LMFDB - Embedded newform 8041.2.a.i.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:	$78$
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)

$f(q)$	$=$	$q-1.80887 q^{2} +0.743622 q^{3} +1.27201 q^{4} +1.40249 q^{5} -1.34511 q^{6} -0.305829 q^{7} +1.31684 q^{8} -2.44703 q^{9} +O(q^{10})$	\(q-1.80887 q^{2} +0.743622 q^{3} +1.27201 q^{4} +1.40249 q^{5} -1.34511 q^{6} -0.305829 q^{7} +1.31684 q^{8} -2.44703 q^{9} -2.53691 q^{10} +1.00000 q^{11} +0.945892 q^{12} +4.42043 q^{13} +0.553205 q^{14} +1.04292 q^{15} -4.92601 q^{16} -1.00000 q^{17} +4.42635 q^{18} +7.16936 q^{19} +1.78397 q^{20} -0.227421 q^{21} -1.80887 q^{22} -6.56536 q^{23} +0.979235 q^{24} -3.03303 q^{25} -7.99597 q^{26} -4.05053 q^{27} -0.389016 q^{28} +7.88823 q^{29} -1.88650 q^{30} +3.50518 q^{31} +6.27682 q^{32} +0.743622 q^{33} +1.80887 q^{34} -0.428921 q^{35} -3.11263 q^{36} +4.24432 q^{37} -12.9684 q^{38} +3.28713 q^{39} +1.84686 q^{40} +10.7010 q^{41} +0.411375 q^{42} -1.00000 q^{43} +1.27201 q^{44} -3.43192 q^{45} +11.8759 q^{46} -4.24257 q^{47} -3.66309 q^{48} -6.90647 q^{49} +5.48636 q^{50} -0.743622 q^{51} +5.62281 q^{52} -7.25189 q^{53} +7.32688 q^{54} +1.40249 q^{55} -0.402729 q^{56} +5.33130 q^{57} -14.2688 q^{58} +12.2876 q^{59} +1.32660 q^{60} -10.1298 q^{61} -6.34042 q^{62} +0.748372 q^{63} -1.50192 q^{64} +6.19959 q^{65} -1.34511 q^{66} -9.17301 q^{67} -1.27201 q^{68} -4.88215 q^{69} +0.775862 q^{70} +11.7531 q^{71} -3.22235 q^{72} +1.47388 q^{73} -7.67741 q^{74} -2.25543 q^{75} +9.11947 q^{76} -0.305829 q^{77} -5.94598 q^{78} +16.0824 q^{79} -6.90866 q^{80} +4.32902 q^{81} -19.3568 q^{82} -7.13085 q^{83} -0.289281 q^{84} -1.40249 q^{85} +1.80887 q^{86} +5.86586 q^{87} +1.31684 q^{88} -5.01147 q^{89} +6.20789 q^{90} -1.35189 q^{91} -8.35118 q^{92} +2.60653 q^{93} +7.67425 q^{94} +10.0549 q^{95} +4.66758 q^{96} +15.7303 q^{97} +12.4929 q^{98} -2.44703 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * 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 $

$2$	−1.80887	−1.27906	−0.639532	−	0.768765i	$-0.720872\pi$
$2$	−1.80887	−1.27906	−0.639532	+	0.768765i	$0.720872\pi$
$3$	0.743622	0.429330	0.214665	−	0.976688i	$-0.431134\pi$
$3$	0.743622	0.429330	0.214665	+	0.976688i	$0.431134\pi$
$4$	1.27201	0.636003
$5$	1.40249	0.627211	0.313605	−	0.949553i	$-0.398463\pi$
$5$	1.40249	0.627211	0.313605	+	0.949553i	$0.398463\pi$
$6$	−1.34511	−0.549141
$7$	−0.305829	−0.115593	−0.0577963	−	0.998328i	$-0.518407\pi$
$7$	−0.305829	−0.115593	−0.0577963	+	0.998328i	$0.518407\pi$
$8$	1.31684	0.465575
$9$	−2.44703	−0.815675
$10$	−2.53691	−0.802242
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.945892	0.273055
$13$	4.42043	1.22601	0.613003	−	0.790081i	$-0.289961\pi$
$13$	4.42043	1.22601	0.613003	+	0.790081i	$0.289961\pi$
$14$	0.553205	0.147850
$15$	1.04292	0.269281
$16$	−4.92601	−1.23150
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	4.42635	1.04330
$19$	7.16936	1.64476	0.822382	−	0.568935i	$-0.192645\pi$
$19$	7.16936	1.64476	0.822382	+	0.568935i	$0.192645\pi$
$20$	1.78397	0.398908
$21$	−0.227421	−0.0496274
$22$	−1.80887	−0.385652
$23$	−6.56536	−1.36897	−0.684486	−	0.729026i	$-0.739973\pi$
$23$	−6.56536	−1.36897	−0.684486	+	0.729026i	$0.739973\pi$
$24$	0.979235	0.199885
$25$	−3.03303	−0.606607
$26$	−7.99597	−1.56814
$27$	−4.05053	−0.779525
$28$	−0.389016	−0.0735172
$29$	7.88823	1.46481	0.732404	−	0.680870i	$-0.238398\pi$
$29$	7.88823	1.46481	0.732404	+	0.680870i	$0.238398\pi$
$30$	−1.88650	−0.344427
$31$	3.50518	0.629550	0.314775	−	0.949166i	$-0.398071\pi$
$31$	3.50518	0.629550	0.314775	+	0.949166i	$0.398071\pi$
$32$	6.27682	1.10960
$33$	0.743622	0.129448
$34$	1.80887	0.310218
$35$	−0.428921	−0.0725009
$36$	−3.11263	−0.518772
$37$	4.24432	0.697761	0.348881	−	0.937167i	$-0.386562\pi$
$37$	4.24432	0.697761	0.348881	+	0.937167i	$0.386562\pi$
$38$	−12.9684	−2.10376
$39$	3.28713	0.526362
$40$	1.84686	0.292014
$41$	10.7010	1.67122	0.835610	−	0.549323i	$-0.185114\pi$
$41$	10.7010	1.67122	0.835610	+	0.549323i	$0.185114\pi$
$42$	0.411375	0.0634766
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.27201	0.191762
$45$	−3.43192	−0.511600
$46$	11.8759	1.75100
$47$	−4.24257	−0.618842	−0.309421	−	0.950925i	$-0.600135\pi$
$47$	−4.24257	−0.618842	−0.309421	+	0.950925i	$0.600135\pi$
$48$	−3.66309	−0.528722
$49$	−6.90647	−0.986638
$50$	5.48636	0.775888
$51$	−0.743622	−0.104128
$52$	5.62281	0.779744
$53$	−7.25189	−0.996124	−0.498062	−	0.867142i	$-0.665955\pi$
$53$	−7.25189	−0.996124	−0.498062	+	0.867142i	$0.665955\pi$
$54$	7.32688	0.997061
$55$	1.40249	0.189111
$56$	−0.402729	−0.0538170
$57$	5.33130	0.706147
$58$	−14.2688	−1.87358
$59$	12.2876	1.59971	0.799857	−	0.600191i	$-0.204909\pi$
$59$	12.2876	1.59971	0.799857	+	0.600191i	$0.204909\pi$
$60$	1.32660	0.171263
$61$	−10.1298	−1.29699	−0.648495	−	0.761219i	$-0.724601\pi$
$61$	−10.1298	−1.29699	−0.648495	+	0.761219i	$0.724601\pi$
$62$	−6.34042	−0.805234
$63$	0.748372	0.0942860
$64$	−1.50192	−0.187740
$65$	6.19959	0.768964
$66$	−1.34511	−0.165572
$67$	−9.17301	−1.12066	−0.560331	−	0.828269i	$-0.689326\pi$
$67$	−9.17301	−1.12066	−0.560331	+	0.828269i	$0.689326\pi$
$68$	−1.27201	−0.154253
$69$	−4.88215	−0.587742
$70$	0.775862	0.0927332
$71$	11.7531	1.39484	0.697418	−	0.716665i	$-0.254332\pi$
$71$	11.7531	1.39484	0.697418	+	0.716665i	$0.254332\pi$
$72$	−3.22235	−0.379758
$73$	1.47388	0.172505	0.0862525	−	0.996273i	$-0.472511\pi$
$73$	1.47388	0.172505	0.0862525	+	0.996273i	$0.472511\pi$
$74$	−7.67741	−0.892481
$75$	−2.25543	−0.260435
$76$	9.11947	1.04608
$77$	−0.305829	−0.0348525
$78$	−5.94598	−0.673250
$79$	16.0824	1.80941	0.904705	−	0.426039i	$-0.140092\pi$
$79$	16.0824	1.80941	0.904705	+	0.426039i	$0.140092\pi$
$80$	−6.90866	−0.772412
$81$	4.32902	0.481002
$82$	−19.3568	−2.13760
$83$	−7.13085	−0.782713	−0.391356	−	0.920239i	$-0.627994\pi$
$83$	−7.13085	−0.782713	−0.391356	+	0.920239i	$0.627994\pi$
$84$	−0.289281	−0.0315632
$85$	−1.40249	−0.152121
$86$	1.80887	0.195055
$87$	5.86586	0.628887
$88$	1.31684	0.140376
$89$	−5.01147	−0.531214	−0.265607	−	0.964081i	$-0.585572\pi$
$89$	−5.01147	−0.531214	−0.265607	+	0.964081i	$0.585572\pi$
$90$	6.20789	0.654369
$91$	−1.35189	−0.141717
$92$	−8.35118	−0.870671
$93$	2.60653	0.270285
$94$	7.67425	0.791539
$95$	10.0549	1.03161
$96$	4.66758	0.476383
$97$	15.7303	1.59717	0.798584	−	0.601883i	$-0.205583\pi$
$97$	15.7303	1.59717	0.798584	+	0.601883i	$0.205583\pi$
$98$	12.4929	1.26197
$99$	−2.44703	−0.245935
$100$	−3.85804	−0.385804
$101$	13.8189	1.37503	0.687515	−	0.726170i	$-0.258702\pi$
$101$	13.8189	1.37503	0.687515	+	0.726170i	$0.258702\pi$
$102$	1.34511	0.133186
$103$	0.963089	0.0948959	0.0474480	−	0.998874i	$-0.484891\pi$
$103$	0.963089	0.0948959	0.0474480	+	0.998874i	$0.484891\pi$
$104$	5.82102	0.570798
$105$	−0.318955	−0.0311268
$106$	13.1177	1.27411
$107$	−2.59418	−0.250789	−0.125394	−	0.992107i	$-0.540020\pi$
$107$	−2.59418	−0.250789	−0.125394	+	0.992107i	$0.540020\pi$
$108$	−5.15230	−0.495780
$109$	−9.46450	−0.906535	−0.453267	−	0.891375i	$-0.649742\pi$
$109$	−9.46450	−0.906535	−0.453267	+	0.891375i	$0.649742\pi$
$110$	−2.53691	−0.241885
$111$	3.15617	0.299570
$112$	1.50652	0.142353
$113$	−1.88070	−0.176922	−0.0884608	−	0.996080i	$-0.528195\pi$
$113$	−1.88070	−0.176922	−0.0884608	+	0.996080i	$0.528195\pi$
$114$	−9.64361	−0.903207
$115$	−9.20783	−0.858634
$116$	10.0339	0.931622
$117$	−10.8169	−1.00002
$118$	−22.2267	−2.04614
$119$	0.305829	0.0280353
$120$	1.37336	0.125370
$121$	1.00000	0.0909091
$122$	18.3235	1.65893
$123$	7.95752	0.717505
$124$	4.45862	0.400396
$125$	−11.2662	−1.00768
$126$	−1.35371	−0.120598
$127$	−13.9245	−1.23560	−0.617802	−	0.786334i	$-0.711977\pi$
$127$	−13.9245	−1.23560	−0.617802	+	0.786334i	$0.711977\pi$
$128$	−9.83686	−0.869464
$129$	−0.743622	−0.0654723
$130$	−11.2142	−0.983554
$131$	−4.81722	−0.420883	−0.210441	−	0.977606i	$-0.567490\pi$
$131$	−4.81722	−0.420883	−0.210441	+	0.977606i	$0.567490\pi$
$132$	0.945892	0.0823293
$133$	−2.19260	−0.190122
$134$	16.5928	1.43340
$135$	−5.68081	−0.488926
$136$	−1.31684	−0.112919
$137$	11.0248	0.941915	0.470957	−	0.882156i	$-0.343909\pi$
$137$	11.0248	0.941915	0.470957	+	0.882156i	$0.343909\pi$
$138$	8.83117	0.751759
$139$	4.88667	0.414482	0.207241	−	0.978290i	$-0.433552\pi$
$139$	4.88667	0.414482	0.207241	+	0.978290i	$0.433552\pi$
$140$	−0.545590	−0.0461108
$141$	−3.15487	−0.265688
$142$	−21.2598	−1.78408
$143$	4.42043	0.369655
$144$	12.0541	1.00451
$145$	11.0631	0.918743
$146$	−2.66606	−0.220645
$147$	−5.13580	−0.423594
$148$	5.39880	0.443778
$149$	−4.66572	−0.382231	−0.191115	−	0.981568i	$-0.561210\pi$
$149$	−4.66572	−0.382231	−0.191115	+	0.981568i	$0.561210\pi$
$150$	4.07978	0.333112
$151$	23.3588	1.90091	0.950455	−	0.310861i	$-0.100617\pi$
$151$	23.3588	1.90091	0.950455	+	0.310861i	$0.100617\pi$
$152$	9.44094	0.765761
$153$	2.44703	0.197830
$154$	0.553205	0.0445785
$155$	4.91597	0.394860
$156$	4.18125	0.334768
$157$	1.96702	0.156986	0.0784928	−	0.996915i	$-0.474989\pi$
$157$	1.96702	0.156986	0.0784928	+	0.996915i	$0.474989\pi$
$158$	−29.0909	−2.31435
$159$	−5.39266	−0.427666
$160$	8.80315	0.695950
$161$	2.00788	0.158243
$162$	−7.83062	−0.615232
$163$	−7.61558	−0.596499	−0.298249	−	0.954488i	$-0.596403\pi$
$163$	−7.61558	−0.596499	−0.298249	+	0.954488i	$0.596403\pi$
$164$	13.6118	1.06290
$165$	1.04292	0.0811912
$166$	12.8988	1.00114
$167$	−22.7161	−1.75783	−0.878914	−	0.476981i	$-0.841731\pi$
$167$	−22.7161	−1.75783	−0.878914	+	0.476981i	$0.841731\pi$
$168$	−0.299478	−0.0231053
$169$	6.54017	0.503090
$170$	2.53691	0.194572
$171$	−17.5436	−1.34159
$172$	−1.27201	−0.0969896
$173$	12.6146	0.959069	0.479535	−	0.877523i	$-0.340805\pi$
$173$	12.6146	0.959069	0.479535	+	0.877523i	$0.340805\pi$
$174$	−10.6106	−0.804386
$175$	0.927590	0.0701192
$176$	−4.92601	−0.371312
$177$	9.13736	0.686806
$178$	9.06509	0.679457
$179$	15.2394	1.13904	0.569522	−	0.821976i	$-0.307128\pi$
$179$	15.2394	1.13904	0.569522	+	0.821976i	$0.307128\pi$
$180$	−4.36542	−0.325379
$181$	−12.0926	−0.898834	−0.449417	−	0.893322i	$-0.648368\pi$
$181$	−12.0926	−0.898834	−0.449417	+	0.893322i	$0.648368\pi$
$182$	2.44540	0.181265
$183$	−7.53276	−0.556837
$184$	−8.64556	−0.637359
$185$	5.95259	0.437643
$186$	−4.71487	−0.345711
$187$	−1.00000	−0.0731272
$188$	−5.39658	−0.393586
$189$	1.23877	0.0901072
$190$	−18.1880	−1.31950
$191$	−3.49870	−0.253157	−0.126579	−	0.991957i	$-0.540400\pi$
$191$	−3.49870	−0.253157	−0.126579	+	0.991957i	$0.540400\pi$
$192$	−1.11686	−0.0806025
$193$	4.07475	0.293307	0.146653	−	0.989188i	$-0.453150\pi$
$193$	4.07475	0.293307	0.146653	+	0.989188i	$0.453150\pi$
$194$	−28.4540	−2.04288
$195$	4.61015	0.330140
$196$	−8.78507	−0.627505
$197$	−6.94473	−0.494792	−0.247396	−	0.968915i	$-0.579575\pi$
$197$	−6.94473	−0.494792	−0.247396	+	0.968915i	$0.579575\pi$
$198$	4.42635	0.314567
$199$	−0.504890	−0.0357907	−0.0178953	−	0.999840i	$-0.505697\pi$
$199$	−0.504890	−0.0357907	−0.0178953	+	0.999840i	$0.505697\pi$
$200$	−3.99403	−0.282421
$201$	−6.82125	−0.481134
$202$	−24.9965	−1.75875
$203$	−2.41245	−0.169321
$204$	−0.945892	−0.0662257
$205$	15.0080	1.04821
$206$	−1.74210	−0.121378
$207$	16.0656	1.11664
$208$	−21.7751	−1.50983
$209$	7.16936	0.495915
$210$	0.576948	0.0398132
$211$	−0.556900	−0.0383386	−0.0191693	−	0.999816i	$-0.506102\pi$
$211$	−0.556900	−0.0383386	−0.0191693	+	0.999816i	$0.506102\pi$
$212$	−9.22445	−0.633538
$213$	8.73986	0.598845
$214$	4.69253	0.320775
$215$	−1.40249	−0.0956487
$216$	−5.33392	−0.362927
$217$	−1.07199	−0.0727712
$218$	17.1200	1.15952
$219$	1.09601	0.0740617
$220$	1.78397	0.120275
$221$	−4.42043	−0.297350
$222$	−5.70909	−0.383169
$223$	−11.6748	−0.781806	−0.390903	−	0.920432i	$-0.627837\pi$
$223$	−11.6748	−0.781806	−0.390903	+	0.920432i	$0.627837\pi$
$224$	−1.91963	−0.128261
$225$	7.42191	0.494794
$226$	3.40194	0.226294
$227$	9.52251	0.632031	0.316016	−	0.948754i	$-0.397655\pi$
$227$	9.52251	0.632031	0.316016	+	0.948754i	$0.397655\pi$
$228$	6.78144	0.449112
$229$	23.5348	1.55522	0.777610	−	0.628747i	$-0.216432\pi$
$229$	23.5348	1.55522	0.777610	+	0.628747i	$0.216432\pi$
$230$	16.6558	1.09825
$231$	−0.227421	−0.0149632
$232$	10.3876	0.681978
$233$	−22.9774	−1.50530	−0.752650	−	0.658421i	$-0.771225\pi$
$233$	−22.9774	−1.50530	−0.752650	+	0.658421i	$0.771225\pi$
$234$	19.5664	1.27909
$235$	−5.95014	−0.388145
$236$	15.6299	1.01742
$237$	11.9592	0.776834
$238$	−0.553205	−0.0358589
$239$	21.4075	1.38473	0.692367	−	0.721545i	$-0.256568\pi$
$239$	21.4075	1.38473	0.692367	+	0.721545i	$0.256568\pi$
$240$	−5.13743	−0.331620
$241$	−0.181928	−0.0117190	−0.00585952	−	0.999983i	$-0.501865\pi$
$241$	−0.181928	−0.0117190	−0.00585952	+	0.999983i	$0.501865\pi$
$242$	−1.80887	−0.116278
$243$	15.3707	0.986033
$244$	−12.8852	−0.824890
$245$	−9.68622	−0.618830
$246$	−14.3941	−0.917735
$247$	31.6916	2.01649
$248$	4.61578	0.293103
$249$	−5.30266	−0.336042
$250$	20.3791	1.28889
$251$	−8.50283	−0.536694	−0.268347	−	0.963322i	$-0.586477\pi$
$251$	−8.50283	−0.536694	−0.268347	+	0.963322i	$0.586477\pi$
$252$	0.951934	0.0599662
$253$	−6.56536	−0.412761
$254$	25.1877	1.58042
$255$	−1.04292	−0.0653101
$256$	20.7974	1.29984
$257$	27.5328	1.71745	0.858723	−	0.512439i	$-0.171258\pi$
$257$	27.5328	1.71745	0.858723	+	0.512439i	$0.171258\pi$
$258$	1.34511	0.0837432
$259$	−1.29804	−0.0806560
$260$	7.88591	0.489064
$261$	−19.3027	−1.19481
$262$	8.71372	0.538335
$263$	18.1306	1.11798	0.558990	−	0.829174i	$-0.311189\pi$
$263$	18.1306	1.11798	0.558990	+	0.829174i	$0.311189\pi$
$264$	0.979235	0.0602677
$265$	−10.1707	−0.624779
$266$	3.96612	0.243179
$267$	−3.72664	−0.228066
$268$	−11.6681	−0.712744
$269$	24.7820	1.51099	0.755493	−	0.655157i	$-0.227397\pi$
$269$	24.7820	1.51099	0.755493	+	0.655157i	$0.227397\pi$
$270$	10.2758	0.625368
$271$	5.28255	0.320892	0.160446	−	0.987045i	$-0.448707\pi$
$271$	5.28255	0.320892	0.160446	+	0.987045i	$0.448707\pi$
$272$	4.92601	0.298683
$273$	−1.00530	−0.0608434
$274$	−19.9425	−1.20477
$275$	−3.03303	−0.182899
$276$	−6.21012	−0.373806
$277$	−2.81766	−0.169297	−0.0846484	−	0.996411i	$-0.526977\pi$
$277$	−2.81766	−0.169297	−0.0846484	+	0.996411i	$0.526977\pi$
$278$	−8.83934	−0.530148
$279$	−8.57728	−0.513508
$280$	−0.564822	−0.0337546
$281$	3.87575	0.231208	0.115604	−	0.993295i	$-0.463120\pi$
$281$	3.87575	0.231208	0.115604	+	0.993295i	$0.463120\pi$
$282$	5.70674	0.339832
$283$	13.9607	0.829879	0.414940	−	0.909849i	$-0.363803\pi$
$283$	13.9607	0.829879	0.414940	+	0.909849i	$0.363803\pi$
$284$	14.9500	0.887120
$285$	7.47707	0.442903
$286$	−7.99597	−0.472812
$287$	−3.27268	−0.193180
$288$	−15.3595	−0.905070
$289$	1.00000	0.0588235
$290$	−20.0118	−1.17513
$291$	11.6974	0.685713
$292$	1.87479	0.109714
$293$	12.9446	0.756233	0.378117	−	0.925758i	$-0.376572\pi$
$293$	12.9446	0.756233	0.378117	+	0.925758i	$0.376572\pi$
$294$	9.28999	0.541803
$295$	17.2332	1.00336
$296$	5.58911	0.324860
$297$	−4.05053	−0.235036
$298$	8.43968	0.488897
$299$	−29.0217	−1.67837
$300$	−2.86892	−0.165637
$301$	0.305829	0.0176277
$302$	−42.2530	−2.43139
$303$	10.2760	0.590342
$304$	−35.3164	−2.02553
$305$	−14.2069	−0.813486
$306$	−4.42635	−0.253038
$307$	19.8089	1.13056	0.565278	−	0.824900i	$-0.308769\pi$
$307$	19.8089	1.13056	0.565278	+	0.824900i	$0.308769\pi$
$308$	−0.389016	−0.0221663
$309$	0.716174	0.0407417
$310$	−8.89235	−0.505051
$311$	0.680814	0.0386054	0.0193027	−	0.999814i	$-0.493855\pi$
$311$	0.680814	0.0386054	0.0193027	+	0.999814i	$0.493855\pi$
$312$	4.32864	0.245061
$313$	−24.0683	−1.36042	−0.680211	−	0.733017i	$-0.738112\pi$
$313$	−24.0683	−1.36042	−0.680211	+	0.733017i	$0.738112\pi$
$314$	−3.55809	−0.200795
$315$	1.04958	0.0591372
$316$	20.4569	1.15079
$317$	20.0187	1.12436	0.562181	−	0.827015i	$-0.309963\pi$
$317$	20.0187	1.12436	0.562181	+	0.827015i	$0.309963\pi$
$318$	9.75462	0.547012
$319$	7.88823	0.441656
$320$	−2.10642	−0.117753
$321$	−1.92909	−0.107671
$322$	−3.63199	−0.202403
$323$	−7.16936	−0.398914
$324$	5.50654	0.305919
$325$	−13.4073	−0.743703
$326$	13.7756	0.762960
$327$	−7.03801	−0.389203
$328$	14.0916	0.778078
$329$	1.29750	0.0715335
$330$	−1.88650	−0.103849
$331$	−4.40156	−0.241932	−0.120966	−	0.992657i	$-0.538599\pi$
$331$	−4.40156	−0.241932	−0.120966	+	0.992657i	$0.538599\pi$
$332$	−9.07049	−0.497808
$333$	−10.3860	−0.569147
$334$	41.0905	2.24837
$335$	−12.8650	−0.702891
$336$	1.12028	0.0611163
$337$	−34.2968	−1.86827	−0.934134	−	0.356924i	$-0.883826\pi$
$337$	−34.2968	−1.86827	−0.934134	+	0.356924i	$0.883826\pi$
$338$	−11.8303	−0.643484
$339$	−1.39853	−0.0759578
$340$	−1.78397	−0.0967494
$341$	3.50518	0.189816
$342$	31.7341	1.71598
$343$	4.25300	0.229641
$344$	−1.31684	−0.0709995
$345$	−6.84714	−0.368638
$346$	−22.8181	−1.22671
$347$	−3.69931	−0.198589	−0.0992946	−	0.995058i	$-0.531659\pi$
$347$	−3.69931	−0.198589	−0.0992946	+	0.995058i	$0.531659\pi$
$348$	7.46141	0.399974
$349$	−12.9491	−0.693148	−0.346574	−	0.938023i	$-0.612655\pi$
$349$	−12.9491	−0.693148	−0.346574	+	0.938023i	$0.612655\pi$
$350$	−1.67789	−0.0896869
$351$	−17.9051	−0.955702
$352$	6.27682	0.334556
$353$	−4.74368	−0.252481	−0.126240	−	0.992000i	$-0.540291\pi$
$353$	−4.74368	−0.252481	−0.126240	+	0.992000i	$0.540291\pi$
$354$	−16.5283	−0.878468
$355$	16.4835	0.874856
$356$	−6.37462	−0.337854
$357$	0.227421	0.0120364
$358$	−27.5660	−1.45691
$359$	7.15512	0.377633	0.188816	−	0.982012i	$-0.439535\pi$
$359$	7.15512	0.377633	0.188816	+	0.982012i	$0.439535\pi$
$360$	−4.51931	−0.238188
$361$	32.3998	1.70525
$362$	21.8739	1.14967
$363$	0.743622	0.0390300
$364$	−1.71962	−0.0901325
$365$	2.06710	0.108197
$366$	13.6258	0.712230
$367$	32.3582	1.68908	0.844542	−	0.535490i	$-0.179873\pi$
$367$	32.3582	1.68908	0.844542	+	0.535490i	$0.179873\pi$
$368$	32.3411	1.68589
$369$	−26.1857	−1.36317
$370$	−10.7675	−0.559774
$371$	2.21784	0.115144
$372$	3.31553	0.171902
$373$	−1.07574	−0.0556999	−0.0278499	−	0.999612i	$-0.508866\pi$
$373$	−1.07574	−0.0556999	−0.0278499	+	0.999612i	$0.508866\pi$
$374$	1.80887	0.0935344
$375$	−8.37781	−0.432628
$376$	−5.58681	−0.288118
$377$	34.8693	1.79586
$378$	−2.24077	−0.115253
$379$	1.69177	0.0869004	0.0434502	−	0.999056i	$-0.486165\pi$
$379$	1.69177	0.0869004	0.0434502	+	0.999056i	$0.486165\pi$
$380$	12.7899	0.656110
$381$	−10.3546	−0.530482
$382$	6.32869	0.323804
$383$	−30.6512	−1.56620	−0.783101	−	0.621894i	$-0.786363\pi$
$383$	−30.6512	−1.56620	−0.783101	+	0.621894i	$0.786363\pi$
$384$	−7.31491	−0.373287
$385$	−0.428921	−0.0218598
$386$	−7.37069	−0.375158
$387$	2.44703	0.124389
$388$	20.0090	1.01580
$389$	−35.1401	−1.78167	−0.890837	−	0.454323i	$-0.849881\pi$
$389$	−35.1401	−1.78167	−0.890837	+	0.454323i	$0.849881\pi$
$390$	−8.33915	−0.422269
$391$	6.56536	0.332025
$392$	−9.09475	−0.459354
$393$	−3.58219	−0.180698
$394$	12.5621	0.632870
$395$	22.5553	1.13488
$396$	−3.11263	−0.156416
$397$	−13.1023	−0.657587	−0.328794	−	0.944402i	$-0.606642\pi$
$397$	−13.1023	−0.657587	−0.328794	+	0.944402i	$0.606642\pi$
$398$	0.913280	0.0457786
$399$	−1.63046	−0.0816253
$400$	14.9408	0.747038
$401$	7.83175	0.391099	0.195549	−	0.980694i	$-0.437351\pi$
$401$	7.83175	0.391099	0.195549	+	0.980694i	$0.437351\pi$
$402$	12.3387	0.615401
$403$	15.4944	0.771831
$404$	17.5777	0.874523
$405$	6.07138	0.301690
$406$	4.36381	0.216572
$407$	4.24432	0.210383
$408$	−0.979235	−0.0484794
$409$	5.67836	0.280777	0.140388	−	0.990096i	$-0.455165\pi$
$409$	5.67836	0.280777	0.140388	+	0.990096i	$0.455165\pi$
$410$	−27.1476	−1.34072
$411$	8.19831	0.404393
$412$	1.22505	0.0603541
$413$	−3.75792	−0.184915
$414$	−29.0606	−1.42825
$415$	−10.0009	−0.490926
$416$	27.7462	1.36037
$417$	3.63383	0.177950
$418$	−12.9684	−0.634307
$419$	−27.8216	−1.35918	−0.679588	−	0.733594i	$-0.737841\pi$
$419$	−27.8216	−1.35918	−0.679588	+	0.733594i	$0.737841\pi$
$420$	−0.405713	−0.0197968
$421$	1.76329	0.0859374	0.0429687	−	0.999076i	$-0.486318\pi$
$421$	1.76329	0.0859374	0.0429687	+	0.999076i	$0.486318\pi$
$422$	1.00736	0.0490375
$423$	10.3817	0.504775
$424$	−9.54961	−0.463770
$425$	3.03303	0.147124
$426$	−15.8093	−0.765961
$427$	3.09799	0.149922
$428$	−3.29981	−0.159502
$429$	3.28713	0.158704
$430$	2.53691	0.122341
$431$	10.4851	0.505051	0.252525	−	0.967590i	$-0.418739\pi$
$431$	10.4851	0.505051	0.252525	+	0.967590i	$0.418739\pi$
$432$	19.9530	0.959987
$433$	−28.0288	−1.34698	−0.673488	−	0.739198i	$-0.735205\pi$
$433$	−28.0288	−1.34698	−0.673488	+	0.739198i	$0.735205\pi$
$434$	1.93908	0.0930790
$435$	8.22679	0.394444
$436$	−12.0389	−0.576559
$437$	−47.0695	−2.25164
$438$	−1.98254	−0.0947295
$439$	−22.6159	−1.07940	−0.539698	−	0.841858i	$-0.681462\pi$
$439$	−22.6159	−1.07940	−0.539698	+	0.841858i	$0.681462\pi$
$440$	1.84686	0.0880454
$441$	16.9003	0.804777
$442$	7.99597	0.380330
$443$	−8.52780	−0.405168	−0.202584	−	0.979265i	$-0.564934\pi$
$443$	−8.52780	−0.405168	−0.202584	+	0.979265i	$0.564934\pi$
$444$	4.01467	0.190528
$445$	−7.02851	−0.333183
$446$	21.1183	0.999979
$447$	−3.46953	−0.164103
$448$	0.459331	0.0217013
$449$	−3.76012	−0.177451	−0.0887255	−	0.996056i	$-0.528279\pi$
$449$	−3.76012	−0.177451	−0.0887255	+	0.996056i	$0.528279\pi$
$450$	−13.4253	−0.632873
$451$	10.7010	0.503892
$452$	−2.39226	−0.112523
$453$	17.3701	0.816119
$454$	−17.2250	−0.808408
$455$	−1.89601	−0.0888865
$456$	7.02049	0.328765
$457$	8.57980	0.401346	0.200673	−	0.979658i	$-0.435687\pi$
$457$	8.57980	0.401346	0.200673	+	0.979658i	$0.435687\pi$
$458$	−42.5713	−1.98923
$459$	4.05053	0.189062
$460$	−11.7124	−0.546094
$461$	−26.7127	−1.24413	−0.622066	−	0.782965i	$-0.713707\pi$
$461$	−26.7127	−1.24413	−0.622066	+	0.782965i	$0.713707\pi$
$462$	0.411375	0.0191389
$463$	4.35965	0.202610	0.101305	−	0.994855i	$-0.467698\pi$
$463$	4.35965	0.202610	0.101305	+	0.994855i	$0.467698\pi$
$464$	−38.8575	−1.80392
$465$	3.65562	0.169526
$466$	41.5631	1.92537
$467$	38.2287	1.76902	0.884508	−	0.466526i	$-0.154494\pi$
$467$	38.2287	1.76902	0.884508	+	0.466526i	$0.154494\pi$
$468$	−13.7592	−0.636018
$469$	2.80537	0.129540
$470$	10.7630	0.496461
$471$	1.46272	0.0673987
$472$	16.1809	0.744787
$473$	−1.00000	−0.0459800
$474$	−21.6326	−0.993620
$475$	−21.7449	−0.997725
$476$	0.389016	0.0178305
$477$	17.7456	0.812514
$478$	−38.7233	−1.77116
$479$	18.3274	0.837401	0.418700	−	0.908124i	$-0.362486\pi$
$479$	18.3274	0.837401	0.418700	+	0.908124i	$0.362486\pi$
$480$	6.54622	0.298793
$481$	18.7617	0.855460
$482$	0.329085	0.0149894
$483$	1.49310	0.0679385
$484$	1.27201	0.0578185
$485$	22.0615	1.00176
$486$	−27.8036	−1.26120
$487$	4.76107	0.215745	0.107872	−	0.994165i	$-0.465596\pi$
$487$	4.76107	0.215745	0.107872	+	0.994165i	$0.465596\pi$
$488$	−13.3394	−0.603846
$489$	−5.66312	−0.256095
$490$	17.5211	0.791523
$491$	12.0024	0.541661	0.270831	−	0.962627i	$-0.412702\pi$
$491$	12.0024	0.541661	0.270831	+	0.962627i	$0.412702\pi$
$492$	10.1220	0.456336
$493$	−7.88823	−0.355268
$494$	−57.3260	−2.57922
$495$	−3.43192	−0.154253
$496$	−17.2666	−0.775292
$497$	−3.59444	−0.161233
$498$	9.59181	0.429819
$499$	−34.8935	−1.56205	−0.781024	−	0.624501i	$-0.785302\pi$
$499$	−34.8935	−1.56205	−0.781024	+	0.624501i	$0.785302\pi$
$500$	−14.3307	−0.640888
$501$	−16.8922	−0.754689
$502$	15.3805	0.686466
$503$	−33.6210	−1.49908	−0.749542	−	0.661956i	$-0.769726\pi$
$503$	−33.6210	−1.49908	−0.749542	+	0.661956i	$0.769726\pi$
$504$	0.985489	0.0438972
$505$	19.3808	0.862434
$506$	11.8759	0.527947
$507$	4.86342	0.215992
$508$	−17.7121	−0.785848
$509$	−44.7318	−1.98270	−0.991352	−	0.131229i	$-0.958108\pi$
$509$	−44.7318	−1.98270	−0.991352	+	0.131229i	$0.958108\pi$
$510$	1.88650	0.0835358
$511$	−0.450756	−0.0199403
$512$	−17.9461	−0.793113
$513$	−29.0397	−1.28213
$514$	−49.8032	−2.19672
$515$	1.35072	0.0595197
$516$	−0.945892	−0.0416406
$517$	−4.24257	−0.186588
$518$	2.34798	0.103164
$519$	9.38049	0.411758
$520$	8.16389	0.358010
$521$	40.1324	1.75823	0.879116	−	0.476607i	$-0.158134\pi$
$521$	40.1324	1.75823	0.879116	+	0.476607i	$0.158134\pi$
$522$	34.9161	1.52823
$523$	27.9218	1.22093	0.610467	−	0.792041i	$-0.290982\pi$
$523$	27.9218	1.22093	0.610467	+	0.792041i	$0.290982\pi$
$524$	−6.12754	−0.267683
$525$	0.689776	0.0301043
$526$	−32.7959	−1.42997
$527$	−3.50518	−0.152688
$528$	−3.66309	−0.159416
$529$	20.1040	0.874086
$530$	18.3974	0.799132
$531$	−30.0682	−1.30485
$532$	−2.78900	−0.120918
$533$	47.3031	2.04892
$534$	6.74100	0.291711
$535$	−3.63830	−0.157297
$536$	−12.0794	−0.521752
$537$	11.3323	0.489026
$538$	−44.8274	−1.93265
$539$	−6.90647	−0.297483
$540$	−7.22603	−0.310959
$541$	−0.779327	−0.0335059	−0.0167529	−	0.999860i	$-0.505333\pi$
$541$	−0.779327	−0.0335059	−0.0167529	+	0.999860i	$0.505333\pi$
$542$	−9.55545	−0.410442
$543$	−8.99230	−0.385897
$544$	−6.27682	−0.269116
$545$	−13.2738	−0.568588
$546$	1.81845	0.0778226
$547$	−3.07606	−0.131523	−0.0657615	−	0.997835i	$-0.520948\pi$
$547$	−3.07606	−0.131523	−0.0657615	+	0.997835i	$0.520948\pi$
$548$	14.0237	0.599061
$549$	24.7879	1.05792
$550$	5.48636	0.233939
$551$	56.5536	2.40926
$552$	−6.42903	−0.273638
$553$	−4.91846	−0.209154
$554$	5.09678	0.216541
$555$	4.42648	0.187894
$556$	6.21587	0.263612
$557$	15.1346	0.641273	0.320636	−	0.947202i	$-0.396103\pi$
$557$	15.1346	0.641273	0.320636	+	0.947202i	$0.396103\pi$
$558$	15.5152	0.656809
$559$	−4.42043	−0.186964
$560$	2.11287	0.0892850
$561$	−0.743622	−0.0313957
$562$	−7.01073	−0.295730
$563$	18.5922	0.783566	0.391783	−	0.920058i	$-0.371858\pi$
$563$	18.5922	0.783566	0.391783	+	0.920058i	$0.371858\pi$
$564$	−4.01301	−0.168978
$565$	−2.63766	−0.110967
$566$	−25.2531	−1.06147
$567$	−1.32394	−0.0556002
$568$	15.4770	0.649401
$569$	38.6283	1.61938	0.809691	−	0.586856i	$-0.199635\pi$
$569$	38.6283	1.61938	0.809691	+	0.586856i	$0.199635\pi$
$570$	−13.5250	−0.566501
$571$	−25.9327	−1.08525	−0.542624	−	0.839976i	$-0.682569\pi$
$571$	−25.9327	−1.08525	−0.542624	+	0.839976i	$0.682569\pi$
$572$	5.62281	0.235102
$573$	−2.60171	−0.108688
$574$	5.91986	0.247090
$575$	19.9130	0.830428
$576$	3.67524	0.153135
$577$	−19.6450	−0.817833	−0.408916	−	0.912572i	$-0.634093\pi$
$577$	−19.6450	−0.817833	−0.408916	+	0.912572i	$0.634093\pi$
$578$	−1.80887	−0.0752390
$579$	3.03007	0.125926
$580$	14.0724	0.584324
$581$	2.18082	0.0904757
$582$	−21.1590	−0.877070
$583$	−7.25189	−0.300343
$584$	1.94088	0.0803140
$585$	−15.1705	−0.627225
$586$	−23.4151	−0.967271
$587$	31.4803	1.29933	0.649666	−	0.760220i	$-0.274909\pi$
$587$	31.4803	1.29933	0.649666	+	0.760220i	$0.274909\pi$
$588$	−6.53277	−0.269407
$589$	25.1299	1.03546
$590$	−31.1727	−1.28336
$591$	−5.16425	−0.212429
$592$	−20.9076	−0.859295
$593$	−4.67485	−0.191973	−0.0959865	−	0.995383i	$-0.530601\pi$
$593$	−4.67485	−0.191973	−0.0959865	+	0.995383i	$0.530601\pi$
$594$	7.32688	0.300625
$595$	0.428921	0.0175840
$596$	−5.93483	−0.243100
$597$	−0.375447	−0.0153660
$598$	52.4965	2.14674
$599$	19.5453	0.798598	0.399299	−	0.916821i	$-0.369254\pi$
$599$	19.5453	0.798598	0.399299	+	0.916821i	$0.369254\pi$
$600$	−2.97005	−0.121252
$601$	19.6562	0.801791	0.400896	−	0.916124i	$-0.368699\pi$
$601$	19.6562	0.801791	0.400896	+	0.916124i	$0.368699\pi$
$602$	−0.553205	−0.0225469
$603$	22.4466	0.914096
$604$	29.7125	1.20899
$605$	1.40249	0.0570192
$606$	−18.5880	−0.755085
$607$	21.7264	0.881849	0.440924	−	0.897544i	$-0.354651\pi$
$607$	21.7264	0.881849	0.440924	+	0.897544i	$0.354651\pi$
$608$	45.0008	1.82502
$609$	−1.79395	−0.0726946
$610$	25.6985	1.04050
$611$	−18.7540	−0.758704
$612$	3.11263	0.125821
$613$	0.804862	0.0325081	0.0162540	−	0.999868i	$-0.494826\pi$
$613$	0.804862	0.0325081	0.0162540	+	0.999868i	$0.494826\pi$
$614$	−35.8318	−1.44605
$615$	11.1603	0.450027
$616$	−0.402729	−0.0162264
$617$	−17.4886	−0.704063	−0.352031	−	0.935988i	$-0.614509\pi$
$617$	−17.4886	−0.704063	−0.352031	+	0.935988i	$0.614509\pi$
$618$	−1.29546	−0.0521112
$619$	23.1821	0.931766	0.465883	−	0.884846i	$-0.345737\pi$
$619$	23.1821	0.931766	0.465883	+	0.884846i	$0.345737\pi$
$620$	6.25315	0.251132
$621$	26.5932	1.06715
$622$	−1.23150	−0.0493788
$623$	1.53265	0.0614044
$624$	−16.1924	−0.648216
$625$	−0.635539	−0.0254216
$626$	43.5364	1.74007
$627$	5.33130	0.212911
$628$	2.50207	0.0998433
$629$	−4.24432	−0.169232
$630$	−1.89855	−0.0756402
$631$	29.7771	1.18541	0.592704	−	0.805420i	$-0.298060\pi$
$631$	29.7771	1.18541	0.592704	+	0.805420i	$0.298060\pi$
$632$	21.1780	0.842416
$633$	−0.414123	−0.0164599
$634$	−36.2112	−1.43813
$635$	−19.5290	−0.774984
$636$	−6.85950	−0.271997
$637$	−30.5295	−1.20962
$638$	−14.2688	−0.564906
$639$	−28.7601	−1.13773
$640$	−13.7961	−0.545337
$641$	8.99717	0.355367	0.177684	−	0.984088i	$-0.443140\pi$
$641$	8.99717	0.355367	0.177684	+	0.984088i	$0.443140\pi$
$642$	3.48947	0.137718
$643$	17.4047	0.686373	0.343187	−	0.939267i	$-0.388494\pi$
$643$	17.4047	0.686373	0.343187	+	0.939267i	$0.388494\pi$
$644$	2.55403	0.100643
$645$	−1.04292	−0.0410649
$646$	12.9684	0.510236
$647$	35.5134	1.39618	0.698088	−	0.716012i	$-0.254035\pi$
$647$	35.5134	1.39618	0.698088	+	0.716012i	$0.254035\pi$
$648$	5.70064	0.223942
$649$	12.2876	0.482332
$650$	24.2521	0.951244
$651$	−0.797153	−0.0312429
$652$	−9.68707	−0.379375
$653$	11.3212	0.443032	0.221516	−	0.975157i	$-0.428900\pi$
$653$	11.3212	0.443032	0.221516	+	0.975157i	$0.428900\pi$
$654$	12.7308	0.497815
$655$	−6.75608	−0.263982
$656$	−52.7134	−2.05811
$657$	−3.60663	−0.140708
$658$	−2.34701	−0.0914959
$659$	−36.3856	−1.41738	−0.708691	−	0.705519i	$-0.750714\pi$
$659$	−36.3856	−1.41738	−0.708691	+	0.705519i	$0.750714\pi$
$660$	1.32660	0.0516378
$661$	31.1787	1.21271	0.606355	−	0.795194i	$-0.292631\pi$
$661$	31.1787	1.21271	0.606355	+	0.795194i	$0.292631\pi$
$662$	7.96185	0.309446
$663$	−3.28713	−0.127661
$664$	−9.39022	−0.364411
$665$	−3.07509	−0.119247
$666$	18.7868	0.727975
$667$	−51.7891	−2.00528
$668$	−28.8951	−1.11798
$669$	−8.68167	−0.335653
$670$	23.2711	0.899042
$671$	−10.1298	−0.391057
$672$	−1.42748	−0.0550663
$673$	48.9069	1.88522	0.942611	−	0.333894i	$-0.108363\pi$
$673$	48.9069	1.88522	0.942611	+	0.333894i	$0.108363\pi$
$674$	62.0385	2.38963
$675$	12.2854	0.472865
$676$	8.31914	0.319967
$677$	39.8252	1.53061	0.765304	−	0.643669i	$-0.222589\pi$
$677$	39.8252	1.53061	0.765304	+	0.643669i	$0.222589\pi$
$678$	2.52976	0.0971548
$679$	−4.81078	−0.184621
$680$	−1.84686	−0.0708237
$681$	7.08115	0.271350
$682$	−6.34042	−0.242787
$683$	−12.9440	−0.495286	−0.247643	−	0.968851i	$-0.579656\pi$
$683$	−12.9440	−0.495286	−0.247643	+	0.968851i	$0.579656\pi$
$684$	−22.3156	−0.853258
$685$	15.4622	0.590779
$686$	−7.69312	−0.293725
$687$	17.5010	0.667703
$688$	4.92601	0.187802
$689$	−32.0564	−1.22125
$690$	12.3856	0.471511
$691$	−14.5793	−0.554622	−0.277311	−	0.960780i	$-0.589443\pi$
$691$	−14.5793	−0.554622	−0.277311	+	0.960780i	$0.589443\pi$
$692$	16.0458	0.609971
$693$	0.748372	0.0284283
$694$	6.69156	0.254008
$695$	6.85348	0.259967
$696$	7.72443	0.292794
$697$	−10.7010	−0.405330
$698$	23.4232	0.886580
$699$	−17.0865	−0.646271
$700$	1.17990	0.0445960
$701$	46.0906	1.74082	0.870410	−	0.492328i	$-0.163854\pi$
$701$	46.0906	1.74082	0.870410	+	0.492328i	$0.163854\pi$
$702$	32.3879	1.22240
$703$	30.4290	1.14765
$704$	−1.50192	−0.0566057
$705$	−4.42466	−0.166642
$706$	8.58070	0.322939
$707$	−4.22621	−0.158943
$708$	11.6228	0.436811
$709$	3.77523	0.141782	0.0708909	−	0.997484i	$-0.477416\pi$
$709$	3.77523	0.141782	0.0708909	+	0.997484i	$0.477416\pi$
$710$	−29.8166	−1.11900
$711$	−39.3540	−1.47589
$712$	−6.59932	−0.247320
$713$	−23.0128	−0.861836
$714$	−0.411375	−0.0153953
$715$	6.19959	0.231851
$716$	19.3846	0.724435
$717$	15.9191	0.594508
$718$	−12.9427	−0.483016
$719$	30.0074	1.11909	0.559544	−	0.828801i	$-0.310976\pi$
$719$	30.0074	1.11909	0.559544	+	0.828801i	$0.310976\pi$
$720$	16.9057	0.630037
$721$	−0.294540	−0.0109693
$722$	−58.6069	−2.18112
$723$	−0.135286	−0.00503134
$724$	−15.3818	−0.571661
$725$	−23.9253	−0.888562
$726$	−1.34511	−0.0499219
$727$	−39.5478	−1.46675	−0.733373	−	0.679827i	$-0.762055\pi$
$727$	−39.5478	−1.46675	−0.733373	+	0.679827i	$0.762055\pi$
$728$	−1.78024	−0.0659799
$729$	−1.55703	−0.0576678
$730$	−3.73911	−0.138391
$731$	1.00000	0.0369863
$732$	−9.58171	−0.354150
$733$	19.3879	0.716108	0.358054	−	0.933701i	$-0.383440\pi$
$733$	19.3879	0.716108	0.358054	+	0.933701i	$0.383440\pi$
$734$	−58.5317	−2.16044
$735$	−7.20289	−0.265683
$736$	−41.2096	−1.51901
$737$	−9.17301	−0.337892
$738$	47.3665	1.74358
$739$	34.8674	1.28262	0.641309	−	0.767283i	$-0.278392\pi$
$739$	34.8674	1.28262	0.641309	+	0.767283i	$0.278392\pi$
$740$	7.57174	0.278343
$741$	23.5666	0.865741
$742$	−4.01178	−0.147277
$743$	−22.9510	−0.841992	−0.420996	−	0.907063i	$-0.638319\pi$
$743$	−22.9510	−0.841992	−0.420996	+	0.907063i	$0.638319\pi$
$744$	3.43240	0.125838
$745$	−6.54361	−0.239739
$746$	1.94588	0.0712437
$747$	17.4494	0.638439
$748$	−1.27201	−0.0465092
$749$	0.793375	0.0289893
$750$	15.1544	0.553359
$751$	−41.3186	−1.50774	−0.753869	−	0.657025i	$-0.771815\pi$
$751$	−41.3186	−1.50774	−0.753869	+	0.657025i	$0.771815\pi$
$752$	20.8990	0.762106
$753$	−6.32289	−0.230419
$754$	−63.0741	−2.29702
$755$	32.7604	1.19227
$756$	1.57572	0.0573085
$757$	24.0794	0.875182	0.437591	−	0.899174i	$-0.355832\pi$
$757$	24.0794	0.875182	0.437591	+	0.899174i	$0.355832\pi$
$758$	−3.06019	−0.111151
$759$	−4.88215	−0.177211
$760$	13.2408	0.480294
$761$	31.3933	1.13801	0.569003	−	0.822335i	$-0.307329\pi$
$761$	31.3933	1.13801	0.569003	+	0.822335i	$0.307329\pi$
$762$	18.7301	0.678520
$763$	2.89452	0.104789
$764$	−4.45037	−0.161009
$765$	3.43192	0.124081
$766$	55.4440	2.00327
$767$	54.3166	1.96126
$768$	15.4654	0.558061
$769$	−35.2224	−1.27015	−0.635077	−	0.772449i	$-0.719032\pi$
$769$	−35.2224	−1.27015	−0.635077	+	0.772449i	$0.719032\pi$
$770$	0.775862	0.0279601
$771$	20.4740	0.737352
$772$	5.18311	0.186544
$773$	6.23078	0.224106	0.112053	−	0.993702i	$-0.464257\pi$
$773$	6.23078	0.224106	0.112053	+	0.993702i	$0.464257\pi$
$774$	−4.42635	−0.159102
$775$	−10.6313	−0.381889
$776$	20.7143	0.743601
$777$	−0.965248	−0.0346281
$778$	63.5638	2.27887
$779$	76.7195	2.74876
$780$	5.86414	0.209970
$781$	11.7531	0.420559
$782$	−11.8759	−0.424681
$783$	−31.9515	−1.14185
$784$	34.0214	1.21505
$785$	2.75872	0.0984630
$786$	6.47971	0.231124
$787$	24.2787	0.865440	0.432720	−	0.901528i	$-0.357554\pi$
$787$	24.2787	0.865440	0.432720	+	0.901528i	$0.357554\pi$
$788$	−8.83374	−0.314689
$789$	13.4823	0.479983
$790$	−40.7996	−1.45158
$791$	0.575173	0.0204508
$792$	−3.22235	−0.114501
$793$	−44.7781	−1.59012
$794$	23.7004	0.841096
$795$	−7.56314	−0.268237
$796$	−0.642223	−0.0227630
$797$	44.8409	1.58835	0.794173	−	0.607692i	$-0.207905\pi$
$797$	44.8409	1.58835	0.794173	+	0.607692i	$0.207905\pi$
$798$	2.94930	0.104404
$799$	4.24257	0.150091
$800$	−19.0378	−0.673088
$801$	12.2632	0.433299
$802$	−14.1666	−0.500240
$803$	1.47388	0.0520122
$804$	−8.67667	−0.306003
$805$	2.81602	0.0992517
$806$	−28.0274	−0.987221
$807$	18.4285	0.648712
$808$	18.1973	0.640180
$809$	45.3872	1.59573	0.797865	−	0.602836i	$-0.205963\pi$
$809$	45.3872	1.59573	0.797865	+	0.602836i	$0.205963\pi$
$810$	−10.9823	−0.385880
$811$	39.3913	1.38322	0.691608	−	0.722273i	$-0.256903\pi$
$811$	39.3913	1.38322	0.691608	+	0.722273i	$0.256903\pi$
$812$	−3.06865	−0.107689
$813$	3.92822	0.137769
$814$	−7.67741	−0.269093
$815$	−10.6807	−0.374130
$816$	3.66309	0.128234
$817$	−7.16936	−0.250824
$818$	−10.2714	−0.359132
$819$	3.30812	0.115595
$820$	19.0903	0.666663
$821$	12.5985	0.439692	0.219846	−	0.975535i	$-0.429445\pi$
$821$	12.5985	0.439692	0.219846	+	0.975535i	$0.429445\pi$
$822$	−14.8297	−0.517244
$823$	19.5740	0.682308	0.341154	−	0.940007i	$-0.389182\pi$
$823$	19.5740	0.682308	0.341154	+	0.940007i	$0.389182\pi$
$824$	1.26824	0.0441812
$825$	−2.25543	−0.0785240
$826$	6.79758	0.236518
$827$	−3.23953	−0.112650	−0.0563248	−	0.998412i	$-0.517938\pi$
$827$	−3.23953	−0.112650	−0.0563248	+	0.998412i	$0.517938\pi$
$828$	20.4356	0.710185
$829$	−17.7198	−0.615434	−0.307717	−	0.951478i	$-0.599565\pi$
$829$	−17.7198	−0.615434	−0.307717	+	0.951478i	$0.599565\pi$
$830$	18.0903	0.627925
$831$	−2.09527	−0.0726843
$832$	−6.63913	−0.230170
$833$	6.90647	0.239295
$834$	−6.57313	−0.227609
$835$	−31.8591	−1.10253
$836$	9.11947	0.315404
$837$	−14.1978	−0.490749
$838$	50.3257	1.73847
$839$	−38.4235	−1.32653	−0.663263	−	0.748386i	$-0.730829\pi$
$839$	−38.4235	−1.32653	−0.663263	+	0.748386i	$0.730829\pi$
$840$	−0.420014	−0.0144919
$841$	33.2242	1.14566
$842$	−3.18956	−0.109919
$843$	2.88209	0.0992646
$844$	−0.708380	−0.0243835
$845$	9.17250	0.315544
$846$	−18.7791	−0.645639
$847$	−0.305829	−0.0105084
$848$	35.7229	1.22673
$849$	10.3815	0.356292
$850$	−5.48636	−0.188181
$851$	−27.8655	−0.955216
$852$	11.1172	0.380868
$853$	4.94254	0.169229	0.0846147	−	0.996414i	$-0.473034\pi$
$853$	4.94254	0.169229	0.0846147	+	0.996414i	$0.473034\pi$
$854$	−5.60386	−0.191760
$855$	−24.6047	−0.841462
$856$	−3.41613	−0.116761
$857$	8.95095	0.305758	0.152879	−	0.988245i	$-0.451145\pi$
$857$	8.95095	0.305758	0.152879	+	0.988245i	$0.451145\pi$
$858$	−5.94598	−0.202992
$859$	9.57945	0.326847	0.163423	−	0.986556i	$-0.447746\pi$
$859$	9.57945	0.326847	0.163423	+	0.986556i	$0.447746\pi$
$860$	−1.78397	−0.0608329
$861$	−2.43364	−0.0829382
$862$	−18.9662	−0.645992
$863$	−7.35886	−0.250498	−0.125249	−	0.992125i	$-0.539973\pi$
$863$	−7.35886	−0.250498	−0.125249	+	0.992125i	$0.539973\pi$
$864$	−25.4244	−0.864957
$865$	17.6918	0.601539
$866$	50.7003	1.72287
$867$	0.743622	0.0252547
$868$	−1.36357	−0.0462827
$869$	16.0824	0.545557
$870$	−14.8812	−0.504519
$871$	−40.5486	−1.37394
$872$	−12.4633	−0.422060
$873$	−38.4924	−1.30277
$874$	85.1425	2.87999
$875$	3.44554	0.116480
$876$	1.39413	0.0471034
$877$	32.5954	1.10067	0.550334	−	0.834945i	$-0.314500\pi$
$877$	32.5954	1.10067	0.550334	+	0.834945i	$0.314500\pi$
$878$	40.9092	1.38062
$879$	9.62591	0.324674
$880$	−6.90866	−0.232891
$881$	4.79497	0.161547	0.0807734	−	0.996732i	$-0.474261\pi$
$881$	4.79497	0.161547	0.0807734	+	0.996732i	$0.474261\pi$
$882$	−30.5704	−1.02936
$883$	27.2051	0.915523	0.457761	−	0.889075i	$-0.348651\pi$
$883$	27.2051	0.915523	0.457761	+	0.889075i	$0.348651\pi$
$884$	−5.62281	−0.189116
$885$	12.8150	0.430772
$886$	15.4257	0.518235
$887$	−50.3215	−1.68963	−0.844816	−	0.535058i	$-0.820290\pi$
$887$	−50.3215	−1.68963	−0.844816	+	0.535058i	$0.820290\pi$
$888$	4.15618	0.139472
$889$	4.25853	0.142827
$890$	12.7137	0.426163
$891$	4.32902	0.145028
$892$	−14.8505	−0.497231
$893$	−30.4165	−1.01785
$894$	6.27593	0.209899
$895$	21.3730	0.714420
$896$	3.00840	0.100504
$897$	−21.5812	−0.720575
$898$	6.80156	0.226971
$899$	27.6497	0.922169
$900$	9.44072	0.314691
$901$	7.25189	0.241595
$902$	−19.3568	−0.644509
$903$	0.227421	0.00756810
$904$	−2.47659	−0.0823702
$905$	−16.9597	−0.563758
$906$	−31.4202	−1.04387
$907$	33.4398	1.11035	0.555176	−	0.831733i	$-0.312651\pi$
$907$	33.4398	1.11035	0.555176	+	0.831733i	$0.312651\pi$
$908$	12.1127	0.401974
$909$	−33.8152	−1.12158
$910$	3.42964	0.113691
$911$	−2.01929	−0.0669021	−0.0334510	−	0.999440i	$-0.510650\pi$
$911$	−2.01929	−0.0669021	−0.0334510	+	0.999440i	$0.510650\pi$
$912$	−26.2620	−0.869623
$913$	−7.13085	−0.235997
$914$	−15.5197	−0.513347
$915$	−10.5646	−0.349254
$916$	29.9364	0.989125
$917$	1.47325	0.0486509
$918$	−7.32688	−0.241823
$919$	−22.5810	−0.744879	−0.372440	−	0.928056i	$-0.621479\pi$
$919$	−22.5810	−0.744879	−0.372440	+	0.928056i	$0.621479\pi$
$920$	−12.1253	−0.399759
$921$	14.7304	0.485382
$922$	48.3197	1.59132
$923$	51.9537	1.71008
$924$	−0.289281	−0.00951665
$925$	−12.8732	−0.423267
$926$	−7.88604	−0.259151
$927$	−2.35670	−0.0774043
$928$	49.5130	1.62534
$929$	1.92382	0.0631185	0.0315593	−	0.999502i	$-0.489953\pi$
$929$	1.92382	0.0631185	0.0315593	+	0.999502i	$0.489953\pi$
$930$	−6.61254	−0.216834
$931$	−49.5150	−1.62279
$932$	−29.2274	−0.957375
$933$	0.506268	0.0165745
$934$	−69.1508	−2.26268
$935$	−1.40249	−0.0458662
$936$	−14.2442	−0.465586
$937$	−31.8217	−1.03957	−0.519784	−	0.854298i	$-0.673988\pi$
$937$	−31.8217	−1.03957	−0.519784	+	0.854298i	$0.673988\pi$
$938$	−5.07455	−0.165690
$939$	−17.8977	−0.584070
$940$	−7.56862	−0.246861
$941$	−13.0996	−0.427034	−0.213517	−	0.976939i	$-0.568492\pi$
$941$	−13.0996	−0.427034	−0.213517	+	0.976939i	$0.568492\pi$
$942$	−2.64587	−0.0862072
$943$	−70.2561	−2.28785
$944$	−60.5290	−1.97005
$945$	1.73736	0.0565162
$946$	1.80887	0.0588114
$947$	24.7576	0.804515	0.402258	−	0.915527i	$-0.368226\pi$
$947$	24.7576	0.804515	0.402258	+	0.915527i	$0.368226\pi$
$948$	15.2122	0.494069
$949$	6.51519	0.211492
$950$	39.3337	1.27615
$951$	14.8863	0.482722
$952$	0.402729	0.0130525
$953$	37.1211	1.20247	0.601235	−	0.799072i	$-0.294676\pi$
$953$	37.1211	1.20247	0.601235	+	0.799072i	$0.294676\pi$
$954$	−32.0994	−1.03926
$955$	−4.90688	−0.158783
$956$	27.2304	0.880695
$957$	5.86586	0.189616
$958$	−33.1519	−1.07109
$959$	−3.37171	−0.108878
$960$	−1.56638	−0.0505547
$961$	−18.7137	−0.603667
$962$	−33.9374	−1.09419
$963$	6.34803	0.204562
$964$	−0.231414	−0.00745335
$965$	5.71478	0.183965
$966$	−2.70083	−0.0868977
$967$	−10.9555	−0.352305	−0.176152	−	0.984363i	$-0.556365\pi$
$967$	−10.9555	−0.352305	−0.176152	+	0.984363i	$0.556365\pi$
$968$	1.31684	0.0423250
$969$	−5.33130	−0.171266
$970$	−39.9064	−1.28132
$971$	36.5279	1.17224	0.586119	−	0.810225i	$-0.300655\pi$
$971$	36.5279	1.17224	0.586119	+	0.810225i	$0.300655\pi$
$972$	19.5517	0.627120
$973$	−1.49448	−0.0479110
$974$	−8.61214	−0.275951
$975$	−9.96997	−0.319294
$976$	49.8996	1.59725
$977$	−37.1990	−1.19010	−0.595050	−	0.803689i	$-0.702868\pi$
$977$	−37.1990	−1.19010	−0.595050	+	0.803689i	$0.702868\pi$
$978$	10.2438	0.327562
$979$	−5.01147	−0.160167
$980$	−12.3209	−0.393578
$981$	23.1599	0.739438
$982$	−21.7108	−0.692819
$983$	2.74907	0.0876817	0.0438408	−	0.999039i	$-0.486041\pi$
$983$	2.74907	0.0876817	0.0438408	+	0.999039i	$0.486041\pi$
$984$	10.4788	0.334053
$985$	−9.73989	−0.310339
$986$	14.2688	0.454410
$987$	0.964850	0.0307115
$988$	40.3120	1.28249
$989$	6.56536	0.208766
$990$	6.20789	0.197300
$991$	11.9613	0.379962	0.189981	−	0.981788i	$-0.439157\pi$
$991$	11.9613	0.379962	0.189981	+	0.981788i	$0.439157\pi$
$992$	22.0014	0.698545
$993$	−3.27310	−0.103869
$994$	6.50187	0.206227
$995$	−0.708101	−0.0224483
$996$	−6.74501	−0.213724
$997$	3.84434	0.121751	0.0608757	−	0.998145i	$-0.480611\pi$
$997$	3.84434	0.121751	0.0608757	+	0.998145i	$0.480611\pi$
$998$	63.1178	1.99796
$999$	−17.1917	−0.543922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.16	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.16	✓	78	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)

\(f(q)\)	\(=\)	\(q-1.80887 q^{2} +0.743622 q^{3} +1.27201 q^{4} +1.40249 q^{5} -1.34511 q^{6} -0.305829 q^{7} +1.31684 q^{8} -2.44703 q^{9} +O(q^{10})\)	\(q-1.80887 q^{2} +0.743622 q^{3} +1.27201 q^{4} +1.40249 q^{5} -1.34511 q^{6} -0.305829 q^{7} +1.31684 q^{8} -2.44703 q^{9} -2.53691 q^{10} +1.00000 q^{11} +0.945892 q^{12} +4.42043 q^{13} +0.553205 q^{14} +1.04292 q^{15} -4.92601 q^{16} -1.00000 q^{17} +4.42635 q^{18} +7.16936 q^{19} +1.78397 q^{20} -0.227421 q^{21} -1.80887 q^{22} -6.56536 q^{23} +0.979235 q^{24} -3.03303 q^{25} -7.99597 q^{26} -4.05053 q^{27} -0.389016 q^{28} +7.88823 q^{29} -1.88650 q^{30} +3.50518 q^{31} +6.27682 q^{32} +0.743622 q^{33} +1.80887 q^{34} -0.428921 q^{35} -3.11263 q^{36} +4.24432 q^{37} -12.9684 q^{38} +3.28713 q^{39} +1.84686 q^{40} +10.7010 q^{41} +0.411375 q^{42} -1.00000 q^{43} +1.27201 q^{44} -3.43192 q^{45} +11.8759 q^{46} -4.24257 q^{47} -3.66309 q^{48} -6.90647 q^{49} +5.48636 q^{50} -0.743622 q^{51} +5.62281 q^{52} -7.25189 q^{53} +7.32688 q^{54} +1.40249 q^{55} -0.402729 q^{56} +5.33130 q^{57} -14.2688 q^{58} +12.2876 q^{59} +1.32660 q^{60} -10.1298 q^{61} -6.34042 q^{62} +0.748372 q^{63} -1.50192 q^{64} +6.19959 q^{65} -1.34511 q^{66} -9.17301 q^{67} -1.27201 q^{68} -4.88215 q^{69} +0.775862 q^{70} +11.7531 q^{71} -3.22235 q^{72} +1.47388 q^{73} -7.67741 q^{74} -2.25543 q^{75} +9.11947 q^{76} -0.305829 q^{77} -5.94598 q^{78} +16.0824 q^{79} -6.90866 q^{80} +4.32902 q^{81} -19.3568 q^{82} -7.13085 q^{83} -0.289281 q^{84} -1.40249 q^{85} +1.80887 q^{86} +5.86586 q^{87} +1.31684 q^{88} -5.01147 q^{89} +6.20789 q^{90} -1.35189 q^{91} -8.35118 q^{92} +2.60653 q^{93} +7.67425 q^{94} +10.0549 q^{95} +4.66758 q^{96} +15.7303 q^{97} +12.4929 q^{98} -2.44703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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