LMFDB - Embedded newform 8049.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20805 q^{2} +1.00000 q^{3} +2.87549 q^{4} -1.04969 q^{5} -2.20805 q^{6} -2.20196 q^{7} -1.93312 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.20805 q^{2} +1.00000 q^{3} +2.87549 q^{4} -1.04969 q^{5} -2.20805 q^{6} -2.20196 q^{7} -1.93312 q^{8} +1.00000 q^{9} +2.31777 q^{10} -0.818928 q^{11} +2.87549 q^{12} +1.22775 q^{13} +4.86204 q^{14} -1.04969 q^{15} -1.48255 q^{16} +2.48081 q^{17} -2.20805 q^{18} -3.95119 q^{19} -3.01838 q^{20} -2.20196 q^{21} +1.80823 q^{22} -1.94620 q^{23} -1.93312 q^{24} -3.89815 q^{25} -2.71093 q^{26} +1.00000 q^{27} -6.33171 q^{28} -5.23583 q^{29} +2.31777 q^{30} -8.62722 q^{31} +7.13978 q^{32} -0.818928 q^{33} -5.47775 q^{34} +2.31138 q^{35} +2.87549 q^{36} +0.290412 q^{37} +8.72442 q^{38} +1.22775 q^{39} +2.02918 q^{40} -9.16186 q^{41} +4.86204 q^{42} +4.75211 q^{43} -2.35482 q^{44} -1.04969 q^{45} +4.29730 q^{46} +1.55257 q^{47} -1.48255 q^{48} -2.15137 q^{49} +8.60731 q^{50} +2.48081 q^{51} +3.53038 q^{52} -10.8457 q^{53} -2.20805 q^{54} +0.859622 q^{55} +4.25665 q^{56} -3.95119 q^{57} +11.5610 q^{58} +0.285078 q^{59} -3.01838 q^{60} +13.1111 q^{61} +19.0493 q^{62} -2.20196 q^{63} -12.7999 q^{64} -1.28876 q^{65} +1.80823 q^{66} +11.0293 q^{67} +7.13353 q^{68} -1.94620 q^{69} -5.10364 q^{70} -4.36779 q^{71} -1.93312 q^{72} +11.0633 q^{73} -0.641245 q^{74} -3.89815 q^{75} -11.3616 q^{76} +1.80325 q^{77} -2.71093 q^{78} +5.16360 q^{79} +1.55622 q^{80} +1.00000 q^{81} +20.2299 q^{82} +6.57845 q^{83} -6.33171 q^{84} -2.60408 q^{85} -10.4929 q^{86} -5.23583 q^{87} +1.58309 q^{88} -2.35105 q^{89} +2.31777 q^{90} -2.70346 q^{91} -5.59627 q^{92} -8.62722 q^{93} -3.42814 q^{94} +4.14753 q^{95} +7.13978 q^{96} +12.1711 q^{97} +4.75033 q^{98} -0.818928 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * 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 $

$2$	−2.20805	−1.56133	−0.780664	−	0.624951i	$-0.785119\pi$
$2$	−2.20805	−1.56133	−0.780664	+	0.624951i	$0.785119\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.87549	1.43774
$5$	−1.04969	−0.469436	−0.234718	−	0.972063i	$-0.575417\pi$
$5$	−1.04969	−0.469436	−0.234718	+	0.972063i	$0.575417\pi$
$6$	−2.20805	−0.901433
$7$	−2.20196	−0.832263	−0.416131	−	0.909304i	$-0.636614\pi$
$7$	−2.20196	−0.832263	−0.416131	+	0.909304i	$0.636614\pi$
$8$	−1.93312	−0.683461
$9$	1.00000	0.333333
$10$	2.31777	0.732944
$11$	−0.818928	−0.246916	−0.123458	−	0.992350i	$-0.539398\pi$
$11$	−0.818928	−0.246916	−0.123458	+	0.992350i	$0.539398\pi$
$12$	2.87549	0.830082
$13$	1.22775	0.340517	0.170258	−	0.985399i	$-0.445540\pi$
$13$	1.22775	0.340517	0.170258	+	0.985399i	$0.445540\pi$
$14$	4.86204	1.29943
$15$	−1.04969	−0.271029
$16$	−1.48255	−0.370637
$17$	2.48081	0.601684	0.300842	−	0.953674i	$-0.402732\pi$
$17$	2.48081	0.601684	0.300842	+	0.953674i	$0.402732\pi$
$18$	−2.20805	−0.520442
$19$	−3.95119	−0.906465	−0.453232	−	0.891392i	$-0.649729\pi$
$19$	−3.95119	−0.906465	−0.453232	+	0.891392i	$0.649729\pi$
$20$	−3.01838	−0.674929
$21$	−2.20196	−0.480507
$22$	1.80823	0.385517
$23$	−1.94620	−0.405810	−0.202905	−	0.979198i	$-0.565038\pi$
$23$	−1.94620	−0.405810	−0.202905	+	0.979198i	$0.565038\pi$
$24$	−1.93312	−0.394596
$25$	−3.89815	−0.779629
$26$	−2.71093	−0.531658
$27$	1.00000	0.192450
$28$	−6.33171	−1.19658
$29$	−5.23583	−0.972268	−0.486134	−	0.873884i	$-0.661593\pi$
$29$	−5.23583	−0.972268	−0.486134	+	0.873884i	$0.661593\pi$
$30$	2.31777	0.423165
$31$	−8.62722	−1.54949	−0.774747	−	0.632271i	$-0.782123\pi$
$31$	−8.62722	−1.54949	−0.774747	+	0.632271i	$0.782123\pi$
$32$	7.13978	1.26215
$33$	−0.818928	−0.142557
$34$	−5.47775	−0.939426
$35$	2.31138	0.390695
$36$	2.87549	0.479248
$37$	0.290412	0.0477435	0.0238717	−	0.999715i	$-0.492401\pi$
$37$	0.290412	0.0477435	0.0238717	+	0.999715i	$0.492401\pi$
$38$	8.72442	1.41529
$39$	1.22775	0.196597
$40$	2.02918	0.320841
$41$	−9.16186	−1.43084	−0.715421	−	0.698693i	$-0.753765\pi$
$41$	−9.16186	−1.43084	−0.715421	+	0.698693i	$0.753765\pi$
$42$	4.86204	0.750229
$43$	4.75211	0.724689	0.362345	−	0.932044i	$-0.381976\pi$
$43$	4.75211	0.724689	0.362345	+	0.932044i	$0.381976\pi$
$44$	−2.35482	−0.355002
$45$	−1.04969	−0.156479
$46$	4.29730	0.633603
$47$	1.55257	0.226465	0.113232	−	0.993569i	$-0.463880\pi$
$47$	1.55257	0.226465	0.113232	+	0.993569i	$0.463880\pi$
$48$	−1.48255	−0.213987
$49$	−2.15137	−0.307339
$50$	8.60731	1.21726
$51$	2.48081	0.347383
$52$	3.53038	0.489576
$53$	−10.8457	−1.48977	−0.744886	−	0.667192i	$-0.767496\pi$
$53$	−10.8457	−1.48977	−0.744886	+	0.667192i	$0.767496\pi$
$54$	−2.20805	−0.300478
$55$	0.859622	0.115911
$56$	4.25665	0.568819
$57$	−3.95119	−0.523348
$58$	11.5610	1.51803
$59$	0.285078	0.0371140	0.0185570	−	0.999828i	$-0.494093\pi$
$59$	0.285078	0.0371140	0.0185570	+	0.999828i	$0.494093\pi$
$60$	−3.01838	−0.389671
$61$	13.1111	1.67871	0.839355	−	0.543584i	$-0.182933\pi$
$61$	13.1111	1.67871	0.839355	+	0.543584i	$0.182933\pi$
$62$	19.0493	2.41927
$63$	−2.20196	−0.277421
$64$	−12.7999	−1.59999
$65$	−1.28876	−0.159851
$66$	1.80823	0.222578
$67$	11.0293	1.34744	0.673721	−	0.738985i	$-0.264695\pi$
$67$	11.0293	1.34744	0.673721	+	0.738985i	$0.264695\pi$
$68$	7.13353	0.865068
$69$	−1.94620	−0.234295
$70$	−5.10364	−0.610002
$71$	−4.36779	−0.518361	−0.259181	−	0.965829i	$-0.583452\pi$
$71$	−4.36779	−0.518361	−0.259181	+	0.965829i	$0.583452\pi$
$72$	−1.93312	−0.227820
$73$	11.0633	1.29486	0.647431	−	0.762124i	$-0.275843\pi$
$73$	11.0633	1.29486	0.647431	+	0.762124i	$0.275843\pi$
$74$	−0.641245	−0.0745432
$75$	−3.89815	−0.450119
$76$	−11.3616	−1.30326
$77$	1.80325	0.205499
$78$	−2.71093	−0.306953
$79$	5.16360	0.580950	0.290475	−	0.956883i	$-0.406187\pi$
$79$	5.16360	0.580950	0.290475	+	0.956883i	$0.406187\pi$
$80$	1.55622	0.173991
$81$	1.00000	0.111111
$82$	20.2299	2.23401
$83$	6.57845	0.722078	0.361039	−	0.932551i	$-0.382422\pi$
$83$	6.57845	0.722078	0.361039	+	0.932551i	$0.382422\pi$
$84$	−6.33171	−0.690846
$85$	−2.60408	−0.282453
$86$	−10.4929	−1.13148
$87$	−5.23583	−0.561339
$88$	1.58309	0.168757
$89$	−2.35105	−0.249210	−0.124605	−	0.992206i	$-0.539766\pi$
$89$	−2.35105	−0.249210	−0.124605	+	0.992206i	$0.539766\pi$
$90$	2.31777	0.244315
$91$	−2.70346	−0.283399
$92$	−5.59627	−0.583451
$93$	−8.62722	−0.894601
$94$	−3.42814	−0.353586
$95$	4.14753	0.425528
$96$	7.13978	0.728701
$97$	12.1711	1.23579	0.617893	−	0.786262i	$-0.287986\pi$
$97$	12.1711	1.23579	0.617893	+	0.786262i	$0.287986\pi$
$98$	4.75033	0.479856
$99$	−0.818928	−0.0823054
$100$	−11.2091	−1.12091
$101$	5.73381	0.570535	0.285268	−	0.958448i	$-0.407918\pi$
$101$	5.73381	0.570535	0.285268	+	0.958448i	$0.407918\pi$
$102$	−5.47775	−0.542378
$103$	6.66151	0.656378	0.328189	−	0.944612i	$-0.393562\pi$
$103$	6.66151	0.656378	0.328189	+	0.944612i	$0.393562\pi$
$104$	−2.37339	−0.232730
$105$	2.31138	0.225568
$106$	23.9479	2.32602
$107$	−7.59392	−0.734132	−0.367066	−	0.930195i	$-0.619638\pi$
$107$	−7.59392	−0.734132	−0.367066	+	0.930195i	$0.619638\pi$
$108$	2.87549	0.276694
$109$	0.985256	0.0943704	0.0471852	−	0.998886i	$-0.484975\pi$
$109$	0.985256	0.0943704	0.0471852	+	0.998886i	$0.484975\pi$
$110$	−1.89809	−0.180976
$111$	0.290412	0.0275647
$112$	3.26451	0.308468
$113$	−4.42597	−0.416360	−0.208180	−	0.978090i	$-0.566754\pi$
$113$	−4.42597	−0.416360	−0.208180	+	0.978090i	$0.566754\pi$
$114$	8.72442	0.817117
$115$	2.04291	0.190502
$116$	−15.0555	−1.39787
$117$	1.22775	0.113506
$118$	−0.629466	−0.0579470
$119$	−5.46264	−0.500759
$120$	2.02918	0.185238
$121$	−10.3294	−0.939032
$122$	−28.9501	−2.62102
$123$	−9.16186	−0.826097
$124$	−24.8075	−2.22778
$125$	9.34031	0.835423
$126$	4.86204	0.433145
$127$	−7.00167	−0.621298	−0.310649	−	0.950525i	$-0.600546\pi$
$127$	−7.00167	−0.621298	−0.310649	+	0.950525i	$0.600546\pi$
$128$	13.9833	1.23596
$129$	4.75211	0.418400
$130$	2.84565	0.249580
$131$	1.71527	0.149864	0.0749319	−	0.997189i	$-0.476126\pi$
$131$	1.71527	0.149864	0.0749319	+	0.997189i	$0.476126\pi$
$132$	−2.35482	−0.204960
$133$	8.70036	0.754417
$134$	−24.3532	−2.10380
$135$	−1.04969	−0.0903431
$136$	−4.79570	−0.411228
$137$	−2.96528	−0.253341	−0.126671	−	0.991945i	$-0.540429\pi$
$137$	−2.96528	−0.253341	−0.126671	+	0.991945i	$0.540429\pi$
$138$	4.29730	0.365811
$139$	1.89874	0.161049	0.0805246	−	0.996753i	$-0.474340\pi$
$139$	1.89874	0.161049	0.0805246	+	0.996753i	$0.474340\pi$
$140$	6.64634	0.561718
$141$	1.55257	0.130750
$142$	9.64430	0.809332
$143$	−1.00544	−0.0840790
$144$	−1.48255	−0.123546
$145$	5.49600	0.456418
$146$	−24.4284	−2.02170
$147$	−2.15137	−0.177442
$148$	0.835077	0.0686429
$149$	−5.82075	−0.476855	−0.238427	−	0.971160i	$-0.576632\pi$
$149$	−5.82075	−0.476855	−0.238427	+	0.971160i	$0.576632\pi$
$150$	8.60731	0.702784
$151$	11.4707	0.933472	0.466736	−	0.884397i	$-0.345430\pi$
$151$	11.4707	0.933472	0.466736	+	0.884397i	$0.345430\pi$
$152$	7.63812	0.619533
$153$	2.48081	0.200561
$154$	−3.98166	−0.320851
$155$	9.05593	0.727389
$156$	3.53038	0.282657
$157$	0.311762	0.0248813	0.0124407	−	0.999923i	$-0.496040\pi$
$157$	0.311762	0.0248813	0.0124407	+	0.999923i	$0.496040\pi$
$158$	−11.4015	−0.907053
$159$	−10.8457	−0.860120
$160$	−7.49457	−0.592498
$161$	4.28545	0.337741
$162$	−2.20805	−0.173481
$163$	−4.03433	−0.315993	−0.157996	−	0.987440i	$-0.550503\pi$
$163$	−4.03433	−0.315993	−0.157996	+	0.987440i	$0.550503\pi$
$164$	−26.3448	−2.05718
$165$	0.859622	0.0669215
$166$	−14.5255	−1.12740
$167$	−5.21059	−0.403208	−0.201604	−	0.979467i	$-0.564615\pi$
$167$	−5.21059	−0.403208	−0.201604	+	0.979467i	$0.564615\pi$
$168$	4.25665	0.328408
$169$	−11.4926	−0.884048
$170$	5.74995	0.441001
$171$	−3.95119	−0.302155
$172$	13.6646	1.04192
$173$	−19.6564	−1.49445	−0.747224	−	0.664572i	$-0.768614\pi$
$173$	−19.6564	−1.49445	−0.747224	+	0.664572i	$0.768614\pi$
$174$	11.5610	0.876435
$175$	8.58357	0.648857
$176$	1.21410	0.0915163
$177$	0.285078	0.0214278
$178$	5.19123	0.389099
$179$	−24.5066	−1.83171	−0.915855	−	0.401510i	$-0.868485\pi$
$179$	−24.5066	−1.83171	−0.915855	+	0.401510i	$0.868485\pi$
$180$	−3.01838	−0.224976
$181$	25.2343	1.87565	0.937826	−	0.347107i	$-0.112836\pi$
$181$	25.2343	1.87565	0.937826	+	0.347107i	$0.112836\pi$
$182$	5.96937	0.442479
$183$	13.1111	0.969203
$184$	3.76223	0.277355
$185$	−0.304843	−0.0224125
$186$	19.0493	1.39677
$187$	−2.03160	−0.148566
$188$	4.46438	0.325598
$189$	−2.20196	−0.160169
$190$	−9.15796	−0.664388
$191$	−17.7703	−1.28582	−0.642909	−	0.765943i	$-0.722272\pi$
$191$	−17.7703	−1.28582	−0.642909	+	0.765943i	$0.722272\pi$
$192$	−12.7999	−0.923753
$193$	6.80526	0.489853	0.244927	−	0.969542i	$-0.421236\pi$
$193$	6.80526	0.489853	0.244927	+	0.969542i	$0.421236\pi$
$194$	−26.8744	−1.92947
$195$	−1.28876	−0.0922900
$196$	−6.18624	−0.441874
$197$	22.4777	1.60147	0.800734	−	0.599020i	$-0.204443\pi$
$197$	22.4777	1.60147	0.800734	+	0.599020i	$0.204443\pi$
$198$	1.80823	0.128506
$199$	−0.956123	−0.0677777	−0.0338889	−	0.999426i	$-0.510789\pi$
$199$	−0.956123	−0.0677777	−0.0338889	+	0.999426i	$0.510789\pi$
$200$	7.53558	0.532846
$201$	11.0293	0.777946
$202$	−12.6605	−0.890792
$203$	11.5291	0.809183
$204$	7.13353	0.499447
$205$	9.61713	0.671690
$206$	−14.7089	−1.02482
$207$	−1.94620	−0.135270
$208$	−1.82020	−0.126208
$209$	3.23574	0.223821
$210$	−5.10364	−0.352185
$211$	−11.7907	−0.811705	−0.405853	−	0.913939i	$-0.633025\pi$
$211$	−11.7907	−0.811705	−0.405853	+	0.913939i	$0.633025\pi$
$212$	−31.1867	−2.14191
$213$	−4.36779	−0.299276
$214$	16.7678	1.14622
$215$	−4.98825	−0.340196
$216$	−1.93312	−0.131532
$217$	18.9968	1.28959
$218$	−2.17549	−0.147343
$219$	11.0633	0.747589
$220$	2.47183	0.166651
$221$	3.04581	0.204883
$222$	−0.641245	−0.0430376
$223$	−3.12185	−0.209055	−0.104527	−	0.994522i	$-0.533333\pi$
$223$	−3.12185	−0.209055	−0.104527	+	0.994522i	$0.533333\pi$
$224$	−15.7215	−1.05044
$225$	−3.89815	−0.259876
$226$	9.77277	0.650075
$227$	7.96720	0.528802	0.264401	−	0.964413i	$-0.414826\pi$
$227$	7.96720	0.528802	0.264401	+	0.964413i	$0.414826\pi$
$228$	−11.3616	−0.752440
$229$	22.6460	1.49649	0.748246	−	0.663421i	$-0.230896\pi$
$229$	22.6460	1.49649	0.748246	+	0.663421i	$0.230896\pi$
$230$	−4.51084	−0.297436
$231$	1.80325	0.118645
$232$	10.1215	0.664507
$233$	−5.16564	−0.338412	−0.169206	−	0.985581i	$-0.554120\pi$
$233$	−5.16564	−0.338412	−0.169206	+	0.985581i	$0.554120\pi$
$234$	−2.71093	−0.177219
$235$	−1.62972	−0.106311
$236$	0.819737	0.0533603
$237$	5.16360	0.335412
$238$	12.0618	0.781849
$239$	2.96868	0.192028	0.0960139	−	0.995380i	$-0.469391\pi$
$239$	2.96868	0.192028	0.0960139	+	0.995380i	$0.469391\pi$
$240$	1.55622	0.100454
$241$	0.816392	0.0525884	0.0262942	−	0.999654i	$-0.491629\pi$
$241$	0.816392	0.0525884	0.0262942	+	0.999654i	$0.491629\pi$
$242$	22.8077	1.46614
$243$	1.00000	0.0641500
$244$	37.7009	2.41355
$245$	2.25828	0.144276
$246$	20.2299	1.28981
$247$	−4.85107	−0.308666
$248$	16.6775	1.05902
$249$	6.57845	0.416892
$250$	−20.6239	−1.30437
$251$	11.3595	0.717008	0.358504	−	0.933528i	$-0.383287\pi$
$251$	11.3595	0.717008	0.358504	+	0.933528i	$0.383287\pi$
$252$	−6.33171	−0.398860
$253$	1.59380	0.100201
$254$	15.4600	0.970050
$255$	−2.60408	−0.163074
$256$	−5.27595	−0.329747
$257$	−12.7278	−0.793939	−0.396970	−	0.917832i	$-0.629938\pi$
$257$	−12.7278	−0.793939	−0.396970	+	0.917832i	$0.629938\pi$
$258$	−10.4929	−0.653259
$259$	−0.639476	−0.0397351
$260$	−3.70581	−0.229825
$261$	−5.23583	−0.324089
$262$	−3.78740	−0.233986
$263$	7.13829	0.440166	0.220083	−	0.975481i	$-0.429367\pi$
$263$	7.13829	0.440166	0.220083	+	0.975481i	$0.429367\pi$
$264$	1.58309	0.0974322
$265$	11.3846	0.699353
$266$	−19.2108	−1.17789
$267$	−2.35105	−0.143882
$268$	31.7146	1.93728
$269$	31.2729	1.90674	0.953371	−	0.301802i	$-0.0975883\pi$
$269$	31.2729	1.90674	0.953371	+	0.301802i	$0.0975883\pi$
$270$	2.31777	0.141055
$271$	23.6403	1.43605	0.718024	−	0.696018i	$-0.245047\pi$
$271$	23.6403	1.43605	0.718024	+	0.696018i	$0.245047\pi$
$272$	−3.67792	−0.223007
$273$	−2.70346	−0.163621
$274$	6.54750	0.395549
$275$	3.19230	0.192503
$276$	−5.59627	−0.336856
$277$	−18.9624	−1.13934	−0.569671	−	0.821873i	$-0.692929\pi$
$277$	−18.9624	−1.13934	−0.569671	+	0.821873i	$0.692929\pi$
$278$	−4.19252	−0.251451
$279$	−8.62722	−0.516498
$280$	−4.46817	−0.267024
$281$	−20.9187	−1.24791	−0.623954	−	0.781461i	$-0.714475\pi$
$281$	−20.9187	−1.24791	−0.623954	+	0.781461i	$0.714475\pi$
$282$	−3.42814	−0.204143
$283$	13.9257	0.827796	0.413898	−	0.910323i	$-0.364167\pi$
$283$	13.9257	0.827796	0.413898	+	0.910323i	$0.364167\pi$
$284$	−12.5595	−0.745270
$285$	4.14753	0.245678
$286$	2.22006	0.131275
$287$	20.1741	1.19084
$288$	7.13978	0.420716
$289$	−10.8456	−0.637976
$290$	−12.1355	−0.712618
$291$	12.1711	0.713481
$292$	31.8124	1.86168
$293$	−15.1223	−0.883455	−0.441727	−	0.897149i	$-0.645634\pi$
$293$	−15.1223	−0.883455	−0.441727	+	0.897149i	$0.645634\pi$
$294$	4.75033	0.277045
$295$	−0.299244	−0.0174226
$296$	−0.561402	−0.0326308
$297$	−0.818928	−0.0475190
$298$	12.8525	0.744526
$299$	−2.38944	−0.138185
$300$	−11.2091	−0.647156
$301$	−10.4639	−0.603132
$302$	−25.3279	−1.45746
$303$	5.73381	0.329399
$304$	5.85783	0.335970
$305$	−13.7627	−0.788047
$306$	−5.47775	−0.313142
$307$	5.66549	0.323346	0.161673	−	0.986844i	$-0.448311\pi$
$307$	5.66549	0.323346	0.161673	+	0.986844i	$0.448311\pi$
$308$	5.18521	0.295455
$309$	6.66151	0.378960
$310$	−19.9959	−1.13569
$311$	26.5860	1.50756	0.753778	−	0.657130i	$-0.228230\pi$
$311$	26.5860	1.50756	0.753778	+	0.657130i	$0.228230\pi$
$312$	−2.37339	−0.134367
$313$	9.66416	0.546251	0.273125	−	0.961978i	$-0.411943\pi$
$313$	9.66416	0.546251	0.273125	+	0.961978i	$0.411943\pi$
$314$	−0.688386	−0.0388479
$315$	2.31138	0.130232
$316$	14.8479	0.835257
$317$	10.2868	0.577761	0.288881	−	0.957365i	$-0.406717\pi$
$317$	10.2868	0.577761	0.288881	+	0.957365i	$0.406717\pi$
$318$	23.9479	1.34293
$319$	4.28776	0.240069
$320$	13.4359	0.751092
$321$	−7.59392	−0.423851
$322$	−9.46249	−0.527324
$323$	−9.80214	−0.545406
$324$	2.87549	0.159749
$325$	−4.78595	−0.265477
$326$	8.90800	0.493368
$327$	0.985256	0.0544848
$328$	17.7110	0.977925
$329$	−3.41869	−0.188478
$330$	−1.89809	−0.104486
$331$	−1.35605	−0.0745353	−0.0372676	−	0.999305i	$-0.511865\pi$
$331$	−1.35605	−0.0745353	−0.0372676	+	0.999305i	$0.511865\pi$
$332$	18.9162	1.03816
$333$	0.290412	0.0159145
$334$	11.5053	0.629540
$335$	−11.5774	−0.632539
$336$	3.26451	0.178094
$337$	−26.4424	−1.44041	−0.720204	−	0.693763i	$-0.755952\pi$
$337$	−26.4424	−1.44041	−0.720204	+	0.693763i	$0.755952\pi$
$338$	25.3763	1.38029
$339$	−4.42597	−0.240386
$340$	−7.48801	−0.406094
$341$	7.06507	0.382595
$342$	8.72442	0.471763
$343$	20.1510	1.08805
$344$	−9.18639	−0.495297
$345$	2.04291	0.109986
$346$	43.4023	2.33332
$347$	12.4064	0.666008	0.333004	−	0.942925i	$-0.391938\pi$
$347$	12.4064	0.666008	0.333004	+	0.942925i	$0.391938\pi$
$348$	−15.0555	−0.807062
$349$	10.6850	0.571953	0.285976	−	0.958237i	$-0.407682\pi$
$349$	10.6850	0.571953	0.285976	+	0.958237i	$0.407682\pi$
$350$	−18.9529	−1.01308
$351$	1.22775	0.0655325
$352$	−5.84697	−0.311644
$353$	0.692406	0.0368531	0.0184265	−	0.999830i	$-0.494134\pi$
$353$	0.692406	0.0368531	0.0184265	+	0.999830i	$0.494134\pi$
$354$	−0.629466	−0.0334557
$355$	4.58483	0.243338
$356$	−6.76040	−0.358301
$357$	−5.46264	−0.289114
$358$	54.1118	2.85990
$359$	22.2052	1.17195	0.585973	−	0.810331i	$-0.300712\pi$
$359$	22.2052	1.17195	0.585973	+	0.810331i	$0.300712\pi$
$360$	2.02918	0.106947
$361$	−3.38811	−0.178322
$362$	−55.7186	−2.92851
$363$	−10.3294	−0.542151
$364$	−7.77376	−0.407456
$365$	−11.6131	−0.607856
$366$	−28.9501	−1.51324
$367$	5.78439	0.301942	0.150971	−	0.988538i	$-0.451760\pi$
$367$	5.78439	0.301942	0.150971	+	0.988538i	$0.451760\pi$
$368$	2.88533	0.150408
$369$	−9.16186	−0.476947
$370$	0.673110	0.0349933
$371$	23.8818	1.23988
$372$	−24.8075	−1.28621
$373$	−1.31553	−0.0681155	−0.0340578	−	0.999420i	$-0.510843\pi$
$373$	−1.31553	−0.0681155	−0.0340578	+	0.999420i	$0.510843\pi$
$374$	4.48588	0.231959
$375$	9.34031	0.482332
$376$	−3.00129	−0.154780
$377$	−6.42829	−0.331074
$378$	4.86204	0.250076
$379$	11.2648	0.578634	0.289317	−	0.957233i	$-0.406572\pi$
$379$	11.2648	0.578634	0.289317	+	0.957233i	$0.406572\pi$
$380$	11.9262	0.611800
$381$	−7.00167	−0.358707
$382$	39.2378	2.00758
$383$	21.1517	1.08080	0.540402	−	0.841407i	$-0.318272\pi$
$383$	21.1517	1.08080	0.540402	+	0.841407i	$0.318272\pi$
$384$	13.9833	0.713580
$385$	−1.89285	−0.0964688
$386$	−15.0264	−0.764822
$387$	4.75211	0.241563
$388$	34.9978	1.77674
$389$	13.8569	0.702573	0.351287	−	0.936268i	$-0.385744\pi$
$389$	13.8569	0.702573	0.351287	+	0.936268i	$0.385744\pi$
$390$	2.84565	0.144095
$391$	−4.82814	−0.244170
$392$	4.15885	0.210054
$393$	1.71527	0.0865239
$394$	−49.6319	−2.50042
$395$	−5.42018	−0.272719
$396$	−2.35482	−0.118334
$397$	12.1815	0.611371	0.305686	−	0.952133i	$-0.401114\pi$
$397$	12.1815	0.611371	0.305686	+	0.952133i	$0.401114\pi$
$398$	2.11117	0.105823
$399$	8.70036	0.435563
$400$	5.77919	0.288960
$401$	−14.6524	−0.731705	−0.365852	−	0.930673i	$-0.619222\pi$
$401$	−14.6524	−0.731705	−0.365852	+	0.930673i	$0.619222\pi$
$402$	−24.3532	−1.21463
$403$	−10.5921	−0.527629
$404$	16.4875	0.820283
$405$	−1.04969	−0.0521596
$406$	−25.4568	−1.26340
$407$	−0.237827	−0.0117886
$408$	−4.79570	−0.237422
$409$	−20.9462	−1.03572	−0.517862	−	0.855464i	$-0.673272\pi$
$409$	−20.9462	−1.03572	−0.517862	+	0.855464i	$0.673272\pi$
$410$	−21.2351	−1.04873
$411$	−2.96528	−0.146267
$412$	19.1551	0.943703
$413$	−0.627730	−0.0308886
$414$	4.29730	0.211201
$415$	−6.90534	−0.338970
$416$	8.76587	0.429782
$417$	1.89874	0.0929818
$418$	−7.14467	−0.349457
$419$	16.1079	0.786925	0.393462	−	0.919341i	$-0.371277\pi$
$419$	16.1079	0.786925	0.393462	+	0.919341i	$0.371277\pi$
$420$	6.64634	0.324308
$421$	−5.63957	−0.274856	−0.137428	−	0.990512i	$-0.543884\pi$
$421$	−5.63957	−0.274856	−0.137428	+	0.990512i	$0.543884\pi$
$422$	26.0345	1.26734
$423$	1.55257	0.0754883
$424$	20.9660	1.01820
$425$	−9.67055	−0.469091
$426$	9.64430	0.467268
$427$	−28.8702	−1.39713
$428$	−21.8362	−1.05549
$429$	−1.00544	−0.0485431
$430$	11.0143	0.531157
$431$	27.4283	1.32117	0.660586	−	0.750750i	$-0.270308\pi$
$431$	27.4283	1.32117	0.660586	+	0.750750i	$0.270308\pi$
$432$	−1.48255	−0.0713292
$433$	34.3404	1.65029	0.825147	−	0.564917i	$-0.191092\pi$
$433$	34.3404	1.65029	0.825147	+	0.564917i	$0.191092\pi$
$434$	−41.9459	−2.01347
$435$	5.49600	0.263513
$436$	2.83309	0.135680
$437$	7.68979	0.367853
$438$	−24.4284	−1.16723
$439$	4.51019	0.215260	0.107630	−	0.994191i	$-0.465674\pi$
$439$	4.51019	0.215260	0.107630	+	0.994191i	$0.465674\pi$
$440$	−1.66175	−0.0792209
$441$	−2.15137	−0.102446
$442$	−6.72531	−0.319890
$443$	−2.44098	−0.115974	−0.0579871	−	0.998317i	$-0.518468\pi$
$443$	−2.44098	−0.115974	−0.0579871	+	0.998317i	$0.518468\pi$
$444$	0.835077	0.0396310
$445$	2.46787	0.116988
$446$	6.89321	0.326403
$447$	−5.82075	−0.275312
$448$	28.1849	1.33161
$449$	9.02011	0.425685	0.212843	−	0.977086i	$-0.431728\pi$
$449$	9.02011	0.425685	0.212843	+	0.977086i	$0.431728\pi$
$450$	8.60731	0.405752
$451$	7.50291	0.353298
$452$	−12.7268	−0.598620
$453$	11.4707	0.538940
$454$	−17.5920	−0.825633
$455$	2.83780	0.133038
$456$	7.63812	0.357688
$457$	−12.5489	−0.587012	−0.293506	−	0.955957i	$-0.594822\pi$
$457$	−12.5489	−0.587012	−0.293506	+	0.955957i	$0.594822\pi$
$458$	−50.0036	−2.33651
$459$	2.48081	0.115794
$460$	5.87435	0.273893
$461$	−25.3624	−1.18125	−0.590623	−	0.806948i	$-0.701118\pi$
$461$	−25.3624	−1.18125	−0.590623	+	0.806948i	$0.701118\pi$
$462$	−3.98166	−0.185244
$463$	−16.3972	−0.762043	−0.381022	−	0.924566i	$-0.624428\pi$
$463$	−16.3972	−0.762043	−0.381022	+	0.924566i	$0.624428\pi$
$464$	7.76237	0.360359
$465$	9.05593	0.419958
$466$	11.4060	0.528372
$467$	−17.0333	−0.788206	−0.394103	−	0.919066i	$-0.628945\pi$
$467$	−17.0333	−0.788206	−0.394103	+	0.919066i	$0.628945\pi$
$468$	3.53038	0.163192
$469$	−24.2861	−1.12143
$470$	3.59849	0.165986
$471$	0.311762	0.0143652
$472$	−0.551089	−0.0253659
$473$	−3.89163	−0.178937
$474$	−11.4015	−0.523687
$475$	15.4023	0.706707
$476$	−15.7078	−0.719964
$477$	−10.8457	−0.496591
$478$	−6.55499	−0.299818
$479$	23.8161	1.08819	0.544093	−	0.839025i	$-0.316874\pi$
$479$	23.8161	1.08819	0.544093	+	0.839025i	$0.316874\pi$
$480$	−7.49457	−0.342079
$481$	0.356554	0.0162575
$482$	−1.80263	−0.0821077
$483$	4.28545	0.194995
$484$	−29.7019	−1.35009
$485$	−12.7759	−0.580123
$486$	−2.20805	−0.100159
$487$	−41.0145	−1.85854	−0.929271	−	0.369398i	$-0.879564\pi$
$487$	−41.0145	−1.85854	−0.929271	+	0.369398i	$0.879564\pi$
$488$	−25.3454	−1.14733
$489$	−4.03433	−0.182439
$490$	−4.98639	−0.225262
$491$	−12.7382	−0.574868	−0.287434	−	0.957800i	$-0.592802\pi$
$491$	−12.7382	−0.574868	−0.287434	+	0.957800i	$0.592802\pi$
$492$	−26.3448	−1.18772
$493$	−12.9891	−0.584999
$494$	10.7114	0.481929
$495$	0.859622	0.0386371
$496$	12.7903	0.574301
$497$	9.61770	0.431413
$498$	−14.5255	−0.650905
$499$	19.1002	0.855042	0.427521	−	0.904005i	$-0.359387\pi$
$499$	19.1002	0.855042	0.427521	+	0.904005i	$0.359387\pi$
$500$	26.8579	1.20112
$501$	−5.21059	−0.232792
$502$	−25.0824	−1.11948
$503$	22.9166	1.02180	0.510899	−	0.859640i	$-0.329312\pi$
$503$	22.9166	1.02180	0.510899	+	0.859640i	$0.329312\pi$
$504$	4.25665	0.189606
$505$	−6.01873	−0.267830
$506$	−3.51918	−0.156447
$507$	−11.4926	−0.510406
$508$	−20.1332	−0.893267
$509$	−27.1612	−1.20390	−0.601950	−	0.798534i	$-0.705609\pi$
$509$	−27.1612	−1.20390	−0.601950	+	0.798534i	$0.705609\pi$
$510$	5.74995	0.254612
$511$	−24.3610	−1.07767
$512$	−16.3170	−0.721115
$513$	−3.95119	−0.174449
$514$	28.1037	1.23960
$515$	−6.99253	−0.308128
$516$	13.6646	0.601551
$517$	−1.27144	−0.0559178
$518$	1.41200	0.0620396
$519$	−19.6564	−0.862820
$520$	2.49133	0.109252
$521$	20.0942	0.880342	0.440171	−	0.897914i	$-0.354918\pi$
$521$	20.0942	0.880342	0.440171	+	0.897914i	$0.354918\pi$
$522$	11.5610	0.506010
$523$	11.3674	0.497063	0.248532	−	0.968624i	$-0.420052\pi$
$523$	11.3674	0.497063	0.248532	+	0.968624i	$0.420052\pi$
$524$	4.93223	0.215466
$525$	8.58357	0.374618
$526$	−15.7617	−0.687243
$527$	−21.4025	−0.932307
$528$	1.21410	0.0528370
$529$	−19.2123	−0.835318
$530$	−25.1379	−1.09192
$531$	0.285078	0.0123713
$532$	25.0178	1.08466
$533$	−11.2485	−0.487226
$534$	5.19123	0.224646
$535$	7.97128	0.344628
$536$	−21.3209	−0.920924
$537$	−24.5066	−1.05754
$538$	−69.0521	−2.97705
$539$	1.76182	0.0758868
$540$	−3.01838	−0.129890
$541$	40.2114	1.72882	0.864411	−	0.502787i	$-0.167692\pi$
$541$	40.2114	1.72882	0.864411	+	0.502787i	$0.167692\pi$
$542$	−52.1991	−2.24214
$543$	25.2343	1.08291
$544$	17.7124	0.759414
$545$	−1.03421	−0.0443009
$546$	5.96937	0.255465
$547$	−42.3251	−1.80969	−0.904846	−	0.425740i	$-0.860014\pi$
$547$	−42.3251	−1.80969	−0.904846	+	0.425740i	$0.860014\pi$
$548$	−8.52664	−0.364240
$549$	13.1111	0.559570
$550$	−7.04876	−0.300560
$551$	20.6877	0.881327
$552$	3.76223	0.160131
$553$	−11.3700	−0.483503
$554$	41.8700	1.77889
$555$	−0.304843	−0.0129399
$556$	5.45981	0.231547
$557$	20.2674	0.858758	0.429379	−	0.903124i	$-0.358733\pi$
$557$	20.2674	0.858758	0.429379	+	0.903124i	$0.358733\pi$
$558$	19.0493	0.806423
$559$	5.83440	0.246769
$560$	−3.42673	−0.144806
$561$	−2.03160	−0.0857743
$562$	46.1896	1.94839
$563$	18.9543	0.798828	0.399414	−	0.916771i	$-0.369214\pi$
$563$	18.9543	0.798828	0.399414	+	0.916771i	$0.369214\pi$
$564$	4.46438	0.187984
$565$	4.64591	0.195455
$566$	−30.7486	−1.29246
$567$	−2.20196	−0.0924736
$568$	8.44346	0.354280
$569$	−6.22158	−0.260822	−0.130411	−	0.991460i	$-0.541630\pi$
$569$	−6.22158	−0.260822	−0.130411	+	0.991460i	$0.541630\pi$
$570$	−9.15796	−0.383585
$571$	20.7978	0.870359	0.435180	−	0.900344i	$-0.356685\pi$
$571$	20.7978	0.870359	0.435180	+	0.900344i	$0.356685\pi$
$572$	−2.89113	−0.120884
$573$	−17.7703	−0.742367
$574$	−44.5453	−1.85929
$575$	7.58657	0.316382
$576$	−12.7999	−0.533329
$577$	9.17102	0.381795	0.190897	−	0.981610i	$-0.438860\pi$
$577$	9.17102	0.381795	0.190897	+	0.981610i	$0.438860\pi$
$578$	23.9476	0.996090
$579$	6.80526	0.282817
$580$	15.8037	0.656212
$581$	−14.4855	−0.600959
$582$	−26.8744	−1.11398
$583$	8.88185	0.367849
$584$	−21.3867	−0.884988
$585$	−1.28876	−0.0532836
$586$	33.3908	1.37936
$587$	33.7394	1.39257	0.696287	−	0.717764i	$-0.254834\pi$
$587$	33.7394	1.39257	0.696287	+	0.717764i	$0.254834\pi$
$588$	−6.18624	−0.255116
$589$	34.0878	1.40456
$590$	0.660745	0.0272024
$591$	22.4777	0.924608
$592$	−0.430550	−0.0176955
$593$	8.04183	0.330238	0.165119	−	0.986274i	$-0.447199\pi$
$593$	8.04183	0.330238	0.165119	+	0.986274i	$0.447199\pi$
$594$	1.80823	0.0741928
$595$	5.73409	0.235075
$596$	−16.7375	−0.685595
$597$	−0.956123	−0.0391315
$598$	5.27601	0.215752
$599$	−25.3509	−1.03581	−0.517904	−	0.855438i	$-0.673288\pi$
$599$	−25.3509	−1.03581	−0.517904	+	0.855438i	$0.673288\pi$
$600$	7.53558	0.307639
$601$	6.78210	0.276648	0.138324	−	0.990387i	$-0.455829\pi$
$601$	6.78210	0.276648	0.138324	+	0.990387i	$0.455829\pi$
$602$	23.1049	0.941686
$603$	11.0293	0.449148
$604$	32.9838	1.34209
$605$	10.8426	0.440816
$606$	−12.6605	−0.514299
$607$	−8.55682	−0.347311	−0.173655	−	0.984807i	$-0.555558\pi$
$607$	−8.55682	−0.347311	−0.173655	+	0.984807i	$0.555558\pi$
$608$	−28.2106	−1.14409
$609$	11.5291	0.467182
$610$	30.3886	1.23040
$611$	1.90616	0.0771151
$612$	7.13353	0.288356
$613$	30.8097	1.24439	0.622195	−	0.782862i	$-0.286241\pi$
$613$	30.8097	1.24439	0.622195	+	0.782862i	$0.286241\pi$
$614$	−12.5097	−0.504850
$615$	9.61713	0.387800
$616$	−3.48589	−0.140451
$617$	−8.23384	−0.331482	−0.165741	−	0.986169i	$-0.553002\pi$
$617$	−8.23384	−0.331482	−0.165741	+	0.986169i	$0.553002\pi$
$618$	−14.7089	−0.591680
$619$	2.18235	0.0877159	0.0438580	−	0.999038i	$-0.486035\pi$
$619$	2.18235	0.0877159	0.0438580	+	0.999038i	$0.486035\pi$
$620$	26.0402	1.04580
$621$	−1.94620	−0.0780982
$622$	−58.7033	−2.35379
$623$	5.17691	0.207408
$624$	−1.82020	−0.0728663
$625$	9.68629	0.387451
$626$	−21.3390	−0.852876
$627$	3.23574	0.129223
$628$	0.896467	0.0357729
$629$	0.720457	0.0287265
$630$	−5.10364	−0.203334
$631$	0.802581	0.0319503	0.0159751	−	0.999872i	$-0.494915\pi$
$631$	0.802581	0.0319503	0.0159751	+	0.999872i	$0.494915\pi$
$632$	−9.98185	−0.397057
$633$	−11.7907	−0.468638
$634$	−22.7137	−0.902075
$635$	7.34960	0.291660
$636$	−31.1867	−1.23663
$637$	−2.64134	−0.104654
$638$	−9.46760	−0.374826
$639$	−4.36779	−0.172787
$640$	−14.6781	−0.580203
$641$	−34.7471	−1.37243	−0.686214	−	0.727400i	$-0.740729\pi$
$641$	−34.7471	−1.37243	−0.686214	+	0.727400i	$0.740729\pi$
$642$	16.7678	0.661771
$643$	−31.4640	−1.24082	−0.620409	−	0.784278i	$-0.713034\pi$
$643$	−31.4640	−1.24082	−0.620409	+	0.784278i	$0.713034\pi$
$644$	12.3228	0.485585
$645$	−4.98825	−0.196412
$646$	21.6436	0.851557
$647$	20.0837	0.789571	0.394786	−	0.918773i	$-0.370819\pi$
$647$	20.0837	0.789571	0.394786	+	0.918773i	$0.370819\pi$
$648$	−1.93312	−0.0759401
$649$	−0.233458	−0.00916403
$650$	10.5676	0.414496
$651$	18.9968	0.744543
$652$	−11.6007	−0.454317
$653$	23.5597	0.921963	0.460982	−	0.887410i	$-0.347497\pi$
$653$	23.5597	0.921963	0.460982	+	0.887410i	$0.347497\pi$
$654$	−2.17549	−0.0850686
$655$	−1.80050	−0.0703515
$656$	13.5829	0.530323
$657$	11.0633	0.431621
$658$	7.54864	0.294276
$659$	−25.0196	−0.974627	−0.487314	−	0.873227i	$-0.662023\pi$
$659$	−25.0196	−0.974627	−0.487314	+	0.873227i	$0.662023\pi$
$660$	2.47183	0.0962159
$661$	35.9571	1.39857	0.699284	−	0.714844i	$-0.253502\pi$
$661$	35.9571	1.39857	0.699284	+	0.714844i	$0.253502\pi$
$662$	2.99423	0.116374
$663$	3.04581	0.118290
$664$	−12.7169	−0.493512
$665$	−9.13270	−0.354151
$666$	−0.641245	−0.0248477
$667$	10.1900	0.394557
$668$	−14.9830	−0.579709
$669$	−3.12185	−0.120698
$670$	25.5634	0.987600
$671$	−10.7371	−0.414500
$672$	−15.7215	−0.606471
$673$	2.27100	0.0875407	0.0437704	−	0.999042i	$-0.486063\pi$
$673$	2.27100	0.0875407	0.0437704	+	0.999042i	$0.486063\pi$
$674$	58.3861	2.24895
$675$	−3.89815	−0.150040
$676$	−33.0469	−1.27103
$677$	−37.3599	−1.43586	−0.717929	−	0.696117i	$-0.754910\pi$
$677$	−37.3599	−1.43586	−0.717929	+	0.696117i	$0.754910\pi$
$678$	9.77277	0.375321
$679$	−26.8002	−1.02850
$680$	5.03400	0.193045
$681$	7.96720	0.305304
$682$	−15.6000	−0.597356
$683$	−34.4535	−1.31833	−0.659163	−	0.752000i	$-0.729089\pi$
$683$	−34.4535	−1.31833	−0.659163	+	0.752000i	$0.729089\pi$
$684$	−11.3616	−0.434421
$685$	3.11264	0.118928
$686$	−44.4943	−1.69880
$687$	22.6460	0.864000
$688$	−7.04523	−0.268597
$689$	−13.3158	−0.507292
$690$	−4.51084	−0.171725
$691$	35.7401	1.35962	0.679808	−	0.733390i	$-0.262063\pi$
$691$	35.7401	1.35962	0.679808	+	0.733390i	$0.262063\pi$
$692$	−56.5217	−2.14863
$693$	1.80325	0.0684997
$694$	−27.3939	−1.03986
$695$	−1.99309	−0.0756024
$696$	10.1215	0.383654
$697$	−22.7288	−0.860915
$698$	−23.5929	−0.893006
$699$	−5.16564	−0.195382
$700$	24.6819	0.932889
$701$	28.9272	1.09257	0.546283	−	0.837601i	$-0.316042\pi$
$701$	28.9272	1.09257	0.546283	+	0.837601i	$0.316042\pi$
$702$	−2.71093	−0.102318
$703$	−1.14747	−0.0432778
$704$	10.4822	0.395063
$705$	−1.62972	−0.0613786
$706$	−1.52887	−0.0575397
$707$	−12.6256	−0.474835
$708$	0.819737	0.0308076
$709$	16.4528	0.617899	0.308950	−	0.951078i	$-0.400023\pi$
$709$	16.4528	0.617899	0.308950	+	0.951078i	$0.400023\pi$
$710$	−10.1235	−0.379930
$711$	5.16360	0.193650
$712$	4.54485	0.170326
$713$	16.7903	0.628801
$714$	12.0618	0.451401
$715$	1.05540	0.0394698
$716$	−70.4684	−2.63353
$717$	2.96868	0.110867
$718$	−49.0302	−1.82979
$719$	−12.8572	−0.479492	−0.239746	−	0.970836i	$-0.577064\pi$
$719$	−12.8572	−0.479492	−0.239746	+	0.970836i	$0.577064\pi$
$720$	1.55622	0.0579969
$721$	−14.6684	−0.546279
$722$	7.48112	0.278418
$723$	0.816392	0.0303619
$724$	72.5609	2.69671
$725$	20.4100	0.758009
$726$	22.8077	0.846475
$727$	36.0825	1.33823	0.669113	−	0.743161i	$-0.266674\pi$
$727$	36.0825	1.33823	0.669113	+	0.743161i	$0.266674\pi$
$728$	5.22611	0.193692
$729$	1.00000	0.0370370
$730$	25.6422	0.949062
$731$	11.7891	0.436034
$732$	37.7009	1.39347
$733$	−14.7320	−0.544140	−0.272070	−	0.962277i	$-0.587708\pi$
$733$	−14.7320	−0.544140	−0.272070	+	0.962277i	$0.587708\pi$
$734$	−12.7722	−0.471431
$735$	2.25828	0.0832977
$736$	−13.8954	−0.512192
$737$	−9.03220	−0.332705
$738$	20.2299	0.744671
$739$	49.4179	1.81787	0.908933	−	0.416941i	$-0.136898\pi$
$739$	49.4179	1.81787	0.908933	+	0.416941i	$0.136898\pi$
$740$	−0.876573	−0.0322235
$741$	−4.85107	−0.178209
$742$	−52.7323	−1.93586
$743$	21.2861	0.780912	0.390456	−	0.920622i	$-0.372317\pi$
$743$	21.2861	0.780912	0.390456	+	0.920622i	$0.372317\pi$
$744$	16.6775	0.611425
$745$	6.11000	0.223853
$746$	2.90476	0.106351
$747$	6.57845	0.240693
$748$	−5.84185	−0.213599
$749$	16.7215	0.610991
$750$	−20.6239	−0.753078
$751$	26.7550	0.976304	0.488152	−	0.872759i	$-0.337671\pi$
$751$	26.7550	0.976304	0.488152	+	0.872759i	$0.337671\pi$
$752$	−2.30175	−0.0839363
$753$	11.3595	0.413965
$754$	14.1940	0.516914
$755$	−12.0407	−0.438206
$756$	−6.33171	−0.230282
$757$	32.3235	1.17482	0.587408	−	0.809291i	$-0.300148\pi$
$757$	32.3235	1.17482	0.587408	+	0.809291i	$0.300148\pi$
$758$	−24.8733	−0.903437
$759$	1.59380	0.0578511
$760$	−8.01767	−0.290831
$761$	−2.75300	−0.0997961	−0.0498981	−	0.998754i	$-0.515890\pi$
$761$	−2.75300	−0.0997961	−0.0498981	+	0.998754i	$0.515890\pi$
$762$	15.4600	0.560058
$763$	−2.16949	−0.0785410
$764$	−51.0984	−1.84868
$765$	−2.60408	−0.0941508
$766$	−46.7041	−1.68749
$767$	0.350004	0.0126379
$768$	−5.27595	−0.190379
$769$	4.89637	0.176568	0.0882839	−	0.996095i	$-0.471862\pi$
$769$	4.89637	0.176568	0.0882839	+	0.996095i	$0.471862\pi$
$770$	4.17952	0.150619
$771$	−12.7278	−0.458381
$772$	19.5684	0.704284
$773$	−5.09233	−0.183158	−0.0915791	−	0.995798i	$-0.529191\pi$
$773$	−5.09233	−0.183158	−0.0915791	+	0.995798i	$0.529191\pi$
$774$	−10.4929	−0.377159
$775$	33.6302	1.20803
$776$	−23.5282	−0.844611
$777$	−0.639476	−0.0229411
$778$	−30.5968	−1.09695
$779$	36.2002	1.29701
$780$	−3.70581	−0.132689
$781$	3.57691	0.127992
$782$	10.6608	0.381229
$783$	−5.23583	−0.187113
$784$	3.18951	0.113911
$785$	−0.327254	−0.0116802
$786$	−3.78740	−0.135092
$787$	5.23593	0.186641	0.0933205	−	0.995636i	$-0.470252\pi$
$787$	5.23593	0.186641	0.0933205	+	0.995636i	$0.470252\pi$
$788$	64.6343	2.30250
$789$	7.13829	0.254130
$790$	11.9680	0.425804
$791$	9.74582	0.346521
$792$	1.58309	0.0562525
$793$	16.0972	0.571628
$794$	−26.8973	−0.954551
$795$	11.3846	0.403772
$796$	−2.74932	−0.0974470
$797$	1.92654	0.0682415	0.0341208	−	0.999418i	$-0.489137\pi$
$797$	1.92654	0.0682415	0.0341208	+	0.999418i	$0.489137\pi$
$798$	−19.2108	−0.680056
$799$	3.85162	0.136260
$800$	−27.8319	−0.984007
$801$	−2.35105	−0.0830701
$802$	32.3532	1.14243
$803$	−9.06006	−0.319722
$804$	31.7146	1.11849
$805$	−4.49840	−0.158548
$806$	23.3878	0.823801
$807$	31.2729	1.10086
$808$	−11.0841	−0.389938
$809$	10.1213	0.355848	0.177924	−	0.984044i	$-0.443062\pi$
$809$	10.1213	0.355848	0.177924	+	0.984044i	$0.443062\pi$
$810$	2.31777	0.0814382
$811$	12.3333	0.433079	0.216540	−	0.976274i	$-0.430523\pi$
$811$	12.3333	0.433079	0.216540	+	0.976274i	$0.430523\pi$
$812$	33.1517	1.16340
$813$	23.6403	0.829103
$814$	0.525134	0.0184059
$815$	4.23480	0.148339
$816$	−3.67792	−0.128753
$817$	−18.7765	−0.656905
$818$	46.2503	1.61710
$819$	−2.70346	−0.0944664
$820$	27.6539	0.965717
$821$	−25.1837	−0.878918	−0.439459	−	0.898263i	$-0.644830\pi$
$821$	−25.1837	−0.878918	−0.439459	+	0.898263i	$0.644830\pi$
$822$	6.54750	0.228370
$823$	28.1525	0.981336	0.490668	−	0.871347i	$-0.336753\pi$
$823$	28.1525	0.981336	0.490668	+	0.871347i	$0.336753\pi$
$824$	−12.8775	−0.448609
$825$	3.19230	0.111142
$826$	1.38606	0.0482272
$827$	9.00515	0.313140	0.156570	−	0.987667i	$-0.449956\pi$
$827$	9.00515	0.313140	0.156570	+	0.987667i	$0.449956\pi$
$828$	−5.59627	−0.194484
$829$	−13.0101	−0.451860	−0.225930	−	0.974144i	$-0.572542\pi$
$829$	−13.0101	−0.451860	−0.225930	+	0.974144i	$0.572542\pi$
$830$	15.2473	0.529243
$831$	−18.9624	−0.657800
$832$	−15.7151	−0.544822
$833$	−5.33714	−0.184921
$834$	−4.19252	−0.145175
$835$	5.46952	0.189280
$836$	9.30432	0.321797
$837$	−8.62722	−0.298200
$838$	−35.5672	−1.22865
$839$	1.77757	0.0613686	0.0306843	−	0.999529i	$-0.490231\pi$
$839$	1.77757	0.0613686	0.0306843	+	0.999529i	$0.490231\pi$
$840$	−4.46817	−0.154167
$841$	−1.58613	−0.0546942
$842$	12.4525	0.429140
$843$	−20.9187	−0.720480
$844$	−33.9040	−1.16702
$845$	12.0637	0.415005
$846$	−3.42814	−0.117862
$847$	22.7448	0.781522
$848$	16.0793	0.552165
$849$	13.9257	0.477928
$850$	21.3531	0.732404
$851$	−0.565200	−0.0193748
$852$	−12.5595	−0.430282
$853$	−21.2891	−0.728926	−0.364463	−	0.931218i	$-0.618747\pi$
$853$	−21.2891	−0.728926	−0.364463	+	0.931218i	$0.618747\pi$
$854$	63.7469	2.18137
$855$	4.14753	0.141843
$856$	14.6800	0.501751
$857$	−33.5282	−1.14530	−0.572650	−	0.819800i	$-0.694085\pi$
$857$	−33.5282	−1.14530	−0.572650	+	0.819800i	$0.694085\pi$
$858$	2.22006	0.0757916
$859$	1.11715	0.0381167	0.0190583	−	0.999818i	$-0.493933\pi$
$859$	1.11715	0.0381167	0.0190583	+	0.999818i	$0.493933\pi$
$860$	−14.3436	−0.489114
$861$	20.1741	0.687530
$862$	−60.5630	−2.06278
$863$	4.06897	0.138509	0.0692547	−	0.997599i	$-0.477938\pi$
$863$	4.06897	0.138509	0.0692547	+	0.997599i	$0.477938\pi$
$864$	7.13978	0.242900
$865$	20.6332	0.701549
$866$	−75.8254	−2.57665
$867$	−10.8456	−0.368336
$868$	54.6251	1.85410
$869$	−4.22861	−0.143446
$870$	−12.1355	−0.411430
$871$	13.5412	0.458827
$872$	−1.90462	−0.0644985
$873$	12.1711	0.411929
$874$	−16.9795	−0.574339
$875$	−20.5670	−0.695291
$876$	31.8124	1.07484
$877$	−31.3788	−1.05959	−0.529793	−	0.848127i	$-0.677730\pi$
$877$	−31.3788	−1.05959	−0.529793	+	0.848127i	$0.677730\pi$
$878$	−9.95874	−0.336091
$879$	−15.1223	−0.510063
$880$	−1.27443	−0.0429611
$881$	−20.1866	−0.680105	−0.340052	−	0.940407i	$-0.610445\pi$
$881$	−20.1866	−0.680105	−0.340052	+	0.940407i	$0.610445\pi$
$882$	4.75033	0.159952
$883$	−28.0604	−0.944308	−0.472154	−	0.881516i	$-0.656523\pi$
$883$	−28.0604	−0.944308	−0.472154	+	0.881516i	$0.656523\pi$
$884$	8.75819	0.294570
$885$	−0.299244	−0.0100590
$886$	5.38980	0.181074
$887$	−38.1961	−1.28250	−0.641251	−	0.767332i	$-0.721584\pi$
$887$	−38.1961	−1.28250	−0.641251	+	0.767332i	$0.721584\pi$
$888$	−0.561402	−0.0188394
$889$	15.4174	0.517083
$890$	−5.44919	−0.182657
$891$	−0.818928	−0.0274351
$892$	−8.97685	−0.300567
$893$	−6.13448	−0.205283
$894$	12.8525	0.429853
$895$	25.7244	0.859871
$896$	−30.7906	−1.02864
$897$	−2.38944	−0.0797812
$898$	−19.9169	−0.664634
$899$	45.1706	1.50652
$900$	−11.2091	−0.373636
$901$	−26.9061	−0.896373
$902$	−16.5668	−0.551614
$903$	−10.4639	−0.348218
$904$	8.55593	0.284566
$905$	−26.4882	−0.880499
$906$	−25.3279	−0.841462
$907$	18.8143	0.624718	0.312359	−	0.949964i	$-0.398881\pi$
$907$	18.8143	0.624718	0.312359	+	0.949964i	$0.398881\pi$
$908$	22.9096	0.760281
$909$	5.73381	0.190178
$910$	−6.26600	−0.207716
$911$	43.6593	1.44650	0.723248	−	0.690589i	$-0.242648\pi$
$911$	43.6593	1.44650	0.723248	+	0.690589i	$0.242648\pi$
$912$	5.85783	0.193972
$913$	−5.38727	−0.178293
$914$	27.7086	0.916518
$915$	−13.7627	−0.454979
$916$	65.1184	2.15157
$917$	−3.77695	−0.124726
$918$	−5.47775	−0.180793
$919$	−10.1179	−0.333758	−0.166879	−	0.985977i	$-0.553369\pi$
$919$	−10.1179	−0.333758	−0.166879	+	0.985977i	$0.553369\pi$
$920$	−3.94918	−0.130201
$921$	5.66549	0.186684
$922$	56.0015	1.84431
$923$	−5.36255	−0.176511
$924$	5.18521	0.170581
$925$	−1.13207	−0.0372222
$926$	36.2059	1.18980
$927$	6.66151	0.218793
$928$	−37.3826	−1.22715
$929$	1.03079	0.0338192	0.0169096	−	0.999857i	$-0.494617\pi$
$929$	1.03079	0.0338192	0.0169096	+	0.999857i	$0.494617\pi$
$930$	−19.9959	−0.655693
$931$	8.50047	0.278592
$932$	−14.8537	−0.486550
$933$	26.5860	0.870387
$934$	37.6103	1.23065
$935$	2.13256	0.0697421
$936$	−2.37339	−0.0775766
$937$	38.2676	1.25015	0.625074	−	0.780566i	$-0.285069\pi$
$937$	38.2676	1.25015	0.625074	+	0.780566i	$0.285069\pi$
$938$	53.6249	1.75091
$939$	9.66416	0.315378
$940$	−4.68622	−0.152848
$941$	−45.7606	−1.49175	−0.745877	−	0.666084i	$-0.767969\pi$
$941$	−45.7606	−1.49175	−0.745877	+	0.666084i	$0.767969\pi$
$942$	−0.688386	−0.0224288
$943$	17.8308	0.580651
$944$	−0.422642	−0.0137558
$945$	2.31138	0.0751892
$946$	8.59292	0.279380
$947$	42.9987	1.39727	0.698636	−	0.715478i	$-0.253791\pi$
$947$	42.9987	1.39727	0.698636	+	0.715478i	$0.253791\pi$
$948$	14.8479	0.482236
$949$	13.5830	0.440922
$950$	−34.0091	−1.10340
$951$	10.2868	0.333571
$952$	10.5599	0.342249
$953$	11.3900	0.368958	0.184479	−	0.982836i	$-0.440940\pi$
$953$	11.3900	0.368958	0.184479	+	0.982836i	$0.440940\pi$
$954$	23.9479	0.775341
$955$	18.6534	0.603609
$956$	8.53639	0.276087
$957$	4.28776	0.138604
$958$	−52.5871	−1.69901
$959$	6.52944	0.210847
$960$	13.4359	0.433643
$961$	43.4290	1.40093
$962$	−0.787289	−0.0253832
$963$	−7.59392	−0.244711
$964$	2.34752	0.0756086
$965$	−7.14343	−0.229955
$966$	−9.46249	−0.304451
$967$	−20.8006	−0.668902	−0.334451	−	0.942413i	$-0.608551\pi$
$967$	−20.8006	−0.668902	−0.334451	+	0.942413i	$0.608551\pi$
$968$	19.9679	0.641792
$969$	−9.80214	−0.314890
$970$	28.2098	0.905762
$971$	24.0738	0.772566	0.386283	−	0.922380i	$-0.373759\pi$
$971$	24.0738	0.772566	0.386283	+	0.922380i	$0.373759\pi$
$972$	2.87549	0.0922313
$973$	−4.18095	−0.134035
$974$	90.5620	2.90179
$975$	−4.78595	−0.153273
$976$	−19.4379	−0.622192
$977$	18.7993	0.601444	0.300722	−	0.953712i	$-0.402772\pi$
$977$	18.7993	0.601444	0.300722	+	0.953712i	$0.402772\pi$
$978$	8.90800	0.284846
$979$	1.92534	0.0615340
$980$	6.49364	0.207432
$981$	0.985256	0.0314568
$982$	28.1266	0.897557
$983$	48.5887	1.54974	0.774869	−	0.632122i	$-0.217816\pi$
$983$	48.5887	1.54974	0.774869	+	0.632122i	$0.217816\pi$
$984$	17.7110	0.564605
$985$	−23.5946	−0.751788
$986$	28.6805	0.913374
$987$	−3.41869	−0.108818
$988$	−13.9492	−0.443783
$989$	−9.24854	−0.294086
$990$	−1.89809	−0.0603252
$991$	−4.23582	−0.134555	−0.0672776	−	0.997734i	$-0.521431\pi$
$991$	−4.23582	−0.134555	−0.0672776	+	0.997734i	$0.521431\pi$
$992$	−61.5965	−1.95569
$993$	−1.35605	−0.0430330
$994$	−21.2364	−0.673577
$995$	1.00363	0.0318173
$996$	18.9162	0.599384
$997$	−37.7993	−1.19712	−0.598558	−	0.801080i	$-0.704259\pi$
$997$	−37.7993	−1.19712	−0.598558	+	0.801080i	$0.704259\pi$
$998$	−42.1742	−1.33500
$999$	0.290412	0.00918824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.d.1.18	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.d.1.18	✓	129	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20805 q^{2} +1.00000 q^{3} +2.87549 q^{4} -1.04969 q^{5} -2.20805 q^{6} -2.20196 q^{7} -1.93312 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.20805 q^{2} +1.00000 q^{3} +2.87549 q^{4} -1.04969 q^{5} -2.20805 q^{6} -2.20196 q^{7} -1.93312 q^{8} +1.00000 q^{9} +2.31777 q^{10} -0.818928 q^{11} +2.87549 q^{12} +1.22775 q^{13} +4.86204 q^{14} -1.04969 q^{15} -1.48255 q^{16} +2.48081 q^{17} -2.20805 q^{18} -3.95119 q^{19} -3.01838 q^{20} -2.20196 q^{21} +1.80823 q^{22} -1.94620 q^{23} -1.93312 q^{24} -3.89815 q^{25} -2.71093 q^{26} +1.00000 q^{27} -6.33171 q^{28} -5.23583 q^{29} +2.31777 q^{30} -8.62722 q^{31} +7.13978 q^{32} -0.818928 q^{33} -5.47775 q^{34} +2.31138 q^{35} +2.87549 q^{36} +0.290412 q^{37} +8.72442 q^{38} +1.22775 q^{39} +2.02918 q^{40} -9.16186 q^{41} +4.86204 q^{42} +4.75211 q^{43} -2.35482 q^{44} -1.04969 q^{45} +4.29730 q^{46} +1.55257 q^{47} -1.48255 q^{48} -2.15137 q^{49} +8.60731 q^{50} +2.48081 q^{51} +3.53038 q^{52} -10.8457 q^{53} -2.20805 q^{54} +0.859622 q^{55} +4.25665 q^{56} -3.95119 q^{57} +11.5610 q^{58} +0.285078 q^{59} -3.01838 q^{60} +13.1111 q^{61} +19.0493 q^{62} -2.20196 q^{63} -12.7999 q^{64} -1.28876 q^{65} +1.80823 q^{66} +11.0293 q^{67} +7.13353 q^{68} -1.94620 q^{69} -5.10364 q^{70} -4.36779 q^{71} -1.93312 q^{72} +11.0633 q^{73} -0.641245 q^{74} -3.89815 q^{75} -11.3616 q^{76} +1.80325 q^{77} -2.71093 q^{78} +5.16360 q^{79} +1.55622 q^{80} +1.00000 q^{81} +20.2299 q^{82} +6.57845 q^{83} -6.33171 q^{84} -2.60408 q^{85} -10.4929 q^{86} -5.23583 q^{87} +1.58309 q^{88} -2.35105 q^{89} +2.31777 q^{90} -2.70346 q^{91} -5.59627 q^{92} -8.62722 q^{93} -3.42814 q^{94} +4.14753 q^{95} +7.13978 q^{96} +12.1711 q^{97} +4.75033 q^{98} -0.818928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * q^99

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