LMFDB - Embedded newform 8014.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$91$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.93164 q^{3} +1.00000 q^{4} -4.27136 q^{5} +2.93164 q^{6} -1.93753 q^{7} -1.00000 q^{8} +5.59453 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.93164 q^{3} +1.00000 q^{4} -4.27136 q^{5} +2.93164 q^{6} -1.93753 q^{7} -1.00000 q^{8} +5.59453 q^{9} +4.27136 q^{10} -0.991936 q^{11} -2.93164 q^{12} -5.90660 q^{13} +1.93753 q^{14} +12.5221 q^{15} +1.00000 q^{16} +4.06954 q^{17} -5.59453 q^{18} +8.21429 q^{19} -4.27136 q^{20} +5.68013 q^{21} +0.991936 q^{22} +2.37774 q^{23} +2.93164 q^{24} +13.2445 q^{25} +5.90660 q^{26} -7.60624 q^{27} -1.93753 q^{28} +5.87852 q^{29} -12.5221 q^{30} +7.14760 q^{31} -1.00000 q^{32} +2.90800 q^{33} -4.06954 q^{34} +8.27587 q^{35} +5.59453 q^{36} +5.93542 q^{37} -8.21429 q^{38} +17.3160 q^{39} +4.27136 q^{40} +5.07474 q^{41} -5.68013 q^{42} -11.2260 q^{43} -0.991936 q^{44} -23.8963 q^{45} -2.37774 q^{46} -8.07082 q^{47} -2.93164 q^{48} -3.24599 q^{49} -13.2445 q^{50} -11.9304 q^{51} -5.90660 q^{52} +5.41517 q^{53} +7.60624 q^{54} +4.23692 q^{55} +1.93753 q^{56} -24.0814 q^{57} -5.87852 q^{58} +10.0829 q^{59} +12.5221 q^{60} -9.14730 q^{61} -7.14760 q^{62} -10.8395 q^{63} +1.00000 q^{64} +25.2292 q^{65} -2.90800 q^{66} +1.78324 q^{67} +4.06954 q^{68} -6.97069 q^{69} -8.27587 q^{70} +1.66759 q^{71} -5.59453 q^{72} +4.78441 q^{73} -5.93542 q^{74} -38.8282 q^{75} +8.21429 q^{76} +1.92190 q^{77} -17.3160 q^{78} -0.911534 q^{79} -4.27136 q^{80} +5.51518 q^{81} -5.07474 q^{82} -4.86446 q^{83} +5.68013 q^{84} -17.3825 q^{85} +11.2260 q^{86} -17.2337 q^{87} +0.991936 q^{88} +3.91663 q^{89} +23.8963 q^{90} +11.4442 q^{91} +2.37774 q^{92} -20.9542 q^{93} +8.07082 q^{94} -35.0862 q^{95} +2.93164 q^{96} -10.3964 q^{97} +3.24599 q^{98} -5.54942 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) $ 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.93164	−1.69258	−0.846292	−	0.532719i	$-0.821170\pi$
$3$	−2.93164	−1.69258	−0.846292	+	0.532719i	$0.821170\pi$
$4$	1.00000	0.500000
$5$	−4.27136	−1.91021	−0.955105	−	0.296267i	$-0.904258\pi$
$5$	−4.27136	−1.91021	−0.955105	+	0.296267i	$0.904258\pi$
$6$	2.93164	1.19684
$7$	−1.93753	−0.732316	−0.366158	−	0.930553i	$-0.619327\pi$
$7$	−1.93753	−0.732316	−0.366158	+	0.930553i	$0.619327\pi$
$8$	−1.00000	−0.353553
$9$	5.59453	1.86484
$10$	4.27136	1.35072
$11$	−0.991936	−0.299080	−0.149540	−	0.988756i	$-0.547779\pi$
$11$	−0.991936	−0.299080	−0.149540	+	0.988756i	$0.547779\pi$
$12$	−2.93164	−0.846292
$13$	−5.90660	−1.63820	−0.819098	−	0.573654i	$-0.805526\pi$
$13$	−5.90660	−1.63820	−0.819098	+	0.573654i	$0.805526\pi$
$14$	1.93753	0.517826
$15$	12.5221	3.23319
$16$	1.00000	0.250000
$17$	4.06954	0.987009	0.493505	−	0.869743i	$-0.335716\pi$
$17$	4.06954	0.987009	0.493505	+	0.869743i	$0.335716\pi$
$18$	−5.59453	−1.31864
$19$	8.21429	1.88449	0.942244	−	0.334929i	$-0.108712\pi$
$19$	8.21429	1.88449	0.942244	+	0.334929i	$0.108712\pi$
$20$	−4.27136	−0.955105
$21$	5.68013	1.23951
$22$	0.991936	0.211482
$23$	2.37774	0.495794	0.247897	−	0.968786i	$-0.420261\pi$
$23$	2.37774	0.495794	0.247897	+	0.968786i	$0.420261\pi$
$24$	2.93164	0.598419
$25$	13.2445	2.64890
$26$	5.90660	1.15838
$27$	−7.60624	−1.46382
$28$	−1.93753	−0.366158
$29$	5.87852	1.09161	0.545806	−	0.837911i	$-0.316223\pi$
$29$	5.87852	1.09161	0.545806	+	0.837911i	$0.316223\pi$
$30$	−12.5221	−2.28621
$31$	7.14760	1.28375	0.641873	−	0.766811i	$-0.278158\pi$
$31$	7.14760	1.28375	0.641873	+	0.766811i	$0.278158\pi$
$32$	−1.00000	−0.176777
$33$	2.90800	0.506218
$34$	−4.06954	−0.697921
$35$	8.27587	1.39888
$36$	5.59453	0.932422
$37$	5.93542	0.975777	0.487888	−	0.872906i	$-0.337767\pi$
$37$	5.93542	0.975777	0.487888	+	0.872906i	$0.337767\pi$
$38$	−8.21429	−1.33253
$39$	17.3160	2.77279
$40$	4.27136	0.675361
$41$	5.07474	0.792541	0.396270	−	0.918134i	$-0.370304\pi$
$41$	5.07474	0.792541	0.396270	+	0.918134i	$0.370304\pi$
$42$	−5.68013	−0.876464
$43$	−11.2260	−1.71195	−0.855975	−	0.517017i	$-0.827042\pi$
$43$	−11.2260	−1.71195	−0.855975	+	0.517017i	$0.827042\pi$
$44$	−0.991936	−0.149540
$45$	−23.8963	−3.56224
$46$	−2.37774	−0.350579
$47$	−8.07082	−1.17725	−0.588625	−	0.808406i	$-0.700331\pi$
$47$	−8.07082	−1.17725	−0.588625	+	0.808406i	$0.700331\pi$
$48$	−2.93164	−0.423146
$49$	−3.24599	−0.463713
$50$	−13.2445	−1.87306
$51$	−11.9304	−1.67060
$52$	−5.90660	−0.819098
$53$	5.41517	0.743830	0.371915	−	0.928267i	$-0.378701\pi$
$53$	5.41517	0.743830	0.371915	+	0.928267i	$0.378701\pi$
$54$	7.60624	1.03508
$55$	4.23692	0.571306
$56$	1.93753	0.258913
$57$	−24.0814	−3.18965
$58$	−5.87852	−0.771887
$59$	10.0829	1.31269	0.656343	−	0.754463i	$-0.272103\pi$
$59$	10.0829	1.31269	0.656343	+	0.754463i	$0.272103\pi$
$60$	12.5221	1.61660
$61$	−9.14730	−1.17119	−0.585596	−	0.810603i	$-0.699139\pi$
$61$	−9.14730	−1.17119	−0.585596	+	0.810603i	$0.699139\pi$
$62$	−7.14760	−0.907746
$63$	−10.8395	−1.36565
$64$	1.00000	0.125000
$65$	25.2292	3.12930
$66$	−2.90800	−0.357950
$67$	1.78324	0.217858	0.108929	−	0.994050i	$-0.465258\pi$
$67$	1.78324	0.217858	0.108929	+	0.994050i	$0.465258\pi$
$68$	4.06954	0.493505
$69$	−6.97069	−0.839173
$70$	−8.27587	−0.989156
$71$	1.66759	0.197906	0.0989531	−	0.995092i	$-0.468451\pi$
$71$	1.66759	0.197906	0.0989531	+	0.995092i	$0.468451\pi$
$72$	−5.59453	−0.659322
$73$	4.78441	0.559973	0.279986	−	0.960004i	$-0.409670\pi$
$73$	4.78441	0.559973	0.279986	+	0.960004i	$0.409670\pi$
$74$	−5.93542	−0.689978
$75$	−38.8282	−4.48349
$76$	8.21429	0.942244
$77$	1.92190	0.219021
$78$	−17.3160	−1.96066
$79$	−0.911534	−0.102556	−0.0512778	−	0.998684i	$-0.516329\pi$
$79$	−0.911534	−0.102556	−0.0512778	+	0.998684i	$0.516329\pi$
$80$	−4.27136	−0.477553
$81$	5.51518	0.612798
$82$	−5.07474	−0.560411
$83$	−4.86446	−0.533944	−0.266972	−	0.963704i	$-0.586023\pi$
$83$	−4.86446	−0.533944	−0.266972	+	0.963704i	$0.586023\pi$
$84$	5.68013	0.619754
$85$	−17.3825	−1.88540
$86$	11.2260	1.21053
$87$	−17.2337	−1.84765
$88$	0.991936	0.105741
$89$	3.91663	0.415162	0.207581	−	0.978218i	$-0.433441\pi$
$89$	3.91663	0.415162	0.207581	+	0.978218i	$0.433441\pi$
$90$	23.8963	2.51889
$91$	11.4442	1.19968
$92$	2.37774	0.247897
$93$	−20.9542	−2.17285
$94$	8.07082	0.832441
$95$	−35.0862	−3.59977
$96$	2.93164	0.299210
$97$	−10.3964	−1.05560	−0.527798	−	0.849370i	$-0.676982\pi$
$97$	−10.3964	−1.05560	−0.527798	+	0.849370i	$0.676982\pi$
$98$	3.24599	0.327895
$99$	−5.54942	−0.557737
$100$	13.2445	1.32445
$101$	9.70253	0.965438	0.482719	−	0.875775i	$-0.339649\pi$
$101$	9.70253	0.965438	0.482719	+	0.875775i	$0.339649\pi$
$102$	11.9304	1.18129
$103$	13.1260	1.29335	0.646673	−	0.762767i	$-0.276160\pi$
$103$	13.1260	1.29335	0.646673	+	0.762767i	$0.276160\pi$
$104$	5.90660	0.579190
$105$	−24.2619	−2.36772
$106$	−5.41517	−0.525967
$107$	1.30213	0.125881	0.0629407	−	0.998017i	$-0.479952\pi$
$107$	1.30213	0.125881	0.0629407	+	0.998017i	$0.479952\pi$
$108$	−7.60624	−0.731911
$109$	7.72615	0.740031	0.370015	−	0.929026i	$-0.379352\pi$
$109$	7.72615	0.740031	0.370015	+	0.929026i	$0.379352\pi$
$110$	−4.23692	−0.403974
$111$	−17.4005	−1.65158
$112$	−1.93753	−0.183079
$113$	14.4944	1.36352	0.681759	−	0.731577i	$-0.261215\pi$
$113$	14.4944	1.36352	0.681759	+	0.731577i	$0.261215\pi$
$114$	24.0814	2.25543
$115$	−10.1562	−0.947070
$116$	5.87852	0.545806
$117$	−33.0447	−3.05498
$118$	−10.0829	−0.928209
$119$	−7.88485	−0.722803
$120$	−12.5221	−1.14311
$121$	−10.0161	−0.910551
$122$	9.14730	0.828157
$123$	−14.8773	−1.34144
$124$	7.14760	0.641873
$125$	−35.2153	−3.14975
$126$	10.8395	0.965664
$127$	1.32137	0.117253	0.0586265	−	0.998280i	$-0.481328\pi$
$127$	1.32137	0.117253	0.0586265	+	0.998280i	$0.481328\pi$
$128$	−1.00000	−0.0883883
$129$	32.9106	2.89762
$130$	−25.2292	−2.21275
$131$	3.54502	0.309730	0.154865	−	0.987936i	$-0.450506\pi$
$131$	3.54502	0.309730	0.154865	+	0.987936i	$0.450506\pi$
$132$	2.90800	0.253109
$133$	−15.9154	−1.38004
$134$	−1.78324	−0.154049
$135$	32.4890	2.79621
$136$	−4.06954	−0.348960
$137$	18.9077	1.61539	0.807695	−	0.589601i	$-0.200715\pi$
$137$	18.9077	1.61539	0.807695	+	0.589601i	$0.200715\pi$
$138$	6.97069	0.593385
$139$	2.16600	0.183718	0.0918590	−	0.995772i	$-0.470719\pi$
$139$	2.16600	0.183718	0.0918590	+	0.995772i	$0.470719\pi$
$140$	8.27587	0.699439
$141$	23.6608	1.99260
$142$	−1.66759	−0.139941
$143$	5.85897	0.489952
$144$	5.59453	0.466211
$145$	−25.1093	−2.08521
$146$	−4.78441	−0.395961
$147$	9.51609	0.784874
$148$	5.93542	0.487888
$149$	−7.31490	−0.599260	−0.299630	−	0.954055i	$-0.596863\pi$
$149$	−7.31490	−0.599260	−0.299630	+	0.954055i	$0.596863\pi$
$150$	38.8282	3.17031
$151$	5.88603	0.478998	0.239499	−	0.970897i	$-0.423017\pi$
$151$	5.88603	0.478998	0.239499	+	0.970897i	$0.423017\pi$
$152$	−8.21429	−0.666267
$153$	22.7672	1.84062
$154$	−1.92190	−0.154871
$155$	−30.5300	−2.45223
$156$	17.3160	1.38639
$157$	−6.74660	−0.538437	−0.269219	−	0.963079i	$-0.586765\pi$
$157$	−6.74660	−0.538437	−0.269219	+	0.963079i	$0.586765\pi$
$158$	0.911534	0.0725177
$159$	−15.8753	−1.25900
$160$	4.27136	0.337681
$161$	−4.60694	−0.363078
$162$	−5.51518	−0.433314
$163$	8.85377	0.693481	0.346740	−	0.937961i	$-0.387289\pi$
$163$	8.85377	0.693481	0.346740	+	0.937961i	$0.387289\pi$
$164$	5.07474	0.396270
$165$	−12.4211	−0.966983
$166$	4.86446	0.377555
$167$	16.6160	1.28579	0.642893	−	0.765956i	$-0.277734\pi$
$167$	16.6160	1.28579	0.642893	+	0.765956i	$0.277734\pi$
$168$	−5.68013	−0.438232
$169$	21.8879	1.68369
$170$	17.3825	1.33318
$171$	45.9551	3.51427
$172$	−11.2260	−0.855975
$173$	4.29830	0.326794	0.163397	−	0.986560i	$-0.447755\pi$
$173$	4.29830	0.326794	0.163397	+	0.986560i	$0.447755\pi$
$174$	17.2337	1.30648
$175$	−25.6616	−1.93983
$176$	−0.991936	−0.0747700
$177$	−29.5595	−2.22183
$178$	−3.91663	−0.293564
$179$	23.4026	1.74919	0.874596	−	0.484852i	$-0.161127\pi$
$179$	23.4026	1.74919	0.874596	+	0.484852i	$0.161127\pi$
$180$	−23.8963	−1.78112
$181$	−2.57332	−0.191274	−0.0956368	−	0.995416i	$-0.530489\pi$
$181$	−2.57332	−0.191274	−0.0956368	+	0.995416i	$0.530489\pi$
$182$	−11.4442	−0.848300
$183$	26.8166	1.98234
$184$	−2.37774	−0.175290
$185$	−25.3523	−1.86394
$186$	20.9542	1.53644
$187$	−4.03673	−0.295195
$188$	−8.07082	−0.588625
$189$	14.7373	1.07198
$190$	35.0862	2.54542
$191$	14.8834	1.07693	0.538463	−	0.842649i	$-0.319005\pi$
$191$	14.8834	1.07693	0.538463	+	0.842649i	$0.319005\pi$
$192$	−2.93164	−0.211573
$193$	7.55743	0.543996	0.271998	−	0.962298i	$-0.412316\pi$
$193$	7.55743	0.543996	0.271998	+	0.962298i	$0.412316\pi$
$194$	10.3964	0.746418
$195$	−73.9631	−5.29660
$196$	−3.24599	−0.231857
$197$	−22.4275	−1.59789	−0.798945	−	0.601404i	$-0.794608\pi$
$197$	−22.4275	−1.59789	−0.798945	+	0.601404i	$0.794608\pi$
$198$	5.54942	0.394380
$199$	−19.7157	−1.39761	−0.698803	−	0.715314i	$-0.746284\pi$
$199$	−19.7157	−1.39761	−0.698803	+	0.715314i	$0.746284\pi$
$200$	−13.2445	−0.936529
$201$	−5.22783	−0.368743
$202$	−9.70253	−0.682668
$203$	−11.3898	−0.799406
$204$	−11.9304	−0.835298
$205$	−21.6760	−1.51392
$206$	−13.1260	−0.914534
$207$	13.3024	0.924578
$208$	−5.90660	−0.409549
$209$	−8.14805	−0.563612
$210$	24.2619	1.67423
$211$	4.87582	0.335665	0.167833	−	0.985815i	$-0.446323\pi$
$211$	4.87582	0.335665	0.167833	+	0.985815i	$0.446323\pi$
$212$	5.41517	0.371915
$213$	−4.88877	−0.334973
$214$	−1.30213	−0.0890116
$215$	47.9503	3.27018
$216$	7.60624	0.517539
$217$	−13.8487	−0.940108
$218$	−7.72615	−0.523281
$219$	−14.0262	−0.947802
$220$	4.23692	0.285653
$221$	−24.0372	−1.61691
$222$	17.4005	1.16785
$223$	−20.0837	−1.34490	−0.672451	−	0.740141i	$-0.734758\pi$
$223$	−20.0837	−1.34490	−0.672451	+	0.740141i	$0.734758\pi$
$224$	1.93753	0.129456
$225$	74.0969	4.93979
$226$	−14.4944	−0.964152
$227$	−22.7888	−1.51254	−0.756272	−	0.654257i	$-0.772981\pi$
$227$	−22.7888	−1.51254	−0.756272	+	0.654257i	$0.772981\pi$
$228$	−24.0814	−1.59483
$229$	−23.6819	−1.56494	−0.782472	−	0.622686i	$-0.786042\pi$
$229$	−23.6819	−1.56494	−0.782472	+	0.622686i	$0.786042\pi$
$230$	10.1562	0.669680
$231$	−5.63433	−0.370712
$232$	−5.87852	−0.385943
$233$	5.86586	0.384286	0.192143	−	0.981367i	$-0.438456\pi$
$233$	5.86586	0.384286	0.192143	+	0.981367i	$0.438456\pi$
$234$	33.0447	2.16020
$235$	34.4734	2.24880
$236$	10.0829	0.656343
$237$	2.67229	0.173584
$238$	7.88485	0.511099
$239$	0.511634	0.0330949	0.0165474	−	0.999863i	$-0.494733\pi$
$239$	0.511634	0.0330949	0.0165474	+	0.999863i	$0.494733\pi$
$240$	12.5221	0.808298
$241$	−18.4508	−1.18852	−0.594259	−	0.804273i	$-0.702555\pi$
$241$	−18.4508	−1.18852	−0.594259	+	0.804273i	$0.702555\pi$
$242$	10.0161	0.643857
$243$	6.65016	0.426608
$244$	−9.14730	−0.585596
$245$	13.8648	0.885790
$246$	14.8773	0.948543
$247$	−48.5185	−3.08716
$248$	−7.14760	−0.453873
$249$	14.2609	0.903745
$250$	35.2153	2.22721
$251$	−24.7520	−1.56233	−0.781166	−	0.624324i	$-0.785375\pi$
$251$	−24.7520	−1.56233	−0.781166	+	0.624324i	$0.785375\pi$
$252$	−10.8395	−0.682827
$253$	−2.35857	−0.148282
$254$	−1.32137	−0.0829104
$255$	50.9592	3.19119
$256$	1.00000	0.0625000
$257$	14.9689	0.933734	0.466867	−	0.884328i	$-0.345383\pi$
$257$	14.9689	0.933734	0.466867	+	0.884328i	$0.345383\pi$
$258$	−32.9106	−2.04893
$259$	−11.5000	−0.714577
$260$	25.2292	1.56465
$261$	32.8875	2.03569
$262$	−3.54502	−0.219012
$263$	2.69400	0.166119	0.0830596	−	0.996545i	$-0.473531\pi$
$263$	2.69400	0.166119	0.0830596	+	0.996545i	$0.473531\pi$
$264$	−2.90800	−0.178975
$265$	−23.1301	−1.42087
$266$	15.9154	0.975836
$267$	−11.4822	−0.702696
$268$	1.78324	0.108929
$269$	−13.5744	−0.827646	−0.413823	−	0.910357i	$-0.635807\pi$
$269$	−13.5744	−0.827646	−0.413823	+	0.910357i	$0.635807\pi$
$270$	−32.4890	−1.97722
$271$	−6.17031	−0.374820	−0.187410	−	0.982282i	$-0.560009\pi$
$271$	−6.17031	−0.374820	−0.187410	+	0.982282i	$0.560009\pi$
$272$	4.06954	0.246752
$273$	−33.5503	−2.03056
$274$	−18.9077	−1.14225
$275$	−13.1377	−0.792234
$276$	−6.97069	−0.419586
$277$	−16.1337	−0.969380	−0.484690	−	0.874686i	$-0.661068\pi$
$277$	−16.1337	−0.969380	−0.484690	+	0.874686i	$0.661068\pi$
$278$	−2.16600	−0.129908
$279$	39.9875	2.39399
$280$	−8.27587	−0.494578
$281$	6.69892	0.399624	0.199812	−	0.979834i	$-0.435967\pi$
$281$	6.69892	0.399624	0.199812	+	0.979834i	$0.435967\pi$
$282$	−23.6608	−1.40898
$283$	7.51085	0.446474	0.223237	−	0.974764i	$-0.428338\pi$
$283$	7.51085	0.446474	0.223237	+	0.974764i	$0.428338\pi$
$284$	1.66759	0.0989531
$285$	102.860	6.09291
$286$	−5.85897	−0.346448
$287$	−9.83244	−0.580390
$288$	−5.59453	−0.329661
$289$	−0.438817	−0.0258128
$290$	25.1093	1.47447
$291$	30.4786	1.78668
$292$	4.78441	0.279986
$293$	−30.2683	−1.76829	−0.884147	−	0.467208i	$-0.845260\pi$
$293$	−30.2683	−1.76829	−0.884147	+	0.467208i	$0.845260\pi$
$294$	−9.51609	−0.554990
$295$	−43.0678	−2.50750
$296$	−5.93542	−0.344989
$297$	7.54490	0.437800
$298$	7.31490	0.423741
$299$	−14.0444	−0.812207
$300$	−38.8282	−2.24175
$301$	21.7507	1.25369
$302$	−5.88603	−0.338703
$303$	−28.4444	−1.63409
$304$	8.21429	0.471122
$305$	39.0714	2.23722
$306$	−22.7672	−1.30151
$307$	21.3794	1.22019	0.610093	−	0.792329i	$-0.291132\pi$
$307$	21.3794	1.22019	0.610093	+	0.792329i	$0.291132\pi$
$308$	1.92190	0.109511
$309$	−38.4809	−2.18910
$310$	30.5300	1.73399
$311$	31.6134	1.79263	0.896315	−	0.443418i	$-0.146234\pi$
$311$	31.6134	1.79263	0.896315	+	0.443418i	$0.146234\pi$
$312$	−17.3160	−0.980328
$313$	−19.8881	−1.12414	−0.562072	−	0.827089i	$-0.689995\pi$
$313$	−19.8881	−1.12414	−0.562072	+	0.827089i	$0.689995\pi$
$314$	6.74660	0.380733
$315$	46.2996	2.60869
$316$	−0.911534	−0.0512778
$317$	19.7643	1.11007	0.555037	−	0.831825i	$-0.312704\pi$
$317$	19.7643	1.11007	0.555037	+	0.831825i	$0.312704\pi$
$318$	15.8753	0.890245
$319$	−5.83111	−0.326480
$320$	−4.27136	−0.238776
$321$	−3.81737	−0.213065
$322$	4.60694	0.256735
$323$	33.4284	1.86001
$324$	5.51518	0.306399
$325$	−78.2301	−4.33942
$326$	−8.85377	−0.490365
$327$	−22.6503	−1.25256
$328$	−5.07474	−0.280206
$329$	15.6374	0.862119
$330$	12.4211	0.683761
$331$	−4.88804	−0.268671	−0.134335	−	0.990936i	$-0.542890\pi$
$331$	−4.88804	−0.268671	−0.134335	+	0.990936i	$0.542890\pi$
$332$	−4.86446	−0.266972
$333$	33.2059	1.81967
$334$	−16.6160	−0.909188
$335$	−7.61687	−0.416154
$336$	5.68013	0.309877
$337$	25.5755	1.39318	0.696592	−	0.717467i	$-0.254699\pi$
$337$	25.5755	1.39318	0.696592	+	0.717467i	$0.254699\pi$
$338$	−21.8879	−1.19055
$339$	−42.4924	−2.30787
$340$	−17.3825	−0.942698
$341$	−7.08996	−0.383943
$342$	−45.9551	−2.48497
$343$	19.8519	1.07190
$344$	11.2260	0.605266
$345$	29.7743	1.60300
$346$	−4.29830	−0.231078
$347$	−13.9253	−0.747550	−0.373775	−	0.927519i	$-0.621937\pi$
$347$	−13.9253	−0.747550	−0.373775	+	0.927519i	$0.621937\pi$
$348$	−17.2337	−0.923824
$349$	33.9521	1.81742	0.908708	−	0.417433i	$-0.137070\pi$
$349$	33.9521	1.81742	0.908708	+	0.417433i	$0.137070\pi$
$350$	25.6616	1.37167
$351$	44.9270	2.39803
$352$	0.991936	0.0528704
$353$	17.0795	0.909050	0.454525	−	0.890734i	$-0.349809\pi$
$353$	17.0795	0.909050	0.454525	+	0.890734i	$0.349809\pi$
$354$	29.5595	1.57107
$355$	−7.12287	−0.378042
$356$	3.91663	0.207581
$357$	23.1156	1.22340
$358$	−23.4026	−1.23687
$359$	−12.6817	−0.669316	−0.334658	−	0.942340i	$-0.608621\pi$
$359$	−12.6817	−0.669316	−0.334658	+	0.942340i	$0.608621\pi$
$360$	23.8963	1.25944
$361$	48.4745	2.55129
$362$	2.57332	0.135251
$363$	29.3635	1.54119
$364$	11.4442	0.599839
$365$	−20.4359	−1.06967
$366$	−26.8166	−1.40173
$367$	5.08326	0.265344	0.132672	−	0.991160i	$-0.457644\pi$
$367$	5.08326	0.265344	0.132672	+	0.991160i	$0.457644\pi$
$368$	2.37774	0.123948
$369$	28.3908	1.47797
$370$	25.3523	1.31800
$371$	−10.4920	−0.544719
$372$	−20.9542	−1.08643
$373$	32.1233	1.66328	0.831640	−	0.555315i	$-0.187402\pi$
$373$	32.1233	1.66328	0.831640	+	0.555315i	$0.187402\pi$
$374$	4.03673	0.208734
$375$	103.239	5.33122
$376$	8.07082	0.416221
$377$	−34.7220	−1.78828
$378$	−14.7373	−0.758004
$379$	9.54377	0.490230	0.245115	−	0.969494i	$-0.421174\pi$
$379$	9.54377	0.490230	0.245115	+	0.969494i	$0.421174\pi$
$380$	−35.0862	−1.79988
$381$	−3.87380	−0.198461
$382$	−14.8834	−0.761501
$383$	27.2952	1.39472	0.697361	−	0.716720i	$-0.254357\pi$
$383$	27.2952	1.39472	0.697361	+	0.716720i	$0.254357\pi$
$384$	2.93164	0.149605
$385$	−8.20914	−0.418376
$386$	−7.55743	−0.384663
$387$	−62.8042	−3.19252
$388$	−10.3964	−0.527798
$389$	32.1193	1.62851	0.814257	−	0.580504i	$-0.197144\pi$
$389$	32.1193	1.62851	0.814257	+	0.580504i	$0.197144\pi$
$390$	73.9631	3.74526
$391$	9.67633	0.489353
$392$	3.24599	0.163947
$393$	−10.3927	−0.524244
$394$	22.4275	1.12988
$395$	3.89349	0.195903
$396$	−5.54942	−0.278869
$397$	26.3751	1.32373	0.661863	−	0.749625i	$-0.269766\pi$
$397$	26.3751	1.32373	0.661863	+	0.749625i	$0.269766\pi$
$398$	19.7157	0.988257
$399$	46.6583	2.33583
$400$	13.2445	0.662226
$401$	25.6700	1.28190	0.640949	−	0.767583i	$-0.278541\pi$
$401$	25.6700	1.28190	0.640949	+	0.767583i	$0.278541\pi$
$402$	5.22783	0.260740
$403$	−42.2180	−2.10303
$404$	9.70253	0.482719
$405$	−23.5573	−1.17057
$406$	11.3898	0.565265
$407$	−5.88755	−0.291835
$408$	11.9304	0.590645
$409$	−26.1737	−1.29421	−0.647104	−	0.762402i	$-0.724020\pi$
$409$	−26.1737	−1.29421	−0.647104	+	0.762402i	$0.724020\pi$
$410$	21.6760	1.07050
$411$	−55.4305	−2.73418
$412$	13.1260	0.646673
$413$	−19.5359	−0.961300
$414$	−13.3024	−0.653775
$415$	20.7779	1.01995
$416$	5.90660	0.289595
$417$	−6.34995	−0.310958
$418$	8.14805	0.398534
$419$	−20.5501	−1.00394	−0.501969	−	0.864886i	$-0.667391\pi$
$419$	−20.5501	−1.00394	−0.501969	+	0.864886i	$0.667391\pi$
$420$	−24.2619	−1.18386
$421$	12.9152	0.629447	0.314723	−	0.949183i	$-0.398088\pi$
$421$	12.9152	0.629447	0.314723	+	0.949183i	$0.398088\pi$
$422$	−4.87582	−0.237351
$423$	−45.1525	−2.19539
$424$	−5.41517	−0.262984
$425$	53.8991	2.61449
$426$	4.88877	0.236862
$427$	17.7231	0.857682
$428$	1.30213	0.0629407
$429$	−17.1764	−0.829285
$430$	−47.9503	−2.31237
$431$	−30.8694	−1.48692	−0.743462	−	0.668778i	$-0.766818\pi$
$431$	−30.8694	−1.48692	−0.743462	+	0.668778i	$0.766818\pi$
$432$	−7.60624	−0.365955
$433$	36.5620	1.75706	0.878528	−	0.477690i	$-0.158526\pi$
$433$	36.5620	1.75706	0.878528	+	0.477690i	$0.158526\pi$
$434$	13.8487	0.664757
$435$	73.6114	3.52940
$436$	7.72615	0.370015
$437$	19.5315	0.934317
$438$	14.0262	0.670197
$439$	−38.4139	−1.83340	−0.916699	−	0.399579i	$-0.869156\pi$
$439$	−38.4139	−1.83340	−0.916699	+	0.399579i	$0.869156\pi$
$440$	−4.23692	−0.201987
$441$	−18.1598	−0.864753
$442$	24.0372	1.14333
$443$	−17.0055	−0.807956	−0.403978	−	0.914769i	$-0.632373\pi$
$443$	−17.0055	−0.807956	−0.403978	+	0.914769i	$0.632373\pi$
$444$	−17.4005	−0.825792
$445$	−16.7293	−0.793046
$446$	20.0837	0.950990
$447$	21.4447	1.01430
$448$	−1.93753	−0.0915395
$449$	32.4174	1.52987	0.764937	−	0.644106i	$-0.222770\pi$
$449$	32.4174	1.52987	0.764937	+	0.644106i	$0.222770\pi$
$450$	−74.0969	−3.49296
$451$	−5.03382	−0.237033
$452$	14.4944	0.681759
$453$	−17.2557	−0.810745
$454$	22.7888	1.06953
$455$	−48.8823	−2.29164
$456$	24.0814	1.12771
$457$	−4.49285	−0.210167	−0.105083	−	0.994463i	$-0.533511\pi$
$457$	−4.49285	−0.210167	−0.105083	+	0.994463i	$0.533511\pi$
$458$	23.6819	1.10658
$459$	−30.9539	−1.44481
$460$	−10.1562	−0.473535
$461$	14.3270	0.667277	0.333639	−	0.942701i	$-0.391724\pi$
$461$	14.3270	0.667277	0.333639	+	0.942701i	$0.391724\pi$
$462$	5.63433	0.262133
$463$	−29.8588	−1.38766	−0.693828	−	0.720141i	$-0.744077\pi$
$463$	−29.8588	−1.38766	−0.693828	+	0.720141i	$0.744077\pi$
$464$	5.87852	0.272903
$465$	89.5030	4.15060
$466$	−5.86586	−0.271731
$467$	−18.5781	−0.859693	−0.429847	−	0.902902i	$-0.641432\pi$
$467$	−18.5781	−0.859693	−0.429847	+	0.902902i	$0.641432\pi$
$468$	−33.0447	−1.52749
$469$	−3.45508	−0.159541
$470$	−34.4734	−1.59014
$471$	19.7786	0.911351
$472$	−10.0829	−0.464104
$473$	11.1355	0.512010
$474$	−2.67229	−0.122742
$475$	108.794	4.99182
$476$	−7.88485	−0.361401
$477$	30.2953	1.38713
$478$	−0.511634	−0.0234016
$479$	8.53897	0.390156	0.195078	−	0.980788i	$-0.437504\pi$
$479$	8.53897	0.390156	0.195078	+	0.980788i	$0.437504\pi$
$480$	−12.5221	−0.571553
$481$	−35.0581	−1.59851
$482$	18.4508	0.840410
$483$	13.5059	0.614540
$484$	−10.0161	−0.455276
$485$	44.4068	2.01641
$486$	−6.65016	−0.301658
$487$	4.97218	0.225311	0.112656	−	0.993634i	$-0.464064\pi$
$487$	4.97218	0.225311	0.112656	+	0.993634i	$0.464064\pi$
$488$	9.14730	0.414079
$489$	−25.9561	−1.17377
$490$	−13.8648	−0.626348
$491$	−17.5836	−0.793535	−0.396767	−	0.917919i	$-0.629868\pi$
$491$	−17.5836	−0.793535	−0.396767	+	0.917919i	$0.629868\pi$
$492$	−14.8773	−0.670721
$493$	23.9229	1.07743
$494$	48.5185	2.18295
$495$	23.7036	1.06540
$496$	7.14760	0.320937
$497$	−3.23099	−0.144930
$498$	−14.2609	−0.639044
$499$	−20.8283	−0.932404	−0.466202	−	0.884678i	$-0.654378\pi$
$499$	−20.8283	−0.932404	−0.466202	+	0.884678i	$0.654378\pi$
$500$	−35.2153	−1.57488
$501$	−48.7122	−2.17630
$502$	24.7520	1.10474
$503$	−24.8856	−1.10960	−0.554798	−	0.831985i	$-0.687204\pi$
$503$	−24.8856	−1.10960	−0.554798	+	0.831985i	$0.687204\pi$
$504$	10.8395	0.482832
$505$	−41.4430	−1.84419
$506$	2.35857	0.104851
$507$	−64.1676	−2.84978
$508$	1.32137	0.0586265
$509$	−15.6936	−0.695606	−0.347803	−	0.937568i	$-0.613072\pi$
$509$	−15.6936	−0.695606	−0.347803	+	0.937568i	$0.613072\pi$
$510$	−50.9592	−2.25651
$511$	−9.26992	−0.410077
$512$	−1.00000	−0.0441942
$513$	−62.4798	−2.75855
$514$	−14.9689	−0.660249
$515$	−56.0660	−2.47056
$516$	32.9106	1.44881
$517$	8.00574	0.352092
$518$	11.5000	0.505282
$519$	−12.6011	−0.553126
$520$	−25.2292	−1.10637
$521$	35.5664	1.55819	0.779096	−	0.626904i	$-0.215678\pi$
$521$	35.5664	1.55819	0.779096	+	0.626904i	$0.215678\pi$
$522$	−32.8875	−1.43945
$523$	−0.318721	−0.0139367	−0.00696834	−	0.999976i	$-0.502218\pi$
$523$	−0.318721	−0.0139367	−0.00696834	+	0.999976i	$0.502218\pi$
$524$	3.54502	0.154865
$525$	75.2306	3.28333
$526$	−2.69400	−0.117464
$527$	29.0875	1.26707
$528$	2.90800	0.126555
$529$	−17.3463	−0.754189
$530$	23.1301	1.00471
$531$	56.4092	2.44795
$532$	−15.9154	−0.690020
$533$	−29.9744	−1.29834
$534$	11.4822	0.496881
$535$	−5.56186	−0.240460
$536$	−1.78324	−0.0770243
$537$	−68.6081	−2.96066
$538$	13.5744	0.585234
$539$	3.21982	0.138687
$540$	32.4890	1.39810
$541$	−1.68519	−0.0724522	−0.0362261	−	0.999344i	$-0.511534\pi$
$541$	−1.68519	−0.0724522	−0.0362261	+	0.999344i	$0.511534\pi$
$542$	6.17031	0.265038
$543$	7.54407	0.323747
$544$	−4.06954	−0.174480
$545$	−33.0012	−1.41361
$546$	33.5503	1.43582
$547$	−13.7451	−0.587698	−0.293849	−	0.955852i	$-0.594936\pi$
$547$	−13.7451	−0.587698	−0.293849	+	0.955852i	$0.594936\pi$
$548$	18.9077	0.807695
$549$	−51.1748	−2.18409
$550$	13.1377	0.560194
$551$	48.2878	2.05713
$552$	6.97069	0.296692
$553$	1.76612	0.0751031
$554$	16.1337	0.685455
$555$	74.3239	3.15487
$556$	2.16600	0.0918590
$557$	24.4871	1.03755	0.518776	−	0.854910i	$-0.326388\pi$
$557$	24.4871	1.03755	0.518776	+	0.854910i	$0.326388\pi$
$558$	−39.9875	−1.69280
$559$	66.3075	2.80451
$560$	8.27587	0.349719
$561$	11.8342	0.499642
$562$	−6.69892	−0.282577
$563$	−6.23287	−0.262684	−0.131342	−	0.991337i	$-0.541929\pi$
$563$	−6.23287	−0.262684	−0.131342	+	0.991337i	$0.541929\pi$
$564$	23.6608	0.996298
$565$	−61.9107	−2.60460
$566$	−7.51085	−0.315705
$567$	−10.6858	−0.448762
$568$	−1.66759	−0.0699704
$569$	−3.47848	−0.145826	−0.0729128	−	0.997338i	$-0.523229\pi$
$569$	−3.47848	−0.145826	−0.0729128	+	0.997338i	$0.523229\pi$
$570$	−102.860	−4.30834
$571$	−2.64597	−0.110730	−0.0553651	−	0.998466i	$-0.517632\pi$
$571$	−2.64597	−0.110730	−0.0553651	+	0.998466i	$0.517632\pi$
$572$	5.85897	0.244976
$573$	−43.6328	−1.82279
$574$	9.83244	0.410398
$575$	31.4921	1.31331
$576$	5.59453	0.233105
$577$	−9.13155	−0.380152	−0.190076	−	0.981769i	$-0.560873\pi$
$577$	−9.13155	−0.380152	−0.190076	+	0.981769i	$0.560873\pi$
$578$	0.438817	0.0182524
$579$	−22.1557	−0.920759
$580$	−25.1093	−1.04261
$581$	9.42502	0.391016
$582$	−30.4786	−1.26338
$583$	−5.37150	−0.222465
$584$	−4.78441	−0.197980
$585$	141.146	5.83565
$586$	30.2683	1.25037
$587$	−15.0161	−0.619783	−0.309891	−	0.950772i	$-0.600293\pi$
$587$	−15.0161	−0.619783	−0.309891	+	0.950772i	$0.600293\pi$
$588$	9.51609	0.392437
$589$	58.7124	2.41920
$590$	43.0678	1.77307
$591$	65.7493	2.70456
$592$	5.93542	0.243944
$593$	2.21802	0.0910833	0.0455417	−	0.998962i	$-0.485499\pi$
$593$	2.21802	0.0910833	0.0455417	+	0.998962i	$0.485499\pi$
$594$	−7.54490	−0.309571
$595$	33.6790	1.38071
$596$	−7.31490	−0.299630
$597$	57.7993	2.36557
$598$	14.0444	0.574317
$599$	−31.0084	−1.26697	−0.633485	−	0.773755i	$-0.718376\pi$
$599$	−31.0084	−1.26697	−0.633485	+	0.773755i	$0.718376\pi$
$600$	38.8282	1.58515
$601$	46.9900	1.91676	0.958381	−	0.285492i	$-0.0921569\pi$
$601$	46.9900	1.91676	0.958381	+	0.285492i	$0.0921569\pi$
$602$	−21.7507	−0.886492
$603$	9.97641	0.406271
$604$	5.88603	0.239499
$605$	42.7822	1.73934
$606$	28.4444	1.15547
$607$	5.79003	0.235010	0.117505	−	0.993072i	$-0.462510\pi$
$607$	5.79003	0.235010	0.117505	+	0.993072i	$0.462510\pi$
$608$	−8.21429	−0.333133
$609$	33.3908	1.35306
$610$	−39.0714	−1.58195
$611$	47.6711	1.92857
$612$	22.7672	0.920309
$613$	19.6412	0.793300	0.396650	−	0.917970i	$-0.370173\pi$
$613$	19.6412	0.793300	0.396650	+	0.917970i	$0.370173\pi$
$614$	−21.3794	−0.862802
$615$	63.5464	2.56244
$616$	−1.92190	−0.0774356
$617$	−4.10250	−0.165160	−0.0825802	−	0.996584i	$-0.526316\pi$
$617$	−4.10250	−0.165160	−0.0825802	+	0.996584i	$0.526316\pi$
$618$	38.4809	1.54793
$619$	37.5159	1.50789	0.753945	−	0.656938i	$-0.228149\pi$
$619$	37.5159	1.50789	0.753945	+	0.656938i	$0.228149\pi$
$620$	−30.5300	−1.22611
$621$	−18.0857	−0.725753
$622$	−31.6134	−1.26758
$623$	−7.58857	−0.304029
$624$	17.3160	0.693196
$625$	84.1947	3.36779
$626$	19.8881	0.794889
$627$	23.8872	0.953962
$628$	−6.74660	−0.269219
$629$	24.1544	0.963100
$630$	−46.2996	−1.84462
$631$	−20.7751	−0.827042	−0.413521	−	0.910495i	$-0.635701\pi$
$631$	−20.7751	−0.827042	−0.413521	+	0.910495i	$0.635701\pi$
$632$	0.911534	0.0362589
$633$	−14.2942	−0.568142
$634$	−19.7643	−0.784941
$635$	−5.64407	−0.223978
$636$	−15.8753	−0.629498
$637$	19.1728	0.759653
$638$	5.83111	0.230856
$639$	9.32937	0.369064
$640$	4.27136	0.168840
$641$	13.2299	0.522549	0.261275	−	0.965265i	$-0.415857\pi$
$641$	13.2299	0.522549	0.261275	+	0.965265i	$0.415857\pi$
$642$	3.81737	0.150660
$643$	−16.2949	−0.642606	−0.321303	−	0.946976i	$-0.604121\pi$
$643$	−16.2949	−0.642606	−0.321303	+	0.946976i	$0.604121\pi$
$644$	−4.60694	−0.181539
$645$	−140.573	−5.53507
$646$	−33.4284	−1.31522
$647$	−17.2253	−0.677197	−0.338599	−	0.940931i	$-0.609953\pi$
$647$	−17.2253	−0.677197	−0.338599	+	0.940931i	$0.609953\pi$
$648$	−5.51518	−0.216657
$649$	−10.0016	−0.392598
$650$	78.2301	3.06844
$651$	40.5993	1.59121
$652$	8.85377	0.346740
$653$	26.2002	1.02529	0.512647	−	0.858600i	$-0.328665\pi$
$653$	26.2002	1.02529	0.512647	+	0.858600i	$0.328665\pi$
$654$	22.6503	0.885697
$655$	−15.1421	−0.591649
$656$	5.07474	0.198135
$657$	26.7665	1.04426
$658$	−15.6374	−0.609610
$659$	−40.8538	−1.59144	−0.795719	−	0.605666i	$-0.792907\pi$
$659$	−40.8538	−1.59144	−0.795719	+	0.605666i	$0.792907\pi$
$660$	−12.4211	−0.483492
$661$	−45.0771	−1.75330	−0.876648	−	0.481133i	$-0.840225\pi$
$661$	−45.0771	−1.75330	−0.876648	+	0.481133i	$0.840225\pi$
$662$	4.88804	0.189979
$663$	70.4684	2.73677
$664$	4.86446	0.188778
$665$	67.9804	2.63617
$666$	−33.2059	−1.28670
$667$	13.9776	0.541215
$668$	16.6160	0.642893
$669$	58.8782	2.27636
$670$	7.61687	0.294265
$671$	9.07353	0.350280
$672$	−5.68013	−0.219116
$673$	31.7318	1.22317	0.611586	−	0.791178i	$-0.290532\pi$
$673$	31.7318	1.22317	0.611586	+	0.791178i	$0.290532\pi$
$674$	−25.5755	−0.985130
$675$	−100.741	−3.87752
$676$	21.8879	0.841843
$677$	0.701481	0.0269601	0.0134801	−	0.999909i	$-0.495709\pi$
$677$	0.701481	0.0269601	0.0134801	+	0.999909i	$0.495709\pi$
$678$	42.4924	1.63191
$679$	20.1433	0.773029
$680$	17.3825	0.666588
$681$	66.8085	2.56011
$682$	7.08996	0.271489
$683$	38.4151	1.46991	0.734957	−	0.678113i	$-0.237202\pi$
$683$	38.4151	1.46991	0.734957	+	0.678113i	$0.237202\pi$
$684$	45.9551	1.75714
$685$	−80.7614	−3.08573
$686$	−19.8519	−0.757948
$687$	69.4269	2.64880
$688$	−11.2260	−0.427988
$689$	−31.9852	−1.21854
$690$	−29.7743	−1.13349
$691$	−20.3235	−0.773144	−0.386572	−	0.922259i	$-0.626341\pi$
$691$	−20.3235	−0.773144	−0.386572	+	0.922259i	$0.626341\pi$
$692$	4.29830	0.163397
$693$	10.7521	0.408440
$694$	13.9253	0.528598
$695$	−9.25178	−0.350940
$696$	17.2337	0.653242
$697$	20.6519	0.782245
$698$	−33.9521	−1.28511
$699$	−17.1966	−0.650436
$700$	−25.6616	−0.969917
$701$	−37.0552	−1.39956	−0.699778	−	0.714360i	$-0.746718\pi$
$701$	−37.0552	−1.39956	−0.699778	+	0.714360i	$0.746718\pi$
$702$	−44.9270	−1.69566
$703$	48.7552	1.83884
$704$	−0.991936	−0.0373850
$705$	−101.064	−3.80628
$706$	−17.0795	−0.642796
$707$	−18.7989	−0.707006
$708$	−29.5595	−1.11092
$709$	−31.3442	−1.17716	−0.588578	−	0.808441i	$-0.700312\pi$
$709$	−31.3442	−1.17716	−0.588578	+	0.808441i	$0.700312\pi$
$710$	7.12287	0.267316
$711$	−5.09960	−0.191250
$712$	−3.91663	−0.146782
$713$	16.9952	0.636473
$714$	−23.1156	−0.865078
$715$	−25.0258	−0.935911
$716$	23.4026	0.874596
$717$	−1.49993	−0.0560159
$718$	12.6817	0.473278
$719$	4.60668	0.171800	0.0859002	−	0.996304i	$-0.472623\pi$
$719$	4.60668	0.171800	0.0859002	+	0.996304i	$0.472623\pi$
$720$	−23.8963	−0.890561
$721$	−25.4320	−0.947138
$722$	−48.4745	−1.80404
$723$	54.0911	2.01167
$724$	−2.57332	−0.0956368
$725$	77.8581	2.89158
$726$	−29.3635	−1.08978
$727$	4.64465	0.172261	0.0861303	−	0.996284i	$-0.472550\pi$
$727$	4.64465	0.172261	0.0861303	+	0.996284i	$0.472550\pi$
$728$	−11.4442	−0.424150
$729$	−36.0415	−1.33487
$730$	20.4359	0.756368
$731$	−45.6847	−1.68971
$732$	26.8166	0.991170
$733$	40.0777	1.48030	0.740151	−	0.672441i	$-0.234754\pi$
$733$	40.0777	1.48030	0.740151	+	0.672441i	$0.234754\pi$
$734$	−5.08326	−0.187626
$735$	−40.6467	−1.49927
$736$	−2.37774	−0.0876448
$737$	−1.76886	−0.0651569
$738$	−28.3908	−1.04508
$739$	0.547955	0.0201568	0.0100784	−	0.999949i	$-0.496792\pi$
$739$	0.547955	0.0201568	0.0100784	+	0.999949i	$0.496792\pi$
$740$	−25.3523	−0.931969
$741$	142.239	5.22528
$742$	10.4920	0.385174
$743$	17.5147	0.642551	0.321275	−	0.946986i	$-0.395888\pi$
$743$	17.5147	0.642551	0.321275	+	0.946986i	$0.395888\pi$
$744$	20.9542	0.768219
$745$	31.2446	1.14471
$746$	−32.1233	−1.17612
$747$	−27.2144	−0.995722
$748$	−4.03673	−0.147597
$749$	−2.52291	−0.0921850
$750$	−103.239	−3.76974
$751$	−18.9497	−0.691485	−0.345742	−	0.938330i	$-0.612373\pi$
$751$	−18.9497	−0.691485	−0.345742	+	0.938330i	$0.612373\pi$
$752$	−8.07082	−0.294313
$753$	72.5640	2.64438
$754$	34.7220	1.26450
$755$	−25.1413	−0.914987
$756$	14.7373	0.535990
$757$	−12.4221	−0.451490	−0.225745	−	0.974186i	$-0.572482\pi$
$757$	−12.4221	−0.451490	−0.225745	+	0.974186i	$0.572482\pi$
$758$	−9.54377	−0.346645
$759$	6.91448	0.250980
$760$	35.0862	1.27271
$761$	−2.94879	−0.106894	−0.0534468	−	0.998571i	$-0.517021\pi$
$761$	−2.94879	−0.106894	−0.0534468	+	0.998571i	$0.517021\pi$
$762$	3.87380	0.140333
$763$	−14.9696	−0.541936
$764$	14.8834	0.538463
$765$	−97.2469	−3.51597
$766$	−27.2952	−0.986217
$767$	−59.5558	−2.15044
$768$	−2.93164	−0.105787
$769$	−8.28102	−0.298621	−0.149311	−	0.988790i	$-0.547705\pi$
$769$	−8.28102	−0.298621	−0.149311	+	0.988790i	$0.547705\pi$
$770$	8.20914	0.295837
$771$	−43.8834	−1.58042
$772$	7.55743	0.271998
$773$	−24.6869	−0.887925	−0.443962	−	0.896045i	$-0.646428\pi$
$773$	−24.6869	−0.887925	−0.443962	+	0.896045i	$0.646428\pi$
$774$	62.8042	2.25745
$775$	94.6665	3.40052
$776$	10.3964	0.373209
$777$	33.7140	1.20948
$778$	−32.1193	−1.15153
$779$	41.6854	1.49353
$780$	−73.9631	−2.64830
$781$	−1.65414	−0.0591898
$782$	−9.67633	−0.346025
$783$	−44.7134	−1.59793
$784$	−3.24599	−0.115928
$785$	28.8172	1.02853
$786$	10.3927	0.370697
$787$	−16.0466	−0.572000	−0.286000	−	0.958230i	$-0.592326\pi$
$787$	−16.0466	−0.572000	−0.286000	+	0.958230i	$0.592326\pi$
$788$	−22.4275	−0.798945
$789$	−7.89785	−0.281171
$790$	−3.89349	−0.138524
$791$	−28.0832	−0.998525
$792$	5.54942	0.197190
$793$	54.0294	1.91864
$794$	−26.3751	−0.936016
$795$	67.8093	2.40495
$796$	−19.7157	−0.698803
$797$	−10.2890	−0.364453	−0.182227	−	0.983257i	$-0.558330\pi$
$797$	−10.2890	−0.364453	−0.182227	+	0.983257i	$0.558330\pi$
$798$	−46.6583	−1.65168
$799$	−32.8445	−1.16196
$800$	−13.2445	−0.468264
$801$	21.9117	0.774212
$802$	−25.6700	−0.906439
$803$	−4.74583	−0.167477
$804$	−5.22783	−0.184371
$805$	19.6779	0.693555
$806$	42.2180	1.48707
$807$	39.7953	1.40086
$808$	−9.70253	−0.341334
$809$	−34.4919	−1.21267	−0.606336	−	0.795209i	$-0.707361\pi$
$809$	−34.4919	−1.21267	−0.606336	+	0.795209i	$0.707361\pi$
$810$	23.5573	0.827721
$811$	4.28503	0.150468	0.0752339	−	0.997166i	$-0.476030\pi$
$811$	4.28503	0.150468	0.0752339	+	0.997166i	$0.476030\pi$
$812$	−11.3898	−0.399703
$813$	18.0892	0.634414
$814$	5.88755	0.206359
$815$	−37.8176	−1.32469
$816$	−11.9304	−0.417649
$817$	−92.2137	−3.22615
$818$	26.1737	0.915143
$819$	64.0249	2.23721
$820$	−21.6760	−0.756960
$821$	−19.5523	−0.682380	−0.341190	−	0.939994i	$-0.610830\pi$
$821$	−19.5523	−0.682380	−0.341190	+	0.939994i	$0.610830\pi$
$822$	55.4305	1.93336
$823$	−37.4041	−1.30382	−0.651912	−	0.758294i	$-0.726033\pi$
$823$	−37.4041	−1.30382	−0.651912	+	0.758294i	$0.726033\pi$
$824$	−13.1260	−0.457267
$825$	38.5151	1.34092
$826$	19.5359	0.679742
$827$	−23.6924	−0.823865	−0.411932	−	0.911214i	$-0.635146\pi$
$827$	−23.6924	−0.823865	−0.411932	+	0.911214i	$0.635146\pi$
$828$	13.3024	0.462289
$829$	−1.56021	−0.0541883	−0.0270942	−	0.999633i	$-0.508625\pi$
$829$	−1.56021	−0.0541883	−0.0270942	+	0.999633i	$0.508625\pi$
$830$	−20.7779	−0.721210
$831$	47.2983	1.64076
$832$	−5.90660	−0.204775
$833$	−13.2097	−0.457689
$834$	6.34995	0.219881
$835$	−70.9730	−2.45612
$836$	−8.14805	−0.281806
$837$	−54.3663	−1.87918
$838$	20.5501	0.709891
$839$	29.7577	1.02735	0.513675	−	0.857985i	$-0.328284\pi$
$839$	29.7577	1.02735	0.513675	+	0.857985i	$0.328284\pi$
$840$	24.2619	0.837115
$841$	5.55694	0.191619
$842$	−12.9152	−0.445086
$843$	−19.6388	−0.676397
$844$	4.87582	0.167833
$845$	−93.4912	−3.21620
$846$	45.1525	1.55237
$847$	19.4064	0.666811
$848$	5.41517	0.185958
$849$	−22.0191	−0.755695
$850$	−53.8991	−1.84873
$851$	14.1129	0.483784
$852$	−4.88877	−0.167487
$853$	−31.5331	−1.07967	−0.539837	−	0.841770i	$-0.681514\pi$
$853$	−31.5331	−1.07967	−0.539837	+	0.841770i	$0.681514\pi$
$854$	−17.7231	−0.606473
$855$	−196.291	−6.71300
$856$	−1.30213	−0.0445058
$857$	−9.96445	−0.340379	−0.170190	−	0.985411i	$-0.554438\pi$
$857$	−9.96445	−0.340379	−0.170190	+	0.985411i	$0.554438\pi$
$858$	17.1764	0.586393
$859$	17.6503	0.602221	0.301111	−	0.953589i	$-0.402643\pi$
$859$	17.6503	0.602221	0.301111	+	0.953589i	$0.402643\pi$
$860$	47.9503	1.63509
$861$	28.8252	0.982360
$862$	30.8694	1.05141
$863$	26.5331	0.903198	0.451599	−	0.892221i	$-0.350854\pi$
$863$	26.5331	0.903198	0.451599	+	0.892221i	$0.350854\pi$
$864$	7.60624	0.258770
$865$	−18.3596	−0.624245
$866$	−36.5620	−1.24243
$867$	1.28646	0.0436903
$868$	−13.8487	−0.470054
$869$	0.904183	0.0306723
$870$	−73.6114	−2.49566
$871$	−10.5329	−0.356894
$872$	−7.72615	−0.261640
$873$	−58.1630	−1.96852
$874$	−19.5315	−0.660662
$875$	68.2306	2.30661
$876$	−14.0262	−0.473901
$877$	−15.8426	−0.534967	−0.267484	−	0.963562i	$-0.586192\pi$
$877$	−15.8426	−0.534967	−0.267484	+	0.963562i	$0.586192\pi$
$878$	38.4139	1.29641
$879$	88.7359	2.99299
$880$	4.23692	0.142826
$881$	13.5051	0.455000	0.227500	−	0.973778i	$-0.426945\pi$
$881$	13.5051	0.455000	0.227500	+	0.973778i	$0.426945\pi$
$882$	18.1598	0.611473
$883$	36.0888	1.21448	0.607242	−	0.794517i	$-0.292276\pi$
$883$	36.0888	1.21448	0.607242	+	0.794517i	$0.292276\pi$
$884$	−24.0372	−0.808457
$885$	126.259	4.24417
$886$	17.0055	0.571311
$887$	−4.05333	−0.136097	−0.0680487	−	0.997682i	$-0.521677\pi$
$887$	−4.05333	−0.136097	−0.0680487	+	0.997682i	$0.521677\pi$
$888$	17.4005	0.583923
$889$	−2.56020	−0.0858663
$890$	16.7293	0.560768
$891$	−5.47071	−0.183276
$892$	−20.0837	−0.672451
$893$	−66.2960	−2.21851
$894$	−21.4447	−0.717217
$895$	−99.9609	−3.34133
$896$	1.93753	0.0647282
$897$	41.1731	1.37473
$898$	−32.4174	−1.08178
$899$	42.0173	1.40135
$900$	74.0969	2.46990
$901$	22.0373	0.734167
$902$	5.03382	0.167608
$903$	−63.7652	−2.12197
$904$	−14.4944	−0.482076
$905$	10.9916	0.365373
$906$	17.2557	0.573283
$907$	−51.5217	−1.71075	−0.855375	−	0.518009i	$-0.826673\pi$
$907$	−51.5217	−1.71075	−0.855375	+	0.518009i	$0.826673\pi$
$908$	−22.7888	−0.756272
$909$	54.2811	1.80039
$910$	48.8823	1.62043
$911$	−12.4438	−0.412280	−0.206140	−	0.978522i	$-0.566090\pi$
$911$	−12.4438	−0.412280	−0.206140	+	0.978522i	$0.566090\pi$
$912$	−24.0814	−0.797414
$913$	4.82523	0.159692
$914$	4.49285	0.148610
$915$	−114.543	−3.78669
$916$	−23.6819	−0.782472
$917$	−6.86857	−0.226820
$918$	30.9539	1.02163
$919$	−42.4957	−1.40180	−0.700902	−	0.713257i	$-0.747219\pi$
$919$	−42.4957	−1.40180	−0.700902	+	0.713257i	$0.747219\pi$
$920$	10.1562	0.334840
$921$	−62.6768	−2.06527
$922$	−14.3270	−0.471836
$923$	−9.84977	−0.324209
$924$	−5.63433	−0.185356
$925$	78.6117	2.58474
$926$	29.8588	0.981221
$927$	73.4340	2.41189
$928$	−5.87852	−0.192972
$929$	16.7659	0.550072	0.275036	−	0.961434i	$-0.411310\pi$
$929$	16.7659	0.550072	0.275036	+	0.961434i	$0.411310\pi$
$930$	−89.5030	−2.93492
$931$	−26.6635	−0.873862
$932$	5.86586	0.192143
$933$	−92.6791	−3.03418
$934$	18.5781	0.607895
$935$	17.2423	0.563884
$936$	33.0447	1.08010
$937$	−16.0756	−0.525167	−0.262583	−	0.964909i	$-0.584574\pi$
$937$	−16.0756	−0.525167	−0.262583	+	0.964909i	$0.584574\pi$
$938$	3.45508	0.112812
$939$	58.3049	1.90271
$940$	34.4734	1.12440
$941$	60.2315	1.96349	0.981746	−	0.190198i	$-0.0609130\pi$
$941$	60.2315	1.96349	0.981746	+	0.190198i	$0.0609130\pi$
$942$	−19.7786	−0.644422
$943$	12.0664	0.392937
$944$	10.0829	0.328171
$945$	−62.9483	−2.04771
$946$	−11.1355	−0.362046
$947$	41.4570	1.34717	0.673585	−	0.739109i	$-0.264753\pi$
$947$	41.4570	1.34717	0.673585	+	0.739109i	$0.264753\pi$
$948$	2.67229	0.0867920
$949$	−28.2596	−0.917345
$950$	−108.794	−3.52975
$951$	−57.9419	−1.87890
$952$	7.88485	0.255549
$953$	19.1447	0.620157	0.310078	−	0.950711i	$-0.399645\pi$
$953$	19.1447	0.620157	0.310078	+	0.950711i	$0.399645\pi$
$954$	−30.2953	−0.980847
$955$	−63.5724	−2.05715
$956$	0.511634	0.0165474
$957$	17.0947	0.552594
$958$	−8.53897	−0.275882
$959$	−36.6341	−1.18298
$960$	12.5221	0.404149
$961$	20.0882	0.648005
$962$	35.0581	1.13032
$963$	7.28479	0.234749
$964$	−18.4508	−0.594259
$965$	−32.2805	−1.03915
$966$	−13.5059	−0.434545
$967$	−49.0512	−1.57738	−0.788689	−	0.614792i	$-0.789240\pi$
$967$	−49.0512	−1.57738	−0.788689	+	0.614792i	$0.789240\pi$
$968$	10.0161	0.321928
$969$	−98.0001	−3.14822
$970$	−44.4068	−1.42582
$971$	−33.5918	−1.07801	−0.539006	−	0.842302i	$-0.681200\pi$
$971$	−33.5918	−1.07801	−0.539006	+	0.842302i	$0.681200\pi$
$972$	6.65016	0.213304
$973$	−4.19669	−0.134540
$974$	−4.97218	−0.159319
$975$	229.343	7.34484
$976$	−9.14730	−0.292798
$977$	15.7654	0.504381	0.252190	−	0.967678i	$-0.418849\pi$
$977$	15.7654	0.504381	0.252190	+	0.967678i	$0.418849\pi$
$978$	25.9561	0.829984
$979$	−3.88504	−0.124167
$980$	13.8648	0.442895
$981$	43.2242	1.38004
$982$	17.5836	0.561114
$983$	40.8062	1.30151	0.650757	−	0.759286i	$-0.274452\pi$
$983$	40.8062	1.30151	0.650757	+	0.759286i	$0.274452\pi$
$984$	14.8773	0.474272
$985$	95.7957	3.05231
$986$	−23.9229	−0.761859
$987$	−45.8433	−1.45921
$988$	−48.5185	−1.54358
$989$	−26.6926	−0.848774
$990$	−23.7036	−0.753349
$991$	30.7285	0.976124	0.488062	−	0.872809i	$-0.337704\pi$
$991$	30.7285	0.976124	0.488062	+	0.872809i	$0.337704\pi$
$992$	−7.14760	−0.226936
$993$	14.3300	0.454748
$994$	3.23099	0.102481
$995$	84.2127	2.66972
$996$	14.2609	0.451873
$997$	15.2656	0.483467	0.241733	−	0.970343i	$-0.422284\pi$
$997$	15.2656	0.483467	0.241733	+	0.970343i	$0.422284\pi$
$998$	20.8283	0.659309
$999$	−45.1462	−1.42836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.e.1.9	✓	91

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.e.1.9	✓	91	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.93164 q^{3} +1.00000 q^{4} -4.27136 q^{5} +2.93164 q^{6} -1.93753 q^{7} -1.00000 q^{8} +5.59453 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.93164 q^{3} +1.00000 q^{4} -4.27136 q^{5} +2.93164 q^{6} -1.93753 q^{7} -1.00000 q^{8} +5.59453 q^{9} +4.27136 q^{10} -0.991936 q^{11} -2.93164 q^{12} -5.90660 q^{13} +1.93753 q^{14} +12.5221 q^{15} +1.00000 q^{16} +4.06954 q^{17} -5.59453 q^{18} +8.21429 q^{19} -4.27136 q^{20} +5.68013 q^{21} +0.991936 q^{22} +2.37774 q^{23} +2.93164 q^{24} +13.2445 q^{25} +5.90660 q^{26} -7.60624 q^{27} -1.93753 q^{28} +5.87852 q^{29} -12.5221 q^{30} +7.14760 q^{31} -1.00000 q^{32} +2.90800 q^{33} -4.06954 q^{34} +8.27587 q^{35} +5.59453 q^{36} +5.93542 q^{37} -8.21429 q^{38} +17.3160 q^{39} +4.27136 q^{40} +5.07474 q^{41} -5.68013 q^{42} -11.2260 q^{43} -0.991936 q^{44} -23.8963 q^{45} -2.37774 q^{46} -8.07082 q^{47} -2.93164 q^{48} -3.24599 q^{49} -13.2445 q^{50} -11.9304 q^{51} -5.90660 q^{52} +5.41517 q^{53} +7.60624 q^{54} +4.23692 q^{55} +1.93753 q^{56} -24.0814 q^{57} -5.87852 q^{58} +10.0829 q^{59} +12.5221 q^{60} -9.14730 q^{61} -7.14760 q^{62} -10.8395 q^{63} +1.00000 q^{64} +25.2292 q^{65} -2.90800 q^{66} +1.78324 q^{67} +4.06954 q^{68} -6.97069 q^{69} -8.27587 q^{70} +1.66759 q^{71} -5.59453 q^{72} +4.78441 q^{73} -5.93542 q^{74} -38.8282 q^{75} +8.21429 q^{76} +1.92190 q^{77} -17.3160 q^{78} -0.911534 q^{79} -4.27136 q^{80} +5.51518 q^{81} -5.07474 q^{82} -4.86446 q^{83} +5.68013 q^{84} -17.3825 q^{85} +11.2260 q^{86} -17.2337 q^{87} +0.991936 q^{88} +3.91663 q^{89} +23.8963 q^{90} +11.4442 q^{91} +2.37774 q^{92} -20.9542 q^{93} +8.07082 q^{94} -35.0862 q^{95} +2.93164 q^{96} -10.3964 q^{97} +3.24599 q^{98} -5.54942 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

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