LMFDB - Embedded newform 8018.2.a.j.1.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.812207 q^{3} +1.00000 q^{4} -3.14651 q^{5} +0.812207 q^{6} +3.94545 q^{7} +1.00000 q^{8} -2.34032 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.812207 q^{3} +1.00000 q^{4} -3.14651 q^{5} +0.812207 q^{6} +3.94545 q^{7} +1.00000 q^{8} -2.34032 q^{9} -3.14651 q^{10} +5.89748 q^{11} +0.812207 q^{12} -4.62153 q^{13} +3.94545 q^{14} -2.55562 q^{15} +1.00000 q^{16} +3.11463 q^{17} -2.34032 q^{18} -1.00000 q^{19} -3.14651 q^{20} +3.20453 q^{21} +5.89748 q^{22} +0.559376 q^{23} +0.812207 q^{24} +4.90052 q^{25} -4.62153 q^{26} -4.33745 q^{27} +3.94545 q^{28} +8.95968 q^{29} -2.55562 q^{30} -1.19504 q^{31} +1.00000 q^{32} +4.78998 q^{33} +3.11463 q^{34} -12.4144 q^{35} -2.34032 q^{36} +3.33021 q^{37} -1.00000 q^{38} -3.75364 q^{39} -3.14651 q^{40} +8.62243 q^{41} +3.20453 q^{42} -2.86688 q^{43} +5.89748 q^{44} +7.36384 q^{45} +0.559376 q^{46} -4.24126 q^{47} +0.812207 q^{48} +8.56661 q^{49} +4.90052 q^{50} +2.52973 q^{51} -4.62153 q^{52} +1.11408 q^{53} -4.33745 q^{54} -18.5565 q^{55} +3.94545 q^{56} -0.812207 q^{57} +8.95968 q^{58} -6.80208 q^{59} -2.55562 q^{60} -3.69242 q^{61} -1.19504 q^{62} -9.23362 q^{63} +1.00000 q^{64} +14.5417 q^{65} +4.78998 q^{66} +3.18287 q^{67} +3.11463 q^{68} +0.454329 q^{69} -12.4144 q^{70} +6.64480 q^{71} -2.34032 q^{72} -15.2776 q^{73} +3.33021 q^{74} +3.98024 q^{75} -1.00000 q^{76} +23.2682 q^{77} -3.75364 q^{78} +12.6917 q^{79} -3.14651 q^{80} +3.49805 q^{81} +8.62243 q^{82} +1.11917 q^{83} +3.20453 q^{84} -9.80023 q^{85} -2.86688 q^{86} +7.27712 q^{87} +5.89748 q^{88} -13.6966 q^{89} +7.36384 q^{90} -18.2340 q^{91} +0.559376 q^{92} -0.970624 q^{93} -4.24126 q^{94} +3.14651 q^{95} +0.812207 q^{96} +16.6072 q^{97} +8.56661 q^{98} -13.8020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.812207	0.468928	0.234464	−	0.972125i	$-0.424666\pi$
$3$	0.812207	0.468928	0.234464	+	0.972125i	$0.424666\pi$
$4$	1.00000	0.500000
$5$	−3.14651	−1.40716	−0.703581	−	0.710615i	$-0.748417\pi$
$5$	−3.14651	−1.40716	−0.703581	+	0.710615i	$0.748417\pi$
$6$	0.812207	0.331582
$7$	3.94545	1.49124	0.745621	−	0.666371i	$-0.232153\pi$
$7$	3.94545	1.49124	0.745621	+	0.666371i	$0.232153\pi$
$8$	1.00000	0.353553
$9$	−2.34032	−0.780106
$10$	−3.14651	−0.995014
$11$	5.89748	1.77816	0.889078	−	0.457755i	$-0.151346\pi$
$11$	5.89748	1.77816	0.889078	+	0.457755i	$0.151346\pi$
$12$	0.812207	0.234464
$13$	−4.62153	−1.28178	−0.640891	−	0.767632i	$-0.721435\pi$
$13$	−4.62153	−1.28178	−0.640891	+	0.767632i	$0.721435\pi$
$14$	3.94545	1.05447
$15$	−2.55562	−0.659858
$16$	1.00000	0.250000
$17$	3.11463	0.755410	0.377705	−	0.925926i	$-0.376713\pi$
$17$	3.11463	0.755410	0.377705	+	0.925926i	$0.376713\pi$
$18$	−2.34032	−0.551618
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.14651	−0.703581
$21$	3.20453	0.699285
$22$	5.89748	1.25735
$23$	0.559376	0.116638	0.0583190	−	0.998298i	$-0.481426\pi$
$23$	0.559376	0.116638	0.0583190	+	0.998298i	$0.481426\pi$
$24$	0.812207	0.165791
$25$	4.90052	0.980105
$26$	−4.62153	−0.906357
$27$	−4.33745	−0.834742
$28$	3.94545	0.745621
$29$	8.95968	1.66377	0.831885	−	0.554948i	$-0.187262\pi$
$29$	8.95968	1.66377	0.831885	+	0.554948i	$0.187262\pi$
$30$	−2.55562	−0.466590
$31$	−1.19504	−0.214636	−0.107318	−	0.994225i	$-0.534226\pi$
$31$	−1.19504	−0.214636	−0.107318	+	0.994225i	$0.534226\pi$
$32$	1.00000	0.176777
$33$	4.78998	0.833828
$34$	3.11463	0.534155
$35$	−12.4144	−2.09842
$36$	−2.34032	−0.390053
$37$	3.33021	0.547483	0.273742	−	0.961803i	$-0.411739\pi$
$37$	3.33021	0.547483	0.273742	+	0.961803i	$0.411739\pi$
$38$	−1.00000	−0.162221
$39$	−3.75364	−0.601064
$40$	−3.14651	−0.497507
$41$	8.62243	1.34660	0.673298	−	0.739371i	$-0.264877\pi$
$41$	8.62243	1.34660	0.673298	+	0.739371i	$0.264877\pi$
$42$	3.20453	0.494469
$43$	−2.86688	−0.437194	−0.218597	−	0.975815i	$-0.570148\pi$
$43$	−2.86688	−0.437194	−0.218597	+	0.975815i	$0.570148\pi$
$44$	5.89748	0.889078
$45$	7.36384	1.09774
$46$	0.559376	0.0824755
$47$	−4.24126	−0.618651	−0.309325	−	0.950956i	$-0.600103\pi$
$47$	−4.24126	−0.618651	−0.309325	+	0.950956i	$0.600103\pi$
$48$	0.812207	0.117232
$49$	8.56661	1.22380
$50$	4.90052	0.693039
$51$	2.52973	0.354233
$52$	−4.62153	−0.640891
$53$	1.11408	0.153030	0.0765152	−	0.997068i	$-0.475621\pi$
$53$	1.11408	0.153030	0.0765152	+	0.997068i	$0.475621\pi$
$54$	−4.33745	−0.590252
$55$	−18.5565	−2.50215
$56$	3.94545	0.527233
$57$	−0.812207	−0.107580
$58$	8.95968	1.17646
$59$	−6.80208	−0.885556	−0.442778	−	0.896631i	$-0.646007\pi$
$59$	−6.80208	−0.885556	−0.442778	+	0.896631i	$0.646007\pi$
$60$	−2.55562	−0.329929
$61$	−3.69242	−0.472766	−0.236383	−	0.971660i	$-0.575962\pi$
$61$	−3.69242	−0.472766	−0.236383	+	0.971660i	$0.575962\pi$
$62$	−1.19504	−0.151771
$63$	−9.23362	−1.16333
$64$	1.00000	0.125000
$65$	14.5417	1.80368
$66$	4.78998	0.589605
$67$	3.18287	0.388849	0.194425	−	0.980917i	$-0.437716\pi$
$67$	3.18287	0.388849	0.194425	+	0.980917i	$0.437716\pi$
$68$	3.11463	0.377705
$69$	0.454329	0.0546948
$70$	−12.4144	−1.48381
$71$	6.64480	0.788592	0.394296	−	0.918983i	$-0.370988\pi$
$71$	6.64480	0.788592	0.394296	+	0.918983i	$0.370988\pi$
$72$	−2.34032	−0.275809
$73$	−15.2776	−1.78811	−0.894053	−	0.447962i	$-0.852150\pi$
$73$	−15.2776	−1.78811	−0.894053	+	0.447962i	$0.852150\pi$
$74$	3.33021	0.387129
$75$	3.98024	0.459599
$76$	−1.00000	−0.114708
$77$	23.2682	2.65166
$78$	−3.75364	−0.425016
$79$	12.6917	1.42792	0.713962	−	0.700184i	$-0.246899\pi$
$79$	12.6917	1.42792	0.713962	+	0.700184i	$0.246899\pi$
$80$	−3.14651	−0.351790
$81$	3.49805	0.388672
$82$	8.62243	0.952188
$83$	1.11917	0.122845	0.0614226	−	0.998112i	$-0.480436\pi$
$83$	1.11917	0.122845	0.0614226	+	0.998112i	$0.480436\pi$
$84$	3.20453	0.349643
$85$	−9.80023	−1.06298
$86$	−2.86688	−0.309143
$87$	7.27712	0.780189
$88$	5.89748	0.628673
$89$	−13.6966	−1.45184	−0.725920	−	0.687779i	$-0.758586\pi$
$89$	−13.6966	−1.45184	−0.725920	+	0.687779i	$0.758586\pi$
$90$	7.36384	0.776217
$91$	−18.2340	−1.91145
$92$	0.559376	0.0583190
$93$	−0.970624	−0.100649
$94$	−4.24126	−0.437452
$95$	3.14651	0.322825
$96$	0.812207	0.0828956
$97$	16.6072	1.68620	0.843102	−	0.537754i	$-0.180727\pi$
$97$	16.6072	1.68620	0.843102	+	0.537754i	$0.180727\pi$
$98$	8.56661	0.865358
$99$	−13.8020	−1.38715
$100$	4.90052	0.490052
$101$	3.44522	0.342812	0.171406	−	0.985200i	$-0.445169\pi$
$101$	3.44522	0.342812	0.171406	+	0.985200i	$0.445169\pi$
$102$	2.52973	0.250481
$103$	−11.8504	−1.16765	−0.583826	−	0.811879i	$-0.698445\pi$
$103$	−11.8504	−1.16765	−0.583826	+	0.811879i	$0.698445\pi$
$104$	−4.62153	−0.453178
$105$	−10.0831	−0.984007
$106$	1.11408	0.108209
$107$	19.4469	1.88001	0.940004	−	0.341165i	$-0.110821\pi$
$107$	19.4469	1.88001	0.940004	+	0.341165i	$0.110821\pi$
$108$	−4.33745	−0.417371
$109$	−3.72383	−0.356678	−0.178339	−	0.983969i	$-0.557072\pi$
$109$	−3.72383	−0.356678	−0.178339	+	0.983969i	$0.557072\pi$
$110$	−18.5565	−1.76929
$111$	2.70482	0.256730
$112$	3.94545	0.372810
$113$	7.22535	0.679704	0.339852	−	0.940479i	$-0.389623\pi$
$113$	7.22535	0.679704	0.339852	+	0.940479i	$0.389623\pi$
$114$	−0.812207	−0.0760702
$115$	−1.76008	−0.164128
$116$	8.95968	0.831885
$117$	10.8159	0.999926
$118$	−6.80208	−0.626182
$119$	12.2886	1.12650
$120$	−2.55562	−0.233295
$121$	23.7803	2.16184
$122$	−3.69242	−0.334296
$123$	7.00320	0.631457
$124$	−1.19504	−0.107318
$125$	0.313001	0.0279957
$126$	−9.23362	−0.822596
$127$	3.04259	0.269986	0.134993	−	0.990847i	$-0.456899\pi$
$127$	3.04259	0.269986	0.134993	+	0.990847i	$0.456899\pi$
$128$	1.00000	0.0883883
$129$	−2.32850	−0.205013
$130$	14.5417	1.27539
$131$	16.8605	1.47311	0.736553	−	0.676380i	$-0.236452\pi$
$131$	16.8605	1.47311	0.736553	+	0.676380i	$0.236452\pi$
$132$	4.78998	0.416914
$133$	−3.94545	−0.342114
$134$	3.18287	0.274958
$135$	13.6478	1.17462
$136$	3.11463	0.267078
$137$	1.18765	0.101467	0.0507337	−	0.998712i	$-0.483844\pi$
$137$	1.18765	0.101467	0.0507337	+	0.998712i	$0.483844\pi$
$138$	0.454329	0.0386751
$139$	−9.50089	−0.805855	−0.402927	−	0.915232i	$-0.632007\pi$
$139$	−9.50089	−0.805855	−0.402927	+	0.915232i	$0.632007\pi$
$140$	−12.4144	−1.04921
$141$	−3.44478	−0.290103
$142$	6.64480	0.557619
$143$	−27.2554	−2.27921
$144$	−2.34032	−0.195027
$145$	−28.1917	−2.34119
$146$	−15.2776	−1.26438
$147$	6.95786	0.573875
$148$	3.33021	0.273742
$149$	2.16669	0.177502	0.0887509	−	0.996054i	$-0.471712\pi$
$149$	2.16669	0.177502	0.0887509	+	0.996054i	$0.471712\pi$
$150$	3.98024	0.324985
$151$	16.2337	1.32108	0.660539	−	0.750792i	$-0.270328\pi$
$151$	16.2337	1.32108	0.660539	+	0.750792i	$0.270328\pi$
$152$	−1.00000	−0.0811107
$153$	−7.28924	−0.589300
$154$	23.2682	1.87501
$155$	3.76022	0.302028
$156$	−3.75364	−0.300532
$157$	10.6839	0.852669	0.426334	−	0.904566i	$-0.359805\pi$
$157$	10.6839	0.852669	0.426334	+	0.904566i	$0.359805\pi$
$158$	12.6917	1.00969
$159$	0.904862	0.0717602
$160$	−3.14651	−0.248753
$161$	2.20699	0.173935
$162$	3.49805	0.274833
$163$	21.8376	1.71046	0.855228	−	0.518253i	$-0.173417\pi$
$163$	21.8376	1.71046	0.855228	+	0.518253i	$0.173417\pi$
$164$	8.62243	0.673298
$165$	−15.0717	−1.17333
$166$	1.11917	0.0868647
$167$	−11.7006	−0.905422	−0.452711	−	0.891657i	$-0.649543\pi$
$167$	−11.7006	−0.905422	−0.452711	+	0.891657i	$0.649543\pi$
$168$	3.20453	0.247235
$169$	8.35855	0.642965
$170$	−9.80023	−0.751643
$171$	2.34032	0.178969
$172$	−2.86688	−0.218597
$173$	2.59413	0.197228	0.0986139	−	0.995126i	$-0.468559\pi$
$173$	2.59413	0.197228	0.0986139	+	0.995126i	$0.468559\pi$
$174$	7.27712	0.551677
$175$	19.3348	1.46157
$176$	5.89748	0.444539
$177$	−5.52470	−0.415262
$178$	−13.6966	−1.02661
$179$	−15.2588	−1.14049	−0.570247	−	0.821473i	$-0.693153\pi$
$179$	−15.2588	−1.14049	−0.570247	+	0.821473i	$0.693153\pi$
$180$	7.36384	0.548868
$181$	14.3141	1.06396	0.531980	−	0.846757i	$-0.321448\pi$
$181$	14.3141	1.06396	0.531980	+	0.846757i	$0.321448\pi$
$182$	−18.2340	−1.35160
$183$	−2.99901	−0.221693
$184$	0.559376	0.0412377
$185$	−10.4785	−0.770398
$186$	−0.970624	−0.0711696
$187$	18.3685	1.34324
$188$	−4.24126	−0.309325
$189$	−17.1132	−1.24480
$190$	3.14651	0.228272
$191$	7.89097	0.570971	0.285485	−	0.958383i	$-0.407845\pi$
$191$	7.89097	0.570971	0.285485	+	0.958383i	$0.407845\pi$
$192$	0.812207	0.0586160
$193$	19.9714	1.43757	0.718786	−	0.695231i	$-0.244698\pi$
$193$	19.9714	1.43757	0.718786	+	0.695231i	$0.244698\pi$
$194$	16.6072	1.19233
$195$	11.8109	0.845794
$196$	8.56661	0.611900
$197$	0.798735	0.0569075	0.0284538	−	0.999595i	$-0.490942\pi$
$197$	0.798735	0.0569075	0.0284538	+	0.999595i	$0.490942\pi$
$198$	−13.8020	−0.980864
$199$	−5.31963	−0.377099	−0.188549	−	0.982064i	$-0.560379\pi$
$199$	−5.31963	−0.377099	−0.188549	+	0.982064i	$0.560379\pi$
$200$	4.90052	0.346519
$201$	2.58515	0.182342
$202$	3.44522	0.242405
$203$	35.3500	2.48108
$204$	2.52973	0.177116
$205$	−27.1305	−1.89488
$206$	−11.8504	−0.825654
$207$	−1.30912	−0.0909900
$208$	−4.62153	−0.320446
$209$	−5.89748	−0.407937
$210$	−10.0831	−0.695798
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	1.11408	0.0765152
$213$	5.39695	0.369793
$214$	19.4469	1.32937
$215$	9.02065	0.615203
$216$	−4.33745	−0.295126
$217$	−4.71499	−0.320075
$218$	−3.72383	−0.252210
$219$	−12.4086	−0.838493
$220$	−18.5565	−1.25108
$221$	−14.3944	−0.968271
$222$	2.70482	0.181536
$223$	−23.1914	−1.55301	−0.776504	−	0.630112i	$-0.783009\pi$
$223$	−23.1914	−1.55301	−0.776504	+	0.630112i	$0.783009\pi$
$224$	3.94545	0.263617
$225$	−11.4688	−0.764586
$226$	7.22535	0.480623
$227$	−19.1359	−1.27009	−0.635046	−	0.772474i	$-0.719019\pi$
$227$	−19.1359	−1.27009	−0.635046	+	0.772474i	$0.719019\pi$
$228$	−0.812207	−0.0537898
$229$	23.5799	1.55821	0.779103	−	0.626896i	$-0.215675\pi$
$229$	23.5799	1.55821	0.779103	+	0.626896i	$0.215675\pi$
$230$	−1.76008	−0.116056
$231$	18.8986	1.24344
$232$	8.95968	0.588232
$233$	−6.29734	−0.412552	−0.206276	−	0.978494i	$-0.566135\pi$
$233$	−6.29734	−0.412552	−0.206276	+	0.978494i	$0.566135\pi$
$234$	10.8159	0.707055
$235$	13.3452	0.870542
$236$	−6.80208	−0.442778
$237$	10.3083	0.669594
$238$	12.2886	0.796555
$239$	−0.815175	−0.0527293	−0.0263646	−	0.999652i	$-0.508393\pi$
$239$	−0.815175	−0.0527293	−0.0263646	+	0.999652i	$0.508393\pi$
$240$	−2.55562	−0.164964
$241$	9.18698	0.591785	0.295893	−	0.955221i	$-0.404383\pi$
$241$	9.18698	0.591785	0.295893	+	0.955221i	$0.404383\pi$
$242$	23.7803	1.52865
$243$	15.8535	1.01700
$244$	−3.69242	−0.236383
$245$	−26.9549	−1.72209
$246$	7.00320	0.446508
$247$	4.62153	0.294061
$248$	−1.19504	−0.0758854
$249$	0.909001	0.0576056
$250$	0.313001	0.0197959
$251$	15.4981	0.978229	0.489115	−	0.872220i	$-0.337320\pi$
$251$	15.4981	0.978229	0.489115	+	0.872220i	$0.337320\pi$
$252$	−9.23362	−0.581663
$253$	3.29891	0.207401
$254$	3.04259	0.190909
$255$	−7.95982	−0.498463
$256$	1.00000	0.0625000
$257$	−16.7457	−1.04457	−0.522285	−	0.852771i	$-0.674920\pi$
$257$	−16.7457	−1.04457	−0.522285	+	0.852771i	$0.674920\pi$
$258$	−2.32850	−0.144966
$259$	13.1392	0.816430
$260$	14.5417	0.901838
$261$	−20.9685	−1.29792
$262$	16.8605	1.04164
$263$	−17.4111	−1.07361	−0.536806	−	0.843706i	$-0.680369\pi$
$263$	−17.4111	−1.07361	−0.536806	+	0.843706i	$0.680369\pi$
$264$	4.78998	0.294803
$265$	−3.50546	−0.215339
$266$	−3.94545	−0.241911
$267$	−11.1245	−0.680808
$268$	3.18287	0.194425
$269$	−16.1930	−0.987304	−0.493652	−	0.869659i	$-0.664338\pi$
$269$	−16.1930	−0.987304	−0.493652	+	0.869659i	$0.664338\pi$
$270$	13.6478	0.830580
$271$	4.47244	0.271681	0.135841	−	0.990731i	$-0.456627\pi$
$271$	4.47244	0.271681	0.135841	+	0.990731i	$0.456627\pi$
$272$	3.11463	0.188852
$273$	−14.8098	−0.896331
$274$	1.18765	0.0717483
$275$	28.9007	1.74278
$276$	0.454329	0.0273474
$277$	−4.58297	−0.275364	−0.137682	−	0.990476i	$-0.543965\pi$
$277$	−4.58297	−0.275364	−0.137682	+	0.990476i	$0.543965\pi$
$278$	−9.50089	−0.569826
$279$	2.79679	0.167439
$280$	−12.4144	−0.741903
$281$	−20.3267	−1.21259	−0.606295	−	0.795240i	$-0.707345\pi$
$281$	−20.3267	−1.21259	−0.606295	+	0.795240i	$0.707345\pi$
$282$	−3.44478	−0.205134
$283$	25.2447	1.50064	0.750321	−	0.661073i	$-0.229899\pi$
$283$	25.2447	1.50064	0.750321	+	0.661073i	$0.229899\pi$
$284$	6.64480	0.394296
$285$	2.55562	0.151382
$286$	−27.2554	−1.61164
$287$	34.0194	2.00810
$288$	−2.34032	−0.137905
$289$	−7.29905	−0.429356
$290$	−28.1917	−1.65547
$291$	13.4885	0.790709
$292$	−15.2776	−0.894053
$293$	14.2089	0.830092	0.415046	−	0.909800i	$-0.363765\pi$
$293$	14.2089	0.830092	0.415046	+	0.909800i	$0.363765\pi$
$294$	6.95786	0.405791
$295$	21.4028	1.24612
$296$	3.33021	0.193565
$297$	−25.5800	−1.48430
$298$	2.16669	0.125513
$299$	−2.58517	−0.149504
$300$	3.98024	0.229799
$301$	−11.3111	−0.651962
$302$	16.2337	0.934143
$303$	2.79823	0.160754
$304$	−1.00000	−0.0573539
$305$	11.6182	0.665258
$306$	−7.28924	−0.416698
$307$	−14.1218	−0.805976	−0.402988	−	0.915205i	$-0.632028\pi$
$307$	−14.1218	−0.805976	−0.402988	+	0.915205i	$0.632028\pi$
$308$	23.2682	1.32583
$309$	−9.62495	−0.547545
$310$	3.76022	0.213566
$311$	−9.05280	−0.513337	−0.256669	−	0.966499i	$-0.582625\pi$
$311$	−9.05280	−0.513337	−0.256669	+	0.966499i	$0.582625\pi$
$312$	−3.75364	−0.212508
$313$	1.95804	0.110675	0.0553376	−	0.998468i	$-0.482377\pi$
$313$	1.95804	0.110675	0.0553376	+	0.998468i	$0.482377\pi$
$314$	10.6839	0.602928
$315$	29.0537	1.63699
$316$	12.6917	0.713962
$317$	−0.780453	−0.0438346	−0.0219173	−	0.999760i	$-0.506977\pi$
$317$	−0.780453	−0.0438346	−0.0219173	+	0.999760i	$0.506977\pi$
$318$	0.904862	0.0507422
$319$	52.8395	2.95844
$320$	−3.14651	−0.175895
$321$	15.7950	0.881588
$322$	2.20699	0.122991
$323$	−3.11463	−0.173303
$324$	3.49805	0.194336
$325$	−22.6479	−1.25628
$326$	21.8376	1.20947
$327$	−3.02452	−0.167257
$328$	8.62243	0.476094
$329$	−16.7337	−0.922558
$330$	−15.0717	−0.829670
$331$	−3.17065	−0.174275	−0.0871374	−	0.996196i	$-0.527772\pi$
$331$	−3.17065	−0.174275	−0.0871374	+	0.996196i	$0.527772\pi$
$332$	1.11917	0.0614226
$333$	−7.79376	−0.427095
$334$	−11.7006	−0.640230
$335$	−10.0149	−0.547174
$336$	3.20453	0.174821
$337$	19.5688	1.06598	0.532991	−	0.846121i	$-0.321068\pi$
$337$	19.5688	1.06598	0.532991	+	0.846121i	$0.321068\pi$
$338$	8.35855	0.454645
$339$	5.86849	0.318732
$340$	−9.80023	−0.531492
$341$	−7.04775	−0.381657
$342$	2.34032	0.126550
$343$	6.18097	0.333741
$344$	−2.86688	−0.154572
$345$	−1.42955	−0.0769645
$346$	2.59413	0.139461
$347$	31.1633	1.67293	0.836466	−	0.548018i	$-0.184618\pi$
$347$	31.1633	1.67293	0.836466	+	0.548018i	$0.184618\pi$
$348$	7.27712	0.390094
$349$	−24.7493	−1.32480	−0.662400	−	0.749151i	$-0.730462\pi$
$349$	−24.7493	−1.32480	−0.662400	+	0.749151i	$0.730462\pi$
$350$	19.3348	1.03349
$351$	20.0456	1.06996
$352$	5.89748	0.314337
$353$	−14.5900	−0.776545	−0.388273	−	0.921545i	$-0.626928\pi$
$353$	−14.5900	−0.776545	−0.388273	+	0.921545i	$0.626928\pi$
$354$	−5.52470	−0.293635
$355$	−20.9079	−1.10968
$356$	−13.6966	−0.725920
$357$	9.98093	0.528247
$358$	−15.2588	−0.806451
$359$	4.82792	0.254808	0.127404	−	0.991851i	$-0.459336\pi$
$359$	4.82792	0.254808	0.127404	+	0.991851i	$0.459336\pi$
$360$	7.36384	0.388108
$361$	1.00000	0.0526316
$362$	14.3141	0.752334
$363$	19.3145	1.01375
$364$	−18.2340	−0.955723
$365$	48.0711	2.51615
$366$	−2.99901	−0.156761
$367$	−8.71358	−0.454845	−0.227423	−	0.973796i	$-0.573030\pi$
$367$	−8.71358	−0.454845	−0.227423	+	0.973796i	$0.573030\pi$
$368$	0.559376	0.0291595
$369$	−20.1792	−1.05049
$370$	−10.4785	−0.544753
$371$	4.39554	0.228205
$372$	−0.970624	−0.0503245
$373$	−6.17229	−0.319589	−0.159795	−	0.987150i	$-0.551083\pi$
$373$	−6.17229	−0.319589	−0.159795	+	0.987150i	$0.551083\pi$
$374$	18.3685	0.949812
$375$	0.254222	0.0131280
$376$	−4.24126	−0.218726
$377$	−41.4074	−2.13259
$378$	−17.1132	−0.880208
$379$	−37.5017	−1.92633	−0.963167	−	0.268903i	$-0.913339\pi$
$379$	−37.5017	−1.92633	−0.963167	+	0.268903i	$0.913339\pi$
$380$	3.14651	0.161413
$381$	2.47121	0.126604
$382$	7.89097	0.403737
$383$	11.4930	0.587266	0.293633	−	0.955918i	$-0.405136\pi$
$383$	11.4930	0.587266	0.293633	+	0.955918i	$0.405136\pi$
$384$	0.812207	0.0414478
$385$	−73.2137	−3.73132
$386$	19.9714	1.01652
$387$	6.70940	0.341058
$388$	16.6072	0.843102
$389$	−14.2930	−0.724685	−0.362343	−	0.932045i	$-0.618023\pi$
$389$	−14.2930	−0.724685	−0.362343	+	0.932045i	$0.618023\pi$
$390$	11.8109	0.598067
$391$	1.74225	0.0881094
$392$	8.56661	0.432679
$393$	13.6942	0.690781
$394$	0.798735	0.0402397
$395$	−39.9345	−2.00932
$396$	−13.8020	−0.693576
$397$	14.3998	0.722703	0.361351	−	0.932430i	$-0.382315\pi$
$397$	14.3998	0.722703	0.361351	+	0.932430i	$0.382315\pi$
$398$	−5.31963	−0.266649
$399$	−3.20453	−0.160427
$400$	4.90052	0.245026
$401$	−17.5473	−0.876268	−0.438134	−	0.898910i	$-0.644360\pi$
$401$	−17.5473	−0.876268	−0.438134	+	0.898910i	$0.644360\pi$
$402$	2.58515	0.128936
$403$	5.52294	0.275117
$404$	3.44522	0.171406
$405$	−11.0067	−0.546925
$406$	35.3500	1.75439
$407$	19.6399	0.973511
$408$	2.52973	0.125240
$409$	−12.3746	−0.611886	−0.305943	−	0.952050i	$-0.598972\pi$
$409$	−12.3746	−0.611886	−0.305943	+	0.952050i	$0.598972\pi$
$410$	−27.1305	−1.33988
$411$	0.964614	0.0475809
$412$	−11.8504	−0.583826
$413$	−26.8373	−1.32058
$414$	−1.30912	−0.0643396
$415$	−3.52149	−0.172863
$416$	−4.62153	−0.226589
$417$	−7.71669	−0.377888
$418$	−5.89748	−0.288455
$419$	26.8159	1.31004	0.655020	−	0.755611i	$-0.272660\pi$
$419$	26.8159	1.31004	0.655020	+	0.755611i	$0.272660\pi$
$420$	−10.0831	−0.492004
$421$	−6.54181	−0.318829	−0.159414	−	0.987212i	$-0.550961\pi$
$421$	−6.54181	−0.318829	−0.159414	+	0.987212i	$0.550961\pi$
$422$	−1.00000	−0.0486792
$423$	9.92589	0.482613
$424$	1.11408	0.0541044
$425$	15.2633	0.740381
$426$	5.39695	0.261483
$427$	−14.5683	−0.705008
$428$	19.4469	0.940004
$429$	−22.1370	−1.06879
$430$	9.02065	0.435014
$431$	−4.02678	−0.193963	−0.0969817	−	0.995286i	$-0.530919\pi$
$431$	−4.02678	−0.193963	−0.0969817	+	0.995286i	$0.530919\pi$
$432$	−4.33745	−0.208686
$433$	33.6474	1.61699	0.808495	−	0.588503i	$-0.200283\pi$
$433$	33.6474	1.61699	0.808495	+	0.588503i	$0.200283\pi$
$434$	−4.71499	−0.226327
$435$	−22.8975	−1.09785
$436$	−3.72383	−0.178339
$437$	−0.559376	−0.0267586
$438$	−12.4086	−0.592904
$439$	4.84095	0.231046	0.115523	−	0.993305i	$-0.463146\pi$
$439$	4.84095	0.231046	0.115523	+	0.993305i	$0.463146\pi$
$440$	−18.5565	−0.884645
$441$	−20.0486	−0.954695
$442$	−14.3944	−0.684671
$443$	3.71385	0.176450	0.0882252	−	0.996101i	$-0.471880\pi$
$443$	3.71385	0.176450	0.0882252	+	0.996101i	$0.471880\pi$
$444$	2.70482	0.128365
$445$	43.0966	2.04297
$446$	−23.1914	−1.09814
$447$	1.75980	0.0832356
$448$	3.94545	0.186405
$449$	−16.0329	−0.756639	−0.378319	−	0.925675i	$-0.623498\pi$
$449$	−16.0329	−0.756639	−0.378319	+	0.925675i	$0.623498\pi$
$450$	−11.4688	−0.540644
$451$	50.8506	2.39446
$452$	7.22535	0.339852
$453$	13.1851	0.619490
$454$	−19.1359	−0.898091
$455$	57.3736	2.68971
$456$	−0.812207	−0.0380351
$457$	17.1488	0.802188	0.401094	−	0.916037i	$-0.368630\pi$
$457$	17.1488	0.802188	0.401094	+	0.916037i	$0.368630\pi$
$458$	23.5799	1.10182
$459$	−13.5096	−0.630572
$460$	−1.76008	−0.0820642
$461$	16.3876	0.763246	0.381623	−	0.924318i	$-0.375365\pi$
$461$	16.3876	0.763246	0.381623	+	0.924318i	$0.375365\pi$
$462$	18.8986	0.879244
$463$	13.4616	0.625613	0.312806	−	0.949817i	$-0.398731\pi$
$463$	13.4616	0.625613	0.312806	+	0.949817i	$0.398731\pi$
$464$	8.95968	0.415943
$465$	3.05408	0.141630
$466$	−6.29734	−0.291718
$467$	25.4096	1.17582	0.587909	−	0.808927i	$-0.299951\pi$
$467$	25.4096	1.17582	0.587909	+	0.808927i	$0.299951\pi$
$468$	10.8159	0.499963
$469$	12.5579	0.579868
$470$	13.3452	0.615566
$471$	8.67755	0.399840
$472$	−6.80208	−0.313091
$473$	−16.9073	−0.777400
$474$	10.3083	0.473474
$475$	−4.90052	−0.224851
$476$	12.2886	0.563249
$477$	−2.60730	−0.119380
$478$	−0.815175	−0.0372852
$479$	−33.7011	−1.53984	−0.769921	−	0.638139i	$-0.779704\pi$
$479$	−33.7011	−1.53984	−0.769921	+	0.638139i	$0.779704\pi$
$480$	−2.55562	−0.116648
$481$	−15.3907	−0.701754
$482$	9.18698	0.418455
$483$	1.79253	0.0815632
$484$	23.7803	1.08092
$485$	−52.2547	−2.37276
$486$	15.8535	0.719129
$487$	9.84622	0.446175	0.223087	−	0.974798i	$-0.428386\pi$
$487$	9.84622	0.446175	0.223087	+	0.974798i	$0.428386\pi$
$488$	−3.69242	−0.167148
$489$	17.7367	0.802081
$490$	−26.9549	−1.21770
$491$	−9.55041	−0.431004	−0.215502	−	0.976503i	$-0.569139\pi$
$491$	−9.55041	−0.431004	−0.215502	+	0.976503i	$0.569139\pi$
$492$	7.00320	0.315729
$493$	27.9061	1.25683
$494$	4.62153	0.207933
$495$	43.4281	1.95195
$496$	−1.19504	−0.0536591
$497$	26.2167	1.17598
$498$	0.909001	0.0407333
$499$	31.4100	1.40610	0.703052	−	0.711138i	$-0.251820\pi$
$499$	31.4100	1.40610	0.703052	+	0.711138i	$0.251820\pi$
$500$	0.313001	0.0139978
$501$	−9.50333	−0.424578
$502$	15.4981	0.691713
$503$	9.42508	0.420243	0.210122	−	0.977675i	$-0.432614\pi$
$503$	9.42508	0.420243	0.210122	+	0.977675i	$0.432614\pi$
$504$	−9.23362	−0.411298
$505$	−10.8404	−0.482392
$506$	3.29891	0.146654
$507$	6.78888	0.301505
$508$	3.04259	0.134993
$509$	29.5443	1.30953	0.654763	−	0.755834i	$-0.272768\pi$
$509$	29.5443	1.30953	0.654763	+	0.755834i	$0.272768\pi$
$510$	−7.95982	−0.352467
$511$	−60.2770	−2.66650
$512$	1.00000	0.0441942
$513$	4.33745	0.191503
$514$	−16.7457	−0.738623
$515$	37.2873	1.64307
$516$	−2.32850	−0.102506
$517$	−25.0127	−1.10006
$518$	13.1392	0.577303
$519$	2.10697	0.0924856
$520$	14.5417	0.637695
$521$	35.0836	1.53704	0.768519	−	0.639827i	$-0.220994\pi$
$521$	35.0836	1.53704	0.768519	+	0.639827i	$0.220994\pi$
$522$	−20.9685	−0.917766
$523$	19.2723	0.842717	0.421359	−	0.906894i	$-0.361553\pi$
$523$	19.2723	0.842717	0.421359	+	0.906894i	$0.361553\pi$
$524$	16.8605	0.736553
$525$	15.7039	0.685373
$526$	−17.4111	−0.759158
$527$	−3.72213	−0.162138
$528$	4.78998	0.208457
$529$	−22.6871	−0.986396
$530$	−3.50546	−0.152267
$531$	15.9190	0.690828
$532$	−3.94545	−0.171057
$533$	−39.8488	−1.72604
$534$	−11.1245	−0.481404
$535$	−61.1900	−2.64547
$536$	3.18287	0.137479
$537$	−12.3933	−0.534810
$538$	−16.1930	−0.698130
$539$	50.5214	2.17611
$540$	13.6478	0.587309
$541$	18.2705	0.785512	0.392756	−	0.919643i	$-0.371522\pi$
$541$	18.2705	0.785512	0.392756	+	0.919643i	$0.371522\pi$
$542$	4.47244	0.192108
$543$	11.6260	0.498921
$544$	3.11463	0.133539
$545$	11.7171	0.501904
$546$	−14.8098	−0.633802
$547$	24.4578	1.04574	0.522870	−	0.852412i	$-0.324861\pi$
$547$	24.4578	1.04574	0.522870	+	0.852412i	$0.324861\pi$
$548$	1.18765	0.0507337
$549$	8.64144	0.368808
$550$	28.9007	1.23233
$551$	−8.95968	−0.381695
$552$	0.454329	0.0193375
$553$	50.0744	2.12938
$554$	−4.58297	−0.194712
$555$	−8.51075	−0.361261
$556$	−9.50089	−0.402927
$557$	−27.4498	−1.16309	−0.581543	−	0.813516i	$-0.697551\pi$
$557$	−27.4498	−1.16309	−0.581543	+	0.813516i	$0.697551\pi$
$558$	2.79679	0.118397
$559$	13.2494	0.560388
$560$	−12.4144	−0.524605
$561$	14.9190	0.629882
$562$	−20.3267	−0.857430
$563$	4.71875	0.198872	0.0994358	−	0.995044i	$-0.468296\pi$
$563$	4.71875	0.198872	0.0994358	+	0.995044i	$0.468296\pi$
$564$	−3.44478	−0.145051
$565$	−22.7346	−0.956454
$566$	25.2447	1.06111
$567$	13.8014	0.579604
$568$	6.64480	0.278809
$569$	−36.7845	−1.54209	−0.771044	−	0.636782i	$-0.780265\pi$
$569$	−36.7845	−1.54209	−0.771044	+	0.636782i	$0.780265\pi$
$570$	2.55562	0.107043
$571$	−16.9116	−0.707727	−0.353864	−	0.935297i	$-0.615132\pi$
$571$	−16.9116	−0.707727	−0.353864	+	0.935297i	$0.615132\pi$
$572$	−27.2554	−1.13960
$573$	6.40911	0.267744
$574$	34.0194	1.41994
$575$	2.74123	0.114317
$576$	−2.34032	−0.0975133
$577$	16.4856	0.686305	0.343153	−	0.939280i	$-0.388505\pi$
$577$	16.4856	0.686305	0.343153	+	0.939280i	$0.388505\pi$
$578$	−7.29905	−0.303600
$579$	16.2209	0.674118
$580$	−28.1917	−1.17060
$581$	4.41565	0.183192
$582$	13.4885	0.559115
$583$	6.57025	0.272112
$584$	−15.2776	−0.632191
$585$	−34.0322	−1.40706
$586$	14.2089	0.586964
$587$	24.8689	1.02645	0.513224	−	0.858255i	$-0.328451\pi$
$587$	24.8689	1.02645	0.513224	+	0.858255i	$0.328451\pi$
$588$	6.95786	0.286937
$589$	1.19504	0.0492410
$590$	21.4028	0.881140
$591$	0.648739	0.0266855
$592$	3.33021	0.136871
$593$	42.1903	1.73255	0.866273	−	0.499571i	$-0.166509\pi$
$593$	42.1903	1.73255	0.866273	+	0.499571i	$0.166509\pi$
$594$	−25.5800	−1.04956
$595$	−38.6664	−1.58517
$596$	2.16669	0.0887509
$597$	−4.32065	−0.176832
$598$	−2.58517	−0.105716
$599$	−48.2496	−1.97143	−0.985713	−	0.168434i	$-0.946129\pi$
$599$	−48.2496	−1.97143	−0.985713	+	0.168434i	$0.946129\pi$
$600$	3.98024	0.162493
$601$	−11.8156	−0.481970	−0.240985	−	0.970529i	$-0.577470\pi$
$601$	−11.8156	−0.481970	−0.240985	+	0.970529i	$0.577470\pi$
$602$	−11.3111	−0.461007
$603$	−7.44893	−0.303344
$604$	16.2337	0.660539
$605$	−74.8248	−3.04206
$606$	2.79823	0.113670
$607$	−6.07064	−0.246400	−0.123200	−	0.992382i	$-0.539316\pi$
$607$	−6.07064	−0.246400	−0.123200	+	0.992382i	$0.539316\pi$
$608$	−1.00000	−0.0405554
$609$	28.7115	1.16345
$610$	11.6182	0.470408
$611$	19.6011	0.792976
$612$	−7.28924	−0.294650
$613$	−22.5825	−0.912100	−0.456050	−	0.889954i	$-0.650736\pi$
$613$	−22.5825	−0.912100	−0.456050	+	0.889954i	$0.650736\pi$
$614$	−14.1218	−0.569911
$615$	−22.0356	−0.888562
$616$	23.2682	0.937504
$617$	−2.58456	−0.104051	−0.0520253	−	0.998646i	$-0.516568\pi$
$617$	−2.58456	−0.104051	−0.0520253	+	0.998646i	$0.516568\pi$
$618$	−9.62495	−0.387172
$619$	16.2317	0.652407	0.326203	−	0.945300i	$-0.394231\pi$
$619$	16.2317	0.652407	0.326203	+	0.945300i	$0.394231\pi$
$620$	3.76022	0.151014
$621$	−2.42626	−0.0973626
$622$	−9.05280	−0.362984
$623$	−54.0394	−2.16504
$624$	−3.75364	−0.150266
$625$	−25.4875	−1.01950
$626$	1.95804	0.0782591
$627$	−4.78998	−0.191293
$628$	10.6839	0.426334
$629$	10.3724	0.413574
$630$	29.0537	1.15753
$631$	−24.2910	−0.967011	−0.483505	−	0.875341i	$-0.660637\pi$
$631$	−24.2910	−0.967011	−0.483505	+	0.875341i	$0.660637\pi$
$632$	12.6917	0.504847
$633$	−0.812207	−0.0322823
$634$	−0.780453	−0.0309958
$635$	−9.57354	−0.379914
$636$	0.904862	0.0358801
$637$	−39.5908	−1.56865
$638$	52.8395	2.09194
$639$	−15.5509	−0.615186
$640$	−3.14651	−0.124377
$641$	7.34521	0.290118	0.145059	−	0.989423i	$-0.453663\pi$
$641$	7.34521	0.290118	0.145059	+	0.989423i	$0.453663\pi$
$642$	15.7950	0.623377
$643$	−5.80170	−0.228797	−0.114398	−	0.993435i	$-0.536494\pi$
$643$	−5.80170	−0.228797	−0.114398	+	0.993435i	$0.536494\pi$
$644$	2.20699	0.0869676
$645$	7.32664	0.288486
$646$	−3.11463	−0.122544
$647$	23.3641	0.918536	0.459268	−	0.888298i	$-0.348112\pi$
$647$	23.3641	0.918536	0.459268	+	0.888298i	$0.348112\pi$
$648$	3.49805	0.137416
$649$	−40.1151	−1.57466
$650$	−22.6479	−0.888325
$651$	−3.82955	−0.150092
$652$	21.8376	0.855228
$653$	−28.5132	−1.11581	−0.557904	−	0.829905i	$-0.688394\pi$
$653$	−28.5132	−1.11581	−0.557904	+	0.829905i	$0.688394\pi$
$654$	−3.02452	−0.118268
$655$	−53.0517	−2.07290
$656$	8.62243	0.336649
$657$	35.7544	1.39491
$658$	−16.7337	−0.652347
$659$	19.8444	0.773028	0.386514	−	0.922284i	$-0.373679\pi$
$659$	19.8444	0.773028	0.386514	+	0.922284i	$0.373679\pi$
$660$	−15.0717	−0.586665
$661$	−22.3700	−0.870093	−0.435047	−	0.900408i	$-0.643268\pi$
$661$	−22.3700	−0.870093	−0.435047	+	0.900408i	$0.643268\pi$
$662$	−3.17065	−0.123231
$663$	−11.6912	−0.454049
$664$	1.11917	0.0434323
$665$	12.4144	0.481410
$666$	−7.79376	−0.302002
$667$	5.01183	0.194059
$668$	−11.7006	−0.452711
$669$	−18.8362	−0.728249
$670$	−10.0149	−0.386911
$671$	−21.7760	−0.840652
$672$	3.20453	0.123617
$673$	43.8604	1.69069	0.845347	−	0.534217i	$-0.179394\pi$
$673$	43.8604	1.69069	0.845347	+	0.534217i	$0.179394\pi$
$674$	19.5688	0.753763
$675$	−21.2558	−0.818135
$676$	8.35855	0.321483
$677$	−38.0383	−1.46193	−0.730966	−	0.682414i	$-0.760930\pi$
$677$	−38.0383	−1.46193	−0.730966	+	0.682414i	$0.760930\pi$
$678$	5.86849	0.225378
$679$	65.5229	2.51454
$680$	−9.80023	−0.375822
$681$	−15.5423	−0.595582
$682$	−7.04775	−0.269872
$683$	−8.45706	−0.323601	−0.161800	−	0.986824i	$-0.551730\pi$
$683$	−8.45706	−0.323601	−0.161800	+	0.986824i	$0.551730\pi$
$684$	2.34032	0.0894843
$685$	−3.73694	−0.142781
$686$	6.18097	0.235991
$687$	19.1518	0.730687
$688$	−2.86688	−0.109299
$689$	−5.14875	−0.196152
$690$	−1.42955	−0.0544221
$691$	−50.1186	−1.90660	−0.953301	−	0.302022i	$-0.902338\pi$
$691$	−50.1186	−1.90660	−0.953301	+	0.302022i	$0.902338\pi$
$692$	2.59413	0.0986139
$693$	−54.4551	−2.06858
$694$	31.1633	1.18294
$695$	29.8946	1.13397
$696$	7.27712	0.275838
$697$	26.8557	1.01723
$698$	−24.7493	−0.936774
$699$	−5.11474	−0.193457
$700$	19.3348	0.730786
$701$	20.0190	0.756106	0.378053	−	0.925784i	$-0.376594\pi$
$701$	20.0190	0.756106	0.378053	+	0.925784i	$0.376594\pi$
$702$	20.0456	0.756574
$703$	−3.33021	−0.125601
$704$	5.89748	0.222270
$705$	10.8390	0.408222
$706$	−14.5900	−0.549100
$707$	13.5929	0.511215
$708$	−5.52470	−0.207631
$709$	−21.4863	−0.806936	−0.403468	−	0.914994i	$-0.632195\pi$
$709$	−21.4863	−0.806936	−0.403468	+	0.914994i	$0.632195\pi$
$710$	−20.9079	−0.784660
$711$	−29.7025	−1.11393
$712$	−13.6966	−0.513303
$713$	−0.668479	−0.0250347
$714$	9.98093	0.373527
$715$	85.7593	3.20722
$716$	−15.2588	−0.570247
$717$	−0.662091	−0.0247263
$718$	4.82792	0.180176
$719$	−38.0383	−1.41859	−0.709294	−	0.704912i	$-0.750986\pi$
$719$	−38.0383	−1.41859	−0.709294	+	0.704912i	$0.750986\pi$
$720$	7.36384	0.274434
$721$	−46.7551	−1.74125
$722$	1.00000	0.0372161
$723$	7.46173	0.277505
$724$	14.3141	0.531980
$725$	43.9071	1.63067
$726$	19.3145	0.716829
$727$	19.3867	0.719011	0.359506	−	0.933143i	$-0.382945\pi$
$727$	19.3867	0.719011	0.359506	+	0.933143i	$0.382945\pi$
$728$	−18.2340	−0.675798
$729$	2.38216	0.0882283
$730$	48.0711	1.77919
$731$	−8.92927	−0.330261
$732$	−2.99901	−0.110847
$733$	−23.3522	−0.862534	−0.431267	−	0.902224i	$-0.641933\pi$
$733$	−23.3522	−0.862534	−0.431267	+	0.902224i	$0.641933\pi$
$734$	−8.71358	−0.321624
$735$	−21.8930	−0.807535
$736$	0.559376	0.0206189
$737$	18.7709	0.691435
$738$	−20.1792	−0.742808
$739$	−0.427399	−0.0157221	−0.00786106	−	0.999969i	$-0.502502\pi$
$739$	−0.427399	−0.0157221	−0.00786106	+	0.999969i	$0.502502\pi$
$740$	−10.4785	−0.385199
$741$	3.75364	0.137893
$742$	4.39554	0.161365
$743$	−30.9128	−1.13408	−0.567040	−	0.823690i	$-0.691911\pi$
$743$	−30.9128	−1.13408	−0.567040	+	0.823690i	$0.691911\pi$
$744$	−0.970624	−0.0355848
$745$	−6.81750	−0.249774
$746$	−6.17229	−0.225984
$747$	−2.61922	−0.0958323
$748$	18.3685	0.671619
$749$	76.7270	2.80354
$750$	0.254222	0.00928287
$751$	5.68644	0.207501	0.103751	−	0.994603i	$-0.466916\pi$
$751$	5.68644	0.207501	0.103751	+	0.994603i	$0.466916\pi$
$752$	−4.24126	−0.154663
$753$	12.5876	0.458719
$754$	−41.4074	−1.50797
$755$	−51.0794	−1.85897
$756$	−17.1132	−0.622401
$757$	−10.6809	−0.388202	−0.194101	−	0.980982i	$-0.562179\pi$
$757$	−10.6809	−0.388202	−0.194101	+	0.980982i	$0.562179\pi$
$758$	−37.5017	−1.36212
$759$	2.67940	0.0972559
$760$	3.14651	0.114136
$761$	−21.6377	−0.784366	−0.392183	−	0.919887i	$-0.628280\pi$
$761$	−21.6377	−0.784366	−0.392183	+	0.919887i	$0.628280\pi$
$762$	2.47121	0.0895226
$763$	−14.6922	−0.531894
$764$	7.89097	0.285485
$765$	22.9357	0.829241
$766$	11.4930	0.415260
$767$	31.4360	1.13509
$768$	0.812207	0.0293080
$769$	7.82956	0.282341	0.141171	−	0.989985i	$-0.454913\pi$
$769$	7.82956	0.282341	0.141171	+	0.989985i	$0.454913\pi$
$770$	−73.2137	−2.63844
$771$	−13.6010	−0.489828
$772$	19.9714	0.718786
$773$	11.2605	0.405014	0.202507	−	0.979281i	$-0.435091\pi$
$773$	11.2605	0.405014	0.202507	+	0.979281i	$0.435091\pi$
$774$	6.70940	0.241165
$775$	−5.85635	−0.210366
$776$	16.6072	0.596163
$777$	10.6718	0.382847
$778$	−14.2930	−0.512430
$779$	−8.62243	−0.308930
$780$	11.8109	0.422897
$781$	39.1875	1.40224
$782$	1.74225	0.0623028
$783$	−38.8621	−1.38882
$784$	8.56661	0.305950
$785$	−33.6170	−1.19984
$786$	13.6942	0.488456
$787$	31.2740	1.11480	0.557400	−	0.830244i	$-0.311799\pi$
$787$	31.2740	1.11480	0.557400	+	0.830244i	$0.311799\pi$
$788$	0.798735	0.0284538
$789$	−14.1414	−0.503447
$790$	−39.9345	−1.42080
$791$	28.5073	1.01360
$792$	−13.8020	−0.490432
$793$	17.0646	0.605983
$794$	14.3998	0.511028
$795$	−2.84716	−0.100978
$796$	−5.31963	−0.188549
$797$	11.7052	0.414618	0.207309	−	0.978275i	$-0.433529\pi$
$797$	11.7052	0.414618	0.207309	+	0.978275i	$0.433529\pi$
$798$	−3.20453	−0.113439
$799$	−13.2100	−0.467335
$800$	4.90052	0.173260
$801$	32.0545	1.13259
$802$	−17.5473	−0.619615
$803$	−90.0992	−3.17953
$804$	2.58515	0.0911712
$805$	−6.94432	−0.244755
$806$	5.52294	0.194537
$807$	−13.1521	−0.462975
$808$	3.44522	0.121202
$809$	−51.2450	−1.80168	−0.900839	−	0.434153i	$-0.857048\pi$
$809$	−51.2450	−1.80168	−0.900839	+	0.434153i	$0.857048\pi$
$810$	−11.0067	−0.386734
$811$	−30.9468	−1.08669	−0.543344	−	0.839510i	$-0.682842\pi$
$811$	−30.9468	−1.08669	−0.543344	+	0.839510i	$0.682842\pi$
$812$	35.3500	1.24054
$813$	3.63255	0.127399
$814$	19.6399	0.688376
$815$	−68.7123	−2.40689
$816$	2.52973	0.0885582
$817$	2.86688	0.100299
$818$	−12.3746	−0.432669
$819$	42.6735	1.49113
$820$	−27.1305	−0.947440
$821$	−6.81092	−0.237703	−0.118851	−	0.992912i	$-0.537921\pi$
$821$	−6.81092	−0.237703	−0.118851	+	0.992912i	$0.537921\pi$
$822$	0.964614	0.0336448
$823$	−11.9737	−0.417378	−0.208689	−	0.977982i	$-0.566920\pi$
$823$	−11.9737	−0.417378	−0.208689	+	0.977982i	$0.566920\pi$
$824$	−11.8504	−0.412827
$825$	23.4734	0.817239
$826$	−26.8373	−0.933789
$827$	−10.8219	−0.376313	−0.188156	−	0.982139i	$-0.560251\pi$
$827$	−10.8219	−0.376313	−0.188156	+	0.982139i	$0.560251\pi$
$828$	−1.30912	−0.0454950
$829$	−27.1443	−0.942760	−0.471380	−	0.881930i	$-0.656244\pi$
$829$	−27.1443	−0.942760	−0.471380	+	0.881930i	$0.656244\pi$
$830$	−3.52149	−0.122233
$831$	−3.72232	−0.129126
$832$	−4.62153	−0.160223
$833$	26.6818	0.924471
$834$	−7.71669	−0.267207
$835$	36.8161	1.27407
$836$	−5.89748	−0.203969
$837$	5.18344	0.179166
$838$	26.8159	0.926339
$839$	−34.4711	−1.19007	−0.595037	−	0.803698i	$-0.702863\pi$
$839$	−34.4711	−1.19007	−0.595037	+	0.803698i	$0.702863\pi$
$840$	−10.0831	−0.347899
$841$	51.2758	1.76813
$842$	−6.54181	−0.225446
$843$	−16.5095	−0.568617
$844$	−1.00000	−0.0344214
$845$	−26.3003	−0.904757
$846$	9.92589	0.341259
$847$	93.8239	3.22383
$848$	1.11408	0.0382576
$849$	20.5039	0.703694
$850$	15.2633	0.523528
$851$	1.86284	0.0638573
$852$	5.39695	0.184897
$853$	32.5120	1.11319	0.556595	−	0.830784i	$-0.312108\pi$
$853$	32.5120	1.11319	0.556595	+	0.830784i	$0.312108\pi$
$854$	−14.5683	−0.498516
$855$	−7.36384	−0.251838
$856$	19.4469	0.664683
$857$	5.35612	0.182962	0.0914808	−	0.995807i	$-0.470840\pi$
$857$	5.35612	0.182962	0.0914808	+	0.995807i	$0.470840\pi$
$858$	−22.1370	−0.755746
$859$	32.4522	1.10726	0.553628	−	0.832764i	$-0.313243\pi$
$859$	32.4522	1.10726	0.553628	+	0.832764i	$0.313243\pi$
$860$	9.02065	0.307602
$861$	27.6308	0.941655
$862$	−4.02678	−0.137153
$863$	−48.4612	−1.64964	−0.824818	−	0.565398i	$-0.808723\pi$
$863$	−48.4612	−1.64964	−0.824818	+	0.565398i	$0.808723\pi$
$864$	−4.33745	−0.147563
$865$	−8.16244	−0.277531
$866$	33.6474	1.14338
$867$	−5.92834	−0.201337
$868$	−4.71499	−0.160037
$869$	74.8488	2.53907
$870$	−22.8975	−0.776299
$871$	−14.7097	−0.498420
$872$	−3.72383	−0.126105
$873$	−38.8661	−1.31542
$874$	−0.559376	−0.0189212
$875$	1.23493	0.0417483
$876$	−12.4086	−0.419247
$877$	0.0515418	0.00174044	0.000870222	−	1.00000i	$-0.499723\pi$
$877$	0.0515418	0.00174044	0.000870222		1.00000i	$0.499723\pi$
$878$	4.84095	0.163374
$879$	11.5406	0.389254
$880$	−18.5565	−0.625539
$881$	44.3994	1.49585	0.747926	−	0.663782i	$-0.231050\pi$
$881$	44.3994	1.49585	0.747926	+	0.663782i	$0.231050\pi$
$882$	−20.0486	−0.675071
$883$	−4.54483	−0.152946	−0.0764729	−	0.997072i	$-0.524366\pi$
$883$	−4.54483	−0.152946	−0.0764729	+	0.997072i	$0.524366\pi$
$884$	−14.3944	−0.484135
$885$	17.3835	0.584341
$886$	3.71385	0.124769
$887$	11.2531	0.377842	0.188921	−	0.981992i	$-0.439501\pi$
$887$	11.2531	0.377842	0.188921	+	0.981992i	$0.439501\pi$
$888$	2.70482	0.0907679
$889$	12.0044	0.402615
$890$	43.0966	1.44460
$891$	20.6297	0.691120
$892$	−23.1914	−0.776504
$893$	4.24126	0.141928
$894$	1.75980	0.0588565
$895$	48.0119	1.60486
$896$	3.94545	0.131808
$897$	−2.09970	−0.0701068
$898$	−16.0329	−0.535024
$899$	−10.7072	−0.357106
$900$	−11.4688	−0.382293
$901$	3.46995	0.115601
$902$	50.8506	1.69314
$903$	−9.18698	−0.305724
$904$	7.22535	0.240312
$905$	−45.0395	−1.49717
$906$	13.1851	0.438046
$907$	−39.8484	−1.32314	−0.661572	−	0.749882i	$-0.730110\pi$
$907$	−39.8484	−1.32314	−0.661572	+	0.749882i	$0.730110\pi$
$908$	−19.1359	−0.635046
$909$	−8.06291	−0.267430
$910$	57.3736	1.90192
$911$	19.5553	0.647897	0.323948	−	0.946075i	$-0.394990\pi$
$911$	19.5553	0.647897	0.323948	+	0.946075i	$0.394990\pi$
$912$	−0.812207	−0.0268949
$913$	6.60030	0.218438
$914$	17.1488	0.567232
$915$	9.43641	0.311958
$916$	23.5799	0.779103
$917$	66.5222	2.19676
$918$	−13.5096	−0.445882
$919$	−17.6205	−0.581247	−0.290624	−	0.956837i	$-0.593863\pi$
$919$	−17.6205	−0.581247	−0.290624	+	0.956837i	$0.593863\pi$
$920$	−1.76008	−0.0580282
$921$	−11.4699	−0.377945
$922$	16.3876	0.539696
$923$	−30.7091	−1.01080
$924$	18.8986	0.621719
$925$	16.3198	0.536591
$926$	13.4616	0.442375
$927$	27.7336	0.910892
$928$	8.95968	0.294116
$929$	−12.2833	−0.403004	−0.201502	−	0.979488i	$-0.564582\pi$
$929$	−12.2833	−0.403004	−0.201502	+	0.979488i	$0.564582\pi$
$930$	3.05408	0.100147
$931$	−8.56661	−0.280759
$932$	−6.29734	−0.206276
$933$	−7.35275	−0.240718
$934$	25.4096	0.831429
$935$	−57.7966	−1.89015
$936$	10.8159	0.353527
$937$	−30.3169	−0.990411	−0.495205	−	0.868776i	$-0.664907\pi$
$937$	−30.3169	−0.990411	−0.495205	+	0.868776i	$0.664907\pi$
$938$	12.5579	0.410029
$939$	1.59034	0.0518987
$940$	13.3452	0.435271
$941$	−56.2444	−1.83351	−0.916757	−	0.399446i	$-0.869203\pi$
$941$	−56.2444	−1.83351	−0.916757	+	0.399446i	$0.869203\pi$
$942$	8.67755	0.282730
$943$	4.82318	0.157064
$944$	−6.80208	−0.221389
$945$	53.8468	1.75164
$946$	−16.9073	−0.549705
$947$	−36.0674	−1.17203	−0.586016	−	0.810299i	$-0.699304\pi$
$947$	−36.0674	−1.17203	−0.586016	+	0.810299i	$0.699304\pi$
$948$	10.3083	0.334797
$949$	70.6058	2.29196
$950$	−4.90052	−0.158994
$951$	−0.633890	−0.0205553
$952$	12.2886	0.398277
$953$	−35.1866	−1.13980	−0.569902	−	0.821712i	$-0.693019\pi$
$953$	−35.1866	−1.13980	−0.569902	+	0.821712i	$0.693019\pi$
$954$	−2.60730	−0.0844144
$955$	−24.8290	−0.803448
$956$	−0.815175	−0.0263646
$957$	42.9166	1.38730
$958$	−33.7011	−1.08883
$959$	4.68580	0.151312
$960$	−2.55562	−0.0824822
$961$	−29.5719	−0.953931
$962$	−15.3907	−0.496215
$963$	−45.5121	−1.46661
$964$	9.18698	0.295893
$965$	−62.8402	−2.02290
$966$	1.79253	0.0576739
$967$	−18.9908	−0.610704	−0.305352	−	0.952240i	$-0.598774\pi$
$967$	−18.9908	−0.610704	−0.305352	+	0.952240i	$0.598774\pi$
$968$	23.7803	0.764327
$969$	−2.52973	−0.0812666
$970$	−52.2547	−1.67780
$971$	−5.58847	−0.179342	−0.0896712	−	0.995971i	$-0.528582\pi$
$971$	−5.58847	−0.179342	−0.0896712	+	0.995971i	$0.528582\pi$
$972$	15.8535	0.508501
$973$	−37.4853	−1.20172
$974$	9.84622	0.315493
$975$	−18.3948	−0.589106
$976$	−3.69242	−0.118191
$977$	−33.9132	−1.08498	−0.542490	−	0.840062i	$-0.682518\pi$
$977$	−33.9132	−1.08498	−0.542490	+	0.840062i	$0.682518\pi$
$978$	17.7367	0.567157
$979$	−80.7756	−2.58160
$980$	−26.9549	−0.861043
$981$	8.71495	0.278247
$982$	−9.55041	−0.304766
$983$	27.5084	0.877382	0.438691	−	0.898638i	$-0.355442\pi$
$983$	27.5084	0.877382	0.438691	+	0.898638i	$0.355442\pi$
$984$	7.00320	0.223254
$985$	−2.51323	−0.0800781
$986$	27.9061	0.888712
$987$	−13.5912	−0.432613
$988$	4.62153	0.147030
$989$	−1.60366	−0.0509934
$990$	43.4281	1.38023
$991$	16.4277	0.521843	0.260922	−	0.965360i	$-0.415974\pi$
$991$	16.4277	0.521843	0.260922	+	0.965360i	$0.415974\pi$
$992$	−1.19504	−0.0379427
$993$	−2.57523	−0.0817224
$994$	26.2167	0.831544
$995$	16.7383	0.530639
$996$	0.909001	0.0288028
$997$	11.7426	0.371892	0.185946	−	0.982560i	$-0.440465\pi$
$997$	11.7426	0.371892	0.185946	+	0.982560i	$0.440465\pi$
$998$	31.4100	0.994266
$999$	−14.4446	−0.457007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.28	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.28	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.812207 q^{3} +1.00000 q^{4} -3.14651 q^{5} +0.812207 q^{6} +3.94545 q^{7} +1.00000 q^{8} -2.34032 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.812207 q^{3} +1.00000 q^{4} -3.14651 q^{5} +0.812207 q^{6} +3.94545 q^{7} +1.00000 q^{8} -2.34032 q^{9} -3.14651 q^{10} +5.89748 q^{11} +0.812207 q^{12} -4.62153 q^{13} +3.94545 q^{14} -2.55562 q^{15} +1.00000 q^{16} +3.11463 q^{17} -2.34032 q^{18} -1.00000 q^{19} -3.14651 q^{20} +3.20453 q^{21} +5.89748 q^{22} +0.559376 q^{23} +0.812207 q^{24} +4.90052 q^{25} -4.62153 q^{26} -4.33745 q^{27} +3.94545 q^{28} +8.95968 q^{29} -2.55562 q^{30} -1.19504 q^{31} +1.00000 q^{32} +4.78998 q^{33} +3.11463 q^{34} -12.4144 q^{35} -2.34032 q^{36} +3.33021 q^{37} -1.00000 q^{38} -3.75364 q^{39} -3.14651 q^{40} +8.62243 q^{41} +3.20453 q^{42} -2.86688 q^{43} +5.89748 q^{44} +7.36384 q^{45} +0.559376 q^{46} -4.24126 q^{47} +0.812207 q^{48} +8.56661 q^{49} +4.90052 q^{50} +2.52973 q^{51} -4.62153 q^{52} +1.11408 q^{53} -4.33745 q^{54} -18.5565 q^{55} +3.94545 q^{56} -0.812207 q^{57} +8.95968 q^{58} -6.80208 q^{59} -2.55562 q^{60} -3.69242 q^{61} -1.19504 q^{62} -9.23362 q^{63} +1.00000 q^{64} +14.5417 q^{65} +4.78998 q^{66} +3.18287 q^{67} +3.11463 q^{68} +0.454329 q^{69} -12.4144 q^{70} +6.64480 q^{71} -2.34032 q^{72} -15.2776 q^{73} +3.33021 q^{74} +3.98024 q^{75} -1.00000 q^{76} +23.2682 q^{77} -3.75364 q^{78} +12.6917 q^{79} -3.14651 q^{80} +3.49805 q^{81} +8.62243 q^{82} +1.11917 q^{83} +3.20453 q^{84} -9.80023 q^{85} -2.86688 q^{86} +7.27712 q^{87} +5.89748 q^{88} -13.6966 q^{89} +7.36384 q^{90} -18.2340 q^{91} +0.559376 q^{92} -0.970624 q^{93} -4.24126 q^{94} +3.14651 q^{95} +0.812207 q^{96} +16.6072 q^{97} +8.56661 q^{98} -13.8020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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