LMFDB - Embedded newform 6018.2.a.ba.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:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 31 x^{10} + 111 x^{9} + 381 x^{8} - 1101 x^{7} - 2301 x^{6} + 4690 x^{5} + \cdots + 5653 $ x^12 - 4x^11 - 31x^10 + 111x^9 + 381x^8 - 1101x^7 - 2301x^6 + 4690x^5 + 6915x^4 - 8325x^3 - 10082x^2 + 5149*x + 5653
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.17036$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.17036 q^{5} +1.00000 q^{6} +1.24708 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.17036 q^{5} +1.00000 q^{6} +1.24708 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.17036 q^{10} -0.523612 q^{11} +1.00000 q^{12} -1.51169 q^{13} +1.24708 q^{14} +2.17036 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +4.77765 q^{19} +2.17036 q^{20} +1.24708 q^{21} -0.523612 q^{22} +5.65951 q^{23} +1.00000 q^{24} -0.289551 q^{25} -1.51169 q^{26} +1.00000 q^{27} +1.24708 q^{28} +1.53004 q^{29} +2.17036 q^{30} +3.38924 q^{31} +1.00000 q^{32} -0.523612 q^{33} -1.00000 q^{34} +2.70661 q^{35} +1.00000 q^{36} +2.69225 q^{37} +4.77765 q^{38} -1.51169 q^{39} +2.17036 q^{40} -9.76511 q^{41} +1.24708 q^{42} +3.60939 q^{43} -0.523612 q^{44} +2.17036 q^{45} +5.65951 q^{46} -1.25410 q^{47} +1.00000 q^{48} -5.44479 q^{49} -0.289551 q^{50} -1.00000 q^{51} -1.51169 q^{52} +6.96173 q^{53} +1.00000 q^{54} -1.13642 q^{55} +1.24708 q^{56} +4.77765 q^{57} +1.53004 q^{58} +1.00000 q^{59} +2.17036 q^{60} -4.29589 q^{61} +3.38924 q^{62} +1.24708 q^{63} +1.00000 q^{64} -3.28090 q^{65} -0.523612 q^{66} -4.91934 q^{67} -1.00000 q^{68} +5.65951 q^{69} +2.70661 q^{70} +14.1242 q^{71} +1.00000 q^{72} -8.38909 q^{73} +2.69225 q^{74} -0.289551 q^{75} +4.77765 q^{76} -0.652986 q^{77} -1.51169 q^{78} -0.117544 q^{79} +2.17036 q^{80} +1.00000 q^{81} -9.76511 q^{82} +2.56861 q^{83} +1.24708 q^{84} -2.17036 q^{85} +3.60939 q^{86} +1.53004 q^{87} -0.523612 q^{88} -10.0215 q^{89} +2.17036 q^{90} -1.88520 q^{91} +5.65951 q^{92} +3.38924 q^{93} -1.25410 q^{94} +10.3692 q^{95} +1.00000 q^{96} +12.4609 q^{97} -5.44479 q^{98} -0.523612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.17036	0.970613	0.485307	−	0.874344i	$-0.338708\pi$
$5$	2.17036	0.970613	0.485307	+	0.874344i	$0.338708\pi$
$6$	1.00000	0.408248
$7$	1.24708	0.471352	0.235676	−	0.971832i	$-0.424270\pi$
$7$	1.24708	0.471352	0.235676	+	0.971832i	$0.424270\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.17036	0.686327
$11$	−0.523612	−0.157875	−0.0789375	−	0.996880i	$-0.525153\pi$
$11$	−0.523612	−0.157875	−0.0789375	+	0.996880i	$0.525153\pi$
$12$	1.00000	0.288675
$13$	−1.51169	−0.419267	−0.209633	−	0.977780i	$-0.567227\pi$
$13$	−1.51169	−0.419267	−0.209633	+	0.977780i	$0.567227\pi$
$14$	1.24708	0.333296
$15$	2.17036	0.560384
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	4.77765	1.09607	0.548034	−	0.836456i	$-0.315377\pi$
$19$	4.77765	1.09607	0.548034	+	0.836456i	$0.315377\pi$
$20$	2.17036	0.485307
$21$	1.24708	0.272135
$22$	−0.523612	−0.111634
$23$	5.65951	1.18009	0.590045	−	0.807370i	$-0.299110\pi$
$23$	5.65951	1.18009	0.590045	+	0.807370i	$0.299110\pi$
$24$	1.00000	0.204124
$25$	−0.289551	−0.0579102
$26$	−1.51169	−0.296467
$27$	1.00000	0.192450
$28$	1.24708	0.235676
$29$	1.53004	0.284122	0.142061	−	0.989858i	$-0.454627\pi$
$29$	1.53004	0.284122	0.142061	+	0.989858i	$0.454627\pi$
$30$	2.17036	0.396251
$31$	3.38924	0.608725	0.304362	−	0.952556i	$-0.401557\pi$
$31$	3.38924	0.608725	0.304362	+	0.952556i	$0.401557\pi$
$32$	1.00000	0.176777
$33$	−0.523612	−0.0911491
$34$	−1.00000	−0.171499
$35$	2.70661	0.457500
$36$	1.00000	0.166667
$37$	2.69225	0.442603	0.221301	−	0.975205i	$-0.428970\pi$
$37$	2.69225	0.442603	0.221301	+	0.975205i	$0.428970\pi$
$38$	4.77765	0.775036
$39$	−1.51169	−0.242064
$40$	2.17036	0.343164
$41$	−9.76511	−1.52505	−0.762527	−	0.646957i	$-0.776041\pi$
$41$	−9.76511	−1.52505	−0.762527	+	0.646957i	$0.776041\pi$
$42$	1.24708	0.192429
$43$	3.60939	0.550427	0.275214	−	0.961383i	$-0.411251\pi$
$43$	3.60939	0.550427	0.275214	+	0.961383i	$0.411251\pi$
$44$	−0.523612	−0.0789375
$45$	2.17036	0.323538
$46$	5.65951	0.834450
$47$	−1.25410	−0.182929	−0.0914646	−	0.995808i	$-0.529155\pi$
$47$	−1.25410	−0.182929	−0.0914646	+	0.995808i	$0.529155\pi$
$48$	1.00000	0.144338
$49$	−5.44479	−0.777827
$50$	−0.289551	−0.0409487
$51$	−1.00000	−0.140028
$52$	−1.51169	−0.209633
$53$	6.96173	0.956267	0.478133	−	0.878287i	$-0.341314\pi$
$53$	6.96173	0.956267	0.478133	+	0.878287i	$0.341314\pi$
$54$	1.00000	0.136083
$55$	−1.13642	−0.153235
$56$	1.24708	0.166648
$57$	4.77765	0.632815
$58$	1.53004	0.200905
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	2.17036	0.280192
$61$	−4.29589	−0.550032	−0.275016	−	0.961440i	$-0.588683\pi$
$61$	−4.29589	−0.550032	−0.275016	+	0.961440i	$0.588683\pi$
$62$	3.38924	0.430433
$63$	1.24708	0.157117
$64$	1.00000	0.125000
$65$	−3.28090	−0.406946
$66$	−0.523612	−0.0644522
$67$	−4.91934	−0.600992	−0.300496	−	0.953783i	$-0.597152\pi$
$67$	−4.91934	−0.600992	−0.300496	+	0.953783i	$0.597152\pi$
$68$	−1.00000	−0.121268
$69$	5.65951	0.681325
$70$	2.70661	0.323502
$71$	14.1242	1.67623	0.838116	−	0.545492i	$-0.183657\pi$
$71$	14.1242	1.67623	0.838116	+	0.545492i	$0.183657\pi$
$72$	1.00000	0.117851
$73$	−8.38909	−0.981869	−0.490934	−	0.871196i	$-0.663345\pi$
$73$	−8.38909	−0.981869	−0.490934	+	0.871196i	$0.663345\pi$
$74$	2.69225	0.312968
$75$	−0.289551	−0.0334345
$76$	4.77765	0.548034
$77$	−0.652986	−0.0744147
$78$	−1.51169	−0.171165
$79$	−0.117544	−0.0132247	−0.00661235	−	0.999978i	$-0.502105\pi$
$79$	−0.117544	−0.0132247	−0.00661235	+	0.999978i	$0.502105\pi$
$80$	2.17036	0.242653
$81$	1.00000	0.111111
$82$	−9.76511	−1.07838
$83$	2.56861	0.281942	0.140971	−	0.990014i	$-0.454978\pi$
$83$	2.56861	0.281942	0.140971	+	0.990014i	$0.454978\pi$
$84$	1.24708	0.136068
$85$	−2.17036	−0.235408
$86$	3.60939	0.389211
$87$	1.53004	0.164038
$88$	−0.523612	−0.0558172
$89$	−10.0215	−1.06228	−0.531140	−	0.847284i	$-0.678236\pi$
$89$	−10.0215	−1.06228	−0.531140	+	0.847284i	$0.678236\pi$
$90$	2.17036	0.228776
$91$	−1.88520	−0.197622
$92$	5.65951	0.590045
$93$	3.38924	0.351447
$94$	−1.25410	−0.129350
$95$	10.3692	1.06386
$96$	1.00000	0.102062
$97$	12.4609	1.26522	0.632608	−	0.774472i	$-0.281984\pi$
$97$	12.4609	1.26522	0.632608	+	0.774472i	$0.281984\pi$
$98$	−5.44479	−0.550007
$99$	−0.523612	−0.0526250
$100$	−0.289551	−0.0289551
$101$	14.7373	1.46642	0.733210	−	0.680003i	$-0.238021\pi$
$101$	14.7373	1.46642	0.733210	+	0.680003i	$0.238021\pi$
$102$	−1.00000	−0.0990148
$103$	13.5352	1.33366	0.666831	−	0.745209i	$-0.267650\pi$
$103$	13.5352	1.33366	0.666831	+	0.745209i	$0.267650\pi$
$104$	−1.51169	−0.148233
$105$	2.70661	0.264138
$106$	6.96173	0.676183
$107$	−7.91596	−0.765265	−0.382632	−	0.923901i	$-0.624982\pi$
$107$	−7.91596	−0.765265	−0.382632	+	0.923901i	$0.624982\pi$
$108$	1.00000	0.0962250
$109$	11.2877	1.08117	0.540585	−	0.841289i	$-0.318203\pi$
$109$	11.2877	1.08117	0.540585	+	0.841289i	$0.318203\pi$
$110$	−1.13642	−0.108354
$111$	2.69225	0.255537
$112$	1.24708	0.117838
$113$	−4.64717	−0.437169	−0.218585	−	0.975818i	$-0.570144\pi$
$113$	−4.64717	−0.437169	−0.218585	+	0.975818i	$0.570144\pi$
$114$	4.77765	0.447467
$115$	12.2832	1.14541
$116$	1.53004	0.142061
$117$	−1.51169	−0.139756
$118$	1.00000	0.0920575
$119$	−1.24708	−0.114320
$120$	2.17036	0.198126
$121$	−10.7258	−0.975076
$122$	−4.29589	−0.388932
$123$	−9.76511	−0.880490
$124$	3.38924	0.304362
$125$	−11.4802	−1.02682
$126$	1.24708	0.111099
$127$	−10.3965	−0.922538	−0.461269	−	0.887260i	$-0.652606\pi$
$127$	−10.3965	−0.922538	−0.461269	+	0.887260i	$0.652606\pi$
$128$	1.00000	0.0883883
$129$	3.60939	0.317789
$130$	−3.28090	−0.287754
$131$	−17.4911	−1.52820	−0.764101	−	0.645097i	$-0.776817\pi$
$131$	−17.4911	−1.52820	−0.764101	+	0.645097i	$0.776817\pi$
$132$	−0.523612	−0.0455746
$133$	5.95811	0.516633
$134$	−4.91934	−0.424966
$135$	2.17036	0.186795
$136$	−1.00000	−0.0857493
$137$	3.10311	0.265117	0.132558	−	0.991175i	$-0.457681\pi$
$137$	3.10311	0.265117	0.132558	+	0.991175i	$0.457681\pi$
$138$	5.65951	0.481770
$139$	15.9070	1.34922	0.674608	−	0.738177i	$-0.264313\pi$
$139$	15.9070	1.34922	0.674608	+	0.738177i	$0.264313\pi$
$140$	2.70661	0.228750
$141$	−1.25410	−0.105614
$142$	14.1242	1.18528
$143$	0.791538	0.0661917
$144$	1.00000	0.0833333
$145$	3.32074	0.275773
$146$	−8.38909	−0.694286
$147$	−5.44479	−0.449079
$148$	2.69225	0.221301
$149$	20.4195	1.67283	0.836417	−	0.548094i	$-0.184646\pi$
$149$	20.4195	1.67283	0.836417	+	0.548094i	$0.184646\pi$
$150$	−0.289551	−0.0236418
$151$	1.97865	0.161020	0.0805102	−	0.996754i	$-0.474345\pi$
$151$	1.97865	0.161020	0.0805102	+	0.996754i	$0.474345\pi$
$152$	4.77765	0.387518
$153$	−1.00000	−0.0808452
$154$	−0.652986	−0.0526191
$155$	7.35585	0.590836
$156$	−1.51169	−0.121032
$157$	−3.45122	−0.275437	−0.137719	−	0.990471i	$-0.543977\pi$
$157$	−3.45122	−0.275437	−0.137719	+	0.990471i	$0.543977\pi$
$158$	−0.117544	−0.00935127
$159$	6.96173	0.552101
$160$	2.17036	0.171582
$161$	7.05787	0.556238
$162$	1.00000	0.0785674
$163$	−4.94496	−0.387319	−0.193660	−	0.981069i	$-0.562036\pi$
$163$	−4.94496	−0.387319	−0.193660	+	0.981069i	$0.562036\pi$
$164$	−9.76511	−0.762527
$165$	−1.13642	−0.0884705
$166$	2.56861	0.199363
$167$	18.7475	1.45073	0.725364	−	0.688366i	$-0.241672\pi$
$167$	18.7475	1.45073	0.725364	+	0.688366i	$0.241672\pi$
$168$	1.24708	0.0962143
$169$	−10.7148	−0.824215
$170$	−2.17036	−0.166459
$171$	4.77765	0.365356
$172$	3.60939	0.275214
$173$	−23.3052	−1.77186	−0.885929	−	0.463820i	$-0.846478\pi$
$173$	−23.3052	−1.77186	−0.885929	+	0.463820i	$0.846478\pi$
$174$	1.53004	0.115992
$175$	−0.361093	−0.0272961
$176$	−0.523612	−0.0394687
$177$	1.00000	0.0751646
$178$	−10.0215	−0.751146
$179$	−3.20300	−0.239403	−0.119702	−	0.992810i	$-0.538194\pi$
$179$	−3.20300	−0.239403	−0.119702	+	0.992810i	$0.538194\pi$
$180$	2.17036	0.161769
$181$	−15.4858	−1.15105	−0.575527	−	0.817783i	$-0.695203\pi$
$181$	−15.4858	−1.15105	−0.575527	+	0.817783i	$0.695203\pi$
$182$	−1.88520	−0.139740
$183$	−4.29589	−0.317561
$184$	5.65951	0.417225
$185$	5.84314	0.429596
$186$	3.38924	0.248511
$187$	0.523612	0.0382903
$188$	−1.25410	−0.0914646
$189$	1.24708	0.0907117
$190$	10.3692	0.752261
$191$	11.4559	0.828921	0.414460	−	0.910067i	$-0.363970\pi$
$191$	11.4559	0.828921	0.414460	+	0.910067i	$0.363970\pi$
$192$	1.00000	0.0721688
$193$	26.8899	1.93558	0.967790	−	0.251760i	$-0.0810093\pi$
$193$	26.8899	1.93558	0.967790	+	0.251760i	$0.0810093\pi$
$194$	12.4609	0.894643
$195$	−3.28090	−0.234950
$196$	−5.44479	−0.388914
$197$	−18.5725	−1.32324	−0.661618	−	0.749841i	$-0.730130\pi$
$197$	−18.5725	−1.32324	−0.661618	+	0.749841i	$0.730130\pi$
$198$	−0.523612	−0.0372115
$199$	−8.42020	−0.596892	−0.298446	−	0.954426i	$-0.596468\pi$
$199$	−8.42020	−0.596892	−0.298446	+	0.954426i	$0.596468\pi$
$200$	−0.289551	−0.0204744
$201$	−4.91934	−0.346983
$202$	14.7373	1.03692
$203$	1.90809	0.133922
$204$	−1.00000	−0.0700140
$205$	−21.1938	−1.48024
$206$	13.5352	0.943041
$207$	5.65951	0.393363
$208$	−1.51169	−0.104817
$209$	−2.50163	−0.173042
$210$	2.70661	0.186774
$211$	−19.9817	−1.37559	−0.687797	−	0.725903i	$-0.741422\pi$
$211$	−19.9817	−1.37559	−0.687797	+	0.725903i	$0.741422\pi$
$212$	6.96173	0.478133
$213$	14.1242	0.967773
$214$	−7.91596	−0.541124
$215$	7.83367	0.534252
$216$	1.00000	0.0680414
$217$	4.22665	0.286924
$218$	11.2877	0.764503
$219$	−8.38909	−0.566882
$220$	−1.13642	−0.0766177
$221$	1.51169	0.101687
$222$	2.69225	0.180692
$223$	−23.1094	−1.54752	−0.773761	−	0.633478i	$-0.781627\pi$
$223$	−23.1094	−1.54752	−0.773761	+	0.633478i	$0.781627\pi$
$224$	1.24708	0.0833240
$225$	−0.289551	−0.0193034
$226$	−4.64717	−0.309125
$227$	−21.4427	−1.42320	−0.711601	−	0.702584i	$-0.752030\pi$
$227$	−21.4427	−1.42320	−0.711601	+	0.702584i	$0.752030\pi$
$228$	4.77765	0.316407
$229$	−19.9185	−1.31625	−0.658126	−	0.752908i	$-0.728651\pi$
$229$	−19.9185	−1.31625	−0.658126	+	0.752908i	$0.728651\pi$
$230$	12.2832	0.809928
$231$	−0.652986	−0.0429633
$232$	1.53004	0.100452
$233$	11.6350	0.762231	0.381116	−	0.924527i	$-0.375540\pi$
$233$	11.6350	0.762231	0.381116	+	0.924527i	$0.375540\pi$
$234$	−1.51169	−0.0988222
$235$	−2.72184	−0.177553
$236$	1.00000	0.0650945
$237$	−0.117544	−0.00763528
$238$	−1.24708	−0.0808362
$239$	10.6456	0.688606	0.344303	−	0.938859i	$-0.388115\pi$
$239$	10.6456	0.688606	0.344303	+	0.938859i	$0.388115\pi$
$240$	2.17036	0.140096
$241$	11.8489	0.763252	0.381626	−	0.924317i	$-0.375364\pi$
$241$	11.8489	0.763252	0.381626	+	0.924317i	$0.375364\pi$
$242$	−10.7258	−0.689483
$243$	1.00000	0.0641500
$244$	−4.29589	−0.275016
$245$	−11.8171	−0.754969
$246$	−9.76511	−0.622600
$247$	−7.22231	−0.459545
$248$	3.38924	0.215217
$249$	2.56861	0.162779
$250$	−11.4802	−0.726072
$251$	−22.6365	−1.42880	−0.714402	−	0.699736i	$-0.753301\pi$
$251$	−22.6365	−1.42880	−0.714402	+	0.699736i	$0.753301\pi$
$252$	1.24708	0.0785587
$253$	−2.96339	−0.186307
$254$	−10.3965	−0.652333
$255$	−2.17036	−0.135913
$256$	1.00000	0.0625000
$257$	−20.8092	−1.29804	−0.649021	−	0.760771i	$-0.724821\pi$
$257$	−20.8092	−1.29804	−0.649021	+	0.760771i	$0.724821\pi$
$258$	3.60939	0.224711
$259$	3.35745	0.208622
$260$	−3.28090	−0.203473
$261$	1.53004	0.0947074
$262$	−17.4911	−1.08060
$263$	−0.891193	−0.0549533	−0.0274767	−	0.999622i	$-0.508747\pi$
$263$	−0.891193	−0.0549533	−0.0274767	+	0.999622i	$0.508747\pi$
$264$	−0.523612	−0.0322261
$265$	15.1094	0.928165
$266$	5.95811	0.365315
$267$	−10.0215	−0.613308
$268$	−4.91934	−0.300496
$269$	12.3034	0.750149	0.375075	−	0.926995i	$-0.377617\pi$
$269$	12.3034	0.750149	0.375075	+	0.926995i	$0.377617\pi$
$270$	2.17036	0.132084
$271$	22.9968	1.39695	0.698477	−	0.715633i	$-0.253862\pi$
$271$	22.9968	1.39695	0.698477	+	0.715633i	$0.253862\pi$
$272$	−1.00000	−0.0606339
$273$	−1.88520	−0.114097
$274$	3.10311	0.187466
$275$	0.151612	0.00914257
$276$	5.65951	0.340663
$277$	15.4961	0.931072	0.465536	−	0.885029i	$-0.345862\pi$
$277$	15.4961	0.931072	0.465536	+	0.885029i	$0.345862\pi$
$278$	15.9070	0.954039
$279$	3.38924	0.202908
$280$	2.70661	0.161751
$281$	14.1241	0.842571	0.421285	−	0.906928i	$-0.361579\pi$
$281$	14.1241	0.842571	0.421285	+	0.906928i	$0.361579\pi$
$282$	−1.25410	−0.0746805
$283$	−20.3792	−1.21142	−0.605710	−	0.795686i	$-0.707111\pi$
$283$	−20.3792	−1.21142	−0.605710	+	0.795686i	$0.707111\pi$
$284$	14.1242	0.838116
$285$	10.3692	0.614218
$286$	0.791538	0.0468046
$287$	−12.1779	−0.718837
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	3.32074	0.195001
$291$	12.4609	0.730473
$292$	−8.38909	−0.490934
$293$	24.8638	1.45256	0.726279	−	0.687401i	$-0.241248\pi$
$293$	24.8638	1.45256	0.726279	+	0.687401i	$0.241248\pi$
$294$	−5.44479	−0.317547
$295$	2.17036	0.126363
$296$	2.69225	0.156484
$297$	−0.523612	−0.0303830
$298$	20.4195	1.18287
$299$	−8.55542	−0.494773
$300$	−0.289551	−0.0167172
$301$	4.50120	0.259445
$302$	1.97865	0.113859
$303$	14.7373	0.846638
$304$	4.77765	0.274017
$305$	−9.32362	−0.533869
$306$	−1.00000	−0.0571662
$307$	−13.4070	−0.765180	−0.382590	−	0.923918i	$-0.624968\pi$
$307$	−13.4070	−0.765180	−0.382590	+	0.923918i	$0.624968\pi$
$308$	−0.652986	−0.0372073
$309$	13.5352	0.769990
$310$	7.35585	0.417784
$311$	−21.8580	−1.23945	−0.619727	−	0.784817i	$-0.712757\pi$
$311$	−21.8580	−1.23945	−0.619727	+	0.784817i	$0.712757\pi$
$312$	−1.51169	−0.0855825
$313$	3.10738	0.175639	0.0878197	−	0.996136i	$-0.472010\pi$
$313$	3.10738	0.175639	0.0878197	+	0.996136i	$0.472010\pi$
$314$	−3.45122	−0.194764
$315$	2.70661	0.152500
$316$	−0.117544	−0.00661235
$317$	1.19358	0.0670379	0.0335189	−	0.999438i	$-0.489329\pi$
$317$	1.19358	0.0670379	0.0335189	+	0.999438i	$0.489329\pi$
$318$	6.96173	0.390394
$319$	−0.801150	−0.0448558
$320$	2.17036	0.121327
$321$	−7.91596	−0.441826
$322$	7.05787	0.393320
$323$	−4.77765	−0.265835
$324$	1.00000	0.0555556
$325$	0.437711	0.0242798
$326$	−4.94496	−0.273876
$327$	11.2877	0.624214
$328$	−9.76511	−0.539188
$329$	−1.56396	−0.0862240
$330$	−1.13642	−0.0625581
$331$	−1.33702	−0.0734892	−0.0367446	−	0.999325i	$-0.511699\pi$
$331$	−1.33702	−0.0734892	−0.0367446	+	0.999325i	$0.511699\pi$
$332$	2.56861	0.140971
$333$	2.69225	0.147534
$334$	18.7475	1.02582
$335$	−10.6767	−0.583331
$336$	1.24708	0.0680338
$337$	−34.3893	−1.87330	−0.936651	−	0.350263i	$-0.886092\pi$
$337$	−34.3893	−1.87330	−0.936651	+	0.350263i	$0.886092\pi$
$338$	−10.7148	−0.582808
$339$	−4.64717	−0.252400
$340$	−2.17036	−0.117704
$341$	−1.77464	−0.0961024
$342$	4.77765	0.258345
$343$	−15.5197	−0.837982
$344$	3.60939	0.194605
$345$	12.2832	0.661303
$346$	−23.3052	−1.25289
$347$	1.67568	0.0899550	0.0449775	−	0.998988i	$-0.485678\pi$
$347$	1.67568	0.0899550	0.0449775	+	0.998988i	$0.485678\pi$
$348$	1.53004	0.0820190
$349$	−3.60263	−0.192844	−0.0964222	−	0.995341i	$-0.530740\pi$
$349$	−3.60263	−0.192844	−0.0964222	+	0.995341i	$0.530740\pi$
$350$	−0.361093	−0.0193013
$351$	−1.51169	−0.0806880
$352$	−0.523612	−0.0279086
$353$	−32.3052	−1.71943	−0.859716	−	0.510773i	$-0.829359\pi$
$353$	−32.3052	−1.71943	−0.859716	+	0.510773i	$0.829359\pi$
$354$	1.00000	0.0531494
$355$	30.6545	1.62697
$356$	−10.0215	−0.531140
$357$	−1.24708	−0.0660025
$358$	−3.20300	−0.169284
$359$	−16.9596	−0.895093	−0.447547	−	0.894261i	$-0.647702\pi$
$359$	−16.9596	−0.895093	−0.447547	+	0.894261i	$0.647702\pi$
$360$	2.17036	0.114388
$361$	3.82590	0.201363
$362$	−15.4858	−0.813917
$363$	−10.7258	−0.562960
$364$	−1.88520	−0.0988111
$365$	−18.2073	−0.953015
$366$	−4.29589	−0.224550
$367$	0.105587	0.00551157	0.00275579	−	0.999996i	$-0.499123\pi$
$367$	0.105587	0.00551157	0.00275579	+	0.999996i	$0.499123\pi$
$368$	5.65951	0.295023
$369$	−9.76511	−0.508351
$370$	5.84314	0.303770
$371$	8.68183	0.450738
$372$	3.38924	0.175724
$373$	25.9839	1.34539	0.672697	−	0.739918i	$-0.265136\pi$
$373$	25.9839	1.34539	0.672697	+	0.739918i	$0.265136\pi$
$374$	0.523612	0.0270753
$375$	−11.4802	−0.592836
$376$	−1.25410	−0.0646752
$377$	−2.31295	−0.119123
$378$	1.24708	0.0641429
$379$	18.8066	0.966029	0.483015	−	0.875612i	$-0.339542\pi$
$379$	18.8066	0.966029	0.483015	+	0.875612i	$0.339542\pi$
$380$	10.3692	0.531929
$381$	−10.3965	−0.532627
$382$	11.4559	0.586136
$383$	19.8157	1.01253	0.506266	−	0.862377i	$-0.331025\pi$
$383$	19.8157	1.01253	0.506266	+	0.862377i	$0.331025\pi$
$384$	1.00000	0.0510310
$385$	−1.41721	−0.0722278
$386$	26.8899	1.36866
$387$	3.60939	0.183476
$388$	12.4609	0.632608
$389$	−27.7689	−1.40794	−0.703968	−	0.710231i	$-0.748590\pi$
$389$	−27.7689	−1.40794	−0.703968	+	0.710231i	$0.748590\pi$
$390$	−3.28090	−0.166135
$391$	−5.65951	−0.286214
$392$	−5.44479	−0.275003
$393$	−17.4911	−0.882308
$394$	−18.5725	−0.935669
$395$	−0.255112	−0.0128361
$396$	−0.523612	−0.0263125
$397$	−7.53440	−0.378140	−0.189070	−	0.981964i	$-0.560547\pi$
$397$	−7.53440	−0.378140	−0.189070	+	0.981964i	$0.560547\pi$
$398$	−8.42020	−0.422066
$399$	5.95811	0.298278
$400$	−0.289551	−0.0144776
$401$	32.2759	1.61178	0.805891	−	0.592064i	$-0.201687\pi$
$401$	32.2759	1.61178	0.805891	+	0.592064i	$0.201687\pi$
$402$	−4.91934	−0.245354
$403$	−5.12347	−0.255218
$404$	14.7373	0.733210
$405$	2.17036	0.107846
$406$	1.90809	0.0946968
$407$	−1.40969	−0.0698759
$408$	−1.00000	−0.0495074
$409$	−3.10227	−0.153397	−0.0766986	−	0.997054i	$-0.524438\pi$
$409$	−3.10227	−0.153397	−0.0766986	+	0.997054i	$0.524438\pi$
$410$	−21.1938	−1.04669
$411$	3.10311	0.153065
$412$	13.5352	0.666831
$413$	1.24708	0.0613648
$414$	5.65951	0.278150
$415$	5.57480	0.273656
$416$	−1.51169	−0.0741166
$417$	15.9070	0.778970
$418$	−2.50163	−0.122359
$419$	37.9098	1.85201	0.926007	−	0.377506i	$-0.123218\pi$
$419$	37.9098	1.85201	0.926007	+	0.377506i	$0.123218\pi$
$420$	2.70661	0.132069
$421$	12.4174	0.605189	0.302594	−	0.953119i	$-0.402147\pi$
$421$	12.4174	0.605189	0.302594	+	0.953119i	$0.402147\pi$
$422$	−19.9817	−0.972692
$423$	−1.25410	−0.0609764
$424$	6.96173	0.338091
$425$	0.289551	0.0140453
$426$	14.1242	0.684319
$427$	−5.35732	−0.259259
$428$	−7.91596	−0.382632
$429$	0.791538	0.0382158
$430$	7.83367	0.377773
$431$	38.3593	1.84770	0.923852	−	0.382749i	$-0.125023\pi$
$431$	38.3593	1.84770	0.923852	+	0.382749i	$0.125023\pi$
$432$	1.00000	0.0481125
$433$	27.4286	1.31813	0.659067	−	0.752085i	$-0.270952\pi$
$433$	27.4286	1.31813	0.659067	+	0.752085i	$0.270952\pi$
$434$	4.22665	0.202886
$435$	3.32074	0.159217
$436$	11.2877	0.540585
$437$	27.0392	1.29346
$438$	−8.38909	−0.400846
$439$	−13.0146	−0.621151	−0.310575	−	0.950549i	$-0.600522\pi$
$439$	−13.0146	−0.621151	−0.310575	+	0.950549i	$0.600522\pi$
$440$	−1.13642	−0.0541769
$441$	−5.44479	−0.259276
$442$	1.51169	0.0719037
$443$	−34.2088	−1.62531	−0.812654	−	0.582746i	$-0.801978\pi$
$443$	−34.2088	−1.62531	−0.812654	+	0.582746i	$0.801978\pi$
$444$	2.69225	0.127768
$445$	−21.7503	−1.03106
$446$	−23.1094	−1.09426
$447$	20.4195	0.965811
$448$	1.24708	0.0589190
$449$	17.9559	0.847391	0.423696	−	0.905805i	$-0.360733\pi$
$449$	17.9559	0.847391	0.423696	+	0.905805i	$0.360733\pi$
$450$	−0.289551	−0.0136496
$451$	5.11313	0.240768
$452$	−4.64717	−0.218585
$453$	1.97865	0.0929652
$454$	−21.4427	−1.00636
$455$	−4.09155	−0.191815
$456$	4.77765	0.223734
$457$	19.0469	0.890976	0.445488	−	0.895288i	$-0.353030\pi$
$457$	19.0469	0.890976	0.445488	+	0.895288i	$0.353030\pi$
$458$	−19.9185	−0.930731
$459$	−1.00000	−0.0466760
$460$	12.2832	0.572705
$461$	9.50153	0.442530	0.221265	−	0.975214i	$-0.428981\pi$
$461$	9.50153	0.442530	0.221265	+	0.975214i	$0.428981\pi$
$462$	−0.652986	−0.0303797
$463$	−5.65280	−0.262708	−0.131354	−	0.991336i	$-0.541932\pi$
$463$	−5.65280	−0.262708	−0.131354	+	0.991336i	$0.541932\pi$
$464$	1.53004	0.0710306
$465$	7.35585	0.341120
$466$	11.6350	0.538979
$467$	17.2722	0.799263	0.399632	−	0.916676i	$-0.369138\pi$
$467$	17.2722	0.799263	0.399632	+	0.916676i	$0.369138\pi$
$468$	−1.51169	−0.0698778
$469$	−6.13480	−0.283279
$470$	−2.72184	−0.125549
$471$	−3.45122	−0.159024
$472$	1.00000	0.0460287
$473$	−1.88992	−0.0868987
$474$	−0.117544	−0.00539896
$475$	−1.38337	−0.0634735
$476$	−1.24708	−0.0571598
$477$	6.96173	0.318756
$478$	10.6456	0.486918
$479$	−17.0940	−0.781047	−0.390523	−	0.920593i	$-0.627706\pi$
$479$	−17.0940	−0.781047	−0.390523	+	0.920593i	$0.627706\pi$
$480$	2.17036	0.0990628
$481$	−4.06984	−0.185569
$482$	11.8489	0.539701
$483$	7.05787	0.321144
$484$	−10.7258	−0.487538
$485$	27.0447	1.22804
$486$	1.00000	0.0453609
$487$	−38.2466	−1.73312	−0.866560	−	0.499073i	$-0.833674\pi$
$487$	−38.2466	−1.73312	−0.866560	+	0.499073i	$0.833674\pi$
$488$	−4.29589	−0.194466
$489$	−4.94496	−0.223619
$490$	−11.8171	−0.533844
$491$	5.31341	0.239791	0.119895	−	0.992787i	$-0.461744\pi$
$491$	5.31341	0.239791	0.119895	+	0.992787i	$0.461744\pi$
$492$	−9.76511	−0.440245
$493$	−1.53004	−0.0689098
$494$	−7.22231	−0.324947
$495$	−1.13642	−0.0510785
$496$	3.38924	0.152181
$497$	17.6140	0.790095
$498$	2.56861	0.115102
$499$	−35.0128	−1.56739	−0.783694	−	0.621147i	$-0.786667\pi$
$499$	−35.0128	−1.56739	−0.783694	+	0.621147i	$0.786667\pi$
$500$	−11.4802	−0.513411
$501$	18.7475	0.837578
$502$	−22.6365	−1.01032
$503$	−30.2670	−1.34954	−0.674768	−	0.738030i	$-0.735756\pi$
$503$	−30.2670	−1.34954	−0.674768	+	0.738030i	$0.735756\pi$
$504$	1.24708	0.0555494
$505$	31.9853	1.42333
$506$	−2.96339	−0.131739
$507$	−10.7148	−0.475861
$508$	−10.3965	−0.461269
$509$	−0.683805	−0.0303091	−0.0151546	−	0.999885i	$-0.504824\pi$
$509$	−0.683805	−0.0303091	−0.0151546	+	0.999885i	$0.504824\pi$
$510$	−2.17036	−0.0961050
$511$	−10.4619	−0.462806
$512$	1.00000	0.0441942
$513$	4.77765	0.210938
$514$	−20.8092	−0.917854
$515$	29.3762	1.29447
$516$	3.60939	0.158895
$517$	0.656661	0.0288799
$518$	3.35745	0.147518
$519$	−23.3052	−1.02298
$520$	−3.28090	−0.143877
$521$	−1.47055	−0.0644261	−0.0322131	−	0.999481i	$-0.510256\pi$
$521$	−1.47055	−0.0644261	−0.0322131	+	0.999481i	$0.510256\pi$
$522$	1.53004	0.0669682
$523$	19.6418	0.858878	0.429439	−	0.903096i	$-0.358711\pi$
$523$	19.6418	0.858878	0.429439	+	0.903096i	$0.358711\pi$
$524$	−17.4911	−0.764101
$525$	−0.361093	−0.0157594
$526$	−0.891193	−0.0388579
$527$	−3.38924	−0.147637
$528$	−0.523612	−0.0227873
$529$	9.03010	0.392613
$530$	15.1094	0.656312
$531$	1.00000	0.0433963
$532$	5.95811	0.258317
$533$	14.7618	0.639405
$534$	−10.0215	−0.433674
$535$	−17.1805	−0.742776
$536$	−4.91934	−0.212483
$537$	−3.20300	−0.138220
$538$	12.3034	0.530436
$539$	2.85096	0.122799
$540$	2.17036	0.0933973
$541$	−34.0654	−1.46459	−0.732293	−	0.680990i	$-0.761550\pi$
$541$	−34.0654	−1.46459	−0.732293	+	0.680990i	$0.761550\pi$
$542$	22.9968	0.987795
$543$	−15.4858	−0.664561
$544$	−1.00000	−0.0428746
$545$	24.4984	1.04940
$546$	−1.88520	−0.0806790
$547$	6.19052	0.264688	0.132344	−	0.991204i	$-0.457750\pi$
$547$	6.19052	0.264688	0.132344	+	0.991204i	$0.457750\pi$
$548$	3.10311	0.132558
$549$	−4.29589	−0.183344
$550$	0.151612	0.00646478
$551$	7.31001	0.311417
$552$	5.65951	0.240885
$553$	−0.146586	−0.00623349
$554$	15.4961	0.658367
$555$	5.84314	0.248027
$556$	15.9070	0.674608
$557$	0.0693521	0.00293854	0.00146927	−	0.999999i	$-0.499532\pi$
$557$	0.0693521	0.00293854	0.00146927	+	0.999999i	$0.499532\pi$
$558$	3.38924	0.143478
$559$	−5.45628	−0.230776
$560$	2.70661	0.114375
$561$	0.523612	0.0221069
$562$	14.1241	0.595788
$563$	−10.2614	−0.432466	−0.216233	−	0.976342i	$-0.569377\pi$
$563$	−10.2614	−0.432466	−0.216233	+	0.976342i	$0.569377\pi$
$564$	−1.25410	−0.0528071
$565$	−10.0860	−0.424322
$566$	−20.3792	−0.856603
$567$	1.24708	0.0523724
$568$	14.1242	0.592638
$569$	−8.49292	−0.356042	−0.178021	−	0.984027i	$-0.556969\pi$
$569$	−8.49292	−0.356042	−0.178021	+	0.984027i	$0.556969\pi$
$570$	10.3692	0.434318
$571$	−23.2098	−0.971302	−0.485651	−	0.874153i	$-0.661417\pi$
$571$	−23.2098	−0.971302	−0.485651	+	0.874153i	$0.661417\pi$
$572$	0.791538	0.0330959
$573$	11.4559	0.478578
$574$	−12.1779	−0.508294
$575$	−1.63872	−0.0683393
$576$	1.00000	0.0416667
$577$	0.458490	0.0190872	0.00954360	−	0.999954i	$-0.496962\pi$
$577$	0.458490	0.0190872	0.00954360	+	0.999954i	$0.496962\pi$
$578$	1.00000	0.0415945
$579$	26.8899	1.11751
$580$	3.32074	0.137886
$581$	3.20326	0.132894
$582$	12.4609	0.516523
$583$	−3.64524	−0.150971
$584$	−8.38909	−0.347143
$585$	−3.28090	−0.135649
$586$	24.8638	1.02711
$587$	38.1754	1.57567	0.787835	−	0.615887i	$-0.211202\pi$
$587$	38.1754	1.57567	0.787835	+	0.615887i	$0.211202\pi$
$588$	−5.44479	−0.224539
$589$	16.1926	0.667203
$590$	2.17036	0.0893522
$591$	−18.5725	−0.763970
$592$	2.69225	0.110651
$593$	−26.0659	−1.07040	−0.535198	−	0.844727i	$-0.679763\pi$
$593$	−26.0659	−1.07040	−0.535198	+	0.844727i	$0.679763\pi$
$594$	−0.523612	−0.0214841
$595$	−2.70661	−0.110960
$596$	20.4195	0.836417
$597$	−8.42020	−0.344616
$598$	−8.55542	−0.349857
$599$	−4.29858	−0.175635	−0.0878176	−	0.996137i	$-0.527989\pi$
$599$	−4.29858	−0.175635	−0.0878176	+	0.996137i	$0.527989\pi$
$600$	−0.289551	−0.0118209
$601$	20.6921	0.844050	0.422025	−	0.906584i	$-0.361319\pi$
$601$	20.6921	0.844050	0.422025	+	0.906584i	$0.361319\pi$
$602$	4.50120	0.183455
$603$	−4.91934	−0.200331
$604$	1.97865	0.0805102
$605$	−23.2789	−0.946421
$606$	14.7373	0.598663
$607$	29.1962	1.18504	0.592519	−	0.805557i	$-0.298134\pi$
$607$	29.1962	1.18504	0.592519	+	0.805557i	$0.298134\pi$
$608$	4.77765	0.193759
$609$	1.90809	0.0773197
$610$	−9.32362	−0.377502
$611$	1.89581	0.0766961
$612$	−1.00000	−0.0404226
$613$	44.9640	1.81608	0.908039	−	0.418885i	$-0.137579\pi$
$613$	44.9640	1.81608	0.908039	+	0.418885i	$0.137579\pi$
$614$	−13.4070	−0.541064
$615$	−21.1938	−0.854615
$616$	−0.652986	−0.0263096
$617$	−15.9196	−0.640898	−0.320449	−	0.947266i	$-0.603834\pi$
$617$	−15.9196	−0.640898	−0.320449	+	0.947266i	$0.603834\pi$
$618$	13.5352	0.544465
$619$	−14.7390	−0.592409	−0.296204	−	0.955125i	$-0.595721\pi$
$619$	−14.7390	−0.592409	−0.296204	+	0.955125i	$0.595721\pi$
$620$	7.35585	0.295418
$621$	5.65951	0.227108
$622$	−21.8580	−0.876427
$623$	−12.4977	−0.500708
$624$	−1.51169	−0.0605160
$625$	−23.4684	−0.938736
$626$	3.10738	0.124196
$627$	−2.50163	−0.0999056
$628$	−3.45122	−0.137719
$629$	−2.69225	−0.107347
$630$	2.70661	0.107834
$631$	−46.3943	−1.84693	−0.923463	−	0.383687i	$-0.874654\pi$
$631$	−46.3943	−1.84693	−0.923463	+	0.383687i	$0.874654\pi$
$632$	−0.117544	−0.00467564
$633$	−19.9817	−0.794200
$634$	1.19358	0.0474029
$635$	−22.5641	−0.895427
$636$	6.96173	0.276050
$637$	8.23083	0.326117
$638$	−0.801150	−0.0317178
$639$	14.1242	0.558744
$640$	2.17036	0.0857909
$641$	6.26206	0.247337	0.123668	−	0.992324i	$-0.460534\pi$
$641$	6.26206	0.247337	0.123668	+	0.992324i	$0.460534\pi$
$642$	−7.91596	−0.312418
$643$	−9.51992	−0.375429	−0.187714	−	0.982224i	$-0.560108\pi$
$643$	−9.51992	−0.375429	−0.187714	+	0.982224i	$0.560108\pi$
$644$	7.05787	0.278119
$645$	7.83367	0.308451
$646$	−4.77765	−0.187974
$647$	−28.7965	−1.13211	−0.566054	−	0.824368i	$-0.691531\pi$
$647$	−28.7965	−1.13211	−0.566054	+	0.824368i	$0.691531\pi$
$648$	1.00000	0.0392837
$649$	−0.523612	−0.0205536
$650$	0.437711	0.0171684
$651$	4.22665	0.165655
$652$	−4.94496	−0.193660
$653$	26.3762	1.03218	0.516089	−	0.856535i	$-0.327387\pi$
$653$	26.3762	1.03218	0.516089	+	0.856535i	$0.327387\pi$
$654$	11.2877	0.441386
$655$	−37.9619	−1.48329
$656$	−9.76511	−0.381263
$657$	−8.38909	−0.327290
$658$	−1.56396	−0.0609696
$659$	10.3802	0.404353	0.202177	−	0.979349i	$-0.435198\pi$
$659$	10.3802	0.404353	0.202177	+	0.979349i	$0.435198\pi$
$660$	−1.13642	−0.0442353
$661$	−18.0459	−0.701903	−0.350951	−	0.936394i	$-0.614142\pi$
$661$	−18.0459	−0.701903	−0.350951	+	0.936394i	$0.614142\pi$
$662$	−1.33702	−0.0519647
$663$	1.51169	0.0587091
$664$	2.56861	0.0996814
$665$	12.9312	0.501451
$666$	2.69225	0.104323
$667$	8.65931	0.335290
$668$	18.7475	0.725364
$669$	−23.1094	−0.893462
$670$	−10.6767	−0.412477
$671$	2.24938	0.0868363
$672$	1.24708	0.0481072
$673$	−4.09771	−0.157955	−0.0789776	−	0.996876i	$-0.525166\pi$
$673$	−4.09771	−0.157955	−0.0789776	+	0.996876i	$0.525166\pi$
$674$	−34.3893	−1.32463
$675$	−0.289551	−0.0111448
$676$	−10.7148	−0.412108
$677$	−26.5433	−1.02014	−0.510072	−	0.860132i	$-0.670381\pi$
$677$	−26.5433	−1.02014	−0.510072	+	0.860132i	$0.670381\pi$
$678$	−4.64717	−0.178474
$679$	15.5398	0.596362
$680$	−2.17036	−0.0832294
$681$	−21.4427	−0.821686
$682$	−1.77464	−0.0679547
$683$	12.7293	0.487072	0.243536	−	0.969892i	$-0.421693\pi$
$683$	12.7293	0.487072	0.243536	+	0.969892i	$0.421693\pi$
$684$	4.77765	0.182678
$685$	6.73486	0.257326
$686$	−15.5197	−0.592543
$687$	−19.9185	−0.759939
$688$	3.60939	0.137607
$689$	−10.5240	−0.400931
$690$	12.2832	0.467612
$691$	−15.6161	−0.594063	−0.297031	−	0.954868i	$-0.595997\pi$
$691$	−15.6161	−0.594063	−0.297031	+	0.954868i	$0.595997\pi$
$692$	−23.3052	−0.885929
$693$	−0.652986	−0.0248049
$694$	1.67568	0.0636078
$695$	34.5239	1.30957
$696$	1.53004	0.0579962
$697$	9.76511	0.369880
$698$	−3.60263	−0.136362
$699$	11.6350	0.440074
$700$	−0.361093	−0.0136481
$701$	48.6095	1.83596	0.917979	−	0.396630i	$-0.129820\pi$
$701$	48.6095	1.83596	0.917979	+	0.396630i	$0.129820\pi$
$702$	−1.51169	−0.0570550
$703$	12.8626	0.485122
$704$	−0.523612	−0.0197344
$705$	−2.72184	−0.102511
$706$	−32.3052	−1.21582
$707$	18.3786	0.691200
$708$	1.00000	0.0375823
$709$	−26.6806	−1.00201	−0.501005	−	0.865444i	$-0.667036\pi$
$709$	−26.6806	−1.00201	−0.501005	+	0.865444i	$0.667036\pi$
$710$	30.6545	1.15044
$711$	−0.117544	−0.00440823
$712$	−10.0215	−0.375573
$713$	19.1814	0.718350
$714$	−1.24708	−0.0466708
$715$	1.71792	0.0642466
$716$	−3.20300	−0.119702
$717$	10.6456	0.397567
$718$	−16.9596	−0.632926
$719$	−28.2127	−1.05216	−0.526078	−	0.850437i	$-0.676338\pi$
$719$	−28.2127	−1.05216	−0.526078	+	0.850437i	$0.676338\pi$
$720$	2.17036	0.0808844
$721$	16.8795	0.628624
$722$	3.82590	0.142385
$723$	11.8489	0.440664
$724$	−15.4858	−0.575527
$725$	−0.443026	−0.0164536
$726$	−10.7258	−0.398073
$727$	16.2987	0.604486	0.302243	−	0.953231i	$-0.402265\pi$
$727$	16.2987	0.604486	0.302243	+	0.953231i	$0.402265\pi$
$728$	−1.88520	−0.0698700
$729$	1.00000	0.0370370
$730$	−18.2073	−0.673883
$731$	−3.60939	−0.133498
$732$	−4.29589	−0.158781
$733$	−38.0165	−1.40417	−0.702085	−	0.712093i	$-0.747747\pi$
$733$	−38.0165	−1.40417	−0.702085	+	0.712093i	$0.747747\pi$
$734$	0.105587	0.00389727
$735$	−11.8171	−0.435882
$736$	5.65951	0.208612
$737$	2.57582	0.0948816
$738$	−9.76511	−0.359459
$739$	−38.5112	−1.41666	−0.708329	−	0.705883i	$-0.750551\pi$
$739$	−38.5112	−1.41666	−0.708329	+	0.705883i	$0.750551\pi$
$740$	5.84314	0.214798
$741$	−7.22231	−0.265318
$742$	8.68183	0.318720
$743$	49.9450	1.83230	0.916152	−	0.400830i	$-0.131278\pi$
$743$	49.9450	1.83230	0.916152	+	0.400830i	$0.131278\pi$
$744$	3.38924	0.124255
$745$	44.3177	1.62367
$746$	25.9839	0.951338
$747$	2.56861	0.0939805
$748$	0.523612	0.0191451
$749$	−9.87184	−0.360709
$750$	−11.4802	−0.419198
$751$	−29.7248	−1.08467	−0.542337	−	0.840161i	$-0.682460\pi$
$751$	−29.7248	−1.08467	−0.542337	+	0.840161i	$0.682460\pi$
$752$	−1.25410	−0.0457323
$753$	−22.6365	−0.824920
$754$	−2.31295	−0.0842327
$755$	4.29438	0.156289
$756$	1.24708	0.0453559
$757$	−7.77069	−0.282430	−0.141215	−	0.989979i	$-0.545101\pi$
$757$	−7.77069	−0.282430	−0.141215	+	0.989979i	$0.545101\pi$
$758$	18.8066	0.683086
$759$	−2.96339	−0.107564
$760$	10.3692	0.376130
$761$	17.4287	0.631790	0.315895	−	0.948794i	$-0.397695\pi$
$761$	17.4287	0.631790	0.315895	+	0.948794i	$0.397695\pi$
$762$	−10.3965	−0.376624
$763$	14.0767	0.509612
$764$	11.4559	0.414460
$765$	−2.17036	−0.0784694
$766$	19.8157	0.715969
$767$	−1.51169	−0.0545839
$768$	1.00000	0.0360844
$769$	15.3833	0.554737	0.277369	−	0.960764i	$-0.410538\pi$
$769$	15.3833	0.554737	0.277369	+	0.960764i	$0.410538\pi$
$770$	−1.41721	−0.0510728
$771$	−20.8092	−0.749425
$772$	26.8899	0.967790
$773$	−26.8806	−0.966827	−0.483414	−	0.875392i	$-0.660603\pi$
$773$	−26.8806	−0.966827	−0.483414	+	0.875392i	$0.660603\pi$
$774$	3.60939	0.129737
$775$	−0.981357	−0.0352514
$776$	12.4609	0.447322
$777$	3.35745	0.120448
$778$	−27.7689	−0.995562
$779$	−46.6542	−1.67156
$780$	−3.28090	−0.117475
$781$	−7.39559	−0.264635
$782$	−5.65951	−0.202384
$783$	1.53004	0.0546793
$784$	−5.44479	−0.194457
$785$	−7.49038	−0.267343
$786$	−17.4911	−0.623886
$787$	−45.3726	−1.61736	−0.808680	−	0.588249i	$-0.799817\pi$
$787$	−45.3726	−1.61736	−0.808680	+	0.588249i	$0.799817\pi$
$788$	−18.5725	−0.661618
$789$	−0.891193	−0.0317273
$790$	−0.255112	−0.00907647
$791$	−5.79540	−0.206061
$792$	−0.523612	−0.0186057
$793$	6.49405	0.230610
$794$	−7.53440	−0.267386
$795$	15.1094	0.535876
$796$	−8.42020	−0.298446
$797$	−6.73614	−0.238606	−0.119303	−	0.992858i	$-0.538066\pi$
$797$	−6.73614	−0.238606	−0.119303	+	0.992858i	$0.538066\pi$
$798$	5.95811	0.210915
$799$	1.25410	0.0443668
$800$	−0.289551	−0.0102372
$801$	−10.0215	−0.354093
$802$	32.2759	1.13970
$803$	4.39263	0.155012
$804$	−4.91934	−0.173492
$805$	15.3181	0.539892
$806$	−5.12347	−0.180467
$807$	12.3034	0.433099
$808$	14.7373	0.518458
$809$	−11.7070	−0.411595	−0.205798	−	0.978595i	$-0.565979\pi$
$809$	−11.7070	−0.411595	−0.205798	+	0.978595i	$0.565979\pi$
$810$	2.17036	0.0762586
$811$	−30.6035	−1.07463	−0.537316	−	0.843381i	$-0.680562\pi$
$811$	−30.6035	−1.07463	−0.537316	+	0.843381i	$0.680562\pi$
$812$	1.90809	0.0669608
$813$	22.9968	0.806531
$814$	−1.40969	−0.0494097
$815$	−10.7323	−0.375937
$816$	−1.00000	−0.0350070
$817$	17.2444	0.603305
$818$	−3.10227	−0.108468
$819$	−1.88520	−0.0658741
$820$	−21.1938	−0.740118
$821$	16.8106	0.586694	0.293347	−	0.956006i	$-0.405231\pi$
$821$	16.8106	0.586694	0.293347	+	0.956006i	$0.405231\pi$
$822$	3.10311	0.108233
$823$	13.2645	0.462373	0.231186	−	0.972910i	$-0.425739\pi$
$823$	13.2645	0.462373	0.231186	+	0.972910i	$0.425739\pi$
$824$	13.5352	0.471521
$825$	0.151612	0.00527847
$826$	1.24708	0.0433915
$827$	1.63548	0.0568712	0.0284356	−	0.999596i	$-0.490947\pi$
$827$	1.63548	0.0568712	0.0284356	+	0.999596i	$0.490947\pi$
$828$	5.65951	0.196682
$829$	−24.3278	−0.844939	−0.422470	−	0.906377i	$-0.638837\pi$
$829$	−24.3278	−0.844939	−0.422470	+	0.906377i	$0.638837\pi$
$830$	5.57480	0.193504
$831$	15.4961	0.537555
$832$	−1.51169	−0.0524084
$833$	5.44479	0.188651
$834$	15.9070	0.550815
$835$	40.6888	1.40809
$836$	−2.50163	−0.0865208
$837$	3.38924	0.117149
$838$	37.9098	1.30957
$839$	26.1603	0.903153	0.451577	−	0.892232i	$-0.350862\pi$
$839$	26.1603	0.903153	0.451577	+	0.892232i	$0.350862\pi$
$840$	2.70661	0.0933869
$841$	−26.6590	−0.919275
$842$	12.4174	0.427933
$843$	14.1241	0.486458
$844$	−19.9817	−0.687797
$845$	−23.2549	−0.799994
$846$	−1.25410	−0.0431168
$847$	−13.3760	−0.459604
$848$	6.96173	0.239067
$849$	−20.3792	−0.699413
$850$	0.289551	0.00993152
$851$	15.2368	0.522311
$852$	14.1242	0.483887
$853$	43.5430	1.49088	0.745441	−	0.666571i	$-0.232239\pi$
$853$	43.5430	1.49088	0.745441	+	0.666571i	$0.232239\pi$
$854$	−5.35732	−0.183324
$855$	10.3692	0.354619
$856$	−7.91596	−0.270562
$857$	−37.7561	−1.28972	−0.644862	−	0.764299i	$-0.723085\pi$
$857$	−37.7561	−1.28972	−0.644862	+	0.764299i	$0.723085\pi$
$858$	0.791538	0.0270227
$859$	45.6072	1.55610	0.778049	−	0.628204i	$-0.216210\pi$
$859$	45.6072	1.55610	0.778049	+	0.628204i	$0.216210\pi$
$860$	7.83367	0.267126
$861$	−12.1779	−0.415021
$862$	38.3593	1.30652
$863$	−42.1106	−1.43346	−0.716731	−	0.697349i	$-0.754363\pi$
$863$	−42.1106	−1.43346	−0.716731	+	0.697349i	$0.754363\pi$
$864$	1.00000	0.0340207
$865$	−50.5805	−1.71979
$866$	27.4286	0.932061
$867$	1.00000	0.0339618
$868$	4.22665	0.143462
$869$	0.0615473	0.00208785
$870$	3.32074	0.112584
$871$	7.43650	0.251976
$872$	11.2877	0.382251
$873$	12.4609	0.421739
$874$	27.0392	0.914613
$875$	−14.3167	−0.483994
$876$	−8.38909	−0.283441
$877$	−27.5520	−0.930365	−0.465183	−	0.885215i	$-0.654011\pi$
$877$	−27.5520	−0.930365	−0.465183	+	0.885215i	$0.654011\pi$
$878$	−13.0146	−0.439220
$879$	24.8638	0.838634
$880$	−1.13642	−0.0383089
$881$	38.7844	1.30668	0.653339	−	0.757065i	$-0.273368\pi$
$881$	38.7844	1.30668	0.653339	+	0.757065i	$0.273368\pi$
$882$	−5.44479	−0.183336
$883$	−50.8085	−1.70984	−0.854921	−	0.518759i	$-0.826394\pi$
$883$	−50.8085	−1.70984	−0.854921	+	0.518759i	$0.826394\pi$
$884$	1.51169	0.0508436
$885$	2.17036	0.0729557
$886$	−34.2088	−1.14927
$887$	20.0731	0.673988	0.336994	−	0.941507i	$-0.390590\pi$
$887$	20.0731	0.673988	0.336994	+	0.941507i	$0.390590\pi$
$888$	2.69225	0.0903459
$889$	−12.9652	−0.434840
$890$	−21.7503	−0.729072
$891$	−0.523612	−0.0175417
$892$	−23.1094	−0.773761
$893$	−5.99164	−0.200503
$894$	20.4195	0.682931
$895$	−6.95165	−0.232368
$896$	1.24708	0.0416620
$897$	−8.55542	−0.285657
$898$	17.9559	0.599196
$899$	5.18568	0.172952
$900$	−0.289551	−0.00965171
$901$	−6.96173	−0.231929
$902$	5.11313	0.170248
$903$	4.50120	0.149791
$904$	−4.64717	−0.154563
$905$	−33.6098	−1.11723
$906$	1.97865	0.0657363
$907$	−15.0491	−0.499696	−0.249848	−	0.968285i	$-0.580381\pi$
$907$	−15.0491	−0.499696	−0.249848	+	0.968285i	$0.580381\pi$
$908$	−21.4427	−0.711601
$909$	14.7373	0.488806
$910$	−4.09155	−0.135634
$911$	−48.0731	−1.59273	−0.796366	−	0.604815i	$-0.793247\pi$
$911$	−48.0731	−1.59273	−0.796366	+	0.604815i	$0.793247\pi$
$912$	4.77765	0.158204
$913$	−1.34495	−0.0445115
$914$	19.0469	0.630015
$915$	−9.32362	−0.308229
$916$	−19.9185	−0.658126
$917$	−21.8128	−0.720321
$918$	−1.00000	−0.0330049
$919$	51.0422	1.68373	0.841864	−	0.539690i	$-0.181458\pi$
$919$	51.0422	1.68373	0.841864	+	0.539690i	$0.181458\pi$
$920$	12.2832	0.404964
$921$	−13.4070	−0.441777
$922$	9.50153	0.312916
$923$	−21.3514	−0.702789
$924$	−0.652986	−0.0214817
$925$	−0.779544	−0.0256312
$926$	−5.65280	−0.185763
$927$	13.5352	0.444554
$928$	1.53004	0.0502262
$929$	27.1887	0.892033	0.446016	−	0.895025i	$-0.352842\pi$
$929$	27.1887	0.892033	0.446016	+	0.895025i	$0.352842\pi$
$930$	7.35585	0.241208
$931$	−26.0133	−0.852551
$932$	11.6350	0.381116
$933$	−21.8580	−0.715600
$934$	17.2722	0.565164
$935$	1.13642	0.0371651
$936$	−1.51169	−0.0494111
$937$	6.88625	0.224964	0.112482	−	0.993654i	$-0.464120\pi$
$937$	6.88625	0.224964	0.112482	+	0.993654i	$0.464120\pi$
$938$	−6.13480	−0.200308
$939$	3.10738	0.101405
$940$	−2.72184	−0.0887767
$941$	−20.0203	−0.652644	−0.326322	−	0.945259i	$-0.605809\pi$
$941$	−20.0203	−0.652644	−0.326322	+	0.945259i	$0.605809\pi$
$942$	−3.45122	−0.112447
$943$	−55.2658	−1.79970
$944$	1.00000	0.0325472
$945$	2.70661	0.0880460
$946$	−1.88992	−0.0614467
$947$	27.6396	0.898165	0.449082	−	0.893490i	$-0.351751\pi$
$947$	27.6396	0.898165	0.449082	+	0.893490i	$0.351751\pi$
$948$	−0.117544	−0.00381764
$949$	12.6817	0.411665
$950$	−1.38337	−0.0448825
$951$	1.19358	0.0387043
$952$	−1.24708	−0.0404181
$953$	−8.39612	−0.271977	−0.135988	−	0.990710i	$-0.543421\pi$
$953$	−8.39612	−0.271977	−0.135988	+	0.990710i	$0.543421\pi$
$954$	6.96173	0.225394
$955$	24.8634	0.804561
$956$	10.6456	0.344303
$957$	−0.801150	−0.0258975
$958$	−17.0940	−0.552283
$959$	3.86983	0.124963
$960$	2.17036	0.0700480
$961$	−19.5131	−0.629454
$962$	−4.06984	−0.131217
$963$	−7.91596	−0.255088
$964$	11.8489	0.381626
$965$	58.3607	1.87870
$966$	7.05787	0.227083
$967$	56.5341	1.81802	0.909008	−	0.416779i	$-0.136841\pi$
$967$	56.5341	1.81802	0.909008	+	0.416779i	$0.136841\pi$
$968$	−10.7258	−0.344741
$969$	−4.77765	−0.153480
$970$	27.0447	0.868353
$971$	−9.93044	−0.318683	−0.159342	−	0.987224i	$-0.550937\pi$
$971$	−9.93044	−0.318683	−0.159342	+	0.987224i	$0.550937\pi$
$972$	1.00000	0.0320750
$973$	19.8373	0.635955
$974$	−38.2466	−1.22550
$975$	0.437711	0.0140180
$976$	−4.29589	−0.137508
$977$	19.7808	0.632842	0.316421	−	0.948619i	$-0.397519\pi$
$977$	19.7808	0.632842	0.316421	+	0.948619i	$0.397519\pi$
$978$	−4.94496	−0.158122
$979$	5.24739	0.167707
$980$	−11.8171	−0.377485
$981$	11.2877	0.360390
$982$	5.31341	0.169558
$983$	53.6136	1.71001	0.855005	−	0.518620i	$-0.173554\pi$
$983$	53.6136	1.71001	0.855005	+	0.518620i	$0.173554\pi$
$984$	−9.76511	−0.311300
$985$	−40.3089	−1.28435
$986$	−1.53004	−0.0487266
$987$	−1.56396	−0.0497815
$988$	−7.22231	−0.229772
$989$	20.4274	0.649554
$990$	−1.13642	−0.0361179
$991$	−37.6500	−1.19599	−0.597995	−	0.801500i	$-0.704036\pi$
$991$	−37.6500	−1.19599	−0.597995	+	0.801500i	$0.704036\pi$
$992$	3.38924	0.107608
$993$	−1.33702	−0.0424290
$994$	17.6140	0.558682
$995$	−18.2748	−0.579351
$996$	2.56861	0.0813895
$997$	−20.5471	−0.650734	−0.325367	−	0.945588i	$-0.605488\pi$
$997$	−20.5471	−0.650734	−0.325367	+	0.945588i	$0.605488\pi$
$998$	−35.0128	−1.10831
$999$	2.69225	0.0851790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.9	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.17036 q^{5} +1.00000 q^{6} +1.24708 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.17036 q^{5} +1.00000 q^{6} +1.24708 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.17036 q^{10} -0.523612 q^{11} +1.00000 q^{12} -1.51169 q^{13} +1.24708 q^{14} +2.17036 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +4.77765 q^{19} +2.17036 q^{20} +1.24708 q^{21} -0.523612 q^{22} +5.65951 q^{23} +1.00000 q^{24} -0.289551 q^{25} -1.51169 q^{26} +1.00000 q^{27} +1.24708 q^{28} +1.53004 q^{29} +2.17036 q^{30} +3.38924 q^{31} +1.00000 q^{32} -0.523612 q^{33} -1.00000 q^{34} +2.70661 q^{35} +1.00000 q^{36} +2.69225 q^{37} +4.77765 q^{38} -1.51169 q^{39} +2.17036 q^{40} -9.76511 q^{41} +1.24708 q^{42} +3.60939 q^{43} -0.523612 q^{44} +2.17036 q^{45} +5.65951 q^{46} -1.25410 q^{47} +1.00000 q^{48} -5.44479 q^{49} -0.289551 q^{50} -1.00000 q^{51} -1.51169 q^{52} +6.96173 q^{53} +1.00000 q^{54} -1.13642 q^{55} +1.24708 q^{56} +4.77765 q^{57} +1.53004 q^{58} +1.00000 q^{59} +2.17036 q^{60} -4.29589 q^{61} +3.38924 q^{62} +1.24708 q^{63} +1.00000 q^{64} -3.28090 q^{65} -0.523612 q^{66} -4.91934 q^{67} -1.00000 q^{68} +5.65951 q^{69} +2.70661 q^{70} +14.1242 q^{71} +1.00000 q^{72} -8.38909 q^{73} +2.69225 q^{74} -0.289551 q^{75} +4.77765 q^{76} -0.652986 q^{77} -1.51169 q^{78} -0.117544 q^{79} +2.17036 q^{80} +1.00000 q^{81} -9.76511 q^{82} +2.56861 q^{83} +1.24708 q^{84} -2.17036 q^{85} +3.60939 q^{86} +1.53004 q^{87} -0.523612 q^{88} -10.0215 q^{89} +2.17036 q^{90} -1.88520 q^{91} +5.65951 q^{92} +3.38924 q^{93} -1.25410 q^{94} +10.3692 q^{95} +1.00000 q^{96} +12.4609 q^{97} -5.44479 q^{98} -0.523612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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