LMFDB - Embedded newform 8015.2.a.m.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55168 q^{2} -1.07267 q^{3} +4.51109 q^{4} +1.00000 q^{5} +2.73711 q^{6} -1.00000 q^{7} -6.40752 q^{8} -1.84938 q^{9} +O(q^{10})$	\(q-2.55168 q^{2} -1.07267 q^{3} +4.51109 q^{4} +1.00000 q^{5} +2.73711 q^{6} -1.00000 q^{7} -6.40752 q^{8} -1.84938 q^{9} -2.55168 q^{10} +5.85501 q^{11} -4.83891 q^{12} -4.03239 q^{13} +2.55168 q^{14} -1.07267 q^{15} +7.32779 q^{16} +2.79109 q^{17} +4.71904 q^{18} +0.0980907 q^{19} +4.51109 q^{20} +1.07267 q^{21} -14.9401 q^{22} +8.83448 q^{23} +6.87315 q^{24} +1.00000 q^{25} +10.2894 q^{26} +5.20178 q^{27} -4.51109 q^{28} +5.54725 q^{29} +2.73711 q^{30} +9.54229 q^{31} -5.88316 q^{32} -6.28049 q^{33} -7.12199 q^{34} -1.00000 q^{35} -8.34274 q^{36} +9.09473 q^{37} -0.250297 q^{38} +4.32542 q^{39} -6.40752 q^{40} +2.31924 q^{41} -2.73711 q^{42} -0.100764 q^{43} +26.4125 q^{44} -1.84938 q^{45} -22.5428 q^{46} +9.36433 q^{47} -7.86029 q^{48} +1.00000 q^{49} -2.55168 q^{50} -2.99392 q^{51} -18.1905 q^{52} -5.59712 q^{53} -13.2733 q^{54} +5.85501 q^{55} +6.40752 q^{56} -0.105219 q^{57} -14.1548 q^{58} +13.0971 q^{59} -4.83891 q^{60} -1.74305 q^{61} -24.3489 q^{62} +1.84938 q^{63} +0.356386 q^{64} -4.03239 q^{65} +16.0258 q^{66} -10.8064 q^{67} +12.5909 q^{68} -9.47647 q^{69} +2.55168 q^{70} +10.5794 q^{71} +11.8500 q^{72} -2.84202 q^{73} -23.2069 q^{74} -1.07267 q^{75} +0.442497 q^{76} -5.85501 q^{77} -11.0371 q^{78} +9.76335 q^{79} +7.32779 q^{80} -0.0316424 q^{81} -5.91797 q^{82} -12.5074 q^{83} +4.83891 q^{84} +2.79109 q^{85} +0.257119 q^{86} -5.95036 q^{87} -37.5161 q^{88} +2.94730 q^{89} +4.71904 q^{90} +4.03239 q^{91} +39.8532 q^{92} -10.2357 q^{93} -23.8948 q^{94} +0.0980907 q^{95} +6.31068 q^{96} -7.11945 q^{97} -2.55168 q^{98} -10.8281 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * 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 $

$2$	−2.55168	−1.80431	−0.902157	−	0.431408i	$-0.858017\pi$
$2$	−2.55168	−1.80431	−0.902157	+	0.431408i	$0.858017\pi$
$3$	−1.07267	−0.619306	−0.309653	−	0.950850i	$-0.600213\pi$
$3$	−1.07267	−0.619306	−0.309653	+	0.950850i	$0.600213\pi$
$4$	4.51109	2.25555
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.73711	1.11742
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.40752	−2.26540
$9$	−1.84938	−0.616461
$10$	−2.55168	−0.806914
$11$	5.85501	1.76535	0.882676	−	0.469982i	$-0.155740\pi$
$11$	5.85501	1.76535	0.882676	+	0.469982i	$0.155740\pi$
$12$	−4.83891	−1.39687
$13$	−4.03239	−1.11838	−0.559192	−	0.829038i	$-0.688888\pi$
$13$	−4.03239	−1.11838	−0.559192	+	0.829038i	$0.688888\pi$
$14$	2.55168	0.681966
$15$	−1.07267	−0.276962
$16$	7.32779	1.83195
$17$	2.79109	0.676939	0.338470	−	0.940977i	$-0.390091\pi$
$17$	2.79109	0.676939	0.338470	+	0.940977i	$0.390091\pi$
$18$	4.71904	1.11229
$19$	0.0980907	0.0225036	0.0112518	−	0.999937i	$-0.496418\pi$
$19$	0.0980907	0.0225036	0.0112518	+	0.999937i	$0.496418\pi$
$20$	4.51109	1.00871
$21$	1.07267	0.234076
$22$	−14.9401	−3.18525
$23$	8.83448	1.84212	0.921058	−	0.389425i	$-0.127326\pi$
$23$	8.83448	1.84212	0.921058	+	0.389425i	$0.127326\pi$
$24$	6.87315	1.40298
$25$	1.00000	0.200000
$26$	10.2894	2.01791
$27$	5.20178	1.00108
$28$	−4.51109	−0.852517
$29$	5.54725	1.03010	0.515049	−	0.857161i	$-0.327774\pi$
$29$	5.54725	1.03010	0.515049	+	0.857161i	$0.327774\pi$
$30$	2.73711	0.499726
$31$	9.54229	1.71385	0.856923	−	0.515444i	$-0.172373\pi$
$31$	9.54229	1.71385	0.856923	+	0.515444i	$0.172373\pi$
$32$	−5.88316	−1.04000
$33$	−6.28049	−1.09329
$34$	−7.12199	−1.22141
$35$	−1.00000	−0.169031
$36$	−8.34274	−1.39046
$37$	9.09473	1.49516	0.747582	−	0.664169i	$-0.231215\pi$
$37$	9.09473	1.49516	0.747582	+	0.664169i	$0.231215\pi$
$38$	−0.250297	−0.0406035
$39$	4.32542	0.692621
$40$	−6.40752	−1.01312
$41$	2.31924	0.362204	0.181102	−	0.983464i	$-0.442034\pi$
$41$	2.31924	0.362204	0.181102	+	0.983464i	$0.442034\pi$
$42$	−2.73711	−0.422346
$43$	−0.100764	−0.0153664	−0.00768322	−	0.999970i	$-0.502446\pi$
$43$	−0.100764	−0.0153664	−0.00768322	+	0.999970i	$0.502446\pi$
$44$	26.4125	3.98184
$45$	−1.84938	−0.275690
$46$	−22.5428	−3.32376
$47$	9.36433	1.36593	0.682964	−	0.730452i	$-0.260691\pi$
$47$	9.36433	1.36593	0.682964	+	0.730452i	$0.260691\pi$
$48$	−7.86029	−1.13453
$49$	1.00000	0.142857
$50$	−2.55168	−0.360863
$51$	−2.99392	−0.419232
$52$	−18.1905	−2.52257
$53$	−5.59712	−0.768824	−0.384412	−	0.923162i	$-0.625596\pi$
$53$	−5.59712	−0.768824	−0.384412	+	0.923162i	$0.625596\pi$
$54$	−13.2733	−1.80627
$55$	5.85501	0.789489
$56$	6.40752	0.856241
$57$	−0.105219	−0.0139366
$58$	−14.1548	−1.85862
$59$	13.0971	1.70510	0.852550	−	0.522645i	$-0.175055\pi$
$59$	13.0971	1.70510	0.852550	+	0.522645i	$0.175055\pi$
$60$	−4.83891	−0.624701
$61$	−1.74305	−0.223175	−0.111587	−	0.993755i	$-0.535593\pi$
$61$	−1.74305	−0.223175	−0.111587	+	0.993755i	$0.535593\pi$
$62$	−24.3489	−3.09232
$63$	1.84938	0.233000
$64$	0.356386	0.0445483
$65$	−4.03239	−0.500156
$66$	16.0258	1.97264
$67$	−10.8064	−1.32022	−0.660109	−	0.751170i	$-0.729490\pi$
$67$	−10.8064	−1.32022	−0.660109	+	0.751170i	$0.729490\pi$
$68$	12.5909	1.52687
$69$	−9.47647	−1.14083
$70$	2.55168	0.304985
$71$	10.5794	1.25554	0.627772	−	0.778397i	$-0.283967\pi$
$71$	10.5794	1.25554	0.627772	+	0.778397i	$0.283967\pi$
$72$	11.8500	1.39653
$73$	−2.84202	−0.332633	−0.166317	−	0.986072i	$-0.553187\pi$
$73$	−2.84202	−0.332633	−0.166317	+	0.986072i	$0.553187\pi$
$74$	−23.2069	−2.69774
$75$	−1.07267	−0.123861
$76$	0.442497	0.0507578
$77$	−5.85501	−0.667240
$78$	−11.0371	−1.24971
$79$	9.76335	1.09846	0.549231	−	0.835670i	$-0.314921\pi$
$79$	9.76335	1.09846	0.549231	+	0.835670i	$0.314921\pi$
$80$	7.32779	0.819271
$81$	−0.0316424	−0.00351582
$82$	−5.91797	−0.653530
$83$	−12.5074	−1.37287	−0.686434	−	0.727192i	$-0.740825\pi$
$83$	−12.5074	−1.37287	−0.686434	+	0.727192i	$0.740825\pi$
$84$	4.83891	0.527968
$85$	2.79109	0.302736
$86$	0.257119	0.0277259
$87$	−5.95036	−0.637946
$88$	−37.5161	−3.99923
$89$	2.94730	0.312413	0.156207	−	0.987724i	$-0.450073\pi$
$89$	2.94730	0.312413	0.156207	+	0.987724i	$0.450073\pi$
$90$	4.71904	0.497430
$91$	4.03239	0.422709
$92$	39.8532	4.15498
$93$	−10.2357	−1.06139
$94$	−23.8948	−2.46456
$95$	0.0980907	0.0100639
$96$	6.31068	0.644081
$97$	−7.11945	−0.722871	−0.361435	−	0.932397i	$-0.617713\pi$
$97$	−7.11945	−0.722871	−0.361435	+	0.932397i	$0.617713\pi$
$98$	−2.55168	−0.257759
$99$	−10.8281	−1.08827
$100$	4.51109	0.451109
$101$	0.335130	0.0333467	0.0166733	−	0.999861i	$-0.494692\pi$
$101$	0.335130	0.0333467	0.0166733	+	0.999861i	$0.494692\pi$
$102$	7.63953	0.756426
$103$	12.6097	1.24248	0.621238	−	0.783622i	$-0.286630\pi$
$103$	12.6097	1.24248	0.621238	+	0.783622i	$0.286630\pi$
$104$	25.8376	2.53359
$105$	1.07267	0.104682
$106$	14.2821	1.38720
$107$	−11.3007	−1.09248	−0.546238	−	0.837630i	$-0.683940\pi$
$107$	−11.3007	−1.09248	−0.546238	+	0.837630i	$0.683940\pi$
$108$	23.4657	2.25799
$109$	−17.8432	−1.70907	−0.854534	−	0.519395i	$-0.826157\pi$
$109$	−17.8432	−1.70907	−0.854534	+	0.519395i	$0.826157\pi$
$110$	−14.9401	−1.42449
$111$	−9.75563	−0.925964
$112$	−7.32779	−0.692411
$113$	−12.4029	−1.16676	−0.583382	−	0.812198i	$-0.698271\pi$
$113$	−12.4029	−1.16676	−0.583382	+	0.812198i	$0.698271\pi$
$114$	0.268485	0.0251460
$115$	8.83448	0.823820
$116$	25.0242	2.32344
$117$	7.45742	0.689439
$118$	−33.4197	−3.07654
$119$	−2.79109	−0.255859
$120$	6.87315	0.627430
$121$	23.2811	2.11647
$122$	4.44772	0.402677
$123$	−2.48778	−0.224315
$124$	43.0462	3.86566
$125$	1.00000	0.0894427
$126$	−4.71904	−0.420405
$127$	7.36364	0.653417	0.326709	−	0.945125i	$-0.394060\pi$
$127$	7.36364	0.653417	0.326709	+	0.945125i	$0.394060\pi$
$128$	10.8569	0.959626
$129$	0.108087	0.00951652
$130$	10.2894	0.902438
$131$	−10.6031	−0.926395	−0.463198	−	0.886255i	$-0.653298\pi$
$131$	−10.6031	−0.926395	−0.463198	+	0.886255i	$0.653298\pi$
$132$	−28.3319	−2.46597
$133$	−0.0980907	−0.00850554
$134$	27.5747	2.38209
$135$	5.20178	0.447698
$136$	−17.8840	−1.53354
$137$	1.11965	0.0956585	0.0478292	−	0.998856i	$-0.484770\pi$
$137$	1.11965	0.0956585	0.0478292	+	0.998856i	$0.484770\pi$
$138$	24.1810	2.05842
$139$	−6.59350	−0.559253	−0.279627	−	0.960109i	$-0.590211\pi$
$139$	−6.59350	−0.559253	−0.279627	+	0.960109i	$0.590211\pi$
$140$	−4.51109	−0.381257
$141$	−10.0448	−0.845927
$142$	−26.9953	−2.26539
$143$	−23.6097	−1.97434
$144$	−13.5519	−1.12932
$145$	5.54725	0.460674
$146$	7.25194	0.600175
$147$	−1.07267	−0.0884722
$148$	41.0272	3.37241
$149$	−6.72784	−0.551166	−0.275583	−	0.961277i	$-0.588871\pi$
$149$	−6.72784	−0.551166	−0.275583	+	0.961277i	$0.588871\pi$
$150$	2.73711	0.223484
$151$	20.6805	1.68295	0.841477	−	0.540292i	$-0.181686\pi$
$151$	20.6805	1.68295	0.841477	+	0.540292i	$0.181686\pi$
$152$	−0.628518	−0.0509796
$153$	−5.16179	−0.417306
$154$	14.9401	1.20391
$155$	9.54229	0.766455
$156$	19.5124	1.56224
$157$	1.27075	0.101417	0.0507085	−	0.998713i	$-0.483852\pi$
$157$	1.27075	0.101417	0.0507085	+	0.998713i	$0.483852\pi$
$158$	−24.9130	−1.98197
$159$	6.00386	0.476137
$160$	−5.88316	−0.465104
$161$	−8.83448	−0.696255
$162$	0.0807413	0.00634364
$163$	−16.8687	−1.32126	−0.660630	−	0.750712i	$-0.729711\pi$
$163$	−16.8687	−1.32126	−0.660630	+	0.750712i	$0.729711\pi$
$164$	10.4623	0.816969
$165$	−6.28049	−0.488935
$166$	31.9150	2.47708
$167$	18.0396	1.39595	0.697973	−	0.716124i	$-0.254085\pi$
$167$	18.0396	1.39595	0.697973	+	0.716124i	$0.254085\pi$
$168$	−6.87315	−0.530275
$169$	3.26015	0.250781
$170$	−7.12199	−0.546231
$171$	−0.181407	−0.0138726
$172$	−0.454558	−0.0346597
$173$	−8.68285	−0.660145	−0.330072	−	0.943956i	$-0.607073\pi$
$173$	−8.68285	−0.660145	−0.330072	+	0.943956i	$0.607073\pi$
$174$	15.1834	1.15105
$175$	−1.00000	−0.0755929
$176$	42.9043	3.23403
$177$	−14.0489	−1.05598
$178$	−7.52058	−0.563691
$179$	−9.56060	−0.714593	−0.357296	−	0.933991i	$-0.616301\pi$
$179$	−9.56060	−0.714593	−0.357296	+	0.933991i	$0.616301\pi$
$180$	−8.34274	−0.621831
$181$	6.54110	0.486196	0.243098	−	0.970002i	$-0.421836\pi$
$181$	6.54110	0.486196	0.243098	+	0.970002i	$0.421836\pi$
$182$	−10.2894	−0.762700
$183$	1.86972	0.138213
$184$	−56.6071	−4.17313
$185$	9.09473	0.668658
$186$	26.1183	1.91509
$187$	16.3419	1.19504
$188$	42.2434	3.08092
$189$	−5.20178	−0.378374
$190$	−0.250297	−0.0181584
$191$	−4.78427	−0.346177	−0.173089	−	0.984906i	$-0.555375\pi$
$191$	−4.78427	−0.346177	−0.173089	+	0.984906i	$0.555375\pi$
$192$	−0.382285	−0.0275890
$193$	5.62831	0.405134	0.202567	−	0.979268i	$-0.435072\pi$
$193$	5.62831	0.405134	0.202567	+	0.979268i	$0.435072\pi$
$194$	18.1666	1.30429
$195$	4.32542	0.309750
$196$	4.51109	0.322221
$197$	−11.8445	−0.843884	−0.421942	−	0.906623i	$-0.638651\pi$
$197$	−11.8445	−0.843884	−0.421942	+	0.906623i	$0.638651\pi$
$198$	27.6300	1.96358
$199$	26.0733	1.84829	0.924143	−	0.382047i	$-0.124781\pi$
$199$	26.0733	1.84829	0.924143	+	0.382047i	$0.124781\pi$
$200$	−6.40752	−0.453080
$201$	11.5917	0.817618
$202$	−0.855146	−0.0601679
$203$	−5.54725	−0.389341
$204$	−13.5058	−0.945598
$205$	2.31924	0.161983
$206$	−32.1761	−2.24182
$207$	−16.3383	−1.13559
$208$	−29.5485	−2.04882
$209$	0.574322	0.0397267
$210$	−2.73711	−0.188879
$211$	17.1736	1.18228	0.591140	−	0.806569i	$-0.298678\pi$
$211$	17.1736	1.18228	0.591140	+	0.806569i	$0.298678\pi$
$212$	−25.2492	−1.73412
$213$	−11.3482	−0.777565
$214$	28.8357	1.97117
$215$	−0.100764	−0.00687208
$216$	−33.3305	−2.26785
$217$	−9.54229	−0.647773
$218$	45.5302	3.08370
$219$	3.04855	0.206002
$220$	26.4125	1.78073
$221$	−11.2548	−0.757077
$222$	24.8933	1.67073
$223$	21.6234	1.44801	0.724005	−	0.689795i	$-0.242299\pi$
$223$	21.6234	1.44801	0.724005	+	0.689795i	$0.242299\pi$
$224$	5.88316	0.393085
$225$	−1.84938	−0.123292
$226$	31.6482	2.10521
$227$	−3.19985	−0.212382	−0.106191	−	0.994346i	$-0.533865\pi$
$227$	−3.19985	−0.212382	−0.106191	+	0.994346i	$0.533865\pi$
$228$	−0.474652	−0.0314346
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−22.5428	−1.48643
$231$	6.28049	0.413226
$232$	−35.5441	−2.33359
$233$	16.3822	1.07323	0.536617	−	0.843826i	$-0.319702\pi$
$233$	16.3822	1.07323	0.536617	+	0.843826i	$0.319702\pi$
$234$	−19.0290	−1.24396
$235$	9.36433	0.610862
$236$	59.0824	3.84594
$237$	−10.4728	−0.680284
$238$	7.12199	0.461650
$239$	8.55525	0.553393	0.276697	−	0.960957i	$-0.410760\pi$
$239$	8.55525	0.553393	0.276697	+	0.960957i	$0.410760\pi$
$240$	−7.86029	−0.507379
$241$	−24.6847	−1.59008	−0.795041	−	0.606556i	$-0.792551\pi$
$241$	−24.6847	−1.59008	−0.795041	+	0.606556i	$0.792551\pi$
$242$	−59.4061	−3.81877
$243$	−15.5714	−0.998906
$244$	−7.86307	−0.503381
$245$	1.00000	0.0638877
$246$	6.34802	0.404735
$247$	−0.395540	−0.0251676
$248$	−61.1424	−3.88255
$249$	13.4163	0.850225
$250$	−2.55168	−0.161383
$251$	13.4515	0.849053	0.424527	−	0.905415i	$-0.360441\pi$
$251$	13.4515	0.849053	0.424527	+	0.905415i	$0.360441\pi$
$252$	8.34274	0.525543
$253$	51.7260	3.25198
$254$	−18.7897	−1.17897
$255$	−2.99392	−0.187486
$256$	−28.4162	−1.77601
$257$	24.3783	1.52068	0.760339	−	0.649527i	$-0.225033\pi$
$257$	24.3783	1.52068	0.760339	+	0.649527i	$0.225033\pi$
$258$	−0.275804	−0.0171708
$259$	−9.09473	−0.565119
$260$	−18.1905	−1.12813
$261$	−10.2590	−0.635015
$262$	27.0557	1.67151
$263$	−19.8082	−1.22143	−0.610714	−	0.791851i	$-0.709117\pi$
$263$	−19.8082	−1.22143	−0.610714	+	0.791851i	$0.709117\pi$
$264$	40.2424	2.47675
$265$	−5.59712	−0.343829
$266$	0.250297	0.0153467
$267$	−3.16148	−0.193479
$268$	−48.7489	−2.97781
$269$	−2.28154	−0.139108	−0.0695539	−	0.997578i	$-0.522158\pi$
$269$	−2.28154	−0.139108	−0.0695539	+	0.997578i	$0.522158\pi$
$270$	−13.2733	−0.807788
$271$	2.06564	0.125479	0.0627394	−	0.998030i	$-0.480016\pi$
$271$	2.06564	0.125479	0.0627394	+	0.998030i	$0.480016\pi$
$272$	20.4525	1.24012
$273$	−4.32542	−0.261786
$274$	−2.85700	−0.172598
$275$	5.85501	0.353070
$276$	−42.7493	−2.57320
$277$	−26.5970	−1.59806	−0.799030	−	0.601291i	$-0.794653\pi$
$277$	−26.5970	−1.59806	−0.799030	+	0.601291i	$0.794653\pi$
$278$	16.8245	1.00907
$279$	−17.6473	−1.05652
$280$	6.40752	0.382923
$281$	−0.516651	−0.0308208	−0.0154104	−	0.999881i	$-0.504905\pi$
$281$	−0.516651	−0.0308208	−0.0154104	+	0.999881i	$0.504905\pi$
$282$	25.6312	1.52632
$283$	5.79010	0.344186	0.172093	−	0.985081i	$-0.444947\pi$
$283$	5.79010	0.344186	0.172093	+	0.985081i	$0.444947\pi$
$284$	47.7247	2.83194
$285$	−0.105219	−0.00623263
$286$	60.2444	3.56233
$287$	−2.31924	−0.136900
$288$	10.8802	0.641122
$289$	−9.20981	−0.541753
$290$	−14.1548	−0.831200
$291$	7.63681	0.447678
$292$	−12.8206	−0.750270
$293$	−20.7738	−1.21362	−0.606810	−	0.794847i	$-0.707551\pi$
$293$	−20.7738	−1.21362	−0.606810	+	0.794847i	$0.707551\pi$
$294$	2.73711	0.159632
$295$	13.0971	0.762544
$296$	−58.2747	−3.38715
$297$	30.4565	1.76726
$298$	17.1673	0.994477
$299$	−35.6241	−2.06019
$300$	−4.83891	−0.279375
$301$	0.100764	0.00580797
$302$	−52.7701	−3.03658
$303$	−0.359483	−0.0206518
$304$	0.718788	0.0412253
$305$	−1.74305	−0.0998068
$306$	13.1713	0.752951
$307$	−0.795707	−0.0454134	−0.0227067	−	0.999742i	$-0.507228\pi$
$307$	−0.795707	−0.0454134	−0.0227067	+	0.999742i	$0.507228\pi$
$308$	−26.4125	−1.50499
$309$	−13.5261	−0.769472
$310$	−24.3489	−1.38293
$311$	−2.19847	−0.124664	−0.0623319	−	0.998055i	$-0.519854\pi$
$311$	−2.19847	−0.124664	−0.0623319	+	0.998055i	$0.519854\pi$
$312$	−27.7152	−1.56906
$313$	−6.50853	−0.367884	−0.183942	−	0.982937i	$-0.558886\pi$
$313$	−6.50853	−0.367884	−0.183942	+	0.982937i	$0.558886\pi$
$314$	−3.24256	−0.182988
$315$	1.84938	0.104201
$316$	44.0434	2.47763
$317$	13.4652	0.756279	0.378140	−	0.925749i	$-0.376564\pi$
$317$	13.4652	0.756279	0.378140	+	0.925749i	$0.376564\pi$
$318$	−15.3200	−0.859101
$319$	32.4792	1.81849
$320$	0.356386	0.0199226
$321$	12.1219	0.676576
$322$	22.5428	1.25626
$323$	0.273780	0.0152335
$324$	−0.142742	−0.00793009
$325$	−4.03239	−0.223677
$326$	43.0436	2.38397
$327$	19.1398	1.05844
$328$	−14.8606	−0.820538
$329$	−9.36433	−0.516272
$330$	16.0258	0.882192
$331$	−25.9104	−1.42416	−0.712082	−	0.702096i	$-0.752248\pi$
$331$	−25.9104	−1.42416	−0.712082	+	0.702096i	$0.752248\pi$
$332$	−56.4222	−3.09657
$333$	−16.8196	−0.921710
$334$	−46.0314	−2.51873
$335$	−10.8064	−0.590419
$336$	7.86029	0.428814
$337$	1.23013	0.0670092	0.0335046	−	0.999439i	$-0.489333\pi$
$337$	1.23013	0.0670092	0.0335046	+	0.999439i	$0.489333\pi$
$338$	−8.31888	−0.452487
$339$	13.3042	0.722583
$340$	12.5909	0.682836
$341$	55.8702	3.02554
$342$	0.462894	0.0250304
$343$	−1.00000	−0.0539949
$344$	0.645650	0.0348111
$345$	−9.47647	−0.510196
$346$	22.1559	1.19111
$347$	1.42542	0.0765207	0.0382604	−	0.999268i	$-0.487818\pi$
$347$	1.42542	0.0765207	0.0382604	+	0.999268i	$0.487818\pi$
$348$	−26.8426	−1.43892
$349$	19.3123	1.03376	0.516881	−	0.856057i	$-0.327093\pi$
$349$	19.3123	1.03376	0.516881	+	0.856057i	$0.327093\pi$
$350$	2.55168	0.136393
$351$	−20.9756	−1.11959
$352$	−34.4459	−1.83597
$353$	10.1988	0.542829	0.271415	−	0.962463i	$-0.412509\pi$
$353$	10.1988	0.542829	0.271415	+	0.962463i	$0.412509\pi$
$354$	35.8483	1.90532
$355$	10.5794	0.561496
$356$	13.2955	0.704663
$357$	2.99392	0.158455
$358$	24.3956	1.28935
$359$	−12.2515	−0.646610	−0.323305	−	0.946295i	$-0.604794\pi$
$359$	−12.2515	−0.646610	−0.323305	+	0.946295i	$0.604794\pi$
$360$	11.8500	0.624547
$361$	−18.9904	−0.999494
$362$	−16.6908	−0.877250
$363$	−24.9730	−1.31074
$364$	18.1905	0.953440
$365$	−2.84202	−0.148758
$366$	−4.77093	−0.249380
$367$	35.1116	1.83281	0.916405	−	0.400253i	$-0.131078\pi$
$367$	35.1116	1.83281	0.916405	+	0.400253i	$0.131078\pi$
$368$	64.7372	3.37466
$369$	−4.28916	−0.223285
$370$	−23.2069	−1.20647
$371$	5.59712	0.290588
$372$	−46.1743	−2.39403
$373$	32.3064	1.67276	0.836381	−	0.548149i	$-0.184667\pi$
$373$	32.3064	1.67276	0.836381	+	0.548149i	$0.184667\pi$
$374$	−41.6993	−2.15622
$375$	−1.07267	−0.0553924
$376$	−60.0022	−3.09437
$377$	−22.3687	−1.15204
$378$	13.2733	0.682705
$379$	−21.9182	−1.12586	−0.562931	−	0.826504i	$-0.690326\pi$
$379$	−21.9182	−1.12586	−0.562931	+	0.826504i	$0.690326\pi$
$380$	0.442497	0.0226996
$381$	−7.89875	−0.404665
$382$	12.2079	0.624613
$383$	−10.7014	−0.546815	−0.273408	−	0.961898i	$-0.588151\pi$
$383$	−10.7014	−0.546815	−0.273408	+	0.961898i	$0.588151\pi$
$384$	−11.6459	−0.594302
$385$	−5.85501	−0.298399
$386$	−14.3617	−0.730989
$387$	0.186352	0.00947280
$388$	−32.1165	−1.63047
$389$	2.10288	0.106620	0.0533100	−	0.998578i	$-0.483023\pi$
$389$	2.10288	0.106620	0.0533100	+	0.998578i	$0.483023\pi$
$390$	−11.0371	−0.558885
$391$	24.6578	1.24700
$392$	−6.40752	−0.323629
$393$	11.3736	0.573722
$394$	30.2234	1.52263
$395$	9.76335	0.491247
$396$	−48.8468	−2.45464
$397$	−26.5937	−1.33470	−0.667349	−	0.744745i	$-0.732571\pi$
$397$	−26.5937	−1.33470	−0.667349	+	0.744745i	$0.732571\pi$
$398$	−66.5308	−3.33489
$399$	0.105219	0.00526753
$400$	7.32779	0.366389
$401$	−15.0189	−0.750006	−0.375003	−	0.927024i	$-0.622358\pi$
$401$	−15.0189	−0.750006	−0.375003	+	0.927024i	$0.622358\pi$
$402$	−29.5785	−1.47524
$403$	−38.4782	−1.91674
$404$	1.51180	0.0752150
$405$	−0.0316424	−0.00157232
$406$	14.1548	0.702492
$407$	53.2497	2.63949
$408$	19.1836	0.949729
$409$	18.7249	0.925885	0.462942	−	0.886388i	$-0.346794\pi$
$409$	18.7249	0.925885	0.462942	+	0.886388i	$0.346794\pi$
$410$	−5.91797	−0.292268
$411$	−1.20102	−0.0592418
$412$	56.8838	2.80246
$413$	−13.0971	−0.644467
$414$	41.6903	2.04896
$415$	−12.5074	−0.613965
$416$	23.7232	1.16312
$417$	7.07264	0.346349
$418$	−1.46549	−0.0716794
$419$	14.8669	0.726297	0.363148	−	0.931731i	$-0.381702\pi$
$419$	14.8669	0.726297	0.363148	+	0.931731i	$0.381702\pi$
$420$	4.83891	0.236115
$421$	−2.85078	−0.138939	−0.0694694	−	0.997584i	$-0.522131\pi$
$421$	−2.85078	−0.138939	−0.0694694	+	0.997584i	$0.522131\pi$
$422$	−43.8216	−2.13320
$423$	−17.3182	−0.842041
$424$	35.8637	1.74170
$425$	2.79109	0.135388
$426$	28.9570	1.40297
$427$	1.74305	0.0843521
$428$	−50.9783	−2.46413
$429$	25.3254	1.22272
$430$	0.257119	0.0123994
$431$	−28.7908	−1.38681	−0.693403	−	0.720550i	$-0.743889\pi$
$431$	−28.7908	−1.38681	−0.693403	+	0.720550i	$0.743889\pi$
$432$	38.1175	1.83393
$433$	−14.1026	−0.677727	−0.338863	−	0.940836i	$-0.610042\pi$
$433$	−14.1026	−0.677727	−0.338863	+	0.940836i	$0.610042\pi$
$434$	24.3489	1.16879
$435$	−5.95036	−0.285298
$436$	−80.4924	−3.85489
$437$	0.866581	0.0414542
$438$	−7.77893	−0.371692
$439$	19.2366	0.918112	0.459056	−	0.888407i	$-0.348188\pi$
$439$	19.2366	0.918112	0.459056	+	0.888407i	$0.348188\pi$
$440$	−37.5161	−1.78851
$441$	−1.84938	−0.0880658
$442$	28.7186	1.36600
$443$	−11.7524	−0.558374	−0.279187	−	0.960237i	$-0.590065\pi$
$443$	−11.7524	−0.558374	−0.279187	+	0.960237i	$0.590065\pi$
$444$	−44.0086	−2.08855
$445$	2.94730	0.139715
$446$	−55.1761	−2.61266
$447$	7.21675	0.341340
$448$	−0.356386	−0.0168377
$449$	−29.5181	−1.39304	−0.696522	−	0.717536i	$-0.745270\pi$
$449$	−29.5181	−1.39304	−0.696522	+	0.717536i	$0.745270\pi$
$450$	4.71904	0.222458
$451$	13.5792	0.639418
$452$	−55.9505	−2.63169
$453$	−22.1833	−1.04226
$454$	8.16501	0.383203
$455$	4.03239	0.189041
$456$	0.674192	0.0315719
$457$	−22.7595	−1.06464	−0.532322	−	0.846542i	$-0.678681\pi$
$457$	−22.7595	−1.06464	−0.532322	+	0.846542i	$0.678681\pi$
$458$	2.55168	0.119232
$459$	14.5186	0.677672
$460$	39.8532	1.85816
$461$	−27.4159	−1.27689	−0.638443	−	0.769669i	$-0.720421\pi$
$461$	−27.4159	−1.27689	−0.638443	+	0.769669i	$0.720421\pi$
$462$	−16.0258	−0.745589
$463$	−29.0558	−1.35034	−0.675169	−	0.737663i	$-0.735930\pi$
$463$	−29.0558	−1.35034	−0.675169	+	0.737663i	$0.735930\pi$
$464$	40.6491	1.88708
$465$	−10.2357	−0.474670
$466$	−41.8022	−1.93645
$467$	29.1084	1.34698	0.673489	−	0.739198i	$-0.264795\pi$
$467$	29.1084	1.34698	0.673489	+	0.739198i	$0.264795\pi$
$468$	33.6411	1.55506
$469$	10.8064	0.498995
$470$	−23.8948	−1.10219
$471$	−1.36310	−0.0628081
$472$	−83.9201	−3.86274
$473$	−0.589977	−0.0271272
$474$	26.7234	1.22745
$475$	0.0980907	0.00450071
$476$	−12.5909	−0.577102
$477$	10.3512	0.473950
$478$	−21.8303	−0.998495
$479$	−11.2724	−0.515048	−0.257524	−	0.966272i	$-0.582907\pi$
$479$	−11.2724	−0.515048	−0.257524	+	0.966272i	$0.582907\pi$
$480$	6.31068	0.288042
$481$	−36.6735	−1.67217
$482$	62.9876	2.86901
$483$	9.47647	0.431194
$484$	105.023	4.77379
$485$	−7.11945	−0.323278
$486$	39.7333	1.80234
$487$	−0.533800	−0.0241888	−0.0120944	−	0.999927i	$-0.503850\pi$
$487$	−0.533800	−0.0241888	−0.0120944	+	0.999927i	$0.503850\pi$
$488$	11.1686	0.505580
$489$	18.0945	0.818264
$490$	−2.55168	−0.115273
$491$	5.30191	0.239272	0.119636	−	0.992818i	$-0.461827\pi$
$491$	5.30191	0.239272	0.119636	+	0.992818i	$0.461827\pi$
$492$	−11.2226	−0.505953
$493$	15.4829	0.697314
$494$	1.00929	0.0454102
$495$	−10.8281	−0.486689
$496$	69.9239	3.13967
$497$	−10.5794	−0.474551
$498$	−34.2342	−1.53407
$499$	−11.3278	−0.507101	−0.253550	−	0.967322i	$-0.581598\pi$
$499$	−11.3278	−0.507101	−0.253550	+	0.967322i	$0.581598\pi$
$500$	4.51109	0.201742
$501$	−19.3505	−0.864518
$502$	−34.3241	−1.53196
$503$	−10.3083	−0.459623	−0.229812	−	0.973235i	$-0.573811\pi$
$503$	−10.3083	−0.459623	−0.229812	+	0.973235i	$0.573811\pi$
$504$	−11.8500	−0.527839
$505$	0.335130	0.0149131
$506$	−131.988	−5.86760
$507$	−3.49706	−0.155310
$508$	33.2181	1.47381
$509$	10.5456	0.467423	0.233712	−	0.972306i	$-0.424913\pi$
$509$	10.5456	0.467423	0.233712	+	0.972306i	$0.424913\pi$
$510$	7.63953	0.338284
$511$	2.84202	0.125724
$512$	50.7954	2.24486
$513$	0.510246	0.0225279
$514$	−62.2058	−2.74378
$515$	12.6097	0.555652
$516$	0.487590	0.0214650
$517$	54.8283	2.41134
$518$	23.2069	1.01965
$519$	9.31382	0.408831
$520$	25.8376	1.13305
$521$	35.8015	1.56849	0.784246	−	0.620450i	$-0.213050\pi$
$521$	35.8015	1.56849	0.784246	+	0.620450i	$0.213050\pi$
$522$	26.1777	1.14577
$523$	21.5033	0.940275	0.470137	−	0.882593i	$-0.344204\pi$
$523$	21.5033	0.940275	0.470137	+	0.882593i	$0.344204\pi$
$524$	−47.8315	−2.08953
$525$	1.07267	0.0468151
$526$	50.5443	2.20384
$527$	26.6334	1.16017
$528$	−46.0221	−2.00285
$529$	55.0481	2.39339
$530$	14.2821	0.620375
$531$	−24.2216	−1.05113
$532$	−0.442497	−0.0191847
$533$	−9.35207	−0.405083
$534$	8.06709	0.349097
$535$	−11.3007	−0.488570
$536$	69.2426	2.99082
$537$	10.2554	0.442551
$538$	5.82177	0.250994
$539$	5.85501	0.252193
$540$	23.4657	1.00980
$541$	−8.45426	−0.363477	−0.181739	−	0.983347i	$-0.558172\pi$
$541$	−8.45426	−0.363477	−0.181739	+	0.983347i	$0.558172\pi$
$542$	−5.27087	−0.226403
$543$	−7.01643	−0.301104
$544$	−16.4204	−0.704020
$545$	−17.8432	−0.764319
$546$	11.0371	0.472344
$547$	−29.4221	−1.25800	−0.628999	−	0.777406i	$-0.716535\pi$
$547$	−29.4221	−1.25800	−0.628999	+	0.777406i	$0.716535\pi$
$548$	5.05086	0.215762
$549$	3.22357	0.137578
$550$	−14.9401	−0.637050
$551$	0.544134	0.0231809
$552$	60.7207	2.58444
$553$	−9.76335	−0.415180
$554$	67.8672	2.88340
$555$	−9.75563	−0.414103
$556$	−29.7439	−1.26142
$557$	31.7655	1.34595	0.672974	−	0.739666i	$-0.265017\pi$
$557$	31.7655	1.34595	0.672974	+	0.739666i	$0.265017\pi$
$558$	45.0304	1.90629
$559$	0.406321	0.0171856
$560$	−7.32779	−0.309655
$561$	−17.5294	−0.740092
$562$	1.31833	0.0556104
$563$	−25.2282	−1.06324	−0.531620	−	0.846983i	$-0.678417\pi$
$563$	−25.2282	−1.06324	−0.531620	+	0.846983i	$0.678417\pi$
$564$	−45.3132	−1.90803
$565$	−12.4029	−0.521792
$566$	−14.7745	−0.621019
$567$	0.0316424	0.00132885
$568$	−67.7877	−2.84431
$569$	−29.6976	−1.24499	−0.622494	−	0.782624i	$-0.713881\pi$
$569$	−29.6976	−1.24499	−0.622494	+	0.782624i	$0.713881\pi$
$570$	0.268485	0.0112456
$571$	−38.6905	−1.61915	−0.809574	−	0.587018i	$-0.800302\pi$
$571$	−38.6905	−1.61915	−0.809574	+	0.587018i	$0.800302\pi$
$572$	−106.505	−4.45322
$573$	5.13193	0.214390
$574$	5.91797	0.247011
$575$	8.83448	0.368423
$576$	−0.659095	−0.0274623
$577$	41.9787	1.74760	0.873799	−	0.486287i	$-0.161649\pi$
$577$	41.9787	1.74760	0.873799	+	0.486287i	$0.161649\pi$
$578$	23.5005	0.977493
$579$	−6.03731	−0.250902
$580$	25.0242	1.03907
$581$	12.5074	0.518895
$582$	−19.4867	−0.807751
$583$	−32.7712	−1.35725
$584$	18.2103	0.753548
$585$	7.45742	0.308327
$586$	53.0083	2.18975
$587$	−10.4092	−0.429632	−0.214816	−	0.976655i	$-0.568915\pi$
$587$	−10.4092	−0.429632	−0.214816	+	0.976655i	$0.568915\pi$
$588$	−4.83891	−0.199553
$589$	0.936010	0.0385676
$590$	−33.4197	−1.37587
$591$	12.7052	0.522622
$592$	66.6442	2.73906
$593$	11.8099	0.484975	0.242487	−	0.970155i	$-0.422037\pi$
$593$	11.8099	0.484975	0.242487	+	0.970155i	$0.422037\pi$
$594$	−77.7153	−3.18870
$595$	−2.79109	−0.114424
$596$	−30.3499	−1.24318
$597$	−27.9680	−1.14465
$598$	90.9014	3.71723
$599$	19.8202	0.809833	0.404916	−	0.914354i	$-0.367301\pi$
$599$	19.8202	0.809833	0.404916	+	0.914354i	$0.367301\pi$
$600$	6.87315	0.280595
$601$	−27.5654	−1.12442	−0.562208	−	0.826996i	$-0.690048\pi$
$601$	−27.5654	−1.12442	−0.562208	+	0.826996i	$0.690048\pi$
$602$	−0.257119	−0.0104794
$603$	19.9853	0.813862
$604$	93.2917	3.79598
$605$	23.2811	0.946513
$606$	0.917288	0.0372623
$607$	25.3783	1.03007	0.515037	−	0.857168i	$-0.327778\pi$
$607$	25.3783	1.03007	0.515037	+	0.857168i	$0.327778\pi$
$608$	−0.577083	−0.0234038
$609$	5.95036	0.241121
$610$	4.44772	0.180083
$611$	−37.7606	−1.52763
$612$	−23.2853	−0.941254
$613$	36.3333	1.46749	0.733744	−	0.679426i	$-0.237771\pi$
$613$	36.3333	1.46749	0.733744	+	0.679426i	$0.237771\pi$
$614$	2.03039	0.0819400
$615$	−2.48778	−0.100317
$616$	37.5161	1.51157
$617$	42.8868	1.72656	0.863280	−	0.504726i	$-0.168406\pi$
$617$	42.8868	1.72656	0.863280	+	0.504726i	$0.168406\pi$
$618$	34.5143	1.38837
$619$	−15.3207	−0.615790	−0.307895	−	0.951420i	$-0.599625\pi$
$619$	−15.3207	−0.615790	−0.307895	+	0.951420i	$0.599625\pi$
$620$	43.0462	1.72878
$621$	45.9550	1.84411
$622$	5.60981	0.224933
$623$	−2.94730	−0.118081
$624$	31.6957	1.26884
$625$	1.00000	0.0400000
$626$	16.6077	0.663778
$627$	−0.616057	−0.0246030
$628$	5.73248	0.228751
$629$	25.3842	1.01214
$630$	−4.71904	−0.188011
$631$	13.5405	0.539039	0.269519	−	0.962995i	$-0.413135\pi$
$631$	13.5405	0.539039	0.269519	+	0.962995i	$0.413135\pi$
$632$	−62.5589	−2.48846
$633$	−18.4216	−0.732193
$634$	−34.3589	−1.36456
$635$	7.36364	0.292217
$636$	27.0840	1.07395
$637$	−4.03239	−0.159769
$638$	−82.8767	−3.28112
$639$	−19.5653	−0.773993
$640$	10.8569	0.429158
$641$	−21.9088	−0.865346	−0.432673	−	0.901551i	$-0.642430\pi$
$641$	−21.9088	−0.865346	−0.432673	+	0.901551i	$0.642430\pi$
$642$	−30.9312	−1.22076
$643$	−1.86606	−0.0735903	−0.0367951	−	0.999323i	$-0.511715\pi$
$643$	−1.86606	−0.0735903	−0.0367951	+	0.999323i	$0.511715\pi$
$644$	−39.8532	−1.57044
$645$	0.108087	0.00425592
$646$	−0.698601	−0.0274861
$647$	3.32447	0.130698	0.0653492	−	0.997862i	$-0.479184\pi$
$647$	3.32447	0.130698	0.0653492	+	0.997862i	$0.479184\pi$
$648$	0.202749	0.00796474
$649$	76.6838	3.01010
$650$	10.2894	0.403583
$651$	10.2357	0.401169
$652$	−76.0964	−2.98016
$653$	38.6272	1.51160	0.755800	−	0.654802i	$-0.227248\pi$
$653$	38.6272	1.51160	0.755800	+	0.654802i	$0.227248\pi$
$654$	−48.8388	−1.90975
$655$	−10.6031	−0.414297
$656$	16.9949	0.663539
$657$	5.25598	0.205055
$658$	23.8948	0.931517
$659$	−36.6792	−1.42882	−0.714410	−	0.699728i	$-0.753305\pi$
$659$	−36.6792	−1.42882	−0.714410	+	0.699728i	$0.753305\pi$
$660$	−28.3319	−1.10282
$661$	17.2762	0.671967	0.335983	−	0.941868i	$-0.390931\pi$
$661$	17.2762	0.671967	0.335983	+	0.941868i	$0.390931\pi$
$662$	66.1152	2.56964
$663$	12.0726	0.468862
$664$	80.1416	3.11010
$665$	−0.0980907	−0.00380379
$666$	42.9184	1.66305
$667$	49.0071	1.89756
$668$	81.3784	3.14862
$669$	−23.1947	−0.896760
$670$	27.5747	1.06530
$671$	−10.2056	−0.393982
$672$	−6.31068	−0.243440
$673$	2.93016	0.112949	0.0564747	−	0.998404i	$-0.482014\pi$
$673$	2.93016	0.112949	0.0564747	+	0.998404i	$0.482014\pi$
$674$	−3.13889	−0.120906
$675$	5.20178	0.200217
$676$	14.7068	0.565648
$677$	−34.0904	−1.31020	−0.655100	−	0.755542i	$-0.727373\pi$
$677$	−34.0904	−1.31020	−0.655100	+	0.755542i	$0.727373\pi$
$678$	−33.9480	−1.30377
$679$	7.11945	0.273219
$680$	−17.8840	−0.685819
$681$	3.43238	0.131529
$682$	−142.563	−5.45903
$683$	−2.79212	−0.106838	−0.0534188	−	0.998572i	$-0.517012\pi$
$683$	−2.79212	−0.106838	−0.0534188	+	0.998572i	$0.517012\pi$
$684$	−0.818345	−0.0312902
$685$	1.11965	0.0427798
$686$	2.55168	0.0974238
$687$	1.07267	0.0409249
$688$	−0.738380	−0.0281505
$689$	22.5698	0.859840
$690$	24.1810	0.920554
$691$	−2.99951	−0.114107	−0.0570534	−	0.998371i	$-0.518171\pi$
$691$	−2.99951	−0.114107	−0.0570534	+	0.998371i	$0.518171\pi$
$692$	−39.1692	−1.48899
$693$	10.8281	0.411327
$694$	−3.63723	−0.138067
$695$	−6.59350	−0.250106
$696$	38.1271	1.44520
$697$	6.47321	0.245190
$698$	−49.2789	−1.86523
$699$	−17.5727	−0.664660
$700$	−4.51109	−0.170503
$701$	12.7027	0.479776	0.239888	−	0.970801i	$-0.422889\pi$
$701$	12.7027	0.479776	0.239888	+	0.970801i	$0.422889\pi$
$702$	53.5231	2.02010
$703$	0.892108	0.0336465
$704$	2.08665	0.0786434
$705$	−10.0448	−0.378310
$706$	−26.0242	−0.979434
$707$	−0.335130	−0.0126039
$708$	−63.3758	−2.38181
$709$	−4.36883	−0.164075	−0.0820374	−	0.996629i	$-0.526143\pi$
$709$	−4.36883	−0.164075	−0.0820374	+	0.996629i	$0.526143\pi$
$710$	−26.9953	−1.01312
$711$	−18.0562	−0.677159
$712$	−18.8849	−0.707741
$713$	84.3012	3.15710
$714$	−7.63953	−0.285902
$715$	−23.6097	−0.882952
$716$	−43.1288	−1.61180
$717$	−9.17695	−0.342720
$718$	31.2620	1.16669
$719$	9.29802	0.346758	0.173379	−	0.984855i	$-0.444531\pi$
$719$	9.29802	0.346758	0.173379	+	0.984855i	$0.444531\pi$
$720$	−13.5519	−0.505049
$721$	−12.6097	−0.469612
$722$	48.4575	1.80340
$723$	26.4785	0.984747
$724$	29.5075	1.09664
$725$	5.54725	0.206020
$726$	63.7231	2.36499
$727$	27.0393	1.00283	0.501416	−	0.865206i	$-0.332813\pi$
$727$	27.0393	1.00283	0.501416	+	0.865206i	$0.332813\pi$
$728$	−25.8376	−0.957606
$729$	16.7979	0.622144
$730$	7.25194	0.268406
$731$	−0.281243	−0.0104021
$732$	8.43447	0.311747
$733$	−29.1689	−1.07738	−0.538688	−	0.842505i	$-0.681080\pi$
$733$	−29.1689	−1.07738	−0.538688	+	0.842505i	$0.681080\pi$
$734$	−89.5937	−3.30696
$735$	−1.07267	−0.0395660
$736$	−51.9746	−1.91581
$737$	−63.2719	−2.33065
$738$	10.9446	0.402876
$739$	4.61148	0.169636	0.0848179	−	0.996396i	$-0.472969\pi$
$739$	4.61148	0.169636	0.0848179	+	0.996396i	$0.472969\pi$
$740$	41.0272	1.50819
$741$	0.424283	0.0155864
$742$	−14.2821	−0.524312
$743$	24.6744	0.905216	0.452608	−	0.891710i	$-0.350494\pi$
$743$	24.6744	0.905216	0.452608	+	0.891710i	$0.350494\pi$
$744$	65.5856	2.40448
$745$	−6.72784	−0.246489
$746$	−82.4357	−3.01819
$747$	23.1310	0.846319
$748$	73.7197	2.69546
$749$	11.3007	0.412917
$750$	2.73711	0.0999452
$751$	5.04962	0.184263	0.0921316	−	0.995747i	$-0.470632\pi$
$751$	5.04962	0.184263	0.0921316	+	0.995747i	$0.470632\pi$
$752$	68.6198	2.50231
$753$	−14.4290	−0.525823
$754$	57.0778	2.07865
$755$	20.6805	0.752640
$756$	−23.4657	−0.853440
$757$	35.1252	1.27665	0.638324	−	0.769768i	$-0.279628\pi$
$757$	35.1252	1.27665	0.638324	+	0.769768i	$0.279628\pi$
$758$	55.9284	2.03141
$759$	−55.4848	−2.01397
$760$	−0.628518	−0.0227988
$761$	−7.23138	−0.262137	−0.131069	−	0.991373i	$-0.541841\pi$
$761$	−7.23138	−0.262137	−0.131069	+	0.991373i	$0.541841\pi$
$762$	20.1551	0.730143
$763$	17.8432	0.645967
$764$	−21.5823	−0.780820
$765$	−5.16179	−0.186625
$766$	27.3066	0.986626
$767$	−52.8127	−1.90696
$768$	30.4812	1.09990
$769$	−31.5596	−1.13807	−0.569034	−	0.822314i	$-0.692683\pi$
$769$	−31.5596	−1.13807	−0.569034	+	0.822314i	$0.692683\pi$
$770$	14.9401	0.538405
$771$	−26.1499	−0.941764
$772$	25.3898	0.913800
$773$	−41.8161	−1.50402	−0.752010	−	0.659152i	$-0.770915\pi$
$773$	−41.8161	−1.50402	−0.752010	+	0.659152i	$0.770915\pi$
$774$	−0.475511	−0.0170919
$775$	9.54229	0.342769
$776$	45.6180	1.63759
$777$	9.75563	0.349981
$778$	−5.36587	−0.192376
$779$	0.227496	0.00815088
$780$	19.5124	0.698655
$781$	61.9425	2.21648
$782$	−62.9190	−2.24998
$783$	28.8556	1.03121
$784$	7.32779	0.261707
$785$	1.27075	0.0453551
$786$	−29.0218	−1.03517
$787$	34.8595	1.24261	0.621303	−	0.783570i	$-0.286604\pi$
$787$	34.8595	1.24261	0.621303	+	0.783570i	$0.286604\pi$
$788$	−53.4315	−1.90342
$789$	21.2477	0.756437
$790$	−24.9130	−0.886364
$791$	12.4029	0.440995
$792$	69.3816	2.46537
$793$	7.02866	0.249595
$794$	67.8586	2.40821
$795$	6.00386	0.212935
$796$	117.619	4.16890
$797$	−23.0943	−0.818043	−0.409021	−	0.912525i	$-0.634130\pi$
$797$	−23.0943	−0.818043	−0.409021	+	0.912525i	$0.634130\pi$
$798$	−0.268485	−0.00950428
$799$	26.1367	0.924650
$800$	−5.88316	−0.208001
$801$	−5.45068	−0.192590
$802$	38.3234	1.35325
$803$	−16.6401	−0.587215
$804$	52.2914	1.84418
$805$	−8.83448	−0.311375
$806$	98.1843	3.45839
$807$	2.44734	0.0861503
$808$	−2.14735	−0.0755436
$809$	−43.1479	−1.51700	−0.758500	−	0.651673i	$-0.774067\pi$
$809$	−43.1479	−1.51700	−0.758500	+	0.651673i	$0.774067\pi$
$810$	0.0807413	0.00283696
$811$	47.3060	1.66114	0.830570	−	0.556915i	$-0.188015\pi$
$811$	47.3060	1.66114	0.830570	+	0.556915i	$0.188015\pi$
$812$	−25.0242	−0.878176
$813$	−2.21575	−0.0777097
$814$	−135.877	−4.76247
$815$	−16.8687	−0.590885
$816$	−21.9388	−0.768011
$817$	−0.00988406	−0.000345799 0
$818$	−47.7799	−1.67059
$819$	−7.45742	−0.260583
$820$	10.4623	0.365360
$821$	−28.8731	−1.00768	−0.503840	−	0.863797i	$-0.668080\pi$
$821$	−28.8731	−1.00768	−0.503840	+	0.863797i	$0.668080\pi$
$822$	3.06462	0.106891
$823$	−22.6817	−0.790634	−0.395317	−	0.918545i	$-0.629365\pi$
$823$	−22.6817	−0.790634	−0.395317	+	0.918545i	$0.629365\pi$
$824$	−80.7972	−2.81471
$825$	−6.28049	−0.218658
$826$	33.4197	1.16282
$827$	49.5758	1.72392	0.861960	−	0.506977i	$-0.169237\pi$
$827$	49.5758	1.72392	0.861960	+	0.506977i	$0.169237\pi$
$828$	−73.7037	−2.56138
$829$	41.4824	1.44074	0.720371	−	0.693589i	$-0.243972\pi$
$829$	41.4824	1.44074	0.720371	+	0.693589i	$0.243972\pi$
$830$	31.9150	1.10779
$831$	28.5298	0.989688
$832$	−1.43709	−0.0498221
$833$	2.79109	0.0967056
$834$	−18.0472	−0.624922
$835$	18.0396	0.624286
$836$	2.59082	0.0896054
$837$	49.6369	1.71570
$838$	−37.9357	−1.31047
$839$	23.7403	0.819605	0.409803	−	0.912174i	$-0.365598\pi$
$839$	23.7403	0.819605	0.409803	+	0.912174i	$0.365598\pi$
$840$	−6.87315	−0.237146
$841$	1.77197	0.0611025
$842$	7.27430	0.250689
$843$	0.554195	0.0190875
$844$	77.4718	2.66669
$845$	3.26015	0.112153
$846$	44.1906	1.51931
$847$	−23.2811	−0.799950
$848$	−41.0145	−1.40844
$849$	−6.21086	−0.213156
$850$	−7.12199	−0.244282
$851$	80.3472	2.75427
$852$	−51.1928	−1.75383
$853$	28.1496	0.963825	0.481913	−	0.876219i	$-0.339942\pi$
$853$	28.1496	0.963825	0.481913	+	0.876219i	$0.339942\pi$
$854$	−4.44772	−0.152198
$855$	−0.181407	−0.00620399
$856$	72.4092	2.47490
$857$	12.4808	0.426337	0.213168	−	0.977016i	$-0.431622\pi$
$857$	12.4808	0.426337	0.213168	+	0.977016i	$0.431622\pi$
$858$	−64.6223	−2.20617
$859$	−2.02466	−0.0690804	−0.0345402	−	0.999403i	$-0.510997\pi$
$859$	−2.02466	−0.0690804	−0.0345402	+	0.999403i	$0.510997\pi$
$860$	−0.454558	−0.0155003
$861$	2.48778	0.0847832
$862$	73.4651	2.50223
$863$	25.1653	0.856636	0.428318	−	0.903628i	$-0.359106\pi$
$863$	25.1653	0.856636	0.428318	+	0.903628i	$0.359106\pi$
$864$	−30.6029	−1.04113
$865$	−8.68285	−0.295226
$866$	35.9853	1.22283
$867$	9.87907	0.335511
$868$	−43.0462	−1.46108
$869$	57.1645	1.93917
$870$	15.1834	0.514767
$871$	43.5758	1.47651
$872$	114.331	3.87173
$873$	13.1666	0.445621
$874$	−2.21124	−0.0747963
$875$	−1.00000	−0.0338062
$876$	13.7523	0.464647
$877$	38.1908	1.28961	0.644806	−	0.764346i	$-0.276938\pi$
$877$	38.1908	1.28961	0.644806	+	0.764346i	$0.276938\pi$
$878$	−49.0857	−1.65656
$879$	22.2834	0.751602
$880$	42.9043	1.44630
$881$	−19.9968	−0.673711	−0.336855	−	0.941556i	$-0.609363\pi$
$881$	−19.9968	−0.673711	−0.336855	+	0.941556i	$0.609363\pi$
$882$	4.71904	0.158898
$883$	3.22115	0.108400	0.0542002	−	0.998530i	$-0.482739\pi$
$883$	3.22115	0.108400	0.0542002	+	0.998530i	$0.482739\pi$
$884$	−50.7713	−1.70762
$885$	−14.0489	−0.472248
$886$	29.9885	1.00748
$887$	13.6206	0.457336	0.228668	−	0.973505i	$-0.426563\pi$
$887$	13.6206	0.457336	0.228668	+	0.973505i	$0.426563\pi$
$888$	62.5094	2.09768
$889$	−7.36364	−0.246969
$890$	−7.52058	−0.252090
$891$	−0.185266	−0.00620666
$892$	97.5452	3.26605
$893$	0.918554	0.0307382
$894$	−18.4149	−0.615885
$895$	−9.56060	−0.319576
$896$	−10.8569	−0.362704
$897$	38.2128	1.27589
$898$	75.3208	2.51349
$899$	52.9335	1.76543
$900$	−8.34274	−0.278091
$901$	−15.6221	−0.520447
$902$	−34.6498	−1.15371
$903$	−0.108087	−0.00359691
$904$	79.4716	2.64319
$905$	6.54110	0.217434
$906$	56.6048	1.88057
$907$	−22.7356	−0.754924	−0.377462	−	0.926025i	$-0.623203\pi$
$907$	−22.7356	−0.754924	−0.377462	+	0.926025i	$0.623203\pi$
$908$	−14.4348	−0.479037
$909$	−0.619783	−0.0205569
$910$	−10.2894	−0.341090
$911$	53.7872	1.78205	0.891025	−	0.453955i	$-0.149987\pi$
$911$	53.7872	1.78205	0.891025	+	0.453955i	$0.149987\pi$
$912$	−0.771021	−0.0255311
$913$	−73.2311	−2.42360
$914$	58.0751	1.92095
$915$	1.86972	0.0618109
$916$	−4.51109	−0.149051
$917$	10.6031	0.350145
$918$	−37.0470	−1.22273
$919$	−34.0444	−1.12302	−0.561511	−	0.827469i	$-0.689780\pi$
$919$	−34.0444	−1.12302	−0.561511	+	0.827469i	$0.689780\pi$
$920$	−56.6071	−1.86628
$921$	0.853530	0.0281248
$922$	69.9567	2.30390
$923$	−42.6602	−1.40418
$924$	28.3319	0.932050
$925$	9.09473	0.299033
$926$	74.1413	2.43643
$927$	−23.3202	−0.765937
$928$	−32.6353	−1.07131
$929$	−37.8607	−1.24217	−0.621084	−	0.783744i	$-0.713307\pi$
$929$	−37.8607	−1.24217	−0.621084	+	0.783744i	$0.713307\pi$
$930$	26.1183	0.856454
$931$	0.0980907	0.00321479
$932$	73.9017	2.42073
$933$	2.35823	0.0772050
$934$	−74.2755	−2.43037
$935$	16.3419	0.534436
$936$	−47.7836	−1.56186
$937$	24.6083	0.803919	0.401960	−	0.915657i	$-0.368329\pi$
$937$	24.6083	0.803919	0.401960	+	0.915657i	$0.368329\pi$
$938$	−27.5747	−0.900344
$939$	6.98149	0.227832
$940$	42.2434	1.37783
$941$	9.74412	0.317649	0.158825	−	0.987307i	$-0.449230\pi$
$941$	9.74412	0.317649	0.158825	+	0.987307i	$0.449230\pi$
$942$	3.47819	0.113326
$943$	20.4893	0.667223
$944$	95.9729	3.12365
$945$	−5.20178	−0.169214
$946$	1.50543	0.0489459
$947$	−9.36576	−0.304346	−0.152173	−	0.988354i	$-0.548627\pi$
$947$	−9.36576	−0.304346	−0.152173	+	0.988354i	$0.548627\pi$
$948$	−47.2440	−1.53441
$949$	11.4601	0.372011
$950$	−0.250297	−0.00812069
$951$	−14.4437	−0.468368
$952$	17.8840	0.579623
$953$	36.5273	1.18324	0.591618	−	0.806218i	$-0.298489\pi$
$953$	36.5273	1.18324	0.591618	+	0.806218i	$0.298489\pi$
$954$	−26.4130	−0.855154
$955$	−4.78427	−0.154815
$956$	38.5936	1.24820
$957$	−34.8394	−1.12620
$958$	28.7636	0.929309
$959$	−1.11965	−0.0361555
$960$	−0.382285	−0.0123382
$961$	60.0553	1.93727
$962$	93.5791	3.01711
$963$	20.8992	0.673468
$964$	−111.355	−3.58651
$965$	5.62831	0.181182
$966$	−24.1810	−0.778010
$967$	29.6716	0.954173	0.477086	−	0.878856i	$-0.341693\pi$
$967$	29.6716	0.954173	0.477086	+	0.878856i	$0.341693\pi$
$968$	−149.174	−4.79465
$969$	−0.293675	−0.00943421
$970$	18.1666	0.583294
$971$	−22.0048	−0.706168	−0.353084	−	0.935592i	$-0.614867\pi$
$971$	−22.0048	−0.706168	−0.353084	+	0.935592i	$0.614867\pi$
$972$	−70.2441	−2.25308
$973$	6.59350	0.211378
$974$	1.36209	0.0436442
$975$	4.32542	0.138524
$976$	−12.7727	−0.408844
$977$	0.304088	0.00972863	0.00486432	−	0.999988i	$-0.498452\pi$
$977$	0.304088	0.00972863	0.00486432	+	0.999988i	$0.498452\pi$
$978$	−46.1716	−1.47640
$979$	17.2565	0.551519
$980$	4.51109	0.144102
$981$	32.9989	1.05357
$982$	−13.5288	−0.431721
$983$	−36.0403	−1.14951	−0.574753	−	0.818327i	$-0.694902\pi$
$983$	−36.0403	−1.14951	−0.574753	+	0.818327i	$0.694902\pi$
$984$	15.9405	0.508164
$985$	−11.8445	−0.377396
$986$	−39.5074	−1.25817
$987$	10.0448	0.319730
$988$	−1.78432	−0.0567667
$989$	−0.890202	−0.0283068
$990$	27.6300	0.878140
$991$	−44.0642	−1.39975	−0.699873	−	0.714268i	$-0.746760\pi$
$991$	−44.0642	−1.39975	−0.699873	+	0.714268i	$0.746760\pi$
$992$	−56.1388	−1.78241
$993$	27.7933	0.881993
$994$	26.9953	0.856238
$995$	26.0733	0.826578
$996$	60.5223	1.91772
$997$	−32.1549	−1.01836	−0.509179	−	0.860661i	$-0.670051\pi$
$997$	−32.1549	−1.01836	−0.509179	+	0.860661i	$0.670051\pi$
$998$	28.9049	0.914969
$999$	47.3088	1.49678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.4	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.4	✓	67	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55168 q^{2} -1.07267 q^{3} +4.51109 q^{4} +1.00000 q^{5} +2.73711 q^{6} -1.00000 q^{7} -6.40752 q^{8} -1.84938 q^{9} +O(q^{10})\)	\(q-2.55168 q^{2} -1.07267 q^{3} +4.51109 q^{4} +1.00000 q^{5} +2.73711 q^{6} -1.00000 q^{7} -6.40752 q^{8} -1.84938 q^{9} -2.55168 q^{10} +5.85501 q^{11} -4.83891 q^{12} -4.03239 q^{13} +2.55168 q^{14} -1.07267 q^{15} +7.32779 q^{16} +2.79109 q^{17} +4.71904 q^{18} +0.0980907 q^{19} +4.51109 q^{20} +1.07267 q^{21} -14.9401 q^{22} +8.83448 q^{23} +6.87315 q^{24} +1.00000 q^{25} +10.2894 q^{26} +5.20178 q^{27} -4.51109 q^{28} +5.54725 q^{29} +2.73711 q^{30} +9.54229 q^{31} -5.88316 q^{32} -6.28049 q^{33} -7.12199 q^{34} -1.00000 q^{35} -8.34274 q^{36} +9.09473 q^{37} -0.250297 q^{38} +4.32542 q^{39} -6.40752 q^{40} +2.31924 q^{41} -2.73711 q^{42} -0.100764 q^{43} +26.4125 q^{44} -1.84938 q^{45} -22.5428 q^{46} +9.36433 q^{47} -7.86029 q^{48} +1.00000 q^{49} -2.55168 q^{50} -2.99392 q^{51} -18.1905 q^{52} -5.59712 q^{53} -13.2733 q^{54} +5.85501 q^{55} +6.40752 q^{56} -0.105219 q^{57} -14.1548 q^{58} +13.0971 q^{59} -4.83891 q^{60} -1.74305 q^{61} -24.3489 q^{62} +1.84938 q^{63} +0.356386 q^{64} -4.03239 q^{65} +16.0258 q^{66} -10.8064 q^{67} +12.5909 q^{68} -9.47647 q^{69} +2.55168 q^{70} +10.5794 q^{71} +11.8500 q^{72} -2.84202 q^{73} -23.2069 q^{74} -1.07267 q^{75} +0.442497 q^{76} -5.85501 q^{77} -11.0371 q^{78} +9.76335 q^{79} +7.32779 q^{80} -0.0316424 q^{81} -5.91797 q^{82} -12.5074 q^{83} +4.83891 q^{84} +2.79109 q^{85} +0.257119 q^{86} -5.95036 q^{87} -37.5161 q^{88} +2.94730 q^{89} +4.71904 q^{90} +4.03239 q^{91} +39.8532 q^{92} -10.2357 q^{93} -23.8948 q^{94} +0.0980907 q^{95} +6.31068 q^{96} -7.11945 q^{97} -2.55168 q^{98} -10.8281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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