LMFDB - Embedded newform 8041.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.96076 q^{2} -1.83181 q^{3} +1.84459 q^{4} -1.45283 q^{5} +3.59175 q^{6} +0.993575 q^{7} +0.304726 q^{8} +0.355533 q^{9} +O(q^{10})$	\(q-1.96076 q^{2} -1.83181 q^{3} +1.84459 q^{4} -1.45283 q^{5} +3.59175 q^{6} +0.993575 q^{7} +0.304726 q^{8} +0.355533 q^{9} +2.84866 q^{10} -1.00000 q^{11} -3.37894 q^{12} +0.254157 q^{13} -1.94816 q^{14} +2.66131 q^{15} -4.28667 q^{16} -1.00000 q^{17} -0.697116 q^{18} -6.56660 q^{19} -2.67988 q^{20} -1.82004 q^{21} +1.96076 q^{22} -1.71714 q^{23} -0.558200 q^{24} -2.88928 q^{25} -0.498342 q^{26} +4.84416 q^{27} +1.83274 q^{28} -4.03686 q^{29} -5.21820 q^{30} +5.05113 q^{31} +7.79569 q^{32} +1.83181 q^{33} +1.96076 q^{34} -1.44350 q^{35} +0.655812 q^{36} -10.8010 q^{37} +12.8755 q^{38} -0.465569 q^{39} -0.442715 q^{40} -3.81116 q^{41} +3.56867 q^{42} +1.00000 q^{43} -1.84459 q^{44} -0.516530 q^{45} +3.36690 q^{46} -11.1603 q^{47} +7.85237 q^{48} -6.01281 q^{49} +5.66519 q^{50} +1.83181 q^{51} +0.468816 q^{52} +7.02133 q^{53} -9.49825 q^{54} +1.45283 q^{55} +0.302768 q^{56} +12.0288 q^{57} +7.91532 q^{58} -8.63232 q^{59} +4.90903 q^{60} -3.66500 q^{61} -9.90406 q^{62} +0.353249 q^{63} -6.71215 q^{64} -0.369248 q^{65} -3.59175 q^{66} +2.19096 q^{67} -1.84459 q^{68} +3.14547 q^{69} +2.83035 q^{70} -5.84594 q^{71} +0.108340 q^{72} -4.67222 q^{73} +21.1783 q^{74} +5.29262 q^{75} -12.1127 q^{76} -0.993575 q^{77} +0.912869 q^{78} -0.350370 q^{79} +6.22781 q^{80} -9.94020 q^{81} +7.47277 q^{82} -3.75535 q^{83} -3.35723 q^{84} +1.45283 q^{85} -1.96076 q^{86} +7.39477 q^{87} -0.304726 q^{88} +10.4301 q^{89} +1.01279 q^{90} +0.252525 q^{91} -3.16741 q^{92} -9.25271 q^{93} +21.8828 q^{94} +9.54016 q^{95} -14.2802 q^{96} +1.74016 q^{97} +11.7897 q^{98} -0.355533 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.96076	−1.38647	−0.693234	−	0.720712i	$-0.743815\pi$
$2$	−1.96076	−1.38647	−0.693234	+	0.720712i	$0.743815\pi$
$3$	−1.83181	−1.05760	−0.528798	−	0.848747i	$-0.677357\pi$
$3$	−1.83181	−1.05760	−0.528798	+	0.848747i	$0.677357\pi$
$4$	1.84459	0.922294
$5$	−1.45283	−0.649726	−0.324863	−	0.945761i	$-0.605318\pi$
$5$	−1.45283	−0.649726	−0.324863	+	0.945761i	$0.605318\pi$
$6$	3.59175	1.46632
$7$	0.993575	0.375536	0.187768	−	0.982213i	$-0.439875\pi$
$7$	0.993575	0.375536	0.187768	+	0.982213i	$0.439875\pi$
$8$	0.304726	0.107737
$9$	0.355533	0.118511
$10$	2.84866	0.900824
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.37894	−0.975415
$13$	0.254157	0.0704906	0.0352453	−	0.999379i	$-0.488779\pi$
$13$	0.254157	0.0704906	0.0352453	+	0.999379i	$0.488779\pi$
$14$	−1.94816	−0.520669
$15$	2.66131	0.687148
$16$	−4.28667	−1.07167
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.697116	−0.164312
$19$	−6.56660	−1.50648	−0.753241	−	0.657745i	$-0.771510\pi$
$19$	−6.56660	−1.50648	−0.753241	+	0.657745i	$0.771510\pi$
$20$	−2.67988	−0.599238
$21$	−1.82004	−0.397166
$22$	1.96076	0.418036
$23$	−1.71714	−0.358048	−0.179024	−	0.983845i	$-0.557294\pi$
$23$	−1.71714	−0.358048	−0.179024	+	0.983845i	$0.557294\pi$
$24$	−0.558200	−0.113942
$25$	−2.88928	−0.577856
$26$	−0.498342	−0.0977330
$27$	4.84416	0.932260
$28$	1.83274	0.346355
$29$	−4.03686	−0.749626	−0.374813	−	0.927100i	$-0.622293\pi$
$29$	−4.03686	−0.749626	−0.374813	+	0.927100i	$0.622293\pi$
$30$	−5.21820	−0.952709
$31$	5.05113	0.907209	0.453605	−	0.891203i	$-0.350138\pi$
$31$	5.05113	0.907209	0.453605	+	0.891203i	$0.350138\pi$
$32$	7.79569	1.37810
$33$	1.83181	0.318877
$34$	1.96076	0.336268
$35$	−1.44350	−0.243996
$36$	0.655812	0.109302
$37$	−10.8010	−1.77568	−0.887840	−	0.460152i	$-0.847795\pi$
$37$	−10.8010	−1.77568	−0.887840	+	0.460152i	$0.847795\pi$
$38$	12.8755	2.08869
$39$	−0.465569	−0.0745506
$40$	−0.442715	−0.0699994
$41$	−3.81116	−0.595202	−0.297601	−	0.954690i	$-0.596187\pi$
$41$	−3.81116	−0.595202	−0.297601	+	0.954690i	$0.596187\pi$
$42$	3.56867	0.550658
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.84459	−0.278082
$45$	−0.516530	−0.0769997
$46$	3.36690	0.496422
$47$	−11.1603	−1.62790	−0.813952	−	0.580933i	$-0.802688\pi$
$47$	−11.1603	−1.62790	−0.813952	+	0.580933i	$0.802688\pi$
$48$	7.85237	1.13339
$49$	−6.01281	−0.858973
$50$	5.66519	0.801179
$51$	1.83181	0.256505
$52$	0.468816	0.0650131
$53$	7.02133	0.964454	0.482227	−	0.876046i	$-0.339828\pi$
$53$	7.02133	0.964454	0.482227	+	0.876046i	$0.339828\pi$
$54$	−9.49825	−1.29255
$55$	1.45283	0.195900
$56$	0.302768	0.0404591
$57$	12.0288	1.59325
$58$	7.91532	1.03933
$59$	−8.63232	−1.12383	−0.561916	−	0.827194i	$-0.689936\pi$
$59$	−8.63232	−1.12383	−0.561916	+	0.827194i	$0.689936\pi$
$60$	4.90903	0.633753
$61$	−3.66500	−0.469255	−0.234627	−	0.972085i	$-0.575387\pi$
$61$	−3.66500	−0.469255	−0.234627	+	0.972085i	$0.575387\pi$
$62$	−9.90406	−1.25782
$63$	0.353249	0.0445052
$64$	−6.71215	−0.839019
$65$	−0.369248	−0.0457996
$66$	−3.59175	−0.442113
$67$	2.19096	0.267668	0.133834	−	0.991004i	$-0.457271\pi$
$67$	2.19096	0.267668	0.133834	+	0.991004i	$0.457271\pi$
$68$	−1.84459	−0.223689
$69$	3.14547	0.378670
$70$	2.83035	0.338292
$71$	−5.84594	−0.693786	−0.346893	−	0.937905i	$-0.612763\pi$
$71$	−5.84594	−0.693786	−0.346893	+	0.937905i	$0.612763\pi$
$72$	0.108340	0.0127680
$73$	−4.67222	−0.546842	−0.273421	−	0.961894i	$-0.588155\pi$
$73$	−4.67222	−0.546842	−0.273421	+	0.961894i	$0.588155\pi$
$74$	21.1783	2.46192
$75$	5.29262	0.611139
$76$	−12.1127	−1.38942
$77$	−0.993575	−0.113228
$78$	0.912869	0.103362
$79$	−0.350370	−0.0394197	−0.0197098	−	0.999806i	$-0.506274\pi$
$79$	−0.350370	−0.0394197	−0.0197098	+	0.999806i	$0.506274\pi$
$80$	6.22781	0.696290
$81$	−9.94020	−1.10447
$82$	7.47277	0.825229
$83$	−3.75535	−0.412203	−0.206101	−	0.978531i	$-0.566078\pi$
$83$	−3.75535	−0.412203	−0.206101	+	0.978531i	$0.566078\pi$
$84$	−3.35723	−0.366304
$85$	1.45283	0.157582
$86$	−1.96076	−0.211434
$87$	7.39477	0.792802
$88$	−0.304726	−0.0324839
$89$	10.4301	1.10559	0.552794	−	0.833318i	$-0.313562\pi$
$89$	10.4301	1.10559	0.552794	+	0.833318i	$0.313562\pi$
$90$	1.01279	0.106758
$91$	0.252525	0.0264718
$92$	−3.16741	−0.330225
$93$	−9.25271	−0.959462
$94$	21.8828	2.25704
$95$	9.54016	0.978800
$96$	−14.2802	−1.45747
$97$	1.74016	0.176687	0.0883433	−	0.996090i	$-0.471843\pi$
$97$	1.74016	0.176687	0.0883433	+	0.996090i	$0.471843\pi$
$98$	11.7897	1.19094
$99$	−0.355533	−0.0357324
$100$	−5.32953	−0.532953
$101$	13.8756	1.38068	0.690338	−	0.723487i	$-0.257462\pi$
$101$	13.8756	1.38068	0.690338	+	0.723487i	$0.257462\pi$
$102$	−3.59175	−0.355636
$103$	−0.810992	−0.0799094	−0.0399547	−	0.999201i	$-0.512721\pi$
$103$	−0.810992	−0.0799094	−0.0399547	+	0.999201i	$0.512721\pi$
$104$	0.0774483	0.00759444
$105$	2.64421	0.258049
$106$	−13.7672	−1.33719
$107$	1.09010	0.105384	0.0526920	−	0.998611i	$-0.483220\pi$
$107$	1.09010	0.105384	0.0526920	+	0.998611i	$0.483220\pi$
$108$	8.93549	0.859818
$109$	2.68824	0.257486	0.128743	−	0.991678i	$-0.458906\pi$
$109$	2.68824	0.257486	0.128743	+	0.991678i	$0.458906\pi$
$110$	−2.84866	−0.271609
$111$	19.7855	1.87795
$112$	−4.25913	−0.402450
$113$	−1.01087	−0.0950945	−0.0475473	−	0.998869i	$-0.515140\pi$
$113$	−1.01087	−0.0950945	−0.0475473	+	0.998869i	$0.515140\pi$
$114$	−23.5856	−2.20899
$115$	2.49471	0.232633
$116$	−7.44634	−0.691376
$117$	0.0903614	0.00835391
$118$	16.9259	1.55816
$119$	−0.993575	−0.0910809
$120$	0.810971	0.0740312
$121$	1.00000	0.0909091
$122$	7.18619	0.650607
$123$	6.98132	0.629484
$124$	9.31725	0.836714
$125$	11.4618	1.02517
$126$	−0.692637	−0.0617050
$127$	−4.60357	−0.408501	−0.204251	−	0.978919i	$-0.565476\pi$
$127$	−4.60357	−0.408501	−0.204251	+	0.978919i	$0.565476\pi$
$128$	−2.43045	−0.214823
$129$	−1.83181	−0.161282
$130$	0.724008	0.0634997
$131$	−12.6440	−1.10471	−0.552356	−	0.833608i	$-0.686271\pi$
$131$	−12.6440	−1.10471	−0.552356	+	0.833608i	$0.686271\pi$
$132$	3.37894	0.294099
$133$	−6.52441	−0.565738
$134$	−4.29594	−0.371113
$135$	−7.03775	−0.605714
$136$	−0.304726	−0.0261300
$137$	7.39241	0.631577	0.315788	−	0.948830i	$-0.397731\pi$
$137$	7.39241	0.631577	0.315788	+	0.948830i	$0.397731\pi$
$138$	−6.16752	−0.525014
$139$	−10.3970	−0.881864	−0.440932	−	0.897541i	$-0.645352\pi$
$139$	−10.3970	−0.881864	−0.440932	+	0.897541i	$0.645352\pi$
$140$	−2.66266	−0.225036
$141$	20.4436	1.72167
$142$	11.4625	0.961912
$143$	−0.254157	−0.0212537
$144$	−1.52405	−0.127004
$145$	5.86488	0.487052
$146$	9.16111	0.758179
$147$	11.0143	0.908447
$148$	−19.9235	−1.63770
$149$	−11.5826	−0.948880	−0.474440	−	0.880288i	$-0.657349\pi$
$149$	−11.5826	−0.948880	−0.474440	+	0.880288i	$0.657349\pi$
$150$	−10.3776	−0.847325
$151$	−7.35482	−0.598527	−0.299263	−	0.954171i	$-0.596741\pi$
$151$	−7.35482	−0.598527	−0.299263	+	0.954171i	$0.596741\pi$
$152$	−2.00101	−0.162304
$153$	−0.355533	−0.0287431
$154$	1.94816	0.156988
$155$	−7.33844	−0.589437
$156$	−0.858782	−0.0687576
$157$	−1.95527	−0.156047	−0.0780237	−	0.996952i	$-0.524861\pi$
$157$	−1.95527	−0.156047	−0.0780237	+	0.996952i	$0.524861\pi$
$158$	0.686992	0.0546541
$159$	−12.8618	−1.02000
$160$	−11.3258	−0.895385
$161$	−1.70610	−0.134460
$162$	19.4904	1.53131
$163$	0.863863	0.0676630	0.0338315	−	0.999428i	$-0.489229\pi$
$163$	0.863863	0.0676630	0.0338315	+	0.999428i	$0.489229\pi$
$164$	−7.03001	−0.548952
$165$	−2.66131	−0.207183
$166$	7.36334	0.571506
$167$	−8.22791	−0.636695	−0.318348	−	0.947974i	$-0.603128\pi$
$167$	−8.22791	−0.636695	−0.318348	+	0.947974i	$0.603128\pi$
$168$	−0.554614	−0.0427894
$169$	−12.9354	−0.995031
$170$	−2.84866	−0.218482
$171$	−2.33464	−0.178535
$172$	1.84459	0.140649
$173$	15.3449	1.16665	0.583327	−	0.812237i	$-0.301750\pi$
$173$	15.3449	1.16665	0.583327	+	0.812237i	$0.301750\pi$
$174$	−14.4994	−1.09920
$175$	−2.87072	−0.217006
$176$	4.28667	0.323120
$177$	15.8128	1.18856
$178$	−20.4509	−1.53286
$179$	−12.8174	−0.958016	−0.479008	−	0.877810i	$-0.659004\pi$
$179$	−12.8174	−0.958016	−0.479008	+	0.877810i	$0.659004\pi$
$180$	−0.952784	−0.0710163
$181$	−17.3475	−1.28943	−0.644714	−	0.764424i	$-0.723023\pi$
$181$	−17.3475	−1.28943	−0.644714	+	0.764424i	$0.723023\pi$
$182$	−0.495141	−0.0367023
$183$	6.71358	0.496282
$184$	−0.523256	−0.0385749
$185$	15.6921	1.15371
$186$	18.1424	1.33026
$187$	1.00000	0.0731272
$188$	−20.5862	−1.50141
$189$	4.81304	0.350097
$190$	−18.7060	−1.35708
$191$	1.78613	0.129240	0.0646199	−	0.997910i	$-0.479417\pi$
$191$	1.78613	0.129240	0.0646199	+	0.997910i	$0.479417\pi$
$192$	12.2954	0.887344
$193$	−16.2308	−1.16832	−0.584159	−	0.811639i	$-0.698575\pi$
$193$	−16.2308	−1.16832	−0.584159	+	0.811639i	$0.698575\pi$
$194$	−3.41204	−0.244970
$195$	0.676393	0.0484375
$196$	−11.0912	−0.792225
$197$	8.94923	0.637606	0.318803	−	0.947821i	$-0.396719\pi$
$197$	8.94923	0.637606	0.318803	+	0.947821i	$0.396719\pi$
$198$	0.697116	0.0495418
$199$	−5.19014	−0.367919	−0.183960	−	0.982934i	$-0.558892\pi$
$199$	−5.19014	−0.367919	−0.183960	+	0.982934i	$0.558892\pi$
$200$	−0.880438	−0.0622564
$201$	−4.01342	−0.283085
$202$	−27.2068	−1.91426
$203$	−4.01092	−0.281512
$204$	3.37894	0.236573
$205$	5.53697	0.386718
$206$	1.59016	0.110792
$207$	−0.610499	−0.0424326
$208$	−1.08949	−0.0755425
$209$	6.56660	0.454221
$210$	−5.18468	−0.357777
$211$	−17.8906	−1.23164	−0.615818	−	0.787888i	$-0.711174\pi$
$211$	−17.8906	−1.23164	−0.615818	+	0.787888i	$0.711174\pi$
$212$	12.9515	0.889510
$213$	10.7087	0.733746
$214$	−2.13743	−0.146111
$215$	−1.45283	−0.0990823
$216$	1.47614	0.100439
$217$	5.01867	0.340690
$218$	−5.27099	−0.356996
$219$	8.55863	0.578338
$220$	2.67988	0.180677
$221$	−0.254157	−0.0170965
$222$	−38.7946	−2.60372
$223$	−13.8823	−0.929628	−0.464814	−	0.885408i	$-0.653879\pi$
$223$	−13.8823	−0.929628	−0.464814	+	0.885408i	$0.653879\pi$
$224$	7.74560	0.517525
$225$	−1.02723	−0.0684823
$226$	1.98207	0.131846
$227$	−25.9690	−1.72362	−0.861811	−	0.507230i	$-0.830669\pi$
$227$	−25.9690	−1.72362	−0.861811	+	0.507230i	$0.830669\pi$
$228$	22.1881	1.46944
$229$	−14.4683	−0.956094	−0.478047	−	0.878334i	$-0.658655\pi$
$229$	−14.4683	−0.956094	−0.478047	+	0.878334i	$0.658655\pi$
$230$	−4.89154	−0.322538
$231$	1.82004	0.119750
$232$	−1.23014	−0.0807624
$233$	−28.4158	−1.86158	−0.930791	−	0.365551i	$-0.880881\pi$
$233$	−28.4158	−1.86158	−0.930791	+	0.365551i	$0.880881\pi$
$234$	−0.177177	−0.0115824
$235$	16.2141	1.05769
$236$	−15.9231	−1.03650
$237$	0.641812	0.0416901
$238$	1.94816	0.126281
$239$	−1.60437	−0.103778	−0.0518889	−	0.998653i	$-0.516524\pi$
$239$	−1.60437	−0.103778	−0.0518889	+	0.998653i	$0.516524\pi$
$240$	−11.4082	−0.736394
$241$	29.4562	1.89744	0.948719	−	0.316121i	$-0.102381\pi$
$241$	29.4562	1.89744	0.948719	+	0.316121i	$0.102381\pi$
$242$	−1.96076	−0.126043
$243$	3.67607	0.235820
$244$	−6.76041	−0.432791
$245$	8.73560	0.558097
$246$	−13.6887	−0.872760
$247$	−1.66895	−0.106193
$248$	1.53921	0.0977399
$249$	6.87909	0.435944
$250$	−22.4739	−1.42137
$251$	9.87406	0.623245	0.311623	−	0.950206i	$-0.399128\pi$
$251$	9.87406	0.623245	0.311623	+	0.950206i	$0.399128\pi$
$252$	0.651598	0.0410468
$253$	1.71714	0.107956
$254$	9.02651	0.566374
$255$	−2.66131	−0.166658
$256$	18.1898	1.13686
$257$	0.740276	0.0461772	0.0230886	−	0.999733i	$-0.492650\pi$
$257$	0.740276	0.0461772	0.0230886	+	0.999733i	$0.492650\pi$
$258$	3.59175	0.223612
$259$	−10.7316	−0.666832
$260$	−0.681110	−0.0422407
$261$	−1.43524	−0.0888389
$262$	24.7919	1.53165
$263$	4.39592	0.271064	0.135532	−	0.990773i	$-0.456726\pi$
$263$	4.39592	0.271064	0.135532	+	0.990773i	$0.456726\pi$
$264$	0.558200	0.0343548
$265$	−10.2008	−0.626631
$266$	12.7928	0.784378
$267$	−19.1060	−1.16927
$268$	4.04141	0.246868
$269$	−18.6023	−1.13420	−0.567101	−	0.823648i	$-0.691935\pi$
$269$	−18.6023	−1.13420	−0.567101	+	0.823648i	$0.691935\pi$
$270$	13.7994	0.839803
$271$	−9.56126	−0.580805	−0.290403	−	0.956905i	$-0.593789\pi$
$271$	−9.56126	−0.580805	−0.290403	+	0.956905i	$0.593789\pi$
$272$	4.28667	0.259918
$273$	−0.462577	−0.0279965
$274$	−14.4948	−0.875661
$275$	2.88928	0.174230
$276$	5.80210	0.349245
$277$	−27.7143	−1.66519	−0.832595	−	0.553883i	$-0.813146\pi$
$277$	−27.7143	−1.66519	−0.832595	+	0.553883i	$0.813146\pi$
$278$	20.3861	1.22268
$279$	1.79584	0.107514
$280$	−0.439871	−0.0262873
$281$	−21.8532	−1.30366	−0.651828	−	0.758367i	$-0.725997\pi$
$281$	−21.8532	−1.30366	−0.651828	+	0.758367i	$0.725997\pi$
$282$	−40.0851	−2.38703
$283$	32.8586	1.95324	0.976620	−	0.214975i	$-0.0689670\pi$
$283$	32.8586	1.95324	0.976620	+	0.214975i	$0.0689670\pi$
$284$	−10.7834	−0.639874
$285$	−17.4758	−1.03518
$286$	0.498342	0.0294676
$287$	−3.78667	−0.223520
$288$	2.77163	0.163320
$289$	1.00000	0.0588235
$290$	−11.4996	−0.675282
$291$	−3.18765	−0.186863
$292$	−8.61832	−0.504349
$293$	6.87054	0.401381	0.200691	−	0.979655i	$-0.435681\pi$
$293$	6.87054	0.401381	0.200691	+	0.979655i	$0.435681\pi$
$294$	−21.5965	−1.25953
$295$	12.5413	0.730183
$296$	−3.29136	−0.191306
$297$	−4.84416	−0.281087
$298$	22.7106	1.31559
$299$	−0.436423	−0.0252390
$300$	9.76270	0.563650
$301$	0.993575	0.0572687
$302$	14.4210	0.829838
$303$	−25.4175	−1.46020
$304$	28.1489	1.61445
$305$	5.32462	0.304887
$306$	0.697116	0.0398514
$307$	−13.0075	−0.742379	−0.371189	−	0.928557i	$-0.621050\pi$
$307$	−13.0075	−0.742379	−0.371189	+	0.928557i	$0.621050\pi$
$308$	−1.83274	−0.104430
$309$	1.48558	0.0845120
$310$	14.3889	0.817236
$311$	7.10855	0.403089	0.201545	−	0.979479i	$-0.435404\pi$
$311$	7.10855	0.403089	0.201545	+	0.979479i	$0.435404\pi$
$312$	−0.141871	−0.00803185
$313$	11.6497	0.658482	0.329241	−	0.944246i	$-0.393207\pi$
$313$	11.6497	0.658482	0.329241	+	0.944246i	$0.393207\pi$
$314$	3.83382	0.216355
$315$	−0.513211	−0.0289162
$316$	−0.646288	−0.0363565
$317$	−11.6045	−0.651774	−0.325887	−	0.945409i	$-0.605663\pi$
$317$	−11.6045	−0.651774	−0.325887	+	0.945409i	$0.605663\pi$
$318$	25.2188	1.41420
$319$	4.03686	0.226021
$320$	9.75163	0.545132
$321$	−1.99686	−0.111454
$322$	3.34527	0.186424
$323$	6.56660	0.365375
$324$	−18.3356	−1.01864
$325$	−0.734332	−0.0407334
$326$	−1.69383	−0.0938125
$327$	−4.92434	−0.272317
$328$	−1.16136	−0.0641252
$329$	−11.0886	−0.611337
$330$	5.21820	0.287253
$331$	12.4942	0.686746	0.343373	−	0.939199i	$-0.388431\pi$
$331$	12.4942	0.686746	0.343373	+	0.939199i	$0.388431\pi$
$332$	−6.92707	−0.380172
$333$	−3.84013	−0.210438
$334$	16.1330	0.882757
$335$	−3.18309	−0.173911
$336$	7.80192	0.425630
$337$	−33.6522	−1.83315	−0.916576	−	0.399861i	$-0.869058\pi$
$337$	−33.6522	−1.83315	−0.916576	+	0.399861i	$0.869058\pi$
$338$	25.3633	1.37958
$339$	1.85172	0.100572
$340$	2.67988	0.145337
$341$	−5.05113	−0.273534
$342$	4.57768	0.247533
$343$	−12.9292	−0.698111
$344$	0.304726	0.0164297
$345$	−4.56984	−0.246032
$346$	−30.0878	−1.61753
$347$	28.0308	1.50477	0.752386	−	0.658722i	$-0.228903\pi$
$347$	28.0308	1.50477	0.752386	+	0.658722i	$0.228903\pi$
$348$	13.6403	0.731197
$349$	−20.3627	−1.08999	−0.544994	−	0.838440i	$-0.683468\pi$
$349$	−20.3627	−1.08999	−0.544994	+	0.838440i	$0.683468\pi$
$350$	5.62879	0.300872
$351$	1.23118	0.0657156
$352$	−7.79569	−0.415512
$353$	29.5474	1.57265	0.786324	−	0.617814i	$-0.211981\pi$
$353$	29.5474	1.57265	0.786324	+	0.617814i	$0.211981\pi$
$354$	−31.0051	−1.64790
$355$	8.49317	0.450771
$356$	19.2392	1.01968
$357$	1.82004	0.0963269
$358$	25.1318	1.32826
$359$	−3.71286	−0.195957	−0.0979786	−	0.995189i	$-0.531238\pi$
$359$	−3.71286	−0.195957	−0.0979786	+	0.995189i	$0.531238\pi$
$360$	−0.157400	−0.00829570
$361$	24.1202	1.26949
$362$	34.0143	1.78775
$363$	−1.83181	−0.0961452
$364$	0.465804	0.0244148
$365$	6.78795	0.355298
$366$	−13.1637	−0.688080
$367$	−24.0343	−1.25458	−0.627291	−	0.778785i	$-0.715836\pi$
$367$	−24.0343	−1.25458	−0.627291	+	0.778785i	$0.715836\pi$
$368$	7.36080	0.383708
$369$	−1.35499	−0.0705380
$370$	−30.7685	−1.59958
$371$	6.97622	0.362187
$372$	−17.0674	−0.884906
$373$	−27.6820	−1.43332	−0.716659	−	0.697424i	$-0.754329\pi$
$373$	−27.6820	−1.43332	−0.716659	+	0.697424i	$0.754329\pi$
$374$	−1.96076	−0.101389
$375$	−20.9958	−1.08422
$376$	−3.40084	−0.175385
$377$	−1.02600	−0.0528416
$378$	−9.43723	−0.485399
$379$	3.83569	0.197026	0.0985131	−	0.995136i	$-0.468591\pi$
$379$	3.83569	0.197026	0.0985131	+	0.995136i	$0.468591\pi$
$380$	17.5977	0.902742
$381$	8.43288	0.432029
$382$	−3.50217	−0.179187
$383$	16.8077	0.858834	0.429417	−	0.903106i	$-0.358719\pi$
$383$	16.8077	0.858834	0.429417	+	0.903106i	$0.358719\pi$
$384$	4.45212	0.227196
$385$	1.44350	0.0735674
$386$	31.8247	1.61983
$387$	0.355533	0.0180728
$388$	3.20988	0.162957
$389$	11.9371	0.605237	0.302619	−	0.953112i	$-0.402139\pi$
$389$	11.9371	0.605237	0.302619	+	0.953112i	$0.402139\pi$
$390$	−1.32625	−0.0671570
$391$	1.71714	0.0868394
$392$	−1.83226	−0.0925430
$393$	23.1614	1.16834
$394$	−17.5473	−0.884021
$395$	0.509028	0.0256120
$396$	−0.655812	−0.0329558
$397$	−20.6677	−1.03728	−0.518642	−	0.854991i	$-0.673562\pi$
$397$	−20.6677	−1.03728	−0.518642	+	0.854991i	$0.673562\pi$
$398$	10.1766	0.510108
$399$	11.9515	0.598323
$400$	12.3854	0.619270
$401$	21.7439	1.08584	0.542919	−	0.839785i	$-0.317319\pi$
$401$	21.7439	1.08584	0.542919	+	0.839785i	$0.317319\pi$
$402$	7.86936	0.392488
$403$	1.28378	0.0639497
$404$	25.5948	1.27339
$405$	14.4414	0.717600
$406$	7.86447	0.390307
$407$	10.8010	0.535388
$408$	0.558200	0.0276350
$409$	−20.8279	−1.02987	−0.514937	−	0.857228i	$-0.672185\pi$
$409$	−20.8279	−1.02987	−0.514937	+	0.857228i	$0.672185\pi$
$410$	−10.8567	−0.536173
$411$	−13.5415	−0.667953
$412$	−1.49595	−0.0737000
$413$	−8.57686	−0.422040
$414$	1.19704	0.0588315
$415$	5.45588	0.267819
$416$	1.98133	0.0971429
$417$	19.0454	0.932656
$418$	−12.8755	−0.629763
$419$	−0.0344564	−0.00168331	−0.000841653	−	1.00000i	$-0.500268\pi$
$419$	−0.0344564	−0.00168331	−0.000841653		1.00000i	$0.500268\pi$
$420$	4.87749	0.237997
$421$	−5.17532	−0.252230	−0.126115	−	0.992016i	$-0.540251\pi$
$421$	−5.17532	−0.252230	−0.126115	+	0.992016i	$0.540251\pi$
$422$	35.0791	1.70762
$423$	−3.96787	−0.192924
$424$	2.13958	0.103907
$425$	2.88928	0.140151
$426$	−20.9971	−1.01731
$427$	−3.64145	−0.176222
$428$	2.01079	0.0971950
$429$	0.465569	0.0224779
$430$	2.84866	0.137374
$431$	34.9734	1.68461	0.842305	−	0.539001i	$-0.181198\pi$
$431$	34.9734	1.68461	0.842305	+	0.539001i	$0.181198\pi$
$432$	−20.7653	−0.999073
$433$	−7.62903	−0.366628	−0.183314	−	0.983054i	$-0.558682\pi$
$433$	−7.62903	−0.366628	−0.183314	+	0.983054i	$0.558682\pi$
$434$	−9.84043	−0.472356
$435$	−10.7433	−0.515104
$436$	4.95869	0.237478
$437$	11.2758	0.539393
$438$	−16.7814	−0.801848
$439$	2.75664	0.131567	0.0657835	−	0.997834i	$-0.479045\pi$
$439$	2.75664	0.131567	0.0657835	+	0.997834i	$0.479045\pi$
$440$	0.442715	0.0211056
$441$	−2.13775	−0.101798
$442$	0.498342	0.0237037
$443$	−28.8544	−1.37092	−0.685458	−	0.728112i	$-0.740398\pi$
$443$	−28.8544	−1.37092	−0.685458	+	0.728112i	$0.740398\pi$
$444$	36.4961	1.73203
$445$	−15.1532	−0.718329
$446$	27.2199	1.28890
$447$	21.2171	1.00353
$448$	−6.66903	−0.315082
$449$	3.78561	0.178654	0.0893269	−	0.996002i	$-0.471528\pi$
$449$	3.78561	0.178654	0.0893269	+	0.996002i	$0.471528\pi$
$450$	2.01416	0.0949485
$451$	3.81116	0.179460
$452$	−1.86464	−0.0877051
$453$	13.4726	0.633000
$454$	50.9190	2.38975
$455$	−0.366876	−0.0171994
$456$	3.66548	0.171652
$457$	13.2182	0.618323	0.309162	−	0.951009i	$-0.399952\pi$
$457$	13.2182	0.618323	0.309162	+	0.951009i	$0.399952\pi$
$458$	28.3689	1.32559
$459$	−4.84416	−0.226106
$460$	4.60171	0.214556
$461$	3.97403	0.185089	0.0925445	−	0.995709i	$-0.470500\pi$
$461$	3.97403	0.185089	0.0925445	+	0.995709i	$0.470500\pi$
$462$	−3.56867	−0.166030
$463$	22.1267	1.02832	0.514159	−	0.857695i	$-0.328104\pi$
$463$	22.1267	1.02832	0.514159	+	0.857695i	$0.328104\pi$
$464$	17.3047	0.803350
$465$	13.4426	0.623387
$466$	55.7167	2.58103
$467$	−20.5774	−0.952210	−0.476105	−	0.879389i	$-0.657952\pi$
$467$	−20.5774	−0.952210	−0.476105	+	0.879389i	$0.657952\pi$
$468$	0.166680	0.00770476
$469$	2.17688	0.100519
$470$	−31.7920	−1.46646
$471$	3.58168	0.165035
$472$	−2.63049	−0.121078
$473$	−1.00000	−0.0459800
$474$	−1.25844	−0.0578020
$475$	18.9728	0.870530
$476$	−1.83274	−0.0840034
$477$	2.49632	0.114298
$478$	3.14578	0.143885
$479$	41.6027	1.90088	0.950438	−	0.310914i	$-0.100635\pi$
$479$	41.6027	1.90088	0.950438	+	0.310914i	$0.100635\pi$
$480$	20.7468	0.946956
$481$	−2.74517	−0.125169
$482$	−57.7565	−2.63074
$483$	3.12526	0.142204
$484$	1.84459	0.0838449
$485$	−2.52816	−0.114798
$486$	−7.20790	−0.326957
$487$	14.0654	0.637363	0.318681	−	0.947862i	$-0.396760\pi$
$487$	14.0654	0.637363	0.318681	+	0.947862i	$0.396760\pi$
$488$	−1.11682	−0.0505560
$489$	−1.58243	−0.0715601
$490$	−17.1284	−0.773784
$491$	−10.8054	−0.487642	−0.243821	−	0.969820i	$-0.578401\pi$
$491$	−10.8054	−0.487642	−0.243821	+	0.969820i	$0.578401\pi$
$492$	12.8777	0.580570
$493$	4.03686	0.181811
$494$	3.27242	0.147233
$495$	0.516530	0.0232163
$496$	−21.6525	−0.972227
$497$	−5.80838	−0.260542
$498$	−13.4882	−0.604423
$499$	14.4939	0.648837	0.324419	−	0.945914i	$-0.394831\pi$
$499$	14.4939	0.648837	0.324419	+	0.945914i	$0.394831\pi$
$500$	21.1423	0.945512
$501$	15.0720	0.673367
$502$	−19.3607	−0.864109
$503$	11.1306	0.496291	0.248145	−	0.968723i	$-0.420179\pi$
$503$	11.1306	0.496291	0.248145	+	0.968723i	$0.420179\pi$
$504$	0.107644	0.00479485
$505$	−20.1589	−0.897061
$506$	−3.36690	−0.149677
$507$	23.6952	1.05234
$508$	−8.49170	−0.376758
$509$	5.70537	0.252886	0.126443	−	0.991974i	$-0.459644\pi$
$509$	5.70537	0.252886	0.126443	+	0.991974i	$0.459644\pi$
$510$	5.21820	0.231066
$511$	−4.64220	−0.205359
$512$	−30.8050	−1.36140
$513$	−31.8097	−1.40443
$514$	−1.45151	−0.0640232
$515$	1.17823	0.0519192
$516$	−3.37894	−0.148749
$517$	11.1603	0.490831
$518$	21.0422	0.924542
$519$	−28.1090	−1.23385
$520$	−0.112519	−0.00493430
$521$	−24.7962	−1.08634	−0.543170	−	0.839622i	$-0.682776\pi$
$521$	−24.7962	−1.08634	−0.543170	+	0.839622i	$0.682776\pi$
$522$	2.81416	0.123172
$523$	−8.47679	−0.370664	−0.185332	−	0.982676i	$-0.559336\pi$
$523$	−8.47679	−0.370664	−0.185332	+	0.982676i	$0.559336\pi$
$524$	−23.3230	−1.01887
$525$	5.25861	0.229505
$526$	−8.61935	−0.375822
$527$	−5.05113	−0.220031
$528$	−7.85237	−0.341731
$529$	−20.0514	−0.871802
$530$	20.0014	0.868804
$531$	−3.06908	−0.133187
$532$	−12.0349	−0.521777
$533$	−0.968634	−0.0419562
$534$	37.4623	1.62115
$535$	−1.58373	−0.0684707
$536$	0.667641	0.0288377
$537$	23.4790	1.01320
$538$	36.4747	1.57254
$539$	6.01281	0.258990
$540$	−12.9818	−0.558646
$541$	−15.7357	−0.676529	−0.338264	−	0.941051i	$-0.609840\pi$
$541$	−15.7357	−0.676529	−0.338264	+	0.941051i	$0.609840\pi$
$542$	18.7474	0.805268
$543$	31.7773	1.36369
$544$	−7.79569	−0.334237
$545$	−3.90555	−0.167296
$546$	0.907004	0.0388162
$547$	16.3198	0.697784	0.348892	−	0.937163i	$-0.386558\pi$
$547$	16.3198	0.697784	0.348892	+	0.937163i	$0.386558\pi$
$548$	13.6360	0.582499
$549$	−1.30303	−0.0556118
$550$	−5.66519	−0.241565
$551$	26.5084	1.12930
$552$	0.958506	0.0407967
$553$	−0.348119	−0.0148035
$554$	54.3411	2.30873
$555$	−28.7450	−1.22016
$556$	−19.1782	−0.813338
$557$	−1.06476	−0.0451153	−0.0225576	−	0.999746i	$-0.507181\pi$
$557$	−1.06476	−0.0451153	−0.0225576	+	0.999746i	$0.507181\pi$
$558$	−3.52122	−0.149065
$559$	0.254157	0.0107497
$560$	6.18780	0.261482
$561$	−1.83181	−0.0773391
$562$	42.8490	1.80748
$563$	−3.95291	−0.166595	−0.0832975	−	0.996525i	$-0.526545\pi$
$563$	−3.95291	−0.166595	−0.0832975	+	0.996525i	$0.526545\pi$
$564$	37.7101	1.58788
$565$	1.46862	0.0617854
$566$	−64.4278	−2.70810
$567$	−9.87633	−0.414767
$568$	−1.78141	−0.0747463
$569$	34.4810	1.44552	0.722760	−	0.691099i	$-0.242873\pi$
$569$	34.4810	1.44552	0.722760	+	0.691099i	$0.242873\pi$
$570$	34.2658	1.43524
$571$	−29.4640	−1.23303	−0.616514	−	0.787344i	$-0.711456\pi$
$571$	−29.4640	−1.23303	−0.616514	+	0.787344i	$0.711456\pi$
$572$	−0.468816	−0.0196022
$573$	−3.27185	−0.136684
$574$	7.42476	0.309903
$575$	4.96129	0.206900
$576$	−2.38639	−0.0994330
$577$	−4.81504	−0.200453	−0.100226	−	0.994965i	$-0.531957\pi$
$577$	−4.81504	−0.200453	−0.100226	+	0.994965i	$0.531957\pi$
$578$	−1.96076	−0.0815570
$579$	29.7317	1.23561
$580$	10.8183	0.449205
$581$	−3.73122	−0.154797
$582$	6.25022	0.259080
$583$	−7.02133	−0.290794
$584$	−1.42375	−0.0589150
$585$	−0.131280	−0.00542775
$586$	−13.4715	−0.556502
$587$	0.783436	0.0323359	0.0161679	−	0.999869i	$-0.494853\pi$
$587$	0.783436	0.0323359	0.0161679	+	0.999869i	$0.494853\pi$
$588$	20.3169	0.837855
$589$	−33.1687	−1.36669
$590$	−24.5905	−1.01238
$591$	−16.3933	−0.674330
$592$	46.3005	1.90294
$593$	4.03693	0.165777	0.0828884	−	0.996559i	$-0.473585\pi$
$593$	4.03693	0.165777	0.0828884	+	0.996559i	$0.473585\pi$
$594$	9.49825	0.389718
$595$	1.44350	0.0591776
$596$	−21.3650	−0.875146
$597$	9.50735	0.389110
$598$	0.855722	0.0349931
$599$	2.78971	0.113984	0.0569921	−	0.998375i	$-0.481849\pi$
$599$	2.78971	0.113984	0.0569921	+	0.998375i	$0.481849\pi$
$600$	1.61280	0.0658422
$601$	23.8234	0.971775	0.485887	−	0.874021i	$-0.338496\pi$
$601$	23.8234	0.971775	0.485887	+	0.874021i	$0.338496\pi$
$602$	−1.94816	−0.0794013
$603$	0.778957	0.0317216
$604$	−13.5666	−0.552017
$605$	−1.45283	−0.0590660
$606$	49.8377	2.02452
$607$	−38.4424	−1.56033	−0.780165	−	0.625574i	$-0.784865\pi$
$607$	−38.4424	−1.56033	−0.780165	+	0.625574i	$0.784865\pi$
$608$	−51.1912	−2.07608
$609$	7.34726	0.297726
$610$	−10.4403	−0.422716
$611$	−2.83649	−0.114752
$612$	−0.655812	−0.0265096
$613$	−28.3037	−1.14317	−0.571587	−	0.820542i	$-0.693672\pi$
$613$	−28.3037	−1.14317	−0.571587	+	0.820542i	$0.693672\pi$
$614$	25.5047	1.02928
$615$	−10.1427	−0.408992
$616$	−0.302768	−0.0121989
$617$	0.288602	0.0116187	0.00580933	−	0.999983i	$-0.498151\pi$
$617$	0.288602	0.0116187	0.00580933	+	0.999983i	$0.498151\pi$
$618$	−2.91288	−0.117173
$619$	21.9947	0.884042	0.442021	−	0.897005i	$-0.354262\pi$
$619$	21.9947	0.884042	0.442021	+	0.897005i	$0.354262\pi$
$620$	−13.5364	−0.543635
$621$	−8.31810	−0.333794
$622$	−13.9382	−0.558870
$623$	10.3631	0.415188
$624$	1.99574	0.0798935
$625$	−2.20565	−0.0882261
$626$	−22.8424	−0.912965
$627$	−12.0288	−0.480383
$628$	−3.60667	−0.143922
$629$	10.8010	0.430666
$630$	1.00628	0.0400913
$631$	31.3044	1.24621	0.623104	−	0.782139i	$-0.285871\pi$
$631$	31.3044	1.24621	0.623104	+	0.782139i	$0.285871\pi$
$632$	−0.106767	−0.00424695
$633$	32.7721	1.30257
$634$	22.7537	0.903664
$635$	6.68822	0.265414
$636$	−23.7246	−0.940743
$637$	−1.52820	−0.0605495
$638$	−7.91532	−0.313371
$639$	−2.07843	−0.0822212
$640$	3.53103	0.139576
$641$	37.1577	1.46764	0.733820	−	0.679344i	$-0.237736\pi$
$641$	37.1577	1.46764	0.733820	+	0.679344i	$0.237736\pi$
$642$	3.91536	0.154527
$643$	−34.1084	−1.34510	−0.672551	−	0.740051i	$-0.734802\pi$
$643$	−34.1084	−1.34510	−0.672551	+	0.740051i	$0.734802\pi$
$644$	−3.14706	−0.124012
$645$	2.66131	0.104789
$646$	−12.8755	−0.506581
$647$	−17.5726	−0.690849	−0.345425	−	0.938446i	$-0.612265\pi$
$647$	−17.5726	−0.690849	−0.345425	+	0.938446i	$0.612265\pi$
$648$	−3.02903	−0.118992
$649$	8.63232	0.338848
$650$	1.43985	0.0564756
$651$	−9.19326	−0.360312
$652$	1.59347	0.0624051
$653$	46.0958	1.80387	0.901935	−	0.431872i	$-0.142147\pi$
$653$	46.0958	1.80387	0.901935	+	0.431872i	$0.142147\pi$
$654$	9.65546	0.377558
$655$	18.3696	0.717760
$656$	16.3372	0.637859
$657$	−1.66113	−0.0648068
$658$	21.7422	0.847599
$659$	−20.0731	−0.781937	−0.390969	−	0.920404i	$-0.627860\pi$
$659$	−20.0731	−0.781937	−0.390969	+	0.920404i	$0.627860\pi$
$660$	−4.90903	−0.191084
$661$	13.4688	0.523874	0.261937	−	0.965085i	$-0.415639\pi$
$661$	13.4688	0.523874	0.261937	+	0.965085i	$0.415639\pi$
$662$	−24.4982	−0.952151
$663$	0.465569	0.0180812
$664$	−1.14435	−0.0444094
$665$	9.47887	0.367575
$666$	7.52958	0.291765
$667$	6.93184	0.268402
$668$	−15.1771	−0.587220
$669$	25.4298	0.983172
$670$	6.24128	0.241122
$671$	3.66500	0.141486
$672$	−14.1885	−0.547333
$673$	18.6161	0.717597	0.358799	−	0.933415i	$-0.383187\pi$
$673$	18.6161	0.717597	0.358799	+	0.933415i	$0.383187\pi$
$674$	65.9839	2.54161
$675$	−13.9962	−0.538712
$676$	−23.8605	−0.917711
$677$	−51.3258	−1.97261	−0.986304	−	0.164935i	$-0.947259\pi$
$677$	−51.3258	−1.97261	−0.986304	+	0.164935i	$0.947259\pi$
$678$	−3.63078	−0.139439
$679$	1.72898	0.0663522
$680$	0.442715	0.0169774
$681$	47.5703	1.82290
$682$	9.90406	0.379246
$683$	−6.57247	−0.251489	−0.125744	−	0.992063i	$-0.540132\pi$
$683$	−6.57247	−0.251489	−0.125744	+	0.992063i	$0.540132\pi$
$684$	−4.30645	−0.164661
$685$	−10.7399	−0.410352
$686$	25.3511	0.967909
$687$	26.5032	1.01116
$688$	−4.28667	−0.163428
$689$	1.78452	0.0679850
$690$	8.96037	0.341115
$691$	3.94842	0.150205	0.0751025	−	0.997176i	$-0.476072\pi$
$691$	3.94842	0.150205	0.0751025	+	0.997176i	$0.476072\pi$
$692$	28.3051	1.07600
$693$	−0.353249	−0.0134188
$694$	−54.9617	−2.08632
$695$	15.1051	0.572970
$696$	2.25338	0.0854140
$697$	3.81116	0.144358
$698$	39.9263	1.51123
$699$	52.0524	1.96880
$700$	−5.29529	−0.200143
$701$	22.9324	0.866146	0.433073	−	0.901359i	$-0.357429\pi$
$701$	22.9324	0.866146	0.433073	+	0.901359i	$0.357429\pi$
$702$	−2.41405	−0.0911125
$703$	70.9261	2.67503
$704$	6.71215	0.252974
$705$	−29.7012	−1.11861
$706$	−57.9354	−2.18043
$707$	13.7865	0.518493
$708$	29.1681	1.09620
$709$	−12.5975	−0.473108	−0.236554	−	0.971618i	$-0.576018\pi$
$709$	−12.5975	−0.473108	−0.236554	+	0.971618i	$0.576018\pi$
$710$	−16.6531	−0.624979
$711$	−0.124568	−0.00467167
$712$	3.17832	0.119113
$713$	−8.67348	−0.324824
$714$	−3.56867	−0.133554
$715$	0.369248	0.0138091
$716$	−23.6428	−0.883573
$717$	2.93889	0.109755
$718$	7.28003	0.271688
$719$	34.2007	1.27547	0.637736	−	0.770255i	$-0.279871\pi$
$719$	34.2007	1.27547	0.637736	+	0.770255i	$0.279871\pi$
$720$	2.21419	0.0825181
$721$	−0.805782	−0.0300089
$722$	−47.2941	−1.76010
$723$	−53.9581	−2.00672
$724$	−31.9989	−1.18923
$725$	11.6636	0.433176
$726$	3.59175	0.133302
$727$	10.7989	0.400509	0.200255	−	0.979744i	$-0.435823\pi$
$727$	10.7989	0.400509	0.200255	+	0.979744i	$0.435823\pi$
$728$	0.0769508	0.00285198
$729$	23.0867	0.855064
$730$	−13.3096	−0.492609
$731$	−1.00000	−0.0369863
$732$	12.3838	0.457718
$733$	−47.1771	−1.74252	−0.871262	−	0.490817i	$-0.836698\pi$
$733$	−47.1771	−1.74252	−0.871262	+	0.490817i	$0.836698\pi$
$734$	47.1256	1.73944
$735$	−16.0020	−0.590241
$736$	−13.3863	−0.493425
$737$	−2.19096	−0.0807049
$738$	2.65682	0.0977987
$739$	37.1935	1.36819	0.684093	−	0.729395i	$-0.260198\pi$
$739$	37.1935	1.36819	0.684093	+	0.729395i	$0.260198\pi$
$740$	28.9455	1.06406
$741$	3.05720	0.112309
$742$	−13.6787	−0.502161
$743$	−5.32706	−0.195431	−0.0977154	−	0.995214i	$-0.531153\pi$
$743$	−5.32706	−0.195431	−0.0977154	+	0.995214i	$0.531153\pi$
$744$	−2.81954	−0.103369
$745$	16.8275	0.616512
$746$	54.2777	1.98725
$747$	−1.33515	−0.0488506
$748$	1.84459	0.0674448
$749$	1.08310	0.0395755
$750$	41.1679	1.50324
$751$	−34.3583	−1.25375	−0.626877	−	0.779119i	$-0.715667\pi$
$751$	−34.3583	−1.25375	−0.626877	+	0.779119i	$0.715667\pi$
$752$	47.8407	1.74457
$753$	−18.0874	−0.659142
$754$	2.01174	0.0732632
$755$	10.6853	0.388878
$756$	8.87808	0.322893
$757$	−3.86787	−0.140580	−0.0702900	−	0.997527i	$-0.522392\pi$
$757$	−3.86787	−0.140580	−0.0702900	+	0.997527i	$0.522392\pi$
$758$	−7.52088	−0.273171
$759$	−3.14547	−0.114173
$760$	2.90713	0.105453
$761$	19.2025	0.696091	0.348046	−	0.937478i	$-0.386845\pi$
$761$	19.2025	0.696091	0.348046	+	0.937478i	$0.386845\pi$
$762$	−16.5349	−0.598995
$763$	2.67096	0.0966954
$764$	3.29467	0.119197
$765$	0.516530	0.0186752
$766$	−32.9559	−1.19075
$767$	−2.19397	−0.0792196
$768$	−33.3203	−1.20234
$769$	47.0401	1.69631	0.848155	−	0.529748i	$-0.177714\pi$
$769$	47.0401	1.69631	0.848155	+	0.529748i	$0.177714\pi$
$770$	−2.83035	−0.101999
$771$	−1.35605	−0.0488368
$772$	−29.9391	−1.07753
$773$	23.8570	0.858075	0.429038	−	0.903287i	$-0.358853\pi$
$773$	23.8570	0.858075	0.429038	+	0.903287i	$0.358853\pi$
$774$	−0.697116	−0.0250573
$775$	−14.5941	−0.524236
$776$	0.530272	0.0190357
$777$	19.6584	0.705240
$778$	−23.4059	−0.839142
$779$	25.0263	0.896661
$780$	1.24767	0.0446736
$781$	5.84594	0.209184
$782$	−3.36690	−0.120400
$783$	−19.5552	−0.698846
$784$	25.7749	0.920533
$785$	2.84068	0.101388
$786$	−45.4141	−1.61987
$787$	29.8475	1.06395	0.531975	−	0.846760i	$-0.321450\pi$
$787$	29.8475	1.06395	0.531975	+	0.846760i	$0.321450\pi$
$788$	16.5076	0.588060
$789$	−8.05249	−0.286676
$790$	−0.998084	−0.0355102
$791$	−1.00437	−0.0357114
$792$	−0.108340	−0.00384970
$793$	−0.931486	−0.0330781
$794$	40.5245	1.43816
$795$	18.6860	0.662723
$796$	−9.57367	−0.339330
$797$	22.8342	0.808829	0.404414	−	0.914576i	$-0.367475\pi$
$797$	22.8342	0.808829	0.404414	+	0.914576i	$0.367475\pi$
$798$	−23.4340	−0.829556
$799$	11.1603	0.394825
$800$	−22.5239	−0.796341
$801$	3.70824	0.131024
$802$	−42.6346	−1.50548
$803$	4.67222	0.164879
$804$	−7.40310	−0.261087
$805$	2.47868	0.0873621
$806$	−2.51719	−0.0886643
$807$	34.0759	1.19953
$808$	4.22826	0.148750
$809$	54.6083	1.91993	0.959964	−	0.280125i	$-0.0903759\pi$
$809$	54.6083	1.91993	0.959964	+	0.280125i	$0.0903759\pi$
$810$	−28.3162	−0.994930
$811$	−55.7582	−1.95793	−0.978967	−	0.204019i	$-0.934599\pi$
$811$	−55.7582	−1.95793	−0.978967	+	0.204019i	$0.934599\pi$
$812$	−7.39850	−0.259637
$813$	17.5144	0.614258
$814$	−21.1783	−0.742298
$815$	−1.25505	−0.0439624
$816$	−7.85237	−0.274888
$817$	−6.56660	−0.229736
$818$	40.8386	1.42789
$819$	0.0897808	0.00313720
$820$	10.2134	0.356668
$821$	28.8767	1.00780	0.503902	−	0.863761i	$-0.331897\pi$
$821$	28.8767	1.00780	0.503902	+	0.863761i	$0.331897\pi$
$822$	26.5517	0.926096
$823$	−32.1815	−1.12178	−0.560888	−	0.827892i	$-0.689540\pi$
$823$	−32.1815	−1.12178	−0.560888	+	0.827892i	$0.689540\pi$
$824$	−0.247130	−0.00860919
$825$	−5.29262	−0.184265
$826$	16.8172	0.585145
$827$	13.2140	0.459497	0.229749	−	0.973250i	$-0.426210\pi$
$827$	13.2140	0.459497	0.229749	+	0.973250i	$0.426210\pi$
$828$	−1.12612	−0.0391353
$829$	−25.7328	−0.893738	−0.446869	−	0.894599i	$-0.647461\pi$
$829$	−25.7328	−0.893738	−0.446869	+	0.894599i	$0.647461\pi$
$830$	−10.6977	−0.371322
$831$	50.7673	1.76110
$832$	−1.70594	−0.0591430
$833$	6.01281	0.208331
$834$	−37.3435	−1.29310
$835$	11.9538	0.413677
$836$	12.1127	0.418926
$837$	24.4685	0.845755
$838$	0.0675608	0.00233385
$839$	1.64847	0.0569116	0.0284558	−	0.999595i	$-0.490941\pi$
$839$	1.64847	0.0569116	0.0284558	+	0.999595i	$0.490941\pi$
$840$	0.805760	0.0278014
$841$	−12.7038	−0.438061
$842$	10.1476	0.349708
$843$	40.0310	1.37874
$844$	−33.0007	−1.13593
$845$	18.7930	0.646498
$846$	7.78005	0.267484
$847$	0.993575	0.0341396
$848$	−30.0981	−1.03357
$849$	−60.1907	−2.06574
$850$	−5.66519	−0.194314
$851$	18.5469	0.635779
$852$	19.7531	0.676729
$853$	1.72997	0.0592330	0.0296165	−	0.999561i	$-0.490571\pi$
$853$	1.72997	0.0592330	0.0296165	+	0.999561i	$0.490571\pi$
$854$	7.14002	0.244326
$855$	3.39184	0.115999
$856$	0.332182	0.0113537
$857$	−45.4779	−1.55350	−0.776748	−	0.629812i	$-0.783132\pi$
$857$	−45.4779	−1.55350	−0.776748	+	0.629812i	$0.783132\pi$
$858$	−0.912869	−0.0311648
$859$	24.6965	0.842635	0.421317	−	0.906913i	$-0.361568\pi$
$859$	24.6965	0.842635	0.421317	+	0.906913i	$0.361568\pi$
$860$	−2.67988	−0.0913830
$861$	6.93646	0.236394
$862$	−68.5746	−2.33566
$863$	−5.48285	−0.186638	−0.0933191	−	0.995636i	$-0.529748\pi$
$863$	−5.48285	−0.186638	−0.0933191	+	0.995636i	$0.529748\pi$
$864$	37.7636	1.28474
$865$	−22.2936	−0.758006
$866$	14.9587	0.508318
$867$	−1.83181	−0.0622116
$868$	9.25739	0.314216
$869$	0.350370	0.0118855
$870$	21.0652	0.714176
$871$	0.556848	0.0188681
$872$	0.819175	0.0277408
$873$	0.618685	0.0209393
$874$	−22.1091	−0.747851
$875$	11.3882	0.384990
$876$	15.7871	0.533398
$877$	55.8487	1.88588	0.942938	−	0.332968i	$-0.108050\pi$
$877$	55.8487	1.88588	0.942938	+	0.332968i	$0.108050\pi$
$878$	−5.40511	−0.182414
$879$	−12.5855	−0.424499
$880$	−6.22781	−0.209939
$881$	−7.39334	−0.249088	−0.124544	−	0.992214i	$-0.539747\pi$
$881$	−7.39334	−0.249088	−0.124544	+	0.992214i	$0.539747\pi$
$882$	4.19162	0.141139
$883$	50.4473	1.69769	0.848843	−	0.528646i	$-0.177300\pi$
$883$	50.4473	1.69769	0.848843	+	0.528646i	$0.177300\pi$
$884$	−0.468816	−0.0157680
$885$	−22.9733	−0.772239
$886$	56.5767	1.90073
$887$	22.3713	0.751154	0.375577	−	0.926791i	$-0.377445\pi$
$887$	22.3713	0.751154	0.375577	+	0.926791i	$0.377445\pi$
$888$	6.02914	0.202325
$889$	−4.57400	−0.153407
$890$	29.7118	0.995941
$891$	9.94020	0.333009
$892$	−25.6071	−0.857390
$893$	73.2855	2.45241
$894$	−41.6016	−1.39137
$895$	18.6215	0.622448
$896$	−2.41483	−0.0806738
$897$	0.799445	0.0266927
$898$	−7.42267	−0.247698
$899$	−20.3907	−0.680068
$900$	−1.89482	−0.0631608
$901$	−7.02133	−0.233915
$902$	−7.47277	−0.248816
$903$	−1.82004	−0.0605672
$904$	−0.308038	−0.0102452
$905$	25.2030	0.837774
$906$	−26.4166	−0.877634
$907$	11.6974	0.388406	0.194203	−	0.980961i	$-0.437788\pi$
$907$	11.6974	0.388406	0.194203	+	0.980961i	$0.437788\pi$
$908$	−47.9021	−1.58969
$909$	4.93324	0.163625
$910$	0.719356	0.0238464
$911$	27.8411	0.922417	0.461208	−	0.887292i	$-0.347416\pi$
$911$	27.8411	0.922417	0.461208	+	0.887292i	$0.347416\pi$
$912$	−51.5634	−1.70743
$913$	3.75535	0.124284
$914$	−25.9178	−0.857286
$915$	−9.75370	−0.322448
$916$	−26.6881	−0.881800
$917$	−12.5628	−0.414859
$918$	9.49825	0.313489
$919$	56.3347	1.85831	0.929156	−	0.369688i	$-0.120535\pi$
$919$	56.3347	1.85831	0.929156	+	0.369688i	$0.120535\pi$
$920$	0.760203	0.0250631
$921$	23.8273	0.785138
$922$	−7.79212	−0.256620
$923$	−1.48579	−0.0489054
$924$	3.35723	0.110445
$925$	31.2072	1.02609
$926$	−43.3853	−1.42573
$927$	−0.288334	−0.00947015
$928$	−31.4701	−1.03306
$929$	−25.0536	−0.821983	−0.410992	−	0.911639i	$-0.634817\pi$
$929$	−25.0536	−0.821983	−0.410992	+	0.911639i	$0.634817\pi$
$930$	−26.3578	−0.864306
$931$	39.4837	1.29403
$932$	−52.4155	−1.71693
$933$	−13.0215	−0.426306
$934$	40.3474	1.32021
$935$	−1.45283	−0.0475127
$936$	0.0275354	0.000900024 0
$937$	−33.4938	−1.09420	−0.547098	−	0.837069i	$-0.684267\pi$
$937$	−33.4938	−1.09420	−0.547098	+	0.837069i	$0.684267\pi$
$938$	−4.26834	−0.139366
$939$	−21.3401	−0.696409
$940$	29.9083	0.975502
$941$	−57.9323	−1.88854	−0.944270	−	0.329171i	$-0.893231\pi$
$941$	−57.9323	−1.88854	−0.944270	+	0.329171i	$0.893231\pi$
$942$	−7.02283	−0.228816
$943$	6.54428	0.213111
$944$	37.0039	1.20438
$945$	−6.99254	−0.227467
$946$	1.96076	0.0637499
$947$	−8.25392	−0.268216	−0.134108	−	0.990967i	$-0.542817\pi$
$947$	−8.25392	−0.268216	−0.134108	+	0.990967i	$0.542817\pi$
$948$	1.18388	0.0384506
$949$	−1.18748	−0.0385472
$950$	−37.2011	−1.20696
$951$	21.2573	0.689314
$952$	−0.302768	−0.00981277
$953$	−23.4335	−0.759087	−0.379543	−	0.925174i	$-0.623919\pi$
$953$	−23.4335	−0.759087	−0.379543	+	0.925174i	$0.623919\pi$
$954$	−4.89468	−0.158471
$955$	−2.59494	−0.0839704
$956$	−2.95939	−0.0957136
$957$	−7.39477	−0.239039
$958$	−81.5730	−2.63550
$959$	7.34492	0.237180
$960$	−17.8631	−0.576530
$961$	−5.48611	−0.176971
$962$	5.38262	0.173543
$963$	0.387566	0.0124892
$964$	54.3345	1.75000
$965$	23.5806	0.759086
$966$	−6.12790	−0.197162
$967$	32.3264	1.03955	0.519774	−	0.854304i	$-0.326016\pi$
$967$	32.3264	1.03955	0.519774	+	0.854304i	$0.326016\pi$
$968$	0.304726	0.00979426
$969$	−12.0288	−0.386420
$970$	4.95712	0.159164
$971$	20.3736	0.653820	0.326910	−	0.945055i	$-0.393993\pi$
$971$	20.3736	0.653820	0.326910	+	0.945055i	$0.393993\pi$
$972$	6.78083	0.217495
$973$	−10.3302	−0.331172
$974$	−27.5788	−0.883683
$975$	1.34516	0.0430795
$976$	15.7106	0.502885
$977$	−16.1078	−0.515335	−0.257667	−	0.966234i	$-0.582954\pi$
$977$	−16.1078	−0.515335	−0.257667	+	0.966234i	$0.582954\pi$
$978$	3.10278	0.0992158
$979$	−10.4301	−0.333347
$980$	16.1136	0.514729
$981$	0.955756	0.0305150
$982$	21.1869	0.676100
$983$	−9.84403	−0.313976	−0.156988	−	0.987601i	$-0.550178\pi$
$983$	−9.84403	−0.313976	−0.156988	+	0.987601i	$0.550178\pi$
$984$	2.12739	0.0678186
$985$	−13.0017	−0.414269
$986$	−7.91532	−0.252075
$987$	20.3123	0.646548
$988$	−3.07853	−0.0979410
$989$	−1.71714	−0.0546018
$990$	−1.01279	−0.0321886
$991$	4.86409	0.154513	0.0772564	−	0.997011i	$-0.475384\pi$
$991$	4.86409	0.154513	0.0772564	+	0.997011i	$0.475384\pi$
$992$	39.3770	1.25022
$993$	−22.8871	−0.726300
$994$	11.3889	0.361233
$995$	7.54040	0.239047
$996$	12.6891	0.402069
$997$	−49.4762	−1.56693	−0.783464	−	0.621438i	$-0.786549\pi$
$997$	−49.4762	−1.56693	−0.783464	+	0.621438i	$0.786549\pi$
$998$	−28.4191	−0.899592
$999$	−52.3220	−1.65540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.10	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.10	✓	66	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.96076 q^{2} -1.83181 q^{3} +1.84459 q^{4} -1.45283 q^{5} +3.59175 q^{6} +0.993575 q^{7} +0.304726 q^{8} +0.355533 q^{9} +O(q^{10})\)	\(q-1.96076 q^{2} -1.83181 q^{3} +1.84459 q^{4} -1.45283 q^{5} +3.59175 q^{6} +0.993575 q^{7} +0.304726 q^{8} +0.355533 q^{9} +2.84866 q^{10} -1.00000 q^{11} -3.37894 q^{12} +0.254157 q^{13} -1.94816 q^{14} +2.66131 q^{15} -4.28667 q^{16} -1.00000 q^{17} -0.697116 q^{18} -6.56660 q^{19} -2.67988 q^{20} -1.82004 q^{21} +1.96076 q^{22} -1.71714 q^{23} -0.558200 q^{24} -2.88928 q^{25} -0.498342 q^{26} +4.84416 q^{27} +1.83274 q^{28} -4.03686 q^{29} -5.21820 q^{30} +5.05113 q^{31} +7.79569 q^{32} +1.83181 q^{33} +1.96076 q^{34} -1.44350 q^{35} +0.655812 q^{36} -10.8010 q^{37} +12.8755 q^{38} -0.465569 q^{39} -0.442715 q^{40} -3.81116 q^{41} +3.56867 q^{42} +1.00000 q^{43} -1.84459 q^{44} -0.516530 q^{45} +3.36690 q^{46} -11.1603 q^{47} +7.85237 q^{48} -6.01281 q^{49} +5.66519 q^{50} +1.83181 q^{51} +0.468816 q^{52} +7.02133 q^{53} -9.49825 q^{54} +1.45283 q^{55} +0.302768 q^{56} +12.0288 q^{57} +7.91532 q^{58} -8.63232 q^{59} +4.90903 q^{60} -3.66500 q^{61} -9.90406 q^{62} +0.353249 q^{63} -6.71215 q^{64} -0.369248 q^{65} -3.59175 q^{66} +2.19096 q^{67} -1.84459 q^{68} +3.14547 q^{69} +2.83035 q^{70} -5.84594 q^{71} +0.108340 q^{72} -4.67222 q^{73} +21.1783 q^{74} +5.29262 q^{75} -12.1127 q^{76} -0.993575 q^{77} +0.912869 q^{78} -0.350370 q^{79} +6.22781 q^{80} -9.94020 q^{81} +7.47277 q^{82} -3.75535 q^{83} -3.35723 q^{84} +1.45283 q^{85} -1.96076 q^{86} +7.39477 q^{87} -0.304726 q^{88} +10.4301 q^{89} +1.01279 q^{90} +0.252525 q^{91} -3.16741 q^{92} -9.25271 q^{93} +21.8828 q^{94} +9.54016 q^{95} -14.2802 q^{96} +1.74016 q^{97} +11.7897 q^{98} -0.355533 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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