LMFDB - Embedded newform 6018.2.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.18461324.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 4x^{4} + 12x^{3} + 3x^{2} - 6x - 2 $ x^6 - 3x^5 - 4x^4 + 12x^3 + 3x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.91714$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.91714 q^{5} +1.00000 q^{6} -1.73720 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.91714 q^{5} +1.00000 q^{6} -1.73720 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.91714 q^{10} +1.28494 q^{11} +1.00000 q^{12} +5.11248 q^{13} -1.73720 q^{14} -1.91714 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -7.73033 q^{19} -1.91714 q^{20} -1.73720 q^{21} +1.28494 q^{22} -6.84877 q^{23} +1.00000 q^{24} -1.32458 q^{25} +5.11248 q^{26} +1.00000 q^{27} -1.73720 q^{28} -8.97540 q^{29} -1.91714 q^{30} -0.566291 q^{31} +1.00000 q^{32} +1.28494 q^{33} -1.00000 q^{34} +3.33045 q^{35} +1.00000 q^{36} +10.2678 q^{37} -7.73033 q^{38} +5.11248 q^{39} -1.91714 q^{40} -1.72781 q^{41} -1.73720 q^{42} +7.67402 q^{43} +1.28494 q^{44} -1.91714 q^{45} -6.84877 q^{46} -3.75247 q^{47} +1.00000 q^{48} -3.98214 q^{49} -1.32458 q^{50} -1.00000 q^{51} +5.11248 q^{52} -1.44997 q^{53} +1.00000 q^{54} -2.46340 q^{55} -1.73720 q^{56} -7.73033 q^{57} -8.97540 q^{58} -1.00000 q^{59} -1.91714 q^{60} +3.44485 q^{61} -0.566291 q^{62} -1.73720 q^{63} +1.00000 q^{64} -9.80134 q^{65} +1.28494 q^{66} -1.48219 q^{67} -1.00000 q^{68} -6.84877 q^{69} +3.33045 q^{70} -5.61916 q^{71} +1.00000 q^{72} -7.84373 q^{73} +10.2678 q^{74} -1.32458 q^{75} -7.73033 q^{76} -2.23219 q^{77} +5.11248 q^{78} -1.87056 q^{79} -1.91714 q^{80} +1.00000 q^{81} -1.72781 q^{82} +1.97044 q^{83} -1.73720 q^{84} +1.91714 q^{85} +7.67402 q^{86} -8.97540 q^{87} +1.28494 q^{88} -2.34832 q^{89} -1.91714 q^{90} -8.88140 q^{91} -6.84877 q^{92} -0.566291 q^{93} -3.75247 q^{94} +14.8201 q^{95} +1.00000 q^{96} -7.86027 q^{97} -3.98214 q^{98} +1.28494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 8 q^{11} + 6 q^{12} - 6 q^{13} - 7 q^{14} - 3 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 3 q^{20} - 7 q^{21} - 8 q^{22} - 8 q^{23} + 6 q^{24} - 13 q^{25} - 6 q^{26} + 6 q^{27} - 7 q^{28} - 21 q^{29} - 3 q^{30} - 5 q^{31} + 6 q^{32} - 8 q^{33} - 6 q^{34} - 12 q^{35} + 6 q^{36} - 13 q^{37} - 14 q^{38} - 6 q^{39} - 3 q^{40} - 18 q^{41} - 7 q^{42} - 4 q^{43} - 8 q^{44} - 3 q^{45} - 8 q^{46} - 4 q^{47} + 6 q^{48} + 5 q^{49} - 13 q^{50} - 6 q^{51} - 6 q^{52} - 25 q^{53} + 6 q^{54} - 8 q^{55} - 7 q^{56} - 14 q^{57} - 21 q^{58} - 6 q^{59} - 3 q^{60} - 5 q^{62} - 7 q^{63} + 6 q^{64} + 6 q^{65} - 8 q^{66} - 13 q^{67} - 6 q^{68} - 8 q^{69} - 12 q^{70} - 12 q^{71} + 6 q^{72} - 4 q^{73} - 13 q^{74} - 13 q^{75} - 14 q^{76} + 4 q^{77} - 6 q^{78} - 12 q^{79} - 3 q^{80} + 6 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 3 q^{85} - 4 q^{86} - 21 q^{87} - 8 q^{88} - 11 q^{89} - 3 q^{90} - 31 q^{91} - 8 q^{92} - 5 q^{93} - 4 q^{94} + 35 q^{95} + 6 q^{96} + 16 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9 - 3 * q^10 - 8 * q^11 + 6 * q^12 - 6 * q^13 - 7 * q^14 - 3 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 3 * q^20 - 7 * q^21 - 8 * q^22 - 8 * q^23 + 6 * q^24 - 13 * q^25 - 6 * q^26 + 6 * q^27 - 7 * q^28 - 21 * q^29 - 3 * q^30 - 5 * q^31 + 6 * q^32 - 8 * q^33 - 6 * q^34 - 12 * q^35 + 6 * q^36 - 13 * q^37 - 14 * q^38 - 6 * q^39 - 3 * q^40 - 18 * q^41 - 7 * q^42 - 4 * q^43 - 8 * q^44 - 3 * q^45 - 8 * q^46 - 4 * q^47 + 6 * q^48 + 5 * q^49 - 13 * q^50 - 6 * q^51 - 6 * q^52 - 25 * q^53 + 6 * q^54 - 8 * q^55 - 7 * q^56 - 14 * q^57 - 21 * q^58 - 6 * q^59 - 3 * q^60 - 5 * q^62 - 7 * q^63 + 6 * q^64 + 6 * q^65 - 8 * q^66 - 13 * q^67 - 6 * q^68 - 8 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 - 4 * q^73 - 13 * q^74 - 13 * q^75 - 14 * q^76 + 4 * q^77 - 6 * q^78 - 12 * q^79 - 3 * q^80 + 6 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 3 * q^85 - 4 * q^86 - 21 * q^87 - 8 * q^88 - 11 * q^89 - 3 * q^90 - 31 * q^91 - 8 * q^92 - 5 * q^93 - 4 * q^94 + 35 * q^95 + 6 * q^96 + 16 * q^97 + 5 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.91714	−0.857371	−0.428685	−	0.903454i	$-0.641023\pi$
$5$	−1.91714	−0.857371	−0.428685	+	0.903454i	$0.641023\pi$
$6$	1.00000	0.408248
$7$	−1.73720	−0.656600	−0.328300	−	0.944574i	$-0.606476\pi$
$7$	−1.73720	−0.656600	−0.328300	+	0.944574i	$0.606476\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.91714	−0.606253
$11$	1.28494	0.387423	0.193711	−	0.981059i	$-0.437947\pi$
$11$	1.28494	0.387423	0.193711	+	0.981059i	$0.437947\pi$
$12$	1.00000	0.288675
$13$	5.11248	1.41795	0.708974	−	0.705235i	$-0.249158\pi$
$13$	5.11248	1.41795	0.708974	+	0.705235i	$0.249158\pi$
$14$	−1.73720	−0.464286
$15$	−1.91714	−0.495003
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−7.73033	−1.77346	−0.886730	−	0.462287i	$-0.847029\pi$
$19$	−7.73033	−1.77346	−0.886730	+	0.462287i	$0.847029\pi$
$20$	−1.91714	−0.428685
$21$	−1.73720	−0.379088
$22$	1.28494	0.273949
$23$	−6.84877	−1.42807	−0.714034	−	0.700111i	$-0.753134\pi$
$23$	−6.84877	−1.42807	−0.714034	+	0.700111i	$0.753134\pi$
$24$	1.00000	0.204124
$25$	−1.32458	−0.264915
$26$	5.11248	1.00264
$27$	1.00000	0.192450
$28$	−1.73720	−0.328300
$29$	−8.97540	−1.66669	−0.833345	−	0.552753i	$-0.813577\pi$
$29$	−8.97540	−1.66669	−0.833345	+	0.552753i	$0.813577\pi$
$30$	−1.91714	−0.350020
$31$	−0.566291	−0.101709	−0.0508544	−	0.998706i	$-0.516194\pi$
$31$	−0.566291	−0.101709	−0.0508544	+	0.998706i	$0.516194\pi$
$32$	1.00000	0.176777
$33$	1.28494	0.223679
$34$	−1.00000	−0.171499
$35$	3.33045	0.562950
$36$	1.00000	0.166667
$37$	10.2678	1.68802	0.844010	−	0.536327i	$-0.180189\pi$
$37$	10.2678	1.68802	0.844010	+	0.536327i	$0.180189\pi$
$38$	−7.73033	−1.25403
$39$	5.11248	0.818652
$40$	−1.91714	−0.303126
$41$	−1.72781	−0.269838	−0.134919	−	0.990857i	$-0.543077\pi$
$41$	−1.72781	−0.269838	−0.134919	+	0.990857i	$0.543077\pi$
$42$	−1.73720	−0.268056
$43$	7.67402	1.17028	0.585139	−	0.810933i	$-0.301040\pi$
$43$	7.67402	1.17028	0.585139	+	0.810933i	$0.301040\pi$
$44$	1.28494	0.193711
$45$	−1.91714	−0.285790
$46$	−6.84877	−1.00980
$47$	−3.75247	−0.547355	−0.273677	−	0.961822i	$-0.588240\pi$
$47$	−3.75247	−0.547355	−0.273677	+	0.961822i	$0.588240\pi$
$48$	1.00000	0.144338
$49$	−3.98214	−0.568877
$50$	−1.32458	−0.187323
$51$	−1.00000	−0.140028
$52$	5.11248	0.708974
$53$	−1.44997	−0.199168	−0.0995841	−	0.995029i	$-0.531751\pi$
$53$	−1.44997	−0.199168	−0.0995841	+	0.995029i	$0.531751\pi$
$54$	1.00000	0.136083
$55$	−2.46340	−0.332165
$56$	−1.73720	−0.232143
$57$	−7.73033	−1.02391
$58$	−8.97540	−1.17853
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−1.91714	−0.247502
$61$	3.44485	0.441067	0.220534	−	0.975379i	$-0.429220\pi$
$61$	3.44485	0.441067	0.220534	+	0.975379i	$0.429220\pi$
$62$	−0.566291	−0.0719190
$63$	−1.73720	−0.218867
$64$	1.00000	0.125000
$65$	−9.80134	−1.21571
$66$	1.28494	0.158165
$67$	−1.48219	−0.181078	−0.0905391	−	0.995893i	$-0.528859\pi$
$67$	−1.48219	−0.181078	−0.0905391	+	0.995893i	$0.528859\pi$
$68$	−1.00000	−0.121268
$69$	−6.84877	−0.824495
$70$	3.33045	0.398066
$71$	−5.61916	−0.666871	−0.333436	−	0.942773i	$-0.608208\pi$
$71$	−5.61916	−0.666871	−0.333436	+	0.942773i	$0.608208\pi$
$72$	1.00000	0.117851
$73$	−7.84373	−0.918039	−0.459020	−	0.888426i	$-0.651799\pi$
$73$	−7.84373	−0.918039	−0.459020	+	0.888426i	$0.651799\pi$
$74$	10.2678	1.19361
$75$	−1.32458	−0.152949
$76$	−7.73033	−0.886730
$77$	−2.23219	−0.254382
$78$	5.11248	0.578875
$79$	−1.87056	−0.210455	−0.105227	−	0.994448i	$-0.533557\pi$
$79$	−1.87056	−0.210455	−0.105227	+	0.994448i	$0.533557\pi$
$80$	−1.91714	−0.214343
$81$	1.00000	0.111111
$82$	−1.72781	−0.190805
$83$	1.97044	0.216283	0.108142	−	0.994135i	$-0.465510\pi$
$83$	1.97044	0.216283	0.108142	+	0.994135i	$0.465510\pi$
$84$	−1.73720	−0.189544
$85$	1.91714	0.207943
$86$	7.67402	0.827511
$87$	−8.97540	−0.962264
$88$	1.28494	0.136975
$89$	−2.34832	−0.248921	−0.124461	−	0.992225i	$-0.539720\pi$
$89$	−2.34832	−0.248921	−0.124461	+	0.992225i	$0.539720\pi$
$90$	−1.91714	−0.202084
$91$	−8.88140	−0.931024
$92$	−6.84877	−0.714034
$93$	−0.566291	−0.0587216
$94$	−3.75247	−0.387038
$95$	14.8201	1.52051
$96$	1.00000	0.102062
$97$	−7.86027	−0.798089	−0.399045	−	0.916931i	$-0.630658\pi$
$97$	−7.86027	−0.798089	−0.399045	+	0.916931i	$0.630658\pi$
$98$	−3.98214	−0.402256
$99$	1.28494	0.129141
$100$	−1.32458	−0.132458
$101$	−1.73371	−0.172510	−0.0862551	−	0.996273i	$-0.527490\pi$
$101$	−1.73371	−0.172510	−0.0862551	+	0.996273i	$0.527490\pi$
$102$	−1.00000	−0.0990148
$103$	−1.41528	−0.139452	−0.0697260	−	0.997566i	$-0.522212\pi$
$103$	−1.41528	−0.139452	−0.0697260	+	0.997566i	$0.522212\pi$
$104$	5.11248	0.501320
$105$	3.33045	0.325019
$106$	−1.44997	−0.140833
$107$	−3.01879	−0.291837	−0.145919	−	0.989297i	$-0.546614\pi$
$107$	−3.01879	−0.291837	−0.145919	+	0.989297i	$0.546614\pi$
$108$	1.00000	0.0962250
$109$	−13.9415	−1.33535	−0.667677	−	0.744451i	$-0.732711\pi$
$109$	−13.9415	−1.33535	−0.667677	+	0.744451i	$0.732711\pi$
$110$	−2.46340	−0.234876
$111$	10.2678	0.974579
$112$	−1.73720	−0.164150
$113$	−5.10698	−0.480424	−0.240212	−	0.970720i	$-0.577217\pi$
$113$	−5.10698	−0.480424	−0.240212	+	0.970720i	$0.577217\pi$
$114$	−7.73033	−0.724012
$115$	13.1301	1.22438
$116$	−8.97540	−0.833345
$117$	5.11248	0.472649
$118$	−1.00000	−0.0920575
$119$	1.73720	0.159249
$120$	−1.91714	−0.175010
$121$	−9.34894	−0.849904
$122$	3.44485	0.311882
$123$	−1.72781	−0.155791
$124$	−0.566291	−0.0508544
$125$	12.1251	1.08450
$126$	−1.73720	−0.154762
$127$	3.30214	0.293017	0.146509	−	0.989209i	$-0.453196\pi$
$127$	3.30214	0.293017	0.146509	+	0.989209i	$0.453196\pi$
$128$	1.00000	0.0883883
$129$	7.67402	0.675660
$130$	−9.80134	−0.859635
$131$	7.71494	0.674058	0.337029	−	0.941494i	$-0.390578\pi$
$131$	7.71494	0.674058	0.337029	+	0.941494i	$0.390578\pi$
$132$	1.28494	0.111839
$133$	13.4291	1.16445
$134$	−1.48219	−0.128042
$135$	−1.91714	−0.165001
$136$	−1.00000	−0.0857493
$137$	−16.2055	−1.38453	−0.692264	−	0.721644i	$-0.743387\pi$
$137$	−16.2055	−1.38453	−0.692264	+	0.721644i	$0.743387\pi$
$138$	−6.84877	−0.583006
$139$	0.110185	0.00934575	0.00467287	−	0.999989i	$-0.498513\pi$
$139$	0.110185	0.00934575	0.00467287	+	0.999989i	$0.498513\pi$
$140$	3.33045	0.281475
$141$	−3.75247	−0.316015
$142$	−5.61916	−0.471549
$143$	6.56921	0.549345
$144$	1.00000	0.0833333
$145$	17.2071	1.42897
$146$	−7.84373	−0.649152
$147$	−3.98214	−0.328441
$148$	10.2678	0.844010
$149$	6.71045	0.549741	0.274871	−	0.961481i	$-0.411365\pi$
$149$	6.71045	0.549741	0.274871	+	0.961481i	$0.411365\pi$
$150$	−1.32458	−0.108151
$151$	−10.5069	−0.855038	−0.427519	−	0.904006i	$-0.640612\pi$
$151$	−10.5069	−0.855038	−0.427519	+	0.904006i	$0.640612\pi$
$152$	−7.73033	−0.627013
$153$	−1.00000	−0.0808452
$154$	−2.23219	−0.179875
$155$	1.08566	0.0872022
$156$	5.11248	0.409326
$157$	12.7990	1.02148	0.510738	−	0.859737i	$-0.329372\pi$
$157$	12.7990	1.02148	0.510738	+	0.859737i	$0.329372\pi$
$158$	−1.87056	−0.148814
$159$	−1.44997	−0.114990
$160$	−1.91714	−0.151563
$161$	11.8977	0.937669
$162$	1.00000	0.0785674
$163$	13.0713	1.02382	0.511910	−	0.859039i	$-0.328938\pi$
$163$	13.0713	1.02382	0.511910	+	0.859039i	$0.328938\pi$
$164$	−1.72781	−0.134919
$165$	−2.46340	−0.191776
$166$	1.97044	0.152935
$167$	6.91888	0.535399	0.267700	−	0.963502i	$-0.413737\pi$
$167$	6.91888	0.535399	0.267700	+	0.963502i	$0.413737\pi$
$168$	−1.73720	−0.134028
$169$	13.1375	1.01058
$170$	1.91714	0.147038
$171$	−7.73033	−0.591153
$172$	7.67402	0.585139
$173$	−15.0096	−1.14116	−0.570579	−	0.821243i	$-0.693281\pi$
$173$	−15.0096	−1.14116	−0.570579	+	0.821243i	$0.693281\pi$
$174$	−8.97540	−0.680424
$175$	2.30105	0.173943
$176$	1.28494	0.0968557
$177$	−1.00000	−0.0751646
$178$	−2.34832	−0.176014
$179$	8.65566	0.646954	0.323477	−	0.946236i	$-0.395148\pi$
$179$	8.65566	0.646954	0.323477	+	0.946236i	$0.395148\pi$
$180$	−1.91714	−0.142895
$181$	−22.3531	−1.66149	−0.830745	−	0.556654i	$-0.812085\pi$
$181$	−22.3531	−1.66149	−0.830745	+	0.556654i	$0.812085\pi$
$182$	−8.88140	−0.658334
$183$	3.44485	0.254650
$184$	−6.84877	−0.504898
$185$	−19.6849	−1.44726
$186$	−0.566291	−0.0415225
$187$	−1.28494	−0.0939638
$188$	−3.75247	−0.273677
$189$	−1.73720	−0.126363
$190$	14.8201	1.07517
$191$	15.1504	1.09624	0.548122	−	0.836399i	$-0.315343\pi$
$191$	15.1504	1.09624	0.548122	+	0.836399i	$0.315343\pi$
$192$	1.00000	0.0721688
$193$	−3.89893	−0.280651	−0.140326	−	0.990105i	$-0.544815\pi$
$193$	−3.89893	−0.280651	−0.140326	+	0.990105i	$0.544815\pi$
$194$	−7.86027	−0.564334
$195$	−9.80134	−0.701889
$196$	−3.98214	−0.284438
$197$	−21.6736	−1.54418	−0.772089	−	0.635514i	$-0.780788\pi$
$197$	−21.6736	−1.54418	−0.772089	+	0.635514i	$0.780788\pi$
$198$	1.28494	0.0913164
$199$	−17.0586	−1.20925	−0.604625	−	0.796510i	$-0.706677\pi$
$199$	−17.0586	−1.20925	−0.604625	+	0.796510i	$0.706677\pi$
$200$	−1.32458	−0.0936616
$201$	−1.48219	−0.104546
$202$	−1.73371	−0.121983
$203$	15.5921	1.09435
$204$	−1.00000	−0.0700140
$205$	3.31245	0.231352
$206$	−1.41528	−0.0986074
$207$	−6.84877	−0.476023
$208$	5.11248	0.354487
$209$	−9.93299	−0.687079
$210$	3.33045	0.229823
$211$	8.03340	0.553042	0.276521	−	0.961008i	$-0.410818\pi$
$211$	8.03340	0.553042	0.276521	+	0.961008i	$0.410818\pi$
$212$	−1.44997	−0.0995841
$213$	−5.61916	−0.385018
$214$	−3.01879	−0.206360
$215$	−14.7122	−1.00336
$216$	1.00000	0.0680414
$217$	0.983761	0.0667820
$218$	−13.9415	−0.944238
$219$	−7.84373	−0.530030
$220$	−2.46340	−0.166083
$221$	−5.11248	−0.343903
$222$	10.2678	0.689131
$223$	15.7871	1.05718	0.528592	−	0.848876i	$-0.322720\pi$
$223$	15.7871	1.05718	0.528592	+	0.848876i	$0.322720\pi$
$224$	−1.73720	−0.116072
$225$	−1.32458	−0.0883050
$226$	−5.10698	−0.339711
$227$	9.87432	0.655382	0.327691	−	0.944785i	$-0.393730\pi$
$227$	9.87432	0.655382	0.327691	+	0.944785i	$0.393730\pi$
$228$	−7.73033	−0.511954
$229$	−20.8962	−1.38086	−0.690429	−	0.723400i	$-0.742578\pi$
$229$	−20.8962	−1.38086	−0.690429	+	0.723400i	$0.742578\pi$
$230$	13.1301	0.865770
$231$	−2.23219	−0.146867
$232$	−8.97540	−0.589264
$233$	−12.5120	−0.819690	−0.409845	−	0.912155i	$-0.634417\pi$
$233$	−12.5120	−0.819690	−0.409845	+	0.912155i	$0.634417\pi$
$234$	5.11248	0.334213
$235$	7.19402	0.469286
$236$	−1.00000	−0.0650945
$237$	−1.87056	−0.121506
$238$	1.73720	0.112606
$239$	−22.7109	−1.46905	−0.734524	−	0.678583i	$-0.762595\pi$
$239$	−22.7109	−1.46905	−0.734524	+	0.678583i	$0.762595\pi$
$240$	−1.91714	−0.123751
$241$	−10.7060	−0.689631	−0.344816	−	0.938670i	$-0.612059\pi$
$241$	−10.7060	−0.689631	−0.344816	+	0.938670i	$0.612059\pi$
$242$	−9.34894	−0.600973
$243$	1.00000	0.0641500
$244$	3.44485	0.220534
$245$	7.63431	0.487738
$246$	−1.72781	−0.110161
$247$	−39.5212	−2.51467
$248$	−0.566291	−0.0359595
$249$	1.97044	0.124871
$250$	12.1251	0.766858
$251$	9.46374	0.597346	0.298673	−	0.954356i	$-0.403456\pi$
$251$	9.46374	0.597346	0.298673	+	0.954356i	$0.403456\pi$
$252$	−1.73720	−0.109433
$253$	−8.80023	−0.553266
$254$	3.30214	0.207194
$255$	1.91714	0.120056
$256$	1.00000	0.0625000
$257$	−14.8435	−0.925913	−0.462956	−	0.886381i	$-0.653211\pi$
$257$	−14.8435	−0.925913	−0.462956	+	0.886381i	$0.653211\pi$
$258$	7.67402	0.477764
$259$	−17.8373	−1.10835
$260$	−9.80134	−0.607853
$261$	−8.97540	−0.555564
$262$	7.71494	0.476631
$263$	−5.74841	−0.354462	−0.177231	−	0.984169i	$-0.556714\pi$
$263$	−5.74841	−0.354462	−0.177231	+	0.984169i	$0.556714\pi$
$264$	1.28494	0.0790824
$265$	2.77979	0.170761
$266$	13.4291	0.823393
$267$	−2.34832	−0.143715
$268$	−1.48219	−0.0905391
$269$	−8.81234	−0.537298	−0.268649	−	0.963238i	$-0.586577\pi$
$269$	−8.81234	−0.537298	−0.268649	+	0.963238i	$0.586577\pi$
$270$	−1.91714	−0.116673
$271$	20.7830	1.26248	0.631238	−	0.775589i	$-0.282547\pi$
$271$	20.7830	1.26248	0.631238	+	0.775589i	$0.282547\pi$
$272$	−1.00000	−0.0606339
$273$	−8.88140	−0.537527
$274$	−16.2055	−0.979010
$275$	−1.70200	−0.102634
$276$	−6.84877	−0.412248
$277$	12.8217	0.770383	0.385192	−	0.922837i	$-0.374135\pi$
$277$	12.8217	0.770383	0.385192	+	0.922837i	$0.374135\pi$
$278$	0.110185	0.00660844
$279$	−0.566291	−0.0339030
$280$	3.33045	0.199033
$281$	−5.85528	−0.349297	−0.174648	−	0.984631i	$-0.555879\pi$
$281$	−5.85528	−0.349297	−0.174648	+	0.984631i	$0.555879\pi$
$282$	−3.75247	−0.223457
$283$	−4.59355	−0.273058	−0.136529	−	0.990636i	$-0.543595\pi$
$283$	−4.59355	−0.273058	−0.136529	+	0.990636i	$0.543595\pi$
$284$	−5.61916	−0.333436
$285$	14.8201	0.877869
$286$	6.56921	0.388446
$287$	3.00155	0.177176
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	17.2071	1.01044
$291$	−7.86027	−0.460777
$292$	−7.84373	−0.459020
$293$	−3.20280	−0.187110	−0.0935548	−	0.995614i	$-0.529823\pi$
$293$	−3.20280	−0.187110	−0.0935548	+	0.995614i	$0.529823\pi$
$294$	−3.98214	−0.232243
$295$	1.91714	0.111620
$296$	10.2678	0.596805
$297$	1.28494	0.0745596
$298$	6.71045	0.388726
$299$	−35.0142	−2.02492
$300$	−1.32458	−0.0764744
$301$	−13.3313	−0.768404
$302$	−10.5069	−0.604603
$303$	−1.73371	−0.0995988
$304$	−7.73033	−0.443365
$305$	−6.60425	−0.378158
$306$	−1.00000	−0.0571662
$307$	13.7350	0.783899	0.391949	−	0.919987i	$-0.371801\pi$
$307$	13.7350	0.783899	0.391949	+	0.919987i	$0.371801\pi$
$308$	−2.23219	−0.127191
$309$	−1.41528	−0.0805126
$310$	1.08566	0.0616613
$311$	−11.8131	−0.669859	−0.334930	−	0.942243i	$-0.608713\pi$
$311$	−11.8131	−0.669859	−0.334930	+	0.942243i	$0.608713\pi$
$312$	5.11248	0.289437
$313$	3.89605	0.220218	0.110109	−	0.993920i	$-0.464880\pi$
$313$	3.89605	0.220218	0.110109	+	0.993920i	$0.464880\pi$
$314$	12.7990	0.722292
$315$	3.33045	0.187650
$316$	−1.87056	−0.105227
$317$	30.0568	1.68816	0.844078	−	0.536220i	$-0.180148\pi$
$317$	30.0568	1.68816	0.844078	+	0.536220i	$0.180148\pi$
$318$	−1.44997	−0.0813101
$319$	−11.5328	−0.645714
$320$	−1.91714	−0.107171
$321$	−3.01879	−0.168492
$322$	11.8977	0.663032
$323$	7.73033	0.430127
$324$	1.00000	0.0555556
$325$	−6.77187	−0.375636
$326$	13.0713	0.723951
$327$	−13.9415	−0.770967
$328$	−1.72781	−0.0954023
$329$	6.51880	0.359393
$330$	−2.46340	−0.135606
$331$	1.37632	0.0756494	0.0378247	−	0.999284i	$-0.487957\pi$
$331$	1.37632	0.0756494	0.0378247	+	0.999284i	$0.487957\pi$
$332$	1.97044	0.108142
$333$	10.2678	0.562673
$334$	6.91888	0.378584
$335$	2.84156	0.155251
$336$	−1.73720	−0.0947720
$337$	−16.0466	−0.874112	−0.437056	−	0.899434i	$-0.643979\pi$
$337$	−16.0466	−0.874112	−0.437056	+	0.899434i	$0.643979\pi$
$338$	13.1375	0.714585
$339$	−5.10698	−0.277373
$340$	1.91714	0.103971
$341$	−0.727648	−0.0394043
$342$	−7.73033	−0.418009
$343$	19.0782	1.03012
$344$	7.67402	0.413755
$345$	13.1301	0.706898
$346$	−15.0096	−0.806921
$347$	−5.57270	−0.299158	−0.149579	−	0.988750i	$-0.547792\pi$
$347$	−5.57270	−0.299158	−0.149579	+	0.988750i	$0.547792\pi$
$348$	−8.97540	−0.481132
$349$	27.5890	1.47681	0.738403	−	0.674360i	$-0.235580\pi$
$349$	27.5890	1.47681	0.738403	+	0.674360i	$0.235580\pi$
$350$	2.30105	0.122996
$351$	5.11248	0.272884
$352$	1.28494	0.0684873
$353$	−0.822979	−0.0438027	−0.0219014	−	0.999760i	$-0.506972\pi$
$353$	−0.822979	−0.0438027	−0.0219014	+	0.999760i	$0.506972\pi$
$354$	−1.00000	−0.0531494
$355$	10.7727	0.571756
$356$	−2.34832	−0.124461
$357$	1.73720	0.0919424
$358$	8.65566	0.457466
$359$	−8.77243	−0.462991	−0.231496	−	0.972836i	$-0.574362\pi$
$359$	−8.77243	−0.462991	−0.231496	+	0.972836i	$0.574362\pi$
$360$	−1.91714	−0.101042
$361$	40.7581	2.14516
$362$	−22.3531	−1.17485
$363$	−9.34894	−0.490692
$364$	−8.88140	−0.465512
$365$	15.0375	0.787100
$366$	3.44485	0.180065
$367$	−26.9735	−1.40800	−0.704002	−	0.710198i	$-0.748606\pi$
$367$	−26.9735	−1.40800	−0.704002	+	0.710198i	$0.748606\pi$
$368$	−6.84877	−0.357017
$369$	−1.72781	−0.0899461
$370$	−19.6849	−1.02337
$371$	2.51888	0.130774
$372$	−0.566291	−0.0293608
$373$	20.8200	1.07802	0.539011	−	0.842299i	$-0.318798\pi$
$373$	20.8200	1.07802	0.539011	+	0.842299i	$0.318798\pi$
$374$	−1.28494	−0.0664425
$375$	12.1251	0.626137
$376$	−3.75247	−0.193519
$377$	−45.8866	−2.36328
$378$	−1.73720	−0.0893519
$379$	−15.5277	−0.797602	−0.398801	−	0.917037i	$-0.630574\pi$
$379$	−15.5277	−0.797602	−0.398801	+	0.917037i	$0.630574\pi$
$380$	14.8201	0.760257
$381$	3.30214	0.169174
$382$	15.1504	0.775161
$383$	26.3858	1.34825	0.674125	−	0.738617i	$-0.264521\pi$
$383$	26.3858	1.34825	0.674125	+	0.738617i	$0.264521\pi$
$384$	1.00000	0.0510310
$385$	4.27942	0.218100
$386$	−3.89893	−0.198450
$387$	7.67402	0.390092
$388$	−7.86027	−0.399045
$389$	−9.77241	−0.495481	−0.247740	−	0.968826i	$-0.579688\pi$
$389$	−9.77241	−0.495481	−0.247740	+	0.968826i	$0.579688\pi$
$390$	−9.80134	−0.496310
$391$	6.84877	0.346357
$392$	−3.98214	−0.201128
$393$	7.71494	0.389167
$394$	−21.6736	−1.09190
$395$	3.58613	0.180438
$396$	1.28494	0.0645705
$397$	36.5480	1.83429	0.917146	−	0.398551i	$-0.130487\pi$
$397$	36.5480	1.83429	0.917146	+	0.398551i	$0.130487\pi$
$398$	−17.0586	−0.855069
$399$	13.4291	0.672298
$400$	−1.32458	−0.0662288
$401$	−29.0374	−1.45006	−0.725028	−	0.688719i	$-0.758173\pi$
$401$	−29.0374	−1.45006	−0.725028	+	0.688719i	$0.758173\pi$
$402$	−1.48219	−0.0739249
$403$	−2.89515	−0.144218
$404$	−1.73371	−0.0862551
$405$	−1.91714	−0.0952634
$406$	15.5921	0.773821
$407$	13.1935	0.653978
$408$	−1.00000	−0.0495074
$409$	−13.9679	−0.690670	−0.345335	−	0.938479i	$-0.612235\pi$
$409$	−13.9679	−0.690670	−0.345335	+	0.938479i	$0.612235\pi$
$410$	3.31245	0.163590
$411$	−16.2055	−0.799358
$412$	−1.41528	−0.0697260
$413$	1.73720	0.0854820
$414$	−6.84877	−0.336599
$415$	−3.77760	−0.185435
$416$	5.11248	0.250660
$417$	0.110185	0.00539577
$418$	−9.93299	−0.485838
$419$	34.0628	1.66408	0.832039	−	0.554717i	$-0.187174\pi$
$419$	34.0628	1.66408	0.832039	+	0.554717i	$0.187174\pi$
$420$	3.33045	0.162510
$421$	16.9425	0.825728	0.412864	−	0.910793i	$-0.364528\pi$
$421$	16.9425	0.825728	0.412864	+	0.910793i	$0.364528\pi$
$422$	8.03340	0.391060
$423$	−3.75247	−0.182452
$424$	−1.44997	−0.0704166
$425$	1.32458	0.0642514
$426$	−5.61916	−0.272249
$427$	−5.98439	−0.289605
$428$	−3.01879	−0.145919
$429$	6.56921	0.317165
$430$	−14.7122	−0.709484
$431$	15.4017	0.741876	0.370938	−	0.928658i	$-0.379036\pi$
$431$	15.4017	0.741876	0.370938	+	0.928658i	$0.379036\pi$
$432$	1.00000	0.0481125
$433$	32.3763	1.55591	0.777954	−	0.628322i	$-0.216258\pi$
$433$	32.3763	1.55591	0.777954	+	0.628322i	$0.216258\pi$
$434$	0.983761	0.0472220
$435$	17.2071	0.825017
$436$	−13.9415	−0.667677
$437$	52.9433	2.53262
$438$	−7.84373	−0.374788
$439$	32.5161	1.55191	0.775953	−	0.630790i	$-0.217269\pi$
$439$	32.5161	1.55191	0.775953	+	0.630790i	$0.217269\pi$
$440$	−2.46340	−0.117438
$441$	−3.98214	−0.189626
$442$	−5.11248	−0.243176
$443$	34.1437	1.62222	0.811108	−	0.584896i	$-0.198865\pi$
$443$	34.1437	1.62222	0.811108	+	0.584896i	$0.198865\pi$
$444$	10.2678	0.487289
$445$	4.50205	0.213418
$446$	15.7871	0.747543
$447$	6.71045	0.317393
$448$	−1.73720	−0.0820750
$449$	−39.8455	−1.88042	−0.940212	−	0.340590i	$-0.889373\pi$
$449$	−39.8455	−1.88042	−0.940212	+	0.340590i	$0.889373\pi$
$450$	−1.32458	−0.0624411
$451$	−2.22012	−0.104542
$452$	−5.10698	−0.240212
$453$	−10.5069	−0.493656
$454$	9.87432	0.463425
$455$	17.0269	0.798233
$456$	−7.73033	−0.362006
$457$	2.00194	0.0936469	0.0468235	−	0.998903i	$-0.485090\pi$
$457$	2.00194	0.0936469	0.0468235	+	0.998903i	$0.485090\pi$
$458$	−20.8962	−0.976414
$459$	−1.00000	−0.0466760
$460$	13.1301	0.612192
$461$	−21.9266	−1.02122	−0.510612	−	0.859811i	$-0.670581\pi$
$461$	−21.9266	−1.02122	−0.510612	+	0.859811i	$0.670581\pi$
$462$	−2.23219	−0.103851
$463$	7.35505	0.341818	0.170909	−	0.985287i	$-0.445330\pi$
$463$	7.35505	0.341818	0.170909	+	0.985287i	$0.445330\pi$
$464$	−8.97540	−0.416673
$465$	1.08566	0.0503462
$466$	−12.5120	−0.579609
$467$	−24.9230	−1.15330	−0.576649	−	0.816992i	$-0.695640\pi$
$467$	−24.9230	−1.15330	−0.576649	+	0.816992i	$0.695640\pi$
$468$	5.11248	0.236325
$469$	2.57486	0.118896
$470$	7.19402	0.331835
$471$	12.7990	0.589749
$472$	−1.00000	−0.0460287
$473$	9.86063	0.453392
$474$	−1.87056	−0.0859179
$475$	10.2394	0.469816
$476$	1.73720	0.0796244
$477$	−1.44997	−0.0663894
$478$	−22.7109	−1.03877
$479$	−4.81095	−0.219818	−0.109909	−	0.993942i	$-0.535056\pi$
$479$	−4.81095	−0.219818	−0.109909	+	0.993942i	$0.535056\pi$
$480$	−1.91714	−0.0875051
$481$	52.4941	2.39352
$482$	−10.7060	−0.487643
$483$	11.8977	0.541363
$484$	−9.34894	−0.424952
$485$	15.0692	0.684259
$486$	1.00000	0.0453609
$487$	0.811925	0.0367918	0.0183959	−	0.999831i	$-0.494144\pi$
$487$	0.811925	0.0367918	0.0183959	+	0.999831i	$0.494144\pi$
$488$	3.44485	0.155941
$489$	13.0713	0.591103
$490$	7.63431	0.344883
$491$	−20.2799	−0.915220	−0.457610	−	0.889153i	$-0.651294\pi$
$491$	−20.2799	−0.915220	−0.457610	+	0.889153i	$0.651294\pi$
$492$	−1.72781	−0.0778956
$493$	8.97540	0.404232
$494$	−39.5212	−1.77814
$495$	−2.46340	−0.110722
$496$	−0.566291	−0.0254272
$497$	9.76160	0.437867
$498$	1.97044	0.0882973
$499$	−41.7313	−1.86815	−0.934074	−	0.357080i	$-0.883772\pi$
$499$	−41.7313	−1.86815	−0.934074	+	0.357080i	$0.883772\pi$
$500$	12.1251	0.542251
$501$	6.91888	0.309113
$502$	9.46374	0.422387
$503$	24.9445	1.11222	0.556110	−	0.831109i	$-0.312293\pi$
$503$	24.9445	1.11222	0.556110	+	0.831109i	$0.312293\pi$
$504$	−1.73720	−0.0773810
$505$	3.32376	0.147905
$506$	−8.80023	−0.391218
$507$	13.1375	0.583456
$508$	3.30214	0.146509
$509$	4.90029	0.217201	0.108601	−	0.994085i	$-0.465363\pi$
$509$	4.90029	0.217201	0.108601	+	0.994085i	$0.465363\pi$
$510$	1.91714	0.0848924
$511$	13.6261	0.602785
$512$	1.00000	0.0441942
$513$	−7.73033	−0.341303
$514$	−14.8435	−0.654719
$515$	2.71329	0.119562
$516$	7.67402	0.337830
$517$	−4.82169	−0.212058
$518$	−17.8373	−0.783725
$519$	−15.0096	−0.658848
$520$	−9.80134	−0.429817
$521$	−11.3212	−0.495989	−0.247995	−	0.968761i	$-0.579772\pi$
$521$	−11.3212	−0.495989	−0.247995	+	0.968761i	$0.579772\pi$
$522$	−8.97540	−0.392843
$523$	4.72874	0.206773	0.103387	−	0.994641i	$-0.467032\pi$
$523$	4.72874	0.206773	0.103387	+	0.994641i	$0.467032\pi$
$524$	7.71494	0.337029
$525$	2.30105	0.100426
$526$	−5.74841	−0.250643
$527$	0.566291	0.0246680
$528$	1.28494	0.0559197
$529$	23.9057	1.03938
$530$	2.77979	0.120746
$531$	−1.00000	−0.0433963
$532$	13.4291	0.582227
$533$	−8.83339	−0.382617
$534$	−2.34832	−0.101622
$535$	5.78744	0.250213
$536$	−1.48219	−0.0640208
$537$	8.65566	0.373519
$538$	−8.81234	−0.379927
$539$	−5.11679	−0.220396
$540$	−1.91714	−0.0825006
$541$	−17.7011	−0.761028	−0.380514	−	0.924775i	$-0.624253\pi$
$541$	−17.7011	−0.761028	−0.380514	+	0.924775i	$0.624253\pi$
$542$	20.7830	0.892705
$543$	−22.3531	−0.959261
$544$	−1.00000	−0.0428746
$545$	26.7278	1.14489
$546$	−8.88140	−0.380089
$547$	14.0475	0.600628	0.300314	−	0.953840i	$-0.402909\pi$
$547$	14.0475	0.600628	0.300314	+	0.953840i	$0.402909\pi$
$548$	−16.2055	−0.692264
$549$	3.44485	0.147022
$550$	−1.70200	−0.0725733
$551$	69.3829	2.95581
$552$	−6.84877	−0.291503
$553$	3.24955	0.138185
$554$	12.8217	0.544743
$555$	−19.6849	−0.835576
$556$	0.110185	0.00467287
$557$	15.8939	0.673445	0.336722	−	0.941604i	$-0.390682\pi$
$557$	15.8939	0.673445	0.336722	+	0.941604i	$0.390682\pi$
$558$	−0.566291	−0.0239730
$559$	39.2333	1.65939
$560$	3.33045	0.140737
$561$	−1.28494	−0.0542500
$562$	−5.85528	−0.246990
$563$	−20.7996	−0.876600	−0.438300	−	0.898829i	$-0.644419\pi$
$563$	−20.7996	−0.876600	−0.438300	+	0.898829i	$0.644419\pi$
$564$	−3.75247	−0.158008
$565$	9.79079	0.411901
$566$	−4.59355	−0.193081
$567$	−1.73720	−0.0729555
$568$	−5.61916	−0.235775
$569$	−32.6274	−1.36781	−0.683905	−	0.729571i	$-0.739720\pi$
$569$	−32.6274	−1.36781	−0.683905	+	0.729571i	$0.739720\pi$
$570$	14.8201	0.620747
$571$	−15.5408	−0.650363	−0.325182	−	0.945652i	$-0.605425\pi$
$571$	−15.5408	−0.650363	−0.325182	+	0.945652i	$0.605425\pi$
$572$	6.56921	0.274673
$573$	15.1504	0.632916
$574$	3.00155	0.125282
$575$	9.07172	0.378317
$576$	1.00000	0.0416667
$577$	40.1762	1.67256	0.836280	−	0.548303i	$-0.184726\pi$
$577$	40.1762	1.67256	0.836280	+	0.548303i	$0.184726\pi$
$578$	1.00000	0.0415945
$579$	−3.89893	−0.162034
$580$	17.2071	0.714486
$581$	−3.42304	−0.142012
$582$	−7.86027	−0.325819
$583$	−1.86311	−0.0771623
$584$	−7.84373	−0.324576
$585$	−9.80134	−0.405236
$586$	−3.20280	−0.132306
$587$	4.20337	0.173492	0.0867459	−	0.996230i	$-0.472353\pi$
$587$	4.20337	0.173492	0.0867459	+	0.996230i	$0.472353\pi$
$588$	−3.98214	−0.164221
$589$	4.37762	0.180377
$590$	1.91714	0.0789274
$591$	−21.6736	−0.891532
$592$	10.2678	0.422005
$593$	5.67986	0.233244	0.116622	−	0.993176i	$-0.462793\pi$
$593$	5.67986	0.233244	0.116622	+	0.993176i	$0.462793\pi$
$594$	1.28494	0.0527216
$595$	−3.33045	−0.136535
$596$	6.71045	0.274871
$597$	−17.0586	−0.698161
$598$	−35.0142	−1.43184
$599$	22.0473	0.900827	0.450413	−	0.892820i	$-0.351277\pi$
$599$	22.0473	0.900827	0.450413	+	0.892820i	$0.351277\pi$
$600$	−1.32458	−0.0540756
$601$	30.3356	1.23742	0.618708	−	0.785621i	$-0.287656\pi$
$601$	30.3356	1.23742	0.618708	+	0.785621i	$0.287656\pi$
$602$	−13.3313	−0.543344
$603$	−1.48219	−0.0603594
$604$	−10.5069	−0.427519
$605$	17.9232	0.728683
$606$	−1.73371	−0.0704270
$607$	22.0852	0.896411	0.448206	−	0.893931i	$-0.352063\pi$
$607$	22.0852	0.896411	0.448206	+	0.893931i	$0.352063\pi$
$608$	−7.73033	−0.313506
$609$	15.5921	0.631823
$610$	−6.60425	−0.267398
$611$	−19.1845	−0.776120
$612$	−1.00000	−0.0404226
$613$	24.0995	0.973370	0.486685	−	0.873577i	$-0.338206\pi$
$613$	24.0995	0.973370	0.486685	+	0.873577i	$0.338206\pi$
$614$	13.7350	0.554300
$615$	3.31245	0.133571
$616$	−2.23219	−0.0899375
$617$	37.8055	1.52199	0.760996	−	0.648756i	$-0.224710\pi$
$617$	37.8055	1.52199	0.760996	+	0.648756i	$0.224710\pi$
$618$	−1.41528	−0.0569310
$619$	−20.2892	−0.815494	−0.407747	−	0.913095i	$-0.633685\pi$
$619$	−20.2892	−0.815494	−0.407747	+	0.913095i	$0.633685\pi$
$620$	1.08566	0.0436011
$621$	−6.84877	−0.274832
$622$	−11.8131	−0.473662
$623$	4.07950	0.163442
$624$	5.11248	0.204663
$625$	−16.6226	−0.664905
$626$	3.89605	0.155718
$627$	−9.93299	−0.396685
$628$	12.7990	0.510738
$629$	−10.2678	−0.409405
$630$	3.33045	0.132689
$631$	−21.9875	−0.875308	−0.437654	−	0.899144i	$-0.644190\pi$
$631$	−21.9875	−0.875308	−0.437654	+	0.899144i	$0.644190\pi$
$632$	−1.87056	−0.0744071
$633$	8.03340	0.319299
$634$	30.0568	1.19371
$635$	−6.33066	−0.251224
$636$	−1.44997	−0.0574949
$637$	−20.3586	−0.806637
$638$	−11.5328	−0.456589
$639$	−5.61916	−0.222290
$640$	−1.91714	−0.0757816
$641$	2.85239	0.112663	0.0563313	−	0.998412i	$-0.482060\pi$
$641$	2.85239	0.112663	0.0563313	+	0.998412i	$0.482060\pi$
$642$	−3.01879	−0.119142
$643$	−5.58227	−0.220143	−0.110072	−	0.993924i	$-0.535108\pi$
$643$	−5.58227	−0.220143	−0.110072	+	0.993924i	$0.535108\pi$
$644$	11.8977	0.468834
$645$	−14.7122	−0.579291
$646$	7.73033	0.304146
$647$	−31.4485	−1.23637	−0.618184	−	0.786034i	$-0.712131\pi$
$647$	−31.4485	−1.23637	−0.618184	+	0.786034i	$0.712131\pi$
$648$	1.00000	0.0392837
$649$	−1.28494	−0.0504382
$650$	−6.77187	−0.265615
$651$	0.983761	0.0385566
$652$	13.0713	0.511910
$653$	9.77199	0.382408	0.191204	−	0.981550i	$-0.438761\pi$
$653$	9.77199	0.382408	0.191204	+	0.981550i	$0.438761\pi$
$654$	−13.9415	−0.545156
$655$	−14.7906	−0.577917
$656$	−1.72781	−0.0674596
$657$	−7.84373	−0.306013
$658$	6.51880	0.254129
$659$	−12.8030	−0.498733	−0.249366	−	0.968409i	$-0.580222\pi$
$659$	−12.8030	−0.498733	−0.249366	+	0.968409i	$0.580222\pi$
$660$	−2.46340	−0.0958878
$661$	31.7658	1.23555	0.617773	−	0.786356i	$-0.288035\pi$
$661$	31.7658	1.23555	0.617773	+	0.786356i	$0.288035\pi$
$662$	1.37632	0.0534922
$663$	−5.11248	−0.198552
$664$	1.97044	0.0764677
$665$	−25.7455	−0.998369
$666$	10.2678	0.397870
$667$	61.4705	2.38015
$668$	6.91888	0.267700
$669$	15.7871	0.610366
$670$	2.84156	0.109779
$671$	4.42641	0.170880
$672$	−1.73720	−0.0670139
$673$	−15.6456	−0.603095	−0.301548	−	0.953451i	$-0.597503\pi$
$673$	−15.6456	−0.603095	−0.301548	+	0.953451i	$0.597503\pi$
$674$	−16.0466	−0.618090
$675$	−1.32458	−0.0509829
$676$	13.1375	0.505288
$677$	−29.9625	−1.15155	−0.575777	−	0.817607i	$-0.695300\pi$
$677$	−29.9625	−1.15155	−0.575777	+	0.817607i	$0.695300\pi$
$678$	−5.10698	−0.196132
$679$	13.6549	0.524025
$680$	1.91714	0.0735189
$681$	9.87432	0.378385
$682$	−0.727648	−0.0278631
$683$	−50.3860	−1.92797	−0.963984	−	0.265959i	$-0.914311\pi$
$683$	−50.3860	−1.92797	−0.963984	+	0.265959i	$0.914311\pi$
$684$	−7.73033	−0.295577
$685$	31.0682	1.18705
$686$	19.0782	0.728408
$687$	−20.8962	−0.797239
$688$	7.67402	0.292569
$689$	−7.41293	−0.282410
$690$	13.1301	0.499852
$691$	17.6172	0.670191	0.335095	−	0.942184i	$-0.391231\pi$
$691$	17.6172	0.670191	0.335095	+	0.942184i	$0.391231\pi$
$692$	−15.0096	−0.570579
$693$	−2.23219	−0.0847939
$694$	−5.57270	−0.211537
$695$	−0.211240	−0.00801277
$696$	−8.97540	−0.340212
$697$	1.72781	0.0654454
$698$	27.5890	1.04426
$699$	−12.5120	−0.473248
$700$	2.30105	0.0869716
$701$	49.8081	1.88123	0.940613	−	0.339481i	$-0.110251\pi$
$701$	49.8081	1.88123	0.940613	+	0.339481i	$0.110251\pi$
$702$	5.11248	0.192958
$703$	−79.3737	−2.99364
$704$	1.28494	0.0484279
$705$	7.19402	0.270942
$706$	−0.822979	−0.0309732
$707$	3.01179	0.113270
$708$	−1.00000	−0.0375823
$709$	7.85726	0.295086	0.147543	−	0.989056i	$-0.452864\pi$
$709$	7.85726	0.295086	0.147543	+	0.989056i	$0.452864\pi$
$710$	10.7727	0.404292
$711$	−1.87056	−0.0701517
$712$	−2.34832	−0.0880070
$713$	3.87840	0.145247
$714$	1.73720	0.0650131
$715$	−12.5941	−0.470993
$716$	8.65566	0.323477
$717$	−22.7109	−0.848155
$718$	−8.77243	−0.327384
$719$	−32.1490	−1.19895	−0.599477	−	0.800392i	$-0.704625\pi$
$719$	−32.1490	−1.19895	−0.599477	+	0.800392i	$0.704625\pi$
$720$	−1.91714	−0.0714476
$721$	2.45863	0.0915641
$722$	40.7581	1.51686
$723$	−10.7060	−0.398159
$724$	−22.3531	−0.830745
$725$	11.8886	0.441532
$726$	−9.34894	−0.346972
$727$	31.4159	1.16515	0.582575	−	0.812777i	$-0.302045\pi$
$727$	31.4159	1.16515	0.582575	+	0.812777i	$0.302045\pi$
$728$	−8.88140	−0.329167
$729$	1.00000	0.0370370
$730$	15.0375	0.556564
$731$	−7.67402	−0.283834
$732$	3.44485	0.127325
$733$	4.71621	0.174197	0.0870987	−	0.996200i	$-0.472240\pi$
$733$	4.71621	0.174197	0.0870987	+	0.996200i	$0.472240\pi$
$734$	−26.9735	−0.995610
$735$	7.63431	0.281596
$736$	−6.84877	−0.252449
$737$	−1.90452	−0.0701538
$738$	−1.72781	−0.0636015
$739$	20.1245	0.740292	0.370146	−	0.928974i	$-0.379308\pi$
$739$	20.1245	0.740292	0.370146	+	0.928974i	$0.379308\pi$
$740$	−19.6849	−0.723630
$741$	−39.5212	−1.45185
$742$	2.51888	0.0924710
$743$	17.0428	0.625241	0.312621	−	0.949878i	$-0.398793\pi$
$743$	17.0428	0.625241	0.312621	+	0.949878i	$0.398793\pi$
$744$	−0.566291	−0.0207612
$745$	−12.8649	−0.471332
$746$	20.8200	0.762276
$747$	1.97044	0.0720945
$748$	−1.28494	−0.0469819
$749$	5.24424	0.191620
$750$	12.1251	0.442746
$751$	−3.34829	−0.122181	−0.0610903	−	0.998132i	$-0.519458\pi$
$751$	−3.34829	−0.122181	−0.0610903	+	0.998132i	$0.519458\pi$
$752$	−3.75247	−0.136839
$753$	9.46374	0.344878
$754$	−45.8866	−1.67109
$755$	20.1432	0.733085
$756$	−1.73720	−0.0631814
$757$	−9.84459	−0.357808	−0.178904	−	0.983867i	$-0.557255\pi$
$757$	−9.84459	−0.357808	−0.178904	+	0.983867i	$0.557255\pi$
$758$	−15.5277	−0.563990
$759$	−8.80023	−0.319428
$760$	14.8201	0.537583
$761$	−13.7456	−0.498279	−0.249139	−	0.968468i	$-0.580148\pi$
$761$	−13.7456	−0.498279	−0.249139	+	0.968468i	$0.580148\pi$
$762$	3.30214	0.119624
$763$	24.2192	0.876793
$764$	15.1504	0.548122
$765$	1.91714	0.0693143
$766$	26.3858	0.953357
$767$	−5.11248	−0.184601
$768$	1.00000	0.0360844
$769$	30.1699	1.08795	0.543977	−	0.839100i	$-0.316918\pi$
$769$	30.1699	1.08795	0.543977	+	0.839100i	$0.316918\pi$
$770$	4.27942	0.154220
$771$	−14.8435	−0.534576
$772$	−3.89893	−0.140326
$773$	15.6568	0.563135	0.281568	−	0.959541i	$-0.409146\pi$
$773$	15.6568	0.563135	0.281568	+	0.959541i	$0.409146\pi$
$774$	7.67402	0.275837
$775$	0.750095	0.0269442
$776$	−7.86027	−0.282167
$777$	−17.8373	−0.639908
$778$	−9.77241	−0.350358
$779$	13.3565	0.478548
$780$	−9.80134	−0.350944
$781$	−7.22026	−0.258361
$782$	6.84877	0.244912
$783$	−8.97540	−0.320755
$784$	−3.98214	−0.142219
$785$	−24.5376	−0.875783
$786$	7.71494	0.275183
$787$	34.8966	1.24393	0.621965	−	0.783045i	$-0.286334\pi$
$787$	34.8966	1.24393	0.621965	+	0.783045i	$0.286334\pi$
$788$	−21.6736	−0.772089
$789$	−5.74841	−0.204649
$790$	3.58613	0.127589
$791$	8.87184	0.315446
$792$	1.28494	0.0456582
$793$	17.6117	0.625411
$794$	36.5480	1.29704
$795$	2.77979	0.0985889
$796$	−17.0586	−0.604625
$797$	−7.17970	−0.254318	−0.127159	−	0.991882i	$-0.540586\pi$
$797$	−7.17970	−0.254318	−0.127159	+	0.991882i	$0.540586\pi$
$798$	13.4291	0.475386
$799$	3.75247	0.132753
$800$	−1.32458	−0.0468308
$801$	−2.34832	−0.0829738
$802$	−29.0374	−1.02534
$803$	−10.0787	−0.355669
$804$	−1.48219	−0.0522728
$805$	−22.8095	−0.803930
$806$	−2.89515	−0.101977
$807$	−8.81234	−0.310209
$808$	−1.73371	−0.0609916
$809$	−1.96543	−0.0691009	−0.0345505	−	0.999403i	$-0.511000\pi$
$809$	−1.96543	−0.0691009	−0.0345505	+	0.999403i	$0.511000\pi$
$810$	−1.91714	−0.0673614
$811$	−24.6148	−0.864341	−0.432171	−	0.901792i	$-0.642252\pi$
$811$	−24.6148	−0.864341	−0.432171	+	0.901792i	$0.642252\pi$
$812$	15.5921	0.547174
$813$	20.7830	0.728891
$814$	13.1935	0.462432
$815$	−25.0594	−0.877794
$816$	−1.00000	−0.0350070
$817$	−59.3227	−2.07544
$818$	−13.9679	−0.488378
$819$	−8.88140	−0.310341
$820$	3.31245	0.115676
$821$	14.3038	0.499207	0.249603	−	0.968348i	$-0.419700\pi$
$821$	14.3038	0.499207	0.249603	+	0.968348i	$0.419700\pi$
$822$	−16.2055	−0.565232
$823$	−32.4256	−1.13028	−0.565142	−	0.824993i	$-0.691179\pi$
$823$	−32.4256	−1.13028	−0.565142	+	0.824993i	$0.691179\pi$
$824$	−1.41528	−0.0493037
$825$	−1.70200	−0.0592559
$826$	1.73720	0.0604449
$827$	32.5012	1.13018	0.565090	−	0.825030i	$-0.308842\pi$
$827$	32.5012	1.13018	0.565090	+	0.825030i	$0.308842\pi$
$828$	−6.84877	−0.238011
$829$	−4.36056	−0.151448	−0.0757242	−	0.997129i	$-0.524127\pi$
$829$	−4.36056	−0.151448	−0.0757242	+	0.997129i	$0.524127\pi$
$830$	−3.77760	−0.131122
$831$	12.8217	0.444781
$832$	5.11248	0.177243
$833$	3.98214	0.137973
$834$	0.110185	0.00381539
$835$	−13.2645	−0.459036
$836$	−9.93299	−0.343539
$837$	−0.566291	−0.0195739
$838$	34.0628	1.17668
$839$	−44.9797	−1.55287	−0.776437	−	0.630195i	$-0.782975\pi$
$839$	−44.9797	−1.55287	−0.776437	+	0.630195i	$0.782975\pi$
$840$	3.33045	0.114912
$841$	51.5579	1.77786
$842$	16.9425	0.583878
$843$	−5.85528	−0.201666
$844$	8.03340	0.276521
$845$	−25.1864	−0.866438
$846$	−3.75247	−0.129013
$847$	16.2410	0.558047
$848$	−1.44997	−0.0497920
$849$	−4.59355	−0.157650
$850$	1.32458	0.0454326
$851$	−70.3220	−2.41061
$852$	−5.61916	−0.192509
$853$	−1.59480	−0.0546050	−0.0273025	−	0.999627i	$-0.508692\pi$
$853$	−1.59480	−0.0546050	−0.0273025	+	0.999627i	$0.508692\pi$
$854$	−5.98439	−0.204782
$855$	14.8201	0.506838
$856$	−3.01879	−0.103180
$857$	−29.7565	−1.01646	−0.508232	−	0.861220i	$-0.669701\pi$
$857$	−29.7565	−1.01646	−0.508232	+	0.861220i	$0.669701\pi$
$858$	6.56921	0.224269
$859$	−13.1623	−0.449092	−0.224546	−	0.974464i	$-0.572090\pi$
$859$	−13.1623	−0.449092	−0.224546	+	0.974464i	$0.572090\pi$
$860$	−14.7122	−0.501681
$861$	3.00155	0.102293
$862$	15.4017	0.524586
$863$	−17.9011	−0.609359	−0.304680	−	0.952455i	$-0.598549\pi$
$863$	−17.9011	−0.609359	−0.304680	+	0.952455i	$0.598549\pi$
$864$	1.00000	0.0340207
$865$	28.7755	0.978396
$866$	32.3763	1.10019
$867$	1.00000	0.0339618
$868$	0.983761	0.0333910
$869$	−2.40356	−0.0815351
$870$	17.2071	0.583375
$871$	−7.57766	−0.256759
$872$	−13.9415	−0.472119
$873$	−7.86027	−0.266030
$874$	52.9433	1.79083
$875$	−21.0637	−0.712084
$876$	−7.84373	−0.265015
$877$	15.1521	0.511649	0.255825	−	0.966723i	$-0.417653\pi$
$877$	15.1521	0.511649	0.255825	+	0.966723i	$0.417653\pi$
$878$	32.5161	1.09736
$879$	−3.20280	−0.108028
$880$	−2.46340	−0.0830413
$881$	29.3670	0.989401	0.494700	−	0.869064i	$-0.335278\pi$
$881$	29.3670	0.989401	0.494700	+	0.869064i	$0.335278\pi$
$882$	−3.98214	−0.134085
$883$	36.1586	1.21683	0.608417	−	0.793618i	$-0.291805\pi$
$883$	36.1586	1.21683	0.608417	+	0.793618i	$0.291805\pi$
$884$	−5.11248	−0.171951
$885$	1.91714	0.0644439
$886$	34.1437	1.14708
$887$	28.1790	0.946157	0.473079	−	0.881020i	$-0.343143\pi$
$887$	28.1790	0.946157	0.473079	+	0.881020i	$0.343143\pi$
$888$	10.2678	0.344566
$889$	−5.73647	−0.192395
$890$	4.50205	0.150909
$891$	1.28494	0.0430470
$892$	15.7871	0.528592
$893$	29.0079	0.970712
$894$	6.71045	0.224431
$895$	−16.5941	−0.554680
$896$	−1.73720	−0.0580358
$897$	−35.0142	−1.16909
$898$	−39.8455	−1.32966
$899$	5.08269	0.169517
$900$	−1.32458	−0.0441525
$901$	1.44997	0.0483054
$902$	−2.22012	−0.0739220
$903$	−13.3313	−0.443638
$904$	−5.10698	−0.169855
$905$	42.8539	1.42451
$906$	−10.5069	−0.349068
$907$	32.7433	1.08722	0.543611	−	0.839337i	$-0.317057\pi$
$907$	32.7433	1.08722	0.543611	+	0.839337i	$0.317057\pi$
$908$	9.87432	0.327691
$909$	−1.73371	−0.0575034
$910$	17.0269	0.564436
$911$	55.7706	1.84776	0.923881	−	0.382680i	$-0.124999\pi$
$911$	55.7706	1.84776	0.923881	+	0.382680i	$0.124999\pi$
$912$	−7.73033	−0.255977
$913$	2.53188	0.0837931
$914$	2.00194	0.0662184
$915$	−6.60425	−0.218330
$916$	−20.8962	−0.690429
$917$	−13.4024	−0.442586
$918$	−1.00000	−0.0330049
$919$	24.8298	0.819058	0.409529	−	0.912297i	$-0.365693\pi$
$919$	24.8298	0.819058	0.409529	+	0.912297i	$0.365693\pi$
$920$	13.1301	0.432885
$921$	13.7350	0.452584
$922$	−21.9266	−0.722115
$923$	−28.7278	−0.945588
$924$	−2.23219	−0.0734337
$925$	−13.6005	−0.447182
$926$	7.35505	0.241702
$927$	−1.41528	−0.0464840
$928$	−8.97540	−0.294632
$929$	−33.1278	−1.08689	−0.543444	−	0.839445i	$-0.682880\pi$
$929$	−33.1278	−1.08689	−0.543444	+	0.839445i	$0.682880\pi$
$930$	1.08566	0.0356002
$931$	30.7832	1.00888
$932$	−12.5120	−0.409845
$933$	−11.8131	−0.386743
$934$	−24.9230	−0.815505
$935$	2.46340	0.0805619
$936$	5.11248	0.167107
$937$	22.3432	0.729921	0.364960	−	0.931023i	$-0.381083\pi$
$937$	22.3432	0.729921	0.364960	+	0.931023i	$0.381083\pi$
$938$	2.57486	0.0840721
$939$	3.89605	0.127143
$940$	7.19402	0.234643
$941$	25.6656	0.836675	0.418337	−	0.908292i	$-0.362613\pi$
$941$	25.6656	0.836675	0.418337	+	0.908292i	$0.362613\pi$
$942$	12.7990	0.417015
$943$	11.8334	0.385347
$944$	−1.00000	−0.0325472
$945$	3.33045	0.108340
$946$	9.86063	0.320597
$947$	34.7603	1.12956	0.564779	−	0.825242i	$-0.308961\pi$
$947$	34.7603	1.12956	0.564779	+	0.825242i	$0.308961\pi$
$948$	−1.87056	−0.0607531
$949$	−40.1009	−1.30173
$950$	10.2394	0.332210
$951$	30.0568	0.974658
$952$	1.73720	0.0563030
$953$	−8.26641	−0.267775	−0.133888	−	0.990997i	$-0.542746\pi$
$953$	−8.26641	−0.267775	−0.133888	+	0.990997i	$0.542746\pi$
$954$	−1.44997	−0.0469444
$955$	−29.0454	−0.939887
$956$	−22.7109	−0.734524
$957$	−11.5328	−0.372803
$958$	−4.81095	−0.155435
$959$	28.1522	0.909081
$960$	−1.91714	−0.0618754
$961$	−30.6793	−0.989655
$962$	52.4941	1.69248
$963$	−3.01879	−0.0972790
$964$	−10.7060	−0.344816
$965$	7.47479	0.240622
$966$	11.8977	0.382802
$967$	11.6130	0.373449	0.186724	−	0.982412i	$-0.440213\pi$
$967$	11.6130	0.373449	0.186724	+	0.982412i	$0.440213\pi$
$968$	−9.34894	−0.300486
$969$	7.73033	0.248334
$970$	15.0692	0.483844
$971$	57.1361	1.83358	0.916792	−	0.399365i	$-0.130769\pi$
$971$	57.1361	1.83358	0.916792	+	0.399365i	$0.130769\pi$
$972$	1.00000	0.0320750
$973$	−0.191413	−0.00613642
$974$	0.811925	0.0260157
$975$	−6.77187	−0.216873
$976$	3.44485	0.110267
$977$	22.7009	0.726266	0.363133	−	0.931737i	$-0.381707\pi$
$977$	22.7009	0.726266	0.363133	+	0.931737i	$0.381707\pi$
$978$	13.0713	0.417973
$979$	−3.01744	−0.0964378
$980$	7.63431	0.243869
$981$	−13.9415	−0.445118
$982$	−20.2799	−0.647158
$983$	43.9320	1.40121	0.700606	−	0.713548i	$-0.252913\pi$
$983$	43.9320	1.40121	0.700606	+	0.713548i	$0.252913\pi$
$984$	−1.72781	−0.0550805
$985$	41.5513	1.32393
$986$	8.97540	0.285835
$987$	6.51880	0.207496
$988$	−39.5212	−1.25734
$989$	−52.5576	−1.67123
$990$	−2.46340	−0.0782921
$991$	1.78501	0.0567026	0.0283513	−	0.999598i	$-0.490974\pi$
$991$	1.78501	0.0567026	0.0283513	+	0.999598i	$0.490974\pi$
$992$	−0.566291	−0.0179798
$993$	1.37632	0.0436762
$994$	9.76160	0.309619
$995$	32.7037	1.03678
$996$	1.97044	0.0624356
$997$	−16.6291	−0.526648	−0.263324	−	0.964708i	$-0.584819\pi$
$997$	−16.6291	−0.526648	−0.263324	+	0.964708i	$0.584819\pi$
$998$	−41.7313	−1.32098
$999$	10.2678	0.324860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.r.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.r.1.2	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.91714 q^{5} +1.00000 q^{6} -1.73720 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.91714 q^{5} +1.00000 q^{6} -1.73720 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.91714 q^{10} +1.28494 q^{11} +1.00000 q^{12} +5.11248 q^{13} -1.73720 q^{14} -1.91714 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -7.73033 q^{19} -1.91714 q^{20} -1.73720 q^{21} +1.28494 q^{22} -6.84877 q^{23} +1.00000 q^{24} -1.32458 q^{25} +5.11248 q^{26} +1.00000 q^{27} -1.73720 q^{28} -8.97540 q^{29} -1.91714 q^{30} -0.566291 q^{31} +1.00000 q^{32} +1.28494 q^{33} -1.00000 q^{34} +3.33045 q^{35} +1.00000 q^{36} +10.2678 q^{37} -7.73033 q^{38} +5.11248 q^{39} -1.91714 q^{40} -1.72781 q^{41} -1.73720 q^{42} +7.67402 q^{43} +1.28494 q^{44} -1.91714 q^{45} -6.84877 q^{46} -3.75247 q^{47} +1.00000 q^{48} -3.98214 q^{49} -1.32458 q^{50} -1.00000 q^{51} +5.11248 q^{52} -1.44997 q^{53} +1.00000 q^{54} -2.46340 q^{55} -1.73720 q^{56} -7.73033 q^{57} -8.97540 q^{58} -1.00000 q^{59} -1.91714 q^{60} +3.44485 q^{61} -0.566291 q^{62} -1.73720 q^{63} +1.00000 q^{64} -9.80134 q^{65} +1.28494 q^{66} -1.48219 q^{67} -1.00000 q^{68} -6.84877 q^{69} +3.33045 q^{70} -5.61916 q^{71} +1.00000 q^{72} -7.84373 q^{73} +10.2678 q^{74} -1.32458 q^{75} -7.73033 q^{76} -2.23219 q^{77} +5.11248 q^{78} -1.87056 q^{79} -1.91714 q^{80} +1.00000 q^{81} -1.72781 q^{82} +1.97044 q^{83} -1.73720 q^{84} +1.91714 q^{85} +7.67402 q^{86} -8.97540 q^{87} +1.28494 q^{88} -2.34832 q^{89} -1.91714 q^{90} -8.88140 q^{91} -6.84877 q^{92} -0.566291 q^{93} -3.75247 q^{94} +14.8201 q^{95} +1.00000 q^{96} -7.86027 q^{97} -3.98214 q^{98} +1.28494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 8 q^{11} + 6 q^{12} - 6 q^{13} - 7 q^{14} - 3 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 3 q^{20} - 7 q^{21} - 8 q^{22} - 8 q^{23} + 6 q^{24} - 13 q^{25} - 6 q^{26} + 6 q^{27} - 7 q^{28} - 21 q^{29} - 3 q^{30} - 5 q^{31} + 6 q^{32} - 8 q^{33} - 6 q^{34} - 12 q^{35} + 6 q^{36} - 13 q^{37} - 14 q^{38} - 6 q^{39} - 3 q^{40} - 18 q^{41} - 7 q^{42} - 4 q^{43} - 8 q^{44} - 3 q^{45} - 8 q^{46} - 4 q^{47} + 6 q^{48} + 5 q^{49} - 13 q^{50} - 6 q^{51} - 6 q^{52} - 25 q^{53} + 6 q^{54} - 8 q^{55} - 7 q^{56} - 14 q^{57} - 21 q^{58} - 6 q^{59} - 3 q^{60} - 5 q^{62} - 7 q^{63} + 6 q^{64} + 6 q^{65} - 8 q^{66} - 13 q^{67} - 6 q^{68} - 8 q^{69} - 12 q^{70} - 12 q^{71} + 6 q^{72} - 4 q^{73} - 13 q^{74} - 13 q^{75} - 14 q^{76} + 4 q^{77} - 6 q^{78} - 12 q^{79} - 3 q^{80} + 6 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 3 q^{85} - 4 q^{86} - 21 q^{87} - 8 q^{88} - 11 q^{89} - 3 q^{90} - 31 q^{91} - 8 q^{92} - 5 q^{93} - 4 q^{94} + 35 q^{95} + 6 q^{96} + 16 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9 - 3 * q^10 - 8 * q^11 + 6 * q^12 - 6 * q^13 - 7 * q^14 - 3 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 3 * q^20 - 7 * q^21 - 8 * q^22 - 8 * q^23 + 6 * q^24 - 13 * q^25 - 6 * q^26 + 6 * q^27 - 7 * q^28 - 21 * q^29 - 3 * q^30 - 5 * q^31 + 6 * q^32 - 8 * q^33 - 6 * q^34 - 12 * q^35 + 6 * q^36 - 13 * q^37 - 14 * q^38 - 6 * q^39 - 3 * q^40 - 18 * q^41 - 7 * q^42 - 4 * q^43 - 8 * q^44 - 3 * q^45 - 8 * q^46 - 4 * q^47 + 6 * q^48 + 5 * q^49 - 13 * q^50 - 6 * q^51 - 6 * q^52 - 25 * q^53 + 6 * q^54 - 8 * q^55 - 7 * q^56 - 14 * q^57 - 21 * q^58 - 6 * q^59 - 3 * q^60 - 5 * q^62 - 7 * q^63 + 6 * q^64 + 6 * q^65 - 8 * q^66 - 13 * q^67 - 6 * q^68 - 8 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 - 4 * q^73 - 13 * q^74 - 13 * q^75 - 14 * q^76 + 4 * q^77 - 6 * q^78 - 12 * q^79 - 3 * q^80 + 6 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 3 * q^85 - 4 * q^86 - 21 * q^87 - 8 * q^88 - 11 * q^89 - 3 * q^90 - 31 * q^91 - 8 * q^92 - 5 * q^93 - 4 * q^94 + 35 * q^95 + 6 * q^96 + 16 * q^97 + 5 * q^98 - 8 * q^99

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