LMFDB - Embedded newform 6018.2.a.m.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:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.48119$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.15633 q^{5} -1.00000 q^{6} -2.28726 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.15633 q^{5} -1.00000 q^{6} -2.28726 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.15633 q^{10} -6.31265 q^{11} +1.00000 q^{12} -2.15633 q^{13} +2.28726 q^{14} -2.15633 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -8.11871 q^{19} -2.15633 q^{20} -2.28726 q^{21} +6.31265 q^{22} +1.32487 q^{23} -1.00000 q^{24} -0.350262 q^{25} +2.15633 q^{26} +1.00000 q^{27} -2.28726 q^{28} -0.806063 q^{29} +2.15633 q^{30} -2.00000 q^{31} -1.00000 q^{32} -6.31265 q^{33} +1.00000 q^{34} +4.93207 q^{35} +1.00000 q^{36} -4.93207 q^{37} +8.11871 q^{38} -2.15633 q^{39} +2.15633 q^{40} +4.19394 q^{41} +2.28726 q^{42} -1.35026 q^{43} -6.31265 q^{44} -2.15633 q^{45} -1.32487 q^{46} -3.19394 q^{47} +1.00000 q^{48} -1.76845 q^{49} +0.350262 q^{50} -1.00000 q^{51} -2.15633 q^{52} +6.41327 q^{53} -1.00000 q^{54} +13.6121 q^{55} +2.28726 q^{56} -8.11871 q^{57} +0.806063 q^{58} -1.00000 q^{59} -2.15633 q^{60} -14.3127 q^{61} +2.00000 q^{62} -2.28726 q^{63} +1.00000 q^{64} +4.64974 q^{65} +6.31265 q^{66} -7.19394 q^{67} -1.00000 q^{68} +1.32487 q^{69} -4.93207 q^{70} +6.93207 q^{71} -1.00000 q^{72} +5.80606 q^{73} +4.93207 q^{74} -0.350262 q^{75} -8.11871 q^{76} +14.4387 q^{77} +2.15633 q^{78} +8.34297 q^{79} -2.15633 q^{80} +1.00000 q^{81} -4.19394 q^{82} +9.34297 q^{83} -2.28726 q^{84} +2.15633 q^{85} +1.35026 q^{86} -0.806063 q^{87} +6.31265 q^{88} -0.687350 q^{89} +2.15633 q^{90} +4.93207 q^{91} +1.32487 q^{92} -2.00000 q^{93} +3.19394 q^{94} +17.5066 q^{95} -1.00000 q^{96} -9.00000 q^{97} +1.76845 q^{98} -6.31265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 3 q^{19} + 4 q^{20} - q^{21} - 2 q^{22} + 9 q^{23} - 3 q^{24} + 9 q^{25} - 4 q^{26} + 3 q^{27} - q^{28} - 2 q^{29} - 4 q^{30} - 6 q^{31} - 3 q^{32} + 2 q^{33} + 3 q^{34} + 6 q^{35} + 3 q^{36} - 6 q^{37} + 3 q^{38} + 4 q^{39} - 4 q^{40} + 13 q^{41} + q^{42} + 6 q^{43} + 2 q^{44} + 4 q^{45} - 9 q^{46} - 10 q^{47} + 3 q^{48} + 6 q^{49} - 9 q^{50} - 3 q^{51} + 4 q^{52} + 5 q^{53} - 3 q^{54} + 40 q^{55} + q^{56} - 3 q^{57} + 2 q^{58} - 3 q^{59} + 4 q^{60} - 22 q^{61} + 6 q^{62} - q^{63} + 3 q^{64} + 24 q^{65} - 2 q^{66} - 22 q^{67} - 3 q^{68} + 9 q^{69} - 6 q^{70} + 12 q^{71} - 3 q^{72} + 17 q^{73} + 6 q^{74} + 9 q^{75} - 3 q^{76} + 14 q^{77} - 4 q^{78} + 2 q^{79} + 4 q^{80} + 3 q^{81} - 13 q^{82} + 5 q^{83} - q^{84} - 4 q^{85} - 6 q^{86} - 2 q^{87} - 2 q^{88} - 23 q^{89} - 4 q^{90} + 6 q^{91} + 9 q^{92} - 6 q^{93} + 10 q^{94} + 32 q^{95} - 3 q^{96} - 27 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 - 4 * q^10 + 2 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 4 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 3 * q^19 + 4 * q^20 - q^21 - 2 * q^22 + 9 * q^23 - 3 * q^24 + 9 * q^25 - 4 * q^26 + 3 * q^27 - q^28 - 2 * q^29 - 4 * q^30 - 6 * q^31 - 3 * q^32 + 2 * q^33 + 3 * q^34 + 6 * q^35 + 3 * q^36 - 6 * q^37 + 3 * q^38 + 4 * q^39 - 4 * q^40 + 13 * q^41 + q^42 + 6 * q^43 + 2 * q^44 + 4 * q^45 - 9 * q^46 - 10 * q^47 + 3 * q^48 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 4 * q^52 + 5 * q^53 - 3 * q^54 + 40 * q^55 + q^56 - 3 * q^57 + 2 * q^58 - 3 * q^59 + 4 * q^60 - 22 * q^61 + 6 * q^62 - q^63 + 3 * q^64 + 24 * q^65 - 2 * q^66 - 22 * q^67 - 3 * q^68 + 9 * q^69 - 6 * q^70 + 12 * q^71 - 3 * q^72 + 17 * q^73 + 6 * q^74 + 9 * q^75 - 3 * q^76 + 14 * q^77 - 4 * q^78 + 2 * q^79 + 4 * q^80 + 3 * q^81 - 13 * q^82 + 5 * q^83 - q^84 - 4 * q^85 - 6 * q^86 - 2 * q^87 - 2 * q^88 - 23 * q^89 - 4 * q^90 + 6 * q^91 + 9 * q^92 - 6 * q^93 + 10 * q^94 + 32 * q^95 - 3 * q^96 - 27 * q^97 - 6 * q^98 + 2 * 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
$5$	−2.15633	−0.964338	−0.482169	−	0.876078i	$-0.660151\pi$
$5$	−2.15633	−0.964338	−0.482169	+	0.876078i	$0.660151\pi$
$6$	−1.00000	−0.408248
$7$	−2.28726	−0.864502	−0.432251	−	0.901753i	$-0.642281\pi$
$7$	−2.28726	−0.864502	−0.432251	+	0.901753i	$0.642281\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.15633	0.681890
$11$	−6.31265	−1.90334	−0.951668	−	0.307129i	$-0.900632\pi$
$11$	−6.31265	−1.90334	−0.951668	+	0.307129i	$0.900632\pi$
$12$	1.00000	0.288675
$13$	−2.15633	−0.598057	−0.299028	−	0.954244i	$-0.596663\pi$
$13$	−2.15633	−0.598057	−0.299028	+	0.954244i	$0.596663\pi$
$14$	2.28726	0.611295
$15$	−2.15633	−0.556761
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−8.11871	−1.86256	−0.931280	−	0.364303i	$-0.881307\pi$
$19$	−8.11871	−1.86256	−0.931280	+	0.364303i	$0.881307\pi$
$20$	−2.15633	−0.482169
$21$	−2.28726	−0.499121
$22$	6.31265	1.34586
$23$	1.32487	0.276254	0.138127	−	0.990415i	$-0.455892\pi$
$23$	1.32487	0.276254	0.138127	+	0.990415i	$0.455892\pi$
$24$	−1.00000	−0.204124
$25$	−0.350262	−0.0700523
$26$	2.15633	0.422890
$27$	1.00000	0.192450
$28$	−2.28726	−0.432251
$29$	−0.806063	−0.149682	−0.0748411	−	0.997195i	$-0.523845\pi$
$29$	−0.806063	−0.149682	−0.0748411	+	0.997195i	$0.523845\pi$
$30$	2.15633	0.393689
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	−6.31265	−1.09889
$34$	1.00000	0.171499
$35$	4.93207	0.833672
$36$	1.00000	0.166667
$37$	−4.93207	−0.810828	−0.405414	−	0.914133i	$-0.632873\pi$
$37$	−4.93207	−0.810828	−0.405414	+	0.914133i	$0.632873\pi$
$38$	8.11871	1.31703
$39$	−2.15633	−0.345288
$40$	2.15633	0.340945
$41$	4.19394	0.654983	0.327491	−	0.944854i	$-0.393797\pi$
$41$	4.19394	0.654983	0.327491	+	0.944854i	$0.393797\pi$
$42$	2.28726	0.352932
$43$	−1.35026	−0.205913	−0.102956	−	0.994686i	$-0.532830\pi$
$43$	−1.35026	−0.205913	−0.102956	+	0.994686i	$0.532830\pi$
$44$	−6.31265	−0.951668
$45$	−2.15633	−0.321446
$46$	−1.32487	−0.195341
$47$	−3.19394	−0.465884	−0.232942	−	0.972491i	$-0.574835\pi$
$47$	−3.19394	−0.465884	−0.232942	+	0.972491i	$0.574835\pi$
$48$	1.00000	0.144338
$49$	−1.76845	−0.252636
$50$	0.350262	0.0495345
$51$	−1.00000	−0.140028
$52$	−2.15633	−0.299028
$53$	6.41327	0.880930	0.440465	−	0.897770i	$-0.354814\pi$
$53$	6.41327	0.880930	0.440465	+	0.897770i	$0.354814\pi$
$54$	−1.00000	−0.136083
$55$	13.6121	1.83546
$56$	2.28726	0.305648
$57$	−8.11871	−1.07535
$58$	0.806063	0.105841
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−2.15633	−0.278380
$61$	−14.3127	−1.83255	−0.916274	−	0.400553i	$-0.868818\pi$
$61$	−14.3127	−1.83255	−0.916274	+	0.400553i	$0.868818\pi$
$62$	2.00000	0.254000
$63$	−2.28726	−0.288167
$64$	1.00000	0.125000
$65$	4.64974	0.576729
$66$	6.31265	0.777034
$67$	−7.19394	−0.878879	−0.439440	−	0.898272i	$-0.644823\pi$
$67$	−7.19394	−0.878879	−0.439440	+	0.898272i	$0.644823\pi$
$68$	−1.00000	−0.121268
$69$	1.32487	0.159496
$70$	−4.93207	−0.589495
$71$	6.93207	0.822686	0.411343	−	0.911481i	$-0.365060\pi$
$71$	6.93207	0.822686	0.411343	+	0.911481i	$0.365060\pi$
$72$	−1.00000	−0.117851
$73$	5.80606	0.679548	0.339774	−	0.940507i	$-0.389649\pi$
$73$	5.80606	0.679548	0.339774	+	0.940507i	$0.389649\pi$
$74$	4.93207	0.573342
$75$	−0.350262	−0.0404447
$76$	−8.11871	−0.931280
$77$	14.4387	1.64544
$78$	2.15633	0.244156
$79$	8.34297	0.938657	0.469329	−	0.883024i	$-0.344496\pi$
$79$	8.34297	0.938657	0.469329	+	0.883024i	$0.344496\pi$
$80$	−2.15633	−0.241084
$81$	1.00000	0.111111
$82$	−4.19394	−0.463143
$83$	9.34297	1.02552	0.512762	−	0.858531i	$-0.328622\pi$
$83$	9.34297	1.02552	0.512762	+	0.858531i	$0.328622\pi$
$84$	−2.28726	−0.249560
$85$	2.15633	0.233886
$86$	1.35026	0.145602
$87$	−0.806063	−0.0864191
$88$	6.31265	0.672931
$89$	−0.687350	−0.0728589	−0.0364295	−	0.999336i	$-0.511598\pi$
$89$	−0.687350	−0.0728589	−0.0364295	+	0.999336i	$0.511598\pi$
$90$	2.15633	0.227297
$91$	4.93207	0.517022
$92$	1.32487	0.138127
$93$	−2.00000	−0.207390
$94$	3.19394	0.329429
$95$	17.5066	1.79614
$96$	−1.00000	−0.102062
$97$	−9.00000	−0.913812	−0.456906	−	0.889515i	$-0.651042\pi$
$97$	−9.00000	−0.913812	−0.456906	+	0.889515i	$0.651042\pi$
$98$	1.76845	0.178641
$99$	−6.31265	−0.634445
$100$	−0.350262	−0.0350262
$101$	0.418190	0.0416115	0.0208057	−	0.999784i	$-0.493377\pi$
$101$	0.418190	0.0416115	0.0208057	+	0.999784i	$0.493377\pi$
$102$	1.00000	0.0990148
$103$	−18.9126	−1.86351	−0.931755	−	0.363088i	$-0.881722\pi$
$103$	−18.9126	−1.86351	−0.931755	+	0.363088i	$0.881722\pi$
$104$	2.15633	0.211445
$105$	4.93207	0.481321
$106$	−6.41327	−0.622911
$107$	1.15633	0.111786	0.0558931	−	0.998437i	$-0.482199\pi$
$107$	1.15633	0.111786	0.0558931	+	0.998437i	$0.482199\pi$
$108$	1.00000	0.0962250
$109$	6.05079	0.579560	0.289780	−	0.957093i	$-0.406418\pi$
$109$	6.05079	0.579560	0.289780	+	0.957093i	$0.406418\pi$
$110$	−13.6121	−1.29787
$111$	−4.93207	−0.468132
$112$	−2.28726	−0.216126
$113$	−14.9175	−1.40332	−0.701659	−	0.712513i	$-0.747557\pi$
$113$	−14.9175	−1.40332	−0.701659	+	0.712513i	$0.747557\pi$
$114$	8.11871	0.760387
$115$	−2.85685	−0.266403
$116$	−0.806063	−0.0748411
$117$	−2.15633	−0.199352
$118$	1.00000	0.0920575
$119$	2.28726	0.209673
$120$	2.15633	0.196845
$121$	28.8496	2.62269
$122$	14.3127	1.29581
$123$	4.19394	0.378155
$124$	−2.00000	−0.179605
$125$	11.5369	1.03189
$126$	2.28726	0.203765
$127$	8.28233	0.734938	0.367469	−	0.930036i	$-0.380224\pi$
$127$	8.28233	0.734938	0.367469	+	0.930036i	$0.380224\pi$
$128$	−1.00000	−0.0883883
$129$	−1.35026	−0.118884
$130$	−4.64974	−0.407809
$131$	13.9551	1.21926	0.609631	−	0.792685i	$-0.291318\pi$
$131$	13.9551	1.21926	0.609631	+	0.792685i	$0.291318\pi$
$132$	−6.31265	−0.549446
$133$	18.5696	1.61019
$134$	7.19394	0.621461
$135$	−2.15633	−0.185587
$136$	1.00000	0.0857493
$137$	6.61942	0.565535	0.282768	−	0.959188i	$-0.408747\pi$
$137$	6.61942	0.565535	0.282768	+	0.959188i	$0.408747\pi$
$138$	−1.32487	−0.112780
$139$	4.73084	0.401265	0.200632	−	0.979667i	$-0.435700\pi$
$139$	4.73084	0.401265	0.200632	+	0.979667i	$0.435700\pi$
$140$	4.93207	0.416836
$141$	−3.19394	−0.268978
$142$	−6.93207	−0.581727
$143$	13.6121	1.13830
$144$	1.00000	0.0833333
$145$	1.73813	0.144344
$146$	−5.80606	−0.480513
$147$	−1.76845	−0.145859
$148$	−4.93207	−0.405414
$149$	−14.0508	−1.15109	−0.575543	−	0.817772i	$-0.695209\pi$
$149$	−14.0508	−1.15109	−0.575543	+	0.817772i	$0.695209\pi$
$150$	0.350262	0.0285988
$151$	−2.95746	−0.240675	−0.120338	−	0.992733i	$-0.538398\pi$
$151$	−2.95746	−0.240675	−0.120338	+	0.992733i	$0.538398\pi$
$152$	8.11871	0.658515
$153$	−1.00000	−0.0808452
$154$	−14.4387	−1.16350
$155$	4.31265	0.346400
$156$	−2.15633	−0.172644
$157$	−12.5999	−1.00558	−0.502791	−	0.864408i	$-0.667693\pi$
$157$	−12.5999	−1.00558	−0.502791	+	0.864408i	$0.667693\pi$
$158$	−8.34297	−0.663731
$159$	6.41327	0.508605
$160$	2.15633	0.170472
$161$	−3.03032	−0.238822
$162$	−1.00000	−0.0785674
$163$	12.8568	1.00703	0.503513	−	0.863988i	$-0.332041\pi$
$163$	12.8568	1.00703	0.503513	+	0.863988i	$0.332041\pi$
$164$	4.19394	0.327491
$165$	13.6121	1.05970
$166$	−9.34297	−0.725155
$167$	−5.86414	−0.453781	−0.226891	−	0.973920i	$-0.572856\pi$
$167$	−5.86414	−0.453781	−0.226891	+	0.973920i	$0.572856\pi$
$168$	2.28726	0.176466
$169$	−8.35026	−0.642328
$170$	−2.15633	−0.165383
$171$	−8.11871	−0.620854
$172$	−1.35026	−0.102956
$173$	−17.3561	−1.31956	−0.659781	−	0.751458i	$-0.729351\pi$
$173$	−17.3561	−1.31956	−0.659781	+	0.751458i	$0.729351\pi$
$174$	0.806063	0.0611075
$175$	0.801139	0.0605604
$176$	−6.31265	−0.475834
$177$	−1.00000	−0.0751646
$178$	0.687350	0.0515190
$179$	13.9380	1.04177	0.520886	−	0.853626i	$-0.325602\pi$
$179$	13.9380	1.04177	0.520886	+	0.853626i	$0.325602\pi$
$180$	−2.15633	−0.160723
$181$	−10.4690	−0.778153	−0.389076	−	0.921205i	$-0.627206\pi$
$181$	−10.4690	−0.778153	−0.389076	+	0.921205i	$0.627206\pi$
$182$	−4.93207	−0.365589
$183$	−14.3127	−1.05802
$184$	−1.32487	−0.0976706
$185$	10.6351	0.781912
$186$	2.00000	0.146647
$187$	6.31265	0.461627
$188$	−3.19394	−0.232942
$189$	−2.28726	−0.166374
$190$	−17.5066	−1.27006
$191$	12.0811	0.874158	0.437079	−	0.899423i	$-0.356013\pi$
$191$	12.0811	0.874158	0.437079	+	0.899423i	$0.356013\pi$
$192$	1.00000	0.0721688
$193$	−14.9321	−1.07483	−0.537417	−	0.843317i	$-0.680600\pi$
$193$	−14.9321	−1.07483	−0.537417	+	0.843317i	$0.680600\pi$
$194$	9.00000	0.646162
$195$	4.64974	0.332975
$196$	−1.76845	−0.126318
$197$	−7.42548	−0.529044	−0.264522	−	0.964380i	$-0.585214\pi$
$197$	−7.42548	−0.529044	−0.264522	+	0.964380i	$0.585214\pi$
$198$	6.31265	0.448621
$199$	12.5696	0.891035	0.445517	−	0.895273i	$-0.353020\pi$
$199$	12.5696	0.891035	0.445517	+	0.895273i	$0.353020\pi$
$200$	0.350262	0.0247672
$201$	−7.19394	−0.507421
$202$	−0.418190	−0.0294238
$203$	1.84367	0.129401
$204$	−1.00000	−0.0700140
$205$	−9.04349	−0.631625
$206$	18.9126	1.31770
$207$	1.32487	0.0920848
$208$	−2.15633	−0.149514
$209$	51.2506	3.54508
$210$	−4.93207	−0.340345
$211$	23.5125	1.61866	0.809332	−	0.587351i	$-0.199829\pi$
$211$	23.5125	1.61866	0.809332	+	0.587351i	$0.199829\pi$
$212$	6.41327	0.440465
$213$	6.93207	0.474978
$214$	−1.15633	−0.0790448
$215$	2.91160	0.198570
$216$	−1.00000	−0.0680414
$217$	4.57452	0.310538
$218$	−6.05079	−0.409811
$219$	5.80606	0.392337
$220$	13.6121	0.917729
$221$	2.15633	0.145050
$222$	4.93207	0.331019
$223$	−1.26916	−0.0849892	−0.0424946	−	0.999097i	$-0.513531\pi$
$223$	−1.26916	−0.0849892	−0.0424946	+	0.999097i	$0.513531\pi$
$224$	2.28726	0.152824
$225$	−0.350262	−0.0233508
$226$	14.9175	0.992296
$227$	3.70782	0.246097	0.123048	−	0.992401i	$-0.460733\pi$
$227$	3.70782	0.246097	0.123048	+	0.992401i	$0.460733\pi$
$228$	−8.11871	−0.537675
$229$	−12.0254	−0.794660	−0.397330	−	0.917676i	$-0.630063\pi$
$229$	−12.0254	−0.794660	−0.397330	+	0.917676i	$0.630063\pi$
$230$	2.85685	0.188375
$231$	14.4387	0.949994
$232$	0.806063	0.0529207
$233$	15.9248	1.04327	0.521633	−	0.853170i	$-0.325323\pi$
$233$	15.9248	1.04327	0.521633	+	0.853170i	$0.325323\pi$
$234$	2.15633	0.140963
$235$	6.88717	0.449269
$236$	−1.00000	−0.0650945
$237$	8.34297	0.541934
$238$	−2.28726	−0.148261
$239$	−1.11871	−0.0723636	−0.0361818	−	0.999345i	$-0.511520\pi$
$239$	−1.11871	−0.0723636	−0.0361818	+	0.999345i	$0.511520\pi$
$240$	−2.15633	−0.139190
$241$	−14.5950	−0.940146	−0.470073	−	0.882628i	$-0.655772\pi$
$241$	−14.5950	−0.940146	−0.470073	+	0.882628i	$0.655772\pi$
$242$	−28.8496	−1.85452
$243$	1.00000	0.0641500
$244$	−14.3127	−0.916274
$245$	3.81336	0.243626
$246$	−4.19394	−0.267396
$247$	17.5066	1.11392
$248$	2.00000	0.127000
$249$	9.34297	0.592087
$250$	−11.5369	−0.729658
$251$	3.25457	0.205427	0.102713	−	0.994711i	$-0.467248\pi$
$251$	3.25457	0.205427	0.102713	+	0.994711i	$0.467248\pi$
$252$	−2.28726	−0.144084
$253$	−8.36344	−0.525805
$254$	−8.28233	−0.519680
$255$	2.15633	0.135034
$256$	1.00000	0.0625000
$257$	0.216960	0.0135336	0.00676678	−	0.999977i	$-0.497846\pi$
$257$	0.216960	0.0135336	0.00676678	+	0.999977i	$0.497846\pi$
$258$	1.35026	0.0840636
$259$	11.2809	0.700962
$260$	4.64974	0.288365
$261$	−0.806063	−0.0498941
$262$	−13.9551	−0.862149
$263$	14.7807	0.911415	0.455708	−	0.890130i	$-0.349386\pi$
$263$	14.7807	0.911415	0.455708	+	0.890130i	$0.349386\pi$
$264$	6.31265	0.388517
$265$	−13.8291	−0.849514
$266$	−18.5696	−1.13857
$267$	−0.687350	−0.0420651
$268$	−7.19394	−0.439440
$269$	−9.71862	−0.592555	−0.296277	−	0.955102i	$-0.595745\pi$
$269$	−9.71862	−0.592555	−0.296277	+	0.955102i	$0.595745\pi$
$270$	2.15633	0.131230
$271$	4.18664	0.254320	0.127160	−	0.991882i	$-0.459414\pi$
$271$	4.18664	0.254320	0.127160	+	0.991882i	$0.459414\pi$
$272$	−1.00000	−0.0606339
$273$	4.93207	0.298503
$274$	−6.61942	−0.399894
$275$	2.21108	0.133333
$276$	1.32487	0.0797478
$277$	24.7767	1.48869	0.744344	−	0.667797i	$-0.232762\pi$
$277$	24.7767	1.48869	0.744344	+	0.667797i	$0.232762\pi$
$278$	−4.73084	−0.283737
$279$	−2.00000	−0.119737
$280$	−4.93207	−0.294748
$281$	−18.2677	−1.08976	−0.544881	−	0.838513i	$-0.683425\pi$
$281$	−18.2677	−1.08976	−0.544881	+	0.838513i	$0.683425\pi$
$282$	3.19394	0.190196
$283$	4.81336	0.286124	0.143062	−	0.989714i	$-0.454305\pi$
$283$	4.81336	0.286124	0.143062	+	0.989714i	$0.454305\pi$
$284$	6.93207	0.411343
$285$	17.5066	1.03700
$286$	−13.6121	−0.804902
$287$	−9.59261	−0.566234
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−1.73813	−0.102067
$291$	−9.00000	−0.527589
$292$	5.80606	0.339774
$293$	−16.5442	−0.966522	−0.483261	−	0.875476i	$-0.660548\pi$
$293$	−16.5442	−0.966522	−0.483261	+	0.875476i	$0.660548\pi$
$294$	1.76845	0.103138
$295$	2.15633	0.125546
$296$	4.93207	0.286671
$297$	−6.31265	−0.366297
$298$	14.0508	0.813940
$299$	−2.85685	−0.165216
$300$	−0.350262	−0.0202224
$301$	3.08840	0.178012
$302$	2.95746	0.170183
$303$	0.418190	0.0240244
$304$	−8.11871	−0.465640
$305$	30.8627	1.76719
$306$	1.00000	0.0571662
$307$	−24.7381	−1.41188	−0.705940	−	0.708272i	$-0.749475\pi$
$307$	−24.7381	−1.41188	−0.705940	+	0.708272i	$0.749475\pi$
$308$	14.4387	0.822719
$309$	−18.9126	−1.07590
$310$	−4.31265	−0.244942
$311$	8.08110	0.458237	0.229119	−	0.973399i	$-0.426416\pi$
$311$	8.08110	0.458237	0.229119	+	0.973399i	$0.426416\pi$
$312$	2.15633	0.122078
$313$	8.26187	0.466988	0.233494	−	0.972358i	$-0.424984\pi$
$313$	8.26187	0.466988	0.233494	+	0.972358i	$0.424984\pi$
$314$	12.5999	0.711054
$315$	4.93207	0.277891
$316$	8.34297	0.469329
$317$	−24.9624	−1.40203	−0.701014	−	0.713148i	$-0.747269\pi$
$317$	−24.9624	−1.40203	−0.701014	+	0.713148i	$0.747269\pi$
$318$	−6.41327	−0.359638
$319$	5.08840	0.284896
$320$	−2.15633	−0.120542
$321$	1.15633	0.0645398
$322$	3.03032	0.168873
$323$	8.11871	0.451737
$324$	1.00000	0.0555556
$325$	0.755278	0.0418953
$326$	−12.8568	−0.712075
$327$	6.05079	0.334609
$328$	−4.19394	−0.231571
$329$	7.30536	0.402757
$330$	−13.6121	−0.749323
$331$	5.85097	0.321598	0.160799	−	0.986987i	$-0.448593\pi$
$331$	5.85097	0.321598	0.160799	+	0.986987i	$0.448593\pi$
$332$	9.34297	0.512762
$333$	−4.93207	−0.270276
$334$	5.86414	0.320872
$335$	15.5125	0.847537
$336$	−2.28726	−0.124780
$337$	5.54420	0.302012	0.151006	−	0.988533i	$-0.451749\pi$
$337$	5.54420	0.302012	0.151006	+	0.988533i	$0.451749\pi$
$338$	8.35026	0.454194
$339$	−14.9175	−0.810206
$340$	2.15633	0.116943
$341$	12.6253	0.683698
$342$	8.11871	0.439010
$343$	20.0557	1.08291
$344$	1.35026	0.0728012
$345$	−2.85685	−0.153808
$346$	17.3561	0.933072
$347$	−28.5804	−1.53428	−0.767138	−	0.641482i	$-0.778320\pi$
$347$	−28.5804	−1.53428	−0.767138	+	0.641482i	$0.778320\pi$
$348$	−0.806063	−0.0432095
$349$	−19.7332	−1.05629	−0.528147	−	0.849153i	$-0.677113\pi$
$349$	−19.7332	−1.05629	−0.528147	+	0.849153i	$0.677113\pi$
$350$	−0.801139	−0.0428227
$351$	−2.15633	−0.115096
$352$	6.31265	0.336465
$353$	16.0943	0.856612	0.428306	−	0.903634i	$-0.359111\pi$
$353$	16.0943	0.856612	0.428306	+	0.903634i	$0.359111\pi$
$354$	1.00000	0.0531494
$355$	−14.9478	−0.793347
$356$	−0.687350	−0.0364295
$357$	2.28726	0.121055
$358$	−13.9380	−0.736644
$359$	3.52610	0.186100	0.0930502	−	0.995661i	$-0.470338\pi$
$359$	3.52610	0.186100	0.0930502	+	0.995661i	$0.470338\pi$
$360$	2.15633	0.113648
$361$	46.9135	2.46913
$362$	10.4690	0.550237
$363$	28.8496	1.51421
$364$	4.93207	0.258511
$365$	−12.5198	−0.655314
$366$	14.3127	0.748134
$367$	14.0508	0.733445	0.366723	−	0.930330i	$-0.380480\pi$
$367$	14.0508	0.733445	0.366723	+	0.930330i	$0.380480\pi$
$368$	1.32487	0.0690636
$369$	4.19394	0.218328
$370$	−10.6351	−0.552895
$371$	−14.6688	−0.761566
$372$	−2.00000	−0.103695
$373$	2.20711	0.114280	0.0571399	−	0.998366i	$-0.481802\pi$
$373$	2.20711	0.114280	0.0571399	+	0.998366i	$0.481802\pi$
$374$	−6.31265	−0.326419
$375$	11.5369	0.595763
$376$	3.19394	0.164715
$377$	1.73813	0.0895185
$378$	2.28726	0.117644
$379$	−23.2750	−1.19556	−0.597779	−	0.801661i	$-0.703950\pi$
$379$	−23.2750	−1.19556	−0.597779	+	0.801661i	$0.703950\pi$
$380$	17.5066	0.898069
$381$	8.28233	0.424317
$382$	−12.0811	−0.618123
$383$	−24.1514	−1.23408	−0.617039	−	0.786932i	$-0.711668\pi$
$383$	−24.1514	−1.23408	−0.617039	+	0.786932i	$0.711668\pi$
$384$	−1.00000	−0.0510310
$385$	−31.1344	−1.58676
$386$	14.9321	0.760022
$387$	−1.35026	−0.0686377
$388$	−9.00000	−0.456906
$389$	1.25931	0.0638496	0.0319248	−	0.999490i	$-0.489836\pi$
$389$	1.25931	0.0638496	0.0319248	+	0.999490i	$0.489836\pi$
$390$	−4.64974	−0.235449
$391$	−1.32487	−0.0670015
$392$	1.76845	0.0893203
$393$	13.9551	0.703941
$394$	7.42548	0.374091
$395$	−17.9902	−0.905183
$396$	−6.31265	−0.317223
$397$	31.9307	1.60255	0.801277	−	0.598294i	$-0.204154\pi$
$397$	31.9307	1.60255	0.801277	+	0.598294i	$0.204154\pi$
$398$	−12.5696	−0.630057
$399$	18.5696	0.929642
$400$	−0.350262	−0.0175131
$401$	−12.3430	−0.616378	−0.308189	−	0.951325i	$-0.599723\pi$
$401$	−12.3430	−0.616378	−0.308189	+	0.951325i	$0.599723\pi$
$402$	7.19394	0.358801
$403$	4.31265	0.214828
$404$	0.418190	0.0208057
$405$	−2.15633	−0.107149
$406$	−1.84367	−0.0915000
$407$	31.1344	1.54328
$408$	1.00000	0.0495074
$409$	−14.5237	−0.718152	−0.359076	−	0.933308i	$-0.616908\pi$
$409$	−14.5237	−0.718152	−0.359076	+	0.933308i	$0.616908\pi$
$410$	9.04349	0.446626
$411$	6.61942	0.326512
$412$	−18.9126	−0.931755
$413$	2.28726	0.112549
$414$	−1.32487	−0.0651138
$415$	−20.1465	−0.988952
$416$	2.15633	0.105723
$417$	4.73084	0.231670
$418$	−51.2506	−2.50675
$419$	−29.5936	−1.44574	−0.722870	−	0.690984i	$-0.757178\pi$
$419$	−29.5936	−1.44574	−0.722870	+	0.690984i	$0.757178\pi$
$420$	4.93207	0.240660
$421$	−2.47390	−0.120571	−0.0602853	−	0.998181i	$-0.519201\pi$
$421$	−2.47390	−0.120571	−0.0602853	+	0.998181i	$0.519201\pi$
$422$	−23.5125	−1.14457
$423$	−3.19394	−0.155295
$424$	−6.41327	−0.311456
$425$	0.350262	0.0169902
$426$	−6.93207	−0.335860
$427$	32.7367	1.58424
$428$	1.15633	0.0558931
$429$	13.6121	0.657200
$430$	−2.91160	−0.140410
$431$	38.4046	1.84988	0.924941	−	0.380110i	$-0.124114\pi$
$431$	38.4046	1.84988	0.924941	+	0.380110i	$0.124114\pi$
$432$	1.00000	0.0481125
$433$	0.476270	0.0228881	0.0114440	−	0.999935i	$-0.496357\pi$
$433$	0.476270	0.0228881	0.0114440	+	0.999935i	$0.496357\pi$
$434$	−4.57452	−0.219584
$435$	1.73813	0.0833372
$436$	6.05079	0.289780
$437$	−10.7562	−0.514540
$438$	−5.80606	−0.277424
$439$	−23.0435	−1.09981	−0.549903	−	0.835229i	$-0.685335\pi$
$439$	−23.0435	−1.09981	−0.549903	+	0.835229i	$0.685335\pi$
$440$	−13.6121	−0.648933
$441$	−1.76845	−0.0842120
$442$	−2.15633	−0.102566
$443$	−30.3620	−1.44254	−0.721272	−	0.692652i	$-0.756442\pi$
$443$	−30.3620	−1.44254	−0.721272	+	0.692652i	$0.756442\pi$
$444$	−4.93207	−0.234066
$445$	1.48215	0.0702606
$446$	1.26916	0.0600964
$447$	−14.0508	−0.664579
$448$	−2.28726	−0.108063
$449$	−36.2506	−1.71077	−0.855386	−	0.517991i	$-0.826680\pi$
$449$	−36.2506	−1.71077	−0.855386	+	0.517991i	$0.826680\pi$
$450$	0.350262	0.0165115
$451$	−26.4749	−1.24665
$452$	−14.9175	−0.701659
$453$	−2.95746	−0.138954
$454$	−3.70782	−0.174017
$455$	−10.6351	−0.498584
$456$	8.11871	0.380194
$457$	−2.02047	−0.0945135	−0.0472568	−	0.998883i	$-0.515048\pi$
$457$	−2.02047	−0.0945135	−0.0472568	+	0.998883i	$0.515048\pi$
$458$	12.0254	0.561910
$459$	−1.00000	−0.0466760
$460$	−2.85685	−0.133201
$461$	31.1138	1.44911	0.724557	−	0.689215i	$-0.242044\pi$
$461$	31.1138	1.44911	0.724557	+	0.689215i	$0.242044\pi$
$462$	−14.4387	−0.671747
$463$	20.5950	0.957130	0.478565	−	0.878052i	$-0.341157\pi$
$463$	20.5950	0.957130	0.478565	+	0.878052i	$0.341157\pi$
$464$	−0.806063	−0.0374206
$465$	4.31265	0.199994
$466$	−15.9248	−0.737701
$467$	21.4617	0.993128	0.496564	−	0.868000i	$-0.334595\pi$
$467$	21.4617	0.993128	0.496564	+	0.868000i	$0.334595\pi$
$468$	−2.15633	−0.0996762
$469$	16.4544	0.759793
$470$	−6.88717	−0.317681
$471$	−12.5999	−0.580573
$472$	1.00000	0.0460287
$473$	8.52373	0.391922
$474$	−8.34297	−0.383205
$475$	2.84367	0.130477
$476$	2.28726	0.104836
$477$	6.41327	0.293643
$478$	1.11871	0.0511688
$479$	16.5139	0.754538	0.377269	−	0.926104i	$-0.376863\pi$
$479$	16.5139	0.754538	0.377269	+	0.926104i	$0.376863\pi$
$480$	2.15633	0.0984223
$481$	10.6351	0.484921
$482$	14.5950	0.664783
$483$	−3.03032	−0.137884
$484$	28.8496	1.31134
$485$	19.4069	0.881223
$486$	−1.00000	−0.0453609
$487$	3.15396	0.142919	0.0714597	−	0.997443i	$-0.477234\pi$
$487$	3.15396	0.142919	0.0714597	+	0.997443i	$0.477234\pi$
$488$	14.3127	0.647903
$489$	12.8568	0.581407
$490$	−3.81336	−0.172270
$491$	17.1187	0.772557	0.386278	−	0.922382i	$-0.373760\pi$
$491$	17.1187	0.772557	0.386278	+	0.922382i	$0.373760\pi$
$492$	4.19394	0.189077
$493$	0.806063	0.0363033
$494$	−17.5066	−0.787659
$495$	13.6121	0.611820
$496$	−2.00000	−0.0898027
$497$	−15.8554	−0.711213
$498$	−9.34297	−0.418668
$499$	−26.2677	−1.17591	−0.587953	−	0.808895i	$-0.700066\pi$
$499$	−26.2677	−1.17591	−0.587953	+	0.808895i	$0.700066\pi$
$500$	11.5369	0.515946
$501$	−5.86414	−0.261991
$502$	−3.25457	−0.145259
$503$	18.9575	0.845272	0.422636	−	0.906300i	$-0.361105\pi$
$503$	18.9575	0.845272	0.422636	+	0.906300i	$0.361105\pi$
$504$	2.28726	0.101883
$505$	−0.901754	−0.0401275
$506$	8.36344	0.371800
$507$	−8.35026	−0.370848
$508$	8.28233	0.367469
$509$	1.35026	0.0598493	0.0299246	−	0.999552i	$-0.490473\pi$
$509$	1.35026	0.0598493	0.0299246	+	0.999552i	$0.490473\pi$
$510$	−2.15633	−0.0954837
$511$	−13.2800	−0.587471
$512$	−1.00000	−0.0441942
$513$	−8.11871	−0.358450
$514$	−0.216960	−0.00956967
$515$	40.7816	1.79705
$516$	−1.35026	−0.0594420
$517$	20.1622	0.886733
$518$	−11.2809	−0.495655
$519$	−17.3561	−0.761850
$520$	−4.64974	−0.203905
$521$	−28.0738	−1.22994	−0.614968	−	0.788552i	$-0.710831\pi$
$521$	−28.0738	−1.22994	−0.614968	+	0.788552i	$0.710831\pi$
$522$	0.806063	0.0352804
$523$	−23.1392	−1.01181	−0.505903	−	0.862590i	$-0.668841\pi$
$523$	−23.1392	−1.01181	−0.505903	+	0.862590i	$0.668841\pi$
$524$	13.9551	0.609631
$525$	0.801139	0.0349646
$526$	−14.7807	−0.644468
$527$	2.00000	0.0871214
$528$	−6.31265	−0.274723
$529$	−21.2447	−0.923684
$530$	13.8291	0.600697
$531$	−1.00000	−0.0433963
$532$	18.5696	0.805094
$533$	−9.04349	−0.391717
$534$	0.687350	0.0297445
$535$	−2.49341	−0.107800
$536$	7.19394	0.310731
$537$	13.9380	0.601467
$538$	9.71862	0.419000
$539$	11.1636	0.480851
$540$	−2.15633	−0.0927935
$541$	0.523730	0.0225169	0.0112585	−	0.999937i	$-0.496416\pi$
$541$	0.523730	0.0225169	0.0112585	+	0.999937i	$0.496416\pi$
$542$	−4.18664	−0.179832
$543$	−10.4690	−0.449267
$544$	1.00000	0.0428746
$545$	−13.0475	−0.558892
$546$	−4.93207	−0.211073
$547$	−40.8383	−1.74612	−0.873060	−	0.487613i	$-0.837868\pi$
$547$	−40.8383	−1.74612	−0.873060	+	0.487613i	$0.837868\pi$
$548$	6.61942	0.282768
$549$	−14.3127	−0.610849
$550$	−2.21108	−0.0942808
$551$	6.54420	0.278792
$552$	−1.32487	−0.0563902
$553$	−19.0825	−0.811471
$554$	−24.7767	−1.05266
$555$	10.6351	0.451437
$556$	4.73084	0.200632
$557$	−0.881286	−0.0373413	−0.0186706	−	0.999826i	$-0.505943\pi$
$557$	−0.881286	−0.0373413	−0.0186706	+	0.999826i	$0.505943\pi$
$558$	2.00000	0.0846668
$559$	2.91160	0.123148
$560$	4.93207	0.208418
$561$	6.31265	0.266520
$562$	18.2677	0.770578
$563$	12.7381	0.536848	0.268424	−	0.963301i	$-0.413497\pi$
$563$	12.7381	0.536848	0.268424	+	0.963301i	$0.413497\pi$
$564$	−3.19394	−0.134489
$565$	32.1669	1.35327
$566$	−4.81336	−0.202321
$567$	−2.28726	−0.0960558
$568$	−6.93207	−0.290863
$569$	27.6497	1.15914	0.579569	−	0.814923i	$-0.303221\pi$
$569$	27.6497	1.15914	0.579569	+	0.814923i	$0.303221\pi$
$570$	−17.5066	−0.733270
$571$	−45.3792	−1.89906	−0.949529	−	0.313678i	$-0.898439\pi$
$571$	−45.3792	−1.89906	−0.949529	+	0.313678i	$0.898439\pi$
$572$	13.6121	0.569152
$573$	12.0811	0.504695
$574$	9.59261	0.400388
$575$	−0.464051	−0.0193523
$576$	1.00000	0.0416667
$577$	−20.0870	−0.836232	−0.418116	−	0.908394i	$-0.637309\pi$
$577$	−20.0870	−0.836232	−0.418116	+	0.908394i	$0.637309\pi$
$578$	−1.00000	−0.0415945
$579$	−14.9321	−0.620556
$580$	1.73813	0.0721721
$581$	−21.3698	−0.886568
$582$	9.00000	0.373062
$583$	−40.4847	−1.67671
$584$	−5.80606	−0.240257
$585$	4.64974	0.192243
$586$	16.5442	0.683435
$587$	−9.31853	−0.384617	−0.192308	−	0.981335i	$-0.561597\pi$
$587$	−9.31853	−0.384617	−0.192308	+	0.981335i	$0.561597\pi$
$588$	−1.76845	−0.0729297
$589$	16.2374	0.669052
$590$	−2.15633	−0.0887745
$591$	−7.42548	−0.305444
$592$	−4.93207	−0.202707
$593$	−20.6009	−0.845976	−0.422988	−	0.906135i	$-0.639019\pi$
$593$	−20.6009	−0.845976	−0.422988	+	0.906135i	$0.639019\pi$
$594$	6.31265	0.259011
$595$	−4.93207	−0.202195
$596$	−14.0508	−0.575543
$597$	12.5696	0.514439
$598$	2.85685	0.116825
$599$	−18.1368	−0.741050	−0.370525	−	0.928822i	$-0.620822\pi$
$599$	−18.1368	−0.741050	−0.370525	+	0.928822i	$0.620822\pi$
$600$	0.350262	0.0142994
$601$	4.73813	0.193273	0.0966363	−	0.995320i	$-0.469192\pi$
$601$	4.73813	0.193273	0.0966363	+	0.995320i	$0.469192\pi$
$602$	−3.08840	−0.125874
$603$	−7.19394	−0.292960
$604$	−2.95746	−0.120338
$605$	−62.2090	−2.52916
$606$	−0.418190	−0.0169878
$607$	20.7464	0.842070	0.421035	−	0.907044i	$-0.361667\pi$
$607$	20.7464	0.842070	0.421035	+	0.907044i	$0.361667\pi$
$608$	8.11871	0.329257
$609$	1.84367	0.0747095
$610$	−30.8627	−1.24960
$611$	6.88717	0.278625
$612$	−1.00000	−0.0404226
$613$	15.0425	0.607562	0.303781	−	0.952742i	$-0.401751\pi$
$613$	15.0425	0.607562	0.303781	+	0.952742i	$0.401751\pi$
$614$	24.7381	0.998350
$615$	−9.04349	−0.364669
$616$	−14.4387	−0.581750
$617$	15.2315	0.613199	0.306600	−	0.951839i	$-0.400809\pi$
$617$	15.2315	0.613199	0.306600	+	0.951839i	$0.400809\pi$
$618$	18.9126	0.760775
$619$	38.5950	1.55126	0.775632	−	0.631186i	$-0.217431\pi$
$619$	38.5950	1.55126	0.775632	+	0.631186i	$0.217431\pi$
$620$	4.31265	0.173200
$621$	1.32487	0.0531652
$622$	−8.08110	−0.324023
$623$	1.57215	0.0629867
$624$	−2.15633	−0.0863221
$625$	−23.1260	−0.925040
$626$	−8.26187	−0.330211
$627$	51.2506	2.04675
$628$	−12.5999	−0.502791
$629$	4.93207	0.196655
$630$	−4.93207	−0.196498
$631$	−12.3733	−0.492573	−0.246286	−	0.969197i	$-0.579210\pi$
$631$	−12.3733	−0.492573	−0.246286	+	0.969197i	$0.579210\pi$
$632$	−8.34297	−0.331865
$633$	23.5125	0.934537
$634$	24.9624	0.991383
$635$	−17.8594	−0.708729
$636$	6.41327	0.254303
$637$	3.81336	0.151091
$638$	−5.08840	−0.201452
$639$	6.93207	0.274229
$640$	2.15633	0.0852362
$641$	25.3185	1.00002	0.500011	−	0.866019i	$-0.333329\pi$
$641$	25.3185	1.00002	0.500011	+	0.866019i	$0.333329\pi$
$642$	−1.15633	−0.0456365
$643$	46.8930	1.84928	0.924641	−	0.380841i	$-0.124365\pi$
$643$	46.8930	1.84928	0.924641	+	0.380841i	$0.124365\pi$
$644$	−3.03032	−0.119411
$645$	2.91160	0.114644
$646$	−8.11871	−0.319427
$647$	18.6243	0.732199	0.366099	−	0.930576i	$-0.380693\pi$
$647$	18.6243	0.732199	0.366099	+	0.930576i	$0.380693\pi$
$648$	−1.00000	−0.0392837
$649$	6.31265	0.247793
$650$	−0.755278	−0.0296244
$651$	4.57452	0.179289
$652$	12.8568	0.503513
$653$	9.28489	0.363346	0.181673	−	0.983359i	$-0.441849\pi$
$653$	9.28489	0.363346	0.181673	+	0.983359i	$0.441849\pi$
$654$	−6.05079	−0.236604
$655$	−30.0917	−1.17578
$656$	4.19394	0.163746
$657$	5.80606	0.226516
$658$	−7.30536	−0.284792
$659$	−4.70782	−0.183391	−0.0916953	−	0.995787i	$-0.529229\pi$
$659$	−4.70782	−0.183391	−0.0916953	+	0.995787i	$0.529229\pi$
$660$	13.6121	0.529851
$661$	39.5369	1.53781	0.768904	−	0.639365i	$-0.220803\pi$
$661$	39.5369	1.53781	0.768904	+	0.639365i	$0.220803\pi$
$662$	−5.85097	−0.227404
$663$	2.15633	0.0837447
$664$	−9.34297	−0.362577
$665$	−40.0421	−1.55277
$666$	4.93207	0.191114
$667$	−1.06793	−0.0413504
$668$	−5.86414	−0.226891
$669$	−1.26916	−0.0490685
$670$	−15.5125	−0.599299
$671$	90.3508	3.48795
$672$	2.28726	0.0882329
$673$	−7.41231	−0.285724	−0.142862	−	0.989743i	$-0.545630\pi$
$673$	−7.41231	−0.285724	−0.142862	+	0.989743i	$0.545630\pi$
$674$	−5.54420	−0.213555
$675$	−0.350262	−0.0134816
$676$	−8.35026	−0.321164
$677$	−18.9584	−0.728631	−0.364316	−	0.931276i	$-0.618697\pi$
$677$	−18.9584	−0.728631	−0.364316	+	0.931276i	$0.618697\pi$
$678$	14.9175	0.572902
$679$	20.5853	0.789992
$680$	−2.15633	−0.0826913
$681$	3.70782	0.142084
$682$	−12.6253	−0.483448
$683$	19.3660	0.741019	0.370510	−	0.928829i	$-0.379183\pi$
$683$	19.3660	0.741019	0.370510	+	0.928829i	$0.379183\pi$
$684$	−8.11871	−0.310427
$685$	−14.2736	−0.545367
$686$	−20.0557	−0.765731
$687$	−12.0254	−0.458797
$688$	−1.35026	−0.0514782
$689$	−13.8291	−0.526846
$690$	2.85685	0.108758
$691$	−50.3971	−1.91720	−0.958598	−	0.284764i	$-0.908085\pi$
$691$	−50.3971	−1.91720	−0.958598	+	0.284764i	$0.908085\pi$
$692$	−17.3561	−0.659781
$693$	14.4387	0.548479
$694$	28.5804	1.08490
$695$	−10.2012	−0.386955
$696$	0.806063	0.0305538
$697$	−4.19394	−0.158857
$698$	19.7332	0.746913
$699$	15.9248	0.602330
$700$	0.801139	0.0302802
$701$	8.71511	0.329165	0.164583	−	0.986363i	$-0.447372\pi$
$701$	8.71511	0.329165	0.164583	+	0.986363i	$0.447372\pi$
$702$	2.15633	0.0813852
$703$	40.0421	1.51022
$704$	−6.31265	−0.237917
$705$	6.88717	0.259386
$706$	−16.0943	−0.605716
$707$	−0.956509	−0.0359732
$708$	−1.00000	−0.0375823
$709$	1.63259	0.0613134	0.0306567	−	0.999530i	$-0.490240\pi$
$709$	1.63259	0.0613134	0.0306567	+	0.999530i	$0.490240\pi$
$710$	14.9478	0.560981
$711$	8.34297	0.312886
$712$	0.687350	0.0257595
$713$	−2.64974	−0.0992335
$714$	−2.28726	−0.0855985
$715$	−29.3522	−1.09771
$716$	13.9380	0.520886
$717$	−1.11871	−0.0417791
$718$	−3.52610	−0.131593
$719$	−8.59498	−0.320539	−0.160269	−	0.987073i	$-0.551236\pi$
$719$	−8.59498	−0.320539	−0.160269	+	0.987073i	$0.551236\pi$
$720$	−2.15633	−0.0803615
$721$	43.2579	1.61101
$722$	−46.9135	−1.74594
$723$	−14.5950	−0.542793
$724$	−10.4690	−0.389076
$725$	0.282333	0.0104856
$726$	−28.8496	−1.07071
$727$	−49.3054	−1.82863	−0.914317	−	0.404999i	$-0.867272\pi$
$727$	−49.3054	−1.82863	−0.914317	+	0.404999i	$0.867272\pi$
$728$	−4.93207	−0.182795
$729$	1.00000	0.0370370
$730$	12.5198	0.463377
$731$	1.35026	0.0499412
$732$	−14.3127	−0.529011
$733$	14.1055	0.521000	0.260500	−	0.965474i	$-0.416113\pi$
$733$	14.1055	0.521000	0.260500	+	0.965474i	$0.416113\pi$
$734$	−14.0508	−0.518624
$735$	3.81336	0.140658
$736$	−1.32487	−0.0488353
$737$	45.4128	1.67280
$738$	−4.19394	−0.154381
$739$	−7.87399	−0.289649	−0.144825	−	0.989457i	$-0.546262\pi$
$739$	−7.87399	−0.289649	−0.144825	+	0.989457i	$0.546262\pi$
$740$	10.6351	0.390956
$741$	17.5066	0.643121
$742$	14.6688	0.538508
$743$	24.9868	0.916678	0.458339	−	0.888778i	$-0.348445\pi$
$743$	24.9868	0.916678	0.458339	+	0.888778i	$0.348445\pi$
$744$	2.00000	0.0733236
$745$	30.2981	1.11004
$746$	−2.20711	−0.0808081
$747$	9.34297	0.341841
$748$	6.31265	0.230813
$749$	−2.64481	−0.0966394
$750$	−11.5369	−0.421268
$751$	2.93207	0.106993	0.0534964	−	0.998568i	$-0.482963\pi$
$751$	2.93207	0.106993	0.0534964	+	0.998568i	$0.482963\pi$
$752$	−3.19394	−0.116471
$753$	3.25457	0.118603
$754$	−1.73813	−0.0632991
$755$	6.37725	0.232092
$756$	−2.28726	−0.0831868
$757$	14.8364	0.539237	0.269619	−	0.962967i	$-0.413102\pi$
$757$	14.8364	0.539237	0.269619	+	0.962967i	$0.413102\pi$
$758$	23.2750	0.845387
$759$	−8.36344	−0.303573
$760$	−17.5066	−0.635031
$761$	36.2784	1.31509	0.657545	−	0.753415i	$-0.271595\pi$
$761$	36.2784	1.31509	0.657545	+	0.753415i	$0.271595\pi$
$762$	−8.28233	−0.300037
$763$	−13.8397	−0.501031
$764$	12.0811	0.437079
$765$	2.15633	0.0779621
$766$	24.1514	0.872626
$767$	2.15633	0.0778604
$768$	1.00000	0.0360844
$769$	12.6556	0.456373	0.228187	−	0.973617i	$-0.426720\pi$
$769$	12.6556	0.456373	0.228187	+	0.973617i	$0.426720\pi$
$770$	31.1344	1.12201
$771$	0.216960	0.00781361
$772$	−14.9321	−0.537417
$773$	−31.7196	−1.14087	−0.570437	−	0.821341i	$-0.693226\pi$
$773$	−31.7196	−1.14087	−0.570437	+	0.821341i	$0.693226\pi$
$774$	1.35026	0.0485342
$775$	0.700523	0.0251635
$776$	9.00000	0.323081
$777$	11.2809	0.404701
$778$	−1.25931	−0.0451485
$779$	−34.0494	−1.21995
$780$	4.64974	0.166487
$781$	−43.7597	−1.56585
$782$	1.32487	0.0473772
$783$	−0.806063	−0.0288064
$784$	−1.76845	−0.0631590
$785$	27.1695	0.969721
$786$	−13.9551	−0.497762
$787$	15.6267	0.557032	0.278516	−	0.960432i	$-0.410157\pi$
$787$	15.6267	0.557032	0.278516	+	0.960432i	$0.410157\pi$
$788$	−7.42548	−0.264522
$789$	14.7807	0.526206
$790$	17.9902	0.640061
$791$	34.1201	1.21317
$792$	6.31265	0.224310
$793$	30.8627	1.09597
$794$	−31.9307	−1.13318
$795$	−13.8291	−0.490467
$796$	12.5696	0.445517
$797$	−16.1319	−0.571421	−0.285710	−	0.958316i	$-0.592230\pi$
$797$	−16.1319	−0.571421	−0.285710	+	0.958316i	$0.592230\pi$
$798$	−18.5696	−0.657356
$799$	3.19394	0.112993
$800$	0.350262	0.0123836
$801$	−0.687350	−0.0242863
$802$	12.3430	0.435845
$803$	−36.6516	−1.29341
$804$	−7.19394	−0.253711
$805$	6.53435	0.230306
$806$	−4.31265	−0.151907
$807$	−9.71862	−0.342112
$808$	−0.418190	−0.0147119
$809$	−25.2447	−0.887557	−0.443779	−	0.896136i	$-0.646362\pi$
$809$	−25.2447	−0.887557	−0.443779	+	0.896136i	$0.646362\pi$
$810$	2.15633	0.0757655
$811$	11.4532	0.402178	0.201089	−	0.979573i	$-0.435552\pi$
$811$	11.4532	0.402178	0.201089	+	0.979573i	$0.435552\pi$
$812$	1.84367	0.0647003
$813$	4.18664	0.146832
$814$	−31.1344	−1.09126
$815$	−27.7235	−0.971113
$816$	−1.00000	−0.0350070
$817$	10.9624	0.383525
$818$	14.5237	0.507810
$819$	4.93207	0.172341
$820$	−9.04349	−0.315812
$821$	46.6869	1.62938	0.814692	−	0.579894i	$-0.196906\pi$
$821$	46.6869	1.62938	0.814692	+	0.579894i	$0.196906\pi$
$822$	−6.61942	−0.230879
$823$	40.2736	1.40385	0.701925	−	0.712251i	$-0.252324\pi$
$823$	40.2736	1.40385	0.701925	+	0.712251i	$0.252324\pi$
$824$	18.9126	0.658850
$825$	2.21108	0.0769799
$826$	−2.28726	−0.0795839
$827$	30.6121	1.06449	0.532244	−	0.846591i	$-0.321349\pi$
$827$	30.6121	1.06449	0.532244	+	0.846591i	$0.321349\pi$
$828$	1.32487	0.0460424
$829$	4.88129	0.169534	0.0847670	−	0.996401i	$-0.472985\pi$
$829$	4.88129	0.169534	0.0847670	+	0.996401i	$0.472985\pi$
$830$	20.1465	0.699294
$831$	24.7767	0.859494
$832$	−2.15633	−0.0747571
$833$	1.76845	0.0612732
$834$	−4.73084	−0.163816
$835$	12.6450	0.437598
$836$	51.2506	1.77254
$837$	−2.00000	−0.0691301
$838$	29.5936	1.02229
$839$	28.9194	0.998408	0.499204	−	0.866484i	$-0.333626\pi$
$839$	28.9194	0.998408	0.499204	+	0.866484i	$0.333626\pi$
$840$	−4.93207	−0.170173
$841$	−28.3503	−0.977595
$842$	2.47390	0.0852562
$843$	−18.2677	−0.629175
$844$	23.5125	0.809332
$845$	18.0059	0.619421
$846$	3.19394	0.109810
$847$	−65.9864	−2.26732
$848$	6.41327	0.220232
$849$	4.81336	0.165194
$850$	−0.350262	−0.0120139
$851$	−6.53435	−0.223995
$852$	6.93207	0.237489
$853$	47.7850	1.63613	0.818063	−	0.575129i	$-0.195048\pi$
$853$	47.7850	1.63613	0.818063	+	0.575129i	$0.195048\pi$
$854$	−32.7367	−1.12023
$855$	17.5066	0.598713
$856$	−1.15633	−0.0395224
$857$	7.38058	0.252116	0.126058	−	0.992023i	$-0.459767\pi$
$857$	7.38058	0.252116	0.126058	+	0.992023i	$0.459767\pi$
$858$	−13.6121	−0.464710
$859$	−31.9161	−1.08896	−0.544481	−	0.838773i	$-0.683273\pi$
$859$	−31.9161	−1.08896	−0.544481	+	0.838773i	$0.683273\pi$
$860$	2.91160	0.0992849
$861$	−9.59261	−0.326915
$862$	−38.4046	−1.30806
$863$	−0.619421	−0.0210853	−0.0105427	−	0.999944i	$-0.503356\pi$
$863$	−0.619421	−0.0210853	−0.0105427	+	0.999944i	$0.503356\pi$
$864$	−1.00000	−0.0340207
$865$	37.4255	1.27250
$866$	−0.476270	−0.0161843
$867$	1.00000	0.0339618
$868$	4.57452	0.155269
$869$	−52.6662	−1.78658
$870$	−1.73813	−0.0589283
$871$	15.5125	0.525620
$872$	−6.05079	−0.204905
$873$	−9.00000	−0.304604
$874$	10.7562	0.363835
$875$	−26.3879	−0.892073
$876$	5.80606	0.196169
$877$	−11.6923	−0.394820	−0.197410	−	0.980321i	$-0.563253\pi$
$877$	−11.6923	−0.394820	−0.197410	+	0.980321i	$0.563253\pi$
$878$	23.0435	0.777680
$879$	−16.5442	−0.558022
$880$	13.6121	0.458865
$881$	−25.8594	−0.871225	−0.435613	−	0.900134i	$-0.643468\pi$
$881$	−25.8594	−0.871225	−0.435613	+	0.900134i	$0.643468\pi$
$882$	1.76845	0.0595469
$883$	−32.8397	−1.10514	−0.552572	−	0.833465i	$-0.686354\pi$
$883$	−32.8397	−1.10514	−0.552572	+	0.833465i	$0.686354\pi$
$884$	2.15633	0.0725251
$885$	2.15633	0.0724841
$886$	30.3620	1.02003
$887$	55.1197	1.85074	0.925369	−	0.379068i	$-0.123755\pi$
$887$	55.1197	1.85074	0.925369	+	0.379068i	$0.123755\pi$
$888$	4.93207	0.165509
$889$	−18.9438	−0.635356
$890$	−1.48215	−0.0496818
$891$	−6.31265	−0.211482
$892$	−1.26916	−0.0424946
$893$	25.9307	0.867736
$894$	14.0508	0.469929
$895$	−30.0548	−1.00462
$896$	2.28726	0.0764119
$897$	−2.85685	−0.0953874
$898$	36.2506	1.20970
$899$	1.61213	0.0537674
$900$	−0.350262	−0.0116754
$901$	−6.41327	−0.213657
$902$	26.4749	0.881516
$903$	3.08840	0.102775
$904$	14.9175	0.496148
$905$	22.5745	0.750402
$906$	2.95746	0.0982552
$907$	8.27645	0.274815	0.137408	−	0.990515i	$-0.456123\pi$
$907$	8.27645	0.274815	0.137408	+	0.990515i	$0.456123\pi$
$908$	3.70782	0.123048
$909$	0.418190	0.0138705
$910$	10.6351	0.352552
$911$	−38.3284	−1.26988	−0.634938	−	0.772563i	$-0.718974\pi$
$911$	−38.3284	−1.26988	−0.634938	+	0.772563i	$0.718974\pi$
$912$	−8.11871	−0.268837
$913$	−58.9789	−1.95192
$914$	2.02047	0.0668311
$915$	30.8627	1.02029
$916$	−12.0254	−0.397330
$917$	−31.9189	−1.05405
$918$	1.00000	0.0330049
$919$	15.2349	0.502552	0.251276	−	0.967915i	$-0.419150\pi$
$919$	15.2349	0.502552	0.251276	+	0.967915i	$0.419150\pi$
$920$	2.85685	0.0941875
$921$	−24.7381	−0.815149
$922$	−31.1138	−1.02468
$923$	−14.9478	−0.492013
$924$	14.4387	0.474997
$925$	1.72752	0.0568004
$926$	−20.5950	−0.676793
$927$	−18.9126	−0.621170
$928$	0.806063	0.0264603
$929$	−13.4109	−0.439997	−0.219999	−	0.975500i	$-0.570605\pi$
$929$	−13.4109	−0.439997	−0.219999	+	0.975500i	$0.570605\pi$
$930$	−4.31265	−0.141417
$931$	14.3576	0.470550
$932$	15.9248	0.521633
$933$	8.08110	0.264563
$934$	−21.4617	−0.702248
$935$	−13.6121	−0.445164
$936$	2.15633	0.0704817
$937$	8.69067	0.283912	0.141956	−	0.989873i	$-0.454661\pi$
$937$	8.69067	0.283912	0.141956	+	0.989873i	$0.454661\pi$
$938$	−16.4544	−0.537255
$939$	8.26187	0.269616
$940$	6.88717	0.224635
$941$	−16.2814	−0.530758	−0.265379	−	0.964144i	$-0.585497\pi$
$941$	−16.2814	−0.530758	−0.265379	+	0.964144i	$0.585497\pi$
$942$	12.5999	0.410527
$943$	5.55642	0.180942
$944$	−1.00000	−0.0325472
$945$	4.93207	0.160440
$946$	−8.52373	−0.277130
$947$	−31.8930	−1.03638	−0.518192	−	0.855264i	$-0.673395\pi$
$947$	−31.8930	−1.03638	−0.518192	+	0.855264i	$0.673395\pi$
$948$	8.34297	0.270967
$949$	−12.5198	−0.406409
$950$	−2.84367	−0.0922610
$951$	−24.9624	−0.809461
$952$	−2.28726	−0.0741304
$953$	7.11283	0.230407	0.115204	−	0.993342i	$-0.463248\pi$
$953$	7.11283	0.230407	0.115204	+	0.993342i	$0.463248\pi$
$954$	−6.41327	−0.207637
$955$	−26.0508	−0.842984
$956$	−1.11871	−0.0361818
$957$	5.08840	0.164485
$958$	−16.5139	−0.533539
$959$	−15.1403	−0.488907
$960$	−2.15633	−0.0695951
$961$	−27.0000	−0.870968
$962$	−10.6351	−0.342891
$963$	1.15633	0.0372621
$964$	−14.5950	−0.470073
$965$	32.1984	1.03650
$966$	3.03032	0.0974989
$967$	−0.0312722	−0.00100565	−0.000502823	−	1.00000i	$-0.500160\pi$
$967$	−0.0312722	−0.00100565	−0.000502823		1.00000i	$0.500160\pi$
$968$	−28.8496	−0.927260
$969$	8.11871	0.260811
$970$	−19.4069	−0.623119
$971$	−14.7104	−0.472078	−0.236039	−	0.971744i	$-0.575849\pi$
$971$	−14.7104	−0.472078	−0.236039	+	0.971744i	$0.575849\pi$
$972$	1.00000	0.0320750
$973$	−10.8207	−0.346894
$974$	−3.15396	−0.101059
$975$	0.755278	0.0241883
$976$	−14.3127	−0.458137
$977$	48.4044	1.54859	0.774297	−	0.632823i	$-0.218104\pi$
$977$	48.4044	1.54859	0.774297	+	0.632823i	$0.218104\pi$
$978$	−12.8568	−0.411117
$979$	4.33900	0.138675
$980$	3.81336	0.121813
$981$	6.05079	0.193187
$982$	−17.1187	−0.546280
$983$	−27.9805	−0.892439	−0.446219	−	0.894924i	$-0.647230\pi$
$983$	−27.9805	−0.892439	−0.446219	+	0.894924i	$0.647230\pi$
$984$	−4.19394	−0.133698
$985$	16.0118	0.510177
$986$	−0.806063	−0.0256703
$987$	7.30536	0.232532
$988$	17.5066	0.556959
$989$	−1.78892	−0.0568843
$990$	−13.6121	−0.432622
$991$	19.3806	0.615644	0.307822	−	0.951444i	$-0.400400\pi$
$991$	19.3806	0.615644	0.307822	+	0.951444i	$0.400400\pi$
$992$	2.00000	0.0635001
$993$	5.85097	0.185675
$994$	15.8554	0.502904
$995$	−27.1041	−0.859259
$996$	9.34297	0.296043
$997$	0.605788	0.0191855	0.00959274	−	0.999954i	$-0.496946\pi$
$997$	0.605788	0.0191855	0.00959274	+	0.999954i	$0.496946\pi$
$998$	26.2677	0.831491
$999$	−4.93207	−0.156044

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.m.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.m.1.1	✓	3	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.15633 q^{5} -1.00000 q^{6} -2.28726 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.15633 q^{5} -1.00000 q^{6} -2.28726 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.15633 q^{10} -6.31265 q^{11} +1.00000 q^{12} -2.15633 q^{13} +2.28726 q^{14} -2.15633 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -8.11871 q^{19} -2.15633 q^{20} -2.28726 q^{21} +6.31265 q^{22} +1.32487 q^{23} -1.00000 q^{24} -0.350262 q^{25} +2.15633 q^{26} +1.00000 q^{27} -2.28726 q^{28} -0.806063 q^{29} +2.15633 q^{30} -2.00000 q^{31} -1.00000 q^{32} -6.31265 q^{33} +1.00000 q^{34} +4.93207 q^{35} +1.00000 q^{36} -4.93207 q^{37} +8.11871 q^{38} -2.15633 q^{39} +2.15633 q^{40} +4.19394 q^{41} +2.28726 q^{42} -1.35026 q^{43} -6.31265 q^{44} -2.15633 q^{45} -1.32487 q^{46} -3.19394 q^{47} +1.00000 q^{48} -1.76845 q^{49} +0.350262 q^{50} -1.00000 q^{51} -2.15633 q^{52} +6.41327 q^{53} -1.00000 q^{54} +13.6121 q^{55} +2.28726 q^{56} -8.11871 q^{57} +0.806063 q^{58} -1.00000 q^{59} -2.15633 q^{60} -14.3127 q^{61} +2.00000 q^{62} -2.28726 q^{63} +1.00000 q^{64} +4.64974 q^{65} +6.31265 q^{66} -7.19394 q^{67} -1.00000 q^{68} +1.32487 q^{69} -4.93207 q^{70} +6.93207 q^{71} -1.00000 q^{72} +5.80606 q^{73} +4.93207 q^{74} -0.350262 q^{75} -8.11871 q^{76} +14.4387 q^{77} +2.15633 q^{78} +8.34297 q^{79} -2.15633 q^{80} +1.00000 q^{81} -4.19394 q^{82} +9.34297 q^{83} -2.28726 q^{84} +2.15633 q^{85} +1.35026 q^{86} -0.806063 q^{87} +6.31265 q^{88} -0.687350 q^{89} +2.15633 q^{90} +4.93207 q^{91} +1.32487 q^{92} -2.00000 q^{93} +3.19394 q^{94} +17.5066 q^{95} -1.00000 q^{96} -9.00000 q^{97} +1.76845 q^{98} -6.31265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 3 q^{19} + 4 q^{20} - q^{21} - 2 q^{22} + 9 q^{23} - 3 q^{24} + 9 q^{25} - 4 q^{26} + 3 q^{27} - q^{28} - 2 q^{29} - 4 q^{30} - 6 q^{31} - 3 q^{32} + 2 q^{33} + 3 q^{34} + 6 q^{35} + 3 q^{36} - 6 q^{37} + 3 q^{38} + 4 q^{39} - 4 q^{40} + 13 q^{41} + q^{42} + 6 q^{43} + 2 q^{44} + 4 q^{45} - 9 q^{46} - 10 q^{47} + 3 q^{48} + 6 q^{49} - 9 q^{50} - 3 q^{51} + 4 q^{52} + 5 q^{53} - 3 q^{54} + 40 q^{55} + q^{56} - 3 q^{57} + 2 q^{58} - 3 q^{59} + 4 q^{60} - 22 q^{61} + 6 q^{62} - q^{63} + 3 q^{64} + 24 q^{65} - 2 q^{66} - 22 q^{67} - 3 q^{68} + 9 q^{69} - 6 q^{70} + 12 q^{71} - 3 q^{72} + 17 q^{73} + 6 q^{74} + 9 q^{75} - 3 q^{76} + 14 q^{77} - 4 q^{78} + 2 q^{79} + 4 q^{80} + 3 q^{81} - 13 q^{82} + 5 q^{83} - q^{84} - 4 q^{85} - 6 q^{86} - 2 q^{87} - 2 q^{88} - 23 q^{89} - 4 q^{90} + 6 q^{91} + 9 q^{92} - 6 q^{93} + 10 q^{94} + 32 q^{95} - 3 q^{96} - 27 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 - 4 * q^10 + 2 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 4 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 3 * q^19 + 4 * q^20 - q^21 - 2 * q^22 + 9 * q^23 - 3 * q^24 + 9 * q^25 - 4 * q^26 + 3 * q^27 - q^28 - 2 * q^29 - 4 * q^30 - 6 * q^31 - 3 * q^32 + 2 * q^33 + 3 * q^34 + 6 * q^35 + 3 * q^36 - 6 * q^37 + 3 * q^38 + 4 * q^39 - 4 * q^40 + 13 * q^41 + q^42 + 6 * q^43 + 2 * q^44 + 4 * q^45 - 9 * q^46 - 10 * q^47 + 3 * q^48 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 4 * q^52 + 5 * q^53 - 3 * q^54 + 40 * q^55 + q^56 - 3 * q^57 + 2 * q^58 - 3 * q^59 + 4 * q^60 - 22 * q^61 + 6 * q^62 - q^63 + 3 * q^64 + 24 * q^65 - 2 * q^66 - 22 * q^67 - 3 * q^68 + 9 * q^69 - 6 * q^70 + 12 * q^71 - 3 * q^72 + 17 * q^73 + 6 * q^74 + 9 * q^75 - 3 * q^76 + 14 * q^77 - 4 * q^78 + 2 * q^79 + 4 * q^80 + 3 * q^81 - 13 * q^82 + 5 * q^83 - q^84 - 4 * q^85 - 6 * q^86 - 2 * q^87 - 2 * q^88 - 23 * q^89 - 4 * q^90 + 6 * q^91 + 9 * q^92 - 6 * q^93 + 10 * q^94 + 32 * q^95 - 3 * q^96 - 27 * q^97 - 6 * q^98 + 2 * q^99

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