LMFDB - Embedded newform 4015.2.a.h.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.829924 q^{2} +2.15264 q^{3} -1.31123 q^{4} +1.00000 q^{5} +1.78653 q^{6} -1.04291 q^{7} -2.74807 q^{8} +1.63385 q^{9} +O(q^{10})$	\(q+0.829924 q^{2} +2.15264 q^{3} -1.31123 q^{4} +1.00000 q^{5} +1.78653 q^{6} -1.04291 q^{7} -2.74807 q^{8} +1.63385 q^{9} +0.829924 q^{10} +1.00000 q^{11} -2.82259 q^{12} -4.99996 q^{13} -0.865533 q^{14} +2.15264 q^{15} +0.341763 q^{16} +2.47904 q^{17} +1.35597 q^{18} +2.20828 q^{19} -1.31123 q^{20} -2.24500 q^{21} +0.829924 q^{22} +5.73620 q^{23} -5.91560 q^{24} +1.00000 q^{25} -4.14959 q^{26} -2.94082 q^{27} +1.36748 q^{28} +7.55345 q^{29} +1.78653 q^{30} +10.9263 q^{31} +5.77977 q^{32} +2.15264 q^{33} +2.05741 q^{34} -1.04291 q^{35} -2.14235 q^{36} -2.81683 q^{37} +1.83271 q^{38} -10.7631 q^{39} -2.74807 q^{40} +4.54516 q^{41} -1.86318 q^{42} +6.23420 q^{43} -1.31123 q^{44} +1.63385 q^{45} +4.76061 q^{46} -7.66300 q^{47} +0.735691 q^{48} -5.91235 q^{49} +0.829924 q^{50} +5.33647 q^{51} +6.55608 q^{52} -4.99682 q^{53} -2.44066 q^{54} +1.00000 q^{55} +2.86598 q^{56} +4.75364 q^{57} +6.26880 q^{58} +12.1875 q^{59} -2.82259 q^{60} -1.05992 q^{61} +9.06802 q^{62} -1.70396 q^{63} +4.11325 q^{64} -4.99996 q^{65} +1.78653 q^{66} +7.00699 q^{67} -3.25058 q^{68} +12.3480 q^{69} -0.865533 q^{70} +13.6462 q^{71} -4.48994 q^{72} +1.00000 q^{73} -2.33775 q^{74} +2.15264 q^{75} -2.89556 q^{76} -1.04291 q^{77} -8.93257 q^{78} +15.2672 q^{79} +0.341763 q^{80} -11.2321 q^{81} +3.77214 q^{82} +3.03747 q^{83} +2.94370 q^{84} +2.47904 q^{85} +5.17392 q^{86} +16.2599 q^{87} -2.74807 q^{88} -16.0244 q^{89} +1.35597 q^{90} +5.21449 q^{91} -7.52145 q^{92} +23.5204 q^{93} -6.35971 q^{94} +2.20828 q^{95} +12.4418 q^{96} +2.92528 q^{97} -4.90680 q^{98} +1.63385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	0.829924	0.586845	0.293423	−	0.955983i	$-0.405206\pi$
$2$	0.829924	0.586845	0.293423	+	0.955983i	$0.405206\pi$
$3$	2.15264	1.24283	0.621413	−	0.783483i	$-0.286559\pi$
$3$	2.15264	1.24283	0.621413	+	0.783483i	$0.286559\pi$
$4$	−1.31123	−0.655613
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.78653	0.729347
$7$	−1.04291	−0.394181	−0.197091	−	0.980385i	$-0.563149\pi$
$7$	−1.04291	−0.394181	−0.197091	+	0.980385i	$0.563149\pi$
$8$	−2.74807	−0.971588
$9$	1.63385	0.544618
$10$	0.829924	0.262445
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.82259	−0.814813
$13$	−4.99996	−1.38674	−0.693370	−	0.720582i	$-0.743875\pi$
$13$	−4.99996	−1.38674	−0.693370	+	0.720582i	$0.743875\pi$
$14$	−0.865533	−0.231323
$15$	2.15264	0.555809
$16$	0.341763	0.0854407
$17$	2.47904	0.601255	0.300627	−	0.953742i	$-0.402804\pi$
$17$	2.47904	0.601255	0.300627	+	0.953742i	$0.402804\pi$
$18$	1.35597	0.319606
$19$	2.20828	0.506615	0.253308	−	0.967386i	$-0.418482\pi$
$19$	2.20828	0.506615	0.253308	+	0.967386i	$0.418482\pi$
$20$	−1.31123	−0.293199
$21$	−2.24500	−0.489899
$22$	0.829924	0.176940
$23$	5.73620	1.19608	0.598040	−	0.801466i	$-0.295946\pi$
$23$	5.73620	1.19608	0.598040	+	0.801466i	$0.295946\pi$
$24$	−5.91560	−1.20752
$25$	1.00000	0.200000
$26$	−4.14959	−0.813802
$27$	−2.94082	−0.565961
$28$	1.36748	0.258430
$29$	7.55345	1.40264	0.701320	−	0.712846i	$-0.252594\pi$
$29$	7.55345	1.40264	0.701320	+	0.712846i	$0.252594\pi$
$30$	1.78653	0.326174
$31$	10.9263	1.96242	0.981212	−	0.192930i	$-0.0617991\pi$
$31$	10.9263	1.96242	0.981212	+	0.192930i	$0.0617991\pi$
$32$	5.77977	1.02173
$33$	2.15264	0.374726
$34$	2.05741	0.352843
$35$	−1.04291	−0.176283
$36$	−2.14235	−0.357058
$37$	−2.81683	−0.463083	−0.231542	−	0.972825i	$-0.574377\pi$
$37$	−2.81683	−0.463083	−0.231542	+	0.972825i	$0.574377\pi$
$38$	1.83271	0.297305
$39$	−10.7631	−1.72348
$40$	−2.74807	−0.434508
$41$	4.54516	0.709834	0.354917	−	0.934898i	$-0.384509\pi$
$41$	4.54516	0.709834	0.354917	+	0.934898i	$0.384509\pi$
$42$	−1.86318	−0.287495
$43$	6.23420	0.950707	0.475354	−	0.879795i	$-0.342320\pi$
$43$	6.23420	0.950707	0.475354	+	0.879795i	$0.342320\pi$
$44$	−1.31123	−0.197675
$45$	1.63385	0.243560
$46$	4.76061	0.701914
$47$	−7.66300	−1.11776	−0.558881	−	0.829248i	$-0.688769\pi$
$47$	−7.66300	−1.11776	−0.558881	+	0.829248i	$0.688769\pi$
$48$	0.735691	0.106188
$49$	−5.91235	−0.844621
$50$	0.829924	0.117369
$51$	5.33647	0.747255
$52$	6.55608	0.909164
$53$	−4.99682	−0.686366	−0.343183	−	0.939269i	$-0.611505\pi$
$53$	−4.99682	−0.686366	−0.343183	+	0.939269i	$0.611505\pi$
$54$	−2.44066	−0.332132
$55$	1.00000	0.134840
$56$	2.86598	0.382982
$57$	4.75364	0.629635
$58$	6.26880	0.823133
$59$	12.1875	1.58668	0.793339	−	0.608780i	$-0.208341\pi$
$59$	12.1875	1.58668	0.793339	+	0.608780i	$0.208341\pi$
$60$	−2.82259	−0.364395
$61$	−1.05992	−0.135709	−0.0678544	−	0.997695i	$-0.521615\pi$
$61$	−1.05992	−0.135709	−0.0678544	+	0.997695i	$0.521615\pi$
$62$	9.06802	1.15164
$63$	−1.70396	−0.214678
$64$	4.11325	0.514156
$65$	−4.99996	−0.620169
$66$	1.78653	0.219906
$67$	7.00699	0.856040	0.428020	−	0.903769i	$-0.359211\pi$
$67$	7.00699	0.856040	0.428020	+	0.903769i	$0.359211\pi$
$68$	−3.25058	−0.394190
$69$	12.3480	1.48652
$70$	−0.865533	−0.103451
$71$	13.6462	1.61951	0.809753	−	0.586770i	$-0.199601\pi$
$71$	13.6462	1.61951	0.809753	+	0.586770i	$0.199601\pi$
$72$	−4.48994	−0.529144
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−2.33775	−0.271758
$75$	2.15264	0.248565
$76$	−2.89556	−0.332143
$77$	−1.04291	−0.118850
$78$	−8.93257	−1.01141
$79$	15.2672	1.71769	0.858845	−	0.512236i	$-0.171183\pi$
$79$	15.2672	1.71769	0.858845	+	0.512236i	$0.171183\pi$
$80$	0.341763	0.0382102
$81$	−11.2321	−1.24801
$82$	3.77214	0.416563
$83$	3.03747	0.333406	0.166703	−	0.986007i	$-0.446688\pi$
$83$	3.03747	0.333406	0.166703	+	0.986007i	$0.446688\pi$
$84$	2.94370	0.321184
$85$	2.47904	0.268889
$86$	5.17392	0.557918
$87$	16.2599	1.74324
$88$	−2.74807	−0.292945
$89$	−16.0244	−1.69859	−0.849293	−	0.527922i	$-0.822972\pi$
$89$	−16.0244	−1.69859	−0.849293	+	0.527922i	$0.822972\pi$
$90$	1.35597	0.142932
$91$	5.21449	0.546627
$92$	−7.52145	−0.784165
$93$	23.5204	2.43895
$94$	−6.35971	−0.655954
$95$	2.20828	0.226565
$96$	12.4418	1.26983
$97$	2.92528	0.297017	0.148508	−	0.988911i	$-0.452553\pi$
$97$	2.92528	0.297017	0.148508	+	0.988911i	$0.452553\pi$
$98$	−4.90680	−0.495662
$99$	1.63385	0.164208
$100$	−1.31123	−0.131123
$101$	10.6303	1.05775	0.528875	−	0.848700i	$-0.322614\pi$
$101$	10.6303	1.05775	0.528875	+	0.848700i	$0.322614\pi$
$102$	4.42887	0.438523
$103$	−13.6587	−1.34584	−0.672918	−	0.739717i	$-0.734959\pi$
$103$	−13.6587	−1.34584	−0.672918	+	0.739717i	$0.734959\pi$
$104$	13.7402	1.34734
$105$	−2.24500	−0.219090
$106$	−4.14698	−0.402790
$107$	−6.82896	−0.660181	−0.330090	−	0.943949i	$-0.607079\pi$
$107$	−6.82896	−0.660181	−0.330090	+	0.943949i	$0.607079\pi$
$108$	3.85608	0.371051
$109$	12.6156	1.20836	0.604178	−	0.796849i	$-0.293502\pi$
$109$	12.6156	1.20836	0.604178	+	0.796849i	$0.293502\pi$
$110$	0.829924	0.0791302
$111$	−6.06361	−0.575532
$112$	−0.356426	−0.0336791
$113$	1.50690	0.141757	0.0708784	−	0.997485i	$-0.477420\pi$
$113$	1.50690	0.141757	0.0708784	+	0.997485i	$0.477420\pi$
$114$	3.94516	0.369498
$115$	5.73620	0.534903
$116$	−9.90428	−0.919589
$117$	−8.16920	−0.755243
$118$	10.1147	0.931134
$119$	−2.58540	−0.237003
$120$	−5.91560	−0.540018
$121$	1.00000	0.0909091
$122$	−0.879653	−0.0796401
$123$	9.78408	0.882201
$124$	−14.3269	−1.28659
$125$	1.00000	0.0894427
$126$	−1.41415	−0.125983
$127$	−4.36742	−0.387546	−0.193773	−	0.981046i	$-0.562072\pi$
$127$	−4.36742	−0.387546	−0.193773	+	0.981046i	$0.562072\pi$
$128$	−8.14586	−0.719999
$129$	13.4200	1.18156
$130$	−4.14959	−0.363943
$131$	16.7683	1.46505	0.732525	−	0.680741i	$-0.238342\pi$
$131$	16.7683	1.46505	0.732525	+	0.680741i	$0.238342\pi$
$132$	−2.82259	−0.245675
$133$	−2.30303	−0.199698
$134$	5.81528	0.502363
$135$	−2.94082	−0.253105
$136$	−6.81256	−0.584172
$137$	−20.5287	−1.75388	−0.876942	−	0.480596i	$-0.840420\pi$
$137$	−20.5287	−1.75388	−0.876942	+	0.480596i	$0.840420\pi$
$138$	10.2479	0.872357
$139$	0.205962	0.0174694	0.00873472	−	0.999962i	$-0.497220\pi$
$139$	0.205962	0.0174694	0.00873472	+	0.999962i	$0.497220\pi$
$140$	1.36748	0.115574
$141$	−16.4957	−1.38919
$142$	11.3253	0.950400
$143$	−4.99996	−0.418118
$144$	0.558390	0.0465325
$145$	7.55345	0.627280
$146$	0.829924	0.0686850
$147$	−12.7271	−1.04972
$148$	3.69349	0.303603
$149$	0.357433	0.0292821	0.0146410	−	0.999893i	$-0.495339\pi$
$149$	0.357433	0.0292821	0.0146410	+	0.999893i	$0.495339\pi$
$150$	1.78653	0.145869
$151$	−5.41786	−0.440900	−0.220450	−	0.975398i	$-0.570753\pi$
$151$	−5.41786	−0.440900	−0.220450	+	0.975398i	$0.570753\pi$
$152$	−6.06851	−0.492221
$153$	4.05038	0.327454
$154$	−0.865533	−0.0697466
$155$	10.9263	0.877623
$156$	14.1129	1.12993
$157$	−12.3225	−0.983441	−0.491720	−	0.870753i	$-0.663632\pi$
$157$	−12.3225	−0.983441	−0.491720	+	0.870753i	$0.663632\pi$
$158$	12.6706	1.00802
$159$	−10.7563	−0.853034
$160$	5.77977	0.456931
$161$	−5.98231	−0.471472
$162$	−9.32178	−0.732388
$163$	7.40490	0.579997	0.289998	−	0.957027i	$-0.406345\pi$
$163$	7.40490	0.579997	0.289998	+	0.957027i	$0.406345\pi$
$164$	−5.95972	−0.465376
$165$	2.15264	0.167583
$166$	2.52087	0.195658
$167$	−18.2133	−1.40939	−0.704695	−	0.709510i	$-0.748916\pi$
$167$	−18.2133	−1.40939	−0.704695	+	0.709510i	$0.748916\pi$
$168$	6.16941	0.475980
$169$	11.9996	0.923047
$170$	2.05741	0.157796
$171$	3.60801	0.275912
$172$	−8.17445	−0.623296
$173$	−11.0730	−0.841866	−0.420933	−	0.907092i	$-0.638297\pi$
$173$	−11.0730	−0.841866	−0.420933	+	0.907092i	$0.638297\pi$
$174$	13.4945	1.02301
$175$	−1.04291	−0.0788363
$176$	0.341763	0.0257613
$177$	26.2353	1.97196
$178$	−13.2991	−0.996807
$179$	−25.4658	−1.90340	−0.951700	−	0.307029i	$-0.900665\pi$
$179$	−25.4658	−1.90340	−0.951700	+	0.307029i	$0.900665\pi$
$180$	−2.14235	−0.159681
$181$	17.9896	1.33716	0.668579	−	0.743641i	$-0.266903\pi$
$181$	17.9896	1.33716	0.668579	+	0.743641i	$0.266903\pi$
$182$	4.32763	0.320785
$183$	−2.28162	−0.168662
$184$	−15.7635	−1.16210
$185$	−2.81683	−0.207097
$186$	19.5202	1.43129
$187$	2.47904	0.181285
$188$	10.0479	0.732820
$189$	3.06700	0.223091
$190$	1.83271	0.132959
$191$	−0.0991286	−0.00717269	−0.00358635	−	0.999994i	$-0.501142\pi$
$191$	−0.0991286	−0.00717269	−0.00358635	+	0.999994i	$0.501142\pi$
$192$	8.85434	0.639007
$193$	−7.35857	−0.529681	−0.264841	−	0.964292i	$-0.585319\pi$
$193$	−7.35857	−0.529681	−0.264841	+	0.964292i	$0.585319\pi$
$194$	2.42776	0.174303
$195$	−10.7631	−0.770762
$196$	7.75242	0.553744
$197$	6.49007	0.462398	0.231199	−	0.972906i	$-0.425735\pi$
$197$	6.49007	0.462398	0.231199	+	0.972906i	$0.425735\pi$
$198$	1.35597	0.0963649
$199$	−0.161833	−0.0114720	−0.00573600	−	0.999984i	$-0.501826\pi$
$199$	−0.161833	−0.0114720	−0.00573600	+	0.999984i	$0.501826\pi$
$200$	−2.74807	−0.194318
$201$	15.0835	1.06391
$202$	8.82231	0.620736
$203$	−7.87754	−0.552895
$204$	−6.99731	−0.489910
$205$	4.54516	0.317448
$206$	−11.3357	−0.789797
$207$	9.37210	0.651406
$208$	−1.70880	−0.118484
$209$	2.20828	0.152750
$210$	−1.86318	−0.128572
$211$	22.5360	1.55144	0.775720	−	0.631078i	$-0.217387\pi$
$211$	22.5360	1.55144	0.775720	+	0.631078i	$0.217387\pi$
$212$	6.55195	0.449990
$213$	29.3753	2.01277
$214$	−5.66752	−0.387424
$215$	6.23420	0.425169
$216$	8.08157	0.549881
$217$	−11.3951	−0.773551
$218$	10.4700	0.709118
$219$	2.15264	0.145462
$220$	−1.31123	−0.0884028
$221$	−12.3951	−0.833784
$222$	−5.03234	−0.337748
$223$	−16.7780	−1.12354	−0.561771	−	0.827293i	$-0.689880\pi$
$223$	−16.7780	−1.12354	−0.561771	+	0.827293i	$0.689880\pi$
$224$	−6.02776	−0.402746
$225$	1.63385	0.108924
$226$	1.25061	0.0831893
$227$	20.4542	1.35759	0.678797	−	0.734326i	$-0.262501\pi$
$227$	20.4542	1.35759	0.678797	+	0.734326i	$0.262501\pi$
$228$	−6.23309	−0.412797
$229$	−9.16392	−0.605569	−0.302784	−	0.953059i	$-0.597916\pi$
$229$	−9.16392	−0.605569	−0.302784	+	0.953059i	$0.597916\pi$
$230$	4.76061	0.313905
$231$	−2.24500	−0.147710
$232$	−20.7574	−1.36279
$233$	−21.2588	−1.39271	−0.696356	−	0.717696i	$-0.745197\pi$
$233$	−21.2588	−1.39271	−0.696356	+	0.717696i	$0.745197\pi$
$234$	−6.77982	−0.443211
$235$	−7.66300	−0.499879
$236$	−15.9806	−1.04025
$237$	32.8647	2.13479
$238$	−2.14569	−0.139084
$239$	−13.2380	−0.856295	−0.428148	−	0.903709i	$-0.640834\pi$
$239$	−13.2380	−0.856295	−0.428148	+	0.903709i	$0.640834\pi$
$240$	0.735691	0.0474887
$241$	−6.99142	−0.450357	−0.225178	−	0.974318i	$-0.572296\pi$
$241$	−6.99142	−0.450357	−0.225178	+	0.974318i	$0.572296\pi$
$242$	0.829924	0.0533496
$243$	−15.3562	−0.985098
$244$	1.38979	0.0889724
$245$	−5.91235	−0.377726
$246$	8.12005	0.517715
$247$	−11.0413	−0.702543
$248$	−30.0263	−1.90667
$249$	6.53858	0.414365
$250$	0.829924	0.0524890
$251$	5.49663	0.346944	0.173472	−	0.984839i	$-0.444501\pi$
$251$	5.49663	0.346944	0.173472	+	0.984839i	$0.444501\pi$
$252$	2.23427	0.140746
$253$	5.73620	0.360632
$254$	−3.62463	−0.227429
$255$	5.33647	0.334183
$256$	−14.9869	−0.936684
$257$	7.03141	0.438608	0.219304	−	0.975657i	$-0.429621\pi$
$257$	7.03141	0.438608	0.219304	+	0.975657i	$0.429621\pi$
$258$	11.1376	0.693395
$259$	2.93768	0.182539
$260$	6.55608	0.406591
$261$	12.3412	0.763903
$262$	13.9164	0.859757
$263$	20.0010	1.23331	0.616656	−	0.787233i	$-0.288487\pi$
$263$	20.0010	1.23331	0.616656	+	0.787233i	$0.288487\pi$
$264$	−5.91560	−0.364080
$265$	−4.99682	−0.306952
$266$	−1.91134	−0.117192
$267$	−34.4948	−2.11105
$268$	−9.18775	−0.561231
$269$	−25.2922	−1.54209	−0.771046	−	0.636779i	$-0.780266\pi$
$269$	−25.2922	−1.54209	−0.771046	+	0.636779i	$0.780266\pi$
$270$	−2.44066	−0.148534
$271$	12.3769	0.751844	0.375922	−	0.926651i	$-0.377326\pi$
$271$	12.3769	0.751844	0.375922	+	0.926651i	$0.377326\pi$
$272$	0.847242	0.0513716
$273$	11.2249	0.679362
$274$	−17.0373	−1.02926
$275$	1.00000	0.0603023
$276$	−16.1910	−0.974581
$277$	−15.2397	−0.915667	−0.457833	−	0.889038i	$-0.651374\pi$
$277$	−15.2397	−0.915667	−0.457833	+	0.889038i	$0.651374\pi$
$278$	0.170933	0.0102519
$279$	17.8520	1.06877
$280$	2.86598	0.171275
$281$	26.7685	1.59687	0.798437	−	0.602078i	$-0.205660\pi$
$281$	26.7685	1.59687	0.798437	+	0.602078i	$0.205660\pi$
$282$	−13.6902	−0.815237
$283$	18.6758	1.11016	0.555082	−	0.831796i	$-0.312687\pi$
$283$	18.6758	1.11016	0.555082	+	0.831796i	$0.312687\pi$
$284$	−17.8933	−1.06177
$285$	4.75364	0.281581
$286$	−4.14959	−0.245370
$287$	−4.74017	−0.279803
$288$	9.44330	0.556452
$289$	−10.8544	−0.638493
$290$	6.26880	0.368116
$291$	6.29706	0.369140
$292$	−1.31123	−0.0767337
$293$	−12.6535	−0.739226	−0.369613	−	0.929186i	$-0.620510\pi$
$293$	−12.6535	−0.739226	−0.369613	+	0.929186i	$0.620510\pi$
$294$	−10.5626	−0.616022
$295$	12.1875	0.709584
$296$	7.74083	0.449926
$297$	−2.94082	−0.170644
$298$	0.296643	0.0171840
$299$	−28.6808	−1.65865
$300$	−2.82259	−0.162963
$301$	−6.50169	−0.374751
$302$	−4.49642	−0.258740
$303$	22.8831	1.31460
$304$	0.754709	0.0432855
$305$	−1.05992	−0.0606908
$306$	3.36151	0.192165
$307$	10.1608	0.579905	0.289953	−	0.957041i	$-0.406360\pi$
$307$	10.1608	0.579905	0.289953	+	0.957041i	$0.406360\pi$
$308$	1.36748	0.0779197
$309$	−29.4023	−1.67264
$310$	9.06802	0.515029
$311$	9.06810	0.514205	0.257102	−	0.966384i	$-0.417232\pi$
$311$	9.06810	0.514205	0.257102	+	0.966384i	$0.417232\pi$
$312$	29.5777	1.67451
$313$	9.61319	0.543369	0.271685	−	0.962386i	$-0.412419\pi$
$313$	9.61319	0.543369	0.271685	+	0.962386i	$0.412419\pi$
$314$	−10.2267	−0.577127
$315$	−1.70396	−0.0960070
$316$	−20.0187	−1.12614
$317$	−3.81576	−0.214315	−0.107157	−	0.994242i	$-0.534175\pi$
$317$	−3.81576	−0.214315	−0.107157	+	0.994242i	$0.534175\pi$
$318$	−8.92695	−0.500599
$319$	7.55345	0.422912
$320$	4.11325	0.229938
$321$	−14.7003	−0.820490
$322$	−4.96487	−0.276681
$323$	5.47442	0.304605
$324$	14.7278	0.818211
$325$	−4.99996	−0.277348
$326$	6.14551	0.340368
$327$	27.1568	1.50178
$328$	−12.4904	−0.689667
$329$	7.99178	0.440601
$330$	1.78653	0.0983451
$331$	3.71474	0.204180	0.102090	−	0.994775i	$-0.467447\pi$
$331$	3.71474	0.204180	0.102090	+	0.994775i	$0.467447\pi$
$332$	−3.98281	−0.218585
$333$	−4.60228	−0.252203
$334$	−15.1157	−0.827094
$335$	7.00699	0.382833
$336$	−0.767257	−0.0418573
$337$	17.0084	0.926504	0.463252	−	0.886227i	$-0.346682\pi$
$337$	17.0084	0.926504	0.463252	+	0.886227i	$0.346682\pi$
$338$	9.95877	0.541686
$339$	3.24380	0.176179
$340$	−3.25058	−0.176287
$341$	10.9263	0.591693
$342$	2.99438	0.161917
$343$	13.4664	0.727115
$344$	−17.1320	−0.923696
$345$	12.3480	0.664792
$346$	−9.18977	−0.494045
$347$	30.3558	1.62959	0.814793	−	0.579751i	$-0.196850\pi$
$347$	30.3558	1.62959	0.814793	+	0.579751i	$0.196850\pi$
$348$	−21.3203	−1.14289
$349$	14.6584	0.784647	0.392323	−	0.919827i	$-0.371671\pi$
$349$	14.6584	0.784647	0.392323	+	0.919827i	$0.371671\pi$
$350$	−0.865533	−0.0462647
$351$	14.7040	0.784841
$352$	5.77977	0.308063
$353$	5.37992	0.286344	0.143172	−	0.989698i	$-0.454270\pi$
$353$	5.37992	0.286344	0.143172	+	0.989698i	$0.454270\pi$
$354$	21.7733	1.15724
$355$	13.6462	0.724265
$356$	21.0116	1.11361
$357$	−5.56544	−0.294554
$358$	−21.1347	−1.11700
$359$	−37.1141	−1.95881	−0.979403	−	0.201917i	$-0.935283\pi$
$359$	−37.1141	−1.95881	−0.979403	+	0.201917i	$0.935283\pi$
$360$	−4.48994	−0.236641
$361$	−14.1235	−0.743341
$362$	14.9300	0.784705
$363$	2.15264	0.112984
$364$	−6.83737	−0.358376
$365$	1.00000	0.0523424
$366$	−1.89358	−0.0989788
$367$	−7.98776	−0.416957	−0.208479	−	0.978027i	$-0.566851\pi$
$367$	−7.98776	−0.416957	−0.208479	+	0.978027i	$0.566851\pi$
$368$	1.96042	0.102194
$369$	7.42612	0.386588
$370$	−2.33775	−0.121534
$371$	5.21121	0.270553
$372$	−30.8406	−1.59901
$373$	5.56022	0.287897	0.143949	−	0.989585i	$-0.454020\pi$
$373$	5.56022	0.287897	0.143949	+	0.989585i	$0.454020\pi$
$374$	2.05741	0.106386
$375$	2.15264	0.111162
$376$	21.0584	1.08601
$377$	−37.7670	−1.94510
$378$	2.54538	0.130920
$379$	−9.54987	−0.490544	−0.245272	−	0.969454i	$-0.578877\pi$
$379$	−9.54987	−0.490544	−0.245272	+	0.969454i	$0.578877\pi$
$380$	−2.89556	−0.148539
$381$	−9.40147	−0.481652
$382$	−0.0822692	−0.00420926
$383$	29.5944	1.51220	0.756102	−	0.654453i	$-0.227101\pi$
$383$	29.5944	1.51220	0.756102	+	0.654453i	$0.227101\pi$
$384$	−17.5351	−0.894834
$385$	−1.04291	−0.0531514
$386$	−6.10705	−0.310841
$387$	10.1858	0.517772
$388$	−3.83570	−0.194728
$389$	6.65207	0.337274	0.168637	−	0.985678i	$-0.446064\pi$
$389$	6.65207	0.337274	0.168637	+	0.985678i	$0.446064\pi$
$390$	−8.93257	−0.452318
$391$	14.2202	0.719148
$392$	16.2475	0.820624
$393$	36.0960	1.82080
$394$	5.38627	0.271356
$395$	15.2672	0.768174
$396$	−2.14235	−0.107657
$397$	21.4150	1.07479	0.537394	−	0.843331i	$-0.319409\pi$
$397$	21.4150	1.07479	0.537394	+	0.843331i	$0.319409\pi$
$398$	−0.134309	−0.00673229
$399$	−4.95760	−0.248190
$400$	0.341763	0.0170881
$401$	−4.03434	−0.201465	−0.100733	−	0.994914i	$-0.532119\pi$
$401$	−4.03434	−0.201465	−0.100733	+	0.994914i	$0.532119\pi$
$402$	12.5182	0.624350
$403$	−54.6312	−2.72137
$404$	−13.9387	−0.693474
$405$	−11.2321	−0.558127
$406$	−6.53776	−0.324464
$407$	−2.81683	−0.139625
$408$	−14.6650	−0.726024
$409$	21.6220	1.06914	0.534570	−	0.845124i	$-0.320474\pi$
$409$	21.6220	1.06914	0.534570	+	0.845124i	$0.320474\pi$
$410$	3.77214	0.186293
$411$	−44.1909	−2.17977
$412$	17.9097	0.882347
$413$	−12.7104	−0.625439
$414$	7.77814	0.382275
$415$	3.03747	0.149104
$416$	−28.8986	−1.41687
$417$	0.443361	0.0217115
$418$	1.83271	0.0896407
$419$	15.0268	0.734106	0.367053	−	0.930200i	$-0.380367\pi$
$419$	15.0268	0.734106	0.367053	+	0.930200i	$0.380367\pi$
$420$	2.94370	0.143638
$421$	−1.89690	−0.0924490	−0.0462245	−	0.998931i	$-0.514719\pi$
$421$	−1.89690	−0.0924490	−0.0462245	+	0.998931i	$0.514719\pi$
$422$	18.7031	0.910455
$423$	−12.5202	−0.608754
$424$	13.7316	0.666865
$425$	2.47904	0.120251
$426$	24.3793	1.18118
$427$	1.10540	0.0534939
$428$	8.95431	0.432823
$429$	−10.7631	−0.519648
$430$	5.17392	0.249509
$431$	−13.3293	−0.642052	−0.321026	−	0.947070i	$-0.604028\pi$
$431$	−13.3293	−0.642052	−0.321026	+	0.947070i	$0.604028\pi$
$432$	−1.00506	−0.0483561
$433$	14.0683	0.676077	0.338039	−	0.941132i	$-0.390237\pi$
$433$	14.0683	0.676077	0.338039	+	0.941132i	$0.390237\pi$
$434$	−9.45709	−0.453955
$435$	16.2599	0.779600
$436$	−16.5419	−0.792214
$437$	12.6672	0.605952
$438$	1.78653	0.0853636
$439$	8.53521	0.407363	0.203682	−	0.979037i	$-0.434709\pi$
$439$	8.53521	0.407363	0.203682	+	0.979037i	$0.434709\pi$
$440$	−2.74807	−0.131009
$441$	−9.65991	−0.459996
$442$	−10.2870	−0.489302
$443$	6.33871	0.301161	0.150581	−	0.988598i	$-0.451886\pi$
$443$	6.33871	0.301161	0.150581	+	0.988598i	$0.451886\pi$
$444$	7.95076	0.377326
$445$	−16.0244	−0.759631
$446$	−13.9245	−0.659345
$447$	0.769425	0.0363925
$448$	−4.28973	−0.202671
$449$	−20.5376	−0.969230	−0.484615	−	0.874727i	$-0.661040\pi$
$449$	−20.5376	−0.969230	−0.484615	+	0.874727i	$0.661040\pi$
$450$	1.35597	0.0639213
$451$	4.54516	0.214023
$452$	−1.97588	−0.0929375
$453$	−11.6627	−0.547962
$454$	16.9755	0.796698
$455$	5.21449	0.244459
$456$	−13.0633	−0.611746
$457$	−16.5418	−0.773792	−0.386896	−	0.922123i	$-0.626453\pi$
$457$	−16.5418	−0.773792	−0.386896	+	0.922123i	$0.626453\pi$
$458$	−7.60536	−0.355375
$459$	−7.29040	−0.340287
$460$	−7.52145	−0.350689
$461$	−10.7185	−0.499212	−0.249606	−	0.968348i	$-0.580301\pi$
$461$	−10.7185	−0.499212	−0.249606	+	0.968348i	$0.580301\pi$
$462$	−1.86318	−0.0866830
$463$	3.22102	0.149693	0.0748467	−	0.997195i	$-0.476153\pi$
$463$	3.22102	0.149693	0.0748467	+	0.997195i	$0.476153\pi$
$464$	2.58149	0.119843
$465$	23.5204	1.09073
$466$	−17.6432	−0.817307
$467$	12.9028	0.597069	0.298534	−	0.954399i	$-0.403502\pi$
$467$	12.9028	0.597069	0.298534	+	0.954399i	$0.403502\pi$
$468$	10.7117	0.495147
$469$	−7.30763	−0.337435
$470$	−6.35971	−0.293351
$471$	−26.5258	−1.22225
$472$	−33.4921	−1.54160
$473$	6.23420	0.286649
$474$	27.2752	1.25279
$475$	2.20828	0.101323
$476$	3.39004	0.155382
$477$	−8.16407	−0.373807
$478$	−10.9865	−0.502513
$479$	−38.6171	−1.76446	−0.882229	−	0.470820i	$-0.843958\pi$
$479$	−38.6171	−1.76446	−0.882229	+	0.470820i	$0.843958\pi$
$480$	12.4418	0.567886
$481$	14.0840	0.642176
$482$	−5.80235	−0.264290
$483$	−12.8778	−0.585958
$484$	−1.31123	−0.0596012
$485$	2.92528	0.132830
$486$	−12.7445	−0.578100
$487$	−15.9532	−0.722907	−0.361453	−	0.932390i	$-0.617719\pi$
$487$	−15.9532	−0.722907	−0.361453	+	0.932390i	$0.617719\pi$
$488$	2.91273	0.131853
$489$	15.9401	0.720835
$490$	−4.90680	−0.221667
$491$	−27.1032	−1.22315	−0.611576	−	0.791186i	$-0.709464\pi$
$491$	−27.1032	−1.22315	−0.611576	+	0.791186i	$0.709464\pi$
$492$	−12.8291	−0.578382
$493$	18.7253	0.843344
$494$	−9.16348	−0.412284
$495$	1.63385	0.0734363
$496$	3.73421	0.167671
$497$	−14.2317	−0.638379
$498$	5.42653	0.243168
$499$	−16.7500	−0.749834	−0.374917	−	0.927058i	$-0.622329\pi$
$499$	−16.7500	−0.749834	−0.374917	+	0.927058i	$0.622329\pi$
$500$	−1.31123	−0.0586398
$501$	−39.2068	−1.75163
$502$	4.56179	0.203603
$503$	−19.2636	−0.858923	−0.429462	−	0.903085i	$-0.641297\pi$
$503$	−19.2636	−0.858923	−0.429462	+	0.903085i	$0.641297\pi$
$504$	4.68258	0.208579
$505$	10.6303	0.473040
$506$	4.76061	0.211635
$507$	25.8308	1.14719
$508$	5.72667	0.254080
$509$	−36.7666	−1.62965	−0.814827	−	0.579705i	$-0.803168\pi$
$509$	−36.7666	−1.62965	−0.814827	+	0.579705i	$0.803168\pi$
$510$	4.42887	0.196114
$511$	−1.04291	−0.0461354
$512$	3.85368	0.170310
$513$	−6.49417	−0.286724
$514$	5.83554	0.257395
$515$	−13.6587	−0.601876
$516$	−17.5966	−0.774649
$517$	−7.66300	−0.337018
$518$	2.43806	0.107122
$519$	−23.8362	−1.04629
$520$	13.7402	0.602549
$521$	34.6661	1.51875	0.759374	−	0.650655i	$-0.225505\pi$
$521$	34.6661	1.51875	0.759374	+	0.650655i	$0.225505\pi$
$522$	10.2423	0.448293
$523$	6.25512	0.273517	0.136759	−	0.990604i	$-0.456332\pi$
$523$	6.25512	0.273517	0.136759	+	0.990604i	$0.456332\pi$
$524$	−21.9870	−0.960505
$525$	−2.24500	−0.0979798
$526$	16.5993	0.723763
$527$	27.0867	1.17992
$528$	0.735691	0.0320169
$529$	9.90395	0.430606
$530$	−4.14698	−0.180133
$531$	19.9126	0.864133
$532$	3.01980	0.130925
$533$	−22.7256	−0.984355
$534$	−28.6281	−1.23886
$535$	−6.82896	−0.295242
$536$	−19.2557	−0.831719
$537$	−54.8186	−2.36560
$538$	−20.9906	−0.904970
$539$	−5.91235	−0.254663
$540$	3.85608	0.165939
$541$	−23.6234	−1.01565	−0.507824	−	0.861461i	$-0.669550\pi$
$541$	−23.6234	−1.01565	−0.507824	+	0.861461i	$0.669550\pi$
$542$	10.2719	0.441216
$543$	38.7252	1.66186
$544$	14.3283	0.614319
$545$	12.6156	0.540393
$546$	9.31583	0.398681
$547$	−12.1926	−0.521320	−0.260660	−	0.965431i	$-0.583940\pi$
$547$	−12.1926	−0.521320	−0.260660	+	0.965431i	$0.583940\pi$
$548$	26.9177	1.14987
$549$	−1.73175	−0.0739094
$550$	0.829924	0.0353881
$551$	16.6802	0.710599
$552$	−33.9330	−1.44429
$553$	−15.9222	−0.677081
$554$	−12.6478	−0.537355
$555$	−6.06361	−0.257386
$556$	−0.270062	−0.0114532
$557$	12.6831	0.537399	0.268700	−	0.963224i	$-0.413406\pi$
$557$	12.6831	0.537399	0.268700	+	0.963224i	$0.413406\pi$
$558$	14.8158	0.627204
$559$	−31.1708	−1.31838
$560$	−0.356426	−0.0150618
$561$	5.33647	0.225306
$562$	22.2158	0.937118
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	21.6295	0.910768
$565$	1.50690	0.0633956
$566$	15.4995	0.651494
$567$	11.7140	0.491942
$568$	−37.5007	−1.57349
$569$	−4.29859	−0.180206	−0.0901032	−	0.995932i	$-0.528720\pi$
$569$	−4.29859	−0.180206	−0.0901032	+	0.995932i	$0.528720\pi$
$570$	3.94516	0.165245
$571$	−9.46649	−0.396160	−0.198080	−	0.980186i	$-0.563471\pi$
$571$	−9.46649	−0.396160	−0.198080	+	0.980186i	$0.563471\pi$
$572$	6.55608	0.274123
$573$	−0.213388	−0.00891441
$574$	−3.93398	−0.164201
$575$	5.73620	0.239216
$576$	6.72044	0.280019
$577$	−34.7090	−1.44495	−0.722477	−	0.691395i	$-0.756997\pi$
$577$	−34.7090	−1.44495	−0.722477	+	0.691395i	$0.756997\pi$
$578$	−9.00832	−0.374697
$579$	−15.8403	−0.658302
$580$	−9.90428	−0.411253
$581$	−3.16780	−0.131422
$582$	5.22608	0.216628
$583$	−4.99682	−0.206947
$584$	−2.74807	−0.113716
$585$	−8.16920	−0.337755
$586$	−10.5015	−0.433811
$587$	21.1630	0.873489	0.436744	−	0.899586i	$-0.356131\pi$
$587$	21.1630	0.873489	0.436744	+	0.899586i	$0.356131\pi$
$588$	16.6882	0.688208
$589$	24.1284	0.994194
$590$	10.1147	0.416416
$591$	13.9708	0.574681
$592$	−0.962686	−0.0395661
$593$	40.2295	1.65203	0.826014	−	0.563649i	$-0.190603\pi$
$593$	40.2295	1.65203	0.826014	+	0.563649i	$0.190603\pi$
$594$	−2.44066	−0.100141
$595$	−2.58540	−0.105991
$596$	−0.468676	−0.0191977
$597$	−0.348367	−0.0142577
$598$	−23.8029	−0.973371
$599$	22.3013	0.911206	0.455603	−	0.890183i	$-0.349424\pi$
$599$	22.3013	0.911206	0.455603	+	0.890183i	$0.349424\pi$
$600$	−5.91560	−0.241503
$601$	16.6444	0.678939	0.339470	−	0.940617i	$-0.389752\pi$
$601$	16.6444	0.678939	0.339470	+	0.940617i	$0.389752\pi$
$602$	−5.39591	−0.219921
$603$	11.4484	0.466215
$604$	7.10404	0.289059
$605$	1.00000	0.0406558
$606$	18.9912	0.771467
$607$	17.8779	0.725641	0.362821	−	0.931859i	$-0.381814\pi$
$607$	17.8779	0.725641	0.362821	+	0.931859i	$0.381814\pi$
$608$	12.7634	0.517623
$609$	−16.9575	−0.687152
$610$	−0.879653	−0.0356161
$611$	38.3147	1.55005
$612$	−5.31096	−0.214683
$613$	35.5502	1.43586	0.717930	−	0.696115i	$-0.245090\pi$
$613$	35.5502	1.43586	0.717930	+	0.696115i	$0.245090\pi$
$614$	8.43266	0.340315
$615$	9.78408	0.394532
$616$	2.86598	0.115473
$617$	2.87315	0.115669	0.0578343	−	0.998326i	$-0.481580\pi$
$617$	2.87315	0.115669	0.0578343	+	0.998326i	$0.481580\pi$
$618$	−24.4017	−0.981581
$619$	−1.78215	−0.0716308	−0.0358154	−	0.999358i	$-0.511403\pi$
$619$	−1.78215	−0.0716308	−0.0358154	+	0.999358i	$0.511403\pi$
$620$	−14.3269	−0.575381
$621$	−16.8691	−0.676934
$622$	7.52584	0.301758
$623$	16.7120	0.669551
$624$	−3.67843	−0.147255
$625$	1.00000	0.0400000
$626$	7.97822	0.318874
$627$	4.75364	0.189842
$628$	16.1575	0.644756
$629$	−6.98301	−0.278431
$630$	−1.41415	−0.0563413
$631$	11.5434	0.459537	0.229768	−	0.973245i	$-0.426203\pi$
$631$	11.5434	0.459537	0.229768	+	0.973245i	$0.426203\pi$
$632$	−41.9552	−1.66889
$633$	48.5118	1.92817
$634$	−3.16680	−0.125770
$635$	−4.36742	−0.173316
$636$	14.1040	0.559260
$637$	29.5615	1.17127
$638$	6.26880	0.248184
$639$	22.2959	0.882012
$640$	−8.14586	−0.321993
$641$	−11.8352	−0.467461	−0.233730	−	0.972301i	$-0.575093\pi$
$641$	−11.8352	−0.467461	−0.233730	+	0.972301i	$0.575093\pi$
$642$	−12.2001	−0.481501
$643$	−20.2651	−0.799177	−0.399589	−	0.916695i	$-0.630847\pi$
$643$	−20.2651	−0.799177	−0.399589	+	0.916695i	$0.630847\pi$
$644$	7.84416	0.309103
$645$	13.4200	0.528412
$646$	4.54335	0.178756
$647$	7.94946	0.312526	0.156263	−	0.987716i	$-0.450055\pi$
$647$	7.94946	0.312526	0.156263	+	0.987716i	$0.450055\pi$
$648$	30.8665	1.21255
$649$	12.1875	0.478401
$650$	−4.14959	−0.162760
$651$	−24.5296	−0.961390
$652$	−9.70949	−0.380253
$653$	−18.0772	−0.707416	−0.353708	−	0.935356i	$-0.615079\pi$
$653$	−18.0772	−0.707416	−0.353708	+	0.935356i	$0.615079\pi$
$654$	22.5381	0.881311
$655$	16.7683	0.655190
$656$	1.55336	0.0606487
$657$	1.63385	0.0637427
$658$	6.63258	0.258565
$659$	−44.4468	−1.73140	−0.865701	−	0.500561i	$-0.833127\pi$
$659$	−44.4468	−1.73140	−0.865701	+	0.500561i	$0.833127\pi$
$660$	−2.82259	−0.109869
$661$	−29.1686	−1.13453	−0.567264	−	0.823536i	$-0.691998\pi$
$661$	−29.1686	−1.13453	−0.567264	+	0.823536i	$0.691998\pi$
$662$	3.08295	0.119822
$663$	−26.6821	−1.03625
$664$	−8.34717	−0.323933
$665$	−2.30303	−0.0893078
$666$	−3.81954	−0.148004
$667$	43.3281	1.67767
$668$	23.8818	0.924015
$669$	−36.1171	−1.39637
$670$	5.81528	0.224664
$671$	−1.05992	−0.0409177
$672$	−12.9756	−0.500544
$673$	12.7086	0.489880	0.244940	−	0.969538i	$-0.421232\pi$
$673$	12.7086	0.489880	0.244940	+	0.969538i	$0.421232\pi$
$674$	14.1157	0.543715
$675$	−2.94082	−0.113192
$676$	−15.7342	−0.605161
$677$	6.19998	0.238285	0.119142	−	0.992877i	$-0.461986\pi$
$677$	6.19998	0.238285	0.119142	+	0.992877i	$0.461986\pi$
$678$	2.69211	0.103390
$679$	−3.05079	−0.117078
$680$	−6.81256	−0.261250
$681$	44.0306	1.68725
$682$	9.06802	0.347232
$683$	19.4045	0.742492	0.371246	−	0.928534i	$-0.378931\pi$
$683$	19.4045	0.742492	0.371246	+	0.928534i	$0.378931\pi$
$684$	−4.73092	−0.180891
$685$	−20.5287	−0.784361
$686$	11.1761	0.426704
$687$	−19.7266	−0.752617
$688$	2.13062	0.0812291
$689$	24.9839	0.951811
$690$	10.2479	0.390130
$691$	38.2011	1.45324	0.726620	−	0.687040i	$-0.241090\pi$
$691$	38.2011	1.45324	0.726620	+	0.687040i	$0.241090\pi$
$692$	14.5192	0.551938
$693$	−1.70396	−0.0647279
$694$	25.1931	0.956315
$695$	0.205962	0.00781257
$696$	−44.6832	−1.69371
$697$	11.2676	0.426791
$698$	12.1654	0.460466
$699$	−45.7626	−1.73090
$700$	1.36748	0.0516861
$701$	7.88516	0.297818	0.148909	−	0.988851i	$-0.452424\pi$
$701$	7.88516	0.297818	0.148909	+	0.988851i	$0.452424\pi$
$702$	12.2032	0.460580
$703$	−6.22035	−0.234605
$704$	4.11325	0.155024
$705$	−16.4957	−0.621263
$706$	4.46493	0.168040
$707$	−11.0864	−0.416945
$708$	−34.4004	−1.29285
$709$	16.2668	0.610913	0.305457	−	0.952206i	$-0.401191\pi$
$709$	16.2668	0.610913	0.305457	+	0.952206i	$0.401191\pi$
$710$	11.3253	0.425032
$711$	24.9443	0.935485
$712$	44.0362	1.65033
$713$	62.6755	2.34722
$714$	−4.61889	−0.172858
$715$	−4.99996	−0.186988
$716$	33.3914	1.24789
$717$	−28.4966	−1.06423
$718$	−30.8019	−1.14952
$719$	10.4846	0.391009	0.195504	−	0.980703i	$-0.437366\pi$
$719$	10.4846	0.391009	0.195504	+	0.980703i	$0.437366\pi$
$720$	0.558390	0.0208100
$721$	14.2448	0.530503
$722$	−11.7214	−0.436226
$723$	−15.0500	−0.559715
$724$	−23.5884	−0.876658
$725$	7.55345	0.280528
$726$	1.78653	0.0663043
$727$	−28.6795	−1.06367	−0.531833	−	0.846850i	$-0.678496\pi$
$727$	−28.6795	−1.06367	−0.531833	+	0.846850i	$0.678496\pi$
$728$	−14.3298	−0.531096
$729$	0.639991	0.0237034
$730$	0.829924	0.0307169
$731$	15.4548	0.571617
$732$	2.99172	0.110577
$733$	9.41565	0.347775	0.173887	−	0.984766i	$-0.444367\pi$
$733$	9.41565	0.347775	0.173887	+	0.984766i	$0.444367\pi$
$734$	−6.62923	−0.244690
$735$	−12.7271	−0.469448
$736$	33.1539	1.22207
$737$	7.00699	0.258106
$738$	6.16312	0.226868
$739$	−28.5927	−1.05180	−0.525900	−	0.850546i	$-0.676271\pi$
$739$	−28.5927	−1.05180	−0.525900	+	0.850546i	$0.676271\pi$
$740$	3.69349	0.135776
$741$	−23.7680	−0.873140
$742$	4.32491	0.158772
$743$	−13.3726	−0.490593	−0.245297	−	0.969448i	$-0.578885\pi$
$743$	−13.3726	−0.490593	−0.245297	+	0.969448i	$0.578885\pi$
$744$	−64.6357	−2.36966
$745$	0.357433	0.0130953
$746$	4.61456	0.168951
$747$	4.96278	0.181579
$748$	−3.25058	−0.118853
$749$	7.12197	0.260231
$750$	1.78653	0.0652348
$751$	7.16088	0.261304	0.130652	−	0.991428i	$-0.458293\pi$
$751$	7.16088	0.261304	0.130652	+	0.991428i	$0.458293\pi$
$752$	−2.61893	−0.0955024
$753$	11.8323	0.431192
$754$	−31.3437	−1.14147
$755$	−5.41786	−0.197176
$756$	−4.02153	−0.146261
$757$	−29.6488	−1.07760	−0.538802	−	0.842433i	$-0.681123\pi$
$757$	−29.6488	−1.07760	−0.538802	+	0.842433i	$0.681123\pi$
$758$	−7.92567	−0.287873
$759$	12.3480	0.448202
$760$	−6.06851	−0.220128
$761$	−38.1278	−1.38213	−0.691066	−	0.722791i	$-0.742859\pi$
$761$	−38.1278	−1.38213	−0.691066	+	0.722791i	$0.742859\pi$
$762$	−7.80251	−0.282655
$763$	−13.1569	−0.476312
$764$	0.129980	0.00470251
$765$	4.05038	0.146442
$766$	24.5611	0.887430
$767$	−60.9370	−2.20031
$768$	−32.2615	−1.16414
$769$	7.37680	0.266014	0.133007	−	0.991115i	$-0.457537\pi$
$769$	7.37680	0.266014	0.133007	+	0.991115i	$0.457537\pi$
$770$	−0.865533	−0.0311916
$771$	15.1361	0.545113
$772$	9.64874	0.347266
$773$	−46.2555	−1.66369	−0.831847	−	0.555004i	$-0.812717\pi$
$773$	−46.2555	−1.66369	−0.831847	+	0.555004i	$0.812717\pi$
$774$	8.45343	0.303852
$775$	10.9263	0.392485
$776$	−8.03885	−0.288578
$777$	6.32377	0.226864
$778$	5.52072	0.197927
$779$	10.0370	0.359613
$780$	14.1129	0.505322
$781$	13.6462	0.488300
$782$	11.8017	0.422029
$783$	−22.2133	−0.793840
$784$	−2.02062	−0.0721650
$785$	−12.3225	−0.439808
$786$	29.9569	1.06853
$787$	−35.5094	−1.26577	−0.632886	−	0.774245i	$-0.718130\pi$
$787$	−35.5094	−1.26577	−0.632886	+	0.774245i	$0.718130\pi$
$788$	−8.50994	−0.303154
$789$	43.0548	1.53279
$790$	12.6706	0.450799
$791$	−1.57155	−0.0558779
$792$	−4.48994	−0.159543
$793$	5.29956	0.188193
$794$	17.7728	0.630734
$795$	−10.7563	−0.381488
$796$	0.212199	0.00752119
$797$	−35.0553	−1.24172	−0.620861	−	0.783920i	$-0.713217\pi$
$797$	−35.0553	−1.24172	−0.620861	+	0.783920i	$0.713217\pi$
$798$	−4.11443	−0.145649
$799$	−18.9968	−0.672060
$800$	5.77977	0.204346
$801$	−26.1816	−0.925080
$802$	−3.34820	−0.118229
$803$	1.00000	0.0352892
$804$	−19.7779	−0.697513
$805$	−5.98231	−0.210849
$806$	−45.3398	−1.59702
$807$	−54.4450	−1.91655
$808$	−29.2127	−1.02770
$809$	42.7463	1.50288	0.751440	−	0.659802i	$-0.229360\pi$
$809$	42.7463	1.50288	0.751440	+	0.659802i	$0.229360\pi$
$810$	−9.32178	−0.327534
$811$	7.93399	0.278600	0.139300	−	0.990250i	$-0.455515\pi$
$811$	7.93399	0.278600	0.139300	+	0.990250i	$0.455515\pi$
$812$	10.3292	0.362485
$813$	26.6430	0.934412
$814$	−2.33775	−0.0819382
$815$	7.40490	0.259382
$816$	1.82381	0.0638460
$817$	13.7669	0.481643
$818$	17.9446	0.627420
$819$	8.51971	0.297703
$820$	−5.95972	−0.208123
$821$	−38.7862	−1.35365	−0.676824	−	0.736145i	$-0.736644\pi$
$821$	−38.7862	−1.35365	−0.676824	+	0.736145i	$0.736644\pi$
$822$	−36.6751	−1.27919
$823$	−23.8084	−0.829908	−0.414954	−	0.909842i	$-0.636202\pi$
$823$	−23.8084	−0.829908	−0.414954	+	0.909842i	$0.636202\pi$
$824$	37.5351	1.30760
$825$	2.15264	0.0749453
$826$	−10.5487	−0.367036
$827$	21.2728	0.739728	0.369864	−	0.929086i	$-0.379404\pi$
$827$	21.2728	0.739728	0.369864	+	0.929086i	$0.379404\pi$
$828$	−12.2889	−0.427070
$829$	32.2902	1.12148	0.560742	−	0.827991i	$-0.310516\pi$
$829$	32.2902	1.12148	0.560742	+	0.827991i	$0.310516\pi$
$830$	2.52087	0.0875007
$831$	−32.8056	−1.13801
$832$	−20.5661	−0.713001
$833$	−14.6569	−0.507832
$834$	0.367956	0.0127413
$835$	−18.2133	−0.630299
$836$	−2.89556	−0.100145
$837$	−32.1323	−1.11066
$838$	12.4711	0.430807
$839$	−3.75627	−0.129681	−0.0648404	−	0.997896i	$-0.520654\pi$
$839$	−3.75627	−0.129681	−0.0648404	+	0.997896i	$0.520654\pi$
$840$	6.16941	0.212865
$841$	28.0546	0.967402
$842$	−1.57428	−0.0542533
$843$	57.6229	1.98464
$844$	−29.5497	−1.01714
$845$	11.9996	0.412799
$846$	−10.3908	−0.357244
$847$	−1.04291	−0.0358347
$848$	−1.70773	−0.0586435
$849$	40.2023	1.37974
$850$	2.05741	0.0705687
$851$	−16.1579	−0.553884
$852$	−38.5177	−1.31959
$853$	14.0599	0.481401	0.240701	−	0.970599i	$-0.422623\pi$
$853$	14.0599	0.481401	0.240701	+	0.970599i	$0.422623\pi$
$854$	0.917396	0.0313926
$855$	3.60801	0.123391
$856$	18.7665	0.641424
$857$	−47.6535	−1.62781	−0.813906	−	0.580997i	$-0.802663\pi$
$857$	−47.6535	−1.62781	−0.813906	+	0.580997i	$0.802663\pi$
$858$	−8.93257	−0.304953
$859$	36.8435	1.25708	0.628542	−	0.777775i	$-0.283652\pi$
$859$	36.8435	1.25708	0.628542	+	0.777775i	$0.283652\pi$
$860$	−8.17445	−0.278746
$861$	−10.2039	−0.347747
$862$	−11.0623	−0.376785
$863$	−39.9755	−1.36078	−0.680391	−	0.732850i	$-0.738190\pi$
$863$	−39.9755	−1.36078	−0.680391	+	0.732850i	$0.738190\pi$
$864$	−16.9973	−0.578259
$865$	−11.0730	−0.376494
$866$	11.6756	0.396753
$867$	−23.3656	−0.793536
$868$	14.9416	0.507150
$869$	15.2672	0.517903
$870$	13.4945	0.457505
$871$	−35.0347	−1.18711
$872$	−34.6685	−1.17402
$873$	4.77947	0.161761
$874$	10.5128	0.355600
$875$	−1.04291	−0.0352567
$876$	−2.82259	−0.0953666
$877$	43.9928	1.48553	0.742766	−	0.669551i	$-0.233513\pi$
$877$	43.9928	1.48553	0.742766	+	0.669551i	$0.233513\pi$
$878$	7.08358	0.239059
$879$	−27.2385	−0.918730
$880$	0.341763	0.0115208
$881$	34.0757	1.14804	0.574019	−	0.818842i	$-0.305383\pi$
$881$	34.0757	1.14804	0.574019	+	0.818842i	$0.305383\pi$
$882$	−8.01699	−0.269946
$883$	0.550601	0.0185292	0.00926460	−	0.999957i	$-0.497051\pi$
$883$	0.550601	0.0185292	0.00926460	+	0.999957i	$0.497051\pi$
$884$	16.2527	0.546639
$885$	26.2353	0.881889
$886$	5.26065	0.176735
$887$	39.0533	1.31128	0.655642	−	0.755072i	$-0.272398\pi$
$887$	39.0533	1.31128	0.655642	+	0.755072i	$0.272398\pi$
$888$	16.6632	0.559180
$889$	4.55481	0.152763
$890$	−13.2991	−0.445786
$891$	−11.2321	−0.376289
$892$	21.9998	0.736608
$893$	−16.9221	−0.566276
$894$	0.638565	0.0213568
$895$	−25.4658	−0.851226
$896$	8.49536	0.283810
$897$	−61.7393	−2.06142
$898$	−17.0447	−0.568788
$899$	82.5314	2.75258
$900$	−2.14235	−0.0714117
$901$	−12.3873	−0.412681
$902$	3.77214	0.125598
$903$	−13.9958	−0.465751
$904$	−4.14105	−0.137729
$905$	17.9896	0.597995
$906$	−9.67916	−0.321569
$907$	27.2645	0.905304	0.452652	−	0.891687i	$-0.350478\pi$
$907$	27.2645	0.905304	0.452652	+	0.891687i	$0.350478\pi$
$908$	−26.8201	−0.890056
$909$	17.3683	0.576070
$910$	4.32763	0.143460
$911$	−46.5648	−1.54276	−0.771380	−	0.636375i	$-0.780433\pi$
$911$	−46.5648	−1.54276	−0.771380	+	0.636375i	$0.780433\pi$
$912$	1.62462	0.0537964
$913$	3.03747	0.100526
$914$	−13.7284	−0.454096
$915$	−2.28162	−0.0754282
$916$	12.0160	0.397019
$917$	−17.4877	−0.577495
$918$	−6.05048	−0.199696
$919$	−50.4399	−1.66386	−0.831930	−	0.554880i	$-0.812764\pi$
$919$	−50.4399	−1.66386	−0.831930	+	0.554880i	$0.812764\pi$
$920$	−15.7635	−0.519706
$921$	21.8724	0.720721
$922$	−8.89557	−0.292960
$923$	−68.2305	−2.24583
$924$	2.94370	0.0968406
$925$	−2.81683	−0.0926167
$926$	2.67320	0.0878469
$927$	−22.3164	−0.732966
$928$	43.6572	1.43312
$929$	44.4410	1.45806	0.729032	−	0.684480i	$-0.239971\pi$
$929$	44.4410	1.45806	0.729032	+	0.684480i	$0.239971\pi$
$930$	19.5202	0.640092
$931$	−13.0561	−0.427898
$932$	27.8751	0.913080
$933$	19.5203	0.639067
$934$	10.7083	0.350387
$935$	2.47904	0.0810732
$936$	22.4495	0.733785
$937$	−48.3906	−1.58085	−0.790427	−	0.612557i	$-0.790141\pi$
$937$	−48.3906	−1.58085	−0.790427	+	0.612557i	$0.790141\pi$
$938$	−6.06478	−0.198022
$939$	20.6937	0.675314
$940$	10.0479	0.327727
$941$	14.2855	0.465694	0.232847	−	0.972513i	$-0.425196\pi$
$941$	14.2855	0.465694	0.232847	+	0.972513i	$0.425196\pi$
$942$	−22.0144	−0.717269
$943$	26.0719	0.849018
$944$	4.16523	0.135567
$945$	3.06700	0.0997695
$946$	5.17392	0.168219
$947$	31.6845	1.02961	0.514805	−	0.857308i	$-0.327864\pi$
$947$	31.6845	1.02961	0.514805	+	0.857308i	$0.327864\pi$
$948$	−43.0930	−1.39960
$949$	−4.99996	−0.162306
$950$	1.83271	0.0594609
$951$	−8.21396	−0.266356
$952$	7.10486	0.230270
$953$	−40.1753	−1.30141	−0.650704	−	0.759332i	$-0.725526\pi$
$953$	−40.1753	−1.30141	−0.650704	+	0.759332i	$0.725526\pi$
$954$	−6.77556	−0.219367
$955$	−0.0991286	−0.00320772
$956$	17.3580	0.561398
$957$	16.2599	0.525606
$958$	−32.0492	−1.03546
$959$	21.4095	0.691349
$960$	8.85434	0.285773
$961$	88.3845	2.85111
$962$	11.6887	0.376858
$963$	−11.1575	−0.359546
$964$	9.16732	0.295260
$965$	−7.35857	−0.236881
$966$	−10.6876	−0.343867
$967$	1.86766	0.0600597	0.0300299	−	0.999549i	$-0.490440\pi$
$967$	1.86766	0.0600597	0.0300299	+	0.999549i	$0.490440\pi$
$968$	−2.74807	−0.0883262
$969$	11.7844	0.378571
$970$	2.42776	0.0779506
$971$	42.4601	1.36261	0.681305	−	0.732000i	$-0.261413\pi$
$971$	42.4601	1.36261	0.681305	+	0.732000i	$0.261413\pi$
$972$	20.1354	0.645843
$973$	−0.214799	−0.00688613
$974$	−13.2399	−0.424235
$975$	−10.7631	−0.344695
$976$	−0.362241	−0.0115950
$977$	6.35485	0.203310	0.101655	−	0.994820i	$-0.467586\pi$
$977$	6.35485	0.203310	0.101655	+	0.994820i	$0.467586\pi$
$978$	13.2291	0.423019
$979$	−16.0244	−0.512143
$980$	7.75242	0.247642
$981$	20.6121	0.658092
$982$	−22.4936	−0.717801
$983$	57.0468	1.81951	0.909755	−	0.415146i	$-0.136270\pi$
$983$	57.0468	1.81951	0.909755	+	0.415146i	$0.136270\pi$
$984$	−26.8873	−0.857136
$985$	6.49007	0.206791
$986$	15.5406	0.494913
$987$	17.2034	0.547591
$988$	14.4777	0.460596
$989$	35.7606	1.13712
$990$	1.35597	0.0430957
$991$	−6.94726	−0.220687	−0.110343	−	0.993894i	$-0.535195\pi$
$991$	−6.94726	−0.220687	−0.110343	+	0.993894i	$0.535195\pi$
$992$	63.1516	2.00507
$993$	7.99649	0.253761
$994$	−11.8112	−0.374630
$995$	−0.161833	−0.00513044
$996$	−8.57355	−0.271663
$997$	−35.7252	−1.13143	−0.565714	−	0.824602i	$-0.691399\pi$
$997$	−35.7252	−1.13143	−0.565714	+	0.824602i	$0.691399\pi$
$998$	−13.9012	−0.440036
$999$	8.28378	0.262087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.22	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.22	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.829924 q^{2} +2.15264 q^{3} -1.31123 q^{4} +1.00000 q^{5} +1.78653 q^{6} -1.04291 q^{7} -2.74807 q^{8} +1.63385 q^{9} +O(q^{10})\)	\(q+0.829924 q^{2} +2.15264 q^{3} -1.31123 q^{4} +1.00000 q^{5} +1.78653 q^{6} -1.04291 q^{7} -2.74807 q^{8} +1.63385 q^{9} +0.829924 q^{10} +1.00000 q^{11} -2.82259 q^{12} -4.99996 q^{13} -0.865533 q^{14} +2.15264 q^{15} +0.341763 q^{16} +2.47904 q^{17} +1.35597 q^{18} +2.20828 q^{19} -1.31123 q^{20} -2.24500 q^{21} +0.829924 q^{22} +5.73620 q^{23} -5.91560 q^{24} +1.00000 q^{25} -4.14959 q^{26} -2.94082 q^{27} +1.36748 q^{28} +7.55345 q^{29} +1.78653 q^{30} +10.9263 q^{31} +5.77977 q^{32} +2.15264 q^{33} +2.05741 q^{34} -1.04291 q^{35} -2.14235 q^{36} -2.81683 q^{37} +1.83271 q^{38} -10.7631 q^{39} -2.74807 q^{40} +4.54516 q^{41} -1.86318 q^{42} +6.23420 q^{43} -1.31123 q^{44} +1.63385 q^{45} +4.76061 q^{46} -7.66300 q^{47} +0.735691 q^{48} -5.91235 q^{49} +0.829924 q^{50} +5.33647 q^{51} +6.55608 q^{52} -4.99682 q^{53} -2.44066 q^{54} +1.00000 q^{55} +2.86598 q^{56} +4.75364 q^{57} +6.26880 q^{58} +12.1875 q^{59} -2.82259 q^{60} -1.05992 q^{61} +9.06802 q^{62} -1.70396 q^{63} +4.11325 q^{64} -4.99996 q^{65} +1.78653 q^{66} +7.00699 q^{67} -3.25058 q^{68} +12.3480 q^{69} -0.865533 q^{70} +13.6462 q^{71} -4.48994 q^{72} +1.00000 q^{73} -2.33775 q^{74} +2.15264 q^{75} -2.89556 q^{76} -1.04291 q^{77} -8.93257 q^{78} +15.2672 q^{79} +0.341763 q^{80} -11.2321 q^{81} +3.77214 q^{82} +3.03747 q^{83} +2.94370 q^{84} +2.47904 q^{85} +5.17392 q^{86} +16.2599 q^{87} -2.74807 q^{88} -16.0244 q^{89} +1.35597 q^{90} +5.21449 q^{91} -7.52145 q^{92} +23.5204 q^{93} -6.35971 q^{94} +2.20828 q^{95} +12.4418 q^{96} +2.92528 q^{97} -4.90680 q^{98} +1.63385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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