LMFDB - Embedded newform 6033.2.a.e.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.19685 q^{2} +1.00000 q^{3} +2.82615 q^{4} +3.79567 q^{5} -2.19685 q^{6} -1.66772 q^{7} -1.81492 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.19685 q^{2} +1.00000 q^{3} +2.82615 q^{4} +3.79567 q^{5} -2.19685 q^{6} -1.66772 q^{7} -1.81492 q^{8} +1.00000 q^{9} -8.33851 q^{10} +4.83986 q^{11} +2.82615 q^{12} -2.74812 q^{13} +3.66373 q^{14} +3.79567 q^{15} -1.66519 q^{16} +3.56654 q^{17} -2.19685 q^{18} -3.74503 q^{19} +10.7271 q^{20} -1.66772 q^{21} -10.6324 q^{22} +2.35015 q^{23} -1.81492 q^{24} +9.40711 q^{25} +6.03720 q^{26} +1.00000 q^{27} -4.71322 q^{28} +1.94030 q^{29} -8.33851 q^{30} -2.18869 q^{31} +7.28801 q^{32} +4.83986 q^{33} -7.83514 q^{34} -6.33012 q^{35} +2.82615 q^{36} -10.8568 q^{37} +8.22726 q^{38} -2.74812 q^{39} -6.88883 q^{40} +0.706976 q^{41} +3.66373 q^{42} +10.4697 q^{43} +13.6782 q^{44} +3.79567 q^{45} -5.16293 q^{46} +7.19902 q^{47} -1.66519 q^{48} -4.21871 q^{49} -20.6660 q^{50} +3.56654 q^{51} -7.76659 q^{52} +3.32017 q^{53} -2.19685 q^{54} +18.3705 q^{55} +3.02678 q^{56} -3.74503 q^{57} -4.26254 q^{58} -5.21288 q^{59} +10.7271 q^{60} +8.93412 q^{61} +4.80823 q^{62} -1.66772 q^{63} -12.6803 q^{64} -10.4310 q^{65} -10.6324 q^{66} -2.51919 q^{67} +10.0796 q^{68} +2.35015 q^{69} +13.9063 q^{70} +3.51929 q^{71} -1.81492 q^{72} +1.31735 q^{73} +23.8509 q^{74} +9.40711 q^{75} -10.5840 q^{76} -8.07154 q^{77} +6.03720 q^{78} -2.41891 q^{79} -6.32051 q^{80} +1.00000 q^{81} -1.55312 q^{82} +2.57053 q^{83} -4.71322 q^{84} +13.5374 q^{85} -23.0004 q^{86} +1.94030 q^{87} -8.78395 q^{88} +2.19869 q^{89} -8.33851 q^{90} +4.58310 q^{91} +6.64187 q^{92} -2.18869 q^{93} -15.8152 q^{94} -14.2149 q^{95} +7.28801 q^{96} -15.5192 q^{97} +9.26786 q^{98} +4.83986 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.19685	−1.55341	−0.776703	−	0.629866i	$-0.783110\pi$
$2$	−2.19685	−1.55341	−0.776703	+	0.629866i	$0.783110\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.82615	1.41307
$5$	3.79567	1.69748	0.848738	−	0.528814i	$-0.177363\pi$
$5$	3.79567	1.69748	0.848738	+	0.528814i	$0.177363\pi$
$6$	−2.19685	−0.896860
$7$	−1.66772	−0.630339	−0.315170	−	0.949035i	$-0.602061\pi$
$7$	−1.66772	−0.630339	−0.315170	+	0.949035i	$0.602061\pi$
$8$	−1.81492	−0.641670
$9$	1.00000	0.333333
$10$	−8.33851	−2.63687
$11$	4.83986	1.45927	0.729637	−	0.683835i	$-0.239689\pi$
$11$	4.83986	1.45927	0.729637	+	0.683835i	$0.239689\pi$
$12$	2.82615	0.815838
$13$	−2.74812	−0.762191	−0.381096	−	0.924536i	$-0.624453\pi$
$13$	−2.74812	−0.762191	−0.381096	+	0.924536i	$0.624453\pi$
$14$	3.66373	0.979174
$15$	3.79567	0.980038
$16$	−1.66519	−0.416298
$17$	3.56654	0.865012	0.432506	−	0.901631i	$-0.357629\pi$
$17$	3.56654	0.865012	0.432506	+	0.901631i	$0.357629\pi$
$18$	−2.19685	−0.517802
$19$	−3.74503	−0.859168	−0.429584	−	0.903027i	$-0.641340\pi$
$19$	−3.74503	−0.859168	−0.429584	+	0.903027i	$0.641340\pi$
$20$	10.7271	2.39866
$21$	−1.66772	−0.363927
$22$	−10.6324	−2.26685
$23$	2.35015	0.490040	0.245020	−	0.969518i	$-0.421205\pi$
$23$	2.35015	0.490040	0.245020	+	0.969518i	$0.421205\pi$
$24$	−1.81492	−0.370469
$25$	9.40711	1.88142
$26$	6.03720	1.18399
$27$	1.00000	0.192450
$28$	−4.71322	−0.890716
$29$	1.94030	0.360304	0.180152	−	0.983639i	$-0.442341\pi$
$29$	1.94030	0.360304	0.180152	+	0.983639i	$0.442341\pi$
$30$	−8.33851	−1.52240
$31$	−2.18869	−0.393101	−0.196550	−	0.980494i	$-0.562974\pi$
$31$	−2.18869	−0.393101	−0.196550	+	0.980494i	$0.562974\pi$
$32$	7.28801	1.28835
$33$	4.83986	0.842512
$34$	−7.83514	−1.34372
$35$	−6.33012	−1.06999
$36$	2.82615	0.471024
$37$	−10.8568	−1.78485	−0.892427	−	0.451191i	$-0.850999\pi$
$37$	−10.8568	−1.78485	−0.892427	+	0.451191i	$0.850999\pi$
$38$	8.22726	1.33464
$39$	−2.74812	−0.440051
$40$	−6.88883	−1.08922
$41$	0.706976	0.110411	0.0552056	−	0.998475i	$-0.482419\pi$
$41$	0.706976	0.110411	0.0552056	+	0.998475i	$0.482419\pi$
$42$	3.66373	0.565326
$43$	10.4697	1.59662	0.798310	−	0.602247i	$-0.205728\pi$
$43$	10.4697	1.59662	0.798310	+	0.602247i	$0.205728\pi$
$44$	13.6782	2.06206
$45$	3.79567	0.565825
$46$	−5.16293	−0.761232
$47$	7.19902	1.05008	0.525042	−	0.851076i	$-0.324050\pi$
$47$	7.19902	1.05008	0.525042	+	0.851076i	$0.324050\pi$
$48$	−1.66519	−0.240350
$49$	−4.21871	−0.602672
$50$	−20.6660	−2.92261
$51$	3.56654	0.499415
$52$	−7.76659	−1.07703
$53$	3.32017	0.456060	0.228030	−	0.973654i	$-0.426772\pi$
$53$	3.32017	0.456060	0.228030	+	0.973654i	$0.426772\pi$
$54$	−2.19685	−0.298953
$55$	18.3705	2.47708
$56$	3.02678	0.404470
$57$	−3.74503	−0.496041
$58$	−4.26254	−0.559699
$59$	−5.21288	−0.678659	−0.339329	−	0.940668i	$-0.610200\pi$
$59$	−5.21288	−0.678659	−0.339329	+	0.940668i	$0.610200\pi$
$60$	10.7271	1.38486
$61$	8.93412	1.14390	0.571949	−	0.820289i	$-0.306188\pi$
$61$	8.93412	1.14390	0.571949	+	0.820289i	$0.306188\pi$
$62$	4.80823	0.610645
$63$	−1.66772	−0.210113
$64$	−12.6803	−1.58503
$65$	−10.4310	−1.29380
$66$	−10.6324	−1.30876
$67$	−2.51919	−0.307768	−0.153884	−	0.988089i	$-0.549178\pi$
$67$	−2.51919	−0.307768	−0.153884	+	0.988089i	$0.549178\pi$
$68$	10.0796	1.22233
$69$	2.35015	0.282925
$70$	13.9063	1.66212
$71$	3.51929	0.417663	0.208831	−	0.977952i	$-0.433034\pi$
$71$	3.51929	0.417663	0.208831	+	0.977952i	$0.433034\pi$
$72$	−1.81492	−0.213890
$73$	1.31735	0.154185	0.0770923	−	0.997024i	$-0.475436\pi$
$73$	1.31735	0.154185	0.0770923	+	0.997024i	$0.475436\pi$
$74$	23.8509	2.77261
$75$	9.40711	1.08624
$76$	−10.5840	−1.21407
$77$	−8.07154	−0.919837
$78$	6.03720	0.683579
$79$	−2.41891	−0.272149	−0.136075	−	0.990699i	$-0.543449\pi$
$79$	−2.41891	−0.272149	−0.136075	+	0.990699i	$0.543449\pi$
$80$	−6.32051	−0.706655
$81$	1.00000	0.111111
$82$	−1.55312	−0.171513
$83$	2.57053	0.282153	0.141076	−	0.989999i	$-0.454944\pi$
$83$	2.57053	0.282153	0.141076	+	0.989999i	$0.454944\pi$
$84$	−4.71322	−0.514255
$85$	13.5374	1.46834
$86$	−23.0004	−2.48020
$87$	1.94030	0.208022
$88$	−8.78395	−0.936372
$89$	2.19869	0.233060	0.116530	−	0.993187i	$-0.462823\pi$
$89$	2.19869	0.233060	0.116530	+	0.993187i	$0.462823\pi$
$90$	−8.33851	−0.878956
$91$	4.58310	0.480439
$92$	6.64187	0.692463
$93$	−2.18869	−0.226957
$94$	−15.8152	−1.63121
$95$	−14.2149	−1.45842
$96$	7.28801	0.743829
$97$	−15.5192	−1.57573	−0.787867	−	0.615846i	$-0.788814\pi$
$97$	−15.5192	−1.57573	−0.787867	+	0.615846i	$0.788814\pi$
$98$	9.26786	0.936195
$99$	4.83986	0.486424
$100$	26.5859	2.65859
$101$	12.3116	1.22505	0.612523	−	0.790453i	$-0.290155\pi$
$101$	12.3116	1.22505	0.612523	+	0.790453i	$0.290155\pi$
$102$	−7.83514	−0.775795
$103$	2.92077	0.287792	0.143896	−	0.989593i	$-0.454037\pi$
$103$	2.92077	0.287792	0.143896	+	0.989593i	$0.454037\pi$
$104$	4.98761	0.489076
$105$	−6.33012	−0.617756
$106$	−7.29391	−0.708447
$107$	3.19193	0.308575	0.154288	−	0.988026i	$-0.450692\pi$
$107$	3.19193	0.308575	0.154288	+	0.988026i	$0.450692\pi$
$108$	2.82615	0.271946
$109$	−2.29237	−0.219569	−0.109785	−	0.993955i	$-0.535016\pi$
$109$	−2.29237	−0.219569	−0.109785	+	0.993955i	$0.535016\pi$
$110$	−40.3573	−3.84791
$111$	−10.8568	−1.03049
$112$	2.77707	0.262409
$113$	5.94731	0.559475	0.279738	−	0.960076i	$-0.409752\pi$
$113$	5.94731	0.559475	0.279738	+	0.960076i	$0.409752\pi$
$114$	8.22726	0.770554
$115$	8.92040	0.831831
$116$	5.48356	0.509136
$117$	−2.74812	−0.254064
$118$	11.4519	1.05423
$119$	−5.94799	−0.545251
$120$	−6.88883	−0.628861
$121$	12.4243	1.12948
$122$	−19.6269	−1.77694
$123$	0.706976	0.0637459
$124$	−6.18556	−0.555480
$125$	16.7279	1.49619
$126$	3.66373	0.326391
$127$	10.6990	0.949379	0.474690	−	0.880153i	$-0.342560\pi$
$127$	10.6990	0.949379	0.474690	+	0.880153i	$0.342560\pi$
$128$	13.2806	1.17385
$129$	10.4697	0.921808
$130$	22.9152	2.00980
$131$	0.809949	0.0707656	0.0353828	−	0.999374i	$-0.488735\pi$
$131$	0.809949	0.0707656	0.0353828	+	0.999374i	$0.488735\pi$
$132$	13.6782	1.19053
$133$	6.24566	0.541568
$134$	5.53429	0.478090
$135$	3.79567	0.326679
$136$	−6.47297	−0.555053
$137$	14.6222	1.24926	0.624630	−	0.780921i	$-0.285250\pi$
$137$	14.6222	1.24926	0.624630	+	0.780921i	$0.285250\pi$
$138$	−5.16293	−0.439497
$139$	19.0862	1.61887	0.809433	−	0.587212i	$-0.199775\pi$
$139$	19.0862	1.61887	0.809433	+	0.587212i	$0.199775\pi$
$140$	−17.8898	−1.51197
$141$	7.19902	0.606266
$142$	−7.73134	−0.648800
$143$	−13.3005	−1.11225
$144$	−1.66519	−0.138766
$145$	7.36472	0.611607
$146$	−2.89403	−0.239511
$147$	−4.21871	−0.347953
$148$	−30.6830	−2.52213
$149$	12.6371	1.03527	0.517636	−	0.855601i	$-0.326812\pi$
$149$	12.6371	1.03527	0.517636	+	0.855601i	$0.326812\pi$
$150$	−20.6660	−1.68737
$151$	0.878917	0.0715252	0.0357626	−	0.999360i	$-0.488614\pi$
$151$	0.878917	0.0715252	0.0357626	+	0.999360i	$0.488614\pi$
$152$	6.79692	0.551303
$153$	3.56654	0.288337
$154$	17.7320	1.42888
$155$	−8.30755	−0.667279
$156$	−7.76659	−0.621825
$157$	16.3344	1.30363	0.651815	−	0.758378i	$-0.274008\pi$
$157$	16.3344	1.30363	0.651815	+	0.758378i	$0.274008\pi$
$158$	5.31399	0.422758
$159$	3.32017	0.263306
$160$	27.6629	2.18694
$161$	−3.91940	−0.308892
$162$	−2.19685	−0.172601
$163$	−3.19445	−0.250209	−0.125104	−	0.992144i	$-0.539927\pi$
$163$	−3.19445	−0.250209	−0.125104	+	0.992144i	$0.539927\pi$
$164$	1.99802	0.156019
$165$	18.3705	1.43014
$166$	−5.64708	−0.438298
$167$	−15.7619	−1.21969	−0.609847	−	0.792519i	$-0.708769\pi$
$167$	−15.7619	−1.21969	−0.609847	+	0.792519i	$0.708769\pi$
$168$	3.02678	0.233521
$169$	−5.44784	−0.419064
$170$	−29.7396	−2.28092
$171$	−3.74503	−0.286389
$172$	29.5890	2.25614
$173$	17.6932	1.34519	0.672594	−	0.740011i	$-0.265180\pi$
$173$	17.6932	1.34519	0.672594	+	0.740011i	$0.265180\pi$
$174$	−4.26254	−0.323142
$175$	−15.6884	−1.18593
$176$	−8.05929	−0.607492
$177$	−5.21288	−0.391824
$178$	−4.83018	−0.362038
$179$	−4.54546	−0.339744	−0.169872	−	0.985466i	$-0.554335\pi$
$179$	−4.54546	−0.339744	−0.169872	+	0.985466i	$0.554335\pi$
$180$	10.7271	0.799552
$181$	18.3425	1.36339	0.681695	−	0.731637i	$-0.261243\pi$
$181$	18.3425	1.36339	0.681695	+	0.731637i	$0.261243\pi$
$182$	−10.0684	−0.746318
$183$	8.93412	0.660429
$184$	−4.26533	−0.314444
$185$	−41.2090	−3.02975
$186$	4.80823	0.352556
$187$	17.2615	1.26229
$188$	20.3455	1.48385
$189$	−1.66772	−0.121309
$190$	31.2280	2.26551
$191$	−13.4368	−0.972256	−0.486128	−	0.873888i	$-0.661591\pi$
$191$	−13.4368	−0.972256	−0.486128	+	0.873888i	$0.661591\pi$
$192$	−12.6803	−0.915120
$193$	−13.5273	−0.973714	−0.486857	−	0.873482i	$-0.661857\pi$
$193$	−13.5273	−0.973714	−0.486857	+	0.873482i	$0.661857\pi$
$194$	34.0933	2.44775
$195$	−10.4310	−0.746976
$196$	−11.9227	−0.851620
$197$	−6.87274	−0.489662	−0.244831	−	0.969566i	$-0.578733\pi$
$197$	−6.87274	−0.489662	−0.244831	+	0.969566i	$0.578733\pi$
$198$	−10.6324	−0.755615
$199$	4.33479	0.307285	0.153642	−	0.988127i	$-0.450900\pi$
$199$	4.33479	0.307285	0.153642	+	0.988127i	$0.450900\pi$
$200$	−17.0731	−1.20725
$201$	−2.51919	−0.177690
$202$	−27.0466	−1.90300
$203$	−3.23587	−0.227114
$204$	10.0796	0.705710
$205$	2.68345	0.187420
$206$	−6.41649	−0.447058
$207$	2.35015	0.163347
$208$	4.57614	0.317299
$209$	−18.1254	−1.25376
$210$	13.9063	0.959627
$211$	5.66151	0.389754	0.194877	−	0.980828i	$-0.437569\pi$
$211$	5.66151	0.389754	0.194877	+	0.980828i	$0.437569\pi$
$212$	9.38328	0.644446
$213$	3.51929	0.241138
$214$	−7.01218	−0.479343
$215$	39.7396	2.71022
$216$	−1.81492	−0.123490
$217$	3.65013	0.247787
$218$	5.03599	0.341081
$219$	1.31735	0.0890185
$220$	51.9178	3.50029
$221$	−9.80127	−0.659305
$222$	23.8509	1.60076
$223$	−14.7044	−0.984677	−0.492339	−	0.870404i	$-0.663858\pi$
$223$	−14.7044	−0.984677	−0.492339	+	0.870404i	$0.663858\pi$
$224$	−12.1544	−0.812098
$225$	9.40711	0.627141
$226$	−13.0653	−0.869093
$227$	6.40836	0.425338	0.212669	−	0.977124i	$-0.431784\pi$
$227$	6.40836	0.425338	0.212669	+	0.977124i	$0.431784\pi$
$228$	−10.5840	−0.700942
$229$	−15.7459	−1.04052	−0.520260	−	0.854008i	$-0.674165\pi$
$229$	−15.7459	−1.04052	−0.520260	+	0.854008i	$0.674165\pi$
$230$	−19.5968	−1.29217
$231$	−8.07154	−0.531068
$232$	−3.52148	−0.231196
$233$	−0.0431460	−0.00282659	−0.00141329	−	0.999999i	$-0.500450\pi$
$233$	−0.0431460	−0.00282659	−0.00141329	+	0.999999i	$0.500450\pi$
$234$	6.03720	0.394664
$235$	27.3251	1.78249
$236$	−14.7324	−0.958995
$237$	−2.41891	−0.157125
$238$	13.0668	0.846997
$239$	−5.39831	−0.349188	−0.174594	−	0.984641i	$-0.555861\pi$
$239$	−5.39831	−0.349188	−0.174594	+	0.984641i	$0.555861\pi$
$240$	−6.32051	−0.407987
$241$	26.7598	1.72375	0.861876	−	0.507119i	$-0.169290\pi$
$241$	26.7598	1.72375	0.861876	+	0.507119i	$0.169290\pi$
$242$	−27.2942	−1.75454
$243$	1.00000	0.0641500
$244$	25.2491	1.61641
$245$	−16.0128	−1.02302
$246$	−1.55312	−0.0990233
$247$	10.2918	0.654851
$248$	3.97230	0.252241
$249$	2.57053	0.162901
$250$	−36.7487	−2.32419
$251$	8.99276	0.567618	0.283809	−	0.958881i	$-0.408402\pi$
$251$	8.99276	0.567618	0.283809	+	0.958881i	$0.408402\pi$
$252$	−4.71322	−0.296905
$253$	11.3744	0.715103
$254$	−23.5040	−1.47477
$255$	13.5374	0.847745
$256$	−3.81499	−0.238437
$257$	19.2715	1.20212	0.601062	−	0.799202i	$-0.294744\pi$
$257$	19.2715	1.20212	0.601062	+	0.799202i	$0.294744\pi$
$258$	−23.0004	−1.43194
$259$	18.1062	1.12506
$260$	−29.4794	−1.82823
$261$	1.94030	0.120101
$262$	−1.77934	−0.109928
$263$	27.3313	1.68532	0.842661	−	0.538445i	$-0.180988\pi$
$263$	27.3313	1.68532	0.842661	+	0.538445i	$0.180988\pi$
$264$	−8.78395	−0.540615
$265$	12.6023	0.774151
$266$	−13.7208	−0.841275
$267$	2.19869	0.134557
$268$	−7.11961	−0.434899
$269$	−29.6604	−1.80843	−0.904214	−	0.427079i	$-0.859543\pi$
$269$	−29.6604	−1.80843	−0.904214	+	0.427079i	$0.859543\pi$
$270$	−8.33851	−0.507466
$271$	−13.2505	−0.804909	−0.402455	−	0.915440i	$-0.631843\pi$
$271$	−13.2505	−0.804909	−0.402455	+	0.915440i	$0.631843\pi$
$272$	−5.93896	−0.360103
$273$	4.58310	0.277382
$274$	−32.1228	−1.94061
$275$	45.5291	2.74551
$276$	6.64187	0.399794
$277$	−3.68387	−0.221342	−0.110671	−	0.993857i	$-0.535300\pi$
$277$	−3.68387	−0.221342	−0.110671	+	0.993857i	$0.535300\pi$
$278$	−41.9294	−2.51476
$279$	−2.18869	−0.131034
$280$	11.4886	0.686578
$281$	−6.04203	−0.360438	−0.180219	−	0.983627i	$-0.557681\pi$
$281$	−6.04203	−0.360438	−0.180219	+	0.983627i	$0.557681\pi$
$282$	−15.8152	−0.941779
$283$	10.2912	0.611748	0.305874	−	0.952072i	$-0.401051\pi$
$283$	10.2912	0.611748	0.305874	+	0.952072i	$0.401051\pi$
$284$	9.94602	0.590188
$285$	−14.2149	−0.842017
$286$	29.2192	1.72777
$287$	−1.17904	−0.0695965
$288$	7.28801	0.429450
$289$	−4.27981	−0.251754
$290$	−16.1792	−0.950075
$291$	−15.5192	−0.909750
$292$	3.72303	0.217874
$293$	18.0546	1.05476	0.527381	−	0.849629i	$-0.323174\pi$
$293$	18.0546	1.05476	0.527381	+	0.849629i	$0.323174\pi$
$294$	9.26786	0.540513
$295$	−19.7864	−1.15201
$296$	19.7043	1.14529
$297$	4.83986	0.280837
$298$	−27.7618	−1.60820
$299$	−6.45850	−0.373504
$300$	26.5859	1.53494
$301$	−17.4606	−1.00641
$302$	−1.93085	−0.111108
$303$	12.3116	0.707281
$304$	6.23619	0.357670
$305$	33.9110	1.94174
$306$	−7.83514	−0.447905
$307$	−12.5628	−0.716999	−0.358500	−	0.933530i	$-0.616712\pi$
$307$	−12.5628	−0.716999	−0.358500	+	0.933530i	$0.616712\pi$
$308$	−22.8114	−1.29980
$309$	2.92077	0.166157
$310$	18.2504	1.03656
$311$	2.97691	0.168805	0.0844024	−	0.996432i	$-0.473102\pi$
$311$	2.97691	0.168805	0.0844024	+	0.996432i	$0.473102\pi$
$312$	4.98761	0.282368
$313$	−25.6863	−1.45187	−0.725937	−	0.687762i	$-0.758593\pi$
$313$	−25.6863	−1.45187	−0.725937	+	0.687762i	$0.758593\pi$
$314$	−35.8843	−2.02507
$315$	−6.33012	−0.356662
$316$	−6.83620	−0.384566
$317$	−18.5714	−1.04308	−0.521538	−	0.853228i	$-0.674641\pi$
$317$	−18.5714	−1.04308	−0.521538	+	0.853228i	$0.674641\pi$
$318$	−7.29391	−0.409022
$319$	9.39077	0.525782
$320$	−48.1301	−2.69056
$321$	3.19193	0.178156
$322$	8.61032	0.479834
$323$	−13.3568	−0.743191
$324$	2.82615	0.157008
$325$	−25.8519	−1.43400
$326$	7.01773	0.388676
$327$	−2.29237	−0.126768
$328$	−1.28310	−0.0708476
$329$	−12.0060	−0.661910
$330$	−40.3573	−2.22159
$331$	−27.4108	−1.50663	−0.753316	−	0.657659i	$-0.771547\pi$
$331$	−27.4108	−1.50663	−0.753316	+	0.657659i	$0.771547\pi$
$332$	7.26470	0.398702
$333$	−10.8568	−0.594951
$334$	34.6266	1.89468
$335$	−9.56203	−0.522429
$336$	2.77707	0.151502
$337$	−19.8883	−1.08339	−0.541693	−	0.840577i	$-0.682216\pi$
$337$	−19.8883	−1.08339	−0.541693	+	0.840577i	$0.682216\pi$
$338$	11.9681	0.650977
$339$	5.94731	0.323013
$340$	38.2587	2.07487
$341$	−10.5930	−0.573641
$342$	8.22726	0.444879
$343$	18.7097	1.01023
$344$	−19.0017	−1.02450
$345$	8.92040	0.480258
$346$	−38.8693	−2.08963
$347$	10.9365	0.587102	0.293551	−	0.955943i	$-0.405163\pi$
$347$	10.9365	0.587102	0.293551	+	0.955943i	$0.405163\pi$
$348$	5.48356	0.293950
$349$	−29.7036	−1.59000	−0.795000	−	0.606610i	$-0.792529\pi$
$349$	−29.7036	−1.59000	−0.795000	+	0.606610i	$0.792529\pi$
$350$	34.4651	1.84224
$351$	−2.74812	−0.146684
$352$	35.2730	1.88005
$353$	8.60188	0.457832	0.228916	−	0.973446i	$-0.426482\pi$
$353$	8.60188	0.457832	0.228916	+	0.973446i	$0.426482\pi$
$354$	11.4519	0.608662
$355$	13.3581	0.708972
$356$	6.21381	0.329331
$357$	−5.94799	−0.314801
$358$	9.98569	0.527760
$359$	−1.09179	−0.0576225	−0.0288113	−	0.999585i	$-0.509172\pi$
$359$	−1.09179	−0.0576225	−0.0288113	+	0.999585i	$0.509172\pi$
$360$	−6.88883	−0.363073
$361$	−4.97477	−0.261830
$362$	−40.2958	−2.11790
$363$	12.4243	0.652105
$364$	12.9525	0.678896
$365$	5.00024	0.261724
$366$	−19.6269	−1.02592
$367$	26.5862	1.38779	0.693895	−	0.720076i	$-0.255893\pi$
$367$	26.5862	1.38779	0.693895	+	0.720076i	$0.255893\pi$
$368$	−3.91345	−0.204003
$369$	0.706976	0.0368037
$370$	90.5300	4.70643
$371$	−5.53711	−0.287473
$372$	−6.18556	−0.320707
$373$	−25.4449	−1.31749	−0.658743	−	0.752368i	$-0.728911\pi$
$373$	−25.4449	−1.31749	−0.658743	+	0.752368i	$0.728911\pi$
$374$	−37.9210	−1.96085
$375$	16.7279	0.863826
$376$	−13.0656	−0.673808
$377$	−5.33217	−0.274621
$378$	3.66373	0.188442
$379$	−13.6810	−0.702745	−0.351372	−	0.936236i	$-0.614285\pi$
$379$	−13.6810	−0.702745	−0.351372	+	0.936236i	$0.614285\pi$
$380$	−40.1733	−2.06085
$381$	10.6990	0.548124
$382$	29.5187	1.51031
$383$	−10.3543	−0.529078	−0.264539	−	0.964375i	$-0.585220\pi$
$383$	−10.3543	−0.529078	−0.264539	+	0.964375i	$0.585220\pi$
$384$	13.2806	0.677724
$385$	−30.6369	−1.56140
$386$	29.7174	1.51257
$387$	10.4697	0.532206
$388$	−43.8594	−2.22663
$389$	−25.8654	−1.31143	−0.655714	−	0.755009i	$-0.727632\pi$
$389$	−25.8654	−1.31143	−0.655714	+	0.755009i	$0.727632\pi$
$390$	22.9152	1.16036
$391$	8.38190	0.423891
$392$	7.65661	0.386717
$393$	0.809949	0.0408565
$394$	15.0984	0.760645
$395$	−9.18140	−0.461966
$396$	13.6782	0.687353
$397$	18.0773	0.907273	0.453637	−	0.891187i	$-0.350126\pi$
$397$	18.0773	0.907273	0.453637	+	0.891187i	$0.350126\pi$
$398$	−9.52287	−0.477339
$399$	6.24566	0.312674
$400$	−15.6646	−0.783231
$401$	−21.7092	−1.08411	−0.542054	−	0.840344i	$-0.682353\pi$
$401$	−21.7092	−1.08411	−0.542054	+	0.840344i	$0.682353\pi$
$402$	5.53429	0.276025
$403$	6.01479	0.299618
$404$	34.7943	1.73108
$405$	3.79567	0.188608
$406$	7.10872	0.352800
$407$	−52.5456	−2.60459
$408$	−6.47297	−0.320460
$409$	−17.7772	−0.879027	−0.439513	−	0.898236i	$-0.644849\pi$
$409$	−17.7772	−0.879027	−0.439513	+	0.898236i	$0.644849\pi$
$410$	−5.89513	−0.291140
$411$	14.6222	0.721261
$412$	8.25452	0.406671
$413$	8.69363	0.427785
$414$	−5.16293	−0.253744
$415$	9.75690	0.478947
$416$	−20.0283	−0.981969
$417$	19.0862	0.934653
$418$	39.8188	1.94760
$419$	2.16711	0.105870	0.0529351	−	0.998598i	$-0.483142\pi$
$419$	2.16711	0.105870	0.0529351	+	0.998598i	$0.483142\pi$
$420$	−17.8898	−0.872935
$421$	−1.16317	−0.0566896	−0.0283448	−	0.999598i	$-0.509024\pi$
$421$	−1.16317	−0.0566896	−0.0283448	+	0.999598i	$0.509024\pi$
$422$	−12.4375	−0.605447
$423$	7.19902	0.350028
$424$	−6.02583	−0.292640
$425$	33.5508	1.62745
$426$	−7.73134	−0.374585
$427$	−14.8996	−0.721044
$428$	9.02085	0.436039
$429$	−13.3005	−0.642155
$430$	−87.3020	−4.21008
$431$	28.0323	1.35027	0.675135	−	0.737694i	$-0.264085\pi$
$431$	28.0323	1.35027	0.675135	+	0.737694i	$0.264085\pi$
$432$	−1.66519	−0.0801165
$433$	−29.1813	−1.40237	−0.701183	−	0.712982i	$-0.747344\pi$
$433$	−29.1813	−1.40237	−0.701183	+	0.712982i	$0.747344\pi$
$434$	−8.01878	−0.384914
$435$	7.36472	0.353111
$436$	−6.47858	−0.310268
$437$	−8.80138	−0.421027
$438$	−2.89403	−0.138282
$439$	11.0078	0.525375	0.262687	−	0.964881i	$-0.415391\pi$
$439$	11.0078	0.525375	0.262687	+	0.964881i	$0.415391\pi$
$440$	−33.3410	−1.58947
$441$	−4.21871	−0.200891
$442$	21.5319	1.02417
$443$	−19.1551	−0.910085	−0.455042	−	0.890470i	$-0.650376\pi$
$443$	−19.1551	−0.910085	−0.455042	+	0.890470i	$0.650376\pi$
$444$	−30.6830	−1.45615
$445$	8.34549	0.395614
$446$	32.3033	1.52960
$447$	12.6371	0.597714
$448$	21.1472	0.999110
$449$	9.07498	0.428275	0.214137	−	0.976804i	$-0.431306\pi$
$449$	9.07498	0.428275	0.214137	+	0.976804i	$0.431306\pi$
$450$	−20.6660	−0.974204
$451$	3.42167	0.161120
$452$	16.8080	0.790580
$453$	0.878917	0.0412951
$454$	−14.0782	−0.660723
$455$	17.3959	0.815534
$456$	6.79692	0.318295
$457$	6.31801	0.295544	0.147772	−	0.989021i	$-0.452790\pi$
$457$	6.31801	0.295544	0.147772	+	0.989021i	$0.452790\pi$
$458$	34.5914	1.61635
$459$	3.56654	0.166472
$460$	25.2103	1.17544
$461$	15.4805	0.720998	0.360499	−	0.932760i	$-0.382606\pi$
$461$	15.4805	0.720998	0.360499	+	0.932760i	$0.382606\pi$
$462$	17.7320	0.824965
$463$	7.87377	0.365925	0.182962	−	0.983120i	$-0.441431\pi$
$463$	7.87377	0.365925	0.182962	+	0.983120i	$0.441431\pi$
$464$	−3.23096	−0.149994
$465$	−8.30755	−0.385254
$466$	0.0947852	0.00439084
$467$	23.5914	1.09168	0.545840	−	0.837889i	$-0.316211\pi$
$467$	23.5914	1.09168	0.545840	+	0.837889i	$0.316211\pi$
$468$	−7.76659	−0.359011
$469$	4.20131	0.193999
$470$	−60.0291	−2.76894
$471$	16.3344	0.752651
$472$	9.46095	0.435475
$473$	50.6721	2.32990
$474$	5.31399	0.244080
$475$	−35.2299	−1.61646
$476$	−16.8099	−0.770480
$477$	3.32017	0.152020
$478$	11.8593	0.542431
$479$	−20.2651	−0.925934	−0.462967	−	0.886376i	$-0.653215\pi$
$479$	−20.2651	−0.925934	−0.462967	+	0.886376i	$0.653215\pi$
$480$	27.6629	1.26263
$481$	29.8359	1.36040
$482$	−58.7873	−2.67769
$483$	−3.91940	−0.178339
$484$	35.1128	1.59604
$485$	−58.9056	−2.67477
$486$	−2.19685	−0.0996511
$487$	38.9109	1.76322	0.881611	−	0.471978i	$-0.156460\pi$
$487$	38.9109	1.76322	0.881611	+	0.471978i	$0.156460\pi$
$488$	−16.2147	−0.734005
$489$	−3.19445	−0.144458
$490$	35.1777	1.58917
$491$	11.3169	0.510723	0.255362	−	0.966846i	$-0.417806\pi$
$491$	11.3169	0.510723	0.255362	+	0.966846i	$0.417806\pi$
$492$	1.99802	0.0900776
$493$	6.92014	0.311667
$494$	−22.6095	−1.01725
$495$	18.3705	0.825693
$496$	3.64459	0.163647
$497$	−5.86919	−0.263269
$498$	−5.64708	−0.253051
$499$	−30.2309	−1.35332	−0.676661	−	0.736295i	$-0.736574\pi$
$499$	−30.2309	−1.35332	−0.676661	+	0.736295i	$0.736574\pi$
$500$	47.2756	2.11423
$501$	−15.7619	−0.704191
$502$	−19.7557	−0.881742
$503$	0.564627	0.0251755	0.0125877	−	0.999921i	$-0.495993\pi$
$503$	0.564627	0.0251755	0.0125877	+	0.999921i	$0.495993\pi$
$504$	3.02678	0.134823
$505$	46.7306	2.07949
$506$	−24.9878	−1.11085
$507$	−5.44784	−0.241947
$508$	30.2368	1.34154
$509$	−7.15138	−0.316979	−0.158490	−	0.987361i	$-0.550662\pi$
$509$	−7.15138	−0.316979	−0.158490	+	0.987361i	$0.550662\pi$
$510$	−29.7396	−1.31689
$511$	−2.19698	−0.0971886
$512$	−18.1803	−0.803463
$513$	−3.74503	−0.165347
$514$	−42.3366	−1.86739
$515$	11.0863	0.488520
$516$	29.5890	1.30258
$517$	34.8422	1.53236
$518$	−39.7766	−1.74768
$519$	17.6932	0.776645
$520$	18.9313	0.830194
$521$	−13.8885	−0.608468	−0.304234	−	0.952597i	$-0.598400\pi$
$521$	−13.8885	−0.608468	−0.304234	+	0.952597i	$0.598400\pi$
$522$	−4.26254	−0.186566
$523$	9.87541	0.431822	0.215911	−	0.976413i	$-0.430728\pi$
$523$	9.87541	0.431822	0.215911	+	0.976413i	$0.430728\pi$
$524$	2.28903	0.0999969
$525$	−15.6884	−0.684699
$526$	−60.0428	−2.61799
$527$	−7.80605	−0.340037
$528$	−8.05929	−0.350736
$529$	−17.4768	−0.759861
$530$	−27.6853	−1.20257
$531$	−5.21288	−0.226220
$532$	17.6512	0.765274
$533$	−1.94286	−0.0841544
$534$	−4.83018	−0.209022
$535$	12.1155	0.523799
$536$	4.57213	0.197486
$537$	−4.54546	−0.196151
$538$	65.1595	2.80923
$539$	−20.4180	−0.879464
$540$	10.7271	0.461622
$541$	14.4652	0.621906	0.310953	−	0.950425i	$-0.399352\pi$
$541$	14.4652	0.621906	0.310953	+	0.950425i	$0.399352\pi$
$542$	29.1093	1.25035
$543$	18.3425	0.787153
$544$	25.9930	1.11444
$545$	−8.70109	−0.372714
$546$	−10.0684	−0.430887
$547$	−36.8662	−1.57628	−0.788142	−	0.615494i	$-0.788957\pi$
$547$	−36.8662	−1.57628	−0.788142	+	0.615494i	$0.788957\pi$
$548$	41.3245	1.76530
$549$	8.93412	0.381299
$550$	−100.021	−4.26489
$551$	−7.26646	−0.309562
$552$	−4.26533	−0.181545
$553$	4.03407	0.171546
$554$	8.09290	0.343834
$555$	−41.2090	−1.74922
$556$	53.9403	2.28758
$557$	−23.1127	−0.979318	−0.489659	−	0.871914i	$-0.662879\pi$
$557$	−23.1127	−0.979318	−0.489659	+	0.871914i	$0.662879\pi$
$558$	4.80823	0.203548
$559$	−28.7721	−1.21693
$560$	10.5409	0.445432
$561$	17.2615	0.728783
$562$	13.2734	0.559906
$563$	4.68282	0.197357	0.0986786	−	0.995119i	$-0.468538\pi$
$563$	4.68282	0.197357	0.0986786	+	0.995119i	$0.468538\pi$
$564$	20.3455	0.856699
$565$	22.5740	0.949696
$566$	−22.6082	−0.950294
$567$	−1.66772	−0.0700377
$568$	−6.38722	−0.268002
$569$	23.7709	0.996528	0.498264	−	0.867025i	$-0.333971\pi$
$569$	23.7709	0.996528	0.498264	+	0.867025i	$0.333971\pi$
$570$	31.2280	1.30800
$571$	−13.1941	−0.552155	−0.276077	−	0.961135i	$-0.589035\pi$
$571$	−13.1941	−0.552155	−0.276077	+	0.961135i	$0.589035\pi$
$572$	−37.5892	−1.57168
$573$	−13.4368	−0.561332
$574$	2.59017	0.108112
$575$	22.1081	0.921972
$576$	−12.6803	−0.528345
$577$	9.85036	0.410076	0.205038	−	0.978754i	$-0.434268\pi$
$577$	9.85036	0.410076	0.205038	+	0.978754i	$0.434268\pi$
$578$	9.40210	0.391076
$579$	−13.5273	−0.562174
$580$	20.8138	0.864245
$581$	−4.28693	−0.177852
$582$	34.0933	1.41321
$583$	16.0692	0.665516
$584$	−2.39089	−0.0989356
$585$	−10.4310	−0.431267
$586$	−39.6632	−1.63847
$587$	27.6488	1.14119	0.570595	−	0.821232i	$-0.306713\pi$
$587$	27.6488	1.14119	0.570595	+	0.821232i	$0.306713\pi$
$588$	−11.9227	−0.491683
$589$	8.19671	0.337740
$590$	43.4677	1.78954
$591$	−6.87274	−0.282707
$592$	18.0787	0.743031
$593$	8.22530	0.337773	0.168886	−	0.985636i	$-0.445983\pi$
$593$	8.22530	0.337773	0.168886	+	0.985636i	$0.445983\pi$
$594$	−10.6324	−0.436255
$595$	−22.5766	−0.925550
$596$	35.7143	1.46291
$597$	4.33479	0.177411
$598$	14.1883	0.580204
$599$	44.2599	1.80841	0.904206	−	0.427097i	$-0.140464\pi$
$599$	44.2599	1.80841	0.904206	+	0.427097i	$0.140464\pi$
$600$	−17.0731	−0.697008
$601$	34.5704	1.41016	0.705078	−	0.709130i	$-0.250912\pi$
$601$	34.5704	1.41016	0.705078	+	0.709130i	$0.250912\pi$
$602$	38.3583	1.56337
$603$	−2.51919	−0.102589
$604$	2.48395	0.101070
$605$	47.1584	1.91726
$606$	−27.0466	−1.09869
$607$	45.1758	1.83363	0.916814	−	0.399314i	$-0.130752\pi$
$607$	45.1758	1.83363	0.916814	+	0.399314i	$0.130752\pi$
$608$	−27.2938	−1.10691
$609$	−3.23587	−0.131124
$610$	−74.4973	−3.01631
$611$	−19.7838	−0.800365
$612$	10.0796	0.407442
$613$	−0.589219	−0.0237983	−0.0118992	−	0.999929i	$-0.503788\pi$
$613$	−0.589219	−0.0237983	−0.0118992	+	0.999929i	$0.503788\pi$
$614$	27.5987	1.11379
$615$	2.68345	0.108207
$616$	14.6492	0.590232
$617$	20.5490	0.827271	0.413635	−	0.910443i	$-0.364259\pi$
$617$	20.5490	0.827271	0.413635	+	0.910443i	$0.364259\pi$
$618$	−6.41649	−0.258109
$619$	−12.7171	−0.511142	−0.255571	−	0.966790i	$-0.582263\pi$
$619$	−12.7171	−0.511142	−0.255571	+	0.966790i	$0.582263\pi$
$620$	−23.4784	−0.942914
$621$	2.35015	0.0943083
$622$	−6.53981	−0.262223
$623$	−3.66680	−0.146907
$624$	4.57614	0.183192
$625$	16.4581	0.658326
$626$	56.4288	2.25535
$627$	−18.1254	−0.723859
$628$	46.1635	1.84212
$629$	−38.7213	−1.54392
$630$	13.9063	0.554041
$631$	17.9990	0.716529	0.358264	−	0.933620i	$-0.383369\pi$
$631$	17.9990	0.716529	0.358264	+	0.933620i	$0.383369\pi$
$632$	4.39013	0.174630
$633$	5.66151	0.225025
$634$	40.7986	1.62032
$635$	40.6097	1.61155
$636$	9.38328	0.372071
$637$	11.5935	0.459352
$638$	−20.6301	−0.816753
$639$	3.51929	0.139221
$640$	50.4089	1.99259
$641$	−28.2356	−1.11524	−0.557620	−	0.830097i	$-0.688285\pi$
$641$	−28.2356	−1.11524	−0.557620	+	0.830097i	$0.688285\pi$
$642$	−7.01218	−0.276749
$643$	−14.2123	−0.560480	−0.280240	−	0.959930i	$-0.590414\pi$
$643$	−14.2123	−0.560480	−0.280240	+	0.959930i	$0.590414\pi$
$644$	−11.0768	−0.436486
$645$	39.7396	1.56475
$646$	29.3428	1.15448
$647$	41.7844	1.64271	0.821357	−	0.570415i	$-0.193218\pi$
$647$	41.7844	1.64271	0.821357	+	0.570415i	$0.193218\pi$
$648$	−1.81492	−0.0712967
$649$	−25.2296	−0.990349
$650$	56.7926	2.22759
$651$	3.65013	0.143060
$652$	−9.02798	−0.353563
$653$	23.7466	0.929276	0.464638	−	0.885501i	$-0.346184\pi$
$653$	23.7466	0.929276	0.464638	+	0.885501i	$0.346184\pi$
$654$	5.03599	0.196923
$655$	3.07430	0.120123
$656$	−1.17725	−0.0459639
$657$	1.31735	0.0513948
$658$	26.3753	1.02821
$659$	−7.50424	−0.292324	−0.146162	−	0.989261i	$-0.546692\pi$
$659$	−7.50424	−0.292324	−0.146162	+	0.989261i	$0.546692\pi$
$660$	51.9178	2.02090
$661$	33.2972	1.29511	0.647556	−	0.762018i	$-0.275791\pi$
$661$	33.2972	1.29511	0.647556	+	0.762018i	$0.275791\pi$
$662$	60.2173	2.34041
$663$	−9.80127	−0.380650
$664$	−4.66531	−0.181049
$665$	23.7065	0.919297
$666$	23.8509	0.924202
$667$	4.55999	0.176563
$668$	−44.5455	−1.72352
$669$	−14.7044	−0.568504
$670$	21.0063	0.811545
$671$	43.2399	1.66926
$672$	−12.1544	−0.468865
$673$	−22.9389	−0.884230	−0.442115	−	0.896958i	$-0.645772\pi$
$673$	−22.9389	−0.884230	−0.442115	+	0.896958i	$0.645772\pi$
$674$	43.6916	1.68294
$675$	9.40711	0.362080
$676$	−15.3964	−0.592169
$677$	33.2790	1.27902	0.639508	−	0.768784i	$-0.279138\pi$
$677$	33.2790	1.27902	0.639508	+	0.768784i	$0.279138\pi$
$678$	−13.0653	−0.501771
$679$	25.8816	0.993247
$680$	−24.5693	−0.942188
$681$	6.40836	0.245569
$682$	23.2712	0.891099
$683$	−0.581526	−0.0222515	−0.0111257	−	0.999938i	$-0.503542\pi$
$683$	−0.581526	−0.0222515	−0.0111257	+	0.999938i	$0.503542\pi$
$684$	−10.5840	−0.404689
$685$	55.5011	2.12059
$686$	−41.1023	−1.56929
$687$	−15.7459	−0.600745
$688$	−17.4341	−0.664669
$689$	−9.12422	−0.347605
$690$	−19.5968	−0.746036
$691$	−32.9466	−1.25335	−0.626674	−	0.779281i	$-0.715584\pi$
$691$	−32.9466	−1.25335	−0.626674	+	0.779281i	$0.715584\pi$
$692$	50.0036	1.90085
$693$	−8.07154	−0.306612
$694$	−24.0258	−0.912008
$695$	72.4447	2.74799
$696$	−3.52148	−0.133481
$697$	2.52146	0.0955070
$698$	65.2544	2.46992
$699$	−0.0431460	−0.00163193
$700$	−44.3378	−1.67581
$701$	31.8516	1.20302	0.601509	−	0.798866i	$-0.294566\pi$
$701$	31.8516	1.20302	0.601509	+	0.798866i	$0.294566\pi$
$702$	6.03720	0.227860
$703$	40.6592	1.53349
$704$	−61.3708	−2.31300
$705$	27.3251	1.02912
$706$	−18.8970	−0.711200
$707$	−20.5323	−0.772195
$708$	−14.7324	−0.553676
$709$	24.0460	0.903065	0.451533	−	0.892255i	$-0.350877\pi$
$709$	24.0460	0.903065	0.451533	+	0.892255i	$0.350877\pi$
$710$	−29.3456	−1.10132
$711$	−2.41891	−0.0907164
$712$	−3.99044	−0.149548
$713$	−5.14376	−0.192635
$714$	13.0668	0.489014
$715$	−50.4844	−1.88801
$716$	−12.8461	−0.480083
$717$	−5.39831	−0.201604
$718$	2.39850	0.0895112
$719$	−37.2021	−1.38740	−0.693701	−	0.720263i	$-0.744021\pi$
$719$	−37.2021	−1.38740	−0.693701	+	0.720263i	$0.744021\pi$
$720$	−6.32051	−0.235552
$721$	−4.87103	−0.181407
$722$	10.9288	0.406729
$723$	26.7598	0.995209
$724$	51.8387	1.92657
$725$	18.2526	0.677884
$726$	−27.2942	−1.01298
$727$	−28.0966	−1.04204	−0.521022	−	0.853543i	$-0.674449\pi$
$727$	−28.0966	−1.04204	−0.521022	+	0.853543i	$0.674449\pi$
$728$	−8.31795	−0.308284
$729$	1.00000	0.0370370
$730$	−10.9848	−0.406564
$731$	37.3407	1.38110
$732$	25.2491	0.933235
$733$	−4.84839	−0.179079	−0.0895397	−	0.995983i	$-0.528540\pi$
$733$	−4.84839	−0.179079	−0.0895397	+	0.995983i	$0.528540\pi$
$734$	−58.4059	−2.15580
$735$	−16.0128	−0.590642
$736$	17.1279	0.631343
$737$	−12.1925	−0.449118
$738$	−1.55312	−0.0571711
$739$	−49.1886	−1.80943	−0.904716	−	0.426015i	$-0.859917\pi$
$739$	−49.1886	−1.80943	−0.904716	+	0.426015i	$0.859917\pi$
$740$	−116.463	−4.28125
$741$	10.2918	0.378078
$742$	12.1642	0.446562
$743$	27.5598	1.01107	0.505536	−	0.862806i	$-0.331295\pi$
$743$	27.5598	1.01107	0.505536	+	0.862806i	$0.331295\pi$
$744$	3.97230	0.145632
$745$	47.9663	1.75735
$746$	55.8985	2.04659
$747$	2.57053	0.0940509
$748$	48.7836	1.78371
$749$	−5.32324	−0.194507
$750$	−36.7487	−1.34187
$751$	−50.6342	−1.84767	−0.923835	−	0.382791i	$-0.874963\pi$
$751$	−50.6342	−1.84767	−0.923835	+	0.382791i	$0.874963\pi$
$752$	−11.9877	−0.437148
$753$	8.99276	0.327714
$754$	11.7140	0.426597
$755$	3.33608	0.121412
$756$	−4.71322	−0.171418
$757$	−6.12982	−0.222792	−0.111396	−	0.993776i	$-0.535532\pi$
$757$	−6.12982	−0.222792	−0.111396	+	0.993776i	$0.535532\pi$
$758$	30.0550	1.09165
$759$	11.3744	0.412865
$760$	25.7989	0.935823
$761$	−9.92811	−0.359894	−0.179947	−	0.983676i	$-0.557593\pi$
$761$	−9.92811	−0.359894	−0.179947	+	0.983676i	$0.557593\pi$
$762$	−23.5040	−0.851460
$763$	3.82304	0.138403
$764$	−37.9745	−1.37387
$765$	13.5374	0.489446
$766$	22.7467	0.821873
$767$	14.3256	0.517268
$768$	−3.81499	−0.137662
$769$	−12.9257	−0.466112	−0.233056	−	0.972463i	$-0.574873\pi$
$769$	−12.9257	−0.466112	−0.233056	+	0.972463i	$0.574873\pi$
$770$	67.3046	2.42549
$771$	19.2715	0.694047
$772$	−38.2300	−1.37593
$773$	33.9105	1.21968	0.609839	−	0.792526i	$-0.291234\pi$
$773$	33.9105	1.21968	0.609839	+	0.792526i	$0.291234\pi$
$774$	−23.0004	−0.826733
$775$	−20.5893	−0.739588
$776$	28.1660	1.01110
$777$	18.1062	0.649556
$778$	56.8224	2.03718
$779$	−2.64764	−0.0948617
$780$	−29.4794	−1.05553
$781$	17.0329	0.609484
$782$	−18.4138	−0.658475
$783$	1.94030	0.0693405
$784$	7.02495	0.250891
$785$	62.0001	2.21288
$786$	−1.77934	−0.0634668
$787$	51.5748	1.83844	0.919222	−	0.393740i	$-0.128819\pi$
$787$	51.5748	1.83844	0.919222	+	0.393740i	$0.128819\pi$
$788$	−19.4234	−0.691929
$789$	27.3313	0.973021
$790$	20.1701	0.717622
$791$	−9.91845	−0.352659
$792$	−8.78395	−0.312124
$793$	−24.5520	−0.871869
$794$	−39.7131	−1.40936
$795$	12.6023	0.446956
$796$	12.2507	0.434216
$797$	22.9664	0.813512	0.406756	−	0.913537i	$-0.366660\pi$
$797$	22.9664	0.813512	0.406756	+	0.913537i	$0.366660\pi$
$798$	−13.7208	−0.485710
$799$	25.6756	0.908336
$800$	68.5591	2.42393
$801$	2.19869	0.0776868
$802$	47.6919	1.68406
$803$	6.37581	0.224997
$804$	−7.11961	−0.251089
$805$	−14.8767	−0.524336
$806$	−13.2136	−0.465429
$807$	−29.6604	−1.04410
$808$	−22.3445	−0.786076
$809$	−43.3099	−1.52270	−0.761348	−	0.648343i	$-0.775462\pi$
$809$	−43.3099	−1.52270	−0.761348	+	0.648343i	$0.775462\pi$
$810$	−8.33851	−0.292985
$811$	−0.00427794	−0.000150219 0	−7.51095e−5	−	1.00000i	$-0.500024\pi$
$811$	−0.00427794	−0.000150219 0	−7.51095e−5		1.00000i	$0.500024\pi$
$812$	−9.14505	−0.320928
$813$	−13.2505	−0.464715
$814$	115.435	4.04599
$815$	−12.1251	−0.424723
$816$	−5.93896	−0.207905
$817$	−39.2094	−1.37176
$818$	39.0539	1.36549
$819$	4.58310	0.160146
$820$	7.58382	0.264838
$821$	−45.8182	−1.59907	−0.799533	−	0.600622i	$-0.794920\pi$
$821$	−45.8182	−1.59907	−0.799533	+	0.600622i	$0.794920\pi$
$822$	−32.1228	−1.12041
$823$	34.8190	1.21371	0.606857	−	0.794811i	$-0.292430\pi$
$823$	34.8190	1.21371	0.606857	+	0.794811i	$0.292430\pi$
$824$	−5.30096	−0.184668
$825$	45.5291	1.58512
$826$	−19.0986	−0.664525
$827$	10.4181	0.362272	0.181136	−	0.983458i	$-0.442023\pi$
$827$	10.4181	0.362272	0.181136	+	0.983458i	$0.442023\pi$
$828$	6.64187	0.230821
$829$	29.4677	1.02345	0.511727	−	0.859148i	$-0.329006\pi$
$829$	29.4677	1.02345	0.511727	+	0.859148i	$0.329006\pi$
$830$	−21.4344	−0.744000
$831$	−3.68387	−0.127792
$832$	34.8469	1.20810
$833$	−15.0462	−0.521319
$834$	−41.9294	−1.45190
$835$	−59.8271	−2.07040
$836$	−51.2251	−1.77166
$837$	−2.18869	−0.0756523
$838$	−4.76081	−0.164460
$839$	27.9975	0.966583	0.483291	−	0.875460i	$-0.339441\pi$
$839$	27.9975	0.966583	0.483291	+	0.875460i	$0.339441\pi$
$840$	11.4886	0.396396
$841$	−25.2353	−0.870181
$842$	2.55532	0.0880620
$843$	−6.04203	−0.208099
$844$	16.0003	0.550752
$845$	−20.6782	−0.711351
$846$	−15.8152	−0.543736
$847$	−20.7202	−0.711955
$848$	−5.52871	−0.189857
$849$	10.2912	0.353193
$850$	−73.7060	−2.52810
$851$	−25.5152	−0.874651
$852$	9.94602	0.340745
$853$	−6.02279	−0.206216	−0.103108	−	0.994670i	$-0.532879\pi$
$853$	−6.02279	−0.206216	−0.103108	+	0.994670i	$0.532879\pi$
$854$	32.7322	1.12007
$855$	−14.2149	−0.486139
$856$	−5.79308	−0.198004
$857$	−35.1195	−1.19966	−0.599830	−	0.800127i	$-0.704765\pi$
$857$	−35.1195	−1.19966	−0.599830	+	0.800127i	$0.704765\pi$
$858$	29.2192	0.997528
$859$	40.2646	1.37381	0.686905	−	0.726747i	$-0.258969\pi$
$859$	40.2646	1.37381	0.686905	+	0.726747i	$0.258969\pi$
$860$	112.310	3.82974
$861$	−1.17904	−0.0401815
$862$	−61.5828	−2.09752
$863$	−6.49336	−0.221037	−0.110518	−	0.993874i	$-0.535251\pi$
$863$	−6.49336	−0.221037	−0.110518	+	0.993874i	$0.535251\pi$
$864$	7.28801	0.247943
$865$	67.1575	2.28342
$866$	64.1070	2.17844
$867$	−4.27981	−0.145350
$868$	10.3158	0.350141
$869$	−11.7072	−0.397140
$870$	−16.1792	−0.548526
$871$	6.92305	0.234578
$872$	4.16047	0.140891
$873$	−15.5192	−0.525244
$874$	19.3353	0.654026
$875$	−27.8975	−0.943108
$876$	3.72303	0.125790
$877$	−47.8832	−1.61690	−0.808451	−	0.588564i	$-0.799694\pi$
$877$	−47.8832	−1.61690	−0.808451	+	0.588564i	$0.799694\pi$
$878$	−24.1825	−0.816121
$879$	18.0546	0.608967
$880$	−30.5904	−1.03120
$881$	44.1310	1.48681	0.743405	−	0.668841i	$-0.233209\pi$
$881$	44.1310	1.48681	0.743405	+	0.668841i	$0.233209\pi$
$882$	9.26786	0.312065
$883$	43.6850	1.47012	0.735059	−	0.678003i	$-0.237154\pi$
$883$	43.6850	1.47012	0.735059	+	0.678003i	$0.237154\pi$
$884$	−27.6998	−0.931646
$885$	−19.7864	−0.665111
$886$	42.0808	1.41373
$887$	25.7670	0.865170	0.432585	−	0.901593i	$-0.357602\pi$
$887$	25.7670	0.865170	0.432585	+	0.901593i	$0.357602\pi$
$888$	19.7043	0.661233
$889$	−17.8429	−0.598431
$890$	−18.3338	−0.614550
$891$	4.83986	0.162141
$892$	−41.5567	−1.39142
$893$	−26.9605	−0.902199
$894$	−27.7618	−0.928494
$895$	−17.2531	−0.576706
$896$	−22.1484	−0.739926
$897$	−6.45850	−0.215643
$898$	−19.9364	−0.665285
$899$	−4.24671	−0.141636
$900$	26.5859	0.886195
$901$	11.8415	0.394498
$902$	−7.51689	−0.250285
$903$	−17.4606	−0.581052
$904$	−10.7939	−0.358999
$905$	69.6222	2.31432
$906$	−1.93085	−0.0641481
$907$	49.0454	1.62852	0.814262	−	0.580497i	$-0.197142\pi$
$907$	49.0454	1.62852	0.814262	+	0.580497i	$0.197142\pi$
$908$	18.1110	0.601033
$909$	12.3116	0.408349
$910$	−38.2162	−1.26686
$911$	8.18703	0.271248	0.135624	−	0.990760i	$-0.456696\pi$
$911$	8.18703	0.271248	0.135624	+	0.990760i	$0.456696\pi$
$912$	6.23619	0.206501
$913$	12.4410	0.411738
$914$	−13.8797	−0.459100
$915$	33.9110	1.12106
$916$	−44.5003	−1.47033
$917$	−1.35077	−0.0446063
$918$	−7.83514	−0.258598
$919$	−43.5659	−1.43711	−0.718553	−	0.695472i	$-0.755195\pi$
$919$	−43.5659	−1.43711	−0.718553	+	0.695472i	$0.755195\pi$
$920$	−16.1898	−0.533761
$921$	−12.5628	−0.413960
$922$	−34.0083	−1.12000
$923$	−9.67142	−0.318339
$924$	−22.8114	−0.750438
$925$	−102.132	−3.35806
$926$	−17.2975	−0.568430
$927$	2.92077	0.0959307
$928$	14.1409	0.464198
$929$	−33.2445	−1.09072	−0.545359	−	0.838203i	$-0.683607\pi$
$929$	−33.2445	−1.09072	−0.545359	+	0.838203i	$0.683607\pi$
$930$	18.2504	0.598456
$931$	15.7992	0.517797
$932$	−0.121937	−0.00399417
$933$	2.97691	0.0974596
$934$	−51.8268	−1.69582
$935$	65.5191	2.14270
$936$	4.98761	0.163025
$937$	−25.5182	−0.833643	−0.416822	−	0.908988i	$-0.636856\pi$
$937$	−25.5182	−0.833643	−0.416822	+	0.908988i	$0.636856\pi$
$938$	−9.22965	−0.301359
$939$	−25.6863	−0.838240
$940$	77.2247	2.51879
$941$	−59.7453	−1.94764	−0.973821	−	0.227316i	$-0.927005\pi$
$941$	−59.7453	−1.94764	−0.973821	+	0.227316i	$0.927005\pi$
$942$	−35.8843	−1.16917
$943$	1.66150	0.0541059
$944$	8.68044	0.282524
$945$	−6.33012	−0.205919
$946$	−111.319	−3.61929
$947$	−2.07011	−0.0672694	−0.0336347	−	0.999434i	$-0.510708\pi$
$947$	−2.07011	−0.0672694	−0.0336347	+	0.999434i	$0.510708\pi$
$948$	−6.83620	−0.222030
$949$	−3.62024	−0.117518
$950$	77.3947	2.51102
$951$	−18.5714	−0.602220
$952$	10.7951	0.349872
$953$	−31.2660	−1.01280	−0.506402	−	0.862298i	$-0.669025\pi$
$953$	−31.2660	−1.01280	−0.506402	+	0.862298i	$0.669025\pi$
$954$	−7.29391	−0.236149
$955$	−51.0018	−1.65038
$956$	−15.2564	−0.493428
$957$	9.39077	0.303560
$958$	44.5193	1.43835
$959$	−24.3858	−0.787458
$960$	−48.1301	−1.55339
$961$	−26.2096	−0.845472
$962$	−65.5450	−2.11326
$963$	3.19193	0.102858
$964$	75.6272	2.43579
$965$	−51.3451	−1.65286
$966$	8.61032	0.277033
$967$	24.3081	0.781697	0.390849	−	0.920455i	$-0.372182\pi$
$967$	24.3081	0.781697	0.390849	+	0.920455i	$0.372182\pi$
$968$	−22.5490	−0.724753
$969$	−13.3568	−0.429082
$970$	129.407	4.15500
$971$	−19.6983	−0.632150	−0.316075	−	0.948734i	$-0.602365\pi$
$971$	−19.6983	−0.632150	−0.316075	+	0.948734i	$0.602365\pi$
$972$	2.82615	0.0906487
$973$	−31.8304	−1.02044
$974$	−85.4814	−2.73900
$975$	−25.8519	−0.827922
$976$	−14.8770	−0.476202
$977$	20.0187	0.640454	0.320227	−	0.947341i	$-0.396241\pi$
$977$	20.0187	0.640454	0.320227	+	0.947341i	$0.396241\pi$
$978$	7.01773	0.224402
$979$	10.6413	0.340099
$980$	−45.2546	−1.44560
$981$	−2.29237	−0.0731898
$982$	−24.8615	−0.793361
$983$	17.1076	0.545646	0.272823	−	0.962064i	$-0.412043\pi$
$983$	17.1076	0.545646	0.272823	+	0.962064i	$0.412043\pi$
$984$	−1.28310	−0.0409039
$985$	−26.0867	−0.831190
$986$	−15.2025	−0.484146
$987$	−12.0060	−0.382154
$988$	29.0861	0.925352
$989$	24.6054	0.782408
$990$	−40.3573	−1.28264
$991$	−36.0834	−1.14623	−0.573113	−	0.819476i	$-0.694264\pi$
$991$	−36.0834	−1.14623	−0.573113	+	0.819476i	$0.694264\pi$
$992$	−15.9512	−0.506451
$993$	−27.4108	−0.869854
$994$	12.8937	0.408964
$995$	16.4534	0.521609
$996$	7.26470	0.230191
$997$	3.04715	0.0965041	0.0482520	−	0.998835i	$-0.484635\pi$
$997$	3.04715	0.0965041	0.0482520	+	0.998835i	$0.484635\pi$
$998$	66.4128	2.10226
$999$	−10.8568	−0.343495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.13	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.19685 q^{2} +1.00000 q^{3} +2.82615 q^{4} +3.79567 q^{5} -2.19685 q^{6} -1.66772 q^{7} -1.81492 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.19685 q^{2} +1.00000 q^{3} +2.82615 q^{4} +3.79567 q^{5} -2.19685 q^{6} -1.66772 q^{7} -1.81492 q^{8} +1.00000 q^{9} -8.33851 q^{10} +4.83986 q^{11} +2.82615 q^{12} -2.74812 q^{13} +3.66373 q^{14} +3.79567 q^{15} -1.66519 q^{16} +3.56654 q^{17} -2.19685 q^{18} -3.74503 q^{19} +10.7271 q^{20} -1.66772 q^{21} -10.6324 q^{22} +2.35015 q^{23} -1.81492 q^{24} +9.40711 q^{25} +6.03720 q^{26} +1.00000 q^{27} -4.71322 q^{28} +1.94030 q^{29} -8.33851 q^{30} -2.18869 q^{31} +7.28801 q^{32} +4.83986 q^{33} -7.83514 q^{34} -6.33012 q^{35} +2.82615 q^{36} -10.8568 q^{37} +8.22726 q^{38} -2.74812 q^{39} -6.88883 q^{40} +0.706976 q^{41} +3.66373 q^{42} +10.4697 q^{43} +13.6782 q^{44} +3.79567 q^{45} -5.16293 q^{46} +7.19902 q^{47} -1.66519 q^{48} -4.21871 q^{49} -20.6660 q^{50} +3.56654 q^{51} -7.76659 q^{52} +3.32017 q^{53} -2.19685 q^{54} +18.3705 q^{55} +3.02678 q^{56} -3.74503 q^{57} -4.26254 q^{58} -5.21288 q^{59} +10.7271 q^{60} +8.93412 q^{61} +4.80823 q^{62} -1.66772 q^{63} -12.6803 q^{64} -10.4310 q^{65} -10.6324 q^{66} -2.51919 q^{67} +10.0796 q^{68} +2.35015 q^{69} +13.9063 q^{70} +3.51929 q^{71} -1.81492 q^{72} +1.31735 q^{73} +23.8509 q^{74} +9.40711 q^{75} -10.5840 q^{76} -8.07154 q^{77} +6.03720 q^{78} -2.41891 q^{79} -6.32051 q^{80} +1.00000 q^{81} -1.55312 q^{82} +2.57053 q^{83} -4.71322 q^{84} +13.5374 q^{85} -23.0004 q^{86} +1.94030 q^{87} -8.78395 q^{88} +2.19869 q^{89} -8.33851 q^{90} +4.58310 q^{91} +6.64187 q^{92} -2.18869 q^{93} -15.8152 q^{94} -14.2149 q^{95} +7.28801 q^{96} -15.5192 q^{97} +9.26786 q^{98} +4.83986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 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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