LMFDB - Embedded newform 8021.2.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.48492 q^{2} -2.97194 q^{3} +4.17482 q^{4} +3.21951 q^{5} +7.38503 q^{6} +2.90175 q^{7} -5.40425 q^{8} +5.83242 q^{9} +O(q^{10})$	\(q-2.48492 q^{2} -2.97194 q^{3} +4.17482 q^{4} +3.21951 q^{5} +7.38503 q^{6} +2.90175 q^{7} -5.40425 q^{8} +5.83242 q^{9} -8.00022 q^{10} -2.09665 q^{11} -12.4073 q^{12} +1.00000 q^{13} -7.21062 q^{14} -9.56819 q^{15} +5.07949 q^{16} +0.183348 q^{17} -14.4931 q^{18} -8.32967 q^{19} +13.4409 q^{20} -8.62384 q^{21} +5.21000 q^{22} -5.93575 q^{23} +16.0611 q^{24} +5.36524 q^{25} -2.48492 q^{26} -8.41779 q^{27} +12.1143 q^{28} -2.88281 q^{29} +23.7762 q^{30} +1.57653 q^{31} -1.81360 q^{32} +6.23111 q^{33} -0.455605 q^{34} +9.34222 q^{35} +24.3493 q^{36} -7.21849 q^{37} +20.6986 q^{38} -2.97194 q^{39} -17.3990 q^{40} +5.76504 q^{41} +21.4295 q^{42} -2.35176 q^{43} -8.75313 q^{44} +18.7775 q^{45} +14.7498 q^{46} -4.35501 q^{47} -15.0959 q^{48} +1.42017 q^{49} -13.3322 q^{50} -0.544899 q^{51} +4.17482 q^{52} +13.5183 q^{53} +20.9175 q^{54} -6.75018 q^{55} -15.6818 q^{56} +24.7553 q^{57} +7.16355 q^{58} +4.68363 q^{59} -39.9455 q^{60} +9.39936 q^{61} -3.91754 q^{62} +16.9243 q^{63} -5.65231 q^{64} +3.21951 q^{65} -15.4838 q^{66} +1.23974 q^{67} +0.765445 q^{68} +17.6407 q^{69} -23.2147 q^{70} +4.77974 q^{71} -31.5199 q^{72} +5.14672 q^{73} +17.9373 q^{74} -15.9452 q^{75} -34.7749 q^{76} -6.08395 q^{77} +7.38503 q^{78} -0.243317 q^{79} +16.3534 q^{80} +7.51990 q^{81} -14.3257 q^{82} -1.78723 q^{83} -36.0030 q^{84} +0.590291 q^{85} +5.84394 q^{86} +8.56754 q^{87} +11.3308 q^{88} +1.59612 q^{89} -46.6607 q^{90} +2.90175 q^{91} -24.7807 q^{92} -4.68535 q^{93} +10.8219 q^{94} -26.8174 q^{95} +5.38992 q^{96} +9.98920 q^{97} -3.52901 q^{98} -12.2285 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.48492	−1.75710	−0.878551	−	0.477648i	$-0.841490\pi$
$2$	−2.48492	−1.75710	−0.878551	+	0.477648i	$0.841490\pi$
$3$	−2.97194	−1.71585	−0.857925	−	0.513775i	$-0.828247\pi$
$3$	−2.97194	−1.71585	−0.857925	+	0.513775i	$0.828247\pi$
$4$	4.17482	2.08741
$5$	3.21951	1.43981	0.719904	−	0.694074i	$-0.244186\pi$
$5$	3.21951	1.43981	0.719904	+	0.694074i	$0.244186\pi$
$6$	7.38503	3.01492
$7$	2.90175	1.09676	0.548380	−	0.836229i	$-0.315245\pi$
$7$	2.90175	1.09676	0.548380	+	0.836229i	$0.315245\pi$
$8$	−5.40425	−1.91069
$9$	5.83242	1.94414
$10$	−8.00022	−2.52989
$11$	−2.09665	−0.632163	−0.316082	−	0.948732i	$-0.602367\pi$
$11$	−2.09665	−0.632163	−0.316082	+	0.948732i	$0.602367\pi$
$12$	−12.4073	−3.58168
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−7.21062	−1.92712
$15$	−9.56819	−2.47049
$16$	5.07949	1.26987
$17$	0.183348	0.0444684	0.0222342	−	0.999753i	$-0.492922\pi$
$17$	0.183348	0.0444684	0.0222342	+	0.999753i	$0.492922\pi$
$18$	−14.4931	−3.41606
$19$	−8.32967	−1.91096	−0.955479	−	0.295060i	$-0.904660\pi$
$19$	−8.32967	−1.91096	−0.955479	+	0.295060i	$0.904660\pi$
$20$	13.4409	3.00547
$21$	−8.62384	−1.88188
$22$	5.21000	1.11078
$23$	−5.93575	−1.23769	−0.618844	−	0.785514i	$-0.712399\pi$
$23$	−5.93575	−1.23769	−0.618844	+	0.785514i	$0.712399\pi$
$24$	16.0611	3.27846
$25$	5.36524	1.07305
$26$	−2.48492	−0.487333
$27$	−8.41779	−1.62000
$28$	12.1143	2.28939
$29$	−2.88281	−0.535325	−0.267662	−	0.963513i	$-0.586251\pi$
$29$	−2.88281	−0.535325	−0.267662	+	0.963513i	$0.586251\pi$
$30$	23.7762	4.34091
$31$	1.57653	0.283153	0.141576	−	0.989927i	$-0.454783\pi$
$31$	1.57653	0.283153	0.141576	+	0.989927i	$0.454783\pi$
$32$	−1.81360	−0.320603
$33$	6.23111	1.08470
$34$	−0.455605	−0.0781356
$35$	9.34222	1.57912
$36$	24.3493	4.05822
$37$	−7.21849	−1.18671	−0.593356	−	0.804940i	$-0.702197\pi$
$37$	−7.21849	−1.18671	−0.593356	+	0.804940i	$0.702197\pi$
$38$	20.6986	3.35775
$39$	−2.97194	−0.475891
$40$	−17.3990	−2.75103
$41$	5.76504	0.900348	0.450174	−	0.892941i	$-0.351362\pi$
$41$	5.76504	0.900348	0.450174	+	0.892941i	$0.351362\pi$
$42$	21.4295	3.30665
$43$	−2.35176	−0.358641	−0.179320	−	0.983791i	$-0.557390\pi$
$43$	−2.35176	−0.358641	−0.179320	+	0.983791i	$0.557390\pi$
$44$	−8.75313	−1.31958
$45$	18.7775	2.79919
$46$	14.7498	2.17475
$47$	−4.35501	−0.635244	−0.317622	−	0.948217i	$-0.602884\pi$
$47$	−4.35501	−0.635244	−0.317622	+	0.948217i	$0.602884\pi$
$48$	−15.0959	−2.17891
$49$	1.42017	0.202882
$50$	−13.3322	−1.88545
$51$	−0.544899	−0.0763011
$52$	4.17482	0.578943
$53$	13.5183	1.85688	0.928442	−	0.371478i	$-0.121149\pi$
$53$	13.5183	1.85688	0.928442	+	0.371478i	$0.121149\pi$
$54$	20.9175	2.84652
$55$	−6.75018	−0.910193
$56$	−15.6818	−2.09557
$57$	24.7553	3.27892
$58$	7.16355	0.940621
$59$	4.68363	0.609757	0.304879	−	0.952391i	$-0.401384\pi$
$59$	4.68363	0.609757	0.304879	+	0.952391i	$0.401384\pi$
$60$	−39.9455	−5.15694
$61$	9.39936	1.20347	0.601733	−	0.798698i	$-0.294477\pi$
$61$	9.39936	1.20347	0.601733	+	0.798698i	$0.294477\pi$
$62$	−3.91754	−0.497528
$63$	16.9243	2.13226
$64$	−5.65231	−0.706539
$65$	3.21951	0.399331
$66$	−15.4838	−1.90592
$67$	1.23974	0.151458	0.0757289	−	0.997128i	$-0.475872\pi$
$67$	1.23974	0.151458	0.0757289	+	0.997128i	$0.475872\pi$
$68$	0.765445	0.0928238
$69$	17.6407	2.12369
$70$	−23.2147	−2.77468
$71$	4.77974	0.567251	0.283625	−	0.958935i	$-0.408463\pi$
$71$	4.77974	0.567251	0.283625	+	0.958935i	$0.408463\pi$
$72$	−31.5199	−3.71465
$73$	5.14672	0.602378	0.301189	−	0.953565i	$-0.402617\pi$
$73$	5.14672	0.602378	0.301189	+	0.953565i	$0.402617\pi$
$74$	17.9373	2.08517
$75$	−15.9452	−1.84119
$76$	−34.7749	−3.98895
$77$	−6.08395	−0.693331
$78$	7.38503	0.836190
$79$	−0.243317	−0.0273753	−0.0136877	−	0.999906i	$-0.504357\pi$
$79$	−0.243317	−0.0273753	−0.0136877	+	0.999906i	$0.504357\pi$
$80$	16.3534	1.82837
$81$	7.51990	0.835544
$82$	−14.3257	−1.58200
$83$	−1.78723	−0.196174	−0.0980869	−	0.995178i	$-0.531272\pi$
$83$	−1.78723	−0.196174	−0.0980869	+	0.995178i	$0.531272\pi$
$84$	−36.0030	−3.92825
$85$	0.590291	0.0640260
$86$	5.84394	0.630168
$87$	8.56754	0.918537
$88$	11.3308	1.20787
$89$	1.59612	0.169189	0.0845943	−	0.996415i	$-0.473041\pi$
$89$	1.59612	0.169189	0.0845943	+	0.996415i	$0.473041\pi$
$90$	−46.6607	−4.91847
$91$	2.90175	0.304186
$92$	−24.7807	−2.58356
$93$	−4.68535	−0.485848
$94$	10.8219	1.11619
$95$	−26.8174	−2.75141
$96$	5.38992	0.550107
$97$	9.98920	1.01425	0.507125	−	0.861873i	$-0.330708\pi$
$97$	9.98920	1.01425	0.507125	+	0.861873i	$0.330708\pi$
$98$	−3.52901	−0.356484
$99$	−12.2285	−1.22901
$100$	22.3989	2.23989
$101$	−12.2968	−1.22358	−0.611790	−	0.791020i	$-0.709550\pi$
$101$	−12.2968	−1.22358	−0.611790	+	0.791020i	$0.709550\pi$
$102$	1.35403	0.134069
$103$	7.46049	0.735104	0.367552	−	0.930003i	$-0.380196\pi$
$103$	7.46049	0.735104	0.367552	+	0.930003i	$0.380196\pi$
$104$	−5.40425	−0.529931
$105$	−27.7645	−2.70954
$106$	−33.5919	−3.26274
$107$	−4.70758	−0.455099	−0.227550	−	0.973766i	$-0.573071\pi$
$107$	−4.70758	−0.455099	−0.227550	+	0.973766i	$0.573071\pi$
$108$	−35.1428	−3.38162
$109$	5.95064	0.569968	0.284984	−	0.958532i	$-0.408012\pi$
$109$	5.95064	0.569968	0.284984	+	0.958532i	$0.408012\pi$
$110$	16.7736	1.59930
$111$	21.4529	2.03622
$112$	14.7394	1.39274
$113$	6.79701	0.639409	0.319705	−	0.947517i	$-0.396416\pi$
$113$	6.79701	0.639409	0.319705	+	0.947517i	$0.396416\pi$
$114$	−61.5148	−5.76139
$115$	−19.1102	−1.78203
$116$	−12.0352	−1.11744
$117$	5.83242	0.539208
$118$	−11.6385	−1.07141
$119$	0.532031	0.0487712
$120$	51.7089	4.72035
$121$	−6.60407	−0.600370
$122$	−23.3567	−2.11461
$123$	−17.1333	−1.54486
$124$	6.58172	0.591056
$125$	1.17589	0.105174
$126$	−42.0554	−3.74659
$127$	4.67102	0.414486	0.207243	−	0.978289i	$-0.433551\pi$
$127$	4.67102	0.414486	0.207243	+	0.978289i	$0.433551\pi$
$128$	17.6727	1.56206
$129$	6.98930	0.615373
$130$	−8.00022	−0.701666
$131$	8.28139	0.723548	0.361774	−	0.932266i	$-0.382171\pi$
$131$	8.28139	0.723548	0.361774	+	0.932266i	$0.382171\pi$
$132$	26.0138	2.26421
$133$	−24.1706	−2.09586
$134$	−3.08064	−0.266127
$135$	−27.1012	−2.33250
$136$	−0.990859	−0.0849654
$137$	−0.0830003	−0.00709119	−0.00354560	−	0.999994i	$-0.501129\pi$
$137$	−0.0830003	−0.00709119	−0.00354560	+	0.999994i	$0.501129\pi$
$138$	−43.8356	−3.73154
$139$	−6.32545	−0.536517	−0.268259	−	0.963347i	$-0.586448\pi$
$139$	−6.32545	−0.536517	−0.268259	+	0.963347i	$0.586448\pi$
$140$	39.0021	3.29628
$141$	12.9428	1.08998
$142$	−11.8773	−0.996718
$143$	−2.09665	−0.175330
$144$	29.6257	2.46881
$145$	−9.28124	−0.770765
$146$	−12.7892	−1.05844
$147$	−4.22067	−0.348115
$148$	−30.1359	−2.47715
$149$	4.21733	0.345497	0.172749	−	0.984966i	$-0.444735\pi$
$149$	4.21733	0.345497	0.172749	+	0.984966i	$0.444735\pi$
$150$	39.6224	3.23516
$151$	−19.0672	−1.55167	−0.775835	−	0.630935i	$-0.782671\pi$
$151$	−19.0672	−1.55167	−0.775835	+	0.630935i	$0.782671\pi$
$152$	45.0156	3.65125
$153$	1.06936	0.0864529
$154$	15.1181	1.21825
$155$	5.07565	0.407686
$156$	−12.4073	−0.993380
$157$	−22.1506	−1.76781	−0.883904	−	0.467669i	$-0.845094\pi$
$157$	−22.1506	−1.76781	−0.883904	+	0.467669i	$0.845094\pi$
$158$	0.604624	0.0481013
$159$	−40.1756	−3.18613
$160$	−5.83892	−0.461607
$161$	−17.2241	−1.35745
$162$	−18.6863	−1.46814
$163$	−3.69841	−0.289682	−0.144841	−	0.989455i	$-0.546267\pi$
$163$	−3.69841	−0.289682	−0.144841	+	0.989455i	$0.546267\pi$
$164$	24.0680	1.87940
$165$	20.0611	1.56176
$166$	4.44112	0.344698
$167$	1.11275	0.0861075	0.0430538	−	0.999073i	$-0.486291\pi$
$167$	1.11275	0.0861075	0.0430538	+	0.999073i	$0.486291\pi$
$168$	46.6054	3.59568
$169$	1.00000	0.0769231
$170$	−1.46682	−0.112500
$171$	−48.5822	−3.71517
$172$	−9.81819	−0.748630
$173$	11.4521	0.870688	0.435344	−	0.900264i	$-0.356627\pi$
$173$	11.4521	0.870688	0.435344	+	0.900264i	$0.356627\pi$
$174$	−21.2896	−1.61396
$175$	15.5686	1.17688
$176$	−10.6499	−0.802766
$177$	−13.9195	−1.04625
$178$	−3.96624	−0.297282
$179$	22.9916	1.71847	0.859237	−	0.511578i	$-0.170939\pi$
$179$	22.9916	1.71847	0.859237	+	0.511578i	$0.170939\pi$
$180$	78.3929	5.84306
$181$	−12.6962	−0.943704	−0.471852	−	0.881678i	$-0.656414\pi$
$181$	−12.6962	−0.943704	−0.471852	+	0.881678i	$0.656414\pi$
$182$	−7.21062	−0.534487
$183$	−27.9343	−2.06497
$184$	32.0783	2.36484
$185$	−23.2400	−1.70864
$186$	11.6427	0.853684
$187$	−0.384416	−0.0281113
$188$	−18.1814	−1.32602
$189$	−24.4264	−1.77676
$190$	66.6392	4.83451
$191$	−16.0887	−1.16414	−0.582070	−	0.813139i	$-0.697757\pi$
$191$	−16.0887	−1.16414	−0.582070	+	0.813139i	$0.697757\pi$
$192$	16.7983	1.21231
$193$	−3.64340	−0.262258	−0.131129	−	0.991365i	$-0.541860\pi$
$193$	−3.64340	−0.262258	−0.131129	+	0.991365i	$0.541860\pi$
$194$	−24.8223	−1.78214
$195$	−9.56819	−0.685192
$196$	5.92897	0.423498
$197$	22.6044	1.61050	0.805248	−	0.592939i	$-0.202032\pi$
$197$	22.6044	1.61050	0.805248	+	0.592939i	$0.202032\pi$
$198$	30.3869	2.15950
$199$	7.00495	0.496568	0.248284	−	0.968687i	$-0.420133\pi$
$199$	7.00495	0.496568	0.248284	+	0.968687i	$0.420133\pi$
$200$	−28.9951	−2.05026
$201$	−3.68442	−0.259879
$202$	30.5566	2.14996
$203$	−8.36521	−0.587123
$204$	−2.27486	−0.159272
$205$	18.5606	1.29633
$206$	−18.5387	−1.29165
$207$	−34.6198	−2.40624
$208$	5.07949	0.352199
$209$	17.4644	1.20804
$210$	68.9926	4.76094
$211$	−9.47921	−0.652576	−0.326288	−	0.945270i	$-0.605798\pi$
$211$	−9.47921	−0.652576	−0.326288	+	0.945270i	$0.605798\pi$
$212$	56.4365	3.87608
$213$	−14.2051	−0.973317
$214$	11.6980	0.799656
$215$	−7.57152	−0.516374
$216$	45.4919	3.09533
$217$	4.57469	0.310551
$218$	−14.7869	−1.00149
$219$	−15.2957	−1.03359
$220$	−28.1808	−1.89995
$221$	0.183348	0.0123333
$222$	−53.3087	−3.57785
$223$	17.5511	1.17531	0.587654	−	0.809112i	$-0.300052\pi$
$223$	17.5511	1.17531	0.587654	+	0.809112i	$0.300052\pi$
$224$	−5.26263	−0.351624
$225$	31.2923	2.08616
$226$	−16.8900	−1.12351
$227$	12.2735	0.814618	0.407309	−	0.913290i	$-0.366467\pi$
$227$	12.2735	0.814618	0.407309	+	0.913290i	$0.366467\pi$
$228$	103.349	6.84444
$229$	−13.0076	−0.859565	−0.429782	−	0.902933i	$-0.641410\pi$
$229$	−13.0076	−0.859565	−0.429782	+	0.902933i	$0.641410\pi$
$230$	47.4873	3.13122
$231$	18.0811	1.18965
$232$	15.5794	1.02284
$233$	14.0818	0.922529	0.461264	−	0.887263i	$-0.347396\pi$
$233$	14.0818	0.922529	0.461264	+	0.887263i	$0.347396\pi$
$234$	−14.4931	−0.947444
$235$	−14.0210	−0.914630
$236$	19.5533	1.27281
$237$	0.723124	0.0469720
$238$	−1.32205	−0.0856960
$239$	−6.81839	−0.441045	−0.220522	−	0.975382i	$-0.570776\pi$
$239$	−6.81839	−0.441045	−0.220522	+	0.975382i	$0.570776\pi$
$240$	−48.6015	−3.13721
$241$	−12.9302	−0.832905	−0.416452	−	0.909157i	$-0.636727\pi$
$241$	−12.9302	−0.832905	−0.416452	+	0.909157i	$0.636727\pi$
$242$	16.4106	1.05491
$243$	2.90470	0.186336
$244$	39.2407	2.51213
$245$	4.57226	0.292111
$246$	42.5750	2.71448
$247$	−8.32967	−0.530004
$248$	−8.51995	−0.541018
$249$	5.31154	0.336605
$250$	−2.92198	−0.184802
$251$	−10.8124	−0.682472	−0.341236	−	0.939978i	$-0.610846\pi$
$251$	−10.8124	−0.682472	−0.341236	+	0.939978i	$0.610846\pi$
$252$	70.6557	4.45089
$253$	12.4452	0.782421
$254$	−11.6071	−0.728295
$255$	−1.75431	−0.109859
$256$	−32.6107	−2.03817
$257$	22.8276	1.42395	0.711974	−	0.702206i	$-0.247801\pi$
$257$	22.8276	1.42395	0.711974	+	0.702206i	$0.247801\pi$
$258$	−17.3678	−1.08127
$259$	−20.9463	−1.30154
$260$	13.4409	0.833568
$261$	−16.8138	−1.04075
$262$	−20.5786	−1.27135
$263$	21.5441	1.32847	0.664235	−	0.747524i	$-0.268758\pi$
$263$	21.5441	1.32847	0.664235	+	0.747524i	$0.268758\pi$
$264$	−33.6745	−2.07252
$265$	43.5223	2.67356
$266$	60.0621	3.68264
$267$	−4.74358	−0.290302
$268$	5.17568	0.316155
$269$	−13.1105	−0.799363	−0.399682	−	0.916654i	$-0.630879\pi$
$269$	−13.1105	−0.799363	−0.399682	+	0.916654i	$0.630879\pi$
$270$	67.3442	4.09844
$271$	4.56445	0.277270	0.138635	−	0.990344i	$-0.455728\pi$
$271$	4.56445	0.277270	0.138635	+	0.990344i	$0.455728\pi$
$272$	0.931314	0.0564692
$273$	−8.62384	−0.521938
$274$	0.206249	0.0124600
$275$	−11.2490	−0.678341
$276$	73.6467	4.43301
$277$	−14.6492	−0.880186	−0.440093	−	0.897952i	$-0.645055\pi$
$277$	−14.6492	−0.880186	−0.440093	+	0.897952i	$0.645055\pi$
$278$	15.7182	0.942716
$279$	9.19498	0.550489
$280$	−50.4877	−3.01722
$281$	−16.8473	−1.00503	−0.502513	−	0.864570i	$-0.667591\pi$
$281$	−16.8473	−1.00503	−0.502513	+	0.864570i	$0.667591\pi$
$282$	−32.1619	−1.91521
$283$	−12.5817	−0.747906	−0.373953	−	0.927448i	$-0.621998\pi$
$283$	−12.5817	−0.747906	−0.373953	+	0.927448i	$0.621998\pi$
$284$	19.9546	1.18409
$285$	79.6998	4.72101
$286$	5.21000	0.308074
$287$	16.7287	0.987465
$288$	−10.5777	−0.623298
$289$	−16.9664	−0.998023
$290$	23.0631	1.35431
$291$	−29.6873	−1.74030
$292$	21.4866	1.25741
$293$	−13.8851	−0.811176	−0.405588	−	0.914056i	$-0.632933\pi$
$293$	−13.8851	−0.811176	−0.405588	+	0.914056i	$0.632933\pi$
$294$	10.4880	0.611673
$295$	15.0790	0.877933
$296$	39.0105	2.26744
$297$	17.6491	1.02411
$298$	−10.4797	−0.607074
$299$	−5.93575	−0.343273
$300$	−66.5682	−3.84332
$301$	−6.82424	−0.393342
$302$	47.3806	2.72644
$303$	36.5454	2.09948
$304$	−42.3104	−2.42667
$305$	30.2613	1.73276
$306$	−2.65728	−0.151907
$307$	−22.8210	−1.30246	−0.651231	−	0.758880i	$-0.725747\pi$
$307$	−22.8210	−1.30246	−0.651231	+	0.758880i	$0.725747\pi$
$308$	−25.3994	−1.44727
$309$	−22.1721	−1.26133
$310$	−12.6126	−0.716346
$311$	−30.3364	−1.72022	−0.860109	−	0.510110i	$-0.829605\pi$
$311$	−30.3364	−1.72022	−0.860109	+	0.510110i	$0.829605\pi$
$312$	16.0611	0.909281
$313$	33.2689	1.88047	0.940235	−	0.340528i	$-0.110606\pi$
$313$	33.2689	1.88047	0.940235	+	0.340528i	$0.110606\pi$
$314$	55.0424	3.10622
$315$	54.4878	3.07004
$316$	−1.01581	−0.0571436
$317$	−3.63936	−0.204407	−0.102203	−	0.994764i	$-0.532589\pi$
$317$	−3.63936	−0.204407	−0.102203	+	0.994764i	$0.532589\pi$
$318$	99.8331	5.59836
$319$	6.04424	0.338412
$320$	−18.1977	−1.01728
$321$	13.9907	0.780882
$322$	42.8004	2.38517
$323$	−1.52723	−0.0849773
$324$	31.3942	1.74412
$325$	5.36524	0.297610
$326$	9.19025	0.509001
$327$	−17.6849	−0.977979
$328$	−31.1557	−1.72029
$329$	−12.6372	−0.696710
$330$	−49.8502	−2.74416
$331$	−1.20071	−0.0659969	−0.0329985	−	0.999455i	$-0.510506\pi$
$331$	−1.20071	−0.0659969	−0.0329985	+	0.999455i	$0.510506\pi$
$332$	−7.46136	−0.409495
$333$	−42.1013	−2.30714
$334$	−2.76510	−0.151300
$335$	3.99134	0.218070
$336$	−43.8046	−2.38974
$337$	33.3699	1.81777	0.908887	−	0.417042i	$-0.136933\pi$
$337$	33.3699	1.81777	0.908887	+	0.417042i	$0.136933\pi$
$338$	−2.48492	−0.135162
$339$	−20.2003	−1.09713
$340$	2.46436	0.133649
$341$	−3.30542	−0.178999
$342$	120.723	6.52794
$343$	−16.1913	−0.874247
$344$	12.7095	0.685251
$345$	56.7943	3.05770
$346$	−28.4576	−1.52989
$347$	−5.77220	−0.309868	−0.154934	−	0.987925i	$-0.549517\pi$
$347$	−5.77220	−0.309868	−0.154934	+	0.987925i	$0.549517\pi$
$348$	35.7679	1.91736
$349$	−31.7550	−1.69980	−0.849902	−	0.526940i	$-0.823339\pi$
$349$	−31.7550	−1.69980	−0.849902	+	0.526940i	$0.823339\pi$
$350$	−38.6867	−2.06789
$351$	−8.41779	−0.449309
$352$	3.80249	0.202673
$353$	−23.6652	−1.25957	−0.629785	−	0.776770i	$-0.716857\pi$
$353$	−23.6652	−1.25957	−0.629785	+	0.776770i	$0.716857\pi$
$354$	34.5888	1.83837
$355$	15.3884	0.816732
$356$	6.66353	0.353166
$357$	−1.58116	−0.0836840
$358$	−57.1323	−3.01953
$359$	−3.84041	−0.202689	−0.101345	−	0.994851i	$-0.532314\pi$
$359$	−3.84041	−0.202689	−0.101345	+	0.994851i	$0.532314\pi$
$360$	−101.479	−5.34839
$361$	50.3834	2.65176
$362$	31.5491	1.65818
$363$	19.6269	1.03014
$364$	12.1143	0.634962
$365$	16.5699	0.867308
$366$	69.4146	3.62836
$367$	−25.3415	−1.32281	−0.661407	−	0.750027i	$-0.730040\pi$
$367$	−25.3415	−1.32281	−0.661407	+	0.750027i	$0.730040\pi$
$368$	−30.1505	−1.57171
$369$	33.6241	1.75040
$370$	57.7495	3.00225
$371$	39.2268	2.03656
$372$	−19.5605	−1.01416
$373$	−25.6899	−1.33017	−0.665087	−	0.746766i	$-0.731606\pi$
$373$	−25.6899	−1.33017	−0.665087	+	0.746766i	$0.731606\pi$
$374$	0.955243	0.0493944
$375$	−3.49466	−0.180464
$376$	23.5356	1.21376
$377$	−2.88281	−0.148472
$378$	60.6975	3.12194
$379$	−17.4252	−0.895073	−0.447537	−	0.894266i	$-0.647699\pi$
$379$	−17.4252	−0.895073	−0.447537	+	0.894266i	$0.647699\pi$
$380$	−111.958	−5.74333
$381$	−13.8820	−0.711196
$382$	39.9792	2.04551
$383$	−36.0833	−1.84377	−0.921885	−	0.387464i	$-0.873351\pi$
$383$	−36.0833	−1.84377	−0.921885	+	0.387464i	$0.873351\pi$
$384$	−52.5223	−2.68027
$385$	−19.5873	−0.998263
$386$	9.05355	0.460814
$387$	−13.7165	−0.697248
$388$	41.7031	2.11715
$389$	−3.90269	−0.197874	−0.0989370	−	0.995094i	$-0.531544\pi$
$389$	−3.90269	−0.197874	−0.0989370	+	0.995094i	$0.531544\pi$
$390$	23.7762	1.20395
$391$	−1.08831	−0.0550381
$392$	−7.67497	−0.387645
$393$	−24.6118	−1.24150
$394$	−56.1700	−2.82981
$395$	−0.783362	−0.0394152
$396$	−51.0519	−2.56546
$397$	24.8256	1.24596	0.622981	−	0.782237i	$-0.285921\pi$
$397$	24.8256	1.24596	0.622981	+	0.782237i	$0.285921\pi$
$398$	−17.4067	−0.872521
$399$	71.8337	3.59618
$400$	27.2526	1.36263
$401$	−24.5023	−1.22359	−0.611793	−	0.791018i	$-0.709552\pi$
$401$	−24.5023	−1.22359	−0.611793	+	0.791018i	$0.709552\pi$
$402$	9.15549	0.456634
$403$	1.57653	0.0785324
$404$	−51.3371	−2.55411
$405$	24.2104	1.20302
$406$	20.7869	1.03163
$407$	15.1346	0.750195
$408$	2.94477	0.145788
$409$	−3.83502	−0.189630	−0.0948148	−	0.995495i	$-0.530226\pi$
$409$	−3.83502	−0.189630	−0.0948148	+	0.995495i	$0.530226\pi$
$410$	−46.1216	−2.27778
$411$	0.246672	0.0121674
$412$	31.1462	1.53446
$413$	13.5908	0.668757
$414$	86.0274	4.22801
$415$	−5.75400	−0.282453
$416$	−1.81360	−0.0889193
$417$	18.7988	0.920583
$418$	−43.3976	−2.12264
$419$	−10.5334	−0.514592	−0.257296	−	0.966333i	$-0.582831\pi$
$419$	−10.5334	−0.514592	−0.257296	+	0.966333i	$0.582831\pi$
$420$	−115.912	−5.65592
$421$	−17.4816	−0.852000	−0.426000	−	0.904723i	$-0.640078\pi$
$421$	−17.4816	−0.852000	−0.426000	+	0.904723i	$0.640078\pi$
$422$	23.5551	1.14664
$423$	−25.4003	−1.23500
$424$	−73.0564	−3.54793
$425$	0.983706	0.0477167
$426$	35.2985	1.71022
$427$	27.2746	1.31991
$428$	−19.6533	−0.949979
$429$	6.23111	0.300841
$430$	18.8146	0.907321
$431$	20.5691	0.990779	0.495390	−	0.868671i	$-0.335025\pi$
$431$	20.5691	0.990779	0.495390	+	0.868671i	$0.335025\pi$
$432$	−42.7581	−2.05720
$433$	−31.5371	−1.51558	−0.757788	−	0.652501i	$-0.773720\pi$
$433$	−31.5371	−1.51558	−0.757788	+	0.652501i	$0.773720\pi$
$434$	−11.3677	−0.545669
$435$	27.5833	1.32252
$436$	24.8428	1.18976
$437$	49.4428	2.36517
$438$	38.0086	1.81612
$439$	3.48597	0.166376	0.0831880	−	0.996534i	$-0.473490\pi$
$439$	3.48597	0.166376	0.0831880	+	0.996534i	$0.473490\pi$
$440$	36.4797	1.73910
$441$	8.28305	0.394431
$442$	−0.455605	−0.0216709
$443$	2.79285	0.132692	0.0663461	−	0.997797i	$-0.478866\pi$
$443$	2.79285	0.132692	0.0663461	+	0.997797i	$0.478866\pi$
$444$	89.5620	4.25043
$445$	5.13873	0.243599
$446$	−43.6130	−2.06514
$447$	−12.5336	−0.592821
$448$	−16.4016	−0.774903
$449$	−32.2595	−1.52242	−0.761209	−	0.648506i	$-0.775394\pi$
$449$	−32.2595	−1.52242	−0.761209	+	0.648506i	$0.775394\pi$
$450$	−77.7589	−3.66559
$451$	−12.0873	−0.569167
$452$	28.3763	1.33471
$453$	56.6667	2.66243
$454$	−30.4985	−1.43137
$455$	9.34222	0.437970
$456$	−133.784	−6.26500
$457$	−36.3839	−1.70197	−0.850983	−	0.525193i	$-0.823993\pi$
$457$	−36.3839	−1.70197	−0.850983	+	0.525193i	$0.823993\pi$
$458$	32.3228	1.51034
$459$	−1.54339	−0.0720391
$460$	−79.7816	−3.71984
$461$	10.2042	0.475255	0.237627	−	0.971356i	$-0.423630\pi$
$461$	10.2042	0.475255	0.237627	+	0.971356i	$0.423630\pi$
$462$	−44.9302	−2.09034
$463$	−2.94791	−0.137001	−0.0685004	−	0.997651i	$-0.521821\pi$
$463$	−2.94791	−0.137001	−0.0685004	+	0.997651i	$0.521821\pi$
$464$	−14.6432	−0.679794
$465$	−15.0845	−0.699527
$466$	−34.9921	−1.62098
$467$	−28.3766	−1.31311	−0.656556	−	0.754277i	$-0.727987\pi$
$467$	−28.3766	−1.31311	−0.656556	+	0.754277i	$0.727987\pi$
$468$	24.3493	1.12555
$469$	3.59741	0.166113
$470$	34.8411	1.60710
$471$	65.8301	3.03329
$472$	−25.3115	−1.16506
$473$	4.93082	0.226719
$474$	−1.79691	−0.0825346
$475$	−44.6907	−2.05055
$476$	2.22113	0.101805
$477$	78.8446	3.61004
$478$	16.9431	0.774961
$479$	−15.1302	−0.691315	−0.345658	−	0.938361i	$-0.612344\pi$
$479$	−15.1302	−0.691315	−0.345658	+	0.938361i	$0.612344\pi$
$480$	17.3529	0.792048
$481$	−7.21849	−0.329135
$482$	32.1304	1.46350
$483$	51.1889	2.32918
$484$	−27.5708	−1.25322
$485$	32.1603	1.46032
$486$	−7.21793	−0.327412
$487$	22.6418	1.02600	0.513000	−	0.858389i	$-0.328534\pi$
$487$	22.6418	1.02600	0.513000	+	0.858389i	$0.328534\pi$
$488$	−50.7965	−2.29945
$489$	10.9914	0.497050
$490$	−11.3617	−0.513269
$491$	39.8025	1.79626	0.898131	−	0.439729i	$-0.144925\pi$
$491$	39.8025	1.79626	0.898131	+	0.439729i	$0.144925\pi$
$492$	−71.5286	−3.22476
$493$	−0.528558	−0.0238050
$494$	20.6986	0.931272
$495$	−39.3699	−1.76954
$496$	8.00795	0.359568
$497$	13.8696	0.622138
$498$	−13.1987	−0.591450
$499$	5.11428	0.228946	0.114473	−	0.993426i	$-0.463482\pi$
$499$	5.11428	0.228946	0.114473	+	0.993426i	$0.463482\pi$
$500$	4.90911	0.219542
$501$	−3.30704	−0.147748
$502$	26.8679	1.19917
$503$	5.84452	0.260594	0.130297	−	0.991475i	$-0.458407\pi$
$503$	5.84452	0.260594	0.130297	+	0.991475i	$0.458407\pi$
$504$	−91.4629	−4.07408
$505$	−39.5898	−1.76172
$506$	−30.9252	−1.37479
$507$	−2.97194	−0.131988
$508$	19.5007	0.865203
$509$	12.9254	0.572909	0.286455	−	0.958094i	$-0.407523\pi$
$509$	12.9254	0.572909	0.286455	+	0.958094i	$0.407523\pi$
$510$	4.35931	0.193034
$511$	14.9345	0.660663
$512$	45.6895	2.01921
$513$	70.1174	3.09576
$514$	−56.7248	−2.50202
$515$	24.0191	1.05841
$516$	29.1791	1.28454
$517$	9.13093	0.401578
$518$	52.0498	2.28694
$519$	−34.0350	−1.49397
$520$	−17.3990	−0.762998
$521$	−43.6812	−1.91371	−0.956854	−	0.290570i	$-0.906155\pi$
$521$	−43.6812	−1.91371	−0.956854	+	0.290570i	$0.906155\pi$
$522$	41.7809	1.82870
$523$	−29.5266	−1.29111	−0.645555	−	0.763714i	$-0.723374\pi$
$523$	−29.5266	−1.29111	−0.645555	+	0.763714i	$0.723374\pi$
$524$	34.5733	1.51034
$525$	−46.2689	−2.01934
$526$	−53.5355	−2.33426
$527$	0.289053	0.0125914
$528$	31.6508	1.37743
$529$	12.2331	0.531873
$530$	−108.149	−4.69771
$531$	27.3169	1.18545
$532$	−100.908	−4.37492
$533$	5.76504	0.249712
$534$	11.7874	0.510091
$535$	−15.1561	−0.655256
$536$	−6.69985	−0.289389
$537$	−68.3297	−2.94864
$538$	32.5786	1.40456
$539$	−2.97760	−0.128254
$540$	−113.142	−4.86888
$541$	−3.99342	−0.171690	−0.0858452	−	0.996308i	$-0.527359\pi$
$541$	−3.99342	−0.171690	−0.0858452	+	0.996308i	$0.527359\pi$
$542$	−11.3423	−0.487193
$543$	37.7324	1.61925
$544$	−0.332521	−0.0142567
$545$	19.1581	0.820644
$546$	21.4295	0.917099
$547$	−8.54036	−0.365160	−0.182580	−	0.983191i	$-0.558445\pi$
$547$	−8.54036	−0.365160	−0.182580	+	0.983191i	$0.558445\pi$
$548$	−0.346511	−0.0148022
$549$	54.8211	2.33971
$550$	27.9529	1.19191
$551$	24.0129	1.02298
$552$	−95.3347	−4.05771
$553$	−0.706047	−0.0300242
$554$	36.4021	1.54658
$555$	69.0678	2.93177
$556$	−26.4076	−1.11993
$557$	−13.6219	−0.577176	−0.288588	−	0.957453i	$-0.593186\pi$
$557$	−13.6219	−0.577176	−0.288588	+	0.957453i	$0.593186\pi$
$558$	−22.8488	−0.967266
$559$	−2.35176	−0.0994690
$560$	47.4537	2.00528
$561$	1.14246	0.0482348
$562$	41.8642	1.76593
$563$	−38.0085	−1.60187	−0.800934	−	0.598752i	$-0.795663\pi$
$563$	−38.0085	−1.60187	−0.800934	+	0.598752i	$0.795663\pi$
$564$	54.0340	2.27524
$565$	21.8830	0.920626
$566$	31.2646	1.31415
$567$	21.8209	0.916391
$568$	−25.8309	−1.08384
$569$	−8.74108	−0.366445	−0.183223	−	0.983071i	$-0.558653\pi$
$569$	−8.74108	−0.366445	−0.183223	+	0.983071i	$0.558653\pi$
$570$	−198.048	−8.29530
$571$	32.3302	1.35298	0.676488	−	0.736454i	$-0.263501\pi$
$571$	32.3302	1.35298	0.676488	+	0.736454i	$0.263501\pi$
$572$	−8.75313	−0.365987
$573$	47.8147	1.99749
$574$	−41.5695	−1.73508
$575$	−31.8467	−1.32810
$576$	−32.9667	−1.37361
$577$	27.6053	1.14922	0.574612	−	0.818426i	$-0.305153\pi$
$577$	27.6053	1.14922	0.574612	+	0.818426i	$0.305153\pi$
$578$	42.1601	1.75363
$579$	10.8280	0.449995
$580$	−38.7475	−1.60890
$581$	−5.18610	−0.215156
$582$	73.7705	3.05789
$583$	−28.3431	−1.17385
$584$	−27.8142	−1.15096
$585$	18.7775	0.776356
$586$	34.5033	1.42532
$587$	−13.3971	−0.552957	−0.276479	−	0.961020i	$-0.589167\pi$
$587$	−13.3971	−0.552957	−0.276479	+	0.961020i	$0.589167\pi$
$588$	−17.6205	−0.726658
$589$	−13.1320	−0.541093
$590$	−37.4701	−1.54262
$591$	−67.1788	−2.76337
$592$	−36.6662	−1.50697
$593$	16.9036	0.694149	0.347074	−	0.937838i	$-0.387175\pi$
$593$	16.9036	0.694149	0.347074	+	0.937838i	$0.387175\pi$
$594$	−43.8567	−1.79946
$595$	1.71288	0.0702211
$596$	17.6066	0.721194
$597$	−20.8183	−0.852036
$598$	14.7498	0.603166
$599$	45.8957	1.87525	0.937625	−	0.347649i	$-0.113020\pi$
$599$	45.8957	1.87525	0.937625	+	0.347649i	$0.113020\pi$
$600$	86.1717	3.51794
$601$	−20.8397	−0.850069	−0.425034	−	0.905177i	$-0.639738\pi$
$601$	−20.8397	−0.850069	−0.425034	+	0.905177i	$0.639738\pi$
$602$	16.9577	0.691143
$603$	7.23067	0.294456
$604$	−79.6023	−3.23897
$605$	−21.2619	−0.864418
$606$	−90.8124	−3.68900
$607$	−0.990550	−0.0402052	−0.0201026	−	0.999798i	$-0.506399\pi$
$607$	−0.990550	−0.0402052	−0.0201026	+	0.999798i	$0.506399\pi$
$608$	15.1067	0.612659
$609$	24.8609	1.00741
$610$	−75.1970	−3.04464
$611$	−4.35501	−0.176185
$612$	4.46440	0.180463
$613$	−26.2120	−1.05869	−0.529347	−	0.848406i	$-0.677563\pi$
$613$	−26.2120	−1.05869	−0.529347	+	0.848406i	$0.677563\pi$
$614$	56.7083	2.28856
$615$	−55.1610	−2.22430
$616$	32.8792	1.32474
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	55.0959	2.21628
$619$	4.04060	0.162406	0.0812028	−	0.996698i	$-0.474124\pi$
$619$	4.04060	0.162406	0.0812028	+	0.996698i	$0.474124\pi$
$620$	21.1899	0.851007
$621$	49.9659	2.00506
$622$	75.3834	3.02260
$623$	4.63155	0.185559
$624$	−15.0959	−0.604321
$625$	−23.0404	−0.921616
$626$	−82.6705	−3.30418
$627$	−51.9031	−2.07281
$628$	−92.4746	−3.69014
$629$	−1.32349	−0.0527712
$630$	−135.398	−5.39437
$631$	−34.5964	−1.37726	−0.688630	−	0.725112i	$-0.741788\pi$
$631$	−34.5964	−1.37726	−0.688630	+	0.725112i	$0.741788\pi$
$632$	1.31495	0.0523058
$633$	28.1716	1.11972
$634$	9.04350	0.359163
$635$	15.0384	0.596781
$636$	−167.726	−6.65077
$637$	1.42017	0.0562693
$638$	−15.0194	−0.594625
$639$	27.8775	1.10282
$640$	56.8976	2.24907
$641$	7.12855	0.281561	0.140780	−	0.990041i	$-0.455039\pi$
$641$	7.12855	0.281561	0.140780	+	0.990041i	$0.455039\pi$
$642$	−34.7656	−1.37209
$643$	21.7734	0.858660	0.429330	−	0.903148i	$-0.358750\pi$
$643$	21.7734	0.858660	0.429330	+	0.903148i	$0.358750\pi$
$644$	−71.9074	−2.83355
$645$	22.5021	0.886020
$646$	3.79504	0.149314
$647$	3.00795	0.118255	0.0591273	−	0.998250i	$-0.481168\pi$
$647$	3.00795	0.118255	0.0591273	+	0.998250i	$0.481168\pi$
$648$	−40.6394	−1.59647
$649$	−9.81993	−0.385466
$650$	−13.3322	−0.522931
$651$	−13.5957	−0.532858
$652$	−15.4402	−0.604685
$653$	−27.3771	−1.07135	−0.535675	−	0.844424i	$-0.679943\pi$
$653$	−27.3771	−1.07135	−0.535675	+	0.844424i	$0.679943\pi$
$654$	43.9456	1.71841
$655$	26.6620	1.04177
$656$	29.2834	1.14333
$657$	30.0178	1.17111
$658$	31.4024	1.22419
$659$	19.1916	0.747599	0.373800	−	0.927510i	$-0.378055\pi$
$659$	19.1916	0.747599	0.373800	+	0.927510i	$0.378055\pi$
$660$	83.7515	3.26002
$661$	−14.8002	−0.575659	−0.287830	−	0.957682i	$-0.592934\pi$
$661$	−14.8002	−0.575659	−0.287830	+	0.957682i	$0.592934\pi$
$662$	2.98366	0.115963
$663$	−0.544899	−0.0211621
$664$	9.65864	0.374828
$665$	−77.8176	−3.01764
$666$	104.618	4.05387
$667$	17.1116	0.662565
$668$	4.64555	0.179742
$669$	−52.1608	−2.01665
$670$	−9.91816	−0.383172
$671$	−19.7072	−0.760786
$672$	15.6402	0.603335
$673$	−14.3569	−0.553418	−0.276709	−	0.960954i	$-0.589244\pi$
$673$	−14.3569	−0.553418	−0.276709	+	0.960954i	$0.589244\pi$
$674$	−82.9215	−3.19402
$675$	−45.1635	−1.73834
$676$	4.17482	0.160570
$677$	−1.98720	−0.0763745	−0.0381872	−	0.999271i	$-0.512158\pi$
$677$	−1.98720	−0.0763745	−0.0381872	+	0.999271i	$0.512158\pi$
$678$	50.1961	1.92777
$679$	28.9862	1.11239
$680$	−3.19008	−0.122334
$681$	−36.4760	−1.39776
$682$	8.21371	0.314519
$683$	−16.9832	−0.649845	−0.324922	−	0.945741i	$-0.605338\pi$
$683$	−16.9832	−0.649845	−0.324922	+	0.945741i	$0.605338\pi$
$684$	−202.822	−7.75509
$685$	−0.267220	−0.0102100
$686$	40.2340	1.53614
$687$	38.6577	1.47488
$688$	−11.9457	−0.455427
$689$	13.5183	0.515007
$690$	−141.129	−5.37270
$691$	−48.6796	−1.85186	−0.925930	−	0.377695i	$-0.876717\pi$
$691$	−48.6796	−1.85186	−0.925930	+	0.377695i	$0.876717\pi$
$692$	47.8105	1.81748
$693$	−35.4842	−1.34793
$694$	14.3435	0.544470
$695$	−20.3648	−0.772482
$696$	−46.3012	−1.75504
$697$	1.05701	0.0400370
$698$	78.9085	2.98673
$699$	−41.8502	−1.58292
$700$	64.9961	2.45662
$701$	−1.24801	−0.0471367	−0.0235684	−	0.999722i	$-0.507503\pi$
$701$	−1.24801	−0.0471367	−0.0235684	+	0.999722i	$0.507503\pi$
$702$	20.9175	0.789481
$703$	60.1276	2.26776
$704$	11.8509	0.446648
$705$	41.6696	1.56937
$706$	58.8060	2.21319
$707$	−35.6824	−1.34197
$708$	−58.1113	−2.18396
$709$	−20.6672	−0.776175	−0.388087	−	0.921623i	$-0.626864\pi$
$709$	−20.6672	−0.776175	−0.388087	+	0.921623i	$0.626864\pi$
$710$	−38.2390	−1.43508
$711$	−1.41913	−0.0532215
$712$	−8.62585	−0.323267
$713$	−9.35787	−0.350455
$714$	3.92906	0.147041
$715$	−6.75018	−0.252442
$716$	95.9858	3.58716
$717$	20.2638	0.756767
$718$	9.54311	0.356146
$719$	−37.6928	−1.40570	−0.702852	−	0.711336i	$-0.748090\pi$
$719$	−37.6928	−1.40570	−0.702852	+	0.711336i	$0.748090\pi$
$720$	95.3803	3.55461
$721$	21.6485	0.806233
$722$	−125.199	−4.65941
$723$	38.4277	1.42914
$724$	−53.0045	−1.96990
$725$	−15.4670	−0.574429
$726$	−48.7712	−1.81007
$727$	1.38852	0.0514975	0.0257488	−	0.999668i	$-0.491803\pi$
$727$	1.38852	0.0514975	0.0257488	+	0.999668i	$0.491803\pi$
$728$	−15.6818	−0.581206
$729$	−31.1923	−1.15527
$730$	−41.1749	−1.52395
$731$	−0.431191	−0.0159482
$732$	−116.621	−4.31043
$733$	−14.5001	−0.535573	−0.267786	−	0.963478i	$-0.586292\pi$
$733$	−14.5001	−0.535573	−0.267786	+	0.963478i	$0.586292\pi$
$734$	62.9715	2.32432
$735$	−13.5885	−0.501218
$736$	10.7651	0.396807
$737$	−2.59929	−0.0957461
$738$	−83.5533	−3.07564
$739$	−19.3119	−0.710401	−0.355201	−	0.934790i	$-0.615587\pi$
$739$	−19.3119	−0.710401	−0.355201	+	0.934790i	$0.615587\pi$
$740$	−97.0227	−3.56663
$741$	24.7553	0.909408
$742$	−97.4755	−3.57844
$743$	−15.9681	−0.585814	−0.292907	−	0.956141i	$-0.594623\pi$
$743$	−15.9681	−0.585814	−0.292907	+	0.956141i	$0.594623\pi$
$744$	25.3208	0.928305
$745$	13.5777	0.497449
$746$	63.8374	2.33725
$747$	−10.4239	−0.381390
$748$	−1.60487	−0.0586798
$749$	−13.6602	−0.499135
$750$	8.68395	0.317093
$751$	−18.6995	−0.682353	−0.341177	−	0.939999i	$-0.610825\pi$
$751$	−18.6995	−0.682353	−0.341177	+	0.939999i	$0.610825\pi$
$752$	−22.1212	−0.806678
$753$	32.1338	1.17102
$754$	7.16355	0.260881
$755$	−61.3872	−2.23411
$756$	−101.976	−3.70882
$757$	5.08915	0.184968	0.0924841	−	0.995714i	$-0.470519\pi$
$757$	5.08915	0.184968	0.0924841	+	0.995714i	$0.470519\pi$
$758$	43.3002	1.57274
$759$	−36.9863	−1.34252
$760$	144.928	5.25710
$761$	18.4394	0.668428	0.334214	−	0.942497i	$-0.391529\pi$
$761$	18.4394	0.668428	0.334214	+	0.942497i	$0.391529\pi$
$762$	34.4956	1.24964
$763$	17.2673	0.625118
$764$	−67.1675	−2.43004
$765$	3.44282	0.124476
$766$	89.6640	3.23969
$767$	4.68363	0.169116
$768$	96.9170	3.49719
$769$	28.5432	1.02929	0.514647	−	0.857402i	$-0.327923\pi$
$769$	28.5432	1.02929	0.514647	+	0.857402i	$0.327923\pi$
$770$	48.6730	1.75405
$771$	−67.8423	−2.44328
$772$	−15.2105	−0.547439
$773$	34.0584	1.22500	0.612498	−	0.790472i	$-0.290165\pi$
$773$	34.0584	1.22500	0.612498	+	0.790472i	$0.290165\pi$
$774$	34.0843	1.22514
$775$	8.45845	0.303836
$776$	−53.9841	−1.93792
$777$	62.2510	2.23324
$778$	9.69786	0.347685
$779$	−48.0209	−1.72053
$780$	−39.9455	−1.43028
$781$	−10.0214	−0.358595
$782$	2.70435	0.0967075
$783$	24.2669	0.867229
$784$	7.21375	0.257634
$785$	−71.3139	−2.54530
$786$	61.1583	2.18144
$787$	31.6915	1.12968	0.564840	−	0.825200i	$-0.308938\pi$
$787$	31.6915	1.12968	0.564840	+	0.825200i	$0.308938\pi$
$788$	94.3692	3.36176
$789$	−64.0279	−2.27945
$790$	1.94659	0.0692566
$791$	19.7233	0.701278
$792$	66.0861	2.34827
$793$	9.39936	0.333781
$794$	−61.6897	−2.18928
$795$	−129.346	−4.58742
$796$	29.2444	1.03654
$797$	−11.4920	−0.407067	−0.203534	−	0.979068i	$-0.565243\pi$
$797$	−11.4920	−0.407067	−0.203534	+	0.979068i	$0.565243\pi$
$798$	−178.501	−6.31886
$799$	−0.798483	−0.0282483
$800$	−9.73042	−0.344022
$801$	9.30926	0.328927
$802$	60.8862	2.14997
$803$	−10.7909	−0.380801
$804$	−15.3818	−0.542474
$805$	−55.4530	−1.95446
$806$	−3.91754	−0.137990
$807$	38.9637	1.37159
$808$	66.4552	2.33788
$809$	−28.5864	−1.00504	−0.502522	−	0.864565i	$-0.667594\pi$
$809$	−28.5864	−1.00504	−0.502522	+	0.864565i	$0.667594\pi$
$810$	−60.1608	−2.11384
$811$	−25.8151	−0.906490	−0.453245	−	0.891386i	$-0.649734\pi$
$811$	−25.8151	−0.906490	−0.453245	+	0.891386i	$0.649734\pi$
$812$	−34.9232	−1.22557
$813$	−13.5653	−0.475754
$814$	−37.6083	−1.31817
$815$	−11.9071	−0.417086
$816$	−2.76781	−0.0968926
$817$	19.5894	0.685347
$818$	9.52972	0.333199
$819$	16.9243	0.591381
$820$	77.4871	2.70597
$821$	−33.5283	−1.17014	−0.585072	−	0.810981i	$-0.698934\pi$
$821$	−33.5283	−1.17014	−0.585072	+	0.810981i	$0.698934\pi$
$822$	−0.612959	−0.0213794
$823$	33.9782	1.18441	0.592203	−	0.805789i	$-0.298258\pi$
$823$	33.9782	1.18441	0.592203	+	0.805789i	$0.298258\pi$
$824$	−40.3184	−1.40456
$825$	33.4314	1.16393
$826$	−33.7719	−1.17508
$827$	−25.2204	−0.877000	−0.438500	−	0.898731i	$-0.644490\pi$
$827$	−25.2204	−0.877000	−0.438500	+	0.898731i	$0.644490\pi$
$828$	−144.531	−5.02281
$829$	44.4689	1.54447	0.772235	−	0.635337i	$-0.219139\pi$
$829$	44.4689	1.54447	0.772235	+	0.635337i	$0.219139\pi$
$830$	14.2982	0.496299
$831$	43.5366	1.51027
$832$	−5.65231	−0.195959
$833$	0.260386	0.00902183
$834$	−46.7136	−1.61756
$835$	3.58252	0.123978
$836$	72.9107	2.52167
$837$	−13.2709	−0.458709
$838$	26.1747	0.904191
$839$	−37.5001	−1.29465	−0.647323	−	0.762215i	$-0.724112\pi$
$839$	−37.5001	−1.29465	−0.647323	+	0.762215i	$0.724112\pi$
$840$	150.046	5.17709
$841$	−20.6894	−0.713427
$842$	43.4403	1.49705
$843$	50.0692	1.72447
$844$	−39.5740	−1.36219
$845$	3.21951	0.110754
$846$	63.1177	2.17003
$847$	−19.1634	−0.658462
$848$	68.6661	2.35800
$849$	37.3921	1.28330
$850$	−2.44443	−0.0838432
$851$	42.8471	1.46878
$852$	−59.3037	−2.03171
$853$	−16.6261	−0.569268	−0.284634	−	0.958636i	$-0.591872\pi$
$853$	−16.6261	−0.569268	−0.284634	+	0.958636i	$0.591872\pi$
$854$	−67.7753	−2.31922
$855$	−156.411	−5.34913
$856$	25.4410	0.869555
$857$	−2.89273	−0.0988138	−0.0494069	−	0.998779i	$-0.515733\pi$
$857$	−2.89273	−0.0988138	−0.0494069	+	0.998779i	$0.515733\pi$
$858$	−15.4838	−0.528608
$859$	−3.45652	−0.117935	−0.0589674	−	0.998260i	$-0.518781\pi$
$859$	−3.45652	−0.117935	−0.0589674	+	0.998260i	$0.518781\pi$
$860$	−31.6097	−1.07788
$861$	−49.7167	−1.69434
$862$	−51.1126	−1.74090
$863$	23.4381	0.797841	0.398921	−	0.916985i	$-0.369385\pi$
$863$	23.4381	0.797841	0.398921	+	0.916985i	$0.369385\pi$
$864$	15.2665	0.519378
$865$	36.8702	1.25362
$866$	78.3671	2.66302
$867$	50.4231	1.71246
$868$	19.0985	0.648246
$869$	0.510151	0.0173057
$870$	−68.5422	−2.32380
$871$	1.23974	0.0420069
$872$	−32.1588	−1.08903
$873$	58.2612	1.97184
$874$	−122.861	−4.15585
$875$	3.41213	0.115351
$876$	−63.8569	−2.15753
$877$	14.1777	0.478747	0.239374	−	0.970928i	$-0.423058\pi$
$877$	14.1777	0.478747	0.239374	+	0.970928i	$0.423058\pi$
$878$	−8.66234	−0.292340
$879$	41.2656	1.39186
$880$	−34.2874	−1.15583
$881$	25.1830	0.848438	0.424219	−	0.905560i	$-0.360549\pi$
$881$	25.1830	0.848438	0.424219	+	0.905560i	$0.360549\pi$
$882$	−20.5827	−0.693056
$883$	0.972485	0.0327267	0.0163634	−	0.999866i	$-0.494791\pi$
$883$	0.972485	0.0327267	0.0163634	+	0.999866i	$0.494791\pi$
$884$	0.765445	0.0257447
$885$	−44.8139	−1.50640
$886$	−6.94000	−0.233154
$887$	−12.0841	−0.405743	−0.202871	−	0.979205i	$-0.565027\pi$
$887$	−12.0841	−0.405743	−0.202871	+	0.979205i	$0.565027\pi$
$888$	−115.937	−3.89059
$889$	13.5542	0.454592
$890$	−12.7693	−0.428029
$891$	−15.7666	−0.528200
$892$	73.2726	2.45335
$893$	36.2758	1.21392
$894$	31.1451	1.04165
$895$	74.0217	2.47427
$896$	51.2819	1.71321
$897$	17.6407	0.589005
$898$	80.1622	2.67505
$899$	−4.54483	−0.151579
$900$	130.640	4.35466
$901$	2.47856	0.0825727
$902$	30.0358	1.00008
$903$	20.2812	0.674917
$904$	−36.7328	−1.22171
$905$	−40.8756	−1.35875
$906$	−140.812	−4.67817
$907$	−36.0959	−1.19854	−0.599272	−	0.800545i	$-0.704543\pi$
$907$	−36.0959	−1.19854	−0.599272	+	0.800545i	$0.704543\pi$
$908$	51.2395	1.70044
$909$	−71.7203	−2.37881
$910$	−23.2147	−0.769558
$911$	36.5614	1.21133	0.605667	−	0.795718i	$-0.292906\pi$
$911$	36.5614	1.21133	0.605667	+	0.795718i	$0.292906\pi$
$912$	125.744	4.16380
$913$	3.74719	0.124014
$914$	90.4110	2.99053
$915$	−89.9349	−2.97315
$916$	−54.3043	−1.79426
$917$	24.0305	0.793559
$918$	3.83519	0.126580
$919$	−30.3768	−1.00204	−0.501019	−	0.865436i	$-0.667041\pi$
$919$	−30.3768	−1.00204	−0.501019	+	0.865436i	$0.667041\pi$
$920$	103.276	3.40492
$921$	67.8226	2.23483
$922$	−25.3565	−0.835072
$923$	4.77974	0.157327
$924$	75.4855	2.48329
$925$	−38.7289	−1.27340
$926$	7.32531	0.240725
$927$	43.5128	1.42915
$928$	5.22828	0.171627
$929$	−43.9017	−1.44037	−0.720183	−	0.693784i	$-0.755942\pi$
$929$	−43.9017	−1.44037	−0.720183	+	0.693784i	$0.755942\pi$
$930$	37.4838	1.22914
$931$	−11.8296	−0.387698
$932$	58.7890	1.92570
$933$	90.1579	2.95164
$934$	70.5135	2.30727
$935$	−1.23763	−0.0404749
$936$	−31.5199	−1.03026
$937$	−42.8830	−1.40093	−0.700463	−	0.713689i	$-0.747023\pi$
$937$	−42.8830	−1.40093	−0.700463	+	0.713689i	$0.747023\pi$
$938$	−8.93927	−0.291877
$939$	−98.8731	−3.22660
$940$	−58.5352	−1.90921
$941$	47.5161	1.54898	0.774490	−	0.632586i	$-0.218007\pi$
$941$	47.5161	1.54898	0.774490	+	0.632586i	$0.218007\pi$
$942$	−163.583	−5.32981
$943$	−34.2198	−1.11435
$944$	23.7905	0.774313
$945$	−78.6409	−2.55819
$946$	−12.2527	−0.398369
$947$	23.1978	0.753826	0.376913	−	0.926249i	$-0.376986\pi$
$947$	23.1978	0.753826	0.376913	+	0.926249i	$0.376986\pi$
$948$	3.01891	0.0980498
$949$	5.14672	0.167069
$950$	111.053	3.60302
$951$	10.8159	0.350731
$952$	−2.87523	−0.0931867
$953$	16.5489	0.536071	0.268035	−	0.963409i	$-0.413626\pi$
$953$	16.5489	0.536071	0.268035	+	0.963409i	$0.413626\pi$
$954$	−195.922	−6.34322
$955$	−51.7978	−1.67614
$956$	−28.4656	−0.920642
$957$	−17.9631	−0.580665
$958$	37.5972	1.21471
$959$	−0.240846	−0.00777734
$960$	54.0824	1.74550
$961$	−28.5146	−0.919825
$962$	17.9373	0.578323
$963$	−27.4566	−0.884777
$964$	−53.9811	−1.73861
$965$	−11.7300	−0.377601
$966$	−127.200	−4.09260
$967$	45.4284	1.46088	0.730439	−	0.682978i	$-0.239316\pi$
$967$	45.4284	1.46088	0.730439	+	0.682978i	$0.239316\pi$
$968$	35.6901	1.14712
$969$	4.53883	0.145808
$970$	−79.9158	−2.56594
$971$	−41.2612	−1.32413	−0.662067	−	0.749445i	$-0.730321\pi$
$971$	−41.2612	−1.32413	−0.662067	+	0.749445i	$0.730321\pi$
$972$	12.1266	0.388960
$973$	−18.3549	−0.588431
$974$	−56.2631	−1.80279
$975$	−15.9452	−0.510654
$976$	47.7439	1.52825
$977$	11.7960	0.377389	0.188695	−	0.982036i	$-0.439574\pi$
$977$	11.7960	0.377389	0.188695	+	0.982036i	$0.439574\pi$
$978$	−27.3129	−0.873369
$979$	−3.34651	−0.106955
$980$	19.0884	0.609755
$981$	34.7066	1.10810
$982$	−98.9060	−3.15622
$983$	53.0743	1.69281	0.846404	−	0.532541i	$-0.178763\pi$
$983$	53.0743	1.69281	0.846404	+	0.532541i	$0.178763\pi$
$984$	92.5929	2.95175
$985$	72.7750	2.31880
$986$	1.31342	0.0418279
$987$	37.5569	1.19545
$988$	−34.7749	−1.10634
$989$	13.9595	0.443885
$990$	97.8310	3.10927
$991$	35.8277	1.13810	0.569052	−	0.822302i	$-0.307310\pi$
$991$	35.8277	1.13810	0.569052	+	0.822302i	$0.307310\pi$
$992$	−2.85920	−0.0907796
$993$	3.56843	0.113241
$994$	−34.4649	−1.09316
$995$	22.5525	0.714963
$996$	22.1747	0.702633
$997$	−50.4661	−1.59828	−0.799138	−	0.601147i	$-0.794710\pi$
$997$	−50.4661	−1.59828	−0.799138	+	0.601147i	$0.794710\pi$
$998$	−12.7086	−0.402282
$999$	60.7637	1.92248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.8	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.8	✓	134	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48492 q^{2} -2.97194 q^{3} +4.17482 q^{4} +3.21951 q^{5} +7.38503 q^{6} +2.90175 q^{7} -5.40425 q^{8} +5.83242 q^{9} +O(q^{10})\)	\(q-2.48492 q^{2} -2.97194 q^{3} +4.17482 q^{4} +3.21951 q^{5} +7.38503 q^{6} +2.90175 q^{7} -5.40425 q^{8} +5.83242 q^{9} -8.00022 q^{10} -2.09665 q^{11} -12.4073 q^{12} +1.00000 q^{13} -7.21062 q^{14} -9.56819 q^{15} +5.07949 q^{16} +0.183348 q^{17} -14.4931 q^{18} -8.32967 q^{19} +13.4409 q^{20} -8.62384 q^{21} +5.21000 q^{22} -5.93575 q^{23} +16.0611 q^{24} +5.36524 q^{25} -2.48492 q^{26} -8.41779 q^{27} +12.1143 q^{28} -2.88281 q^{29} +23.7762 q^{30} +1.57653 q^{31} -1.81360 q^{32} +6.23111 q^{33} -0.455605 q^{34} +9.34222 q^{35} +24.3493 q^{36} -7.21849 q^{37} +20.6986 q^{38} -2.97194 q^{39} -17.3990 q^{40} +5.76504 q^{41} +21.4295 q^{42} -2.35176 q^{43} -8.75313 q^{44} +18.7775 q^{45} +14.7498 q^{46} -4.35501 q^{47} -15.0959 q^{48} +1.42017 q^{49} -13.3322 q^{50} -0.544899 q^{51} +4.17482 q^{52} +13.5183 q^{53} +20.9175 q^{54} -6.75018 q^{55} -15.6818 q^{56} +24.7553 q^{57} +7.16355 q^{58} +4.68363 q^{59} -39.9455 q^{60} +9.39936 q^{61} -3.91754 q^{62} +16.9243 q^{63} -5.65231 q^{64} +3.21951 q^{65} -15.4838 q^{66} +1.23974 q^{67} +0.765445 q^{68} +17.6407 q^{69} -23.2147 q^{70} +4.77974 q^{71} -31.5199 q^{72} +5.14672 q^{73} +17.9373 q^{74} -15.9452 q^{75} -34.7749 q^{76} -6.08395 q^{77} +7.38503 q^{78} -0.243317 q^{79} +16.3534 q^{80} +7.51990 q^{81} -14.3257 q^{82} -1.78723 q^{83} -36.0030 q^{84} +0.590291 q^{85} +5.84394 q^{86} +8.56754 q^{87} +11.3308 q^{88} +1.59612 q^{89} -46.6607 q^{90} +2.90175 q^{91} -24.7807 q^{92} -4.68535 q^{93} +10.8219 q^{94} -26.8174 q^{95} +5.38992 q^{96} +9.98920 q^{97} -3.52901 q^{98} -12.2285 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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