LMFDB - Embedded newform 6018.2.a.v.1.9

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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 21x^{7} + 42x^{6} + 121x^{5} - 127x^{4} - 141x^{3} + 27x^{2} + 26x - 1 $ x^9 - 3x^8 - 21x^7 + 42x^6 + 121x^5 - 127x^4 - 141x^3 + 27x^2 + 26x - 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			1.9
Root			$-3.19847$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.19847 q^{5} +1.00000 q^{6} -2.69790 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.19847 q^{5} +1.00000 q^{6} -2.69790 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.19847 q^{10} +1.19484 q^{11} -1.00000 q^{12} -4.58356 q^{13} +2.69790 q^{14} -4.19847 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -1.48304 q^{19} +4.19847 q^{20} +2.69790 q^{21} -1.19484 q^{22} -7.59828 q^{23} +1.00000 q^{24} +12.6271 q^{25} +4.58356 q^{26} -1.00000 q^{27} -2.69790 q^{28} +1.17977 q^{29} +4.19847 q^{30} +4.98944 q^{31} -1.00000 q^{32} -1.19484 q^{33} +1.00000 q^{34} -11.3271 q^{35} +1.00000 q^{36} +0.394811 q^{37} +1.48304 q^{38} +4.58356 q^{39} -4.19847 q^{40} +8.27729 q^{41} -2.69790 q^{42} -0.00309616 q^{43} +1.19484 q^{44} +4.19847 q^{45} +7.59828 q^{46} +2.16664 q^{47} -1.00000 q^{48} +0.278679 q^{49} -12.6271 q^{50} +1.00000 q^{51} -4.58356 q^{52} -4.75723 q^{53} +1.00000 q^{54} +5.01649 q^{55} +2.69790 q^{56} +1.48304 q^{57} -1.17977 q^{58} -1.00000 q^{59} -4.19847 q^{60} +3.91284 q^{61} -4.98944 q^{62} -2.69790 q^{63} +1.00000 q^{64} -19.2439 q^{65} +1.19484 q^{66} +13.6349 q^{67} -1.00000 q^{68} +7.59828 q^{69} +11.3271 q^{70} -12.7395 q^{71} -1.00000 q^{72} -2.98757 q^{73} -0.394811 q^{74} -12.6271 q^{75} -1.48304 q^{76} -3.22356 q^{77} -4.58356 q^{78} +6.59838 q^{79} +4.19847 q^{80} +1.00000 q^{81} -8.27729 q^{82} -15.7167 q^{83} +2.69790 q^{84} -4.19847 q^{85} +0.00309616 q^{86} -1.17977 q^{87} -1.19484 q^{88} +2.83334 q^{89} -4.19847 q^{90} +12.3660 q^{91} -7.59828 q^{92} -4.98944 q^{93} -2.16664 q^{94} -6.22651 q^{95} +1.00000 q^{96} -19.2681 q^{97} -0.278679 q^{98} +1.19484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9} - 6 q^{10} + q^{11} - 9 q^{12} + 4 q^{13} + 11 q^{14} - 6 q^{15} + 9 q^{16} - 9 q^{17} - 9 q^{18} - 13 q^{19} + 6 q^{20} + 11 q^{21} - q^{22} - 6 q^{23} + 9 q^{24} + 9 q^{25} - 4 q^{26} - 9 q^{27} - 11 q^{28} + 10 q^{29} + 6 q^{30} + q^{31} - 9 q^{32} - q^{33} + 9 q^{34} + 6 q^{35} + 9 q^{36} - 2 q^{37} + 13 q^{38} - 4 q^{39} - 6 q^{40} + 20 q^{41} - 11 q^{42} - 17 q^{43} + q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 9 q^{48} + 2 q^{49} - 9 q^{50} + 9 q^{51} + 4 q^{52} + 16 q^{53} + 9 q^{54} - 17 q^{55} + 11 q^{56} + 13 q^{57} - 10 q^{58} - 9 q^{59} - 6 q^{60} - 9 q^{61} - q^{62} - 11 q^{63} + 9 q^{64} + q^{66} - 8 q^{67} - 9 q^{68} + 6 q^{69} - 6 q^{70} - 8 q^{71} - 9 q^{72} - 20 q^{73} + 2 q^{74} - 9 q^{75} - 13 q^{76} - 32 q^{77} + 4 q^{78} - 29 q^{79} + 6 q^{80} + 9 q^{81} - 20 q^{82} - 16 q^{83} + 11 q^{84} - 6 q^{85} + 17 q^{86} - 10 q^{87} - q^{88} + 11 q^{89} - 6 q^{90} - 13 q^{91} - 6 q^{92} - q^{93} - 4 q^{94} + 5 q^{95} + 9 q^{96} + 17 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9 - 6 * q^10 + q^11 - 9 * q^12 + 4 * q^13 + 11 * q^14 - 6 * q^15 + 9 * q^16 - 9 * q^17 - 9 * q^18 - 13 * q^19 + 6 * q^20 + 11 * q^21 - q^22 - 6 * q^23 + 9 * q^24 + 9 * q^25 - 4 * q^26 - 9 * q^27 - 11 * q^28 + 10 * q^29 + 6 * q^30 + q^31 - 9 * q^32 - q^33 + 9 * q^34 + 6 * q^35 + 9 * q^36 - 2 * q^37 + 13 * q^38 - 4 * q^39 - 6 * q^40 + 20 * q^41 - 11 * q^42 - 17 * q^43 + q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 - 9 * q^50 + 9 * q^51 + 4 * q^52 + 16 * q^53 + 9 * q^54 - 17 * q^55 + 11 * q^56 + 13 * q^57 - 10 * q^58 - 9 * q^59 - 6 * q^60 - 9 * q^61 - q^62 - 11 * q^63 + 9 * q^64 + q^66 - 8 * q^67 - 9 * q^68 + 6 * q^69 - 6 * q^70 - 8 * q^71 - 9 * q^72 - 20 * q^73 + 2 * q^74 - 9 * q^75 - 13 * q^76 - 32 * q^77 + 4 * q^78 - 29 * q^79 + 6 * q^80 + 9 * q^81 - 20 * q^82 - 16 * q^83 + 11 * q^84 - 6 * q^85 + 17 * q^86 - 10 * q^87 - q^88 + 11 * q^89 - 6 * q^90 - 13 * q^91 - 6 * q^92 - q^93 - 4 * q^94 + 5 * q^95 + 9 * q^96 + 17 * q^97 - 2 * q^98 + 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
$5$	4.19847	1.87761	0.938806	−	0.344447i	$-0.111934\pi$
$5$	4.19847	1.87761	0.938806	+	0.344447i	$0.111934\pi$
$6$	1.00000	0.408248
$7$	−2.69790	−1.01971	−0.509856	−	0.860260i	$-0.670301\pi$
$7$	−2.69790	−1.01971	−0.509856	+	0.860260i	$0.670301\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.19847	−1.32767
$11$	1.19484	0.360258	0.180129	−	0.983643i	$-0.442349\pi$
$11$	1.19484	0.360258	0.180129	+	0.983643i	$0.442349\pi$
$12$	−1.00000	−0.288675
$13$	−4.58356	−1.27125	−0.635625	−	0.771998i	$-0.719258\pi$
$13$	−4.58356	−1.27125	−0.635625	+	0.771998i	$0.719258\pi$
$14$	2.69790	0.721045
$15$	−4.19847	−1.08404
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−1.48304	−0.340233	−0.170117	−	0.985424i	$-0.554414\pi$
$19$	−1.48304	−0.340233	−0.170117	+	0.985424i	$0.554414\pi$
$20$	4.19847	0.938806
$21$	2.69790	0.588731
$22$	−1.19484	−0.254741
$23$	−7.59828	−1.58435	−0.792176	−	0.610293i	$-0.791052\pi$
$23$	−7.59828	−1.58435	−0.792176	+	0.610293i	$0.791052\pi$
$24$	1.00000	0.204124
$25$	12.6271	2.52542
$26$	4.58356	0.898910
$27$	−1.00000	−0.192450
$28$	−2.69790	−0.509856
$29$	1.17977	0.219077	0.109539	−	0.993983i	$-0.465063\pi$
$29$	1.17977	0.219077	0.109539	+	0.993983i	$0.465063\pi$
$30$	4.19847	0.766532
$31$	4.98944	0.896129	0.448065	−	0.894001i	$-0.352113\pi$
$31$	4.98944	0.896129	0.448065	+	0.894001i	$0.352113\pi$
$32$	−1.00000	−0.176777
$33$	−1.19484	−0.207995
$34$	1.00000	0.171499
$35$	−11.3271	−1.91462
$36$	1.00000	0.166667
$37$	0.394811	0.0649066	0.0324533	−	0.999473i	$-0.489668\pi$
$37$	0.394811	0.0649066	0.0324533	+	0.999473i	$0.489668\pi$
$38$	1.48304	0.240581
$39$	4.58356	0.733957
$40$	−4.19847	−0.663836
$41$	8.27729	1.29270	0.646348	−	0.763043i	$-0.276296\pi$
$41$	8.27729	1.29270	0.646348	+	0.763043i	$0.276296\pi$
$42$	−2.69790	−0.416295
$43$	−0.00309616	−0.000472160 0	−0.000236080	−	1.00000i	$-0.500075\pi$
$43$	−0.00309616	−0.000472160 0	−0.000236080		1.00000i	$0.500075\pi$
$44$	1.19484	0.180129
$45$	4.19847	0.625870
$46$	7.59828	1.12031
$47$	2.16664	0.316037	0.158018	−	0.987436i	$-0.449489\pi$
$47$	2.16664	0.316037	0.158018	+	0.987436i	$0.449489\pi$
$48$	−1.00000	−0.144338
$49$	0.278679	0.0398113
$50$	−12.6271	−1.78574
$51$	1.00000	0.140028
$52$	−4.58356	−0.635625
$53$	−4.75723	−0.653455	−0.326728	−	0.945119i	$-0.605946\pi$
$53$	−4.75723	−0.653455	−0.326728	+	0.945119i	$0.605946\pi$
$54$	1.00000	0.136083
$55$	5.01649	0.676424
$56$	2.69790	0.360522
$57$	1.48304	0.196434
$58$	−1.17977	−0.154911
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−4.19847	−0.542020
$61$	3.91284	0.500988	0.250494	−	0.968118i	$-0.419407\pi$
$61$	3.91284	0.500988	0.250494	+	0.968118i	$0.419407\pi$
$62$	−4.98944	−0.633659
$63$	−2.69790	−0.339904
$64$	1.00000	0.125000
$65$	−19.2439	−2.38691
$66$	1.19484	0.147075
$67$	13.6349	1.66577	0.832886	−	0.553445i	$-0.186687\pi$
$67$	13.6349	1.66577	0.832886	+	0.553445i	$0.186687\pi$
$68$	−1.00000	−0.121268
$69$	7.59828	0.914726
$70$	11.3271	1.35384
$71$	−12.7395	−1.51190	−0.755949	−	0.654631i	$-0.772824\pi$
$71$	−12.7395	−1.51190	−0.755949	+	0.654631i	$0.772824\pi$
$72$	−1.00000	−0.117851
$73$	−2.98757	−0.349669	−0.174834	−	0.984598i	$-0.555939\pi$
$73$	−2.98757	−0.349669	−0.174834	+	0.984598i	$0.555939\pi$
$74$	−0.394811	−0.0458959
$75$	−12.6271	−1.45805
$76$	−1.48304	−0.170117
$77$	−3.22356	−0.367359
$78$	−4.58356	−0.518986
$79$	6.59838	0.742375	0.371188	−	0.928558i	$-0.378951\pi$
$79$	6.59838	0.742375	0.371188	+	0.928558i	$0.378951\pi$
$80$	4.19847	0.469403
$81$	1.00000	0.111111
$82$	−8.27729	−0.914073
$83$	−15.7167	−1.72513	−0.862566	−	0.505945i	$-0.831144\pi$
$83$	−15.7167	−1.72513	−0.862566	+	0.505945i	$0.831144\pi$
$84$	2.69790	0.294365
$85$	−4.19847	−0.455388
$86$	0.00309616	0.000333867 0
$87$	−1.17977	−0.126484
$88$	−1.19484	−0.127370
$89$	2.83334	0.300334	0.150167	−	0.988661i	$-0.452019\pi$
$89$	2.83334	0.300334	0.150167	+	0.988661i	$0.452019\pi$
$90$	−4.19847	−0.442557
$91$	12.3660	1.29631
$92$	−7.59828	−0.792176
$93$	−4.98944	−0.517380
$94$	−2.16664	−0.223472
$95$	−6.22651	−0.638826
$96$	1.00000	0.102062
$97$	−19.2681	−1.95638	−0.978191	−	0.207707i	$-0.933400\pi$
$97$	−19.2681	−1.95638	−0.978191	+	0.207707i	$0.933400\pi$
$98$	−0.278679	−0.0281508
$99$	1.19484	0.120086
$100$	12.6271	1.26271
$101$	4.25817	0.423704	0.211852	−	0.977302i	$-0.432051\pi$
$101$	4.25817	0.423704	0.211852	+	0.977302i	$0.432051\pi$
$102$	−1.00000	−0.0990148
$103$	3.05007	0.300533	0.150266	−	0.988646i	$-0.451987\pi$
$103$	3.05007	0.300533	0.150266	+	0.988646i	$0.451987\pi$
$104$	4.58356	0.449455
$105$	11.3271	1.10541
$106$	4.75723	0.462063
$107$	−16.9305	−1.63673	−0.818365	−	0.574698i	$-0.805119\pi$
$107$	−16.9305	−1.63673	−0.818365	+	0.574698i	$0.805119\pi$
$108$	−1.00000	−0.0962250
$109$	−1.60794	−0.154012	−0.0770062	−	0.997031i	$-0.524536\pi$
$109$	−1.60794	−0.154012	−0.0770062	+	0.997031i	$0.524536\pi$
$110$	−5.01649	−0.478304
$111$	−0.394811	−0.0374738
$112$	−2.69790	−0.254928
$113$	8.51072	0.800621	0.400310	−	0.916380i	$-0.368902\pi$
$113$	8.51072	0.800621	0.400310	+	0.916380i	$0.368902\pi$
$114$	−1.48304	−0.138900
$115$	−31.9011	−2.97480
$116$	1.17977	0.109539
$117$	−4.58356	−0.423750
$118$	1.00000	0.0920575
$119$	2.69790	0.247316
$120$	4.19847	0.383266
$121$	−9.57236	−0.870214
$122$	−3.91284	−0.354252
$123$	−8.27729	−0.746338
$124$	4.98944	0.448065
$125$	32.0222	2.86415
$126$	2.69790	0.240348
$127$	−17.2206	−1.52808	−0.764039	−	0.645170i	$-0.776787\pi$
$127$	−17.2206	−1.52808	−0.764039	+	0.645170i	$0.776787\pi$
$128$	−1.00000	−0.0883883
$129$	0.00309616	0.000272602 0
$130$	19.2439	1.68780
$131$	−1.15783	−0.101160	−0.0505801	−	0.998720i	$-0.516107\pi$
$131$	−1.15783	−0.101160	−0.0505801	+	0.998720i	$0.516107\pi$
$132$	−1.19484	−0.103997
$133$	4.00111	0.346940
$134$	−13.6349	−1.17788
$135$	−4.19847	−0.361346
$136$	1.00000	0.0857493
$137$	−8.37755	−0.715742	−0.357871	−	0.933771i	$-0.616497\pi$
$137$	−8.37755	−0.715742	−0.357871	+	0.933771i	$0.616497\pi$
$138$	−7.59828	−0.646809
$139$	−17.2546	−1.46351	−0.731756	−	0.681567i	$-0.761299\pi$
$139$	−17.2546	−1.46351	−0.731756	+	0.681567i	$0.761299\pi$
$140$	−11.3271	−0.957311
$141$	−2.16664	−0.182464
$142$	12.7395	1.06907
$143$	−5.47662	−0.457978
$144$	1.00000	0.0833333
$145$	4.95322	0.411342
$146$	2.98757	0.247253
$147$	−0.278679	−0.0229851
$148$	0.394811	0.0324533
$149$	3.14451	0.257608	0.128804	−	0.991670i	$-0.458886\pi$
$149$	3.14451	0.257608	0.128804	+	0.991670i	$0.458886\pi$
$150$	12.6271	1.03100
$151$	−13.6425	−1.11021	−0.555107	−	0.831779i	$-0.687323\pi$
$151$	−13.6425	−1.11021	−0.555107	+	0.831779i	$0.687323\pi$
$152$	1.48304	0.120291
$153$	−1.00000	−0.0808452
$154$	3.22356	0.259762
$155$	20.9480	1.68258
$156$	4.58356	0.366978
$157$	−15.5140	−1.23815	−0.619076	−	0.785331i	$-0.712493\pi$
$157$	−15.5140	−1.23815	−0.619076	+	0.785331i	$0.712493\pi$
$158$	−6.59838	−0.524939
$159$	4.75723	0.377273
$160$	−4.19847	−0.331918
$161$	20.4994	1.61558
$162$	−1.00000	−0.0785674
$163$	8.51597	0.667022	0.333511	−	0.942746i	$-0.391767\pi$
$163$	8.51597	0.667022	0.333511	+	0.942746i	$0.391767\pi$
$164$	8.27729	0.646348
$165$	−5.01649	−0.390533
$166$	15.7167	1.21985
$167$	−19.0854	−1.47687	−0.738435	−	0.674325i	$-0.764435\pi$
$167$	−19.0854	−1.47687	−0.738435	+	0.674325i	$0.764435\pi$
$168$	−2.69790	−0.208148
$169$	8.00901	0.616078
$170$	4.19847	0.322008
$171$	−1.48304	−0.113411
$172$	−0.00309616	−0.000236080 0
$173$	12.8947	0.980367	0.490184	−	0.871619i	$-0.336930\pi$
$173$	12.8947	0.980367	0.490184	+	0.871619i	$0.336930\pi$
$174$	1.17977	0.0894380
$175$	−34.0667	−2.57520
$176$	1.19484	0.0900644
$177$	1.00000	0.0751646
$178$	−2.83334	−0.212368
$179$	−23.4879	−1.75557	−0.877783	−	0.479059i	$-0.840978\pi$
$179$	−23.4879	−1.75557	−0.877783	+	0.479059i	$0.840978\pi$
$180$	4.19847	0.312935
$181$	4.21008	0.312933	0.156466	−	0.987683i	$-0.449990\pi$
$181$	4.21008	0.312933	0.156466	+	0.987683i	$0.449990\pi$
$182$	−12.3660	−0.916629
$183$	−3.91284	−0.289246
$184$	7.59828	0.560153
$185$	1.65760	0.121869
$186$	4.98944	0.365843
$187$	−1.19484	−0.0873753
$188$	2.16664	0.158018
$189$	2.69790	0.196244
$190$	6.22651	0.451718
$191$	16.7182	1.20969	0.604845	−	0.796343i	$-0.293235\pi$
$191$	16.7182	1.20969	0.604845	+	0.796343i	$0.293235\pi$
$192$	−1.00000	−0.0721688
$193$	9.00012	0.647843	0.323922	−	0.946084i	$-0.394999\pi$
$193$	9.00012	0.647843	0.323922	+	0.946084i	$0.394999\pi$
$194$	19.2681	1.38337
$195$	19.2439	1.37809
$196$	0.278679	0.0199056
$197$	−22.3042	−1.58911	−0.794555	−	0.607192i	$-0.792296\pi$
$197$	−22.3042	−1.58911	−0.794555	+	0.607192i	$0.792296\pi$
$198$	−1.19484	−0.0849135
$199$	−14.2741	−1.01187	−0.505934	−	0.862572i	$-0.668852\pi$
$199$	−14.2741	−1.01187	−0.505934	+	0.862572i	$0.668852\pi$
$200$	−12.6271	−0.892872
$201$	−13.6349	−0.961733
$202$	−4.25817	−0.299604
$203$	−3.18290	−0.223396
$204$	1.00000	0.0700140
$205$	34.7519	2.42718
$206$	−3.05007	−0.212509
$207$	−7.59828	−0.528117
$208$	−4.58356	−0.317813
$209$	−1.77200	−0.122572
$210$	−11.3271	−0.781641
$211$	0.526892	0.0362728	0.0181364	−	0.999836i	$-0.494227\pi$
$211$	0.526892	0.0362728	0.0181364	+	0.999836i	$0.494227\pi$
$212$	−4.75723	−0.326728
$213$	12.7395	0.872894
$214$	16.9305	1.15734
$215$	−0.0129991	−0.000886533 0
$216$	1.00000	0.0680414
$217$	−13.4610	−0.913793
$218$	1.60794	0.108903
$219$	2.98757	0.201881
$220$	5.01649	0.338212
$221$	4.58356	0.308324
$222$	0.394811	0.0264980
$223$	10.6178	0.711018	0.355509	−	0.934673i	$-0.384308\pi$
$223$	10.6178	0.711018	0.355509	+	0.934673i	$0.384308\pi$
$224$	2.69790	0.180261
$225$	12.6271	0.841808
$226$	−8.51072	−0.566125
$227$	20.6494	1.37055	0.685274	−	0.728286i	$-0.259683\pi$
$227$	20.6494	1.37055	0.685274	+	0.728286i	$0.259683\pi$
$228$	1.48304	0.0982169
$229$	16.4578	1.08756	0.543779	−	0.839228i	$-0.316993\pi$
$229$	16.4578	1.08756	0.543779	+	0.839228i	$0.316993\pi$
$230$	31.9011	2.10350
$231$	3.22356	0.212095
$232$	−1.17977	−0.0774556
$233$	22.0591	1.44514	0.722570	−	0.691298i	$-0.242961\pi$
$233$	22.0591	1.44514	0.722570	+	0.691298i	$0.242961\pi$
$234$	4.58356	0.299637
$235$	9.09657	0.593395
$236$	−1.00000	−0.0650945
$237$	−6.59838	−0.428611
$238$	−2.69790	−0.174879
$239$	−23.0551	−1.49131	−0.745657	−	0.666330i	$-0.767864\pi$
$239$	−23.0551	−1.49131	−0.745657	+	0.666330i	$0.767864\pi$
$240$	−4.19847	−0.271010
$241$	−10.4425	−0.672659	−0.336329	−	0.941744i	$-0.609186\pi$
$241$	−10.4425	−0.672659	−0.336329	+	0.941744i	$0.609186\pi$
$242$	9.57236	0.615335
$243$	−1.00000	−0.0641500
$244$	3.91284	0.250494
$245$	1.17002	0.0747501
$246$	8.27729	0.527741
$247$	6.79761	0.432522
$248$	−4.98944	−0.316830
$249$	15.7167	0.996005
$250$	−32.0222	−2.02526
$251$	−21.2266	−1.33981	−0.669906	−	0.742446i	$-0.733666\pi$
$251$	−21.2266	−1.33981	−0.669906	+	0.742446i	$0.733666\pi$
$252$	−2.69790	−0.169952
$253$	−9.07873	−0.570775
$254$	17.2206	1.08051
$255$	4.19847	0.262918
$256$	1.00000	0.0625000
$257$	14.0172	0.874369	0.437185	−	0.899372i	$-0.355976\pi$
$257$	14.0172	0.874369	0.437185	+	0.899372i	$0.355976\pi$
$258$	−0.00309616	−0.000192758 0
$259$	−1.06516	−0.0661860
$260$	−19.2439	−1.19346
$261$	1.17977	0.0730258
$262$	1.15783	0.0715310
$263$	16.1830	0.997888	0.498944	−	0.866634i	$-0.333721\pi$
$263$	16.1830	0.997888	0.498944	+	0.866634i	$0.333721\pi$
$264$	1.19484	0.0735373
$265$	−19.9731	−1.22694
$266$	−4.00111	−0.245324
$267$	−2.83334	−0.173398
$268$	13.6349	0.832886
$269$	−8.28383	−0.505074	−0.252537	−	0.967587i	$-0.581265\pi$
$269$	−8.28383	−0.505074	−0.252537	+	0.967587i	$0.581265\pi$
$270$	4.19847	0.255511
$271$	8.74541	0.531246	0.265623	−	0.964077i	$-0.414422\pi$
$271$	8.74541	0.531246	0.265623	+	0.964077i	$0.414422\pi$
$272$	−1.00000	−0.0606339
$273$	−12.3660	−0.748424
$274$	8.37755	0.506106
$275$	15.0874	0.909803
$276$	7.59828	0.457363
$277$	11.5607	0.694615	0.347307	−	0.937751i	$-0.387096\pi$
$277$	11.5607	0.694615	0.347307	+	0.937751i	$0.387096\pi$
$278$	17.2546	1.03486
$279$	4.98944	0.298710
$280$	11.3271	0.676921
$281$	−19.8564	−1.18453	−0.592267	−	0.805742i	$-0.701767\pi$
$281$	−19.8564	−1.18453	−0.592267	+	0.805742i	$0.701767\pi$
$282$	2.16664	0.129022
$283$	−26.0905	−1.55092	−0.775459	−	0.631398i	$-0.782481\pi$
$283$	−26.0905	−1.55092	−0.775459	+	0.631398i	$0.782481\pi$
$284$	−12.7395	−0.755949
$285$	6.22651	0.368826
$286$	5.47662	0.323839
$287$	−22.3313	−1.31818
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−4.95322	−0.290863
$291$	19.2681	1.12952
$292$	−2.98757	−0.174834
$293$	−0.456074	−0.0266441	−0.0133221	−	0.999911i	$-0.504241\pi$
$293$	−0.456074	−0.0266441	−0.0133221	+	0.999911i	$0.504241\pi$
$294$	0.278679	0.0162529
$295$	−4.19847	−0.244444
$296$	−0.394811	−0.0229480
$297$	−1.19484	−0.0693316
$298$	−3.14451	−0.182156
$299$	34.8272	2.01411
$300$	−12.6271	−0.729027
$301$	0.00835314	0.000481467 0
$302$	13.6425	0.785040
$303$	−4.25817	−0.244625
$304$	−1.48304	−0.0850583
$305$	16.4279	0.940661
$306$	1.00000	0.0571662
$307$	−11.9152	−0.680036	−0.340018	−	0.940419i	$-0.610433\pi$
$307$	−11.9152	−0.680036	−0.340018	+	0.940419i	$0.610433\pi$
$308$	−3.22356	−0.183679
$309$	−3.05007	−0.173513
$310$	−20.9480	−1.18977
$311$	−2.00912	−0.113927	−0.0569635	−	0.998376i	$-0.518142\pi$
$311$	−2.00912	−0.113927	−0.0569635	+	0.998376i	$0.518142\pi$
$312$	−4.58356	−0.259493
$313$	−17.1578	−0.969817	−0.484909	−	0.874565i	$-0.661147\pi$
$313$	−17.1578	−0.969817	−0.484909	+	0.874565i	$0.661147\pi$
$314$	15.5140	0.875505
$315$	−11.3271	−0.638207
$316$	6.59838	0.371188
$317$	17.5375	0.985002	0.492501	−	0.870312i	$-0.336083\pi$
$317$	17.5375	0.985002	0.492501	+	0.870312i	$0.336083\pi$
$318$	−4.75723	−0.266772
$319$	1.40963	0.0789243
$320$	4.19847	0.234701
$321$	16.9305	0.944967
$322$	−20.4994	−1.14239
$323$	1.48304	0.0825187
$324$	1.00000	0.0555556
$325$	−57.8772	−3.21045
$326$	−8.51597	−0.471656
$327$	1.60794	0.0889191
$328$	−8.27729	−0.457037
$329$	−5.84539	−0.322267
$330$	5.01649	0.276149
$331$	23.8985	1.31358	0.656791	−	0.754072i	$-0.271913\pi$
$331$	23.8985	1.31358	0.656791	+	0.754072i	$0.271913\pi$
$332$	−15.7167	−0.862566
$333$	0.394811	0.0216355
$334$	19.0854	1.04430
$335$	57.2458	3.12767
$336$	2.69790	0.147183
$337$	−11.9721	−0.652162	−0.326081	−	0.945342i	$-0.605728\pi$
$337$	−11.9721	−0.652162	−0.326081	+	0.945342i	$0.605728\pi$
$338$	−8.00901	−0.435633
$339$	−8.51072	−0.462239
$340$	−4.19847	−0.227694
$341$	5.96157	0.322837
$342$	1.48304	0.0801938
$343$	18.1335	0.979115
$344$	0.00309616	0.000166934 0
$345$	31.9011	1.71750
$346$	−12.8947	−0.693224
$347$	21.6651	1.16304	0.581521	−	0.813531i	$-0.302458\pi$
$347$	21.6651	1.16304	0.581521	+	0.813531i	$0.302458\pi$
$348$	−1.17977	−0.0632422
$349$	7.89422	0.422568	0.211284	−	0.977425i	$-0.432235\pi$
$349$	7.89422	0.422568	0.211284	+	0.977425i	$0.432235\pi$
$350$	34.0667	1.82094
$351$	4.58356	0.244652
$352$	−1.19484	−0.0636851
$353$	8.98725	0.478343	0.239172	−	0.970977i	$-0.423124\pi$
$353$	8.98725	0.478343	0.239172	+	0.970977i	$0.423124\pi$
$354$	−1.00000	−0.0531494
$355$	−53.4862	−2.83876
$356$	2.83334	0.150167
$357$	−2.69790	−0.142788
$358$	23.4879	1.24137
$359$	−23.5234	−1.24152	−0.620758	−	0.784002i	$-0.713175\pi$
$359$	−23.5234	−1.24152	−0.620758	+	0.784002i	$0.713175\pi$
$360$	−4.19847	−0.221279
$361$	−16.8006	−0.884241
$362$	−4.21008	−0.221277
$363$	9.57236	0.502419
$364$	12.3660	0.648154
$365$	−12.5432	−0.656542
$366$	3.91284	0.204528
$367$	−16.8854	−0.881408	−0.440704	−	0.897652i	$-0.645271\pi$
$367$	−16.8854	−0.881408	−0.440704	+	0.897652i	$0.645271\pi$
$368$	−7.59828	−0.396088
$369$	8.27729	0.430898
$370$	−1.65760	−0.0861747
$371$	12.8345	0.666336
$372$	−4.98944	−0.258690
$373$	−36.9662	−1.91404	−0.957020	−	0.290023i	$-0.906337\pi$
$373$	−36.9662	−1.91404	−0.957020	+	0.290023i	$0.906337\pi$
$374$	1.19484	0.0617837
$375$	−32.0222	−1.65362
$376$	−2.16664	−0.111736
$377$	−5.40754	−0.278502
$378$	−2.69790	−0.138765
$379$	−19.9787	−1.02624	−0.513118	−	0.858318i	$-0.671510\pi$
$379$	−19.9787	−1.02624	−0.513118	+	0.858318i	$0.671510\pi$
$380$	−6.22651	−0.319413
$381$	17.2206	0.882236
$382$	−16.7182	−0.855380
$383$	−26.5265	−1.35544	−0.677721	−	0.735319i	$-0.737032\pi$
$383$	−26.5265	−1.35544	−0.677721	+	0.735319i	$0.737032\pi$
$384$	1.00000	0.0510310
$385$	−13.5340	−0.689757
$386$	−9.00012	−0.458094
$387$	−0.00309616	−0.000157387 0
$388$	−19.2681	−0.978191
$389$	−7.67469	−0.389122	−0.194561	−	0.980890i	$-0.562328\pi$
$389$	−7.67469	−0.389122	−0.194561	+	0.980890i	$0.562328\pi$
$390$	−19.2439	−0.974454
$391$	7.59828	0.384262
$392$	−0.278679	−0.0140754
$393$	1.15783	0.0584048
$394$	22.3042	1.12367
$395$	27.7031	1.39389
$396$	1.19484	0.0600429
$397$	−4.97104	−0.249489	−0.124745	−	0.992189i	$-0.539811\pi$
$397$	−4.97104	−0.249489	−0.124745	+	0.992189i	$0.539811\pi$
$398$	14.2741	0.715498
$399$	−4.00111	−0.200306
$400$	12.6271	0.631356
$401$	20.0279	1.00014	0.500072	−	0.865984i	$-0.333307\pi$
$401$	20.0279	1.00014	0.500072	+	0.865984i	$0.333307\pi$
$402$	13.6349	0.680048
$403$	−22.8694	−1.13920
$404$	4.25817	0.211852
$405$	4.19847	0.208623
$406$	3.18290	0.157965
$407$	0.471736	0.0233831
$408$	−1.00000	−0.0495074
$409$	−25.3721	−1.25457	−0.627285	−	0.778790i	$-0.715834\pi$
$409$	−25.3721	−1.25457	−0.627285	+	0.778790i	$0.715834\pi$
$410$	−34.7519	−1.71627
$411$	8.37755	0.413234
$412$	3.05007	0.150266
$413$	2.69790	0.132755
$414$	7.59828	0.373435
$415$	−65.9860	−3.23913
$416$	4.58356	0.224727
$417$	17.2546	0.844959
$418$	1.77200	0.0866712
$419$	−8.42914	−0.411790	−0.205895	−	0.978574i	$-0.566011\pi$
$419$	−8.42914	−0.411790	−0.205895	+	0.978574i	$0.566011\pi$
$420$	11.3271	0.552704
$421$	15.0393	0.732970	0.366485	−	0.930424i	$-0.380561\pi$
$421$	15.0393	0.732970	0.366485	+	0.930424i	$0.380561\pi$
$422$	−0.526892	−0.0256487
$423$	2.16664	0.105346
$424$	4.75723	0.231031
$425$	−12.6271	−0.612505
$426$	−12.7395	−0.617229
$427$	−10.5565	−0.510864
$428$	−16.9305	−0.818365
$429$	5.47662	0.264414
$430$	0.0129991	0.000626873 0
$431$	16.3765	0.788829	0.394415	−	0.918933i	$-0.370947\pi$
$431$	16.3765	0.788829	0.394415	+	0.918933i	$0.370947\pi$
$432$	−1.00000	−0.0481125
$433$	28.2109	1.35573	0.677865	−	0.735186i	$-0.262905\pi$
$433$	28.2109	1.35573	0.677865	+	0.735186i	$0.262905\pi$
$434$	13.4610	0.646149
$435$	−4.95322	−0.237489
$436$	−1.60794	−0.0770062
$437$	11.2686	0.539049
$438$	−2.98757	−0.142752
$439$	−32.4774	−1.55006	−0.775031	−	0.631923i	$-0.782266\pi$
$439$	−32.4774	−1.55006	−0.775031	+	0.631923i	$0.782266\pi$
$440$	−5.01649	−0.239152
$441$	0.278679	0.0132704
$442$	−4.58356	−0.218018
$443$	18.4578	0.876959	0.438479	−	0.898741i	$-0.355517\pi$
$443$	18.4578	0.876959	0.438479	+	0.898741i	$0.355517\pi$
$444$	−0.394811	−0.0187369
$445$	11.8957	0.563910
$446$	−10.6178	−0.502766
$447$	−3.14451	−0.148730
$448$	−2.69790	−0.127464
$449$	17.5260	0.827103	0.413551	−	0.910481i	$-0.364288\pi$
$449$	17.5260	0.827103	0.413551	+	0.910481i	$0.364288\pi$
$450$	−12.6271	−0.595248
$451$	9.89003	0.465703
$452$	8.51072	0.400310
$453$	13.6425	0.640983
$454$	−20.6494	−0.969123
$455$	51.9182	2.43396
$456$	−1.48304	−0.0694498
$457$	−36.1590	−1.69145	−0.845723	−	0.533622i	$-0.820831\pi$
$457$	−36.1590	−1.69145	−0.845723	+	0.533622i	$0.820831\pi$
$458$	−16.4578	−0.769020
$459$	1.00000	0.0466760
$460$	−31.9011	−1.48740
$461$	−31.5020	−1.46720	−0.733598	−	0.679584i	$-0.762160\pi$
$461$	−31.5020	−1.46720	−0.733598	+	0.679584i	$0.762160\pi$
$462$	−3.22356	−0.149974
$463$	26.1280	1.21427	0.607135	−	0.794599i	$-0.292319\pi$
$463$	26.1280	1.21427	0.607135	+	0.794599i	$0.292319\pi$
$464$	1.17977	0.0547694
$465$	−20.9480	−0.971439
$466$	−22.0591	−1.02187
$467$	32.2031	1.49018	0.745091	−	0.666963i	$-0.232406\pi$
$467$	32.2031	1.49018	0.745091	+	0.666963i	$0.232406\pi$
$468$	−4.58356	−0.211875
$469$	−36.7857	−1.69861
$470$	−9.09657	−0.419593
$471$	15.5140	0.714847
$472$	1.00000	0.0460287
$473$	−0.00369941	−0.000170099 0
$474$	6.59838	0.303073
$475$	−18.7266	−0.859234
$476$	2.69790	0.123658
$477$	−4.75723	−0.217818
$478$	23.0551	1.05452
$479$	−2.51462	−0.114896	−0.0574480	−	0.998349i	$-0.518296\pi$
$479$	−2.51462	−0.114896	−0.0574480	+	0.998349i	$0.518296\pi$
$480$	4.19847	0.191633
$481$	−1.80964	−0.0825126
$482$	10.4425	0.475641
$483$	−20.4994	−0.932756
$484$	−9.57236	−0.435107
$485$	−80.8966	−3.67333
$486$	1.00000	0.0453609
$487$	−13.3330	−0.604178	−0.302089	−	0.953280i	$-0.597684\pi$
$487$	−13.3330	−0.604178	−0.302089	+	0.953280i	$0.597684\pi$
$488$	−3.91284	−0.177126
$489$	−8.51597	−0.385105
$490$	−1.17002	−0.0528563
$491$	−18.9410	−0.854797	−0.427399	−	0.904063i	$-0.640570\pi$
$491$	−18.9410	−0.854797	−0.427399	+	0.904063i	$0.640570\pi$
$492$	−8.27729	−0.373169
$493$	−1.17977	−0.0531341
$494$	−6.79761	−0.305839
$495$	5.01649	0.225475
$496$	4.98944	0.224032
$497$	34.3699	1.54170
$498$	−15.7167	−0.704282
$499$	11.1322	0.498348	0.249174	−	0.968459i	$-0.419841\pi$
$499$	11.1322	0.498348	0.249174	+	0.968459i	$0.419841\pi$
$500$	32.0222	1.43208
$501$	19.0854	0.852671
$502$	21.2266	0.947390
$503$	27.7505	1.23733	0.618667	−	0.785653i	$-0.287673\pi$
$503$	27.7505	1.23733	0.618667	+	0.785653i	$0.287673\pi$
$504$	2.69790	0.120174
$505$	17.8778	0.795551
$506$	9.07873	0.403599
$507$	−8.00901	−0.355693
$508$	−17.2206	−0.764039
$509$	−5.80368	−0.257244	−0.128622	−	0.991694i	$-0.541055\pi$
$509$	−5.80368	−0.257244	−0.128622	+	0.991694i	$0.541055\pi$
$510$	−4.19847	−0.185911
$511$	8.06017	0.356561
$512$	−1.00000	−0.0441942
$513$	1.48304	0.0654779
$514$	−14.0172	−0.618273
$515$	12.8056	0.564284
$516$	0.00309616	0.000136301 0
$517$	2.58879	0.113855
$518$	1.06516	0.0468006
$519$	−12.8947	−0.566015
$520$	19.2439	0.843902
$521$	9.88249	0.432960	0.216480	−	0.976287i	$-0.430542\pi$
$521$	9.88249	0.432960	0.216480	+	0.976287i	$0.430542\pi$
$522$	−1.17977	−0.0516370
$523$	39.0168	1.70608	0.853042	−	0.521843i	$-0.174755\pi$
$523$	39.0168	1.70608	0.853042	+	0.521843i	$0.174755\pi$
$524$	−1.15783	−0.0505801
$525$	34.0667	1.48679
$526$	−16.1830	−0.705613
$527$	−4.98944	−0.217343
$528$	−1.19484	−0.0519987
$529$	34.7339	1.51017
$530$	19.9731	0.867574
$531$	−1.00000	−0.0433963
$532$	4.00111	0.173470
$533$	−37.9394	−1.64334
$534$	2.83334	0.122611
$535$	−71.0820	−3.07314
$536$	−13.6349	−0.588939
$537$	23.4879	1.01358
$538$	8.28383	0.357141
$539$	0.332977	0.0143423
$540$	−4.19847	−0.180673
$541$	7.71873	0.331854	0.165927	−	0.986138i	$-0.446938\pi$
$541$	7.71873	0.331854	0.165927	+	0.986138i	$0.446938\pi$
$542$	−8.74541	−0.375648
$543$	−4.21008	−0.180672
$544$	1.00000	0.0428746
$545$	−6.75087	−0.289175
$546$	12.3660	0.529216
$547$	−37.1533	−1.58856	−0.794280	−	0.607552i	$-0.792152\pi$
$547$	−37.1533	−1.58856	−0.794280	+	0.607552i	$0.792152\pi$
$548$	−8.37755	−0.357871
$549$	3.91284	0.166996
$550$	−15.0874	−0.643328
$551$	−1.74965	−0.0745375
$552$	−7.59828	−0.323404
$553$	−17.8018	−0.757009
$554$	−11.5607	−0.491167
$555$	−1.65760	−0.0703613
$556$	−17.2546	−0.731756
$557$	−4.13364	−0.175148	−0.0875739	−	0.996158i	$-0.527911\pi$
$557$	−4.13364	−0.175148	−0.0875739	+	0.996158i	$0.527911\pi$
$558$	−4.98944	−0.211220
$559$	0.0141914	0.000600233 0
$560$	−11.3271	−0.478655
$561$	1.19484	0.0504462
$562$	19.8564	0.837591
$563$	−17.6175	−0.742487	−0.371244	−	0.928536i	$-0.621069\pi$
$563$	−17.6175	−0.742487	−0.371244	+	0.928536i	$0.621069\pi$
$564$	−2.16664	−0.0912320
$565$	35.7320	1.50326
$566$	26.0905	1.09666
$567$	−2.69790	−0.113301
$568$	12.7395	0.534536
$569$	34.0968	1.42941	0.714706	−	0.699425i	$-0.246560\pi$
$569$	34.0968	1.42941	0.714706	+	0.699425i	$0.246560\pi$
$570$	−6.22651	−0.260800
$571$	43.8889	1.83669	0.918347	−	0.395775i	$-0.129524\pi$
$571$	43.8889	1.83669	0.918347	+	0.395775i	$0.129524\pi$
$572$	−5.47662	−0.228989
$573$	−16.7182	−0.698415
$574$	22.3313	0.932091
$575$	−95.9445	−4.00116
$576$	1.00000	0.0416667
$577$	17.2849	0.719579	0.359789	−	0.933034i	$-0.382849\pi$
$577$	17.2849	0.719579	0.359789	+	0.933034i	$0.382849\pi$
$578$	−1.00000	−0.0415945
$579$	−9.00012	−0.374032
$580$	4.95322	0.205671
$581$	42.4021	1.75914
$582$	−19.2681	−0.798690
$583$	−5.68412	−0.235412
$584$	2.98757	0.123627
$585$	−19.2439	−0.795638
$586$	0.456074	0.0188402
$587$	−34.7778	−1.43543	−0.717717	−	0.696334i	$-0.754813\pi$
$587$	−34.7778	−1.43543	−0.717717	+	0.696334i	$0.754813\pi$
$588$	−0.278679	−0.0114925
$589$	−7.39955	−0.304893
$590$	4.19847	0.172848
$591$	22.3042	0.917473
$592$	0.394811	0.0162267
$593$	−7.30253	−0.299879	−0.149939	−	0.988695i	$-0.547908\pi$
$593$	−7.30253	−0.299879	−0.149939	+	0.988695i	$0.547908\pi$
$594$	1.19484	0.0490248
$595$	11.3271	0.464364
$596$	3.14451	0.128804
$597$	14.2741	0.584202
$598$	−34.8272	−1.42419
$599$	0.379085	0.0154890	0.00774449	−	0.999970i	$-0.497535\pi$
$599$	0.379085	0.0154890	0.00774449	+	0.999970i	$0.497535\pi$
$600$	12.6271	0.515500
$601$	−40.1286	−1.63688	−0.818439	−	0.574593i	$-0.805160\pi$
$601$	−40.1286	−1.63688	−0.818439	+	0.574593i	$0.805160\pi$
$602$	−0.00835314	−0.000340448 0
$603$	13.6349	0.555257
$604$	−13.6425	−0.555107
$605$	−40.1892	−1.63392
$606$	4.25817	0.172976
$607$	−14.0355	−0.569683	−0.284842	−	0.958575i	$-0.591941\pi$
$607$	−14.0355	−0.569683	−0.284842	+	0.958575i	$0.591941\pi$
$608$	1.48304	0.0601453
$609$	3.18290	0.128978
$610$	−16.4279	−0.665148
$611$	−9.93092	−0.401762
$612$	−1.00000	−0.0404226
$613$	−34.8230	−1.40649	−0.703244	−	0.710949i	$-0.748266\pi$
$613$	−34.8230	−1.40649	−0.703244	+	0.710949i	$0.748266\pi$
$614$	11.9152	0.480858
$615$	−34.7519	−1.40133
$616$	3.22356	0.129881
$617$	10.5734	0.425669	0.212835	−	0.977088i	$-0.431730\pi$
$617$	10.5734	0.425669	0.212835	+	0.977088i	$0.431730\pi$
$618$	3.05007	0.122692
$619$	−29.1329	−1.17095	−0.585475	−	0.810690i	$-0.699092\pi$
$619$	−29.1329	−1.17095	−0.585475	+	0.810690i	$0.699092\pi$
$620$	20.9480	0.841291
$621$	7.59828	0.304909
$622$	2.00912	0.0805585
$623$	−7.64408	−0.306254
$624$	4.58356	0.183489
$625$	71.3086	2.85234
$626$	17.1578	0.685764
$627$	1.77200	0.0707668
$628$	−15.5140	−0.619076
$629$	−0.394811	−0.0157422
$630$	11.3271	0.451281
$631$	−21.6812	−0.863115	−0.431557	−	0.902085i	$-0.642036\pi$
$631$	−21.6812	−0.863115	−0.431557	+	0.902085i	$0.642036\pi$
$632$	−6.59838	−0.262469
$633$	−0.526892	−0.0209421
$634$	−17.5375	−0.696502
$635$	−72.3000	−2.86914
$636$	4.75723	0.188636
$637$	−1.27734	−0.0506101
$638$	−1.40963	−0.0558079
$639$	−12.7395	−0.503966
$640$	−4.19847	−0.165959
$641$	39.1476	1.54624	0.773118	−	0.634262i	$-0.218696\pi$
$641$	39.1476	1.54624	0.773118	+	0.634262i	$0.218696\pi$
$642$	−16.9305	−0.668192
$643$	−4.72890	−0.186490	−0.0932448	−	0.995643i	$-0.529724\pi$
$643$	−4.72890	−0.186490	−0.0932448	+	0.995643i	$0.529724\pi$
$644$	20.4994	0.807791
$645$	0.0129991	0.000511840 0
$646$	−1.48304	−0.0583495
$647$	−33.2863	−1.30862	−0.654309	−	0.756227i	$-0.727041\pi$
$647$	−33.2863	−1.30862	−0.654309	+	0.756227i	$0.727041\pi$
$648$	−1.00000	−0.0392837
$649$	−1.19484	−0.0469015
$650$	57.8772	2.27013
$651$	13.4610	0.527579
$652$	8.51597	0.333511
$653$	−21.4046	−0.837628	−0.418814	−	0.908072i	$-0.637554\pi$
$653$	−21.4046	−0.837628	−0.418814	+	0.908072i	$0.637554\pi$
$654$	−1.60794	−0.0628753
$655$	−4.86111	−0.189939
$656$	8.27729	0.323174
$657$	−2.98757	−0.116556
$658$	5.84539	0.227877
$659$	−4.95365	−0.192967	−0.0964833	−	0.995335i	$-0.530759\pi$
$659$	−4.95365	−0.192967	−0.0964833	+	0.995335i	$0.530759\pi$
$660$	−5.01649	−0.195267
$661$	−5.30500	−0.206340	−0.103170	−	0.994664i	$-0.532899\pi$
$661$	−5.30500	−0.206340	−0.103170	+	0.994664i	$0.532899\pi$
$662$	−23.8985	−0.928843
$663$	−4.58356	−0.178011
$664$	15.7167	0.609926
$665$	16.7985	0.651418
$666$	−0.394811	−0.0152986
$667$	−8.96421	−0.347096
$668$	−19.0854	−0.738435
$669$	−10.6178	−0.410507
$670$	−57.2458	−2.21160
$671$	4.67522	0.180485
$672$	−2.69790	−0.104074
$673$	−28.2830	−1.09023	−0.545114	−	0.838362i	$-0.683514\pi$
$673$	−28.2830	−1.09023	−0.545114	+	0.838362i	$0.683514\pi$
$674$	11.9721	0.461148
$675$	−12.6271	−0.486018
$676$	8.00901	0.308039
$677$	−26.0471	−1.00107	−0.500535	−	0.865716i	$-0.666863\pi$
$677$	−26.0471	−1.00107	−0.500535	+	0.865716i	$0.666863\pi$
$678$	8.51072	0.326852
$679$	51.9835	1.99495
$680$	4.19847	0.161004
$681$	−20.6494	−0.791286
$682$	−5.96157	−0.228280
$683$	11.2193	0.429296	0.214648	−	0.976691i	$-0.431140\pi$
$683$	11.2193	0.429296	0.214648	+	0.976691i	$0.431140\pi$
$684$	−1.48304	−0.0567056
$685$	−35.1729	−1.34389
$686$	−18.1335	−0.692339
$687$	−16.4578	−0.627902
$688$	−0.00309616	−0.000118040 0
$689$	21.8050	0.830705
$690$	−31.9011	−1.21446
$691$	−6.68850	−0.254443	−0.127221	−	0.991874i	$-0.540606\pi$
$691$	−6.68850	−0.254443	−0.127221	+	0.991874i	$0.540606\pi$
$692$	12.8947	0.490184
$693$	−3.22356	−0.122453
$694$	−21.6651	−0.822395
$695$	−72.4427	−2.74791
$696$	1.17977	0.0447190
$697$	−8.27729	−0.313525
$698$	−7.89422	−0.298801
$699$	−22.0591	−0.834352
$700$	−34.0667	−1.28760
$701$	−1.41881	−0.0535877	−0.0267938	−	0.999641i	$-0.508530\pi$
$701$	−1.41881	−0.0535877	−0.0267938	+	0.999641i	$0.508530\pi$
$702$	−4.58356	−0.172995
$703$	−0.585522	−0.0220834
$704$	1.19484	0.0450322
$705$	−9.09657	−0.342597
$706$	−8.98725	−0.338240
$707$	−11.4881	−0.432055
$708$	1.00000	0.0375823
$709$	−39.4208	−1.48048	−0.740240	−	0.672343i	$-0.765288\pi$
$709$	−39.4208	−1.48048	−0.740240	+	0.672343i	$0.765288\pi$
$710$	53.4862	2.00730
$711$	6.59838	0.247458
$712$	−2.83334	−0.106184
$713$	−37.9112	−1.41978
$714$	2.69790	0.100966
$715$	−22.9934	−0.859904
$716$	−23.4879	−0.877783
$717$	23.0551	0.861010
$718$	23.5234	0.877884
$719$	−3.43560	−0.128126	−0.0640632	−	0.997946i	$-0.520406\pi$
$719$	−3.43560	−0.128126	−0.0640632	+	0.997946i	$0.520406\pi$
$720$	4.19847	0.156468
$721$	−8.22881	−0.306457
$722$	16.8006	0.625253
$723$	10.4425	0.388360
$724$	4.21008	0.156466
$725$	14.8971	0.553263
$726$	−9.57236	−0.355264
$727$	36.8297	1.36594	0.682969	−	0.730447i	$-0.260688\pi$
$727$	36.8297	1.36594	0.682969	+	0.730447i	$0.260688\pi$
$728$	−12.3660	−0.458314
$729$	1.00000	0.0370370
$730$	12.5432	0.464245
$731$	0.00309616	0.000114516 0
$732$	−3.91284	−0.144623
$733$	35.1475	1.29820	0.649101	−	0.760702i	$-0.275145\pi$
$733$	35.1475	1.29820	0.649101	+	0.760702i	$0.275145\pi$
$734$	16.8854	0.623250
$735$	−1.17002	−0.0431570
$736$	7.59828	0.280076
$737$	16.2915	0.600107
$738$	−8.27729	−0.304691
$739$	16.0872	0.591778	0.295889	−	0.955222i	$-0.404384\pi$
$739$	16.0872	0.591778	0.295889	+	0.955222i	$0.404384\pi$
$740$	1.65760	0.0609347
$741$	−6.79761	−0.249717
$742$	−12.8345	−0.471171
$743$	−16.3815	−0.600979	−0.300490	−	0.953785i	$-0.597150\pi$
$743$	−16.3815	−0.600979	−0.300490	+	0.953785i	$0.597150\pi$
$744$	4.98944	0.182922
$745$	13.2021	0.483688
$746$	36.9662	1.35343
$747$	−15.7167	−0.575044
$748$	−1.19484	−0.0436876
$749$	45.6768	1.66899
$750$	32.0222	1.16929
$751$	−3.55772	−0.129823	−0.0649115	−	0.997891i	$-0.520677\pi$
$751$	−3.55772	−0.129823	−0.0649115	+	0.997891i	$0.520677\pi$
$752$	2.16664	0.0790092
$753$	21.2266	0.773541
$754$	5.40754	0.196931
$755$	−57.2778	−2.08455
$756$	2.69790	0.0981218
$757$	−34.5050	−1.25410	−0.627052	−	0.778977i	$-0.715739\pi$
$757$	−34.5050	−1.25410	−0.627052	+	0.778977i	$0.715739\pi$
$758$	19.9787	0.725659
$759$	9.07873	0.329537
$760$	6.22651	0.225859
$761$	8.48265	0.307496	0.153748	−	0.988110i	$-0.450866\pi$
$761$	8.48265	0.307496	0.153748	+	0.988110i	$0.450866\pi$
$762$	−17.2206	−0.623835
$763$	4.33805	0.157048
$764$	16.7182	0.604845
$765$	−4.19847	−0.151796
$766$	26.5265	0.958442
$767$	4.58356	0.165503
$768$	−1.00000	−0.0360844
$769$	5.46433	0.197049	0.0985244	−	0.995135i	$-0.468588\pi$
$769$	5.46433	0.197049	0.0985244	+	0.995135i	$0.468588\pi$
$770$	13.5340	0.487732
$771$	−14.0172	−0.504817
$772$	9.00012	0.323922
$773$	−12.5930	−0.452938	−0.226469	−	0.974018i	$-0.572718\pi$
$773$	−12.5930	−0.452938	−0.226469	+	0.974018i	$0.572718\pi$
$774$	0.00309616	0.000111289 0
$775$	63.0022	2.26311
$776$	19.2681	0.691686
$777$	1.06516	0.0382125
$778$	7.67469	0.275151
$779$	−12.2756	−0.439818
$780$	19.2439	0.689043
$781$	−15.2216	−0.544672
$782$	−7.59828	−0.271714
$783$	−1.17977	−0.0421615
$784$	0.278679	0.00995282
$785$	−65.1350	−2.32477
$786$	−1.15783	−0.0412984
$787$	23.3494	0.832315	0.416157	−	0.909293i	$-0.363377\pi$
$787$	23.3494	0.832315	0.416157	+	0.909293i	$0.363377\pi$
$788$	−22.3042	−0.794555
$789$	−16.1830	−0.576131
$790$	−27.7031	−0.985631
$791$	−22.9611	−0.816402
$792$	−1.19484	−0.0424568
$793$	−17.9348	−0.636882
$794$	4.97104	0.176416
$795$	19.9731	0.708371
$796$	−14.2741	−0.505934
$797$	4.72836	0.167487	0.0837435	−	0.996487i	$-0.473312\pi$
$797$	4.72836	0.167487	0.0837435	+	0.996487i	$0.473312\pi$
$798$	4.00111	0.141638
$799$	−2.16664	−0.0766502
$800$	−12.6271	−0.446436
$801$	2.83334	0.100111
$802$	−20.0279	−0.707209
$803$	−3.56967	−0.125971
$804$	−13.6349	−0.480867
$805$	86.0662	3.03343
$806$	22.8694	0.805539
$807$	8.28383	0.291604
$808$	−4.25817	−0.149802
$809$	−1.35501	−0.0476397	−0.0238198	−	0.999716i	$-0.507583\pi$
$809$	−1.35501	−0.0476397	−0.0238198	+	0.999716i	$0.507583\pi$
$810$	−4.19847	−0.147519
$811$	0.916552	0.0321845	0.0160923	−	0.999871i	$-0.494877\pi$
$811$	0.916552	0.0321845	0.0160923	+	0.999871i	$0.494877\pi$
$812$	−3.18290	−0.111698
$813$	−8.74541	−0.306715
$814$	−0.471736	−0.0165343
$815$	35.7540	1.25241
$816$	1.00000	0.0350070
$817$	0.00459174	0.000160645 0
$818$	25.3721	0.887115
$819$	12.3660	0.432103
$820$	34.7519	1.21359
$821$	−19.4100	−0.677413	−0.338706	−	0.940892i	$-0.609989\pi$
$821$	−19.4100	−0.677413	−0.338706	+	0.940892i	$0.609989\pi$
$822$	−8.37755	−0.292201
$823$	−52.9535	−1.84584	−0.922922	−	0.384988i	$-0.874206\pi$
$823$	−52.9535	−1.84584	−0.922922	+	0.384988i	$0.874206\pi$
$824$	−3.05007	−0.106254
$825$	−15.0874	−0.525275
$826$	−2.69790	−0.0938720
$827$	29.8963	1.03960	0.519798	−	0.854289i	$-0.326007\pi$
$827$	29.8963	1.03960	0.519798	+	0.854289i	$0.326007\pi$
$828$	−7.59828	−0.264059
$829$	43.6469	1.51592	0.757959	−	0.652302i	$-0.226196\pi$
$829$	43.6469	1.51592	0.757959	+	0.652302i	$0.226196\pi$
$830$	65.9860	2.29041
$831$	−11.5607	−0.401036
$832$	−4.58356	−0.158906
$833$	−0.278679	−0.00965566
$834$	−17.2546	−0.597476
$835$	−80.1293	−2.77299
$836$	−1.77200	−0.0612858
$837$	−4.98944	−0.172460
$838$	8.42914	0.291180
$839$	5.72457	0.197634	0.0988170	−	0.995106i	$-0.468494\pi$
$839$	5.72457	0.197634	0.0988170	+	0.995106i	$0.468494\pi$
$840$	−11.3271	−0.390821
$841$	−27.6081	−0.952005
$842$	−15.0393	−0.518288
$843$	19.8564	0.683891
$844$	0.526892	0.0181364
$845$	33.6256	1.15675
$846$	−2.16664	−0.0744906
$847$	25.8253	0.887368
$848$	−4.75723	−0.163364
$849$	26.0905	0.895423
$850$	12.6271	0.433107
$851$	−2.99989	−0.102835
$852$	12.7395	0.436447
$853$	25.5278	0.874055	0.437027	−	0.899448i	$-0.356031\pi$
$853$	25.5278	0.874055	0.437027	+	0.899448i	$0.356031\pi$
$854$	10.5565	0.361235
$855$	−6.22651	−0.212942
$856$	16.9305	0.578672
$857$	10.7253	0.366368	0.183184	−	0.983079i	$-0.441360\pi$
$857$	10.7253	0.366368	0.183184	+	0.983079i	$0.441360\pi$
$858$	−5.47662	−0.186969
$859$	−19.3214	−0.659239	−0.329619	−	0.944114i	$-0.606920\pi$
$859$	−19.3214	−0.659239	−0.329619	+	0.944114i	$0.606920\pi$
$860$	−0.0129991	−0.000443266 0
$861$	22.3313	0.761049
$862$	−16.3765	−0.557787
$863$	5.00098	0.170235	0.0851177	−	0.996371i	$-0.472873\pi$
$863$	5.00098	0.170235	0.0851177	+	0.996371i	$0.472873\pi$
$864$	1.00000	0.0340207
$865$	54.1380	1.84075
$866$	−28.2109	−0.958646
$867$	−1.00000	−0.0339618
$868$	−13.4610	−0.456897
$869$	7.88400	0.267446
$870$	4.95322	0.167930
$871$	−62.4965	−2.11761
$872$	1.60794	0.0544516
$873$	−19.2681	−0.652127
$874$	−11.2686	−0.381165
$875$	−86.3928	−2.92061
$876$	2.98757	0.100941
$877$	−38.5332	−1.30117	−0.650587	−	0.759432i	$-0.725477\pi$
$877$	−38.5332	−1.30117	−0.650587	+	0.759432i	$0.725477\pi$
$878$	32.4774	1.09606
$879$	0.456074	0.0153830
$880$	5.01649	0.169106
$881$	50.2667	1.69353	0.846763	−	0.531970i	$-0.178548\pi$
$881$	50.2667	1.69353	0.846763	+	0.531970i	$0.178548\pi$
$882$	−0.278679	−0.00938361
$883$	19.0191	0.640044	0.320022	−	0.947410i	$-0.396310\pi$
$883$	19.0191	0.640044	0.320022	+	0.947410i	$0.396310\pi$
$884$	4.58356	0.154162
$885$	4.19847	0.141130
$886$	−18.4578	−0.620103
$887$	27.5450	0.924871	0.462435	−	0.886653i	$-0.346976\pi$
$887$	27.5450	0.924871	0.462435	+	0.886653i	$0.346976\pi$
$888$	0.394811	0.0132490
$889$	46.4594	1.55820
$890$	−11.8957	−0.398745
$891$	1.19484	0.0400286
$892$	10.6178	0.355509
$893$	−3.21322	−0.107526
$894$	3.14451	0.105168
$895$	−98.6130	−3.29627
$896$	2.69790	0.0901306
$897$	−34.8272	−1.16285
$898$	−17.5260	−0.584850
$899$	5.88638	0.196322
$900$	12.6271	0.420904
$901$	4.75723	0.158486
$902$	−9.89003	−0.329302
$903$	−0.00835314	−0.000277975 0
$904$	−8.51072	−0.283062
$905$	17.6759	0.587566
$906$	−13.6425	−0.453243
$907$	45.7710	1.51980	0.759900	−	0.650040i	$-0.225248\pi$
$907$	45.7710	1.51980	0.759900	+	0.650040i	$0.225248\pi$
$908$	20.6494	0.685274
$909$	4.25817	0.141235
$910$	−51.9182	−1.72107
$911$	9.75352	0.323149	0.161574	−	0.986861i	$-0.448343\pi$
$911$	9.75352	0.323149	0.161574	+	0.986861i	$0.448343\pi$
$912$	1.48304	0.0491085
$913$	−18.7789	−0.621492
$914$	36.1590	1.19603
$915$	−16.4279	−0.543091
$916$	16.4578	0.543779
$917$	3.12371	0.103154
$918$	−1.00000	−0.0330049
$919$	39.2274	1.29399	0.646997	−	0.762492i	$-0.276025\pi$
$919$	39.2274	1.29399	0.646997	+	0.762492i	$0.276025\pi$
$920$	31.9011	1.05175
$921$	11.9152	0.392619
$922$	31.5020	1.03746
$923$	58.3921	1.92200
$924$	3.22356	0.106047
$925$	4.98533	0.163917
$926$	−26.1280	−0.858618
$927$	3.05007	0.100178
$928$	−1.17977	−0.0387278
$929$	5.00221	0.164117	0.0820585	−	0.996628i	$-0.473851\pi$
$929$	5.00221	0.164117	0.0820585	+	0.996628i	$0.473851\pi$
$930$	20.9480	0.686911
$931$	−0.413293	−0.0135451
$932$	22.0591	0.722570
$933$	2.00912	0.0657758
$934$	−32.2031	−1.05372
$935$	−5.01649	−0.164057
$936$	4.58356	0.149818
$937$	49.3851	1.61334	0.806670	−	0.591002i	$-0.201268\pi$
$937$	49.3851	1.61334	0.806670	+	0.591002i	$0.201268\pi$
$938$	36.7857	1.20110
$939$	17.1578	0.559924
$940$	9.09657	0.296697
$941$	38.6219	1.25904	0.629519	−	0.776985i	$-0.283252\pi$
$941$	38.6219	1.25904	0.629519	+	0.776985i	$0.283252\pi$
$942$	−15.5140	−0.505473
$943$	−62.8932	−2.04808
$944$	−1.00000	−0.0325472
$945$	11.3271	0.368469
$946$	0.00369941	0.000120278 0
$947$	55.7665	1.81217	0.906084	−	0.423097i	$-0.139057\pi$
$947$	55.7665	1.81217	0.906084	+	0.423097i	$0.139057\pi$
$948$	−6.59838	−0.214305
$949$	13.6937	0.444516
$950$	18.7266	0.607570
$951$	−17.5375	−0.568691
$952$	−2.69790	−0.0874395
$953$	9.30617	0.301456	0.150728	−	0.988575i	$-0.451838\pi$
$953$	9.30617	0.301456	0.150728	+	0.988575i	$0.451838\pi$
$954$	4.75723	0.154021
$955$	70.1910	2.27133
$956$	−23.0551	−0.745657
$957$	−1.40963	−0.0455670
$958$	2.51462	0.0812437
$959$	22.6018	0.729851
$960$	−4.19847	−0.135505
$961$	−6.10553	−0.196952
$962$	1.80964	0.0583452
$963$	−16.9305	−0.545577
$964$	−10.4425	−0.336329
$965$	37.7867	1.21640
$966$	20.4994	0.659558
$967$	22.5182	0.724135	0.362068	−	0.932152i	$-0.382071\pi$
$967$	22.5182	0.724135	0.362068	+	0.932152i	$0.382071\pi$
$968$	9.57236	0.307667
$969$	−1.48304	−0.0476422
$970$	80.8966	2.59743
$971$	−2.81385	−0.0903006	−0.0451503	−	0.998980i	$-0.514377\pi$
$971$	−2.81385	−0.0903006	−0.0451503	+	0.998980i	$0.514377\pi$
$972$	−1.00000	−0.0320750
$973$	46.5511	1.49236
$974$	13.3330	0.427218
$975$	57.8772	1.85355
$976$	3.91284	0.125247
$977$	25.0660	0.801933	0.400966	−	0.916093i	$-0.368674\pi$
$977$	25.0660	0.801933	0.400966	+	0.916093i	$0.368674\pi$
$978$	8.51597	0.272311
$979$	3.38539	0.108198
$980$	1.17002	0.0373751
$981$	−1.60794	−0.0513374
$982$	18.9410	0.604433
$983$	−33.5511	−1.07012	−0.535058	−	0.844816i	$-0.679710\pi$
$983$	−33.5511	−1.07012	−0.535058	+	0.844816i	$0.679710\pi$
$984$	8.27729	0.263870
$985$	−93.6436	−2.98373
$986$	1.17977	0.0375715
$987$	5.84539	0.186061
$988$	6.79761	0.216261
$989$	0.0235255	0.000748067 0
$990$	−5.01649	−0.159435
$991$	−3.05090	−0.0969151	−0.0484575	−	0.998825i	$-0.515431\pi$
$991$	−3.05090	−0.0969151	−0.0484575	+	0.998825i	$0.515431\pi$
$992$	−4.98944	−0.158415
$993$	−23.8985	−0.758397
$994$	−34.3699	−1.09015
$995$	−59.9295	−1.89989
$996$	15.7167	0.498003
$997$	14.2363	0.450868	0.225434	−	0.974258i	$-0.427620\pi$
$997$	14.2363	0.450868	0.225434	+	0.974258i	$0.427620\pi$
$998$	−11.1322	−0.352385
$999$	−0.394811	−0.0124913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.v.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.v.1.9	✓	9	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.19847 q^{5} +1.00000 q^{6} -2.69790 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.19847 q^{5} +1.00000 q^{6} -2.69790 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.19847 q^{10} +1.19484 q^{11} -1.00000 q^{12} -4.58356 q^{13} +2.69790 q^{14} -4.19847 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -1.48304 q^{19} +4.19847 q^{20} +2.69790 q^{21} -1.19484 q^{22} -7.59828 q^{23} +1.00000 q^{24} +12.6271 q^{25} +4.58356 q^{26} -1.00000 q^{27} -2.69790 q^{28} +1.17977 q^{29} +4.19847 q^{30} +4.98944 q^{31} -1.00000 q^{32} -1.19484 q^{33} +1.00000 q^{34} -11.3271 q^{35} +1.00000 q^{36} +0.394811 q^{37} +1.48304 q^{38} +4.58356 q^{39} -4.19847 q^{40} +8.27729 q^{41} -2.69790 q^{42} -0.00309616 q^{43} +1.19484 q^{44} +4.19847 q^{45} +7.59828 q^{46} +2.16664 q^{47} -1.00000 q^{48} +0.278679 q^{49} -12.6271 q^{50} +1.00000 q^{51} -4.58356 q^{52} -4.75723 q^{53} +1.00000 q^{54} +5.01649 q^{55} +2.69790 q^{56} +1.48304 q^{57} -1.17977 q^{58} -1.00000 q^{59} -4.19847 q^{60} +3.91284 q^{61} -4.98944 q^{62} -2.69790 q^{63} +1.00000 q^{64} -19.2439 q^{65} +1.19484 q^{66} +13.6349 q^{67} -1.00000 q^{68} +7.59828 q^{69} +11.3271 q^{70} -12.7395 q^{71} -1.00000 q^{72} -2.98757 q^{73} -0.394811 q^{74} -12.6271 q^{75} -1.48304 q^{76} -3.22356 q^{77} -4.58356 q^{78} +6.59838 q^{79} +4.19847 q^{80} +1.00000 q^{81} -8.27729 q^{82} -15.7167 q^{83} +2.69790 q^{84} -4.19847 q^{85} +0.00309616 q^{86} -1.17977 q^{87} -1.19484 q^{88} +2.83334 q^{89} -4.19847 q^{90} +12.3660 q^{91} -7.59828 q^{92} -4.98944 q^{93} -2.16664 q^{94} -6.22651 q^{95} +1.00000 q^{96} -19.2681 q^{97} -0.278679 q^{98} +1.19484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9} - 6 q^{10} + q^{11} - 9 q^{12} + 4 q^{13} + 11 q^{14} - 6 q^{15} + 9 q^{16} - 9 q^{17} - 9 q^{18} - 13 q^{19} + 6 q^{20} + 11 q^{21} - q^{22} - 6 q^{23} + 9 q^{24} + 9 q^{25} - 4 q^{26} - 9 q^{27} - 11 q^{28} + 10 q^{29} + 6 q^{30} + q^{31} - 9 q^{32} - q^{33} + 9 q^{34} + 6 q^{35} + 9 q^{36} - 2 q^{37} + 13 q^{38} - 4 q^{39} - 6 q^{40} + 20 q^{41} - 11 q^{42} - 17 q^{43} + q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 9 q^{48} + 2 q^{49} - 9 q^{50} + 9 q^{51} + 4 q^{52} + 16 q^{53} + 9 q^{54} - 17 q^{55} + 11 q^{56} + 13 q^{57} - 10 q^{58} - 9 q^{59} - 6 q^{60} - 9 q^{61} - q^{62} - 11 q^{63} + 9 q^{64} + q^{66} - 8 q^{67} - 9 q^{68} + 6 q^{69} - 6 q^{70} - 8 q^{71} - 9 q^{72} - 20 q^{73} + 2 q^{74} - 9 q^{75} - 13 q^{76} - 32 q^{77} + 4 q^{78} - 29 q^{79} + 6 q^{80} + 9 q^{81} - 20 q^{82} - 16 q^{83} + 11 q^{84} - 6 q^{85} + 17 q^{86} - 10 q^{87} - q^{88} + 11 q^{89} - 6 q^{90} - 13 q^{91} - 6 q^{92} - q^{93} - 4 q^{94} + 5 q^{95} + 9 q^{96} + 17 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9 - 6 * q^10 + q^11 - 9 * q^12 + 4 * q^13 + 11 * q^14 - 6 * q^15 + 9 * q^16 - 9 * q^17 - 9 * q^18 - 13 * q^19 + 6 * q^20 + 11 * q^21 - q^22 - 6 * q^23 + 9 * q^24 + 9 * q^25 - 4 * q^26 - 9 * q^27 - 11 * q^28 + 10 * q^29 + 6 * q^30 + q^31 - 9 * q^32 - q^33 + 9 * q^34 + 6 * q^35 + 9 * q^36 - 2 * q^37 + 13 * q^38 - 4 * q^39 - 6 * q^40 + 20 * q^41 - 11 * q^42 - 17 * q^43 + q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 - 9 * q^50 + 9 * q^51 + 4 * q^52 + 16 * q^53 + 9 * q^54 - 17 * q^55 + 11 * q^56 + 13 * q^57 - 10 * q^58 - 9 * q^59 - 6 * q^60 - 9 * q^61 - q^62 - 11 * q^63 + 9 * q^64 + q^66 - 8 * q^67 - 9 * q^68 + 6 * q^69 - 6 * q^70 - 8 * q^71 - 9 * q^72 - 20 * q^73 + 2 * q^74 - 9 * q^75 - 13 * q^76 - 32 * q^77 + 4 * q^78 - 29 * q^79 + 6 * q^80 + 9 * q^81 - 20 * q^82 - 16 * q^83 + 11 * q^84 - 6 * q^85 + 17 * q^86 - 10 * q^87 - q^88 + 11 * q^89 - 6 * q^90 - 13 * q^91 - 6 * q^92 - q^93 - 4 * q^94 + 5 * q^95 + 9 * q^96 + 17 * q^97 - 2 * q^98 + q^99

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