LMFDB - Embedded newform 6041.2.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$112$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71246 q^{2} -0.244067 q^{3} +5.35744 q^{4} -2.10613 q^{5} +0.662022 q^{6} -1.00000 q^{7} -9.10692 q^{8} -2.94043 q^{9} +O(q^{10})$	\(q-2.71246 q^{2} -0.244067 q^{3} +5.35744 q^{4} -2.10613 q^{5} +0.662022 q^{6} -1.00000 q^{7} -9.10692 q^{8} -2.94043 q^{9} +5.71281 q^{10} -5.79283 q^{11} -1.30757 q^{12} +6.38359 q^{13} +2.71246 q^{14} +0.514038 q^{15} +13.9873 q^{16} -2.07387 q^{17} +7.97580 q^{18} -8.19526 q^{19} -11.2835 q^{20} +0.244067 q^{21} +15.7128 q^{22} +4.78009 q^{23} +2.22270 q^{24} -0.564196 q^{25} -17.3152 q^{26} +1.44986 q^{27} -5.35744 q^{28} +4.34456 q^{29} -1.39431 q^{30} +3.75853 q^{31} -19.7261 q^{32} +1.41384 q^{33} +5.62529 q^{34} +2.10613 q^{35} -15.7532 q^{36} -4.73131 q^{37} +22.2293 q^{38} -1.55803 q^{39} +19.1804 q^{40} -7.81088 q^{41} -0.662022 q^{42} +1.43726 q^{43} -31.0348 q^{44} +6.19294 q^{45} -12.9658 q^{46} +7.69111 q^{47} -3.41383 q^{48} +1.00000 q^{49} +1.53036 q^{50} +0.506164 q^{51} +34.1997 q^{52} -6.96631 q^{53} -3.93270 q^{54} +12.2005 q^{55} +9.10692 q^{56} +2.00019 q^{57} -11.7844 q^{58} -10.8931 q^{59} +2.75393 q^{60} -7.29851 q^{61} -10.1948 q^{62} +2.94043 q^{63} +25.5317 q^{64} -13.4447 q^{65} -3.83499 q^{66} -10.2315 q^{67} -11.1106 q^{68} -1.16666 q^{69} -5.71281 q^{70} -13.2849 q^{71} +26.7783 q^{72} -5.04928 q^{73} +12.8335 q^{74} +0.137702 q^{75} -43.9056 q^{76} +5.79283 q^{77} +4.22608 q^{78} -7.12174 q^{79} -29.4591 q^{80} +8.46743 q^{81} +21.1867 q^{82} -13.0426 q^{83} +1.30757 q^{84} +4.36785 q^{85} -3.89852 q^{86} -1.06036 q^{87} +52.7549 q^{88} +11.0012 q^{89} -16.7981 q^{90} -6.38359 q^{91} +25.6090 q^{92} -0.917333 q^{93} -20.8618 q^{94} +17.2603 q^{95} +4.81449 q^{96} -3.68194 q^{97} -2.71246 q^{98} +17.0334 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) $ 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * 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 $

$2$	−2.71246	−1.91800	−0.958999	−	0.283408i	$-0.908535\pi$
$2$	−2.71246	−1.91800	−0.958999	+	0.283408i	$0.908535\pi$
$3$	−0.244067	−0.140912	−0.0704561	−	0.997515i	$-0.522445\pi$
$3$	−0.244067	−0.140912	−0.0704561	+	0.997515i	$0.522445\pi$
$4$	5.35744	2.67872
$5$	−2.10613	−0.941892	−0.470946	−	0.882162i	$-0.656087\pi$
$5$	−2.10613	−0.941892	−0.470946	+	0.882162i	$0.656087\pi$
$6$	0.662022	0.270270
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−9.10692	−3.21978
$9$	−2.94043	−0.980144
$10$	5.71281	1.80655
$11$	−5.79283	−1.74661	−0.873303	−	0.487178i	$-0.838026\pi$
$11$	−5.79283	−1.74661	−0.873303	+	0.487178i	$0.838026\pi$
$12$	−1.30757	−0.377464
$13$	6.38359	1.77049	0.885245	−	0.465125i	$-0.153991\pi$
$13$	6.38359	1.77049	0.885245	+	0.465125i	$0.153991\pi$
$14$	2.71246	0.724935
$15$	0.514038	0.132724
$16$	13.9873	3.49682
$17$	−2.07387	−0.502987	−0.251494	−	0.967859i	$-0.580922\pi$
$17$	−2.07387	−0.502987	−0.251494	+	0.967859i	$0.580922\pi$
$18$	7.97580	1.87991
$19$	−8.19526	−1.88012	−0.940061	−	0.341007i	$-0.889232\pi$
$19$	−8.19526	−1.88012	−0.940061	+	0.341007i	$0.889232\pi$
$20$	−11.2835	−2.52306
$21$	0.244067	0.0532598
$22$	15.7128	3.34999
$23$	4.78009	0.996717	0.498359	−	0.866971i	$-0.333936\pi$
$23$	4.78009	0.996717	0.498359	+	0.866971i	$0.333936\pi$
$24$	2.22270	0.453707
$25$	−0.564196	−0.112839
$26$	−17.3152	−3.39580
$27$	1.44986	0.279026
$28$	−5.35744	−1.01246
$29$	4.34456	0.806765	0.403382	−	0.915032i	$-0.367834\pi$
$29$	4.34456	0.806765	0.403382	+	0.915032i	$0.367834\pi$
$30$	−1.39431	−0.254565
$31$	3.75853	0.675051	0.337526	−	0.941316i	$-0.390410\pi$
$31$	3.75853	0.675051	0.337526	+	0.941316i	$0.390410\pi$
$32$	−19.7261	−3.48711
$33$	1.41384	0.246118
$34$	5.62529	0.964729
$35$	2.10613	0.356002
$36$	−15.7532	−2.62553
$37$	−4.73131	−0.777822	−0.388911	−	0.921275i	$-0.627149\pi$
$37$	−4.73131	−0.777822	−0.388911	+	0.921275i	$0.627149\pi$
$38$	22.2293	3.60607
$39$	−1.55803	−0.249484
$40$	19.1804	3.03269
$41$	−7.81088	−1.21985	−0.609927	−	0.792457i	$-0.708801\pi$
$41$	−7.81088	−1.21985	−0.609927	+	0.792457i	$0.708801\pi$
$42$	−0.662022	−0.102152
$43$	1.43726	0.219181	0.109590	−	0.993977i	$-0.465046\pi$
$43$	1.43726	0.219181	0.109590	+	0.993977i	$0.465046\pi$
$44$	−31.0348	−4.67867
$45$	6.19294	0.923190
$46$	−12.9658	−1.91170
$47$	7.69111	1.12186	0.560932	−	0.827862i	$-0.310443\pi$
$47$	7.69111	1.12186	0.560932	+	0.827862i	$0.310443\pi$
$48$	−3.41383	−0.492744
$49$	1.00000	0.142857
$50$	1.53036	0.216426
$51$	0.506164	0.0708771
$52$	34.1997	4.74265
$53$	−6.96631	−0.956896	−0.478448	−	0.878116i	$-0.658800\pi$
$53$	−6.96631	−0.956896	−0.478448	+	0.878116i	$0.658800\pi$
$54$	−3.93270	−0.535172
$55$	12.2005	1.64511
$56$	9.10692	1.21696
$57$	2.00019	0.264932
$58$	−11.7844	−1.54737
$59$	−10.8931	−1.41816	−0.709078	−	0.705130i	$-0.750888\pi$
$59$	−10.8931	−1.41816	−0.709078	+	0.705130i	$0.750888\pi$
$60$	2.75393	0.355531
$61$	−7.29851	−0.934479	−0.467239	−	0.884131i	$-0.654751\pi$
$61$	−7.29851	−0.934479	−0.467239	+	0.884131i	$0.654751\pi$
$62$	−10.1948	−1.29475
$63$	2.94043	0.370460
$64$	25.5317	3.19146
$65$	−13.4447	−1.66761
$66$	−3.83499	−0.472054
$67$	−10.2315	−1.24997	−0.624987	−	0.780635i	$-0.714896\pi$
$67$	−10.2315	−1.24997	−0.624987	+	0.780635i	$0.714896\pi$
$68$	−11.1106	−1.34736
$69$	−1.16666	−0.140450
$70$	−5.71281	−0.682811
$71$	−13.2849	−1.57663	−0.788314	−	0.615274i	$-0.789046\pi$
$71$	−13.2849	−1.57663	−0.788314	+	0.615274i	$0.789046\pi$
$72$	26.7783	3.15585
$73$	−5.04928	−0.590973	−0.295487	−	0.955347i	$-0.595482\pi$
$73$	−5.04928	−0.590973	−0.295487	+	0.955347i	$0.595482\pi$
$74$	12.8335	1.49186
$75$	0.137702	0.0159004
$76$	−43.9056	−5.03632
$77$	5.79283	0.660155
$78$	4.22608	0.478510
$79$	−7.12174	−0.801258	−0.400629	−	0.916240i	$-0.631208\pi$
$79$	−7.12174	−0.801258	−0.400629	+	0.916240i	$0.631208\pi$
$80$	−29.4591	−3.29363
$81$	8.46743	0.940825
$82$	21.1867	2.33968
$83$	−13.0426	−1.43161	−0.715807	−	0.698298i	$-0.753941\pi$
$83$	−13.0426	−1.43161	−0.715807	+	0.698298i	$0.753941\pi$
$84$	1.30757	0.142668
$85$	4.36785	0.473760
$86$	−3.89852	−0.420388
$87$	−1.06036	−0.113683
$88$	52.7549	5.62369
$89$	11.0012	1.16613	0.583064	−	0.812426i	$-0.301854\pi$
$89$	11.0012	1.16613	0.583064	+	0.812426i	$0.301854\pi$
$90$	−16.7981	−1.77068
$91$	−6.38359	−0.669182
$92$	25.6090	2.66993
$93$	−0.917333	−0.0951230
$94$	−20.8618	−2.15173
$95$	17.2603	1.77087
$96$	4.81449	0.491377
$97$	−3.68194	−0.373844	−0.186922	−	0.982375i	$-0.559851\pi$
$97$	−3.68194	−0.373844	−0.186922	+	0.982375i	$0.559851\pi$
$98$	−2.71246	−0.274000
$99$	17.0334	1.71192
$100$	−3.02265	−0.302265
$101$	−15.7267	−1.56487	−0.782434	−	0.622733i	$-0.786022\pi$
$101$	−15.7267	−1.56487	−0.782434	+	0.622733i	$0.786022\pi$
$102$	−1.37295	−0.135942
$103$	−10.7354	−1.05779	−0.528897	−	0.848686i	$-0.677394\pi$
$103$	−10.7354	−1.05779	−0.528897	+	0.848686i	$0.677394\pi$
$104$	−58.1349	−5.70059
$105$	−0.514038	−0.0501650
$106$	18.8958	1.83532
$107$	−9.45487	−0.914037	−0.457018	−	0.889457i	$-0.651083\pi$
$107$	−9.45487	−0.914037	−0.457018	+	0.889457i	$0.651083\pi$
$108$	7.76756	0.747434
$109$	−12.1214	−1.16102	−0.580511	−	0.814252i	$-0.697147\pi$
$109$	−12.1214	−1.16102	−0.580511	+	0.814252i	$0.697147\pi$
$110$	−33.0933	−3.15533
$111$	1.15476	0.109605
$112$	−13.9873	−1.32167
$113$	−10.7445	−1.01075	−0.505377	−	0.862899i	$-0.668647\pi$
$113$	−10.7445	−1.01075	−0.505377	+	0.862899i	$0.668647\pi$
$114$	−5.42544	−0.508139
$115$	−10.0675	−0.938800
$116$	23.2757	2.16110
$117$	−18.7705	−1.73534
$118$	29.5470	2.72002
$119$	2.07387	0.190111
$120$	−4.68130	−0.427343
$121$	22.5569	2.05063
$122$	19.7969	1.79233
$123$	1.90638	0.171892
$124$	20.1361	1.80827
$125$	11.7189	1.04817
$126$	−7.97580	−0.710541
$127$	6.95688	0.617323	0.308661	−	0.951172i	$-0.400119\pi$
$127$	6.95688	0.617323	0.308661	+	0.951172i	$0.400119\pi$
$128$	−29.8014	−2.63410
$129$	−0.350789	−0.0308852
$130$	36.4682	3.19848
$131$	−19.9888	−1.74643	−0.873216	−	0.487333i	$-0.837970\pi$
$131$	−19.9888	−1.74643	−0.873216	+	0.487333i	$0.837970\pi$
$132$	7.57456	0.659281
$133$	8.19526	0.710619
$134$	27.7525	2.39745
$135$	−3.05361	−0.262813
$136$	18.8866	1.61951
$137$	−13.3450	−1.14014	−0.570069	−	0.821597i	$-0.693084\pi$
$137$	−13.3450	−1.14014	−0.570069	+	0.821597i	$0.693084\pi$
$138$	3.16453	0.269382
$139$	9.55328	0.810298	0.405149	−	0.914251i	$-0.367220\pi$
$139$	9.55328	0.810298	0.405149	+	0.914251i	$0.367220\pi$
$140$	11.2835	0.953629
$141$	−1.87715	−0.158084
$142$	36.0348	3.02397
$143$	−36.9791	−3.09235
$144$	−41.1286	−3.42738
$145$	−9.15023	−0.759885
$146$	13.6960	1.13349
$147$	−0.244067	−0.0201303
$148$	−25.3477	−2.08357
$149$	−19.4316	−1.59190	−0.795951	−	0.605361i	$-0.793029\pi$
$149$	−19.4316	−1.59190	−0.795951	+	0.605361i	$0.793029\pi$
$150$	−0.373510	−0.0304970
$151$	20.6043	1.67675	0.838375	−	0.545094i	$-0.183506\pi$
$151$	20.6043	1.67675	0.838375	+	0.545094i	$0.183506\pi$
$152$	74.6335	6.05358
$153$	6.09807	0.493000
$154$	−15.7128	−1.26618
$155$	−7.91596	−0.635825
$156$	−8.34703	−0.668297
$157$	10.6114	0.846882	0.423441	−	0.905924i	$-0.360822\pi$
$157$	10.6114	0.846882	0.423441	+	0.905924i	$0.360822\pi$
$158$	19.3174	1.53681
$159$	1.70025	0.134838
$160$	41.5458	3.28448
$161$	−4.78009	−0.376724
$162$	−22.9676	−1.80450
$163$	6.22430	0.487525	0.243762	−	0.969835i	$-0.421618\pi$
$163$	6.22430	0.487525	0.243762	+	0.969835i	$0.421618\pi$
$164$	−41.8463	−3.26765
$165$	−2.97774	−0.231817
$166$	35.3776	2.74583
$167$	16.7804	1.29851	0.649254	−	0.760571i	$-0.275081\pi$
$167$	16.7804	1.29851	0.649254	+	0.760571i	$0.275081\pi$
$168$	−2.22270	−0.171485
$169$	27.7503	2.13464
$170$	−11.8476	−0.908671
$171$	24.0976	1.84279
$172$	7.70005	0.587123
$173$	−10.8929	−0.828170	−0.414085	−	0.910238i	$-0.635898\pi$
$173$	−10.8929	−0.828170	−0.414085	+	0.910238i	$0.635898\pi$
$174$	2.87620	0.218044
$175$	0.564196	0.0426492
$176$	−81.0260	−6.10756
$177$	2.65864	0.199835
$178$	−29.8404	−2.23663
$179$	17.1634	1.28286	0.641428	−	0.767183i	$-0.278342\pi$
$179$	17.1634	1.28286	0.641428	+	0.767183i	$0.278342\pi$
$180$	33.1783	2.47297
$181$	−17.7318	−1.31799	−0.658997	−	0.752146i	$-0.729019\pi$
$181$	−17.7318	−1.31799	−0.658997	+	0.752146i	$0.729019\pi$
$182$	17.3152	1.28349
$183$	1.78133	0.131679
$184$	−43.5319	−3.20921
$185$	9.96477	0.732625
$186$	2.48823	0.182446
$187$	12.0136	0.878521
$188$	41.2047	3.00516
$189$	−1.44986	−0.105462
$190$	−46.8179	−3.39653
$191$	9.91899	0.717713	0.358857	−	0.933393i	$-0.383167\pi$
$191$	9.91899	0.717713	0.358857	+	0.933393i	$0.383167\pi$
$192$	−6.23144	−0.449715
$193$	1.52598	0.109842	0.0549212	−	0.998491i	$-0.482509\pi$
$193$	1.52598	0.109842	0.0549212	+	0.998491i	$0.482509\pi$
$194$	9.98711	0.717033
$195$	3.28141	0.234987
$196$	5.35744	0.382674
$197$	−0.256632	−0.0182843	−0.00914214	−	0.999958i	$-0.502910\pi$
$197$	−0.256632	−0.0182843	−0.00914214	+	0.999958i	$0.502910\pi$
$198$	−46.2025	−3.28347
$199$	24.0375	1.70397	0.851986	−	0.523564i	$-0.175398\pi$
$199$	24.0375	1.70397	0.851986	+	0.523564i	$0.175398\pi$
$200$	5.13809	0.363318
$201$	2.49717	0.176137
$202$	42.6581	3.00142
$203$	−4.34456	−0.304928
$204$	2.71174	0.189860
$205$	16.4508	1.14897
$206$	29.1195	2.02885
$207$	−14.0555	−0.976926
$208$	89.2891	6.19108
$209$	47.4738	3.28383
$210$	1.39431	0.0962164
$211$	16.4980	1.13577	0.567886	−	0.823107i	$-0.307761\pi$
$211$	16.4980	1.13577	0.567886	+	0.823107i	$0.307761\pi$
$212$	−37.3216	−2.56326
$213$	3.24241	0.222166
$214$	25.6459	1.75312
$215$	−3.02707	−0.206444
$216$	−13.2038	−0.898404
$217$	−3.75853	−0.255145
$218$	32.8789	2.22684
$219$	1.23236	0.0832753
$220$	65.3634	4.40680
$221$	−13.2387	−0.890534
$222$	−3.13223	−0.210222
$223$	−11.4031	−0.763609	−0.381805	−	0.924243i	$-0.624697\pi$
$223$	−11.4031	−0.763609	−0.381805	+	0.924243i	$0.624697\pi$
$224$	19.7261	1.31800
$225$	1.65898	0.110599
$226$	29.1439	1.93862
$227$	−5.59800	−0.371552	−0.185776	−	0.982592i	$-0.559480\pi$
$227$	−5.59800	−0.371552	−0.185776	+	0.982592i	$0.559480\pi$
$228$	10.7159	0.709679
$229$	−22.3341	−1.47588	−0.737940	−	0.674866i	$-0.764201\pi$
$229$	−22.3341	−1.47588	−0.737940	+	0.674866i	$0.764201\pi$
$230$	27.3077	1.80062
$231$	−1.41384	−0.0930239
$232$	−39.5656	−2.59761
$233$	8.44993	0.553573	0.276787	−	0.960931i	$-0.410731\pi$
$233$	8.44993	0.553573	0.276787	+	0.960931i	$0.410731\pi$
$234$	50.9143	3.32837
$235$	−16.1985	−1.05667
$236$	−58.3589	−3.79884
$237$	1.73818	0.112907
$238$	−5.62529	−0.364633
$239$	−3.09804	−0.200396	−0.100198	−	0.994968i	$-0.531948\pi$
$239$	−3.09804	−0.200396	−0.100198	+	0.994968i	$0.531948\pi$
$240$	7.18999	0.464112
$241$	10.8986	0.702038	0.351019	−	0.936368i	$-0.385835\pi$
$241$	10.8986	0.702038	0.351019	+	0.936368i	$0.385835\pi$
$242$	−61.1848	−3.93311
$243$	−6.41621	−0.411600
$244$	−39.1013	−2.50321
$245$	−2.10613	−0.134556
$246$	−5.17098	−0.329690
$247$	−52.3152	−3.32874
$248$	−34.2286	−2.17352
$249$	3.18328	0.201732
$250$	−31.7872	−2.01040
$251$	7.54609	0.476305	0.238152	−	0.971228i	$-0.423458\pi$
$251$	7.54609	0.476305	0.238152	+	0.971228i	$0.423458\pi$
$252$	15.7532	0.992357
$253$	−27.6903	−1.74087
$254$	−18.8702	−1.18402
$255$	−1.06605	−0.0667586
$256$	29.7719	1.86074
$257$	−12.1926	−0.760553	−0.380277	−	0.924873i	$-0.624171\pi$
$257$	−12.1926	−0.760553	−0.380277	+	0.924873i	$0.624171\pi$
$258$	0.951500	0.0592378
$259$	4.73131	0.293989
$260$	−72.0292	−4.46706
$261$	−12.7749	−0.790745
$262$	54.2189	3.34965
$263$	−3.37165	−0.207905	−0.103952	−	0.994582i	$-0.533149\pi$
$263$	−3.37165	−0.207905	−0.103952	+	0.994582i	$0.533149\pi$
$264$	−12.8757	−0.792446
$265$	14.6720	0.901293
$266$	−22.2293	−1.36297
$267$	−2.68504	−0.164322
$268$	−54.8145	−3.34833
$269$	−9.32435	−0.568516	−0.284258	−	0.958748i	$-0.591747\pi$
$269$	−9.32435	−0.568516	−0.284258	+	0.958748i	$0.591747\pi$
$270$	8.28279	0.504075
$271$	2.59297	0.157512	0.0787558	−	0.996894i	$-0.474905\pi$
$271$	2.59297	0.157512	0.0787558	+	0.996894i	$0.474905\pi$
$272$	−29.0078	−1.75886
$273$	1.55803	0.0942960
$274$	36.1977	2.18678
$275$	3.26830	0.197086
$276$	−6.25032	−0.376225
$277$	−4.68116	−0.281263	−0.140632	−	0.990062i	$-0.544913\pi$
$277$	−4.68116	−0.281263	−0.140632	+	0.990062i	$0.544913\pi$
$278$	−25.9129	−1.55415
$279$	−11.0517	−0.661647
$280$	−19.1804	−1.14625
$281$	13.8732	0.827608	0.413804	−	0.910366i	$-0.364200\pi$
$281$	13.8732	0.827608	0.413804	+	0.910366i	$0.364200\pi$
$282$	5.09169	0.303206
$283$	10.8489	0.644902	0.322451	−	0.946586i	$-0.395493\pi$
$283$	10.8489	0.644902	0.322451	+	0.946586i	$0.395493\pi$
$284$	−71.1730	−4.22334
$285$	−4.21268	−0.249537
$286$	100.304	5.93112
$287$	7.81088	0.461062
$288$	58.0032	3.41787
$289$	−12.6991	−0.747004
$290$	24.8196	1.45746
$291$	0.898641	0.0526792
$292$	−27.0512	−1.58305
$293$	−1.70950	−0.0998700	−0.0499350	−	0.998752i	$-0.515901\pi$
$293$	−1.70950	−0.0998700	−0.0499350	+	0.998752i	$0.515901\pi$
$294$	0.662022	0.0386099
$295$	22.9422	1.33575
$296$	43.0876	2.50442
$297$	−8.39882	−0.487349
$298$	52.7076	3.05327
$299$	30.5141	1.76468
$300$	0.737729	0.0425928
$301$	−1.43726	−0.0828424
$302$	−55.8882	−3.21601
$303$	3.83838	0.220509
$304$	−114.629	−6.57444
$305$	15.3716	0.880178
$306$	−16.5408	−0.945573
$307$	12.8873	0.735519	0.367759	−	0.929921i	$-0.380125\pi$
$307$	12.8873	0.735519	0.367759	+	0.929921i	$0.380125\pi$
$308$	31.0348	1.76837
$309$	2.62017	0.149056
$310$	21.4717	1.21951
$311$	15.4677	0.877095	0.438548	−	0.898708i	$-0.355493\pi$
$311$	15.4677	0.877095	0.438548	+	0.898708i	$0.355493\pi$
$312$	14.1888	0.803283
$313$	−28.8099	−1.62843	−0.814217	−	0.580560i	$-0.802834\pi$
$313$	−28.8099	−1.62843	−0.814217	+	0.580560i	$0.802834\pi$
$314$	−28.7830	−1.62432
$315$	−6.19294	−0.348933
$316$	−38.1543	−2.14635
$317$	−2.80442	−0.157512	−0.0787559	−	0.996894i	$-0.525095\pi$
$317$	−2.80442	−0.157512	−0.0787559	+	0.996894i	$0.525095\pi$
$318$	−4.61185	−0.258620
$319$	−25.1673	−1.40910
$320$	−53.7731	−3.00601
$321$	2.30762	0.128799
$322$	12.9658	0.722556
$323$	16.9959	0.945677
$324$	45.3637	2.52021
$325$	−3.60160	−0.199781
$326$	−16.8832	−0.935072
$327$	2.95844	0.163602
$328$	71.1331	3.92767
$329$	−7.69111	−0.424025
$330$	8.07700	0.444624
$331$	−2.88773	−0.158724	−0.0793619	−	0.996846i	$-0.525288\pi$
$331$	−2.88773	−0.158724	−0.0793619	+	0.996846i	$0.525288\pi$
$332$	−69.8751	−3.83489
$333$	13.9121	0.762377
$334$	−45.5162	−2.49054
$335$	21.5489	1.17734
$336$	3.41383	0.186240
$337$	−26.1141	−1.42253	−0.711264	−	0.702925i	$-0.751877\pi$
$337$	−26.1141	−1.42253	−0.711264	+	0.702925i	$0.751877\pi$
$338$	−75.2715	−4.09423
$339$	2.62237	0.142428
$340$	23.4005	1.26907
$341$	−21.7725	−1.17905
$342$	−65.3638	−3.53447
$343$	−1.00000	−0.0539949
$344$	−13.0890	−0.705713
$345$	2.45715	0.132288
$346$	29.5465	1.58843
$347$	−1.67430	−0.0898814	−0.0449407	−	0.998990i	$-0.514310\pi$
$347$	−1.67430	−0.0898814	−0.0449407	+	0.998990i	$0.514310\pi$
$348$	−5.68084	−0.304525
$349$	3.31969	0.177699	0.0888494	−	0.996045i	$-0.471681\pi$
$349$	3.31969	0.177699	0.0888494	+	0.996045i	$0.471681\pi$
$350$	−1.53036	−0.0818012
$351$	9.25534	0.494014
$352$	114.270	6.09061
$353$	−1.52611	−0.0812268	−0.0406134	−	0.999175i	$-0.512931\pi$
$353$	−1.52611	−0.0812268	−0.0406134	+	0.999175i	$0.512931\pi$
$354$	−7.21145	−0.383284
$355$	27.9798	1.48501
$356$	58.9384	3.12373
$357$	−0.506164	−0.0267890
$358$	−46.5551	−2.46052
$359$	−24.6302	−1.29993	−0.649967	−	0.759963i	$-0.725217\pi$
$359$	−24.6302	−1.29993	−0.649967	+	0.759963i	$0.725217\pi$
$360$	−56.3986	−2.97247
$361$	48.1623	2.53486
$362$	48.0968	2.52791
$363$	−5.50541	−0.288959
$364$	−34.1997	−1.79255
$365$	10.6345	0.556633
$366$	−4.83178	−0.252561
$367$	−16.3042	−0.851074	−0.425537	−	0.904941i	$-0.639915\pi$
$367$	−16.3042	−0.851074	−0.425537	+	0.904941i	$0.639915\pi$
$368$	66.8604	3.48534
$369$	22.9674	1.19563
$370$	−27.0290	−1.40517
$371$	6.96631	0.361673
$372$	−4.91455	−0.254808
$373$	−19.1883	−0.993530	−0.496765	−	0.867885i	$-0.665479\pi$
$373$	−19.1883	−0.993530	−0.496765	+	0.867885i	$0.665479\pi$
$374$	−32.5864	−1.68500
$375$	−2.86021	−0.147701
$376$	−70.0423	−3.61216
$377$	27.7339	1.42837
$378$	3.93270	0.202276
$379$	−12.8381	−0.659451	−0.329726	−	0.944077i	$-0.606956\pi$
$379$	−12.8381	−0.659451	−0.329726	+	0.944077i	$0.606956\pi$
$380$	92.4711	4.74367
$381$	−1.69795	−0.0869884
$382$	−26.9049	−1.37657
$383$	−11.3848	−0.581736	−0.290868	−	0.956763i	$-0.593944\pi$
$383$	−11.3848	−0.581736	−0.290868	+	0.956763i	$0.593944\pi$
$384$	7.27355	0.371177
$385$	−12.2005	−0.621795
$386$	−4.13916	−0.210678
$387$	−4.22617	−0.214828
$388$	−19.7258	−1.00142
$389$	31.1393	1.57883	0.789413	−	0.613863i	$-0.210385\pi$
$389$	31.1393	1.57883	0.789413	+	0.613863i	$0.210385\pi$
$390$	−8.90070	−0.450704
$391$	−9.91328	−0.501336
$392$	−9.10692	−0.459969
$393$	4.87862	0.246094
$394$	0.696104	0.0350692
$395$	14.9993	0.754699
$396$	91.2556	4.58576
$397$	7.02653	0.352651	0.176326	−	0.984332i	$-0.443579\pi$
$397$	7.02653	0.352651	0.176326	+	0.984332i	$0.443579\pi$
$398$	−65.2007	−3.26822
$399$	−2.00019	−0.100135
$400$	−7.89157	−0.394578
$401$	33.9693	1.69635	0.848173	−	0.529719i	$-0.177703\pi$
$401$	33.9693	1.69635	0.848173	+	0.529719i	$0.177703\pi$
$402$	−6.77347	−0.337830
$403$	23.9929	1.19517
$404$	−84.2550	−4.19184
$405$	−17.8335	−0.886156
$406$	11.7844	0.584852
$407$	27.4077	1.35855
$408$	−4.60959	−0.228209
$409$	−22.7654	−1.12568	−0.562838	−	0.826568i	$-0.690290\pi$
$409$	−22.7654	−1.12568	−0.562838	+	0.826568i	$0.690290\pi$
$410$	−44.6221	−2.20373
$411$	3.25707	0.160659
$412$	−57.5145	−2.83353
$413$	10.8931	0.536012
$414$	38.1250	1.87374
$415$	27.4695	1.34843
$416$	−125.923	−6.17390
$417$	−2.33164	−0.114181
$418$	−128.771	−6.29838
$419$	13.4448	0.656822	0.328411	−	0.944535i	$-0.393487\pi$
$419$	13.4448	0.656822	0.328411	+	0.944535i	$0.393487\pi$
$420$	−2.75393	−0.134378
$421$	14.4876	0.706084	0.353042	−	0.935607i	$-0.385147\pi$
$421$	14.4876	0.706084	0.353042	+	0.935607i	$0.385147\pi$
$422$	−44.7503	−2.17841
$423$	−22.6152	−1.09959
$424$	63.4416	3.08100
$425$	1.17007	0.0567567
$426$	−8.79490	−0.426114
$427$	7.29851	0.353200
$428$	−50.6539	−2.44845
$429$	9.02538	0.435750
$430$	8.21080	0.395960
$431$	29.9457	1.44243	0.721216	−	0.692710i	$-0.243583\pi$
$431$	29.9457	1.44243	0.721216	+	0.692710i	$0.243583\pi$
$432$	20.2796	0.975705
$433$	29.5979	1.42239	0.711193	−	0.702997i	$-0.248155\pi$
$433$	29.5979	1.42239	0.711193	+	0.702997i	$0.248155\pi$
$434$	10.1948	0.489368
$435$	2.23327	0.107077
$436$	−64.9398	−3.11005
$437$	−39.1741	−1.87395
$438$	−3.34273	−0.159722
$439$	6.57417	0.313768	0.156884	−	0.987617i	$-0.449855\pi$
$439$	6.57417	0.313768	0.156884	+	0.987617i	$0.449855\pi$
$440$	−111.109	−5.29691
$441$	−2.94043	−0.140021
$442$	35.9096	1.70804
$443$	26.5960	1.26361	0.631806	−	0.775126i	$-0.282314\pi$
$443$	26.5960	1.26361	0.631806	+	0.775126i	$0.282314\pi$
$444$	6.18654	0.293600
$445$	−23.1701	−1.09837
$446$	30.9305	1.46460
$447$	4.74263	0.224319
$448$	−25.5317	−1.20626
$449$	3.59934	0.169864	0.0849318	−	0.996387i	$-0.472933\pi$
$449$	3.59934	0.169864	0.0849318	+	0.996387i	$0.472933\pi$
$450$	−4.49992	−0.212128
$451$	45.2472	2.13061
$452$	−57.5628	−2.70753
$453$	−5.02882	−0.236275
$454$	15.1844	0.712637
$455$	13.4447	0.630298
$456$	−18.2156	−0.853023
$457$	−14.1643	−0.662579	−0.331289	−	0.943529i	$-0.607484\pi$
$457$	−14.1643	−0.662579	−0.331289	+	0.943529i	$0.607484\pi$
$458$	60.5804	2.83074
$459$	−3.00683	−0.140347
$460$	−53.9361	−2.51478
$461$	1.05865	0.0493065	0.0246532	−	0.999696i	$-0.492152\pi$
$461$	1.05865	0.0493065	0.0246532	+	0.999696i	$0.492152\pi$
$462$	3.83499	0.178420
$463$	−42.6168	−1.98057	−0.990284	−	0.139057i	$-0.955593\pi$
$463$	−42.6168	−1.98057	−0.990284	+	0.139057i	$0.955593\pi$
$464$	60.7686	2.82111
$465$	1.93203	0.0895956
$466$	−22.9201	−1.06175
$467$	15.1910	0.702957	0.351478	−	0.936196i	$-0.385679\pi$
$467$	15.1910	0.702957	0.351478	+	0.936196i	$0.385679\pi$
$468$	−100.562	−4.64848
$469$	10.2315	0.472446
$470$	43.9378	2.02670
$471$	−2.58990	−0.119336
$472$	99.2022	4.56615
$473$	−8.32582	−0.382822
$474$	−4.71475	−0.216556
$475$	4.62373	0.212151
$476$	11.1106	0.509255
$477$	20.4839	0.937895
$478$	8.40332	0.384359
$479$	20.7233	0.946871	0.473435	−	0.880829i	$-0.343014\pi$
$479$	20.7233	0.946871	0.473435	+	0.880829i	$0.343014\pi$
$480$	−10.1400	−0.462824
$481$	−30.2027	−1.37713
$482$	−29.5619	−1.34651
$483$	1.16666	0.0530850
$484$	120.847	5.49306
$485$	7.75466	0.352121
$486$	17.4037	0.789449
$487$	27.7567	1.25778	0.628889	−	0.777495i	$-0.283510\pi$
$487$	27.7567	1.25778	0.628889	+	0.777495i	$0.283510\pi$
$488$	66.4669	3.00882
$489$	−1.51915	−0.0686982
$490$	5.71281	0.258078
$491$	−15.1008	−0.681491	−0.340745	−	0.940156i	$-0.610679\pi$
$491$	−15.1008	−0.681491	−0.340745	+	0.940156i	$0.610679\pi$
$492$	10.2133	0.460452
$493$	−9.01006	−0.405793
$494$	141.903	6.38451
$495$	−35.8747	−1.61245
$496$	52.5715	2.36053
$497$	13.2849	0.595909
$498$	−8.63451	−0.386922
$499$	−7.66426	−0.343099	−0.171550	−	0.985175i	$-0.554877\pi$
$499$	−7.66426	−0.343099	−0.171550	+	0.985175i	$0.554877\pi$
$500$	62.7835	2.80777
$501$	−4.09555	−0.182976
$502$	−20.4685	−0.913552
$503$	−10.8203	−0.482455	−0.241228	−	0.970469i	$-0.577550\pi$
$503$	−10.8203	−0.482455	−0.241228	+	0.970469i	$0.577550\pi$
$504$	−26.7783	−1.19280
$505$	33.1226	1.47394
$506$	75.1087	3.33899
$507$	−6.77293	−0.300796
$508$	37.2710	1.65363
$509$	−4.04069	−0.179100	−0.0895502	−	0.995982i	$-0.528543\pi$
$509$	−4.04069	−0.179100	−0.0895502	+	0.995982i	$0.528543\pi$
$510$	2.89161	0.128043
$511$	5.04928	0.223367
$512$	−21.1522	−0.934803
$513$	−11.8820	−0.524604
$514$	33.0719	1.45874
$515$	22.6103	0.996328
$516$	−1.87933	−0.0827328
$517$	−44.5533	−1.95945
$518$	−12.8335	−0.563871
$519$	2.65859	0.116699
$520$	122.440	5.36934
$521$	−30.3360	−1.32904	−0.664522	−	0.747269i	$-0.731365\pi$
$521$	−30.3360	−1.32904	−0.664522	+	0.747269i	$0.731365\pi$
$522$	34.6514	1.51665
$523$	−24.8607	−1.08708	−0.543540	−	0.839383i	$-0.682917\pi$
$523$	−24.8607	−1.08708	−0.543540	+	0.839383i	$0.682917\pi$
$524$	−107.089	−4.67820
$525$	−0.137702	−0.00600980
$526$	9.14547	0.398761
$527$	−7.79470	−0.339542
$528$	19.7758	0.860630
$529$	−0.150758	−0.00655471
$530$	−39.7972	−1.72868
$531$	32.0303	1.39000
$532$	43.9056	1.90355
$533$	−49.8615	−2.15974
$534$	7.28306	0.315169
$535$	19.9132	0.860924
$536$	93.1772	4.02464
$537$	−4.18903	−0.180770
$538$	25.2919	1.09041
$539$	−5.79283	−0.249515
$540$	−16.3595	−0.704002
$541$	−33.4651	−1.43878	−0.719388	−	0.694609i	$-0.755577\pi$
$541$	−33.4651	−1.43878	−0.719388	+	0.694609i	$0.755577\pi$
$542$	−7.03332	−0.302107
$543$	4.32775	0.185721
$544$	40.9093	1.75397
$545$	25.5294	1.09356
$546$	−4.22608	−0.180860
$547$	32.6367	1.39544	0.697722	−	0.716369i	$-0.254197\pi$
$547$	32.6367	1.39544	0.697722	+	0.716369i	$0.254197\pi$
$548$	−71.4949	−3.05411
$549$	21.4608	0.915923
$550$	−8.86512	−0.378010
$551$	−35.6048	−1.51682
$552$	10.6247	0.452217
$553$	7.12174	0.302847
$554$	12.6974	0.539463
$555$	−2.43207	−0.103236
$556$	51.1811	2.17056
$557$	26.5599	1.12538	0.562689	−	0.826669i	$-0.309767\pi$
$557$	26.5599	1.12538	0.562689	+	0.826669i	$0.309767\pi$
$558$	29.9773	1.26904
$559$	9.17490	0.388057
$560$	29.4591	1.24487
$561$	−2.93212	−0.123794
$562$	−37.6306	−1.58735
$563$	−21.0957	−0.889080	−0.444540	−	0.895759i	$-0.646633\pi$
$563$	−21.0957	−0.889080	−0.444540	+	0.895759i	$0.646633\pi$
$564$	−10.0567	−0.423464
$565$	22.6293	0.952021
$566$	−29.4273	−1.23692
$567$	−8.46743	−0.355599
$568$	120.984	5.07640
$569$	27.5918	1.15671	0.578355	−	0.815785i	$-0.303695\pi$
$569$	27.5918	1.15671	0.578355	+	0.815785i	$0.303695\pi$
$570$	11.4267	0.478613
$571$	3.43717	0.143841	0.0719205	−	0.997410i	$-0.477087\pi$
$571$	3.43717	0.143841	0.0719205	+	0.997410i	$0.477087\pi$
$572$	−198.113	−8.28353
$573$	−2.42090	−0.101135
$574$	−21.1867	−0.884316
$575$	−2.69691	−0.112469
$576$	−75.0741	−3.12809
$577$	−19.2595	−0.801782	−0.400891	−	0.916126i	$-0.631299\pi$
$577$	−19.2595	−0.801782	−0.400891	+	0.916126i	$0.631299\pi$
$578$	34.4457	1.43275
$579$	−0.372442	−0.0154781
$580$	−49.0218	−2.03552
$581$	13.0426	0.541099
$582$	−2.43753	−0.101039
$583$	40.3547	1.67132
$584$	45.9833	1.90280
$585$	39.5332	1.63450
$586$	4.63695	0.191551
$587$	36.1468	1.49194	0.745970	−	0.665980i	$-0.231986\pi$
$587$	36.1468	1.49194	0.745970	+	0.665980i	$0.231986\pi$
$588$	−1.30757	−0.0539235
$589$	−30.8021	−1.26918
$590$	−62.2299	−2.56197
$591$	0.0626355	0.00257648
$592$	−66.1781	−2.71990
$593$	10.4099	0.427483	0.213741	−	0.976890i	$-0.431435\pi$
$593$	10.4099	0.427483	0.213741	+	0.976890i	$0.431435\pi$
$594$	22.7815	0.934735
$595$	−4.36785	−0.179064
$596$	−104.104	−4.26426
$597$	−5.86676	−0.240111
$598$	−82.7684	−3.38465
$599$	−37.8971	−1.54843	−0.774217	−	0.632921i	$-0.781856\pi$
$599$	−37.8971	−1.54843	−0.774217	+	0.632921i	$0.781856\pi$
$600$	−1.25404	−0.0511959
$601$	−10.8412	−0.442222	−0.221111	−	0.975249i	$-0.570968\pi$
$601$	−10.8412	−0.442222	−0.221111	+	0.975249i	$0.570968\pi$
$602$	3.89852	0.158892
$603$	30.0850	1.22515
$604$	110.386	4.49154
$605$	−47.5079	−1.93147
$606$	−10.4115	−0.422936
$607$	5.46484	0.221811	0.110905	−	0.993831i	$-0.464625\pi$
$607$	5.46484	0.221811	0.110905	+	0.993831i	$0.464625\pi$
$608$	161.660	6.55619
$609$	1.06036	0.0429681
$610$	−41.6950	−1.68818
$611$	49.0969	1.98625
$612$	32.6701	1.32061
$613$	−10.3904	−0.419664	−0.209832	−	0.977737i	$-0.567292\pi$
$613$	−10.3904	−0.419664	−0.209832	+	0.977737i	$0.567292\pi$
$614$	−34.9564	−1.41072
$615$	−4.01509	−0.161904
$616$	−52.7549	−2.12555
$617$	18.7406	0.754467	0.377234	−	0.926118i	$-0.376875\pi$
$617$	18.7406	0.754467	0.377234	+	0.926118i	$0.376875\pi$
$618$	−7.10710	−0.285890
$619$	34.3178	1.37935	0.689674	−	0.724120i	$-0.257754\pi$
$619$	34.3178	1.37935	0.689674	+	0.724120i	$0.257754\pi$
$620$	−42.4093	−1.70320
$621$	6.93048	0.278111
$622$	−41.9556	−1.68227
$623$	−11.0012	−0.440755
$624$	−21.7925	−0.872399
$625$	−21.8607	−0.874428
$626$	78.1458	3.12334
$627$	−11.5868	−0.462732
$628$	56.8500	2.26856
$629$	9.81212	0.391235
$630$	16.7981	0.669253
$631$	−20.6228	−0.820981	−0.410491	−	0.911865i	$-0.634643\pi$
$631$	−20.6228	−0.820981	−0.410491	+	0.911865i	$0.634643\pi$
$632$	64.8571	2.57988
$633$	−4.02663	−0.160044
$634$	7.60688	0.302108
$635$	−14.6521	−0.581452
$636$	9.10897	0.361194
$637$	6.38359	0.252927
$638$	68.2653	2.70265
$639$	39.0633	1.54532
$640$	62.7658	2.48104
$641$	18.1420	0.716565	0.358282	−	0.933613i	$-0.383363\pi$
$641$	18.1420	0.716565	0.358282	+	0.933613i	$0.383363\pi$
$642$	−6.25933	−0.247036
$643$	−7.52660	−0.296820	−0.148410	−	0.988926i	$-0.547416\pi$
$643$	−7.52660	−0.296820	−0.148410	+	0.988926i	$0.547416\pi$
$644$	−25.6090	−1.00914
$645$	0.738808	0.0290905
$646$	−46.1007	−1.81381
$647$	15.6837	0.616591	0.308296	−	0.951291i	$-0.400241\pi$
$647$	15.6837	0.616591	0.308296	+	0.951291i	$0.400241\pi$
$648$	−77.1122	−3.02925
$649$	63.1017	2.47696
$650$	9.76919	0.383179
$651$	0.917333	0.0359531
$652$	33.3463	1.30594
$653$	7.55905	0.295809	0.147904	−	0.989002i	$-0.452747\pi$
$653$	7.55905	0.295809	0.147904	+	0.989002i	$0.452747\pi$
$654$	−8.02465	−0.313789
$655$	42.0992	1.64495
$656$	−109.253	−4.26561
$657$	14.8470	0.579239
$658$	20.8618	0.813279
$659$	−32.1712	−1.25321	−0.626606	−	0.779336i	$-0.715556\pi$
$659$	−32.1712	−1.25321	−0.626606	+	0.779336i	$0.715556\pi$
$660$	−15.9531	−0.620972
$661$	−2.17677	−0.0846664	−0.0423332	−	0.999104i	$-0.513479\pi$
$661$	−2.17677	−0.0846664	−0.0423332	+	0.999104i	$0.513479\pi$
$662$	7.83285	0.304432
$663$	3.23114	0.125487
$664$	118.778	4.60948
$665$	−17.2603	−0.669326
$666$	−37.7360	−1.46224
$667$	20.7674	0.804116
$668$	89.9001	3.47834
$669$	2.78313	0.107602
$670$	−58.4504	−2.25814
$671$	42.2791	1.63217
$672$	−4.81449	−0.185723
$673$	−32.8534	−1.26640	−0.633202	−	0.773986i	$-0.718260\pi$
$673$	−32.8534	−1.26640	−0.633202	+	0.773986i	$0.718260\pi$
$674$	70.8335	2.72841
$675$	−0.818008	−0.0314851
$676$	148.670	5.71809
$677$	1.20402	0.0462741	0.0231370	−	0.999732i	$-0.492635\pi$
$677$	1.20402	0.0462741	0.0231370	+	0.999732i	$0.492635\pi$
$678$	−7.11307	−0.273176
$679$	3.68194	0.141300
$680$	−39.7777	−1.52540
$681$	1.36629	0.0523563
$682$	59.0571	2.26141
$683$	15.8691	0.607214	0.303607	−	0.952797i	$-0.401809\pi$
$683$	15.8691	0.607214	0.303607	+	0.952797i	$0.401809\pi$
$684$	129.101	4.93631
$685$	28.1063	1.07389
$686$	2.71246	0.103562
$687$	5.45102	0.207970
$688$	20.1034	0.766434
$689$	−44.4701	−1.69417
$690$	−6.66492	−0.253729
$691$	7.11255	0.270574	0.135287	−	0.990806i	$-0.456804\pi$
$691$	7.11255	0.270574	0.135287	+	0.990806i	$0.456804\pi$
$692$	−58.3579	−2.21844
$693$	−17.0334	−0.647047
$694$	4.54148	0.172392
$695$	−20.1205	−0.763214
$696$	9.65665	0.366034
$697$	16.1988	0.613572
$698$	−9.00452	−0.340826
$699$	−2.06235	−0.0780052
$700$	3.02265	0.114245
$701$	48.0908	1.81636	0.908182	−	0.418576i	$-0.137471\pi$
$701$	48.0908	1.81636	0.908182	+	0.418576i	$0.137471\pi$
$702$	−25.1047	−0.947518
$703$	38.7743	1.46240
$704$	−147.901	−5.57422
$705$	3.95353	0.148898
$706$	4.13952	0.155793
$707$	15.7267	0.591465
$708$	14.2435	0.535303
$709$	14.2638	0.535688	0.267844	−	0.963462i	$-0.413689\pi$
$709$	14.2638	0.535688	0.267844	+	0.963462i	$0.413689\pi$
$710$	−75.8941	−2.84825
$711$	20.9410	0.785348
$712$	−100.187	−3.75468
$713$	17.9661	0.672835
$714$	1.37295	0.0513813
$715$	77.8830	2.91266
$716$	91.9521	3.43641
$717$	0.756131	0.0282382
$718$	66.8085	2.49327
$719$	−18.1393	−0.676481	−0.338240	−	0.941060i	$-0.609832\pi$
$719$	−18.1393	−0.676481	−0.338240	+	0.941060i	$0.609832\pi$
$720$	86.6224	3.22823
$721$	10.7354	0.399809
$722$	−130.638	−4.86185
$723$	−2.65998	−0.0989257
$724$	−94.9970	−3.53054
$725$	−2.45118	−0.0910347
$726$	14.9332	0.554223
$727$	3.27575	0.121491	0.0607455	−	0.998153i	$-0.480652\pi$
$727$	3.27575	0.121491	0.0607455	+	0.998153i	$0.480652\pi$
$728$	58.1349	2.15462
$729$	−23.8363	−0.882826
$730$	−28.8455	−1.06762
$731$	−2.98070	−0.110245
$732$	9.54335	0.352732
$733$	44.7122	1.65148	0.825741	−	0.564049i	$-0.190757\pi$
$733$	44.7122	1.65148	0.825741	+	0.564049i	$0.190757\pi$
$734$	44.2246	1.63236
$735$	0.514038	0.0189606
$736$	−94.2924	−3.47566
$737$	59.2692	2.18321
$738$	−62.2981	−2.29322
$739$	−47.8915	−1.76172	−0.880859	−	0.473378i	$-0.843034\pi$
$739$	−47.8915	−1.76172	−0.880859	+	0.473378i	$0.843034\pi$
$740$	53.3857	1.96250
$741$	12.7684	0.469060
$742$	−18.8958	−0.693688
$743$	35.9242	1.31793	0.658965	−	0.752174i	$-0.270994\pi$
$743$	35.9242	1.31793	0.658965	+	0.752174i	$0.270994\pi$
$744$	8.35407	0.306275
$745$	40.9257	1.49940
$746$	52.0474	1.90559
$747$	38.3509	1.40319
$748$	64.3621	2.35331
$749$	9.45487	0.345473
$750$	7.75821	0.283290
$751$	12.7184	0.464099	0.232050	−	0.972704i	$-0.425457\pi$
$751$	12.7184	0.464099	0.232050	+	0.972704i	$0.425457\pi$
$752$	107.578	3.92295
$753$	−1.84175	−0.0671172
$754$	−75.2271	−2.73961
$755$	−43.3953	−1.57932
$756$	−7.76756	−0.282503
$757$	−34.1089	−1.23971	−0.619854	−	0.784717i	$-0.712808\pi$
$757$	−34.1089	−1.23971	−0.619854	+	0.784717i	$0.712808\pi$
$758$	34.8229	1.26483
$759$	6.75828	0.245310
$760$	−157.188	−5.70182
$761$	−31.8129	−1.15322	−0.576609	−	0.817020i	$-0.695624\pi$
$761$	−31.8129	−1.15322	−0.576609	+	0.817020i	$0.695624\pi$
$762$	4.60561	0.166844
$763$	12.1214	0.438825
$764$	53.1404	1.92255
$765$	−12.8434	−0.464353
$766$	30.8808	1.11577
$767$	−69.5369	−2.51083
$768$	−7.26634	−0.262201
$769$	1.20258	0.0433663	0.0216832	−	0.999765i	$-0.493097\pi$
$769$	1.20258	0.0433663	0.0216832	+	0.999765i	$0.493097\pi$
$770$	33.0933	1.19260
$771$	2.97581	0.107171
$772$	8.17534	0.294237
$773$	−37.2151	−1.33853	−0.669266	−	0.743022i	$-0.733392\pi$
$773$	−37.2151	−1.33853	−0.669266	+	0.743022i	$0.733392\pi$
$774$	11.4633	0.412041
$775$	−2.12055	−0.0761723
$776$	33.5311	1.20370
$777$	−1.15476	−0.0414267
$778$	−84.4641	−3.02818
$779$	64.0122	2.29348
$780$	17.5800	0.629464
$781$	76.9572	2.75375
$782$	26.8894	0.961562
$783$	6.29902	0.225109
$784$	13.9873	0.499545
$785$	−22.3491	−0.797672
$786$	−13.2331	−0.472007
$787$	−3.23594	−0.115349	−0.0576744	−	0.998335i	$-0.518369\pi$
$787$	−3.23594	−0.115349	−0.0576744	+	0.998335i	$0.518369\pi$
$788$	−1.37489	−0.0489784
$789$	0.822909	0.0292963
$790$	−40.6851	−1.44751
$791$	10.7445	0.382029
$792$	−155.122	−5.51202
$793$	−46.5907	−1.65449
$794$	−19.0592	−0.676385
$795$	−3.58095	−0.127003
$796$	128.779	4.56446
$797$	35.2135	1.24733	0.623663	−	0.781693i	$-0.285644\pi$
$797$	35.2135	1.24733	0.623663	+	0.781693i	$0.285644\pi$
$798$	5.42544	0.192059
$799$	−15.9504	−0.564284
$800$	11.1294	0.393483
$801$	−32.3483	−1.14297
$802$	−92.1404	−3.25359
$803$	29.2496	1.03220
$804$	13.3784	0.471821
$805$	10.0675	0.354833
$806$	−65.0798	−2.29234
$807$	2.27577	0.0801108
$808$	143.222	5.03854
$809$	2.37003	0.0833257	0.0416629	−	0.999132i	$-0.486734\pi$
$809$	2.37003	0.0833257	0.0416629	+	0.999132i	$0.486734\pi$
$810$	48.3728	1.69965
$811$	28.9553	1.01676	0.508379	−	0.861134i	$-0.330245\pi$
$811$	28.9553	1.01676	0.508379	+	0.861134i	$0.330245\pi$
$812$	−23.2757	−0.816818
$813$	−0.632858	−0.0221953
$814$	−74.3422	−2.60569
$815$	−13.1092	−0.459196
$816$	7.07985	0.247844
$817$	−11.7787	−0.412086
$818$	61.7502	2.15904
$819$	18.7705	0.655895
$820$	88.1340	3.07777
$821$	−43.1210	−1.50493	−0.752466	−	0.658631i	$-0.771136\pi$
$821$	−43.1210	−1.50493	−0.752466	+	0.658631i	$0.771136\pi$
$822$	−8.83467	−0.308145
$823$	−22.5444	−0.785850	−0.392925	−	0.919571i	$-0.628537\pi$
$823$	−22.5444	−0.785850	−0.392925	+	0.919571i	$0.628537\pi$
$824$	97.7668	3.40587
$825$	−0.797683	−0.0277718
$826$	−29.5470	−1.02807
$827$	31.2651	1.08719	0.543597	−	0.839346i	$-0.317062\pi$
$827$	31.2651	1.08719	0.543597	+	0.839346i	$0.317062\pi$
$828$	−75.3016	−2.61691
$829$	8.74143	0.303602	0.151801	−	0.988411i	$-0.451493\pi$
$829$	8.74143	0.303602	0.151801	+	0.988411i	$0.451493\pi$
$830$	−74.5100	−2.58628
$831$	1.14252	0.0396335
$832$	162.984	5.65044
$833$	−2.07387	−0.0718554
$834$	6.32448	0.218999
$835$	−35.3418	−1.22305
$836$	254.338	8.79646
$837$	5.44935	0.188357
$838$	−36.4685	−1.25978
$839$	6.40904	0.221264	0.110632	−	0.993861i	$-0.464712\pi$
$839$	6.40904	0.221264	0.110632	+	0.993861i	$0.464712\pi$
$840$	4.68130	0.161520
$841$	−10.1248	−0.349131
$842$	−39.2971	−1.35427
$843$	−3.38600	−0.116620
$844$	88.3873	3.04242
$845$	−58.4458	−2.01060
$846$	61.3428	2.10901
$847$	−22.5569	−0.775065
$848$	−97.4396	−3.34609
$849$	−2.64787	−0.0908746
$850$	−3.17377	−0.108859
$851$	−22.6161	−0.775269
$852$	17.3710	0.595121
$853$	20.3964	0.698360	0.349180	−	0.937056i	$-0.386460\pi$
$853$	20.3964	0.698360	0.349180	+	0.937056i	$0.386460\pi$
$854$	−19.7969	−0.677437
$855$	−50.7528	−1.73571
$856$	86.1047	2.94300
$857$	19.6153	0.670046	0.335023	−	0.942210i	$-0.391256\pi$
$857$	19.6153	0.670046	0.335023	+	0.942210i	$0.391256\pi$
$858$	−24.4810	−0.835767
$859$	−4.89257	−0.166932	−0.0834662	−	0.996511i	$-0.526599\pi$
$859$	−4.89257	−0.166932	−0.0834662	+	0.996511i	$0.526599\pi$
$860$	−16.2173	−0.553007
$861$	−1.90638	−0.0649693
$862$	−81.2264	−2.76658
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−28.6001	−0.972996
$865$	22.9419	0.780047
$866$	−80.2832	−2.72813
$867$	3.09942	0.105262
$868$	−20.1361	−0.683463
$869$	41.2551	1.39948
$870$	−6.05766	−0.205374
$871$	−65.3136	−2.21307
$872$	110.389	3.73824
$873$	10.8265	0.366421
$874$	106.258	3.59423
$875$	−11.7189	−0.396173
$876$	6.60231	0.223071
$877$	−4.87286	−0.164545	−0.0822724	−	0.996610i	$-0.526218\pi$
$877$	−4.87286	−0.164545	−0.0822724	+	0.996610i	$0.526218\pi$
$878$	−17.8322	−0.601806
$879$	0.417233	0.0140729
$880$	170.652	5.75266
$881$	−20.5112	−0.691038	−0.345519	−	0.938412i	$-0.612297\pi$
$881$	−20.5112	−0.691038	−0.345519	+	0.938412i	$0.612297\pi$
$882$	7.97580	0.268559
$883$	−15.5921	−0.524716	−0.262358	−	0.964971i	$-0.584500\pi$
$883$	−15.5921	−0.524716	−0.262358	+	0.964971i	$0.584500\pi$
$884$	−70.9258	−2.38549
$885$	−5.59945	−0.188223
$886$	−72.1405	−2.42361
$887$	13.0787	0.439141	0.219571	−	0.975597i	$-0.429534\pi$
$887$	13.0787	0.439141	0.219571	+	0.975597i	$0.429534\pi$
$888$	−10.5163	−0.352903
$889$	−6.95688	−0.233326
$890$	62.8479	2.10666
$891$	−49.0504	−1.64325
$892$	−61.0915	−2.04549
$893$	−63.0307	−2.10924
$894$	−12.8642	−0.430243
$895$	−36.1485	−1.20831
$896$	29.8014	0.995596
$897$	−7.44750	−0.248665
$898$	−9.76308	−0.325798
$899$	16.3291	0.544607
$900$	8.88788	0.296263
$901$	14.4472	0.481307
$902$	−122.731	−4.08650
$903$	0.350789	0.0116735
$904$	97.8489	3.25441
$905$	37.3455	1.24141
$906$	13.6405	0.453174
$907$	5.71947	0.189912	0.0949560	−	0.995481i	$-0.469729\pi$
$907$	5.71947	0.189912	0.0949560	+	0.995481i	$0.469729\pi$
$908$	−29.9910	−0.995285
$909$	46.2434	1.53380
$910$	−36.4682	−1.20891
$911$	3.16036	0.104707	0.0523537	−	0.998629i	$-0.483328\pi$
$911$	3.16036	0.104707	0.0523537	+	0.998629i	$0.483328\pi$
$912$	27.9772	0.926419
$913$	75.5538	2.50046
$914$	38.4201	1.27083
$915$	−3.75171	−0.124028
$916$	−119.654	−3.95347
$917$	19.9888	0.660089
$918$	8.15591	0.269185
$919$	42.2495	1.39368	0.696841	−	0.717226i	$-0.254588\pi$
$919$	42.2495	1.39368	0.696841	+	0.717226i	$0.254588\pi$
$920$	91.6840	3.02273
$921$	−3.14537	−0.103644
$922$	−2.87156	−0.0945697
$923$	−84.8054	−2.79140
$924$	−7.57456	−0.249185
$925$	2.66939	0.0877689
$926$	115.596	3.79873
$927$	31.5668	1.03679
$928$	−85.7012	−2.81328
$929$	49.8591	1.63582	0.817912	−	0.575343i	$-0.195131\pi$
$929$	49.8591	1.63582	0.817912	+	0.575343i	$0.195131\pi$
$930$	−5.24054	−0.171844
$931$	−8.19526	−0.268589
$932$	45.2700	1.48287
$933$	−3.77517	−0.123593
$934$	−41.2050	−1.34827
$935$	−25.3022	−0.827472
$936$	170.942	5.58740
$937$	10.6386	0.347547	0.173773	−	0.984786i	$-0.444404\pi$
$937$	10.6386	0.347547	0.173773	+	0.984786i	$0.444404\pi$
$938$	−27.7525	−0.906150
$939$	7.03156	0.229466
$940$	−86.7826	−2.83054
$941$	−0.297868	−0.00971022	−0.00485511	−	0.999988i	$-0.501545\pi$
$941$	−0.297868	−0.00971022	−0.00485511	+	0.999988i	$0.501545\pi$
$942$	7.02499	0.228886
$943$	−37.3367	−1.21585
$944$	−152.364	−4.95903
$945$	3.05361	0.0993339
$946$	22.5835	0.734252
$947$	21.8728	0.710770	0.355385	−	0.934720i	$-0.384350\pi$
$947$	21.8728	0.710770	0.355385	+	0.934720i	$0.384350\pi$
$948$	9.31221	0.302446
$949$	−32.2325	−1.04631
$950$	−12.5417	−0.406906
$951$	0.684467	0.0221954
$952$	−18.8866	−0.612117
$953$	−4.29236	−0.139043	−0.0695215	−	0.997580i	$-0.522147\pi$
$953$	−4.29236	−0.139043	−0.0695215	+	0.997580i	$0.522147\pi$
$954$	−55.5619	−1.79888
$955$	−20.8907	−0.676008
$956$	−16.5976	−0.536804
$957$	6.14252	0.198559
$958$	−56.2111	−1.81610
$959$	13.3450	0.430932
$960$	13.1243	0.423583
$961$	−16.8735	−0.544306
$962$	81.9237	2.64133
$963$	27.8014	0.895887
$964$	58.3883	1.88056
$965$	−3.21392	−0.103460
$966$	−3.16453	−0.101817
$967$	−33.4520	−1.07574	−0.537871	−	0.843027i	$-0.680771\pi$
$967$	−33.4520	−1.07574	−0.537871	+	0.843027i	$0.680771\pi$
$968$	−205.424	−6.60258
$969$	−4.14814	−0.133258
$970$	−21.0342	−0.675368
$971$	−22.5941	−0.725080	−0.362540	−	0.931968i	$-0.618090\pi$
$971$	−22.5941	−0.725080	−0.362540	+	0.931968i	$0.618090\pi$
$972$	−34.3745	−1.10256
$973$	−9.55328	−0.306264
$974$	−75.2891	−2.41242
$975$	0.879032	0.0281516
$976$	−102.086	−3.26770
$977$	5.52100	0.176632	0.0883162	−	0.996092i	$-0.471851\pi$
$977$	5.52100	0.176632	0.0883162	+	0.996092i	$0.471851\pi$
$978$	4.12063	0.131763
$979$	−63.7283	−2.03676
$980$	−11.2835	−0.360438
$981$	35.6422	1.13797
$982$	40.9604	1.30710
$983$	−9.92257	−0.316481	−0.158240	−	0.987401i	$-0.550582\pi$
$983$	−9.92257	−0.316481	−0.158240	+	0.987401i	$0.550582\pi$
$984$	−17.3612	−0.553456
$985$	0.540502	0.0172218
$986$	24.4394	0.778310
$987$	1.87715	0.0597503
$988$	−280.275	−8.91675
$989$	6.87024	0.218461
$990$	97.3087	3.09267
$991$	31.6811	1.00638	0.503191	−	0.864175i	$-0.332159\pi$
$991$	31.6811	1.00638	0.503191	+	0.864175i	$0.332159\pi$
$992$	−74.1410	−2.35398
$993$	0.704800	0.0223661
$994$	−36.0348	−1.14295
$995$	−50.6262	−1.60496
$996$	17.0542	0.540383
$997$	15.3370	0.485727	0.242863	−	0.970060i	$-0.421913\pi$
$997$	15.3370	0.485727	0.242863	+	0.970060i	$0.421913\pi$
$998$	20.7890	0.658064
$999$	−6.85975	−0.217033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.e.1.5	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.e.1.5	✓	112	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71246 q^{2} -0.244067 q^{3} +5.35744 q^{4} -2.10613 q^{5} +0.662022 q^{6} -1.00000 q^{7} -9.10692 q^{8} -2.94043 q^{9} +O(q^{10})\)	\(q-2.71246 q^{2} -0.244067 q^{3} +5.35744 q^{4} -2.10613 q^{5} +0.662022 q^{6} -1.00000 q^{7} -9.10692 q^{8} -2.94043 q^{9} +5.71281 q^{10} -5.79283 q^{11} -1.30757 q^{12} +6.38359 q^{13} +2.71246 q^{14} +0.514038 q^{15} +13.9873 q^{16} -2.07387 q^{17} +7.97580 q^{18} -8.19526 q^{19} -11.2835 q^{20} +0.244067 q^{21} +15.7128 q^{22} +4.78009 q^{23} +2.22270 q^{24} -0.564196 q^{25} -17.3152 q^{26} +1.44986 q^{27} -5.35744 q^{28} +4.34456 q^{29} -1.39431 q^{30} +3.75853 q^{31} -19.7261 q^{32} +1.41384 q^{33} +5.62529 q^{34} +2.10613 q^{35} -15.7532 q^{36} -4.73131 q^{37} +22.2293 q^{38} -1.55803 q^{39} +19.1804 q^{40} -7.81088 q^{41} -0.662022 q^{42} +1.43726 q^{43} -31.0348 q^{44} +6.19294 q^{45} -12.9658 q^{46} +7.69111 q^{47} -3.41383 q^{48} +1.00000 q^{49} +1.53036 q^{50} +0.506164 q^{51} +34.1997 q^{52} -6.96631 q^{53} -3.93270 q^{54} +12.2005 q^{55} +9.10692 q^{56} +2.00019 q^{57} -11.7844 q^{58} -10.8931 q^{59} +2.75393 q^{60} -7.29851 q^{61} -10.1948 q^{62} +2.94043 q^{63} +25.5317 q^{64} -13.4447 q^{65} -3.83499 q^{66} -10.2315 q^{67} -11.1106 q^{68} -1.16666 q^{69} -5.71281 q^{70} -13.2849 q^{71} +26.7783 q^{72} -5.04928 q^{73} +12.8335 q^{74} +0.137702 q^{75} -43.9056 q^{76} +5.79283 q^{77} +4.22608 q^{78} -7.12174 q^{79} -29.4591 q^{80} +8.46743 q^{81} +21.1867 q^{82} -13.0426 q^{83} +1.30757 q^{84} +4.36785 q^{85} -3.89852 q^{86} -1.06036 q^{87} +52.7549 q^{88} +11.0012 q^{89} -16.7981 q^{90} -6.38359 q^{91} +25.6090 q^{92} -0.917333 q^{93} -20.8618 q^{94} +17.2603 q^{95} +4.81449 q^{96} -3.68194 q^{97} -2.71246 q^{98} +17.0334 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * q^99

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