LMFDB - Embedded newform 6018.2.a.bb.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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} + \cdots + 128 $ x^13 - 4x^12 - 41x^11 + 179x^10 + 540x^9 - 2773x^8 - 2260x^7 + 17621x^6 - 838x^5 - 44478x^4 + 16472x^3 + 29944x^2 - 6856x + 128
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			$2.66604$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.66604 q^{5} +1.00000 q^{6} +4.24276 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.66604 q^{5} +1.00000 q^{6} +4.24276 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.66604 q^{10} -0.269084 q^{11} +1.00000 q^{12} +5.45233 q^{13} +4.24276 q^{14} +2.66604 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -5.29629 q^{19} +2.66604 q^{20} +4.24276 q^{21} -0.269084 q^{22} +1.99447 q^{23} +1.00000 q^{24} +2.10775 q^{25} +5.45233 q^{26} +1.00000 q^{27} +4.24276 q^{28} -5.03017 q^{29} +2.66604 q^{30} -5.57443 q^{31} +1.00000 q^{32} -0.269084 q^{33} +1.00000 q^{34} +11.3113 q^{35} +1.00000 q^{36} -3.75782 q^{37} -5.29629 q^{38} +5.45233 q^{39} +2.66604 q^{40} -9.45106 q^{41} +4.24276 q^{42} +6.32915 q^{43} -0.269084 q^{44} +2.66604 q^{45} +1.99447 q^{46} +13.0885 q^{47} +1.00000 q^{48} +11.0010 q^{49} +2.10775 q^{50} +1.00000 q^{51} +5.45233 q^{52} -5.54800 q^{53} +1.00000 q^{54} -0.717387 q^{55} +4.24276 q^{56} -5.29629 q^{57} -5.03017 q^{58} -1.00000 q^{59} +2.66604 q^{60} +1.10999 q^{61} -5.57443 q^{62} +4.24276 q^{63} +1.00000 q^{64} +14.5361 q^{65} -0.269084 q^{66} -1.40536 q^{67} +1.00000 q^{68} +1.99447 q^{69} +11.3113 q^{70} -4.21979 q^{71} +1.00000 q^{72} -11.6711 q^{73} -3.75782 q^{74} +2.10775 q^{75} -5.29629 q^{76} -1.14166 q^{77} +5.45233 q^{78} -15.4850 q^{79} +2.66604 q^{80} +1.00000 q^{81} -9.45106 q^{82} -0.968600 q^{83} +4.24276 q^{84} +2.66604 q^{85} +6.32915 q^{86} -5.03017 q^{87} -0.269084 q^{88} +7.37102 q^{89} +2.66604 q^{90} +23.1329 q^{91} +1.99447 q^{92} -5.57443 q^{93} +13.0885 q^{94} -14.1201 q^{95} +1.00000 q^{96} +2.52617 q^{97} +11.0010 q^{98} -0.269084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * 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
$5$	2.66604	1.19229	0.596144	−	0.802878i	$-0.296699\pi$
$5$	2.66604	1.19229	0.596144	+	0.802878i	$0.296699\pi$
$6$	1.00000	0.408248
$7$	4.24276	1.60361	0.801806	−	0.597585i	$-0.203873\pi$
$7$	4.24276	1.60361	0.801806	+	0.597585i	$0.203873\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.66604	0.843074
$11$	−0.269084	−0.0811319	−0.0405659	−	0.999177i	$-0.512916\pi$
$11$	−0.269084	−0.0811319	−0.0405659	+	0.999177i	$0.512916\pi$
$12$	1.00000	0.288675
$13$	5.45233	1.51220	0.756101	−	0.654454i	$-0.227102\pi$
$13$	5.45233	1.51220	0.756101	+	0.654454i	$0.227102\pi$
$14$	4.24276	1.13392
$15$	2.66604	0.688367
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−5.29629	−1.21505	−0.607526	−	0.794300i	$-0.707838\pi$
$19$	−5.29629	−1.21505	−0.607526	+	0.794300i	$0.707838\pi$
$20$	2.66604	0.596144
$21$	4.24276	0.925845
$22$	−0.269084	−0.0573689
$23$	1.99447	0.415876	0.207938	−	0.978142i	$-0.433325\pi$
$23$	1.99447	0.415876	0.207938	+	0.978142i	$0.433325\pi$
$24$	1.00000	0.204124
$25$	2.10775	0.421549
$26$	5.45233	1.06929
$27$	1.00000	0.192450
$28$	4.24276	0.801806
$29$	−5.03017	−0.934078	−0.467039	−	0.884237i	$-0.654679\pi$
$29$	−5.03017	−0.934078	−0.467039	+	0.884237i	$0.654679\pi$
$30$	2.66604	0.486749
$31$	−5.57443	−1.00120	−0.500599	−	0.865680i	$-0.666887\pi$
$31$	−5.57443	−1.00120	−0.500599	+	0.865680i	$0.666887\pi$
$32$	1.00000	0.176777
$33$	−0.269084	−0.0468415
$34$	1.00000	0.171499
$35$	11.3113	1.91197
$36$	1.00000	0.166667
$37$	−3.75782	−0.617781	−0.308891	−	0.951098i	$-0.599958\pi$
$37$	−3.75782	−0.617781	−0.308891	+	0.951098i	$0.599958\pi$
$38$	−5.29629	−0.859172
$39$	5.45233	0.873071
$40$	2.66604	0.421537
$41$	−9.45106	−1.47601	−0.738004	−	0.674797i	$-0.764231\pi$
$41$	−9.45106	−1.47601	−0.738004	+	0.674797i	$0.764231\pi$
$42$	4.24276	0.654672
$43$	6.32915	0.965186	0.482593	−	0.875845i	$-0.339695\pi$
$43$	6.32915	0.965186	0.482593	+	0.875845i	$0.339695\pi$
$44$	−0.269084	−0.0405659
$45$	2.66604	0.397429
$46$	1.99447	0.294069
$47$	13.0885	1.90916	0.954580	−	0.297955i	$-0.0963046\pi$
$47$	13.0885	1.90916	0.954580	+	0.297955i	$0.0963046\pi$
$48$	1.00000	0.144338
$49$	11.0010	1.57157
$50$	2.10775	0.298080
$51$	1.00000	0.140028
$52$	5.45233	0.756101
$53$	−5.54800	−0.762076	−0.381038	−	0.924559i	$-0.624433\pi$
$53$	−5.54800	−0.762076	−0.381038	+	0.924559i	$0.624433\pi$
$54$	1.00000	0.136083
$55$	−0.717387	−0.0967325
$56$	4.24276	0.566962
$57$	−5.29629	−0.701511
$58$	−5.03017	−0.660493
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	2.66604	0.344184
$61$	1.10999	0.142120	0.0710600	−	0.997472i	$-0.477362\pi$
$61$	1.10999	0.142120	0.0710600	+	0.997472i	$0.477362\pi$
$62$	−5.57443	−0.707953
$63$	4.24276	0.534537
$64$	1.00000	0.125000
$65$	14.5361	1.80298
$66$	−0.269084	−0.0331219
$67$	−1.40536	−0.171692	−0.0858459	−	0.996308i	$-0.527359\pi$
$67$	−1.40536	−0.171692	−0.0858459	+	0.996308i	$0.527359\pi$
$68$	1.00000	0.121268
$69$	1.99447	0.240106
$70$	11.3113	1.35196
$71$	−4.21979	−0.500797	−0.250399	−	0.968143i	$-0.580562\pi$
$71$	−4.21979	−0.500797	−0.250399	+	0.968143i	$0.580562\pi$
$72$	1.00000	0.117851
$73$	−11.6711	−1.36600	−0.682999	−	0.730419i	$-0.739325\pi$
$73$	−11.6711	−1.36600	−0.682999	+	0.730419i	$0.739325\pi$
$74$	−3.75782	−0.436837
$75$	2.10775	0.243381
$76$	−5.29629	−0.607526
$77$	−1.14166	−0.130104
$78$	5.45233	0.617354
$79$	−15.4850	−1.74219	−0.871097	−	0.491110i	$-0.836591\pi$
$79$	−15.4850	−1.74219	−0.871097	+	0.491110i	$0.836591\pi$
$80$	2.66604	0.298072
$81$	1.00000	0.111111
$82$	−9.45106	−1.04369
$83$	−0.968600	−0.106318	−0.0531588	−	0.998586i	$-0.516929\pi$
$83$	−0.968600	−0.106318	−0.0531588	+	0.998586i	$0.516929\pi$
$84$	4.24276	0.462923
$85$	2.66604	0.289172
$86$	6.32915	0.682489
$87$	−5.03017	−0.539290
$88$	−0.269084	−0.0286844
$89$	7.37102	0.781327	0.390664	−	0.920534i	$-0.372246\pi$
$89$	7.37102	0.781327	0.390664	+	0.920534i	$0.372246\pi$
$90$	2.66604	0.281025
$91$	23.1329	2.42499
$92$	1.99447	0.207938
$93$	−5.57443	−0.578041
$94$	13.0885	1.34998
$95$	−14.1201	−1.44869
$96$	1.00000	0.102062
$97$	2.52617	0.256494	0.128247	−	0.991742i	$-0.459065\pi$
$97$	2.52617	0.256494	0.128247	+	0.991742i	$0.459065\pi$
$98$	11.0010	1.11127
$99$	−0.269084	−0.0270440
$100$	2.10775	0.210775
$101$	7.30932	0.727304	0.363652	−	0.931535i	$-0.381530\pi$
$101$	7.30932	0.727304	0.363652	+	0.931535i	$0.381530\pi$
$102$	1.00000	0.0990148
$103$	−3.50199	−0.345061	−0.172531	−	0.985004i	$-0.555194\pi$
$103$	−3.50199	−0.345061	−0.172531	+	0.985004i	$0.555194\pi$
$104$	5.45233	0.534644
$105$	11.3113	1.10387
$106$	−5.54800	−0.538869
$107$	−13.1729	−1.27347	−0.636734	−	0.771083i	$-0.719715\pi$
$107$	−13.1729	−1.27347	−0.636734	+	0.771083i	$0.719715\pi$
$108$	1.00000	0.0962250
$109$	−18.0756	−1.73133	−0.865666	−	0.500622i	$-0.833105\pi$
$109$	−18.0756	−1.73133	−0.865666	+	0.500622i	$0.833105\pi$
$110$	−0.717387	−0.0684002
$111$	−3.75782	−0.356676
$112$	4.24276	0.400903
$113$	−12.8538	−1.20918	−0.604592	−	0.796535i	$-0.706664\pi$
$113$	−12.8538	−1.20918	−0.604592	+	0.796535i	$0.706664\pi$
$114$	−5.29629	−0.496043
$115$	5.31734	0.495844
$116$	−5.03017	−0.467039
$117$	5.45233	0.504068
$118$	−1.00000	−0.0920575
$119$	4.24276	0.388933
$120$	2.66604	0.243375
$121$	−10.9276	−0.993418
$122$	1.10999	0.100494
$123$	−9.45106	−0.852173
$124$	−5.57443	−0.500599
$125$	−7.71085	−0.689680
$126$	4.24276	0.377975
$127$	0.366455	0.0325176	0.0162588	−	0.999868i	$-0.494824\pi$
$127$	0.366455	0.0325176	0.0162588	+	0.999868i	$0.494824\pi$
$128$	1.00000	0.0883883
$129$	6.32915	0.557250
$130$	14.5361	1.27490
$131$	−8.71109	−0.761091	−0.380546	−	0.924762i	$-0.624264\pi$
$131$	−8.71109	−0.761091	−0.380546	+	0.924762i	$0.624264\pi$
$132$	−0.269084	−0.0234208
$133$	−22.4709	−1.94847
$134$	−1.40536	−0.121404
$135$	2.66604	0.229456
$136$	1.00000	0.0857493
$137$	11.0929	0.947729	0.473864	−	0.880598i	$-0.342859\pi$
$137$	11.0929	0.947729	0.473864	+	0.880598i	$0.342859\pi$
$138$	1.99447	0.169781
$139$	−8.42488	−0.714589	−0.357294	−	0.933992i	$-0.616301\pi$
$139$	−8.42488	−0.714589	−0.357294	+	0.933992i	$0.616301\pi$
$140$	11.3113	0.955983
$141$	13.0885	1.10225
$142$	−4.21979	−0.354117
$143$	−1.46713	−0.122688
$144$	1.00000	0.0833333
$145$	−13.4106	−1.11369
$146$	−11.6711	−0.965906
$147$	11.0010	0.907346
$148$	−3.75782	−0.308891
$149$	21.6171	1.77094	0.885471	−	0.464694i	$-0.153836\pi$
$149$	21.6171	1.77094	0.885471	+	0.464694i	$0.153836\pi$
$150$	2.10775	0.172097
$151$	−6.23210	−0.507161	−0.253581	−	0.967314i	$-0.581608\pi$
$151$	−6.23210	−0.507161	−0.253581	+	0.967314i	$0.581608\pi$
$152$	−5.29629	−0.429586
$153$	1.00000	0.0808452
$154$	−1.14166	−0.0919974
$155$	−14.8616	−1.19371
$156$	5.45233	0.436535
$157$	−24.9109	−1.98811	−0.994053	−	0.108901i	$-0.965267\pi$
$157$	−24.9109	−1.98811	−0.994053	+	0.108901i	$0.965267\pi$
$158$	−15.4850	−1.23192
$159$	−5.54800	−0.439985
$160$	2.66604	0.210769
$161$	8.46206	0.666904
$162$	1.00000	0.0785674
$163$	18.6976	1.46451	0.732253	−	0.681033i	$-0.238469\pi$
$163$	18.6976	1.46451	0.732253	+	0.681033i	$0.238469\pi$
$164$	−9.45106	−0.738004
$165$	−0.717387	−0.0558485
$166$	−0.968600	−0.0751779
$167$	15.3134	1.18499	0.592494	−	0.805575i	$-0.298143\pi$
$167$	15.3134	1.18499	0.592494	+	0.805575i	$0.298143\pi$
$168$	4.24276	0.327336
$169$	16.7278	1.28676
$170$	2.66604	0.204476
$171$	−5.29629	−0.405017
$172$	6.32915	0.482593
$173$	21.7413	1.65296	0.826481	−	0.562965i	$-0.190339\pi$
$173$	21.7413	1.65296	0.826481	+	0.562965i	$0.190339\pi$
$174$	−5.03017	−0.381336
$175$	8.94265	0.676001
$176$	−0.269084	−0.0202830
$177$	−1.00000	−0.0751646
$178$	7.37102	0.552482
$179$	−18.4184	−1.37666	−0.688330	−	0.725398i	$-0.741656\pi$
$179$	−18.4184	−1.37666	−0.688330	+	0.725398i	$0.741656\pi$
$180$	2.66604	0.198715
$181$	12.4615	0.926254	0.463127	−	0.886292i	$-0.346727\pi$
$181$	12.4615	0.926254	0.463127	+	0.886292i	$0.346727\pi$
$182$	23.1329	1.71472
$183$	1.10999	0.0820530
$184$	1.99447	0.147034
$185$	−10.0185	−0.736572
$186$	−5.57443	−0.408737
$187$	−0.269084	−0.0196774
$188$	13.0885	0.954580
$189$	4.24276	0.308615
$190$	−14.1201	−1.02438
$191$	8.02566	0.580717	0.290358	−	0.956918i	$-0.406226\pi$
$191$	8.02566	0.580717	0.290358	+	0.956918i	$0.406226\pi$
$192$	1.00000	0.0721688
$193$	18.6029	1.33907	0.669534	−	0.742781i	$-0.266494\pi$
$193$	18.6029	1.33907	0.669534	+	0.742781i	$0.266494\pi$
$194$	2.52617	0.181368
$195$	14.5361	1.04095
$196$	11.0010	0.785784
$197$	17.3241	1.23429	0.617146	−	0.786849i	$-0.288289\pi$
$197$	17.3241	1.23429	0.617146	+	0.786849i	$0.288289\pi$
$198$	−0.269084	−0.0191230
$199$	−23.7109	−1.68082	−0.840410	−	0.541951i	$-0.817686\pi$
$199$	−23.7109	−1.68082	−0.840410	+	0.541951i	$0.817686\pi$
$200$	2.10775	0.149040
$201$	−1.40536	−0.0991264
$202$	7.30932	0.514282
$203$	−21.3418	−1.49790
$204$	1.00000	0.0700140
$205$	−25.1969	−1.75982
$206$	−3.50199	−0.243995
$207$	1.99447	0.138625
$208$	5.45233	0.378051
$209$	1.42515	0.0985795
$210$	11.3113	0.780557
$211$	−21.2553	−1.46328	−0.731638	−	0.681693i	$-0.761244\pi$
$211$	−21.2553	−1.46328	−0.731638	+	0.681693i	$0.761244\pi$
$212$	−5.54800	−0.381038
$213$	−4.21979	−0.289135
$214$	−13.1729	−0.900479
$215$	16.8737	1.15078
$216$	1.00000	0.0680414
$217$	−23.6509	−1.60553
$218$	−18.0756	−1.22424
$219$	−11.6711	−0.788659
$220$	−0.717387	−0.0483662
$221$	5.45233	0.366763
$222$	−3.75782	−0.252208
$223$	14.7912	0.990490	0.495245	−	0.868753i	$-0.335078\pi$
$223$	14.7912	0.990490	0.495245	+	0.868753i	$0.335078\pi$
$224$	4.24276	0.283481
$225$	2.10775	0.140516
$226$	−12.8538	−0.855022
$227$	13.8685	0.920483	0.460242	−	0.887794i	$-0.347763\pi$
$227$	13.8685	0.920483	0.460242	+	0.887794i	$0.347763\pi$
$228$	−5.29629	−0.350755
$229$	29.6505	1.95936	0.979679	−	0.200570i	$-0.0642793\pi$
$229$	29.6505	1.95936	0.979679	+	0.200570i	$0.0642793\pi$
$230$	5.31734	0.350615
$231$	−1.14166	−0.0751156
$232$	−5.03017	−0.330247
$233$	11.2060	0.734131	0.367066	−	0.930195i	$-0.380362\pi$
$233$	11.2060	0.734131	0.367066	+	0.930195i	$0.380362\pi$
$234$	5.45233	0.356430
$235$	34.8945	2.27627
$236$	−1.00000	−0.0650945
$237$	−15.4850	−1.00586
$238$	4.24276	0.275017
$239$	−6.01571	−0.389124	−0.194562	−	0.980890i	$-0.562329\pi$
$239$	−6.01571	−0.389124	−0.194562	+	0.980890i	$0.562329\pi$
$240$	2.66604	0.172092
$241$	2.92713	0.188553	0.0942766	−	0.995546i	$-0.469946\pi$
$241$	2.92713	0.188553	0.0942766	+	0.995546i	$0.469946\pi$
$242$	−10.9276	−0.702452
$243$	1.00000	0.0641500
$244$	1.10999	0.0710600
$245$	29.3290	1.87376
$246$	−9.45106	−0.602577
$247$	−28.8771	−1.83741
$248$	−5.57443	−0.353977
$249$	−0.968600	−0.0613825
$250$	−7.71085	−0.487677
$251$	−17.2275	−1.08739	−0.543695	−	0.839283i	$-0.682975\pi$
$251$	−17.2275	−1.08739	−0.543695	+	0.839283i	$0.682975\pi$
$252$	4.24276	0.267269
$253$	−0.536681	−0.0337408
$254$	0.366455	0.0229934
$255$	2.66604	0.166954
$256$	1.00000	0.0625000
$257$	−17.5046	−1.09191	−0.545955	−	0.837815i	$-0.683833\pi$
$257$	−17.5046	−1.09191	−0.545955	+	0.837815i	$0.683833\pi$
$258$	6.32915	0.394035
$259$	−15.9435	−0.990681
$260$	14.5361	0.901490
$261$	−5.03017	−0.311359
$262$	−8.71109	−0.538173
$263$	−19.7411	−1.21729	−0.608645	−	0.793442i	$-0.708287\pi$
$263$	−19.7411	−1.21729	−0.608645	+	0.793442i	$0.708287\pi$
$264$	−0.269084	−0.0165610
$265$	−14.7912	−0.908614
$266$	−22.4709	−1.37778
$267$	7.37102	0.451099
$268$	−1.40536	−0.0858459
$269$	14.9580	0.912006	0.456003	−	0.889978i	$-0.349281\pi$
$269$	14.9580	0.912006	0.456003	+	0.889978i	$0.349281\pi$
$270$	2.66604	0.162250
$271$	20.2941	1.23278	0.616390	−	0.787441i	$-0.288594\pi$
$271$	20.2941	1.23278	0.616390	+	0.787441i	$0.288594\pi$
$272$	1.00000	0.0606339
$273$	23.1329	1.40007
$274$	11.0929	0.670145
$275$	−0.567160	−0.0342011
$276$	1.99447	0.120053
$277$	0.430732	0.0258802	0.0129401	−	0.999916i	$-0.495881\pi$
$277$	0.430732	0.0258802	0.0129401	+	0.999916i	$0.495881\pi$
$278$	−8.42488	−0.505291
$279$	−5.57443	−0.333732
$280$	11.3113	0.675982
$281$	20.0042	1.19335	0.596676	−	0.802482i	$-0.296488\pi$
$281$	20.0042	1.19335	0.596676	+	0.802482i	$0.296488\pi$
$282$	13.0885	0.779411
$283$	−30.7966	−1.83067	−0.915333	−	0.402698i	$-0.868073\pi$
$283$	−30.7966	−1.83067	−0.915333	+	0.402698i	$0.868073\pi$
$284$	−4.21979	−0.250399
$285$	−14.1201	−0.836402
$286$	−1.46713	−0.0867534
$287$	−40.0985	−2.36694
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−13.4106	−0.787497
$291$	2.52617	0.148087
$292$	−11.6711	−0.682999
$293$	25.8380	1.50947	0.754736	−	0.656029i	$-0.227765\pi$
$293$	25.8380	1.50947	0.754736	+	0.656029i	$0.227765\pi$
$294$	11.0010	0.641590
$295$	−2.66604	−0.155223
$296$	−3.75782	−0.218419
$297$	−0.269084	−0.0156138
$298$	21.6171	1.25225
$299$	10.8745	0.628889
$300$	2.10775	0.121691
$301$	26.8530	1.54778
$302$	−6.23210	−0.358617
$303$	7.30932	0.419909
$304$	−5.29629	−0.303763
$305$	2.95928	0.169448
$306$	1.00000	0.0571662
$307$	26.1206	1.49078	0.745390	−	0.666629i	$-0.232263\pi$
$307$	26.1206	1.49078	0.745390	+	0.666629i	$0.232263\pi$
$308$	−1.14166	−0.0650520
$309$	−3.50199	−0.199221
$310$	−14.8616	−0.844084
$311$	9.57209	0.542784	0.271392	−	0.962469i	$-0.412516\pi$
$311$	9.57209	0.542784	0.271392	+	0.962469i	$0.412516\pi$
$312$	5.45233	0.308677
$313$	−26.6917	−1.50870	−0.754351	−	0.656472i	$-0.772048\pi$
$313$	−26.6917	−1.50870	−0.754351	+	0.656472i	$0.772048\pi$
$314$	−24.9109	−1.40580
$315$	11.3113	0.637322
$316$	−15.4850	−0.871097
$317$	−17.2506	−0.968892	−0.484446	−	0.874821i	$-0.660979\pi$
$317$	−17.2506	−0.968892	−0.484446	+	0.874821i	$0.660979\pi$
$318$	−5.54800	−0.311116
$319$	1.35354	0.0757835
$320$	2.66604	0.149036
$321$	−13.1729	−0.735238
$322$	8.46206	0.471572
$323$	−5.29629	−0.294694
$324$	1.00000	0.0555556
$325$	11.4921	0.637468
$326$	18.6976	1.03556
$327$	−18.0756	−0.999585
$328$	−9.45106	−0.521847
$329$	55.5315	3.06155
$330$	−0.717387	−0.0394909
$331$	16.5855	0.911620	0.455810	−	0.890077i	$-0.349350\pi$
$331$	16.5855	0.911620	0.455810	+	0.890077i	$0.349350\pi$
$332$	−0.968600	−0.0531588
$333$	−3.75782	−0.205927
$334$	15.3134	0.837913
$335$	−3.74674	−0.204706
$336$	4.24276	0.231461
$337$	23.7902	1.29594	0.647968	−	0.761668i	$-0.275619\pi$
$337$	23.7902	1.29594	0.647968	+	0.761668i	$0.275619\pi$
$338$	16.7278	0.909875
$339$	−12.8538	−0.698123
$340$	2.66604	0.144586
$341$	1.49999	0.0812290
$342$	−5.29629	−0.286391
$343$	16.9752	0.916574
$344$	6.32915	0.341245
$345$	5.31734	0.286276
$346$	21.7413	1.16882
$347$	−0.199391	−0.0107039	−0.00535193	−	0.999986i	$-0.501704\pi$
$347$	−0.199391	−0.0107039	−0.00535193	+	0.999986i	$0.501704\pi$
$348$	−5.03017	−0.269645
$349$	−11.8597	−0.634835	−0.317418	−	0.948286i	$-0.602816\pi$
$349$	−11.8597	−0.634835	−0.317418	+	0.948286i	$0.602816\pi$
$350$	8.94265	0.478005
$351$	5.45233	0.291024
$352$	−0.269084	−0.0143422
$353$	−26.8945	−1.43145	−0.715724	−	0.698383i	$-0.753903\pi$
$353$	−26.8945	−1.43145	−0.715724	+	0.698383i	$0.753903\pi$
$354$	−1.00000	−0.0531494
$355$	−11.2501	−0.597094
$356$	7.37102	0.390664
$357$	4.24276	0.224550
$358$	−18.4184	−0.973445
$359$	18.8144	0.992984	0.496492	−	0.868041i	$-0.334621\pi$
$359$	18.8144	0.992984	0.496492	+	0.868041i	$0.334621\pi$
$360$	2.66604	0.140512
$361$	9.05070	0.476352
$362$	12.4615	0.654961
$363$	−10.9276	−0.573550
$364$	23.1329	1.21249
$365$	−31.1155	−1.62866
$366$	1.10999	0.0580202
$367$	21.3939	1.11675	0.558377	−	0.829588i	$-0.311424\pi$
$367$	21.3939	1.11675	0.558377	+	0.829588i	$0.311424\pi$
$368$	1.99447	0.103969
$369$	−9.45106	−0.492002
$370$	−10.0185	−0.520835
$371$	−23.5388	−1.22207
$372$	−5.57443	−0.289021
$373$	16.9637	0.878348	0.439174	−	0.898402i	$-0.355271\pi$
$373$	16.9637	0.878348	0.439174	+	0.898402i	$0.355271\pi$
$374$	−0.269084	−0.0139140
$375$	−7.71085	−0.398187
$376$	13.0885	0.674990
$377$	−27.4261	−1.41252
$378$	4.24276	0.218224
$379$	13.3890	0.687747	0.343873	−	0.939016i	$-0.388261\pi$
$379$	13.3890	0.687747	0.343873	+	0.939016i	$0.388261\pi$
$380$	−14.1201	−0.724346
$381$	0.366455	0.0187741
$382$	8.02566	0.410629
$383$	−6.67925	−0.341294	−0.170647	−	0.985332i	$-0.554586\pi$
$383$	−6.67925	−0.341294	−0.170647	+	0.985332i	$0.554586\pi$
$384$	1.00000	0.0510310
$385$	−3.04370	−0.155121
$386$	18.6029	0.946864
$387$	6.32915	0.321729
$388$	2.52617	0.128247
$389$	18.0389	0.914611	0.457305	−	0.889310i	$-0.348815\pi$
$389$	18.0389	0.914611	0.457305	+	0.889310i	$0.348815\pi$
$390$	14.5361	0.736064
$391$	1.99447	0.100865
$392$	11.0010	0.555633
$393$	−8.71109	−0.439416
$394$	17.3241	0.872776
$395$	−41.2835	−2.07720
$396$	−0.269084	−0.0135220
$397$	−26.1599	−1.31293	−0.656463	−	0.754359i	$-0.727948\pi$
$397$	−26.1599	−1.31293	−0.656463	+	0.754359i	$0.727948\pi$
$398$	−23.7109	−1.18852
$399$	−22.4709	−1.12495
$400$	2.10775	0.105387
$401$	−31.6007	−1.57806	−0.789032	−	0.614352i	$-0.789418\pi$
$401$	−31.6007	−1.57806	−0.789032	+	0.614352i	$0.789418\pi$
$402$	−1.40536	−0.0700929
$403$	−30.3936	−1.51401
$404$	7.30932	0.363652
$405$	2.66604	0.132476
$406$	−21.3418	−1.05917
$407$	1.01117	0.0501217
$408$	1.00000	0.0495074
$409$	28.7375	1.42098	0.710490	−	0.703707i	$-0.248473\pi$
$409$	28.7375	1.42098	0.710490	+	0.703707i	$0.248473\pi$
$410$	−25.1969	−1.24438
$411$	11.0929	0.547171
$412$	−3.50199	−0.172531
$413$	−4.24276	−0.208772
$414$	1.99447	0.0980230
$415$	−2.58232	−0.126761
$416$	5.45233	0.267322
$417$	−8.42488	−0.412568
$418$	1.42515	0.0697062
$419$	−1.81670	−0.0887518	−0.0443759	−	0.999015i	$-0.514130\pi$
$419$	−1.81670	−0.0887518	−0.0443759	+	0.999015i	$0.514130\pi$
$420$	11.3113	0.551937
$421$	25.1182	1.22418	0.612092	−	0.790786i	$-0.290328\pi$
$421$	25.1182	1.22418	0.612092	+	0.790786i	$0.290328\pi$
$422$	−21.2553	−1.03469
$423$	13.0885	0.636387
$424$	−5.54800	−0.269435
$425$	2.10775	0.102241
$426$	−4.21979	−0.204450
$427$	4.70943	0.227905
$428$	−13.1729	−0.636734
$429$	−1.46713	−0.0708339
$430$	16.8737	0.813724
$431$	−8.75445	−0.421687	−0.210844	−	0.977520i	$-0.567621\pi$
$431$	−8.75445	−0.421687	−0.210844	+	0.977520i	$0.567621\pi$
$432$	1.00000	0.0481125
$433$	0.964357	0.0463441	0.0231720	−	0.999731i	$-0.492623\pi$
$433$	0.964357	0.0463441	0.0231720	+	0.999731i	$0.492623\pi$
$434$	−23.6509	−1.13528
$435$	−13.4106	−0.642989
$436$	−18.0756	−0.865666
$437$	−10.5633	−0.505312
$438$	−11.6711	−0.557666
$439$	37.3974	1.78488	0.892441	−	0.451165i	$-0.148991\pi$
$439$	37.3974	1.78488	0.892441	+	0.451165i	$0.148991\pi$
$440$	−0.717387	−0.0342001
$441$	11.0010	0.523856
$442$	5.45233	0.259341
$443$	16.2776	0.773374	0.386687	−	0.922211i	$-0.373619\pi$
$443$	16.2776	0.773374	0.386687	+	0.922211i	$0.373619\pi$
$444$	−3.75782	−0.178338
$445$	19.6514	0.931566
$446$	14.7912	0.700382
$447$	21.6171	1.02245
$448$	4.24276	0.200451
$449$	18.8547	0.889808	0.444904	−	0.895578i	$-0.353238\pi$
$449$	18.8547	0.889808	0.444904	+	0.895578i	$0.353238\pi$
$450$	2.10775	0.0993601
$451$	2.54313	0.119751
$452$	−12.8538	−0.604592
$453$	−6.23210	−0.292810
$454$	13.8685	0.650880
$455$	61.6731	2.89128
$456$	−5.29629	−0.248022
$457$	−40.2484	−1.88274	−0.941370	−	0.337376i	$-0.890461\pi$
$457$	−40.2484	−1.88274	−0.941370	+	0.337376i	$0.890461\pi$
$458$	29.6505	1.38548
$459$	1.00000	0.0466760
$460$	5.31734	0.247922
$461$	27.8216	1.29578	0.647890	−	0.761734i	$-0.275652\pi$
$461$	27.8216	1.29578	0.647890	+	0.761734i	$0.275652\pi$
$462$	−1.14166	−0.0531147
$463$	9.59595	0.445961	0.222981	−	0.974823i	$-0.428421\pi$
$463$	9.59595	0.445961	0.222981	+	0.974823i	$0.428421\pi$
$464$	−5.03017	−0.233520
$465$	−14.8616	−0.689191
$466$	11.2060	0.519109
$467$	3.22329	0.149156	0.0745780	−	0.997215i	$-0.476239\pi$
$467$	3.22329	0.149156	0.0745780	+	0.997215i	$0.476239\pi$
$468$	5.45233	0.252034
$469$	−5.96259	−0.275327
$470$	34.8945	1.60956
$471$	−24.9109	−1.14783
$472$	−1.00000	−0.0460287
$473$	−1.70307	−0.0783073
$474$	−15.4850	−0.711248
$475$	−11.1632	−0.512204
$476$	4.24276	0.194466
$477$	−5.54800	−0.254025
$478$	−6.01571	−0.275152
$479$	7.90214	0.361058	0.180529	−	0.983570i	$-0.442219\pi$
$479$	7.90214	0.361058	0.180529	+	0.983570i	$0.442219\pi$
$480$	2.66604	0.121687
$481$	−20.4888	−0.934210
$482$	2.92713	0.133327
$483$	8.46206	0.385037
$484$	−10.9276	−0.496709
$485$	6.73486	0.305814
$486$	1.00000	0.0453609
$487$	9.68996	0.439094	0.219547	−	0.975602i	$-0.429542\pi$
$487$	9.68996	0.439094	0.219547	+	0.975602i	$0.429542\pi$
$488$	1.10999	0.0502470
$489$	18.6976	0.845533
$490$	29.3290	1.32495
$491$	−5.92485	−0.267385	−0.133692	−	0.991023i	$-0.542683\pi$
$491$	−5.92485	−0.267385	−0.133692	+	0.991023i	$0.542683\pi$
$492$	−9.45106	−0.426087
$493$	−5.03017	−0.226547
$494$	−28.8771	−1.29924
$495$	−0.717387	−0.0322442
$496$	−5.57443	−0.250299
$497$	−17.9035	−0.803084
$498$	−0.968600	−0.0434040
$499$	−12.9895	−0.581488	−0.290744	−	0.956801i	$-0.593903\pi$
$499$	−12.9895	−0.581488	−0.290744	+	0.956801i	$0.593903\pi$
$500$	−7.71085	−0.344840
$501$	15.3134	0.684153
$502$	−17.2275	−0.768902
$503$	23.2454	1.03646	0.518231	−	0.855241i	$-0.326591\pi$
$503$	23.2454	1.03646	0.518231	+	0.855241i	$0.326591\pi$
$504$	4.24276	0.188987
$505$	19.4869	0.867156
$506$	−0.536681	−0.0238584
$507$	16.7278	0.742910
$508$	0.366455	0.0162588
$509$	−0.229244	−0.0101610	−0.00508052	−	0.999987i	$-0.501617\pi$
$509$	−0.229244	−0.0101610	−0.00508052	+	0.999987i	$0.501617\pi$
$510$	2.66604	0.118054
$511$	−49.5176	−2.19053
$512$	1.00000	0.0441942
$513$	−5.29629	−0.233837
$514$	−17.5046	−0.772096
$515$	−9.33642	−0.411412
$516$	6.32915	0.278625
$517$	−3.52192	−0.154894
$518$	−15.9435	−0.700517
$519$	21.7413	0.954338
$520$	14.5361	0.637450
$521$	−5.19776	−0.227718	−0.113859	−	0.993497i	$-0.536321\pi$
$521$	−5.19776	−0.227718	−0.113859	+	0.993497i	$0.536321\pi$
$522$	−5.03017	−0.220164
$523$	−37.3665	−1.63392	−0.816961	−	0.576693i	$-0.804343\pi$
$523$	−37.3665	−1.63392	−0.816961	+	0.576693i	$0.804343\pi$
$524$	−8.71109	−0.380546
$525$	8.94265	0.390289
$526$	−19.7411	−0.860755
$527$	−5.57443	−0.242826
$528$	−0.269084	−0.0117104
$529$	−19.0221	−0.827047
$530$	−14.7912	−0.642487
$531$	−1.00000	−0.0433963
$532$	−22.4709	−0.974236
$533$	−51.5302	−2.23202
$534$	7.37102	0.318975
$535$	−35.1193	−1.51834
$536$	−1.40536	−0.0607022
$537$	−18.4184	−0.794815
$538$	14.9580	0.644886
$539$	−2.96019	−0.127504
$540$	2.66604	0.114728
$541$	32.2931	1.38839	0.694195	−	0.719787i	$-0.255761\pi$
$541$	32.2931	1.38839	0.694195	+	0.719787i	$0.255761\pi$
$542$	20.2941	0.871707
$543$	12.4615	0.534773
$544$	1.00000	0.0428746
$545$	−48.1903	−2.06425
$546$	23.1329	0.989996
$547$	7.24160	0.309629	0.154814	−	0.987944i	$-0.450522\pi$
$547$	7.24160	0.309629	0.154814	+	0.987944i	$0.450522\pi$
$548$	11.0929	0.473864
$549$	1.10999	0.0473733
$550$	−0.567160	−0.0241838
$551$	26.6412	1.13495
$552$	1.99447	0.0848904
$553$	−65.6989	−2.79380
$554$	0.430732	0.0183001
$555$	−10.0185	−0.425260
$556$	−8.42488	−0.357294
$557$	7.49451	0.317553	0.158776	−	0.987315i	$-0.449245\pi$
$557$	7.49451	0.317553	0.158776	+	0.987315i	$0.449245\pi$
$558$	−5.57443	−0.235984
$559$	34.5086	1.45956
$560$	11.3113	0.477991
$561$	−0.269084	−0.0113607
$562$	20.0042	0.843828
$563$	11.8549	0.499625	0.249813	−	0.968294i	$-0.419631\pi$
$563$	11.8549	0.499625	0.249813	+	0.968294i	$0.419631\pi$
$564$	13.0885	0.551127
$565$	−34.2687	−1.44170
$566$	−30.7966	−1.29448
$567$	4.24276	0.178179
$568$	−4.21979	−0.177059
$569$	21.1129	0.885100	0.442550	−	0.896744i	$-0.354074\pi$
$569$	21.1129	0.885100	0.442550	+	0.896744i	$0.354074\pi$
$570$	−14.1201	−0.591426
$571$	−7.55518	−0.316174	−0.158087	−	0.987425i	$-0.550533\pi$
$571$	−7.55518	−0.316174	−0.158087	+	0.987425i	$0.550533\pi$
$572$	−1.46713	−0.0613439
$573$	8.02566	0.335277
$574$	−40.0985	−1.67368
$575$	4.20384	0.175312
$576$	1.00000	0.0416667
$577$	30.5912	1.27353	0.636764	−	0.771058i	$-0.280272\pi$
$577$	30.5912	1.27353	0.636764	+	0.771058i	$0.280272\pi$
$578$	1.00000	0.0415945
$579$	18.6029	0.773112
$580$	−13.4106	−0.556845
$581$	−4.10953	−0.170492
$582$	2.52617	0.104713
$583$	1.49288	0.0618286
$584$	−11.6711	−0.482953
$585$	14.5361	0.600993
$586$	25.8380	1.06736
$587$	12.5949	0.519848	0.259924	−	0.965629i	$-0.416303\pi$
$587$	12.5949	0.519848	0.259924	+	0.965629i	$0.416303\pi$
$588$	11.0010	0.453673
$589$	29.5238	1.21651
$590$	−2.66604	−0.109759
$591$	17.3241	0.712619
$592$	−3.75782	−0.154445
$593$	12.6387	0.519010	0.259505	−	0.965742i	$-0.416441\pi$
$593$	12.6387	0.519010	0.259505	+	0.965742i	$0.416441\pi$
$594$	−0.269084	−0.0110406
$595$	11.3113	0.463720
$596$	21.6171	0.885471
$597$	−23.7109	−0.970422
$598$	10.8745	0.444692
$599$	−35.6326	−1.45591	−0.727954	−	0.685626i	$-0.759528\pi$
$599$	−35.6326	−1.45591	−0.727954	+	0.685626i	$0.759528\pi$
$600$	2.10775	0.0860483
$601$	−8.12852	−0.331569	−0.165785	−	0.986162i	$-0.553016\pi$
$601$	−8.12852	−0.331569	−0.165785	+	0.986162i	$0.553016\pi$
$602$	26.8530	1.09445
$603$	−1.40536	−0.0572306
$604$	−6.23210	−0.253581
$605$	−29.1334	−1.18444
$606$	7.30932	0.296921
$607$	−0.791598	−0.0321300	−0.0160650	−	0.999871i	$-0.505114\pi$
$607$	−0.791598	−0.0321300	−0.0160650	+	0.999871i	$0.505114\pi$
$608$	−5.29629	−0.214793
$609$	−21.3418	−0.864812
$610$	2.95928	0.119818
$611$	71.3630	2.88704
$612$	1.00000	0.0404226
$613$	26.8960	1.08632	0.543160	−	0.839629i	$-0.317228\pi$
$613$	26.8960	1.08632	0.543160	+	0.839629i	$0.317228\pi$
$614$	26.1206	1.05414
$615$	−25.1969	−1.01604
$616$	−1.14166	−0.0459987
$617$	27.1580	1.09334	0.546669	−	0.837348i	$-0.315895\pi$
$617$	27.1580	1.09334	0.546669	+	0.837348i	$0.315895\pi$
$618$	−3.50199	−0.140871
$619$	36.9674	1.48585	0.742923	−	0.669377i	$-0.233439\pi$
$619$	36.9674	1.48585	0.742923	+	0.669377i	$0.233439\pi$
$620$	−14.8616	−0.596857
$621$	1.99447	0.0800354
$622$	9.57209	0.383806
$623$	31.2735	1.25294
$624$	5.45233	0.218268
$625$	−31.0961	−1.24385
$626$	−26.6917	−1.06681
$627$	1.42515	0.0569149
$628$	−24.9109	−0.994053
$629$	−3.75782	−0.149834
$630$	11.3113	0.450655
$631$	45.2959	1.80320	0.901602	−	0.432568i	$-0.142392\pi$
$631$	45.2959	1.80320	0.901602	+	0.432568i	$0.142392\pi$
$632$	−15.4850	−0.615959
$633$	−21.2553	−0.844823
$634$	−17.2506	−0.685110
$635$	0.976982	0.0387704
$636$	−5.54800	−0.219992
$637$	59.9809	2.37653
$638$	1.35354	0.0535870
$639$	−4.21979	−0.166932
$640$	2.66604	0.105384
$641$	−35.4371	−1.39968	−0.699841	−	0.714299i	$-0.746746\pi$
$641$	−35.4371	−1.39968	−0.699841	+	0.714299i	$0.746746\pi$
$642$	−13.1729	−0.519892
$643$	−45.0891	−1.77814	−0.889071	−	0.457770i	$-0.848648\pi$
$643$	−45.0891	−1.77814	−0.889071	+	0.457770i	$0.848648\pi$
$644$	8.46206	0.333452
$645$	16.8737	0.664402
$646$	−5.29629	−0.208380
$647$	31.5617	1.24082	0.620409	−	0.784278i	$-0.286966\pi$
$647$	31.5617	1.24082	0.620409	+	0.784278i	$0.286966\pi$
$648$	1.00000	0.0392837
$649$	0.269084	0.0105625
$650$	11.4921	0.450758
$651$	−23.6509	−0.926954
$652$	18.6976	0.732253
$653$	44.0900	1.72537	0.862687	−	0.505738i	$-0.168780\pi$
$653$	44.0900	1.72537	0.862687	+	0.505738i	$0.168780\pi$
$654$	−18.0756	−0.706813
$655$	−23.2241	−0.907439
$656$	−9.45106	−0.369002
$657$	−11.6711	−0.455333
$658$	55.5315	2.16484
$659$	9.58845	0.373513	0.186757	−	0.982406i	$-0.440202\pi$
$659$	9.58845	0.373513	0.186757	+	0.982406i	$0.440202\pi$
$660$	−0.717387	−0.0279243
$661$	−0.940501	−0.0365813	−0.0182906	−	0.999833i	$-0.505822\pi$
$661$	−0.940501	−0.0365813	−0.0182906	+	0.999833i	$0.505822\pi$
$662$	16.5855	0.644613
$663$	5.45233	0.211751
$664$	−0.968600	−0.0375890
$665$	−59.9081	−2.32314
$666$	−3.75782	−0.145612
$667$	−10.0325	−0.388461
$668$	15.3134	0.592494
$669$	14.7912	0.571859
$670$	−3.74674	−0.144749
$671$	−0.298681	−0.0115305
$672$	4.24276	0.163668
$673$	−26.1153	−1.00667	−0.503336	−	0.864091i	$-0.667894\pi$
$673$	−26.1153	−1.00667	−0.503336	+	0.864091i	$0.667894\pi$
$674$	23.7902	0.916365
$675$	2.10775	0.0811272
$676$	16.7278	0.643379
$677$	9.35248	0.359445	0.179723	−	0.983717i	$-0.442480\pi$
$677$	9.35248	0.359445	0.179723	+	0.983717i	$0.442480\pi$
$678$	−12.8538	−0.493647
$679$	10.7179	0.411316
$680$	2.66604	0.102238
$681$	13.8685	0.531441
$682$	1.49999	0.0574376
$683$	23.7337	0.908143	0.454071	−	0.890965i	$-0.349971\pi$
$683$	23.7337	0.908143	0.454071	+	0.890965i	$0.349971\pi$
$684$	−5.29629	−0.202509
$685$	29.5740	1.12997
$686$	16.9752	0.648116
$687$	29.6505	1.13124
$688$	6.32915	0.241296
$689$	−30.2495	−1.15241
$690$	5.31734	0.202427
$691$	34.7528	1.32206	0.661029	−	0.750361i	$-0.270120\pi$
$691$	34.7528	1.32206	0.661029	+	0.750361i	$0.270120\pi$
$692$	21.7413	0.826481
$693$	−1.14166	−0.0433680
$694$	−0.199391	−0.00756878
$695$	−22.4610	−0.851995
$696$	−5.03017	−0.190668
$697$	−9.45106	−0.357984
$698$	−11.8597	−0.448896
$699$	11.2060	0.423851
$700$	8.94265	0.338000
$701$	−21.6406	−0.817356	−0.408678	−	0.912679i	$-0.634010\pi$
$701$	−21.6406	−0.817356	−0.408678	+	0.912679i	$0.634010\pi$
$702$	5.45233	0.205785
$703$	19.9025	0.750636
$704$	−0.269084	−0.0101415
$705$	34.8945	1.31420
$706$	−26.8945	−1.01219
$707$	31.0117	1.16631
$708$	−1.00000	−0.0375823
$709$	13.5834	0.510137	0.255068	−	0.966923i	$-0.417902\pi$
$709$	13.5834	0.510137	0.255068	+	0.966923i	$0.417902\pi$
$710$	−11.2501	−0.422209
$711$	−15.4850	−0.580732
$712$	7.37102	0.276241
$713$	−11.1180	−0.416374
$714$	4.24276	0.158781
$715$	−3.91143	−0.146279
$716$	−18.4184	−0.688330
$717$	−6.01571	−0.224661
$718$	18.8144	0.702146
$719$	35.9438	1.34048	0.670240	−	0.742145i	$-0.266191\pi$
$719$	35.9438	1.34048	0.670240	+	0.742145i	$0.266191\pi$
$720$	2.66604	0.0993573
$721$	−14.8581	−0.553344
$722$	9.05070	0.336832
$723$	2.92713	0.108861
$724$	12.4615	0.463127
$725$	−10.6023	−0.393760
$726$	−10.9276	−0.405561
$727$	−41.6916	−1.54626	−0.773128	−	0.634250i	$-0.781309\pi$
$727$	−41.6916	−1.54626	−0.773128	+	0.634250i	$0.781309\pi$
$728$	23.1329	0.857362
$729$	1.00000	0.0370370
$730$	−31.1155	−1.15164
$731$	6.32915	0.234092
$732$	1.10999	0.0410265
$733$	−1.65697	−0.0612018	−0.0306009	−	0.999532i	$-0.509742\pi$
$733$	−1.65697	−0.0612018	−0.0306009	+	0.999532i	$0.509742\pi$
$734$	21.3939	0.789664
$735$	29.3290	1.08182
$736$	1.99447	0.0735172
$737$	0.378159	0.0139297
$738$	−9.45106	−0.347898
$739$	−29.6751	−1.09162	−0.545809	−	0.837910i	$-0.683777\pi$
$739$	−29.6751	−1.09162	−0.545809	+	0.837910i	$0.683777\pi$
$740$	−10.0185	−0.368286
$741$	−28.8771	−1.06083
$742$	−23.5388	−0.864136
$743$	−40.8560	−1.49886	−0.749431	−	0.662083i	$-0.769673\pi$
$743$	−40.8560	−1.49886	−0.749431	+	0.662083i	$0.769673\pi$
$744$	−5.57443	−0.204369
$745$	57.6320	2.11147
$746$	16.9637	0.621086
$747$	−0.968600	−0.0354392
$748$	−0.269084	−0.00983868
$749$	−55.8893	−2.04215
$750$	−7.71085	−0.281561
$751$	−13.0994	−0.478002	−0.239001	−	0.971019i	$-0.576820\pi$
$751$	−13.0994	−0.478002	−0.239001	+	0.971019i	$0.576820\pi$
$752$	13.0885	0.477290
$753$	−17.2275	−0.627805
$754$	−27.4261	−0.998799
$755$	−16.6150	−0.604682
$756$	4.24276	0.154308
$757$	−7.57068	−0.275161	−0.137581	−	0.990491i	$-0.543933\pi$
$757$	−7.57068	−0.275161	−0.137581	+	0.990491i	$0.543933\pi$
$758$	13.3890	0.486310
$759$	−0.536681	−0.0194803
$760$	−14.1201	−0.512190
$761$	45.0163	1.63184	0.815919	−	0.578166i	$-0.196231\pi$
$761$	45.0163	1.63184	0.815919	+	0.578166i	$0.196231\pi$
$762$	0.366455	0.0132753
$763$	−76.6905	−2.77638
$764$	8.02566	0.290358
$765$	2.66604	0.0963907
$766$	−6.67925	−0.241331
$767$	−5.45233	−0.196872
$768$	1.00000	0.0360844
$769$	−15.4197	−0.556050	−0.278025	−	0.960574i	$-0.589680\pi$
$769$	−15.4197	−0.556050	−0.278025	+	0.960574i	$0.589680\pi$
$770$	−3.04370	−0.109687
$771$	−17.5046	−0.630414
$772$	18.6029	0.669534
$773$	−18.7020	−0.672664	−0.336332	−	0.941744i	$-0.609186\pi$
$773$	−18.7020	−0.672664	−0.336332	+	0.941744i	$0.609186\pi$
$774$	6.32915	0.227496
$775$	−11.7495	−0.422054
$776$	2.52617	0.0906842
$777$	−15.9435	−0.571970
$778$	18.0389	0.646727
$779$	50.0555	1.79343
$780$	14.5361	0.520476
$781$	1.13548	0.0406306
$782$	1.99447	0.0713222
$783$	−5.03017	−0.179763
$784$	11.0010	0.392892
$785$	−66.4133	−2.37039
$786$	−8.71109	−0.310714
$787$	−18.4957	−0.659299	−0.329650	−	0.944103i	$-0.606931\pi$
$787$	−18.4957	−0.659299	−0.329650	+	0.944103i	$0.606931\pi$
$788$	17.3241	0.617146
$789$	−19.7411	−0.702803
$790$	−41.2835	−1.46880
$791$	−54.5356	−1.93906
$792$	−0.269084	−0.00956148
$793$	6.05204	0.214914
$794$	−26.1599	−0.928378
$795$	−14.7912	−0.524588
$796$	−23.7109	−0.840410
$797$	40.8682	1.44763	0.723814	−	0.689995i	$-0.242387\pi$
$797$	40.8682	1.44763	0.723814	+	0.689995i	$0.242387\pi$
$798$	−22.4709	−0.795460
$799$	13.0885	0.463039
$800$	2.10775	0.0745200
$801$	7.37102	0.260442
$802$	−31.6007	−1.11586
$803$	3.14050	0.110826
$804$	−1.40536	−0.0495632
$805$	22.5602	0.795141
$806$	−30.3936	−1.07057
$807$	14.9580	0.526547
$808$	7.30932	0.257141
$809$	−8.37130	−0.294319	−0.147160	−	0.989113i	$-0.547013\pi$
$809$	−8.37130	−0.294319	−0.147160	+	0.989113i	$0.547013\pi$
$810$	2.66604	0.0936749
$811$	−36.1487	−1.26935	−0.634677	−	0.772778i	$-0.718867\pi$
$811$	−36.1487	−1.26935	−0.634677	+	0.772778i	$0.718867\pi$
$812$	−21.3418	−0.748949
$813$	20.2941	0.711746
$814$	1.01117	0.0354414
$815$	49.8483	1.74611
$816$	1.00000	0.0350070
$817$	−33.5210	−1.17275
$818$	28.7375	1.00478
$819$	23.1329	0.808329
$820$	−25.1969	−0.879912
$821$	15.1947	0.530300	0.265150	−	0.964207i	$-0.414579\pi$
$821$	15.1947	0.530300	0.265150	+	0.964207i	$0.414579\pi$
$822$	11.0929	0.386909
$823$	16.0756	0.560361	0.280180	−	0.959947i	$-0.409606\pi$
$823$	16.0756	0.560361	0.280180	+	0.959947i	$0.409606\pi$
$824$	−3.50199	−0.121998
$825$	−0.567160	−0.0197460
$826$	−4.24276	−0.147624
$827$	−17.4309	−0.606131	−0.303065	−	0.952970i	$-0.598010\pi$
$827$	−17.4309	−0.606131	−0.303065	+	0.952970i	$0.598010\pi$
$828$	1.99447	0.0693127
$829$	2.16891	0.0753295	0.0376647	−	0.999290i	$-0.488008\pi$
$829$	2.16891	0.0753295	0.0376647	+	0.999290i	$0.488008\pi$
$830$	−2.58232	−0.0896337
$831$	0.430732	0.0149419
$832$	5.45233	0.189025
$833$	11.0010	0.381161
$834$	−8.42488	−0.291730
$835$	40.8261	1.41285
$836$	1.42515	0.0492897
$837$	−5.57443	−0.192680
$838$	−1.81670	−0.0627570
$839$	−39.5970	−1.36704	−0.683520	−	0.729932i	$-0.739552\pi$
$839$	−39.5970	−1.36704	−0.683520	+	0.729932i	$0.739552\pi$
$840$	11.3113	0.390278
$841$	−3.69744	−0.127498
$842$	25.1182	0.865629
$843$	20.0042	0.688982
$844$	−21.2553	−0.731638
$845$	44.5970	1.53418
$846$	13.0885	0.449993
$847$	−46.3631	−1.59306
$848$	−5.54800	−0.190519
$849$	−30.7966	−1.05694
$850$	2.10775	0.0722951
$851$	−7.49486	−0.256921
$852$	−4.21979	−0.144568
$853$	50.6945	1.73575	0.867873	−	0.496786i	$-0.165487\pi$
$853$	50.6945	1.73575	0.867873	+	0.496786i	$0.165487\pi$
$854$	4.70943	0.161153
$855$	−14.1201	−0.482897
$856$	−13.1729	−0.450239
$857$	26.9223	0.919650	0.459825	−	0.888010i	$-0.347912\pi$
$857$	26.9223	0.919650	0.459825	+	0.888010i	$0.347912\pi$
$858$	−1.46713	−0.0500871
$859$	−49.5243	−1.68975	−0.844874	−	0.534965i	$-0.820325\pi$
$859$	−49.5243	−1.68975	−0.844874	+	0.534965i	$0.820325\pi$
$860$	16.8737	0.575389
$861$	−40.0985	−1.36655
$862$	−8.75445	−0.298178
$863$	−38.3597	−1.30578	−0.652889	−	0.757453i	$-0.726443\pi$
$863$	−38.3597	−1.30578	−0.652889	+	0.757453i	$0.726443\pi$
$864$	1.00000	0.0340207
$865$	57.9631	1.97080
$866$	0.964357	0.0327702
$867$	1.00000	0.0339618
$868$	−23.6509	−0.802765
$869$	4.16676	0.141348
$870$	−13.4106	−0.454662
$871$	−7.66247	−0.259633
$872$	−18.0756	−0.612118
$873$	2.52617	0.0854979
$874$	−10.5633	−0.357309
$875$	−32.7153	−1.10598
$876$	−11.6711	−0.394330
$877$	−20.4304	−0.689887	−0.344943	−	0.938624i	$-0.612102\pi$
$877$	−20.4304	−0.689887	−0.344943	+	0.938624i	$0.612102\pi$
$878$	37.3974	1.26210
$879$	25.8380	0.871494
$880$	−0.717387	−0.0241831
$881$	−40.3371	−1.35899	−0.679495	−	0.733680i	$-0.737801\pi$
$881$	−40.3371	−1.35899	−0.679495	+	0.733680i	$0.737801\pi$
$882$	11.0010	0.370422
$883$	−44.8633	−1.50977	−0.754886	−	0.655856i	$-0.772308\pi$
$883$	−44.8633	−1.50977	−0.754886	+	0.655856i	$0.772308\pi$
$884$	5.45233	0.183382
$885$	−2.66604	−0.0896178
$886$	16.2776	0.546858
$887$	−19.8737	−0.667292	−0.333646	−	0.942698i	$-0.608279\pi$
$887$	−19.8737	−0.667292	−0.333646	+	0.942698i	$0.608279\pi$
$888$	−3.75782	−0.126104
$889$	1.55478	0.0521456
$890$	19.6514	0.658717
$891$	−0.269084	−0.00901465
$892$	14.7912	0.495245
$893$	−69.3207	−2.31973
$894$	21.6171	0.722984
$895$	−49.1042	−1.64137
$896$	4.24276	0.141741
$897$	10.8745	0.363089
$898$	18.8547	0.629190
$899$	28.0403	0.935196
$900$	2.10775	0.0702582
$901$	−5.54800	−0.184831
$902$	2.54313	0.0846769
$903$	26.8530	0.893613
$904$	−12.8538	−0.427511
$905$	33.2227	1.10436
$906$	−6.23210	−0.207048
$907$	1.24471	0.0413301	0.0206650	−	0.999786i	$-0.493422\pi$
$907$	1.24471	0.0413301	0.0206650	+	0.999786i	$0.493422\pi$
$908$	13.8685	0.460242
$909$	7.30932	0.242435
$910$	61.6731	2.04444
$911$	45.6923	1.51385	0.756926	−	0.653501i	$-0.226700\pi$
$911$	45.6923	1.51385	0.756926	+	0.653501i	$0.226700\pi$
$912$	−5.29629	−0.175378
$913$	0.260635	0.00862575
$914$	−40.2484	−1.33130
$915$	2.95928	0.0978307
$916$	29.6505	0.979679
$917$	−36.9590	−1.22049
$918$	1.00000	0.0330049
$919$	9.10718	0.300418	0.150209	−	0.988654i	$-0.452005\pi$
$919$	9.10718	0.300418	0.150209	+	0.988654i	$0.452005\pi$
$920$	5.31734	0.175307
$921$	26.1206	0.860702
$922$	27.8216	0.916255
$923$	−23.0077	−0.757307
$924$	−1.14166	−0.0375578
$925$	−7.92052	−0.260425
$926$	9.59595	0.315342
$927$	−3.50199	−0.115020
$928$	−5.03017	−0.165123
$929$	45.6297	1.49706	0.748531	−	0.663100i	$-0.230759\pi$
$929$	45.6297	1.49706	0.748531	+	0.663100i	$0.230759\pi$
$930$	−14.8616	−0.487332
$931$	−58.2644	−1.90954
$932$	11.2060	0.367066
$933$	9.57209	0.313376
$934$	3.22329	0.105469
$935$	−0.717387	−0.0234611
$936$	5.45233	0.178215
$937$	−22.5760	−0.737527	−0.368764	−	0.929523i	$-0.620219\pi$
$937$	−22.5760	−0.737527	−0.368764	+	0.929523i	$0.620219\pi$
$938$	−5.96259	−0.194686
$939$	−26.6917	−0.871049
$940$	34.8945	1.13813
$941$	−27.0542	−0.881942	−0.440971	−	0.897521i	$-0.645366\pi$
$941$	−27.0542	−0.881942	−0.440971	+	0.897521i	$0.645366\pi$
$942$	−24.9109	−0.811641
$943$	−18.8499	−0.613836
$944$	−1.00000	−0.0325472
$945$	11.3113	0.367958
$946$	−1.70307	−0.0553716
$947$	−22.0564	−0.716738	−0.358369	−	0.933580i	$-0.616667\pi$
$947$	−22.0564	−0.716738	−0.358369	+	0.933580i	$0.616667\pi$
$948$	−15.4850	−0.502928
$949$	−63.6346	−2.06567
$950$	−11.1632	−0.362183
$951$	−17.2506	−0.559390
$952$	4.24276	0.137509
$953$	43.2423	1.40076	0.700378	−	0.713772i	$-0.253015\pi$
$953$	43.2423	1.40076	0.700378	+	0.713772i	$0.253015\pi$
$954$	−5.54800	−0.179623
$955$	21.3967	0.692381
$956$	−6.01571	−0.194562
$957$	1.35354	0.0437536
$958$	7.90214	0.255307
$959$	47.0644	1.51979
$960$	2.66604	0.0860459
$961$	0.0742644	0.00239562
$962$	−20.4888	−0.660586
$963$	−13.1729	−0.424490
$964$	2.92713	0.0942766
$965$	49.5961	1.59655
$966$	8.46206	0.272262
$967$	−43.4373	−1.39685	−0.698425	−	0.715683i	$-0.746116\pi$
$967$	−43.4373	−1.39685	−0.698425	+	0.715683i	$0.746116\pi$
$968$	−10.9276	−0.351226
$969$	−5.29629	−0.170141
$970$	6.73486	0.216243
$971$	−29.3240	−0.941053	−0.470527	−	0.882386i	$-0.655936\pi$
$971$	−29.3240	−0.941053	−0.470527	+	0.882386i	$0.655936\pi$
$972$	1.00000	0.0320750
$973$	−35.7447	−1.14592
$974$	9.68996	0.310486
$975$	11.4921	0.368042
$976$	1.10999	0.0355300
$977$	−5.14960	−0.164750	−0.0823751	−	0.996601i	$-0.526251\pi$
$977$	−5.14960	−0.164750	−0.0823751	+	0.996601i	$0.526251\pi$
$978$	18.6976	0.597882
$979$	−1.98342	−0.0633905
$980$	29.3290	0.936881
$981$	−18.0756	−0.577111
$982$	−5.92485	−0.189070
$983$	−23.6934	−0.755701	−0.377851	−	0.925867i	$-0.623337\pi$
$983$	−23.6934	−0.755701	−0.377851	+	0.925867i	$0.623337\pi$
$984$	−9.45106	−0.301289
$985$	46.1867	1.47163
$986$	−5.03017	−0.160193
$987$	55.5315	1.76759
$988$	−28.8771	−0.918703
$989$	12.6233	0.401398
$990$	−0.717387	−0.0228001
$991$	16.1932	0.514394	0.257197	−	0.966359i	$-0.417201\pi$
$991$	16.1932	0.514394	0.257197	+	0.966359i	$0.417201\pi$
$992$	−5.57443	−0.176988
$993$	16.5855	0.526324
$994$	−17.9035	−0.567866
$995$	−63.2141	−2.00402
$996$	−0.968600	−0.0306913
$997$	−1.94096	−0.0614709	−0.0307354	−	0.999528i	$-0.509785\pi$
$997$	−1.94096	−0.0614709	−0.0307354	+	0.999528i	$0.509785\pi$
$998$	−12.9895	−0.411174
$999$	−3.75782	−0.118892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.9	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.9	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.66604 q^{5} +1.00000 q^{6} +4.24276 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.66604 q^{5} +1.00000 q^{6} +4.24276 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.66604 q^{10} -0.269084 q^{11} +1.00000 q^{12} +5.45233 q^{13} +4.24276 q^{14} +2.66604 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -5.29629 q^{19} +2.66604 q^{20} +4.24276 q^{21} -0.269084 q^{22} +1.99447 q^{23} +1.00000 q^{24} +2.10775 q^{25} +5.45233 q^{26} +1.00000 q^{27} +4.24276 q^{28} -5.03017 q^{29} +2.66604 q^{30} -5.57443 q^{31} +1.00000 q^{32} -0.269084 q^{33} +1.00000 q^{34} +11.3113 q^{35} +1.00000 q^{36} -3.75782 q^{37} -5.29629 q^{38} +5.45233 q^{39} +2.66604 q^{40} -9.45106 q^{41} +4.24276 q^{42} +6.32915 q^{43} -0.269084 q^{44} +2.66604 q^{45} +1.99447 q^{46} +13.0885 q^{47} +1.00000 q^{48} +11.0010 q^{49} +2.10775 q^{50} +1.00000 q^{51} +5.45233 q^{52} -5.54800 q^{53} +1.00000 q^{54} -0.717387 q^{55} +4.24276 q^{56} -5.29629 q^{57} -5.03017 q^{58} -1.00000 q^{59} +2.66604 q^{60} +1.10999 q^{61} -5.57443 q^{62} +4.24276 q^{63} +1.00000 q^{64} +14.5361 q^{65} -0.269084 q^{66} -1.40536 q^{67} +1.00000 q^{68} +1.99447 q^{69} +11.3113 q^{70} -4.21979 q^{71} +1.00000 q^{72} -11.6711 q^{73} -3.75782 q^{74} +2.10775 q^{75} -5.29629 q^{76} -1.14166 q^{77} +5.45233 q^{78} -15.4850 q^{79} +2.66604 q^{80} +1.00000 q^{81} -9.45106 q^{82} -0.968600 q^{83} +4.24276 q^{84} +2.66604 q^{85} +6.32915 q^{86} -5.03017 q^{87} -0.269084 q^{88} +7.37102 q^{89} +2.66604 q^{90} +23.1329 q^{91} +1.99447 q^{92} -5.57443 q^{93} +13.0885 q^{94} -14.1201 q^{95} +1.00000 q^{96} +2.52617 q^{97} +11.0010 q^{98} -0.269084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * q^99

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