LMFDB - Embedded newform 6015.2.a.e.1.23

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:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
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)

$f(q)$	$=$	$q+1.39305 q^{2} -1.00000 q^{3} -0.0594164 q^{4} -1.00000 q^{5} -1.39305 q^{6} -2.63479 q^{7} -2.86887 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.39305 q^{2} -1.00000 q^{3} -0.0594164 q^{4} -1.00000 q^{5} -1.39305 q^{6} -2.63479 q^{7} -2.86887 q^{8} +1.00000 q^{9} -1.39305 q^{10} -6.12960 q^{11} +0.0594164 q^{12} -4.25969 q^{13} -3.67039 q^{14} +1.00000 q^{15} -3.87764 q^{16} -0.114637 q^{17} +1.39305 q^{18} -4.89254 q^{19} +0.0594164 q^{20} +2.63479 q^{21} -8.53883 q^{22} +1.07466 q^{23} +2.86887 q^{24} +1.00000 q^{25} -5.93395 q^{26} -1.00000 q^{27} +0.156550 q^{28} -7.76026 q^{29} +1.39305 q^{30} +0.623574 q^{31} +0.335997 q^{32} +6.12960 q^{33} -0.159696 q^{34} +2.63479 q^{35} -0.0594164 q^{36} +1.43634 q^{37} -6.81554 q^{38} +4.25969 q^{39} +2.86887 q^{40} -2.55222 q^{41} +3.67039 q^{42} -5.42082 q^{43} +0.364199 q^{44} -1.00000 q^{45} +1.49705 q^{46} -2.89624 q^{47} +3.87764 q^{48} -0.0578718 q^{49} +1.39305 q^{50} +0.114637 q^{51} +0.253095 q^{52} +0.713581 q^{53} -1.39305 q^{54} +6.12960 q^{55} +7.55887 q^{56} +4.89254 q^{57} -10.8104 q^{58} -12.4880 q^{59} -0.0594164 q^{60} -0.909596 q^{61} +0.868669 q^{62} -2.63479 q^{63} +8.22333 q^{64} +4.25969 q^{65} +8.53883 q^{66} -14.2593 q^{67} +0.00681134 q^{68} -1.07466 q^{69} +3.67039 q^{70} +11.4549 q^{71} -2.86887 q^{72} -11.2580 q^{73} +2.00089 q^{74} -1.00000 q^{75} +0.290697 q^{76} +16.1502 q^{77} +5.93395 q^{78} +8.76451 q^{79} +3.87764 q^{80} +1.00000 q^{81} -3.55536 q^{82} +6.20815 q^{83} -0.156550 q^{84} +0.114637 q^{85} -7.55146 q^{86} +7.76026 q^{87} +17.5850 q^{88} -2.01016 q^{89} -1.39305 q^{90} +11.2234 q^{91} -0.0638521 q^{92} -0.623574 q^{93} -4.03461 q^{94} +4.89254 q^{95} -0.335997 q^{96} +10.5717 q^{97} -0.0806182 q^{98} -6.12960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * 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 $

$2$	1.39305	0.985034	0.492517	−	0.870303i	$-0.336077\pi$
$2$	1.39305	0.985034	0.492517	+	0.870303i	$0.336077\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.0594164	−0.0297082
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.39305	−0.568710
$7$	−2.63479	−0.995858	−0.497929	−	0.867218i	$-0.665906\pi$
$7$	−2.63479	−0.995858	−0.497929	+	0.867218i	$0.665906\pi$
$8$	−2.86887	−1.01430
$9$	1.00000	0.333333
$10$	−1.39305	−0.440521
$11$	−6.12960	−1.84814	−0.924072	−	0.382219i	$-0.875160\pi$
$11$	−6.12960	−1.84814	−0.924072	+	0.382219i	$0.875160\pi$
$12$	0.0594164	0.0171520
$13$	−4.25969	−1.18143	−0.590713	−	0.806882i	$-0.701153\pi$
$13$	−4.25969	−1.18143	−0.590713	+	0.806882i	$0.701153\pi$
$14$	−3.67039	−0.980954
$15$	1.00000	0.258199
$16$	−3.87764	−0.969409
$17$	−0.114637	−0.0278037	−0.0139018	−	0.999903i	$-0.504425\pi$
$17$	−0.114637	−0.0278037	−0.0139018	+	0.999903i	$0.504425\pi$
$18$	1.39305	0.328345
$19$	−4.89254	−1.12243	−0.561213	−	0.827672i	$-0.689665\pi$
$19$	−4.89254	−1.12243	−0.561213	+	0.827672i	$0.689665\pi$
$20$	0.0594164	0.0132859
$21$	2.63479	0.574959
$22$	−8.53883	−1.82048
$23$	1.07466	0.224081	0.112041	−	0.993704i	$-0.464261\pi$
$23$	1.07466	0.224081	0.112041	+	0.993704i	$0.464261\pi$
$24$	2.86887	0.585605
$25$	1.00000	0.200000
$26$	−5.93395	−1.16374
$27$	−1.00000	−0.192450
$28$	0.156550	0.0295851
$29$	−7.76026	−1.44104	−0.720522	−	0.693432i	$-0.756098\pi$
$29$	−7.76026	−1.44104	−0.720522	+	0.693432i	$0.756098\pi$
$30$	1.39305	0.254335
$31$	0.623574	0.111997	0.0559986	−	0.998431i	$-0.482166\pi$
$31$	0.623574	0.111997	0.0559986	+	0.998431i	$0.482166\pi$
$32$	0.335997	0.0593965
$33$	6.12960	1.06703
$34$	−0.159696	−0.0273876
$35$	2.63479	0.445361
$36$	−0.0594164	−0.00990273
$37$	1.43634	0.236133	0.118066	−	0.993006i	$-0.462330\pi$
$37$	1.43634	0.236133	0.118066	+	0.993006i	$0.462330\pi$
$38$	−6.81554	−1.10563
$39$	4.25969	0.682096
$40$	2.86887	0.453608
$41$	−2.55222	−0.398589	−0.199295	−	0.979940i	$-0.563865\pi$
$41$	−2.55222	−0.398589	−0.199295	+	0.979940i	$0.563865\pi$
$42$	3.67039	0.566354
$43$	−5.42082	−0.826667	−0.413334	−	0.910580i	$-0.635636\pi$
$43$	−5.42082	−0.826667	−0.413334	+	0.910580i	$0.635636\pi$
$44$	0.364199	0.0549050
$45$	−1.00000	−0.149071
$46$	1.49705	0.220727
$47$	−2.89624	−0.422460	−0.211230	−	0.977436i	$-0.567747\pi$
$47$	−2.89624	−0.422460	−0.211230	+	0.977436i	$0.567747\pi$
$48$	3.87764	0.559689
$49$	−0.0578718	−0.00826740
$50$	1.39305	0.197007
$51$	0.114637	0.0160525
$52$	0.253095	0.0350980
$53$	0.713581	0.0980179	0.0490089	−	0.998798i	$-0.484394\pi$
$53$	0.713581	0.0980179	0.0490089	+	0.998798i	$0.484394\pi$
$54$	−1.39305	−0.189570
$55$	6.12960	0.826515
$56$	7.55887	1.01010
$57$	4.89254	0.648033
$58$	−10.8104	−1.41948
$59$	−12.4880	−1.62580	−0.812898	−	0.582406i	$-0.802111\pi$
$59$	−12.4880	−1.62580	−0.812898	+	0.582406i	$0.802111\pi$
$60$	−0.0594164	−0.00767062
$61$	−0.909596	−0.116462	−0.0582309	−	0.998303i	$-0.518546\pi$
$61$	−0.909596	−0.116462	−0.0582309	+	0.998303i	$0.518546\pi$
$62$	0.868669	0.110321
$63$	−2.63479	−0.331953
$64$	8.22333	1.02792
$65$	4.25969	0.528349
$66$	8.53883	1.05106
$67$	−14.2593	−1.74205	−0.871024	−	0.491241i	$-0.836543\pi$
$67$	−14.2593	−1.74205	−0.871024	+	0.491241i	$0.836543\pi$
$68$	0.00681134	0.000825996 0
$69$	−1.07466	−0.129373
$70$	3.67039	0.438696
$71$	11.4549	1.35945	0.679723	−	0.733469i	$-0.262100\pi$
$71$	11.4549	1.35945	0.679723	+	0.733469i	$0.262100\pi$
$72$	−2.86887	−0.338099
$73$	−11.2580	−1.31765	−0.658827	−	0.752294i	$-0.728947\pi$
$73$	−11.2580	−1.31765	−0.658827	+	0.752294i	$0.728947\pi$
$74$	2.00089	0.232599
$75$	−1.00000	−0.115470
$76$	0.290697	0.0333452
$77$	16.1502	1.84049
$78$	5.93395	0.671888
$79$	8.76451	0.986084	0.493042	−	0.870005i	$-0.335885\pi$
$79$	8.76451	0.986084	0.493042	+	0.870005i	$0.335885\pi$
$80$	3.87764	0.433533
$81$	1.00000	0.111111
$82$	−3.55536	−0.392624
$83$	6.20815	0.681433	0.340717	−	0.940166i	$-0.389330\pi$
$83$	6.20815	0.681433	0.340717	+	0.940166i	$0.389330\pi$
$84$	−0.156550	−0.0170810
$85$	0.114637	0.0124342
$86$	−7.55146	−0.814295
$87$	7.76026	0.831987
$88$	17.5850	1.87457
$89$	−2.01016	−0.213077	−0.106539	−	0.994309i	$-0.533977\pi$
$89$	−2.01016	−0.213077	−0.106539	+	0.994309i	$0.533977\pi$
$90$	−1.39305	−0.146840
$91$	11.2234	1.17653
$92$	−0.0638521	−0.00665704
$93$	−0.623574	−0.0646616
$94$	−4.03461	−0.416138
$95$	4.89254	0.501964
$96$	−0.335997	−0.0342926
$97$	10.5717	1.07339	0.536695	−	0.843776i	$-0.319673\pi$
$97$	10.5717	1.07339	0.536695	+	0.843776i	$0.319673\pi$
$98$	−0.0806182	−0.00814367
$99$	−6.12960	−0.616048
$100$	−0.0594164	−0.00594164
$101$	12.6327	1.25700	0.628498	−	0.777811i	$-0.283670\pi$
$101$	12.6327	1.25700	0.628498	+	0.777811i	$0.283670\pi$
$102$	0.159696	0.0158122
$103$	10.6864	1.05296	0.526482	−	0.850186i	$-0.323511\pi$
$103$	10.6864	1.05296	0.526482	+	0.850186i	$0.323511\pi$
$104$	12.2205	1.19832
$105$	−2.63479	−0.257129
$106$	0.994053	0.0965510
$107$	−15.9276	−1.53978	−0.769890	−	0.638176i	$-0.779689\pi$
$107$	−15.9276	−1.53978	−0.769890	+	0.638176i	$0.779689\pi$
$108$	0.0594164	0.00571734
$109$	5.75126	0.550871	0.275436	−	0.961320i	$-0.411178\pi$
$109$	5.75126	0.550871	0.275436	+	0.961320i	$0.411178\pi$
$110$	8.53883	0.814145
$111$	−1.43634	−0.136331
$112$	10.2168	0.965394
$113$	4.22448	0.397405	0.198703	−	0.980060i	$-0.436327\pi$
$113$	4.22448	0.397405	0.198703	+	0.980060i	$0.436327\pi$
$114$	6.81554	0.638334
$115$	−1.07466	−0.100212
$116$	0.461086	0.0428108
$117$	−4.25969	−0.393808
$118$	−17.3964	−1.60146
$119$	0.302046	0.0276885
$120$	−2.86887	−0.261890
$121$	26.5720	2.41564
$122$	−1.26711	−0.114719
$123$	2.55222	0.230125
$124$	−0.0370505	−0.00332723
$125$	−1.00000	−0.0894427
$126$	−3.67039	−0.326985
$127$	−17.3005	−1.53517	−0.767584	−	0.640949i	$-0.778541\pi$
$127$	−17.3005	−1.53517	−0.767584	+	0.640949i	$0.778541\pi$
$128$	10.7835	0.953136
$129$	5.42082	0.477277
$130$	5.93395	0.520442
$131$	2.28387	0.199542	0.0997712	−	0.995010i	$-0.468189\pi$
$131$	2.28387	0.199542	0.0997712	+	0.995010i	$0.468189\pi$
$132$	−0.364199	−0.0316994
$133$	12.8908	1.11778
$134$	−19.8639	−1.71598
$135$	1.00000	0.0860663
$136$	0.328880	0.0282012
$137$	−9.77078	−0.834774	−0.417387	−	0.908729i	$-0.637054\pi$
$137$	−9.77078	−0.834774	−0.417387	+	0.908729i	$0.637054\pi$
$138$	−1.49705	−0.127437
$139$	7.36131	0.624378	0.312189	−	0.950020i	$-0.398938\pi$
$139$	7.36131	0.624378	0.312189	+	0.950020i	$0.398938\pi$
$140$	−0.156550	−0.0132309
$141$	2.89624	0.243908
$142$	15.9572	1.33910
$143$	26.1102	2.18344
$144$	−3.87764	−0.323136
$145$	7.76026	0.644455
$146$	−15.6830	−1.29793
$147$	0.0578718	0.00477319
$148$	−0.0853421	−0.00701508
$149$	−17.5568	−1.43831	−0.719156	−	0.694849i	$-0.755471\pi$
$149$	−17.5568	−1.43831	−0.719156	+	0.694849i	$0.755471\pi$
$150$	−1.39305	−0.113742
$151$	−6.44976	−0.524874	−0.262437	−	0.964949i	$-0.584526\pi$
$151$	−6.44976	−0.524874	−0.262437	+	0.964949i	$0.584526\pi$
$152$	14.0360	1.13847
$153$	−0.114637	−0.00926789
$154$	22.4980	1.81294
$155$	−0.623574	−0.0500867
$156$	−0.253095	−0.0202638
$157$	5.41559	0.432211	0.216105	−	0.976370i	$-0.430664\pi$
$157$	5.41559	0.432211	0.216105	+	0.976370i	$0.430664\pi$
$158$	12.2094	0.971326
$159$	−0.713581	−0.0565907
$160$	−0.335997	−0.0265629
$161$	−2.83149	−0.223153
$162$	1.39305	0.109448
$163$	−14.8502	−1.16316	−0.581579	−	0.813490i	$-0.697565\pi$
$163$	−14.8502	−1.16316	−0.581579	+	0.813490i	$0.697565\pi$
$164$	0.151643	0.0118414
$165$	−6.12960	−0.477189
$166$	8.64825	0.671235
$167$	−2.87203	−0.222245	−0.111122	−	0.993807i	$-0.535445\pi$
$167$	−2.87203	−0.222245	−0.111122	+	0.993807i	$0.535445\pi$
$168$	−7.55887	−0.583179
$169$	5.14495	0.395766
$170$	0.159696	0.0122481
$171$	−4.89254	−0.374142
$172$	0.322085	0.0245588
$173$	−16.5926	−1.26152	−0.630758	−	0.775980i	$-0.717256\pi$
$173$	−16.5926	−1.26152	−0.630758	+	0.775980i	$0.717256\pi$
$174$	10.8104	0.819536
$175$	−2.63479	−0.199172
$176$	23.7684	1.79161
$177$	12.4880	0.938654
$178$	−2.80026	−0.209888
$179$	−6.27637	−0.469118	−0.234559	−	0.972102i	$-0.575365\pi$
$179$	−6.27637	−0.469118	−0.234559	+	0.972102i	$0.575365\pi$
$180$	0.0594164	0.00442863
$181$	−24.6315	−1.83084	−0.915422	−	0.402495i	$-0.868143\pi$
$181$	−24.6315	−1.83084	−0.915422	+	0.402495i	$0.868143\pi$
$182$	15.6347	1.15892
$183$	0.909596	0.0672393
$184$	−3.08304	−0.227285
$185$	−1.43634	−0.105602
$186$	−0.868669	−0.0636939
$187$	0.702682	0.0513852
$188$	0.172084	0.0125505
$189$	2.63479	0.191653
$190$	6.81554	0.494452
$191$	12.2327	0.885124	0.442562	−	0.896738i	$-0.354070\pi$
$191$	12.2327	0.885124	0.442562	+	0.896738i	$0.354070\pi$
$192$	−8.22333	−0.593468
$193$	−11.7428	−0.845265	−0.422633	−	0.906301i	$-0.638894\pi$
$193$	−11.7428	−0.845265	−0.422633	+	0.906301i	$0.638894\pi$
$194$	14.7268	1.05733
$195$	−4.25969	−0.305043
$196$	0.00343853	0.000245609 0
$197$	22.0479	1.57085	0.785424	−	0.618958i	$-0.212445\pi$
$197$	22.0479	1.57085	0.785424	+	0.618958i	$0.212445\pi$
$198$	−8.53883	−0.606828
$199$	−19.0314	−1.34910	−0.674549	−	0.738231i	$-0.735662\pi$
$199$	−19.0314	−1.34910	−0.674549	+	0.738231i	$0.735662\pi$
$200$	−2.86887	−0.202859
$201$	14.2593	1.00577
$202$	17.5979	1.23818
$203$	20.4467	1.43507
$204$	−0.00681134	−0.000476889 0
$205$	2.55222	0.178254
$206$	14.8867	1.03721
$207$	1.07466	0.0746937
$208$	16.5175	1.14528
$209$	29.9893	2.07440
$210$	−3.67039	−0.253281
$211$	−2.80728	−0.193261	−0.0966305	−	0.995320i	$-0.530807\pi$
$211$	−2.80728	−0.193261	−0.0966305	+	0.995320i	$0.530807\pi$
$212$	−0.0423984	−0.00291193
$213$	−11.4549	−0.784876
$214$	−22.1879	−1.51674
$215$	5.42082	0.369697
$216$	2.86887	0.195202
$217$	−1.64299	−0.111533
$218$	8.01179	0.542627
$219$	11.2580	0.760748
$220$	−0.364199	−0.0245543
$221$	0.488320	0.0328480
$222$	−2.00089	−0.134291
$223$	−3.17836	−0.212839	−0.106419	−	0.994321i	$-0.533939\pi$
$223$	−3.17836	−0.212839	−0.106419	+	0.994321i	$0.533939\pi$
$224$	−0.885283	−0.0591505
$225$	1.00000	0.0666667
$226$	5.88490	0.391458
$227$	−8.38539	−0.556558	−0.278279	−	0.960500i	$-0.589764\pi$
$227$	−8.38539	−0.556558	−0.278279	+	0.960500i	$0.589764\pi$
$228$	−0.290697	−0.0192519
$229$	−2.47887	−0.163808	−0.0819041	−	0.996640i	$-0.526100\pi$
$229$	−2.47887	−0.163808	−0.0819041	+	0.996640i	$0.526100\pi$
$230$	−1.49705	−0.0987123
$231$	−16.1502	−1.06261
$232$	22.2632	1.46165
$233$	−15.1925	−0.995295	−0.497648	−	0.867379i	$-0.665803\pi$
$233$	−15.1925	−0.995295	−0.497648	+	0.867379i	$0.665803\pi$
$234$	−5.93395	−0.387915
$235$	2.89624	0.188930
$236$	0.741990	0.0482994
$237$	−8.76451	−0.569316
$238$	0.420764	0.0272741
$239$	2.35413	0.152276	0.0761379	−	0.997097i	$-0.475741\pi$
$239$	2.35413	0.152276	0.0761379	+	0.997097i	$0.475741\pi$
$240$	−3.87764	−0.250300
$241$	4.38122	0.282219	0.141109	−	0.989994i	$-0.454933\pi$
$241$	4.38122	0.282219	0.141109	+	0.989994i	$0.454933\pi$
$242$	37.0161	2.37948
$243$	−1.00000	−0.0641500
$244$	0.0540449	0.00345987
$245$	0.0578718	0.00369729
$246$	3.55536	0.226681
$247$	20.8407	1.32606
$248$	−1.78895	−0.113598
$249$	−6.20815	−0.393426
$250$	−1.39305	−0.0881041
$251$	−15.9159	−1.00460	−0.502300	−	0.864693i	$-0.667513\pi$
$251$	−15.9159	−1.00460	−0.502300	+	0.864693i	$0.667513\pi$
$252$	0.156550	0.00986171
$253$	−6.58721	−0.414134
$254$	−24.1004	−1.51219
$255$	−0.114637	−0.00717888
$256$	−1.42472	−0.0890451
$257$	9.32338	0.581577	0.290788	−	0.956787i	$-0.406082\pi$
$257$	9.32338	0.581577	0.290788	+	0.956787i	$0.406082\pi$
$258$	7.55146	0.470134
$259$	−3.78446	−0.235155
$260$	−0.253095	−0.0156963
$261$	−7.76026	−0.480348
$262$	3.18154	0.196556
$263$	12.9082	0.795956	0.397978	−	0.917395i	$-0.369712\pi$
$263$	12.9082	0.795956	0.397978	+	0.917395i	$0.369712\pi$
$264$	−17.5850	−1.08228
$265$	−0.713581	−0.0438349
$266$	17.9575	1.10105
$267$	2.01016	0.123020
$268$	0.847234	0.0517531
$269$	−20.0911	−1.22498	−0.612489	−	0.790479i	$-0.709832\pi$
$269$	−20.0911	−1.22498	−0.612489	+	0.790479i	$0.709832\pi$
$270$	1.39305	0.0847782
$271$	−1.54527	−0.0938686	−0.0469343	−	0.998898i	$-0.514945\pi$
$271$	−1.54527	−0.0938686	−0.0469343	+	0.998898i	$0.514945\pi$
$272$	0.444522	0.0269531
$273$	−11.2234	−0.679271
$274$	−13.6112	−0.822281
$275$	−6.12960	−0.369629
$276$	0.0638521	0.00384345
$277$	6.72933	0.404326	0.202163	−	0.979352i	$-0.435203\pi$
$277$	6.72933	0.404326	0.202163	+	0.979352i	$0.435203\pi$
$278$	10.2547	0.615034
$279$	0.623574	0.0373324
$280$	−7.55887	−0.451729
$281$	17.0503	1.01714	0.508568	−	0.861022i	$-0.330175\pi$
$281$	17.0503	1.01714	0.508568	+	0.861022i	$0.330175\pi$
$282$	4.03461	0.240257
$283$	−7.33317	−0.435912	−0.217956	−	0.975959i	$-0.569939\pi$
$283$	−7.33317	−0.435912	−0.217956	+	0.975959i	$0.569939\pi$
$284$	−0.680608	−0.0403867
$285$	−4.89254	−0.289809
$286$	36.3728	2.15077
$287$	6.72456	0.396938
$288$	0.335997	0.0197988
$289$	−16.9869	−0.999227
$290$	10.8104	0.634810
$291$	−10.5717	−0.619722
$292$	0.668912	0.0391451
$293$	16.6469	0.972522	0.486261	−	0.873813i	$-0.338360\pi$
$293$	16.6469	0.972522	0.486261	+	0.873813i	$0.338360\pi$
$294$	0.0806182	0.00470175
$295$	12.4880	0.727078
$296$	−4.12067	−0.239509
$297$	6.12960	0.355675
$298$	−24.4575	−1.41679
$299$	−4.57770	−0.264735
$300$	0.0594164	0.00343041
$301$	14.2827	0.823243
$302$	−8.98482	−0.517019
$303$	−12.6327	−0.725727
$304$	18.9715	1.08809
$305$	0.909596	0.0520833
$306$	−0.159696	−0.00912919
$307$	10.4895	0.598669	0.299335	−	0.954148i	$-0.403235\pi$
$307$	10.4895	0.598669	0.299335	+	0.954148i	$0.403235\pi$
$308$	−0.959587	−0.0546776
$309$	−10.6864	−0.607929
$310$	−0.868669	−0.0493371
$311$	−18.5814	−1.05365	−0.526826	−	0.849973i	$-0.676618\pi$
$311$	−18.5814	−1.05365	−0.526826	+	0.849973i	$0.676618\pi$
$312$	−12.2205	−0.691848
$313$	−9.18709	−0.519285	−0.259643	−	0.965705i	$-0.583605\pi$
$313$	−9.18709	−0.519285	−0.259643	+	0.965705i	$0.583605\pi$
$314$	7.54418	0.425742
$315$	2.63479	0.148454
$316$	−0.520755	−0.0292948
$317$	9.85203	0.553345	0.276672	−	0.960964i	$-0.410768\pi$
$317$	9.85203	0.553345	0.276672	+	0.960964i	$0.410768\pi$
$318$	−0.994053	−0.0557437
$319$	47.5673	2.66326
$320$	−8.22333	−0.459698
$321$	15.9276	0.888993
$322$	−3.94441	−0.219813
$323$	0.560868	0.0312075
$324$	−0.0594164	−0.00330091
$325$	−4.25969	−0.236285
$326$	−20.6870	−1.14575
$327$	−5.75126	−0.318046
$328$	7.32196	0.404288
$329$	7.63099	0.420710
$330$	−8.53883	−0.470047
$331$	−31.2124	−1.71559	−0.857796	−	0.513991i	$-0.828166\pi$
$331$	−31.2124	−1.71559	−0.857796	+	0.513991i	$0.828166\pi$
$332$	−0.368866	−0.0202441
$333$	1.43634	0.0787110
$334$	−4.00088	−0.218919
$335$	14.2593	0.779067
$336$	−10.2168	−0.557370
$337$	6.27927	0.342054	0.171027	−	0.985266i	$-0.445292\pi$
$337$	6.27927	0.342054	0.171027	+	0.985266i	$0.445292\pi$
$338$	7.16717	0.389843
$339$	−4.22448	−0.229442
$340$	−0.00681134	−0.000369397 0
$341$	−3.82226	−0.206987
$342$	−6.81554	−0.368542
$343$	18.5960	1.00409
$344$	15.5516	0.838487
$345$	1.07466	0.0578575
$346$	−23.1144	−1.24264
$347$	21.8057	1.17059	0.585296	−	0.810819i	$-0.300978\pi$
$347$	21.8057	1.17059	0.585296	+	0.810819i	$0.300978\pi$
$348$	−0.461086	−0.0247168
$349$	25.2731	1.35284	0.676418	−	0.736518i	$-0.263531\pi$
$349$	25.2731	1.35284	0.676418	+	0.736518i	$0.263531\pi$
$350$	−3.67039	−0.196191
$351$	4.25969	0.227365
$352$	−2.05953	−0.109773
$353$	7.80930	0.415647	0.207824	−	0.978166i	$-0.433362\pi$
$353$	7.80930	0.415647	0.207824	+	0.978166i	$0.433362\pi$
$354$	17.3964	0.924606
$355$	−11.4549	−0.607963
$356$	0.119437	0.00633013
$357$	−0.302046	−0.0159860
$358$	−8.74328	−0.462097
$359$	−22.5508	−1.19019	−0.595093	−	0.803657i	$-0.702885\pi$
$359$	−22.5508	−1.19019	−0.595093	+	0.803657i	$0.702885\pi$
$360$	2.86887	0.151203
$361$	4.93695	0.259839
$362$	−34.3129	−1.80344
$363$	−26.5720	−1.39467
$364$	−0.666853	−0.0349526
$365$	11.2580	0.589273
$366$	1.26711	0.0662329
$367$	−2.67970	−0.139879	−0.0699396	−	0.997551i	$-0.522281\pi$
$367$	−2.67970	−0.139879	−0.0699396	+	0.997551i	$0.522281\pi$
$368$	−4.16712	−0.217226
$369$	−2.55222	−0.132863
$370$	−2.00089	−0.104021
$371$	−1.88014	−0.0976119
$372$	0.0370505	0.00192098
$373$	−21.5729	−1.11700	−0.558501	−	0.829504i	$-0.688623\pi$
$373$	−21.5729	−1.11700	−0.558501	+	0.829504i	$0.688623\pi$
$374$	0.978869	0.0506161
$375$	1.00000	0.0516398
$376$	8.30893	0.428500
$377$	33.0563	1.70249
$378$	3.67039	0.188785
$379$	−31.5927	−1.62281	−0.811405	−	0.584484i	$-0.801297\pi$
$379$	−31.5927	−1.62281	−0.811405	+	0.584484i	$0.801297\pi$
$380$	−0.290697	−0.0149124
$381$	17.3005	0.886329
$382$	17.0407	0.871877
$383$	1.19682	0.0611544	0.0305772	−	0.999532i	$-0.490265\pi$
$383$	1.19682	0.0611544	0.0305772	+	0.999532i	$0.490265\pi$
$384$	−10.7835	−0.550294
$385$	−16.1502	−0.823091
$386$	−16.3583	−0.832615
$387$	−5.42082	−0.275556
$388$	−0.628130	−0.0318885
$389$	18.1137	0.918401	0.459200	−	0.888333i	$-0.348136\pi$
$389$	18.1137	0.918401	0.459200	+	0.888333i	$0.348136\pi$
$390$	−5.93395	−0.300477
$391$	−0.123196	−0.00623028
$392$	0.166026	0.00838560
$393$	−2.28387	−0.115206
$394$	30.7138	1.54734
$395$	−8.76451	−0.440990
$396$	0.364199	0.0183017
$397$	30.6316	1.53736	0.768679	−	0.639634i	$-0.220914\pi$
$397$	30.6316	1.53736	0.768679	+	0.639634i	$0.220914\pi$
$398$	−26.5116	−1.32891
$399$	−12.8908	−0.645348
$400$	−3.87764	−0.193882
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	19.8639	0.990719
$403$	−2.65623	−0.132316
$404$	−0.750586	−0.0373431
$405$	−1.00000	−0.0496904
$406$	28.4832	1.41360
$407$	−8.80419	−0.436408
$408$	−0.328880	−0.0162820
$409$	21.2497	1.05073	0.525366	−	0.850877i	$-0.323929\pi$
$409$	21.2497	1.05073	0.525366	+	0.850877i	$0.323929\pi$
$410$	3.55536	0.175587
$411$	9.77078	0.481957
$412$	−0.634948	−0.0312817
$413$	32.9032	1.61906
$414$	1.49705	0.0735758
$415$	−6.20815	−0.304746
$416$	−1.43124	−0.0701725
$417$	−7.36131	−0.360485
$418$	41.7766	2.04336
$419$	−24.7485	−1.20904	−0.604522	−	0.796588i	$-0.706636\pi$
$419$	−24.7485	−1.20904	−0.604522	+	0.796588i	$0.706636\pi$
$420$	0.156550	0.00763885
$421$	23.3498	1.13800	0.569000	−	0.822338i	$-0.307331\pi$
$421$	23.3498	1.13800	0.569000	+	0.822338i	$0.307331\pi$
$422$	−3.91067	−0.190369
$423$	−2.89624	−0.140820
$424$	−2.04717	−0.0994193
$425$	−0.114637	−0.00556073
$426$	−15.9572	−0.773130
$427$	2.39660	0.115979
$428$	0.946361	0.0457441
$429$	−26.1102	−1.26061
$430$	7.55146	0.364164
$431$	4.00626	0.192975	0.0964874	−	0.995334i	$-0.469239\pi$
$431$	4.00626	0.192975	0.0964874	+	0.995334i	$0.469239\pi$
$432$	3.87764	0.186563
$433$	0.549688	0.0264163	0.0132082	−	0.999913i	$-0.495796\pi$
$433$	0.549688	0.0264163	0.0132082	+	0.999913i	$0.495796\pi$
$434$	−2.28876	−0.109864
$435$	−7.76026	−0.372076
$436$	−0.341719	−0.0163654
$437$	−5.25779	−0.251514
$438$	15.6830	0.749363
$439$	−8.29181	−0.395747	−0.197873	−	0.980228i	$-0.563403\pi$
$439$	−8.29181	−0.395747	−0.197873	+	0.980228i	$0.563403\pi$
$440$	−17.5850	−0.838332
$441$	−0.0578718	−0.00275580
$442$	0.680253	0.0323563
$443$	−13.9671	−0.663596	−0.331798	−	0.943351i	$-0.607655\pi$
$443$	−13.9671	−0.663596	−0.331798	+	0.943351i	$0.607655\pi$
$444$	0.0853421	0.00405016
$445$	2.01016	0.0952910
$446$	−4.42761	−0.209654
$447$	17.5568	0.830410
$448$	−21.6668	−1.02366
$449$	−34.3286	−1.62007	−0.810035	−	0.586382i	$-0.800552\pi$
$449$	−34.3286	−1.62007	−0.810035	+	0.586382i	$0.800552\pi$
$450$	1.39305	0.0656689
$451$	15.6441	0.736650
$452$	−0.251003	−0.0118062
$453$	6.44976	0.303036
$454$	−11.6813	−0.548228
$455$	−11.2234	−0.526161
$456$	−14.0360	−0.657298
$457$	−27.8911	−1.30469	−0.652345	−	0.757923i	$-0.726214\pi$
$457$	−27.8911	−1.30469	−0.652345	+	0.757923i	$0.726214\pi$
$458$	−3.45318	−0.161357
$459$	0.114637	0.00535082
$460$	0.0638521	0.00297712
$461$	−10.6919	−0.497974	−0.248987	−	0.968507i	$-0.580098\pi$
$461$	−10.6919	−0.497974	−0.248987	+	0.968507i	$0.580098\pi$
$462$	−22.4980	−1.04670
$463$	15.0872	0.701160	0.350580	−	0.936533i	$-0.385985\pi$
$463$	15.0872	0.701160	0.350580	+	0.936533i	$0.385985\pi$
$464$	30.0915	1.39696
$465$	0.623574	0.0289176
$466$	−21.1639	−0.980400
$467$	11.9437	0.552691	0.276345	−	0.961058i	$-0.410877\pi$
$467$	11.9437	0.552691	0.276345	+	0.961058i	$0.410877\pi$
$468$	0.253095	0.0116993
$469$	37.5702	1.73483
$470$	4.03461	0.186102
$471$	−5.41559	−0.249537
$472$	35.8263	1.64904
$473$	33.2275	1.52780
$474$	−12.2094	−0.560796
$475$	−4.89254	−0.224485
$476$	−0.0179465	−0.000822575 0
$477$	0.713581	0.0326726
$478$	3.27941	0.149997
$479$	−20.0730	−0.917157	−0.458579	−	0.888654i	$-0.651641\pi$
$479$	−20.0730	−0.917157	−0.458579	+	0.888654i	$0.651641\pi$
$480$	0.335997	0.0153361
$481$	−6.11836	−0.278973
$482$	6.10325	0.277995
$483$	2.83149	0.128837
$484$	−1.57881	−0.0717641
$485$	−10.5717	−0.480035
$486$	−1.39305	−0.0631900
$487$	21.6517	0.981133	0.490567	−	0.871404i	$-0.336790\pi$
$487$	21.6517	0.981133	0.490567	+	0.871404i	$0.336790\pi$
$488$	2.60951	0.118127
$489$	14.8502	0.671549
$490$	0.0806182	0.00364196
$491$	−14.0681	−0.634883	−0.317442	−	0.948278i	$-0.602824\pi$
$491$	−14.0681	−0.634883	−0.317442	+	0.948278i	$0.602824\pi$
$492$	−0.151643	−0.00683661
$493$	0.889616	0.0400663
$494$	29.0321	1.30622
$495$	6.12960	0.275505
$496$	−2.41799	−0.108571
$497$	−30.1813	−1.35381
$498$	−8.64825	−0.387538
$499$	19.8331	0.887852	0.443926	−	0.896064i	$-0.353585\pi$
$499$	19.8331	0.887852	0.443926	+	0.896064i	$0.353585\pi$
$500$	0.0594164	0.00265718
$501$	2.87203	0.128313
$502$	−22.1716	−0.989566
$503$	−8.12987	−0.362493	−0.181247	−	0.983438i	$-0.558013\pi$
$503$	−8.12987	−0.362493	−0.181247	+	0.983438i	$0.558013\pi$
$504$	7.55887	0.336699
$505$	−12.6327	−0.562146
$506$	−9.17630	−0.407936
$507$	−5.14495	−0.228495
$508$	1.02793	0.0456070
$509$	−16.5687	−0.734394	−0.367197	−	0.930143i	$-0.619682\pi$
$509$	−16.5687	−0.734394	−0.367197	+	0.930143i	$0.619682\pi$
$510$	−0.159696	−0.00707144
$511$	29.6626	1.31220
$512$	−23.5517	−1.04085
$513$	4.89254	0.216011
$514$	12.9879	0.572873
$515$	−10.6864	−0.470900
$516$	−0.322085	−0.0141790
$517$	17.7528	0.780767
$518$	−5.27193	−0.231635
$519$	16.5926	0.728336
$520$	−12.2205	−0.535904
$521$	−6.06893	−0.265885	−0.132942	−	0.991124i	$-0.542442\pi$
$521$	−6.06893	−0.265885	−0.132942	+	0.991124i	$0.542442\pi$
$522$	−10.8104	−0.473159
$523$	−35.2804	−1.54271	−0.771353	−	0.636408i	$-0.780420\pi$
$523$	−35.2804	−1.54271	−0.771353	+	0.636408i	$0.780420\pi$
$524$	−0.135699	−0.00592804
$525$	2.63479	0.114992
$526$	17.9818	0.784044
$527$	−0.0714849	−0.00311393
$528$	−23.7684	−1.03439
$529$	−21.8451	−0.949788
$530$	−0.994053	−0.0431789
$531$	−12.4880	−0.541932
$532$	−0.765926	−0.0332071
$533$	10.8716	0.470903
$534$	2.80026	0.121179
$535$	15.9276	0.688611
$536$	40.9079	1.76695
$537$	6.27637	0.270845
$538$	−27.9879	−1.20664
$539$	0.354731	0.0152793
$540$	−0.0594164	−0.00255687
$541$	7.73459	0.332536	0.166268	−	0.986081i	$-0.446828\pi$
$541$	7.73459	0.332536	0.166268	+	0.986081i	$0.446828\pi$
$542$	−2.15264	−0.0924637
$543$	24.6315	1.05704
$544$	−0.0385179	−0.00165144
$545$	−5.75126	−0.246357
$546$	−15.6347	−0.669105
$547$	39.9104	1.70644	0.853222	−	0.521547i	$-0.174645\pi$
$547$	39.9104	1.70644	0.853222	+	0.521547i	$0.174645\pi$
$548$	0.580544	0.0247996
$549$	−0.909596	−0.0388206
$550$	−8.53883	−0.364097
$551$	37.9674	1.61746
$552$	3.08304	0.131223
$553$	−23.0927	−0.982000
$554$	9.37428	0.398275
$555$	1.43634	0.0609693
$556$	−0.437382	−0.0185491
$557$	28.8073	1.22060	0.610302	−	0.792169i	$-0.291048\pi$
$557$	28.8073	1.22060	0.610302	+	0.792169i	$0.291048\pi$
$558$	0.868669	0.0367737
$559$	23.0910	0.976646
$560$	−10.2168	−0.431737
$561$	−0.702682	−0.0296672
$562$	23.7519	1.00191
$563$	17.4065	0.733597	0.366799	−	0.930300i	$-0.380454\pi$
$563$	17.4065	0.733597	0.366799	+	0.930300i	$0.380454\pi$
$564$	−0.172084	−0.00724605
$565$	−4.22448	−0.177725
$566$	−10.2155	−0.429388
$567$	−2.63479	−0.110651
$568$	−32.8626	−1.37888
$569$	38.0552	1.59536	0.797678	−	0.603083i	$-0.206061\pi$
$569$	38.0552	1.59536	0.797678	+	0.603083i	$0.206061\pi$
$570$	−6.81554	−0.285472
$571$	−39.8449	−1.66746	−0.833729	−	0.552173i	$-0.813799\pi$
$571$	−39.8449	−1.66746	−0.833729	+	0.552173i	$0.813799\pi$
$572$	−1.55137	−0.0648661
$573$	−12.2327	−0.511026
$574$	9.36763	0.390997
$575$	1.07466	0.0448162
$576$	8.22333	0.342639
$577$	−8.14064	−0.338899	−0.169450	−	0.985539i	$-0.554199\pi$
$577$	−8.14064	−0.338899	−0.169450	+	0.985539i	$0.554199\pi$
$578$	−23.6635	−0.984272
$579$	11.7428	0.488014
$580$	−0.461086	−0.0191456
$581$	−16.3572	−0.678610
$582$	−14.7268	−0.610447
$583$	−4.37397	−0.181151
$584$	32.2978	1.33649
$585$	4.25969	0.176116
$586$	23.1899	0.957968
$587$	18.7694	0.774697	0.387348	−	0.921933i	$-0.373391\pi$
$587$	18.7694	0.774697	0.387348	+	0.921933i	$0.373391\pi$
$588$	−0.00343853	−0.000141803 0
$589$	−3.05086	−0.125709
$590$	17.3964	0.716197
$591$	−22.0479	−0.906929
$592$	−5.56961	−0.228909
$593$	6.97072	0.286253	0.143127	−	0.989704i	$-0.454284\pi$
$593$	6.97072	0.286253	0.143127	+	0.989704i	$0.454284\pi$
$594$	8.53883	0.350352
$595$	−0.302046	−0.0123827
$596$	1.04316	0.0427296
$597$	19.0314	0.778902
$598$	−6.37695	−0.260773
$599$	−30.4761	−1.24522	−0.622610	−	0.782533i	$-0.713928\pi$
$599$	−30.4761	−1.24522	−0.622610	+	0.782533i	$0.713928\pi$
$600$	2.86887	0.117121
$601$	−12.2482	−0.499616	−0.249808	−	0.968295i	$-0.580367\pi$
$601$	−12.2482	−0.499616	−0.249808	+	0.968295i	$0.580367\pi$
$602$	19.8965	0.810922
$603$	−14.2593	−0.580682
$604$	0.383221	0.0155930
$605$	−26.5720	−1.08030
$606$	−17.5979	−0.714866
$607$	−14.7881	−0.600230	−0.300115	−	0.953903i	$-0.597025\pi$
$607$	−14.7881	−0.600230	−0.300115	+	0.953903i	$0.597025\pi$
$608$	−1.64388	−0.0666682
$609$	−20.4467	−0.828541
$610$	1.26711	0.0513038
$611$	12.3371	0.499105
$612$	0.00681134	0.000275332 0
$613$	15.6875	0.633612	0.316806	−	0.948490i	$-0.397390\pi$
$613$	15.6875	0.633612	0.316806	+	0.948490i	$0.397390\pi$
$614$	14.6124	0.589710
$615$	−2.55222	−0.102915
$616$	−46.3328	−1.86680
$617$	−12.7409	−0.512930	−0.256465	−	0.966554i	$-0.582558\pi$
$617$	−12.7409	−0.512930	−0.256465	+	0.966554i	$0.582558\pi$
$618$	−14.8867	−0.598831
$619$	−31.9455	−1.28400	−0.641999	−	0.766706i	$-0.721895\pi$
$619$	−31.9455	−1.28400	−0.641999	+	0.766706i	$0.721895\pi$
$620$	0.0370505	0.00148798
$621$	−1.07466	−0.0431244
$622$	−25.8848	−1.03788
$623$	5.29637	0.212194
$624$	−16.5175	−0.661230
$625$	1.00000	0.0400000
$626$	−12.7981	−0.511513
$627$	−29.9893	−1.19766
$628$	−0.321775	−0.0128402
$629$	−0.164658	−0.00656536
$630$	3.67039	0.146232
$631$	−37.7137	−1.50136	−0.750679	−	0.660667i	$-0.770274\pi$
$631$	−37.7137	−1.50136	−0.750679	+	0.660667i	$0.770274\pi$
$632$	−25.1442	−1.00018
$633$	2.80728	0.111579
$634$	13.7243	0.545063
$635$	17.3005	0.686548
$636$	0.0423984	0.00168121
$637$	0.246516	0.00976732
$638$	66.2635	2.62340
$639$	11.4549	0.453149
$640$	−10.7835	−0.426256
$641$	14.2034	0.561001	0.280500	−	0.959854i	$-0.409500\pi$
$641$	14.2034	0.561001	0.280500	+	0.959854i	$0.409500\pi$
$642$	22.1879	0.875688
$643$	17.4078	0.686497	0.343249	−	0.939245i	$-0.388473\pi$
$643$	17.4078	0.686497	0.343249	+	0.939245i	$0.388473\pi$
$644$	0.168237	0.00662947
$645$	−5.42082	−0.213445
$646$	0.781317	0.0307405
$647$	−16.2991	−0.640783	−0.320392	−	0.947285i	$-0.603814\pi$
$647$	−16.2991	−0.640783	−0.320392	+	0.947285i	$0.603814\pi$
$648$	−2.86887	−0.112700
$649$	76.5463	3.00470
$650$	−5.93395	−0.232749
$651$	1.64299	0.0643938
$652$	0.882345	0.0345553
$653$	−47.4211	−1.85573	−0.927866	−	0.372915i	$-0.878358\pi$
$653$	−47.4211	−1.85573	−0.927866	+	0.372915i	$0.878358\pi$
$654$	−8.01179	−0.313286
$655$	−2.28387	−0.0892381
$656$	9.89656	0.386396
$657$	−11.2580	−0.439218
$658$	10.6303	0.414414
$659$	−12.8070	−0.498889	−0.249445	−	0.968389i	$-0.580248\pi$
$659$	−12.8070	−0.498889	−0.249445	+	0.968389i	$0.580248\pi$
$660$	0.364199	0.0141764
$661$	−30.8512	−1.19997	−0.599986	−	0.800010i	$-0.704827\pi$
$661$	−30.8512	−1.19997	−0.599986	+	0.800010i	$0.704827\pi$
$662$	−43.4804	−1.68992
$663$	−0.488320	−0.0189648
$664$	−17.8104	−0.691176
$665$	−12.8908	−0.499885
$666$	2.00089	0.0775330
$667$	−8.33960	−0.322911
$668$	0.170646	0.00660249
$669$	3.17836	0.122883
$670$	19.8639	0.767408
$671$	5.57546	0.215238
$672$	0.885283	0.0341505
$673$	39.3012	1.51495	0.757476	−	0.652863i	$-0.226432\pi$
$673$	39.3012	1.51495	0.757476	+	0.652863i	$0.226432\pi$
$674$	8.74732	0.336934
$675$	−1.00000	−0.0384900
$676$	−0.305694	−0.0117575
$677$	−24.4591	−0.940040	−0.470020	−	0.882656i	$-0.655753\pi$
$677$	−24.4591	−0.940040	−0.470020	+	0.882656i	$0.655753\pi$
$678$	−5.88490	−0.226008
$679$	−27.8541	−1.06894
$680$	−0.328880	−0.0126120
$681$	8.38539	0.321329
$682$	−5.32459	−0.203889
$683$	−31.2488	−1.19570	−0.597850	−	0.801608i	$-0.703978\pi$
$683$	−31.2488	−1.19570	−0.597850	+	0.801608i	$0.703978\pi$
$684$	0.290697	0.0111151
$685$	9.77078	0.373322
$686$	25.9052	0.989064
$687$	2.47887	0.0945747
$688$	21.0200	0.801379
$689$	−3.03963	−0.115801
$690$	1.49705	0.0569916
$691$	−26.3044	−1.00067	−0.500334	−	0.865833i	$-0.666789\pi$
$691$	−26.3044	−1.00067	−0.500334	+	0.865833i	$0.666789\pi$
$692$	0.985875	0.0374773
$693$	16.1502	0.613496
$694$	30.3764	1.15307
$695$	−7.36131	−0.279230
$696$	−22.2632	−0.843883
$697$	0.292579	0.0110822
$698$	35.2066	1.33259
$699$	15.1925	0.574634
$700$	0.156550	0.00591702
$701$	−16.3630	−0.618023	−0.309012	−	0.951058i	$-0.599998\pi$
$701$	−16.3630	−0.618023	−0.309012	+	0.951058i	$0.599998\pi$
$702$	5.93395	0.223963
$703$	−7.02735	−0.265042
$704$	−50.4057	−1.89974
$705$	−2.89624	−0.109079
$706$	10.8787	0.409426
$707$	−33.2844	−1.25179
$708$	−0.741990	−0.0278857
$709$	−20.8997	−0.784903	−0.392452	−	0.919773i	$-0.628373\pi$
$709$	−20.8997	−0.784903	−0.392452	+	0.919773i	$0.628373\pi$
$710$	−15.9572	−0.598864
$711$	8.76451	0.328695
$712$	5.76689	0.216124
$713$	0.670127	0.0250965
$714$	−0.420764	−0.0157467
$715$	−26.1102	−0.976466
$716$	0.372919	0.0139366
$717$	−2.35413	−0.0879164
$718$	−31.4144	−1.17237
$719$	−45.6190	−1.70130	−0.850651	−	0.525731i	$-0.823792\pi$
$719$	−45.6190	−1.70130	−0.850651	+	0.525731i	$0.823792\pi$
$720$	3.87764	0.144511
$721$	−28.1565	−1.04860
$722$	6.87741	0.255951
$723$	−4.38122	−0.162939
$724$	1.46351	0.0543911
$725$	−7.76026	−0.288209
$726$	−37.0161	−1.37379
$727$	8.39859	0.311487	0.155743	−	0.987798i	$-0.450223\pi$
$727$	8.39859	0.311487	0.155743	+	0.987798i	$0.450223\pi$
$728$	−32.1984	−1.19335
$729$	1.00000	0.0370370
$730$	15.6830	0.580454
$731$	0.621429	0.0229844
$732$	−0.0540449	−0.00199756
$733$	−31.5562	−1.16556	−0.582778	−	0.812631i	$-0.698034\pi$
$733$	−31.5562	−1.16556	−0.582778	+	0.812631i	$0.698034\pi$
$734$	−3.73295	−0.137786
$735$	−0.0578718	−0.00213463
$736$	0.361081	0.0133096
$737$	87.4036	3.21955
$738$	−3.55536	−0.130875
$739$	−4.53012	−0.166643	−0.0833216	−	0.996523i	$-0.526553\pi$
$739$	−4.53012	−0.166643	−0.0833216	+	0.996523i	$0.526553\pi$
$740$	0.0853421	0.00313724
$741$	−20.8407	−0.765602
$742$	−2.61912	−0.0961510
$743$	4.74060	0.173916	0.0869579	−	0.996212i	$-0.472285\pi$
$743$	4.74060	0.173916	0.0869579	+	0.996212i	$0.472285\pi$
$744$	1.78895	0.0655861
$745$	17.5568	0.643233
$746$	−30.0521	−1.10028
$747$	6.20815	0.227144
$748$	−0.0417508	−0.00152656
$749$	41.9660	1.53340
$750$	1.39305	0.0508669
$751$	−43.8927	−1.60167	−0.800833	−	0.598888i	$-0.795610\pi$
$751$	−43.8927	−1.60167	−0.800833	+	0.598888i	$0.795610\pi$
$752$	11.2306	0.409537
$753$	15.9159	0.580007
$754$	46.0490	1.67701
$755$	6.44976	0.234731
$756$	−0.156550	−0.00569366
$757$	12.0766	0.438930	0.219465	−	0.975620i	$-0.429569\pi$
$757$	12.0766	0.438930	0.219465	+	0.975620i	$0.429569\pi$
$758$	−44.0102	−1.59852
$759$	6.58721	0.239100
$760$	−14.0360	−0.509141
$761$	−14.6985	−0.532819	−0.266410	−	0.963860i	$-0.585837\pi$
$761$	−14.6985	−0.532819	−0.266410	+	0.963860i	$0.585837\pi$
$762$	24.1004	0.873065
$763$	−15.1534	−0.548589
$764$	−0.726820	−0.0262954
$765$	0.114637	0.00414473
$766$	1.66722	0.0602392
$767$	53.1949	1.92076
$768$	1.42472	0.0514102
$769$	15.1984	0.548070	0.274035	−	0.961720i	$-0.411642\pi$
$769$	15.1984	0.548070	0.274035	+	0.961720i	$0.411642\pi$
$770$	−22.4980	−0.810773
$771$	−9.32338	−0.335773
$772$	0.697715	0.0251113
$773$	5.77567	0.207737	0.103868	−	0.994591i	$-0.466878\pi$
$773$	5.77567	0.207737	0.103868	+	0.994591i	$0.466878\pi$
$774$	−7.55146	−0.271432
$775$	0.623574	0.0223994
$776$	−30.3287	−1.08874
$777$	3.78446	0.135767
$778$	25.2333	0.904656
$779$	12.4868	0.447387
$780$	0.253095	0.00906226
$781$	−70.2139	−2.51245
$782$	−0.171618	−0.00613703
$783$	7.76026	0.277329
$784$	0.224406	0.00801449
$785$	−5.41559	−0.193291
$786$	−3.18154	−0.113482
$787$	−16.2255	−0.578378	−0.289189	−	0.957272i	$-0.593386\pi$
$787$	−16.2255	−0.578378	−0.289189	+	0.957272i	$0.593386\pi$
$788$	−1.31001	−0.0466670
$789$	−12.9082	−0.459545
$790$	−12.2094	−0.434390
$791$	−11.1306	−0.395759
$792$	17.5850	0.624856
$793$	3.87460	0.137591
$794$	42.6714	1.51435
$795$	0.713581	0.0253081
$796$	1.13077	0.0400792
$797$	22.8406	0.809056	0.404528	−	0.914526i	$-0.367436\pi$
$797$	22.8406	0.809056	0.404528	+	0.914526i	$0.367436\pi$
$798$	−17.9575	−0.635690
$799$	0.332018	0.0117459
$800$	0.335997	0.0118793
$801$	−2.01016	−0.0710257
$802$	1.39305	0.0491902
$803$	69.0073	2.43522
$804$	−0.847234	−0.0298796
$805$	2.83149	0.0997970
$806$	−3.70026	−0.130336
$807$	20.0911	0.707241
$808$	−36.2414	−1.27497
$809$	29.0378	1.02092	0.510458	−	0.859903i	$-0.329476\pi$
$809$	29.0378	1.02092	0.510458	+	0.859903i	$0.329476\pi$
$810$	−1.39305	−0.0489467
$811$	−42.3135	−1.48583	−0.742914	−	0.669387i	$-0.766557\pi$
$811$	−42.3135	−1.48583	−0.742914	+	0.669387i	$0.766557\pi$
$812$	−1.21487	−0.0426335
$813$	1.54527	0.0541950
$814$	−12.2647	−0.429876
$815$	14.8502	0.520180
$816$	−0.444522	−0.0155614
$817$	26.5216	0.927873
$818$	29.6019	1.03501
$819$	11.2234	0.392177
$820$	−0.151643	−0.00529562
$821$	−31.6343	−1.10405	−0.552023	−	0.833829i	$-0.686144\pi$
$821$	−31.6343	−1.10405	−0.552023	+	0.833829i	$0.686144\pi$
$822$	13.6112	0.474744
$823$	−18.3398	−0.639284	−0.319642	−	0.947538i	$-0.603563\pi$
$823$	−18.3398	−0.639284	−0.319642	+	0.947538i	$0.603563\pi$
$824$	−30.6579	−1.06802
$825$	6.12960	0.213405
$826$	45.8358	1.59483
$827$	30.5053	1.06077	0.530387	−	0.847756i	$-0.322047\pi$
$827$	30.5053	1.06077	0.530387	+	0.847756i	$0.322047\pi$
$828$	−0.0638521	−0.00221901
$829$	4.69335	0.163007	0.0815033	−	0.996673i	$-0.474028\pi$
$829$	4.69335	0.163007	0.0815033	+	0.996673i	$0.474028\pi$
$830$	−8.64825	−0.300185
$831$	−6.72933	−0.233438
$832$	−35.0289	−1.21441
$833$	0.00663428	0.000229864 0
$834$	−10.2547	−0.355090
$835$	2.87203	0.0993909
$836$	−1.78186	−0.0616268
$837$	−0.623574	−0.0215539
$838$	−34.4759	−1.19095
$839$	27.8247	0.960616	0.480308	−	0.877100i	$-0.340525\pi$
$839$	27.8247	0.960616	0.480308	+	0.877100i	$0.340525\pi$
$840$	7.55887	0.260806
$841$	31.2216	1.07661
$842$	32.5274	1.12097
$843$	−17.0503	−0.587244
$844$	0.166798	0.00574143
$845$	−5.14495	−0.176992
$846$	−4.03461	−0.138713
$847$	−70.0117	−2.40563
$848$	−2.76701	−0.0950195
$849$	7.33317	0.251674
$850$	−0.159696	−0.00547751
$851$	1.54357	0.0529129
$852$	0.680608	0.0233172
$853$	1.02195	0.0349910	0.0174955	−	0.999847i	$-0.494431\pi$
$853$	1.02195	0.0349910	0.0174955	+	0.999847i	$0.494431\pi$
$854$	3.33857	0.114244
$855$	4.89254	0.167321
$856$	45.6942	1.56180
$857$	16.0908	0.549650	0.274825	−	0.961494i	$-0.411380\pi$
$857$	16.0908	0.549650	0.274825	+	0.961494i	$0.411380\pi$
$858$	−36.3728	−1.24175
$859$	−2.13245	−0.0727582	−0.0363791	−	0.999338i	$-0.511582\pi$
$859$	−2.13245	−0.0727582	−0.0363791	+	0.999338i	$0.511582\pi$
$860$	−0.322085	−0.0109830
$861$	−6.72456	−0.229172
$862$	5.58092	0.190087
$863$	−37.7814	−1.28609	−0.643047	−	0.765827i	$-0.722330\pi$
$863$	−37.7814	−1.28609	−0.643047	+	0.765827i	$0.722330\pi$
$864$	−0.335997	−0.0114309
$865$	16.5926	0.564167
$866$	0.765743	0.0260210
$867$	16.9869	0.576904
$868$	0.0976204	0.00331345
$869$	−53.7229	−1.82243
$870$	−10.8104	−0.366507
$871$	60.7401	2.05810
$872$	−16.4996	−0.558747
$873$	10.5717	0.357797
$874$	−7.32436	−0.247750
$875$	2.63479	0.0890722
$876$	−0.668912	−0.0226005
$877$	−33.8992	−1.14469	−0.572347	−	0.820011i	$-0.693967\pi$
$877$	−33.8992	−1.14469	−0.572347	+	0.820011i	$0.693967\pi$
$878$	−11.5509	−0.389824
$879$	−16.6469	−0.561486
$880$	−23.7684	−0.801231
$881$	52.3230	1.76281	0.881403	−	0.472365i	$-0.156600\pi$
$881$	52.3230	1.76281	0.881403	+	0.472365i	$0.156600\pi$
$882$	−0.0806182	−0.00271456
$883$	34.9533	1.17627	0.588136	−	0.808762i	$-0.299862\pi$
$883$	34.9533	1.17627	0.588136	+	0.808762i	$0.299862\pi$
$884$	−0.0290142	−0.000975853 0
$885$	−12.4880	−0.419779
$886$	−19.4568	−0.653664
$887$	23.1560	0.777504	0.388752	−	0.921342i	$-0.372906\pi$
$887$	23.1560	0.777504	0.388752	+	0.921342i	$0.372906\pi$
$888$	4.12067	0.138281
$889$	45.5831	1.52881
$890$	2.80026	0.0938648
$891$	−6.12960	−0.205349
$892$	0.188847	0.00632306
$893$	14.1700	0.474180
$894$	24.4575	0.817982
$895$	6.27637	0.209796
$896$	−28.4123	−0.949188
$897$	4.57770	0.152845
$898$	−47.8215	−1.59582
$899$	−4.83910	−0.161393
$900$	−0.0594164	−0.00198055
$901$	−0.0818031	−0.00272526
$902$	21.7929	0.725625
$903$	−14.2827	−0.475300
$904$	−12.1195	−0.403087
$905$	24.6315	0.818779
$906$	8.98482	0.298501
$907$	−25.3756	−0.842584	−0.421292	−	0.906925i	$-0.638423\pi$
$907$	−25.3756	−0.842584	−0.421292	+	0.906925i	$0.638423\pi$
$908$	0.498229	0.0165343
$909$	12.6327	0.418999
$910$	−15.6347	−0.518286
$911$	40.6785	1.34774	0.673869	−	0.738851i	$-0.264631\pi$
$911$	40.6785	1.34774	0.673869	+	0.738851i	$0.264631\pi$
$912$	−18.9715	−0.628209
$913$	−38.0535	−1.25939
$914$	−38.8536	−1.28516
$915$	−0.909596	−0.0300703
$916$	0.147285	0.00486644
$917$	−6.01752	−0.198716
$918$	0.159696	0.00527074
$919$	−57.8316	−1.90769	−0.953844	−	0.300304i	$-0.902912\pi$
$919$	−57.8316	−1.90769	−0.953844	+	0.300304i	$0.902912\pi$
$920$	3.08304	0.101645
$921$	−10.4895	−0.345642
$922$	−14.8944	−0.490521
$923$	−48.7943	−1.60608
$924$	0.959587	0.0315681
$925$	1.43634	0.0472266
$926$	21.0171	0.690666
$927$	10.6864	0.350988
$928$	−2.60743	−0.0855930
$929$	−20.9622	−0.687746	−0.343873	−	0.939016i	$-0.611739\pi$
$929$	−20.9622	−0.687746	−0.343873	+	0.939016i	$0.611739\pi$
$930$	0.868669	0.0284848
$931$	0.283140	0.00927954
$932$	0.902685	0.0295684
$933$	18.5814	0.608327
$934$	16.6382	0.544419
$935$	−0.702682	−0.0229801
$936$	12.2205	0.399439
$937$	19.4340	0.634881	0.317441	−	0.948278i	$-0.397177\pi$
$937$	19.4340	0.634881	0.317441	+	0.948278i	$0.397177\pi$
$938$	52.3371	1.70887
$939$	9.18709	0.299809
$940$	−0.172084	−0.00561277
$941$	39.5232	1.28842	0.644209	−	0.764849i	$-0.277187\pi$
$941$	39.5232	1.28842	0.644209	+	0.764849i	$0.277187\pi$
$942$	−7.54418	−0.245803
$943$	−2.74275	−0.0893163
$944$	48.4238	1.57606
$945$	−2.63479	−0.0857098
$946$	46.2875	1.50493
$947$	45.0639	1.46438	0.732190	−	0.681101i	$-0.238498\pi$
$947$	45.0639	1.46438	0.732190	+	0.681101i	$0.238498\pi$
$948$	0.520755	0.0169133
$949$	47.9558	1.55671
$950$	−6.81554	−0.221125
$951$	−9.85203	−0.319474
$952$	−0.866529	−0.0280844
$953$	−1.25700	−0.0407182	−0.0203591	−	0.999793i	$-0.506481\pi$
$953$	−1.25700	−0.0407182	−0.0203591	+	0.999793i	$0.506481\pi$
$954$	0.994053	0.0321837
$955$	−12.2327	−0.395839
$956$	−0.139874	−0.00452384
$957$	−47.5673	−1.53763
$958$	−27.9626	−0.903431
$959$	25.7440	0.831316
$960$	8.22333	0.265407
$961$	−30.6112	−0.987457
$962$	−8.52318	−0.274798
$963$	−15.9276	−0.513260
$964$	−0.260316	−0.00838421
$965$	11.7428	0.378014
$966$	3.94441	0.126909
$967$	10.8042	0.347440	0.173720	−	0.984795i	$-0.444421\pi$
$967$	10.8042	0.347440	0.173720	+	0.984795i	$0.444421\pi$
$968$	−76.2315	−2.45017
$969$	−0.560868	−0.0180177
$970$	−14.7268	−0.472850
$971$	11.3502	0.364244	0.182122	−	0.983276i	$-0.441703\pi$
$971$	11.3502	0.364244	0.182122	+	0.983276i	$0.441703\pi$
$972$	0.0594164	0.00190578
$973$	−19.3955	−0.621792
$974$	30.1619	0.966449
$975$	4.25969	0.136419
$976$	3.52708	0.112899
$977$	−0.154109	−0.00493038	−0.00246519	−	0.999997i	$-0.500785\pi$
$977$	−0.154109	−0.00493038	−0.00246519	+	0.999997i	$0.500785\pi$
$978$	20.6870	0.661499
$979$	12.3215	0.393797
$980$	−0.00343853	−0.000109840 0
$981$	5.75126	0.183624
$982$	−19.5975	−0.625382
$983$	−19.3825	−0.618207	−0.309104	−	0.951028i	$-0.600029\pi$
$983$	−19.3825	−0.618207	−0.309104	+	0.951028i	$0.600029\pi$
$984$	−7.32196	−0.233416
$985$	−22.0479	−0.702504
$986$	1.23928	0.0394667
$987$	−7.63099	−0.242897
$988$	−1.23828	−0.0393949
$989$	−5.82551	−0.185241
$990$	8.53883	0.271382
$991$	8.46224	0.268812	0.134406	−	0.990926i	$-0.457087\pi$
$991$	8.46224	0.268812	0.134406	+	0.990926i	$0.457087\pi$
$992$	0.209519	0.00665224
$993$	31.2124	0.990497
$994$	−42.0440	−1.33355
$995$	19.0314	0.603335
$996$	0.368866	0.0116880
$997$	−20.4735	−0.648401	−0.324201	−	0.945988i	$-0.605095\pi$
$997$	−20.4735	−0.648401	−0.324201	+	0.945988i	$0.605095\pi$
$998$	27.6285	0.874564
$999$	−1.43634	−0.0454438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.e.1.23	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.e.1.23	✓	31	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)

\(f(q)\)	\(=\)	\(q+1.39305 q^{2} -1.00000 q^{3} -0.0594164 q^{4} -1.00000 q^{5} -1.39305 q^{6} -2.63479 q^{7} -2.86887 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.39305 q^{2} -1.00000 q^{3} -0.0594164 q^{4} -1.00000 q^{5} -1.39305 q^{6} -2.63479 q^{7} -2.86887 q^{8} +1.00000 q^{9} -1.39305 q^{10} -6.12960 q^{11} +0.0594164 q^{12} -4.25969 q^{13} -3.67039 q^{14} +1.00000 q^{15} -3.87764 q^{16} -0.114637 q^{17} +1.39305 q^{18} -4.89254 q^{19} +0.0594164 q^{20} +2.63479 q^{21} -8.53883 q^{22} +1.07466 q^{23} +2.86887 q^{24} +1.00000 q^{25} -5.93395 q^{26} -1.00000 q^{27} +0.156550 q^{28} -7.76026 q^{29} +1.39305 q^{30} +0.623574 q^{31} +0.335997 q^{32} +6.12960 q^{33} -0.159696 q^{34} +2.63479 q^{35} -0.0594164 q^{36} +1.43634 q^{37} -6.81554 q^{38} +4.25969 q^{39} +2.86887 q^{40} -2.55222 q^{41} +3.67039 q^{42} -5.42082 q^{43} +0.364199 q^{44} -1.00000 q^{45} +1.49705 q^{46} -2.89624 q^{47} +3.87764 q^{48} -0.0578718 q^{49} +1.39305 q^{50} +0.114637 q^{51} +0.253095 q^{52} +0.713581 q^{53} -1.39305 q^{54} +6.12960 q^{55} +7.55887 q^{56} +4.89254 q^{57} -10.8104 q^{58} -12.4880 q^{59} -0.0594164 q^{60} -0.909596 q^{61} +0.868669 q^{62} -2.63479 q^{63} +8.22333 q^{64} +4.25969 q^{65} +8.53883 q^{66} -14.2593 q^{67} +0.00681134 q^{68} -1.07466 q^{69} +3.67039 q^{70} +11.4549 q^{71} -2.86887 q^{72} -11.2580 q^{73} +2.00089 q^{74} -1.00000 q^{75} +0.290697 q^{76} +16.1502 q^{77} +5.93395 q^{78} +8.76451 q^{79} +3.87764 q^{80} +1.00000 q^{81} -3.55536 q^{82} +6.20815 q^{83} -0.156550 q^{84} +0.114637 q^{85} -7.55146 q^{86} +7.76026 q^{87} +17.5850 q^{88} -2.01016 q^{89} -1.39305 q^{90} +11.2234 q^{91} -0.0638521 q^{92} -0.623574 q^{93} -4.03461 q^{94} +4.89254 q^{95} -0.335997 q^{96} +10.5717 q^{97} -0.0806182 q^{98} -6.12960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

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