17862	0.221467
$357$	1.48607	0.0786510
$358$	−10.9797	−0.580293
$359$	−23.8662	−1.25961	−0.629805	−	0.776753i	$-0.716865\pi$
$359$	−23.8662	−1.25961	−0.629805	+	0.776753i	$0.716865\pi$
$360$	−3.07242	−0.161931
$361$	−18.8599	−0.992627
$362$	−1.47824	−0.0776945
$363$	13.0562	0.685275
$364$	5.50874	0.288737
$365$	−12.7744	−0.668641
$366$	−8.24709	−0.431082
$367$	−26.5582	−1.38633	−0.693163	−	0.720781i	$-0.743783\pi$
$367$	−26.5582	−1.38633	−0.693163	+	0.720781i	$0.743783\pi$
$368$	−3.75854	−0.195928
$369$	−7.48927	−0.389876
$370$	−25.8909	−1.34600
$371$	−0.880787	−0.0457282
$372$	5.86726	0.304203
$373$	−27.3731	−1.41733	−0.708664	−	0.705547i	$-0.750702\pi$
$373$	−27.3731	−1.41733	−0.708664	+	0.705547i	$0.750702\pi$
$374$	−4.90472	−0.253617
$375$	1.72128	0.0888867
$376$	5.58129	0.287833
$377$	−14.9635	−0.770660
$378$	−1.48607	−0.0764350
$379$	−1.78947	−0.0919187	−0.0459593	−	0.998943i	$-0.514634\pi$
$379$	−1.78947	−0.0919187	−0.0459593	+	0.998943i	$0.514634\pi$
$380$	−1.14997	−0.0589925
$381$	−6.32721	−0.324153
$382$	−14.2651	−0.729864
$383$	6.54895	0.334636	0.167318	−	0.985903i	$-0.446489\pi$
$383$	6.54895	0.334636	0.167318	+	0.985903i	$0.446489\pi$
$384$	1.00000	0.0510310
$385$	22.3941	1.14131
$386$	−5.60510	−0.285292
$387$	3.86423	0.196430
$388$	15.5954	0.791735
$389$	14.5692	0.738686	0.369343	−	0.929293i	$-0.379583\pi$
$389$	14.5692	0.738686	0.369343	+	0.929293i	$0.379583\pi$
$390$	11.3892	0.576717
$391$	3.75854	0.190078
$392$	−4.79160	−0.242013
$393$	−5.60154	−0.282560
$394$	3.61666	0.182205
$395$	−15.1472	−0.762137
$396$	4.90472	0.246471
$397$	26.4432	1.32714	0.663572	−	0.748112i	$-0.269040\pi$
$397$	26.4432	1.32714	0.663572	+	0.748112i	$0.269040\pi$
$398$	28.1123	1.40914
$399$	−0.556220	−0.0278458
$400$	4.43976	0.221988
$401$	−21.6256	−1.07993	−0.539966	−	0.841687i	$-0.681563\pi$
$401$	−21.6256	−1.07993	−0.539966	+	0.841687i	$0.681563\pi$
$402$	2.59730	0.129542
$403$	−21.7495	−1.08342
$404$	5.53545	0.275399
$405$	−3.07242	−0.152670
$406$	−5.99871	−0.297711
$407$	41.3314	2.04872
$408$	−1.00000	−0.0495074
$409$	−5.01952	−0.248199	−0.124100	−	0.992270i	$-0.539604\pi$
$409$	−5.01952	−0.248199	−0.124100	+	0.992270i	$0.539604\pi$
$410$	23.0102	1.13639
$411$	17.4376	0.860135
$412$	7.92686	0.390528
$413$	−1.48607	−0.0731246
$414$	−3.75854	−0.184722
$415$	−48.2441	−2.36821
$416$	−3.70693	−0.181747
$417$	14.1517	0.693012
$418$	1.83578	0.0897912
$419$	−21.4162	−1.04625	−0.523124	−	0.852256i	$-0.675234\pi$
$419$	−21.4162	−1.04625	−0.523124	+	0.852256i	$0.675234\pi$
$420$	4.56582	0.222789
$421$	−6.28069	−0.306102	−0.153051	−	0.988218i	$-0.548910\pi$
$421$	−6.28069	−0.306102	−0.153051	+	0.988218i	$0.548910\pi$
$422$	22.6597	1.10305
$423$	5.58129	0.271371
$424$	0.592697	0.0287839
$425$	−4.43976	−0.215360
$426$	0.437051	0.0211752
$427$	12.2557	0.593096
$428$	10.8555	0.524718
$429$	−18.1814	−0.877808
$430$	−11.8725	−0.572545
$431$	−7.56132	−0.364216	−0.182108	−	0.983279i	$-0.558292\pi$
$431$	−7.56132	−0.364216	−0.182108	+	0.983279i	$0.558292\pi$
$432$	1.00000	0.0481125
$433$	−1.99310	−0.0957824	−0.0478912	−	0.998853i	$-0.515250\pi$
$433$	−1.99310	−0.0957824	−0.0478912	+	0.998853i	$0.515250\pi$
$434$	−8.71915	−0.418532
$435$	−12.4022	−0.594642
$436$	−13.9208	−0.666684
$437$	−1.40678	−0.0672956
$438$	4.15775	0.198665
$439$	2.58245	0.123254	0.0616268	−	0.998099i	$-0.480371\pi$
$439$	2.58245	0.123254	0.0616268	+	0.998099i	$0.480371\pi$
$440$	−15.0693	−0.718403
$441$	−4.79160	−0.228172
$442$	3.70693	0.176321
$443$	1.77660	0.0844088	0.0422044	−	0.999109i	$-0.486562\pi$
$443$	1.77660	0.0844088	0.0422044	+	0.999109i	$0.486562\pi$
$444$	8.42687	0.399921
$445$	−12.8385	−0.608603
$446$	21.5439	1.02013
$447$	9.48677	0.448709
$448$	−1.48607	−0.0702101
$449$	27.4572	1.29579	0.647893	−	0.761731i	$-0.275650\pi$
$449$	27.4572	1.29579	0.647893	+	0.761731i	$0.275650\pi$
$450$	4.43976	0.209292
$451$	−36.7327	−1.72968
$452$	4.37971	0.206004
$453$	21.9372	1.03070
$454$	12.9102	0.605907
$455$	−16.9252	−0.793465
$456$	0.374290	0.0175277
$457$	−0.932760	−0.0436327	−0.0218163	−	0.999762i	$-0.506945\pi$
$457$	−0.932760	−0.0436327	−0.0218163	+	0.999762i	$0.506945\pi$
$458$	−26.5168	−1.23905
$459$	−1.00000	−0.0466760
$460$	11.5478	0.538420
$461$	8.38031	0.390310	0.195155	−	0.980772i	$-0.437479\pi$
$461$	8.38031	0.390310	0.195155	+	0.980772i	$0.437479\pi$
$462$	−7.28874	−0.339103
$463$	−14.6428	−0.680510	−0.340255	−	0.940333i	$-0.610513\pi$
$463$	−14.6428	−0.680510	−0.340255	+	0.940333i	$0.610513\pi$
$464$	4.03663	0.187396
$465$	−18.0267	−0.835968
$466$	7.54608	0.349566
$467$	11.3626	0.525800	0.262900	−	0.964823i	$-0.415321\pi$
$467$	11.3626	0.525800	0.262900	+	0.964823i	$0.415321\pi$
$468$	−3.70693	−0.171353
$469$	−3.85977	−0.178227
$470$	−17.1481	−0.790981
$471$	−16.7394	−0.771312
$472$	1.00000	0.0460287
$473$	18.9530	0.871458
$474$	4.93005	0.226445
$475$	1.66176	0.0762467
$476$	1.48607	0.0681138
$477$	0.592697	0.0271377
$478$	16.5904	0.758827
$479$	36.1930	1.65370	0.826850	−	0.562423i	$-0.190131\pi$
$479$	36.1930	1.65370	0.826850	+	0.562423i	$0.190131\pi$
$480$	−3.07242	−0.140236
$481$	−31.2378	−1.42432
$482$	−5.88902	−0.268237
$483$	5.58544	0.254147
$484$	13.0562	0.593466
$485$	−47.9155	−2.17573
$486$	1.00000	0.0453609
$487$	26.0075	1.17851	0.589256	−	0.807946i	$-0.299421\pi$
$487$	26.0075	1.17851	0.589256	+	0.807946i	$0.299421\pi$
$488$	−8.24709	−0.373328
$489$	−3.99279	−0.180560
$490$	14.7218	0.665064
$491$	16.8295	0.759506	0.379753	−	0.925088i	$-0.376009\pi$
$491$	16.8295	0.759506	0.379753	+	0.925088i	$0.376009\pi$
$492$	−7.48927	−0.337642
$493$	−4.03663	−0.181801
$494$	−1.38747	−0.0624250
$495$	−15.0693	−0.677317
$496$	5.86726	0.263448
$497$	−0.649487	−0.0291335
$498$	15.7023	0.703638
$499$	13.7666	0.616278	0.308139	−	0.951341i	$-0.400294\pi$
$499$	13.7666	0.616278	0.308139	+	0.951341i	$0.400294\pi$
$500$	1.72128	0.0769782
$501$	−4.73486	−0.211538
$502$	4.15036	0.185239
$503$	21.4555	0.956654	0.478327	−	0.878182i	$-0.341243\pi$
$503$	21.4555	0.956654	0.478327	+	0.878182i	$0.341243\pi$
$504$	−1.48607	−0.0661947
$505$	−17.0072	−0.756812
$506$	−18.4346	−0.819517
$507$	0.741324	0.0329233
$508$	−6.32721	−0.280724
$509$	−25.9375	−1.14966	−0.574829	−	0.818273i	$-0.694932\pi$
$509$	−25.9375	−1.14966	−0.574829	+	0.818273i	$0.694932\pi$
$510$	3.07242	0.136049
$511$	−6.17870	−0.273330
$512$	1.00000	0.0441942
$513$	0.374290	0.0165253
$514$	2.71311	0.119670
$515$	−24.3546	−1.07319
$516$	3.86423	0.170113
$517$	27.3746	1.20393
$518$	−12.5229	−0.550224
$519$	−13.5074	−0.592909
$520$	11.3892	0.499451
$521$	−13.9685	−0.611973	−0.305986	−	0.952036i	$-0.598986\pi$
$521$	−13.9685	−0.611973	−0.305986	+	0.952036i	$0.598986\pi$
$522$	4.03663	0.176679
$523$	−44.9948	−1.96749	−0.983744	−	0.179579i	$-0.942527\pi$
$523$	−44.9948	−1.96749	−0.983744	+	0.179579i	$0.942527\pi$
$524$	−5.60154	−0.244705
$525$	−6.59778	−0.287951
$526$	9.32648	0.406654
$527$	−5.86726	−0.255582
$528$	4.90472	0.213450
$529$	−8.87336	−0.385798
$530$	−1.82101	−0.0790998
$531$	1.00000	0.0433963
$532$	−0.556220	−0.0241152
$533$	27.7622	1.20251
$534$	4.17862	0.180827
$535$	−33.3525	−1.44196
$536$	2.59730	0.112186
$537$	−10.9797	−0.473807
$538$	−5.67392	−0.244620
$539$	−23.5015	−1.01228
$540$	−3.07242	−0.132216
$541$	−30.2071	−1.29871	−0.649353	−	0.760488i	$-0.724960\pi$
$541$	−30.2071	−1.29871	−0.649353	+	0.760488i	$0.724960\pi$
$542$	−26.5429	−1.14011
$543$	−1.47824	−0.0634373
$544$	−1.00000	−0.0428746
$545$	42.7704	1.83208
$546$	5.50874	0.235753
$547$	−9.69919	−0.414708	−0.207354	−	0.978266i	$-0.566485\pi$
$547$	−9.69919	−0.414708	−0.207354	+	0.978266i	$0.566485\pi$
$548$	17.4376	0.744899
$549$	−8.24709	−0.351977
$550$	21.7758	0.928522
$551$	1.51087	0.0643653
$552$	−3.75854	−0.159974
$553$	−7.32638	−0.311550
$554$	−22.6634	−0.962876
$555$	−25.8909	−1.09901
$556$	14.1517	0.600166
$557$	41.9832	1.77889	0.889443	−	0.457046i	$-0.151093\pi$
$557$	41.9832	1.77889	0.889443	+	0.457046i	$0.151093\pi$
$558$	5.86726	0.248381
$559$	−14.3244	−0.605859
$560$	4.56582	0.192941
$561$	−4.90472	−0.207077
$562$	25.1519	1.06097
$563$	−36.1328	−1.52282	−0.761408	−	0.648273i	$-0.775492\pi$
$563$	−36.1328	−1.52282	−0.761408	+	0.648273i	$0.775492\pi$
$564$	5.58129	0.235015
$565$	−13.4563	−0.566111
$566$	1.87698	0.0788954
$567$	−1.48607	−0.0624089
$568$	0.437051	0.0183382
$569$	12.4073	0.520142	0.260071	−	0.965590i	$-0.416254\pi$
$569$	12.4073	0.520142	0.260071	+	0.965590i	$0.416254\pi$
$570$	−1.14997	−0.0481672
$571$	29.9416	1.25302	0.626509	−	0.779414i	$-0.284483\pi$
$571$	29.9416	1.25302	0.626509	+	0.779414i	$0.284483\pi$
$572$	−18.1814	−0.760204
$573$	−14.2651	−0.595931
$574$	11.1296	0.464538
$575$	−16.6870	−0.695897
$576$	1.00000	0.0416667
$577$	−13.1288	−0.546558	−0.273279	−	0.961935i	$-0.588108\pi$
$577$	−13.1288	−0.546558	−0.273279	+	0.961935i	$0.588108\pi$
$578$	1.00000	0.0415945
$579$	−5.60510	−0.232940
$580$	−12.4022	−0.514975
$581$	−23.3347	−0.968086
$582$	15.5954	0.646449
$583$	2.90701	0.120396
$584$	4.15775	0.172049
$585$	11.3892	0.470887
$586$	−13.3308	−0.550689
$587$	−4.64008	−0.191517	−0.0957583	−	0.995405i	$-0.530528\pi$
$587$	−4.64008	−0.191517	−0.0957583	+	0.995405i	$0.530528\pi$
$588$	−4.79160	−0.197602
$589$	2.19606	0.0904869
$590$	−3.07242	−0.126490
$591$	3.61666	0.148770
$592$	8.42687	0.346342
$593$	−17.3899	−0.714118	−0.357059	−	0.934082i	$-0.616221\pi$
$593$	−17.3899	−0.714118	−0.357059	+	0.934082i	$0.616221\pi$
$594$	4.90472	0.201243
$595$	−4.56582	−0.187180
$596$	9.48677	0.388593
$597$	28.1123	1.15056
$598$	13.9326	0.569748
$599$	−18.3020	−0.747798	−0.373899	−	0.927470i	$-0.621979\pi$
$599$	−18.3020	−0.747798	−0.373899	+	0.927470i	$0.621979\pi$
$600$	4.43976	0.181253
$601$	−24.3955	−0.995113	−0.497557	−	0.867432i	$-0.665769\pi$
$601$	−24.3955	−0.995113	−0.497557	+	0.867432i	$0.665769\pi$
$602$	−5.74251	−0.234047
$603$	2.59730	0.105770
$604$	21.9372	0.892611
$605$	−40.1143	−1.63088
$606$	5.53545	0.224862
$607$	−22.3995	−0.909166	−0.454583	−	0.890704i	$-0.650212\pi$
$607$	−22.3995	−0.909166	−0.454583	+	0.890704i	$0.650212\pi$
$608$	0.374290	0.0151795
$609$	−5.99871	−0.243080
$610$	25.3385	1.02593
$611$	−20.6894	−0.837005
$612$	−1.00000	−0.0404226
$613$	7.59723	0.306849	0.153425	−	0.988160i	$-0.450970\pi$
$613$	7.59723	0.306849	0.153425	+	0.988160i	$0.450970\pi$
$614$	−5.72146	−0.230899
$615$	23.0102	0.927860
$616$	−7.28874	−0.293672
$617$	−11.2213	−0.451753	−0.225876	−	0.974156i	$-0.572525\pi$
$617$	−11.2213	−0.451753	−0.225876	+	0.974156i	$0.572525\pi$
$618$	7.92686	0.318865
$619$	−20.1388	−0.809445	−0.404723	−	0.914440i	$-0.632632\pi$
$619$	−20.1388	−0.809445	−0.404723	+	0.914440i	$0.632632\pi$
$620$	−18.0267	−0.723969
$621$	−3.75854	−0.150825
$622$	24.6873	0.989870
$623$	−6.20971	−0.248787
$624$	−3.70693	−0.148396
$625$	−27.4873	−1.09949
$626$	−10.0874	−0.403173
$627$	1.83578	0.0733142
$628$	−16.7394	−0.667976
$629$	−8.42687	−0.336001
$630$	4.56582	0.181907
$631$	−26.3608	−1.04941	−0.524703	−	0.851286i	$-0.675824\pi$
$631$	−26.3608	−1.04941	−0.524703	+	0.851286i	$0.675824\pi$
$632$	4.93005	0.196107
$633$	22.6597	0.900641
$634$	−12.7798	−0.507551
$635$	19.4398	0.771446
$636$	0.592697	0.0235020
$637$	17.7621	0.703762
$638$	19.7986	0.783832
$639$	0.437051	0.0172895
$640$	−3.07242	−0.121448
$641$	−33.7365	−1.33251	−0.666256	−	0.745723i	$-0.732104\pi$
$641$	−33.7365	−1.33251	−0.666256	+	0.745723i	$0.732104\pi$
$642$	10.8555	0.428431
$643$	−24.3662	−0.960911	−0.480455	−	0.877019i	$-0.659529\pi$
$643$	−24.3662	−0.960911	−0.480455	+	0.877019i	$0.659529\pi$
$644$	5.58544	0.220097
$645$	−11.8725	−0.467481
$646$	−0.374290	−0.0147262
$647$	39.9572	1.57088	0.785441	−	0.618937i	$-0.212436\pi$
$647$	39.9572	1.57088	0.785441	+	0.618937i	$0.212436\pi$
$648$	1.00000	0.0392837
$649$	4.90472	0.192527
$650$	−16.4579	−0.645531
$651$	−8.71915	−0.341730
$652$	−3.99279	−0.156370
$653$	47.0895	1.84275	0.921377	−	0.388671i	$-0.127066\pi$
$653$	47.0895	1.84275	0.921377	+	0.388671i	$0.127066\pi$
$654$	−13.9208	−0.544345
$655$	17.2103	0.672462
$656$	−7.48927	−0.292407
$657$	4.15775	0.162209
$658$	−8.29416	−0.323340
$659$	41.6347	1.62186	0.810929	−	0.585144i	$-0.198962\pi$
$659$	41.6347	1.62186	0.810929	+	0.585144i	$0.198962\pi$
$660$	−15.0693	−0.586574
$661$	−13.6537	−0.531069	−0.265534	−	0.964101i	$-0.585548\pi$
$661$	−13.6537	−0.531069	−0.265534	+	0.964101i	$0.585548\pi$
$662$	4.29789	0.167042
$663$	3.70693	0.143965
$664$	15.7023	0.609368
$665$	1.70894	0.0662698
$666$	8.42687	0.326534
$667$	−15.1719	−0.587457
$668$	−4.73486	−0.183197
$669$	21.5439	0.832936
$670$	−7.98000	−0.308294
$671$	−40.4497	−1.56154
$672$	−1.48607	−0.0573263
$673$	18.7863	0.724160	0.362080	−	0.932147i	$-0.382067\pi$
$673$	18.7863	0.724160	0.362080	+	0.932147i	$0.382067\pi$
$674$	16.8587	0.649373
$675$	4.43976	0.170887
$676$	0.741324	0.0285124
$677$	1.64149	0.0630874	0.0315437	−	0.999502i	$-0.489958\pi$
$677$	1.64149	0.0630874	0.0315437	+	0.999502i	$0.489958\pi$
$678$	4.37971	0.168202
$679$	−23.1758	−0.889404
$680$	3.07242	0.117822
$681$	12.9102	0.494721
$682$	28.7773	1.10194
$683$	48.1596	1.84277	0.921387	−	0.388646i	$-0.127057\pi$
$683$	48.1596	1.84277	0.921387	+	0.388646i	$0.127057\pi$
$684$	0.374290	0.0143113
$685$	−53.5757	−2.04702
$686$	17.5231	0.669036
$687$	−26.5168	−1.01168
$688$	3.86423	0.147322
$689$	−2.19708	−0.0837023
$690$	11.5478	0.439618
$691$	8.42822	0.320625	0.160312	−	0.987066i	$-0.448750\pi$
$691$	8.42822	0.320625	0.160312	+	0.987066i	$0.448750\pi$
$692$	−13.5074	−0.513474
$693$	−7.28874	−0.276876
$694$	32.4580	1.23209
$695$	−43.4800	−1.64929
$696$	4.03663	0.153008
$697$	7.48927	0.283676
$698$	−27.5200	−1.04165
$699$	7.54608	0.285419
$700$	−6.59778	−0.249373
$701$	−36.0337	−1.36097	−0.680486	−	0.732761i	$-0.738231\pi$
$701$	−36.0337	−1.36097	−0.680486	+	0.732761i	$0.738231\pi$
$702$	−3.70693	−0.139909
$703$	3.15409	0.118959
$704$	4.90472	0.184853
$705$	−17.1481	−0.645833
$706$	−12.1060	−0.455616
$707$	−8.22605	−0.309372
$708$	1.00000	0.0375823
$709$	2.56945	0.0964977	0.0482489	−	0.998835i	$-0.484636\pi$
$709$	2.56945	0.0964977	0.0482489	+	0.998835i	$0.484636\pi$
$710$	−1.34280	−0.0503945
$711$	4.93005	0.184891
$712$	4.17862	0.156601
$713$	−22.0524	−0.825867
$714$	1.48607	0.0556147
$715$	55.8610	2.08908
$716$	−10.9797	−0.410329
$717$	16.5904	0.619579
$718$	−23.8662	−0.890679
$719$	−14.6417	−0.546044	−0.273022	−	0.962008i	$-0.588023\pi$
$719$	−14.6417	−0.546044	−0.273022	+	0.962008i	$0.588023\pi$
$720$	−3.07242	−0.114502
$721$	−11.7798	−0.438704
$722$	−18.8599	−0.701893
$723$	−5.88902	−0.219015
$724$	−1.47824	−0.0549383
$725$	17.9217	0.665595
$726$	13.0562	0.484563
$727$	3.26550	0.121111	0.0605553	−	0.998165i	$-0.480713\pi$
$727$	3.26550	0.121111	0.0605553	+	0.998165i	$0.480713\pi$
$728$	5.50874	0.204168
$729$	1.00000	0.0370370
$730$	−12.7744	−0.472800
$731$	−3.86423	−0.142924
$732$	−8.24709	−0.304821
$733$	−2.83866	−0.104848	−0.0524241	−	0.998625i	$-0.516695\pi$
$733$	−2.83866	−0.104848	−0.0524241	+	0.998625i	$0.516695\pi$
$734$	−26.5582	−0.980280
$735$	14.7218	0.543023
$736$	−3.75854	−0.138542
$737$	12.7390	0.469248
$738$	−7.48927	−0.275684
$739$	14.0946	0.518478	0.259239	−	0.965813i	$-0.416528\pi$
$739$	14.0946	0.518478	0.259239	+	0.965813i	$0.416528\pi$
$740$	−25.8909	−0.951767
$741$	−1.38747	−0.0509698
$742$	−0.880787	−0.0323347
$743$	−39.5161	−1.44971	−0.724853	−	0.688903i	$-0.758092\pi$
$743$	−39.5161	−1.44971	−0.724853	+	0.688903i	$0.758092\pi$
$744$	5.86726	0.215104
$745$	−29.1473	−1.06788
$746$	−27.3731	−1.00220
$747$	15.7023	0.574518
$748$	−4.90472	−0.179334
$749$	−16.1319	−0.589448
$750$	1.72128	0.0628524
$751$	7.12299	0.259922	0.129961	−	0.991519i	$-0.458515\pi$
$751$	7.12299	0.259922	0.129961	+	0.991519i	$0.458515\pi$
$752$	5.58129	0.203529
$753$	4.15036	0.151247
$754$	−14.9635	−0.544939
$755$	−67.4002	−2.45294
$756$	−1.48607	−0.0540477
$757$	−33.8460	−1.23015	−0.615076	−	0.788468i	$-0.710875\pi$
$757$	−33.8460	−1.23015	−0.615076	+	0.788468i	$0.710875\pi$
$758$	−1.78947	−0.0649963
$759$	−18.4346	−0.669133
$760$	−1.14997	−0.0417140
$761$	−13.8722	−0.502865	−0.251433	−	0.967875i	$-0.580902\pi$
$761$	−13.8722	−0.502865	−0.251433	+	0.967875i	$0.580902\pi$
$762$	−6.32721	−0.229210
$763$	20.6872	0.748926
$764$	−14.2651	−0.516092
$765$	3.07242	0.111084
$766$	6.54895	0.236623
$767$	−3.70693	−0.133849
$768$	1.00000	0.0360844
$769$	19.4819	0.702535	0.351267	−	0.936275i	$-0.385751\pi$
$769$	19.4819	0.702535	0.351267	+	0.936275i	$0.385751\pi$
$770$	22.3941	0.807026
$771$	2.71311	0.0977103
$772$	−5.60510	−0.201732
$773$	3.61538	0.130036	0.0650180	−	0.997884i	$-0.479290\pi$
$773$	3.61538	0.130036	0.0650180	+	0.997884i	$0.479290\pi$
$774$	3.86423	0.138897
$775$	26.0493	0.935717
$776$	15.5954	0.559841
$777$	−12.5229	−0.449256
$778$	14.5692	0.522330
$779$	−2.80316	−0.100433
$780$	11.3892	0.407800
$781$	2.14361	0.0767044
$782$	3.75854	0.134405
$783$	4.03663	0.144258
$784$	−4.79160	−0.171129
$785$	51.4306	1.83564
$786$	−5.60154	−0.199800
$787$	38.3935	1.36858	0.684290	−	0.729210i	$-0.260112\pi$
$787$	38.3935	1.36858	0.684290	+	0.729210i	$0.260112\pi$
$788$	3.61666	0.128838
$789$	9.32648	0.332031
$790$	−15.1472	−0.538913
$791$	−6.50854	−0.231417
$792$	4.90472	0.174282
$793$	30.5714	1.08562
$794$	26.4432	0.938433
$795$	−1.82101	−0.0645847
$796$	28.1123	0.996414
$797$	−25.9396	−0.918827	−0.459414	−	0.888222i	$-0.651940\pi$
$797$	−25.9396	−0.918827	−0.459414	+	0.888222i	$0.651940\pi$
$798$	−0.556220	−0.0196900
$799$	−5.58129	−0.197452
$800$	4.43976	0.156969
$801$	4.17862	0.147644
$802$	−21.6256	−0.763628
$803$	20.3926	0.719639
$804$	2.59730	0.0915998
$805$	−17.1608	−0.604840
$806$	−21.7495	−0.766094
$807$	−5.67392	−0.199731
$808$	5.53545	0.194736
$809$	21.6605	0.761542	0.380771	−	0.924669i	$-0.375659\pi$
$809$	21.6605	0.761542	0.380771	+	0.924669i	$0.375659\pi$
$810$	−3.07242	−0.107954
$811$	−18.7910	−0.659842	−0.329921	−	0.944009i	$-0.607022\pi$
$811$	−18.7910	−0.659842	−0.329921	+	0.944009i	$0.607022\pi$
$812$	−5.99871	−0.210513
$813$	−26.5429	−0.930899
$814$	41.3314	1.44866
$815$	12.2675	0.429712
$816$	−1.00000	−0.0350070
$817$	1.44634	0.0506011
$818$	−5.01952	−0.175504
$819$	5.50874	0.192491
$820$	23.0102	0.803550
$821$	−7.83921	−0.273590	−0.136795	−	0.990599i	$-0.543680\pi$
$821$	−7.83921	−0.273590	−0.136795	+	0.990599i	$0.543680\pi$
$822$	17.4376	0.608207
$823$	−3.33181	−0.116140	−0.0580699	−	0.998313i	$-0.518495\pi$
$823$	−3.33181	−0.116140	−0.0580699	+	0.998313i	$0.518495\pi$
$824$	7.92686	0.276145
$825$	21.7758	0.758135
$826$	−1.48607	−0.0517069
$827$	17.1001	0.594627	0.297314	−	0.954780i	$-0.403909\pi$
$827$	17.1001	0.594627	0.297314	+	0.954780i	$0.403909\pi$
$828$	−3.75854	−0.130618
$829$	−48.9101	−1.69872	−0.849359	−	0.527816i	$-0.823011\pi$
$829$	−48.9101	−1.69872	−0.849359	+	0.527816i	$0.823011\pi$
$830$	−48.2441	−1.67458
$831$	−22.6634	−0.786185
$832$	−3.70693	−0.128515
$833$	4.79160	0.166019
$834$	14.1517	0.490033
$835$	14.5475	0.503436
$836$	1.83578	0.0634919
$837$	5.86726	0.202802
$838$	−21.4162	−0.739809
$839$	−4.00138	−0.138143	−0.0690714	−	0.997612i	$-0.522004\pi$
$839$	−4.00138	−0.138143	−0.0690714	+	0.997612i	$0.522004\pi$
$840$	4.56582	0.157536
$841$	−12.7056	−0.438123
$842$	−6.28069	−0.216447
$843$	25.1519	0.866278
$844$	22.6597	0.779978
$845$	−2.27766	−0.0783538
$846$	5.58129	0.191889
$847$	−19.4025	−0.666676
$848$	0.592697	0.0203533
$849$	1.87698	0.0644179
$850$	−4.43976	−0.152283
$851$	−31.6727	−1.08573
$852$	0.437051	0.0149731
$853$	16.3072	0.558347	0.279173	−	0.960241i	$-0.409940\pi$
$853$	16.3072	0.558347	0.279173	+	0.960241i	$0.409940\pi$
$854$	12.2557	0.419383
$855$	−1.14997	−0.0393283
$856$	10.8555	0.371032
$857$	16.9992	0.580683	0.290341	−	0.956923i	$-0.406231\pi$
$857$	16.9992	0.580683	0.290341	+	0.956923i	$0.406231\pi$
$858$	−18.1814	−0.620704
$859$	−19.8463	−0.677146	−0.338573	−	0.940940i	$-0.609944\pi$
$859$	−19.8463	−0.677146	−0.338573	+	0.940940i	$0.609944\pi$
$860$	−11.8725	−0.404850
$861$	11.1296	0.379294
$862$	−7.56132	−0.257539
$863$	−20.1157	−0.684745	−0.342372	−	0.939564i	$-0.611230\pi$
$863$	−20.1157	−0.684745	−0.342372	+	0.939564i	$0.611230\pi$
$864$	1.00000	0.0340207
$865$	41.5004	1.41106
$866$	−1.99310	−0.0677284
$867$	1.00000	0.0339618
$868$	−8.71915	−0.295947
$869$	24.1805	0.820267
$870$	−12.4022	−0.420475
$871$	−9.62802	−0.326233
$872$	−13.9208	−0.471416
$873$	15.5954	0.527823
$874$	−1.40678	−0.0475852
$875$	−2.55794	−0.0864743
$876$	4.15775	0.140477
$877$	9.88412	0.333763	0.166881	−	0.985977i	$-0.446630\pi$
$877$	9.88412	0.333763	0.166881	+	0.985977i	$0.446630\pi$
$878$	2.58245	0.0871535
$879$	−13.3308	−0.449635
$880$	−15.0693	−0.507988
$881$	10.1000	0.340276	0.170138	−	0.985420i	$-0.445579\pi$
$881$	10.1000	0.340276	0.170138	+	0.985420i	$0.445579\pi$
$882$	−4.79160	−0.161342
$883$	4.47217	0.150501	0.0752503	−	0.997165i	$-0.476024\pi$
$883$	4.47217	0.150501	0.0752503	+	0.997165i	$0.476024\pi$
$884$	3.70693	0.124678
$885$	−3.07242	−0.103278
$886$	1.77660	0.0596860
$887$	−26.2046	−0.879864	−0.439932	−	0.898031i	$-0.644997\pi$
$887$	−26.2046	−0.879864	−0.439932	+	0.898031i	$0.644997\pi$
$888$	8.42687	0.282787
$889$	9.40265	0.315355
$890$	−12.8385	−0.430347
$891$	4.90472	0.164314
$892$	21.5439	0.721344
$893$	2.08902	0.0699063
$894$	9.48677	0.317285
$895$	33.7341	1.12761
$896$	−1.48607	−0.0496460
$897$	13.9326	0.465198
$898$	27.4572	0.916259
$899$	23.6840	0.789906
$900$	4.43976	0.147992
$901$	−0.592697	−0.0197456
$902$	−36.7327	−1.22307
$903$	−5.74251	−0.191099
$904$	4.37971	0.145667
$905$	4.54177	0.150973
$906$	21.9372	0.728813
$907$	18.9377	0.628815	0.314408	−	0.949288i	$-0.398194\pi$
$907$	18.9377	0.628815	0.314408	+	0.949288i	$0.398194\pi$
$908$	12.9102	0.428441
$909$	5.53545	0.183599
$910$	−16.9252	−0.561064
$911$	−10.7129	−0.354936	−0.177468	−	0.984127i	$-0.556791\pi$
$911$	−10.7129	−0.354936	−0.177468	+	0.984127i	$0.556791\pi$
$912$	0.374290	0.0123940
$913$	77.0154	2.54884
$914$	−0.932760	−0.0308529
$915$	25.3385	0.837666
$916$	−26.5168	−0.876141
$917$	8.32427	0.274892
$918$	−1.00000	−0.0330049
$919$	−4.39371	−0.144935	−0.0724675	−	0.997371i	$-0.523087\pi$
$919$	−4.39371	−0.144935	−0.0724675	+	0.997371i	$0.523087\pi$
$920$	11.5478	0.380720
$921$	−5.72146	−0.188529
$922$	8.38031	0.275991
$923$	−1.62012	−0.0533268
$924$	−7.28874	−0.239782
$925$	37.4133	1.23014
$926$	−14.6428	−0.481193
$927$	7.92686	0.260352
$928$	4.03663	0.132509
$929$	−47.1557	−1.54713	−0.773564	−	0.633718i	$-0.781528\pi$
$929$	−47.1557	−1.54713	−0.773564	+	0.633718i	$0.781528\pi$
$930$	−18.0267	−0.591119
$931$	−1.79345	−0.0587779
$932$	7.54608	0.247180
$933$	24.6873	0.808226
$934$	11.3626	0.371797
$935$	15.0693	0.492820
$936$	−3.70693	−0.121165
$937$	−10.4365	−0.340945	−0.170472	−	0.985362i	$-0.554529\pi$
$937$	−10.4365	−0.340945	−0.170472	+	0.985362i	$0.554529\pi$
$938$	−3.85977	−0.126026
$939$	−10.0874	−0.329190
$940$	−17.1481	−0.559308
$941$	49.6539	1.61867	0.809335	−	0.587348i	$-0.199828\pi$
$941$	49.6539	1.61867	0.809335	+	0.587348i	$0.199828\pi$
$942$	−16.7394	−0.545400
$943$	28.1487	0.916648
$944$	1.00000	0.0325472
$945$	4.56582	0.148526
$946$	18.9530	0.616214
$947$	8.33011	0.270692	0.135346	−	0.990798i	$-0.456785\pi$
$947$	8.33011	0.270692	0.135346	+	0.990798i	$0.456785\pi$
$948$	4.93005	0.160121
$949$	−15.4125	−0.500311
$950$	1.66176	0.0539145
$951$	−12.7798	−0.414414
$952$	1.48607	0.0481637
$953$	20.3421	0.658947	0.329473	−	0.944165i	$-0.393129\pi$
$953$	20.3421	0.658947	0.329473	+	0.944165i	$0.393129\pi$
$954$	0.592697	0.0191893
$955$	43.8282	1.41825
$956$	16.5904	0.536572
$957$	19.7986	0.639996
$958$	36.1930	1.16934
$959$	−25.9135	−0.836790
$960$	−3.07242	−0.0991619
$961$	3.42477	0.110476
$962$	−31.2378	−1.00715
$963$	10.8555	0.349812
$964$	−5.88902	−0.189673
$965$	17.2212	0.554371
$966$	5.58544	0.179709
$967$	−10.5458	−0.339130	−0.169565	−	0.985519i	$-0.554236\pi$
$967$	−10.5458	−0.339130	−0.169565	+	0.985519i	$0.554236\pi$
$968$	13.0562	0.419644
$969$	−0.374290	−0.0120239
$970$	−47.9155	−1.53847
$971$	49.1877	1.57851	0.789255	−	0.614066i	$-0.210467\pi$
$971$	49.1877	1.57851	0.789255	+	0.614066i	$0.210467\pi$
$972$	1.00000	0.0320750
$973$	−21.0304	−0.674203
$974$	26.0075	0.833334
$975$	−16.4579	−0.527074
$976$	−8.24709	−0.263983
$977$	7.63098	0.244137	0.122068	−	0.992522i	$-0.461047\pi$
$977$	7.63098	0.244137	0.122068	+	0.992522i	$0.461047\pi$
$978$	−3.99279	−0.127675
$979$	20.4950	0.655022
$980$	14.7218	0.470271
$981$	−13.9208	−0.444456
$982$	16.8295	0.537052
$983$	−57.0839	−1.82069	−0.910346	−	0.413847i	$-0.864185\pi$
$983$	−57.0839	−1.82069	−0.910346	+	0.413847i	$0.864185\pi$
$984$	−7.48927	−0.238749
$985$	−11.1119	−0.354055
$986$	−4.03663	−0.128553
$987$	−8.29416	−0.264006
$988$	−1.38747	−0.0441412
$989$	−14.5239	−0.461832
$990$	−15.0693	−0.478935
$991$	−39.2841	−1.24790	−0.623949	−	0.781465i	$-0.714473\pi$
$991$	−39.2841	−1.24790	−0.623949	+	0.781465i	$0.714473\pi$
$992$	5.86726	0.186286
$993$	4.29789	0.136389
$994$	−0.649487	−0.0206005
$995$	−86.3728	−2.73820
$996$	15.7023	0.497547
$997$	44.2977	1.40292	0.701462	−	0.712707i	$-0.252531\pi$
$997$	44.2977	1.40292	0.701462	+	0.712707i	$0.252531\pi$
$998$	13.7666	0.435774
$999$	8.42687	0.266614

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.07242 q^{5} +1.00000 q^{6} -1.48607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.07242 q^{5} +1.00000 q^{6} -1.48607 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.07242 q^{10} +4.90472 q^{11} +1.00000 q^{12} -3.70693 q^{13} -1.48607 q^{14} -3.07242 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +0.374290 q^{19} -3.07242 q^{20} -1.48607 q^{21} +4.90472 q^{22} -3.75854 q^{23} +1.00000 q^{24} +4.43976 q^{25} -3.70693 q^{26} +1.00000 q^{27} -1.48607 q^{28} +4.03663 q^{29} -3.07242 q^{30} +5.86726 q^{31} +1.00000 q^{32} +4.90472 q^{33} -1.00000 q^{34} +4.56582 q^{35} +1.00000 q^{36} +8.42687 q^{37} +0.374290 q^{38} -3.70693 q^{39} -3.07242 q^{40} -7.48927 q^{41} -1.48607 q^{42} +3.86423 q^{43} +4.90472 q^{44} -3.07242 q^{45} -3.75854 q^{46} +5.58129 q^{47} +1.00000 q^{48} -4.79160 q^{49} +4.43976 q^{50} -1.00000 q^{51} -3.70693 q^{52} +0.592697 q^{53} +1.00000 q^{54} -15.0693 q^{55} -1.48607 q^{56} +0.374290 q^{57} +4.03663 q^{58} +1.00000 q^{59} -3.07242 q^{60} -8.24709 q^{61} +5.86726 q^{62} -1.48607 q^{63} +1.00000 q^{64} +11.3892 q^{65} +4.90472 q^{66} +2.59730 q^{67} -1.00000 q^{68} -3.75854 q^{69} +4.56582 q^{70} +0.437051 q^{71} +1.00000 q^{72} +4.15775 q^{73} +8.42687 q^{74} +4.43976 q^{75} +0.374290 q^{76} -7.28874 q^{77} -3.70693 q^{78} +4.93005 q^{79} -3.07242 q^{80} +1.00000 q^{81} -7.48927 q^{82} +15.7023 q^{83} -1.48607 q^{84} +3.07242 q^{85} +3.86423 q^{86} +4.03663 q^{87} +4.90472 q^{88} +4.17862 q^{89} -3.07242 q^{90} +5.50874 q^{91} -3.75854 q^{92} +5.86726 q^{93} +5.58129 q^{94} -1.14997 q^{95} +1.00000 q^{96} +15.5954 q^{97} -4.79160 q^{98} +4.90472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 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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