LMFDB - Embedded newform 8033.2.a.d.1.10

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:	$168$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.52738 q^{2} -1.64022 q^{3} +4.38763 q^{4} +1.90507 q^{5} +4.14544 q^{6} -1.36071 q^{7} -6.03443 q^{8} -0.309688 q^{9} +O(q^{10})$	\(q-2.52738 q^{2} -1.64022 q^{3} +4.38763 q^{4} +1.90507 q^{5} +4.14544 q^{6} -1.36071 q^{7} -6.03443 q^{8} -0.309688 q^{9} -4.81483 q^{10} +3.85055 q^{11} -7.19666 q^{12} +2.26492 q^{13} +3.43902 q^{14} -3.12473 q^{15} +6.47602 q^{16} -1.41342 q^{17} +0.782698 q^{18} -1.27377 q^{19} +8.35874 q^{20} +2.23185 q^{21} -9.73179 q^{22} +3.51082 q^{23} +9.89777 q^{24} -1.37070 q^{25} -5.72430 q^{26} +5.42861 q^{27} -5.97027 q^{28} +1.00000 q^{29} +7.89737 q^{30} -5.84809 q^{31} -4.29846 q^{32} -6.31574 q^{33} +3.57224 q^{34} -2.59224 q^{35} -1.35880 q^{36} +1.18449 q^{37} +3.21929 q^{38} -3.71496 q^{39} -11.4960 q^{40} +8.78516 q^{41} -5.64073 q^{42} +3.91961 q^{43} +16.8948 q^{44} -0.589978 q^{45} -8.87317 q^{46} -0.0758263 q^{47} -10.6221 q^{48} -5.14848 q^{49} +3.46428 q^{50} +2.31831 q^{51} +9.93762 q^{52} -1.09529 q^{53} -13.7201 q^{54} +7.33558 q^{55} +8.21109 q^{56} +2.08925 q^{57} -2.52738 q^{58} +2.14637 q^{59} -13.7101 q^{60} -4.40254 q^{61} +14.7803 q^{62} +0.421395 q^{63} -2.08820 q^{64} +4.31483 q^{65} +15.9622 q^{66} +12.6300 q^{67} -6.20156 q^{68} -5.75851 q^{69} +6.55157 q^{70} -7.57012 q^{71} +1.86879 q^{72} +4.11424 q^{73} -2.99364 q^{74} +2.24825 q^{75} -5.58882 q^{76} -5.23947 q^{77} +9.38909 q^{78} -3.96657 q^{79} +12.3373 q^{80} -7.97503 q^{81} -22.2034 q^{82} -11.4408 q^{83} +9.79254 q^{84} -2.69266 q^{85} -9.90633 q^{86} -1.64022 q^{87} -23.2359 q^{88} +10.6424 q^{89} +1.49110 q^{90} -3.08189 q^{91} +15.4042 q^{92} +9.59214 q^{93} +0.191642 q^{94} -2.42662 q^{95} +7.05041 q^{96} +18.0801 q^{97} +13.0121 q^{98} -1.19247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) $ 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * 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 $

$2$	−2.52738	−1.78712	−0.893562	−	0.448939i	$-0.851802\pi$
$2$	−2.52738	−1.78712	−0.893562	+	0.448939i	$0.851802\pi$
$3$	−1.64022	−0.946980	−0.473490	−	0.880799i	$-0.657006\pi$
$3$	−1.64022	−0.946980	−0.473490	+	0.880799i	$0.657006\pi$
$4$	4.38763	2.19381
$5$	1.90507	0.851974	0.425987	−	0.904729i	$-0.359927\pi$
$5$	1.90507	0.851974	0.425987	+	0.904729i	$0.359927\pi$
$6$	4.14544	1.69237
$7$	−1.36071	−0.514299	−0.257149	−	0.966372i	$-0.582783\pi$
$7$	−1.36071	−0.514299	−0.257149	+	0.966372i	$0.582783\pi$
$8$	−6.03443	−2.13349
$9$	−0.309688	−0.103229
$10$	−4.81483	−1.52258
$11$	3.85055	1.16099	0.580493	−	0.814266i	$-0.302860\pi$
$11$	3.85055	1.16099	0.580493	+	0.814266i	$0.302860\pi$
$12$	−7.19666	−2.07750
$13$	2.26492	0.628175	0.314088	−	0.949394i	$-0.398301\pi$
$13$	2.26492	0.628175	0.314088	+	0.949394i	$0.398301\pi$
$14$	3.43902	0.919116
$15$	−3.12473	−0.806802
$16$	6.47602	1.61900
$17$	−1.41342	−0.342804	−0.171402	−	0.985201i	$-0.554830\pi$
$17$	−1.41342	−0.342804	−0.171402	+	0.985201i	$0.554830\pi$
$18$	0.782698	0.184484
$19$	−1.27377	−0.292222	−0.146111	−	0.989268i	$-0.546676\pi$
$19$	−1.27377	−0.292222	−0.146111	+	0.989268i	$0.546676\pi$
$20$	8.35874	1.86907
$21$	2.23185	0.487030
$22$	−9.73179	−2.07482
$23$	3.51082	0.732058	0.366029	−	0.930604i	$-0.380717\pi$
$23$	3.51082	0.732058	0.366029	+	0.930604i	$0.380717\pi$
$24$	9.89777	2.02037
$25$	−1.37070	−0.274141
$26$	−5.72430	−1.12263
$27$	5.42861	1.04474
$28$	−5.97027	−1.12828
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	7.89737	1.44186
$31$	−5.84809	−1.05035	−0.525174	−	0.850995i	$-0.676000\pi$
$31$	−5.84809	−1.05035	−0.525174	+	0.850995i	$0.676000\pi$
$32$	−4.29846	−0.759868
$33$	−6.31574	−1.09943
$34$	3.57224	0.612634
$35$	−2.59224	−0.438169
$36$	−1.35880	−0.226466
$37$	1.18449	0.194728	0.0973641	−	0.995249i	$-0.468959\pi$
$37$	1.18449	0.194728	0.0973641	+	0.995249i	$0.468959\pi$
$38$	3.21929	0.522238
$39$	−3.71496	−0.594869
$40$	−11.4960	−1.81768
$41$	8.78516	1.37201	0.686006	−	0.727596i	$-0.259362\pi$
$41$	8.78516	1.37201	0.686006	+	0.727596i	$0.259362\pi$
$42$	−5.64073	−0.870384
$43$	3.91961	0.597735	0.298868	−	0.954295i	$-0.403391\pi$
$43$	3.91961	0.597735	0.298868	+	0.954295i	$0.403391\pi$
$44$	16.8948	2.54698
$45$	−0.589978	−0.0879487
$46$	−8.87317	−1.30828
$47$	−0.0758263	−0.0110604	−0.00553020	−	0.999985i	$-0.501760\pi$
$47$	−0.0758263	−0.0110604	−0.00553020	+	0.999985i	$0.501760\pi$
$48$	−10.6221	−1.53316
$49$	−5.14848	−0.735497
$50$	3.46428	0.489924
$51$	2.31831	0.324629
$52$	9.93762	1.37810
$53$	−1.09529	−0.150450	−0.0752249	−	0.997167i	$-0.523967\pi$
$53$	−1.09529	−0.150450	−0.0752249	+	0.997167i	$0.523967\pi$
$54$	−13.7201	−1.86707
$55$	7.33558	0.989129
$56$	8.21109	1.09725
$57$	2.08925	0.276729
$58$	−2.52738	−0.331861
$59$	2.14637	0.279434	0.139717	−	0.990191i	$-0.455381\pi$
$59$	2.14637	0.279434	0.139717	+	0.990191i	$0.455381\pi$
$60$	−13.7101	−1.76997
$61$	−4.40254	−0.563687	−0.281844	−	0.959460i	$-0.590946\pi$
$61$	−4.40254	−0.563687	−0.281844	+	0.959460i	$0.590946\pi$
$62$	14.7803	1.87710
$63$	0.421395	0.0530907
$64$	−2.08820	−0.261025
$65$	4.31483	0.535189
$66$	15.9622	1.96482
$67$	12.6300	1.54300	0.771500	−	0.636229i	$-0.219507\pi$
$67$	12.6300	1.54300	0.771500	+	0.636229i	$0.219507\pi$
$68$	−6.20156	−0.752049
$69$	−5.75851	−0.693244
$70$	6.55157	0.783062
$71$	−7.57012	−0.898408	−0.449204	−	0.893429i	$-0.648292\pi$
$71$	−7.57012	−0.898408	−0.449204	+	0.893429i	$0.648292\pi$
$72$	1.86879	0.220239
$73$	4.11424	0.481535	0.240768	−	0.970583i	$-0.422601\pi$
$73$	4.11424	0.481535	0.240768	+	0.970583i	$0.422601\pi$
$74$	−2.99364	−0.348003
$75$	2.24825	0.259606
$76$	−5.58882	−0.641081
$77$	−5.23947	−0.597093
$78$	9.38909	1.06311
$79$	−3.96657	−0.446275	−0.223137	−	0.974787i	$-0.571630\pi$
$79$	−3.96657	−0.446275	−0.223137	+	0.974787i	$0.571630\pi$
$80$	12.3373	1.37935
$81$	−7.97503	−0.886114
$82$	−22.2034	−2.45196
$83$	−11.4408	−1.25580	−0.627898	−	0.778296i	$-0.716084\pi$
$83$	−11.4408	−1.25580	−0.627898	+	0.778296i	$0.716084\pi$
$84$	9.79254	1.06845
$85$	−2.69266	−0.292060
$86$	−9.90633	−1.06823
$87$	−1.64022	−0.175850
$88$	−23.2359	−2.47695
$89$	10.6424	1.12810	0.564048	−	0.825742i	$-0.309243\pi$
$89$	10.6424	1.12810	0.564048	+	0.825742i	$0.309243\pi$
$90$	1.49110	0.157175
$91$	−3.08189	−0.323070
$92$	15.4042	1.60600
$93$	9.59214	0.994658
$94$	0.191642	0.0197663
$95$	−2.42662	−0.248966
$96$	7.05041	0.719580
$97$	18.0801	1.83575	0.917877	−	0.396865i	$-0.129902\pi$
$97$	18.0801	1.83575	0.917877	+	0.396865i	$0.129902\pi$
$98$	13.0121	1.31442
$99$	−1.19247	−0.119848
$100$	−6.01414	−0.601414
$101$	−12.4435	−1.23818	−0.619088	−	0.785322i	$-0.712498\pi$
$101$	−12.4435	−1.23818	−0.619088	+	0.785322i	$0.712498\pi$
$102$	−5.85925	−0.580152
$103$	−3.50549	−0.345407	−0.172703	−	0.984974i	$-0.555250\pi$
$103$	−3.50549	−0.345407	−0.172703	+	0.984974i	$0.555250\pi$
$104$	−13.6675	−1.34021
$105$	4.25184	0.414937
$106$	2.76821	0.268873
$107$	11.2162	1.08431	0.542155	−	0.840279i	$-0.317609\pi$
$107$	11.2162	1.08431	0.542155	+	0.840279i	$0.317609\pi$
$108$	23.8187	2.29196
$109$	0.543097	0.0520193	0.0260096	−	0.999662i	$-0.491720\pi$
$109$	0.543097	0.0520193	0.0260096	+	0.999662i	$0.491720\pi$
$110$	−18.5398	−1.76770
$111$	−1.94281	−0.184404
$112$	−8.81196	−0.832652
$113$	−8.07929	−0.760035	−0.380018	−	0.924979i	$-0.624082\pi$
$113$	−8.07929	−0.760035	−0.380018	+	0.924979i	$0.624082\pi$
$114$	−5.28033	−0.494548
$115$	6.68837	0.623694
$116$	4.38763	0.407381
$117$	−0.701418	−0.0648462
$118$	−5.42469	−0.499383
$119$	1.92325	0.176304
$120$	18.8560	1.72131
$121$	3.82675	0.347887
$122$	11.1269	1.00738
$123$	−14.4096	−1.29927
$124$	−25.6592	−2.30427
$125$	−12.1366	−1.08553
$126$	−1.06502	−0.0948798
$127$	−8.85851	−0.786065	−0.393033	−	0.919525i	$-0.628574\pi$
$127$	−8.85851	−0.786065	−0.393033	+	0.919525i	$0.628574\pi$
$128$	13.8746	1.22635
$129$	−6.42901	−0.566043
$130$	−10.9052	−0.956449
$131$	−2.50314	−0.218701	−0.109350	−	0.994003i	$-0.534877\pi$
$131$	−2.50314	−0.218701	−0.109350	+	0.994003i	$0.534877\pi$
$132$	−27.7111	−2.41194
$133$	1.73322	0.150290
$134$	−31.9207	−2.75753
$135$	10.3419	0.890087
$136$	8.52918	0.731371
$137$	22.0735	1.88586	0.942932	−	0.332986i	$-0.108056\pi$
$137$	22.0735	1.88586	0.942932	+	0.332986i	$0.108056\pi$
$138$	14.5539	1.23891
$139$	11.6081	0.984588	0.492294	−	0.870429i	$-0.336159\pi$
$139$	11.6081	0.984588	0.492294	+	0.870429i	$0.336159\pi$
$140$	−11.3738	−0.961261
$141$	0.124372	0.0104740
$142$	19.1325	1.60557
$143$	8.72119	0.729302
$144$	−2.00555	−0.167129
$145$	1.90507	0.158208
$146$	−10.3982	−0.860563
$147$	8.44462	0.696501
$148$	5.19708	0.427197
$149$	10.9082	0.893638	0.446819	−	0.894624i	$-0.352557\pi$
$149$	10.9082	0.893638	0.446819	+	0.894624i	$0.352557\pi$
$150$	−5.68218	−0.463948
$151$	6.89676	0.561250	0.280625	−	0.959817i	$-0.409458\pi$
$151$	6.89676	0.561250	0.280625	+	0.959817i	$0.409458\pi$
$152$	7.68646	0.623454
$153$	0.437719	0.0353875
$154$	13.2421	1.06708
$155$	−11.1410	−0.894869
$156$	−16.2998	−1.30503
$157$	−8.01868	−0.639960	−0.319980	−	0.947424i	$-0.603676\pi$
$157$	−8.01868	−0.639960	−0.319980	+	0.947424i	$0.603676\pi$
$158$	10.0250	0.797548
$159$	1.79652	0.142473
$160$	−8.18888	−0.647388
$161$	−4.77720	−0.376496
$162$	20.1559	1.58360
$163$	19.7396	1.54613	0.773063	−	0.634329i	$-0.218724\pi$
$163$	19.7396	1.54613	0.773063	+	0.634329i	$0.218724\pi$
$164$	38.5460	3.00994
$165$	−12.0319	−0.936685
$166$	28.9153	2.24426
$167$	23.2143	1.79638	0.898188	−	0.439613i	$-0.144884\pi$
$167$	23.2143	1.79638	0.898188	+	0.439613i	$0.144884\pi$
$168$	−13.4680	−1.03908
$169$	−7.87015	−0.605396
$170$	6.80537	0.521948
$171$	0.394471	0.0301659
$172$	17.1978	1.31132
$173$	−13.0028	−0.988585	−0.494292	−	0.869296i	$-0.664573\pi$
$173$	−13.0028	−0.988585	−0.494292	+	0.869296i	$0.664573\pi$
$174$	4.14544	0.314265
$175$	1.86513	0.140990
$176$	24.9362	1.87964
$177$	−3.52052	−0.264618
$178$	−26.8974	−2.01605
$179$	−19.7312	−1.47478	−0.737390	−	0.675468i	$-0.763942\pi$
$179$	−19.7312	−1.47478	−0.737390	+	0.675468i	$0.763942\pi$
$180$	−2.58860	−0.192943
$181$	8.45569	0.628506	0.314253	−	0.949339i	$-0.398246\pi$
$181$	8.45569	0.628506	0.314253	+	0.949339i	$0.398246\pi$
$182$	7.78909	0.577366
$183$	7.22112	0.533800
$184$	−21.1858	−1.56184
$185$	2.25653	0.165903
$186$	−24.2429	−1.77758
$187$	−5.44244	−0.397991
$188$	−0.332698	−0.0242645
$189$	−7.38674	−0.537306
$190$	6.13297	0.444933
$191$	0.812428	0.0587852	0.0293926	−	0.999568i	$-0.490643\pi$
$191$	0.812428	0.0587852	0.0293926	+	0.999568i	$0.490643\pi$
$192$	3.42510	0.247185
$193$	21.4137	1.54139	0.770695	−	0.637205i	$-0.219909\pi$
$193$	21.4137	1.54139	0.770695	+	0.637205i	$0.219909\pi$
$194$	−45.6951	−3.28072
$195$	−7.07726	−0.506813
$196$	−22.5896	−1.61354
$197$	7.15445	0.509733	0.254867	−	0.966976i	$-0.417968\pi$
$197$	7.15445	0.509733	0.254867	+	0.966976i	$0.417968\pi$
$198$	3.01382	0.214183
$199$	−5.36599	−0.380385	−0.190192	−	0.981747i	$-0.560911\pi$
$199$	−5.36599	−0.380385	−0.190192	+	0.981747i	$0.560911\pi$
$200$	8.27142	0.584878
$201$	−20.7159	−1.46119
$202$	31.4494	2.21277
$203$	−1.36071	−0.0955029
$204$	10.1719	0.712175
$205$	16.7364	1.16892
$206$	8.85970	0.617285
$207$	−1.08726	−0.0755699
$208$	14.6676	1.01702
$209$	−4.90471	−0.339266
$210$	−10.7460	−0.741544
$211$	18.3978	1.26656	0.633279	−	0.773923i	$-0.281709\pi$
$211$	18.3978	1.26656	0.633279	+	0.773923i	$0.281709\pi$
$212$	−4.80573	−0.330059
$213$	12.4166	0.850775
$214$	−28.3475	−1.93780
$215$	7.46714	0.509254
$216$	−32.7585	−2.22894
$217$	7.95753	0.540192
$218$	−1.37261	−0.0929649
$219$	−6.74824	−0.456004
$220$	32.1858	2.16996
$221$	−3.20128	−0.215341
$222$	4.91022	0.329552
$223$	23.8346	1.59608	0.798042	−	0.602602i	$-0.205869\pi$
$223$	23.8346	1.59608	0.798042	+	0.602602i	$0.205869\pi$
$224$	5.84895	0.390799
$225$	0.424491	0.0282994
$226$	20.4194	1.35828
$227$	−15.0930	−1.00176	−0.500879	−	0.865517i	$-0.666990\pi$
$227$	−15.0930	−1.00176	−0.500879	+	0.865517i	$0.666990\pi$
$228$	9.16687	0.607091
$229$	21.3268	1.40932	0.704658	−	0.709547i	$-0.251100\pi$
$229$	21.3268	1.40932	0.704658	+	0.709547i	$0.251100\pi$
$230$	−16.9040	−1.11462
$231$	8.59387	0.565435
$232$	−6.03443	−0.396180
$233$	−11.1247	−0.728805	−0.364403	−	0.931242i	$-0.618727\pi$
$233$	−11.1247	−0.728805	−0.364403	+	0.931242i	$0.618727\pi$
$234$	1.77275	0.115888
$235$	−0.144455	−0.00942317
$236$	9.41749	0.613026
$237$	6.50604	0.422613
$238$	−4.86077	−0.315077
$239$	9.14848	0.591766	0.295883	−	0.955224i	$-0.404386\pi$
$239$	9.14848	0.591766	0.295883	+	0.955224i	$0.404386\pi$
$240$	−20.2358	−1.30622
$241$	−29.1091	−1.87508	−0.937540	−	0.347878i	$-0.886902\pi$
$241$	−29.1091	−1.87508	−0.937540	+	0.347878i	$0.886902\pi$
$242$	−9.67164	−0.621717
$243$	−3.20504	−0.205604
$244$	−19.3167	−1.23662
$245$	−9.80822	−0.626624
$246$	36.4184	2.32195
$247$	−2.88498	−0.183567
$248$	35.2899	2.24091
$249$	18.7655	1.18921
$250$	30.6739	1.93999
$251$	11.0270	0.696015	0.348008	−	0.937492i	$-0.386858\pi$
$251$	11.0270	0.696015	0.348008	+	0.937492i	$0.386858\pi$
$252$	1.84892	0.116471
$253$	13.5186	0.849908
$254$	22.3888	1.40480
$255$	4.41655	0.276575
$256$	−30.8899	−1.93062
$257$	−22.6860	−1.41511	−0.707555	−	0.706658i	$-0.750202\pi$
$257$	−22.6860	−1.41511	−0.707555	+	0.706658i	$0.750202\pi$
$258$	16.2485	1.01159
$259$	−1.61174	−0.100148
$260$	18.9319	1.17410
$261$	−0.309688	−0.0191692
$262$	6.32638	0.390845
$263$	−24.3156	−1.49936	−0.749682	−	0.661798i	$-0.769793\pi$
$263$	−24.3156	−1.49936	−0.749682	+	0.661798i	$0.769793\pi$
$264$	38.1119	2.34563
$265$	−2.08661	−0.128179
$266$	−4.38051	−0.268586
$267$	−17.4559	−1.06828
$268$	55.4157	3.38505
$269$	3.19562	0.194840	0.0974202	−	0.995243i	$-0.468941\pi$
$269$	3.19562	0.194840	0.0974202	+	0.995243i	$0.468941\pi$
$270$	−26.1378	−1.59070
$271$	2.73082	0.165885	0.0829426	−	0.996554i	$-0.473568\pi$
$271$	2.73082	0.165885	0.0829426	+	0.996554i	$0.473568\pi$
$272$	−9.15332	−0.555002
$273$	5.05497	0.305940
$274$	−55.7879	−3.37027
$275$	−5.27797	−0.318273
$276$	−25.2662	−1.52085
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	−29.3381	−1.75958
$279$	1.81108	0.108427
$280$	15.6427	0.934830
$281$	−31.2295	−1.86300	−0.931499	−	0.363745i	$-0.881498\pi$
$281$	−31.2295	−1.86300	−0.931499	+	0.363745i	$0.881498\pi$
$282$	−0.314334	−0.0187183
$283$	0.837774	0.0498005	0.0249003	−	0.999690i	$-0.492073\pi$
$283$	0.837774	0.0498005	0.0249003	+	0.999690i	$0.492073\pi$
$284$	−33.2149	−1.97094
$285$	3.98018	0.235765
$286$	−22.0417	−1.30335
$287$	−11.9540	−0.705624
$288$	1.33118	0.0784408
$289$	−15.0022	−0.882485
$290$	−4.81483	−0.282737
$291$	−29.6552	−1.73842
$292$	18.0517	1.05640
$293$	23.7509	1.38754	0.693770	−	0.720197i	$-0.255949\pi$
$293$	23.7509	1.38754	0.693770	+	0.720197i	$0.255949\pi$
$294$	−21.3427	−1.24473
$295$	4.08899	0.238070
$296$	−7.14769	−0.415451
$297$	20.9031	1.21292
$298$	−27.5692	−1.59704
$299$	7.95173	0.459860
$300$	9.86449	0.569527
$301$	−5.33344	−0.307414
$302$	−17.4307	−1.00302
$303$	20.4101	1.17253
$304$	−8.24894	−0.473109
$305$	−8.38715	−0.480247
$306$	−1.10628	−0.0632419
$307$	−15.9077	−0.907903	−0.453951	−	0.891026i	$-0.649986\pi$
$307$	−15.9077	−0.907903	−0.453951	+	0.891026i	$0.649986\pi$
$308$	−22.9888	−1.30991
$309$	5.74977	0.327093
$310$	28.1576	1.59924
$311$	24.2011	1.37232	0.686161	−	0.727450i	$-0.259295\pi$
$311$	24.2011	1.37232	0.686161	+	0.727450i	$0.259295\pi$
$312$	22.4176	1.26915
$313$	−11.7052	−0.661618	−0.330809	−	0.943698i	$-0.607322\pi$
$313$	−11.7052	−0.661618	−0.330809	+	0.943698i	$0.607322\pi$
$314$	20.2662	1.14369
$315$	0.802787	0.0452319
$316$	−17.4038	−0.979043
$317$	−5.08267	−0.285471	−0.142736	−	0.989761i	$-0.545590\pi$
$317$	−5.08267	−0.285471	−0.142736	+	0.989761i	$0.545590\pi$
$318$	−4.54047	−0.254617
$319$	3.85055	0.215590
$320$	−3.97817	−0.222386
$321$	−18.3970	−1.02682
$322$	12.0738	0.672846
$323$	1.80037	0.100175
$324$	−34.9914	−1.94397
$325$	−3.10453	−0.172208
$326$	−49.8894	−2.76312
$327$	−0.890798	−0.0492612
$328$	−53.0135	−2.92718
$329$	0.103177	0.00568835
$330$	30.4092	1.67397
$331$	−3.96768	−0.218083	−0.109042	−	0.994037i	$-0.534778\pi$
$331$	−3.96768	−0.218083	−0.109042	+	0.994037i	$0.534778\pi$
$332$	−50.1981	−2.75498
$333$	−0.366821	−0.0201017
$334$	−58.6712	−3.21035
$335$	24.0610	1.31460
$336$	14.4535	0.788504
$337$	−19.5390	−1.06436	−0.532178	−	0.846632i	$-0.678626\pi$
$337$	−19.5390	−1.06436	−0.532178	+	0.846632i	$0.678626\pi$
$338$	19.8908	1.08192
$339$	13.2518	0.719738
$340$	−11.8144	−0.640726
$341$	−22.5184	−1.21944
$342$	−0.996976	−0.0539103
$343$	16.5305	0.892564
$344$	−23.6526	−1.27526
$345$	−10.9704	−0.590625
$346$	32.8630	1.76672
$347$	6.80799	0.365472	0.182736	−	0.983162i	$-0.441505\pi$
$347$	6.80799	0.365472	0.182736	+	0.983162i	$0.441505\pi$
$348$	−7.19666	−0.385781
$349$	17.0243	0.911288	0.455644	−	0.890162i	$-0.349409\pi$
$349$	17.0243	0.911288	0.455644	+	0.890162i	$0.349409\pi$
$350$	−4.71387	−0.251967
$351$	12.2953	0.656277
$352$	−16.5515	−0.882196
$353$	1.10269	0.0586905	0.0293453	−	0.999569i	$-0.490658\pi$
$353$	1.10269	0.0586905	0.0293453	+	0.999569i	$0.490658\pi$
$354$	8.89767	0.472906
$355$	−14.4216	−0.765420
$356$	46.6950	2.47483
$357$	−3.15454	−0.166956
$358$	49.8682	2.63561
$359$	−24.7158	−1.30445	−0.652225	−	0.758025i	$-0.726164\pi$
$359$	−24.7158	−1.30445	−0.652225	+	0.758025i	$0.726164\pi$
$360$	3.56018	0.187638
$361$	−17.3775	−0.914606
$362$	−21.3707	−1.12322
$363$	−6.27670	−0.329442
$364$	−13.5222	−0.708755
$365$	7.83792	0.410255
$366$	−18.2505	−0.953968
$367$	−16.2181	−0.846579	−0.423290	−	0.905994i	$-0.639125\pi$
$367$	−16.2181	−0.846579	−0.423290	+	0.905994i	$0.639125\pi$
$368$	22.7362	1.18520
$369$	−2.72066	−0.141632
$370$	−5.70310	−0.296490
$371$	1.49037	0.0773762
$372$	42.0867	2.18209
$373$	28.8757	1.49513	0.747563	−	0.664191i	$-0.231224\pi$
$373$	28.8757	1.49513	0.747563	+	0.664191i	$0.231224\pi$
$374$	13.7551	0.711259
$375$	19.9067	1.02798
$376$	0.457569	0.0235973
$377$	2.26492	0.116649
$378$	18.6691	0.960233
$379$	−24.3228	−1.24938	−0.624690	−	0.780873i	$-0.714775\pi$
$379$	−24.3228	−1.24938	−0.624690	+	0.780873i	$0.714775\pi$
$380$	−10.6471	−0.546184
$381$	14.5299	0.744388
$382$	−2.05331	−0.105056
$383$	−24.2985	−1.24159	−0.620797	−	0.783972i	$-0.713191\pi$
$383$	−24.2985	−1.24159	−0.620797	+	0.783972i	$0.713191\pi$
$384$	−22.7573	−1.16133
$385$	−9.98156	−0.508708
$386$	−54.1204	−2.75465
$387$	−1.21386	−0.0617038
$388$	79.3286	4.02730
$389$	24.2047	1.22723	0.613614	−	0.789606i	$-0.289715\pi$
$389$	24.2047	1.22723	0.613614	+	0.789606i	$0.289715\pi$
$390$	17.8869	0.905738
$391$	−4.96227	−0.250953
$392$	31.0681	1.56918
$393$	4.10570	0.207105
$394$	−18.0820	−0.910957
$395$	−7.55661	−0.380214
$396$	−5.23212	−0.262924
$397$	34.6014	1.73660	0.868298	−	0.496042i	$-0.165214\pi$
$397$	34.6014	1.73660	0.868298	+	0.496042i	$0.165214\pi$
$398$	13.5619	0.679795
$399$	−2.84286	−0.142321
$400$	−8.87670	−0.443835
$401$	9.54407	0.476608	0.238304	−	0.971191i	$-0.423409\pi$
$401$	9.54407	0.476608	0.238304	+	0.971191i	$0.423409\pi$
$402$	52.3570	2.61133
$403$	−13.2454	−0.659803
$404$	−54.5975	−2.71633
$405$	−15.1930	−0.754946
$406$	3.43902	0.170675
$407$	4.56092	0.226077
$408$	−13.9897	−0.692593
$409$	10.3732	0.512922	0.256461	−	0.966555i	$-0.417444\pi$
$409$	10.3732	0.512922	0.256461	+	0.966555i	$0.417444\pi$
$410$	−42.2991	−2.08900
$411$	−36.2053	−1.78587
$412$	−15.3808	−0.757758
$413$	−2.92058	−0.143713
$414$	2.74792	0.135053
$415$	−21.7956	−1.06990
$416$	−9.73567	−0.477330
$417$	−19.0398	−0.932385
$418$	12.3960	0.606310
$419$	10.4665	0.511324	0.255662	−	0.966766i	$-0.417707\pi$
$419$	10.4665	0.511324	0.255662	+	0.966766i	$0.417707\pi$
$420$	18.6555	0.910295
$421$	−4.27085	−0.208149	−0.104074	−	0.994570i	$-0.533188\pi$
$421$	−4.27085	−0.208149	−0.104074	+	0.994570i	$0.533188\pi$
$422$	−46.4982	−2.26350
$423$	0.0234825	0.00114176
$424$	6.60946	0.320984
$425$	1.93738	0.0939767
$426$	−31.3815	−1.52044
$427$	5.99056	0.289904
$428$	49.2124	2.37877
$429$	−14.3046	−0.690634
$430$	−18.8723	−0.910101
$431$	−33.4044	−1.60903	−0.804516	−	0.593931i	$-0.797575\pi$
$431$	−33.4044	−1.60903	−0.804516	+	0.593931i	$0.797575\pi$
$432$	35.1557	1.69143
$433$	−7.46421	−0.358707	−0.179353	−	0.983785i	$-0.557401\pi$
$433$	−7.46421	−0.358707	−0.179353	+	0.983785i	$0.557401\pi$
$434$	−20.1117	−0.965391
$435$	−3.12473	−0.149819
$436$	2.38291	0.114121
$437$	−4.47197	−0.213924
$438$	17.0553	0.814936
$439$	−11.6900	−0.557933	−0.278967	−	0.960301i	$-0.589992\pi$
$439$	−11.6900	−0.557933	−0.278967	+	0.960301i	$0.589992\pi$
$440$	−44.2660	−2.11030
$441$	1.59442	0.0759249
$442$	8.09083	0.384842
$443$	6.63058	0.315029	0.157514	−	0.987517i	$-0.449652\pi$
$443$	6.63058	0.315029	0.157514	+	0.987517i	$0.449652\pi$
$444$	−8.52434	−0.404547
$445$	20.2746	0.961107
$446$	−60.2390	−2.85240
$447$	−17.8919	−0.846257
$448$	2.84142	0.134245
$449$	−14.2325	−0.671675	−0.335837	−	0.941920i	$-0.609019\pi$
$449$	−14.2325	−0.671675	−0.335837	+	0.941920i	$0.609019\pi$
$450$	−1.07285	−0.0505745
$451$	33.8277	1.59289
$452$	−35.4489	−1.66738
$453$	−11.3122	−0.531493
$454$	38.1457	1.79027
$455$	−5.87122	−0.275247
$456$	−12.6075	−0.590398
$457$	−27.1593	−1.27046	−0.635228	−	0.772324i	$-0.719094\pi$
$457$	−27.1593	−1.27046	−0.635228	+	0.772324i	$0.719094\pi$
$458$	−53.9009	−2.51862
$459$	−7.67290	−0.358140
$460$	29.3461	1.36827
$461$	−11.1290	−0.518328	−0.259164	−	0.965833i	$-0.583447\pi$
$461$	−11.1290	−0.518328	−0.259164	+	0.965833i	$0.583447\pi$
$462$	−21.7199	−1.01050
$463$	32.7933	1.52403	0.762017	−	0.647557i	$-0.224209\pi$
$463$	32.7933	1.52403	0.762017	+	0.647557i	$0.224209\pi$
$464$	6.47602	0.300641
$465$	18.2737	0.847423
$466$	28.1164	1.30247
$467$	−8.47940	−0.392380	−0.196190	−	0.980566i	$-0.562857\pi$
$467$	−8.47940	−0.392380	−0.196190	+	0.980566i	$0.562857\pi$
$468$	−3.07756	−0.142260
$469$	−17.1857	−0.793563
$470$	0.365091	0.0168404
$471$	13.1524	0.606029
$472$	−12.9521	−0.596171
$473$	15.0927	0.693961
$474$	−16.4432	−0.755262
$475$	1.74596	0.0801101
$476$	8.43850	0.386778
$477$	0.339199	0.0155308
$478$	−23.1217	−1.05756
$479$	37.9955	1.73606	0.868029	−	0.496514i	$-0.165387\pi$
$479$	37.9955	1.73606	0.868029	+	0.496514i	$0.165387\pi$
$480$	13.4315	0.613063
$481$	2.68276	0.122323
$482$	73.5695	3.35100
$483$	7.83565	0.356534
$484$	16.7904	0.763198
$485$	34.4438	1.56401
$486$	8.10035	0.367439
$487$	10.1065	0.457969	0.228984	−	0.973430i	$-0.426460\pi$
$487$	10.1065	0.457969	0.228984	+	0.973430i	$0.426460\pi$
$488$	26.5668	1.20262
$489$	−32.3773	−1.46415
$490$	24.7890	1.11986
$491$	20.3836	0.919898	0.459949	−	0.887945i	$-0.347868\pi$
$491$	20.3836	0.919898	0.459949	+	0.887945i	$0.347868\pi$
$492$	−63.2238	−2.85035
$493$	−1.41342	−0.0636572
$494$	7.29142	0.328057
$495$	−2.27174	−0.102107
$496$	−37.8723	−1.70052
$497$	10.3007	0.462050
$498$	−47.4274	−2.12527
$499$	−2.13177	−0.0954311	−0.0477155	−	0.998861i	$-0.515194\pi$
$499$	−2.13177	−0.0954311	−0.0477155	+	0.998861i	$0.515194\pi$
$500$	−53.2511	−2.38146
$501$	−38.0765	−1.70113
$502$	−27.8693	−1.24387
$503$	14.7447	0.657434	0.328717	−	0.944428i	$-0.393384\pi$
$503$	14.7447	0.657434	0.328717	+	0.944428i	$0.393384\pi$
$504$	−2.54288	−0.113269
$505$	−23.7058	−1.05489
$506$	−34.1666	−1.51889
$507$	12.9087	0.573298
$508$	−38.8678	−1.72448
$509$	−41.5648	−1.84233	−0.921164	−	0.389176i	$-0.872760\pi$
$509$	−41.5648	−1.84233	−0.921164	+	0.389176i	$0.872760\pi$
$510$	−11.1623	−0.494274
$511$	−5.59827	−0.247653
$512$	50.3212	2.22390
$513$	−6.91478	−0.305295
$514$	57.3359	2.52898
$515$	−6.67822	−0.294277
$516$	−28.2081	−1.24179
$517$	−0.291973	−0.0128410
$518$	4.07346	0.178978
$519$	21.3274	0.936170
$520$	−26.0375	−1.14182
$521$	−28.6450	−1.25496	−0.627480	−	0.778632i	$-0.715914\pi$
$521$	−28.6450	−1.25496	−0.627480	+	0.778632i	$0.715914\pi$
$522$	0.782698	0.0342578
$523$	36.6406	1.60218	0.801090	−	0.598544i	$-0.204254\pi$
$523$	36.6406	1.60218	0.801090	+	0.598544i	$0.204254\pi$
$524$	−10.9829	−0.479789
$525$	−3.05921	−0.133515
$526$	61.4546	2.67955
$527$	8.26580	0.360064
$528$	−40.9008	−1.77998
$529$	−10.6741	−0.464092
$530$	5.27364	0.229072
$531$	−0.664707	−0.0288458
$532$	7.60474	0.329707
$533$	19.8977	0.861864
$534$	44.1176	1.90915
$535$	21.3676	0.923803
$536$	−76.2148	−3.29198
$537$	32.3634	1.39659
$538$	−8.07654	−0.348204
$539$	−19.8245	−0.853901
$540$	45.3763	1.95269
$541$	4.73804	0.203704	0.101852	−	0.994800i	$-0.467523\pi$
$541$	4.73804	0.203704	0.101852	+	0.994800i	$0.467523\pi$
$542$	−6.90180	−0.296458
$543$	−13.8692	−0.595183
$544$	6.07553	0.260486
$545$	1.03464	0.0443191
$546$	−12.7758	−0.546754
$547$	2.77109	0.118483	0.0592417	−	0.998244i	$-0.481132\pi$
$547$	2.77109	0.118483	0.0592417	+	0.998244i	$0.481132\pi$
$548$	96.8501	4.13723
$549$	1.36341	0.0581891
$550$	13.3394	0.568794
$551$	−1.27377	−0.0542643
$552$	34.7493	1.47903
$553$	5.39734	0.229518
$554$	2.52738	0.107378
$555$	−3.70120	−0.157107
$556$	50.9321	2.16000
$557$	−34.9314	−1.48009	−0.740045	−	0.672558i	$-0.765196\pi$
$557$	−34.9314	−1.48009	−0.740045	+	0.672558i	$0.765196\pi$
$558$	−4.57729	−0.193772
$559$	8.87760	0.375482
$560$	−16.7874	−0.709397
$561$	8.92679	0.376889
$562$	78.9287	3.32941
$563$	16.9414	0.713997	0.356998	−	0.934105i	$-0.383800\pi$
$563$	16.9414	0.713997	0.356998	+	0.934105i	$0.383800\pi$
$564$	0.545696	0.0229780
$565$	−15.3916	−0.647530
$566$	−2.11737	−0.0889997
$567$	10.8517	0.455727
$568$	45.6814	1.91675
$569$	−42.4889	−1.78123	−0.890614	−	0.454761i	$-0.849725\pi$
$569$	−42.4889	−1.78123	−0.890614	+	0.454761i	$0.849725\pi$
$570$	−10.0594	−0.421342
$571$	43.9511	1.83930	0.919648	−	0.392743i	$-0.128474\pi$
$571$	43.9511	1.83930	0.919648	+	0.392743i	$0.128474\pi$
$572$	38.2653	1.59995
$573$	−1.33256	−0.0556684
$574$	30.2123	1.26104
$575$	−4.81230	−0.200687
$576$	0.646690	0.0269454
$577$	−29.7442	−1.23827	−0.619134	−	0.785285i	$-0.712516\pi$
$577$	−29.7442	−1.23827	−0.619134	+	0.785285i	$0.712516\pi$
$578$	37.9163	1.57711
$579$	−35.1231	−1.45966
$580$	8.35874	0.347078
$581$	15.5676	0.645854
$582$	74.9499	3.10678
$583$	−4.21748	−0.174670
$584$	−24.8271	−1.02735
$585$	−1.33625	−0.0552472
$586$	−60.0273	−2.47971
$587$	23.1915	0.957214	0.478607	−	0.878029i	$-0.341142\pi$
$587$	23.1915	0.957214	0.478607	+	0.878029i	$0.341142\pi$
$588$	37.0518	1.52799
$589$	7.44911	0.306935
$590$	−10.3344	−0.425461
$591$	−11.7348	−0.482707
$592$	7.67075	0.315266
$593$	0.0820388	0.00336893	0.00168446	−	0.999999i	$-0.499464\pi$
$593$	0.0820388	0.00336893	0.00168446	+	0.999999i	$0.499464\pi$
$594$	−52.8301	−2.16764
$595$	3.66392	0.150206
$596$	47.8613	1.96048
$597$	8.80138	0.360217
$598$	−20.0970	−0.821828
$599$	3.80221	0.155354	0.0776770	−	0.996979i	$-0.475250\pi$
$599$	3.80221	0.155354	0.0776770	+	0.996979i	$0.475250\pi$
$600$	−13.5669	−0.553867
$601$	−14.5099	−0.591870	−0.295935	−	0.955208i	$-0.595631\pi$
$601$	−14.5099	−0.591870	−0.295935	+	0.955208i	$0.595631\pi$
$602$	13.4796	0.549388
$603$	−3.91136	−0.159283
$604$	30.2604	1.23128
$605$	7.29024	0.296390
$606$	−51.5839	−2.09545
$607$	10.0078	0.406205	0.203102	−	0.979157i	$-0.434898\pi$
$607$	10.0078	0.406205	0.203102	+	0.979157i	$0.434898\pi$
$608$	5.47524	0.222050
$609$	2.23185	0.0904393
$610$	21.1975	0.858261
$611$	−0.171740	−0.00694787
$612$	1.92055	0.0776336
$613$	36.3878	1.46969	0.734845	−	0.678235i	$-0.237255\pi$
$613$	36.3878	1.46969	0.734845	+	0.678235i	$0.237255\pi$
$614$	40.2048	1.62254
$615$	−27.4513	−1.10694
$616$	31.6172	1.27389
$617$	−9.62813	−0.387614	−0.193807	−	0.981040i	$-0.562084\pi$
$617$	−9.62813	−0.387614	−0.193807	+	0.981040i	$0.562084\pi$
$618$	−14.5318	−0.584556
$619$	25.9954	1.04484	0.522421	−	0.852688i	$-0.325029\pi$
$619$	25.9954	1.04484	0.522421	+	0.852688i	$0.325029\pi$
$620$	−48.8827	−1.96318
$621$	19.0589	0.764807
$622$	−61.1654	−2.45251
$623$	−14.4812	−0.580178
$624$	−24.0581	−0.963096
$625$	−16.2676	−0.650706
$626$	29.5835	1.18239
$627$	8.04478	0.321278
$628$	−35.1830	−1.40395
$629$	−1.67417	−0.0667537
$630$	−2.02894	−0.0808351
$631$	48.0818	1.91411	0.957054	−	0.289910i	$-0.0936254\pi$
$631$	48.0818	1.91411	0.957054	+	0.289910i	$0.0936254\pi$
$632$	23.9360	0.952124
$633$	−30.1764	−1.19940
$634$	12.8458	0.510173
$635$	−16.8761	−0.669707
$636$	7.88244	0.312559
$637$	−11.6609	−0.462021
$638$	−9.73179	−0.385285
$639$	2.34438	0.0927422
$640$	26.4321	1.04482
$641$	3.64417	0.143936	0.0719680	−	0.997407i	$-0.477072\pi$
$641$	3.64417	0.143936	0.0719680	+	0.997407i	$0.477072\pi$
$642$	46.4961	1.83505
$643$	6.82967	0.269336	0.134668	−	0.990891i	$-0.457003\pi$
$643$	6.82967	0.269336	0.134668	+	0.990891i	$0.457003\pi$
$644$	−20.9606	−0.825962
$645$	−12.2477	−0.482254
$646$	−4.55020	−0.179025
$647$	−43.9314	−1.72712	−0.863561	−	0.504244i	$-0.831771\pi$
$647$	−43.9314	−1.72712	−0.863561	+	0.504244i	$0.831771\pi$
$648$	48.1247	1.89052
$649$	8.26472	0.324419
$650$	7.84632	0.307758
$651$	−13.0521	−0.511551
$652$	86.6101	3.39191
$653$	6.42796	0.251546	0.125773	−	0.992059i	$-0.459859\pi$
$653$	6.42796	0.251546	0.125773	+	0.992059i	$0.459859\pi$
$654$	2.25138	0.0880359
$655$	−4.76867	−0.186327
$656$	56.8929	2.22129
$657$	−1.27413	−0.0497086
$658$	−0.260768	−0.0101658
$659$	−10.6180	−0.413619	−0.206809	−	0.978381i	$-0.566308\pi$
$659$	−10.6180	−0.413619	−0.206809	+	0.978381i	$0.566308\pi$
$660$	−52.7916	−2.05491
$661$	21.3709	0.831230	0.415615	−	0.909541i	$-0.363566\pi$
$661$	21.3709	0.831230	0.415615	+	0.909541i	$0.363566\pi$
$662$	10.0278	0.389742
$663$	5.25079	0.203924
$664$	69.0390	2.67923
$665$	3.30191	0.128043
$666$	0.927095	0.0359242
$667$	3.51082	0.135940
$668$	101.856	3.94091
$669$	−39.0939	−1.51146
$670$	−60.8113	−2.34935
$671$	−16.9522	−0.654433
$672$	−9.59354	−0.370079
$673$	12.3742	0.476990	0.238495	−	0.971144i	$-0.423346\pi$
$673$	12.3742	0.476990	0.238495	+	0.971144i	$0.423346\pi$
$674$	49.3823	1.90214
$675$	−7.44101	−0.286405
$676$	−34.5313	−1.32813
$677$	48.0995	1.84861	0.924307	−	0.381650i	$-0.124644\pi$
$677$	48.0995	1.84861	0.924307	+	0.381650i	$0.124644\pi$
$678$	−33.4922	−1.28626
$679$	−24.6017	−0.944126
$680$	16.2487	0.623109
$681$	24.7558	0.948645
$682$	56.9124	2.17929
$683$	22.9806	0.879329	0.439665	−	0.898162i	$-0.355097\pi$
$683$	22.9806	0.879329	0.439665	+	0.898162i	$0.355097\pi$
$684$	1.73079	0.0661784
$685$	42.0515	1.60671
$686$	−41.7788	−1.59512
$687$	−34.9806	−1.33459
$688$	25.3835	0.967735
$689$	−2.48075	−0.0945089
$690$	27.7263	1.05552
$691$	31.9390	1.21502	0.607509	−	0.794313i	$-0.292169\pi$
$691$	31.9390	1.21502	0.607509	+	0.794313i	$0.292169\pi$
$692$	−57.0515	−2.16877
$693$	1.62260	0.0616376
$694$	−17.2063	−0.653144
$695$	22.1143	0.838843
$696$	9.89777	0.375174
$697$	−12.4171	−0.470332
$698$	−43.0267	−1.62859
$699$	18.2470	0.690164
$700$	8.18348	0.309306
$701$	−2.63447	−0.0995026	−0.0497513	−	0.998762i	$-0.515843\pi$
$701$	−2.63447	−0.0995026	−0.0497513	+	0.998762i	$0.515843\pi$
$702$	−31.0750	−1.17285
$703$	−1.50876	−0.0569039
$704$	−8.04072	−0.303046
$705$	0.236937	0.00892356
$706$	−2.78692	−0.104887
$707$	16.9320	0.636792
$708$	−15.4467	−0.580523
$709$	2.64625	0.0993820	0.0496910	−	0.998765i	$-0.484176\pi$
$709$	2.64625	0.0993820	0.0496910	+	0.998765i	$0.484176\pi$
$710$	36.4489	1.36790
$711$	1.22840	0.0460687
$712$	−64.2210	−2.40678
$713$	−20.5316	−0.768915
$714$	7.97272	0.298371
$715$	16.6145	0.621346
$716$	−86.5731	−3.23539
$717$	−15.0055	−0.560391
$718$	62.4661	2.33122
$719$	48.2643	1.79996	0.899978	−	0.435935i	$-0.143582\pi$
$719$	48.2643	1.79996	0.899978	+	0.435935i	$0.143582\pi$
$720$	−3.82071	−0.142389
$721$	4.76995	0.177642
$722$	43.9195	1.63451
$723$	47.7452	1.77566
$724$	37.1004	1.37883
$725$	−1.37070	−0.0509067
$726$	15.8636	0.588753
$727$	−46.5064	−1.72483	−0.862413	−	0.506205i	$-0.831048\pi$
$727$	−46.5064	−1.72483	−0.862413	+	0.506205i	$0.831048\pi$
$728$	18.5974	0.689267
$729$	29.1821	1.08082
$730$	−19.8094	−0.733177
$731$	−5.54005	−0.204906
$732$	31.6836	1.17106
$733$	32.0208	1.18271	0.591357	−	0.806410i	$-0.298592\pi$
$733$	32.0208	1.18271	0.591357	+	0.806410i	$0.298592\pi$
$734$	40.9893	1.51294
$735$	16.0876	0.593400
$736$	−15.0912	−0.556267
$737$	48.6325	1.79140
$738$	6.87613	0.253114
$739$	28.0944	1.03347	0.516735	−	0.856146i	$-0.327147\pi$
$739$	28.0944	1.03347	0.516735	+	0.856146i	$0.327147\pi$
$740$	9.90081	0.363961
$741$	4.73199	0.173834
$742$	−3.76672	−0.138281
$743$	17.3928	0.638080	0.319040	−	0.947741i	$-0.396640\pi$
$743$	17.3928	0.638080	0.319040	+	0.947741i	$0.396640\pi$
$744$	−57.8831	−2.12210
$745$	20.7810	0.761356
$746$	−72.9796	−2.67197
$747$	3.54309	0.129635
$748$	−23.8794	−0.873118
$749$	−15.2619	−0.557659
$750$	−50.3118	−1.83713
$751$	−19.6431	−0.716787	−0.358393	−	0.933571i	$-0.616675\pi$
$751$	−19.6431	−0.716787	−0.358393	+	0.933571i	$0.616675\pi$
$752$	−0.491052	−0.0179068
$753$	−18.0866	−0.659113
$754$	−5.72430	−0.208467
$755$	13.1388	0.478170
$756$	−32.4103	−1.17875
$757$	16.1700	0.587709	0.293855	−	0.955850i	$-0.405062\pi$
$757$	16.1700	0.587709	0.293855	+	0.955850i	$0.405062\pi$
$758$	61.4730	2.23280
$759$	−22.1735	−0.804846
$760$	14.6433	0.531167
$761$	11.2120	0.406434	0.203217	−	0.979134i	$-0.434860\pi$
$761$	11.2120	0.406434	0.203217	+	0.979134i	$0.434860\pi$
$762$	−36.7224	−1.33031
$763$	−0.738996	−0.0267535
$764$	3.56463	0.128964
$765$	0.833886	0.0301492
$766$	61.4113	2.21888
$767$	4.86136	0.175534
$768$	50.6661	1.82826
$769$	18.9992	0.685129	0.342564	−	0.939494i	$-0.388705\pi$
$769$	18.9992	0.685129	0.342564	+	0.939494i	$0.388705\pi$
$770$	25.2272	0.909124
$771$	37.2099	1.34008
$772$	93.9552	3.38152
$773$	5.10139	0.183484	0.0917422	−	0.995783i	$-0.470756\pi$
$773$	5.10139	0.183484	0.0917422	+	0.995783i	$0.470756\pi$
$774$	3.06787	0.110272
$775$	8.01600	0.287943
$776$	−109.103	−3.91657
$777$	2.64360	0.0948385
$778$	−61.1744	−2.19321
$779$	−11.1903	−0.400932
$780$	−31.0524	−1.11185
$781$	−29.1492	−1.04304
$782$	12.5415	0.448484
$783$	5.42861	0.194003
$784$	−33.3416	−1.19077
$785$	−15.2761	−0.545229
$786$	−10.3766	−0.370123
$787$	−36.8507	−1.31358	−0.656792	−	0.754071i	$-0.728087\pi$
$787$	−36.8507	−1.31358	−0.656792	+	0.754071i	$0.728087\pi$
$788$	31.3910	1.11826
$789$	39.8828	1.41987
$790$	19.0984	0.679490
$791$	10.9935	0.390885
$792$	7.19588	0.255694
$793$	−9.97139	−0.354094
$794$	−87.4508	−3.10351
$795$	3.42249	0.121383
$796$	−23.5440	−0.834493
$797$	−38.4727	−1.36277	−0.681386	−	0.731924i	$-0.738623\pi$
$797$	−38.4727	−1.36277	−0.681386	+	0.731924i	$0.738623\pi$
$798$	7.18498	0.254346
$799$	0.107174	0.00379156
$800$	5.89192	0.208311
$801$	−3.29583	−0.116453
$802$	−24.1214	−0.851758
$803$	15.8421	0.559055
$804$	−90.8938	−3.20558
$805$	−9.10091	−0.320765
$806$	33.4762	1.17915
$807$	−5.24151	−0.184510
$808$	75.0895	2.64164
$809$	25.4742	0.895626	0.447813	−	0.894127i	$-0.352203\pi$
$809$	25.4742	0.895626	0.447813	+	0.894127i	$0.352203\pi$
$810$	38.3984	1.34918
$811$	30.4438	1.06902	0.534512	−	0.845161i	$-0.320495\pi$
$811$	30.4438	1.06902	0.534512	+	0.845161i	$0.320495\pi$
$812$	−5.97027	−0.209515
$813$	−4.47913	−0.157090
$814$	−11.5272	−0.404027
$815$	37.6054	1.31726
$816$	15.0134	0.525575
$817$	−4.99267	−0.174671
$818$	−26.2170	−0.916655
$819$	0.954425	0.0333503
$820$	73.4329	2.56439
$821$	20.8851	0.728896	0.364448	−	0.931224i	$-0.381258\pi$
$821$	20.8851	0.728896	0.364448	+	0.931224i	$0.381258\pi$
$822$	91.5043	3.19158
$823$	−7.19419	−0.250774	−0.125387	−	0.992108i	$-0.540017\pi$
$823$	−7.19419	−0.250774	−0.125387	+	0.992108i	$0.540017\pi$
$824$	21.1537	0.736923
$825$	8.65701	0.301399
$826$	7.38141	0.256832
$827$	−20.9757	−0.729397	−0.364698	−	0.931126i	$-0.618828\pi$
$827$	−20.9757	−0.729397	−0.364698	+	0.931126i	$0.618828\pi$
$828$	−4.77050	−0.165786
$829$	43.8486	1.52292	0.761462	−	0.648209i	$-0.224482\pi$
$829$	43.8486	1.52292	0.761462	+	0.648209i	$0.224482\pi$
$830$	55.0857	1.91205
$831$	1.64022	0.0568985
$832$	−4.72960	−0.163969
$833$	7.27696	0.252132
$834$	48.1208	1.66629
$835$	44.2249	1.53046
$836$	−21.5200	−0.744286
$837$	−31.7470	−1.09734
$838$	−26.4529	−0.913800
$839$	14.5505	0.502337	0.251169	−	0.967943i	$-0.419185\pi$
$839$	14.5505	0.502337	0.251169	+	0.967943i	$0.419185\pi$
$840$	−25.6574	−0.885265
$841$	1.00000	0.0344828
$842$	10.7940	0.371987
$843$	51.2232	1.76422
$844$	80.7228	2.77859
$845$	−14.9932	−0.515781
$846$	−0.0593491	−0.00204047
$847$	−5.20709	−0.178918
$848$	−7.09312	−0.243579
$849$	−1.37413	−0.0471601
$850$	−4.89649	−0.167948
$851$	4.15852	0.142552
$852$	54.4796	1.86644
$853$	40.6583	1.39211	0.696056	−	0.717987i	$-0.254936\pi$
$853$	40.6583	1.39211	0.696056	+	0.717987i	$0.254936\pi$
$854$	−15.1404	−0.518094
$855$	0.751495	0.0257006
$856$	−67.6833	−2.31337
$857$	−12.9715	−0.443097	−0.221548	−	0.975149i	$-0.571111\pi$
$857$	−12.9715	−0.443097	−0.221548	+	0.975149i	$0.571111\pi$
$858$	36.1532	1.23425
$859$	48.0121	1.63815	0.819076	−	0.573685i	$-0.194486\pi$
$859$	48.0121	1.63815	0.819076	+	0.573685i	$0.194486\pi$
$860$	32.7630	1.11721
$861$	19.6072	0.668212
$862$	84.4254	2.87554
$863$	44.6498	1.51990	0.759948	−	0.649984i	$-0.225224\pi$
$863$	44.6498	1.51990	0.759948	+	0.649984i	$0.225224\pi$
$864$	−23.3347	−0.793862
$865$	−24.7713	−0.842248
$866$	18.8649	0.641054
$867$	24.6069	0.835695
$868$	34.9147	1.18508
$869$	−15.2735	−0.518118
$870$	7.89737	0.267746
$871$	28.6059	0.969274
$872$	−3.27728	−0.110983
$873$	−5.59919	−0.189504
$874$	11.3024	0.382308
$875$	16.5144	0.558289
$876$	−29.6088	−1.00039
$877$	−31.3904	−1.05998	−0.529989	−	0.848004i	$-0.677804\pi$
$877$	−31.3904	−1.05998	−0.529989	+	0.848004i	$0.677804\pi$
$878$	29.5450	0.997096
$879$	−38.9566	−1.31397
$880$	47.5053	1.60140
$881$	−5.10338	−0.171937	−0.0859687	−	0.996298i	$-0.527398\pi$
$881$	−5.10338	−0.171937	−0.0859687	+	0.996298i	$0.527398\pi$
$882$	−4.02971	−0.135687
$883$	6.58916	0.221743	0.110871	−	0.993835i	$-0.464636\pi$
$883$	6.58916	0.221743	0.110871	+	0.993835i	$0.464636\pi$
$884$	−14.0460	−0.472419
$885$	−6.70684	−0.225448
$886$	−16.7580	−0.562995
$887$	56.2131	1.88745	0.943726	−	0.330729i	$-0.107295\pi$
$887$	56.2131	1.88745	0.943726	+	0.330729i	$0.107295\pi$
$888$	11.7238	0.393424
$889$	12.0538	0.404272
$890$	−51.2415	−1.71762
$891$	−30.7083	−1.02877
$892$	104.577	3.50151
$893$	0.0965851	0.00323210
$894$	45.2195	1.51237
$895$	−37.5893	−1.25647
$896$	−18.8792	−0.630711
$897$	−13.0426	−0.435478
$898$	35.9709	1.20037
$899$	−5.84809	−0.195045
$900$	1.86251	0.0620836
$901$	1.54811	0.0515749
$902$	−85.4954	−2.84668
$903$	8.74800	0.291115
$904$	48.7539	1.62153
$905$	16.1087	0.535471
$906$	28.5901	0.949843
$907$	16.3040	0.541364	0.270682	−	0.962669i	$-0.412751\pi$
$907$	16.3040	0.541364	0.270682	+	0.962669i	$0.412751\pi$
$908$	−66.2225	−2.19767
$909$	3.85361	0.127816
$910$	14.8388	0.491900
$911$	7.42084	0.245863	0.122932	−	0.992415i	$-0.460770\pi$
$911$	7.42084	0.245863	0.122932	+	0.992415i	$0.460770\pi$
$912$	13.5300	0.448025
$913$	−44.0536	−1.45796
$914$	68.6416	2.27046
$915$	13.7567	0.454784
$916$	93.5742	3.09178
$917$	3.40604	0.112477
$918$	19.3923	0.640041
$919$	28.8395	0.951327	0.475663	−	0.879627i	$-0.342208\pi$
$919$	28.8395	0.951327	0.475663	+	0.879627i	$0.342208\pi$
$920$	−40.3605	−1.33065
$921$	26.0921	0.859765
$922$	28.1271	0.926316
$923$	−17.1457	−0.564358
$924$	37.7067	1.24046
$925$	−1.62358	−0.0533829
$926$	−82.8810	−2.72364
$927$	1.08561	0.0356561
$928$	−4.29846	−0.141104
$929$	−43.6664	−1.43265	−0.716324	−	0.697767i	$-0.754177\pi$
$929$	−43.6664	−1.43265	−0.716324	+	0.697767i	$0.754177\pi$
$930$	−46.1845	−1.51445
$931$	6.55796	0.214929
$932$	−48.8112	−1.59886
$933$	−39.6951	−1.29956
$934$	21.4306	0.701232
$935$	−10.3682	−0.339078
$936$	4.23266	0.138349
$937$	15.1038	0.493419	0.246709	−	0.969090i	$-0.420651\pi$
$937$	15.1038	0.493419	0.246709	+	0.969090i	$0.420651\pi$
$938$	43.4348	1.41820
$939$	19.1991	0.626539
$940$	−0.633813	−0.0206727
$941$	−43.8383	−1.42909	−0.714544	−	0.699590i	$-0.753366\pi$
$941$	−43.8383	−1.42909	−0.714544	+	0.699590i	$0.753366\pi$
$942$	−33.2410	−1.08305
$943$	30.8432	1.00439
$944$	13.8999	0.452405
$945$	−14.0723	−0.457771
$946$	−38.1448	−1.24020
$947$	10.6518	0.346138	0.173069	−	0.984910i	$-0.444632\pi$
$947$	10.6518	0.346138	0.173069	+	0.984910i	$0.444632\pi$
$948$	28.5461	0.927134
$949$	9.31841	0.302488
$950$	−4.41269	−0.143167
$951$	8.33668	0.270335
$952$	−11.6057	−0.376143
$953$	40.5089	1.31221	0.656106	−	0.754669i	$-0.272202\pi$
$953$	40.5089	1.31221	0.656106	+	0.754669i	$0.272202\pi$
$954$	−0.857283	−0.0277556
$955$	1.54773	0.0500834
$956$	40.1401	1.29822
$957$	−6.31574	−0.204159
$958$	−96.0288	−3.10255
$959$	−30.0355	−0.969897
$960$	6.52506	0.210595
$961$	3.20015	0.103231
$962$	−6.78035	−0.218607
$963$	−3.47352	−0.111933
$964$	−127.720	−4.11358
$965$	40.7946	1.31322
$966$	−19.8036	−0.637171
$967$	−33.9157	−1.09066	−0.545328	−	0.838223i	$-0.683595\pi$
$967$	−33.9157	−1.09066	−0.545328	+	0.838223i	$0.683595\pi$
$968$	−23.0923	−0.742214
$969$	−2.95299	−0.0948638
$970$	−87.0525	−2.79509
$971$	28.6168	0.918356	0.459178	−	0.888344i	$-0.348144\pi$
$971$	28.6168	0.918356	0.459178	+	0.888344i	$0.348144\pi$
$972$	−14.0625	−0.451056
$973$	−15.7952	−0.506372
$974$	−25.5429	−0.818447
$975$	5.09211	0.163078
$976$	−28.5109	−0.912612
$977$	21.4131	0.685065	0.342532	−	0.939506i	$-0.388715\pi$
$977$	21.4131	0.685065	0.342532	+	0.939506i	$0.388715\pi$
$978$	81.8295	2.61662
$979$	40.9792	1.30970
$980$	−43.0348	−1.37470
$981$	−0.168191	−0.00536992
$982$	−51.5170	−1.64397
$983$	8.30456	0.264874	0.132437	−	0.991191i	$-0.457720\pi$
$983$	8.30456	0.264874	0.132437	+	0.991191i	$0.457720\pi$
$984$	86.9536	2.77198
$985$	13.6297	0.434279
$986$	3.57224	0.113763
$987$	−0.169233	−0.00538675
$988$	−12.6582	−0.402711
$989$	13.7611	0.437576
$990$	5.74154	0.182478
$991$	−15.8098	−0.502216	−0.251108	−	0.967959i	$-0.580795\pi$
$991$	−15.8098	−0.502216	−0.251108	+	0.967959i	$0.580795\pi$
$992$	25.1378	0.798126
$993$	6.50786	0.206521
$994$	−26.0338	−0.825741
$995$	−10.2226	−0.324078
$996$	82.3359	2.60891
$997$	20.9278	0.662789	0.331395	−	0.943492i	$-0.392481\pi$
$997$	20.9278	0.662789	0.331395	+	0.943492i	$0.392481\pi$
$998$	5.38778	0.170547
$999$	6.43010	0.203440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.d.1.10	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.d.1.10	✓	168	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)

\(f(q)\)	\(=\)	\(q-2.52738 q^{2} -1.64022 q^{3} +4.38763 q^{4} +1.90507 q^{5} +4.14544 q^{6} -1.36071 q^{7} -6.03443 q^{8} -0.309688 q^{9} +O(q^{10})\)	\(q-2.52738 q^{2} -1.64022 q^{3} +4.38763 q^{4} +1.90507 q^{5} +4.14544 q^{6} -1.36071 q^{7} -6.03443 q^{8} -0.309688 q^{9} -4.81483 q^{10} +3.85055 q^{11} -7.19666 q^{12} +2.26492 q^{13} +3.43902 q^{14} -3.12473 q^{15} +6.47602 q^{16} -1.41342 q^{17} +0.782698 q^{18} -1.27377 q^{19} +8.35874 q^{20} +2.23185 q^{21} -9.73179 q^{22} +3.51082 q^{23} +9.89777 q^{24} -1.37070 q^{25} -5.72430 q^{26} +5.42861 q^{27} -5.97027 q^{28} +1.00000 q^{29} +7.89737 q^{30} -5.84809 q^{31} -4.29846 q^{32} -6.31574 q^{33} +3.57224 q^{34} -2.59224 q^{35} -1.35880 q^{36} +1.18449 q^{37} +3.21929 q^{38} -3.71496 q^{39} -11.4960 q^{40} +8.78516 q^{41} -5.64073 q^{42} +3.91961 q^{43} +16.8948 q^{44} -0.589978 q^{45} -8.87317 q^{46} -0.0758263 q^{47} -10.6221 q^{48} -5.14848 q^{49} +3.46428 q^{50} +2.31831 q^{51} +9.93762 q^{52} -1.09529 q^{53} -13.7201 q^{54} +7.33558 q^{55} +8.21109 q^{56} +2.08925 q^{57} -2.52738 q^{58} +2.14637 q^{59} -13.7101 q^{60} -4.40254 q^{61} +14.7803 q^{62} +0.421395 q^{63} -2.08820 q^{64} +4.31483 q^{65} +15.9622 q^{66} +12.6300 q^{67} -6.20156 q^{68} -5.75851 q^{69} +6.55157 q^{70} -7.57012 q^{71} +1.86879 q^{72} +4.11424 q^{73} -2.99364 q^{74} +2.24825 q^{75} -5.58882 q^{76} -5.23947 q^{77} +9.38909 q^{78} -3.96657 q^{79} +12.3373 q^{80} -7.97503 q^{81} -22.2034 q^{82} -11.4408 q^{83} +9.79254 q^{84} -2.69266 q^{85} -9.90633 q^{86} -1.64022 q^{87} -23.2359 q^{88} +10.6424 q^{89} +1.49110 q^{90} -3.08189 q^{91} +15.4042 q^{92} +9.59214 q^{93} +0.191642 q^{94} -2.42662 q^{95} +7.05041 q^{96} +18.0801 q^{97} +13.0121 q^{98} -1.19247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * q^99

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