LMFDB - Embedded newform 6005.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81643 q^{2} -3.03025 q^{3} +5.93229 q^{4} -1.00000 q^{5} +8.53449 q^{6} +1.00907 q^{7} -11.0750 q^{8} +6.18240 q^{9} +O(q^{10})$	\(q-2.81643 q^{2} -3.03025 q^{3} +5.93229 q^{4} -1.00000 q^{5} +8.53449 q^{6} +1.00907 q^{7} -11.0750 q^{8} +6.18240 q^{9} +2.81643 q^{10} -3.27932 q^{11} -17.9763 q^{12} -1.81381 q^{13} -2.84198 q^{14} +3.03025 q^{15} +19.3275 q^{16} +6.07453 q^{17} -17.4123 q^{18} +4.67603 q^{19} -5.93229 q^{20} -3.05774 q^{21} +9.23598 q^{22} -7.64438 q^{23} +33.5601 q^{24} +1.00000 q^{25} +5.10846 q^{26} -9.64347 q^{27} +5.98611 q^{28} +3.00018 q^{29} -8.53449 q^{30} +10.0752 q^{31} -32.2845 q^{32} +9.93715 q^{33} -17.1085 q^{34} -1.00907 q^{35} +36.6758 q^{36} +0.0838401 q^{37} -13.1697 q^{38} +5.49628 q^{39} +11.0750 q^{40} -6.65761 q^{41} +8.61191 q^{42} +6.15844 q^{43} -19.4539 q^{44} -6.18240 q^{45} +21.5299 q^{46} +2.74840 q^{47} -58.5670 q^{48} -5.98177 q^{49} -2.81643 q^{50} -18.4073 q^{51} -10.7600 q^{52} +8.65472 q^{53} +27.1602 q^{54} +3.27932 q^{55} -11.1755 q^{56} -14.1695 q^{57} -8.44979 q^{58} +12.0477 q^{59} +17.9763 q^{60} -13.1689 q^{61} -28.3761 q^{62} +6.23849 q^{63} +52.2720 q^{64} +1.81381 q^{65} -27.9873 q^{66} +11.3860 q^{67} +36.0359 q^{68} +23.1644 q^{69} +2.84198 q^{70} -8.87706 q^{71} -68.4702 q^{72} -0.140761 q^{73} -0.236130 q^{74} -3.03025 q^{75} +27.7396 q^{76} -3.30907 q^{77} -15.4799 q^{78} -4.88628 q^{79} -19.3275 q^{80} +10.6749 q^{81} +18.7507 q^{82} +3.63623 q^{83} -18.1394 q^{84} -6.07453 q^{85} -17.3448 q^{86} -9.09127 q^{87} +36.3185 q^{88} +11.1926 q^{89} +17.4123 q^{90} -1.83026 q^{91} -45.3487 q^{92} -30.5304 q^{93} -7.74069 q^{94} -4.67603 q^{95} +97.8299 q^{96} +7.12709 q^{97} +16.8473 q^{98} -20.2741 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) $ 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * 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 $

$2$	−2.81643	−1.99152	−0.995759	−	0.0919997i	$-0.970674\pi$
$2$	−2.81643	−1.99152	−0.995759	+	0.0919997i	$0.970674\pi$
$3$	−3.03025	−1.74951	−0.874757	−	0.484562i	$-0.838979\pi$
$3$	−3.03025	−1.74951	−0.874757	+	0.484562i	$0.838979\pi$
$4$	5.93229	2.96614
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	8.53449	3.48419
$7$	1.00907	0.381393	0.190697	−	0.981649i	$-0.438925\pi$
$7$	1.00907	0.381393	0.190697	+	0.981649i	$0.438925\pi$
$8$	−11.0750	−3.91561
$9$	6.18240	2.06080
$10$	2.81643	0.890634
$11$	−3.27932	−0.988752	−0.494376	−	0.869248i	$-0.664603\pi$
$11$	−3.27932	−0.988752	−0.494376	+	0.869248i	$0.664603\pi$
$12$	−17.9763	−5.18931
$13$	−1.81381	−0.503060	−0.251530	−	0.967850i	$-0.580934\pi$
$13$	−1.81381	−0.503060	−0.251530	+	0.967850i	$0.580934\pi$
$14$	−2.84198	−0.759552
$15$	3.03025	0.782407
$16$	19.3275	4.83187
$17$	6.07453	1.47329	0.736645	−	0.676280i	$-0.236409\pi$
$17$	6.07453	1.47329	0.736645	+	0.676280i	$0.236409\pi$
$18$	−17.4123	−4.10412
$19$	4.67603	1.07276	0.536378	−	0.843978i	$-0.319792\pi$
$19$	4.67603	1.07276	0.536378	+	0.843978i	$0.319792\pi$
$20$	−5.93229	−1.32650
$21$	−3.05774	−0.667253
$22$	9.23598	1.96912
$23$	−7.64438	−1.59396	−0.796982	−	0.604003i	$-0.793571\pi$
$23$	−7.64438	−1.59396	−0.796982	+	0.604003i	$0.793571\pi$
$24$	33.5601	6.85042
$25$	1.00000	0.200000
$26$	5.10846	1.00185
$27$	−9.64347	−1.85589
$28$	5.98611	1.13127
$29$	3.00018	0.557119	0.278559	−	0.960419i	$-0.410143\pi$
$29$	3.00018	0.557119	0.278559	+	0.960419i	$0.410143\pi$
$30$	−8.53449	−1.55818
$31$	10.0752	1.80956	0.904780	−	0.425880i	$-0.140035\pi$
$31$	10.0752	1.80956	0.904780	+	0.425880i	$0.140035\pi$
$32$	−32.2845	−5.70714
$33$	9.93715	1.72984
$34$	−17.1085	−2.93408
$35$	−1.00907	−0.170564
$36$	36.6758	6.11263
$37$	0.0838401	0.0137832	0.00689161	−	0.999976i	$-0.497806\pi$
$37$	0.0838401	0.0137832	0.00689161	+	0.999976i	$0.497806\pi$
$38$	−13.1697	−2.13641
$39$	5.49628	0.880110
$40$	11.0750	1.75111
$41$	−6.65761	−1.03974	−0.519872	−	0.854244i	$-0.674020\pi$
$41$	−6.65761	−1.03974	−0.519872	+	0.854244i	$0.674020\pi$
$42$	8.61191	1.32885
$43$	6.15844	0.939153	0.469577	−	0.882892i	$-0.344407\pi$
$43$	6.15844	0.939153	0.469577	+	0.882892i	$0.344407\pi$
$44$	−19.4539	−2.93278
$45$	−6.18240	−0.921618
$46$	21.5299	3.17441
$47$	2.74840	0.400896	0.200448	−	0.979704i	$-0.435760\pi$
$47$	2.74840	0.400896	0.200448	+	0.979704i	$0.435760\pi$
$48$	−58.5670	−8.45342
$49$	−5.98177	−0.854539
$50$	−2.81643	−0.398304
$51$	−18.4073	−2.57754
$52$	−10.7600	−1.49215
$53$	8.65472	1.18882	0.594409	−	0.804163i	$-0.297386\pi$
$53$	8.65472	1.18882	0.594409	+	0.804163i	$0.297386\pi$
$54$	27.1602	3.69603
$55$	3.27932	0.442183
$56$	−11.1755	−1.49339
$57$	−14.1695	−1.87680
$58$	−8.44979	−1.10951
$59$	12.0477	1.56848	0.784238	−	0.620460i	$-0.213054\pi$
$59$	12.0477	1.56848	0.784238	+	0.620460i	$0.213054\pi$
$60$	17.9763	2.32073
$61$	−13.1689	−1.68611	−0.843054	−	0.537829i	$-0.819244\pi$
$61$	−13.1689	−1.68611	−0.843054	+	0.537829i	$0.819244\pi$
$62$	−28.3761	−3.60377
$63$	6.23849	0.785976
$64$	52.2720	6.53400
$65$	1.81381	0.224975
$66$	−27.9873	−3.44500
$67$	11.3860	1.39103	0.695513	−	0.718513i	$-0.255177\pi$
$67$	11.3860	1.39103	0.695513	+	0.718513i	$0.255177\pi$
$68$	36.0359	4.36999
$69$	23.1644	2.78866
$70$	2.84198	0.339682
$71$	−8.87706	−1.05351	−0.526757	−	0.850016i	$-0.676592\pi$
$71$	−8.87706	−1.05351	−0.526757	+	0.850016i	$0.676592\pi$
$72$	−68.4702	−8.06929
$73$	−0.140761	−0.0164748	−0.00823740	−	0.999966i	$-0.502622\pi$
$73$	−0.140761	−0.0164748	−0.00823740	+	0.999966i	$0.502622\pi$
$74$	−0.236130	−0.0274495
$75$	−3.03025	−0.349903
$76$	27.7396	3.18195
$77$	−3.30907	−0.377104
$78$	−15.4799	−1.75275
$79$	−4.88628	−0.549750	−0.274875	−	0.961480i	$-0.588636\pi$
$79$	−4.88628	−0.549750	−0.274875	+	0.961480i	$0.588636\pi$
$80$	−19.3275	−2.16088
$81$	10.6749	1.18610
$82$	18.7507	2.07067
$83$	3.63623	0.399128	0.199564	−	0.979885i	$-0.436047\pi$
$83$	3.63623	0.399128	0.199564	+	0.979885i	$0.436047\pi$
$84$	−18.1394	−1.97917
$85$	−6.07453	−0.658875
$86$	−17.3448	−1.87034
$87$	−9.09127	−0.974687
$88$	36.3185	3.87157
$89$	11.1926	1.18642	0.593209	−	0.805049i	$-0.297861\pi$
$89$	11.1926	1.18642	0.593209	+	0.805049i	$0.297861\pi$
$90$	17.4123	1.83542
$91$	−1.83026	−0.191864
$92$	−45.3487	−4.72793
$93$	−30.5304	−3.16585
$94$	−7.74069	−0.798391
$95$	−4.67603	−0.479751
$96$	97.8299	9.98472
$97$	7.12709	0.723647	0.361823	−	0.932247i	$-0.382154\pi$
$97$	7.12709	0.723647	0.361823	+	0.932247i	$0.382154\pi$
$98$	16.8473	1.70183
$99$	−20.2741	−2.03762
$100$	5.93229	0.593229
$101$	13.5995	1.35320	0.676600	−	0.736351i	$-0.263453\pi$
$101$	13.5995	1.35320	0.676600	+	0.736351i	$0.263453\pi$
$102$	51.8430	5.13322
$103$	1.50617	0.148407	0.0742034	−	0.997243i	$-0.476359\pi$
$103$	1.50617	0.148407	0.0742034	+	0.997243i	$0.476359\pi$
$104$	20.0880	1.96979
$105$	3.05774	0.298405
$106$	−24.3754	−2.36755
$107$	6.96297	0.673136	0.336568	−	0.941659i	$-0.390734\pi$
$107$	6.96297	0.673136	0.336568	+	0.941659i	$0.390734\pi$
$108$	−57.2078	−5.50482
$109$	15.2087	1.45673	0.728366	−	0.685189i	$-0.240280\pi$
$109$	15.2087	1.45673	0.728366	+	0.685189i	$0.240280\pi$
$110$	−9.23598	−0.880616
$111$	−0.254056	−0.0241139
$112$	19.5028	1.84284
$113$	−3.00305	−0.282503	−0.141251	−	0.989974i	$-0.545113\pi$
$113$	−3.00305	−0.282503	−0.141251	+	0.989974i	$0.545113\pi$
$114$	39.9075	3.73768
$115$	7.64438	0.712842
$116$	17.7979	1.65249
$117$	−11.2137	−1.03671
$118$	−33.9315	−3.12365
$119$	6.12964	0.561903
$120$	−33.5601	−3.06360
$121$	−0.246061	−0.0223692
$122$	37.0894	3.35791
$123$	20.1742	1.81905
$124$	59.7690	5.36741
$125$	−1.00000	−0.0894427
$126$	−17.5703	−1.56528
$127$	18.2599	1.62031	0.810153	−	0.586219i	$-0.199384\pi$
$127$	18.2599	1.62031	0.810153	+	0.586219i	$0.199384\pi$
$128$	−82.6517	−7.30545
$129$	−18.6616	−1.64306
$130$	−5.10846	−0.448042
$131$	6.45391	0.563881	0.281940	−	0.959432i	$-0.409022\pi$
$131$	6.45391	0.563881	0.281940	+	0.959432i	$0.409022\pi$
$132$	58.9501	5.13094
$133$	4.71845	0.409142
$134$	−32.0680	−2.77025
$135$	9.64347	0.829977
$136$	−67.2756	−5.76883
$137$	−21.4150	−1.82960	−0.914802	−	0.403903i	$-0.867653\pi$
$137$	−21.4150	−1.82960	−0.914802	+	0.403903i	$0.867653\pi$
$138$	−65.2409	−5.55367
$139$	5.76397	0.488894	0.244447	−	0.969663i	$-0.421394\pi$
$139$	5.76397	0.488894	0.244447	+	0.969663i	$0.421394\pi$
$140$	−5.98611	−0.505918
$141$	−8.32834	−0.701373
$142$	25.0016	2.09809
$143$	5.94805	0.497401
$144$	119.490	9.95751
$145$	−3.00018	−0.249151
$146$	0.396443	0.0328099
$147$	18.1263	1.49503
$148$	0.497363	0.0408830
$149$	−0.810940	−0.0664348	−0.0332174	−	0.999448i	$-0.510575\pi$
$149$	−0.810940	−0.0664348	−0.0332174	+	0.999448i	$0.510575\pi$
$150$	8.53449	0.696838
$151$	−20.6790	−1.68283	−0.841417	−	0.540386i	$-0.818278\pi$
$151$	−20.6790	−1.68283	−0.841417	+	0.540386i	$0.818278\pi$
$152$	−51.7871	−4.20049
$153$	37.5552	3.03616
$154$	9.31977	0.751009
$155$	−10.0752	−0.809260
$156$	32.6055	2.61053
$157$	−11.8330	−0.944380	−0.472190	−	0.881497i	$-0.656536\pi$
$157$	−11.8330	−0.944380	−0.472190	+	0.881497i	$0.656536\pi$
$158$	13.7619	1.09484
$159$	−26.2260	−2.07985
$160$	32.2845	2.55231
$161$	−7.71373	−0.607927
$162$	−30.0651	−2.36214
$163$	−6.96274	−0.545364	−0.272682	−	0.962104i	$-0.587911\pi$
$163$	−6.96274	−0.545364	−0.272682	+	0.962104i	$0.587911\pi$
$164$	−39.4949	−3.08403
$165$	−9.93715	−0.773606
$166$	−10.2412	−0.794871
$167$	8.17983	0.632974	0.316487	−	0.948597i	$-0.397497\pi$
$167$	8.17983	0.632974	0.316487	+	0.948597i	$0.397497\pi$
$168$	33.8645	2.61270
$169$	−9.71010	−0.746931
$170$	17.1085	1.31216
$171$	28.9091	2.21073
$172$	36.5336	2.78566
$173$	0.998153	0.0758881	0.0379441	−	0.999280i	$-0.487919\pi$
$173$	0.998153	0.0758881	0.0379441	+	0.999280i	$0.487919\pi$
$174$	25.6050	1.94111
$175$	1.00907	0.0762787
$176$	−63.3810	−4.77752
$177$	−36.5075	−2.74407
$178$	−31.5233	−2.36277
$179$	21.0768	1.57535	0.787676	−	0.616090i	$-0.211284\pi$
$179$	21.0768	1.57535	0.787676	+	0.616090i	$0.211284\pi$
$180$	−36.6758	−2.73365
$181$	−6.49502	−0.482771	−0.241386	−	0.970429i	$-0.577602\pi$
$181$	−6.49502	−0.482771	−0.241386	+	0.970429i	$0.577602\pi$
$182$	5.15481	0.382100
$183$	39.9051	2.94987
$184$	84.6617	6.24134
$185$	−0.0838401	−0.00616404
$186$	85.9867	6.30485
$187$	−19.9203	−1.45672
$188$	16.3043	1.18911
$189$	−9.73095	−0.707823
$190$	13.1697	0.955432
$191$	13.1371	0.950565	0.475282	−	0.879833i	$-0.342346\pi$
$191$	13.1371	0.950565	0.475282	+	0.879833i	$0.342346\pi$
$192$	−158.397	−11.4313
$193$	−7.26989	−0.523298	−0.261649	−	0.965163i	$-0.584266\pi$
$193$	−7.26989	−0.523298	−0.261649	+	0.965163i	$0.584266\pi$
$194$	−20.0730	−1.44116
$195$	−5.49628	−0.393597
$196$	−35.4856	−2.53469
$197$	0.583517	0.0415739	0.0207869	−	0.999784i	$-0.493383\pi$
$197$	0.583517	0.0415739	0.0207869	+	0.999784i	$0.493383\pi$
$198$	57.1005	4.05796
$199$	14.0574	0.996501	0.498250	−	0.867033i	$-0.333976\pi$
$199$	14.0574	0.996501	0.498250	+	0.867033i	$0.333976\pi$
$200$	−11.0750	−0.783122
$201$	−34.5025	−2.43362
$202$	−38.3020	−2.69492
$203$	3.02739	0.212481
$204$	−109.198	−7.64536
$205$	6.65761	0.464988
$206$	−4.24201	−0.295555
$207$	−47.2606	−3.28484
$208$	−35.0563	−2.43072
$209$	−15.3342	−1.06069
$210$	−8.61191	−0.594278
$211$	16.6012	1.14287	0.571436	−	0.820646i	$-0.306386\pi$
$211$	16.6012	1.14287	0.571436	+	0.820646i	$0.306386\pi$
$212$	51.3423	3.52620
$213$	26.8997	1.84314
$214$	−19.6107	−1.34056
$215$	−6.15844	−0.420002
$216$	106.802	7.26693
$217$	10.1666	0.690154
$218$	−42.8343	−2.90111
$219$	0.426540	0.0288229
$220$	19.4539	1.31158
$221$	−11.0180	−0.741153
$222$	0.715532	0.0480233
$223$	−23.2006	−1.55362	−0.776812	−	0.629732i	$-0.783165\pi$
$223$	−23.2006	−1.55362	−0.776812	+	0.629732i	$0.783165\pi$
$224$	−32.5773	−2.17667
$225$	6.18240	0.412160
$226$	8.45787	0.562609
$227$	−10.7208	−0.711563	−0.355781	−	0.934569i	$-0.615785\pi$
$227$	−10.7208	−0.711563	−0.355781	+	0.934569i	$0.615785\pi$
$228$	−84.0577	−5.56686
$229$	−11.9920	−0.792454	−0.396227	−	0.918153i	$-0.629681\pi$
$229$	−11.9920	−0.792454	−0.396227	+	0.918153i	$0.629681\pi$
$230$	−21.5299	−1.41964
$231$	10.0273	0.659748
$232$	−33.2270	−2.18146
$233$	−21.3658	−1.39972	−0.699860	−	0.714280i	$-0.746754\pi$
$233$	−21.3658	−1.39972	−0.699860	+	0.714280i	$0.746754\pi$
$234$	31.5826	2.06462
$235$	−2.74840	−0.179286
$236$	71.4704	4.65233
$237$	14.8066	0.961795
$238$	−17.2637	−1.11904
$239$	−16.8652	−1.09092	−0.545461	−	0.838136i	$-0.683645\pi$
$239$	−16.8652	−1.09092	−0.545461	+	0.838136i	$0.683645\pi$
$240$	58.5670	3.78048
$241$	−16.7784	−1.08079	−0.540397	−	0.841410i	$-0.681726\pi$
$241$	−16.7784	−1.08079	−0.540397	+	0.841410i	$0.681726\pi$
$242$	0.693014	0.0445486
$243$	−3.41715	−0.219210
$244$	−78.1218	−5.00124
$245$	5.98177	0.382161
$246$	−56.8193	−3.62267
$247$	−8.48142	−0.539660
$248$	−111.583	−7.08553
$249$	−11.0187	−0.698281
$250$	2.81643	0.178127
$251$	−9.61348	−0.606797	−0.303399	−	0.952864i	$-0.598121\pi$
$251$	−9.61348	−0.606797	−0.303399	+	0.952864i	$0.598121\pi$
$252$	37.0085	2.33132
$253$	25.0684	1.57603
$254$	−51.4278	−3.22687
$255$	18.4073	1.15271
$256$	128.239	8.01493
$257$	11.5656	0.721443	0.360722	−	0.932674i	$-0.382530\pi$
$257$	11.5656	0.721443	0.360722	+	0.932674i	$0.382530\pi$
$258$	52.5591	3.27219
$259$	0.0846007	0.00525683
$260$	10.7600	0.667308
$261$	18.5483	1.14811
$262$	−18.1770	−1.12298
$263$	16.1334	0.994830	0.497415	−	0.867513i	$-0.334283\pi$
$263$	16.1334	0.994830	0.497415	+	0.867513i	$0.334283\pi$
$264$	−110.054	−6.77337
$265$	−8.65472	−0.531655
$266$	−13.2892	−0.814813
$267$	−33.9165	−2.07565
$268$	67.5453	4.12599
$269$	−24.9749	−1.52275	−0.761374	−	0.648312i	$-0.775475\pi$
$269$	−24.9749	−1.52275	−0.761374	+	0.648312i	$0.775475\pi$
$270$	−27.1602	−1.65291
$271$	−24.3532	−1.47935	−0.739675	−	0.672964i	$-0.765021\pi$
$271$	−24.3532	−1.47935	−0.739675	+	0.672964i	$0.765021\pi$
$272$	117.405	7.11874
$273$	5.54615	0.335668
$274$	60.3138	3.64369
$275$	−3.27932	−0.197750
$276$	137.418	8.27157
$277$	−20.2879	−1.21898	−0.609491	−	0.792793i	$-0.708626\pi$
$277$	−20.2879	−1.21898	−0.609491	+	0.792793i	$0.708626\pi$
$278$	−16.2338	−0.973641
$279$	62.2889	3.72914
$280$	11.1755	0.667864
$281$	−24.1839	−1.44269	−0.721347	−	0.692574i	$-0.756476\pi$
$281$	−24.1839	−1.44269	−0.721347	+	0.692574i	$0.756476\pi$
$282$	23.4562	1.39680
$283$	7.47520	0.444354	0.222177	−	0.975006i	$-0.428684\pi$
$283$	7.47520	0.444354	0.222177	+	0.975006i	$0.428684\pi$
$284$	−52.6613	−3.12487
$285$	14.1695	0.839331
$286$	−16.7523	−0.990583
$287$	−6.71801	−0.396552
$288$	−199.595	−11.7613
$289$	19.8999	1.17058
$290$	8.44979	0.496189
$291$	−21.5969	−1.26603
$292$	−0.835034	−0.0488667
$293$	8.92165	0.521208	0.260604	−	0.965446i	$-0.416078\pi$
$293$	8.92165	0.521208	0.260604	+	0.965446i	$0.416078\pi$
$294$	−51.0514	−2.97738
$295$	−12.0477	−0.701444
$296$	−0.928530	−0.0539697
$297$	31.6240	1.83501
$298$	2.28396	0.132306
$299$	13.8654	0.801859
$300$	−17.9763	−1.03786
$301$	6.21431	0.358187
$302$	58.2411	3.35140
$303$	−41.2098	−2.36744
$304$	90.3758	5.18341
$305$	13.1689	0.754050
$306$	−105.772	−6.04656
$307$	1.18844	0.0678277	0.0339138	−	0.999425i	$-0.489203\pi$
$307$	1.18844	0.0678277	0.0339138	+	0.999425i	$0.489203\pi$
$308$	−19.6304	−1.11854
$309$	−4.56405	−0.259640
$310$	28.3761	1.61165
$311$	−14.1758	−0.803837	−0.401919	−	0.915675i	$-0.631657\pi$
$311$	−14.1758	−0.803837	−0.401919	+	0.915675i	$0.631657\pi$
$312$	−60.8715	−3.44617
$313$	−14.7069	−0.831285	−0.415643	−	0.909528i	$-0.636443\pi$
$313$	−14.7069	−0.831285	−0.415643	+	0.909528i	$0.636443\pi$
$314$	33.3270	1.88075
$315$	−6.23849	−0.351499
$316$	−28.9868	−1.63064
$317$	27.8048	1.56167	0.780836	−	0.624737i	$-0.214794\pi$
$317$	27.8048	1.56167	0.780836	+	0.624737i	$0.214794\pi$
$318$	73.8636	4.14207
$319$	−9.83853	−0.550852
$320$	−52.2720	−2.92210
$321$	−21.0995	−1.17766
$322$	21.7252	1.21070
$323$	28.4047	1.58048
$324$	63.3265	3.51814
$325$	−1.81381	−0.100612
$326$	19.6101	1.08610
$327$	−46.0862	−2.54857
$328$	73.7332	4.07124
$329$	2.77334	0.152899
$330$	27.9873	1.54065
$331$	−2.69762	−0.148275	−0.0741373	−	0.997248i	$-0.523620\pi$
$331$	−2.69762	−0.148275	−0.0741373	+	0.997248i	$0.523620\pi$
$332$	21.5712	1.18387
$333$	0.518333	0.0284045
$334$	−23.0379	−1.26058
$335$	−11.3860	−0.622086
$336$	−59.0983	−3.22408
$337$	−1.57444	−0.0857652	−0.0428826	−	0.999080i	$-0.513654\pi$
$337$	−1.57444	−0.0857652	−0.0428826	+	0.999080i	$0.513654\pi$
$338$	27.3478	1.48753
$339$	9.09997	0.494243
$340$	−36.0359	−1.95432
$341$	−33.0398	−1.78921
$342$	−81.4205	−4.40272
$343$	−13.0995	−0.707309
$344$	−68.2049	−3.67736
$345$	−23.1644	−1.24713
$346$	−2.81123	−0.151133
$347$	−7.41450	−0.398031	−0.199016	−	0.979996i	$-0.563774\pi$
$347$	−7.41450	−0.398031	−0.199016	+	0.979996i	$0.563774\pi$
$348$	−53.9321	−2.89106
$349$	14.2800	0.764392	0.382196	−	0.924081i	$-0.375168\pi$
$349$	14.2800	0.764392	0.382196	+	0.924081i	$0.375168\pi$
$350$	−2.84198	−0.151910
$351$	17.4914	0.933621
$352$	105.871	5.64295
$353$	12.7203	0.677032	0.338516	−	0.940961i	$-0.390075\pi$
$353$	12.7203	0.677032	0.338516	+	0.940961i	$0.390075\pi$
$354$	102.821	5.46487
$355$	8.87706	0.471145
$356$	66.3980	3.51908
$357$	−18.5743	−0.983058
$358$	−59.3613	−3.13734
$359$	−29.4849	−1.55615	−0.778075	−	0.628171i	$-0.783804\pi$
$359$	−29.4849	−1.55615	−0.778075	+	0.628171i	$0.783804\pi$
$360$	68.4702	3.60870
$361$	2.86526	0.150803
$362$	18.2928	0.961448
$363$	0.745626	0.0391352
$364$	−10.8576	−0.569095
$365$	0.140761	0.00736776
$366$	−112.390	−5.87472
$367$	8.34693	0.435706	0.217853	−	0.975982i	$-0.430095\pi$
$367$	8.34693	0.435706	0.217853	+	0.975982i	$0.430095\pi$
$368$	−147.747	−7.70182
$369$	−41.1600	−2.14271
$370$	0.236130	0.0122758
$371$	8.73324	0.453407
$372$	−181.115	−9.39037
$373$	−35.0898	−1.81688	−0.908440	−	0.418014i	$-0.862726\pi$
$373$	−35.0898	−1.81688	−0.908440	+	0.418014i	$0.862726\pi$
$374$	56.1042	2.90108
$375$	3.03025	0.156481
$376$	−30.4386	−1.56975
$377$	−5.44174	−0.280264
$378$	27.4066	1.40964
$379$	16.1930	0.831779	0.415890	−	0.909415i	$-0.363470\pi$
$379$	16.1930	0.831779	0.415890	+	0.909415i	$0.363470\pi$
$380$	−27.7396	−1.42301
$381$	−55.3321	−2.83475
$382$	−36.9997	−1.89307
$383$	17.6660	0.902690	0.451345	−	0.892350i	$-0.350944\pi$
$383$	17.6660	0.902690	0.451345	+	0.892350i	$0.350944\pi$
$384$	250.455	12.7810
$385$	3.30907	0.168646
$386$	20.4751	1.04216
$387$	38.0740	1.93541
$388$	42.2800	2.14644
$389$	4.49136	0.227721	0.113860	−	0.993497i	$-0.463678\pi$
$389$	4.49136	0.227721	0.113860	+	0.993497i	$0.463678\pi$
$390$	15.4799	0.783856
$391$	−46.4360	−2.34837
$392$	66.2483	3.34604
$393$	−19.5569	−0.986517
$394$	−1.64344	−0.0827952
$395$	4.88628	0.245855
$396$	−120.272	−6.04388
$397$	35.1368	1.76347	0.881734	−	0.471747i	$-0.156377\pi$
$397$	35.1368	1.76347	0.881734	+	0.471747i	$0.156377\pi$
$398$	−39.5916	−1.98455
$399$	−14.2981	−0.715799
$400$	19.3275	0.966373
$401$	−19.7514	−0.986336	−0.493168	−	0.869934i	$-0.664161\pi$
$401$	−19.7514	−0.986336	−0.493168	+	0.869934i	$0.664161\pi$
$402$	97.1740	4.84660
$403$	−18.2745	−0.910316
$404$	80.6761	4.01379
$405$	−10.6749	−0.530439
$406$	−8.52645	−0.423160
$407$	−0.274938	−0.0136282
$408$	203.862	10.0927
$409$	21.1617	1.04638	0.523190	−	0.852216i	$-0.324742\pi$
$409$	21.1617	1.04638	0.523190	+	0.852216i	$0.324742\pi$
$410$	−18.7507	−0.926032
$411$	64.8926	3.20092
$412$	8.93501	0.440196
$413$	12.1570	0.598207
$414$	133.106	6.54182
$415$	−3.63623	−0.178496
$416$	58.5578	2.87103
$417$	−17.4663	−0.855327
$418$	43.1877	2.11238
$419$	−1.38577	−0.0676994	−0.0338497	−	0.999427i	$-0.510777\pi$
$419$	−1.38577	−0.0676994	−0.0338497	+	0.999427i	$0.510777\pi$
$420$	18.1394	0.885111
$421$	9.34652	0.455521	0.227761	−	0.973717i	$-0.426860\pi$
$421$	9.34652	0.455521	0.227761	+	0.973717i	$0.426860\pi$
$422$	−46.7561	−2.27605
$423$	16.9917	0.826166
$424$	−95.8512	−4.65495
$425$	6.07453	0.294658
$426$	−75.7611	−3.67064
$427$	−13.2884	−0.643070
$428$	41.3064	1.99662
$429$	−18.0241	−0.870211
$430$	17.3448	0.836442
$431$	14.8713	0.716325	0.358163	−	0.933659i	$-0.383403\pi$
$431$	14.8713	0.716325	0.358163	+	0.933659i	$0.383403\pi$
$432$	−186.384	−8.96739
$433$	31.9655	1.53616	0.768082	−	0.640351i	$-0.221211\pi$
$433$	31.9655	1.53616	0.768082	+	0.640351i	$0.221211\pi$
$434$	−28.6335	−1.37445
$435$	9.09127	0.435893
$436$	90.2225	4.32088
$437$	−35.7454	−1.70993
$438$	−1.20132	−0.0574014
$439$	−9.01111	−0.430077	−0.215038	−	0.976606i	$-0.568988\pi$
$439$	−9.01111	−0.430077	−0.215038	+	0.976606i	$0.568988\pi$
$440$	−36.3185	−1.73142
$441$	−36.9817	−1.76103
$442$	31.0315	1.47602
$443$	−9.17235	−0.435792	−0.217896	−	0.975972i	$-0.569919\pi$
$443$	−9.17235	−0.435792	−0.217896	+	0.975972i	$0.569919\pi$
$444$	−1.50713	−0.0715254
$445$	−11.1926	−0.530582
$446$	65.3428	3.09407
$447$	2.45735	0.116229
$448$	52.7462	2.49203
$449$	−10.6967	−0.504808	−0.252404	−	0.967622i	$-0.581221\pi$
$449$	−10.6967	−0.504808	−0.252404	+	0.967622i	$0.581221\pi$
$450$	−17.4123	−0.820824
$451$	21.8324	1.02805
$452$	−17.8149	−0.837944
$453$	62.6626	2.94414
$454$	30.1943	1.41709
$455$	1.83026	0.0858040
$456$	156.928	7.34882
$457$	14.4201	0.674545	0.337273	−	0.941407i	$-0.390496\pi$
$457$	14.4201	0.674545	0.337273	+	0.941407i	$0.390496\pi$
$458$	33.7747	1.57819
$459$	−58.5795	−2.73426
$460$	45.3487	2.11439
$461$	16.9174	0.787923	0.393962	−	0.919127i	$-0.371104\pi$
$461$	16.9174	0.787923	0.393962	+	0.919127i	$0.371104\pi$
$462$	−28.2412	−1.31390
$463$	−11.2183	−0.521360	−0.260680	−	0.965425i	$-0.583947\pi$
$463$	−11.2183	−0.521360	−0.260680	+	0.965425i	$0.583947\pi$
$464$	57.9858	2.69192
$465$	30.5304	1.41581
$466$	60.1753	2.78757
$467$	28.6998	1.32807	0.664034	−	0.747703i	$-0.268843\pi$
$467$	28.6998	1.32807	0.664034	+	0.747703i	$0.268843\pi$
$468$	−66.5228	−3.07502
$469$	11.4893	0.530528
$470$	7.74069	0.357051
$471$	35.8571	1.65221
$472$	−133.429	−6.14154
$473$	−20.1955	−0.928590
$474$	−41.7019	−1.91543
$475$	4.67603	0.214551
$476$	36.3628	1.66669
$477$	53.5070	2.44992
$478$	47.4998	2.17259
$479$	37.2118	1.70025	0.850125	−	0.526581i	$-0.176526\pi$
$479$	37.2118	1.70025	0.850125	+	0.526581i	$0.176526\pi$
$480$	−97.8299	−4.46530
$481$	−0.152070	−0.00693378
$482$	47.2553	2.15242
$483$	23.3745	1.06358
$484$	−1.45970	−0.0663502
$485$	−7.12709	−0.323625
$486$	9.62417	0.436561
$487$	12.7657	0.578467	0.289234	−	0.957259i	$-0.406600\pi$
$487$	12.7657	0.578467	0.289234	+	0.957259i	$0.406600\pi$
$488$	145.846	6.60214
$489$	21.0988	0.954122
$490$	−16.8473	−0.761082
$491$	24.6689	1.11329	0.556645	−	0.830750i	$-0.312088\pi$
$491$	24.6689	1.11329	0.556645	+	0.830750i	$0.312088\pi$
$492$	119.679	5.39556
$493$	18.2247	0.820797
$494$	23.8873	1.07474
$495$	20.2741	0.911252
$496$	194.728	8.74355
$497$	−8.95759	−0.401803
$498$	31.0334	1.39064
$499$	5.99127	0.268206	0.134103	−	0.990967i	$-0.457185\pi$
$499$	5.99127	0.268206	0.134103	+	0.990967i	$0.457185\pi$
$500$	−5.93229	−0.265300
$501$	−24.7869	−1.10740
$502$	27.0757	1.20845
$503$	−16.8542	−0.751490	−0.375745	−	0.926723i	$-0.622613\pi$
$503$	−16.8542	−0.751490	−0.375745	+	0.926723i	$0.622613\pi$
$504$	−69.0914	−3.07758
$505$	−13.5995	−0.605169
$506$	−70.6034	−3.13870
$507$	29.4240	1.30677
$508$	108.323	4.80606
$509$	−25.7368	−1.14076	−0.570382	−	0.821380i	$-0.693205\pi$
$509$	−25.7368	−1.14076	−0.570382	+	0.821380i	$0.693205\pi$
$510$	−51.8430	−2.29565
$511$	−0.142038	−0.00628338
$512$	−195.872	−8.65642
$513$	−45.0931	−1.99091
$514$	−32.5738	−1.43677
$515$	−1.50617	−0.0663696
$516$	−110.706	−4.87356
$517$	−9.01289	−0.396386
$518$	−0.238272	−0.0104691
$519$	−3.02465	−0.132767
$520$	−20.0880	−0.880915
$521$	−5.38651	−0.235987	−0.117994	−	0.993014i	$-0.537646\pi$
$521$	−5.38651	−0.235987	−0.117994	+	0.993014i	$0.537646\pi$
$522$	−52.2400	−2.28648
$523$	20.6671	0.903711	0.451856	−	0.892091i	$-0.350762\pi$
$523$	20.6671	0.903711	0.451856	+	0.892091i	$0.350762\pi$
$524$	38.2864	1.67255
$525$	−3.05774	−0.133451
$526$	−45.4387	−1.98122
$527$	61.2021	2.66601
$528$	192.060	8.35834
$529$	35.4366	1.54072
$530$	24.3754	1.05880
$531$	74.4837	3.23232
$532$	27.9912	1.21357
$533$	12.0756	0.523053
$534$	95.5234	4.13370
$535$	−6.96297	−0.301036
$536$	−126.101	−5.44672
$537$	−63.8678	−2.75610
$538$	70.3402	3.03258
$539$	19.6161	0.844927
$540$	57.2078	2.46183
$541$	8.56025	0.368034	0.184017	−	0.982923i	$-0.441090\pi$
$541$	8.56025	0.368034	0.184017	+	0.982923i	$0.441090\pi$
$542$	68.5891	2.94615
$543$	19.6815	0.844615
$544$	−196.113	−8.40827
$545$	−15.2087	−0.651470
$546$	−15.6203	−0.668489
$547$	−0.0726079	−0.00310449	−0.00155224	−	0.999999i	$-0.500494\pi$
$547$	−0.0726079	−0.00310449	−0.00155224	+	0.999999i	$0.500494\pi$
$548$	−127.040	−5.42687
$549$	−81.4156	−3.47473
$550$	9.23598	0.393824
$551$	14.0289	0.597652
$552$	−256.546	−10.9193
$553$	−4.93061	−0.209671
$554$	57.1395	2.42763
$555$	0.254056	0.0107841
$556$	34.1936	1.45013
$557$	−2.08545	−0.0883635	−0.0441818	−	0.999024i	$-0.514068\pi$
$557$	−2.08545	−0.0883635	−0.0441818	+	0.999024i	$0.514068\pi$
$558$	−175.433	−7.42665
$559$	−11.1702	−0.472450
$560$	−19.5028	−0.824144
$561$	60.3635	2.54855
$562$	68.1124	2.87315
$563$	−10.3249	−0.435142	−0.217571	−	0.976044i	$-0.569813\pi$
$563$	−10.3249	−0.435142	−0.217571	+	0.976044i	$0.569813\pi$
$564$	−49.4061	−2.08037
$565$	3.00305	0.126339
$566$	−21.0534	−0.884940
$567$	10.7717	0.452370
$568$	98.3136	4.12515
$569$	−20.2906	−0.850628	−0.425314	−	0.905046i	$-0.639836\pi$
$569$	−20.2906	−0.850628	−0.425314	+	0.905046i	$0.639836\pi$
$570$	−39.9075	−1.67154
$571$	16.2475	0.679936	0.339968	−	0.940437i	$-0.389584\pi$
$571$	16.2475	0.679936	0.339968	+	0.940437i	$0.389584\pi$
$572$	35.2856	1.47536
$573$	−39.8086	−1.66303
$574$	18.9208	0.789740
$575$	−7.64438	−0.318793
$576$	323.167	13.4653
$577$	2.58551	0.107636	0.0538182	−	0.998551i	$-0.482861\pi$
$577$	2.58551	0.107636	0.0538182	+	0.998551i	$0.482861\pi$
$578$	−56.0468	−2.33124
$579$	22.0296	0.915517
$580$	−17.7979	−0.739018
$581$	3.66922	0.152225
$582$	60.8261	2.52132
$583$	−28.3816	−1.17545
$584$	1.55893	0.0645090
$585$	11.2137	0.463629
$586$	−25.1272	−1.03800
$587$	−31.6815	−1.30764	−0.653818	−	0.756652i	$-0.726834\pi$
$587$	−31.6815	−1.30764	−0.653818	+	0.756652i	$0.726834\pi$
$588$	107.530	4.43447
$589$	47.1119	1.94121
$590$	33.9315	1.39694
$591$	−1.76820	−0.0727341
$592$	1.62042	0.0665987
$593$	33.7278	1.38503	0.692517	−	0.721402i	$-0.256502\pi$
$593$	33.7278	1.38503	0.692517	+	0.721402i	$0.256502\pi$
$594$	−89.0669	−3.65446
$595$	−6.12964	−0.251291
$596$	−4.81073	−0.197055
$597$	−42.5973	−1.74339
$598$	−39.0510	−1.59692
$599$	19.7690	0.807740	0.403870	−	0.914816i	$-0.367665\pi$
$599$	19.7690	0.807740	0.403870	+	0.914816i	$0.367665\pi$
$600$	33.5601	1.37008
$601$	−12.1783	−0.496763	−0.248382	−	0.968662i	$-0.579899\pi$
$601$	−12.1783	−0.496763	−0.248382	+	0.968662i	$0.579899\pi$
$602$	−17.5022	−0.713336
$603$	70.3931	2.86663
$604$	−122.674	−4.99153
$605$	0.246061	0.0100038
$606$	116.065	4.71480
$607$	18.7036	0.759154	0.379577	−	0.925160i	$-0.376069\pi$
$607$	18.7036	0.759154	0.379577	+	0.925160i	$0.376069\pi$
$608$	−150.963	−6.12236
$609$	−9.17375	−0.371739
$610$	−37.0894	−1.50170
$611$	−4.98507	−0.201674
$612$	222.788	9.00568
$613$	−33.5877	−1.35660	−0.678298	−	0.734787i	$-0.737282\pi$
$613$	−33.5877	−1.35660	−0.678298	+	0.734787i	$0.737282\pi$
$614$	−3.34715	−0.135080
$615$	−20.1742	−0.813503
$616$	36.6480	1.47659
$617$	−20.2675	−0.815937	−0.407969	−	0.912996i	$-0.633763\pi$
$617$	−20.2675	−0.815937	−0.407969	+	0.912996i	$0.633763\pi$
$618$	12.8543	0.517078
$619$	−21.9138	−0.880789	−0.440395	−	0.897804i	$-0.645161\pi$
$619$	−21.9138	−0.880789	−0.440395	+	0.897804i	$0.645161\pi$
$620$	−59.7690	−2.40038
$621$	73.7183	2.95821
$622$	39.9252	1.60086
$623$	11.2942	0.452492
$624$	106.229	4.25257
$625$	1.00000	0.0400000
$626$	41.4211	1.65552
$627$	46.4664	1.85569
$628$	−70.1970	−2.80117
$629$	0.509289	0.0203067
$630$	17.5703	0.700017
$631$	−13.3058	−0.529697	−0.264848	−	0.964290i	$-0.585322\pi$
$631$	−13.3058	−0.529697	−0.264848	+	0.964290i	$0.585322\pi$
$632$	54.1157	2.15261
$633$	−50.3057	−1.99947
$634$	−78.3102	−3.11010
$635$	−18.2599	−0.724623
$636$	−155.580	−6.16914
$637$	10.8498	0.429884
$638$	27.7096	1.09703
$639$	−54.8816	−2.17108
$640$	82.6517	3.26710
$641$	10.4738	0.413689	0.206845	−	0.978374i	$-0.433681\pi$
$641$	10.4738	0.413689	0.206845	+	0.978374i	$0.433681\pi$
$642$	59.4254	2.34533
$643$	−23.9232	−0.943439	−0.471720	−	0.881749i	$-0.656367\pi$
$643$	−23.9232	−0.943439	−0.471720	+	0.881749i	$0.656367\pi$
$644$	−45.7601	−1.80320
$645$	18.6616	0.734800
$646$	−79.9999	−3.14755
$647$	4.68960	0.184367	0.0921836	−	0.995742i	$-0.470615\pi$
$647$	4.68960	0.184367	0.0921836	+	0.995742i	$0.470615\pi$
$648$	−118.225	−4.64430
$649$	−39.5083	−1.55083
$650$	5.10846	0.200370
$651$	−30.8073	−1.20743
$652$	−41.3050	−1.61763
$653$	16.2152	0.634550	0.317275	−	0.948334i	$-0.397232\pi$
$653$	16.2152	0.634550	0.317275	+	0.948334i	$0.397232\pi$
$654$	129.799	5.07553
$655$	−6.45391	−0.252175
$656$	−128.675	−5.02391
$657$	−0.870240	−0.0339513
$658$	−7.81091	−0.304501
$659$	5.71958	0.222803	0.111402	−	0.993775i	$-0.464466\pi$
$659$	5.71958	0.222803	0.111402	+	0.993775i	$0.464466\pi$
$660$	−58.9501	−2.29463
$661$	37.5998	1.46246	0.731232	−	0.682129i	$-0.238946\pi$
$661$	37.5998	1.46246	0.731232	+	0.682129i	$0.238946\pi$
$662$	7.59766	0.295291
$663$	33.3873	1.29666
$664$	−40.2714	−1.56283
$665$	−4.71845	−0.182974
$666$	−1.45985	−0.0565680
$667$	−22.9345	−0.888027
$668$	48.5251	1.87749
$669$	70.3034	2.71809
$670$	32.0680	1.23890
$671$	43.1851	1.66714
$672$	98.7174	3.80811
$673$	−5.51334	−0.212523	−0.106262	−	0.994338i	$-0.533888\pi$
$673$	−5.51334	−0.212523	−0.106262	+	0.994338i	$0.533888\pi$
$674$	4.43430	0.170803
$675$	−9.64347	−0.371177
$676$	−57.6031	−2.21551
$677$	−22.9372	−0.881550	−0.440775	−	0.897618i	$-0.645296\pi$
$677$	−22.9372	−0.881550	−0.440775	+	0.897618i	$0.645296\pi$
$678$	−25.6294	−0.984293
$679$	7.19175	0.275994
$680$	67.2756	2.57990
$681$	32.4866	1.24489
$682$	93.0544	3.56324
$683$	−27.8646	−1.06621	−0.533105	−	0.846049i	$-0.678975\pi$
$683$	−27.8646	−1.06621	−0.533105	+	0.846049i	$0.678975\pi$
$684$	171.497	6.55736
$685$	21.4150	0.818223
$686$	36.8940	1.40862
$687$	36.3387	1.38641
$688$	119.027	4.53786
$689$	−15.6980	−0.598046
$690$	65.2409	2.48368
$691$	23.7561	0.903725	0.451863	−	0.892088i	$-0.350760\pi$
$691$	23.7561	0.903725	0.451863	+	0.892088i	$0.350760\pi$
$692$	5.92133	0.225095
$693$	−20.4580	−0.777135
$694$	20.8824	0.792687
$695$	−5.76397	−0.218640
$696$	100.686	3.81650
$697$	−40.4419	−1.53185
$698$	−40.2187	−1.52230
$699$	64.7437	2.44883
$700$	5.98611	0.226254
$701$	25.7236	0.971566	0.485783	−	0.874079i	$-0.338535\pi$
$701$	25.7236	0.971566	0.485783	+	0.874079i	$0.338535\pi$
$702$	−49.2633	−1.85932
$703$	0.392039	0.0147860
$704$	−171.417	−6.46051
$705$	8.32834	0.313663
$706$	−35.8258	−1.34832
$707$	13.7229	0.516102
$708$	−216.573	−8.13931
$709$	2.76471	0.103831	0.0519154	−	0.998651i	$-0.483467\pi$
$709$	2.76471	0.103831	0.0519154	+	0.998651i	$0.483467\pi$
$710$	−25.0016	−0.938295
$711$	−30.2089	−1.13292
$712$	−123.959	−4.64555
$713$	−77.0187	−2.88437
$714$	52.3133	1.95778
$715$	−5.94805	−0.222445
$716$	125.033	4.67272
$717$	51.1059	1.90858
$718$	83.0421	3.09910
$719$	−39.8545	−1.48632	−0.743162	−	0.669112i	$-0.766675\pi$
$719$	−39.8545	−1.48632	−0.743162	+	0.669112i	$0.766675\pi$
$720$	−119.490	−4.45314
$721$	1.51983	0.0566014
$722$	−8.06982	−0.300328
$723$	50.8428	1.89086
$724$	−38.5303	−1.43197
$725$	3.00018	0.111424
$726$	−2.10000	−0.0779384
$727$	24.8104	0.920165	0.460083	−	0.887876i	$-0.347820\pi$
$727$	24.8104	0.920165	0.460083	+	0.887876i	$0.347820\pi$
$728$	20.2702	0.751263
$729$	−21.6698	−0.802587
$730$	−0.396443	−0.0146730
$731$	37.4096	1.38365
$732$	236.729	8.74974
$733$	−20.2193	−0.746817	−0.373408	−	0.927667i	$-0.621811\pi$
$733$	−20.2193	−0.746817	−0.373408	+	0.927667i	$0.621811\pi$
$734$	−23.5086	−0.867717
$735$	−18.1263	−0.668597
$736$	246.795	9.09697
$737$	−37.3385	−1.37538
$738$	115.924	4.26724
$739$	−1.40576	−0.0517117	−0.0258558	−	0.999666i	$-0.508231\pi$
$739$	−1.40576	−0.0517117	−0.0258558	+	0.999666i	$0.508231\pi$
$740$	−0.497363	−0.0182834
$741$	25.7008	0.944142
$742$	−24.5966	−0.902969
$743$	43.2531	1.58680	0.793402	−	0.608699i	$-0.208308\pi$
$743$	43.2531	1.58680	0.793402	+	0.608699i	$0.208308\pi$
$744$	338.124	12.3962
$745$	0.810940	0.0297105
$746$	98.8280	3.61835
$747$	22.4806	0.822524
$748$	−118.173	−4.32084
$749$	7.02614	0.256730
$750$	−8.53449	−0.311635
$751$	−19.7081	−0.719159	−0.359580	−	0.933114i	$-0.617080\pi$
$751$	−19.7081	−0.719159	−0.359580	+	0.933114i	$0.617080\pi$
$752$	53.1196	1.93707
$753$	29.1312	1.06160
$754$	15.3263	0.558150
$755$	20.6790	0.752587
$756$	−57.7268	−2.09950
$757$	−39.0063	−1.41771	−0.708854	−	0.705355i	$-0.750787\pi$
$757$	−39.0063	−1.41771	−0.708854	+	0.705355i	$0.750787\pi$
$758$	−45.6065	−1.65650
$759$	−75.9634	−2.75730
$760$	51.7871	1.87852
$761$	25.5423	0.925907	0.462953	−	0.886383i	$-0.346790\pi$
$761$	25.5423	0.925907	0.462953	+	0.886383i	$0.346790\pi$
$762$	155.839	5.64545
$763$	15.3467	0.555588
$764$	77.9329	2.81951
$765$	−37.5552	−1.35781
$766$	−49.7551	−1.79772
$767$	−21.8522	−0.789037
$768$	−388.595	−14.0222
$769$	51.0449	1.84072	0.920362	−	0.391067i	$-0.127894\pi$
$769$	51.0449	1.84072	0.920362	+	0.391067i	$0.127894\pi$
$770$	−9.31977	−0.335861
$771$	−35.0467	−1.26218
$772$	−43.1271	−1.55218
$773$	15.7032	0.564804	0.282402	−	0.959296i	$-0.408869\pi$
$773$	15.7032	0.564804	0.282402	+	0.959296i	$0.408869\pi$
$774$	−107.233	−3.85440
$775$	10.0752	0.361912
$776$	−78.9327	−2.83352
$777$	−0.256361	−0.00919690
$778$	−12.6496	−0.453510
$779$	−31.1312	−1.11539
$780$	−32.6055	−1.16747
$781$	29.1107	1.04166
$782$	130.784	4.67682
$783$	−28.9321	−1.03395
$784$	−115.613	−4.12902
$785$	11.8330	0.422340
$786$	55.0808	1.96467
$787$	−32.6085	−1.16237	−0.581184	−	0.813772i	$-0.697410\pi$
$787$	−32.6085	−1.16237	−0.581184	+	0.813772i	$0.697410\pi$
$788$	3.46159	0.123314
$789$	−48.8883	−1.74047
$790$	−13.7619	−0.489626
$791$	−3.03029	−0.107745
$792$	224.536	7.97853
$793$	23.8859	0.848212
$794$	−98.9605	−3.51198
$795$	26.2260	0.930139
$796$	83.3924	2.95576
$797$	7.76163	0.274931	0.137466	−	0.990507i	$-0.456104\pi$
$797$	7.76163	0.274931	0.137466	+	0.990507i	$0.456104\pi$
$798$	40.2696	1.42553
$799$	16.6952	0.590635
$800$	−32.2845	−1.14143
$801$	69.1974	2.44497
$802$	55.6284	1.96431
$803$	0.461600	0.0162895
$804$	−204.679	−7.21847
$805$	7.71373	0.271873
$806$	51.4688	1.81291
$807$	75.6802	2.66407
$808$	−150.615	−5.29861
$809$	−16.6813	−0.586485	−0.293242	−	0.956038i	$-0.594734\pi$
$809$	−16.6813	−0.586485	−0.293242	+	0.956038i	$0.594734\pi$
$810$	30.0651	1.05638
$811$	−14.8768	−0.522395	−0.261198	−	0.965285i	$-0.584117\pi$
$811$	−14.8768	−0.522395	−0.261198	+	0.965285i	$0.584117\pi$
$812$	17.9594	0.630250
$813$	73.7962	2.58815
$814$	0.774345	0.0271408
$815$	6.96274	0.243894
$816$	−355.767	−12.4543
$817$	28.7971	1.00748
$818$	−59.6006	−2.08388
$819$	−11.3154	−0.395393
$820$	39.4949	1.37922
$821$	−25.1073	−0.876252	−0.438126	−	0.898914i	$-0.644358\pi$
$821$	−25.1073	−0.876252	−0.438126	+	0.898914i	$0.644358\pi$
$822$	−182.766	−6.37468
$823$	20.6145	0.718575	0.359288	−	0.933227i	$-0.383020\pi$
$823$	20.6145	0.718575	0.359288	+	0.933227i	$0.383020\pi$
$824$	−16.6808	−0.581104
$825$	9.93715	0.345967
$826$	−34.2393	−1.19134
$827$	−23.2976	−0.810135	−0.405068	−	0.914287i	$-0.632752\pi$
$827$	−23.2976	−0.810135	−0.405068	+	0.914287i	$0.632752\pi$
$828$	−280.364	−9.74331
$829$	−5.18339	−0.180027	−0.0900133	−	0.995941i	$-0.528691\pi$
$829$	−5.18339	−0.180027	−0.0900133	+	0.995941i	$0.528691\pi$
$830$	10.2412	0.355477
$831$	61.4774	2.13263
$832$	−94.8114	−3.28699
$833$	−36.3365	−1.25898
$834$	49.1926	1.70340
$835$	−8.17983	−0.283075
$836$	−90.9669	−3.14616
$837$	−97.1598	−3.35834
$838$	3.90293	0.134824
$839$	−20.0497	−0.692192	−0.346096	−	0.938199i	$-0.612493\pi$
$839$	−20.0497	−0.692192	−0.346096	+	0.938199i	$0.612493\pi$
$840$	−33.8645	−1.16844
$841$	−19.9989	−0.689619
$842$	−26.3238	−0.907179
$843$	73.2833	2.52401
$844$	98.4830	3.38993
$845$	9.71010	0.334038
$846$	−47.8560	−1.64532
$847$	−0.248293	−0.00853146
$848$	167.274	5.74421
$849$	−22.6517	−0.777404
$850$	−17.1085	−0.586817
$851$	−0.640905	−0.0219699
$852$	159.577	5.46701
$853$	11.8213	0.404754	0.202377	−	0.979308i	$-0.435133\pi$
$853$	11.8213	0.404754	0.202377	+	0.979308i	$0.435133\pi$
$854$	37.4258	1.28069
$855$	−28.9091	−0.988670
$856$	−77.1151	−2.63574
$857$	47.7162	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$857$	47.7162	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$858$	50.7636	1.73304
$859$	−9.97683	−0.340405	−0.170202	−	0.985409i	$-0.554442\pi$
$859$	−9.97683	−0.340405	−0.170202	+	0.985409i	$0.554442\pi$
$860$	−36.5336	−1.24579
$861$	20.3572	0.693773
$862$	−41.8840	−1.42657
$863$	22.2724	0.758161	0.379081	−	0.925364i	$-0.376240\pi$
$863$	22.2724	0.758161	0.379081	+	0.925364i	$0.376240\pi$
$864$	311.334	10.5918
$865$	−0.998153	−0.0339382
$866$	−90.0287	−3.05930
$867$	−60.3017	−2.04795
$868$	60.3112	2.04710
$869$	16.0237	0.543566
$870$	−25.6050	−0.868089
$871$	−20.6521	−0.699769
$872$	−168.437	−5.70399
$873$	44.0625	1.49129
$874$	100.674	3.40536
$875$	−1.00907	−0.0341129
$876$	2.53036	0.0854929
$877$	48.3019	1.63104	0.815520	−	0.578729i	$-0.196451\pi$
$877$	48.3019	1.63104	0.815520	+	0.578729i	$0.196451\pi$
$878$	25.3792	0.856506
$879$	−27.0348	−0.911862
$880$	63.3810	2.13657
$881$	30.8990	1.04101	0.520507	−	0.853857i	$-0.325743\pi$
$881$	30.8990	1.04101	0.520507	+	0.853857i	$0.325743\pi$
$882$	104.157	3.50713
$883$	40.0757	1.34865	0.674327	−	0.738433i	$-0.264434\pi$
$883$	40.0757	1.34865	0.674327	+	0.738433i	$0.264434\pi$
$884$	−65.3621	−2.19837
$885$	36.5075	1.22719
$886$	25.8333	0.867887
$887$	12.1177	0.406871	0.203436	−	0.979088i	$-0.434789\pi$
$887$	12.1177	0.406871	0.203436	+	0.979088i	$0.434789\pi$
$888$	2.81368	0.0944208
$889$	18.4256	0.617974
$890$	31.5233	1.05666
$891$	−35.0064	−1.17276
$892$	−137.632	−4.60827
$893$	12.8516	0.430063
$894$	−6.92096	−0.231471
$895$	−21.0768	−0.704519
$896$	−83.4015	−2.78625
$897$	−42.0157	−1.40286
$898$	30.1265	1.00533
$899$	30.2274	1.00814
$900$	36.6758	1.22253
$901$	52.5734	1.75147
$902$	−61.4896	−2.04738
$903$	−18.8309	−0.626653
$904$	33.2588	1.10617
$905$	6.49502	0.215902
$906$	−176.485	−5.86332
$907$	40.3293	1.33911	0.669556	−	0.742762i	$-0.266484\pi$
$907$	40.3293	1.33911	0.669556	+	0.742762i	$0.266484\pi$
$908$	−63.5987	−2.11060
$909$	84.0775	2.78868
$910$	−5.15481	−0.170880
$911$	12.4219	0.411555	0.205777	−	0.978599i	$-0.434028\pi$
$911$	12.4219	0.411555	0.205777	+	0.978599i	$0.434028\pi$
$912$	−273.861	−9.06845
$913$	−11.9244	−0.394639
$914$	−40.6133	−1.34337
$915$	−39.9051	−1.31922
$916$	−71.1400	−2.35053
$917$	6.51246	0.215060
$918$	164.985	5.44532
$919$	3.65770	0.120656	0.0603282	−	0.998179i	$-0.480785\pi$
$919$	3.65770	0.120656	0.0603282	+	0.998179i	$0.480785\pi$
$920$	−84.6617	−2.79121
$921$	−3.60126	−0.118665
$922$	−47.6468	−1.56916
$923$	16.1013	0.529980
$924$	59.4849	1.95691
$925$	0.0838401	0.00275664
$926$	31.5957	1.03830
$927$	9.31172	0.305837
$928$	−96.8590	−3.17955
$929$	−13.8979	−0.455977	−0.227988	−	0.973664i	$-0.573215\pi$
$929$	−13.8979	−0.455977	−0.227988	+	0.973664i	$0.573215\pi$
$930$	−85.9867	−2.81961
$931$	−27.9710	−0.916711
$932$	−126.748	−4.15177
$933$	42.9563	1.40632
$934$	−80.8310	−2.64487
$935$	19.9203	0.651464
$936$	124.192	4.05934
$937$	13.6774	0.446821	0.223411	−	0.974724i	$-0.428281\pi$
$937$	13.6774	0.446821	0.223411	+	0.974724i	$0.428281\pi$
$938$	−32.3589	−1.05656
$939$	44.5657	1.45435
$940$	−16.3043	−0.531788
$941$	−48.9810	−1.59674	−0.798368	−	0.602170i	$-0.794303\pi$
$941$	−48.9810	−1.59674	−0.798368	+	0.602170i	$0.794303\pi$
$942$	−100.989	−3.29040
$943$	50.8933	1.65731
$944$	232.851	7.57867
$945$	9.73095	0.316548
$946$	56.8792	1.84930
$947$	14.4282	0.468854	0.234427	−	0.972134i	$-0.424679\pi$
$947$	14.4282	0.468854	0.234427	+	0.972134i	$0.424679\pi$
$948$	87.8373	2.85282
$949$	0.255313	0.00828781
$950$	−13.1697	−0.427282
$951$	−84.2553	−2.73217
$952$	−67.8859	−2.20019
$953$	41.3904	1.34077	0.670383	−	0.742015i	$-0.266130\pi$
$953$	41.3904	1.34077	0.670383	+	0.742015i	$0.266130\pi$
$954$	−150.699	−4.87905
$955$	−13.1371	−0.425106
$956$	−100.049	−3.23583
$957$	29.8132	0.963724
$958$	−104.804	−3.38608
$959$	−21.6092	−0.697799
$960$	158.397	5.11225
$961$	70.5097	2.27451
$962$	0.428294	0.0138087
$963$	43.0479	1.38720
$964$	−99.5345	−3.20579
$965$	7.26989	0.234026
$966$	−65.8327	−2.11813
$967$	20.5559	0.661034	0.330517	−	0.943800i	$-0.392777\pi$
$967$	20.5559	0.661034	0.330517	+	0.943800i	$0.392777\pi$
$968$	2.72513	0.0875890
$969$	−86.0732	−2.76507
$970$	20.0730	0.644504
$971$	16.1797	0.519233	0.259616	−	0.965712i	$-0.416404\pi$
$971$	16.1797	0.519233	0.259616	+	0.965712i	$0.416404\pi$
$972$	−20.2715	−0.650210
$973$	5.81626	0.186461
$974$	−35.9536	−1.15203
$975$	5.49628	0.176022
$976$	−254.522	−8.14705
$977$	15.5250	0.496690	0.248345	−	0.968672i	$-0.420113\pi$
$977$	15.5250	0.496690	0.248345	+	0.968672i	$0.420113\pi$
$978$	−59.4234	−1.90015
$979$	−36.7042	−1.17307
$980$	35.4856	1.13355
$981$	94.0264	3.00203
$982$	−69.4782	−2.21714
$983$	−11.7838	−0.375846	−0.187923	−	0.982184i	$-0.560175\pi$
$983$	−11.7838	−0.375846	−0.187923	+	0.982184i	$0.560175\pi$
$984$	−223.430	−7.12269
$985$	−0.583517	−0.0185924
$986$	−51.3285	−1.63463
$987$	−8.40389	−0.267499
$988$	−50.3142	−1.60071
$989$	−47.0775	−1.49698
$990$	−57.1005	−1.81477
$991$	18.9334	0.601438	0.300719	−	0.953713i	$-0.402773\pi$
$991$	18.9334	0.601438	0.300719	+	0.953713i	$0.402773\pi$
$992$	−325.272	−10.3274
$993$	8.17445	0.259408
$994$	25.2285	0.800198
$995$	−14.0574	−0.445649
$996$	−65.3660	−2.07120
$997$	11.3408	0.359166	0.179583	−	0.983743i	$-0.442525\pi$
$997$	11.3408	0.359166	0.179583	+	0.983743i	$0.442525\pi$
$998$	−16.8740	−0.534137
$999$	−0.808509	−0.0255801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.1	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.1	✓	113	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.81643 q^{2} -3.03025 q^{3} +5.93229 q^{4} -1.00000 q^{5} +8.53449 q^{6} +1.00907 q^{7} -11.0750 q^{8} +6.18240 q^{9} +O(q^{10})\)	\(q-2.81643 q^{2} -3.03025 q^{3} +5.93229 q^{4} -1.00000 q^{5} +8.53449 q^{6} +1.00907 q^{7} -11.0750 q^{8} +6.18240 q^{9} +2.81643 q^{10} -3.27932 q^{11} -17.9763 q^{12} -1.81381 q^{13} -2.84198 q^{14} +3.03025 q^{15} +19.3275 q^{16} +6.07453 q^{17} -17.4123 q^{18} +4.67603 q^{19} -5.93229 q^{20} -3.05774 q^{21} +9.23598 q^{22} -7.64438 q^{23} +33.5601 q^{24} +1.00000 q^{25} +5.10846 q^{26} -9.64347 q^{27} +5.98611 q^{28} +3.00018 q^{29} -8.53449 q^{30} +10.0752 q^{31} -32.2845 q^{32} +9.93715 q^{33} -17.1085 q^{34} -1.00907 q^{35} +36.6758 q^{36} +0.0838401 q^{37} -13.1697 q^{38} +5.49628 q^{39} +11.0750 q^{40} -6.65761 q^{41} +8.61191 q^{42} +6.15844 q^{43} -19.4539 q^{44} -6.18240 q^{45} +21.5299 q^{46} +2.74840 q^{47} -58.5670 q^{48} -5.98177 q^{49} -2.81643 q^{50} -18.4073 q^{51} -10.7600 q^{52} +8.65472 q^{53} +27.1602 q^{54} +3.27932 q^{55} -11.1755 q^{56} -14.1695 q^{57} -8.44979 q^{58} +12.0477 q^{59} +17.9763 q^{60} -13.1689 q^{61} -28.3761 q^{62} +6.23849 q^{63} +52.2720 q^{64} +1.81381 q^{65} -27.9873 q^{66} +11.3860 q^{67} +36.0359 q^{68} +23.1644 q^{69} +2.84198 q^{70} -8.87706 q^{71} -68.4702 q^{72} -0.140761 q^{73} -0.236130 q^{74} -3.03025 q^{75} +27.7396 q^{76} -3.30907 q^{77} -15.4799 q^{78} -4.88628 q^{79} -19.3275 q^{80} +10.6749 q^{81} +18.7507 q^{82} +3.63623 q^{83} -18.1394 q^{84} -6.07453 q^{85} -17.3448 q^{86} -9.09127 q^{87} +36.3185 q^{88} +11.1926 q^{89} +17.4123 q^{90} -1.83026 q^{91} -45.3487 q^{92} -30.5304 q^{93} -7.74069 q^{94} -4.67603 q^{95} +97.8299 q^{96} +7.12709 q^{97} +16.8473 q^{98} -20.2741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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