LMFDB - Embedded newform 4033.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67574 q^{2} +1.31893 q^{3} +0.808091 q^{4} -4.46158 q^{5} -2.21019 q^{6} +0.153470 q^{7} +1.99732 q^{8} -1.26041 q^{9} +O(q^{10})$	\(q-1.67574 q^{2} +1.31893 q^{3} +0.808091 q^{4} -4.46158 q^{5} -2.21019 q^{6} +0.153470 q^{7} +1.99732 q^{8} -1.26041 q^{9} +7.47643 q^{10} -2.02860 q^{11} +1.06582 q^{12} -0.641377 q^{13} -0.257174 q^{14} -5.88453 q^{15} -4.96317 q^{16} +4.82713 q^{17} +2.11212 q^{18} -5.72216 q^{19} -3.60536 q^{20} +0.202416 q^{21} +3.39940 q^{22} -7.85045 q^{23} +2.63434 q^{24} +14.9057 q^{25} +1.07478 q^{26} -5.61920 q^{27} +0.124017 q^{28} +3.40426 q^{29} +9.86092 q^{30} -9.46396 q^{31} +4.32231 q^{32} -2.67559 q^{33} -8.08899 q^{34} -0.684717 q^{35} -1.01853 q^{36} +1.00000 q^{37} +9.58884 q^{38} -0.845934 q^{39} -8.91123 q^{40} -6.28903 q^{41} -0.339196 q^{42} -4.53674 q^{43} -1.63929 q^{44} +5.62343 q^{45} +13.1553 q^{46} +6.13454 q^{47} -6.54610 q^{48} -6.97645 q^{49} -24.9780 q^{50} +6.36666 q^{51} -0.518291 q^{52} +1.29314 q^{53} +9.41630 q^{54} +9.05076 q^{55} +0.306529 q^{56} -7.54716 q^{57} -5.70464 q^{58} -2.52877 q^{59} -4.75524 q^{60} -7.78879 q^{61} +15.8591 q^{62} -0.193435 q^{63} +2.68328 q^{64} +2.86156 q^{65} +4.48358 q^{66} -5.17506 q^{67} +3.90076 q^{68} -10.3542 q^{69} +1.14740 q^{70} +6.99021 q^{71} -2.51745 q^{72} -3.90986 q^{73} -1.67574 q^{74} +19.6596 q^{75} -4.62403 q^{76} -0.311328 q^{77} +1.41756 q^{78} +2.27090 q^{79} +22.1436 q^{80} -3.63012 q^{81} +10.5388 q^{82} +1.48552 q^{83} +0.163571 q^{84} -21.5366 q^{85} +7.60239 q^{86} +4.48999 q^{87} -4.05177 q^{88} +16.3116 q^{89} -9.42339 q^{90} -0.0984319 q^{91} -6.34388 q^{92} -12.4823 q^{93} -10.2799 q^{94} +25.5299 q^{95} +5.70085 q^{96} -13.6877 q^{97} +11.6907 q^{98} +2.55687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.67574	−1.18492	−0.592462	−	0.805598i	$-0.701844\pi$
$2$	−1.67574	−1.18492	−0.592462	+	0.805598i	$0.701844\pi$
$3$	1.31893	0.761487	0.380744	−	0.924681i	$-0.375668\pi$
$3$	1.31893	0.761487	0.380744	+	0.924681i	$0.375668\pi$
$4$	0.808091	0.404046
$5$	−4.46158	−1.99528	−0.997640	−	0.0686650i	$-0.978126\pi$
$5$	−4.46158	−1.99528	−0.997640	+	0.0686650i	$0.978126\pi$
$6$	−2.21019	−0.902305
$7$	0.153470	0.0580060	0.0290030	−	0.999579i	$-0.490767\pi$
$7$	0.153470	0.0580060	0.0290030	+	0.999579i	$0.490767\pi$
$8$	1.99732	0.706161
$9$	−1.26041	−0.420137
$10$	7.47643	2.36426
$11$	−2.02860	−0.611646	−0.305823	−	0.952088i	$-0.598932\pi$
$11$	−2.02860	−0.611646	−0.305823	+	0.952088i	$0.598932\pi$
$12$	1.06582	0.307675
$13$	−0.641377	−0.177886	−0.0889430	−	0.996037i	$-0.528349\pi$
$13$	−0.641377	−0.177886	−0.0889430	+	0.996037i	$0.528349\pi$
$14$	−0.257174	−0.0687328
$15$	−5.88453	−1.51938
$16$	−4.96317	−1.24079
$17$	4.82713	1.17075	0.585375	−	0.810763i	$-0.300947\pi$
$17$	4.82713	1.17075	0.585375	+	0.810763i	$0.300947\pi$
$18$	2.11212	0.497831
$19$	−5.72216	−1.31275	−0.656377	−	0.754433i	$-0.727912\pi$
$19$	−5.72216	−1.31275	−0.656377	+	0.754433i	$0.727912\pi$
$20$	−3.60536	−0.806184
$21$	0.202416	0.0441709
$22$	3.39940	0.724754
$23$	−7.85045	−1.63693	−0.818466	−	0.574555i	$-0.805175\pi$
$23$	−7.85045	−1.63693	−0.818466	+	0.574555i	$0.805175\pi$
$24$	2.63434	0.537732
$25$	14.9057	2.98114
$26$	1.07478	0.210781
$27$	−5.61920	−1.08142
$28$	0.124017	0.0234371
$29$	3.40426	0.632155	0.316078	−	0.948733i	$-0.397634\pi$
$29$	3.40426	0.632155	0.316078	+	0.948733i	$0.397634\pi$
$30$	9.86092	1.80035
$31$	−9.46396	−1.69978	−0.849889	−	0.526962i	$-0.823331\pi$
$31$	−9.46396	−1.69978	−0.849889	+	0.526962i	$0.823331\pi$
$32$	4.32231	0.764085
$33$	−2.67559	−0.465760
$34$	−8.08899	−1.38725
$35$	−0.684717	−0.115738
$36$	−1.01853	−0.169755
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	9.58884	1.55551
$39$	−0.845934	−0.135458
$40$	−8.91123	−1.40899
$41$	−6.28903	−0.982182	−0.491091	−	0.871108i	$-0.663402\pi$
$41$	−6.28903	−0.982182	−0.491091	+	0.871108i	$0.663402\pi$
$42$	−0.339196	−0.0523391
$43$	−4.53674	−0.691847	−0.345924	−	0.938263i	$-0.612434\pi$
$43$	−4.53674	−0.691847	−0.345924	+	0.938263i	$0.612434\pi$
$44$	−1.63929	−0.247133
$45$	5.62343	0.838292
$46$	13.1553	1.93964
$47$	6.13454	0.894814	0.447407	−	0.894330i	$-0.352348\pi$
$47$	6.13454	0.894814	0.447407	+	0.894330i	$0.352348\pi$
$48$	−6.54610	−0.944848
$49$	−6.97645	−0.996635
$50$	−24.9780	−3.53243
$51$	6.36666	0.891511
$52$	−0.518291	−0.0718740
$53$	1.29314	0.177626	0.0888130	−	0.996048i	$-0.471693\pi$
$53$	1.29314	0.177626	0.0888130	+	0.996048i	$0.471693\pi$
$54$	9.41630	1.28140
$55$	9.05076	1.22040
$56$	0.306529	0.0409616
$57$	−7.54716	−0.999646
$58$	−5.70464	−0.749056
$59$	−2.52877	−0.329218	−0.164609	−	0.986359i	$-0.552636\pi$
$59$	−2.52877	−0.329218	−0.164609	+	0.986359i	$0.552636\pi$
$60$	−4.75524	−0.613899
$61$	−7.78879	−0.997253	−0.498626	−	0.866817i	$-0.666162\pi$
$61$	−7.78879	−0.997253	−0.498626	+	0.866817i	$0.666162\pi$
$62$	15.8591	2.01411
$63$	−0.193435	−0.0243705
$64$	2.68328	0.335410
$65$	2.86156	0.354932
$66$	4.48358	0.551891
$67$	−5.17506	−0.632234	−0.316117	−	0.948720i	$-0.602379\pi$
$67$	−5.17506	−0.632234	−0.316117	+	0.948720i	$0.602379\pi$
$68$	3.90076	0.473036
$69$	−10.3542	−1.24650
$70$	1.14740	0.137141
$71$	6.99021	0.829585	0.414793	−	0.909916i	$-0.363854\pi$
$71$	6.99021	0.829585	0.414793	+	0.909916i	$0.363854\pi$
$72$	−2.51745	−0.296685
$73$	−3.90986	−0.457614	−0.228807	−	0.973472i	$-0.573482\pi$
$73$	−3.90986	−0.457614	−0.228807	+	0.973472i	$0.573482\pi$
$74$	−1.67574	−0.194800
$75$	19.6596	2.27010
$76$	−4.62403	−0.530413
$77$	−0.311328	−0.0354791
$78$	1.41756	0.160507
$79$	2.27090	0.255496	0.127748	−	0.991807i	$-0.459225\pi$
$79$	2.27090	0.255496	0.127748	+	0.991807i	$0.459225\pi$
$80$	22.1436	2.47573
$81$	−3.63012	−0.403347
$82$	10.5388	1.16381
$83$	1.48552	0.163057	0.0815283	−	0.996671i	$-0.474020\pi$
$83$	1.48552	0.163057	0.0815283	+	0.996671i	$0.474020\pi$
$84$	0.163571	0.0178470
$85$	−21.5366	−2.33597
$86$	7.60239	0.819786
$87$	4.48999	0.481378
$88$	−4.05177	−0.431920
$89$	16.3116	1.72903	0.864515	−	0.502607i	$-0.167626\pi$
$89$	16.3116	1.72903	0.864515	+	0.502607i	$0.167626\pi$
$90$	−9.42339	−0.993312
$91$	−0.0984319	−0.0103185
$92$	−6.34388	−0.661395
$93$	−12.4823	−1.29436
$94$	−10.2799	−1.06029
$95$	25.5299	2.61931
$96$	5.70085	0.581840
$97$	−13.6877	−1.38978	−0.694889	−	0.719117i	$-0.744546\pi$
$97$	−13.6877	−1.38978	−0.694889	+	0.719117i	$0.744546\pi$
$98$	11.6907	1.18094
$99$	2.55687	0.256975
$100$	12.0452	1.20452
$101$	0.406458	0.0404441	0.0202220	−	0.999796i	$-0.493563\pi$
$101$	0.406458	0.0404441	0.0202220	+	0.999796i	$0.493563\pi$
$102$	−10.6688	−1.05637
$103$	−12.1679	−1.19894	−0.599470	−	0.800397i	$-0.704622\pi$
$103$	−12.1679	−1.19894	−0.599470	+	0.800397i	$0.704622\pi$
$104$	−1.28104	−0.125616
$105$	−0.903097	−0.0881332
$106$	−2.16696	−0.210473
$107$	−19.0438	−1.84103	−0.920516	−	0.390706i	$-0.872231\pi$
$107$	−19.0438	−1.84103	−0.920516	+	0.390706i	$0.872231\pi$
$108$	−4.54083	−0.436941
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−15.1667	−1.44609
$111$	1.31893	0.125188
$112$	−0.761696	−0.0719735
$113$	−10.5792	−0.995203	−0.497602	−	0.867406i	$-0.665786\pi$
$113$	−10.5792	−0.995203	−0.497602	+	0.867406i	$0.665786\pi$
$114$	12.6470	1.18450
$115$	35.0254	3.26614
$116$	2.75095	0.255419
$117$	0.808400	0.0747366
$118$	4.23756	0.390099
$119$	0.740817	0.0679106
$120$	−11.7533	−1.07293
$121$	−6.88479	−0.625890
$122$	13.0520	1.18167
$123$	−8.29482	−0.747919
$124$	−7.64774	−0.686787
$125$	−44.1951	−3.95293
$126$	0.324146	0.0288772
$127$	4.01781	0.356523	0.178261	−	0.983983i	$-0.442953\pi$
$127$	4.01781	0.356523	0.178261	+	0.983983i	$0.442953\pi$
$128$	−13.1411	−1.16152
$129$	−5.98367	−0.526833
$130$	−4.79521	−0.420568
$131$	11.8040	1.03132	0.515662	−	0.856792i	$-0.327546\pi$
$131$	11.8040	1.03132	0.515662	+	0.856792i	$0.327546\pi$
$132$	−2.16212	−0.188188
$133$	−0.878178	−0.0761477
$134$	8.67203	0.749150
$135$	25.0705	2.15773
$136$	9.64134	0.826738
$137$	6.89832	0.589363	0.294682	−	0.955596i	$-0.404786\pi$
$137$	6.89832	0.589363	0.294682	+	0.955596i	$0.404786\pi$
$138$	17.3510	1.47701
$139$	19.1239	1.62207	0.811033	−	0.585000i	$-0.198905\pi$
$139$	19.1239	1.62207	0.811033	+	0.585000i	$0.198905\pi$
$140$	−0.553314	−0.0467635
$141$	8.09105	0.681389
$142$	−11.7137	−0.982996
$143$	1.30110	0.108803
$144$	6.25564	0.521303
$145$	−15.1884	−1.26133
$146$	6.55189	0.542238
$147$	−9.20148	−0.758925
$148$	0.808091	0.0664247
$149$	5.79483	0.474731	0.237365	−	0.971420i	$-0.423716\pi$
$149$	5.79483	0.474731	0.237365	+	0.971420i	$0.423716\pi$
$150$	−32.9444	−2.68990
$151$	10.8220	0.880680	0.440340	−	0.897831i	$-0.354858\pi$
$151$	10.8220	0.880680	0.440340	+	0.897831i	$0.354858\pi$
$152$	−11.4290	−0.927016
$153$	−6.08417	−0.491876
$154$	0.521704	0.0420401
$155$	42.2242	3.39153
$156$	−0.683592	−0.0547312
$157$	8.58264	0.684969	0.342485	−	0.939523i	$-0.388732\pi$
$157$	8.58264	0.684969	0.342485	+	0.939523i	$0.388732\pi$
$158$	−3.80542	−0.302743
$159$	1.70556	0.135260
$160$	−19.2844	−1.52456
$161$	−1.20481	−0.0949520
$162$	6.08313	0.477936
$163$	−2.78158	−0.217870	−0.108935	−	0.994049i	$-0.534744\pi$
$163$	−2.78158	−0.217870	−0.108935	+	0.994049i	$0.534744\pi$
$164$	−5.08211	−0.396846
$165$	11.9374	0.929322
$166$	−2.48933	−0.193210
$167$	5.14086	0.397812	0.198906	−	0.980019i	$-0.436261\pi$
$167$	5.14086	0.397812	0.198906	+	0.980019i	$0.436261\pi$
$168$	0.404291	0.0311917
$169$	−12.5886	−0.968357
$170$	36.0897	2.76795
$171$	7.21229	0.551537
$172$	−3.66610	−0.279538
$173$	8.64474	0.657247	0.328624	−	0.944461i	$-0.393415\pi$
$173$	8.64474	0.657247	0.328624	+	0.944461i	$0.393415\pi$
$174$	−7.52405	−0.570396
$175$	2.28757	0.172924
$176$	10.0683	0.758925
$177$	−3.33529	−0.250695
$178$	−27.3340	−2.04877
$179$	11.9934	0.896429	0.448215	−	0.893926i	$-0.352060\pi$
$179$	11.9934	0.896429	0.448215	+	0.893926i	$0.352060\pi$
$180$	4.54424	0.338708
$181$	10.1340	0.753254	0.376627	−	0.926365i	$-0.377084\pi$
$181$	10.1340	0.753254	0.376627	+	0.926365i	$0.377084\pi$
$182$	0.164946	0.0122266
$183$	−10.2729	−0.759395
$184$	−15.6799	−1.15594
$185$	−4.46158	−0.328022
$186$	20.9171	1.53372
$187$	−9.79230	−0.716084
$188$	4.95726	0.361546
$189$	−0.862377	−0.0627287
$190$	−42.7814	−3.10369
$191$	17.7409	1.28368	0.641842	−	0.766837i	$-0.278171\pi$
$191$	17.7409	1.28368	0.641842	+	0.766837i	$0.278171\pi$
$192$	3.53907	0.255411
$193$	8.06832	0.580771	0.290385	−	0.956910i	$-0.406217\pi$
$193$	8.06832	0.580771	0.290385	+	0.956910i	$0.406217\pi$
$194$	22.9370	1.64678
$195$	3.77420	0.270276
$196$	−5.63760	−0.402686
$197$	−4.70969	−0.335551	−0.167776	−	0.985825i	$-0.553658\pi$
$197$	−4.70969	−0.335551	−0.167776	+	0.985825i	$0.553658\pi$
$198$	−4.28464	−0.304496
$199$	11.2513	0.797585	0.398793	−	0.917041i	$-0.369429\pi$
$199$	11.2513	0.797585	0.398793	+	0.917041i	$0.369429\pi$
$200$	29.7715	2.10516
$201$	−6.82556	−0.481438
$202$	−0.681116	−0.0479232
$203$	0.522450	0.0366688
$204$	5.14484	0.360211
$205$	28.0590	1.95973
$206$	20.3902	1.42065
$207$	9.89480	0.687736
$208$	3.18326	0.220720
$209$	11.6080	0.802941
$210$	1.51335	0.104431
$211$	−26.9066	−1.85232	−0.926162	−	0.377126i	$-0.876912\pi$
$211$	−26.9066	−1.85232	−0.926162	+	0.377126i	$0.876912\pi$
$212$	1.04497	0.0717690
$213$	9.21963	0.631719
$214$	31.9123	2.18148
$215$	20.2411	1.38043
$216$	−11.2234	−0.763654
$217$	−1.45243	−0.0985974
$218$	1.67574	0.113495
$219$	−5.15684	−0.348467
$220$	7.31384	0.493099
$221$	−3.09601	−0.208260
$222$	−2.21019	−0.148338
$223$	15.3948	1.03091	0.515457	−	0.856915i	$-0.327622\pi$
$223$	15.3948	1.03091	0.515457	+	0.856915i	$0.327622\pi$
$224$	0.663344	0.0443215
$225$	−18.7873	−1.25249
$226$	17.7279	1.17924
$227$	3.31210	0.219832	0.109916	−	0.993941i	$-0.464942\pi$
$227$	3.31210	0.219832	0.109916	+	0.993941i	$0.464942\pi$
$228$	−6.09879	−0.403902
$229$	−15.1489	−1.00107	−0.500535	−	0.865717i	$-0.666863\pi$
$229$	−15.1489	−1.00107	−0.500535	+	0.865717i	$0.666863\pi$
$230$	−58.6934	−3.87013
$231$	−0.410621	−0.0270169
$232$	6.79941	0.446403
$233$	28.5028	1.86728	0.933641	−	0.358211i	$-0.116613\pi$
$233$	28.5028	1.86728	0.933641	+	0.358211i	$0.116613\pi$
$234$	−1.35466	−0.0885572
$235$	−27.3697	−1.78540
$236$	−2.04348	−0.133019
$237$	2.99516	0.194557
$238$	−1.24141	−0.0804689
$239$	7.32458	0.473788	0.236894	−	0.971536i	$-0.423871\pi$
$239$	7.32458	0.473788	0.236894	+	0.971536i	$0.423871\pi$
$240$	29.2059	1.88524
$241$	13.4407	0.865792	0.432896	−	0.901444i	$-0.357492\pi$
$241$	13.4407	0.865792	0.432896	+	0.901444i	$0.357492\pi$
$242$	11.5371	0.741632
$243$	12.0697	0.774273
$244$	−6.29405	−0.402935
$245$	31.1260	1.98857
$246$	13.8999	0.886227
$247$	3.67007	0.233521
$248$	−18.9026	−1.20032
$249$	1.95930	0.124165
$250$	74.0593	4.68392
$251$	−1.47113	−0.0928566	−0.0464283	−	0.998922i	$-0.514784\pi$
$251$	−1.47113	−0.0928566	−0.0464283	+	0.998922i	$0.514784\pi$
$252$	−0.156313	−0.00984680
$253$	15.9254	1.00122
$254$	−6.73278	−0.422452
$255$	−28.4054	−1.77881
$256$	16.6545	1.04090
$257$	−17.6787	−1.10277	−0.551384	−	0.834252i	$-0.685900\pi$
$257$	−17.6787	−1.10277	−0.551384	+	0.834252i	$0.685900\pi$
$258$	10.0270	0.624257
$259$	0.153470	0.00953614
$260$	2.31240	0.143409
$261$	−4.29077	−0.265592
$262$	−19.7805	−1.22204
$263$	10.4354	0.643473	0.321737	−	0.946829i	$-0.395733\pi$
$263$	10.4354	0.643473	0.321737	+	0.946829i	$0.395733\pi$
$264$	−5.34402	−0.328902
$265$	−5.76944	−0.354414
$266$	1.47159	0.0902293
$267$	21.5140	1.31663
$268$	−4.18192	−0.255451
$269$	−9.05288	−0.551964	−0.275982	−	0.961163i	$-0.589003\pi$
$269$	−9.05288	−0.551964	−0.275982	+	0.961163i	$0.589003\pi$
$270$	−42.0116	−2.55674
$271$	10.8294	0.657837	0.328919	−	0.944358i	$-0.393316\pi$
$271$	10.8294	0.657837	0.328919	+	0.944358i	$0.393316\pi$
$272$	−23.9578	−1.45266
$273$	−0.129825	−0.00785738
$274$	−11.5598	−0.698351
$275$	−30.2377	−1.82340
$276$	−8.36716	−0.503644
$277$	18.4815	1.11045	0.555223	−	0.831702i	$-0.312633\pi$
$277$	18.4815	1.11045	0.555223	+	0.831702i	$0.312633\pi$
$278$	−32.0466	−1.92203
$279$	11.9285	0.714140
$280$	−1.36760	−0.0817299
$281$	1.60098	0.0955062	0.0477531	−	0.998859i	$-0.484794\pi$
$281$	1.60098	0.0955062	0.0477531	+	0.998859i	$0.484794\pi$
$282$	−13.5585	−0.807395
$283$	17.0393	1.01288	0.506442	−	0.862274i	$-0.330960\pi$
$283$	17.0393	1.01288	0.506442	+	0.862274i	$0.330960\pi$
$284$	5.64873	0.335190
$285$	33.6723	1.99457
$286$	−2.18029	−0.128924
$287$	−0.965175	−0.0569725
$288$	−5.44790	−0.321021
$289$	6.30114	0.370655
$290$	25.4517	1.49458
$291$	−18.0532	−1.05830
$292$	−3.15952	−0.184897
$293$	8.59821	0.502313	0.251156	−	0.967947i	$-0.419189\pi$
$293$	8.59821	0.502313	0.251156	+	0.967947i	$0.419189\pi$
$294$	15.4192	0.899269
$295$	11.2823	0.656882
$296$	1.99732	0.116092
$297$	11.3991	0.661443
$298$	−9.71060	−0.562520
$299$	5.03510	0.291187
$300$	15.8868	0.917224
$301$	−0.696252	−0.0401313
$302$	−18.1348	−1.04354
$303$	0.536091	0.0307976
$304$	28.4001	1.62886
$305$	34.7503	1.98980
$306$	10.1955	0.582836
$307$	−2.71832	−0.155143	−0.0775713	−	0.996987i	$-0.524717\pi$
$307$	−2.71832	−0.155143	−0.0775713	+	0.996987i	$0.524717\pi$
$308$	−0.251582	−0.0143352
$309$	−16.0487	−0.912978
$310$	−70.7566	−4.01871
$311$	−0.471741	−0.0267500	−0.0133750	−	0.999911i	$-0.504258\pi$
$311$	−0.471741	−0.0267500	−0.0133750	+	0.999911i	$0.504258\pi$
$312$	−1.68961	−0.0956551
$313$	−7.41533	−0.419139	−0.209570	−	0.977794i	$-0.567206\pi$
$313$	−7.41533	−0.419139	−0.209570	+	0.977794i	$0.567206\pi$
$314$	−14.3822	−0.811636
$315$	0.863026	0.0486260
$316$	1.83509	0.103232
$317$	−32.0167	−1.79824	−0.899120	−	0.437703i	$-0.855792\pi$
$317$	−32.0167	−1.79824	−0.899120	+	0.437703i	$0.855792\pi$
$318$	−2.85807	−0.160273
$319$	−6.90588	−0.386655
$320$	−11.9717	−0.669238
$321$	−25.1175	−1.40192
$322$	2.01894	0.112511
$323$	−27.6216	−1.53691
$324$	−2.93347	−0.162971
$325$	−9.56018	−0.530303
$326$	4.66119	0.258159
$327$	−1.31893	−0.0729372
$328$	−12.5612	−0.693578
$329$	0.941465	0.0519046
$330$	−20.0039	−1.10118
$331$	−20.8827	−1.14782	−0.573910	−	0.818919i	$-0.694574\pi$
$331$	−20.8827	−1.14782	−0.573910	+	0.818919i	$0.694574\pi$
$332$	1.20043	0.0658823
$333$	−1.26041	−0.0690702
$334$	−8.61473	−0.471377
$335$	23.0889	1.26148
$336$	−1.00463	−0.0548069
$337$	14.3925	0.784008	0.392004	−	0.919964i	$-0.371782\pi$
$337$	14.3925	0.784008	0.392004	+	0.919964i	$0.371782\pi$
$338$	21.0952	1.14743
$339$	−13.9532	−0.757835
$340$	−17.4035	−0.943840
$341$	19.1986	1.03966
$342$	−12.0859	−0.653530
$343$	−2.14496	−0.115817
$344$	−9.06135	−0.488555
$345$	46.1962	2.48712
$346$	−14.4863	−0.778788
$347$	−16.6072	−0.891519	−0.445760	−	0.895153i	$-0.647066\pi$
$347$	−16.6072	−0.891519	−0.445760	+	0.895153i	$0.647066\pi$
$348$	3.62832	0.194499
$349$	−17.6196	−0.943158	−0.471579	−	0.881824i	$-0.656316\pi$
$349$	−17.6196	−0.943158	−0.471579	+	0.881824i	$0.656316\pi$
$350$	−3.83337	−0.204902
$351$	3.60403	0.192369
$352$	−8.76824	−0.467349
$353$	−31.4761	−1.67530	−0.837652	−	0.546204i	$-0.816072\pi$
$353$	−31.4761	−1.67530	−0.837652	+	0.546204i	$0.816072\pi$
$354$	5.58906	0.297055
$355$	−31.1874	−1.65525
$356$	13.1813	0.698607
$357$	0.977089	0.0517130
$358$	−20.0978	−1.06220
$359$	6.20620	0.327551	0.163775	−	0.986498i	$-0.447633\pi$
$359$	6.20620	0.327551	0.163775	+	0.986498i	$0.447633\pi$
$360$	11.2318	0.591969
$361$	13.7432	0.723325
$362$	−16.9819	−0.892549
$363$	−9.08058	−0.476607
$364$	−0.0795419	−0.00416913
$365$	17.4441	0.913068
$366$	17.2147	0.899826
$367$	6.05050	0.315833	0.157917	−	0.987452i	$-0.449522\pi$
$367$	6.05050	0.315833	0.157917	+	0.987452i	$0.449522\pi$
$368$	38.9631	2.03109
$369$	7.92677	0.412651
$370$	7.47643	0.388681
$371$	0.198457	0.0103034
$372$	−10.0869	−0.522980
$373$	9.37059	0.485191	0.242595	−	0.970128i	$-0.422001\pi$
$373$	9.37059	0.485191	0.242595	+	0.970128i	$0.422001\pi$
$374$	16.4093	0.848505
$375$	−58.2904	−3.01010
$376$	12.2527	0.631883
$377$	−2.18341	−0.112452
$378$	1.44512	0.0743287
$379$	3.05433	0.156890	0.0784452	−	0.996918i	$-0.475004\pi$
$379$	3.05433	0.156890	0.0784452	+	0.996918i	$0.475004\pi$
$380$	20.6305	1.05832
$381$	5.29922	0.271487
$382$	−29.7290	−1.52107
$383$	17.6483	0.901785	0.450893	−	0.892578i	$-0.351106\pi$
$383$	17.6483	0.901785	0.450893	+	0.892578i	$0.351106\pi$
$384$	−17.3323	−0.884483
$385$	1.38902	0.0707908
$386$	−13.5204	−0.688169
$387$	5.71817	0.290671
$388$	−11.0609	−0.561534
$389$	−0.0515818	−0.00261530	−0.00130765	−	0.999999i	$-0.500416\pi$
$389$	−0.0515818	−0.00261530	−0.00130765	+	0.999999i	$0.500416\pi$
$390$	−6.32457	−0.320257
$391$	−37.8951	−1.91644
$392$	−13.9342	−0.703785
$393$	15.5688	0.785340
$394$	7.89219	0.397603
$395$	−10.1318	−0.509786
$396$	2.06618	0.103830
$397$	7.63554	0.383217	0.191608	−	0.981471i	$-0.438630\pi$
$397$	7.63554	0.383217	0.191608	+	0.981471i	$0.438630\pi$
$398$	−18.8542	−0.945078
$399$	−1.15826	−0.0579855
$400$	−73.9795	−3.69898
$401$	−12.8734	−0.642868	−0.321434	−	0.946932i	$-0.604165\pi$
$401$	−12.8734	−0.642868	−0.321434	+	0.946932i	$0.604165\pi$
$402$	11.4378	0.570468
$403$	6.06997	0.302367
$404$	0.328455	0.0163412
$405$	16.1961	0.804790
$406$	−0.875489	−0.0434498
$407$	−2.02860	−0.100554
$408$	12.7163	0.629550
$409$	−18.0254	−0.891299	−0.445649	−	0.895208i	$-0.647027\pi$
$409$	−18.0254	−0.891299	−0.445649	+	0.895208i	$0.647027\pi$
$410$	−47.0195	−2.32213
$411$	9.09843	0.448792
$412$	−9.83279	−0.484427
$413$	−0.388090	−0.0190966
$414$	−16.5811	−0.814916
$415$	−6.62775	−0.325343
$416$	−2.77223	−0.135920
$417$	25.2231	1.23518
$418$	−19.4519	−0.951424
$419$	33.6446	1.64365	0.821824	−	0.569741i	$-0.192957\pi$
$419$	33.6446	1.64365	0.821824	+	0.569741i	$0.192957\pi$
$420$	−0.729784	−0.0356098
$421$	5.64937	0.275334	0.137667	−	0.990479i	$-0.456040\pi$
$421$	5.64937	0.275334	0.137667	+	0.990479i	$0.456040\pi$
$422$	45.0883	2.19486
$423$	−7.73205	−0.375945
$424$	2.58282	0.125433
$425$	71.9517	3.49017
$426$	−15.4497	−0.748539
$427$	−1.19534	−0.0578467
$428$	−15.3891	−0.743861
$429$	1.71606	0.0828522
$430$	−33.9187	−1.63570
$431$	26.3292	1.26824	0.634118	−	0.773237i	$-0.281363\pi$
$431$	26.3292	1.26824	0.634118	+	0.773237i	$0.281363\pi$
$432$	27.8891	1.34181
$433$	4.76137	0.228817	0.114409	−	0.993434i	$-0.463503\pi$
$433$	4.76137	0.228817	0.114409	+	0.993434i	$0.463503\pi$
$434$	2.43389	0.116830
$435$	−20.0325	−0.960484
$436$	−0.808091	−0.0387005
$437$	44.9216	2.14889
$438$	8.64151	0.412907
$439$	13.1522	0.627722	0.313861	−	0.949469i	$-0.398377\pi$
$439$	13.1522	0.627722	0.313861	+	0.949469i	$0.398377\pi$
$440$	18.0773	0.861801
$441$	8.79320	0.418724
$442$	5.18809	0.246772
$443$	11.2474	0.534380	0.267190	−	0.963644i	$-0.413905\pi$
$443$	11.2474	0.534380	0.267190	+	0.963644i	$0.413905\pi$
$444$	1.06582	0.0505815
$445$	−72.7757	−3.44990
$446$	−25.7977	−1.22156
$447$	7.64300	0.361501
$448$	0.411802	0.0194558
$449$	−35.2363	−1.66290	−0.831451	−	0.555598i	$-0.812489\pi$
$449$	−35.2363	−1.66290	−0.831451	+	0.555598i	$0.812489\pi$
$450$	31.4826	1.48410
$451$	12.7579	0.600747
$452$	−8.54892	−0.402107
$453$	14.2735	0.670626
$454$	−5.55020	−0.260484
$455$	0.439162	0.0205882
$456$	−15.0741	−0.705911
$457$	−16.9482	−0.792801	−0.396401	−	0.918078i	$-0.629741\pi$
$457$	−16.9482	−0.792801	−0.396401	+	0.918078i	$0.629741\pi$
$458$	25.3856	1.18619
$459$	−27.1246	−1.26607
$460$	28.3037	1.31967
$461$	16.6647	0.776155	0.388077	−	0.921627i	$-0.373139\pi$
$461$	16.6647	0.776155	0.388077	+	0.921627i	$0.373139\pi$
$462$	0.688093	0.0320130
$463$	17.1884	0.798812	0.399406	−	0.916774i	$-0.369216\pi$
$463$	17.1884	0.798812	0.399406	+	0.916774i	$0.369216\pi$
$464$	−16.8959	−0.784373
$465$	55.6910	2.58261
$466$	−47.7632	−2.21259
$467$	17.9660	0.831368	0.415684	−	0.909509i	$-0.363542\pi$
$467$	17.9660	0.831368	0.415684	+	0.909509i	$0.363542\pi$
$468$	0.653260	0.0301970
$469$	−0.794214	−0.0366734
$470$	45.8644	2.11557
$471$	11.3199	0.521595
$472$	−5.05078	−0.232481
$473$	9.20323	0.423165
$474$	−5.01910	−0.230535
$475$	−85.2929	−3.91351
$476$	0.598647	0.0274390
$477$	−1.62989	−0.0746274
$478$	−12.2741	−0.561403
$479$	−17.3024	−0.790565	−0.395282	−	0.918560i	$-0.629353\pi$
$479$	−17.3024	−0.790565	−0.395282	+	0.918560i	$0.629353\pi$
$480$	−25.4348	−1.16093
$481$	−0.641377	−0.0292443
$482$	−22.5231	−1.02590
$483$	−1.58906	−0.0723047
$484$	−5.56353	−0.252888
$485$	61.0689	2.77300
$486$	−20.2257	−0.917454
$487$	−27.9162	−1.26500	−0.632502	−	0.774559i	$-0.717972\pi$
$487$	−27.9162	−1.26500	−0.632502	+	0.774559i	$0.717972\pi$
$488$	−15.5567	−0.704221
$489$	−3.66872	−0.165905
$490$	−52.1589	−2.35630
$491$	37.1406	1.67613	0.838065	−	0.545570i	$-0.183687\pi$
$491$	37.1406	1.67613	0.838065	+	0.545570i	$0.183687\pi$
$492$	−6.70297	−0.302193
$493$	16.4328	0.740095
$494$	−6.15006	−0.276704
$495$	−11.4077	−0.512737
$496$	46.9712	2.10907
$497$	1.07278	0.0481210
$498$	−3.28327	−0.147127
$499$	−17.6921	−0.792007	−0.396004	−	0.918249i	$-0.629603\pi$
$499$	−17.6921	−0.792007	−0.396004	+	0.918249i	$0.629603\pi$
$500$	−35.7137	−1.59716
$501$	6.78046	0.302929
$502$	2.46522	0.110028
$503$	24.1713	1.07774	0.538872	−	0.842388i	$-0.318851\pi$
$503$	24.1713	1.07774	0.538872	+	0.842388i	$0.318851\pi$
$504$	−0.386352	−0.0172095
$505$	−1.81344	−0.0806972
$506$	−26.6868	−1.18637
$507$	−16.6036	−0.737391
$508$	3.24675	0.144051
$509$	12.9107	0.572256	0.286128	−	0.958191i	$-0.407632\pi$
$509$	12.9107	0.572256	0.286128	+	0.958191i	$0.407632\pi$
$510$	47.5999	2.10776
$511$	−0.600044	−0.0265444
$512$	−1.62626	−0.0718712
$513$	32.1540	1.41963
$514$	29.6248	1.30670
$515$	54.2882	2.39222
$516$	−4.83535	−0.212864
$517$	−12.4445	−0.547309
$518$	−0.257174	−0.0112996
$519$	11.4018	0.500485
$520$	5.71546	0.250639
$521$	39.7298	1.74059	0.870297	−	0.492528i	$-0.163927\pi$
$521$	39.7298	1.74059	0.870297	+	0.492528i	$0.163927\pi$
$522$	7.19020	0.314706
$523$	35.6685	1.55968	0.779838	−	0.625982i	$-0.215302\pi$
$523$	35.6685	1.55968	0.779838	+	0.625982i	$0.215302\pi$
$524$	9.53874	0.416702
$525$	3.01716	0.131680
$526$	−17.4869	−0.762467
$527$	−45.6837	−1.99001
$528$	13.2794	0.577912
$529$	38.6296	1.67955
$530$	9.66805	0.419953
$531$	3.18730	0.138317
$532$	−0.709648	−0.0307671
$533$	4.03364	0.174716
$534$	−36.0517	−1.56011
$535$	84.9653	3.67337
$536$	−10.3363	−0.446459
$537$	15.8185	0.682619
$538$	15.1702	0.654035
$539$	14.1524	0.609588
$540$	20.2593	0.871820
$541$	−22.8304	−0.981556	−0.490778	−	0.871285i	$-0.663287\pi$
$541$	−22.8304	−0.981556	−0.490778	+	0.871285i	$0.663287\pi$
$542$	−18.1472	−0.779487
$543$	13.3661	0.573593
$544$	20.8644	0.894552
$545$	4.46158	0.191113
$546$	0.217553	0.00931040
$547$	−12.1051	−0.517575	−0.258788	−	0.965934i	$-0.583323\pi$
$547$	−12.1051	−0.517575	−0.258788	+	0.965934i	$0.583323\pi$
$548$	5.57447	0.238130
$549$	9.81709	0.418983
$550$	50.6704	2.16059
$551$	−19.4797	−0.829865
$552$	−20.6808	−0.880231
$553$	0.348514	0.0148203
$554$	−30.9701	−1.31579
$555$	−5.88453	−0.249784
$556$	15.4538	0.655389
$557$	−18.1528	−0.769160	−0.384580	−	0.923092i	$-0.625654\pi$
$557$	−18.1528	−0.769160	−0.384580	+	0.923092i	$0.625654\pi$
$558$	−19.9890	−0.846202
$559$	2.90976	0.123070
$560$	3.39837	0.143607
$561$	−12.9154	−0.545289
$562$	−2.68281	−0.113168
$563$	−26.8044	−1.12967	−0.564836	−	0.825203i	$-0.691061\pi$
$563$	−26.8044	−1.12967	−0.564836	+	0.825203i	$0.691061\pi$
$564$	6.53831	0.275312
$565$	47.1998	1.98571
$566$	−28.5534	−1.20019
$567$	−0.557114	−0.0233966
$568$	13.9617	0.585821
$569$	1.27982	0.0536526	0.0268263	−	0.999640i	$-0.491460\pi$
$569$	1.27982	0.0536526	0.0268263	+	0.999640i	$0.491460\pi$
$570$	−56.4258	−2.36342
$571$	19.9893	0.836527	0.418264	−	0.908326i	$-0.362639\pi$
$571$	19.9893	0.836527	0.418264	+	0.908326i	$0.362639\pi$
$572$	1.05140	0.0439614
$573$	23.3990	0.977509
$574$	1.61738	0.0675081
$575$	−117.016	−4.87992
$576$	−3.38204	−0.140918
$577$	−23.2353	−0.967297	−0.483648	−	0.875262i	$-0.660689\pi$
$577$	−23.2353	−0.967297	−0.483648	+	0.875262i	$0.660689\pi$
$578$	−10.5590	−0.439198
$579$	10.6416	0.442249
$580$	−12.2736	−0.509633
$581$	0.227981	0.00945826
$582$	30.2524	1.25400
$583$	−2.62326	−0.108644
$584$	−7.80925	−0.323149
$585$	−3.60674	−0.149120
$586$	−14.4083	−0.595202
$587$	−39.7308	−1.63987	−0.819933	−	0.572460i	$-0.805989\pi$
$587$	−39.7308	−1.63987	−0.819933	+	0.572460i	$0.805989\pi$
$588$	−7.43563	−0.306640
$589$	54.1543	2.23139
$590$	−18.9062	−0.778356
$591$	−6.21177	−0.255518
$592$	−4.96317	−0.203985
$593$	35.8883	1.47376	0.736879	−	0.676025i	$-0.236299\pi$
$593$	35.8883	1.47376	0.736879	+	0.676025i	$0.236299\pi$
$594$	−19.1019	−0.783760
$595$	−3.30521	−0.135501
$596$	4.68275	0.191813
$597$	14.8398	0.607351
$598$	−8.43750	−0.345035
$599$	−26.9746	−1.10215	−0.551076	−	0.834455i	$-0.685783\pi$
$599$	−26.9746	−1.10215	−0.551076	+	0.834455i	$0.685783\pi$
$600$	39.2667	1.60306
$601$	−40.1900	−1.63939	−0.819693	−	0.572803i	$-0.805856\pi$
$601$	−40.1900	−1.63939	−0.819693	+	0.572803i	$0.805856\pi$
$602$	1.16673	0.0475526
$603$	6.52271	0.265625
$604$	8.74514	0.355835
$605$	30.7170	1.24882
$606$	−0.898347	−0.0364929
$607$	26.9356	1.09328	0.546641	−	0.837367i	$-0.315906\pi$
$607$	26.9356	1.09328	0.546641	+	0.837367i	$0.315906\pi$
$608$	−24.7330	−1.00306
$609$	0.689078	0.0279228
$610$	−58.2324	−2.35776
$611$	−3.93455	−0.159175
$612$	−4.91656	−0.198740
$613$	−23.5851	−0.952594	−0.476297	−	0.879284i	$-0.658021\pi$
$613$	−23.5851	−0.952594	−0.476297	+	0.879284i	$0.658021\pi$
$614$	4.55518	0.183832
$615$	37.0080	1.49231
$616$	−0.621824	−0.0250540
$617$	−44.2803	−1.78266	−0.891330	−	0.453355i	$-0.850227\pi$
$617$	−44.2803	−1.78266	−0.891330	+	0.453355i	$0.850227\pi$
$618$	26.8934	1.08181
$619$	−23.7990	−0.956562	−0.478281	−	0.878207i	$-0.658740\pi$
$619$	−23.7990	−0.956562	−0.478281	+	0.878207i	$0.658740\pi$
$620$	34.1210	1.37033
$621$	44.1133	1.77021
$622$	0.790513	0.0316967
$623$	2.50334	0.100294
$624$	4.19852	0.168075
$625$	122.651	4.90606
$626$	12.4261	0.496648
$627$	15.3102	0.611429
$628$	6.93555	0.276759
$629$	4.82713	0.192470
$630$	−1.44620	−0.0576181
$631$	−9.24950	−0.368217	−0.184108	−	0.982906i	$-0.558940\pi$
$631$	−9.24950	−0.368217	−0.184108	+	0.982906i	$0.558940\pi$
$632$	4.53572	0.180421
$633$	−35.4880	−1.41052
$634$	53.6516	2.13078
$635$	−17.9258	−0.711363
$636$	1.37825	0.0546512
$637$	4.47453	0.177287
$638$	11.5724	0.458157
$639$	−8.81055	−0.348540
$640$	58.6301	2.31756
$641$	18.8887	0.746060	0.373030	−	0.927819i	$-0.378319\pi$
$641$	18.8887	0.746060	0.373030	+	0.927819i	$0.378319\pi$
$642$	42.0903	1.66117
$643$	−40.3848	−1.59262	−0.796311	−	0.604887i	$-0.793218\pi$
$643$	−40.3848	−1.59262	−0.796311	+	0.604887i	$0.793218\pi$
$644$	−0.973592	−0.0383649
$645$	26.6966	1.05118
$646$	46.2865	1.82112
$647$	6.12486	0.240793	0.120397	−	0.992726i	$-0.461583\pi$
$647$	6.12486	0.240793	0.120397	+	0.992726i	$0.461583\pi$
$648$	−7.25054	−0.284828
$649$	5.12987	0.201365
$650$	16.0203	0.628369
$651$	−1.91566	−0.0750806
$652$	−2.24777	−0.0880294
$653$	−31.4355	−1.23017	−0.615084	−	0.788462i	$-0.710878\pi$
$653$	−31.4355	−1.23017	−0.615084	+	0.788462i	$0.710878\pi$
$654$	2.21019	0.0864251
$655$	−52.6647	−2.05778
$656$	31.2135	1.21868
$657$	4.92803	0.192261
$658$	−1.57765	−0.0615031
$659$	22.0639	0.859487	0.429744	−	0.902951i	$-0.358604\pi$
$659$	22.0639	0.859487	0.429744	+	0.902951i	$0.358604\pi$
$660$	9.64647	0.375488
$661$	13.1323	0.510788	0.255394	−	0.966837i	$-0.417795\pi$
$661$	13.1323	0.510788	0.255394	+	0.966837i	$0.417795\pi$
$662$	34.9940	1.36008
$663$	−4.08343	−0.158587
$664$	2.96706	0.115144
$665$	3.91806	0.151936
$666$	2.11212	0.0818429
$667$	−26.7250	−1.03480
$668$	4.15428	0.160734
$669$	20.3048	0.785028
$670$	−38.6910	−1.49476
$671$	15.8003	0.609965
$672$	0.874907	0.0337503
$673$	3.38035	0.130303	0.0651514	−	0.997875i	$-0.479247\pi$
$673$	3.38035	0.130303	0.0651514	+	0.997875i	$0.479247\pi$
$674$	−24.1180	−0.928990
$675$	−83.7582	−3.22385
$676$	−10.1728	−0.391260
$677$	24.8002	0.953147	0.476574	−	0.879135i	$-0.341879\pi$
$677$	24.8002	0.953147	0.476574	+	0.879135i	$0.341879\pi$
$678$	23.3819	0.897976
$679$	−2.10065	−0.0806155
$680$	−43.0156	−1.64957
$681$	4.36844	0.167399
$682$	−32.1717	−1.23192
$683$	36.7428	1.40593	0.702963	−	0.711226i	$-0.251860\pi$
$683$	36.7428	1.40593	0.702963	+	0.711226i	$0.251860\pi$
$684$	5.82818	0.222846
$685$	−30.7774	−1.17594
$686$	3.59439	0.137234
$687$	−19.9804	−0.762301
$688$	22.5166	0.858439
$689$	−0.829389	−0.0315972
$690$	−77.4127	−2.94705
$691$	17.0966	0.650384	0.325192	−	0.945648i	$-0.394571\pi$
$691$	17.0966	0.650384	0.325192	+	0.945648i	$0.394571\pi$
$692$	6.98574	0.265558
$693$	0.392402	0.0149061
$694$	27.8292	1.05638
$695$	−85.3228	−3.23648
$696$	8.96798	0.339930
$697$	−30.3579	−1.14989
$698$	29.5259	1.11757
$699$	37.5933	1.42191
$700$	1.84857	0.0698692
$701$	−21.0036	−0.793295	−0.396647	−	0.917971i	$-0.629826\pi$
$701$	−21.0036	−0.793295	−0.396647	+	0.917971i	$0.629826\pi$
$702$	−6.03940	−0.227942
$703$	−5.72216	−0.215816
$704$	−5.44331	−0.205152
$705$	−36.0989	−1.35956
$706$	52.7457	1.98511
$707$	0.0623789	0.00234600
$708$	−2.69521	−0.101292
$709$	−48.1637	−1.80883	−0.904413	−	0.426659i	$-0.859691\pi$
$709$	−48.1637	−1.80883	−0.904413	+	0.426659i	$0.859691\pi$
$710$	52.2618	1.96135
$711$	−2.86227	−0.107343
$712$	32.5796	1.22097
$713$	74.2963	2.78242
$714$	−1.63734	−0.0612760
$715$	−5.80495	−0.217093
$716$	9.69176	0.362198
$717$	9.66064	0.360783
$718$	−10.3999	−0.388123
$719$	24.7294	0.922249	0.461125	−	0.887335i	$-0.347446\pi$
$719$	24.7294	0.922249	0.461125	+	0.887335i	$0.347446\pi$
$720$	−27.9100	−1.04015
$721$	−1.86741	−0.0695458
$722$	−23.0299	−0.857085
$723$	17.7274	0.659289
$724$	8.18919	0.304349
$725$	50.7429	1.88454
$726$	15.2167	0.564743
$727$	43.8033	1.62457	0.812287	−	0.583258i	$-0.198222\pi$
$727$	43.8033	1.62457	0.812287	+	0.583258i	$0.198222\pi$
$728$	−0.196600	−0.00728650
$729$	26.8095	0.992946
$730$	−29.2318	−1.08192
$731$	−21.8994	−0.809980
$732$	−8.30144	−0.306830
$733$	51.8337	1.91452	0.957261	−	0.289227i	$-0.0933981\pi$
$733$	51.8337	1.91452	0.957261	+	0.289227i	$0.0933981\pi$
$734$	−10.1390	−0.374239
$735$	41.0531	1.51427
$736$	−33.9321	−1.25075
$737$	10.4981	0.386703
$738$	−13.2832	−0.488961
$739$	−20.4067	−0.750672	−0.375336	−	0.926889i	$-0.622473\pi$
$739$	−20.4067	−0.750672	−0.375336	+	0.926889i	$0.622473\pi$
$740$	−3.60536	−0.132536
$741$	4.84058	0.177823
$742$	−0.332562	−0.0122087
$743$	5.00059	0.183454	0.0917270	−	0.995784i	$-0.470761\pi$
$743$	5.00059	0.183454	0.0917270	+	0.995784i	$0.470761\pi$
$744$	−24.9313	−0.914025
$745$	−25.8541	−0.947221
$746$	−15.7026	−0.574915
$747$	−1.87236	−0.0685061
$748$	−7.91307	−0.289331
$749$	−2.92264	−0.106791
$750$	97.6794	3.56675
$751$	21.4224	0.781716	0.390858	−	0.920451i	$-0.372178\pi$
$751$	21.4224	0.781716	0.390858	+	0.920451i	$0.372178\pi$
$752$	−30.4468	−1.11028
$753$	−1.94032	−0.0707091
$754$	3.65883	0.133247
$755$	−48.2831	−1.75720
$756$	−0.696879	−0.0253452
$757$	−31.0047	−1.12689	−0.563443	−	0.826155i	$-0.690524\pi$
$757$	−31.0047	−1.12689	−0.563443	+	0.826155i	$0.690524\pi$
$758$	−5.11825	−0.185903
$759$	21.0046	0.762418
$760$	50.9915	1.84966
$761$	32.8588	1.19113	0.595566	−	0.803306i	$-0.296928\pi$
$761$	32.8588	1.19113	0.595566	+	0.803306i	$0.296928\pi$
$762$	−8.88010	−0.321692
$763$	−0.153470	−0.00555597
$764$	14.3362	0.518667
$765$	27.1450	0.981430
$766$	−29.5739	−1.06855
$767$	1.62190	0.0585633
$768$	21.9661	0.792634
$769$	31.8058	1.14695	0.573473	−	0.819224i	$-0.305596\pi$
$769$	31.8058	1.14695	0.573473	+	0.819224i	$0.305596\pi$
$770$	−2.32762	−0.0838817
$771$	−23.3170	−0.839743
$772$	6.51994	0.234658
$773$	−40.1636	−1.44458	−0.722292	−	0.691588i	$-0.756911\pi$
$773$	−40.1636	−1.44458	−0.722292	+	0.691588i	$0.756911\pi$
$774$	−9.58214	−0.344423
$775$	−141.067	−5.06727
$776$	−27.3388	−0.981407
$777$	0.202416	0.00726164
$778$	0.0864375	0.00309893
$779$	35.9869	1.28936
$780$	3.04990	0.109204
$781$	−14.1803	−0.507412
$782$	63.5022	2.27083
$783$	−19.1292	−0.683623
$784$	34.6253	1.23662
$785$	−38.2921	−1.36670
$786$	−26.0891	−0.930568
$787$	−27.0310	−0.963551	−0.481775	−	0.876295i	$-0.660008\pi$
$787$	−27.0310	−0.963551	−0.481775	+	0.876295i	$0.660008\pi$
$788$	−3.80586	−0.135578
$789$	13.7636	0.489996
$790$	16.9782	0.604057
$791$	−1.62358	−0.0577278
$792$	5.10690	0.181466
$793$	4.99555	0.177397
$794$	−12.7951	−0.454083
$795$	−7.60951	−0.269881
$796$	9.09209	0.322261
$797$	−3.57575	−0.126660	−0.0633298	−	0.997993i	$-0.520172\pi$
$797$	−3.57575	−0.126660	−0.0633298	+	0.997993i	$0.520172\pi$
$798$	1.94094	0.0687084
$799$	29.6122	1.04760
$800$	64.4271	2.27784
$801$	−20.5594	−0.726430
$802$	21.5725	0.761750
$803$	7.93153	0.279898
$804$	−5.51568	−0.194523
$805$	5.37534	0.189456
$806$	−10.1717	−0.358281
$807$	−11.9402	−0.420313
$808$	0.811828	0.0285600
$809$	−1.95987	−0.0689055	−0.0344527	−	0.999406i	$-0.510969\pi$
$809$	−1.95987	−0.0689055	−0.0344527	+	0.999406i	$0.510969\pi$
$810$	−27.1404	−0.953616
$811$	41.9428	1.47281	0.736406	−	0.676540i	$-0.236522\pi$
$811$	41.9428	1.47281	0.736406	+	0.676540i	$0.236522\pi$
$812$	0.422187	0.0148159
$813$	14.2832	0.500934
$814$	3.39940	0.119149
$815$	12.4102	0.434712
$816$	−31.5988	−1.10618
$817$	25.9600	0.908225
$818$	30.2058	1.05612
$819$	0.124065	0.00433517
$820$	22.6742	0.791819
$821$	−48.2157	−1.68274	−0.841370	−	0.540459i	$-0.818251\pi$
$821$	−48.2157	−1.68274	−0.841370	+	0.540459i	$0.818251\pi$
$822$	−15.2466	−0.531785
$823$	−15.0514	−0.524660	−0.262330	−	0.964978i	$-0.584491\pi$
$823$	−15.0514	−0.524660	−0.262330	+	0.964978i	$0.584491\pi$
$824$	−24.3033	−0.846645
$825$	−39.8815	−1.38850
$826$	0.650336	0.0226281
$827$	13.6704	0.475366	0.237683	−	0.971343i	$-0.423612\pi$
$827$	13.6704	0.475366	0.237683	+	0.971343i	$0.423612\pi$
$828$	7.99590	0.277877
$829$	−0.116293	−0.00403903	−0.00201952	−	0.999998i	$-0.500643\pi$
$829$	−0.116293	−0.00403903	−0.00201952	+	0.999998i	$0.500643\pi$
$830$	11.1064	0.385507
$831$	24.3759	0.845590
$832$	−1.72100	−0.0596648
$833$	−33.6762	−1.16681
$834$	−42.2673	−1.46360
$835$	−22.9364	−0.793746
$836$	9.38030	0.324425
$837$	53.1799	1.83817
$838$	−56.3795	−1.94760
$839$	23.6555	0.816678	0.408339	−	0.912830i	$-0.366108\pi$
$839$	23.6555	0.816678	0.408339	+	0.912830i	$0.366108\pi$
$840$	−1.80378	−0.0622362
$841$	−17.4110	−0.600380
$842$	−9.46686	−0.326249
$843$	2.11158	0.0727267
$844$	−21.7429	−0.748423
$845$	56.1652	1.93214
$846$	12.9569	0.445466
$847$	−1.05661	−0.0363054
$848$	−6.41806	−0.220397
$849$	22.4738	0.771298
$850$	−120.572	−4.13559
$851$	−7.85045	−0.269110
$852$	7.45030	0.255243
$853$	−13.9385	−0.477245	−0.238622	−	0.971112i	$-0.576696\pi$
$853$	−13.9385	−0.477245	−0.238622	+	0.971112i	$0.576696\pi$
$854$	2.00308	0.0685439
$855$	−32.1782	−1.10047
$856$	−38.0366	−1.30006
$857$	−38.0360	−1.29929	−0.649643	−	0.760240i	$-0.725082\pi$
$857$	−38.0360	−1.29929	−0.649643	+	0.760240i	$0.725082\pi$
$858$	−2.87567	−0.0981736
$859$	−16.9867	−0.579578	−0.289789	−	0.957091i	$-0.593585\pi$
$859$	−16.9867	−0.579578	−0.289789	+	0.957091i	$0.593585\pi$
$860$	16.3566	0.557756
$861$	−1.27300	−0.0433838
$862$	−44.1209	−1.50276
$863$	1.32622	0.0451449	0.0225725	−	0.999745i	$-0.492814\pi$
$863$	1.32622	0.0451449	0.0225725	+	0.999745i	$0.492814\pi$
$864$	−24.2880	−0.826293
$865$	−38.5692	−1.31139
$866$	−7.97881	−0.271131
$867$	8.31079	0.282249
$868$	−1.17370	−0.0398378
$869$	−4.60674	−0.156273
$870$	33.5691	1.13810
$871$	3.31916	0.112466
$872$	−1.99732	−0.0676379
$873$	17.2522	0.583898
$874$	−75.2767	−2.54627
$875$	−6.78260	−0.229294
$876$	−4.16720	−0.140797
$877$	15.2829	0.516066	0.258033	−	0.966136i	$-0.416926\pi$
$877$	15.2829	0.516066	0.258033	+	0.966136i	$0.416926\pi$
$878$	−22.0397	−0.743803
$879$	11.3405	0.382505
$880$	−44.9205	−1.51427
$881$	−51.7188	−1.74245	−0.871225	−	0.490883i	$-0.836674\pi$
$881$	−51.7188	−1.74245	−0.871225	+	0.490883i	$0.836674\pi$
$882$	−14.7351	−0.496156
$883$	−41.5272	−1.39750	−0.698750	−	0.715366i	$-0.746260\pi$
$883$	−41.5272	−1.39750	−0.698750	+	0.715366i	$0.746260\pi$
$884$	−2.50186	−0.0841465
$885$	14.8806	0.500207
$886$	−18.8477	−0.633200
$887$	2.05411	0.0689702	0.0344851	−	0.999405i	$-0.489021\pi$
$887$	2.05411	0.0689702	0.0344851	+	0.999405i	$0.489021\pi$
$888$	2.63434	0.0884027
$889$	0.616611	0.0206805
$890$	121.953	4.08787
$891$	7.36407	0.246705
$892$	12.4404	0.416537
$893$	−35.1028	−1.17467
$894$	−12.8076	−0.428352
$895$	−53.5095	−1.78863
$896$	−2.01676	−0.0673752
$897$	6.64097	0.221735
$898$	59.0467	1.97041
$899$	−32.2178	−1.07452
$900$	−15.1819	−0.506062
$901$	6.24214	0.207956
$902$	−21.3789	−0.711840
$903$	−0.918311	−0.0305595
$904$	−21.1300	−0.702774
$905$	−45.2136	−1.50295
$906$	−23.9186	−0.794641
$907$	−0.825008	−0.0273939	−0.0136970	−	0.999906i	$-0.504360\pi$
$907$	−0.825008	−0.0273939	−0.0136970	+	0.999906i	$0.504360\pi$
$908$	2.67648	0.0888219
$909$	−0.512305	−0.0169921
$910$	−0.735919	−0.0243955
$911$	3.44846	0.114253	0.0571263	−	0.998367i	$-0.481806\pi$
$911$	3.44846	0.114253	0.0571263	+	0.998367i	$0.481806\pi$
$912$	37.4578	1.24035
$913$	−3.01352	−0.0997328
$914$	28.4006	0.939409
$915$	45.8334	1.51521
$916$	−12.2417	−0.404478
$917$	1.81156	0.0598230
$918$	45.4537	1.50019
$919$	7.79335	0.257079	0.128539	−	0.991704i	$-0.458971\pi$
$919$	7.79335	0.257079	0.128539	+	0.991704i	$0.458971\pi$
$920$	69.9571	2.30642
$921$	−3.58528	−0.118139
$922$	−27.9257	−0.919685
$923$	−4.48336	−0.147572
$924$	−0.331820	−0.0109161
$925$	14.9057	0.490096
$926$	−28.8032	−0.946531
$927$	15.3366	0.503720
$928$	14.7143	0.483020
$929$	−33.0017	−1.08275	−0.541376	−	0.840781i	$-0.682096\pi$
$929$	−33.0017	−1.08275	−0.541376	+	0.840781i	$0.682096\pi$
$930$	−93.3234	−3.06019
$931$	39.9204	1.30834
$932$	23.0329	0.754467
$933$	−0.622195	−0.0203698
$934$	−30.1063	−0.985108
$935$	43.6891	1.42879
$936$	1.61464	0.0527760
$937$	−27.5557	−0.900204	−0.450102	−	0.892977i	$-0.648612\pi$
$937$	−27.5557	−0.900204	−0.450102	+	0.892977i	$0.648612\pi$
$938$	1.33089	0.0434552
$939$	−9.78034	−0.319169
$940$	−22.1172	−0.721385
$941$	−30.3946	−0.990835	−0.495418	−	0.868655i	$-0.664985\pi$
$941$	−30.3946	−0.990835	−0.495418	+	0.868655i	$0.664985\pi$
$942$	−18.9692	−0.618051
$943$	49.3717	1.60776
$944$	12.5507	0.408492
$945$	3.84756	0.125161
$946$	−15.4222	−0.501419
$947$	−45.5105	−1.47889	−0.739446	−	0.673215i	$-0.764913\pi$
$947$	−45.5105	−1.47889	−0.739446	+	0.673215i	$0.764913\pi$
$948$	2.42037	0.0786098
$949$	2.50769	0.0814031
$950$	142.928	4.63721
$951$	−42.2280	−1.36934
$952$	1.47965	0.0479558
$953$	−29.2668	−0.948046	−0.474023	−	0.880513i	$-0.657199\pi$
$953$	−29.2668	−0.948046	−0.474023	+	0.880513i	$0.657199\pi$
$954$	2.73126	0.0884278
$955$	−79.1523	−2.56131
$956$	5.91893	0.191432
$957$	−9.10840	−0.294433
$958$	28.9942	0.936759
$959$	1.05868	0.0341866
$960$	−15.7899	−0.509616
$961$	58.5665	1.88924
$962$	1.07478	0.0346523
$963$	24.0030	0.773486
$964$	10.8613	0.349819
$965$	−35.9975	−1.15880
$966$	2.66284	0.0856756
$967$	13.4930	0.433906	0.216953	−	0.976182i	$-0.430388\pi$
$967$	13.4930	0.433906	0.216953	+	0.976182i	$0.430388\pi$
$968$	−13.7512	−0.441979
$969$	−36.4311	−1.17034
$970$	−102.335	−3.28579
$971$	−0.866740	−0.0278150	−0.0139075	−	0.999903i	$-0.504427\pi$
$971$	−0.866740	−0.0278150	−0.0139075	+	0.999903i	$0.504427\pi$
$972$	9.75343	0.312841
$973$	2.93493	0.0940897
$974$	46.7802	1.49893
$975$	−12.6092	−0.403819
$976$	38.6571	1.23738
$977$	−22.6329	−0.724092	−0.362046	−	0.932160i	$-0.617922\pi$
$977$	−22.6329	−0.724092	−0.362046	+	0.932160i	$0.617922\pi$
$978$	6.14780	0.196585
$979$	−33.0898	−1.05755
$980$	25.1526	0.803471
$981$	1.26041	0.0402419
$982$	−62.2378	−1.98609
$983$	15.5448	0.495803	0.247901	−	0.968785i	$-0.420259\pi$
$983$	15.5448	0.495803	0.247901	+	0.968785i	$0.420259\pi$
$984$	−16.5674	−0.528151
$985$	21.0127	0.669519
$986$	−27.5370	−0.876957
$987$	1.24173	0.0395247
$988$	2.96575	0.0943530
$989$	35.6155	1.13251
$990$	19.1163	0.607555
$991$	16.2076	0.514851	0.257425	−	0.966298i	$-0.417126\pi$
$991$	16.2076	0.514851	0.257425	+	0.966298i	$0.417126\pi$
$992$	−40.9062	−1.29877
$993$	−27.5430	−0.874049
$994$	−1.79770	−0.0570197
$995$	−50.1987	−1.59141
$996$	1.58329	0.0501685
$997$	39.7542	1.25903	0.629514	−	0.776990i	$-0.283254\pi$
$997$	39.7542	1.25903	0.629514	+	0.776990i	$0.283254\pi$
$998$	29.6473	0.938468
$999$	−5.61920	−0.177784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.19	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.19	✓	85	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67574 q^{2} +1.31893 q^{3} +0.808091 q^{4} -4.46158 q^{5} -2.21019 q^{6} +0.153470 q^{7} +1.99732 q^{8} -1.26041 q^{9} +O(q^{10})\)	\(q-1.67574 q^{2} +1.31893 q^{3} +0.808091 q^{4} -4.46158 q^{5} -2.21019 q^{6} +0.153470 q^{7} +1.99732 q^{8} -1.26041 q^{9} +7.47643 q^{10} -2.02860 q^{11} +1.06582 q^{12} -0.641377 q^{13} -0.257174 q^{14} -5.88453 q^{15} -4.96317 q^{16} +4.82713 q^{17} +2.11212 q^{18} -5.72216 q^{19} -3.60536 q^{20} +0.202416 q^{21} +3.39940 q^{22} -7.85045 q^{23} +2.63434 q^{24} +14.9057 q^{25} +1.07478 q^{26} -5.61920 q^{27} +0.124017 q^{28} +3.40426 q^{29} +9.86092 q^{30} -9.46396 q^{31} +4.32231 q^{32} -2.67559 q^{33} -8.08899 q^{34} -0.684717 q^{35} -1.01853 q^{36} +1.00000 q^{37} +9.58884 q^{38} -0.845934 q^{39} -8.91123 q^{40} -6.28903 q^{41} -0.339196 q^{42} -4.53674 q^{43} -1.63929 q^{44} +5.62343 q^{45} +13.1553 q^{46} +6.13454 q^{47} -6.54610 q^{48} -6.97645 q^{49} -24.9780 q^{50} +6.36666 q^{51} -0.518291 q^{52} +1.29314 q^{53} +9.41630 q^{54} +9.05076 q^{55} +0.306529 q^{56} -7.54716 q^{57} -5.70464 q^{58} -2.52877 q^{59} -4.75524 q^{60} -7.78879 q^{61} +15.8591 q^{62} -0.193435 q^{63} +2.68328 q^{64} +2.86156 q^{65} +4.48358 q^{66} -5.17506 q^{67} +3.90076 q^{68} -10.3542 q^{69} +1.14740 q^{70} +6.99021 q^{71} -2.51745 q^{72} -3.90986 q^{73} -1.67574 q^{74} +19.6596 q^{75} -4.62403 q^{76} -0.311328 q^{77} +1.41756 q^{78} +2.27090 q^{79} +22.1436 q^{80} -3.63012 q^{81} +10.5388 q^{82} +1.48552 q^{83} +0.163571 q^{84} -21.5366 q^{85} +7.60239 q^{86} +4.48999 q^{87} -4.05177 q^{88} +16.3116 q^{89} -9.42339 q^{90} -0.0984319 q^{91} -6.34388 q^{92} -12.4823 q^{93} -10.2799 q^{94} +25.5299 q^{95} +5.70085 q^{96} -13.6877 q^{97} +11.6907 q^{98} +2.55687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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