LMFDB - Embedded newform 8021.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51883 q^{2} -2.43350 q^{3} +4.34452 q^{4} -0.221192 q^{5} +6.12959 q^{6} -1.84924 q^{7} -5.90546 q^{8} +2.92194 q^{9} +O(q^{10})$	\(q-2.51883 q^{2} -2.43350 q^{3} +4.34452 q^{4} -0.221192 q^{5} +6.12959 q^{6} -1.84924 q^{7} -5.90546 q^{8} +2.92194 q^{9} +0.557145 q^{10} -0.570132 q^{11} -10.5724 q^{12} +1.00000 q^{13} +4.65793 q^{14} +0.538271 q^{15} +6.18583 q^{16} -2.72385 q^{17} -7.35988 q^{18} +0.725895 q^{19} -0.960972 q^{20} +4.50014 q^{21} +1.43607 q^{22} +9.23887 q^{23} +14.3710 q^{24} -4.95107 q^{25} -2.51883 q^{26} +0.189961 q^{27} -8.03407 q^{28} -5.17059 q^{29} -1.35581 q^{30} -1.94484 q^{31} -3.77015 q^{32} +1.38742 q^{33} +6.86093 q^{34} +0.409037 q^{35} +12.6944 q^{36} +3.04393 q^{37} -1.82841 q^{38} -2.43350 q^{39} +1.30624 q^{40} -10.8334 q^{41} -11.3351 q^{42} +1.96107 q^{43} -2.47695 q^{44} -0.646308 q^{45} -23.2712 q^{46} -6.01145 q^{47} -15.0532 q^{48} -3.58031 q^{49} +12.4709 q^{50} +6.62850 q^{51} +4.34452 q^{52} +8.41021 q^{53} -0.478479 q^{54} +0.126109 q^{55} +10.9206 q^{56} -1.76647 q^{57} +13.0238 q^{58} +12.7351 q^{59} +2.33853 q^{60} +4.56498 q^{61} +4.89874 q^{62} -5.40337 q^{63} -2.87528 q^{64} -0.221192 q^{65} -3.49468 q^{66} -7.92183 q^{67} -11.8338 q^{68} -22.4828 q^{69} -1.03030 q^{70} -1.61023 q^{71} -17.2554 q^{72} +10.2770 q^{73} -7.66716 q^{74} +12.0485 q^{75} +3.15367 q^{76} +1.05431 q^{77} +6.12959 q^{78} -9.24103 q^{79} -1.36825 q^{80} -9.22809 q^{81} +27.2875 q^{82} +16.4887 q^{83} +19.5509 q^{84} +0.602493 q^{85} -4.93960 q^{86} +12.5826 q^{87} +3.36689 q^{88} +12.2808 q^{89} +1.62794 q^{90} -1.84924 q^{91} +40.1385 q^{92} +4.73279 q^{93} +15.1418 q^{94} -0.160562 q^{95} +9.17467 q^{96} -8.85175 q^{97} +9.01819 q^{98} -1.66589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * 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 $

$2$	−2.51883	−1.78108	−0.890542	−	0.454901i	$-0.849675\pi$
$2$	−2.51883	−1.78108	−0.890542	+	0.454901i	$0.849675\pi$
$3$	−2.43350	−1.40498	−0.702492	−	0.711692i	$-0.747929\pi$
$3$	−2.43350	−1.40498	−0.702492	+	0.711692i	$0.747929\pi$
$4$	4.34452	2.17226
$5$	−0.221192	−0.0989199	−0.0494599	−	0.998776i	$-0.515750\pi$
$5$	−0.221192	−0.0989199	−0.0494599	+	0.998776i	$0.515750\pi$
$6$	6.12959	2.50239
$7$	−1.84924	−0.698948	−0.349474	−	0.936946i	$-0.613640\pi$
$7$	−1.84924	−0.698948	−0.349474	+	0.936946i	$0.613640\pi$
$8$	−5.90546	−2.08790
$9$	2.92194	0.973980
$10$	0.557145	0.176185
$11$	−0.570132	−0.171901	−0.0859507	−	0.996299i	$-0.527393\pi$
$11$	−0.570132	−0.171901	−0.0859507	+	0.996299i	$0.527393\pi$
$12$	−10.5724	−3.05199
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.65793	1.24488
$15$	0.538271	0.138981
$16$	6.18583	1.54646
$17$	−2.72385	−0.660631	−0.330315	−	0.943871i	$-0.607155\pi$
$17$	−2.72385	−0.660631	−0.330315	+	0.943871i	$0.607155\pi$
$18$	−7.35988	−1.73474
$19$	0.725895	0.166532	0.0832659	−	0.996527i	$-0.473465\pi$
$19$	0.725895	0.166532	0.0832659	+	0.996527i	$0.473465\pi$
$20$	−0.960972	−0.214880
$21$	4.50014	0.982010
$22$	1.43607	0.306171
$23$	9.23887	1.92644	0.963218	−	0.268720i	$-0.0866005\pi$
$23$	9.23887	1.92644	0.963218	+	0.268720i	$0.0866005\pi$
$24$	14.3710	2.93346
$25$	−4.95107	−0.990215
$26$	−2.51883	−0.493984
$27$	0.189961	0.0365579
$28$	−8.03407	−1.51830
$29$	−5.17059	−0.960154	−0.480077	−	0.877226i	$-0.659391\pi$
$29$	−5.17059	−0.960154	−0.480077	+	0.877226i	$0.659391\pi$
$30$	−1.35581	−0.247537
$31$	−1.94484	−0.349304	−0.174652	−	0.984630i	$-0.555880\pi$
$31$	−1.94484	−0.349304	−0.174652	+	0.984630i	$0.555880\pi$
$32$	−3.77015	−0.666474
$33$	1.38742	0.241519
$34$	6.86093	1.17664
$35$	0.409037	0.0691398
$36$	12.6944	2.11574
$37$	3.04393	0.500419	0.250210	−	0.968192i	$-0.419500\pi$
$37$	3.04393	0.500419	0.250210	+	0.968192i	$0.419500\pi$
$38$	−1.82841	−0.296607
$39$	−2.43350	−0.389672
$40$	1.30624	0.206534
$41$	−10.8334	−1.69189	−0.845946	−	0.533269i	$-0.820963\pi$
$41$	−10.8334	−1.69189	−0.845946	+	0.533269i	$0.820963\pi$
$42$	−11.3351	−1.74904
$43$	1.96107	0.299060	0.149530	−	0.988757i	$-0.452224\pi$
$43$	1.96107	0.299060	0.149530	+	0.988757i	$0.452224\pi$
$44$	−2.47695	−0.373415
$45$	−0.646308	−0.0963460
$46$	−23.2712	−3.43115
$47$	−6.01145	−0.876860	−0.438430	−	0.898765i	$-0.644465\pi$
$47$	−6.01145	−0.876860	−0.438430	+	0.898765i	$0.644465\pi$
$48$	−15.0532	−2.17275
$49$	−3.58031	−0.511472
$50$	12.4709	1.76366
$51$	6.62850	0.928176
$52$	4.34452	0.602477
$53$	8.41021	1.15523	0.577615	−	0.816309i	$-0.303983\pi$
$53$	8.41021	1.15523	0.577615	+	0.816309i	$0.303983\pi$
$54$	−0.478479	−0.0651127
$55$	0.126109	0.0170045
$56$	10.9206	1.45933
$57$	−1.76647	−0.233975
$58$	13.0238	1.71011
$59$	12.7351	1.65797	0.828987	−	0.559268i	$-0.188918\pi$
$59$	12.7351	1.65797	0.828987	+	0.559268i	$0.188918\pi$
$60$	2.33853	0.301903
$61$	4.56498	0.584486	0.292243	−	0.956344i	$-0.405598\pi$
$61$	4.56498	0.584486	0.292243	+	0.956344i	$0.405598\pi$
$62$	4.89874	0.622141
$63$	−5.40337	−0.680761
$64$	−2.87528	−0.359410
$65$	−0.221192	−0.0274354
$66$	−3.49468	−0.430165
$67$	−7.92183	−0.967805	−0.483903	−	0.875122i	$-0.660781\pi$
$67$	−7.92183	−0.967805	−0.483903	+	0.875122i	$0.660781\pi$
$68$	−11.8338	−1.43506
$69$	−22.4828	−2.70661
$70$	−1.03030	−0.123144
$71$	−1.61023	−0.191099	−0.0955495	−	0.995425i	$-0.530461\pi$
$71$	−1.61023	−0.191099	−0.0955495	+	0.995425i	$0.530461\pi$
$72$	−17.2554	−2.03357
$73$	10.2770	1.20284	0.601418	−	0.798934i	$-0.294603\pi$
$73$	10.2770	1.20284	0.601418	+	0.798934i	$0.294603\pi$
$74$	−7.66716	−0.891289
$75$	12.0485	1.39124
$76$	3.15367	0.361751
$77$	1.05431	0.120150
$78$	6.12959	0.694039
$79$	−9.24103	−1.03970	−0.519849	−	0.854258i	$-0.674012\pi$
$79$	−9.24103	−1.03970	−0.519849	+	0.854258i	$0.674012\pi$
$80$	−1.36825	−0.152975
$81$	−9.22809	−1.02534
$82$	27.2875	3.01340
$83$	16.4887	1.80987	0.904937	−	0.425545i	$-0.139918\pi$
$83$	16.4887	1.80987	0.904937	+	0.425545i	$0.139918\pi$
$84$	19.5509	2.13318
$85$	0.602493	0.0653495
$86$	−4.93960	−0.532651
$87$	12.5826	1.34900
$88$	3.36689	0.358912
$89$	12.2808	1.30176	0.650879	−	0.759182i	$-0.274401\pi$
$89$	12.2808	1.30176	0.650879	+	0.759182i	$0.274401\pi$
$90$	1.62794	0.171600
$91$	−1.84924	−0.193853
$92$	40.1385	4.18472
$93$	4.73279	0.490767
$94$	15.1418	1.56176
$95$	−0.160562	−0.0164733
$96$	9.17467	0.936386
$97$	−8.85175	−0.898759	−0.449380	−	0.893341i	$-0.648355\pi$
$97$	−8.85175	−0.898759	−0.449380	+	0.893341i	$0.648355\pi$
$98$	9.01819	0.910975
$99$	−1.66589	−0.167429
$100$	−21.5101	−2.15101
$101$	−7.08468	−0.704952	−0.352476	−	0.935821i	$-0.614660\pi$
$101$	−7.08468	−0.704952	−0.352476	+	0.935821i	$0.614660\pi$
$102$	−16.6961	−1.65316
$103$	−4.57406	−0.450696	−0.225348	−	0.974278i	$-0.572352\pi$
$103$	−4.57406	−0.450696	−0.225348	+	0.974278i	$0.572352\pi$
$104$	−5.90546	−0.579078
$105$	−0.995392	−0.0971403
$106$	−21.1839	−2.05756
$107$	−16.3395	−1.57959	−0.789797	−	0.613368i	$-0.789814\pi$
$107$	−16.3395	−1.57959	−0.789797	+	0.613368i	$0.789814\pi$
$108$	0.825288	0.0794134
$109$	5.94027	0.568975	0.284487	−	0.958680i	$-0.408177\pi$
$109$	5.94027	0.568975	0.284487	+	0.958680i	$0.408177\pi$
$110$	−0.317646	−0.0302864
$111$	−7.40742	−0.703081
$112$	−11.4391	−1.08089
$113$	2.62243	0.246697	0.123349	−	0.992363i	$-0.460637\pi$
$113$	2.62243	0.246697	0.123349	+	0.992363i	$0.460637\pi$
$114$	4.44944	0.416728
$115$	−2.04356	−0.190563
$116$	−22.4637	−2.08570
$117$	2.92194	0.270133
$118$	−32.0777	−2.95299
$119$	5.03706	0.461746
$120$	−3.17874	−0.290178
$121$	−10.6749	−0.970450
$122$	−11.4984	−1.04102
$123$	26.3631	2.37708
$124$	−8.44942	−0.758780
$125$	2.20109	0.196872
$126$	13.6102	1.21249
$127$	4.62182	0.410120	0.205060	−	0.978749i	$-0.434261\pi$
$127$	4.62182	0.410120	0.205060	+	0.978749i	$0.434261\pi$
$128$	14.7826	1.30661
$129$	−4.77226	−0.420174
$130$	0.557145	0.0488648
$131$	−11.0299	−0.963691	−0.481845	−	0.876256i	$-0.660033\pi$
$131$	−11.0299	−0.963691	−0.481845	+	0.876256i	$0.660033\pi$
$132$	6.02767	0.524642
$133$	−1.34236	−0.116397
$134$	19.9538	1.72374
$135$	−0.0420177	−0.00361631
$136$	16.0856	1.37933
$137$	2.40317	0.205316	0.102658	−	0.994717i	$-0.467265\pi$
$137$	2.40317	0.205316	0.102658	+	0.994717i	$0.467265\pi$
$138$	56.6305	4.82071
$139$	−1.55707	−0.132069	−0.0660345	−	0.997817i	$-0.521035\pi$
$139$	−1.55707	−0.132069	−0.0660345	+	0.997817i	$0.521035\pi$
$140$	1.77707	0.150190
$141$	14.6289	1.23197
$142$	4.05590	0.340363
$143$	−0.570132	−0.0476769
$144$	18.0746	1.50622
$145$	1.14369	0.0949783
$146$	−25.8862	−2.14235
$147$	8.71269	0.718610
$148$	13.2244	1.08704
$149$	11.1268	0.911541	0.455770	−	0.890097i	$-0.349364\pi$
$149$	11.1268	0.911541	0.455770	+	0.890097i	$0.349364\pi$
$150$	−30.3481	−2.47791
$151$	8.31701	0.676829	0.338414	−	0.940997i	$-0.390109\pi$
$151$	8.31701	0.676829	0.338414	+	0.940997i	$0.390109\pi$
$152$	−4.28675	−0.347701
$153$	−7.95893	−0.643441
$154$	−2.65564	−0.213997
$155$	0.430183	0.0345532
$156$	−10.5724	−0.846470
$157$	−10.5305	−0.840423	−0.420212	−	0.907426i	$-0.638044\pi$
$157$	−10.5305	−0.840423	−0.420212	+	0.907426i	$0.638044\pi$
$158$	23.2766	1.85179
$159$	−20.4663	−1.62308
$160$	0.833925	0.0659276
$161$	−17.0849	−1.34648
$162$	23.2440	1.82622
$163$	−4.92927	−0.386090	−0.193045	−	0.981190i	$-0.561836\pi$
$163$	−4.92927	−0.386090	−0.193045	+	0.981190i	$0.561836\pi$
$164$	−47.0659	−3.67523
$165$	−0.306886	−0.0238910
$166$	−41.5324	−3.22354
$167$	−15.5438	−1.20281	−0.601406	−	0.798944i	$-0.705393\pi$
$167$	−15.5438	−1.20281	−0.601406	+	0.798944i	$0.705393\pi$
$168$	−26.5754	−2.05033
$169$	1.00000	0.0769231
$170$	−1.51758	−0.116393
$171$	2.12102	0.162199
$172$	8.51989	0.649636
$173$	15.5327	1.18093	0.590465	−	0.807063i	$-0.298944\pi$
$173$	15.5327	1.18093	0.590465	+	0.807063i	$0.298944\pi$
$174$	−31.6936	−2.40268
$175$	9.15573	0.692108
$176$	−3.52674	−0.265838
$177$	−30.9910	−2.32943
$178$	−30.9332	−2.31854
$179$	7.93161	0.592836	0.296418	−	0.955058i	$-0.404208\pi$
$179$	7.93161	0.592836	0.296418	+	0.955058i	$0.404208\pi$
$180$	−2.80790	−0.209289
$181$	−7.42017	−0.551537	−0.275769	−	0.961224i	$-0.588932\pi$
$181$	−7.42017	−0.551537	−0.275769	+	0.961224i	$0.588932\pi$
$182$	4.65793	0.345269
$183$	−11.1089	−0.821194
$184$	−54.5598	−4.02220
$185$	−0.673292	−0.0495014
$186$	−11.9211	−0.874097
$187$	1.55296	0.113563
$188$	−26.1169	−1.90477
$189$	−0.351283	−0.0255521
$190$	0.404429	0.0293404
$191$	5.40208	0.390881	0.195440	−	0.980716i	$-0.437386\pi$
$191$	5.40208	0.390881	0.195440	+	0.980716i	$0.437386\pi$
$192$	6.99700	0.504965
$193$	19.0924	1.37430	0.687151	−	0.726515i	$-0.258861\pi$
$193$	19.0924	1.37430	0.687151	+	0.726515i	$0.258861\pi$
$194$	22.2961	1.60077
$195$	0.538271	0.0385464
$196$	−15.5547	−1.11105
$197$	4.96836	0.353981	0.176990	−	0.984213i	$-0.443364\pi$
$197$	4.96836	0.353981	0.176990	+	0.984213i	$0.443364\pi$
$198$	4.19611	0.298204
$199$	−12.2242	−0.866553	−0.433276	−	0.901261i	$-0.642643\pi$
$199$	−12.2242	−0.866553	−0.433276	+	0.901261i	$0.642643\pi$
$200$	29.2384	2.06747
$201$	19.2778	1.35975
$202$	17.8451	1.25558
$203$	9.56166	0.671097
$204$	28.7977	2.01624
$205$	2.39626	0.167362
$206$	11.5213	0.802727
$207$	26.9954	1.87631
$208$	6.18583	0.428910
$209$	−0.413857	−0.0286271
$210$	2.50723	0.173015
$211$	18.0902	1.24538	0.622691	−	0.782468i	$-0.286039\pi$
$211$	18.0902	1.24538	0.622691	+	0.782468i	$0.286039\pi$
$212$	36.5383	2.50946
$213$	3.91850	0.268491
$214$	41.1564	2.81339
$215$	−0.433771	−0.0295830
$216$	−1.12180	−0.0763291
$217$	3.59649	0.244145
$218$	−14.9626	−1.01339
$219$	−25.0092	−1.68997
$220$	0.547881	0.0369381
$221$	−2.72385	−0.183226
$222$	18.6581	1.25225
$223$	−9.93760	−0.665471	−0.332736	−	0.943020i	$-0.607972\pi$
$223$	−9.93760	−0.665471	−0.332736	+	0.943020i	$0.607972\pi$
$224$	6.97191	0.465831
$225$	−14.4667	−0.964449
$226$	−6.60545	−0.439388
$227$	−1.44380	−0.0958283	−0.0479142	−	0.998851i	$-0.515257\pi$
$227$	−1.44380	−0.0958283	−0.0479142	+	0.998851i	$0.515257\pi$
$228$	−7.67446	−0.508254
$229$	3.36100	0.222101	0.111051	−	0.993815i	$-0.464578\pi$
$229$	3.36100	0.222101	0.111051	+	0.993815i	$0.464578\pi$
$230$	5.14739	0.339409
$231$	−2.56567	−0.168809
$232$	30.5347	2.00470
$233$	13.8966	0.910400	0.455200	−	0.890389i	$-0.349568\pi$
$233$	13.8966	0.910400	0.455200	+	0.890389i	$0.349568\pi$
$234$	−7.35988	−0.481130
$235$	1.32968	0.0867389
$236$	55.3281	3.60155
$237$	22.4881	1.46076
$238$	−12.6875	−0.822409
$239$	−8.83495	−0.571485	−0.285743	−	0.958306i	$-0.592240\pi$
$239$	−8.83495	−0.571485	−0.285743	+	0.958306i	$0.592240\pi$
$240$	3.32965	0.214928
$241$	10.5701	0.680883	0.340441	−	0.940266i	$-0.389424\pi$
$241$	10.5701	0.680883	0.340441	+	0.940266i	$0.389424\pi$
$242$	26.8884	1.72845
$243$	21.8867	1.40403
$244$	19.8327	1.26966
$245$	0.791934	0.0505948
$246$	−66.4043	−4.23378
$247$	0.725895	0.0461876
$248$	11.4852	0.729311
$249$	−40.1254	−2.54284
$250$	−5.54419	−0.350645
$251$	10.9621	0.691923	0.345961	−	0.938249i	$-0.387553\pi$
$251$	10.9621	0.691923	0.345961	+	0.938249i	$0.387553\pi$
$252$	−23.4751	−1.47879
$253$	−5.26738	−0.331157
$254$	−11.6416	−0.730459
$255$	−1.46617	−0.0918151
$256$	−31.4845	−1.96778
$257$	22.1898	1.38416	0.692080	−	0.721821i	$-0.256695\pi$
$257$	22.1898	1.38416	0.692080	+	0.721821i	$0.256695\pi$
$258$	12.0205	0.748366
$259$	−5.62896	−0.349767
$260$	−0.960972	−0.0595969
$261$	−15.1081	−0.935170
$262$	27.7826	1.71641
$263$	−4.69101	−0.289260	−0.144630	−	0.989486i	$-0.546199\pi$
$263$	−4.69101	−0.289260	−0.144630	+	0.989486i	$0.546199\pi$
$264$	−8.19335	−0.504266
$265$	−1.86027	−0.114275
$266$	3.38117	0.207313
$267$	−29.8853	−1.82895
$268$	−34.4165	−2.10233
$269$	27.3934	1.67021	0.835104	−	0.550092i	$-0.185407\pi$
$269$	27.3934	1.67021	0.835104	+	0.550092i	$0.185407\pi$
$270$	0.105836	0.00644095
$271$	−6.28478	−0.381773	−0.190887	−	0.981612i	$-0.561136\pi$
$271$	−6.28478	−0.381773	−0.190887	+	0.981612i	$0.561136\pi$
$272$	−16.8493	−1.02164
$273$	4.50014	0.272361
$274$	−6.05317	−0.365686
$275$	2.82277	0.170219
$276$	−97.6771	−5.87947
$277$	16.3770	0.983996	0.491998	−	0.870596i	$-0.336267\pi$
$277$	16.3770	0.983996	0.491998	+	0.870596i	$0.336267\pi$
$278$	3.92200	0.235226
$279$	−5.68272	−0.340215
$280$	−2.41555	−0.144357
$281$	−8.13368	−0.485215	−0.242607	−	0.970125i	$-0.578003\pi$
$281$	−8.13368	−0.485215	−0.242607	+	0.970125i	$0.578003\pi$
$282$	−36.8477	−2.19425
$283$	15.6804	0.932104	0.466052	−	0.884757i	$-0.345676\pi$
$283$	15.6804	0.932104	0.466052	+	0.884757i	$0.345676\pi$
$284$	−6.99567	−0.415117
$285$	0.390728	0.0231447
$286$	1.43607	0.0849165
$287$	20.0336	1.18254
$288$	−11.0161	−0.649133
$289$	−9.58063	−0.563567
$290$	−2.88077	−0.169164
$291$	21.5408	1.26274
$292$	44.6488	2.61287
$293$	18.8635	1.10202	0.551008	−	0.834500i	$-0.314243\pi$
$293$	18.8635	1.10202	0.551008	+	0.834500i	$0.314243\pi$
$294$	−21.9458	−1.27991
$295$	−2.81691	−0.164007
$296$	−17.9758	−1.04482
$297$	−0.108303	−0.00628436
$298$	−28.0265	−1.62353
$299$	9.23887	0.534297
$300$	52.3448	3.02213
$301$	−3.62648	−0.209027
$302$	−20.9492	−1.20549
$303$	17.2406	0.990447
$304$	4.49026	0.257534
$305$	−1.00974	−0.0578173
$306$	20.0472	1.14602
$307$	−22.7774	−1.29997	−0.649987	−	0.759945i	$-0.725226\pi$
$307$	−22.7774	−1.29997	−0.649987	+	0.759945i	$0.725226\pi$
$308$	4.58048	0.260997
$309$	11.1310	0.633220
$310$	−1.08356	−0.0615421
$311$	−9.62933	−0.546029	−0.273014	−	0.962010i	$-0.588021\pi$
$311$	−9.62933	−0.546029	−0.273014	+	0.962010i	$0.588021\pi$
$312$	14.3710	0.813595
$313$	−30.0545	−1.69878	−0.849391	−	0.527765i	$-0.823030\pi$
$313$	−30.0545	−1.69878	−0.849391	+	0.527765i	$0.823030\pi$
$314$	26.5245	1.49686
$315$	1.19518	0.0673408
$316$	−40.1479	−2.25849
$317$	−9.99419	−0.561330	−0.280665	−	0.959806i	$-0.590555\pi$
$317$	−9.99419	−0.561330	−0.280665	+	0.959806i	$0.590555\pi$
$318$	51.5511	2.89084
$319$	2.94792	0.165052
$320$	0.635988	0.0355528
$321$	39.7621	2.21931
$322$	43.0340	2.39819
$323$	−1.97723	−0.110016
$324$	−40.0916	−2.22731
$325$	−4.95107	−0.274636
$326$	12.4160	0.687660
$327$	−14.4557	−0.799400
$328$	63.9762	3.53249
$329$	11.1166	0.612879
$330$	0.772994	0.0425519
$331$	−1.61217	−0.0886128	−0.0443064	−	0.999018i	$-0.514108\pi$
$331$	−1.61217	−0.0886128	−0.0443064	+	0.999018i	$0.514108\pi$
$332$	71.6357	3.93152
$333$	8.89418	0.487398
$334$	39.1521	2.14231
$335$	1.75224	0.0957352
$336$	27.8371	1.51864
$337$	26.2381	1.42928	0.714640	−	0.699493i	$-0.246591\pi$
$337$	26.2381	1.42928	0.714640	+	0.699493i	$0.246591\pi$
$338$	−2.51883	−0.137006
$339$	−6.38168	−0.346605
$340$	2.61754	0.141956
$341$	1.10882	0.0600459
$342$	−5.34250	−0.288889
$343$	19.5655	1.05644
$344$	−11.5810	−0.624406
$345$	4.97301	0.267738
$346$	−39.1243	−2.10334
$347$	−9.84301	−0.528401	−0.264200	−	0.964468i	$-0.585108\pi$
$347$	−9.84301	−0.528401	−0.264200	+	0.964468i	$0.585108\pi$
$348$	54.6656	2.93038
$349$	32.5097	1.74020	0.870102	−	0.492872i	$-0.164053\pi$
$349$	32.5097	1.74020	0.870102	+	0.492872i	$0.164053\pi$
$350$	−23.0618	−1.23270
$351$	0.189961	0.0101393
$352$	2.14948	0.114568
$353$	35.8101	1.90598	0.952991	−	0.303000i	$-0.0979882\pi$
$353$	35.8101	1.90598	0.952991	+	0.303000i	$0.0979882\pi$
$354$	78.0612	4.14891
$355$	0.356169	0.0189035
$356$	53.3540	2.82776
$357$	−12.2577	−0.648746
$358$	−19.9784	−1.05589
$359$	12.8975	0.680706	0.340353	−	0.940298i	$-0.389453\pi$
$359$	12.8975	0.680706	0.340353	+	0.940298i	$0.389453\pi$
$360$	3.81675	0.201160
$361$	−18.4731	−0.972267
$362$	18.6902	0.982334
$363$	25.9775	1.36347
$364$	−8.03407	−0.421100
$365$	−2.27319	−0.118984
$366$	27.9815	1.46262
$367$	28.5603	1.49084	0.745419	−	0.666596i	$-0.232249\pi$
$367$	28.5603	1.49084	0.745419	+	0.666596i	$0.232249\pi$
$368$	57.1500	2.97915
$369$	−31.6545	−1.64787
$370$	1.69591	0.0881662
$371$	−15.5525	−0.807446
$372$	20.5617	1.06607
$373$	0.246560	0.0127664	0.00638318	−	0.999980i	$-0.497968\pi$
$373$	0.246560	0.0127664	0.00638318	+	0.999980i	$0.497968\pi$
$374$	−3.91164	−0.202266
$375$	−5.35637	−0.276602
$376$	35.5004	1.83079
$377$	−5.17059	−0.266299
$378$	0.884823	0.0455104
$379$	−10.8613	−0.557905	−0.278953	−	0.960305i	$-0.589987\pi$
$379$	−10.8613	−0.557905	−0.278953	+	0.960305i	$0.589987\pi$
$380$	−0.697565	−0.0357843
$381$	−11.2472	−0.576212
$382$	−13.6069	−0.696192
$383$	22.8063	1.16535	0.582674	−	0.812706i	$-0.302006\pi$
$383$	22.8063	1.16535	0.582674	+	0.812706i	$0.302006\pi$
$384$	−35.9736	−1.83577
$385$	−0.233205	−0.0118852
$386$	−48.0906	−2.44775
$387$	5.73012	0.291278
$388$	−38.4566	−1.95234
$389$	−17.0529	−0.864618	−0.432309	−	0.901726i	$-0.642301\pi$
$389$	−17.0529	−0.864618	−0.432309	+	0.901726i	$0.642301\pi$
$390$	−1.35581	−0.0686543
$391$	−25.1653	−1.27266
$392$	21.1434	1.06790
$393$	26.8414	1.35397
$394$	−12.5145	−0.630470
$395$	2.04404	0.102847
$396$	−7.23751	−0.363698
$397$	26.8577	1.34795	0.673975	−	0.738754i	$-0.264585\pi$
$397$	26.8577	1.34795	0.673975	+	0.738754i	$0.264585\pi$
$398$	30.7908	1.54340
$399$	3.26663	0.163536
$400$	−30.6265	−1.53132
$401$	23.9948	1.19824	0.599122	−	0.800658i	$-0.295516\pi$
$401$	23.9948	1.19824	0.599122	+	0.800658i	$0.295516\pi$
$402$	−48.5575	−2.42183
$403$	−1.94484	−0.0968796
$404$	−30.7796	−1.53134
$405$	2.04118	0.101427
$406$	−24.0842	−1.19528
$407$	−1.73544	−0.0860228
$408$	−39.1444	−1.93793
$409$	3.97701	0.196650	0.0983251	−	0.995154i	$-0.468651\pi$
$409$	3.97701	0.196650	0.0983251	+	0.995154i	$0.468651\pi$
$410$	−6.03577	−0.298085
$411$	−5.84811	−0.288466
$412$	−19.8721	−0.979028
$413$	−23.5504	−1.15884
$414$	−67.9969	−3.34187
$415$	−3.64717	−0.179033
$416$	−3.77015	−0.184847
$417$	3.78914	0.185555
$418$	1.04244	0.0509872
$419$	−7.30573	−0.356908	−0.178454	−	0.983948i	$-0.557110\pi$
$419$	−7.30573	−0.356908	−0.178454	+	0.983948i	$0.557110\pi$
$420$	−4.32450	−0.211014
$421$	−17.6314	−0.859301	−0.429650	−	0.902995i	$-0.641363\pi$
$421$	−17.6314	−0.859301	−0.429650	+	0.902995i	$0.641363\pi$
$422$	−45.5663	−2.21813
$423$	−17.5651	−0.854044
$424$	−49.6661	−2.41200
$425$	13.4860	0.654167
$426$	−9.87004	−0.478205
$427$	−8.44176	−0.408525
$428$	−70.9871	−3.43129
$429$	1.38742	0.0669852
$430$	1.09260	0.0526897
$431$	−10.8027	−0.520348	−0.260174	−	0.965562i	$-0.583780\pi$
$431$	−10.8027	−0.520348	−0.260174	+	0.965562i	$0.583780\pi$
$432$	1.17506	0.0565353
$433$	0.408217	0.0196177	0.00980883	−	0.999952i	$-0.496878\pi$
$433$	0.408217	0.0196177	0.00980883	+	0.999952i	$0.496878\pi$
$434$	−9.05895	−0.434844
$435$	−2.78317	−0.133443
$436$	25.8076	1.23596
$437$	6.70645	0.320813
$438$	62.9940	3.00997
$439$	−19.1821	−0.915510	−0.457755	−	0.889078i	$-0.651346\pi$
$439$	−19.1821	−0.915510	−0.457755	+	0.889078i	$0.651346\pi$
$440$	−0.744729	−0.0355036
$441$	−10.4614	−0.498164
$442$	6.86093	0.326341
$443$	15.8699	0.754001	0.377001	−	0.926213i	$-0.376955\pi$
$443$	15.8699	0.754001	0.377001	+	0.926213i	$0.376955\pi$
$444$	−32.1817	−1.52728
$445$	−2.71640	−0.128770
$446$	25.0312	1.18526
$447$	−27.0770	−1.28070
$448$	5.31709	0.251209
$449$	−26.3949	−1.24565	−0.622825	−	0.782361i	$-0.714015\pi$
$449$	−26.3949	−1.24565	−0.622825	+	0.782361i	$0.714015\pi$
$450$	36.4393	1.71777
$451$	6.17647	0.290839
$452$	11.3932	0.535890
$453$	−20.2395	−0.950934
$454$	3.63669	0.170678
$455$	0.409037	0.0191759
$456$	10.4318	0.488514
$457$	4.92449	0.230358	0.115179	−	0.993345i	$-0.463256\pi$
$457$	4.92449	0.230358	0.115179	+	0.993345i	$0.463256\pi$
$458$	−8.46580	−0.395581
$459$	−0.517424	−0.0241513
$460$	−8.87829	−0.413952
$461$	34.8301	1.62220	0.811101	−	0.584907i	$-0.198869\pi$
$461$	34.8301	1.62220	0.811101	+	0.584907i	$0.198869\pi$
$462$	6.46250	0.300663
$463$	−0.487675	−0.0226642	−0.0113321	−	0.999936i	$-0.503607\pi$
$463$	−0.487675	−0.0226642	−0.0113321	+	0.999936i	$0.503607\pi$
$464$	−31.9844	−1.48484
$465$	−1.04685	−0.0485466
$466$	−35.0033	−1.62150
$467$	−37.9178	−1.75463	−0.877313	−	0.479918i	$-0.840666\pi$
$467$	−37.9178	−1.75463	−0.877313	+	0.479918i	$0.840666\pi$
$468$	12.6944	0.586800
$469$	14.6494	0.676445
$470$	−3.34925	−0.154489
$471$	25.6259	1.18078
$472$	−75.2069	−3.46168
$473$	−1.11807	−0.0514088
$474$	−56.6438	−2.60173
$475$	−3.59396	−0.164902
$476$	21.8836	1.00303
$477$	24.5741	1.12517
$478$	22.2538	1.01786
$479$	−11.6961	−0.534406	−0.267203	−	0.963640i	$-0.586099\pi$
$479$	−11.6961	−0.534406	−0.267203	+	0.963640i	$0.586099\pi$
$480$	−2.02936	−0.0926272
$481$	3.04393	0.138791
$482$	−26.6244	−1.21271
$483$	41.5762	1.89178
$484$	−46.3776	−2.10807
$485$	1.95793	0.0889051
$486$	−55.1290	−2.50070
$487$	−14.6131	−0.662182	−0.331091	−	0.943599i	$-0.607417\pi$
$487$	−14.6131	−0.662182	−0.331091	+	0.943599i	$0.607417\pi$
$488$	−26.9583	−1.22035
$489$	11.9954	0.542451
$490$	−1.99475	−0.0901136
$491$	−4.38216	−0.197764	−0.0988821	−	0.995099i	$-0.531527\pi$
$491$	−4.38216	−0.197764	−0.0988821	+	0.995099i	$0.531527\pi$
$492$	114.535	5.16364
$493$	14.0839	0.634307
$494$	−1.82841	−0.0822640
$495$	0.368481	0.0165620
$496$	−12.0305	−0.540184
$497$	2.97770	0.133568
$498$	101.069	4.52902
$499$	8.36464	0.374453	0.187226	−	0.982317i	$-0.440050\pi$
$499$	8.36464	0.374453	0.187226	+	0.982317i	$0.440050\pi$
$500$	9.56270	0.427657
$501$	37.8258	1.68993
$502$	−27.6117	−1.23237
$503$	30.5505	1.36218	0.681089	−	0.732201i	$-0.261507\pi$
$503$	30.5505	1.36218	0.681089	+	0.732201i	$0.261507\pi$
$504$	31.9094	1.42136
$505$	1.56707	0.0697338
$506$	13.2676	0.589819
$507$	−2.43350	−0.108076
$508$	20.0796	0.890888
$509$	0.301504	0.0133639	0.00668196	−	0.999978i	$-0.497873\pi$
$509$	0.301504	0.0133639	0.00668196	+	0.999978i	$0.497873\pi$
$510$	3.69304	0.163530
$511$	−19.0047	−0.840720
$512$	49.7388	2.19817
$513$	0.137891	0.00608806
$514$	−55.8923	−2.46530
$515$	1.01174	0.0445828
$516$	−20.7332	−0.912728
$517$	3.42732	0.150734
$518$	14.1784	0.622964
$519$	−37.7989	−1.65919
$520$	1.30624	0.0572823
$521$	−23.4929	−1.02924	−0.514621	−	0.857418i	$-0.672067\pi$
$521$	−23.4929	−1.02924	−0.514621	+	0.857418i	$0.672067\pi$
$522$	38.0549	1.66562
$523$	19.8954	0.869965	0.434983	−	0.900439i	$-0.356754\pi$
$523$	19.8954	0.869965	0.434983	+	0.900439i	$0.356754\pi$
$524$	−47.9198	−2.09339
$525$	−22.2805	−0.972401
$526$	11.8159	0.515197
$527$	5.29747	0.230761
$528$	8.58234	0.373498
$529$	62.3567	2.71116
$530$	4.68570	0.203534
$531$	37.2113	1.61483
$532$	−5.83189	−0.252845
$533$	−10.8334	−0.469246
$534$	75.2760	3.25751
$535$	3.61415	0.156253
$536$	46.7820	2.02068
$537$	−19.3016	−0.832925
$538$	−68.9995	−2.97478
$539$	2.04125	0.0879228
$540$	−0.182547	−0.00785556
$541$	−7.50470	−0.322652	−0.161326	−	0.986901i	$-0.551577\pi$
$541$	−7.50470	−0.322652	−0.161326	+	0.986901i	$0.551577\pi$
$542$	15.8303	0.679970
$543$	18.0570	0.774901
$544$	10.2693	0.440294
$545$	−1.31394	−0.0562829
$546$	−11.3351	−0.485097
$547$	19.3190	0.826020	0.413010	−	0.910727i	$-0.364478\pi$
$547$	19.3190	0.826020	0.413010	+	0.910727i	$0.364478\pi$
$548$	10.4406	0.446001
$549$	13.3386	0.569278
$550$	−7.11008	−0.303175
$551$	−3.75331	−0.159896
$552$	132.771	5.65112
$553$	17.0889	0.726694
$554$	−41.2508	−1.75258
$555$	1.63846	0.0695487
$556$	−6.76473	−0.286889
$557$	22.6330	0.958992	0.479496	−	0.877544i	$-0.340819\pi$
$557$	22.6330	0.958992	0.479496	+	0.877544i	$0.340819\pi$
$558$	14.3138	0.605952
$559$	1.96107	0.0829443
$560$	2.53023	0.106922
$561$	−3.77912	−0.159555
$562$	20.4874	0.864208
$563$	−10.2983	−0.434020	−0.217010	−	0.976169i	$-0.569630\pi$
$563$	−10.2983	−0.434020	−0.217010	+	0.976169i	$0.569630\pi$
$564$	63.5555	2.67617
$565$	−0.580059	−0.0244033
$566$	−39.4964	−1.66016
$567$	17.0650	0.716661
$568$	9.50914	0.398995
$569$	−5.28019	−0.221357	−0.110678	−	0.993856i	$-0.535302\pi$
$569$	−5.28019	−0.221357	−0.110678	+	0.993856i	$0.535302\pi$
$570$	−0.984179	−0.0412227
$571$	−19.4225	−0.812808	−0.406404	−	0.913694i	$-0.633217\pi$
$571$	−19.4225	−0.812808	−0.406404	+	0.913694i	$0.633217\pi$
$572$	−2.47695	−0.103567
$573$	−13.1460	−0.549181
$574$	−50.4612	−2.10621
$575$	−45.7423	−1.90759
$576$	−8.40139	−0.350058
$577$	−32.0820	−1.33559	−0.667796	−	0.744344i	$-0.732762\pi$
$577$	−32.0820	−1.33559	−0.667796	+	0.744344i	$0.732762\pi$
$578$	24.1320	1.00376
$579$	−46.4614	−1.93087
$580$	4.96879	0.206318
$581$	−30.4917	−1.26501
$582$	−54.2576	−2.24905
$583$	−4.79493	−0.198586
$584$	−60.6907	−2.51140
$585$	−0.646308	−0.0267216
$586$	−47.5139	−1.96278
$587$	10.4229	0.430198	0.215099	−	0.976592i	$-0.430993\pi$
$587$	10.4229	0.430198	0.215099	+	0.976592i	$0.430993\pi$
$588$	37.8525	1.56101
$589$	−1.41175	−0.0581703
$590$	7.09532	0.292110
$591$	−12.0905	−0.497338
$592$	18.8292	0.773877
$593$	36.0999	1.48244	0.741222	−	0.671260i	$-0.234247\pi$
$593$	36.0999	1.48244	0.741222	+	0.671260i	$0.234247\pi$
$594$	0.272796	0.0111930
$595$	−1.11416	−0.0456759
$596$	48.3405	1.98010
$597$	29.7477	1.21749
$598$	−23.2712	−0.951629
$599$	37.9352	1.54999	0.774996	−	0.631966i	$-0.217752\pi$
$599$	37.9352	1.54999	0.774996	+	0.631966i	$0.217752\pi$
$600$	−71.1517	−2.90476
$601$	−24.4848	−0.998755	−0.499377	−	0.866385i	$-0.666438\pi$
$601$	−24.4848	−0.998755	−0.499377	+	0.866385i	$0.666438\pi$
$602$	9.13451	0.372295
$603$	−23.1471	−0.942623
$604$	36.1334	1.47025
$605$	2.36121	0.0959968
$606$	−43.4262	−1.76407
$607$	−33.6918	−1.36751	−0.683753	−	0.729713i	$-0.739654\pi$
$607$	−33.6918	−1.36751	−0.683753	+	0.729713i	$0.739654\pi$
$608$	−2.73673	−0.110989
$609$	−23.2683	−0.942881
$610$	2.54336	0.102977
$611$	−6.01145	−0.243197
$612$	−34.5777	−1.39772
$613$	0.00186567	7.53535e−5 0	3.76768e−5	−	1.00000i	$-0.499988\pi$
$613$	0.00186567	7.53535e−5 0	3.76768e−5		1.00000i	$0.499988\pi$
$614$	57.3724	2.31536
$615$	−5.83130	−0.235141
$616$	−6.22620	−0.250861
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−28.0371	−1.12782
$619$	−39.5169	−1.58832	−0.794158	−	0.607711i	$-0.792088\pi$
$619$	−39.5169	−1.58832	−0.794158	+	0.607711i	$0.792088\pi$
$620$	1.86894	0.0750585
$621$	1.75502	0.0704265
$622$	24.2547	0.972524
$623$	−22.7101	−0.909861
$624$	−15.0532	−0.602612
$625$	24.2685	0.970740
$626$	75.7023	3.02567
$627$	1.00712	0.0402206
$628$	−45.7499	−1.82562
$629$	−8.29122	−0.330592
$630$	−3.01046	−0.119940
$631$	5.96338	0.237398	0.118699	−	0.992930i	$-0.462128\pi$
$631$	5.96338	0.237398	0.118699	+	0.992930i	$0.462128\pi$
$632$	54.5726	2.17078
$633$	−44.0226	−1.74974
$634$	25.1737	0.999775
$635$	−1.02231	−0.0405691
$636$	−88.9161	−3.52575
$637$	−3.58031	−0.141857
$638$	−7.42532	−0.293971
$639$	−4.70499	−0.186126
$640$	−3.26980	−0.129250
$641$	−3.04033	−0.120086	−0.0600428	−	0.998196i	$-0.519124\pi$
$641$	−3.04033	−0.120086	−0.0600428	+	0.998196i	$0.519124\pi$
$642$	−100.154	−3.95277
$643$	−34.8329	−1.37368	−0.686838	−	0.726811i	$-0.741002\pi$
$643$	−34.8329	−1.37368	−0.686838	+	0.726811i	$0.741002\pi$
$644$	−74.2257	−2.92490
$645$	1.05558	0.0415636
$646$	4.98032	0.195948
$647$	−2.21360	−0.0870256	−0.0435128	−	0.999053i	$-0.513855\pi$
$647$	−2.21360	−0.0870256	−0.0435128	+	0.999053i	$0.513855\pi$
$648$	54.4961	2.14081
$649$	−7.26072	−0.285008
$650$	12.4709	0.489150
$651$	−8.75206	−0.343020
$652$	−21.4153	−0.838689
$653$	−28.7597	−1.12545	−0.562726	−	0.826643i	$-0.690247\pi$
$653$	−28.7597	−1.12545	−0.562726	+	0.826643i	$0.690247\pi$
$654$	36.4114	1.42380
$655$	2.43973	0.0953282
$656$	−67.0135	−2.61644
$657$	30.0289	1.17154
$658$	−28.0009	−1.09159
$659$	21.6371	0.842864	0.421432	−	0.906860i	$-0.361528\pi$
$659$	21.6371	0.842864	0.421432	+	0.906860i	$0.361528\pi$
$660$	−1.33327	−0.0518975
$661$	13.0069	0.505909	0.252955	−	0.967478i	$-0.418598\pi$
$661$	13.0069	0.505909	0.252955	+	0.967478i	$0.418598\pi$
$662$	4.06078	0.157827
$663$	6.62850	0.257430
$664$	−97.3736	−3.77883
$665$	0.296918	0.0115140
$666$	−22.4030	−0.868097
$667$	−47.7704	−1.84968
$668$	−67.5302	−2.61282
$669$	24.1832	0.934976
$670$	−4.41360	−0.170512
$671$	−2.60264	−0.100474
$672$	−16.9662	−0.654485
$673$	−17.9639	−0.692456	−0.346228	−	0.938150i	$-0.612538\pi$
$673$	−17.9639	−0.692456	−0.346228	+	0.938150i	$0.612538\pi$
$674$	−66.0893	−2.54567
$675$	−0.940509	−0.0362002
$676$	4.34452	0.167097
$677$	−0.826149	−0.0317515	−0.0158757	−	0.999874i	$-0.505054\pi$
$677$	−0.826149	−0.0317515	−0.0158757	+	0.999874i	$0.505054\pi$
$678$	16.0744	0.617334
$679$	16.3690	0.628185
$680$	−3.55800	−0.136443
$681$	3.51349	0.134637
$682$	−2.79293	−0.106947
$683$	21.0033	0.803670	0.401835	−	0.915712i	$-0.368373\pi$
$683$	21.0033	0.803670	0.401835	+	0.915712i	$0.368373\pi$
$684$	9.21483	0.352338
$685$	−0.531560	−0.0203099
$686$	−49.2823	−1.88161
$687$	−8.17900	−0.312048
$688$	12.1308	0.462483
$689$	8.41021	0.320403
$690$	−12.5262	−0.476864
$691$	−23.2297	−0.883699	−0.441850	−	0.897089i	$-0.645678\pi$
$691$	−23.2297	−0.883699	−0.441850	+	0.897089i	$0.645678\pi$
$692$	67.4822	2.56529
$693$	3.08064	0.117024
$694$	24.7929	0.941126
$695$	0.344411	0.0130643
$696$	−74.3063	−2.81657
$697$	29.5086	1.11772
$698$	−81.8865	−3.09945
$699$	−33.8175	−1.27910
$700$	39.7773	1.50344
$701$	−21.3033	−0.804613	−0.402307	−	0.915505i	$-0.631791\pi$
$701$	−21.3033	−0.804613	−0.402307	+	0.915505i	$0.631791\pi$
$702$	−0.478479	−0.0180590
$703$	2.20958	0.0833357
$704$	1.63929	0.0617831
$705$	−3.23579	−0.121867
$706$	−90.1998	−3.39471
$707$	13.1013	0.492725
$708$	−134.641	−5.06012
$709$	−35.1976	−1.32188	−0.660938	−	0.750441i	$-0.729841\pi$
$709$	−35.1976	−1.32188	−0.660938	+	0.750441i	$0.729841\pi$
$710$	−0.897130	−0.0336687
$711$	−27.0017	−1.01264
$712$	−72.5235	−2.71793
$713$	−17.9682	−0.672913
$714$	30.8751	1.15547
$715$	0.126109	0.00471619
$716$	34.4590	1.28779
$717$	21.4999	0.802928
$718$	−32.4867	−1.21239
$719$	−8.73898	−0.325909	−0.162954	−	0.986634i	$-0.552102\pi$
$719$	−8.73898	−0.325909	−0.162954	+	0.986634i	$0.552102\pi$
$720$	−3.99795	−0.148995
$721$	8.45854	0.315013
$722$	46.5306	1.73169
$723$	−25.7225	−0.956629
$724$	−32.2371	−1.19808
$725$	25.6000	0.950759
$726$	−65.4331	−2.42845
$727$	8.74126	0.324195	0.162098	−	0.986775i	$-0.448174\pi$
$727$	8.74126	0.324195	0.162098	+	0.986775i	$0.448174\pi$
$728$	10.9206	0.404745
$729$	−25.5771	−0.947300
$730$	5.72580	0.211921
$731$	−5.34165	−0.197568
$732$	−48.2629	−1.78385
$733$	−24.1822	−0.893189	−0.446594	−	0.894736i	$-0.647363\pi$
$733$	−24.1822	−0.893189	−0.446594	+	0.894736i	$0.647363\pi$
$734$	−71.9388	−2.65531
$735$	−1.92717	−0.0710849
$736$	−34.8319	−1.28392
$737$	4.51649	0.166367
$738$	79.7325	2.93499
$739$	−52.8767	−1.94510	−0.972550	−	0.232695i	$-0.925246\pi$
$739$	−52.8767	−1.94510	−0.972550	+	0.232695i	$0.925246\pi$
$740$	−2.92513	−0.107530
$741$	−1.76647	−0.0648929
$742$	39.1742	1.43813
$743$	42.1241	1.54538	0.772691	−	0.634782i	$-0.218910\pi$
$743$	42.1241	1.54538	0.772691	+	0.634782i	$0.218910\pi$
$744$	−27.9493	−1.02467
$745$	−2.46115	−0.0901695
$746$	−0.621042	−0.0227380
$747$	48.1791	1.76278
$748$	6.74685	0.246689
$749$	30.2156	1.10405
$750$	13.4918	0.492651
$751$	−18.7486	−0.684145	−0.342073	−	0.939673i	$-0.611129\pi$
$751$	−18.7486	−0.684145	−0.342073	+	0.939673i	$0.611129\pi$
$752$	−37.1858	−1.35603
$753$	−26.6764	−0.972140
$754$	13.0238	0.474300
$755$	−1.83965	−0.0669518
$756$	−1.52616	−0.0555058
$757$	−30.3567	−1.10333	−0.551667	−	0.834065i	$-0.686008\pi$
$757$	−30.3567	−1.10333	−0.551667	+	0.834065i	$0.686008\pi$
$758$	27.3577	0.993676
$759$	12.8182	0.465271
$760$	0.948192	0.0343946
$761$	50.4071	1.82726	0.913629	−	0.406550i	$-0.133268\pi$
$761$	50.4071	1.82726	0.913629	+	0.406550i	$0.133268\pi$
$762$	28.3299	1.02628
$763$	−10.9850	−0.397683
$764$	23.4695	0.849095
$765$	1.76045	0.0636491
$766$	−57.4453	−2.07558
$767$	12.7351	0.459839
$768$	76.6176	2.76470
$769$	36.5832	1.31922	0.659611	−	0.751607i	$-0.270721\pi$
$769$	36.5832	1.31922	0.659611	+	0.751607i	$0.270721\pi$
$770$	0.587405	0.0211686
$771$	−53.9989	−1.94472
$772$	82.9474	2.98534
$773$	−27.5777	−0.991902	−0.495951	−	0.868350i	$-0.665181\pi$
$773$	−27.5777	−0.991902	−0.495951	+	0.868350i	$0.665181\pi$
$774$	−14.4332	−0.518791
$775$	9.62907	0.345886
$776$	52.2737	1.87652
$777$	13.6981	0.491417
$778$	42.9535	1.53996
$779$	−7.86391	−0.281754
$780$	2.33853	0.0837327
$781$	0.918043	0.0328502
$782$	63.3872	2.26672
$783$	−0.982207	−0.0351012
$784$	−22.1472	−0.790970
$785$	2.32925	0.0831346
$786$	−67.6090	−2.41153
$787$	13.9134	0.495961	0.247980	−	0.968765i	$-0.420233\pi$
$787$	13.9134	0.495961	0.247980	+	0.968765i	$0.420233\pi$
$788$	21.5851	0.768939
$789$	11.4156	0.406406
$790$	−5.14859	−0.183179
$791$	−4.84950	−0.172428
$792$	9.83786	0.349573
$793$	4.56498	0.162107
$794$	−67.6501	−2.40081
$795$	4.52697	0.160555
$796$	−53.1084	−1.88238
$797$	−24.5998	−0.871369	−0.435685	−	0.900099i	$-0.643494\pi$
$797$	−24.5998	−0.871369	−0.435685	+	0.900099i	$0.643494\pi$
$798$	−8.22809	−0.291271
$799$	16.3743	0.579281
$800$	18.6663	0.659953
$801$	35.8836	1.26789
$802$	−60.4390	−2.13417
$803$	−5.85927	−0.206769
$804$	83.7528	2.95373
$805$	3.77904	0.133193
$806$	4.89874	0.172551
$807$	−66.6620	−2.34661
$808$	41.8383	1.47187
$809$	−8.80674	−0.309629	−0.154814	−	0.987944i	$-0.549478\pi$
$809$	−8.80674	−0.309629	−0.154814	+	0.987944i	$0.549478\pi$
$810$	−5.14138	−0.180650
$811$	−48.2903	−1.69570	−0.847851	−	0.530235i	$-0.822104\pi$
$811$	−48.2903	−1.69570	−0.847851	+	0.530235i	$0.822104\pi$
$812$	41.5409	1.45780
$813$	15.2940	0.536385
$814$	4.37129	0.153214
$815$	1.09031	0.0381920
$816$	41.0028	1.43538
$817$	1.42353	0.0498030
$818$	−10.0174	−0.350251
$819$	−5.40337	−0.188809
$820$	10.4106	0.363553
$821$	−8.02008	−0.279903	−0.139951	−	0.990158i	$-0.544695\pi$
$821$	−8.02008	−0.279903	−0.139951	+	0.990158i	$0.544695\pi$
$822$	14.7304	0.513782
$823$	−46.9705	−1.63729	−0.818644	−	0.574302i	$-0.805274\pi$
$823$	−46.9705	−1.63729	−0.818644	+	0.574302i	$0.805274\pi$
$824$	27.0119	0.941005
$825$	−6.86922	−0.239155
$826$	59.3194	2.06399
$827$	−45.7058	−1.58935	−0.794674	−	0.607037i	$-0.792358\pi$
$827$	−45.7058	−1.58935	−0.794674	+	0.607037i	$0.792358\pi$
$828$	117.282	4.07584
$829$	−34.2326	−1.18895	−0.594474	−	0.804115i	$-0.702640\pi$
$829$	−34.2326	−1.18895	−0.594474	+	0.804115i	$0.702640\pi$
$830$	9.18662	0.318872
$831$	−39.8534	−1.38250
$832$	−2.87528	−0.0996824
$833$	9.75222	0.337894
$834$	−9.54421	−0.330489
$835$	3.43815	0.118982
$836$	−1.79801	−0.0621854
$837$	−0.369444	−0.0127698
$838$	18.4019	0.635684
$839$	12.2617	0.423322	0.211661	−	0.977343i	$-0.432113\pi$
$839$	12.2617	0.423322	0.211661	+	0.977343i	$0.432113\pi$
$840$	5.87825	0.202819
$841$	−2.26504	−0.0781047
$842$	44.4105	1.53049
$843$	19.7933	0.681719
$844$	78.5934	2.70530
$845$	−0.221192	−0.00760922
$846$	44.2436	1.52112
$847$	19.7406	0.678294
$848$	52.0241	1.78651
$849$	−38.1584	−1.30959
$850$	−33.9690	−1.16513
$851$	28.1225	0.964026
$852$	17.0240	0.583232
$853$	33.6911	1.15356	0.576781	−	0.816899i	$-0.304309\pi$
$853$	33.6911	1.15356	0.576781	+	0.816899i	$0.304309\pi$
$854$	21.2634	0.727618
$855$	−0.469152	−0.0160447
$856$	96.4920	3.29803
$857$	0.603596	0.0206184	0.0103092	−	0.999947i	$-0.496718\pi$
$857$	0.603596	0.0206184	0.0103092	+	0.999947i	$0.496718\pi$
$858$	−3.49468	−0.119306
$859$	1.05988	0.0361626	0.0180813	−	0.999837i	$-0.494244\pi$
$859$	1.05988	0.0361626	0.0180813	+	0.999837i	$0.494244\pi$
$860$	−1.88453	−0.0642619
$861$	−48.7517	−1.66145
$862$	27.2102	0.926783
$863$	−26.6849	−0.908363	−0.454181	−	0.890909i	$-0.650068\pi$
$863$	−26.6849	−0.908363	−0.454181	+	0.890909i	$0.650068\pi$
$864$	−0.716179	−0.0243649
$865$	−3.43570	−0.116817
$866$	−1.02823	−0.0349407
$867$	23.3145	0.791802
$868$	15.6250	0.530348
$869$	5.26861	0.178725
$870$	7.01035	0.237673
$871$	−7.92183	−0.268421
$872$	−35.0800	−1.18796
$873$	−25.8643	−0.875373
$874$	−16.8924	−0.571395
$875$	−4.07035	−0.137603
$876$	−108.653	−3.67105
$877$	−50.2110	−1.69550	−0.847752	−	0.530393i	$-0.822044\pi$
$877$	−50.2110	−1.69550	−0.847752	+	0.530393i	$0.822044\pi$
$878$	48.3164	1.63060
$879$	−45.9043	−1.54831
$880$	0.780086	0.0262967
$881$	−41.5979	−1.40147	−0.700735	−	0.713422i	$-0.747144\pi$
$881$	−41.5979	−1.40147	−0.700735	+	0.713422i	$0.747144\pi$
$882$	26.3506	0.887272
$883$	−38.4833	−1.29507	−0.647533	−	0.762037i	$-0.724199\pi$
$883$	−38.4833	−1.29507	−0.647533	+	0.762037i	$0.724199\pi$
$884$	−11.8338	−0.398015
$885$	6.85495	0.230427
$886$	−39.9736	−1.34294
$887$	−9.38989	−0.315282	−0.157641	−	0.987497i	$-0.550389\pi$
$887$	−9.38989	−0.315282	−0.157641	+	0.987497i	$0.550389\pi$
$888$	43.7442	1.46796
$889$	−8.54686	−0.286653
$890$	6.84216	0.229350
$891$	5.26123	0.176258
$892$	−43.1741	−1.44558
$893$	−4.36369	−0.146025
$894$	68.2026	2.28103
$895$	−1.75440	−0.0586433
$896$	−27.3367	−0.913254
$897$	−22.4828	−0.750679
$898$	66.4843	2.21861
$899$	10.0560	0.335386
$900$	−62.8511	−2.09504
$901$	−22.9082	−0.763181
$902$	−15.5575	−0.518008
$903$	8.82506	0.293680
$904$	−15.4866	−0.515078
$905$	1.64128	0.0545580
$906$	50.9799	1.69369
$907$	37.4461	1.24338	0.621688	−	0.783265i	$-0.286447\pi$
$907$	37.4461	1.24338	0.621688	+	0.783265i	$0.286447\pi$
$908$	−6.27262	−0.208164
$909$	−20.7010	−0.686610
$910$	−1.03030	−0.0341540
$911$	−12.3835	−0.410283	−0.205142	−	0.978732i	$-0.565765\pi$
$911$	−12.3835	−0.410283	−0.205142	+	0.978732i	$0.565765\pi$
$912$	−10.9271	−0.361832
$913$	−9.40077	−0.311120
$914$	−12.4040	−0.410287
$915$	2.45720	0.0812324
$916$	14.6019	0.482461
$917$	20.3970	0.673569
$918$	1.30331	0.0430155
$919$	−48.5944	−1.60298	−0.801491	−	0.598007i	$-0.795960\pi$
$919$	−48.5944	−1.60298	−0.801491	+	0.598007i	$0.795960\pi$
$920$	12.0682	0.397875
$921$	55.4288	1.82644
$922$	−87.7313	−2.88928
$923$	−1.61023	−0.0530013
$924$	−11.1466	−0.366697
$925$	−15.0707	−0.495523
$926$	1.22837	0.0403668
$927$	−13.3651	−0.438968
$928$	19.4939	0.639918
$929$	−23.5622	−0.773051	−0.386526	−	0.922279i	$-0.626325\pi$
$929$	−23.5622	−0.773051	−0.386526	+	0.922279i	$0.626325\pi$
$930$	2.63685	0.0864656
$931$	−2.59893	−0.0851764
$932$	60.3743	1.97763
$933$	23.4330	0.767162
$934$	95.5086	3.12514
$935$	−0.343501	−0.0112337
$936$	−17.2554	−0.564010
$937$	29.6586	0.968904	0.484452	−	0.874818i	$-0.339019\pi$
$937$	29.6586	0.968904	0.484452	+	0.874818i	$0.339019\pi$
$938$	−36.8993	−1.20481
$939$	73.1378	2.38676
$940$	5.77684	0.188420
$941$	0.179871	0.00586362	0.00293181	−	0.999996i	$-0.499067\pi$
$941$	0.179871	0.00586362	0.00293181	+	0.999996i	$0.499067\pi$
$942$	−64.5475	−2.10307
$943$	−100.088	−3.25932
$944$	78.7774	2.56399
$945$	0.0777008	0.00252761
$946$	2.81623	0.0915634
$947$	−55.6536	−1.80850	−0.904250	−	0.427003i	$-0.859569\pi$
$947$	−55.6536	−1.80850	−0.904250	+	0.427003i	$0.859569\pi$
$948$	97.7000	3.17315
$949$	10.2770	0.333607
$950$	9.05259	0.293705
$951$	24.3209	0.788659
$952$	−29.7462	−0.964078
$953$	−44.7982	−1.45116	−0.725578	−	0.688140i	$-0.758427\pi$
$953$	−44.7982	−1.45116	−0.725578	+	0.688140i	$0.758427\pi$
$954$	−61.8981	−2.00402
$955$	−1.19490	−0.0386659
$956$	−38.3836	−1.24142
$957$	−7.17377	−0.231895
$958$	29.4604	0.951823
$959$	−4.44403	−0.143505
$960$	−1.54768	−0.0499511
$961$	−27.2176	−0.877986
$962$	−7.66716	−0.247199
$963$	−47.7429	−1.53849
$964$	45.9222	1.47905
$965$	−4.22308	−0.135946
$966$	−104.723	−3.36942
$967$	−21.1099	−0.678850	−0.339425	−	0.940633i	$-0.610232\pi$
$967$	−21.1099	−0.678850	−0.339425	+	0.940633i	$0.610232\pi$
$968$	63.0405	2.02620
$969$	4.81160	0.154571
$970$	−4.93171	−0.158348
$971$	−24.4654	−0.785134	−0.392567	−	0.919724i	$-0.628413\pi$
$971$	−24.4654	−0.785134	−0.392567	+	0.919724i	$0.628413\pi$
$972$	95.0873	3.04993
$973$	2.87940	0.0923094
$974$	36.8079	1.17940
$975$	12.0485	0.385859
$976$	28.2382	0.903883
$977$	5.96340	0.190786	0.0953930	−	0.995440i	$-0.469589\pi$
$977$	5.96340	0.190786	0.0953930	+	0.995440i	$0.469589\pi$
$978$	−30.2144	−0.966151
$979$	−7.00166	−0.223774
$980$	3.44057	0.109905
$981$	17.3571	0.554170
$982$	11.0379	0.352235
$983$	−51.6942	−1.64879	−0.824395	−	0.566016i	$-0.808484\pi$
$983$	−51.6942	−1.64879	−0.824395	+	0.566016i	$0.808484\pi$
$984$	−155.686	−4.96310
$985$	−1.09896	−0.0350158
$986$	−35.4750	−1.12975
$987$	−27.0523	−0.861086
$988$	3.15367	0.100332
$989$	18.1180	0.576120
$990$	−0.928143	−0.0294983
$991$	51.1752	1.62563	0.812816	−	0.582520i	$-0.197933\pi$
$991$	51.1752	1.62563	0.812816	+	0.582520i	$0.197933\pi$
$992$	7.33235	0.232802
$993$	3.92322	0.124500
$994$	−7.50033	−0.237896
$995$	2.70390	0.0857193
$996$	−174.326	−5.52372
$997$	17.4998	0.554223	0.277112	−	0.960838i	$-0.410623\pi$
$997$	17.4998	0.554223	0.277112	+	0.960838i	$0.410623\pi$
$998$	−21.0691	−0.666932
$999$	0.578227	0.0182943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.7	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.7	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51883 q^{2} -2.43350 q^{3} +4.34452 q^{4} -0.221192 q^{5} +6.12959 q^{6} -1.84924 q^{7} -5.90546 q^{8} +2.92194 q^{9} +O(q^{10})\)	\(q-2.51883 q^{2} -2.43350 q^{3} +4.34452 q^{4} -0.221192 q^{5} +6.12959 q^{6} -1.84924 q^{7} -5.90546 q^{8} +2.92194 q^{9} +0.557145 q^{10} -0.570132 q^{11} -10.5724 q^{12} +1.00000 q^{13} +4.65793 q^{14} +0.538271 q^{15} +6.18583 q^{16} -2.72385 q^{17} -7.35988 q^{18} +0.725895 q^{19} -0.960972 q^{20} +4.50014 q^{21} +1.43607 q^{22} +9.23887 q^{23} +14.3710 q^{24} -4.95107 q^{25} -2.51883 q^{26} +0.189961 q^{27} -8.03407 q^{28} -5.17059 q^{29} -1.35581 q^{30} -1.94484 q^{31} -3.77015 q^{32} +1.38742 q^{33} +6.86093 q^{34} +0.409037 q^{35} +12.6944 q^{36} +3.04393 q^{37} -1.82841 q^{38} -2.43350 q^{39} +1.30624 q^{40} -10.8334 q^{41} -11.3351 q^{42} +1.96107 q^{43} -2.47695 q^{44} -0.646308 q^{45} -23.2712 q^{46} -6.01145 q^{47} -15.0532 q^{48} -3.58031 q^{49} +12.4709 q^{50} +6.62850 q^{51} +4.34452 q^{52} +8.41021 q^{53} -0.478479 q^{54} +0.126109 q^{55} +10.9206 q^{56} -1.76647 q^{57} +13.0238 q^{58} +12.7351 q^{59} +2.33853 q^{60} +4.56498 q^{61} +4.89874 q^{62} -5.40337 q^{63} -2.87528 q^{64} -0.221192 q^{65} -3.49468 q^{66} -7.92183 q^{67} -11.8338 q^{68} -22.4828 q^{69} -1.03030 q^{70} -1.61023 q^{71} -17.2554 q^{72} +10.2770 q^{73} -7.66716 q^{74} +12.0485 q^{75} +3.15367 q^{76} +1.05431 q^{77} +6.12959 q^{78} -9.24103 q^{79} -1.36825 q^{80} -9.22809 q^{81} +27.2875 q^{82} +16.4887 q^{83} +19.5509 q^{84} +0.602493 q^{85} -4.93960 q^{86} +12.5826 q^{87} +3.36689 q^{88} +12.2808 q^{89} +1.62794 q^{90} -1.84924 q^{91} +40.1385 q^{92} +4.73279 q^{93} +15.1418 q^{94} -0.160562 q^{95} +9.17467 q^{96} -8.85175 q^{97} +9.01819 q^{98} -1.66589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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