LMFDB - Embedded newform 8042.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$1$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.26666 q^{3} +1.00000 q^{4} +1.36820 q^{5} +3.26666 q^{6} -2.10777 q^{7} -1.00000 q^{8} +7.67104 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.26666 q^{3} +1.00000 q^{4} +1.36820 q^{5} +3.26666 q^{6} -2.10777 q^{7} -1.00000 q^{8} +7.67104 q^{9} -1.36820 q^{10} -4.86841 q^{11} -3.26666 q^{12} -1.75983 q^{13} +2.10777 q^{14} -4.46942 q^{15} +1.00000 q^{16} -2.56637 q^{17} -7.67104 q^{18} +5.19834 q^{19} +1.36820 q^{20} +6.88537 q^{21} +4.86841 q^{22} -8.67659 q^{23} +3.26666 q^{24} -3.12804 q^{25} +1.75983 q^{26} -15.2587 q^{27} -2.10777 q^{28} +9.95534 q^{29} +4.46942 q^{30} -2.79883 q^{31} -1.00000 q^{32} +15.9034 q^{33} +2.56637 q^{34} -2.88385 q^{35} +7.67104 q^{36} +10.2066 q^{37} -5.19834 q^{38} +5.74877 q^{39} -1.36820 q^{40} +1.32182 q^{41} -6.88537 q^{42} +5.83776 q^{43} -4.86841 q^{44} +10.4955 q^{45} +8.67659 q^{46} -1.26757 q^{47} -3.26666 q^{48} -2.55729 q^{49} +3.12804 q^{50} +8.38343 q^{51} -1.75983 q^{52} +6.80090 q^{53} +15.2587 q^{54} -6.66094 q^{55} +2.10777 q^{56} -16.9812 q^{57} -9.95534 q^{58} +10.8668 q^{59} -4.46942 q^{60} -5.95750 q^{61} +2.79883 q^{62} -16.1688 q^{63} +1.00000 q^{64} -2.40780 q^{65} -15.9034 q^{66} -12.2416 q^{67} -2.56637 q^{68} +28.3434 q^{69} +2.88385 q^{70} -0.326875 q^{71} -7.67104 q^{72} -13.6322 q^{73} -10.2066 q^{74} +10.2182 q^{75} +5.19834 q^{76} +10.2615 q^{77} -5.74877 q^{78} +15.2922 q^{79} +1.36820 q^{80} +26.8317 q^{81} -1.32182 q^{82} -3.57097 q^{83} +6.88537 q^{84} -3.51129 q^{85} -5.83776 q^{86} -32.5207 q^{87} +4.86841 q^{88} -5.88216 q^{89} -10.4955 q^{90} +3.70933 q^{91} -8.67659 q^{92} +9.14281 q^{93} +1.26757 q^{94} +7.11234 q^{95} +3.26666 q^{96} +11.2147 q^{97} +2.55729 q^{98} -37.3458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q - 82 q^{2} - 13 q^{3} + 82 q^{4} + 3 q^{5} + 13 q^{6} - 37 q^{7} - 82 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q - 82 * q^2 - 13 * q^3 + 82 * q^4 + 3 * q^5 + 13 * q^6 - 37 * q^7 - 82 * q^8 + 91 * q^9	\( 82 q - 82 q^{2} - 13 q^{3} + 82 q^{4} + 3 q^{5} + 13 q^{6} - 37 q^{7} - 82 q^{8} + 91 q^{9} - 3 q^{10} - 16 q^{11} - 13 q^{12} - 42 q^{13} + 37 q^{14} - 9 q^{15} + 82 q^{16} + 3 q^{17} - 91 q^{18} - 42 q^{19} + 3 q^{20} - q^{21} + 16 q^{22} - 6 q^{23} + 13 q^{24} + 53 q^{25} + 42 q^{26} - 49 q^{27} - 37 q^{28} + 15 q^{29} + 9 q^{30} - 40 q^{31} - 82 q^{32} - 37 q^{33} - 3 q^{34} - 42 q^{35} + 91 q^{36} - 72 q^{37} + 42 q^{38} - 14 q^{39} - 3 q^{40} + 8 q^{41} + q^{42} - 93 q^{43} - 16 q^{44} - 11 q^{45} + 6 q^{46} + 7 q^{47} - 13 q^{48} + 61 q^{49} - 53 q^{50} - 70 q^{51} - 42 q^{52} + 18 q^{53} + 49 q^{54} - 62 q^{55} + 37 q^{56} - 51 q^{57} - 15 q^{58} - 47 q^{59} - 9 q^{60} - 14 q^{61} + 40 q^{62} - 100 q^{63} + 82 q^{64} + q^{65} + 37 q^{66} - 150 q^{67} + 3 q^{68} + 31 q^{69} + 42 q^{70} + 7 q^{71} - 91 q^{72} - 78 q^{73} + 72 q^{74} - 49 q^{75} - 42 q^{76} + 29 q^{77} + 14 q^{78} - 59 q^{79} + 3 q^{80} + 122 q^{81} - 8 q^{82} - 52 q^{83} - q^{84} - 108 q^{85} + 93 q^{86} - 49 q^{87} + 16 q^{88} + 38 q^{89} + 11 q^{90} - 69 q^{91} - 6 q^{92} - 63 q^{93} - 7 q^{94} + 5 q^{95} + 13 q^{96} - 74 q^{97} - 61 q^{98} - 89 q^{99}+O(q^{100}) \) 82 * q - 82 * q^2 - 13 * q^3 + 82 * q^4 + 3 * q^5 + 13 * q^6 - 37 * q^7 - 82 * q^8 + 91 * q^9 - 3 * q^10 - 16 * q^11 - 13 * q^12 - 42 * q^13 + 37 * q^14 - 9 * q^15 + 82 * q^16 + 3 * q^17 - 91 * q^18 - 42 * q^19 + 3 * q^20 - q^21 + 16 * q^22 - 6 * q^23 + 13 * q^24 + 53 * q^25 + 42 * q^26 - 49 * q^27 - 37 * q^28 + 15 * q^29 + 9 * q^30 - 40 * q^31 - 82 * q^32 - 37 * q^33 - 3 * q^34 - 42 * q^35 + 91 * q^36 - 72 * q^37 + 42 * q^38 - 14 * q^39 - 3 * q^40 + 8 * q^41 + q^42 - 93 * q^43 - 16 * q^44 - 11 * q^45 + 6 * q^46 + 7 * q^47 - 13 * q^48 + 61 * q^49 - 53 * q^50 - 70 * q^51 - 42 * q^52 + 18 * q^53 + 49 * q^54 - 62 * q^55 + 37 * q^56 - 51 * q^57 - 15 * q^58 - 47 * q^59 - 9 * q^60 - 14 * q^61 + 40 * q^62 - 100 * q^63 + 82 * q^64 + q^65 + 37 * q^66 - 150 * q^67 + 3 * q^68 + 31 * q^69 + 42 * q^70 + 7 * q^71 - 91 * q^72 - 78 * q^73 + 72 * q^74 - 49 * q^75 - 42 * q^76 + 29 * q^77 + 14 * q^78 - 59 * q^79 + 3 * q^80 + 122 * q^81 - 8 * q^82 - 52 * q^83 - q^84 - 108 * q^85 + 93 * q^86 - 49 * q^87 + 16 * q^88 + 38 * q^89 + 11 * q^90 - 69 * q^91 - 6 * q^92 - 63 * q^93 - 7 * q^94 + 5 * q^95 + 13 * q^96 - 74 * q^97 - 61 * q^98 - 89 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.26666	−1.88600	−0.943002	−	0.332786i	$-0.892011\pi$
$3$	−3.26666	−1.88600	−0.943002	+	0.332786i	$0.892011\pi$
$4$	1.00000	0.500000
$5$	1.36820	0.611876	0.305938	−	0.952052i	$-0.401030\pi$
$5$	1.36820	0.611876	0.305938	+	0.952052i	$0.401030\pi$
$6$	3.26666	1.33361
$7$	−2.10777	−0.796664	−0.398332	−	0.917241i	$-0.630411\pi$
$7$	−2.10777	−0.796664	−0.398332	+	0.917241i	$0.630411\pi$
$8$	−1.00000	−0.353553
$9$	7.67104	2.55701
$10$	−1.36820	−0.432661
$11$	−4.86841	−1.46788	−0.733941	−	0.679213i	$-0.762321\pi$
$11$	−4.86841	−1.46788	−0.733941	+	0.679213i	$0.762321\pi$
$12$	−3.26666	−0.943002
$13$	−1.75983	−0.488090	−0.244045	−	0.969764i	$-0.578474\pi$
$13$	−1.75983	−0.488090	−0.244045	+	0.969764i	$0.578474\pi$
$14$	2.10777	0.563326
$15$	−4.46942	−1.15400
$16$	1.00000	0.250000
$17$	−2.56637	−0.622435	−0.311218	−	0.950339i	$-0.600737\pi$
$17$	−2.56637	−0.622435	−0.311218	+	0.950339i	$0.600737\pi$
$18$	−7.67104	−1.80808
$19$	5.19834	1.19258	0.596290	−	0.802769i	$-0.296641\pi$
$19$	5.19834	1.19258	0.596290	+	0.802769i	$0.296641\pi$
$20$	1.36820	0.305938
$21$	6.88537	1.50251
$22$	4.86841	1.03795
$23$	−8.67659	−1.80919	−0.904597	−	0.426267i	$-0.859828\pi$
$23$	−8.67659	−1.80919	−0.904597	+	0.426267i	$0.859828\pi$
$24$	3.26666	0.666803
$25$	−3.12804	−0.625608
$26$	1.75983	0.345132
$27$	−15.2587	−2.93653
$28$	−2.10777	−0.398332
$29$	9.95534	1.84866	0.924330	−	0.381594i	$-0.124625\pi$
$29$	9.95534	1.84866	0.924330	+	0.381594i	$0.124625\pi$
$30$	4.46942	0.816001
$31$	−2.79883	−0.502684	−0.251342	−	0.967898i	$-0.580872\pi$
$31$	−2.79883	−0.502684	−0.251342	+	0.967898i	$0.580872\pi$
$32$	−1.00000	−0.176777
$33$	15.9034	2.76843
$34$	2.56637	0.440128
$35$	−2.88385	−0.487459
$36$	7.67104	1.27851
$37$	10.2066	1.67795	0.838974	−	0.544172i	$-0.183156\pi$
$37$	10.2066	1.67795	0.838974	+	0.544172i	$0.183156\pi$
$38$	−5.19834	−0.843281
$39$	5.74877	0.920540
$40$	−1.36820	−0.216331
$41$	1.32182	0.206433	0.103217	−	0.994659i	$-0.467087\pi$
$41$	1.32182	0.206433	0.103217	+	0.994659i	$0.467087\pi$
$42$	−6.88537	−1.06244
$43$	5.83776	0.890250	0.445125	−	0.895468i	$-0.353159\pi$
$43$	5.83776	0.890250	0.445125	+	0.895468i	$0.353159\pi$
$44$	−4.86841	−0.733941
$45$	10.4955	1.56457
$46$	8.67659	1.27929
$47$	−1.26757	−0.184894	−0.0924468	−	0.995718i	$-0.529469\pi$
$47$	−1.26757	−0.184894	−0.0924468	+	0.995718i	$0.529469\pi$
$48$	−3.26666	−0.471501
$49$	−2.55729	−0.365327
$50$	3.12804	0.442372
$51$	8.38343	1.17392
$52$	−1.75983	−0.244045
$53$	6.80090	0.934175	0.467088	−	0.884211i	$-0.345303\pi$
$53$	6.80090	0.934175	0.467088	+	0.884211i	$0.345303\pi$
$54$	15.2587	2.07644
$55$	−6.66094	−0.898161
$56$	2.10777	0.281663
$57$	−16.9812	−2.24921
$58$	−9.95534	−1.30720
$59$	10.8668	1.41474	0.707369	−	0.706844i	$-0.249882\pi$
$59$	10.8668	1.41474	0.707369	+	0.706844i	$0.249882\pi$
$60$	−4.46942	−0.577000
$61$	−5.95750	−0.762779	−0.381390	−	0.924414i	$-0.624554\pi$
$61$	−5.95750	−0.762779	−0.381390	+	0.924414i	$0.624554\pi$
$62$	2.79883	0.355451
$63$	−16.1688	−2.03708
$64$	1.00000	0.125000
$65$	−2.40780	−0.298650
$66$	−15.9034	−1.95758
$67$	−12.2416	−1.49555	−0.747777	−	0.663950i	$-0.768879\pi$
$67$	−12.2416	−1.49555	−0.747777	+	0.663950i	$0.768879\pi$
$68$	−2.56637	−0.311218
$69$	28.3434	3.41215
$70$	2.88385	0.344686
$71$	−0.326875	−0.0387929	−0.0193965	−	0.999812i	$-0.506174\pi$
$71$	−0.326875	−0.0387929	−0.0193965	+	0.999812i	$0.506174\pi$
$72$	−7.67104	−0.904041
$73$	−13.6322	−1.59553	−0.797764	−	0.602969i	$-0.793984\pi$
$73$	−13.6322	−1.59553	−0.797764	+	0.602969i	$0.793984\pi$
$74$	−10.2066	−1.18649
$75$	10.2182	1.17990
$76$	5.19834	0.596290
$77$	10.2615	1.16941
$78$	−5.74877	−0.650920
$79$	15.2922	1.72050	0.860252	−	0.509868i	$-0.170306\pi$
$79$	15.2922	1.72050	0.860252	+	0.509868i	$0.170306\pi$
$80$	1.36820	0.152969
$81$	26.8317	2.98130
$82$	−1.32182	−0.145970
$83$	−3.57097	−0.391965	−0.195983	−	0.980607i	$-0.562790\pi$
$83$	−3.57097	−0.391965	−0.195983	+	0.980607i	$0.562790\pi$
$84$	6.88537	0.751256
$85$	−3.51129	−0.380853
$86$	−5.83776	−0.629502
$87$	−32.5207	−3.48658
$88$	4.86841	0.518975
$89$	−5.88216	−0.623508	−0.311754	−	0.950163i	$-0.600916\pi$
$89$	−5.88216	−0.623508	−0.311754	+	0.950163i	$0.600916\pi$
$90$	−10.4955	−1.10632
$91$	3.70933	0.388843
$92$	−8.67659	−0.904597
$93$	9.14281	0.948065
$94$	1.26757	0.130740
$95$	7.11234	0.729711
$96$	3.26666	0.333402
$97$	11.2147	1.13868	0.569341	−	0.822102i	$-0.307199\pi$
$97$	11.2147	1.13868	0.569341	+	0.822102i	$0.307199\pi$
$98$	2.55729	0.258325
$99$	−37.3458	−3.75339
$100$	−3.12804	−0.312804
$101$	15.4063	1.53299	0.766494	−	0.642252i	$-0.222000\pi$
$101$	15.4063	1.53299	0.766494	+	0.642252i	$0.222000\pi$
$102$	−8.38343	−0.830084
$103$	9.43172	0.929335	0.464667	−	0.885485i	$-0.346174\pi$
$103$	9.43172	0.929335	0.464667	+	0.885485i	$0.346174\pi$
$104$	1.75983	0.172566
$105$	9.42053	0.919350
$106$	−6.80090	−0.660562
$107$	7.67129	0.741612	0.370806	−	0.928710i	$-0.379082\pi$
$107$	7.67129	0.741612	0.370806	+	0.928710i	$0.379082\pi$
$108$	−15.2587	−1.46827
$109$	−17.7477	−1.69992	−0.849961	−	0.526846i	$-0.823374\pi$
$109$	−17.7477	−1.69992	−0.849961	+	0.526846i	$0.823374\pi$
$110$	6.66094	0.635096
$111$	−33.3413	−3.16462
$112$	−2.10777	−0.199166
$113$	8.69671	0.818118	0.409059	−	0.912508i	$-0.365857\pi$
$113$	8.69671	0.818118	0.409059	+	0.912508i	$0.365857\pi$
$114$	16.9812	1.59043
$115$	−11.8713	−1.10700
$116$	9.95534	0.924330
$117$	−13.4997	−1.24805
$118$	−10.8668	−1.00037
$119$	5.40932	0.495871
$120$	4.46942	0.408001
$121$	12.7014	1.15468
$122$	5.95750	0.539367
$123$	−4.31792	−0.389334
$124$	−2.79883	−0.251342
$125$	−11.1207	−0.994670
$126$	16.1688	1.44043
$127$	−19.1780	−1.70177	−0.850887	−	0.525348i	$-0.823935\pi$
$127$	−19.1780	−1.70177	−0.850887	+	0.525348i	$0.823935\pi$
$128$	−1.00000	−0.0883883
$129$	−19.0700	−1.67902
$130$	2.40780	0.211178
$131$	−5.52894	−0.483066	−0.241533	−	0.970393i	$-0.577650\pi$
$131$	−5.52894	−0.483066	−0.241533	+	0.970393i	$0.577650\pi$
$132$	15.9034	1.38422
$133$	−10.9569	−0.950085
$134$	12.2416	1.05752
$135$	−20.8769	−1.79679
$136$	2.56637	0.220064
$137$	0.221098	0.0188897	0.00944485	−	0.999955i	$-0.496994\pi$
$137$	0.221098	0.0188897	0.00944485	+	0.999955i	$0.496994\pi$
$138$	−28.3434	−2.41275
$139$	7.83492	0.664549	0.332275	−	0.943183i	$-0.392184\pi$
$139$	7.83492	0.664549	0.332275	+	0.943183i	$0.392184\pi$
$140$	−2.88385	−0.243729
$141$	4.14070	0.348710
$142$	0.326875	0.0274308
$143$	8.56759	0.716458
$144$	7.67104	0.639253
$145$	13.6209	1.13115
$146$	13.6322	1.12821
$147$	8.35379	0.689009
$148$	10.2066	0.838974
$149$	5.95357	0.487735	0.243868	−	0.969809i	$-0.421584\pi$
$149$	5.95357	0.487735	0.243868	+	0.969809i	$0.421584\pi$
$150$	−10.2182	−0.834315
$151$	−4.37692	−0.356188	−0.178094	−	0.984013i	$-0.556993\pi$
$151$	−4.37692	−0.356188	−0.178094	+	0.984013i	$0.556993\pi$
$152$	−5.19834	−0.421641
$153$	−19.6867	−1.59157
$154$	−10.2615	−0.826896
$155$	−3.82934	−0.307580
$156$	5.74877	0.460270
$157$	3.56267	0.284332	0.142166	−	0.989843i	$-0.454593\pi$
$157$	3.56267	0.284332	0.142166	+	0.989843i	$0.454593\pi$
$158$	−15.2922	−1.21658
$159$	−22.2162	−1.76186
$160$	−1.36820	−0.108165
$161$	18.2883	1.44132
$162$	−26.8317	−2.10810
$163$	−23.7956	−1.86382	−0.931909	−	0.362692i	$-0.881858\pi$
$163$	−23.7956	−1.86382	−0.931909	+	0.362692i	$0.881858\pi$
$164$	1.32182	0.103217
$165$	21.7590	1.69394
$166$	3.57097	0.277161
$167$	25.1525	1.94636	0.973180	−	0.230043i	$-0.0738868\pi$
$167$	25.1525	1.94636	0.973180	+	0.230043i	$0.0738868\pi$
$168$	−6.88537	−0.531218
$169$	−9.90299	−0.761768
$170$	3.51129	0.269304
$171$	39.8766	3.04944
$172$	5.83776	0.445125
$173$	9.14436	0.695232	0.347616	−	0.937637i	$-0.386991\pi$
$173$	9.14436	0.695232	0.347616	+	0.937637i	$0.386991\pi$
$174$	32.5207	2.46539
$175$	6.59320	0.498399
$176$	−4.86841	−0.366970
$177$	−35.4981	−2.66820
$178$	5.88216	0.440886
$179$	−5.93982	−0.443963	−0.221981	−	0.975051i	$-0.571252\pi$
$179$	−5.93982	−0.443963	−0.221981	+	0.975051i	$0.571252\pi$
$180$	10.4955	0.782287
$181$	24.3459	1.80962	0.904809	−	0.425818i	$-0.140014\pi$
$181$	24.3459	1.80962	0.904809	+	0.425818i	$0.140014\pi$
$182$	−3.70933	−0.274954
$183$	19.4611	1.43861
$184$	8.67659	0.639647
$185$	13.9646	1.02670
$186$	−9.14281	−0.670383
$187$	12.4941	0.913661
$188$	−1.26757	−0.0924468
$189$	32.1618	2.33943
$190$	−7.11234	−0.515983
$191$	4.56048	0.329985	0.164993	−	0.986295i	$-0.447240\pi$
$191$	4.56048	0.329985	0.164993	+	0.986295i	$0.447240\pi$
$192$	−3.26666	−0.235751
$193$	15.0988	1.08684	0.543418	−	0.839462i	$-0.317130\pi$
$193$	15.0988	1.08684	0.543418	+	0.839462i	$0.317130\pi$
$194$	−11.2147	−0.805169
$195$	7.86544	0.563256
$196$	−2.55729	−0.182664
$197$	−8.29533	−0.591018	−0.295509	−	0.955340i	$-0.595489\pi$
$197$	−8.29533	−0.591018	−0.295509	+	0.955340i	$0.595489\pi$
$198$	37.3458	2.65405
$199$	5.73149	0.406295	0.203147	−	0.979148i	$-0.434883\pi$
$199$	5.73149	0.406295	0.203147	+	0.979148i	$0.434883\pi$
$200$	3.12804	0.221186
$201$	39.9892	2.82062
$202$	−15.4063	−1.08399
$203$	−20.9836	−1.47276
$204$	8.38343	0.586958
$205$	1.80850	0.126311
$206$	−9.43172	−0.657139
$207$	−66.5585	−4.62613
$208$	−1.75983	−0.122022
$209$	−25.3076	−1.75057
$210$	−9.42053	−0.650079
$211$	18.7572	1.29130	0.645650	−	0.763634i	$-0.276587\pi$
$211$	18.7572	1.29130	0.645650	+	0.763634i	$0.276587\pi$
$212$	6.80090	0.467088
$213$	1.06779	0.0731637
$214$	−7.67129	−0.524399
$215$	7.98720	0.544722
$216$	15.2587	1.03822
$217$	5.89930	0.400470
$218$	17.7477	1.20203
$219$	44.5317	3.00917
$220$	−6.66094	−0.449080
$221$	4.51637	0.303804
$222$	33.3413	2.23772
$223$	−5.16269	−0.345720	−0.172860	−	0.984946i	$-0.555301\pi$
$223$	−5.16269	−0.345720	−0.172860	+	0.984946i	$0.555301\pi$
$224$	2.10777	0.140832
$225$	−23.9953	−1.59969
$226$	−8.69671	−0.578497
$227$	13.1823	0.874943	0.437472	−	0.899232i	$-0.355874\pi$
$227$	13.1823	0.874943	0.437472	+	0.899232i	$0.355874\pi$
$228$	−16.9812	−1.12461
$229$	−22.4258	−1.48194	−0.740969	−	0.671539i	$-0.765634\pi$
$229$	−22.4258	−1.48194	−0.740969	+	0.671539i	$0.765634\pi$
$230$	11.8713	0.782769
$231$	−33.5208	−2.20551
$232$	−9.95534	−0.653600
$233$	21.6062	1.41547	0.707733	−	0.706480i	$-0.249718\pi$
$233$	21.6062	1.41547	0.707733	+	0.706480i	$0.249718\pi$
$234$	13.4997	0.882506
$235$	−1.73428	−0.113132
$236$	10.8668	0.707369
$237$	−49.9543	−3.24488
$238$	−5.40932	−0.350634
$239$	0.295749	0.0191304	0.00956520	−	0.999954i	$-0.496955\pi$
$239$	0.295749	0.0191304	0.00956520	+	0.999954i	$0.496955\pi$
$240$	−4.46942	−0.288500
$241$	12.7323	0.820159	0.410079	−	0.912050i	$-0.365501\pi$
$241$	12.7323	0.820159	0.410079	+	0.912050i	$0.365501\pi$
$242$	−12.7014	−0.816479
$243$	−41.8740	−2.68622
$244$	−5.95750	−0.381390
$245$	−3.49887	−0.223535
$246$	4.31792	0.275301
$247$	−9.14820	−0.582086
$248$	2.79883	0.177726
$249$	11.6651	0.739248
$250$	11.1207	0.703338
$251$	17.9360	1.13211	0.566056	−	0.824367i	$-0.308469\pi$
$251$	17.9360	1.13211	0.566056	+	0.824367i	$0.308469\pi$
$252$	−16.1688	−1.01854
$253$	42.2412	2.65568
$254$	19.1780	1.20334
$255$	11.4702	0.718290
$256$	1.00000	0.0625000
$257$	−0.393261	−0.0245310	−0.0122655	−	0.999925i	$-0.503904\pi$
$257$	−0.393261	−0.0245310	−0.0122655	+	0.999925i	$0.503904\pi$
$258$	19.0700	1.18724
$259$	−21.5131	−1.33676
$260$	−2.40780	−0.149325
$261$	76.3678	4.72705
$262$	5.52894	0.341579
$263$	−10.5219	−0.648811	−0.324405	−	0.945918i	$-0.605164\pi$
$263$	−10.5219	−0.648811	−0.324405	+	0.945918i	$0.605164\pi$
$264$	−15.9034	−0.978788
$265$	9.30496	0.571599
$266$	10.9569	0.671812
$267$	19.2150	1.17594
$268$	−12.2416	−0.747777
$269$	9.41679	0.574152	0.287076	−	0.957908i	$-0.407317\pi$
$269$	9.41679	0.574152	0.287076	+	0.957908i	$0.407317\pi$
$270$	20.8769	1.27053
$271$	−2.31695	−0.140745	−0.0703723	−	0.997521i	$-0.522419\pi$
$271$	−2.31695	−0.140745	−0.0703723	+	0.997521i	$0.522419\pi$
$272$	−2.56637	−0.155609
$273$	−12.1171	−0.733360
$274$	−0.221098	−0.0133570
$275$	15.2286	0.918319
$276$	28.3434	1.70607
$277$	−3.85239	−0.231468	−0.115734	−	0.993280i	$-0.536922\pi$
$277$	−3.85239	−0.231468	−0.115734	+	0.993280i	$0.536922\pi$
$278$	−7.83492	−0.469907
$279$	−21.4699	−1.28537
$280$	2.88385	0.172343
$281$	−10.2685	−0.612568	−0.306284	−	0.951940i	$-0.599086\pi$
$281$	−10.2685	−0.612568	−0.306284	+	0.951940i	$0.599086\pi$
$282$	−4.14070	−0.246575
$283$	3.21291	0.190988	0.0954938	−	0.995430i	$-0.469557\pi$
$283$	3.21291	0.190988	0.0954938	+	0.995430i	$0.469557\pi$
$284$	−0.326875	−0.0193965
$285$	−23.2336	−1.37624
$286$	−8.56759	−0.506612
$287$	−2.78609	−0.164458
$288$	−7.67104	−0.452020
$289$	−10.4138	−0.612575
$290$	−13.6209	−0.799844
$291$	−36.6346	−2.14756
$292$	−13.6322	−0.797764
$293$	−26.4775	−1.54683	−0.773415	−	0.633900i	$-0.781453\pi$
$293$	−26.4775	−1.54683	−0.773415	+	0.633900i	$0.781453\pi$
$294$	−8.35379	−0.487203
$295$	14.8679	0.865644
$296$	−10.2066	−0.593244
$297$	74.2856	4.31048
$298$	−5.95357	−0.344881
$299$	15.2694	0.883049
$300$	10.2182	0.589950
$301$	−12.3047	−0.709230
$302$	4.37692	0.251863
$303$	−50.3272	−2.89122
$304$	5.19834	0.298145
$305$	−8.15102	−0.466726
$306$	19.6867	1.12541
$307$	−26.4159	−1.50763	−0.753817	−	0.657084i	$-0.771790\pi$
$307$	−26.4159	−1.50763	−0.753817	+	0.657084i	$0.771790\pi$
$308$	10.2615	0.584704
$309$	−30.8102	−1.75273
$310$	3.82934	0.217492
$311$	−25.9104	−1.46925	−0.734623	−	0.678476i	$-0.762641\pi$
$311$	−25.9104	−1.46925	−0.734623	+	0.678476i	$0.762641\pi$
$312$	−5.74877	−0.325460
$313$	7.09101	0.400808	0.200404	−	0.979713i	$-0.435775\pi$
$313$	7.09101	0.400808	0.200404	+	0.979713i	$0.435775\pi$
$314$	−3.56267	−0.201053
$315$	−22.1221	−1.24644
$316$	15.2922	0.860252
$317$	−33.9371	−1.90610	−0.953048	−	0.302820i	$-0.902072\pi$
$317$	−33.9371	−1.90610	−0.953048	+	0.302820i	$0.902072\pi$
$318$	22.2162	1.24582
$319$	−48.4667	−2.71361
$320$	1.36820	0.0764844
$321$	−25.0595	−1.39868
$322$	−18.2883	−1.01917
$323$	−13.3408	−0.742304
$324$	26.8317	1.49065
$325$	5.50483	0.305353
$326$	23.7956	1.31792
$327$	57.9756	3.20606
$328$	−1.32182	−0.0729851
$329$	2.67174	0.147298
$330$	−21.7590	−1.19779
$331$	15.3668	0.844637	0.422319	−	0.906447i	$-0.361216\pi$
$331$	15.3668	0.844637	0.422319	+	0.906447i	$0.361216\pi$
$332$	−3.57097	−0.195983
$333$	78.2949	4.29053
$334$	−25.1525	−1.37628
$335$	−16.7490	−0.915093
$336$	6.88537	0.375628
$337$	24.4687	1.33290	0.666449	−	0.745551i	$-0.267814\pi$
$337$	24.4687	1.33290	0.666449	+	0.745551i	$0.267814\pi$
$338$	9.90299	0.538652
$339$	−28.4092	−1.54297
$340$	−3.51129	−0.190426
$341$	13.6258	0.737881
$342$	−39.8766	−2.15628
$343$	20.1446	1.08771
$344$	−5.83776	−0.314751
$345$	38.7794	2.08781
$346$	−9.14436	−0.491604
$347$	20.4446	1.09752	0.548761	−	0.835979i	$-0.315100\pi$
$347$	20.4446	1.09752	0.548761	+	0.835979i	$0.315100\pi$
$348$	−32.5207	−1.74329
$349$	−24.0060	−1.28501	−0.642507	−	0.766280i	$-0.722106\pi$
$349$	−24.0060	−1.28501	−0.642507	+	0.766280i	$0.722106\pi$
$350$	−6.59320	−0.352422
$351$	26.8527	1.43329
$352$	4.86841	0.259487
$353$	5.78721	0.308022	0.154011	−	0.988069i	$-0.450781\pi$
$353$	5.78721	0.308022	0.154011	+	0.988069i	$0.450781\pi$
$354$	35.4981	1.88671
$355$	−0.447229	−0.0237365
$356$	−5.88216	−0.311754
$357$	−17.6704	−0.935216
$358$	5.93982	0.313929
$359$	25.0971	1.32457	0.662287	−	0.749250i	$-0.269586\pi$
$359$	25.0971	1.32457	0.662287	+	0.749250i	$0.269586\pi$
$360$	−10.4955	−0.553160
$361$	8.02270	0.422247
$362$	−24.3459	−1.27959
$363$	−41.4912	−2.17772
$364$	3.70933	0.194422
$365$	−18.6515	−0.976265
$366$	−19.4611	−1.01725
$367$	7.95965	0.415490	0.207745	−	0.978183i	$-0.433388\pi$
$367$	7.95965	0.415490	0.207745	+	0.978183i	$0.433388\pi$
$368$	−8.67659	−0.452299
$369$	10.1397	0.527852
$370$	−13.9646	−0.725983
$371$	−14.3348	−0.744223
$372$	9.14281	0.474032
$373$	34.7801	1.80085	0.900424	−	0.435013i	$-0.143256\pi$
$373$	34.7801	1.80085	0.900424	+	0.435013i	$0.143256\pi$
$374$	−12.4941	−0.646056
$375$	36.3277	1.87595
$376$	1.26757	0.0653698
$377$	−17.5197	−0.902312
$378$	−32.1618	−1.65423
$379$	−18.4592	−0.948184	−0.474092	−	0.880475i	$-0.657224\pi$
$379$	−18.4592	−0.948184	−0.474092	+	0.880475i	$0.657224\pi$
$380$	7.11234	0.364855
$381$	62.6480	3.20956
$382$	−4.56048	−0.233335
$383$	28.0851	1.43508	0.717542	−	0.696516i	$-0.245267\pi$
$383$	28.0851	1.43508	0.717542	+	0.696516i	$0.245267\pi$
$384$	3.26666	0.166701
$385$	14.0398	0.715532
$386$	−15.0988	−0.768510
$387$	44.7817	2.27638
$388$	11.2147	0.569341
$389$	23.0812	1.17026	0.585132	−	0.810938i	$-0.301043\pi$
$389$	23.0812	1.17026	0.585132	+	0.810938i	$0.301043\pi$
$390$	−7.86544	−0.398282
$391$	22.2673	1.12611
$392$	2.55729	0.129163
$393$	18.0611	0.911064
$394$	8.29533	0.417913
$395$	20.9227	1.05273
$396$	−37.3458	−1.87670
$397$	18.7516	0.941115	0.470558	−	0.882369i	$-0.344053\pi$
$397$	18.7516	0.941115	0.470558	+	0.882369i	$0.344053\pi$
$398$	−5.73149	−0.287294
$399$	35.7925	1.79186
$400$	−3.12804	−0.156402
$401$	12.1174	0.605113	0.302556	−	0.953132i	$-0.402160\pi$
$401$	12.1174	0.605113	0.302556	+	0.953132i	$0.402160\pi$
$402$	−39.9892	−1.99448
$403$	4.92547	0.245355
$404$	15.4063	0.766494
$405$	36.7111	1.82419
$406$	20.9836	1.04140
$407$	−49.6897	−2.46303
$408$	−8.38343	−0.415042
$409$	−0.110895	−0.00548341	−0.00274170	−	0.999996i	$-0.500873\pi$
$409$	−0.110895	−0.00548341	−0.00274170	+	0.999996i	$0.500873\pi$
$410$	−1.80850	−0.0893157
$411$	−0.722252	−0.0356260
$412$	9.43172	0.464667
$413$	−22.9048	−1.12707
$414$	66.5585	3.27117
$415$	−4.88579	−0.239834
$416$	1.75983	0.0862829
$417$	−25.5940	−1.25334
$418$	25.3076	1.23784
$419$	−25.0420	−1.22338	−0.611692	−	0.791096i	$-0.709511\pi$
$419$	−25.0420	−1.22338	−0.611692	+	0.791096i	$0.709511\pi$
$420$	9.42053	0.459675
$421$	−37.1393	−1.81006	−0.905028	−	0.425351i	$-0.860151\pi$
$421$	−37.1393	−1.81006	−0.905028	+	0.425351i	$0.860151\pi$
$422$	−18.7572	−0.913087
$423$	−9.72356	−0.472776
$424$	−6.80090	−0.330281
$425$	8.02770	0.389401
$426$	−1.06779	−0.0517345
$427$	12.5571	0.607679
$428$	7.67129	0.370806
$429$	−27.9874	−1.35124
$430$	−7.98720	−0.385177
$431$	19.5730	0.942799	0.471400	−	0.881920i	$-0.343749\pi$
$431$	19.5730	0.942799	0.471400	+	0.881920i	$0.343749\pi$
$432$	−15.2587	−0.734134
$433$	3.00246	0.144289	0.0721446	−	0.997394i	$-0.477016\pi$
$433$	3.00246	0.144289	0.0721446	+	0.997394i	$0.477016\pi$
$434$	−5.89930	−0.283175
$435$	−44.4946	−2.13335
$436$	−17.7477	−0.849961
$437$	−45.1038	−2.15761
$438$	−44.5317	−2.12781
$439$	−34.4736	−1.64533	−0.822667	−	0.568523i	$-0.807515\pi$
$439$	−34.4736	−1.64533	−0.822667	+	0.568523i	$0.807515\pi$
$440$	6.66094	0.317548
$441$	−19.6171	−0.934146
$442$	−4.51637	−0.214822
$443$	−21.8159	−1.03651	−0.518253	−	0.855227i	$-0.673418\pi$
$443$	−21.8159	−1.03651	−0.518253	+	0.855227i	$0.673418\pi$
$444$	−33.3413	−1.58231
$445$	−8.04794	−0.381509
$446$	5.16269	0.244461
$447$	−19.4482	−0.919871
$448$	−2.10777	−0.0995829
$449$	6.79348	0.320604	0.160302	−	0.987068i	$-0.448753\pi$
$449$	6.79348	0.320604	0.160302	+	0.987068i	$0.448753\pi$
$450$	23.9953	1.13115
$451$	−6.43515	−0.303019
$452$	8.69671	0.409059
$453$	14.2979	0.671773
$454$	−13.1823	−0.618678
$455$	5.07509	0.237924
$456$	16.9812	0.795216
$457$	−40.3185	−1.88602	−0.943010	−	0.332765i	$-0.892018\pi$
$457$	−40.3185	−1.88602	−0.943010	+	0.332765i	$0.892018\pi$
$458$	22.4258	1.04789
$459$	39.1594	1.82780
$460$	−11.8713	−0.553501
$461$	−31.8444	−1.48314	−0.741571	−	0.670875i	$-0.765919\pi$
$461$	−31.8444	−1.48314	−0.741571	+	0.670875i	$0.765919\pi$
$462$	33.5208	1.55953
$463$	−5.69460	−0.264651	−0.132325	−	0.991206i	$-0.542244\pi$
$463$	−5.69460	−0.264651	−0.132325	+	0.991206i	$0.542244\pi$
$464$	9.95534	0.462165
$465$	12.5091	0.580098
$466$	−21.6062	−1.00089
$467$	22.0782	1.02166	0.510828	−	0.859683i	$-0.329339\pi$
$467$	22.0782	1.02166	0.510828	+	0.859683i	$0.329339\pi$
$468$	−13.4997	−0.624026
$469$	25.8026	1.19145
$470$	1.73428	0.0799963
$471$	−11.6380	−0.536251
$472$	−10.8668	−0.500186
$473$	−28.4206	−1.30678
$474$	49.9543	2.29448
$475$	−16.2606	−0.746088
$476$	5.40932	0.247936
$477$	52.1700	2.38870
$478$	−0.295749	−0.0135272
$479$	−14.3295	−0.654730	−0.327365	−	0.944898i	$-0.606161\pi$
$479$	−14.3295	−0.654730	−0.327365	+	0.944898i	$0.606161\pi$
$480$	4.46942	0.204000
$481$	−17.9618	−0.818989
$482$	−12.7323	−0.579940
$483$	−59.7416	−2.71833
$484$	12.7014	0.577338
$485$	15.3439	0.696731
$486$	41.8740	1.89944
$487$	−33.8088	−1.53202	−0.766012	−	0.642826i	$-0.777762\pi$
$487$	−33.8088	−1.53202	−0.766012	+	0.642826i	$0.777762\pi$
$488$	5.95750	0.269683
$489$	77.7322	3.51517
$490$	3.49887	0.158063
$491$	3.54659	0.160055	0.0800277	−	0.996793i	$-0.474499\pi$
$491$	3.54659	0.160055	0.0800277	+	0.996793i	$0.474499\pi$
$492$	−4.31792	−0.194667
$493$	−25.5490	−1.15067
$494$	9.14820	0.411597
$495$	−51.0963	−2.29661
$496$	−2.79883	−0.125671
$497$	0.688979	0.0309049
$498$	−11.6651	−0.522727
$499$	6.93022	0.310239	0.155120	−	0.987896i	$-0.450424\pi$
$499$	6.93022	0.310239	0.155120	+	0.987896i	$0.450424\pi$
$500$	−11.1207	−0.497335
$501$	−82.1646	−3.67085
$502$	−17.9360	−0.800524
$503$	16.5699	0.738815	0.369407	−	0.929268i	$-0.379561\pi$
$503$	16.5699	0.738815	0.369407	+	0.929268i	$0.379561\pi$
$504$	16.1688	0.720216
$505$	21.0789	0.937997
$506$	−42.2412	−1.87785
$507$	32.3497	1.43670
$508$	−19.1780	−0.850887
$509$	−12.4018	−0.549699	−0.274849	−	0.961487i	$-0.588628\pi$
$509$	−12.4018	−0.549699	−0.274849	+	0.961487i	$0.588628\pi$
$510$	−11.4702	−0.507908
$511$	28.7336	1.27110
$512$	−1.00000	−0.0441942
$513$	−79.3198	−3.50205
$514$	0.393261	0.0173460
$515$	12.9044	0.568637
$516$	−19.0700	−0.839508
$517$	6.17104	0.271402
$518$	21.5131	0.945232
$519$	−29.8715	−1.31121
$520$	2.40780	0.105589
$521$	−13.5510	−0.593682	−0.296841	−	0.954927i	$-0.595933\pi$
$521$	−13.5510	−0.593682	−0.296841	+	0.954927i	$0.595933\pi$
$522$	−76.3678	−3.34253
$523$	43.7392	1.91258	0.956290	−	0.292420i	$-0.0944607\pi$
$523$	43.7392	1.91258	0.956290	+	0.292420i	$0.0944607\pi$
$524$	−5.52894	−0.241533
$525$	−21.5377	−0.939983
$526$	10.5219	0.458778
$527$	7.18282	0.312888
$528$	15.9034	0.692108
$529$	52.2832	2.27318
$530$	−9.30496	−0.404182
$531$	83.3598	3.61751
$532$	−10.9569	−0.475043
$533$	−2.32618	−0.100758
$534$	−19.2150	−0.831514
$535$	10.4958	0.453774
$536$	12.2416	0.528758
$537$	19.4033	0.837316
$538$	−9.41679	−0.405987
$539$	12.4499	0.536257
$540$	−20.8769	−0.898397
$541$	−10.8353	−0.465844	−0.232922	−	0.972495i	$-0.574829\pi$
$541$	−10.8353	−0.465844	−0.232922	+	0.972495i	$0.574829\pi$
$542$	2.31695	0.0995214
$543$	−79.5297	−3.41295
$544$	2.56637	0.110032
$545$	−24.2823	−1.04014
$546$	12.1171	0.518564
$547$	1.29493	0.0553673	0.0276836	−	0.999617i	$-0.491187\pi$
$547$	1.29493	0.0553673	0.0276836	+	0.999617i	$0.491187\pi$
$548$	0.221098	0.00944485
$549$	−45.7002	−1.95044
$550$	−15.2286	−0.649350
$551$	51.7512	2.20468
$552$	−28.3434	−1.20638
$553$	−32.2325	−1.37066
$554$	3.85239	0.163672
$555$	−45.6174	−1.93635
$556$	7.83492	0.332275
$557$	−43.9401	−1.86180	−0.930901	−	0.365271i	$-0.880976\pi$
$557$	−43.9401	−1.86180	−0.930901	+	0.365271i	$0.880976\pi$
$558$	21.4699	0.908894
$559$	−10.2735	−0.434522
$560$	−2.88385	−0.121865
$561$	−40.8140	−1.72317
$562$	10.2685	0.433151
$563$	−36.0805	−1.52061	−0.760306	−	0.649565i	$-0.774951\pi$
$563$	−36.0805	−1.52061	−0.760306	+	0.649565i	$0.774951\pi$
$564$	4.14070	0.174355
$565$	11.8988	0.500586
$566$	−3.21291	−0.135049
$567$	−56.5552	−2.37510
$568$	0.326875	0.0137154
$569$	−15.3005	−0.641431	−0.320715	−	0.947176i	$-0.603923\pi$
$569$	−15.3005	−0.641431	−0.320715	+	0.947176i	$0.603923\pi$
$570$	23.2336	0.973147
$571$	−6.52668	−0.273133	−0.136567	−	0.990631i	$-0.543607\pi$
$571$	−6.52668	−0.273133	−0.136567	+	0.990631i	$0.543607\pi$
$572$	8.56759	0.358229
$573$	−14.8975	−0.622353
$574$	2.78609	0.116289
$575$	27.1407	1.13185
$576$	7.67104	0.319627
$577$	−15.0875	−0.628103	−0.314051	−	0.949406i	$-0.601686\pi$
$577$	−15.0875	−0.628103	−0.314051	+	0.949406i	$0.601686\pi$
$578$	10.4138	0.433156
$579$	−49.3227	−2.04978
$580$	13.6209	0.565575
$581$	7.52680	0.312264
$582$	36.6346	1.51855
$583$	−33.1096	−1.37126
$584$	13.6322	0.564105
$585$	−18.4703	−0.763653
$586$	26.4775	1.09377
$587$	34.0517	1.40546	0.702732	−	0.711454i	$-0.251963\pi$
$587$	34.0517	1.40546	0.702732	+	0.711454i	$0.251963\pi$
$588$	8.35379	0.344504
$589$	−14.5492	−0.599491
$590$	−14.8679	−0.612103
$591$	27.0980	1.11466
$592$	10.2066	0.419487
$593$	−22.9841	−0.943842	−0.471921	−	0.881641i	$-0.656439\pi$
$593$	−22.9841	−0.943842	−0.471921	+	0.881641i	$0.656439\pi$
$594$	−74.2856	−3.04797
$595$	7.40100	0.303412
$596$	5.95357	0.243868
$597$	−18.7228	−0.766274
$598$	−15.2694	−0.624410
$599$	3.45037	0.140978	0.0704892	−	0.997513i	$-0.477544\pi$
$599$	3.45037	0.140978	0.0704892	+	0.997513i	$0.477544\pi$
$600$	−10.2182	−0.417158
$601$	36.2095	1.47701	0.738507	−	0.674245i	$-0.235531\pi$
$601$	36.2095	1.47701	0.738507	+	0.674245i	$0.235531\pi$
$602$	12.3047	0.501501
$603$	−93.9061	−3.82415
$604$	−4.37692	−0.178094
$605$	17.3780	0.706518
$606$	50.3272	2.04440
$607$	−31.1693	−1.26512	−0.632561	−	0.774511i	$-0.717996\pi$
$607$	−31.1693	−1.26512	−0.632561	+	0.774511i	$0.717996\pi$
$608$	−5.19834	−0.210820
$609$	68.5462	2.77763
$610$	8.15102	0.330025
$611$	2.23071	0.0902447
$612$	−19.6867	−0.795787
$613$	−6.43977	−0.260100	−0.130050	−	0.991507i	$-0.541514\pi$
$613$	−6.43977	−0.260100	−0.130050	+	0.991507i	$0.541514\pi$
$614$	26.4159	1.06606
$615$	−5.90776	−0.238224
$616$	−10.2615	−0.413448
$617$	−28.4409	−1.14499	−0.572493	−	0.819910i	$-0.694024\pi$
$617$	−28.4409	−1.14499	−0.572493	+	0.819910i	$0.694024\pi$
$618$	30.8102	1.23937
$619$	−17.1573	−0.689609	−0.344804	−	0.938675i	$-0.612055\pi$
$619$	−17.1573	−0.689609	−0.344804	+	0.938675i	$0.612055\pi$
$620$	−3.82934	−0.153790
$621$	132.393	5.31276
$622$	25.9104	1.03891
$623$	12.3983	0.496726
$624$	5.74877	0.230135
$625$	0.424851	0.0169940
$626$	−7.09101	−0.283414
$627$	82.6714	3.30158
$628$	3.56267	0.142166
$629$	−26.1938	−1.04441
$630$	22.1221	0.881366
$631$	−37.1493	−1.47889	−0.739446	−	0.673216i	$-0.764912\pi$
$631$	−37.1493	−1.47889	−0.739446	+	0.673216i	$0.764912\pi$
$632$	−15.2922	−0.608290
$633$	−61.2734	−2.43540
$634$	33.9371	1.34781
$635$	−26.2393	−1.04127
$636$	−22.2162	−0.880930
$637$	4.50040	0.178312
$638$	48.4667	1.91882
$639$	−2.50747	−0.0991941
$640$	−1.36820	−0.0540827
$641$	12.4117	0.490235	0.245117	−	0.969493i	$-0.421174\pi$
$641$	12.4117	0.490235	0.245117	+	0.969493i	$0.421174\pi$
$642$	25.0595	0.989018
$643$	19.1434	0.754941	0.377470	−	0.926022i	$-0.376794\pi$
$643$	19.1434	0.754941	0.377470	+	0.926022i	$0.376794\pi$
$644$	18.2883	0.720660
$645$	−26.0914	−1.02735
$646$	13.3408	0.524888
$647$	−29.6230	−1.16460	−0.582301	−	0.812973i	$-0.697847\pi$
$647$	−29.6230	−1.16460	−0.582301	+	0.812973i	$0.697847\pi$
$648$	−26.8317	−1.05405
$649$	−52.9041	−2.07667
$650$	−5.50483	−0.215917
$651$	−19.2710	−0.755289
$652$	−23.7956	−0.931909
$653$	12.4620	0.487677	0.243839	−	0.969816i	$-0.421593\pi$
$653$	12.4620	0.487677	0.243839	+	0.969816i	$0.421593\pi$
$654$	−57.9756	−2.26703
$655$	−7.56467	−0.295576
$656$	1.32182	0.0516083
$657$	−104.573	−4.07979
$658$	−2.67174	−0.104155
$659$	−24.8681	−0.968723	−0.484362	−	0.874868i	$-0.660948\pi$
$659$	−24.8681	−0.968723	−0.484362	+	0.874868i	$0.660948\pi$
$660$	21.7590	0.846968
$661$	−38.0100	−1.47842	−0.739209	−	0.673476i	$-0.764800\pi$
$661$	−38.0100	−1.47842	−0.739209	+	0.673476i	$0.764800\pi$
$662$	−15.3668	−0.597249
$663$	−14.7534	−0.572976
$664$	3.57097	0.138581
$665$	−14.9912	−0.581334
$666$	−78.2949	−3.03387
$667$	−86.3784	−3.34459
$668$	25.1525	0.973180
$669$	16.8647	0.652029
$670$	16.7490	0.647069
$671$	29.0036	1.11967
$672$	−6.88537	−0.265609
$673$	−14.8124	−0.570976	−0.285488	−	0.958382i	$-0.592156\pi$
$673$	−14.8124	−0.570976	−0.285488	+	0.958382i	$0.592156\pi$
$674$	−24.4687	−0.942501
$675$	47.7298	1.83712
$676$	−9.90299	−0.380884
$677$	−6.00381	−0.230745	−0.115373	−	0.993322i	$-0.536806\pi$
$677$	−6.00381	−0.230745	−0.115373	+	0.993322i	$0.536806\pi$
$678$	28.4092	1.09105
$679$	−23.6381	−0.907146
$680$	3.51129	0.134652
$681$	−43.0622	−1.65015
$682$	−13.6258	−0.521761
$683$	−21.0724	−0.806313	−0.403157	−	0.915131i	$-0.632087\pi$
$683$	−21.0724	−0.806313	−0.403157	+	0.915131i	$0.632087\pi$
$684$	39.8766	1.52472
$685$	0.302506	0.0115581
$686$	−20.1446	−0.769125
$687$	73.2574	2.79494
$688$	5.83776	0.222563
$689$	−11.9684	−0.455962
$690$	−38.7794	−1.47631
$691$	−19.4128	−0.738499	−0.369249	−	0.929330i	$-0.620385\pi$
$691$	−19.4128	−0.738499	−0.369249	+	0.929330i	$0.620385\pi$
$692$	9.14436	0.347616
$693$	78.7165	2.99019
$694$	−20.4446	−0.776065
$695$	10.7197	0.406621
$696$	32.5207	1.23269
$697$	−3.39227	−0.128491
$698$	24.0060	0.908642
$699$	−70.5799	−2.66958
$700$	6.59320	0.249200
$701$	−22.4056	−0.846250	−0.423125	−	0.906071i	$-0.639067\pi$
$701$	−22.4056	−0.846250	−0.423125	+	0.906071i	$0.639067\pi$
$702$	−26.8527	−1.01349
$703$	53.0571	2.00109
$704$	−4.86841	−0.183485
$705$	5.66529	0.213367
$706$	−5.78721	−0.217805
$707$	−32.4731	−1.22128
$708$	−35.4981	−1.33410
$709$	−35.9065	−1.34850	−0.674248	−	0.738505i	$-0.735532\pi$
$709$	−35.9065	−1.34850	−0.674248	+	0.738505i	$0.735532\pi$
$710$	0.447229	0.0167842
$711$	117.307	4.39935
$712$	5.88216	0.220443
$713$	24.2843	0.909454
$714$	17.6704	0.661297
$715$	11.7221	0.438383
$716$	−5.93982	−0.221981
$717$	−0.966109	−0.0360800
$718$	−25.0971	−0.936615
$719$	−30.6661	−1.14365	−0.571825	−	0.820375i	$-0.693765\pi$
$719$	−30.6661	−1.14365	−0.571825	+	0.820375i	$0.693765\pi$
$720$	10.4955	0.391144
$721$	−19.8799	−0.740367
$722$	−8.02270	−0.298574
$723$	−41.5920	−1.54682
$724$	24.3459	0.904809
$725$	−31.1407	−1.15654
$726$	41.4912	1.53988
$727$	32.3142	1.19847	0.599233	−	0.800575i	$-0.295472\pi$
$727$	32.3142	1.19847	0.599233	+	0.800575i	$0.295472\pi$
$728$	−3.70933	−0.137477
$729$	56.2928	2.08492
$730$	18.6515	0.690324
$731$	−14.9818	−0.554123
$732$	19.4611	0.719303
$733$	13.4399	0.496415	0.248208	−	0.968707i	$-0.420158\pi$
$733$	13.4399	0.496415	0.248208	+	0.968707i	$0.420158\pi$
$734$	−7.95965	−0.293796
$735$	11.4296	0.421588
$736$	8.67659	0.319823
$737$	59.5974	2.19530
$738$	−10.1397	−0.373248
$739$	31.4506	1.15693	0.578464	−	0.815708i	$-0.303652\pi$
$739$	31.4506	1.15693	0.578464	+	0.815708i	$0.303652\pi$
$740$	13.9646	0.513348
$741$	29.8840	1.09782
$742$	14.3348	0.526245
$743$	−4.69016	−0.172065	−0.0860326	−	0.996292i	$-0.527419\pi$
$743$	−4.69016	−0.172065	−0.0860326	+	0.996292i	$0.527419\pi$
$744$	−9.14281	−0.335192
$745$	8.14564	0.298433
$746$	−34.7801	−1.27339
$747$	−27.3931	−1.00226
$748$	12.4941	0.456830
$749$	−16.1693	−0.590815
$750$	−36.3277	−1.32650
$751$	33.1799	1.21075	0.605376	−	0.795940i	$-0.293023\pi$
$751$	33.1799	1.21075	0.605376	+	0.795940i	$0.293023\pi$
$752$	−1.26757	−0.0462234
$753$	−58.5908	−2.13517
$754$	17.5197	0.638031
$755$	−5.98848	−0.217943
$756$	32.1618	1.16972
$757$	−7.93736	−0.288488	−0.144244	−	0.989542i	$-0.546075\pi$
$757$	−7.93736	−0.288488	−0.144244	+	0.989542i	$0.546075\pi$
$758$	18.4592	0.670467
$759$	−137.988	−5.00863
$760$	−7.11234	−0.257992
$761$	−12.4691	−0.452004	−0.226002	−	0.974127i	$-0.572566\pi$
$761$	−12.4691	−0.452004	−0.226002	+	0.974127i	$0.572566\pi$
$762$	−62.6480	−2.26950
$763$	37.4081	1.35427
$764$	4.56048	0.164993
$765$	−26.9352	−0.973846
$766$	−28.0851	−1.01476
$767$	−19.1238	−0.690520
$768$	−3.26666	−0.117875
$769$	−47.6952	−1.71993	−0.859967	−	0.510349i	$-0.829516\pi$
$769$	−47.6952	−1.71993	−0.859967	+	0.510349i	$0.829516\pi$
$770$	−14.0398	−0.505958
$771$	1.28465	0.0462655
$772$	15.0988	0.543418
$773$	−32.6065	−1.17278	−0.586388	−	0.810030i	$-0.699451\pi$
$773$	−32.6065	−1.17278	−0.586388	+	0.810030i	$0.699451\pi$
$774$	−44.7817	−1.60965
$775$	8.75485	0.314483
$776$	−11.2147	−0.402585
$777$	70.2759	2.52114
$778$	−23.0812	−0.827502
$779$	6.87125	0.246188
$780$	7.86544	0.281628
$781$	1.59136	0.0569434
$782$	−22.2673	−0.796277
$783$	−151.905	−5.42865
$784$	−2.55729	−0.0913318
$785$	4.87443	0.173976
$786$	−18.0611	−0.644220
$787$	13.6140	0.485287	0.242643	−	0.970116i	$-0.421986\pi$
$787$	13.6140	0.485287	0.242643	+	0.970116i	$0.421986\pi$
$788$	−8.29533	−0.295509
$789$	34.3716	1.22366
$790$	−20.9227	−0.744396
$791$	−18.3307	−0.651764
$792$	37.3458	1.32702
$793$	10.4842	0.372305
$794$	−18.7516	−0.665469
$795$	−30.3961	−1.07804
$796$	5.73149	0.203147
$797$	−20.5388	−0.727521	−0.363761	−	0.931492i	$-0.618507\pi$
$797$	−20.5388	−0.727521	−0.363761	+	0.931492i	$0.618507\pi$
$798$	−35.7925	−1.26704
$799$	3.25304	0.115084
$800$	3.12804	0.110593
$801$	−45.1223	−1.59432
$802$	−12.1174	−0.427879
$803$	66.3672	2.34205
$804$	39.9892	1.41031
$805$	25.0220	0.881908
$806$	−4.92547	−0.173492
$807$	−30.7614	−1.08285
$808$	−15.4063	−0.541993
$809$	29.5648	1.03944	0.519721	−	0.854336i	$-0.326036\pi$
$809$	29.5648	1.03944	0.519721	+	0.854336i	$0.326036\pi$
$810$	−36.7111	−1.28990
$811$	−53.6405	−1.88357	−0.941787	−	0.336210i	$-0.890855\pi$
$811$	−53.6405	−1.88357	−0.941787	+	0.336210i	$0.890855\pi$
$812$	−20.9836	−0.736380
$813$	7.56867	0.265445
$814$	49.6897	1.74162
$815$	−32.5571	−1.14042
$816$	8.38343	0.293479
$817$	30.3466	1.06169
$818$	0.110895	0.00387735
$819$	28.4544	0.994278
$820$	1.80850	0.0631557
$821$	40.2909	1.40616	0.703081	−	0.711110i	$-0.251807\pi$
$821$	40.2909	1.40616	0.703081	+	0.711110i	$0.251807\pi$
$822$	0.722252	0.0251914
$823$	−26.5047	−0.923895	−0.461948	−	0.886907i	$-0.652849\pi$
$823$	−26.5047	−0.923895	−0.461948	+	0.886907i	$0.652849\pi$
$824$	−9.43172	−0.328569
$825$	−49.7466	−1.73195
$826$	22.9048	0.796960
$827$	−20.0913	−0.698644	−0.349322	−	0.937003i	$-0.613588\pi$
$827$	−20.0913	−0.698644	−0.349322	+	0.937003i	$0.613588\pi$
$828$	−66.5585	−2.31307
$829$	−3.45420	−0.119969	−0.0599846	−	0.998199i	$-0.519105\pi$
$829$	−3.45420	−0.119969	−0.0599846	+	0.998199i	$0.519105\pi$
$830$	4.88579	0.169588
$831$	12.5844	0.436549
$832$	−1.75983	−0.0610112
$833$	6.56294	0.227392
$834$	25.5940	0.886247
$835$	34.4136	1.19093
$836$	−25.3076	−0.875283
$837$	42.7064	1.47615
$838$	25.0420	0.865063
$839$	32.0966	1.10810	0.554049	−	0.832484i	$-0.313082\pi$
$839$	32.0966	1.10810	0.554049	+	0.832484i	$0.313082\pi$
$840$	−9.42053	−0.325039
$841$	70.1088	2.41754
$842$	37.1393	1.27990
$843$	33.5437	1.15531
$844$	18.7572	0.645650
$845$	−13.5492	−0.466107
$846$	9.72356	0.334303
$847$	−26.7718	−0.919889
$848$	6.80090	0.233544
$849$	−10.4955	−0.360203
$850$	−8.02770	−0.275348
$851$	−88.5581	−3.03573
$852$	1.06779	0.0365818
$853$	−36.3161	−1.24344	−0.621720	−	0.783240i	$-0.713566\pi$
$853$	−36.3161	−1.24344	−0.621720	+	0.783240i	$0.713566\pi$
$854$	−12.5571	−0.429694
$855$	54.5590	1.86588
$856$	−7.67129	−0.262199
$857$	35.9066	1.22654	0.613272	−	0.789872i	$-0.289853\pi$
$857$	35.9066	1.22654	0.613272	+	0.789872i	$0.289853\pi$
$858$	27.9874	0.955473
$859$	6.96123	0.237514	0.118757	−	0.992923i	$-0.462109\pi$
$859$	6.96123	0.237514	0.118757	+	0.992923i	$0.462109\pi$
$860$	7.98720	0.272361
$861$	9.10120	0.310168
$862$	−19.5730	−0.666660
$863$	−15.7157	−0.534969	−0.267485	−	0.963562i	$-0.586192\pi$
$863$	−15.7157	−0.534969	−0.267485	+	0.963562i	$0.586192\pi$
$864$	15.2587	0.519111
$865$	12.5113	0.425396
$866$	−3.00246	−0.102028
$867$	34.0182	1.15532
$868$	5.89930	0.200235
$869$	−74.4486	−2.52550
$870$	44.4946	1.50851
$871$	21.5432	0.729965
$872$	17.7477	0.601013
$873$	86.0285	2.91162
$874$	45.1038	1.52566
$875$	23.4400	0.792417
$876$	44.5317	1.50459
$877$	2.00718	0.0677778	0.0338889	−	0.999426i	$-0.489211\pi$
$877$	2.00718	0.0677778	0.0338889	+	0.999426i	$0.489211\pi$
$878$	34.4736	1.16343
$879$	86.4928	2.91733
$880$	−6.66094	−0.224540
$881$	−40.0825	−1.35041	−0.675207	−	0.737628i	$-0.735946\pi$
$881$	−40.0825	−1.35041	−0.675207	+	0.737628i	$0.735946\pi$
$882$	19.6171	0.660541
$883$	−31.6168	−1.06399	−0.531995	−	0.846748i	$-0.678557\pi$
$883$	−31.6168	−1.06399	−0.531995	+	0.846748i	$0.678557\pi$
$884$	4.51637	0.151902
$885$	−48.5684	−1.63261
$886$	21.8159	0.732921
$887$	29.2692	0.982763	0.491381	−	0.870944i	$-0.336492\pi$
$887$	29.2692	0.982763	0.491381	+	0.870944i	$0.336492\pi$
$888$	33.3413	1.11886
$889$	40.4229	1.35574
$890$	8.04794	0.269768
$891$	−130.628	−4.37620
$892$	−5.16269	−0.172860
$893$	−6.58924	−0.220500
$894$	19.4482	0.650447
$895$	−8.12683	−0.271650
$896$	2.10777	0.0704158
$897$	−49.8797	−1.66544
$898$	−6.79348	−0.226701
$899$	−27.8633	−0.929293
$900$	−23.9953	−0.799844
$901$	−17.4536	−0.581464
$902$	6.43515	0.214267
$903$	40.1952	1.33761
$904$	−8.69671	−0.289248
$905$	33.3100	1.10726
$906$	−14.2979	−0.475015
$907$	−10.5253	−0.349486	−0.174743	−	0.984614i	$-0.555909\pi$
$907$	−10.5253	−0.349486	−0.174743	+	0.984614i	$0.555909\pi$
$908$	13.1823	0.437472
$909$	118.183	3.91987
$910$	−5.07509	−0.168238
$911$	22.4853	0.744970	0.372485	−	0.928038i	$-0.378506\pi$
$911$	22.4853	0.744970	0.372485	+	0.928038i	$0.378506\pi$
$912$	−16.9812	−0.562303
$913$	17.3850	0.575359
$914$	40.3185	1.33362
$915$	26.6266	0.880248
$916$	−22.4258	−0.740969
$917$	11.6538	0.384841
$918$	−39.1594	−1.29245
$919$	3.43645	0.113358	0.0566790	−	0.998392i	$-0.481949\pi$
$919$	3.43645	0.113358	0.0566790	+	0.998392i	$0.481949\pi$
$920$	11.8713	0.391384
$921$	86.2916	2.84341
$922$	31.8444	1.04874
$923$	0.575246	0.0189344
$924$	−33.5208	−1.10275
$925$	−31.9265	−1.04974
$926$	5.69460	0.187136
$927$	72.3511	2.37632
$928$	−9.95534	−0.326800
$929$	−9.16913	−0.300830	−0.150415	−	0.988623i	$-0.548061\pi$
$929$	−9.16913	−0.300830	−0.150415	+	0.988623i	$0.548061\pi$
$930$	−12.5091	−0.410191
$931$	−13.2937	−0.435682
$932$	21.6062	0.707733
$933$	84.6404	2.77100
$934$	−22.0782	−0.722420
$935$	17.0944	0.559047
$936$	13.4997	0.441253
$937$	−19.9714	−0.652438	−0.326219	−	0.945294i	$-0.605775\pi$
$937$	−19.9714	−0.652438	−0.326219	+	0.945294i	$0.605775\pi$
$938$	−25.8026	−0.842485
$939$	−23.1639	−0.755925
$940$	−1.73428	−0.0565659
$941$	−5.12082	−0.166934	−0.0834670	−	0.996511i	$-0.526599\pi$
$941$	−5.12082	−0.166934	−0.0834670	+	0.996511i	$0.526599\pi$
$942$	11.6380	0.379187
$943$	−11.4689	−0.373478
$944$	10.8668	0.353685
$945$	44.0037	1.43144
$946$	28.4206	0.924034
$947$	4.48636	0.145787	0.0728936	−	0.997340i	$-0.476777\pi$
$947$	4.48636	0.145787	0.0728936	+	0.997340i	$0.476777\pi$
$948$	−49.9543	−1.62244
$949$	23.9904	0.778761
$950$	16.2606	0.527564
$951$	110.861	3.59490
$952$	−5.40932	−0.175317
$953$	−2.84151	−0.0920454	−0.0460227	−	0.998940i	$-0.514655\pi$
$953$	−2.84151	−0.0920454	−0.0460227	+	0.998940i	$0.514655\pi$
$954$	−52.1700	−1.68907
$955$	6.23963	0.201910
$956$	0.295749	0.00956520
$957$	158.324	5.11789
$958$	14.3295	0.462964
$959$	−0.466025	−0.0150487
$960$	−4.46942	−0.144250
$961$	−23.1666	−0.747308
$962$	17.9618	0.579113
$963$	58.8468	1.89631
$964$	12.7323	0.410079
$965$	20.6581	0.665009
$966$	59.7416	1.92215
$967$	−15.5309	−0.499440	−0.249720	−	0.968318i	$-0.580339\pi$
$967$	−15.5309	−0.499440	−0.249720	+	0.968318i	$0.580339\pi$
$968$	−12.7014	−0.408240
$969$	43.5799	1.39999
$970$	−15.3439	−0.492664
$971$	−27.8610	−0.894103	−0.447051	−	0.894508i	$-0.647526\pi$
$971$	−27.8610	−0.894103	−0.447051	+	0.894508i	$0.647526\pi$
$972$	−41.8740	−1.34311
$973$	−16.5142	−0.529422
$974$	33.8088	1.08330
$975$	−17.9824	−0.575897
$976$	−5.95750	−0.190695
$977$	3.96637	0.126895	0.0634477	−	0.997985i	$-0.479790\pi$
$977$	3.96637	0.126895	0.0634477	+	0.997985i	$0.479790\pi$
$978$	−77.7322	−2.48560
$979$	28.6368	0.915235
$980$	−3.49887	−0.111767
$981$	−136.143	−4.34672
$982$	−3.54659	−0.113176
$983$	22.6725	0.723142	0.361571	−	0.932345i	$-0.382241\pi$
$983$	22.6725	0.723142	0.361571	+	0.932345i	$0.382241\pi$
$984$	4.31792	0.137650
$985$	−11.3496	−0.361629
$986$	25.5490	0.813647
$987$	−8.72767	−0.277805
$988$	−9.14820	−0.291043
$989$	−50.6519	−1.61064
$990$	51.0963	1.62395
$991$	−50.0356	−1.58943	−0.794717	−	0.606980i	$-0.792381\pi$
$991$	−50.0356	−1.58943	−0.794717	+	0.606980i	$0.792381\pi$
$992$	2.79883	0.0888629
$993$	−50.1981	−1.59299
$994$	−0.688979	−0.0218531
$995$	7.84180	0.248602
$996$	11.6651	0.369624
$997$	−27.3368	−0.865764	−0.432882	−	0.901451i	$-0.642503\pi$
$997$	−27.3368	−0.865764	−0.432882	+	0.901451i	$0.642503\pi$
$998$	−6.93022	−0.219372
$999$	−155.739	−4.92735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.b.1.4	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.b.1.4	✓	82	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.26666 q^{3} +1.00000 q^{4} +1.36820 q^{5} +3.26666 q^{6} -2.10777 q^{7} -1.00000 q^{8} +7.67104 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.26666 q^{3} +1.00000 q^{4} +1.36820 q^{5} +3.26666 q^{6} -2.10777 q^{7} -1.00000 q^{8} +7.67104 q^{9} -1.36820 q^{10} -4.86841 q^{11} -3.26666 q^{12} -1.75983 q^{13} +2.10777 q^{14} -4.46942 q^{15} +1.00000 q^{16} -2.56637 q^{17} -7.67104 q^{18} +5.19834 q^{19} +1.36820 q^{20} +6.88537 q^{21} +4.86841 q^{22} -8.67659 q^{23} +3.26666 q^{24} -3.12804 q^{25} +1.75983 q^{26} -15.2587 q^{27} -2.10777 q^{28} +9.95534 q^{29} +4.46942 q^{30} -2.79883 q^{31} -1.00000 q^{32} +15.9034 q^{33} +2.56637 q^{34} -2.88385 q^{35} +7.67104 q^{36} +10.2066 q^{37} -5.19834 q^{38} +5.74877 q^{39} -1.36820 q^{40} +1.32182 q^{41} -6.88537 q^{42} +5.83776 q^{43} -4.86841 q^{44} +10.4955 q^{45} +8.67659 q^{46} -1.26757 q^{47} -3.26666 q^{48} -2.55729 q^{49} +3.12804 q^{50} +8.38343 q^{51} -1.75983 q^{52} +6.80090 q^{53} +15.2587 q^{54} -6.66094 q^{55} +2.10777 q^{56} -16.9812 q^{57} -9.95534 q^{58} +10.8668 q^{59} -4.46942 q^{60} -5.95750 q^{61} +2.79883 q^{62} -16.1688 q^{63} +1.00000 q^{64} -2.40780 q^{65} -15.9034 q^{66} -12.2416 q^{67} -2.56637 q^{68} +28.3434 q^{69} +2.88385 q^{70} -0.326875 q^{71} -7.67104 q^{72} -13.6322 q^{73} -10.2066 q^{74} +10.2182 q^{75} +5.19834 q^{76} +10.2615 q^{77} -5.74877 q^{78} +15.2922 q^{79} +1.36820 q^{80} +26.8317 q^{81} -1.32182 q^{82} -3.57097 q^{83} +6.88537 q^{84} -3.51129 q^{85} -5.83776 q^{86} -32.5207 q^{87} +4.86841 q^{88} -5.88216 q^{89} -10.4955 q^{90} +3.70933 q^{91} -8.67659 q^{92} +9.14281 q^{93} +1.26757 q^{94} +7.11234 q^{95} +3.26666 q^{96} +11.2147 q^{97} +2.55729 q^{98} -37.3458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q - 82 q^{2} - 13 q^{3} + 82 q^{4} + 3 q^{5} + 13 q^{6} - 37 q^{7} - 82 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q - 82 * q^2 - 13 * q^3 + 82 * q^4 + 3 * q^5 + 13 * q^6 - 37 * q^7 - 82 * q^8 + 91 * q^9	\( 82 q - 82 q^{2} - 13 q^{3} + 82 q^{4} + 3 q^{5} + 13 q^{6} - 37 q^{7} - 82 q^{8} + 91 q^{9} - 3 q^{10} - 16 q^{11} - 13 q^{12} - 42 q^{13} + 37 q^{14} - 9 q^{15} + 82 q^{16} + 3 q^{17} - 91 q^{18} - 42 q^{19} + 3 q^{20} - q^{21} + 16 q^{22} - 6 q^{23} + 13 q^{24} + 53 q^{25} + 42 q^{26} - 49 q^{27} - 37 q^{28} + 15 q^{29} + 9 q^{30} - 40 q^{31} - 82 q^{32} - 37 q^{33} - 3 q^{34} - 42 q^{35} + 91 q^{36} - 72 q^{37} + 42 q^{38} - 14 q^{39} - 3 q^{40} + 8 q^{41} + q^{42} - 93 q^{43} - 16 q^{44} - 11 q^{45} + 6 q^{46} + 7 q^{47} - 13 q^{48} + 61 q^{49} - 53 q^{50} - 70 q^{51} - 42 q^{52} + 18 q^{53} + 49 q^{54} - 62 q^{55} + 37 q^{56} - 51 q^{57} - 15 q^{58} - 47 q^{59} - 9 q^{60} - 14 q^{61} + 40 q^{62} - 100 q^{63} + 82 q^{64} + q^{65} + 37 q^{66} - 150 q^{67} + 3 q^{68} + 31 q^{69} + 42 q^{70} + 7 q^{71} - 91 q^{72} - 78 q^{73} + 72 q^{74} - 49 q^{75} - 42 q^{76} + 29 q^{77} + 14 q^{78} - 59 q^{79} + 3 q^{80} + 122 q^{81} - 8 q^{82} - 52 q^{83} - q^{84} - 108 q^{85} + 93 q^{86} - 49 q^{87} + 16 q^{88} + 38 q^{89} + 11 q^{90} - 69 q^{91} - 6 q^{92} - 63 q^{93} - 7 q^{94} + 5 q^{95} + 13 q^{96} - 74 q^{97} - 61 q^{98} - 89 q^{99}+O(q^{100}) \) 82 * q - 82 * q^2 - 13 * q^3 + 82 * q^4 + 3 * q^5 + 13 * q^6 - 37 * q^7 - 82 * q^8 + 91 * q^9 - 3 * q^10 - 16 * q^11 - 13 * q^12 - 42 * q^13 + 37 * q^14 - 9 * q^15 + 82 * q^16 + 3 * q^17 - 91 * q^18 - 42 * q^19 + 3 * q^20 - q^21 + 16 * q^22 - 6 * q^23 + 13 * q^24 + 53 * q^25 + 42 * q^26 - 49 * q^27 - 37 * q^28 + 15 * q^29 + 9 * q^30 - 40 * q^31 - 82 * q^32 - 37 * q^33 - 3 * q^34 - 42 * q^35 + 91 * q^36 - 72 * q^37 + 42 * q^38 - 14 * q^39 - 3 * q^40 + 8 * q^41 + q^42 - 93 * q^43 - 16 * q^44 - 11 * q^45 + 6 * q^46 + 7 * q^47 - 13 * q^48 + 61 * q^49 - 53 * q^50 - 70 * q^51 - 42 * q^52 + 18 * q^53 + 49 * q^54 - 62 * q^55 + 37 * q^56 - 51 * q^57 - 15 * q^58 - 47 * q^59 - 9 * q^60 - 14 * q^61 + 40 * q^62 - 100 * q^63 + 82 * q^64 + q^65 + 37 * q^66 - 150 * q^67 + 3 * q^68 + 31 * q^69 + 42 * q^70 + 7 * q^71 - 91 * q^72 - 78 * q^73 + 72 * q^74 - 49 * q^75 - 42 * q^76 + 29 * q^77 + 14 * q^78 - 59 * q^79 + 3 * q^80 + 122 * q^81 - 8 * q^82 - 52 * q^83 - q^84 - 108 * q^85 + 93 * q^86 - 49 * q^87 + 16 * q^88 + 38 * q^89 + 11 * q^90 - 69 * q^91 - 6 * q^92 - 63 * q^93 - 7 * q^94 + 5 * q^95 + 13 * q^96 - 74 * q^97 - 61 * q^98 - 89 * q^99

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