LMFDB - Embedded newform 6005.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43196 q^{2} -2.45366 q^{3} +3.91445 q^{4} -1.00000 q^{5} +5.96721 q^{6} -1.89640 q^{7} -4.65586 q^{8} +3.02044 q^{9} +O(q^{10})$	\(q-2.43196 q^{2} -2.45366 q^{3} +3.91445 q^{4} -1.00000 q^{5} +5.96721 q^{6} -1.89640 q^{7} -4.65586 q^{8} +3.02044 q^{9} +2.43196 q^{10} -3.71453 q^{11} -9.60472 q^{12} +4.94359 q^{13} +4.61199 q^{14} +2.45366 q^{15} +3.49399 q^{16} +3.66014 q^{17} -7.34561 q^{18} -6.10112 q^{19} -3.91445 q^{20} +4.65313 q^{21} +9.03361 q^{22} -0.343760 q^{23} +11.4239 q^{24} +1.00000 q^{25} -12.0226 q^{26} -0.0501619 q^{27} -7.42337 q^{28} -0.905167 q^{29} -5.96721 q^{30} -6.56706 q^{31} +0.814461 q^{32} +9.11420 q^{33} -8.90133 q^{34} +1.89640 q^{35} +11.8234 q^{36} +0.246586 q^{37} +14.8377 q^{38} -12.1299 q^{39} +4.65586 q^{40} +2.53826 q^{41} -11.3162 q^{42} +0.967901 q^{43} -14.5403 q^{44} -3.02044 q^{45} +0.836012 q^{46} -2.38343 q^{47} -8.57307 q^{48} -3.40365 q^{49} -2.43196 q^{50} -8.98074 q^{51} +19.3514 q^{52} -2.25731 q^{53} +0.121992 q^{54} +3.71453 q^{55} +8.82940 q^{56} +14.9701 q^{57} +2.20133 q^{58} +9.37732 q^{59} +9.60472 q^{60} -7.65800 q^{61} +15.9709 q^{62} -5.72798 q^{63} -8.96872 q^{64} -4.94359 q^{65} -22.1654 q^{66} -1.24306 q^{67} +14.3274 q^{68} +0.843470 q^{69} -4.61199 q^{70} +15.2494 q^{71} -14.0628 q^{72} -2.13297 q^{73} -0.599689 q^{74} -2.45366 q^{75} -23.8825 q^{76} +7.04426 q^{77} +29.4994 q^{78} -5.38326 q^{79} -3.49399 q^{80} -8.93825 q^{81} -6.17296 q^{82} +4.37731 q^{83} +18.2144 q^{84} -3.66014 q^{85} -2.35390 q^{86} +2.22097 q^{87} +17.2944 q^{88} -3.94489 q^{89} +7.34561 q^{90} -9.37505 q^{91} -1.34563 q^{92} +16.1133 q^{93} +5.79642 q^{94} +6.10112 q^{95} -1.99841 q^{96} +1.90366 q^{97} +8.27755 q^{98} -11.2195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) $ 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * 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 $

$2$	−2.43196	−1.71966	−0.859829	−	0.510582i	$-0.829430\pi$
$2$	−2.43196	−1.71966	−0.859829	+	0.510582i	$0.829430\pi$
$3$	−2.45366	−1.41662	−0.708310	−	0.705901i	$-0.750542\pi$
$3$	−2.45366	−1.41662	−0.708310	+	0.705901i	$0.750542\pi$
$4$	3.91445	1.95722
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.96721	2.43610
$7$	−1.89640	−0.716774	−0.358387	−	0.933573i	$-0.616673\pi$
$7$	−1.89640	−0.716774	−0.358387	+	0.933573i	$0.616673\pi$
$8$	−4.65586	−1.64610
$9$	3.02044	1.00681
$10$	2.43196	0.769054
$11$	−3.71453	−1.11997	−0.559987	−	0.828501i	$-0.689194\pi$
$11$	−3.71453	−1.11997	−0.559987	+	0.828501i	$0.689194\pi$
$12$	−9.60472	−2.77264
$13$	4.94359	1.37110	0.685552	−	0.728023i	$-0.259561\pi$
$13$	4.94359	1.37110	0.685552	+	0.728023i	$0.259561\pi$
$14$	4.61199	1.23261
$15$	2.45366	0.633532
$16$	3.49399	0.873498
$17$	3.66014	0.887714	0.443857	−	0.896098i	$-0.353610\pi$
$17$	3.66014	0.887714	0.443857	+	0.896098i	$0.353610\pi$
$18$	−7.34561	−1.73138
$19$	−6.10112	−1.39969	−0.699846	−	0.714293i	$-0.746748\pi$
$19$	−6.10112	−1.39969	−0.699846	+	0.714293i	$0.746748\pi$
$20$	−3.91445	−0.875297
$21$	4.65313	1.01540
$22$	9.03361	1.92597
$23$	−0.343760	−0.0716789	−0.0358395	−	0.999358i	$-0.511411\pi$
$23$	−0.343760	−0.0716789	−0.0358395	+	0.999358i	$0.511411\pi$
$24$	11.4239	2.33189
$25$	1.00000	0.200000
$26$	−12.0226	−2.35783
$27$	−0.0501619	−0.00965366
$28$	−7.42337	−1.40289
$29$	−0.905167	−0.168085	−0.0840427	−	0.996462i	$-0.526783\pi$
$29$	−0.905167	−0.168085	−0.0840427	+	0.996462i	$0.526783\pi$
$30$	−5.96721	−1.08946
$31$	−6.56706	−1.17948	−0.589739	−	0.807594i	$-0.700770\pi$
$31$	−6.56706	−1.17948	−0.589739	+	0.807594i	$0.700770\pi$
$32$	0.814461	0.143978
$33$	9.11420	1.58658
$34$	−8.90133	−1.52656
$35$	1.89640	0.320551
$36$	11.8234	1.97056
$37$	0.246586	0.0405385	0.0202693	−	0.999795i	$-0.493548\pi$
$37$	0.246586	0.0405385	0.0202693	+	0.999795i	$0.493548\pi$
$38$	14.8377	2.40699
$39$	−12.1299	−1.94234
$40$	4.65586	0.736156
$41$	2.53826	0.396410	0.198205	−	0.980161i	$-0.436489\pi$
$41$	2.53826	0.396410	0.198205	+	0.980161i	$0.436489\pi$
$42$	−11.3162	−1.74613
$43$	0.967901	0.147604	0.0738018	−	0.997273i	$-0.476487\pi$
$43$	0.967901	0.147604	0.0738018	+	0.997273i	$0.476487\pi$
$44$	−14.5403	−2.19204
$45$	−3.02044	−0.450261
$46$	0.836012	0.123263
$47$	−2.38343	−0.347659	−0.173830	−	0.984776i	$-0.555614\pi$
$47$	−2.38343	−0.347659	−0.173830	+	0.984776i	$0.555614\pi$
$48$	−8.57307	−1.23742
$49$	−3.40365	−0.486236
$50$	−2.43196	−0.343932
$51$	−8.98074	−1.25755
$52$	19.3514	2.68356
$53$	−2.25731	−0.310065	−0.155033	−	0.987909i	$-0.549548\pi$
$53$	−2.25731	−0.310065	−0.155033	+	0.987909i	$0.549548\pi$
$54$	0.121992	0.0166010
$55$	3.71453	0.500868
$56$	8.82940	1.17988
$57$	14.9701	1.98283
$58$	2.20133	0.289049
$59$	9.37732	1.22082	0.610412	−	0.792084i	$-0.291004\pi$
$59$	9.37732	1.22082	0.610412	+	0.792084i	$0.291004\pi$
$60$	9.60472	1.23996
$61$	−7.65800	−0.980507	−0.490253	−	0.871580i	$-0.663096\pi$
$61$	−7.65800	−0.980507	−0.490253	+	0.871580i	$0.663096\pi$
$62$	15.9709	2.02830
$63$	−5.72798	−0.721658
$64$	−8.96872	−1.12109
$65$	−4.94359	−0.613177
$66$	−22.1654	−2.72837
$67$	−1.24306	−0.151863	−0.0759317	−	0.997113i	$-0.524193\pi$
$67$	−1.24306	−0.151863	−0.0759317	+	0.997113i	$0.524193\pi$
$68$	14.3274	1.73745
$69$	0.843470	0.101542
$70$	−4.61199	−0.551238
$71$	15.2494	1.80977	0.904885	−	0.425657i	$-0.139957\pi$
$71$	15.2494	1.80977	0.904885	+	0.425657i	$0.139957\pi$
$72$	−14.0628	−1.65731
$73$	−2.13297	−0.249645	−0.124823	−	0.992179i	$-0.539836\pi$
$73$	−2.13297	−0.249645	−0.124823	+	0.992179i	$0.539836\pi$
$74$	−0.599689	−0.0697124
$75$	−2.45366	−0.283324
$76$	−23.8825	−2.73951
$77$	7.04426	0.802768
$78$	29.4994	3.34015
$79$	−5.38326	−0.605664	−0.302832	−	0.953044i	$-0.597932\pi$
$79$	−5.38326	−0.605664	−0.302832	+	0.953044i	$0.597932\pi$
$80$	−3.49399	−0.390640
$81$	−8.93825	−0.993139
$82$	−6.17296	−0.681690
$83$	4.37731	0.480472	0.240236	−	0.970715i	$-0.422775\pi$
$83$	4.37731	0.480472	0.240236	+	0.970715i	$0.422775\pi$
$84$	18.2144	1.98736
$85$	−3.66014	−0.396998
$86$	−2.35390	−0.253828
$87$	2.22097	0.238113
$88$	17.2944	1.84358
$89$	−3.94489	−0.418158	−0.209079	−	0.977899i	$-0.567047\pi$
$89$	−3.94489	−0.418158	−0.209079	+	0.977899i	$0.567047\pi$
$90$	7.34561	0.774295
$91$	−9.37505	−0.982772
$92$	−1.34563	−0.140292
$93$	16.1133	1.67087
$94$	5.79642	0.597855
$95$	6.10112	0.625962
$96$	−1.99841	−0.203962
$97$	1.90366	0.193288	0.0966438	−	0.995319i	$-0.469189\pi$
$97$	1.90366	0.193288	0.0966438	+	0.995319i	$0.469189\pi$
$98$	8.27755	0.836159
$99$	−11.2195	−1.12761
$100$	3.91445	0.391445
$101$	2.54141	0.252879	0.126440	−	0.991974i	$-0.459645\pi$
$101$	2.54141	0.252879	0.126440	+	0.991974i	$0.459645\pi$
$102$	21.8408	2.16256
$103$	1.97008	0.194118	0.0970590	−	0.995279i	$-0.469056\pi$
$103$	1.97008	0.194118	0.0970590	+	0.995279i	$0.469056\pi$
$104$	−23.0167	−2.25697
$105$	−4.65313	−0.454099
$106$	5.48969	0.533206
$107$	−9.02372	−0.872356	−0.436178	−	0.899860i	$-0.643668\pi$
$107$	−9.02372	−0.872356	−0.436178	+	0.899860i	$0.643668\pi$
$108$	−0.196356	−0.0188944
$109$	11.4096	1.09285	0.546423	−	0.837509i	$-0.315989\pi$
$109$	11.4096	1.09285	0.546423	+	0.837509i	$0.315989\pi$
$110$	−9.03361	−0.861321
$111$	−0.605039	−0.0574277
$112$	−6.62602	−0.626100
$113$	17.4079	1.63760	0.818799	−	0.574080i	$-0.194640\pi$
$113$	17.4079	1.63760	0.818799	+	0.574080i	$0.194640\pi$
$114$	−36.4067	−3.40980
$115$	0.343760	0.0320558
$116$	−3.54323	−0.328980
$117$	14.9318	1.38045
$118$	−22.8053	−2.09940
$119$	−6.94111	−0.636290
$120$	−11.4239	−1.04285
$121$	2.79776	0.254342
$122$	18.6240	1.68614
$123$	−6.22803	−0.561563
$124$	−25.7064	−2.30850
$125$	−1.00000	−0.0894427
$126$	13.9302	1.24101
$127$	−15.0030	−1.33130	−0.665649	−	0.746265i	$-0.731845\pi$
$127$	−15.0030	−1.33130	−0.665649	+	0.746265i	$0.731845\pi$
$128$	20.1827	1.78391
$129$	−2.37490	−0.209098
$130$	12.0226	1.05445
$131$	−8.80686	−0.769459	−0.384730	−	0.923029i	$-0.625705\pi$
$131$	−8.80686	−0.769459	−0.384730	+	0.923029i	$0.625705\pi$
$132$	35.6770	3.10529
$133$	11.5702	1.00326
$134$	3.02307	0.261153
$135$	0.0501619	0.00431725
$136$	−17.0411	−1.46126
$137$	−2.84504	−0.243068	−0.121534	−	0.992587i	$-0.538781\pi$
$137$	−2.84504	−0.243068	−0.121534	+	0.992587i	$0.538781\pi$
$138$	−2.05129	−0.174617
$139$	−3.82070	−0.324068	−0.162034	−	0.986785i	$-0.551805\pi$
$139$	−3.82070	−0.324068	−0.162034	+	0.986785i	$0.551805\pi$
$140$	7.42337	0.627390
$141$	5.84813	0.492501
$142$	−37.0859	−3.11218
$143$	−18.3631	−1.53560
$144$	10.5534	0.879451
$145$	0.905167	0.0751701
$146$	5.18730	0.429304
$147$	8.35139	0.688811
$148$	0.965249	0.0793430
$149$	15.2587	1.25004	0.625020	−	0.780609i	$-0.285091\pi$
$149$	15.2587	1.25004	0.625020	+	0.780609i	$0.285091\pi$
$150$	5.96721	0.487221
$151$	7.23810	0.589028	0.294514	−	0.955647i	$-0.404842\pi$
$151$	7.23810	0.589028	0.294514	+	0.955647i	$0.404842\pi$
$152$	28.4060	2.30403
$153$	11.0552	0.893764
$154$	−17.1314	−1.38049
$155$	6.56706	0.527479
$156$	−47.4818	−3.80158
$157$	12.4675	0.995017	0.497508	−	0.867459i	$-0.334248\pi$
$157$	12.4675	0.995017	0.497508	+	0.867459i	$0.334248\pi$
$158$	13.0919	1.04153
$159$	5.53867	0.439245
$160$	−0.814461	−0.0643888
$161$	0.651908	0.0513776
$162$	21.7375	1.70786
$163$	−4.29345	−0.336289	−0.168144	−	0.985762i	$-0.553777\pi$
$163$	−4.29345	−0.336289	−0.168144	+	0.985762i	$0.553777\pi$
$164$	9.93590	0.775863
$165$	−9.11420	−0.709540
$166$	−10.6454	−0.826247
$167$	7.40736	0.573199	0.286599	−	0.958051i	$-0.407475\pi$
$167$	7.40736	0.573199	0.286599	+	0.958051i	$0.407475\pi$
$168$	−21.6643	−1.67144
$169$	11.4391	0.879929
$170$	8.90133	0.682701
$171$	−18.4281	−1.40923
$172$	3.78880	0.288893
$173$	4.99159	0.379503	0.189752	−	0.981832i	$-0.439232\pi$
$173$	4.99159	0.379503	0.189752	+	0.981832i	$0.439232\pi$
$174$	−5.40132	−0.409473
$175$	−1.89640	−0.143355
$176$	−12.9786	−0.978295
$177$	−23.0088	−1.72944
$178$	9.59383	0.719088
$179$	15.1926	1.13555	0.567773	−	0.823185i	$-0.307805\pi$
$179$	15.1926	1.13555	0.567773	+	0.823185i	$0.307805\pi$
$180$	−11.8234	−0.881261
$181$	−4.74681	−0.352828	−0.176414	−	0.984316i	$-0.556450\pi$
$181$	−4.74681	−0.352828	−0.176414	+	0.984316i	$0.556450\pi$
$182$	22.7998	1.69003
$183$	18.7901	1.38901
$184$	1.60050	0.117990
$185$	−0.246586	−0.0181294
$186$	−39.1870	−2.87333
$187$	−13.5957	−0.994217
$188$	−9.32981	−0.680446
$189$	0.0951272	0.00691949
$190$	−14.8377	−1.07644
$191$	−10.9138	−0.789694	−0.394847	−	0.918747i	$-0.629202\pi$
$191$	−10.9138	−0.789694	−0.394847	+	0.918747i	$0.629202\pi$
$192$	22.0062	1.58816
$193$	8.73116	0.628482	0.314241	−	0.949343i	$-0.398250\pi$
$193$	8.73116	0.628482	0.314241	+	0.949343i	$0.398250\pi$
$194$	−4.62964	−0.332389
$195$	12.1299	0.868639
$196$	−13.3234	−0.951671
$197$	−6.01764	−0.428739	−0.214369	−	0.976753i	$-0.568770\pi$
$197$	−6.01764	−0.428739	−0.214369	+	0.976753i	$0.568770\pi$
$198$	27.2855	1.93910
$199$	−0.644829	−0.0457107	−0.0228554	−	0.999739i	$-0.507276\pi$
$199$	−0.644829	−0.0457107	−0.0228554	+	0.999739i	$0.507276\pi$
$200$	−4.65586	−0.329219
$201$	3.05004	0.215133
$202$	−6.18061	−0.434866
$203$	1.71656	0.120479
$204$	−35.1546	−2.46131
$205$	−2.53826	−0.177280
$206$	−4.79117	−0.333817
$207$	−1.03831	−0.0721674
$208$	17.2729	1.19766
$209$	22.6628	1.56762
$210$	11.3162	0.780895
$211$	6.22843	0.428783	0.214391	−	0.976748i	$-0.431223\pi$
$211$	6.22843	0.428783	0.214391	+	0.976748i	$0.431223\pi$
$212$	−8.83611	−0.606867
$213$	−37.4168	−2.56376
$214$	21.9454	1.50015
$215$	−0.967901	−0.0660103
$216$	0.233547	0.0158908
$217$	12.4538	0.845419
$218$	−27.7478	−1.87932
$219$	5.23358	0.353653
$220$	14.5403	0.980309
$221$	18.0942	1.21715
$222$	1.47143	0.0987561
$223$	2.44484	0.163719	0.0818594	−	0.996644i	$-0.473914\pi$
$223$	2.44484	0.163719	0.0818594	+	0.996644i	$0.473914\pi$
$224$	−1.54455	−0.103199
$225$	3.02044	0.201363
$226$	−42.3354	−2.81611
$227$	7.13994	0.473894	0.236947	−	0.971523i	$-0.423853\pi$
$227$	7.13994	0.473894	0.236947	+	0.971523i	$0.423853\pi$
$228$	58.5995	3.88085
$229$	3.98758	0.263507	0.131753	−	0.991283i	$-0.457939\pi$
$229$	3.98758	0.263507	0.131753	+	0.991283i	$0.457939\pi$
$230$	−0.836012	−0.0551250
$231$	−17.2842	−1.13722
$232$	4.21433	0.276685
$233$	20.6302	1.35153	0.675763	−	0.737119i	$-0.263814\pi$
$233$	20.6302	1.35153	0.675763	+	0.737119i	$0.263814\pi$
$234$	−36.3137	−2.37390
$235$	2.38343	0.155478
$236$	36.7070	2.38942
$237$	13.2087	0.857996
$238$	16.8805	1.09420
$239$	20.5838	1.33146	0.665728	−	0.746194i	$-0.268121\pi$
$239$	20.5838	1.33146	0.665728	+	0.746194i	$0.268121\pi$
$240$	8.57307	0.553389
$241$	19.7302	1.27094	0.635468	−	0.772127i	$-0.280807\pi$
$241$	19.7302	1.27094	0.635468	+	0.772127i	$0.280807\pi$
$242$	−6.80405	−0.437381
$243$	22.0819	1.41656
$244$	−29.9768	−1.91907
$245$	3.40365	0.217451
$246$	15.1464	0.965696
$247$	−30.1614	−1.91913
$248$	30.5753	1.94153
$249$	−10.7404	−0.680646
$250$	2.43196	0.153811
$251$	−1.95490	−0.123392	−0.0616962	−	0.998095i	$-0.519651\pi$
$251$	−1.95490	−0.123392	−0.0616962	+	0.998095i	$0.519651\pi$
$252$	−22.4219	−1.41245
$253$	1.27691	0.0802786
$254$	36.4867	2.28938
$255$	8.98074	0.562396
$256$	−31.1461	−1.94663
$257$	21.4570	1.33845	0.669226	−	0.743059i	$-0.266626\pi$
$257$	21.4570	1.33845	0.669226	+	0.743059i	$0.266626\pi$
$258$	5.77567	0.359578
$259$	−0.467627	−0.0290570
$260$	−19.3514	−1.20012
$261$	−2.73401	−0.169231
$262$	21.4180	1.32321
$263$	−4.08817	−0.252087	−0.126044	−	0.992025i	$-0.540228\pi$
$263$	−4.08817	−0.252087	−0.126044	+	0.992025i	$0.540228\pi$
$264$	−42.4344	−2.61166
$265$	2.25731	0.138665
$266$	−28.1383	−1.72527
$267$	9.67942	0.592371
$268$	−4.86588	−0.297231
$269$	−3.05679	−0.186376	−0.0931879	−	0.995649i	$-0.529706\pi$
$269$	−3.05679	−0.186376	−0.0931879	+	0.995649i	$0.529706\pi$
$270$	−0.121992	−0.00742419
$271$	29.3999	1.78592	0.892960	−	0.450136i	$-0.148625\pi$
$271$	29.3999	1.78592	0.892960	+	0.450136i	$0.148625\pi$
$272$	12.7885	0.775417
$273$	23.0032	1.39222
$274$	6.91904	0.417994
$275$	−3.71453	−0.223995
$276$	3.30172	0.198740
$277$	10.1416	0.609350	0.304675	−	0.952456i	$-0.401452\pi$
$277$	10.1416	0.609350	0.304675	+	0.952456i	$0.401452\pi$
$278$	9.29181	0.557286
$279$	−19.8354	−1.18752
$280$	−8.82940	−0.527657
$281$	−15.8590	−0.946070	−0.473035	−	0.881044i	$-0.656842\pi$
$281$	−15.8590	−0.946070	−0.473035	+	0.881044i	$0.656842\pi$
$282$	−14.2224	−0.846934
$283$	−12.7140	−0.755767	−0.377883	−	0.925853i	$-0.623348\pi$
$283$	−12.7140	−0.755767	−0.377883	+	0.925853i	$0.623348\pi$
$284$	59.6929	3.54212
$285$	−14.9701	−0.886750
$286$	44.6585	2.64071
$287$	−4.81358	−0.284136
$288$	2.46003	0.144959
$289$	−3.60337	−0.211963
$290$	−2.20133	−0.129267
$291$	−4.67094	−0.273815
$292$	−8.34939	−0.488611
$293$	6.64804	0.388383	0.194191	−	0.980964i	$-0.437792\pi$
$293$	6.64804	0.388383	0.194191	+	0.980964i	$0.437792\pi$
$294$	−20.3103	−1.18452
$295$	−9.37732	−0.545969
$296$	−1.14807	−0.0667303
$297$	0.186328	0.0108118
$298$	−37.1086	−2.14964
$299$	−1.69941	−0.0982794
$300$	−9.60472	−0.554528
$301$	−1.83553	−0.105798
$302$	−17.6028	−1.01293
$303$	−6.23575	−0.358234
$304$	−21.3173	−1.22263
$305$	7.65800	0.438496
$306$	−26.8860	−1.53697
$307$	6.36012	0.362991	0.181496	−	0.983392i	$-0.441906\pi$
$307$	6.36012	0.362991	0.181496	+	0.983392i	$0.441906\pi$
$308$	27.5744	1.57120
$309$	−4.83391	−0.274992
$310$	−15.9709	−0.907083
$311$	−4.49738	−0.255023	−0.127512	−	0.991837i	$-0.540699\pi$
$311$	−4.49738	−0.255023	−0.127512	+	0.991837i	$0.540699\pi$
$312$	56.4750	3.19727
$313$	17.1849	0.971348	0.485674	−	0.874140i	$-0.338574\pi$
$313$	17.1849	0.971348	0.485674	+	0.874140i	$0.338574\pi$
$314$	−30.3206	−1.71109
$315$	5.72798	0.322735
$316$	−21.0725	−1.18542
$317$	−0.769929	−0.0432435	−0.0216218	−	0.999766i	$-0.506883\pi$
$317$	−0.769929	−0.0432435	−0.0216218	+	0.999766i	$0.506883\pi$
$318$	−13.4698	−0.755351
$319$	3.36227	0.188251
$320$	8.96872	0.501367
$321$	22.1411	1.23580
$322$	−1.58542	−0.0883519
$323$	−22.3310	−1.24253
$324$	−34.9883	−1.94379
$325$	4.94359	0.274221
$326$	10.4415	0.578301
$327$	−27.9954	−1.54815
$328$	−11.8178	−0.652529
$329$	4.51995	0.249193
$330$	22.1654	1.22017
$331$	−16.6597	−0.915701	−0.457851	−	0.889029i	$-0.651381\pi$
$331$	−16.6597	−0.915701	−0.457851	+	0.889029i	$0.651381\pi$
$332$	17.1347	0.940390
$333$	0.744800	0.0408148
$334$	−18.0144	−0.985705
$335$	1.24306	0.0679154
$336$	16.2580	0.886947
$337$	21.9183	1.19397	0.596984	−	0.802253i	$-0.296366\pi$
$337$	21.9183	1.19397	0.596984	+	0.802253i	$0.296366\pi$
$338$	−27.8194	−1.51318
$339$	−42.7131	−2.31986
$340$	−14.3274	−0.777013
$341$	24.3936	1.32099
$342$	44.8164	2.42340
$343$	19.7295	1.06529
$344$	−4.50641	−0.242970
$345$	−0.843470	−0.0454109
$346$	−12.1394	−0.652616
$347$	28.3676	1.52285	0.761427	−	0.648251i	$-0.224499\pi$
$347$	28.3676	1.52285	0.761427	+	0.648251i	$0.224499\pi$
$348$	8.69387	0.466041
$349$	−13.4205	−0.718381	−0.359190	−	0.933264i	$-0.616947\pi$
$349$	−13.4205	−0.718381	−0.359190	+	0.933264i	$0.616947\pi$
$350$	4.61199	0.246521
$351$	−0.247980	−0.0132362
$352$	−3.02534	−0.161251
$353$	−6.17209	−0.328507	−0.164254	−	0.986418i	$-0.552522\pi$
$353$	−6.17209	−0.328507	−0.164254	+	0.986418i	$0.552522\pi$
$354$	55.9564	2.97405
$355$	−15.2494	−0.809353
$356$	−15.4421	−0.818428
$357$	17.0311	0.901382
$358$	−36.9478	−1.95275
$359$	−5.00323	−0.264060	−0.132030	−	0.991246i	$-0.542150\pi$
$359$	−5.00323	−0.264060	−0.132030	+	0.991246i	$0.542150\pi$
$360$	14.0628	0.741173
$361$	18.2237	0.959140
$362$	11.5441	0.606743
$363$	−6.86475	−0.360306
$364$	−36.6981	−1.92350
$365$	2.13297	0.111645
$366$	−45.6969	−2.38862
$367$	−6.05927	−0.316291	−0.158146	−	0.987416i	$-0.550552\pi$
$367$	−6.05927	−0.316291	−0.158146	+	0.987416i	$0.550552\pi$
$368$	−1.20110	−0.0626114
$369$	7.66668	0.399112
$370$	0.599689	0.0311763
$371$	4.28077	0.222247
$372$	63.0748	3.27027
$373$	−24.4183	−1.26433	−0.632167	−	0.774833i	$-0.717834\pi$
$373$	−24.4183	−1.26433	−0.632167	+	0.774833i	$0.717834\pi$
$374$	33.0643	1.70971
$375$	2.45366	0.126706
$376$	11.0969	0.572280
$377$	−4.47478	−0.230463
$378$	−0.231346	−0.0118992
$379$	8.21962	0.422213	0.211107	−	0.977463i	$-0.432293\pi$
$379$	8.21962	0.422213	0.211107	+	0.977463i	$0.432293\pi$
$380$	23.8825	1.22515
$381$	36.8122	1.88595
$382$	26.5419	1.35800
$383$	−2.90549	−0.148464	−0.0742318	−	0.997241i	$-0.523650\pi$
$383$	−2.90549	−0.148464	−0.0742318	+	0.997241i	$0.523650\pi$
$384$	−49.5214	−2.52713
$385$	−7.04426	−0.359009
$386$	−21.2339	−1.08077
$387$	2.92349	0.148609
$388$	7.45178	0.378307
$389$	−15.8338	−0.802807	−0.401404	−	0.915901i	$-0.631478\pi$
$389$	−15.8338	−0.802807	−0.401404	+	0.915901i	$0.631478\pi$
$390$	−29.4994	−1.49376
$391$	−1.25821	−0.0636304
$392$	15.8469	0.800390
$393$	21.6090	1.09003
$394$	14.6347	0.737284
$395$	5.38326	0.270861
$396$	−43.9183	−2.20698
$397$	34.4896	1.73098	0.865492	−	0.500923i	$-0.167006\pi$
$397$	34.4896	1.73098	0.865492	+	0.500923i	$0.167006\pi$
$398$	1.56820	0.0786068
$399$	−28.3893	−1.42124
$400$	3.49399	0.174700
$401$	17.3624	0.867037	0.433519	−	0.901145i	$-0.357272\pi$
$401$	17.3624	0.867037	0.433519	+	0.901145i	$0.357272\pi$
$402$	−7.41758	−0.369955
$403$	−32.4649	−1.61719
$404$	9.94820	0.494941
$405$	8.93825	0.444145
$406$	−4.17462	−0.207183
$407$	−0.915953	−0.0454021
$408$	41.8131	2.07006
$409$	−1.42491	−0.0704573	−0.0352287	−	0.999379i	$-0.511216\pi$
$409$	−1.42491	−0.0704573	−0.0352287	+	0.999379i	$0.511216\pi$
$410$	6.17296	0.304861
$411$	6.98076	0.344336
$412$	7.71178	0.379932
$413$	−17.7832	−0.875054
$414$	2.52513	0.124103
$415$	−4.37731	−0.214874
$416$	4.02636	0.197409
$417$	9.37471	0.459081
$418$	−55.1151	−2.69577
$419$	21.8259	1.06627	0.533134	−	0.846031i	$-0.321014\pi$
$419$	21.8259	1.06627	0.533134	+	0.846031i	$0.321014\pi$
$420$	−18.2144	−0.888773
$421$	19.4516	0.948011	0.474005	−	0.880522i	$-0.342808\pi$
$421$	19.4516	0.948011	0.474005	+	0.880522i	$0.342808\pi$
$422$	−15.1473	−0.737360
$423$	−7.19902	−0.350028
$424$	10.5097	0.510397
$425$	3.66014	0.177543
$426$	90.9963	4.40878
$427$	14.5227	0.702802
$428$	−35.3229	−1.70739
$429$	45.0569	2.17537
$430$	2.35390	0.113515
$431$	0.0292691	0.00140984	0.000704921	−	1.00000i	$-0.499776\pi$
$431$	0.0292691	0.00140984	0.000704921		1.00000i	$0.499776\pi$
$432$	−0.175265	−0.00843245
$433$	0.262278	0.0126043	0.00630215	−	0.999980i	$-0.497994\pi$
$433$	0.262278	0.0126043	0.00630215	+	0.999980i	$0.497994\pi$
$434$	−30.2872	−1.45383
$435$	−2.22097	−0.106487
$436$	44.6624	2.13894
$437$	2.09732	0.100329
$438$	−12.7279	−0.608161
$439$	−25.2195	−1.20366	−0.601832	−	0.798623i	$-0.705562\pi$
$439$	−25.2195	−1.20366	−0.601832	+	0.798623i	$0.705562\pi$
$440$	−17.2944	−0.824476
$441$	−10.2805	−0.489549
$442$	−44.0045	−2.09308
$443$	−36.2626	−1.72289	−0.861444	−	0.507853i	$-0.830439\pi$
$443$	−36.2626	−1.72289	−0.861444	+	0.507853i	$0.830439\pi$
$444$	−2.36839	−0.112399
$445$	3.94489	0.187006
$446$	−5.94577	−0.281540
$447$	−37.4396	−1.77083
$448$	17.0083	0.803568
$449$	−17.0119	−0.802839	−0.401420	−	0.915894i	$-0.631483\pi$
$449$	−17.0119	−0.802839	−0.401420	+	0.915894i	$0.631483\pi$
$450$	−7.34561	−0.346275
$451$	−9.42847	−0.443969
$452$	68.1423	3.20515
$453$	−17.7598	−0.834430
$454$	−17.3641	−0.814936
$455$	9.37505	0.439509
$456$	−69.6986	−3.26393
$457$	−6.56526	−0.307110	−0.153555	−	0.988140i	$-0.549072\pi$
$457$	−6.56526	−0.307110	−0.153555	+	0.988140i	$0.549072\pi$
$458$	−9.69765	−0.453141
$459$	−0.183600	−0.00856969
$460$	1.34563	0.0627403
$461$	−32.1999	−1.49970	−0.749848	−	0.661610i	$-0.769874\pi$
$461$	−32.1999	−1.49970	−0.749848	+	0.661610i	$0.769874\pi$
$462$	42.0346	1.95563
$463$	−6.23788	−0.289899	−0.144949	−	0.989439i	$-0.546302\pi$
$463$	−6.23788	−0.289899	−0.144949	+	0.989439i	$0.546302\pi$
$464$	−3.16265	−0.146822
$465$	−16.1133	−0.747238
$466$	−50.1718	−2.32416
$467$	−29.7179	−1.37518	−0.687589	−	0.726100i	$-0.741331\pi$
$467$	−29.7179	−1.37518	−0.687589	+	0.726100i	$0.741331\pi$
$468$	58.4498	2.70184
$469$	2.35734	0.108852
$470$	−5.79642	−0.267369
$471$	−30.5911	−1.40956
$472$	−43.6595	−2.00959
$473$	−3.59530	−0.165312
$474$	−32.1230	−1.47546
$475$	−6.10112	−0.279939
$476$	−27.1706	−1.24536
$477$	−6.81808	−0.312178
$478$	−50.0591	−2.28965
$479$	21.6800	0.990585	0.495292	−	0.868726i	$-0.335061\pi$
$479$	21.6800	0.990585	0.495292	+	0.868726i	$0.335061\pi$
$480$	1.99841	0.0912145
$481$	1.21902	0.0555826
$482$	−47.9832	−2.18558
$483$	−1.59956	−0.0727826
$484$	10.9517	0.497804
$485$	−1.90366	−0.0864409
$486$	−53.7024	−2.43599
$487$	3.71524	0.168353	0.0841767	−	0.996451i	$-0.473174\pi$
$487$	3.71524	0.168353	0.0841767	+	0.996451i	$0.473174\pi$
$488$	35.6546	1.61401
$489$	10.5347	0.476393
$490$	−8.27755	−0.373942
$491$	−18.8349	−0.850008	−0.425004	−	0.905191i	$-0.639727\pi$
$491$	−18.8349	−0.850008	−0.425004	+	0.905191i	$0.639727\pi$
$492$	−24.3793	−1.09910
$493$	−3.31304	−0.149212
$494$	73.3515	3.30024
$495$	11.2195	0.504281
$496$	−22.9453	−1.03027
$497$	−28.9190	−1.29719
$498$	26.1203	1.17048
$499$	−27.8628	−1.24731	−0.623655	−	0.781700i	$-0.714353\pi$
$499$	−27.8628	−1.24731	−0.623655	+	0.781700i	$0.714353\pi$
$500$	−3.91445	−0.175059
$501$	−18.1751	−0.812005
$502$	4.75425	0.212193
$503$	−24.1021	−1.07466	−0.537329	−	0.843373i	$-0.680567\pi$
$503$	−24.1021	−1.07466	−0.537329	+	0.843373i	$0.680567\pi$
$504$	26.6687	1.18792
$505$	−2.54141	−0.113091
$506$	−3.10540	−0.138052
$507$	−28.0676	−1.24653
$508$	−58.7283	−2.60565
$509$	2.41277	0.106944	0.0534720	−	0.998569i	$-0.482971\pi$
$509$	2.41277	0.106944	0.0534720	+	0.998569i	$0.482971\pi$
$510$	−21.8408	−0.967128
$511$	4.04497	0.178939
$512$	35.3808	1.56363
$513$	0.306044	0.0135122
$514$	−52.1827	−2.30168
$515$	−1.97008	−0.0868122
$516$	−9.29642	−0.409252
$517$	8.85334	0.389369
$518$	1.13725	0.0499680
$519$	−12.2477	−0.537612
$520$	23.0167	1.00935
$521$	−35.2392	−1.54386	−0.771929	−	0.635709i	$-0.780708\pi$
$521$	−35.2392	−1.54386	−0.771929	+	0.635709i	$0.780708\pi$
$522$	6.64900	0.291019
$523$	−3.06407	−0.133983	−0.0669913	−	0.997754i	$-0.521340\pi$
$523$	−3.06407	−0.133983	−0.0669913	+	0.997754i	$0.521340\pi$
$524$	−34.4740	−1.50600
$525$	4.65313	0.203079
$526$	9.94227	0.433504
$527$	−24.0364	−1.04704
$528$	31.8449	1.38587
$529$	−22.8818	−0.994862
$530$	−5.48969	−0.238457
$531$	28.3237	1.22914
$532$	45.2909	1.96361
$533$	12.5481	0.543520
$534$	−23.5400	−1.01867
$535$	9.02372	0.390129
$536$	5.78750	0.249982
$537$	−37.2774	−1.60864
$538$	7.43400	0.320503
$539$	12.6430	0.544571
$540$	0.196356	0.00844981
$541$	−30.4343	−1.30847	−0.654237	−	0.756289i	$-0.727010\pi$
$541$	−30.4343	−1.30847	−0.654237	+	0.756289i	$0.727010\pi$
$542$	−71.4996	−3.07117
$543$	11.6471	0.499823
$544$	2.98104	0.127811
$545$	−11.4096	−0.488735
$546$	−55.9429	−2.39413
$547$	−11.5578	−0.494178	−0.247089	−	0.968993i	$-0.579474\pi$
$547$	−11.5578	−0.494178	−0.247089	+	0.968993i	$0.579474\pi$
$548$	−11.1368	−0.475739
$549$	−23.1306	−0.987189
$550$	9.03361	0.385194
$551$	5.52253	0.235268
$552$	−3.92708	−0.167148
$553$	10.2088	0.434124
$554$	−24.6640	−1.04787
$555$	0.605039	0.0256825
$556$	−14.9559	−0.634273
$557$	−20.1837	−0.855209	−0.427604	−	0.903966i	$-0.640642\pi$
$557$	−20.1837	−0.855209	−0.427604	+	0.903966i	$0.640642\pi$
$558$	48.2391	2.04212
$559$	4.78491	0.202380
$560$	6.62602	0.280001
$561$	33.3593	1.40843
$562$	38.5686	1.62692
$563$	−27.8746	−1.17477	−0.587387	−	0.809306i	$-0.699843\pi$
$563$	−27.8746	−1.17477	−0.587387	+	0.809306i	$0.699843\pi$
$564$	22.8922	0.963935
$565$	−17.4079	−0.732356
$566$	30.9199	1.29966
$567$	16.9505	0.711856
$568$	−70.9990	−2.97905
$569$	13.0297	0.546232	0.273116	−	0.961981i	$-0.411946\pi$
$569$	13.0297	0.546232	0.273116	+	0.961981i	$0.411946\pi$
$570$	36.4067	1.52491
$571$	−30.7611	−1.28731	−0.643656	−	0.765315i	$-0.722583\pi$
$571$	−30.7611	−1.28731	−0.643656	+	0.765315i	$0.722583\pi$
$572$	−71.8815	−3.00551
$573$	26.7787	1.11870
$574$	11.7064	0.488617
$575$	−0.343760	−0.0143358
$576$	−27.0895	−1.12873
$577$	−2.79133	−0.116204	−0.0581022	−	0.998311i	$-0.518505\pi$
$577$	−2.79133	−0.116204	−0.0581022	+	0.998311i	$0.518505\pi$
$578$	8.76327	0.364504
$579$	−21.4233	−0.890321
$580$	3.54323	0.147125
$581$	−8.30115	−0.344390
$582$	11.3596	0.470869
$583$	8.38485	0.347265
$584$	9.93081	0.410940
$585$	−14.9318	−0.617355
$586$	−16.1678	−0.667885
$587$	−37.2892	−1.53909	−0.769546	−	0.638592i	$-0.779517\pi$
$587$	−37.2892	−1.53909	−0.769546	+	0.638592i	$0.779517\pi$
$588$	32.6911	1.34816
$589$	40.0664	1.65091
$590$	22.8053	0.938879
$591$	14.7652	0.607360
$592$	0.861571	0.0354103
$593$	11.6142	0.476937	0.238468	−	0.971150i	$-0.423355\pi$
$593$	11.6142	0.476937	0.238468	+	0.971150i	$0.423355\pi$
$594$	−0.453143	−0.0185927
$595$	6.94111	0.284558
$596$	59.7293	2.44661
$597$	1.58219	0.0647548
$598$	4.13290	0.169007
$599$	6.33519	0.258849	0.129424	−	0.991589i	$-0.458687\pi$
$599$	6.33519	0.258849	0.129424	+	0.991589i	$0.458687\pi$
$600$	11.4239	0.466379
$601$	−14.1929	−0.578939	−0.289469	−	0.957187i	$-0.593479\pi$
$601$	−14.1929	−0.578939	−0.289469	+	0.957187i	$0.593479\pi$
$602$	4.46395	0.181937
$603$	−3.75458	−0.152898
$604$	28.3332	1.15286
$605$	−2.79776	−0.113745
$606$	15.1651	0.616040
$607$	−7.01029	−0.284539	−0.142269	−	0.989828i	$-0.545440\pi$
$607$	−7.01029	−0.284539	−0.142269	+	0.989828i	$0.545440\pi$
$608$	−4.96913	−0.201525
$609$	−4.21186	−0.170673
$610$	−18.6240	−0.754063
$611$	−11.7827	−0.476677
$612$	43.2752	1.74929
$613$	−44.2353	−1.78665	−0.893324	−	0.449414i	$-0.851633\pi$
$613$	−44.2353	−1.78665	−0.893324	+	0.449414i	$0.851633\pi$
$614$	−15.4676	−0.624221
$615$	6.22803	0.251139
$616$	−32.7971	−1.32143
$617$	−10.8133	−0.435327	−0.217664	−	0.976024i	$-0.569844\pi$
$617$	−10.8133	−0.435327	−0.217664	+	0.976024i	$0.569844\pi$
$618$	11.7559	0.472892
$619$	2.04523	0.0822049	0.0411025	−	0.999155i	$-0.486913\pi$
$619$	2.04523	0.0822049	0.0411025	+	0.999155i	$0.486913\pi$
$620$	25.7064	1.03239
$621$	0.0172437	0.000691964 0
$622$	10.9375	0.438553
$623$	7.48111	0.299724
$624$	−42.3817	−1.69663
$625$	1.00000	0.0400000
$626$	−41.7931	−1.67039
$627$	−55.6068	−2.22072
$628$	48.8035	1.94747
$629$	0.902541	0.0359866
$630$	−13.9302	−0.554994
$631$	6.68121	0.265975	0.132987	−	0.991118i	$-0.457543\pi$
$631$	6.68121	0.265975	0.132987	+	0.991118i	$0.457543\pi$
$632$	25.0637	0.996980
$633$	−15.2825	−0.607423
$634$	1.87244	0.0743640
$635$	15.0030	0.595375
$636$	21.6808	0.859700
$637$	−16.8262	−0.666680
$638$	−8.17693	−0.323728
$639$	46.0599	1.82210
$640$	−20.1827	−0.797791
$641$	37.5772	1.48421	0.742106	−	0.670283i	$-0.233827\pi$
$641$	37.5772	1.48421	0.742106	+	0.670283i	$0.233827\pi$
$642$	−53.8464	−2.12515
$643$	19.3468	0.762964	0.381482	−	0.924376i	$-0.375414\pi$
$643$	19.3468	0.762964	0.381482	+	0.924376i	$0.375414\pi$
$644$	2.55186	0.100557
$645$	2.37490	0.0935116
$646$	54.3081	2.13672
$647$	49.3661	1.94078	0.970390	−	0.241542i	$-0.0776531\pi$
$647$	49.3661	1.94078	0.970390	+	0.241542i	$0.0776531\pi$
$648$	41.6153	1.63480
$649$	−34.8324	−1.36729
$650$	−12.0226	−0.471566
$651$	−30.5574	−1.19764
$652$	−16.8065	−0.658192
$653$	3.60569	0.141101	0.0705507	−	0.997508i	$-0.477524\pi$
$653$	3.60569	0.141101	0.0705507	+	0.997508i	$0.477524\pi$
$654$	68.0837	2.66228
$655$	8.80686	0.344113
$656$	8.86867	0.346264
$657$	−6.44251	−0.251346
$658$	−10.9924	−0.428527
$659$	41.1501	1.60298	0.801491	−	0.598007i	$-0.204041\pi$
$659$	41.1501	1.60298	0.801491	+	0.598007i	$0.204041\pi$
$660$	−35.6770	−1.38873
$661$	−36.3721	−1.41471	−0.707355	−	0.706858i	$-0.750112\pi$
$661$	−36.3721	−1.41471	−0.707355	+	0.706858i	$0.750112\pi$
$662$	40.5158	1.57469
$663$	−44.3971	−1.72424
$664$	−20.3801	−0.790902
$665$	−11.5702	−0.448673
$666$	−1.81133	−0.0701875
$667$	0.311160	0.0120482
$668$	28.9957	1.12188
$669$	−5.99882	−0.231928
$670$	−3.02307	−0.116791
$671$	28.4459	1.09814
$672$	3.78980	0.146195
$673$	−17.7225	−0.683152	−0.341576	−	0.939854i	$-0.610961\pi$
$673$	−17.7225	−0.683152	−0.341576	+	0.939854i	$0.610961\pi$
$674$	−53.3046	−2.05321
$675$	−0.0501619	−0.00193073
$676$	44.7776	1.72222
$677$	−21.3192	−0.819364	−0.409682	−	0.912228i	$-0.634360\pi$
$677$	−21.3192	−0.819364	−0.409682	+	0.912228i	$0.634360\pi$
$678$	103.877	3.98936
$679$	−3.61011	−0.138543
$680$	17.0411	0.653497
$681$	−17.5190	−0.671329
$682$	−59.3243	−2.27164
$683$	13.6702	0.523074	0.261537	−	0.965193i	$-0.415771\pi$
$683$	13.6702	0.523074	0.261537	+	0.965193i	$0.415771\pi$
$684$	−72.1357	−2.75818
$685$	2.84504	0.108703
$686$	−47.9815	−1.83194
$687$	−9.78416	−0.373289
$688$	3.38184	0.128931
$689$	−11.1592	−0.425132
$690$	2.05129	0.0780912
$691$	4.12296	0.156845	0.0784224	−	0.996920i	$-0.475012\pi$
$691$	4.12296	0.156845	0.0784224	+	0.996920i	$0.475012\pi$
$692$	19.5393	0.742773
$693$	21.2768	0.808238
$694$	−68.9890	−2.61879
$695$	3.82070	0.144928
$696$	−10.3405	−0.391957
$697$	9.29040	0.351899
$698$	32.6381	1.23537
$699$	−50.6194	−1.91460
$700$	−7.42337	−0.280577
$701$	11.6481	0.439941	0.219970	−	0.975507i	$-0.429404\pi$
$701$	11.6481	0.439941	0.219970	+	0.975507i	$0.429404\pi$
$702$	0.603078	0.0227617
$703$	−1.50445	−0.0567415
$704$	33.3146	1.25559
$705$	−5.84813	−0.220253
$706$	15.0103	0.564920
$707$	−4.81954	−0.181257
$708$	−90.0665	−3.38491
$709$	−8.30323	−0.311834	−0.155917	−	0.987770i	$-0.549833\pi$
$709$	−8.30323	−0.311834	−0.155917	+	0.987770i	$0.549833\pi$
$710$	37.0859	1.39181
$711$	−16.2598	−0.609791
$712$	18.3669	0.688327
$713$	2.25749	0.0845438
$714$	−41.4190	−1.55007
$715$	18.3631	0.686742
$716$	59.4705	2.22252
$717$	−50.5057	−1.88617
$718$	12.1677	0.454093
$719$	−1.26184	−0.0470588	−0.0235294	−	0.999723i	$-0.507490\pi$
$719$	−1.26184	−0.0470588	−0.0235294	+	0.999723i	$0.507490\pi$
$720$	−10.5534	−0.393302
$721$	−3.73608	−0.139139
$722$	−44.3193	−1.64939
$723$	−48.4113	−1.80044
$724$	−18.5811	−0.690562
$725$	−0.905167	−0.0336171
$726$	16.6948	0.619603
$727$	−1.56607	−0.0580824	−0.0290412	−	0.999578i	$-0.509245\pi$
$727$	−1.56607	−0.0580824	−0.0290412	+	0.999578i	$0.509245\pi$
$728$	43.6489	1.61774
$729$	−27.3667	−1.01358
$730$	−5.18730	−0.191991
$731$	3.54266	0.131030
$732$	73.5529	2.71860
$733$	−36.6602	−1.35408	−0.677038	−	0.735948i	$-0.736737\pi$
$733$	−36.6602	−1.35408	−0.677038	+	0.735948i	$0.736737\pi$
$734$	14.7359	0.543913
$735$	−8.35139	−0.308046
$736$	−0.279979	−0.0103202
$737$	4.61737	0.170083
$738$	−18.6451	−0.686335
$739$	−7.66035	−0.281791	−0.140895	−	0.990024i	$-0.544998\pi$
$739$	−7.66035	−0.281791	−0.140895	+	0.990024i	$0.544998\pi$
$740$	−0.965249	−0.0354832
$741$	74.0059	2.71867
$742$	−10.4107	−0.382188
$743$	−1.72493	−0.0632816	−0.0316408	−	0.999499i	$-0.510073\pi$
$743$	−1.72493	−0.0632816	−0.0316408	+	0.999499i	$0.510073\pi$
$744$	−75.0214	−2.75042
$745$	−15.2587	−0.559035
$746$	59.3845	2.17422
$747$	13.2214	0.483746
$748$	−53.2197	−1.94590
$749$	17.1126	0.625282
$750$	−5.96721	−0.217892
$751$	38.0805	1.38958	0.694788	−	0.719215i	$-0.255498\pi$
$751$	38.0805	1.38958	0.694788	+	0.719215i	$0.255498\pi$
$752$	−8.32769	−0.303680
$753$	4.79666	0.174800
$754$	10.8825	0.396317
$755$	−7.23810	−0.263421
$756$	0.372370	0.0135430
$757$	16.8768	0.613396	0.306698	−	0.951807i	$-0.400776\pi$
$757$	16.8768	0.613396	0.306698	+	0.951807i	$0.400776\pi$
$758$	−19.9898	−0.726063
$759$	−3.13310	−0.113724
$760$	−28.4060	−1.03039
$761$	−22.7454	−0.824519	−0.412260	−	0.911066i	$-0.635260\pi$
$761$	−22.7454	−0.824519	−0.412260	+	0.911066i	$0.635260\pi$
$762$	−89.5259	−3.24318
$763$	−21.6373	−0.783323
$764$	−42.7214	−1.54561
$765$	−11.0552	−0.399703
$766$	7.06604	0.255307
$767$	46.3576	1.67388
$768$	76.4219	2.75764
$769$	−7.52500	−0.271358	−0.135679	−	0.990753i	$-0.543322\pi$
$769$	−7.52500	−0.271358	−0.135679	+	0.990753i	$0.543322\pi$
$770$	17.1314	0.617372
$771$	−52.6482	−1.89608
$772$	34.1776	1.23008
$773$	−2.56593	−0.0922901	−0.0461451	−	0.998935i	$-0.514694\pi$
$773$	−2.56593	−0.0922901	−0.0461451	+	0.998935i	$0.514694\pi$
$774$	−7.10982	−0.255557
$775$	−6.56706	−0.235896
$776$	−8.86319	−0.318170
$777$	1.14740	0.0411627
$778$	38.5073	1.38055
$779$	−15.4863	−0.554853
$780$	47.4818	1.70012
$781$	−56.6444	−2.02689
$782$	3.05992	0.109423
$783$	0.0454049	0.00162264
$784$	−11.8923	−0.424726
$785$	−12.4675	−0.444985
$786$	−52.5524	−1.87448
$787$	14.9756	0.533821	0.266910	−	0.963721i	$-0.413997\pi$
$787$	14.9756	0.533821	0.266910	+	0.963721i	$0.413997\pi$
$788$	−23.5557	−0.839138
$789$	10.0310	0.357112
$790$	−13.0919	−0.465788
$791$	−33.0125	−1.17379
$792$	52.2366	1.85615
$793$	−37.8580	−1.34438
$794$	−83.8775	−2.97670
$795$	−5.53867	−0.196436
$796$	−2.52415	−0.0894661
$797$	−22.8400	−0.809035	−0.404517	−	0.914530i	$-0.632560\pi$
$797$	−22.8400	−0.809035	−0.404517	+	0.914530i	$0.632560\pi$
$798$	69.0418	2.44405
$799$	−8.72369	−0.308622
$800$	0.814461	0.0287956
$801$	−11.9153	−0.421007
$802$	−42.2247	−1.49101
$803$	7.92299	0.279596
$804$	11.9392	0.421063
$805$	−0.651908	−0.0229768
$806$	78.9533	2.78101
$807$	7.50032	0.264024
$808$	−11.8324	−0.416264
$809$	5.31743	0.186951	0.0934754	−	0.995622i	$-0.470202\pi$
$809$	5.31743	0.186951	0.0934754	+	0.995622i	$0.470202\pi$
$810$	−21.7375	−0.763778
$811$	−24.0678	−0.845135	−0.422568	−	0.906331i	$-0.638871\pi$
$811$	−24.0678	−0.845135	−0.422568	+	0.906331i	$0.638871\pi$
$812$	6.71939	0.235805
$813$	−72.1374	−2.52997
$814$	2.22756	0.0780761
$815$	4.29345	0.150393
$816$	−31.3786	−1.09847
$817$	−5.90528	−0.206600
$818$	3.46533	0.121162
$819$	−28.3168	−0.989469
$820$	−9.93590	−0.346977
$821$	22.9658	0.801513	0.400756	−	0.916185i	$-0.368747\pi$
$821$	22.9658	0.801513	0.400756	+	0.916185i	$0.368747\pi$
$822$	−16.9770	−0.592139
$823$	−8.42835	−0.293794	−0.146897	−	0.989152i	$-0.546929\pi$
$823$	−8.42835	−0.293794	−0.146897	+	0.989152i	$0.546929\pi$
$824$	−9.17243	−0.319537
$825$	9.11420	0.317316
$826$	43.2481	1.50479
$827$	−17.2457	−0.599693	−0.299846	−	0.953987i	$-0.596935\pi$
$827$	−17.2457	−0.599693	−0.299846	+	0.953987i	$0.596935\pi$
$828$	−4.06440	−0.141248
$829$	−20.0714	−0.697109	−0.348555	−	0.937288i	$-0.613327\pi$
$829$	−20.0714	−0.697109	−0.348555	+	0.937288i	$0.613327\pi$
$830$	10.6454	0.369509
$831$	−24.8841	−0.863218
$832$	−44.3377	−1.53713
$833$	−12.4578	−0.431638
$834$	−22.7989	−0.789463
$835$	−7.40736	−0.256342
$836$	88.7124	3.06818
$837$	0.329416	0.0113863
$838$	−53.0799	−1.83361
$839$	9.69158	0.334590	0.167295	−	0.985907i	$-0.446497\pi$
$839$	9.69158	0.334590	0.167295	+	0.985907i	$0.446497\pi$
$840$	21.6643	0.747490
$841$	−28.1807	−0.971747
$842$	−47.3055	−1.63025
$843$	38.9127	1.34022
$844$	24.3809	0.839224
$845$	−11.4391	−0.393516
$846$	17.5078	0.601929
$847$	−5.30569	−0.182306
$848$	−7.88702	−0.270841
$849$	31.1957	1.07063
$850$	−8.90133	−0.305313
$851$	−0.0847665	−0.00290576
$852$	−146.466	−5.01784
$853$	9.92082	0.339682	0.169841	−	0.985471i	$-0.445675\pi$
$853$	9.92082	0.339682	0.169841	+	0.985471i	$0.445675\pi$
$854$	−35.3186	−1.20858
$855$	18.4281	0.630227
$856$	42.0132	1.43598
$857$	5.24795	0.179267	0.0896333	−	0.995975i	$-0.471430\pi$
$857$	5.24795	0.179267	0.0896333	+	0.995975i	$0.471430\pi$
$858$	−109.577	−3.74088
$859$	21.1417	0.721344	0.360672	−	0.932693i	$-0.382547\pi$
$859$	21.1417	0.721344	0.360672	+	0.932693i	$0.382547\pi$
$860$	−3.78880	−0.129197
$861$	11.8109	0.402514
$862$	−0.0711813	−0.00242445
$863$	55.9612	1.90494	0.952470	−	0.304633i	$-0.0985337\pi$
$863$	55.9612	1.90494	0.952470	+	0.304633i	$0.0985337\pi$
$864$	−0.0408549	−0.00138991
$865$	−4.99159	−0.169719
$866$	−0.637852	−0.0216751
$867$	8.84145	0.300271
$868$	48.7497	1.65467
$869$	19.9963	0.678328
$870$	5.40132	0.183122
$871$	−6.14516	−0.208221
$872$	−53.1217	−1.79893
$873$	5.74991	0.194605
$874$	−5.10061	−0.172531
$875$	1.89640	0.0641102
$876$	20.4866	0.692177
$877$	−11.5162	−0.388873	−0.194437	−	0.980915i	$-0.562288\pi$
$877$	−11.5162	−0.388873	−0.194437	+	0.980915i	$0.562288\pi$
$878$	61.3330	2.06989
$879$	−16.3120	−0.550191
$880$	12.9786	0.437507
$881$	−57.0173	−1.92096	−0.960480	−	0.278348i	$-0.910213\pi$
$881$	−57.0173	−1.92096	−0.960480	+	0.278348i	$0.910213\pi$
$882$	25.0019	0.841857
$883$	−34.7548	−1.16959	−0.584796	−	0.811180i	$-0.698826\pi$
$883$	−34.7548	−1.16959	−0.584796	+	0.811180i	$0.698826\pi$
$884$	70.8289	2.38223
$885$	23.0088	0.773431
$886$	88.1893	2.96278
$887$	22.4963	0.755353	0.377676	−	0.925938i	$-0.376723\pi$
$887$	22.4963	0.755353	0.377676	+	0.925938i	$0.376723\pi$
$888$	2.81698	0.0945315
$889$	28.4517	0.954240
$890$	−9.59383	−0.321586
$891$	33.2014	1.11229
$892$	9.57021	0.320434
$893$	14.5416	0.486616
$894$	91.0518	3.04523
$895$	−15.1926	−0.507832
$896$	−38.2745	−1.27866
$897$	4.16977	0.139225
$898$	41.3722	1.38061
$899$	5.94429	0.198253
$900$	11.8234	0.394112
$901$	−8.26207	−0.275249
$902$	22.9297	0.763475
$903$	4.50377	0.149876
$904$	−81.0488	−2.69564
$905$	4.74681	0.157789
$906$	43.1913	1.43493
$907$	43.7603	1.45304	0.726518	−	0.687148i	$-0.241137\pi$
$907$	43.7603	1.45304	0.726518	+	0.687148i	$0.241137\pi$
$908$	27.9489	0.927517
$909$	7.67618	0.254603
$910$	−22.7998	−0.755805
$911$	54.9812	1.82161	0.910804	−	0.412839i	$-0.135463\pi$
$911$	54.9812	1.82161	0.910804	+	0.412839i	$0.135463\pi$
$912$	52.3053	1.73200
$913$	−16.2597	−0.538116
$914$	15.9665	0.528124
$915$	−18.7901	−0.621183
$916$	15.6092	0.515741
$917$	16.7014	0.551528
$918$	0.446507	0.0147369
$919$	−48.1406	−1.58801	−0.794006	−	0.607910i	$-0.792008\pi$
$919$	−48.1406	−1.58801	−0.794006	+	0.607910i	$0.792008\pi$
$920$	−1.60050	−0.0527669
$921$	−15.6056	−0.514221
$922$	78.3089	2.57897
$923$	75.3867	2.48138
$924$	−67.6581	−2.22579
$925$	0.246586	0.00810771
$926$	15.1703	0.498527
$927$	5.95053	0.195441
$928$	−0.737224	−0.0242006
$929$	42.7166	1.40149	0.700744	−	0.713413i	$-0.252852\pi$
$929$	42.7166	1.40149	0.700744	+	0.713413i	$0.252852\pi$
$930$	39.1870	1.28499
$931$	20.7661	0.680580
$932$	80.7556	2.64524
$933$	11.0350	0.361271
$934$	72.2728	2.36484
$935$	13.5957	0.444627
$936$	−69.5205	−2.27235
$937$	17.8041	0.581635	0.290818	−	0.956778i	$-0.406073\pi$
$937$	17.8041	0.581635	0.290818	+	0.956778i	$0.406073\pi$
$938$	−5.73296	−0.187188
$939$	−42.1659	−1.37603
$940$	9.32981	0.304305
$941$	−40.8299	−1.33102	−0.665509	−	0.746390i	$-0.731785\pi$
$941$	−40.8299	−1.33102	−0.665509	+	0.746390i	$0.731785\pi$
$942$	74.3963	2.42396
$943$	−0.872554	−0.0284143
$944$	32.7643	1.06639
$945$	−0.0951272	−0.00309449
$946$	8.74364	0.284280
$947$	−6.64647	−0.215981	−0.107991	−	0.994152i	$-0.534442\pi$
$947$	−6.64647	−0.215981	−0.107991	+	0.994152i	$0.534442\pi$
$948$	51.7046	1.67929
$949$	−10.5445	−0.342290
$950$	14.8377	0.481399
$951$	1.88914	0.0612597
$952$	32.3168	1.04739
$953$	−46.3707	−1.50210	−0.751048	−	0.660248i	$-0.770451\pi$
$953$	−46.3707	−1.50210	−0.751048	+	0.660248i	$0.770451\pi$
$954$	16.5813	0.536840
$955$	10.9138	0.353162
$956$	80.5742	2.60596
$957$	−8.24988	−0.266681
$958$	−52.7250	−1.70347
$959$	5.39535	0.174225
$960$	−22.0062	−0.710247
$961$	12.1263	0.391171
$962$	−2.96462	−0.0955830
$963$	−27.2556	−0.878301
$964$	77.2330	2.48751
$965$	−8.73116	−0.281066
$966$	3.89007	0.125161
$967$	20.5687	0.661446	0.330723	−	0.943728i	$-0.392707\pi$
$967$	20.5687	0.661446	0.330723	+	0.943728i	$0.392707\pi$
$968$	−13.0260	−0.418671
$969$	54.7926	1.76019
$970$	4.62964	0.148649
$971$	−58.3117	−1.87131	−0.935655	−	0.352915i	$-0.885191\pi$
$971$	−58.3117	−1.87131	−0.935655	+	0.352915i	$0.885191\pi$
$972$	86.4384	2.77251
$973$	7.24560	0.232283
$974$	−9.03532	−0.289510
$975$	−12.1299	−0.388467
$976$	−26.7570	−0.856471
$977$	27.2328	0.871254	0.435627	−	0.900127i	$-0.356527\pi$
$977$	27.2328	0.871254	0.435627	+	0.900127i	$0.356527\pi$
$978$	−25.6199	−0.819234
$979$	14.6534	0.468326
$980$	13.3234	0.425600
$981$	34.4622	1.10029
$982$	45.8058	1.46172
$983$	−27.3078	−0.870985	−0.435493	−	0.900192i	$-0.643426\pi$
$983$	−27.3078	−0.870985	−0.435493	+	0.900192i	$0.643426\pi$
$984$	28.9969	0.924386
$985$	6.01764	0.191738
$986$	8.05719	0.256593
$987$	−11.0904	−0.353012
$988$	−118.065	−3.75616
$989$	−0.332726	−0.0105801
$990$	−27.2855	−0.867190
$991$	−9.24942	−0.293817	−0.146909	−	0.989150i	$-0.546932\pi$
$991$	−9.24942	−0.293817	−0.146909	+	0.989150i	$0.546932\pi$
$992$	−5.34862	−0.169819
$993$	40.8773	1.29720
$994$	70.3300	2.23073
$995$	0.644829	0.0204425
$996$	−42.0428	−1.33218
$997$	31.0812	0.984350	0.492175	−	0.870496i	$-0.336202\pi$
$997$	31.0812	0.984350	0.492175	+	0.870496i	$0.336202\pi$
$998$	67.7613	2.14495
$999$	−0.0123692	−0.000391345 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.d.1.5	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.d.1.5	✓	83	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43196 q^{2} -2.45366 q^{3} +3.91445 q^{4} -1.00000 q^{5} +5.96721 q^{6} -1.89640 q^{7} -4.65586 q^{8} +3.02044 q^{9} +O(q^{10})\)	\(q-2.43196 q^{2} -2.45366 q^{3} +3.91445 q^{4} -1.00000 q^{5} +5.96721 q^{6} -1.89640 q^{7} -4.65586 q^{8} +3.02044 q^{9} +2.43196 q^{10} -3.71453 q^{11} -9.60472 q^{12} +4.94359 q^{13} +4.61199 q^{14} +2.45366 q^{15} +3.49399 q^{16} +3.66014 q^{17} -7.34561 q^{18} -6.10112 q^{19} -3.91445 q^{20} +4.65313 q^{21} +9.03361 q^{22} -0.343760 q^{23} +11.4239 q^{24} +1.00000 q^{25} -12.0226 q^{26} -0.0501619 q^{27} -7.42337 q^{28} -0.905167 q^{29} -5.96721 q^{30} -6.56706 q^{31} +0.814461 q^{32} +9.11420 q^{33} -8.90133 q^{34} +1.89640 q^{35} +11.8234 q^{36} +0.246586 q^{37} +14.8377 q^{38} -12.1299 q^{39} +4.65586 q^{40} +2.53826 q^{41} -11.3162 q^{42} +0.967901 q^{43} -14.5403 q^{44} -3.02044 q^{45} +0.836012 q^{46} -2.38343 q^{47} -8.57307 q^{48} -3.40365 q^{49} -2.43196 q^{50} -8.98074 q^{51} +19.3514 q^{52} -2.25731 q^{53} +0.121992 q^{54} +3.71453 q^{55} +8.82940 q^{56} +14.9701 q^{57} +2.20133 q^{58} +9.37732 q^{59} +9.60472 q^{60} -7.65800 q^{61} +15.9709 q^{62} -5.72798 q^{63} -8.96872 q^{64} -4.94359 q^{65} -22.1654 q^{66} -1.24306 q^{67} +14.3274 q^{68} +0.843470 q^{69} -4.61199 q^{70} +15.2494 q^{71} -14.0628 q^{72} -2.13297 q^{73} -0.599689 q^{74} -2.45366 q^{75} -23.8825 q^{76} +7.04426 q^{77} +29.4994 q^{78} -5.38326 q^{79} -3.49399 q^{80} -8.93825 q^{81} -6.17296 q^{82} +4.37731 q^{83} +18.2144 q^{84} -3.66014 q^{85} -2.35390 q^{86} +2.22097 q^{87} +17.2944 q^{88} -3.94489 q^{89} +7.34561 q^{90} -9.37505 q^{91} -1.34563 q^{92} +16.1133 q^{93} +5.79642 q^{94} +6.10112 q^{95} -1.99841 q^{96} +1.90366 q^{97} +8.27755 q^{98} -11.2195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * q^99

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