LMFDB - Embedded newform 6001.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10824 q^{2} -2.66682 q^{3} +2.44469 q^{4} -3.46040 q^{5} +5.62230 q^{6} -1.09952 q^{7} -0.937516 q^{8} +4.11192 q^{9} +O(q^{10})$	\(q-2.10824 q^{2} -2.66682 q^{3} +2.44469 q^{4} -3.46040 q^{5} +5.62230 q^{6} -1.09952 q^{7} -0.937516 q^{8} +4.11192 q^{9} +7.29537 q^{10} -2.77755 q^{11} -6.51955 q^{12} +4.41425 q^{13} +2.31806 q^{14} +9.22827 q^{15} -2.91287 q^{16} +1.00000 q^{17} -8.66894 q^{18} +7.84839 q^{19} -8.45961 q^{20} +2.93223 q^{21} +5.85576 q^{22} -5.90976 q^{23} +2.50019 q^{24} +6.97438 q^{25} -9.30632 q^{26} -2.96530 q^{27} -2.68800 q^{28} -9.04005 q^{29} -19.4554 q^{30} -8.72445 q^{31} +8.01607 q^{32} +7.40723 q^{33} -2.10824 q^{34} +3.80479 q^{35} +10.0524 q^{36} -8.47027 q^{37} -16.5463 q^{38} -11.7720 q^{39} +3.24418 q^{40} +5.14486 q^{41} -6.18186 q^{42} -4.00114 q^{43} -6.79026 q^{44} -14.2289 q^{45} +12.4592 q^{46} +9.30498 q^{47} +7.76810 q^{48} -5.79105 q^{49} -14.7037 q^{50} -2.66682 q^{51} +10.7915 q^{52} -13.3821 q^{53} +6.25157 q^{54} +9.61145 q^{55} +1.03082 q^{56} -20.9302 q^{57} +19.0586 q^{58} -7.54072 q^{59} +22.5603 q^{60} +15.1285 q^{61} +18.3933 q^{62} -4.52116 q^{63} -11.0741 q^{64} -15.2751 q^{65} -15.6162 q^{66} +1.64619 q^{67} +2.44469 q^{68} +15.7603 q^{69} -8.02143 q^{70} +0.983333 q^{71} -3.85499 q^{72} +8.86134 q^{73} +17.8574 q^{74} -18.5994 q^{75} +19.1869 q^{76} +3.05399 q^{77} +24.8183 q^{78} +11.9057 q^{79} +10.0797 q^{80} -4.42785 q^{81} -10.8466 q^{82} +16.2677 q^{83} +7.16840 q^{84} -3.46040 q^{85} +8.43538 q^{86} +24.1082 q^{87} +2.60400 q^{88} -12.3401 q^{89} +29.9980 q^{90} -4.85358 q^{91} -14.4475 q^{92} +23.2665 q^{93} -19.6172 q^{94} -27.1586 q^{95} -21.3774 q^{96} +2.51011 q^{97} +12.2089 q^{98} -11.4211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.10824	−1.49075	−0.745377	−	0.666644i	$-0.767730\pi$
$2$	−2.10824	−1.49075	−0.745377	+	0.666644i	$0.767730\pi$
$3$	−2.66682	−1.53969	−0.769844	−	0.638232i	$-0.779666\pi$
$3$	−2.66682	−1.53969	−0.769844	+	0.638232i	$0.779666\pi$
$4$	2.44469	1.22235
$5$	−3.46040	−1.54754	−0.773770	−	0.633467i	$-0.781631\pi$
$5$	−3.46040	−1.54754	−0.773770	+	0.633467i	$0.781631\pi$
$6$	5.62230	2.29530
$7$	−1.09952	−0.415581	−0.207790	−	0.978173i	$-0.566627\pi$
$7$	−1.09952	−0.415581	−0.207790	+	0.978173i	$0.566627\pi$
$8$	−0.937516	−0.331462
$9$	4.11192	1.37064
$10$	7.29537	2.30700
$11$	−2.77755	−0.837464	−0.418732	−	0.908110i	$-0.637525\pi$
$11$	−2.77755	−0.837464	−0.418732	+	0.908110i	$0.637525\pi$
$12$	−6.51955	−1.88203
$13$	4.41425	1.22429	0.612147	−	0.790744i	$-0.290306\pi$
$13$	4.41425	1.22429	0.612147	+	0.790744i	$0.290306\pi$
$14$	2.31806	0.619529
$15$	9.22827	2.38273
$16$	−2.91287	−0.728217
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−8.66894	−2.04329
$19$	7.84839	1.80054	0.900272	−	0.435328i	$-0.143367\pi$
$19$	7.84839	1.80054	0.900272	+	0.435328i	$0.143367\pi$
$20$	−8.45961	−1.89163
$21$	2.93223	0.639865
$22$	5.85576	1.24845
$23$	−5.90976	−1.23227	−0.616135	−	0.787640i	$-0.711303\pi$
$23$	−5.90976	−1.23227	−0.616135	+	0.787640i	$0.711303\pi$
$24$	2.50019	0.510348
$25$	6.97438	1.39488
$26$	−9.30632	−1.82512
$27$	−2.96530	−0.570672
$28$	−2.68800	−0.507983
$29$	−9.04005	−1.67870	−0.839348	−	0.543594i	$-0.817063\pi$
$29$	−9.04005	−1.67870	−0.839348	+	0.543594i	$0.817063\pi$
$30$	−19.4554	−3.55206
$31$	−8.72445	−1.56696	−0.783479	−	0.621418i	$-0.786557\pi$
$31$	−8.72445	−1.56696	−0.783479	+	0.621418i	$0.786557\pi$
$32$	8.01607	1.41705
$33$	7.40723	1.28943
$34$	−2.10824	−0.361561
$35$	3.80479	0.643128
$36$	10.0524	1.67540
$37$	−8.47027	−1.39250	−0.696252	−	0.717797i	$-0.745151\pi$
$37$	−8.47027	−1.39250	−0.696252	+	0.717797i	$0.745151\pi$
$38$	−16.5463	−2.68417
$39$	−11.7720	−1.88503
$40$	3.24418	0.512950
$41$	5.14486	0.803493	0.401746	−	0.915751i	$-0.368403\pi$
$41$	5.14486	0.803493	0.401746	+	0.915751i	$0.368403\pi$
$42$	−6.18186	−0.953881
$43$	−4.00114	−0.610169	−0.305084	−	0.952325i	$-0.598685\pi$
$43$	−4.00114	−0.610169	−0.305084	+	0.952325i	$0.598685\pi$
$44$	−6.79026	−1.02367
$45$	−14.2289	−2.12112
$46$	12.4592	1.83701
$47$	9.30498	1.35727	0.678635	−	0.734475i	$-0.262572\pi$
$47$	9.30498	1.35727	0.678635	+	0.734475i	$0.262572\pi$
$48$	7.76810	1.12123
$49$	−5.79105	−0.827292
$50$	−14.7037	−2.07942
$51$	−2.66682	−0.373429
$52$	10.7915	1.49651
$53$	−13.3821	−1.83817	−0.919087	−	0.394054i	$-0.871072\pi$
$53$	−13.3821	−1.83817	−0.919087	+	0.394054i	$0.871072\pi$
$54$	6.25157	0.850732
$55$	9.61145	1.29601
$56$	1.03082	0.137749
$57$	−20.9302	−2.77228
$58$	19.0586	2.50252
$59$	−7.54072	−0.981718	−0.490859	−	0.871239i	$-0.663317\pi$
$59$	−7.54072	−0.981718	−0.490859	+	0.871239i	$0.663317\pi$
$60$	22.5603	2.91252
$61$	15.1285	1.93701	0.968506	−	0.248991i	$-0.0800990\pi$
$61$	15.1285	1.93701	0.968506	+	0.248991i	$0.0800990\pi$
$62$	18.3933	2.33595
$63$	−4.52116	−0.569612
$64$	−11.0741	−1.38426
$65$	−15.2751	−1.89464
$66$	−15.6162	−1.92223
$67$	1.64619	0.201115	0.100557	−	0.994931i	$-0.467937\pi$
$67$	1.64619	0.201115	0.100557	+	0.994931i	$0.467937\pi$
$68$	2.44469	0.296462
$69$	15.7603	1.89731
$70$	−8.02143	−0.958745
$71$	0.983333	0.116700	0.0583501	−	0.998296i	$-0.481416\pi$
$71$	0.983333	0.116700	0.0583501	+	0.998296i	$0.481416\pi$
$72$	−3.85499	−0.454315
$73$	8.86134	1.03714	0.518571	−	0.855035i	$-0.326464\pi$
$73$	8.86134	1.03714	0.518571	+	0.855035i	$0.326464\pi$
$74$	17.8574	2.07588
$75$	−18.5994	−2.14768
$76$	19.1869	2.20089
$77$	3.05399	0.348034
$78$	24.8183	2.81012
$79$	11.9057	1.33950	0.669749	−	0.742587i	$-0.266402\pi$
$79$	11.9057	1.33950	0.669749	+	0.742587i	$0.266402\pi$
$80$	10.0797	1.12694
$81$	−4.42785	−0.491984
$82$	−10.8466	−1.19781
$83$	16.2677	1.78561	0.892806	−	0.450442i	$-0.148734\pi$
$83$	16.2677	1.78561	0.892806	+	0.450442i	$0.148734\pi$
$84$	7.16840	0.782136
$85$	−3.46040	−0.375333
$86$	8.43538	0.909611
$87$	24.1082	2.58467
$88$	2.60400	0.277587
$89$	−12.3401	−1.30805	−0.654024	−	0.756474i	$-0.726920\pi$
$89$	−12.3401	−1.30805	−0.654024	+	0.756474i	$0.726920\pi$
$90$	29.9980	3.16207
$91$	−4.85358	−0.508793
$92$	−14.4475	−1.50626
$93$	23.2665	2.41263
$94$	−19.6172	−2.02336
$95$	−27.1586	−2.78641
$96$	−21.3774	−2.18182
$97$	2.51011	0.254864	0.127432	−	0.991847i	$-0.459327\pi$
$97$	2.51011	0.254864	0.127432	+	0.991847i	$0.459327\pi$
$98$	12.2089	1.23329
$99$	−11.4211	−1.14786
$100$	17.0502	1.70502
$101$	7.78793	0.774928	0.387464	−	0.921885i	$-0.373351\pi$
$101$	7.78793	0.774928	0.387464	+	0.921885i	$0.373351\pi$
$102$	5.62230	0.556691
$103$	−11.5730	−1.14032	−0.570161	−	0.821533i	$-0.693119\pi$
$103$	−11.5730	−1.14032	−0.570161	+	0.821533i	$0.693119\pi$
$104$	−4.13843	−0.405807
$105$	−10.1467	−0.990216
$106$	28.2128	2.74027
$107$	−6.57110	−0.635252	−0.317626	−	0.948216i	$-0.602886\pi$
$107$	−6.57110	−0.635252	−0.317626	+	0.948216i	$0.602886\pi$
$108$	−7.24924	−0.697559
$109$	4.20640	0.402901	0.201450	−	0.979499i	$-0.435435\pi$
$109$	4.20640	0.402901	0.201450	+	0.979499i	$0.435435\pi$
$110$	−20.2633	−1.93203
$111$	22.5887	2.14402
$112$	3.20277	0.302633
$113$	−0.987392	−0.0928860	−0.0464430	−	0.998921i	$-0.514789\pi$
$113$	−0.987392	−0.0928860	−0.0464430	+	0.998921i	$0.514789\pi$
$114$	44.1260	4.13278
$115$	20.4502	1.90699
$116$	−22.1001	−2.05195
$117$	18.1511	1.67807
$118$	15.8977	1.46350
$119$	−1.09952	−0.100793
$120$	−8.65165	−0.789784
$121$	−3.28520	−0.298654
$122$	−31.8947	−2.88761
$123$	−13.7204	−1.23713
$124$	−21.3286	−1.91536
$125$	−6.83217	−0.611088
$126$	9.53170	0.849152
$127$	7.07572	0.627869	0.313934	−	0.949445i	$-0.398353\pi$
$127$	7.07572	0.627869	0.313934	+	0.949445i	$0.398353\pi$
$128$	7.31473	0.646537
$129$	10.6703	0.939470
$130$	32.2036	2.82444
$131$	−0.989227	−0.0864292	−0.0432146	−	0.999066i	$-0.513760\pi$
$131$	−0.989227	−0.0864292	−0.0432146	+	0.999066i	$0.513760\pi$
$132$	18.1084	1.57613
$133$	−8.62949	−0.748272
$134$	−3.47058	−0.299812
$135$	10.2611	0.883138
$136$	−0.937516	−0.0803913
$137$	3.90498	0.333625	0.166813	−	0.985989i	$-0.446652\pi$
$137$	3.90498	0.333625	0.166813	+	0.985989i	$0.446652\pi$
$138$	−33.2265	−2.82843
$139$	3.31759	0.281394	0.140697	−	0.990053i	$-0.455066\pi$
$139$	3.31759	0.281394	0.140697	+	0.990053i	$0.455066\pi$
$140$	9.30155	0.786124
$141$	−24.8147	−2.08977
$142$	−2.07311	−0.173971
$143$	−12.2608	−1.02530
$144$	−11.9775	−0.998125
$145$	31.2822	2.59785
$146$	−18.6819	−1.54612
$147$	15.4437	1.27377
$148$	−20.7072	−1.70212
$149$	13.0474	1.06888	0.534442	−	0.845205i	$-0.320522\pi$
$149$	13.0474	1.06888	0.534442	+	0.845205i	$0.320522\pi$
$150$	39.2121	3.20166
$151$	−16.5677	−1.34826	−0.674129	−	0.738614i	$-0.735481\pi$
$151$	−16.5677	−1.34826	−0.674129	+	0.738614i	$0.735481\pi$
$152$	−7.35799	−0.596812
$153$	4.11192	0.332429
$154$	−6.43855	−0.518833
$155$	30.1901	2.42493
$156$	−28.7789	−2.30416
$157$	12.6183	1.00705	0.503523	−	0.863982i	$-0.332037\pi$
$157$	12.6183	1.00705	0.503523	+	0.863982i	$0.332037\pi$
$158$	−25.1002	−1.99686
$159$	35.6877	2.83022
$160$	−27.7388	−2.19295
$161$	6.49793	0.512108
$162$	9.33499	0.733426
$163$	14.2228	1.11402	0.557009	−	0.830507i	$-0.311949\pi$
$163$	14.2228	1.11402	0.557009	+	0.830507i	$0.311949\pi$
$164$	12.5776	0.982146
$165$	−25.6320	−1.99545
$166$	−34.2963	−2.66191
$167$	−11.3087	−0.875097	−0.437548	−	0.899195i	$-0.644153\pi$
$167$	−11.3087	−0.875097	−0.437548	+	0.899195i	$0.644153\pi$
$168$	−2.74901	−0.212091
$169$	6.48563	0.498895
$170$	7.29537	0.559529
$171$	32.2720	2.46790
$172$	−9.78156	−0.745837
$173$	18.4774	1.40481	0.702404	−	0.711779i	$-0.252110\pi$
$173$	18.4774	1.40481	0.702404	+	0.711779i	$0.252110\pi$
$174$	−50.8259	−3.85310
$175$	−7.66850	−0.579684
$176$	8.09065	0.609856
$177$	20.1097	1.51154
$178$	26.0159	1.94998
$179$	−20.0292	−1.49705	−0.748526	−	0.663106i	$-0.769238\pi$
$179$	−20.0292	−1.49705	−0.748526	+	0.663106i	$0.769238\pi$
$180$	−34.7853	−2.59274
$181$	7.58523	0.563806	0.281903	−	0.959443i	$-0.409034\pi$
$181$	7.58523	0.563806	0.281903	+	0.959443i	$0.409034\pi$
$182$	10.2325	0.758485
$183$	−40.3451	−2.98239
$184$	5.54050	0.408451
$185$	29.3106	2.15496
$186$	−49.0515	−3.59663
$187$	−2.77755	−0.203115
$188$	22.7478	1.65905
$189$	3.26042	0.237161
$190$	57.2569	4.15385
$191$	−18.8268	−1.36226	−0.681128	−	0.732164i	$-0.738510\pi$
$191$	−18.8268	−1.36226	−0.681128	+	0.732164i	$0.738510\pi$
$192$	29.5326	2.13133
$193$	1.46391	0.105374	0.0526872	−	0.998611i	$-0.483221\pi$
$193$	1.46391	0.105374	0.0526872	+	0.998611i	$0.483221\pi$
$194$	−5.29193	−0.379939
$195$	40.7359	2.91716
$196$	−14.1573	−1.01124
$197$	12.9636	0.923618	0.461809	−	0.886979i	$-0.347200\pi$
$197$	12.9636	0.923618	0.461809	+	0.886979i	$0.347200\pi$
$198$	24.0784	1.71118
$199$	16.9078	1.19856	0.599281	−	0.800539i	$-0.295453\pi$
$199$	16.9078	1.19856	0.599281	+	0.800539i	$0.295453\pi$
$200$	−6.53860	−0.462349
$201$	−4.39010	−0.309654
$202$	−16.4189	−1.15523
$203$	9.93975	0.697634
$204$	−6.51955	−0.456460
$205$	−17.8033	−1.24344
$206$	24.3987	1.69994
$207$	−24.3005	−1.68900
$208$	−12.8581	−0.891552
$209$	−21.7993	−1.50789
$210$	21.3917	1.47617
$211$	0.663214	0.0456576	0.0228288	−	0.999739i	$-0.492733\pi$
$211$	0.663214	0.0456576	0.0228288	+	0.999739i	$0.492733\pi$
$212$	−32.7151	−2.24688
$213$	−2.62237	−0.179682
$214$	13.8535	0.947004
$215$	13.8456	0.944260
$216$	2.78002	0.189156
$217$	9.59274	0.651198
$218$	−8.86813	−0.600625
$219$	−23.6316	−1.59687
$220$	23.4970	1.58417
$221$	4.41425	0.296935
$222$	−47.6225	−3.19621
$223$	17.5812	1.17732	0.588661	−	0.808380i	$-0.299655\pi$
$223$	17.5812	1.17732	0.588661	+	0.808380i	$0.299655\pi$
$224$	−8.81386	−0.588901
$225$	28.6781	1.91188
$226$	2.08166	0.138470
$227$	0.310250	0.0205920	0.0102960	−	0.999947i	$-0.496723\pi$
$227$	0.310250	0.0205920	0.0102960	+	0.999947i	$0.496723\pi$
$228$	−51.1680	−3.38868
$229$	−1.53337	−0.101328	−0.0506641	−	0.998716i	$-0.516134\pi$
$229$	−1.53337	−0.101328	−0.0506641	+	0.998716i	$0.516134\pi$
$230$	−43.1139	−2.84285
$231$	−8.14443	−0.535864
$232$	8.47520	0.556424
$233$	30.3026	1.98519	0.992596	−	0.121461i	$-0.0387580\pi$
$233$	30.3026	1.98519	0.992596	+	0.121461i	$0.0387580\pi$
$234$	−38.2669	−2.50158
$235$	−32.1990	−2.10043
$236$	−18.4347	−1.20000
$237$	−31.7504	−2.06241
$238$	2.31806	0.150258
$239$	−19.8755	−1.28564	−0.642821	−	0.766017i	$-0.722236\pi$
$239$	−19.8755	−1.28564	−0.642821	+	0.766017i	$0.722236\pi$
$240$	−26.8807	−1.73514
$241$	−11.2526	−0.724846	−0.362423	−	0.932014i	$-0.618050\pi$
$241$	−11.2526	−0.724846	−0.362423	+	0.932014i	$0.618050\pi$
$242$	6.92600	0.445220
$243$	20.7042	1.32817
$244$	36.9846	2.36770
$245$	20.0394	1.28027
$246$	28.9260	1.84425
$247$	34.6448	2.20439
$248$	8.17931	0.519387
$249$	−43.3830	−2.74929
$250$	14.4039	0.910981
$251$	7.74777	0.489035	0.244517	−	0.969645i	$-0.421370\pi$
$251$	7.74777	0.489035	0.244517	+	0.969645i	$0.421370\pi$
$252$	−11.0528	−0.696263
$253$	16.4147	1.03198
$254$	−14.9173	−0.935997
$255$	9.22827	0.577897
$256$	6.72693	0.420433
$257$	24.2754	1.51426	0.757129	−	0.653266i	$-0.226602\pi$
$257$	24.2754	1.51426	0.757129	+	0.653266i	$0.226602\pi$
$258$	−22.4956	−1.40052
$259$	9.31327	0.578698
$260$	−37.3429	−2.31591
$261$	−37.1720	−2.30089
$262$	2.08553	0.128845
$263$	12.5628	0.774657	0.387328	−	0.921942i	$-0.373398\pi$
$263$	12.5628	0.774657	0.387328	+	0.921942i	$0.373398\pi$
$264$	−6.94440	−0.427398
$265$	46.3075	2.84465
$266$	18.1931	1.11549
$267$	32.9088	2.01399
$268$	4.02444	0.245832
$269$	−17.0970	−1.04242	−0.521211	−	0.853428i	$-0.674520\pi$
$269$	−17.0970	−1.04242	−0.521211	+	0.853428i	$0.674520\pi$
$270$	−21.6330	−1.31654
$271$	−7.68225	−0.466664	−0.233332	−	0.972397i	$-0.574963\pi$
$271$	−7.68225	−0.466664	−0.233332	+	0.972397i	$0.574963\pi$
$272$	−2.91287	−0.176619
$273$	12.9436	0.783383
$274$	−8.23266	−0.497353
$275$	−19.3717	−1.16816
$276$	38.5290	2.31917
$277$	6.57498	0.395052	0.197526	−	0.980298i	$-0.436709\pi$
$277$	6.57498	0.395052	0.197526	+	0.980298i	$0.436709\pi$
$278$	−6.99428	−0.419489
$279$	−35.8743	−2.14774
$280$	−3.56706	−0.213172
$281$	−6.03721	−0.360150	−0.180075	−	0.983653i	$-0.557634\pi$
$281$	−6.03721	−0.360150	−0.180075	+	0.983653i	$0.557634\pi$
$282$	52.3154	3.11534
$283$	10.0544	0.597673	0.298836	−	0.954304i	$-0.403401\pi$
$283$	10.0544	0.597673	0.298836	+	0.954304i	$0.403401\pi$
$284$	2.40395	0.142648
$285$	72.4270	4.29021
$286$	25.8488	1.52847
$287$	−5.65690	−0.333916
$288$	32.9615	1.94227
$289$	1.00000	0.0588235
$290$	−65.9505	−3.87275
$291$	−6.69402	−0.392410
$292$	21.6632	1.26774
$293$	17.7221	1.03534	0.517669	−	0.855581i	$-0.326800\pi$
$293$	17.7221	1.03534	0.517669	+	0.855581i	$0.326800\pi$
$294$	−32.5590	−1.89888
$295$	26.0939	1.51925
$296$	7.94102	0.461562
$297$	8.23628	0.477917
$298$	−27.5071	−1.59344
$299$	−26.0872	−1.50866
$300$	−45.4698	−2.62520
$301$	4.39935	0.253574
$302$	34.9287	2.00992
$303$	−20.7690	−1.19315
$304$	−22.8613	−1.31119
$305$	−52.3509	−2.99760
$306$	−8.66894	−0.495570
$307$	−25.8245	−1.47388	−0.736941	−	0.675957i	$-0.763731\pi$
$307$	−25.8245	−1.47388	−0.736941	+	0.675957i	$0.763731\pi$
$308$	7.46605	0.425418
$309$	30.8631	1.75574
$310$	−63.6481	−3.61497
$311$	−12.6362	−0.716532	−0.358266	−	0.933620i	$-0.616632\pi$
$311$	−12.6362	−0.716532	−0.358266	+	0.933620i	$0.616632\pi$
$312$	11.0365	0.624816
$313$	−10.5786	−0.597936	−0.298968	−	0.954263i	$-0.596642\pi$
$313$	−10.5786	−0.597936	−0.298968	+	0.954263i	$0.596642\pi$
$314$	−26.6023	−1.50126
$315$	15.6450	0.881497
$316$	29.1058	1.63733
$317$	14.2061	0.797893	0.398947	−	0.916974i	$-0.369376\pi$
$317$	14.2061	0.797893	0.398947	+	0.916974i	$0.369376\pi$
$318$	−75.2383	−4.21916
$319$	25.1092	1.40585
$320$	38.3208	2.14220
$321$	17.5239	0.978091
$322$	−13.6992	−0.763427
$323$	7.84839	0.436696
$324$	−10.8247	−0.601374
$325$	30.7867	1.70774
$326$	−29.9852	−1.66072
$327$	−11.2177	−0.620341
$328$	−4.82339	−0.266327
$329$	−10.2310	−0.564056
$330$	54.0385	2.97472
$331$	19.2837	1.05993	0.529965	−	0.848020i	$-0.322205\pi$
$331$	19.2837	1.05993	0.529965	+	0.848020i	$0.322205\pi$
$332$	39.7695	2.18263
$333$	−34.8291	−1.90862
$334$	23.8416	1.30455
$335$	−5.69649	−0.311233
$336$	−8.54121	−0.465961
$337$	−4.51321	−0.245850	−0.122925	−	0.992416i	$-0.539227\pi$
$337$	−4.51321	−0.245850	−0.122925	+	0.992416i	$0.539227\pi$
$338$	−13.6733	−0.743729
$339$	2.63320	0.143016
$340$	−8.45961	−0.458787
$341$	24.2326	1.31227
$342$	−68.0372	−3.67903
$343$	14.0641	0.759388
$344$	3.75114	0.202248
$345$	−54.5369	−2.93617
$346$	−38.9548	−2.09422
$347$	−14.4680	−0.776685	−0.388342	−	0.921515i	$-0.626952\pi$
$347$	−14.4680	−0.776685	−0.388342	+	0.921515i	$0.626952\pi$
$348$	58.9371	3.15936
$349$	15.8445	0.848136	0.424068	−	0.905630i	$-0.360602\pi$
$349$	15.8445	0.848136	0.424068	+	0.905630i	$0.360602\pi$
$350$	16.1671	0.864166
$351$	−13.0896	−0.698670
$352$	−22.2651	−1.18673
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−42.3962	−2.25333
$355$	−3.40273	−0.180598
$356$	−30.1677	−1.59889
$357$	2.93223	0.155190
$358$	42.2264	2.23173
$359$	17.1219	0.903658	0.451829	−	0.892105i	$-0.350772\pi$
$359$	17.1219	0.903658	0.451829	+	0.892105i	$0.350772\pi$
$360$	13.3398	0.703071
$361$	42.5972	2.24196
$362$	−15.9915	−0.840496
$363$	8.76103	0.459835
$364$	−11.8655	−0.621921
$365$	−30.6638	−1.60502
$366$	85.0573	4.44601
$367$	−13.4138	−0.700192	−0.350096	−	0.936714i	$-0.613851\pi$
$367$	−13.4138	−0.700192	−0.350096	+	0.936714i	$0.613851\pi$
$368$	17.2144	0.897361
$369$	21.1553	1.10130
$370$	−61.7938	−3.21251
$371$	14.7140	0.763910
$372$	56.8795	2.94906
$373$	−32.5154	−1.68358	−0.841792	−	0.539802i	$-0.818499\pi$
$373$	−32.5154	−1.68358	−0.841792	+	0.539802i	$0.818499\pi$
$374$	5.85576	0.302794
$375$	18.2202	0.940885
$376$	−8.72357	−0.449884
$377$	−39.9051	−2.05522
$378$	−6.87376	−0.353548
$379$	−0.0410933	−0.00211082	−0.00105541	−	0.999999i	$-0.500336\pi$
$379$	−0.0410933	−0.00211082	−0.00105541	+	0.999999i	$0.500336\pi$
$380$	−66.3943	−3.40596
$381$	−18.8697	−0.966722
$382$	39.6914	2.03079
$383$	−5.36933	−0.274360	−0.137180	−	0.990546i	$-0.543804\pi$
$383$	−5.36933	−0.274360	−0.137180	+	0.990546i	$0.543804\pi$
$384$	−19.5071	−0.995466
$385$	−10.5680	−0.538596
$386$	−3.08627	−0.157087
$387$	−16.4524	−0.836322
$388$	6.13645	0.311531
$389$	18.2017	0.922864	0.461432	−	0.887176i	$-0.347336\pi$
$389$	18.2017	0.922864	0.461432	+	0.887176i	$0.347336\pi$
$390$	−85.8812	−4.34876
$391$	−5.90976	−0.298870
$392$	5.42920	0.274216
$393$	2.63809	0.133074
$394$	−27.3304	−1.37689
$395$	−41.1986	−2.07293
$396$	−27.9210	−1.40308
$397$	−14.8207	−0.743830	−0.371915	−	0.928267i	$-0.621299\pi$
$397$	−14.8207	−0.743830	−0.371915	+	0.928267i	$0.621299\pi$
$398$	−35.6457	−1.78676
$399$	23.0133	1.15211
$400$	−20.3155	−1.01577
$401$	14.2644	0.712331	0.356165	−	0.934423i	$-0.384084\pi$
$401$	14.2644	0.712331	0.356165	+	0.934423i	$0.384084\pi$
$402$	9.25540	0.461618
$403$	−38.5119	−1.91842
$404$	19.0391	0.947230
$405$	15.3222	0.761364
$406$	−20.9554	−1.04000
$407$	23.5266	1.16617
$408$	2.50019	0.123778
$409$	29.1103	1.43941	0.719706	−	0.694279i	$-0.244277\pi$
$409$	29.1103	1.43941	0.719706	+	0.694279i	$0.244277\pi$
$410$	37.5337	1.85366
$411$	−10.4139	−0.513679
$412$	−28.2924	−1.39387
$413$	8.29120	0.407983
$414$	51.2314	2.51788
$415$	−56.2928	−2.76330
$416$	35.3850	1.73489
$417$	−8.84741	−0.433259
$418$	45.9583	2.24789
$419$	−11.8324	−0.578052	−0.289026	−	0.957321i	$-0.593331\pi$
$419$	−11.8324	−0.578052	−0.289026	+	0.957321i	$0.593331\pi$
$420$	−24.8055	−1.21039
$421$	31.6285	1.54148	0.770739	−	0.637151i	$-0.219887\pi$
$421$	31.6285	1.54148	0.770739	+	0.637151i	$0.219887\pi$
$422$	−1.39822	−0.0680642
$423$	38.2614	1.86033
$424$	12.5459	0.609285
$425$	6.97438	0.338307
$426$	5.52860	0.267861
$427$	−16.6342	−0.804985
$428$	−16.0643	−0.776498
$429$	32.6974	1.57865
$430$	−29.1898	−1.40766
$431$	−24.6588	−1.18777	−0.593885	−	0.804550i	$-0.702407\pi$
$431$	−24.6588	−1.18777	−0.593885	+	0.804550i	$0.702407\pi$
$432$	8.63753	0.415573
$433$	−32.2412	−1.54942	−0.774708	−	0.632320i	$-0.782103\pi$
$433$	−32.2412	−1.54942	−0.774708	+	0.632320i	$0.782103\pi$
$434$	−20.2238	−0.970775
$435$	−83.4240	−3.99988
$436$	10.2834	0.492484
$437$	−46.3821	−2.21876
$438$	49.8211	2.38055
$439$	1.41788	0.0676716	0.0338358	−	0.999427i	$-0.489228\pi$
$439$	1.41788	0.0676716	0.0338358	+	0.999427i	$0.489228\pi$
$440$	−9.01089	−0.429577
$441$	−23.8123	−1.13392
$442$	−9.30632	−0.442657
$443$	36.7112	1.74420	0.872100	−	0.489327i	$-0.162758\pi$
$443$	36.7112	1.74420	0.872100	+	0.489327i	$0.162758\pi$
$444$	55.2224	2.62074
$445$	42.7017	2.02426
$446$	−37.0654	−1.75510
$447$	−34.7950	−1.64575
$448$	12.1762	0.575272
$449$	−8.69800	−0.410484	−0.205242	−	0.978711i	$-0.565798\pi$
$449$	−8.69800	−0.410484	−0.205242	+	0.978711i	$0.565798\pi$
$450$	−60.4605	−2.85014
$451$	−14.2901	−0.672896
$452$	−2.41387	−0.113539
$453$	44.1830	2.07590
$454$	−0.654083	−0.0306976
$455$	16.7953	0.787377
$456$	19.6224	0.918905
$457$	−4.73505	−0.221496	−0.110748	−	0.993849i	$-0.535325\pi$
$457$	−4.73505	−0.221496	−0.110748	+	0.993849i	$0.535325\pi$
$458$	3.23272	0.151055
$459$	−2.96530	−0.138408
$460$	49.9943	2.33100
$461$	20.3578	0.948155	0.474078	−	0.880483i	$-0.342782\pi$
$461$	20.3578	0.948155	0.474078	+	0.880483i	$0.342782\pi$
$462$	17.1704	0.798841
$463$	−4.92241	−0.228764	−0.114382	−	0.993437i	$-0.536489\pi$
$463$	−4.92241	−0.228764	−0.114382	+	0.993437i	$0.536489\pi$
$464$	26.3325	1.22246
$465$	−80.5116	−3.73364
$466$	−63.8854	−2.95943
$467$	3.38256	0.156526	0.0782630	−	0.996933i	$-0.475063\pi$
$467$	3.38256	0.156526	0.0782630	+	0.996933i	$0.475063\pi$
$468$	44.3738	2.05118
$469$	−1.81003	−0.0835794
$470$	67.8833	3.13122
$471$	−33.6506	−1.55054
$472$	7.06955	0.325402
$473$	11.1134	0.510994
$474$	66.9376	3.07455
$475$	54.7377	2.51154
$476$	−2.68800	−0.123204
$477$	−55.0262	−2.51948
$478$	41.9025	1.91657
$479$	6.21983	0.284191	0.142096	−	0.989853i	$-0.454616\pi$
$479$	6.21983	0.284191	0.142096	+	0.989853i	$0.454616\pi$
$480$	73.9744	3.37646
$481$	−37.3899	−1.70483
$482$	23.7233	1.08057
$483$	−17.3288	−0.788487
$484$	−8.03130	−0.365059
$485$	−8.68601	−0.394411
$486$	−43.6495	−1.97998
$487$	−33.6068	−1.52287	−0.761435	−	0.648241i	$-0.775505\pi$
$487$	−33.6068	−1.52287	−0.761435	+	0.648241i	$0.775505\pi$
$488$	−14.1833	−0.642046
$489$	−37.9297	−1.71524
$490$	−42.2478	−1.90856
$491$	−16.2926	−0.735277	−0.367638	−	0.929969i	$-0.619834\pi$
$491$	−16.2926	−0.735277	−0.367638	+	0.929969i	$0.619834\pi$
$492$	−33.5422	−1.51220
$493$	−9.04005	−0.407144
$494$	−73.0396	−3.28621
$495$	39.5216	1.77636
$496$	25.4132	1.14109
$497$	−1.08120	−0.0484984
$498$	91.4619	4.09851
$499$	−14.9769	−0.670457	−0.335228	−	0.942137i	$-0.608813\pi$
$499$	−14.9769	−0.670457	−0.335228	+	0.942137i	$0.608813\pi$
$500$	−16.7025	−0.746960
$501$	30.1584	1.34738
$502$	−16.3342	−0.729030
$503$	40.6196	1.81114	0.905569	−	0.424199i	$-0.139444\pi$
$503$	40.6196	1.81114	0.905569	+	0.424199i	$0.139444\pi$
$504$	4.23866	0.188805
$505$	−26.9494	−1.19923
$506$	−34.6061	−1.53843
$507$	−17.2960	−0.768143
$508$	17.2979	0.767472
$509$	−13.5307	−0.599740	−0.299870	−	0.953980i	$-0.596943\pi$
$509$	−13.5307	−0.599740	−0.299870	+	0.953980i	$0.596943\pi$
$510$	−19.4554	−0.861501
$511$	−9.74325	−0.431016
$512$	−28.8115	−1.27330
$513$	−23.2728	−1.02752
$514$	−51.1784	−2.25738
$515$	40.0472	1.76469
$516$	26.0856	1.14836
$517$	−25.8451	−1.13667
$518$	−19.6346	−0.862696
$519$	−49.2758	−2.16297
$520$	14.3206	0.628002
$521$	−19.5015	−0.854378	−0.427189	−	0.904162i	$-0.640496\pi$
$521$	−19.5015	−0.854378	−0.427189	+	0.904162i	$0.640496\pi$
$522$	78.3677	3.43006
$523$	−26.6832	−1.16677	−0.583387	−	0.812194i	$-0.698273\pi$
$523$	−26.6832	−1.16677	−0.583387	+	0.812194i	$0.698273\pi$
$524$	−2.41835	−0.105646
$525$	20.4505	0.892533
$526$	−26.4855	−1.15482
$527$	−8.72445	−0.380043
$528$	−21.5763	−0.938988
$529$	11.9253	0.518492
$530$	−97.6275	−4.24067
$531$	−31.0069	−1.34558
$532$	−21.0964	−0.914647
$533$	22.7107	0.983711
$534$	−69.3798	−3.00236
$535$	22.7386	0.983078
$536$	−1.54333	−0.0666618
$537$	53.4142	2.30499
$538$	36.0446	1.55399
$539$	16.0849	0.692827
$540$	25.0853	1.07950
$541$	−16.9566	−0.729021	−0.364511	−	0.931199i	$-0.618764\pi$
$541$	−16.9566	−0.729021	−0.364511	+	0.931199i	$0.618764\pi$
$542$	16.1961	0.695680
$543$	−20.2284	−0.868086
$544$	8.01607	0.343686
$545$	−14.5559	−0.623504
$546$	−27.2883	−1.16783
$547$	−10.0239	−0.428591	−0.214296	−	0.976769i	$-0.568746\pi$
$547$	−10.0239	−0.428591	−0.214296	+	0.976769i	$0.568746\pi$
$548$	9.54648	0.407805
$549$	62.2074	2.65495
$550$	40.8403	1.74144
$551$	−70.9499	−3.02257
$552$	−14.7755	−0.628887
$553$	−13.0906	−0.556670
$554$	−13.8617	−0.588925
$555$	−78.1660	−3.31796
$556$	8.11048	0.343961
$557$	29.4122	1.24624	0.623118	−	0.782128i	$-0.285866\pi$
$557$	29.4122	1.24624	0.623118	+	0.782128i	$0.285866\pi$
$558$	75.6317	3.20175
$559$	−17.6621	−0.747025
$560$	−11.0829	−0.468337
$561$	7.40723	0.312734
$562$	12.7279	0.536894
$563$	39.2636	1.65477	0.827383	−	0.561639i	$-0.189829\pi$
$563$	39.2636	1.65477	0.827383	+	0.561639i	$0.189829\pi$
$564$	−60.6643	−2.55443
$565$	3.41677	0.143745
$566$	−21.1972	−0.890983
$567$	4.86853	0.204459
$568$	−0.921890	−0.0386817
$569$	27.7414	1.16298	0.581489	−	0.813554i	$-0.302470\pi$
$569$	27.7414	1.16298	0.581489	+	0.813554i	$0.302470\pi$
$570$	−152.694	−6.39564
$571$	−33.0550	−1.38331	−0.691655	−	0.722228i	$-0.743118\pi$
$571$	−33.0550	−1.38331	−0.691655	+	0.722228i	$0.743118\pi$
$572$	−29.9739	−1.25327
$573$	50.2075	2.09745
$574$	11.9261	0.497787
$575$	−41.2170	−1.71887
$576$	−45.5358	−1.89733
$577$	36.2137	1.50760	0.753798	−	0.657106i	$-0.228219\pi$
$577$	36.2137	1.50760	0.753798	+	0.657106i	$0.228219\pi$
$578$	−2.10824	−0.0876914
$579$	−3.90397	−0.162244
$580$	76.4754	3.17547
$581$	−17.8867	−0.742066
$582$	14.1126	0.584987
$583$	37.1695	1.53940
$584$	−8.30765	−0.343773
$585$	−62.8100	−2.59687
$586$	−37.3626	−1.54343
$587$	−20.6469	−0.852187	−0.426094	−	0.904679i	$-0.640111\pi$
$587$	−20.6469	−0.852187	−0.426094	+	0.904679i	$0.640111\pi$
$588$	37.7550	1.55699
$589$	−68.4729	−2.82138
$590$	−55.0124	−2.26482
$591$	−34.5716	−1.42208
$592$	24.6728	1.01405
$593$	13.6932	0.562311	0.281155	−	0.959662i	$-0.409282\pi$
$593$	13.6932	0.562311	0.281155	+	0.959662i	$0.409282\pi$
$594$	−17.3641	−0.712457
$595$	3.80479	0.155981
$596$	31.8968	1.30654
$597$	−45.0900	−1.84541
$598$	54.9982	2.24904
$599$	−5.80474	−0.237175	−0.118588	−	0.992944i	$-0.537837\pi$
$599$	−5.80474	−0.237175	−0.118588	+	0.992944i	$0.537837\pi$
$600$	17.4373	0.711873
$601$	1.65581	0.0675420	0.0337710	−	0.999430i	$-0.489248\pi$
$601$	1.65581	0.0675420	0.0337710	+	0.999430i	$0.489248\pi$
$602$	−9.27490	−0.378017
$603$	6.76903	0.275656
$604$	−40.5028	−1.64804
$605$	11.3681	0.462179
$606$	43.7861	1.77869
$607$	31.5026	1.27865	0.639327	−	0.768935i	$-0.279213\pi$
$607$	31.5026	1.27865	0.639327	+	0.768935i	$0.279213\pi$
$608$	62.9132	2.55147
$609$	−26.5075	−1.07414
$610$	110.368	4.46868
$611$	41.0745	1.66170
$612$	10.0524	0.406343
$613$	17.3656	0.701389	0.350695	−	0.936490i	$-0.385945\pi$
$613$	17.3656	0.701389	0.350695	+	0.936490i	$0.385945\pi$
$614$	54.4444	2.19720
$615$	47.4782	1.91451
$616$	−2.86316	−0.115360
$617$	24.3412	0.979941	0.489971	−	0.871739i	$-0.337007\pi$
$617$	24.3412	0.979941	0.489971	+	0.871739i	$0.337007\pi$
$618$	−65.0669	−2.61738
$619$	19.0596	0.766068	0.383034	−	0.923734i	$-0.374879\pi$
$619$	19.0596	0.766068	0.383034	+	0.923734i	$0.374879\pi$
$620$	73.8055	2.96410
$621$	17.5242	0.703223
$622$	26.6401	1.06817
$623$	13.5682	0.543600
$624$	34.2903	1.37271
$625$	−11.2299	−0.449195
$626$	22.3022	0.891375
$627$	58.1348	2.32168
$628$	30.8477	1.23096
$629$	−8.47027	−0.337732
$630$	−32.9835	−1.31410
$631$	10.8712	0.432777	0.216389	−	0.976307i	$-0.430572\pi$
$631$	10.8712	0.432777	0.216389	+	0.976307i	$0.430572\pi$
$632$	−11.1618	−0.443993
$633$	−1.76867	−0.0702984
$634$	−29.9499	−1.18946
$635$	−24.4848	−0.971651
$636$	87.2453	3.45950
$637$	−25.5631	−1.01285
$638$	−52.9364	−2.09577
$639$	4.04339	0.159954
$640$	−25.3119	−1.00054
$641$	−14.3699	−0.567577	−0.283788	−	0.958887i	$-0.591591\pi$
$641$	−14.3699	−0.567577	−0.283788	+	0.958887i	$0.591591\pi$
$642$	−36.9447	−1.45809
$643$	32.9196	1.29822	0.649112	−	0.760693i	$-0.275141\pi$
$643$	32.9196	1.29822	0.649112	+	0.760693i	$0.275141\pi$
$644$	15.8854	0.625973
$645$	−36.9236	−1.45387
$646$	−16.5463	−0.651006
$647$	−45.6054	−1.79293	−0.896467	−	0.443110i	$-0.853875\pi$
$647$	−45.6054	−1.79293	−0.896467	+	0.443110i	$0.853875\pi$
$648$	4.15118	0.163074
$649$	20.9448	0.822153
$650$	−64.9059	−2.54582
$651$	−25.5821	−1.00264
$652$	34.7704	1.36171
$653$	−4.55485	−0.178245	−0.0891225	−	0.996021i	$-0.528406\pi$
$653$	−4.55485	−0.178245	−0.0891225	+	0.996021i	$0.528406\pi$
$654$	23.6497	0.924776
$655$	3.42312	0.133753
$656$	−14.9863	−0.585117
$657$	36.4372	1.42155
$658$	21.5695	0.840868
$659$	−7.90075	−0.307769	−0.153885	−	0.988089i	$-0.549178\pi$
$659$	−7.90075	−0.307769	−0.153885	+	0.988089i	$0.549178\pi$
$660$	−62.6623	−2.43913
$661$	8.81131	0.342720	0.171360	−	0.985208i	$-0.445184\pi$
$661$	8.81131	0.342720	0.171360	+	0.985208i	$0.445184\pi$
$662$	−40.6548	−1.58009
$663$	−11.7720	−0.457187
$664$	−15.2512	−0.591862
$665$	29.8615	1.15798
$666$	73.4283	2.84529
$667$	53.4246	2.06861
$668$	−27.6464	−1.06967
$669$	−46.8858	−1.81271
$670$	12.0096	0.463971
$671$	−42.0203	−1.62218
$672$	23.5050	0.906724
$673$	6.46726	0.249294	0.124647	−	0.992201i	$-0.460220\pi$
$673$	6.46726	0.249294	0.124647	+	0.992201i	$0.460220\pi$
$674$	9.51494	0.366502
$675$	−20.6811	−0.796018
$676$	15.8554	0.609822
$677$	33.1350	1.27348	0.636741	−	0.771078i	$-0.280282\pi$
$677$	33.1350	1.27348	0.636741	+	0.771078i	$0.280282\pi$
$678$	−5.55142	−0.213201
$679$	−2.75993	−0.105916
$680$	3.24418	0.124409
$681$	−0.827381	−0.0317053
$682$	−51.0883	−1.95627
$683$	2.33896	0.0894980	0.0447490	−	0.998998i	$-0.485751\pi$
$683$	2.33896	0.0894980	0.0447490	+	0.998998i	$0.485751\pi$
$684$	78.8950	3.01663
$685$	−13.5128	−0.516298
$686$	−29.6505	−1.13206
$687$	4.08923	0.156014
$688$	11.6548	0.444335
$689$	−59.0720	−2.25047
$690$	114.977	4.37710
$691$	37.1582	1.41356	0.706781	−	0.707432i	$-0.250146\pi$
$691$	37.1582	1.41356	0.706781	+	0.707432i	$0.250146\pi$
$692$	45.1714	1.71716
$693$	12.5578	0.477030
$694$	30.5021	1.15785
$695$	−11.4802	−0.435468
$696$	−22.6018	−0.856720
$697$	5.14486	0.194876
$698$	−33.4041	−1.26436
$699$	−80.8117	−3.05658
$700$	−18.7471	−0.708574
$701$	−7.28344	−0.275092	−0.137546	−	0.990495i	$-0.543921\pi$
$701$	−7.28344	−0.275092	−0.137546	+	0.990495i	$0.543921\pi$
$702$	27.5960	1.04155
$703$	−66.4780	−2.50727
$704$	30.7589	1.15927
$705$	85.8688	3.23401
$706$	−2.10824	−0.0793448
$707$	−8.56302	−0.322045
$708$	49.1621	1.84762
$709$	−49.1251	−1.84493	−0.922467	−	0.386077i	$-0.873830\pi$
$709$	−49.1251	−1.84493	−0.922467	+	0.386077i	$0.873830\pi$
$710$	7.17378	0.269227
$711$	48.9554	1.83597
$712$	11.5690	0.433568
$713$	51.5595	1.93092
$714$	−6.18186	−0.231350
$715$	42.4274	1.58669
$716$	−48.9652	−1.82991
$717$	53.0045	1.97949
$718$	−36.0971	−1.34713
$719$	−39.6517	−1.47876	−0.739380	−	0.673288i	$-0.764881\pi$
$719$	−39.6517	−1.47876	−0.739380	+	0.673288i	$0.764881\pi$
$720$	41.4470	1.54464
$721$	12.7248	0.473896
$722$	−89.8053	−3.34221
$723$	30.0087	1.11604
$724$	18.5436	0.689166
$725$	−63.0488	−2.34157
$726$	−18.4704	−0.685500
$727$	9.13797	0.338909	0.169454	−	0.985538i	$-0.445800\pi$
$727$	9.13797	0.338909	0.169454	+	0.985538i	$0.445800\pi$
$728$	4.55031	0.168646
$729$	−41.9308	−1.55299
$730$	64.6468	2.39268
$731$	−4.00114	−0.147988
$732$	−98.6313	−3.64552
$733$	−4.18278	−0.154495	−0.0772473	−	0.997012i	$-0.524613\pi$
$733$	−4.18278	−0.154495	−0.0772473	+	0.997012i	$0.524613\pi$
$734$	28.2795	1.04381
$735$	−53.4413	−1.97121
$736$	−47.3731	−1.74619
$737$	−4.57239	−0.168426
$738$	−44.6005	−1.64177
$739$	−43.2103	−1.58952	−0.794758	−	0.606926i	$-0.792402\pi$
$739$	−43.2103	−1.58952	−0.794758	+	0.606926i	$0.792402\pi$
$740$	71.6552	2.63410
$741$	−92.3914	−3.39408
$742$	−31.0206	−1.13880
$743$	−21.7408	−0.797593	−0.398796	−	0.917040i	$-0.630572\pi$
$743$	−21.7408	−0.797593	−0.398796	+	0.917040i	$0.630572\pi$
$744$	−21.8128	−0.799694
$745$	−45.1492	−1.65414
$746$	68.5504	2.50981
$747$	66.8915	2.44743
$748$	−6.79026	−0.248276
$749$	7.22508	0.263999
$750$	−38.4125	−1.40263
$751$	−23.1640	−0.845265	−0.422632	−	0.906301i	$-0.638894\pi$
$751$	−23.1640	−0.845265	−0.422632	+	0.906301i	$0.638894\pi$
$752$	−27.1042	−0.988388
$753$	−20.6619	−0.752961
$754$	84.1296	3.06382
$755$	57.3308	2.08648
$756$	7.97071	0.289892
$757$	−8.33446	−0.302921	−0.151461	−	0.988463i	$-0.548398\pi$
$757$	−8.33446	−0.302921	−0.151461	+	0.988463i	$0.548398\pi$
$758$	0.0866347	0.00314671
$759$	−43.7750	−1.58893
$760$	25.4616	0.923590
$761$	−37.8193	−1.37095	−0.685474	−	0.728097i	$-0.740405\pi$
$761$	−37.8193	−1.37095	−0.685474	+	0.728097i	$0.740405\pi$
$762$	39.7819	1.44114
$763$	−4.62504	−0.167438
$764$	−46.0256	−1.66515
$765$	−14.2289	−0.514447
$766$	11.3199	0.409003
$767$	−33.2867	−1.20191
$768$	−17.9395	−0.647337
$769$	40.3994	1.45684	0.728420	−	0.685131i	$-0.240255\pi$
$769$	40.3994	1.45684	0.728420	+	0.685131i	$0.240255\pi$
$770$	22.2800	0.802914
$771$	−64.7381	−2.33149
$772$	3.57880	0.128804
$773$	−32.7166	−1.17673	−0.588367	−	0.808594i	$-0.700229\pi$
$773$	−32.7166	−1.17673	−0.588367	+	0.808594i	$0.700229\pi$
$774$	34.6857	1.24675
$775$	−60.8477	−2.18571
$776$	−2.35327	−0.0844776
$777$	−24.8368	−0.891015
$778$	−38.3737	−1.37576
$779$	40.3789	1.44672
$780$	99.5867	3.56578
$781$	−2.73126	−0.0977322
$782$	12.4592	0.445541
$783$	26.8065	0.957985
$784$	16.8686	0.602449
$785$	−43.6642	−1.55844
$786$	−5.56173	−0.198381
$787$	25.4707	0.907932	0.453966	−	0.891019i	$-0.350009\pi$
$787$	25.4707	0.907932	0.453966	+	0.891019i	$0.350009\pi$
$788$	31.6920	1.12898
$789$	−33.5028	−1.19273
$790$	86.8567	3.09022
$791$	1.08566	0.0386017
$792$	10.7075	0.380473
$793$	66.7812	2.37147
$794$	31.2457	1.10887
$795$	−123.494	−4.37987
$796$	41.3343	1.46506
$797$	−2.37704	−0.0841991	−0.0420996	−	0.999113i	$-0.513405\pi$
$797$	−2.37704	−0.0841991	−0.0420996	+	0.999113i	$0.513405\pi$
$798$	−48.5176	−1.71751
$799$	9.30498	0.329187
$800$	55.9072	1.97662
$801$	−50.7416	−1.79286
$802$	−30.0729	−1.06191
$803$	−24.6128	−0.868568
$804$	−10.7324	−0.378504
$805$	−22.4854	−0.792508
$806$	81.1926	2.85989
$807$	45.5946	1.60501
$808$	−7.30131	−0.256859
$809$	−14.7344	−0.518035	−0.259017	−	0.965873i	$-0.583399\pi$
$809$	−14.7344	−0.518035	−0.259017	+	0.965873i	$0.583399\pi$
$810$	−32.3028	−1.13501
$811$	−7.21156	−0.253232	−0.126616	−	0.991952i	$-0.540412\pi$
$811$	−7.21156	−0.253232	−0.126616	+	0.991952i	$0.540412\pi$
$812$	24.2996	0.852750
$813$	20.4872	0.718517
$814$	−49.5999	−1.73847
$815$	−49.2167	−1.72399
$816$	7.76810	0.271938
$817$	−31.4025	−1.09864
$818$	−61.3716	−2.14581
$819$	−19.9575	−0.697373
$820$	−43.5236	−1.51991
$821$	22.7725	0.794765	0.397383	−	0.917653i	$-0.369919\pi$
$821$	22.7725	0.794765	0.397383	+	0.917653i	$0.369919\pi$
$822$	21.9550	0.765769
$823$	−36.5536	−1.27418	−0.637089	−	0.770790i	$-0.719862\pi$
$823$	−36.5536	−1.27418	−0.637089	+	0.770790i	$0.719862\pi$
$824$	10.8499	0.377973
$825$	51.6609	1.79860
$826$	−17.4799	−0.608203
$827$	3.65442	0.127077	0.0635383	−	0.997979i	$-0.479761\pi$
$827$	3.65442	0.127077	0.0635383	+	0.997979i	$0.479761\pi$
$828$	−59.4072	−2.06454
$829$	−46.8615	−1.62757	−0.813784	−	0.581168i	$-0.802596\pi$
$829$	−46.8615	−1.62757	−0.813784	+	0.581168i	$0.802596\pi$
$830$	118.679	4.11940
$831$	−17.5343	−0.608257
$832$	−48.8838	−1.69474
$833$	−5.79105	−0.200648
$834$	18.6525	0.645883
$835$	39.1328	1.35425
$836$	−53.2926	−1.84316
$837$	25.8706	0.894219
$838$	24.9456	0.861733
$839$	−18.8861	−0.652022	−0.326011	−	0.945366i	$-0.605705\pi$
$839$	−18.8861	−0.652022	−0.326011	+	0.945366i	$0.605705\pi$
$840$	9.51269	0.328219
$841$	52.7226	1.81802
$842$	−66.6805	−2.29796
$843$	16.1001	0.554518
$844$	1.62135	0.0558093
$845$	−22.4429	−0.772059
$846$	−80.6643	−2.77330
$847$	3.61215	0.124115
$848$	38.9804	1.33859
$849$	−26.8133	−0.920230
$850$	−14.7037	−0.504333
$851$	50.0573	1.71594
$852$	−6.41089	−0.219633
$853$	−18.3337	−0.627733	−0.313867	−	0.949467i	$-0.601624\pi$
$853$	−18.3337	−0.627733	−0.313867	+	0.949467i	$0.601624\pi$
$854$	35.0689	1.20003
$855$	−111.674	−3.81917
$856$	6.16051	0.210562
$857$	12.6696	0.432786	0.216393	−	0.976306i	$-0.430571\pi$
$857$	12.6696	0.432786	0.216393	+	0.976306i	$0.430571\pi$
$858$	−68.9341	−2.35337
$859$	56.8643	1.94018	0.970092	−	0.242738i	$-0.0780456\pi$
$859$	56.8643	1.94018	0.970092	+	0.242738i	$0.0780456\pi$
$860$	33.8481	1.15421
$861$	15.0859	0.514127
$862$	51.9867	1.77067
$863$	−6.18825	−0.210650	−0.105325	−	0.994438i	$-0.533588\pi$
$863$	−6.18825	−0.210650	−0.105325	+	0.994438i	$0.533588\pi$
$864$	−23.7701	−0.808674
$865$	−63.9391	−2.17399
$866$	67.9724	2.30980
$867$	−2.66682	−0.0905699
$868$	23.4513	0.795989
$869$	−33.0688	−1.12178
$870$	175.878	5.96283
$871$	7.26672	0.246223
$872$	−3.94357	−0.133546
$873$	10.3214	0.349326
$874$	97.7848	3.30762
$875$	7.51213	0.253956
$876$	−57.7719	−1.95193
$877$	13.6697	0.461593	0.230796	−	0.973002i	$-0.425867\pi$
$877$	13.6697	0.461593	0.230796	+	0.973002i	$0.425867\pi$
$878$	−2.98923	−0.100882
$879$	−47.2618	−1.59410
$880$	−27.9969	−0.943775
$881$	39.2014	1.32073	0.660365	−	0.750945i	$-0.270402\pi$
$881$	39.2014	1.32073	0.660365	+	0.750945i	$0.270402\pi$
$882$	50.2022	1.69040
$883$	30.2275	1.01724	0.508618	−	0.860992i	$-0.330156\pi$
$883$	30.2275	1.01724	0.508618	+	0.860992i	$0.330156\pi$
$884$	10.7915	0.362957
$885$	−69.5878	−2.33917
$886$	−77.3961	−2.60017
$887$	−14.4501	−0.485189	−0.242594	−	0.970128i	$-0.577998\pi$
$887$	−14.4501	−0.485189	−0.242594	+	0.970128i	$0.577998\pi$
$888$	−21.1773	−0.710662
$889$	−7.77992	−0.260930
$890$	−90.0256	−3.01767
$891$	12.2986	0.412018
$892$	42.9805	1.43909
$893$	73.0291	2.44383
$894$	73.3563	2.45340
$895$	69.3090	2.31675
$896$	−8.04272	−0.268689
$897$	69.5698	2.32287
$898$	18.3375	0.611931
$899$	78.8695	2.63045
$900$	70.1092	2.33697
$901$	−13.3821	−0.445823
$902$	30.1271	1.00312
$903$	−11.7323	−0.390426
$904$	0.925696	0.0307882
$905$	−26.2480	−0.872512
$906$	−93.1484	−3.09465
$907$	20.7556	0.689179	0.344589	−	0.938754i	$-0.388018\pi$
$907$	20.7556	0.689179	0.344589	+	0.938754i	$0.388018\pi$
$908$	0.758466	0.0251706
$909$	32.0234	1.06215
$910$	−35.4086	−1.17378
$911$	3.11546	0.103220	0.0516099	−	0.998667i	$-0.483565\pi$
$911$	3.11546	0.103220	0.0516099	+	0.998667i	$0.483565\pi$
$912$	60.9670	2.01882
$913$	−45.1844	−1.49538
$914$	9.98263	0.330196
$915$	139.610	4.61537
$916$	−3.74862	−0.123858
$917$	1.08768	0.0359183
$918$	6.25157	0.206333
$919$	21.3465	0.704154	0.352077	−	0.935971i	$-0.385475\pi$
$919$	21.3465	0.704154	0.352077	+	0.935971i	$0.385475\pi$
$920$	−19.1724	−0.632094
$921$	68.8693	2.26932
$922$	−42.9191	−1.41347
$923$	4.34068	0.142875
$924$	−19.9106	−0.655011
$925$	−59.0750	−1.94237
$926$	10.3776	0.341031
$927$	−47.5873	−1.56297
$928$	−72.4657	−2.37880
$929$	15.1055	0.495596	0.247798	−	0.968812i	$-0.420293\pi$
$929$	15.1055	0.495596	0.247798	+	0.968812i	$0.420293\pi$
$930$	169.738	5.56593
$931$	−45.4504	−1.48958
$932$	74.0806	2.42659
$933$	33.6984	1.10324
$934$	−7.13125	−0.233342
$935$	9.61145	0.314328
$936$	−17.0169	−0.556215
$937$	−25.4242	−0.830571	−0.415286	−	0.909691i	$-0.636318\pi$
$937$	−25.4242	−0.830571	−0.415286	+	0.909691i	$0.636318\pi$
$938$	3.81598	0.124596
$939$	28.2111	0.920636
$940$	−78.7165	−2.56745
$941$	−30.1292	−0.982185	−0.491093	−	0.871107i	$-0.663402\pi$
$941$	−30.1292	−0.982185	−0.491093	+	0.871107i	$0.663402\pi$
$942$	70.9437	2.31147
$943$	−30.4049	−0.990121
$944$	21.9651	0.714904
$945$	−11.2824	−0.367015
$946$	−23.4297	−0.761766
$947$	4.17795	0.135765	0.0678825	−	0.997693i	$-0.478376\pi$
$947$	4.17795	0.135765	0.0678825	+	0.997693i	$0.478376\pi$
$948$	−77.6199	−2.52098
$949$	39.1162	1.26977
$950$	−115.400	−3.74408
$951$	−37.8851	−1.22851
$952$	1.03082	0.0334091
$953$	−42.2006	−1.36701	−0.683505	−	0.729946i	$-0.739545\pi$
$953$	−42.2006	−1.36701	−0.683505	+	0.729946i	$0.739545\pi$
$954$	116.009	3.75592
$955$	65.1481	2.10814
$956$	−48.5895	−1.57150
$957$	−66.9618	−2.16457
$958$	−13.1129	−0.423659
$959$	−4.29362	−0.138648
$960$	−102.195	−3.29832
$961$	45.1161	1.45536
$962$	78.8271	2.54149
$963$	−27.0199	−0.870703
$964$	−27.5092	−0.886012
$965$	−5.06571	−0.163071
$966$	36.5333	1.17544
$967$	17.9202	0.576274	0.288137	−	0.957589i	$-0.406964\pi$
$967$	17.9202	0.576274	0.288137	+	0.957589i	$0.406964\pi$
$968$	3.07993	0.0989926
$969$	−20.9302	−0.672376
$970$	18.3122	0.587970
$971$	−17.7063	−0.568224	−0.284112	−	0.958791i	$-0.591699\pi$
$971$	−17.7063	−0.568224	−0.284112	+	0.958791i	$0.591699\pi$
$972$	50.6153	1.62349
$973$	−3.64777	−0.116942
$974$	70.8514	2.27022
$975$	−82.1026	−2.62939
$976$	−44.0675	−1.41057
$977$	−5.91382	−0.189200	−0.0945999	−	0.995515i	$-0.530157\pi$
$977$	−5.91382	−0.189200	−0.0945999	+	0.995515i	$0.530157\pi$
$978$	79.9650	2.55700
$979$	34.2753	1.09544
$980$	48.9900	1.56493
$981$	17.2964	0.552232
$982$	34.3489	1.09612
$983$	37.5704	1.19831	0.599155	−	0.800633i	$-0.295503\pi$
$983$	37.5704	1.19831	0.599155	+	0.800633i	$0.295503\pi$
$984$	12.8631	0.410061
$985$	−44.8593	−1.42934
$986$	19.0586	0.606951
$987$	27.2844	0.868470
$988$	84.6958	2.69453
$989$	23.6458	0.751893
$990$	−83.3211	−2.64812
$991$	−27.0336	−0.858751	−0.429375	−	0.903126i	$-0.641266\pi$
$991$	−27.0336	−0.858751	−0.429375	+	0.903126i	$0.641266\pi$
$992$	−69.9358	−2.22046
$993$	−51.4262	−1.63196
$994$	2.27943	0.0722991
$995$	−58.5078	−1.85482
$996$	−106.058	−3.36058
$997$	24.3875	0.772361	0.386180	−	0.922423i	$-0.373794\pi$
$997$	24.3875	0.772361	0.386180	+	0.922423i	$0.373794\pi$
$998$	31.5749	0.999485
$999$	25.1169	0.794664

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.19	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.19	✓	114	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10824 q^{2} -2.66682 q^{3} +2.44469 q^{4} -3.46040 q^{5} +5.62230 q^{6} -1.09952 q^{7} -0.937516 q^{8} +4.11192 q^{9} +O(q^{10})\)	\(q-2.10824 q^{2} -2.66682 q^{3} +2.44469 q^{4} -3.46040 q^{5} +5.62230 q^{6} -1.09952 q^{7} -0.937516 q^{8} +4.11192 q^{9} +7.29537 q^{10} -2.77755 q^{11} -6.51955 q^{12} +4.41425 q^{13} +2.31806 q^{14} +9.22827 q^{15} -2.91287 q^{16} +1.00000 q^{17} -8.66894 q^{18} +7.84839 q^{19} -8.45961 q^{20} +2.93223 q^{21} +5.85576 q^{22} -5.90976 q^{23} +2.50019 q^{24} +6.97438 q^{25} -9.30632 q^{26} -2.96530 q^{27} -2.68800 q^{28} -9.04005 q^{29} -19.4554 q^{30} -8.72445 q^{31} +8.01607 q^{32} +7.40723 q^{33} -2.10824 q^{34} +3.80479 q^{35} +10.0524 q^{36} -8.47027 q^{37} -16.5463 q^{38} -11.7720 q^{39} +3.24418 q^{40} +5.14486 q^{41} -6.18186 q^{42} -4.00114 q^{43} -6.79026 q^{44} -14.2289 q^{45} +12.4592 q^{46} +9.30498 q^{47} +7.76810 q^{48} -5.79105 q^{49} -14.7037 q^{50} -2.66682 q^{51} +10.7915 q^{52} -13.3821 q^{53} +6.25157 q^{54} +9.61145 q^{55} +1.03082 q^{56} -20.9302 q^{57} +19.0586 q^{58} -7.54072 q^{59} +22.5603 q^{60} +15.1285 q^{61} +18.3933 q^{62} -4.52116 q^{63} -11.0741 q^{64} -15.2751 q^{65} -15.6162 q^{66} +1.64619 q^{67} +2.44469 q^{68} +15.7603 q^{69} -8.02143 q^{70} +0.983333 q^{71} -3.85499 q^{72} +8.86134 q^{73} +17.8574 q^{74} -18.5994 q^{75} +19.1869 q^{76} +3.05399 q^{77} +24.8183 q^{78} +11.9057 q^{79} +10.0797 q^{80} -4.42785 q^{81} -10.8466 q^{82} +16.2677 q^{83} +7.16840 q^{84} -3.46040 q^{85} +8.43538 q^{86} +24.1082 q^{87} +2.60400 q^{88} -12.3401 q^{89} +29.9980 q^{90} -4.85358 q^{91} -14.4475 q^{92} +23.2665 q^{93} -19.6172 q^{94} -27.1586 q^{95} -21.3774 q^{96} +2.51011 q^{97} +12.2089 q^{98} -11.4211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

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