LMFDB - Embedded newform 6035.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.134450 q^{2} -0.934655 q^{3} -1.98192 q^{4} +1.00000 q^{5} +0.125664 q^{6} -1.20552 q^{7} +0.535370 q^{8} -2.12642 q^{9} +O(q^{10})$	\(q-0.134450 q^{2} -0.934655 q^{3} -1.98192 q^{4} +1.00000 q^{5} +0.125664 q^{6} -1.20552 q^{7} +0.535370 q^{8} -2.12642 q^{9} -0.134450 q^{10} +2.09838 q^{11} +1.85241 q^{12} +2.95082 q^{13} +0.162082 q^{14} -0.934655 q^{15} +3.89187 q^{16} -1.00000 q^{17} +0.285897 q^{18} -5.68082 q^{19} -1.98192 q^{20} +1.12674 q^{21} -0.282127 q^{22} -2.33008 q^{23} -0.500386 q^{24} +1.00000 q^{25} -0.396738 q^{26} +4.79143 q^{27} +2.38925 q^{28} -1.32871 q^{29} +0.125664 q^{30} +7.54332 q^{31} -1.59400 q^{32} -1.96126 q^{33} +0.134450 q^{34} -1.20552 q^{35} +4.21440 q^{36} -5.16566 q^{37} +0.763786 q^{38} -2.75800 q^{39} +0.535370 q^{40} -1.36334 q^{41} -0.151491 q^{42} -1.22252 q^{43} -4.15883 q^{44} -2.12642 q^{45} +0.313280 q^{46} +1.31621 q^{47} -3.63755 q^{48} -5.54672 q^{49} -0.134450 q^{50} +0.934655 q^{51} -5.84830 q^{52} +6.50530 q^{53} -0.644208 q^{54} +2.09838 q^{55} -0.645399 q^{56} +5.30960 q^{57} +0.178645 q^{58} +0.797029 q^{59} +1.85241 q^{60} +5.57830 q^{61} -1.01420 q^{62} +2.56344 q^{63} -7.56942 q^{64} +2.95082 q^{65} +0.263692 q^{66} -7.09408 q^{67} +1.98192 q^{68} +2.17782 q^{69} +0.162082 q^{70} +1.00000 q^{71} -1.13842 q^{72} +13.0062 q^{73} +0.694524 q^{74} -0.934655 q^{75} +11.2589 q^{76} -2.52964 q^{77} +0.370813 q^{78} +9.72040 q^{79} +3.89187 q^{80} +1.90093 q^{81} +0.183301 q^{82} +13.6291 q^{83} -2.23312 q^{84} -1.00000 q^{85} +0.164368 q^{86} +1.24189 q^{87} +1.12341 q^{88} +9.99162 q^{89} +0.285897 q^{90} -3.55727 q^{91} +4.61805 q^{92} -7.05040 q^{93} -0.176964 q^{94} -5.68082 q^{95} +1.48984 q^{96} -4.26259 q^{97} +0.745757 q^{98} -4.46204 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * 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 $

$2$	−0.134450	−0.0950705	−0.0475353	−	0.998870i	$-0.515137\pi$
$2$	−0.134450	−0.0950705	−0.0475353	+	0.998870i	$0.515137\pi$
$3$	−0.934655	−0.539623	−0.269812	−	0.962913i	$-0.586961\pi$
$3$	−0.934655	−0.539623	−0.269812	+	0.962913i	$0.586961\pi$
$4$	−1.98192	−0.990962
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.125664	0.0513022
$7$	−1.20552	−0.455644	−0.227822	−	0.973703i	$-0.573160\pi$
$7$	−1.20552	−0.455644	−0.227822	+	0.973703i	$0.573160\pi$
$8$	0.535370	0.189282
$9$	−2.12642	−0.708807
$10$	−0.134450	−0.0425168
$11$	2.09838	0.632686	0.316343	−	0.948645i	$-0.397545\pi$
$11$	2.09838	0.632686	0.316343	+	0.948645i	$0.397545\pi$
$12$	1.85241	0.534746
$13$	2.95082	0.818410	0.409205	−	0.912442i	$-0.365806\pi$
$13$	2.95082	0.818410	0.409205	+	0.912442i	$0.365806\pi$
$14$	0.162082	0.0433183
$15$	−0.934655	−0.241327
$16$	3.89187	0.972966
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.285897	0.0673866
$19$	−5.68082	−1.30327	−0.651635	−	0.758533i	$-0.725916\pi$
$19$	−5.68082	−1.30327	−0.651635	+	0.758533i	$0.725916\pi$
$20$	−1.98192	−0.443171
$21$	1.12674	0.245876
$22$	−0.282127	−0.0601497
$23$	−2.33008	−0.485856	−0.242928	−	0.970044i	$-0.578108\pi$
$23$	−2.33008	−0.485856	−0.242928	+	0.970044i	$0.578108\pi$
$24$	−0.500386	−0.102141
$25$	1.00000	0.200000
$26$	−0.396738	−0.0778067
$27$	4.79143	0.922112
$28$	2.38925	0.451525
$29$	−1.32871	−0.246735	−0.123368	−	0.992361i	$-0.539369\pi$
$29$	−1.32871	−0.246735	−0.123368	+	0.992361i	$0.539369\pi$
$30$	0.125664	0.0229431
$31$	7.54332	1.35482	0.677410	−	0.735606i	$-0.263102\pi$
$31$	7.54332	1.35482	0.677410	+	0.735606i	$0.263102\pi$
$32$	−1.59400	−0.281782
$33$	−1.96126	−0.341412
$34$	0.134450	0.0230580
$35$	−1.20552	−0.203770
$36$	4.21440	0.702400
$37$	−5.16566	−0.849230	−0.424615	−	0.905374i	$-0.639591\pi$
$37$	−5.16566	−0.849230	−0.424615	+	0.905374i	$0.639591\pi$
$38$	0.763786	0.123902
$39$	−2.75800	−0.441633
$40$	0.535370	0.0846494
$41$	−1.36334	−0.212917	−0.106459	−	0.994317i	$-0.533951\pi$
$41$	−1.36334	−0.212917	−0.106459	+	0.994317i	$0.533951\pi$
$42$	−0.151491	−0.0233755
$43$	−1.22252	−0.186433	−0.0932166	−	0.995646i	$-0.529715\pi$
$43$	−1.22252	−0.186433	−0.0932166	+	0.995646i	$0.529715\pi$
$44$	−4.15883	−0.626967
$45$	−2.12642	−0.316988
$46$	0.313280	0.0461906
$47$	1.31621	0.191989	0.0959943	−	0.995382i	$-0.469397\pi$
$47$	1.31621	0.191989	0.0959943	+	0.995382i	$0.469397\pi$
$48$	−3.63755	−0.525035
$49$	−5.54672	−0.792389
$50$	−0.134450	−0.0190141
$51$	0.934655	0.130878
$52$	−5.84830	−0.811013
$53$	6.50530	0.893572	0.446786	−	0.894641i	$-0.352569\pi$
$53$	6.50530	0.893572	0.446786	+	0.894641i	$0.352569\pi$
$54$	−0.644208	−0.0876656
$55$	2.09838	0.282946
$56$	−0.645399	−0.0862450
$57$	5.30960	0.703274
$58$	0.178645	0.0234573
$59$	0.797029	0.103764	0.0518822	−	0.998653i	$-0.483478\pi$
$59$	0.797029	0.103764	0.0518822	+	0.998653i	$0.483478\pi$
$60$	1.85241	0.239146
$61$	5.57830	0.714228	0.357114	−	0.934061i	$-0.383761\pi$
$61$	5.57830	0.714228	0.357114	+	0.934061i	$0.383761\pi$
$62$	−1.01420	−0.128803
$63$	2.56344	0.322963
$64$	−7.56942	−0.946177
$65$	2.95082	0.366004
$66$	0.263692	0.0324582
$67$	−7.09408	−0.866680	−0.433340	−	0.901231i	$-0.642665\pi$
$67$	−7.09408	−0.866680	−0.433340	+	0.901231i	$0.642665\pi$
$68$	1.98192	0.240343
$69$	2.17782	0.262179
$70$	0.162082	0.0193725
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−1.13842	−0.134164
$73$	13.0062	1.52226	0.761128	−	0.648602i	$-0.224646\pi$
$73$	13.0062	1.52226	0.761128	+	0.648602i	$0.224646\pi$
$74$	0.694524	0.0807367
$75$	−0.934655	−0.107925
$76$	11.2589	1.29149
$77$	−2.52964	−0.288279
$78$	0.370813	0.0419863
$79$	9.72040	1.09363	0.546815	−	0.837253i	$-0.315840\pi$
$79$	9.72040	1.09363	0.546815	+	0.837253i	$0.315840\pi$
$80$	3.89187	0.435124
$81$	1.90093	0.211214
$82$	0.183301	0.0202422
$83$	13.6291	1.49599	0.747994	−	0.663706i	$-0.231017\pi$
$83$	13.6291	1.49599	0.747994	+	0.663706i	$0.231017\pi$
$84$	−2.23312	−0.243654
$85$	−1.00000	−0.108465
$86$	0.164368	0.0177243
$87$	1.24189	0.133144
$88$	1.12341	0.119756
$89$	9.99162	1.05911	0.529555	−	0.848276i	$-0.322359\pi$
$89$	9.99162	1.05911	0.529555	+	0.848276i	$0.322359\pi$
$90$	0.285897	0.0301362
$91$	−3.55727	−0.372904
$92$	4.61805	0.481465
$93$	−7.05040	−0.731092
$94$	−0.176964	−0.0182525
$95$	−5.68082	−0.582840
$96$	1.48984	0.152056
$97$	−4.26259	−0.432800	−0.216400	−	0.976305i	$-0.569432\pi$
$97$	−4.26259	−0.432800	−0.216400	+	0.976305i	$0.569432\pi$
$98$	0.745757	0.0753328
$99$	−4.46204	−0.448452
$100$	−1.98192	−0.198192
$101$	4.03033	0.401032	0.200516	−	0.979690i	$-0.435738\pi$
$101$	4.03033	0.401032	0.200516	+	0.979690i	$0.435738\pi$
$102$	−0.125664	−0.0124426
$103$	−3.07591	−0.303078	−0.151539	−	0.988451i	$-0.548423\pi$
$103$	−3.07591	−0.303078	−0.151539	+	0.988451i	$0.548423\pi$
$104$	1.57978	0.154910
$105$	1.12674	0.109959
$106$	−0.874638	−0.0849523
$107$	−18.2006	−1.75952	−0.879758	−	0.475422i	$-0.842295\pi$
$107$	−18.2006	−1.75952	−0.879758	+	0.475422i	$0.842295\pi$
$108$	−9.49625	−0.913777
$109$	−6.83244	−0.654429	−0.327214	−	0.944950i	$-0.606110\pi$
$109$	−6.83244	−0.654429	−0.327214	+	0.944950i	$0.606110\pi$
$110$	−0.282127	−0.0268998
$111$	4.82811	0.458264
$112$	−4.69172	−0.443326
$113$	−10.6185	−0.998903	−0.499451	−	0.866342i	$-0.666465\pi$
$113$	−10.6185	−0.998903	−0.499451	+	0.866342i	$0.666465\pi$
$114$	−0.713876	−0.0668606
$115$	−2.33008	−0.217282
$116$	2.63340	0.244505
$117$	−6.27469	−0.580095
$118$	−0.107161	−0.00986493
$119$	1.20552	0.110510
$120$	−0.500386	−0.0456788
$121$	−6.59680	−0.599709
$122$	−0.750002	−0.0679020
$123$	1.27425	0.114895
$124$	−14.9503	−1.34257
$125$	1.00000	0.0894427
$126$	−0.344655	−0.0307043
$127$	8.08323	0.717270	0.358635	−	0.933478i	$-0.383242\pi$
$127$	8.08323	0.717270	0.358635	+	0.933478i	$0.383242\pi$
$128$	4.20571	0.371736
$129$	1.14264	0.100604
$130$	−0.396738	−0.0347962
$131$	−2.43507	−0.212753	−0.106376	−	0.994326i	$-0.533925\pi$
$131$	−2.43507	−0.212753	−0.106376	+	0.994326i	$0.533925\pi$
$132$	3.88707	0.338326
$133$	6.84834	0.593827
$134$	0.953799	0.0823957
$135$	4.79143	0.412381
$136$	−0.535370	−0.0459076
$137$	−10.7789	−0.920906	−0.460453	−	0.887684i	$-0.652313\pi$
$137$	−10.7789	−0.920906	−0.460453	+	0.887684i	$0.652313\pi$
$138$	−0.292809	−0.0249255
$139$	−6.54940	−0.555512	−0.277756	−	0.960652i	$-0.589591\pi$
$139$	−6.54940	−0.555512	−0.277756	+	0.960652i	$0.589591\pi$
$140$	2.38925	0.201928
$141$	−1.23020	−0.103602
$142$	−0.134450	−0.0112828
$143$	6.19194	0.517796
$144$	−8.27574	−0.689645
$145$	−1.32871	−0.110343
$146$	−1.74868	−0.144722
$147$	5.18427	0.427591
$148$	10.2379	0.841554
$149$	−6.03792	−0.494646	−0.247323	−	0.968933i	$-0.579551\pi$
$149$	−6.03792	−0.494646	−0.247323	+	0.968933i	$0.579551\pi$
$150$	0.125664	0.0102604
$151$	5.99509	0.487873	0.243937	−	0.969791i	$-0.421561\pi$
$151$	5.99509	0.487873	0.243937	+	0.969791i	$0.421561\pi$
$152$	−3.04134	−0.246685
$153$	2.12642	0.171911
$154$	0.340110	0.0274069
$155$	7.54332	0.605894
$156$	5.46614	0.437641
$157$	14.1710	1.13097	0.565483	−	0.824760i	$-0.308690\pi$
$157$	14.1710	1.13097	0.565483	+	0.824760i	$0.308690\pi$
$158$	−1.30691	−0.103972
$159$	−6.08021	−0.482192
$160$	−1.59400	−0.126017
$161$	2.80896	0.221377
$162$	−0.255580	−0.0200802
$163$	−5.18268	−0.405939	−0.202970	−	0.979185i	$-0.565059\pi$
$163$	−5.18268	−0.405939	−0.202970	+	0.979185i	$0.565059\pi$
$164$	2.70203	0.210993
$165$	−1.96126	−0.152684
$166$	−1.83243	−0.142224
$167$	17.6498	1.36578	0.682892	−	0.730519i	$-0.260722\pi$
$167$	17.6498	1.36578	0.682892	+	0.730519i	$0.260722\pi$
$168$	0.603225	0.0465398
$169$	−4.29266	−0.330205
$170$	0.134450	0.0103118
$171$	12.0798	0.923766
$172$	2.42295	0.184748
$173$	−11.6601	−0.886501	−0.443251	−	0.896398i	$-0.646175\pi$
$173$	−11.6601	−0.886501	−0.443251	+	0.896398i	$0.646175\pi$
$174$	−0.166972	−0.0126581
$175$	−1.20552	−0.0911288
$176$	8.16662	0.615582
$177$	−0.744947	−0.0559937
$178$	−1.34337	−0.100690
$179$	16.3889	1.22496	0.612481	−	0.790485i	$-0.290172\pi$
$179$	16.3889	1.22496	0.612481	+	0.790485i	$0.290172\pi$
$180$	4.21440	0.314123
$181$	−18.2106	−1.35358	−0.676791	−	0.736175i	$-0.736630\pi$
$181$	−18.2106	−1.35358	−0.676791	+	0.736175i	$0.736630\pi$
$182$	0.478275	0.0354521
$183$	−5.21378	−0.385414
$184$	−1.24746	−0.0919637
$185$	−5.16566	−0.379787
$186$	0.947926	0.0695053
$187$	−2.09838	−0.153449
$188$	−2.60862	−0.190253
$189$	−5.77617	−0.420154
$190$	0.763786	0.0554109
$191$	−19.1569	−1.38614	−0.693072	−	0.720869i	$-0.743743\pi$
$191$	−19.1569	−1.38614	−0.693072	+	0.720869i	$0.743743\pi$
$192$	7.07479	0.510579
$193$	−16.2615	−1.17053	−0.585265	−	0.810842i	$-0.699009\pi$
$193$	−16.2615	−1.17053	−0.585265	+	0.810842i	$0.699009\pi$
$194$	0.573105	0.0411465
$195$	−2.75800	−0.197504
$196$	10.9932	0.785227
$197$	−3.43445	−0.244694	−0.122347	−	0.992487i	$-0.539042\pi$
$197$	−3.43445	−0.244694	−0.122347	+	0.992487i	$0.539042\pi$
$198$	0.599921	0.0426346
$199$	17.1665	1.21690	0.608449	−	0.793593i	$-0.291792\pi$
$199$	17.1665	1.21690	0.608449	+	0.793593i	$0.291792\pi$
$200$	0.535370	0.0378563
$201$	6.63051	0.467680
$202$	−0.541877	−0.0381264
$203$	1.60179	0.112423
$204$	−1.85241	−0.129695
$205$	−1.36334	−0.0952195
$206$	0.413556	0.0288138
$207$	4.95474	0.344378
$208$	11.4842	0.796286
$209$	−11.9205	−0.824560
$210$	−0.151491	−0.0104539
$211$	−21.4298	−1.47529	−0.737643	−	0.675191i	$-0.764061\pi$
$211$	−21.4298	−1.47529	−0.737643	+	0.675191i	$0.764061\pi$
$212$	−12.8930	−0.885495
$213$	−0.934655	−0.0640415
$214$	2.44707	0.167278
$215$	−1.22252	−0.0833755
$216$	2.56519	0.174539
$217$	−9.09362	−0.617315
$218$	0.918621	0.0622169
$219$	−12.1563	−0.821444
$220$	−4.15883	−0.280388
$221$	−2.95082	−0.198494
$222$	−0.649140	−0.0435674
$223$	0.693289	0.0464261	0.0232130	−	0.999731i	$-0.492610\pi$
$223$	0.693289	0.0464261	0.0232130	+	0.999731i	$0.492610\pi$
$224$	1.92160	0.128392
$225$	−2.12642	−0.141761
$226$	1.42765	0.0949662
$227$	−4.61662	−0.306416	−0.153208	−	0.988194i	$-0.548960\pi$
$227$	−4.61662	−0.306416	−0.153208	+	0.988194i	$0.548960\pi$
$228$	−10.5232	−0.696918
$229$	−1.92796	−0.127403	−0.0637015	−	0.997969i	$-0.520291\pi$
$229$	−1.92796	−0.127403	−0.0637015	+	0.997969i	$0.520291\pi$
$230$	0.313280	0.0206571
$231$	2.36434	0.155562
$232$	−0.711352	−0.0467025
$233$	−0.508852	−0.0333360	−0.0166680	−	0.999861i	$-0.505306\pi$
$233$	−0.508852	−0.0333360	−0.0166680	+	0.999861i	$0.505306\pi$
$234$	0.843632	0.0551499
$235$	1.31621	0.0858599
$236$	−1.57965	−0.102827
$237$	−9.08521	−0.590148
$238$	−0.162082	−0.0105062
$239$	−21.1307	−1.36683	−0.683415	−	0.730030i	$-0.739506\pi$
$239$	−21.1307	−1.36683	−0.683415	+	0.730030i	$0.739506\pi$
$240$	−3.63755	−0.234803
$241$	15.0513	0.969542	0.484771	−	0.874641i	$-0.338903\pi$
$241$	15.0513	0.969542	0.484771	+	0.874641i	$0.338903\pi$
$242$	0.886940	0.0570146
$243$	−16.1510	−1.03609
$244$	−11.0558	−0.707772
$245$	−5.54672	−0.354367
$246$	−0.171323	−0.0109231
$247$	−16.7631	−1.06661
$248$	4.03846	0.256443
$249$	−12.7385	−0.807269
$250$	−0.134450	−0.00850337
$251$	−23.1706	−1.46252	−0.731258	−	0.682101i	$-0.761067\pi$
$251$	−23.1706	−1.46252	−0.731258	+	0.682101i	$0.761067\pi$
$252$	−5.08055	−0.320044
$253$	−4.88941	−0.307394
$254$	−1.08679	−0.0681913
$255$	0.934655	0.0585303
$256$	14.5734	0.910836
$257$	24.8194	1.54819	0.774096	−	0.633068i	$-0.218205\pi$
$257$	24.8194	1.54819	0.774096	+	0.633068i	$0.218205\pi$
$258$	−0.153628	−0.00956445
$259$	6.22731	0.386946
$260$	−5.84830	−0.362696
$261$	2.82540	0.174888
$262$	0.327395	0.0202265
$263$	−13.0625	−0.805465	−0.402733	−	0.915318i	$-0.631940\pi$
$263$	−13.0625	−0.805465	−0.402733	+	0.915318i	$0.631940\pi$
$264$	−1.05000	−0.0646230
$265$	6.50530	0.399617
$266$	−0.920760	−0.0564554
$267$	−9.33871	−0.571520
$268$	14.0599	0.858846
$269$	17.0957	1.04234	0.521172	−	0.853452i	$-0.325495\pi$
$269$	17.0957	1.04234	0.521172	+	0.853452i	$0.325495\pi$
$270$	−0.644208	−0.0392053
$271$	10.9990	0.668144	0.334072	−	0.942548i	$-0.391577\pi$
$271$	10.9990	0.668144	0.334072	+	0.942548i	$0.391577\pi$
$272$	−3.89187	−0.235979
$273$	3.32482	0.201227
$274$	1.44923	0.0875510
$275$	2.09838	0.126537
$276$	−4.31628	−0.259810
$277$	5.26177	0.316149	0.158075	−	0.987427i	$-0.449471\pi$
$277$	5.26177	0.316149	0.158075	+	0.987427i	$0.449471\pi$
$278$	0.880566	0.0528129
$279$	−16.0403	−0.960306
$280$	−0.645399	−0.0385700
$281$	−32.7060	−1.95108	−0.975539	−	0.219827i	$-0.929451\pi$
$281$	−32.7060	−1.95108	−0.975539	+	0.219827i	$0.929451\pi$
$282$	0.165400	0.00984945
$283$	−9.52979	−0.566487	−0.283244	−	0.959048i	$-0.591411\pi$
$283$	−9.52979	−0.566487	−0.283244	+	0.959048i	$0.591411\pi$
$284$	−1.98192	−0.117606
$285$	5.30960	0.314514
$286$	−0.832507	−0.0492272
$287$	1.64353	0.0970145
$288$	3.38952	0.199729
$289$	1.00000	0.0588235
$290$	0.178645	0.0104904
$291$	3.98405	0.233549
$292$	−25.7772	−1.50850
$293$	−7.59705	−0.443824	−0.221912	−	0.975067i	$-0.571230\pi$
$293$	−7.59705	−0.443824	−0.221912	+	0.975067i	$0.571230\pi$
$294$	−0.697025	−0.0406513
$295$	0.797029	0.0464048
$296$	−2.76554	−0.160744
$297$	10.0543	0.583407
$298$	0.811799	0.0470262
$299$	−6.87566	−0.397630
$300$	1.85241	0.106949
$301$	1.47378	0.0849472
$302$	−0.806040	−0.0463824
$303$	−3.76696	−0.216406
$304$	−22.1090	−1.26804
$305$	5.57830	0.319412
$306$	−0.285897	−0.0163437
$307$	−16.0145	−0.913997	−0.456998	−	0.889468i	$-0.651075\pi$
$307$	−16.0145	−0.913997	−0.456998	+	0.889468i	$0.651075\pi$
$308$	5.01355	0.285674
$309$	2.87491	0.163548
$310$	−1.01420	−0.0576026
$311$	−12.6773	−0.718861	−0.359431	−	0.933172i	$-0.617029\pi$
$311$	−12.6773	−0.718861	−0.359431	+	0.933172i	$0.617029\pi$
$312$	−1.47655	−0.0835931
$313$	−28.1952	−1.59369	−0.796845	−	0.604184i	$-0.793499\pi$
$313$	−28.1952	−1.59369	−0.796845	+	0.604184i	$0.793499\pi$
$314$	−1.90529	−0.107522
$315$	2.56344	0.144434
$316$	−19.2651	−1.08375
$317$	−21.1076	−1.18552	−0.592762	−	0.805378i	$-0.701962\pi$
$317$	−21.1076	−1.18552	−0.592762	+	0.805378i	$0.701962\pi$
$318$	0.817484	0.0458422
$319$	−2.78814	−0.156106
$320$	−7.56942	−0.423143
$321$	17.0112	0.949475
$322$	−0.377665	−0.0210465
$323$	5.68082	0.316089
$324$	−3.76749	−0.209305
$325$	2.95082	0.163682
$326$	0.696812	0.0385928
$327$	6.38597	0.353145
$328$	−0.729889	−0.0403014
$329$	−1.58672	−0.0874784
$330$	0.263692	0.0145157
$331$	9.29325	0.510803	0.255402	−	0.966835i	$-0.417792\pi$
$331$	9.29325	0.510803	0.255402	+	0.966835i	$0.417792\pi$
$332$	−27.0118	−1.48247
$333$	10.9844	0.601940
$334$	−2.37302	−0.129846
$335$	−7.09408	−0.387591
$336$	4.38514	0.239229
$337$	−1.75506	−0.0956044	−0.0478022	−	0.998857i	$-0.515222\pi$
$337$	−1.75506	−0.0956044	−0.0478022	+	0.998857i	$0.515222\pi$
$338$	0.577148	0.0313927
$339$	9.92461	0.539031
$340$	1.98192	0.107485
$341$	15.8288	0.857175
$342$	−1.62413	−0.0878229
$343$	15.1253	0.816691
$344$	−0.654503	−0.0352884
$345$	2.17782	0.117250
$346$	1.56770	0.0842801
$347$	−1.08126	−0.0580453	−0.0290227	−	0.999579i	$-0.509239\pi$
$347$	−1.08126	−0.0580453	−0.0290227	+	0.999579i	$0.509239\pi$
$348$	−2.46132	−0.131941
$349$	−24.4311	−1.30777	−0.653883	−	0.756596i	$-0.726861\pi$
$349$	−24.4311	−1.30777	−0.653883	+	0.756596i	$0.726861\pi$
$350$	0.162082	0.00866366
$351$	14.1387	0.754666
$352$	−3.34482	−0.178280
$353$	−30.8737	−1.64324	−0.821621	−	0.570034i	$-0.806930\pi$
$353$	−30.8737	−1.64324	−0.821621	+	0.570034i	$0.806930\pi$
$354$	0.100158	0.00532335
$355$	1.00000	0.0530745
$356$	−19.8026	−1.04954
$357$	−1.12674	−0.0596337
$358$	−2.20348	−0.116458
$359$	−5.21820	−0.275406	−0.137703	−	0.990474i	$-0.543972\pi$
$359$	−5.21820	−0.275406	−0.137703	+	0.990474i	$0.543972\pi$
$360$	−1.13842	−0.0600001
$361$	13.2717	0.698511
$362$	2.44841	0.128686
$363$	6.16573	0.323617
$364$	7.05024	0.369533
$365$	13.0062	0.680774
$366$	0.700993	0.0366415
$367$	−17.4810	−0.912502	−0.456251	−	0.889851i	$-0.650808\pi$
$367$	−17.4810	−0.912502	−0.456251	+	0.889851i	$0.650808\pi$
$368$	−9.06838	−0.472722
$369$	2.89903	0.150917
$370$	0.694524	0.0361066
$371$	−7.84227	−0.407150
$372$	13.9733	0.724484
$373$	−14.9322	−0.773159	−0.386579	−	0.922256i	$-0.626343\pi$
$373$	−14.9322	−0.773159	−0.386579	+	0.922256i	$0.626343\pi$
$374$	0.282127	0.0145885
$375$	−0.934655	−0.0482654
$376$	0.704658	0.0363399
$377$	−3.92079	−0.201931
$378$	0.776606	0.0399443
$379$	−12.4716	−0.640621	−0.320311	−	0.947313i	$-0.603787\pi$
$379$	−12.4716	−0.640621	−0.320311	+	0.947313i	$0.603787\pi$
$380$	11.2589	0.577572
$381$	−7.55502	−0.387056
$382$	2.57564	0.131781
$383$	12.3439	0.630743	0.315371	−	0.948968i	$-0.397871\pi$
$383$	12.3439	0.630743	0.315371	+	0.948968i	$0.397871\pi$
$384$	−3.93089	−0.200597
$385$	−2.52964	−0.128922
$386$	2.18636	0.111283
$387$	2.59960	0.132145
$388$	8.44812	0.428888
$389$	13.7866	0.699006	0.349503	−	0.936935i	$-0.386350\pi$
$389$	13.7866	0.699006	0.349503	+	0.936935i	$0.386350\pi$
$390$	0.370813	0.0187768
$391$	2.33008	0.117837
$392$	−2.96955	−0.149985
$393$	2.27595	0.114806
$394$	0.461762	0.0232632
$395$	9.72040	0.489086
$396$	8.84342	0.444399
$397$	18.3184	0.919373	0.459687	−	0.888081i	$-0.347962\pi$
$397$	18.3184	0.919373	0.459687	+	0.888081i	$0.347962\pi$
$398$	−2.30803	−0.115691
$399$	−6.40083	−0.320443
$400$	3.89187	0.194593
$401$	−22.4180	−1.11950	−0.559750	−	0.828662i	$-0.689103\pi$
$401$	−22.4180	−1.11950	−0.559750	+	0.828662i	$0.689103\pi$
$402$	−0.891473	−0.0444626
$403$	22.2590	1.10880
$404$	−7.98780	−0.397408
$405$	1.90093	0.0944579
$406$	−0.215360	−0.0106882
$407$	−10.8395	−0.537296
$408$	0.500386	0.0247728
$409$	−28.4739	−1.40794	−0.703971	−	0.710228i	$-0.748592\pi$
$409$	−28.4739	−1.40794	−0.703971	+	0.710228i	$0.748592\pi$
$410$	0.183301	0.00905257
$411$	10.0746	0.496942
$412$	6.09622	0.300339
$413$	−0.960835	−0.0472796
$414$	−0.666165	−0.0327402
$415$	13.6291	0.669026
$416$	−4.70361	−0.230613
$417$	6.12142	0.299767
$418$	1.60271	0.0783913
$419$	−11.0568	−0.540162	−0.270081	−	0.962838i	$-0.587051\pi$
$419$	−11.0568	−0.540162	−0.270081	+	0.962838i	$0.587051\pi$
$420$	−2.23312	−0.108965
$421$	−28.9215	−1.40955	−0.704775	−	0.709431i	$-0.748952\pi$
$421$	−28.9215	−1.40955	−0.704775	+	0.709431i	$0.748952\pi$
$422$	2.88123	0.140256
$423$	−2.79881	−0.136083
$424$	3.48274	0.169137
$425$	−1.00000	−0.0485071
$426$	0.125664	0.00608846
$427$	−6.72475	−0.325433
$428$	36.0721	1.74361
$429$	−5.78733	−0.279415
$430$	0.164368	0.00792655
$431$	−12.8774	−0.620282	−0.310141	−	0.950691i	$-0.600376\pi$
$431$	−12.8774	−0.620282	−0.310141	+	0.950691i	$0.600376\pi$
$432$	18.6476	0.897184
$433$	39.1450	1.88119	0.940595	−	0.339532i	$-0.110269\pi$
$433$	39.1450	1.88119	0.940595	+	0.339532i	$0.110269\pi$
$434$	1.22264	0.0586885
$435$	1.24189	0.0595439
$436$	13.5414	0.648514
$437$	13.2368	0.633202
$438$	1.63441	0.0780951
$439$	31.6769	1.51185	0.755927	−	0.654656i	$-0.227186\pi$
$439$	31.6769	1.51185	0.755927	+	0.654656i	$0.227186\pi$
$440$	1.12341	0.0535564
$441$	11.7947	0.561651
$442$	0.396738	0.0188709
$443$	32.4633	1.54238	0.771190	−	0.636605i	$-0.219662\pi$
$443$	32.4633	1.54238	0.771190	+	0.636605i	$0.219662\pi$
$444$	−9.56895	−0.454122
$445$	9.99162	0.473648
$446$	−0.0932127	−0.00441375
$447$	5.64337	0.266922
$448$	9.12509	0.431120
$449$	0.255135	0.0120406	0.00602028	−	0.999982i	$-0.498084\pi$
$449$	0.255135	0.0120406	0.00602028	+	0.999982i	$0.498084\pi$
$450$	0.285897	0.0134773
$451$	−2.86080	−0.134710
$452$	21.0450	0.989874
$453$	−5.60334	−0.263268
$454$	0.620704	0.0291311
$455$	−3.55727	−0.166768
$456$	2.84260	0.133117
$457$	21.4545	1.00360	0.501799	−	0.864984i	$-0.332672\pi$
$457$	21.4545	1.00360	0.501799	+	0.864984i	$0.332672\pi$
$458$	0.259214	0.0121123
$459$	−4.79143	−0.223645
$460$	4.61805	0.215318
$461$	−24.3293	−1.13313	−0.566563	−	0.824018i	$-0.691727\pi$
$461$	−24.3293	−1.13313	−0.566563	+	0.824018i	$0.691727\pi$
$462$	−0.317886	−0.0147894
$463$	5.41863	0.251825	0.125913	−	0.992041i	$-0.459814\pi$
$463$	5.41863	0.251825	0.125913	+	0.992041i	$0.459814\pi$
$464$	−5.17117	−0.240065
$465$	−7.05040	−0.326954
$466$	0.0684151	0.00316927
$467$	−28.8881	−1.33678	−0.668392	−	0.743810i	$-0.733017\pi$
$467$	−28.8881	−1.33678	−0.668392	+	0.743810i	$0.733017\pi$
$468$	12.4359	0.574852
$469$	8.55205	0.394897
$470$	−0.176964	−0.00816275
$471$	−13.2450	−0.610296
$472$	0.426705	0.0196407
$473$	−2.56532	−0.117954
$474$	1.22151	0.0561057
$475$	−5.68082	−0.260654
$476$	−2.38925	−0.109511
$477$	−13.8330	−0.633370
$478$	2.84102	0.129945
$479$	−15.8602	−0.724673	−0.362336	−	0.932047i	$-0.618021\pi$
$479$	−15.8602	−0.724673	−0.362336	+	0.932047i	$0.618021\pi$
$480$	1.48984	0.0680016
$481$	−15.2429	−0.695018
$482$	−2.02365	−0.0921748
$483$	−2.62541	−0.119460
$484$	13.0743	0.594289
$485$	−4.26259	−0.193554
$486$	2.17150	0.0985014
$487$	16.1186	0.730403	0.365202	−	0.930928i	$-0.381000\pi$
$487$	16.1186	0.730403	0.365202	+	0.930928i	$0.381000\pi$
$488$	2.98645	0.135190
$489$	4.84402	0.219054
$490$	0.745757	0.0336899
$491$	−11.7963	−0.532362	−0.266181	−	0.963923i	$-0.585762\pi$
$491$	−11.7963	−0.532362	−0.266181	+	0.963923i	$0.585762\pi$
$492$	−2.52546	−0.113857
$493$	1.32871	0.0598421
$494$	2.25380	0.101403
$495$	−4.46204	−0.200554
$496$	29.3576	1.31819
$497$	−1.20552	−0.0540750
$498$	1.71269	0.0767475
$499$	9.71165	0.434753	0.217377	−	0.976088i	$-0.430250\pi$
$499$	9.71165	0.434753	0.217377	+	0.976088i	$0.430250\pi$
$500$	−1.98192	−0.0886343
$501$	−16.4965	−0.737009
$502$	3.11529	0.139042
$503$	8.86599	0.395315	0.197658	−	0.980271i	$-0.436667\pi$
$503$	8.86599	0.395315	0.197658	+	0.980271i	$0.436667\pi$
$504$	1.37239	0.0611311
$505$	4.03033	0.179347
$506$	0.657381	0.0292241
$507$	4.01215	0.178186
$508$	−16.0203	−0.710787
$509$	11.2139	0.497049	0.248525	−	0.968626i	$-0.420054\pi$
$509$	11.2139	0.497049	0.248525	+	0.968626i	$0.420054\pi$
$510$	−0.125664	−0.00556451
$511$	−15.6792	−0.693606
$512$	−10.3708	−0.458329
$513$	−27.2193	−1.20176
$514$	−3.33697	−0.147187
$515$	−3.07591	−0.135541
$516$	−2.26462	−0.0996944
$517$	2.76191	0.121468
$518$	−0.837262	−0.0367872
$519$	10.8982	0.478377
$520$	1.57978	0.0692779
$521$	−33.5868	−1.47146	−0.735732	−	0.677273i	$-0.763162\pi$
$521$	−33.5868	−1.47146	−0.735732	+	0.677273i	$0.763162\pi$
$522$	−0.379875	−0.0166267
$523$	−23.7919	−1.04035	−0.520173	−	0.854061i	$-0.674133\pi$
$523$	−23.7919	−1.04035	−0.520173	+	0.854061i	$0.674133\pi$
$524$	4.82612	0.210830
$525$	1.12674	0.0491752
$526$	1.75625	0.0765760
$527$	−7.54332	−0.328592
$528$	−7.63297	−0.332182
$529$	−17.5707	−0.763944
$530$	−0.874638	−0.0379918
$531$	−1.69482	−0.0735489
$532$	−13.5729	−0.588459
$533$	−4.02296	−0.174254
$534$	1.25559	0.0543347
$535$	−18.2006	−0.786879
$536$	−3.79795	−0.164047
$537$	−15.3179	−0.661018
$538$	−2.29852	−0.0990962
$539$	−11.6391	−0.501333
$540$	−9.49625	−0.408654
$541$	31.7996	1.36717	0.683587	−	0.729869i	$-0.260419\pi$
$541$	31.7996	1.36717	0.683587	+	0.729869i	$0.260419\pi$
$542$	−1.47882	−0.0635208
$543$	17.0206	0.730424
$544$	1.59400	0.0683422
$545$	−6.83244	−0.292670
$546$	−0.447022	−0.0191308
$547$	25.4868	1.08974	0.544869	−	0.838521i	$-0.316580\pi$
$547$	25.4868	1.08974	0.544869	+	0.838521i	$0.316580\pi$
$548$	21.3630	0.912582
$549$	−11.8618	−0.506249
$550$	−0.282127	−0.0120299
$551$	7.54817	0.321563
$552$	1.16594	0.0496257
$553$	−11.7181	−0.498306
$554$	−0.707445	−0.0300565
$555$	4.82811	0.204942
$556$	12.9804	0.550492
$557$	−25.7387	−1.09059	−0.545293	−	0.838246i	$-0.683581\pi$
$557$	−25.7387	−1.09059	−0.545293	+	0.838246i	$0.683581\pi$
$558$	2.15661	0.0912967
$559$	−3.60745	−0.152579
$560$	−4.69172	−0.198261
$561$	1.96126	0.0828045
$562$	4.39733	0.185490
$563$	31.6450	1.33368	0.666840	−	0.745201i	$-0.267647\pi$
$563$	31.6450	1.33368	0.666840	+	0.745201i	$0.267647\pi$
$564$	2.43816	0.102665
$565$	−10.6185	−0.446723
$566$	1.28128	0.0538562
$567$	−2.29161	−0.0962384
$568$	0.535370	0.0224636
$569$	−13.0924	−0.548862	−0.274431	−	0.961607i	$-0.588490\pi$
$569$	−13.0924	−0.548862	−0.274431	+	0.961607i	$0.588490\pi$
$570$	−0.713876	−0.0299010
$571$	1.65797	0.0693841	0.0346920	−	0.999398i	$-0.488955\pi$
$571$	1.65797	0.0693841	0.0346920	+	0.999398i	$0.488955\pi$
$572$	−12.2720	−0.513116
$573$	17.9051	0.747995
$574$	−0.220973	−0.00922322
$575$	−2.33008	−0.0971713
$576$	16.0958	0.670657
$577$	−19.4043	−0.807812	−0.403906	−	0.914801i	$-0.632348\pi$
$577$	−19.4043	−0.807812	−0.403906	+	0.914801i	$0.632348\pi$
$578$	−0.134450	−0.00559238
$579$	15.1989	0.631645
$580$	2.63340	0.109346
$581$	−16.4301	−0.681637
$582$	−0.535655	−0.0222036
$583$	13.6506	0.565350
$584$	6.96310	0.288135
$585$	−6.27469	−0.259426
$586$	1.02142	0.0421946
$587$	42.5896	1.75786	0.878931	−	0.476948i	$-0.158257\pi$
$587$	42.5896	1.75786	0.878931	+	0.476948i	$0.158257\pi$
$588$	−10.2748	−0.423727
$589$	−42.8522	−1.76569
$590$	−0.107161	−0.00441173
$591$	3.21002	0.132043
$592$	−20.1041	−0.826272
$593$	−18.6899	−0.767503	−0.383752	−	0.923436i	$-0.625368\pi$
$593$	−18.6899	−0.767503	−0.383752	+	0.923436i	$0.625368\pi$
$594$	−1.35179	−0.0554648
$595$	1.20552	0.0494215
$596$	11.9667	0.490175
$597$	−16.0447	−0.656666
$598$	0.924433	0.0378029
$599$	−6.79762	−0.277743	−0.138872	−	0.990310i	$-0.544348\pi$
$599$	−6.79762	−0.277743	−0.138872	+	0.990310i	$0.544348\pi$
$600$	−0.500386	−0.0204282
$601$	−28.2623	−1.15284	−0.576421	−	0.817153i	$-0.695551\pi$
$601$	−28.2623	−1.15284	−0.576421	+	0.817153i	$0.695551\pi$
$602$	−0.198150	−0.00807597
$603$	15.0850	0.614309
$604$	−11.8818	−0.483464
$605$	−6.59680	−0.268198
$606$	0.506468	0.0205739
$607$	2.08738	0.0847240	0.0423620	−	0.999102i	$-0.486512\pi$
$607$	2.08738	0.0847240	0.0423620	+	0.999102i	$0.486512\pi$
$608$	9.05523	0.367238
$609$	−1.49712	−0.0606663
$610$	−0.750002	−0.0303667
$611$	3.88389	0.157126
$612$	−4.21440	−0.170357
$613$	1.71512	0.0692730	0.0346365	−	0.999400i	$-0.488973\pi$
$613$	1.71512	0.0692730	0.0346365	+	0.999400i	$0.488973\pi$
$614$	2.15315	0.0868941
$615$	1.27425	0.0513827
$616$	−1.35429	−0.0545660
$617$	−13.2022	−0.531501	−0.265750	−	0.964042i	$-0.585620\pi$
$617$	−13.2022	−0.531501	−0.265750	+	0.964042i	$0.585620\pi$
$618$	−0.386532	−0.0155486
$619$	−10.9560	−0.440359	−0.220179	−	0.975459i	$-0.570664\pi$
$619$	−10.9560	−0.440359	−0.220179	+	0.975459i	$0.570664\pi$
$620$	−14.9503	−0.600417
$621$	−11.1644	−0.448014
$622$	1.70446	0.0683425
$623$	−12.0451	−0.482577
$624$	−10.7338	−0.429694
$625$	1.00000	0.0400000
$626$	3.79085	0.151513
$627$	11.1416	0.444951
$628$	−28.0858	−1.12074
$629$	5.16566	0.205969
$630$	−0.344655	−0.0137314
$631$	17.8248	0.709595	0.354798	−	0.934943i	$-0.384550\pi$
$631$	17.8248	0.709595	0.354798	+	0.934943i	$0.384550\pi$
$632$	5.20401	0.207004
$633$	20.0294	0.796098
$634$	2.83792	0.112708
$635$	8.08323	0.320773
$636$	12.0505	0.477834
$637$	−16.3674	−0.648499
$638$	0.374866	0.0148411
$639$	−2.12642	−0.0841199
$640$	4.20571	0.166245
$641$	−31.9867	−1.26340	−0.631699	−	0.775214i	$-0.717642\pi$
$641$	−31.9867	−1.26340	−0.631699	+	0.775214i	$0.717642\pi$
$642$	−2.28716	−0.0902671
$643$	4.61619	0.182045	0.0910224	−	0.995849i	$-0.470987\pi$
$643$	4.61619	0.182045	0.0910224	+	0.995849i	$0.470987\pi$
$644$	−5.56715	−0.219376
$645$	1.14264	0.0449913
$646$	−0.763786	−0.0300508
$647$	21.5782	0.848326	0.424163	−	0.905586i	$-0.360568\pi$
$647$	21.5782	0.848326	0.424163	+	0.905586i	$0.360568\pi$
$648$	1.01770	0.0399790
$649$	1.67247	0.0656502
$650$	−0.396738	−0.0155613
$651$	8.49939	0.333118
$652$	10.2717	0.402270
$653$	−11.6730	−0.456799	−0.228399	−	0.973568i	$-0.573349\pi$
$653$	−11.6730	−0.456799	−0.228399	+	0.973568i	$0.573349\pi$
$654$	−0.858594	−0.0335737
$655$	−2.43507	−0.0951460
$656$	−5.30592	−0.207161
$657$	−27.6566	−1.07899
$658$	0.213334	0.00831662
$659$	−3.82296	−0.148922	−0.0744608	−	0.997224i	$-0.523724\pi$
$659$	−3.82296	−0.148922	−0.0744608	+	0.997224i	$0.523724\pi$
$660$	3.88707	0.151304
$661$	16.9313	0.658552	0.329276	−	0.944234i	$-0.393195\pi$
$661$	16.9313	0.658552	0.329276	+	0.944234i	$0.393195\pi$
$662$	−1.24948	−0.0485623
$663$	2.75800	0.107112
$664$	7.29660	0.283163
$665$	6.84834	0.265567
$666$	−1.47685	−0.0572267
$667$	3.09601	0.119878
$668$	−34.9806	−1.35344
$669$	−0.647986	−0.0250526
$670$	0.953799	0.0368485
$671$	11.7054	0.451882
$672$	−1.79603	−0.0692834
$673$	−9.60049	−0.370072	−0.185036	−	0.982732i	$-0.559240\pi$
$673$	−9.60049	−0.370072	−0.185036	+	0.982732i	$0.559240\pi$
$674$	0.235968	0.00908916
$675$	4.79143	0.184422
$676$	8.50772	0.327220
$677$	5.76742	0.221660	0.110830	−	0.993839i	$-0.464649\pi$
$677$	5.76742	0.221660	0.110830	+	0.993839i	$0.464649\pi$
$678$	−1.33436	−0.0512459
$679$	5.13863	0.197203
$680$	−0.535370	−0.0205305
$681$	4.31494	0.165349
$682$	−2.12818	−0.0814921
$683$	4.13919	0.158382	0.0791908	−	0.996859i	$-0.474766\pi$
$683$	4.13919	0.158382	0.0791908	+	0.996859i	$0.474766\pi$
$684$	−23.9413	−0.915417
$685$	−10.7789	−0.411842
$686$	−2.03360	−0.0776432
$687$	1.80197	0.0687496
$688$	−4.75790	−0.181393
$689$	19.1960	0.731308
$690$	−0.292809	−0.0111470
$691$	27.8389	1.05904	0.529521	−	0.848297i	$-0.322372\pi$
$691$	27.8389	1.05904	0.529521	+	0.848297i	$0.322372\pi$
$692$	23.1094	0.878489
$693$	5.37908	0.204334
$694$	0.145376	0.00551840
$695$	−6.54940	−0.248433
$696$	0.664868	0.0252018
$697$	1.36334	0.0516401
$698$	3.28476	0.124330
$699$	0.475600	0.0179889
$700$	2.38925	0.0903051
$701$	26.8117	1.01266	0.506331	−	0.862339i	$-0.331001\pi$
$701$	26.8117	1.01266	0.506331	+	0.862339i	$0.331001\pi$
$702$	−1.90094	−0.0717465
$703$	29.3452	1.10678
$704$	−15.8835	−0.598633
$705$	−1.23020	−0.0463320
$706$	4.15097	0.156224
$707$	−4.85864	−0.182728
$708$	1.47643	0.0554876
$709$	−46.9647	−1.76380	−0.881898	−	0.471439i	$-0.843735\pi$
$709$	−46.9647	−1.76380	−0.881898	+	0.471439i	$0.843735\pi$
$710$	−0.134450	−0.00504582
$711$	−20.6697	−0.775173
$712$	5.34921	0.200470
$713$	−17.5766	−0.658248
$714$	0.151491	0.00566940
$715$	6.19194	0.231566
$716$	−32.4815	−1.21389
$717$	19.7499	0.737574
$718$	0.701587	0.0261830
$719$	−33.0619	−1.23300	−0.616501	−	0.787354i	$-0.711450\pi$
$719$	−33.0619	−1.23300	−0.616501	+	0.787354i	$0.711450\pi$
$720$	−8.27574	−0.308419
$721$	3.70807	0.138096
$722$	−1.78438	−0.0664078
$723$	−14.0678	−0.523187
$724$	36.0920	1.34135
$725$	−1.32871	−0.0493471
$726$	−0.828982	−0.0307664
$727$	−4.20371	−0.155907	−0.0779534	−	0.996957i	$-0.524839\pi$
$727$	−4.20371	−0.155907	−0.0779534	+	0.996957i	$0.524839\pi$
$728$	−1.90446	−0.0705838
$729$	9.39283	0.347883
$730$	−1.74868	−0.0647215
$731$	1.22252	0.0452167
$732$	10.3333	0.381930
$733$	−2.11437	−0.0780960	−0.0390480	−	0.999237i	$-0.512433\pi$
$733$	−2.11437	−0.0780960	−0.0390480	+	0.999237i	$0.512433\pi$
$734$	2.35032	0.0867520
$735$	5.18427	0.191225
$736$	3.71416	0.136906
$737$	−14.8861	−0.548336
$738$	−0.389774	−0.0143478
$739$	−47.2537	−1.73826	−0.869128	−	0.494588i	$-0.835319\pi$
$739$	−47.2537	−1.73826	−0.869128	+	0.494588i	$0.835319\pi$
$740$	10.2379	0.376354
$741$	15.6677	0.575567
$742$	1.05439	0.0387080
$743$	−33.8897	−1.24329	−0.621646	−	0.783298i	$-0.713536\pi$
$743$	−33.8897	−1.24329	−0.621646	+	0.783298i	$0.713536\pi$
$744$	−3.77457	−0.138382
$745$	−6.03792	−0.221212
$746$	2.00763	0.0735046
$747$	−28.9812	−1.06037
$748$	4.15883	0.152062
$749$	21.9412	0.801712
$750$	0.125664	0.00458861
$751$	5.48481	0.200144	0.100072	−	0.994980i	$-0.468093\pi$
$751$	5.48481	0.200144	0.100072	+	0.994980i	$0.468093\pi$
$752$	5.12250	0.186799
$753$	21.6565	0.789208
$754$	0.527150	0.0191977
$755$	5.99509	0.218184
$756$	11.4479	0.416357
$757$	−3.52347	−0.128063	−0.0640313	−	0.997948i	$-0.520396\pi$
$757$	−3.52347	−0.128063	−0.0640313	+	0.997948i	$0.520396\pi$
$758$	1.67680	0.0609042
$759$	4.56991	0.165877
$760$	−3.04134	−0.110321
$761$	40.6900	1.47501	0.737506	−	0.675340i	$-0.236003\pi$
$761$	40.6900	1.47501	0.737506	+	0.675340i	$0.236003\pi$
$762$	1.01577	0.0367976
$763$	8.23664	0.298186
$764$	37.9675	1.37361
$765$	2.12642	0.0768809
$766$	−1.65963	−0.0599650
$767$	2.35189	0.0849218
$768$	−13.6211	−0.491508
$769$	36.6684	1.32230	0.661148	−	0.750255i	$-0.270069\pi$
$769$	36.6684	1.32230	0.661148	+	0.750255i	$0.270069\pi$
$770$	0.340110	0.0122567
$771$	−23.1976	−0.835440
$772$	32.2291	1.15995
$773$	42.2930	1.52117	0.760586	−	0.649237i	$-0.224912\pi$
$773$	42.2930	1.52117	0.760586	+	0.649237i	$0.224912\pi$
$774$	−0.349517	−0.0125631
$775$	7.54332	0.270964
$776$	−2.28206	−0.0819212
$777$	−5.82039	−0.208805
$778$	−1.85360	−0.0664549
$779$	7.74487	0.277489
$780$	5.46614	0.195719
$781$	2.09838	0.0750860
$782$	−0.313280	−0.0112029
$783$	−6.36643	−0.227518
$784$	−21.5871	−0.770968
$785$	14.1710	0.505784
$786$	−0.306001	−0.0109147
$787$	−15.2262	−0.542754	−0.271377	−	0.962473i	$-0.587479\pi$
$787$	−15.2262	−0.542754	−0.271377	+	0.962473i	$0.587479\pi$
$788$	6.80681	0.242483
$789$	12.2089	0.434648
$790$	−1.30691	−0.0464977
$791$	12.8008	0.455144
$792$	−2.38884	−0.0848838
$793$	16.4605	0.584531
$794$	−2.46291	−0.0874053
$795$	−6.08021	−0.215643
$796$	−34.0226	−1.20590
$797$	−23.7911	−0.842725	−0.421363	−	0.906892i	$-0.638448\pi$
$797$	−23.7911	−0.842725	−0.421363	+	0.906892i	$0.638448\pi$
$798$	0.860592	0.0304646
$799$	−1.31621	−0.0465641
$800$	−1.59400	−0.0563564
$801$	−21.2464	−0.750704
$802$	3.01410	0.106431
$803$	27.2919	0.963109
$804$	−13.1412	−0.463453
$805$	2.80896	0.0990030
$806$	−2.99272	−0.105414
$807$	−15.9786	−0.562473
$808$	2.15771	0.0759081
$809$	−8.98746	−0.315982	−0.157991	−	0.987441i	$-0.550502\pi$
$809$	−8.98746	−0.315982	−0.157991	+	0.987441i	$0.550502\pi$
$810$	−0.255580	−0.00898016
$811$	−42.7743	−1.50201	−0.751004	−	0.660298i	$-0.770430\pi$
$811$	−42.7743	−1.50201	−0.751004	+	0.660298i	$0.770430\pi$
$812$	−3.17462	−0.111407
$813$	−10.2803	−0.360546
$814$	1.45737	0.0510810
$815$	−5.18268	−0.181541
$816$	3.63755	0.127340
$817$	6.94494	0.242973
$818$	3.82831	0.133854
$819$	7.56426	0.264317
$820$	2.70203	0.0943589
$821$	−27.1381	−0.947128	−0.473564	−	0.880760i	$-0.657033\pi$
$821$	−27.1381	−0.947128	−0.473564	+	0.880760i	$0.657033\pi$
$822$	−1.35453	−0.0472445
$823$	8.41200	0.293224	0.146612	−	0.989194i	$-0.453163\pi$
$823$	8.41200	0.293224	0.146612	+	0.989194i	$0.453163\pi$
$824$	−1.64675	−0.0573672
$825$	−1.96126	−0.0682824
$826$	0.129184	0.00449490
$827$	−28.0412	−0.975088	−0.487544	−	0.873099i	$-0.662107\pi$
$827$	−28.0412	−0.975088	−0.487544	+	0.873099i	$0.662107\pi$
$828$	−9.81992	−0.341266
$829$	−25.6225	−0.889907	−0.444953	−	0.895554i	$-0.646780\pi$
$829$	−25.6225	−0.889907	−0.444953	+	0.895554i	$0.646780\pi$
$830$	−1.83243	−0.0636046
$831$	−4.91794	−0.170601
$832$	−22.3360	−0.774361
$833$	5.54672	0.192182
$834$	−0.823025	−0.0284990
$835$	17.6498	0.610797
$836$	23.6256	0.817107
$837$	36.1433	1.24930
$838$	1.48659	0.0513535
$839$	−27.8095	−0.960091	−0.480045	−	0.877244i	$-0.659380\pi$
$839$	−27.8095	−0.960091	−0.480045	+	0.877244i	$0.659380\pi$
$840$	0.603225	0.0208132
$841$	−27.2345	−0.939122
$842$	3.88850	0.134007
$843$	30.5688	1.05285
$844$	42.4721	1.46195
$845$	−4.29266	−0.147672
$846$	0.376300	0.0129375
$847$	7.95257	0.273254
$848$	25.3178	0.869415
$849$	8.90706	0.305690
$850$	0.134450	0.00461160
$851$	12.0364	0.412604
$852$	1.85241	0.0634626
$853$	30.4096	1.04121	0.520603	−	0.853799i	$-0.325707\pi$
$853$	30.4096	1.04121	0.520603	+	0.853799i	$0.325707\pi$
$854$	0.904142	0.0309391
$855$	12.0798	0.413121
$856$	−9.74403	−0.333044
$857$	−0.859880	−0.0293730	−0.0146865	−	0.999892i	$-0.504675\pi$
$857$	−0.859880	−0.0293730	−0.0146865	+	0.999892i	$0.504675\pi$
$858$	0.778106	0.0265641
$859$	19.1640	0.653868	0.326934	−	0.945047i	$-0.393984\pi$
$859$	19.1640	0.653868	0.326934	+	0.945047i	$0.393984\pi$
$860$	2.42295	0.0826219
$861$	−1.53613	−0.0523513
$862$	1.73137	0.0589705
$863$	42.2102	1.43685	0.718426	−	0.695603i	$-0.244863\pi$
$863$	42.2102	1.43685	0.718426	+	0.695603i	$0.244863\pi$
$864$	−7.63755	−0.259835
$865$	−11.6601	−0.396455
$866$	−5.26305	−0.178846
$867$	−0.934655	−0.0317425
$868$	18.0229	0.611736
$869$	20.3971	0.691924
$870$	−0.166972	−0.00566087
$871$	−20.9334	−0.709300
$872$	−3.65788	−0.123871
$873$	9.06405	0.306772
$874$	−1.77969	−0.0601988
$875$	−1.20552	−0.0407540
$876$	24.0928	0.814020
$877$	36.4293	1.23013	0.615065	−	0.788476i	$-0.289130\pi$
$877$	36.4293	1.23013	0.615065	+	0.788476i	$0.289130\pi$
$878$	−4.25895	−0.143733
$879$	7.10062	0.239498
$880$	8.16662	0.275297
$881$	41.4640	1.39696	0.698479	−	0.715630i	$-0.253860\pi$
$881$	41.4640	1.39696	0.698479	+	0.715630i	$0.253860\pi$
$882$	−1.58579	−0.0533964
$883$	32.4677	1.09263	0.546313	−	0.837581i	$-0.316031\pi$
$883$	32.4677	1.09263	0.546313	+	0.837581i	$0.316031\pi$
$884$	5.84830	0.196700
$885$	−0.744947	−0.0250411
$886$	−4.36470	−0.146635
$887$	24.9582	0.838016	0.419008	−	0.907983i	$-0.362378\pi$
$887$	24.9582	0.838016	0.419008	+	0.907983i	$0.362378\pi$
$888$	2.58482	0.0867410
$889$	−9.74449	−0.326820
$890$	−1.34337	−0.0450300
$891$	3.98887	0.133632
$892$	−1.37405	−0.0460065
$893$	−7.47714	−0.250213
$894$	−0.758751	−0.0253764
$895$	16.3889	0.547820
$896$	−5.07007	−0.169379
$897$	6.42637	0.214570
$898$	−0.0343029	−0.00114470
$899$	−10.0229	−0.334282
$900$	4.21440	0.140480
$901$	−6.50530	−0.216723
$902$	0.384634	0.0128069
$903$	−1.37747	−0.0458395
$904$	−5.68481	−0.189074
$905$	−18.2106	−0.605340
$906$	0.753369	0.0250290
$907$	−24.5069	−0.813737	−0.406868	−	0.913487i	$-0.633379\pi$
$907$	−24.5069	−0.813737	−0.406868	+	0.913487i	$0.633379\pi$
$908$	9.14978	0.303646
$909$	−8.57017	−0.284255
$910$	0.478275	0.0158547
$911$	21.9067	0.725803	0.362901	−	0.931828i	$-0.381786\pi$
$911$	21.9067	0.725803	0.362901	+	0.931828i	$0.381786\pi$
$912$	20.6643	0.684262
$913$	28.5990	0.946490
$914$	−2.88456	−0.0954127
$915$	−5.21378	−0.172362
$916$	3.82106	0.126251
$917$	2.93552	0.0969395
$918$	0.644208	0.0212620
$919$	−13.6163	−0.449159	−0.224580	−	0.974456i	$-0.572101\pi$
$919$	−13.6163	−0.449159	−0.224580	+	0.974456i	$0.572101\pi$
$920$	−1.24746	−0.0411274
$921$	14.9680	0.493214
$922$	3.27107	0.107727
$923$	2.95082	0.0971274
$924$	−4.68594	−0.154156
$925$	−5.16566	−0.169846
$926$	−0.728535	−0.0239411
$927$	6.54068	0.214824
$928$	2.11797	0.0695257
$929$	−12.3897	−0.406493	−0.203246	−	0.979128i	$-0.565149\pi$
$929$	−12.3897	−0.406493	−0.203246	+	0.979128i	$0.565149\pi$
$930$	0.947926	0.0310837
$931$	31.5099	1.03270
$932$	1.00850	0.0330347
$933$	11.8489	0.387914
$934$	3.88401	0.127089
$935$	−2.09838	−0.0686244
$936$	−3.35928	−0.109801
$937$	−24.8357	−0.811346	−0.405673	−	0.914018i	$-0.632963\pi$
$937$	−24.8357	−0.811346	−0.405673	+	0.914018i	$0.632963\pi$
$938$	−1.14982	−0.0375431
$939$	26.3528	0.859992
$940$	−2.60862	−0.0850839
$941$	29.5593	0.963604	0.481802	−	0.876280i	$-0.339982\pi$
$941$	29.5593	0.963604	0.481802	+	0.876280i	$0.339982\pi$
$942$	1.78079	0.0580211
$943$	3.17669	0.103447
$944$	3.10193	0.100959
$945$	−5.77617	−0.187899
$946$	0.344908	0.0112139
$947$	−6.34089	−0.206051	−0.103026	−	0.994679i	$-0.532852\pi$
$947$	−6.34089	−0.206051	−0.103026	+	0.994679i	$0.532852\pi$
$948$	18.0062	0.584814
$949$	38.3788	1.24583
$950$	0.763786	0.0247805
$951$	19.7284	0.639736
$952$	0.645399	0.0209175
$953$	−22.7511	−0.736982	−0.368491	−	0.929631i	$-0.620125\pi$
$953$	−22.7511	−0.736982	−0.368491	+	0.929631i	$0.620125\pi$
$954$	1.85985	0.0602148
$955$	−19.1569	−0.619902
$956$	41.8794	1.35448
$957$	2.60595	0.0842384
$958$	2.13241	0.0688950
$959$	12.9942	0.419605
$960$	7.07479	0.228338
$961$	25.9016	0.835536
$962$	2.04941	0.0660758
$963$	38.7021	1.24716
$964$	−29.8306	−0.960779
$965$	−16.2615	−0.523477
$966$	0.352987	0.0113572
$967$	10.7643	0.346157	0.173078	−	0.984908i	$-0.444629\pi$
$967$	10.7643	0.346157	0.173078	+	0.984908i	$0.444629\pi$
$968$	−3.53173	−0.113514
$969$	−5.30960	−0.170569
$970$	0.573105	0.0184013
$971$	19.1061	0.613145	0.306572	−	0.951847i	$-0.400818\pi$
$971$	19.1061	0.613145	0.306572	+	0.951847i	$0.400818\pi$
$972$	32.0101	1.02672
$973$	7.89543	0.253116
$974$	−2.16714	−0.0694398
$975$	−2.75800	−0.0883266
$976$	21.7100	0.694919
$977$	25.2806	0.808799	0.404400	−	0.914582i	$-0.367480\pi$
$977$	25.2806	0.808799	0.404400	+	0.914582i	$0.367480\pi$
$978$	−0.651278	−0.0208256
$979$	20.9662	0.670083
$980$	10.9932	0.351164
$981$	14.5286	0.463864
$982$	1.58602	0.0506119
$983$	−11.8439	−0.377763	−0.188881	−	0.982000i	$-0.560486\pi$
$983$	−11.8439	−0.377763	−0.188881	+	0.982000i	$0.560486\pi$
$984$	0.682194	0.0217476
$985$	−3.43445	−0.109431
$986$	−0.178645	−0.00568922
$987$	1.48303	0.0472054
$988$	33.2231	1.05697
$989$	2.84859	0.0905798
$990$	0.599921	0.0190668
$991$	−18.7547	−0.595762	−0.297881	−	0.954603i	$-0.596280\pi$
$991$	−18.7547	−0.595762	−0.297881	+	0.954603i	$0.596280\pi$
$992$	−12.0241	−0.381764
$993$	−8.68598	−0.275641
$994$	0.162082	0.00514093
$995$	17.1665	0.544213
$996$	25.2467	0.799973
$997$	−4.71773	−0.149412	−0.0747061	−	0.997206i	$-0.523802\pi$
$997$	−4.71773	−0.149412	−0.0747061	+	0.997206i	$0.523802\pi$
$998$	−1.30573	−0.0413322
$999$	−24.7509	−0.783085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.b.1.18	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.b.1.18	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-0.134450 q^{2} -0.934655 q^{3} -1.98192 q^{4} +1.00000 q^{5} +0.125664 q^{6} -1.20552 q^{7} +0.535370 q^{8} -2.12642 q^{9} +O(q^{10})\)	\(q-0.134450 q^{2} -0.934655 q^{3} -1.98192 q^{4} +1.00000 q^{5} +0.125664 q^{6} -1.20552 q^{7} +0.535370 q^{8} -2.12642 q^{9} -0.134450 q^{10} +2.09838 q^{11} +1.85241 q^{12} +2.95082 q^{13} +0.162082 q^{14} -0.934655 q^{15} +3.89187 q^{16} -1.00000 q^{17} +0.285897 q^{18} -5.68082 q^{19} -1.98192 q^{20} +1.12674 q^{21} -0.282127 q^{22} -2.33008 q^{23} -0.500386 q^{24} +1.00000 q^{25} -0.396738 q^{26} +4.79143 q^{27} +2.38925 q^{28} -1.32871 q^{29} +0.125664 q^{30} +7.54332 q^{31} -1.59400 q^{32} -1.96126 q^{33} +0.134450 q^{34} -1.20552 q^{35} +4.21440 q^{36} -5.16566 q^{37} +0.763786 q^{38} -2.75800 q^{39} +0.535370 q^{40} -1.36334 q^{41} -0.151491 q^{42} -1.22252 q^{43} -4.15883 q^{44} -2.12642 q^{45} +0.313280 q^{46} +1.31621 q^{47} -3.63755 q^{48} -5.54672 q^{49} -0.134450 q^{50} +0.934655 q^{51} -5.84830 q^{52} +6.50530 q^{53} -0.644208 q^{54} +2.09838 q^{55} -0.645399 q^{56} +5.30960 q^{57} +0.178645 q^{58} +0.797029 q^{59} +1.85241 q^{60} +5.57830 q^{61} -1.01420 q^{62} +2.56344 q^{63} -7.56942 q^{64} +2.95082 q^{65} +0.263692 q^{66} -7.09408 q^{67} +1.98192 q^{68} +2.17782 q^{69} +0.162082 q^{70} +1.00000 q^{71} -1.13842 q^{72} +13.0062 q^{73} +0.694524 q^{74} -0.934655 q^{75} +11.2589 q^{76} -2.52964 q^{77} +0.370813 q^{78} +9.72040 q^{79} +3.89187 q^{80} +1.90093 q^{81} +0.183301 q^{82} +13.6291 q^{83} -2.23312 q^{84} -1.00000 q^{85} +0.164368 q^{86} +1.24189 q^{87} +1.12341 q^{88} +9.99162 q^{89} +0.285897 q^{90} -3.55727 q^{91} +4.61805 q^{92} -7.05040 q^{93} -0.176964 q^{94} -5.68082 q^{95} +1.48984 q^{96} -4.26259 q^{97} +0.745757 q^{98} -4.46204 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * q^99

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