LMFDB - Embedded newform 8018.2.a.g.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:	$34$
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.129854 q^{3} +1.00000 q^{4} +1.90646 q^{5} +0.129854 q^{6} -0.0260326 q^{7} -1.00000 q^{8} -2.98314 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.129854 q^{3} +1.00000 q^{4} +1.90646 q^{5} +0.129854 q^{6} -0.0260326 q^{7} -1.00000 q^{8} -2.98314 q^{9} -1.90646 q^{10} +2.55961 q^{11} -0.129854 q^{12} -4.06204 q^{13} +0.0260326 q^{14} -0.247562 q^{15} +1.00000 q^{16} -4.11815 q^{17} +2.98314 q^{18} +1.00000 q^{19} +1.90646 q^{20} +0.00338044 q^{21} -2.55961 q^{22} +3.49020 q^{23} +0.129854 q^{24} -1.36541 q^{25} +4.06204 q^{26} +0.776935 q^{27} -0.0260326 q^{28} -4.54364 q^{29} +0.247562 q^{30} +4.14167 q^{31} -1.00000 q^{32} -0.332376 q^{33} +4.11815 q^{34} -0.0496300 q^{35} -2.98314 q^{36} +9.52484 q^{37} -1.00000 q^{38} +0.527473 q^{39} -1.90646 q^{40} +6.26253 q^{41} -0.00338044 q^{42} -3.53186 q^{43} +2.55961 q^{44} -5.68723 q^{45} -3.49020 q^{46} +4.46347 q^{47} -0.129854 q^{48} -6.99932 q^{49} +1.36541 q^{50} +0.534759 q^{51} -4.06204 q^{52} -11.6139 q^{53} -0.776935 q^{54} +4.87979 q^{55} +0.0260326 q^{56} -0.129854 q^{57} +4.54364 q^{58} +3.30491 q^{59} -0.247562 q^{60} +5.56733 q^{61} -4.14167 q^{62} +0.0776587 q^{63} +1.00000 q^{64} -7.74412 q^{65} +0.332376 q^{66} +3.69793 q^{67} -4.11815 q^{68} -0.453217 q^{69} +0.0496300 q^{70} +10.6752 q^{71} +2.98314 q^{72} -6.37745 q^{73} -9.52484 q^{74} +0.177304 q^{75} +1.00000 q^{76} -0.0666331 q^{77} -0.527473 q^{78} +17.2377 q^{79} +1.90646 q^{80} +8.84853 q^{81} -6.26253 q^{82} +5.79776 q^{83} +0.00338044 q^{84} -7.85110 q^{85} +3.53186 q^{86} +0.590011 q^{87} -2.55961 q^{88} -16.4227 q^{89} +5.68723 q^{90} +0.105745 q^{91} +3.49020 q^{92} -0.537813 q^{93} -4.46347 q^{94} +1.90646 q^{95} +0.129854 q^{96} -16.7557 q^{97} +6.99932 q^{98} -7.63566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * 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
$3$	−0.129854	−0.0749713	−0.0374857	−	0.999297i	$-0.511935\pi$
$3$	−0.129854	−0.0749713	−0.0374857	+	0.999297i	$0.511935\pi$
$4$	1.00000	0.500000
$5$	1.90646	0.852595	0.426298	−	0.904583i	$-0.359818\pi$
$5$	1.90646	0.852595	0.426298	+	0.904583i	$0.359818\pi$
$6$	0.129854	0.0530127
$7$	−0.0260326	−0.00983938	−0.00491969	−	0.999988i	$-0.501566\pi$
$7$	−0.0260326	−0.00983938	−0.00491969	+	0.999988i	$0.501566\pi$
$8$	−1.00000	−0.353553
$9$	−2.98314	−0.994379
$10$	−1.90646	−0.602876
$11$	2.55961	0.771750	0.385875	−	0.922551i	$-0.373900\pi$
$11$	2.55961	0.771750	0.385875	+	0.922551i	$0.373900\pi$
$12$	−0.129854	−0.0374857
$13$	−4.06204	−1.12661	−0.563303	−	0.826250i	$-0.690470\pi$
$13$	−4.06204	−1.12661	−0.563303	+	0.826250i	$0.690470\pi$
$14$	0.0260326	0.00695749
$15$	−0.247562	−0.0639202
$16$	1.00000	0.250000
$17$	−4.11815	−0.998799	−0.499399	−	0.866372i	$-0.666446\pi$
$17$	−4.11815	−0.998799	−0.499399	+	0.866372i	$0.666446\pi$
$18$	2.98314	0.703132
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.90646	0.426298
$21$	0.00338044	0.000737672 0
$22$	−2.55961	−0.545710
$23$	3.49020	0.727757	0.363878	−	0.931446i	$-0.381452\pi$
$23$	3.49020	0.727757	0.363878	+	0.931446i	$0.381452\pi$
$24$	0.129854	0.0265064
$25$	−1.36541	−0.273082
$26$	4.06204	0.796631
$27$	0.776935	0.149521
$28$	−0.0260326	−0.00491969
$29$	−4.54364	−0.843734	−0.421867	−	0.906658i	$-0.638625\pi$
$29$	−4.54364	−0.843734	−0.421867	+	0.906658i	$0.638625\pi$
$30$	0.247562	0.0451984
$31$	4.14167	0.743866	0.371933	−	0.928260i	$-0.378695\pi$
$31$	4.14167	0.743866	0.371933	+	0.928260i	$0.378695\pi$
$32$	−1.00000	−0.176777
$33$	−0.332376	−0.0578592
$34$	4.11815	0.706257
$35$	−0.0496300	−0.00838901
$36$	−2.98314	−0.497190
$37$	9.52484	1.56587	0.782937	−	0.622101i	$-0.213721\pi$
$37$	9.52484	1.56587	0.782937	+	0.622101i	$0.213721\pi$
$38$	−1.00000	−0.162221
$39$	0.527473	0.0844632
$40$	−1.90646	−0.301438
$41$	6.26253	0.978042	0.489021	−	0.872272i	$-0.337354\pi$
$41$	6.26253	0.978042	0.489021	+	0.872272i	$0.337354\pi$
$42$	−0.00338044	−0.000521613 0
$43$	−3.53186	−0.538604	−0.269302	−	0.963056i	$-0.586793\pi$
$43$	−3.53186	−0.538604	−0.269302	+	0.963056i	$0.586793\pi$
$44$	2.55961	0.385875
$45$	−5.68723	−0.847803
$46$	−3.49020	−0.514602
$47$	4.46347	0.651064	0.325532	−	0.945531i	$-0.394457\pi$
$47$	4.46347	0.651064	0.325532	+	0.945531i	$0.394457\pi$
$48$	−0.129854	−0.0187428
$49$	−6.99932	−0.999903
$50$	1.36541	0.193098
$51$	0.534759	0.0748813
$52$	−4.06204	−0.563303
$53$	−11.6139	−1.59530	−0.797648	−	0.603123i	$-0.793923\pi$
$53$	−11.6139	−1.59530	−0.797648	+	0.603123i	$0.793923\pi$
$54$	−0.776935	−0.105728
$55$	4.87979	0.657990
$56$	0.0260326	0.00347875
$57$	−0.129854	−0.0171996
$58$	4.54364	0.596610
$59$	3.30491	0.430263	0.215132	−	0.976585i	$-0.430982\pi$
$59$	3.30491	0.430263	0.215132	+	0.976585i	$0.430982\pi$
$60$	−0.247562	−0.0319601
$61$	5.56733	0.712823	0.356412	−	0.934329i	$-0.384000\pi$
$61$	5.56733	0.712823	0.356412	+	0.934329i	$0.384000\pi$
$62$	−4.14167	−0.525993
$63$	0.0776587	0.00978408
$64$	1.00000	0.125000
$65$	−7.74412	−0.960539
$66$	0.332376	0.0409126
$67$	3.69793	0.451775	0.225887	−	0.974153i	$-0.427472\pi$
$67$	3.69793	0.451775	0.225887	+	0.974153i	$0.427472\pi$
$68$	−4.11815	−0.499399
$69$	−0.453217	−0.0545609
$70$	0.0496300	0.00593193
$71$	10.6752	1.26691	0.633457	−	0.773778i	$-0.281635\pi$
$71$	10.6752	1.26691	0.633457	+	0.773778i	$0.281635\pi$
$72$	2.98314	0.351566
$73$	−6.37745	−0.746424	−0.373212	−	0.927746i	$-0.621744\pi$
$73$	−6.37745	−0.746424	−0.373212	+	0.927746i	$0.621744\pi$
$74$	−9.52484	−1.10724
$75$	0.177304	0.0204733
$76$	1.00000	0.114708
$77$	−0.0666331	−0.00759355
$78$	−0.527473	−0.0597245
$79$	17.2377	1.93939	0.969697	−	0.244309i	$-0.0785612\pi$
$79$	17.2377	1.93939	0.969697	+	0.244309i	$0.0785612\pi$
$80$	1.90646	0.213149
$81$	8.84853	0.983169
$82$	−6.26253	−0.691580
$83$	5.79776	0.636387	0.318193	−	0.948026i	$-0.396924\pi$
$83$	5.79776	0.636387	0.318193	+	0.948026i	$0.396924\pi$
$84$	0.00338044	0.000368836 0
$85$	−7.85110	−0.851571
$86$	3.53186	0.380850
$87$	0.590011	0.0632558
$88$	−2.55961	−0.272855
$89$	−16.4227	−1.74081	−0.870403	−	0.492340i	$-0.836142\pi$
$89$	−16.4227	−1.74081	−0.870403	+	0.492340i	$0.836142\pi$
$90$	5.68723	0.599487
$91$	0.105745	0.0110851
$92$	3.49020	0.363878
$93$	−0.537813	−0.0557686
$94$	−4.46347	−0.460372
$95$	1.90646	0.195599
$96$	0.129854	0.0132532
$97$	−16.7557	−1.70129	−0.850644	−	0.525742i	$-0.823788\pi$
$97$	−16.7557	−1.70129	−0.850644	+	0.525742i	$0.823788\pi$
$98$	6.99932	0.707038
$99$	−7.63566	−0.767413
$100$	−1.36541	−0.136541
$101$	16.9602	1.68760	0.843802	−	0.536655i	$-0.180312\pi$
$101$	16.9602	1.68760	0.843802	+	0.536655i	$0.180312\pi$
$102$	−0.534759	−0.0529491
$103$	−1.66446	−0.164005	−0.0820023	−	0.996632i	$-0.526131\pi$
$103$	−1.66446	−0.164005	−0.0820023	+	0.996632i	$0.526131\pi$
$104$	4.06204	0.398316
$105$	0.00644467	0.000628935 0
$106$	11.6139	1.12804
$107$	−9.83140	−0.950437	−0.475219	−	0.879868i	$-0.657631\pi$
$107$	−9.83140	−0.950437	−0.475219	+	0.879868i	$0.657631\pi$
$108$	0.776935	0.0747606
$109$	−7.67629	−0.735255	−0.367628	−	0.929973i	$-0.619830\pi$
$109$	−7.67629	−0.735255	−0.367628	+	0.929973i	$0.619830\pi$
$110$	−4.87979	−0.465270
$111$	−1.23684	−0.117396
$112$	−0.0260326	−0.00245985
$113$	−8.08198	−0.760289	−0.380144	−	0.924927i	$-0.624126\pi$
$113$	−8.08198	−0.760289	−0.380144	+	0.924927i	$0.624126\pi$
$114$	0.129854	0.0121620
$115$	6.65393	0.620482
$116$	−4.54364	−0.421867
$117$	12.1176	1.12027
$118$	−3.30491	−0.304242
$119$	0.107206	0.00982756
$120$	0.247562	0.0225992
$121$	−4.44842	−0.404401
$122$	−5.56733	−0.504042
$123$	−0.813215	−0.0733251
$124$	4.14167	0.371933
$125$	−12.1354	−1.08542
$126$	−0.0776587	−0.00691839
$127$	−7.74025	−0.686836	−0.343418	−	0.939183i	$-0.611585\pi$
$127$	−7.74025	−0.686836	−0.343418	+	0.939183i	$0.611585\pi$
$128$	−1.00000	−0.0883883
$129$	0.458627	0.0403798
$130$	7.74412	0.679204
$131$	−19.6458	−1.71646	−0.858232	−	0.513262i	$-0.828437\pi$
$131$	−19.6458	−1.71646	−0.858232	+	0.513262i	$0.828437\pi$
$132$	−0.332376	−0.0289296
$133$	−0.0260326	−0.00225731
$134$	−3.69793	−0.319453
$135$	1.48120	0.127481
$136$	4.11815	0.353129
$137$	−13.6508	−1.16627	−0.583134	−	0.812376i	$-0.698174\pi$
$137$	−13.6508	−1.16627	−0.583134	+	0.812376i	$0.698174\pi$
$138$	0.453217	0.0385804
$139$	−11.3017	−0.958602	−0.479301	−	0.877651i	$-0.659110\pi$
$139$	−11.3017	−0.958602	−0.479301	+	0.877651i	$0.659110\pi$
$140$	−0.0496300	−0.00419450
$141$	−0.579600	−0.0488112
$142$	−10.6752	−0.895844
$143$	−10.3972	−0.869459
$144$	−2.98314	−0.248595
$145$	−8.66228	−0.719363
$146$	6.37745	0.527802
$147$	0.908891	0.0749641
$148$	9.52484	0.782937
$149$	−12.4614	−1.02088	−0.510441	−	0.859913i	$-0.670518\pi$
$149$	−12.4614	−1.02088	−0.510441	+	0.859913i	$0.670518\pi$
$150$	−0.177304	−0.0144768
$151$	−5.11154	−0.415971	−0.207986	−	0.978132i	$-0.566691\pi$
$151$	−5.11154	−0.415971	−0.207986	+	0.978132i	$0.566691\pi$
$152$	−1.00000	−0.0811107
$153$	12.2850	0.993185
$154$	0.0666331	0.00536945
$155$	7.89593	0.634216
$156$	0.527473	0.0422316
$157$	−5.34105	−0.426262	−0.213131	−	0.977024i	$-0.568366\pi$
$157$	−5.34105	−0.426262	−0.213131	+	0.977024i	$0.568366\pi$
$158$	−17.2377	−1.37136
$159$	1.50812	0.119601
$160$	−1.90646	−0.150719
$161$	−0.0908588	−0.00716068
$162$	−8.84853	−0.695206
$163$	−5.24517	−0.410833	−0.205417	−	0.978675i	$-0.565855\pi$
$163$	−5.24517	−0.410833	−0.205417	+	0.978675i	$0.565855\pi$
$164$	6.26253	0.489021
$165$	−0.633661	−0.0493304
$166$	−5.79776	−0.449993
$167$	7.86052	0.608265	0.304133	−	0.952630i	$-0.401633\pi$
$167$	7.86052	0.608265	0.304133	+	0.952630i	$0.401633\pi$
$168$	−0.00338044	−0.000260806 0
$169$	3.50015	0.269243
$170$	7.85110	0.602151
$171$	−2.98314	−0.228126
$172$	−3.53186	−0.269302
$173$	12.4635	0.947585	0.473793	−	0.880636i	$-0.342885\pi$
$173$	12.4635	0.947585	0.473793	+	0.880636i	$0.342885\pi$
$174$	−0.590011	−0.0447286
$175$	0.0355451	0.00268696
$176$	2.55961	0.192938
$177$	−0.429157	−0.0322574
$178$	16.4227	1.23094
$179$	−8.94688	−0.668721	−0.334361	−	0.942445i	$-0.608520\pi$
$179$	−8.94688	−0.668721	−0.334361	+	0.942445i	$0.608520\pi$
$180$	−5.68723	−0.423901
$181$	13.3738	0.994065	0.497032	−	0.867732i	$-0.334423\pi$
$181$	13.3738	0.994065	0.497032	+	0.867732i	$0.334423\pi$
$182$	−0.105745	−0.00783836
$183$	−0.722941	−0.0534413
$184$	−3.49020	−0.257301
$185$	18.1587	1.33506
$186$	0.537813	0.0394344
$187$	−10.5408	−0.770823
$188$	4.46347	0.325532
$189$	−0.0202256	−0.00147120
$190$	−1.90646	−0.138309
$191$	−19.4462	−1.40708	−0.703538	−	0.710658i	$-0.748397\pi$
$191$	−19.4462	−1.40708	−0.703538	+	0.710658i	$0.748397\pi$
$192$	−0.129854	−0.00937142
$193$	−9.15865	−0.659254	−0.329627	−	0.944111i	$-0.606923\pi$
$193$	−9.15865	−0.659254	−0.329627	+	0.944111i	$0.606923\pi$
$194$	16.7557	1.20299
$195$	1.00561	0.0720129
$196$	−6.99932	−0.499952
$197$	−5.87844	−0.418821	−0.209411	−	0.977828i	$-0.567155\pi$
$197$	−5.87844	−0.418821	−0.209411	+	0.977828i	$0.567155\pi$
$198$	7.63566	0.542643
$199$	−20.5661	−1.45789	−0.728946	−	0.684572i	$-0.759989\pi$
$199$	−20.5661	−1.45789	−0.728946	+	0.684572i	$0.759989\pi$
$200$	1.36541	0.0965490
$201$	−0.480192	−0.0338701
$202$	−16.9602	−1.19332
$203$	0.118283	0.00830182
$204$	0.534759	0.0374406
$205$	11.9393	0.833874
$206$	1.66446	0.115969
$207$	−10.4117	−0.723666
$208$	−4.06204	−0.281652
$209$	2.55961	0.177052
$210$	−0.00644467	−0.000444724 0
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−11.6139	−0.797648
$213$	−1.38622	−0.0949822
$214$	9.83140	0.672061
$215$	−6.73335	−0.459211
$216$	−0.776935	−0.0528638
$217$	−0.107818	−0.00731918
$218$	7.67629	0.519904
$219$	0.828139	0.0559604
$220$	4.87979	0.328995
$221$	16.7281	1.12525
$222$	1.23684	0.0830112
$223$	7.17524	0.480490	0.240245	−	0.970712i	$-0.422772\pi$
$223$	7.17524	0.480490	0.240245	+	0.970712i	$0.422772\pi$
$224$	0.0260326	0.00173937
$225$	4.07320	0.271547
$226$	8.08198	0.537605
$227$	−14.0659	−0.933585	−0.466792	−	0.884367i	$-0.654590\pi$
$227$	−14.0659	−0.933585	−0.466792	+	0.884367i	$0.654590\pi$
$228$	−0.129854	−0.00859980
$229$	11.3752	0.751693	0.375847	−	0.926682i	$-0.377352\pi$
$229$	11.3752	0.751693	0.375847	+	0.926682i	$0.377352\pi$
$230$	−6.65393	−0.438747
$231$	0.00865259	0.000569298 0
$232$	4.54364	0.298305
$233$	−6.85094	−0.448820	−0.224410	−	0.974495i	$-0.572045\pi$
$233$	−6.85094	−0.448820	−0.224410	+	0.974495i	$0.572045\pi$
$234$	−12.1176	−0.792154
$235$	8.50943	0.555094
$236$	3.30491	0.215132
$237$	−2.23839	−0.145399
$238$	−0.107206	−0.00694914
$239$	22.1924	1.43551	0.717754	−	0.696297i	$-0.245170\pi$
$239$	22.1924	1.43551	0.717754	+	0.696297i	$0.245170\pi$
$240$	−0.247562	−0.0159800
$241$	−3.53563	−0.227750	−0.113875	−	0.993495i	$-0.536326\pi$
$241$	−3.53563	−0.227750	−0.113875	+	0.993495i	$0.536326\pi$
$242$	4.44842	0.285955
$243$	−3.47982	−0.223231
$244$	5.56733	0.356412
$245$	−13.3439	−0.852513
$246$	0.813215	0.0518487
$247$	−4.06204	−0.258461
$248$	−4.14167	−0.262996
$249$	−0.752863	−0.0477108
$250$	12.1354	0.767510
$251$	−22.3216	−1.40892	−0.704462	−	0.709741i	$-0.748812\pi$
$251$	−22.3216	−1.40892	−0.704462	+	0.709741i	$0.748812\pi$
$252$	0.0776587	0.00489204
$253$	8.93353	0.561646
$254$	7.74025	0.485666
$255$	1.01950	0.0638434
$256$	1.00000	0.0625000
$257$	−24.8532	−1.55030	−0.775151	−	0.631776i	$-0.782326\pi$
$257$	−24.8532	−1.55030	−0.775151	+	0.631776i	$0.782326\pi$
$258$	−0.458627	−0.0285529
$259$	−0.247956	−0.0154072
$260$	−7.74412	−0.480270
$261$	13.5543	0.838991
$262$	19.6458	1.21372
$263$	24.6194	1.51810	0.759048	−	0.651035i	$-0.225665\pi$
$263$	24.6194	1.51810	0.759048	+	0.651035i	$0.225665\pi$
$264$	0.332376	0.0204563
$265$	−22.1415	−1.36014
$266$	0.0260326	0.00159616
$267$	2.13256	0.130511
$268$	3.69793	0.225887
$269$	−15.9965	−0.975322	−0.487661	−	0.873033i	$-0.662150\pi$
$269$	−15.9965	−0.975322	−0.487661	+	0.873033i	$0.662150\pi$
$270$	−1.48120	−0.0901428
$271$	−6.44389	−0.391438	−0.195719	−	0.980660i	$-0.562704\pi$
$271$	−6.44389	−0.391438	−0.195719	+	0.980660i	$0.562704\pi$
$272$	−4.11815	−0.249700
$273$	−0.0137315	−0.000831066 0
$274$	13.6508	0.824676
$275$	−3.49491	−0.210751
$276$	−0.453217	−0.0272804
$277$	−16.5087	−0.991910	−0.495955	−	0.868348i	$-0.665182\pi$
$277$	−16.5087	−0.991910	−0.495955	+	0.868348i	$0.665182\pi$
$278$	11.3017	0.677834
$279$	−12.3552	−0.739685
$280$	0.0496300	0.00296596
$281$	13.5215	0.806624	0.403312	−	0.915063i	$-0.367859\pi$
$281$	13.5215	0.806624	0.403312	+	0.915063i	$0.367859\pi$
$282$	0.579600	0.0345147
$283$	27.7683	1.65065	0.825326	−	0.564656i	$-0.190991\pi$
$283$	27.7683	1.65065	0.825326	+	0.564656i	$0.190991\pi$
$284$	10.6752	0.633457
$285$	−0.247562	−0.0146643
$286$	10.3972	0.614800
$287$	−0.163030	−0.00962333
$288$	2.98314	0.175783
$289$	−0.0408198	−0.00240117
$290$	8.66228	0.508667
$291$	2.17580	0.127548
$292$	−6.37745	−0.373212
$293$	−19.8566	−1.16004	−0.580018	−	0.814603i	$-0.696955\pi$
$293$	−19.8566	−1.16004	−0.580018	+	0.814603i	$0.696955\pi$
$294$	−0.908891	−0.0530076
$295$	6.30069	0.366840
$296$	−9.52484	−0.553620
$297$	1.98865	0.115393
$298$	12.4614	0.721872
$299$	−14.1773	−0.819896
$300$	0.177304	0.0102366
$301$	0.0919434	0.00529953
$302$	5.11154	0.294136
$303$	−2.20235	−0.126522
$304$	1.00000	0.0573539
$305$	10.6139	0.607750
$306$	−12.2850	−0.702288
$307$	18.2513	1.04166	0.520830	−	0.853661i	$-0.325623\pi$
$307$	18.2513	1.04166	0.520830	+	0.853661i	$0.325623\pi$
$308$	−0.0666331	−0.00379677
$309$	0.216138	0.0122956
$310$	−7.89593	−0.448459
$311$	−9.52642	−0.540194	−0.270097	−	0.962833i	$-0.587056\pi$
$311$	−9.52642	−0.540194	−0.270097	+	0.962833i	$0.587056\pi$
$312$	−0.527473	−0.0298623
$313$	−4.10385	−0.231963	−0.115982	−	0.993251i	$-0.537001\pi$
$313$	−4.10385	−0.231963	−0.115982	+	0.993251i	$0.537001\pi$
$314$	5.34105	0.301413
$315$	0.148053	0.00834186
$316$	17.2377	0.969697
$317$	2.18893	0.122943	0.0614713	−	0.998109i	$-0.480421\pi$
$317$	2.18893	0.122943	0.0614713	+	0.998109i	$0.480421\pi$
$318$	−1.50812	−0.0845710
$319$	−11.6299	−0.651152
$320$	1.90646	0.106574
$321$	1.27665	0.0712556
$322$	0.0908588	0.00506336
$323$	−4.11815	−0.229140
$324$	8.84853	0.491585
$325$	5.54634	0.307656
$326$	5.24517	0.290503
$327$	0.996798	0.0551231
$328$	−6.26253	−0.345790
$329$	−0.116196	−0.00640607
$330$	0.633661	0.0348819
$331$	24.4787	1.34547	0.672737	−	0.739882i	$-0.265119\pi$
$331$	24.4787	1.34547	0.672737	+	0.739882i	$0.265119\pi$
$332$	5.79776	0.318193
$333$	−28.4139	−1.55707
$334$	−7.86052	−0.430109
$335$	7.04996	0.385181
$336$	0.00338044	0.000184418 0
$337$	−7.75670	−0.422535	−0.211267	−	0.977428i	$-0.567759\pi$
$337$	−7.75670	−0.422535	−0.211267	+	0.977428i	$0.567759\pi$
$338$	−3.50015	−0.190383
$339$	1.04948	0.0569998
$340$	−7.85110	−0.425785
$341$	10.6010	0.574079
$342$	2.98314	0.161310
$343$	0.364438	0.0196778
$344$	3.53186	0.190425
$345$	−0.864040	−0.0465183
$346$	−12.4635	−0.670044
$347$	−13.1846	−0.707788	−0.353894	−	0.935285i	$-0.615143\pi$
$347$	−13.1846	−0.707788	−0.353894	+	0.935285i	$0.615143\pi$
$348$	0.590011	0.0316279
$349$	−5.04955	−0.270296	−0.135148	−	0.990825i	$-0.543151\pi$
$349$	−5.04955	−0.270296	−0.135148	+	0.990825i	$0.543151\pi$
$350$	−0.0355451	−0.00189996
$351$	−3.15594	−0.168452
$352$	−2.55961	−0.136427
$353$	−28.8582	−1.53597	−0.767983	−	0.640471i	$-0.778739\pi$
$353$	−28.8582	−1.53597	−0.767983	+	0.640471i	$0.778739\pi$
$354$	0.429157	0.0228094
$355$	20.3519	1.08016
$356$	−16.4227	−0.870403
$357$	−0.0139212	−0.000736786 0
$358$	8.94688	0.472857
$359$	11.1856	0.590355	0.295177	−	0.955442i	$-0.404621\pi$
$359$	11.1856	0.590355	0.295177	+	0.955442i	$0.404621\pi$
$360$	5.68723	0.299744
$361$	1.00000	0.0526316
$362$	−13.3738	−0.702910
$363$	0.577645	0.0303185
$364$	0.105745	0.00554256
$365$	−12.1584	−0.636398
$366$	0.722941	0.0377887
$367$	−28.5624	−1.49095	−0.745473	−	0.666536i	$-0.767776\pi$
$367$	−28.5624	−1.49095	−0.745473	+	0.666536i	$0.767776\pi$
$368$	3.49020	0.181939
$369$	−18.6820	−0.972545
$370$	−18.1587	−0.944027
$371$	0.302340	0.0156967
$372$	−0.537813	−0.0278843
$373$	−35.4286	−1.83442	−0.917212	−	0.398400i	$-0.869566\pi$
$373$	−35.4286	−1.83442	−0.917212	+	0.398400i	$0.869566\pi$
$374$	10.5408	0.545054
$375$	1.57583	0.0813756
$376$	−4.46347	−0.230186
$377$	18.4565	0.950556
$378$	0.0202256	0.00104029
$379$	−24.7277	−1.27018	−0.635089	−	0.772439i	$-0.719037\pi$
$379$	−24.7277	−1.27018	−0.635089	+	0.772439i	$0.719037\pi$
$380$	1.90646	0.0977994
$381$	1.00510	0.0514930
$382$	19.4462	0.994953
$383$	29.5815	1.51155	0.755773	−	0.654834i	$-0.227262\pi$
$383$	29.5815	1.51155	0.755773	+	0.654834i	$0.227262\pi$
$384$	0.129854	0.00662659
$385$	−0.127033	−0.00647422
$386$	9.15865	0.466163
$387$	10.5360	0.535576
$388$	−16.7557	−0.850644
$389$	0.731565	0.0370918	0.0185459	−	0.999828i	$-0.494096\pi$
$389$	0.731565	0.0370918	0.0185459	+	0.999828i	$0.494096\pi$
$390$	−1.00561	−0.0509208
$391$	−14.3732	−0.726882
$392$	6.99932	0.353519
$393$	2.55109	0.128686
$394$	5.87844	0.296151
$395$	32.8630	1.65352
$396$	−7.63566	−0.383706
$397$	30.3229	1.52186	0.760931	−	0.648833i	$-0.224743\pi$
$397$	30.3229	1.52186	0.760931	+	0.648833i	$0.224743\pi$
$398$	20.5661	1.03088
$399$	0.00338044	0.000169233 0
$400$	−1.36541	−0.0682704
$401$	33.3030	1.66307	0.831537	−	0.555469i	$-0.187461\pi$
$401$	33.3030	1.66307	0.831537	+	0.555469i	$0.187461\pi$
$402$	0.480192	0.0239498
$403$	−16.8236	−0.838044
$404$	16.9602	0.843802
$405$	16.8694	0.838245
$406$	−0.118283	−0.00587027
$407$	24.3798	1.20846
$408$	−0.534759	−0.0264745
$409$	−11.3924	−0.563317	−0.281659	−	0.959515i	$-0.590885\pi$
$409$	−11.3924	−0.563317	−0.281659	+	0.959515i	$0.590885\pi$
$410$	−11.9393	−0.589638
$411$	1.77261	0.0874366
$412$	−1.66446	−0.0820023
$413$	−0.0860354	−0.00423352
$414$	10.4117	0.511709
$415$	11.0532	0.542580
$416$	4.06204	0.199158
$417$	1.46758	0.0718677
$418$	−2.55961	−0.125194
$419$	−7.89341	−0.385618	−0.192809	−	0.981236i	$-0.561760\pi$
$419$	−7.89341	−0.385618	−0.192809	+	0.981236i	$0.561760\pi$
$420$	0.00644467	0.000314468 0
$421$	13.8119	0.673149	0.336575	−	0.941657i	$-0.390732\pi$
$421$	13.8119	0.673149	0.336575	+	0.941657i	$0.390732\pi$
$422$	−1.00000	−0.0486792
$423$	−13.3152	−0.647405
$424$	11.6139	0.564022
$425$	5.62296	0.272754
$426$	1.38622	0.0671626
$427$	−0.144932	−0.00701374
$428$	−9.83140	−0.475219
$429$	1.35012	0.0651845
$430$	6.73335	0.324711
$431$	−32.6378	−1.57211	−0.786053	−	0.618159i	$-0.787879\pi$
$431$	−32.6378	−1.57211	−0.786053	+	0.618159i	$0.787879\pi$
$432$	0.776935	0.0373803
$433$	7.81939	0.375776	0.187888	−	0.982190i	$-0.439836\pi$
$433$	7.81939	0.375776	0.187888	+	0.982190i	$0.439836\pi$
$434$	0.107818	0.00517544
$435$	1.12483	0.0539316
$436$	−7.67629	−0.367628
$437$	3.49020	0.166959
$438$	−0.828139	−0.0395700
$439$	11.0042	0.525202	0.262601	−	0.964904i	$-0.415420\pi$
$439$	11.0042	0.525202	0.262601	+	0.964904i	$0.415420\pi$
$440$	−4.87979	−0.232635
$441$	20.8799	0.994283
$442$	−16.7281	−0.795674
$443$	6.52477	0.310001	0.155001	−	0.987914i	$-0.450462\pi$
$443$	6.52477	0.310001	0.155001	+	0.987914i	$0.450462\pi$
$444$	−1.23684	−0.0586978
$445$	−31.3093	−1.48420
$446$	−7.17524	−0.339758
$447$	1.61817	0.0765368
$448$	−0.0260326	−0.00122992
$449$	16.9505	0.799944	0.399972	−	0.916527i	$-0.369020\pi$
$449$	16.9505	0.799944	0.399972	+	0.916527i	$0.369020\pi$
$450$	−4.07320	−0.192013
$451$	16.0296	0.754804
$452$	−8.08198	−0.380144
$453$	0.663755	0.0311859
$454$	14.0659	0.660144
$455$	0.201599	0.00945111
$456$	0.129854	0.00608098
$457$	−9.91752	−0.463922	−0.231961	−	0.972725i	$-0.574514\pi$
$457$	−9.91752	−0.463922	−0.231961	+	0.972725i	$0.574514\pi$
$458$	−11.3752	−0.531528
$459$	−3.19954	−0.149342
$460$	6.65393	0.310241
$461$	17.5041	0.815245	0.407623	−	0.913150i	$-0.366358\pi$
$461$	17.5041	0.815245	0.407623	+	0.913150i	$0.366358\pi$
$462$	−0.00865259	−0.000402555 0
$463$	39.0738	1.81591	0.907957	−	0.419064i	$-0.137642\pi$
$463$	39.0738	1.81591	0.907957	+	0.419064i	$0.137642\pi$
$464$	−4.54364	−0.210933
$465$	−1.02532	−0.0475481
$466$	6.85094	0.317364
$467$	−22.3337	−1.03348	−0.516740	−	0.856142i	$-0.672855\pi$
$467$	−22.3337	−1.03348	−0.516740	+	0.856142i	$0.672855\pi$
$468$	12.1176	0.560137
$469$	−0.0962667	−0.00444518
$470$	−8.50943	−0.392511
$471$	0.693557	0.0319574
$472$	−3.30491	−0.152121
$473$	−9.04017	−0.415668
$474$	2.23839	0.102813
$475$	−1.36541	−0.0626492
$476$	0.107206	0.00491378
$477$	34.6460	1.58633
$478$	−22.1924	−1.01506
$479$	−18.2646	−0.834529	−0.417265	−	0.908785i	$-0.637011\pi$
$479$	−18.2646	−0.834529	−0.417265	+	0.908785i	$0.637011\pi$
$480$	0.247562	0.0112996
$481$	−38.6902	−1.76412
$482$	3.53563	0.161044
$483$	0.0117984	0.000536846 0
$484$	−4.44842	−0.202201
$485$	−31.9442	−1.45051
$486$	3.47982	0.157848
$487$	−12.2545	−0.555304	−0.277652	−	0.960682i	$-0.589556\pi$
$487$	−12.2545	−0.555304	−0.277652	+	0.960682i	$0.589556\pi$
$488$	−5.56733	−0.252021
$489$	0.681107	0.0308007
$490$	13.3439	0.602817
$491$	28.8555	1.30223	0.651116	−	0.758978i	$-0.274301\pi$
$491$	28.8555	1.30223	0.651116	+	0.758978i	$0.274301\pi$
$492$	−0.813215	−0.0366626
$493$	18.7114	0.842720
$494$	4.06204	0.182760
$495$	−14.5571	−0.654292
$496$	4.14167	0.185966
$497$	−0.277903	−0.0124657
$498$	0.752863	0.0337366
$499$	−4.80541	−0.215120	−0.107560	−	0.994199i	$-0.534304\pi$
$499$	−4.80541	−0.215120	−0.107560	+	0.994199i	$0.534304\pi$
$500$	−12.1354	−0.542712
$501$	−1.02072	−0.0456025
$502$	22.3216	0.996260
$503$	3.23046	0.144039	0.0720196	−	0.997403i	$-0.477056\pi$
$503$	3.23046	0.144039	0.0720196	+	0.997403i	$0.477056\pi$
$504$	−0.0776587	−0.00345919
$505$	32.3340	1.43884
$506$	−8.93353	−0.397144
$507$	−0.454510	−0.0201855
$508$	−7.74025	−0.343418
$509$	−8.10055	−0.359051	−0.179525	−	0.983753i	$-0.557456\pi$
$509$	−8.10055	−0.359051	−0.179525	+	0.983753i	$0.557456\pi$
$510$	−1.01950	−0.0451441
$511$	0.166021	0.00734435
$512$	−1.00000	−0.0441942
$513$	0.776935	0.0343025
$514$	24.8532	1.09623
$515$	−3.17324	−0.139829
$516$	0.458627	0.0201899
$517$	11.4247	0.502459
$518$	0.247956	0.0108946
$519$	−1.61844	−0.0710417
$520$	7.74412	0.339602
$521$	20.5254	0.899233	0.449617	−	0.893222i	$-0.351561\pi$
$521$	20.5254	0.899233	0.449617	+	0.893222i	$0.351561\pi$
$522$	−13.5543	−0.593256
$523$	−24.5082	−1.07167	−0.535834	−	0.844323i	$-0.680003\pi$
$523$	−24.5082	−1.07167	−0.535834	+	0.844323i	$0.680003\pi$
$524$	−19.6458	−0.858232
$525$	−0.00461568	−0.000201445 0
$526$	−24.6194	−1.07346
$527$	−17.0560	−0.742972
$528$	−0.332376	−0.0144648
$529$	−10.8185	−0.470370
$530$	22.1415	0.961765
$531$	−9.85901	−0.427845
$532$	−0.0260326	−0.00112865
$533$	−25.4386	−1.10187
$534$	−2.13256	−0.0922849
$535$	−18.7432	−0.810338
$536$	−3.69793	−0.159726
$537$	1.16179	0.0501349
$538$	15.9965	0.689657
$539$	−17.9155	−0.771676
$540$	1.48120	0.0637406
$541$	−14.8930	−0.640298	−0.320149	−	0.947367i	$-0.603733\pi$
$541$	−14.8930	−0.640298	−0.320149	+	0.947367i	$0.603733\pi$
$542$	6.44389	0.276789
$543$	−1.73664	−0.0745264
$544$	4.11815	0.176564
$545$	−14.6345	−0.626875
$546$	0.0137315	0.000587652 0
$547$	15.7712	0.674326	0.337163	−	0.941446i	$-0.390533\pi$
$547$	15.7712	0.674326	0.337163	+	0.941446i	$0.390533\pi$
$548$	−13.6508	−0.583134
$549$	−16.6081	−0.708817
$550$	3.49491	0.149023
$551$	−4.54364	−0.193566
$552$	0.453217	0.0192902
$553$	−0.448742	−0.0190824
$554$	16.5087	0.701386
$555$	−2.35799	−0.100091
$556$	−11.3017	−0.479301
$557$	42.9146	1.81835	0.909176	−	0.416412i	$-0.136713\pi$
$557$	42.9146	1.81835	0.909176	+	0.416412i	$0.136713\pi$
$558$	12.3552	0.523036
$559$	14.3466	0.606795
$560$	−0.0496300	−0.00209725
$561$	1.36877	0.0577896
$562$	−13.5215	−0.570369
$563$	6.62311	0.279131	0.139565	−	0.990213i	$-0.455429\pi$
$563$	6.62311	0.279131	0.139565	+	0.990213i	$0.455429\pi$
$564$	−0.579600	−0.0244056
$565$	−15.4080	−0.648218
$566$	−27.7683	−1.16719
$567$	−0.230350	−0.00967378
$568$	−10.6752	−0.447922
$569$	27.1241	1.13710	0.568551	−	0.822648i	$-0.307504\pi$
$569$	27.1241	1.13710	0.568551	+	0.822648i	$0.307504\pi$
$570$	0.247562	0.0103692
$571$	21.9259	0.917571	0.458785	−	0.888547i	$-0.348285\pi$
$571$	21.9259	0.917571	0.458785	+	0.888547i	$0.348285\pi$
$572$	−10.3972	−0.434730
$573$	2.52517	0.105490
$574$	0.163030	0.00680472
$575$	−4.76555	−0.198737
$576$	−2.98314	−0.124297
$577$	−7.14959	−0.297641	−0.148821	−	0.988864i	$-0.547548\pi$
$577$	−7.14959	−0.297641	−0.148821	+	0.988864i	$0.547548\pi$
$578$	0.0408198	0.00169788
$579$	1.18929	0.0494252
$580$	−8.66228	−0.359682
$581$	−0.150930	−0.00626165
$582$	−2.17580	−0.0901900
$583$	−29.7271	−1.23117
$584$	6.37745	0.263901
$585$	23.1018	0.955140
$586$	19.8566	0.820270
$587$	−15.8897	−0.655839	−0.327919	−	0.944706i	$-0.606347\pi$
$587$	−15.8897	−0.655839	−0.327919	+	0.944706i	$0.606347\pi$
$588$	0.908891	0.0374820
$589$	4.14167	0.170655
$590$	−6.30069	−0.259395
$591$	0.763340	0.0313996
$592$	9.52484	0.391468
$593$	−18.9839	−0.779576	−0.389788	−	0.920905i	$-0.627452\pi$
$593$	−18.9839	−0.779576	−0.389788	+	0.920905i	$0.627452\pi$
$594$	−1.98865	−0.0815952
$595$	0.204384	0.00837893
$596$	−12.4614	−0.510441
$597$	2.67059	0.109300
$598$	14.1773	0.579754
$599$	28.5384	1.16605	0.583023	−	0.812456i	$-0.301870\pi$
$599$	28.5384	1.16605	0.583023	+	0.812456i	$0.301870\pi$
$600$	−0.177304	−0.00723840
$601$	26.2970	1.07268	0.536338	−	0.844003i	$-0.319807\pi$
$601$	26.2970	1.07268	0.536338	+	0.844003i	$0.319807\pi$
$602$	−0.0919434	−0.00374733
$603$	−11.0314	−0.449235
$604$	−5.11154	−0.207986
$605$	−8.48073	−0.344791
$606$	2.20235	0.0894645
$607$	37.9715	1.54122	0.770608	−	0.637309i	$-0.219953\pi$
$607$	37.9715	1.54122	0.770608	+	0.637309i	$0.219953\pi$
$608$	−1.00000	−0.0405554
$609$	−0.0153595	−0.000622398 0
$610$	−10.6139	−0.429744
$611$	−18.1308	−0.733493
$612$	12.2850	0.496592
$613$	−31.8095	−1.28478	−0.642388	−	0.766380i	$-0.722056\pi$
$613$	−31.8095	−1.28478	−0.642388	+	0.766380i	$0.722056\pi$
$614$	−18.2513	−0.736564
$615$	−1.55036	−0.0625166
$616$	0.0666331	0.00268472
$617$	−4.24033	−0.170709	−0.0853547	−	0.996351i	$-0.527202\pi$
$617$	−4.24033	−0.170709	−0.0853547	+	0.996351i	$0.527202\pi$
$618$	−0.216138	−0.00869433
$619$	−39.3563	−1.58186	−0.790932	−	0.611904i	$-0.790404\pi$
$619$	−39.3563	−1.58186	−0.790932	+	0.611904i	$0.790404\pi$
$620$	7.89593	0.317108
$621$	2.71166	0.108815
$622$	9.52642	0.381975
$623$	0.427526	0.0171285
$624$	0.527473	0.0211158
$625$	−16.3086	−0.652345
$626$	4.10385	0.164023
$627$	−0.332376	−0.0132738
$628$	−5.34105	−0.213131
$629$	−39.2247	−1.56399
$630$	−0.148053	−0.00589858
$631$	2.60782	0.103816	0.0519079	−	0.998652i	$-0.483470\pi$
$631$	2.60782	0.103816	0.0519079	+	0.998652i	$0.483470\pi$
$632$	−17.2377	−0.685680
$633$	−0.129854	−0.00516124
$634$	−2.18893	−0.0869336
$635$	−14.7565	−0.585593
$636$	1.50812	0.0598007
$637$	28.4315	1.12650
$638$	11.6299	0.460434
$639$	−31.8456	−1.25979
$640$	−1.90646	−0.0753595
$641$	−12.8501	−0.507550	−0.253775	−	0.967263i	$-0.581672\pi$
$641$	−12.8501	−0.507550	−0.253775	+	0.967263i	$0.581672\pi$
$642$	−1.27665	−0.0503853
$643$	−17.6980	−0.697941	−0.348971	−	0.937134i	$-0.613469\pi$
$643$	−17.6980	−0.697941	−0.348971	+	0.937134i	$0.613469\pi$
$644$	−0.0908588	−0.00358034
$645$	0.874354	0.0344277
$646$	4.11815	0.162027
$647$	−13.1528	−0.517091	−0.258546	−	0.965999i	$-0.583243\pi$
$647$	−13.1528	−0.517091	−0.258546	+	0.965999i	$0.583243\pi$
$648$	−8.84853	−0.347603
$649$	8.45928	0.332056
$650$	−5.54634	−0.217545
$651$	0.0140007	0.000548729 0
$652$	−5.24517	−0.205417
$653$	−25.8709	−1.01241	−0.506203	−	0.862414i	$-0.668952\pi$
$653$	−25.8709	−1.01241	−0.506203	+	0.862414i	$0.668952\pi$
$654$	−0.996798	−0.0389779
$655$	−37.4540	−1.46345
$656$	6.26253	0.244511
$657$	19.0248	0.742229
$658$	0.116196	0.00452978
$659$	6.01604	0.234352	0.117176	−	0.993111i	$-0.462616\pi$
$659$	6.01604	0.234352	0.117176	+	0.993111i	$0.462616\pi$
$660$	−0.633661	−0.0246652
$661$	−26.7586	−1.04079	−0.520395	−	0.853926i	$-0.674215\pi$
$661$	−26.7586	−1.04079	−0.520395	+	0.853926i	$0.674215\pi$
$662$	−24.4787	−0.951393
$663$	−2.17221	−0.0843617
$664$	−5.79776	−0.224997
$665$	−0.0496300	−0.00192457
$666$	28.4139	1.10102
$667$	−15.8582	−0.614033
$668$	7.86052	0.304133
$669$	−0.931735	−0.0360230
$670$	−7.04996	−0.272364
$671$	14.2502	0.550122
$672$	−0.00338044	−0.000130403 0
$673$	−28.5944	−1.10223	−0.551117	−	0.834428i	$-0.685798\pi$
$673$	−28.5944	−1.10223	−0.551117	+	0.834428i	$0.685798\pi$
$674$	7.75670	0.298777
$675$	−1.06083	−0.0408315
$676$	3.50015	0.134621
$677$	43.0010	1.65266	0.826331	−	0.563185i	$-0.190424\pi$
$677$	43.0010	1.65266	0.826331	+	0.563185i	$0.190424\pi$
$678$	−1.04948	−0.0403050
$679$	0.436195	0.0167396
$680$	7.85110	0.301076
$681$	1.82651	0.0699921
$682$	−10.6010	−0.405935
$683$	10.7437	0.411097	0.205548	−	0.978647i	$-0.434102\pi$
$683$	10.7437	0.411097	0.205548	+	0.978647i	$0.434102\pi$
$684$	−2.98314	−0.114063
$685$	−26.0247	−0.994354
$686$	−0.364438	−0.0139143
$687$	−1.47712	−0.0563555
$688$	−3.53186	−0.134651
$689$	47.1762	1.79727
$690$	0.864040	0.0328934
$691$	−12.5308	−0.476694	−0.238347	−	0.971180i	$-0.576606\pi$
$691$	−12.5308	−0.476694	−0.238347	+	0.971180i	$0.576606\pi$
$692$	12.4635	0.473793
$693$	0.198776	0.00755087
$694$	13.1846	0.500482
$695$	−21.5463	−0.817299
$696$	−0.590011	−0.0223643
$697$	−25.7900	−0.976867
$698$	5.04955	0.191128
$699$	0.889623	0.0336486
$700$	0.0355451	0.00134348
$701$	2.44438	0.0923229	0.0461614	−	0.998934i	$-0.485301\pi$
$701$	2.44438	0.0923229	0.0461614	+	0.998934i	$0.485301\pi$
$702$	3.15594	0.119113
$703$	9.52484	0.359236
$704$	2.55961	0.0964688
$705$	−1.10499	−0.0416162
$706$	28.8582	1.08609
$707$	−0.441518	−0.0166050
$708$	−0.429157	−0.0161287
$709$	−40.4879	−1.52055	−0.760277	−	0.649599i	$-0.774937\pi$
$709$	−40.4879	−1.52055	−0.760277	+	0.649599i	$0.774937\pi$
$710$	−20.3519	−0.763792
$711$	−51.4225	−1.92849
$712$	16.4227	0.615468
$713$	14.4553	0.541353
$714$	0.0139212	0.000520986 0
$715$	−19.8219	−0.741296
$716$	−8.94688	−0.334361
$717$	−2.88178	−0.107622
$718$	−11.1856	−0.417444
$719$	−6.24616	−0.232943	−0.116471	−	0.993194i	$-0.537158\pi$
$719$	−6.24616	−0.232943	−0.116471	+	0.993194i	$0.537158\pi$
$720$	−5.68723	−0.211951
$721$	0.0433303	0.00161370
$722$	−1.00000	−0.0372161
$723$	0.459117	0.0170747
$724$	13.3738	0.497032
$725$	6.20393	0.230408
$726$	−0.577645	−0.0214384
$727$	−31.5213	−1.16906	−0.584529	−	0.811372i	$-0.698721\pi$
$727$	−31.5213	−1.16906	−0.584529	+	0.811372i	$0.698721\pi$
$728$	−0.105745	−0.00391918
$729$	−26.0937	−0.966434
$730$	12.1584	0.450001
$731$	14.5447	0.537957
$732$	−0.722941	−0.0267207
$733$	50.2882	1.85744	0.928719	−	0.370785i	$-0.120911\pi$
$733$	50.2882	1.85744	0.928719	+	0.370785i	$0.120911\pi$
$734$	28.5624	1.05426
$735$	1.73277	0.0639140
$736$	−3.49020	−0.128650
$737$	9.46525	0.348657
$738$	18.6820	0.687693
$739$	10.4341	0.383825	0.191912	−	0.981412i	$-0.438531\pi$
$739$	10.4341	0.383825	0.191912	+	0.981412i	$0.438531\pi$
$740$	18.1587	0.667528
$741$	0.527473	0.0193772
$742$	−0.302340	−0.0110993
$743$	1.46491	0.0537424	0.0268712	−	0.999639i	$-0.491446\pi$
$743$	1.46491	0.0537424	0.0268712	+	0.999639i	$0.491446\pi$
$744$	0.537813	0.0197172
$745$	−23.7573	−0.870398
$746$	35.4286	1.29713
$747$	−17.2955	−0.632810
$748$	−10.5408	−0.385412
$749$	0.255936	0.00935172
$750$	−1.57583	−0.0575413
$751$	−14.3760	−0.524588	−0.262294	−	0.964988i	$-0.584479\pi$
$751$	−14.3760	−0.524588	−0.262294	+	0.964988i	$0.584479\pi$
$752$	4.46347	0.162766
$753$	2.89855	0.105629
$754$	−18.4565	−0.672145
$755$	−9.74495	−0.354655
$756$	−0.0202256	−0.000735599 0
$757$	−18.0931	−0.657605	−0.328802	−	0.944399i	$-0.606645\pi$
$757$	−18.0931	−0.657605	−0.328802	+	0.944399i	$0.606645\pi$
$758$	24.7277	0.898152
$759$	−1.16006	−0.0421074
$760$	−1.90646	−0.0691546
$761$	−25.5575	−0.926460	−0.463230	−	0.886238i	$-0.653310\pi$
$761$	−25.5575	−0.926460	−0.463230	+	0.886238i	$0.653310\pi$
$762$	−1.00510	−0.0364111
$763$	0.199833	0.00723446
$764$	−19.4462	−0.703538
$765$	23.4209	0.846784
$766$	−29.5815	−1.06882
$767$	−13.4247	−0.484737
$768$	−0.129854	−0.00468571
$769$	29.1125	1.04982	0.524912	−	0.851157i	$-0.324098\pi$
$769$	29.1125	1.04982	0.524912	+	0.851157i	$0.324098\pi$
$770$	0.127033	0.00457797
$771$	3.22729	0.116228
$772$	−9.15865	−0.329627
$773$	−22.7768	−0.819224	−0.409612	−	0.912260i	$-0.634336\pi$
$773$	−22.7768	−0.819224	−0.409612	+	0.912260i	$0.634336\pi$
$774$	−10.5360	−0.378710
$775$	−5.65507	−0.203136
$776$	16.7557	0.601496
$777$	0.0321981	0.00115510
$778$	−0.731565	−0.0262279
$779$	6.26253	0.224378
$780$	1.00561	0.0360065
$781$	27.3243	0.977741
$782$	14.3732	0.513984
$783$	−3.53012	−0.126156
$784$	−6.99932	−0.249976
$785$	−10.1825	−0.363429
$786$	−2.55109	−0.0909944
$787$	−43.6116	−1.55458	−0.777292	−	0.629140i	$-0.783407\pi$
$787$	−43.6116	−1.55458	−0.777292	+	0.629140i	$0.783407\pi$
$788$	−5.87844	−0.209411
$789$	−3.19693	−0.113814
$790$	−32.8630	−1.16921
$791$	0.210395	0.00748077
$792$	7.63566	0.271321
$793$	−22.6147	−0.803071
$794$	−30.3229	−1.07612
$795$	2.87517	0.101972
$796$	−20.5661	−0.728946
$797$	15.8335	0.560853	0.280426	−	0.959876i	$-0.409524\pi$
$797$	15.8335	0.560853	0.280426	+	0.959876i	$0.409524\pi$
$798$	−0.00338044	−0.000119666 0
$799$	−18.3813	−0.650282
$800$	1.36541	0.0482745
$801$	48.9913	1.73102
$802$	−33.3030	−1.17597
$803$	−16.3238	−0.576053
$804$	−0.480192	−0.0169351
$805$	−0.173219	−0.00610516
$806$	16.8236	0.592587
$807$	2.07721	0.0731212
$808$	−16.9602	−0.596658
$809$	−11.2945	−0.397092	−0.198546	−	0.980092i	$-0.563622\pi$
$809$	−11.2945	−0.397092	−0.198546	+	0.980092i	$0.563622\pi$
$810$	−16.8694	−0.592729
$811$	19.6970	0.691655	0.345828	−	0.938298i	$-0.387598\pi$
$811$	19.6970	0.691655	0.345828	+	0.938298i	$0.387598\pi$
$812$	0.118283	0.00415091
$813$	0.836765	0.0293466
$814$	−24.3798	−0.854513
$815$	−9.99970	−0.350274
$816$	0.534759	0.0187203
$817$	−3.53186	−0.123564
$818$	11.3924	0.398326
$819$	−0.315453	−0.0110228
$820$	11.9393	0.416937
$821$	30.7395	1.07282	0.536409	−	0.843958i	$-0.319781\pi$
$821$	30.7395	1.07282	0.536409	+	0.843958i	$0.319781\pi$
$822$	−1.77261	−0.0618270
$823$	−1.26032	−0.0439319	−0.0219659	−	0.999759i	$-0.506993\pi$
$823$	−1.26032	−0.0439319	−0.0219659	+	0.999759i	$0.506993\pi$
$824$	1.66446	0.0579844
$825$	0.453828	0.0158003
$826$	0.0860354	0.00299355
$827$	5.67367	0.197293	0.0986464	−	0.995123i	$-0.468549\pi$
$827$	5.67367	0.197293	0.0986464	+	0.995123i	$0.468549\pi$
$828$	−10.4117	−0.361833
$829$	25.5983	0.889067	0.444533	−	0.895762i	$-0.353370\pi$
$829$	25.5983	0.889067	0.444533	+	0.895762i	$0.353370\pi$
$830$	−11.0532	−0.383662
$831$	2.14372	0.0743648
$832$	−4.06204	−0.140826
$833$	28.8243	0.998702
$834$	−1.46758	−0.0508181
$835$	14.9858	0.518604
$836$	2.55961	0.0885258
$837$	3.21781	0.111224
$838$	7.89341	0.272673
$839$	19.8083	0.683859	0.341929	−	0.939726i	$-0.388920\pi$
$839$	19.8083	0.683859	0.341929	+	0.939726i	$0.388920\pi$
$840$	−0.00644467	−0.000222362 0
$841$	−8.35530	−0.288114
$842$	−13.8119	−0.475988
$843$	−1.75582	−0.0604737
$844$	1.00000	0.0344214
$845$	6.67291	0.229555
$846$	13.3152	0.457784
$847$	0.115804	0.00397906
$848$	−11.6139	−0.398824
$849$	−3.60583	−0.123752
$850$	−5.62296	−0.192866
$851$	33.2436	1.13957
$852$	−1.38622	−0.0474911
$853$	9.58017	0.328019	0.164009	−	0.986459i	$-0.447557\pi$
$853$	9.58017	0.328019	0.164009	+	0.986459i	$0.447557\pi$
$854$	0.144932	0.00495946
$855$	−5.68723	−0.194499
$856$	9.83140	0.336030
$857$	34.1107	1.16520	0.582600	−	0.812759i	$-0.302035\pi$
$857$	34.1107	1.16520	0.582600	+	0.812759i	$0.302035\pi$
$858$	−1.35012	−0.0460924
$859$	−29.3924	−1.00285	−0.501427	−	0.865200i	$-0.667192\pi$
$859$	−29.3924	−1.00285	−0.501427	+	0.865200i	$0.667192\pi$
$860$	−6.73335	−0.229605
$861$	0.0211701	0.000721474 0
$862$	32.6378	1.11165
$863$	−54.8792	−1.86811	−0.934055	−	0.357129i	$-0.883756\pi$
$863$	−54.8792	−1.86811	−0.934055	+	0.357129i	$0.883756\pi$
$864$	−0.776935	−0.0264319
$865$	23.7612	0.807907
$866$	−7.81939	−0.265714
$867$	0.00530062	0.000180019 0
$868$	−0.107818	−0.00365959
$869$	44.1218	1.49673
$870$	−1.12483	−0.0381354
$871$	−15.0211	−0.508972
$872$	7.67629	0.259952
$873$	49.9847	1.69173
$874$	−3.49020	−0.118058
$875$	0.315916	0.0106799
$876$	0.828139	0.0279802
$877$	−30.9993	−1.04677	−0.523386	−	0.852096i	$-0.675331\pi$
$877$	−30.9993	−1.04677	−0.523386	+	0.852096i	$0.675331\pi$
$878$	−11.0042	−0.371374
$879$	2.57847	0.0869695
$880$	4.87979	0.164498
$881$	−6.57642	−0.221565	−0.110783	−	0.993845i	$-0.535336\pi$
$881$	−6.57642	−0.221565	−0.110783	+	0.993845i	$0.535336\pi$
$882$	−20.8799	−0.703064
$883$	−22.2287	−0.748055	−0.374028	−	0.927418i	$-0.622023\pi$
$883$	−22.2287	−0.748055	−0.374028	+	0.927418i	$0.622023\pi$
$884$	16.7281	0.562627
$885$	−0.818170	−0.0275025
$886$	−6.52477	−0.219204
$887$	51.5247	1.73003	0.865016	−	0.501745i	$-0.167308\pi$
$887$	51.5247	1.73003	0.865016	+	0.501745i	$0.167308\pi$
$888$	1.23684	0.0415056
$889$	0.201499	0.00675804
$890$	31.3093	1.04949
$891$	22.6487	0.758761
$892$	7.17524	0.240245
$893$	4.46347	0.149364
$894$	−1.61817	−0.0541197
$895$	−17.0569	−0.570148
$896$	0.0260326	0.000869687 0
$897$	1.84098	0.0614687
$898$	−16.9505	−0.565646
$899$	−18.8183	−0.627625
$900$	4.07320	0.135773
$901$	47.8279	1.59338
$902$	−16.0296	−0.533727
$903$	−0.0119392	−0.000397313 0
$904$	8.08198	0.268803
$905$	25.4966	0.847535
$906$	−0.663755	−0.0220518
$907$	−33.8786	−1.12492	−0.562460	−	0.826825i	$-0.690145\pi$
$907$	−33.8786	−1.12492	−0.562460	+	0.826825i	$0.690145\pi$
$908$	−14.0659	−0.466792
$909$	−50.5946	−1.67812
$910$	−0.201599	−0.00668295
$911$	27.9007	0.924390	0.462195	−	0.886778i	$-0.347062\pi$
$911$	27.9007	0.924390	0.462195	+	0.886778i	$0.347062\pi$
$912$	−0.129854	−0.00429990
$913$	14.8400	0.491132
$914$	9.91752	0.328042
$915$	−1.37826	−0.0455638
$916$	11.3752	0.375847
$917$	0.511431	0.0168889
$918$	3.19954	0.105601
$919$	−16.7413	−0.552245	−0.276123	−	0.961122i	$-0.589050\pi$
$919$	−16.7413	−0.552245	−0.276123	+	0.961122i	$0.589050\pi$
$920$	−6.65393	−0.219373
$921$	−2.37001	−0.0780946
$922$	−17.5041	−0.576466
$923$	−43.3631	−1.42731
$924$	0.00865259	0.000284649 0
$925$	−13.0053	−0.427611
$926$	−39.0738	−1.28404
$927$	4.96533	0.163083
$928$	4.54364	0.149152
$929$	−33.9172	−1.11279	−0.556394	−	0.830919i	$-0.687815\pi$
$929$	−33.9172	−1.11279	−0.556394	+	0.830919i	$0.687815\pi$
$930$	1.02532	0.0336216
$931$	−6.99932	−0.229394
$932$	−6.85094	−0.224410
$933$	1.23705	0.0404991
$934$	22.3337	0.730781
$935$	−20.0957	−0.657200
$936$	−12.1176	−0.396077
$937$	−1.58389	−0.0517434	−0.0258717	−	0.999665i	$-0.508236\pi$
$937$	−1.58389	−0.0517434	−0.0258717	+	0.999665i	$0.508236\pi$
$938$	0.0962667	0.00314322
$939$	0.532902	0.0173906
$940$	8.50943	0.277547
$941$	−42.2146	−1.37616	−0.688078	−	0.725636i	$-0.741545\pi$
$941$	−42.2146	−1.37616	−0.688078	+	0.725636i	$0.741545\pi$
$942$	−0.693557	−0.0225973
$943$	21.8575	0.711777
$944$	3.30491	0.107566
$945$	−0.0385593	−0.00125434
$946$	9.04017	0.293921
$947$	−57.2371	−1.85996	−0.929978	−	0.367616i	$-0.880174\pi$
$947$	−57.2371	−1.85996	−0.929978	+	0.367616i	$0.880174\pi$
$948$	−2.23839	−0.0726995
$949$	25.9055	0.840927
$950$	1.36541	0.0442997
$951$	−0.284242	−0.00921718
$952$	−0.107206	−0.00347457
$953$	39.0532	1.26506	0.632529	−	0.774536i	$-0.282017\pi$
$953$	39.0532	1.26506	0.632529	+	0.774536i	$0.282017\pi$
$954$	−34.6460	−1.12170
$955$	−37.0734	−1.19967
$956$	22.1924	0.717754
$957$	1.51020	0.0488177
$958$	18.2646	0.590101
$959$	0.355366	0.0114754
$960$	−0.247562	−0.00799002
$961$	−13.8466	−0.446663
$962$	38.6902	1.24742
$963$	29.3284	0.945095
$964$	−3.53563	−0.113875
$965$	−17.4606	−0.562077
$966$	−0.0117984	−0.000379607 0
$967$	−17.9411	−0.576947	−0.288473	−	0.957488i	$-0.593148\pi$
$967$	−17.9411	−0.576947	−0.288473	+	0.957488i	$0.593148\pi$
$968$	4.44842	0.142978
$969$	0.534759	0.0171789
$970$	31.9442	1.02567
$971$	−15.9441	−0.511671	−0.255835	−	0.966720i	$-0.582350\pi$
$971$	−15.9441	−0.511671	−0.255835	+	0.966720i	$0.582350\pi$
$972$	−3.47982	−0.111615
$973$	0.294213	0.00943205
$974$	12.2545	0.392659
$975$	−0.720216	−0.0230654
$976$	5.56733	0.178206
$977$	53.3414	1.70654	0.853271	−	0.521467i	$-0.174615\pi$
$977$	53.3414	1.70654	0.853271	+	0.521467i	$0.174615\pi$
$978$	−0.681107	−0.0217794
$979$	−42.0357	−1.34347
$980$	−13.3439	−0.426256
$981$	22.8994	0.731123
$982$	−28.8555	−0.920817
$983$	−8.46589	−0.270020	−0.135010	−	0.990844i	$-0.543107\pi$
$983$	−8.46589	−0.270020	−0.135010	+	0.990844i	$0.543107\pi$
$984$	0.813215	0.0259244
$985$	−11.2070	−0.357085
$986$	−18.7114	−0.595893
$987$	0.0150885	0.000480272 0
$988$	−4.06204	−0.129231
$989$	−12.3269	−0.391973
$990$	14.5571	0.462654
$991$	−2.54523	−0.0808520	−0.0404260	−	0.999183i	$-0.512872\pi$
$991$	−2.54523	−0.0808520	−0.0404260	+	0.999183i	$0.512872\pi$
$992$	−4.14167	−0.131498
$993$	−3.17867	−0.100872
$994$	0.277903	0.00881455
$995$	−39.2084	−1.24299
$996$	−0.752863	−0.0238554
$997$	−7.84842	−0.248562	−0.124281	−	0.992247i	$-0.539662\pi$
$997$	−7.84842	−0.248562	−0.124281	+	0.992247i	$0.539662\pi$
$998$	4.80541	0.152113
$999$	7.40018	0.234131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.g.1.17	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.g.1.17	✓	34	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.129854 q^{3} +1.00000 q^{4} +1.90646 q^{5} +0.129854 q^{6} -0.0260326 q^{7} -1.00000 q^{8} -2.98314 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.129854 q^{3} +1.00000 q^{4} +1.90646 q^{5} +0.129854 q^{6} -0.0260326 q^{7} -1.00000 q^{8} -2.98314 q^{9} -1.90646 q^{10} +2.55961 q^{11} -0.129854 q^{12} -4.06204 q^{13} +0.0260326 q^{14} -0.247562 q^{15} +1.00000 q^{16} -4.11815 q^{17} +2.98314 q^{18} +1.00000 q^{19} +1.90646 q^{20} +0.00338044 q^{21} -2.55961 q^{22} +3.49020 q^{23} +0.129854 q^{24} -1.36541 q^{25} +4.06204 q^{26} +0.776935 q^{27} -0.0260326 q^{28} -4.54364 q^{29} +0.247562 q^{30} +4.14167 q^{31} -1.00000 q^{32} -0.332376 q^{33} +4.11815 q^{34} -0.0496300 q^{35} -2.98314 q^{36} +9.52484 q^{37} -1.00000 q^{38} +0.527473 q^{39} -1.90646 q^{40} +6.26253 q^{41} -0.00338044 q^{42} -3.53186 q^{43} +2.55961 q^{44} -5.68723 q^{45} -3.49020 q^{46} +4.46347 q^{47} -0.129854 q^{48} -6.99932 q^{49} +1.36541 q^{50} +0.534759 q^{51} -4.06204 q^{52} -11.6139 q^{53} -0.776935 q^{54} +4.87979 q^{55} +0.0260326 q^{56} -0.129854 q^{57} +4.54364 q^{58} +3.30491 q^{59} -0.247562 q^{60} +5.56733 q^{61} -4.14167 q^{62} +0.0776587 q^{63} +1.00000 q^{64} -7.74412 q^{65} +0.332376 q^{66} +3.69793 q^{67} -4.11815 q^{68} -0.453217 q^{69} +0.0496300 q^{70} +10.6752 q^{71} +2.98314 q^{72} -6.37745 q^{73} -9.52484 q^{74} +0.177304 q^{75} +1.00000 q^{76} -0.0666331 q^{77} -0.527473 q^{78} +17.2377 q^{79} +1.90646 q^{80} +8.84853 q^{81} -6.26253 q^{82} +5.79776 q^{83} +0.00338044 q^{84} -7.85110 q^{85} +3.53186 q^{86} +0.590011 q^{87} -2.55961 q^{88} -16.4227 q^{89} +5.68723 q^{90} +0.105745 q^{91} +3.49020 q^{92} -0.537813 q^{93} -4.46347 q^{94} +1.90646 q^{95} +0.129854 q^{96} -16.7557 q^{97} +6.99932 q^{98} -7.63566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

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