LMFDB - Embedded newform 3009.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3009,2,Mod(1,3009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3009 = 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3009.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:	$24.0269859682$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	3009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10017 q^{2} +1.00000 q^{3} +2.41071 q^{4} -2.30678 q^{5} -2.10017 q^{6} +4.51480 q^{7} -0.862553 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.10017 q^{2} +1.00000 q^{3} +2.41071 q^{4} -2.30678 q^{5} -2.10017 q^{6} +4.51480 q^{7} -0.862553 q^{8} +1.00000 q^{9} +4.84464 q^{10} -3.88210 q^{11} +2.41071 q^{12} -2.10288 q^{13} -9.48184 q^{14} -2.30678 q^{15} -3.00991 q^{16} -1.00000 q^{17} -2.10017 q^{18} -4.56971 q^{19} -5.56098 q^{20} +4.51480 q^{21} +8.15306 q^{22} -2.70687 q^{23} -0.862553 q^{24} +0.321256 q^{25} +4.41640 q^{26} +1.00000 q^{27} +10.8839 q^{28} -1.80504 q^{29} +4.84464 q^{30} +1.68580 q^{31} +8.04642 q^{32} -3.88210 q^{33} +2.10017 q^{34} -10.4147 q^{35} +2.41071 q^{36} +8.51916 q^{37} +9.59715 q^{38} -2.10288 q^{39} +1.98972 q^{40} +1.10866 q^{41} -9.48184 q^{42} +8.34430 q^{43} -9.35860 q^{44} -2.30678 q^{45} +5.68488 q^{46} +10.1035 q^{47} -3.00991 q^{48} +13.3834 q^{49} -0.674692 q^{50} -1.00000 q^{51} -5.06943 q^{52} +4.71276 q^{53} -2.10017 q^{54} +8.95516 q^{55} -3.89426 q^{56} -4.56971 q^{57} +3.79088 q^{58} -1.00000 q^{59} -5.56098 q^{60} -3.91583 q^{61} -3.54047 q^{62} +4.51480 q^{63} -10.8790 q^{64} +4.85089 q^{65} +8.15306 q^{66} +13.1112 q^{67} -2.41071 q^{68} -2.70687 q^{69} +21.8726 q^{70} -3.91855 q^{71} -0.862553 q^{72} -3.15443 q^{73} -17.8917 q^{74} +0.321256 q^{75} -11.0162 q^{76} -17.5269 q^{77} +4.41640 q^{78} +6.51359 q^{79} +6.94321 q^{80} +1.00000 q^{81} -2.32838 q^{82} -15.5265 q^{83} +10.8839 q^{84} +2.30678 q^{85} -17.5244 q^{86} -1.80504 q^{87} +3.34851 q^{88} -6.03654 q^{89} +4.84464 q^{90} -9.49409 q^{91} -6.52547 q^{92} +1.68580 q^{93} -21.2192 q^{94} +10.5413 q^{95} +8.04642 q^{96} +13.4902 q^{97} -28.1075 q^{98} -3.88210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 24 q^{3} + 34 q^{4} - 3 q^{5} + 2 q^{6} + 19 q^{7} + 3 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 24 * q^3 + 34 * q^4 - 3 * q^5 + 2 * q^6 + 19 * q^7 + 3 * q^8 + 24 * q^9	\( 24 q + 2 q^{2} + 24 q^{3} + 34 q^{4} - 3 q^{5} + 2 q^{6} + 19 q^{7} + 3 q^{8} + 24 q^{9} + 10 q^{10} + 11 q^{11} + 34 q^{12} + 21 q^{13} + 9 q^{14} - 3 q^{15} + 50 q^{16} - 24 q^{17} + 2 q^{18} + 13 q^{19} + q^{20} + 19 q^{21} + 5 q^{22} + 18 q^{23} + 3 q^{24} + 39 q^{25} - 7 q^{26} + 24 q^{27} + 40 q^{28} - 10 q^{29} + 10 q^{30} + 47 q^{31} + 18 q^{32} + 11 q^{33} - 2 q^{34} + 5 q^{35} + 34 q^{36} + 54 q^{37} + 5 q^{38} + 21 q^{39} + 29 q^{40} + 9 q^{42} + 16 q^{43} + 7 q^{44} - 3 q^{45} - 8 q^{46} + 10 q^{47} + 50 q^{48} + 55 q^{49} + 21 q^{50} - 24 q^{51} + 68 q^{52} + 6 q^{53} + 2 q^{54} + 15 q^{55} - 5 q^{56} + 13 q^{57} + q^{58} - 24 q^{59} + q^{60} + 42 q^{61} - 7 q^{62} + 19 q^{63} + 53 q^{64} - 9 q^{65} + 5 q^{66} + 28 q^{67} - 34 q^{68} + 18 q^{69} - 20 q^{70} + 54 q^{71} + 3 q^{72} + 33 q^{73} - 17 q^{74} + 39 q^{75} - 56 q^{76} - 23 q^{77} - 7 q^{78} + 35 q^{79} + 3 q^{80} + 24 q^{81} - 12 q^{82} - 17 q^{83} + 40 q^{84} + 3 q^{85} + 36 q^{86} - 10 q^{87} + 47 q^{88} + 15 q^{89} + 10 q^{90} + 74 q^{91} + 6 q^{92} + 47 q^{93} + 9 q^{94} + 12 q^{95} + 18 q^{96} + 52 q^{97} - 48 q^{98} + 11 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 24 * q^3 + 34 * q^4 - 3 * q^5 + 2 * q^6 + 19 * q^7 + 3 * q^8 + 24 * q^9 + 10 * q^10 + 11 * q^11 + 34 * q^12 + 21 * q^13 + 9 * q^14 - 3 * q^15 + 50 * q^16 - 24 * q^17 + 2 * q^18 + 13 * q^19 + q^20 + 19 * q^21 + 5 * q^22 + 18 * q^23 + 3 * q^24 + 39 * q^25 - 7 * q^26 + 24 * q^27 + 40 * q^28 - 10 * q^29 + 10 * q^30 + 47 * q^31 + 18 * q^32 + 11 * q^33 - 2 * q^34 + 5 * q^35 + 34 * q^36 + 54 * q^37 + 5 * q^38 + 21 * q^39 + 29 * q^40 + 9 * q^42 + 16 * q^43 + 7 * q^44 - 3 * q^45 - 8 * q^46 + 10 * q^47 + 50 * q^48 + 55 * q^49 + 21 * q^50 - 24 * q^51 + 68 * q^52 + 6 * q^53 + 2 * q^54 + 15 * q^55 - 5 * q^56 + 13 * q^57 + q^58 - 24 * q^59 + q^60 + 42 * q^61 - 7 * q^62 + 19 * q^63 + 53 * q^64 - 9 * q^65 + 5 * q^66 + 28 * q^67 - 34 * q^68 + 18 * q^69 - 20 * q^70 + 54 * q^71 + 3 * q^72 + 33 * q^73 - 17 * q^74 + 39 * q^75 - 56 * q^76 - 23 * q^77 - 7 * q^78 + 35 * q^79 + 3 * q^80 + 24 * q^81 - 12 * q^82 - 17 * q^83 + 40 * q^84 + 3 * q^85 + 36 * q^86 - 10 * q^87 + 47 * q^88 + 15 * q^89 + 10 * q^90 + 74 * q^91 + 6 * q^92 + 47 * q^93 + 9 * q^94 + 12 * q^95 + 18 * q^96 + 52 * q^97 - 48 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.10017	−1.48504	−0.742522	−	0.669822i	$-0.766370\pi$
$2$	−2.10017	−1.48504	−0.742522	+	0.669822i	$0.766370\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.41071	1.20535
$5$	−2.30678	−1.03163	−0.515813	−	0.856701i	$-0.672510\pi$
$5$	−2.30678	−1.03163	−0.515813	+	0.856701i	$0.672510\pi$
$6$	−2.10017	−0.857390
$7$	4.51480	1.70643	0.853217	−	0.521555i	$-0.174648\pi$
$7$	4.51480	1.70643	0.853217	+	0.521555i	$0.174648\pi$
$8$	−0.862553	−0.304959
$9$	1.00000	0.333333
$10$	4.84464	1.53201
$11$	−3.88210	−1.17050	−0.585248	−	0.810854i	$-0.699003\pi$
$11$	−3.88210	−1.17050	−0.585248	+	0.810854i	$0.699003\pi$
$12$	2.41071	0.695911
$13$	−2.10288	−0.583234	−0.291617	−	0.956535i	$-0.594193\pi$
$13$	−2.10288	−0.583234	−0.291617	+	0.956535i	$0.594193\pi$
$14$	−9.48184	−2.53413
$15$	−2.30678	−0.595609
$16$	−3.00991	−0.752477
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.10017	−0.495014
$19$	−4.56971	−1.04836	−0.524181	−	0.851607i	$-0.675629\pi$
$19$	−4.56971	−1.04836	−0.524181	+	0.851607i	$0.675629\pi$
$20$	−5.56098	−1.24347
$21$	4.51480	0.985211
$22$	8.15306	1.73824
$23$	−2.70687	−0.564422	−0.282211	−	0.959352i	$-0.591068\pi$
$23$	−2.70687	−0.564422	−0.282211	+	0.959352i	$0.591068\pi$
$24$	−0.862553	−0.176068
$25$	0.321256	0.0642512
$26$	4.41640	0.866128
$27$	1.00000	0.192450
$28$	10.8839	2.05686
$29$	−1.80504	−0.335187	−0.167594	−	0.985856i	$-0.553600\pi$
$29$	−1.80504	−0.335187	−0.167594	+	0.985856i	$0.553600\pi$
$30$	4.84464	0.884506
$31$	1.68580	0.302779	0.151390	−	0.988474i	$-0.451625\pi$
$31$	1.68580	0.302779	0.151390	+	0.988474i	$0.451625\pi$
$32$	8.04642	1.42242
$33$	−3.88210	−0.675786
$34$	2.10017	0.360176
$35$	−10.4147	−1.76040
$36$	2.41071	0.401784
$37$	8.51916	1.40054	0.700271	−	0.713877i	$-0.253062\pi$
$37$	8.51916	1.40054	0.700271	+	0.713877i	$0.253062\pi$
$38$	9.59715	1.55686
$39$	−2.10288	−0.336730
$40$	1.98972	0.314603
$41$	1.10866	0.173144	0.0865720	−	0.996246i	$-0.472409\pi$
$41$	1.10866	0.173144	0.0865720	+	0.996246i	$0.472409\pi$
$42$	−9.48184	−1.46308
$43$	8.34430	1.27249	0.636247	−	0.771486i	$-0.280486\pi$
$43$	8.34430	1.27249	0.636247	+	0.771486i	$0.280486\pi$
$44$	−9.35860	−1.41086
$45$	−2.30678	−0.343875
$46$	5.68488	0.838190
$47$	10.1035	1.47375	0.736877	−	0.676027i	$-0.236300\pi$
$47$	10.1035	1.47375	0.736877	+	0.676027i	$0.236300\pi$
$48$	−3.00991	−0.434443
$49$	13.3834	1.91192
$50$	−0.674692	−0.0954158
$51$	−1.00000	−0.140028
$52$	−5.06943	−0.703003
$53$	4.71276	0.647347	0.323674	−	0.946169i	$-0.395082\pi$
$53$	4.71276	0.647347	0.323674	+	0.946169i	$0.395082\pi$
$54$	−2.10017	−0.285797
$55$	8.95516	1.20751
$56$	−3.89426	−0.520392
$57$	−4.56971	−0.605272
$58$	3.79088	0.497767
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−5.56098	−0.717920
$61$	−3.91583	−0.501371	−0.250685	−	0.968069i	$-0.580656\pi$
$61$	−3.91583	−0.501371	−0.250685	+	0.968069i	$0.580656\pi$
$62$	−3.54047	−0.449640
$63$	4.51480	0.568812
$64$	−10.8790	−1.35988
$65$	4.85089	0.601679
$66$	8.15306	1.00357
$67$	13.1112	1.60179	0.800893	−	0.598808i	$-0.204359\pi$
$67$	13.1112	1.60179	0.800893	+	0.598808i	$0.204359\pi$
$68$	−2.41071	−0.292341
$69$	−2.70687	−0.325869
$70$	21.8726	2.61427
$71$	−3.91855	−0.465046	−0.232523	−	0.972591i	$-0.574698\pi$
$71$	−3.91855	−0.465046	−0.232523	+	0.972591i	$0.574698\pi$
$72$	−0.862553	−0.101653
$73$	−3.15443	−0.369198	−0.184599	−	0.982814i	$-0.559099\pi$
$73$	−3.15443	−0.369198	−0.184599	+	0.982814i	$0.559099\pi$
$74$	−17.8917	−2.07987
$75$	0.321256	0.0370955
$76$	−11.0162	−1.26365
$77$	−17.5269	−1.99738
$78$	4.41640	0.500059
$79$	6.51359	0.732837	0.366418	−	0.930450i	$-0.380584\pi$
$79$	6.51359	0.732837	0.366418	+	0.930450i	$0.380584\pi$
$80$	6.94321	0.776274
$81$	1.00000	0.111111
$82$	−2.32838	−0.257126
$83$	−15.5265	−1.70425	−0.852126	−	0.523337i	$-0.824687\pi$
$83$	−15.5265	−1.70425	−0.852126	+	0.523337i	$0.824687\pi$
$84$	10.8839	1.18753
$85$	2.30678	0.250206
$86$	−17.5244	−1.88971
$87$	−1.80504	−0.193520
$88$	3.34851	0.356953
$89$	−6.03654	−0.639872	−0.319936	−	0.947439i	$-0.603661\pi$
$89$	−6.03654	−0.639872	−0.319936	+	0.947439i	$0.603661\pi$
$90$	4.84464	0.510669
$91$	−9.49409	−0.995251
$92$	−6.52547	−0.680327
$93$	1.68580	0.174810
$94$	−21.2192	−2.18859
$95$	10.5413	1.08152
$96$	8.04642	0.821234
$97$	13.4902	1.36973	0.684863	−	0.728672i	$-0.259862\pi$
$97$	13.4902	1.36973	0.684863	+	0.728672i	$0.259862\pi$
$98$	−28.1075	−2.83928
$99$	−3.88210	−0.390165
$100$	0.774454	0.0774454
$101$	−8.50500	−0.846279	−0.423140	−	0.906065i	$-0.639072\pi$
$101$	−8.50500	−0.846279	−0.423140	+	0.906065i	$0.639072\pi$
$102$	2.10017	0.207948
$103$	−5.09592	−0.502116	−0.251058	−	0.967972i	$-0.580779\pi$
$103$	−5.09592	−0.502116	−0.251058	+	0.967972i	$0.580779\pi$
$104$	1.81385	0.177862
$105$	−10.4147	−1.01637
$106$	−9.89759	−0.961339
$107$	17.5791	1.69943	0.849716	−	0.527241i	$-0.176773\pi$
$107$	17.5791	1.69943	0.849716	+	0.527241i	$0.176773\pi$
$108$	2.41071	0.231970
$109$	−14.7562	−1.41339	−0.706696	−	0.707517i	$-0.749815\pi$
$109$	−14.7562	−1.41339	−0.706696	+	0.707517i	$0.749815\pi$
$110$	−18.8073	−1.79321
$111$	8.51916	0.808603
$112$	−13.5891	−1.28405
$113$	16.8773	1.58768	0.793842	−	0.608124i	$-0.208078\pi$
$113$	16.8773	1.58768	0.793842	+	0.608124i	$0.208078\pi$
$114$	9.59715	0.898856
$115$	6.24417	0.582272
$116$	−4.35142	−0.404019
$117$	−2.10288	−0.194411
$118$	2.10017	0.193336
$119$	−4.51480	−0.413871
$120$	1.98972	0.181636
$121$	4.07068	0.370061
$122$	8.22390	0.744557
$123$	1.10866	0.0999647
$124$	4.06398	0.364956
$125$	10.7929	0.965342
$126$	−9.48184	−0.844710
$127$	0.935504	0.0830126	0.0415063	−	0.999138i	$-0.486784\pi$
$127$	0.935504	0.0830126	0.0415063	+	0.999138i	$0.486784\pi$
$128$	6.75493	0.597057
$129$	8.34430	0.734675
$130$	−10.1877	−0.893520
$131$	10.7050	0.935301	0.467651	−	0.883913i	$-0.345101\pi$
$131$	10.7050	0.935301	0.467651	+	0.883913i	$0.345101\pi$
$132$	−9.35860	−0.814561
$133$	−20.6313	−1.78896
$134$	−27.5357	−2.37872
$135$	−2.30678	−0.198536
$136$	0.862553	0.0739633
$137$	18.3907	1.57122	0.785611	−	0.618721i	$-0.212349\pi$
$137$	18.3907	1.57122	0.785611	+	0.618721i	$0.212349\pi$
$138$	5.68488	0.483929
$139$	8.06594	0.684144	0.342072	−	0.939674i	$-0.388871\pi$
$139$	8.06594	0.684144	0.342072	+	0.939674i	$0.388871\pi$
$140$	−25.1067	−2.12191
$141$	10.1035	0.850872
$142$	8.22962	0.690614
$143$	8.16359	0.682673
$144$	−3.00991	−0.250826
$145$	4.16383	0.345788
$146$	6.62484	0.548276
$147$	13.3834	1.10385
$148$	20.5372	1.68815
$149$	7.59683	0.622357	0.311178	−	0.950352i	$-0.399276\pi$
$149$	7.59683	0.622357	0.311178	+	0.950352i	$0.399276\pi$
$150$	−0.674692	−0.0550884
$151$	16.1171	1.31159	0.655797	−	0.754937i	$-0.272333\pi$
$151$	16.1171	1.31159	0.655797	+	0.754937i	$0.272333\pi$
$152$	3.94161	0.319707
$153$	−1.00000	−0.0808452
$154$	36.8094	2.96619
$155$	−3.88879	−0.312355
$156$	−5.06943	−0.405879
$157$	15.9310	1.27143	0.635715	−	0.771924i	$-0.280705\pi$
$157$	15.9310	1.27143	0.635715	+	0.771924i	$0.280705\pi$
$158$	−13.6796	−1.08829
$159$	4.71276	0.373746
$160$	−18.5614	−1.46740
$161$	−12.2210	−0.963149
$162$	−2.10017	−0.165005
$163$	−6.59354	−0.516446	−0.258223	−	0.966085i	$-0.583137\pi$
$163$	−6.59354	−0.516446	−0.258223	+	0.966085i	$0.583137\pi$
$164$	2.67266	0.208700
$165$	8.95516	0.697158
$166$	32.6082	2.53089
$167$	−9.38923	−0.726560	−0.363280	−	0.931680i	$-0.618343\pi$
$167$	−9.38923	−0.726560	−0.363280	+	0.931680i	$0.618343\pi$
$168$	−3.89426	−0.300448
$169$	−8.57789	−0.659838
$170$	−4.84464	−0.371567
$171$	−4.56971	−0.349454
$172$	20.1157	1.53380
$173$	6.79701	0.516767	0.258384	−	0.966042i	$-0.416810\pi$
$173$	6.79701	0.516767	0.258384	+	0.966042i	$0.416810\pi$
$174$	3.79088	0.287386
$175$	1.45041	0.109641
$176$	11.6848	0.880771
$177$	−1.00000	−0.0751646
$178$	12.6777	0.950237
$179$	3.19822	0.239046	0.119523	−	0.992831i	$-0.461864\pi$
$179$	3.19822	0.239046	0.119523	+	0.992831i	$0.461864\pi$
$180$	−5.56098	−0.414491
$181$	−16.8898	−1.25541	−0.627704	−	0.778452i	$-0.716005\pi$
$181$	−16.8898	−1.25541	−0.627704	+	0.778452i	$0.716005\pi$
$182$	19.9392	1.47799
$183$	−3.91583	−0.289466
$184$	2.33482	0.172125
$185$	−19.6519	−1.44483
$186$	−3.54047	−0.259600
$187$	3.88210	0.283887
$188$	24.3567	1.77639
$189$	4.51480	0.328404
$190$	−22.1386	−1.60610
$191$	26.9463	1.94977	0.974883	−	0.222718i	$-0.0714930\pi$
$191$	26.9463	1.94977	0.974883	+	0.222718i	$0.0714930\pi$
$192$	−10.8790	−0.785125
$193$	16.4020	1.18065	0.590323	−	0.807167i	$-0.299001\pi$
$193$	16.4020	1.18065	0.590323	+	0.807167i	$0.299001\pi$
$194$	−28.3318	−2.03410
$195$	4.85089	0.347380
$196$	32.2635	2.30454
$197$	−3.45189	−0.245937	−0.122968	−	0.992411i	$-0.539241\pi$
$197$	−3.45189	−0.245937	−0.122968	+	0.992411i	$0.539241\pi$
$198$	8.15306	0.579413
$199$	8.65187	0.613315	0.306657	−	0.951820i	$-0.400789\pi$
$199$	8.65187	0.613315	0.306657	+	0.951820i	$0.400789\pi$
$200$	−0.277100	−0.0195940
$201$	13.1112	0.924791
$202$	17.8619	1.25676
$203$	−8.14939	−0.571975
$204$	−2.41071	−0.168783
$205$	−2.55744	−0.178620
$206$	10.7023	0.745664
$207$	−2.70687	−0.188141
$208$	6.32948	0.438870
$209$	17.7400	1.22710
$210$	21.8726	1.50935
$211$	−18.5611	−1.27780	−0.638900	−	0.769290i	$-0.720610\pi$
$211$	−18.5611	−1.27780	−0.638900	+	0.769290i	$0.720610\pi$
$212$	11.3611	0.780282
$213$	−3.91855	−0.268495
$214$	−36.9190	−2.52373
$215$	−19.2485	−1.31274
$216$	−0.862553	−0.0586893
$217$	7.61107	0.516673
$218$	30.9906	2.09895
$219$	−3.15443	−0.213157
$220$	21.5883	1.45548
$221$	2.10288	0.141455
$222$	−17.8917	−1.20081
$223$	−17.0243	−1.14003	−0.570017	−	0.821633i	$-0.693063\pi$
$223$	−17.0243	−1.14003	−0.570017	+	0.821633i	$0.693063\pi$
$224$	36.3280	2.42727
$225$	0.321256	0.0214171
$226$	−35.4452	−2.35778
$227$	−9.96647	−0.661498	−0.330749	−	0.943719i	$-0.607301\pi$
$227$	−9.96647	−0.661498	−0.330749	+	0.943719i	$0.607301\pi$
$228$	−11.0162	−0.729567
$229$	−6.02183	−0.397934	−0.198967	−	0.980006i	$-0.563759\pi$
$229$	−6.02183	−0.397934	−0.198967	+	0.980006i	$0.563759\pi$
$230$	−13.1138	−0.864699
$231$	−17.5269	−1.15319
$232$	1.55694	0.102218
$233$	23.6217	1.54751	0.773755	−	0.633485i	$-0.218376\pi$
$233$	23.6217	1.54751	0.773755	+	0.633485i	$0.218376\pi$
$234$	4.41640	0.288709
$235$	−23.3067	−1.52036
$236$	−2.41071	−0.156924
$237$	6.51359	0.423103
$238$	9.48184	0.614617
$239$	−13.4612	−0.870733	−0.435367	−	0.900253i	$-0.643381\pi$
$239$	−13.4612	−0.870733	−0.435367	+	0.900253i	$0.643381\pi$
$240$	6.94321	0.448182
$241$	13.0684	0.841807	0.420903	−	0.907106i	$-0.361713\pi$
$241$	13.0684	0.841807	0.420903	+	0.907106i	$0.361713\pi$
$242$	−8.54911	−0.549557
$243$	1.00000	0.0641500
$244$	−9.43992	−0.604329
$245$	−30.8727	−1.97239
$246$	−2.32838	−0.148452
$247$	9.60955	0.611441
$248$	−1.45410	−0.0923351
$249$	−15.5265	−0.983950
$250$	−22.6668	−1.43358
$251$	−7.67180	−0.484240	−0.242120	−	0.970246i	$-0.577843\pi$
$251$	−7.67180	−0.484240	−0.242120	+	0.970246i	$0.577843\pi$
$252$	10.8839	0.685619
$253$	10.5083	0.660653
$254$	−1.96472	−0.123277
$255$	2.30678	0.144456
$256$	7.57154	0.473222
$257$	−16.0802	−1.00305	−0.501526	−	0.865142i	$-0.667228\pi$
$257$	−16.0802	−1.00305	−0.501526	+	0.865142i	$0.667228\pi$
$258$	−17.5244	−1.09102
$259$	38.4623	2.38993
$260$	11.6941	0.725236
$261$	−1.80504	−0.111729
$262$	−22.4823	−1.38896
$263$	19.1252	1.17931	0.589656	−	0.807654i	$-0.299263\pi$
$263$	19.1252	1.17931	0.589656	+	0.807654i	$0.299263\pi$
$264$	3.34851	0.206087
$265$	−10.8713	−0.667820
$266$	43.3292	2.65669
$267$	−6.03654	−0.369430
$268$	31.6072	1.93072
$269$	−27.8237	−1.69644	−0.848221	−	0.529643i	$-0.822326\pi$
$269$	−27.8237	−1.69644	−0.848221	+	0.529643i	$0.822326\pi$
$270$	4.84464	0.294835
$271$	−9.03969	−0.549122	−0.274561	−	0.961570i	$-0.588532\pi$
$271$	−9.03969	−0.549122	−0.274561	+	0.961570i	$0.588532\pi$
$272$	3.00991	0.182502
$273$	−9.49409	−0.574609
$274$	−38.6235	−2.33333
$275$	−1.24715	−0.0752058
$276$	−6.52547	−0.392787
$277$	13.3912	0.804601	0.402301	−	0.915508i	$-0.368211\pi$
$277$	13.3912	0.804601	0.402301	+	0.915508i	$0.368211\pi$
$278$	−16.9398	−1.01598
$279$	1.68580	0.100926
$280$	8.98321	0.536850
$281$	19.4798	1.16207	0.581033	−	0.813880i	$-0.302649\pi$
$281$	19.4798	1.16207	0.581033	+	0.813880i	$0.302649\pi$
$282$	−21.2192	−1.26358
$283$	4.19744	0.249512	0.124756	−	0.992187i	$-0.460185\pi$
$283$	4.19744	0.249512	0.124756	+	0.992187i	$0.460185\pi$
$284$	−9.44648	−0.560545
$285$	10.5413	0.624414
$286$	−17.1449	−1.01380
$287$	5.00539	0.295459
$288$	8.04642	0.474140
$289$	1.00000	0.0588235
$290$	−8.74475	−0.513509
$291$	13.4902	0.790812
$292$	−7.60441	−0.445015
$293$	22.1989	1.29687	0.648436	−	0.761269i	$-0.275423\pi$
$293$	22.1989	1.29687	0.648436	+	0.761269i	$0.275423\pi$
$294$	−28.1075	−1.63926
$295$	2.30678	0.134306
$296$	−7.34823	−0.427107
$297$	−3.88210	−0.225262
$298$	−15.9546	−0.924226
$299$	5.69223	0.329190
$300$	0.774454	0.0447131
$301$	37.6729	2.17143
$302$	−33.8487	−1.94778
$303$	−8.50500	−0.488599
$304$	13.7544	0.788868
$305$	9.03298	0.517227
$306$	2.10017	0.120059
$307$	−1.42930	−0.0815746	−0.0407873	−	0.999168i	$-0.512987\pi$
$307$	−1.42930	−0.0815746	−0.0407873	+	0.999168i	$0.512987\pi$
$308$	−42.2522	−2.40754
$309$	−5.09592	−0.289897
$310$	8.16711	0.463861
$311$	−12.1203	−0.687280	−0.343640	−	0.939102i	$-0.611660\pi$
$311$	−12.1203	−0.687280	−0.343640	+	0.939102i	$0.611660\pi$
$312$	1.81385	0.102689
$313$	−4.92301	−0.278265	−0.139133	−	0.990274i	$-0.544431\pi$
$313$	−4.92301	−0.278265	−0.139133	+	0.990274i	$0.544431\pi$
$314$	−33.4577	−1.88813
$315$	−10.4147	−0.586801
$316$	15.7024	0.883327
$317$	20.4685	1.14963	0.574814	−	0.818284i	$-0.305075\pi$
$317$	20.4685	1.14963	0.574814	+	0.818284i	$0.305075\pi$
$318$	−9.89759	−0.555029
$319$	7.00733	0.392335
$320$	25.0955	1.40288
$321$	17.5791	0.981168
$322$	25.6661	1.43032
$323$	4.56971	0.254265
$324$	2.41071	0.133928
$325$	−0.675563	−0.0374735
$326$	13.8476	0.766945
$327$	−14.7562	−0.816022
$328$	−0.956280	−0.0528017
$329$	45.6155	2.51487
$330$	−18.8073	−1.03531
$331$	−7.63062	−0.419417	−0.209709	−	0.977764i	$-0.567252\pi$
$331$	−7.63062	−0.419417	−0.209709	+	0.977764i	$0.567252\pi$
$332$	−37.4298	−2.05422
$333$	8.51916	0.466847
$334$	19.7190	1.07897
$335$	−30.2447	−1.65244
$336$	−13.5891	−0.741348
$337$	−15.2833	−0.832536	−0.416268	−	0.909242i	$-0.636662\pi$
$337$	−15.2833	−0.832536	−0.416268	+	0.909242i	$0.636662\pi$
$338$	18.0150	0.979888
$339$	16.8773	0.916650
$340$	5.56098	0.301587
$341$	−6.54446	−0.354402
$342$	9.59715	0.518955
$343$	28.8200	1.55613
$344$	−7.19740	−0.388058
$345$	6.24417	0.336175
$346$	−14.2749	−0.767422
$347$	11.9854	0.643409	0.321705	−	0.946840i	$-0.395744\pi$
$347$	11.9854	0.643409	0.321705	+	0.946840i	$0.395744\pi$
$348$	−4.35142	−0.233260
$349$	−1.42775	−0.0764255	−0.0382127	−	0.999270i	$-0.512166\pi$
$349$	−1.42775	−0.0764255	−0.0382127	+	0.999270i	$0.512166\pi$
$350$	−3.04610	−0.162821
$351$	−2.10288	−0.112243
$352$	−31.2370	−1.66494
$353$	24.5749	1.30799	0.653994	−	0.756499i	$-0.273092\pi$
$353$	24.5749	1.30799	0.653994	+	0.756499i	$0.273092\pi$
$354$	2.10017	0.111623
$355$	9.03925	0.479754
$356$	−14.5523	−0.771272
$357$	−4.51480	−0.238949
$358$	−6.71679	−0.354993
$359$	15.5965	0.823153	0.411576	−	0.911375i	$-0.364978\pi$
$359$	15.5965	0.823153	0.411576	+	0.911375i	$0.364978\pi$
$360$	1.98972	0.104868
$361$	1.88222	0.0990641
$362$	35.4714	1.86434
$363$	4.07068	0.213655
$364$	−22.8875	−1.19963
$365$	7.27660	0.380875
$366$	8.22390	0.429870
$367$	25.2605	1.31859	0.659294	−	0.751885i	$-0.270855\pi$
$367$	25.2605	1.31859	0.659294	+	0.751885i	$0.270855\pi$
$368$	8.14743	0.424714
$369$	1.10866	0.0577146
$370$	41.2723	2.14564
$371$	21.2772	1.10466
$372$	4.06398	0.210708
$373$	−18.9136	−0.979308	−0.489654	−	0.871917i	$-0.662877\pi$
$373$	−18.9136	−0.979308	−0.489654	+	0.871917i	$0.662877\pi$
$374$	−8.15306	−0.421585
$375$	10.7929	0.557341
$376$	−8.71485	−0.449434
$377$	3.79578	0.195493
$378$	−9.48184	−0.487693
$379$	−36.2133	−1.86015	−0.930076	−	0.367368i	$-0.880259\pi$
$379$	−36.2133	−1.86015	−0.930076	+	0.367368i	$0.880259\pi$
$380$	25.4121	1.30361
$381$	0.935504	0.0479273
$382$	−56.5918	−2.89549
$383$	−15.1569	−0.774483	−0.387241	−	0.921978i	$-0.626572\pi$
$383$	−15.1569	−0.774483	−0.387241	+	0.921978i	$0.626572\pi$
$384$	6.75493	0.344711
$385$	40.4308	2.06054
$386$	−34.4471	−1.75331
$387$	8.34430	0.424165
$388$	32.5210	1.65100
$389$	−19.9540	−1.01171	−0.505853	−	0.862620i	$-0.668822\pi$
$389$	−19.9540	−1.01171	−0.505853	+	0.862620i	$0.668822\pi$
$390$	−10.1877	−0.515874
$391$	2.70687	0.136892
$392$	−11.5439	−0.583056
$393$	10.7050	0.539996
$394$	7.24954	0.365227
$395$	−15.0255	−0.756013
$396$	−9.35860	−0.470287
$397$	11.1566	0.559934	0.279967	−	0.960010i	$-0.409677\pi$
$397$	11.1566	0.559934	0.279967	+	0.960010i	$0.409677\pi$
$398$	−18.1704	−0.910799
$399$	−20.6313	−1.03286
$400$	−0.966951	−0.0483476
$401$	13.8699	0.692631	0.346315	−	0.938118i	$-0.387433\pi$
$401$	13.8699	0.692631	0.346315	+	0.938118i	$0.387433\pi$
$402$	−27.5357	−1.37336
$403$	−3.54505	−0.176591
$404$	−20.5031	−1.02007
$405$	−2.30678	−0.114625
$406$	17.1151	0.849407
$407$	−33.0722	−1.63933
$408$	0.862553	0.0427027
$409$	35.2301	1.74201	0.871007	−	0.491270i	$-0.163467\pi$
$409$	35.2301	1.74201	0.871007	+	0.491270i	$0.163467\pi$
$410$	5.37106	0.265258
$411$	18.3907	0.907145
$412$	−12.2848	−0.605228
$413$	−4.51480	−0.222159
$414$	5.68488	0.279397
$415$	35.8162	1.75815
$416$	−16.9207	−0.829603
$417$	8.06594	0.394991
$418$	−37.2571	−1.82230
$419$	29.5716	1.44467	0.722333	−	0.691545i	$-0.243070\pi$
$419$	29.5716	1.44467	0.722333	+	0.691545i	$0.243070\pi$
$420$	−25.1067	−1.22508
$421$	8.04388	0.392035	0.196017	−	0.980600i	$-0.437199\pi$
$421$	8.04388	0.392035	0.196017	+	0.980600i	$0.437199\pi$
$422$	38.9815	1.89759
$423$	10.1035	0.491251
$424$	−4.06500	−0.197414
$425$	−0.321256	−0.0155832
$426$	8.22962	0.398726
$427$	−17.6792	−0.855556
$428$	42.3780	2.04842
$429$	8.16359	0.394142
$430$	40.4251	1.94947
$431$	−30.3068	−1.45983	−0.729913	−	0.683540i	$-0.760440\pi$
$431$	−30.3068	−1.45983	−0.729913	+	0.683540i	$0.760440\pi$
$432$	−3.00991	−0.144814
$433$	22.6918	1.09050	0.545248	−	0.838275i	$-0.316435\pi$
$433$	22.6918	1.09050	0.545248	+	0.838275i	$0.316435\pi$
$434$	−15.9845	−0.767282
$435$	4.16383	0.199641
$436$	−35.5730	−1.70364
$437$	12.3696	0.591719
$438$	6.62484	0.316547
$439$	−15.4745	−0.738560	−0.369280	−	0.929318i	$-0.620396\pi$
$439$	−15.4745	−0.738560	−0.369280	+	0.929318i	$0.620396\pi$
$440$	−7.72430	−0.368242
$441$	13.3834	0.637307
$442$	−4.41640	−0.210067
$443$	26.2278	1.24612	0.623059	−	0.782175i	$-0.285890\pi$
$443$	26.2278	1.24612	0.623059	+	0.782175i	$0.285890\pi$
$444$	20.5372	0.974653
$445$	13.9250	0.660108
$446$	35.7539	1.69300
$447$	7.59683	0.359318
$448$	−49.1166	−2.32054
$449$	−26.5724	−1.25403	−0.627014	−	0.779008i	$-0.715723\pi$
$449$	−26.5724	−1.25403	−0.627014	+	0.779008i	$0.715723\pi$
$450$	−0.674692	−0.0318053
$451$	−4.30393	−0.202664
$452$	40.6863	1.91372
$453$	16.1171	0.757250
$454$	20.9313	0.982353
$455$	21.9008	1.02673
$456$	3.94161	0.184583
$457$	−20.0503	−0.937911	−0.468956	−	0.883222i	$-0.655370\pi$
$457$	−20.0503	−0.937911	−0.468956	+	0.883222i	$0.655370\pi$
$458$	12.6469	0.590949
$459$	−1.00000	−0.0466760
$460$	15.0529	0.701843
$461$	26.1566	1.21824	0.609118	−	0.793079i	$-0.291523\pi$
$461$	26.1566	1.21824	0.609118	+	0.793079i	$0.291523\pi$
$462$	36.8094	1.71253
$463$	19.2819	0.896106	0.448053	−	0.894007i	$-0.352118\pi$
$463$	19.2819	0.896106	0.448053	+	0.894007i	$0.352118\pi$
$464$	5.43299	0.252220
$465$	−3.88879	−0.180338
$466$	−49.6096	−2.29812
$467$	−3.38575	−0.156674	−0.0783369	−	0.996927i	$-0.524961\pi$
$467$	−3.38575	−0.156674	−0.0783369	+	0.996927i	$0.524961\pi$
$468$	−5.06943	−0.234334
$469$	59.1944	2.73334
$470$	48.9480	2.25780
$471$	15.9310	0.734061
$472$	0.862553	0.0397022
$473$	−32.3934	−1.48945
$474$	−13.6796	−0.628327
$475$	−1.46805	−0.0673586
$476$	−10.8839	−0.498861
$477$	4.71276	0.215782
$478$	28.2708	1.29308
$479$	−0.702324	−0.0320900	−0.0160450	−	0.999871i	$-0.505108\pi$
$479$	−0.702324	−0.0320900	−0.0160450	+	0.999871i	$0.505108\pi$
$480$	−18.5614	−0.847206
$481$	−17.9148	−0.816844
$482$	−27.4457	−1.25012
$483$	−12.2210	−0.556074
$484$	9.81321	0.446055
$485$	−31.1191	−1.41304
$486$	−2.10017	−0.0952656
$487$	−11.3938	−0.516301	−0.258151	−	0.966105i	$-0.583113\pi$
$487$	−11.3938	−0.516301	−0.258151	+	0.966105i	$0.583113\pi$
$488$	3.37761	0.152897
$489$	−6.59354	−0.298170
$490$	64.8379	2.92908
$491$	−37.2721	−1.68207	−0.841034	−	0.540983i	$-0.818052\pi$
$491$	−37.2721	−1.68207	−0.841034	+	0.540983i	$0.818052\pi$
$492$	2.67266	0.120493
$493$	1.80504	0.0812948
$494$	−20.1817	−0.908016
$495$	8.95516	0.402505
$496$	−5.07411	−0.227834
$497$	−17.6915	−0.793571
$498$	32.6082	1.46121
$499$	18.4823	0.827383	0.413691	−	0.910417i	$-0.364239\pi$
$499$	18.4823	0.827383	0.413691	+	0.910417i	$0.364239\pi$
$500$	26.0184	1.16358
$501$	−9.38923	−0.419480
$502$	16.1121	0.719117
$503$	−17.9752	−0.801473	−0.400736	−	0.916193i	$-0.631246\pi$
$503$	−17.9752	−0.801473	−0.400736	+	0.916193i	$0.631246\pi$
$504$	−3.89426	−0.173464
$505$	19.6192	0.873043
$506$	−22.0693	−0.981099
$507$	−8.57789	−0.380958
$508$	2.25523	0.100060
$509$	15.3785	0.681639	0.340819	−	0.940129i	$-0.389296\pi$
$509$	15.3785	0.681639	0.340819	+	0.940129i	$0.389296\pi$
$510$	−4.84464	−0.214524
$511$	−14.2416	−0.630013
$512$	−29.4114	−1.29981
$513$	−4.56971	−0.201757
$514$	33.7710	1.48958
$515$	11.7552	0.517996
$516$	20.1157	0.885542
$517$	−39.2230	−1.72502
$518$	−80.7774	−3.54915
$519$	6.79701	0.298356
$520$	−4.18415	−0.183487
$521$	8.23943	0.360976	0.180488	−	0.983577i	$-0.442232\pi$
$521$	8.23943	0.360976	0.180488	+	0.983577i	$0.442232\pi$
$522$	3.79088	0.165922
$523$	−43.2960	−1.89320	−0.946600	−	0.322410i	$-0.895507\pi$
$523$	−43.2960	−1.89320	−0.946600	+	0.322410i	$0.895507\pi$
$524$	25.8066	1.12737
$525$	1.45041	0.0633010
$526$	−40.1662	−1.75133
$527$	−1.68580	−0.0734348
$528$	11.6848	0.508513
$529$	−15.6728	−0.681428
$530$	22.8316	0.991742
$531$	−1.00000	−0.0433963
$532$	−49.7361	−2.15633
$533$	−2.33138	−0.100983
$534$	12.6777	0.548620
$535$	−40.5511	−1.75318
$536$	−11.3091	−0.488478
$537$	3.19822	0.138013
$538$	58.4345	2.51929
$539$	−51.9558	−2.23790
$540$	−5.56098	−0.239307
$541$	4.64721	0.199799	0.0998995	−	0.994998i	$-0.468148\pi$
$541$	4.64721	0.199799	0.0998995	+	0.994998i	$0.468148\pi$
$542$	18.9849	0.815470
$543$	−16.8898	−0.724810
$544$	−8.04642	−0.344987
$545$	34.0395	1.45809
$546$	19.9392	0.853319
$547$	4.22818	0.180784	0.0903920	−	0.995906i	$-0.471188\pi$
$547$	4.22818	0.180784	0.0903920	+	0.995906i	$0.471188\pi$
$548$	44.3345	1.89388
$549$	−3.91583	−0.167124
$550$	2.61922	0.111684
$551$	8.24849	0.351398
$552$	2.33482	0.0993765
$553$	29.4076	1.25054
$554$	−28.1238	−1.19487
$555$	−19.6519	−0.834176
$556$	19.4446	0.824636
$557$	30.7888	1.30456	0.652282	−	0.757976i	$-0.273812\pi$
$557$	30.7888	1.30456	0.652282	+	0.757976i	$0.273812\pi$
$558$	−3.54047	−0.149880
$559$	−17.5471	−0.742162
$560$	31.3472	1.32466
$561$	3.88210	0.163902
$562$	−40.9108	−1.72572
$563$	−6.71743	−0.283106	−0.141553	−	0.989931i	$-0.545210\pi$
$563$	−6.71743	−0.283106	−0.141553	+	0.989931i	$0.545210\pi$
$564$	24.3567	1.02560
$565$	−38.9323	−1.63790
$566$	−8.81533	−0.370536
$567$	4.51480	0.189604
$568$	3.37996	0.141820
$569$	20.0294	0.839676	0.419838	−	0.907599i	$-0.362087\pi$
$569$	20.0294	0.839676	0.419838	+	0.907599i	$0.362087\pi$
$570$	−22.1386	−0.927282
$571$	44.5126	1.86279	0.931396	−	0.364007i	$-0.118592\pi$
$571$	44.5126	1.86279	0.931396	+	0.364007i	$0.118592\pi$
$572$	19.6800	0.822863
$573$	26.9463	1.12570
$574$	−10.5122	−0.438769
$575$	−0.869599	−0.0362648
$576$	−10.8790	−0.453292
$577$	37.5728	1.56418	0.782089	−	0.623167i	$-0.214154\pi$
$577$	37.5728	1.56418	0.782089	+	0.623167i	$0.214154\pi$
$578$	−2.10017	−0.0873555
$579$	16.4020	0.681646
$580$	10.0378	0.416796
$581$	−70.0989	−2.90819
$582$	−28.3318	−1.17439
$583$	−18.2954	−0.757718
$584$	2.72087	0.112590
$585$	4.85089	0.200560
$586$	−46.6214	−1.92591
$587$	−27.9033	−1.15169	−0.575847	−	0.817558i	$-0.695327\pi$
$587$	−27.9033	−1.15169	−0.575847	+	0.817558i	$0.695327\pi$
$588$	32.2635	1.33053
$589$	−7.70363	−0.317423
$590$	−4.84464	−0.199451
$591$	−3.45189	−0.141992
$592$	−25.6419	−1.05388
$593$	−29.9035	−1.22799	−0.613995	−	0.789310i	$-0.710439\pi$
$593$	−29.9035	−1.22799	−0.613995	+	0.789310i	$0.710439\pi$
$594$	8.15306	0.334524
$595$	10.4147	0.426960
$596$	18.3137	0.750160
$597$	8.65187	0.354098
$598$	−11.9546	−0.488861
$599$	−1.52281	−0.0622203	−0.0311101	−	0.999516i	$-0.509904\pi$
$599$	−1.52281	−0.0622203	−0.0311101	+	0.999516i	$0.509904\pi$
$600$	−0.277100	−0.0113126
$601$	−33.8978	−1.38272	−0.691359	−	0.722511i	$-0.742988\pi$
$601$	−33.8978	−1.38272	−0.691359	+	0.722511i	$0.742988\pi$
$602$	−79.1193	−3.22466
$603$	13.1112	0.533929
$604$	38.8537	1.58094
$605$	−9.39017	−0.381765
$606$	17.8619	0.725591
$607$	28.6840	1.16425	0.582124	−	0.813100i	$-0.302222\pi$
$607$	28.6840	1.16425	0.582124	+	0.813100i	$0.302222\pi$
$608$	−36.7698	−1.49121
$609$	−8.14939	−0.330230
$610$	−18.9708	−0.768104
$611$	−21.2466	−0.859544
$612$	−2.41071	−0.0974470
$613$	39.0863	1.57868	0.789341	−	0.613955i	$-0.210422\pi$
$613$	39.0863	1.57868	0.789341	+	0.613955i	$0.210422\pi$
$614$	3.00178	0.121142
$615$	−2.55744	−0.103126
$616$	15.1179	0.609117
$617$	9.41263	0.378938	0.189469	−	0.981887i	$-0.439323\pi$
$617$	9.41263	0.378938	0.189469	+	0.981887i	$0.439323\pi$
$618$	10.7023	0.430510
$619$	35.1721	1.41369	0.706844	−	0.707370i	$-0.250118\pi$
$619$	35.1721	1.41369	0.706844	+	0.707370i	$0.250118\pi$
$620$	−9.37473	−0.376498
$621$	−2.70687	−0.108623
$622$	25.4547	1.02064
$623$	−27.2538	−1.09190
$624$	6.32948	0.253382
$625$	−26.5031	−1.06012
$626$	10.3392	0.413236
$627$	17.7400	0.708469
$628$	38.4049	1.53252
$629$	−8.51916	−0.339681
$630$	21.8726	0.871424
$631$	25.3838	1.01051	0.505256	−	0.862970i	$-0.331398\pi$
$631$	25.3838	1.01051	0.505256	+	0.862970i	$0.331398\pi$
$632$	−5.61832	−0.223485
$633$	−18.5611	−0.737738
$634$	−42.9874	−1.70725
$635$	−2.15801	−0.0856379
$636$	11.3611	0.450496
$637$	−28.1438	−1.11510
$638$	−14.7166	−0.582635
$639$	−3.91855	−0.155015
$640$	−15.5822	−0.615939
$641$	19.3147	0.762886	0.381443	−	0.924392i	$-0.375427\pi$
$641$	19.3147	0.762886	0.381443	+	0.924392i	$0.375427\pi$
$642$	−36.9190	−1.45708
$643$	−13.0669	−0.515307	−0.257654	−	0.966237i	$-0.582949\pi$
$643$	−13.0669	−0.515307	−0.257654	+	0.966237i	$0.582949\pi$
$644$	−29.4612	−1.16093
$645$	−19.2485	−0.757909
$646$	−9.59715	−0.377595
$647$	−21.8728	−0.859907	−0.429954	−	0.902851i	$-0.641470\pi$
$647$	−21.8728	−0.859907	−0.429954	+	0.902851i	$0.641470\pi$
$648$	−0.862553	−0.0338843
$649$	3.88210	0.152386
$650$	1.41880	0.0556498
$651$	7.61107	0.298301
$652$	−15.8951	−0.622500
$653$	−14.1947	−0.555481	−0.277740	−	0.960656i	$-0.589586\pi$
$653$	−14.1947	−0.555481	−0.277740	+	0.960656i	$0.589586\pi$
$654$	30.9906	1.21183
$655$	−24.6942	−0.964881
$656$	−3.33697	−0.130287
$657$	−3.15443	−0.123066
$658$	−95.8003	−3.73468
$659$	−2.63833	−0.102775	−0.0513875	−	0.998679i	$-0.516364\pi$
$659$	−2.63833	−0.102775	−0.0513875	+	0.998679i	$0.516364\pi$
$660$	21.5883	0.840322
$661$	−5.86329	−0.228056	−0.114028	−	0.993478i	$-0.536375\pi$
$661$	−5.86329	−0.228056	−0.114028	+	0.993478i	$0.536375\pi$
$662$	16.0256	0.622852
$663$	2.10288	0.0816691
$664$	13.3924	0.519726
$665$	47.5920	1.84554
$666$	−17.8917	−0.693288
$667$	4.88600	0.189187
$668$	−22.6347	−0.875762
$669$	−17.0243	−0.658198
$670$	63.5189	2.45395
$671$	15.2016	0.586852
$672$	36.3280	1.40138
$673$	20.3970	0.786248	0.393124	−	0.919485i	$-0.371394\pi$
$673$	20.3970	0.786248	0.393124	+	0.919485i	$0.371394\pi$
$674$	32.0976	1.23635
$675$	0.321256	0.0123652
$676$	−20.6788	−0.795338
$677$	−4.41467	−0.169670	−0.0848349	−	0.996395i	$-0.527036\pi$
$677$	−4.41467	−0.169670	−0.0848349	+	0.996395i	$0.527036\pi$
$678$	−35.4452	−1.36126
$679$	60.9058	2.33735
$680$	−1.98972	−0.0763024
$681$	−9.96647	−0.381916
$682$	13.7445	0.526302
$683$	44.8987	1.71800	0.859001	−	0.511974i	$-0.171085\pi$
$683$	44.8987	1.71800	0.859001	+	0.511974i	$0.171085\pi$
$684$	−11.0162	−0.421216
$685$	−42.4233	−1.62091
$686$	−60.5268	−2.31092
$687$	−6.02183	−0.229747
$688$	−25.1156	−0.957522
$689$	−9.91037	−0.377555
$690$	−13.1138	−0.499234
$691$	−14.8725	−0.565777	−0.282889	−	0.959153i	$-0.591293\pi$
$691$	−14.8725	−0.565777	−0.282889	+	0.959153i	$0.591293\pi$
$692$	16.3856	0.622887
$693$	−17.5269	−0.665792
$694$	−25.1713	−0.955490
$695$	−18.6064	−0.705781
$696$	1.55694	0.0590157
$697$	−1.10866	−0.0419936
$698$	2.99851	0.113495
$699$	23.6217	0.893456
$700$	3.49651	0.132156
$701$	−19.4166	−0.733356	−0.366678	−	0.930348i	$-0.619505\pi$
$701$	−19.4166	−0.733356	−0.366678	+	0.930348i	$0.619505\pi$
$702$	4.41640	0.166686
$703$	−38.9301	−1.46828
$704$	42.2334	1.59173
$705$	−23.3067	−0.877782
$706$	−51.6114	−1.94242
$707$	−38.3984	−1.44412
$708$	−2.41071	−0.0905999
$709$	−29.8929	−1.12265	−0.561326	−	0.827595i	$-0.689709\pi$
$709$	−29.8929	−1.12265	−0.561326	+	0.827595i	$0.689709\pi$
$710$	−18.9840	−0.712455
$711$	6.51359	0.244279
$712$	5.20683	0.195134
$713$	−4.56325	−0.170895
$714$	9.48184	0.354849
$715$	−18.8316	−0.704263
$716$	7.70996	0.288135
$717$	−13.4612	−0.502718
$718$	−32.7553	−1.22242
$719$	25.8668	0.964668	0.482334	−	0.875987i	$-0.339789\pi$
$719$	25.8668	0.964668	0.482334	+	0.875987i	$0.339789\pi$
$720$	6.94321	0.258758
$721$	−23.0071	−0.856829
$722$	−3.95298	−0.147115
$723$	13.0684	0.486017
$724$	−40.7163	−1.51321
$725$	−0.579879	−0.0215362
$726$	−8.54911	−0.317287
$727$	−20.1442	−0.747105	−0.373553	−	0.927609i	$-0.621860\pi$
$727$	−20.1442	−0.747105	−0.373553	+	0.927609i	$0.621860\pi$
$728$	8.18916	0.303510
$729$	1.00000	0.0370370
$730$	−15.2821	−0.565615
$731$	−8.34430	−0.308625
$732$	−9.43992	−0.348909
$733$	−18.9876	−0.701323	−0.350661	−	0.936502i	$-0.614043\pi$
$733$	−18.9876	−0.701323	−0.350661	+	0.936502i	$0.614043\pi$
$734$	−53.0513	−1.95816
$735$	−30.8727	−1.13876
$736$	−21.7806	−0.802844
$737$	−50.8989	−1.87488
$738$	−2.32838	−0.0857087
$739$	37.0452	1.36273	0.681365	−	0.731944i	$-0.261387\pi$
$739$	37.0452	1.36273	0.681365	+	0.731944i	$0.261387\pi$
$740$	−47.3749	−1.74154
$741$	9.60955	0.353016
$742$	−44.6857	−1.64046
$743$	−12.0107	−0.440631	−0.220316	−	0.975429i	$-0.570709\pi$
$743$	−12.0107	−0.440631	−0.220316	+	0.975429i	$0.570709\pi$
$744$	−1.45410	−0.0533097
$745$	−17.5243	−0.642039
$746$	39.7217	1.45431
$747$	−15.5265	−0.568084
$748$	9.35860	0.342184
$749$	79.3660	2.89997
$750$	−22.6668	−0.827675
$751$	1.49051	0.0543896	0.0271948	−	0.999630i	$-0.491343\pi$
$751$	1.49051	0.0543896	0.0271948	+	0.999630i	$0.491343\pi$
$752$	−30.4107	−1.10897
$753$	−7.67180	−0.279576
$754$	−7.97177	−0.290315
$755$	−37.1788	−1.35307
$756$	10.8839	0.395842
$757$	−14.3861	−0.522870	−0.261435	−	0.965221i	$-0.584196\pi$
$757$	−14.3861	−0.522870	−0.261435	+	0.965221i	$0.584196\pi$
$758$	76.0540	2.76241
$759$	10.5083	0.381428
$760$	−9.09246	−0.329818
$761$	37.1200	1.34560	0.672800	−	0.739825i	$-0.265092\pi$
$761$	37.1200	1.34560	0.672800	+	0.739825i	$0.265092\pi$
$762$	−1.96472	−0.0711742
$763$	−66.6215	−2.41186
$764$	64.9596	2.35016
$765$	2.30678	0.0834020
$766$	31.8321	1.15014
$767$	2.10288	0.0759306
$768$	7.57154	0.273215
$769$	39.6193	1.42871	0.714354	−	0.699784i	$-0.246720\pi$
$769$	39.6193	1.42871	0.714354	+	0.699784i	$0.246720\pi$
$770$	−84.9115	−3.06000
$771$	−16.0802	−0.579113
$772$	39.5405	1.42309
$773$	−1.10324	−0.0396807	−0.0198404	−	0.999803i	$-0.506316\pi$
$773$	−1.10324	−0.0396807	−0.0198404	+	0.999803i	$0.506316\pi$
$774$	−17.5244	−0.629903
$775$	0.541575	0.0194539
$776$	−11.6360	−0.417710
$777$	38.4623	1.37983
$778$	41.9067	1.50243
$779$	−5.06626	−0.181518
$780$	11.6941	0.418715
$781$	15.2122	0.544335
$782$	−5.68488	−0.203291
$783$	−1.80504	−0.0645068
$784$	−40.2829	−1.43868
$785$	−36.7493	−1.31164
$786$	−22.4823	−0.801918
$787$	1.04346	0.0371953	0.0185977	−	0.999827i	$-0.494080\pi$
$787$	1.04346	0.0371953	0.0185977	+	0.999827i	$0.494080\pi$
$788$	−8.32149	−0.296441
$789$	19.1252	0.680876
$790$	31.5560	1.12271
$791$	76.1977	2.70928
$792$	3.34851	0.118984
$793$	8.23452	0.292416
$794$	−23.4307	−0.831526
$795$	−10.8713	−0.385566
$796$	20.8571	0.739261
$797$	47.1482	1.67008	0.835038	−	0.550192i	$-0.185445\pi$
$797$	47.1482	1.67008	0.835038	+	0.550192i	$0.185445\pi$
$798$	43.3292	1.53384
$799$	−10.1035	−0.357438
$800$	2.58496	0.0913922
$801$	−6.03654	−0.213291
$802$	−29.1292	−1.02859
$803$	12.2458	0.432145
$804$	31.6072	1.11470
$805$	28.1912	0.993609
$806$	7.44519	0.262246
$807$	−27.8237	−0.979441
$808$	7.33601	0.258080
$809$	−20.8110	−0.731675	−0.365837	−	0.930679i	$-0.619217\pi$
$809$	−20.8110	−0.731675	−0.365837	+	0.930679i	$0.619217\pi$
$810$	4.84464	0.170223
$811$	−36.4991	−1.28166	−0.640828	−	0.767685i	$-0.721409\pi$
$811$	−36.4991	−1.28166	−0.640828	+	0.767685i	$0.721409\pi$
$812$	−19.6458	−0.689432
$813$	−9.03969	−0.317036
$814$	69.4572	2.43447
$815$	15.2099	0.532779
$816$	3.00991	0.105368
$817$	−38.1310	−1.33403
$818$	−73.9891	−2.58697
$819$	−9.49409	−0.331750
$820$	−6.16525	−0.215300
$821$	16.3589	0.570930	0.285465	−	0.958389i	$-0.407852\pi$
$821$	16.3589	0.570930	0.285465	+	0.958389i	$0.407852\pi$
$822$	−38.6235	−1.34715
$823$	4.97004	0.173245	0.0866224	−	0.996241i	$-0.472393\pi$
$823$	4.97004	0.173245	0.0866224	+	0.996241i	$0.472393\pi$
$824$	4.39550	0.153125
$825$	−1.24715	−0.0434201
$826$	9.48184	0.329916
$827$	37.4464	1.30214	0.651070	−	0.759018i	$-0.274320\pi$
$827$	37.4464	1.30214	0.651070	+	0.759018i	$0.274320\pi$
$828$	−6.52547	−0.226776
$829$	8.65185	0.300491	0.150246	−	0.988649i	$-0.451994\pi$
$829$	8.65185	0.300491	0.150246	+	0.988649i	$0.451994\pi$
$830$	−75.2201	−2.61093
$831$	13.3912	0.464537
$832$	22.8773	0.793127
$833$	−13.3834	−0.463709
$834$	−16.9398	−0.586579
$835$	21.6589	0.749538
$836$	42.7660	1.47909
$837$	1.68580	0.0582699
$838$	−62.1053	−2.14539
$839$	13.4693	0.465013	0.232507	−	0.972595i	$-0.425307\pi$
$839$	13.4693	0.465013	0.232507	+	0.972595i	$0.425307\pi$
$840$	8.98321	0.309950
$841$	−25.7418	−0.887650
$842$	−16.8935	−0.582188
$843$	19.4798	0.670919
$844$	−44.7454	−1.54020
$845$	19.7874	0.680706
$846$	−21.2192	−0.729529
$847$	18.3783	0.631486
$848$	−14.1850	−0.487114
$849$	4.19744	0.144056
$850$	0.674692	0.0231417
$851$	−23.0603	−0.790496
$852$	−9.44648	−0.323631
$853$	−15.1364	−0.518261	−0.259130	−	0.965842i	$-0.583436\pi$
$853$	−15.1364	−0.518261	−0.259130	+	0.965842i	$0.583436\pi$
$854$	37.1293	1.27054
$855$	10.5413	0.360506
$856$	−15.1629	−0.518256
$857$	−46.7584	−1.59724	−0.798618	−	0.601838i	$-0.794435\pi$
$857$	−46.7584	−1.59724	−0.798618	+	0.601838i	$0.794435\pi$
$858$	−17.1449	−0.585317
$859$	−18.9518	−0.646629	−0.323314	−	0.946292i	$-0.604797\pi$
$859$	−18.9518	−0.646629	−0.323314	+	0.946292i	$0.604797\pi$
$860$	−46.4025	−1.58231
$861$	5.00539	0.170583
$862$	63.6494	2.16791
$863$	0.683193	0.0232562	0.0116281	−	0.999932i	$-0.496299\pi$
$863$	0.683193	0.0232562	0.0116281	+	0.999932i	$0.496299\pi$
$864$	8.04642	0.273745
$865$	−15.6792	−0.533110
$866$	−47.6565	−1.61943
$867$	1.00000	0.0339618
$868$	18.3481	0.622774
$869$	−25.2864	−0.857783
$870$	−8.74475	−0.296475
$871$	−27.5712	−0.934216
$872$	12.7280	0.431026
$873$	13.4902	0.456576
$874$	−25.9783	−0.878728
$875$	48.7276	1.64729
$876$	−7.60441	−0.256929
$877$	2.91649	0.0984828	0.0492414	−	0.998787i	$-0.484320\pi$
$877$	2.91649	0.0984828	0.0492414	+	0.998787i	$0.484320\pi$
$878$	32.4991	1.09679
$879$	22.1989	0.748749
$880$	−26.9542	−0.908626
$881$	−12.0223	−0.405043	−0.202522	−	0.979278i	$-0.564914\pi$
$881$	−12.0223	−0.405043	−0.202522	+	0.979278i	$0.564914\pi$
$882$	−28.1075	−0.946428
$883$	−26.0110	−0.875340	−0.437670	−	0.899136i	$-0.644196\pi$
$883$	−26.0110	−0.875340	−0.437670	+	0.899136i	$0.644196\pi$
$884$	5.06943	0.170503
$885$	2.30678	0.0775417
$886$	−55.0827	−1.85054
$887$	45.9354	1.54236	0.771180	−	0.636617i	$-0.219667\pi$
$887$	45.9354	1.54236	0.771180	+	0.636617i	$0.219667\pi$
$888$	−7.34823	−0.246590
$889$	4.22362	0.141656
$890$	−29.2448	−0.980289
$891$	−3.88210	−0.130055
$892$	−41.0407	−1.37414
$893$	−46.1703	−1.54503
$894$	−15.9546	−0.533602
$895$	−7.37759	−0.246606
$896$	30.4972	1.01884
$897$	5.69223	0.190058
$898$	55.8064	1.86228
$899$	−3.04294	−0.101488
$900$	0.774454	0.0258151
$901$	−4.71276	−0.157005
$902$	9.03898	0.300965
$903$	37.6729	1.25367
$904$	−14.5576	−0.484178
$905$	38.9611	1.29511
$906$	−33.8487	−1.12455
$907$	−36.2034	−1.20211	−0.601057	−	0.799206i	$-0.705253\pi$
$907$	−36.2034	−1.20211	−0.601057	+	0.799206i	$0.705253\pi$
$908$	−24.0262	−0.797339
$909$	−8.50500	−0.282093
$910$	−45.9954	−1.52473
$911$	−16.7461	−0.554821	−0.277411	−	0.960751i	$-0.589476\pi$
$911$	−16.7461	−0.554821	−0.277411	+	0.960751i	$0.589476\pi$
$912$	13.7544	0.455453
$913$	60.2752	1.99482
$914$	42.1089	1.39284
$915$	9.03298	0.298621
$916$	−14.5169	−0.479651
$917$	48.3310	1.59603
$918$	2.10017	0.0693159
$919$	29.7233	0.980480	0.490240	−	0.871587i	$-0.336909\pi$
$919$	29.7233	0.980480	0.490240	+	0.871587i	$0.336909\pi$
$920$	−5.38593	−0.177569
$921$	−1.42930	−0.0470971
$922$	−54.9334	−1.80913
$923$	8.24025	0.271231
$924$	−42.2522	−1.39000
$925$	2.73683	0.0899865
$926$	−40.4952	−1.33076
$927$	−5.09592	−0.167372
$928$	−14.5241	−0.476776
$929$	−12.5057	−0.410298	−0.205149	−	0.978731i	$-0.565768\pi$
$929$	−12.5057	−0.410298	−0.205149	+	0.978731i	$0.565768\pi$
$930$	8.16711	0.267810
$931$	−61.1584	−2.00439
$932$	56.9450	1.86530
$933$	−12.1203	−0.396801
$934$	7.11064	0.232667
$935$	−8.95516	−0.292865
$936$	1.81385	0.0592874
$937$	−16.0944	−0.525780	−0.262890	−	0.964826i	$-0.584676\pi$
$937$	−16.0944	−0.525780	−0.262890	+	0.964826i	$0.584676\pi$
$938$	−124.318	−4.05913
$939$	−4.92301	−0.160656
$940$	−56.1856	−1.83257
$941$	48.8862	1.59365	0.796823	−	0.604213i	$-0.206512\pi$
$941$	48.8862	1.59365	0.796823	+	0.604213i	$0.206512\pi$
$942$	−33.4577	−1.09011
$943$	−3.00101	−0.0977262
$944$	3.00991	0.0979641
$945$	−10.4147	−0.338789
$946$	68.0315	2.21190
$947$	−36.5527	−1.18780	−0.593902	−	0.804537i	$-0.702413\pi$
$947$	−36.5527	−1.18780	−0.593902	+	0.804537i	$0.702413\pi$
$948$	15.7024	0.509989
$949$	6.63340	0.215329
$950$	3.08314	0.100030
$951$	20.4685	0.663738
$952$	3.89426	0.126214
$953$	−20.4996	−0.664046	−0.332023	−	0.943271i	$-0.607731\pi$
$953$	−20.4996	−0.664046	−0.332023	+	0.943271i	$0.607731\pi$
$954$	−9.89759	−0.320446
$955$	−62.1593	−2.01143
$956$	−32.4510	−1.04954
$957$	7.00733	0.226515
$958$	1.47500	0.0476550
$959$	83.0303	2.68119
$960$	25.0955	0.809955
$961$	−28.1581	−0.908325
$962$	37.6241	1.21305
$963$	17.5791	0.566477
$964$	31.5040	1.01467
$965$	−37.8360	−1.21798
$966$	25.6661	0.825794
$967$	−36.6475	−1.17850	−0.589252	−	0.807949i	$-0.700577\pi$
$967$	−36.6475	−1.17850	−0.589252	+	0.807949i	$0.700577\pi$
$968$	−3.51117	−0.112853
$969$	4.56971	0.146800
$970$	65.3553	2.09843
$971$	−50.7446	−1.62847	−0.814235	−	0.580535i	$-0.802843\pi$
$971$	−50.7446	−1.62847	−0.814235	+	0.580535i	$0.802843\pi$
$972$	2.41071	0.0773235
$973$	36.4161	1.16745
$974$	23.9289	0.766730
$975$	−0.675563	−0.0216353
$976$	11.7863	0.377270
$977$	27.8266	0.890253	0.445126	−	0.895468i	$-0.353159\pi$
$977$	27.8266	0.890253	0.445126	+	0.895468i	$0.353159\pi$
$978$	13.8476	0.442796
$979$	23.4344	0.748968
$980$	−74.4251	−2.37742
$981$	−14.7562	−0.471131
$982$	78.2777	2.49794
$983$	35.2725	1.12502	0.562509	−	0.826791i	$-0.309836\pi$
$983$	35.2725	1.12502	0.562509	+	0.826791i	$0.309836\pi$
$984$	−0.956280	−0.0304851
$985$	7.96276	0.253715
$986$	−3.79088	−0.120726
$987$	45.6155	1.45196
$988$	23.1658	0.737002
$989$	−22.5869	−0.718223
$990$	−18.8073	−0.597737
$991$	−15.8594	−0.503789	−0.251894	−	0.967755i	$-0.581054\pi$
$991$	−15.8594	−0.503789	−0.251894	+	0.967755i	$0.581054\pi$
$992$	13.5647	0.430679
$993$	−7.63062	−0.242151
$994$	37.1551	1.17849
$995$	−19.9580	−0.632711
$996$	−37.4298	−1.18601
$997$	−49.9654	−1.58242	−0.791210	−	0.611544i	$-0.790549\pi$
$997$	−49.9654	−1.58242	−0.791210	+	0.611544i	$0.790549\pi$
$998$	−38.8160	−1.22870
$999$	8.51916	0.269534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3009.2.a.j.1.5	✓	24
3.2	odd	2		9027.2.a.t.1.20		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3009.2.a.j.1.5	✓	24	1.1	even	1	trivial
9027.2.a.t.1.20		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 3009 = 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10017 q^{2} +1.00000 q^{3} +2.41071 q^{4} -2.30678 q^{5} -2.10017 q^{6} +4.51480 q^{7} -0.862553 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.10017 q^{2} +1.00000 q^{3} +2.41071 q^{4} -2.30678 q^{5} -2.10017 q^{6} +4.51480 q^{7} -0.862553 q^{8} +1.00000 q^{9} +4.84464 q^{10} -3.88210 q^{11} +2.41071 q^{12} -2.10288 q^{13} -9.48184 q^{14} -2.30678 q^{15} -3.00991 q^{16} -1.00000 q^{17} -2.10017 q^{18} -4.56971 q^{19} -5.56098 q^{20} +4.51480 q^{21} +8.15306 q^{22} -2.70687 q^{23} -0.862553 q^{24} +0.321256 q^{25} +4.41640 q^{26} +1.00000 q^{27} +10.8839 q^{28} -1.80504 q^{29} +4.84464 q^{30} +1.68580 q^{31} +8.04642 q^{32} -3.88210 q^{33} +2.10017 q^{34} -10.4147 q^{35} +2.41071 q^{36} +8.51916 q^{37} +9.59715 q^{38} -2.10288 q^{39} +1.98972 q^{40} +1.10866 q^{41} -9.48184 q^{42} +8.34430 q^{43} -9.35860 q^{44} -2.30678 q^{45} +5.68488 q^{46} +10.1035 q^{47} -3.00991 q^{48} +13.3834 q^{49} -0.674692 q^{50} -1.00000 q^{51} -5.06943 q^{52} +4.71276 q^{53} -2.10017 q^{54} +8.95516 q^{55} -3.89426 q^{56} -4.56971 q^{57} +3.79088 q^{58} -1.00000 q^{59} -5.56098 q^{60} -3.91583 q^{61} -3.54047 q^{62} +4.51480 q^{63} -10.8790 q^{64} +4.85089 q^{65} +8.15306 q^{66} +13.1112 q^{67} -2.41071 q^{68} -2.70687 q^{69} +21.8726 q^{70} -3.91855 q^{71} -0.862553 q^{72} -3.15443 q^{73} -17.8917 q^{74} +0.321256 q^{75} -11.0162 q^{76} -17.5269 q^{77} +4.41640 q^{78} +6.51359 q^{79} +6.94321 q^{80} +1.00000 q^{81} -2.32838 q^{82} -15.5265 q^{83} +10.8839 q^{84} +2.30678 q^{85} -17.5244 q^{86} -1.80504 q^{87} +3.34851 q^{88} -6.03654 q^{89} +4.84464 q^{90} -9.49409 q^{91} -6.52547 q^{92} +1.68580 q^{93} -21.2192 q^{94} +10.5413 q^{95} +8.04642 q^{96} +13.4902 q^{97} -28.1075 q^{98} -3.88210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 24 q^{3} + 34 q^{4} - 3 q^{5} + 2 q^{6} + 19 q^{7} + 3 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 24 * q^3 + 34 * q^4 - 3 * q^5 + 2 * q^6 + 19 * q^7 + 3 * q^8 + 24 * q^9	\( 24 q + 2 q^{2} + 24 q^{3} + 34 q^{4} - 3 q^{5} + 2 q^{6} + 19 q^{7} + 3 q^{8} + 24 q^{9} + 10 q^{10} + 11 q^{11} + 34 q^{12} + 21 q^{13} + 9 q^{14} - 3 q^{15} + 50 q^{16} - 24 q^{17} + 2 q^{18} + 13 q^{19} + q^{20} + 19 q^{21} + 5 q^{22} + 18 q^{23} + 3 q^{24} + 39 q^{25} - 7 q^{26} + 24 q^{27} + 40 q^{28} - 10 q^{29} + 10 q^{30} + 47 q^{31} + 18 q^{32} + 11 q^{33} - 2 q^{34} + 5 q^{35} + 34 q^{36} + 54 q^{37} + 5 q^{38} + 21 q^{39} + 29 q^{40} + 9 q^{42} + 16 q^{43} + 7 q^{44} - 3 q^{45} - 8 q^{46} + 10 q^{47} + 50 q^{48} + 55 q^{49} + 21 q^{50} - 24 q^{51} + 68 q^{52} + 6 q^{53} + 2 q^{54} + 15 q^{55} - 5 q^{56} + 13 q^{57} + q^{58} - 24 q^{59} + q^{60} + 42 q^{61} - 7 q^{62} + 19 q^{63} + 53 q^{64} - 9 q^{65} + 5 q^{66} + 28 q^{67} - 34 q^{68} + 18 q^{69} - 20 q^{70} + 54 q^{71} + 3 q^{72} + 33 q^{73} - 17 q^{74} + 39 q^{75} - 56 q^{76} - 23 q^{77} - 7 q^{78} + 35 q^{79} + 3 q^{80} + 24 q^{81} - 12 q^{82} - 17 q^{83} + 40 q^{84} + 3 q^{85} + 36 q^{86} - 10 q^{87} + 47 q^{88} + 15 q^{89} + 10 q^{90} + 74 q^{91} + 6 q^{92} + 47 q^{93} + 9 q^{94} + 12 q^{95} + 18 q^{96} + 52 q^{97} - 48 q^{98} + 11 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 24 * q^3 + 34 * q^4 - 3 * q^5 + 2 * q^6 + 19 * q^7 + 3 * q^8 + 24 * q^9 + 10 * q^10 + 11 * q^11 + 34 * q^12 + 21 * q^13 + 9 * q^14 - 3 * q^15 + 50 * q^16 - 24 * q^17 + 2 * q^18 + 13 * q^19 + q^20 + 19 * q^21 + 5 * q^22 + 18 * q^23 + 3 * q^24 + 39 * q^25 - 7 * q^26 + 24 * q^27 + 40 * q^28 - 10 * q^29 + 10 * q^30 + 47 * q^31 + 18 * q^32 + 11 * q^33 - 2 * q^34 + 5 * q^35 + 34 * q^36 + 54 * q^37 + 5 * q^38 + 21 * q^39 + 29 * q^40 + 9 * q^42 + 16 * q^43 + 7 * q^44 - 3 * q^45 - 8 * q^46 + 10 * q^47 + 50 * q^48 + 55 * q^49 + 21 * q^50 - 24 * q^51 + 68 * q^52 + 6 * q^53 + 2 * q^54 + 15 * q^55 - 5 * q^56 + 13 * q^57 + q^58 - 24 * q^59 + q^60 + 42 * q^61 - 7 * q^62 + 19 * q^63 + 53 * q^64 - 9 * q^65 + 5 * q^66 + 28 * q^67 - 34 * q^68 + 18 * q^69 - 20 * q^70 + 54 * q^71 + 3 * q^72 + 33 * q^73 - 17 * q^74 + 39 * q^75 - 56 * q^76 - 23 * q^77 - 7 * q^78 + 35 * q^79 + 3 * q^80 + 24 * q^81 - 12 * q^82 - 17 * q^83 + 40 * q^84 + 3 * q^85 + 36 * q^86 - 10 * q^87 + 47 * q^88 + 15 * q^89 + 10 * q^90 + 74 * q^91 + 6 * q^92 + 47 * q^93 + 9 * q^94 + 12 * q^95 + 18 * q^96 + 52 * q^97 - 48 * q^98 + 11 * q^99

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