LMFDB - Embedded newform 8041.2.a.e.1.16

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			1.16
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)

$f(q)$	$=$	$q-1.40918 q^{2} +0.980513 q^{3} -0.0142062 q^{4} +1.84997 q^{5} -1.38172 q^{6} -3.81355 q^{7} +2.83838 q^{8} -2.03859 q^{9} +O(q^{10})$	\(q-1.40918 q^{2} +0.980513 q^{3} -0.0142062 q^{4} +1.84997 q^{5} -1.38172 q^{6} -3.81355 q^{7} +2.83838 q^{8} -2.03859 q^{9} -2.60695 q^{10} -1.00000 q^{11} -0.0139294 q^{12} -2.03990 q^{13} +5.37399 q^{14} +1.81392 q^{15} -3.97139 q^{16} -1.00000 q^{17} +2.87275 q^{18} -3.73725 q^{19} -0.0262812 q^{20} -3.73924 q^{21} +1.40918 q^{22} -7.09931 q^{23} +2.78307 q^{24} -1.57759 q^{25} +2.87459 q^{26} -4.94041 q^{27} +0.0541762 q^{28} -2.16283 q^{29} -2.55615 q^{30} -7.57807 q^{31} -0.0803611 q^{32} -0.980513 q^{33} +1.40918 q^{34} -7.05497 q^{35} +0.0289607 q^{36} -6.96480 q^{37} +5.26646 q^{38} -2.00015 q^{39} +5.25094 q^{40} -0.575981 q^{41} +5.26926 q^{42} +1.00000 q^{43} +0.0142062 q^{44} -3.77135 q^{45} +10.0042 q^{46} +6.77612 q^{47} -3.89400 q^{48} +7.54317 q^{49} +2.22312 q^{50} -0.980513 q^{51} +0.0289793 q^{52} -5.28310 q^{53} +6.96193 q^{54} -1.84997 q^{55} -10.8243 q^{56} -3.66442 q^{57} +3.04782 q^{58} -0.0805972 q^{59} -0.0257690 q^{60} +2.92910 q^{61} +10.6789 q^{62} +7.77428 q^{63} +8.05601 q^{64} -3.77376 q^{65} +1.38172 q^{66} +11.9351 q^{67} +0.0142062 q^{68} -6.96096 q^{69} +9.94174 q^{70} +13.6753 q^{71} -5.78631 q^{72} +3.53743 q^{73} +9.81466 q^{74} -1.54685 q^{75} +0.0530922 q^{76} +3.81355 q^{77} +2.81857 q^{78} -9.70231 q^{79} -7.34696 q^{80} +1.27165 q^{81} +0.811662 q^{82} +3.86137 q^{83} +0.0531205 q^{84} -1.84997 q^{85} -1.40918 q^{86} -2.12068 q^{87} -2.83838 q^{88} -7.39523 q^{89} +5.31452 q^{90} +7.77926 q^{91} +0.100854 q^{92} -7.43040 q^{93} -9.54879 q^{94} -6.91382 q^{95} -0.0787951 q^{96} +0.591741 q^{97} -10.6297 q^{98} +2.03859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.40918	−0.996442	−0.498221	−	0.867050i	$-0.666013\pi$
$2$	−1.40918	−0.996442	−0.498221	+	0.867050i	$0.666013\pi$
$3$	0.980513	0.566099	0.283050	−	0.959105i	$-0.408654\pi$
$3$	0.980513	0.566099	0.283050	+	0.959105i	$0.408654\pi$
$4$	−0.0142062	−0.00710312
$5$	1.84997	0.827334	0.413667	−	0.910428i	$-0.364248\pi$
$5$	1.84997	0.827334	0.413667	+	0.910428i	$0.364248\pi$
$6$	−1.38172	−0.564085
$7$	−3.81355	−1.44139	−0.720693	−	0.693254i	$-0.756176\pi$
$7$	−3.81355	−1.44139	−0.720693	+	0.693254i	$0.756176\pi$
$8$	2.83838	1.00352
$9$	−2.03859	−0.679531
$10$	−2.60695	−0.824390
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.0139294	−0.00402107
$13$	−2.03990	−0.565766	−0.282883	−	0.959154i	$-0.591291\pi$
$13$	−2.03990	−0.565766	−0.282883	+	0.959154i	$0.591291\pi$
$14$	5.37399	1.43626
$15$	1.81392	0.468353
$16$	−3.97139	−0.992846
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.87275	0.677114
$19$	−3.73725	−0.857384	−0.428692	−	0.903451i	$-0.641025\pi$
$19$	−3.73725	−0.857384	−0.428692	+	0.903451i	$0.641025\pi$
$20$	−0.0262812	−0.00587665
$21$	−3.73924	−0.815968
$22$	1.40918	0.300439
$23$	−7.09931	−1.48031	−0.740154	−	0.672438i	$-0.765247\pi$
$23$	−7.09931	−1.48031	−0.740154	+	0.672438i	$0.765247\pi$
$24$	2.78307	0.568092
$25$	−1.57759	−0.315519
$26$	2.87459	0.563754
$27$	−4.94041	−0.950782
$28$	0.0541762	0.0102383
$29$	−2.16283	−0.401627	−0.200813	−	0.979630i	$-0.564358\pi$
$29$	−2.16283	−0.401627	−0.200813	+	0.979630i	$0.564358\pi$
$30$	−2.55615	−0.466687
$31$	−7.57807	−1.36106	−0.680531	−	0.732719i	$-0.738251\pi$
$31$	−7.57807	−1.36106	−0.680531	+	0.732719i	$0.738251\pi$
$32$	−0.0803611	−0.0142060
$33$	−0.980513	−0.170685
$34$	1.40918	0.241673
$35$	−7.05497	−1.19251
$36$	0.0289607	0.00482679
$37$	−6.96480	−1.14501	−0.572503	−	0.819903i	$-0.694027\pi$
$37$	−6.96480	−1.14501	−0.572503	+	0.819903i	$0.694027\pi$
$38$	5.26646	0.854333
$39$	−2.00015	−0.320280
$40$	5.25094	0.830246
$41$	−0.575981	−0.0899531	−0.0449765	−	0.998988i	$-0.514321\pi$
$41$	−0.575981	−0.0899531	−0.0449765	+	0.998988i	$0.514321\pi$
$42$	5.26926	0.813065
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.0142062	0.00214167
$45$	−3.77135	−0.562199
$46$	10.0042	1.47504
$47$	6.77612	0.988399	0.494199	−	0.869349i	$-0.335461\pi$
$47$	6.77612	0.988399	0.494199	+	0.869349i	$0.335461\pi$
$48$	−3.89400	−0.562050
$49$	7.54317	1.07760
$50$	2.22312	0.314396
$51$	−0.980513	−0.137299
$52$	0.0289793	0.00401871
$53$	−5.28310	−0.725689	−0.362845	−	0.931850i	$-0.618194\pi$
$53$	−5.28310	−0.725689	−0.362845	+	0.931850i	$0.618194\pi$
$54$	6.96193	0.947399
$55$	−1.84997	−0.249451
$56$	−10.8243	−1.44646
$57$	−3.66442	−0.485365
$58$	3.04782	0.400198
$59$	−0.0805972	−0.0104929	−0.00524643	−	0.999986i	$-0.501670\pi$
$59$	−0.0805972	−0.0104929	−0.00524643	+	0.999986i	$0.501670\pi$
$60$	−0.0257690	−0.00332677
$61$	2.92910	0.375032	0.187516	−	0.982262i	$-0.439956\pi$
$61$	2.92910	0.375032	0.187516	+	0.982262i	$0.439956\pi$
$62$	10.6789	1.35622
$63$	7.77428	0.979468
$64$	8.05601	1.00700
$65$	−3.77376	−0.468078
$66$	1.38172	0.170078
$67$	11.9351	1.45811	0.729055	−	0.684455i	$-0.239960\pi$
$67$	11.9351	1.45811	0.729055	+	0.684455i	$0.239960\pi$
$68$	0.0142062	0.00172276
$69$	−6.96096	−0.838001
$70$	9.94174	1.18827
$71$	13.6753	1.62296	0.811478	−	0.584383i	$-0.198663\pi$
$71$	13.6753	1.62296	0.811478	+	0.584383i	$0.198663\pi$
$72$	−5.78631	−0.681923
$73$	3.53743	0.414024	0.207012	−	0.978338i	$-0.433626\pi$
$73$	3.53743	0.414024	0.207012	+	0.978338i	$0.433626\pi$
$74$	9.81466	1.14093
$75$	−1.54685	−0.178615
$76$	0.0530922	0.00609010
$77$	3.81355	0.434594
$78$	2.81857	0.319141
$79$	−9.70231	−1.09160	−0.545798	−	0.837917i	$-0.683773\pi$
$79$	−9.70231	−1.09160	−0.545798	+	0.837917i	$0.683773\pi$
$80$	−7.34696	−0.821415
$81$	1.27165	0.141294
$82$	0.811662	0.0896330
$83$	3.86137	0.423840	0.211920	−	0.977287i	$-0.432028\pi$
$83$	3.86137	0.423840	0.211920	+	0.977287i	$0.432028\pi$
$84$	0.0531205	0.00579592
$85$	−1.84997	−0.200658
$86$	−1.40918	−0.151956
$87$	−2.12068	−0.227361
$88$	−2.83838	−0.302573
$89$	−7.39523	−0.783893	−0.391946	−	0.919988i	$-0.628198\pi$
$89$	−7.39523	−0.783893	−0.391946	+	0.919988i	$0.628198\pi$
$90$	5.31452	0.560199
$91$	7.77926	0.815488
$92$	0.100854	0.0105148
$93$	−7.43040	−0.770497
$94$	−9.54879	−0.984882
$95$	−6.91382	−0.709343
$96$	−0.0787951	−0.00804199
$97$	0.591741	0.0600822	0.0300411	−	0.999549i	$-0.490436\pi$
$97$	0.591741	0.0600822	0.0300411	+	0.999549i	$0.490436\pi$
$98$	−10.6297	−1.07376
$99$	2.03859	0.204886
$100$	0.0224117	0.00224117
$101$	17.8253	1.77368	0.886840	−	0.462077i	$-0.152895\pi$
$101$	17.8253	1.77368	0.886840	+	0.462077i	$0.152895\pi$
$102$	1.38172	0.136811
$103$	8.11589	0.799683	0.399841	−	0.916584i	$-0.369065\pi$
$103$	8.11589	0.799683	0.399841	+	0.916584i	$0.369065\pi$
$104$	−5.79002	−0.567758
$105$	−6.91749	−0.675078
$106$	7.44485	0.723107
$107$	5.16890	0.499696	0.249848	−	0.968285i	$-0.419619\pi$
$107$	5.16890	0.499696	0.249848	+	0.968285i	$0.419619\pi$
$108$	0.0701846	0.00675351
$109$	0.494613	0.0473753	0.0236876	−	0.999719i	$-0.492459\pi$
$109$	0.494613	0.0473753	0.0236876	+	0.999719i	$0.492459\pi$
$110$	2.60695	0.248563
$111$	−6.82907	−0.648187
$112$	15.1451	1.43108
$113$	−6.63282	−0.623964	−0.311982	−	0.950088i	$-0.600993\pi$
$113$	−6.63282	−0.623964	−0.311982	+	0.950088i	$0.600993\pi$
$114$	5.16384	0.483638
$115$	−13.1335	−1.22471
$116$	0.0307256	0.00285280
$117$	4.15853	0.384456
$118$	0.113576	0.0104555
$119$	3.81355	0.349588
$120$	5.14861	0.470002
$121$	1.00000	0.0909091
$122$	−4.12763	−0.373698
$123$	−0.564757	−0.0509224
$124$	0.107656	0.00966778
$125$	−12.1684	−1.08837
$126$	−10.9554	−0.975983
$127$	−6.34970	−0.563445	−0.281722	−	0.959496i	$-0.590906\pi$
$127$	−6.34970	−0.563445	−0.281722	+	0.959496i	$0.590906\pi$
$128$	−11.1917	−0.989213
$129$	0.980513	0.0863294
$130$	5.31792	0.466412
$131$	−19.1622	−1.67421	−0.837105	−	0.547043i	$-0.815754\pi$
$131$	−19.1622	−1.67421	−0.837105	+	0.547043i	$0.815754\pi$
$132$	0.0139294	0.00121240
$133$	14.2522	1.23582
$134$	−16.8188	−1.45292
$135$	−9.13963	−0.786614
$136$	−2.83838	−0.243389
$137$	−6.84697	−0.584976	−0.292488	−	0.956269i	$-0.594483\pi$
$137$	−6.84697	−0.584976	−0.292488	+	0.956269i	$0.594483\pi$
$138$	9.80926	0.835020
$139$	19.7531	1.67544	0.837720	−	0.546100i	$-0.183888\pi$
$139$	19.7531	1.67544	0.837720	+	0.546100i	$0.183888\pi$
$140$	0.100225	0.00847052
$141$	6.64408	0.559532
$142$	−19.2709	−1.61718
$143$	2.03990	0.170585
$144$	8.09604	0.674670
$145$	−4.00117	−0.332279
$146$	−4.98488	−0.412551
$147$	7.39618	0.610027
$148$	0.0989435	0.00813311
$149$	7.50186	0.614576	0.307288	−	0.951617i	$-0.400578\pi$
$149$	7.50186	0.614576	0.307288	+	0.951617i	$0.400578\pi$
$150$	2.17979	0.177979
$151$	10.4373	0.849373	0.424687	−	0.905340i	$-0.360384\pi$
$151$	10.4373	0.849373	0.424687	+	0.905340i	$0.360384\pi$
$152$	−10.6077	−0.860402
$153$	2.03859	0.164811
$154$	−5.37399	−0.433048
$155$	−14.0192	−1.12605
$156$	0.0284146	0.00227499
$157$	8.59256	0.685761	0.342881	−	0.939379i	$-0.388597\pi$
$157$	8.59256	0.685761	0.342881	+	0.939379i	$0.388597\pi$
$158$	13.6723	1.08771
$159$	−5.18015	−0.410812
$160$	−0.148666	−0.0117531
$161$	27.0736	2.13370
$162$	−1.79198	−0.140792
$163$	10.0024	0.783446	0.391723	−	0.920083i	$-0.371879\pi$
$163$	10.0024	0.783446	0.391723	+	0.920083i	$0.371879\pi$
$164$	0.00818252	0.000638947 0
$165$	−1.81392	−0.141214
$166$	−5.44137	−0.422332
$167$	−6.16249	−0.476868	−0.238434	−	0.971159i	$-0.576634\pi$
$167$	−6.16249	−0.476868	−0.238434	+	0.971159i	$0.576634\pi$
$168$	−10.6134	−0.818841
$169$	−8.83881	−0.679908
$170$	2.60695	0.199944
$171$	7.61873	0.582619
$172$	−0.0142062	−0.00108322
$173$	5.59791	0.425602	0.212801	−	0.977096i	$-0.431741\pi$
$173$	5.59791	0.425602	0.212801	+	0.977096i	$0.431741\pi$
$174$	2.98842	0.226552
$175$	6.01623	0.454785
$176$	3.97139	0.299354
$177$	−0.0790266	−0.00594000
$178$	10.4212	0.781104
$179$	−15.2068	−1.13661	−0.568306	−	0.822818i	$-0.692401\pi$
$179$	−15.2068	−1.13661	−0.568306	+	0.822818i	$0.692401\pi$
$180$	0.0535766	0.00399337
$181$	14.2150	1.05659	0.528296	−	0.849060i	$-0.322831\pi$
$181$	14.2150	1.05659	0.528296	+	0.849060i	$0.322831\pi$
$182$	−10.9624	−0.812587
$183$	2.87202	0.212306
$184$	−20.1506	−1.48552
$185$	−12.8847	−0.947302
$186$	10.4708	0.767755
$187$	1.00000	0.0731272
$188$	−0.0962632	−0.00702071
$189$	18.8405	1.37044
$190$	9.74283	0.706819
$191$	−8.71054	−0.630273	−0.315136	−	0.949046i	$-0.602050\pi$
$191$	−8.71054	−0.630273	−0.315136	+	0.949046i	$0.602050\pi$
$192$	7.89903	0.570063
$193$	−15.0353	−1.08226	−0.541131	−	0.840938i	$-0.682004\pi$
$193$	−15.0353	−1.08226	−0.541131	+	0.840938i	$0.682004\pi$
$194$	−0.833871	−0.0598685
$195$	−3.70022	−0.264979
$196$	−0.107160	−0.00765429
$197$	3.01193	0.214591	0.107296	−	0.994227i	$-0.465781\pi$
$197$	3.01193	0.214591	0.107296	+	0.994227i	$0.465781\pi$
$198$	−2.87275	−0.204157
$199$	16.0109	1.13498	0.567492	−	0.823379i	$-0.307914\pi$
$199$	16.0109	1.13498	0.567492	+	0.823379i	$0.307914\pi$
$200$	−4.47781	−0.316629
$201$	11.7026	0.825435
$202$	−25.1190	−1.76737
$203$	8.24805	0.578900
$204$	0.0139294	0.000975253 0
$205$	−1.06555	−0.0744212
$206$	−11.4368	−0.796838
$207$	14.4726	1.00592
$208$	8.10123	0.561719
$209$	3.73725	0.258511
$210$	9.74801	0.672676
$211$	−2.96659	−0.204229	−0.102114	−	0.994773i	$-0.532561\pi$
$211$	−2.96659	−0.204229	−0.102114	+	0.994773i	$0.532561\pi$
$212$	0.0750529	0.00515466
$213$	13.4088	0.918755
$214$	−7.28391	−0.497918
$215$	1.84997	0.126167
$216$	−14.0228	−0.954129
$217$	28.8994	1.96182
$218$	−0.696999	−0.0472067
$219$	3.46849	0.234379
$220$	0.0262812	0.00177188
$221$	2.03990	0.137219
$222$	9.62341	0.645881
$223$	−22.4102	−1.50070	−0.750348	−	0.661043i	$-0.770114\pi$
$223$	−22.4102	−1.50070	−0.750348	+	0.661043i	$0.770114\pi$
$224$	0.306461	0.0204763
$225$	3.21607	0.214405
$226$	9.34685	0.621744
$227$	22.5927	1.49953	0.749765	−	0.661704i	$-0.230167\pi$
$227$	22.5927	1.49953	0.749765	+	0.661704i	$0.230167\pi$
$228$	0.0520576	0.00344760
$229$	−16.3369	−1.07957	−0.539785	−	0.841803i	$-0.681495\pi$
$229$	−16.3369	−1.07957	−0.539785	+	0.841803i	$0.681495\pi$
$230$	18.5075	1.22035
$231$	3.73924	0.246024
$232$	−6.13893	−0.403041
$233$	−3.20546	−0.209997	−0.104998	−	0.994472i	$-0.533484\pi$
$233$	−3.20546	−0.209997	−0.104998	+	0.994472i	$0.533484\pi$
$234$	−5.86012	−0.383088
$235$	12.5357	0.817736
$236$	0.00114498	7.45320e−5 0
$237$	−9.51325	−0.617952
$238$	−5.37399	−0.348344
$239$	−9.72642	−0.629150	−0.314575	−	0.949233i	$-0.601862\pi$
$239$	−9.72642	−0.629150	−0.314575	+	0.949233i	$0.601862\pi$
$240$	−7.20379	−0.465003
$241$	15.1559	0.976278	0.488139	−	0.872766i	$-0.337676\pi$
$241$	15.1559	0.976278	0.488139	+	0.872766i	$0.337676\pi$
$242$	−1.40918	−0.0905856
$243$	16.0681	1.03077
$244$	−0.0416114	−0.00266390
$245$	13.9547	0.891532
$246$	0.795845	0.0507412
$247$	7.62362	0.485079
$248$	−21.5095	−1.36585
$249$	3.78612	0.239936
$250$	17.1475	1.08450
$251$	−24.8846	−1.57070	−0.785350	−	0.619052i	$-0.787517\pi$
$251$	−24.8846	−1.57070	−0.785350	+	0.619052i	$0.787517\pi$
$252$	−0.110443	−0.00695727
$253$	7.09931	0.446330
$254$	8.94788	0.561440
$255$	−1.81392	−0.113592
$256$	−0.340932	−0.0213083
$257$	31.0074	1.93419	0.967095	−	0.254417i	$-0.0818835\pi$
$257$	31.0074	1.93419	0.967095	+	0.254417i	$0.0818835\pi$
$258$	−1.38172	−0.0860222
$259$	26.5606	1.65040
$260$	0.0536110	0.00332481
$261$	4.40913	0.272918
$262$	27.0030	1.66825
$263$	−19.7919	−1.22042	−0.610210	−	0.792240i	$-0.708915\pi$
$263$	−19.7919	−1.22042	−0.610210	+	0.792240i	$0.708915\pi$
$264$	−2.78307	−0.171286
$265$	−9.77360	−0.600387
$266$	−20.0839	−1.23142
$267$	−7.25112	−0.443761
$268$	−0.169553	−0.0103571
$269$	−25.9662	−1.58319	−0.791594	−	0.611048i	$-0.790748\pi$
$269$	−25.9662	−1.58319	−0.791594	+	0.611048i	$0.790748\pi$
$270$	12.8794	0.783815
$271$	25.5941	1.55473	0.777366	−	0.629049i	$-0.216556\pi$
$271$	25.5941	1.55473	0.777366	+	0.629049i	$0.216556\pi$
$272$	3.97139	0.240801
$273$	7.62767	0.461648
$274$	9.64863	0.582895
$275$	1.57759	0.0951325
$276$	0.0988891	0.00595242
$277$	8.73069	0.524576	0.262288	−	0.964990i	$-0.415523\pi$
$277$	8.73069	0.524576	0.262288	+	0.964990i	$0.415523\pi$
$278$	−27.8358	−1.66948
$279$	15.4486	0.924885
$280$	−20.0247	−1.19671
$281$	0.127721	0.00761923	0.00380961	−	0.999993i	$-0.498787\pi$
$281$	0.127721	0.00761923	0.00380961	+	0.999993i	$0.498787\pi$
$282$	−9.36271	−0.557541
$283$	0.836178	0.0497056	0.0248528	−	0.999691i	$-0.492088\pi$
$283$	0.836178	0.0497056	0.0248528	+	0.999691i	$0.492088\pi$
$284$	−0.194274	−0.0115280
$285$	−6.77909	−0.401559
$286$	−2.87459	−0.169978
$287$	2.19653	0.129657
$288$	0.163824	0.00965340
$289$	1.00000	0.0588235
$290$	5.63838	0.331097
$291$	0.580210	0.0340125
$292$	−0.0502535	−0.00294086
$293$	−25.0402	−1.46287	−0.731433	−	0.681914i	$-0.761148\pi$
$293$	−25.0402	−1.46287	−0.731433	+	0.681914i	$0.761148\pi$
$294$	−10.4226	−0.607856
$295$	−0.149103	−0.00868110
$296$	−19.7688	−1.14904
$297$	4.94041	0.286672
$298$	−10.5715	−0.612390
$299$	14.4819	0.837508
$300$	0.0219749	0.00126872
$301$	−3.81355	−0.219809
$302$	−14.7080	−0.846351
$303$	17.4779	1.00408
$304$	14.8421	0.851250
$305$	5.41876	0.310277
$306$	−2.87275	−0.164224
$307$	11.4579	0.653935	0.326967	−	0.945036i	$-0.393973\pi$
$307$	11.4579	0.653935	0.326967	+	0.945036i	$0.393973\pi$
$308$	−0.0541762	−0.00308698
$309$	7.95774	0.452700
$310$	19.7557	1.12205
$311$	33.1566	1.88014	0.940070	−	0.340982i	$-0.110759\pi$
$311$	33.1566	1.88014	0.940070	+	0.340982i	$0.110759\pi$
$312$	−5.67719	−0.321407
$313$	−2.95854	−0.167226	−0.0836132	−	0.996498i	$-0.526646\pi$
$313$	−2.95854	−0.167226	−0.0836132	+	0.996498i	$0.526646\pi$
$314$	−12.1085	−0.683321
$315$	14.3822	0.810347
$316$	0.137833	0.00775373
$317$	−14.3080	−0.803616	−0.401808	−	0.915724i	$-0.631618\pi$
$317$	−14.3080	−0.803616	−0.401808	+	0.915724i	$0.631618\pi$
$318$	7.29977	0.409351
$319$	2.16283	0.121095
$320$	14.9034	0.833127
$321$	5.06817	0.282878
$322$	−38.1516	−2.12610
$323$	3.73725	0.207946
$324$	−0.0180653	−0.00100363
$325$	3.21813	0.178510
$326$	−14.0952	−0.780659
$327$	0.484974	0.0268191
$328$	−1.63485	−0.0902697
$329$	−25.8411	−1.42467
$330$	2.55615	0.140711
$331$	−12.6754	−0.696701	−0.348351	−	0.937364i	$-0.613258\pi$
$331$	−12.6754	−0.696701	−0.348351	+	0.937364i	$0.613258\pi$
$332$	−0.0548555	−0.00301059
$333$	14.1984	0.778067
$334$	8.68407	0.475171
$335$	22.0797	1.20634
$336$	14.8500	0.810131
$337$	−9.50599	−0.517824	−0.258912	−	0.965901i	$-0.583364\pi$
$337$	−9.50599	−0.517824	−0.258912	+	0.965901i	$0.583364\pi$
$338$	12.4555	0.677489
$339$	−6.50357	−0.353225
$340$	0.0262812	0.00142530
$341$	7.57807	0.410376
$342$	−10.7362	−0.580546
$343$	−2.07142	−0.111846
$344$	2.83838	0.153035
$345$	−12.8776	−0.693307
$346$	−7.88848	−0.424087
$347$	26.8373	1.44070	0.720350	−	0.693610i	$-0.243981\pi$
$347$	26.8373	1.44070	0.720350	+	0.693610i	$0.243981\pi$
$348$	0.0301269	0.00161497
$349$	−12.1934	−0.652698	−0.326349	−	0.945249i	$-0.605818\pi$
$349$	−12.1934	−0.652698	−0.326349	+	0.945249i	$0.605818\pi$
$350$	−8.47797	−0.453166
$351$	10.0779	0.537920
$352$	0.0803611	0.00428326
$353$	−36.7657	−1.95684	−0.978420	−	0.206627i	$-0.933751\pi$
$353$	−36.7657	−1.95684	−0.978420	+	0.206627i	$0.933751\pi$
$354$	0.111363	0.00591887
$355$	25.2989	1.34273
$356$	0.105058	0.00556808
$357$	3.73924	0.197901
$358$	21.4292	1.13257
$359$	14.3401	0.756844	0.378422	−	0.925633i	$-0.376467\pi$
$359$	14.3401	0.756844	0.378422	+	0.925633i	$0.376467\pi$
$360$	−10.7045	−0.564178
$361$	−5.03297	−0.264893
$362$	−20.0315	−1.05283
$363$	0.980513	0.0514636
$364$	−0.110514	−0.00579251
$365$	6.54415	0.342536
$366$	−4.04720	−0.211550
$367$	16.3962	0.855873	0.427937	−	0.903809i	$-0.359241\pi$
$367$	16.3962	0.855873	0.427937	+	0.903809i	$0.359241\pi$
$368$	28.1941	1.46972
$369$	1.17419	0.0611259
$370$	18.1569	0.943931
$371$	20.1474	1.04600
$372$	0.105558	0.00547293
$373$	−25.4679	−1.31868	−0.659339	−	0.751846i	$-0.729164\pi$
$373$	−25.4679	−1.31868	−0.659339	+	0.751846i	$0.729164\pi$
$374$	−1.40918	−0.0728671
$375$	−11.9313	−0.616127
$376$	19.2332	0.991878
$377$	4.41195	0.227227
$378$	−26.5497	−1.36557
$379$	0.376204	0.0193243	0.00966216	−	0.999953i	$-0.496924\pi$
$379$	0.376204	0.0193243	0.00966216	+	0.999953i	$0.496924\pi$
$380$	0.0982193	0.00503854
$381$	−6.22596	−0.318966
$382$	12.2747	0.628030
$383$	−0.819796	−0.0418896	−0.0209448	−	0.999781i	$-0.506667\pi$
$383$	−0.819796	−0.0418896	−0.0209448	+	0.999781i	$0.506667\pi$
$384$	−10.9736	−0.559993
$385$	7.05497	0.359555
$386$	21.1874	1.07841
$387$	−2.03859	−0.103628
$388$	−0.00840642	−0.000426771 0
$389$	32.3790	1.64168	0.820841	−	0.571156i	$-0.193505\pi$
$389$	32.3790	1.64168	0.820841	+	0.571156i	$0.193505\pi$
$390$	5.21429	0.264036
$391$	7.09931	0.359027
$392$	21.4104	1.08139
$393$	−18.7888	−0.947769
$394$	−4.24436	−0.213828
$395$	−17.9490	−0.903114
$396$	−0.0289607	−0.00145533
$397$	−27.3688	−1.37360	−0.686801	−	0.726845i	$-0.740986\pi$
$397$	−27.3688	−1.37360	−0.686801	+	0.726845i	$0.740986\pi$
$398$	−22.5623	−1.13095
$399$	13.9745	0.699598
$400$	6.26523	0.313262
$401$	−33.7650	−1.68614	−0.843072	−	0.537800i	$-0.819256\pi$
$401$	−33.7650	−1.68614	−0.843072	+	0.537800i	$0.819256\pi$
$402$	−16.4910	−0.822498
$403$	15.4585	0.770043
$404$	−0.253230	−0.0125987
$405$	2.35252	0.116898
$406$	−11.6230	−0.576840
$407$	6.96480	0.345232
$408$	−2.78307	−0.137783
$409$	−22.3053	−1.10292	−0.551462	−	0.834200i	$-0.685930\pi$
$409$	−22.3053	−1.10292	−0.551462	+	0.834200i	$0.685930\pi$
$410$	1.50155	0.0741564
$411$	−6.71355	−0.331155
$412$	−0.115296	−0.00568024
$413$	0.307362	0.0151243
$414$	−20.3945	−1.00234
$415$	7.14343	0.350657
$416$	0.163929	0.00803726
$417$	19.3682	0.948466
$418$	−5.26646	−0.257591
$419$	−20.9767	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$419$	−20.9767	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$420$	0.0982715	0.00479516
$421$	27.7300	1.35148	0.675740	−	0.737140i	$-0.263824\pi$
$421$	27.7300	1.35148	0.675740	+	0.737140i	$0.263824\pi$
$422$	4.18047	0.203502
$423$	−13.8138	−0.671648
$424$	−14.9955	−0.728244
$425$	1.57759	0.0765245
$426$	−18.8954	−0.915486
$427$	−11.1703	−0.540567
$428$	−0.0734305	−0.00354940
$429$	2.00015	0.0965681
$430$	−2.60695	−0.125718
$431$	11.1309	0.536155	0.268077	−	0.963397i	$-0.413612\pi$
$431$	11.1309	0.536155	0.268077	+	0.963397i	$0.413612\pi$
$432$	19.6203	0.943980
$433$	−22.7204	−1.09187	−0.545937	−	0.837826i	$-0.683826\pi$
$433$	−22.7204	−1.09187	−0.545937	+	0.837826i	$0.683826\pi$
$434$	−40.7245	−1.95484
$435$	−3.92320	−0.188103
$436$	−0.00702658	−0.000336512 0
$437$	26.5319	1.26919
$438$	−4.88774	−0.233545
$439$	7.18941	0.343132	0.171566	−	0.985173i	$-0.445117\pi$
$439$	7.18941	0.343132	0.171566	+	0.985173i	$0.445117\pi$
$440$	−5.25094	−0.250329
$441$	−15.3775	−0.732260
$442$	−2.87459	−0.136730
$443$	−36.1893	−1.71941	−0.859703	−	0.510794i	$-0.829351\pi$
$443$	−36.1893	−1.71941	−0.859703	+	0.510794i	$0.829351\pi$
$444$	0.0970154	0.00460415
$445$	−13.6810	−0.648541
$446$	31.5800	1.49536
$447$	7.35567	0.347911
$448$	−30.7220	−1.45148
$449$	−28.4892	−1.34449	−0.672245	−	0.740329i	$-0.734670\pi$
$449$	−28.4892	−1.34449	−0.672245	+	0.740329i	$0.734670\pi$
$450$	−4.53203	−0.213642
$451$	0.575981	0.0271219
$452$	0.0942274	0.00443209
$453$	10.2339	0.480830
$454$	−31.8372	−1.49419
$455$	14.3914	0.674681
$456$	−10.4010	−0.487073
$457$	33.9430	1.58779	0.793893	−	0.608058i	$-0.208051\pi$
$457$	33.9430	1.58779	0.793893	+	0.608058i	$0.208051\pi$
$458$	23.0216	1.07573
$459$	4.94041	0.230598
$460$	0.186578	0.00869925
$461$	−25.9534	−1.20877	−0.604386	−	0.796692i	$-0.706581\pi$
$461$	−25.9534	−1.20877	−0.604386	+	0.796692i	$0.706581\pi$
$462$	−5.26926	−0.245148
$463$	12.8086	0.595267	0.297633	−	0.954680i	$-0.403803\pi$
$463$	12.8086	0.595267	0.297633	+	0.954680i	$0.403803\pi$
$464$	8.58942	0.398754
$465$	−13.7461	−0.637458
$466$	4.51708	0.209250
$467$	−35.6960	−1.65182	−0.825908	−	0.563805i	$-0.809337\pi$
$467$	−35.6960	−1.65182	−0.825908	+	0.563805i	$0.809337\pi$
$468$	−0.0590770	−0.00273084
$469$	−45.5153	−2.10170
$470$	−17.6650	−0.814826
$471$	8.42512	0.388209
$472$	−0.228766	−0.0105298
$473$	−1.00000	−0.0459800
$474$	13.4059	0.615753
$475$	5.89586	0.270521
$476$	−0.0541762	−0.00248316
$477$	10.7701	0.493129
$478$	13.7063	0.626911
$479$	27.4034	1.25209	0.626047	−	0.779785i	$-0.284672\pi$
$479$	27.4034	1.25209	0.626047	+	0.779785i	$0.284672\pi$
$480$	−0.145769	−0.00665341
$481$	14.2075	0.647806
$482$	−21.3574	−0.972804
$483$	26.5460	1.20788
$484$	−0.0142062	−0.000645738 0
$485$	1.09471	0.0497081
$486$	−22.6429	−1.02710
$487$	−21.0586	−0.954255	−0.477128	−	0.878834i	$-0.658322\pi$
$487$	−21.0586	−0.954255	−0.477128	+	0.878834i	$0.658322\pi$
$488$	8.31390	0.376353
$489$	9.80745	0.443508
$490$	−19.6647	−0.888360
$491$	5.93404	0.267799	0.133900	−	0.990995i	$-0.457250\pi$
$491$	5.93404	0.267799	0.133900	+	0.990995i	$0.457250\pi$
$492$	0.00802306	0.000361708 0
$493$	2.16283	0.0974088
$494$	−10.7431	−0.483353
$495$	3.77135	0.169509
$496$	30.0955	1.35133
$497$	−52.1514	−2.33931
$498$	−5.33533	−0.239082
$499$	−36.6009	−1.63848	−0.819241	−	0.573449i	$-0.805605\pi$
$499$	−36.6009	−1.63848	−0.819241	+	0.573449i	$0.805605\pi$
$500$	0.172867	0.00773084
$501$	−6.04240	−0.269955
$502$	35.0669	1.56511
$503$	−43.6309	−1.94540	−0.972702	−	0.232057i	$-0.925454\pi$
$503$	−43.6309	−1.94540	−0.972702	+	0.232057i	$0.925454\pi$
$504$	22.0664	0.982915
$505$	32.9763	1.46743
$506$	−10.0042	−0.444742
$507$	−8.66657	−0.384896
$508$	0.0902053	0.00400221
$509$	15.0059	0.665124	0.332562	−	0.943081i	$-0.392087\pi$
$509$	15.0059	0.665124	0.332562	+	0.943081i	$0.392087\pi$
$510$	2.55615	0.113188
$511$	−13.4902	−0.596769
$512$	22.8638	1.01045
$513$	18.4635	0.815185
$514$	−43.6951	−1.92731
$515$	15.0142	0.661605
$516$	−0.0139294	−0.000613208 0
$517$	−6.77612	−0.298013
$518$	−37.4287	−1.64452
$519$	5.48883	0.240933
$520$	−10.7114	−0.469725
$521$	38.3315	1.67933	0.839666	−	0.543103i	$-0.182751\pi$
$521$	38.3315	1.67933	0.839666	+	0.543103i	$0.182751\pi$
$522$	−6.21326	−0.271947
$523$	35.6213	1.55761	0.778806	−	0.627265i	$-0.215826\pi$
$523$	35.6213	1.55761	0.778806	+	0.627265i	$0.215826\pi$
$524$	0.272223	0.0118921
$525$	5.89900	0.257453
$526$	27.8904	1.21608
$527$	7.57807	0.330106
$528$	3.89400	0.169464
$529$	27.4002	1.19131
$530$	13.7728	0.598251
$531$	0.164305	0.00713023
$532$	−0.202470	−0.00877819
$533$	1.17494	0.0508924
$534$	10.2181	0.442183
$535$	9.56233	0.413415
$536$	33.8765	1.46324
$537$	−14.9105	−0.643435
$538$	36.5911	1.57755
$539$	−7.54317	−0.324907
$540$	0.129840	0.00558741
$541$	14.2417	0.612300	0.306150	−	0.951983i	$-0.400959\pi$
$541$	14.2417	0.612300	0.306150	+	0.951983i	$0.400959\pi$
$542$	−36.0668	−1.54920
$543$	13.9380	0.598136
$544$	0.0803611	0.00344545
$545$	0.915021	0.0391952
$546$	−10.7488	−0.460005
$547$	36.8726	1.57656	0.788280	−	0.615317i	$-0.210972\pi$
$547$	36.8726	1.57656	0.788280	+	0.615317i	$0.210972\pi$
$548$	0.0972697	0.00415516
$549$	−5.97124	−0.254846
$550$	−2.22312	−0.0947940
$551$	8.08302	0.344348
$552$	−19.7579	−0.840951
$553$	37.0003	1.57341
$554$	−12.3031	−0.522710
$555$	−12.6336	−0.536267
$556$	−0.280618	−0.0119008
$557$	8.75292	0.370873	0.185437	−	0.982656i	$-0.440630\pi$
$557$	8.75292	0.370873	0.185437	+	0.982656i	$0.440630\pi$
$558$	−21.7699	−0.921594
$559$	−2.03990	−0.0862786
$560$	28.0180	1.18398
$561$	0.980513	0.0413973
$562$	−0.179983	−0.00759212
$563$	12.0643	0.508450	0.254225	−	0.967145i	$-0.418180\pi$
$563$	12.0643	0.508450	0.254225	+	0.967145i	$0.418180\pi$
$564$	−0.0943873	−0.00397442
$565$	−12.2706	−0.516226
$566$	−1.17833	−0.0495288
$567$	−4.84950	−0.203660
$568$	38.8157	1.62867
$569$	−44.4893	−1.86509	−0.932544	−	0.361057i	$-0.882416\pi$
$569$	−44.4893	−1.86509	−0.932544	+	0.361057i	$0.882416\pi$
$570$	9.55297	0.400130
$571$	21.8313	0.913612	0.456806	−	0.889566i	$-0.348993\pi$
$571$	21.8313	0.913612	0.456806	+	0.889566i	$0.348993\pi$
$572$	−0.0289793	−0.00121169
$573$	−8.54080	−0.356797
$574$	−3.09531	−0.129196
$575$	11.1998	0.467065
$576$	−16.4229	−0.684289
$577$	16.8750	0.702515	0.351258	−	0.936279i	$-0.385754\pi$
$577$	16.8750	0.702515	0.351258	+	0.936279i	$0.385754\pi$
$578$	−1.40918	−0.0586142
$579$	−14.7423	−0.612668
$580$	0.0568416	0.00236022
$581$	−14.7255	−0.610918
$582$	−0.817622	−0.0338915
$583$	5.28310	0.218804
$584$	10.0406	0.415482
$585$	7.69317	0.318074
$586$	35.2862	1.45766
$587$	13.9698	0.576594	0.288297	−	0.957541i	$-0.406911\pi$
$587$	13.9698	0.576594	0.288297	+	0.957541i	$0.406911\pi$
$588$	−0.105072	−0.00433309
$589$	28.3212	1.16695
$590$	0.210113	0.00865021
$591$	2.95324	0.121480
$592$	27.6599	1.13681
$593$	29.6131	1.21606	0.608032	−	0.793913i	$-0.291959\pi$
$593$	29.6131	1.21606	0.608032	+	0.793913i	$0.291959\pi$
$594$	−6.96193	−0.285652
$595$	7.05497	0.289226
$596$	−0.106573	−0.00436541
$597$	15.6989	0.642514
$598$	−20.4076	−0.834529
$599$	2.15225	0.0879386	0.0439693	−	0.999033i	$-0.486000\pi$
$599$	2.15225	0.0879386	0.0439693	+	0.999033i	$0.486000\pi$
$600$	−4.39056	−0.179244
$601$	40.1898	1.63938	0.819688	−	0.572811i	$-0.194147\pi$
$601$	40.1898	1.63938	0.819688	+	0.572811i	$0.194147\pi$
$602$	5.37399	0.219027
$603$	−24.3309	−0.990831
$604$	−0.148274	−0.00603320
$605$	1.84997	0.0752122
$606$	−24.6295	−1.00051
$607$	5.12571	0.208046	0.104023	−	0.994575i	$-0.466828\pi$
$607$	5.12571	0.208046	0.104023	+	0.994575i	$0.466828\pi$
$608$	0.300329	0.0121800
$609$	8.08732	0.327715
$610$	−7.63601	−0.309173
$611$	−13.8226	−0.559203
$612$	−0.0289607	−0.00117067
$613$	−23.2503	−0.939069	−0.469535	−	0.882914i	$-0.655578\pi$
$613$	−23.2503	−0.939069	−0.469535	+	0.882914i	$0.655578\pi$
$614$	−16.1462	−0.651608
$615$	−1.04479	−0.0421298
$616$	10.8243	0.436124
$617$	26.2894	1.05837	0.529185	−	0.848507i	$-0.322498\pi$
$617$	26.2894	1.05837	0.529185	+	0.848507i	$0.322498\pi$
$618$	−11.2139	−0.451089
$619$	−17.8396	−0.717036	−0.358518	−	0.933523i	$-0.616718\pi$
$619$	−17.8396	−0.717036	−0.358518	+	0.933523i	$0.616718\pi$
$620$	0.199161	0.00799848
$621$	35.0735	1.40745
$622$	−46.7237	−1.87345
$623$	28.2021	1.12989
$624$	7.94336	0.317989
$625$	−14.6232	−0.584929
$626$	4.16912	0.166631
$627$	3.66442	0.146343
$628$	−0.122068	−0.00487104
$629$	6.96480	0.277705
$630$	−20.2672	−0.807464
$631$	−49.8419	−1.98418	−0.992088	−	0.125543i	$-0.959933\pi$
$631$	−49.8419	−1.98418	−0.992088	+	0.125543i	$0.959933\pi$
$632$	−27.5389	−1.09544
$633$	−2.90878	−0.115614
$634$	20.1625	0.800756
$635$	−11.7468	−0.466157
$636$	0.0735904	0.00291805
$637$	−15.3873	−0.609668
$638$	−3.04782	−0.120664
$639$	−27.8783	−1.10285
$640$	−20.7043	−0.818409
$641$	−24.7894	−0.979123	−0.489562	−	0.871969i	$-0.662843\pi$
$641$	−24.7894	−0.979123	−0.489562	+	0.871969i	$0.662843\pi$
$642$	−7.14197	−0.281871
$643$	−34.1548	−1.34693	−0.673466	−	0.739218i	$-0.735195\pi$
$643$	−34.1548	−1.34693	−0.673466	+	0.739218i	$0.735195\pi$
$644$	−0.384613	−0.0151559
$645$	1.81392	0.0714232
$646$	−5.26646	−0.207206
$647$	10.6595	0.419067	0.209533	−	0.977802i	$-0.432806\pi$
$647$	10.6595	0.419067	0.209533	+	0.977802i	$0.432806\pi$
$648$	3.60943	0.141792
$649$	0.0805972	0.00316372
$650$	−4.53493	−0.177875
$651$	28.3362	1.11058
$652$	−0.142096	−0.00556491
$653$	−7.57850	−0.296569	−0.148285	−	0.988945i	$-0.547375\pi$
$653$	−7.57850	−0.296569	−0.148285	+	0.988945i	$0.547375\pi$
$654$	−0.683417	−0.0267237
$655$	−35.4496	−1.38513
$656$	2.28744	0.0893096
$657$	−7.21138	−0.281343
$658$	36.4148	1.41960
$659$	23.9948	0.934704	0.467352	−	0.884071i	$-0.345208\pi$
$659$	23.9948	0.934704	0.467352	+	0.884071i	$0.345208\pi$
$660$	0.0257690	0.00100306
$661$	−40.0590	−1.55811	−0.779056	−	0.626954i	$-0.784301\pi$
$661$	−40.0590	−1.55811	−0.779056	+	0.626954i	$0.784301\pi$
$662$	17.8619	0.694222
$663$	2.00015	0.0776793
$664$	10.9600	0.425332
$665$	26.3662	1.02244
$666$	−20.0081	−0.775299
$667$	15.3546	0.594531
$668$	0.0875458	0.00338725
$669$	−21.9735	−0.849543
$670$	−31.1143	−1.20205
$671$	−2.92910	−0.113077
$672$	0.300489	0.0115916
$673$	−37.0477	−1.42809	−0.714043	−	0.700102i	$-0.753138\pi$
$673$	−37.0477	−1.42809	−0.714043	+	0.700102i	$0.753138\pi$
$674$	13.3957	0.515982
$675$	7.79395	0.299989
$676$	0.125566	0.00482947
$677$	40.2429	1.54666	0.773330	−	0.634004i	$-0.218590\pi$
$677$	40.2429	1.54666	0.773330	+	0.634004i	$0.218590\pi$
$678$	9.16471	0.351969
$679$	−2.25664	−0.0866018
$680$	−5.25094	−0.201364
$681$	22.1524	0.848883
$682$	−10.6789	−0.408916
$683$	2.77129	0.106041	0.0530203	−	0.998593i	$-0.483115\pi$
$683$	2.77129	0.106041	0.0530203	+	0.998593i	$0.483115\pi$
$684$	−0.108234	−0.00413841
$685$	−12.6667	−0.483971
$686$	2.91900	0.111448
$687$	−16.0185	−0.611144
$688$	−3.97139	−0.151408
$689$	10.7770	0.410571
$690$	18.1469	0.690840
$691$	15.5670	0.592198	0.296099	−	0.955157i	$-0.404314\pi$
$691$	15.5670	0.592198	0.296099	+	0.955157i	$0.404314\pi$
$692$	−0.0795253	−0.00302310
$693$	−7.77428	−0.295321
$694$	−37.8186	−1.43557
$695$	36.5428	1.38615
$696$	−6.01930	−0.228161
$697$	0.575981	0.0218168
$698$	17.1827	0.650375
$699$	−3.14300	−0.118879
$700$	−0.0854680	−0.00323039
$701$	−8.36031	−0.315765	−0.157882	−	0.987458i	$-0.550467\pi$
$701$	−8.36031	−0.315765	−0.157882	+	0.987458i	$0.550467\pi$
$702$	−14.2016	−0.536007
$703$	26.0292	0.981709
$704$	−8.05601	−0.303622
$705$	12.2914	0.462920
$706$	51.8095	1.94988
$707$	−67.9776	−2.55656
$708$	0.00112267	4.21925e−5 0
$709$	−14.6469	−0.550076	−0.275038	−	0.961433i	$-0.588690\pi$
$709$	−14.6469	−0.550076	−0.275038	+	0.961433i	$0.588690\pi$
$710$	−35.6508	−1.33795
$711$	19.7791	0.741773
$712$	−20.9905	−0.786652
$713$	53.7991	2.01479
$714$	−5.26926	−0.197197
$715$	3.77376	0.141131
$716$	0.216032	0.00807348
$717$	−9.53688	−0.356161
$718$	−20.2079	−0.754151
$719$	30.4669	1.13622	0.568112	−	0.822951i	$-0.307674\pi$
$719$	30.4669	1.13622	0.568112	+	0.822951i	$0.307674\pi$
$720$	14.9775	0.558178
$721$	−30.9504	−1.15265
$722$	7.09237	0.263951
$723$	14.8606	0.552670
$724$	−0.201941	−0.00750510
$725$	3.41206	0.126721
$726$	−1.38172	−0.0512805
$727$	−12.9065	−0.478674	−0.239337	−	0.970937i	$-0.576930\pi$
$727$	−12.9065	−0.478674	−0.239337	+	0.970937i	$0.576930\pi$
$728$	22.0805	0.818359
$729$	11.9400	0.442223
$730$	−9.22190	−0.341318
$731$	−1.00000	−0.0369863
$732$	−0.0408006	−0.00150803
$733$	−1.48408	−0.0548157	−0.0274079	−	0.999624i	$-0.508725\pi$
$733$	−1.48408	−0.0548157	−0.0274079	+	0.999624i	$0.508725\pi$
$734$	−23.1052	−0.852828
$735$	13.6827	0.504696
$736$	0.570508	0.0210292
$737$	−11.9351	−0.439637
$738$	−1.65465	−0.0609085
$739$	40.1985	1.47873	0.739363	−	0.673307i	$-0.235127\pi$
$739$	40.1985	1.47873	0.739363	+	0.673307i	$0.235127\pi$
$740$	0.183043	0.00672879
$741$	7.47505	0.274603
$742$	−28.3913	−1.04228
$743$	−3.08358	−0.113126	−0.0565628	−	0.998399i	$-0.518014\pi$
$743$	−3.08358	−0.113126	−0.0565628	+	0.998399i	$0.518014\pi$
$744$	−21.0903	−0.773209
$745$	13.8782	0.508460
$746$	35.8889	1.31399
$747$	−7.87176	−0.288013
$748$	−0.0142062	−0.000519431 0
$749$	−19.7118	−0.720255
$750$	16.8133	0.613935
$751$	9.67794	0.353153	0.176577	−	0.984287i	$-0.443498\pi$
$751$	9.67794	0.353153	0.176577	+	0.984287i	$0.443498\pi$
$752$	−26.9106	−0.981328
$753$	−24.3996	−0.889172
$754$	−6.21724	−0.226419
$755$	19.3087	0.702715
$756$	−0.267652	−0.00973443
$757$	−27.1815	−0.987927	−0.493964	−	0.869483i	$-0.664452\pi$
$757$	−27.1815	−0.987927	−0.493964	+	0.869483i	$0.664452\pi$
$758$	−0.530140	−0.0192556
$759$	6.96096	0.252667
$760$	−19.6241	−0.711840
$761$	−47.4197	−1.71896	−0.859482	−	0.511167i	$-0.829213\pi$
$761$	−47.4197	−1.71896	−0.859482	+	0.511167i	$0.829213\pi$
$762$	8.77352	0.317831
$763$	−1.88623	−0.0682861
$764$	0.123744	0.00447690
$765$	3.77135	0.136353
$766$	1.15524	0.0417406
$767$	0.164410	0.00593651
$768$	−0.334289	−0.0120626
$769$	14.7691	0.532587	0.266294	−	0.963892i	$-0.414201\pi$
$769$	14.7691	0.532587	0.266294	+	0.963892i	$0.414201\pi$
$770$	−9.94174	−0.358275
$771$	30.4032	1.09494
$772$	0.213595	0.00768744
$773$	42.8824	1.54237	0.771187	−	0.636609i	$-0.219663\pi$
$773$	42.8824	1.54237	0.771187	+	0.636609i	$0.219663\pi$
$774$	2.87275	0.103259
$775$	11.9551	0.429441
$776$	1.67959	0.0602937
$777$	26.0430	0.934288
$778$	−45.6280	−1.63584
$779$	2.15258	0.0771243
$780$	0.0525662	0.00188217
$781$	−13.6753	−0.489340
$782$	−10.0042	−0.357750
$783$	10.6852	0.381860
$784$	−29.9568	−1.06989
$785$	15.8960	0.567353
$786$	26.4768	0.944397
$787$	−43.0197	−1.53349	−0.766743	−	0.641954i	$-0.778124\pi$
$787$	−43.0197	−1.53349	−0.766743	+	0.641954i	$0.778124\pi$
$788$	−0.0427882	−0.00152427
$789$	−19.4062	−0.690879
$790$	25.2935	0.899901
$791$	25.2946	0.899373
$792$	5.78631	0.205608
$793$	−5.97507	−0.212181
$794$	38.5677	1.36872
$795$	−9.58314	−0.339879
$796$	−0.227455	−0.00806193
$797$	30.3420	1.07477	0.537384	−	0.843338i	$-0.319413\pi$
$797$	30.3420	1.07477	0.537384	+	0.843338i	$0.319413\pi$
$798$	−19.6926	−0.697109
$799$	−6.77612	−0.239722
$800$	0.126777	0.00448225
$801$	15.0759	0.532680
$802$	47.5811	1.68015
$803$	−3.53743	−0.124833
$804$	−0.166249	−0.00586316
$805$	50.0854	1.76528
$806$	−21.7839	−0.767304
$807$	−25.4602	−0.896242
$808$	50.5949	1.77992
$809$	−28.4356	−0.999742	−0.499871	−	0.866100i	$-0.666619\pi$
$809$	−28.4356	−0.999742	−0.499871	+	0.866100i	$0.666619\pi$
$810$	−3.31513	−0.116482
$811$	22.8316	0.801726	0.400863	−	0.916138i	$-0.368710\pi$
$811$	22.8316	0.801726	0.400863	+	0.916138i	$0.368710\pi$
$812$	−0.117174	−0.00411199
$813$	25.0954	0.880132
$814$	−9.81466	−0.344004
$815$	18.5041	0.648171
$816$	3.89400	0.136317
$817$	−3.73725	−0.130750
$818$	31.4322	1.09900
$819$	−15.8588	−0.554150
$820$	0.0151374	0.000528623 0
$821$	11.9771	0.418005	0.209002	−	0.977915i	$-0.432978\pi$
$821$	11.9771	0.418005	0.209002	+	0.977915i	$0.432978\pi$
$822$	9.46061	0.329977
$823$	−0.0598099	−0.00208484	−0.00104242	−	0.999999i	$-0.500332\pi$
$823$	−0.0598099	−0.00208484	−0.00104242	+	0.999999i	$0.500332\pi$
$824$	23.0360	0.802498
$825$	1.54685	0.0538544
$826$	−0.433128	−0.0150705
$827$	16.4468	0.571911	0.285956	−	0.958243i	$-0.407689\pi$
$827$	16.4468	0.571911	0.285956	+	0.958243i	$0.407689\pi$
$828$	−0.205601	−0.00714514
$829$	3.07652	0.106852	0.0534261	−	0.998572i	$-0.482986\pi$
$829$	3.07652	0.106852	0.0534261	+	0.998572i	$0.482986\pi$
$830$	−10.0664	−0.349410
$831$	8.56055	0.296962
$832$	−16.4335	−0.569728
$833$	−7.54317	−0.261355
$834$	−27.2933	−0.945091
$835$	−11.4005	−0.394529
$836$	−0.0530922	−0.00183623
$837$	37.4388	1.29407
$838$	29.5600	1.02113
$839$	33.8811	1.16971	0.584853	−	0.811139i	$-0.301152\pi$
$839$	33.8811	1.16971	0.584853	+	0.811139i	$0.301152\pi$
$840$	−19.6345	−0.677454
$841$	−24.3222	−0.838696
$842$	−39.0767	−1.34667
$843$	0.125233	0.00431324
$844$	0.0421441	0.00145066
$845$	−16.3516	−0.562511
$846$	19.4661	0.669258
$847$	−3.81355	−0.131035
$848$	20.9812	0.720498
$849$	0.819883	0.0281383
$850$	−2.22312	−0.0762523
$851$	49.4452	1.69496
$852$	−0.190488	−0.00652602
$853$	22.9296	0.785094	0.392547	−	0.919732i	$-0.371594\pi$
$853$	22.9296	0.785094	0.392547	+	0.919732i	$0.371594\pi$
$854$	15.7409	0.538644
$855$	14.0945	0.482021
$856$	14.6713	0.501455
$857$	28.5538	0.975381	0.487690	−	0.873017i	$-0.337840\pi$
$857$	28.5538	0.975381	0.487690	+	0.873017i	$0.337840\pi$
$858$	−2.81857	−0.0962245
$859$	−30.1616	−1.02910	−0.514550	−	0.857460i	$-0.672041\pi$
$859$	−30.1616	−1.02910	−0.514550	+	0.857460i	$0.672041\pi$
$860$	−0.0262812	−0.000896181 0
$861$	2.15373	0.0733989
$862$	−15.6854	−0.534247
$863$	3.46269	0.117871	0.0589357	−	0.998262i	$-0.481229\pi$
$863$	3.46269	0.117871	0.0589357	+	0.998262i	$0.481229\pi$
$864$	0.397016	0.0135068
$865$	10.3560	0.352115
$866$	32.0172	1.08799
$867$	0.980513	0.0333000
$868$	−0.410551	−0.0139350
$869$	9.70231	0.329128
$870$	5.52851	0.187434
$871$	−24.3465	−0.824949
$872$	1.40390	0.0475421
$873$	−1.20632	−0.0408278
$874$	−37.3882	−1.26468
$875$	46.4047	1.56877
$876$	−0.0492742	−0.00166482
$877$	10.8232	0.365472	0.182736	−	0.983162i	$-0.441505\pi$
$877$	10.8232	0.365472	0.182736	+	0.983162i	$0.441505\pi$
$878$	−10.1312	−0.341911
$879$	−24.5523	−0.828127
$880$	7.34696	0.247666
$881$	11.9556	0.402795	0.201398	−	0.979510i	$-0.435452\pi$
$881$	11.9556	0.402795	0.201398	+	0.979510i	$0.435452\pi$
$882$	21.6697	0.729655
$883$	−31.7518	−1.06853	−0.534267	−	0.845316i	$-0.679412\pi$
$883$	−31.7518	−1.06853	−0.534267	+	0.845316i	$0.679412\pi$
$884$	−0.0289793	−0.000974679 0
$885$	−0.146197	−0.00491437
$886$	50.9973	1.71329
$887$	−0.609048	−0.0204498	−0.0102249	−	0.999948i	$-0.503255\pi$
$887$	−0.609048	−0.0204498	−0.0102249	+	0.999948i	$0.503255\pi$
$888$	−19.3835	−0.650469
$889$	24.2149	0.812142
$890$	19.2790	0.646234
$891$	−1.27165	−0.0426018
$892$	0.318364	0.0106596
$893$	−25.3241	−0.847437
$894$	−10.3655	−0.346673
$895$	−28.1322	−0.940357
$896$	42.6800	1.42584
$897$	14.1997	0.474113
$898$	40.1465	1.33971
$899$	16.3901	0.546639
$900$	−0.0456883	−0.00152294
$901$	5.28310	0.176005
$902$	−0.811662	−0.0270254
$903$	−3.73924	−0.124434
$904$	−18.8265	−0.626160
$905$	26.2974	0.874154
$906$	−14.4214	−0.479119
$907$	−27.4036	−0.909922	−0.454961	−	0.890511i	$-0.650347\pi$
$907$	−27.4036	−0.909922	−0.454961	+	0.890511i	$0.650347\pi$
$908$	−0.320957	−0.0106513
$909$	−36.3385	−1.20527
$910$	−20.2802	−0.672281
$911$	58.8817	1.95084	0.975418	−	0.220361i	$-0.0707235\pi$
$911$	58.8817	1.95084	0.975418	+	0.220361i	$0.0707235\pi$
$912$	14.5528	0.481892
$913$	−3.86137	−0.127793
$914$	−47.8318	−1.58214
$915$	5.31316	0.175648
$916$	0.232085	0.00766831
$917$	73.0760	2.41318
$918$	−6.96193	−0.229778
$919$	−15.4645	−0.510127	−0.255064	−	0.966924i	$-0.582096\pi$
$919$	−15.4645	−0.510127	−0.255064	+	0.966924i	$0.582096\pi$
$920$	−37.2780	−1.22902
$921$	11.2346	0.370192
$922$	36.5731	1.20447
$923$	−27.8962	−0.918214
$924$	−0.0531205	−0.00174754
$925$	10.9876	0.361271
$926$	−18.0497	−0.593149
$927$	−16.5450	−0.543410
$928$	0.173807	0.00570550
$929$	−26.3769	−0.865398	−0.432699	−	0.901539i	$-0.642439\pi$
$929$	−26.3769	−0.865398	−0.432699	+	0.901539i	$0.642439\pi$
$930$	19.3707	0.635190
$931$	−28.1907	−0.923913
$932$	0.0455375	0.00149163
$933$	32.5105	1.06435
$934$	50.3022	1.64594
$935$	1.84997	0.0605006
$936$	11.8035	0.385809
$937$	19.8441	0.648280	0.324140	−	0.946009i	$-0.394925\pi$
$937$	19.8441	0.648280	0.324140	+	0.946009i	$0.394925\pi$
$938$	64.1393	2.09422
$939$	−2.90088	−0.0946668
$940$	−0.178084	−0.00580847
$941$	−6.98553	−0.227722	−0.113861	−	0.993497i	$-0.536322\pi$
$941$	−6.98553	−0.227722	−0.113861	+	0.993497i	$0.536322\pi$
$942$	−11.8725	−0.386828
$943$	4.08906	0.133158
$944$	0.320083	0.0104178
$945$	34.8544	1.13382
$946$	1.40918	0.0458165
$947$	2.01789	0.0655727	0.0327864	−	0.999462i	$-0.489562\pi$
$947$	2.01789	0.0655727	0.0327864	+	0.999462i	$0.489562\pi$
$948$	0.135147	0.00438938
$949$	−7.21599	−0.234241
$950$	−8.30834	−0.269558
$951$	−14.0292	−0.454926
$952$	10.8243	0.350818
$953$	−24.3408	−0.788475	−0.394238	−	0.919009i	$-0.628991\pi$
$953$	−24.3408	−0.788475	−0.394238	+	0.919009i	$0.628991\pi$
$954$	−15.1770	−0.491374
$955$	−16.1143	−0.521446
$956$	0.138176	0.00446892
$957$	2.12068	0.0685518
$958$	−38.6164	−1.24764
$959$	26.1113	0.843177
$960$	14.6130	0.471633
$961$	26.4272	0.852490
$962$	−20.0209	−0.645501
$963$	−10.5373	−0.339559
$964$	−0.215308	−0.00693461
$965$	−27.8149	−0.895392
$966$	−37.4081	−1.20359
$967$	29.1421	0.937148	0.468574	−	0.883424i	$-0.344768\pi$
$967$	29.1421	0.937148	0.468574	+	0.883424i	$0.344768\pi$
$968$	2.83838	0.0912291
$969$	3.66442	0.117718
$970$	−1.54264	−0.0495312
$971$	46.2990	1.48581	0.742903	−	0.669399i	$-0.233448\pi$
$971$	46.2990	1.48581	0.742903	+	0.669399i	$0.233448\pi$
$972$	−0.228267	−0.00732167
$973$	−75.3296	−2.41496
$974$	29.6754	0.950860
$975$	3.15542	0.101054
$976$	−11.6326	−0.372350
$977$	−37.7629	−1.20814	−0.604071	−	0.796930i	$-0.706456\pi$
$977$	−37.7629	−1.20814	−0.604071	+	0.796930i	$0.706456\pi$
$978$	−13.8205	−0.441930
$979$	7.39523	0.236353
$980$	−0.198243	−0.00633265
$981$	−1.00831	−0.0321930
$982$	−8.36214	−0.266847
$983$	10.2586	0.327198	0.163599	−	0.986527i	$-0.447690\pi$
$983$	10.2586	0.327198	0.163599	+	0.986527i	$0.447690\pi$
$984$	−1.60300	−0.0511016
$985$	5.57200	0.177539
$986$	−3.04782	−0.0970622
$987$	−25.3375	−0.806502
$988$	−0.108303	−0.00344557
$989$	−7.09931	−0.225745
$990$	−5.31452	−0.168906
$991$	40.9975	1.30233	0.651165	−	0.758937i	$-0.274281\pi$
$991$	40.9975	1.30233	0.651165	+	0.758937i	$0.274281\pi$
$992$	0.608982	0.0193352
$993$	−12.4284	−0.394402
$994$	73.4907	2.33098
$995$	29.6198	0.939011
$996$	−0.0537865	−0.00170429
$997$	34.7476	1.10047	0.550233	−	0.835011i	$-0.314539\pi$
$997$	34.7476	1.10047	0.550233	+	0.835011i	$0.314539\pi$
$998$	51.5774	1.63265
$999$	34.4089	1.08865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.16	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-1.40918 q^{2} +0.980513 q^{3} -0.0142062 q^{4} +1.84997 q^{5} -1.38172 q^{6} -3.81355 q^{7} +2.83838 q^{8} -2.03859 q^{9} +O(q^{10})\)	\(q-1.40918 q^{2} +0.980513 q^{3} -0.0142062 q^{4} +1.84997 q^{5} -1.38172 q^{6} -3.81355 q^{7} +2.83838 q^{8} -2.03859 q^{9} -2.60695 q^{10} -1.00000 q^{11} -0.0139294 q^{12} -2.03990 q^{13} +5.37399 q^{14} +1.81392 q^{15} -3.97139 q^{16} -1.00000 q^{17} +2.87275 q^{18} -3.73725 q^{19} -0.0262812 q^{20} -3.73924 q^{21} +1.40918 q^{22} -7.09931 q^{23} +2.78307 q^{24} -1.57759 q^{25} +2.87459 q^{26} -4.94041 q^{27} +0.0541762 q^{28} -2.16283 q^{29} -2.55615 q^{30} -7.57807 q^{31} -0.0803611 q^{32} -0.980513 q^{33} +1.40918 q^{34} -7.05497 q^{35} +0.0289607 q^{36} -6.96480 q^{37} +5.26646 q^{38} -2.00015 q^{39} +5.25094 q^{40} -0.575981 q^{41} +5.26926 q^{42} +1.00000 q^{43} +0.0142062 q^{44} -3.77135 q^{45} +10.0042 q^{46} +6.77612 q^{47} -3.89400 q^{48} +7.54317 q^{49} +2.22312 q^{50} -0.980513 q^{51} +0.0289793 q^{52} -5.28310 q^{53} +6.96193 q^{54} -1.84997 q^{55} -10.8243 q^{56} -3.66442 q^{57} +3.04782 q^{58} -0.0805972 q^{59} -0.0257690 q^{60} +2.92910 q^{61} +10.6789 q^{62} +7.77428 q^{63} +8.05601 q^{64} -3.77376 q^{65} +1.38172 q^{66} +11.9351 q^{67} +0.0142062 q^{68} -6.96096 q^{69} +9.94174 q^{70} +13.6753 q^{71} -5.78631 q^{72} +3.53743 q^{73} +9.81466 q^{74} -1.54685 q^{75} +0.0530922 q^{76} +3.81355 q^{77} +2.81857 q^{78} -9.70231 q^{79} -7.34696 q^{80} +1.27165 q^{81} +0.811662 q^{82} +3.86137 q^{83} +0.0531205 q^{84} -1.84997 q^{85} -1.40918 q^{86} -2.12068 q^{87} -2.83838 q^{88} -7.39523 q^{89} +5.31452 q^{90} +7.77926 q^{91} +0.100854 q^{92} -7.43040 q^{93} -9.54879 q^{94} -6.91382 q^{95} -0.0787951 q^{96} +0.591741 q^{97} -10.6297 q^{98} +2.03859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 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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