LMFDB - Embedded newform 4017.2.a.g.1.13

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			1.13
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)

$f(q)$	$=$	$q+0.543206 q^{2} -1.00000 q^{3} -1.70493 q^{4} +2.45290 q^{5} -0.543206 q^{6} +0.874109 q^{7} -2.01254 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.543206 q^{2} -1.00000 q^{3} -1.70493 q^{4} +2.45290 q^{5} -0.543206 q^{6} +0.874109 q^{7} -2.01254 q^{8} +1.00000 q^{9} +1.33243 q^{10} -4.72327 q^{11} +1.70493 q^{12} -1.00000 q^{13} +0.474821 q^{14} -2.45290 q^{15} +2.31663 q^{16} -1.13931 q^{17} +0.543206 q^{18} +3.87568 q^{19} -4.18202 q^{20} -0.874109 q^{21} -2.56571 q^{22} +0.738530 q^{23} +2.01254 q^{24} +1.01673 q^{25} -0.543206 q^{26} -1.00000 q^{27} -1.49029 q^{28} +0.947901 q^{29} -1.33243 q^{30} -3.64768 q^{31} +5.28348 q^{32} +4.72327 q^{33} -0.618878 q^{34} +2.14410 q^{35} -1.70493 q^{36} +3.19911 q^{37} +2.10529 q^{38} +1.00000 q^{39} -4.93656 q^{40} -0.380271 q^{41} -0.474821 q^{42} -2.38858 q^{43} +8.05284 q^{44} +2.45290 q^{45} +0.401174 q^{46} +5.91658 q^{47} -2.31663 q^{48} -6.23593 q^{49} +0.552295 q^{50} +1.13931 q^{51} +1.70493 q^{52} +8.85124 q^{53} -0.543206 q^{54} -11.5857 q^{55} -1.75918 q^{56} -3.87568 q^{57} +0.514905 q^{58} +12.0866 q^{59} +4.18202 q^{60} -4.69689 q^{61} -1.98144 q^{62} +0.874109 q^{63} -1.76325 q^{64} -2.45290 q^{65} +2.56571 q^{66} +16.1559 q^{67} +1.94244 q^{68} -0.738530 q^{69} +1.16469 q^{70} +2.39836 q^{71} -2.01254 q^{72} -10.2947 q^{73} +1.73777 q^{74} -1.01673 q^{75} -6.60776 q^{76} -4.12866 q^{77} +0.543206 q^{78} +15.0397 q^{79} +5.68248 q^{80} +1.00000 q^{81} -0.206565 q^{82} -4.05379 q^{83} +1.49029 q^{84} -2.79461 q^{85} -1.29749 q^{86} -0.947901 q^{87} +9.50577 q^{88} +4.49947 q^{89} +1.33243 q^{90} -0.874109 q^{91} -1.25914 q^{92} +3.64768 q^{93} +3.21392 q^{94} +9.50667 q^{95} -5.28348 q^{96} +0.478339 q^{97} -3.38739 q^{98} -4.72327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.543206	0.384104	0.192052	−	0.981385i	$-0.438486\pi$
$2$	0.543206	0.384104	0.192052	+	0.981385i	$0.438486\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.70493	−0.852464
$5$	2.45290	1.09697	0.548486	−	0.836160i	$-0.315204\pi$
$5$	2.45290	1.09697	0.548486	+	0.836160i	$0.315204\pi$
$6$	−0.543206	−0.221763
$7$	0.874109	0.330382	0.165191	−	0.986262i	$-0.447176\pi$
$7$	0.874109	0.330382	0.165191	+	0.986262i	$0.447176\pi$
$8$	−2.01254	−0.711540
$9$	1.00000	0.333333
$10$	1.33243	0.421352
$11$	−4.72327	−1.42412	−0.712060	−	0.702118i	$-0.752238\pi$
$11$	−4.72327	−1.42412	−0.712060	+	0.702118i	$0.752238\pi$
$12$	1.70493	0.492170
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.474821	0.126901
$15$	−2.45290	−0.633337
$16$	2.31663	0.579158
$17$	−1.13931	−0.276323	−0.138161	−	0.990410i	$-0.544119\pi$
$17$	−1.13931	−0.276323	−0.138161	+	0.990410i	$0.544119\pi$
$18$	0.543206	0.128035
$19$	3.87568	0.889142	0.444571	−	0.895744i	$-0.353356\pi$
$19$	3.87568	0.889142	0.444571	+	0.895744i	$0.353356\pi$
$20$	−4.18202	−0.935129
$21$	−0.874109	−0.190746
$22$	−2.56571	−0.547011
$23$	0.738530	0.153994	0.0769971	−	0.997031i	$-0.475467\pi$
$23$	0.738530	0.153994	0.0769971	+	0.997031i	$0.475467\pi$
$24$	2.01254	0.410808
$25$	1.01673	0.203347
$26$	−0.543206	−0.106531
$27$	−1.00000	−0.192450
$28$	−1.49029	−0.281639
$29$	0.947901	0.176021	0.0880104	−	0.996120i	$-0.471949\pi$
$29$	0.947901	0.176021	0.0880104	+	0.996120i	$0.471949\pi$
$30$	−1.33243	−0.243267
$31$	−3.64768	−0.655142	−0.327571	−	0.944827i	$-0.606230\pi$
$31$	−3.64768	−0.655142	−0.327571	+	0.944827i	$0.606230\pi$
$32$	5.28348	0.933997
$33$	4.72327	0.822217
$34$	−0.618878	−0.106137
$35$	2.14410	0.362420
$36$	−1.70493	−0.284155
$37$	3.19911	0.525930	0.262965	−	0.964805i	$-0.415300\pi$
$37$	3.19911	0.525930	0.262965	+	0.964805i	$0.415300\pi$
$38$	2.10529	0.341524
$39$	1.00000	0.160128
$40$	−4.93656	−0.780539
$41$	−0.380271	−0.0593883	−0.0296942	−	0.999559i	$-0.509453\pi$
$41$	−0.380271	−0.0593883	−0.0296942	+	0.999559i	$0.509453\pi$
$42$	−0.474821	−0.0732665
$43$	−2.38858	−0.364256	−0.182128	−	0.983275i	$-0.558298\pi$
$43$	−2.38858	−0.364256	−0.182128	+	0.983275i	$0.558298\pi$
$44$	8.05284	1.21401
$45$	2.45290	0.365657
$46$	0.401174	0.0591498
$47$	5.91658	0.863022	0.431511	−	0.902108i	$-0.357981\pi$
$47$	5.91658	0.863022	0.431511	+	0.902108i	$0.357981\pi$
$48$	−2.31663	−0.334377
$49$	−6.23593	−0.890848
$50$	0.552295	0.0781064
$51$	1.13931	0.159535
$52$	1.70493	0.236431
$53$	8.85124	1.21581	0.607906	−	0.794009i	$-0.292010\pi$
$53$	8.85124	1.21581	0.607906	+	0.794009i	$0.292010\pi$
$54$	−0.543206	−0.0739209
$55$	−11.5857	−1.56222
$56$	−1.75918	−0.235080
$57$	−3.87568	−0.513347
$58$	0.514905	0.0676104
$59$	12.0866	1.57354	0.786772	−	0.617243i	$-0.211751\pi$
$59$	12.0866	1.57354	0.786772	+	0.617243i	$0.211751\pi$
$60$	4.18202	0.539897
$61$	−4.69689	−0.601375	−0.300687	−	0.953723i	$-0.597216\pi$
$61$	−4.69689	−0.601375	−0.300687	+	0.953723i	$0.597216\pi$
$62$	−1.98144	−0.251643
$63$	0.874109	0.110127
$64$	−1.76325	−0.220406
$65$	−2.45290	−0.304245
$66$	2.56571	0.315817
$67$	16.1559	1.97375	0.986876	−	0.161478i	$-0.0516261\pi$
$67$	16.1559	1.97375	0.986876	+	0.161478i	$0.0516261\pi$
$68$	1.94244	0.235555
$69$	−0.738530	−0.0889085
$70$	1.16469	0.139207
$71$	2.39836	0.284632	0.142316	−	0.989821i	$-0.454545\pi$
$71$	2.39836	0.284632	0.142316	+	0.989821i	$0.454545\pi$
$72$	−2.01254	−0.237180
$73$	−10.2947	−1.20490	−0.602449	−	0.798157i	$-0.705808\pi$
$73$	−10.2947	−1.20490	−0.602449	+	0.798157i	$0.705808\pi$
$74$	1.73777	0.202012
$75$	−1.01673	−0.117402
$76$	−6.60776	−0.757962
$77$	−4.12866	−0.470504
$78$	0.543206	0.0615059
$79$	15.0397	1.69210	0.846049	−	0.533106i	$-0.178975\pi$
$79$	15.0397	1.69210	0.846049	+	0.533106i	$0.178975\pi$
$80$	5.68248	0.635320
$81$	1.00000	0.111111
$82$	−0.206565	−0.0228113
$83$	−4.05379	−0.444961	−0.222480	−	0.974937i	$-0.571415\pi$
$83$	−4.05379	−0.444961	−0.222480	+	0.974937i	$0.571415\pi$
$84$	1.49029	0.162604
$85$	−2.79461	−0.303118
$86$	−1.29749	−0.139912
$87$	−0.947901	−0.101626
$88$	9.50577	1.01332
$89$	4.49947	0.476943	0.238471	−	0.971150i	$-0.423354\pi$
$89$	4.49947	0.476943	0.238471	+	0.971150i	$0.423354\pi$
$90$	1.33243	0.140451
$91$	−0.874109	−0.0916315
$92$	−1.25914	−0.131274
$93$	3.64768	0.378246
$94$	3.21392	0.331491
$95$	9.50667	0.975364
$96$	−5.28348	−0.539243
$97$	0.478339	0.0485680	0.0242840	−	0.999705i	$-0.492269\pi$
$97$	0.478339	0.0485680	0.0242840	+	0.999705i	$0.492269\pi$
$98$	−3.38739	−0.342179
$99$	−4.72327	−0.474707
$100$	−1.73346	−0.173346
$101$	−12.1057	−1.20456	−0.602279	−	0.798285i	$-0.705741\pi$
$101$	−12.1057	−1.20456	−0.602279	+	0.798285i	$0.705741\pi$
$102$	0.618878	0.0612781
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.01254	0.197346
$105$	−2.14410	−0.209243
$106$	4.80805	0.466999
$107$	−11.1204	−1.07505	−0.537525	−	0.843248i	$-0.680641\pi$
$107$	−11.1204	−1.07505	−0.537525	+	0.843248i	$0.680641\pi$
$108$	1.70493	0.164057
$109$	13.6869	1.31097	0.655483	−	0.755210i	$-0.272465\pi$
$109$	13.6869	1.31097	0.655483	+	0.755210i	$0.272465\pi$
$110$	−6.29344	−0.600056
$111$	−3.19911	−0.303646
$112$	2.02499	0.191344
$113$	−1.48413	−0.139615	−0.0698075	−	0.997560i	$-0.522238\pi$
$113$	−1.48413	−0.139615	−0.0698075	+	0.997560i	$0.522238\pi$
$114$	−2.10529	−0.197179
$115$	1.81154	0.168927
$116$	−1.61610	−0.150051
$117$	−1.00000	−0.0924500
$118$	6.56552	0.604406
$119$	−0.995878	−0.0912920
$120$	4.93656	0.450644
$121$	11.3093	1.02812
$122$	−2.55138	−0.230991
$123$	0.380271	0.0342879
$124$	6.21902	0.558485
$125$	−9.77057	−0.873906
$126$	0.474821	0.0423004
$127$	−2.32503	−0.206313	−0.103156	−	0.994665i	$-0.532894\pi$
$127$	−2.32503	−0.206313	−0.103156	+	0.994665i	$0.532894\pi$
$128$	−11.5248	−1.01866
$129$	2.38858	0.210303
$130$	−1.33243	−0.116862
$131$	7.82082	0.683308	0.341654	−	0.939826i	$-0.389013\pi$
$131$	7.82082	0.683308	0.341654	+	0.939826i	$0.389013\pi$
$132$	−8.05284	−0.700910
$133$	3.38777	0.293757
$134$	8.77596	0.758127
$135$	−2.45290	−0.211112
$136$	2.29290	0.196614
$137$	18.1155	1.54771	0.773857	−	0.633361i	$-0.218325\pi$
$137$	18.1155	1.54771	0.773857	+	0.633361i	$0.218325\pi$
$138$	−0.401174	−0.0341502
$139$	11.9775	1.01592	0.507959	−	0.861381i	$-0.330400\pi$
$139$	11.9775	1.01592	0.507959	+	0.861381i	$0.330400\pi$
$140$	−3.65554	−0.308950
$141$	−5.91658	−0.498266
$142$	1.30280	0.109329
$143$	4.72327	0.394980
$144$	2.31663	0.193053
$145$	2.32511	0.193090
$146$	−5.59212	−0.462807
$147$	6.23593	0.514331
$148$	−5.45425	−0.448336
$149$	−2.40587	−0.197096	−0.0985482	−	0.995132i	$-0.531420\pi$
$149$	−2.40587	−0.197096	−0.0985482	+	0.995132i	$0.531420\pi$
$150$	−0.552295	−0.0450947
$151$	7.94663	0.646688	0.323344	−	0.946282i	$-0.395193\pi$
$151$	7.94663	0.646688	0.323344	+	0.946282i	$0.395193\pi$
$152$	−7.79996	−0.632660
$153$	−1.13931	−0.0921075
$154$	−2.24271	−0.180723
$155$	−8.94739	−0.718672
$156$	−1.70493	−0.136503
$157$	8.48925	0.677516	0.338758	−	0.940874i	$-0.389993\pi$
$157$	8.48925	0.677516	0.338758	+	0.940874i	$0.389993\pi$
$158$	8.16964	0.649942
$159$	−8.85124	−0.701949
$160$	12.9599	1.02457
$161$	0.645556	0.0508769
$162$	0.543206	0.0426783
$163$	−5.72861	−0.448699	−0.224350	−	0.974509i	$-0.572026\pi$
$163$	−5.72861	−0.448699	−0.224350	+	0.974509i	$0.572026\pi$
$164$	0.648334	0.0506264
$165$	11.5857	0.901948
$166$	−2.20204	−0.170911
$167$	8.39701	0.649780	0.324890	−	0.945752i	$-0.394673\pi$
$167$	8.39701	0.649780	0.324890	+	0.945752i	$0.394673\pi$
$168$	1.75918	0.135723
$169$	1.00000	0.0769231
$170$	−1.51805	−0.116429
$171$	3.87568	0.296381
$172$	4.07236	0.310515
$173$	−3.10312	−0.235926	−0.117963	−	0.993018i	$-0.537636\pi$
$173$	−3.10312	−0.235926	−0.117963	+	0.993018i	$0.537636\pi$
$174$	−0.514905	−0.0390349
$175$	0.888736	0.0671821
$176$	−10.9421	−0.824791
$177$	−12.0866	−0.908487
$178$	2.44414	0.183196
$179$	11.3658	0.849518	0.424759	−	0.905306i	$-0.360359\pi$
$179$	11.3658	0.849518	0.424759	+	0.905306i	$0.360359\pi$
$180$	−4.18202	−0.311710
$181$	6.70214	0.498166	0.249083	−	0.968482i	$-0.419871\pi$
$181$	6.70214	0.498166	0.249083	+	0.968482i	$0.419871\pi$
$182$	−0.474821	−0.0351961
$183$	4.69689	0.347204
$184$	−1.48632	−0.109573
$185$	7.84710	0.576930
$186$	1.98144	0.145286
$187$	5.38126	0.393517
$188$	−10.0873	−0.735695
$189$	−0.874109	−0.0635821
$190$	5.16408	0.374642
$191$	21.1839	1.53282	0.766408	−	0.642354i	$-0.222042\pi$
$191$	21.1839	1.53282	0.766408	+	0.642354i	$0.222042\pi$
$192$	1.76325	0.127251
$193$	−3.15996	−0.227459	−0.113730	−	0.993512i	$-0.536280\pi$
$193$	−3.15996	−0.227459	−0.113730	+	0.993512i	$0.536280\pi$
$194$	0.259837	0.0186552
$195$	2.45290	0.175656
$196$	10.6318	0.759415
$197$	0.847773	0.0604013	0.0302007	−	0.999544i	$-0.490385\pi$
$197$	0.847773	0.0604013	0.0302007	+	0.999544i	$0.490385\pi$
$198$	−2.56571	−0.182337
$199$	−14.8027	−1.04934	−0.524668	−	0.851307i	$-0.675810\pi$
$199$	−14.8027	−1.04934	−0.524668	+	0.851307i	$0.675810\pi$
$200$	−2.04621	−0.144689
$201$	−16.1559	−1.13955
$202$	−6.57587	−0.462676
$203$	0.828569	0.0581541
$204$	−1.94244	−0.135998
$205$	−0.932767	−0.0651473
$206$	0.543206	0.0378469
$207$	0.738530	0.0513314
$208$	−2.31663	−0.160630
$209$	−18.3059	−1.26625
$210$	−1.16469	−0.0803712
$211$	17.0767	1.17561	0.587804	−	0.809003i	$-0.299993\pi$
$211$	17.0767	1.17561	0.587804	+	0.809003i	$0.299993\pi$
$212$	−15.0907	−1.03644
$213$	−2.39836	−0.164333
$214$	−6.04067	−0.412932
$215$	−5.85897	−0.399578
$216$	2.01254	0.136936
$217$	−3.18847	−0.216447
$218$	7.43480	0.503548
$219$	10.2947	0.695649
$220$	19.7528	1.33174
$221$	1.13931	0.0766381
$222$	−1.73777	−0.116632
$223$	20.4566	1.36988	0.684939	−	0.728600i	$-0.259829\pi$
$223$	20.4566	1.36988	0.684939	+	0.728600i	$0.259829\pi$
$224$	4.61834	0.308576
$225$	1.01673	0.0677822
$226$	−0.806186	−0.0536267
$227$	29.2951	1.94438	0.972191	−	0.234190i	$-0.0752438\pi$
$227$	29.2951	1.94438	0.972191	+	0.234190i	$0.0752438\pi$
$228$	6.60776	0.437609
$229$	−12.6431	−0.835477	−0.417738	−	0.908567i	$-0.637177\pi$
$229$	−12.6431	−0.835477	−0.417738	+	0.908567i	$0.637177\pi$
$230$	0.984040	0.0648857
$231$	4.12866	0.271646
$232$	−1.90769	−0.125246
$233$	0.167504	0.0109736	0.00548678	−	0.999985i	$-0.498253\pi$
$233$	0.167504	0.0109736	0.00548678	+	0.999985i	$0.498253\pi$
$234$	−0.543206	−0.0355105
$235$	14.5128	0.946711
$236$	−20.6068	−1.34139
$237$	−15.0397	−0.976933
$238$	−0.540967	−0.0350657
$239$	16.0189	1.03618	0.518089	−	0.855327i	$-0.326644\pi$
$239$	16.0189	1.03618	0.518089	+	0.855327i	$0.326644\pi$
$240$	−5.68248	−0.366802
$241$	−2.29564	−0.147875	−0.0739376	−	0.997263i	$-0.523557\pi$
$241$	−2.29564	−0.147875	−0.0739376	+	0.997263i	$0.523557\pi$
$242$	6.14329	0.394906
$243$	−1.00000	−0.0641500
$244$	8.00785	0.512650
$245$	−15.2961	−0.977235
$246$	0.206565	0.0131701
$247$	−3.87568	−0.246604
$248$	7.34108	0.466159
$249$	4.05379	0.256898
$250$	−5.30743	−0.335671
$251$	20.4151	1.28859	0.644295	−	0.764777i	$-0.277151\pi$
$251$	20.4151	1.28859	0.644295	+	0.764777i	$0.277151\pi$
$252$	−1.49029	−0.0938796
$253$	−3.48828	−0.219306
$254$	−1.26297	−0.0792456
$255$	2.79461	0.175005
$256$	−2.73383	−0.170864
$257$	−16.1232	−1.00574	−0.502869	−	0.864363i	$-0.667722\pi$
$257$	−16.1232	−1.00574	−0.502869	+	0.864363i	$0.667722\pi$
$258$	1.29749	0.0807784
$259$	2.79637	0.173758
$260$	4.18202	0.259358
$261$	0.947901	0.0586736
$262$	4.24832	0.262462
$263$	1.09876	0.0677526	0.0338763	−	0.999426i	$-0.489215\pi$
$263$	1.09876	0.0677526	0.0338763	+	0.999426i	$0.489215\pi$
$264$	−9.50577	−0.585040
$265$	21.7112	1.33371
$266$	1.84025	0.112833
$267$	−4.49947	−0.275363
$268$	−27.5446	−1.68255
$269$	28.6912	1.74934	0.874668	−	0.484723i	$-0.161080\pi$
$269$	28.6912	1.74934	0.874668	+	0.484723i	$0.161080\pi$
$270$	−1.33243	−0.0810892
$271$	−14.6710	−0.891197	−0.445598	−	0.895233i	$-0.647009\pi$
$271$	−14.6710	−0.891197	−0.445598	+	0.895233i	$0.647009\pi$
$272$	−2.63936	−0.160034
$273$	0.874109	0.0529035
$274$	9.84046	0.594484
$275$	−4.80231	−0.289590
$276$	1.25914	0.0757913
$277$	−5.30418	−0.318698	−0.159349	−	0.987222i	$-0.550939\pi$
$277$	−5.30418	−0.318698	−0.159349	+	0.987222i	$0.550939\pi$
$278$	6.50625	0.390219
$279$	−3.64768	−0.218381
$280$	−4.31509	−0.257876
$281$	−16.4273	−0.979972	−0.489986	−	0.871730i	$-0.662998\pi$
$281$	−16.4273	−0.979972	−0.489986	+	0.871730i	$0.662998\pi$
$282$	−3.21392	−0.191386
$283$	9.52273	0.566067	0.283034	−	0.959110i	$-0.408659\pi$
$283$	9.52273	0.566067	0.283034	+	0.959110i	$0.408659\pi$
$284$	−4.08902	−0.242639
$285$	−9.50667	−0.563127
$286$	2.56571	0.151714
$287$	−0.332398	−0.0196208
$288$	5.28348	0.311332
$289$	−15.7020	−0.923646
$290$	1.26301	0.0741667
$291$	−0.478339	−0.0280407
$292$	17.5517	1.02713
$293$	30.6087	1.78818	0.894091	−	0.447885i	$-0.147823\pi$
$293$	30.6087	1.78818	0.894091	+	0.447885i	$0.147823\pi$
$294$	3.38739	0.197557
$295$	29.6473	1.72613
$296$	−6.43832	−0.374220
$297$	4.72327	0.274072
$298$	−1.30688	−0.0757056
$299$	−0.738530	−0.0427103
$300$	1.73346	0.100081
$301$	−2.08788	−0.120344
$302$	4.31666	0.248396
$303$	12.1057	0.695452
$304$	8.97853	0.514954
$305$	−11.5210	−0.659691
$306$	−0.618878	−0.0353789
$307$	−27.2078	−1.55283	−0.776415	−	0.630222i	$-0.782964\pi$
$307$	−27.2078	−1.55283	−0.776415	+	0.630222i	$0.782964\pi$
$308$	7.03906	0.401088
$309$	−1.00000	−0.0568880
$310$	−4.86028	−0.276045
$311$	15.6719	0.888671	0.444335	−	0.895861i	$-0.353440\pi$
$311$	15.6719	0.888671	0.444335	+	0.895861i	$0.353440\pi$
$312$	−2.01254	−0.113938
$313$	22.1557	1.25232	0.626158	−	0.779696i	$-0.284626\pi$
$313$	22.1557	1.25232	0.626158	+	0.779696i	$0.284626\pi$
$314$	4.61141	0.260237
$315$	2.14410	0.120807
$316$	−25.6416	−1.44245
$317$	10.5618	0.593209	0.296605	−	0.955000i	$-0.404146\pi$
$317$	10.5618	0.593209	0.296605	+	0.955000i	$0.404146\pi$
$318$	−4.80805	−0.269622
$319$	−4.47720	−0.250675
$320$	−4.32507	−0.241779
$321$	11.1204	0.620681
$322$	0.350669	0.0195420
$323$	−4.41559	−0.245690
$324$	−1.70493	−0.0947182
$325$	−1.01673	−0.0563982
$326$	−3.11181	−0.172347
$327$	−13.6869	−0.756887
$328$	0.765309	0.0422571
$329$	5.17174	0.285127
$330$	6.29344	0.346442
$331$	32.6559	1.79493	0.897466	−	0.441083i	$-0.145406\pi$
$331$	32.6559	1.79493	0.897466	+	0.441083i	$0.145406\pi$
$332$	6.91141	0.379313
$333$	3.19911	0.175310
$334$	4.56130	0.249583
$335$	39.6288	2.16515
$336$	−2.02499	−0.110472
$337$	4.88789	0.266260	0.133130	−	0.991099i	$-0.457497\pi$
$337$	4.88789	0.266260	0.133130	+	0.991099i	$0.457497\pi$
$338$	0.543206	0.0295465
$339$	1.48413	0.0806067
$340$	4.76461	0.258397
$341$	17.2290	0.933001
$342$	2.10529	0.113841
$343$	−11.5696	−0.624702
$344$	4.80712	0.259182
$345$	−1.81154	−0.0975302
$346$	−1.68563	−0.0906202
$347$	−17.8602	−0.958783	−0.479392	−	0.877601i	$-0.659143\pi$
$347$	−17.8602	−0.958783	−0.479392	+	0.877601i	$0.659143\pi$
$348$	1.61610	0.0866322
$349$	−12.8492	−0.687803	−0.343901	−	0.939006i	$-0.611749\pi$
$349$	−12.8492	−0.687803	−0.343901	+	0.939006i	$0.611749\pi$
$350$	0.482766	0.0258049
$351$	1.00000	0.0533761
$352$	−24.9553	−1.33012
$353$	−3.65503	−0.194537	−0.0972687	−	0.995258i	$-0.531011\pi$
$353$	−3.65503	−0.194537	−0.0972687	+	0.995258i	$0.531011\pi$
$354$	−6.56552	−0.348954
$355$	5.88293	0.312234
$356$	−7.67127	−0.406577
$357$	0.995878	0.0527075
$358$	6.17396	0.326304
$359$	0.615252	0.0324718	0.0162359	−	0.999868i	$-0.494832\pi$
$359$	0.615252	0.0324718	0.0162359	+	0.999868i	$0.494832\pi$
$360$	−4.93656	−0.260180
$361$	−3.97909	−0.209426
$362$	3.64064	0.191348
$363$	−11.3093	−0.593585
$364$	1.49029	0.0781125
$365$	−25.2518	−1.32174
$366$	2.55138	0.133363
$367$	16.0289	0.836701	0.418350	−	0.908286i	$-0.362608\pi$
$367$	16.0289	0.836701	0.418350	+	0.908286i	$0.362608\pi$
$368$	1.71090	0.0891870
$369$	−0.380271	−0.0197961
$370$	4.26259	0.221601
$371$	7.73695	0.401682
$372$	−6.21902	−0.322441
$373$	4.02349	0.208328	0.104164	−	0.994560i	$-0.466783\pi$
$373$	4.02349	0.208328	0.104164	+	0.994560i	$0.466783\pi$
$374$	2.92313	0.151152
$375$	9.77057	0.504550
$376$	−11.9073	−0.614075
$377$	−0.947901	−0.0488194
$378$	−0.474821	−0.0244222
$379$	−4.15842	−0.213604	−0.106802	−	0.994280i	$-0.534061\pi$
$379$	−4.15842	−0.213604	−0.106802	+	0.994280i	$0.534061\pi$
$380$	−16.2082	−0.831462
$381$	2.32503	0.119115
$382$	11.5072	0.588762
$383$	17.2715	0.882533	0.441267	−	0.897376i	$-0.354529\pi$
$383$	17.2715	0.882533	0.441267	+	0.897376i	$0.354529\pi$
$384$	11.5248	0.588121
$385$	−10.1272	−0.516130
$386$	−1.71651	−0.0873681
$387$	−2.38858	−0.121419
$388$	−0.815534	−0.0414025
$389$	−19.8662	−1.00726	−0.503628	−	0.863921i	$-0.668002\pi$
$389$	−19.8662	−1.00726	−0.503628	+	0.863921i	$0.668002\pi$
$390$	1.33243	0.0674703
$391$	−0.841412	−0.0425520
$392$	12.5501	0.633873
$393$	−7.82082	−0.394508
$394$	0.460515	0.0232004
$395$	36.8909	1.85618
$396$	8.05284	0.404670
$397$	14.3697	0.721194	0.360597	−	0.932722i	$-0.382573\pi$
$397$	14.3697	0.721194	0.360597	+	0.932722i	$0.382573\pi$
$398$	−8.04091	−0.403054
$399$	−3.38777	−0.169601
$400$	2.35540	0.117770
$401$	22.9493	1.14603	0.573016	−	0.819544i	$-0.305773\pi$
$401$	22.9493	1.14603	0.573016	+	0.819544i	$0.305773\pi$
$402$	−8.77596	−0.437705
$403$	3.64768	0.181704
$404$	20.6393	1.02684
$405$	2.45290	0.121886
$406$	0.450083	0.0223373
$407$	−15.1103	−0.748988
$408$	−2.29290	−0.113515
$409$	−7.01008	−0.346626	−0.173313	−	0.984867i	$-0.555447\pi$
$409$	−7.01008	−0.346626	−0.173313	+	0.984867i	$0.555447\pi$
$410$	−0.506685	−0.0250234
$411$	−18.1155	−0.893573
$412$	−1.70493	−0.0839958
$413$	10.5650	0.519871
$414$	0.401174	0.0197166
$415$	−9.94355	−0.488110
$416$	−5.28348	−0.259044
$417$	−11.9775	−0.586541
$418$	−9.94387	−0.486371
$419$	−27.4635	−1.34168	−0.670840	−	0.741602i	$-0.734066\pi$
$419$	−27.4635	−1.34168	−0.670840	+	0.741602i	$0.734066\pi$
$420$	3.65554	0.178372
$421$	6.66965	0.325059	0.162529	−	0.986704i	$-0.448035\pi$
$421$	6.66965	0.325059	0.162529	+	0.986704i	$0.448035\pi$
$422$	9.27616	0.451556
$423$	5.91658	0.287674
$424$	−17.8135	−0.865098
$425$	−1.15837	−0.0561893
$426$	−1.30280	−0.0631209
$427$	−4.10559	−0.198683
$428$	18.9595	0.916442
$429$	−4.72327	−0.228042
$430$	−3.18262	−0.153480
$431$	−39.1915	−1.88779	−0.943894	−	0.330249i	$-0.892867\pi$
$431$	−39.1915	−1.88779	−0.943894	+	0.330249i	$0.892867\pi$
$432$	−2.31663	−0.111459
$433$	8.02746	0.385775	0.192888	−	0.981221i	$-0.438215\pi$
$433$	8.02746	0.385775	0.192888	+	0.981221i	$0.438215\pi$
$434$	−1.73199	−0.0831383
$435$	−2.32511	−0.111480
$436$	−23.3352	−1.11755
$437$	2.86231	0.136923
$438$	5.59212	0.267202
$439$	−30.7097	−1.46570	−0.732848	−	0.680392i	$-0.761809\pi$
$439$	−30.7097	−1.46570	−0.732848	+	0.680392i	$0.761809\pi$
$440$	23.3167	1.11158
$441$	−6.23593	−0.296949
$442$	0.618878	0.0294370
$443$	−13.9772	−0.664075	−0.332038	−	0.943266i	$-0.607736\pi$
$443$	−13.9772	−0.664075	−0.332038	+	0.943266i	$0.607736\pi$
$444$	5.45425	0.258847
$445$	11.0368	0.523193
$446$	11.1122	0.526176
$447$	2.40587	0.113794
$448$	−1.54127	−0.0728182
$449$	33.1319	1.56359	0.781796	−	0.623534i	$-0.214304\pi$
$449$	33.1319	1.56359	0.781796	+	0.623534i	$0.214304\pi$
$450$	0.552295	0.0260355
$451$	1.79612	0.0845761
$452$	2.53033	0.119017
$453$	−7.94663	−0.373365
$454$	15.9132	0.746846
$455$	−2.14410	−0.100517
$456$	7.79996	0.365266
$457$	20.1152	0.940952	0.470476	−	0.882413i	$-0.344082\pi$
$457$	20.1152	0.940952	0.470476	+	0.882413i	$0.344082\pi$
$458$	−6.86778	−0.320910
$459$	1.13931	0.0531783
$460$	−3.08855	−0.144004
$461$	−19.1274	−0.890851	−0.445426	−	0.895319i	$-0.646948\pi$
$461$	−19.1274	−0.890851	−0.445426	+	0.895319i	$0.646948\pi$
$462$	2.24271	0.104340
$463$	−28.9045	−1.34330	−0.671652	−	0.740866i	$-0.734415\pi$
$463$	−28.9045	−1.34330	−0.671652	+	0.740866i	$0.734415\pi$
$464$	2.19594	0.101944
$465$	8.94739	0.414925
$466$	0.0909892	0.00421499
$467$	7.35954	0.340559	0.170279	−	0.985396i	$-0.445533\pi$
$467$	7.35954	0.340559	0.170279	+	0.985396i	$0.445533\pi$
$468$	1.70493	0.0788103
$469$	14.1220	0.652093
$470$	7.88344	0.363636
$471$	−8.48925	−0.391164
$472$	−24.3248	−1.11964
$473$	11.2819	0.518744
$474$	−8.16964	−0.375244
$475$	3.94053	0.180804
$476$	1.69790	0.0778231
$477$	8.85124	0.405271
$478$	8.70157	0.398001
$479$	−2.12245	−0.0969772	−0.0484886	−	0.998824i	$-0.515440\pi$
$479$	−2.12245	−0.0969772	−0.0484886	+	0.998824i	$0.515440\pi$
$480$	−12.9599	−0.591535
$481$	−3.19911	−0.145867
$482$	−1.24701	−0.0567995
$483$	−0.645556	−0.0293738
$484$	−19.2816	−0.876435
$485$	1.17332	0.0532777
$486$	−0.543206	−0.0246403
$487$	−6.42767	−0.291265	−0.145633	−	0.989339i	$-0.546522\pi$
$487$	−6.42767	−0.291265	−0.145633	+	0.989339i	$0.546522\pi$
$488$	9.45266	0.427902
$489$	5.72861	0.259056
$490$	−8.30895	−0.375360
$491$	9.83079	0.443657	0.221829	−	0.975086i	$-0.428797\pi$
$491$	9.83079	0.443657	0.221829	+	0.975086i	$0.428797\pi$
$492$	−0.648334	−0.0292292
$493$	−1.07995	−0.0486385
$494$	−2.10529	−0.0947216
$495$	−11.5857	−0.520740
$496$	−8.45032	−0.379431
$497$	2.09642	0.0940375
$498$	2.20204	0.0986758
$499$	21.1561	0.947078	0.473539	−	0.880773i	$-0.342976\pi$
$499$	21.1561	0.947078	0.473539	+	0.880773i	$0.342976\pi$
$500$	16.6581	0.744973
$501$	−8.39701	−0.375151
$502$	11.0896	0.494953
$503$	2.64013	0.117717	0.0588587	−	0.998266i	$-0.481254\pi$
$503$	2.64013	0.117717	0.0588587	+	0.998266i	$0.481254\pi$
$504$	−1.75918	−0.0783600
$505$	−29.6940	−1.32137
$506$	−1.89485	−0.0842365
$507$	−1.00000	−0.0444116
$508$	3.96400	0.175874
$509$	−34.9693	−1.54999	−0.774993	−	0.631970i	$-0.782247\pi$
$509$	−34.9693	−1.54999	−0.774993	+	0.631970i	$0.782247\pi$
$510$	1.51805	0.0672203
$511$	−8.99865	−0.398077
$512$	21.5645	0.953026
$513$	−3.87568	−0.171116
$514$	−8.75822	−0.386308
$515$	2.45290	0.108088
$516$	−4.07236	−0.179276
$517$	−27.9456	−1.22905
$518$	1.51900	0.0667412
$519$	3.10312	0.136212
$520$	4.93656	0.216482
$521$	−6.82238	−0.298894	−0.149447	−	0.988770i	$-0.547749\pi$
$521$	−6.82238	−0.298894	−0.149447	+	0.988770i	$0.547749\pi$
$522$	0.514905	0.0225368
$523$	−27.4275	−1.19932	−0.599660	−	0.800255i	$-0.704698\pi$
$523$	−27.4275	−1.19932	−0.599660	+	0.800255i	$0.704698\pi$
$524$	−13.3339	−0.582496
$525$	−0.888736	−0.0387876
$526$	0.596854	0.0260241
$527$	4.15582	0.181030
$528$	10.9421	0.476193
$529$	−22.4546	−0.976286
$530$	11.7937	0.512284
$531$	12.0866	0.524515
$532$	−5.77590	−0.250417
$533$	0.380271	0.0164714
$534$	−2.44414	−0.105768
$535$	−27.2773	−1.17930
$536$	−32.5143	−1.40440
$537$	−11.3658	−0.490470
$538$	15.5852	0.671927
$539$	29.4540	1.26867
$540$	4.18202	0.179966
$541$	−12.6218	−0.542652	−0.271326	−	0.962488i	$-0.587462\pi$
$541$	−12.6218	−0.542652	−0.271326	+	0.962488i	$0.587462\pi$
$542$	−7.96935	−0.342313
$543$	−6.70214	−0.287616
$544$	−6.01951	−0.258084
$545$	33.5726	1.43809
$546$	0.474821	0.0203205
$547$	−2.77976	−0.118854	−0.0594269	−	0.998233i	$-0.518927\pi$
$547$	−2.77976	−0.118854	−0.0594269	+	0.998233i	$0.518927\pi$
$548$	−30.8857	−1.31937
$549$	−4.69689	−0.200458
$550$	−2.60864	−0.111233
$551$	3.67376	0.156508
$552$	1.48632	0.0632620
$553$	13.1463	0.559039
$554$	−2.88126	−0.122413
$555$	−7.84710	−0.333091
$556$	−20.4208	−0.866034
$557$	−20.4961	−0.868446	−0.434223	−	0.900805i	$-0.642977\pi$
$557$	−20.4961	−0.868446	−0.434223	+	0.900805i	$0.642977\pi$
$558$	−1.98144	−0.0838810
$559$	2.38858	0.101026
$560$	4.96710	0.209898
$561$	−5.38126	−0.227197
$562$	−8.92342	−0.376412
$563$	−3.66744	−0.154564	−0.0772820	−	0.997009i	$-0.524624\pi$
$563$	−3.66744	−0.154564	−0.0772820	+	0.997009i	$0.524624\pi$
$564$	10.0873	0.424754
$565$	−3.64042	−0.153154
$566$	5.17280	0.217429
$567$	0.874109	0.0367091
$568$	−4.82678	−0.202527
$569$	21.3867	0.896579	0.448289	−	0.893888i	$-0.352033\pi$
$569$	21.3867	0.896579	0.448289	+	0.893888i	$0.352033\pi$
$570$	−5.16408	−0.216299
$571$	−36.2259	−1.51601	−0.758003	−	0.652252i	$-0.773825\pi$
$571$	−36.2259	−1.51601	−0.758003	+	0.652252i	$0.773825\pi$
$572$	−8.05284	−0.336706
$573$	−21.1839	−0.884972
$574$	−0.180561	−0.00753645
$575$	0.750888	0.0313142
$576$	−1.76325	−0.0734686
$577$	−1.68765	−0.0702578	−0.0351289	−	0.999383i	$-0.511184\pi$
$577$	−1.68765	−0.0702578	−0.0351289	+	0.999383i	$0.511184\pi$
$578$	−8.52941	−0.354776
$579$	3.15996	0.131324
$580$	−3.96414	−0.164602
$581$	−3.54345	−0.147007
$582$	−0.259837	−0.0107706
$583$	−41.8069	−1.73146
$584$	20.7184	0.857333
$585$	−2.45290	−0.101415
$586$	16.6268	0.686849
$587$	−7.33376	−0.302697	−0.151348	−	0.988480i	$-0.548362\pi$
$587$	−7.33376	−0.302697	−0.151348	+	0.988480i	$0.548362\pi$
$588$	−10.6318	−0.438449
$589$	−14.1372	−0.582514
$590$	16.1046	0.663016
$591$	−0.847773	−0.0348727
$592$	7.41116	0.304597
$593$	9.13724	0.375222	0.187611	−	0.982243i	$-0.439926\pi$
$593$	9.13724	0.375222	0.187611	+	0.982243i	$0.439926\pi$
$594$	2.56571	0.105272
$595$	−2.44279	−0.100145
$596$	4.10183	0.168018
$597$	14.8027	0.605834
$598$	−0.401174	−0.0164052
$599$	−8.14586	−0.332831	−0.166415	−	0.986056i	$-0.553219\pi$
$599$	−8.14586	−0.332831	−0.166415	+	0.986056i	$0.553219\pi$
$600$	2.04621	0.0835363
$601$	−28.7811	−1.17401	−0.587003	−	0.809585i	$-0.699692\pi$
$601$	−28.7811	−1.17401	−0.587003	+	0.809585i	$0.699692\pi$
$602$	−1.13415	−0.0462245
$603$	16.1559	0.657918
$604$	−13.5484	−0.551278
$605$	27.7407	1.12782
$606$	6.57587	0.267126
$607$	18.1625	0.737195	0.368597	−	0.929589i	$-0.379838\pi$
$607$	18.1625	0.737195	0.368597	+	0.929589i	$0.379838\pi$
$608$	20.4771	0.830456
$609$	−0.828569	−0.0335753
$610$	−6.25828	−0.253390
$611$	−5.91658	−0.239359
$612$	1.94244	0.0785183
$613$	20.6241	0.832998	0.416499	−	0.909136i	$-0.363257\pi$
$613$	20.6241	0.832998	0.416499	+	0.909136i	$0.363257\pi$
$614$	−14.7794	−0.596449
$615$	0.932767	0.0376128
$616$	8.30908	0.334782
$617$	−28.6472	−1.15329	−0.576646	−	0.816994i	$-0.695639\pi$
$617$	−28.6472	−1.15329	−0.576646	+	0.816994i	$0.695639\pi$
$618$	−0.543206	−0.0218509
$619$	45.0266	1.80977	0.904886	−	0.425653i	$-0.139956\pi$
$619$	45.0266	1.80977	0.904886	+	0.425653i	$0.139956\pi$
$620$	15.2547	0.612642
$621$	−0.738530	−0.0296362
$622$	8.51305	0.341342
$623$	3.93303	0.157573
$624$	2.31663	0.0927395
$625$	−29.0499	−1.16200
$626$	12.0351	0.481020
$627$	18.3059	0.731068
$628$	−14.4736	−0.577558
$629$	−3.64476	−0.145326
$630$	1.16469	0.0464023
$631$	22.3372	0.889230	0.444615	−	0.895722i	$-0.353340\pi$
$631$	22.3372	0.889230	0.444615	+	0.895722i	$0.353340\pi$
$632$	−30.2679	−1.20399
$633$	−17.0767	−0.678738
$634$	5.73722	0.227854
$635$	−5.70306	−0.226319
$636$	15.0907	0.598386
$637$	6.23593	0.247077
$638$	−2.43204	−0.0962854
$639$	2.39836	0.0948775
$640$	−28.2692	−1.11744
$641$	−27.9960	−1.10578	−0.552888	−	0.833256i	$-0.686474\pi$
$641$	−27.9960	−1.10578	−0.552888	+	0.833256i	$0.686474\pi$
$642$	6.04067	0.238406
$643$	−4.75342	−0.187457	−0.0937283	−	0.995598i	$-0.529878\pi$
$643$	−4.75342	−0.187457	−0.0937283	+	0.995598i	$0.529878\pi$
$644$	−1.10063	−0.0433707
$645$	5.85897	0.230697
$646$	−2.39857	−0.0943706
$647$	−28.9235	−1.13710	−0.568550	−	0.822648i	$-0.692496\pi$
$647$	−28.9235	−1.13710	−0.568550	+	0.822648i	$0.692496\pi$
$648$	−2.01254	−0.0790600
$649$	−57.0885	−2.24092
$650$	−0.552295	−0.0216628
$651$	3.18847	0.124966
$652$	9.76686	0.382500
$653$	10.7203	0.419518	0.209759	−	0.977753i	$-0.432732\pi$
$653$	10.7203	0.419518	0.209759	+	0.977753i	$0.432732\pi$
$654$	−7.43480	−0.290724
$655$	19.1837	0.749570
$656$	−0.880948	−0.0343952
$657$	−10.2947	−0.401633
$658$	2.80932	0.109519
$659$	−26.3136	−1.02503	−0.512515	−	0.858678i	$-0.671286\pi$
$659$	−26.3136	−1.02503	−0.512515	+	0.858678i	$0.671286\pi$
$660$	−19.7528	−0.768878
$661$	15.7151	0.611245	0.305622	−	0.952153i	$-0.401135\pi$
$661$	15.7151	0.611245	0.305622	+	0.952153i	$0.401135\pi$
$662$	17.7389	0.689442
$663$	−1.13931	−0.0442470
$664$	8.15840	0.316607
$665$	8.30987	0.322243
$666$	1.73777	0.0673373
$667$	0.700053	0.0271062
$668$	−14.3163	−0.553914
$669$	−20.4566	−0.790899
$670$	21.5266	0.831644
$671$	22.1847	0.856430
$672$	−4.61834	−0.178156
$673$	−2.92500	−0.112750	−0.0563752	−	0.998410i	$-0.517954\pi$
$673$	−2.92500	−0.112750	−0.0563752	+	0.998410i	$0.517954\pi$
$674$	2.65513	0.102272
$675$	−1.01673	−0.0391341
$676$	−1.70493	−0.0655741
$677$	−26.7989	−1.02996	−0.514982	−	0.857201i	$-0.672201\pi$
$677$	−26.7989	−1.02996	−0.514982	+	0.857201i	$0.672201\pi$
$678$	0.806186	0.0309614
$679$	0.418121	0.0160460
$680$	5.62426	0.215680
$681$	−29.2951	−1.12259
$682$	9.35888	0.358370
$683$	22.8745	0.875268	0.437634	−	0.899153i	$-0.355817\pi$
$683$	22.8745	0.875268	0.437634	+	0.899153i	$0.355817\pi$
$684$	−6.60776	−0.252654
$685$	44.4356	1.69780
$686$	−6.28470	−0.239951
$687$	12.6431	0.482363
$688$	−5.53347	−0.210962
$689$	−8.85124	−0.337206
$690$	−0.984040	−0.0374618
$691$	−31.4547	−1.19659	−0.598296	−	0.801275i	$-0.704155\pi$
$691$	−31.4547	−1.19659	−0.598296	+	0.801275i	$0.704155\pi$
$692$	5.29060	0.201118
$693$	−4.12866	−0.156835
$694$	−9.70174	−0.368273
$695$	29.3797	1.11443
$696$	1.90769	0.0723107
$697$	0.433245	0.0164103
$698$	−6.97977	−0.264188
$699$	−0.167504	−0.00633559
$700$	−1.51523	−0.0572703
$701$	−19.0881	−0.720949	−0.360474	−	0.932769i	$-0.617385\pi$
$701$	−19.0881	−0.720949	−0.360474	+	0.932769i	$0.617385\pi$
$702$	0.543206	0.0205020
$703$	12.3987	0.467627
$704$	8.32830	0.313885
$705$	−14.5128	−0.546584
$706$	−1.98543	−0.0747227
$707$	−10.5817	−0.397965
$708$	20.6068	0.774452
$709$	−30.8393	−1.15819	−0.579097	−	0.815259i	$-0.696595\pi$
$709$	−30.8393	−1.15819	−0.579097	+	0.815259i	$0.696595\pi$
$710$	3.19564	0.119930
$711$	15.0397	0.564032
$712$	−9.05535	−0.339364
$713$	−2.69392	−0.100888
$714$	0.540967	0.0202452
$715$	11.5857	0.433282
$716$	−19.3778	−0.724184
$717$	−16.0189	−0.598238
$718$	0.334208	0.0124725
$719$	40.1561	1.49757	0.748785	−	0.662813i	$-0.230638\pi$
$719$	40.1561	1.49757	0.748785	+	0.662813i	$0.230638\pi$
$720$	5.68248	0.211773
$721$	0.874109	0.0325535
$722$	−2.16147	−0.0804414
$723$	2.29564	0.0853758
$724$	−11.4267	−0.424669
$725$	0.963763	0.0357933
$726$	−6.14329	−0.227999
$727$	−37.9051	−1.40582	−0.702911	−	0.711278i	$-0.748117\pi$
$727$	−37.9051	−1.40582	−0.702911	+	0.711278i	$0.748117\pi$
$728$	1.75918	0.0651994
$729$	1.00000	0.0370370
$730$	−13.7169	−0.507686
$731$	2.72133	0.100652
$732$	−8.00785	−0.295979
$733$	−53.9961	−1.99439	−0.997196	−	0.0748328i	$-0.976158\pi$
$733$	−53.9961	−1.99439	−0.997196	+	0.0748328i	$0.976158\pi$
$734$	8.70698	0.321380
$735$	15.2961	0.564207
$736$	3.90201	0.143830
$737$	−76.3086	−2.81086
$738$	−0.206565	−0.00760377
$739$	−38.1604	−1.40375	−0.701877	−	0.712298i	$-0.747654\pi$
$739$	−38.1604	−1.40375	−0.701877	+	0.712298i	$0.747654\pi$
$740$	−13.3787	−0.491812
$741$	3.87568	0.142377
$742$	4.20276	0.154288
$743$	21.1552	0.776107	0.388054	−	0.921637i	$-0.373148\pi$
$743$	21.1552	0.776107	0.388054	+	0.921637i	$0.373148\pi$
$744$	−7.34108	−0.269137
$745$	−5.90136	−0.216209
$746$	2.18558	0.0800199
$747$	−4.05379	−0.148320
$748$	−9.17466	−0.335459
$749$	−9.72045	−0.355178
$750$	5.30743	0.193800
$751$	−15.9611	−0.582430	−0.291215	−	0.956658i	$-0.594059\pi$
$751$	−15.9611	−0.582430	−0.291215	+	0.956658i	$0.594059\pi$
$752$	13.7066	0.499827
$753$	−20.4151	−0.743968
$754$	−0.514905	−0.0187517
$755$	19.4923	0.709398
$756$	1.49029	0.0542014
$757$	−51.5171	−1.87242	−0.936211	−	0.351440i	$-0.885692\pi$
$757$	−51.5171	−1.87242	−0.936211	+	0.351440i	$0.885692\pi$
$758$	−2.25888	−0.0820462
$759$	3.48828	0.126617
$760$	−19.1325	−0.694010
$761$	27.4304	0.994353	0.497176	−	0.867649i	$-0.334370\pi$
$761$	27.4304	0.994353	0.497176	+	0.867649i	$0.334370\pi$
$762$	1.26297	0.0457525
$763$	11.9638	0.433120
$764$	−36.1171	−1.30667
$765$	−2.79461	−0.101039
$766$	9.38199	0.338985
$767$	−12.0866	−0.436423
$768$	2.73383	0.0986486
$769$	32.8775	1.18559	0.592796	−	0.805352i	$-0.298024\pi$
$769$	32.8775	1.18559	0.592796	+	0.805352i	$0.298024\pi$
$770$	−5.50115	−0.198248
$771$	16.1232	0.580663
$772$	5.38751	0.193901
$773$	21.0273	0.756301	0.378151	−	0.925744i	$-0.376560\pi$
$773$	21.0273	0.756301	0.378151	+	0.925744i	$0.376560\pi$
$774$	−1.29749	−0.0466374
$775$	−3.70871	−0.133221
$776$	−0.962676	−0.0345581
$777$	−2.79637	−0.100319
$778$	−10.7914	−0.386892
$779$	−1.47381	−0.0528047
$780$	−4.18202	−0.149740
$781$	−11.3281	−0.405351
$782$	−0.457060	−0.0163444
$783$	−0.947901	−0.0338752
$784$	−14.4464	−0.515942
$785$	20.8233	0.743216
$786$	−4.24832	−0.151532
$787$	−44.7932	−1.59671	−0.798353	−	0.602190i	$-0.794295\pi$
$787$	−44.7932	−1.59671	−0.798353	+	0.602190i	$0.794295\pi$
$788$	−1.44539	−0.0514899
$789$	−1.09876	−0.0391170
$790$	20.0393	0.712968
$791$	−1.29729	−0.0461263
$792$	9.50577	0.337773
$793$	4.69689	0.166791
$794$	7.80569	0.277014
$795$	−21.7112	−0.770018
$796$	25.2375	0.894520
$797$	19.9674	0.707281	0.353641	−	0.935381i	$-0.384944\pi$
$797$	19.9674	0.707281	0.353641	+	0.935381i	$0.384944\pi$
$798$	−1.84025	−0.0651443
$799$	−6.74080	−0.238473
$800$	5.37189	0.189925
$801$	4.49947	0.158981
$802$	12.4662	0.440196
$803$	48.6245	1.71592
$804$	27.5446	0.971422
$805$	1.58349	0.0558105
$806$	1.98144	0.0697932
$807$	−28.6912	−1.00998
$808$	24.3631	0.857091
$809$	37.9429	1.33400	0.667001	−	0.745057i	$-0.267578\pi$
$809$	37.9429	1.33400	0.667001	+	0.745057i	$0.267578\pi$
$810$	1.33243	0.0468169
$811$	−36.9905	−1.29891	−0.649456	−	0.760400i	$-0.725003\pi$
$811$	−36.9905	−1.29891	−0.649456	+	0.760400i	$0.725003\pi$
$812$	−1.41265	−0.0495743
$813$	14.6710	0.514533
$814$	−8.20798	−0.287690
$815$	−14.0517	−0.492210
$816$	2.63936	0.0923959
$817$	−9.25739	−0.323875
$818$	−3.80792	−0.133141
$819$	−0.874109	−0.0305438
$820$	1.59030	0.0555357
$821$	−8.59722	−0.300045	−0.150023	−	0.988683i	$-0.547935\pi$
$821$	−8.59722	−0.300045	−0.150023	+	0.988683i	$0.547935\pi$
$822$	−9.84046	−0.343225
$823$	31.5103	1.09838	0.549189	−	0.835698i	$-0.314937\pi$
$823$	31.5103	1.09838	0.549189	+	0.835698i	$0.314937\pi$
$824$	−2.01254	−0.0701101
$825$	4.80231	0.167195
$826$	5.73898	0.199685
$827$	−1.24592	−0.0433249	−0.0216624	−	0.999765i	$-0.506896\pi$
$827$	−1.24592	−0.0433249	−0.0216624	+	0.999765i	$0.506896\pi$
$828$	−1.25914	−0.0437581
$829$	41.2542	1.43282	0.716409	−	0.697681i	$-0.245785\pi$
$829$	41.2542	1.43282	0.716409	+	0.697681i	$0.245785\pi$
$830$	−5.40139	−0.187485
$831$	5.30418	0.184000
$832$	1.76325	0.0611296
$833$	7.10464	0.246161
$834$	−6.50625	−0.225293
$835$	20.5971	0.712790
$836$	31.2102	1.07943
$837$	3.64768	0.126082
$838$	−14.9183	−0.515345
$839$	26.0917	0.900787	0.450393	−	0.892830i	$-0.351284\pi$
$839$	26.0917	0.900787	0.450393	+	0.892830i	$0.351284\pi$
$840$	4.31509	0.148885
$841$	−28.1015	−0.969017
$842$	3.62299	0.124857
$843$	16.4273	0.565787
$844$	−29.1145	−1.00216
$845$	2.45290	0.0843824
$846$	3.21392	0.110497
$847$	9.88558	0.339672
$848$	20.5051	0.704148
$849$	−9.52273	−0.326819
$850$	−0.629234	−0.0215825
$851$	2.36264	0.0809901
$852$	4.08902	0.140088
$853$	−33.9307	−1.16177	−0.580883	−	0.813987i	$-0.697293\pi$
$853$	−33.9307	−1.16177	−0.580883	+	0.813987i	$0.697293\pi$
$854$	−2.23018	−0.0763152
$855$	9.50667	0.325121
$856$	22.3802	0.764941
$857$	−48.8798	−1.66970	−0.834850	−	0.550477i	$-0.814446\pi$
$857$	−48.8798	−1.66970	−0.834850	+	0.550477i	$0.814446\pi$
$858$	−2.56571	−0.0875919
$859$	−48.8971	−1.66835	−0.834174	−	0.551501i	$-0.814055\pi$
$859$	−48.8971	−1.66835	−0.834174	+	0.551501i	$0.814055\pi$
$860$	9.98911	0.340626
$861$	0.332398	0.0113281
$862$	−21.2890	−0.725108
$863$	15.3107	0.521182	0.260591	−	0.965449i	$-0.416083\pi$
$863$	15.3107	0.521182	0.260591	+	0.965449i	$0.416083\pi$
$864$	−5.28348	−0.179748
$865$	−7.61166	−0.258804
$866$	4.36056	0.148178
$867$	15.7020	0.533267
$868$	5.43610	0.184513
$869$	−71.0366	−2.40975
$870$	−1.26301	−0.0428202
$871$	−16.1559	−0.547420
$872$	−27.5454	−0.932804
$873$	0.478339	0.0161893
$874$	1.55482	0.0525926
$875$	−8.54054	−0.288723
$876$	−17.5517	−0.593015
$877$	1.42018	0.0479562	0.0239781	−	0.999712i	$-0.492367\pi$
$877$	1.42018	0.0479562	0.0239781	+	0.999712i	$0.492367\pi$
$878$	−16.6817	−0.562980
$879$	−30.6087	−1.03241
$880$	−26.8399	−0.904773
$881$	35.9831	1.21230	0.606151	−	0.795350i	$-0.292713\pi$
$881$	35.9831	1.21230	0.606151	+	0.795350i	$0.292713\pi$
$882$	−3.38739	−0.114060
$883$	6.06242	0.204017	0.102008	−	0.994784i	$-0.467473\pi$
$883$	6.06242	0.204017	0.102008	+	0.994784i	$0.467473\pi$
$884$	−1.94244	−0.0653312
$885$	−29.6473	−0.996584
$886$	−7.59248	−0.255074
$887$	20.2959	0.681471	0.340735	−	0.940159i	$-0.389324\pi$
$887$	20.2959	0.681471	0.340735	+	0.940159i	$0.389324\pi$
$888$	6.43832	0.216056
$889$	−2.03233	−0.0681620
$890$	5.99523	0.200961
$891$	−4.72327	−0.158236
$892$	−34.8771	−1.16777
$893$	22.9308	0.767350
$894$	1.30688	0.0437087
$895$	27.8792	0.931897
$896$	−10.0739	−0.336546
$897$	0.738530	0.0246588
$898$	17.9975	0.600583
$899$	−3.45764	−0.115319
$900$	−1.73346	−0.0577819
$901$	−10.0843	−0.335956
$902$	0.975664	0.0324861
$903$	2.08788	0.0694804
$904$	2.98686	0.0993415
$905$	16.4397	0.546474
$906$	−4.31666	−0.143411
$907$	48.8957	1.62355	0.811777	−	0.583967i	$-0.198500\pi$
$907$	48.8957	1.62355	0.811777	+	0.583967i	$0.198500\pi$
$908$	−49.9460	−1.65751
$909$	−12.1057	−0.401520
$910$	−1.16469	−0.0386091
$911$	58.4479	1.93647	0.968233	−	0.250050i	$-0.0804472\pi$
$911$	58.4479	1.93647	0.968233	+	0.250050i	$0.0804472\pi$
$912$	−8.97853	−0.297309
$913$	19.1471	0.633678
$914$	10.9267	0.361424
$915$	11.5210	0.380873
$916$	21.5555	0.712214
$917$	6.83625	0.225753
$918$	0.618878	0.0204260
$919$	7.34680	0.242349	0.121174	−	0.992631i	$-0.461334\pi$
$919$	7.34680	0.242349	0.121174	+	0.992631i	$0.461334\pi$
$920$	−3.64580	−0.120198
$921$	27.2078	0.896527
$922$	−10.3901	−0.342180
$923$	−2.39836	−0.0789428
$924$	−7.03906	−0.231568
$925$	3.25264	0.106946
$926$	−15.7011	−0.515969
$927$	1.00000	0.0328443
$928$	5.00822	0.164403
$929$	31.0292	1.01803	0.509017	−	0.860756i	$-0.330009\pi$
$929$	31.0292	1.01803	0.509017	+	0.860756i	$0.330009\pi$
$930$	4.86028	0.159375
$931$	−24.1685	−0.792090
$932$	−0.285582	−0.00935456
$933$	−15.6719	−0.513074
$934$	3.99774	0.130810
$935$	13.1997	0.431677
$936$	2.01254	0.0657819
$937$	19.4387	0.635033	0.317517	−	0.948253i	$-0.397151\pi$
$937$	19.4387	0.635033	0.317517	+	0.948253i	$0.397151\pi$
$938$	7.67114	0.250472
$939$	−22.1557	−0.723025
$940$	−24.7433	−0.807037
$941$	40.6139	1.32398	0.661988	−	0.749514i	$-0.269713\pi$
$941$	40.6139	1.32398	0.661988	+	0.749514i	$0.269713\pi$
$942$	−4.61141	−0.150248
$943$	−0.280841	−0.00914545
$944$	28.0003	0.911331
$945$	−2.14410	−0.0697477
$946$	6.12841	0.199252
$947$	−28.4552	−0.924668	−0.462334	−	0.886706i	$-0.652988\pi$
$947$	−28.4552	−0.924668	−0.462334	+	0.886706i	$0.652988\pi$
$948$	25.6416	0.832800
$949$	10.2947	0.334179
$950$	2.14052	0.0694477
$951$	−10.5618	−0.342489
$952$	2.00424	0.0649579
$953$	−11.1528	−0.361276	−0.180638	−	0.983550i	$-0.557816\pi$
$953$	−11.1528	−0.361276	−0.180638	+	0.983550i	$0.557816\pi$
$954$	4.80805	0.155666
$955$	51.9622	1.68146
$956$	−27.3111	−0.883304
$957$	4.47720	0.144727
$958$	−1.15293	−0.0372494
$959$	15.8349	0.511337
$960$	4.32507	0.139591
$961$	−17.6945	−0.570789
$962$	−1.73777	−0.0560281
$963$	−11.1204	−0.358350
$964$	3.91390	0.126058
$965$	−7.75109	−0.249516
$966$	−0.350669	−0.0112826
$967$	−16.7408	−0.538349	−0.269175	−	0.963091i	$-0.586751\pi$
$967$	−16.7408	−0.538349	−0.269175	+	0.963091i	$0.586751\pi$
$968$	−22.7604	−0.731548
$969$	4.41559	0.141849
$970$	0.637354	0.0204642
$971$	10.0103	0.321246	0.160623	−	0.987016i	$-0.448650\pi$
$971$	10.0103	0.321246	0.160623	+	0.987016i	$0.448650\pi$
$972$	1.70493	0.0546856
$973$	10.4696	0.335641
$974$	−3.49155	−0.111876
$975$	1.01673	0.0325615
$976$	−10.8810	−0.348291
$977$	−54.9072	−1.75664	−0.878318	−	0.478076i	$-0.841334\pi$
$977$	−54.9072	−1.75664	−0.878318	+	0.478076i	$0.841334\pi$
$978$	3.11181	0.0995048
$979$	−21.2522	−0.679224
$980$	26.0788	0.833057
$981$	13.6869	0.436989
$982$	5.34014	0.170411
$983$	33.9975	1.08435	0.542175	−	0.840265i	$-0.317601\pi$
$983$	33.9975	1.08435	0.542175	+	0.840265i	$0.317601\pi$
$984$	−0.765309	−0.0243972
$985$	2.07950	0.0662585
$986$	−0.586635	−0.0186823
$987$	−5.17174	−0.164618
$988$	6.60776	0.210221
$989$	−1.76404	−0.0560932
$990$	−6.29344	−0.200019
$991$	−49.9609	−1.58706	−0.793530	−	0.608531i	$-0.791759\pi$
$991$	−49.9609	−1.58706	−0.793530	+	0.608531i	$0.791759\pi$
$992$	−19.2724	−0.611900
$993$	−32.6559	−1.03630
$994$	1.13879	0.0361202
$995$	−36.3096	−1.15109
$996$	−6.91141	−0.218997
$997$	−2.48157	−0.0785920	−0.0392960	−	0.999228i	$-0.512512\pi$
$997$	−2.48157	−0.0785920	−0.0392960	+	0.999228i	$0.512512\pi$
$998$	11.4921	0.363777
$999$	−3.19911	−0.101215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.13	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+0.543206 q^{2} -1.00000 q^{3} -1.70493 q^{4} +2.45290 q^{5} -0.543206 q^{6} +0.874109 q^{7} -2.01254 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.543206 q^{2} -1.00000 q^{3} -1.70493 q^{4} +2.45290 q^{5} -0.543206 q^{6} +0.874109 q^{7} -2.01254 q^{8} +1.00000 q^{9} +1.33243 q^{10} -4.72327 q^{11} +1.70493 q^{12} -1.00000 q^{13} +0.474821 q^{14} -2.45290 q^{15} +2.31663 q^{16} -1.13931 q^{17} +0.543206 q^{18} +3.87568 q^{19} -4.18202 q^{20} -0.874109 q^{21} -2.56571 q^{22} +0.738530 q^{23} +2.01254 q^{24} +1.01673 q^{25} -0.543206 q^{26} -1.00000 q^{27} -1.49029 q^{28} +0.947901 q^{29} -1.33243 q^{30} -3.64768 q^{31} +5.28348 q^{32} +4.72327 q^{33} -0.618878 q^{34} +2.14410 q^{35} -1.70493 q^{36} +3.19911 q^{37} +2.10529 q^{38} +1.00000 q^{39} -4.93656 q^{40} -0.380271 q^{41} -0.474821 q^{42} -2.38858 q^{43} +8.05284 q^{44} +2.45290 q^{45} +0.401174 q^{46} +5.91658 q^{47} -2.31663 q^{48} -6.23593 q^{49} +0.552295 q^{50} +1.13931 q^{51} +1.70493 q^{52} +8.85124 q^{53} -0.543206 q^{54} -11.5857 q^{55} -1.75918 q^{56} -3.87568 q^{57} +0.514905 q^{58} +12.0866 q^{59} +4.18202 q^{60} -4.69689 q^{61} -1.98144 q^{62} +0.874109 q^{63} -1.76325 q^{64} -2.45290 q^{65} +2.56571 q^{66} +16.1559 q^{67} +1.94244 q^{68} -0.738530 q^{69} +1.16469 q^{70} +2.39836 q^{71} -2.01254 q^{72} -10.2947 q^{73} +1.73777 q^{74} -1.01673 q^{75} -6.60776 q^{76} -4.12866 q^{77} +0.543206 q^{78} +15.0397 q^{79} +5.68248 q^{80} +1.00000 q^{81} -0.206565 q^{82} -4.05379 q^{83} +1.49029 q^{84} -2.79461 q^{85} -1.29749 q^{86} -0.947901 q^{87} +9.50577 q^{88} +4.49947 q^{89} +1.33243 q^{90} -0.874109 q^{91} -1.25914 q^{92} +3.64768 q^{93} +3.21392 q^{94} +9.50667 q^{95} -5.28348 q^{96} +0.478339 q^{97} -3.38739 q^{98} -4.72327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 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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