LMFDB - Embedded newform 8015.2.a.l.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.76681 q^{2} +2.93332 q^{3} +1.12163 q^{4} -1.00000 q^{5} -5.18264 q^{6} -1.00000 q^{7} +1.55191 q^{8} +5.60439 q^{9} +O(q^{10})$	\(q-1.76681 q^{2} +2.93332 q^{3} +1.12163 q^{4} -1.00000 q^{5} -5.18264 q^{6} -1.00000 q^{7} +1.55191 q^{8} +5.60439 q^{9} +1.76681 q^{10} +5.57251 q^{11} +3.29012 q^{12} +2.46065 q^{13} +1.76681 q^{14} -2.93332 q^{15} -4.98520 q^{16} +6.99936 q^{17} -9.90191 q^{18} -7.29290 q^{19} -1.12163 q^{20} -2.93332 q^{21} -9.84559 q^{22} +7.80740 q^{23} +4.55225 q^{24} +1.00000 q^{25} -4.34751 q^{26} +7.63951 q^{27} -1.12163 q^{28} -0.282924 q^{29} +5.18264 q^{30} +9.08665 q^{31} +5.70412 q^{32} +16.3460 q^{33} -12.3666 q^{34} +1.00000 q^{35} +6.28607 q^{36} +3.25443 q^{37} +12.8852 q^{38} +7.21787 q^{39} -1.55191 q^{40} +5.90197 q^{41} +5.18264 q^{42} -7.89879 q^{43} +6.25032 q^{44} -5.60439 q^{45} -13.7942 q^{46} +6.99295 q^{47} -14.6232 q^{48} +1.00000 q^{49} -1.76681 q^{50} +20.5314 q^{51} +2.75995 q^{52} -9.58756 q^{53} -13.4976 q^{54} -5.57251 q^{55} -1.55191 q^{56} -21.3924 q^{57} +0.499874 q^{58} -2.15310 q^{59} -3.29012 q^{60} +4.50495 q^{61} -16.0544 q^{62} -5.60439 q^{63} -0.107708 q^{64} -2.46065 q^{65} -28.8803 q^{66} -8.61501 q^{67} +7.85073 q^{68} +22.9016 q^{69} -1.76681 q^{70} +14.1801 q^{71} +8.69750 q^{72} -12.7551 q^{73} -5.74998 q^{74} +2.93332 q^{75} -8.17997 q^{76} -5.57251 q^{77} -12.7526 q^{78} -10.9668 q^{79} +4.98520 q^{80} +5.59598 q^{81} -10.4277 q^{82} -0.554755 q^{83} -3.29012 q^{84} -6.99936 q^{85} +13.9557 q^{86} -0.829907 q^{87} +8.64802 q^{88} +11.4222 q^{89} +9.90191 q^{90} -2.46065 q^{91} +8.75705 q^{92} +26.6541 q^{93} -12.3553 q^{94} +7.29290 q^{95} +16.7320 q^{96} +9.69786 q^{97} -1.76681 q^{98} +31.2305 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.76681	−1.24933	−0.624663	−	0.780894i	$-0.714764\pi$
$2$	−1.76681	−1.24933	−0.624663	+	0.780894i	$0.714764\pi$
$3$	2.93332	1.69356	0.846778	−	0.531947i	$-0.178540\pi$
$3$	2.93332	1.69356	0.846778	+	0.531947i	$0.178540\pi$
$4$	1.12163	0.560817
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.18264	−2.11580
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.55191	0.548683
$9$	5.60439	1.86813
$10$	1.76681	0.558716
$11$	5.57251	1.68017	0.840087	−	0.542452i	$-0.182504\pi$
$11$	5.57251	1.68017	0.840087	+	0.542452i	$0.182504\pi$
$12$	3.29012	0.949775
$13$	2.46065	0.682461	0.341230	−	0.939980i	$-0.389156\pi$
$13$	2.46065	0.682461	0.341230	+	0.939980i	$0.389156\pi$
$14$	1.76681	0.472201
$15$	−2.93332	−0.757381
$16$	−4.98520	−1.24630
$17$	6.99936	1.69759	0.848797	−	0.528719i	$-0.177327\pi$
$17$	6.99936	1.69759	0.848797	+	0.528719i	$0.177327\pi$
$18$	−9.90191	−2.33390
$19$	−7.29290	−1.67311	−0.836553	−	0.547886i	$-0.815433\pi$
$19$	−7.29290	−1.67311	−0.836553	+	0.547886i	$0.815433\pi$
$20$	−1.12163	−0.250805
$21$	−2.93332	−0.640104
$22$	−9.84559	−2.09909
$23$	7.80740	1.62795	0.813977	−	0.580896i	$-0.197298\pi$
$23$	7.80740	1.62795	0.813977	+	0.580896i	$0.197298\pi$
$24$	4.55225	0.929224
$25$	1.00000	0.200000
$26$	−4.34751	−0.852616
$27$	7.63951	1.47022
$28$	−1.12163	−0.211969
$29$	−0.282924	−0.0525376	−0.0262688	−	0.999655i	$-0.508363\pi$
$29$	−0.282924	−0.0525376	−0.0262688	+	0.999655i	$0.508363\pi$
$30$	5.18264	0.946216
$31$	9.08665	1.63201	0.816005	−	0.578044i	$-0.196184\pi$
$31$	9.08665	1.63201	0.816005	+	0.578044i	$0.196184\pi$
$32$	5.70412	1.00835
$33$	16.3460	2.84547
$34$	−12.3666	−2.12085
$35$	1.00000	0.169031
$36$	6.28607	1.04768
$37$	3.25443	0.535026	0.267513	−	0.963554i	$-0.413798\pi$
$37$	3.25443	0.535026	0.267513	+	0.963554i	$0.413798\pi$
$38$	12.8852	2.09026
$39$	7.21787	1.15578
$40$	−1.55191	−0.245378
$41$	5.90197	0.921733	0.460866	−	0.887470i	$-0.347539\pi$
$41$	5.90197	0.921733	0.460866	+	0.887470i	$0.347539\pi$
$42$	5.18264	0.799699
$43$	−7.89879	−1.20455	−0.602277	−	0.798287i	$-0.705740\pi$
$43$	−7.89879	−1.20455	−0.602277	+	0.798287i	$0.705740\pi$
$44$	6.25032	0.942271
$45$	−5.60439	−0.835453
$46$	−13.7942	−2.03385
$47$	6.99295	1.02003	0.510014	−	0.860166i	$-0.329640\pi$
$47$	6.99295	1.02003	0.510014	+	0.860166i	$0.329640\pi$
$48$	−14.6232	−2.11068
$49$	1.00000	0.142857
$50$	−1.76681	−0.249865
$51$	20.5314	2.87497
$52$	2.75995	0.382736
$53$	−9.58756	−1.31695	−0.658476	−	0.752602i	$-0.728799\pi$
$53$	−9.58756	−1.31695	−0.658476	+	0.752602i	$0.728799\pi$
$54$	−13.4976	−1.83679
$55$	−5.57251	−0.751397
$56$	−1.55191	−0.207383
$57$	−21.3924	−2.83350
$58$	0.499874	0.0656367
$59$	−2.15310	−0.280310	−0.140155	−	0.990130i	$-0.544760\pi$
$59$	−2.15310	−0.280310	−0.140155	+	0.990130i	$0.544760\pi$
$60$	−3.29012	−0.424752
$61$	4.50495	0.576800	0.288400	−	0.957510i	$-0.406877\pi$
$61$	4.50495	0.576800	0.288400	+	0.957510i	$0.406877\pi$
$62$	−16.0544	−2.03891
$63$	−5.60439	−0.706086
$64$	−0.107708	−0.0134635
$65$	−2.46065	−0.305206
$66$	−28.8803	−3.55492
$67$	−8.61501	−1.05249	−0.526245	−	0.850333i	$-0.676401\pi$
$67$	−8.61501	−1.05249	−0.526245	+	0.850333i	$0.676401\pi$
$68$	7.85073	0.952040
$69$	22.9016	2.75703
$70$	−1.76681	−0.211175
$71$	14.1801	1.68287	0.841434	−	0.540359i	$-0.181712\pi$
$71$	14.1801	1.68287	0.841434	+	0.540359i	$0.181712\pi$
$72$	8.69750	1.02501
$73$	−12.7551	−1.49287	−0.746436	−	0.665457i	$-0.768237\pi$
$73$	−12.7551	−1.49287	−0.746436	+	0.665457i	$0.768237\pi$
$74$	−5.74998	−0.668422
$75$	2.93332	0.338711
$76$	−8.17997	−0.938307
$77$	−5.57251	−0.635046
$78$	−12.7526	−1.44395
$79$	−10.9668	−1.23386	−0.616930	−	0.787018i	$-0.711624\pi$
$79$	−10.9668	−1.23386	−0.616930	+	0.787018i	$0.711624\pi$
$80$	4.98520	0.557363
$81$	5.59598	0.621776
$82$	−10.4277	−1.15155
$83$	−0.554755	−0.0608922	−0.0304461	−	0.999536i	$-0.509693\pi$
$83$	−0.554755	−0.0608922	−0.0304461	+	0.999536i	$0.509693\pi$
$84$	−3.29012	−0.358981
$85$	−6.99936	−0.759187
$86$	13.9557	1.50488
$87$	−0.829907	−0.0889754
$88$	8.64802	0.921882
$89$	11.4222	1.21075	0.605374	−	0.795941i	$-0.293023\pi$
$89$	11.4222	1.21075	0.605374	+	0.795941i	$0.293023\pi$
$90$	9.90191	1.04375
$91$	−2.46065	−0.257946
$92$	8.75705	0.912985
$93$	26.6541	2.76390
$94$	−12.3553	−1.27435
$95$	7.29290	0.748236
$96$	16.7320	1.70770
$97$	9.69786	0.984668	0.492334	−	0.870406i	$-0.336144\pi$
$97$	9.69786	0.984668	0.492334	+	0.870406i	$0.336144\pi$
$98$	−1.76681	−0.178475
$99$	31.2305	3.13878
$100$	1.12163	0.112163
$101$	−3.30049	−0.328411	−0.164206	−	0.986426i	$-0.552506\pi$
$101$	−3.30049	−0.328411	−0.164206	+	0.986426i	$0.552506\pi$
$102$	−36.2752	−3.59178
$103$	−11.3910	−1.12239	−0.561193	−	0.827685i	$-0.689657\pi$
$103$	−11.3910	−1.12239	−0.561193	+	0.827685i	$0.689657\pi$
$104$	3.81870	0.374454
$105$	2.93332	0.286263
$106$	16.9394	1.64530
$107$	14.6507	1.41634	0.708168	−	0.706044i	$-0.249522\pi$
$107$	14.6507	1.41634	0.708168	+	0.706044i	$0.249522\pi$
$108$	8.56873	0.824527
$109$	−6.01512	−0.576144	−0.288072	−	0.957609i	$-0.593014\pi$
$109$	−6.01512	−0.576144	−0.288072	+	0.957609i	$0.593014\pi$
$110$	9.84559	0.938740
$111$	9.54631	0.906096
$112$	4.98520	0.471058
$113$	−10.9393	−1.02908	−0.514539	−	0.857467i	$-0.672037\pi$
$113$	−10.9393	−1.02908	−0.514539	+	0.857467i	$0.672037\pi$
$114$	37.7965	3.53996
$115$	−7.80740	−0.728044
$116$	−0.317337	−0.0294640
$117$	13.7904	1.27492
$118$	3.80413	0.350199
$119$	−6.99936	−0.641630
$120$	−4.55225	−0.415562
$121$	20.0528	1.82299
$122$	−7.95942	−0.720612
$123$	17.3124	1.56101
$124$	10.1919	0.915260
$125$	−1.00000	−0.0894427
$126$	9.90191	0.882132
$127$	−0.0780272	−0.00692380	−0.00346190	−	0.999994i	$-0.501102\pi$
$127$	−0.0780272	−0.00692380	−0.00346190	+	0.999994i	$0.501102\pi$
$128$	−11.2179	−0.991535
$129$	−23.1697	−2.03998
$130$	4.34751	0.381302
$131$	−11.7880	−1.02992	−0.514960	−	0.857214i	$-0.672193\pi$
$131$	−11.7880	−1.02992	−0.514960	+	0.857214i	$0.672193\pi$
$132$	18.3342	1.59579
$133$	7.29290	0.632375
$134$	15.2211	1.31490
$135$	−7.63951	−0.657504
$136$	10.8624	0.931441
$137$	2.46593	0.210679	0.105339	−	0.994436i	$-0.466407\pi$
$137$	2.46593	0.210679	0.105339	+	0.994436i	$0.466407\pi$
$138$	−40.4629	−3.44443
$139$	12.0994	1.02626	0.513129	−	0.858312i	$-0.328486\pi$
$139$	12.0994	1.02626	0.513129	+	0.858312i	$0.328486\pi$
$140$	1.12163	0.0947954
$141$	20.5126	1.72747
$142$	−25.0536	−2.10245
$143$	13.7120	1.14665
$144$	−27.9390	−2.32825
$145$	0.282924	0.0234955
$146$	22.5359	1.86509
$147$	2.93332	0.241936
$148$	3.65029	0.300052
$149$	−2.35083	−0.192588	−0.0962938	−	0.995353i	$-0.530699\pi$
$149$	−2.35083	−0.192588	−0.0962938	+	0.995353i	$0.530699\pi$
$150$	−5.18264	−0.423161
$151$	−11.8960	−0.968086	−0.484043	−	0.875044i	$-0.660832\pi$
$151$	−11.8960	−0.968086	−0.484043	+	0.875044i	$0.660832\pi$
$152$	−11.3179	−0.918004
$153$	39.2271	3.17132
$154$	9.84559	0.793380
$155$	−9.08665	−0.729857
$156$	8.09582	0.648184
$157$	−16.0234	−1.27880	−0.639402	−	0.768873i	$-0.720818\pi$
$157$	−16.0234	−1.27880	−0.639402	+	0.768873i	$0.720818\pi$
$158$	19.3763	1.54149
$159$	−28.1234	−2.23033
$160$	−5.70412	−0.450950
$161$	−7.80740	−0.615309
$162$	−9.88707	−0.776801
$163$	2.75757	0.215989	0.107995	−	0.994151i	$-0.465557\pi$
$163$	2.75757	0.215989	0.107995	+	0.994151i	$0.465557\pi$
$164$	6.61985	0.516924
$165$	−16.3460	−1.27253
$166$	0.980149	0.0760743
$167$	−22.0299	−1.70472	−0.852361	−	0.522953i	$-0.824830\pi$
$167$	−22.0299	−1.70472	−0.852361	+	0.522953i	$0.824830\pi$
$168$	−4.55225	−0.351214
$169$	−6.94522	−0.534248
$170$	12.3666	0.948473
$171$	−40.8722	−3.12558
$172$	−8.85955	−0.675535
$173$	23.7596	1.80641	0.903206	−	0.429207i	$-0.141207\pi$
$173$	23.7596	1.80641	0.903206	+	0.429207i	$0.141207\pi$
$174$	1.46629	0.111159
$175$	−1.00000	−0.0755929
$176$	−27.7801	−2.09400
$177$	−6.31574	−0.474720
$178$	−20.1809	−1.51262
$179$	11.5524	0.863467	0.431734	−	0.902001i	$-0.357902\pi$
$179$	11.5524	0.863467	0.431734	+	0.902001i	$0.357902\pi$
$180$	−6.28607	−0.468536
$181$	−25.8028	−1.91791	−0.958953	−	0.283565i	$-0.908483\pi$
$181$	−25.8028	−1.91791	−0.958953	+	0.283565i	$0.908483\pi$
$182$	4.34751	0.322259
$183$	13.2145	0.976843
$184$	12.1164	0.893231
$185$	−3.25443	−0.239271
$186$	−47.0928	−3.45301
$187$	39.0040	2.85225
$188$	7.84354	0.572049
$189$	−7.63951	−0.555692
$190$	−12.8852	−0.934791
$191$	27.0255	1.95549	0.977747	−	0.209786i	$-0.0672768\pi$
$191$	27.0255	1.95549	0.977747	+	0.209786i	$0.0672768\pi$
$192$	−0.315942	−0.0228012
$193$	−8.88805	−0.639776	−0.319888	−	0.947455i	$-0.603645\pi$
$193$	−8.88805	−0.639776	−0.319888	+	0.947455i	$0.603645\pi$
$194$	−17.1343	−1.23017
$195$	−7.21787	−0.516883
$196$	1.12163	0.0801168
$197$	−18.1670	−1.29435	−0.647173	−	0.762343i	$-0.724049\pi$
$197$	−18.1670	−1.29435	−0.647173	+	0.762343i	$0.724049\pi$
$198$	−55.1785	−3.92136
$199$	−20.1135	−1.42581	−0.712904	−	0.701262i	$-0.752620\pi$
$199$	−20.1135	−1.42581	−0.712904	+	0.701262i	$0.752620\pi$
$200$	1.55191	0.109737
$201$	−25.2706	−1.78245
$202$	5.83136	0.410293
$203$	0.282924	0.0198574
$204$	23.0287	1.61233
$205$	−5.90197	−0.412211
$206$	20.1257	1.40223
$207$	43.7557	3.04123
$208$	−12.2668	−0.850551
$209$	−40.6398	−2.81111
$210$	−5.18264	−0.357636
$211$	25.6863	1.76832	0.884160	−	0.467183i	$-0.154731\pi$
$211$	25.6863	1.76832	0.884160	+	0.467183i	$0.154731\pi$
$212$	−10.7537	−0.738570
$213$	41.5948	2.85003
$214$	−25.8851	−1.76947
$215$	7.89879	0.538693
$216$	11.8558	0.806686
$217$	−9.08665	−0.616842
$218$	10.6276	0.719793
$219$	−37.4148	−2.52826
$220$	−6.25032	−0.421396
$221$	17.2230	1.15854
$222$	−16.8666	−1.13201
$223$	3.72658	0.249550	0.124775	−	0.992185i	$-0.460179\pi$
$223$	3.72658	0.249550	0.124775	+	0.992185i	$0.460179\pi$
$224$	−5.70412	−0.381122
$225$	5.60439	0.373626
$226$	19.3276	1.28566
$227$	10.1304	0.672379	0.336189	−	0.941794i	$-0.390862\pi$
$227$	10.1304	0.672379	0.336189	+	0.941794i	$0.390862\pi$
$228$	−23.9945	−1.58907
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	13.7942	0.909564
$231$	−16.3460	−1.07549
$232$	−0.439072	−0.0288265
$233$	1.22517	0.0802634	0.0401317	−	0.999194i	$-0.487222\pi$
$233$	1.22517	0.0802634	0.0401317	+	0.999194i	$0.487222\pi$
$234$	−24.3651	−1.59280
$235$	−6.99295	−0.456170
$236$	−2.41499	−0.157203
$237$	−32.1691	−2.08961
$238$	12.3666	0.801606
$239$	−25.2747	−1.63489	−0.817443	−	0.576009i	$-0.804609\pi$
$239$	−25.2747	−1.63489	−0.817443	+	0.576009i	$0.804609\pi$
$240$	14.6232	0.943925
$241$	−2.54854	−0.164166	−0.0820831	−	0.996625i	$-0.526157\pi$
$241$	−2.54854	−0.164166	−0.0820831	+	0.996625i	$0.526157\pi$
$242$	−35.4297	−2.27750
$243$	−6.50369	−0.417212
$244$	5.05291	0.323480
$245$	−1.00000	−0.0638877
$246$	−30.5878	−1.95021
$247$	−17.9453	−1.14183
$248$	14.1017	0.895456
$249$	−1.62728	−0.103124
$250$	1.76681	0.111743
$251$	4.34906	0.274510	0.137255	−	0.990536i	$-0.456172\pi$
$251$	4.34906	0.274510	0.137255	+	0.990536i	$0.456172\pi$
$252$	−6.28607	−0.395985
$253$	43.5068	2.73525
$254$	0.137860	0.00865009
$255$	−20.5314	−1.28573
$256$	20.0354	1.25221
$257$	16.0884	1.00356	0.501782	−	0.864994i	$-0.332678\pi$
$257$	16.0884	1.00356	0.501782	+	0.864994i	$0.332678\pi$
$258$	40.9366	2.54860
$259$	−3.25443	−0.202221
$260$	−2.75995	−0.171165
$261$	−1.58561	−0.0981471
$262$	20.8272	1.28671
$263$	15.1036	0.931330	0.465665	−	0.884961i	$-0.345815\pi$
$263$	15.1036	0.931330	0.465665	+	0.884961i	$0.345815\pi$
$264$	25.3674	1.56126
$265$	9.58756	0.588959
$266$	−12.8852	−0.790043
$267$	33.5049	2.05047
$268$	−9.66289	−0.590255
$269$	−21.9389	−1.33764	−0.668820	−	0.743424i	$-0.733200\pi$
$269$	−21.9389	−1.33764	−0.668820	+	0.743424i	$0.733200\pi$
$270$	13.4976	0.821437
$271$	−21.9172	−1.33138	−0.665689	−	0.746230i	$-0.731862\pi$
$271$	−21.9172	−1.33138	−0.665689	+	0.746230i	$0.731862\pi$
$272$	−34.8932	−2.11571
$273$	−7.21787	−0.436845
$274$	−4.35685	−0.263207
$275$	5.57251	0.336035
$276$	25.6873	1.54619
$277$	−1.46742	−0.0881685	−0.0440843	−	0.999028i	$-0.514037\pi$
$277$	−1.46742	−0.0881685	−0.0440843	+	0.999028i	$0.514037\pi$
$278$	−21.3774	−1.28213
$279$	50.9251	3.04881
$280$	1.55191	0.0927443
$281$	9.73542	0.580766	0.290383	−	0.956910i	$-0.406217\pi$
$281$	9.73542	0.580766	0.290383	+	0.956910i	$0.406217\pi$
$282$	−36.2420	−2.15818
$283$	−4.69544	−0.279115	−0.139558	−	0.990214i	$-0.544568\pi$
$283$	−4.69544	−0.279115	−0.139558	+	0.990214i	$0.544568\pi$
$284$	15.9049	0.943782
$285$	21.3924	1.26718
$286$	−24.2265	−1.43254
$287$	−5.90197	−0.348382
$288$	31.9681	1.88374
$289$	31.9911	1.88183
$290$	−0.499874	−0.0293536
$291$	28.4470	1.66759
$292$	−14.3066	−0.837229
$293$	19.8129	1.15748	0.578740	−	0.815512i	$-0.303545\pi$
$293$	19.8129	1.15748	0.578740	+	0.815512i	$0.303545\pi$
$294$	−5.18264	−0.302258
$295$	2.15310	0.125358
$296$	5.05059	0.293559
$297$	42.5712	2.47023
$298$	4.15348	0.240605
$299$	19.2112	1.11101
$300$	3.29012	0.189955
$301$	7.89879	0.455279
$302$	21.0181	1.20946
$303$	−9.68141	−0.556182
$304$	36.3566	2.08519
$305$	−4.50495	−0.257953
$306$	−69.3071	−3.96202
$307$	−22.2882	−1.27206	−0.636028	−	0.771666i	$-0.719424\pi$
$307$	−22.2882	−1.27206	−0.636028	+	0.771666i	$0.719424\pi$
$308$	−6.25032	−0.356145
$309$	−33.4134	−1.90082
$310$	16.0544	0.911830
$311$	−8.81128	−0.499642	−0.249821	−	0.968292i	$-0.580372\pi$
$311$	−8.81128	−0.499642	−0.249821	+	0.968292i	$0.580372\pi$
$312$	11.2015	0.634159
$313$	17.5808	0.993724	0.496862	−	0.867829i	$-0.334485\pi$
$313$	17.5808	0.993724	0.496862	+	0.867829i	$0.334485\pi$
$314$	28.3103	1.59764
$315$	5.60439	0.315771
$316$	−12.3007	−0.691970
$317$	−24.6180	−1.38269	−0.691343	−	0.722526i	$-0.742981\pi$
$317$	−24.6180	−1.38269	−0.691343	+	0.722526i	$0.742981\pi$
$318$	49.6888	2.78641
$319$	−1.57660	−0.0882724
$320$	0.107708	0.00602106
$321$	42.9752	2.39864
$322$	13.7942	0.768722
$323$	−51.0457	−2.84026
$324$	6.27665	0.348703
$325$	2.46065	0.136492
$326$	−4.87211	−0.269841
$327$	−17.6443	−0.975732
$328$	9.15932	0.505739
$329$	−6.99295	−0.385534
$330$	28.8803	1.58981
$331$	17.0015	0.934484	0.467242	−	0.884129i	$-0.345248\pi$
$331$	17.0015	0.934484	0.467242	+	0.884129i	$0.345248\pi$
$332$	−0.622232	−0.0341494
$333$	18.2391	0.999497
$334$	38.9227	2.12976
$335$	8.61501	0.470688
$336$	14.6232	0.797762
$337$	−6.26804	−0.341442	−0.170721	−	0.985319i	$-0.554610\pi$
$337$	−6.26804	−0.341442	−0.170721	+	0.985319i	$0.554610\pi$
$338$	12.2709	0.667450
$339$	−32.0884	−1.74280
$340$	−7.85073	−0.425765
$341$	50.6354	2.74206
$342$	72.2137	3.90487
$343$	−1.00000	−0.0539949
$344$	−12.2582	−0.660918
$345$	−22.9016	−1.23298
$346$	−41.9789	−2.25680
$347$	11.0320	0.592230	0.296115	−	0.955152i	$-0.404309\pi$
$347$	11.0320	0.592230	0.296115	+	0.955152i	$0.404309\pi$
$348$	−0.930853	−0.0498989
$349$	−23.9723	−1.28321	−0.641603	−	0.767037i	$-0.721730\pi$
$349$	−23.9723	−1.28321	−0.641603	+	0.767037i	$0.721730\pi$
$350$	1.76681	0.0944402
$351$	18.7981	1.00337
$352$	31.7862	1.69421
$353$	−14.6943	−0.782101	−0.391051	−	0.920369i	$-0.627888\pi$
$353$	−14.6943	−0.782101	−0.391051	+	0.920369i	$0.627888\pi$
$354$	11.1587	0.593081
$355$	−14.1801	−0.752602
$356$	12.8115	0.679009
$357$	−20.5314	−1.08664
$358$	−20.4110	−1.07875
$359$	8.60763	0.454294	0.227147	−	0.973861i	$-0.427060\pi$
$359$	8.60763	0.454294	0.227147	+	0.973861i	$0.427060\pi$
$360$	−8.69750	−0.458398
$361$	34.1864	1.79929
$362$	45.5887	2.39609
$363$	58.8215	3.08733
$364$	−2.75995	−0.144660
$365$	12.7551	0.667633
$366$	−23.3476	−1.22040
$367$	−0.831519	−0.0434049	−0.0217025	−	0.999764i	$-0.506909\pi$
$367$	−0.831519	−0.0434049	−0.0217025	+	0.999764i	$0.506909\pi$
$368$	−38.9215	−2.02892
$369$	33.0769	1.72192
$370$	5.74998	0.298927
$371$	9.58756	0.497761
$372$	29.8961	1.55004
$373$	9.85102	0.510066	0.255033	−	0.966932i	$-0.417914\pi$
$373$	9.85102	0.510066	0.255033	+	0.966932i	$0.417914\pi$
$374$	−68.9128	−3.56340
$375$	−2.93332	−0.151476
$376$	10.8524	0.559671
$377$	−0.696176	−0.0358549
$378$	13.4976	0.694241
$379$	4.68612	0.240710	0.120355	−	0.992731i	$-0.461597\pi$
$379$	4.68612	0.240710	0.120355	+	0.992731i	$0.461597\pi$
$380$	8.17997	0.419624
$381$	−0.228879	−0.0117258
$382$	−47.7490	−2.44305
$383$	20.9263	1.06928	0.534641	−	0.845079i	$-0.320447\pi$
$383$	20.9263	1.06928	0.534641	+	0.845079i	$0.320447\pi$
$384$	−32.9058	−1.67922
$385$	5.57251	0.284001
$386$	15.7035	0.799289
$387$	−44.2678	−2.25026
$388$	10.8775	0.552219
$389$	12.4828	0.632905	0.316452	−	0.948608i	$-0.397508\pi$
$389$	12.4828	0.632905	0.316452	+	0.948608i	$0.397508\pi$
$390$	12.7526	0.645755
$391$	54.6468	2.76361
$392$	1.55191	0.0783832
$393$	−34.5779	−1.74423
$394$	32.0978	1.61706
$395$	10.9668	0.551799
$396$	35.0292	1.76028
$397$	23.1029	1.15950	0.579751	−	0.814794i	$-0.303150\pi$
$397$	23.1029	1.15950	0.579751	+	0.814794i	$0.303150\pi$
$398$	35.5368	1.78130
$399$	21.3924	1.07096
$400$	−4.98520	−0.249260
$401$	−0.559463	−0.0279382	−0.0139691	−	0.999902i	$-0.504447\pi$
$401$	−0.559463	−0.0279382	−0.0139691	+	0.999902i	$0.504447\pi$
$402$	44.6485	2.22686
$403$	22.3590	1.11378
$404$	−3.70195	−0.184179
$405$	−5.59598	−0.278067
$406$	−0.499874	−0.0248083
$407$	18.1354	0.898936
$408$	31.8628	1.57745
$409$	17.5238	0.866498	0.433249	−	0.901274i	$-0.357367\pi$
$409$	17.5238	0.866498	0.433249	+	0.901274i	$0.357367\pi$
$410$	10.4277	0.514987
$411$	7.23338	0.356796
$412$	−12.7765	−0.629453
$413$	2.15310	0.105947
$414$	−77.3082	−3.79949
$415$	0.554755	0.0272318
$416$	14.0358	0.688162
$417$	35.4915	1.73802
$418$	71.8029	3.51200
$419$	−30.6310	−1.49642	−0.748210	−	0.663462i	$-0.769086\pi$
$419$	−30.6310	−1.49642	−0.748210	+	0.663462i	$0.769086\pi$
$420$	3.29012	0.160541
$421$	−4.02979	−0.196400	−0.0981999	−	0.995167i	$-0.531308\pi$
$421$	−4.02979	−0.196400	−0.0981999	+	0.995167i	$0.531308\pi$
$422$	−45.3830	−2.20921
$423$	39.1912	1.90554
$424$	−14.8790	−0.722589
$425$	6.99936	0.339519
$426$	−73.4904	−3.56062
$427$	−4.50495	−0.218010
$428$	16.4327	0.794306
$429$	40.2216	1.94192
$430$	−13.9557	−0.673003
$431$	−24.0938	−1.16056	−0.580279	−	0.814418i	$-0.697056\pi$
$431$	−24.0938	−1.16056	−0.580279	+	0.814418i	$0.697056\pi$
$432$	−38.0845	−1.83234
$433$	6.12482	0.294340	0.147170	−	0.989111i	$-0.452984\pi$
$433$	6.12482	0.294340	0.147170	+	0.989111i	$0.452984\pi$
$434$	16.0544	0.770637
$435$	0.829907	0.0397910
$436$	−6.74677	−0.323112
$437$	−56.9386	−2.72374
$438$	66.1051	3.15862
$439$	−10.8531	−0.517990	−0.258995	−	0.965879i	$-0.583391\pi$
$439$	−10.8531	−0.517990	−0.258995	+	0.965879i	$0.583391\pi$
$440$	−8.64802	−0.412278
$441$	5.60439	0.266876
$442$	−30.4298	−1.44740
$443$	16.6982	0.793354	0.396677	−	0.917958i	$-0.370163\pi$
$443$	16.6982	0.793354	0.396677	+	0.917958i	$0.370163\pi$
$444$	10.7075	0.508154
$445$	−11.4222	−0.541463
$446$	−6.58417	−0.311770
$447$	−6.89575	−0.326158
$448$	0.107708	0.00508872
$449$	13.9150	0.656691	0.328345	−	0.944558i	$-0.393509\pi$
$449$	13.9150	0.656691	0.328345	+	0.944558i	$0.393509\pi$
$450$	−9.90191	−0.466781
$451$	32.8888	1.54867
$452$	−12.2698	−0.577125
$453$	−34.8949	−1.63951
$454$	−17.8986	−0.840021
$455$	2.46065	0.115357
$456$	−33.1991	−1.55469
$457$	23.5948	1.10372	0.551859	−	0.833937i	$-0.313919\pi$
$457$	23.5948	1.10372	0.551859	+	0.833937i	$0.313919\pi$
$458$	−1.76681	−0.0825578
$459$	53.4717	2.49584
$460$	−8.75705	−0.408299
$461$	7.28675	0.339378	0.169689	−	0.985498i	$-0.445724\pi$
$461$	7.28675	0.339378	0.169689	+	0.985498i	$0.445724\pi$
$462$	28.8803	1.34363
$463$	−2.00582	−0.0932182	−0.0466091	−	0.998913i	$-0.514842\pi$
$463$	−2.00582	−0.0932182	−0.0466091	+	0.998913i	$0.514842\pi$
$464$	1.41043	0.0654777
$465$	−26.6541	−1.23605
$466$	−2.16465	−0.100275
$467$	−13.6741	−0.632760	−0.316380	−	0.948632i	$-0.602468\pi$
$467$	−13.6741	−0.632760	−0.316380	+	0.948632i	$0.602468\pi$
$468$	15.4678	0.715000
$469$	8.61501	0.397804
$470$	12.3553	0.569905
$471$	−47.0017	−2.16572
$472$	−3.34142	−0.153801
$473$	−44.0160	−2.02386
$474$	56.8369	2.61061
$475$	−7.29290	−0.334621
$476$	−7.85073	−0.359837
$477$	−53.7324	−2.46024
$478$	44.6558	2.04251
$479$	−15.8846	−0.725787	−0.362893	−	0.931831i	$-0.618211\pi$
$479$	−15.8846	−0.725787	−0.362893	+	0.931831i	$0.618211\pi$
$480$	−16.7320	−0.763709
$481$	8.00801	0.365134
$482$	4.50280	0.205097
$483$	−22.9016	−1.04206
$484$	22.4920	1.02236
$485$	−9.69786	−0.440357
$486$	11.4908	0.521234
$487$	35.2183	1.59589	0.797947	−	0.602727i	$-0.205919\pi$
$487$	35.2183	1.59589	0.797947	+	0.602727i	$0.205919\pi$
$488$	6.99128	0.316480
$489$	8.08884	0.365790
$490$	1.76681	0.0798166
$491$	0.185421	0.00836795	0.00418398	−	0.999991i	$-0.498668\pi$
$491$	0.185421	0.00836795	0.00418398	+	0.999991i	$0.498668\pi$
$492$	19.4182	0.875439
$493$	−1.98029	−0.0891876
$494$	31.7059	1.42652
$495$	−31.2305	−1.40371
$496$	−45.2988	−2.03398
$497$	−14.1801	−0.636065
$498$	2.87509	0.128836
$499$	15.3955	0.689199	0.344599	−	0.938750i	$-0.388015\pi$
$499$	15.3955	0.689199	0.344599	+	0.938750i	$0.388015\pi$
$500$	−1.12163	−0.0501610
$501$	−64.6207	−2.88704
$502$	−7.68398	−0.342953
$503$	−12.4786	−0.556394	−0.278197	−	0.960524i	$-0.589737\pi$
$503$	−12.4786	−0.556394	−0.278197	+	0.960524i	$0.589737\pi$
$504$	−8.69750	−0.387417
$505$	3.30049	0.146870
$506$	−76.8684	−3.41722
$507$	−20.3726	−0.904778
$508$	−0.0875181	−0.00388299
$509$	23.9865	1.06318	0.531592	−	0.847001i	$-0.321594\pi$
$509$	23.9865	1.06318	0.531592	+	0.847001i	$0.321594\pi$
$510$	36.2752	1.60629
$511$	12.7551	0.564253
$512$	−12.9630	−0.572890
$513$	−55.7142	−2.45984
$514$	−28.4251	−1.25378
$515$	11.3910	0.501946
$516$	−25.9879	−1.14406
$517$	38.9683	1.71382
$518$	5.74998	0.252640
$519$	69.6947	3.05926
$520$	−3.81870	−0.167461
$521$	2.06211	0.0903427	0.0451713	−	0.998979i	$-0.485617\pi$
$521$	2.06211	0.0903427	0.0451713	+	0.998979i	$0.485617\pi$
$522$	2.80149	0.122618
$523$	−16.8449	−0.736577	−0.368288	−	0.929712i	$-0.620056\pi$
$523$	−16.8449	−0.736577	−0.368288	+	0.929712i	$0.620056\pi$
$524$	−13.2218	−0.577597
$525$	−2.93332	−0.128021
$526$	−26.6853	−1.16354
$527$	63.6007	2.77049
$528$	−81.4880	−3.54631
$529$	37.9555	1.65024
$530$	−16.9394	−0.735802
$531$	−12.0668	−0.523655
$532$	8.17997	0.354647
$533$	14.5227	0.629046
$534$	−59.1970	−2.56171
$535$	−14.6507	−0.633405
$536$	−13.3697	−0.577483
$537$	33.8869	1.46233
$538$	38.7620	1.67115
$539$	5.57251	0.240025
$540$	−8.56873	−0.368740
$541$	−2.13928	−0.0919747	−0.0459874	−	0.998942i	$-0.514643\pi$
$541$	−2.13928	−0.0919747	−0.0459874	+	0.998942i	$0.514643\pi$
$542$	38.7237	1.66333
$543$	−75.6879	−3.24808
$544$	39.9252	1.71178
$545$	6.01512	0.257660
$546$	12.7526	0.545763
$547$	−38.9611	−1.66585	−0.832927	−	0.553382i	$-0.813337\pi$
$547$	−38.9611	−1.66585	−0.832927	+	0.553382i	$0.813337\pi$
$548$	2.76588	0.118152
$549$	25.2475	1.07754
$550$	−9.84559	−0.419817
$551$	2.06334	0.0879011
$552$	35.5412	1.51274
$553$	10.9668	0.466355
$554$	2.59265	0.110151
$555$	−9.54631	−0.405218
$556$	13.5711	0.575543
$557$	24.3258	1.03072	0.515359	−	0.856974i	$-0.327658\pi$
$557$	24.3258	1.03072	0.515359	+	0.856974i	$0.327658\pi$
$558$	−89.9752	−3.80895
$559$	−19.4361	−0.822060
$560$	−4.98520	−0.210663
$561$	114.411	4.83045
$562$	−17.2007	−0.725567
$563$	33.5731	1.41494	0.707469	−	0.706744i	$-0.249837\pi$
$563$	33.5731	1.41494	0.707469	+	0.706744i	$0.249837\pi$
$564$	23.0076	0.968796
$565$	10.9393	0.460218
$566$	8.29598	0.348706
$567$	−5.59598	−0.235009
$568$	22.0062	0.923361
$569$	−7.83718	−0.328552	−0.164276	−	0.986414i	$-0.552529\pi$
$569$	−7.83718	−0.328552	−0.164276	+	0.986414i	$0.552529\pi$
$570$	−37.7965	−1.58312
$571$	−27.0736	−1.13299	−0.566497	−	0.824064i	$-0.691702\pi$
$571$	−27.0736	−1.13299	−0.566497	+	0.824064i	$0.691702\pi$
$572$	15.3798	0.643063
$573$	79.2744	3.31174
$574$	10.4277	0.435243
$575$	7.80740	0.325591
$576$	−0.603637	−0.0251515
$577$	4.95258	0.206179	0.103089	−	0.994672i	$-0.467127\pi$
$577$	4.95258	0.206179	0.103089	+	0.994672i	$0.467127\pi$
$578$	−56.5223	−2.35102
$579$	−26.0715	−1.08350
$580$	0.317337	0.0131767
$581$	0.554755	0.0230151
$582$	−50.2605	−2.08337
$583$	−53.4267	−2.21271
$584$	−19.7948	−0.819113
$585$	−13.7904	−0.570163
$586$	−35.0057	−1.44607
$587$	23.0449	0.951163	0.475581	−	0.879672i	$-0.342238\pi$
$587$	23.0449	0.951163	0.475581	+	0.879672i	$0.342238\pi$
$588$	3.29012	0.135682
$589$	−66.2681	−2.73053
$590$	−3.80413	−0.156614
$591$	−53.2897	−2.19205
$592$	−16.2240	−0.666803
$593$	13.5697	0.557242	0.278621	−	0.960401i	$-0.410123\pi$
$593$	13.5697	0.557242	0.278621	+	0.960401i	$0.410123\pi$
$594$	−75.2154	−3.08613
$595$	6.99936	0.286946
$596$	−2.63677	−0.108006
$597$	−58.9994	−2.41468
$598$	−33.9427	−1.38802
$599$	−33.6379	−1.37441	−0.687203	−	0.726465i	$-0.741162\pi$
$599$	−33.6379	−1.37441	−0.687203	+	0.726465i	$0.741162\pi$
$600$	4.55225	0.185845
$601$	38.3161	1.56295	0.781474	−	0.623938i	$-0.214468\pi$
$601$	38.3161	1.56295	0.781474	+	0.623938i	$0.214468\pi$
$602$	−13.9557	−0.568792
$603$	−48.2818	−1.96619
$604$	−13.3430	−0.542919
$605$	−20.0528	−0.815264
$606$	17.1053	0.694854
$607$	3.05677	0.124071	0.0620353	−	0.998074i	$-0.480241\pi$
$607$	3.05677	0.124071	0.0620353	+	0.998074i	$0.480241\pi$
$608$	−41.5996	−1.68709
$609$	0.829907	0.0336295
$610$	7.95942	0.322267
$611$	17.2072	0.696128
$612$	43.9985	1.77853
$613$	19.0380	0.768936	0.384468	−	0.923138i	$-0.374385\pi$
$613$	19.0380	0.768936	0.384468	+	0.923138i	$0.374385\pi$
$614$	39.3791	1.58921
$615$	−17.3124	−0.698103
$616$	−8.64802	−0.348439
$617$	−1.04915	−0.0422371	−0.0211185	−	0.999777i	$-0.506723\pi$
$617$	−1.04915	−0.0422371	−0.0211185	+	0.999777i	$0.506723\pi$
$618$	59.0353	2.37475
$619$	2.01296	0.0809076	0.0404538	−	0.999181i	$-0.487120\pi$
$619$	2.01296	0.0809076	0.0404538	+	0.999181i	$0.487120\pi$
$620$	−10.1919	−0.409317
$621$	59.6447	2.39346
$622$	15.5679	0.624216
$623$	−11.4222	−0.457620
$624$	−35.9826	−1.44046
$625$	1.00000	0.0400000
$626$	−31.0620	−1.24149
$627$	−119.210	−4.76077
$628$	−17.9724	−0.717175
$629$	22.7790	0.908257
$630$	−9.90191	−0.394502
$631$	−19.6968	−0.784117	−0.392059	−	0.919940i	$-0.628237\pi$
$631$	−19.6968	−0.784117	−0.392059	+	0.919940i	$0.628237\pi$
$632$	−17.0195	−0.676998
$633$	75.3463	2.99475
$634$	43.4955	1.72743
$635$	0.0780272	0.00309642
$636$	−31.5442	−1.25081
$637$	2.46065	0.0974944
$638$	2.78555	0.110281
$639$	79.4708	3.14381
$640$	11.2179	0.443428
$641$	−8.70703	−0.343907	−0.171954	−	0.985105i	$-0.555008\pi$
$641$	−8.70703	−0.343907	−0.171954	+	0.985105i	$0.555008\pi$
$642$	−75.9293	−2.99669
$643$	17.7885	0.701511	0.350756	−	0.936467i	$-0.385925\pi$
$643$	17.7885	0.701511	0.350756	+	0.936467i	$0.385925\pi$
$644$	−8.75705	−0.345076
$645$	23.1697	0.912306
$646$	90.1882	3.54841
$647$	−31.1355	−1.22406	−0.612032	−	0.790833i	$-0.709648\pi$
$647$	−31.1355	−1.22406	−0.612032	+	0.790833i	$0.709648\pi$
$648$	8.68445	0.341158
$649$	−11.9982	−0.470969
$650$	−4.34751	−0.170523
$651$	−26.6541	−1.04466
$652$	3.09298	0.121131
$653$	−11.9099	−0.466069	−0.233035	−	0.972468i	$-0.574866\pi$
$653$	−11.9099	−0.466069	−0.233035	+	0.972468i	$0.574866\pi$
$654$	31.1742	1.21901
$655$	11.7880	0.460594
$656$	−29.4225	−1.14876
$657$	−71.4845	−2.78888
$658$	12.3553	0.481658
$659$	−12.2728	−0.478079	−0.239040	−	0.971010i	$-0.576833\pi$
$659$	−12.2728	−0.478079	−0.239040	+	0.971010i	$0.576833\pi$
$660$	−18.3342	−0.713658
$661$	21.5059	0.836481	0.418240	−	0.908336i	$-0.362647\pi$
$661$	21.5059	0.836481	0.418240	+	0.908336i	$0.362647\pi$
$662$	−30.0384	−1.16748
$663$	50.5205	1.96205
$664$	−0.860929	−0.0334105
$665$	−7.29290	−0.282807
$666$	−32.2251	−1.24870
$667$	−2.20890	−0.0855289
$668$	−24.7095	−0.956038
$669$	10.9313	0.422627
$670$	−15.2211	−0.588043
$671$	25.1039	0.969125
$672$	−16.7320	−0.645452
$673$	−15.2023	−0.586006	−0.293003	−	0.956111i	$-0.594655\pi$
$673$	−15.2023	−0.586006	−0.293003	+	0.956111i	$0.594655\pi$
$674$	11.0745	0.426572
$675$	7.63951	0.294045
$676$	−7.79000	−0.299615
$677$	28.2617	1.08618	0.543092	−	0.839673i	$-0.317253\pi$
$677$	28.2617	1.08618	0.543092	+	0.839673i	$0.317253\pi$
$678$	56.6942	2.17733
$679$	−9.69786	−0.372170
$680$	−10.8624	−0.416553
$681$	29.7158	1.13871
$682$	−89.4634	−3.42573
$683$	−21.5966	−0.826372	−0.413186	−	0.910647i	$-0.635584\pi$
$683$	−21.5966	−0.826372	−0.413186	+	0.910647i	$0.635584\pi$
$684$	−45.8437	−1.75288
$685$	−2.46593	−0.0942185
$686$	1.76681	0.0674573
$687$	2.93332	0.111913
$688$	39.3771	1.50124
$689$	−23.5916	−0.898768
$690$	40.4629	1.54040
$691$	2.53457	0.0964197	0.0482098	−	0.998837i	$-0.484648\pi$
$691$	2.53457	0.0964197	0.0482098	+	0.998837i	$0.484648\pi$
$692$	26.6496	1.01307
$693$	−31.2305	−1.18635
$694$	−19.4916	−0.739889
$695$	−12.0994	−0.458957
$696$	−1.28794	−0.0488193
$697$	41.3100	1.56473
$698$	42.3546	1.60314
$699$	3.59381	0.135931
$700$	−1.12163	−0.0423938
$701$	−34.1597	−1.29019	−0.645097	−	0.764100i	$-0.723183\pi$
$701$	−34.1597	−1.29019	−0.645097	+	0.764100i	$0.723183\pi$
$702$	−33.2128	−1.25354
$703$	−23.7343	−0.895155
$704$	−0.600203	−0.0226210
$705$	−20.5126	−0.772549
$706$	25.9622	0.977100
$707$	3.30049	0.124128
$708$	−7.08396	−0.266231
$709$	−32.1055	−1.20575	−0.602875	−	0.797836i	$-0.705978\pi$
$709$	−32.1055	−1.20575	−0.602875	+	0.797836i	$0.705978\pi$
$710$	25.0536	0.940245
$711$	−61.4621	−2.30501
$712$	17.7262	0.664317
$713$	70.9431	2.65684
$714$	36.2752	1.35756
$715$	−13.7120	−0.512799
$716$	12.9576	0.484247
$717$	−74.1390	−2.76877
$718$	−15.2081	−0.567561
$719$	8.31992	0.310280	0.155140	−	0.987892i	$-0.450417\pi$
$719$	8.31992	0.310280	0.155140	+	0.987892i	$0.450417\pi$
$720$	27.9390	1.04123
$721$	11.3910	0.424222
$722$	−60.4011	−2.24790
$723$	−7.47570	−0.278024
$724$	−28.9413	−1.07560
$725$	−0.282924	−0.0105075
$726$	−103.927	−3.85708
$727$	9.85286	0.365422	0.182711	−	0.983167i	$-0.441513\pi$
$727$	9.85286	0.365422	0.182711	+	0.983167i	$0.441513\pi$
$728$	−3.81870	−0.141530
$729$	−35.8654	−1.32835
$730$	−22.5359	−0.834091
$731$	−55.2865	−2.04484
$732$	14.8218	0.547830
$733$	18.2883	0.675494	0.337747	−	0.941237i	$-0.390335\pi$
$733$	18.2883	0.675494	0.337747	+	0.941237i	$0.390335\pi$
$734$	1.46914	0.0542270
$735$	−2.93332	−0.108197
$736$	44.5343	1.64156
$737$	−48.0072	−1.76837
$738$	−58.4408	−2.15124
$739$	33.3823	1.22799	0.613994	−	0.789311i	$-0.289562\pi$
$739$	33.3823	1.22799	0.613994	+	0.789311i	$0.289562\pi$
$740$	−3.65029	−0.134187
$741$	−52.6392	−1.93375
$742$	−16.9394	−0.621866
$743$	−11.9424	−0.438123	−0.219062	−	0.975711i	$-0.570300\pi$
$743$	−11.9424	−0.438123	−0.219062	+	0.975711i	$0.570300\pi$
$744$	41.3647	1.51650
$745$	2.35083	0.0861278
$746$	−17.4049	−0.637239
$747$	−3.10906	−0.113755
$748$	43.7482	1.59959
$749$	−14.6507	−0.535325
$750$	5.18264	0.189243
$751$	−8.69916	−0.317437	−0.158718	−	0.987324i	$-0.550736\pi$
$751$	−8.69916	−0.317437	−0.158718	+	0.987324i	$0.550736\pi$
$752$	−34.8613	−1.27126
$753$	12.7572	0.464898
$754$	1.23001	0.0447944
$755$	11.8960	0.432941
$756$	−8.56873	−0.311642
$757$	−19.9289	−0.724327	−0.362164	−	0.932115i	$-0.617962\pi$
$757$	−19.9289	−0.724327	−0.362164	+	0.932115i	$0.617962\pi$
$758$	−8.27950	−0.300725
$759$	127.619	4.63229
$760$	11.3179	0.410544
$761$	−22.0167	−0.798104	−0.399052	−	0.916928i	$-0.630661\pi$
$761$	−22.0167	−0.798104	−0.399052	+	0.916928i	$0.630661\pi$
$762$	0.404387	0.0146494
$763$	6.01512	0.217762
$764$	30.3127	1.09668
$765$	−39.2271	−1.41826
$766$	−36.9728	−1.33588
$767$	−5.29802	−0.191300
$768$	58.7704	2.12069
$769$	10.3014	0.371477	0.185738	−	0.982599i	$-0.440532\pi$
$769$	10.3014	0.371477	0.185738	+	0.982599i	$0.440532\pi$
$770$	−9.84559	−0.354810
$771$	47.1923	1.69959
$772$	−9.96914	−0.358797
$773$	1.42750	0.0513435	0.0256717	−	0.999670i	$-0.491828\pi$
$773$	1.42750	0.0513435	0.0256717	+	0.999670i	$0.491828\pi$
$774$	78.2131	2.81131
$775$	9.08665	0.326402
$776$	15.0502	0.540270
$777$	−9.54631	−0.342472
$778$	−22.0549	−0.790705
$779$	−43.0425	−1.54216
$780$	−8.09582	−0.289877
$781$	79.0187	2.82751
$782$	−96.5508	−3.45265
$783$	−2.16140	−0.0772421
$784$	−4.98520	−0.178043
$785$	16.0234	0.571898
$786$	61.0928	2.17911
$787$	53.7310	1.91530	0.957652	−	0.287927i	$-0.0929660\pi$
$787$	53.7310	1.91530	0.957652	+	0.287927i	$0.0929660\pi$
$788$	−20.3768	−0.725892
$789$	44.3039	1.57726
$790$	−19.3763	−0.689377
$791$	10.9393	0.388955
$792$	48.4669	1.72219
$793$	11.0851	0.393643
$794$	−40.8185	−1.44860
$795$	28.1234	0.997434
$796$	−22.5600	−0.799618
$797$	−38.5582	−1.36580	−0.682900	−	0.730512i	$-0.739282\pi$
$797$	−38.5582	−1.36580	−0.682900	+	0.730512i	$0.739282\pi$
$798$	−37.7965	−1.33798
$799$	48.9462	1.73159
$800$	5.70412	0.201671
$801$	64.0143	2.26183
$802$	0.988467	0.0349040
$803$	−71.0779	−2.50829
$804$	−28.3444	−0.999629
$805$	7.80740	0.275175
$806$	−39.5043	−1.39148
$807$	−64.3540	−2.26537
$808$	−5.12206	−0.180194
$809$	8.74409	0.307426	0.153713	−	0.988116i	$-0.450877\pi$
$809$	8.74409	0.307426	0.153713	+	0.988116i	$0.450877\pi$
$810$	9.88707	0.347396
$811$	−6.36588	−0.223536	−0.111768	−	0.993734i	$-0.535651\pi$
$811$	−6.36588	−0.223536	−0.111768	+	0.993734i	$0.535651\pi$
$812$	0.317337	0.0111364
$813$	−64.2903	−2.25476
$814$	−32.0418	−1.12307
$815$	−2.75757	−0.0965934
$816$	−102.353	−3.58308
$817$	57.6051	2.01535
$818$	−30.9614	−1.08254
$819$	−13.7904	−0.481876
$820$	−6.61985	−0.231175
$821$	−28.5401	−0.996057	−0.498028	−	0.867161i	$-0.665942\pi$
$821$	−28.5401	−0.996057	−0.498028	+	0.867161i	$0.665942\pi$
$822$	−12.7800	−0.445755
$823$	29.1255	1.01525	0.507626	−	0.861578i	$-0.330523\pi$
$823$	29.1255	1.01525	0.507626	+	0.861578i	$0.330523\pi$
$824$	−17.6777	−0.615833
$825$	16.3460	0.569093
$826$	−3.80413	−0.132363
$827$	−31.5453	−1.09694	−0.548468	−	0.836172i	$-0.684789\pi$
$827$	−31.5453	−1.09694	−0.548468	+	0.836172i	$0.684789\pi$
$828$	49.0779	1.70557
$829$	21.9470	0.762251	0.381126	−	0.924523i	$-0.375537\pi$
$829$	21.9470	0.762251	0.381126	+	0.924523i	$0.375537\pi$
$830$	−0.980149	−0.0340215
$831$	−4.30441	−0.149318
$832$	−0.265031	−0.00918830
$833$	6.99936	0.242513
$834$	−62.7068	−2.17136
$835$	22.0299	0.762375
$836$	−45.5830	−1.57652
$837$	69.4175	2.39942
$838$	54.1192	1.86952
$839$	13.1665	0.454558	0.227279	−	0.973830i	$-0.427017\pi$
$839$	13.1665	0.454558	0.227279	+	0.973830i	$0.427017\pi$
$840$	4.55225	0.157068
$841$	−28.9200	−0.997240
$842$	7.11989	0.245368
$843$	28.5571	0.983560
$844$	28.8107	0.991705
$845$	6.94522	0.238923
$846$	−69.2436	−2.38064
$847$	−20.0528	−0.689024
$848$	47.7959	1.64132
$849$	−13.7733	−0.472697
$850$	−12.3666	−0.424170
$851$	25.4087	0.870998
$852$	46.6542	1.59835
$853$	9.97282	0.341463	0.170731	−	0.985318i	$-0.445387\pi$
$853$	9.97282	0.341463	0.170731	+	0.985318i	$0.445387\pi$
$854$	7.95942	0.272366
$855$	40.8722	1.39780
$856$	22.7366	0.777119
$857$	−13.1891	−0.450533	−0.225266	−	0.974297i	$-0.572325\pi$
$857$	−13.1891	−0.450533	−0.225266	+	0.974297i	$0.572325\pi$
$858$	−71.0642	−2.42609
$859$	1.16310	0.0396844	0.0198422	−	0.999803i	$-0.493684\pi$
$859$	1.16310	0.0396844	0.0198422	+	0.999803i	$0.493684\pi$
$860$	8.85955	0.302108
$861$	−17.3124	−0.590005
$862$	42.5693	1.44992
$863$	55.1620	1.87774	0.938868	−	0.344278i	$-0.111876\pi$
$863$	55.1620	1.87774	0.938868	+	0.344278i	$0.111876\pi$
$864$	43.5766	1.48251
$865$	−23.7596	−0.807852
$866$	−10.8214	−0.367727
$867$	93.8401	3.18698
$868$	−10.1919	−0.345936
$869$	−61.1125	−2.07310
$870$	−1.46629	−0.0497120
$871$	−21.1985	−0.718283
$872$	−9.33492	−0.316120
$873$	54.3505	1.83949
$874$	100.600	3.40284
$875$	1.00000	0.0338062
$876$	−41.9658	−1.41789
$877$	−8.97353	−0.303015	−0.151507	−	0.988456i	$-0.548413\pi$
$877$	−8.97353	−0.303015	−0.151507	+	0.988456i	$0.548413\pi$
$878$	19.1754	0.647139
$879$	58.1175	1.96026
$880$	27.7801	0.936467
$881$	52.7878	1.77847	0.889233	−	0.457454i	$-0.151239\pi$
$881$	52.7878	1.77847	0.889233	+	0.457454i	$0.151239\pi$
$882$	−9.90191	−0.333415
$883$	7.46113	0.251087	0.125544	−	0.992088i	$-0.459933\pi$
$883$	7.46113	0.251087	0.125544	+	0.992088i	$0.459933\pi$
$884$	19.3179	0.649730
$885$	6.31574	0.212301
$886$	−29.5026	−0.991158
$887$	5.05704	0.169799	0.0848995	−	0.996390i	$-0.472943\pi$
$887$	5.05704	0.169799	0.0848995	+	0.996390i	$0.472943\pi$
$888$	14.8150	0.497159
$889$	0.0780272	0.00261695
$890$	20.1809	0.676464
$891$	31.1837	1.04469
$892$	4.17986	0.139952
$893$	−50.9989	−1.70661
$894$	12.1835	0.407478
$895$	−11.5524	−0.386154
$896$	11.2179	0.374765
$897$	56.3528	1.88156
$898$	−24.5853	−0.820421
$899$	−2.57083	−0.0857420
$900$	6.28607	0.209536
$901$	−67.1068	−2.23565
$902$	−58.1084	−1.93480
$903$	23.1697	0.771039
$904$	−16.9767	−0.564638
$905$	25.8028	0.857714
$906$	61.6529	2.04828
$907$	−21.4264	−0.711453	−0.355726	−	0.934590i	$-0.615767\pi$
$907$	−21.4264	−0.711453	−0.355726	+	0.934590i	$0.615767\pi$
$908$	11.3626	0.377082
$909$	−18.4972	−0.613514
$910$	−4.34751	−0.144118
$911$	11.2098	0.371398	0.185699	−	0.982607i	$-0.440545\pi$
$911$	11.2098	0.371398	0.185699	+	0.982607i	$0.440545\pi$
$912$	106.646	3.53139
$913$	−3.09138	−0.102310
$914$	−41.6877	−1.37891
$915$	−13.2145	−0.436857
$916$	1.12163	0.0370599
$917$	11.7880	0.389273
$918$	−94.4745	−3.11812
$919$	33.1011	1.09191	0.545953	−	0.837816i	$-0.316168\pi$
$919$	33.1011	1.09191	0.545953	+	0.837816i	$0.316168\pi$
$920$	−12.1164	−0.399465
$921$	−65.3785	−2.15430
$922$	−12.8743	−0.423994
$923$	34.8922	1.14849
$924$	−18.3342	−0.603151
$925$	3.25443	0.107005
$926$	3.54391	0.116460
$927$	−63.8394	−2.09676
$928$	−1.61383	−0.0529766
$929$	20.2164	0.663278	0.331639	−	0.943406i	$-0.392398\pi$
$929$	20.2164	0.663278	0.331639	+	0.943406i	$0.392398\pi$
$930$	47.0928	1.54423
$931$	−7.29290	−0.239015
$932$	1.37419	0.0450131
$933$	−25.8463	−0.846171
$934$	24.1595	0.790524
$935$	−39.0040	−1.27557
$936$	21.4015	0.699529
$937$	1.88144	0.0614639	0.0307319	−	0.999528i	$-0.490216\pi$
$937$	1.88144	0.0614639	0.0307319	+	0.999528i	$0.490216\pi$
$938$	−15.2211	−0.496987
$939$	51.5701	1.68293
$940$	−7.84354	−0.255828
$941$	−16.9898	−0.553851	−0.276925	−	0.960891i	$-0.589316\pi$
$941$	−16.9898	−0.553851	−0.276925	+	0.960891i	$0.589316\pi$
$942$	83.0433	2.70570
$943$	46.0790	1.50054
$944$	10.7337	0.349351
$945$	7.63951	0.248513
$946$	77.7682	2.52846
$947$	19.4492	0.632013	0.316007	−	0.948757i	$-0.397658\pi$
$947$	19.4492	0.632013	0.316007	+	0.948757i	$0.397658\pi$
$948$	−36.0820	−1.17189
$949$	−31.3858	−1.01883
$950$	12.8852	0.418051
$951$	−72.2127	−2.34166
$952$	−10.8624	−0.352051
$953$	15.6168	0.505877	0.252939	−	0.967482i	$-0.418603\pi$
$953$	15.6168	0.505877	0.252939	+	0.967482i	$0.418603\pi$
$954$	94.9351	3.07364
$955$	−27.0255	−0.874524
$956$	−28.3490	−0.916873
$957$	−4.62466	−0.149494
$958$	28.0652	0.906745
$959$	−2.46593	−0.0796292
$960$	0.315942	0.0101970
$961$	51.5672	1.66346
$962$	−14.1487	−0.456172
$963$	82.1082	2.64590
$964$	−2.85853	−0.0920672
$965$	8.88805	0.286116
$966$	40.4629	1.30187
$967$	6.17907	0.198705	0.0993527	−	0.995052i	$-0.468323\pi$
$967$	6.17907	0.198705	0.0993527	+	0.995052i	$0.468323\pi$
$968$	31.1202	1.00024
$969$	−149.733	−4.81013
$970$	17.1343	0.550150
$971$	−42.0542	−1.34958	−0.674791	−	0.738008i	$-0.735766\pi$
$971$	−42.0542	−1.34958	−0.674791	+	0.738008i	$0.735766\pi$
$972$	−7.29476	−0.233980
$973$	−12.0994	−0.387889
$974$	−62.2243	−1.99379
$975$	7.21787	0.231157
$976$	−22.4581	−0.718867
$977$	−1.79994	−0.0575851	−0.0287925	−	0.999585i	$-0.509166\pi$
$977$	−1.79994	−0.0575851	−0.0287925	+	0.999585i	$0.509166\pi$
$978$	−14.2915	−0.456991
$979$	63.6502	2.03427
$980$	−1.12163	−0.0358293
$981$	−33.7111	−1.07631
$982$	−0.327605	−0.0104543
$983$	3.13320	0.0999336	0.0499668	−	0.998751i	$-0.484088\pi$
$983$	3.13320	0.0999336	0.0499668	+	0.998751i	$0.484088\pi$
$984$	26.8672	0.856496
$985$	18.1670	0.578849
$986$	3.49880	0.111424
$987$	−20.5126	−0.652923
$988$	−20.1280	−0.640358
$989$	−61.6690	−1.96096
$990$	55.1785	1.75369
$991$	8.04171	0.255453	0.127727	−	0.991809i	$-0.459232\pi$
$991$	8.04171	0.255453	0.127727	+	0.991809i	$0.459232\pi$
$992$	51.8313	1.64565
$993$	49.8708	1.58260
$994$	25.0536	0.794652
$995$	20.1135	0.637641
$996$	−1.82521	−0.0578339
$997$	36.6604	1.16105	0.580523	−	0.814244i	$-0.302848\pi$
$997$	36.6604	1.16105	0.580523	+	0.814244i	$0.302848\pi$
$998$	−27.2011	−0.861035
$999$	24.8623	0.786607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.14	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.14	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.76681 q^{2} +2.93332 q^{3} +1.12163 q^{4} -1.00000 q^{5} -5.18264 q^{6} -1.00000 q^{7} +1.55191 q^{8} +5.60439 q^{9} +O(q^{10})\)	\(q-1.76681 q^{2} +2.93332 q^{3} +1.12163 q^{4} -1.00000 q^{5} -5.18264 q^{6} -1.00000 q^{7} +1.55191 q^{8} +5.60439 q^{9} +1.76681 q^{10} +5.57251 q^{11} +3.29012 q^{12} +2.46065 q^{13} +1.76681 q^{14} -2.93332 q^{15} -4.98520 q^{16} +6.99936 q^{17} -9.90191 q^{18} -7.29290 q^{19} -1.12163 q^{20} -2.93332 q^{21} -9.84559 q^{22} +7.80740 q^{23} +4.55225 q^{24} +1.00000 q^{25} -4.34751 q^{26} +7.63951 q^{27} -1.12163 q^{28} -0.282924 q^{29} +5.18264 q^{30} +9.08665 q^{31} +5.70412 q^{32} +16.3460 q^{33} -12.3666 q^{34} +1.00000 q^{35} +6.28607 q^{36} +3.25443 q^{37} +12.8852 q^{38} +7.21787 q^{39} -1.55191 q^{40} +5.90197 q^{41} +5.18264 q^{42} -7.89879 q^{43} +6.25032 q^{44} -5.60439 q^{45} -13.7942 q^{46} +6.99295 q^{47} -14.6232 q^{48} +1.00000 q^{49} -1.76681 q^{50} +20.5314 q^{51} +2.75995 q^{52} -9.58756 q^{53} -13.4976 q^{54} -5.57251 q^{55} -1.55191 q^{56} -21.3924 q^{57} +0.499874 q^{58} -2.15310 q^{59} -3.29012 q^{60} +4.50495 q^{61} -16.0544 q^{62} -5.60439 q^{63} -0.107708 q^{64} -2.46065 q^{65} -28.8803 q^{66} -8.61501 q^{67} +7.85073 q^{68} +22.9016 q^{69} -1.76681 q^{70} +14.1801 q^{71} +8.69750 q^{72} -12.7551 q^{73} -5.74998 q^{74} +2.93332 q^{75} -8.17997 q^{76} -5.57251 q^{77} -12.7526 q^{78} -10.9668 q^{79} +4.98520 q^{80} +5.59598 q^{81} -10.4277 q^{82} -0.554755 q^{83} -3.29012 q^{84} -6.99936 q^{85} +13.9557 q^{86} -0.829907 q^{87} +8.64802 q^{88} +11.4222 q^{89} +9.90191 q^{90} -2.46065 q^{91} +8.75705 q^{92} +26.6541 q^{93} -12.3553 q^{94} +7.29290 q^{95} +16.7320 q^{96} +9.69786 q^{97} -1.76681 q^{98} +31.2305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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