LMFDB - Embedded newform 8043.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62597 q^{2} +1.00000 q^{3} +4.89573 q^{4} -3.97585 q^{5} -2.62597 q^{6} -1.00000 q^{7} -7.60410 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62597 q^{2} +1.00000 q^{3} +4.89573 q^{4} -3.97585 q^{5} -2.62597 q^{6} -1.00000 q^{7} -7.60410 q^{8} +1.00000 q^{9} +10.4405 q^{10} +3.07295 q^{11} +4.89573 q^{12} -5.58232 q^{13} +2.62597 q^{14} -3.97585 q^{15} +10.1767 q^{16} -3.53245 q^{17} -2.62597 q^{18} +4.27331 q^{19} -19.4647 q^{20} -1.00000 q^{21} -8.06948 q^{22} -8.48709 q^{23} -7.60410 q^{24} +10.8074 q^{25} +14.6590 q^{26} +1.00000 q^{27} -4.89573 q^{28} -2.33440 q^{29} +10.4405 q^{30} -3.48403 q^{31} -11.5155 q^{32} +3.07295 q^{33} +9.27610 q^{34} +3.97585 q^{35} +4.89573 q^{36} -0.0532022 q^{37} -11.2216 q^{38} -5.58232 q^{39} +30.2328 q^{40} +4.90456 q^{41} +2.62597 q^{42} +11.8781 q^{43} +15.0443 q^{44} -3.97585 q^{45} +22.2869 q^{46} +9.25963 q^{47} +10.1767 q^{48} +1.00000 q^{49} -28.3799 q^{50} -3.53245 q^{51} -27.3295 q^{52} -2.19168 q^{53} -2.62597 q^{54} -12.2176 q^{55} +7.60410 q^{56} +4.27331 q^{57} +6.13006 q^{58} -1.18101 q^{59} -19.4647 q^{60} +14.8098 q^{61} +9.14897 q^{62} -1.00000 q^{63} +9.88607 q^{64} +22.1945 q^{65} -8.06948 q^{66} +14.0586 q^{67} -17.2939 q^{68} -8.48709 q^{69} -10.4405 q^{70} +6.00643 q^{71} -7.60410 q^{72} -11.7779 q^{73} +0.139708 q^{74} +10.8074 q^{75} +20.9210 q^{76} -3.07295 q^{77} +14.6590 q^{78} +2.69910 q^{79} -40.4611 q^{80} +1.00000 q^{81} -12.8792 q^{82} -12.8920 q^{83} -4.89573 q^{84} +14.0445 q^{85} -31.1916 q^{86} -2.33440 q^{87} -23.3670 q^{88} -2.44993 q^{89} +10.4405 q^{90} +5.58232 q^{91} -41.5505 q^{92} -3.48403 q^{93} -24.3155 q^{94} -16.9900 q^{95} -11.5155 q^{96} +0.516461 q^{97} -2.62597 q^{98} +3.07295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.62597	−1.85684	−0.928421	−	0.371529i	$-0.878834\pi$
$2$	−2.62597	−1.85684	−0.928421	+	0.371529i	$0.878834\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.89573	2.44786
$5$	−3.97585	−1.77805	−0.889027	−	0.457855i	$-0.848618\pi$
$5$	−3.97585	−1.77805	−0.889027	+	0.457855i	$0.848618\pi$
$6$	−2.62597	−1.07205
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.60410	−2.68846
$9$	1.00000	0.333333
$10$	10.4405	3.30157
$11$	3.07295	0.926529	0.463265	−	0.886220i	$-0.346678\pi$
$11$	3.07295	0.926529	0.463265	+	0.886220i	$0.346678\pi$
$12$	4.89573	1.41328
$13$	−5.58232	−1.54826	−0.774129	−	0.633028i	$-0.781812\pi$
$13$	−5.58232	−1.54826	−0.774129	+	0.633028i	$0.781812\pi$
$14$	2.62597	0.701821
$15$	−3.97585	−1.02656
$16$	10.1767	2.54418
$17$	−3.53245	−0.856744	−0.428372	−	0.903602i	$-0.640913\pi$
$17$	−3.53245	−0.856744	−0.428372	+	0.903602i	$0.640913\pi$
$18$	−2.62597	−0.618948
$19$	4.27331	0.980365	0.490182	−	0.871620i	$-0.336930\pi$
$19$	4.27331	0.980365	0.490182	+	0.871620i	$0.336930\pi$
$20$	−19.4647	−4.35244
$21$	−1.00000	−0.218218
$22$	−8.06948	−1.72042
$23$	−8.48709	−1.76968	−0.884840	−	0.465895i	$-0.845732\pi$
$23$	−8.48709	−1.76968	−0.884840	+	0.465895i	$0.845732\pi$
$24$	−7.60410	−1.55218
$25$	10.8074	2.16148
$26$	14.6590	2.87487
$27$	1.00000	0.192450
$28$	−4.89573	−0.925206
$29$	−2.33440	−0.433487	−0.216743	−	0.976229i	$-0.569543\pi$
$29$	−2.33440	−0.433487	−0.216743	+	0.976229i	$0.569543\pi$
$30$	10.4405	1.90616
$31$	−3.48403	−0.625751	−0.312875	−	0.949794i	$-0.601292\pi$
$31$	−3.48403	−0.625751	−0.312875	+	0.949794i	$0.601292\pi$
$32$	−11.5155	−2.03568
$33$	3.07295	0.534932
$34$	9.27610	1.59084
$35$	3.97585	0.672041
$36$	4.89573	0.815955
$37$	−0.0532022	−0.00874639	−0.00437320	−	0.999990i	$-0.501392\pi$
$37$	−0.0532022	−0.00874639	−0.00437320	+	0.999990i	$0.501392\pi$
$38$	−11.2216	−1.82038
$39$	−5.58232	−0.893887
$40$	30.2328	4.78022
$41$	4.90456	0.765964	0.382982	−	0.923756i	$-0.374897\pi$
$41$	4.90456	0.765964	0.382982	+	0.923756i	$0.374897\pi$
$42$	2.62597	0.405196
$43$	11.8781	1.81140	0.905698	−	0.423924i	$-0.139348\pi$
$43$	11.8781	1.81140	0.905698	+	0.423924i	$0.139348\pi$
$44$	15.0443	2.26802
$45$	−3.97585	−0.592685
$46$	22.2869	3.28602
$47$	9.25963	1.35066	0.675328	−	0.737518i	$-0.264002\pi$
$47$	9.25963	1.35066	0.675328	+	0.737518i	$0.264002\pi$
$48$	10.1767	1.46888
$49$	1.00000	0.142857
$50$	−28.3799	−4.01352
$51$	−3.53245	−0.494641
$52$	−27.3295	−3.78993
$53$	−2.19168	−0.301050	−0.150525	−	0.988606i	$-0.548096\pi$
$53$	−2.19168	−0.301050	−0.150525	+	0.988606i	$0.548096\pi$
$54$	−2.62597	−0.357350
$55$	−12.2176	−1.64742
$56$	7.60410	1.01614
$57$	4.27331	0.566014
$58$	6.13006	0.804917
$59$	−1.18101	−0.153754	−0.0768770	−	0.997041i	$-0.524495\pi$
$59$	−1.18101	−0.153754	−0.0768770	+	0.997041i	$0.524495\pi$
$60$	−19.4647	−2.51288
$61$	14.8098	1.89620	0.948098	−	0.317978i	$-0.103004\pi$
$61$	14.8098	1.89620	0.948098	+	0.317978i	$0.103004\pi$
$62$	9.14897	1.16192
$63$	−1.00000	−0.125988
$64$	9.88607	1.23576
$65$	22.1945	2.75289
$66$	−8.06948	−0.993284
$67$	14.0586	1.71753	0.858765	−	0.512370i	$-0.171232\pi$
$67$	14.0586	1.71753	0.858765	+	0.512370i	$0.171232\pi$
$68$	−17.2939	−2.09719
$69$	−8.48709	−1.02173
$70$	−10.4405	−1.24787
$71$	6.00643	0.712832	0.356416	−	0.934327i	$-0.383999\pi$
$71$	6.00643	0.712832	0.356416	+	0.934327i	$0.383999\pi$
$72$	−7.60410	−0.896152
$73$	−11.7779	−1.37850	−0.689249	−	0.724524i	$-0.742059\pi$
$73$	−11.7779	−1.37850	−0.689249	+	0.724524i	$0.742059\pi$
$74$	0.139708	0.0162407
$75$	10.8074	1.24793
$76$	20.9210	2.39980
$77$	−3.07295	−0.350195
$78$	14.6590	1.65981
$79$	2.69910	0.303672	0.151836	−	0.988406i	$-0.451481\pi$
$79$	2.69910	0.303672	0.151836	+	0.988406i	$0.451481\pi$
$80$	−40.4611	−4.52368
$81$	1.00000	0.111111
$82$	−12.8792	−1.42227
$83$	−12.8920	−1.41508	−0.707542	−	0.706671i	$-0.750196\pi$
$83$	−12.8920	−1.41508	−0.707542	+	0.706671i	$0.750196\pi$
$84$	−4.89573	−0.534168
$85$	14.0445	1.52334
$86$	−31.1916	−3.36348
$87$	−2.33440	−0.250274
$88$	−23.3670	−2.49093
$89$	−2.44993	−0.259692	−0.129846	−	0.991534i	$-0.541448\pi$
$89$	−2.44993	−0.259692	−0.129846	+	0.991534i	$0.541448\pi$
$90$	10.4405	1.10052
$91$	5.58232	0.585186
$92$	−41.5505	−4.33194
$93$	−3.48403	−0.361277
$94$	−24.3155	−2.50796
$95$	−16.9900	−1.74314
$96$	−11.5155	−1.17530
$97$	0.516461	0.0524386	0.0262193	−	0.999656i	$-0.491653\pi$
$97$	0.516461	0.0524386	0.0262193	+	0.999656i	$0.491653\pi$
$98$	−2.62597	−0.265263
$99$	3.07295	0.308843
$100$	52.9100	5.29100
$101$	−6.65915	−0.662610	−0.331305	−	0.943524i	$-0.607489\pi$
$101$	−6.65915	−0.662610	−0.331305	+	0.943524i	$0.607489\pi$
$102$	9.27610	0.918471
$103$	−9.17575	−0.904114	−0.452057	−	0.891989i	$-0.649310\pi$
$103$	−9.17575	−0.904114	−0.452057	+	0.891989i	$0.649310\pi$
$104$	42.4486	4.16242
$105$	3.97585	0.388003
$106$	5.75528	0.559002
$107$	17.3572	1.67798	0.838990	−	0.544147i	$-0.183147\pi$
$107$	17.3572	1.67798	0.838990	+	0.544147i	$0.183147\pi$
$108$	4.89573	0.471092
$109$	−7.00848	−0.671291	−0.335645	−	0.941988i	$-0.608954\pi$
$109$	−7.00848	−0.671291	−0.335645	+	0.941988i	$0.608954\pi$
$110$	32.0830	3.05900
$111$	−0.0532022	−0.00504973
$112$	−10.1767	−0.961608
$113$	−2.46642	−0.232022	−0.116011	−	0.993248i	$-0.537011\pi$
$113$	−2.46642	−0.232022	−0.116011	+	0.993248i	$0.537011\pi$
$114$	−11.2216	−1.05100
$115$	33.7434	3.14659
$116$	−11.4286	−1.06112
$117$	−5.58232	−0.516086
$118$	3.10129	0.285497
$119$	3.53245	0.323819
$120$	30.2328	2.75986
$121$	−1.55698	−0.141543
$122$	−38.8900	−3.52094
$123$	4.90456	0.442230
$124$	−17.0569	−1.53175
$125$	−23.0893	−2.06517
$126$	2.62597	0.233940
$127$	−0.454073	−0.0402925	−0.0201462	−	0.999797i	$-0.506413\pi$
$127$	−0.454073	−0.0402925	−0.0201462	+	0.999797i	$0.506413\pi$
$128$	−2.92946	−0.258930
$129$	11.8781	1.04581
$130$	−58.2821	−5.11168
$131$	−11.1216	−0.971701	−0.485851	−	0.874042i	$-0.661490\pi$
$131$	−11.1216	−0.971701	−0.485851	+	0.874042i	$0.661490\pi$
$132$	15.0443	1.30944
$133$	−4.27331	−0.370543
$134$	−36.9175	−3.18918
$135$	−3.97585	−0.342187
$136$	26.8611	2.30332
$137$	−3.57602	−0.305520	−0.152760	−	0.988263i	$-0.548816\pi$
$137$	−3.57602	−0.305520	−0.152760	+	0.988263i	$0.548816\pi$
$138$	22.2869	1.89718
$139$	−17.0610	−1.44709	−0.723547	−	0.690275i	$-0.757489\pi$
$139$	−17.0610	−1.44709	−0.723547	+	0.690275i	$0.757489\pi$
$140$	19.4647	1.64507
$141$	9.25963	0.779802
$142$	−15.7727	−1.32362
$143$	−17.1542	−1.43451
$144$	10.1767	0.848059
$145$	9.28121	0.770763
$146$	30.9284	2.55965
$147$	1.00000	0.0824786
$148$	−0.260464	−0.0214100
$149$	19.4761	1.59554	0.797771	−	0.602960i	$-0.206012\pi$
$149$	19.4761	1.59554	0.797771	+	0.602960i	$0.206012\pi$
$150$	−28.3799	−2.31721
$151$	−3.41627	−0.278012	−0.139006	−	0.990292i	$-0.544391\pi$
$151$	−3.41627	−0.278012	−0.139006	+	0.990292i	$0.544391\pi$
$152$	−32.4947	−2.63567
$153$	−3.53245	−0.285581
$154$	8.06948	0.650257
$155$	13.8520	1.11262
$156$	−27.3295	−2.18811
$157$	−7.86181	−0.627441	−0.313721	−	0.949515i	$-0.601576\pi$
$157$	−7.86181	−0.627441	−0.313721	+	0.949515i	$0.601576\pi$
$158$	−7.08775	−0.563871
$159$	−2.19168	−0.173811
$160$	45.7840	3.61955
$161$	8.48709	0.668876
$162$	−2.62597	−0.206316
$163$	19.0347	1.49092	0.745458	−	0.666553i	$-0.232231\pi$
$163$	19.0347	1.49092	0.745458	+	0.666553i	$0.232231\pi$
$164$	24.0114	1.87498
$165$	−12.2176	−0.951138
$166$	33.8541	2.62759
$167$	20.0336	1.55025	0.775123	−	0.631810i	$-0.217688\pi$
$167$	20.0336	1.55025	0.775123	+	0.631810i	$0.217688\pi$
$168$	7.60410	0.586669
$169$	18.1623	1.39710
$170$	−36.8804	−2.82860
$171$	4.27331	0.326788
$172$	58.1520	4.43405
$173$	17.8021	1.35347	0.676735	−	0.736226i	$-0.263394\pi$
$173$	17.8021	1.35347	0.676735	+	0.736226i	$0.263394\pi$
$174$	6.13006	0.464719
$175$	−10.8074	−0.816961
$176$	31.2725	2.35725
$177$	−1.18101	−0.0887699
$178$	6.43346	0.482208
$179$	9.45774	0.706904	0.353452	−	0.935453i	$-0.385008\pi$
$179$	9.45774	0.706904	0.353452	+	0.935453i	$0.385008\pi$
$180$	−19.4647	−1.45081
$181$	23.2912	1.73122	0.865609	−	0.500720i	$-0.166931\pi$
$181$	23.2912	1.73122	0.865609	+	0.500720i	$0.166931\pi$
$182$	−14.6590	−1.08660
$183$	14.8098	1.09477
$184$	64.5367	4.75771
$185$	0.211524	0.0155516
$186$	9.14897	0.670835
$187$	−10.8550	−0.793798
$188$	45.3326	3.30622
$189$	−1.00000	−0.0727393
$190$	44.6154	3.23674
$191$	−11.0449	−0.799181	−0.399590	−	0.916694i	$-0.630848\pi$
$191$	−11.0449	−0.799181	−0.399590	+	0.916694i	$0.630848\pi$
$192$	9.88607	0.713465
$193$	−12.0473	−0.867183	−0.433591	−	0.901110i	$-0.642754\pi$
$193$	−12.0473	−0.867183	−0.433591	+	0.901110i	$0.642754\pi$
$194$	−1.35621	−0.0973703
$195$	22.1945	1.58938
$196$	4.89573	0.349695
$197$	−14.8302	−1.05661	−0.528305	−	0.849055i	$-0.677172\pi$
$197$	−14.8302	−1.05661	−0.528305	+	0.849055i	$0.677172\pi$
$198$	−8.06948	−0.573473
$199$	−6.27849	−0.445071	−0.222535	−	0.974925i	$-0.571433\pi$
$199$	−6.27849	−0.445071	−0.222535	+	0.974925i	$0.571433\pi$
$200$	−82.1804	−5.81104
$201$	14.0586	0.991616
$202$	17.4867	1.23036
$203$	2.33440	0.163843
$204$	−17.2939	−1.21082
$205$	−19.4998	−1.36193
$206$	24.0953	1.67880
$207$	−8.48709	−0.589893
$208$	−56.8097	−3.93904
$209$	13.1317	0.908337
$210$	−10.4405	−0.720461
$211$	28.2274	1.94326	0.971628	−	0.236516i	$-0.0760054\pi$
$211$	28.2274	1.94326	0.971628	+	0.236516i	$0.0760054\pi$
$212$	−10.7299	−0.736930
$213$	6.00643	0.411554
$214$	−45.5794	−3.11575
$215$	−47.2256	−3.22076
$216$	−7.60410	−0.517394
$217$	3.48403	0.236512
$218$	18.4041	1.24648
$219$	−11.7779	−0.795876
$220$	−59.8140	−4.03266
$221$	19.7193	1.32646
$222$	0.139708	0.00937656
$223$	−19.8724	−1.33075	−0.665377	−	0.746508i	$-0.731729\pi$
$223$	−19.8724	−1.33075	−0.665377	+	0.746508i	$0.731729\pi$
$224$	11.5155	0.769414
$225$	10.8074	0.720492
$226$	6.47676	0.430828
$227$	5.22666	0.346906	0.173453	−	0.984842i	$-0.444508\pi$
$227$	5.22666	0.346906	0.173453	+	0.984842i	$0.444508\pi$
$228$	20.9210	1.38553
$229$	−4.42137	−0.292172	−0.146086	−	0.989272i	$-0.546668\pi$
$229$	−4.42137	−0.292172	−0.146086	+	0.989272i	$0.546668\pi$
$230$	−88.6092	−5.84272
$231$	−3.07295	−0.202185
$232$	17.7510	1.16541
$233$	−18.0277	−1.18104	−0.590518	−	0.807025i	$-0.701076\pi$
$233$	−18.0277	−1.18104	−0.590518	+	0.807025i	$0.701076\pi$
$234$	14.6590	0.958290
$235$	−36.8149	−2.40154
$236$	−5.78189	−0.376369
$237$	2.69910	0.175325
$238$	−9.27610	−0.601281
$239$	−6.39593	−0.413718	−0.206859	−	0.978371i	$-0.566324\pi$
$239$	−6.39593	−0.413718	−0.206859	+	0.978371i	$0.566324\pi$
$240$	−40.4611	−2.61175
$241$	5.11788	0.329672	0.164836	−	0.986321i	$-0.447291\pi$
$241$	5.11788	0.329672	0.164836	+	0.986321i	$0.447291\pi$
$242$	4.08858	0.262824
$243$	1.00000	0.0641500
$244$	72.5046	4.64163
$245$	−3.97585	−0.254008
$246$	−12.8792	−0.821151
$247$	−23.8550	−1.51786
$248$	26.4929	1.68230
$249$	−12.8920	−0.816999
$250$	60.6318	3.83469
$251$	4.32880	0.273232	0.136616	−	0.990624i	$-0.456377\pi$
$251$	4.32880	0.273232	0.136616	+	0.990624i	$0.456377\pi$
$252$	−4.89573	−0.308402
$253$	−26.0804	−1.63966
$254$	1.19238	0.0748168
$255$	14.0445	0.879499
$256$	−12.0795	−0.754966
$257$	−16.8812	−1.05302	−0.526511	−	0.850168i	$-0.676500\pi$
$257$	−16.8812	−1.05302	−0.526511	+	0.850168i	$0.676500\pi$
$258$	−31.1916	−1.94190
$259$	0.0532022	0.00330583
$260$	108.658	6.73869
$261$	−2.33440	−0.144496
$262$	29.2051	1.80430
$263$	−0.841148	−0.0518674	−0.0259337	−	0.999664i	$-0.508256\pi$
$263$	−0.841148	−0.0518674	−0.0259337	+	0.999664i	$0.508256\pi$
$264$	−23.3670	−1.43814
$265$	8.71378	0.535283
$266$	11.2216	0.688040
$267$	−2.44993	−0.149933
$268$	68.8270	4.20428
$269$	−16.4028	−1.00009	−0.500047	−	0.865998i	$-0.666684\pi$
$269$	−16.4028	−1.00009	−0.500047	+	0.865998i	$0.666684\pi$
$270$	10.4405	0.635387
$271$	11.8176	0.717871	0.358935	−	0.933362i	$-0.383140\pi$
$271$	11.8176	0.717871	0.358935	+	0.933362i	$0.383140\pi$
$272$	−35.9487	−2.17971
$273$	5.58232	0.337858
$274$	9.39052	0.567302
$275$	33.2105	2.00267
$276$	−41.5505	−2.50104
$277$	4.29660	0.258157	0.129079	−	0.991634i	$-0.458798\pi$
$277$	4.29660	0.258157	0.129079	+	0.991634i	$0.458798\pi$
$278$	44.8017	2.68702
$279$	−3.48403	−0.208584
$280$	−30.2328	−1.80675
$281$	7.76321	0.463115	0.231557	−	0.972821i	$-0.425618\pi$
$281$	7.76321	0.463115	0.231557	+	0.972821i	$0.425618\pi$
$282$	−24.3155	−1.44797
$283$	−1.31516	−0.0781782	−0.0390891	−	0.999236i	$-0.512446\pi$
$283$	−1.31516	−0.0781782	−0.0390891	+	0.999236i	$0.512446\pi$
$284$	29.4058	1.74492
$285$	−16.9900	−1.00640
$286$	45.0464	2.66365
$287$	−4.90456	−0.289507
$288$	−11.5155	−0.678559
$289$	−4.52183	−0.265990
$290$	−24.3722	−1.43119
$291$	0.516461	0.0302755
$292$	−57.6614	−3.37438
$293$	−26.7529	−1.56292	−0.781461	−	0.623954i	$-0.785525\pi$
$293$	−26.7529	−1.56292	−0.781461	+	0.623954i	$0.785525\pi$
$294$	−2.62597	−0.153150
$295$	4.69551	0.273383
$296$	0.404555	0.0235143
$297$	3.07295	0.178311
$298$	−51.1436	−2.96267
$299$	47.3777	2.73992
$300$	52.9100	3.05476
$301$	−11.8781	−0.684643
$302$	8.97102	0.516224
$303$	−6.65915	−0.382558
$304$	43.4882	2.49422
$305$	−58.8814	−3.37154
$306$	9.27610	0.530280
$307$	−8.19727	−0.467843	−0.233921	−	0.972256i	$-0.575156\pi$
$307$	−8.19727	−0.467843	−0.233921	+	0.972256i	$0.575156\pi$
$308$	−15.0443	−0.857230
$309$	−9.17575	−0.521990
$310$	−36.3749	−2.06596
$311$	−19.8503	−1.12561	−0.562804	−	0.826590i	$-0.690278\pi$
$311$	−19.8503	−1.12561	−0.562804	+	0.826590i	$0.690278\pi$
$312$	42.4486	2.40318
$313$	−2.30566	−0.130323	−0.0651617	−	0.997875i	$-0.520756\pi$
$313$	−2.30566	−0.130323	−0.0651617	+	0.997875i	$0.520756\pi$
$314$	20.6449	1.16506
$315$	3.97585	0.224014
$316$	13.2140	0.743348
$317$	19.1053	1.07306	0.536530	−	0.843881i	$-0.319735\pi$
$317$	19.1053	1.07306	0.536530	+	0.843881i	$0.319735\pi$
$318$	5.75528	0.322740
$319$	−7.17349	−0.401638
$320$	−39.3055	−2.19724
$321$	17.3572	0.968782
$322$	−22.2869	−1.24200
$323$	−15.0952	−0.839922
$324$	4.89573	0.271985
$325$	−60.3303	−3.34652
$326$	−49.9847	−2.76839
$327$	−7.00848	−0.387570
$328$	−37.2948	−2.05926
$329$	−9.25963	−0.510500
$330$	32.0830	1.76611
$331$	−0.245813	−0.0135111	−0.00675555	−	0.999977i	$-0.502150\pi$
$331$	−0.245813	−0.0135111	−0.00675555	+	0.999977i	$0.502150\pi$
$332$	−63.1159	−3.46393
$333$	−0.0532022	−0.00291546
$334$	−52.6077	−2.87856
$335$	−55.8948	−3.05386
$336$	−10.1767	−0.555185
$337$	2.84439	0.154944	0.0774720	−	0.996995i	$-0.475315\pi$
$337$	2.84439	0.154944	0.0774720	+	0.996995i	$0.475315\pi$
$338$	−47.6938	−2.59420
$339$	−2.46642	−0.133958
$340$	68.7579	3.72892
$341$	−10.7063	−0.579776
$342$	−11.2216	−0.606794
$343$	−1.00000	−0.0539949
$344$	−90.3224	−4.86986
$345$	33.7434	1.81668
$346$	−46.7479	−2.51318
$347$	−16.0986	−0.864219	−0.432109	−	0.901821i	$-0.642231\pi$
$347$	−16.0986	−0.864219	−0.432109	+	0.901821i	$0.642231\pi$
$348$	−11.4286	−0.612636
$349$	31.2266	1.67152	0.835761	−	0.549093i	$-0.185027\pi$
$349$	31.2266	1.67152	0.835761	+	0.549093i	$0.185027\pi$
$350$	28.3799	1.51697
$351$	−5.58232	−0.297962
$352$	−35.3867	−1.88612
$353$	21.7758	1.15901	0.579503	−	0.814970i	$-0.303247\pi$
$353$	21.7758	1.15901	0.579503	+	0.814970i	$0.303247\pi$
$354$	3.10129	0.164832
$355$	−23.8807	−1.26745
$356$	−11.9942	−0.635692
$357$	3.53245	0.186957
$358$	−24.8357	−1.31261
$359$	−1.73246	−0.0914359	−0.0457180	−	0.998954i	$-0.514558\pi$
$359$	−1.73246	−0.0914359	−0.0457180	+	0.998954i	$0.514558\pi$
$360$	30.2328	1.59341
$361$	−0.738807	−0.0388846
$362$	−61.1619	−3.21460
$363$	−1.55698	−0.0817202
$364$	27.3295	1.43246
$365$	46.8271	2.45104
$366$	−38.8900	−2.03281
$367$	15.4549	0.806738	0.403369	−	0.915037i	$-0.367839\pi$
$367$	15.4549	0.806738	0.403369	+	0.915037i	$0.367839\pi$
$368$	−86.3706	−4.50238
$369$	4.90456	0.255321
$370$	−0.555456	−0.0288768
$371$	2.19168	0.113786
$372$	−17.0569	−0.884358
$373$	−16.8848	−0.874260	−0.437130	−	0.899398i	$-0.644005\pi$
$373$	−16.8848	−0.874260	−0.437130	+	0.899398i	$0.644005\pi$
$374$	28.5050	1.47396
$375$	−23.0893	−1.19233
$376$	−70.4112	−3.63118
$377$	13.0314	0.671149
$378$	2.62597	0.135065
$379$	19.9346	1.02397	0.511985	−	0.858994i	$-0.328910\pi$
$379$	19.9346	1.02397	0.511985	+	0.858994i	$0.328910\pi$
$380$	−83.1787	−4.26698
$381$	−0.454073	−0.0232629
$382$	29.0036	1.48395
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−2.92946	−0.149493
$385$	12.2176	0.622666
$386$	31.6358	1.61022
$387$	11.8781	0.603799
$388$	2.52845	0.128363
$389$	−6.94662	−0.352208	−0.176104	−	0.984372i	$-0.556349\pi$
$389$	−6.94662	−0.352208	−0.176104	+	0.984372i	$0.556349\pi$
$390$	−58.2821	−2.95123
$391$	29.9802	1.51616
$392$	−7.60410	−0.384065
$393$	−11.1216	−0.561012
$394$	38.9437	1.96196
$395$	−10.7312	−0.539945
$396$	15.0443	0.756006
$397$	35.4582	1.77960	0.889798	−	0.456355i	$-0.150845\pi$
$397$	35.4582	1.77960	0.889798	+	0.456355i	$0.150845\pi$
$398$	16.4872	0.826426
$399$	−4.27331	−0.213933
$400$	109.984	5.49918
$401$	29.0736	1.45187	0.725933	−	0.687765i	$-0.241408\pi$
$401$	29.0736	1.45187	0.725933	+	0.687765i	$0.241408\pi$
$402$	−36.9175	−1.84128
$403$	19.4490	0.968824
$404$	−32.6014	−1.62198
$405$	−3.97585	−0.197562
$406$	−6.13006	−0.304230
$407$	−0.163488	−0.00810379
$408$	26.8611	1.32982
$409$	−14.2116	−0.702719	−0.351359	−	0.936241i	$-0.614280\pi$
$409$	−14.2116	−0.702719	−0.351359	+	0.936241i	$0.614280\pi$
$410$	51.2059	2.52888
$411$	−3.57602	−0.176392
$412$	−44.9220	−2.21315
$413$	1.18101	0.0581136
$414$	22.2869	1.09534
$415$	51.2568	2.51610
$416$	64.2834	3.15176
$417$	−17.0610	−0.835480
$418$	−34.4834	−1.68664
$419$	−29.3810	−1.43536	−0.717679	−	0.696374i	$-0.754795\pi$
$419$	−29.3810	−1.43536	−0.717679	+	0.696374i	$0.754795\pi$
$420$	19.4647	0.949779
$421$	−3.83791	−0.187048	−0.0935241	−	0.995617i	$-0.529813\pi$
$421$	−3.83791	−0.187048	−0.0935241	+	0.995617i	$0.529813\pi$
$422$	−74.1244	−3.60832
$423$	9.25963	0.450219
$424$	16.6657	0.809360
$425$	−38.1765	−1.85183
$426$	−15.7727	−0.764190
$427$	−14.8098	−0.716695
$428$	84.9760	4.10747
$429$	−17.1542	−0.828213
$430$	124.013	5.98044
$431$	26.4846	1.27572	0.637858	−	0.770154i	$-0.279821\pi$
$431$	26.4846	1.27572	0.637858	+	0.770154i	$0.279821\pi$
$432$	10.1767	0.489627
$433$	−6.37756	−0.306486	−0.153243	−	0.988189i	$-0.548972\pi$
$433$	−6.37756	−0.306486	−0.153243	+	0.988189i	$0.548972\pi$
$434$	−9.14897	−0.439165
$435$	9.28121	0.445000
$436$	−34.3116	−1.64323
$437$	−36.2680	−1.73493
$438$	30.9284	1.47782
$439$	−23.0867	−1.10187	−0.550934	−	0.834549i	$-0.685728\pi$
$439$	−23.0867	−1.10187	−0.550934	+	0.834549i	$0.685728\pi$
$440$	92.9038	4.42901
$441$	1.00000	0.0476190
$442$	−51.7822	−2.46303
$443$	−32.8474	−1.56063	−0.780314	−	0.625387i	$-0.784941\pi$
$443$	−32.8474	−1.56063	−0.780314	+	0.625387i	$0.784941\pi$
$444$	−0.260464	−0.0123611
$445$	9.74057	0.461747
$446$	52.1843	2.47100
$447$	19.4761	0.921187
$448$	−9.88607	−0.467073
$449$	−15.4129	−0.727378	−0.363689	−	0.931520i	$-0.618483\pi$
$449$	−15.4129	−0.727378	−0.363689	+	0.931520i	$0.618483\pi$
$450$	−28.3799	−1.33784
$451$	15.0715	0.709688
$452$	−12.0749	−0.567958
$453$	−3.41627	−0.160510
$454$	−13.7251	−0.644150
$455$	−22.1945	−1.04049
$456$	−32.4947	−1.52170
$457$	2.37964	0.111315	0.0556575	−	0.998450i	$-0.482275\pi$
$457$	2.37964	0.111315	0.0556575	+	0.998450i	$0.482275\pi$
$458$	11.6104	0.542518
$459$	−3.53245	−0.164880
$460$	165.198	7.70242
$461$	−22.8786	−1.06556	−0.532780	−	0.846254i	$-0.678853\pi$
$461$	−22.8786	−1.06556	−0.532780	+	0.846254i	$0.678853\pi$
$462$	8.06948	0.375426
$463$	−24.5234	−1.13970	−0.569851	−	0.821748i	$-0.692999\pi$
$463$	−24.5234	−1.13970	−0.569851	+	0.821748i	$0.692999\pi$
$464$	−23.7565	−1.10287
$465$	13.8520	0.642371
$466$	47.3403	2.19300
$467$	−13.9390	−0.645020	−0.322510	−	0.946566i	$-0.604527\pi$
$467$	−13.9390	−0.645020	−0.322510	+	0.946566i	$0.604527\pi$
$468$	−27.3295	−1.26331
$469$	−14.0586	−0.649165
$470$	96.6749	4.45928
$471$	−7.86181	−0.362253
$472$	8.98050	0.413361
$473$	36.5009	1.67831
$474$	−7.08775	−0.325551
$475$	46.1833	2.11904
$476$	17.2939	0.792664
$477$	−2.19168	−0.100350
$478$	16.7955	0.768210
$479$	−8.17027	−0.373309	−0.186655	−	0.982426i	$-0.559765\pi$
$479$	−8.17027	−0.373309	−0.186655	+	0.982426i	$0.559765\pi$
$480$	45.7840	2.08975
$481$	0.296992	0.0135417
$482$	−13.4394	−0.612148
$483$	8.48709	0.386176
$484$	−7.62254	−0.346479
$485$	−2.05337	−0.0932387
$486$	−2.62597	−0.119117
$487$	−5.00809	−0.226938	−0.113469	−	0.993542i	$-0.536196\pi$
$487$	−5.00809	−0.226938	−0.113469	+	0.993542i	$0.536196\pi$
$488$	−112.615	−5.09784
$489$	19.0347	0.860780
$490$	10.4405	0.471652
$491$	−15.2169	−0.686730	−0.343365	−	0.939202i	$-0.611567\pi$
$491$	−15.2169	−0.686730	−0.343365	+	0.939202i	$0.611567\pi$
$492$	24.0114	1.08252
$493$	8.24613	0.371387
$494$	62.6426	2.81842
$495$	−12.2176	−0.549140
$496$	−35.4560	−1.59202
$497$	−6.00643	−0.269425
$498$	33.8541	1.51704
$499$	−1.91609	−0.0857759	−0.0428880	−	0.999080i	$-0.513656\pi$
$499$	−1.91609	−0.0857759	−0.0428880	+	0.999080i	$0.513656\pi$
$500$	−113.039	−5.05525
$501$	20.0336	0.895035
$502$	−11.3673	−0.507348
$503$	43.1125	1.92229	0.961147	−	0.276038i	$-0.0890216\pi$
$503$	43.1125	1.92229	0.961147	+	0.276038i	$0.0890216\pi$
$504$	7.60410	0.338714
$505$	26.4758	1.17816
$506$	68.4864	3.04459
$507$	18.1623	0.806617
$508$	−2.22302	−0.0986305
$509$	34.2547	1.51831	0.759157	−	0.650907i	$-0.225611\pi$
$509$	34.2547	1.51831	0.759157	+	0.650907i	$0.225611\pi$
$510$	−36.8804	−1.63309
$511$	11.7779	0.521023
$512$	37.5792	1.66078
$513$	4.27331	0.188671
$514$	44.3296	1.95530
$515$	36.4814	1.60756
$516$	58.1520	2.56000
$517$	28.4544	1.25142
$518$	−0.139708	−0.00613840
$519$	17.8021	0.781427
$520$	−168.769	−7.40101
$521$	32.3247	1.41617	0.708085	−	0.706128i	$-0.249560\pi$
$521$	32.3247	1.41617	0.708085	+	0.706128i	$0.249560\pi$
$522$	6.13006	0.268306
$523$	−6.91305	−0.302287	−0.151143	−	0.988512i	$-0.548295\pi$
$523$	−6.91305	−0.302287	−0.151143	+	0.988512i	$0.548295\pi$
$524$	−54.4485	−2.37859
$525$	−10.8074	−0.471673
$526$	2.20883	0.0963096
$527$	12.3072	0.536108
$528$	31.2725	1.36096
$529$	49.0306	2.13177
$530$	−22.8821	−0.993937
$531$	−1.18101	−0.0512513
$532$	−20.9210	−0.907039
$533$	−27.3789	−1.18591
$534$	6.43346	0.278403
$535$	−69.0095	−2.98354
$536$	−106.903	−4.61750
$537$	9.45774	0.408131
$538$	43.0732	1.85702
$539$	3.07295	0.132361
$540$	−19.4647	−0.837627
$541$	3.89387	0.167410	0.0837052	−	0.996491i	$-0.473325\pi$
$541$	3.89387	0.167410	0.0837052	+	0.996491i	$0.473325\pi$
$542$	−31.0328	−1.33297
$543$	23.2912	0.999519
$544$	40.6780	1.74406
$545$	27.8647	1.19359
$546$	−14.6590	−0.627348
$547$	−43.6121	−1.86472	−0.932360	−	0.361531i	$-0.882254\pi$
$547$	−43.6121	−1.86472	−0.932360	+	0.361531i	$0.882254\pi$
$548$	−17.5072	−0.747871
$549$	14.8098	0.632065
$550$	−87.2100	−3.71864
$551$	−9.97561	−0.424975
$552$	64.5367	2.74686
$553$	−2.69910	−0.114777
$554$	−11.2827	−0.479358
$555$	0.211524	0.00897870
$556$	−83.5259	−3.54229
$557$	−19.8851	−0.842559	−0.421279	−	0.906931i	$-0.638419\pi$
$557$	−19.8851	−0.842559	−0.421279	+	0.906931i	$0.638419\pi$
$558$	9.14897	0.387307
$559$	−66.3075	−2.80451
$560$	40.4611	1.70979
$561$	−10.8550	−0.458300
$562$	−20.3860	−0.859931
$563$	36.8636	1.55362	0.776808	−	0.629738i	$-0.216838\pi$
$563$	36.8636	1.55362	0.776808	+	0.629738i	$0.216838\pi$
$564$	45.3326	1.90885
$565$	9.80613	0.412547
$566$	3.45357	0.145165
$567$	−1.00000	−0.0419961
$568$	−45.6735	−1.91642
$569$	9.89135	0.414667	0.207333	−	0.978270i	$-0.433521\pi$
$569$	9.89135	0.414667	0.207333	+	0.978270i	$0.433521\pi$
$570$	44.6154	1.86873
$571$	−34.2897	−1.43498	−0.717489	−	0.696570i	$-0.754709\pi$
$571$	−34.2897	−1.43498	−0.717489	+	0.696570i	$0.754709\pi$
$572$	−83.9823	−3.51148
$573$	−11.0449	−0.461407
$574$	12.8792	0.537569
$575$	−91.7232	−3.82512
$576$	9.88607	0.411919
$577$	−39.5004	−1.64442	−0.822211	−	0.569183i	$-0.807260\pi$
$577$	−39.5004	−1.64442	−0.822211	+	0.569183i	$0.807260\pi$
$578$	11.8742	0.493901
$579$	−12.0473	−0.500668
$580$	45.4383	1.88672
$581$	12.8920	0.534852
$582$	−1.35621	−0.0562168
$583$	−6.73491	−0.278932
$584$	89.5603	3.70603
$585$	22.1945	0.917629
$586$	70.2524	2.90210
$587$	25.5133	1.05305	0.526523	−	0.850161i	$-0.323495\pi$
$587$	25.5133	1.05305	0.526523	+	0.850161i	$0.323495\pi$
$588$	4.89573	0.201896
$589$	−14.8884	−0.613464
$590$	−12.3303	−0.507629
$591$	−14.8302	−0.610034
$592$	−0.541423	−0.0222524
$593$	32.6707	1.34163	0.670813	−	0.741626i	$-0.265945\pi$
$593$	32.6707	1.34163	0.670813	+	0.741626i	$0.265945\pi$
$594$	−8.06948	−0.331095
$595$	−14.0445	−0.575767
$596$	95.3496	3.90567
$597$	−6.27849	−0.256962
$598$	−124.412	−5.08760
$599$	−7.38376	−0.301692	−0.150846	−	0.988557i	$-0.548200\pi$
$599$	−7.38376	−0.301692	−0.150846	+	0.988557i	$0.548200\pi$
$600$	−82.1804	−3.35500
$601$	−21.5967	−0.880946	−0.440473	−	0.897766i	$-0.645189\pi$
$601$	−21.5967	−0.880946	−0.440473	+	0.897766i	$0.645189\pi$
$602$	31.1916	1.27127
$603$	14.0586	0.572510
$604$	−16.7251	−0.680536
$605$	6.19031	0.251672
$606$	17.4867	0.710350
$607$	12.7017	0.515546	0.257773	−	0.966206i	$-0.417011\pi$
$607$	12.7017	0.515546	0.257773	+	0.966206i	$0.417011\pi$
$608$	−49.2095	−1.99571
$609$	2.33440	0.0945946
$610$	154.621	6.26042
$611$	−51.6902	−2.09116
$612$	−17.2939	−0.699064
$613$	−16.1259	−0.651319	−0.325659	−	0.945487i	$-0.605586\pi$
$613$	−16.1259	−0.651319	−0.325659	+	0.945487i	$0.605586\pi$
$614$	21.5258	0.868710
$615$	−19.4998	−0.786308
$616$	23.3670	0.941484
$617$	−16.3664	−0.658886	−0.329443	−	0.944175i	$-0.606861\pi$
$617$	−16.3664	−0.658886	−0.329443	+	0.944175i	$0.606861\pi$
$618$	24.0953	0.969254
$619$	−33.1615	−1.33287	−0.666436	−	0.745562i	$-0.732181\pi$
$619$	−33.1615	−1.33287	−0.666436	+	0.745562i	$0.732181\pi$
$620$	67.8156	2.72354
$621$	−8.48709	−0.340575
$622$	52.1264	2.09008
$623$	2.44993	0.0981545
$624$	−56.8097	−2.27421
$625$	37.7626	1.51050
$626$	6.05459	0.241990
$627$	13.1317	0.524429
$628$	−38.4893	−1.53589
$629$	0.187934	0.00749342
$630$	−10.4405	−0.415958
$631$	−30.1527	−1.20036	−0.600179	−	0.799866i	$-0.704904\pi$
$631$	−30.1527	−1.20036	−0.600179	+	0.799866i	$0.704904\pi$
$632$	−20.5242	−0.816409
$633$	28.2274	1.12194
$634$	−50.1699	−1.99250
$635$	1.80533	0.0716422
$636$	−10.7299	−0.425467
$637$	−5.58232	−0.221180
$638$	18.8374	0.745779
$639$	6.00643	0.237611
$640$	11.6471	0.460392
$641$	33.5624	1.32564	0.662818	−	0.748781i	$-0.269360\pi$
$641$	33.5624	1.32564	0.662818	+	0.748781i	$0.269360\pi$
$642$	−45.5794	−1.79888
$643$	−22.3092	−0.879790	−0.439895	−	0.898049i	$-0.644984\pi$
$643$	−22.3092	−0.879790	−0.439895	+	0.898049i	$0.644984\pi$
$644$	41.5505	1.63732
$645$	−47.2256	−1.85951
$646$	39.6397	1.55960
$647$	−25.0343	−0.984198	−0.492099	−	0.870539i	$-0.663770\pi$
$647$	−25.0343	−0.984198	−0.492099	+	0.870539i	$0.663770\pi$
$648$	−7.60410	−0.298717
$649$	−3.62918	−0.142458
$650$	158.426	6.21397
$651$	3.48403	0.136550
$652$	93.1889	3.64956
$653$	−23.1742	−0.906876	−0.453438	−	0.891288i	$-0.649803\pi$
$653$	−23.1742	−0.906876	−0.453438	+	0.891288i	$0.649803\pi$
$654$	18.4041	0.719656
$655$	44.2179	1.72774
$656$	49.9123	1.94875
$657$	−11.7779	−0.459499
$658$	24.3155	0.947918
$659$	−26.6065	−1.03644	−0.518222	−	0.855246i	$-0.673406\pi$
$659$	−26.6065	−1.03644	−0.518222	+	0.855246i	$0.673406\pi$
$660$	−59.8140	−2.32826
$661$	−0.642933	−0.0250072	−0.0125036	−	0.999922i	$-0.503980\pi$
$661$	−0.642933	−0.0250072	−0.0125036	+	0.999922i	$0.503980\pi$
$662$	0.645498	0.0250880
$663$	19.7193	0.765832
$664$	98.0323	3.80439
$665$	16.9900	0.658846
$666$	0.139708	0.00541356
$667$	19.8122	0.767133
$668$	98.0791	3.79479
$669$	−19.8724	−0.768311
$670$	146.778	5.67054
$671$	45.5097	1.75688
$672$	11.5155	0.444221
$673$	−31.4814	−1.21352	−0.606759	−	0.794886i	$-0.707531\pi$
$673$	−31.4814	−1.21352	−0.606759	+	0.794886i	$0.707531\pi$
$674$	−7.46930	−0.287707
$675$	10.8074	0.415976
$676$	88.9178	3.41992
$677$	−2.13104	−0.0819027	−0.0409513	−	0.999161i	$-0.513039\pi$
$677$	−2.13104	−0.0819027	−0.0409513	+	0.999161i	$0.513039\pi$
$678$	6.47676	0.248738
$679$	−0.516461	−0.0198199
$680$	−106.796	−4.09543
$681$	5.22666	0.200286
$682$	28.1143	1.07655
$683$	−46.7258	−1.78791	−0.893956	−	0.448155i	$-0.852081\pi$
$683$	−46.7258	−1.78791	−0.893956	+	0.448155i	$0.852081\pi$
$684$	20.9210	0.799934
$685$	14.2177	0.543231
$686$	2.62597	0.100260
$687$	−4.42137	−0.168686
$688$	120.880	4.60851
$689$	12.2346	0.466103
$690$	−88.6092	−3.37329
$691$	−23.7227	−0.902454	−0.451227	−	0.892409i	$-0.649013\pi$
$691$	−23.7227	−0.902454	−0.451227	+	0.892409i	$0.649013\pi$
$692$	87.1544	3.31311
$693$	−3.07295	−0.116732
$694$	42.2745	1.60472
$695$	67.8319	2.57301
$696$	17.7510	0.672850
$697$	−17.3251	−0.656235
$698$	−82.0002	−3.10376
$699$	−18.0277	−0.681871
$700$	−52.9100	−1.99981
$701$	−4.62036	−0.174508	−0.0872542	−	0.996186i	$-0.527809\pi$
$701$	−4.62036	−0.174508	−0.0872542	+	0.996186i	$0.527809\pi$
$702$	14.6590	0.553269
$703$	−0.227350	−0.00857466
$704$	30.3794	1.14497
$705$	−36.8149	−1.38653
$706$	−57.1825	−2.15209
$707$	6.65915	0.250443
$708$	−5.78189	−0.217297
$709$	−10.7505	−0.403745	−0.201873	−	0.979412i	$-0.564703\pi$
$709$	−10.7505	−0.403745	−0.201873	+	0.979412i	$0.564703\pi$
$710$	62.7099	2.35346
$711$	2.69910	0.101224
$712$	18.6295	0.698172
$713$	29.5693	1.10738
$714$	−9.27610	−0.347149
$715$	68.2025	2.55063
$716$	46.3025	1.73041
$717$	−6.39593	−0.238860
$718$	4.54940	0.169782
$719$	−20.3307	−0.758207	−0.379104	−	0.925354i	$-0.623768\pi$
$719$	−20.3307	−0.758207	−0.379104	+	0.925354i	$0.623768\pi$
$720$	−40.4611	−1.50789
$721$	9.17575	0.341723
$722$	1.94009	0.0722025
$723$	5.11788	0.190336
$724$	114.027	4.23779
$725$	−25.2287	−0.936971
$726$	4.08858	0.151741
$727$	−35.9061	−1.33168	−0.665841	−	0.746093i	$-0.731927\pi$
$727$	−35.9061	−1.33168	−0.665841	+	0.746093i	$0.731927\pi$
$728$	−42.4486	−1.57325
$729$	1.00000	0.0370370
$730$	−122.967	−4.55120
$731$	−41.9588	−1.55190
$732$	72.5046	2.67985
$733$	45.2456	1.67118	0.835592	−	0.549350i	$-0.185125\pi$
$733$	45.2456	1.67118	0.835592	+	0.549350i	$0.185125\pi$
$734$	−40.5841	−1.49799
$735$	−3.97585	−0.146651
$736$	97.7333	3.60250
$737$	43.2013	1.59134
$738$	−12.8792	−0.474092
$739$	−4.22855	−0.155550	−0.0777748	−	0.996971i	$-0.524782\pi$
$739$	−4.22855	−0.155550	−0.0777748	+	0.996971i	$0.524782\pi$
$740$	1.03556	0.0380681
$741$	−23.8550	−0.876336
$742$	−5.75528	−0.211283
$743$	−33.3507	−1.22352	−0.611758	−	0.791045i	$-0.709538\pi$
$743$	−33.3507	−1.22352	−0.611758	+	0.791045i	$0.709538\pi$
$744$	26.4929	0.971279
$745$	−77.4340	−2.83696
$746$	44.3389	1.62336
$747$	−12.8920	−0.471695
$748$	−53.1433	−1.94311
$749$	−17.3572	−0.634217
$750$	60.6318	2.21396
$751$	0.565731	0.0206438	0.0103219	−	0.999947i	$-0.496714\pi$
$751$	0.565731	0.0206438	0.0103219	+	0.999947i	$0.496714\pi$
$752$	94.2325	3.43631
$753$	4.32880	0.157750
$754$	−34.2200	−1.24622
$755$	13.5826	0.494320
$756$	−4.89573	−0.178056
$757$	−14.1218	−0.513266	−0.256633	−	0.966509i	$-0.582613\pi$
$757$	−14.1218	−0.513266	−0.256633	+	0.966509i	$0.582613\pi$
$758$	−52.3476	−1.90135
$759$	−26.0804	−0.946658
$760$	129.194	4.68636
$761$	−4.22765	−0.153252	−0.0766261	−	0.997060i	$-0.524415\pi$
$761$	−4.22765	−0.153252	−0.0766261	+	0.997060i	$0.524415\pi$
$762$	1.19238	0.0431955
$763$	7.00848	0.253724
$764$	−54.0728	−1.95629
$765$	14.0445	0.507779
$766$	−2.62597	−0.0948802
$767$	6.59276	0.238051
$768$	−12.0795	−0.435880
$769$	9.37348	0.338016	0.169008	−	0.985615i	$-0.445944\pi$
$769$	9.37348	0.338016	0.169008	+	0.985615i	$0.445944\pi$
$770$	−32.0830	−1.15619
$771$	−16.8812	−0.607963
$772$	−58.9803	−2.12275
$773$	48.5239	1.74529	0.872643	−	0.488359i	$-0.162405\pi$
$773$	48.5239	1.74529	0.872643	+	0.488359i	$0.162405\pi$
$774$	−31.1916	−1.12116
$775$	−37.6533	−1.35255
$776$	−3.92722	−0.140979
$777$	0.0532022	0.00190862
$778$	18.2416	0.653994
$779$	20.9587	0.750924
$780$	108.658	3.89059
$781$	18.4575	0.660460
$782$	−78.7271	−2.81528
$783$	−2.33440	−0.0834246
$784$	10.1767	0.363454
$785$	31.2574	1.11562
$786$	29.2051	1.04171
$787$	0.369000	0.0131534	0.00657672	−	0.999978i	$-0.497907\pi$
$787$	0.369000	0.0131534	0.00657672	+	0.999978i	$0.497907\pi$
$788$	−72.6047	−2.58644
$789$	−0.841148	−0.0299457
$790$	28.1798	1.00259
$791$	2.46642	0.0876959
$792$	−23.3670	−0.830311
$793$	−82.6729	−2.93580
$794$	−93.1122	−3.30443
$795$	8.71378	0.309046
$796$	−30.7378	−1.08947
$797$	1.27622	0.0452060	0.0226030	−	0.999745i	$-0.492805\pi$
$797$	1.27622	0.0452060	0.0226030	+	0.999745i	$0.492805\pi$
$798$	11.2216	0.397240
$799$	−32.7091	−1.15717
$800$	−124.453	−4.40007
$801$	−2.44993	−0.0865641
$802$	−76.3465	−2.69589
$803$	−36.1929	−1.27722
$804$	68.8270	2.42734
$805$	−33.7434	−1.18930
$806$	−51.0725	−1.79895
$807$	−16.4028	−0.577404
$808$	50.6368	1.78140
$809$	44.8312	1.57618	0.788091	−	0.615559i	$-0.211070\pi$
$809$	44.8312	1.57618	0.788091	+	0.615559i	$0.211070\pi$
$810$	10.4405	0.366841
$811$	−53.1829	−1.86750	−0.933751	−	0.357922i	$-0.883485\pi$
$811$	−53.1829	−1.86750	−0.933751	+	0.357922i	$0.883485\pi$
$812$	11.4286	0.401064
$813$	11.8176	0.414463
$814$	0.429314	0.0150475
$815$	−75.6792	−2.65093
$816$	−35.9487	−1.25845
$817$	50.7589	1.77583
$818$	37.3193	1.30484
$819$	5.58232	0.195062
$820$	−95.4658	−3.33381
$821$	43.8771	1.53132	0.765661	−	0.643245i	$-0.222412\pi$
$821$	43.8771	1.53132	0.765661	+	0.643245i	$0.222412\pi$
$822$	9.39052	0.327532
$823$	−6.56420	−0.228814	−0.114407	−	0.993434i	$-0.536497\pi$
$823$	−6.56420	−0.228814	−0.114407	+	0.993434i	$0.536497\pi$
$824$	69.7734	2.43067
$825$	33.2105	1.15624
$826$	−3.10129	−0.107908
$827$	−14.2172	−0.494381	−0.247190	−	0.968967i	$-0.579507\pi$
$827$	−14.2172	−0.494381	−0.247190	+	0.968967i	$0.579507\pi$
$828$	−41.5505	−1.44398
$829$	−45.8349	−1.59191	−0.795955	−	0.605355i	$-0.793031\pi$
$829$	−45.8349	−1.59191	−0.795955	+	0.605355i	$0.793031\pi$
$830$	−134.599	−4.67200
$831$	4.29660	0.149047
$832$	−55.1872	−1.91327
$833$	−3.53245	−0.122392
$834$	44.8017	1.55135
$835$	−79.6506	−2.75642
$836$	64.2891	2.22349
$837$	−3.48403	−0.120426
$838$	77.1538	2.66523
$839$	−23.6047	−0.814923	−0.407462	−	0.913222i	$-0.633586\pi$
$839$	−23.6047	−0.814923	−0.407462	+	0.913222i	$0.633586\pi$
$840$	−30.2328	−1.04313
$841$	−23.5506	−0.812089
$842$	10.0782	0.347319
$843$	7.76321	0.267379
$844$	138.194	4.75683
$845$	−72.2107	−2.48412
$846$	−24.3155	−0.835985
$847$	1.55698	0.0534984
$848$	−22.3041	−0.765924
$849$	−1.31516	−0.0451362
$850$	100.250	3.43856
$851$	0.451532	0.0154783
$852$	29.4058	1.00743
$853$	1.77198	0.0606716	0.0303358	−	0.999540i	$-0.490342\pi$
$853$	1.77198	0.0606716	0.0303358	+	0.999540i	$0.490342\pi$
$854$	38.8900	1.33079
$855$	−16.9900	−0.581047
$856$	−131.986	−4.51118
$857$	−28.2393	−0.964636	−0.482318	−	0.875996i	$-0.660205\pi$
$857$	−28.2393	−0.964636	−0.482318	+	0.875996i	$0.660205\pi$
$858$	45.0464	1.53786
$859$	55.1065	1.88021	0.940105	−	0.340885i	$-0.110727\pi$
$859$	55.1065	1.88021	0.940105	+	0.340885i	$0.110727\pi$
$860$	−231.204	−7.88398
$861$	−4.90456	−0.167147
$862$	−69.5477	−2.36880
$863$	19.7827	0.673410	0.336705	−	0.941610i	$-0.390687\pi$
$863$	19.7827	0.673410	0.336705	+	0.941610i	$0.390687\pi$
$864$	−11.5155	−0.391766
$865$	−70.7786	−2.40654
$866$	16.7473	0.569096
$867$	−4.52183	−0.153569
$868$	17.0569	0.578948
$869$	8.29419	0.281361
$870$	−24.3722	−0.826295
$871$	−78.4796	−2.65918
$872$	53.2932	1.80474
$873$	0.516461	0.0174795
$874$	95.2387	3.22150
$875$	23.0893	0.780560
$876$	−57.6614	−1.94820
$877$	−6.46797	−0.218408	−0.109204	−	0.994019i	$-0.534830\pi$
$877$	−6.46797	−0.218408	−0.109204	+	0.994019i	$0.534830\pi$
$878$	60.6250	2.04599
$879$	−26.7529	−0.902353
$880$	−124.335	−4.19132
$881$	−7.51583	−0.253215	−0.126607	−	0.991953i	$-0.540409\pi$
$881$	−7.51583	−0.253215	−0.126607	+	0.991953i	$0.540409\pi$
$882$	−2.62597	−0.0884211
$883$	38.2423	1.28696	0.643478	−	0.765465i	$-0.277491\pi$
$883$	38.2423	1.28696	0.643478	+	0.765465i	$0.277491\pi$
$884$	96.5401	3.24700
$885$	4.69551	0.157838
$886$	86.2565	2.89784
$887$	10.7302	0.360286	0.180143	−	0.983640i	$-0.442344\pi$
$887$	10.7302	0.360286	0.180143	+	0.983640i	$0.442344\pi$
$888$	0.404555	0.0135760
$889$	0.454073	0.0152291
$890$	−25.5785	−0.857392
$891$	3.07295	0.102948
$892$	−97.2899	−3.25751
$893$	39.5693	1.32414
$894$	−51.1436	−1.71050
$895$	−37.6025	−1.25691
$896$	2.92946	0.0978663
$897$	47.3777	1.58189
$898$	40.4738	1.35063
$899$	8.13312	0.271255
$900$	52.9100	1.76367
$901$	7.74198	0.257923
$902$	−39.5773	−1.31778
$903$	−11.8781	−0.395279
$904$	18.7549	0.623780
$905$	−92.6022	−3.07820
$906$	8.97102	0.298042
$907$	33.5047	1.11251	0.556253	−	0.831013i	$-0.312239\pi$
$907$	33.5047	1.11251	0.556253	+	0.831013i	$0.312239\pi$
$908$	25.5883	0.849179
$909$	−6.65915	−0.220870
$910$	58.2821	1.93203
$911$	9.92181	0.328724	0.164362	−	0.986400i	$-0.447443\pi$
$911$	9.92181	0.328724	0.164362	+	0.986400i	$0.447443\pi$
$912$	43.4882	1.44004
$913$	−39.6166	−1.31112
$914$	−6.24887	−0.206694
$915$	−58.8814	−1.94656
$916$	−21.6458	−0.715198
$917$	11.1216	0.367269
$918$	9.27610	0.306157
$919$	35.3163	1.16498	0.582488	−	0.812839i	$-0.302079\pi$
$919$	35.3163	1.16498	0.582488	+	0.812839i	$0.302079\pi$
$920$	−256.588	−8.45946
$921$	−8.19727	−0.270109
$922$	60.0785	1.97858
$923$	−33.5298	−1.10365
$924$	−15.0443	−0.494922
$925$	−0.574977	−0.0189051
$926$	64.3979	2.11625
$927$	−9.17575	−0.301371
$928$	26.8818	0.882440
$929$	−3.25816	−0.106897	−0.0534483	−	0.998571i	$-0.517021\pi$
$929$	−3.25816	−0.106897	−0.0534483	+	0.998571i	$0.517021\pi$
$930$	−36.3749	−1.19278
$931$	4.27331	0.140052
$932$	−88.2589	−2.89102
$933$	−19.8503	−0.649870
$934$	36.6034	1.19770
$935$	43.1580	1.41142
$936$	42.4486	1.38747
$937$	−43.0123	−1.40515	−0.702575	−	0.711610i	$-0.747966\pi$
$937$	−43.0123	−1.40515	−0.702575	+	0.711610i	$0.747966\pi$
$938$	36.9175	1.20540
$939$	−2.30566	−0.0752423
$940$	−180.236	−5.87864
$941$	18.1033	0.590150	0.295075	−	0.955474i	$-0.404655\pi$
$941$	18.1033	0.590150	0.295075	+	0.955474i	$0.404655\pi$
$942$	20.6449	0.672647
$943$	−41.6255	−1.35551
$944$	−12.0188	−0.391177
$945$	3.97585	0.129334
$946$	−95.8502	−3.11636
$947$	33.1097	1.07592	0.537960	−	0.842970i	$-0.319195\pi$
$947$	33.1097	1.07592	0.537960	+	0.842970i	$0.319195\pi$
$948$	13.2140	0.429172
$949$	65.7480	2.13427
$950$	−121.276	−3.93472
$951$	19.1053	0.619531
$952$	−26.8611	−0.870573
$953$	−7.08241	−0.229422	−0.114711	−	0.993399i	$-0.536594\pi$
$953$	−7.08241	−0.229422	−0.114711	+	0.993399i	$0.536594\pi$
$954$	5.75528	0.186334
$955$	43.9129	1.42099
$956$	−31.3128	−1.01273
$957$	−7.17349	−0.231886
$958$	21.4549	0.693176
$959$	3.57602	0.115476
$960$	−39.3055	−1.26858
$961$	−18.8615	−0.608436
$962$	−0.779893	−0.0251448
$963$	17.3572	0.559327
$964$	25.0557	0.806991
$965$	47.8982	1.54190
$966$	−22.2869	−0.717068
$967$	−4.01091	−0.128982	−0.0644911	−	0.997918i	$-0.520542\pi$
$967$	−4.01091	−0.128982	−0.0644911	+	0.997918i	$0.520542\pi$
$968$	11.8394	0.380533
$969$	−15.0952	−0.484929
$970$	5.39209	0.173130
$971$	−44.6057	−1.43147	−0.715733	−	0.698374i	$-0.753907\pi$
$971$	−44.6057	−1.43147	−0.715733	+	0.698374i	$0.753907\pi$
$972$	4.89573	0.157031
$973$	17.0610	0.546950
$974$	13.1511	0.421388
$975$	−60.3303	−1.93212
$976$	150.715	4.82426
$977$	42.8677	1.37146	0.685730	−	0.727856i	$-0.259483\pi$
$977$	42.8677	1.37146	0.685730	+	0.727856i	$0.259483\pi$
$978$	−49.9847	−1.59833
$979$	−7.52852	−0.240613
$980$	−19.4647	−0.621777
$981$	−7.00848	−0.223764
$982$	39.9592	1.27515
$983$	4.78631	0.152660	0.0763298	−	0.997083i	$-0.475680\pi$
$983$	4.78631	0.152660	0.0763298	+	0.997083i	$0.475680\pi$
$984$	−37.2948	−1.18892
$985$	58.9627	1.87871
$986$	−21.6541	−0.689608
$987$	−9.25963	−0.294737
$988$	−116.788	−3.71551
$989$	−100.811	−3.20559
$990$	32.0830	1.01967
$991$	−18.1980	−0.578079	−0.289039	−	0.957317i	$-0.593336\pi$
$991$	−18.1980	−0.578079	−0.289039	+	0.957317i	$0.593336\pi$
$992$	40.1205	1.27383
$993$	−0.245813	−0.00780064
$994$	15.7727	0.500280
$995$	24.9624	0.791360
$996$	−63.1159	−1.99990
$997$	−33.7449	−1.06871	−0.534356	−	0.845260i	$-0.679446\pi$
$997$	−33.7449	−1.06871	−0.534356	+	0.845260i	$0.679446\pi$
$998$	5.03160	0.159272
$999$	−0.0532022	−0.00168324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.2	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.2	✓	44	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62597 q^{2} +1.00000 q^{3} +4.89573 q^{4} -3.97585 q^{5} -2.62597 q^{6} -1.00000 q^{7} -7.60410 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62597 q^{2} +1.00000 q^{3} +4.89573 q^{4} -3.97585 q^{5} -2.62597 q^{6} -1.00000 q^{7} -7.60410 q^{8} +1.00000 q^{9} +10.4405 q^{10} +3.07295 q^{11} +4.89573 q^{12} -5.58232 q^{13} +2.62597 q^{14} -3.97585 q^{15} +10.1767 q^{16} -3.53245 q^{17} -2.62597 q^{18} +4.27331 q^{19} -19.4647 q^{20} -1.00000 q^{21} -8.06948 q^{22} -8.48709 q^{23} -7.60410 q^{24} +10.8074 q^{25} +14.6590 q^{26} +1.00000 q^{27} -4.89573 q^{28} -2.33440 q^{29} +10.4405 q^{30} -3.48403 q^{31} -11.5155 q^{32} +3.07295 q^{33} +9.27610 q^{34} +3.97585 q^{35} +4.89573 q^{36} -0.0532022 q^{37} -11.2216 q^{38} -5.58232 q^{39} +30.2328 q^{40} +4.90456 q^{41} +2.62597 q^{42} +11.8781 q^{43} +15.0443 q^{44} -3.97585 q^{45} +22.2869 q^{46} +9.25963 q^{47} +10.1767 q^{48} +1.00000 q^{49} -28.3799 q^{50} -3.53245 q^{51} -27.3295 q^{52} -2.19168 q^{53} -2.62597 q^{54} -12.2176 q^{55} +7.60410 q^{56} +4.27331 q^{57} +6.13006 q^{58} -1.18101 q^{59} -19.4647 q^{60} +14.8098 q^{61} +9.14897 q^{62} -1.00000 q^{63} +9.88607 q^{64} +22.1945 q^{65} -8.06948 q^{66} +14.0586 q^{67} -17.2939 q^{68} -8.48709 q^{69} -10.4405 q^{70} +6.00643 q^{71} -7.60410 q^{72} -11.7779 q^{73} +0.139708 q^{74} +10.8074 q^{75} +20.9210 q^{76} -3.07295 q^{77} +14.6590 q^{78} +2.69910 q^{79} -40.4611 q^{80} +1.00000 q^{81} -12.8792 q^{82} -12.8920 q^{83} -4.89573 q^{84} +14.0445 q^{85} -31.1916 q^{86} -2.33440 q^{87} -23.3670 q^{88} -2.44993 q^{89} +10.4405 q^{90} +5.58232 q^{91} -41.5505 q^{92} -3.48403 q^{93} -24.3155 q^{94} -16.9900 q^{95} -11.5155 q^{96} +0.516461 q^{97} -2.62597 q^{98} +3.07295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

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