LMFDB - Embedded newform 8018.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.0920586 q^{3} +1.00000 q^{4} +2.87697 q^{5} -0.0920586 q^{6} +2.64672 q^{7} +1.00000 q^{8} -2.99153 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.0920586 q^{3} +1.00000 q^{4} +2.87697 q^{5} -0.0920586 q^{6} +2.64672 q^{7} +1.00000 q^{8} -2.99153 q^{9} +2.87697 q^{10} -0.542435 q^{11} -0.0920586 q^{12} -5.81038 q^{13} +2.64672 q^{14} -0.264850 q^{15} +1.00000 q^{16} -5.96467 q^{17} -2.99153 q^{18} -1.00000 q^{19} +2.87697 q^{20} -0.243653 q^{21} -0.542435 q^{22} -6.88660 q^{23} -0.0920586 q^{24} +3.27695 q^{25} -5.81038 q^{26} +0.551572 q^{27} +2.64672 q^{28} +3.48435 q^{29} -0.264850 q^{30} -7.61790 q^{31} +1.00000 q^{32} +0.0499358 q^{33} -5.96467 q^{34} +7.61453 q^{35} -2.99153 q^{36} +3.09057 q^{37} -1.00000 q^{38} +0.534895 q^{39} +2.87697 q^{40} -8.13918 q^{41} -0.243653 q^{42} +0.880796 q^{43} -0.542435 q^{44} -8.60653 q^{45} -6.88660 q^{46} +7.38140 q^{47} -0.0920586 q^{48} +0.00511548 q^{49} +3.27695 q^{50} +0.549099 q^{51} -5.81038 q^{52} +0.697997 q^{53} +0.551572 q^{54} -1.56057 q^{55} +2.64672 q^{56} +0.0920586 q^{57} +3.48435 q^{58} +3.10936 q^{59} -0.264850 q^{60} +3.67649 q^{61} -7.61790 q^{62} -7.91772 q^{63} +1.00000 q^{64} -16.7163 q^{65} +0.0499358 q^{66} -8.09242 q^{67} -5.96467 q^{68} +0.633971 q^{69} +7.61453 q^{70} -7.80107 q^{71} -2.99153 q^{72} -7.08049 q^{73} +3.09057 q^{74} -0.301672 q^{75} -1.00000 q^{76} -1.43567 q^{77} +0.534895 q^{78} -2.35822 q^{79} +2.87697 q^{80} +8.92380 q^{81} -8.13918 q^{82} -6.43207 q^{83} -0.243653 q^{84} -17.1602 q^{85} +0.880796 q^{86} -0.320765 q^{87} -0.542435 q^{88} +3.95828 q^{89} -8.60653 q^{90} -15.3784 q^{91} -6.88660 q^{92} +0.701293 q^{93} +7.38140 q^{94} -2.87697 q^{95} -0.0920586 q^{96} +9.40667 q^{97} +0.00511548 q^{98} +1.62271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * 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
$3$	−0.0920586	−0.0531501	−0.0265750	−	0.999647i	$-0.508460\pi$
$3$	−0.0920586	−0.0531501	−0.0265750	+	0.999647i	$0.508460\pi$
$4$	1.00000	0.500000
$5$	2.87697	1.28662	0.643310	−	0.765606i	$-0.277561\pi$
$5$	2.87697	1.28662	0.643310	+	0.765606i	$0.277561\pi$
$6$	−0.0920586	−0.0375828
$7$	2.64672	1.00037	0.500183	−	0.865920i	$-0.333266\pi$
$7$	2.64672	1.00037	0.500183	+	0.865920i	$0.333266\pi$
$8$	1.00000	0.353553
$9$	−2.99153	−0.997175
$10$	2.87697	0.909778
$11$	−0.542435	−0.163550	−0.0817751	−	0.996651i	$-0.526059\pi$
$11$	−0.542435	−0.163550	−0.0817751	+	0.996651i	$0.526059\pi$
$12$	−0.0920586	−0.0265750
$13$	−5.81038	−1.61151	−0.805755	−	0.592250i	$-0.798240\pi$
$13$	−5.81038	−1.61151	−0.805755	+	0.592250i	$0.798240\pi$
$14$	2.64672	0.707365
$15$	−0.264850	−0.0683839
$16$	1.00000	0.250000
$17$	−5.96467	−1.44664	−0.723322	−	0.690510i	$-0.757386\pi$
$17$	−5.96467	−1.44664	−0.723322	+	0.690510i	$0.757386\pi$
$18$	−2.99153	−0.705109
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.87697	0.643310
$21$	−0.243653	−0.0531695
$22$	−0.542435	−0.115647
$23$	−6.88660	−1.43596	−0.717978	−	0.696066i	$-0.754932\pi$
$23$	−6.88660	−1.43596	−0.717978	+	0.696066i	$0.754932\pi$
$24$	−0.0920586	−0.0187914
$25$	3.27695	0.655391
$26$	−5.81038	−1.13951
$27$	0.551572	0.106150
$28$	2.64672	0.500183
$29$	3.48435	0.647028	0.323514	−	0.946223i	$-0.395136\pi$
$29$	3.48435	0.647028	0.323514	+	0.946223i	$0.395136\pi$
$30$	−0.264850	−0.0483547
$31$	−7.61790	−1.36821	−0.684107	−	0.729381i	$-0.739808\pi$
$31$	−7.61790	−1.36821	−0.684107	+	0.729381i	$0.739808\pi$
$32$	1.00000	0.176777
$33$	0.0499358	0.00869270
$34$	−5.96467	−1.02293
$35$	7.61453	1.28709
$36$	−2.99153	−0.498588
$37$	3.09057	0.508086	0.254043	−	0.967193i	$-0.418240\pi$
$37$	3.09057	0.508086	0.254043	+	0.967193i	$0.418240\pi$
$38$	−1.00000	−0.162221
$39$	0.534895	0.0856518
$40$	2.87697	0.454889
$41$	−8.13918	−1.27113	−0.635563	−	0.772049i	$-0.719232\pi$
$41$	−8.13918	−1.27113	−0.635563	+	0.772049i	$0.719232\pi$
$42$	−0.243653	−0.0375965
$43$	0.880796	0.134320	0.0671600	−	0.997742i	$-0.478606\pi$
$43$	0.880796	0.134320	0.0671600	+	0.997742i	$0.478606\pi$
$44$	−0.542435	−0.0817751
$45$	−8.60653	−1.28299
$46$	−6.88660	−1.01537
$47$	7.38140	1.07669	0.538344	−	0.842725i	$-0.319050\pi$
$47$	7.38140	1.07669	0.538344	+	0.842725i	$0.319050\pi$
$48$	−0.0920586	−0.0132875
$49$	0.00511548	0.000730783 0
$50$	3.27695	0.463431
$51$	0.549099	0.0768893
$52$	−5.81038	−0.805755
$53$	0.697997	0.0958772	0.0479386	−	0.998850i	$-0.484735\pi$
$53$	0.697997	0.0958772	0.0479386	+	0.998850i	$0.484735\pi$
$54$	0.551572	0.0750594
$55$	−1.56057	−0.210427
$56$	2.64672	0.353683
$57$	0.0920586	0.0121935
$58$	3.48435	0.457518
$59$	3.10936	0.404804	0.202402	−	0.979302i	$-0.435125\pi$
$59$	3.10936	0.404804	0.202402	+	0.979302i	$0.435125\pi$
$60$	−0.264850	−0.0341920
$61$	3.67649	0.470726	0.235363	−	0.971908i	$-0.424372\pi$
$61$	3.67649	0.470726	0.235363	+	0.971908i	$0.424372\pi$
$62$	−7.61790	−0.967474
$63$	−7.91772	−0.997539
$64$	1.00000	0.125000
$65$	−16.7163	−2.07340
$66$	0.0499358	0.00614667
$67$	−8.09242	−0.988647	−0.494323	−	0.869278i	$-0.664584\pi$
$67$	−8.09242	−0.988647	−0.494323	+	0.869278i	$0.664584\pi$
$68$	−5.96467	−0.723322
$69$	0.633971	0.0763211
$70$	7.61453	0.910110
$71$	−7.80107	−0.925817	−0.462909	−	0.886406i	$-0.653194\pi$
$71$	−7.80107	−0.925817	−0.462909	+	0.886406i	$0.653194\pi$
$72$	−2.99153	−0.352555
$73$	−7.08049	−0.828708	−0.414354	−	0.910116i	$-0.635993\pi$
$73$	−7.08049	−0.828708	−0.414354	+	0.910116i	$0.635993\pi$
$74$	3.09057	0.359271
$75$	−0.301672	−0.0348341
$76$	−1.00000	−0.114708
$77$	−1.43567	−0.163610
$78$	0.534895	0.0605650
$79$	−2.35822	−0.265320	−0.132660	−	0.991162i	$-0.542352\pi$
$79$	−2.35822	−0.265320	−0.132660	+	0.991162i	$0.542352\pi$
$80$	2.87697	0.321655
$81$	8.92380	0.991533
$82$	−8.13918	−0.898822
$83$	−6.43207	−0.706012	−0.353006	−	0.935621i	$-0.614840\pi$
$83$	−6.43207	−0.706012	−0.353006	+	0.935621i	$0.614840\pi$
$84$	−0.243653	−0.0265847
$85$	−17.1602	−1.86128
$86$	0.880796	0.0949786
$87$	−0.320765	−0.0343896
$88$	−0.542435	−0.0578237
$89$	3.95828	0.419577	0.209788	−	0.977747i	$-0.432722\pi$
$89$	3.95828	0.419577	0.209788	+	0.977747i	$0.432722\pi$
$90$	−8.60653	−0.907208
$91$	−15.3784	−1.61210
$92$	−6.88660	−0.717978
$93$	0.701293	0.0727207
$94$	7.38140	0.761334
$95$	−2.87697	−0.295171
$96$	−0.0920586	−0.00939569
$97$	9.40667	0.955103	0.477552	−	0.878604i	$-0.341524\pi$
$97$	9.40667	0.955103	0.477552	+	0.878604i	$0.341524\pi$
$98$	0.00511548	0.000516742 0
$99$	1.62271	0.163088
$100$	3.27695	0.327695
$101$	−12.5799	−1.25175	−0.625874	−	0.779924i	$-0.715258\pi$
$101$	−12.5799	−1.25175	−0.625874	+	0.779924i	$0.715258\pi$
$102$	0.549099	0.0543689
$103$	−10.1310	−0.998234	−0.499117	−	0.866534i	$-0.666342\pi$
$103$	−10.1310	−0.998234	−0.499117	+	0.866534i	$0.666342\pi$
$104$	−5.81038	−0.569754
$105$	−0.700983	−0.0684089
$106$	0.697997	0.0677954
$107$	−6.56706	−0.634862	−0.317431	−	0.948281i	$-0.602820\pi$
$107$	−6.56706	−0.634862	−0.317431	+	0.948281i	$0.602820\pi$
$108$	0.551572	0.0530750
$109$	10.4085	0.996951	0.498476	−	0.866904i	$-0.333893\pi$
$109$	10.4085	0.996951	0.498476	+	0.866904i	$0.333893\pi$
$110$	−1.56057	−0.148794
$111$	−0.284513	−0.0270048
$112$	2.64672	0.250091
$113$	10.9015	1.02553	0.512765	−	0.858529i	$-0.328621\pi$
$113$	10.9015	1.02553	0.512765	+	0.858529i	$0.328621\pi$
$114$	0.0920586	0.00862208
$115$	−19.8125	−1.84753
$116$	3.48435	0.323514
$117$	17.3819	1.60696
$118$	3.10936	0.286240
$119$	−15.7868	−1.44717
$120$	−0.264850	−0.0241774
$121$	−10.7058	−0.973251
$122$	3.67649	0.332853
$123$	0.749281	0.0675604
$124$	−7.61790	−0.684107
$125$	−4.95715	−0.443381
$126$	−7.91772	−0.705367
$127$	4.79969	0.425903	0.212952	−	0.977063i	$-0.431692\pi$
$127$	4.79969	0.425903	0.212952	+	0.977063i	$0.431692\pi$
$128$	1.00000	0.0883883
$129$	−0.0810848	−0.00713912
$130$	−16.7163	−1.46611
$131$	−6.08860	−0.531963	−0.265982	−	0.963978i	$-0.585696\pi$
$131$	−6.08860	−0.531963	−0.265982	+	0.963978i	$0.585696\pi$
$132$	0.0499358	0.00434635
$133$	−2.64672	−0.229500
$134$	−8.09242	−0.699079
$135$	1.58685	0.136575
$136$	−5.96467	−0.511466
$137$	2.56861	0.219451	0.109726	−	0.993962i	$-0.465003\pi$
$137$	2.56861	0.219451	0.109726	+	0.993962i	$0.465003\pi$
$138$	0.633971	0.0539672
$139$	2.34384	0.198802	0.0994008	−	0.995047i	$-0.468307\pi$
$139$	2.34384	0.198802	0.0994008	+	0.995047i	$0.468307\pi$
$140$	7.61453	0.643545
$141$	−0.679522	−0.0572261
$142$	−7.80107	−0.654652
$143$	3.15175	0.263563
$144$	−2.99153	−0.249294
$145$	10.0244	0.832479
$146$	−7.08049	−0.585985
$147$	−0.000470924 0	−3.88412e−5 0
$148$	3.09057	0.254043
$149$	−13.0596	−1.06988	−0.534940	−	0.844890i	$-0.679666\pi$
$149$	−13.0596	−1.06988	−0.534940	+	0.844890i	$0.679666\pi$
$150$	−0.301672	−0.0246314
$151$	−15.1534	−1.23316	−0.616581	−	0.787291i	$-0.711483\pi$
$151$	−15.1534	−1.23316	−0.616581	+	0.787291i	$0.711483\pi$
$152$	−1.00000	−0.0811107
$153$	17.8435	1.44256
$154$	−1.43567	−0.115690
$155$	−21.9165	−1.76037
$156$	0.534895	0.0428259
$157$	21.2604	1.69676	0.848381	−	0.529385i	$-0.177577\pi$
$157$	21.2604	1.69676	0.848381	+	0.529385i	$0.177577\pi$
$158$	−2.35822	−0.187610
$159$	−0.0642566	−0.00509588
$160$	2.87697	0.227444
$161$	−18.2269	−1.43648
$162$	8.92380	0.701120
$163$	15.5887	1.22100	0.610500	−	0.792016i	$-0.290968\pi$
$163$	15.5887	1.22100	0.610500	+	0.792016i	$0.290968\pi$
$164$	−8.13918	−0.635563
$165$	0.143664	0.0111842
$166$	−6.43207	−0.499226
$167$	17.5498	1.35805	0.679024	−	0.734116i	$-0.262403\pi$
$167$	17.5498	1.35805	0.679024	+	0.734116i	$0.262403\pi$
$168$	−0.243653	−0.0187983
$169$	20.7605	1.59696
$170$	−17.1602	−1.31613
$171$	2.99153	0.228768
$172$	0.880796	0.0671600
$173$	23.2044	1.76420	0.882100	−	0.471062i	$-0.156129\pi$
$173$	23.2044	1.76420	0.882100	+	0.471062i	$0.156129\pi$
$174$	−0.320765	−0.0243171
$175$	8.67317	0.655630
$176$	−0.542435	−0.0408875
$177$	−0.286244	−0.0215154
$178$	3.95828	0.296686
$179$	13.8335	1.03396	0.516981	−	0.855997i	$-0.327056\pi$
$179$	13.8335	1.03396	0.516981	+	0.855997i	$0.327056\pi$
$180$	−8.60653	−0.641493
$181$	5.34522	0.397307	0.198653	−	0.980070i	$-0.436343\pi$
$181$	5.34522	0.397307	0.198653	+	0.980070i	$0.436343\pi$
$182$	−15.3784	−1.13993
$183$	−0.338452	−0.0250191
$184$	−6.88660	−0.507687
$185$	8.89147	0.653714
$186$	0.701293	0.0514213
$187$	3.23544	0.236599
$188$	7.38140	0.538344
$189$	1.45985	0.106189
$190$	−2.87697	−0.208717
$191$	−0.187305	−0.0135529	−0.00677645	−	0.999977i	$-0.502157\pi$
$191$	−0.187305	−0.0135529	−0.00677645	+	0.999977i	$0.502157\pi$
$192$	−0.0920586	−0.00664376
$193$	−12.7511	−0.917843	−0.458921	−	0.888477i	$-0.651764\pi$
$193$	−12.7511	−0.917843	−0.458921	+	0.888477i	$0.651764\pi$
$194$	9.40667	0.675360
$195$	1.53888	0.110201
$196$	0.00511548	0.000365392 0
$197$	−11.6395	−0.829280	−0.414640	−	0.909986i	$-0.636092\pi$
$197$	−11.6395	−0.829280	−0.414640	+	0.909986i	$0.636092\pi$
$198$	1.62271	0.115321
$199$	−9.73478	−0.690080	−0.345040	−	0.938588i	$-0.612135\pi$
$199$	−9.73478	−0.690080	−0.345040	+	0.938588i	$0.612135\pi$
$200$	3.27695	0.231716
$201$	0.744977	0.0525466
$202$	−12.5799	−0.885120
$203$	9.22209	0.647264
$204$	0.549099	0.0384446
$205$	−23.4162	−1.63546
$206$	−10.1310	−0.705858
$207$	20.6014	1.43190
$208$	−5.81038	−0.402877
$209$	0.542435	0.0375210
$210$	−0.700983	−0.0483724
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	0.697997	0.0479386
$213$	0.718156	0.0492072
$214$	−6.56706	−0.448915
$215$	2.53402	0.172819
$216$	0.551572	0.0375297
$217$	−20.1624	−1.36871
$218$	10.4085	0.704951
$219$	0.651820	0.0440459
$220$	−1.56057	−0.105213
$221$	34.6570	2.33128
$222$	−0.284513	−0.0190953
$223$	−18.2905	−1.22482	−0.612411	−	0.790540i	$-0.709800\pi$
$223$	−18.2905	−1.22482	−0.612411	+	0.790540i	$0.709800\pi$
$224$	2.64672	0.176841
$225$	−9.80309	−0.653539
$226$	10.9015	0.725160
$227$	−15.7614	−1.04612	−0.523059	−	0.852296i	$-0.675209\pi$
$227$	−15.7614	−1.04612	−0.523059	+	0.852296i	$0.675209\pi$
$228$	0.0920586	0.00609673
$229$	8.91359	0.589026	0.294513	−	0.955647i	$-0.404842\pi$
$229$	8.91359	0.589026	0.294513	+	0.955647i	$0.404842\pi$
$230$	−19.8125	−1.30640
$231$	0.132166	0.00869588
$232$	3.48435	0.228759
$233$	−11.2475	−0.736849	−0.368425	−	0.929658i	$-0.620103\pi$
$233$	−11.2475	−0.736849	−0.368425	+	0.929658i	$0.620103\pi$
$234$	17.3819	1.13629
$235$	21.2361	1.38529
$236$	3.10936	0.202402
$237$	0.217094	0.0141018
$238$	−15.7868	−1.02331
$239$	6.00199	0.388237	0.194118	−	0.980978i	$-0.437815\pi$
$239$	6.00199	0.388237	0.194118	+	0.980978i	$0.437815\pi$
$240$	−0.264850	−0.0170960
$241$	−6.88941	−0.443786	−0.221893	−	0.975071i	$-0.571224\pi$
$241$	−6.88941	−0.443786	−0.221893	+	0.975071i	$0.571224\pi$
$242$	−10.7058	−0.688193
$243$	−2.47623	−0.158850
$244$	3.67649	0.235363
$245$	0.0147171	0.000940240 0
$246$	0.749281	0.0477724
$247$	5.81038	0.369706
$248$	−7.61790	−0.483737
$249$	0.592128	0.0375246
$250$	−4.95715	−0.313518
$251$	28.2154	1.78094	0.890471	−	0.455041i	$-0.150375\pi$
$251$	28.2154	1.78094	0.890471	+	0.455041i	$0.150375\pi$
$252$	−7.91772	−0.498770
$253$	3.73553	0.234851
$254$	4.79969	0.301159
$255$	1.57974	0.0989273
$256$	1.00000	0.0625000
$257$	−10.5117	−0.655702	−0.327851	−	0.944729i	$-0.606324\pi$
$257$	−10.5117	−0.655702	−0.327851	+	0.944729i	$0.606324\pi$
$258$	−0.0810848	−0.00504812
$259$	8.17986	0.508272
$260$	−16.7163	−1.03670
$261$	−10.4235	−0.645200
$262$	−6.08860	−0.376155
$263$	21.2950	1.31310	0.656552	−	0.754280i	$-0.272014\pi$
$263$	21.2950	1.31310	0.656552	+	0.754280i	$0.272014\pi$
$264$	0.0499358	0.00307333
$265$	2.00812	0.123358
$266$	−2.64672	−0.162281
$267$	−0.364394	−0.0223005
$268$	−8.09242	−0.494323
$269$	−13.4940	−0.822745	−0.411373	−	0.911467i	$-0.634951\pi$
$269$	−13.4940	−0.822745	−0.411373	+	0.911467i	$0.634951\pi$
$270$	1.58685	0.0965729
$271$	6.50735	0.395294	0.197647	−	0.980273i	$-0.436670\pi$
$271$	6.50735	0.395294	0.197647	+	0.980273i	$0.436670\pi$
$272$	−5.96467	−0.361661
$273$	1.41572	0.0856831
$274$	2.56861	0.155175
$275$	−1.77753	−0.107189
$276$	0.633971	0.0381606
$277$	4.96122	0.298091	0.149045	−	0.988830i	$-0.452380\pi$
$277$	4.96122	0.298091	0.149045	+	0.988830i	$0.452380\pi$
$278$	2.34384	0.140574
$279$	22.7891	1.36435
$280$	7.61453	0.455055
$281$	−8.97354	−0.535317	−0.267658	−	0.963514i	$-0.586250\pi$
$281$	−8.97354	−0.535317	−0.267658	+	0.963514i	$0.586250\pi$
$282$	−0.679522	−0.0404649
$283$	15.2547	0.906796	0.453398	−	0.891308i	$-0.350212\pi$
$283$	15.2547	0.906796	0.453398	+	0.891308i	$0.350212\pi$
$284$	−7.80107	−0.462909
$285$	0.264850	0.0156884
$286$	3.15175	0.186367
$287$	−21.5421	−1.27159
$288$	−2.99153	−0.176277
$289$	18.5773	1.09278
$290$	10.0244	0.588651
$291$	−0.865965	−0.0507638
$292$	−7.08049	−0.414354
$293$	24.3035	1.41983	0.709914	−	0.704288i	$-0.248734\pi$
$293$	24.3035	1.41983	0.709914	+	0.704288i	$0.248734\pi$
$294$	−0.000470924 0	−2.74649e−5 0
$295$	8.94554	0.520829
$296$	3.09057	0.179636
$297$	−0.299191	−0.0173609
$298$	−13.0596	−0.756520
$299$	40.0138	2.31406
$300$	−0.301672	−0.0174170
$301$	2.33122	0.134369
$302$	−15.1534	−0.871978
$303$	1.15809	0.0665305
$304$	−1.00000	−0.0573539
$305$	10.5771	0.605645
$306$	17.8435	1.02004
$307$	19.6796	1.12317	0.561586	−	0.827418i	$-0.310191\pi$
$307$	19.6796	1.12317	0.561586	+	0.827418i	$0.310191\pi$
$308$	−1.43567	−0.0818050
$309$	0.932643	0.0530562
$310$	−21.9165	−1.24477
$311$	6.29615	0.357022	0.178511	−	0.983938i	$-0.442872\pi$
$311$	6.29615	0.357022	0.178511	+	0.983938i	$0.442872\pi$
$312$	0.534895	0.0302825
$313$	−15.1556	−0.856643	−0.428322	−	0.903626i	$-0.640895\pi$
$313$	−15.1556	−0.856643	−0.428322	+	0.903626i	$0.640895\pi$
$314$	21.2604	1.19979
$315$	−22.7790	−1.28345
$316$	−2.35822	−0.132660
$317$	5.19447	0.291751	0.145875	−	0.989303i	$-0.453400\pi$
$317$	5.19447	0.291751	0.145875	+	0.989303i	$0.453400\pi$
$318$	−0.0642566	−0.00360333
$319$	−1.89003	−0.105822
$320$	2.87697	0.160827
$321$	0.604555	0.0337430
$322$	−18.2269	−1.01574
$323$	5.96467	0.331883
$324$	8.92380	0.495767
$325$	−19.0403	−1.05617
$326$	15.5887	0.863378
$327$	−0.958190	−0.0529880
$328$	−8.13918	−0.449411
$329$	19.5365	1.07708
$330$	0.143664	0.00790843
$331$	−17.0334	−0.936238	−0.468119	−	0.883665i	$-0.655068\pi$
$331$	−17.0334	−0.936238	−0.468119	+	0.883665i	$0.655068\pi$
$332$	−6.43207	−0.353006
$333$	−9.24551	−0.506651
$334$	17.5498	0.960284
$335$	−23.2817	−1.27201
$336$	−0.243653	−0.0132924
$337$	−14.4821	−0.788889	−0.394445	−	0.918920i	$-0.629063\pi$
$337$	−14.4821	−0.788889	−0.394445	+	0.918920i	$0.629063\pi$
$338$	20.7605	1.12922
$339$	−1.00358	−0.0545070
$340$	−17.1602	−0.930641
$341$	4.13221	0.223772
$342$	2.99153	0.161763
$343$	−18.5135	−0.999634
$344$	0.880796	0.0474893
$345$	1.82391	0.0981963
$346$	23.2044	1.24748
$347$	−10.7978	−0.579658	−0.289829	−	0.957078i	$-0.593598\pi$
$347$	−10.7978	−0.579658	−0.289829	+	0.957078i	$0.593598\pi$
$348$	−0.320765	−0.0171948
$349$	20.8969	1.11859	0.559293	−	0.828970i	$-0.311073\pi$
$349$	20.8969	1.11859	0.559293	+	0.828970i	$0.311073\pi$
$350$	8.67317	0.463601
$351$	−3.20484	−0.171062
$352$	−0.542435	−0.0289119
$353$	−17.1021	−0.910255	−0.455128	−	0.890426i	$-0.650406\pi$
$353$	−17.1021	−0.910255	−0.455128	+	0.890426i	$0.650406\pi$
$354$	−0.286244	−0.0152137
$355$	−22.4435	−1.19117
$356$	3.95828	0.209788
$357$	1.45331	0.0769174
$358$	13.8335	0.731121
$359$	24.6473	1.30083	0.650416	−	0.759578i	$-0.274594\pi$
$359$	24.6473	1.30083	0.650416	+	0.759578i	$0.274594\pi$
$360$	−8.60653	−0.453604
$361$	1.00000	0.0526316
$362$	5.34522	0.280938
$363$	0.985558	0.0517284
$364$	−15.3784	−0.806049
$365$	−20.3703	−1.06623
$366$	−0.338452	−0.0176912
$367$	−3.10543	−0.162102	−0.0810510	−	0.996710i	$-0.525828\pi$
$367$	−3.10543	−0.162102	−0.0810510	+	0.996710i	$0.525828\pi$
$368$	−6.88660	−0.358989
$369$	24.3485	1.26753
$370$	8.89147	0.462245
$371$	1.84740	0.0959122
$372$	0.701293	0.0363603
$373$	−17.8715	−0.925351	−0.462676	−	0.886528i	$-0.653111\pi$
$373$	−17.8715	−0.925351	−0.462676	+	0.886528i	$0.653111\pi$
$374$	3.23544	0.167301
$375$	0.456348	0.0235657
$376$	7.38140	0.380667
$377$	−20.2454	−1.04269
$378$	1.45985	0.0750868
$379$	−35.9048	−1.84430	−0.922152	−	0.386828i	$-0.873571\pi$
$379$	−35.9048	−1.84430	−0.922152	+	0.386828i	$0.873571\pi$
$380$	−2.87697	−0.147585
$381$	−0.441852	−0.0226368
$382$	−0.187305	−0.00958334
$383$	−28.5247	−1.45754	−0.728771	−	0.684757i	$-0.759908\pi$
$383$	−28.5247	−1.45754	−0.728771	+	0.684757i	$0.759908\pi$
$384$	−0.0920586	−0.00469785
$385$	−4.13038	−0.210504
$386$	−12.7511	−0.649013
$387$	−2.63492	−0.133941
$388$	9.40667	0.477552
$389$	−28.1844	−1.42901	−0.714504	−	0.699631i	$-0.753348\pi$
$389$	−28.1844	−1.42901	−0.714504	+	0.699631i	$0.753348\pi$
$390$	1.53888	0.0779241
$391$	41.0763	2.07732
$392$	0.00511548	0.000258371 0
$393$	0.560508	0.0282739
$394$	−11.6395	−0.586389
$395$	−6.78451	−0.341366
$396$	1.62271	0.0815441
$397$	25.8496	1.29735	0.648677	−	0.761064i	$-0.275323\pi$
$397$	25.8496	1.29735	0.648677	+	0.761064i	$0.275323\pi$
$398$	−9.73478	−0.487960
$399$	0.243653	0.0121979
$400$	3.27695	0.163848
$401$	−8.85312	−0.442104	−0.221052	−	0.975262i	$-0.570949\pi$
$401$	−8.85312	−0.442104	−0.221052	+	0.975262i	$0.570949\pi$
$402$	0.744977	0.0371561
$403$	44.2629	2.20489
$404$	−12.5799	−0.625874
$405$	25.6735	1.27573
$406$	9.22209	0.457685
$407$	−1.67643	−0.0830976
$408$	0.549099	0.0271845
$409$	21.6552	1.07078	0.535390	−	0.844605i	$-0.320165\pi$
$409$	21.6552	1.07078	0.535390	+	0.844605i	$0.320165\pi$
$410$	−23.4162	−1.15644
$411$	−0.236463	−0.0116638
$412$	−10.1310	−0.499117
$413$	8.22960	0.404952
$414$	20.6014	1.01251
$415$	−18.5049	−0.908369
$416$	−5.81038	−0.284877
$417$	−0.215770	−0.0105663
$418$	0.542435	0.0265313
$419$	32.5263	1.58902	0.794508	−	0.607254i	$-0.207729\pi$
$419$	32.5263	1.58902	0.794508	+	0.607254i	$0.207729\pi$
$420$	−0.700983	−0.0342045
$421$	17.0950	0.833159	0.416579	−	0.909099i	$-0.363229\pi$
$421$	17.0950	0.833159	0.416579	+	0.909099i	$0.363229\pi$
$422$	1.00000	0.0486792
$423$	−22.0817	−1.07365
$424$	0.697997	0.0338977
$425$	−19.5459	−0.948118
$426$	0.718156	0.0347948
$427$	9.73062	0.470898
$428$	−6.56706	−0.317431
$429$	−0.290146	−0.0140084
$430$	2.53402	0.122201
$431$	−10.9052	−0.525285	−0.262642	−	0.964893i	$-0.584594\pi$
$431$	−10.9052	−0.525285	−0.262642	+	0.964893i	$0.584594\pi$
$432$	0.551572	0.0265375
$433$	−22.1371	−1.06384	−0.531922	−	0.846794i	$-0.678530\pi$
$433$	−22.1371	−1.06384	−0.531922	+	0.846794i	$0.678530\pi$
$434$	−20.1624	−0.967827
$435$	−0.922830	−0.0442463
$436$	10.4085	0.498476
$437$	6.88660	0.329431
$438$	0.651820	0.0311452
$439$	−11.9879	−0.572152	−0.286076	−	0.958207i	$-0.592351\pi$
$439$	−11.9879	−0.572152	−0.286076	+	0.958207i	$0.592351\pi$
$440$	−1.56057	−0.0743972
$441$	−0.0153031	−0.000728719 0
$442$	34.6570	1.64846
$443$	−0.960487	−0.0456341	−0.0228171	−	0.999740i	$-0.507264\pi$
$443$	−0.960487	−0.0456341	−0.0228171	+	0.999740i	$0.507264\pi$
$444$	−0.284513	−0.0135024
$445$	11.3879	0.539836
$446$	−18.2905	−0.866079
$447$	1.20224	0.0568642
$448$	2.64672	0.125046
$449$	−6.42730	−0.303323	−0.151662	−	0.988432i	$-0.548462\pi$
$449$	−6.42730	−0.303323	−0.151662	+	0.988432i	$0.548462\pi$
$450$	−9.80309	−0.462122
$451$	4.41497	0.207893
$452$	10.9015	0.512765
$453$	1.39500	0.0655427
$454$	−15.7614	−0.739718
$455$	−44.2433	−2.07416
$456$	0.0920586	0.00431104
$457$	37.2803	1.74390	0.871950	−	0.489595i	$-0.162855\pi$
$457$	37.2803	1.74390	0.871950	+	0.489595i	$0.162855\pi$
$458$	8.91359	0.416505
$459$	−3.28994	−0.153561
$460$	−19.8125	−0.923764
$461$	20.1292	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$461$	20.1292	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$462$	0.132166	0.00614891
$463$	−39.5151	−1.83642	−0.918211	−	0.396092i	$-0.870366\pi$
$463$	−39.5151	−1.83642	−0.918211	+	0.396092i	$0.870366\pi$
$464$	3.48435	0.161757
$465$	2.01760	0.0935639
$466$	−11.2475	−0.521031
$467$	−17.0751	−0.790139	−0.395070	−	0.918651i	$-0.629280\pi$
$467$	−17.0751	−0.790139	−0.395070	+	0.918651i	$0.629280\pi$
$468$	17.3819	0.803478
$469$	−21.4184	−0.989008
$470$	21.2361	0.979547
$471$	−1.95720	−0.0901831
$472$	3.10936	0.143120
$473$	−0.477774	−0.0219681
$474$	0.217094	0.00997146
$475$	−3.27695	−0.150357
$476$	−15.7868	−0.723587
$477$	−2.08807	−0.0956064
$478$	6.00199	0.274525
$479$	42.9526	1.96255	0.981277	−	0.192604i	$-0.0616934\pi$
$479$	42.9526	1.96255	0.981277	+	0.192604i	$0.0616934\pi$
$480$	−0.264850	−0.0120887
$481$	−17.9574	−0.818785
$482$	−6.88941	−0.313804
$483$	1.67794	0.0763490
$484$	−10.7058	−0.486626
$485$	27.0627	1.22885
$486$	−2.47623	−0.112324
$487$	−20.1515	−0.913150	−0.456575	−	0.889685i	$-0.650924\pi$
$487$	−20.1515	−0.913150	−0.456575	+	0.889685i	$0.650924\pi$
$488$	3.67649	0.166427
$489$	−1.43507	−0.0648962
$490$	0.0147171	0.000664850 0
$491$	24.9429	1.12566	0.562828	−	0.826574i	$-0.309713\pi$
$491$	24.9429	1.12566	0.562828	+	0.826574i	$0.309713\pi$
$492$	0.749281	0.0337802
$493$	−20.7830	−0.936019
$494$	5.81038	0.261421
$495$	4.66848	0.209832
$496$	−7.61790	−0.342054
$497$	−20.6472	−0.926155
$498$	0.592128	0.0265339
$499$	−19.4085	−0.868843	−0.434422	−	0.900710i	$-0.643047\pi$
$499$	−19.4085	−0.868843	−0.434422	+	0.900710i	$0.643047\pi$
$500$	−4.95715	−0.221691
$501$	−1.61561	−0.0721803
$502$	28.2154	1.25932
$503$	−6.80367	−0.303361	−0.151680	−	0.988430i	$-0.548468\pi$
$503$	−6.80367	−0.303361	−0.151680	+	0.988430i	$0.548468\pi$
$504$	−7.91772	−0.352683
$505$	−36.1920	−1.61052
$506$	3.73553	0.166065
$507$	−1.91118	−0.0848786
$508$	4.79969	0.212952
$509$	−27.3386	−1.21176	−0.605881	−	0.795556i	$-0.707179\pi$
$509$	−27.3386	−1.21176	−0.605881	+	0.795556i	$0.707179\pi$
$510$	1.57974	0.0699521
$511$	−18.7401	−0.829011
$512$	1.00000	0.0441942
$513$	−0.551572	−0.0243525
$514$	−10.5117	−0.463651
$515$	−29.1465	−1.28435
$516$	−0.0810848	−0.00356956
$517$	−4.00393	−0.176093
$518$	8.17986	0.359402
$519$	−2.13617	−0.0937674
$520$	−16.7163	−0.733057
$521$	−9.12509	−0.399777	−0.199889	−	0.979819i	$-0.564058\pi$
$521$	−9.12509	−0.399777	−0.199889	+	0.979819i	$0.564058\pi$
$522$	−10.4235	−0.456225
$523$	38.9497	1.70315	0.851577	−	0.524230i	$-0.175647\pi$
$523$	38.9497	1.70315	0.851577	+	0.524230i	$0.175647\pi$
$524$	−6.08860	−0.265982
$525$	−0.798440	−0.0348468
$526$	21.2950	0.928505
$527$	45.4382	1.97932
$528$	0.0499358	0.00217318
$529$	24.4253	1.06197
$530$	2.00812	0.0872270
$531$	−9.30173	−0.403661
$532$	−2.64672	−0.114750
$533$	47.2917	2.04843
$534$	−0.364394	−0.0157689
$535$	−18.8932	−0.816826
$536$	−8.09242	−0.349539
$537$	−1.27349	−0.0549551
$538$	−13.4940	−0.581769
$539$	−0.00277481	−0.000119520 0
$540$	1.58685	0.0682873
$541$	3.76901	0.162042	0.0810211	−	0.996712i	$-0.474182\pi$
$541$	3.76901	0.162042	0.0810211	+	0.996712i	$0.474182\pi$
$542$	6.50735	0.279515
$543$	−0.492073	−0.0211169
$544$	−5.96467	−0.255733
$545$	29.9449	1.28270
$546$	1.41572	0.0605871
$547$	1.54075	0.0658778	0.0329389	−	0.999457i	$-0.489513\pi$
$547$	1.54075	0.0658778	0.0329389	+	0.999457i	$0.489513\pi$
$548$	2.56861	0.109726
$549$	−10.9983	−0.469396
$550$	−1.77753	−0.0757943
$551$	−3.48435	−0.148438
$552$	0.633971	0.0269836
$553$	−6.24153	−0.265417
$554$	4.96122	0.210782
$555$	−0.818536	−0.0347449
$556$	2.34384	0.0994008
$557$	−27.0430	−1.14585	−0.572925	−	0.819608i	$-0.694191\pi$
$557$	−27.0430	−1.14585	−0.572925	+	0.819608i	$0.694191\pi$
$558$	22.7891	0.964741
$559$	−5.11776	−0.216458
$560$	7.61453	0.321772
$561$	−0.297850	−0.0125753
$562$	−8.97354	−0.378526
$563$	12.6035	0.531174	0.265587	−	0.964087i	$-0.414434\pi$
$563$	12.6035	0.531174	0.265587	+	0.964087i	$0.414434\pi$
$564$	−0.679522	−0.0286130
$565$	31.3634	1.31947
$566$	15.2547	0.641201
$567$	23.6188	0.991895
$568$	−7.80107	−0.327326
$569$	−10.6185	−0.445153	−0.222576	−	0.974915i	$-0.571447\pi$
$569$	−10.6185	−0.445153	−0.222576	+	0.974915i	$0.571447\pi$
$570$	0.264850	0.0110933
$571$	−32.4370	−1.35745	−0.678724	−	0.734393i	$-0.737467\pi$
$571$	−32.4370	−1.35745	−0.678724	+	0.734393i	$0.737467\pi$
$572$	3.15175	0.131781
$573$	0.0172430	0.000720337 0
$574$	−21.5421	−0.899150
$575$	−22.5671	−0.941112
$576$	−2.99153	−0.124647
$577$	−47.5213	−1.97834	−0.989169	−	0.146781i	$-0.953109\pi$
$577$	−47.5213	−1.97834	−0.989169	+	0.146781i	$0.953109\pi$
$578$	18.5773	0.772713
$579$	1.17385	0.0487834
$580$	10.0244	0.416239
$581$	−17.0239	−0.706270
$582$	−0.865965	−0.0358954
$583$	−0.378618	−0.0156807
$584$	−7.08049	−0.292993
$585$	50.0072	2.06754
$586$	24.3035	1.00397
$587$	31.2702	1.29066	0.645329	−	0.763904i	$-0.276720\pi$
$587$	31.2702	1.29066	0.645329	+	0.763904i	$0.276720\pi$
$588$	−0.000470924 0	−1.94206e−5 0
$589$	7.61790	0.313890
$590$	8.94554	0.368282
$591$	1.07152	0.0440763
$592$	3.09057	0.127022
$593$	5.33677	0.219155	0.109577	−	0.993978i	$-0.465050\pi$
$593$	5.33677	0.219155	0.109577	+	0.993978i	$0.465050\pi$
$594$	−0.299191	−0.0122760
$595$	−45.4181	−1.86196
$596$	−13.0596	−0.534940
$597$	0.896170	0.0366778
$598$	40.0138	1.63628
$599$	−10.4015	−0.424994	−0.212497	−	0.977162i	$-0.568159\pi$
$599$	−10.4015	−0.424994	−0.212497	+	0.977162i	$0.568159\pi$
$600$	−0.301672	−0.0123157
$601$	6.98711	0.285010	0.142505	−	0.989794i	$-0.454484\pi$
$601$	6.98711	0.285010	0.142505	+	0.989794i	$0.454484\pi$
$602$	2.33122	0.0950133
$603$	24.2087	0.985854
$604$	−15.1534	−0.616581
$605$	−30.8002	−1.25220
$606$	1.15809	0.0470442
$607$	−38.8289	−1.57602	−0.788009	−	0.615664i	$-0.788888\pi$
$607$	−38.8289	−1.57602	−0.788009	+	0.615664i	$0.788888\pi$
$608$	−1.00000	−0.0405554
$609$	−0.848973	−0.0344021
$610$	10.5771	0.428256
$611$	−42.8888	−1.73509
$612$	17.8435	0.721279
$613$	36.1291	1.45924	0.729620	−	0.683852i	$-0.239697\pi$
$613$	36.1291	1.45924	0.729620	+	0.683852i	$0.239697\pi$
$614$	19.6796	0.794203
$615$	2.15566	0.0869246
$616$	−1.43567	−0.0578448
$617$	10.6105	0.427162	0.213581	−	0.976925i	$-0.431487\pi$
$617$	10.6105	0.427162	0.213581	+	0.976925i	$0.431487\pi$
$618$	0.932643	0.0375164
$619$	9.01687	0.362419	0.181209	−	0.983445i	$-0.441999\pi$
$619$	9.01687	0.362419	0.181209	+	0.983445i	$0.441999\pi$
$620$	−21.9165	−0.880186
$621$	−3.79845	−0.152427
$622$	6.29615	0.252452
$623$	10.4765	0.419730
$624$	0.534895	0.0214130
$625$	−30.6463	−1.22585
$626$	−15.1556	−0.605738
$627$	−0.0499358	−0.00199424
$628$	21.2604	0.848381
$629$	−18.4342	−0.735020
$630$	−22.7790	−0.907539
$631$	−5.85991	−0.233279	−0.116640	−	0.993174i	$-0.537212\pi$
$631$	−5.85991	−0.233279	−0.116640	+	0.993174i	$0.537212\pi$
$632$	−2.35822	−0.0938048
$633$	−0.0920586	−0.00365900
$634$	5.19447	0.206299
$635$	13.8085	0.547976
$636$	−0.0642566	−0.00254794
$637$	−0.0297229	−0.00117766
$638$	−1.89003	−0.0748271
$639$	23.3371	0.923202
$640$	2.87697	0.113722
$641$	−26.6199	−1.05142	−0.525712	−	0.850662i	$-0.676201\pi$
$641$	−26.6199	−1.05142	−0.525712	+	0.850662i	$0.676201\pi$
$642$	0.604555	0.0238599
$643$	0.913113	0.0360097	0.0180048	−	0.999838i	$-0.494269\pi$
$643$	0.913113	0.0360097	0.0180048	+	0.999838i	$0.494269\pi$
$644$	−18.2269	−0.718240
$645$	−0.233279	−0.00918533
$646$	5.96467	0.234677
$647$	−1.80404	−0.0709242	−0.0354621	−	0.999371i	$-0.511290\pi$
$647$	−1.80404	−0.0709242	−0.0354621	+	0.999371i	$0.511290\pi$
$648$	8.92380	0.350560
$649$	−1.68663	−0.0662058
$650$	−19.0403	−0.746824
$651$	1.85612	0.0727472
$652$	15.5887	0.610500
$653$	−37.8948	−1.48294	−0.741470	−	0.670986i	$-0.765871\pi$
$653$	−37.8948	−1.48294	−0.741470	+	0.670986i	$0.765871\pi$
$654$	−0.958190	−0.0374682
$655$	−17.5167	−0.684434
$656$	−8.13918	−0.317781
$657$	21.1815	0.826367
$658$	19.5365	0.761612
$659$	37.9217	1.47722	0.738611	−	0.674132i	$-0.235482\pi$
$659$	37.9217	1.47722	0.738611	+	0.674132i	$0.235482\pi$
$660$	0.143664	0.00559210
$661$	48.5060	1.88667	0.943333	−	0.331847i	$-0.107672\pi$
$661$	48.5060	1.88667	0.943333	+	0.331847i	$0.107672\pi$
$662$	−17.0334	−0.662020
$663$	−3.19047	−0.123908
$664$	−6.43207	−0.249613
$665$	−7.61453	−0.295279
$666$	−9.24551	−0.358256
$667$	−23.9953	−0.929103
$668$	17.5498	0.679024
$669$	1.68380	0.0650993
$670$	−23.2817	−0.899449
$671$	−1.99425	−0.0769873
$672$	−0.243653	−0.00939913
$673$	−4.68425	−0.180565	−0.0902823	−	0.995916i	$-0.528777\pi$
$673$	−4.68425	−0.180565	−0.0902823	+	0.995916i	$0.528777\pi$
$674$	−14.4821	−0.557829
$675$	1.80747	0.0695697
$676$	20.7605	0.798481
$677$	−30.3838	−1.16774	−0.583872	−	0.811846i	$-0.698463\pi$
$677$	−30.3838	−1.16774	−0.583872	+	0.811846i	$0.698463\pi$
$678$	−1.00358	−0.0385423
$679$	24.8968	0.955452
$680$	−17.1602	−0.658063
$681$	1.45097	0.0556013
$682$	4.13221	0.158230
$683$	−17.6202	−0.674217	−0.337108	−	0.941466i	$-0.609449\pi$
$683$	−17.6202	−0.674217	−0.337108	+	0.941466i	$0.609449\pi$
$684$	2.99153	0.114384
$685$	7.38981	0.282350
$686$	−18.5135	−0.706848
$687$	−0.820573	−0.0313068
$688$	0.880796	0.0335800
$689$	−4.05563	−0.154507
$690$	1.82391	0.0694353
$691$	24.9352	0.948578	0.474289	−	0.880369i	$-0.342705\pi$
$691$	24.9352	0.948578	0.474289	+	0.880369i	$0.342705\pi$
$692$	23.2044	0.882100
$693$	4.29485	0.163148
$694$	−10.7978	−0.409880
$695$	6.74315	0.255782
$696$	−0.320765	−0.0121585
$697$	48.5475	1.83887
$698$	20.8969	0.790960
$699$	1.03543	0.0391636
$700$	8.67317	0.327815
$701$	−15.1106	−0.570721	−0.285361	−	0.958420i	$-0.592113\pi$
$701$	−15.1106	−0.570721	−0.285361	+	0.958420i	$0.592113\pi$
$702$	−3.20484	−0.120959
$703$	−3.09057	−0.116563
$704$	−0.542435	−0.0204438
$705$	−1.95496	−0.0736282
$706$	−17.1021	−0.643648
$707$	−33.2955	−1.25221
$708$	−0.286244	−0.0107577
$709$	−47.3648	−1.77882	−0.889410	−	0.457110i	$-0.848885\pi$
$709$	−47.3648	−1.77882	−0.889410	+	0.457110i	$0.848885\pi$
$710$	−22.4435	−0.842288
$711$	7.05466	0.264570
$712$	3.95828	0.148343
$713$	52.4614	1.96469
$714$	1.45331	0.0543888
$715$	9.06749	0.339105
$716$	13.8335	0.516981
$717$	−0.552535	−0.0206348
$718$	24.6473	0.919827
$719$	−28.0067	−1.04447	−0.522236	−	0.852801i	$-0.674902\pi$
$719$	−28.0067	−1.04447	−0.522236	+	0.852801i	$0.674902\pi$
$720$	−8.60653	−0.320746
$721$	−26.8138	−0.998599
$722$	1.00000	0.0372161
$723$	0.634229	0.0235872
$724$	5.34522	0.198653
$725$	11.4181	0.424056
$726$	0.985558	0.0365775
$727$	−15.2525	−0.565685	−0.282842	−	0.959166i	$-0.591277\pi$
$727$	−15.2525	−0.565685	−0.282842	+	0.959166i	$0.591277\pi$
$728$	−15.3784	−0.569963
$729$	−26.5434	−0.983090
$730$	−20.3703	−0.753940
$731$	−5.25365	−0.194313
$732$	−0.338452	−0.0125096
$733$	41.0403	1.51586	0.757928	−	0.652338i	$-0.226212\pi$
$733$	41.0403	1.51586	0.757928	+	0.652338i	$0.226212\pi$
$734$	−3.10543	−0.114623
$735$	−0.00135483	−4.99738e−5 0
$736$	−6.88660	−0.253843
$737$	4.38961	0.161693
$738$	24.3485	0.896282
$739$	25.6226	0.942544	0.471272	−	0.881988i	$-0.343795\pi$
$739$	25.6226	0.942544	0.471272	+	0.881988i	$0.343795\pi$
$740$	8.89147	0.326857
$741$	−0.534895	−0.0196499
$742$	1.84740	0.0678202
$743$	−1.97392	−0.0724162	−0.0362081	−	0.999344i	$-0.511528\pi$
$743$	−1.97392	−0.0724162	−0.0362081	+	0.999344i	$0.511528\pi$
$744$	0.701293	0.0257106
$745$	−37.5719	−1.37653
$746$	−17.8715	−0.654322
$747$	19.2417	0.704017
$748$	3.23544	0.118300
$749$	−17.3812	−0.635094
$750$	0.456348	0.0166635
$751$	−18.8743	−0.688732	−0.344366	−	0.938836i	$-0.611906\pi$
$751$	−18.8743	−0.688732	−0.344366	+	0.938836i	$0.611906\pi$
$752$	7.38140	0.269172
$753$	−2.59747	−0.0946571
$754$	−20.2454	−0.737294
$755$	−43.5957	−1.58661
$756$	1.45985	0.0530944
$757$	−38.8049	−1.41039	−0.705195	−	0.709014i	$-0.749140\pi$
$757$	−38.8049	−1.41039	−0.705195	+	0.709014i	$0.749140\pi$
$758$	−35.9048	−1.30412
$759$	−0.343888	−0.0124823
$760$	−2.87697	−0.104359
$761$	−50.0165	−1.81310	−0.906549	−	0.422101i	$-0.861293\pi$
$761$	−50.0165	−1.81310	−0.906549	+	0.422101i	$0.861293\pi$
$762$	−0.441852	−0.0160066
$763$	27.5483	0.997316
$764$	−0.187305	−0.00677645
$765$	51.3351	1.85602
$766$	−28.5247	−1.03064
$767$	−18.0666	−0.652346
$768$	−0.0920586	−0.00332188
$769$	3.85431	0.138990	0.0694950	−	0.997582i	$-0.477861\pi$
$769$	3.85431	0.138990	0.0694950	+	0.997582i	$0.477861\pi$
$770$	−4.13038	−0.148849
$771$	0.967693	0.0348506
$772$	−12.7511	−0.458921
$773$	3.57679	0.128648	0.0643240	−	0.997929i	$-0.479511\pi$
$773$	3.57679	0.128648	0.0643240	+	0.997929i	$0.479511\pi$
$774$	−2.63492	−0.0947103
$775$	−24.9635	−0.896715
$776$	9.40667	0.337680
$777$	−0.753026	−0.0270147
$778$	−28.1844	−1.01046
$779$	8.13918	0.291616
$780$	1.53888	0.0551007
$781$	4.23157	0.151418
$782$	41.0763	1.46889
$783$	1.92187	0.0686820
$784$	0.00511548	0.000182696 0
$785$	61.1655	2.18309
$786$	0.560508	0.0199926
$787$	−11.4932	−0.409690	−0.204845	−	0.978794i	$-0.565669\pi$
$787$	−11.4932	−0.409690	−0.204845	+	0.978794i	$0.565669\pi$
$788$	−11.6395	−0.414640
$789$	−1.96039	−0.0697916
$790$	−6.78451	−0.241382
$791$	28.8533	1.02591
$792$	1.62271	0.0576604
$793$	−21.3618	−0.758579
$794$	25.8496	0.917368
$795$	−0.184864	−0.00655646
$796$	−9.73478	−0.345040
$797$	−38.3398	−1.35806	−0.679032	−	0.734109i	$-0.737600\pi$
$797$	−38.3398	−1.35806	−0.679032	+	0.734109i	$0.737600\pi$
$798$	0.243653	0.00862523
$799$	−44.0276	−1.55759
$800$	3.27695	0.115858
$801$	−11.8413	−0.418392
$802$	−8.85312	−0.312614
$803$	3.84070	0.135535
$804$	0.744977	0.0262733
$805$	−52.4382	−1.84820
$806$	44.2629	1.55909
$807$	1.24224	0.0437290
$808$	−12.5799	−0.442560
$809$	−10.2595	−0.360704	−0.180352	−	0.983602i	$-0.557724\pi$
$809$	−10.2595	−0.360704	−0.180352	+	0.983602i	$0.557724\pi$
$810$	25.6735	0.902075
$811$	−2.12295	−0.0745469	−0.0372734	−	0.999305i	$-0.511867\pi$
$811$	−2.12295	−0.0745469	−0.0372734	+	0.999305i	$0.511867\pi$
$812$	9.22209	0.323632
$813$	−0.599058	−0.0210099
$814$	−1.67643	−0.0587589
$815$	44.8482	1.57096
$816$	0.549099	0.0192223
$817$	−0.880796	−0.0308151
$818$	21.6552	0.757155
$819$	46.0050	1.60754
$820$	−23.4162	−0.817728
$821$	40.8475	1.42559	0.712794	−	0.701374i	$-0.247430\pi$
$821$	40.8475	1.42559	0.712794	+	0.701374i	$0.247430\pi$
$822$	−0.236463	−0.00824758
$823$	10.4746	0.365120	0.182560	−	0.983195i	$-0.441562\pi$
$823$	10.4746	0.365120	0.182560	+	0.983195i	$0.441562\pi$
$824$	−10.1310	−0.352929
$825$	0.163637	0.00569712
$826$	8.22960	0.286344
$827$	6.97944	0.242699	0.121350	−	0.992610i	$-0.461278\pi$
$827$	6.97944	0.242699	0.121350	+	0.992610i	$0.461278\pi$
$828$	20.6014	0.715949
$829$	−37.0566	−1.28703	−0.643514	−	0.765434i	$-0.722524\pi$
$829$	−37.0566	−1.28703	−0.643514	+	0.765434i	$0.722524\pi$
$830$	−18.5049	−0.642314
$831$	−0.456723	−0.0158435
$832$	−5.81038	−0.201439
$833$	−0.0305122	−0.00105718
$834$	−0.215770	−0.00747152
$835$	50.4903	1.74729
$836$	0.542435	0.0187605
$837$	−4.20181	−0.145236
$838$	32.5263	1.12360
$839$	−3.89170	−0.134357	−0.0671783	−	0.997741i	$-0.521400\pi$
$839$	−3.89170	−0.134357	−0.0671783	+	0.997741i	$0.521400\pi$
$840$	−0.700983	−0.0241862
$841$	−16.8593	−0.581355
$842$	17.0950	0.589132
$843$	0.826092	0.0284521
$844$	1.00000	0.0344214
$845$	59.7273	2.05468
$846$	−22.0817	−0.759183
$847$	−28.3351	−0.973607
$848$	0.697997	0.0239693
$849$	−1.40432	−0.0481962
$850$	−19.5459	−0.670421
$851$	−21.2835	−0.729589
$852$	0.718156	0.0246036
$853$	−16.3741	−0.560639	−0.280319	−	0.959907i	$-0.590440\pi$
$853$	−16.3741	−0.560639	−0.280319	+	0.959907i	$0.590440\pi$
$854$	9.73062	0.332975
$855$	8.60653	0.294337
$856$	−6.56706	−0.224458
$857$	−5.28223	−0.180437	−0.0902187	−	0.995922i	$-0.528757\pi$
$857$	−5.28223	−0.180437	−0.0902187	+	0.995922i	$0.528757\pi$
$858$	−0.290146	−0.00990541
$859$	24.5565	0.837858	0.418929	−	0.908019i	$-0.362406\pi$
$859$	24.5565	0.837858	0.418929	+	0.908019i	$0.362406\pi$
$860$	2.53402	0.0864094
$861$	1.98314	0.0675851
$862$	−10.9052	−0.371432
$863$	−28.8156	−0.980895	−0.490448	−	0.871471i	$-0.663167\pi$
$863$	−28.8156	−0.980895	−0.490448	+	0.871471i	$0.663167\pi$
$864$	0.551572	0.0187648
$865$	66.7585	2.26986
$866$	−22.1371	−0.752251
$867$	−1.71020	−0.0580814
$868$	−20.1624	−0.684357
$869$	1.27918	0.0433931
$870$	−0.922830	−0.0312869
$871$	47.0200	1.59321
$872$	10.4085	0.352476
$873$	−28.1403	−0.952405
$874$	6.88660	0.232943
$875$	−13.1202	−0.443543
$876$	0.651820	0.0220230
$877$	−32.8577	−1.10953	−0.554763	−	0.832008i	$-0.687191\pi$
$877$	−32.8577	−1.10953	−0.554763	+	0.832008i	$0.687191\pi$
$878$	−11.9879	−0.404573
$879$	−2.23735	−0.0754640
$880$	−1.56057	−0.0526067
$881$	−5.90571	−0.198968	−0.0994842	−	0.995039i	$-0.531719\pi$
$881$	−5.90571	−0.198968	−0.0994842	+	0.995039i	$0.531719\pi$
$882$	−0.0153031	−0.000515282 0
$883$	36.6575	1.23362	0.616812	−	0.787111i	$-0.288424\pi$
$883$	36.6575	1.23362	0.616812	+	0.787111i	$0.288424\pi$
$884$	34.6570	1.16564
$885$	−0.823514	−0.0276821
$886$	−0.960487	−0.0322682
$887$	−2.94702	−0.0989513	−0.0494756	−	0.998775i	$-0.515755\pi$
$887$	−2.94702	−0.0989513	−0.0494756	+	0.998775i	$0.515755\pi$
$888$	−0.284513	−0.00954764
$889$	12.7034	0.426059
$890$	11.3879	0.381722
$891$	−4.84058	−0.162165
$892$	−18.2905	−0.612411
$893$	−7.38140	−0.247009
$894$	1.20224	0.0402091
$895$	39.7985	1.33032
$896$	2.64672	0.0884206
$897$	−3.68361	−0.122992
$898$	−6.42730	−0.214482
$899$	−26.5434	−0.885273
$900$	−9.80309	−0.326770
$901$	−4.16332	−0.138700
$902$	4.41497	0.147002
$903$	−0.214609	−0.00714173
$904$	10.9015	0.362580
$905$	15.3780	0.511183
$906$	1.39500	0.0463457
$907$	−1.81441	−0.0602464	−0.0301232	−	0.999546i	$-0.509590\pi$
$907$	−1.81441	−0.0602464	−0.0301232	+	0.999546i	$0.509590\pi$
$908$	−15.7614	−0.523059
$909$	37.6331	1.24821
$910$	−44.2433	−1.46665
$911$	26.5697	0.880293	0.440146	−	0.897926i	$-0.354927\pi$
$911$	26.5697	0.880293	0.440146	+	0.897926i	$0.354927\pi$
$912$	0.0920586	0.00304837
$913$	3.48898	0.115468
$914$	37.2803	1.23312
$915$	−0.973717	−0.0321901
$916$	8.91359	0.294513
$917$	−16.1148	−0.532157
$918$	−3.28994	−0.108584
$919$	3.56472	0.117589	0.0587946	−	0.998270i	$-0.481274\pi$
$919$	3.56472	0.117589	0.0587946	+	0.998270i	$0.481274\pi$
$920$	−19.8125	−0.653200
$921$	−1.81167	−0.0596967
$922$	20.1292	0.662919
$923$	45.3272	1.49196
$924$	0.132166	0.00434794
$925$	10.1276	0.332995
$926$	−39.5151	−1.29855
$927$	30.3071	0.995414
$928$	3.48435	0.114379
$929$	−9.81585	−0.322048	−0.161024	−	0.986951i	$-0.551480\pi$
$929$	−9.81585	−0.322048	−0.161024	+	0.986951i	$0.551480\pi$
$930$	2.01760	0.0661597
$931$	−0.00511548	−0.000167653 0
$932$	−11.2475	−0.368425
$933$	−0.579615	−0.0189757
$934$	−17.0751	−0.558713
$935$	9.30827	0.304413
$936$	17.3819	0.568145
$937$	43.7730	1.43000	0.715001	−	0.699123i	$-0.246426\pi$
$937$	43.7730	1.43000	0.715001	+	0.699123i	$0.246426\pi$
$938$	−21.4184	−0.699334
$939$	1.39520	0.0455306
$940$	21.2361	0.692644
$941$	−13.7896	−0.449527	−0.224763	−	0.974413i	$-0.572161\pi$
$941$	−13.7896	−0.449527	−0.224763	+	0.974413i	$0.572161\pi$
$942$	−1.95720	−0.0637691
$943$	56.0512	1.82528
$944$	3.10936	0.101201
$945$	4.19996	0.136625
$946$	−0.477774	−0.0155338
$947$	14.0991	0.458158	0.229079	−	0.973408i	$-0.426429\pi$
$947$	14.0991	0.458158	0.229079	+	0.973408i	$0.426429\pi$
$948$	0.217094	0.00705089
$949$	41.1403	1.33547
$950$	−3.27695	−0.106318
$951$	−0.478196	−0.0155066
$952$	−15.7868	−0.511653
$953$	−30.9245	−1.00174	−0.500871	−	0.865522i	$-0.666987\pi$
$953$	−30.9245	−1.00174	−0.500871	+	0.865522i	$0.666987\pi$
$954$	−2.08807	−0.0676039
$955$	−0.538870	−0.0174374
$956$	6.00199	0.194118
$957$	0.173994	0.00562442
$958$	42.9526	1.38773
$959$	6.79838	0.219531
$960$	−0.264850	−0.00854799
$961$	27.0323	0.872011
$962$	−17.9574	−0.578969
$963$	19.6455	0.633069
$964$	−6.88941	−0.221893
$965$	−36.6845	−1.18091
$966$	1.67794	0.0539869
$967$	32.5347	1.04624	0.523122	−	0.852258i	$-0.324767\pi$
$967$	32.5347	1.04624	0.523122	+	0.852258i	$0.324767\pi$
$968$	−10.7058	−0.344096
$969$	−0.549099	−0.0176396
$970$	27.0627	0.868931
$971$	33.8716	1.08699	0.543496	−	0.839412i	$-0.317100\pi$
$971$	33.8716	1.08699	0.543496	+	0.839412i	$0.317100\pi$
$972$	−2.47623	−0.0794250
$973$	6.20347	0.198874
$974$	−20.1515	−0.645694
$975$	1.75283	0.0561354
$976$	3.67649	0.117681
$977$	20.0596	0.641763	0.320882	−	0.947119i	$-0.396021\pi$
$977$	20.0596	0.641763	0.320882	+	0.947119i	$0.396021\pi$
$978$	−1.43507	−0.0458886
$979$	−2.14711	−0.0686219
$980$	0.0147171	0.000470120 0
$981$	−31.1372	−0.994135
$982$	24.9429	0.795958
$983$	−7.68278	−0.245043	−0.122521	−	0.992466i	$-0.539098\pi$
$983$	−7.68278	−0.245043	−0.122521	+	0.992466i	$0.539098\pi$
$984$	0.749281	0.0238862
$985$	−33.4865	−1.06697
$986$	−20.7830	−0.661866
$987$	−1.79850	−0.0572470
$988$	5.81038	0.184853
$989$	−6.06569	−0.192878
$990$	4.66848	0.148374
$991$	22.4711	0.713819	0.356910	−	0.934139i	$-0.383830\pi$
$991$	22.4711	0.713819	0.356910	+	0.934139i	$0.383830\pi$
$992$	−7.61790	−0.241868
$993$	1.56807	0.0497611
$994$	−20.6472	−0.654891
$995$	−28.0067	−0.887871
$996$	0.592128	0.0187623
$997$	−0.969289	−0.0306977	−0.0153488	−	0.999882i	$-0.504886\pi$
$997$	−0.969289	−0.0306977	−0.0153488	+	0.999882i	$0.504886\pi$
$998$	−19.4085	−0.614365
$999$	1.70467	0.0539333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.17	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.17	✓	32	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.0920586 q^{3} +1.00000 q^{4} +2.87697 q^{5} -0.0920586 q^{6} +2.64672 q^{7} +1.00000 q^{8} -2.99153 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.0920586 q^{3} +1.00000 q^{4} +2.87697 q^{5} -0.0920586 q^{6} +2.64672 q^{7} +1.00000 q^{8} -2.99153 q^{9} +2.87697 q^{10} -0.542435 q^{11} -0.0920586 q^{12} -5.81038 q^{13} +2.64672 q^{14} -0.264850 q^{15} +1.00000 q^{16} -5.96467 q^{17} -2.99153 q^{18} -1.00000 q^{19} +2.87697 q^{20} -0.243653 q^{21} -0.542435 q^{22} -6.88660 q^{23} -0.0920586 q^{24} +3.27695 q^{25} -5.81038 q^{26} +0.551572 q^{27} +2.64672 q^{28} +3.48435 q^{29} -0.264850 q^{30} -7.61790 q^{31} +1.00000 q^{32} +0.0499358 q^{33} -5.96467 q^{34} +7.61453 q^{35} -2.99153 q^{36} +3.09057 q^{37} -1.00000 q^{38} +0.534895 q^{39} +2.87697 q^{40} -8.13918 q^{41} -0.243653 q^{42} +0.880796 q^{43} -0.542435 q^{44} -8.60653 q^{45} -6.88660 q^{46} +7.38140 q^{47} -0.0920586 q^{48} +0.00511548 q^{49} +3.27695 q^{50} +0.549099 q^{51} -5.81038 q^{52} +0.697997 q^{53} +0.551572 q^{54} -1.56057 q^{55} +2.64672 q^{56} +0.0920586 q^{57} +3.48435 q^{58} +3.10936 q^{59} -0.264850 q^{60} +3.67649 q^{61} -7.61790 q^{62} -7.91772 q^{63} +1.00000 q^{64} -16.7163 q^{65} +0.0499358 q^{66} -8.09242 q^{67} -5.96467 q^{68} +0.633971 q^{69} +7.61453 q^{70} -7.80107 q^{71} -2.99153 q^{72} -7.08049 q^{73} +3.09057 q^{74} -0.301672 q^{75} -1.00000 q^{76} -1.43567 q^{77} +0.534895 q^{78} -2.35822 q^{79} +2.87697 q^{80} +8.92380 q^{81} -8.13918 q^{82} -6.43207 q^{83} -0.243653 q^{84} -17.1602 q^{85} +0.880796 q^{86} -0.320765 q^{87} -0.542435 q^{88} +3.95828 q^{89} -8.60653 q^{90} -15.3784 q^{91} -6.88660 q^{92} +0.701293 q^{93} +7.38140 q^{94} -2.87697 q^{95} -0.0920586 q^{96} +9.40667 q^{97} +0.00511548 q^{98} +1.62271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

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