LMFDB - Embedded newform 6045.2.a.bi.1.7

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			1.7
Root			$-0.603996$ 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)

$f(q)$	$=$	$q-0.603996 q^{2} +1.00000 q^{3} -1.63519 q^{4} +1.00000 q^{5} -0.603996 q^{6} +0.896809 q^{7} +2.19564 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.603996 q^{2} +1.00000 q^{3} -1.63519 q^{4} +1.00000 q^{5} -0.603996 q^{6} +0.896809 q^{7} +2.19564 q^{8} +1.00000 q^{9} -0.603996 q^{10} +5.79548 q^{11} -1.63519 q^{12} -1.00000 q^{13} -0.541669 q^{14} +1.00000 q^{15} +1.94422 q^{16} -2.12077 q^{17} -0.603996 q^{18} +3.54711 q^{19} -1.63519 q^{20} +0.896809 q^{21} -3.50044 q^{22} +4.20640 q^{23} +2.19564 q^{24} +1.00000 q^{25} +0.603996 q^{26} +1.00000 q^{27} -1.46645 q^{28} +4.56328 q^{29} -0.603996 q^{30} +1.00000 q^{31} -5.56558 q^{32} +5.79548 q^{33} +1.28094 q^{34} +0.896809 q^{35} -1.63519 q^{36} +2.53347 q^{37} -2.14244 q^{38} -1.00000 q^{39} +2.19564 q^{40} +4.85363 q^{41} -0.541669 q^{42} +9.32856 q^{43} -9.47671 q^{44} +1.00000 q^{45} -2.54065 q^{46} -2.29901 q^{47} +1.94422 q^{48} -6.19573 q^{49} -0.603996 q^{50} -2.12077 q^{51} +1.63519 q^{52} -9.13114 q^{53} -0.603996 q^{54} +5.79548 q^{55} +1.96907 q^{56} +3.54711 q^{57} -2.75620 q^{58} -5.84233 q^{59} -1.63519 q^{60} +1.19298 q^{61} -0.603996 q^{62} +0.896809 q^{63} -0.526862 q^{64} -1.00000 q^{65} -3.50044 q^{66} +7.68535 q^{67} +3.46786 q^{68} +4.20640 q^{69} -0.541669 q^{70} -10.1886 q^{71} +2.19564 q^{72} +10.0552 q^{73} -1.53020 q^{74} +1.00000 q^{75} -5.80020 q^{76} +5.19744 q^{77} +0.603996 q^{78} -15.8217 q^{79} +1.94422 q^{80} +1.00000 q^{81} -2.93157 q^{82} +11.9488 q^{83} -1.46645 q^{84} -2.12077 q^{85} -5.63441 q^{86} +4.56328 q^{87} +12.7248 q^{88} -0.655353 q^{89} -0.603996 q^{90} -0.896809 q^{91} -6.87826 q^{92} +1.00000 q^{93} +1.38859 q^{94} +3.54711 q^{95} -5.56558 q^{96} +9.49130 q^{97} +3.74220 q^{98} +5.79548 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.603996	−0.427089	−0.213545	−	0.976933i	$-0.568501\pi$
$2$	−0.603996	−0.427089	−0.213545	+	0.976933i	$0.568501\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.63519	−0.817595
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.603996	−0.246580
$7$	0.896809	0.338962	0.169481	−	0.985533i	$-0.445791\pi$
$7$	0.896809	0.338962	0.169481	+	0.985533i	$0.445791\pi$
$8$	2.19564	0.776275
$9$	1.00000	0.333333
$10$	−0.603996	−0.191000
$11$	5.79548	1.74740	0.873701	−	0.486463i	$-0.161713\pi$
$11$	5.79548	1.74740	0.873701	+	0.486463i	$0.161713\pi$
$12$	−1.63519	−0.472039
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.541669	−0.144767
$15$	1.00000	0.258199
$16$	1.94422	0.486056
$17$	−2.12077	−0.514363	−0.257181	−	0.966363i	$-0.582794\pi$
$17$	−2.12077	−0.514363	−0.257181	+	0.966363i	$0.582794\pi$
$18$	−0.603996	−0.142363
$19$	3.54711	0.813764	0.406882	−	0.913481i	$-0.366616\pi$
$19$	3.54711	0.813764	0.406882	+	0.913481i	$0.366616\pi$
$20$	−1.63519	−0.365639
$21$	0.896809	0.195700
$22$	−3.50044	−0.746297
$23$	4.20640	0.877095	0.438548	−	0.898708i	$-0.355493\pi$
$23$	4.20640	0.877095	0.438548	+	0.898708i	$0.355493\pi$
$24$	2.19564	0.448183
$25$	1.00000	0.200000
$26$	0.603996	0.118453
$27$	1.00000	0.192450
$28$	−1.46645	−0.277133
$29$	4.56328	0.847380	0.423690	−	0.905807i	$-0.360735\pi$
$29$	4.56328	0.847380	0.423690	+	0.905807i	$0.360735\pi$
$30$	−0.603996	−0.110274
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−5.56558	−0.983865
$33$	5.79548	1.00886
$34$	1.28094	0.219679
$35$	0.896809	0.151588
$36$	−1.63519	−0.272532
$37$	2.53347	0.416499	0.208250	−	0.978076i	$-0.433223\pi$
$37$	2.53347	0.416499	0.208250	+	0.978076i	$0.433223\pi$
$38$	−2.14244	−0.347550
$39$	−1.00000	−0.160128
$40$	2.19564	0.347161
$41$	4.85363	0.758010	0.379005	−	0.925395i	$-0.376266\pi$
$41$	4.85363	0.758010	0.379005	+	0.925395i	$0.376266\pi$
$42$	−0.541669	−0.0835813
$43$	9.32856	1.42259	0.711296	−	0.702892i	$-0.248108\pi$
$43$	9.32856	1.42259	0.711296	+	0.702892i	$0.248108\pi$
$44$	−9.47671	−1.42867
$45$	1.00000	0.149071
$46$	−2.54065	−0.374598
$47$	−2.29901	−0.335345	−0.167672	−	0.985843i	$-0.553625\pi$
$47$	−2.29901	−0.335345	−0.167672	+	0.985843i	$0.553625\pi$
$48$	1.94422	0.280624
$49$	−6.19573	−0.885105
$50$	−0.603996	−0.0854179
$51$	−2.12077	−0.296967
$52$	1.63519	0.226760
$53$	−9.13114	−1.25426	−0.627130	−	0.778915i	$-0.715770\pi$
$53$	−9.13114	−1.25426	−0.627130	+	0.778915i	$0.715770\pi$
$54$	−0.603996	−0.0821934
$55$	5.79548	0.781462
$56$	1.96907	0.263128
$57$	3.54711	0.469827
$58$	−2.75620	−0.361907
$59$	−5.84233	−0.760607	−0.380303	−	0.924862i	$-0.624180\pi$
$59$	−5.84233	−0.760607	−0.380303	+	0.924862i	$0.624180\pi$
$60$	−1.63519	−0.211102
$61$	1.19298	0.152746	0.0763730	−	0.997079i	$-0.475666\pi$
$61$	1.19298	0.152746	0.0763730	+	0.997079i	$0.475666\pi$
$62$	−0.603996	−0.0767075
$63$	0.896809	0.112987
$64$	−0.526862	−0.0658577
$65$	−1.00000	−0.124035
$66$	−3.50044	−0.430875
$67$	7.68535	0.938915	0.469458	−	0.882955i	$-0.344449\pi$
$67$	7.68535	0.938915	0.469458	+	0.882955i	$0.344449\pi$
$68$	3.46786	0.420540
$69$	4.20640	0.506391
$70$	−0.541669	−0.0647418
$71$	−10.1886	−1.20916	−0.604580	−	0.796545i	$-0.706659\pi$
$71$	−10.1886	−1.20916	−0.604580	+	0.796545i	$0.706659\pi$
$72$	2.19564	0.258758
$73$	10.0552	1.17688	0.588438	−	0.808542i	$-0.299743\pi$
$73$	10.0552	1.17688	0.588438	+	0.808542i	$0.299743\pi$
$74$	−1.53020	−0.177882
$75$	1.00000	0.115470
$76$	−5.80020	−0.665329
$77$	5.19744	0.592303
$78$	0.603996	0.0683890
$79$	−15.8217	−1.78008	−0.890039	−	0.455884i	$-0.849323\pi$
$79$	−15.8217	−1.78008	−0.890039	+	0.455884i	$0.849323\pi$
$80$	1.94422	0.217371
$81$	1.00000	0.111111
$82$	−2.93157	−0.323738
$83$	11.9488	1.31156	0.655778	−	0.754954i	$-0.272341\pi$
$83$	11.9488	1.31156	0.655778	+	0.754954i	$0.272341\pi$
$84$	−1.46645	−0.160003
$85$	−2.12077	−0.230030
$86$	−5.63441	−0.607574
$87$	4.56328	0.489235
$88$	12.7248	1.35647
$89$	−0.655353	−0.0694673	−0.0347336	−	0.999397i	$-0.511058\pi$
$89$	−0.655353	−0.0694673	−0.0347336	+	0.999397i	$0.511058\pi$
$90$	−0.603996	−0.0636667
$91$	−0.896809	−0.0940111
$92$	−6.87826	−0.717109
$93$	1.00000	0.103695
$94$	1.38859	0.143222
$95$	3.54711	0.363926
$96$	−5.56558	−0.568034
$97$	9.49130	0.963696	0.481848	−	0.876255i	$-0.339966\pi$
$97$	9.49130	0.963696	0.481848	+	0.876255i	$0.339966\pi$
$98$	3.74220	0.378019
$99$	5.79548	0.582468
$100$	−1.63519	−0.163519
$101$	9.17750	0.913196	0.456598	−	0.889673i	$-0.349068\pi$
$101$	9.17750	0.913196	0.456598	+	0.889673i	$0.349068\pi$
$102$	1.28094	0.126832
$103$	0.146651	0.0144500	0.00722499	−	0.999974i	$-0.497700\pi$
$103$	0.146651	0.0144500	0.00722499	+	0.999974i	$0.497700\pi$
$104$	−2.19564	−0.215300
$105$	0.896809	0.0875196
$106$	5.51517	0.535681
$107$	−9.29438	−0.898522	−0.449261	−	0.893401i	$-0.648313\pi$
$107$	−9.29438	−0.898522	−0.449261	+	0.893401i	$0.648313\pi$
$108$	−1.63519	−0.157346
$109$	−16.4853	−1.57900	−0.789501	−	0.613750i	$-0.789660\pi$
$109$	−16.4853	−1.57900	−0.789501	+	0.613750i	$0.789660\pi$
$110$	−3.50044	−0.333754
$111$	2.53347	0.240466
$112$	1.74360	0.164754
$113$	−4.31119	−0.405562	−0.202781	−	0.979224i	$-0.564998\pi$
$113$	−4.31119	−0.405562	−0.202781	+	0.979224i	$0.564998\pi$
$114$	−2.14244	−0.200658
$115$	4.20640	0.392249
$116$	−7.46183	−0.692813
$117$	−1.00000	−0.0924500
$118$	3.52874	0.324847
$119$	−1.90193	−0.174349
$120$	2.19564	0.200433
$121$	22.5876	2.05342
$122$	−0.720557	−0.0652362
$123$	4.85363	0.437637
$124$	−1.63519	−0.146844
$125$	1.00000	0.0894427
$126$	−0.541669	−0.0482557
$127$	1.49034	0.132247	0.0661233	−	0.997811i	$-0.478937\pi$
$127$	1.49034	0.132247	0.0661233	+	0.997811i	$0.478937\pi$
$128$	11.4494	1.01199
$129$	9.32856	0.821334
$130$	0.603996	0.0529739
$131$	−12.7324	−1.11244	−0.556218	−	0.831036i	$-0.687748\pi$
$131$	−12.7324	−1.11244	−0.556218	+	0.831036i	$0.687748\pi$
$132$	−9.47671	−0.824841
$133$	3.18108	0.275835
$134$	−4.64192	−0.401001
$135$	1.00000	0.0860663
$136$	−4.65645	−0.399287
$137$	−3.86747	−0.330421	−0.165210	−	0.986258i	$-0.552830\pi$
$137$	−3.86747	−0.330421	−0.165210	+	0.986258i	$0.552830\pi$
$138$	−2.54065	−0.216274
$139$	−7.62441	−0.646694	−0.323347	−	0.946280i	$-0.604808\pi$
$139$	−7.62441	−0.646694	−0.323347	+	0.946280i	$0.604808\pi$
$140$	−1.46645	−0.123938
$141$	−2.29901	−0.193611
$142$	6.15384	0.516419
$143$	−5.79548	−0.484642
$144$	1.94422	0.162019
$145$	4.56328	0.378960
$146$	−6.07332	−0.502631
$147$	−6.19573	−0.511015
$148$	−4.14270	−0.340528
$149$	16.9148	1.38571	0.692857	−	0.721075i	$-0.256352\pi$
$149$	16.9148	1.38571	0.692857	+	0.721075i	$0.256352\pi$
$150$	−0.603996	−0.0493160
$151$	6.41237	0.521831	0.260916	−	0.965362i	$-0.415976\pi$
$151$	6.41237	0.521831	0.260916	+	0.965362i	$0.415976\pi$
$152$	7.78818	0.631705
$153$	−2.12077	−0.171454
$154$	−3.13923	−0.252966
$155$	1.00000	0.0803219
$156$	1.63519	0.130920
$157$	−12.0292	−0.960032	−0.480016	−	0.877260i	$-0.659369\pi$
$157$	−12.0292	−0.960032	−0.480016	+	0.877260i	$0.659369\pi$
$158$	9.55622	0.760252
$159$	−9.13114	−0.724147
$160$	−5.56558	−0.439998
$161$	3.77234	0.297302
$162$	−0.603996	−0.0474544
$163$	6.89962	0.540420	0.270210	−	0.962801i	$-0.412907\pi$
$163$	6.89962	0.540420	0.270210	+	0.962801i	$0.412907\pi$
$164$	−7.93661	−0.619745
$165$	5.79548	0.451177
$166$	−7.21705	−0.560151
$167$	−7.75276	−0.599926	−0.299963	−	0.953951i	$-0.596974\pi$
$167$	−7.75276	−0.599926	−0.299963	+	0.953951i	$0.596974\pi$
$168$	1.96907	0.151917
$169$	1.00000	0.0769231
$170$	1.28094	0.0982433
$171$	3.54711	0.271255
$172$	−15.2540	−1.16310
$173$	−15.1202	−1.14956	−0.574782	−	0.818306i	$-0.694913\pi$
$173$	−15.1202	−1.14956	−0.574782	+	0.818306i	$0.694913\pi$
$174$	−2.75620	−0.208947
$175$	0.896809	0.0677924
$176$	11.2677	0.849335
$177$	−5.84233	−0.439136
$178$	0.395830	0.0296687
$179$	23.7773	1.77720	0.888601	−	0.458681i	$-0.151678\pi$
$179$	23.7773	1.77720	0.888601	+	0.458681i	$0.151678\pi$
$180$	−1.63519	−0.121880
$181$	6.33758	0.471068	0.235534	−	0.971866i	$-0.424316\pi$
$181$	6.33758	0.471068	0.235534	+	0.971866i	$0.424316\pi$
$182$	0.541669	0.0401512
$183$	1.19298	0.0881880
$184$	9.23574	0.680868
$185$	2.53347	0.186264
$186$	−0.603996	−0.0442871
$187$	−12.2909	−0.898799
$188$	3.75931	0.274176
$189$	0.896809	0.0652333
$190$	−2.14244	−0.155429
$191$	−20.7431	−1.50092	−0.750458	−	0.660918i	$-0.770167\pi$
$191$	−20.7431	−1.50092	−0.750458	+	0.660918i	$0.770167\pi$
$192$	−0.526862	−0.0380230
$193$	−3.44124	−0.247706	−0.123853	−	0.992301i	$-0.539525\pi$
$193$	−3.44124	−0.247706	−0.123853	+	0.992301i	$0.539525\pi$
$194$	−5.73270	−0.411584
$195$	−1.00000	−0.0716115
$196$	10.1312	0.723657
$197$	−8.77889	−0.625470	−0.312735	−	0.949840i	$-0.601245\pi$
$197$	−8.77889	−0.625470	−0.312735	+	0.949840i	$0.601245\pi$
$198$	−3.50044	−0.248766
$199$	−3.64065	−0.258079	−0.129039	−	0.991639i	$-0.541189\pi$
$199$	−3.64065	−0.258079	−0.129039	+	0.991639i	$0.541189\pi$
$200$	2.19564	0.155255
$201$	7.68535	0.542083
$202$	−5.54317	−0.390016
$203$	4.09239	0.287230
$204$	3.46786	0.242799
$205$	4.85363	0.338992
$206$	−0.0885768	−0.00617144
$207$	4.20640	0.292365
$208$	−1.94422	−0.134808
$209$	20.5572	1.42197
$210$	−0.541669	−0.0373787
$211$	−23.9105	−1.64607	−0.823034	−	0.567991i	$-0.807721\pi$
$211$	−23.9105	−1.64607	−0.823034	+	0.567991i	$0.807721\pi$
$212$	14.9311	1.02548
$213$	−10.1886	−0.698108
$214$	5.61376	0.383749
$215$	9.32856	0.636203
$216$	2.19564	0.149394
$217$	0.896809	0.0608794
$218$	9.95702	0.674375
$219$	10.0552	0.679470
$220$	−9.47671	−0.638919
$221$	2.12077	0.142659
$222$	−1.53020	−0.102701
$223$	−18.0854	−1.21109	−0.605545	−	0.795811i	$-0.707045\pi$
$223$	−18.0854	−1.21109	−0.605545	+	0.795811i	$0.707045\pi$
$224$	−4.99126	−0.333493
$225$	1.00000	0.0666667
$226$	2.60394	0.173211
$227$	17.6795	1.17343	0.586713	−	0.809795i	$-0.300422\pi$
$227$	17.6795	1.17343	0.586713	+	0.809795i	$0.300422\pi$
$228$	−5.80020	−0.384128
$229$	7.13501	0.471495	0.235747	−	0.971814i	$-0.424246\pi$
$229$	7.13501	0.471495	0.235747	+	0.971814i	$0.424246\pi$
$230$	−2.54065	−0.167525
$231$	5.19744	0.341966
$232$	10.0193	0.657800
$233$	−0.262039	−0.0171667	−0.00858337	−	0.999963i	$-0.502732\pi$
$233$	−0.262039	−0.0171667	−0.00858337	+	0.999963i	$0.502732\pi$
$234$	0.603996	0.0394844
$235$	−2.29901	−0.149971
$236$	9.55332	0.621868
$237$	−15.8217	−1.02773
$238$	1.14876	0.0744627
$239$	9.07460	0.586987	0.293493	−	0.955961i	$-0.405182\pi$
$239$	9.07460	0.586987	0.293493	+	0.955961i	$0.405182\pi$
$240$	1.94422	0.125499
$241$	16.5769	1.06781	0.533907	−	0.845543i	$-0.320723\pi$
$241$	16.5769	1.06781	0.533907	+	0.845543i	$0.320723\pi$
$242$	−13.6428	−0.876992
$243$	1.00000	0.0641500
$244$	−1.95076	−0.124884
$245$	−6.19573	−0.395831
$246$	−2.93157	−0.186910
$247$	−3.54711	−0.225697
$248$	2.19564	0.139423
$249$	11.9488	0.757227
$250$	−0.603996	−0.0382000
$251$	−3.90081	−0.246217	−0.123108	−	0.992393i	$-0.539286\pi$
$251$	−3.90081	−0.246217	−0.123108	+	0.992393i	$0.539286\pi$
$252$	−1.46645	−0.0923778
$253$	24.3781	1.53264
$254$	−0.900161	−0.0564811
$255$	−2.12077	−0.132808
$256$	−5.86165	−0.366353
$257$	3.88448	0.242307	0.121154	−	0.992634i	$-0.461341\pi$
$257$	3.88448	0.242307	0.121154	+	0.992634i	$0.461341\pi$
$258$	−5.63441	−0.350783
$259$	2.27204	0.141177
$260$	1.63519	0.101410
$261$	4.56328	0.282460
$262$	7.69032	0.475110
$263$	18.0090	1.11048	0.555240	−	0.831690i	$-0.312626\pi$
$263$	18.0090	1.11048	0.555240	+	0.831690i	$0.312626\pi$
$264$	12.7248	0.783156
$265$	−9.13114	−0.560922
$266$	−1.92136	−0.117806
$267$	−0.655353	−0.0401070
$268$	−12.5670	−0.767652
$269$	−22.9636	−1.40012	−0.700058	−	0.714086i	$-0.746843\pi$
$269$	−22.9636	−1.40012	−0.700058	+	0.714086i	$0.746843\pi$
$270$	−0.603996	−0.0367580
$271$	−1.67627	−0.101826	−0.0509130	−	0.998703i	$-0.516213\pi$
$271$	−1.67627	−0.101826	−0.0509130	+	0.998703i	$0.516213\pi$
$272$	−4.12325	−0.250009
$273$	−0.896809	−0.0542774
$274$	2.33594	0.141119
$275$	5.79548	0.349481
$276$	−6.87826	−0.414023
$277$	17.4921	1.05100	0.525500	−	0.850794i	$-0.323878\pi$
$277$	17.4921	1.05100	0.525500	+	0.850794i	$0.323878\pi$
$278$	4.60511	0.276196
$279$	1.00000	0.0598684
$280$	1.96907	0.117674
$281$	23.5804	1.40669	0.703345	−	0.710849i	$-0.251689\pi$
$281$	23.5804	1.40669	0.703345	+	0.710849i	$0.251689\pi$
$282$	1.38859	0.0826893
$283$	1.30403	0.0775163	0.0387581	−	0.999249i	$-0.487660\pi$
$283$	1.30403	0.0775163	0.0387581	+	0.999249i	$0.487660\pi$
$284$	16.6602	0.988602
$285$	3.54711	0.210113
$286$	3.50044	0.206986
$287$	4.35278	0.256937
$288$	−5.56558	−0.327955
$289$	−12.5023	−0.735431
$290$	−2.75620	−0.161850
$291$	9.49130	0.556390
$292$	−16.4422	−0.962208
$293$	29.0626	1.69785	0.848927	−	0.528509i	$-0.177249\pi$
$293$	29.0626	1.69785	0.848927	+	0.528509i	$0.177249\pi$
$294$	3.74220	0.218249
$295$	−5.84233	−0.340154
$296$	5.56258	0.323318
$297$	5.79548	0.336288
$298$	−10.2165	−0.591824
$299$	−4.20640	−0.243263
$300$	−1.63519	−0.0944077
$301$	8.36594	0.482205
$302$	−3.87304	−0.222869
$303$	9.17750	0.527234
$304$	6.89638	0.395534
$305$	1.19298	0.0683101
$306$	1.28094	0.0732263
$307$	2.55036	0.145557	0.0727784	−	0.997348i	$-0.476813\pi$
$307$	2.55036	0.145557	0.0727784	+	0.997348i	$0.476813\pi$
$308$	−8.49880	−0.484264
$309$	0.146651	0.00834270
$310$	−0.603996	−0.0343046
$311$	−13.0781	−0.741589	−0.370794	−	0.928715i	$-0.620915\pi$
$311$	−13.0781	−0.741589	−0.370794	+	0.928715i	$0.620915\pi$
$312$	−2.19564	−0.124304
$313$	26.7291	1.51082	0.755410	−	0.655253i	$-0.227438\pi$
$313$	26.7291	1.51082	0.755410	+	0.655253i	$0.227438\pi$
$314$	7.26556	0.410019
$315$	0.896809	0.0505295
$316$	25.8714	1.45538
$317$	−22.1016	−1.24135	−0.620676	−	0.784067i	$-0.713142\pi$
$317$	−22.1016	−1.24135	−0.620676	+	0.784067i	$0.713142\pi$
$318$	5.51517	0.309275
$319$	26.4464	1.48071
$320$	−0.526862	−0.0294525
$321$	−9.29438	−0.518762
$322$	−2.27848	−0.126975
$323$	−7.52262	−0.418570
$324$	−1.63519	−0.0908439
$325$	−1.00000	−0.0554700
$326$	−4.16734	−0.230808
$327$	−16.4853	−0.911637
$328$	10.6568	0.588424
$329$	−2.06177	−0.113669
$330$	−3.50044	−0.192693
$331$	−20.6234	−1.13357	−0.566783	−	0.823867i	$-0.691812\pi$
$331$	−20.6234	−1.13357	−0.566783	+	0.823867i	$0.691812\pi$
$332$	−19.5386	−1.07232
$333$	2.53347	0.138833
$334$	4.68263	0.256222
$335$	7.68535	0.419896
$336$	1.74360	0.0951210
$337$	10.9645	0.597275	0.298638	−	0.954367i	$-0.403468\pi$
$337$	10.9645	0.597275	0.298638	+	0.954367i	$0.403468\pi$
$338$	−0.603996	−0.0328530
$339$	−4.31119	−0.234152
$340$	3.46786	0.188071
$341$	5.79548	0.313843
$342$	−2.14244	−0.115850
$343$	−11.8341	−0.638979
$344$	20.4821	1.10432
$345$	4.20640	0.226465
$346$	9.13251	0.490967
$347$	15.7815	0.847195	0.423598	−	0.905850i	$-0.360767\pi$
$347$	15.7815	0.847195	0.423598	+	0.905850i	$0.360767\pi$
$348$	−7.46183	−0.399996
$349$	15.5742	0.833668	0.416834	−	0.908983i	$-0.363140\pi$
$349$	15.5742	0.833668	0.416834	+	0.908983i	$0.363140\pi$
$350$	−0.541669	−0.0289534
$351$	−1.00000	−0.0533761
$352$	−32.2552	−1.71921
$353$	28.1738	1.49954	0.749771	−	0.661697i	$-0.230164\pi$
$353$	28.1738	1.49954	0.749771	+	0.661697i	$0.230164\pi$
$354$	3.52874	0.187550
$355$	−10.1886	−0.540752
$356$	1.07163	0.0567961
$357$	−1.90193	−0.100661
$358$	−14.3614	−0.759024
$359$	1.79160	0.0945570	0.0472785	−	0.998882i	$-0.484945\pi$
$359$	1.79160	0.0945570	0.0472785	+	0.998882i	$0.484945\pi$
$360$	2.19564	0.115720
$361$	−6.41799	−0.337789
$362$	−3.82787	−0.201188
$363$	22.5876	1.18554
$364$	1.46645	0.0768630
$365$	10.0552	0.526315
$366$	−0.720557	−0.0376641
$367$	6.98025	0.364366	0.182183	−	0.983265i	$-0.441684\pi$
$367$	6.98025	0.364366	0.182183	+	0.983265i	$0.441684\pi$
$368$	8.17818	0.426317
$369$	4.85363	0.252670
$370$	−1.53020	−0.0795515
$371$	−8.18889	−0.425146
$372$	−1.63519	−0.0847806
$373$	13.6784	0.708239	0.354119	−	0.935200i	$-0.384781\pi$
$373$	13.6784	0.708239	0.354119	+	0.935200i	$0.384781\pi$
$374$	7.42364	0.383867
$375$	1.00000	0.0516398
$376$	−5.04779	−0.260320
$377$	−4.56328	−0.235021
$378$	−0.541669	−0.0278604
$379$	14.7037	0.755279	0.377639	−	0.925953i	$-0.376736\pi$
$379$	14.7037	0.755279	0.377639	+	0.925953i	$0.376736\pi$
$380$	−5.80020	−0.297544
$381$	1.49034	0.0763526
$382$	12.5287	0.641026
$383$	11.2613	0.575424	0.287712	−	0.957717i	$-0.407105\pi$
$383$	11.2613	0.575424	0.287712	+	0.957717i	$0.407105\pi$
$384$	11.4494	0.584274
$385$	5.19744	0.264886
$386$	2.07850	0.105793
$387$	9.32856	0.474197
$388$	−15.5201	−0.787912
$389$	1.68703	0.0855356	0.0427678	−	0.999085i	$-0.486382\pi$
$389$	1.68703	0.0855356	0.0427678	+	0.999085i	$0.486382\pi$
$390$	0.603996	0.0305845
$391$	−8.92082	−0.451145
$392$	−13.6036	−0.687085
$393$	−12.7324	−0.642265
$394$	5.30241	0.267132
$395$	−15.8217	−0.796075
$396$	−9.47671	−0.476222
$397$	8.41578	0.422376	0.211188	−	0.977445i	$-0.432267\pi$
$397$	8.41578	0.422376	0.211188	+	0.977445i	$0.432267\pi$
$398$	2.19894	0.110223
$399$	3.18108	0.159253
$400$	1.94422	0.0972112
$401$	21.7665	1.08697	0.543484	−	0.839420i	$-0.317105\pi$
$401$	21.7665	1.08697	0.543484	+	0.839420i	$0.317105\pi$
$402$	−4.64192	−0.231518
$403$	−1.00000	−0.0498135
$404$	−15.0070	−0.746624
$405$	1.00000	0.0496904
$406$	−2.47179	−0.122673
$407$	14.6827	0.727792
$408$	−4.65645	−0.230528
$409$	−8.74215	−0.432271	−0.216136	−	0.976363i	$-0.569345\pi$
$409$	−8.74215	−0.432271	−0.216136	+	0.976363i	$0.569345\pi$
$410$	−2.93157	−0.144780
$411$	−3.86747	−0.190768
$412$	−0.239803	−0.0118142
$413$	−5.23945	−0.257817
$414$	−2.54065	−0.124866
$415$	11.9488	0.586546
$416$	5.56558	0.272875
$417$	−7.62441	−0.373369
$418$	−12.4165	−0.607309
$419$	−6.79271	−0.331846	−0.165923	−	0.986139i	$-0.553060\pi$
$419$	−6.79271	−0.331846	−0.165923	+	0.986139i	$0.553060\pi$
$420$	−1.46645	−0.0715556
$421$	−20.9284	−1.01999	−0.509995	−	0.860177i	$-0.670353\pi$
$421$	−20.9284	−1.01999	−0.509995	+	0.860177i	$0.670353\pi$
$422$	14.4419	0.703018
$423$	−2.29901	−0.111782
$424$	−20.0487	−0.973650
$425$	−2.12077	−0.102873
$426$	6.15384	0.298155
$427$	1.06988	0.0517751
$428$	15.1981	0.734627
$429$	−5.79548	−0.279808
$430$	−5.63441	−0.271715
$431$	32.7280	1.57645	0.788226	−	0.615385i	$-0.211000\pi$
$431$	32.7280	1.57645	0.788226	+	0.615385i	$0.211000\pi$
$432$	1.94422	0.0935415
$433$	−1.44643	−0.0695109	−0.0347555	−	0.999396i	$-0.511065\pi$
$433$	−1.44643	−0.0695109	−0.0347555	+	0.999396i	$0.511065\pi$
$434$	−0.541669	−0.0260009
$435$	4.56328	0.218793
$436$	26.9565	1.29098
$437$	14.9206	0.713748
$438$	−6.07332	−0.290194
$439$	−21.2056	−1.01209	−0.506044	−	0.862508i	$-0.668893\pi$
$439$	−21.2056	−1.01209	−0.506044	+	0.862508i	$0.668893\pi$
$440$	12.7248	0.606630
$441$	−6.19573	−0.295035
$442$	−1.28094	−0.0609279
$443$	18.1078	0.860326	0.430163	−	0.902751i	$-0.358456\pi$
$443$	18.1078	0.860326	0.430163	+	0.902751i	$0.358456\pi$
$444$	−4.14270	−0.196604
$445$	−0.655353	−0.0310667
$446$	10.9235	0.517244
$447$	16.9148	0.800043
$448$	−0.472494	−0.0223233
$449$	−5.08064	−0.239770	−0.119885	−	0.992788i	$-0.538253\pi$
$449$	−5.08064	−0.239770	−0.119885	+	0.992788i	$0.538253\pi$
$450$	−0.603996	−0.0284726
$451$	28.1291	1.32455
$452$	7.04961	0.331586
$453$	6.41237	0.301280
$454$	−10.6783	−0.501158
$455$	−0.896809	−0.0420431
$456$	7.78818	0.364715
$457$	−10.4510	−0.488877	−0.244439	−	0.969665i	$-0.578604\pi$
$457$	−10.4510	−0.488877	−0.244439	+	0.969665i	$0.578604\pi$
$458$	−4.30951	−0.201370
$459$	−2.12077	−0.0989891
$460$	−6.87826	−0.320701
$461$	−9.54543	−0.444575	−0.222288	−	0.974981i	$-0.571352\pi$
$461$	−9.54543	−0.444575	−0.222288	+	0.974981i	$0.571352\pi$
$462$	−3.13923	−0.146050
$463$	1.39505	0.0648336	0.0324168	−	0.999474i	$-0.489680\pi$
$463$	1.39505	0.0648336	0.0324168	+	0.999474i	$0.489680\pi$
$464$	8.87204	0.411874
$465$	1.00000	0.0463739
$466$	0.158270	0.00733173
$467$	−28.2978	−1.30947	−0.654734	−	0.755860i	$-0.727219\pi$
$467$	−28.2978	−1.30947	−0.654734	+	0.755860i	$0.727219\pi$
$468$	1.63519	0.0755867
$469$	6.89230	0.318257
$470$	1.38859	0.0640509
$471$	−12.0292	−0.554274
$472$	−12.8276	−0.590440
$473$	54.0635	2.48584
$474$	9.55622	0.438932
$475$	3.54711	0.162753
$476$	3.11001	0.142547
$477$	−9.13114	−0.418086
$478$	−5.48102	−0.250696
$479$	13.6588	0.624087	0.312044	−	0.950068i	$-0.398987\pi$
$479$	13.6588	0.624087	0.312044	+	0.950068i	$0.398987\pi$
$480$	−5.56558	−0.254033
$481$	−2.53347	−0.115516
$482$	−10.0124	−0.456052
$483$	3.77234	0.171647
$484$	−36.9350	−1.67886
$485$	9.49130	0.430978
$486$	−0.603996	−0.0273978
$487$	26.4005	1.19632	0.598161	−	0.801376i	$-0.295898\pi$
$487$	26.4005	1.19632	0.598161	+	0.801376i	$0.295898\pi$
$488$	2.61936	0.118573
$489$	6.89962	0.312012
$490$	3.74220	0.169055
$491$	23.7050	1.06979	0.534896	−	0.844918i	$-0.320351\pi$
$491$	23.7050	1.06979	0.534896	+	0.844918i	$0.320351\pi$
$492$	−7.93661	−0.357810
$493$	−9.67768	−0.435861
$494$	2.14244	0.0963930
$495$	5.79548	0.260487
$496$	1.94422	0.0872982
$497$	−9.13719	−0.409859
$498$	−7.21705	−0.323404
$499$	−11.5601	−0.517501	−0.258751	−	0.965944i	$-0.583311\pi$
$499$	−11.5601	−0.517501	−0.258751	+	0.965944i	$0.583311\pi$
$500$	−1.63519	−0.0731279
$501$	−7.75276	−0.346368
$502$	2.35607	0.105157
$503$	9.65806	0.430631	0.215316	−	0.976544i	$-0.430922\pi$
$503$	9.65806	0.430631	0.215316	+	0.976544i	$0.430922\pi$
$504$	1.96907	0.0877093
$505$	9.17750	0.408394
$506$	−14.7243	−0.654574
$507$	1.00000	0.0444116
$508$	−2.43699	−0.108124
$509$	17.5018	0.775754	0.387877	−	0.921711i	$-0.373209\pi$
$509$	17.5018	0.775754	0.387877	+	0.921711i	$0.373209\pi$
$510$	1.28094	0.0567208
$511$	9.01763	0.398916
$512$	−19.3583	−0.855526
$513$	3.54711	0.156609
$514$	−2.34621	−0.103487
$515$	0.146651	0.00646223
$516$	−15.2540	−0.671518
$517$	−13.3238	−0.585982
$518$	−1.37230	−0.0602954
$519$	−15.1202	−0.663701
$520$	−2.19564	−0.0962851
$521$	42.0420	1.84189	0.920946	−	0.389690i	$-0.127418\pi$
$521$	42.0420	1.84189	0.920946	+	0.389690i	$0.127418\pi$
$522$	−2.75620	−0.120636
$523$	−12.3745	−0.541098	−0.270549	−	0.962706i	$-0.587205\pi$
$523$	−12.3745	−0.541098	−0.270549	+	0.962706i	$0.587205\pi$
$524$	20.8199	0.909522
$525$	0.896809	0.0391400
$526$	−10.8773	−0.474274
$527$	−2.12077	−0.0923822
$528$	11.2677	0.490364
$529$	−5.30618	−0.230703
$530$	5.51517	0.239564
$531$	−5.84233	−0.253536
$532$	−5.20167	−0.225521
$533$	−4.85363	−0.210234
$534$	0.395830	0.0171293
$535$	−9.29438	−0.401831
$536$	16.8743	0.728857
$537$	23.7773	1.02607
$538$	13.8699	0.597975
$539$	−35.9072	−1.54663
$540$	−1.63519	−0.0703673
$541$	−17.4066	−0.748370	−0.374185	−	0.927354i	$-0.622078\pi$
$541$	−17.4066	−0.748370	−0.374185	+	0.927354i	$0.622078\pi$
$542$	1.01246	0.0434888
$543$	6.33758	0.271971
$544$	11.8033	0.506063
$545$	−16.4853	−0.706151
$546$	0.541669	0.0231813
$547$	−11.2282	−0.480083	−0.240042	−	0.970763i	$-0.577161\pi$
$547$	−11.2282	−0.480083	−0.240042	+	0.970763i	$0.577161\pi$
$548$	6.32405	0.270150
$549$	1.19298	0.0509153
$550$	−3.50044	−0.149259
$551$	16.1865	0.689567
$552$	9.23574	0.393099
$553$	−14.1890	−0.603379
$554$	−10.5652	−0.448871
$555$	2.53347	0.107540
$556$	12.4674	0.528734
$557$	−12.9487	−0.548654	−0.274327	−	0.961636i	$-0.588455\pi$
$557$	−12.9487	−0.548654	−0.274327	+	0.961636i	$0.588455\pi$
$558$	−0.603996	−0.0255692
$559$	−9.32856	−0.394556
$560$	1.74360	0.0736804
$561$	−12.2909	−0.518922
$562$	−14.2425	−0.600782
$563$	−43.9216	−1.85107	−0.925536	−	0.378659i	$-0.876385\pi$
$563$	−43.9216	−1.85107	−0.925536	+	0.378659i	$0.876385\pi$
$564$	3.75931	0.158296
$565$	−4.31119	−0.181373
$566$	−0.787626	−0.0331064
$567$	0.896809	0.0376624
$568$	−22.3704	−0.938640
$569$	−12.6259	−0.529305	−0.264652	−	0.964344i	$-0.585257\pi$
$569$	−12.6259	−0.529305	−0.264652	+	0.964344i	$0.585257\pi$
$570$	−2.14244	−0.0897370
$571$	45.3893	1.89948	0.949741	−	0.313038i	$-0.101347\pi$
$571$	45.3893	1.89948	0.949741	+	0.313038i	$0.101347\pi$
$572$	9.47671	0.396241
$573$	−20.7431	−0.866555
$574$	−2.62906	−0.109735
$575$	4.20640	0.175419
$576$	−0.526862	−0.0219526
$577$	−20.9880	−0.873743	−0.436872	−	0.899524i	$-0.643914\pi$
$577$	−20.9880	−0.873743	−0.436872	+	0.899524i	$0.643914\pi$
$578$	7.55135	0.314095
$579$	−3.44124	−0.143013
$580$	−7.46183	−0.309836
$581$	10.7158	0.444568
$582$	−5.73270	−0.237628
$583$	−52.9194	−2.19170
$584$	22.0777	0.913580
$585$	−1.00000	−0.0413449
$586$	−17.5537	−0.725136
$587$	21.2616	0.877559	0.438780	−	0.898595i	$-0.355411\pi$
$587$	21.2616	0.877559	0.438780	+	0.898595i	$0.355411\pi$
$588$	10.1312	0.417804
$589$	3.54711	0.146156
$590$	3.52874	0.145276
$591$	−8.77889	−0.361115
$592$	4.92563	0.202442
$593$	9.90331	0.406680	0.203340	−	0.979108i	$-0.434820\pi$
$593$	9.90331	0.406680	0.203340	+	0.979108i	$0.434820\pi$
$594$	−3.50044	−0.143625
$595$	−1.90193	−0.0779714
$596$	−27.6589	−1.13295
$597$	−3.64065	−0.149002
$598$	2.54065	0.103895
$599$	−24.4581	−0.999329	−0.499665	−	0.866219i	$-0.666543\pi$
$599$	−24.4581	−0.999329	−0.499665	+	0.866219i	$0.666543\pi$
$600$	2.19564	0.0896366
$601$	−37.6591	−1.53615	−0.768073	−	0.640362i	$-0.778784\pi$
$601$	−37.6591	−1.53615	−0.768073	+	0.640362i	$0.778784\pi$
$602$	−5.05299	−0.205944
$603$	7.68535	0.312972
$604$	−10.4854	−0.426647
$605$	22.5876	0.918316
$606$	−5.54317	−0.225176
$607$	17.2556	0.700385	0.350193	−	0.936678i	$-0.386116\pi$
$607$	17.2556	0.700385	0.350193	+	0.936678i	$0.386116\pi$
$608$	−19.7417	−0.800633
$609$	4.09239	0.165832
$610$	−0.720557	−0.0291745
$611$	2.29901	0.0930079
$612$	3.46786	0.140180
$613$	17.5707	0.709675	0.354838	−	0.934928i	$-0.384536\pi$
$613$	17.5707	0.709675	0.354838	+	0.934928i	$0.384536\pi$
$614$	−1.54041	−0.0621657
$615$	4.85363	0.195717
$616$	11.4117	0.459790
$617$	9.85911	0.396913	0.198456	−	0.980110i	$-0.436407\pi$
$617$	9.85911	0.396913	0.198456	+	0.980110i	$0.436407\pi$
$618$	−0.0885768	−0.00356308
$619$	−29.4715	−1.18456	−0.592281	−	0.805732i	$-0.701772\pi$
$619$	−29.4715	−1.18456	−0.592281	+	0.805732i	$0.701772\pi$
$620$	−1.63519	−0.0656708
$621$	4.20640	0.168797
$622$	7.89909	0.316725
$623$	−0.587727	−0.0235468
$624$	−1.94422	−0.0778312
$625$	1.00000	0.0400000
$626$	−16.1443	−0.645255
$627$	20.5572	0.820976
$628$	19.6700	0.784917
$629$	−5.37290	−0.214232
$630$	−0.541669	−0.0215806
$631$	−3.76310	−0.149807	−0.0749033	−	0.997191i	$-0.523865\pi$
$631$	−3.76310	−0.149807	−0.0749033	+	0.997191i	$0.523865\pi$
$632$	−34.7387	−1.38183
$633$	−23.9105	−0.950358
$634$	13.3493	0.530168
$635$	1.49034	0.0591425
$636$	14.9311	0.592059
$637$	6.19573	0.245484
$638$	−15.9735	−0.632397
$639$	−10.1886	−0.403053
$640$	11.4494	0.452576
$641$	48.9092	1.93180	0.965898	−	0.258923i	$-0.0833676\pi$
$641$	48.9092	1.93180	0.965898	+	0.258923i	$0.0833676\pi$
$642$	5.61376	0.221558
$643$	−7.95820	−0.313841	−0.156920	−	0.987611i	$-0.550157\pi$
$643$	−7.95820	−0.313841	−0.156920	+	0.987611i	$0.550157\pi$
$644$	−6.16849	−0.243073
$645$	9.32856	0.367312
$646$	4.54363	0.178767
$647$	−19.2791	−0.757940	−0.378970	−	0.925409i	$-0.623722\pi$
$647$	−19.2791	−0.757940	−0.378970	+	0.925409i	$0.623722\pi$
$648$	2.19564	0.0862528
$649$	−33.8591	−1.32909
$650$	0.603996	0.0236907
$651$	0.896809	0.0351487
$652$	−11.2822	−0.441844
$653$	22.4458	0.878372	0.439186	−	0.898396i	$-0.355267\pi$
$653$	22.4458	0.878372	0.439186	+	0.898396i	$0.355267\pi$
$654$	9.95702	0.389350
$655$	−12.7324	−0.497497
$656$	9.43654	0.368435
$657$	10.0552	0.392292
$658$	1.24530	0.0485468
$659$	−2.52492	−0.0983568	−0.0491784	−	0.998790i	$-0.515660\pi$
$659$	−2.52492	−0.0983568	−0.0491784	+	0.998790i	$0.515660\pi$
$660$	−9.47671	−0.368880
$661$	−4.11650	−0.160113	−0.0800567	−	0.996790i	$-0.525510\pi$
$661$	−4.11650	−0.160113	−0.0800567	+	0.996790i	$0.525510\pi$
$662$	12.4565	0.484134
$663$	2.12077	0.0823639
$664$	26.2353	1.01813
$665$	3.18108	0.123357
$666$	−1.53020	−0.0592942
$667$	19.1950	0.743233
$668$	12.6772	0.490497
$669$	−18.0854	−0.699224
$670$	−4.64192	−0.179333
$671$	6.91392	0.266909
$672$	−4.99126	−0.192542
$673$	−37.7807	−1.45634	−0.728170	−	0.685397i	$-0.759629\pi$
$673$	−37.7807	−1.45634	−0.728170	+	0.685397i	$0.759629\pi$
$674$	−6.62252	−0.255090
$675$	1.00000	0.0384900
$676$	−1.63519	−0.0628919
$677$	11.8126	0.453993	0.226997	−	0.973896i	$-0.427109\pi$
$677$	11.8126	0.453993	0.226997	+	0.973896i	$0.427109\pi$
$678$	2.60394	0.100004
$679$	8.51188	0.326656
$680$	−4.65645	−0.178567
$681$	17.6795	0.677478
$682$	−3.50044	−0.134039
$683$	−12.3588	−0.472896	−0.236448	−	0.971644i	$-0.575983\pi$
$683$	−12.3588	−0.472896	−0.236448	+	0.971644i	$0.575983\pi$
$684$	−5.80020	−0.221776
$685$	−3.86747	−0.147769
$686$	7.14772	0.272901
$687$	7.13501	0.272218
$688$	18.1368	0.691459
$689$	9.13114	0.347869
$690$	−2.54065	−0.0967208
$691$	1.72579	0.0656520	0.0328260	−	0.999461i	$-0.489549\pi$
$691$	1.72579	0.0656520	0.0328260	+	0.999461i	$0.489549\pi$
$692$	24.7243	0.939878
$693$	5.19744	0.197434
$694$	−9.53196	−0.361828
$695$	−7.62441	−0.289210
$696$	10.0193	0.379781
$697$	−10.2934	−0.389892
$698$	−9.40675	−0.356051
$699$	−0.262039	−0.00991122
$700$	−1.46645	−0.0554267
$701$	−5.41286	−0.204441	−0.102220	−	0.994762i	$-0.532595\pi$
$701$	−5.41286	−0.204441	−0.102220	+	0.994762i	$0.532595\pi$
$702$	0.603996	0.0227963
$703$	8.98650	0.338932
$704$	−3.05342	−0.115080
$705$	−2.29901	−0.0865856
$706$	−17.0169	−0.640439
$707$	8.23047	0.309539
$708$	9.55332	0.359036
$709$	33.4839	1.25752	0.628758	−	0.777601i	$-0.283564\pi$
$709$	33.4839	1.25752	0.628758	+	0.777601i	$0.283564\pi$
$710$	6.15384	0.230950
$711$	−15.8217	−0.593359
$712$	−1.43892	−0.0539257
$713$	4.20640	0.157531
$714$	1.14876	0.0429911
$715$	−5.79548	−0.216739
$716$	−38.8805	−1.45303
$717$	9.07460	0.338897
$718$	−1.08212	−0.0403843
$719$	33.3011	1.24192	0.620961	−	0.783842i	$-0.286743\pi$
$719$	33.3011	1.24192	0.620961	+	0.783842i	$0.286743\pi$
$720$	1.94422	0.0724569
$721$	0.131518	0.00489800
$722$	3.87644	0.144266
$723$	16.5769	0.616502
$724$	−10.3631	−0.385143
$725$	4.56328	0.169476
$726$	−13.6428	−0.506332
$727$	−7.71784	−0.286239	−0.143119	−	0.989705i	$-0.545713\pi$
$727$	−7.71784	−0.286239	−0.143119	+	0.989705i	$0.545713\pi$
$728$	−1.96907	−0.0729785
$729$	1.00000	0.0370370
$730$	−6.07332	−0.224784
$731$	−19.7837	−0.731728
$732$	−1.95076	−0.0721020
$733$	28.4788	1.05189	0.525944	−	0.850519i	$-0.323712\pi$
$733$	28.4788	1.05189	0.525944	+	0.850519i	$0.323712\pi$
$734$	−4.21604	−0.155617
$735$	−6.19573	−0.228533
$736$	−23.4111	−0.862943
$737$	44.5403	1.64066
$738$	−2.93157	−0.107913
$739$	−33.7419	−1.24122	−0.620608	−	0.784121i	$-0.713114\pi$
$739$	−33.7419	−1.24122	−0.620608	+	0.784121i	$0.713114\pi$
$740$	−4.14270	−0.152289
$741$	−3.54711	−0.130306
$742$	4.94605	0.181575
$743$	1.89522	0.0695288	0.0347644	−	0.999396i	$-0.488932\pi$
$743$	1.89522	0.0695288	0.0347644	+	0.999396i	$0.488932\pi$
$744$	2.19564	0.0804960
$745$	16.9148	0.619710
$746$	−8.26167	−0.302481
$747$	11.9488	0.437185
$748$	20.0979	0.734853
$749$	−8.33528	−0.304565
$750$	−0.603996	−0.0220548
$751$	−16.4785	−0.601308	−0.300654	−	0.953733i	$-0.597205\pi$
$751$	−16.4785	−0.601308	−0.300654	+	0.953733i	$0.597205\pi$
$752$	−4.46978	−0.162996
$753$	−3.90081	−0.142153
$754$	2.75620	0.100375
$755$	6.41237	0.233370
$756$	−1.46645	−0.0533344
$757$	−36.5517	−1.32849	−0.664246	−	0.747514i	$-0.731247\pi$
$757$	−36.5517	−1.32849	−0.664246	+	0.747514i	$0.731247\pi$
$758$	−8.88097	−0.322571
$759$	24.3781	0.884870
$760$	7.78818	0.282507
$761$	−14.7606	−0.535070	−0.267535	−	0.963548i	$-0.586209\pi$
$761$	−14.7606	−0.535070	−0.267535	+	0.963548i	$0.586209\pi$
$762$	−0.900161	−0.0326094
$763$	−14.7841	−0.535221
$764$	33.9189	1.22714
$765$	−2.12077	−0.0766766
$766$	−6.80175	−0.245757
$767$	5.84233	0.210954
$768$	−5.86165	−0.211514
$769$	−30.2915	−1.09234	−0.546169	−	0.837675i	$-0.683915\pi$
$769$	−30.2915	−1.09234	−0.546169	+	0.837675i	$0.683915\pi$
$770$	−3.13923	−0.113130
$771$	3.88448	0.139896
$772$	5.62708	0.202523
$773$	−10.4721	−0.376655	−0.188327	−	0.982106i	$-0.560307\pi$
$773$	−10.4721	−0.376655	−0.188327	+	0.982106i	$0.560307\pi$
$774$	−5.63441	−0.202525
$775$	1.00000	0.0359211
$776$	20.8395	0.748093
$777$	2.27204	0.0815089
$778$	−1.01896	−0.0365313
$779$	17.2164	0.616841
$780$	1.63519	0.0585492
$781$	−59.0476	−2.11289
$782$	5.38813	0.192679
$783$	4.56328	0.163078
$784$	−12.0459	−0.430210
$785$	−12.0292	−0.429339
$786$	7.69032	0.274305
$787$	−45.1709	−1.61017	−0.805084	−	0.593161i	$-0.797880\pi$
$787$	−45.1709	−1.61017	−0.805084	+	0.593161i	$0.797880\pi$
$788$	14.3551	0.511381
$789$	18.0090	0.641136
$790$	9.55622	0.339995
$791$	−3.86631	−0.137470
$792$	12.7248	0.452155
$793$	−1.19298	−0.0423641
$794$	−5.08309	−0.180392
$795$	−9.13114	−0.323848
$796$	5.95315	0.211004
$797$	−24.9150	−0.882533	−0.441267	−	0.897376i	$-0.645471\pi$
$797$	−24.9150	−0.882533	−0.441267	+	0.897376i	$0.645471\pi$
$798$	−1.92136	−0.0680154
$799$	4.87567	0.172489
$800$	−5.56558	−0.196773
$801$	−0.655353	−0.0231558
$802$	−13.1469	−0.464232
$803$	58.2749	2.05648
$804$	−12.5670	−0.443204
$805$	3.77234	0.132957
$806$	0.603996	0.0212748
$807$	−22.9636	−0.808358
$808$	20.1505	0.708891
$809$	−36.4791	−1.28254	−0.641269	−	0.767316i	$-0.721592\pi$
$809$	−36.4791	−1.28254	−0.641269	+	0.767316i	$0.721592\pi$
$810$	−0.603996	−0.0212222
$811$	−15.0034	−0.526841	−0.263421	−	0.964681i	$-0.584851\pi$
$811$	−15.0034	−0.526841	−0.263421	+	0.964681i	$0.584851\pi$
$812$	−6.69184	−0.234837
$813$	−1.67627	−0.0587893
$814$	−8.86826	−0.310832
$815$	6.89962	0.241683
$816$	−4.12325	−0.144343
$817$	33.0895	1.15765
$818$	5.28022	0.184618
$819$	−0.896809	−0.0313370
$820$	−7.93661	−0.277158
$821$	−18.8782	−0.658855	−0.329427	−	0.944181i	$-0.606856\pi$
$821$	−18.8782	−0.658855	−0.329427	+	0.944181i	$0.606856\pi$
$822$	2.33594	0.0814751
$823$	−1.10450	−0.0385004	−0.0192502	−	0.999815i	$-0.506128\pi$
$823$	−1.10450	−0.0385004	−0.0192502	+	0.999815i	$0.506128\pi$
$824$	0.321993	0.0112172
$825$	5.79548	0.201773
$826$	3.16461	0.110111
$827$	−6.30885	−0.219380	−0.109690	−	0.993966i	$-0.534986\pi$
$827$	−6.30885	−0.219380	−0.109690	+	0.993966i	$0.534986\pi$
$828$	−6.87826	−0.239036
$829$	−19.4123	−0.674216	−0.337108	−	0.941466i	$-0.609449\pi$
$829$	−19.4123	−0.674216	−0.337108	+	0.941466i	$0.609449\pi$
$830$	−7.21705	−0.250507
$831$	17.4921	0.606795
$832$	0.526862	0.0182656
$833$	13.1397	0.455265
$834$	4.60511	0.159462
$835$	−7.75276	−0.268295
$836$	−33.6149	−1.16260
$837$	1.00000	0.0345651
$838$	4.10277	0.141728
$839$	6.48920	0.224032	0.112016	−	0.993706i	$-0.464269\pi$
$839$	6.48920	0.224032	0.112016	+	0.993706i	$0.464269\pi$
$840$	1.96907	0.0679393
$841$	−8.17646	−0.281947
$842$	12.6407	0.435627
$843$	23.5804	0.812153
$844$	39.0982	1.34582
$845$	1.00000	0.0344010
$846$	1.38859	0.0477407
$847$	20.2567	0.696030
$848$	−17.7530	−0.609640
$849$	1.30403	0.0447540
$850$	1.28094	0.0439358
$851$	10.6568	0.365310
$852$	16.6602	0.570770
$853$	36.7181	1.25720	0.628602	−	0.777727i	$-0.283628\pi$
$853$	36.7181	1.25720	0.628602	+	0.777727i	$0.283628\pi$
$854$	−0.646202	−0.0221126
$855$	3.54711	0.121309
$856$	−20.4071	−0.697500
$857$	27.7063	0.946431	0.473215	−	0.880947i	$-0.343093\pi$
$857$	27.7063	0.946431	0.473215	+	0.880947i	$0.343093\pi$
$858$	3.50044	0.119503
$859$	5.04352	0.172083	0.0860414	−	0.996292i	$-0.472578\pi$
$859$	5.04352	0.172083	0.0860414	+	0.996292i	$0.472578\pi$
$860$	−15.2540	−0.520156
$861$	4.35278	0.148342
$862$	−19.7676	−0.673286
$863$	23.1251	0.787186	0.393593	−	0.919285i	$-0.371232\pi$
$863$	23.1251	0.787186	0.393593	+	0.919285i	$0.371232\pi$
$864$	−5.56558	−0.189345
$865$	−15.1202	−0.514101
$866$	0.873636	0.0296874
$867$	−12.5023	−0.424601
$868$	−1.46645	−0.0497746
$869$	−91.6942	−3.11051
$870$	−2.75620	−0.0934440
$871$	−7.68535	−0.260408
$872$	−36.1957	−1.22574
$873$	9.49130	0.321232
$874$	−9.01197	−0.304834
$875$	0.896809	0.0303177
$876$	−16.4422	−0.555531
$877$	13.9998	0.472739	0.236369	−	0.971663i	$-0.424042\pi$
$877$	13.9998	0.472739	0.236369	+	0.971663i	$0.424042\pi$
$878$	12.8081	0.432252
$879$	29.0626	0.980257
$880$	11.2677	0.379834
$881$	29.8609	1.00604	0.503019	−	0.864275i	$-0.332222\pi$
$881$	29.8609	1.00604	0.503019	+	0.864275i	$0.332222\pi$
$882$	3.74220	0.126006
$883$	22.8871	0.770211	0.385105	−	0.922873i	$-0.374165\pi$
$883$	22.8871	0.770211	0.385105	+	0.922873i	$0.374165\pi$
$884$	−3.46786	−0.116637
$885$	−5.84233	−0.196388
$886$	−10.9370	−0.367436
$887$	−24.3031	−0.816018	−0.408009	−	0.912978i	$-0.633777\pi$
$887$	−24.3031	−0.816018	−0.408009	+	0.912978i	$0.633777\pi$
$888$	5.56258	0.186668
$889$	1.33655	0.0448266
$890$	0.395830	0.0132683
$891$	5.79548	0.194156
$892$	29.5731	0.990181
$893$	−8.15484	−0.272891
$894$	−10.2165	−0.341690
$895$	23.7773	0.794789
$896$	10.2679	0.343027
$897$	−4.20640	−0.140448
$898$	3.06868	0.102403
$899$	4.56328	0.152194
$900$	−1.63519	−0.0545063
$901$	19.3651	0.645144
$902$	−16.9899	−0.565701
$903$	8.36594	0.278401
$904$	−9.46581	−0.314828
$905$	6.33758	0.210668
$906$	−3.87304	−0.128673
$907$	−9.71157	−0.322467	−0.161234	−	0.986916i	$-0.551547\pi$
$907$	−9.71157	−0.322467	−0.161234	+	0.986916i	$0.551547\pi$
$908$	−28.9093	−0.959387
$909$	9.17750	0.304399
$910$	0.541669	0.0179561
$911$	−0.444044	−0.0147118	−0.00735592	−	0.999973i	$-0.502341\pi$
$911$	−0.444044	−0.0147118	−0.00735592	+	0.999973i	$0.502341\pi$
$912$	6.89638	0.228362
$913$	69.2493	2.29182
$914$	6.31236	0.208794
$915$	1.19298	0.0394389
$916$	−11.6671	−0.385491
$917$	−11.4185	−0.377074
$918$	1.28094	0.0422772
$919$	17.5250	0.578095	0.289048	−	0.957315i	$-0.406661\pi$
$919$	17.5250	0.578095	0.289048	+	0.957315i	$0.406661\pi$
$920$	9.23574	0.304493
$921$	2.55036	0.0840372
$922$	5.76540	0.189873
$923$	10.1886	0.335360
$924$	−8.49880	−0.279590
$925$	2.53347	0.0832999
$926$	−0.842606	−0.0276897
$927$	0.146651	0.00481666
$928$	−25.3973	−0.833707
$929$	−14.2745	−0.468332	−0.234166	−	0.972197i	$-0.575236\pi$
$929$	−14.2745	−0.468332	−0.234166	+	0.972197i	$0.575236\pi$
$930$	−0.603996	−0.0198058
$931$	−21.9770	−0.720266
$932$	0.428483	0.0140354
$933$	−13.0781	−0.428156
$934$	17.0918	0.559259
$935$	−12.2909	−0.401955
$936$	−2.19564	−0.0717667
$937$	26.0156	0.849893	0.424947	−	0.905218i	$-0.360293\pi$
$937$	26.0156	0.849893	0.424947	+	0.905218i	$0.360293\pi$
$938$	−4.16292	−0.135924
$939$	26.7291	0.872272
$940$	3.75931	0.122615
$941$	19.0945	0.622462	0.311231	−	0.950334i	$-0.399259\pi$
$941$	19.0945	0.622462	0.311231	+	0.950334i	$0.399259\pi$
$942$	7.26556	0.236725
$943$	20.4163	0.664847
$944$	−11.3588	−0.369697
$945$	0.896809	0.0291732
$946$	−32.6541	−1.06168
$947$	−30.1935	−0.981158	−0.490579	−	0.871397i	$-0.663215\pi$
$947$	−30.1935	−0.981158	−0.490579	+	0.871397i	$0.663215\pi$
$948$	25.8714	0.840265
$949$	−10.0552	−0.326407
$950$	−2.14244	−0.0695099
$951$	−22.1016	−0.716695
$952$	−4.17594	−0.135343
$953$	−19.6386	−0.636155	−0.318078	−	0.948065i	$-0.603037\pi$
$953$	−19.6386	−0.636155	−0.318078	+	0.948065i	$0.603037\pi$
$954$	5.51517	0.178560
$955$	−20.7431	−0.671230
$956$	−14.8387	−0.479917
$957$	26.4464	0.854891
$958$	−8.24986	−0.266541
$959$	−3.46838	−0.112000
$960$	−0.526862	−0.0170044
$961$	1.00000	0.0322581
$962$	1.53020	0.0493357
$963$	−9.29438	−0.299507
$964$	−27.1064	−0.873038
$965$	−3.44124	−0.110778
$966$	−2.27848	−0.0733088
$967$	−25.7564	−0.828271	−0.414136	−	0.910215i	$-0.635916\pi$
$967$	−25.7564	−0.828271	−0.414136	+	0.910215i	$0.635916\pi$
$968$	49.5942	1.59402
$969$	−7.52262	−0.241661
$970$	−5.73270	−0.184066
$971$	−29.1205	−0.934521	−0.467261	−	0.884120i	$-0.654759\pi$
$971$	−29.1205	−0.934521	−0.467261	+	0.884120i	$0.654759\pi$
$972$	−1.63519	−0.0524487
$973$	−6.83764	−0.219205
$974$	−15.9458	−0.510936
$975$	−1.00000	−0.0320256
$976$	2.31943	0.0742431
$977$	−9.97575	−0.319153	−0.159576	−	0.987186i	$-0.551013\pi$
$977$	−9.97575	−0.319153	−0.159576	+	0.987186i	$0.551013\pi$
$978$	−4.16734	−0.133257
$979$	−3.79809	−0.121387
$980$	10.1312	0.323629
$981$	−16.4853	−0.526334
$982$	−14.3177	−0.456897
$983$	19.2153	0.612874	0.306437	−	0.951891i	$-0.400863\pi$
$983$	19.2153	0.612874	0.306437	+	0.951891i	$0.400863\pi$
$984$	10.6568	0.339727
$985$	−8.77889	−0.279719
$986$	5.84527	0.186151
$987$	−2.06177	−0.0656269
$988$	5.80020	0.184529
$989$	39.2397	1.24775
$990$	−3.50044	−0.111251
$991$	−13.4899	−0.428519	−0.214260	−	0.976777i	$-0.568734\pi$
$991$	−13.4899	−0.428519	−0.214260	+	0.976777i	$0.568734\pi$
$992$	−5.56558	−0.176707
$993$	−20.6234	−0.654465
$994$	5.51882	0.175046
$995$	−3.64065	−0.115416
$996$	−19.5386	−0.619105
$997$	−36.3976	−1.15272	−0.576361	−	0.817195i	$-0.695528\pi$
$997$	−36.3976	−1.15272	−0.576361	+	0.817195i	$0.695528\pi$
$998$	6.98225	0.221019
$999$	2.53347	0.0801554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bi.1.7	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bi.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-0.603996 q^{2} +1.00000 q^{3} -1.63519 q^{4} +1.00000 q^{5} -0.603996 q^{6} +0.896809 q^{7} +2.19564 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.603996 q^{2} +1.00000 q^{3} -1.63519 q^{4} +1.00000 q^{5} -0.603996 q^{6} +0.896809 q^{7} +2.19564 q^{8} +1.00000 q^{9} -0.603996 q^{10} +5.79548 q^{11} -1.63519 q^{12} -1.00000 q^{13} -0.541669 q^{14} +1.00000 q^{15} +1.94422 q^{16} -2.12077 q^{17} -0.603996 q^{18} +3.54711 q^{19} -1.63519 q^{20} +0.896809 q^{21} -3.50044 q^{22} +4.20640 q^{23} +2.19564 q^{24} +1.00000 q^{25} +0.603996 q^{26} +1.00000 q^{27} -1.46645 q^{28} +4.56328 q^{29} -0.603996 q^{30} +1.00000 q^{31} -5.56558 q^{32} +5.79548 q^{33} +1.28094 q^{34} +0.896809 q^{35} -1.63519 q^{36} +2.53347 q^{37} -2.14244 q^{38} -1.00000 q^{39} +2.19564 q^{40} +4.85363 q^{41} -0.541669 q^{42} +9.32856 q^{43} -9.47671 q^{44} +1.00000 q^{45} -2.54065 q^{46} -2.29901 q^{47} +1.94422 q^{48} -6.19573 q^{49} -0.603996 q^{50} -2.12077 q^{51} +1.63519 q^{52} -9.13114 q^{53} -0.603996 q^{54} +5.79548 q^{55} +1.96907 q^{56} +3.54711 q^{57} -2.75620 q^{58} -5.84233 q^{59} -1.63519 q^{60} +1.19298 q^{61} -0.603996 q^{62} +0.896809 q^{63} -0.526862 q^{64} -1.00000 q^{65} -3.50044 q^{66} +7.68535 q^{67} +3.46786 q^{68} +4.20640 q^{69} -0.541669 q^{70} -10.1886 q^{71} +2.19564 q^{72} +10.0552 q^{73} -1.53020 q^{74} +1.00000 q^{75} -5.80020 q^{76} +5.19744 q^{77} +0.603996 q^{78} -15.8217 q^{79} +1.94422 q^{80} +1.00000 q^{81} -2.93157 q^{82} +11.9488 q^{83} -1.46645 q^{84} -2.12077 q^{85} -5.63441 q^{86} +4.56328 q^{87} +12.7248 q^{88} -0.655353 q^{89} -0.603996 q^{90} -0.896809 q^{91} -6.87826 q^{92} +1.00000 q^{93} +1.38859 q^{94} +3.54711 q^{95} -5.56558 q^{96} +9.49130 q^{97} +3.74220 q^{98} +5.79548 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 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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