LMFDB - Embedded newform 6045.2.a.bi.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 21 x^{16} + 97 x^{15} + 156 x^{14} - 935 x^{13} - 411 x^{12} + 4582 x^{11} + \cdots - 112 $ x^18 - 4x^17 - 21x^16 + 97x^15 + 156x^14 - 935x^13 - 411x^12 + 4582x^11 - 446x^10 - 12159x^9 + 4398x^8 + 17347x^7 - 7839x^6 - 12832x^5 + 4744x^4 + 5064x^3 - 746x^2 - 892*x - 112
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.698229$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.698229 q^{2} +1.00000 q^{3} -1.51248 q^{4} +1.00000 q^{5} -0.698229 q^{6} +4.99716 q^{7} +2.45251 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.698229 q^{2} +1.00000 q^{3} -1.51248 q^{4} +1.00000 q^{5} -0.698229 q^{6} +4.99716 q^{7} +2.45251 q^{8} +1.00000 q^{9} -0.698229 q^{10} -1.57000 q^{11} -1.51248 q^{12} -1.00000 q^{13} -3.48916 q^{14} +1.00000 q^{15} +1.31253 q^{16} +0.300188 q^{17} -0.698229 q^{18} -6.71723 q^{19} -1.51248 q^{20} +4.99716 q^{21} +1.09622 q^{22} +3.87456 q^{23} +2.45251 q^{24} +1.00000 q^{25} +0.698229 q^{26} +1.00000 q^{27} -7.55808 q^{28} -3.73496 q^{29} -0.698229 q^{30} +1.00000 q^{31} -5.82148 q^{32} -1.57000 q^{33} -0.209600 q^{34} +4.99716 q^{35} -1.51248 q^{36} -5.41626 q^{37} +4.69016 q^{38} -1.00000 q^{39} +2.45251 q^{40} -2.60170 q^{41} -3.48916 q^{42} +10.5490 q^{43} +2.37458 q^{44} +1.00000 q^{45} -2.70533 q^{46} +5.68914 q^{47} +1.31253 q^{48} +17.9716 q^{49} -0.698229 q^{50} +0.300188 q^{51} +1.51248 q^{52} +6.83072 q^{53} -0.698229 q^{54} -1.57000 q^{55} +12.2556 q^{56} -6.71723 q^{57} +2.60786 q^{58} +12.5928 q^{59} -1.51248 q^{60} +13.6921 q^{61} -0.698229 q^{62} +4.99716 q^{63} +1.43966 q^{64} -1.00000 q^{65} +1.09622 q^{66} -8.54291 q^{67} -0.454027 q^{68} +3.87456 q^{69} -3.48916 q^{70} -12.6665 q^{71} +2.45251 q^{72} -3.14470 q^{73} +3.78179 q^{74} +1.00000 q^{75} +10.1596 q^{76} -7.84553 q^{77} +0.698229 q^{78} +6.81473 q^{79} +1.31253 q^{80} +1.00000 q^{81} +1.81659 q^{82} +12.0190 q^{83} -7.55808 q^{84} +0.300188 q^{85} -7.36563 q^{86} -3.73496 q^{87} -3.85044 q^{88} +4.84865 q^{89} -0.698229 q^{90} -4.99716 q^{91} -5.86017 q^{92} +1.00000 q^{93} -3.97232 q^{94} -6.71723 q^{95} -5.82148 q^{96} -7.32782 q^{97} -12.5483 q^{98} -1.57000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * 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 $

$2$	−0.698229	−0.493723	−0.246861	−	0.969051i	$-0.579399\pi$
$2$	−0.698229	−0.493723	−0.246861	+	0.969051i	$0.579399\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.51248	−0.756238
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.698229	−0.285051
$7$	4.99716	1.88875	0.944374	−	0.328872i	$-0.106669\pi$
$7$	4.99716	1.88875	0.944374	+	0.328872i	$0.106669\pi$
$8$	2.45251	0.867094
$9$	1.00000	0.333333
$10$	−0.698229	−0.220799
$11$	−1.57000	−0.473372	−0.236686	−	0.971586i	$-0.576061\pi$
$11$	−1.57000	−0.473372	−0.236686	+	0.971586i	$0.576061\pi$
$12$	−1.51248	−0.436614
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.48916	−0.932518
$15$	1.00000	0.258199
$16$	1.31253	0.328134
$17$	0.300188	0.0728063	0.0364032	−	0.999337i	$-0.488410\pi$
$17$	0.300188	0.0728063	0.0364032	+	0.999337i	$0.488410\pi$
$18$	−0.698229	−0.164574
$19$	−6.71723	−1.54104	−0.770519	−	0.637417i	$-0.780003\pi$
$19$	−6.71723	−1.54104	−0.770519	+	0.637417i	$0.780003\pi$
$20$	−1.51248	−0.338200
$21$	4.99716	1.09047
$22$	1.09622	0.233715
$23$	3.87456	0.807901	0.403950	−	0.914781i	$-0.367637\pi$
$23$	3.87456	0.807901	0.403950	+	0.914781i	$0.367637\pi$
$24$	2.45251	0.500617
$25$	1.00000	0.200000
$26$	0.698229	0.136934
$27$	1.00000	0.192450
$28$	−7.55808	−1.42834
$29$	−3.73496	−0.693565	−0.346783	−	0.937946i	$-0.612726\pi$
$29$	−3.73496	−0.693565	−0.346783	+	0.937946i	$0.612726\pi$
$30$	−0.698229	−0.127479
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−5.82148	−1.02910
$33$	−1.57000	−0.273302
$34$	−0.209600	−0.0359461
$35$	4.99716	0.844674
$36$	−1.51248	−0.252079
$37$	−5.41626	−0.890428	−0.445214	−	0.895424i	$-0.646872\pi$
$37$	−5.41626	−0.890428	−0.445214	+	0.895424i	$0.646872\pi$
$38$	4.69016	0.760845
$39$	−1.00000	−0.160128
$40$	2.45251	0.387776
$41$	−2.60170	−0.406318	−0.203159	−	0.979146i	$-0.565121\pi$
$41$	−2.60170	−0.406318	−0.203159	+	0.979146i	$0.565121\pi$
$42$	−3.48916	−0.538390
$43$	10.5490	1.60871	0.804355	−	0.594149i	$-0.202511\pi$
$43$	10.5490	1.60871	0.804355	+	0.594149i	$0.202511\pi$
$44$	2.37458	0.357982
$45$	1.00000	0.149071
$46$	−2.70533	−0.398879
$47$	5.68914	0.829846	0.414923	−	0.909856i	$-0.363808\pi$
$47$	5.68914	0.829846	0.414923	+	0.909856i	$0.363808\pi$
$48$	1.31253	0.189448
$49$	17.9716	2.56737
$50$	−0.698229	−0.0987445
$51$	0.300188	0.0420348
$52$	1.51248	0.209743
$53$	6.83072	0.938271	0.469136	−	0.883126i	$-0.344566\pi$
$53$	6.83072	0.938271	0.469136	+	0.883126i	$0.344566\pi$
$54$	−0.698229	−0.0950170
$55$	−1.57000	−0.211699
$56$	12.2556	1.63772
$57$	−6.71723	−0.889718
$58$	2.60786	0.342429
$59$	12.5928	1.63945	0.819724	−	0.572758i	$-0.194127\pi$
$59$	12.5928	1.63945	0.819724	+	0.572758i	$0.194127\pi$
$60$	−1.51248	−0.195260
$61$	13.6921	1.75309	0.876546	−	0.481318i	$-0.159842\pi$
$61$	13.6921	1.75309	0.876546	+	0.481318i	$0.159842\pi$
$62$	−0.698229	−0.0886752
$63$	4.99716	0.629583
$64$	1.43966	0.179957
$65$	−1.00000	−0.124035
$66$	1.09622	0.134935
$67$	−8.54291	−1.04368	−0.521841	−	0.853043i	$-0.674755\pi$
$67$	−8.54291	−1.04368	−0.521841	+	0.853043i	$0.674755\pi$
$68$	−0.454027	−0.0550589
$69$	3.87456	0.466442
$70$	−3.48916	−0.417035
$71$	−12.6665	−1.50324	−0.751621	−	0.659595i	$-0.770728\pi$
$71$	−12.6665	−1.50324	−0.751621	+	0.659595i	$0.770728\pi$
$72$	2.45251	0.289031
$73$	−3.14470	−0.368059	−0.184029	−	0.982921i	$-0.558914\pi$
$73$	−3.14470	−0.368059	−0.184029	+	0.982921i	$0.558914\pi$
$74$	3.78179	0.439625
$75$	1.00000	0.115470
$76$	10.1596	1.16539
$77$	−7.84553	−0.894081
$78$	0.698229	0.0790589
$79$	6.81473	0.766717	0.383358	−	0.923600i	$-0.374767\pi$
$79$	6.81473	0.766717	0.383358	+	0.923600i	$0.374767\pi$
$80$	1.31253	0.146746
$81$	1.00000	0.111111
$82$	1.81659	0.200608
$83$	12.0190	1.31926	0.659630	−	0.751591i	$-0.270713\pi$
$83$	12.0190	1.31926	0.659630	+	0.751591i	$0.270713\pi$
$84$	−7.55808	−0.824654
$85$	0.300188	0.0325600
$86$	−7.36563	−0.794257
$87$	−3.73496	−0.400430
$88$	−3.85044	−0.410459
$89$	4.84865	0.513956	0.256978	−	0.966417i	$-0.417273\pi$
$89$	4.84865	0.513956	0.256978	+	0.966417i	$0.417273\pi$
$90$	−0.698229	−0.0735998
$91$	−4.99716	−0.523845
$92$	−5.86017	−0.610965
$93$	1.00000	0.103695
$94$	−3.97232	−0.409714
$95$	−6.71723	−0.689173
$96$	−5.82148	−0.594152
$97$	−7.32782	−0.744027	−0.372014	−	0.928227i	$-0.621333\pi$
$97$	−7.32782	−0.744027	−0.372014	+	0.928227i	$0.621333\pi$
$98$	−12.5483	−1.26757
$99$	−1.57000	−0.157791
$100$	−1.51248	−0.151248
$101$	13.7783	1.37100	0.685498	−	0.728075i	$-0.259585\pi$
$101$	13.7783	1.37100	0.685498	+	0.728075i	$0.259585\pi$
$102$	−0.209600	−0.0207535
$103$	−6.82192	−0.672184	−0.336092	−	0.941829i	$-0.609105\pi$
$103$	−6.82192	−0.672184	−0.336092	+	0.941829i	$0.609105\pi$
$104$	−2.45251	−0.240489
$105$	4.99716	0.487673
$106$	−4.76941	−0.463246
$107$	14.2092	1.37366	0.686829	−	0.726819i	$-0.259002\pi$
$107$	14.2092	1.37366	0.686829	+	0.726819i	$0.259002\pi$
$108$	−1.51248	−0.145538
$109$	11.2659	1.07908	0.539541	−	0.841959i	$-0.318598\pi$
$109$	11.2659	1.07908	0.539541	+	0.841959i	$0.318598\pi$
$110$	1.09622	0.104520
$111$	−5.41626	−0.514089
$112$	6.55895	0.619762
$113$	1.55385	0.146174	0.0730869	−	0.997326i	$-0.476715\pi$
$113$	1.55385	0.146174	0.0730869	+	0.997326i	$0.476715\pi$
$114$	4.69016	0.439274
$115$	3.87456	0.361304
$116$	5.64904	0.524500
$117$	−1.00000	−0.0924500
$118$	−8.79269	−0.809433
$119$	1.50009	0.137513
$120$	2.45251	0.223883
$121$	−8.53510	−0.775919
$122$	−9.56022	−0.865541
$123$	−2.60170	−0.234588
$124$	−1.51248	−0.135824
$125$	1.00000	0.0894427
$126$	−3.48916	−0.310839
$127$	−13.3727	−1.18663	−0.593316	−	0.804970i	$-0.702182\pi$
$127$	−13.3727	−1.18663	−0.593316	+	0.804970i	$0.702182\pi$
$128$	10.6377	0.940253
$129$	10.5490	0.928789
$130$	0.698229	0.0612388
$131$	−16.5313	−1.44435	−0.722174	−	0.691712i	$-0.756857\pi$
$131$	−16.5313	−1.44435	−0.722174	+	0.691712i	$0.756857\pi$
$132$	2.37458	0.206681
$133$	−33.5671	−2.91063
$134$	5.96491	0.515290
$135$	1.00000	0.0860663
$136$	0.736216	0.0631300
$137$	5.55654	0.474727	0.237364	−	0.971421i	$-0.423717\pi$
$137$	5.55654	0.474727	0.237364	+	0.971421i	$0.423717\pi$
$138$	−2.70533	−0.230293
$139$	5.26118	0.446248	0.223124	−	0.974790i	$-0.428375\pi$
$139$	5.26118	0.446248	0.223124	+	0.974790i	$0.428375\pi$
$140$	−7.55808	−0.638775
$141$	5.68914	0.479112
$142$	8.84415	0.742185
$143$	1.57000	0.131290
$144$	1.31253	0.109378
$145$	−3.73496	−0.310172
$146$	2.19572	0.181719
$147$	17.9716	1.48227
$148$	8.19197	0.673375
$149$	7.90778	0.647831	0.323915	−	0.946086i	$-0.395001\pi$
$149$	7.90778	0.647831	0.323915	+	0.946086i	$0.395001\pi$
$150$	−0.698229	−0.0570102
$151$	−3.31042	−0.269398	−0.134699	−	0.990887i	$-0.543007\pi$
$151$	−3.31042	−0.269398	−0.134699	+	0.990887i	$0.543007\pi$
$152$	−16.4741	−1.33623
$153$	0.300188	0.0242688
$154$	5.47798	0.441428
$155$	1.00000	0.0803219
$156$	1.51248	0.121095
$157$	1.06279	0.0848198	0.0424099	−	0.999100i	$-0.486496\pi$
$157$	1.06279	0.0848198	0.0424099	+	0.999100i	$0.486496\pi$
$158$	−4.75824	−0.378545
$159$	6.83072	0.541711
$160$	−5.82148	−0.460228
$161$	19.3618	1.52592
$162$	−0.698229	−0.0548581
$163$	5.12384	0.401330	0.200665	−	0.979660i	$-0.435690\pi$
$163$	5.12384	0.401330	0.200665	+	0.979660i	$0.435690\pi$
$164$	3.93501	0.307273
$165$	−1.57000	−0.122224
$166$	−8.39204	−0.651349
$167$	−13.0843	−1.01249	−0.506247	−	0.862389i	$-0.668968\pi$
$167$	−13.0843	−1.01249	−0.506247	+	0.862389i	$0.668968\pi$
$168$	12.2556	0.945540
$169$	1.00000	0.0769231
$170$	−0.209600	−0.0160756
$171$	−6.71723	−0.513679
$172$	−15.9551	−1.21657
$173$	25.8571	1.96588	0.982940	−	0.183928i	$-0.0588812\pi$
$173$	25.8571	1.96588	0.982940	+	0.183928i	$0.0588812\pi$
$174$	2.60786	0.197701
$175$	4.99716	0.377750
$176$	−2.06068	−0.155329
$177$	12.5928	0.946536
$178$	−3.38547	−0.253752
$179$	−1.59705	−0.119369	−0.0596846	−	0.998217i	$-0.519009\pi$
$179$	−1.59705	−0.119369	−0.0596846	+	0.998217i	$0.519009\pi$
$180$	−1.51248	−0.112733
$181$	12.7798	0.949916	0.474958	−	0.880009i	$-0.342463\pi$
$181$	12.7798	0.949916	0.474958	+	0.880009i	$0.342463\pi$
$182$	3.48916	0.258634
$183$	13.6921	1.01215
$184$	9.50240	0.700526
$185$	−5.41626	−0.398212
$186$	−0.698229	−0.0511967
$187$	−0.471295	−0.0344645
$188$	−8.60469	−0.627561
$189$	4.99716	0.363490
$190$	4.69016	0.340260
$191$	20.0443	1.45036	0.725178	−	0.688561i	$-0.241757\pi$
$191$	20.0443	1.45036	0.725178	+	0.688561i	$0.241757\pi$
$192$	1.43966	0.103898
$193$	−8.51290	−0.612772	−0.306386	−	0.951907i	$-0.599120\pi$
$193$	−8.51290	−0.612772	−0.306386	+	0.951907i	$0.599120\pi$
$194$	5.11650	0.367343
$195$	−1.00000	−0.0716115
$196$	−27.1816	−1.94154
$197$	−23.8567	−1.69972	−0.849860	−	0.527009i	$-0.823313\pi$
$197$	−23.8567	−1.69972	−0.849860	+	0.527009i	$0.823313\pi$
$198$	1.09622	0.0779049
$199$	1.76246	0.124938	0.0624689	−	0.998047i	$-0.480103\pi$
$199$	1.76246	0.124938	0.0624689	+	0.998047i	$0.480103\pi$
$200$	2.45251	0.173419
$201$	−8.54291	−0.602570
$202$	−9.62044	−0.676892
$203$	−18.6642	−1.30997
$204$	−0.454027	−0.0317883
$205$	−2.60170	−0.181711
$206$	4.76327	0.331873
$207$	3.87456	0.269300
$208$	−1.31253	−0.0910079
$209$	10.5460	0.729485
$210$	−3.48916	−0.240775
$211$	19.0301	1.31009	0.655043	−	0.755592i	$-0.272650\pi$
$211$	19.0301	1.31009	0.655043	+	0.755592i	$0.272650\pi$
$212$	−10.3313	−0.709556
$213$	−12.6665	−0.867897
$214$	−9.92130	−0.678206
$215$	10.5490	0.719437
$216$	2.45251	0.166872
$217$	4.99716	0.339229
$218$	−7.86622	−0.532767
$219$	−3.14470	−0.212499
$220$	2.37458	0.160094
$221$	−0.300188	−0.0201928
$222$	3.78179	0.253817
$223$	4.03550	0.270237	0.135119	−	0.990829i	$-0.456858\pi$
$223$	4.03550	0.270237	0.135119	+	0.990829i	$0.456858\pi$
$224$	−29.0909	−1.94371
$225$	1.00000	0.0666667
$226$	−1.08494	−0.0721693
$227$	−26.1796	−1.73760	−0.868801	−	0.495162i	$-0.835109\pi$
$227$	−26.1796	−1.73760	−0.868801	+	0.495162i	$0.835109\pi$
$228$	10.1596	0.672839
$229$	−26.4530	−1.74807	−0.874033	−	0.485866i	$-0.838504\pi$
$229$	−26.4530	−1.74807	−0.874033	+	0.485866i	$0.838504\pi$
$230$	−2.70533	−0.178384
$231$	−7.84553	−0.516198
$232$	−9.16005	−0.601387
$233$	3.89182	0.254961	0.127481	−	0.991841i	$-0.459311\pi$
$233$	3.89182	0.254961	0.127481	+	0.991841i	$0.459311\pi$
$234$	0.698229	0.0456447
$235$	5.68914	0.371119
$236$	−19.0464	−1.23981
$237$	6.81473	0.442664
$238$	−1.04741	−0.0678932
$239$	−7.98768	−0.516680	−0.258340	−	0.966054i	$-0.583176\pi$
$239$	−7.98768	−0.516680	−0.258340	+	0.966054i	$0.583176\pi$
$240$	1.31253	0.0847238
$241$	24.5037	1.57842	0.789210	−	0.614123i	$-0.210490\pi$
$241$	24.5037	1.57842	0.789210	+	0.614123i	$0.210490\pi$
$242$	5.95946	0.383089
$243$	1.00000	0.0641500
$244$	−20.7090	−1.32575
$245$	17.9716	1.14816
$246$	1.81659	0.115821
$247$	6.71723	0.427407
$248$	2.45251	0.155735
$249$	12.0190	0.761675
$250$	−0.698229	−0.0441599
$251$	6.18882	0.390635	0.195317	−	0.980740i	$-0.437426\pi$
$251$	6.18882	0.390635	0.195317	+	0.980740i	$0.437426\pi$
$252$	−7.55808	−0.476114
$253$	−6.08305	−0.382438
$254$	9.33719	0.585867
$255$	0.300188	0.0187985
$256$	−10.3069	−0.644181
$257$	2.13527	0.133195	0.0665974	−	0.997780i	$-0.478786\pi$
$257$	2.13527	0.133195	0.0665974	+	0.997780i	$0.478786\pi$
$258$	−7.36563	−0.458564
$259$	−27.0659	−1.68179
$260$	1.51248	0.0937998
$261$	−3.73496	−0.231188
$262$	11.5426	0.713107
$263$	18.8394	1.16169	0.580844	−	0.814015i	$-0.302723\pi$
$263$	18.8394	1.16169	0.580844	+	0.814015i	$0.302723\pi$
$264$	−3.85044	−0.236978
$265$	6.83072	0.419608
$266$	23.4375	1.43705
$267$	4.84865	0.296732
$268$	12.9209	0.789272
$269$	−25.9975	−1.58510	−0.792548	−	0.609809i	$-0.791246\pi$
$269$	−25.9975	−1.58510	−0.792548	+	0.609809i	$0.791246\pi$
$270$	−0.698229	−0.0424929
$271$	−3.82778	−0.232521	−0.116260	−	0.993219i	$-0.537091\pi$
$271$	−3.82778	−0.232521	−0.116260	+	0.993219i	$0.537091\pi$
$272$	0.394008	0.0238902
$273$	−4.99716	−0.302442
$274$	−3.87974	−0.234384
$275$	−1.57000	−0.0946745
$276$	−5.86017	−0.352741
$277$	4.98695	0.299637	0.149818	−	0.988714i	$-0.452131\pi$
$277$	4.98695	0.299637	0.149818	+	0.988714i	$0.452131\pi$
$278$	−3.67351	−0.220323
$279$	1.00000	0.0598684
$280$	12.2556	0.732412
$281$	6.67810	0.398382	0.199191	−	0.979961i	$-0.436169\pi$
$281$	6.67810	0.398382	0.199191	+	0.979961i	$0.436169\pi$
$282$	−3.97232	−0.236549
$283$	−24.9380	−1.48241	−0.741204	−	0.671280i	$-0.765745\pi$
$283$	−24.9380	−1.48241	−0.741204	+	0.671280i	$0.765745\pi$
$284$	19.1578	1.13681
$285$	−6.71723	−0.397894
$286$	−1.09622	−0.0648208
$287$	−13.0011	−0.767432
$288$	−5.82148	−0.343034
$289$	−16.9099	−0.994699
$290$	2.60786	0.153139
$291$	−7.32782	−0.429564
$292$	4.75628	0.278340
$293$	−13.8839	−0.811106	−0.405553	−	0.914072i	$-0.632921\pi$
$293$	−13.8839	−0.811106	−0.405553	+	0.914072i	$0.632921\pi$
$294$	−12.5483	−0.731832
$295$	12.5928	0.733184
$296$	−13.2835	−0.772085
$297$	−1.57000	−0.0911006
$298$	−5.52145	−0.319849
$299$	−3.87456	−0.224071
$300$	−1.51248	−0.0873228
$301$	52.7151	3.03845
$302$	2.31143	0.133008
$303$	13.7783	0.791545
$304$	−8.81659	−0.505666
$305$	13.6921	0.784007
$306$	−0.209600	−0.0119820
$307$	26.0504	1.48677	0.743387	−	0.668861i	$-0.233218\pi$
$307$	26.0504	1.48677	0.743387	+	0.668861i	$0.233218\pi$
$308$	11.8662	0.676138
$309$	−6.82192	−0.388086
$310$	−0.698229	−0.0396568
$311$	−1.97857	−0.112194	−0.0560971	−	0.998425i	$-0.517866\pi$
$311$	−1.97857	−0.112194	−0.0560971	+	0.998425i	$0.517866\pi$
$312$	−2.45251	−0.138846
$313$	−27.5938	−1.55969	−0.779846	−	0.625971i	$-0.784703\pi$
$313$	−27.5938	−1.55969	−0.779846	+	0.625971i	$0.784703\pi$
$314$	−0.742070	−0.0418774
$315$	4.99716	0.281558
$316$	−10.3071	−0.579820
$317$	22.4370	1.26019	0.630095	−	0.776518i	$-0.283016\pi$
$317$	22.4370	1.26019	0.630095	+	0.776518i	$0.283016\pi$
$318$	−4.76941	−0.267455
$319$	5.86389	0.328315
$320$	1.43966	0.0804792
$321$	14.2092	0.793082
$322$	−13.5190	−0.753382
$323$	−2.01643	−0.112197
$324$	−1.51248	−0.0840264
$325$	−1.00000	−0.0554700
$326$	−3.57761	−0.198146
$327$	11.2659	0.623008
$328$	−6.38071	−0.352316
$329$	28.4295	1.56737
$330$	1.09622	0.0603449
$331$	2.60392	0.143124	0.0715622	−	0.997436i	$-0.477202\pi$
$331$	2.60392	0.143124	0.0715622	+	0.997436i	$0.477202\pi$
$332$	−18.1785	−0.997674
$333$	−5.41626	−0.296809
$334$	9.13585	0.499891
$335$	−8.54291	−0.466749
$336$	6.55895	0.357820
$337$	0.945259	0.0514915	0.0257458	−	0.999669i	$-0.491804\pi$
$337$	0.945259	0.0514915	0.0257458	+	0.999669i	$0.491804\pi$
$338$	−0.698229	−0.0379787
$339$	1.55385	0.0843935
$340$	−0.454027	−0.0246231
$341$	−1.57000	−0.0850202
$342$	4.69016	0.253615
$343$	54.8268	2.96037
$344$	25.8716	1.39490
$345$	3.87456	0.208599
$346$	−18.0542	−0.970599
$347$	−17.1586	−0.921120	−0.460560	−	0.887629i	$-0.652351\pi$
$347$	−17.1586	−0.921120	−0.460560	+	0.887629i	$0.652351\pi$
$348$	5.64904	0.302820
$349$	25.1360	1.34550	0.672749	−	0.739871i	$-0.265113\pi$
$349$	25.1360	1.34550	0.672749	+	0.739871i	$0.265113\pi$
$350$	−3.48916	−0.186504
$351$	−1.00000	−0.0533761
$352$	9.13971	0.487148
$353$	23.9901	1.27687	0.638433	−	0.769677i	$-0.279583\pi$
$353$	23.9901	1.27687	0.638433	+	0.769677i	$0.279583\pi$
$354$	−8.79269	−0.467326
$355$	−12.6665	−0.672270
$356$	−7.33346	−0.388673
$357$	1.50009	0.0793931
$358$	1.11511	0.0589353
$359$	9.94698	0.524982	0.262491	−	0.964935i	$-0.415456\pi$
$359$	9.94698	0.524982	0.262491	+	0.964935i	$0.415456\pi$
$360$	2.45251	0.129259
$361$	26.1211	1.37480
$362$	−8.92324	−0.468995
$363$	−8.53510	−0.447977
$364$	7.55808	0.396151
$365$	−3.14470	−0.164601
$366$	−9.56022	−0.499721
$367$	3.23794	0.169019	0.0845096	−	0.996423i	$-0.473068\pi$
$367$	3.23794	0.169019	0.0845096	+	0.996423i	$0.473068\pi$
$368$	5.08549	0.265099
$369$	−2.60170	−0.135439
$370$	3.78179	0.196606
$371$	34.1342	1.77216
$372$	−1.51248	−0.0784182
$373$	−24.0562	−1.24558	−0.622791	−	0.782388i	$-0.714001\pi$
$373$	−24.0562	−1.24558	−0.622791	+	0.782388i	$0.714001\pi$
$374$	0.329072	0.0170159
$375$	1.00000	0.0516398
$376$	13.9527	0.719555
$377$	3.73496	0.192360
$378$	−3.48916	−0.179463
$379$	13.0055	0.668046	0.334023	−	0.942565i	$-0.391594\pi$
$379$	13.0055	0.668046	0.334023	+	0.942565i	$0.391594\pi$
$380$	10.1596	0.521179
$381$	−13.3727	−0.685102
$382$	−13.9955	−0.716074
$383$	26.7026	1.36444	0.682220	−	0.731147i	$-0.261015\pi$
$383$	26.7026	1.36444	0.682220	+	0.731147i	$0.261015\pi$
$384$	10.6377	0.542855
$385$	−7.84553	−0.399845
$386$	5.94395	0.302539
$387$	10.5490	0.536237
$388$	11.0831	0.562662
$389$	22.5353	1.14259	0.571294	−	0.820746i	$-0.306442\pi$
$389$	22.5353	1.14259	0.571294	+	0.820746i	$0.306442\pi$
$390$	0.698229	0.0353562
$391$	1.16310	0.0588203
$392$	44.0756	2.22615
$393$	−16.5313	−0.833894
$394$	16.6574	0.839190
$395$	6.81473	0.342886
$396$	2.37458	0.119327
$397$	−0.526066	−0.0264025	−0.0132013	−	0.999913i	$-0.504202\pi$
$397$	−0.526066	−0.0264025	−0.0132013	+	0.999913i	$0.504202\pi$
$398$	−1.23060	−0.0616846
$399$	−33.5671	−1.68045
$400$	1.31253	0.0656267
$401$	−6.28168	−0.313692	−0.156846	−	0.987623i	$-0.550133\pi$
$401$	−6.28168	−0.313692	−0.156846	+	0.987623i	$0.550133\pi$
$402$	5.96491	0.297503
$403$	−1.00000	−0.0498135
$404$	−20.8394	−1.03680
$405$	1.00000	0.0496904
$406$	13.0319	0.646762
$407$	8.50352	0.421504
$408$	0.736216	0.0364481
$409$	18.0606	0.893039	0.446520	−	0.894774i	$-0.352663\pi$
$409$	18.0606	0.893039	0.446520	+	0.894774i	$0.352663\pi$
$410$	1.81659	0.0897148
$411$	5.55654	0.274084
$412$	10.3180	0.508331
$413$	62.9285	3.09651
$414$	−2.70533	−0.132960
$415$	12.0190	0.589991
$416$	5.82148	0.285421
$417$	5.26118	0.257641
$418$	−7.36355	−0.360163
$419$	−15.7937	−0.771573	−0.385786	−	0.922588i	$-0.626070\pi$
$419$	−15.7937	−0.771573	−0.385786	+	0.922588i	$0.626070\pi$
$420$	−7.55808	−0.368797
$421$	8.72011	0.424992	0.212496	−	0.977162i	$-0.431841\pi$
$421$	8.72011	0.424992	0.212496	+	0.977162i	$0.431841\pi$
$422$	−13.2874	−0.646819
$423$	5.68914	0.276615
$424$	16.7524	0.813570
$425$	0.300188	0.0145613
$426$	8.84415	0.428501
$427$	68.4216	3.31115
$428$	−21.4911	−1.03881
$429$	1.57000	0.0758002
$430$	−7.36563	−0.355202
$431$	30.5610	1.47207	0.736037	−	0.676942i	$-0.236695\pi$
$431$	30.5610	1.47207	0.736037	+	0.676942i	$0.236695\pi$
$432$	1.31253	0.0631494
$433$	−6.35843	−0.305567	−0.152783	−	0.988260i	$-0.548824\pi$
$433$	−6.35843	−0.305567	−0.152783	+	0.988260i	$0.548824\pi$
$434$	−3.48916	−0.167485
$435$	−3.73496	−0.179078
$436$	−17.0395	−0.816043
$437$	−26.0263	−1.24501
$438$	2.19572	0.104915
$439$	−30.8275	−1.47131	−0.735657	−	0.677354i	$-0.763127\pi$
$439$	−30.8275	−1.47131	−0.735657	+	0.677354i	$0.763127\pi$
$440$	−3.85044	−0.183563
$441$	17.9716	0.855791
$442$	0.209600	0.00996967
$443$	−0.460557	−0.0218817	−0.0109409	−	0.999940i	$-0.503483\pi$
$443$	−0.460557	−0.0218817	−0.0109409	+	0.999940i	$0.503483\pi$
$444$	8.19197	0.388773
$445$	4.84865	0.229848
$446$	−2.81771	−0.133422
$447$	7.90778	0.374025
$448$	7.19419	0.339894
$449$	21.7022	1.02419	0.512095	−	0.858929i	$-0.328869\pi$
$449$	21.7022	1.02419	0.512095	+	0.858929i	$0.328869\pi$
$450$	−0.698229	−0.0329148
$451$	4.08467	0.192340
$452$	−2.35016	−0.110542
$453$	−3.31042	−0.155537
$454$	18.2794	0.857893
$455$	−4.99716	−0.234270
$456$	−16.4741	−0.771470
$457$	−25.6149	−1.19821	−0.599106	−	0.800670i	$-0.704477\pi$
$457$	−25.6149	−1.19821	−0.599106	+	0.800670i	$0.704477\pi$
$458$	18.4703	0.863060
$459$	0.300188	0.0140116
$460$	−5.86017	−0.273232
$461$	1.88780	0.0879236	0.0439618	−	0.999033i	$-0.486002\pi$
$461$	1.88780	0.0879236	0.0439618	+	0.999033i	$0.486002\pi$
$462$	5.47798	0.254859
$463$	−2.52465	−0.117330	−0.0586651	−	0.998278i	$-0.518684\pi$
$463$	−2.52465	−0.117330	−0.0586651	+	0.998278i	$0.518684\pi$
$464$	−4.90227	−0.227582
$465$	1.00000	0.0463739
$466$	−2.71738	−0.125880
$467$	16.4319	0.760379	0.380189	−	0.924909i	$-0.375859\pi$
$467$	16.4319	0.760379	0.380189	+	0.924909i	$0.375859\pi$
$468$	1.51248	0.0699142
$469$	−42.6903	−1.97125
$470$	−3.97232	−0.183230
$471$	1.06279	0.0489707
$472$	30.8841	1.42156
$473$	−16.5619	−0.761519
$474$	−4.75824	−0.218553
$475$	−6.71723	−0.308208
$476$	−2.26885	−0.103992
$477$	6.83072	0.312757
$478$	5.57724	0.255097
$479$	−28.9971	−1.32491	−0.662455	−	0.749101i	$-0.730486\pi$
$479$	−28.9971	−1.32491	−0.662455	+	0.749101i	$0.730486\pi$
$480$	−5.82148	−0.265713
$481$	5.41626	0.246960
$482$	−17.1092	−0.779302
$483$	19.3618	0.880991
$484$	12.9091	0.586779
$485$	−7.32782	−0.332739
$486$	−0.698229	−0.0316723
$487$	−37.1309	−1.68256	−0.841280	−	0.540600i	$-0.818197\pi$
$487$	−37.1309	−1.68256	−0.841280	+	0.540600i	$0.818197\pi$
$488$	33.5800	1.52010
$489$	5.12384	0.231708
$490$	−12.5483	−0.566874
$491$	17.1574	0.774303	0.387151	−	0.922016i	$-0.373459\pi$
$491$	17.1574	0.774303	0.387151	+	0.922016i	$0.373459\pi$
$492$	3.93501	0.177404
$493$	−1.12119	−0.0504959
$494$	−4.69016	−0.211020
$495$	−1.57000	−0.0705662
$496$	1.31253	0.0589346
$497$	−63.2967	−2.83925
$498$	−8.39204	−0.376056
$499$	27.3192	1.22297	0.611487	−	0.791254i	$-0.290572\pi$
$499$	27.3192	1.22297	0.611487	+	0.791254i	$0.290572\pi$
$500$	−1.51248	−0.0676400
$501$	−13.0843	−0.584564
$502$	−4.32122	−0.192865
$503$	1.03096	0.0459684	0.0229842	−	0.999736i	$-0.492683\pi$
$503$	1.03096	0.0459684	0.0229842	+	0.999736i	$0.492683\pi$
$504$	12.2556	0.545908
$505$	13.7783	0.613128
$506$	4.24736	0.188818
$507$	1.00000	0.0444116
$508$	20.2258	0.897376
$509$	6.58424	0.291841	0.145921	−	0.989296i	$-0.453386\pi$
$509$	6.58424	0.291841	0.145921	+	0.989296i	$0.453386\pi$
$510$	−0.209600	−0.00928125
$511$	−15.7145	−0.695171
$512$	−14.0789	−0.622206
$513$	−6.71723	−0.296573
$514$	−1.49091	−0.0657613
$515$	−6.82192	−0.300610
$516$	−15.9551	−0.702386
$517$	−8.93194	−0.392826
$518$	18.8982	0.830340
$519$	25.8571	1.13500
$520$	−2.45251	−0.107550
$521$	−8.87936	−0.389012	−0.194506	−	0.980901i	$-0.562310\pi$
$521$	−8.87936	−0.389012	−0.194506	+	0.980901i	$0.562310\pi$
$522$	2.60786	0.114143
$523$	−2.41219	−0.105478	−0.0527388	−	0.998608i	$-0.516795\pi$
$523$	−2.41219	−0.105478	−0.0527388	+	0.998608i	$0.516795\pi$
$524$	25.0032	1.09227
$525$	4.99716	0.218094
$526$	−13.1542	−0.573551
$527$	0.300188	0.0130764
$528$	−2.06068	−0.0896795
$529$	−7.98782	−0.347296
$530$	−4.76941	−0.207170
$531$	12.5928	0.546483
$532$	50.7694	2.20113
$533$	2.60170	0.112692
$534$	−3.38547	−0.146504
$535$	14.2092	0.614318
$536$	−20.9516	−0.904971
$537$	−1.59705	−0.0689178
$538$	18.1522	0.782598
$539$	−28.2154	−1.21532
$540$	−1.51248	−0.0650866
$541$	−44.3911	−1.90852	−0.954261	−	0.298974i	$-0.903356\pi$
$541$	−44.3911	−1.90852	−0.954261	+	0.298974i	$0.903356\pi$
$542$	2.67267	0.114801
$543$	12.7798	0.548434
$544$	−1.74754	−0.0749251
$545$	11.2659	0.482580
$546$	3.48916	0.149322
$547$	−26.6185	−1.13812	−0.569062	−	0.822294i	$-0.692694\pi$
$547$	−26.6185	−1.13812	−0.569062	+	0.822294i	$0.692694\pi$
$548$	−8.40413	−0.359007
$549$	13.6921	0.584364
$550$	1.09622	0.0467429
$551$	25.0886	1.06881
$552$	9.50240	0.404449
$553$	34.0543	1.44814
$554$	−3.48203	−0.147937
$555$	−5.41626	−0.229908
$556$	−7.95741	−0.337469
$557$	−2.34093	−0.0991885	−0.0495942	−	0.998769i	$-0.515793\pi$
$557$	−2.34093	−0.0991885	−0.0495942	+	0.998769i	$0.515793\pi$
$558$	−0.698229	−0.0295584
$559$	−10.5490	−0.446176
$560$	6.55895	0.277166
$561$	−0.471295	−0.0198981
$562$	−4.66285	−0.196690
$563$	18.0781	0.761900	0.380950	−	0.924596i	$-0.375597\pi$
$563$	18.0781	0.761900	0.380950	+	0.924596i	$0.375597\pi$
$564$	−8.60469	−0.362323
$565$	1.55385	0.0653709
$566$	17.4124	0.731899
$567$	4.99716	0.209861
$568$	−31.0649	−1.30345
$569$	24.8565	1.04204	0.521019	−	0.853545i	$-0.325552\pi$
$569$	24.8565	1.04204	0.521019	+	0.853545i	$0.325552\pi$
$570$	4.69016	0.196449
$571$	29.4920	1.23420	0.617101	−	0.786884i	$-0.288307\pi$
$571$	29.4920	1.23420	0.617101	+	0.786884i	$0.288307\pi$
$572$	−2.37458	−0.0992864
$573$	20.0443	0.837364
$574$	9.07777	0.378899
$575$	3.87456	0.161580
$576$	1.43966	0.0599857
$577$	−29.9111	−1.24522	−0.622608	−	0.782534i	$-0.713927\pi$
$577$	−29.9111	−1.24522	−0.622608	+	0.782534i	$0.713927\pi$
$578$	11.8070	0.491106
$579$	−8.51290	−0.353784
$580$	5.64904	0.234564
$581$	60.0610	2.49175
$582$	5.11650	0.212086
$583$	−10.7242	−0.444152
$584$	−7.71241	−0.319142
$585$	−1.00000	−0.0413449
$586$	9.69414	0.400461
$587$	−22.7618	−0.939481	−0.469740	−	0.882805i	$-0.655652\pi$
$587$	−22.7618	−0.939481	−0.469740	+	0.882805i	$0.655652\pi$
$588$	−27.1816	−1.12095
$589$	−6.71723	−0.276779
$590$	−8.79269	−0.361989
$591$	−23.8567	−0.981333
$592$	−7.10903	−0.292179
$593$	−5.30347	−0.217788	−0.108894	−	0.994053i	$-0.534731\pi$
$593$	−5.30347	−0.217788	−0.108894	+	0.994053i	$0.534731\pi$
$594$	1.09622	0.0449784
$595$	1.50009	0.0614976
$596$	−11.9603	−0.489914
$597$	1.76246	0.0721328
$598$	2.70533	0.110629
$599$	38.7148	1.58184	0.790921	−	0.611918i	$-0.209602\pi$
$599$	38.7148	1.58184	0.790921	+	0.611918i	$0.209602\pi$
$600$	2.45251	0.100123
$601$	−27.1366	−1.10693	−0.553463	−	0.832874i	$-0.686694\pi$
$601$	−27.1366	−1.10693	−0.553463	+	0.832874i	$0.686694\pi$
$602$	−36.8072	−1.50015
$603$	−8.54291	−0.347894
$604$	5.00692	0.203729
$605$	−8.53510	−0.347001
$606$	−9.62044	−0.390804
$607$	−12.0370	−0.488568	−0.244284	−	0.969704i	$-0.578553\pi$
$607$	−12.0370	−0.488568	−0.244284	+	0.969704i	$0.578553\pi$
$608$	39.1042	1.58588
$609$	−18.6642	−0.756312
$610$	−9.56022	−0.387082
$611$	−5.68914	−0.230158
$612$	−0.454027	−0.0183530
$613$	8.25755	0.333519	0.166760	−	0.985998i	$-0.446670\pi$
$613$	8.25755	0.333519	0.166760	+	0.985998i	$0.446670\pi$
$614$	−18.1891	−0.734054
$615$	−2.60170	−0.104911
$616$	−19.2413	−0.775253
$617$	27.0352	1.08839	0.544197	−	0.838957i	$-0.316834\pi$
$617$	27.0352	1.08839	0.544197	+	0.838957i	$0.316834\pi$
$618$	4.76327	0.191607
$619$	−38.5805	−1.55068	−0.775341	−	0.631543i	$-0.782422\pi$
$619$	−38.5805	−1.55068	−0.775341	+	0.631543i	$0.782422\pi$
$620$	−1.51248	−0.0607425
$621$	3.87456	0.155481
$622$	1.38149	0.0553928
$623$	24.2295	0.970733
$624$	−1.31253	−0.0525434
$625$	1.00000	0.0400000
$626$	19.2668	0.770056
$627$	10.5460	0.421168
$628$	−1.60744	−0.0641439
$629$	−1.62590	−0.0648288
$630$	−3.48916	−0.139012
$631$	−42.9628	−1.71032	−0.855161	−	0.518363i	$-0.826542\pi$
$631$	−42.9628	−1.71032	−0.855161	+	0.518363i	$0.826542\pi$
$632$	16.7132	0.664816
$633$	19.0301	0.756379
$634$	−15.6662	−0.622184
$635$	−13.3727	−0.530678
$636$	−10.3313	−0.409663
$637$	−17.9716	−0.712061
$638$	−4.09434	−0.162096
$639$	−12.6665	−0.501081
$640$	10.6377	0.420494
$641$	−26.8557	−1.06074	−0.530368	−	0.847767i	$-0.677946\pi$
$641$	−26.8557	−1.06074	−0.530368	+	0.847767i	$0.677946\pi$
$642$	−9.92130	−0.391562
$643$	0.874168	0.0344738	0.0172369	−	0.999851i	$-0.494513\pi$
$643$	0.874168	0.0344738	0.0172369	+	0.999851i	$0.494513\pi$
$644$	−29.2842	−1.15396
$645$	10.5490	0.415367
$646$	1.40793	0.0553944
$647$	16.5610	0.651080	0.325540	−	0.945528i	$-0.394454\pi$
$647$	16.5610	0.651080	0.325540	+	0.945528i	$0.394454\pi$
$648$	2.45251	0.0963438
$649$	−19.7707	−0.776070
$650$	0.698229	0.0273868
$651$	4.99716	0.195854
$652$	−7.74968	−0.303501
$653$	13.8547	0.542175	0.271088	−	0.962555i	$-0.412617\pi$
$653$	13.8547	0.542175	0.271088	+	0.962555i	$0.412617\pi$
$654$	−7.86622	−0.307593
$655$	−16.5313	−0.645932
$656$	−3.41483	−0.133327
$657$	−3.14470	−0.122686
$658$	−19.8503	−0.773847
$659$	−18.5705	−0.723404	−0.361702	−	0.932294i	$-0.617804\pi$
$659$	−18.5705	−0.723404	−0.361702	+	0.932294i	$0.617804\pi$
$660$	2.37458	0.0924306
$661$	23.9137	0.930135	0.465068	−	0.885275i	$-0.346030\pi$
$661$	23.9137	0.930135	0.465068	+	0.885275i	$0.346030\pi$
$662$	−1.81813	−0.0706638
$663$	−0.300188	−0.0116583
$664$	29.4768	1.14392
$665$	−33.5671	−1.30167
$666$	3.78179	0.146542
$667$	−14.4713	−0.560332
$668$	19.7897	0.765686
$669$	4.03550	0.156022
$670$	5.96491	0.230445
$671$	−21.4966	−0.829866
$672$	−29.0909	−1.12220
$673$	−26.3067	−1.01405	−0.507025	−	0.861932i	$-0.669255\pi$
$673$	−26.3067	−1.01405	−0.507025	+	0.861932i	$0.669255\pi$
$674$	−0.660008	−0.0254225
$675$	1.00000	0.0384900
$676$	−1.51248	−0.0581721
$677$	2.64029	0.101474	0.0507372	−	0.998712i	$-0.483843\pi$
$677$	2.64029	0.101474	0.0507372	+	0.998712i	$0.483843\pi$
$678$	−1.08494	−0.0416670
$679$	−36.6183	−1.40528
$680$	0.736216	0.0282326
$681$	−26.1796	−1.00320
$682$	1.09622	0.0419764
$683$	18.9685	0.725810	0.362905	−	0.931826i	$-0.381785\pi$
$683$	18.9685	0.725810	0.362905	+	0.931826i	$0.381785\pi$
$684$	10.1596	0.388464
$685$	5.55654	0.212305
$686$	−38.2817	−1.46160
$687$	−26.4530	−1.00925
$688$	13.8460	0.527872
$689$	−6.83072	−0.260230
$690$	−2.70533	−0.102990
$691$	−47.9826	−1.82534	−0.912672	−	0.408694i	$-0.865984\pi$
$691$	−47.9826	−1.82534	−0.912672	+	0.408694i	$0.865984\pi$
$692$	−39.1083	−1.48667
$693$	−7.84553	−0.298027
$694$	11.9806	0.454778
$695$	5.26118	0.199568
$696$	−9.16005	−0.347211
$697$	−0.781001	−0.0295825
$698$	−17.5507	−0.664303
$699$	3.89182	0.147202
$700$	−7.55808	−0.285669
$701$	12.7469	0.481444	0.240722	−	0.970594i	$-0.422616\pi$
$701$	12.7469	0.481444	0.240722	+	0.970594i	$0.422616\pi$
$702$	0.698229	0.0263530
$703$	36.3823	1.37218
$704$	−2.26026	−0.0851867
$705$	5.68914	0.214265
$706$	−16.7506	−0.630418
$707$	68.8525	2.58947
$708$	−19.0464	−0.715807
$709$	17.2263	0.646948	0.323474	−	0.946237i	$-0.395149\pi$
$709$	17.2263	0.646948	0.323474	+	0.946237i	$0.395149\pi$
$710$	8.84415	0.331915
$711$	6.81473	0.255572
$712$	11.8914	0.445648
$713$	3.87456	0.145103
$714$	−1.04741	−0.0391982
$715$	1.57000	0.0587146
$716$	2.41550	0.0902715
$717$	−7.98768	−0.298306
$718$	−6.94527	−0.259195
$719$	6.82307	0.254458	0.127229	−	0.991873i	$-0.459392\pi$
$719$	6.82307	0.254458	0.127229	+	0.991873i	$0.459392\pi$
$720$	1.31253	0.0489153
$721$	−34.0902	−1.26959
$722$	−18.2385	−0.678768
$723$	24.5037	0.911302
$724$	−19.3292	−0.718362
$725$	−3.73496	−0.138713
$726$	5.95946	0.221176
$727$	44.8838	1.66465	0.832325	−	0.554288i	$-0.187009\pi$
$727$	44.8838	1.66465	0.832325	+	0.554288i	$0.187009\pi$
$728$	−12.2556	−0.454223
$729$	1.00000	0.0370370
$730$	2.19572	0.0812672
$731$	3.16669	0.117124
$732$	−20.7090	−0.765425
$733$	32.4330	1.19794	0.598969	−	0.800772i	$-0.295577\pi$
$733$	32.4330	1.19794	0.598969	+	0.800772i	$0.295577\pi$
$734$	−2.26083	−0.0834486
$735$	17.9716	0.662893
$736$	−22.5556	−0.831412
$737$	13.4124	0.494050
$738$	1.81659	0.0668694
$739$	−15.6515	−0.575750	−0.287875	−	0.957668i	$-0.592949\pi$
$739$	−15.6515	−0.575750	−0.287875	+	0.957668i	$0.592949\pi$
$740$	8.19197	0.301143
$741$	6.71723	0.246764
$742$	−23.8335	−0.874955
$743$	44.4277	1.62989	0.814947	−	0.579535i	$-0.196766\pi$
$743$	44.4277	1.62989	0.814947	+	0.579535i	$0.196766\pi$
$744$	2.45251	0.0899135
$745$	7.90778	0.289719
$746$	16.7967	0.614972
$747$	12.0190	0.439753
$748$	0.712822	0.0260634
$749$	71.0058	2.59449
$750$	−0.698229	−0.0254957
$751$	−23.7432	−0.866401	−0.433201	−	0.901298i	$-0.642616\pi$
$751$	−23.7432	−0.866401	−0.433201	+	0.901298i	$0.642616\pi$
$752$	7.46720	0.272301
$753$	6.18882	0.225533
$754$	−2.60786	−0.0949727
$755$	−3.31042	−0.120478
$756$	−7.55808	−0.274885
$757$	38.4500	1.39749	0.698744	−	0.715372i	$-0.253743\pi$
$757$	38.4500	1.39749	0.698744	+	0.715372i	$0.253743\pi$
$758$	−9.08080	−0.329830
$759$	−6.08305	−0.220801
$760$	−16.4741	−0.597578
$761$	−25.8364	−0.936570	−0.468285	−	0.883577i	$-0.655128\pi$
$761$	−25.8364	−0.936570	−0.468285	+	0.883577i	$0.655128\pi$
$762$	9.33719	0.338251
$763$	56.2977	2.03812
$764$	−30.3166	−1.09681
$765$	0.300188	0.0108533
$766$	−18.6445	−0.673655
$767$	−12.5928	−0.454701
$768$	−10.3069	−0.371918
$769$	−2.42672	−0.0875097	−0.0437549	−	0.999042i	$-0.513932\pi$
$769$	−2.42672	−0.0875097	−0.0437549	+	0.999042i	$0.513932\pi$
$770$	5.47798	0.197413
$771$	2.13527	0.0769000
$772$	12.8755	0.463401
$773$	22.8561	0.822077	0.411039	−	0.911618i	$-0.365166\pi$
$773$	22.8561	0.822077	0.411039	+	0.911618i	$0.365166\pi$
$774$	−7.36563	−0.264752
$775$	1.00000	0.0359211
$776$	−17.9716	−0.645142
$777$	−27.0659	−0.970985
$778$	−15.7348	−0.564121
$779$	17.4762	0.626151
$780$	1.51248	0.0541553
$781$	19.8865	0.711593
$782$	−0.812108	−0.0290409
$783$	−3.73496	−0.133477
$784$	23.5884	0.842441
$785$	1.06279	0.0379326
$786$	11.5426	0.411713
$787$	24.1899	0.862275	0.431138	−	0.902286i	$-0.358112\pi$
$787$	24.1899	0.862275	0.431138	+	0.902286i	$0.358112\pi$
$788$	36.0827	1.28539
$789$	18.8394	0.670700
$790$	−4.75824	−0.169291
$791$	7.76483	0.276086
$792$	−3.85044	−0.136820
$793$	−13.6921	−0.486220
$794$	0.367315	0.0130355
$795$	6.83072	0.242261
$796$	−2.66568	−0.0944826
$797$	30.0620	1.06485	0.532426	−	0.846477i	$-0.321280\pi$
$797$	30.0620	1.06485	0.532426	+	0.846477i	$0.321280\pi$
$798$	23.4375	0.829679
$799$	1.70781	0.0604181
$800$	−5.82148	−0.205820
$801$	4.84865	0.171319
$802$	4.38605	0.154877
$803$	4.93717	0.174229
$804$	12.9209	0.455686
$805$	19.3618	0.682413
$806$	0.698229	0.0245941
$807$	−25.9975	−0.915156
$808$	33.7916	1.18878
$809$	−28.7205	−1.00976	−0.504880	−	0.863190i	$-0.668463\pi$
$809$	−28.7205	−1.00976	−0.504880	+	0.863190i	$0.668463\pi$
$810$	−0.698229	−0.0245333
$811$	−16.5656	−0.581696	−0.290848	−	0.956769i	$-0.593937\pi$
$811$	−16.5656	−0.581696	−0.290848	+	0.956769i	$0.593937\pi$
$812$	28.2292	0.990649
$813$	−3.82778	−0.134246
$814$	−5.93741	−0.208106
$815$	5.12384	0.179480
$816$	0.394008	0.0137930
$817$	−70.8601	−2.47908
$818$	−12.6104	−0.440914
$819$	−4.99716	−0.174615
$820$	3.93501	0.137417
$821$	−8.49421	−0.296450	−0.148225	−	0.988954i	$-0.547356\pi$
$821$	−8.49421	−0.296450	−0.148225	+	0.988954i	$0.547356\pi$
$822$	−3.87974	−0.135321
$823$	−53.5804	−1.86769	−0.933847	−	0.357672i	$-0.883571\pi$
$823$	−53.5804	−1.86769	−0.933847	+	0.357672i	$0.883571\pi$
$824$	−16.7309	−0.582847
$825$	−1.57000	−0.0546603
$826$	−43.9385	−1.52882
$827$	−20.1976	−0.702338	−0.351169	−	0.936312i	$-0.614216\pi$
$827$	−20.1976	−0.702338	−0.351169	+	0.936312i	$0.614216\pi$
$828$	−5.86017	−0.203655
$829$	−30.4332	−1.05699	−0.528495	−	0.848936i	$-0.677243\pi$
$829$	−30.4332	−1.05699	−0.528495	+	0.848936i	$0.677243\pi$
$830$	−8.39204	−0.291292
$831$	4.98695	0.172995
$832$	−1.43966	−0.0499111
$833$	5.39486	0.186921
$834$	−3.67351	−0.127203
$835$	−13.0843	−0.452801
$836$	−15.9506	−0.551664
$837$	1.00000	0.0345651
$838$	11.0276	0.380943
$839$	7.43140	0.256560	0.128280	−	0.991738i	$-0.459054\pi$
$839$	7.43140	0.256560	0.128280	+	0.991738i	$0.459054\pi$
$840$	12.2556	0.422858
$841$	−15.0501	−0.518967
$842$	−6.08863	−0.209828
$843$	6.67810	0.230006
$844$	−28.7826	−0.990737
$845$	1.00000	0.0344010
$846$	−3.97232	−0.136571
$847$	−42.6513	−1.46552
$848$	8.96555	0.307878
$849$	−24.9380	−0.855869
$850$	−0.209600	−0.00718923
$851$	−20.9856	−0.719378
$852$	19.1578	0.656337
$853$	17.3135	0.592802	0.296401	−	0.955064i	$-0.404214\pi$
$853$	17.3135	0.592802	0.296401	+	0.955064i	$0.404214\pi$
$854$	−47.7739	−1.63479
$855$	−6.71723	−0.229724
$856$	34.8483	1.19109
$857$	−10.0500	−0.343302	−0.171651	−	0.985158i	$-0.554910\pi$
$857$	−10.0500	−0.343302	−0.171651	+	0.985158i	$0.554910\pi$
$858$	−1.09622	−0.0374243
$859$	11.6017	0.395846	0.197923	−	0.980218i	$-0.436580\pi$
$859$	11.6017	0.395846	0.197923	+	0.980218i	$0.436580\pi$
$860$	−15.9551	−0.544066
$861$	−13.0011	−0.443077
$862$	−21.3386	−0.726796
$863$	−43.5733	−1.48325	−0.741627	−	0.670813i	$-0.765946\pi$
$863$	−43.5733	−1.48325	−0.741627	+	0.670813i	$0.765946\pi$
$864$	−5.82148	−0.198051
$865$	25.8571	0.879168
$866$	4.43964	0.150865
$867$	−16.9099	−0.574290
$868$	−7.55808	−0.256538
$869$	−10.6991	−0.362942
$870$	2.60786	0.0884148
$871$	8.54291	0.289465
$872$	27.6299	0.935666
$873$	−7.32782	−0.248009
$874$	18.1723	0.614687
$875$	4.99716	0.168935
$876$	4.75628	0.160700
$877$	−8.80291	−0.297253	−0.148627	−	0.988893i	$-0.547485\pi$
$877$	−8.80291	−0.297253	−0.148627	+	0.988893i	$0.547485\pi$
$878$	21.5246	0.726421
$879$	−13.8839	−0.468292
$880$	−2.06068	−0.0694654
$881$	46.9276	1.58103	0.790516	−	0.612441i	$-0.209812\pi$
$881$	46.9276	1.58103	0.790516	+	0.612441i	$0.209812\pi$
$882$	−12.5483	−0.422523
$883$	−11.3219	−0.381012	−0.190506	−	0.981686i	$-0.561013\pi$
$883$	−11.3219	−0.381012	−0.190506	+	0.981686i	$0.561013\pi$
$884$	0.454027	0.0152706
$885$	12.5928	0.423304
$886$	0.321574	0.0108035
$887$	−31.8914	−1.07081	−0.535404	−	0.844596i	$-0.679841\pi$
$887$	−31.8914	−1.07081	−0.535404	+	0.844596i	$0.679841\pi$
$888$	−13.2835	−0.445764
$889$	−66.8253	−2.24125
$890$	−3.38547	−0.113481
$891$	−1.57000	−0.0525969
$892$	−6.10360	−0.204364
$893$	−38.2153	−1.27882
$894$	−5.52145	−0.184665
$895$	−1.59705	−0.0533835
$896$	53.1585	1.77590
$897$	−3.87456	−0.129368
$898$	−15.1531	−0.505666
$899$	−3.73496	−0.124568
$900$	−1.51248	−0.0504159
$901$	2.05050	0.0683121
$902$	−2.85204	−0.0949624
$903$	52.7151	1.75425
$904$	3.81083	0.126746
$905$	12.7798	0.424815
$906$	2.31143	0.0767921
$907$	−6.95687	−0.230999	−0.115500	−	0.993308i	$-0.536847\pi$
$907$	−6.95687	−0.230999	−0.115500	+	0.993308i	$0.536847\pi$
$908$	39.5960	1.31404
$909$	13.7783	0.456999
$910$	3.48916	0.115665
$911$	−21.0332	−0.696860	−0.348430	−	0.937335i	$-0.613285\pi$
$911$	−21.0332	−0.696860	−0.348430	+	0.937335i	$0.613285\pi$
$912$	−8.81659	−0.291947
$913$	−18.8699	−0.624501
$914$	17.8850	0.591585
$915$	13.6921	0.452647
$916$	40.0096	1.32195
$917$	−82.6096	−2.72801
$918$	−0.209600	−0.00691784
$919$	2.99197	0.0986959	0.0493479	−	0.998782i	$-0.484286\pi$
$919$	2.99197	0.0986959	0.0493479	+	0.998782i	$0.484286\pi$
$920$	9.50240	0.313285
$921$	26.0504	0.858390
$922$	−1.31812	−0.0434099
$923$	12.6665	0.416924
$924$	11.8662	0.390369
$925$	−5.41626	−0.178086
$926$	1.76278	0.0579286
$927$	−6.82192	−0.224061
$928$	21.7430	0.713749
$929$	−34.4310	−1.12964	−0.564822	−	0.825213i	$-0.691055\pi$
$929$	−34.4310	−1.12964	−0.564822	+	0.825213i	$0.691055\pi$
$930$	−0.698229	−0.0228958
$931$	−120.719	−3.95642
$932$	−5.88628	−0.192811
$933$	−1.97857	−0.0647753
$934$	−11.4733	−0.375416
$935$	−0.471295	−0.0154130
$936$	−2.45251	−0.0801629
$937$	40.5106	1.32342	0.661712	−	0.749758i	$-0.269830\pi$
$937$	40.5106	1.32342	0.661712	+	0.749758i	$0.269830\pi$
$938$	29.8076	0.973252
$939$	−27.5938	−0.900489
$940$	−8.60469	−0.280654
$941$	−35.1711	−1.14654	−0.573272	−	0.819365i	$-0.694326\pi$
$941$	−35.1711	−1.14654	−0.573272	+	0.819365i	$0.694326\pi$
$942$	−0.742070	−0.0241780
$943$	−10.0804	−0.328264
$944$	16.5285	0.537958
$945$	4.99716	0.162558
$946$	11.5640	0.375979
$947$	16.6805	0.542044	0.271022	−	0.962573i	$-0.412638\pi$
$947$	16.6805	0.542044	0.271022	+	0.962573i	$0.412638\pi$
$948$	−10.3071	−0.334759
$949$	3.14470	0.102081
$950$	4.69016	0.152169
$951$	22.4370	0.727571
$952$	3.67899	0.119237
$953$	41.9849	1.36002	0.680012	−	0.733201i	$-0.261974\pi$
$953$	41.9849	1.36002	0.680012	+	0.733201i	$0.261974\pi$
$954$	−4.76941	−0.154415
$955$	20.0443	0.648619
$956$	12.0812	0.390733
$957$	5.86389	0.189553
$958$	20.2466	0.654139
$959$	27.7669	0.896641
$960$	1.43966	0.0464647
$961$	1.00000	0.0322581
$962$	−3.78179	−0.121930
$963$	14.2092	0.457886
$964$	−37.0612	−1.19366
$965$	−8.51290	−0.274040
$966$	−13.5190	−0.434965
$967$	−29.8124	−0.958703	−0.479351	−	0.877623i	$-0.659128\pi$
$967$	−29.8124	−0.958703	−0.479351	+	0.877623i	$0.659128\pi$
$968$	−20.9325	−0.672795
$969$	−2.01643	−0.0647771
$970$	5.11650	0.164281
$971$	−33.6067	−1.07849	−0.539245	−	0.842149i	$-0.681290\pi$
$971$	−33.6067	−1.07849	−0.539245	+	0.842149i	$0.681290\pi$
$972$	−1.51248	−0.0485127
$973$	26.2910	0.842850
$974$	25.9259	0.830718
$975$	−1.00000	−0.0320256
$976$	17.9713	0.575249
$977$	−32.2904	−1.03306	−0.516531	−	0.856268i	$-0.672777\pi$
$977$	−32.2904	−1.03306	−0.516531	+	0.856268i	$0.672777\pi$
$978$	−3.57761	−0.114399
$979$	−7.61237	−0.243292
$980$	−27.1816	−0.868285
$981$	11.2659	0.359694
$982$	−11.9798	−0.382291
$983$	10.2692	0.327537	0.163769	−	0.986499i	$-0.447635\pi$
$983$	10.2692	0.327537	0.163769	+	0.986499i	$0.447635\pi$
$984$	−6.38071	−0.203410
$985$	−23.8567	−0.760137
$986$	0.782849	0.0249310
$987$	28.4295	0.904922
$988$	−10.1596	−0.323221
$989$	40.8728	1.29968
$990$	1.09622	0.0348401
$991$	−26.7165	−0.848678	−0.424339	−	0.905503i	$-0.639493\pi$
$991$	−26.7165	−0.848678	−0.424339	+	0.905503i	$0.639493\pi$
$992$	−5.82148	−0.184832
$993$	2.60392	0.0826330
$994$	44.1956	1.40180
$995$	1.76246	0.0558739
$996$	−18.1785	−0.576008
$997$	24.2982	0.769533	0.384766	−	0.923014i	$-0.374282\pi$
$997$	24.2982	0.769533	0.384766	+	0.923014i	$0.374282\pi$
$998$	−19.0750	−0.603810
$999$	−5.41626	−0.171363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bi.1.6	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bi.1.6	✓	18	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-0.698229 q^{2} +1.00000 q^{3} -1.51248 q^{4} +1.00000 q^{5} -0.698229 q^{6} +4.99716 q^{7} +2.45251 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.698229 q^{2} +1.00000 q^{3} -1.51248 q^{4} +1.00000 q^{5} -0.698229 q^{6} +4.99716 q^{7} +2.45251 q^{8} +1.00000 q^{9} -0.698229 q^{10} -1.57000 q^{11} -1.51248 q^{12} -1.00000 q^{13} -3.48916 q^{14} +1.00000 q^{15} +1.31253 q^{16} +0.300188 q^{17} -0.698229 q^{18} -6.71723 q^{19} -1.51248 q^{20} +4.99716 q^{21} +1.09622 q^{22} +3.87456 q^{23} +2.45251 q^{24} +1.00000 q^{25} +0.698229 q^{26} +1.00000 q^{27} -7.55808 q^{28} -3.73496 q^{29} -0.698229 q^{30} +1.00000 q^{31} -5.82148 q^{32} -1.57000 q^{33} -0.209600 q^{34} +4.99716 q^{35} -1.51248 q^{36} -5.41626 q^{37} +4.69016 q^{38} -1.00000 q^{39} +2.45251 q^{40} -2.60170 q^{41} -3.48916 q^{42} +10.5490 q^{43} +2.37458 q^{44} +1.00000 q^{45} -2.70533 q^{46} +5.68914 q^{47} +1.31253 q^{48} +17.9716 q^{49} -0.698229 q^{50} +0.300188 q^{51} +1.51248 q^{52} +6.83072 q^{53} -0.698229 q^{54} -1.57000 q^{55} +12.2556 q^{56} -6.71723 q^{57} +2.60786 q^{58} +12.5928 q^{59} -1.51248 q^{60} +13.6921 q^{61} -0.698229 q^{62} +4.99716 q^{63} +1.43966 q^{64} -1.00000 q^{65} +1.09622 q^{66} -8.54291 q^{67} -0.454027 q^{68} +3.87456 q^{69} -3.48916 q^{70} -12.6665 q^{71} +2.45251 q^{72} -3.14470 q^{73} +3.78179 q^{74} +1.00000 q^{75} +10.1596 q^{76} -7.84553 q^{77} +0.698229 q^{78} +6.81473 q^{79} +1.31253 q^{80} +1.00000 q^{81} +1.81659 q^{82} +12.0190 q^{83} -7.55808 q^{84} +0.300188 q^{85} -7.36563 q^{86} -3.73496 q^{87} -3.85044 q^{88} +4.84865 q^{89} -0.698229 q^{90} -4.99716 q^{91} -5.86017 q^{92} +1.00000 q^{93} -3.97232 q^{94} -6.71723 q^{95} -5.82148 q^{96} -7.32782 q^{97} -12.5483 q^{98} -1.57000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * q^99

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