LMFDB - Embedded newform 8041.2.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44026 q^{2} -2.32024 q^{3} +3.95484 q^{4} -3.72812 q^{5} +5.66197 q^{6} -3.99727 q^{7} -4.77032 q^{8} +2.38350 q^{9} +O(q^{10})$	\(q-2.44026 q^{2} -2.32024 q^{3} +3.95484 q^{4} -3.72812 q^{5} +5.66197 q^{6} -3.99727 q^{7} -4.77032 q^{8} +2.38350 q^{9} +9.09757 q^{10} -1.00000 q^{11} -9.17617 q^{12} +1.34992 q^{13} +9.75436 q^{14} +8.65012 q^{15} +3.73111 q^{16} -1.00000 q^{17} -5.81634 q^{18} -2.39617 q^{19} -14.7441 q^{20} +9.27462 q^{21} +2.44026 q^{22} +6.85983 q^{23} +11.0683 q^{24} +8.89889 q^{25} -3.29414 q^{26} +1.43043 q^{27} -15.8086 q^{28} +5.00840 q^{29} -21.1085 q^{30} +5.80641 q^{31} +0.435786 q^{32} +2.32024 q^{33} +2.44026 q^{34} +14.9023 q^{35} +9.42636 q^{36} -5.46719 q^{37} +5.84727 q^{38} -3.13212 q^{39} +17.7843 q^{40} +10.8260 q^{41} -22.6324 q^{42} +1.00000 q^{43} -3.95484 q^{44} -8.88596 q^{45} -16.7397 q^{46} +7.26962 q^{47} -8.65705 q^{48} +8.97819 q^{49} -21.7156 q^{50} +2.32024 q^{51} +5.33871 q^{52} -11.6838 q^{53} -3.49062 q^{54} +3.72812 q^{55} +19.0683 q^{56} +5.55969 q^{57} -12.2218 q^{58} +3.34085 q^{59} +34.2099 q^{60} +2.30403 q^{61} -14.1691 q^{62} -9.52748 q^{63} -8.52564 q^{64} -5.03265 q^{65} -5.66197 q^{66} +5.30216 q^{67} -3.95484 q^{68} -15.9164 q^{69} -36.3655 q^{70} +13.4015 q^{71} -11.3700 q^{72} +11.2234 q^{73} +13.3413 q^{74} -20.6475 q^{75} -9.47649 q^{76} +3.99727 q^{77} +7.64318 q^{78} +3.87049 q^{79} -13.9100 q^{80} -10.4694 q^{81} -26.4182 q^{82} -3.77164 q^{83} +36.6797 q^{84} +3.72812 q^{85} -2.44026 q^{86} -11.6207 q^{87} +4.77032 q^{88} +2.44945 q^{89} +21.6840 q^{90} -5.39598 q^{91} +27.1296 q^{92} -13.4722 q^{93} -17.7397 q^{94} +8.93323 q^{95} -1.01113 q^{96} +7.34508 q^{97} -21.9091 q^{98} -2.38350 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * 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 $

$2$	−2.44026	−1.72552	−0.862760	−	0.505613i	$-0.831266\pi$
$2$	−2.44026	−1.72552	−0.862760	+	0.505613i	$0.831266\pi$
$3$	−2.32024	−1.33959	−0.669795	−	0.742547i	$-0.733618\pi$
$3$	−2.32024	−1.33959	−0.669795	+	0.742547i	$0.733618\pi$
$4$	3.95484	1.97742
$5$	−3.72812	−1.66727	−0.833633	−	0.552318i	$-0.813743\pi$
$5$	−3.72812	−1.66727	−0.833633	+	0.552318i	$0.813743\pi$
$6$	5.66197	2.31149
$7$	−3.99727	−1.51083	−0.755414	−	0.655248i	$-0.772564\pi$
$7$	−3.99727	−1.51083	−0.755414	+	0.655248i	$0.772564\pi$
$8$	−4.77032	−1.68656
$9$	2.38350	0.794499
$10$	9.09757	2.87690
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−9.17617	−2.64893
$13$	1.34992	0.374399	0.187200	−	0.982322i	$-0.440059\pi$
$13$	1.34992	0.374399	0.187200	+	0.982322i	$0.440059\pi$
$14$	9.75436	2.60696
$15$	8.65012	2.23345
$16$	3.73111	0.932777
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−5.81634	−1.37092
$19$	−2.39617	−0.549720	−0.274860	−	0.961484i	$-0.588631\pi$
$19$	−2.39617	−0.549720	−0.274860	+	0.961484i	$0.588631\pi$
$20$	−14.7441	−3.29689
$21$	9.27462	2.02389
$22$	2.44026	0.520264
$23$	6.85983	1.43037	0.715187	−	0.698934i	$-0.246342\pi$
$23$	6.85983	1.43037	0.715187	+	0.698934i	$0.246342\pi$
$24$	11.0683	2.25930
$25$	8.89889	1.77978
$26$	−3.29414	−0.646034
$27$	1.43043	0.275287
$28$	−15.8086	−2.98754
$29$	5.00840	0.930037	0.465018	−	0.885301i	$-0.346048\pi$
$29$	5.00840	0.930037	0.465018	+	0.885301i	$0.346048\pi$
$30$	−21.1085	−3.85387
$31$	5.80641	1.04286	0.521431	−	0.853294i	$-0.325398\pi$
$31$	5.80641	1.04286	0.521431	+	0.853294i	$0.325398\pi$
$32$	0.435786	0.0770369
$33$	2.32024	0.403901
$34$	2.44026	0.418500
$35$	14.9023	2.51895
$36$	9.42636	1.57106
$37$	−5.46719	−0.898801	−0.449400	−	0.893330i	$-0.648362\pi$
$37$	−5.46719	−0.898801	−0.449400	+	0.893330i	$0.648362\pi$
$38$	5.84727	0.948553
$39$	−3.13212	−0.501541
$40$	17.7843	2.81195
$41$	10.8260	1.69074	0.845368	−	0.534184i	$-0.179381\pi$
$41$	10.8260	1.69074	0.845368	+	0.534184i	$0.179381\pi$
$42$	−22.6324	−3.49226
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−3.95484	−0.596215
$45$	−8.88596	−1.32464
$46$	−16.7397	−2.46814
$47$	7.26962	1.06038	0.530192	−	0.847878i	$-0.322120\pi$
$47$	7.26962	1.06038	0.530192	+	0.847878i	$0.322120\pi$
$48$	−8.65705	−1.24954
$49$	8.97819	1.28260
$50$	−21.7156	−3.07104
$51$	2.32024	0.324898
$52$	5.33871	0.740345
$53$	−11.6838	−1.60489	−0.802445	−	0.596726i	$-0.796468\pi$
$53$	−11.6838	−1.60489	−0.802445	+	0.596726i	$0.796468\pi$
$54$	−3.49062	−0.475014
$55$	3.72812	0.502700
$56$	19.0683	2.54810
$57$	5.55969	0.736399
$58$	−12.2218	−1.60480
$59$	3.34085	0.434942	0.217471	−	0.976067i	$-0.430219\pi$
$59$	3.34085	0.434942	0.217471	+	0.976067i	$0.430219\pi$
$60$	34.2099	4.41648
$61$	2.30403	0.295001	0.147501	−	0.989062i	$-0.452877\pi$
$61$	2.30403	0.295001	0.147501	+	0.989062i	$0.452877\pi$
$62$	−14.1691	−1.79948
$63$	−9.52748	−1.20035
$64$	−8.52564	−1.06571
$65$	−5.03265	−0.624223
$66$	−5.66197	−0.696940
$67$	5.30216	0.647762	0.323881	−	0.946098i	$-0.395012\pi$
$67$	5.30216	0.647762	0.323881	+	0.946098i	$0.395012\pi$
$68$	−3.95484	−0.479595
$69$	−15.9164	−1.91611
$70$	−36.3655	−4.34650
$71$	13.4015	1.59046	0.795232	−	0.606306i	$-0.207349\pi$
$71$	13.4015	1.59046	0.795232	+	0.606306i	$0.207349\pi$
$72$	−11.3700	−1.33997
$73$	11.2234	1.31360	0.656801	−	0.754064i	$-0.271909\pi$
$73$	11.2234	1.31360	0.656801	+	0.754064i	$0.271909\pi$
$74$	13.3413	1.55090
$75$	−20.6475	−2.38417
$76$	−9.47649	−1.08703
$77$	3.99727	0.455531
$78$	7.64318	0.865419
$79$	3.87049	0.435464	0.217732	−	0.976009i	$-0.430134\pi$
$79$	3.87049	0.435464	0.217732	+	0.976009i	$0.430134\pi$
$80$	−13.9100	−1.55519
$81$	−10.4694	−1.16327
$82$	−26.4182	−2.91740
$83$	−3.77164	−0.413991	−0.206996	−	0.978342i	$-0.566369\pi$
$83$	−3.77164	−0.413991	−0.206996	+	0.978342i	$0.566369\pi$
$84$	36.6797	4.00208
$85$	3.72812	0.404372
$86$	−2.44026	−0.263139
$87$	−11.6207	−1.24587
$88$	4.77032	0.508518
$89$	2.44945	0.259642	0.129821	−	0.991537i	$-0.458560\pi$
$89$	2.44945	0.259642	0.129821	+	0.991537i	$0.458560\pi$
$90$	21.6840	2.28570
$91$	−5.39598	−0.565652
$92$	27.1296	2.82845
$93$	−13.4722	−1.39701
$94$	−17.7397	−1.82971
$95$	8.93323	0.916530
$96$	−1.01113	−0.103198
$97$	7.34508	0.745780	0.372890	−	0.927876i	$-0.378367\pi$
$97$	7.34508	0.745780	0.372890	+	0.927876i	$0.378367\pi$
$98$	−21.9091	−2.21315
$99$	−2.38350	−0.239550
$100$	35.1937	3.51937
$101$	16.4938	1.64119	0.820596	−	0.571509i	$-0.193642\pi$
$101$	16.4938	1.64119	0.820596	+	0.571509i	$0.193642\pi$
$102$	−5.66197	−0.560618
$103$	−3.48645	−0.343530	−0.171765	−	0.985138i	$-0.554947\pi$
$103$	−3.48645	−0.343530	−0.171765	+	0.985138i	$0.554947\pi$
$104$	−6.43953	−0.631448
$105$	−34.5769	−3.37436
$106$	28.5114	2.76927
$107$	−10.1002	−0.976420	−0.488210	−	0.872726i	$-0.662350\pi$
$107$	−10.1002	−0.976420	−0.488210	+	0.872726i	$0.662350\pi$
$108$	5.65715	0.544359
$109$	10.5922	1.01455	0.507276	−	0.861784i	$-0.330653\pi$
$109$	10.5922	1.01455	0.507276	+	0.861784i	$0.330653\pi$
$110$	−9.09757	−0.867419
$111$	12.6852	1.20402
$112$	−14.9143	−1.40926
$113$	11.1761	1.05136	0.525678	−	0.850684i	$-0.323812\pi$
$113$	11.1761	1.05136	0.525678	+	0.850684i	$0.323812\pi$
$114$	−13.5671	−1.27067
$115$	−25.5743	−2.38481
$116$	19.8074	1.83907
$117$	3.21752	0.297460
$118$	−8.15253	−0.750502
$119$	3.99727	0.366429
$120$	−41.2638	−3.76686
$121$	1.00000	0.0909091
$122$	−5.62243	−0.509031
$123$	−25.1189	−2.26489
$124$	22.9634	2.06218
$125$	−14.5355	−1.30010
$126$	23.2495	2.07123
$127$	−9.03498	−0.801725	−0.400862	−	0.916138i	$-0.631289\pi$
$127$	−9.03498	−0.801725	−0.400862	+	0.916138i	$0.631289\pi$
$128$	19.9332	1.76186
$129$	−2.32024	−0.204285
$130$	12.2809	1.07711
$131$	−2.10263	−0.183707	−0.0918537	−	0.995773i	$-0.529279\pi$
$131$	−2.10263	−0.183707	−0.0918537	+	0.995773i	$0.529279\pi$
$132$	9.17617	0.798683
$133$	9.57816	0.830532
$134$	−12.9386	−1.11773
$135$	−5.33283	−0.458977
$136$	4.77032	0.409052
$137$	−10.0886	−0.861928	−0.430964	−	0.902369i	$-0.641826\pi$
$137$	−10.0886	−0.861928	−0.430964	+	0.902369i	$0.641826\pi$
$138$	38.8401	3.30629
$139$	−7.52776	−0.638497	−0.319248	−	0.947671i	$-0.603430\pi$
$139$	−7.52776	−0.638497	−0.319248	+	0.947671i	$0.603430\pi$
$140$	58.9364	4.98103
$141$	−16.8672	−1.42048
$142$	−32.7030	−2.74438
$143$	−1.34992	−0.112886
$144$	8.89308	0.741090
$145$	−18.6719	−1.55062
$146$	−27.3880	−2.26665
$147$	−20.8315	−1.71815
$148$	−21.6219	−1.77731
$149$	8.08455	0.662312	0.331156	−	0.943576i	$-0.392561\pi$
$149$	8.08455	0.662312	0.331156	+	0.943576i	$0.392561\pi$
$150$	50.3852	4.11394
$151$	9.92002	0.807280	0.403640	−	0.914918i	$-0.367745\pi$
$151$	9.92002	0.807280	0.403640	+	0.914918i	$0.367745\pi$
$152$	11.4305	0.927137
$153$	−2.38350	−0.192694
$154$	−9.75436	−0.786029
$155$	−21.6470	−1.73873
$156$	−12.3871	−0.991758
$157$	−5.95343	−0.475135	−0.237568	−	0.971371i	$-0.576350\pi$
$157$	−5.95343	−0.475135	−0.237568	+	0.971371i	$0.576350\pi$
$158$	−9.44498	−0.751403
$159$	27.1091	2.14989
$160$	−1.62466	−0.128441
$161$	−27.4206	−2.16105
$162$	25.5481	2.00725
$163$	−8.43986	−0.661060	−0.330530	−	0.943795i	$-0.607228\pi$
$163$	−8.43986	−0.661060	−0.330530	+	0.943795i	$0.607228\pi$
$164$	42.8151	3.34330
$165$	−8.65012	−0.673411
$166$	9.20377	0.714351
$167$	−0.316537	−0.0244943	−0.0122472	−	0.999925i	$-0.503898\pi$
$167$	−0.316537	−0.0244943	−0.0122472	+	0.999925i	$0.503898\pi$
$168$	−44.2429	−3.41341
$169$	−11.1777	−0.859825
$170$	−9.09757	−0.697752
$171$	−5.71127	−0.436752
$172$	3.95484	0.301554
$173$	−3.94677	−0.300068	−0.150034	−	0.988681i	$-0.547938\pi$
$173$	−3.94677	−0.300068	−0.150034	+	0.988681i	$0.547938\pi$
$174$	28.3574	2.14977
$175$	−35.5713	−2.68894
$176$	−3.73111	−0.281243
$177$	−7.75157	−0.582644
$178$	−5.97729	−0.448017
$179$	10.5359	0.787489	0.393744	−	0.919220i	$-0.371179\pi$
$179$	10.5359	0.787489	0.393744	+	0.919220i	$0.371179\pi$
$180$	−35.1426	−2.61938
$181$	−5.61968	−0.417708	−0.208854	−	0.977947i	$-0.566973\pi$
$181$	−5.61968	−0.417708	−0.208854	+	0.977947i	$0.566973\pi$
$182$	13.1676	0.976045
$183$	−5.34590	−0.395180
$184$	−32.7236	−2.41241
$185$	20.3824	1.49854
$186$	32.8757	2.41056
$187$	1.00000	0.0731272
$188$	28.7502	2.09683
$189$	−5.71784	−0.415911
$190$	−21.7993	−1.58149
$191$	17.1781	1.24296	0.621480	−	0.783430i	$-0.286532\pi$
$191$	17.1781	1.24296	0.621480	+	0.783430i	$0.286532\pi$
$192$	19.7815	1.42761
$193$	21.7032	1.56223	0.781114	−	0.624389i	$-0.214652\pi$
$193$	21.7032	1.56223	0.781114	+	0.624389i	$0.214652\pi$
$194$	−17.9239	−1.28686
$195$	11.6769	0.836203
$196$	35.5073	2.53624
$197$	12.4748	0.888790	0.444395	−	0.895831i	$-0.353419\pi$
$197$	12.4748	0.888790	0.444395	+	0.895831i	$0.353419\pi$
$198$	5.81634	0.413349
$199$	2.93368	0.207963	0.103981	−	0.994579i	$-0.466842\pi$
$199$	2.93368	0.207963	0.103981	+	0.994579i	$0.466842\pi$
$200$	−42.4505	−3.00171
$201$	−12.3023	−0.867735
$202$	−40.2490	−2.83191
$203$	−20.0199	−1.40512
$204$	9.17617	0.642461
$205$	−40.3606	−2.81891
$206$	8.50782	0.592768
$207$	16.3504	1.13643
$208$	5.03668	0.349231
$209$	2.39617	0.165747
$210$	84.3765	5.82253
$211$	4.21228	0.289985	0.144993	−	0.989433i	$-0.453684\pi$
$211$	4.21228	0.289985	0.144993	+	0.989433i	$0.453684\pi$
$212$	−46.2075	−3.17355
$213$	−31.0946	−2.13057
$214$	24.6470	1.68483
$215$	−3.72812	−0.254256
$216$	−6.82363	−0.464289
$217$	−23.2098	−1.57558
$218$	−25.8477	−1.75063
$219$	−26.0410	−1.75969
$220$	14.7441	0.994050
$221$	−1.34992	−0.0908051
$222$	−30.9551	−2.07757
$223$	−9.60880	−0.643453	−0.321726	−	0.946833i	$-0.604263\pi$
$223$	−9.60880	−0.643453	−0.321726	+	0.946833i	$0.604263\pi$
$224$	−1.74196	−0.116389
$225$	21.2105	1.41403
$226$	−27.2724	−1.81414
$227$	25.2201	1.67391	0.836957	−	0.547269i	$-0.184333\pi$
$227$	25.2201	1.67391	0.836957	+	0.547269i	$0.184333\pi$
$228$	21.9877	1.45617
$229$	7.28800	0.481604	0.240802	−	0.970574i	$-0.422590\pi$
$229$	7.28800	0.481604	0.240802	+	0.970574i	$0.422590\pi$
$230$	62.4077	4.11505
$231$	−9.27462	−0.610225
$232$	−23.8917	−1.56856
$233$	16.8704	1.10522	0.552609	−	0.833440i	$-0.313632\pi$
$233$	16.8704	1.10522	0.552609	+	0.833440i	$0.313632\pi$
$234$	−7.85156	−0.513273
$235$	−27.1020	−1.76794
$236$	13.2126	0.860064
$237$	−8.98045	−0.583343
$238$	−9.75436	−0.632282
$239$	6.62588	0.428593	0.214296	−	0.976769i	$-0.431254\pi$
$239$	6.62588	0.428593	0.214296	+	0.976769i	$0.431254\pi$
$240$	32.2745	2.08331
$241$	1.48316	0.0955385	0.0477693	−	0.998858i	$-0.484789\pi$
$241$	1.48316	0.0955385	0.0477693	+	0.998858i	$0.484789\pi$
$242$	−2.44026	−0.156866
$243$	20.0003	1.28302
$244$	9.11209	0.583342
$245$	−33.4718	−2.13843
$246$	61.2964	3.90812
$247$	−3.23463	−0.205815
$248$	−27.6984	−1.75885
$249$	8.75110	0.554578
$250$	35.4704	2.24335
$251$	29.7778	1.87956	0.939779	−	0.341782i	$-0.111030\pi$
$251$	29.7778	1.87956	0.939779	+	0.341782i	$0.111030\pi$
$252$	−37.6797	−2.37360
$253$	−6.85983	−0.431274
$254$	22.0477	1.38339
$255$	−8.65012	−0.541692
$256$	−31.5907	−1.97442
$257$	3.08090	0.192182	0.0960908	−	0.995373i	$-0.469366\pi$
$257$	3.08090	0.192182	0.0960908	+	0.995373i	$0.469366\pi$
$258$	5.66197	0.352499
$259$	21.8539	1.35793
$260$	−19.9033	−1.23435
$261$	11.9375	0.738913
$262$	5.13095	0.316991
$263$	18.5801	1.14570	0.572850	−	0.819660i	$-0.305838\pi$
$263$	18.5801	1.14570	0.572850	+	0.819660i	$0.305838\pi$
$264$	−11.0683	−0.681205
$265$	43.5585	2.67578
$266$	−23.3731	−1.43310
$267$	−5.68331	−0.347813
$268$	20.9692	1.28090
$269$	−21.9613	−1.33900	−0.669501	−	0.742811i	$-0.733492\pi$
$269$	−21.9613	−1.33900	−0.669501	+	0.742811i	$0.733492\pi$
$270$	13.0135	0.791975
$271$	−4.32913	−0.262976	−0.131488	−	0.991318i	$-0.541975\pi$
$271$	−4.32913	−0.262976	−0.131488	+	0.991318i	$0.541975\pi$
$272$	−3.73111	−0.226232
$273$	12.5199	0.757742
$274$	24.6188	1.48727
$275$	−8.89889	−0.536623
$276$	−62.9470	−3.78896
$277$	−10.5859	−0.636043	−0.318021	−	0.948084i	$-0.603018\pi$
$277$	−10.5859	−0.636043	−0.318021	+	0.948084i	$0.603018\pi$
$278$	18.3697	1.10174
$279$	13.8396	0.828552
$280$	−71.0888	−4.24837
$281$	3.64238	0.217286	0.108643	−	0.994081i	$-0.465349\pi$
$281$	3.64238	0.217286	0.108643	+	0.994081i	$0.465349\pi$
$282$	41.1604	2.45106
$283$	−1.97729	−0.117538	−0.0587689	−	0.998272i	$-0.518717\pi$
$283$	−1.97729	−0.117538	−0.0587689	+	0.998272i	$0.518717\pi$
$284$	53.0008	3.14502
$285$	−20.7272	−1.22777
$286$	3.29414	0.194786
$287$	−43.2745	−2.55441
$288$	1.03870	0.0612057
$289$	1.00000	0.0588235
$290$	45.5643	2.67563
$291$	−17.0423	−0.999039
$292$	44.3869	2.59755
$293$	−28.7438	−1.67923	−0.839617	−	0.543179i	$-0.817220\pi$
$293$	−28.7438	−1.67923	−0.839617	+	0.543179i	$0.817220\pi$
$294$	50.8342	2.96471
$295$	−12.4551	−0.725164
$296$	26.0803	1.51588
$297$	−1.43043	−0.0830022
$298$	−19.7284	−1.14283
$299$	9.26019	0.535530
$300$	−81.6578	−4.71451
$301$	−3.99727	−0.230399
$302$	−24.2074	−1.39298
$303$	−38.2695	−2.19852
$304$	−8.94038	−0.512766
$305$	−8.58972	−0.491846
$306$	5.81634	0.332498
$307$	−4.15201	−0.236968	−0.118484	−	0.992956i	$-0.537803\pi$
$307$	−4.15201	−0.236968	−0.118484	+	0.992956i	$0.537803\pi$
$308$	15.8086	0.900778
$309$	8.08938	0.460189
$310$	52.8242	3.00021
$311$	−10.1124	−0.573420	−0.286710	−	0.958017i	$-0.592562\pi$
$311$	−10.1124	−0.573420	−0.286710	+	0.958017i	$0.592562\pi$
$312$	14.9412	0.845880
$313$	−18.6328	−1.05319	−0.526593	−	0.850117i	$-0.676531\pi$
$313$	−18.6328	−1.05319	−0.526593	+	0.850117i	$0.676531\pi$
$314$	14.5279	0.819856
$315$	35.5196	2.00130
$316$	15.3072	0.861097
$317$	7.35737	0.413231	0.206616	−	0.978422i	$-0.433755\pi$
$317$	7.35737	0.413231	0.206616	+	0.978422i	$0.433755\pi$
$318$	−66.1532	−3.70969
$319$	−5.00840	−0.280417
$320$	31.7846	1.77682
$321$	23.4348	1.30800
$322$	66.9133	3.72893
$323$	2.39617	0.133327
$324$	−41.4050	−2.30028
$325$	12.0127	0.666347
$326$	20.5954	1.14067
$327$	−24.5765	−1.35908
$328$	−51.6435	−2.85153
$329$	−29.0587	−1.60206
$330$	21.1085	1.16198
$331$	−16.3267	−0.897397	−0.448699	−	0.893683i	$-0.648112\pi$
$331$	−16.3267	−0.897397	−0.448699	+	0.893683i	$0.648112\pi$
$332$	−14.9163	−0.818636
$333$	−13.0310	−0.714096
$334$	0.772430	0.0422655
$335$	−19.7671	−1.07999
$336$	34.6046	1.88784
$337$	−6.31242	−0.343860	−0.171930	−	0.985109i	$-0.555000\pi$
$337$	−6.31242	−0.343860	−0.171930	+	0.985109i	$0.555000\pi$
$338$	27.2765	1.48365
$339$	−25.9311	−1.40838
$340$	14.7441	0.799613
$341$	−5.80641	−0.314435
$342$	13.9370	0.753624
$343$	−7.90736	−0.426957
$344$	−4.77032	−0.257198
$345$	59.3384	3.19467
$346$	9.63113	0.517773
$347$	19.7136	1.05828	0.529140	−	0.848535i	$-0.322515\pi$
$347$	19.7136	1.05828	0.529140	+	0.848535i	$0.322515\pi$
$348$	−45.9579	−2.46360
$349$	−6.05616	−0.324179	−0.162089	−	0.986776i	$-0.551823\pi$
$349$	−6.05616	−0.324179	−0.162089	+	0.986776i	$0.551823\pi$
$350$	86.8030	4.63982
$351$	1.93096	0.103067
$352$	−0.435786	−0.0232275
$353$	28.1128	1.49630	0.748148	−	0.663532i	$-0.230943\pi$
$353$	28.1128	1.49630	0.748148	+	0.663532i	$0.230943\pi$
$354$	18.9158	1.00536
$355$	−49.9624	−2.65173
$356$	9.68721	0.513421
$357$	−9.27462	−0.490865
$358$	−25.7102	−1.35883
$359$	−8.52540	−0.449954	−0.224977	−	0.974364i	$-0.572231\pi$
$359$	−8.52540	−0.449954	−0.224977	+	0.974364i	$0.572231\pi$
$360$	42.3889	2.23409
$361$	−13.2584	−0.697808
$362$	13.7135	0.720764
$363$	−2.32024	−0.121781
$364$	−21.3403	−1.11853
$365$	−41.8423	−2.19013
$366$	13.0454	0.681892
$367$	−17.7678	−0.927472	−0.463736	−	0.885973i	$-0.653491\pi$
$367$	−17.7678	−0.927472	−0.463736	+	0.885973i	$0.653491\pi$
$368$	25.5948	1.33422
$369$	25.8037	1.34329
$370$	−49.7382	−2.58576
$371$	46.7032	2.42471
$372$	−53.2806	−2.76247
$373$	−27.4449	−1.42104	−0.710521	−	0.703676i	$-0.751541\pi$
$373$	−27.4449	−1.42104	−0.710521	+	0.703676i	$0.751541\pi$
$374$	−2.44026	−0.126183
$375$	33.7259	1.74160
$376$	−34.6784	−1.78840
$377$	6.76092	0.348205
$378$	13.9530	0.717664
$379$	−14.7536	−0.757843	−0.378921	−	0.925429i	$-0.623705\pi$
$379$	−14.7536	−0.757843	−0.378921	+	0.925429i	$0.623705\pi$
$380$	35.3295	1.81237
$381$	20.9633	1.07398
$382$	−41.9188	−2.14475
$383$	24.3653	1.24501	0.622505	−	0.782616i	$-0.286115\pi$
$383$	24.3653	1.24501	0.622505	+	0.782616i	$0.286115\pi$
$384$	−46.2497	−2.36017
$385$	−14.9023	−0.759492
$386$	−52.9612	−2.69566
$387$	2.38350	0.121160
$388$	29.0487	1.47472
$389$	−10.3820	−0.526390	−0.263195	−	0.964743i	$-0.584776\pi$
$389$	−10.3820	−0.526390	−0.263195	+	0.964743i	$0.584776\pi$
$390$	−28.4947	−1.44288
$391$	−6.85983	−0.346916
$392$	−42.8288	−2.16318
$393$	4.87859	0.246093
$394$	−30.4416	−1.53363
$395$	−14.4297	−0.726035
$396$	−9.42636	−0.473692
$397$	29.6457	1.48788	0.743939	−	0.668248i	$-0.232955\pi$
$397$	29.6457	1.48788	0.743939	+	0.668248i	$0.232955\pi$
$398$	−7.15892	−0.358844
$399$	−22.2236	−1.11257
$400$	33.2027	1.66014
$401$	30.3324	1.51473	0.757363	−	0.652994i	$-0.226487\pi$
$401$	30.3324	1.51473	0.757363	+	0.652994i	$0.226487\pi$
$402$	30.0207	1.49729
$403$	7.83816	0.390446
$404$	65.2303	3.24533
$405$	39.0313	1.93948
$406$	48.8538	2.42457
$407$	5.46719	0.270999
$408$	−11.0683	−0.547961
$409$	12.9997	0.642794	0.321397	−	0.946945i	$-0.395848\pi$
$409$	12.9997	0.642794	0.321397	+	0.946945i	$0.395848\pi$
$410$	98.4902	4.86409
$411$	23.4080	1.15463
$412$	−13.7884	−0.679304
$413$	−13.3543	−0.657122
$414$	−39.8991	−1.96093
$415$	14.0611	0.690234
$416$	0.588275	0.0288425
$417$	17.4662	0.855323
$418$	−5.84727	−0.286000
$419$	27.1269	1.32524	0.662619	−	0.748957i	$-0.269445\pi$
$419$	27.1269	1.32524	0.662619	+	0.748957i	$0.269445\pi$
$420$	−136.746	−6.67253
$421$	34.3762	1.67539	0.837697	−	0.546136i	$-0.183902\pi$
$421$	34.3762	1.67539	0.837697	+	0.546136i	$0.183902\pi$
$422$	−10.2790	−0.500375
$423$	17.3271	0.842473
$424$	55.7353	2.70675
$425$	−8.89889	−0.431660
$426$	75.8788	3.67634
$427$	−9.20985	−0.445696
$428$	−39.9446	−1.93079
$429$	3.13212	0.151220
$430$	9.09757	0.438724
$431$	8.56561	0.412591	0.206296	−	0.978490i	$-0.433859\pi$
$431$	8.56561	0.412591	0.206296	+	0.978490i	$0.433859\pi$
$432$	5.33710	0.256781
$433$	−36.3292	−1.74587	−0.872934	−	0.487838i	$-0.837786\pi$
$433$	−36.3292	−1.74587	−0.872934	+	0.487838i	$0.837786\pi$
$434$	56.6378	2.71870
$435$	43.3233	2.07719
$436$	41.8906	2.00620
$437$	−16.4373	−0.786304
$438$	63.5467	3.03638
$439$	10.2903	0.491131	0.245565	−	0.969380i	$-0.421026\pi$
$439$	10.2903	0.491131	0.245565	+	0.969380i	$0.421026\pi$
$440$	−17.7843	−0.847835
$441$	21.3995	1.01902
$442$	3.29414	0.156686
$443$	−30.7792	−1.46236	−0.731182	−	0.682182i	$-0.761031\pi$
$443$	−30.7792	−1.46236	−0.731182	+	0.682182i	$0.761031\pi$
$444$	50.1679	2.38086
$445$	−9.13186	−0.432892
$446$	23.4479	1.11029
$447$	−18.7581	−0.887226
$448$	34.0793	1.61010
$449$	−11.3499	−0.535633	−0.267816	−	0.963470i	$-0.586302\pi$
$449$	−11.3499	−0.535633	−0.267816	+	0.963470i	$0.586302\pi$
$450$	−51.7590	−2.43994
$451$	−10.8260	−0.509776
$452$	44.1996	2.07897
$453$	−23.0168	−1.08142
$454$	−61.5434	−2.88837
$455$	20.1169	0.943093
$456$	−26.5215	−1.24198
$457$	−29.4238	−1.37639	−0.688193	−	0.725527i	$-0.741596\pi$
$457$	−29.4238	−1.37639	−0.688193	+	0.725527i	$0.741596\pi$
$458$	−17.7846	−0.831018
$459$	−1.43043	−0.0667669
$460$	−101.142	−4.71578
$461$	−38.5655	−1.79618	−0.898088	−	0.439816i	$-0.855044\pi$
$461$	−38.5655	−1.79618	−0.898088	+	0.439816i	$0.855044\pi$
$462$	22.6324	1.05296
$463$	19.2410	0.894205	0.447102	−	0.894483i	$-0.352456\pi$
$463$	19.2410	0.894205	0.447102	+	0.894483i	$0.352456\pi$
$464$	18.6869	0.867516
$465$	50.2261	2.32918
$466$	−41.1681	−1.90708
$467$	4.32499	0.200137	0.100068	−	0.994981i	$-0.468094\pi$
$467$	4.32499	0.200137	0.100068	+	0.994981i	$0.468094\pi$
$468$	12.7248	0.588203
$469$	−21.1942	−0.978656
$470$	66.1359	3.05062
$471$	13.8134	0.636486
$472$	−15.9369	−0.733557
$473$	−1.00000	−0.0459800
$474$	21.9146	1.00657
$475$	−21.3233	−0.978379
$476$	15.8086	0.724586
$477$	−27.8482	−1.27508
$478$	−16.1688	−0.739546
$479$	−31.5267	−1.44049	−0.720245	−	0.693720i	$-0.755971\pi$
$479$	−31.5267	−1.44049	−0.720245	+	0.693720i	$0.755971\pi$
$480$	3.76960	0.172058
$481$	−7.38025	−0.336510
$482$	−3.61928	−0.164854
$483$	63.6223	2.89491
$484$	3.95484	0.179766
$485$	−27.3834	−1.24341
$486$	−48.8057	−2.21387
$487$	17.0996	0.774855	0.387428	−	0.921900i	$-0.373364\pi$
$487$	17.0996	0.774855	0.387428	+	0.921900i	$0.373364\pi$
$488$	−10.9910	−0.497538
$489$	19.5825	0.885549
$490$	81.6797	3.68991
$491$	27.3992	1.23651	0.618255	−	0.785977i	$-0.287840\pi$
$491$	27.3992	1.23651	0.618255	+	0.785977i	$0.287840\pi$
$492$	−99.3412	−4.47865
$493$	−5.00840	−0.225567
$494$	7.89332	0.355137
$495$	8.88596	0.399394
$496$	21.6643	0.972757
$497$	−53.5694	−2.40292
$498$	−21.3549	−0.956937
$499$	−13.0728	−0.585221	−0.292610	−	0.956232i	$-0.594524\pi$
$499$	−13.0728	−0.585221	−0.292610	+	0.956232i	$0.594524\pi$
$500$	−57.4858	−2.57084
$501$	0.734440	0.0328123
$502$	−72.6654	−3.24322
$503$	−3.17242	−0.141451	−0.0707257	−	0.997496i	$-0.522532\pi$
$503$	−3.17242	−0.141451	−0.0707257	+	0.997496i	$0.522532\pi$
$504$	45.4491	2.02447
$505$	−61.4908	−2.73630
$506$	16.7397	0.744172
$507$	25.9350	1.15181
$508$	−35.7319	−1.58535
$509$	−2.92974	−0.129859	−0.0649293	−	0.997890i	$-0.520682\pi$
$509$	−2.92974	−0.129859	−0.0649293	+	0.997890i	$0.520682\pi$
$510$	21.1085	0.934700
$511$	−44.8631	−1.98463
$512$	37.2231	1.64504
$513$	−3.42757	−0.151331
$514$	−7.51819	−0.331613
$515$	12.9979	0.572756
$516$	−9.17617	−0.403959
$517$	−7.26962	−0.319718
$518$	−53.3290	−2.34314
$519$	9.15745	0.401967
$520$	24.0073	1.05279
$521$	−10.3777	−0.454655	−0.227327	−	0.973818i	$-0.572999\pi$
$521$	−10.3777	−0.454655	−0.227327	+	0.973818i	$0.572999\pi$
$522$	−29.1306	−1.27501
$523$	−29.3371	−1.28282	−0.641411	−	0.767197i	$-0.721651\pi$
$523$	−29.3371	−1.28282	−0.641411	+	0.767197i	$0.721651\pi$
$524$	−8.31557	−0.363267
$525$	82.5338	3.60207
$526$	−45.3402	−1.97693
$527$	−5.80641	−0.252931
$528$	8.65705	0.376750
$529$	24.0572	1.04597
$530$	−106.294	−4.61711
$531$	7.96291	0.345561
$532$	37.8801	1.64231
$533$	14.6142	0.633010
$534$	13.8687	0.600158
$535$	37.6546	1.62795
$536$	−25.2930	−1.09249
$537$	−24.4457	−1.05491
$538$	53.5911	2.31048
$539$	−8.97819	−0.386718
$540$	−21.0905	−0.907592
$541$	28.0860	1.20751	0.603756	−	0.797169i	$-0.293670\pi$
$541$	28.0860	1.20751	0.603756	+	0.797169i	$0.293670\pi$
$542$	10.5642	0.453770
$543$	13.0390	0.559557
$544$	−0.435786	−0.0186842
$545$	−39.4891	−1.69153
$546$	−30.5519	−1.30750
$547$	9.08891	0.388614	0.194307	−	0.980941i	$-0.437754\pi$
$547$	9.08891	0.388614	0.194307	+	0.980941i	$0.437754\pi$
$548$	−39.8989	−1.70440
$549$	5.49166	0.234378
$550$	21.7156	0.925955
$551$	−12.0010	−0.511260
$552$	75.9264	3.23164
$553$	−15.4714	−0.657911
$554$	25.8322	1.09751
$555$	−47.2919	−2.00743
$556$	−29.7711	−1.26258
$557$	21.1781	0.897345	0.448673	−	0.893696i	$-0.351897\pi$
$557$	21.1781	0.897345	0.448673	+	0.893696i	$0.351897\pi$
$558$	−33.7720	−1.42968
$559$	1.34992	0.0570953
$560$	55.6021	2.34962
$561$	−2.32024	−0.0979605
$562$	−8.88834	−0.374932
$563$	−2.56497	−0.108100	−0.0540502	−	0.998538i	$-0.517213\pi$
$563$	−2.56497	−0.108100	−0.0540502	+	0.998538i	$0.517213\pi$
$564$	−66.7073	−2.80888
$565$	−41.6657	−1.75289
$566$	4.82509	0.202814
$567$	41.8492	1.75750
$568$	−63.9294	−2.68242
$569$	−17.5368	−0.735182	−0.367591	−	0.929988i	$-0.619817\pi$
$569$	−17.5368	−0.735182	−0.367591	+	0.929988i	$0.619817\pi$
$570$	50.5796	2.11855
$571$	34.5237	1.44477	0.722387	−	0.691489i	$-0.243045\pi$
$571$	34.5237	1.44477	0.722387	+	0.691489i	$0.243045\pi$
$572$	−5.33871	−0.223222
$573$	−39.8572	−1.66506
$574$	105.601	4.40769
$575$	61.0449	2.54575
$576$	−20.3208	−0.846702
$577$	−28.4685	−1.18516	−0.592579	−	0.805512i	$-0.701890\pi$
$577$	−28.4685	−1.18516	−0.592579	+	0.805512i	$0.701890\pi$
$578$	−2.44026	−0.101501
$579$	−50.3564	−2.09274
$580$	−73.8446	−3.06623
$581$	15.0763	0.625469
$582$	41.5876	1.72386
$583$	11.6838	0.483893
$584$	−53.5393	−2.21547
$585$	−11.9953	−0.495945
$586$	70.1423	2.89755
$587$	35.4427	1.46288	0.731438	−	0.681908i	$-0.238850\pi$
$587$	35.4427	1.46288	0.731438	+	0.681908i	$0.238850\pi$
$588$	−82.3854	−3.39752
$589$	−13.9132	−0.573282
$590$	30.3936	1.25129
$591$	−28.9444	−1.19061
$592$	−20.3987	−0.838381
$593$	12.3816	0.508451	0.254226	−	0.967145i	$-0.418179\pi$
$593$	12.3816	0.508451	0.254226	+	0.967145i	$0.418179\pi$
$594$	3.49062	0.143222
$595$	−14.9023	−0.610935
$596$	31.9731	1.30967
$597$	−6.80682	−0.278585
$598$	−22.5972	−0.924069
$599$	30.1565	1.23216	0.616081	−	0.787683i	$-0.288719\pi$
$599$	30.1565	1.23216	0.616081	+	0.787683i	$0.288719\pi$
$600$	98.4953	4.02105
$601$	7.57151	0.308848	0.154424	−	0.988005i	$-0.450648\pi$
$601$	7.57151	0.308848	0.154424	+	0.988005i	$0.450648\pi$
$602$	9.75436	0.397558
$603$	12.6377	0.514646
$604$	39.2321	1.59633
$605$	−3.72812	−0.151570
$606$	93.3872	3.79360
$607$	28.2960	1.14850	0.574249	−	0.818681i	$-0.305294\pi$
$607$	28.2960	1.14850	0.574249	+	0.818681i	$0.305294\pi$
$608$	−1.04422	−0.0423487
$609$	46.4510	1.88229
$610$	20.9611	0.848690
$611$	9.81337	0.397007
$612$	−9.42636	−0.381038
$613$	22.7590	0.919226	0.459613	−	0.888119i	$-0.347988\pi$
$613$	22.7590	0.919226	0.459613	+	0.888119i	$0.347988\pi$
$614$	10.1320	0.408893
$615$	93.6462	3.77618
$616$	−19.0683	−0.768282
$617$	39.4845	1.58959	0.794793	−	0.606880i	$-0.207579\pi$
$617$	39.4845	1.58959	0.794793	+	0.606880i	$0.207579\pi$
$618$	−19.7402	−0.794066
$619$	−21.6124	−0.868674	−0.434337	−	0.900750i	$-0.643017\pi$
$619$	−21.6124	−0.868674	−0.434337	+	0.900750i	$0.643017\pi$
$620$	−85.6105	−3.43820
$621$	9.81253	0.393763
$622$	24.6767	0.989447
$623$	−9.79113	−0.392273
$624$	−11.6863	−0.467826
$625$	9.69579	0.387832
$626$	45.4687	1.81730
$627$	−5.55969	−0.222033
$628$	−23.5449	−0.939544
$629$	5.46719	0.217991
$630$	−86.6769	−3.45329
$631$	31.6669	1.26064	0.630320	−	0.776335i	$-0.282924\pi$
$631$	31.6669	1.26064	0.630320	+	0.776335i	$0.282924\pi$
$632$	−18.4635	−0.734438
$633$	−9.77348	−0.388461
$634$	−17.9539	−0.713039
$635$	33.6835	1.33669
$636$	107.212	4.25125
$637$	12.1198	0.480204
$638$	12.2218	0.483865
$639$	31.9424	1.26362
$640$	−74.3133	−2.93749
$641$	3.48031	0.137464	0.0687320	−	0.997635i	$-0.478105\pi$
$641$	3.48031	0.137464	0.0687320	+	0.997635i	$0.478105\pi$
$642$	−57.1868	−2.25698
$643$	−9.78658	−0.385945	−0.192973	−	0.981204i	$-0.561813\pi$
$643$	−9.78658	−0.385945	−0.192973	+	0.981204i	$0.561813\pi$
$644$	−108.444	−4.27330
$645$	8.65012	0.340598
$646$	−5.84727	−0.230058
$647$	16.7087	0.656887	0.328444	−	0.944524i	$-0.393476\pi$
$647$	16.7087	0.656887	0.328444	+	0.944524i	$0.393476\pi$
$648$	49.9425	1.96193
$649$	−3.34085	−0.131140
$650$	−29.3142	−1.14980
$651$	53.8522	2.11063
$652$	−33.3783	−1.30720
$653$	−15.7024	−0.614483	−0.307241	−	0.951632i	$-0.599406\pi$
$653$	−15.7024	−0.614483	−0.307241	+	0.951632i	$0.599406\pi$
$654$	59.9729	2.34512
$655$	7.83885	0.306289
$656$	40.3930	1.57708
$657$	26.7510	1.04366
$658$	70.9105	2.76438
$659$	43.1995	1.68281	0.841406	−	0.540404i	$-0.181728\pi$
$659$	43.1995	1.68281	0.841406	+	0.540404i	$0.181728\pi$
$660$	−34.2099	−1.33162
$661$	28.9489	1.12598	0.562990	−	0.826464i	$-0.309651\pi$
$661$	28.9489	1.12598	0.562990	+	0.826464i	$0.309651\pi$
$662$	39.8413	1.54848
$663$	3.13212	0.121642
$664$	17.9919	0.698223
$665$	−35.7085	−1.38472
$666$	31.7990	1.23219
$667$	34.3568	1.33030
$668$	−1.25185	−0.0484357
$669$	22.2947	0.861962
$670$	48.2368	1.86355
$671$	−2.30403	−0.0889462
$672$	4.04175	0.155914
$673$	27.8169	1.07226	0.536131	−	0.844135i	$-0.319885\pi$
$673$	27.8169	1.07226	0.536131	+	0.844135i	$0.319885\pi$
$674$	15.4039	0.593337
$675$	12.7293	0.489950
$676$	−44.2062	−1.70024
$677$	−40.5007	−1.55657	−0.778284	−	0.627913i	$-0.783909\pi$
$677$	−40.5007	−1.55657	−0.778284	+	0.627913i	$0.783909\pi$
$678$	63.2785	2.43020
$679$	−29.3603	−1.12674
$680$	−17.7843	−0.681998
$681$	−58.5165	−2.24236
$682$	14.1691	0.542563
$683$	−23.1123	−0.884366	−0.442183	−	0.896925i	$-0.645796\pi$
$683$	−23.1123	−0.884366	−0.442183	+	0.896925i	$0.645796\pi$
$684$	−22.5872	−0.863643
$685$	37.6116	1.43706
$686$	19.2960	0.736724
$687$	−16.9099	−0.645152
$688$	3.73111	0.142247
$689$	−15.7721	−0.600869
$690$	−144.801	−5.51247
$691$	31.5235	1.19921	0.599606	−	0.800296i	$-0.295324\pi$
$691$	31.5235	1.19921	0.599606	+	0.800296i	$0.295324\pi$
$692$	−15.6089	−0.593360
$693$	9.52748	0.361919
$694$	−48.1061	−1.82608
$695$	28.0644	1.06454
$696$	55.4343	2.10123
$697$	−10.8260	−0.410064
$698$	14.7786	0.559377
$699$	−39.1434	−1.48054
$700$	−140.679	−5.31716
$701$	17.0045	0.642251	0.321125	−	0.947037i	$-0.395939\pi$
$701$	17.0045	0.642251	0.321125	+	0.947037i	$0.395939\pi$
$702$	−4.71205	−0.177845
$703$	13.1003	0.494089
$704$	8.52564	0.321322
$705$	62.8831	2.36832
$706$	−68.6025	−2.58189
$707$	−65.9301	−2.47956
$708$	−30.6563	−1.15213
$709$	39.9077	1.49876	0.749382	−	0.662137i	$-0.230350\pi$
$709$	39.9077	1.49876	0.749382	+	0.662137i	$0.230350\pi$
$710$	121.921	4.57561
$711$	9.22530	0.345976
$712$	−11.6847	−0.437902
$713$	39.8310	1.49168
$714$	22.6324	0.846997
$715$	5.03265	0.188210
$716$	41.6678	1.55720
$717$	−15.3736	−0.574138
$718$	20.8042	0.776404
$719$	−38.7081	−1.44357	−0.721784	−	0.692118i	$-0.756678\pi$
$719$	−38.7081	−1.44357	−0.721784	+	0.692118i	$0.756678\pi$
$720$	−33.1545	−1.23559
$721$	13.9363	0.519014
$722$	32.3538	1.20408
$723$	−3.44127	−0.127982
$724$	−22.2250	−0.825985
$725$	44.5692	1.65526
$726$	5.66197	0.210135
$727$	46.9640	1.74180	0.870899	−	0.491462i	$-0.163537\pi$
$727$	46.9640	1.74180	0.870899	+	0.491462i	$0.163537\pi$
$728$	25.7405	0.954008
$729$	−14.9970	−0.555445
$730$	102.106	3.77911
$731$	−1.00000	−0.0369863
$732$	−21.1422	−0.781439
$733$	−21.9534	−0.810869	−0.405435	−	0.914124i	$-0.632880\pi$
$733$	−21.9534	−0.810869	−0.405435	+	0.914124i	$0.632880\pi$
$734$	43.3580	1.60037
$735$	77.6624	2.86462
$736$	2.98942	0.110191
$737$	−5.30216	−0.195308
$738$	−62.9677	−2.31787
$739$	44.3040	1.62975	0.814875	−	0.579637i	$-0.196805\pi$
$739$	44.3040	1.62975	0.814875	+	0.579637i	$0.196805\pi$
$740$	80.6091	2.96325
$741$	7.50511	0.275707
$742$	−113.968	−4.18389
$743$	−35.7741	−1.31242	−0.656212	−	0.754577i	$-0.727842\pi$
$743$	−35.7741	−1.31242	−0.656212	+	0.754577i	$0.727842\pi$
$744$	64.2669	2.35614
$745$	−30.1402	−1.10425
$746$	66.9725	2.45204
$747$	−8.98969	−0.328916
$748$	3.95484	0.144603
$749$	40.3731	1.47520
$750$	−82.2997	−3.00516
$751$	46.7727	1.70676	0.853380	−	0.521289i	$-0.174549\pi$
$751$	46.7727	1.70676	0.853380	+	0.521289i	$0.174549\pi$
$752$	27.1237	0.989101
$753$	−69.0915	−2.51784
$754$	−16.4984	−0.600835
$755$	−36.9830	−1.34595
$756$	−22.6132	−0.822432
$757$	15.9340	0.579130	0.289565	−	0.957158i	$-0.406489\pi$
$757$	15.9340	0.579130	0.289565	+	0.957158i	$0.406489\pi$
$758$	36.0026	1.30767
$759$	15.9164	0.577730
$760$	−42.6143	−1.54578
$761$	−43.5805	−1.57979	−0.789896	−	0.613240i	$-0.789866\pi$
$761$	−43.5805	−1.57979	−0.789896	+	0.613240i	$0.789866\pi$
$762$	−51.1558	−1.85318
$763$	−42.3400	−1.53281
$764$	67.9366	2.45786
$765$	8.88596	0.321273
$766$	−59.4576	−2.14829
$767$	4.50987	0.162842
$768$	73.2980	2.64491
$769$	−44.4680	−1.60356	−0.801779	−	0.597620i	$-0.796113\pi$
$769$	−44.4680	−1.60356	−0.801779	+	0.597620i	$0.796113\pi$
$770$	36.3655	1.31052
$771$	−7.14843	−0.257444
$772$	85.8326	3.08918
$773$	−29.8683	−1.07429	−0.537143	−	0.843491i	$-0.680497\pi$
$773$	−29.8683	−1.07429	−0.537143	+	0.843491i	$0.680497\pi$
$774$	−5.81634	−0.209064
$775$	51.6706	1.85606
$776$	−35.0384	−1.25781
$777$	−50.7061	−1.81907
$778$	25.3348	0.908297
$779$	−25.9410	−0.929431
$780$	46.1805	1.65353
$781$	−13.4015	−0.479543
$782$	16.7397	0.598612
$783$	7.16419	0.256027
$784$	33.4986	1.19638
$785$	22.1951	0.792178
$786$	−11.9050	−0.424638
$787$	−17.1447	−0.611144	−0.305572	−	0.952169i	$-0.598848\pi$
$787$	−17.1447	−0.611144	−0.305572	+	0.952169i	$0.598848\pi$
$788$	49.3357	1.75751
$789$	−43.1103	−1.53477
$790$	35.2120	1.25279
$791$	−44.6738	−1.58842
$792$	11.3700	0.404017
$793$	3.11025	0.110448
$794$	−72.3432	−2.56736
$795$	−101.066	−3.58444
$796$	11.6022	0.411230
$797$	19.2056	0.680297	0.340148	−	0.940372i	$-0.389523\pi$
$797$	19.2056	0.680297	0.340148	+	0.940372i	$0.389523\pi$
$798$	54.2312	1.91976
$799$	−7.26962	−0.257181
$800$	3.87801	0.137109
$801$	5.83826	0.206285
$802$	−74.0187	−2.61369
$803$	−11.2234	−0.396066
$804$	−48.6536	−1.71588
$805$	102.227	3.60304
$806$	−19.1271	−0.673724
$807$	50.9554	1.79371
$808$	−78.6806	−2.76797
$809$	35.3656	1.24339	0.621695	−	0.783259i	$-0.286444\pi$
$809$	35.3656	1.24339	0.621695	+	0.783259i	$0.286444\pi$
$810$	−95.2464	−3.34662
$811$	41.7345	1.46550	0.732748	−	0.680500i	$-0.238237\pi$
$811$	41.7345	1.46550	0.732748	+	0.680500i	$0.238237\pi$
$812$	−79.1758	−2.77852
$813$	10.0446	0.352280
$814$	−13.3413	−0.467614
$815$	31.4648	1.10216
$816$	8.65705	0.303057
$817$	−2.39617	−0.0838315
$818$	−31.7226	−1.10915
$819$	−12.8613	−0.449410
$820$	−159.620	−5.57417
$821$	−8.93965	−0.311996	−0.155998	−	0.987757i	$-0.549859\pi$
$821$	−8.93965	−0.311996	−0.155998	+	0.987757i	$0.549859\pi$
$822$	−57.1214	−1.99234
$823$	16.8317	0.586717	0.293359	−	0.956002i	$-0.405227\pi$
$823$	16.8317	0.586717	0.293359	+	0.956002i	$0.405227\pi$
$824$	16.6315	0.579385
$825$	20.6475	0.718855
$826$	32.5879	1.13388
$827$	30.1275	1.04763	0.523817	−	0.851831i	$-0.324508\pi$
$827$	30.1275	1.04763	0.523817	+	0.851831i	$0.324508\pi$
$828$	64.6632	2.24720
$829$	−48.6901	−1.69108	−0.845538	−	0.533915i	$-0.820720\pi$
$829$	−48.6901	−1.69108	−0.845538	+	0.533915i	$0.820720\pi$
$830$	−34.3128	−1.19101
$831$	24.5617	0.852036
$832$	−11.5089	−0.398999
$833$	−8.97819	−0.311076
$834$	−42.6220	−1.47588
$835$	1.18009	0.0408386
$836$	9.47649	0.327751
$837$	8.30568	0.287086
$838$	−66.1967	−2.28673
$839$	44.1500	1.52423	0.762113	−	0.647444i	$-0.224162\pi$
$839$	44.1500	1.52423	0.762113	+	0.647444i	$0.224162\pi$
$840$	164.943	5.69107
$841$	−3.91593	−0.135032
$842$	−83.8867	−2.89093
$843$	−8.45119	−0.291074
$844$	16.6589	0.573423
$845$	41.6719	1.43356
$846$	−42.2826	−1.45371
$847$	−3.99727	−0.137348
$848$	−43.5934	−1.49700
$849$	4.58778	0.157452
$850$	21.7156	0.744838
$851$	−37.5040	−1.28562
$852$	−122.974	−4.21303
$853$	42.8216	1.46618	0.733091	−	0.680130i	$-0.238077\pi$
$853$	42.8216	1.46618	0.733091	+	0.680130i	$0.238077\pi$
$854$	22.4744	0.769058
$855$	21.2923	0.728182
$856$	48.1810	1.64679
$857$	52.5338	1.79452	0.897261	−	0.441501i	$-0.145554\pi$
$857$	52.5338	1.79452	0.897261	+	0.441501i	$0.145554\pi$
$858$	−7.64318	−0.260934
$859$	0.323499	0.0110377	0.00551883	−	0.999985i	$-0.498243\pi$
$859$	0.323499	0.0110377	0.00551883	+	0.999985i	$0.498243\pi$
$860$	−14.7441	−0.502771
$861$	100.407	3.42186
$862$	−20.9023	−0.711934
$863$	11.5588	0.393465	0.196732	−	0.980457i	$-0.436967\pi$
$863$	11.5588	0.393465	0.196732	+	0.980457i	$0.436967\pi$
$864$	0.623364	0.0212073
$865$	14.7141	0.500293
$866$	88.6524	3.01253
$867$	−2.32024	−0.0787994
$868$	−91.7911	−3.11559
$869$	−3.87049	−0.131297
$870$	−105.720	−3.58424
$871$	7.15747	0.242522
$872$	−50.5283	−1.71110
$873$	17.5070	0.592521
$874$	40.1113	1.35678
$875$	58.1025	1.96422
$876$	−102.988	−3.47965
$877$	−25.1351	−0.848753	−0.424377	−	0.905486i	$-0.639507\pi$
$877$	−25.1351	−0.848753	−0.424377	+	0.905486i	$0.639507\pi$
$878$	−25.1110	−0.847456
$879$	66.6925	2.24948
$880$	13.9100	0.468907
$881$	0.0626347	0.00211022	0.00105511	−	0.999999i	$-0.499664\pi$
$881$	0.0626347	0.00211022	0.00105511	+	0.999999i	$0.499664\pi$
$882$	−52.2202	−1.75835
$883$	−21.9388	−0.738301	−0.369150	−	0.929370i	$-0.620351\pi$
$883$	−21.9388	−0.738301	−0.369150	+	0.929370i	$0.620351\pi$
$884$	−5.33871	−0.179560
$885$	28.8988	0.971422
$886$	75.1091	2.52334
$887$	8.92672	0.299730	0.149865	−	0.988706i	$-0.452116\pi$
$887$	8.92672	0.299730	0.149865	+	0.988706i	$0.452116\pi$
$888$	−60.5124	−2.03066
$889$	36.1153	1.21127
$890$	22.2841	0.746964
$891$	10.4694	0.350739
$892$	−38.0013	−1.27238
$893$	−17.4193	−0.582914
$894$	45.7745	1.53093
$895$	−39.2791	−1.31295
$896$	−79.6783	−2.66187
$897$	−21.4858	−0.717391
$898$	27.6965	0.924245
$899$	29.0808	0.969899
$900$	83.8841	2.79614
$901$	11.6838	0.389243
$902$	26.4182	0.879630
$903$	9.27462	0.308640
$904$	−53.3134	−1.77318
$905$	20.9509	0.696430
$906$	56.1668	1.86602
$907$	17.5204	0.581756	0.290878	−	0.956760i	$-0.406053\pi$
$907$	17.5204	0.581756	0.290878	+	0.956760i	$0.406053\pi$
$908$	99.7414	3.31003
$909$	39.3128	1.30392
$910$	−49.0903	−1.62733
$911$	−32.6039	−1.08021	−0.540107	−	0.841596i	$-0.681616\pi$
$911$	−32.6039	−1.08021	−0.540107	+	0.841596i	$0.681616\pi$
$912$	20.7438	0.686896
$913$	3.77164	0.124823
$914$	71.8016	2.37498
$915$	19.9302	0.658871
$916$	28.8229	0.952335
$917$	8.40478	0.277550
$918$	3.49062	0.115208
$919$	−35.8513	−1.18262	−0.591312	−	0.806443i	$-0.701390\pi$
$919$	−35.8513	−1.18262	−0.591312	+	0.806443i	$0.701390\pi$
$920$	121.997	4.02214
$921$	9.63365	0.317440
$922$	94.1097	3.09934
$923$	18.0909	0.595468
$924$	−36.6797	−1.20667
$925$	−48.6519	−1.59967
$926$	−46.9529	−1.54297
$927$	−8.30994	−0.272934
$928$	2.18259	0.0716471
$929$	−57.7497	−1.89471	−0.947354	−	0.320189i	$-0.896254\pi$
$929$	−57.7497	−1.89471	−0.947354	+	0.320189i	$0.896254\pi$
$930$	−122.565	−4.01905
$931$	−21.5133	−0.705070
$932$	66.7199	2.18548
$933$	23.4631	0.768147
$934$	−10.5541	−0.345340
$935$	−3.72812	−0.121923
$936$	−15.3486	−0.501684
$937$	47.6690	1.55728	0.778640	−	0.627471i	$-0.215910\pi$
$937$	47.6690	1.55728	0.778640	+	0.627471i	$0.215910\pi$
$938$	51.7192	1.68869
$939$	43.2324	1.41084
$940$	−107.184	−3.49597
$941$	38.8124	1.26525	0.632624	−	0.774459i	$-0.281978\pi$
$941$	38.8124	1.26525	0.632624	+	0.774459i	$0.281978\pi$
$942$	−33.7081	−1.09827
$943$	74.2645	2.41838
$944$	12.4651	0.405704
$945$	21.3168	0.693435
$946$	2.44026	0.0793395
$947$	2.29175	0.0744720	0.0372360	−	0.999307i	$-0.488145\pi$
$947$	2.29175	0.0744720	0.0372360	+	0.999307i	$0.488145\pi$
$948$	−35.5163	−1.15352
$949$	15.1507	0.491812
$950$	52.0342	1.68821
$951$	−17.0708	−0.553560
$952$	−19.0683	−0.618006
$953$	−30.1445	−0.976476	−0.488238	−	0.872710i	$-0.662360\pi$
$953$	−30.1445	−0.976476	−0.488238	+	0.872710i	$0.662360\pi$
$954$	67.9568	2.20018
$955$	−64.0419	−2.07235
$956$	26.2043	0.847509
$957$	11.6207	0.375643
$958$	76.9331	2.48560
$959$	40.3269	1.30222
$960$	−73.7479	−2.38020
$961$	2.71437	0.0875603
$962$	18.0097	0.580656
$963$	−24.0737	−0.775764
$964$	5.86565	0.188920
$965$	−80.9120	−2.60465
$966$	−155.255	−4.99523
$967$	20.2799	0.652156	0.326078	−	0.945343i	$-0.394273\pi$
$967$	20.2799	0.652156	0.326078	+	0.945343i	$0.394273\pi$
$968$	−4.77032	−0.153324
$969$	−5.55969	−0.178603
$970$	66.8224	2.14554
$971$	31.6245	1.01488	0.507439	−	0.861688i	$-0.330592\pi$
$971$	31.6245	1.01488	0.507439	+	0.861688i	$0.330592\pi$
$972$	79.0979	2.53707
$973$	30.0905	0.964658
$974$	−41.7273	−1.33703
$975$	−27.8724	−0.892632
$976$	8.59660	0.275170
$977$	−18.3243	−0.586247	−0.293123	−	0.956075i	$-0.594695\pi$
$977$	−18.3243	−0.586247	−0.293123	+	0.956075i	$0.594695\pi$
$978$	−47.7862	−1.52803
$979$	−2.44945	−0.0782849
$980$	−132.376	−4.22859
$981$	25.2465	0.806060
$982$	−66.8612	−2.13363
$983$	−4.26658	−0.136083	−0.0680413	−	0.997683i	$-0.521675\pi$
$983$	−4.26658	−0.136083	−0.0680413	+	0.997683i	$0.521675\pi$
$984$	119.825	3.81988
$985$	−46.5074	−1.48185
$986$	12.2218	0.389221
$987$	67.4230	2.14610
$988$	−12.7925	−0.406982
$989$	6.85983	0.218130
$990$	−21.6840	−0.689163
$991$	−36.1753	−1.14915	−0.574573	−	0.818453i	$-0.694832\pi$
$991$	−36.1753	−1.14915	−0.574573	+	0.818453i	$0.694832\pi$
$992$	2.53035	0.0803388
$993$	37.8818	1.20214
$994$	130.723	4.14628
$995$	−10.9371	−0.346729
$996$	34.6092	1.09664
$997$	0.394534	0.0124950	0.00624750	−	0.999980i	$-0.498011\pi$
$997$	0.394534	0.0124950	0.00624750	+	0.999980i	$0.498011\pi$
$998$	31.9011	1.00981
$999$	−7.82046	−0.247428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.5	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.5	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44026 q^{2} -2.32024 q^{3} +3.95484 q^{4} -3.72812 q^{5} +5.66197 q^{6} -3.99727 q^{7} -4.77032 q^{8} +2.38350 q^{9} +O(q^{10})\)	\(q-2.44026 q^{2} -2.32024 q^{3} +3.95484 q^{4} -3.72812 q^{5} +5.66197 q^{6} -3.99727 q^{7} -4.77032 q^{8} +2.38350 q^{9} +9.09757 q^{10} -1.00000 q^{11} -9.17617 q^{12} +1.34992 q^{13} +9.75436 q^{14} +8.65012 q^{15} +3.73111 q^{16} -1.00000 q^{17} -5.81634 q^{18} -2.39617 q^{19} -14.7441 q^{20} +9.27462 q^{21} +2.44026 q^{22} +6.85983 q^{23} +11.0683 q^{24} +8.89889 q^{25} -3.29414 q^{26} +1.43043 q^{27} -15.8086 q^{28} +5.00840 q^{29} -21.1085 q^{30} +5.80641 q^{31} +0.435786 q^{32} +2.32024 q^{33} +2.44026 q^{34} +14.9023 q^{35} +9.42636 q^{36} -5.46719 q^{37} +5.84727 q^{38} -3.13212 q^{39} +17.7843 q^{40} +10.8260 q^{41} -22.6324 q^{42} +1.00000 q^{43} -3.95484 q^{44} -8.88596 q^{45} -16.7397 q^{46} +7.26962 q^{47} -8.65705 q^{48} +8.97819 q^{49} -21.7156 q^{50} +2.32024 q^{51} +5.33871 q^{52} -11.6838 q^{53} -3.49062 q^{54} +3.72812 q^{55} +19.0683 q^{56} +5.55969 q^{57} -12.2218 q^{58} +3.34085 q^{59} +34.2099 q^{60} +2.30403 q^{61} -14.1691 q^{62} -9.52748 q^{63} -8.52564 q^{64} -5.03265 q^{65} -5.66197 q^{66} +5.30216 q^{67} -3.95484 q^{68} -15.9164 q^{69} -36.3655 q^{70} +13.4015 q^{71} -11.3700 q^{72} +11.2234 q^{73} +13.3413 q^{74} -20.6475 q^{75} -9.47649 q^{76} +3.99727 q^{77} +7.64318 q^{78} +3.87049 q^{79} -13.9100 q^{80} -10.4694 q^{81} -26.4182 q^{82} -3.77164 q^{83} +36.6797 q^{84} +3.72812 q^{85} -2.44026 q^{86} -11.6207 q^{87} +4.77032 q^{88} +2.44945 q^{89} +21.6840 q^{90} -5.39598 q^{91} +27.1296 q^{92} -13.4722 q^{93} -17.7397 q^{94} +8.93323 q^{95} -1.01113 q^{96} +7.34508 q^{97} -21.9091 q^{98} -2.38350 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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