LMFDB - Embedded newform 6015.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98559 q^{2} -1.00000 q^{3} +1.94257 q^{4} -1.00000 q^{5} +1.98559 q^{6} +4.82942 q^{7} +0.114041 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.98559 q^{2} -1.00000 q^{3} +1.94257 q^{4} -1.00000 q^{5} +1.98559 q^{6} +4.82942 q^{7} +0.114041 q^{8} +1.00000 q^{9} +1.98559 q^{10} -3.26217 q^{11} -1.94257 q^{12} +4.27685 q^{13} -9.58925 q^{14} +1.00000 q^{15} -4.11157 q^{16} +0.810913 q^{17} -1.98559 q^{18} +1.34101 q^{19} -1.94257 q^{20} -4.82942 q^{21} +6.47733 q^{22} +7.26846 q^{23} -0.114041 q^{24} +1.00000 q^{25} -8.49207 q^{26} -1.00000 q^{27} +9.38147 q^{28} +3.20730 q^{29} -1.98559 q^{30} -7.76023 q^{31} +7.93581 q^{32} +3.26217 q^{33} -1.61014 q^{34} -4.82942 q^{35} +1.94257 q^{36} -3.62204 q^{37} -2.66269 q^{38} -4.27685 q^{39} -0.114041 q^{40} -11.7377 q^{41} +9.58925 q^{42} -3.17031 q^{43} -6.33698 q^{44} -1.00000 q^{45} -14.4322 q^{46} -12.4432 q^{47} +4.11157 q^{48} +16.3233 q^{49} -1.98559 q^{50} -0.810913 q^{51} +8.30807 q^{52} -7.31283 q^{53} +1.98559 q^{54} +3.26217 q^{55} +0.550751 q^{56} -1.34101 q^{57} -6.36839 q^{58} +0.540754 q^{59} +1.94257 q^{60} +5.50037 q^{61} +15.4086 q^{62} +4.82942 q^{63} -7.53412 q^{64} -4.27685 q^{65} -6.47733 q^{66} +6.91798 q^{67} +1.57525 q^{68} -7.26846 q^{69} +9.58925 q^{70} -7.94024 q^{71} +0.114041 q^{72} -9.45462 q^{73} +7.19189 q^{74} -1.00000 q^{75} +2.60500 q^{76} -15.7544 q^{77} +8.49207 q^{78} -6.39666 q^{79} +4.11157 q^{80} +1.00000 q^{81} +23.3063 q^{82} -0.821857 q^{83} -9.38147 q^{84} -0.810913 q^{85} +6.29493 q^{86} -3.20730 q^{87} -0.372020 q^{88} -18.5985 q^{89} +1.98559 q^{90} +20.6547 q^{91} +14.1195 q^{92} +7.76023 q^{93} +24.7071 q^{94} -1.34101 q^{95} -7.93581 q^{96} +0.781410 q^{97} -32.4114 q^{98} -3.26217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - 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 $

$2$	−1.98559	−1.40402	−0.702012	−	0.712165i	$-0.747715\pi$
$2$	−1.98559	−1.40402	−0.702012	+	0.712165i	$0.747715\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.94257	0.971283
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.98559	0.810614
$7$	4.82942	1.82535	0.912675	−	0.408686i	$-0.134013\pi$
$7$	4.82942	1.82535	0.912675	+	0.408686i	$0.134013\pi$
$8$	0.114041	0.0403195
$9$	1.00000	0.333333
$10$	1.98559	0.627899
$11$	−3.26217	−0.983582	−0.491791	−	0.870713i	$-0.663658\pi$
$11$	−3.26217	−0.983582	−0.491791	+	0.870713i	$0.663658\pi$
$12$	−1.94257	−0.560770
$13$	4.27685	1.18619	0.593093	−	0.805134i	$-0.297907\pi$
$13$	4.27685	1.18619	0.593093	+	0.805134i	$0.297907\pi$
$14$	−9.58925	−2.56283
$15$	1.00000	0.258199
$16$	−4.11157	−1.02789
$17$	0.810913	0.196675	0.0983376	−	0.995153i	$-0.468648\pi$
$17$	0.810913	0.196675	0.0983376	+	0.995153i	$0.468648\pi$
$18$	−1.98559	−0.468008
$19$	1.34101	0.307648	0.153824	−	0.988098i	$-0.450841\pi$
$19$	1.34101	0.307648	0.153824	+	0.988098i	$0.450841\pi$
$20$	−1.94257	−0.434371
$21$	−4.82942	−1.05387
$22$	6.47733	1.38097
$23$	7.26846	1.51558	0.757789	−	0.652500i	$-0.226280\pi$
$23$	7.26846	1.51558	0.757789	+	0.652500i	$0.226280\pi$
$24$	−0.114041	−0.0232785
$25$	1.00000	0.200000
$26$	−8.49207	−1.66543
$27$	−1.00000	−0.192450
$28$	9.38147	1.77293
$29$	3.20730	0.595581	0.297791	−	0.954631i	$-0.403750\pi$
$29$	3.20730	0.595581	0.297791	+	0.954631i	$0.403750\pi$
$30$	−1.98559	−0.362517
$31$	−7.76023	−1.39378	−0.696890	−	0.717178i	$-0.745433\pi$
$31$	−7.76023	−1.39378	−0.696890	+	0.717178i	$0.745433\pi$
$32$	7.93581	1.40287
$33$	3.26217	0.567871
$34$	−1.61014	−0.276137
$35$	−4.82942	−0.816321
$36$	1.94257	0.323761
$37$	−3.62204	−0.595460	−0.297730	−	0.954650i	$-0.596229\pi$
$37$	−3.62204	−0.595460	−0.297730	+	0.954650i	$0.596229\pi$
$38$	−2.66269	−0.431946
$39$	−4.27685	−0.684844
$40$	−0.114041	−0.0180314
$41$	−11.7377	−1.83312	−0.916561	−	0.399896i	$-0.869046\pi$
$41$	−11.7377	−1.83312	−0.916561	+	0.399896i	$0.869046\pi$
$42$	9.58925	1.47965
$43$	−3.17031	−0.483468	−0.241734	−	0.970343i	$-0.577716\pi$
$43$	−3.17031	−0.483468	−0.241734	+	0.970343i	$0.577716\pi$
$44$	−6.33698	−0.955336
$45$	−1.00000	−0.149071
$46$	−14.4322	−2.12791
$47$	−12.4432	−1.81503	−0.907513	−	0.420025i	$-0.862021\pi$
$47$	−12.4432	−1.81503	−0.907513	+	0.420025i	$0.862021\pi$
$48$	4.11157	0.593454
$49$	16.3233	2.33190
$50$	−1.98559	−0.280805
$51$	−0.810913	−0.113550
$52$	8.30807	1.15212
$53$	−7.31283	−1.00449	−0.502247	−	0.864724i	$-0.667493\pi$
$53$	−7.31283	−1.00449	−0.502247	+	0.864724i	$0.667493\pi$
$54$	1.98559	0.270205
$55$	3.26217	0.439871
$56$	0.550751	0.0735972
$57$	−1.34101	−0.177621
$58$	−6.36839	−0.836210
$59$	0.540754	0.0704002	0.0352001	−	0.999380i	$-0.488793\pi$
$59$	0.540754	0.0704002	0.0352001	+	0.999380i	$0.488793\pi$
$60$	1.94257	0.250784
$61$	5.50037	0.704250	0.352125	−	0.935953i	$-0.385459\pi$
$61$	5.50037	0.704250	0.352125	+	0.935953i	$0.385459\pi$
$62$	15.4086	1.95690
$63$	4.82942	0.608450
$64$	−7.53412	−0.941765
$65$	−4.27685	−0.530478
$66$	−6.47733	−0.797305
$67$	6.91798	0.845166	0.422583	−	0.906324i	$-0.361123\pi$
$67$	6.91798	0.845166	0.422583	+	0.906324i	$0.361123\pi$
$68$	1.57525	0.191027
$69$	−7.26846	−0.875019
$70$	9.58925	1.14613
$71$	−7.94024	−0.942333	−0.471167	−	0.882044i	$-0.656167\pi$
$71$	−7.94024	−0.942333	−0.471167	+	0.882044i	$0.656167\pi$
$72$	0.114041	0.0134398
$73$	−9.45462	−1.10658	−0.553290	−	0.832989i	$-0.686628\pi$
$73$	−9.45462	−1.10658	−0.553290	+	0.832989i	$0.686628\pi$
$74$	7.19189	0.836040
$75$	−1.00000	−0.115470
$76$	2.60500	0.298814
$77$	−15.7544	−1.79538
$78$	8.49207	0.961538
$79$	−6.39666	−0.719680	−0.359840	−	0.933014i	$-0.617169\pi$
$79$	−6.39666	−0.719680	−0.359840	+	0.933014i	$0.617169\pi$
$80$	4.11157	0.459687
$81$	1.00000	0.111111
$82$	23.3063	2.57375
$83$	−0.821857	−0.0902105	−0.0451052	−	0.998982i	$-0.514362\pi$
$83$	−0.821857	−0.0902105	−0.0451052	+	0.998982i	$0.514362\pi$
$84$	−9.38147	−1.02360
$85$	−0.810913	−0.0879558
$86$	6.29493	0.678800
$87$	−3.20730	−0.343859
$88$	−0.372020	−0.0396575
$89$	−18.5985	−1.97144	−0.985721	−	0.168386i	$-0.946144\pi$
$89$	−18.5985	−1.97144	−0.985721	+	0.168386i	$0.946144\pi$
$90$	1.98559	0.209300
$91$	20.6547	2.16520
$92$	14.1195	1.47205
$93$	7.76023	0.804699
$94$	24.7071	2.54834
$95$	−1.34101	−0.137584
$96$	−7.93581	−0.809945
$97$	0.781410	0.0793401	0.0396701	−	0.999213i	$-0.487369\pi$
$97$	0.781410	0.0793401	0.0396701	+	0.999213i	$0.487369\pi$
$98$	−32.4114	−3.27405
$99$	−3.26217	−0.327861
$100$	1.94257	0.194257
$101$	−11.5602	−1.15028	−0.575141	−	0.818054i	$-0.695053\pi$
$101$	−11.5602	−1.15028	−0.575141	+	0.818054i	$0.695053\pi$
$102$	1.61014	0.159428
$103$	−4.44128	−0.437613	−0.218806	−	0.975768i	$-0.570216\pi$
$103$	−4.44128	−0.437613	−0.218806	+	0.975768i	$0.570216\pi$
$104$	0.487735	0.0478264
$105$	4.82942	0.471303
$106$	14.5203	1.41033
$107$	−13.3638	−1.29193	−0.645963	−	0.763368i	$-0.723544\pi$
$107$	−13.3638	−1.29193	−0.645963	+	0.763368i	$0.723544\pi$
$108$	−1.94257	−0.186923
$109$	−13.7348	−1.31556	−0.657779	−	0.753211i	$-0.728504\pi$
$109$	−13.7348	−1.31556	−0.657779	+	0.753211i	$0.728504\pi$
$110$	−6.47733	−0.617590
$111$	3.62204	0.343789
$112$	−19.8565	−1.87626
$113$	−1.89605	−0.178365	−0.0891827	−	0.996015i	$-0.528425\pi$
$113$	−1.89605	−0.178365	−0.0891827	+	0.996015i	$0.528425\pi$
$114$	2.66269	0.249384
$115$	−7.26846	−0.677787
$116$	6.23040	0.578478
$117$	4.27685	0.395395
$118$	−1.07372	−0.0988436
$119$	3.91624	0.359001
$120$	0.114041	0.0104104
$121$	−0.358235	−0.0325668
$122$	−10.9215	−0.988784
$123$	11.7377	1.05835
$124$	−15.0748	−1.35375
$125$	−1.00000	−0.0894427
$126$	−9.58925	−0.854278
$127$	17.2115	1.52727	0.763635	−	0.645648i	$-0.223413\pi$
$127$	17.2115	1.52727	0.763635	+	0.645648i	$0.223413\pi$
$128$	−0.911949	−0.0806057
$129$	3.17031	0.279130
$130$	8.49207	0.744804
$131$	−14.4900	−1.26600	−0.633000	−	0.774152i	$-0.718177\pi$
$131$	−14.4900	−1.26600	−0.633000	+	0.774152i	$0.718177\pi$
$132$	6.33698	0.551564
$133$	6.47629	0.561566
$134$	−13.7363	−1.18663
$135$	1.00000	0.0860663
$136$	0.0924770	0.00792984
$137$	−9.81322	−0.838400	−0.419200	−	0.907894i	$-0.637689\pi$
$137$	−9.81322	−0.838400	−0.419200	+	0.907894i	$0.637689\pi$
$138$	14.4322	1.22855
$139$	−10.5945	−0.898616	−0.449308	−	0.893377i	$-0.648329\pi$
$139$	−10.5945	−0.898616	−0.449308	+	0.893377i	$0.648329\pi$
$140$	−9.38147	−0.792879
$141$	12.4432	1.04791
$142$	15.7661	1.32306
$143$	−13.9518	−1.16671
$144$	−4.11157	−0.342631
$145$	−3.20730	−0.266352
$146$	18.7730	1.55366
$147$	−16.3233	−1.34632
$148$	−7.03605	−0.578360
$149$	21.8815	1.79260	0.896302	−	0.443444i	$-0.146244\pi$
$149$	21.8815	1.79260	0.896302	+	0.443444i	$0.146244\pi$
$150$	1.98559	0.162123
$151$	4.35127	0.354102	0.177051	−	0.984202i	$-0.443344\pi$
$151$	4.35127	0.354102	0.177051	+	0.984202i	$0.443344\pi$
$152$	0.152929	0.0124042
$153$	0.810913	0.0655584
$154$	31.2818	2.52076
$155$	7.76023	0.623317
$156$	−8.30807	−0.665178
$157$	−14.1743	−1.13123	−0.565615	−	0.824670i	$-0.691361\pi$
$157$	−14.1743	−1.13123	−0.565615	+	0.824670i	$0.691361\pi$
$158$	12.7011	1.01045
$159$	7.31283	0.579945
$160$	−7.93581	−0.627381
$161$	35.1024	2.76646
$162$	−1.98559	−0.156003
$163$	11.6016	0.908706	0.454353	−	0.890822i	$-0.349871\pi$
$163$	11.6016	0.908706	0.454353	+	0.890822i	$0.349871\pi$
$164$	−22.8013	−1.78048
$165$	−3.26217	−0.253960
$166$	1.63187	0.126658
$167$	−4.28180	−0.331336	−0.165668	−	0.986182i	$-0.552978\pi$
$167$	−4.28180	−0.331336	−0.165668	+	0.986182i	$0.552978\pi$
$168$	−0.550751	−0.0424913
$169$	5.29146	0.407036
$170$	1.61014	0.123492
$171$	1.34101	0.102549
$172$	−6.15854	−0.469584
$173$	14.4066	1.09531	0.547656	−	0.836704i	$-0.315520\pi$
$173$	14.4066	1.09531	0.547656	+	0.836704i	$0.315520\pi$
$174$	6.36839	0.482786
$175$	4.82942	0.365070
$176$	13.4126	1.01102
$177$	−0.540754	−0.0406456
$178$	36.9291	2.76795
$179$	7.48119	0.559170	0.279585	−	0.960121i	$-0.409803\pi$
$179$	7.48119	0.559170	0.279585	+	0.960121i	$0.409803\pi$
$180$	−1.94257	−0.144790
$181$	5.53400	0.411339	0.205670	−	0.978622i	$-0.434063\pi$
$181$	5.53400	0.411339	0.205670	+	0.978622i	$0.434063\pi$
$182$	−41.0118	−3.04000
$183$	−5.50037	−0.406599
$184$	0.828900	0.0611073
$185$	3.62204	0.266298
$186$	−15.4086	−1.12982
$187$	−2.64534	−0.193446
$188$	−24.1717	−1.76290
$189$	−4.82942	−0.351289
$190$	2.66269	0.193172
$191$	8.85244	0.640540	0.320270	−	0.947326i	$-0.396226\pi$
$191$	8.85244	0.640540	0.320270	+	0.947326i	$0.396226\pi$
$192$	7.53412	0.543728
$193$	−5.08324	−0.365900	−0.182950	−	0.983122i	$-0.558565\pi$
$193$	−5.08324	−0.365900	−0.182950	+	0.983122i	$0.558565\pi$
$194$	−1.55156	−0.111395
$195$	4.27685	0.306272
$196$	31.7091	2.26494
$197$	6.10507	0.434968	0.217484	−	0.976064i	$-0.430215\pi$
$197$	6.10507	0.434968	0.217484	+	0.976064i	$0.430215\pi$
$198$	6.47733	0.460324
$199$	−16.5954	−1.17641	−0.588207	−	0.808711i	$-0.700166\pi$
$199$	−16.5954	−1.17641	−0.588207	+	0.808711i	$0.700166\pi$
$200$	0.114041	0.00806389
$201$	−6.91798	−0.487957
$202$	22.9538	1.61502
$203$	15.4894	1.08714
$204$	−1.57525	−0.110290
$205$	11.7377	0.819797
$206$	8.81856	0.614418
$207$	7.26846	0.505193
$208$	−17.5846	−1.21927
$209$	−4.37460	−0.302597
$210$	−9.58925	−0.661721
$211$	3.58923	0.247093	0.123546	−	0.992339i	$-0.460573\pi$
$211$	3.58923	0.247093	0.123546	+	0.992339i	$0.460573\pi$
$212$	−14.2057	−0.975648
$213$	7.94024	0.544056
$214$	26.5350	1.81390
$215$	3.17031	0.216213
$216$	−0.114041	−0.00775949
$217$	−37.4775	−2.54414
$218$	27.2717	1.84707
$219$	9.45462	0.638884
$220$	6.33698	0.427239
$221$	3.46815	0.233293
$222$	−7.19189	−0.482688
$223$	−11.0048	−0.736939	−0.368470	−	0.929640i	$-0.620118\pi$
$223$	−11.0048	−0.736939	−0.368470	+	0.929640i	$0.620118\pi$
$224$	38.3254	2.56072
$225$	1.00000	0.0666667
$226$	3.76478	0.250429
$227$	−12.5150	−0.830651	−0.415325	−	0.909673i	$-0.636332\pi$
$227$	−12.5150	−0.830651	−0.415325	+	0.909673i	$0.636332\pi$
$228$	−2.60500	−0.172520
$229$	25.4804	1.68379	0.841896	−	0.539640i	$-0.181440\pi$
$229$	25.4804	1.68379	0.841896	+	0.539640i	$0.181440\pi$
$230$	14.4322	0.951629
$231$	15.7544	1.03656
$232$	0.365763	0.0240135
$233$	0.302135	0.0197935	0.00989675	−	0.999951i	$-0.496850\pi$
$233$	0.302135	0.0197935	0.00989675	+	0.999951i	$0.496850\pi$
$234$	−8.49207	−0.555144
$235$	12.4432	0.811704
$236$	1.05045	0.0683785
$237$	6.39666	0.415507
$238$	−7.77604	−0.504046
$239$	26.9069	1.74047	0.870233	−	0.492641i	$-0.163968\pi$
$239$	26.9069	1.74047	0.870233	+	0.492641i	$0.163968\pi$
$240$	−4.11157	−0.265401
$241$	17.3882	1.12007	0.560037	−	0.828467i	$-0.310787\pi$
$241$	17.3882	1.12007	0.560037	+	0.828467i	$0.310787\pi$
$242$	0.711308	0.0457246
$243$	−1.00000	−0.0641500
$244$	10.6848	0.684026
$245$	−16.3233	−1.04286
$246$	−23.3063	−1.48595
$247$	5.73529	0.364928
$248$	−0.884983	−0.0561964
$249$	0.821857	0.0520830
$250$	1.98559	0.125580
$251$	16.0999	1.01621	0.508107	−	0.861294i	$-0.330345\pi$
$251$	16.0999	1.01621	0.508107	+	0.861294i	$0.330345\pi$
$252$	9.38147	0.590977
$253$	−23.7110	−1.49069
$254$	−34.1749	−2.14432
$255$	0.810913	0.0507813
$256$	16.8790	1.05494
$257$	5.73726	0.357880	0.178940	−	0.983860i	$-0.442733\pi$
$257$	5.73726	0.357880	0.178940	+	0.983860i	$0.442733\pi$
$258$	−6.29493	−0.391906
$259$	−17.4924	−1.08692
$260$	−8.30807	−0.515244
$261$	3.20730	0.198527
$262$	28.7712	1.77749
$263$	12.4972	0.770611	0.385306	−	0.922789i	$-0.374096\pi$
$263$	12.4972	0.770611	0.385306	+	0.922789i	$0.374096\pi$
$264$	0.372020	0.0228963
$265$	7.31283	0.449224
$266$	−12.8593	−0.788452
$267$	18.5985	1.13821
$268$	13.4386	0.820896
$269$	−14.4780	−0.882737	−0.441369	−	0.897326i	$-0.645507\pi$
$269$	−14.4780	−0.882737	−0.441369	+	0.897326i	$0.645507\pi$
$270$	−1.98559	−0.120839
$271$	11.5535	0.701824	0.350912	−	0.936409i	$-0.385872\pi$
$271$	11.5535	0.701824	0.350912	+	0.936409i	$0.385872\pi$
$272$	−3.33412	−0.202161
$273$	−20.6547	−1.25008
$274$	19.4850	1.17713
$275$	−3.26217	−0.196716
$276$	−14.1195	−0.849891
$277$	8.93449	0.536821	0.268411	−	0.963305i	$-0.413502\pi$
$277$	8.93449	0.536821	0.268411	+	0.963305i	$0.413502\pi$
$278$	21.0364	1.26168
$279$	−7.76023	−0.464593
$280$	−0.550751	−0.0329136
$281$	13.7345	0.819331	0.409665	−	0.912236i	$-0.365645\pi$
$281$	13.7345	0.819331	0.409665	+	0.912236i	$0.365645\pi$
$282$	−24.7071	−1.47128
$283$	−12.1138	−0.720092	−0.360046	−	0.932934i	$-0.617239\pi$
$283$	−12.1138	−0.720092	−0.360046	+	0.932934i	$0.617239\pi$
$284$	−15.4244	−0.915272
$285$	1.34101	0.0794344
$286$	27.7026	1.63809
$287$	−56.6863	−3.34609
$288$	7.93581	0.467622
$289$	−16.3424	−0.961319
$290$	6.36839	0.373965
$291$	−0.781410	−0.0458071
$292$	−18.3662	−1.07480
$293$	−22.6616	−1.32390	−0.661951	−	0.749547i	$-0.730272\pi$
$293$	−22.6616	−1.32390	−0.661951	+	0.749547i	$0.730272\pi$
$294$	32.4114	1.89027
$295$	−0.540754	−0.0314839
$296$	−0.413060	−0.0240086
$297$	3.26217	0.189290
$298$	−43.4477	−2.51686
$299$	31.0861	1.79776
$300$	−1.94257	−0.112154
$301$	−15.3108	−0.882498
$302$	−8.63984	−0.497167
$303$	11.5602	0.664116
$304$	−5.51365	−0.316229
$305$	−5.50037	−0.314950
$306$	−1.61014	−0.0920455
$307$	10.3409	0.590189	0.295094	−	0.955468i	$-0.404649\pi$
$307$	10.3409	0.590189	0.295094	+	0.955468i	$0.404649\pi$
$308$	−30.6040	−1.74382
$309$	4.44128	0.252656
$310$	−15.4086	−0.875152
$311$	−13.9419	−0.790572	−0.395286	−	0.918558i	$-0.629354\pi$
$311$	−13.9419	−0.790572	−0.395286	+	0.918558i	$0.629354\pi$
$312$	−0.487735	−0.0276126
$313$	−19.7976	−1.11903	−0.559514	−	0.828821i	$-0.689012\pi$
$313$	−19.7976	−1.11903	−0.559514	+	0.828821i	$0.689012\pi$
$314$	28.1443	1.58827
$315$	−4.82942	−0.272107
$316$	−12.4259	−0.699013
$317$	16.4447	0.923627	0.461813	−	0.886977i	$-0.347199\pi$
$317$	16.4447	0.923627	0.461813	+	0.886977i	$0.347199\pi$
$318$	−14.5203	−0.814257
$319$	−10.4628	−0.585803
$320$	7.53412	0.421170
$321$	13.3638	0.745894
$322$	−69.6990	−3.88418
$323$	1.08744	0.0605068
$324$	1.94257	0.107920
$325$	4.27685	0.237237
$326$	−23.0360	−1.27584
$327$	13.7348	0.759537
$328$	−1.33858	−0.0739105
$329$	−60.0934	−3.31306
$330$	6.47733	0.356566
$331$	21.7076	1.19316	0.596579	−	0.802554i	$-0.296526\pi$
$331$	21.7076	1.19316	0.596579	+	0.802554i	$0.296526\pi$
$332$	−1.59651	−0.0876199
$333$	−3.62204	−0.198487
$334$	8.50190	0.465203
$335$	−6.91798	−0.377970
$336$	19.8565	1.08326
$337$	−28.7592	−1.56661	−0.783307	−	0.621636i	$-0.786468\pi$
$337$	−28.7592	−1.56661	−0.783307	+	0.621636i	$0.786468\pi$
$338$	−10.5067	−0.571488
$339$	1.89605	0.102979
$340$	−1.57525	−0.0854300
$341$	25.3152	1.37090
$342$	−2.66269	−0.143982
$343$	45.0262	2.43119
$344$	−0.361544	−0.0194932
$345$	7.26846	0.391321
$346$	−28.6056	−1.53784
$347$	−23.8178	−1.27861	−0.639305	−	0.768954i	$-0.720778\pi$
$347$	−23.8178	−1.27861	−0.639305	+	0.768954i	$0.720778\pi$
$348$	−6.23040	−0.333984
$349$	−0.268134	−0.0143529	−0.00717644	−	0.999974i	$-0.502284\pi$
$349$	−0.268134	−0.0143529	−0.00717644	+	0.999974i	$0.502284\pi$
$350$	−9.58925	−0.512567
$351$	−4.27685	−0.228281
$352$	−25.8880	−1.37983
$353$	0.715691	0.0380924	0.0190462	−	0.999819i	$-0.493937\pi$
$353$	0.715691	0.0380924	0.0190462	+	0.999819i	$0.493937\pi$
$354$	1.07372	0.0570674
$355$	7.94024	0.421424
$356$	−36.1289	−1.91483
$357$	−3.91624	−0.207269
$358$	−14.8546	−0.785088
$359$	20.9315	1.10472	0.552360	−	0.833605i	$-0.313727\pi$
$359$	20.9315	1.10472	0.552360	+	0.833605i	$0.313727\pi$
$360$	−0.114041	−0.00601047
$361$	−17.2017	−0.905353
$362$	−10.9883	−0.577530
$363$	0.358235	0.0188025
$364$	40.1232	2.10302
$365$	9.45462	0.494877
$366$	10.9215	0.570875
$367$	5.52928	0.288626	0.144313	−	0.989532i	$-0.453903\pi$
$367$	5.52928	0.288626	0.144313	+	0.989532i	$0.453903\pi$
$368$	−29.8848	−1.55785
$369$	−11.7377	−0.611040
$370$	−7.19189	−0.373888
$371$	−35.3167	−1.83355
$372$	15.0748	0.781590
$373$	−30.1954	−1.56346	−0.781729	−	0.623619i	$-0.785662\pi$
$373$	−30.1954	−1.56346	−0.781729	+	0.623619i	$0.785662\pi$
$374$	5.25255	0.271603
$375$	1.00000	0.0516398
$376$	−1.41903	−0.0731809
$377$	13.7172	0.706470
$378$	9.58925	0.493218
$379$	−27.2694	−1.40074	−0.700368	−	0.713782i	$-0.746981\pi$
$379$	−27.2694	−1.40074	−0.700368	+	0.713782i	$0.746981\pi$
$380$	−2.60500	−0.133633
$381$	−17.2115	−0.881770
$382$	−17.5773	−0.899334
$383$	−24.8031	−1.26738	−0.633690	−	0.773587i	$-0.718461\pi$
$383$	−24.8031	−1.26738	−0.633690	+	0.773587i	$0.718461\pi$
$384$	0.911949	0.0465377
$385$	15.7544	0.802919
$386$	10.0932	0.513732
$387$	−3.17031	−0.161156
$388$	1.51794	0.0770617
$389$	31.5999	1.60218	0.801089	−	0.598546i	$-0.204255\pi$
$389$	31.5999	1.60218	0.801089	+	0.598546i	$0.204255\pi$
$390$	−8.49207	−0.430013
$391$	5.89408	0.298077
$392$	1.86152	0.0940211
$393$	14.4900	0.730925
$394$	−12.1222	−0.610706
$395$	6.39666	0.321851
$396$	−6.33698	−0.318445
$397$	−26.8727	−1.34870	−0.674351	−	0.738411i	$-0.735577\pi$
$397$	−26.8727	−1.34870	−0.674351	+	0.738411i	$0.735577\pi$
$398$	32.9516	1.65171
$399$	−6.47629	−0.324220
$400$	−4.11157	−0.205578
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	13.7363	0.685103
$403$	−33.1894	−1.65328
$404$	−22.4564	−1.11725
$405$	−1.00000	−0.0496904
$406$	−30.7556	−1.52638
$407$	11.8157	0.585683
$408$	−0.0924770	−0.00457830
$409$	9.39258	0.464433	0.232217	−	0.972664i	$-0.425402\pi$
$409$	9.39258	0.464433	0.232217	+	0.972664i	$0.425402\pi$
$410$	−23.3063	−1.15101
$411$	9.81322	0.484051
$412$	−8.62748	−0.425046
$413$	2.61153	0.128505
$414$	−14.4322	−0.709302
$415$	0.821857	0.0403434
$416$	33.9403	1.66406
$417$	10.5945	0.518816
$418$	8.68616	0.424854
$419$	−12.2643	−0.599149	−0.299574	−	0.954073i	$-0.596845\pi$
$419$	−12.2643	−0.599149	−0.299574	+	0.954073i	$0.596845\pi$
$420$	9.38147	0.457769
$421$	17.3510	0.845635	0.422818	−	0.906215i	$-0.361041\pi$
$421$	17.3510	0.845635	0.422818	+	0.906215i	$0.361041\pi$
$422$	−7.12674	−0.346924
$423$	−12.4432	−0.605008
$424$	−0.833960	−0.0405007
$425$	0.810913	0.0393350
$426$	−15.7661	−0.763868
$427$	26.5636	1.28550
$428$	−25.9600	−1.25483
$429$	13.9518	0.673600
$430$	−6.29493	−0.303569
$431$	30.6787	1.47774	0.738870	−	0.673848i	$-0.235360\pi$
$431$	30.6787	1.47774	0.738870	+	0.673848i	$0.235360\pi$
$432$	4.11157	0.197818
$433$	9.67546	0.464973	0.232486	−	0.972600i	$-0.425314\pi$
$433$	9.67546	0.464973	0.232486	+	0.972600i	$0.425314\pi$
$434$	74.4148	3.57203
$435$	3.20730	0.153778
$436$	−26.6808	−1.27778
$437$	9.74706	0.466265
$438$	−18.7730	−0.897008
$439$	−24.7489	−1.18120	−0.590601	−	0.806964i	$-0.701109\pi$
$439$	−24.7489	−1.18120	−0.590601	+	0.806964i	$0.701109\pi$
$440$	0.372020	0.0177354
$441$	16.3233	0.777301
$442$	−6.88633	−0.327549
$443$	−2.69509	−0.128047	−0.0640237	−	0.997948i	$-0.520393\pi$
$443$	−2.69509	−0.128047	−0.0640237	+	0.997948i	$0.520393\pi$
$444$	7.03605	0.333916
$445$	18.5985	0.881656
$446$	21.8511	1.03468
$447$	−21.8815	−1.03496
$448$	−36.3854	−1.71905
$449$	−7.25925	−0.342585	−0.171293	−	0.985220i	$-0.554794\pi$
$449$	−7.25925	−0.342585	−0.171293	+	0.985220i	$0.554794\pi$
$450$	−1.98559	−0.0936016
$451$	38.2904	1.80302
$452$	−3.68320	−0.173243
$453$	−4.35127	−0.204441
$454$	24.8497	1.16625
$455$	−20.6547	−0.968308
$456$	−0.152929	−0.00716158
$457$	14.4793	0.677315	0.338658	−	0.940910i	$-0.390027\pi$
$457$	14.4793	0.677315	0.338658	+	0.940910i	$0.390027\pi$
$458$	−50.5936	−2.36408
$459$	−0.810913	−0.0378502
$460$	−14.1195	−0.658323
$461$	−22.4667	−1.04638	−0.523190	−	0.852216i	$-0.675258\pi$
$461$	−22.4667	−1.04638	−0.523190	+	0.852216i	$0.675258\pi$
$462$	−31.2818	−1.45536
$463$	−1.19690	−0.0556245	−0.0278122	−	0.999613i	$-0.508854\pi$
$463$	−1.19690	−0.0556245	−0.0278122	+	0.999613i	$0.508854\pi$
$464$	−13.1871	−0.612193
$465$	−7.76023	−0.359872
$466$	−0.599915	−0.0277905
$467$	8.30867	0.384480	0.192240	−	0.981348i	$-0.438425\pi$
$467$	8.30867	0.384480	0.192240	+	0.981348i	$0.438425\pi$
$468$	8.30807	0.384040
$469$	33.4099	1.54272
$470$	−24.7071	−1.13965
$471$	14.1743	0.653116
$472$	0.0616680	0.00283850
$473$	10.3421	0.475530
$474$	−12.7011	−0.583382
$475$	1.34101	0.0615297
$476$	7.60755	0.348692
$477$	−7.31283	−0.334831
$478$	−53.4261	−2.44365
$479$	−22.2804	−1.01802	−0.509008	−	0.860762i	$-0.669988\pi$
$479$	−22.2804	−1.01802	−0.509008	+	0.860762i	$0.669988\pi$
$480$	7.93581	0.362218
$481$	−15.4909	−0.706326
$482$	−34.5259	−1.57261
$483$	−35.1024	−1.59722
$484$	−0.695895	−0.0316316
$485$	−0.781410	−0.0354820
$486$	1.98559	0.0900682
$487$	−10.5170	−0.476571	−0.238285	−	0.971195i	$-0.576585\pi$
$487$	−10.5170	−0.476571	−0.238285	+	0.971195i	$0.576585\pi$
$488$	0.627266	0.0283950
$489$	−11.6016	−0.524642
$490$	32.4114	1.46420
$491$	−10.9280	−0.493176	−0.246588	−	0.969120i	$-0.579309\pi$
$491$	−10.9280	−0.493176	−0.246588	+	0.969120i	$0.579309\pi$
$492$	22.8013	1.02796
$493$	2.60084	0.117136
$494$	−11.3879	−0.512367
$495$	3.26217	0.146624
$496$	31.9067	1.43266
$497$	−38.3468	−1.72009
$498$	−1.63187	−0.0731258
$499$	−22.8342	−1.02220	−0.511099	−	0.859522i	$-0.670761\pi$
$499$	−22.8342	−1.02220	−0.511099	+	0.859522i	$0.670761\pi$
$500$	−1.94257	−0.0868742
$501$	4.28180	0.191297
$502$	−31.9677	−1.42679
$503$	−17.2723	−0.770132	−0.385066	−	0.922889i	$-0.625821\pi$
$503$	−17.2723	−0.770132	−0.385066	+	0.922889i	$0.625821\pi$
$504$	0.550751	0.0245324
$505$	11.5602	0.514422
$506$	47.0802	2.09297
$507$	−5.29146	−0.235002
$508$	33.4344	1.48341
$509$	11.5628	0.512514	0.256257	−	0.966609i	$-0.417511\pi$
$509$	11.5628	0.512514	0.256257	+	0.966609i	$0.417511\pi$
$510$	−1.61014	−0.0712982
$511$	−45.6603	−2.01989
$512$	−31.6909	−1.40055
$513$	−1.34101	−0.0592069
$514$	−11.3918	−0.502473
$515$	4.44128	0.195706
$516$	6.15854	0.271114
$517$	40.5918	1.78523
$518$	34.7327	1.52607
$519$	−14.4066	−0.632379
$520$	−0.487735	−0.0213886
$521$	−27.1656	−1.19015	−0.595073	−	0.803672i	$-0.702877\pi$
$521$	−27.1656	−1.19015	−0.595073	+	0.803672i	$0.702877\pi$
$522$	−6.36839	−0.278737
$523$	34.6343	1.51445	0.757226	−	0.653153i	$-0.226554\pi$
$523$	34.6343	1.51445	0.757226	+	0.653153i	$0.226554\pi$
$524$	−28.1478	−1.22964
$525$	−4.82942	−0.210773
$526$	−24.8143	−1.08196
$527$	−6.29287	−0.274122
$528$	−13.4126	−0.583711
$529$	29.8305	1.29698
$530$	−14.5203	−0.630721
$531$	0.540754	0.0234667
$532$	12.5806	0.545439
$533$	−50.2004	−2.17442
$534$	−36.9291	−1.59808
$535$	13.3638	0.577767
$536$	0.788932	0.0340767
$537$	−7.48119	−0.322837
$538$	28.7473	1.23938
$539$	−53.2495	−2.29362
$540$	1.94257	0.0835947
$541$	−35.9675	−1.54637	−0.773183	−	0.634183i	$-0.781337\pi$
$541$	−35.9675	−1.54637	−0.773183	+	0.634183i	$0.781337\pi$
$542$	−22.9405	−0.985377
$543$	−5.53400	−0.237487
$544$	6.43525	0.275909
$545$	13.7348	0.588335
$546$	41.0118	1.75514
$547$	3.67365	0.157074	0.0785369	−	0.996911i	$-0.474975\pi$
$547$	3.67365	0.157074	0.0785369	+	0.996911i	$0.474975\pi$
$548$	−19.0628	−0.814324
$549$	5.50037	0.234750
$550$	6.47733	0.276194
$551$	4.30102	0.183230
$552$	−0.828900	−0.0352803
$553$	−30.8921	−1.31367
$554$	−17.7402	−0.753710
$555$	−3.62204	−0.153747
$556$	−20.5806	−0.872810
$557$	−0.775371	−0.0328535	−0.0164268	−	0.999865i	$-0.505229\pi$
$557$	−0.775371	−0.0328535	−0.0164268	+	0.999865i	$0.505229\pi$
$558$	15.4086	0.652300
$559$	−13.5589	−0.573482
$560$	19.8565	0.839091
$561$	2.64534	0.111686
$562$	−27.2710	−1.15036
$563$	12.0767	0.508974	0.254487	−	0.967076i	$-0.418093\pi$
$563$	12.0767	0.508974	0.254487	+	0.967076i	$0.418093\pi$
$564$	24.1717	1.01781
$565$	1.89605	0.0797674
$566$	24.0531	1.01103
$567$	4.82942	0.202817
$568$	−0.905511	−0.0379944
$569$	−25.1522	−1.05444	−0.527219	−	0.849730i	$-0.676765\pi$
$569$	−25.1522	−1.05444	−0.527219	+	0.849730i	$0.676765\pi$
$570$	−2.66269	−0.111528
$571$	−24.4001	−1.02111	−0.510556	−	0.859845i	$-0.670560\pi$
$571$	−24.4001	−1.02111	−0.510556	+	0.859845i	$0.670560\pi$
$572$	−27.1023	−1.13321
$573$	−8.85244	−0.369816
$574$	112.556	4.69799
$575$	7.26846	0.303116
$576$	−7.53412	−0.313922
$577$	21.0316	0.875558	0.437779	−	0.899083i	$-0.355765\pi$
$577$	21.0316	0.875558	0.437779	+	0.899083i	$0.355765\pi$
$578$	32.4493	1.34971
$579$	5.08324	0.211252
$580$	−6.23040	−0.258703
$581$	−3.96909	−0.164666
$582$	1.55156	0.0643142
$583$	23.8557	0.988002
$584$	−1.07821	−0.0446167
$585$	−4.27685	−0.176826
$586$	44.9966	1.85879
$587$	33.0707	1.36497	0.682486	−	0.730898i	$-0.260899\pi$
$587$	33.0707	1.36497	0.682486	+	0.730898i	$0.260899\pi$
$588$	−31.7091	−1.30766
$589$	−10.4065	−0.428794
$590$	1.07372	0.0442042
$591$	−6.10507	−0.251129
$592$	14.8923	0.612069
$593$	41.5572	1.70655	0.853275	−	0.521461i	$-0.174613\pi$
$593$	41.5572	1.70655	0.853275	+	0.521461i	$0.174613\pi$
$594$	−6.47733	−0.265768
$595$	−3.91624	−0.160550
$596$	42.5063	1.74113
$597$	16.5954	0.679203
$598$	−61.7243	−2.52409
$599$	−35.5513	−1.45259	−0.726293	−	0.687385i	$-0.758759\pi$
$599$	−35.5513	−1.45259	−0.726293	+	0.687385i	$0.758759\pi$
$600$	−0.114041	−0.00465569
$601$	21.0376	0.858141	0.429071	−	0.903271i	$-0.358841\pi$
$601$	21.0376	0.858141	0.429071	+	0.903271i	$0.358841\pi$
$602$	30.4009	1.23905
$603$	6.91798	0.281722
$604$	8.45263	0.343933
$605$	0.358235	0.0145643
$606$	−22.9538	−0.932435
$607$	−29.7416	−1.20717	−0.603587	−	0.797297i	$-0.706262\pi$
$607$	−29.7416	−1.20717	−0.603587	+	0.797297i	$0.706262\pi$
$608$	10.6420	0.431589
$609$	−15.4894	−0.627663
$610$	10.9215	0.442198
$611$	−53.2177	−2.15296
$612$	1.57525	0.0636757
$613$	−5.82973	−0.235460	−0.117730	−	0.993046i	$-0.537562\pi$
$613$	−5.82973	−0.235460	−0.117730	+	0.993046i	$0.537562\pi$
$614$	−20.5329	−0.828639
$615$	−11.7377	−0.473310
$616$	−1.79664	−0.0723888
$617$	40.2102	1.61880	0.809402	−	0.587255i	$-0.199792\pi$
$617$	40.2102	1.61880	0.809402	+	0.587255i	$0.199792\pi$
$618$	−8.81856	−0.354735
$619$	−17.4137	−0.699918	−0.349959	−	0.936765i	$-0.613804\pi$
$619$	−17.4137	−0.699918	−0.349959	+	0.936765i	$0.613804\pi$
$620$	15.0748	0.605417
$621$	−7.26846	−0.291673
$622$	27.6829	1.10998
$623$	−89.8202	−3.59857
$624$	17.5846	0.703946
$625$	1.00000	0.0400000
$626$	39.3100	1.57114
$627$	4.37460	0.174705
$628$	−27.5344	−1.09874
$629$	−2.93716	−0.117112
$630$	9.58925	0.382045
$631$	−17.4494	−0.694652	−0.347326	−	0.937745i	$-0.612910\pi$
$631$	−17.4494	−0.694652	−0.347326	+	0.937745i	$0.612910\pi$
$632$	−0.729479	−0.0290171
$633$	−3.58923	−0.142659
$634$	−32.6524	−1.29679
$635$	−17.2115	−0.683016
$636$	14.2057	0.563291
$637$	69.8124	2.76607
$638$	20.7748	0.822481
$639$	−7.94024	−0.314111
$640$	0.911949	0.0360480
$641$	−28.1395	−1.11144	−0.555721	−	0.831369i	$-0.687558\pi$
$641$	−28.1395	−1.11144	−0.555721	+	0.831369i	$0.687558\pi$
$642$	−26.5350	−1.04725
$643$	2.79793	0.110340	0.0551698	−	0.998477i	$-0.482430\pi$
$643$	2.79793	0.110340	0.0551698	+	0.998477i	$0.482430\pi$
$644$	68.1888	2.68702
$645$	−3.17031	−0.124831
$646$	−2.15921	−0.0849530
$647$	12.7037	0.499432	0.249716	−	0.968319i	$-0.419663\pi$
$647$	12.7037	0.499432	0.249716	+	0.968319i	$0.419663\pi$
$648$	0.114041	0.00447994
$649$	−1.76403	−0.0692444
$650$	−8.49207	−0.333086
$651$	37.4775	1.46886
$652$	22.5368	0.882610
$653$	3.56966	0.139692	0.0698458	−	0.997558i	$-0.477749\pi$
$653$	3.56966	0.139692	0.0698458	+	0.997558i	$0.477749\pi$
$654$	−27.2717	−1.06641
$655$	14.4900	0.566172
$656$	48.2604	1.88425
$657$	−9.45462	−0.368860
$658$	119.321	4.65161
$659$	−29.5594	−1.15147	−0.575735	−	0.817636i	$-0.695284\pi$
$659$	−29.5594	−1.15147	−0.575735	+	0.817636i	$0.695284\pi$
$660$	−6.33698	−0.246667
$661$	−22.2285	−0.864588	−0.432294	−	0.901733i	$-0.642296\pi$
$661$	−22.2285	−0.864588	−0.432294	+	0.901733i	$0.642296\pi$
$662$	−43.1024	−1.67522
$663$	−3.46815	−0.134692
$664$	−0.0937251	−0.00363724
$665$	−6.47629	−0.251140
$666$	7.19189	0.278680
$667$	23.3121	0.902650
$668$	−8.31768	−0.321821
$669$	11.0048	0.425472
$670$	13.7363	0.530679
$671$	−17.9432	−0.692688
$672$	−38.3254	−1.47843
$673$	−16.9189	−0.652175	−0.326088	−	0.945340i	$-0.605730\pi$
$673$	−16.9189	−0.652175	−0.326088	+	0.945340i	$0.605730\pi$
$674$	57.1040	2.19956
$675$	−1.00000	−0.0384900
$676$	10.2790	0.395347
$677$	−1.96936	−0.0756886	−0.0378443	−	0.999284i	$-0.512049\pi$
$677$	−1.96936	−0.0756886	−0.0378443	+	0.999284i	$0.512049\pi$
$678$	−3.76478	−0.144585
$679$	3.77376	0.144824
$680$	−0.0924770	−0.00354633
$681$	12.5150	0.479576
$682$	−50.2656	−1.92477
$683$	−9.40198	−0.359757	−0.179878	−	0.983689i	$-0.557570\pi$
$683$	−9.40198	−0.359757	−0.179878	+	0.983689i	$0.557570\pi$
$684$	2.60500	0.0996045
$685$	9.81322	0.374944
$686$	−89.4036	−3.41345
$687$	−25.4804	−0.972138
$688$	13.0350	0.496953
$689$	−31.2759	−1.19152
$690$	−14.4322	−0.549423
$691$	10.0121	0.380880	0.190440	−	0.981699i	$-0.439009\pi$
$691$	10.0121	0.380880	0.190440	+	0.981699i	$0.439009\pi$
$692$	27.9857	1.06386
$693$	−15.7544	−0.598460
$694$	47.2925	1.79520
$695$	10.5945	0.401873
$696$	−0.365763	−0.0138642
$697$	−9.51825	−0.360529
$698$	0.532404	0.0201518
$699$	−0.302135	−0.0114278
$700$	9.38147	0.354586
$701$	39.5605	1.49418	0.747089	−	0.664724i	$-0.231451\pi$
$701$	39.5605	1.49418	0.747089	+	0.664724i	$0.231451\pi$
$702$	8.49207	0.320513
$703$	−4.85719	−0.183192
$704$	24.5776	0.926303
$705$	−12.4432	−0.468638
$706$	−1.42107	−0.0534826
$707$	−55.8291	−2.09967
$708$	−1.05045	−0.0394784
$709$	−15.8851	−0.596577	−0.298289	−	0.954476i	$-0.596416\pi$
$709$	−15.8851	−0.596577	−0.298289	+	0.954476i	$0.596416\pi$
$710$	−15.7661	−0.591690
$711$	−6.39666	−0.239893
$712$	−2.12099	−0.0794875
$713$	−56.4049	−2.11238
$714$	7.77604	0.291011
$715$	13.9518	0.521769
$716$	14.5327	0.543112
$717$	−26.9069	−1.00486
$718$	−41.5613	−1.55105
$719$	−11.3894	−0.424752	−0.212376	−	0.977188i	$-0.568120\pi$
$719$	−11.3894	−0.424752	−0.212376	+	0.977188i	$0.568120\pi$
$720$	4.11157	0.153229
$721$	−21.4488	−0.798796
$722$	34.1555	1.27114
$723$	−17.3882	−0.646676
$724$	10.7502	0.399527
$725$	3.20730	0.119116
$726$	−0.711308	−0.0263991
$727$	−4.06388	−0.150721	−0.0753605	−	0.997156i	$-0.524011\pi$
$727$	−4.06388	−0.150721	−0.0753605	+	0.997156i	$0.524011\pi$
$728$	2.35548	0.0872999
$729$	1.00000	0.0370370
$730$	−18.7730	−0.694820
$731$	−2.57084	−0.0950861
$732$	−10.6848	−0.394923
$733$	12.6385	0.466814	0.233407	−	0.972379i	$-0.425013\pi$
$733$	12.6385	0.466814	0.233407	+	0.972379i	$0.425013\pi$
$734$	−10.9789	−0.405238
$735$	16.3233	0.602095
$736$	57.6811	2.12615
$737$	−22.5677	−0.831290
$738$	23.3063	0.857915
$739$	48.2666	1.77551	0.887757	−	0.460312i	$-0.152262\pi$
$739$	48.2666	1.77551	0.887757	+	0.460312i	$0.152262\pi$
$740$	7.03605	0.258650
$741$	−5.73529	−0.210691
$742$	70.1245	2.57435
$743$	43.8800	1.60980	0.804900	−	0.593410i	$-0.202219\pi$
$743$	43.8800	1.60980	0.804900	+	0.593410i	$0.202219\pi$
$744$	0.884983	0.0324450
$745$	−21.8815	−0.801677
$746$	59.9556	2.19513
$747$	−0.821857	−0.0300702
$748$	−5.13874	−0.187891
$749$	−64.5394	−2.35822
$750$	−1.98559	−0.0725035
$751$	−8.33341	−0.304090	−0.152045	−	0.988374i	$-0.548586\pi$
$751$	−8.33341	−0.304090	−0.152045	+	0.988374i	$0.548586\pi$
$752$	51.1610	1.86565
$753$	−16.0999	−0.586712
$754$	−27.2367	−0.991900
$755$	−4.35127	−0.158359
$756$	−9.38147	−0.341201
$757$	−11.0420	−0.401327	−0.200664	−	0.979660i	$-0.564310\pi$
$757$	−11.0420	−0.401327	−0.200664	+	0.979660i	$0.564310\pi$
$758$	54.1459	1.96667
$759$	23.7110	0.860653
$760$	−0.152929	−0.00554733
$761$	−1.74735	−0.0633412	−0.0316706	−	0.999498i	$-0.510083\pi$
$761$	−1.74735	−0.0633412	−0.0316706	+	0.999498i	$0.510083\pi$
$762$	34.1749	1.23803
$763$	−66.3313	−2.40135
$764$	17.1964	0.622146
$765$	−0.810913	−0.0293186
$766$	49.2488	1.77943
$767$	2.31273	0.0835077
$768$	−16.8790	−0.609068
$769$	39.1269	1.41095	0.705475	−	0.708734i	$-0.250734\pi$
$769$	39.1269	1.41095	0.705475	+	0.708734i	$0.250734\pi$
$770$	−31.2818	−1.12732
$771$	−5.73726	−0.206622
$772$	−9.87454	−0.355392
$773$	14.8710	0.534871	0.267435	−	0.963576i	$-0.413824\pi$
$773$	14.8710	0.534871	0.267435	+	0.963576i	$0.413824\pi$
$774$	6.29493	0.226267
$775$	−7.76023	−0.278756
$776$	0.0891125	0.00319895
$777$	17.4924	0.627535
$778$	−62.7444	−2.24950
$779$	−15.7404	−0.563957
$780$	8.30807	0.297476
$781$	25.9024	0.926862
$782$	−11.7032	−0.418507
$783$	−3.20730	−0.114620
$784$	−67.1145	−2.39695
$785$	14.1743	0.505901
$786$	−28.7712	−1.02624
$787$	25.8786	0.922471	0.461236	−	0.887278i	$-0.347406\pi$
$787$	25.8786	0.922471	0.461236	+	0.887278i	$0.347406\pi$
$788$	11.8595	0.422477
$789$	−12.4972	−0.444913
$790$	−12.7011	−0.451886
$791$	−9.15682	−0.325579
$792$	−0.372020	−0.0132192
$793$	23.5243	0.835371
$794$	53.3581	1.89361
$795$	−7.31283	−0.259359
$796$	−32.2376	−1.14263
$797$	−27.6450	−0.979234	−0.489617	−	0.871937i	$-0.662863\pi$
$797$	−27.6450	−0.979234	−0.489617	+	0.871937i	$0.662863\pi$
$798$	12.8593	0.455213
$799$	−10.0903	−0.356970
$800$	7.93581	0.280573
$801$	−18.5985	−0.657147
$802$	1.98559	0.0701136
$803$	30.8426	1.08841
$804$	−13.4386	−0.473944
$805$	−35.1024	−1.23720
$806$	65.9005	2.32125
$807$	14.4780	0.509649
$808$	−1.31833	−0.0463788
$809$	21.5285	0.756903	0.378452	−	0.925621i	$-0.376457\pi$
$809$	21.5285	0.756903	0.378452	+	0.925621i	$0.376457\pi$
$810$	1.98559	0.0697665
$811$	3.98877	0.140065	0.0700324	−	0.997545i	$-0.477690\pi$
$811$	3.98877	0.140065	0.0700324	+	0.997545i	$0.477690\pi$
$812$	30.0892	1.05592
$813$	−11.5535	−0.405198
$814$	−23.4612	−0.822314
$815$	−11.6016	−0.406386
$816$	3.33412	0.116718
$817$	−4.25141	−0.148738
$818$	−18.6498	−0.652075
$819$	20.6547	0.721734
$820$	22.8013	0.796255
$821$	37.1286	1.29580	0.647898	−	0.761727i	$-0.275648\pi$
$821$	37.1286	1.29580	0.647898	+	0.761727i	$0.275648\pi$
$822$	−19.4850	−0.679619
$823$	−5.05326	−0.176146	−0.0880728	−	0.996114i	$-0.528071\pi$
$823$	−5.05326	−0.176146	−0.0880728	+	0.996114i	$0.528071\pi$
$824$	−0.506487	−0.0176443
$825$	3.26217	0.113574
$826$	−5.18543	−0.180424
$827$	55.0774	1.91523	0.957614	−	0.288056i	$-0.0930089\pi$
$827$	55.0774	1.91523	0.957614	+	0.288056i	$0.0930089\pi$
$828$	14.1195	0.490685
$829$	−39.9408	−1.38720	−0.693601	−	0.720359i	$-0.743977\pi$
$829$	−39.9408	−1.38720	−0.693601	+	0.720359i	$0.743977\pi$
$830$	−1.63187	−0.0566430
$831$	−8.93449	−0.309934
$832$	−32.2223	−1.11711
$833$	13.2368	0.458627
$834$	−21.0364	−0.728430
$835$	4.28180	0.148178
$836$	−8.49794	−0.293908
$837$	7.76023	0.268233
$838$	24.3518	0.841219
$839$	15.2511	0.526528	0.263264	−	0.964724i	$-0.415201\pi$
$839$	15.2511	0.526528	0.263264	+	0.964724i	$0.415201\pi$
$840$	0.550751	0.0190027
$841$	−18.7132	−0.645283
$842$	−34.4519	−1.18729
$843$	−13.7345	−0.473041
$844$	6.97232	0.239997
$845$	−5.29146	−0.182032
$846$	24.7071	0.849446
$847$	−1.73007	−0.0594459
$848$	30.0672	1.03251
$849$	12.1138	0.415745
$850$	−1.61014	−0.0552273
$851$	−26.3266	−0.902466
$852$	15.4244	0.528433
$853$	−35.4398	−1.21344	−0.606718	−	0.794917i	$-0.707514\pi$
$853$	−35.4398	−1.21344	−0.606718	+	0.794917i	$0.707514\pi$
$854$	−52.7444	−1.80488
$855$	−1.34101	−0.0458615
$856$	−1.52402	−0.0520898
$857$	11.9470	0.408103	0.204051	−	0.978960i	$-0.434589\pi$
$857$	11.9470	0.408103	0.204051	+	0.978960i	$0.434589\pi$
$858$	−27.7026	−0.945751
$859$	8.18533	0.279280	0.139640	−	0.990202i	$-0.455405\pi$
$859$	8.18533	0.279280	0.139640	+	0.990202i	$0.455405\pi$
$860$	6.15854	0.210004
$861$	56.6863	1.93186
$862$	−60.9153	−2.07478
$863$	5.62173	0.191366	0.0956829	−	0.995412i	$-0.469497\pi$
$863$	5.62173	0.191366	0.0956829	+	0.995412i	$0.469497\pi$
$864$	−7.93581	−0.269982
$865$	−14.4066	−0.489838
$866$	−19.2115	−0.652833
$867$	16.3424	0.555018
$868$	−72.8024	−2.47108
$869$	20.8670	0.707864
$870$	−6.36839	−0.215909
$871$	29.5872	1.00252
$872$	−1.56633	−0.0530426
$873$	0.781410	0.0264467
$874$	−19.3537	−0.654647
$875$	−4.82942	−0.163264
$876$	18.3662	0.620537
$877$	25.8176	0.871800	0.435900	−	0.899995i	$-0.356430\pi$
$877$	25.8176	0.871800	0.435900	+	0.899995i	$0.356430\pi$
$878$	49.1412	1.65843
$879$	22.6616	0.764356
$880$	−13.4126	−0.452140
$881$	−2.42796	−0.0818002	−0.0409001	−	0.999163i	$-0.513023\pi$
$881$	−2.42796	−0.0818002	−0.0409001	+	0.999163i	$0.513023\pi$
$882$	−32.4114	−1.09135
$883$	12.4348	0.418465	0.209232	−	0.977866i	$-0.432904\pi$
$883$	12.4348	0.418465	0.209232	+	0.977866i	$0.432904\pi$
$884$	6.73712	0.226594
$885$	0.540754	0.0181773
$886$	5.35134	0.179782
$887$	12.5656	0.421910	0.210955	−	0.977496i	$-0.432343\pi$
$887$	12.5656	0.421910	0.210955	+	0.977496i	$0.432343\pi$
$888$	0.413060	0.0138614
$889$	83.1214	2.78780
$890$	−36.9291	−1.23787
$891$	−3.26217	−0.109287
$892$	−21.3776	−0.715776
$893$	−16.6864	−0.558389
$894$	43.4477	1.45311
$895$	−7.48119	−0.250069
$896$	−4.40419	−0.147134
$897$	−31.0861	−1.03794
$898$	14.4139	0.480998
$899$	−24.8894	−0.830109
$900$	1.94257	0.0647522
$901$	−5.93006	−0.197559
$902$	−76.0290	−2.53149
$903$	15.3108	0.509510
$904$	−0.216227	−0.00719160
$905$	−5.53400	−0.183956
$906$	8.63984	0.287040
$907$	10.4500	0.346988	0.173494	−	0.984835i	$-0.444494\pi$
$907$	10.4500	0.346988	0.173494	+	0.984835i	$0.444494\pi$
$908$	−24.3112	−0.806797
$909$	−11.5602	−0.383427
$910$	41.0118	1.35953
$911$	−6.10750	−0.202350	−0.101175	−	0.994869i	$-0.532260\pi$
$911$	−6.10750	−0.202350	−0.101175	+	0.994869i	$0.532260\pi$
$912$	5.51365	0.182575
$913$	2.68104	0.0887294
$914$	−28.7500	−0.950967
$915$	5.50037	0.181837
$916$	49.4973	1.63544
$917$	−69.9785	−2.31089
$918$	1.61014	0.0531425
$919$	20.8078	0.686385	0.343192	−	0.939265i	$-0.388492\pi$
$919$	20.8078	0.686385	0.343192	+	0.939265i	$0.388492\pi$
$920$	−0.828900	−0.0273280
$921$	−10.3409	−0.340746
$922$	44.6097	1.46914
$923$	−33.9592	−1.11778
$924$	30.6040	1.00680
$925$	−3.62204	−0.119092
$926$	2.37654	0.0780981
$927$	−4.44128	−0.145871
$928$	25.4525	0.835521
$929$	12.5078	0.410367	0.205184	−	0.978723i	$-0.434221\pi$
$929$	12.5078	0.410367	0.205184	+	0.978723i	$0.434221\pi$
$930$	15.4086	0.505269
$931$	21.8897	0.717406
$932$	0.586916	0.0192251
$933$	13.9419	0.456437
$934$	−16.4976	−0.539818
$935$	2.64534	0.0865117
$936$	0.487735	0.0159421
$937$	26.4332	0.863534	0.431767	−	0.901985i	$-0.357890\pi$
$937$	26.4332	0.863534	0.431767	+	0.901985i	$0.357890\pi$
$938$	−66.3383	−2.16602
$939$	19.7976	0.646071
$940$	24.1717	0.788394
$941$	38.5043	1.25520	0.627602	−	0.778534i	$-0.284036\pi$
$941$	38.5043	1.25520	0.627602	+	0.778534i	$0.284036\pi$
$942$	−28.1443	−0.916990
$943$	−85.3150	−2.77824
$944$	−2.22335	−0.0723639
$945$	4.82942	0.157101
$946$	−20.5352	−0.667656
$947$	19.1397	0.621957	0.310979	−	0.950417i	$-0.399343\pi$
$947$	19.1397	0.621957	0.310979	+	0.950417i	$0.399343\pi$
$948$	12.4259	0.403575
$949$	−40.4360	−1.31261
$950$	−2.66269	−0.0863891
$951$	−16.4447	−0.533256
$952$	0.446611	0.0144747
$953$	−34.8066	−1.12750	−0.563748	−	0.825947i	$-0.690641\pi$
$953$	−34.8066	−1.12750	−0.563748	+	0.825947i	$0.690641\pi$
$954$	14.5203	0.470111
$955$	−8.85244	−0.286458
$956$	52.2685	1.69048
$957$	10.4628	0.338213
$958$	44.2397	1.42932
$959$	−47.3922	−1.53037
$960$	−7.53412	−0.243163
$961$	29.2212	0.942621
$962$	30.7586	0.991698
$963$	−13.3638	−0.430642
$964$	33.7778	1.08791
$965$	5.08324	0.163635
$966$	69.6990	2.24253
$967$	−11.6732	−0.375386	−0.187693	−	0.982228i	$-0.560101\pi$
$967$	−11.6732	−0.375386	−0.187693	+	0.982228i	$0.560101\pi$
$968$	−0.0408534	−0.00131308
$969$	−1.08744	−0.0349336
$970$	1.55156	0.0498176
$971$	46.9841	1.50779	0.753895	−	0.656995i	$-0.228173\pi$
$971$	46.9841	1.50779	0.753895	+	0.656995i	$0.228173\pi$
$972$	−1.94257	−0.0623078
$973$	−51.1654	−1.64029
$974$	20.8824	0.669116
$975$	−4.27685	−0.136969
$976$	−22.6152	−0.723894
$977$	−20.5769	−0.658314	−0.329157	−	0.944275i	$-0.606765\pi$
$977$	−20.5769	−0.658314	−0.329157	+	0.944275i	$0.606765\pi$
$978$	23.0360	0.736609
$979$	60.6717	1.93907
$980$	−31.7091	−1.01291
$981$	−13.7348	−0.438519
$982$	21.6986	0.692430
$983$	−44.4148	−1.41661	−0.708306	−	0.705905i	$-0.750540\pi$
$983$	−44.4148	−1.41661	−0.708306	+	0.705905i	$0.750540\pi$
$984$	1.33858	0.0426722
$985$	−6.10507	−0.194524
$986$	−5.16421	−0.164462
$987$	60.0934	1.91279
$988$	11.1412	0.354448
$989$	−23.0433	−0.732733
$990$	−6.47733	−0.205863
$991$	−59.2571	−1.88236	−0.941182	−	0.337900i	$-0.890283\pi$
$991$	−59.2571	−1.88236	−0.941182	+	0.337900i	$0.890283\pi$
$992$	−61.5837	−1.95529
$993$	−21.7076	−0.688870
$994$	76.1410	2.41504
$995$	16.5954	0.526108
$996$	1.59651	0.0505874
$997$	15.1679	0.480373	0.240187	−	0.970727i	$-0.422791\pi$
$997$	15.1679	0.480373	0.240187	+	0.970727i	$0.422791\pi$
$998$	45.3393	1.43519
$999$	3.62204	0.114596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.10	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.10	✓	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.98559 q^{2} -1.00000 q^{3} +1.94257 q^{4} -1.00000 q^{5} +1.98559 q^{6} +4.82942 q^{7} +0.114041 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.98559 q^{2} -1.00000 q^{3} +1.94257 q^{4} -1.00000 q^{5} +1.98559 q^{6} +4.82942 q^{7} +0.114041 q^{8} +1.00000 q^{9} +1.98559 q^{10} -3.26217 q^{11} -1.94257 q^{12} +4.27685 q^{13} -9.58925 q^{14} +1.00000 q^{15} -4.11157 q^{16} +0.810913 q^{17} -1.98559 q^{18} +1.34101 q^{19} -1.94257 q^{20} -4.82942 q^{21} +6.47733 q^{22} +7.26846 q^{23} -0.114041 q^{24} +1.00000 q^{25} -8.49207 q^{26} -1.00000 q^{27} +9.38147 q^{28} +3.20730 q^{29} -1.98559 q^{30} -7.76023 q^{31} +7.93581 q^{32} +3.26217 q^{33} -1.61014 q^{34} -4.82942 q^{35} +1.94257 q^{36} -3.62204 q^{37} -2.66269 q^{38} -4.27685 q^{39} -0.114041 q^{40} -11.7377 q^{41} +9.58925 q^{42} -3.17031 q^{43} -6.33698 q^{44} -1.00000 q^{45} -14.4322 q^{46} -12.4432 q^{47} +4.11157 q^{48} +16.3233 q^{49} -1.98559 q^{50} -0.810913 q^{51} +8.30807 q^{52} -7.31283 q^{53} +1.98559 q^{54} +3.26217 q^{55} +0.550751 q^{56} -1.34101 q^{57} -6.36839 q^{58} +0.540754 q^{59} +1.94257 q^{60} +5.50037 q^{61} +15.4086 q^{62} +4.82942 q^{63} -7.53412 q^{64} -4.27685 q^{65} -6.47733 q^{66} +6.91798 q^{67} +1.57525 q^{68} -7.26846 q^{69} +9.58925 q^{70} -7.94024 q^{71} +0.114041 q^{72} -9.45462 q^{73} +7.19189 q^{74} -1.00000 q^{75} +2.60500 q^{76} -15.7544 q^{77} +8.49207 q^{78} -6.39666 q^{79} +4.11157 q^{80} +1.00000 q^{81} +23.3063 q^{82} -0.821857 q^{83} -9.38147 q^{84} -0.810913 q^{85} +6.29493 q^{86} -3.20730 q^{87} -0.372020 q^{88} -18.5985 q^{89} +1.98559 q^{90} +20.6547 q^{91} +14.1195 q^{92} +7.76023 q^{93} +24.7071 q^{94} -1.34101 q^{95} -7.93581 q^{96} +0.781410 q^{97} -32.4114 q^{98} -3.26217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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