LMFDB - Embedded newform 6033.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$97$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41345 q^{2} +1.00000 q^{3} +3.82475 q^{4} +3.09815 q^{5} -2.41345 q^{6} +4.57422 q^{7} -4.40394 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.41345 q^{2} +1.00000 q^{3} +3.82475 q^{4} +3.09815 q^{5} -2.41345 q^{6} +4.57422 q^{7} -4.40394 q^{8} +1.00000 q^{9} -7.47724 q^{10} +1.31483 q^{11} +3.82475 q^{12} -6.35814 q^{13} -11.0396 q^{14} +3.09815 q^{15} +2.97920 q^{16} +4.74827 q^{17} -2.41345 q^{18} +5.71036 q^{19} +11.8496 q^{20} +4.57422 q^{21} -3.17328 q^{22} +1.26469 q^{23} -4.40394 q^{24} +4.59854 q^{25} +15.3451 q^{26} +1.00000 q^{27} +17.4952 q^{28} -1.31274 q^{29} -7.47724 q^{30} +7.17950 q^{31} +1.61772 q^{32} +1.31483 q^{33} -11.4597 q^{34} +14.1716 q^{35} +3.82475 q^{36} +0.200429 q^{37} -13.7817 q^{38} -6.35814 q^{39} -13.6441 q^{40} -5.28470 q^{41} -11.0396 q^{42} -5.82686 q^{43} +5.02890 q^{44} +3.09815 q^{45} -3.05226 q^{46} +3.63640 q^{47} +2.97920 q^{48} +13.9234 q^{49} -11.0984 q^{50} +4.74827 q^{51} -24.3183 q^{52} -8.67253 q^{53} -2.41345 q^{54} +4.07355 q^{55} -20.1446 q^{56} +5.71036 q^{57} +3.16823 q^{58} -13.0537 q^{59} +11.8496 q^{60} +3.27359 q^{61} -17.3274 q^{62} +4.57422 q^{63} -9.86270 q^{64} -19.6985 q^{65} -3.17328 q^{66} +2.57141 q^{67} +18.1609 q^{68} +1.26469 q^{69} -34.2025 q^{70} -7.53223 q^{71} -4.40394 q^{72} +3.90099 q^{73} -0.483726 q^{74} +4.59854 q^{75} +21.8407 q^{76} +6.01432 q^{77} +15.3451 q^{78} +8.41894 q^{79} +9.23002 q^{80} +1.00000 q^{81} +12.7544 q^{82} +9.28891 q^{83} +17.4952 q^{84} +14.7108 q^{85} +14.0628 q^{86} -1.31274 q^{87} -5.79044 q^{88} +4.24085 q^{89} -7.47724 q^{90} -29.0835 q^{91} +4.83711 q^{92} +7.17950 q^{93} -8.77626 q^{94} +17.6916 q^{95} +1.61772 q^{96} +15.1350 q^{97} -33.6036 q^{98} +1.31483 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) $ 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * 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 $

$2$	−2.41345	−1.70657	−0.853284	−	0.521447i	$-0.825393\pi$
$2$	−2.41345	−1.70657	−0.853284	+	0.521447i	$0.825393\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.82475	1.91237
$5$	3.09815	1.38554	0.692768	−	0.721161i	$-0.256391\pi$
$5$	3.09815	1.38554	0.692768	+	0.721161i	$0.256391\pi$
$6$	−2.41345	−0.985287
$7$	4.57422	1.72889	0.864445	−	0.502727i	$-0.167670\pi$
$7$	4.57422	1.72889	0.864445	+	0.502727i	$0.167670\pi$
$8$	−4.40394	−1.55703
$9$	1.00000	0.333333
$10$	−7.47724	−2.36451
$11$	1.31483	0.396437	0.198218	−	0.980158i	$-0.436484\pi$
$11$	1.31483	0.396437	0.198218	+	0.980158i	$0.436484\pi$
$12$	3.82475	1.10411
$13$	−6.35814	−1.76343	−0.881715	−	0.471782i	$-0.843611\pi$
$13$	−6.35814	−1.76343	−0.881715	+	0.471782i	$0.843611\pi$
$14$	−11.0396	−2.95047
$15$	3.09815	0.799939
$16$	2.97920	0.744800
$17$	4.74827	1.15162	0.575812	−	0.817582i	$-0.304686\pi$
$17$	4.74827	1.15162	0.575812	+	0.817582i	$0.304686\pi$
$18$	−2.41345	−0.568856
$19$	5.71036	1.31005	0.655024	−	0.755608i	$-0.272659\pi$
$19$	5.71036	1.31005	0.655024	+	0.755608i	$0.272659\pi$
$20$	11.8496	2.64966
$21$	4.57422	0.998176
$22$	−3.17328	−0.676546
$23$	1.26469	0.263706	0.131853	−	0.991269i	$-0.457907\pi$
$23$	1.26469	0.263706	0.131853	+	0.991269i	$0.457907\pi$
$24$	−4.40394	−0.898951
$25$	4.59854	0.919708
$26$	15.3451	3.00941
$27$	1.00000	0.192450
$28$	17.4952	3.30629
$29$	−1.31274	−0.243769	−0.121885	−	0.992544i	$-0.538894\pi$
$29$	−1.31274	−0.243769	−0.121885	+	0.992544i	$0.538894\pi$
$30$	−7.47724	−1.36515
$31$	7.17950	1.28948	0.644738	−	0.764404i	$-0.276967\pi$
$31$	7.17950	1.28948	0.644738	+	0.764404i	$0.276967\pi$
$32$	1.61772	0.285976
$33$	1.31483	0.228883
$34$	−11.4597	−1.96532
$35$	14.1716	2.39544
$36$	3.82475	0.637458
$37$	0.200429	0.0329503	0.0164752	−	0.999864i	$-0.494756\pi$
$37$	0.200429	0.0329503	0.0164752	+	0.999864i	$0.494756\pi$
$38$	−13.7817	−2.23569
$39$	−6.35814	−1.01812
$40$	−13.6441	−2.15732
$41$	−5.28470	−0.825332	−0.412666	−	0.910882i	$-0.635402\pi$
$41$	−5.28470	−0.825332	−0.412666	+	0.910882i	$0.635402\pi$
$42$	−11.0396	−1.70345
$43$	−5.82686	−0.888588	−0.444294	−	0.895881i	$-0.646545\pi$
$43$	−5.82686	−0.888588	−0.444294	+	0.895881i	$0.646545\pi$
$44$	5.02890	0.758135
$45$	3.09815	0.461845
$46$	−3.05226	−0.450031
$47$	3.63640	0.530423	0.265211	−	0.964190i	$-0.414558\pi$
$47$	3.63640	0.530423	0.265211	+	0.964190i	$0.414558\pi$
$48$	2.97920	0.430011
$49$	13.9234	1.98906
$50$	−11.0984	−1.56954
$51$	4.74827	0.664890
$52$	−24.3183	−3.37234
$53$	−8.67253	−1.19126	−0.595632	−	0.803258i	$-0.703098\pi$
$53$	−8.67253	−1.19126	−0.595632	+	0.803258i	$0.703098\pi$
$54$	−2.41345	−0.328429
$55$	4.07355	0.549277
$56$	−20.1446	−2.69193
$57$	5.71036	0.756356
$58$	3.16823	0.416009
$59$	−13.0537	−1.69945	−0.849723	−	0.527229i	$-0.823231\pi$
$59$	−13.0537	−1.69945	−0.849723	+	0.527229i	$0.823231\pi$
$60$	11.8496	1.52978
$61$	3.27359	0.419140	0.209570	−	0.977794i	$-0.432794\pi$
$61$	3.27359	0.419140	0.209570	+	0.977794i	$0.432794\pi$
$62$	−17.3274	−2.20058
$63$	4.57422	0.576297
$64$	−9.86270	−1.23284
$65$	−19.6985	−2.44329
$66$	−3.17328	−0.390604
$67$	2.57141	0.314148	0.157074	−	0.987587i	$-0.449794\pi$
$67$	2.57141	0.314148	0.157074	+	0.987587i	$0.449794\pi$
$68$	18.1609	2.20234
$69$	1.26469	0.152250
$70$	−34.2025	−4.08798
$71$	−7.53223	−0.893911	−0.446955	−	0.894556i	$-0.647492\pi$
$71$	−7.53223	−0.893911	−0.446955	+	0.894556i	$0.647492\pi$
$72$	−4.40394	−0.519009
$73$	3.90099	0.456576	0.228288	−	0.973594i	$-0.426687\pi$
$73$	3.90099	0.456576	0.228288	+	0.973594i	$0.426687\pi$
$74$	−0.483726	−0.0562320
$75$	4.59854	0.530994
$76$	21.8407	2.50530
$77$	6.01432	0.685396
$78$	15.3451	1.73749
$79$	8.41894	0.947205	0.473603	−	0.880739i	$-0.342953\pi$
$79$	8.41894	0.947205	0.473603	+	0.880739i	$0.342953\pi$
$80$	9.23002	1.03195
$81$	1.00000	0.111111
$82$	12.7544	1.40848
$83$	9.28891	1.01959	0.509795	−	0.860296i	$-0.329721\pi$
$83$	9.28891	1.01959	0.509795	+	0.860296i	$0.329721\pi$
$84$	17.4952	1.90889
$85$	14.7108	1.59562
$86$	14.0628	1.51644
$87$	−1.31274	−0.140740
$88$	−5.79044	−0.617263
$89$	4.24085	0.449529	0.224765	−	0.974413i	$-0.427839\pi$
$89$	4.24085	0.449529	0.224765	+	0.974413i	$0.427839\pi$
$90$	−7.47724	−0.788170
$91$	−29.0835	−3.04878
$92$	4.83711	0.504304
$93$	7.17950	0.744479
$94$	−8.77626	−0.905202
$95$	17.6916	1.81512
$96$	1.61772	0.165108
$97$	15.1350	1.53673	0.768363	−	0.640015i	$-0.221072\pi$
$97$	15.1350	1.53673	0.768363	+	0.640015i	$0.221072\pi$
$98$	−33.6036	−3.39447
$99$	1.31483	0.132146
$100$	17.5883	1.75883
$101$	−15.5054	−1.54284	−0.771421	−	0.636325i	$-0.780454\pi$
$101$	−15.5054	−1.54284	−0.771421	+	0.636325i	$0.780454\pi$
$102$	−11.4597	−1.13468
$103$	−3.10551	−0.305995	−0.152998	−	0.988227i	$-0.548893\pi$
$103$	−3.10551	−0.305995	−0.152998	+	0.988227i	$0.548893\pi$
$104$	28.0009	2.74571
$105$	14.1716	1.38301
$106$	20.9307	2.03297
$107$	−10.5949	−1.02424	−0.512122	−	0.858913i	$-0.671140\pi$
$107$	−10.5949	−1.02424	−0.512122	+	0.858913i	$0.671140\pi$
$108$	3.82475	0.368037
$109$	19.5697	1.87444	0.937218	−	0.348744i	$-0.113392\pi$
$109$	19.5697	1.87444	0.937218	+	0.348744i	$0.113392\pi$
$110$	−9.83131	−0.937378
$111$	0.200429	0.0190239
$112$	13.6275	1.28768
$113$	16.4971	1.55192	0.775960	−	0.630783i	$-0.217266\pi$
$113$	16.4971	1.55192	0.775960	+	0.630783i	$0.217266\pi$
$114$	−13.7817	−1.29077
$115$	3.91819	0.365373
$116$	−5.02090	−0.466178
$117$	−6.35814	−0.587810
$118$	31.5045	2.90022
$119$	21.7196	1.99103
$120$	−13.6441	−1.24553
$121$	−9.27122	−0.842838
$122$	−7.90065	−0.715291
$123$	−5.28470	−0.476506
$124$	27.4598	2.46596
$125$	−1.24379	−0.111248
$126$	−11.0396	−0.983490
$127$	1.09073	0.0967869	0.0483935	−	0.998828i	$-0.484590\pi$
$127$	1.09073	0.0967869	0.0483935	+	0.998828i	$0.484590\pi$
$128$	20.5677	1.81795
$129$	−5.82686	−0.513026
$130$	47.5413	4.16965
$131$	−6.24355	−0.545501	−0.272751	−	0.962085i	$-0.587933\pi$
$131$	−6.24355	−0.545501	−0.272751	+	0.962085i	$0.587933\pi$
$132$	5.02890	0.437710
$133$	26.1204	2.26493
$134$	−6.20599	−0.536115
$135$	3.09815	0.266646
$136$	−20.9111	−1.79311
$137$	11.4463	0.977920	0.488960	−	0.872306i	$-0.337376\pi$
$137$	11.4463	0.977920	0.488960	+	0.872306i	$0.337376\pi$
$138$	−3.05226	−0.259826
$139$	7.54247	0.639744	0.319872	−	0.947461i	$-0.396360\pi$
$139$	7.54247	0.639744	0.319872	+	0.947461i	$0.396360\pi$
$140$	54.2028	4.58098
$141$	3.63640	0.306240
$142$	18.1787	1.52552
$143$	−8.35988	−0.699088
$144$	2.97920	0.248267
$145$	−4.06706	−0.337751
$146$	−9.41485	−0.779178
$147$	13.9234	1.14839
$148$	0.766591	0.0630134
$149$	1.62550	0.133166	0.0665831	−	0.997781i	$-0.478790\pi$
$149$	1.62550	0.133166	0.0665831	+	0.997781i	$0.478790\pi$
$150$	−11.0984	−0.906176
$151$	4.88036	0.397158	0.198579	−	0.980085i	$-0.436367\pi$
$151$	4.88036	0.397158	0.198579	+	0.980085i	$0.436367\pi$
$152$	−25.1481	−2.03978
$153$	4.74827	0.383875
$154$	−14.5153	−1.16967
$155$	22.2432	1.78661
$156$	−24.3183	−1.94702
$157$	11.6400	0.928976	0.464488	−	0.885579i	$-0.346238\pi$
$157$	11.6400	0.928976	0.464488	+	0.885579i	$0.346238\pi$
$158$	−20.3187	−1.61647
$159$	−8.67253	−0.687776
$160$	5.01195	0.396230
$161$	5.78495	0.455918
$162$	−2.41345	−0.189619
$163$	−20.5032	−1.60593	−0.802966	−	0.596025i	$-0.796746\pi$
$163$	−20.5032	−1.60593	−0.802966	+	0.596025i	$0.796746\pi$
$164$	−20.2127	−1.57834
$165$	4.07355	0.317125
$166$	−22.4183	−1.74000
$167$	−13.7833	−1.06658	−0.533291	−	0.845932i	$-0.679045\pi$
$167$	−13.7833	−1.06658	−0.533291	+	0.845932i	$0.679045\pi$
$168$	−20.1446	−1.55419
$169$	27.4259	2.10969
$170$	−35.5039	−2.72303
$171$	5.71036	0.436683
$172$	−22.2863	−1.69931
$173$	−14.8155	−1.12640	−0.563201	−	0.826320i	$-0.690430\pi$
$173$	−14.8155	−1.12640	−0.563201	+	0.826320i	$0.690430\pi$
$174$	3.16823	0.240183
$175$	21.0347	1.59007
$176$	3.91715	0.295266
$177$	−13.0537	−0.981176
$178$	−10.2351	−0.767152
$179$	−17.3131	−1.29404	−0.647022	−	0.762471i	$-0.723986\pi$
$179$	−17.3131	−1.29404	−0.647022	+	0.762471i	$0.723986\pi$
$180$	11.8496	0.883220
$181$	−26.7666	−1.98955	−0.994774	−	0.102104i	$-0.967442\pi$
$181$	−26.7666	−1.98955	−0.994774	+	0.102104i	$0.967442\pi$
$182$	70.1916	5.20295
$183$	3.27359	0.241991
$184$	−5.56961	−0.410597
$185$	0.620960	0.0456539
$186$	−17.3274	−1.27050
$187$	6.24317	0.456546
$188$	13.9083	1.01437
$189$	4.57422	0.332725
$190$	−42.6977	−3.09762
$191$	−0.755718	−0.0546819	−0.0273409	−	0.999626i	$-0.508704\pi$
$191$	−0.755718	−0.0546819	−0.0273409	+	0.999626i	$0.508704\pi$
$192$	−9.86270	−0.711779
$193$	20.9901	1.51090	0.755450	−	0.655206i	$-0.227418\pi$
$193$	20.9901	1.51090	0.755450	+	0.655206i	$0.227418\pi$
$194$	−36.5276	−2.62253
$195$	−19.6985	−1.41064
$196$	53.2537	3.80383
$197$	3.01118	0.214538	0.107269	−	0.994230i	$-0.465789\pi$
$197$	3.01118	0.214538	0.107269	+	0.994230i	$0.465789\pi$
$198$	−3.17328	−0.225515
$199$	−17.4845	−1.23945	−0.619723	−	0.784821i	$-0.712755\pi$
$199$	−17.4845	−1.23945	−0.619723	+	0.784821i	$0.712755\pi$
$200$	−20.2517	−1.43201
$201$	2.57141	0.181374
$202$	37.4214	2.63296
$203$	−6.00475	−0.421451
$204$	18.1609	1.27152
$205$	−16.3728	−1.14353
$206$	7.49500	0.522202
$207$	1.26469	0.0879019
$208$	−18.9422	−1.31340
$209$	7.50817	0.519351
$210$	−34.2025	−2.36020
$211$	23.8817	1.64408	0.822042	−	0.569427i	$-0.192835\pi$
$211$	23.8817	1.64408	0.822042	+	0.569427i	$0.192835\pi$
$212$	−33.1702	−2.27814
$213$	−7.53223	−0.516100
$214$	25.5702	1.74794
$215$	−18.0525	−1.23117
$216$	−4.40394	−0.299650
$217$	32.8406	2.22936
$218$	−47.2305	−3.19885
$219$	3.90099	0.263604
$220$	15.5803	1.05042
$221$	−30.1901	−2.03081
$222$	−0.483726	−0.0324656
$223$	−1.30410	−0.0873293	−0.0436646	−	0.999046i	$-0.513903\pi$
$223$	−1.30410	−0.0873293	−0.0436646	+	0.999046i	$0.513903\pi$
$224$	7.39982	0.494421
$225$	4.59854	0.306569
$226$	−39.8150	−2.64846
$227$	−12.4882	−0.828868	−0.414434	−	0.910079i	$-0.636020\pi$
$227$	−12.4882	−0.828868	−0.414434	+	0.910079i	$0.636020\pi$
$228$	21.8407	1.44644
$229$	24.2400	1.60183	0.800913	−	0.598781i	$-0.204348\pi$
$229$	24.2400	1.60183	0.800913	+	0.598781i	$0.204348\pi$
$230$	−9.45637	−0.623534
$231$	6.01432	0.395713
$232$	5.78122	0.379556
$233$	28.1910	1.84685	0.923426	−	0.383776i	$-0.125377\pi$
$233$	28.1910	1.84685	0.923426	+	0.383776i	$0.125377\pi$
$234$	15.3451	1.00314
$235$	11.2661	0.734919
$236$	−49.9271	−3.24998
$237$	8.41894	0.546869
$238$	−52.4192	−3.39783
$239$	5.12904	0.331770	0.165885	−	0.986145i	$-0.446952\pi$
$239$	5.12904	0.331770	0.165885	+	0.986145i	$0.446952\pi$
$240$	9.23002	0.595795
$241$	−19.4892	−1.25541	−0.627704	−	0.778452i	$-0.716005\pi$
$241$	−19.4892	−1.25541	−0.627704	+	0.778452i	$0.716005\pi$
$242$	22.3756	1.43836
$243$	1.00000	0.0641500
$244$	12.5206	0.801552
$245$	43.1369	2.75592
$246$	12.7544	0.813189
$247$	−36.3073	−2.31018
$248$	−31.6181	−2.00775
$249$	9.28891	0.588660
$250$	3.00182	0.189852
$251$	−11.5239	−0.727381	−0.363691	−	0.931520i	$-0.618483\pi$
$251$	−11.5239	−0.727381	−0.363691	+	0.931520i	$0.618483\pi$
$252$	17.4952	1.10210
$253$	1.66285	0.104543
$254$	−2.63243	−0.165173
$255$	14.7108	0.921229
$256$	−29.9137	−1.86961
$257$	−28.6952	−1.78996	−0.894979	−	0.446108i	$-0.852810\pi$
$257$	−28.6952	−1.78996	−0.894979	+	0.446108i	$0.852810\pi$
$258$	14.0628	0.875514
$259$	0.916806	0.0569675
$260$	−75.3417	−4.67249
$261$	−1.31274	−0.0812565
$262$	15.0685	0.930935
$263$	26.2290	1.61735	0.808675	−	0.588255i	$-0.200185\pi$
$263$	26.2290	1.61735	0.808675	+	0.588255i	$0.200185\pi$
$264$	−5.79044	−0.356377
$265$	−26.8688	−1.65054
$266$	−63.0404	−3.86526
$267$	4.24085	0.259536
$268$	9.83501	0.600769
$269$	16.9341	1.03249	0.516245	−	0.856441i	$-0.327329\pi$
$269$	16.9341	1.03249	0.516245	+	0.856441i	$0.327329\pi$
$270$	−7.47724	−0.455050
$271$	1.18075	0.0717253	0.0358627	−	0.999357i	$-0.488582\pi$
$271$	1.18075	0.0717253	0.0358627	+	0.999357i	$0.488582\pi$
$272$	14.1460	0.857730
$273$	−29.0835	−1.76021
$274$	−27.6250	−1.66889
$275$	6.04630	0.364606
$276$	4.83711	0.291160
$277$	5.38258	0.323408	0.161704	−	0.986839i	$-0.448301\pi$
$277$	5.38258	0.323408	0.161704	+	0.986839i	$0.448301\pi$
$278$	−18.2034	−1.09177
$279$	7.17950	0.429825
$280$	−62.4109	−3.72977
$281$	0.842565	0.0502632	0.0251316	−	0.999684i	$-0.492000\pi$
$281$	0.842565	0.0502632	0.0251316	+	0.999684i	$0.492000\pi$
$282$	−8.77626	−0.522619
$283$	−20.1750	−1.19928	−0.599641	−	0.800269i	$-0.704690\pi$
$283$	−20.1750	−1.19928	−0.599641	+	0.800269i	$0.704690\pi$
$284$	−28.8089	−1.70949
$285$	17.6916	1.04796
$286$	20.1762	1.19304
$287$	−24.1734	−1.42691
$288$	1.61772	0.0953253
$289$	5.54605	0.326238
$290$	9.81566	0.576395
$291$	15.1350	0.887229
$292$	14.9203	0.873145
$293$	−24.7623	−1.44663	−0.723314	−	0.690519i	$-0.757382\pi$
$293$	−24.7623	−1.44663	−0.723314	+	0.690519i	$0.757382\pi$
$294$	−33.6036	−1.95980
$295$	−40.4423	−2.35464
$296$	−0.882678	−0.0513046
$297$	1.31483	0.0762943
$298$	−3.92307	−0.227257
$299$	−8.04106	−0.465026
$300$	17.5883	1.01546
$301$	−26.6533	−1.53627
$302$	−11.7785	−0.677777
$303$	−15.5054	−0.890760
$304$	17.0123	0.975724
$305$	10.1421	0.580733
$306$	−11.4597	−0.655108
$307$	10.9602	0.625529	0.312764	−	0.949831i	$-0.398745\pi$
$307$	10.9602	0.625529	0.312764	+	0.949831i	$0.398745\pi$
$308$	23.0033	1.31073
$309$	−3.10551	−0.176666
$310$	−53.6828	−3.04898
$311$	21.9918	1.24704	0.623522	−	0.781806i	$-0.285701\pi$
$311$	21.9918	1.24704	0.623522	+	0.781806i	$0.285701\pi$
$312$	28.0009	1.58524
$313$	−24.6281	−1.39206	−0.696031	−	0.718012i	$-0.745052\pi$
$313$	−24.6281	−1.39206	−0.696031	+	0.718012i	$0.745052\pi$
$314$	−28.0927	−1.58536
$315$	14.1716	0.798480
$316$	32.2003	1.81141
$317$	21.5737	1.21170	0.605849	−	0.795580i	$-0.292834\pi$
$317$	21.5737	1.21170	0.605849	+	0.795580i	$0.292834\pi$
$318$	20.9307	1.17374
$319$	−1.72603	−0.0966392
$320$	−30.5561	−1.70814
$321$	−10.5949	−0.591347
$322$	−13.9617	−0.778055
$323$	27.1143	1.50868
$324$	3.82475	0.212486
$325$	−29.2381	−1.62184
$326$	49.4834	2.74063
$327$	19.5697	1.08221
$328$	23.2735	1.28506
$329$	16.6337	0.917043
$330$	−9.83131	−0.541196
$331$	−23.3593	−1.28394	−0.641970	−	0.766729i	$-0.721883\pi$
$331$	−23.3593	−1.28394	−0.641970	+	0.766729i	$0.721883\pi$
$332$	35.5277	1.94984
$333$	0.200429	0.0109834
$334$	33.2653	1.82020
$335$	7.96663	0.435264
$336$	13.6275	0.743442
$337$	11.7449	0.639788	0.319894	−	0.947453i	$-0.396353\pi$
$337$	11.7449	0.639788	0.319894	+	0.947453i	$0.396353\pi$
$338$	−66.1911	−3.60032
$339$	16.4971	0.896001
$340$	56.2653	3.05141
$341$	9.43983	0.511195
$342$	−13.7817	−0.745228
$343$	31.6693	1.70998
$344$	25.6611	1.38356
$345$	3.91819	0.210948
$346$	35.7565	1.92228
$347$	−8.47268	−0.454838	−0.227419	−	0.973797i	$-0.573029\pi$
$347$	−8.47268	−0.454838	−0.227419	+	0.973797i	$0.573029\pi$
$348$	−5.02090	−0.269148
$349$	22.4170	1.19995	0.599976	−	0.800018i	$-0.295177\pi$
$349$	22.4170	1.19995	0.599976	+	0.800018i	$0.295177\pi$
$350$	−50.7662	−2.71357
$351$	−6.35814	−0.339372
$352$	2.12703	0.113371
$353$	−11.2194	−0.597147	−0.298574	−	0.954387i	$-0.596511\pi$
$353$	−11.2194	−0.597147	−0.298574	+	0.954387i	$0.596511\pi$
$354$	31.5045	1.67444
$355$	−23.3360	−1.23855
$356$	16.2202	0.859668
$357$	21.7196	1.14952
$358$	41.7844	2.20837
$359$	0.649602	0.0342847	0.0171423	−	0.999853i	$-0.494543\pi$
$359$	0.649602	0.0342847	0.0171423	+	0.999853i	$0.494543\pi$
$360$	−13.6441	−0.719106
$361$	13.6083	0.716225
$362$	64.5999	3.39530
$363$	−9.27122	−0.486613
$364$	−111.237	−5.83040
$365$	12.0859	0.632602
$366$	−7.90065	−0.412973
$367$	−19.0285	−0.993279	−0.496639	−	0.867957i	$-0.665433\pi$
$367$	−19.0285	−0.993279	−0.496639	+	0.867957i	$0.665433\pi$
$368$	3.76776	0.196408
$369$	−5.28470	−0.275111
$370$	−1.49866	−0.0779114
$371$	−39.6700	−2.05956
$372$	27.4598	1.42372
$373$	−13.5504	−0.701613	−0.350807	−	0.936448i	$-0.614093\pi$
$373$	−13.5504	−0.701613	−0.350807	+	0.936448i	$0.614093\pi$
$374$	−15.0676	−0.779127
$375$	−1.24379	−0.0642289
$376$	−16.0145	−0.825883
$377$	8.34658	0.429870
$378$	−11.0396	−0.567818
$379$	−2.94693	−0.151374	−0.0756868	−	0.997132i	$-0.524115\pi$
$379$	−2.94693	−0.151374	−0.0756868	+	0.997132i	$0.524115\pi$
$380$	67.6658	3.47118
$381$	1.09073	0.0558800
$382$	1.82389	0.0933183
$383$	28.8447	1.47389	0.736947	−	0.675950i	$-0.236267\pi$
$383$	28.8447	1.47389	0.736947	+	0.675950i	$0.236267\pi$
$384$	20.5677	1.04959
$385$	18.6333	0.949640
$386$	−50.6586	−2.57845
$387$	−5.82686	−0.296196
$388$	57.8875	2.93879
$389$	−7.34530	−0.372422	−0.186211	−	0.982510i	$-0.559621\pi$
$389$	−7.34530	−0.372422	−0.186211	+	0.982510i	$0.559621\pi$
$390$	47.5413	2.40735
$391$	6.00507	0.303690
$392$	−61.3180	−3.09703
$393$	−6.24355	−0.314945
$394$	−7.26734	−0.366124
$395$	26.0832	1.31239
$396$	5.02890	0.252712
$397$	−11.9003	−0.597258	−0.298629	−	0.954369i	$-0.596529\pi$
$397$	−11.9003	−0.597258	−0.298629	+	0.954369i	$0.596529\pi$
$398$	42.1981	2.11520
$399$	26.1204	1.30766
$400$	13.7000	0.684999
$401$	0.330391	0.0164989	0.00824947	−	0.999966i	$-0.497374\pi$
$401$	0.330391	0.0164989	0.00824947	+	0.999966i	$0.497374\pi$
$402$	−6.20599	−0.309526
$403$	−45.6482	−2.27390
$404$	−59.3041	−2.95049
$405$	3.09815	0.153948
$406$	14.4922	0.719235
$407$	0.263530	0.0130627
$408$	−20.9111	−1.03525
$409$	25.1530	1.24373	0.621867	−	0.783123i	$-0.286374\pi$
$409$	25.1530	1.24373	0.621867	+	0.783123i	$0.286374\pi$
$410$	39.5150	1.95151
$411$	11.4463	0.564603
$412$	−11.8778	−0.585177
$413$	−59.7104	−2.93816
$414$	−3.05226	−0.150010
$415$	28.7784	1.41268
$416$	−10.2857	−0.504298
$417$	7.54247	0.369356
$418$	−18.1206	−0.886308
$419$	−9.60593	−0.469280	−0.234640	−	0.972082i	$-0.575391\pi$
$419$	−9.60593	−0.469280	−0.234640	+	0.972082i	$0.575391\pi$
$420$	54.2028	2.64483
$421$	−40.5703	−1.97728	−0.988638	−	0.150313i	$-0.951972\pi$
$421$	−40.5703	−1.97728	−0.988638	+	0.150313i	$0.951972\pi$
$422$	−57.6373	−2.80574
$423$	3.63640	0.176808
$424$	38.1933	1.85483
$425$	21.8351	1.05916
$426$	18.1787	0.880759
$427$	14.9741	0.724647
$428$	−40.5227	−1.95874
$429$	−8.35988	−0.403619
$430$	43.5688	2.10107
$431$	29.4879	1.42038	0.710191	−	0.704009i	$-0.248609\pi$
$431$	29.4879	1.42038	0.710191	+	0.704009i	$0.248609\pi$
$432$	2.97920	0.143337
$433$	12.1429	0.583550	0.291775	−	0.956487i	$-0.405754\pi$
$433$	12.1429	0.583550	0.291775	+	0.956487i	$0.405754\pi$
$434$	−79.2591	−3.80456
$435$	−4.06706	−0.195001
$436$	74.8491	3.58462
$437$	7.22183	0.345467
$438$	−9.41485	−0.449859
$439$	−23.5947	−1.12612	−0.563058	−	0.826418i	$-0.690375\pi$
$439$	−23.5947	−1.12612	−0.563058	+	0.826418i	$0.690375\pi$
$440$	−17.9397	−0.855240
$441$	13.9234	0.663021
$442$	72.8624	3.46571
$443$	−12.0439	−0.572223	−0.286111	−	0.958196i	$-0.592363\pi$
$443$	−12.0439	−0.572223	−0.286111	+	0.958196i	$0.592363\pi$
$444$	0.766591	0.0363808
$445$	13.1388	0.622839
$446$	3.14739	0.149033
$447$	1.62550	0.0768836
$448$	−45.1141	−2.13144
$449$	−4.00434	−0.188976	−0.0944882	−	0.995526i	$-0.530121\pi$
$449$	−4.00434	−0.188976	−0.0944882	+	0.995526i	$0.530121\pi$
$450$	−11.0984	−0.523181
$451$	−6.94849	−0.327192
$452$	63.0974	2.96785
$453$	4.88036	0.229299
$454$	30.1396	1.41452
$455$	−90.1051	−4.22419
$456$	−25.1481	−1.17767
$457$	2.88160	0.134795	0.0673977	−	0.997726i	$-0.478530\pi$
$457$	2.88160	0.134795	0.0673977	+	0.997726i	$0.478530\pi$
$458$	−58.5021	−2.73363
$459$	4.74827	0.221630
$460$	14.9861	0.698731
$461$	−2.82187	−0.131428	−0.0657139	−	0.997839i	$-0.520932\pi$
$461$	−2.82187	−0.131428	−0.0657139	+	0.997839i	$0.520932\pi$
$462$	−14.5153	−0.675312
$463$	26.8451	1.24760	0.623799	−	0.781584i	$-0.285588\pi$
$463$	26.8451	1.24760	0.623799	+	0.781584i	$0.285588\pi$
$464$	−3.91091	−0.181560
$465$	22.2432	1.03150
$466$	−68.0376	−3.15178
$467$	−16.7718	−0.776104	−0.388052	−	0.921637i	$-0.626852\pi$
$467$	−16.7718	−0.776104	−0.388052	+	0.921637i	$0.626852\pi$
$468$	−24.3183	−1.12411
$469$	11.7622	0.543128
$470$	−27.1902	−1.25419
$471$	11.6400	0.536345
$472$	57.4877	2.64609
$473$	−7.66134	−0.352269
$474$	−20.3187	−0.933269
$475$	26.2593	1.20486
$476$	83.0720	3.80760
$477$	−8.67253	−0.397088
$478$	−12.3787	−0.566188
$479$	12.1143	0.553518	0.276759	−	0.960939i	$-0.410740\pi$
$479$	12.1143	0.553518	0.276759	+	0.960939i	$0.410740\pi$
$480$	5.01195	0.228763
$481$	−1.27436	−0.0581056
$482$	47.0361	2.14244
$483$	5.78495	0.263224
$484$	−35.4601	−1.61182
$485$	46.8905	2.12919
$486$	−2.41345	−0.109476
$487$	−11.0985	−0.502921	−0.251461	−	0.967868i	$-0.580911\pi$
$487$	−11.0985	−0.502921	−0.251461	+	0.967868i	$0.580911\pi$
$488$	−14.4167	−0.652613
$489$	−20.5032	−0.927185
$490$	−104.109	−4.70316
$491$	−28.7193	−1.29608	−0.648041	−	0.761605i	$-0.724412\pi$
$491$	−28.7193	−1.29608	−0.648041	+	0.761605i	$0.724412\pi$
$492$	−20.2127	−0.911257
$493$	−6.23324	−0.280731
$494$	87.6259	3.94247
$495$	4.07355	0.183092
$496$	21.3892	0.960402
$497$	−34.4540	−1.54547
$498$	−22.4183	−1.00459
$499$	15.2615	0.683197	0.341599	−	0.939846i	$-0.389032\pi$
$499$	15.2615	0.683197	0.341599	+	0.939846i	$0.389032\pi$
$500$	−4.75717	−0.212747
$501$	−13.7833	−0.615792
$502$	27.8123	1.24133
$503$	−14.9480	−0.666498	−0.333249	−	0.942839i	$-0.608145\pi$
$503$	−14.9480	−0.666498	−0.333249	+	0.942839i	$0.608145\pi$
$504$	−20.1446	−0.897311
$505$	−48.0380	−2.13766
$506$	−4.01321	−0.178409
$507$	27.4259	1.21803
$508$	4.17178	0.185093
$509$	−3.64956	−0.161764	−0.0808820	−	0.996724i	$-0.525774\pi$
$509$	−3.64956	−0.161764	−0.0808820	+	0.996724i	$0.525774\pi$
$510$	−35.5039	−1.57214
$511$	17.8440	0.789371
$512$	31.0600	1.37267
$513$	5.71036	0.252119
$514$	69.2545	3.05469
$515$	−9.62135	−0.423967
$516$	−22.2863	−0.981098
$517$	4.78125	0.210279
$518$	−2.21267	−0.0972190
$519$	−14.8155	−0.650328
$520$	86.7509	3.80428
$521$	−32.9400	−1.44313	−0.721563	−	0.692349i	$-0.756576\pi$
$521$	−32.9400	−1.44313	−0.721563	+	0.692349i	$0.756576\pi$
$522$	3.16823	0.138670
$523$	−10.5628	−0.461881	−0.230941	−	0.972968i	$-0.574180\pi$
$523$	−10.5628	−0.461881	−0.230941	+	0.972968i	$0.574180\pi$
$524$	−23.8800	−1.04320
$525$	21.0347	0.918030
$526$	−63.3025	−2.76012
$527$	34.0902	1.48499
$528$	3.91715	0.170472
$529$	−21.4006	−0.930459
$530$	64.8466	2.81675
$531$	−13.0537	−0.566482
$532$	99.9041	4.33139
$533$	33.6009	1.45542
$534$	−10.2351	−0.442915
$535$	−32.8245	−1.41913
$536$	−11.3244	−0.489138
$537$	−17.3131	−0.747117
$538$	−40.8696	−1.76201
$539$	18.3070	0.788538
$540$	11.8496	0.509928
$541$	−40.2496	−1.73046	−0.865232	−	0.501371i	$-0.832829\pi$
$541$	−40.2496	−1.73046	−0.865232	+	0.501371i	$0.832829\pi$
$542$	−2.84968	−0.122404
$543$	−26.7666	−1.14867
$544$	7.68138	0.329337
$545$	60.6298	2.59710
$546$	70.1916	3.00392
$547$	10.8260	0.462886	0.231443	−	0.972849i	$-0.425655\pi$
$547$	10.8260	0.462886	0.231443	+	0.972849i	$0.425655\pi$
$548$	43.7791	1.87015
$549$	3.27359	0.139713
$550$	−14.5925	−0.622225
$551$	−7.49622	−0.319350
$552$	−5.56961	−0.237058
$553$	38.5101	1.63761
$554$	−12.9906	−0.551918
$555$	0.620960	0.0263583
$556$	28.8480	1.22343
$557$	−30.9379	−1.31088	−0.655441	−	0.755246i	$-0.727517\pi$
$557$	−30.9379	−1.31088	−0.655441	+	0.755246i	$0.727517\pi$
$558$	−17.3274	−0.733526
$559$	37.0480	1.56696
$560$	42.2201	1.78412
$561$	6.24317	0.263587
$562$	−2.03349	−0.0857776
$563$	−3.88846	−0.163879	−0.0819396	−	0.996637i	$-0.526111\pi$
$563$	−3.88846	−0.163879	−0.0819396	+	0.996637i	$0.526111\pi$
$564$	13.9083	0.585645
$565$	51.1106	2.15024
$566$	48.6915	2.04666
$567$	4.57422	0.192099
$568$	33.1715	1.39184
$569$	−41.3991	−1.73554	−0.867770	−	0.496966i	$-0.834447\pi$
$569$	−41.3991	−1.73554	−0.867770	+	0.496966i	$0.834447\pi$
$570$	−42.6977	−1.78841
$571$	41.9500	1.75555	0.877777	−	0.479069i	$-0.159026\pi$
$571$	41.9500	1.75555	0.877777	+	0.479069i	$0.159026\pi$
$572$	−31.9744	−1.33692
$573$	−0.755718	−0.0315706
$574$	58.3412	2.43512
$575$	5.81571	0.242532
$576$	−9.86270	−0.410946
$577$	11.1143	0.462696	0.231348	−	0.972871i	$-0.425686\pi$
$577$	11.1143	0.462696	0.231348	+	0.972871i	$0.425686\pi$
$578$	−13.3851	−0.556747
$579$	20.9901	0.872319
$580$	−15.5555	−0.645907
$581$	42.4895	1.76276
$582$	−36.5276	−1.51412
$583$	−11.4029	−0.472260
$584$	−17.1797	−0.710902
$585$	−19.6985	−0.814432
$586$	59.7626	2.46877
$587$	1.52602	0.0629856	0.0314928	−	0.999504i	$-0.489974\pi$
$587$	1.52602	0.0629856	0.0314928	+	0.999504i	$0.489974\pi$
$588$	53.2537	2.19614
$589$	40.9975	1.68927
$590$	97.6055	4.01836
$591$	3.01118	0.123864
$592$	0.597119	0.0245414
$593$	5.40111	0.221797	0.110899	−	0.993832i	$-0.464627\pi$
$593$	5.40111	0.221797	0.110899	+	0.993832i	$0.464627\pi$
$594$	−3.17328	−0.130201
$595$	67.2906	2.75865
$596$	6.21713	0.254664
$597$	−17.4845	−0.715594
$598$	19.4067	0.793599
$599$	−22.1738	−0.905998	−0.452999	−	0.891511i	$-0.649646\pi$
$599$	−22.1738	−0.905998	−0.452999	+	0.891511i	$0.649646\pi$
$600$	−20.2517	−0.826772
$601$	−14.1685	−0.577944	−0.288972	−	0.957337i	$-0.593314\pi$
$601$	−14.1685	−0.577944	−0.288972	+	0.957337i	$0.593314\pi$
$602$	64.3265	2.62175
$603$	2.57141	0.104716
$604$	18.6661	0.759514
$605$	−28.7236	−1.16778
$606$	37.4214	1.52014
$607$	17.7221	0.719316	0.359658	−	0.933084i	$-0.382893\pi$
$607$	17.7221	0.719316	0.359658	+	0.933084i	$0.382893\pi$
$608$	9.23779	0.374642
$609$	−6.00475	−0.243325
$610$	−24.4774	−0.991061
$611$	−23.1207	−0.935364
$612$	18.1609	0.734112
$613$	2.67570	0.108071	0.0540353	−	0.998539i	$-0.482792\pi$
$613$	2.67570	0.108071	0.0540353	+	0.998539i	$0.482792\pi$
$614$	−26.4518	−1.06751
$615$	−16.3728	−0.660215
$616$	−26.4867	−1.06718
$617$	12.4823	0.502519	0.251260	−	0.967920i	$-0.419155\pi$
$617$	12.4823	0.502519	0.251260	+	0.967920i	$0.419155\pi$
$618$	7.49500	0.301493
$619$	−18.7317	−0.752889	−0.376445	−	0.926439i	$-0.622853\pi$
$619$	−18.7317	−0.752889	−0.376445	+	0.926439i	$0.622853\pi$
$620$	85.0745	3.41667
$621$	1.26469	0.0507502
$622$	−53.0762	−2.12816
$623$	19.3986	0.777187
$624$	−18.9422	−0.758294
$625$	−26.8461	−1.07385
$626$	59.4387	2.37565
$627$	7.50817	0.299847
$628$	44.5202	1.77655
$629$	0.951691	0.0379464
$630$	−34.2025	−1.36266
$631$	16.5028	0.656967	0.328483	−	0.944510i	$-0.393463\pi$
$631$	16.5028	0.656967	0.328483	+	0.944510i	$0.393463\pi$
$632$	−37.0765	−1.47483
$633$	23.8817	0.949212
$634$	−52.0670	−2.06784
$635$	3.37926	0.134102
$636$	−33.1702	−1.31529
$637$	−88.5272	−3.50758
$638$	4.16569	0.164921
$639$	−7.53223	−0.297970
$640$	63.7218	2.51883
$641$	−2.15835	−0.0852498	−0.0426249	−	0.999091i	$-0.513572\pi$
$641$	−2.15835	−0.0852498	−0.0426249	+	0.999091i	$0.513572\pi$
$642$	25.5702	1.00917
$643$	−1.80467	−0.0711691	−0.0355845	−	0.999367i	$-0.511329\pi$
$643$	−1.80467	−0.0711691	−0.0355845	+	0.999367i	$0.511329\pi$
$644$	22.1260	0.871886
$645$	−18.0525	−0.710816
$646$	−65.4391	−2.57467
$647$	−43.8849	−1.72529	−0.862647	−	0.505807i	$-0.831195\pi$
$647$	−43.8849	−1.72529	−0.862647	+	0.505807i	$0.831195\pi$
$648$	−4.40394	−0.173003
$649$	−17.1634	−0.673723
$650$	70.5648	2.76778
$651$	32.8406	1.28712
$652$	−78.4195	−3.07114
$653$	12.9536	0.506913	0.253457	−	0.967347i	$-0.418432\pi$
$653$	12.9536	0.506913	0.253457	+	0.967347i	$0.418432\pi$
$654$	−47.2305	−1.84686
$655$	−19.3435	−0.755811
$656$	−15.7442	−0.614707
$657$	3.90099	0.152192
$658$	−40.1445	−1.56500
$659$	−23.6300	−0.920494	−0.460247	−	0.887791i	$-0.652239\pi$
$659$	−23.6300	−0.920494	−0.460247	+	0.887791i	$0.652239\pi$
$660$	15.5803	0.606462
$661$	1.48979	0.0579460	0.0289730	−	0.999580i	$-0.490776\pi$
$661$	1.48979	0.0579460	0.0289730	+	0.999580i	$0.490776\pi$
$662$	56.3764	2.19113
$663$	−30.1901	−1.17249
$664$	−40.9078	−1.58753
$665$	80.9251	3.13814
$666$	−0.483726	−0.0187440
$667$	−1.66020	−0.0642834
$668$	−52.7176	−2.03971
$669$	−1.30410	−0.0504196
$670$	−19.2271	−0.742807
$671$	4.30422	0.166162
$672$	7.39982	0.285454
$673$	−31.9437	−1.23134	−0.615669	−	0.788005i	$-0.711114\pi$
$673$	−31.9437	−1.23134	−0.615669	+	0.788005i	$0.711114\pi$
$674$	−28.3458	−1.09184
$675$	4.59854	0.176998
$676$	104.897	4.03451
$677$	4.19507	0.161230	0.0806148	−	0.996745i	$-0.474312\pi$
$677$	4.19507	0.161230	0.0806148	+	0.996745i	$0.474312\pi$
$678$	−39.8150	−1.52909
$679$	69.2307	2.65683
$680$	−64.7857	−2.48442
$681$	−12.4882	−0.478547
$682$	−22.7826	−0.872390
$683$	24.3586	0.932054	0.466027	−	0.884770i	$-0.345685\pi$
$683$	24.3586	0.932054	0.466027	+	0.884770i	$0.345685\pi$
$684$	21.8407	0.835100
$685$	35.4623	1.35494
$686$	−76.4324	−2.91820
$687$	24.2400	0.924815
$688$	−17.3594	−0.661821
$689$	55.1411	2.10071
$690$	−9.45637	−0.359998
$691$	−5.41142	−0.205860	−0.102930	−	0.994689i	$-0.532822\pi$
$691$	−5.41142	−0.205860	−0.102930	+	0.994689i	$0.532822\pi$
$692$	−56.6656	−2.15410
$693$	6.01432	0.228465
$694$	20.4484	0.776211
$695$	23.3677	0.886388
$696$	5.78122	0.219137
$697$	−25.0932	−0.950472
$698$	−54.1023	−2.04780
$699$	28.1910	1.06628
$700$	80.4525	3.04082
$701$	45.1869	1.70669	0.853343	−	0.521350i	$-0.174571\pi$
$701$	45.1869	1.70669	0.853343	+	0.521350i	$0.174571\pi$
$702$	15.3451	0.579162
$703$	1.14452	0.0431665
$704$	−12.9678	−0.488742
$705$	11.2661	0.424306
$706$	27.0774	1.01907
$707$	−70.9249	−2.66740
$708$	−49.9271	−1.87637
$709$	45.5997	1.71253	0.856266	−	0.516535i	$-0.172779\pi$
$709$	45.5997	1.71253	0.856266	+	0.516535i	$0.172779\pi$
$710$	56.3202	2.11366
$711$	8.41894	0.315735
$712$	−18.6765	−0.699930
$713$	9.07982	0.340042
$714$	−52.4192	−1.96174
$715$	−25.9002	−0.968612
$716$	−66.2184	−2.47470
$717$	5.12904	0.191548
$718$	−1.56778	−0.0585091
$719$	−7.64098	−0.284960	−0.142480	−	0.989798i	$-0.545508\pi$
$719$	−7.64098	−0.284960	−0.142480	+	0.989798i	$0.545508\pi$
$720$	9.23002	0.343982
$721$	−14.2053	−0.529032
$722$	−32.8429	−1.22229
$723$	−19.4892	−0.724810
$724$	−102.376	−3.80476
$725$	−6.03668	−0.224197
$726$	22.3756	0.830438
$727$	37.8926	1.40536	0.702680	−	0.711507i	$-0.251987\pi$
$727$	37.8926	1.40536	0.702680	+	0.711507i	$0.251987\pi$
$728$	128.082	4.74703
$729$	1.00000	0.0370370
$730$	−29.1686	−1.07958
$731$	−27.6675	−1.02332
$732$	12.5206	0.462776
$733$	−49.1819	−1.81658	−0.908288	−	0.418346i	$-0.862610\pi$
$733$	−49.1819	−1.81658	−0.908288	+	0.418346i	$0.862610\pi$
$734$	45.9243	1.69510
$735$	43.1369	1.59113
$736$	2.04591	0.0754134
$737$	3.38098	0.124540
$738$	12.7544	0.469495
$739$	0.803553	0.0295592	0.0147796	−	0.999891i	$-0.495295\pi$
$739$	0.803553	0.0295592	0.0147796	+	0.999891i	$0.495295\pi$
$740$	2.37501	0.0873072
$741$	−36.3073	−1.33378
$742$	95.7417	3.51479
$743$	19.9017	0.730123	0.365061	−	0.930983i	$-0.381048\pi$
$743$	19.9017	0.730123	0.365061	+	0.930983i	$0.381048\pi$
$744$	−31.6181	−1.15918
$745$	5.03605	0.184506
$746$	32.7032	1.19735
$747$	9.28891	0.339863
$748$	23.8786	0.873087
$749$	−48.4631	−1.77080
$750$	3.00182	0.109611
$751$	7.43726	0.271389	0.135695	−	0.990751i	$-0.456673\pi$
$751$	7.43726	0.271389	0.135695	+	0.990751i	$0.456673\pi$
$752$	10.8336	0.395059
$753$	−11.5239	−0.419954
$754$	−20.1441	−0.733603
$755$	15.1201	0.550276
$756$	17.4952	0.636295
$757$	1.44087	0.0523692	0.0261846	−	0.999657i	$-0.491664\pi$
$757$	1.44087	0.0523692	0.0261846	+	0.999657i	$0.491664\pi$
$758$	7.11227	0.258329
$759$	1.66285	0.0603577
$760$	−77.9126	−2.82619
$761$	−3.11192	−0.112807	−0.0564035	−	0.998408i	$-0.517963\pi$
$761$	−3.11192	−0.112807	−0.0564035	+	0.998408i	$0.517963\pi$
$762$	−2.63243	−0.0953629
$763$	89.5160	3.24070
$764$	−2.89043	−0.104572
$765$	14.7108	0.531872
$766$	−69.6152	−2.51530
$767$	82.9972	2.99685
$768$	−29.9137	−1.07942
$769$	8.62599	0.311061	0.155531	−	0.987831i	$-0.450291\pi$
$769$	8.62599	0.311061	0.155531	+	0.987831i	$0.450291\pi$
$770$	−44.9705	−1.62062
$771$	−28.6952	−1.03343
$772$	80.2818	2.88941
$773$	36.2190	1.30271	0.651354	−	0.758774i	$-0.274201\pi$
$773$	36.2190	1.30271	0.651354	+	0.758774i	$0.274201\pi$
$774$	14.0628	0.505479
$775$	33.0152	1.18594
$776$	−66.6536	−2.39272
$777$	0.916806	0.0328902
$778$	17.7275	0.635563
$779$	−30.1776	−1.08122
$780$	−75.3417	−2.69767
$781$	−9.90361	−0.354379
$782$	−14.4930	−0.518267
$783$	−1.31274	−0.0469135
$784$	41.4808	1.48146
$785$	36.0626	1.28713
$786$	15.0685	0.537476
$787$	34.6900	1.23656	0.618282	−	0.785956i	$-0.287829\pi$
$787$	34.6900	1.23656	0.618282	+	0.785956i	$0.287829\pi$
$788$	11.5170	0.410277
$789$	26.2290	0.933778
$790$	−62.9504	−2.23968
$791$	75.4614	2.68310
$792$	−5.79044	−0.205754
$793$	−20.8139	−0.739124
$794$	28.7208	1.01926
$795$	−26.8688	−0.952938
$796$	−66.8739	−2.37028
$797$	23.7019	0.839563	0.419781	−	0.907625i	$-0.362107\pi$
$797$	23.7019	0.839563	0.419781	+	0.907625i	$0.362107\pi$
$798$	−63.0404	−2.23161
$799$	17.2666	0.610848
$800$	7.43916	0.263014
$801$	4.24085	0.149843
$802$	−0.797383	−0.0281566
$803$	5.12914	0.181004
$804$	9.83501	0.346854
$805$	17.9227	0.631691
$806$	110.170	3.88057
$807$	16.9341	0.596108
$808$	68.2847	2.40225
$809$	−16.1191	−0.566717	−0.283359	−	0.959014i	$-0.591449\pi$
$809$	−16.1191	−0.566717	−0.283359	+	0.959014i	$0.591449\pi$
$810$	−7.47724	−0.262723
$811$	29.3069	1.02911	0.514553	−	0.857459i	$-0.327958\pi$
$811$	29.3069	1.02911	0.514553	+	0.857459i	$0.327958\pi$
$812$	−22.9667	−0.805972
$813$	1.18075	0.0414106
$814$	−0.636018	−0.0222924
$815$	−63.5219	−2.22508
$816$	14.1460	0.495211
$817$	−33.2735	−1.16409
$818$	−60.7055	−2.12252
$819$	−29.0835	−1.01626
$820$	−62.6219	−2.18685
$821$	−10.1129	−0.352942	−0.176471	−	0.984306i	$-0.556468\pi$
$821$	−10.1129	−0.352942	−0.176471	+	0.984306i	$0.556468\pi$
$822$	−27.6250	−0.963533
$823$	−38.6979	−1.34892	−0.674462	−	0.738310i	$-0.735624\pi$
$823$	−38.6979	−1.34892	−0.674462	+	0.738310i	$0.735624\pi$
$824$	13.6765	0.476443
$825$	6.04630	0.210505
$826$	144.108	5.01416
$827$	7.10608	0.247103	0.123551	−	0.992338i	$-0.460572\pi$
$827$	7.10608	0.247103	0.123551	+	0.992338i	$0.460572\pi$
$828$	4.83711	0.168101
$829$	54.4181	1.89002	0.945010	−	0.327042i	$-0.106052\pi$
$829$	54.4181	1.89002	0.945010	+	0.327042i	$0.106052\pi$
$830$	−69.4553	−2.41083
$831$	5.38258	0.186720
$832$	62.7084	2.17402
$833$	66.1123	2.29065
$834$	−18.2034	−0.630332
$835$	−42.7027	−1.47779
$836$	28.7169	0.993193
$837$	7.17950	0.248160
$838$	23.1834	0.800859
$839$	−51.4868	−1.77752	−0.888760	−	0.458373i	$-0.848432\pi$
$839$	−51.4868	−1.77752	−0.888760	+	0.458373i	$0.848432\pi$
$840$	−62.4109	−2.15338
$841$	−27.2767	−0.940576
$842$	97.9145	3.37436
$843$	0.842565	0.0290195
$844$	91.3415	3.14410
$845$	84.9696	2.92304
$846$	−8.77626	−0.301734
$847$	−42.4085	−1.45717
$848$	−25.8372	−0.887253
$849$	−20.1750	−0.692405
$850$	−52.6979	−1.80752
$851$	0.253480	0.00868919
$852$	−28.8089	−0.986976
$853$	35.9756	1.23178	0.615890	−	0.787832i	$-0.288797\pi$
$853$	35.9756	1.23178	0.615890	+	0.787832i	$0.288797\pi$
$854$	−36.1393	−1.23666
$855$	17.6916	0.605039
$856$	46.6591	1.59478
$857$	−16.0640	−0.548737	−0.274368	−	0.961625i	$-0.588469\pi$
$857$	−16.0640	−0.548737	−0.274368	+	0.961625i	$0.588469\pi$
$858$	20.1762	0.688803
$859$	−17.0865	−0.582983	−0.291492	−	0.956573i	$-0.594152\pi$
$859$	−17.0865	−0.582983	−0.291492	+	0.956573i	$0.594152\pi$
$860$	−69.0462	−2.35446
$861$	−24.1734	−0.823826
$862$	−71.1676	−2.42398
$863$	−33.6466	−1.14534	−0.572672	−	0.819784i	$-0.694093\pi$
$863$	−33.6466	−1.14534	−0.572672	+	0.819784i	$0.694093\pi$
$864$	1.61772	0.0550361
$865$	−45.9007	−1.56067
$866$	−29.3063	−0.995868
$867$	5.54605	0.188354
$868$	125.607	4.26338
$869$	11.0695	0.375507
$870$	9.81566	0.332782
$871$	−16.3494	−0.553979
$872$	−86.1837	−2.91855
$873$	15.1350	0.512242
$874$	−17.4295	−0.589563
$875$	−5.68935	−0.192335
$876$	14.9203	0.504110
$877$	−31.9000	−1.07719	−0.538594	−	0.842566i	$-0.681044\pi$
$877$	−31.9000	−1.07719	−0.538594	+	0.842566i	$0.681044\pi$
$878$	56.9447	1.92179
$879$	−24.7623	−0.835212
$880$	12.1359	0.409102
$881$	−2.20650	−0.0743387	−0.0371694	−	0.999309i	$-0.511834\pi$
$881$	−2.20650	−0.0743387	−0.0371694	+	0.999309i	$0.511834\pi$
$882$	−33.6036	−1.13149
$883$	25.0139	0.841784	0.420892	−	0.907111i	$-0.361717\pi$
$883$	25.0139	0.841784	0.420892	+	0.907111i	$0.361717\pi$
$884$	−115.470	−3.88367
$885$	−40.4423	−1.35945
$886$	29.0674	0.976537
$887$	−6.37474	−0.214043	−0.107021	−	0.994257i	$-0.534131\pi$
$887$	−6.37474	−0.214043	−0.107021	+	0.994257i	$0.534131\pi$
$888$	−0.882678	−0.0296207
$889$	4.98925	0.167334
$890$	−31.7098	−1.06292
$891$	1.31483	0.0440485
$892$	−4.98787	−0.167006
$893$	20.7651	0.694879
$894$	−3.92307	−0.131207
$895$	−53.6387	−1.79294
$896$	94.0811	3.14303
$897$	−8.04106	−0.268483
$898$	9.66427	0.322501
$899$	−9.42481	−0.314335
$900$	17.5883	0.586275
$901$	−41.1795	−1.37189
$902$	16.7699	0.558375
$903$	−26.6533	−0.886967
$904$	−72.6524	−2.41638
$905$	−82.9270	−2.75659
$906$	−11.7785	−0.391315
$907$	−23.0268	−0.764594	−0.382297	−	0.924040i	$-0.624867\pi$
$907$	−23.0268	−0.764594	−0.382297	+	0.924040i	$0.624867\pi$
$908$	−47.7640	−1.58511
$909$	−15.5054	−0.514280
$910$	217.464	7.20887
$911$	35.1563	1.16478	0.582390	−	0.812909i	$-0.302118\pi$
$911$	35.1563	1.16478	0.582390	+	0.812909i	$0.302118\pi$
$912$	17.0123	0.563334
$913$	12.2133	0.404203
$914$	−6.95459	−0.230037
$915$	10.1421	0.335286
$916$	92.7120	3.06329
$917$	−28.5593	−0.943112
$918$	−11.4597	−0.378227
$919$	2.82221	0.0930962	0.0465481	−	0.998916i	$-0.485178\pi$
$919$	2.82221	0.0930962	0.0465481	+	0.998916i	$0.485178\pi$
$920$	−17.2555	−0.568897
$921$	10.9602	0.361149
$922$	6.81046	0.224290
$923$	47.8909	1.57635
$924$	23.0033	0.756752
$925$	0.921681	0.0303047
$926$	−64.7894	−2.12911
$927$	−3.10551	−0.101998
$928$	−2.12365	−0.0697122
$929$	−25.9197	−0.850397	−0.425198	−	0.905100i	$-0.639796\pi$
$929$	−25.9197	−0.850397	−0.425198	+	0.905100i	$0.639796\pi$
$930$	−53.6828	−1.76033
$931$	79.5080	2.60577
$932$	107.823	3.53187
$933$	21.9918	0.719981
$934$	40.4778	1.32447
$935$	19.3423	0.632561
$936$	28.0009	0.915237
$937$	45.2116	1.47700	0.738499	−	0.674254i	$-0.235535\pi$
$937$	45.2116	1.47700	0.738499	+	0.674254i	$0.235535\pi$
$938$	−28.3875	−0.926885
$939$	−24.6281	−0.803707
$940$	43.0900	1.40544
$941$	18.9527	0.617841	0.308920	−	0.951088i	$-0.400032\pi$
$941$	18.9527	0.617841	0.308920	+	0.951088i	$0.400032\pi$
$942$	−28.0927	−0.915309
$943$	−6.68350	−0.217645
$944$	−38.8896	−1.26575
$945$	14.1716	0.461002
$946$	18.4903	0.601171
$947$	−13.1479	−0.427250	−0.213625	−	0.976916i	$-0.568527\pi$
$947$	−13.1479	−0.427250	−0.213625	+	0.976916i	$0.568527\pi$
$948$	32.2003	1.04582
$949$	−24.8030	−0.805140
$950$	−63.3756	−2.05618
$951$	21.5737	0.699574
$952$	−95.6518	−3.10009
$953$	−0.457280	−0.0148128	−0.00740638	−	0.999973i	$-0.502358\pi$
$953$	−0.457280	−0.0148128	−0.00740638	+	0.999973i	$0.502358\pi$
$954$	20.9307	0.677657
$955$	−2.34133	−0.0757636
$956$	19.6173	0.634469
$957$	−1.72603	−0.0557946
$958$	−29.2373	−0.944616
$959$	52.3577	1.69072
$960$	−30.5561	−0.986195
$961$	20.5452	0.662748
$962$	3.07560	0.0991612
$963$	−10.5949	−0.341414
$964$	−74.5411	−2.40081
$965$	65.0305	2.09341
$966$	−13.9617	−0.449210
$967$	45.3664	1.45888	0.729442	−	0.684043i	$-0.239780\pi$
$967$	45.3664	1.45888	0.729442	+	0.684043i	$0.239780\pi$
$968$	40.8299	1.31232
$969$	27.1143	0.871038
$970$	−113.168	−3.63360
$971$	−29.9244	−0.960319	−0.480159	−	0.877181i	$-0.659421\pi$
$971$	−29.9244	−0.960319	−0.480159	+	0.877181i	$0.659421\pi$
$972$	3.82475	0.122679
$973$	34.5009	1.10605
$974$	26.7857	0.858270
$975$	−29.2381	−0.936370
$976$	9.75268	0.312176
$977$	38.7472	1.23963	0.619817	−	0.784747i	$-0.287207\pi$
$977$	38.7472	1.23963	0.619817	+	0.784747i	$0.287207\pi$
$978$	49.4834	1.58230
$979$	5.57600	0.178210
$980$	164.988	5.27035
$981$	19.5697	0.624812
$982$	69.3126	2.21185
$983$	17.1114	0.545770	0.272885	−	0.962047i	$-0.412022\pi$
$983$	17.1114	0.545770	0.272885	+	0.962047i	$0.412022\pi$
$984$	23.2735	0.741933
$985$	9.32910	0.297250
$986$	15.0436	0.479086
$987$	16.6337	0.529455
$988$	−138.866	−4.41792
$989$	−7.36916	−0.234326
$990$	−9.83131	−0.312459
$991$	39.9042	1.26760	0.633799	−	0.773497i	$-0.281494\pi$
$991$	39.9042	1.26760	0.633799	+	0.773497i	$0.281494\pi$
$992$	11.6144	0.368759
$993$	−23.3593	−0.741284
$994$	83.1531	2.63746
$995$	−54.1697	−1.71730
$996$	35.5277	1.12574
$997$	−39.6576	−1.25597	−0.627985	−	0.778225i	$-0.716120\pi$
$997$	−39.6576	−1.25597	−0.627985	+	0.778225i	$0.716120\pi$
$998$	−36.8328	−1.16592
$999$	0.200429	0.00634130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.9	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.9	✓	97	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41345 q^{2} +1.00000 q^{3} +3.82475 q^{4} +3.09815 q^{5} -2.41345 q^{6} +4.57422 q^{7} -4.40394 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.41345 q^{2} +1.00000 q^{3} +3.82475 q^{4} +3.09815 q^{5} -2.41345 q^{6} +4.57422 q^{7} -4.40394 q^{8} +1.00000 q^{9} -7.47724 q^{10} +1.31483 q^{11} +3.82475 q^{12} -6.35814 q^{13} -11.0396 q^{14} +3.09815 q^{15} +2.97920 q^{16} +4.74827 q^{17} -2.41345 q^{18} +5.71036 q^{19} +11.8496 q^{20} +4.57422 q^{21} -3.17328 q^{22} +1.26469 q^{23} -4.40394 q^{24} +4.59854 q^{25} +15.3451 q^{26} +1.00000 q^{27} +17.4952 q^{28} -1.31274 q^{29} -7.47724 q^{30} +7.17950 q^{31} +1.61772 q^{32} +1.31483 q^{33} -11.4597 q^{34} +14.1716 q^{35} +3.82475 q^{36} +0.200429 q^{37} -13.7817 q^{38} -6.35814 q^{39} -13.6441 q^{40} -5.28470 q^{41} -11.0396 q^{42} -5.82686 q^{43} +5.02890 q^{44} +3.09815 q^{45} -3.05226 q^{46} +3.63640 q^{47} +2.97920 q^{48} +13.9234 q^{49} -11.0984 q^{50} +4.74827 q^{51} -24.3183 q^{52} -8.67253 q^{53} -2.41345 q^{54} +4.07355 q^{55} -20.1446 q^{56} +5.71036 q^{57} +3.16823 q^{58} -13.0537 q^{59} +11.8496 q^{60} +3.27359 q^{61} -17.3274 q^{62} +4.57422 q^{63} -9.86270 q^{64} -19.6985 q^{65} -3.17328 q^{66} +2.57141 q^{67} +18.1609 q^{68} +1.26469 q^{69} -34.2025 q^{70} -7.53223 q^{71} -4.40394 q^{72} +3.90099 q^{73} -0.483726 q^{74} +4.59854 q^{75} +21.8407 q^{76} +6.01432 q^{77} +15.3451 q^{78} +8.41894 q^{79} +9.23002 q^{80} +1.00000 q^{81} +12.7544 q^{82} +9.28891 q^{83} +17.4952 q^{84} +14.7108 q^{85} +14.0628 q^{86} -1.31274 q^{87} -5.79044 q^{88} +4.24085 q^{89} -7.47724 q^{90} -29.0835 q^{91} +4.83711 q^{92} +7.17950 q^{93} -8.77626 q^{94} +17.6916 q^{95} +1.61772 q^{96} +15.1350 q^{97} -33.6036 q^{98} +1.31483 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

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