LMFDB - Embedded newform 8015.2.a.i.1.18

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:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-0.612476 q^{2} -1.57448 q^{3} -1.62487 q^{4} +1.00000 q^{5} +0.964330 q^{6} -1.00000 q^{7} +2.22015 q^{8} -0.521024 q^{9} +O(q^{10})$	\(q-0.612476 q^{2} -1.57448 q^{3} -1.62487 q^{4} +1.00000 q^{5} +0.964330 q^{6} -1.00000 q^{7} +2.22015 q^{8} -0.521024 q^{9} -0.612476 q^{10} -3.36841 q^{11} +2.55832 q^{12} -6.96057 q^{13} +0.612476 q^{14} -1.57448 q^{15} +1.88996 q^{16} +0.396526 q^{17} +0.319115 q^{18} -1.72732 q^{19} -1.62487 q^{20} +1.57448 q^{21} +2.06307 q^{22} -1.95243 q^{23} -3.49557 q^{24} +1.00000 q^{25} +4.26319 q^{26} +5.54377 q^{27} +1.62487 q^{28} +3.51292 q^{29} +0.964330 q^{30} -3.01953 q^{31} -5.59785 q^{32} +5.30348 q^{33} -0.242863 q^{34} -1.00000 q^{35} +0.846597 q^{36} +7.83936 q^{37} +1.05794 q^{38} +10.9593 q^{39} +2.22015 q^{40} +10.8318 q^{41} -0.964330 q^{42} +6.95621 q^{43} +5.47324 q^{44} -0.521024 q^{45} +1.19582 q^{46} +0.580967 q^{47} -2.97569 q^{48} +1.00000 q^{49} -0.612476 q^{50} -0.624321 q^{51} +11.3100 q^{52} -6.72794 q^{53} -3.39543 q^{54} -3.36841 q^{55} -2.22015 q^{56} +2.71962 q^{57} -2.15158 q^{58} +2.93021 q^{59} +2.55832 q^{60} -5.89533 q^{61} +1.84939 q^{62} +0.521024 q^{63} -0.351363 q^{64} -6.96057 q^{65} -3.24826 q^{66} +3.33986 q^{67} -0.644304 q^{68} +3.07406 q^{69} +0.612476 q^{70} +5.08136 q^{71} -1.15675 q^{72} +4.67864 q^{73} -4.80142 q^{74} -1.57448 q^{75} +2.80667 q^{76} +3.36841 q^{77} -6.71229 q^{78} -0.892529 q^{79} +1.88996 q^{80} -7.16546 q^{81} -6.63422 q^{82} +9.82177 q^{83} -2.55832 q^{84} +0.396526 q^{85} -4.26051 q^{86} -5.53101 q^{87} -7.47837 q^{88} +1.07271 q^{89} +0.319115 q^{90} +6.96057 q^{91} +3.17245 q^{92} +4.75417 q^{93} -0.355828 q^{94} -1.72732 q^{95} +8.81369 q^{96} -2.02580 q^{97} -0.612476 q^{98} +1.75502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * 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 $

$2$	−0.612476	−0.433086	−0.216543	−	0.976273i	$-0.569478\pi$
$2$	−0.612476	−0.433086	−0.216543	+	0.976273i	$0.569478\pi$
$3$	−1.57448	−0.909024	−0.454512	−	0.890741i	$-0.650186\pi$
$3$	−1.57448	−0.909024	−0.454512	+	0.890741i	$0.650186\pi$
$4$	−1.62487	−0.812436
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.964330	0.393686
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.22015	0.784941
$9$	−0.521024	−0.173675
$10$	−0.612476	−0.193682
$11$	−3.36841	−1.01561	−0.507807	−	0.861471i	$-0.669544\pi$
$11$	−3.36841	−1.01561	−0.507807	+	0.861471i	$0.669544\pi$
$12$	2.55832	0.738525
$13$	−6.96057	−1.93052	−0.965258	−	0.261300i	$-0.915849\pi$
$13$	−6.96057	−1.93052	−0.965258	+	0.261300i	$0.915849\pi$
$14$	0.612476	0.163691
$15$	−1.57448	−0.406528
$16$	1.88996	0.472489
$17$	0.396526	0.0961717	0.0480858	−	0.998843i	$-0.484688\pi$
$17$	0.396526	0.0961717	0.0480858	+	0.998843i	$0.484688\pi$
$18$	0.319115	0.0752161
$19$	−1.72732	−0.396274	−0.198137	−	0.980174i	$-0.563489\pi$
$19$	−1.72732	−0.396274	−0.198137	+	0.980174i	$0.563489\pi$
$20$	−1.62487	−0.363333
$21$	1.57448	0.343579
$22$	2.06307	0.439848
$23$	−1.95243	−0.407110	−0.203555	−	0.979064i	$-0.565250\pi$
$23$	−1.95243	−0.407110	−0.203555	+	0.979064i	$0.565250\pi$
$24$	−3.49557	−0.713531
$25$	1.00000	0.200000
$26$	4.26319	0.836079
$27$	5.54377	1.06690
$28$	1.62487	0.307072
$29$	3.51292	0.652332	0.326166	−	0.945312i	$-0.394243\pi$
$29$	3.51292	0.652332	0.326166	+	0.945312i	$0.394243\pi$
$30$	0.964330	0.176062
$31$	−3.01953	−0.542323	−0.271161	−	0.962534i	$-0.587408\pi$
$31$	−3.01953	−0.542323	−0.271161	+	0.962534i	$0.587408\pi$
$32$	−5.59785	−0.989570
$33$	5.30348	0.923217
$34$	−0.242863	−0.0416506
$35$	−1.00000	−0.169031
$36$	0.846597	0.141100
$37$	7.83936	1.28878	0.644391	−	0.764696i	$-0.277111\pi$
$37$	7.83936	1.28878	0.644391	+	0.764696i	$0.277111\pi$
$38$	1.05794	0.171621
$39$	10.9593	1.75489
$40$	2.22015	0.351036
$41$	10.8318	1.69164	0.845821	−	0.533467i	$-0.179111\pi$
$41$	10.8318	1.69164	0.845821	+	0.533467i	$0.179111\pi$
$42$	−0.964330	−0.148799
$43$	6.95621	1.06081	0.530406	−	0.847744i	$-0.322040\pi$
$43$	6.95621	1.06081	0.530406	+	0.847744i	$0.322040\pi$
$44$	5.47324	0.825121
$45$	−0.521024	−0.0776696
$46$	1.19582	0.176314
$47$	0.580967	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$47$	0.580967	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$48$	−2.97569	−0.429504
$49$	1.00000	0.142857
$50$	−0.612476	−0.0866172
$51$	−0.624321	−0.0874224
$52$	11.3100	1.56842
$53$	−6.72794	−0.924154	−0.462077	−	0.886840i	$-0.652896\pi$
$53$	−6.72794	−0.924154	−0.462077	+	0.886840i	$0.652896\pi$
$54$	−3.39543	−0.462059
$55$	−3.36841	−0.454196
$56$	−2.22015	−0.296680
$57$	2.71962	0.360222
$58$	−2.15158	−0.282516
$59$	2.93021	0.381481	0.190740	−	0.981641i	$-0.438911\pi$
$59$	2.93021	0.381481	0.190740	+	0.981641i	$0.438911\pi$
$60$	2.55832	0.330278
$61$	−5.89533	−0.754820	−0.377410	−	0.926046i	$-0.623185\pi$
$61$	−5.89533	−0.754820	−0.377410	+	0.926046i	$0.623185\pi$
$62$	1.84939	0.234872
$63$	0.521024	0.0656428
$64$	−0.351363	−0.0439203
$65$	−6.96057	−0.863353
$66$	−3.24826	−0.399833
$67$	3.33986	0.408028	0.204014	−	0.978968i	$-0.434601\pi$
$67$	3.33986	0.408028	0.204014	+	0.978968i	$0.434601\pi$
$68$	−0.644304	−0.0781333
$69$	3.07406	0.370073
$70$	0.612476	0.0732049
$71$	5.08136	0.603046	0.301523	−	0.953459i	$-0.402505\pi$
$71$	5.08136	0.603046	0.301523	+	0.953459i	$0.402505\pi$
$72$	−1.15675	−0.136324
$73$	4.67864	0.547593	0.273797	−	0.961788i	$-0.411720\pi$
$73$	4.67864	0.547593	0.273797	+	0.961788i	$0.411720\pi$
$74$	−4.80142	−0.558154
$75$	−1.57448	−0.181805
$76$	2.80667	0.321947
$77$	3.36841	0.383866
$78$	−6.71229	−0.760017
$79$	−0.892529	−0.100417	−0.0502087	−	0.998739i	$-0.515989\pi$
$79$	−0.892529	−0.100417	−0.0502087	+	0.998739i	$0.515989\pi$
$80$	1.88996	0.211304
$81$	−7.16546	−0.796163
$82$	−6.63422	−0.732627
$83$	9.82177	1.07808	0.539040	−	0.842280i	$-0.318787\pi$
$83$	9.82177	1.07808	0.539040	+	0.842280i	$0.318787\pi$
$84$	−2.55832	−0.279136
$85$	0.396526	0.0430093
$86$	−4.26051	−0.459423
$87$	−5.53101	−0.592986
$88$	−7.47837	−0.797197
$89$	1.07271	0.113708	0.0568538	−	0.998383i	$-0.481893\pi$
$89$	1.07271	0.113708	0.0568538	+	0.998383i	$0.481893\pi$
$90$	0.319115	0.0336376
$91$	6.96057	0.729666
$92$	3.17245	0.330751
$93$	4.75417	0.492985
$94$	−0.355828	−0.0367009
$95$	−1.72732	−0.177219
$96$	8.81369	0.899543
$97$	−2.02580	−0.205689	−0.102845	−	0.994697i	$-0.532794\pi$
$97$	−2.02580	−0.205689	−0.102845	+	0.994697i	$0.532794\pi$
$98$	−0.612476	−0.0618695
$99$	1.75502	0.176386
$100$	−1.62487	−0.162487
$101$	−14.6725	−1.45997	−0.729984	−	0.683464i	$-0.760472\pi$
$101$	−14.6725	−1.45997	−0.729984	+	0.683464i	$0.760472\pi$
$102$	0.382382	0.0378614
$103$	−7.12284	−0.701834	−0.350917	−	0.936407i	$-0.614130\pi$
$103$	−7.12284	−0.701834	−0.350917	+	0.936407i	$0.614130\pi$
$104$	−15.4535	−1.51534
$105$	1.57448	0.153653
$106$	4.12070	0.400238
$107$	11.9699	1.15717	0.578587	−	0.815621i	$-0.303604\pi$
$107$	11.9699	1.15717	0.578587	+	0.815621i	$0.303604\pi$
$108$	−9.00792	−0.866787
$109$	−10.4837	−1.00415	−0.502076	−	0.864823i	$-0.667430\pi$
$109$	−10.4837	−1.00415	−0.502076	+	0.864823i	$0.667430\pi$
$110$	2.06307	0.196706
$111$	−12.3429	−1.17154
$112$	−1.88996	−0.178584
$113$	−2.19705	−0.206681	−0.103341	−	0.994646i	$-0.532953\pi$
$113$	−2.19705	−0.206681	−0.103341	+	0.994646i	$0.532953\pi$
$114$	−1.66570	−0.156007
$115$	−1.95243	−0.182065
$116$	−5.70804	−0.529978
$117$	3.62662	0.335281
$118$	−1.79468	−0.165214
$119$	−0.396526	−0.0363495
$120$	−3.49557	−0.319101
$121$	0.346177	0.0314707
$122$	3.61075	0.326902
$123$	−17.0544	−1.53774
$124$	4.90634	0.440603
$125$	1.00000	0.0894427
$126$	−0.319115	−0.0284290
$127$	6.78581	0.602143	0.301071	−	0.953602i	$-0.402656\pi$
$127$	6.78581	0.602143	0.301071	+	0.953602i	$0.402656\pi$
$128$	11.4109	1.00859
$129$	−10.9524	−0.964304
$130$	4.26319	0.373906
$131$	−9.59070	−0.837943	−0.418972	−	0.907999i	$-0.637609\pi$
$131$	−9.59070	−0.837943	−0.418972	+	0.907999i	$0.637609\pi$
$132$	−8.61748	−0.750055
$133$	1.72732	0.149777
$134$	−2.04558	−0.176711
$135$	5.54377	0.477132
$136$	0.880346	0.0754891
$137$	−1.71260	−0.146318	−0.0731588	−	0.997320i	$-0.523308\pi$
$137$	−1.71260	−0.146318	−0.0731588	+	0.997320i	$0.523308\pi$
$138$	−1.88279	−0.160273
$139$	16.5937	1.40746	0.703729	−	0.710468i	$-0.251517\pi$
$139$	16.5937	1.40746	0.703729	+	0.710468i	$0.251517\pi$
$140$	1.62487	0.137327
$141$	−0.914718	−0.0770332
$142$	−3.11221	−0.261171
$143$	23.4461	1.96066
$144$	−0.984712	−0.0820594
$145$	3.51292	0.291732
$146$	−2.86556	−0.237155
$147$	−1.57448	−0.129861
$148$	−12.7380	−1.04705
$149$	8.32626	0.682114	0.341057	−	0.940043i	$-0.389215\pi$
$149$	8.32626	0.682114	0.341057	+	0.940043i	$0.389215\pi$
$150$	0.964330	0.0787372
$151$	12.5168	1.01861	0.509303	−	0.860587i	$-0.329903\pi$
$151$	12.5168	1.01861	0.509303	+	0.860587i	$0.329903\pi$
$152$	−3.83490	−0.311051
$153$	−0.206599	−0.0167026
$154$	−2.06307	−0.166247
$155$	−3.01953	−0.242534
$156$	−17.8074	−1.42573
$157$	6.87590	0.548757	0.274378	−	0.961622i	$-0.411528\pi$
$157$	6.87590	0.548757	0.274378	+	0.961622i	$0.411528\pi$
$158$	0.546653	0.0434894
$159$	10.5930	0.840078
$160$	−5.59785	−0.442549
$161$	1.95243	0.153873
$162$	4.38868	0.344807
$163$	−8.97732	−0.703158	−0.351579	−	0.936158i	$-0.614355\pi$
$163$	−8.97732	−0.703158	−0.351579	+	0.936158i	$0.614355\pi$
$164$	−17.6003	−1.37435
$165$	5.30348	0.412875
$166$	−6.01560	−0.466901
$167$	−20.5063	−1.58683	−0.793413	−	0.608683i	$-0.791698\pi$
$167$	−20.5063	−1.58683	−0.793413	+	0.608683i	$0.791698\pi$
$168$	3.49557	0.269689
$169$	35.4496	2.72689
$170$	−0.242863	−0.0186267
$171$	0.899973	0.0688226
$172$	−11.3030	−0.861842
$173$	−4.40338	−0.334783	−0.167391	−	0.985891i	$-0.553534\pi$
$173$	−4.40338	−0.334783	−0.167391	+	0.985891i	$0.553534\pi$
$174$	3.38761	0.256814
$175$	−1.00000	−0.0755929
$176$	−6.36615	−0.479866
$177$	−4.61354	−0.346775
$178$	−0.657012	−0.0492452
$179$	−6.72424	−0.502594	−0.251297	−	0.967910i	$-0.580857\pi$
$179$	−6.72424	−0.502594	−0.251297	+	0.967910i	$0.580857\pi$
$180$	0.846597	0.0631016
$181$	−2.51472	−0.186918	−0.0934589	−	0.995623i	$-0.529792\pi$
$181$	−2.51472	−0.186918	−0.0934589	+	0.995623i	$0.529792\pi$
$182$	−4.26319	−0.316008
$183$	9.28206	0.686149
$184$	−4.33469	−0.319557
$185$	7.83936	0.576361
$186$	−2.91182	−0.213505
$187$	−1.33566	−0.0976732
$188$	−0.943997	−0.0688481
$189$	−5.54377	−0.403250
$190$	1.05794	0.0767511
$191$	11.5268	0.834047	0.417023	−	0.908896i	$-0.363073\pi$
$191$	11.5268	0.834047	0.417023	+	0.908896i	$0.363073\pi$
$192$	0.553212	0.0399246
$193$	−0.590583	−0.0425111	−0.0212555	−	0.999774i	$-0.506766\pi$
$193$	−0.590583	−0.0425111	−0.0212555	+	0.999774i	$0.506766\pi$
$194$	1.24076	0.0890811
$195$	10.9593	0.784809
$196$	−1.62487	−0.116062
$197$	12.6362	0.900293	0.450147	−	0.892955i	$-0.351372\pi$
$197$	12.6362	0.900293	0.450147	+	0.892955i	$0.351372\pi$
$198$	−1.07491	−0.0763904
$199$	1.75135	0.124150	0.0620751	−	0.998071i	$-0.480228\pi$
$199$	1.75135	0.124150	0.0620751	+	0.998071i	$0.480228\pi$
$200$	2.22015	0.156988
$201$	−5.25853	−0.370908
$202$	8.98656	0.632292
$203$	−3.51292	−0.246558
$204$	1.01444	0.0710251
$205$	10.8318	0.756525
$206$	4.36257	0.303955
$207$	1.01726	0.0707047
$208$	−13.1552	−0.912148
$209$	5.81831	0.402461
$210$	−0.964330	−0.0665451
$211$	15.9016	1.09471	0.547357	−	0.836899i	$-0.315634\pi$
$211$	15.9016	1.09471	0.547357	+	0.836899i	$0.315634\pi$
$212$	10.9320	0.750816
$213$	−8.00048	−0.548184
$214$	−7.33128	−0.501156
$215$	6.95621	0.474409
$216$	12.3080	0.837453
$217$	3.01953	0.204979
$218$	6.42100	0.434885
$219$	−7.36641	−0.497776
$220$	5.47324	0.369005
$221$	−2.76005	−0.185661
$222$	7.55973	0.507376
$223$	15.9429	1.06761	0.533806	−	0.845607i	$-0.320761\pi$
$223$	15.9429	1.06761	0.533806	+	0.845607i	$0.320761\pi$
$224$	5.59785	0.374022
$225$	−0.521024	−0.0347349
$226$	1.34564	0.0895109
$227$	23.4297	1.55508	0.777541	−	0.628832i	$-0.216467\pi$
$227$	23.4297	1.55508	0.777541	+	0.628832i	$0.216467\pi$
$228$	−4.41904	−0.292658
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	1.19582	0.0788499
$231$	−5.30348	−0.348943
$232$	7.79920	0.512042
$233$	−17.4759	−1.14488	−0.572442	−	0.819945i	$-0.694004\pi$
$233$	−17.4759	−1.14488	−0.572442	+	0.819945i	$0.694004\pi$
$234$	−2.22122	−0.145206
$235$	0.580967	0.0378981
$236$	−4.76122	−0.309929
$237$	1.40527	0.0912818
$238$	0.242863	0.0157425
$239$	10.6670	0.689988	0.344994	−	0.938605i	$-0.387881\pi$
$239$	10.6670	0.689988	0.344994	+	0.938605i	$0.387881\pi$
$240$	−2.97569	−0.192080
$241$	−3.44923	−0.222185	−0.111092	−	0.993810i	$-0.535435\pi$
$241$	−3.44923	−0.222185	−0.111092	+	0.993810i	$0.535435\pi$
$242$	−0.212025	−0.0136295
$243$	−5.34945	−0.343168
$244$	9.57916	0.613243
$245$	1.00000	0.0638877
$246$	10.4454	0.665976
$247$	12.0231	0.765012
$248$	−6.70380	−0.425691
$249$	−15.4641	−0.980000
$250$	−0.612476	−0.0387364
$251$	−21.1776	−1.33672	−0.668359	−	0.743839i	$-0.733003\pi$
$251$	−21.1776	−1.33672	−0.668359	+	0.743839i	$0.733003\pi$
$252$	−0.846597	−0.0533306
$253$	6.57659	0.413466
$254$	−4.15615	−0.260780
$255$	−0.624321	−0.0390965
$256$	−6.28618	−0.392886
$257$	−17.8262	−1.11197	−0.555984	−	0.831193i	$-0.687659\pi$
$257$	−17.8262	−1.11197	−0.555984	+	0.831193i	$0.687659\pi$
$258$	6.70808	0.417627
$259$	−7.83936	−0.487114
$260$	11.3100	0.701419
$261$	−1.83031	−0.113294
$262$	5.87407	0.362902
$263$	−16.2433	−1.00161	−0.500803	−	0.865561i	$-0.666962\pi$
$263$	−16.2433	−1.00161	−0.500803	+	0.865561i	$0.666962\pi$
$264$	11.7745	0.724671
$265$	−6.72794	−0.413294
$266$	−1.05794	−0.0648665
$267$	−1.68896	−0.103363
$268$	−5.42684	−0.331497
$269$	8.54028	0.520710	0.260355	−	0.965513i	$-0.416160\pi$
$269$	8.54028	0.520710	0.260355	+	0.965513i	$0.416160\pi$
$270$	−3.39543	−0.206639
$271$	−6.24639	−0.379441	−0.189721	−	0.981838i	$-0.560758\pi$
$271$	−6.24639	−0.379441	−0.189721	+	0.981838i	$0.560758\pi$
$272$	0.749417	0.0454401
$273$	−10.9593	−0.663284
$274$	1.04893	0.0633681
$275$	−3.36841	−0.203123
$276$	−4.99495	−0.300661
$277$	−0.232246	−0.0139543	−0.00697715	−	0.999976i	$-0.502221\pi$
$277$	−0.232246	−0.0139543	−0.00697715	+	0.999976i	$0.502221\pi$
$278$	−10.1632	−0.609551
$279$	1.57324	0.0941877
$280$	−2.22015	−0.132679
$281$	−10.4699	−0.624585	−0.312292	−	0.949986i	$-0.601097\pi$
$281$	−10.4699	−0.624585	−0.312292	+	0.949986i	$0.601097\pi$
$282$	0.560243	0.0333620
$283$	−13.0618	−0.776441	−0.388220	−	0.921567i	$-0.626910\pi$
$283$	−13.0618	−0.776441	−0.388220	+	0.921567i	$0.626910\pi$
$284$	−8.25656	−0.489937
$285$	2.71962	0.161096
$286$	−14.3602	−0.849134
$287$	−10.8318	−0.639381
$288$	2.91661	0.171863
$289$	−16.8428	−0.990751
$290$	−2.15158	−0.126345
$291$	3.18958	0.186976
$292$	−7.60219	−0.444885
$293$	11.5993	0.677640	0.338820	−	0.940851i	$-0.389972\pi$
$293$	11.5993	0.677640	0.338820	+	0.940851i	$0.389972\pi$
$294$	0.964330	0.0562408
$295$	2.93021	0.170603
$296$	17.4045	1.01162
$297$	−18.6737	−1.08356
$298$	−5.09964	−0.295414
$299$	13.5900	0.785932
$300$	2.55832	0.147705
$301$	−6.95621	−0.400949
$302$	−7.66626	−0.441144
$303$	23.1015	1.32715
$304$	−3.26455	−0.187235
$305$	−5.89533	−0.337566
$306$	0.126537	0.00723365
$307$	−2.71542	−0.154977	−0.0774885	−	0.996993i	$-0.524690\pi$
$307$	−2.71542	−0.154977	−0.0774885	+	0.996993i	$0.524690\pi$
$308$	−5.47324	−0.311867
$309$	11.2147	0.637984
$310$	1.84939	0.105038
$311$	−13.7518	−0.779795	−0.389898	−	0.920858i	$-0.627490\pi$
$311$	−13.7518	−0.779795	−0.389898	+	0.920858i	$0.627490\pi$
$312$	24.3312	1.37748
$313$	−5.32854	−0.301187	−0.150593	−	0.988596i	$-0.548118\pi$
$313$	−5.32854	−0.301187	−0.150593	+	0.988596i	$0.548118\pi$
$314$	−4.21133	−0.237659
$315$	0.521024	0.0293564
$316$	1.45025	0.0815827
$317$	−16.4172	−0.922084	−0.461042	−	0.887378i	$-0.652524\pi$
$317$	−16.4172	−0.922084	−0.461042	+	0.887378i	$0.652524\pi$
$318$	−6.48795	−0.363826
$319$	−11.8329	−0.662517
$320$	−0.351363	−0.0196418
$321$	−18.8463	−1.05190
$322$	−1.19582	−0.0666403
$323$	−0.684926	−0.0381103
$324$	11.6430	0.646831
$325$	−6.96057	−0.386103
$326$	5.49839	0.304528
$327$	16.5063	0.912800
$328$	24.0482	1.32784
$329$	−0.580967	−0.0320297
$330$	−3.24826	−0.178811
$331$	23.2658	1.27881	0.639403	−	0.768872i	$-0.279181\pi$
$331$	23.2658	1.27881	0.639403	+	0.768872i	$0.279181\pi$
$332$	−15.9591	−0.875871
$333$	−4.08449	−0.223829
$334$	12.5596	0.687233
$335$	3.33986	0.182476
$336$	2.97569	0.162337
$337$	3.76608	0.205152	0.102576	−	0.994725i	$-0.467292\pi$
$337$	3.76608	0.205152	0.102576	+	0.994725i	$0.467292\pi$
$338$	−21.7120	−1.18098
$339$	3.45921	0.187879
$340$	−0.644304	−0.0349423
$341$	10.1710	0.550790
$342$	−0.551212	−0.0298061
$343$	−1.00000	−0.0539949
$344$	15.4438	0.832675
$345$	3.07406	0.165502
$346$	2.69697	0.144990
$347$	−1.84107	−0.0988340	−0.0494170	−	0.998778i	$-0.515736\pi$
$347$	−1.84107	−0.0988340	−0.0494170	+	0.998778i	$0.515736\pi$
$348$	8.98718	0.481763
$349$	−2.07528	−0.111087	−0.0555436	−	0.998456i	$-0.517689\pi$
$349$	−2.07528	−0.111087	−0.0555436	+	0.998456i	$0.517689\pi$
$350$	0.612476	0.0327382
$351$	−38.5878	−2.05966
$352$	18.8559	1.00502
$353$	10.1247	0.538885	0.269443	−	0.963016i	$-0.413161\pi$
$353$	10.1247	0.538885	0.269443	+	0.963016i	$0.413161\pi$
$354$	2.82569	0.150184
$355$	5.08136	0.269691
$356$	−1.74303	−0.0923801
$357$	0.624321	0.0330426
$358$	4.11844	0.217666
$359$	−24.8699	−1.31258	−0.656291	−	0.754508i	$-0.727875\pi$
$359$	−24.8699	−1.31258	−0.656291	+	0.754508i	$0.727875\pi$
$360$	−1.15675	−0.0609661
$361$	−16.0164	−0.842967
$362$	1.54021	0.0809515
$363$	−0.545048	−0.0286076
$364$	−11.3100	−0.592807
$365$	4.67864	0.244891
$366$	−5.68504	−0.297162
$367$	26.0380	1.35917	0.679586	−	0.733596i	$-0.262160\pi$
$367$	26.0380	1.35917	0.679586	+	0.733596i	$0.262160\pi$
$368$	−3.69001	−0.192355
$369$	−5.64362	−0.293795
$370$	−4.80142	−0.249614
$371$	6.72794	0.349297
$372$	−7.72492	−0.400519
$373$	17.9692	0.930411	0.465206	−	0.885203i	$-0.345980\pi$
$373$	17.9692	0.930411	0.465206	+	0.885203i	$0.345980\pi$
$374$	0.818061	0.0423009
$375$	−1.57448	−0.0813056
$376$	1.28983	0.0665180
$377$	−24.4519	−1.25934
$378$	3.39543	0.174642
$379$	−1.45232	−0.0746006	−0.0373003	−	0.999304i	$-0.511876\pi$
$379$	−1.45232	−0.0746006	−0.0373003	+	0.999304i	$0.511876\pi$
$380$	2.80667	0.143979
$381$	−10.6841	−0.547363
$382$	−7.05987	−0.361214
$383$	37.8856	1.93586	0.967931	−	0.251217i	$-0.0808307\pi$
$383$	37.8856	1.93586	0.967931	+	0.251217i	$0.0808307\pi$
$384$	−17.9662	−0.916834
$385$	3.36841	0.171670
$386$	0.361718	0.0184110
$387$	−3.62435	−0.184236
$388$	3.29167	0.167109
$389$	−8.90403	−0.451452	−0.225726	−	0.974191i	$-0.572475\pi$
$389$	−8.90403	−0.451452	−0.225726	+	0.974191i	$0.572475\pi$
$390$	−6.71229	−0.339890
$391$	−0.774189	−0.0391524
$392$	2.22015	0.112134
$393$	15.1003	0.761711
$394$	−7.73938	−0.389904
$395$	−0.892529	−0.0449080
$396$	−2.85169	−0.143303
$397$	15.4334	0.774581	0.387291	−	0.921958i	$-0.373411\pi$
$397$	15.4334	0.774581	0.387291	+	0.921958i	$0.373411\pi$
$398$	−1.07266	−0.0537677
$399$	−2.71962	−0.136151
$400$	1.88996	0.0944978
$401$	−0.382894	−0.0191208	−0.00956041	−	0.999954i	$-0.503043\pi$
$401$	−0.382894	−0.0191208	−0.00956041	+	0.999954i	$0.503043\pi$
$402$	3.22072	0.160635
$403$	21.0176	1.04696
$404$	23.8409	1.18613
$405$	−7.16546	−0.356055
$406$	2.15158	0.106781
$407$	−26.4062	−1.30891
$408$	−1.38608	−0.0686214
$409$	−11.6267	−0.574901	−0.287451	−	0.957795i	$-0.592808\pi$
$409$	−11.6267	−0.574901	−0.287451	+	0.957795i	$0.592808\pi$
$410$	−6.63422	−0.327641
$411$	2.69645	0.133006
$412$	11.5737	0.570196
$413$	−2.93021	−0.144186
$414$	−0.623049	−0.0306212
$415$	9.82177	0.482132
$416$	38.9642	1.91038
$417$	−26.1264	−1.27941
$418$	−3.56358	−0.174300
$419$	−31.4083	−1.53439	−0.767197	−	0.641411i	$-0.778349\pi$
$419$	−31.4083	−1.53439	−0.767197	+	0.641411i	$0.778349\pi$
$420$	−2.55832	−0.124833
$421$	0.136448	0.00665009	0.00332504	−	0.999994i	$-0.498942\pi$
$421$	0.136448	0.00665009	0.00332504	+	0.999994i	$0.498942\pi$
$422$	−9.73937	−0.474105
$423$	−0.302697	−0.0147177
$424$	−14.9370	−0.725406
$425$	0.396526	0.0192343
$426$	4.90010	0.237411
$427$	5.89533	0.285295
$428$	−19.4496	−0.940130
$429$	−36.9153	−1.78229
$430$	−4.26051	−0.205460
$431$	−9.12045	−0.439317	−0.219658	−	0.975577i	$-0.570494\pi$
$431$	−9.12045	−0.439317	−0.219658	+	0.975577i	$0.570494\pi$
$432$	10.4775	0.504098
$433$	4.78121	0.229770	0.114885	−	0.993379i	$-0.463350\pi$
$433$	4.78121	0.229770	0.114885	+	0.993379i	$0.463350\pi$
$434$	−1.84939	−0.0887735
$435$	−5.53101	−0.265191
$436$	17.0346	0.815810
$437$	3.37247	0.161327
$438$	4.51175	0.215580
$439$	15.2137	0.726108	0.363054	−	0.931768i	$-0.381734\pi$
$439$	15.2137	0.726108	0.363054	+	0.931768i	$0.381734\pi$
$440$	−7.47837	−0.356517
$441$	−0.521024	−0.0248107
$442$	1.69046	0.0804071
$443$	5.39075	0.256122	0.128061	−	0.991766i	$-0.459125\pi$
$443$	5.39075	0.256122	0.128061	+	0.991766i	$0.459125\pi$
$444$	20.0556	0.951798
$445$	1.07271	0.0508516
$446$	−9.76462	−0.462368
$447$	−13.1095	−0.620058
$448$	0.351363	0.0166003
$449$	−8.49042	−0.400688	−0.200344	−	0.979726i	$-0.564206\pi$
$449$	−8.49042	−0.400688	−0.200344	+	0.979726i	$0.564206\pi$
$450$	0.319115	0.0150432
$451$	−36.4859	−1.71805
$452$	3.56993	0.167916
$453$	−19.7075	−0.925937
$454$	−14.3501	−0.673485
$455$	6.96057	0.326317
$456$	6.03796	0.282753
$457$	3.17542	0.148540	0.0742699	−	0.997238i	$-0.476337\pi$
$457$	3.17542	0.148540	0.0742699	+	0.997238i	$0.476337\pi$
$458$	−0.612476	−0.0286191
$459$	2.19825	0.102605
$460$	3.17245	0.147916
$461$	−14.9848	−0.697912	−0.348956	−	0.937139i	$-0.613464\pi$
$461$	−14.9848	−0.697912	−0.348956	+	0.937139i	$0.613464\pi$
$462$	3.24826	0.151123
$463$	18.5610	0.862605	0.431302	−	0.902207i	$-0.358054\pi$
$463$	18.5610	0.862605	0.431302	+	0.902207i	$0.358054\pi$
$464$	6.63926	0.308220
$465$	4.75417	0.220469
$466$	10.7036	0.495833
$467$	12.2138	0.565187	0.282593	−	0.959240i	$-0.408805\pi$
$467$	12.2138	0.565187	0.282593	+	0.959240i	$0.408805\pi$
$468$	−5.89280	−0.272395
$469$	−3.33986	−0.154220
$470$	−0.355828	−0.0164131
$471$	−10.8259	−0.498833
$472$	6.50550	0.299440
$473$	−23.4314	−1.07737
$474$	−0.860692	−0.0395329
$475$	−1.72732	−0.0792547
$476$	0.644304	0.0295316
$477$	3.50542	0.160502
$478$	−6.53326	−0.298824
$479$	30.1491	1.37755	0.688774	−	0.724976i	$-0.258149\pi$
$479$	30.1491	1.37755	0.688774	+	0.724976i	$0.258149\pi$
$480$	8.81369	0.402288
$481$	−54.5664	−2.48802
$482$	2.11257	0.0962251
$483$	−3.07406	−0.139874
$484$	−0.562494	−0.0255679
$485$	−2.02580	−0.0919870
$486$	3.27641	0.148621
$487$	−13.4649	−0.610151	−0.305076	−	0.952328i	$-0.598682\pi$
$487$	−13.4649	−0.610151	−0.305076	+	0.952328i	$0.598682\pi$
$488$	−13.0885	−0.592489
$489$	14.1346	0.639187
$490$	−0.612476	−0.0276689
$491$	−22.1051	−0.997590	−0.498795	−	0.866720i	$-0.666224\pi$
$491$	−22.1051	−0.997590	−0.498795	+	0.866720i	$0.666224\pi$
$492$	27.7112	1.24932
$493$	1.39296	0.0627359
$494$	−7.36387	−0.331316
$495$	1.75502	0.0788823
$496$	−5.70677	−0.256242
$497$	−5.08136	−0.227930
$498$	9.47142	0.424425
$499$	28.2162	1.26313	0.631565	−	0.775323i	$-0.282413\pi$
$499$	28.2162	1.26313	0.631565	+	0.775323i	$0.282413\pi$
$500$	−1.62487	−0.0726665
$501$	32.2867	1.44246
$502$	12.9708	0.578914
$503$	7.87865	0.351292	0.175646	−	0.984453i	$-0.443799\pi$
$503$	7.87865	0.351292	0.175646	+	0.984453i	$0.443799\pi$
$504$	1.15675	0.0515257
$505$	−14.6725	−0.652917
$506$	−4.02800	−0.179067
$507$	−55.8145	−2.47881
$508$	−11.0261	−0.489203
$509$	14.9441	0.662388	0.331194	−	0.943563i	$-0.392549\pi$
$509$	14.9441	0.662388	0.331194	+	0.943563i	$0.392549\pi$
$510$	0.382382	0.0169321
$511$	−4.67864	−0.206971
$512$	−18.9717	−0.838437
$513$	−9.57584	−0.422784
$514$	10.9181	0.481578
$515$	−7.12284	−0.313870
$516$	17.7962	0.783436
$517$	−1.95693	−0.0860658
$518$	4.80142	0.210962
$519$	6.93302	0.304326
$520$	−15.4535	−0.677681
$521$	−29.1690	−1.27792	−0.638960	−	0.769240i	$-0.720635\pi$
$521$	−29.1690	−1.27792	−0.638960	+	0.769240i	$0.720635\pi$
$522$	1.12102	0.0490659
$523$	−33.5578	−1.46738	−0.733691	−	0.679484i	$-0.762204\pi$
$523$	−33.5578	−1.46738	−0.733691	+	0.679484i	$0.762204\pi$
$524$	15.5837	0.680775
$525$	1.57448	0.0687158
$526$	9.94865	0.433782
$527$	−1.19732	−0.0521561
$528$	10.0233	0.436210
$529$	−19.1880	−0.834261
$530$	4.12070	0.178992
$531$	−1.52671	−0.0662535
$532$	−2.80667	−0.121685
$533$	−75.3955	−3.26574
$534$	1.03445	0.0447651
$535$	11.9699	0.517504
$536$	7.41498	0.320278
$537$	10.5872	0.456870
$538$	−5.23072	−0.225512
$539$	−3.36841	−0.145088
$540$	−9.00792	−0.387639
$541$	−2.01853	−0.0867835	−0.0433918	−	0.999058i	$-0.513816\pi$
$541$	−2.01853	−0.0867835	−0.0433918	+	0.999058i	$0.513816\pi$
$542$	3.82577	0.164331
$543$	3.95937	0.169913
$544$	−2.21969	−0.0951685
$545$	−10.4837	−0.449071
$546$	6.71229	0.287259
$547$	−13.3127	−0.569212	−0.284606	−	0.958645i	$-0.591863\pi$
$547$	−13.3127	−0.569212	−0.284606	+	0.958645i	$0.591863\pi$
$548$	2.78276	0.118874
$549$	3.07161	0.131093
$550$	2.06307	0.0879696
$551$	−6.06792	−0.258502
$552$	6.82486	0.290485
$553$	0.892529	0.0379542
$554$	0.142245	0.00604341
$555$	−12.3429	−0.523926
$556$	−26.9626	−1.14347
$557$	15.2510	0.646204	0.323102	−	0.946364i	$-0.395274\pi$
$557$	15.2510	0.646204	0.323102	+	0.946364i	$0.395274\pi$
$558$	−0.963575	−0.0407914
$559$	−48.4192	−2.04791
$560$	−1.88996	−0.0798653
$561$	2.10297	0.0887873
$562$	6.41260	0.270499
$563$	−6.97638	−0.294019	−0.147010	−	0.989135i	$-0.546965\pi$
$563$	−6.97638	−0.294019	−0.147010	+	0.989135i	$0.546965\pi$
$564$	1.48630	0.0625846
$565$	−2.19705	−0.0924308
$566$	8.00002	0.336266
$567$	7.16546	0.300921
$568$	11.2814	0.473356
$569$	−30.4875	−1.27810	−0.639051	−	0.769164i	$-0.720673\pi$
$569$	−30.4875	−1.27810	−0.639051	+	0.769164i	$0.720673\pi$
$570$	−1.66570	−0.0697686
$571$	−39.3526	−1.64685	−0.823427	−	0.567422i	$-0.807941\pi$
$571$	−39.3526	−1.64685	−0.823427	+	0.567422i	$0.807941\pi$
$572$	−38.0968	−1.59291
$573$	−18.1486	−0.758169
$574$	6.63422	0.276907
$575$	−1.95243	−0.0814220
$576$	0.183068	0.00762784
$577$	10.2984	0.428730	0.214365	−	0.976754i	$-0.431232\pi$
$577$	10.2984	0.428730	0.214365	+	0.976754i	$0.431232\pi$
$578$	10.3158	0.429081
$579$	0.929859	0.0386436
$580$	−5.70804	−0.237014
$581$	−9.82177	−0.407476
$582$	−1.95354	−0.0809769
$583$	22.6624	0.938583
$584$	10.3873	0.429828
$585$	3.62662	0.149942
$586$	−7.10431	−0.293476
$587$	−17.6636	−0.729053	−0.364527	−	0.931193i	$-0.618769\pi$
$587$	−17.6636	−0.729053	−0.364527	+	0.931193i	$0.618769\pi$
$588$	2.55832	0.105504
$589$	5.21568	0.214908
$590$	−1.79468	−0.0738859
$591$	−19.8954	−0.818388
$592$	14.8161	0.608936
$593$	2.38205	0.0978189	0.0489094	−	0.998803i	$-0.484425\pi$
$593$	2.38205	0.0978189	0.0489094	+	0.998803i	$0.484425\pi$
$594$	11.4372	0.469273
$595$	−0.396526	−0.0162560
$596$	−13.5291	−0.554174
$597$	−2.75747	−0.112856
$598$	−8.32357	−0.340376
$599$	−48.5759	−1.98476	−0.992379	−	0.123225i	$-0.960676\pi$
$599$	−48.5759	−1.98476	−0.992379	+	0.123225i	$0.960676\pi$
$600$	−3.49557	−0.142706
$601$	−45.7742	−1.86717	−0.933584	−	0.358360i	$-0.883336\pi$
$601$	−45.7742	−1.86717	−0.933584	+	0.358360i	$0.883336\pi$
$602$	4.26051	0.173646
$603$	−1.74014	−0.0708642
$604$	−20.3383	−0.827552
$605$	0.346177	0.0140741
$606$	−14.1491	−0.574769
$607$	15.8081	0.641629	0.320814	−	0.947142i	$-0.396043\pi$
$607$	15.8081	0.641629	0.320814	+	0.947142i	$0.396043\pi$
$608$	9.66926	0.392140
$609$	5.53101	0.224128
$610$	3.61075	0.146195
$611$	−4.04386	−0.163597
$612$	0.335698	0.0135698
$613$	18.3314	0.740398	0.370199	−	0.928953i	$-0.379290\pi$
$613$	18.3314	0.740398	0.370199	+	0.928953i	$0.379290\pi$
$614$	1.66313	0.0671184
$615$	−17.0544	−0.687700
$616$	7.47837	0.301312
$617$	−2.56537	−0.103278	−0.0516390	−	0.998666i	$-0.516445\pi$
$617$	−2.56537	−0.103278	−0.0516390	+	0.998666i	$0.516445\pi$
$618$	−6.86876	−0.276302
$619$	−12.3447	−0.496176	−0.248088	−	0.968738i	$-0.579802\pi$
$619$	−12.3447	−0.496176	−0.248088	+	0.968738i	$0.579802\pi$
$620$	4.90634	0.197044
$621$	−10.8238	−0.434345
$622$	8.42268	0.337719
$623$	−1.07271	−0.0429774
$624$	20.7125	0.829165
$625$	1.00000	0.0400000
$626$	3.26361	0.130440
$627$	−9.16079	−0.365847
$628$	−11.1725	−0.445830
$629$	3.10851	0.123944
$630$	−0.319115	−0.0127138
$631$	−11.0147	−0.438488	−0.219244	−	0.975670i	$-0.570359\pi$
$631$	−11.0147	−0.438488	−0.219244	+	0.975670i	$0.570359\pi$
$632$	−1.98155	−0.0788217
$633$	−25.0367	−0.995121
$634$	10.0552	0.399342
$635$	6.78581	0.269287
$636$	−17.2122	−0.682510
$637$	−6.96057	−0.275788
$638$	7.24740	0.286927
$639$	−2.64751	−0.104734
$640$	11.4109	0.451056
$641$	18.6376	0.736139	0.368070	−	0.929798i	$-0.380019\pi$
$641$	18.6376	0.736139	0.368070	+	0.929798i	$0.380019\pi$
$642$	11.5429	0.455563
$643$	−0.583961	−0.0230292	−0.0115146	−	0.999934i	$-0.503665\pi$
$643$	−0.583961	−0.0230292	−0.0115146	+	0.999934i	$0.503665\pi$
$644$	−3.17245	−0.125012
$645$	−10.9524	−0.431250
$646$	0.419501	0.0165050
$647$	−46.4706	−1.82695	−0.913474	−	0.406897i	$-0.866611\pi$
$647$	−46.4706	−1.82695	−0.913474	+	0.406897i	$0.866611\pi$
$648$	−15.9084	−0.624941
$649$	−9.87014	−0.387437
$650$	4.26319	0.167216
$651$	−4.75417	−0.186331
$652$	14.5870	0.571271
$653$	22.8641	0.894742	0.447371	−	0.894348i	$-0.352360\pi$
$653$	22.8641	0.894742	0.447371	+	0.894348i	$0.352360\pi$
$654$	−10.1097	−0.395321
$655$	−9.59070	−0.374740
$656$	20.4716	0.799283
$657$	−2.43768	−0.0951030
$658$	0.355828	0.0138716
$659$	4.54047	0.176872	0.0884359	−	0.996082i	$-0.471813\pi$
$659$	4.54047	0.176872	0.0884359	+	0.996082i	$0.471813\pi$
$660$	−8.61748	−0.335435
$661$	−27.7304	−1.07859	−0.539293	−	0.842118i	$-0.681309\pi$
$661$	−27.7304	−1.07859	−0.539293	+	0.842118i	$0.681309\pi$
$662$	−14.2498	−0.553833
$663$	4.34563	0.168770
$664$	21.8058	0.846229
$665$	1.72732	0.0669825
$666$	2.50166	0.0969372
$667$	−6.85873	−0.265571
$668$	33.3202	1.28920
$669$	−25.1017	−0.970486
$670$	−2.04558	−0.0790278
$671$	19.8579	0.766605
$672$	−8.81369	−0.339995
$673$	1.47199	0.0567409	0.0283705	−	0.999597i	$-0.490968\pi$
$673$	1.47199	0.0567409	0.0283705	+	0.999597i	$0.490968\pi$
$674$	−2.30664	−0.0888483
$675$	5.54377	0.213380
$676$	−57.6010	−2.21542
$677$	−13.8846	−0.533629	−0.266814	−	0.963748i	$-0.585971\pi$
$677$	−13.8846	−0.533629	−0.266814	+	0.963748i	$0.585971\pi$
$678$	−2.11868	−0.0813676
$679$	2.02580	0.0777432
$680$	0.880346	0.0337597
$681$	−36.8895	−1.41361
$682$	−6.22949	−0.238540
$683$	27.7372	1.06133	0.530667	−	0.847581i	$-0.321942\pi$
$683$	27.7372	1.06133	0.530667	+	0.847581i	$0.321942\pi$
$684$	−1.46234	−0.0559140
$685$	−1.71260	−0.0654352
$686$	0.612476	0.0233845
$687$	−1.57448	−0.0600700
$688$	13.1469	0.501222
$689$	46.8303	1.78409
$690$	−1.88279	−0.0716765
$691$	0.179249	0.00681896	0.00340948	−	0.999994i	$-0.498915\pi$
$691$	0.179249	0.00681896	0.00340948	+	0.999994i	$0.498915\pi$
$692$	7.15493	0.271990
$693$	−1.75502	−0.0666677
$694$	1.12761	0.0428037
$695$	16.5937	0.629435
$696$	−12.2797	−0.465459
$697$	4.29509	0.162688
$698$	1.27106	0.0481103
$699$	27.5154	1.04073
$700$	1.62487	0.0614144
$701$	−43.4457	−1.64092	−0.820460	−	0.571703i	$-0.806283\pi$
$701$	−43.4457	−1.64092	−0.820460	+	0.571703i	$0.806283\pi$
$702$	23.6341	0.892012
$703$	−13.5411	−0.510711
$704$	1.18353	0.0446061
$705$	−0.914718	−0.0344503
$706$	−6.20116	−0.233384
$707$	14.6725	0.551816
$708$	7.49642	0.281733
$709$	3.42905	0.128781	0.0643903	−	0.997925i	$-0.479490\pi$
$709$	3.42905	0.128781	0.0643903	+	0.997925i	$0.479490\pi$
$710$	−3.11221	−0.116799
$711$	0.465029	0.0174399
$712$	2.38159	0.0892537
$713$	5.89541	0.220785
$714$	−0.382382	−0.0143103
$715$	23.4461	0.876833
$716$	10.9260	0.408325
$717$	−16.7949	−0.627216
$718$	15.2322	0.568461
$719$	36.3037	1.35390	0.676949	−	0.736029i	$-0.263302\pi$
$719$	36.3037	1.35390	0.676949	+	0.736029i	$0.263302\pi$
$720$	−0.984712	−0.0366981
$721$	7.12284	0.265268
$722$	9.80965	0.365077
$723$	5.43074	0.201971
$724$	4.08610	0.151859
$725$	3.51292	0.130466
$726$	0.333829	0.0123896
$727$	−11.6455	−0.431907	−0.215954	−	0.976404i	$-0.569286\pi$
$727$	−11.6455	−0.431907	−0.215954	+	0.976404i	$0.569286\pi$
$728$	15.4535	0.572745
$729$	29.9190	1.10811
$730$	−2.86556	−0.106059
$731$	2.75832	0.102020
$732$	−15.0822	−0.557453
$733$	9.20368	0.339946	0.169973	−	0.985449i	$-0.445632\pi$
$733$	9.20368	0.339946	0.169973	+	0.985449i	$0.445632\pi$
$734$	−15.9476	−0.588638
$735$	−1.57448	−0.0580754
$736$	10.9294	0.402864
$737$	−11.2500	−0.414399
$738$	3.45659	0.127239
$739$	−25.0024	−0.919728	−0.459864	−	0.887989i	$-0.652102\pi$
$739$	−25.0024	−0.919728	−0.459864	+	0.887989i	$0.652102\pi$
$740$	−12.7380	−0.468257
$741$	−18.9301	−0.695415
$742$	−4.12070	−0.151276
$743$	−18.0585	−0.662503	−0.331251	−	0.943543i	$-0.607471\pi$
$743$	−18.0585	−0.662503	−0.331251	+	0.943543i	$0.607471\pi$
$744$	10.5550	0.386964
$745$	8.32626	0.305051
$746$	−11.0057	−0.402948
$747$	−5.11738	−0.187235
$748$	2.17028	0.0793533
$749$	−11.9699	−0.437371
$750$	0.964330	0.0352123
$751$	19.5258	0.712507	0.356254	−	0.934389i	$-0.384054\pi$
$751$	19.5258	0.712507	0.356254	+	0.934389i	$0.384054\pi$
$752$	1.09800	0.0400400
$753$	33.3436	1.21511
$754$	14.9762	0.545402
$755$	12.5168	0.455534
$756$	9.00792	0.327615
$757$	21.6324	0.786243	0.393122	−	0.919487i	$-0.371395\pi$
$757$	21.6324	0.786243	0.393122	+	0.919487i	$0.371395\pi$
$758$	0.889511	0.0323085
$759$	−10.3547	−0.375851
$760$	−3.83490	−0.139106
$761$	−34.8862	−1.26462	−0.632311	−	0.774715i	$-0.717894\pi$
$761$	−34.8862	−1.26462	−0.632311	+	0.774715i	$0.717894\pi$
$762$	6.54375	0.237055
$763$	10.4837	0.379534
$764$	−18.7295	−0.677610
$765$	−0.206599	−0.00746962
$766$	−23.2040	−0.838395
$767$	−20.3959	−0.736454
$768$	9.89745	0.357143
$769$	6.38280	0.230170	0.115085	−	0.993356i	$-0.463286\pi$
$769$	6.38280	0.230170	0.115085	+	0.993356i	$0.463286\pi$
$770$	−2.06307	−0.0743479
$771$	28.0670	1.01081
$772$	0.959622	0.0345376
$773$	−8.76731	−0.315338	−0.157669	−	0.987492i	$-0.550398\pi$
$773$	−8.76731	−0.315338	−0.157669	+	0.987492i	$0.550398\pi$
$774$	2.21983	0.0797901
$775$	−3.01953	−0.108465
$776$	−4.49758	−0.161454
$777$	12.3429	0.442799
$778$	5.45351	0.195518
$779$	−18.7099	−0.670353
$780$	−17.8074	−0.637607
$781$	−17.1161	−0.612462
$782$	0.474173	0.0169564
$783$	19.4748	0.695973
$784$	1.88996	0.0674985
$785$	6.87590	0.245411
$786$	−9.24859	−0.329886
$787$	10.2451	0.365199	0.182600	−	0.983187i	$-0.441549\pi$
$787$	10.2451	0.365199	0.182600	+	0.983187i	$0.441549\pi$
$788$	−20.5322	−0.731431
$789$	25.5747	0.910485
$790$	0.546653	0.0194490
$791$	2.19705	0.0781183
$792$	3.89641	0.138453
$793$	41.0349	1.45719
$794$	−9.45261	−0.335461
$795$	10.5930	0.375694
$796$	−2.84573	−0.100864
$797$	30.9643	1.09681	0.548405	−	0.836213i	$-0.315235\pi$
$797$	30.9643	1.09681	0.548405	+	0.836213i	$0.315235\pi$
$798$	1.66570	0.0589652
$799$	0.230368	0.00814985
$800$	−5.59785	−0.197914
$801$	−0.558910	−0.0197481
$802$	0.234514	0.00828096
$803$	−15.7596	−0.556143
$804$	8.54444	0.301339
$805$	1.95243	0.0688141
$806$	−12.8728	−0.453425
$807$	−13.4465	−0.473338
$808$	−32.5751	−1.14599
$809$	30.9346	1.08760	0.543801	−	0.839214i	$-0.316985\pi$
$809$	30.9346	1.08760	0.543801	+	0.839214i	$0.316985\pi$
$810$	4.38868	0.154202
$811$	3.78151	0.132787	0.0663933	−	0.997794i	$-0.478851\pi$
$811$	3.78151	0.132787	0.0663933	+	0.997794i	$0.478851\pi$
$812$	5.70804	0.200313
$813$	9.83480	0.344922
$814$	16.1732	0.566869
$815$	−8.97732	−0.314462
$816$	−1.17994	−0.0413061
$817$	−12.0156	−0.420372
$818$	7.12105	0.248982
$819$	−3.62662	−0.126724
$820$	−17.6003	−0.614629
$821$	40.9094	1.42775	0.713874	−	0.700274i	$-0.246939\pi$
$821$	40.9094	1.42775	0.713874	+	0.700274i	$0.246939\pi$
$822$	−1.65151	−0.0576031
$823$	−51.7948	−1.80545	−0.902726	−	0.430216i	$-0.858438\pi$
$823$	−51.7948	−1.80545	−0.902726	+	0.430216i	$0.858438\pi$
$824$	−15.8138	−0.550898
$825$	5.30348	0.184643
$826$	1.79468	0.0624450
$827$	−16.3724	−0.569325	−0.284662	−	0.958628i	$-0.591881\pi$
$827$	−16.3724	−0.569325	−0.284662	+	0.958628i	$0.591881\pi$
$828$	−1.65292	−0.0574430
$829$	−46.1871	−1.60414	−0.802072	−	0.597227i	$-0.796269\pi$
$829$	−46.1871	−1.60414	−0.802072	+	0.597227i	$0.796269\pi$
$830$	−6.01560	−0.208805
$831$	0.365666	0.0126848
$832$	2.44568	0.0847888
$833$	0.396526	0.0137388
$834$	16.0018	0.554097
$835$	−20.5063	−0.709651
$836$	−9.45401	−0.326974
$837$	−16.7396	−0.578604
$838$	19.2368	0.664525
$839$	48.7911	1.68446	0.842228	−	0.539121i	$-0.181243\pi$
$839$	48.7911	1.68446	0.842228	+	0.539121i	$0.181243\pi$
$840$	3.49557	0.120609
$841$	−16.6594	−0.574463
$842$	−0.0835714	−0.00288006
$843$	16.4847	0.567763
$844$	−25.8381	−0.889385
$845$	35.4496	1.21950
$846$	0.185395	0.00637401
$847$	−0.346177	−0.0118948
$848$	−12.7155	−0.436653
$849$	20.5654	0.705804
$850$	−0.242863	−0.00833012
$851$	−15.3058	−0.524676
$852$	12.9998	0.445365
$853$	−11.2558	−0.385392	−0.192696	−	0.981259i	$-0.561723\pi$
$853$	−11.2558	−0.385392	−0.192696	+	0.981259i	$0.561723\pi$
$854$	−3.61075	−0.123557
$855$	0.899973	0.0307784
$856$	26.5750	0.908313
$857$	29.0439	0.992120	0.496060	−	0.868288i	$-0.334780\pi$
$857$	29.0439	0.992120	0.496060	+	0.868288i	$0.334780\pi$
$858$	22.6097	0.771883
$859$	−25.7261	−0.877763	−0.438881	−	0.898545i	$-0.644625\pi$
$859$	−25.7261	−0.877763	−0.438881	+	0.898545i	$0.644625\pi$
$860$	−11.3030	−0.385428
$861$	17.0544	0.581213
$862$	5.58606	0.190262
$863$	33.3426	1.13500	0.567498	−	0.823375i	$-0.307912\pi$
$863$	33.3426	1.13500	0.567498	+	0.823375i	$0.307912\pi$
$864$	−31.0332	−1.05577
$865$	−4.40338	−0.149719
$866$	−2.92838	−0.0995103
$867$	26.5185	0.900617
$868$	−4.90634	−0.166532
$869$	3.00640	0.101985
$870$	3.38761	0.114851
$871$	−23.2473	−0.787705
$872$	−23.2753	−0.788201
$873$	1.05549	0.0357230
$874$	−2.06556	−0.0698685
$875$	−1.00000	−0.0338062
$876$	11.9695	0.404411
$877$	40.3728	1.36329	0.681646	−	0.731682i	$-0.261264\pi$
$877$	40.3728	1.36329	0.681646	+	0.731682i	$0.261264\pi$
$878$	−9.31801	−0.314467
$879$	−18.2629	−0.615991
$880$	−6.36615	−0.214603
$881$	−20.5201	−0.691340	−0.345670	−	0.938356i	$-0.612348\pi$
$881$	−20.5201	−0.691340	−0.345670	+	0.938356i	$0.612348\pi$
$882$	0.319115	0.0107452
$883$	−20.8431	−0.701427	−0.350713	−	0.936483i	$-0.614061\pi$
$883$	−20.8431	−0.701427	−0.350713	+	0.936483i	$0.614061\pi$
$884$	4.48472	0.150838
$885$	−4.61354	−0.155083
$886$	−3.30171	−0.110923
$887$	−47.7303	−1.60263	−0.801313	−	0.598245i	$-0.795865\pi$
$887$	−47.7303	−1.60263	−0.801313	+	0.598245i	$0.795865\pi$
$888$	−27.4030	−0.919586
$889$	−6.78581	−0.227589
$890$	−0.657012	−0.0220231
$891$	24.1362	0.808593
$892$	−25.9051	−0.867368
$893$	−1.00351	−0.0335813
$894$	8.02926	0.268539
$895$	−6.72424	−0.224767
$896$	−11.4109	−0.381212
$897$	−21.3972	−0.714431
$898$	5.20018	0.173532
$899$	−10.6073	−0.353775
$900$	0.846597	0.0282199
$901$	−2.66780	−0.0888774
$902$	22.3468	0.744066
$903$	10.9524	0.364473
$904$	−4.87779	−0.162233
$905$	−2.51472	−0.0835922
$906$	12.0704	0.401011
$907$	36.3773	1.20789	0.603945	−	0.797026i	$-0.293595\pi$
$907$	36.3773	1.20789	0.603945	+	0.797026i	$0.293595\pi$
$908$	−38.0702	−1.26341
$909$	7.64472	0.253559
$910$	−4.26319	−0.141323
$911$	33.9220	1.12389	0.561943	−	0.827176i	$-0.310054\pi$
$911$	33.9220	1.12389	0.561943	+	0.827176i	$0.310054\pi$
$912$	5.13996	0.170201
$913$	−33.0837	−1.09491
$914$	−1.94487	−0.0643305
$915$	9.28206	0.306855
$916$	−1.62487	−0.0536873
$917$	9.59070	0.316713
$918$	−1.34637	−0.0444370
$919$	40.2585	1.32801	0.664003	−	0.747730i	$-0.268856\pi$
$919$	40.2585	1.32801	0.664003	+	0.747730i	$0.268856\pi$
$920$	−4.33469	−0.142910
$921$	4.27536	0.140878
$922$	9.17784	0.302256
$923$	−35.3692	−1.16419
$924$	8.61748	0.283494
$925$	7.83936	0.257757
$926$	−11.3682	−0.373582
$927$	3.71117	0.121891
$928$	−19.6648	−0.645528
$929$	26.0069	0.853259	0.426629	−	0.904427i	$-0.359701\pi$
$929$	26.0069	0.853259	0.426629	+	0.904427i	$0.359701\pi$
$930$	−2.91182	−0.0954823
$931$	−1.72732	−0.0566105
$932$	28.3961	0.930145
$933$	21.6520	0.708853
$934$	−7.48066	−0.244775
$935$	−1.33566	−0.0436808
$936$	8.05164	0.263176
$937$	3.95982	0.129362	0.0646809	−	0.997906i	$-0.479397\pi$
$937$	3.95982	0.129362	0.0646809	+	0.997906i	$0.479397\pi$
$938$	2.04558	0.0667907
$939$	8.38966	0.273786
$940$	−0.943997	−0.0307898
$941$	−48.8073	−1.59107	−0.795536	−	0.605907i	$-0.792810\pi$
$941$	−48.8073	−1.59107	−0.795536	+	0.605907i	$0.792810\pi$
$942$	6.63063	0.216038
$943$	−21.1483	−0.688684
$944$	5.53797	0.180245
$945$	−5.54377	−0.180339
$946$	14.3511	0.466596
$947$	17.6585	0.573825	0.286913	−	0.957957i	$-0.407371\pi$
$947$	17.6585	0.573825	0.286913	+	0.957957i	$0.407371\pi$
$948$	−2.28338	−0.0741607
$949$	−32.5660	−1.05714
$950$	1.05794	0.0343241
$951$	25.8486	0.838197
$952$	−0.880346	−0.0285322
$953$	−36.4772	−1.18161	−0.590806	−	0.806814i	$-0.701190\pi$
$953$	−36.4772	−1.18161	−0.590806	+	0.806814i	$0.701190\pi$
$954$	−2.14698	−0.0695112
$955$	11.5268	0.372997
$956$	−17.3324	−0.560571
$957$	18.6307	0.602245
$958$	−18.4656	−0.596597
$959$	1.71260	0.0553028
$960$	0.553212	0.0178548
$961$	−21.8825	−0.705886
$962$	33.4206	1.07752
$963$	−6.23660	−0.200972
$964$	5.60457	0.180511
$965$	−0.590583	−0.0190115
$966$	1.88279	0.0605777
$967$	−22.2611	−0.715867	−0.357934	−	0.933747i	$-0.616519\pi$
$967$	−22.2611	−0.715867	−0.357934	+	0.933747i	$0.616519\pi$
$968$	0.768565	0.0247026
$969$	1.07840	0.0346432
$970$	1.24076	0.0398383
$971$	−29.9544	−0.961282	−0.480641	−	0.876917i	$-0.659596\pi$
$971$	−29.9544	−0.961282	−0.480641	+	0.876917i	$0.659596\pi$
$972$	8.69218	0.278802
$973$	−16.5937	−0.531969
$974$	8.24691	0.264248
$975$	10.9593	0.350977
$976$	−11.1419	−0.356644
$977$	44.5082	1.42394	0.711971	−	0.702209i	$-0.247803\pi$
$977$	44.5082	1.42394	0.711971	+	0.702209i	$0.247803\pi$
$978$	−8.65709	−0.276823
$979$	−3.61334	−0.115483
$980$	−1.62487	−0.0519047
$981$	5.46224	0.174396
$982$	13.5389	0.432042
$983$	56.6408	1.80656	0.903280	−	0.429052i	$-0.141152\pi$
$983$	56.6408	1.80656	0.903280	+	0.429052i	$0.141152\pi$
$984$	−37.8633	−1.20704
$985$	12.6362	0.402623
$986$	−0.853157	−0.0271700
$987$	0.914718	0.0291158
$988$	−19.5360	−0.621524
$989$	−13.5815	−0.431867
$990$	−1.07491	−0.0341628
$991$	8.34006	0.264931	0.132465	−	0.991188i	$-0.457711\pi$
$991$	8.34006	0.264931	0.132465	+	0.991188i	$0.457711\pi$
$992$	16.9029	0.536666
$993$	−36.6315	−1.16247
$994$	3.11221	0.0987134
$995$	1.75135	0.0555216
$996$	25.1273	0.796188
$997$	11.9314	0.377871	0.188935	−	0.981990i	$-0.439496\pi$
$997$	11.9314	0.377871	0.188935	+	0.981990i	$0.439496\pi$
$998$	−17.2817	−0.547044
$999$	43.4596	1.37500

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.18	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.18	✓	44	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)

\(f(q)\)	\(=\)	\(q-0.612476 q^{2} -1.57448 q^{3} -1.62487 q^{4} +1.00000 q^{5} +0.964330 q^{6} -1.00000 q^{7} +2.22015 q^{8} -0.521024 q^{9} +O(q^{10})\)	\(q-0.612476 q^{2} -1.57448 q^{3} -1.62487 q^{4} +1.00000 q^{5} +0.964330 q^{6} -1.00000 q^{7} +2.22015 q^{8} -0.521024 q^{9} -0.612476 q^{10} -3.36841 q^{11} +2.55832 q^{12} -6.96057 q^{13} +0.612476 q^{14} -1.57448 q^{15} +1.88996 q^{16} +0.396526 q^{17} +0.319115 q^{18} -1.72732 q^{19} -1.62487 q^{20} +1.57448 q^{21} +2.06307 q^{22} -1.95243 q^{23} -3.49557 q^{24} +1.00000 q^{25} +4.26319 q^{26} +5.54377 q^{27} +1.62487 q^{28} +3.51292 q^{29} +0.964330 q^{30} -3.01953 q^{31} -5.59785 q^{32} +5.30348 q^{33} -0.242863 q^{34} -1.00000 q^{35} +0.846597 q^{36} +7.83936 q^{37} +1.05794 q^{38} +10.9593 q^{39} +2.22015 q^{40} +10.8318 q^{41} -0.964330 q^{42} +6.95621 q^{43} +5.47324 q^{44} -0.521024 q^{45} +1.19582 q^{46} +0.580967 q^{47} -2.97569 q^{48} +1.00000 q^{49} -0.612476 q^{50} -0.624321 q^{51} +11.3100 q^{52} -6.72794 q^{53} -3.39543 q^{54} -3.36841 q^{55} -2.22015 q^{56} +2.71962 q^{57} -2.15158 q^{58} +2.93021 q^{59} +2.55832 q^{60} -5.89533 q^{61} +1.84939 q^{62} +0.521024 q^{63} -0.351363 q^{64} -6.96057 q^{65} -3.24826 q^{66} +3.33986 q^{67} -0.644304 q^{68} +3.07406 q^{69} +0.612476 q^{70} +5.08136 q^{71} -1.15675 q^{72} +4.67864 q^{73} -4.80142 q^{74} -1.57448 q^{75} +2.80667 q^{76} +3.36841 q^{77} -6.71229 q^{78} -0.892529 q^{79} +1.88996 q^{80} -7.16546 q^{81} -6.63422 q^{82} +9.82177 q^{83} -2.55832 q^{84} +0.396526 q^{85} -4.26051 q^{86} -5.53101 q^{87} -7.47837 q^{88} +1.07271 q^{89} +0.319115 q^{90} +6.96057 q^{91} +3.17245 q^{92} +4.75417 q^{93} -0.355828 q^{94} -1.72732 q^{95} +8.81369 q^{96} -2.02580 q^{97} -0.612476 q^{98} +1.75502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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