LMFDB - Embedded newform 6001.2.a.b.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.61975 q^{2} -2.31872 q^{3} +4.86309 q^{4} +0.216177 q^{5} +6.07447 q^{6} +3.38406 q^{7} -7.50057 q^{8} +2.37647 q^{9} +O(q^{10})$	\(q-2.61975 q^{2} -2.31872 q^{3} +4.86309 q^{4} +0.216177 q^{5} +6.07447 q^{6} +3.38406 q^{7} -7.50057 q^{8} +2.37647 q^{9} -0.566328 q^{10} +0.605807 q^{11} -11.2761 q^{12} -3.04846 q^{13} -8.86539 q^{14} -0.501253 q^{15} +9.92345 q^{16} +1.00000 q^{17} -6.22574 q^{18} +4.98478 q^{19} +1.05129 q^{20} -7.84669 q^{21} -1.58706 q^{22} +1.60592 q^{23} +17.3917 q^{24} -4.95327 q^{25} +7.98621 q^{26} +1.44580 q^{27} +16.4570 q^{28} -10.5141 q^{29} +1.31316 q^{30} +5.87827 q^{31} -10.9958 q^{32} -1.40470 q^{33} -2.61975 q^{34} +0.731555 q^{35} +11.5570 q^{36} -3.75203 q^{37} -13.0589 q^{38} +7.06853 q^{39} -1.62145 q^{40} -0.864890 q^{41} +20.5564 q^{42} +6.40616 q^{43} +2.94609 q^{44} +0.513736 q^{45} -4.20712 q^{46} +0.621685 q^{47} -23.0097 q^{48} +4.45187 q^{49} +12.9763 q^{50} -2.31872 q^{51} -14.8249 q^{52} +9.64958 q^{53} -3.78764 q^{54} +0.130961 q^{55} -25.3824 q^{56} -11.5583 q^{57} +27.5443 q^{58} -5.81342 q^{59} -2.43764 q^{60} -6.34225 q^{61} -15.3996 q^{62} +8.04211 q^{63} +8.95936 q^{64} -0.659006 q^{65} +3.67995 q^{66} +8.53186 q^{67} +4.86309 q^{68} -3.72369 q^{69} -1.91649 q^{70} -12.8904 q^{71} -17.8249 q^{72} +16.5475 q^{73} +9.82938 q^{74} +11.4852 q^{75} +24.2414 q^{76} +2.05009 q^{77} -18.5178 q^{78} +0.298557 q^{79} +2.14522 q^{80} -10.4818 q^{81} +2.26579 q^{82} +3.17470 q^{83} -38.1592 q^{84} +0.216177 q^{85} -16.7825 q^{86} +24.3793 q^{87} -4.54390 q^{88} -6.23133 q^{89} -1.34586 q^{90} -10.3162 q^{91} +7.80974 q^{92} -13.6301 q^{93} -1.62866 q^{94} +1.07759 q^{95} +25.4962 q^{96} -18.2172 q^{97} -11.6628 q^{98} +1.43968 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.61975	−1.85244	−0.926221	−	0.376980i	$-0.876963\pi$
$2$	−2.61975	−1.85244	−0.926221	+	0.376980i	$0.876963\pi$
$3$	−2.31872	−1.33871	−0.669357	−	0.742941i	$-0.733430\pi$
$3$	−2.31872	−1.33871	−0.669357	+	0.742941i	$0.733430\pi$
$4$	4.86309	2.43154
$5$	0.216177	0.0966771	0.0483385	−	0.998831i	$-0.484607\pi$
$5$	0.216177	0.0966771	0.0483385	+	0.998831i	$0.484607\pi$
$6$	6.07447	2.47989
$7$	3.38406	1.27905	0.639527	−	0.768768i	$-0.279130\pi$
$7$	3.38406	1.27905	0.639527	+	0.768768i	$0.279130\pi$
$8$	−7.50057	−2.65185
$9$	2.37647	0.792155
$10$	−0.566328	−0.179089
$11$	0.605807	0.182658	0.0913288	−	0.995821i	$-0.470889\pi$
$11$	0.605807	0.182658	0.0913288	+	0.995821i	$0.470889\pi$
$12$	−11.2761	−3.25514
$13$	−3.04846	−0.845491	−0.422746	−	0.906248i	$-0.638934\pi$
$13$	−3.04846	−0.845491	−0.422746	+	0.906248i	$0.638934\pi$
$14$	−8.86539	−2.36938
$15$	−0.501253	−0.129423
$16$	9.92345	2.48086
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−6.22574	−1.46742
$19$	4.98478	1.14359	0.571793	−	0.820398i	$-0.306248\pi$
$19$	4.98478	1.14359	0.571793	+	0.820398i	$0.306248\pi$
$20$	1.05129	0.235075
$21$	−7.84669	−1.71229
$22$	−1.58706	−0.338363
$23$	1.60592	0.334858	0.167429	−	0.985884i	$-0.446453\pi$
$23$	1.60592	0.334858	0.167429	+	0.985884i	$0.446453\pi$
$24$	17.3917	3.55007
$25$	−4.95327	−0.990654
$26$	7.98621	1.56622
$27$	1.44580	0.278245
$28$	16.4570	3.11008
$29$	−10.5141	−1.95242	−0.976211	−	0.216824i	$-0.930430\pi$
$29$	−10.5141	−1.95242	−0.976211	+	0.216824i	$0.930430\pi$
$30$	1.31316	0.239749
$31$	5.87827	1.05577	0.527884	−	0.849317i	$-0.322986\pi$
$31$	5.87827	1.05577	0.527884	+	0.849317i	$0.322986\pi$
$32$	−10.9958	−1.94380
$33$	−1.40470	−0.244526
$34$	−2.61975	−0.449283
$35$	0.731555	0.123655
$36$	11.5570	1.92616
$37$	−3.75203	−0.616830	−0.308415	−	0.951252i	$-0.599799\pi$
$37$	−3.75203	−0.616830	−0.308415	+	0.951252i	$0.599799\pi$
$38$	−13.0589	−2.11843
$39$	7.06853	1.13187
$40$	−1.62145	−0.256373
$41$	−0.864890	−0.135073	−0.0675366	−	0.997717i	$-0.521514\pi$
$41$	−0.864890	−0.135073	−0.0675366	+	0.997717i	$0.521514\pi$
$42$	20.5564	3.17192
$43$	6.40616	0.976930	0.488465	−	0.872583i	$-0.337557\pi$
$43$	6.40616	0.976930	0.488465	+	0.872583i	$0.337557\pi$
$44$	2.94609	0.444140
$45$	0.513736	0.0765832
$46$	−4.20712	−0.620305
$47$	0.621685	0.0906821	0.0453411	−	0.998972i	$-0.485563\pi$
$47$	0.621685	0.0906821	0.0453411	+	0.998972i	$0.485563\pi$
$48$	−23.0097	−3.32117
$49$	4.45187	0.635982
$50$	12.9763	1.83513
$51$	−2.31872	−0.324686
$52$	−14.8249	−2.05585
$53$	9.64958	1.32547	0.662736	−	0.748853i	$-0.269395\pi$
$53$	9.64958	1.32547	0.662736	+	0.748853i	$0.269395\pi$
$54$	−3.78764	−0.515432
$55$	0.130961	0.0176588
$56$	−25.3824	−3.39187
$57$	−11.5583	−1.53094
$58$	27.5443	3.61675
$59$	−5.81342	−0.756843	−0.378422	−	0.925633i	$-0.623533\pi$
$59$	−5.81342	−0.756843	−0.378422	+	0.925633i	$0.623533\pi$
$60$	−2.43764	−0.314698
$61$	−6.34225	−0.812042	−0.406021	−	0.913864i	$-0.633084\pi$
$61$	−6.34225	−0.812042	−0.406021	+	0.913864i	$0.633084\pi$
$62$	−15.3996	−1.95575
$63$	8.04211	1.01321
$64$	8.95936	1.11992
$65$	−0.659006	−0.0817396
$66$	3.67995	0.452971
$67$	8.53186	1.04233	0.521166	−	0.853455i	$-0.325497\pi$
$67$	8.53186	1.04233	0.521166	+	0.853455i	$0.325497\pi$
$68$	4.86309	0.589736
$69$	−3.72369	−0.448279
$70$	−1.91649	−0.229064
$71$	−12.8904	−1.52981	−0.764904	−	0.644144i	$-0.777214\pi$
$71$	−12.8904	−1.52981	−0.764904	+	0.644144i	$0.777214\pi$
$72$	−17.8249	−2.10068
$73$	16.5475	1.93673	0.968367	−	0.249530i	$-0.0802762\pi$
$73$	16.5475	1.93673	0.968367	+	0.249530i	$0.0802762\pi$
$74$	9.82938	1.14264
$75$	11.4852	1.32620
$76$	24.2414	2.78068
$77$	2.05009	0.233629
$78$	−18.5178	−2.09673
$79$	0.298557	0.0335902	0.0167951	−	0.999859i	$-0.494654\pi$
$79$	0.298557	0.0335902	0.0167951	+	0.999859i	$0.494654\pi$
$80$	2.14522	0.239843
$81$	−10.4818	−1.16465
$82$	2.26579	0.250215
$83$	3.17470	0.348468	0.174234	−	0.984704i	$-0.444255\pi$
$83$	3.17470	0.348468	0.174234	+	0.984704i	$0.444255\pi$
$84$	−38.1592	−4.16351
$85$	0.216177	0.0234476
$86$	−16.7825	−1.80971
$87$	24.3793	2.61373
$88$	−4.54390	−0.484381
$89$	−6.23133	−0.660520	−0.330260	−	0.943890i	$-0.607136\pi$
$89$	−6.23133	−0.660520	−0.330260	+	0.943890i	$0.607136\pi$
$90$	−1.34586	−0.141866
$91$	−10.3162	−1.08143
$92$	7.80974	0.814222
$93$	−13.6301	−1.41337
$94$	−1.62866	−0.167983
$95$	1.07759	0.110559
$96$	25.4962	2.60220
$97$	−18.2172	−1.84967	−0.924837	−	0.380363i	$-0.875799\pi$
$97$	−18.2172	−1.84967	−0.924837	+	0.380363i	$0.875799\pi$
$98$	−11.6628	−1.17812
$99$	1.43968	0.144693
$100$	−24.0882	−2.40882
$101$	−14.5345	−1.44624	−0.723119	−	0.690724i	$-0.757292\pi$
$101$	−14.5345	−1.44624	−0.723119	+	0.690724i	$0.757292\pi$
$102$	6.07447	0.601462
$103$	−4.71810	−0.464888	−0.232444	−	0.972610i	$-0.574672\pi$
$103$	−4.71810	−0.464888	−0.232444	+	0.972610i	$0.574672\pi$
$104$	22.8652	2.24212
$105$	−1.69627	−0.165539
$106$	−25.2795	−2.45536
$107$	−15.4790	−1.49642	−0.748208	−	0.663465i	$-0.769085\pi$
$107$	−15.4790	−1.49642	−0.748208	+	0.663465i	$0.769085\pi$
$108$	7.03106	0.676564
$109$	−17.9470	−1.71902	−0.859508	−	0.511123i	$-0.829230\pi$
$109$	−17.9470	−1.71902	−0.859508	+	0.511123i	$0.829230\pi$
$110$	−0.343085	−0.0327119
$111$	8.69991	0.825759
$112$	33.5816	3.17316
$113$	−6.04866	−0.569010	−0.284505	−	0.958675i	$-0.591829\pi$
$113$	−6.04866	−0.569010	−0.284505	+	0.958675i	$0.591829\pi$
$114$	30.2799	2.83597
$115$	0.347163	0.0323731
$116$	−51.1310	−4.74740
$117$	−7.24457	−0.669760
$118$	15.2297	1.40201
$119$	3.38406	0.310216
$120$	3.75968	0.343211
$121$	−10.6330	−0.966636
$122$	16.6151	1.50426
$123$	2.00544	0.180824
$124$	28.5865	2.56715
$125$	−2.15166	−0.192451
$126$	−21.0683	−1.87691
$127$	−15.5307	−1.37812	−0.689062	−	0.724702i	$-0.741977\pi$
$127$	−15.5307	−1.37812	−0.689062	+	0.724702i	$0.741977\pi$
$128$	−1.47967	−0.130786
$129$	−14.8541	−1.30783
$130$	1.72643	0.151418
$131$	2.50539	0.218897	0.109449	−	0.993992i	$-0.465091\pi$
$131$	2.50539	0.218897	0.109449	+	0.993992i	$0.465091\pi$
$132$	−6.83116	−0.594576
$133$	16.8688	1.46271
$134$	−22.3513	−1.93086
$135$	0.312548	0.0268999
$136$	−7.50057	−0.643169
$137$	13.0927	1.11859	0.559294	−	0.828969i	$-0.311072\pi$
$137$	13.0927	1.11859	0.559294	+	0.828969i	$0.311072\pi$
$138$	9.75513	0.830411
$139$	15.5926	1.32254	0.661272	−	0.750146i	$-0.270017\pi$
$139$	15.5926	1.32254	0.661272	+	0.750146i	$0.270017\pi$
$140$	3.55761	0.300673
$141$	−1.44151	−0.121397
$142$	33.7696	2.83388
$143$	−1.84678	−0.154435
$144$	23.5827	1.96523
$145$	−2.27290	−0.188754
$146$	−43.3502	−3.58769
$147$	−10.3226	−0.851398
$148$	−18.2465	−1.49985
$149$	−16.3563	−1.33996	−0.669979	−	0.742380i	$-0.733697\pi$
$149$	−16.3563	−1.33996	−0.669979	+	0.742380i	$0.733697\pi$
$150$	−30.0885	−2.45671
$151$	8.22364	0.669230	0.334615	−	0.942355i	$-0.391394\pi$
$151$	8.22364	0.669230	0.334615	+	0.942355i	$0.391394\pi$
$152$	−37.3887	−3.03263
$153$	2.37647	0.192126
$154$	−5.37071	−0.432784
$155$	1.27074	0.102069
$156$	34.3749	2.75219
$157$	8.76181	0.699269	0.349634	−	0.936886i	$-0.386306\pi$
$157$	8.76181	0.699269	0.349634	+	0.936886i	$0.386306\pi$
$158$	−0.782144	−0.0622240
$159$	−22.3747	−1.77443
$160$	−2.37704	−0.187921
$161$	5.43454	0.428302
$162$	27.4597	2.15744
$163$	21.0887	1.65179	0.825896	−	0.563823i	$-0.190670\pi$
$163$	21.0887	1.65179	0.825896	+	0.563823i	$0.190670\pi$
$164$	−4.20604	−0.328436
$165$	−0.303662	−0.0236401
$166$	−8.31691	−0.645517
$167$	2.81554	0.217873	0.108937	−	0.994049i	$-0.465255\pi$
$167$	2.81554	0.217873	0.108937	+	0.994049i	$0.465255\pi$
$168$	58.8547	4.54074
$169$	−3.70688	−0.285144
$170$	−0.566328	−0.0434354
$171$	11.8462	0.905898
$172$	31.1537	2.37545
$173$	21.6542	1.64634	0.823170	−	0.567795i	$-0.192203\pi$
$173$	21.6542	1.64634	0.823170	+	0.567795i	$0.192203\pi$
$174$	−63.8676	−4.84179
$175$	−16.7622	−1.26710
$176$	6.01169	0.453148
$177$	13.4797	1.01320
$178$	16.3245	1.22358
$179$	21.6382	1.61732	0.808659	−	0.588277i	$-0.200194\pi$
$179$	21.6382	1.61732	0.808659	+	0.588277i	$0.200194\pi$
$180$	2.49834	0.186216
$181$	13.4427	0.999187	0.499594	−	0.866260i	$-0.333483\pi$
$181$	13.4427	0.999187	0.499594	+	0.866260i	$0.333483\pi$
$182$	27.0258	2.00329
$183$	14.7059	1.08709
$184$	−12.0453	−0.887994
$185$	−0.811101	−0.0596333
$186$	35.7073	2.61819
$187$	0.605807	0.0443010
$188$	3.02331	0.220498
$189$	4.89268	0.355890
$190$	−2.82302	−0.204804
$191$	−17.6388	−1.27630	−0.638148	−	0.769914i	$-0.720299\pi$
$191$	−17.6388	−1.27630	−0.638148	+	0.769914i	$0.720299\pi$
$192$	−20.7743	−1.49925
$193$	−13.6671	−0.983779	−0.491890	−	0.870658i	$-0.663694\pi$
$193$	−13.6671	−0.983779	−0.491890	+	0.870658i	$0.663694\pi$
$194$	47.7244	3.42642
$195$	1.52805	0.109426
$196$	21.6498	1.54642
$197$	−22.5607	−1.60738	−0.803691	−	0.595046i	$-0.797134\pi$
$197$	−22.5607	−1.60738	−0.803691	+	0.595046i	$0.797134\pi$
$198$	−3.77160	−0.268036
$199$	−18.0931	−1.28259	−0.641294	−	0.767295i	$-0.721602\pi$
$199$	−18.0931	−1.28259	−0.641294	+	0.767295i	$0.721602\pi$
$200$	37.1524	2.62707
$201$	−19.7830	−1.39538
$202$	38.0768	2.67907
$203$	−35.5804	−2.49725
$204$	−11.2761	−0.789488
$205$	−0.186969	−0.0130585
$206$	12.3602	0.861179
$207$	3.81642	0.265260
$208$	−30.2513	−2.09755
$209$	3.01981	0.208885
$210$	4.44380	0.306652
$211$	20.1155	1.38481	0.692403	−	0.721511i	$-0.256552\pi$
$211$	20.1155	1.38481	0.692403	+	0.721511i	$0.256552\pi$
$212$	46.9268	3.22294
$213$	29.8892	2.04798
$214$	40.5512	2.77202
$215$	1.38486	0.0944468
$216$	−10.8443	−0.737864
$217$	19.8924	1.35038
$218$	47.0168	3.18438
$219$	−38.3689	−2.59273
$220$	0.636876	0.0429382
$221$	−3.04846	−0.205062
$222$	−22.7916	−1.52967
$223$	−6.23690	−0.417653	−0.208827	−	0.977953i	$-0.566964\pi$
$223$	−6.23690	−0.417653	−0.208827	+	0.977953i	$0.566964\pi$
$224$	−37.2105	−2.48623
$225$	−11.7713	−0.784751
$226$	15.8460	1.05406
$227$	13.0031	0.863049	0.431524	−	0.902101i	$-0.357976\pi$
$227$	13.0031	0.863049	0.431524	+	0.902101i	$0.357976\pi$
$228$	−56.2091	−3.72254
$229$	13.9959	0.924878	0.462439	−	0.886651i	$-0.346974\pi$
$229$	13.9959	0.924878	0.462439	+	0.886651i	$0.346974\pi$
$230$	−0.909480	−0.0599693
$231$	−4.75358	−0.312763
$232$	78.8619	5.17754
$233$	−17.3041	−1.13363	−0.566815	−	0.823845i	$-0.691825\pi$
$233$	−17.3041	−1.13363	−0.566815	+	0.823845i	$0.691825\pi$
$234$	18.9790	1.24069
$235$	0.134394	0.00876688
$236$	−28.2712	−1.84030
$237$	−0.692270	−0.0449677
$238$	−8.86539	−0.574658
$239$	29.9641	1.93822	0.969109	−	0.246634i	$-0.0793247\pi$
$239$	29.9641	1.93822	0.969109	+	0.246634i	$0.0793247\pi$
$240$	−4.97416	−0.321081
$241$	27.1082	1.74619	0.873097	−	0.487546i	$-0.162108\pi$
$241$	27.1082	1.74619	0.873097	+	0.487546i	$0.162108\pi$
$242$	27.8558	1.79064
$243$	19.9670	1.28088
$244$	−30.8429	−1.97452
$245$	0.962390	0.0614848
$246$	−5.25375	−0.334967
$247$	−15.1959	−0.966893
$248$	−44.0904	−2.79974
$249$	−7.36123	−0.466499
$250$	5.63682	0.356504
$251$	3.10278	0.195846	0.0979228	−	0.995194i	$-0.468780\pi$
$251$	3.10278	0.195846	0.0979228	+	0.995194i	$0.468780\pi$
$252$	39.1095	2.46366
$253$	0.972879	0.0611644
$254$	40.6865	2.55290
$255$	−0.501253	−0.0313897
$256$	−14.0424	−0.877647
$257$	−3.18613	−0.198745	−0.0993726	−	0.995050i	$-0.531684\pi$
$257$	−3.18613	−0.198745	−0.0993726	+	0.995050i	$0.531684\pi$
$258$	38.9140	2.42268
$259$	−12.6971	−0.788960
$260$	−3.20480	−0.198754
$261$	−24.9864	−1.54662
$262$	−6.56351	−0.405495
$263$	−0.0320315	−0.00197515	−0.000987573	−	1.00000i	$-0.500314\pi$
$263$	−0.0320315	−0.00197515	−0.000987573		1.00000i	$0.500314\pi$
$264$	10.5360	0.648448
$265$	2.08601	0.128143
$266$	−44.1920	−2.70959
$267$	14.4487	0.884247
$268$	41.4912	2.53448
$269$	−12.0236	−0.733094	−0.366547	−	0.930399i	$-0.619460\pi$
$269$	−12.0236	−0.733094	−0.366547	+	0.930399i	$0.619460\pi$
$270$	−0.818799	−0.0498305
$271$	−7.27379	−0.441851	−0.220926	−	0.975291i	$-0.570908\pi$
$271$	−7.27379	−0.441851	−0.220926	+	0.975291i	$0.570908\pi$
$272$	9.92345	0.601698
$273$	23.9204	1.44773
$274$	−34.2997	−2.07212
$275$	−3.00072	−0.180950
$276$	−18.1086	−1.09001
$277$	15.7552	0.946640	0.473320	−	0.880891i	$-0.343055\pi$
$277$	15.7552	0.946640	0.473320	+	0.880891i	$0.343055\pi$
$278$	−40.8486	−2.44994
$279$	13.9695	0.836332
$280$	−5.48708	−0.327916
$281$	−16.0943	−0.960108	−0.480054	−	0.877239i	$-0.659383\pi$
$281$	−16.0943	−0.960108	−0.480054	+	0.877239i	$0.659383\pi$
$282$	3.77641	0.224882
$283$	−13.7318	−0.816272	−0.408136	−	0.912921i	$-0.633821\pi$
$283$	−13.7318	−0.816272	−0.408136	+	0.912921i	$0.633821\pi$
$284$	−62.6871	−3.71980
$285$	−2.49864	−0.148006
$286$	4.83810	0.286083
$287$	−2.92684	−0.172766
$288$	−26.1312	−1.53979
$289$	1.00000	0.0588235
$290$	5.95444	0.349657
$291$	42.2405	2.47618
$292$	80.4718	4.70925
$293$	15.4912	0.905005	0.452502	−	0.891763i	$-0.350531\pi$
$293$	15.4912	0.905005	0.452502	+	0.891763i	$0.350531\pi$
$294$	27.0427	1.57717
$295$	−1.25673	−0.0731694
$296$	28.1424	1.63574
$297$	0.875876	0.0508235
$298$	42.8493	2.48219
$299$	−4.89560	−0.283120
$300$	55.8538	3.22472
$301$	21.6788	1.24955
$302$	−21.5439	−1.23971
$303$	33.7015	1.93610
$304$	49.4662	2.83708
$305$	−1.37105	−0.0785059
$306$	−6.22574	−0.355902
$307$	10.4733	0.597743	0.298872	−	0.954293i	$-0.403390\pi$
$307$	10.4733	0.597743	0.298872	+	0.954293i	$0.403390\pi$
$308$	9.96975	0.568079
$309$	10.9400	0.622352
$310$	−3.32903	−0.189076
$311$	−8.12547	−0.460753	−0.230377	−	0.973102i	$-0.573996\pi$
$311$	−8.12547	−0.460753	−0.230377	+	0.973102i	$0.573996\pi$
$312$	−53.0181	−3.00156
$313$	−9.96182	−0.563075	−0.281538	−	0.959550i	$-0.590844\pi$
$313$	−9.96182	−0.563075	−0.281538	+	0.959550i	$0.590844\pi$
$314$	−22.9537	−1.29535
$315$	1.73851	0.0979542
$316$	1.45191	0.0816762
$317$	15.0746	0.846671	0.423336	−	0.905973i	$-0.360859\pi$
$317$	15.0746	0.846671	0.423336	+	0.905973i	$0.360859\pi$
$318$	58.6161	3.28703
$319$	−6.36952	−0.356625
$320$	1.93680	0.108271
$321$	35.8916	2.00327
$322$	−14.2371	−0.793405
$323$	4.98478	0.277361
$324$	−50.9740	−2.83189
$325$	15.0999	0.837589
$326$	−55.2470	−3.05985
$327$	41.6142	2.30127
$328$	6.48717	0.358194
$329$	2.10382	0.115987
$330$	0.795519	0.0437919
$331$	33.4525	1.83872	0.919359	−	0.393420i	$-0.128708\pi$
$331$	33.4525	1.83872	0.919359	+	0.393420i	$0.128708\pi$
$332$	15.4388	0.847316
$333$	−8.91657	−0.488625
$334$	−7.37601	−0.403597
$335$	1.84439	0.100770
$336$	−77.8663	−4.24795
$337$	−20.3557	−1.10885	−0.554423	−	0.832235i	$-0.687061\pi$
$337$	−20.3557	−1.10885	−0.554423	+	0.832235i	$0.687061\pi$
$338$	9.71109	0.528213
$339$	14.0252	0.761742
$340$	1.05129	0.0570140
$341$	3.56109	0.192844
$342$	−31.0340	−1.67812
$343$	−8.62302	−0.465600
$344$	−48.0499	−2.59068
$345$	−0.804973	−0.0433383
$346$	−56.7286	−3.04975
$347$	−7.32242	−0.393088	−0.196544	−	0.980495i	$-0.562972\pi$
$347$	−7.32242	−0.393088	−0.196544	+	0.980495i	$0.562972\pi$
$348$	118.559	6.35541
$349$	16.7811	0.898271	0.449136	−	0.893464i	$-0.351732\pi$
$349$	16.7811	0.898271	0.449136	+	0.893464i	$0.351732\pi$
$350$	43.9127	2.34723
$351$	−4.40747	−0.235254
$352$	−6.66133	−0.355050
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−35.3135	−1.87689
$355$	−2.78660	−0.147897
$356$	−30.3035	−1.60608
$357$	−7.84669	−0.415291
$358$	−56.6868	−2.99599
$359$	−30.3103	−1.59972	−0.799859	−	0.600189i	$-0.795092\pi$
$359$	−30.3103	−1.59972	−0.799859	+	0.600189i	$0.795092\pi$
$360$	−3.85332	−0.203088
$361$	5.84803	0.307791
$362$	−35.2165	−1.85094
$363$	24.6550	1.29405
$364$	−50.1685	−2.62954
$365$	3.57717	0.187238
$366$	−38.5258	−2.01378
$367$	−32.4415	−1.69343	−0.846717	−	0.532043i	$-0.821424\pi$
$367$	−32.4415	−1.69343	−0.846717	+	0.532043i	$0.821424\pi$
$368$	15.9363	0.830737
$369$	−2.05538	−0.106999
$370$	2.12488	0.110467
$371$	32.6548	1.69535
$372$	−66.2842	−3.43667
$373$	−33.0668	−1.71214	−0.856068	−	0.516864i	$-0.827099\pi$
$373$	−33.0668	−1.71214	−0.856068	+	0.516864i	$0.827099\pi$
$374$	−1.58706	−0.0820650
$375$	4.98910	0.257636
$376$	−4.66300	−0.240476
$377$	32.0519	1.65076
$378$	−12.8176	−0.659266
$379$	−18.7297	−0.962082	−0.481041	−	0.876698i	$-0.659741\pi$
$379$	−18.7297	−0.962082	−0.481041	+	0.876698i	$0.659741\pi$
$380$	5.24043	0.268828
$381$	36.0113	1.84491
$382$	46.2091	2.36426
$383$	−31.5763	−1.61347	−0.806737	−	0.590911i	$-0.798769\pi$
$383$	−31.5763	−1.61347	−0.806737	+	0.590911i	$0.798769\pi$
$384$	3.43094	0.175085
$385$	0.443181	0.0225866
$386$	35.8044	1.82239
$387$	15.2240	0.773880
$388$	−88.5917	−4.49756
$389$	2.38448	0.120898	0.0604489	−	0.998171i	$-0.480747\pi$
$389$	2.38448	0.120898	0.0604489	+	0.998171i	$0.480747\pi$
$390$	−4.00311	−0.202705
$391$	1.60592	0.0812150
$392$	−33.3916	−1.68653
$393$	−5.80931	−0.293041
$394$	59.1034	2.97758
$395$	0.0645409	0.00324741
$396$	7.00128	0.351828
$397$	24.2645	1.21780	0.608900	−	0.793247i	$-0.291611\pi$
$397$	24.2645	1.21780	0.608900	+	0.793247i	$0.291611\pi$
$398$	47.3995	2.37592
$399$	−39.1140	−1.95815
$400$	−49.1535	−2.45768
$401$	20.7258	1.03500	0.517498	−	0.855684i	$-0.326863\pi$
$401$	20.7258	1.03500	0.517498	+	0.855684i	$0.326863\pi$
$402$	51.8265	2.58487
$403$	−17.9197	−0.892642
$404$	−70.6826	−3.51659
$405$	−2.26592	−0.112595
$406$	93.2117	4.62602
$407$	−2.27301	−0.112669
$408$	17.3917	0.861019
$409$	−14.0876	−0.696585	−0.348292	−	0.937386i	$-0.613238\pi$
$409$	−14.0876	−0.696585	−0.348292	+	0.937386i	$0.613238\pi$
$410$	0.489812	0.0241901
$411$	−30.3584	−1.49747
$412$	−22.9445	−1.13040
$413$	−19.6730	−0.968044
$414$	−9.99807	−0.491378
$415$	0.686295	0.0336889
$416$	33.5203	1.64347
$417$	−36.1548	−1.77051
$418$	−7.91115	−0.386947
$419$	10.5781	0.516773	0.258386	−	0.966042i	$-0.416809\pi$
$419$	10.5781	0.516773	0.258386	+	0.966042i	$0.416809\pi$
$420$	−8.24911	−0.402516
$421$	−21.1281	−1.02972	−0.514860	−	0.857274i	$-0.672156\pi$
$421$	−21.1281	−1.02972	−0.514860	+	0.857274i	$0.672156\pi$
$422$	−52.6975	−2.56528
$423$	1.47741	0.0718343
$424$	−72.3774	−3.51496
$425$	−4.95327	−0.240269
$426$	−78.3023	−3.79376
$427$	−21.4626	−1.03865
$428$	−75.2759	−3.63860
$429$	4.28216	0.206745
$430$	−3.62799	−0.174957
$431$	−29.5237	−1.42211	−0.711054	−	0.703138i	$-0.751782\pi$
$431$	−29.5237	−1.42211	−0.711054	+	0.703138i	$0.751782\pi$
$432$	14.3473	0.690287
$433$	−23.1646	−1.11322	−0.556609	−	0.830774i	$-0.687898\pi$
$433$	−23.1646	−1.11322	−0.556609	+	0.830774i	$0.687898\pi$
$434$	−52.1131	−2.50151
$435$	5.27023	0.252688
$436$	−87.2781	−4.17986
$437$	8.00517	0.382939
$438$	100.517	4.80289
$439$	31.8923	1.52214	0.761068	−	0.648672i	$-0.224675\pi$
$439$	31.8923	1.52214	0.761068	+	0.648672i	$0.224675\pi$
$440$	−0.982284	−0.0468285
$441$	10.5797	0.503796
$442$	7.98621	0.379865
$443$	−30.0347	−1.42699	−0.713497	−	0.700658i	$-0.752890\pi$
$443$	−30.0347	−1.42699	−0.713497	+	0.700658i	$0.752890\pi$
$444$	42.3084	2.00787
$445$	−1.34707	−0.0638571
$446$	16.3391	0.773679
$447$	37.9256	1.79382
$448$	30.3190	1.43244
$449$	−32.2392	−1.52146	−0.760732	−	0.649066i	$-0.775160\pi$
$449$	−32.2392	−1.52146	−0.760732	+	0.649066i	$0.775160\pi$
$450$	30.8378	1.45371
$451$	−0.523956	−0.0246721
$452$	−29.4152	−1.38357
$453$	−19.0683	−0.895908
$454$	−34.0650	−1.59875
$455$	−2.23012	−0.104549
$456$	86.6940	4.05982
$457$	40.0897	1.87532	0.937658	−	0.347560i	$-0.112990\pi$
$457$	40.0897	1.87532	0.937658	+	0.347560i	$0.112990\pi$
$458$	−36.6659	−1.71328
$459$	1.44580	0.0674843
$460$	1.68828	0.0787166
$461$	−37.9134	−1.76580	−0.882901	−	0.469559i	$-0.844413\pi$
$461$	−37.9134	−1.76580	−0.882901	+	0.469559i	$0.844413\pi$
$462$	12.4532	0.579375
$463$	−4.18769	−0.194618	−0.0973092	−	0.995254i	$-0.531024\pi$
$463$	−4.18769	−0.194618	−0.0973092	+	0.995254i	$0.531024\pi$
$464$	−104.336	−4.84369
$465$	−2.94650	−0.136641
$466$	45.3324	2.09998
$467$	10.6805	0.494236	0.247118	−	0.968985i	$-0.420517\pi$
$467$	10.6805	0.494236	0.247118	+	0.968985i	$0.420517\pi$
$468$	−35.2310	−1.62855
$469$	28.8723	1.33320
$470$	−0.352078	−0.0162401
$471$	−20.3162	−0.936121
$472$	43.6040	2.00704
$473$	3.88089	0.178444
$474$	1.81357	0.0833002
$475$	−24.6909	−1.13290
$476$	16.4570	0.754305
$477$	22.9319	1.04998
$478$	−78.4985	−3.59044
$479$	21.8653	0.999051	0.499525	−	0.866299i	$-0.333508\pi$
$479$	21.8653	0.999051	0.499525	+	0.866299i	$0.333508\pi$
$480$	5.51168	0.251573
$481$	11.4379	0.521525
$482$	−71.0168	−3.23473
$483$	−12.6012	−0.573374
$484$	−51.7092	−2.35042
$485$	−3.93813	−0.178821
$486$	−52.3085	−2.37276
$487$	27.2950	1.23685	0.618427	−	0.785842i	$-0.287770\pi$
$487$	27.2950	1.23685	0.618427	+	0.785842i	$0.287770\pi$
$488$	47.5705	2.15342
$489$	−48.8987	−2.21128
$490$	−2.52122	−0.113897
$491$	1.76167	0.0795031	0.0397516	−	0.999210i	$-0.487343\pi$
$491$	1.76167	0.0795031	0.0397516	+	0.999210i	$0.487343\pi$
$492$	9.75262	0.439682
$493$	−10.5141	−0.473532
$494$	39.8095	1.79111
$495$	0.311225	0.0139885
$496$	58.3327	2.61921
$497$	−43.6219	−1.95671
$498$	19.2846	0.864163
$499$	24.6671	1.10425	0.552126	−	0.833761i	$-0.313817\pi$
$499$	24.6671	1.10425	0.552126	+	0.833761i	$0.313817\pi$
$500$	−10.4637	−0.467952
$501$	−6.52845	−0.291670
$502$	−8.12850	−0.362793
$503$	20.7548	0.925409	0.462704	−	0.886513i	$-0.346879\pi$
$503$	20.7548	0.925409	0.462704	+	0.886513i	$0.346879\pi$
$504$	−60.3204	−2.68688
$505$	−3.14202	−0.139818
$506$	−2.54870	−0.113303
$507$	8.59521	0.381727
$508$	−75.5270	−3.35097
$509$	−34.9462	−1.54896	−0.774481	−	0.632597i	$-0.781989\pi$
$509$	−34.9462	−1.54896	−0.774481	+	0.632597i	$0.781989\pi$
$510$	1.31316	0.0581476
$511$	55.9976	2.47719
$512$	39.7468	1.75658
$513$	7.20701	0.318197
$514$	8.34686	0.368164
$515$	−1.01994	−0.0449440
$516$	−72.2368	−3.18005
$517$	0.376621	0.0165638
$518$	33.2632	1.46150
$519$	−50.2101	−2.20398
$520$	4.94292	0.216762
$521$	14.1237	0.618771	0.309385	−	0.950937i	$-0.399877\pi$
$521$	14.1237	0.618771	0.309385	+	0.950937i	$0.399877\pi$
$522$	65.4582	2.86503
$523$	−2.80695	−0.122739	−0.0613697	−	0.998115i	$-0.519547\pi$
$523$	−2.80695	−0.122739	−0.0613697	+	0.998115i	$0.519547\pi$
$524$	12.1840	0.532259
$525$	38.8668	1.69628
$526$	0.0839145	0.00365885
$527$	5.87827	0.256061
$528$	−13.9394	−0.606636
$529$	−20.4210	−0.887870
$530$	−5.46483	−0.237377
$531$	−13.8154	−0.599537
$532$	82.0345	3.55665
$533$	2.63658	0.114203
$534$	−37.8520	−1.63802
$535$	−3.34620	−0.144669
$536$	−63.9938	−2.76411
$537$	−50.1730	−2.16513
$538$	31.4989	1.35802
$539$	2.69697	0.116167
$540$	1.51995	0.0654083
$541$	−21.7805	−0.936418	−0.468209	−	0.883618i	$-0.655100\pi$
$541$	−21.7805	−0.936418	−0.468209	+	0.883618i	$0.655100\pi$
$542$	19.0555	0.818504
$543$	−31.1698	−1.33763
$544$	−10.9958	−0.471441
$545$	−3.87973	−0.166189
$546$	−62.6653	−2.68183
$547$	17.0651	0.729651	0.364825	−	0.931076i	$-0.381129\pi$
$547$	17.0651	0.729651	0.364825	+	0.931076i	$0.381129\pi$
$548$	63.6712	2.71990
$549$	−15.0721	−0.643264
$550$	7.86114	0.335200
$551$	−52.4105	−2.23276
$552$	27.9298	1.18877
$553$	1.01033	0.0429638
$554$	−41.2748	−1.75360
$555$	1.88072	0.0798320
$556$	75.8280	3.21582
$557$	40.2072	1.70363	0.851816	−	0.523840i	$-0.175501\pi$
$557$	40.2072	1.70363	0.851816	+	0.523840i	$0.175501\pi$
$558$	−36.5966	−1.54926
$559$	−19.5289	−0.825986
$560$	7.25955	0.306772
$561$	−1.40470	−0.0593063
$562$	42.1632	1.77855
$563$	−6.67822	−0.281453	−0.140727	−	0.990048i	$-0.544944\pi$
$563$	−6.67822	−0.281453	−0.140727	+	0.990048i	$0.544944\pi$
$564$	−7.01021	−0.295183
$565$	−1.30758	−0.0550103
$566$	35.9739	1.51210
$567$	−35.4711	−1.48965
$568$	96.6853	4.05683
$569$	−0.960867	−0.0402816	−0.0201408	−	0.999797i	$-0.506411\pi$
$569$	−0.960867	−0.0402816	−0.0201408	+	0.999797i	$0.506411\pi$
$570$	6.54580	0.274173
$571$	10.5338	0.440827	0.220414	−	0.975407i	$-0.429259\pi$
$571$	10.5338	0.440827	0.220414	+	0.975407i	$0.429259\pi$
$572$	−8.98105	−0.375517
$573$	40.8993	1.70859
$574$	7.66759	0.320039
$575$	−7.95457	−0.331728
$576$	21.2916	0.887151
$577$	27.7951	1.15712	0.578562	−	0.815638i	$-0.303614\pi$
$577$	27.7951	1.15712	0.578562	+	0.815638i	$0.303614\pi$
$578$	−2.61975	−0.108967
$579$	31.6902	1.31700
$580$	−11.0533	−0.458965
$581$	10.7434	0.445710
$582$	−110.660	−4.58699
$583$	5.84578	0.242107
$584$	−124.115	−5.13593
$585$	−1.56611	−0.0647505
$586$	−40.5830	−1.67647
$587$	16.9858	0.701081	0.350540	−	0.936548i	$-0.385998\pi$
$587$	16.9858	0.701081	0.350540	+	0.936548i	$0.385998\pi$
$588$	−50.1999	−2.07021
$589$	29.3019	1.20736
$590$	3.29231	0.135542
$591$	52.3120	2.15183
$592$	−37.2331	−1.53027
$593$	−5.88610	−0.241713	−0.120857	−	0.992670i	$-0.538564\pi$
$593$	−5.88610	−0.241713	−0.120857	+	0.992670i	$0.538564\pi$
$594$	−2.29458	−0.0941476
$595$	0.731555	0.0299908
$596$	−79.5419	−3.25816
$597$	41.9529	1.71702
$598$	12.8252	0.524463
$599$	39.5784	1.61713	0.808565	−	0.588407i	$-0.200245\pi$
$599$	39.5784	1.61713	0.808565	+	0.588407i	$0.200245\pi$
$600$	−86.1459	−3.51689
$601$	−10.2614	−0.418573	−0.209286	−	0.977854i	$-0.567114\pi$
$601$	−10.2614	−0.418573	−0.209286	+	0.977854i	$0.567114\pi$
$602$	−56.7931	−2.31472
$603$	20.2757	0.825689
$604$	39.9923	1.62726
$605$	−2.29860	−0.0934516
$606$	−88.2894	−3.58651
$607$	−33.6135	−1.36433	−0.682164	−	0.731199i	$-0.738961\pi$
$607$	−33.6135	−1.36433	−0.682164	+	0.731199i	$0.738961\pi$
$608$	−54.8117	−2.22291
$609$	82.5010	3.34311
$610$	3.59180	0.145428
$611$	−1.89518	−0.0766709
$612$	11.5570	0.467163
$613$	1.09646	0.0442858	0.0221429	−	0.999755i	$-0.492951\pi$
$613$	1.09646	0.0442858	0.0221429	+	0.999755i	$0.492951\pi$
$614$	−27.4374	−1.10728
$615$	0.433529	0.0174816
$616$	−15.3768	−0.619550
$617$	21.2959	0.857341	0.428670	−	0.903461i	$-0.358982\pi$
$617$	21.2959	0.857341	0.428670	+	0.903461i	$0.358982\pi$
$618$	−28.6599	−1.15287
$619$	−1.95401	−0.0785383	−0.0392691	−	0.999229i	$-0.512503\pi$
$619$	−1.95401	−0.0785383	−0.0392691	+	0.999229i	$0.512503\pi$
$620$	6.17973	0.248184
$621$	2.32185	0.0931725
$622$	21.2867	0.853519
$623$	−21.0872	−0.844841
$624$	70.1442	2.80802
$625$	24.3012	0.972048
$626$	26.0975	1.04306
$627$	−7.00210	−0.279637
$628$	42.6095	1.70030
$629$	−3.75203	−0.149603
$630$	−4.55447	−0.181455
$631$	−3.11124	−0.123857	−0.0619283	−	0.998081i	$-0.519725\pi$
$631$	−3.11124	−0.123857	−0.0619283	+	0.998081i	$0.519725\pi$
$632$	−2.23935	−0.0890764
$633$	−46.6422	−1.85386
$634$	−39.4916	−1.56841
$635$	−3.35737	−0.133233
$636$	−108.810	−4.31460
$637$	−13.5714	−0.537717
$638$	16.6865	0.660627
$639$	−30.6336	−1.21185
$640$	−0.319870	−0.0126440
$641$	−2.50666	−0.0990071	−0.0495036	−	0.998774i	$-0.515764\pi$
$641$	−2.50666	−0.0990071	−0.0495036	+	0.998774i	$0.515764\pi$
$642$	−94.0269	−3.71095
$643$	31.7764	1.25314	0.626570	−	0.779365i	$-0.284458\pi$
$643$	31.7764	1.25314	0.626570	+	0.779365i	$0.284458\pi$
$644$	26.4287	1.04143
$645$	−3.21111	−0.126437
$646$	−13.0589	−0.513795
$647$	−28.3128	−1.11309	−0.556546	−	0.830816i	$-0.687874\pi$
$647$	−28.3128	−1.11309	−0.556546	+	0.830816i	$0.687874\pi$
$648$	78.6196	3.08847
$649$	−3.52181	−0.138243
$650$	−39.5578	−1.55159
$651$	−46.1249	−1.80778
$652$	102.556	4.01640
$653$	−27.6210	−1.08089	−0.540447	−	0.841378i	$-0.681745\pi$
$653$	−27.6210	−1.08089	−0.540447	+	0.841378i	$0.681745\pi$
$654$	−109.019	−4.26297
$655$	0.541607	0.0211624
$656$	−8.58269	−0.335098
$657$	39.3245	1.53419
$658$	−5.51148	−0.214860
$659$	2.81302	0.109580	0.0547899	−	0.998498i	$-0.482551\pi$
$659$	2.81302	0.109580	0.0547899	+	0.998498i	$0.482551\pi$
$660$	−1.47674	−0.0574819
$661$	−3.28095	−0.127614	−0.0638070	−	0.997962i	$-0.520324\pi$
$661$	−3.28095	−0.127614	−0.0638070	+	0.997962i	$0.520324\pi$
$662$	−87.6373	−3.40612
$663$	7.06853	0.274519
$664$	−23.8120	−0.924086
$665$	3.64664	0.141411
$666$	23.3592	0.905150
$667$	−16.8848	−0.653784
$668$	13.6922	0.529768
$669$	14.4616	0.559118
$670$	−4.83183	−0.186670
$671$	−3.84218	−0.148326
$672$	86.2807	3.32835
$673$	−11.7832	−0.454208	−0.227104	−	0.973871i	$-0.572926\pi$
$673$	−11.7832	−0.454208	−0.227104	+	0.973871i	$0.572926\pi$
$674$	53.3269	2.05407
$675$	−7.16144	−0.275644
$676$	−18.0269	−0.693341
$677$	−42.7536	−1.64315	−0.821577	−	0.570097i	$-0.806906\pi$
$677$	−42.7536	−1.64315	−0.821577	+	0.570097i	$0.806906\pi$
$678$	−36.7424	−1.41108
$679$	−61.6480	−2.36583
$680$	−1.62145	−0.0621797
$681$	−30.1506	−1.15538
$682$	−9.32917	−0.357232
$683$	13.4457	0.514486	0.257243	−	0.966347i	$-0.417186\pi$
$683$	13.4457	0.514486	0.257243	+	0.966347i	$0.417186\pi$
$684$	57.6089	2.20273
$685$	2.83034	0.108142
$686$	22.5902	0.862496
$687$	−32.4527	−1.23815
$688$	63.5712	2.42363
$689$	−29.4164	−1.12067
$690$	2.10883	0.0802817
$691$	−36.2653	−1.37960	−0.689798	−	0.724002i	$-0.742301\pi$
$691$	−36.2653	−1.37960	−0.689798	+	0.724002i	$0.742301\pi$
$692$	105.306	4.00315
$693$	4.87196	0.185070
$694$	19.1829	0.728173
$695$	3.37075	0.127860
$696$	−182.859	−6.93124
$697$	−0.864890	−0.0327600
$698$	−43.9623	−1.66400
$699$	40.1234	1.51761
$700$	−81.5159	−3.08101
$701$	2.98235	0.112642	0.0563210	−	0.998413i	$-0.482063\pi$
$701$	2.98235	0.112642	0.0563210	+	0.998413i	$0.482063\pi$
$702$	11.5465	0.435794
$703$	−18.7031	−0.705399
$704$	5.42764	0.204562
$705$	−0.311622	−0.0117363
$706$	−2.61975	−0.0985956
$707$	−49.1857	−1.84982
$708$	65.5530	2.46363
$709$	27.2729	1.02426	0.512128	−	0.858909i	$-0.328857\pi$
$709$	27.2729	1.02426	0.512128	+	0.858909i	$0.328857\pi$
$710$	7.30019	0.273971
$711$	0.709510	0.0266087
$712$	46.7386	1.75160
$713$	9.44004	0.353532
$714$	20.5564	0.769303
$715$	−0.399230	−0.0149304
$716$	105.229	3.93258
$717$	−69.4784	−2.59472
$718$	79.4054	2.96338
$719$	8.97679	0.334778	0.167389	−	0.985891i	$-0.446466\pi$
$719$	8.97679	0.334778	0.167389	+	0.985891i	$0.446466\pi$
$720$	5.09803	0.189993
$721$	−15.9663	−0.594618
$722$	−15.3204	−0.570165
$723$	−62.8564	−2.33766
$724$	65.3730	2.42957
$725$	52.0792	1.93417
$726$	−64.5898	−2.39715
$727$	−45.6766	−1.69405	−0.847025	−	0.531553i	$-0.821609\pi$
$727$	−45.6766	−1.69405	−0.847025	+	0.531553i	$0.821609\pi$
$728$	77.3773	2.86779
$729$	−14.8524	−0.550090
$730$	−9.37130	−0.346847
$731$	6.40616	0.236940
$732$	71.5162	2.64331
$733$	−6.77664	−0.250301	−0.125150	−	0.992138i	$-0.539941\pi$
$733$	−6.77664	−0.250301	−0.125150	+	0.992138i	$0.539941\pi$
$734$	84.9887	3.13699
$735$	−2.23151	−0.0823106
$736$	−17.6584	−0.650898
$737$	5.16866	0.190390
$738$	5.38458	0.198209
$739$	−26.2113	−0.964197	−0.482099	−	0.876117i	$-0.660125\pi$
$739$	−26.2113	−0.964197	−0.482099	+	0.876117i	$0.660125\pi$
$740$	−3.94446	−0.145001
$741$	35.2351	1.29439
$742$	−85.5473	−3.14054
$743$	−49.0933	−1.80106	−0.900529	−	0.434796i	$-0.856820\pi$
$743$	−49.0933	−1.80106	−0.900529	+	0.434796i	$0.856820\pi$
$744$	102.233	3.74805
$745$	−3.53584	−0.129543
$746$	86.6268	3.17163
$747$	7.54456	0.276041
$748$	2.94609	0.107720
$749$	−52.3820	−1.91400
$750$	−13.0702	−0.477256
$751$	−47.5002	−1.73331	−0.866654	−	0.498910i	$-0.833734\pi$
$751$	−47.5002	−1.73331	−0.866654	+	0.498910i	$0.833734\pi$
$752$	6.16926	0.224970
$753$	−7.19447	−0.262181
$754$	−83.9679	−3.05793
$755$	1.77776	0.0646992
$756$	23.7935	0.865363
$757$	11.3486	0.412471	0.206235	−	0.978502i	$-0.433879\pi$
$757$	11.3486	0.412471	0.206235	+	0.978502i	$0.433879\pi$
$758$	49.0672	1.78220
$759$	−2.25583	−0.0818816
$760$	−8.08256	−0.293185
$761$	17.2748	0.626213	0.313106	−	0.949718i	$-0.398630\pi$
$761$	17.2748	0.626213	0.313106	+	0.949718i	$0.398630\pi$
$762$	−94.3405	−3.41760
$763$	−60.7339	−2.19871
$764$	−85.7788	−3.10337
$765$	0.513736	0.0185742
$766$	82.7220	2.98887
$767$	17.7220	0.639905
$768$	32.5603	1.17492
$769$	26.1758	0.943924	0.471962	−	0.881619i	$-0.343546\pi$
$769$	26.1758	0.943924	0.471962	+	0.881619i	$0.343546\pi$
$770$	−1.16102	−0.0418403
$771$	7.38774	0.266063
$772$	−66.4643	−2.39210
$773$	4.03438	0.145107	0.0725533	−	0.997365i	$-0.476885\pi$
$773$	4.03438	0.145107	0.0725533	+	0.997365i	$0.476885\pi$
$774$	−39.8831	−1.43357
$775$	−29.1166	−1.04590
$776$	136.639	4.90507
$777$	29.4410	1.05619
$778$	−6.24674	−0.223956
$779$	−4.31129	−0.154468
$780$	7.43105	0.266074
$781$	−7.80908	−0.279431
$782$	−4.20712	−0.150446
$783$	−15.2013	−0.543251
$784$	44.1779	1.57778
$785$	1.89410	0.0676032
$786$	15.2189	0.542842
$787$	−39.5086	−1.40833	−0.704165	−	0.710036i	$-0.748679\pi$
$787$	−39.5086	−1.40833	−0.704165	+	0.710036i	$0.748679\pi$
$788$	−109.715	−3.90842
$789$	0.0742721	0.00264416
$790$	−0.169081	−0.00601564
$791$	−20.4690	−0.727795
$792$	−10.7984	−0.383705
$793$	19.3341	0.686575
$794$	−63.5669	−2.25590
$795$	−4.83688	−0.171546
$796$	−87.9885	−3.11867
$797$	−23.1479	−0.819940	−0.409970	−	0.912099i	$-0.634461\pi$
$797$	−23.1479	−0.819940	−0.409970	+	0.912099i	$0.634461\pi$
$798$	102.469	3.62736
$799$	0.621685	0.0219936
$800$	54.4652	1.92563
$801$	−14.8085	−0.523234
$802$	−54.2964	−1.91727
$803$	10.0246	0.353759
$804$	−96.2064	−3.39294
$805$	1.17482	0.0414070
$806$	46.9451	1.65357
$807$	27.8795	0.981404
$808$	109.017	3.83521
$809$	−12.0620	−0.424077	−0.212038	−	0.977261i	$-0.568010\pi$
$809$	−12.0620	−0.424077	−0.212038	+	0.977261i	$0.568010\pi$
$810$	5.93614	0.208575
$811$	−16.9298	−0.594484	−0.297242	−	0.954802i	$-0.596067\pi$
$811$	−16.9298	−0.594484	−0.297242	+	0.954802i	$0.596067\pi$
$812$	−173.031	−6.07218
$813$	16.8659	0.591512
$814$	5.95471	0.208712
$815$	4.55887	0.159690
$816$	−23.0097	−0.805501
$817$	31.9333	1.11720
$818$	36.9059	1.29038
$819$	−24.5161	−0.856660
$820$	−0.909246	−0.0317523
$821$	32.5308	1.13533	0.567666	−	0.823259i	$-0.307847\pi$
$821$	32.5308	1.13533	0.567666	+	0.823259i	$0.307847\pi$
$822$	79.5315	2.77398
$823$	−36.8163	−1.28334	−0.641668	−	0.766983i	$-0.721757\pi$
$823$	−36.8163	−1.28334	−0.641668	+	0.766983i	$0.721757\pi$
$824$	35.3885	1.23282
$825$	6.95784	0.242241
$826$	51.5383	1.79325
$827$	27.8455	0.968283	0.484142	−	0.874990i	$-0.339132\pi$
$827$	27.8455	0.968283	0.484142	+	0.874990i	$0.339132\pi$
$828$	18.5596	0.644990
$829$	−34.8659	−1.21094	−0.605471	−	0.795868i	$-0.707015\pi$
$829$	−34.8659	−1.21094	−0.605471	+	0.795868i	$0.707015\pi$
$830$	−1.79792	−0.0624067
$831$	−36.5320	−1.26728
$832$	−27.3123	−0.946883
$833$	4.45187	0.154248
$834$	94.7165	3.27976
$835$	0.608654	0.0210633
$836$	14.6856	0.507913
$837$	8.49881	0.293762
$838$	−27.7119	−0.957292
$839$	−9.84127	−0.339759	−0.169879	−	0.985465i	$-0.554338\pi$
$839$	−9.84127	−0.339759	−0.169879	+	0.985465i	$0.554338\pi$
$840$	12.7230	0.438985
$841$	81.5465	2.81195
$842$	55.3503	1.90750
$843$	37.3183	1.28531
$844$	97.8234	3.36722
$845$	−0.801339	−0.0275669
$846$	−3.87045	−0.133069
$847$	−35.9827	−1.23638
$848$	95.7571	3.28831
$849$	31.8403	1.09275
$850$	12.9763	0.445084
$851$	−6.02547	−0.206551
$852$	145.354	4.97974
$853$	−15.8307	−0.542033	−0.271016	−	0.962575i	$-0.587360\pi$
$853$	−15.8307	−0.542033	−0.271016	+	0.962575i	$0.587360\pi$
$854$	56.2266	1.92403
$855$	2.56086	0.0875796
$856$	116.102	3.96827
$857$	3.53704	0.120823	0.0604114	−	0.998174i	$-0.480759\pi$
$857$	3.53704	0.120823	0.0604114	+	0.998174i	$0.480759\pi$
$858$	−11.2182	−0.382983
$859$	−0.251805	−0.00859147	−0.00429573	−	0.999991i	$-0.501367\pi$
$859$	−0.251805	−0.00859147	−0.00429573	+	0.999991i	$0.501367\pi$
$860$	6.73470	0.229651
$861$	6.78653	0.231284
$862$	77.3447	2.63437
$863$	−27.1322	−0.923591	−0.461796	−	0.886986i	$-0.652795\pi$
$863$	−27.1322	−0.923591	−0.461796	+	0.886986i	$0.652795\pi$
$864$	−15.8978	−0.540853
$865$	4.68113	0.159163
$866$	60.6854	2.06217
$867$	−2.31872	−0.0787479
$868$	96.7385	3.28352
$869$	0.180868	0.00613551
$870$	−13.8067	−0.468090
$871$	−26.0090	−0.881283
$872$	134.613	4.55858
$873$	−43.2925	−1.46523
$874$	−20.9715	−0.709373
$875$	−7.28136	−0.246155
$876$	−186.592	−6.30434
$877$	31.9378	1.07846	0.539231	−	0.842158i	$-0.318715\pi$
$877$	31.9378	1.07846	0.539231	+	0.842158i	$0.318715\pi$
$878$	−83.5498	−2.81967
$879$	−35.9197	−1.21154
$880$	1.29959	0.0438091
$881$	−2.65980	−0.0896110	−0.0448055	−	0.998996i	$-0.514267\pi$
$881$	−2.65980	−0.0896110	−0.0448055	+	0.998996i	$0.514267\pi$
$882$	−27.7162	−0.933254
$883$	−17.9088	−0.602678	−0.301339	−	0.953517i	$-0.597434\pi$
$883$	−17.9088	−0.602678	−0.301339	+	0.953517i	$0.597434\pi$
$884$	−14.8249	−0.498617
$885$	2.91400	0.0979529
$886$	78.6835	2.64342
$887$	49.1193	1.64927	0.824633	−	0.565668i	$-0.191382\pi$
$887$	49.1193	1.64927	0.824633	+	0.565668i	$0.191382\pi$
$888$	−65.2543	−2.18979
$889$	−52.5567	−1.76270
$890$	3.52898	0.118292
$891$	−6.34995	−0.212731
$892$	−30.3306	−1.01554
$893$	3.09896	0.103703
$894$	−99.3556	−3.32295
$895$	4.67768	0.156358
$896$	−5.00730	−0.167282
$897$	11.3515	0.379016
$898$	84.4587	2.81842
$899$	−61.8047	−2.06130
$900$	−57.2447	−1.90816
$901$	9.64958	0.321474
$902$	1.37263	0.0457037
$903$	−50.2672	−1.67279
$904$	45.3684	1.50893
$905$	2.90599	0.0965985
$906$	49.9542	1.65962
$907$	−12.9245	−0.429150	−0.214575	−	0.976708i	$-0.568837\pi$
$907$	−12.9245	−0.429150	−0.214575	+	0.976708i	$0.568837\pi$
$908$	63.2354	2.09854
$909$	−34.5408	−1.14564
$910$	5.84235	0.193672
$911$	−23.5415	−0.779966	−0.389983	−	0.920822i	$-0.627519\pi$
$911$	−23.5415	−0.779966	−0.389983	+	0.920822i	$0.627519\pi$
$912$	−114.698	−3.79804
$913$	1.92325	0.0636503
$914$	−105.025	−3.47391
$915$	3.17907	0.105097
$916$	68.0635	2.24888
$917$	8.47841	0.279982
$918$	−3.78764	−0.125011
$919$	−30.5981	−1.00934	−0.504670	−	0.863312i	$-0.668386\pi$
$919$	−30.5981	−1.00934	−0.504670	+	0.863312i	$0.668386\pi$
$920$	−2.60392	−0.0858487
$921$	−24.2847	−0.800207
$922$	99.3236	3.27105
$923$	39.2959	1.29344
$924$	−23.1171	−0.760496
$925$	18.5848	0.611065
$926$	10.9707	0.360519
$927$	−11.2124	−0.368264
$928$	115.611	3.79512
$929$	8.54374	0.280311	0.140155	−	0.990130i	$-0.455240\pi$
$929$	8.54374	0.280311	0.140155	+	0.990130i	$0.455240\pi$
$930$	7.71909	0.253119
$931$	22.1916	0.727300
$932$	−84.1514	−2.75647
$933$	18.8407	0.616817
$934$	−27.9803	−0.915543
$935$	0.130961	0.00428289
$936$	54.3384	1.77611
$937$	−10.6927	−0.349315	−0.174657	−	0.984629i	$-0.555882\pi$
$937$	−10.6927	−0.349315	−0.174657	+	0.984629i	$0.555882\pi$
$938$	−75.6383	−2.46968
$939$	23.0987	0.753797
$940$	0.653569	0.0213171
$941$	−27.1679	−0.885648	−0.442824	−	0.896609i	$-0.646023\pi$
$941$	−27.1679	−0.885648	−0.442824	+	0.896609i	$0.646023\pi$
$942$	53.2233	1.73411
$943$	−1.38895	−0.0452303
$944$	−57.6892	−1.87762
$945$	1.05768	0.0344064
$946$	−10.1670	−0.330557
$947$	1.95002	0.0633671	0.0316835	−	0.999498i	$-0.489913\pi$
$947$	1.95002	0.0633671	0.0316835	+	0.999498i	$0.489913\pi$
$948$	−3.36657	−0.109341
$949$	−50.4443	−1.63749
$950$	64.6841	2.09863
$951$	−34.9537	−1.13345
$952$	−25.3824	−0.822648
$953$	55.5344	1.79893	0.899467	−	0.436988i	$-0.143955\pi$
$953$	55.5344	1.79893	0.899467	+	0.436988i	$0.143955\pi$
$954$	−60.0758	−1.94503
$955$	−3.81308	−0.123389
$956$	145.718	4.71286
$957$	14.7691	0.477418
$958$	−57.2816	−1.85068
$959$	44.3067	1.43074
$960$	−4.49091	−0.144943
$961$	3.55400	0.114645
$962$	−29.9645	−0.966095
$963$	−36.7854	−1.18539
$964$	131.830	4.24595
$965$	−2.95451	−0.0951089
$966$	33.0119	1.06214
$967$	34.5966	1.11255	0.556276	−	0.830998i	$-0.312230\pi$
$967$	34.5966	1.11255	0.556276	+	0.830998i	$0.312230\pi$
$968$	79.7536	2.56338
$969$	−11.5583	−0.371306
$970$	10.3169	0.331256
$971$	−12.5948	−0.404188	−0.202094	−	0.979366i	$-0.564775\pi$
$971$	−12.5948	−0.404188	−0.202094	+	0.979366i	$0.564775\pi$
$972$	97.1012	3.11452
$973$	52.7662	1.69161
$974$	−71.5060	−2.29120
$975$	−35.0123	−1.12129
$976$	−62.9370	−2.01457
$977$	22.4304	0.717612	0.358806	−	0.933412i	$-0.383184\pi$
$977$	22.4304	0.717612	0.358806	+	0.933412i	$0.383184\pi$
$978$	128.102	4.09626
$979$	−3.77498	−0.120649
$980$	4.68019	0.149503
$981$	−42.6505	−1.36173
$982$	−4.61514	−0.147275
$983$	18.6869	0.596020	0.298010	−	0.954563i	$-0.403677\pi$
$983$	18.6869	0.596020	0.298010	+	0.954563i	$0.403677\pi$
$984$	−15.0419	−0.479519
$985$	−4.87709	−0.155397
$986$	27.5443	0.877190
$987$	−4.87817	−0.155274
$988$	−73.8991	−2.35104
$989$	10.2878	0.327133
$990$	−0.815331	−0.0259129
$991$	−25.3301	−0.804639	−0.402319	−	0.915499i	$-0.631796\pi$
$991$	−25.3301	−0.804639	−0.402319	+	0.915499i	$0.631796\pi$
$992$	−64.6363	−2.05220
$993$	−77.5671	−2.46152
$994$	114.278	3.62469
$995$	−3.91131	−0.123997
$996$	−35.7983	−1.13431
$997$	13.6496	0.432286	0.216143	−	0.976362i	$-0.430652\pi$
$997$	13.6496	0.432286	0.216143	+	0.976362i	$0.430652\pi$
$998$	−64.6216	−2.04556
$999$	−5.42470	−0.171630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.7	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.61975 q^{2} -2.31872 q^{3} +4.86309 q^{4} +0.216177 q^{5} +6.07447 q^{6} +3.38406 q^{7} -7.50057 q^{8} +2.37647 q^{9} +O(q^{10})\)	\(q-2.61975 q^{2} -2.31872 q^{3} +4.86309 q^{4} +0.216177 q^{5} +6.07447 q^{6} +3.38406 q^{7} -7.50057 q^{8} +2.37647 q^{9} -0.566328 q^{10} +0.605807 q^{11} -11.2761 q^{12} -3.04846 q^{13} -8.86539 q^{14} -0.501253 q^{15} +9.92345 q^{16} +1.00000 q^{17} -6.22574 q^{18} +4.98478 q^{19} +1.05129 q^{20} -7.84669 q^{21} -1.58706 q^{22} +1.60592 q^{23} +17.3917 q^{24} -4.95327 q^{25} +7.98621 q^{26} +1.44580 q^{27} +16.4570 q^{28} -10.5141 q^{29} +1.31316 q^{30} +5.87827 q^{31} -10.9958 q^{32} -1.40470 q^{33} -2.61975 q^{34} +0.731555 q^{35} +11.5570 q^{36} -3.75203 q^{37} -13.0589 q^{38} +7.06853 q^{39} -1.62145 q^{40} -0.864890 q^{41} +20.5564 q^{42} +6.40616 q^{43} +2.94609 q^{44} +0.513736 q^{45} -4.20712 q^{46} +0.621685 q^{47} -23.0097 q^{48} +4.45187 q^{49} +12.9763 q^{50} -2.31872 q^{51} -14.8249 q^{52} +9.64958 q^{53} -3.78764 q^{54} +0.130961 q^{55} -25.3824 q^{56} -11.5583 q^{57} +27.5443 q^{58} -5.81342 q^{59} -2.43764 q^{60} -6.34225 q^{61} -15.3996 q^{62} +8.04211 q^{63} +8.95936 q^{64} -0.659006 q^{65} +3.67995 q^{66} +8.53186 q^{67} +4.86309 q^{68} -3.72369 q^{69} -1.91649 q^{70} -12.8904 q^{71} -17.8249 q^{72} +16.5475 q^{73} +9.82938 q^{74} +11.4852 q^{75} +24.2414 q^{76} +2.05009 q^{77} -18.5178 q^{78} +0.298557 q^{79} +2.14522 q^{80} -10.4818 q^{81} +2.26579 q^{82} +3.17470 q^{83} -38.1592 q^{84} +0.216177 q^{85} -16.7825 q^{86} +24.3793 q^{87} -4.54390 q^{88} -6.23133 q^{89} -1.34586 q^{90} -10.3162 q^{91} +7.80974 q^{92} -13.6301 q^{93} -1.62866 q^{94} +1.07759 q^{95} +25.4962 q^{96} -18.2172 q^{97} -11.6628 q^{98} +1.43968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 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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