LMFDB - Embedded newform 8021.2.a.b.1.10

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:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.49397 q^{2} -2.62257 q^{3} +4.21989 q^{4} +0.472078 q^{5} +6.54061 q^{6} +1.90995 q^{7} -5.53635 q^{8} +3.87786 q^{9} +O(q^{10})$	\(q-2.49397 q^{2} -2.62257 q^{3} +4.21989 q^{4} +0.472078 q^{5} +6.54061 q^{6} +1.90995 q^{7} -5.53635 q^{8} +3.87786 q^{9} -1.17735 q^{10} +3.36001 q^{11} -11.0670 q^{12} -1.00000 q^{13} -4.76337 q^{14} -1.23805 q^{15} +5.36772 q^{16} +2.14871 q^{17} -9.67126 q^{18} -4.14154 q^{19} +1.99212 q^{20} -5.00898 q^{21} -8.37976 q^{22} -3.70878 q^{23} +14.5195 q^{24} -4.77714 q^{25} +2.49397 q^{26} -2.30224 q^{27} +8.05979 q^{28} +1.67163 q^{29} +3.08767 q^{30} +5.46965 q^{31} -2.31423 q^{32} -8.81184 q^{33} -5.35882 q^{34} +0.901645 q^{35} +16.3641 q^{36} +6.98863 q^{37} +10.3289 q^{38} +2.62257 q^{39} -2.61359 q^{40} +3.67027 q^{41} +12.4922 q^{42} +8.18904 q^{43} +14.1789 q^{44} +1.83065 q^{45} +9.24959 q^{46} -0.944725 q^{47} -14.0772 q^{48} -3.35208 q^{49} +11.9141 q^{50} -5.63513 q^{51} -4.21989 q^{52} -4.91546 q^{53} +5.74172 q^{54} +1.58618 q^{55} -10.5742 q^{56} +10.8615 q^{57} -4.16900 q^{58} -5.76343 q^{59} -5.22446 q^{60} -8.85032 q^{61} -13.6411 q^{62} +7.40652 q^{63} -4.96381 q^{64} -0.472078 q^{65} +21.9765 q^{66} +12.5050 q^{67} +9.06733 q^{68} +9.72653 q^{69} -2.24868 q^{70} -15.2993 q^{71} -21.4692 q^{72} +5.39973 q^{73} -17.4295 q^{74} +12.5284 q^{75} -17.4768 q^{76} +6.41745 q^{77} -6.54061 q^{78} -16.9780 q^{79} +2.53398 q^{80} -5.59580 q^{81} -9.15356 q^{82} +8.08775 q^{83} -21.1373 q^{84} +1.01436 q^{85} -20.4232 q^{86} -4.38396 q^{87} -18.6022 q^{88} +6.81346 q^{89} -4.56559 q^{90} -1.90995 q^{91} -15.6507 q^{92} -14.3445 q^{93} +2.35612 q^{94} -1.95513 q^{95} +6.06923 q^{96} +0.921790 q^{97} +8.36000 q^{98} +13.0296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) $ 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * 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 $

$2$	−2.49397	−1.76350	−0.881752	−	0.471713i	$-0.843636\pi$
$2$	−2.49397	−1.76350	−0.881752	+	0.471713i	$0.843636\pi$
$3$	−2.62257	−1.51414	−0.757070	−	0.653334i	$-0.773370\pi$
$3$	−2.62257	−1.51414	−0.757070	+	0.653334i	$0.773370\pi$
$4$	4.21989	2.10995
$5$	0.472078	0.211119	0.105560	−	0.994413i	$-0.466337\pi$
$5$	0.472078	0.211119	0.105560	+	0.994413i	$0.466337\pi$
$6$	6.54061	2.67019
$7$	1.90995	0.721894	0.360947	−	0.932586i	$-0.382454\pi$
$7$	1.90995	0.721894	0.360947	+	0.932586i	$0.382454\pi$
$8$	−5.53635	−1.95740
$9$	3.87786	1.29262
$10$	−1.17735	−0.372310
$11$	3.36001	1.01308	0.506540	−	0.862217i	$-0.330924\pi$
$11$	3.36001	1.01308	0.506540	+	0.862217i	$0.330924\pi$
$12$	−11.0670	−3.19475
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.76337	−1.27306
$15$	−1.23805	−0.319664
$16$	5.36772	1.34193
$17$	2.14871	0.521139	0.260569	−	0.965455i	$-0.416090\pi$
$17$	2.14871	0.521139	0.260569	+	0.965455i	$0.416090\pi$
$18$	−9.67126	−2.27954
$19$	−4.14154	−0.950133	−0.475067	−	0.879950i	$-0.657576\pi$
$19$	−4.14154	−0.950133	−0.475067	+	0.879950i	$0.657576\pi$
$20$	1.99212	0.445451
$21$	−5.00898	−1.09305
$22$	−8.37976	−1.78657
$23$	−3.70878	−0.773334	−0.386667	−	0.922219i	$-0.626374\pi$
$23$	−3.70878	−0.773334	−0.386667	+	0.922219i	$0.626374\pi$
$24$	14.5195	2.96377
$25$	−4.77714	−0.955429
$26$	2.49397	0.489108
$27$	−2.30224	−0.443066
$28$	8.05979	1.52316
$29$	1.67163	0.310414	0.155207	−	0.987882i	$-0.450396\pi$
$29$	1.67163	0.310414	0.155207	+	0.987882i	$0.450396\pi$
$30$	3.08767	0.563730
$31$	5.46965	0.982378	0.491189	−	0.871053i	$-0.336562\pi$
$31$	5.46965	0.982378	0.491189	+	0.871053i	$0.336562\pi$
$32$	−2.31423	−0.409103
$33$	−8.81184	−1.53394
$34$	−5.35882	−0.919030
$35$	0.901645	0.152406
$36$	16.3641	2.72736
$37$	6.98863	1.14892	0.574462	−	0.818531i	$-0.305211\pi$
$37$	6.98863	1.14892	0.574462	+	0.818531i	$0.305211\pi$
$38$	10.3289	1.67556
$39$	2.62257	0.419947
$40$	−2.61359	−0.413245
$41$	3.67027	0.573200	0.286600	−	0.958050i	$-0.407475\pi$
$41$	3.67027	0.573200	0.286600	+	0.958050i	$0.407475\pi$
$42$	12.4922	1.92760
$43$	8.18904	1.24882	0.624409	−	0.781098i	$-0.285340\pi$
$43$	8.18904	1.24882	0.624409	+	0.781098i	$0.285340\pi$
$44$	14.1789	2.13754
$45$	1.83065	0.272897
$46$	9.24959	1.36378
$47$	−0.944725	−0.137802	−0.0689011	−	0.997623i	$-0.521949\pi$
$47$	−0.944725	−0.137802	−0.0689011	+	0.997623i	$0.521949\pi$
$48$	−14.0772	−2.03187
$49$	−3.35208	−0.478869
$50$	11.9141	1.68490
$51$	−5.63513	−0.789077
$52$	−4.21989	−0.585194
$53$	−4.91546	−0.675190	−0.337595	−	0.941291i	$-0.609613\pi$
$53$	−4.91546	−0.675190	−0.337595	+	0.941291i	$0.609613\pi$
$54$	5.74172	0.781349
$55$	1.58618	0.213881
$56$	−10.5742	−1.41303
$57$	10.8615	1.43863
$58$	−4.16900	−0.547416
$59$	−5.76343	−0.750334	−0.375167	−	0.926957i	$-0.622415\pi$
$59$	−5.76343	−0.750334	−0.375167	+	0.926957i	$0.622415\pi$
$60$	−5.22446	−0.674475
$61$	−8.85032	−1.13317	−0.566584	−	0.824004i	$-0.691735\pi$
$61$	−8.85032	−1.13317	−0.566584	+	0.824004i	$0.691735\pi$
$62$	−13.6411	−1.73243
$63$	7.40652	0.933134
$64$	−4.96381	−0.620476
$65$	−0.472078	−0.0585540
$66$	21.9765	2.70512
$67$	12.5050	1.52773	0.763866	−	0.645374i	$-0.223299\pi$
$67$	12.5050	1.52773	0.763866	+	0.645374i	$0.223299\pi$
$68$	9.06733	1.09958
$69$	9.72653	1.17094
$70$	−2.24868	−0.268768
$71$	−15.2993	−1.81570	−0.907848	−	0.419300i	$-0.862276\pi$
$71$	−15.2993	−1.81570	−0.907848	+	0.419300i	$0.862276\pi$
$72$	−21.4692	−2.53017
$73$	5.39973	0.631991	0.315996	−	0.948761i	$-0.397662\pi$
$73$	5.39973	0.631991	0.315996	+	0.948761i	$0.397662\pi$
$74$	−17.4295	−2.02613
$75$	12.5284	1.44665
$76$	−17.4768	−2.00473
$77$	6.41745	0.731336
$78$	−6.54061	−0.740578
$79$	−16.9780	−1.91018	−0.955090	−	0.296317i	$-0.904241\pi$
$79$	−16.9780	−1.91018	−0.955090	+	0.296317i	$0.904241\pi$
$80$	2.53398	0.283308
$81$	−5.59580	−0.621755
$82$	−9.15356	−1.01084
$83$	8.08775	0.887746	0.443873	−	0.896090i	$-0.353604\pi$
$83$	8.08775	0.887746	0.443873	+	0.896090i	$0.353604\pi$
$84$	−21.1373	−2.30627
$85$	1.01436	0.110023
$86$	−20.4232	−2.20229
$87$	−4.38396	−0.470010
$88$	−18.6022	−1.98300
$89$	6.81346	0.722225	0.361113	−	0.932522i	$-0.382397\pi$
$89$	6.81346	0.722225	0.361113	+	0.932522i	$0.382397\pi$
$90$	−4.56559	−0.481255
$91$	−1.90995	−0.200217
$92$	−15.6507	−1.63169
$93$	−14.3445	−1.48746
$94$	2.35612	0.243015
$95$	−1.95513	−0.200592
$96$	6.06923	0.619438
$97$	0.921790	0.0935936	0.0467968	−	0.998904i	$-0.485099\pi$
$97$	0.921790	0.0935936	0.0467968	+	0.998904i	$0.485099\pi$
$98$	8.36000	0.844488
$99$	13.0296	1.30953
$100$	−20.1590	−2.01590
$101$	−8.24638	−0.820546	−0.410273	−	0.911963i	$-0.634567\pi$
$101$	−8.24638	−0.820546	−0.410273	+	0.911963i	$0.634567\pi$
$102$	14.0539	1.39154
$103$	−7.58995	−0.747860	−0.373930	−	0.927457i	$-0.621990\pi$
$103$	−7.58995	−0.747860	−0.373930	+	0.927457i	$0.621990\pi$
$104$	5.53635	0.542884
$105$	−2.36463	−0.230764
$106$	12.2590	1.19070
$107$	−0.503638	−0.0486885	−0.0243443	−	0.999704i	$-0.507750\pi$
$107$	−0.503638	−0.0486885	−0.0243443	+	0.999704i	$0.507750\pi$
$108$	−9.71520	−0.934846
$109$	−14.3684	−1.37624	−0.688121	−	0.725596i	$-0.741564\pi$
$109$	−14.3684	−1.37624	−0.688121	+	0.725596i	$0.741564\pi$
$110$	−3.95590	−0.377180
$111$	−18.3282	−1.73963
$112$	10.2521	0.968731
$113$	18.4850	1.73893	0.869463	−	0.493997i	$-0.164465\pi$
$113$	18.4850	1.73893	0.869463	+	0.493997i	$0.164465\pi$
$114$	−27.0882	−2.53704
$115$	−1.75083	−0.163266
$116$	7.05410	0.654957
$117$	−3.87786	−0.358508
$118$	14.3738	1.32322
$119$	4.10393	0.376207
$120$	6.85431	0.625710
$121$	0.289636	0.0263305
$122$	22.0724	1.99835
$123$	−9.62554	−0.867905
$124$	23.0813	2.07277
$125$	−4.61557	−0.412829
$126$	−18.4716	−1.64559
$127$	−4.70640	−0.417625	−0.208813	−	0.977956i	$-0.566960\pi$
$127$	−4.70640	−0.417625	−0.208813	+	0.977956i	$0.566960\pi$
$128$	17.0081	1.50331
$129$	−21.4763	−1.89088
$130$	1.17735	0.103260
$131$	1.59412	0.139279	0.0696396	−	0.997572i	$-0.477815\pi$
$131$	1.59412	0.139279	0.0696396	+	0.997572i	$0.477815\pi$
$132$	−37.1850	−3.23654
$133$	−7.91013	−0.685895
$134$	−31.1872	−2.69416
$135$	−1.08683	−0.0935398
$136$	−11.8960	−1.02007
$137$	−16.7146	−1.42803	−0.714014	−	0.700132i	$-0.753125\pi$
$137$	−16.7146	−1.42803	−0.714014	+	0.700132i	$0.753125\pi$
$138$	−24.2577	−2.06495
$139$	−13.8243	−1.17256	−0.586282	−	0.810107i	$-0.699409\pi$
$139$	−13.8243	−1.17256	−0.586282	+	0.810107i	$0.699409\pi$
$140$	3.80485	0.321568
$141$	2.47760	0.208652
$142$	38.1561	3.20199
$143$	−3.36001	−0.280978
$144$	20.8152	1.73460
$145$	0.789139	0.0655344
$146$	−13.4668	−1.11452
$147$	8.79107	0.725075
$148$	29.4913	2.42417
$149$	−0.609647	−0.0499442	−0.0249721	−	0.999688i	$-0.507950\pi$
$149$	−0.609647	−0.0499442	−0.0249721	+	0.999688i	$0.507950\pi$
$150$	−31.2454	−2.55118
$151$	11.5499	0.939916	0.469958	−	0.882689i	$-0.344269\pi$
$151$	11.5499	0.939916	0.469958	+	0.882689i	$0.344269\pi$
$152$	22.9290	1.85979
$153$	8.33239	0.673634
$154$	−16.0049	−1.28971
$155$	2.58210	0.207399
$156$	11.0670	0.886066
$157$	−1.29767	−0.103565	−0.0517827	−	0.998658i	$-0.516490\pi$
$157$	−1.29767	−0.103565	−0.0517827	+	0.998658i	$0.516490\pi$
$158$	42.3428	3.36861
$159$	12.8911	1.02233
$160$	−1.09250	−0.0863695
$161$	−7.08359	−0.558265
$162$	13.9558	1.09647
$163$	−18.0864	−1.41663	−0.708317	−	0.705895i	$-0.750545\pi$
$163$	−18.0864	−1.41663	−0.708317	+	0.705895i	$0.750545\pi$
$164$	15.4882	1.20942
$165$	−4.15987	−0.323846
$166$	−20.1706	−1.56554
$167$	−10.0534	−0.777953	−0.388976	−	0.921248i	$-0.627171\pi$
$167$	−10.0534	−0.777953	−0.388976	+	0.921248i	$0.627171\pi$
$168$	27.7315	2.13953
$169$	1.00000	0.0769231
$170$	−2.52978	−0.194025
$171$	−16.0603	−1.22816
$172$	34.5569	2.63494
$173$	5.22718	0.397415	0.198708	−	0.980059i	$-0.436326\pi$
$173$	5.22718	0.397415	0.198708	+	0.980059i	$0.436326\pi$
$174$	10.9335	0.828865
$175$	−9.12411	−0.689718
$176$	18.0356	1.35948
$177$	15.1150	1.13611
$178$	−16.9926	−1.27365
$179$	8.20850	0.613532	0.306766	−	0.951785i	$-0.400753\pi$
$179$	8.20850	0.613532	0.306766	+	0.951785i	$0.400753\pi$
$180$	7.72515	0.575798
$181$	17.4321	1.29571	0.647857	−	0.761762i	$-0.275665\pi$
$181$	17.4321	1.29571	0.647857	+	0.761762i	$0.275665\pi$
$182$	4.76337	0.353084
$183$	23.2106	1.71577
$184$	20.5331	1.51372
$185$	3.29918	0.242560
$186$	35.7748	2.62314
$187$	7.21968	0.527955
$188$	−3.98664	−0.290755
$189$	−4.39716	−0.319847
$190$	4.87603	0.353744
$191$	1.68647	0.122029	0.0610145	−	0.998137i	$-0.480566\pi$
$191$	1.68647	0.122029	0.0610145	+	0.998137i	$0.480566\pi$
$192$	13.0179	0.939487
$193$	−19.7774	−1.42361	−0.711804	−	0.702378i	$-0.752121\pi$
$193$	−19.7774	−1.42361	−0.711804	+	0.702378i	$0.752121\pi$
$194$	−2.29892	−0.165053
$195$	1.23805	0.0886590
$196$	−14.1454	−1.01039
$197$	10.4621	0.745394	0.372697	−	0.927953i	$-0.378433\pi$
$197$	10.4621	0.745394	0.372697	+	0.927953i	$0.378433\pi$
$198$	−32.4955	−2.30935
$199$	−12.5828	−0.891974	−0.445987	−	0.895039i	$-0.647147\pi$
$199$	−12.5828	−0.891974	−0.445987	+	0.895039i	$0.647147\pi$
$200$	26.4480	1.87015
$201$	−32.7953	−2.31320
$202$	20.5662	1.44704
$203$	3.19273	0.224086
$204$	−23.7797	−1.66491
$205$	1.73265	0.121014
$206$	18.9291	1.31885
$207$	−14.3821	−0.999626
$208$	−5.36772	−0.372184
$209$	−13.9156	−0.962561
$210$	5.89731	0.406953
$211$	9.43985	0.649866	0.324933	−	0.945737i	$-0.394658\pi$
$211$	9.43985	0.649866	0.324933	+	0.945737i	$0.394658\pi$
$212$	−20.7427	−1.42462
$213$	40.1235	2.74922
$214$	1.25606	0.0858624
$215$	3.86586	0.263650
$216$	12.7460	0.867256
$217$	10.4468	0.709173
$218$	35.8343	2.42701
$219$	−14.1612	−0.956923
$220$	6.69352	0.451277
$221$	−2.14871	−0.144538
$222$	45.7099	3.06785
$223$	−2.78526	−0.186515	−0.0932575	−	0.995642i	$-0.529728\pi$
$223$	−2.78526	−0.186515	−0.0932575	+	0.995642i	$0.529728\pi$
$224$	−4.42007	−0.295329
$225$	−18.5251	−1.23501
$226$	−46.1012	−3.06660
$227$	−21.0620	−1.39794	−0.698969	−	0.715152i	$-0.746357\pi$
$227$	−21.0620	−1.39794	−0.698969	+	0.715152i	$0.746357\pi$
$228$	45.8342	3.03544
$229$	−24.6549	−1.62924	−0.814622	−	0.579992i	$-0.803056\pi$
$229$	−24.6549	−1.62924	−0.814622	+	0.579992i	$0.803056\pi$
$230$	4.36653	0.287920
$231$	−16.8302	−1.10734
$232$	−9.25474	−0.607603
$233$	6.37348	0.417540	0.208770	−	0.977965i	$-0.433054\pi$
$233$	6.37348	0.417540	0.208770	+	0.977965i	$0.433054\pi$
$234$	9.67126	0.632230
$235$	−0.445983	−0.0290927
$236$	−24.3211	−1.58317
$237$	44.5261	2.89228
$238$	−10.2351	−0.663442
$239$	13.6164	0.880771	0.440386	−	0.897809i	$-0.354842\pi$
$239$	13.6164	0.880771	0.440386	+	0.897809i	$0.354842\pi$
$240$	−6.64553	−0.428967
$241$	−4.97250	−0.320307	−0.160154	−	0.987092i	$-0.551199\pi$
$241$	−4.97250	−0.320307	−0.160154	+	0.987092i	$0.551199\pi$
$242$	−0.722343	−0.0464340
$243$	21.5821	1.38449
$244$	−37.3474	−2.39092
$245$	−1.58244	−0.101099
$246$	24.0058	1.53055
$247$	4.14154	0.263520
$248$	−30.2819	−1.92290
$249$	−21.2107	−1.34417
$250$	11.5111	0.728026
$251$	−5.78223	−0.364971	−0.182485	−	0.983209i	$-0.558414\pi$
$251$	−5.78223	−0.364971	−0.182485	+	0.983209i	$0.558414\pi$
$252$	31.2547	1.96886
$253$	−12.4615	−0.783449
$254$	11.7376	0.736484
$255$	−2.66022	−0.166589
$256$	−32.4900	−2.03063
$257$	13.4908	0.841532	0.420766	−	0.907169i	$-0.361761\pi$
$257$	13.4908	0.841532	0.420766	+	0.907169i	$0.361761\pi$
$258$	53.5613	3.33458
$259$	13.3480	0.829401
$260$	−1.99212	−0.123546
$261$	6.48234	0.401247
$262$	−3.97570	−0.245620
$263$	−12.5210	−0.772078	−0.386039	−	0.922483i	$-0.626157\pi$
$263$	−12.5210	−0.772078	−0.386039	+	0.922483i	$0.626157\pi$
$264$	48.7855	3.00254
$265$	−2.32048	−0.142546
$266$	19.7276	1.20958
$267$	−17.8688	−1.09355
$268$	52.7699	3.22344
$269$	−15.9495	−0.972459	−0.486230	−	0.873831i	$-0.661628\pi$
$269$	−15.9495	−0.972459	−0.486230	+	0.873831i	$0.661628\pi$
$270$	2.71054	0.164958
$271$	3.75954	0.228376	0.114188	−	0.993459i	$-0.463573\pi$
$271$	3.75954	0.228376	0.114188	+	0.993459i	$0.463573\pi$
$272$	11.5337	0.699332
$273$	5.00898	0.303157
$274$	41.6858	2.51833
$275$	−16.0512	−0.967925
$276$	41.0449	2.47061
$277$	11.4043	0.685220	0.342610	−	0.939478i	$-0.388689\pi$
$277$	11.4043	0.685220	0.342610	+	0.939478i	$0.388689\pi$
$278$	34.4775	2.06782
$279$	21.2105	1.26984
$280$	−4.99183	−0.298319
$281$	12.6196	0.752820	0.376410	−	0.926453i	$-0.377158\pi$
$281$	12.6196	0.752820	0.376410	+	0.926453i	$0.377158\pi$
$282$	−6.17907	−0.367958
$283$	−32.2223	−1.91542	−0.957708	−	0.287742i	$-0.907095\pi$
$283$	−32.2223	−1.91542	−0.957708	+	0.287742i	$0.907095\pi$
$284$	−64.5615	−3.83102
$285$	5.12745	0.303724
$286$	8.37976	0.495505
$287$	7.01004	0.413790
$288$	−8.97427	−0.528814
$289$	−12.3830	−0.728415
$290$	−1.96809	−0.115570
$291$	−2.41746	−0.141714
$292$	22.7863	1.33347
$293$	19.2245	1.12311	0.561554	−	0.827440i	$-0.310204\pi$
$293$	19.2245	1.12311	0.561554	+	0.827440i	$0.310204\pi$
$294$	−21.9247	−1.27867
$295$	−2.72078	−0.158410
$296$	−38.6915	−2.24890
$297$	−7.73553	−0.448861
$298$	1.52044	0.0880768
$299$	3.70878	0.214484
$300$	52.8684	3.05236
$301$	15.6407	0.901514
$302$	−28.8051	−1.65755
$303$	21.6267	1.24242
$304$	−22.2306	−1.27501
$305$	−4.17804	−0.239234
$306$	−20.7807	−1.18796
$307$	31.0992	1.77493	0.887463	−	0.460878i	$-0.152466\pi$
$307$	31.0992	1.77493	0.887463	+	0.460878i	$0.152466\pi$
$308$	27.0810	1.54308
$309$	19.9051	1.13236
$310$	−6.43968	−0.365749
$311$	28.5119	1.61676	0.808380	−	0.588661i	$-0.200345\pi$
$311$	28.5119	1.61676	0.808380	+	0.588661i	$0.200345\pi$
$312$	−14.5195	−0.822002
$313$	−13.9850	−0.790480	−0.395240	−	0.918578i	$-0.629339\pi$
$313$	−13.9850	−0.790480	−0.395240	+	0.918578i	$0.629339\pi$
$314$	3.23635	0.182638
$315$	3.49645	0.197003
$316$	−71.6456	−4.03038
$317$	16.1397	0.906497	0.453249	−	0.891384i	$-0.350265\pi$
$317$	16.1397	0.906497	0.453249	+	0.891384i	$0.350265\pi$
$318$	−32.1501	−1.80289
$319$	5.61669	0.314474
$320$	−2.34330	−0.130995
$321$	1.32082	0.0737212
$322$	17.6663	0.984503
$323$	−8.89896	−0.495151
$324$	−23.6137	−1.31187
$325$	4.77714	0.264988
$326$	45.1069	2.49824
$327$	37.6820	2.08382
$328$	−20.3199	−1.12198
$329$	−1.80438	−0.0994786
$330$	10.3746	0.571103
$331$	−14.3539	−0.788963	−0.394482	−	0.918904i	$-0.629076\pi$
$331$	−14.3539	−0.788963	−0.394482	+	0.918904i	$0.629076\pi$
$332$	34.1295	1.87310
$333$	27.1009	1.48512
$334$	25.0728	1.37192
$335$	5.90334	0.322534
$336$	−26.8868	−1.46679
$337$	−27.5175	−1.49897	−0.749486	−	0.662020i	$-0.769699\pi$
$337$	−27.5175	−1.49897	−0.749486	+	0.662020i	$0.769699\pi$
$338$	−2.49397	−0.135654
$339$	−48.4783	−2.63298
$340$	4.28048	0.232142
$341$	18.3780	0.995227
$342$	40.0539	2.16587
$343$	−19.7720	−1.06759
$344$	−45.3374	−2.44443
$345$	4.59167	0.247207
$346$	−13.0364	−0.700844
$347$	3.27463	0.175792	0.0878958	−	0.996130i	$-0.471986\pi$
$347$	3.27463	0.175792	0.0878958	+	0.996130i	$0.471986\pi$
$348$	−18.4999	−0.991697
$349$	22.5850	1.20895	0.604474	−	0.796625i	$-0.293383\pi$
$349$	22.5850	1.20895	0.604474	+	0.796625i	$0.293383\pi$
$350$	22.7553	1.21632
$351$	2.30224	0.122884
$352$	−7.77584	−0.414454
$353$	6.46375	0.344031	0.172015	−	0.985094i	$-0.444972\pi$
$353$	6.46375	0.344031	0.172015	+	0.985094i	$0.444972\pi$
$354$	−37.6963	−2.00354
$355$	−7.22247	−0.383329
$356$	28.7521	1.52386
$357$	−10.7628	−0.569630
$358$	−20.4718	−1.08197
$359$	2.28780	0.120746	0.0603728	−	0.998176i	$-0.480771\pi$
$359$	2.28780	0.120746	0.0603728	+	0.998176i	$0.480771\pi$
$360$	−10.1351	−0.534168
$361$	−1.84768	−0.0972465
$362$	−43.4750	−2.28500
$363$	−0.759589	−0.0398681
$364$	−8.05979	−0.422448
$365$	2.54909	0.133426
$366$	−57.8865	−3.02577
$367$	12.4349	0.649097	0.324549	−	0.945869i	$-0.394788\pi$
$367$	12.4349	0.649097	0.324549	+	0.945869i	$0.394788\pi$
$368$	−19.9077	−1.03776
$369$	14.2328	0.740930
$370$	−8.22805	−0.427756
$371$	−9.38829	−0.487415
$372$	−60.5324	−3.13846
$373$	−29.6858	−1.53707	−0.768535	−	0.639807i	$-0.779014\pi$
$373$	−29.6858	−1.53707	−0.768535	+	0.639807i	$0.779014\pi$
$374$	−18.0057	−0.931051
$375$	12.1046	0.625081
$376$	5.23033	0.269734
$377$	−1.67163	−0.0860934
$378$	10.9664	0.564051
$379$	1.82721	0.0938573	0.0469286	−	0.998898i	$-0.485057\pi$
$379$	1.82721	0.0938573	0.0469286	+	0.998898i	$0.485057\pi$
$380$	−8.25042	−0.423238
$381$	12.3428	0.632343
$382$	−4.20602	−0.215199
$383$	28.0394	1.43274	0.716372	−	0.697718i	$-0.245801\pi$
$383$	28.0394	1.43274	0.716372	+	0.697718i	$0.245801\pi$
$384$	−44.6048	−2.27623
$385$	3.02953	0.154399
$386$	49.3242	2.51054
$387$	31.7559	1.61424
$388$	3.88986	0.197478
$389$	20.7191	1.05050	0.525249	−	0.850948i	$-0.323972\pi$
$389$	20.7191	1.05050	0.525249	+	0.850948i	$0.323972\pi$
$390$	−3.08767	−0.156350
$391$	−7.96909	−0.403014
$392$	18.5583	0.937337
$393$	−4.18070	−0.210888
$394$	−26.0922	−1.31451
$395$	−8.01495	−0.403276
$396$	54.9836	2.76303
$397$	22.0246	1.10538	0.552690	−	0.833387i	$-0.313601\pi$
$397$	22.0246	1.10538	0.552690	+	0.833387i	$0.313601\pi$
$398$	31.3813	1.57300
$399$	20.7449	1.03854
$400$	−25.6424	−1.28212
$401$	4.44663	0.222054	0.111027	−	0.993817i	$-0.464586\pi$
$401$	4.44663	0.222054	0.111027	+	0.993817i	$0.464586\pi$
$402$	81.7905	4.07934
$403$	−5.46965	−0.272463
$404$	−34.7989	−1.73131
$405$	−2.64165	−0.131265
$406$	−7.96259	−0.395177
$407$	23.4818	1.16395
$408$	31.1981	1.54454
$409$	0.525516	0.0259851	0.0129925	−	0.999916i	$-0.495864\pi$
$409$	0.525516	0.0259851	0.0129925	+	0.999916i	$0.495864\pi$
$410$	−4.32119	−0.213408
$411$	43.8353	2.16223
$412$	−32.0288	−1.57794
$413$	−11.0079	−0.541662
$414$	35.8686	1.76285
$415$	3.81805	0.187421
$416$	2.31423	0.113465
$417$	36.2552	1.77542
$418$	34.7051	1.69748
$419$	−7.08806	−0.346274	−0.173137	−	0.984898i	$-0.555390\pi$
$419$	−7.08806	−0.346274	−0.173137	+	0.984898i	$0.555390\pi$
$420$	−9.97847	−0.486899
$421$	−9.70263	−0.472877	−0.236439	−	0.971646i	$-0.575980\pi$
$421$	−9.70263	−0.472877	−0.236439	+	0.971646i	$0.575980\pi$
$422$	−23.5427	−1.14604
$423$	−3.66351	−0.178126
$424$	27.2137	1.32161
$425$	−10.2647	−0.497911
$426$	−100.067	−4.84826
$427$	−16.9037	−0.818027
$428$	−2.12530	−0.102730
$429$	8.81184	0.425440
$430$	−9.64135	−0.464947
$431$	17.9090	0.862646	0.431323	−	0.902198i	$-0.358047\pi$
$431$	17.9090	0.862646	0.431323	+	0.902198i	$0.358047\pi$
$432$	−12.3578	−0.594563
$433$	16.3611	0.786263	0.393132	−	0.919482i	$-0.371392\pi$
$433$	16.3611	0.786263	0.393132	+	0.919482i	$0.371392\pi$
$434$	−26.0539	−1.25063
$435$	−2.06957	−0.0992283
$436$	−60.6331	−2.90380
$437$	15.3600	0.734771
$438$	35.3175	1.68754
$439$	−8.25010	−0.393756	−0.196878	−	0.980428i	$-0.563080\pi$
$439$	−8.25010	−0.393756	−0.196878	+	0.980428i	$0.563080\pi$
$440$	−8.78167	−0.418650
$441$	−12.9989	−0.618995
$442$	5.35882	0.254893
$443$	−3.11747	−0.148115	−0.0740577	−	0.997254i	$-0.523595\pi$
$443$	−3.11747	−0.148115	−0.0740577	+	0.997254i	$0.523595\pi$
$444$	−77.3429	−3.67053
$445$	3.21648	0.152476
$446$	6.94637	0.328920
$447$	1.59884	0.0756225
$448$	−9.48063	−0.447918
$449$	40.3905	1.90615	0.953073	−	0.302740i	$-0.0979012\pi$
$449$	40.3905	1.90615	0.953073	+	0.302740i	$0.0979012\pi$
$450$	46.2010	2.17794
$451$	12.3321	0.580698
$452$	78.0049	3.66904
$453$	−30.2903	−1.42316
$454$	52.5281	2.46527
$455$	−0.901645	−0.0422698
$456$	−60.1328	−2.81598
$457$	18.4120	0.861275	0.430638	−	0.902525i	$-0.358289\pi$
$457$	18.4120	0.861275	0.430638	+	0.902525i	$0.358289\pi$
$458$	61.4887	2.87318
$459$	−4.94684	−0.230899
$460$	−7.38833	−0.344483
$461$	1.76692	0.0822935	0.0411467	−	0.999153i	$-0.486899\pi$
$461$	1.76692	0.0822935	0.0411467	+	0.999153i	$0.486899\pi$
$462$	41.9740	1.95281
$463$	21.2553	0.987817	0.493909	−	0.869514i	$-0.335568\pi$
$463$	21.2553	0.987817	0.493909	+	0.869514i	$0.335568\pi$
$464$	8.97284	0.416554
$465$	−6.77173	−0.314031
$466$	−15.8953	−0.736334
$467$	−5.90321	−0.273168	−0.136584	−	0.990628i	$-0.543612\pi$
$467$	−5.90321	−0.273168	−0.136584	+	0.990628i	$0.543612\pi$
$468$	−16.3641	−0.756433
$469$	23.8840	1.10286
$470$	1.11227	0.0513052
$471$	3.40323	0.156812
$472$	31.9084	1.46870
$473$	27.5152	1.26515
$474$	−111.047	−5.10054
$475$	19.7847	0.907785
$476$	17.3182	0.793776
$477$	−19.0614	−0.872763
$478$	−33.9589	−1.55324
$479$	4.61711	0.210961	0.105481	−	0.994421i	$-0.466362\pi$
$479$	4.61711	0.210961	0.105481	+	0.994421i	$0.466362\pi$
$480$	2.86515	0.130776
$481$	−6.98863	−0.318654
$482$	12.4013	0.564863
$483$	18.5772	0.845292
$484$	1.22223	0.0555560
$485$	0.435157	0.0197594
$486$	−53.8251	−2.44155
$487$	−3.02429	−0.137044	−0.0685218	−	0.997650i	$-0.521828\pi$
$487$	−3.02429	−0.137044	−0.0685218	+	0.997650i	$0.521828\pi$
$488$	48.9985	2.21806
$489$	47.4327	2.14498
$490$	3.94657	0.178288
$491$	13.5621	0.612048	0.306024	−	0.952024i	$-0.401001\pi$
$491$	13.5621	0.612048	0.306024	+	0.952024i	$0.401001\pi$
$492$	−40.6187	−1.83123
$493$	3.59185	0.161769
$494$	−10.3289	−0.464718
$495$	6.15099	0.276466
$496$	29.3595	1.31828
$497$	−29.2210	−1.31074
$498$	52.8988	2.37045
$499$	−22.9486	−1.02732	−0.513660	−	0.857994i	$-0.671711\pi$
$499$	−22.9486	−1.02732	−0.513660	+	0.857994i	$0.671711\pi$
$500$	−19.4772	−0.871048
$501$	26.3656	1.17793
$502$	14.4207	0.643628
$503$	−26.2628	−1.17100	−0.585500	−	0.810673i	$-0.699102\pi$
$503$	−26.2628	−1.17100	−0.585500	+	0.810673i	$0.699102\pi$
$504$	−41.0051	−1.82651
$505$	−3.89293	−0.173233
$506$	31.0787	1.38162
$507$	−2.62257	−0.116472
$508$	−19.8605	−0.881167
$509$	−39.3983	−1.74630	−0.873149	−	0.487453i	$-0.837926\pi$
$509$	−39.3983	−1.74630	−0.873149	+	0.487453i	$0.837926\pi$
$510$	6.63451	0.293781
$511$	10.3132	0.456231
$512$	47.0130	2.07770
$513$	9.53480	0.420972
$514$	−33.6456	−1.48405
$515$	−3.58304	−0.157888
$516$	−90.6278	−3.98966
$517$	−3.17428	−0.139605
$518$	−33.2894	−1.46265
$519$	−13.7086	−0.601742
$520$	2.61359	0.114613
$521$	16.1790	0.708813	0.354407	−	0.935091i	$-0.384683\pi$
$521$	16.1790	0.708813	0.354407	+	0.935091i	$0.384683\pi$
$522$	−16.1668	−0.707601
$523$	−23.7001	−1.03633	−0.518167	−	0.855279i	$-0.673386\pi$
$523$	−23.7001	−1.03633	−0.518167	+	0.855279i	$0.673386\pi$
$524$	6.72703	0.293872
$525$	23.9286	1.04433
$526$	31.2270	1.36156
$527$	11.7527	0.511955
$528$	−47.2995	−2.05845
$529$	−9.24494	−0.401954
$530$	5.78720	0.251380
$531$	−22.3497	−0.969896
$532$	−33.3799	−1.44720
$533$	−3.67027	−0.158977
$534$	44.5642	1.92848
$535$	−0.237756	−0.0102791
$536$	−69.2323	−2.99038
$537$	−21.5273	−0.928973
$538$	39.7776	1.71494
$539$	−11.2630	−0.485133
$540$	−4.58633	−0.197364
$541$	−35.7849	−1.53851	−0.769257	−	0.638939i	$-0.779373\pi$
$541$	−35.7849	−1.53851	−0.769257	+	0.638939i	$0.779373\pi$
$542$	−9.37618	−0.402742
$543$	−45.7167	−1.96189
$544$	−4.97262	−0.213199
$545$	−6.78299	−0.290551
$546$	−12.4922	−0.534619
$547$	−23.0482	−0.985471	−0.492736	−	0.870179i	$-0.664003\pi$
$547$	−23.0482	−0.985471	−0.492736	+	0.870179i	$0.664003\pi$
$548$	−70.5340	−3.01306
$549$	−34.3203	−1.46475
$550$	40.0313	1.70694
$551$	−6.92312	−0.294935
$552$	−53.8495	−2.29199
$553$	−32.4272	−1.37895
$554$	−28.4421	−1.20839
$555$	−8.65231	−0.367270
$556$	−58.3372	−2.47405
$557$	−10.7458	−0.455316	−0.227658	−	0.973741i	$-0.573107\pi$
$557$	−10.7458	−0.455316	−0.227658	+	0.973741i	$0.573107\pi$
$558$	−52.8984	−2.23937
$559$	−8.18904	−0.346360
$560$	4.83978	0.204518
$561$	−18.9341	−0.799398
$562$	−31.4728	−1.32760
$563$	−29.7763	−1.25492	−0.627461	−	0.778648i	$-0.715906\pi$
$563$	−29.7763	−1.25492	−0.627461	+	0.778648i	$0.715906\pi$
$564$	10.4552	0.440244
$565$	8.72637	0.367121
$566$	80.3615	3.37784
$567$	−10.6877	−0.448841
$568$	84.7025	3.55404
$569$	−7.04140	−0.295191	−0.147595	−	0.989048i	$-0.547153\pi$
$569$	−7.04140	−0.295191	−0.147595	+	0.989048i	$0.547153\pi$
$570$	−12.7877	−0.535618
$571$	14.5432	0.608615	0.304308	−	0.952574i	$-0.401575\pi$
$571$	14.5432	0.608615	0.304308	+	0.952574i	$0.401575\pi$
$572$	−14.1789	−0.592848
$573$	−4.42289	−0.184769
$574$	−17.4829	−0.729720
$575$	17.7174	0.738866
$576$	−19.2489	−0.802039
$577$	−4.40835	−0.183522	−0.0917610	−	0.995781i	$-0.529250\pi$
$577$	−4.40835	−0.183522	−0.0917610	+	0.995781i	$0.529250\pi$
$578$	30.8830	1.28456
$579$	51.8675	2.15554
$580$	3.33008	0.138274
$581$	15.4472	0.640859
$582$	6.02907	0.249913
$583$	−16.5160	−0.684021
$584$	−29.8948	−1.23706
$585$	−1.83065	−0.0756880
$586$	−47.9454	−1.98061
$587$	−13.4383	−0.554657	−0.277329	−	0.960775i	$-0.589449\pi$
$587$	−13.4383	−0.554657	−0.277329	+	0.960775i	$0.589449\pi$
$588$	37.0974	1.52987
$589$	−22.6527	−0.933390
$590$	6.78556	0.279357
$591$	−27.4376	−1.12863
$592$	37.5130	1.54178
$593$	47.1075	1.93447	0.967237	−	0.253875i	$-0.0817052\pi$
$593$	47.1075	1.93447	0.967237	+	0.253875i	$0.0817052\pi$
$594$	19.2922	0.791568
$595$	1.93737	0.0794246
$596$	−2.57264	−0.105380
$597$	32.9993	1.35057
$598$	−9.24959	−0.378244
$599$	30.0599	1.22822	0.614108	−	0.789222i	$-0.289516\pi$
$599$	30.0599	1.22822	0.614108	+	0.789222i	$0.289516\pi$
$600$	−69.3615	−2.83167
$601$	−12.8955	−0.526019	−0.263009	−	0.964793i	$-0.584715\pi$
$601$	−12.8955	−0.526019	−0.263009	+	0.964793i	$0.584715\pi$
$602$	−39.0074	−1.58982
$603$	48.4927	1.97478
$604$	48.7393	1.98317
$605$	0.136730	0.00555889
$606$	−53.9363	−2.19101
$607$	23.0234	0.934492	0.467246	−	0.884127i	$-0.345246\pi$
$607$	23.0234	0.934492	0.467246	+	0.884127i	$0.345246\pi$
$608$	9.58448	0.388702
$609$	−8.37316	−0.339297
$610$	10.4199	0.421890
$611$	0.944725	0.0382195
$612$	35.1618	1.42133
$613$	−24.8783	−1.00482	−0.502412	−	0.864628i	$-0.667554\pi$
$613$	−24.8783	−1.00482	−0.502412	+	0.864628i	$0.667554\pi$
$614$	−77.5606	−3.13009
$615$	−4.54400	−0.183232
$616$	−35.5293	−1.43151
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	−49.6429	−1.99693
$619$	−25.9164	−1.04167	−0.520835	−	0.853657i	$-0.674379\pi$
$619$	−25.9164	−1.04167	−0.520835	+	0.853657i	$0.674379\pi$
$620$	10.8962	0.437601
$621$	8.53850	0.342638
$622$	−71.1078	−2.85116
$623$	13.0134	0.521370
$624$	14.0772	0.563539
$625$	21.7068	0.868272
$626$	34.8783	1.39402
$627$	36.4945	1.45745
$628$	−5.47603	−0.218517
$629$	15.0165	0.598749
$630$	−8.72005	−0.347415
$631$	−4.44902	−0.177113	−0.0885563	−	0.996071i	$-0.528225\pi$
$631$	−4.44902	−0.177113	−0.0885563	+	0.996071i	$0.528225\pi$
$632$	93.9965	3.73898
$633$	−24.7566	−0.983988
$634$	−40.2520	−1.59861
$635$	−2.22178	−0.0881688
$636$	54.3991	2.15707
$637$	3.35208	0.132814
$638$	−14.0079	−0.554576
$639$	−59.3286	−2.34700
$640$	8.02912	0.317379
$641$	−6.70745	−0.264928	−0.132464	−	0.991188i	$-0.542289\pi$
$641$	−6.70745	−0.264928	−0.132464	+	0.991188i	$0.542289\pi$
$642$	−3.29410	−0.130008
$643$	−36.2756	−1.43057	−0.715285	−	0.698832i	$-0.753703\pi$
$643$	−36.2756	−1.43057	−0.715285	+	0.698832i	$0.753703\pi$
$644$	−29.8920	−1.17791
$645$	−10.1385	−0.399202
$646$	22.1937	0.873201
$647$	−43.2753	−1.70133	−0.850664	−	0.525709i	$-0.823800\pi$
$647$	−43.2753	−1.70133	−0.850664	+	0.525709i	$0.823800\pi$
$648$	30.9803	1.21702
$649$	−19.3651	−0.760149
$650$	−11.9141	−0.467308
$651$	−27.3973	−1.07379
$652$	−76.3225	−2.98902
$653$	13.6155	0.532816	0.266408	−	0.963860i	$-0.414163\pi$
$653$	13.6155	0.532816	0.266408	+	0.963860i	$0.414163\pi$
$654$	−93.9780	−3.67483
$655$	0.752550	0.0294046
$656$	19.7010	0.769195
$657$	20.9394	0.816924
$658$	4.50007	0.175431
$659$	−32.5298	−1.26718	−0.633590	−	0.773669i	$-0.718419\pi$
$659$	−32.5298	−1.26718	−0.633590	+	0.773669i	$0.718419\pi$
$660$	−17.5542	−0.683297
$661$	21.0210	0.817621	0.408811	−	0.912619i	$-0.365944\pi$
$661$	21.0210	0.817621	0.408811	+	0.912619i	$0.365944\pi$
$662$	35.7983	1.39134
$663$	5.63513	0.218850
$664$	−44.7767	−1.73767
$665$	−3.73420	−0.144806
$666$	−67.5889	−2.61902
$667$	−6.19971	−0.240054
$668$	−42.4241	−1.64144
$669$	7.30454	0.282410
$670$	−14.7228	−0.568790
$671$	−29.7371	−1.14799
$672$	11.5919	0.447169
$673$	−28.1420	−1.08479	−0.542397	−	0.840122i	$-0.682483\pi$
$673$	−28.1420	−1.08479	−0.542397	+	0.840122i	$0.682483\pi$
$674$	68.6278	2.64344
$675$	10.9981	0.423318
$676$	4.21989	0.162304
$677$	36.4138	1.39950	0.699748	−	0.714390i	$-0.253296\pi$
$677$	36.4138	1.39950	0.699748	+	0.714390i	$0.253296\pi$
$678$	120.903	4.64327
$679$	1.76058	0.0675647
$680$	−5.61584	−0.215358
$681$	55.2366	2.11667
$682$	−45.8343	−1.75509
$683$	−28.4458	−1.08845	−0.544224	−	0.838940i	$-0.683176\pi$
$683$	−28.4458	−1.08845	−0.544224	+	0.838940i	$0.683176\pi$
$684$	−67.7727	−2.59135
$685$	−7.89060	−0.301484
$686$	49.3108	1.88269
$687$	64.6592	2.46690
$688$	43.9565	1.67583
$689$	4.91546	0.187264
$690$	−11.4515	−0.435951
$691$	−26.7130	−1.01621	−0.508104	−	0.861295i	$-0.669654\pi$
$691$	−26.7130	−1.01621	−0.508104	+	0.861295i	$0.669654\pi$
$692$	22.0582	0.838525
$693$	24.8859	0.945339
$694$	−8.16684	−0.310009
$695$	−6.52615	−0.247551
$696$	24.2712	0.919996
$697$	7.88635	0.298717
$698$	−56.3264	−2.13199
$699$	−16.7149	−0.632214
$700$	−38.5028	−1.45527
$701$	−38.7206	−1.46246	−0.731229	−	0.682132i	$-0.761053\pi$
$701$	−38.7206	−1.46246	−0.731229	+	0.682132i	$0.761053\pi$
$702$	−5.74172	−0.216707
$703$	−28.9437	−1.09163
$704$	−16.6784	−0.628591
$705$	1.16962	0.0440505
$706$	−16.1204	−0.606700
$707$	−15.7502	−0.592347
$708$	63.7836	2.39713
$709$	12.5779	0.472373	0.236187	−	0.971708i	$-0.424102\pi$
$709$	12.5779	0.472373	0.236187	+	0.971708i	$0.424102\pi$
$710$	18.0126	0.676002
$711$	−65.8384	−2.46913
$712$	−37.7217	−1.41368
$713$	−20.2857	−0.759707
$714$	26.8422	1.00454
$715$	−1.58618	−0.0593199
$716$	34.6390	1.29452
$717$	−35.7099	−1.33361
$718$	−5.70571	−0.212935
$719$	35.3438	1.31810	0.659050	−	0.752099i	$-0.270959\pi$
$719$	35.3438	1.31810	0.659050	+	0.752099i	$0.270959\pi$
$720$	9.82641	0.366209
$721$	−14.4964	−0.539875
$722$	4.60807	0.171495
$723$	13.0407	0.484990
$724$	73.5614	2.73389
$725$	−7.98562	−0.296578
$726$	1.89439	0.0703075
$727$	−4.00405	−0.148502	−0.0742509	−	0.997240i	$-0.523657\pi$
$727$	−4.00405	−0.148502	−0.0742509	+	0.997240i	$0.523657\pi$
$728$	10.5742	0.391905
$729$	−39.8130	−1.47456
$730$	−6.35737	−0.235297
$731$	17.5959	0.650807
$732$	97.9461	3.62019
$733$	−34.4572	−1.27271	−0.636353	−	0.771398i	$-0.719558\pi$
$733$	−34.4572	−1.27271	−0.636353	+	0.771398i	$0.719558\pi$
$734$	−31.0123	−1.14469
$735$	4.15006	0.153077
$736$	8.58299	0.316373
$737$	42.0170	1.54772
$738$	−35.4962	−1.30663
$739$	−21.1267	−0.777157	−0.388579	−	0.921416i	$-0.627034\pi$
$739$	−21.1267	−0.777157	−0.388579	+	0.921416i	$0.627034\pi$
$740$	13.9222	0.511789
$741$	−10.8615	−0.399005
$742$	23.4141	0.859559
$743$	1.18871	0.0436097	0.0218049	−	0.999762i	$-0.493059\pi$
$743$	1.18871	0.0436097	0.0218049	+	0.999762i	$0.493059\pi$
$744$	79.4163	2.91154
$745$	−0.287801	−0.0105442
$746$	74.0355	2.71063
$747$	31.3631	1.14752
$748$	30.4663	1.11396
$749$	−0.961924	−0.0351479
$750$	−30.1886	−1.10233
$751$	25.5593	0.932673	0.466337	−	0.884607i	$-0.345574\pi$
$751$	25.5593	0.932673	0.466337	+	0.884607i	$0.345574\pi$
$752$	−5.07102	−0.184921
$753$	15.1643	0.552617
$754$	4.16900	0.151826
$755$	5.45244	0.198435
$756$	−18.5556	−0.674859
$757$	9.72091	0.353313	0.176656	−	0.984273i	$-0.443472\pi$
$757$	9.72091	0.353313	0.176656	+	0.984273i	$0.443472\pi$
$758$	−4.55700	−0.165518
$759$	32.6812	1.18625
$760$	10.8243	0.392637
$761$	−48.2328	−1.74844	−0.874220	−	0.485531i	$-0.838626\pi$
$761$	−48.2328	−1.74844	−0.874220	+	0.485531i	$0.838626\pi$
$762$	−30.7827	−1.11514
$763$	−27.4429	−0.993500
$764$	7.11674	0.257475
$765$	3.93353	0.142217
$766$	−69.9294	−2.52665
$767$	5.76343	0.208105
$768$	85.2072	3.07465
$769$	39.3971	1.42070	0.710348	−	0.703850i	$-0.248537\pi$
$769$	39.3971	1.42070	0.710348	+	0.703850i	$0.248537\pi$
$770$	−7.55557	−0.272284
$771$	−35.3805	−1.27420
$772$	−83.4585	−3.00374
$773$	−26.8227	−0.964745	−0.482372	−	0.875966i	$-0.660225\pi$
$773$	−26.8227	−0.964745	−0.482372	+	0.875966i	$0.660225\pi$
$774$	−79.1984	−2.84673
$775$	−26.1293	−0.938592
$776$	−5.10336	−0.183200
$777$	−35.0059	−1.25583
$778$	−51.6728	−1.85256
$779$	−15.2006	−0.544617
$780$	5.22446	0.187066
$781$	−51.4058	−1.83944
$782$	19.8747	0.710718
$783$	−3.84849	−0.137534
$784$	−17.9931	−0.642609
$785$	−0.612601	−0.0218647
$786$	10.4265	0.371902
$787$	−28.0790	−1.00091	−0.500454	−	0.865763i	$-0.666833\pi$
$787$	−28.0790	−1.00091	−0.500454	+	0.865763i	$0.666833\pi$
$788$	44.1490	1.57274
$789$	32.8371	1.16903
$790$	19.9891	0.711179
$791$	35.3055	1.25532
$792$	−72.1366	−2.56326
$793$	8.85032	0.314284
$794$	−54.9286	−1.94934
$795$	6.08561	0.215834
$796$	−53.0983	−1.88202
$797$	15.8581	0.561721	0.280861	−	0.959749i	$-0.409380\pi$
$797$	15.8581	0.561721	0.280861	+	0.959749i	$0.409380\pi$
$798$	−51.7371	−1.83147
$799$	−2.02994	−0.0718141
$800$	11.0554	0.390868
$801$	26.4216	0.933562
$802$	−11.0898	−0.391594
$803$	18.1431	0.640257
$804$	−138.393	−4.88073
$805$	−3.34400	−0.117861
$806$	13.6411	0.480489
$807$	41.8287	1.47244
$808$	45.6549	1.60613
$809$	55.0447	1.93527	0.967634	−	0.252359i	$-0.0812062\pi$
$809$	55.0447	1.93527	0.967634	+	0.252359i	$0.0812062\pi$
$810$	6.58820	0.231486
$811$	50.5560	1.77526	0.887631	−	0.460555i	$-0.152350\pi$
$811$	50.5560	1.77526	0.887631	+	0.460555i	$0.152350\pi$
$812$	13.4730	0.472810
$813$	−9.85964	−0.345793
$814$	−58.5631	−2.05263
$815$	−8.53817	−0.299079
$816$	−30.2478	−1.05889
$817$	−33.9152	−1.18654
$818$	−1.31062	−0.0458248
$819$	−7.40652	−0.258805
$820$	7.31161	0.255333
$821$	48.5533	1.69452	0.847262	−	0.531176i	$-0.178250\pi$
$821$	48.5533	1.69452	0.847262	+	0.531176i	$0.178250\pi$
$822$	−109.324	−3.81311
$823$	17.2255	0.600444	0.300222	−	0.953869i	$-0.402939\pi$
$823$	17.2255	0.600444	0.300222	+	0.953869i	$0.402939\pi$
$824$	42.0206	1.46386
$825$	42.0954	1.46557
$826$	27.4533	0.955223
$827$	−53.5472	−1.86202	−0.931009	−	0.364996i	$-0.881070\pi$
$827$	−53.5472	−1.86202	−0.931009	+	0.364996i	$0.881070\pi$
$828$	−60.6910	−2.10916
$829$	3.35715	0.116599	0.0582994	−	0.998299i	$-0.481432\pi$
$829$	3.35715	0.116599	0.0582994	+	0.998299i	$0.481432\pi$
$830$	−9.52210	−0.330517
$831$	−29.9086	−1.03752
$832$	4.96381	0.172089
$833$	−7.20266	−0.249557
$834$	−90.4194	−3.13097
$835$	−4.74597	−0.164241
$836$	−58.7223	−2.03095
$837$	−12.5924	−0.435258
$838$	17.6774	0.610656
$839$	−36.8934	−1.27370	−0.636851	−	0.770986i	$-0.719764\pi$
$839$	−36.8934	−1.27370	−0.636851	+	0.770986i	$0.719764\pi$
$840$	13.0914	0.451696
$841$	−26.2057	−0.903643
$842$	24.1981	0.833921
$843$	−33.0956	−1.13987
$844$	39.8352	1.37118
$845$	0.472078	0.0162400
$846$	9.13668	0.314126
$847$	0.553190	0.0190078
$848$	−26.3848	−0.906058
$849$	84.5051	2.90021
$850$	25.5999	0.878068
$851$	−25.9193	−0.888502
$852$	169.317	5.80070
$853$	19.6223	0.671853	0.335927	−	0.941888i	$-0.390951\pi$
$853$	19.6223	0.671853	0.335927	+	0.941888i	$0.390951\pi$
$854$	42.1573	1.44259
$855$	−7.58170	−0.259289
$856$	2.78832	0.0953027
$857$	16.3947	0.560031	0.280016	−	0.959995i	$-0.409660\pi$
$857$	16.3947	0.560031	0.280016	+	0.959995i	$0.409660\pi$
$858$	−21.9765	−0.750264
$859$	−36.1186	−1.23235	−0.616176	−	0.787609i	$-0.711319\pi$
$859$	−36.1186	−1.23235	−0.616176	+	0.787609i	$0.711319\pi$
$860$	16.3135	0.556287
$861$	−18.3843	−0.626536
$862$	−44.6645	−1.52128
$863$	6.12026	0.208336	0.104168	−	0.994560i	$-0.466782\pi$
$863$	6.12026	0.208336	0.104168	+	0.994560i	$0.466782\pi$
$864$	5.32792	0.181259
$865$	2.46764	0.0839021
$866$	−40.8041	−1.38658
$867$	32.4754	1.10292
$868$	44.0842	1.49632
$869$	−57.0463	−1.93516
$870$	5.16145	0.174990
$871$	−12.5050	−0.423717
$872$	79.5485	2.69385
$873$	3.57457	0.120981
$874$	−38.3075	−1.29577
$875$	−8.81551	−0.298019
$876$	−59.7586	−2.01906
$877$	55.9948	1.89081	0.945405	−	0.325898i	$-0.105667\pi$
$877$	55.9948	1.89081	0.945405	+	0.325898i	$0.105667\pi$
$878$	20.5755	0.694390
$879$	−50.4176	−1.70054
$880$	8.51419	0.287013
$881$	13.7330	0.462676	0.231338	−	0.972873i	$-0.425690\pi$
$881$	13.7330	0.462676	0.231338	+	0.972873i	$0.425690\pi$
$882$	32.4189	1.09160
$883$	−10.2881	−0.346222	−0.173111	−	0.984902i	$-0.555382\pi$
$883$	−10.2881	−0.346222	−0.173111	+	0.984902i	$0.555382\pi$
$884$	−9.06733	−0.304967
$885$	7.13544	0.239855
$886$	7.77488	0.261202
$887$	−28.1096	−0.943826	−0.471913	−	0.881645i	$-0.656436\pi$
$887$	−28.1096	−0.943826	−0.471913	+	0.881645i	$0.656436\pi$
$888$	101.471	3.40515
$889$	−8.98899	−0.301481
$890$	−8.02182	−0.268892
$891$	−18.8019	−0.629888
$892$	−11.7535	−0.393537
$893$	3.91261	0.130931
$894$	−3.98746	−0.133361
$895$	3.87505	0.129529
$896$	32.4846	1.08523
$897$	−9.72653	−0.324759
$898$	−100.733	−3.36150
$899$	9.14323	0.304944
$900$	−78.1739	−2.60580
$901$	−10.5619	−0.351868
$902$	−30.7560	−1.02406
$903$	−41.0187	−1.36502
$904$	−102.340	−3.40377
$905$	8.22928	0.273551
$906$	75.5433	2.50976
$907$	19.9072	0.661007	0.330503	−	0.943805i	$-0.392781\pi$
$907$	19.9072	0.661007	0.330503	+	0.943805i	$0.392781\pi$
$908$	−88.8796	−2.94957
$909$	−31.9783	−1.06065
$910$	2.24868	0.0745429
$911$	7.29923	0.241834	0.120917	−	0.992663i	$-0.461416\pi$
$911$	7.29923	0.241834	0.120917	+	0.992663i	$0.461416\pi$
$912$	58.3012	1.93055
$913$	27.1749	0.899358
$914$	−45.9189	−1.51886
$915$	10.9572	0.362233
$916$	−104.041	−3.43762
$917$	3.04470	0.100545
$918$	12.3373	0.407191
$919$	−50.9480	−1.68062	−0.840309	−	0.542107i	$-0.817627\pi$
$919$	−50.9480	−1.68062	−0.840309	+	0.542107i	$0.817627\pi$
$920$	9.69323	0.319576
$921$	−81.5598	−2.68749
$922$	−4.40664	−0.145125
$923$	15.2993	0.503583
$924$	−71.0216	−2.33644
$925$	−33.3857	−1.09772
$926$	−53.0101	−1.74202
$927$	−29.4327	−0.966698
$928$	−3.86854	−0.126991
$929$	−8.99158	−0.295004	−0.147502	−	0.989062i	$-0.547123\pi$
$929$	−8.99158	−0.295004	−0.147502	+	0.989062i	$0.547123\pi$
$930$	16.8885	0.553795
$931$	13.8828	0.454990
$932$	26.8954	0.880988
$933$	−74.7743	−2.44800
$934$	14.7224	0.481733
$935$	3.40825	0.111462
$936$	21.4692	0.701742
$937$	46.2615	1.51130	0.755649	−	0.654977i	$-0.227322\pi$
$937$	46.2615	1.51130	0.755649	+	0.654977i	$0.227322\pi$
$938$	−59.5660	−1.94490
$939$	36.6767	1.19690
$940$	−1.88200	−0.0613841
$941$	5.29816	0.172715	0.0863575	−	0.996264i	$-0.472477\pi$
$941$	5.29816	0.172715	0.0863575	+	0.996264i	$0.472477\pi$
$942$	−8.48755	−0.276539
$943$	−13.6122	−0.443275
$944$	−30.9365	−1.00690
$945$	−2.07580	−0.0675258
$946$	−68.6222	−2.23110
$947$	−4.05079	−0.131633	−0.0658166	−	0.997832i	$-0.520965\pi$
$947$	−4.05079	−0.131633	−0.0658166	+	0.997832i	$0.520965\pi$
$948$	187.895	6.10255
$949$	−5.39973	−0.175283
$950$	−49.3425	−1.60088
$951$	−42.3275	−1.37256
$952$	−22.7208	−0.736386
$953$	46.2710	1.49886	0.749432	−	0.662081i	$-0.230327\pi$
$953$	46.2710	1.49886	0.749432	+	0.662081i	$0.230327\pi$
$954$	47.5387	1.53912
$955$	0.796146	0.0257627
$956$	57.4597	1.85838
$957$	−14.7301	−0.476158
$958$	−11.5149	−0.372031
$959$	−31.9241	−1.03088
$960$	6.14546	0.198344
$961$	−1.08294	−0.0349335
$962$	17.4295	0.561948
$963$	−1.95304	−0.0629357
$964$	−20.9834	−0.675831
$965$	−9.33646	−0.300551
$966$	−46.3310	−1.49068
$967$	24.7862	0.797069	0.398535	−	0.917153i	$-0.369519\pi$
$967$	24.7862	0.797069	0.398535	+	0.917153i	$0.369519\pi$
$968$	−1.60353	−0.0515393
$969$	23.3381	0.749728
$970$	−1.08527	−0.0348459
$971$	36.7196	1.17839	0.589194	−	0.807991i	$-0.299445\pi$
$971$	36.7196	1.17839	0.589194	+	0.807991i	$0.299445\pi$
$972$	91.0740	2.92120
$973$	−26.4038	−0.846466
$974$	7.54249	0.241677
$975$	−12.5284	−0.401229
$976$	−47.5060	−1.52063
$977$	9.25290	0.296027	0.148013	−	0.988985i	$-0.452712\pi$
$977$	9.25290	0.296027	0.148013	+	0.988985i	$0.452712\pi$
$978$	−118.296	−3.78268
$979$	22.8933	0.731672
$980$	−6.67775	−0.213313
$981$	−55.7185	−1.77896
$982$	−33.8234	−1.07935
$983$	−26.5832	−0.847873	−0.423937	−	0.905692i	$-0.639352\pi$
$983$	−26.5832	−0.847873	−0.423937	+	0.905692i	$0.639352\pi$
$984$	53.2904	1.69883
$985$	4.93893	0.157367
$986$	−8.95797	−0.285280
$987$	4.73210	0.150624
$988$	17.4768	0.556012
$989$	−30.3714	−0.965753
$990$	−15.3404	−0.487550
$991$	25.4981	0.809975	0.404987	−	0.914322i	$-0.367276\pi$
$991$	25.4981	0.809975	0.404987	+	0.914322i	$0.367276\pi$
$992$	−12.6580	−0.401893
$993$	37.6441	1.19460
$994$	72.8763	2.31149
$995$	−5.94008	−0.188313
$996$	−89.5068	−2.83613
$997$	−37.4032	−1.18457	−0.592285	−	0.805728i	$-0.701774\pi$
$997$	−37.4032	−1.18457	−0.592285	+	0.805728i	$0.701774\pi$
$998$	57.2331	1.81168
$999$	−16.0895	−0.509049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.10	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.10	✓	140	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)

\(f(q)\)	\(=\)	\(q-2.49397 q^{2} -2.62257 q^{3} +4.21989 q^{4} +0.472078 q^{5} +6.54061 q^{6} +1.90995 q^{7} -5.53635 q^{8} +3.87786 q^{9} +O(q^{10})\)	\(q-2.49397 q^{2} -2.62257 q^{3} +4.21989 q^{4} +0.472078 q^{5} +6.54061 q^{6} +1.90995 q^{7} -5.53635 q^{8} +3.87786 q^{9} -1.17735 q^{10} +3.36001 q^{11} -11.0670 q^{12} -1.00000 q^{13} -4.76337 q^{14} -1.23805 q^{15} +5.36772 q^{16} +2.14871 q^{17} -9.67126 q^{18} -4.14154 q^{19} +1.99212 q^{20} -5.00898 q^{21} -8.37976 q^{22} -3.70878 q^{23} +14.5195 q^{24} -4.77714 q^{25} +2.49397 q^{26} -2.30224 q^{27} +8.05979 q^{28} +1.67163 q^{29} +3.08767 q^{30} +5.46965 q^{31} -2.31423 q^{32} -8.81184 q^{33} -5.35882 q^{34} +0.901645 q^{35} +16.3641 q^{36} +6.98863 q^{37} +10.3289 q^{38} +2.62257 q^{39} -2.61359 q^{40} +3.67027 q^{41} +12.4922 q^{42} +8.18904 q^{43} +14.1789 q^{44} +1.83065 q^{45} +9.24959 q^{46} -0.944725 q^{47} -14.0772 q^{48} -3.35208 q^{49} +11.9141 q^{50} -5.63513 q^{51} -4.21989 q^{52} -4.91546 q^{53} +5.74172 q^{54} +1.58618 q^{55} -10.5742 q^{56} +10.8615 q^{57} -4.16900 q^{58} -5.76343 q^{59} -5.22446 q^{60} -8.85032 q^{61} -13.6411 q^{62} +7.40652 q^{63} -4.96381 q^{64} -0.472078 q^{65} +21.9765 q^{66} +12.5050 q^{67} +9.06733 q^{68} +9.72653 q^{69} -2.24868 q^{70} -15.2993 q^{71} -21.4692 q^{72} +5.39973 q^{73} -17.4295 q^{74} +12.5284 q^{75} -17.4768 q^{76} +6.41745 q^{77} -6.54061 q^{78} -16.9780 q^{79} +2.53398 q^{80} -5.59580 q^{81} -9.15356 q^{82} +8.08775 q^{83} -21.1373 q^{84} +1.01436 q^{85} -20.4232 q^{86} -4.38396 q^{87} -18.6022 q^{88} +6.81346 q^{89} -4.56559 q^{90} -1.90995 q^{91} -15.6507 q^{92} -14.3445 q^{93} +2.35612 q^{94} -1.95513 q^{95} +6.06923 q^{96} +0.921790 q^{97} +8.36000 q^{98} +13.0296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * q^99

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