LMFDB - Embedded newform 8021.2.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.47091 q^{2} +2.70447 q^{3} +4.10542 q^{4} -1.18660 q^{5} -6.68251 q^{6} -3.35758 q^{7} -5.20231 q^{8} +4.31416 q^{9} +O(q^{10})$	\(q-2.47091 q^{2} +2.70447 q^{3} +4.10542 q^{4} -1.18660 q^{5} -6.68251 q^{6} -3.35758 q^{7} -5.20231 q^{8} +4.31416 q^{9} +2.93198 q^{10} -0.397844 q^{11} +11.1030 q^{12} -1.00000 q^{13} +8.29629 q^{14} -3.20911 q^{15} +4.64362 q^{16} +1.58904 q^{17} -10.6599 q^{18} +3.65161 q^{19} -4.87147 q^{20} -9.08047 q^{21} +0.983039 q^{22} -3.64860 q^{23} -14.0695 q^{24} -3.59199 q^{25} +2.47091 q^{26} +3.55409 q^{27} -13.7843 q^{28} +6.13080 q^{29} +7.92944 q^{30} +1.02999 q^{31} -1.06938 q^{32} -1.07596 q^{33} -3.92639 q^{34} +3.98409 q^{35} +17.7114 q^{36} +1.95918 q^{37} -9.02281 q^{38} -2.70447 q^{39} +6.17304 q^{40} -9.17373 q^{41} +22.4371 q^{42} +9.66577 q^{43} -1.63332 q^{44} -5.11916 q^{45} +9.01538 q^{46} +3.69308 q^{47} +12.5585 q^{48} +4.27333 q^{49} +8.87550 q^{50} +4.29752 q^{51} -4.10542 q^{52} +8.76086 q^{53} -8.78186 q^{54} +0.472081 q^{55} +17.4672 q^{56} +9.87566 q^{57} -15.1487 q^{58} -1.33299 q^{59} -13.1748 q^{60} -11.1078 q^{61} -2.54502 q^{62} -14.4851 q^{63} -6.64490 q^{64} +1.18660 q^{65} +2.65860 q^{66} +1.99570 q^{67} +6.52369 q^{68} -9.86753 q^{69} -9.84434 q^{70} +5.04421 q^{71} -22.4436 q^{72} -7.01703 q^{73} -4.84096 q^{74} -9.71443 q^{75} +14.9914 q^{76} +1.33579 q^{77} +6.68251 q^{78} +13.4380 q^{79} -5.51011 q^{80} -3.33053 q^{81} +22.6675 q^{82} -9.73127 q^{83} -37.2791 q^{84} -1.88555 q^{85} -23.8833 q^{86} +16.5806 q^{87} +2.06971 q^{88} -11.2978 q^{89} +12.6490 q^{90} +3.35758 q^{91} -14.9790 q^{92} +2.78557 q^{93} -9.12529 q^{94} -4.33298 q^{95} -2.89210 q^{96} -15.5059 q^{97} -10.5590 q^{98} -1.71636 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.47091	−1.74720	−0.873600	−	0.486644i	$-0.838221\pi$
$2$	−2.47091	−1.74720	−0.873600	+	0.486644i	$0.838221\pi$
$3$	2.70447	1.56143	0.780713	−	0.624890i	$-0.214856\pi$
$3$	2.70447	1.56143	0.780713	+	0.624890i	$0.214856\pi$
$4$	4.10542	2.05271
$5$	−1.18660	−0.530662	−0.265331	−	0.964157i	$-0.585481\pi$
$5$	−1.18660	−0.530662	−0.265331	+	0.964157i	$0.585481\pi$
$6$	−6.68251	−2.72812
$7$	−3.35758	−1.26905	−0.634523	−	0.772904i	$-0.718803\pi$
$7$	−3.35758	−1.26905	−0.634523	+	0.772904i	$0.718803\pi$
$8$	−5.20231	−1.83929
$9$	4.31416	1.43805
$10$	2.93198	0.927173
$11$	−0.397844	−0.119955	−0.0599773	−	0.998200i	$-0.519103\pi$
$11$	−0.397844	−0.119955	−0.0599773	+	0.998200i	$0.519103\pi$
$12$	11.1030	3.20515
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	8.29629	2.21728
$15$	−3.20911	−0.828589
$16$	4.64362	1.16091
$17$	1.58904	0.385400	0.192700	−	0.981258i	$-0.438276\pi$
$17$	1.58904	0.385400	0.192700	+	0.981258i	$0.438276\pi$
$18$	−10.6599	−2.51256
$19$	3.65161	0.837736	0.418868	−	0.908047i	$-0.362427\pi$
$19$	3.65161	0.837736	0.418868	+	0.908047i	$0.362427\pi$
$20$	−4.87147	−1.08929
$21$	−9.08047	−1.98152
$22$	0.983039	0.209585
$23$	−3.64860	−0.760786	−0.380393	−	0.924825i	$-0.624211\pi$
$23$	−3.64860	−0.760786	−0.380393	+	0.924825i	$0.624211\pi$
$24$	−14.0695	−2.87192
$25$	−3.59199	−0.718398
$26$	2.47091	0.484586
$27$	3.55409	0.683986
$28$	−13.7843	−2.60498
$29$	6.13080	1.13846	0.569230	−	0.822178i	$-0.307241\pi$
$29$	6.13080	1.13846	0.569230	+	0.822178i	$0.307241\pi$
$30$	7.92944	1.44771
$31$	1.02999	0.184992	0.0924958	−	0.995713i	$-0.470516\pi$
$31$	1.02999	0.184992	0.0924958	+	0.995713i	$0.470516\pi$
$32$	−1.06938	−0.189041
$33$	−1.07596	−0.187300
$34$	−3.92639	−0.673371
$35$	3.98409	0.673434
$36$	17.7114	2.95190
$37$	1.95918	0.322087	0.161043	−	0.986947i	$-0.448514\pi$
$37$	1.95918	0.322087	0.161043	+	0.986947i	$0.448514\pi$
$38$	−9.02281	−1.46369
$39$	−2.70447	−0.433062
$40$	6.17304	0.976043
$41$	−9.17373	−1.43270	−0.716348	−	0.697743i	$-0.754188\pi$
$41$	−9.17373	−1.43270	−0.716348	+	0.697743i	$0.754188\pi$
$42$	22.4371	3.46211
$43$	9.66577	1.47402	0.737008	−	0.675884i	$-0.236238\pi$
$43$	9.66577	1.47402	0.737008	+	0.675884i	$0.236238\pi$
$44$	−1.63332	−0.246232
$45$	−5.11916	−0.763119
$46$	9.01538	1.32925
$47$	3.69308	0.538692	0.269346	−	0.963044i	$-0.413193\pi$
$47$	3.69308	0.538692	0.269346	+	0.963044i	$0.413193\pi$
$48$	12.5585	1.81267
$49$	4.27333	0.610475
$50$	8.87550	1.25519
$51$	4.29752	0.601774
$52$	−4.10542	−0.569319
$53$	8.76086	1.20340	0.601699	−	0.798723i	$-0.294491\pi$
$53$	8.76086	1.20340	0.601699	+	0.798723i	$0.294491\pi$
$54$	−8.78186	−1.19506
$55$	0.472081	0.0636553
$56$	17.4672	2.33415
$57$	9.87566	1.30806
$58$	−15.1487	−1.98912
$59$	−1.33299	−0.173541	−0.0867704	−	0.996228i	$-0.527655\pi$
$59$	−1.33299	−0.173541	−0.0867704	+	0.996228i	$0.527655\pi$
$60$	−13.1748	−1.70085
$61$	−11.1078	−1.42221	−0.711106	−	0.703085i	$-0.751806\pi$
$61$	−11.1078	−1.42221	−0.711106	+	0.703085i	$0.751806\pi$
$62$	−2.54502	−0.323217
$63$	−14.4851	−1.82495
$64$	−6.64490	−0.830613
$65$	1.18660	0.147179
$66$	2.65860	0.327251
$67$	1.99570	0.243813	0.121907	−	0.992542i	$-0.461099\pi$
$67$	1.99570	0.243813	0.121907	+	0.992542i	$0.461099\pi$
$68$	6.52369	0.791114
$69$	−9.86753	−1.18791
$70$	−9.84434	−1.17662
$71$	5.04421	0.598637	0.299319	−	0.954153i	$-0.403241\pi$
$71$	5.04421	0.598637	0.299319	+	0.954153i	$0.403241\pi$
$72$	−22.4436	−2.64500
$73$	−7.01703	−0.821281	−0.410641	−	0.911797i	$-0.634695\pi$
$73$	−7.01703	−0.821281	−0.410641	+	0.911797i	$0.634695\pi$
$74$	−4.84096	−0.562750
$75$	−9.71443	−1.12173
$76$	14.9914	1.71963
$77$	1.33579	0.152228
$78$	6.68251	0.756646
$79$	13.4380	1.51189	0.755944	−	0.654636i	$-0.227178\pi$
$79$	13.4380	1.51189	0.755944	+	0.654636i	$0.227178\pi$
$80$	−5.51011	−0.616049
$81$	−3.33053	−0.370059
$82$	22.6675	2.50321
$83$	−9.73127	−1.06815	−0.534073	−	0.845438i	$-0.679339\pi$
$83$	−9.73127	−1.06815	−0.534073	+	0.845438i	$0.679339\pi$
$84$	−37.2791	−4.06749
$85$	−1.88555	−0.204517
$86$	−23.8833	−2.57540
$87$	16.5806	1.77762
$88$	2.06971	0.220632
$89$	−11.2978	−1.19756	−0.598782	−	0.800912i	$-0.704349\pi$
$89$	−11.2978	−1.19756	−0.598782	+	0.800912i	$0.704349\pi$
$90$	12.6490	1.33332
$91$	3.35758	0.351970
$92$	−14.9790	−1.56167
$93$	2.78557	0.288851
$94$	−9.12529	−0.941202
$95$	−4.33298	−0.444555
$96$	−2.89210	−0.295174
$97$	−15.5059	−1.57439	−0.787193	−	0.616707i	$-0.788467\pi$
$97$	−15.5059	−1.57439	−0.787193	+	0.616707i	$0.788467\pi$
$98$	−10.5590	−1.06662
$99$	−1.71636	−0.172501
$100$	−14.7466	−1.47466
$101$	14.1519	1.40816	0.704081	−	0.710119i	$-0.251359\pi$
$101$	14.1519	1.40816	0.704081	+	0.710119i	$0.251359\pi$
$102$	−10.6188	−1.05142
$103$	11.7306	1.15585	0.577925	−	0.816090i	$-0.303863\pi$
$103$	11.7306	1.15585	0.577925	+	0.816090i	$0.303863\pi$
$104$	5.20231	0.510128
$105$	10.7748	1.05152
$106$	−21.6473	−2.10258
$107$	−5.73692	−0.554609	−0.277304	−	0.960782i	$-0.589441\pi$
$107$	−5.73692	−0.554609	−0.277304	+	0.960782i	$0.589441\pi$
$108$	14.5910	1.40402
$109$	−18.5302	−1.77487	−0.887436	−	0.460931i	$-0.847516\pi$
$109$	−18.5302	−1.77487	−0.887436	+	0.460931i	$0.847516\pi$
$110$	−1.16647	−0.111219
$111$	5.29853	0.502914
$112$	−15.5913	−1.47324
$113$	−3.35374	−0.315493	−0.157747	−	0.987480i	$-0.550423\pi$
$113$	−3.35374	−0.315493	−0.157747	+	0.987480i	$0.550423\pi$
$114$	−24.4019	−2.28545
$115$	4.32942	0.403720
$116$	25.1695	2.33693
$117$	−4.31416	−0.398844
$118$	3.29371	0.303211
$119$	−5.33534	−0.489090
$120$	16.6948	1.52402
$121$	−10.8417	−0.985611
$122$	27.4465	2.48489
$123$	−24.8101	−2.23705
$124$	4.22854	0.379734
$125$	10.1952	0.911888
$126$	35.7915	3.18856
$127$	−2.13766	−0.189686	−0.0948432	−	0.995492i	$-0.530235\pi$
$127$	−2.13766	−0.189686	−0.0948432	+	0.995492i	$0.530235\pi$
$128$	18.5577	1.64029
$129$	26.1408	2.30157
$130$	−2.93198	−0.257151
$131$	13.6661	1.19402	0.597008	−	0.802235i	$-0.296356\pi$
$131$	13.6661	1.19402	0.597008	+	0.802235i	$0.296356\pi$
$132$	−4.41726	−0.384473
$133$	−12.2606	−1.06313
$134$	−4.93120	−0.425991
$135$	−4.21727	−0.362965
$136$	−8.26670	−0.708864
$137$	13.2347	1.13071	0.565357	−	0.824847i	$-0.308739\pi$
$137$	13.2347	1.13071	0.565357	+	0.824847i	$0.308739\pi$
$138$	24.3818	2.07552
$139$	−0.671381	−0.0569458	−0.0284729	−	0.999595i	$-0.509064\pi$
$139$	−0.671381	−0.0569458	−0.0284729	+	0.999595i	$0.509064\pi$
$140$	16.3564	1.38236
$141$	9.98783	0.841127
$142$	−12.4638	−1.04594
$143$	0.397844	0.0332694
$144$	20.0333	1.66944
$145$	−7.27478	−0.604138
$146$	17.3385	1.43494
$147$	11.5571	0.953212
$148$	8.04324	0.661150
$149$	−22.6028	−1.85170	−0.925849	−	0.377895i	$-0.876648\pi$
$149$	−22.6028	−1.85170	−0.925849	+	0.377895i	$0.876648\pi$
$150$	24.0035	1.95988
$151$	16.3177	1.32792	0.663958	−	0.747770i	$-0.268875\pi$
$151$	16.3177	1.32792	0.663958	+	0.747770i	$0.268875\pi$
$152$	−18.9968	−1.54084
$153$	6.85539	0.554225
$154$	−3.30063	−0.265972
$155$	−1.22218	−0.0981680
$156$	−11.1030	−0.888950
$157$	5.46967	0.436527	0.218264	−	0.975890i	$-0.429961\pi$
$157$	5.46967	0.436527	0.218264	+	0.975890i	$0.429961\pi$
$158$	−33.2041	−2.64157
$159$	23.6935	1.87902
$160$	1.26892	0.100317
$161$	12.2505	0.965472
$162$	8.22945	0.646566
$163$	−12.3159	−0.964656	−0.482328	−	0.875991i	$-0.660209\pi$
$163$	−12.3159	−0.964656	−0.482328	+	0.875991i	$0.660209\pi$
$164$	−37.6620	−2.94091
$165$	1.27673	0.0993931
$166$	24.0451	1.86627
$167$	0.309704	0.0239656	0.0119828	−	0.999928i	$-0.496186\pi$
$167$	0.309704	0.0239656	0.0119828	+	0.999928i	$0.496186\pi$
$168$	47.2394	3.64460
$169$	1.00000	0.0769231
$170$	4.65904	0.357332
$171$	15.7536	1.20471
$172$	39.6820	3.02573
$173$	−8.57255	−0.651759	−0.325879	−	0.945411i	$-0.605660\pi$
$173$	−8.57255	−0.651759	−0.325879	+	0.945411i	$0.605660\pi$
$174$	−40.9691	−3.10586
$175$	12.0604	0.911679
$176$	−1.84744	−0.139256
$177$	−3.60504	−0.270971
$178$	27.9159	2.09239
$179$	−10.6446	−0.795618	−0.397809	−	0.917468i	$-0.630229\pi$
$179$	−10.6446	−0.795618	−0.397809	+	0.917468i	$0.630229\pi$
$180$	−21.0163	−1.56646
$181$	−20.7326	−1.54104	−0.770520	−	0.637416i	$-0.780003\pi$
$181$	−20.7326	−1.54104	−0.770520	+	0.637416i	$0.780003\pi$
$182$	−8.29629	−0.614962
$183$	−30.0408	−2.22068
$184$	18.9812	1.39931
$185$	−2.32475	−0.170919
$186$	−6.88292	−0.504680
$187$	−0.632193	−0.0462305
$188$	15.1617	1.10578
$189$	−11.9331	−0.868009
$190$	10.7064	0.776726
$191$	1.69353	0.122540	0.0612698	−	0.998121i	$-0.480485\pi$
$191$	1.69353	0.122540	0.0612698	+	0.998121i	$0.480485\pi$
$192$	−17.9709	−1.29694
$193$	3.19666	0.230100	0.115050	−	0.993360i	$-0.463297\pi$
$193$	3.19666	0.230100	0.115050	+	0.993360i	$0.463297\pi$
$194$	38.3138	2.75077
$195$	3.20911	0.229809
$196$	17.5438	1.25313
$197$	12.2652	0.873858	0.436929	−	0.899496i	$-0.356066\pi$
$197$	12.2652	0.873858	0.436929	+	0.899496i	$0.356066\pi$
$198$	4.24099	0.301394
$199$	−5.42921	−0.384867	−0.192433	−	0.981310i	$-0.561638\pi$
$199$	−5.42921	−0.384867	−0.192433	+	0.981310i	$0.561638\pi$
$200$	18.6866	1.32134
$201$	5.39730	0.380697
$202$	−34.9680	−2.46034
$203$	−20.5846	−1.44476
$204$	17.6431	1.23527
$205$	10.8855	0.760277
$206$	−28.9853	−2.01950
$207$	−15.7406	−1.09405
$208$	−4.64362	−0.321977
$209$	−1.45277	−0.100490
$210$	−26.6237	−1.83721
$211$	9.02952	0.621618	0.310809	−	0.950472i	$-0.399400\pi$
$211$	9.02952	0.621618	0.310809	+	0.950472i	$0.399400\pi$
$212$	35.9670	2.47022
$213$	13.6419	0.934728
$214$	14.1754	0.969012
$215$	−11.4694	−0.782205
$216$	−18.4895	−1.25805
$217$	−3.45827	−0.234763
$218$	45.7866	3.10106
$219$	−18.9773	−1.28237
$220$	1.93809	0.130666
$221$	−1.58904	−0.106891
$222$	−13.0922	−0.878692
$223$	−7.85466	−0.525987	−0.262993	−	0.964798i	$-0.584710\pi$
$223$	−7.85466	−0.525987	−0.262993	+	0.964798i	$0.584710\pi$
$224$	3.59052	0.239902
$225$	−15.4964	−1.03309
$226$	8.28680	0.551230
$227$	21.3537	1.41729	0.708646	−	0.705564i	$-0.249306\pi$
$227$	21.3537	1.41729	0.708646	+	0.705564i	$0.249306\pi$
$228$	40.5437	2.68507
$229$	−19.5706	−1.29326	−0.646632	−	0.762802i	$-0.723823\pi$
$229$	−19.5706	−1.29326	−0.646632	+	0.762802i	$0.723823\pi$
$230$	−10.6976	−0.705380
$231$	3.61261	0.237692
$232$	−31.8943	−2.09396
$233$	−16.4314	−1.07646	−0.538228	−	0.842799i	$-0.680906\pi$
$233$	−16.4314	−1.07646	−0.538228	+	0.842799i	$0.680906\pi$
$234$	10.6599	0.696860
$235$	−4.38220	−0.285863
$236$	−5.47249	−0.356229
$237$	36.3426	2.36070
$238$	13.1832	0.854538
$239$	17.1175	1.10724	0.553619	−	0.832770i	$-0.313247\pi$
$239$	17.1175	1.10724	0.553619	+	0.832770i	$0.313247\pi$
$240$	−14.9019	−0.961914
$241$	5.35024	0.344639	0.172320	−	0.985041i	$-0.444874\pi$
$241$	5.35024	0.344639	0.172320	+	0.985041i	$0.444874\pi$
$242$	26.7890	1.72206
$243$	−19.6696	−1.26180
$244$	−45.6023	−2.91939
$245$	−5.07071	−0.323956
$246$	61.3036	3.90857
$247$	−3.65161	−0.232346
$248$	−5.35832	−0.340254
$249$	−26.3179	−1.66783
$250$	−25.1915	−1.59325
$251$	−3.44006	−0.217135	−0.108567	−	0.994089i	$-0.534626\pi$
$251$	−3.44006	−0.217135	−0.108567	+	0.994089i	$0.534626\pi$
$252$	−59.4675	−3.74610
$253$	1.45158	0.0912598
$254$	5.28197	0.331420
$255$	−5.09942	−0.319338
$256$	−32.5648	−2.03530
$257$	11.7371	0.732141	0.366070	−	0.930587i	$-0.380703\pi$
$257$	11.7371	0.732141	0.366070	+	0.930587i	$0.380703\pi$
$258$	−64.5917	−4.02130
$259$	−6.57809	−0.408742
$260$	4.87147	0.302116
$261$	26.4492	1.63717
$262$	−33.7679	−2.08619
$263$	−6.01350	−0.370808	−0.185404	−	0.982662i	$-0.559359\pi$
$263$	−6.01350	−0.370808	−0.185404	+	0.982662i	$0.559359\pi$
$264$	5.59747	0.344500
$265$	−10.3956	−0.638597
$266$	30.2948	1.85749
$267$	−30.5546	−1.86991
$268$	8.19318	0.500478
$269$	−19.5663	−1.19298	−0.596488	−	0.802622i	$-0.703438\pi$
$269$	−19.5663	−1.19298	−0.596488	+	0.802622i	$0.703438\pi$
$270$	10.4205	0.634173
$271$	−21.7750	−1.32274	−0.661368	−	0.750061i	$-0.730024\pi$
$271$	−21.7750	−1.32274	−0.661368	+	0.750061i	$0.730024\pi$
$272$	7.37893	0.447413
$273$	9.08047	0.549575
$274$	−32.7017	−1.97558
$275$	1.42905	0.0861751
$276$	−40.5103	−2.43844
$277$	−23.2306	−1.39579	−0.697896	−	0.716199i	$-0.745880\pi$
$277$	−23.2306	−1.39579	−0.697896	+	0.716199i	$0.745880\pi$
$278$	1.65893	0.0994957
$279$	4.44353	0.266027
$280$	−20.7265	−1.23864
$281$	−18.6376	−1.11182	−0.555912	−	0.831241i	$-0.687631\pi$
$281$	−18.6376	−1.11182	−0.555912	+	0.831241i	$0.687631\pi$
$282$	−24.6791	−1.46962
$283$	−18.1653	−1.07982	−0.539908	−	0.841724i	$-0.681541\pi$
$283$	−18.1653	−1.07982	−0.539908	+	0.841724i	$0.681541\pi$
$284$	20.7086	1.22883
$285$	−11.7184	−0.694139
$286$	−0.983039	−0.0581283
$287$	30.8015	1.81816
$288$	−4.61347	−0.271851
$289$	−14.4749	−0.851467
$290$	17.9754	1.05555
$291$	−41.9353	−2.45829
$292$	−28.8078	−1.68585
$293$	−24.5943	−1.43681	−0.718406	−	0.695624i	$-0.755128\pi$
$293$	−24.5943	−1.43681	−0.718406	+	0.695624i	$0.755128\pi$
$294$	−28.5566	−1.66545
$295$	1.58172	0.0920915
$296$	−10.1922	−0.592412
$297$	−1.41398	−0.0820472
$298$	55.8497	3.23529
$299$	3.64860	0.211004
$300$	−39.8818	−2.30258
$301$	−32.4536	−1.87059
$302$	−40.3197	−2.32014
$303$	38.2733	2.19874
$304$	16.9567	0.972533
$305$	13.1805	0.754714
$306$	−16.9391	−0.968342
$307$	−6.13119	−0.349926	−0.174963	−	0.984575i	$-0.555981\pi$
$307$	−6.13119	−0.349926	−0.174963	+	0.984575i	$0.555981\pi$
$308$	5.48399	0.312479
$309$	31.7250	1.80477
$310$	3.01991	0.171519
$311$	−21.0541	−1.19387	−0.596933	−	0.802291i	$-0.703614\pi$
$311$	−21.0541	−1.19387	−0.596933	+	0.802291i	$0.703614\pi$
$312$	14.0695	0.796528
$313$	−26.5730	−1.50200	−0.750999	−	0.660304i	$-0.770428\pi$
$313$	−26.5730	−1.50200	−0.750999	+	0.660304i	$0.770428\pi$
$314$	−13.5151	−0.762701
$315$	17.1880	0.968433
$316$	55.1684	3.10347
$317$	10.4578	0.587371	0.293685	−	0.955902i	$-0.405118\pi$
$317$	10.4578	0.587371	0.293685	+	0.955902i	$0.405118\pi$
$318$	−58.5446	−3.28302
$319$	−2.43910	−0.136564
$320$	7.88482	0.440775
$321$	−15.5153	−0.865980
$322$	−30.2698	−1.68687
$323$	5.80257	0.322864
$324$	−13.6732	−0.759623
$325$	3.59199	0.199248
$326$	30.4315	1.68545
$327$	−50.1144	−2.77133
$328$	47.7246	2.63515
$329$	−12.3998	−0.683624
$330$	−3.15468	−0.173660
$331$	0.264430	0.0145344	0.00726720	−	0.999974i	$-0.497687\pi$
$331$	0.264430	0.0145344	0.00726720	+	0.999974i	$0.497687\pi$
$332$	−39.9510	−2.19259
$333$	8.45219	0.463177
$334$	−0.765252	−0.0418727
$335$	−2.36809	−0.129382
$336$	−42.1663	−2.30036
$337$	−20.3606	−1.10911	−0.554556	−	0.832146i	$-0.687112\pi$
$337$	−20.3606	−1.10911	−0.554556	+	0.832146i	$0.687112\pi$
$338$	−2.47091	−0.134400
$339$	−9.07008	−0.492619
$340$	−7.74099	−0.419814
$341$	−0.409775	−0.0221906
$342$	−38.9258	−2.10487
$343$	9.15501	0.494324
$344$	−50.2843	−2.71115
$345$	11.7088	0.630379
$346$	21.1820	1.13875
$347$	18.5107	0.993706	0.496853	−	0.867835i	$-0.334489\pi$
$347$	18.5107	0.993706	0.496853	+	0.867835i	$0.334489\pi$
$348$	68.0701	3.64894
$349$	1.92534	0.103061	0.0515305	−	0.998671i	$-0.483590\pi$
$349$	1.92534	0.103061	0.0515305	+	0.998671i	$0.483590\pi$
$350$	−29.8002	−1.59289
$351$	−3.55409	−0.189704
$352$	0.425446	0.0226764
$353$	12.0838	0.643157	0.321579	−	0.946883i	$-0.395787\pi$
$353$	12.0838	0.643157	0.321579	+	0.946883i	$0.395787\pi$
$354$	8.90774	0.473441
$355$	−5.98543	−0.317674
$356$	−46.3822	−2.45825
$357$	−14.4293	−0.763678
$358$	26.3020	1.39010
$359$	7.70645	0.406731	0.203366	−	0.979103i	$-0.434812\pi$
$359$	7.70645	0.406731	0.203366	+	0.979103i	$0.434812\pi$
$360$	26.6315	1.40360
$361$	−5.66576	−0.298198
$362$	51.2284	2.69251
$363$	−29.3211	−1.53896
$364$	13.7843	0.722492
$365$	8.32638	0.435823
$366$	74.2283	3.87997
$367$	−20.3216	−1.06078	−0.530391	−	0.847753i	$-0.677955\pi$
$367$	−20.3216	−1.06078	−0.530391	+	0.847753i	$0.677955\pi$
$368$	−16.9427	−0.883201
$369$	−39.5769	−2.06029
$370$	5.74426	0.298630
$371$	−29.4153	−1.52717
$372$	11.4359	0.592926
$373$	19.4787	1.00857	0.504286	−	0.863537i	$-0.331756\pi$
$373$	19.4787	1.00857	0.504286	+	0.863537i	$0.331756\pi$
$374$	1.56209	0.0807739
$375$	27.5727	1.42385
$376$	−19.2126	−0.990812
$377$	−6.13080	−0.315752
$378$	29.4858	1.51659
$379$	−34.4835	−1.77130	−0.885649	−	0.464356i	$-0.846286\pi$
$379$	−34.4835	−1.77130	−0.885649	+	0.464356i	$0.846286\pi$
$380$	−17.7887	−0.912542
$381$	−5.78123	−0.296181
$382$	−4.18457	−0.214101
$383$	10.8996	0.556942	0.278471	−	0.960445i	$-0.410172\pi$
$383$	10.8996	0.556942	0.278471	+	0.960445i	$0.410172\pi$
$384$	50.1889	2.56119
$385$	−1.58505	−0.0807815
$386$	−7.89867	−0.402032
$387$	41.6997	2.11971
$388$	−63.6582	−3.23176
$389$	16.7767	0.850612	0.425306	−	0.905050i	$-0.360167\pi$
$389$	16.7767	0.850612	0.425306	+	0.905050i	$0.360167\pi$
$390$	−7.92944	−0.401523
$391$	−5.79779	−0.293207
$392$	−22.2312	−1.12284
$393$	36.9597	1.86437
$394$	−30.3062	−1.52681
$395$	−15.9454	−0.802302
$396$	−7.04639	−0.354094
$397$	20.5242	1.03008	0.515040	−	0.857166i	$-0.327777\pi$
$397$	20.5242	1.03008	0.515040	+	0.857166i	$0.327777\pi$
$398$	13.4151	0.672439
$399$	−33.1583	−1.65999
$400$	−16.6798	−0.833992
$401$	4.05740	0.202617	0.101308	−	0.994855i	$-0.467697\pi$
$401$	4.05740	0.202617	0.101308	+	0.994855i	$0.467697\pi$
$402$	−13.3363	−0.665153
$403$	−1.02999	−0.0513074
$404$	58.0993	2.89055
$405$	3.95199	0.196376
$406$	50.8629	2.52428
$407$	−0.779447	−0.0386358
$408$	−22.3570	−1.10684
$409$	12.9242	0.639061	0.319531	−	0.947576i	$-0.396475\pi$
$409$	12.9242	0.639061	0.319531	+	0.947576i	$0.396475\pi$
$410$	−26.8972	−1.32836
$411$	35.7927	1.76553
$412$	48.1590	2.37262
$413$	4.47562	0.220231
$414$	38.8938	1.91152
$415$	11.5471	0.566824
$416$	1.06938	0.0524306
$417$	−1.81573	−0.0889167
$418$	3.58967	0.175577
$419$	−8.11277	−0.396335	−0.198167	−	0.980168i	$-0.563499\pi$
$419$	−8.11277	−0.396335	−0.198167	+	0.980168i	$0.563499\pi$
$420$	44.2353	2.15846
$421$	−29.2736	−1.42671	−0.713354	−	0.700803i	$-0.752825\pi$
$421$	−29.2736	−1.42671	−0.713354	+	0.700803i	$0.752825\pi$
$422$	−22.3112	−1.08609
$423$	15.9325	0.774666
$424$	−45.5767	−2.21340
$425$	−5.70783	−0.276871
$426$	−33.7080	−1.63316
$427$	37.2954	1.80485
$428$	−23.5524	−1.13845
$429$	1.07596	0.0519477
$430$	28.3398	1.36667
$431$	−3.04112	−0.146486	−0.0732428	−	0.997314i	$-0.523335\pi$
$431$	−3.04112	−0.146486	−0.0732428	+	0.997314i	$0.523335\pi$
$432$	16.5039	0.794043
$433$	21.0417	1.01120	0.505600	−	0.862768i	$-0.331271\pi$
$433$	21.0417	1.01120	0.505600	+	0.862768i	$0.331271\pi$
$434$	8.54509	0.410177
$435$	−19.6744	−0.943316
$436$	−76.0743	−3.64330
$437$	−13.3233	−0.637338
$438$	46.8914	2.24056
$439$	3.05218	0.145673	0.0728364	−	0.997344i	$-0.476795\pi$
$439$	3.05218	0.145673	0.0728364	+	0.997344i	$0.476795\pi$
$440$	−2.45591	−0.117081
$441$	18.4358	0.877895
$442$	3.92639	0.186760
$443$	−12.4991	−0.593851	−0.296926	−	0.954901i	$-0.595961\pi$
$443$	−12.4991	−0.593851	−0.296926	+	0.954901i	$0.595961\pi$
$444$	21.7527	1.03234
$445$	13.4059	0.635502
$446$	19.4082	0.919004
$447$	−61.1287	−2.89129
$448$	22.3108	1.05409
$449$	−19.8737	−0.937896	−0.468948	−	0.883226i	$-0.655367\pi$
$449$	−19.8737	−0.937896	−0.468948	+	0.883226i	$0.655367\pi$
$450$	38.2903	1.80502
$451$	3.64972	0.171858
$452$	−13.7685	−0.647616
$453$	44.1307	2.07344
$454$	−52.7630	−2.47629
$455$	−3.98409	−0.186777
$456$	−51.3762	−2.40591
$457$	18.4005	0.860738	0.430369	−	0.902653i	$-0.358383\pi$
$457$	18.4005	0.860738	0.430369	+	0.902653i	$0.358383\pi$
$458$	48.3574	2.25959
$459$	5.64762	0.263608
$460$	17.7741	0.828720
$461$	−9.06559	−0.422227	−0.211113	−	0.977462i	$-0.567709\pi$
$461$	−9.06559	−0.422227	−0.211113	+	0.977462i	$0.567709\pi$
$462$	−8.92646	−0.415296
$463$	7.64674	0.355374	0.177687	−	0.984087i	$-0.443139\pi$
$463$	7.64674	0.355374	0.177687	+	0.984087i	$0.443139\pi$
$464$	28.4691	1.32165
$465$	−3.30535	−0.153282
$466$	40.6006	1.88078
$467$	−21.7429	−1.00614	−0.503070	−	0.864246i	$-0.667796\pi$
$467$	−21.7429	−1.00614	−0.503070	+	0.864246i	$0.667796\pi$
$468$	−17.7114	−0.818710
$469$	−6.70071	−0.309410
$470$	10.8280	0.499460
$471$	14.7926	0.681605
$472$	6.93464	0.319193
$473$	−3.84547	−0.176815
$474$	−89.7993	−4.12462
$475$	−13.1165	−0.601828
$476$	−21.9038	−1.00396
$477$	37.7957	1.73055
$478$	−42.2958	−1.93457
$479$	−1.75633	−0.0802488	−0.0401244	−	0.999195i	$-0.512775\pi$
$479$	−1.75633	−0.0802488	−0.0401244	+	0.999195i	$0.512775\pi$
$480$	3.43176	0.156638
$481$	−1.95918	−0.0893307
$482$	−13.2200	−0.602154
$483$	33.1310	1.50751
$484$	−44.5098	−2.02317
$485$	18.3992	0.835467
$486$	48.6019	2.20463
$487$	−21.6685	−0.981892	−0.490946	−	0.871190i	$-0.663349\pi$
$487$	−21.6685	−0.981892	−0.490946	+	0.871190i	$0.663349\pi$
$488$	57.7864	2.61587
$489$	−33.3080	−1.50624
$490$	12.5293	0.566016
$491$	−24.9850	−1.12756	−0.563780	−	0.825925i	$-0.690653\pi$
$491$	−24.9850	−1.12756	−0.563780	+	0.825925i	$0.690653\pi$
$492$	−101.856	−4.59201
$493$	9.74211	0.438763
$494$	9.02281	0.405955
$495$	2.03663	0.0915397
$496$	4.78288	0.214758
$497$	−16.9363	−0.759697
$498$	65.0294	2.91404
$499$	−24.6498	−1.10348	−0.551738	−	0.834018i	$-0.686035\pi$
$499$	−24.6498	−1.10348	−0.551738	+	0.834018i	$0.686035\pi$
$500$	41.8556	1.87184
$501$	0.837585	0.0374205
$502$	8.50010	0.379378
$503$	2.90205	0.129396	0.0646981	−	0.997905i	$-0.479392\pi$
$503$	2.90205	0.129396	0.0646981	+	0.997905i	$0.479392\pi$
$504$	75.3560	3.35662
$505$	−16.7925	−0.747258
$506$	−3.58672	−0.159449
$507$	2.70447	0.120110
$508$	−8.77597	−0.389371
$509$	−28.0913	−1.24513	−0.622563	−	0.782569i	$-0.713909\pi$
$509$	−28.0913	−1.24513	−0.622563	+	0.782569i	$0.713909\pi$
$510$	12.6002	0.557948
$511$	23.5602	1.04224
$512$	43.3493	1.91579
$513$	12.9782	0.573000
$514$	−29.0014	−1.27920
$515$	−13.9195	−0.613365
$516$	107.319	4.72445
$517$	−1.46927	−0.0646185
$518$	16.2539	0.714155
$519$	−23.1842	−1.01767
$520$	−6.17304	−0.270706
$521$	2.00728	0.0879405	0.0439702	−	0.999033i	$-0.485999\pi$
$521$	2.00728	0.0879405	0.0439702	+	0.999033i	$0.485999\pi$
$522$	−65.3538	−2.86046
$523$	44.7537	1.95694	0.978471	−	0.206383i	$-0.0661693\pi$
$523$	44.7537	1.95694	0.978471	+	0.206383i	$0.0661693\pi$
$524$	56.1052	2.45097
$525$	32.6169	1.42352
$526$	14.8588	0.647876
$527$	1.63670	0.0712957
$528$	−4.99634	−0.217438
$529$	−9.68771	−0.421205
$530$	25.6867	1.11576
$531$	−5.75074	−0.249561
$532$	−50.3347	−2.18229
$533$	9.17373	0.397358
$534$	75.4977	3.26711
$535$	6.80740	0.294310
$536$	−10.3822	−0.448444
$537$	−28.7881	−1.24230
$538$	48.3466	2.08437
$539$	−1.70012	−0.0732293
$540$	−17.3137	−0.745062
$541$	−6.84492	−0.294286	−0.147143	−	0.989115i	$-0.547008\pi$
$541$	−6.84492	−0.294286	−0.147143	+	0.989115i	$0.547008\pi$
$542$	53.8041	2.31109
$543$	−56.0706	−2.40622
$544$	−1.69929	−0.0728565
$545$	21.9879	0.941857
$546$	−22.4371	−0.960217
$547$	−13.7367	−0.587339	−0.293669	−	0.955907i	$-0.594876\pi$
$547$	−13.7367	−0.587339	−0.293669	+	0.955907i	$0.594876\pi$
$548$	54.3338	2.32103
$549$	−47.9209	−2.04522
$550$	−3.53107	−0.150565
$551$	22.3873	0.953730
$552$	51.3340	2.18492
$553$	−45.1190	−1.91865
$554$	57.4008	2.43873
$555$	−6.28722	−0.266878
$556$	−2.75630	−0.116893
$557$	17.5082	0.741846	0.370923	−	0.928664i	$-0.379041\pi$
$557$	17.5082	0.741846	0.370923	+	0.928664i	$0.379041\pi$
$558$	−10.9796	−0.464803
$559$	−9.66577	−0.408819
$560$	18.5006	0.781793
$561$	−1.70975	−0.0721855
$562$	46.0518	1.94258
$563$	35.8394	1.51045	0.755226	−	0.655464i	$-0.227527\pi$
$563$	35.8394	1.51045	0.755226	+	0.655464i	$0.227527\pi$
$564$	41.0042	1.72659
$565$	3.97953	0.167420
$566$	44.8849	1.88666
$567$	11.1825	0.469621
$568$	−26.2415	−1.10107
$569$	41.0997	1.72299	0.861495	−	0.507766i	$-0.169528\pi$
$569$	41.0997	1.72299	0.861495	+	0.507766i	$0.169528\pi$
$570$	28.9552	1.21280
$571$	−24.8244	−1.03887	−0.519434	−	0.854511i	$-0.673857\pi$
$571$	−24.8244	−1.03887	−0.519434	+	0.854511i	$0.673857\pi$
$572$	1.63332	0.0682924
$573$	4.58010	0.191337
$574$	−76.1079	−3.17668
$575$	13.1057	0.546547
$576$	−28.6671	−1.19446
$577$	−28.5731	−1.18951	−0.594756	−	0.803906i	$-0.702751\pi$
$577$	−28.5731	−1.18951	−0.594756	+	0.803906i	$0.702751\pi$
$578$	35.7663	1.48768
$579$	8.64526	0.359285
$580$	−29.8660	−1.24012
$581$	32.6735	1.35553
$582$	103.618	4.29512
$583$	−3.48546	−0.144353
$584$	36.5047	1.51058
$585$	5.11916	0.211651
$586$	60.7703	2.51040
$587$	17.6023	0.726525	0.363263	−	0.931687i	$-0.381663\pi$
$587$	17.6023	0.726525	0.363263	+	0.931687i	$0.381663\pi$
$588$	47.4467	1.95667
$589$	3.76112	0.154974
$590$	−3.90830	−0.160902
$591$	33.1708	1.36447
$592$	9.09768	0.373912
$593$	34.5433	1.41852	0.709262	−	0.704945i	$-0.249028\pi$
$593$	34.5433	1.41852	0.709262	+	0.704945i	$0.249028\pi$
$594$	3.49382	0.143353
$595$	6.33090	0.259541
$596$	−92.7941	−3.80100
$597$	−14.6831	−0.600941
$598$	−9.01538	−0.368666
$599$	−31.5988	−1.29109	−0.645547	−	0.763721i	$-0.723371\pi$
$599$	−31.5988	−1.29109	−0.645547	+	0.763721i	$0.723371\pi$
$600$	50.5374	2.06318
$601$	−33.2462	−1.35614	−0.678071	−	0.734996i	$-0.737184\pi$
$601$	−33.2462	−1.35614	−0.678071	+	0.734996i	$0.737184\pi$
$602$	80.1900	3.26830
$603$	8.60975	0.350616
$604$	66.9910	2.72583
$605$	12.8647	0.523026
$606$	−94.5700	−3.84164
$607$	6.78057	0.275215	0.137607	−	0.990487i	$-0.456059\pi$
$607$	6.78057	0.275215	0.137607	+	0.990487i	$0.456059\pi$
$608$	−3.90495	−0.158367
$609$	−55.6705	−2.25588
$610$	−32.5679	−1.31864
$611$	−3.69308	−0.149406
$612$	28.1442	1.13766
$613$	5.83058	0.235495	0.117747	−	0.993044i	$-0.462433\pi$
$613$	5.83058	0.235495	0.117747	+	0.993044i	$0.462433\pi$
$614$	15.1497	0.611390
$615$	29.4395	1.18712
$616$	−6.94921	−0.279992
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	−78.3898	−3.15330
$619$	−21.6611	−0.870635	−0.435318	−	0.900277i	$-0.643364\pi$
$619$	−21.6611	−0.870635	−0.435318	+	0.900277i	$0.643364\pi$
$620$	−5.01757	−0.201510
$621$	−12.9675	−0.520367
$622$	52.0228	2.08592
$623$	37.9332	1.51976
$624$	−12.5585	−0.502744
$625$	5.86234	0.234494
$626$	65.6597	2.62429
$627$	−3.92898	−0.156908
$628$	22.4553	0.896064
$629$	3.11322	0.124132
$630$	−42.4700	−1.69205
$631$	15.0244	0.598111	0.299055	−	0.954236i	$-0.403328\pi$
$631$	15.0244	0.598111	0.299055	+	0.954236i	$0.403328\pi$
$632$	−69.9084	−2.78081
$633$	24.4201	0.970611
$634$	−25.8404	−1.02625
$635$	2.53653	0.100659
$636$	97.2717	3.85707
$637$	−4.27333	−0.169315
$638$	6.02682	0.238604
$639$	21.7615	0.860871
$640$	−22.0205	−0.870439
$641$	−1.14360	−0.0451694	−0.0225847	−	0.999745i	$-0.507190\pi$
$641$	−1.14360	−0.0451694	−0.0225847	+	0.999745i	$0.507190\pi$
$642$	38.3370	1.51304
$643$	5.40533	0.213166	0.106583	−	0.994304i	$-0.466009\pi$
$643$	5.40533	0.213166	0.106583	+	0.994304i	$0.466009\pi$
$644$	50.2933	1.98183
$645$	−31.0186	−1.22135
$646$	−14.3377	−0.564107
$647$	−39.6935	−1.56051	−0.780257	−	0.625459i	$-0.784912\pi$
$647$	−39.6935	−1.56051	−0.780257	+	0.625459i	$0.784912\pi$
$648$	17.3264	0.680646
$649$	0.530323	0.0208170
$650$	−8.87550	−0.348126
$651$	−9.35278	−0.366565
$652$	−50.5619	−1.98016
$653$	46.5719	1.82250	0.911249	−	0.411856i	$-0.135119\pi$
$653$	46.5719	1.82250	0.911249	+	0.411856i	$0.135119\pi$
$654$	123.828	4.84207
$655$	−16.2162	−0.633619
$656$	−42.5993	−1.66322
$657$	−30.2726	−1.18104
$658$	30.6389	1.19443
$659$	44.7847	1.74456	0.872281	−	0.489004i	$-0.162640\pi$
$659$	44.7847	1.74456	0.872281	+	0.489004i	$0.162640\pi$
$660$	5.24150	0.204025
$661$	43.8441	1.70534	0.852668	−	0.522453i	$-0.174983\pi$
$661$	43.8441	1.70534	0.852668	+	0.522453i	$0.174983\pi$
$662$	−0.653385	−0.0253945
$663$	−4.29752	−0.166902
$664$	50.6251	1.96463
$665$	14.5483	0.564160
$666$	−20.8846	−0.809263
$667$	−22.3688	−0.866125
$668$	1.27146	0.0491944
$669$	−21.2427	−0.821289
$670$	5.85134	0.226057
$671$	4.41919	0.170601
$672$	9.71046	0.374589
$673$	−47.7872	−1.84206	−0.921030	−	0.389491i	$-0.872651\pi$
$673$	−47.7872	−1.84206	−0.921030	+	0.389491i	$0.872651\pi$
$674$	50.3093	1.93784
$675$	−12.7663	−0.491374
$676$	4.10542	0.157901
$677$	30.7462	1.18167	0.590836	−	0.806792i	$-0.298798\pi$
$677$	30.7462	1.18167	0.590836	+	0.806792i	$0.298798\pi$
$678$	22.4114	0.860704
$679$	52.0623	1.99797
$680$	9.80924	0.376167
$681$	57.7503	2.21300
$682$	1.01252	0.0387714
$683$	−21.0384	−0.805011	−0.402506	−	0.915418i	$-0.631861\pi$
$683$	−21.0384	−0.805011	−0.402506	+	0.915418i	$0.631861\pi$
$684$	64.6751	2.47292
$685$	−15.7042	−0.600026
$686$	−22.6213	−0.863683
$687$	−52.9282	−2.01934
$688$	44.8842	1.71119
$689$	−8.76086	−0.333762
$690$	−28.9314	−1.10140
$691$	46.3471	1.76313	0.881564	−	0.472064i	$-0.156491\pi$
$691$	46.3471	1.76313	0.881564	+	0.472064i	$0.156491\pi$
$692$	−35.1939	−1.33787
$693$	5.76282	0.218911
$694$	−45.7383	−1.73620
$695$	0.796658	0.0302190
$696$	−86.2572	−3.26957
$697$	−14.5775	−0.552161
$698$	−4.75734	−0.180068
$699$	−44.4382	−1.68081
$700$	49.5129	1.87141
$701$	4.14168	0.156429	0.0782145	−	0.996937i	$-0.475078\pi$
$701$	4.14168	0.156429	0.0782145	+	0.996937i	$0.475078\pi$
$702$	8.78186	0.331450
$703$	7.15414	0.269824
$704$	2.64364	0.0996358
$705$	−11.8515	−0.446354
$706$	−29.8581	−1.12372
$707$	−47.5160	−1.78702
$708$	−14.8002	−0.556225
$709$	−51.1256	−1.92006	−0.960031	−	0.279895i	$-0.909700\pi$
$709$	−51.1256	−1.92006	−0.960031	+	0.279895i	$0.909700\pi$
$710$	14.7895	0.555040
$711$	57.9735	2.17417
$712$	58.7746	2.20267
$713$	−3.75802	−0.140739
$714$	35.6535	1.33430
$715$	−0.472081	−0.0176548
$716$	−43.7007	−1.63317
$717$	46.2937	1.72887
$718$	−19.0420	−0.710641
$719$	−45.6058	−1.70081	−0.850405	−	0.526129i	$-0.823643\pi$
$719$	−45.6058	−1.70081	−0.850405	+	0.526129i	$0.823643\pi$
$720$	−23.7715	−0.885910
$721$	−39.3864	−1.46683
$722$	13.9996	0.521011
$723$	14.4696	0.538129
$724$	−85.1159	−3.16331
$725$	−22.0218	−0.817868
$726$	72.4499	2.68887
$727$	−15.8506	−0.587867	−0.293933	−	0.955826i	$-0.594964\pi$
$727$	−15.8506	−0.587867	−0.293933	+	0.955826i	$0.594964\pi$
$728$	−17.4672	−0.647376
$729$	−43.2042	−1.60016
$730$	−20.5738	−0.761469
$731$	15.3593	0.568086
$732$	−123.330	−4.55841
$733$	32.7681	1.21032	0.605158	−	0.796105i	$-0.293110\pi$
$733$	32.7681	1.21032	0.605158	+	0.796105i	$0.293110\pi$
$734$	50.2131	1.85340
$735$	−13.7136	−0.505834
$736$	3.90174	0.143820
$737$	−0.793977	−0.0292465
$738$	97.7911	3.59974
$739$	10.9067	0.401210	0.200605	−	0.979672i	$-0.435709\pi$
$739$	10.9067	0.401210	0.200605	+	0.979672i	$0.435709\pi$
$740$	−9.54407	−0.350847
$741$	−9.87566	−0.362792
$742$	72.6826	2.66826
$743$	−35.0057	−1.28424	−0.642118	−	0.766606i	$-0.721944\pi$
$743$	−35.0057	−1.28424	−0.642118	+	0.766606i	$0.721944\pi$
$744$	−14.4914	−0.531281
$745$	26.8204	0.982625
$746$	−48.1303	−1.76218
$747$	−41.9822	−1.53605
$748$	−2.59541	−0.0948978
$749$	19.2621	0.703823
$750$	−68.1297	−2.48774
$751$	−36.4608	−1.33047	−0.665237	−	0.746632i	$-0.731670\pi$
$751$	−36.4608	−1.33047	−0.665237	+	0.746632i	$0.731670\pi$
$752$	17.1493	0.625370
$753$	−9.30354	−0.339040
$754$	15.1487	0.551682
$755$	−19.3625	−0.704675
$756$	−48.9906	−1.78177
$757$	15.0582	0.547299	0.273649	−	0.961829i	$-0.411769\pi$
$757$	15.0582	0.547299	0.273649	+	0.961829i	$0.411769\pi$
$758$	85.2057	3.09481
$759$	3.92574	0.142495
$760$	22.5415	0.817667
$761$	27.6565	1.00255	0.501274	−	0.865289i	$-0.332865\pi$
$761$	27.6565	1.00255	0.501274	+	0.865289i	$0.332865\pi$
$762$	14.2849	0.517488
$763$	62.2166	2.25239
$764$	6.95265	0.251538
$765$	−8.13458	−0.294106
$766$	−26.9319	−0.973090
$767$	1.33299	0.0481316
$768$	−88.0705	−3.17797
$769$	−44.9542	−1.62109	−0.810545	−	0.585676i	$-0.800829\pi$
$769$	−44.9542	−1.62109	−0.810545	+	0.585676i	$0.800829\pi$
$770$	3.91652	0.141141
$771$	31.7427	1.14318
$772$	13.1236	0.472329
$773$	35.2206	1.26680	0.633398	−	0.773826i	$-0.281660\pi$
$773$	35.2206	1.26680	0.633398	+	0.773826i	$0.281660\pi$
$774$	−103.036	−3.70356
$775$	−3.69971	−0.132898
$776$	80.6665	2.89576
$777$	−17.7902	−0.638221
$778$	−41.4537	−1.48619
$779$	−33.4989	−1.20022
$780$	13.1748	0.471732
$781$	−2.00681	−0.0718093
$782$	14.3258	0.512291
$783$	21.7894	0.778691
$784$	19.8437	0.708705
$785$	−6.49029	−0.231648
$786$	−91.3242	−3.25742
$787$	−26.5071	−0.944877	−0.472439	−	0.881364i	$-0.656626\pi$
$787$	−26.5071	−0.944877	−0.472439	+	0.881364i	$0.656626\pi$
$788$	50.3537	1.79378
$789$	−16.2633	−0.578990
$790$	39.3998	1.40178
$791$	11.2604	0.400375
$792$	8.92905	0.317280
$793$	11.1078	0.394451
$794$	−50.7135	−1.79975
$795$	−28.1146	−0.997122
$796$	−22.2892	−0.790020
$797$	28.4434	1.00752	0.503758	−	0.863845i	$-0.331950\pi$
$797$	28.4434	1.00752	0.503758	+	0.863845i	$0.331950\pi$
$798$	81.9313	2.90034
$799$	5.86848	0.207612
$800$	3.84120	0.135807
$801$	−48.7405	−1.72216
$802$	−10.0255	−0.354012
$803$	2.79169	0.0985164
$804$	22.1582	0.781459
$805$	−14.5364	−0.512339
$806$	2.54502	0.0896443
$807$	−52.9164	−1.86274
$808$	−73.6223	−2.59002
$809$	19.7489	0.694334	0.347167	−	0.937803i	$-0.387144\pi$
$809$	19.7489	0.694334	0.347167	+	0.937803i	$0.387144\pi$
$810$	−9.76503	−0.343108
$811$	5.37131	0.188612	0.0943061	−	0.995543i	$-0.469937\pi$
$811$	5.37131	0.188612	0.0943061	+	0.995543i	$0.469937\pi$
$812$	−84.5085	−2.96567
$813$	−58.8898	−2.06536
$814$	1.92595	0.0675044
$815$	14.6140	0.511906
$816$	19.9561	0.698603
$817$	35.2956	1.23484
$818$	−31.9346	−1.11657
$819$	14.4851	0.506151
$820$	44.6896	1.56063
$821$	45.2215	1.57824	0.789121	−	0.614237i	$-0.210536\pi$
$821$	45.2215	1.57824	0.789121	+	0.614237i	$0.210536\pi$
$822$	−88.4408	−3.08473
$823$	−7.51927	−0.262105	−0.131053	−	0.991375i	$-0.541836\pi$
$823$	−7.51927	−0.262105	−0.131053	+	0.991375i	$0.541836\pi$
$824$	−61.0262	−2.12595
$825$	3.86483	0.134556
$826$	−11.0589	−0.384788
$827$	−18.5977	−0.646705	−0.323352	−	0.946279i	$-0.604810\pi$
$827$	−18.5977	−0.646705	−0.323352	+	0.946279i	$0.604810\pi$
$828$	−64.6219	−2.24577
$829$	−38.1151	−1.32379	−0.661896	−	0.749596i	$-0.730248\pi$
$829$	−38.1151	−1.32379	−0.661896	+	0.749596i	$0.730248\pi$
$830$	−28.5319	−0.990356
$831$	−62.8264	−2.17943
$832$	6.64490	0.230371
$833$	6.79051	0.235277
$834$	4.48651	0.155355
$835$	−0.367493	−0.0127176
$836$	−5.96424	−0.206277
$837$	3.66068	0.126532
$838$	20.0460	0.692476
$839$	20.1275	0.694878	0.347439	−	0.937703i	$-0.387051\pi$
$839$	20.1275	0.694878	0.347439	+	0.937703i	$0.387051\pi$
$840$	−56.0541	−1.93405
$841$	8.58668	0.296092
$842$	72.3326	2.49275
$843$	−50.4047	−1.73603
$844$	37.0700	1.27600
$845$	−1.18660	−0.0408201
$846$	−39.3679	−1.35350
$847$	36.4019	1.25078
$848$	40.6821	1.39703
$849$	−49.1276	−1.68605
$850$	14.1036	0.483748
$851$	−7.14825	−0.245039
$852$	56.0057	1.91872
$853$	4.06683	0.139246	0.0696228	−	0.997573i	$-0.477820\pi$
$853$	4.06683	0.139246	0.0696228	+	0.997573i	$0.477820\pi$
$854$	−92.1538	−3.15344
$855$	−18.6932	−0.639293
$856$	29.8452	1.02009
$857$	−18.9943	−0.648834	−0.324417	−	0.945914i	$-0.605168\pi$
$857$	−18.9943	−0.648834	−0.324417	+	0.945914i	$0.605168\pi$
$858$	−2.65860	−0.0907631
$859$	56.3029	1.92103	0.960516	−	0.278225i	$-0.0897462\pi$
$859$	56.3029	1.92103	0.960516	+	0.278225i	$0.0897462\pi$
$860$	−47.0866	−1.60564
$861$	83.3017	2.83892
$862$	7.51435	0.255940
$863$	−30.6129	−1.04208	−0.521038	−	0.853533i	$-0.674455\pi$
$863$	−30.6129	−1.04208	−0.521038	+	0.853533i	$0.674455\pi$
$864$	−3.80067	−0.129302
$865$	10.1721	0.345863
$866$	−51.9923	−1.76677
$867$	−39.1470	−1.32950
$868$	−14.1976	−0.481899
$869$	−5.34622	−0.181358
$870$	48.6138	1.64816
$871$	−1.99570	−0.0676216
$872$	96.3999	3.26451
$873$	−66.8949	−2.26405
$874$	32.9206	1.11356
$875$	−34.2312	−1.15723
$876$	−77.9099	−2.63233
$877$	1.83925	0.0621072	0.0310536	−	0.999518i	$-0.490114\pi$
$877$	1.83925	0.0621072	0.0310536	+	0.999518i	$0.490114\pi$
$878$	−7.54169	−0.254520
$879$	−66.5144	−2.24348
$880$	2.19216	0.0738978
$881$	4.36279	0.146986	0.0734931	−	0.997296i	$-0.476585\pi$
$881$	4.36279	0.146986	0.0734931	+	0.997296i	$0.476585\pi$
$882$	−45.5533	−1.53386
$883$	−0.0625382	−0.00210458	−0.00105229	−	0.999999i	$-0.500335\pi$
$883$	−0.0625382	−0.00210458	−0.00105229	+	0.999999i	$0.500335\pi$
$884$	−6.52369	−0.219416
$885$	4.27772	0.143794
$886$	30.8843	1.03758
$887$	−26.8619	−0.901935	−0.450968	−	0.892540i	$-0.648921\pi$
$887$	−26.8619	−0.901935	−0.450968	+	0.892540i	$0.648921\pi$
$888$	−27.5646	−0.925008
$889$	7.17735	0.240721
$890$	−33.1249	−1.11035
$891$	1.32503	0.0443902
$892$	−32.2466	−1.07970
$893$	13.4857	0.451281
$894$	151.044	5.05166
$895$	12.6309	0.422204
$896$	−62.3091	−2.08160
$897$	9.86753	0.329467
$898$	49.1061	1.63869
$899$	6.31466	0.210606
$900$	−63.6192	−2.12064
$901$	13.9214	0.463789
$902$	−9.01814	−0.300271
$903$	−87.7697	−2.92079
$904$	17.4472	0.580284
$905$	24.6012	0.817771
$906$	−109.043	−3.62272
$907$	−44.5906	−1.48061	−0.740303	−	0.672273i	$-0.765318\pi$
$907$	−44.5906	−1.48061	−0.740303	+	0.672273i	$0.765318\pi$
$908$	87.6657	2.90929
$909$	61.0533	2.02501
$910$	9.84434	0.326337
$911$	−0.00316878	−0.000104986 0	−5.24932e−5	−	1.00000i	$-0.500017\pi$
$911$	−0.00316878	−0.000104986 0	−5.24932e−5		1.00000i	$0.500017\pi$
$912$	45.8589	1.51854
$913$	3.87153	0.128129
$914$	−45.4660	−1.50388
$915$	35.6463	1.17843
$916$	−80.3457	−2.65470
$917$	−45.8851	−1.51526
$918$	−13.9548	−0.460576
$919$	20.7922	0.685870	0.342935	−	0.939359i	$-0.388579\pi$
$919$	20.7922	0.685870	0.342935	+	0.939359i	$0.388579\pi$
$920$	−22.5230	−0.742560
$921$	−16.5816	−0.546383
$922$	22.4003	0.737715
$923$	−5.04421	−0.166032
$924$	14.8313	0.487914
$925$	−7.03734	−0.231386
$926$	−18.8944	−0.620910
$927$	50.6076	1.66217
$928$	−6.55614	−0.215216
$929$	2.23522	0.0733351	0.0366676	−	0.999328i	$-0.488326\pi$
$929$	2.23522	0.0733351	0.0366676	+	0.999328i	$0.488326\pi$
$930$	8.16724	0.267814
$931$	15.6045	0.511417
$932$	−67.4577	−2.20965
$933$	−56.9401	−1.86413
$934$	53.7248	1.75793
$935$	0.750157	0.0245328
$936$	22.4436	0.733591
$937$	−22.9905	−0.751066	−0.375533	−	0.926809i	$-0.622540\pi$
$937$	−22.9905	−0.751066	−0.375533	+	0.926809i	$0.622540\pi$
$938$	16.5569	0.540601
$939$	−71.8660	−2.34526
$940$	−17.9908	−0.586794
$941$	8.93959	0.291422	0.145711	−	0.989327i	$-0.453453\pi$
$941$	8.93959	0.291422	0.145711	+	0.989327i	$0.453453\pi$
$942$	−36.5511	−1.19090
$943$	33.4713	1.08997
$944$	−6.18991	−0.201465
$945$	14.1598	0.460619
$946$	9.50184	0.308931
$947$	−41.4965	−1.34845	−0.674227	−	0.738524i	$-0.735523\pi$
$947$	−41.4965	−1.34845	−0.674227	+	0.738524i	$0.735523\pi$
$948$	149.201	4.84584
$949$	7.01703	0.227782
$950$	32.4098	1.05151
$951$	28.2829	0.917136
$952$	27.7561	0.899580
$953$	−22.0771	−0.715147	−0.357573	−	0.933885i	$-0.616396\pi$
$953$	−22.0771	−0.715147	−0.357573	+	0.933885i	$0.616396\pi$
$954$	−93.3900	−3.02361
$955$	−2.00954	−0.0650271
$956$	70.2744	2.27284
$957$	−6.59648	−0.213234
$958$	4.33974	0.140211
$959$	−44.4364	−1.43493
$960$	21.3242	0.688237
$961$	−29.9391	−0.965778
$962$	4.84096	0.156079
$963$	−24.7499	−0.797556
$964$	21.9650	0.707445
$965$	−3.79314	−0.122106
$966$	−81.8639	−2.63393
$967$	31.4940	1.01278	0.506390	−	0.862304i	$-0.330980\pi$
$967$	31.4940	1.01278	0.506390	+	0.862304i	$0.330980\pi$
$968$	56.4020	1.81283
$969$	15.6929	0.504128
$970$	−45.4630	−1.45973
$971$	26.9678	0.865437	0.432719	−	0.901529i	$-0.357554\pi$
$971$	26.9678	0.865437	0.432719	+	0.901529i	$0.357554\pi$
$972$	−80.7519	−2.59012
$973$	2.25421	0.0722668
$974$	53.5409	1.71556
$975$	9.71443	0.311111
$976$	−51.5806	−1.65105
$977$	−6.68288	−0.213804	−0.106902	−	0.994270i	$-0.534093\pi$
$977$	−6.68288	−0.213804	−0.106902	+	0.994270i	$0.534093\pi$
$978$	82.3011	2.63170
$979$	4.49477	0.143653
$980$	−20.8174	−0.664988
$981$	−79.9422	−2.55236
$982$	61.7359	1.97007
$983$	−29.6564	−0.945892	−0.472946	−	0.881091i	$-0.656809\pi$
$983$	−29.6564	−0.945892	−0.472946	+	0.881091i	$0.656809\pi$
$984$	129.070	4.11459
$985$	−14.5538	−0.463723
$986$	−24.0719	−0.766606
$987$	−33.5349	−1.06743
$988$	−14.9914	−0.476939
$989$	−35.2666	−1.12141
$990$	−5.03234	−0.159938
$991$	−9.34751	−0.296933	−0.148467	−	0.988917i	$-0.547434\pi$
$991$	−9.34751	−0.296933	−0.148467	+	0.988917i	$0.547434\pi$
$992$	−1.10145	−0.0349710
$993$	0.715144	0.0226944
$994$	41.8482	1.32734
$995$	6.44228	0.204234
$996$	−108.046	−3.42357
$997$	−13.6082	−0.430976	−0.215488	−	0.976506i	$-0.569134\pi$
$997$	−13.6082	−0.430976	−0.215488	+	0.976506i	$0.569134\pi$
$998$	60.9075	1.92799
$999$	6.96310	0.220303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.11	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.47091 q^{2} +2.70447 q^{3} +4.10542 q^{4} -1.18660 q^{5} -6.68251 q^{6} -3.35758 q^{7} -5.20231 q^{8} +4.31416 q^{9} +O(q^{10})\)	\(q-2.47091 q^{2} +2.70447 q^{3} +4.10542 q^{4} -1.18660 q^{5} -6.68251 q^{6} -3.35758 q^{7} -5.20231 q^{8} +4.31416 q^{9} +2.93198 q^{10} -0.397844 q^{11} +11.1030 q^{12} -1.00000 q^{13} +8.29629 q^{14} -3.20911 q^{15} +4.64362 q^{16} +1.58904 q^{17} -10.6599 q^{18} +3.65161 q^{19} -4.87147 q^{20} -9.08047 q^{21} +0.983039 q^{22} -3.64860 q^{23} -14.0695 q^{24} -3.59199 q^{25} +2.47091 q^{26} +3.55409 q^{27} -13.7843 q^{28} +6.13080 q^{29} +7.92944 q^{30} +1.02999 q^{31} -1.06938 q^{32} -1.07596 q^{33} -3.92639 q^{34} +3.98409 q^{35} +17.7114 q^{36} +1.95918 q^{37} -9.02281 q^{38} -2.70447 q^{39} +6.17304 q^{40} -9.17373 q^{41} +22.4371 q^{42} +9.66577 q^{43} -1.63332 q^{44} -5.11916 q^{45} +9.01538 q^{46} +3.69308 q^{47} +12.5585 q^{48} +4.27333 q^{49} +8.87550 q^{50} +4.29752 q^{51} -4.10542 q^{52} +8.76086 q^{53} -8.78186 q^{54} +0.472081 q^{55} +17.4672 q^{56} +9.87566 q^{57} -15.1487 q^{58} -1.33299 q^{59} -13.1748 q^{60} -11.1078 q^{61} -2.54502 q^{62} -14.4851 q^{63} -6.64490 q^{64} +1.18660 q^{65} +2.65860 q^{66} +1.99570 q^{67} +6.52369 q^{68} -9.86753 q^{69} -9.84434 q^{70} +5.04421 q^{71} -22.4436 q^{72} -7.01703 q^{73} -4.84096 q^{74} -9.71443 q^{75} +14.9914 q^{76} +1.33579 q^{77} +6.68251 q^{78} +13.4380 q^{79} -5.51011 q^{80} -3.33053 q^{81} +22.6675 q^{82} -9.73127 q^{83} -37.2791 q^{84} -1.88555 q^{85} -23.8833 q^{86} +16.5806 q^{87} +2.06971 q^{88} -11.2978 q^{89} +12.6490 q^{90} +3.35758 q^{91} -14.9790 q^{92} +2.78557 q^{93} -9.12529 q^{94} -4.33298 q^{95} -2.89210 q^{96} -15.5059 q^{97} -10.5590 q^{98} -1.71636 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 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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