LMFDB - Embedded newform 4017.2.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.794802 q^{2} -1.00000 q^{3} -1.36829 q^{4} -2.06654 q^{5} -0.794802 q^{6} -0.419104 q^{7} -2.67712 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.794802 q^{2} -1.00000 q^{3} -1.36829 q^{4} -2.06654 q^{5} -0.794802 q^{6} -0.419104 q^{7} -2.67712 q^{8} +1.00000 q^{9} -1.64249 q^{10} -4.33558 q^{11} +1.36829 q^{12} -1.00000 q^{13} -0.333104 q^{14} +2.06654 q^{15} +0.608797 q^{16} -7.64093 q^{17} +0.794802 q^{18} -5.46114 q^{19} +2.82763 q^{20} +0.419104 q^{21} -3.44593 q^{22} +4.58181 q^{23} +2.67712 q^{24} -0.729414 q^{25} -0.794802 q^{26} -1.00000 q^{27} +0.573455 q^{28} -8.93627 q^{29} +1.64249 q^{30} +3.38103 q^{31} +5.83812 q^{32} +4.33558 q^{33} -6.07302 q^{34} +0.866094 q^{35} -1.36829 q^{36} -9.44913 q^{37} -4.34053 q^{38} +1.00000 q^{39} +5.53238 q^{40} +4.87737 q^{41} +0.333104 q^{42} -4.63862 q^{43} +5.93233 q^{44} -2.06654 q^{45} +3.64163 q^{46} -8.00181 q^{47} -0.608797 q^{48} -6.82435 q^{49} -0.579740 q^{50} +7.64093 q^{51} +1.36829 q^{52} +11.6159 q^{53} -0.794802 q^{54} +8.95964 q^{55} +1.12199 q^{56} +5.46114 q^{57} -7.10257 q^{58} +1.23130 q^{59} -2.82763 q^{60} +2.85235 q^{61} +2.68725 q^{62} -0.419104 q^{63} +3.42255 q^{64} +2.06654 q^{65} +3.44593 q^{66} -7.89062 q^{67} +10.4550 q^{68} -4.58181 q^{69} +0.688373 q^{70} +4.14678 q^{71} -2.67712 q^{72} -14.4858 q^{73} -7.51019 q^{74} +0.729414 q^{75} +7.47243 q^{76} +1.81706 q^{77} +0.794802 q^{78} -15.4353 q^{79} -1.25810 q^{80} +1.00000 q^{81} +3.87654 q^{82} +2.01066 q^{83} -0.573455 q^{84} +15.7903 q^{85} -3.68678 q^{86} +8.93627 q^{87} +11.6069 q^{88} +6.93386 q^{89} -1.64249 q^{90} +0.419104 q^{91} -6.26924 q^{92} -3.38103 q^{93} -6.35985 q^{94} +11.2857 q^{95} -5.83812 q^{96} +16.6255 q^{97} -5.42401 q^{98} -4.33558 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * 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 $

$2$	0.794802	0.562010	0.281005	−	0.959706i	$-0.409332\pi$
$2$	0.794802	0.562010	0.281005	+	0.959706i	$0.409332\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.36829	−0.684145
$5$	−2.06654	−0.924185	−0.462092	−	0.886832i	$-0.652901\pi$
$5$	−2.06654	−0.924185	−0.462092	+	0.886832i	$0.652901\pi$
$6$	−0.794802	−0.324477
$7$	−0.419104	−0.158406	−0.0792032	−	0.996858i	$-0.525238\pi$
$7$	−0.419104	−0.158406	−0.0792032	+	0.996858i	$0.525238\pi$
$8$	−2.67712	−0.946506
$9$	1.00000	0.333333
$10$	−1.64249	−0.519401
$11$	−4.33558	−1.30723	−0.653613	−	0.756829i	$-0.726748\pi$
$11$	−4.33558	−1.30723	−0.653613	+	0.756829i	$0.726748\pi$
$12$	1.36829	0.394991
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.333104	−0.0890259
$15$	2.06654	0.533578
$16$	0.608797	0.152199
$17$	−7.64093	−1.85320	−0.926598	−	0.376053i	$-0.877281\pi$
$17$	−7.64093	−1.85320	−0.926598	+	0.376053i	$0.877281\pi$
$18$	0.794802	0.187337
$19$	−5.46114	−1.25287	−0.626436	−	0.779473i	$-0.715487\pi$
$19$	−5.46114	−1.25287	−0.626436	+	0.779473i	$0.715487\pi$
$20$	2.82763	0.632276
$21$	0.419104	0.0914559
$22$	−3.44593	−0.734674
$23$	4.58181	0.955373	0.477686	−	0.878530i	$-0.341476\pi$
$23$	4.58181	0.955373	0.477686	+	0.878530i	$0.341476\pi$
$24$	2.67712	0.546465
$25$	−0.729414	−0.145883
$26$	−0.794802	−0.155873
$27$	−1.00000	−0.192450
$28$	0.573455	0.108373
$29$	−8.93627	−1.65942	−0.829712	−	0.558191i	$-0.811495\pi$
$29$	−8.93627	−1.65942	−0.829712	+	0.558191i	$0.811495\pi$
$30$	1.64249	0.299876
$31$	3.38103	0.607252	0.303626	−	0.952791i	$-0.401803\pi$
$31$	3.38103	0.607252	0.303626	+	0.952791i	$0.401803\pi$
$32$	5.83812	1.03204
$33$	4.33558	0.754727
$34$	−6.07302	−1.04151
$35$	0.866094	0.146397
$36$	−1.36829	−0.228048
$37$	−9.44913	−1.55343	−0.776714	−	0.629854i	$-0.783115\pi$
$37$	−9.44913	−1.55343	−0.776714	+	0.629854i	$0.783115\pi$
$38$	−4.34053	−0.704127
$39$	1.00000	0.160128
$40$	5.53238	0.874746
$41$	4.87737	0.761717	0.380858	−	0.924633i	$-0.375629\pi$
$41$	4.87737	0.761717	0.380858	+	0.924633i	$0.375629\pi$
$42$	0.333104	0.0513991
$43$	−4.63862	−0.707383	−0.353691	−	0.935362i	$-0.615074\pi$
$43$	−4.63862	−0.707383	−0.353691	+	0.935362i	$0.615074\pi$
$44$	5.93233	0.894332
$45$	−2.06654	−0.308062
$46$	3.64163	0.536929
$47$	−8.00181	−1.16718	−0.583592	−	0.812047i	$-0.698353\pi$
$47$	−8.00181	−1.16718	−0.583592	+	0.812047i	$0.698353\pi$
$48$	−0.608797	−0.0878723
$49$	−6.82435	−0.974907
$50$	−0.579740	−0.0819876
$51$	7.64093	1.06994
$52$	1.36829	0.189748
$53$	11.6159	1.59557	0.797786	−	0.602940i	$-0.206004\pi$
$53$	11.6159	1.59557	0.797786	+	0.602940i	$0.206004\pi$
$54$	−0.794802	−0.108159
$55$	8.95964	1.20812
$56$	1.12199	0.149933
$57$	5.46114	0.723346
$58$	−7.10257	−0.932613
$59$	1.23130	0.160302	0.0801511	−	0.996783i	$-0.474460\pi$
$59$	1.23130	0.160302	0.0801511	+	0.996783i	$0.474460\pi$
$60$	−2.82763	−0.365045
$61$	2.85235	0.365205	0.182603	−	0.983187i	$-0.441548\pi$
$61$	2.85235	0.365205	0.182603	+	0.983187i	$0.441548\pi$
$62$	2.68725	0.341281
$63$	−0.419104	−0.0528021
$64$	3.42255	0.427819
$65$	2.06654	0.256323
$66$	3.44593	0.424164
$67$	−7.89062	−0.963993	−0.481996	−	0.876173i	$-0.660088\pi$
$67$	−7.89062	−0.963993	−0.481996	+	0.876173i	$0.660088\pi$
$68$	10.4550	1.26786
$69$	−4.58181	−0.551585
$70$	0.688373	0.0822764
$71$	4.14678	0.492133	0.246066	−	0.969253i	$-0.420862\pi$
$71$	4.14678	0.492133	0.246066	+	0.969253i	$0.420862\pi$
$72$	−2.67712	−0.315502
$73$	−14.4858	−1.69544	−0.847719	−	0.530445i	$-0.822025\pi$
$73$	−14.4858	−1.69544	−0.847719	+	0.530445i	$0.822025\pi$
$74$	−7.51019	−0.873042
$75$	0.729414	0.0842255
$76$	7.47243	0.857146
$77$	1.81706	0.207073
$78$	0.794802	0.0899936
$79$	−15.4353	−1.73661	−0.868304	−	0.496033i	$-0.834790\pi$
$79$	−15.4353	−1.73661	−0.868304	+	0.496033i	$0.834790\pi$
$80$	−1.25810	−0.140660
$81$	1.00000	0.111111
$82$	3.87654	0.428092
$83$	2.01066	0.220699	0.110349	−	0.993893i	$-0.464803\pi$
$83$	2.01066	0.220699	0.110349	+	0.993893i	$0.464803\pi$
$84$	−0.573455	−0.0625691
$85$	15.7903	1.71270
$86$	−3.68678	−0.397556
$87$	8.93627	0.958069
$88$	11.6069	1.23730
$89$	6.93386	0.734987	0.367494	−	0.930026i	$-0.380216\pi$
$89$	6.93386	0.734987	0.367494	+	0.930026i	$0.380216\pi$
$90$	−1.64249	−0.173134
$91$	0.419104	0.0439340
$92$	−6.26924	−0.653613
$93$	−3.38103	−0.350597
$94$	−6.35985	−0.655969
$95$	11.2857	1.15789
$96$	−5.83812	−0.595851
$97$	16.6255	1.68806	0.844031	−	0.536295i	$-0.180176\pi$
$97$	16.6255	1.68806	0.844031	+	0.536295i	$0.180176\pi$
$98$	−5.42401	−0.547908
$99$	−4.33558	−0.435742
$100$	0.998050	0.0998050
$101$	5.67256	0.564441	0.282220	−	0.959350i	$-0.408929\pi$
$101$	5.67256	0.564441	0.282220	+	0.959350i	$0.408929\pi$
$102$	6.07302	0.601319
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.67712	0.262514
$105$	−0.866094	−0.0845222
$106$	9.23237	0.896727
$107$	−8.51172	−0.822859	−0.411430	−	0.911442i	$-0.634970\pi$
$107$	−8.51172	−0.822859	−0.411430	+	0.911442i	$0.634970\pi$
$108$	1.36829	0.131664
$109$	2.24876	0.215392	0.107696	−	0.994184i	$-0.465653\pi$
$109$	2.24876	0.215392	0.107696	+	0.994184i	$0.465653\pi$
$110$	7.12114	0.678974
$111$	9.44913	0.896872
$112$	−0.255149	−0.0241093
$113$	13.4569	1.26592	0.632961	−	0.774184i	$-0.281839\pi$
$113$	13.4569	1.26592	0.632961	+	0.774184i	$0.281839\pi$
$114$	4.34053	0.406528
$115$	−9.46848	−0.882941
$116$	12.2274	1.13529
$117$	−1.00000	−0.0924500
$118$	0.978643	0.0900914
$119$	3.20234	0.293558
$120$	−5.53238	−0.505035
$121$	7.79724	0.708840
$122$	2.26705	0.205249
$123$	−4.87737	−0.439777
$124$	−4.62624	−0.415448
$125$	11.8401	1.05901
$126$	−0.333104	−0.0296753
$127$	−6.91632	−0.613724	−0.306862	−	0.951754i	$-0.599279\pi$
$127$	−6.91632	−0.613724	−0.306862	+	0.951754i	$0.599279\pi$
$128$	−8.95599	−0.791605
$129$	4.63862	0.408407
$130$	1.64249	0.144056
$131$	−7.41147	−0.647543	−0.323771	−	0.946135i	$-0.604951\pi$
$131$	−7.41147	−0.647543	−0.323771	+	0.946135i	$0.604951\pi$
$132$	−5.93233	−0.516343
$133$	2.28879	0.198463
$134$	−6.27148	−0.541774
$135$	2.06654	0.177859
$136$	20.4557	1.75406
$137$	13.0081	1.11136	0.555679	−	0.831397i	$-0.312458\pi$
$137$	13.0081	1.11136	0.555679	+	0.831397i	$0.312458\pi$
$138$	−3.64163	−0.309996
$139$	−10.7084	−0.908275	−0.454138	−	0.890932i	$-0.650053\pi$
$139$	−10.7084	−0.908275	−0.454138	+	0.890932i	$0.650053\pi$
$140$	−1.18507	−0.100157
$141$	8.00181	0.673874
$142$	3.29587	0.276583
$143$	4.33558	0.362559
$144$	0.608797	0.0507331
$145$	18.4672	1.53361
$146$	−11.5134	−0.952853
$147$	6.82435	0.562863
$148$	12.9292	1.06277
$149$	−2.57410	−0.210879	−0.105439	−	0.994426i	$-0.533625\pi$
$149$	−2.57410	−0.210879	−0.105439	+	0.994426i	$0.533625\pi$
$150$	0.579740	0.0473356
$151$	−16.6540	−1.35528	−0.677642	−	0.735392i	$-0.736998\pi$
$151$	−16.6540	−1.35528	−0.677642	+	0.735392i	$0.736998\pi$
$152$	14.6202	1.18585
$153$	−7.64093	−0.617732
$154$	1.44420	0.116377
$155$	−6.98704	−0.561213
$156$	−1.36829	−0.109551
$157$	−0.710797	−0.0567278	−0.0283639	−	0.999598i	$-0.509030\pi$
$157$	−0.710797	−0.0567278	−0.0283639	+	0.999598i	$0.509030\pi$
$158$	−12.2680	−0.975991
$159$	−11.6159	−0.921204
$160$	−12.0647	−0.953799
$161$	−1.92025	−0.151337
$162$	0.794802	0.0624455
$163$	13.0101	1.01903	0.509514	−	0.860462i	$-0.329825\pi$
$163$	13.0101	1.01903	0.509514	+	0.860462i	$0.329825\pi$
$164$	−6.67365	−0.521125
$165$	−8.95964	−0.697507
$166$	1.59808	0.124035
$167$	7.10169	0.549546	0.274773	−	0.961509i	$-0.411397\pi$
$167$	7.10169	0.549546	0.274773	+	0.961509i	$0.411397\pi$
$168$	−1.12199	−0.0865636
$169$	1.00000	0.0769231
$170$	12.5501	0.962552
$171$	−5.46114	−0.417624
$172$	6.34697	0.483952
$173$	10.1334	0.770429	0.385215	−	0.922827i	$-0.374127\pi$
$173$	10.1334	0.770429	0.385215	+	0.922827i	$0.374127\pi$
$174$	7.10257	0.538444
$175$	0.305700	0.0231088
$176$	−2.63949	−0.198959
$177$	−1.23130	−0.0925505
$178$	5.51104	0.413070
$179$	15.7177	1.17479	0.587397	−	0.809299i	$-0.300153\pi$
$179$	15.7177	1.17479	0.587397	+	0.809299i	$0.300153\pi$
$180$	2.82763	0.210759
$181$	−26.3182	−1.95622	−0.978108	−	0.208099i	$-0.933272\pi$
$181$	−26.3182	−1.95622	−0.978108	+	0.208099i	$0.933272\pi$
$182$	0.333104	0.0246913
$183$	−2.85235	−0.210851
$184$	−12.2661	−0.904266
$185$	19.5270	1.43565
$186$	−2.68725	−0.197039
$187$	33.1278	2.42255
$188$	10.9488	0.798523
$189$	0.419104	0.0304853
$190$	8.96987	0.650743
$191$	−14.0606	−1.01739	−0.508695	−	0.860947i	$-0.669872\pi$
$191$	−14.0606	−1.01739	−0.508695	+	0.860947i	$0.669872\pi$
$192$	−3.42255	−0.247002
$193$	−0.311517	−0.0224235	−0.0112117	−	0.999937i	$-0.503569\pi$
$193$	−0.311517	−0.0224235	−0.0112117	+	0.999937i	$0.503569\pi$
$194$	13.2140	0.948707
$195$	−2.06654	−0.147988
$196$	9.33769	0.666978
$197$	−17.1412	−1.22126	−0.610630	−	0.791916i	$-0.709084\pi$
$197$	−17.1412	−1.22126	−0.610630	+	0.791916i	$0.709084\pi$
$198$	−3.44593	−0.244891
$199$	11.9466	0.846873	0.423436	−	0.905926i	$-0.360824\pi$
$199$	11.9466	0.846873	0.423436	+	0.905926i	$0.360824\pi$
$200$	1.95273	0.138079
$201$	7.89062	0.556562
$202$	4.50856	0.317221
$203$	3.74523	0.262863
$204$	−10.4550	−0.731997
$205$	−10.0793	−0.703967
$206$	0.794802	0.0553765
$207$	4.58181	0.318458
$208$	−0.608797	−0.0422125
$209$	23.6772	1.63779
$210$	−0.688373	−0.0475023
$211$	21.4688	1.47797	0.738985	−	0.673722i	$-0.235305\pi$
$211$	21.4688	1.47797	0.738985	+	0.673722i	$0.235305\pi$
$212$	−15.8940	−1.09160
$213$	−4.14678	−0.284133
$214$	−6.76513	−0.462455
$215$	9.58589	0.653752
$216$	2.67712	0.182155
$217$	−1.41700	−0.0961925
$218$	1.78732	0.121052
$219$	14.4858	0.978862
$220$	−12.2594	−0.826528
$221$	7.64093	0.513984
$222$	7.51019	0.504051
$223$	3.95705	0.264984	0.132492	−	0.991184i	$-0.457702\pi$
$223$	3.95705	0.264984	0.132492	+	0.991184i	$0.457702\pi$
$224$	−2.44678	−0.163482
$225$	−0.729414	−0.0486276
$226$	10.6956	0.711461
$227$	−18.4414	−1.22400	−0.612000	−	0.790858i	$-0.709635\pi$
$227$	−18.4414	−1.22400	−0.612000	+	0.790858i	$0.709635\pi$
$228$	−7.47243	−0.494874
$229$	2.23072	0.147410	0.0737049	−	0.997280i	$-0.476518\pi$
$229$	2.23072	0.147410	0.0737049	+	0.997280i	$0.476518\pi$
$230$	−7.52557	−0.496221
$231$	−1.81706	−0.119554
$232$	23.9235	1.57066
$233$	7.20583	0.472070	0.236035	−	0.971745i	$-0.424152\pi$
$233$	7.20583	0.472070	0.236035	+	0.971745i	$0.424152\pi$
$234$	−0.794802	−0.0519578
$235$	16.5361	1.07869
$236$	−1.68478	−0.109670
$237$	15.4353	1.00263
$238$	2.54523	0.164982
$239$	19.1264	1.23718	0.618592	−	0.785713i	$-0.287704\pi$
$239$	19.1264	1.23718	0.618592	+	0.785713i	$0.287704\pi$
$240$	1.25810	0.0812103
$241$	−0.761662	−0.0490630	−0.0245315	−	0.999699i	$-0.507809\pi$
$241$	−0.761662	−0.0490630	−0.0245315	+	0.999699i	$0.507809\pi$
$242$	6.19726	0.398375
$243$	−1.00000	−0.0641500
$244$	−3.90284	−0.249853
$245$	14.1028	0.900994
$246$	−3.87654	−0.247159
$247$	5.46114	0.347484
$248$	−9.05145	−0.574767
$249$	−2.01066	−0.127420
$250$	9.41050	0.595172
$251$	7.46705	0.471316	0.235658	−	0.971836i	$-0.424275\pi$
$251$	7.46705	0.471316	0.235658	+	0.971836i	$0.424275\pi$
$252$	0.573455	0.0361243
$253$	−19.8648	−1.24889
$254$	−5.49711	−0.344919
$255$	−15.7903	−0.988825
$256$	−13.9633	−0.872709
$257$	−8.82563	−0.550527	−0.275264	−	0.961369i	$-0.588765\pi$
$257$	−8.82563	−0.550527	−0.275264	+	0.961369i	$0.588765\pi$
$258$	3.68678	0.229529
$259$	3.96017	0.246073
$260$	−2.82763	−0.175362
$261$	−8.93627	−0.553141
$262$	−5.89065	−0.363925
$263$	12.7982	0.789172	0.394586	−	0.918859i	$-0.370888\pi$
$263$	12.7982	0.789172	0.394586	+	0.918859i	$0.370888\pi$
$264$	−11.6069	−0.714354
$265$	−24.0048	−1.47460
$266$	1.81913	0.111538
$267$	−6.93386	−0.424345
$268$	10.7967	0.659511
$269$	−20.6790	−1.26082	−0.630410	−	0.776262i	$-0.717113\pi$
$269$	−20.6790	−1.26082	−0.630410	+	0.776262i	$0.717113\pi$
$270$	1.64249	0.0999587
$271$	−25.4090	−1.54349	−0.771744	−	0.635934i	$-0.780615\pi$
$271$	−25.4090	−1.54349	−0.771744	+	0.635934i	$0.780615\pi$
$272$	−4.65178	−0.282055
$273$	−0.419104	−0.0253653
$274$	10.3389	0.624594
$275$	3.16243	0.190702
$276$	6.26924	0.377364
$277$	14.2162	0.854172	0.427086	−	0.904211i	$-0.359540\pi$
$277$	14.2162	0.854172	0.427086	+	0.904211i	$0.359540\pi$
$278$	−8.51106	−0.510460
$279$	3.38103	0.202417
$280$	−2.31864	−0.138565
$281$	−3.65110	−0.217807	−0.108903	−	0.994052i	$-0.534734\pi$
$281$	−3.65110	−0.217807	−0.108903	+	0.994052i	$0.534734\pi$
$282$	6.35985	0.378724
$283$	8.52173	0.506564	0.253282	−	0.967392i	$-0.418490\pi$
$283$	8.52173	0.506564	0.253282	+	0.967392i	$0.418490\pi$
$284$	−5.67400	−0.336690
$285$	−11.2857	−0.668506
$286$	3.44593	0.203762
$287$	−2.04412	−0.120661
$288$	5.83812	0.344015
$289$	41.3837	2.43434
$290$	14.6777	0.861906
$291$	−16.6255	−0.974603
$292$	19.8208	1.15993
$293$	−28.5871	−1.67007	−0.835037	−	0.550194i	$-0.814554\pi$
$293$	−28.5871	−1.67007	−0.835037	+	0.550194i	$0.814554\pi$
$294$	5.42401	0.316335
$295$	−2.54454	−0.148149
$296$	25.2965	1.47033
$297$	4.33558	0.251576
$298$	−2.04590	−0.118516
$299$	−4.58181	−0.264973
$300$	−0.998050	−0.0576225
$301$	1.94406	0.112054
$302$	−13.2366	−0.761682
$303$	−5.67256	−0.325880
$304$	−3.32473	−0.190686
$305$	−5.89448	−0.337517
$306$	−6.07302	−0.347172
$307$	−12.2009	−0.696345	−0.348172	−	0.937430i	$-0.613198\pi$
$307$	−12.2009	−0.696345	−0.348172	+	0.937430i	$0.613198\pi$
$308$	−2.48626	−0.141668
$309$	−1.00000	−0.0568880
$310$	−5.55331	−0.315407
$311$	9.75699	0.553268	0.276634	−	0.960975i	$-0.410781\pi$
$311$	9.75699	0.553268	0.276634	+	0.960975i	$0.410781\pi$
$312$	−2.67712	−0.151562
$313$	−23.7658	−1.34332	−0.671661	−	0.740858i	$-0.734419\pi$
$313$	−23.7658	−1.34332	−0.671661	+	0.740858i	$0.734419\pi$
$314$	−0.564943	−0.0318816
$315$	0.866094	0.0487989
$316$	21.1200	1.18809
$317$	−31.3673	−1.76177	−0.880883	−	0.473335i	$-0.843050\pi$
$317$	−31.3673	−1.76177	−0.880883	+	0.473335i	$0.843050\pi$
$318$	−9.23237	−0.517726
$319$	38.7439	2.16924
$320$	−7.07284	−0.395384
$321$	8.51172	0.475078
$322$	−1.52622	−0.0850529
$323$	41.7282	2.32182
$324$	−1.36829	−0.0760161
$325$	0.729414	0.0404606
$326$	10.3404	0.572704
$327$	−2.24876	−0.124357
$328$	−13.0573	−0.720969
$329$	3.35359	0.184889
$330$	−7.12114	−0.392006
$331$	7.75473	0.426239	0.213119	−	0.977026i	$-0.431638\pi$
$331$	7.75473	0.426239	0.213119	+	0.977026i	$0.431638\pi$
$332$	−2.75117	−0.150990
$333$	−9.44913	−0.517809
$334$	5.64444	0.308850
$335$	16.3063	0.890907
$336$	0.255149	0.0139195
$337$	−4.47279	−0.243648	−0.121824	−	0.992552i	$-0.538874\pi$
$337$	−4.47279	−0.243648	−0.121824	+	0.992552i	$0.538874\pi$
$338$	0.794802	0.0432315
$339$	−13.4569	−0.730881
$340$	−21.6057	−1.17173
$341$	−14.6587	−0.793815
$342$	−4.34053	−0.234709
$343$	5.79384	0.312838
$344$	12.4182	0.669542
$345$	9.46848	0.509766
$346$	8.05406	0.432989
$347$	−7.82810	−0.420234	−0.210117	−	0.977676i	$-0.567385\pi$
$347$	−7.82810	−0.420234	−0.210117	+	0.977676i	$0.567385\pi$
$348$	−12.2274	−0.655458
$349$	−23.0081	−1.23160	−0.615798	−	0.787904i	$-0.711166\pi$
$349$	−23.0081	−1.23160	−0.615798	+	0.787904i	$0.711166\pi$
$350$	0.242971	0.0129874
$351$	1.00000	0.0533761
$352$	−25.3116	−1.34911
$353$	−10.9972	−0.585322	−0.292661	−	0.956216i	$-0.594541\pi$
$353$	−10.9972	−0.585322	−0.292661	+	0.956216i	$0.594541\pi$
$354$	−0.978643	−0.0520143
$355$	−8.56949	−0.454822
$356$	−9.48753	−0.502838
$357$	−3.20234	−0.169486
$358$	12.4924	0.660246
$359$	−6.57949	−0.347252	−0.173626	−	0.984812i	$-0.555548\pi$
$359$	−6.57949	−0.347252	−0.173626	+	0.984812i	$0.555548\pi$
$360$	5.53238	0.291582
$361$	10.8241	0.569690
$362$	−20.9177	−1.09941
$363$	−7.79724	−0.409249
$364$	−0.573455	−0.0300572
$365$	29.9355	1.56690
$366$	−2.26705	−0.118501
$367$	23.5096	1.22719	0.613596	−	0.789620i	$-0.289722\pi$
$367$	23.5096	1.22719	0.613596	+	0.789620i	$0.289722\pi$
$368$	2.78939	0.145407
$369$	4.87737	0.253906
$370$	15.5201	0.806852
$371$	−4.86828	−0.252749
$372$	4.62624	0.239859
$373$	0.0810038	0.00419422	0.00209711	−	0.999998i	$-0.499332\pi$
$373$	0.0810038	0.00419422	0.00209711	+	0.999998i	$0.499332\pi$
$374$	26.3301	1.36150
$375$	−11.8401	−0.611418
$376$	21.4218	1.10475
$377$	8.93627	0.460242
$378$	0.333104	0.0171330
$379$	24.2181	1.24400	0.621999	−	0.783018i	$-0.286321\pi$
$379$	24.2181	1.24400	0.621999	+	0.783018i	$0.286321\pi$
$380$	−15.4421	−0.792162
$381$	6.91632	0.354334
$382$	−11.1754	−0.571783
$383$	−31.1296	−1.59065	−0.795324	−	0.606184i	$-0.792699\pi$
$383$	−31.1296	−1.59065	−0.795324	+	0.606184i	$0.792699\pi$
$384$	8.95599	0.457033
$385$	−3.75502	−0.191374
$386$	−0.247594	−0.0126022
$387$	−4.63862	−0.235794
$388$	−22.7485	−1.15488
$389$	32.8837	1.66727	0.833636	−	0.552315i	$-0.186255\pi$
$389$	32.8837	1.66727	0.833636	+	0.552315i	$0.186255\pi$
$390$	−1.64249	−0.0831707
$391$	−35.0092	−1.77049
$392$	18.2696	0.922756
$393$	7.41147	0.373859
$394$	−13.6239	−0.686360
$395$	31.8977	1.60495
$396$	5.93233	0.298111
$397$	−30.7254	−1.54206	−0.771031	−	0.636797i	$-0.780259\pi$
$397$	−30.7254	−1.54206	−0.771031	+	0.636797i	$0.780259\pi$
$398$	9.49519	0.475951
$399$	−2.28879	−0.114583
$400$	−0.444066	−0.0222033
$401$	−31.9019	−1.59310	−0.796552	−	0.604570i	$-0.793345\pi$
$401$	−31.9019	−1.59310	−0.796552	+	0.604570i	$0.793345\pi$
$402$	6.27148	0.312793
$403$	−3.38103	−0.168421
$404$	−7.76171	−0.386159
$405$	−2.06654	−0.102687
$406$	2.97671	0.147732
$407$	40.9675	2.03068
$408$	−20.4557	−1.01271
$409$	1.62541	0.0803713	0.0401857	−	0.999192i	$-0.487205\pi$
$409$	1.62541	0.0803713	0.0401857	+	0.999192i	$0.487205\pi$
$410$	−8.01102	−0.395636
$411$	−13.0081	−0.641643
$412$	−1.36829	−0.0674108
$413$	−0.516044	−0.0253929
$414$	3.64163	0.178976
$415$	−4.15511	−0.203966
$416$	−5.83812	−0.286237
$417$	10.7084	0.524393
$418$	18.8187	0.920453
$419$	−29.4160	−1.43707	−0.718534	−	0.695492i	$-0.755186\pi$
$419$	−29.4160	−1.43707	−0.718534	+	0.695492i	$0.755186\pi$
$420$	1.18507	0.0578254
$421$	−31.4197	−1.53130	−0.765650	−	0.643257i	$-0.777583\pi$
$421$	−31.4197	−1.53130	−0.765650	+	0.643257i	$0.777583\pi$
$422$	17.0634	0.830634
$423$	−8.00181	−0.389061
$424$	−31.0973	−1.51022
$425$	5.57340	0.270350
$426$	−3.29587	−0.159686
$427$	−1.19543	−0.0578508
$428$	11.6465	0.562955
$429$	−4.33558	−0.209324
$430$	7.61888	0.367415
$431$	−1.62450	−0.0782494	−0.0391247	−	0.999234i	$-0.512457\pi$
$431$	−1.62450	−0.0782494	−0.0391247	+	0.999234i	$0.512457\pi$
$432$	−0.608797	−0.0292908
$433$	−21.4453	−1.03060	−0.515298	−	0.857011i	$-0.672319\pi$
$433$	−21.4453	−1.03060	−0.515298	+	0.857011i	$0.672319\pi$
$434$	−1.12624	−0.0540611
$435$	−18.4672	−0.885433
$436$	−3.07695	−0.147359
$437$	−25.0219	−1.19696
$438$	11.5134	0.550130
$439$	8.43624	0.402640	0.201320	−	0.979526i	$-0.435477\pi$
$439$	8.43624	0.402640	0.201320	+	0.979526i	$0.435477\pi$
$440$	−23.9861	−1.14349
$441$	−6.82435	−0.324969
$442$	6.07302	0.288864
$443$	16.4670	0.782371	0.391185	−	0.920312i	$-0.372065\pi$
$443$	16.4670	0.782371	0.391185	+	0.920312i	$0.372065\pi$
$444$	−12.9292	−0.613590
$445$	−14.3291	−0.679264
$446$	3.14507	0.148923
$447$	2.57410	0.121751
$448$	−1.43440	−0.0677693
$449$	26.9062	1.26978	0.634890	−	0.772602i	$-0.281045\pi$
$449$	26.9062	1.26978	0.634890	+	0.772602i	$0.281045\pi$
$450$	−0.579740	−0.0273292
$451$	−21.1462	−0.995736
$452$	−18.4130	−0.866074
$453$	16.6540	0.782473
$454$	−14.6573	−0.687900
$455$	−0.866094	−0.0406031
$456$	−14.6202	−0.684652
$457$	−25.6821	−1.20136	−0.600679	−	0.799491i	$-0.705103\pi$
$457$	−25.6821	−1.20136	−0.600679	+	0.799491i	$0.705103\pi$
$458$	1.77298	0.0828458
$459$	7.64093	0.356648
$460$	12.9556	0.604059
$461$	17.1038	0.796604	0.398302	−	0.917254i	$-0.369600\pi$
$461$	17.1038	0.796604	0.398302	+	0.917254i	$0.369600\pi$
$462$	−1.44420	−0.0671903
$463$	25.5652	1.18811	0.594057	−	0.804423i	$-0.297525\pi$
$463$	25.5652	1.18811	0.594057	+	0.804423i	$0.297525\pi$
$464$	−5.44038	−0.252563
$465$	6.98704	0.324016
$466$	5.72721	0.265308
$467$	1.00933	0.0467064	0.0233532	−	0.999727i	$-0.492566\pi$
$467$	1.00933	0.0467064	0.0233532	+	0.999727i	$0.492566\pi$
$468$	1.36829	0.0632492
$469$	3.30699	0.152703
$470$	13.1429	0.606236
$471$	0.710797	0.0327518
$472$	−3.29635	−0.151727
$473$	20.1111	0.924709
$474$	12.2680	0.563488
$475$	3.98344	0.182773
$476$	−4.38173	−0.200836
$477$	11.6159	0.531858
$478$	15.2017	0.695309
$479$	−2.37629	−0.108576	−0.0542878	−	0.998525i	$-0.517289\pi$
$479$	−2.37629	−0.108576	−0.0542878	+	0.998525i	$0.517289\pi$
$480$	12.0647	0.550676
$481$	9.44913	0.430843
$482$	−0.605371	−0.0275739
$483$	1.92025	0.0873745
$484$	−10.6689	−0.484949
$485$	−34.3572	−1.56008
$486$	−0.794802	−0.0360529
$487$	−4.98754	−0.226007	−0.113004	−	0.993595i	$-0.536047\pi$
$487$	−4.98754	−0.226007	−0.113004	+	0.993595i	$0.536047\pi$
$488$	−7.63608	−0.345669
$489$	−13.0101	−0.588336
$490$	11.2089	0.506368
$491$	−8.65530	−0.390608	−0.195304	−	0.980743i	$-0.562569\pi$
$491$	−8.65530	−0.390608	−0.195304	+	0.980743i	$0.562569\pi$
$492$	6.67365	0.300871
$493$	68.2814	3.07524
$494$	4.34053	0.195290
$495$	8.95964	0.402706
$496$	2.05836	0.0924233
$497$	−1.73793	−0.0779569
$498$	−1.59808	−0.0716115
$499$	−33.5377	−1.50136	−0.750678	−	0.660669i	$-0.770273\pi$
$499$	−33.5377	−1.50136	−0.750678	+	0.660669i	$0.770273\pi$
$500$	−16.2006	−0.724515
$501$	−7.10169	−0.317280
$502$	5.93483	0.264884
$503$	−2.42893	−0.108301	−0.0541503	−	0.998533i	$-0.517245\pi$
$503$	−2.42893	−0.108301	−0.0541503	+	0.998533i	$0.517245\pi$
$504$	1.12199	0.0499775
$505$	−11.7226	−0.521647
$506$	−15.7886	−0.701887
$507$	−1.00000	−0.0444116
$508$	9.46353	0.419876
$509$	−13.3176	−0.590292	−0.295146	−	0.955452i	$-0.595368\pi$
$509$	−13.3176	−0.590292	−0.295146	+	0.955452i	$0.595368\pi$
$510$	−12.5501	−0.555730
$511$	6.07107	0.268568
$512$	6.81388	0.301134
$513$	5.46114	0.241115
$514$	−7.01462	−0.309402
$515$	−2.06654	−0.0910626
$516$	−6.34697	−0.279410
$517$	34.6925	1.52577
$518$	3.14755	0.138295
$519$	−10.1334	−0.444808
$520$	−5.53238	−0.242611
$521$	4.82651	0.211453	0.105727	−	0.994395i	$-0.466283\pi$
$521$	4.82651	0.211453	0.105727	+	0.994395i	$0.466283\pi$
$522$	−7.10257	−0.310871
$523$	30.0187	1.31263	0.656314	−	0.754488i	$-0.272115\pi$
$523$	30.0187	1.31263	0.656314	+	0.754488i	$0.272115\pi$
$524$	10.1410	0.443013
$525$	−0.305700	−0.0133419
$526$	10.1720	0.443522
$527$	−25.8342	−1.12536
$528$	2.63949	0.114869
$529$	−2.00705	−0.0872629
$530$	−19.0791	−0.828742
$531$	1.23130	0.0534341
$532$	−3.13172	−0.135777
$533$	−4.87737	−0.211262
$534$	−5.51104	−0.238486
$535$	17.5898	0.760474
$536$	21.1242	0.912425
$537$	−15.7177	−0.678268
$538$	−16.4357	−0.708594
$539$	29.5875	1.27442
$540$	−2.82763	−0.121682
$541$	−40.5682	−1.74416	−0.872081	−	0.489362i	$-0.837230\pi$
$541$	−40.5682	−1.74416	−0.872081	+	0.489362i	$0.837230\pi$
$542$	−20.1951	−0.867455
$543$	26.3182	1.12942
$544$	−44.6086	−1.91258
$545$	−4.64715	−0.199062
$546$	−0.333104	−0.0142556
$547$	−33.1437	−1.41712	−0.708562	−	0.705648i	$-0.750656\pi$
$547$	−33.1437	−1.41712	−0.708562	+	0.705648i	$0.750656\pi$
$548$	−17.7989	−0.760330
$549$	2.85235	0.121735
$550$	2.51351	0.107176
$551$	48.8023	2.07905
$552$	12.2661	0.522078
$553$	6.46899	0.275090
$554$	11.2991	0.480053
$555$	−19.5270	−0.828875
$556$	14.6522	0.621392
$557$	−3.24302	−0.137411	−0.0687055	−	0.997637i	$-0.521887\pi$
$557$	−3.24302	−0.137411	−0.0687055	+	0.997637i	$0.521887\pi$
$558$	2.68725	0.113760
$559$	4.63862	0.196193
$560$	0.527276	0.0222815
$561$	−33.1278	−1.39866
$562$	−2.90190	−0.122409
$563$	−12.7205	−0.536105	−0.268053	−	0.963404i	$-0.586380\pi$
$563$	−12.7205	−0.536105	−0.268053	+	0.963404i	$0.586380\pi$
$564$	−10.9488	−0.461027
$565$	−27.8093	−1.16995
$566$	6.77309	0.284694
$567$	−0.419104	−0.0176007
$568$	−11.1015	−0.465807
$569$	8.83470	0.370370	0.185185	−	0.982704i	$-0.440712\pi$
$569$	8.83470	0.370370	0.185185	+	0.982704i	$0.440712\pi$
$570$	−8.96987	−0.375707
$571$	−17.7994	−0.744880	−0.372440	−	0.928056i	$-0.621479\pi$
$571$	−17.7994	−0.744880	−0.372440	+	0.928056i	$0.621479\pi$
$572$	−5.93233	−0.248043
$573$	14.0606	0.587390
$574$	−1.62467	−0.0678125
$575$	−3.34204	−0.139373
$576$	3.42255	0.142606
$577$	13.9102	0.579089	0.289545	−	0.957164i	$-0.406496\pi$
$577$	13.9102	0.579089	0.289545	+	0.957164i	$0.406496\pi$
$578$	32.8919	1.36812
$579$	0.311517	0.0129462
$580$	−25.2684	−1.04921
$581$	−0.842675	−0.0349601
$582$	−13.2140	−0.547736
$583$	−50.3618	−2.08577
$584$	38.7804	1.60474
$585$	2.06654	0.0854409
$586$	−22.7211	−0.938598
$587$	−18.1814	−0.750427	−0.375213	−	0.926938i	$-0.622431\pi$
$587$	−18.1814	−0.750427	−0.375213	+	0.926938i	$0.622431\pi$
$588$	−9.33769	−0.385080
$589$	−18.4643	−0.760809
$590$	−2.02240	−0.0832611
$591$	17.1412	0.705094
$592$	−5.75261	−0.236431
$593$	−39.2261	−1.61082	−0.805412	−	0.592715i	$-0.798056\pi$
$593$	−39.2261	−1.61082	−0.805412	+	0.592715i	$0.798056\pi$
$594$	3.44593	0.141388
$595$	−6.61776	−0.271302
$596$	3.52212	0.144272
$597$	−11.9466	−0.488942
$598$	−3.64163	−0.148917
$599$	−25.9434	−1.06002	−0.530008	−	0.847992i	$-0.677811\pi$
$599$	−25.9434	−1.06002	−0.530008	+	0.847992i	$0.677811\pi$
$600$	−1.95273	−0.0797200
$601$	17.4054	0.709979	0.354990	−	0.934870i	$-0.384484\pi$
$601$	17.4054	0.709979	0.354990	+	0.934870i	$0.384484\pi$
$602$	1.54514	0.0629754
$603$	−7.89062	−0.321331
$604$	22.7875	0.927210
$605$	−16.1133	−0.655099
$606$	−4.50856	−0.183148
$607$	−1.01366	−0.0411431	−0.0205716	−	0.999788i	$-0.506549\pi$
$607$	−1.01366	−0.0411431	−0.0205716	+	0.999788i	$0.506549\pi$
$608$	−31.8828	−1.29302
$609$	−3.74523	−0.151764
$610$	−4.68495	−0.189688
$611$	8.00181	0.323718
$612$	10.4550	0.422618
$613$	−24.1419	−0.975082	−0.487541	−	0.873100i	$-0.662106\pi$
$613$	−24.1419	−0.975082	−0.487541	+	0.873100i	$0.662106\pi$
$614$	−9.69734	−0.391353
$615$	10.0793	0.406435
$616$	−4.86449	−0.195996
$617$	14.3888	0.579270	0.289635	−	0.957137i	$-0.406466\pi$
$617$	14.3888	0.579270	0.289635	+	0.957137i	$0.406466\pi$
$618$	−0.794802	−0.0319716
$619$	15.7976	0.634958	0.317479	−	0.948265i	$-0.397164\pi$
$619$	15.7976	0.634958	0.317479	+	0.948265i	$0.397164\pi$
$620$	9.56030	0.383951
$621$	−4.58181	−0.183862
$622$	7.75487	0.310942
$623$	−2.90601	−0.116427
$624$	0.608797	0.0243714
$625$	−20.8209	−0.832835
$626$	−18.8891	−0.754961
$627$	−23.6772	−0.945577
$628$	0.972577	0.0388100
$629$	72.2001	2.87881
$630$	0.688373	0.0274255
$631$	0.860446	0.0342538	0.0171269	−	0.999853i	$-0.494548\pi$
$631$	0.860446	0.0342538	0.0171269	+	0.999853i	$0.494548\pi$
$632$	41.3222	1.64371
$633$	−21.4688	−0.853306
$634$	−24.9308	−0.990129
$635$	14.2929	0.567195
$636$	15.8940	0.630237
$637$	6.82435	0.270391
$638$	30.7937	1.21914
$639$	4.14678	0.164044
$640$	18.5079	0.731589
$641$	23.7422	0.937761	0.468881	−	0.883262i	$-0.344657\pi$
$641$	23.7422	0.937761	0.468881	+	0.883262i	$0.344657\pi$
$642$	6.76513	0.266998
$643$	7.56253	0.298237	0.149119	−	0.988819i	$-0.452356\pi$
$643$	7.56253	0.298237	0.149119	+	0.988819i	$0.452356\pi$
$644$	2.62746	0.103536
$645$	−9.58589	−0.377444
$646$	33.1657	1.30489
$647$	7.40752	0.291220	0.145610	−	0.989342i	$-0.453486\pi$
$647$	7.40752	0.291220	0.145610	+	0.989342i	$0.453486\pi$
$648$	−2.67712	−0.105167
$649$	−5.33842	−0.209551
$650$	0.579740	0.0227393
$651$	1.41700	0.0555368
$652$	−17.8016	−0.697163
$653$	18.5843	0.727258	0.363629	−	0.931544i	$-0.381538\pi$
$653$	18.5843	0.727258	0.363629	+	0.931544i	$0.381538\pi$
$654$	−1.78732	−0.0698897
$655$	15.3161	0.598449
$656$	2.96933	0.115933
$657$	−14.4858	−0.565146
$658$	2.66544	0.103910
$659$	13.3582	0.520360	0.260180	−	0.965560i	$-0.416218\pi$
$659$	13.3582	0.520360	0.260180	+	0.965560i	$0.416218\pi$
$660$	12.2594	0.477196
$661$	−30.5211	−1.18713	−0.593567	−	0.804785i	$-0.702281\pi$
$661$	−30.5211	−1.18713	−0.593567	+	0.804785i	$0.702281\pi$
$662$	6.16348	0.239550
$663$	−7.64093	−0.296749
$664$	−5.38279	−0.208893
$665$	−4.72987	−0.183416
$666$	−7.51019	−0.291014
$667$	−40.9443	−1.58537
$668$	−9.71718	−0.375969
$669$	−3.95705	−0.152988
$670$	12.9603	0.500699
$671$	−12.3666	−0.477406
$672$	2.44678	0.0943865
$673$	−10.9338	−0.421469	−0.210734	−	0.977543i	$-0.567586\pi$
$673$	−10.9338	−0.421469	−0.210734	+	0.977543i	$0.567586\pi$
$674$	−3.55498	−0.136933
$675$	0.729414	0.0280752
$676$	−1.36829	−0.0526265
$677$	−11.7378	−0.451120	−0.225560	−	0.974229i	$-0.572421\pi$
$677$	−11.7378	−0.451120	−0.225560	+	0.974229i	$0.572421\pi$
$678$	−10.6956	−0.410762
$679$	−6.96780	−0.267400
$680$	−42.2725	−1.62108
$681$	18.4414	0.706677
$682$	−11.6508	−0.446132
$683$	6.16534	0.235910	0.117955	−	0.993019i	$-0.462366\pi$
$683$	6.16534	0.235910	0.117955	+	0.993019i	$0.462366\pi$
$684$	7.47243	0.285715
$685$	−26.8818	−1.02710
$686$	4.60495	0.175818
$687$	−2.23072	−0.0851071
$688$	−2.82398	−0.107663
$689$	−11.6159	−0.442532
$690$	7.52557	0.286494
$691$	−41.6485	−1.58438	−0.792191	−	0.610273i	$-0.791060\pi$
$691$	−41.6485	−1.58438	−0.792191	+	0.610273i	$0.791060\pi$
$692$	−13.8655	−0.527085
$693$	1.81706	0.0690243
$694$	−6.22178	−0.236176
$695$	22.1293	0.839414
$696$	−23.9235	−0.906818
$697$	−37.2676	−1.41161
$698$	−18.2869	−0.692169
$699$	−7.20583	−0.272550
$700$	−0.418287	−0.0158097
$701$	−40.1708	−1.51723	−0.758615	−	0.651539i	$-0.774124\pi$
$701$	−40.1708	−1.51723	−0.758615	+	0.651539i	$0.774124\pi$
$702$	0.794802	0.0299979
$703$	51.6031	1.94625
$704$	−14.8388	−0.559256
$705$	−16.5361	−0.622784
$706$	−8.74060	−0.328957
$707$	−2.37739	−0.0894110
$708$	1.68478	0.0633180
$709$	20.5042	0.770051	0.385026	−	0.922906i	$-0.374193\pi$
$709$	20.5042	0.770051	0.385026	+	0.922906i	$0.374193\pi$
$710$	−6.81105	−0.255614
$711$	−15.4353	−0.578869
$712$	−18.5628	−0.695670
$713$	15.4912	0.580152
$714$	−2.54523	−0.0952527
$715$	−8.95964	−0.335072
$716$	−21.5063	−0.803729
$717$	−19.1264	−0.714288
$718$	−5.22939	−0.195159
$719$	−41.5080	−1.54799	−0.773994	−	0.633193i	$-0.781744\pi$
$719$	−41.5080	−1.54799	−0.773994	+	0.633193i	$0.781744\pi$
$720$	−1.25810	−0.0468868
$721$	−0.419104	−0.0156082
$722$	8.60302	0.320171
$723$	0.761662	0.0283265
$724$	36.0109	1.33834
$725$	6.51825	0.242082
$726$	−6.19726	−0.230002
$727$	45.9288	1.70340	0.851702	−	0.524027i	$-0.175571\pi$
$727$	45.9288	1.70340	0.851702	+	0.524027i	$0.175571\pi$
$728$	−1.12199	−0.0415838
$729$	1.00000	0.0370370
$730$	23.7928	0.880612
$731$	35.4433	1.31092
$732$	3.90284	0.144253
$733$	−24.4100	−0.901605	−0.450802	−	0.892624i	$-0.648862\pi$
$733$	−24.4100	−0.901605	−0.450802	+	0.892624i	$0.648862\pi$
$734$	18.6855	0.689694
$735$	−14.1028	−0.520189
$736$	26.7491	0.985986
$737$	34.2104	1.26016
$738$	3.87654	0.142697
$739$	43.2555	1.59118	0.795590	−	0.605836i	$-0.207161\pi$
$739$	43.2555	1.59118	0.795590	+	0.605836i	$0.207161\pi$
$740$	−26.7186	−0.982196
$741$	−5.46114	−0.200620
$742$	−3.86932	−0.142047
$743$	37.3333	1.36962	0.684812	−	0.728719i	$-0.259884\pi$
$743$	37.3333	1.36962	0.684812	+	0.728719i	$0.259884\pi$
$744$	9.05145	0.331842
$745$	5.31949	0.194891
$746$	0.0643819	0.00235719
$747$	2.01066	0.0735662
$748$	−45.3285	−1.65737
$749$	3.56729	0.130346
$750$	−9.41050	−0.343623
$751$	−3.99968	−0.145950	−0.0729752	−	0.997334i	$-0.523249\pi$
$751$	−3.99968	−0.145950	−0.0729752	+	0.997334i	$0.523249\pi$
$752$	−4.87148	−0.177645
$753$	−7.46705	−0.272114
$754$	7.10257	0.258660
$755$	34.4161	1.25253
$756$	−0.573455	−0.0208564
$757$	−44.0325	−1.60039	−0.800193	−	0.599742i	$-0.795270\pi$
$757$	−44.0325	−1.60039	−0.800193	+	0.599742i	$0.795270\pi$
$758$	19.2486	0.699140
$759$	19.8648	0.721046
$760$	−30.2131	−1.09595
$761$	12.2617	0.444485	0.222242	−	0.974991i	$-0.428662\pi$
$761$	12.2617	0.444485	0.222242	+	0.974991i	$0.428662\pi$
$762$	5.49711	0.199139
$763$	−0.942463	−0.0341195
$764$	19.2390	0.696042
$765$	15.7903	0.570899
$766$	−24.7419	−0.893960
$767$	−1.23130	−0.0444598
$768$	13.9633	0.503859
$769$	−31.3860	−1.13181	−0.565903	−	0.824472i	$-0.691473\pi$
$769$	−31.3860	−1.13181	−0.565903	+	0.824472i	$0.691473\pi$
$770$	−2.98450	−0.107554
$771$	8.82563	0.317847
$772$	0.426245	0.0153409
$773$	6.96256	0.250426	0.125213	−	0.992130i	$-0.460039\pi$
$773$	6.96256	0.250426	0.125213	+	0.992130i	$0.460039\pi$
$774$	−3.68678	−0.132519
$775$	−2.46617	−0.0885876
$776$	−44.5085	−1.59776
$777$	−3.96017	−0.142070
$778$	26.1361	0.937023
$779$	−26.6360	−0.954334
$780$	2.82763	0.101245
$781$	−17.9787	−0.643329
$782$	−27.8254	−0.995035
$783$	8.93627	0.319356
$784$	−4.15465	−0.148380
$785$	1.46889	0.0524270
$786$	5.89065	0.210112
$787$	−1.28337	−0.0457472	−0.0228736	−	0.999738i	$-0.507282\pi$
$787$	−1.28337	−0.0457472	−0.0228736	+	0.999738i	$0.507282\pi$
$788$	23.4541	0.835519
$789$	−12.7982	−0.455629
$790$	25.3523	0.901995
$791$	−5.63985	−0.200530
$792$	11.6069	0.412432
$793$	−2.85235	−0.101290
$794$	−24.4206	−0.866654
$795$	24.0048	0.851363
$796$	−16.3464	−0.579384
$797$	−19.8952	−0.704724	−0.352362	−	0.935864i	$-0.614621\pi$
$797$	−19.8952	−0.704724	−0.352362	+	0.935864i	$0.614621\pi$
$798$	−1.81913	−0.0643966
$799$	61.1412	2.16302
$800$	−4.25841	−0.150557
$801$	6.93386	0.244996
$802$	−25.3557	−0.895340
$803$	62.8045	2.21632
$804$	−10.7967	−0.380769
$805$	3.96828	0.139863
$806$	−2.68725	−0.0946544
$807$	20.6790	0.727935
$808$	−15.1861	−0.534247
$809$	−53.0680	−1.86577	−0.932886	−	0.360171i	$-0.882718\pi$
$809$	−53.0680	−1.86577	−0.932886	+	0.360171i	$0.882718\pi$
$810$	−1.64249	−0.0577112
$811$	38.2282	1.34238	0.671188	−	0.741288i	$-0.265784\pi$
$811$	38.2282	1.34238	0.671188	+	0.741288i	$0.265784\pi$
$812$	−5.12455	−0.179837
$813$	25.4090	0.891133
$814$	32.5610	1.14126
$815$	−26.8859	−0.941771
$816$	4.65178	0.162845
$817$	25.3322	0.886260
$818$	1.29188	0.0451695
$819$	0.419104	0.0146447
$820$	13.7914	0.481615
$821$	−4.98130	−0.173848	−0.0869242	−	0.996215i	$-0.527704\pi$
$821$	−4.98130	−0.173848	−0.0869242	+	0.996215i	$0.527704\pi$
$822$	−10.3389	−0.360609
$823$	16.8882	0.588686	0.294343	−	0.955700i	$-0.404899\pi$
$823$	16.8882	0.588686	0.294343	+	0.955700i	$0.404899\pi$
$824$	−2.67712	−0.0932620
$825$	−3.16243	−0.110102
$826$	−0.410153	−0.0142710
$827$	6.76345	0.235188	0.117594	−	0.993062i	$-0.462482\pi$
$827$	6.76345	0.235188	0.117594	+	0.993062i	$0.462482\pi$
$828$	−6.26924	−0.217871
$829$	35.0874	1.21864	0.609318	−	0.792926i	$-0.291443\pi$
$829$	35.0874	1.21864	0.609318	+	0.792926i	$0.291443\pi$
$830$	−3.30249	−0.114631
$831$	−14.2162	−0.493156
$832$	−3.42255	−0.118656
$833$	52.1444	1.80670
$834$	8.51106	0.294714
$835$	−14.6759	−0.507882
$836$	−32.3973	−1.12048
$837$	−3.38103	−0.116866
$838$	−23.3799	−0.807646
$839$	2.39431	0.0826608	0.0413304	−	0.999146i	$-0.486840\pi$
$839$	2.39431	0.0826608	0.0413304	+	0.999146i	$0.486840\pi$
$840$	2.31864	0.0800007
$841$	50.8570	1.75369
$842$	−24.9724	−0.860606
$843$	3.65110	0.125751
$844$	−29.3755	−1.01115
$845$	−2.06654	−0.0710911
$846$	−6.35985	−0.218656
$847$	−3.26785	−0.112285
$848$	7.07176	0.242845
$849$	−8.52173	−0.292465
$850$	4.42975	0.151939
$851$	−43.2941	−1.48410
$852$	5.67400	0.194388
$853$	4.39113	0.150350	0.0751748	−	0.997170i	$-0.476049\pi$
$853$	4.39113	0.150350	0.0751748	+	0.997170i	$0.476049\pi$
$854$	−0.950129	−0.0325127
$855$	11.2857	0.385962
$856$	22.7869	0.778841
$857$	40.0899	1.36945	0.684723	−	0.728804i	$-0.259923\pi$
$857$	40.0899	1.36945	0.684723	+	0.728804i	$0.259923\pi$
$858$	−3.44593	−0.117642
$859$	29.2646	0.998494	0.499247	−	0.866460i	$-0.333610\pi$
$859$	29.2646	0.998494	0.499247	+	0.866460i	$0.333610\pi$
$860$	−13.1163	−0.447261
$861$	2.04412	0.0696635
$862$	−1.29116	−0.0439769
$863$	10.1867	0.346760	0.173380	−	0.984855i	$-0.444531\pi$
$863$	10.1867	0.346760	0.173380	+	0.984855i	$0.444531\pi$
$864$	−5.83812	−0.198617
$865$	−20.9411	−0.712019
$866$	−17.0448	−0.579205
$867$	−41.3837	−1.40547
$868$	1.93887	0.0658096
$869$	66.9210	2.27014
$870$	−14.6777	−0.497622
$871$	7.89062	0.267364
$872$	−6.02020	−0.203870
$873$	16.6255	0.562687
$874$	−19.8875	−0.672703
$875$	−4.96221	−0.167753
$876$	−19.8208	−0.669683
$877$	33.3980	1.12777	0.563886	−	0.825853i	$-0.309306\pi$
$877$	33.3980	1.12777	0.563886	+	0.825853i	$0.309306\pi$
$878$	6.70514	0.226288
$879$	28.5871	0.964218
$880$	5.45461	0.183875
$881$	−20.8660	−0.702993	−0.351497	−	0.936189i	$-0.614327\pi$
$881$	−20.8660	−0.702993	−0.351497	+	0.936189i	$0.614327\pi$
$882$	−5.42401	−0.182636
$883$	−17.2350	−0.580005	−0.290002	−	0.957026i	$-0.593656\pi$
$883$	−17.2350	−0.580005	−0.290002	+	0.957026i	$0.593656\pi$
$884$	−10.4550	−0.351640
$885$	2.54454	0.0855338
$886$	13.0880	0.439700
$887$	41.3475	1.38831	0.694156	−	0.719824i	$-0.255778\pi$
$887$	41.3475	1.38831	0.694156	+	0.719824i	$0.255778\pi$
$888$	−25.2965	−0.848895
$889$	2.89866	0.0972178
$890$	−11.3888	−0.381753
$891$	−4.33558	−0.145247
$892$	−5.41439	−0.181287
$893$	43.6990	1.46233
$894$	2.04590	0.0684252
$895$	−32.4812	−1.08573
$896$	3.75349	0.125395
$897$	4.58181	0.152982
$898$	21.3851	0.713629
$899$	−30.2138	−1.00769
$900$	0.998050	0.0332683
$901$	−88.7566	−2.95691
$902$	−16.8070	−0.559613
$903$	−1.94406	−0.0646943
$904$	−36.0259	−1.19820
$905$	54.3876	1.80790
$906$	13.2366	0.439758
$907$	19.8815	0.660155	0.330077	−	0.943954i	$-0.392925\pi$
$907$	19.8815	0.660155	0.330077	+	0.943954i	$0.392925\pi$
$908$	25.2332	0.837393
$909$	5.67256	0.188147
$910$	−0.688373	−0.0228194
$911$	13.7720	0.456286	0.228143	−	0.973628i	$-0.426735\pi$
$911$	13.7720	0.456286	0.228143	+	0.973628i	$0.426735\pi$
$912$	3.32473	0.110093
$913$	−8.71737	−0.288503
$914$	−20.4122	−0.675174
$915$	5.89448	0.194866
$916$	−3.05227	−0.100850
$917$	3.10617	0.102575
$918$	6.07302	0.200440
$919$	12.0948	0.398972	0.199486	−	0.979901i	$-0.436073\pi$
$919$	12.0948	0.398972	0.199486	+	0.979901i	$0.436073\pi$
$920$	25.3483	0.835709
$921$	12.2009	0.402035
$922$	13.5941	0.447699
$923$	−4.14678	−0.136493
$924$	2.48626	0.0817920
$925$	6.89233	0.226618
$926$	20.3192	0.667731
$927$	1.00000	0.0328443
$928$	−52.1710	−1.71260
$929$	19.4836	0.639238	0.319619	−	0.947546i	$-0.396445\pi$
$929$	19.4836	0.639238	0.319619	+	0.947546i	$0.396445\pi$
$930$	5.55331	0.182100
$931$	37.2688	1.22143
$932$	−9.85967	−0.322964
$933$	−9.75699	−0.319429
$934$	0.802220	0.0262495
$935$	−68.4600	−2.23888
$936$	2.67712	0.0875045
$937$	−2.88482	−0.0942429	−0.0471215	−	0.998889i	$-0.515005\pi$
$937$	−2.88482	−0.0942429	−0.0471215	+	0.998889i	$0.515005\pi$
$938$	2.62840	0.0858203
$939$	23.7658	0.775568
$940$	−22.6261	−0.737982
$941$	1.12551	0.0366907	0.0183454	−	0.999832i	$-0.494160\pi$
$941$	1.12551	0.0366907	0.0183454	+	0.999832i	$0.494160\pi$
$942$	0.564943	0.0184068
$943$	22.3472	0.727723
$944$	0.749615	0.0243979
$945$	−0.866094	−0.0281741
$946$	15.9843	0.519695
$947$	0.624895	0.0203064	0.0101532	−	0.999948i	$-0.496768\pi$
$947$	0.624895	0.0203064	0.0101532	+	0.999948i	$0.496768\pi$
$948$	−21.1200	−0.685945
$949$	14.4858	0.470230
$950$	3.16604	0.102720
$951$	31.3673	1.01716
$952$	−8.57306	−0.277854
$953$	56.1730	1.81962	0.909810	−	0.415025i	$-0.136227\pi$
$953$	56.1730	1.81962	0.909810	+	0.415025i	$0.136227\pi$
$954$	9.23237	0.298909
$955$	29.0568	0.940255
$956$	−26.1704	−0.846413
$957$	−38.7439	−1.25241
$958$	−1.88868	−0.0610206
$959$	−5.45174	−0.176046
$960$	7.07284	0.228275
$961$	−19.5686	−0.631245
$962$	7.51019	0.242138
$963$	−8.51172	−0.274286
$964$	1.04218	0.0335662
$965$	0.643762	0.0207234
$966$	1.52622	0.0491053
$967$	57.7806	1.85810	0.929050	−	0.369955i	$-0.120627\pi$
$967$	57.7806	1.85810	0.929050	+	0.369955i	$0.120627\pi$
$968$	−20.8742	−0.670921
$969$	−41.7282	−1.34050
$970$	−27.3072	−0.876781
$971$	−22.3554	−0.717418	−0.358709	−	0.933449i	$-0.616783\pi$
$971$	−22.3554	−0.717418	−0.358709	+	0.933449i	$0.616783\pi$
$972$	1.36829	0.0438879
$973$	4.48793	0.143877
$974$	−3.96411	−0.127018
$975$	−0.729414	−0.0233600
$976$	1.73650	0.0555840
$977$	33.3943	1.06838	0.534190	−	0.845365i	$-0.320617\pi$
$977$	33.3943	1.06838	0.534190	+	0.845365i	$0.320617\pi$
$978$	−10.3404	−0.330651
$979$	−30.0623	−0.960795
$980$	−19.2967	−0.616411
$981$	2.24876	0.0717973
$982$	−6.87925	−0.219526
$983$	−16.3853	−0.522611	−0.261305	−	0.965256i	$-0.584153\pi$
$983$	−16.3853	−0.522611	−0.261305	+	0.965256i	$0.584153\pi$
$984$	13.0573	0.416252
$985$	35.4230	1.12867
$986$	54.2702	1.72831
$987$	−3.35359	−0.106746
$988$	−7.47243	−0.237730
$989$	−21.2532	−0.675814
$990$	7.12114	0.226325
$991$	25.4574	0.808682	0.404341	−	0.914608i	$-0.367501\pi$
$991$	25.4574	0.808682	0.404341	+	0.914608i	$0.367501\pi$
$992$	19.7389	0.626710
$993$	−7.75473	−0.246089
$994$	−1.38131	−0.0438126
$995$	−24.6881	−0.782667
$996$	2.75117	0.0871740
$997$	15.3055	0.484731	0.242365	−	0.970185i	$-0.422077\pi$
$997$	15.3055	0.484731	0.242365	+	0.970185i	$0.422077\pi$
$998$	−26.6559	−0.843776
$999$	9.44913	0.298957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.15	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.15	✓	24	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+0.794802 q^{2} -1.00000 q^{3} -1.36829 q^{4} -2.06654 q^{5} -0.794802 q^{6} -0.419104 q^{7} -2.67712 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.794802 q^{2} -1.00000 q^{3} -1.36829 q^{4} -2.06654 q^{5} -0.794802 q^{6} -0.419104 q^{7} -2.67712 q^{8} +1.00000 q^{9} -1.64249 q^{10} -4.33558 q^{11} +1.36829 q^{12} -1.00000 q^{13} -0.333104 q^{14} +2.06654 q^{15} +0.608797 q^{16} -7.64093 q^{17} +0.794802 q^{18} -5.46114 q^{19} +2.82763 q^{20} +0.419104 q^{21} -3.44593 q^{22} +4.58181 q^{23} +2.67712 q^{24} -0.729414 q^{25} -0.794802 q^{26} -1.00000 q^{27} +0.573455 q^{28} -8.93627 q^{29} +1.64249 q^{30} +3.38103 q^{31} +5.83812 q^{32} +4.33558 q^{33} -6.07302 q^{34} +0.866094 q^{35} -1.36829 q^{36} -9.44913 q^{37} -4.34053 q^{38} +1.00000 q^{39} +5.53238 q^{40} +4.87737 q^{41} +0.333104 q^{42} -4.63862 q^{43} +5.93233 q^{44} -2.06654 q^{45} +3.64163 q^{46} -8.00181 q^{47} -0.608797 q^{48} -6.82435 q^{49} -0.579740 q^{50} +7.64093 q^{51} +1.36829 q^{52} +11.6159 q^{53} -0.794802 q^{54} +8.95964 q^{55} +1.12199 q^{56} +5.46114 q^{57} -7.10257 q^{58} +1.23130 q^{59} -2.82763 q^{60} +2.85235 q^{61} +2.68725 q^{62} -0.419104 q^{63} +3.42255 q^{64} +2.06654 q^{65} +3.44593 q^{66} -7.89062 q^{67} +10.4550 q^{68} -4.58181 q^{69} +0.688373 q^{70} +4.14678 q^{71} -2.67712 q^{72} -14.4858 q^{73} -7.51019 q^{74} +0.729414 q^{75} +7.47243 q^{76} +1.81706 q^{77} +0.794802 q^{78} -15.4353 q^{79} -1.25810 q^{80} +1.00000 q^{81} +3.87654 q^{82} +2.01066 q^{83} -0.573455 q^{84} +15.7903 q^{85} -3.68678 q^{86} +8.93627 q^{87} +11.6069 q^{88} +6.93386 q^{89} -1.64249 q^{90} +0.419104 q^{91} -6.26924 q^{92} -3.38103 q^{93} -6.35985 q^{94} +11.2857 q^{95} -5.83812 q^{96} +16.6255 q^{97} -5.42401 q^{98} -4.33558 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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