LMFDB - Embedded newform 8018.2.a.f.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.11253 q^{3} +1.00000 q^{4} -2.63739 q^{5} +1.11253 q^{6} -4.04134 q^{7} -1.00000 q^{8} -1.76228 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.11253 q^{3} +1.00000 q^{4} -2.63739 q^{5} +1.11253 q^{6} -4.04134 q^{7} -1.00000 q^{8} -1.76228 q^{9} +2.63739 q^{10} -0.240117 q^{11} -1.11253 q^{12} -4.90150 q^{13} +4.04134 q^{14} +2.93417 q^{15} +1.00000 q^{16} -2.68375 q^{17} +1.76228 q^{18} -1.00000 q^{19} -2.63739 q^{20} +4.49610 q^{21} +0.240117 q^{22} +4.56012 q^{23} +1.11253 q^{24} +1.95582 q^{25} +4.90150 q^{26} +5.29817 q^{27} -4.04134 q^{28} -3.19444 q^{29} -2.93417 q^{30} +4.37170 q^{31} -1.00000 q^{32} +0.267137 q^{33} +2.68375 q^{34} +10.6586 q^{35} -1.76228 q^{36} -9.88907 q^{37} +1.00000 q^{38} +5.45305 q^{39} +2.63739 q^{40} -0.240486 q^{41} -4.49610 q^{42} +11.1937 q^{43} -0.240117 q^{44} +4.64783 q^{45} -4.56012 q^{46} +5.99061 q^{47} -1.11253 q^{48} +9.33245 q^{49} -1.95582 q^{50} +2.98575 q^{51} -4.90150 q^{52} -11.9229 q^{53} -5.29817 q^{54} +0.633283 q^{55} +4.04134 q^{56} +1.11253 q^{57} +3.19444 q^{58} -3.67352 q^{59} +2.93417 q^{60} +4.10473 q^{61} -4.37170 q^{62} +7.12199 q^{63} +1.00000 q^{64} +12.9272 q^{65} -0.267137 q^{66} +13.1464 q^{67} -2.68375 q^{68} -5.07326 q^{69} -10.6586 q^{70} +6.19117 q^{71} +1.76228 q^{72} +0.320560 q^{73} +9.88907 q^{74} -2.17591 q^{75} -1.00000 q^{76} +0.970397 q^{77} -5.45305 q^{78} +3.48112 q^{79} -2.63739 q^{80} -0.607511 q^{81} +0.240486 q^{82} +1.60709 q^{83} +4.49610 q^{84} +7.07809 q^{85} -11.1937 q^{86} +3.55390 q^{87} +0.240117 q^{88} +1.30673 q^{89} -4.64783 q^{90} +19.8086 q^{91} +4.56012 q^{92} -4.86364 q^{93} -5.99061 q^{94} +2.63739 q^{95} +1.11253 q^{96} -15.2653 q^{97} -9.33245 q^{98} +0.423155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	−1.11253	−0.642318	−0.321159	−	0.947025i	$-0.604072\pi$
$3$	−1.11253	−0.642318	−0.321159	+	0.947025i	$0.604072\pi$
$4$	1.00000	0.500000
$5$	−2.63739	−1.17948	−0.589738	−	0.807594i	$-0.700769\pi$
$5$	−2.63739	−1.17948	−0.589738	+	0.807594i	$0.700769\pi$
$6$	1.11253	0.454187
$7$	−4.04134	−1.52748	−0.763742	−	0.645522i	$-0.776640\pi$
$7$	−4.04134	−1.52748	−0.763742	+	0.645522i	$0.776640\pi$
$8$	−1.00000	−0.353553
$9$	−1.76228	−0.587428
$10$	2.63739	0.834016
$11$	−0.240117	−0.0723981	−0.0361991	−	0.999345i	$-0.511525\pi$
$11$	−0.240117	−0.0723981	−0.0361991	+	0.999345i	$0.511525\pi$
$12$	−1.11253	−0.321159
$13$	−4.90150	−1.35943	−0.679716	−	0.733476i	$-0.737897\pi$
$13$	−4.90150	−1.35943	−0.679716	+	0.733476i	$0.737897\pi$
$14$	4.04134	1.08009
$15$	2.93417	0.757599
$16$	1.00000	0.250000
$17$	−2.68375	−0.650905	−0.325453	−	0.945558i	$-0.605517\pi$
$17$	−2.68375	−0.650905	−0.325453	+	0.945558i	$0.605517\pi$
$18$	1.76228	0.415374
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.63739	−0.589738
$21$	4.49610	0.981130
$22$	0.240117	0.0511932
$23$	4.56012	0.950850	0.475425	−	0.879756i	$-0.342294\pi$
$23$	4.56012	0.950850	0.475425	+	0.879756i	$0.342294\pi$
$24$	1.11253	0.227094
$25$	1.95582	0.391165
$26$	4.90150	0.961263
$27$	5.29817	1.01963
$28$	−4.04134	−0.763742
$29$	−3.19444	−0.593193	−0.296597	−	0.955003i	$-0.595852\pi$
$29$	−3.19444	−0.593193	−0.296597	+	0.955003i	$0.595852\pi$
$30$	−2.93417	−0.535703
$31$	4.37170	0.785180	0.392590	−	0.919714i	$-0.371579\pi$
$31$	4.37170	0.785180	0.392590	+	0.919714i	$0.371579\pi$
$32$	−1.00000	−0.176777
$33$	0.267137	0.0465026
$34$	2.68375	0.460259
$35$	10.6586	1.80163
$36$	−1.76228	−0.293714
$37$	−9.88907	−1.62575	−0.812877	−	0.582436i	$-0.802100\pi$
$37$	−9.88907	−1.62575	−0.812877	+	0.582436i	$0.802100\pi$
$38$	1.00000	0.162221
$39$	5.45305	0.873187
$40$	2.63739	0.417008
$41$	−0.240486	−0.0375575	−0.0187788	−	0.999824i	$-0.505978\pi$
$41$	−0.240486	−0.0375575	−0.0187788	+	0.999824i	$0.505978\pi$
$42$	−4.49610	−0.693764
$43$	11.1937	1.70702	0.853508	−	0.521080i	$-0.174471\pi$
$43$	11.1937	1.70702	0.853508	+	0.521080i	$0.174471\pi$
$44$	−0.240117	−0.0361991
$45$	4.64783	0.692857
$46$	−4.56012	−0.672353
$47$	5.99061	0.873821	0.436910	−	0.899505i	$-0.356073\pi$
$47$	5.99061	0.873821	0.436910	+	0.899505i	$0.356073\pi$
$48$	−1.11253	−0.160580
$49$	9.33245	1.33321
$50$	−1.95582	−0.276595
$51$	2.98575	0.418088
$52$	−4.90150	−0.679716
$53$	−11.9229	−1.63773	−0.818867	−	0.573983i	$-0.805398\pi$
$53$	−11.9229	−1.63773	−0.818867	+	0.573983i	$0.805398\pi$
$54$	−5.29817	−0.720990
$55$	0.633283	0.0853919
$56$	4.04134	0.540047
$57$	1.11253	0.147358
$58$	3.19444	0.419451
$59$	−3.67352	−0.478251	−0.239126	−	0.970989i	$-0.576861\pi$
$59$	−3.67352	−0.478251	−0.239126	+	0.970989i	$0.576861\pi$
$60$	2.93417	0.378799
$61$	4.10473	0.525557	0.262779	−	0.964856i	$-0.415361\pi$
$61$	4.10473	0.525557	0.262779	+	0.964856i	$0.415361\pi$
$62$	−4.37170	−0.555206
$63$	7.12199	0.897286
$64$	1.00000	0.125000
$65$	12.9272	1.60342
$66$	−0.267137	−0.0328823
$67$	13.1464	1.60608	0.803042	−	0.595922i	$-0.203213\pi$
$67$	13.1464	1.60608	0.803042	+	0.595922i	$0.203213\pi$
$68$	−2.68375	−0.325453
$69$	−5.07326	−0.610748
$70$	−10.6586	−1.27395
$71$	6.19117	0.734757	0.367379	−	0.930071i	$-0.380255\pi$
$71$	6.19117	0.734757	0.367379	+	0.930071i	$0.380255\pi$
$72$	1.76228	0.207687
$73$	0.320560	0.0375187	0.0187594	−	0.999824i	$-0.494028\pi$
$73$	0.320560	0.0375187	0.0187594	+	0.999824i	$0.494028\pi$
$74$	9.88907	1.14958
$75$	−2.17591	−0.251252
$76$	−1.00000	−0.114708
$77$	0.970397	0.110587
$78$	−5.45305	−0.617437
$79$	3.48112	0.391656	0.195828	−	0.980638i	$-0.437261\pi$
$79$	3.48112	0.391656	0.195828	+	0.980638i	$0.437261\pi$
$80$	−2.63739	−0.294869
$81$	−0.607511	−0.0675013
$82$	0.240486	0.0265572
$83$	1.60709	0.176401	0.0882005	−	0.996103i	$-0.471888\pi$
$83$	1.60709	0.176401	0.0882005	+	0.996103i	$0.471888\pi$
$84$	4.49610	0.490565
$85$	7.07809	0.767727
$86$	−11.1937	−1.20704
$87$	3.55390	0.381019
$88$	0.240117	0.0255966
$89$	1.30673	0.138513	0.0692565	−	0.997599i	$-0.477937\pi$
$89$	1.30673	0.138513	0.0692565	+	0.997599i	$0.477937\pi$
$90$	−4.64783	−0.489924
$91$	19.8086	2.07651
$92$	4.56012	0.475425
$93$	−4.86364	−0.504335
$94$	−5.99061	−0.617885
$95$	2.63739	0.270590
$96$	1.11253	0.113547
$97$	−15.2653	−1.54996	−0.774978	−	0.631988i	$-0.782239\pi$
$97$	−15.2653	−1.54996	−0.774978	+	0.631988i	$0.782239\pi$
$98$	−9.33245	−0.942720
$99$	0.423155	0.0425287
$100$	1.95582	0.195582
$101$	9.93722	0.988790	0.494395	−	0.869237i	$-0.335390\pi$
$101$	9.93722	0.988790	0.494395	+	0.869237i	$0.335390\pi$
$102$	−2.98575	−0.295633
$103$	4.46964	0.440407	0.220204	−	0.975454i	$-0.429328\pi$
$103$	4.46964	0.440407	0.220204	+	0.975454i	$0.429328\pi$
$104$	4.90150	0.480632
$105$	−11.8580	−1.15722
$106$	11.9229	1.15805
$107$	3.94388	0.381269	0.190635	−	0.981661i	$-0.438945\pi$
$107$	3.94388	0.381269	0.190635	+	0.981661i	$0.438945\pi$
$108$	5.29817	0.509817
$109$	8.89273	0.851769	0.425885	−	0.904778i	$-0.359963\pi$
$109$	8.89273	0.851769	0.425885	+	0.904778i	$0.359963\pi$
$110$	−0.633283	−0.0603812
$111$	11.0019	1.04425
$112$	−4.04134	−0.381871
$113$	−16.3838	−1.54126	−0.770628	−	0.637286i	$-0.780057\pi$
$113$	−16.3838	−1.54126	−0.770628	+	0.637286i	$0.780057\pi$
$114$	−1.11253	−0.104198
$115$	−12.0268	−1.12151
$116$	−3.19444	−0.296597
$117$	8.63783	0.798568
$118$	3.67352	0.338175
$119$	10.8460	0.994247
$120$	−2.93417	−0.267852
$121$	−10.9423	−0.994759
$122$	−4.10473	−0.371625
$123$	0.267547	0.0241239
$124$	4.37170	0.392590
$125$	8.02868	0.718107
$126$	−7.12199	−0.634477
$127$	−0.665924	−0.0590912	−0.0295456	−	0.999563i	$-0.509406\pi$
$127$	−0.665924	−0.0590912	−0.0295456	+	0.999563i	$0.509406\pi$
$128$	−1.00000	−0.0883883
$129$	−12.4532	−1.09645
$130$	−12.9272	−1.13379
$131$	10.6208	0.927947	0.463973	−	0.885849i	$-0.346423\pi$
$131$	10.6208	0.927947	0.463973	+	0.885849i	$0.346423\pi$
$132$	0.267137	0.0232513
$133$	4.04134	0.350429
$134$	−13.1464	−1.13567
$135$	−13.9733	−1.20263
$136$	2.68375	0.230130
$137$	11.3837	0.972574	0.486287	−	0.873799i	$-0.338351\pi$
$137$	11.3837	0.972574	0.486287	+	0.873799i	$0.338351\pi$
$138$	5.07326	0.431864
$139$	−3.41808	−0.289918	−0.144959	−	0.989438i	$-0.546305\pi$
$139$	−3.41808	−0.289918	−0.144959	+	0.989438i	$0.546305\pi$
$140$	10.6586	0.900816
$141$	−6.66472	−0.561271
$142$	−6.19117	−0.519552
$143$	1.17694	0.0984203
$144$	−1.76228	−0.146857
$145$	8.42499	0.699657
$146$	−0.320560	−0.0265298
$147$	−10.3826	−0.856343
$148$	−9.88907	−0.812877
$149$	0.185320	0.0151820	0.00759101	−	0.999971i	$-0.497584\pi$
$149$	0.185320	0.0151820	0.00759101	+	0.999971i	$0.497584\pi$
$150$	2.17591	0.177662
$151$	0.925829	0.0753429	0.0376714	−	0.999290i	$-0.488006\pi$
$151$	0.925829	0.0753429	0.0376714	+	0.999290i	$0.488006\pi$
$152$	1.00000	0.0811107
$153$	4.72953	0.382360
$154$	−0.970397	−0.0781968
$155$	−11.5299	−0.926102
$156$	5.45305	0.436594
$157$	1.64724	0.131464	0.0657318	−	0.997837i	$-0.479062\pi$
$157$	1.64724	0.131464	0.0657318	+	0.997837i	$0.479062\pi$
$158$	−3.48112	−0.276943
$159$	13.2645	1.05195
$160$	2.63739	0.208504
$161$	−18.4290	−1.45241
$162$	0.607511	0.0477306
$163$	−20.6772	−1.61956	−0.809781	−	0.586733i	$-0.800414\pi$
$163$	−20.6772	−1.61956	−0.809781	+	0.586733i	$0.800414\pi$
$164$	−0.240486	−0.0187788
$165$	−0.704545	−0.0548487
$166$	−1.60709	−0.124734
$167$	−20.6628	−1.59894	−0.799469	−	0.600708i	$-0.794885\pi$
$167$	−20.6628	−1.59894	−0.799469	+	0.600708i	$0.794885\pi$
$168$	−4.49610	−0.346882
$169$	11.0247	0.848054
$170$	−7.07809	−0.542865
$171$	1.76228	0.134765
$172$	11.1937	0.853508
$173$	4.07508	0.309823	0.154911	−	0.987928i	$-0.450491\pi$
$173$	4.07508	0.309823	0.154911	+	0.987928i	$0.450491\pi$
$174$	−3.55390	−0.269421
$175$	−7.90415	−0.597498
$176$	−0.240117	−0.0180995
$177$	4.08689	0.307190
$178$	−1.30673	−0.0979434
$179$	8.87378	0.663258	0.331629	−	0.943410i	$-0.392402\pi$
$179$	8.87378	0.663258	0.331629	+	0.943410i	$0.392402\pi$
$180$	4.64783	0.346428
$181$	21.5901	1.60478	0.802391	−	0.596799i	$-0.203561\pi$
$181$	21.5901	1.60478	0.802391	+	0.596799i	$0.203561\pi$
$182$	−19.8086	−1.46831
$183$	−4.56663	−0.337575
$184$	−4.56012	−0.336176
$185$	26.0813	1.91754
$186$	4.86364	0.356619
$187$	0.644415	0.0471243
$188$	5.99061	0.436910
$189$	−21.4117	−1.55747
$190$	−2.63739	−0.191336
$191$	−1.66451	−0.120440	−0.0602200	−	0.998185i	$-0.519180\pi$
$191$	−1.66451	−0.120440	−0.0602200	+	0.998185i	$0.519180\pi$
$192$	−1.11253	−0.0802898
$193$	−6.70278	−0.482476	−0.241238	−	0.970466i	$-0.577553\pi$
$193$	−6.70278	−0.482476	−0.241238	+	0.970466i	$0.577553\pi$
$194$	15.2653	1.09598
$195$	−14.3818	−1.02990
$196$	9.33245	0.666604
$197$	14.5377	1.03577	0.517885	−	0.855451i	$-0.326720\pi$
$197$	14.5377	1.03577	0.517885	+	0.855451i	$0.326720\pi$
$198$	−0.423155	−0.0300723
$199$	−5.89512	−0.417894	−0.208947	−	0.977927i	$-0.567004\pi$
$199$	−5.89512	−0.417894	−0.208947	+	0.977927i	$0.567004\pi$
$200$	−1.95582	−0.138298
$201$	−14.6257	−1.03162
$202$	−9.93722	−0.699180
$203$	12.9098	0.906093
$204$	2.98575	0.209044
$205$	0.634254	0.0442982
$206$	−4.46964	−0.311415
$207$	−8.03622	−0.558556
$208$	−4.90150	−0.339858
$209$	0.240117	0.0166093
$210$	11.8580	0.818278
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−11.9229	−0.818867
$213$	−6.88785	−0.471948
$214$	−3.94388	−0.269598
$215$	−29.5220	−2.01339
$216$	−5.29817	−0.360495
$217$	−17.6675	−1.19935
$218$	−8.89273	−0.602292
$219$	−0.356632	−0.0240990
$220$	0.633283	0.0426959
$221$	13.1544	0.884861
$222$	−11.0019	−0.738397
$223$	10.7285	0.718431	0.359216	−	0.933255i	$-0.383044\pi$
$223$	10.7285	0.718431	0.359216	+	0.933255i	$0.383044\pi$
$224$	4.04134	0.270024
$225$	−3.44671	−0.229781
$226$	16.3838	1.08983
$227$	2.86126	0.189909	0.0949543	−	0.995482i	$-0.469730\pi$
$227$	2.86126	0.189909	0.0949543	+	0.995482i	$0.469730\pi$
$228$	1.11253	0.0736789
$229$	−6.49370	−0.429116	−0.214558	−	0.976711i	$-0.568831\pi$
$229$	−6.49370	−0.429116	−0.214558	+	0.976711i	$0.568831\pi$
$230$	12.0268	0.793024
$231$	−1.07959	−0.0710320
$232$	3.19444	0.209725
$233$	−16.1920	−1.06077	−0.530387	−	0.847756i	$-0.677953\pi$
$233$	−16.1920	−1.06077	−0.530387	+	0.847756i	$0.677953\pi$
$234$	−8.63783	−0.564673
$235$	−15.7996	−1.03065
$236$	−3.67352	−0.239126
$237$	−3.87284	−0.251568
$238$	−10.8460	−0.703039
$239$	−7.58705	−0.490765	−0.245383	−	0.969426i	$-0.578914\pi$
$239$	−7.58705	−0.490765	−0.245383	+	0.969426i	$0.578914\pi$
$240$	2.93417	0.189400
$241$	20.2339	1.30338	0.651689	−	0.758486i	$-0.274061\pi$
$241$	20.2339	1.30338	0.651689	+	0.758486i	$0.274061\pi$
$242$	10.9423	0.703400
$243$	−15.2186	−0.976276
$244$	4.10473	0.262779
$245$	−24.6133	−1.57249
$246$	−0.267547	−0.0170582
$247$	4.90150	0.311875
$248$	−4.37170	−0.277603
$249$	−1.78793	−0.113306
$250$	−8.02868	−0.507778
$251$	−7.07907	−0.446827	−0.223414	−	0.974724i	$-0.571720\pi$
$251$	−7.07907	−0.446827	−0.223414	+	0.974724i	$0.571720\pi$
$252$	7.12199	0.448643
$253$	−1.09496	−0.0688398
$254$	0.665924	0.0417838
$255$	−7.87457	−0.493125
$256$	1.00000	0.0625000
$257$	17.7435	1.10681	0.553403	−	0.832913i	$-0.313329\pi$
$257$	17.7435	1.10681	0.553403	+	0.832913i	$0.313329\pi$
$258$	12.4532	0.775305
$259$	39.9651	2.48331
$260$	12.9272	0.801709
$261$	5.62951	0.348458
$262$	−10.6208	−0.656158
$263$	−0.728201	−0.0449028	−0.0224514	−	0.999748i	$-0.507147\pi$
$263$	−0.728201	−0.0449028	−0.0224514	+	0.999748i	$0.507147\pi$
$264$	−0.267137	−0.0164412
$265$	31.4453	1.93167
$266$	−4.04134	−0.247791
$267$	−1.45377	−0.0889694
$268$	13.1464	0.803042
$269$	−22.3864	−1.36492	−0.682461	−	0.730922i	$-0.739090\pi$
$269$	−22.3864	−1.36492	−0.682461	+	0.730922i	$0.739090\pi$
$270$	13.9733	0.850390
$271$	−4.48730	−0.272584	−0.136292	−	0.990669i	$-0.543519\pi$
$271$	−4.48730	−0.272584	−0.136292	+	0.990669i	$0.543519\pi$
$272$	−2.68375	−0.162726
$273$	−22.0377	−1.33378
$274$	−11.3837	−0.687714
$275$	−0.469627	−0.0283196
$276$	−5.07326	−0.305374
$277$	−4.33567	−0.260505	−0.130253	−	0.991481i	$-0.541579\pi$
$277$	−4.33567	−0.260505	−0.130253	+	0.991481i	$0.541579\pi$
$278$	3.41808	0.205003
$279$	−7.70417	−0.461237
$280$	−10.6586	−0.636973
$281$	7.06389	0.421396	0.210698	−	0.977551i	$-0.432426\pi$
$281$	7.06389	0.421396	0.210698	+	0.977551i	$0.432426\pi$
$282$	6.66472	0.396878
$283$	−16.6476	−0.989596	−0.494798	−	0.869008i	$-0.664758\pi$
$283$	−16.6476	−0.989596	−0.494798	+	0.869008i	$0.664758\pi$
$284$	6.19117	0.367379
$285$	−2.93417	−0.173805
$286$	−1.17694	−0.0695937
$287$	0.971884	0.0573685
$288$	1.76228	0.103844
$289$	−9.79748	−0.576323
$290$	−8.42499	−0.494732
$291$	16.9831	0.995565
$292$	0.320560	0.0187594
$293$	31.9214	1.86487	0.932435	−	0.361339i	$-0.117680\pi$
$293$	31.9214	1.86487	0.932435	+	0.361339i	$0.117680\pi$
$294$	10.3826	0.605526
$295$	9.68850	0.564086
$296$	9.88907	0.574791
$297$	−1.27218	−0.0738196
$298$	−0.185320	−0.0107353
$299$	−22.3514	−1.29262
$300$	−2.17591	−0.125626
$301$	−45.2374	−2.60744
$302$	−0.925829	−0.0532755
$303$	−11.0554	−0.635118
$304$	−1.00000	−0.0573539
$305$	−10.8258	−0.619882
$306$	−4.72953	−0.270369
$307$	4.25202	0.242676	0.121338	−	0.992611i	$-0.461282\pi$
$307$	4.25202	0.242676	0.121338	+	0.992611i	$0.461282\pi$
$308$	0.970397	0.0552935
$309$	−4.97260	−0.282881
$310$	11.5299	0.654853
$311$	−19.7674	−1.12091	−0.560454	−	0.828185i	$-0.689373\pi$
$311$	−19.7674	−1.12091	−0.560454	+	0.828185i	$0.689373\pi$
$312$	−5.45305	−0.308718
$313$	4.71903	0.266735	0.133368	−	0.991067i	$-0.457421\pi$
$313$	4.71903	0.266735	0.133368	+	0.991067i	$0.457421\pi$
$314$	−1.64724	−0.0929589
$315$	−18.7835	−1.05833
$316$	3.48112	0.195828
$317$	−4.74019	−0.266236	−0.133118	−	0.991100i	$-0.542499\pi$
$317$	−4.74019	−0.266236	−0.133118	+	0.991100i	$0.542499\pi$
$318$	−13.2645	−0.743838
$319$	0.767041	0.0429461
$320$	−2.63739	−0.147435
$321$	−4.38768	−0.244896
$322$	18.4290	1.02701
$323$	2.68375	0.149328
$324$	−0.607511	−0.0337506
$325$	−9.58647	−0.531761
$326$	20.6772	1.14520
$327$	−9.89341	−0.547107
$328$	0.240486	0.0132786
$329$	−24.2101	−1.33475
$330$	0.704545	0.0387839
$331$	16.5217	0.908116	0.454058	−	0.890972i	$-0.349976\pi$
$331$	16.5217	0.908116	0.454058	+	0.890972i	$0.349976\pi$
$332$	1.60709	0.0882005
$333$	17.4273	0.955012
$334$	20.6628	1.13062
$335$	−34.6721	−1.89434
$336$	4.49610	0.245283
$337$	−1.01955	−0.0555382	−0.0277691	−	0.999614i	$-0.508840\pi$
$337$	−1.01955	−0.0555382	−0.0277691	+	0.999614i	$0.508840\pi$
$338$	−11.0247	−0.599665
$339$	18.2274	0.989976
$340$	7.07809	0.383864
$341$	−1.04972	−0.0568456
$342$	−1.76228	−0.0952933
$343$	−9.42624	−0.508969
$344$	−11.1937	−0.603521
$345$	13.3802	0.720363
$346$	−4.07508	−0.219078
$347$	24.1571	1.29682	0.648411	−	0.761291i	$-0.275434\pi$
$347$	24.1571	1.29682	0.648411	+	0.761291i	$0.275434\pi$
$348$	3.55390	0.190509
$349$	−18.5645	−0.993736	−0.496868	−	0.867826i	$-0.665517\pi$
$349$	−18.5645	−0.993736	−0.496868	+	0.867826i	$0.665517\pi$
$350$	7.90415	0.422495
$351$	−25.9690	−1.38612
$352$	0.240117	0.0127983
$353$	1.94911	0.103741	0.0518704	−	0.998654i	$-0.483482\pi$
$353$	1.94911	0.103741	0.0518704	+	0.998654i	$0.483482\pi$
$354$	−4.08689	−0.217216
$355$	−16.3285	−0.866629
$356$	1.30673	0.0692565
$357$	−12.0664	−0.638623
$358$	−8.87378	−0.468994
$359$	10.9179	0.576225	0.288112	−	0.957597i	$-0.406972\pi$
$359$	10.9179	0.576225	0.288112	+	0.957597i	$0.406972\pi$
$360$	−4.64783	−0.244962
$361$	1.00000	0.0526316
$362$	−21.5901	−1.13475
$363$	12.1737	0.638951
$364$	19.8086	1.03825
$365$	−0.845442	−0.0442525
$366$	4.56663	0.238701
$367$	−9.96585	−0.520213	−0.260107	−	0.965580i	$-0.583758\pi$
$367$	−9.96585	−0.520213	−0.260107	+	0.965580i	$0.583758\pi$
$368$	4.56012	0.237713
$369$	0.423803	0.0220623
$370$	−26.0813	−1.35590
$371$	48.1845	2.50161
$372$	−4.86364	−0.252168
$373$	−21.0215	−1.08845	−0.544225	−	0.838939i	$-0.683176\pi$
$373$	−21.0215	−1.08845	−0.544225	+	0.838939i	$0.683176\pi$
$374$	−0.644415	−0.0333219
$375$	−8.93213	−0.461253
$376$	−5.99061	−0.308942
$377$	15.6576	0.806405
$378$	21.4117	1.10130
$379$	16.0239	0.823090	0.411545	−	0.911389i	$-0.364989\pi$
$379$	16.0239	0.823090	0.411545	+	0.911389i	$0.364989\pi$
$380$	2.63739	0.135295
$381$	0.740858	0.0379553
$382$	1.66451	0.0851640
$383$	−9.09873	−0.464923	−0.232462	−	0.972606i	$-0.574678\pi$
$383$	−9.09873	−0.464923	−0.232462	+	0.972606i	$0.574678\pi$
$384$	1.11253	0.0567734
$385$	−2.55931	−0.130435
$386$	6.70278	0.341162
$387$	−19.7264	−1.00275
$388$	−15.2653	−0.774978
$389$	−7.90064	−0.400578	−0.200289	−	0.979737i	$-0.564188\pi$
$389$	−7.90064	−0.400578	−0.200289	+	0.979737i	$0.564188\pi$
$390$	14.3818	0.728252
$391$	−12.2382	−0.618913
$392$	−9.33245	−0.471360
$393$	−11.8160	−0.596037
$394$	−14.5377	−0.732399
$395$	−9.18106	−0.461949
$396$	0.423155	0.0212643
$397$	23.4712	1.17798	0.588992	−	0.808139i	$-0.299525\pi$
$397$	23.4712	1.17798	0.588992	+	0.808139i	$0.299525\pi$
$398$	5.89512	0.295496
$399$	−4.49610	−0.225087
$400$	1.95582	0.0977911
$401$	39.4713	1.97110	0.985552	−	0.169374i	$-0.0541745\pi$
$401$	39.4713	1.97110	0.985552	+	0.169374i	$0.0541745\pi$
$402$	14.6257	0.729463
$403$	−21.4279	−1.06740
$404$	9.93722	0.494395
$405$	1.60224	0.0796162
$406$	−12.9098	−0.640704
$407$	2.37454	0.117701
$408$	−2.98575	−0.147816
$409$	26.1666	1.29385	0.646927	−	0.762552i	$-0.276054\pi$
$409$	26.1666	1.29385	0.646927	+	0.762552i	$0.276054\pi$
$410$	−0.634254	−0.0313236
$411$	−12.6647	−0.624702
$412$	4.46964	0.220204
$413$	14.8459	0.730521
$414$	8.03622	0.394959
$415$	−4.23852	−0.208061
$416$	4.90150	0.240316
$417$	3.80271	0.186219
$418$	−0.240117	−0.0117445
$419$	39.0719	1.90879	0.954393	−	0.298553i	$-0.0965039\pi$
$419$	39.0719	1.90879	0.954393	+	0.298553i	$0.0965039\pi$
$420$	−11.8580	−0.578610
$421$	−38.6123	−1.88185	−0.940923	−	0.338620i	$-0.890040\pi$
$421$	−38.6123	−1.88185	−0.940923	+	0.338620i	$0.890040\pi$
$422$	1.00000	0.0486792
$423$	−10.5572	−0.513306
$424$	11.9229	0.579027
$425$	−5.24894	−0.254611
$426$	6.88785	0.333717
$427$	−16.5886	−0.802780
$428$	3.94388	0.190635
$429$	−1.30937	−0.0632171
$430$	29.5220	1.42368
$431$	−3.77651	−0.181908	−0.0909540	−	0.995855i	$-0.528992\pi$
$431$	−3.77651	−0.181908	−0.0909540	+	0.995855i	$0.528992\pi$
$432$	5.29817	0.254908
$433$	−28.8779	−1.38778	−0.693891	−	0.720080i	$-0.744105\pi$
$433$	−28.8779	−1.38778	−0.693891	+	0.720080i	$0.744105\pi$
$434$	17.6675	0.848069
$435$	−9.37303	−0.449402
$436$	8.89273	0.425885
$437$	−4.56012	−0.218140
$438$	0.356632	0.0170405
$439$	−22.3702	−1.06767	−0.533836	−	0.845588i	$-0.679250\pi$
$439$	−22.3702	−1.06767	−0.533836	+	0.845588i	$0.679250\pi$
$440$	−0.633283	−0.0301906
$441$	−16.4464	−0.783163
$442$	−13.1544	−0.625691
$443$	−25.0821	−1.19169	−0.595844	−	0.803100i	$-0.703182\pi$
$443$	−25.0821	−1.19169	−0.595844	+	0.803100i	$0.703182\pi$
$444$	11.0019	0.522125
$445$	−3.44635	−0.163373
$446$	−10.7285	−0.508008
$447$	−0.206174	−0.00975169
$448$	−4.04134	−0.190935
$449$	−0.763087	−0.0360123	−0.0180062	−	0.999838i	$-0.505732\pi$
$449$	−0.763087	−0.0360123	−0.0180062	+	0.999838i	$0.505732\pi$
$450$	3.44671	0.162480
$451$	0.0577448	0.00271910
$452$	−16.3838	−0.770628
$453$	−1.03001	−0.0483941
$454$	−2.86126	−0.134286
$455$	−52.2431	−2.44919
$456$	−1.11253	−0.0520989
$457$	3.10779	0.145376	0.0726882	−	0.997355i	$-0.476842\pi$
$457$	3.10779	0.145376	0.0726882	+	0.997355i	$0.476842\pi$
$458$	6.49370	0.303431
$459$	−14.2190	−0.663685
$460$	−12.0268	−0.560753
$461$	−4.63610	−0.215925	−0.107962	−	0.994155i	$-0.534433\pi$
$461$	−4.63610	−0.215925	−0.107962	+	0.994155i	$0.534433\pi$
$462$	1.07959	0.0502272
$463$	0.137750	0.00640177	0.00320089	−	0.999995i	$-0.498981\pi$
$463$	0.137750	0.00640177	0.00320089	+	0.999995i	$0.498981\pi$
$464$	−3.19444	−0.148298
$465$	12.8273	0.594852
$466$	16.1920	0.750081
$467$	32.7027	1.51330	0.756649	−	0.653821i	$-0.226835\pi$
$467$	32.7027	1.51330	0.756649	+	0.653821i	$0.226835\pi$
$468$	8.63783	0.399284
$469$	−53.1290	−2.45327
$470$	15.7996	0.728780
$471$	−1.83259	−0.0844415
$472$	3.67352	0.169087
$473$	−2.68779	−0.123585
$474$	3.87284	0.177885
$475$	−1.95582	−0.0897393
$476$	10.8460	0.497124
$477$	21.0115	0.962050
$478$	7.58705	0.347023
$479$	16.5721	0.757198	0.378599	−	0.925561i	$-0.376406\pi$
$479$	16.5721	0.757198	0.378599	+	0.925561i	$0.376406\pi$
$480$	−2.93417	−0.133926
$481$	48.4713	2.21010
$482$	−20.2339	−0.921627
$483$	20.5028	0.932908
$484$	−10.9423	−0.497379
$485$	40.2605	1.82814
$486$	15.2186	0.690331
$487$	1.90081	0.0861341	0.0430671	−	0.999072i	$-0.486287\pi$
$487$	1.90081	0.0861341	0.0430671	+	0.999072i	$0.486287\pi$
$488$	−4.10473	−0.185813
$489$	23.0039	1.04027
$490$	24.6133	1.11192
$491$	14.8056	0.668170	0.334085	−	0.942543i	$-0.391573\pi$
$491$	14.8056	0.668170	0.334085	+	0.942543i	$0.391573\pi$
$492$	0.267547	0.0120619
$493$	8.57309	0.386112
$494$	−4.90150	−0.220529
$495$	−1.11602	−0.0501616
$496$	4.37170	0.196295
$497$	−25.0207	−1.12233
$498$	1.78793	0.0801191
$499$	5.92541	0.265258	0.132629	−	0.991166i	$-0.457658\pi$
$499$	5.92541	0.265258	0.132629	+	0.991166i	$0.457658\pi$
$500$	8.02868	0.359054
$501$	22.9880	1.02703
$502$	7.07907	0.315955
$503$	−21.3962	−0.954010	−0.477005	−	0.878901i	$-0.658278\pi$
$503$	−21.3962	−0.954010	−0.477005	+	0.878901i	$0.658278\pi$
$504$	−7.12199	−0.317239
$505$	−26.2083	−1.16625
$506$	1.09496	0.0486771
$507$	−12.2653	−0.544720
$508$	−0.665924	−0.0295456
$509$	−2.77983	−0.123214	−0.0616068	−	0.998100i	$-0.519622\pi$
$509$	−2.77983	−0.123214	−0.0616068	+	0.998100i	$0.519622\pi$
$510$	7.87457	0.348692
$511$	−1.29549	−0.0573093
$512$	−1.00000	−0.0441942
$513$	−5.29817	−0.233920
$514$	−17.7435	−0.782630
$515$	−11.7882	−0.519450
$516$	−12.4532	−0.548224
$517$	−1.43845	−0.0632630
$518$	−39.9651	−1.75597
$519$	−4.53364	−0.199005
$520$	−12.9272	−0.566894
$521$	24.1864	1.05962	0.529812	−	0.848115i	$-0.322262\pi$
$521$	24.1864	1.05962	0.529812	+	0.848115i	$0.322262\pi$
$522$	−5.62951	−0.246397
$523$	−16.0536	−0.701976	−0.350988	−	0.936380i	$-0.614154\pi$
$523$	−16.0536	−0.701976	−0.350988	+	0.936380i	$0.614154\pi$
$524$	10.6208	0.463973
$525$	8.79358	0.383783
$526$	0.728201	0.0317511
$527$	−11.7325	−0.511078
$528$	0.267137	0.0116257
$529$	−2.20532	−0.0958834
$530$	−31.4453	−1.36590
$531$	6.47378	0.280938
$532$	4.04134	0.175214
$533$	1.17874	0.0510569
$534$	1.45377	0.0629108
$535$	−10.4016	−0.449698
$536$	−13.1464	−0.567837
$537$	−9.87233	−0.426022
$538$	22.3864	0.965145
$539$	−2.24088	−0.0965217
$540$	−13.9733	−0.601317
$541$	14.4094	0.619511	0.309755	−	0.950816i	$-0.399753\pi$
$541$	14.4094	0.619511	0.309755	+	0.950816i	$0.399753\pi$
$542$	4.48730	0.192746
$543$	−24.0196	−1.03078
$544$	2.68375	0.115065
$545$	−23.4536	−1.00464
$546$	22.0377	0.943125
$547$	−15.3359	−0.655715	−0.327857	−	0.944727i	$-0.606327\pi$
$547$	−15.3359	−0.655715	−0.327857	+	0.944727i	$0.606327\pi$
$548$	11.3837	0.486287
$549$	−7.23370	−0.308727
$550$	0.469627	0.0200250
$551$	3.19444	0.136088
$552$	5.07326	0.215932
$553$	−14.0684	−0.598249
$554$	4.33567	0.184205
$555$	−29.0162	−1.23167
$556$	−3.41808	−0.144959
$557$	−3.09288	−0.131050	−0.0655248	−	0.997851i	$-0.520872\pi$
$557$	−3.09288	−0.131050	−0.0655248	+	0.997851i	$0.520872\pi$
$558$	7.70417	0.326144
$559$	−54.8657	−2.32057
$560$	10.6586	0.450408
$561$	−0.716930	−0.0302688
$562$	−7.06389	−0.297972
$563$	−1.88851	−0.0795913	−0.0397957	−	0.999208i	$-0.512671\pi$
$563$	−1.88851	−0.0795913	−0.0397957	+	0.999208i	$0.512671\pi$
$564$	−6.66472	−0.280635
$565$	43.2104	1.81787
$566$	16.6476	0.699750
$567$	2.45516	0.103107
$568$	−6.19117	−0.259776
$569$	−2.89516	−0.121372	−0.0606858	−	0.998157i	$-0.519329\pi$
$569$	−2.89516	−0.121372	−0.0606858	+	0.998157i	$0.519329\pi$
$570$	2.93417	0.122899
$571$	4.16620	0.174350	0.0871751	−	0.996193i	$-0.472216\pi$
$571$	4.16620	0.174350	0.0871751	+	0.996193i	$0.472216\pi$
$572$	1.17694	0.0492102
$573$	1.85182	0.0773608
$574$	−0.971884	−0.0405657
$575$	8.91878	0.371939
$576$	−1.76228	−0.0734284
$577$	−8.66978	−0.360928	−0.180464	−	0.983582i	$-0.557760\pi$
$577$	−8.66978	−0.360928	−0.180464	+	0.983582i	$0.557760\pi$
$578$	9.79748	0.407522
$579$	7.45702	0.309903
$580$	8.42499	0.349829
$581$	−6.49480	−0.269450
$582$	−16.9831	−0.703971
$583$	2.86289	0.118569
$584$	−0.320560	−0.0132649
$585$	−22.7813	−0.941892
$586$	−31.9214	−1.31866
$587$	47.3551	1.95455	0.977276	−	0.211970i	$-0.0679879\pi$
$587$	47.3551	1.95455	0.977276	+	0.211970i	$0.0679879\pi$
$588$	−10.3826	−0.428172
$589$	−4.37170	−0.180133
$590$	−9.68850	−0.398869
$591$	−16.1736	−0.665293
$592$	−9.88907	−0.406438
$593$	30.7889	1.26435	0.632174	−	0.774827i	$-0.282163\pi$
$593$	30.7889	1.26435	0.632174	+	0.774827i	$0.282163\pi$
$594$	1.27218	0.0521983
$595$	−28.6050	−1.17269
$596$	0.185320	0.00759101
$597$	6.55848	0.268421
$598$	22.3514	0.914018
$599$	−44.1625	−1.80443	−0.902215	−	0.431286i	$-0.858060\pi$
$599$	−44.1625	−1.80443	−0.902215	+	0.431286i	$0.858060\pi$
$600$	2.17591	0.0888310
$601$	16.0161	0.653311	0.326656	−	0.945143i	$-0.394078\pi$
$601$	16.0161	0.653311	0.326656	+	0.945143i	$0.394078\pi$
$602$	45.2374	1.84374
$603$	−23.1676	−0.943458
$604$	0.925829	0.0376714
$605$	28.8592	1.17329
$606$	11.0554	0.449096
$607$	−35.2017	−1.42879	−0.714397	−	0.699741i	$-0.753299\pi$
$607$	−35.2017	−1.42879	−0.714397	+	0.699741i	$0.753299\pi$
$608$	1.00000	0.0405554
$609$	−14.3625	−0.582000
$610$	10.8258	0.438323
$611$	−29.3630	−1.18790
$612$	4.72953	0.191180
$613$	−29.7543	−1.20177	−0.600883	−	0.799337i	$-0.705184\pi$
$613$	−29.7543	−1.20177	−0.600883	+	0.799337i	$0.705184\pi$
$614$	−4.25202	−0.171598
$615$	−0.705625	−0.0284535
$616$	−0.970397	−0.0390984
$617$	−8.71022	−0.350660	−0.175330	−	0.984510i	$-0.556099\pi$
$617$	−8.71022	−0.350660	−0.175330	+	0.984510i	$0.556099\pi$
$618$	4.97260	0.200027
$619$	6.02889	0.242322	0.121161	−	0.992633i	$-0.461338\pi$
$619$	6.02889	0.242322	0.121161	+	0.992633i	$0.461338\pi$
$620$	−11.5299	−0.463051
$621$	24.1603	0.969519
$622$	19.7674	0.792602
$623$	−5.28094	−0.211576
$624$	5.45305	0.218297
$625$	−30.9539	−1.23815
$626$	−4.71903	−0.188610
$627$	−0.267137	−0.0106684
$628$	1.64724	0.0657318
$629$	26.5398	1.05821
$630$	18.7835	0.748351
$631$	6.91748	0.275381	0.137690	−	0.990475i	$-0.456032\pi$
$631$	6.91748	0.275381	0.137690	+	0.990475i	$0.456032\pi$
$632$	−3.48112	−0.138471
$633$	1.11253	0.0442190
$634$	4.74019	0.188257
$635$	1.75630	0.0696967
$636$	13.2645	0.525973
$637$	−45.7430	−1.81240
$638$	−0.767041	−0.0303675
$639$	−10.9106	−0.431617
$640$	2.63739	0.104252
$641$	20.0416	0.791595	0.395798	−	0.918338i	$-0.370468\pi$
$641$	20.0416	0.791595	0.395798	+	0.918338i	$0.370468\pi$
$642$	4.38768	0.173168
$643$	−3.64402	−0.143706	−0.0718531	−	0.997415i	$-0.522891\pi$
$643$	−3.64402	−0.143706	−0.0718531	+	0.997415i	$0.522891\pi$
$644$	−18.4290	−0.726204
$645$	32.8441	1.29323
$646$	−2.68375	−0.105591
$647$	29.5775	1.16281	0.581406	−	0.813614i	$-0.302503\pi$
$647$	29.5775	1.16281	0.581406	+	0.813614i	$0.302503\pi$
$648$	0.607511	0.0238653
$649$	0.882076	0.0346245
$650$	9.58647	0.376012
$651$	19.6556	0.770364
$652$	−20.6772	−0.809781
$653$	−17.3919	−0.680596	−0.340298	−	0.940318i	$-0.610528\pi$
$653$	−17.3919	−0.680596	−0.340298	+	0.940318i	$0.610528\pi$
$654$	9.89341	0.386863
$655$	−28.0113	−1.09449
$656$	−0.240486	−0.00938938
$657$	−0.564918	−0.0220395
$658$	24.2101	0.943809
$659$	−17.3694	−0.676615	−0.338308	−	0.941036i	$-0.609854\pi$
$659$	−17.3694	−0.676615	−0.338308	+	0.941036i	$0.609854\pi$
$660$	−0.704545	−0.0274244
$661$	−20.0851	−0.781220	−0.390610	−	0.920556i	$-0.627736\pi$
$661$	−20.0851	−0.781220	−0.390610	+	0.920556i	$0.627736\pi$
$662$	−16.5217	−0.642135
$663$	−14.6346	−0.568362
$664$	−1.60709	−0.0623672
$665$	−10.6586	−0.413323
$666$	−17.4273	−0.675296
$667$	−14.5670	−0.564038
$668$	−20.6628	−0.799469
$669$	−11.9357	−0.461461
$670$	34.6721	1.33950
$671$	−0.985618	−0.0380494
$672$	−4.49610	−0.173441
$673$	2.17284	0.0837568	0.0418784	−	0.999123i	$-0.486666\pi$
$673$	2.17284	0.0837568	0.0418784	+	0.999123i	$0.486666\pi$
$674$	1.01955	0.0392714
$675$	10.3623	0.398844
$676$	11.0247	0.424027
$677$	−9.56754	−0.367710	−0.183855	−	0.982953i	$-0.558858\pi$
$677$	−9.56754	−0.367710	−0.183855	+	0.982953i	$0.558858\pi$
$678$	−18.2274	−0.700019
$679$	61.6923	2.36753
$680$	−7.07809	−0.271433
$681$	−3.18323	−0.121982
$682$	1.04972	0.0401959
$683$	24.9655	0.955280	0.477640	−	0.878556i	$-0.341492\pi$
$683$	24.9655	0.955280	0.477640	+	0.878556i	$0.341492\pi$
$684$	1.76228	0.0673826
$685$	−30.0232	−1.14713
$686$	9.42624	0.359895
$687$	7.22442	0.275629
$688$	11.1937	0.426754
$689$	58.4400	2.22639
$690$	−13.3802	−0.509374
$691$	44.3186	1.68596	0.842980	−	0.537945i	$-0.180799\pi$
$691$	44.3186	1.68596	0.842980	+	0.537945i	$0.180799\pi$
$692$	4.07508	0.154911
$693$	−1.71011	−0.0649618
$694$	−24.1571	−0.916991
$695$	9.01481	0.341951
$696$	−3.55390	−0.134710
$697$	0.645403	0.0244464
$698$	18.5645	0.702677
$699$	18.0141	0.681355
$700$	−7.90415	−0.298749
$701$	26.5774	1.00381	0.501907	−	0.864921i	$-0.332632\pi$
$701$	26.5774	1.00381	0.501907	+	0.864921i	$0.332632\pi$
$702$	25.9690	0.980136
$703$	9.88907	0.372973
$704$	−0.240117	−0.00904977
$705$	17.5775	0.662006
$706$	−1.94911	−0.0733558
$707$	−40.1597	−1.51036
$708$	4.08689	0.153595
$709$	37.6406	1.41362	0.706812	−	0.707402i	$-0.250133\pi$
$709$	37.6406	1.41362	0.706812	+	0.707402i	$0.250133\pi$
$710$	16.3285	0.612799
$711$	−6.13471	−0.230070
$712$	−1.30673	−0.0489717
$713$	19.9355	0.746589
$714$	12.0664	0.451575
$715$	−3.10404	−0.116084
$716$	8.87378	0.331629
$717$	8.44080	0.315227
$718$	−10.9179	−0.407452
$719$	34.4837	1.28603	0.643013	−	0.765856i	$-0.277684\pi$
$719$	34.4837	1.28603	0.643013	+	0.765856i	$0.277684\pi$
$720$	4.64783	0.173214
$721$	−18.0634	−0.672715
$722$	−1.00000	−0.0372161
$723$	−22.5107	−0.837183
$724$	21.5901	0.802391
$725$	−6.24776	−0.232036
$726$	−12.1737	−0.451807
$727$	−25.4792	−0.944969	−0.472485	−	0.881339i	$-0.656643\pi$
$727$	−25.4792	−0.944969	−0.472485	+	0.881339i	$0.656643\pi$
$728$	−19.8086	−0.734157
$729$	18.7537	0.694581
$730$	0.845442	0.0312912
$731$	−30.0410	−1.11111
$732$	−4.56663	−0.168787
$733$	−27.0738	−0.999995	−0.499998	−	0.866027i	$-0.666666\pi$
$733$	−27.0738	−0.999995	−0.499998	+	0.866027i	$0.666666\pi$
$734$	9.96585	0.367846
$735$	27.3830	1.01004
$736$	−4.56012	−0.168088
$737$	−3.15667	−0.116278
$738$	−0.423803	−0.0156004
$739$	24.6132	0.905411	0.452705	−	0.891660i	$-0.350459\pi$
$739$	24.6132	0.905411	0.452705	+	0.891660i	$0.350459\pi$
$740$	26.0813	0.958769
$741$	−5.45305	−0.200323
$742$	−48.1845	−1.76891
$743$	−14.1354	−0.518579	−0.259289	−	0.965800i	$-0.583488\pi$
$743$	−14.1354	−0.518579	−0.259289	+	0.965800i	$0.583488\pi$
$744$	4.86364	0.178310
$745$	−0.488762	−0.0179068
$746$	21.0215	0.769651
$747$	−2.83215	−0.103623
$748$	0.644415	0.0235622
$749$	−15.9386	−0.582383
$750$	8.93213	0.326155
$751$	−40.5619	−1.48013	−0.740063	−	0.672538i	$-0.765204\pi$
$751$	−40.5619	−1.48013	−0.740063	+	0.672538i	$0.765204\pi$
$752$	5.99061	0.218455
$753$	7.87566	0.287005
$754$	−15.6576	−0.570215
$755$	−2.44177	−0.0888651
$756$	−21.4117	−0.778737
$757$	−37.4358	−1.36063	−0.680313	−	0.732922i	$-0.738156\pi$
$757$	−37.4358	−1.36063	−0.680313	+	0.732922i	$0.738156\pi$
$758$	−16.0239	−0.582013
$759$	1.21818	0.0442170
$760$	−2.63739	−0.0956682
$761$	29.8262	1.08120	0.540600	−	0.841280i	$-0.318197\pi$
$761$	29.8262	1.08120	0.540600	+	0.841280i	$0.318197\pi$
$762$	−0.740858	−0.0268385
$763$	−35.9386	−1.30106
$764$	−1.66451	−0.0602200
$765$	−12.4736	−0.450984
$766$	9.09873	0.328750
$767$	18.0058	0.650150
$768$	−1.11253	−0.0401449
$769$	19.9827	0.720593	0.360296	−	0.932838i	$-0.382676\pi$
$769$	19.9827	0.720593	0.360296	+	0.932838i	$0.382676\pi$
$770$	2.55931	0.0922313
$771$	−19.7401	−0.710922
$772$	−6.70278	−0.241238
$773$	−7.02999	−0.252851	−0.126426	−	0.991976i	$-0.540350\pi$
$773$	−7.02999	−0.252851	−0.126426	+	0.991976i	$0.540350\pi$
$774$	19.7264	0.709050
$775$	8.55027	0.307135
$776$	15.2653	0.547992
$777$	−44.4623	−1.59508
$778$	7.90064	0.283252
$779$	0.240486	0.00861629
$780$	−14.3818	−0.514952
$781$	−1.48661	−0.0531950
$782$	12.2382	0.437638
$783$	−16.9247	−0.604839
$784$	9.33245	0.333302
$785$	−4.34440	−0.155058
$786$	11.8160	0.421462
$787$	42.4992	1.51493	0.757466	−	0.652874i	$-0.226437\pi$
$787$	42.4992	1.51493	0.757466	+	0.652874i	$0.226437\pi$
$788$	14.5377	0.517885
$789$	0.810144	0.0288419
$790$	9.18106	0.326648
$791$	66.2124	2.35424
$792$	−0.423155	−0.0150362
$793$	−20.1194	−0.714459
$794$	−23.4712	−0.832960
$795$	−34.9838	−1.24075
$796$	−5.89512	−0.208947
$797$	21.6865	0.768174	0.384087	−	0.923297i	$-0.374516\pi$
$797$	21.6865	0.768174	0.384087	+	0.923297i	$0.374516\pi$
$798$	4.49610	0.159160
$799$	−16.0773	−0.568774
$800$	−1.95582	−0.0691488
$801$	−2.30282	−0.0813663
$802$	−39.4713	−1.39378
$803$	−0.0769721	−0.00271629
$804$	−14.6257	−0.515809
$805$	48.6045	1.71308
$806$	21.4279	0.754765
$807$	24.9055	0.876714
$808$	−9.93722	−0.349590
$809$	7.52737	0.264648	0.132324	−	0.991206i	$-0.457756\pi$
$809$	7.52737	0.264648	0.132324	+	0.991206i	$0.457756\pi$
$810$	−1.60224	−0.0562971
$811$	−17.3928	−0.610745	−0.305373	−	0.952233i	$-0.598781\pi$
$811$	−17.3928	−0.610745	−0.305373	+	0.952233i	$0.598781\pi$
$812$	12.9098	0.453046
$813$	4.99224	0.175086
$814$	−2.37454	−0.0832275
$815$	54.5338	1.91023
$816$	2.98575	0.104522
$817$	−11.1937	−0.391616
$818$	−26.1666	−0.914893
$819$	−34.9084	−1.21980
$820$	0.634254	0.0221491
$821$	−12.9496	−0.451944	−0.225972	−	0.974134i	$-0.572556\pi$
$821$	−12.9496	−0.451944	−0.225972	+	0.974134i	$0.572556\pi$
$822$	12.6647	0.441731
$823$	37.5911	1.31034	0.655172	−	0.755480i	$-0.272596\pi$
$823$	37.5911	1.31034	0.655172	+	0.755480i	$0.272596\pi$
$824$	−4.46964	−0.155707
$825$	0.522473	0.0181902
$826$	−14.8459	−0.516557
$827$	−5.78087	−0.201020	−0.100510	−	0.994936i	$-0.532048\pi$
$827$	−5.78087	−0.201020	−0.100510	+	0.994936i	$0.532048\pi$
$828$	−8.03622	−0.279278
$829$	22.6678	0.787285	0.393642	−	0.919264i	$-0.371215\pi$
$829$	22.6678	0.787285	0.393642	+	0.919264i	$0.371215\pi$
$830$	4.23852	0.147121
$831$	4.82355	0.167327
$832$	−4.90150	−0.169929
$833$	−25.0460	−0.867791
$834$	−3.80271	−0.131677
$835$	54.4959	1.88591
$836$	0.240117	0.00830464
$837$	23.1620	0.800596
$838$	−39.0719	−1.34972
$839$	−38.5355	−1.33039	−0.665197	−	0.746668i	$-0.731652\pi$
$839$	−38.5355	−1.33039	−0.665197	+	0.746668i	$0.731652\pi$
$840$	11.8580	0.409139
$841$	−18.7955	−0.648122
$842$	38.6123	1.33067
$843$	−7.85877	−0.270670
$844$	−1.00000	−0.0344214
$845$	−29.0764	−1.00026
$846$	10.5572	0.362962
$847$	44.2218	1.51948
$848$	−11.9229	−0.409434
$849$	18.5209	0.635635
$850$	5.24894	0.180037
$851$	−45.0953	−1.54585
$852$	−6.88785	−0.235974
$853$	−18.9154	−0.647649	−0.323825	−	0.946117i	$-0.604969\pi$
$853$	−18.9154	−0.647649	−0.323825	+	0.946117i	$0.604969\pi$
$854$	16.5886	0.567651
$855$	−4.64783	−0.158952
$856$	−3.94388	−0.134799
$857$	−52.2864	−1.78607	−0.893034	−	0.449989i	$-0.851428\pi$
$857$	−52.2864	−1.78607	−0.893034	+	0.449989i	$0.851428\pi$
$858$	1.30937	0.0447013
$859$	9.19712	0.313802	0.156901	−	0.987614i	$-0.449850\pi$
$859$	9.19712	0.313802	0.156901	+	0.987614i	$0.449850\pi$
$860$	−29.5220	−1.00669
$861$	−1.08125	−0.0368488
$862$	3.77651	0.128628
$863$	35.6821	1.21463	0.607316	−	0.794460i	$-0.292246\pi$
$863$	35.6821	1.21463	0.607316	+	0.794460i	$0.292246\pi$
$864$	−5.29817	−0.180247
$865$	−10.7476	−0.365429
$866$	28.8779	0.981311
$867$	10.9000	0.370182
$868$	−17.6675	−0.599675
$869$	−0.835877	−0.0283552
$870$	9.37303	0.317776
$871$	−64.4369	−2.18336
$872$	−8.89273	−0.301146
$873$	26.9018	0.910487
$874$	4.56012	0.154248
$875$	−32.4467	−1.09690
$876$	−0.356632	−0.0120495
$877$	−44.1936	−1.49231	−0.746156	−	0.665771i	$-0.768103\pi$
$877$	−44.1936	−1.49231	−0.746156	+	0.665771i	$0.768103\pi$
$878$	22.3702	0.754958
$879$	−35.5135	−1.19784
$880$	0.633283	0.0213480
$881$	−9.54827	−0.321689	−0.160845	−	0.986980i	$-0.551422\pi$
$881$	−9.54827	−0.321689	−0.160845	+	0.986980i	$0.551422\pi$
$882$	16.4464	0.553780
$883$	−36.6577	−1.23363	−0.616815	−	0.787108i	$-0.711577\pi$
$883$	−36.6577	−1.23363	−0.616815	+	0.787108i	$0.711577\pi$
$884$	13.1544	0.442430
$885$	−10.7787	−0.362323
$886$	25.0821	0.842651
$887$	−29.1701	−0.979435	−0.489718	−	0.871881i	$-0.662900\pi$
$887$	−29.1701	−0.979435	−0.489718	+	0.871881i	$0.662900\pi$
$888$	−11.0019	−0.369198
$889$	2.69123	0.0902608
$890$	3.44635	0.115522
$891$	0.145874	0.00488697
$892$	10.7285	0.359216
$893$	−5.99061	−0.200468
$894$	0.206174	0.00689548
$895$	−23.4036	−0.782297
$896$	4.04134	0.135012
$897$	24.8666	0.830271
$898$	0.763087	0.0254646
$899$	−13.9651	−0.465764
$900$	−3.44671	−0.114890
$901$	31.9981	1.06601
$902$	−0.0577448	−0.00192269
$903$	50.3278	1.67481
$904$	16.3838	0.544916
$905$	−56.9416	−1.89280
$906$	1.03001	0.0342198
$907$	13.6328	0.452669	0.226335	−	0.974050i	$-0.427326\pi$
$907$	13.6328	0.452669	0.226335	+	0.974050i	$0.427326\pi$
$908$	2.86126	0.0949543
$909$	−17.5122	−0.580842
$910$	52.2431	1.73184
$911$	43.8365	1.45237	0.726184	−	0.687501i	$-0.241292\pi$
$911$	43.8365	1.45237	0.726184	+	0.687501i	$0.241292\pi$
$912$	1.11253	0.0368395
$913$	−0.385890	−0.0127711
$914$	−3.10779	−0.102797
$915$	12.0440	0.398162
$916$	−6.49370	−0.214558
$917$	−42.9225	−1.41742
$918$	14.2190	0.469296
$919$	31.7893	1.04863	0.524317	−	0.851523i	$-0.324321\pi$
$919$	31.7893	1.04863	0.524317	+	0.851523i	$0.324321\pi$
$920$	12.0268	0.396512
$921$	−4.73049	−0.155875
$922$	4.63610	0.152682
$923$	−30.3460	−0.998852
$924$	−1.07959	−0.0355160
$925$	−19.3413	−0.635937
$926$	−0.137750	−0.00452674
$927$	−7.87678	−0.258707
$928$	3.19444	0.104863
$929$	−16.1920	−0.531241	−0.265620	−	0.964078i	$-0.585577\pi$
$929$	−16.1920	−0.531241	−0.265620	+	0.964078i	$0.585577\pi$
$930$	−12.8273	−0.420624
$931$	−9.33245	−0.305859
$932$	−16.1920	−0.530387
$933$	21.9918	0.719980
$934$	−32.7027	−1.07006
$935$	−1.69957	−0.0555820
$936$	−8.63783	−0.282336
$937$	−46.1222	−1.50675	−0.753373	−	0.657594i	$-0.771574\pi$
$937$	−46.1222	−1.50675	−0.753373	+	0.657594i	$0.771574\pi$
$938$	53.1290	1.73472
$939$	−5.25005	−0.171329
$940$	−15.7996	−0.515325
$941$	3.47118	0.113157	0.0565787	−	0.998398i	$-0.481981\pi$
$941$	3.47118	0.113157	0.0565787	+	0.998398i	$0.481981\pi$
$942$	1.83259	0.0597092
$943$	−1.09664	−0.0357116
$944$	−3.67352	−0.119563
$945$	56.4710	1.83700
$946$	2.68779	0.0873876
$947$	46.7599	1.51949	0.759747	−	0.650219i	$-0.225323\pi$
$947$	46.7599	1.51949	0.759747	+	0.650219i	$0.225323\pi$
$948$	−3.87284	−0.125784
$949$	−1.57123	−0.0510042
$950$	1.95582	0.0634553
$951$	5.27359	0.171008
$952$	−10.8460	−0.351519
$953$	−34.4097	−1.11464	−0.557319	−	0.830298i	$-0.688170\pi$
$953$	−34.4097	−1.11464	−0.557319	+	0.830298i	$0.688170\pi$
$954$	−21.0115	−0.680272
$955$	4.38997	0.142056
$956$	−7.58705	−0.245383
$957$	−0.853355	−0.0275850
$958$	−16.5721	−0.535420
$959$	−46.0054	−1.48559
$960$	2.93417	0.0946999
$961$	−11.8882	−0.383492
$962$	−48.4713	−1.56278
$963$	−6.95024	−0.223968
$964$	20.2339	0.651689
$965$	17.6778	0.569069
$966$	−20.5028	−0.659666
$967$	−2.41118	−0.0775383	−0.0387692	−	0.999248i	$-0.512344\pi$
$967$	−2.41118	−0.0775383	−0.0387692	+	0.999248i	$0.512344\pi$
$968$	10.9423	0.351700
$969$	−2.98575	−0.0959160
$970$	−40.2605	−1.29269
$971$	−15.0196	−0.482001	−0.241000	−	0.970525i	$-0.577476\pi$
$971$	−15.0196	−0.482001	−0.241000	+	0.970525i	$0.577476\pi$
$972$	−15.2186	−0.488138
$973$	13.8136	0.442845
$974$	−1.90081	−0.0609060
$975$	10.6652	0.341560
$976$	4.10473	0.131389
$977$	−8.09269	−0.258908	−0.129454	−	0.991585i	$-0.541322\pi$
$977$	−8.09269	−0.258908	−0.129454	+	0.991585i	$0.541322\pi$
$978$	−23.0039	−0.735584
$979$	−0.313768	−0.0100281
$980$	−24.6133	−0.786243
$981$	−15.6715	−0.500353
$982$	−14.8056	−0.472467
$983$	−54.2942	−1.73172	−0.865858	−	0.500289i	$-0.833227\pi$
$983$	−54.2942	−1.73172	−0.865858	+	0.500289i	$0.833227\pi$
$984$	−0.267547	−0.00852908
$985$	−38.3416	−1.22167
$986$	−8.57309	−0.273023
$987$	26.9344	0.857332
$988$	4.90150	0.155937
$989$	51.0444	1.62312
$990$	1.11602	0.0354696
$991$	−24.7944	−0.787619	−0.393809	−	0.919192i	$-0.628843\pi$
$991$	−24.7944	−0.787619	−0.393809	+	0.919192i	$0.628843\pi$
$992$	−4.37170	−0.138802
$993$	−18.3809	−0.583300
$994$	25.0207	0.793607
$995$	15.5477	0.492896
$996$	−1.78793	−0.0566528
$997$	−51.1748	−1.62072	−0.810361	−	0.585931i	$-0.800729\pi$
$997$	−51.1748	−1.62072	−0.810361	+	0.585931i	$0.800729\pi$
$998$	−5.92541	−0.187566
$999$	−52.3940	−1.65767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.14	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.11253 q^{3} +1.00000 q^{4} -2.63739 q^{5} +1.11253 q^{6} -4.04134 q^{7} -1.00000 q^{8} -1.76228 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.11253 q^{3} +1.00000 q^{4} -2.63739 q^{5} +1.11253 q^{6} -4.04134 q^{7} -1.00000 q^{8} -1.76228 q^{9} +2.63739 q^{10} -0.240117 q^{11} -1.11253 q^{12} -4.90150 q^{13} +4.04134 q^{14} +2.93417 q^{15} +1.00000 q^{16} -2.68375 q^{17} +1.76228 q^{18} -1.00000 q^{19} -2.63739 q^{20} +4.49610 q^{21} +0.240117 q^{22} +4.56012 q^{23} +1.11253 q^{24} +1.95582 q^{25} +4.90150 q^{26} +5.29817 q^{27} -4.04134 q^{28} -3.19444 q^{29} -2.93417 q^{30} +4.37170 q^{31} -1.00000 q^{32} +0.267137 q^{33} +2.68375 q^{34} +10.6586 q^{35} -1.76228 q^{36} -9.88907 q^{37} +1.00000 q^{38} +5.45305 q^{39} +2.63739 q^{40} -0.240486 q^{41} -4.49610 q^{42} +11.1937 q^{43} -0.240117 q^{44} +4.64783 q^{45} -4.56012 q^{46} +5.99061 q^{47} -1.11253 q^{48} +9.33245 q^{49} -1.95582 q^{50} +2.98575 q^{51} -4.90150 q^{52} -11.9229 q^{53} -5.29817 q^{54} +0.633283 q^{55} +4.04134 q^{56} +1.11253 q^{57} +3.19444 q^{58} -3.67352 q^{59} +2.93417 q^{60} +4.10473 q^{61} -4.37170 q^{62} +7.12199 q^{63} +1.00000 q^{64} +12.9272 q^{65} -0.267137 q^{66} +13.1464 q^{67} -2.68375 q^{68} -5.07326 q^{69} -10.6586 q^{70} +6.19117 q^{71} +1.76228 q^{72} +0.320560 q^{73} +9.88907 q^{74} -2.17591 q^{75} -1.00000 q^{76} +0.970397 q^{77} -5.45305 q^{78} +3.48112 q^{79} -2.63739 q^{80} -0.607511 q^{81} +0.240486 q^{82} +1.60709 q^{83} +4.49610 q^{84} +7.07809 q^{85} -11.1937 q^{86} +3.55390 q^{87} +0.240117 q^{88} +1.30673 q^{89} -4.64783 q^{90} +19.8086 q^{91} +4.56012 q^{92} -4.86364 q^{93} -5.99061 q^{94} +2.63739 q^{95} +1.11253 q^{96} -15.2653 q^{97} -9.33245 q^{98} +0.423155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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