LMFDB - Embedded newform 8033.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30642 q^{2} +0.966593 q^{3} +3.31956 q^{4} +1.65248 q^{5} -2.22937 q^{6} -3.04982 q^{7} -3.04346 q^{8} -2.06570 q^{9} +O(q^{10})$	\(q-2.30642 q^{2} +0.966593 q^{3} +3.31956 q^{4} +1.65248 q^{5} -2.22937 q^{6} -3.04982 q^{7} -3.04346 q^{8} -2.06570 q^{9} -3.81132 q^{10} -5.94583 q^{11} +3.20867 q^{12} +0.739240 q^{13} +7.03416 q^{14} +1.59728 q^{15} +0.380375 q^{16} -7.08266 q^{17} +4.76436 q^{18} -0.578575 q^{19} +5.48553 q^{20} -2.94793 q^{21} +13.7136 q^{22} -5.03953 q^{23} -2.94179 q^{24} -2.26929 q^{25} -1.70500 q^{26} -4.89647 q^{27} -10.1241 q^{28} -1.00000 q^{29} -3.68400 q^{30} +0.576747 q^{31} +5.20963 q^{32} -5.74720 q^{33} +16.3356 q^{34} -5.03978 q^{35} -6.85721 q^{36} +3.08223 q^{37} +1.33444 q^{38} +0.714545 q^{39} -5.02928 q^{40} -3.32934 q^{41} +6.79917 q^{42} +0.471486 q^{43} -19.7375 q^{44} -3.41353 q^{45} +11.6233 q^{46} +2.24321 q^{47} +0.367668 q^{48} +2.30139 q^{49} +5.23394 q^{50} -6.84605 q^{51} +2.45395 q^{52} -7.55455 q^{53} +11.2933 q^{54} -9.82539 q^{55} +9.28201 q^{56} -0.559247 q^{57} +2.30642 q^{58} +5.26245 q^{59} +5.30227 q^{60} -0.150316 q^{61} -1.33022 q^{62} +6.30000 q^{63} -12.7763 q^{64} +1.22158 q^{65} +13.2554 q^{66} -2.08023 q^{67} -23.5113 q^{68} -4.87118 q^{69} +11.6238 q^{70} -1.09650 q^{71} +6.28688 q^{72} +8.22117 q^{73} -7.10891 q^{74} -2.19349 q^{75} -1.92062 q^{76} +18.1337 q^{77} -1.64804 q^{78} -3.30975 q^{79} +0.628563 q^{80} +1.46420 q^{81} +7.67884 q^{82} -1.95197 q^{83} -9.78586 q^{84} -11.7040 q^{85} -1.08744 q^{86} -0.966593 q^{87} +18.0959 q^{88} -8.82476 q^{89} +7.87303 q^{90} -2.25455 q^{91} -16.7290 q^{92} +0.557480 q^{93} -5.17379 q^{94} -0.956086 q^{95} +5.03559 q^{96} -3.46996 q^{97} -5.30797 q^{98} +12.2823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) $ 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.30642	−1.63088	−0.815442	−	0.578839i	$-0.803506\pi$
$2$	−2.30642	−1.63088	−0.815442	+	0.578839i	$0.803506\pi$
$3$	0.966593	0.558063	0.279031	−	0.960282i	$-0.409987\pi$
$3$	0.966593	0.558063	0.279031	+	0.960282i	$0.409987\pi$
$4$	3.31956	1.65978
$5$	1.65248	0.739014	0.369507	−	0.929228i	$-0.379527\pi$
$5$	1.65248	0.739014	0.369507	+	0.929228i	$0.379527\pi$
$6$	−2.22937	−0.910136
$7$	−3.04982	−1.15272	−0.576361	−	0.817195i	$-0.695528\pi$
$7$	−3.04982	−1.15272	−0.576361	+	0.817195i	$0.695528\pi$
$8$	−3.04346	−1.07603
$9$	−2.06570	−0.688566
$10$	−3.81132	−1.20525
$11$	−5.94583	−1.79273	−0.896367	−	0.443313i	$-0.853803\pi$
$11$	−5.94583	−1.79273	−0.896367	+	0.443313i	$0.853803\pi$
$12$	3.20867	0.926263
$13$	0.739240	0.205028	0.102514	−	0.994732i	$-0.467311\pi$
$13$	0.739240	0.205028	0.102514	+	0.994732i	$0.467311\pi$
$14$	7.03416	1.87996
$15$	1.59728	0.412416
$16$	0.380375	0.0950936
$17$	−7.08266	−1.71780	−0.858898	−	0.512146i	$-0.828851\pi$
$17$	−7.08266	−1.71780	−0.858898	+	0.512146i	$0.828851\pi$
$18$	4.76436	1.12297
$19$	−0.578575	−0.132734	−0.0663671	−	0.997795i	$-0.521141\pi$
$19$	−0.578575	−0.132734	−0.0663671	+	0.997795i	$0.521141\pi$
$20$	5.48553	1.22660
$21$	−2.94793	−0.643292
$22$	13.7136	2.92374
$23$	−5.03953	−1.05081	−0.525407	−	0.850851i	$-0.676087\pi$
$23$	−5.03953	−1.05081	−0.525407	+	0.850851i	$0.676087\pi$
$24$	−2.94179	−0.600491
$25$	−2.26929	−0.453859
$26$	−1.70500	−0.334377
$27$	−4.89647	−0.942326
$28$	−10.1241	−1.91327
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−3.68400	−0.672603
$31$	0.576747	0.103587	0.0517934	−	0.998658i	$-0.483506\pi$
$31$	0.576747	0.103587	0.0517934	+	0.998658i	$0.483506\pi$
$32$	5.20963	0.920941
$33$	−5.74720	−1.00046
$34$	16.3356	2.80153
$35$	−5.03978	−0.851878
$36$	−6.85721	−1.14287
$37$	3.08223	0.506715	0.253358	−	0.967373i	$-0.418465\pi$
$37$	3.08223	0.506715	0.253358	+	0.967373i	$0.418465\pi$
$38$	1.33444	0.216474
$39$	0.714545	0.114419
$40$	−5.02928	−0.795199
$41$	−3.32934	−0.519955	−0.259977	−	0.965615i	$-0.583715\pi$
$41$	−3.32934	−0.519955	−0.259977	+	0.965615i	$0.583715\pi$
$42$	6.79917	1.04913
$43$	0.471486	0.0719010	0.0359505	−	0.999354i	$-0.488554\pi$
$43$	0.471486	0.0719010	0.0359505	+	0.999354i	$0.488554\pi$
$44$	−19.7375	−2.97555
$45$	−3.41353	−0.508859
$46$	11.6233	1.71376
$47$	2.24321	0.327206	0.163603	−	0.986526i	$-0.447688\pi$
$47$	2.24321	0.327206	0.163603	+	0.986526i	$0.447688\pi$
$48$	0.367668	0.0530682
$49$	2.30139	0.328770
$50$	5.23394	0.740191
$51$	−6.84605	−0.958639
$52$	2.45395	0.340302
$53$	−7.55455	−1.03770	−0.518849	−	0.854866i	$-0.673639\pi$
$53$	−7.55455	−1.03770	−0.518849	+	0.854866i	$0.673639\pi$
$54$	11.2933	1.53682
$55$	−9.82539	−1.32485
$56$	9.28201	1.24036
$57$	−0.559247	−0.0740741
$58$	2.30642	0.302848
$59$	5.26245	0.685113	0.342556	−	0.939497i	$-0.388707\pi$
$59$	5.26245	0.685113	0.342556	+	0.939497i	$0.388707\pi$
$60$	5.30227	0.684521
$61$	−0.150316	−0.0192459	−0.00962297	−	0.999954i	$-0.503063\pi$
$61$	−0.150316	−0.0192459	−0.00962297	+	0.999954i	$0.503063\pi$
$62$	−1.33022	−0.168938
$63$	6.30000	0.793725
$64$	−12.7763	−1.59704
$65$	1.22158	0.151519
$66$	13.2554	1.63163
$67$	−2.08023	−0.254140	−0.127070	−	0.991894i	$-0.540557\pi$
$67$	−2.08023	−0.254140	−0.127070	+	0.991894i	$0.540557\pi$
$68$	−23.5113	−2.85117
$69$	−4.87118	−0.586421
$70$	11.6238	1.38931
$71$	−1.09650	−0.130131	−0.0650655	−	0.997881i	$-0.520726\pi$
$71$	−1.09650	−0.130131	−0.0650655	+	0.997881i	$0.520726\pi$
$72$	6.28688	0.740915
$73$	8.22117	0.962216	0.481108	−	0.876661i	$-0.340235\pi$
$73$	8.22117	0.962216	0.481108	+	0.876661i	$0.340235\pi$
$74$	−7.10891	−0.826394
$75$	−2.19349	−0.253282
$76$	−1.92062	−0.220310
$77$	18.1337	2.06653
$78$	−1.64804	−0.186604
$79$	−3.30975	−0.372376	−0.186188	−	0.982514i	$-0.559613\pi$
$79$	−3.30975	−0.372376	−0.186188	+	0.982514i	$0.559613\pi$
$80$	0.628563	0.0702755
$81$	1.46420	0.162688
$82$	7.67884	0.847986
$83$	−1.95197	−0.214256	−0.107128	−	0.994245i	$-0.534166\pi$
$83$	−1.95197	−0.214256	−0.107128	+	0.994245i	$0.534166\pi$
$84$	−9.78586	−1.06772
$85$	−11.7040	−1.26947
$86$	−1.08744	−0.117262
$87$	−0.966593	−0.103630
$88$	18.0959	1.92903
$89$	−8.82476	−0.935423	−0.467712	−	0.883881i	$-0.654921\pi$
$89$	−8.82476	−0.935423	−0.467712	+	0.883881i	$0.654921\pi$
$90$	7.87303	0.829890
$91$	−2.25455	−0.236341
$92$	−16.7290	−1.74412
$93$	0.557480	0.0578080
$94$	−5.17379	−0.533636
$95$	−0.956086	−0.0980924
$96$	5.03559	0.513943
$97$	−3.46996	−0.352321	−0.176161	−	0.984361i	$-0.556368\pi$
$97$	−3.46996	−0.352321	−0.176161	+	0.984361i	$0.556368\pi$
$98$	−5.30797	−0.536186
$99$	12.2823	1.23442
$100$	−7.53307	−0.753307
$101$	−13.8660	−1.37972	−0.689861	−	0.723942i	$-0.742328\pi$
$101$	−13.8660	−1.37972	−0.689861	+	0.723942i	$0.742328\pi$
$102$	15.7898	1.56343
$103$	5.97151	0.588390	0.294195	−	0.955745i	$-0.404948\pi$
$103$	5.97151	0.588390	0.294195	+	0.955745i	$0.404948\pi$
$104$	−2.24985	−0.220616
$105$	−4.87142	−0.475402
$106$	17.4239	1.69236
$107$	−19.5148	−1.88657	−0.943285	−	0.331983i	$-0.892282\pi$
$107$	−19.5148	−1.88657	−0.943285	+	0.331983i	$0.892282\pi$
$108$	−16.2541	−1.56406
$109$	−2.80032	−0.268222	−0.134111	−	0.990966i	$-0.542818\pi$
$109$	−2.80032	−0.268222	−0.134111	+	0.990966i	$0.542818\pi$
$110$	22.6614	2.16068
$111$	2.97926	0.282779
$112$	−1.16007	−0.109617
$113$	−6.96077	−0.654814	−0.327407	−	0.944883i	$-0.606175\pi$
$113$	−6.96077	−0.654814	−0.327407	+	0.944883i	$0.606175\pi$
$114$	1.28986	0.120806
$115$	−8.32774	−0.776566
$116$	−3.31956	−0.308214
$117$	−1.52705	−0.141175
$118$	−12.1374	−1.11734
$119$	21.6008	1.98014
$120$	−4.86127	−0.443771
$121$	24.3528	2.21389
$122$	0.346690	0.0313879
$123$	−3.21811	−0.290168
$124$	1.91455	0.171931
$125$	−12.0124	−1.07442
$126$	−14.5304	−1.29447
$127$	5.70351	0.506105	0.253053	−	0.967453i	$-0.418565\pi$
$127$	5.70351	0.506105	0.253053	+	0.967453i	$0.418565\pi$
$128$	19.0483	1.68365
$129$	0.455736	0.0401253
$130$	−2.81748	−0.247109
$131$	2.85877	0.249772	0.124886	−	0.992171i	$-0.460144\pi$
$131$	2.85877	0.249772	0.124886	+	0.992171i	$0.460144\pi$
$132$	−19.0782	−1.66054
$133$	1.76455	0.153006
$134$	4.79788	0.414473
$135$	−8.09134	−0.696392
$136$	21.5558	1.84840
$137$	10.3119	0.881005	0.440502	−	0.897751i	$-0.354800\pi$
$137$	10.3119	0.881005	0.440502	+	0.897751i	$0.354800\pi$
$138$	11.2350	0.956384
$139$	2.38680	0.202446	0.101223	−	0.994864i	$-0.467724\pi$
$139$	2.38680	0.202446	0.101223	+	0.994864i	$0.467724\pi$
$140$	−16.7299	−1.41393
$141$	2.16828	0.182602
$142$	2.52899	0.212228
$143$	−4.39539	−0.367561
$144$	−0.785739	−0.0654782
$145$	−1.65248	−0.137231
$146$	−18.9615	−1.56926
$147$	2.22451	0.183475
$148$	10.2317	0.841037
$149$	11.4199	0.935559	0.467779	−	0.883845i	$-0.345054\pi$
$149$	11.4199	0.935559	0.467779	+	0.883845i	$0.345054\pi$
$150$	5.05909	0.413073
$151$	−4.53704	−0.369219	−0.184610	−	0.982812i	$-0.559102\pi$
$151$	−4.53704	−0.369219	−0.184610	+	0.982812i	$0.559102\pi$
$152$	1.76087	0.142826
$153$	14.6306	1.18282
$154$	−41.8239	−3.37026
$155$	0.953065	0.0765520
$156$	2.37198	0.189910
$157$	−5.64207	−0.450286	−0.225143	−	0.974326i	$-0.572285\pi$
$157$	−5.64207	−0.450286	−0.225143	+	0.974326i	$0.572285\pi$
$158$	7.63366	0.607302
$159$	−7.30218	−0.579100
$160$	8.60883	0.680588
$161$	15.3696	1.21130
$162$	−3.37705	−0.265326
$163$	−18.3420	−1.43665	−0.718326	−	0.695706i	$-0.755091\pi$
$163$	−18.3420	−1.43665	−0.718326	+	0.695706i	$0.755091\pi$
$164$	−11.0519	−0.863012
$165$	−9.49715	−0.739352
$166$	4.50206	0.349427
$167$	18.3887	1.42296	0.711481	−	0.702706i	$-0.248025\pi$
$167$	18.3887	1.42296	0.711481	+	0.702706i	$0.248025\pi$
$168$	8.97193	0.692200
$169$	−12.4535	−0.957963
$170$	26.9943	2.07037
$171$	1.19516	0.0913962
$172$	1.56513	0.119340
$173$	−10.8134	−0.822126	−0.411063	−	0.911607i	$-0.634842\pi$
$173$	−10.8134	−0.822126	−0.411063	+	0.911607i	$0.634842\pi$
$174$	2.22937	0.169008
$175$	6.92094	0.523174
$176$	−2.26164	−0.170478
$177$	5.08665	0.382336
$178$	20.3536	1.52557
$179$	−2.13443	−0.159535	−0.0797673	−	0.996814i	$-0.525418\pi$
$179$	−2.13443	−0.159535	−0.0797673	+	0.996814i	$0.525418\pi$
$180$	−11.3314	−0.844596
$181$	−17.7657	−1.32052	−0.660258	−	0.751039i	$-0.729553\pi$
$181$	−17.7657	−1.32052	−0.660258	+	0.751039i	$0.729553\pi$
$182$	5.19993	0.385444
$183$	−0.145294	−0.0107404
$184$	15.3376	1.13071
$185$	5.09333	0.374469
$186$	−1.28578	−0.0942780
$187$	42.1122	3.07955
$188$	7.44649	0.543091
$189$	14.9333	1.08624
$190$	2.20513	0.159977
$191$	19.0366	1.37744	0.688720	−	0.725027i	$-0.258173\pi$
$191$	19.0366	1.37744	0.688720	+	0.725027i	$0.258173\pi$
$192$	−12.3495	−0.891249
$193$	−3.65422	−0.263036	−0.131518	−	0.991314i	$-0.541985\pi$
$193$	−3.65422	−0.263036	−0.131518	+	0.991314i	$0.541985\pi$
$194$	8.00318	0.574595
$195$	1.18077	0.0845570
$196$	7.63962	0.545687
$197$	16.2750	1.15954	0.579771	−	0.814779i	$-0.303142\pi$
$197$	16.2750	1.15954	0.579771	+	0.814779i	$0.303142\pi$
$198$	−28.3281	−2.01319
$199$	6.22332	0.441160	0.220580	−	0.975369i	$-0.429205\pi$
$199$	6.22332	0.441160	0.220580	+	0.975369i	$0.429205\pi$
$200$	6.90652	0.488365
$201$	−2.01074	−0.141826
$202$	31.9809	2.25017
$203$	3.04982	0.214055
$204$	−22.7259	−1.59113
$205$	−5.50168	−0.384254
$206$	−13.7728	−0.959596
$207$	10.4101	0.723555
$208$	0.281188	0.0194969
$209$	3.44011	0.237957
$210$	11.2355	0.775325
$211$	17.2723	1.18908	0.594538	−	0.804067i	$-0.297335\pi$
$211$	17.2723	1.18908	0.594538	+	0.804067i	$0.297335\pi$
$212$	−25.0778	−1.72235
$213$	−1.05987	−0.0726213
$214$	45.0094	3.07678
$215$	0.779124	0.0531358
$216$	14.9022	1.01397
$217$	−1.75897	−0.119407
$218$	6.45871	0.437439
$219$	7.94653	0.536977
$220$	−32.6160	−2.19897
$221$	−5.23578	−0.352197
$222$	−6.87142	−0.461180
$223$	18.3595	1.22944	0.614722	−	0.788744i	$-0.289268\pi$
$223$	18.3595	1.22944	0.614722	+	0.788744i	$0.289268\pi$
$224$	−15.8884	−1.06159
$225$	4.68768	0.312512
$226$	16.0544	1.06793
$227$	5.16220	0.342627	0.171314	−	0.985217i	$-0.445199\pi$
$227$	5.16220	0.342627	0.171314	+	0.985217i	$0.445199\pi$
$228$	−1.85646	−0.122947
$229$	0.807086	0.0533338	0.0266669	−	0.999644i	$-0.491511\pi$
$229$	0.807086	0.0533338	0.0266669	+	0.999644i	$0.491511\pi$
$230$	19.2073	1.26649
$231$	17.5279	1.15325
$232$	3.04346	0.199813
$233$	−5.71308	−0.374276	−0.187138	−	0.982334i	$-0.559921\pi$
$233$	−5.71308	−0.374276	−0.187138	+	0.982334i	$0.559921\pi$
$234$	3.52201	0.230241
$235$	3.70688	0.241810
$236$	17.4690	1.13714
$237$	−3.19918	−0.207809
$238$	−49.8205	−3.22938
$239$	4.48971	0.290415	0.145208	−	0.989401i	$-0.453615\pi$
$239$	4.48971	0.290415	0.145208	+	0.989401i	$0.453615\pi$
$240$	0.607565	0.0392181
$241$	11.9055	0.766900	0.383450	−	0.923562i	$-0.374736\pi$
$241$	11.9055	0.766900	0.383450	+	0.923562i	$0.374736\pi$
$242$	−56.1678	−3.61061
$243$	16.1047	1.03312
$244$	−0.498982	−0.0319440
$245$	3.80301	0.242966
$246$	7.42232	0.473230
$247$	−0.427706	−0.0272143
$248$	−1.75531	−0.111462
$249$	−1.88676	−0.119569
$250$	27.7056	1.75226
$251$	−0.882322	−0.0556917	−0.0278458	−	0.999612i	$-0.508865\pi$
$251$	−0.882322	−0.0556917	−0.0278458	+	0.999612i	$0.508865\pi$
$252$	20.9133	1.31741
$253$	29.9642	1.88383
$254$	−13.1547	−0.825399
$255$	−11.3130	−0.708447
$256$	−18.3807	−1.14879
$257$	17.8933	1.11615	0.558076	−	0.829790i	$-0.311540\pi$
$257$	17.8933	1.11615	0.558076	+	0.829790i	$0.311540\pi$
$258$	−1.05112	−0.0654397
$259$	−9.40024	−0.584102
$260$	4.05512	0.251488
$261$	2.06570	0.127863
$262$	−6.59351	−0.407349
$263$	−25.9419	−1.59965	−0.799823	−	0.600236i	$-0.795073\pi$
$263$	−25.9419	−1.59965	−0.799823	+	0.600236i	$0.795073\pi$
$264$	17.4914	1.07652
$265$	−12.4838	−0.766872
$266$	−4.06979	−0.249535
$267$	−8.52996	−0.522025
$268$	−6.90545	−0.421818
$269$	−3.63920	−0.221886	−0.110943	−	0.993827i	$-0.535387\pi$
$269$	−3.63920	−0.221886	−0.110943	+	0.993827i	$0.535387\pi$
$270$	18.6620	1.13573
$271$	15.5895	0.946997	0.473499	−	0.880795i	$-0.342991\pi$
$271$	15.5895	0.946997	0.473499	+	0.880795i	$0.342991\pi$
$272$	−2.69406	−0.163352
$273$	−2.17923	−0.131893
$274$	−23.7835	−1.43682
$275$	13.4928	0.813648
$276$	−16.1702	−0.973330
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−5.50496	−0.330166
$279$	−1.19138	−0.0713263
$280$	15.3384	0.916644
$281$	26.3446	1.57159	0.785793	−	0.618490i	$-0.212255\pi$
$281$	26.3446	1.57159	0.785793	+	0.618490i	$0.212255\pi$
$282$	−5.00095	−0.297802
$283$	−8.13163	−0.483375	−0.241688	−	0.970354i	$-0.577701\pi$
$283$	−8.13163	−0.483375	−0.241688	+	0.970354i	$0.577701\pi$
$284$	−3.63991	−0.215989
$285$	−0.924147	−0.0547417
$286$	10.1376	0.599450
$287$	10.1539	0.599364
$288$	−10.7615	−0.634128
$289$	33.1640	1.95082
$290$	3.81132	0.223808
$291$	−3.35404	−0.196617
$292$	27.2907	1.59707
$293$	16.9925	0.992713	0.496356	−	0.868119i	$-0.334671\pi$
$293$	16.9925	0.992713	0.496356	+	0.868119i	$0.334671\pi$
$294$	−5.13065	−0.299226
$295$	8.69612	0.506308
$296$	−9.38065	−0.545239
$297$	29.1136	1.68934
$298$	−26.3392	−1.52579
$299$	−3.72542	−0.215447
$300$	−7.28141	−0.420393
$301$	−1.43795	−0.0828819
$302$	10.4643	0.602154
$303$	−13.4028	−0.769972
$304$	−0.220075	−0.0126222
$305$	−0.248394	−0.0142230
$306$	−33.7443	−1.92903
$307$	−6.45243	−0.368260	−0.184130	−	0.982902i	$-0.558947\pi$
$307$	−6.45243	−0.368260	−0.184130	+	0.982902i	$0.558947\pi$
$308$	60.1959	3.42998
$309$	5.77202	0.328359
$310$	−2.19817	−0.124847
$311$	−2.64154	−0.149788	−0.0748939	−	0.997192i	$-0.523862\pi$
$311$	−2.64154	−0.149788	−0.0748939	+	0.997192i	$0.523862\pi$
$312$	−2.17469	−0.123118
$313$	−1.51667	−0.0857272	−0.0428636	−	0.999081i	$-0.513648\pi$
$313$	−1.51667	−0.0857272	−0.0428636	+	0.999081i	$0.513648\pi$
$314$	13.0130	0.734364
$315$	10.4107	0.586574
$316$	−10.9869	−0.618063
$317$	−26.9494	−1.51363	−0.756815	−	0.653630i	$-0.773245\pi$
$317$	−26.9494	−1.51363	−0.756815	+	0.653630i	$0.773245\pi$
$318$	16.8419	0.944445
$319$	5.94583	0.332902
$320$	−21.1127	−1.18023
$321$	−18.8629	−1.05283
$322$	−35.4488	−1.97549
$323$	4.09785	0.228010
$324$	4.86049	0.270027
$325$	−1.67755	−0.0930539
$326$	42.3042	2.34301
$327$	−2.70677	−0.149685
$328$	10.1327	0.559486
$329$	−6.84140	−0.377178
$330$	21.9044	1.20580
$331$	−16.8573	−0.926562	−0.463281	−	0.886212i	$-0.653328\pi$
$331$	−16.8573	−0.926562	−0.463281	+	0.886212i	$0.653328\pi$
$332$	−6.47968	−0.355619
$333$	−6.36695	−0.348907
$334$	−42.4120	−2.32068
$335$	−3.43755	−0.187813
$336$	−1.12132	−0.0611730
$337$	5.84870	0.318599	0.159300	−	0.987230i	$-0.449076\pi$
$337$	5.84870	0.318599	0.159300	+	0.987230i	$0.449076\pi$
$338$	28.7230	1.56233
$339$	−6.72823	−0.365427
$340$	−38.8521	−2.10705
$341$	−3.42924	−0.185704
$342$	−2.75654	−0.149057
$343$	14.3299	0.773742
$344$	−1.43495	−0.0773674
$345$	−8.04954	−0.433373
$346$	24.9402	1.34079
$347$	28.7533	1.54356	0.771778	−	0.635892i	$-0.219367\pi$
$347$	28.7533	1.54356	0.771778	+	0.635892i	$0.219367\pi$
$348$	−3.20867	−0.172003
$349$	−7.96494	−0.426354	−0.213177	−	0.977014i	$-0.568381\pi$
$349$	−7.96494	−0.426354	−0.213177	+	0.977014i	$0.568381\pi$
$350$	−15.9626	−0.853235
$351$	−3.61967	−0.193203
$352$	−30.9755	−1.65100
$353$	3.55025	0.188961	0.0944804	−	0.995527i	$-0.469881\pi$
$353$	3.55025	0.188961	0.0944804	+	0.995527i	$0.469881\pi$
$354$	−11.7319	−0.623546
$355$	−1.81195	−0.0961685
$356$	−29.2944	−1.55260
$357$	20.8792	1.10504
$358$	4.92288	0.260182
$359$	−20.0630	−1.05888	−0.529441	−	0.848347i	$-0.677598\pi$
$359$	−20.0630	−1.05888	−0.529441	+	0.848347i	$0.677598\pi$
$360$	10.3890	0.547547
$361$	−18.6653	−0.982382
$362$	40.9752	2.15361
$363$	23.5393	1.23549
$364$	−7.48411	−0.392274
$365$	13.5854	0.711090
$366$	0.335109	0.0175164
$367$	−18.5822	−0.969981	−0.484991	−	0.874519i	$-0.661177\pi$
$367$	−18.5822	−0.969981	−0.484991	+	0.874519i	$0.661177\pi$
$368$	−1.91691	−0.0999258
$369$	6.87740	0.358023
$370$	−11.7474	−0.610716
$371$	23.0400	1.19618
$372$	1.85059	0.0959486
$373$	22.2706	1.15313	0.576563	−	0.817053i	$-0.304393\pi$
$373$	22.2706	1.15313	0.576563	+	0.817053i	$0.304393\pi$
$374$	−97.1284	−5.02239
$375$	−11.6111	−0.599595
$376$	−6.82714	−0.352083
$377$	−0.739240	−0.0380728
$378$	−34.4425	−1.77153
$379$	10.9000	0.559895	0.279947	−	0.960015i	$-0.409683\pi$
$379$	10.9000	0.559895	0.279947	+	0.960015i	$0.409683\pi$
$380$	−3.17379	−0.162812
$381$	5.51298	0.282439
$382$	−43.9064	−2.24645
$383$	−6.52879	−0.333606	−0.166803	−	0.985990i	$-0.553344\pi$
$383$	−6.52879	−0.333606	−0.166803	+	0.985990i	$0.553344\pi$
$384$	18.4120	0.939581
$385$	29.9656	1.52719
$386$	8.42816	0.428982
$387$	−0.973948	−0.0495086
$388$	−11.5188	−0.584776
$389$	−29.6762	−1.50465	−0.752323	−	0.658795i	$-0.771067\pi$
$389$	−29.6762	−1.50465	−0.752323	+	0.658795i	$0.771067\pi$
$390$	−2.72336	−0.137903
$391$	35.6933	1.80509
$392$	−7.00420	−0.353766
$393$	2.76327	0.139388
$394$	−37.5369	−1.89108
$395$	−5.46931	−0.275191
$396$	40.7718	2.04886
$397$	−18.0352	−0.905159	−0.452580	−	0.891724i	$-0.649496\pi$
$397$	−18.0352	−0.905159	−0.452580	+	0.891724i	$0.649496\pi$
$398$	−14.3536	−0.719480
$399$	1.70560	0.0853869
$400$	−0.863182	−0.0431591
$401$	3.87036	0.193277	0.0966383	−	0.995320i	$-0.469191\pi$
$401$	3.87036	0.193277	0.0966383	+	0.995320i	$0.469191\pi$
$402$	4.63760	0.231302
$403$	0.426354	0.0212382
$404$	−46.0292	−2.29004
$405$	2.41956	0.120229
$406$	−7.03416	−0.349099
$407$	−18.3264	−0.908406
$408$	20.8357	1.03152
$409$	−11.4706	−0.567185	−0.283593	−	0.958945i	$-0.591526\pi$
$409$	−11.4706	−0.567185	−0.283593	+	0.958945i	$0.591526\pi$
$410$	12.6892	0.626673
$411$	9.96741	0.491656
$412$	19.8228	0.976599
$413$	−16.0495	−0.789745
$414$	−24.0101	−1.18003
$415$	−3.22560	−0.158338
$416$	3.85116	0.188819
$417$	2.30707	0.112978
$418$	−7.93432	−0.388080
$419$	−5.05258	−0.246835	−0.123417	−	0.992355i	$-0.539385\pi$
$419$	−5.05258	−0.246835	−0.123417	+	0.992355i	$0.539385\pi$
$420$	−16.1710	−0.789063
$421$	21.2110	1.03376	0.516881	−	0.856057i	$-0.327093\pi$
$421$	21.2110	1.03376	0.516881	+	0.856057i	$0.327093\pi$
$422$	−39.8372	−1.93925
$423$	−4.63380	−0.225303
$424$	22.9920	1.11659
$425$	16.0726	0.779637
$426$	2.44451	0.118437
$427$	0.458435	0.0221852
$428$	−64.7807	−3.13130
$429$	−4.24856	−0.205122
$430$	−1.79699	−0.0866583
$431$	−1.89633	−0.0913429	−0.0456715	−	0.998957i	$-0.514543\pi$
$431$	−1.89633	−0.0913429	−0.0456715	+	0.998957i	$0.514543\pi$
$432$	−1.86249	−0.0896092
$433$	2.87597	0.138210	0.0691052	−	0.997609i	$-0.477986\pi$
$433$	2.87597	0.138210	0.0691052	+	0.997609i	$0.477986\pi$
$434$	4.05693	0.194739
$435$	−1.59728	−0.0765838
$436$	−9.29585	−0.445190
$437$	2.91575	0.139479
$438$	−18.3280	−0.875747
$439$	8.32442	0.397303	0.198651	−	0.980070i	$-0.436344\pi$
$439$	8.32442	0.397303	0.198651	+	0.980070i	$0.436344\pi$
$440$	29.9032	1.42558
$441$	−4.75398	−0.226380
$442$	12.0759	0.574392
$443$	−35.7543	−1.69874	−0.849369	−	0.527800i	$-0.823017\pi$
$443$	−35.7543	−1.69874	−0.849369	+	0.527800i	$0.823017\pi$
$444$	9.88985	0.469351
$445$	−14.5828	−0.691290
$446$	−42.3447	−2.00508
$447$	11.0384	0.522101
$448$	38.9655	1.84095
$449$	−22.6938	−1.07099	−0.535494	−	0.844539i	$-0.679875\pi$
$449$	−22.6938	−1.07099	−0.535494	+	0.844539i	$0.679875\pi$
$450$	−10.8117	−0.509670
$451$	19.7957	0.932141
$452$	−23.1067	−1.08685
$453$	−4.38548	−0.206048
$454$	−11.9062	−0.558785
$455$	−3.72561	−0.174659
$456$	1.70205	0.0797057
$457$	11.5098	0.538406	0.269203	−	0.963083i	$-0.413240\pi$
$457$	11.5098	0.538406	0.269203	+	0.963083i	$0.413240\pi$
$458$	−1.86148	−0.0869812
$459$	34.6800	1.61872
$460$	−27.6445	−1.28893
$461$	−16.7299	−0.779191	−0.389595	−	0.920986i	$-0.627385\pi$
$461$	−16.7299	−0.779191	−0.389595	+	0.920986i	$0.627385\pi$
$462$	−40.4267	−1.88082
$463$	−33.9004	−1.57549	−0.787743	−	0.616005i	$-0.788750\pi$
$463$	−33.9004	−1.57549	−0.787743	+	0.616005i	$0.788750\pi$
$464$	−0.380375	−0.0176584
$465$	0.921227	0.0427209
$466$	13.1767	0.610401
$467$	8.81538	0.407927	0.203964	−	0.978978i	$-0.434618\pi$
$467$	8.81538	0.407927	0.203964	+	0.978978i	$0.434618\pi$
$468$	−5.06913	−0.234320
$469$	6.34432	0.292953
$470$	−8.54961	−0.394364
$471$	−5.45359	−0.251288
$472$	−16.0161	−0.737200
$473$	−2.80338	−0.128899
$474$	7.37865	0.338913
$475$	1.31296	0.0602426
$476$	71.7053	3.28661
$477$	15.6054	0.714523
$478$	−10.3552	−0.473634
$479$	−6.37803	−0.291419	−0.145710	−	0.989327i	$-0.546547\pi$
$479$	−6.37803	−0.291419	−0.145710	+	0.989327i	$0.546547\pi$
$480$	8.32124	0.379811
$481$	2.27851	0.103891
$482$	−27.4590	−1.25072
$483$	14.8562	0.675981
$484$	80.8408	3.67458
$485$	−5.73406	−0.260370
$486$	−37.1441	−1.68489
$487$	24.7312	1.12068	0.560340	−	0.828263i	$-0.310671\pi$
$487$	24.7312	1.12068	0.560340	+	0.828263i	$0.310671\pi$
$488$	0.457480	0.0207091
$489$	−17.7292	−0.801743
$490$	−8.77134	−0.396249
$491$	−19.1702	−0.865139	−0.432569	−	0.901601i	$-0.642393\pi$
$491$	−19.1702	−0.865139	−0.432569	+	0.901601i	$0.642393\pi$
$492$	−10.6827	−0.481615
$493$	7.08266	0.318987
$494$	0.986468	0.0443833
$495$	20.2963	0.912249
$496$	0.219380	0.00985044
$497$	3.34413	0.150005
$498$	4.35166	0.195002
$499$	−40.2371	−1.80126	−0.900630	−	0.434587i	$-0.856894\pi$
$499$	−40.2371	−1.80126	−0.900630	+	0.434587i	$0.856894\pi$
$500$	−39.8759	−1.78331
$501$	17.7744	0.794102
$502$	2.03500	0.0908266
$503$	1.58034	0.0704638	0.0352319	−	0.999379i	$-0.488783\pi$
$503$	1.58034	0.0704638	0.0352319	+	0.999379i	$0.488783\pi$
$504$	−19.1738	−0.854070
$505$	−22.9134	−1.01963
$506$	−69.1099	−3.07231
$507$	−12.0375	−0.534604
$508$	18.9332	0.840024
$509$	−27.6565	−1.22585	−0.612927	−	0.790140i	$-0.710008\pi$
$509$	−27.6565	−1.22585	−0.612927	+	0.790140i	$0.710008\pi$
$510$	26.0925	1.15539
$511$	−25.0731	−1.10917
$512$	4.29692	0.189899
$513$	2.83298	0.125079
$514$	−41.2694	−1.82031
$515$	9.86783	0.434828
$516$	1.51284	0.0665992
$517$	−13.3378	−0.586594
$518$	21.6809	0.952603
$519$	−10.4521	−0.458798
$520$	−3.71784	−0.163038
$521$	−18.8369	−0.825260	−0.412630	−	0.910899i	$-0.635390\pi$
$521$	−18.8369	−0.825260	−0.412630	+	0.910899i	$0.635390\pi$
$522$	−4.76436	−0.208530
$523$	15.4880	0.677244	0.338622	−	0.940922i	$-0.390039\pi$
$523$	15.4880	0.677244	0.338622	+	0.940922i	$0.390039\pi$
$524$	9.48986	0.414567
$525$	6.68973	0.291964
$526$	59.8329	2.60884
$527$	−4.08490	−0.177941
$528$	−2.18609	−0.0951372
$529$	2.39686	0.104211
$530$	28.7928	1.25068
$531$	−10.8706	−0.471745
$532$	5.85753	0.253956
$533$	−2.46118	−0.106605
$534$	19.6737	0.851362
$535$	−32.2480	−1.39420
$536$	6.33110	0.273462
$537$	−2.06312	−0.0890304
$538$	8.39352	0.361870
$539$	−13.6837	−0.589398
$540$	−26.8597	−1.15586
$541$	−29.1578	−1.25359	−0.626796	−	0.779183i	$-0.715634\pi$
$541$	−29.1578	−1.25359	−0.626796	+	0.779183i	$0.715634\pi$
$542$	−35.9560	−1.54444
$543$	−17.1722	−0.736931
$544$	−36.8980	−1.58199
$545$	−4.62749	−0.198220
$546$	5.02622	0.215102
$547$	13.9441	0.596206	0.298103	−	0.954534i	$-0.403646\pi$
$547$	13.9441	0.596206	0.298103	+	0.954534i	$0.403646\pi$
$548$	34.2310	1.46228
$549$	0.310506	0.0132521
$550$	−31.1201	−1.32697
$551$	0.578575	0.0246481
$552$	14.8253	0.631005
$553$	10.0941	0.429246
$554$	−2.30642	−0.0979903
$555$	4.92318	0.208978
$556$	7.92314	0.336016
$557$	−16.3536	−0.692924	−0.346462	−	0.938064i	$-0.612617\pi$
$557$	−16.3536	−0.692924	−0.346462	+	0.938064i	$0.612617\pi$
$558$	2.74783	0.116325
$559$	0.348542	0.0147417
$560$	−1.91700	−0.0810082
$561$	40.7054	1.71858
$562$	−60.7616	−2.56307
$563$	39.8939	1.68133	0.840665	−	0.541556i	$-0.182165\pi$
$563$	39.8939	1.68133	0.840665	+	0.541556i	$0.182165\pi$
$564$	7.19773	0.303079
$565$	−11.5026	−0.483916
$566$	18.7549	0.788329
$567$	−4.46553	−0.187535
$568$	3.33717	0.140024
$569$	2.22933	0.0934583	0.0467292	−	0.998908i	$-0.485120\pi$
$569$	2.22933	0.0934583	0.0467292	+	0.998908i	$0.485120\pi$
$570$	2.13147	0.0892774
$571$	37.8027	1.58200	0.790998	−	0.611819i	$-0.209562\pi$
$571$	37.8027	1.58200	0.790998	+	0.611819i	$0.209562\pi$
$572$	−14.5908	−0.610071
$573$	18.4007	0.768699
$574$	−23.4191	−0.977493
$575$	11.4362	0.476922
$576$	26.3920	1.09967
$577$	−0.389323	−0.0162077	−0.00810386	−	0.999967i	$-0.502580\pi$
$577$	−0.389323	−0.0162077	−0.00810386	+	0.999967i	$0.502580\pi$
$578$	−76.4901	−3.18157
$579$	−3.53214	−0.146791
$580$	−5.48553	−0.227774
$581$	5.95315	0.246978
$582$	7.73582	0.320660
$583$	44.9180	1.86031
$584$	−25.0209	−1.03537
$585$	−2.52342	−0.104331
$586$	−39.1918	−1.61900
$587$	26.8215	1.10704	0.553521	−	0.832835i	$-0.313284\pi$
$587$	26.8215	1.10704	0.553521	+	0.832835i	$0.313284\pi$
$588$	7.38440	0.304528
$589$	−0.333691	−0.0137495
$590$	−20.0569	−0.825729
$591$	15.7313	0.647098
$592$	1.17240	0.0481854
$593$	−37.6579	−1.54643	−0.773213	−	0.634146i	$-0.781352\pi$
$593$	−37.6579	−1.54643	−0.773213	+	0.634146i	$0.781352\pi$
$594$	−67.1480	−2.75512
$595$	35.6950	1.46335
$596$	37.9092	1.55282
$597$	6.01542	0.246195
$598$	8.59238	0.351369
$599$	−10.9297	−0.446575	−0.223287	−	0.974753i	$-0.571679\pi$
$599$	−10.9297	−0.446575	−0.223287	+	0.974753i	$0.571679\pi$
$600$	6.67580	0.272538
$601$	3.12024	0.127277	0.0636386	−	0.997973i	$-0.479730\pi$
$601$	3.12024	0.127277	0.0636386	+	0.997973i	$0.479730\pi$
$602$	3.31651	0.135171
$603$	4.29712	0.174992
$604$	−15.0610	−0.612824
$605$	40.2427	1.63610
$606$	30.9125	1.25573
$607$	29.7880	1.20906	0.604530	−	0.796583i	$-0.293361\pi$
$607$	29.7880	1.20906	0.604530	+	0.796583i	$0.293361\pi$
$608$	−3.01416	−0.122240
$609$	2.94793	0.119456
$610$	0.572901	0.0231961
$611$	1.65827	0.0670866
$612$	48.5673	1.96322
$613$	−7.85282	−0.317172	−0.158586	−	0.987345i	$-0.550694\pi$
$613$	−7.85282	−0.317172	−0.158586	+	0.987345i	$0.550694\pi$
$614$	14.8820	0.600589
$615$	−5.31788	−0.214438
$616$	−55.1892	−2.22364
$617$	14.7015	0.591860	0.295930	−	0.955210i	$-0.404370\pi$
$617$	14.7015	0.591860	0.295930	+	0.955210i	$0.404370\pi$
$618$	−13.3127	−0.535515
$619$	−30.1072	−1.21011	−0.605055	−	0.796184i	$-0.706849\pi$
$619$	−30.1072	−1.21011	−0.605055	+	0.796184i	$0.706849\pi$
$620$	3.16376	0.127060
$621$	24.6759	0.990210
$622$	6.09249	0.244287
$623$	26.9139	1.07828
$624$	0.271795	0.0108805
$625$	−8.50383	−0.340153
$626$	3.49807	0.139811
$627$	3.32518	0.132795
$628$	−18.7292	−0.747377
$629$	−21.8304	−0.870434
$630$	−24.0113	−0.956634
$631$	13.6045	0.541588	0.270794	−	0.962637i	$-0.412714\pi$
$631$	13.6045	0.541588	0.270794	+	0.962637i	$0.412714\pi$
$632$	10.0731	0.400687
$633$	16.6953	0.663580
$634$	62.1566	2.46855
$635$	9.42497	0.374019
$636$	−24.2400	−0.961180
$637$	1.70128	0.0674072
$638$	−13.7136	−0.542925
$639$	2.26504	0.0896037
$640$	31.4770	1.24424
$641$	13.3054	0.525532	0.262766	−	0.964860i	$-0.415365\pi$
$641$	13.3054	0.525532	0.262766	+	0.964860i	$0.415365\pi$
$642$	43.5058	1.71704
$643$	36.2101	1.42799	0.713994	−	0.700152i	$-0.246884\pi$
$643$	36.2101	1.42799	0.713994	+	0.700152i	$0.246884\pi$
$644$	51.0205	2.01049
$645$	0.753096	0.0296531
$646$	−9.45135	−0.371858
$647$	−19.9747	−0.785288	−0.392644	−	0.919691i	$-0.628439\pi$
$647$	−19.9747	−0.785288	−0.392644	+	0.919691i	$0.628439\pi$
$648$	−4.45623	−0.175057
$649$	−31.2896	−1.22823
$650$	3.86914	0.151760
$651$	−1.70021	−0.0666366
$652$	−60.8873	−2.38453
$653$	10.5103	0.411299	0.205649	−	0.978626i	$-0.434069\pi$
$653$	10.5103	0.411299	0.205649	+	0.978626i	$0.434069\pi$
$654$	6.24295	0.244119
$655$	4.72407	0.184585
$656$	−1.26639	−0.0494444
$657$	−16.9825	−0.662549
$658$	15.7791	0.615134
$659$	5.83404	0.227262	0.113631	−	0.993523i	$-0.463752\pi$
$659$	5.83404	0.227262	0.113631	+	0.993523i	$0.463752\pi$
$660$	−31.5264	−1.22716
$661$	−5.28812	−0.205684	−0.102842	−	0.994698i	$-0.532794\pi$
$661$	−5.28812	−0.205684	−0.102842	+	0.994698i	$0.532794\pi$
$662$	38.8800	1.51111
$663$	−5.06087	−0.196548
$664$	5.94075	0.230546
$665$	2.91589	0.113073
$666$	14.6848	0.569026
$667$	5.03953	0.195131
$668$	61.0425	2.36180
$669$	17.7462	0.686107
$670$	7.92842	0.306301
$671$	0.893750	0.0345028
$672$	−15.3576	−0.592434
$673$	8.89497	0.342876	0.171438	−	0.985195i	$-0.445159\pi$
$673$	8.89497	0.342876	0.171438	+	0.985195i	$0.445159\pi$
$674$	−13.4895	−0.519598
$675$	11.1115	0.427683
$676$	−41.3403	−1.59001
$677$	−9.82429	−0.377578	−0.188789	−	0.982018i	$-0.560456\pi$
$677$	−9.82429	−0.377578	−0.188789	+	0.982018i	$0.560456\pi$
$678$	15.5181	0.595969
$679$	10.5827	0.406129
$680$	35.6206	1.36599
$681$	4.98975	0.191208
$682$	7.90925	0.302861
$683$	−50.6502	−1.93808	−0.969039	−	0.246909i	$-0.920585\pi$
$683$	−50.6502	−1.93808	−0.969039	+	0.246909i	$0.920585\pi$
$684$	3.96741	0.151698
$685$	17.0403	0.651075
$686$	−33.0507	−1.26188
$687$	0.780124	0.0297636
$688$	0.179341	0.00683733
$689$	−5.58463	−0.212757
$690$	18.5656	0.706781
$691$	28.6381	1.08944	0.544722	−	0.838617i	$-0.316635\pi$
$691$	28.6381	1.08944	0.544722	+	0.838617i	$0.316635\pi$
$692$	−35.8957	−1.36455
$693$	−37.4587	−1.42294
$694$	−66.3171	−2.51736
$695$	3.94415	0.149610
$696$	2.94179	0.111508
$697$	23.5805	0.893177
$698$	18.3705	0.695333
$699$	−5.52222	−0.208870
$700$	22.9745	0.868354
$701$	1.71273	0.0646890	0.0323445	−	0.999477i	$-0.489703\pi$
$701$	1.71273	0.0646890	0.0323445	+	0.999477i	$0.489703\pi$
$702$	8.34846	0.315092
$703$	−1.78330	−0.0672585
$704$	75.9658	2.86307
$705$	3.58304	0.134945
$706$	−8.18836	−0.308173
$707$	42.2889	1.59044
$708$	16.8855	0.634595
$709$	21.3771	0.802835	0.401417	−	0.915895i	$-0.368518\pi$
$709$	21.3771	0.802835	0.401417	+	0.915895i	$0.368518\pi$
$710$	4.17912	0.156840
$711$	6.83694	0.256405
$712$	26.8579	1.00654
$713$	−2.90653	−0.108851
$714$	−48.1562	−1.80220
$715$	−7.26332	−0.271633
$716$	−7.08537	−0.264793
$717$	4.33973	0.162070
$718$	46.2736	1.72691
$719$	14.9516	0.557600	0.278800	−	0.960349i	$-0.410063\pi$
$719$	14.9516	0.557600	0.278800	+	0.960349i	$0.410063\pi$
$720$	−1.29842	−0.0483893
$721$	−18.2120	−0.678251
$722$	43.0499	1.60215
$723$	11.5078	0.427978
$724$	−58.9744	−2.19177
$725$	2.26929	0.0842795
$726$	−54.2915	−2.01495
$727$	−9.95784	−0.369316	−0.184658	−	0.982803i	$-0.559118\pi$
$727$	−9.95784	−0.369316	−0.184658	+	0.982803i	$0.559118\pi$
$728$	6.86164	0.254309
$729$	11.1741	0.413856
$730$	−31.3335	−1.15971
$731$	−3.33938	−0.123511
$732$	−0.482313	−0.0178268
$733$	−16.5544	−0.611452	−0.305726	−	0.952119i	$-0.598899\pi$
$733$	−16.5544	−0.611452	−0.305726	+	0.952119i	$0.598899\pi$
$734$	42.8583	1.58193
$735$	3.67597	0.135590
$736$	−26.2541	−0.967738
$737$	12.3687	0.455606
$738$	−15.8622	−0.583894
$739$	35.2802	1.29780	0.648902	−	0.760872i	$-0.275229\pi$
$739$	35.2802	1.29780	0.648902	+	0.760872i	$0.275229\pi$
$740$	16.9076	0.621538
$741$	−0.413418	−0.0151873
$742$	−53.1399	−1.95083
$743$	30.2298	1.10902	0.554512	−	0.832176i	$-0.312905\pi$
$743$	30.2298	1.10902	0.554512	+	0.832176i	$0.312905\pi$
$744$	−1.69667	−0.0622029
$745$	18.8713	0.691391
$746$	−51.3652	−1.88061
$747$	4.03218	0.147530
$748$	139.794	5.11138
$749$	59.5167	2.17469
$750$	26.7801	0.977870
$751$	33.2851	1.21459	0.607295	−	0.794477i	$-0.292255\pi$
$751$	33.2851	1.21459	0.607295	+	0.794477i	$0.292255\pi$
$752$	0.853262	0.0311152
$753$	−0.852847	−0.0310795
$754$	1.70500	0.0620923
$755$	−7.49740	−0.272858
$756$	49.5722	1.80292
$757$	6.15053	0.223545	0.111772	−	0.993734i	$-0.464347\pi$
$757$	6.15053	0.223545	0.111772	+	0.993734i	$0.464347\pi$
$758$	−25.1399	−0.913123
$759$	28.9632	1.05130
$760$	2.90982	0.105550
$761$	28.4391	1.03092	0.515458	−	0.856915i	$-0.327622\pi$
$761$	28.4391	1.03092	0.515458	+	0.856915i	$0.327622\pi$
$762$	−12.7152	−0.460624
$763$	8.54047	0.309186
$764$	63.1932	2.28625
$765$	24.1769	0.874117
$766$	15.0581	0.544072
$767$	3.89021	0.140468
$768$	−17.7666	−0.641098
$769$	−30.8748	−1.11337	−0.556687	−	0.830722i	$-0.687928\pi$
$769$	−30.8748	−1.11337	−0.556687	+	0.830722i	$0.687928\pi$
$770$	−69.1133	−2.49067
$771$	17.2955	0.622883
$772$	−12.1304	−0.436583
$773$	4.00506	0.144052	0.0720260	−	0.997403i	$-0.477054\pi$
$773$	4.00506	0.144052	0.0720260	+	0.997403i	$0.477054\pi$
$774$	2.24633	0.0807427
$775$	−1.30881	−0.0470138
$776$	10.5607	0.379107
$777$	−9.08621	−0.325966
$778$	68.4458	2.45390
$779$	1.92627	0.0690158
$780$	3.91965	0.140346
$781$	6.51962	0.233290
$782$	−82.3236	−2.94388
$783$	4.89647	0.174986
$784$	0.875391	0.0312640
$785$	−9.32343	−0.332768
$786$	−6.37325	−0.227326
$787$	35.9215	1.28046	0.640232	−	0.768182i	$-0.278838\pi$
$787$	35.9215	1.28046	0.640232	+	0.768182i	$0.278838\pi$
$788$	54.0258	1.92459
$789$	−25.0753	−0.892703
$790$	12.6145	0.448804
$791$	21.2291	0.754819
$792$	−37.3807	−1.32826
$793$	−0.111119	−0.00394596
$794$	41.5966	1.47621
$795$	−12.0667	−0.427963
$796$	20.6587	0.732228
$797$	9.30778	0.329699	0.164849	−	0.986319i	$-0.447286\pi$
$797$	9.30778	0.329699	0.164849	+	0.986319i	$0.447286\pi$
$798$	−3.93383	−0.139256
$799$	−15.8879	−0.562074
$800$	−11.8222	−0.417977
$801$	18.2293	0.644100
$802$	−8.92667	−0.315212
$803$	−48.8817	−1.72500
$804$	−6.67476	−0.235401
$805$	25.3981	0.895166
$806$	−0.983351	−0.0346371
$807$	−3.51763	−0.123826
$808$	42.2008	1.48462
$809$	−30.7392	−1.08073	−0.540367	−	0.841429i	$-0.681715\pi$
$809$	−30.7392	−1.08073	−0.540367	+	0.841429i	$0.681715\pi$
$810$	−5.58052	−0.196079
$811$	−23.9943	−0.842554	−0.421277	−	0.906932i	$-0.638418\pi$
$811$	−23.9943	−0.842554	−0.421277	+	0.906932i	$0.638418\pi$
$812$	10.1241	0.355285
$813$	15.0687	0.528484
$814$	42.2683	1.48150
$815$	−30.3098	−1.06171
$816$	−2.60406	−0.0911604
$817$	−0.272790	−0.00954372
$818$	26.4560	0.925013
$819$	4.65721	0.162736
$820$	−18.2632	−0.637777
$821$	−32.3020	−1.12735	−0.563674	−	0.825998i	$-0.690612\pi$
$821$	−32.3020	−1.12735	−0.563674	+	0.825998i	$0.690612\pi$
$822$	−22.9890	−0.801834
$823$	15.7017	0.547325	0.273663	−	0.961826i	$-0.411765\pi$
$823$	15.7017	0.547325	0.273663	+	0.961826i	$0.411765\pi$
$824$	−18.1741	−0.633124
$825$	13.0421	0.454067
$826$	37.0169	1.28798
$827$	1.43382	0.0498586	0.0249293	−	0.999689i	$-0.492064\pi$
$827$	1.43382	0.0498586	0.0249293	+	0.999689i	$0.492064\pi$
$828$	34.5571	1.20094
$829$	6.25445	0.217226	0.108613	−	0.994084i	$-0.465359\pi$
$829$	6.25445	0.217226	0.108613	+	0.994084i	$0.465359\pi$
$830$	7.43958	0.258231
$831$	0.966593	0.0335308
$832$	−9.44477	−0.327439
$833$	−16.3000	−0.564760
$834$	−5.32106	−0.184253
$835$	30.3871	1.05159
$836$	11.4197	0.394957
$837$	−2.82402	−0.0976125
$838$	11.6534	0.402559
$839$	−9.32277	−0.321858	−0.160929	−	0.986966i	$-0.551449\pi$
$839$	−9.32277	−0.321858	−0.160929	+	0.986966i	$0.551449\pi$
$840$	14.8260	0.511545
$841$	1.00000	0.0344828
$842$	−48.9215	−1.68595
$843$	25.4645	0.877044
$844$	57.3366	1.97361
$845$	−20.5793	−0.707948
$846$	10.6875	0.367443
$847$	−74.2717	−2.55201
$848$	−2.87356	−0.0986784
$849$	−7.85998	−0.269754
$850$	−37.0702	−1.27150
$851$	−15.5330	−0.532464
$852$	−3.51831	−0.120535
$853$	−0.174006	−0.00595787	−0.00297893	−	0.999996i	$-0.500948\pi$
$853$	−0.174006	−0.00595787	−0.00297893	+	0.999996i	$0.500948\pi$
$854$	−1.05734	−0.0361815
$855$	1.97498	0.0675431
$856$	59.3927	2.03000
$857$	−6.50148	−0.222086	−0.111043	−	0.993816i	$-0.535419\pi$
$857$	−6.50148	−0.222086	−0.111043	+	0.993816i	$0.535419\pi$
$858$	9.79895	0.334531
$859$	0.710874	0.0242547	0.0121273	−	0.999926i	$-0.496140\pi$
$859$	0.710874	0.0242547	0.0121273	+	0.999926i	$0.496140\pi$
$860$	2.58635	0.0881939
$861$	9.81467	0.334483
$862$	4.37373	0.148970
$863$	4.23123	0.144033	0.0720164	−	0.997403i	$-0.477057\pi$
$863$	4.23123	0.144033	0.0720164	+	0.997403i	$0.477057\pi$
$864$	−25.5088	−0.867826
$865$	−17.8689	−0.607562
$866$	−6.63319	−0.225405
$867$	32.0561	1.08868
$868$	−5.83902	−0.198189
$869$	19.6792	0.667571
$870$	3.68400	0.124899
$871$	−1.53779	−0.0521060
$872$	8.52268	0.288614
$873$	7.16789	0.242596
$874$	−6.72493	−0.227474
$875$	36.6356	1.23851
$876$	26.3790	0.891265
$877$	−40.7527	−1.37612	−0.688060	−	0.725653i	$-0.741538\pi$
$877$	−40.7527	−1.37612	−0.688060	+	0.725653i	$0.741538\pi$
$878$	−19.1996	−0.647955
$879$	16.4248	0.553996
$880$	−3.73733	−0.125985
$881$	−7.48158	−0.252061	−0.126030	−	0.992026i	$-0.540224\pi$
$881$	−7.48158	−0.252061	−0.126030	+	0.992026i	$0.540224\pi$
$882$	10.9647	0.369199
$883$	−4.37157	−0.147115	−0.0735575	−	0.997291i	$-0.523435\pi$
$883$	−4.37157	−0.147115	−0.0735575	+	0.997291i	$0.523435\pi$
$884$	−17.3805	−0.584570
$885$	8.40561	0.282552
$886$	82.4643	2.77044
$887$	−57.1741	−1.91972	−0.959860	−	0.280481i	$-0.909506\pi$
$887$	−57.1741	−1.91972	−0.959860	+	0.280481i	$0.909506\pi$
$888$	−9.06728	−0.304278
$889$	−17.3947	−0.583399
$890$	33.6340	1.12741
$891$	−8.70585	−0.291657
$892$	60.9456	2.04061
$893$	−1.29787	−0.0434315
$894$	−25.4593	−0.851485
$895$	−3.52711	−0.117898
$896$	−58.0938	−1.94078
$897$	−3.60097	−0.120233
$898$	52.3415	1.74666
$899$	−0.576747	−0.0192356
$900$	15.5610	0.518701
$901$	53.5063	1.78255
$902$	−45.6570	−1.52021
$903$	−1.38991	−0.0462533
$904$	21.1848	0.704597
$905$	−29.3576	−0.975879
$906$	10.1147	0.336040
$907$	−18.9262	−0.628436	−0.314218	−	0.949351i	$-0.601742\pi$
$907$	−18.9262	−0.628436	−0.314218	+	0.949351i	$0.601742\pi$
$908$	17.1363	0.568687
$909$	28.6430	0.950029
$910$	8.59280	0.284849
$911$	−43.3444	−1.43606	−0.718031	−	0.696011i	$-0.754957\pi$
$911$	−43.3444	−1.43606	−0.718031	+	0.696011i	$0.754957\pi$
$912$	−0.212723	−0.00704397
$913$	11.6061	0.384105
$914$	−26.5464	−0.878077
$915$	−0.240096	−0.00793733
$916$	2.67917	0.0885224
$917$	−8.71872	−0.287918
$918$	−79.9866	−2.63995
$919$	−25.5043	−0.841310	−0.420655	−	0.907221i	$-0.638200\pi$
$919$	−25.5043	−0.841310	−0.420655	+	0.907221i	$0.638200\pi$
$920$	25.3452	0.835606
$921$	−6.23688	−0.205512
$922$	38.5862	1.27077
$923$	−0.810579	−0.0266805
$924$	58.1850	1.91415
$925$	−6.99448	−0.229977
$926$	78.1885	2.56943
$927$	−12.3353	−0.405145
$928$	−5.20963	−0.171014
$929$	4.31350	0.141521	0.0707606	−	0.997493i	$-0.477457\pi$
$929$	4.31350	0.141521	0.0707606	+	0.997493i	$0.477457\pi$
$930$	−2.12473	−0.0696728
$931$	−1.33153	−0.0436391
$932$	−18.9649	−0.621217
$933$	−2.55329	−0.0835911
$934$	−20.3320	−0.665282
$935$	69.5898	2.27583
$936$	4.64751	0.151909
$937$	−7.94592	−0.259582	−0.129791	−	0.991541i	$-0.541431\pi$
$937$	−7.94592	−0.259582	−0.129791	+	0.991541i	$0.541431\pi$
$938$	−14.6327	−0.477773
$939$	−1.46600	−0.0478412
$940$	12.3052	0.401352
$941$	−58.4210	−1.90447	−0.952235	−	0.305367i	$-0.901221\pi$
$941$	−58.4210	−1.90447	−0.952235	+	0.305367i	$0.901221\pi$
$942$	12.5782	0.409822
$943$	16.7783	0.546376
$944$	2.00170	0.0651499
$945$	24.6771	0.802747
$946$	6.46576	0.210220
$947$	−12.1906	−0.396140	−0.198070	−	0.980188i	$-0.563467\pi$
$947$	−12.1906	−0.396140	−0.198070	+	0.980188i	$0.563467\pi$
$948$	−10.6199	−0.344918
$949$	6.07742	0.197281
$950$	−3.02823	−0.0982487
$951$	−26.0491	−0.844700
$952$	−65.7413	−2.13069
$953$	37.6807	1.22060	0.610299	−	0.792171i	$-0.291049\pi$
$953$	37.6807	1.22060	0.610299	+	0.792171i	$0.291049\pi$
$954$	−35.9926	−1.16530
$955$	31.4577	1.01795
$956$	14.9039	0.482026
$957$	5.74720	0.185780
$958$	14.7104	0.475271
$959$	−31.4494	−1.01555
$960$	−20.4074	−0.658645
$961$	−30.6674	−0.989270
$962$	−5.25519	−0.169434
$963$	40.3117	1.29903
$964$	39.5210	1.27289
$965$	−6.03854	−0.194388
$966$	−34.2646	−1.10245
$967$	−52.0053	−1.67238	−0.836189	−	0.548441i	$-0.815222\pi$
$967$	−52.0053	−1.67238	−0.836189	+	0.548441i	$0.815222\pi$
$968$	−74.1170	−2.38221
$969$	3.96095	0.127244
$970$	13.2251	0.424633
$971$	49.8929	1.60114	0.800569	−	0.599240i	$-0.204531\pi$
$971$	49.8929	1.60114	0.800569	+	0.599240i	$0.204531\pi$
$972$	53.4605	1.71475
$973$	−7.27931	−0.233364
$974$	−57.0406	−1.82770
$975$	−1.62151	−0.0519300
$976$	−0.0571762	−0.00183017
$977$	21.9071	0.700870	0.350435	−	0.936587i	$-0.386034\pi$
$977$	21.9071	0.700870	0.350435	+	0.936587i	$0.386034\pi$
$978$	40.8910	1.30755
$979$	52.4705	1.67696
$980$	12.6243	0.403270
$981$	5.78462	0.184689
$982$	44.2145	1.41094
$983$	−28.0375	−0.894257	−0.447128	−	0.894470i	$-0.647553\pi$
$983$	−28.0375	−0.894257	−0.447128	+	0.894470i	$0.647553\pi$
$984$	9.79422	0.312228
$985$	26.8941	0.856918
$986$	−16.3356	−0.520230
$987$	−6.61285	−0.210489
$988$	−1.41980	−0.0451698
$989$	−2.37607	−0.0755546
$990$	−46.8117	−1.48777
$991$	17.8635	0.567454	0.283727	−	0.958905i	$-0.408429\pi$
$991$	17.8635	0.567454	0.283727	+	0.958905i	$0.408429\pi$
$992$	3.00464	0.0953973
$993$	−16.2942	−0.517080
$994$	−7.71297	−0.244641
$995$	10.2839	0.326023
$996$	−6.26322	−0.198458
$997$	21.7450	0.688670	0.344335	−	0.938847i	$-0.388104\pi$
$997$	21.7450	0.688670	0.344335	+	0.938847i	$0.388104\pi$
$998$	92.8035	2.93764
$999$	−15.0920	−0.477491

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.e.1.19	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.e.1.19	✓	169	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30642 q^{2} +0.966593 q^{3} +3.31956 q^{4} +1.65248 q^{5} -2.22937 q^{6} -3.04982 q^{7} -3.04346 q^{8} -2.06570 q^{9} +O(q^{10})\)	\(q-2.30642 q^{2} +0.966593 q^{3} +3.31956 q^{4} +1.65248 q^{5} -2.22937 q^{6} -3.04982 q^{7} -3.04346 q^{8} -2.06570 q^{9} -3.81132 q^{10} -5.94583 q^{11} +3.20867 q^{12} +0.739240 q^{13} +7.03416 q^{14} +1.59728 q^{15} +0.380375 q^{16} -7.08266 q^{17} +4.76436 q^{18} -0.578575 q^{19} +5.48553 q^{20} -2.94793 q^{21} +13.7136 q^{22} -5.03953 q^{23} -2.94179 q^{24} -2.26929 q^{25} -1.70500 q^{26} -4.89647 q^{27} -10.1241 q^{28} -1.00000 q^{29} -3.68400 q^{30} +0.576747 q^{31} +5.20963 q^{32} -5.74720 q^{33} +16.3356 q^{34} -5.03978 q^{35} -6.85721 q^{36} +3.08223 q^{37} +1.33444 q^{38} +0.714545 q^{39} -5.02928 q^{40} -3.32934 q^{41} +6.79917 q^{42} +0.471486 q^{43} -19.7375 q^{44} -3.41353 q^{45} +11.6233 q^{46} +2.24321 q^{47} +0.367668 q^{48} +2.30139 q^{49} +5.23394 q^{50} -6.84605 q^{51} +2.45395 q^{52} -7.55455 q^{53} +11.2933 q^{54} -9.82539 q^{55} +9.28201 q^{56} -0.559247 q^{57} +2.30642 q^{58} +5.26245 q^{59} +5.30227 q^{60} -0.150316 q^{61} -1.33022 q^{62} +6.30000 q^{63} -12.7763 q^{64} +1.22158 q^{65} +13.2554 q^{66} -2.08023 q^{67} -23.5113 q^{68} -4.87118 q^{69} +11.6238 q^{70} -1.09650 q^{71} +6.28688 q^{72} +8.22117 q^{73} -7.10891 q^{74} -2.19349 q^{75} -1.92062 q^{76} +18.1337 q^{77} -1.64804 q^{78} -3.30975 q^{79} +0.628563 q^{80} +1.46420 q^{81} +7.67884 q^{82} -1.95197 q^{83} -9.78586 q^{84} -11.7040 q^{85} -1.08744 q^{86} -0.966593 q^{87} +18.0959 q^{88} -8.82476 q^{89} +7.87303 q^{90} -2.25455 q^{91} -16.7290 q^{92} +0.557480 q^{93} -5.17379 q^{94} -0.956086 q^{95} +5.03559 q^{96} -3.46996 q^{97} -5.30797 q^{98} +12.2823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

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