LMFDB - Embedded newform 6038.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.56837 q^{3} +1.00000 q^{4} -1.56733 q^{5} -1.56837 q^{6} +2.76703 q^{7} +1.00000 q^{8} -0.540224 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.56837 q^{3} +1.00000 q^{4} -1.56733 q^{5} -1.56837 q^{6} +2.76703 q^{7} +1.00000 q^{8} -0.540224 q^{9} -1.56733 q^{10} -3.47008 q^{11} -1.56837 q^{12} +2.06412 q^{13} +2.76703 q^{14} +2.45814 q^{15} +1.00000 q^{16} -7.03851 q^{17} -0.540224 q^{18} -0.425853 q^{19} -1.56733 q^{20} -4.33971 q^{21} -3.47008 q^{22} +8.61264 q^{23} -1.56837 q^{24} -2.54349 q^{25} +2.06412 q^{26} +5.55237 q^{27} +2.76703 q^{28} +8.75787 q^{29} +2.45814 q^{30} +9.08268 q^{31} +1.00000 q^{32} +5.44236 q^{33} -7.03851 q^{34} -4.33683 q^{35} -0.540224 q^{36} -10.5791 q^{37} -0.425853 q^{38} -3.23730 q^{39} -1.56733 q^{40} +4.87722 q^{41} -4.33971 q^{42} -5.96758 q^{43} -3.47008 q^{44} +0.846706 q^{45} +8.61264 q^{46} -10.4383 q^{47} -1.56837 q^{48} +0.656434 q^{49} -2.54349 q^{50} +11.0390 q^{51} +2.06412 q^{52} -5.95366 q^{53} +5.55237 q^{54} +5.43874 q^{55} +2.76703 q^{56} +0.667893 q^{57} +8.75787 q^{58} +3.45065 q^{59} +2.45814 q^{60} +3.56279 q^{61} +9.08268 q^{62} -1.49481 q^{63} +1.00000 q^{64} -3.23514 q^{65} +5.44236 q^{66} -6.93553 q^{67} -7.03851 q^{68} -13.5078 q^{69} -4.33683 q^{70} +5.28501 q^{71} -0.540224 q^{72} -15.5878 q^{73} -10.5791 q^{74} +3.98913 q^{75} -0.425853 q^{76} -9.60180 q^{77} -3.23730 q^{78} +2.64999 q^{79} -1.56733 q^{80} -7.08749 q^{81} +4.87722 q^{82} +6.14014 q^{83} -4.33971 q^{84} +11.0316 q^{85} -5.96758 q^{86} -13.7356 q^{87} -3.47008 q^{88} -2.24404 q^{89} +0.846706 q^{90} +5.71147 q^{91} +8.61264 q^{92} -14.2450 q^{93} -10.4383 q^{94} +0.667449 q^{95} -1.56837 q^{96} -15.7435 q^{97} +0.656434 q^{98} +1.87462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9} - 14 q^{10} - 31 q^{11} - 21 q^{12} - 34 q^{13} - 44 q^{14} - 22 q^{15} + 54 q^{16} - 40 q^{17} + 39 q^{18} - 44 q^{19} - 14 q^{20} - 3 q^{21} - 31 q^{22} - 33 q^{23} - 21 q^{24} + 14 q^{25} - 34 q^{26} - 66 q^{27} - 44 q^{28} - 22 q^{30} - 65 q^{31} + 54 q^{32} - 43 q^{33} - 40 q^{34} - 46 q^{35} + 39 q^{36} - 58 q^{37} - 44 q^{38} - 36 q^{39} - 14 q^{40} - 49 q^{41} - 3 q^{42} - 47 q^{43} - 31 q^{44} - 45 q^{45} - 33 q^{46} - 66 q^{47} - 21 q^{48} + 16 q^{49} + 14 q^{50} - 33 q^{51} - 34 q^{52} - 16 q^{53} - 66 q^{54} - 50 q^{55} - 44 q^{56} - 33 q^{57} - 70 q^{59} - 22 q^{60} - 40 q^{61} - 65 q^{62} - 117 q^{63} + 54 q^{64} - 33 q^{65} - 43 q^{66} - 82 q^{67} - 40 q^{68} - q^{69} - 46 q^{70} - 60 q^{71} + 39 q^{72} - 92 q^{73} - 58 q^{74} - 68 q^{75} - 44 q^{76} + 13 q^{77} - 36 q^{78} - 57 q^{79} - 14 q^{80} + 26 q^{81} - 49 q^{82} - 77 q^{83} - 3 q^{84} - 24 q^{85} - 47 q^{86} - 61 q^{87} - 31 q^{88} - 54 q^{89} - 45 q^{90} - 46 q^{91} - 33 q^{92} - 24 q^{93} - 66 q^{94} - 66 q^{95} - 21 q^{96} - 137 q^{97} + 16 q^{98} - 71 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9 - 14 * q^10 - 31 * q^11 - 21 * q^12 - 34 * q^13 - 44 * q^14 - 22 * q^15 + 54 * q^16 - 40 * q^17 + 39 * q^18 - 44 * q^19 - 14 * q^20 - 3 * q^21 - 31 * q^22 - 33 * q^23 - 21 * q^24 + 14 * q^25 - 34 * q^26 - 66 * q^27 - 44 * q^28 - 22 * q^30 - 65 * q^31 + 54 * q^32 - 43 * q^33 - 40 * q^34 - 46 * q^35 + 39 * q^36 - 58 * q^37 - 44 * q^38 - 36 * q^39 - 14 * q^40 - 49 * q^41 - 3 * q^42 - 47 * q^43 - 31 * q^44 - 45 * q^45 - 33 * q^46 - 66 * q^47 - 21 * q^48 + 16 * q^49 + 14 * q^50 - 33 * q^51 - 34 * q^52 - 16 * q^53 - 66 * q^54 - 50 * q^55 - 44 * q^56 - 33 * q^57 - 70 * q^59 - 22 * q^60 - 40 * q^61 - 65 * q^62 - 117 * q^63 + 54 * q^64 - 33 * q^65 - 43 * q^66 - 82 * q^67 - 40 * q^68 - q^69 - 46 * q^70 - 60 * q^71 + 39 * q^72 - 92 * q^73 - 58 * q^74 - 68 * q^75 - 44 * q^76 + 13 * q^77 - 36 * q^78 - 57 * q^79 - 14 * q^80 + 26 * q^81 - 49 * q^82 - 77 * q^83 - 3 * q^84 - 24 * q^85 - 47 * q^86 - 61 * q^87 - 31 * q^88 - 54 * q^89 - 45 * q^90 - 46 * q^91 - 33 * q^92 - 24 * q^93 - 66 * q^94 - 66 * q^95 - 21 * q^96 - 137 * q^97 + 16 * q^98 - 71 * 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
$3$	−1.56837	−0.905497	−0.452749	−	0.891638i	$-0.649557\pi$
$3$	−1.56837	−0.905497	−0.452749	+	0.891638i	$0.649557\pi$
$4$	1.00000	0.500000
$5$	−1.56733	−0.700929	−0.350465	−	0.936576i	$-0.613976\pi$
$5$	−1.56733	−0.700929	−0.350465	+	0.936576i	$0.613976\pi$
$6$	−1.56837	−0.640283
$7$	2.76703	1.04584	0.522919	−	0.852382i	$-0.324843\pi$
$7$	2.76703	1.04584	0.522919	+	0.852382i	$0.324843\pi$
$8$	1.00000	0.353553
$9$	−0.540224	−0.180075
$10$	−1.56733	−0.495632
$11$	−3.47008	−1.04627	−0.523134	−	0.852250i	$-0.675237\pi$
$11$	−3.47008	−1.04627	−0.523134	+	0.852250i	$0.675237\pi$
$12$	−1.56837	−0.452749
$13$	2.06412	0.572483	0.286242	−	0.958157i	$-0.407594\pi$
$13$	2.06412	0.572483	0.286242	+	0.958157i	$0.407594\pi$
$14$	2.76703	0.739519
$15$	2.45814	0.634689
$16$	1.00000	0.250000
$17$	−7.03851	−1.70709	−0.853545	−	0.521019i	$-0.825552\pi$
$17$	−7.03851	−1.70709	−0.853545	+	0.521019i	$0.825552\pi$
$18$	−0.540224	−0.127332
$19$	−0.425853	−0.0976973	−0.0488486	−	0.998806i	$-0.515555\pi$
$19$	−0.425853	−0.0976973	−0.0488486	+	0.998806i	$0.515555\pi$
$20$	−1.56733	−0.350465
$21$	−4.33971	−0.947003
$22$	−3.47008	−0.739824
$23$	8.61264	1.79586	0.897930	−	0.440139i	$-0.145071\pi$
$23$	8.61264	1.79586	0.897930	+	0.440139i	$0.145071\pi$
$24$	−1.56837	−0.320142
$25$	−2.54349	−0.508698
$26$	2.06412	0.404807
$27$	5.55237	1.06855
$28$	2.76703	0.522919
$29$	8.75787	1.62629	0.813147	−	0.582058i	$-0.197752\pi$
$29$	8.75787	1.62629	0.813147	+	0.582058i	$0.197752\pi$
$30$	2.45814	0.448793
$31$	9.08268	1.63130	0.815648	−	0.578548i	$-0.196380\pi$
$31$	9.08268	1.63130	0.815648	+	0.578548i	$0.196380\pi$
$32$	1.00000	0.176777
$33$	5.44236	0.947394
$34$	−7.03851	−1.20710
$35$	−4.33683	−0.733058
$36$	−0.540224	−0.0900373
$37$	−10.5791	−1.73919	−0.869597	−	0.493762i	$-0.835621\pi$
$37$	−10.5791	−1.73919	−0.869597	+	0.493762i	$0.835621\pi$
$38$	−0.425853	−0.0690824
$39$	−3.23730	−0.518382
$40$	−1.56733	−0.247816
$41$	4.87722	0.761695	0.380847	−	0.924638i	$-0.375632\pi$
$41$	4.87722	0.761695	0.380847	+	0.924638i	$0.375632\pi$
$42$	−4.33971	−0.669632
$43$	−5.96758	−0.910048	−0.455024	−	0.890479i	$-0.650369\pi$
$43$	−5.96758	−0.910048	−0.455024	+	0.890479i	$0.650369\pi$
$44$	−3.47008	−0.523134
$45$	0.846706	0.126219
$46$	8.61264	1.26986
$47$	−10.4383	−1.52258	−0.761288	−	0.648414i	$-0.775433\pi$
$47$	−10.4383	−1.52258	−0.761288	+	0.648414i	$0.775433\pi$
$48$	−1.56837	−0.226374
$49$	0.656434	0.0937763
$50$	−2.54349	−0.359704
$51$	11.0390	1.54577
$52$	2.06412	0.286242
$53$	−5.95366	−0.817798	−0.408899	−	0.912580i	$-0.634087\pi$
$53$	−5.95366	−0.817798	−0.408899	+	0.912580i	$0.634087\pi$
$54$	5.55237	0.755582
$55$	5.43874	0.733360
$56$	2.76703	0.369759
$57$	0.667893	0.0884646
$58$	8.75787	1.14996
$59$	3.45065	0.449237	0.224618	−	0.974447i	$-0.427886\pi$
$59$	3.45065	0.449237	0.224618	+	0.974447i	$0.427886\pi$
$60$	2.45814	0.317345
$61$	3.56279	0.456169	0.228084	−	0.973641i	$-0.426754\pi$
$61$	3.56279	0.456169	0.228084	+	0.973641i	$0.426754\pi$
$62$	9.08268	1.15350
$63$	−1.49481	−0.188329
$64$	1.00000	0.125000
$65$	−3.23514	−0.401270
$66$	5.44236	0.669908
$67$	−6.93553	−0.847310	−0.423655	−	0.905824i	$-0.639253\pi$
$67$	−6.93553	−0.847310	−0.423655	+	0.905824i	$0.639253\pi$
$68$	−7.03851	−0.853545
$69$	−13.5078	−1.62615
$70$	−4.33683	−0.518350
$71$	5.28501	0.627215	0.313607	−	0.949553i	$-0.398462\pi$
$71$	5.28501	0.627215	0.313607	+	0.949553i	$0.398462\pi$
$72$	−0.540224	−0.0636660
$73$	−15.5878	−1.82441	−0.912207	−	0.409730i	$-0.865623\pi$
$73$	−15.5878	−1.82441	−0.912207	+	0.409730i	$0.865623\pi$
$74$	−10.5791	−1.22980
$75$	3.98913	0.460625
$76$	−0.425853	−0.0488486
$77$	−9.60180	−1.09423
$78$	−3.23730	−0.366551
$79$	2.64999	0.298147	0.149073	−	0.988826i	$-0.452371\pi$
$79$	2.64999	0.298147	0.149073	+	0.988826i	$0.452371\pi$
$80$	−1.56733	−0.175232
$81$	−7.08749	−0.787499
$82$	4.87722	0.538599
$83$	6.14014	0.673968	0.336984	−	0.941510i	$-0.390593\pi$
$83$	6.14014	0.673968	0.336984	+	0.941510i	$0.390593\pi$
$84$	−4.33971	−0.473502
$85$	11.0316	1.19655
$86$	−5.96758	−0.643501
$87$	−13.7356	−1.47261
$88$	−3.47008	−0.369912
$89$	−2.24404	−0.237868	−0.118934	−	0.992902i	$-0.537948\pi$
$89$	−2.24404	−0.237868	−0.118934	+	0.992902i	$0.537948\pi$
$90$	0.846706	0.0892506
$91$	5.71147	0.598725
$92$	8.61264	0.897930
$93$	−14.2450	−1.47714
$94$	−10.4383	−1.07662
$95$	0.667449	0.0684789
$96$	−1.56837	−0.160071
$97$	−15.7435	−1.59851	−0.799257	−	0.600990i	$-0.794773\pi$
$97$	−15.7435	−1.59851	−0.799257	+	0.600990i	$0.794773\pi$
$98$	0.656434	0.0663099
$99$	1.87462	0.188406
$100$	−2.54349	−0.254349
$101$	11.2826	1.12266	0.561328	−	0.827594i	$-0.310291\pi$
$101$	11.2826	1.12266	0.561328	+	0.827594i	$0.310291\pi$
$102$	11.0390	1.09302
$103$	−10.9342	−1.07738	−0.538689	−	0.842505i	$-0.681080\pi$
$103$	−10.9342	−1.07738	−0.538689	+	0.842505i	$0.681080\pi$
$104$	2.06412	0.202403
$105$	6.80174	0.663782
$106$	−5.95366	−0.578271
$107$	6.41345	0.620012	0.310006	−	0.950735i	$-0.399669\pi$
$107$	6.41345	0.620012	0.310006	+	0.950735i	$0.399669\pi$
$108$	5.55237	0.534277
$109$	−0.696528	−0.0667153	−0.0333576	−	0.999443i	$-0.510620\pi$
$109$	−0.696528	−0.0667153	−0.0333576	+	0.999443i	$0.510620\pi$
$110$	5.43874	0.518564
$111$	16.5919	1.57484
$112$	2.76703	0.261459
$113$	1.29557	0.121877	0.0609383	−	0.998142i	$-0.480591\pi$
$113$	1.29557	0.121877	0.0609383	+	0.998142i	$0.480591\pi$
$114$	0.667893	0.0625539
$115$	−13.4988	−1.25877
$116$	8.75787	0.813147
$117$	−1.11509	−0.103090
$118$	3.45065	0.317658
$119$	−19.4758	−1.78534
$120$	2.45814	0.224397
$121$	1.04146	0.0946783
$122$	3.56279	0.322560
$123$	−7.64928	−0.689712
$124$	9.08268	0.815648
$125$	11.8231	1.05749
$126$	−1.49481	−0.133169
$127$	11.8644	1.05280	0.526399	−	0.850238i	$-0.323542\pi$
$127$	11.8644	1.05280	0.526399	+	0.850238i	$0.323542\pi$
$128$	1.00000	0.0883883
$129$	9.35936	0.824046
$130$	−3.23514	−0.283741
$131$	3.90377	0.341074	0.170537	−	0.985351i	$-0.445450\pi$
$131$	3.90377	0.341074	0.170537	+	0.985351i	$0.445450\pi$
$132$	5.44236	0.473697
$133$	−1.17835	−0.102175
$134$	−6.93553	−0.599139
$135$	−8.70237	−0.748981
$136$	−7.03851	−0.603548
$137$	−19.0680	−1.62909	−0.814546	−	0.580099i	$-0.803014\pi$
$137$	−19.0680	−1.62909	−0.814546	+	0.580099i	$0.803014\pi$
$138$	−13.5078	−1.14986
$139$	−15.7655	−1.33721	−0.668606	−	0.743617i	$-0.733109\pi$
$139$	−15.7655	−1.33721	−0.668606	+	0.743617i	$0.733109\pi$
$140$	−4.33683	−0.366529
$141$	16.3710	1.37869
$142$	5.28501	0.443508
$143$	−7.16266	−0.598971
$144$	−0.540224	−0.0450186
$145$	−13.7264	−1.13992
$146$	−15.5878	−1.29006
$147$	−1.02953	−0.0849142
$148$	−10.5791	−0.869597
$149$	−20.2985	−1.66291	−0.831457	−	0.555589i	$-0.812493\pi$
$149$	−20.2985	−1.66291	−0.831457	+	0.555589i	$0.812493\pi$
$150$	3.98913	0.325711
$151$	−17.7675	−1.44589	−0.722947	−	0.690903i	$-0.757213\pi$
$151$	−17.7675	−1.44589	−0.722947	+	0.690903i	$0.757213\pi$
$152$	−0.425853	−0.0345412
$153$	3.80237	0.307403
$154$	−9.60180	−0.773735
$155$	−14.2355	−1.14342
$156$	−3.23730	−0.259191
$157$	−21.0628	−1.68100	−0.840499	−	0.541814i	$-0.817738\pi$
$157$	−21.0628	−1.68100	−0.840499	+	0.541814i	$0.817738\pi$
$158$	2.64999	0.210822
$159$	9.33753	0.740514
$160$	−1.56733	−0.123908
$161$	23.8314	1.87818
$162$	−7.08749	−0.556846
$163$	5.83404	0.456957	0.228479	−	0.973549i	$-0.426625\pi$
$163$	5.83404	0.456957	0.228479	+	0.973549i	$0.426625\pi$
$164$	4.87722	0.380847
$165$	−8.52995	−0.664056
$166$	6.14014	0.476567
$167$	1.01528	0.0785643	0.0392822	−	0.999228i	$-0.487493\pi$
$167$	1.01528	0.0785643	0.0392822	+	0.999228i	$0.487493\pi$
$168$	−4.33971	−0.334816
$169$	−8.73942	−0.672263
$170$	11.0316	0.846088
$171$	0.230056	0.0175928
$172$	−5.96758	−0.455024
$173$	12.9348	0.983416	0.491708	−	0.870760i	$-0.336373\pi$
$173$	12.9348	0.983416	0.491708	+	0.870760i	$0.336373\pi$
$174$	−13.7356	−1.04129
$175$	−7.03791	−0.532016
$176$	−3.47008	−0.261567
$177$	−5.41189	−0.406783
$178$	−2.24404	−0.168198
$179$	1.71791	0.128403	0.0642013	−	0.997937i	$-0.479550\pi$
$179$	1.71791	0.128403	0.0642013	+	0.997937i	$0.479550\pi$
$180$	0.846706	0.0631097
$181$	5.19300	0.385993	0.192996	−	0.981199i	$-0.438179\pi$
$181$	5.19300	0.385993	0.192996	+	0.981199i	$0.438179\pi$
$182$	5.71147	0.423362
$183$	−5.58777	−0.413060
$184$	8.61264	0.634932
$185$	16.5809	1.21905
$186$	−14.2450	−1.04449
$187$	24.4242	1.78608
$188$	−10.4383	−0.761288
$189$	15.3636	1.11753
$190$	0.667449	0.0484219
$191$	−12.0180	−0.869595	−0.434798	−	0.900528i	$-0.643180\pi$
$191$	−12.0180	−0.869595	−0.434798	+	0.900528i	$0.643180\pi$
$192$	−1.56837	−0.113187
$193$	18.2371	1.31274	0.656369	−	0.754440i	$-0.272091\pi$
$193$	18.2371	1.31274	0.656369	+	0.754440i	$0.272091\pi$
$194$	−15.7435	−1.13032
$195$	5.07389	0.363349
$196$	0.656434	0.0468882
$197$	2.80007	0.199496	0.0997482	−	0.995013i	$-0.468196\pi$
$197$	2.80007	0.199496	0.0997482	+	0.995013i	$0.468196\pi$
$198$	1.87462	0.133223
$199$	−7.37003	−0.522447	−0.261224	−	0.965278i	$-0.584126\pi$
$199$	−7.37003	−0.522447	−0.261224	+	0.965278i	$0.584126\pi$
$200$	−2.54349	−0.179852
$201$	10.8775	0.767237
$202$	11.2826	0.793837
$203$	24.2332	1.70084
$204$	11.0390	0.772883
$205$	−7.64420	−0.533894
$206$	−10.9342	−0.761821
$207$	−4.65275	−0.323389
$208$	2.06412	0.143121
$209$	1.47774	0.102218
$210$	6.80174	0.469365
$211$	24.9392	1.71688	0.858442	−	0.512910i	$-0.171433\pi$
$211$	24.9392	1.71688	0.858442	+	0.512910i	$0.171433\pi$
$212$	−5.95366	−0.408899
$213$	−8.28883	−0.567941
$214$	6.41345	0.438415
$215$	9.35314	0.637879
$216$	5.55237	0.377791
$217$	25.1320	1.70607
$218$	−0.696528	−0.0471748
$219$	24.4474	1.65200
$220$	5.43874	0.366680
$221$	−14.5283	−0.977281
$222$	16.5919	1.11358
$223$	−25.6032	−1.71452	−0.857260	−	0.514884i	$-0.827835\pi$
$223$	−25.6032	−1.71452	−0.857260	+	0.514884i	$0.827835\pi$
$224$	2.76703	0.184880
$225$	1.37405	0.0916036
$226$	1.29557	0.0861797
$227$	−20.2813	−1.34612	−0.673058	−	0.739590i	$-0.735020\pi$
$227$	−20.2813	−1.34612	−0.673058	+	0.739590i	$0.735020\pi$
$228$	0.667893	0.0442323
$229$	22.3992	1.48018	0.740090	−	0.672508i	$-0.234783\pi$
$229$	22.3992	1.48018	0.740090	+	0.672508i	$0.234783\pi$
$230$	−13.4988	−0.890085
$231$	15.0592	0.990820
$232$	8.75787	0.574982
$233$	−8.60681	−0.563851	−0.281926	−	0.959436i	$-0.590973\pi$
$233$	−8.60681	−0.563851	−0.281926	+	0.959436i	$0.590973\pi$
$234$	−1.11509	−0.0728954
$235$	16.3601	1.06722
$236$	3.45065	0.224618
$237$	−4.15615	−0.269971
$238$	−19.4758	−1.26243
$239$	−7.45410	−0.482165	−0.241083	−	0.970505i	$-0.577502\pi$
$239$	−7.45410	−0.482165	−0.241083	+	0.970505i	$0.577502\pi$
$240$	2.45814	0.158672
$241$	−13.5963	−0.875817	−0.437909	−	0.899019i	$-0.644281\pi$
$241$	−13.5963	−0.875817	−0.437909	+	0.899019i	$0.644281\pi$
$242$	1.04146	0.0669477
$243$	−5.54133	−0.355476
$244$	3.56279	0.228084
$245$	−1.02885	−0.0657306
$246$	−7.64928	−0.487700
$247$	−0.879010	−0.0559301
$248$	9.08268	0.576751
$249$	−9.62999	−0.610276
$250$	11.8231	0.747759
$251$	6.82335	0.430686	0.215343	−	0.976539i	$-0.430913\pi$
$251$	6.82335	0.430686	0.215343	+	0.976539i	$0.430913\pi$
$252$	−1.49481	−0.0941644
$253$	−29.8866	−1.87895
$254$	11.8644	0.744441
$255$	−17.3017	−1.08347
$256$	1.00000	0.0625000
$257$	−11.9287	−0.744091	−0.372046	−	0.928214i	$-0.621343\pi$
$257$	−11.9287	−0.744091	−0.372046	+	0.928214i	$0.621343\pi$
$258$	9.35936	0.582688
$259$	−29.2727	−1.81892
$260$	−3.23514	−0.200635
$261$	−4.73121	−0.292854
$262$	3.90377	0.241176
$263$	22.5053	1.38774	0.693868	−	0.720102i	$-0.255905\pi$
$263$	22.5053	1.38774	0.693868	+	0.720102i	$0.255905\pi$
$264$	5.44236	0.334954
$265$	9.33132	0.573219
$266$	−1.17835	−0.0722490
$267$	3.51949	0.215389
$268$	−6.93553	−0.423655
$269$	11.9742	0.730081	0.365041	−	0.930992i	$-0.381055\pi$
$269$	11.9742	0.730081	0.365041	+	0.930992i	$0.381055\pi$
$270$	−8.70237	−0.529609
$271$	−26.8768	−1.63265	−0.816325	−	0.577593i	$-0.803992\pi$
$271$	−26.8768	−1.63265	−0.816325	+	0.577593i	$0.803992\pi$
$272$	−7.03851	−0.426773
$273$	−8.95768	−0.542143
$274$	−19.0680	−1.15194
$275$	8.82612	0.532235
$276$	−13.5078	−0.813073
$277$	11.7231	0.704375	0.352188	−	0.935929i	$-0.385438\pi$
$277$	11.7231	0.704375	0.352188	+	0.935929i	$0.385438\pi$
$278$	−15.7655	−0.945552
$279$	−4.90668	−0.293755
$280$	−4.33683	−0.259175
$281$	−28.0769	−1.67493	−0.837463	−	0.546493i	$-0.815962\pi$
$281$	−28.0769	−1.67493	−0.837463	+	0.546493i	$0.815962\pi$
$282$	16.3710	0.974880
$283$	−18.9231	−1.12486	−0.562431	−	0.826844i	$-0.690134\pi$
$283$	−18.9231	−1.12486	−0.562431	+	0.826844i	$0.690134\pi$
$284$	5.28501	0.313607
$285$	−1.04681	−0.0620074
$286$	−7.16266	−0.423537
$287$	13.4954	0.796609
$288$	−0.540224	−0.0318330
$289$	32.5407	1.91416
$290$	−13.7264	−0.806043
$291$	24.6916	1.44745
$292$	−15.5878	−0.912207
$293$	−4.37031	−0.255317	−0.127658	−	0.991818i	$-0.540746\pi$
$293$	−4.37031	−0.255317	−0.127658	+	0.991818i	$0.540746\pi$
$294$	−1.02953	−0.0600434
$295$	−5.40830	−0.314883
$296$	−10.5791	−0.614898
$297$	−19.2672	−1.11800
$298$	−20.2985	−1.17586
$299$	17.7775	1.02810
$300$	3.98913	0.230313
$301$	−16.5125	−0.951762
$302$	−17.7675	−1.02240
$303$	−17.6952	−1.01656
$304$	−0.425853	−0.0244243
$305$	−5.58405	−0.319742
$306$	3.80237	0.217367
$307$	−22.4104	−1.27903	−0.639514	−	0.768779i	$-0.720864\pi$
$307$	−22.4104	−1.27903	−0.639514	+	0.768779i	$0.720864\pi$
$308$	−9.60180	−0.547114
$309$	17.1488	0.975563
$310$	−14.2355	−0.808522
$311$	21.7445	1.23302	0.616510	−	0.787347i	$-0.288546\pi$
$311$	21.7445	1.23302	0.616510	+	0.787347i	$0.288546\pi$
$312$	−3.23730	−0.183276
$313$	−28.5761	−1.61521	−0.807607	−	0.589721i	$-0.799238\pi$
$313$	−28.5761	−1.61521	−0.807607	+	0.589721i	$0.799238\pi$
$314$	−21.0628	−1.18864
$315$	2.34286	0.132005
$316$	2.64999	0.149073
$317$	−18.4883	−1.03841	−0.519204	−	0.854651i	$-0.673771\pi$
$317$	−18.4883	−1.03841	−0.519204	+	0.854651i	$0.673771\pi$
$318$	9.33753	0.523623
$319$	−30.3905	−1.70154
$320$	−1.56733	−0.0876161
$321$	−10.0587	−0.561419
$322$	23.8314	1.32807
$323$	2.99737	0.166778
$324$	−7.08749	−0.393749
$325$	−5.25007	−0.291221
$326$	5.83404	0.323118
$327$	1.09241	0.0604105
$328$	4.87722	0.269300
$329$	−28.8829	−1.59237
$330$	−8.52995	−0.469558
$331$	−10.0989	−0.555087	−0.277544	−	0.960713i	$-0.589520\pi$
$331$	−10.0989	−0.555087	−0.277544	+	0.960713i	$0.589520\pi$
$332$	6.14014	0.336984
$333$	5.71508	0.313185
$334$	1.01528	0.0555534
$335$	10.8702	0.593904
$336$	−4.33971	−0.236751
$337$	2.09886	0.114332	0.0571662	−	0.998365i	$-0.481794\pi$
$337$	2.09886	0.114332	0.0571662	+	0.998365i	$0.481794\pi$
$338$	−8.73942	−0.475362
$339$	−2.03192	−0.110359
$340$	11.0316	0.598275
$341$	−31.5176	−1.70677
$342$	0.230056	0.0124400
$343$	−17.5528	−0.947763
$344$	−5.96758	−0.321750
$345$	21.1711	1.13981
$346$	12.9348	0.695380
$347$	15.8588	0.851345	0.425672	−	0.904877i	$-0.360038\pi$
$347$	15.8588	0.851345	0.425672	+	0.904877i	$0.360038\pi$
$348$	−13.7356	−0.736303
$349$	−6.01437	−0.321942	−0.160971	−	0.986959i	$-0.551463\pi$
$349$	−6.01437	−0.321942	−0.160971	+	0.986959i	$0.551463\pi$
$350$	−7.03791	−0.376192
$351$	11.4607	0.611730
$352$	−3.47008	−0.184956
$353$	−28.1698	−1.49933	−0.749663	−	0.661819i	$-0.769785\pi$
$353$	−28.1698	−1.49933	−0.749663	+	0.661819i	$0.769785\pi$
$354$	−5.41189	−0.287639
$355$	−8.28332	−0.439633
$356$	−2.24404	−0.118934
$357$	30.5451	1.61662
$358$	1.71791	0.0907944
$359$	1.90534	0.100560	0.0502799	−	0.998735i	$-0.483989\pi$
$359$	1.90534	0.100560	0.0502799	+	0.998735i	$0.483989\pi$
$360$	0.846706	0.0446253
$361$	−18.8186	−0.990455
$362$	5.19300	0.272938
$363$	−1.63339	−0.0857310
$364$	5.71147	0.299362
$365$	24.4311	1.27878
$366$	−5.58777	−0.292077
$367$	−21.0986	−1.10134	−0.550669	−	0.834724i	$-0.685627\pi$
$367$	−21.0986	−1.10134	−0.550669	+	0.834724i	$0.685627\pi$
$368$	8.61264	0.448965
$369$	−2.63479	−0.137162
$370$	16.5809	0.862000
$371$	−16.4739	−0.855284
$372$	−14.2450	−0.738568
$373$	−0.829688	−0.0429596	−0.0214798	−	0.999769i	$-0.506838\pi$
$373$	−0.829688	−0.0429596	−0.0214798	+	0.999769i	$0.506838\pi$
$374$	24.4242	1.26295
$375$	−18.5430	−0.957555
$376$	−10.4383	−0.538312
$377$	18.0773	0.931027
$378$	15.3636	0.790216
$379$	−19.3774	−0.995351	−0.497675	−	0.867363i	$-0.665813\pi$
$379$	−19.3774	−0.995351	−0.497675	+	0.867363i	$0.665813\pi$
$380$	0.667449	0.0342394
$381$	−18.6078	−0.953306
$382$	−12.0180	−0.614897
$383$	−7.56405	−0.386505	−0.193253	−	0.981149i	$-0.561904\pi$
$383$	−7.56405	−0.386505	−0.193253	+	0.981149i	$0.561904\pi$
$384$	−1.56837	−0.0800354
$385$	15.0491	0.766976
$386$	18.2371	0.928246
$387$	3.22383	0.163876
$388$	−15.7435	−0.799257
$389$	−13.6744	−0.693317	−0.346659	−	0.937991i	$-0.612684\pi$
$389$	−13.6744	−0.693317	−0.346659	+	0.937991i	$0.612684\pi$
$390$	5.07389	0.256927
$391$	−60.6202	−3.06569
$392$	0.656434	0.0331549
$393$	−6.12255	−0.308842
$394$	2.80007	0.141065
$395$	−4.15339	−0.208980
$396$	1.87462	0.0942032
$397$	−1.16827	−0.0586336	−0.0293168	−	0.999570i	$-0.509333\pi$
$397$	−1.16827	−0.0586336	−0.0293168	+	0.999570i	$0.509333\pi$
$398$	−7.37003	−0.369426
$399$	1.84808	0.0925196
$400$	−2.54349	−0.127175
$401$	30.5440	1.52529	0.762646	−	0.646816i	$-0.223900\pi$
$401$	30.5440	1.52529	0.762646	+	0.646816i	$0.223900\pi$
$402$	10.8775	0.542518
$403$	18.7477	0.933890
$404$	11.2826	0.561328
$405$	11.1084	0.551981
$406$	24.2332	1.20268
$407$	36.7104	1.81966
$408$	11.0390	0.546511
$409$	−30.4095	−1.50365	−0.751826	−	0.659361i	$-0.770827\pi$
$409$	−30.4095	−1.50365	−0.751826	+	0.659361i	$0.770827\pi$
$410$	−7.64420	−0.377520
$411$	29.9057	1.47514
$412$	−10.9342	−0.538689
$413$	9.54805	0.469829
$414$	−4.65275	−0.228670
$415$	−9.62359	−0.472404
$416$	2.06412	0.101202
$417$	24.7261	1.21084
$418$	1.47774	0.0722788
$419$	14.2192	0.694651	0.347326	−	0.937745i	$-0.387090\pi$
$419$	14.2192	0.694651	0.347326	+	0.937745i	$0.387090\pi$
$420$	6.80174	0.331891
$421$	35.9753	1.75333	0.876663	−	0.481104i	$-0.159764\pi$
$421$	35.9753	1.75333	0.876663	+	0.481104i	$0.159764\pi$
$422$	24.9392	1.21402
$423$	5.63899	0.274177
$424$	−5.95366	−0.289135
$425$	17.9024	0.868394
$426$	−8.28883	−0.401595
$427$	9.85834	0.477078
$428$	6.41345	0.310006
$429$	11.2337	0.542367
$430$	9.35314	0.451048
$431$	−35.3473	−1.70262	−0.851309	−	0.524664i	$-0.824191\pi$
$431$	−35.3473	−1.70262	−0.851309	+	0.524664i	$0.824191\pi$
$432$	5.55237	0.267139
$433$	16.7556	0.805224	0.402612	−	0.915371i	$-0.368102\pi$
$433$	16.7556	0.805224	0.402612	+	0.915371i	$0.368102\pi$
$434$	25.1320	1.20637
$435$	21.5281	1.03219
$436$	−0.696528	−0.0333576
$437$	−3.66771	−0.175451
$438$	24.4474	1.16814
$439$	34.8296	1.66232	0.831162	−	0.556030i	$-0.187676\pi$
$439$	34.8296	1.66232	0.831162	+	0.556030i	$0.187676\pi$
$440$	5.43874	0.259282
$441$	−0.354621	−0.0168867
$442$	−14.5283	−0.691042
$443$	−17.7363	−0.842676	−0.421338	−	0.906904i	$-0.638439\pi$
$443$	−17.7363	−0.842676	−0.421338	+	0.906904i	$0.638439\pi$
$444$	16.5919	0.787418
$445$	3.51715	0.166729
$446$	−25.6032	−1.21235
$447$	31.8354	1.50576
$448$	2.76703	0.130730
$449$	36.6686	1.73050	0.865249	−	0.501342i	$-0.167160\pi$
$449$	36.6686	1.73050	0.865249	+	0.501342i	$0.167160\pi$
$450$	1.37405	0.0647736
$451$	−16.9244	−0.796937
$452$	1.29557	0.0609383
$453$	27.8659	1.30925
$454$	−20.2813	−0.951848
$455$	−8.95173	−0.419663
$456$	0.667893	0.0312770
$457$	−20.0209	−0.936538	−0.468269	−	0.883586i	$-0.655122\pi$
$457$	−20.0209	−0.936538	−0.468269	+	0.883586i	$0.655122\pi$
$458$	22.3992	1.04665
$459$	−39.0804	−1.82412
$460$	−13.4988	−0.629385
$461$	−26.9454	−1.25497	−0.627486	−	0.778628i	$-0.715916\pi$
$461$	−26.9454	−1.25497	−0.627486	+	0.778628i	$0.715916\pi$
$462$	15.0592	0.700615
$463$	−10.5519	−0.490388	−0.245194	−	0.969474i	$-0.578852\pi$
$463$	−10.5519	−0.490388	−0.245194	+	0.969474i	$0.578852\pi$
$464$	8.75787	0.406574
$465$	22.3265	1.03537
$466$	−8.60681	−0.398703
$467$	31.1473	1.44132	0.720662	−	0.693286i	$-0.243838\pi$
$467$	31.1473	1.44132	0.720662	+	0.693286i	$0.243838\pi$
$468$	−1.11509	−0.0515448
$469$	−19.1908	−0.886149
$470$	16.3601	0.754637
$471$	33.0343	1.52214
$472$	3.45065	0.158829
$473$	20.7080	0.952154
$474$	−4.15615	−0.190898
$475$	1.08315	0.0496984
$476$	−19.4758	−0.892670
$477$	3.21631	0.147265
$478$	−7.45410	−0.340942
$479$	−11.2780	−0.515306	−0.257653	−	0.966238i	$-0.582949\pi$
$479$	−11.2780	−0.515306	−0.257653	+	0.966238i	$0.582949\pi$
$480$	2.45814	0.112198
$481$	−21.8365	−0.995660
$482$	−13.5963	−0.619296
$483$	−37.3764	−1.70068
$484$	1.04146	0.0473392
$485$	24.6752	1.12044
$486$	−5.54133	−0.251360
$487$	27.2349	1.23413	0.617067	−	0.786911i	$-0.288321\pi$
$487$	27.2349	1.23413	0.617067	+	0.786911i	$0.288321\pi$
$488$	3.56279	0.161280
$489$	−9.14992	−0.413774
$490$	−1.02885	−0.0464785
$491$	29.9497	1.35161	0.675807	−	0.737079i	$-0.263795\pi$
$491$	29.9497	1.35161	0.675807	+	0.737079i	$0.263795\pi$
$492$	−7.64928	−0.344856
$493$	−61.6424	−2.77623
$494$	−0.879010	−0.0395485
$495$	−2.93814	−0.132059
$496$	9.08268	0.407824
$497$	14.6237	0.655965
$498$	−9.62999	−0.431530
$499$	−11.4793	−0.513885	−0.256943	−	0.966427i	$-0.582715\pi$
$499$	−11.4793	−0.513885	−0.256943	+	0.966427i	$0.582715\pi$
$500$	11.8231	0.528745
$501$	−1.59232	−0.0711398
$502$	6.82335	0.304541
$503$	5.17284	0.230646	0.115323	−	0.993328i	$-0.463210\pi$
$503$	5.17284	0.230646	0.115323	+	0.993328i	$0.463210\pi$
$504$	−1.49481	−0.0665843
$505$	−17.6834	−0.786902
$506$	−29.8866	−1.32862
$507$	13.7066	0.608732
$508$	11.8644	0.526399
$509$	−9.31975	−0.413091	−0.206545	−	0.978437i	$-0.566222\pi$
$509$	−9.31975	−0.413091	−0.206545	+	0.978437i	$0.566222\pi$
$510$	−17.3017	−0.766130
$511$	−43.1319	−1.90804
$512$	1.00000	0.0441942
$513$	−2.36449	−0.104395
$514$	−11.9287	−0.526152
$515$	17.1374	0.755165
$516$	9.35936	0.412023
$517$	36.2216	1.59302
$518$	−29.2727	−1.28617
$519$	−20.2865	−0.890480
$520$	−3.23514	−0.141870
$521$	17.7351	0.776990	0.388495	−	0.921451i	$-0.372995\pi$
$521$	17.7351	0.776990	0.388495	+	0.921451i	$0.372995\pi$
$522$	−4.73121	−0.207079
$523$	−4.69151	−0.205145	−0.102573	−	0.994726i	$-0.532707\pi$
$523$	−4.69151	−0.205145	−0.102573	+	0.994726i	$0.532707\pi$
$524$	3.90377	0.170537
$525$	11.0380	0.481739
$526$	22.5053	0.981278
$527$	−63.9285	−2.78477
$528$	5.44236	0.236848
$529$	51.1775	2.22511
$530$	9.33132	0.405327
$531$	−1.86412	−0.0808961
$532$	−1.17835	−0.0510877
$533$	10.0672	0.436057
$534$	3.51949	0.152303
$535$	−10.0520	−0.434584
$536$	−6.93553	−0.299569
$537$	−2.69431	−0.116268
$538$	11.9742	0.516245
$539$	−2.27788	−0.0981153
$540$	−8.70237	−0.374490
$541$	−7.13290	−0.306667	−0.153334	−	0.988174i	$-0.549001\pi$
$541$	−7.13290	−0.306667	−0.153334	+	0.988174i	$0.549001\pi$
$542$	−26.8768	−1.15446
$543$	−8.14453	−0.349515
$544$	−7.03851	−0.301774
$545$	1.09169	0.0467627
$546$	−8.95768	−0.383353
$547$	−27.6908	−1.18397	−0.591987	−	0.805947i	$-0.701657\pi$
$547$	−27.6908	−1.18397	−0.591987	+	0.805947i	$0.701657\pi$
$548$	−19.0680	−0.814546
$549$	−1.92470	−0.0821444
$550$	8.82612	0.376347
$551$	−3.72956	−0.158885
$552$	−13.5078	−0.574929
$553$	7.33258	0.311813
$554$	11.7231	0.498069
$555$	−26.0049	−1.10385
$556$	−15.7655	−0.668606
$557$	20.1772	0.854935	0.427467	−	0.904031i	$-0.359406\pi$
$557$	20.1772	0.854935	0.427467	+	0.904031i	$0.359406\pi$
$558$	−4.90668	−0.207716
$559$	−12.3178	−0.520987
$560$	−4.33683	−0.183264
$561$	−38.3061	−1.61729
$562$	−28.0769	−1.18435
$563$	20.6770	0.871431	0.435716	−	0.900084i	$-0.356495\pi$
$563$	20.6770	0.871431	0.435716	+	0.900084i	$0.356495\pi$
$564$	16.3710	0.689344
$565$	−2.03057	−0.0854268
$566$	−18.9231	−0.795398
$567$	−19.6113	−0.823596
$568$	5.28501	0.221754
$569$	33.4083	1.40055	0.700274	−	0.713874i	$-0.253061\pi$
$569$	33.4083	1.40055	0.700274	+	0.713874i	$0.253061\pi$
$570$	−1.04681	−0.0438459
$571$	7.93176	0.331934	0.165967	−	0.986131i	$-0.446925\pi$
$571$	7.93176	0.331934	0.165967	+	0.986131i	$0.446925\pi$
$572$	−7.16266	−0.299486
$573$	18.8487	0.787416
$574$	13.4954	0.563288
$575$	−21.9062	−0.913551
$576$	−0.540224	−0.0225093
$577$	28.5121	1.18697	0.593486	−	0.804844i	$-0.297751\pi$
$577$	28.5121	1.18697	0.593486	+	0.804844i	$0.297751\pi$
$578$	32.5407	1.35351
$579$	−28.6025	−1.18868
$580$	−13.7264	−0.569959
$581$	16.9899	0.704861
$582$	24.6916	1.02350
$583$	20.6597	0.855637
$584$	−15.5878	−0.645028
$585$	1.74770	0.0722585
$586$	−4.37031	−0.180536
$587$	28.6392	1.18207	0.591033	−	0.806647i	$-0.298720\pi$
$587$	28.6392	1.18207	0.591033	+	0.806647i	$0.298720\pi$
$588$	−1.02953	−0.0424571
$589$	−3.86788	−0.159373
$590$	−5.40830	−0.222656
$591$	−4.39153	−0.180644
$592$	−10.5791	−0.434799
$593$	−26.2274	−1.07703	−0.538514	−	0.842616i	$-0.681014\pi$
$593$	−26.2274	−1.07703	−0.538514	+	0.842616i	$0.681014\pi$
$594$	−19.2672	−0.790542
$595$	30.5248	1.25140
$596$	−20.2985	−0.831457
$597$	11.5589	0.473075
$598$	17.7775	0.726976
$599$	−8.99258	−0.367427	−0.183713	−	0.982980i	$-0.558812\pi$
$599$	−8.99258	−0.367427	−0.183713	+	0.982980i	$0.558812\pi$
$600$	3.98913	0.162856
$601$	1.47016	0.0599690	0.0299845	−	0.999550i	$-0.490454\pi$
$601$	1.47016	0.0599690	0.0299845	+	0.999550i	$0.490454\pi$
$602$	−16.5125	−0.672997
$603$	3.74674	0.152579
$604$	−17.7675	−0.722947
$605$	−1.63231	−0.0663628
$606$	−17.6952	−0.718818
$607$	−19.8266	−0.804737	−0.402368	−	0.915478i	$-0.631813\pi$
$607$	−19.8266	−0.804737	−0.402368	+	0.915478i	$0.631813\pi$
$608$	−0.425853	−0.0172706
$609$	−38.0066	−1.54011
$610$	−5.58405	−0.226092
$611$	−21.5458	−0.871650
$612$	3.80237	0.153702
$613$	29.6470	1.19743	0.598715	−	0.800962i	$-0.295678\pi$
$613$	29.6470	1.19743	0.598715	+	0.800962i	$0.295678\pi$
$614$	−22.4104	−0.904410
$615$	11.9889	0.483439
$616$	−9.60180	−0.386868
$617$	38.9098	1.56645	0.783225	−	0.621738i	$-0.213573\pi$
$617$	38.9098	1.56645	0.783225	+	0.621738i	$0.213573\pi$
$618$	17.1488	0.689827
$619$	3.47014	0.139477	0.0697383	−	0.997565i	$-0.477784\pi$
$619$	3.47014	0.139477	0.0697383	+	0.997565i	$0.477784\pi$
$620$	−14.2355	−0.571712
$621$	47.8206	1.91897
$622$	21.7445	0.871876
$623$	−6.20933	−0.248771
$624$	−3.23730	−0.129596
$625$	−5.81319	−0.232527
$626$	−28.5761	−1.14213
$627$	−2.31764	−0.0925578
$628$	−21.0628	−0.840499
$629$	74.4612	2.96896
$630$	2.34286	0.0933417
$631$	42.7582	1.70218	0.851088	−	0.525024i	$-0.175944\pi$
$631$	42.7582	1.70218	0.851088	+	0.525024i	$0.175944\pi$
$632$	2.64999	0.105411
$633$	−39.1138	−1.55463
$634$	−18.4883	−0.734265
$635$	−18.5954	−0.737937
$636$	9.33753	0.370257
$637$	1.35496	0.0536854
$638$	−30.3905	−1.20317
$639$	−2.85508	−0.112945
$640$	−1.56733	−0.0619540
$641$	4.04931	0.159938	0.0799690	−	0.996797i	$-0.474518\pi$
$641$	4.04931	0.159938	0.0799690	+	0.996797i	$0.474518\pi$
$642$	−10.0587	−0.396983
$643$	−4.44333	−0.175228	−0.0876140	−	0.996155i	$-0.527924\pi$
$643$	−4.44333	−0.175228	−0.0876140	+	0.996155i	$0.527924\pi$
$644$	23.8314	0.939089
$645$	−14.6692	−0.577598
$646$	2.99737	0.117930
$647$	−26.3253	−1.03495	−0.517476	−	0.855698i	$-0.673128\pi$
$647$	−26.3253	−1.03495	−0.517476	+	0.855698i	$0.673128\pi$
$648$	−7.08749	−0.278423
$649$	−11.9740	−0.470022
$650$	−5.25007	−0.205925
$651$	−39.4162	−1.54484
$652$	5.83404	0.228479
$653$	25.1132	0.982757	0.491379	−	0.870946i	$-0.336493\pi$
$653$	25.1132	0.982757	0.491379	+	0.870946i	$0.336493\pi$
$654$	1.09241	0.0427167
$655$	−6.11848	−0.239069
$656$	4.87722	0.190424
$657$	8.42090	0.328530
$658$	−28.8829	−1.12597
$659$	−31.9717	−1.24544	−0.622720	−	0.782444i	$-0.713973\pi$
$659$	−31.9717	−1.24544	−0.622720	+	0.782444i	$0.713973\pi$
$660$	−8.52995	−0.332028
$661$	−15.0016	−0.583495	−0.291748	−	0.956495i	$-0.594237\pi$
$661$	−15.0016	−0.583495	−0.291748	+	0.956495i	$0.594237\pi$
$662$	−10.0989	−0.392506
$663$	22.7857	0.884925
$664$	6.14014	0.238284
$665$	1.84685	0.0716178
$666$	5.71508	0.221455
$667$	75.4283	2.92060
$668$	1.01528	0.0392822
$669$	40.1553	1.55249
$670$	10.8702	0.419954
$671$	−12.3632	−0.477275
$672$	−4.33971	−0.167408
$673$	10.0070	0.385740	0.192870	−	0.981224i	$-0.438220\pi$
$673$	10.0070	0.385740	0.192870	+	0.981224i	$0.438220\pi$
$674$	2.09886	0.0808452
$675$	−14.1224	−0.543572
$676$	−8.73942	−0.336131
$677$	14.2788	0.548779	0.274390	−	0.961619i	$-0.411524\pi$
$677$	14.2788	0.548779	0.274390	+	0.961619i	$0.411524\pi$
$678$	−2.03192	−0.0780355
$679$	−43.5628	−1.67179
$680$	11.0316	0.423044
$681$	31.8085	1.21890
$682$	−31.5176	−1.20687
$683$	35.2196	1.34764	0.673819	−	0.738896i	$-0.264653\pi$
$683$	35.2196	1.34764	0.673819	+	0.738896i	$0.264653\pi$
$684$	0.230056	0.00879639
$685$	29.8858	1.14188
$686$	−17.5528	−0.670170
$687$	−35.1302	−1.34030
$688$	−5.96758	−0.227512
$689$	−12.2891	−0.468176
$690$	21.1711	0.805969
$691$	−0.0958459	−0.00364615	−0.00182307	−	0.999998i	$-0.500580\pi$
$691$	−0.0958459	−0.00364615	−0.00182307	+	0.999998i	$0.500580\pi$
$692$	12.9348	0.491708
$693$	5.18712	0.197042
$694$	15.8588	0.601991
$695$	24.7097	0.937291
$696$	−13.7356	−0.520645
$697$	−34.3284	−1.30028
$698$	−6.01437	−0.227647
$699$	13.4986	0.510566
$700$	−7.03791	−0.266008
$701$	16.8093	0.634878	0.317439	−	0.948279i	$-0.397177\pi$
$701$	16.8093	0.634878	0.317439	+	0.948279i	$0.397177\pi$
$702$	11.4607	0.432558
$703$	4.50514	0.169915
$704$	−3.47008	−0.130784
$705$	−25.6587	−0.966363
$706$	−28.1698	−1.06018
$707$	31.2191	1.17412
$708$	−5.41189	−0.203391
$709$	−30.8711	−1.15939	−0.579694	−	0.814834i	$-0.696828\pi$
$709$	−30.8711	−1.15939	−0.579694	+	0.814834i	$0.696828\pi$
$710$	−8.28332	−0.310867
$711$	−1.43159	−0.0536887
$712$	−2.24404	−0.0840991
$713$	78.2258	2.92958
$714$	30.5451	1.14312
$715$	11.2262	0.419836
$716$	1.71791	0.0642013
$717$	11.6908	0.436599
$718$	1.90534	0.0711065
$719$	−29.6293	−1.10499	−0.552493	−	0.833517i	$-0.686323\pi$
$719$	−29.6293	−1.10499	−0.552493	+	0.833517i	$0.686323\pi$
$720$	0.846706	0.0315549
$721$	−30.2552	−1.12676
$722$	−18.8186	−0.700358
$723$	21.3241	0.793050
$724$	5.19300	0.192996
$725$	−22.2756	−0.827294
$726$	−1.63339	−0.0606209
$727$	−6.06473	−0.224928	−0.112464	−	0.993656i	$-0.535874\pi$
$727$	−6.06473	−0.224928	−0.112464	+	0.993656i	$0.535874\pi$
$728$	5.71147	0.211681
$729$	29.9533	1.10938
$730$	24.4311	0.904237
$731$	42.0029	1.55353
$732$	−5.58777	−0.206530
$733$	29.8088	1.10101	0.550507	−	0.834831i	$-0.314435\pi$
$733$	29.8088	1.10101	0.550507	+	0.834831i	$0.314435\pi$
$734$	−21.0986	−0.778764
$735$	1.61361	0.0595188
$736$	8.61264	0.317466
$737$	24.0669	0.886514
$738$	−2.63479	−0.0969880
$739$	6.42612	0.236389	0.118194	−	0.992990i	$-0.462289\pi$
$739$	6.42612	0.236389	0.118194	+	0.992990i	$0.462289\pi$
$740$	16.5809	0.609526
$741$	1.37861	0.0506445
$742$	−16.4739	−0.604777
$743$	−17.7018	−0.649417	−0.324709	−	0.945814i	$-0.605266\pi$
$743$	−17.7018	−0.649417	−0.324709	+	0.945814i	$0.605266\pi$
$744$	−14.2450	−0.522246
$745$	31.8143	1.16559
$746$	−0.829688	−0.0303770
$747$	−3.31705	−0.121364
$748$	24.4242	0.893038
$749$	17.7462	0.648432
$750$	−18.5430	−0.677094
$751$	−30.7821	−1.12326	−0.561628	−	0.827390i	$-0.689825\pi$
$751$	−30.7821	−1.12326	−0.561628	+	0.827390i	$0.689825\pi$
$752$	−10.4383	−0.380644
$753$	−10.7015	−0.389985
$754$	18.0773	0.658335
$755$	27.8474	1.01347
$756$	15.3636	0.558767
$757$	−32.6522	−1.18676	−0.593382	−	0.804921i	$-0.702208\pi$
$757$	−32.6522	−1.18676	−0.593382	+	0.804921i	$0.702208\pi$
$758$	−19.3774	−0.703819
$759$	46.8731	1.70139
$760$	0.667449	0.0242109
$761$	−20.8784	−0.756840	−0.378420	−	0.925634i	$-0.623533\pi$
$761$	−20.8784	−0.756840	−0.378420	+	0.925634i	$0.623533\pi$
$762$	−18.6078	−0.674089
$763$	−1.92731	−0.0697733
$764$	−12.0180	−0.434798
$765$	−5.95955	−0.215468
$766$	−7.56405	−0.273300
$767$	7.12256	0.257181
$768$	−1.56837	−0.0565936
$769$	29.5224	1.06461	0.532303	−	0.846554i	$-0.321327\pi$
$769$	29.5224	1.06461	0.532303	+	0.846554i	$0.321327\pi$
$770$	15.0491	0.542334
$771$	18.7086	0.673773
$772$	18.2371	0.656369
$773$	−36.0114	−1.29524	−0.647621	−	0.761963i	$-0.724236\pi$
$773$	−36.0114	−1.29524	−0.647621	+	0.761963i	$0.724236\pi$
$774$	3.22383	0.115878
$775$	−23.1017	−0.829838
$776$	−15.7435	−0.565160
$777$	45.9103	1.64702
$778$	−13.6744	−0.490249
$779$	−2.07698	−0.0744155
$780$	5.07389	0.181675
$781$	−18.3394	−0.656235
$782$	−60.6202	−2.16777
$783$	48.6269	1.73778
$784$	0.656434	0.0234441
$785$	33.0123	1.17826
$786$	−6.12255	−0.218384
$787$	11.8927	0.423931	0.211965	−	0.977277i	$-0.432014\pi$
$787$	11.8927	0.423931	0.211965	+	0.977277i	$0.432014\pi$
$788$	2.80007	0.0997482
$789$	−35.2966	−1.25659
$790$	−4.15339	−0.147771
$791$	3.58486	0.127463
$792$	1.87462	0.0666117
$793$	7.35402	0.261149
$794$	−1.16827	−0.0414602
$795$	−14.6349	−0.519048
$796$	−7.37003	−0.261224
$797$	−53.4956	−1.89491	−0.947455	−	0.319889i	$-0.896354\pi$
$797$	−53.4956	−1.89491	−0.947455	+	0.319889i	$0.896354\pi$
$798$	1.84808	0.0654213
$799$	73.4698	2.59918
$800$	−2.54349	−0.0899260
$801$	1.21229	0.0428340
$802$	30.5440	1.07854
$803$	54.0909	1.90883
$804$	10.8775	0.383618
$805$	−37.3515	−1.31647
$806$	18.7477	0.660360
$807$	−18.7800	−0.661087
$808$	11.2826	0.396919
$809$	17.0973	0.601108	0.300554	−	0.953765i	$-0.402828\pi$
$809$	17.0973	0.601108	0.300554	+	0.953765i	$0.402828\pi$
$810$	11.1084	0.390309
$811$	−6.01433	−0.211192	−0.105596	−	0.994409i	$-0.533675\pi$
$811$	−6.01433	−0.211192	−0.105596	+	0.994409i	$0.533675\pi$
$812$	24.2332	0.850420
$813$	42.1527	1.47836
$814$	36.7104	1.28670
$815$	−9.14384	−0.320295
$816$	11.0390	0.386441
$817$	2.54131	0.0889092
$818$	−30.4095	−1.06324
$819$	−3.08547	−0.107815
$820$	−7.64420	−0.266947
$821$	7.34096	0.256201	0.128101	−	0.991761i	$-0.459112\pi$
$821$	7.34096	0.256201	0.128101	+	0.991761i	$0.459112\pi$
$822$	29.9057	1.04308
$823$	−24.1397	−0.841458	−0.420729	−	0.907186i	$-0.638226\pi$
$823$	−24.1397	−0.841458	−0.420729	+	0.907186i	$0.638226\pi$
$824$	−10.9342	−0.380910
$825$	−13.8426	−0.481938
$826$	9.54805	0.332219
$827$	−4.81670	−0.167493	−0.0837466	−	0.996487i	$-0.526689\pi$
$827$	−4.81670	−0.167493	−0.0837466	+	0.996487i	$0.526689\pi$
$828$	−4.65275	−0.161694
$829$	19.3160	0.670871	0.335435	−	0.942063i	$-0.391117\pi$
$829$	19.3160	0.670871	0.335435	+	0.942063i	$0.391117\pi$
$830$	−9.62359	−0.334040
$831$	−18.3862	−0.637810
$832$	2.06412	0.0715604
$833$	−4.62032	−0.160085
$834$	24.7261	0.856195
$835$	−1.59127	−0.0550680
$836$	1.47774	0.0511088
$837$	50.4304	1.74313
$838$	14.2192	0.491193
$839$	−17.6375	−0.608913	−0.304457	−	0.952526i	$-0.598475\pi$
$839$	−17.6375	−0.608913	−0.304457	+	0.952526i	$0.598475\pi$
$840$	6.80174	0.234682
$841$	47.7002	1.64483
$842$	35.9753	1.23979
$843$	44.0349	1.51664
$844$	24.9392	0.858442
$845$	13.6975	0.471209
$846$	5.63899	0.193873
$847$	2.88175	0.0990181
$848$	−5.95366	−0.204450
$849$	29.6784	1.01856
$850$	17.9024	0.614047
$851$	−91.1140	−3.12335
$852$	−8.28883	−0.283971
$853$	−42.0450	−1.43959	−0.719797	−	0.694185i	$-0.755765\pi$
$853$	−42.0450	−1.43959	−0.719797	+	0.694185i	$0.755765\pi$
$854$	9.85834	0.337345
$855$	−0.360572	−0.0123313
$856$	6.41345	0.219207
$857$	−19.9039	−0.679903	−0.339951	−	0.940443i	$-0.610411\pi$
$857$	−19.9039	−0.679903	−0.339951	+	0.940443i	$0.610411\pi$
$858$	11.2337	0.383511
$859$	47.3914	1.61697	0.808487	−	0.588514i	$-0.200287\pi$
$859$	47.3914	1.61697	0.808487	+	0.588514i	$0.200287\pi$
$860$	9.35314	0.318939
$861$	−21.1658	−0.721327
$862$	−35.3473	−1.20393
$863$	9.42450	0.320814	0.160407	−	0.987051i	$-0.448719\pi$
$863$	9.42450	0.320814	0.160407	+	0.987051i	$0.448719\pi$
$864$	5.55237	0.188896
$865$	−20.2731	−0.689305
$866$	16.7556	0.569379
$867$	−51.0357	−1.73326
$868$	25.1320	0.853036
$869$	−9.19567	−0.311942
$870$	21.5281	0.729870
$871$	−14.3158	−0.485071
$872$	−0.696528	−0.0235874
$873$	8.50503	0.287852
$874$	−3.66771	−0.124062
$875$	32.7148	1.10596
$876$	24.4474	0.826001
$877$	−22.2296	−0.750641	−0.375320	−	0.926895i	$-0.622467\pi$
$877$	−22.2296	−0.750641	−0.375320	+	0.926895i	$0.622467\pi$
$878$	34.8296	1.17544
$879$	6.85426	0.231188
$880$	5.43874	0.183340
$881$	49.8957	1.68103	0.840515	−	0.541788i	$-0.182252\pi$
$881$	49.8957	1.68103	0.840515	+	0.541788i	$0.182252\pi$
$882$	−0.354621	−0.0119407
$883$	11.7879	0.396696	0.198348	−	0.980132i	$-0.436442\pi$
$883$	11.7879	0.396696	0.198348	+	0.980132i	$0.436442\pi$
$884$	−14.5283	−0.488640
$885$	8.48220	0.285126
$886$	−17.7363	−0.595862
$887$	55.2539	1.85525	0.927623	−	0.373518i	$-0.121849\pi$
$887$	55.2539	1.85525	0.927623	+	0.373518i	$0.121849\pi$
$888$	16.5919	0.556789
$889$	32.8292	1.10106
$890$	3.51715	0.117895
$891$	24.5942	0.823935
$892$	−25.6032	−0.857260
$893$	4.44516	0.148752
$894$	31.8354	1.06474
$895$	−2.69252	−0.0900011
$896$	2.76703	0.0924399
$897$	−27.8817	−0.930941
$898$	36.6686	1.22365
$899$	79.5449	2.65297
$900$	1.37405	0.0458018
$901$	41.9049	1.39606
$902$	−16.9244	−0.563520
$903$	25.8976	0.861818
$904$	1.29557	0.0430899
$905$	−8.13912	−0.270553
$906$	27.8659	0.925782
$907$	26.2737	0.872403	0.436201	−	0.899849i	$-0.356324\pi$
$907$	26.2737	0.872403	0.436201	+	0.899849i	$0.356324\pi$
$908$	−20.2813	−0.673058
$909$	−6.09510	−0.202162
$910$	−8.95173	−0.296747
$911$	−42.2604	−1.40015	−0.700074	−	0.714070i	$-0.746850\pi$
$911$	−42.2604	−1.40015	−0.700074	+	0.714070i	$0.746850\pi$
$912$	0.667893	0.0221162
$913$	−21.3068	−0.705151
$914$	−20.0209	−0.662232
$915$	8.75785	0.289526
$916$	22.3992	0.740090
$917$	10.8018	0.356708
$918$	−39.0804	−1.28985
$919$	29.2871	0.966093	0.483046	−	0.875595i	$-0.339530\pi$
$919$	29.2871	0.966093	0.483046	+	0.875595i	$0.339530\pi$
$920$	−13.4988	−0.445042
$921$	35.1477	1.15816
$922$	−26.9454	−0.887399
$923$	10.9089	0.359070
$924$	15.0592	0.495410
$925$	26.9079	0.884726
$926$	−10.5519	−0.346757
$927$	5.90691	0.194008
$928$	8.75787	0.287491
$929$	−2.75745	−0.0904689	−0.0452344	−	0.998976i	$-0.514403\pi$
$929$	−2.75745	−0.0904689	−0.0452344	+	0.998976i	$0.514403\pi$
$930$	22.3265	0.732115
$931$	−0.279544	−0.00916169
$932$	−8.60681	−0.281926
$933$	−34.1034	−1.11650
$934$	31.1473	1.01917
$935$	−38.2807	−1.25191
$936$	−1.11509	−0.0364477
$937$	58.9796	1.92678	0.963390	−	0.268102i	$-0.0863966\pi$
$937$	58.9796	1.92678	0.963390	+	0.268102i	$0.0863966\pi$
$938$	−19.1908	−0.626602
$939$	44.8178	1.46257
$940$	16.3601	0.533609
$941$	−52.7412	−1.71932	−0.859658	−	0.510870i	$-0.829323\pi$
$941$	−52.7412	−1.71932	−0.859658	+	0.510870i	$0.829323\pi$
$942$	33.0343	1.07631
$943$	42.0058	1.36790
$944$	3.45065	0.112309
$945$	−24.0797	−0.783312
$946$	20.7080	0.673275
$947$	−37.7156	−1.22559	−0.612797	−	0.790241i	$-0.709956\pi$
$947$	−37.7156	−1.22559	−0.612797	+	0.790241i	$0.709956\pi$
$948$	−4.15615	−0.134986
$949$	−32.1751	−1.04445
$950$	1.08315	0.0351421
$951$	28.9965	0.940275
$952$	−19.4758	−0.631213
$953$	59.5864	1.93019	0.965096	−	0.261895i	$-0.0843475\pi$
$953$	59.5864	1.93019	0.965096	+	0.261895i	$0.0843475\pi$
$954$	3.21631	0.104132
$955$	18.8362	0.609524
$956$	−7.45410	−0.241083
$957$	47.6635	1.54074
$958$	−11.2780	−0.364376
$959$	−52.7617	−1.70377
$960$	2.45814	0.0793362
$961$	51.4950	1.66113
$962$	−21.8365	−0.704038
$963$	−3.46470	−0.111648
$964$	−13.5963	−0.437909
$965$	−28.5835	−0.920136
$966$	−37.3764	−1.20257
$967$	−32.8926	−1.05776	−0.528878	−	0.848698i	$-0.677387\pi$
$967$	−32.8926	−1.05776	−0.528878	+	0.848698i	$0.677387\pi$
$968$	1.04146	0.0334738
$969$	−4.70098	−0.151017
$970$	24.6752	0.792274
$971$	−26.5255	−0.851244	−0.425622	−	0.904901i	$-0.639945\pi$
$971$	−26.5255	−0.851244	−0.425622	+	0.904901i	$0.639945\pi$
$972$	−5.54133	−0.177738
$973$	−43.6236	−1.39851
$974$	27.2349	0.872664
$975$	8.23403	0.263700
$976$	3.56279	0.114042
$977$	36.7454	1.17559	0.587795	−	0.809010i	$-0.299996\pi$
$977$	36.7454	1.17559	0.587795	+	0.809010i	$0.299996\pi$
$978$	−9.14992	−0.292582
$979$	7.78701	0.248874
$980$	−1.02885	−0.0328653
$981$	0.376281	0.0120137
$982$	29.9497	0.955735
$983$	−2.81659	−0.0898353	−0.0449177	−	0.998991i	$-0.514303\pi$
$983$	−2.81659	−0.0898353	−0.0449177	+	0.998991i	$0.514303\pi$
$984$	−7.64928	−0.243850
$985$	−4.38861	−0.139833
$986$	−61.6424	−1.96309
$987$	45.2991	1.44188
$988$	−0.879010	−0.0279650
$989$	−51.3966	−1.63432
$990$	−2.93814	−0.0933802
$991$	0.811160	0.0257673	0.0128837	−	0.999917i	$-0.495899\pi$
$991$	0.811160	0.0257673	0.0128837	+	0.999917i	$0.495899\pi$
$992$	9.08268	0.288375
$993$	15.8388	0.502630
$994$	14.6237	0.463837
$995$	11.5512	0.366199
$996$	−9.62999	−0.305138
$997$	−61.6833	−1.95353	−0.976765	−	0.214311i	$-0.931249\pi$
$997$	−61.6833	−1.95353	−0.976765	+	0.214311i	$0.931249\pi$
$998$	−11.4793	−0.363372
$999$	−58.7391	−1.85842

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.b.1.19	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.b.1.19	✓	54	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.56837 q^{3} +1.00000 q^{4} -1.56733 q^{5} -1.56837 q^{6} +2.76703 q^{7} +1.00000 q^{8} -0.540224 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.56837 q^{3} +1.00000 q^{4} -1.56733 q^{5} -1.56837 q^{6} +2.76703 q^{7} +1.00000 q^{8} -0.540224 q^{9} -1.56733 q^{10} -3.47008 q^{11} -1.56837 q^{12} +2.06412 q^{13} +2.76703 q^{14} +2.45814 q^{15} +1.00000 q^{16} -7.03851 q^{17} -0.540224 q^{18} -0.425853 q^{19} -1.56733 q^{20} -4.33971 q^{21} -3.47008 q^{22} +8.61264 q^{23} -1.56837 q^{24} -2.54349 q^{25} +2.06412 q^{26} +5.55237 q^{27} +2.76703 q^{28} +8.75787 q^{29} +2.45814 q^{30} +9.08268 q^{31} +1.00000 q^{32} +5.44236 q^{33} -7.03851 q^{34} -4.33683 q^{35} -0.540224 q^{36} -10.5791 q^{37} -0.425853 q^{38} -3.23730 q^{39} -1.56733 q^{40} +4.87722 q^{41} -4.33971 q^{42} -5.96758 q^{43} -3.47008 q^{44} +0.846706 q^{45} +8.61264 q^{46} -10.4383 q^{47} -1.56837 q^{48} +0.656434 q^{49} -2.54349 q^{50} +11.0390 q^{51} +2.06412 q^{52} -5.95366 q^{53} +5.55237 q^{54} +5.43874 q^{55} +2.76703 q^{56} +0.667893 q^{57} +8.75787 q^{58} +3.45065 q^{59} +2.45814 q^{60} +3.56279 q^{61} +9.08268 q^{62} -1.49481 q^{63} +1.00000 q^{64} -3.23514 q^{65} +5.44236 q^{66} -6.93553 q^{67} -7.03851 q^{68} -13.5078 q^{69} -4.33683 q^{70} +5.28501 q^{71} -0.540224 q^{72} -15.5878 q^{73} -10.5791 q^{74} +3.98913 q^{75} -0.425853 q^{76} -9.60180 q^{77} -3.23730 q^{78} +2.64999 q^{79} -1.56733 q^{80} -7.08749 q^{81} +4.87722 q^{82} +6.14014 q^{83} -4.33971 q^{84} +11.0316 q^{85} -5.96758 q^{86} -13.7356 q^{87} -3.47008 q^{88} -2.24404 q^{89} +0.846706 q^{90} +5.71147 q^{91} +8.61264 q^{92} -14.2450 q^{93} -10.4383 q^{94} +0.667449 q^{95} -1.56837 q^{96} -15.7435 q^{97} +0.656434 q^{98} +1.87462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9} - 14 q^{10} - 31 q^{11} - 21 q^{12} - 34 q^{13} - 44 q^{14} - 22 q^{15} + 54 q^{16} - 40 q^{17} + 39 q^{18} - 44 q^{19} - 14 q^{20} - 3 q^{21} - 31 q^{22} - 33 q^{23} - 21 q^{24} + 14 q^{25} - 34 q^{26} - 66 q^{27} - 44 q^{28} - 22 q^{30} - 65 q^{31} + 54 q^{32} - 43 q^{33} - 40 q^{34} - 46 q^{35} + 39 q^{36} - 58 q^{37} - 44 q^{38} - 36 q^{39} - 14 q^{40} - 49 q^{41} - 3 q^{42} - 47 q^{43} - 31 q^{44} - 45 q^{45} - 33 q^{46} - 66 q^{47} - 21 q^{48} + 16 q^{49} + 14 q^{50} - 33 q^{51} - 34 q^{52} - 16 q^{53} - 66 q^{54} - 50 q^{55} - 44 q^{56} - 33 q^{57} - 70 q^{59} - 22 q^{60} - 40 q^{61} - 65 q^{62} - 117 q^{63} + 54 q^{64} - 33 q^{65} - 43 q^{66} - 82 q^{67} - 40 q^{68} - q^{69} - 46 q^{70} - 60 q^{71} + 39 q^{72} - 92 q^{73} - 58 q^{74} - 68 q^{75} - 44 q^{76} + 13 q^{77} - 36 q^{78} - 57 q^{79} - 14 q^{80} + 26 q^{81} - 49 q^{82} - 77 q^{83} - 3 q^{84} - 24 q^{85} - 47 q^{86} - 61 q^{87} - 31 q^{88} - 54 q^{89} - 45 q^{90} - 46 q^{91} - 33 q^{92} - 24 q^{93} - 66 q^{94} - 66 q^{95} - 21 q^{96} - 137 q^{97} + 16 q^{98} - 71 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9 - 14 * q^10 - 31 * q^11 - 21 * q^12 - 34 * q^13 - 44 * q^14 - 22 * q^15 + 54 * q^16 - 40 * q^17 + 39 * q^18 - 44 * q^19 - 14 * q^20 - 3 * q^21 - 31 * q^22 - 33 * q^23 - 21 * q^24 + 14 * q^25 - 34 * q^26 - 66 * q^27 - 44 * q^28 - 22 * q^30 - 65 * q^31 + 54 * q^32 - 43 * q^33 - 40 * q^34 - 46 * q^35 + 39 * q^36 - 58 * q^37 - 44 * q^38 - 36 * q^39 - 14 * q^40 - 49 * q^41 - 3 * q^42 - 47 * q^43 - 31 * q^44 - 45 * q^45 - 33 * q^46 - 66 * q^47 - 21 * q^48 + 16 * q^49 + 14 * q^50 - 33 * q^51 - 34 * q^52 - 16 * q^53 - 66 * q^54 - 50 * q^55 - 44 * q^56 - 33 * q^57 - 70 * q^59 - 22 * q^60 - 40 * q^61 - 65 * q^62 - 117 * q^63 + 54 * q^64 - 33 * q^65 - 43 * q^66 - 82 * q^67 - 40 * q^68 - q^69 - 46 * q^70 - 60 * q^71 + 39 * q^72 - 92 * q^73 - 58 * q^74 - 68 * q^75 - 44 * q^76 + 13 * q^77 - 36 * q^78 - 57 * q^79 - 14 * q^80 + 26 * q^81 - 49 * q^82 - 77 * q^83 - 3 * q^84 - 24 * q^85 - 47 * q^86 - 61 * q^87 - 31 * q^88 - 54 * q^89 - 45 * q^90 - 46 * q^91 - 33 * q^92 - 24 * q^93 - 66 * q^94 - 66 * q^95 - 21 * q^96 - 137 * q^97 + 16 * q^98 - 71 * q^99

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