LMFDB - Embedded newform 4017.2.a.h.1.12

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:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-0.633751 q^{2} -1.00000 q^{3} -1.59836 q^{4} +3.72594 q^{5} +0.633751 q^{6} -0.819859 q^{7} +2.28046 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.633751 q^{2} -1.00000 q^{3} -1.59836 q^{4} +3.72594 q^{5} +0.633751 q^{6} -0.819859 q^{7} +2.28046 q^{8} +1.00000 q^{9} -2.36132 q^{10} -5.95407 q^{11} +1.59836 q^{12} +1.00000 q^{13} +0.519586 q^{14} -3.72594 q^{15} +1.75147 q^{16} +0.220680 q^{17} -0.633751 q^{18} +3.58549 q^{19} -5.95539 q^{20} +0.819859 q^{21} +3.77340 q^{22} -6.39569 q^{23} -2.28046 q^{24} +8.88262 q^{25} -0.633751 q^{26} -1.00000 q^{27} +1.31043 q^{28} +2.80146 q^{29} +2.36132 q^{30} +2.92031 q^{31} -5.67093 q^{32} +5.95407 q^{33} -0.139856 q^{34} -3.05474 q^{35} -1.59836 q^{36} -1.86799 q^{37} -2.27231 q^{38} -1.00000 q^{39} +8.49687 q^{40} +2.27753 q^{41} -0.519586 q^{42} -4.99809 q^{43} +9.51674 q^{44} +3.72594 q^{45} +4.05328 q^{46} +0.499059 q^{47} -1.75147 q^{48} -6.32783 q^{49} -5.62937 q^{50} -0.220680 q^{51} -1.59836 q^{52} -6.32497 q^{53} +0.633751 q^{54} -22.1845 q^{55} -1.86966 q^{56} -3.58549 q^{57} -1.77543 q^{58} +0.203697 q^{59} +5.95539 q^{60} +4.63396 q^{61} -1.85075 q^{62} -0.819859 q^{63} +0.0910118 q^{64} +3.72594 q^{65} -3.77340 q^{66} -12.1610 q^{67} -0.352726 q^{68} +6.39569 q^{69} +1.93595 q^{70} +8.37368 q^{71} +2.28046 q^{72} -11.4059 q^{73} +1.18384 q^{74} -8.88262 q^{75} -5.73090 q^{76} +4.88149 q^{77} +0.633751 q^{78} +2.25221 q^{79} +6.52588 q^{80} +1.00000 q^{81} -1.44339 q^{82} -2.79727 q^{83} -1.31043 q^{84} +0.822241 q^{85} +3.16755 q^{86} -2.80146 q^{87} -13.5780 q^{88} -2.90084 q^{89} -2.36132 q^{90} -0.819859 q^{91} +10.2226 q^{92} -2.92031 q^{93} -0.316279 q^{94} +13.3593 q^{95} +5.67093 q^{96} +8.31381 q^{97} +4.01027 q^{98} -5.95407 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * 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 $

$2$	−0.633751	−0.448130	−0.224065	−	0.974574i	$-0.571933\pi$
$2$	−0.633751	−0.448130	−0.224065	+	0.974574i	$0.571933\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.59836	−0.799180
$5$	3.72594	1.66629	0.833145	−	0.553054i	$-0.186538\pi$
$5$	3.72594	1.66629	0.833145	+	0.553054i	$0.186538\pi$
$6$	0.633751	0.258728
$7$	−0.819859	−0.309877	−0.154939	−	0.987924i	$-0.549518\pi$
$7$	−0.819859	−0.309877	−0.154939	+	0.987924i	$0.549518\pi$
$8$	2.28046	0.806266
$9$	1.00000	0.333333
$10$	−2.36132	−0.746714
$11$	−5.95407	−1.79522	−0.897610	−	0.440791i	$-0.854698\pi$
$11$	−5.95407	−1.79522	−0.897610	+	0.440791i	$0.854698\pi$
$12$	1.59836	0.461407
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.519586	0.138865
$15$	−3.72594	−0.962033
$16$	1.75147	0.437868
$17$	0.220680	0.0535228	0.0267614	−	0.999642i	$-0.491481\pi$
$17$	0.220680	0.0535228	0.0267614	+	0.999642i	$0.491481\pi$
$18$	−0.633751	−0.149377
$19$	3.58549	0.822567	0.411284	−	0.911507i	$-0.365081\pi$
$19$	3.58549	0.822567	0.411284	+	0.911507i	$0.365081\pi$
$20$	−5.95539	−1.33167
$21$	0.819859	0.178908
$22$	3.77340	0.804491
$23$	−6.39569	−1.33359	−0.666797	−	0.745240i	$-0.732335\pi$
$23$	−6.39569	−1.33359	−0.666797	+	0.745240i	$0.732335\pi$
$24$	−2.28046	−0.465498
$25$	8.88262	1.77652
$26$	−0.633751	−0.124289
$27$	−1.00000	−0.192450
$28$	1.31043	0.247648
$29$	2.80146	0.520218	0.260109	−	0.965579i	$-0.416242\pi$
$29$	2.80146	0.520218	0.260109	+	0.965579i	$0.416242\pi$
$30$	2.36132	0.431116
$31$	2.92031	0.524504	0.262252	−	0.964999i	$-0.415535\pi$
$31$	2.92031	0.524504	0.262252	+	0.964999i	$0.415535\pi$
$32$	−5.67093	−1.00249
$33$	5.95407	1.03647
$34$	−0.139856	−0.0239852
$35$	−3.05474	−0.516346
$36$	−1.59836	−0.266393
$37$	−1.86799	−0.307095	−0.153548	−	0.988141i	$-0.549070\pi$
$37$	−1.86799	−0.307095	−0.153548	+	0.988141i	$0.549070\pi$
$38$	−2.27231	−0.368617
$39$	−1.00000	−0.160128
$40$	8.49687	1.34347
$41$	2.27753	0.355690	0.177845	−	0.984058i	$-0.443087\pi$
$41$	2.27753	0.355690	0.177845	+	0.984058i	$0.443087\pi$
$42$	−0.519586	−0.0801739
$43$	−4.99809	−0.762202	−0.381101	−	0.924533i	$-0.624455\pi$
$43$	−4.99809	−0.762202	−0.381101	+	0.924533i	$0.624455\pi$
$44$	9.51674	1.43470
$45$	3.72594	0.555430
$46$	4.05328	0.597623
$47$	0.499059	0.0727952	0.0363976	−	0.999337i	$-0.488412\pi$
$47$	0.499059	0.0727952	0.0363976	+	0.999337i	$0.488412\pi$
$48$	−1.75147	−0.252803
$49$	−6.32783	−0.903976
$50$	−5.62937	−0.796113
$51$	−0.220680	−0.0309014
$52$	−1.59836	−0.221653
$53$	−6.32497	−0.868802	−0.434401	−	0.900720i	$-0.643040\pi$
$53$	−6.32497	−0.868802	−0.434401	+	0.900720i	$0.643040\pi$
$54$	0.633751	0.0862426
$55$	−22.1845	−2.99136
$56$	−1.86966	−0.249844
$57$	−3.58549	−0.474909
$58$	−1.77543	−0.233125
$59$	0.203697	0.0265191	0.0132596	−	0.999912i	$-0.495779\pi$
$59$	0.203697	0.0265191	0.0132596	+	0.999912i	$0.495779\pi$
$60$	5.95539	0.768837
$61$	4.63396	0.593317	0.296659	−	0.954984i	$-0.404128\pi$
$61$	4.63396	0.593317	0.296659	+	0.954984i	$0.404128\pi$
$62$	−1.85075	−0.235046
$63$	−0.819859	−0.103292
$64$	0.0910118	0.0113765
$65$	3.72594	0.462146
$66$	−3.77340	−0.464473
$67$	−12.1610	−1.48570	−0.742852	−	0.669456i	$-0.766527\pi$
$67$	−12.1610	−1.48570	−0.742852	+	0.669456i	$0.766527\pi$
$68$	−0.352726	−0.0427743
$69$	6.39569	0.769951
$70$	1.93595	0.231390
$71$	8.37368	0.993772	0.496886	−	0.867816i	$-0.334477\pi$
$71$	8.37368	0.993772	0.496886	+	0.867816i	$0.334477\pi$
$72$	2.28046	0.268755
$73$	−11.4059	−1.33496	−0.667480	−	0.744628i	$-0.732627\pi$
$73$	−11.4059	−1.33496	−0.667480	+	0.744628i	$0.732627\pi$
$74$	1.18384	0.137618
$75$	−8.88262	−1.02568
$76$	−5.73090	−0.657379
$77$	4.88149	0.556298
$78$	0.633751	0.0717582
$79$	2.25221	0.253393	0.126697	−	0.991942i	$-0.459563\pi$
$79$	2.25221	0.253393	0.126697	+	0.991942i	$0.459563\pi$
$80$	6.52588	0.729615
$81$	1.00000	0.111111
$82$	−1.44339	−0.159395
$83$	−2.79727	−0.307041	−0.153520	−	0.988145i	$-0.549061\pi$
$83$	−2.79727	−0.307041	−0.153520	+	0.988145i	$0.549061\pi$
$84$	−1.31043	−0.142980
$85$	0.822241	0.0891845
$86$	3.16755	0.341565
$87$	−2.80146	−0.300348
$88$	−13.5780	−1.44742
$89$	−2.90084	−0.307488	−0.153744	−	0.988111i	$-0.549133\pi$
$89$	−2.90084	−0.307488	−0.153744	+	0.988111i	$0.549133\pi$
$90$	−2.36132	−0.248905
$91$	−0.819859	−0.0859445
$92$	10.2226	1.06578
$93$	−2.92031	−0.302822
$94$	−0.316279	−0.0326217
$95$	13.3593	1.37064
$96$	5.67093	0.578786
$97$	8.31381	0.844140	0.422070	−	0.906563i	$-0.361304\pi$
$97$	8.31381	0.844140	0.422070	+	0.906563i	$0.361304\pi$
$98$	4.01027	0.405099
$99$	−5.95407	−0.598406
$100$	−14.1976	−1.41976
$101$	7.98978	0.795013	0.397507	−	0.917599i	$-0.369876\pi$
$101$	7.98978	0.795013	0.397507	+	0.917599i	$0.369876\pi$
$102$	0.139856	0.0138478
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.28046	0.223618
$105$	3.05474	0.298112
$106$	4.00846	0.389336
$107$	7.10369	0.686739	0.343370	−	0.939200i	$-0.388432\pi$
$107$	7.10369	0.686739	0.343370	+	0.939200i	$0.388432\pi$
$108$	1.59836	0.153802
$109$	5.69163	0.545160	0.272580	−	0.962133i	$-0.412123\pi$
$109$	5.69163	0.545160	0.272580	+	0.962133i	$0.412123\pi$
$110$	14.0594	1.34052
$111$	1.86799	0.177301
$112$	−1.43596	−0.135685
$113$	−5.34769	−0.503068	−0.251534	−	0.967848i	$-0.580935\pi$
$113$	−5.34769	−0.503068	−0.251534	+	0.967848i	$0.580935\pi$
$114$	2.27231	0.212821
$115$	−23.8299	−2.22215
$116$	−4.47774	−0.415747
$117$	1.00000	0.0924500
$118$	−0.129093	−0.0118840
$119$	−0.180927	−0.0165855
$120$	−8.49687	−0.775655
$121$	24.4509	2.22281
$122$	−2.93678	−0.265883
$123$	−2.27753	−0.205358
$124$	−4.66771	−0.419173
$125$	14.4664	1.29391
$126$	0.519586	0.0462884
$127$	−9.01284	−0.799760	−0.399880	−	0.916567i	$-0.630948\pi$
$127$	−9.01284	−0.799760	−0.399880	+	0.916567i	$0.630948\pi$
$128$	11.2842	0.997389
$129$	4.99809	0.440057
$130$	−2.36132	−0.207101
$131$	−9.45932	−0.826465	−0.413232	−	0.910626i	$-0.635600\pi$
$131$	−9.45932	−0.826465	−0.413232	+	0.910626i	$0.635600\pi$
$132$	−9.51674	−0.828326
$133$	−2.93959	−0.254895
$134$	7.70705	0.665788
$135$	−3.72594	−0.320678
$136$	0.503253	0.0431536
$137$	−14.0750	−1.20251	−0.601256	−	0.799057i	$-0.705333\pi$
$137$	−14.0750	−1.20251	−0.601256	+	0.799057i	$0.705333\pi$
$138$	−4.05328	−0.345038
$139$	11.6301	0.986451	0.493226	−	0.869901i	$-0.335818\pi$
$139$	11.6301	0.986451	0.493226	+	0.869901i	$0.335818\pi$
$140$	4.88258	0.412653
$141$	−0.499059	−0.0420283
$142$	−5.30683	−0.445339
$143$	−5.95407	−0.497904
$144$	1.75147	0.145956
$145$	10.4381	0.866834
$146$	7.22850	0.598235
$147$	6.32783	0.521911
$148$	2.98571	0.245424
$149$	−23.6249	−1.93543	−0.967713	−	0.252056i	$-0.918893\pi$
$149$	−23.6249	−1.93543	−0.967713	+	0.252056i	$0.918893\pi$
$150$	5.62937	0.459636
$151$	−10.5878	−0.861620	−0.430810	−	0.902443i	$-0.641772\pi$
$151$	−10.5878	−0.861620	−0.430810	+	0.902443i	$0.641772\pi$
$152$	8.17657	0.663208
$153$	0.220680	0.0178409
$154$	−3.09365	−0.249294
$155$	10.8809	0.873976
$156$	1.59836	0.127971
$157$	5.30126	0.423086	0.211543	−	0.977369i	$-0.432151\pi$
$157$	5.30126	0.423086	0.211543	+	0.977369i	$0.432151\pi$
$158$	−1.42734	−0.113553
$159$	6.32497	0.501603
$160$	−21.1295	−1.67044
$161$	5.24356	0.413251
$162$	−0.633751	−0.0497922
$163$	8.10953	0.635188	0.317594	−	0.948227i	$-0.397125\pi$
$163$	8.10953	0.635188	0.317594	+	0.948227i	$0.397125\pi$
$164$	−3.64031	−0.284260
$165$	22.1845	1.72706
$166$	1.77278	0.137594
$167$	−17.2940	−1.33825	−0.669123	−	0.743152i	$-0.733330\pi$
$167$	−17.2940	−1.33825	−0.669123	+	0.743152i	$0.733330\pi$
$168$	1.86966	0.144247
$169$	1.00000	0.0769231
$170$	−0.521096	−0.0399662
$171$	3.58549	0.274189
$172$	7.98875	0.609136
$173$	20.1569	1.53250	0.766252	−	0.642541i	$-0.222120\pi$
$173$	20.1569	1.53250	0.766252	+	0.642541i	$0.222120\pi$
$174$	1.77543	0.134595
$175$	−7.28249	−0.550505
$176$	−10.4284	−0.786069
$177$	−0.203697	−0.0153108
$178$	1.83841	0.137795
$179$	−21.7398	−1.62491	−0.812453	−	0.583027i	$-0.801868\pi$
$179$	−21.7398	−1.62491	−0.812453	+	0.583027i	$0.801868\pi$
$180$	−5.95539	−0.443889
$181$	−16.3644	−1.21635	−0.608177	−	0.793802i	$-0.708099\pi$
$181$	−16.3644	−1.21635	−0.608177	+	0.793802i	$0.708099\pi$
$182$	0.519586	0.0385143
$183$	−4.63396	−0.342552
$184$	−14.5851	−1.07523
$185$	−6.96000	−0.511709
$186$	1.85075	0.135704
$187$	−1.31395	−0.0960852
$188$	−0.797676	−0.0581765
$189$	0.819859	0.0596359
$190$	−8.46647	−0.614223
$191$	−0.944271	−0.0683251	−0.0341625	−	0.999416i	$-0.510876\pi$
$191$	−0.944271	−0.0683251	−0.0341625	+	0.999416i	$0.510876\pi$
$192$	−0.0910118	−0.00656821
$193$	−3.13041	−0.225332	−0.112666	−	0.993633i	$-0.535939\pi$
$193$	−3.13041	−0.225332	−0.112666	+	0.993633i	$0.535939\pi$
$194$	−5.26889	−0.378284
$195$	−3.72594	−0.266820
$196$	10.1142	0.722439
$197$	10.8515	0.773136	0.386568	−	0.922261i	$-0.373660\pi$
$197$	10.8515	0.773136	0.386568	+	0.922261i	$0.373660\pi$
$198$	3.77340	0.268164
$199$	9.89589	0.701501	0.350751	−	0.936469i	$-0.385926\pi$
$199$	9.89589	0.701501	0.350751	+	0.936469i	$0.385926\pi$
$200$	20.2565	1.43235
$201$	12.1610	0.857772
$202$	−5.06353	−0.356269
$203$	−2.29680	−0.161204
$204$	0.352726	0.0246958
$205$	8.48593	0.592683
$206$	−0.633751	−0.0441555
$207$	−6.39569	−0.444531
$208$	1.75147	0.121443
$209$	−21.3482	−1.47669
$210$	−1.93595	−0.133593
$211$	−22.4668	−1.54668	−0.773339	−	0.633993i	$-0.781415\pi$
$211$	−22.4668	−1.54668	−0.773339	+	0.633993i	$0.781415\pi$
$212$	10.1096	0.694329
$213$	−8.37368	−0.573755
$214$	−4.50197	−0.307748
$215$	−18.6226	−1.27005
$216$	−2.28046	−0.155166
$217$	−2.39424	−0.162532
$218$	−3.60708	−0.244302
$219$	11.4059	0.770739
$220$	35.4588	2.39063
$221$	0.220680	0.0148446
$222$	−1.18384	−0.0794540
$223$	24.6739	1.65229	0.826145	−	0.563458i	$-0.190529\pi$
$223$	24.6739	1.65229	0.826145	+	0.563458i	$0.190529\pi$
$224$	4.64936	0.310648
$225$	8.88262	0.592175
$226$	3.38910	0.225440
$227$	−5.94923	−0.394864	−0.197432	−	0.980317i	$-0.563260\pi$
$227$	−5.94923	−0.394864	−0.197432	+	0.980317i	$0.563260\pi$
$228$	5.73090	0.379538
$229$	13.1281	0.867529	0.433764	−	0.901026i	$-0.357185\pi$
$229$	13.1281	0.867529	0.433764	+	0.901026i	$0.357185\pi$
$230$	15.1023	0.995813
$231$	−4.88149	−0.321179
$232$	6.38863	0.419434
$233$	−0.710407	−0.0465403	−0.0232702	−	0.999729i	$-0.507408\pi$
$233$	−0.710407	−0.0465403	−0.0232702	+	0.999729i	$0.507408\pi$
$234$	−0.633751	−0.0414296
$235$	1.85946	0.121298
$236$	−0.325581	−0.0211935
$237$	−2.25221	−0.146297
$238$	0.114662	0.00743246
$239$	−24.3204	−1.57316	−0.786579	−	0.617490i	$-0.788150\pi$
$239$	−24.3204	−1.57316	−0.786579	+	0.617490i	$0.788150\pi$
$240$	−6.52588	−0.421244
$241$	−24.8948	−1.60362	−0.801809	−	0.597581i	$-0.796129\pi$
$241$	−24.8948	−1.60362	−0.801809	+	0.597581i	$0.796129\pi$
$242$	−15.4958	−0.996108
$243$	−1.00000	−0.0641500
$244$	−7.40673	−0.474167
$245$	−23.5771	−1.50629
$246$	1.44339	0.0920270
$247$	3.58549	0.228139
$248$	6.65967	0.422890
$249$	2.79727	0.177270
$250$	−9.16810	−0.579841
$251$	−14.7408	−0.930430	−0.465215	−	0.885198i	$-0.654023\pi$
$251$	−14.7408	−0.930430	−0.465215	+	0.885198i	$0.654023\pi$
$252$	1.31043	0.0825493
$253$	38.0804	2.39409
$254$	5.71190	0.358396
$255$	−0.822241	−0.0514907
$256$	−7.33338	−0.458336
$257$	−6.26766	−0.390966	−0.195483	−	0.980707i	$-0.562627\pi$
$257$	−6.26766	−0.390966	−0.195483	+	0.980707i	$0.562627\pi$
$258$	−3.16755	−0.197203
$259$	1.53148	0.0951618
$260$	−5.95539	−0.369338
$261$	2.80146	0.173406
$262$	5.99485	0.370363
$263$	−17.3034	−1.06697	−0.533487	−	0.845808i	$-0.679119\pi$
$263$	−17.3034	−1.06697	−0.533487	+	0.845808i	$0.679119\pi$
$264$	13.5780	0.835671
$265$	−23.5665	−1.44768
$266$	1.86297	0.114226
$267$	2.90084	0.177528
$268$	19.4377	1.18734
$269$	−18.0570	−1.10096	−0.550479	−	0.834849i	$-0.685555\pi$
$269$	−18.0570	−1.10096	−0.550479	+	0.834849i	$0.685555\pi$
$270$	2.36132	0.143705
$271$	−1.08642	−0.0659952	−0.0329976	−	0.999455i	$-0.510505\pi$
$271$	−1.08642	−0.0659952	−0.0329976	+	0.999455i	$0.510505\pi$
$272$	0.386515	0.0234359
$273$	0.819859	0.0496201
$274$	8.92007	0.538881
$275$	−52.8877	−3.18925
$276$	−10.2226	−0.615329
$277$	−31.0755	−1.86715	−0.933573	−	0.358387i	$-0.883327\pi$
$277$	−31.0755	−1.86715	−0.933573	+	0.358387i	$0.883327\pi$
$278$	−7.37058	−0.442058
$279$	2.92031	0.174835
$280$	−6.96623	−0.416312
$281$	23.3058	1.39031	0.695155	−	0.718860i	$-0.255336\pi$
$281$	23.3058	1.39031	0.695155	+	0.718860i	$0.255336\pi$
$282$	0.316279	0.0188342
$283$	−5.93959	−0.353072	−0.176536	−	0.984294i	$-0.556489\pi$
$283$	−5.93959	−0.353072	−0.176536	+	0.984294i	$0.556489\pi$
$284$	−13.3841	−0.794203
$285$	−13.3593	−0.791337
$286$	3.77340	0.223126
$287$	−1.86725	−0.110220
$288$	−5.67093	−0.334163
$289$	−16.9513	−0.997135
$290$	−6.61513	−0.388454
$291$	−8.31381	−0.487364
$292$	18.2307	1.06687
$293$	−18.4670	−1.07885	−0.539427	−	0.842032i	$-0.681359\pi$
$293$	−18.4670	−1.07885	−0.539427	+	0.842032i	$0.681359\pi$
$294$	−4.01027	−0.233884
$295$	0.758964	0.0441886
$296$	−4.25988	−0.247600
$297$	5.95407	0.345490
$298$	14.9723	0.867322
$299$	−6.39569	−0.369872
$300$	14.1976	0.819700
$301$	4.09773	0.236189
$302$	6.71001	0.386117
$303$	−7.98978	−0.459001
$304$	6.27988	0.360176
$305$	17.2658	0.988639
$306$	−0.139856	−0.00799505
$307$	−28.3681	−1.61905	−0.809526	−	0.587084i	$-0.800276\pi$
$307$	−28.3681	−1.61905	−0.809526	+	0.587084i	$0.800276\pi$
$308$	−7.80238	−0.444582
$309$	−1.00000	−0.0568880
$310$	−6.89579	−0.391655
$311$	−18.6698	−1.05867	−0.529334	−	0.848414i	$-0.677558\pi$
$311$	−18.6698	−1.05867	−0.529334	+	0.848414i	$0.677558\pi$
$312$	−2.28046	−0.129106
$313$	28.9811	1.63811	0.819055	−	0.573715i	$-0.194498\pi$
$313$	28.9811	1.63811	0.819055	+	0.573715i	$0.194498\pi$
$314$	−3.35968	−0.189598
$315$	−3.05474	−0.172115
$316$	−3.59984	−0.202507
$317$	19.8437	1.11453	0.557266	−	0.830334i	$-0.311851\pi$
$317$	19.8437	1.11453	0.557266	+	0.830334i	$0.311851\pi$
$318$	−4.00846	−0.224783
$319$	−16.6801	−0.933905
$320$	0.339104	0.0189565
$321$	−7.10369	−0.396489
$322$	−3.32311	−0.185190
$323$	0.791246	0.0440261
$324$	−1.59836	−0.0887977
$325$	8.88262	0.492719
$326$	−5.13943	−0.284646
$327$	−5.69163	−0.314748
$328$	5.19382	0.286781
$329$	−0.409158	−0.0225576
$330$	−14.0594	−0.773947
$331$	−4.28222	−0.235372	−0.117686	−	0.993051i	$-0.537548\pi$
$331$	−4.28222	−0.235372	−0.117686	+	0.993051i	$0.537548\pi$
$332$	4.47105	0.245381
$333$	−1.86799	−0.102365
$334$	10.9601	0.599708
$335$	−45.3112	−2.47561
$336$	1.43596	0.0783380
$337$	−27.8211	−1.51551	−0.757756	−	0.652538i	$-0.773704\pi$
$337$	−27.8211	−1.51551	−0.757756	+	0.652538i	$0.773704\pi$
$338$	−0.633751	−0.0344715
$339$	5.34769	0.290447
$340$	−1.31424	−0.0712745
$341$	−17.3878	−0.941600
$342$	−2.27231	−0.122872
$343$	10.9269	0.589999
$344$	−11.3980	−0.614537
$345$	23.8299	1.28296
$346$	−12.7745	−0.686760
$347$	12.2846	0.659471	0.329735	−	0.944073i	$-0.393040\pi$
$347$	12.2846	0.659471	0.329735	+	0.944073i	$0.393040\pi$
$348$	4.47774	0.240032
$349$	9.73559	0.521134	0.260567	−	0.965456i	$-0.416091\pi$
$349$	9.73559	0.521134	0.260567	+	0.965456i	$0.416091\pi$
$350$	4.61529	0.246697
$351$	−1.00000	−0.0533761
$352$	33.7651	1.79969
$353$	11.2815	0.600453	0.300227	−	0.953868i	$-0.402938\pi$
$353$	11.2815	0.600453	0.300227	+	0.953868i	$0.402938\pi$
$354$	0.129093	0.00686124
$355$	31.1998	1.65591
$356$	4.63658	0.245738
$357$	0.180927	0.00957565
$358$	13.7776	0.728169
$359$	3.49815	0.184625	0.0923126	−	0.995730i	$-0.470574\pi$
$359$	3.49815	0.184625	0.0923126	+	0.995730i	$0.470574\pi$
$360$	8.49687	0.447824
$361$	−6.14429	−0.323384
$362$	10.3709	0.545084
$363$	−24.4509	−1.28334
$364$	1.31043	0.0686851
$365$	−42.4977	−2.22443
$366$	2.93678	0.153508
$367$	−18.1107	−0.945370	−0.472685	−	0.881232i	$-0.656715\pi$
$367$	−18.1107	−0.945370	−0.472685	+	0.881232i	$0.656715\pi$
$368$	−11.2019	−0.583938
$369$	2.27753	0.118563
$370$	4.41091	0.229312
$371$	5.18558	0.269222
$372$	4.66771	0.242010
$373$	−23.6461	−1.22435	−0.612176	−	0.790722i	$-0.709705\pi$
$373$	−23.6461	−1.22435	−0.612176	+	0.790722i	$0.709705\pi$
$374$	0.832714	0.0430586
$375$	−14.4664	−0.747042
$376$	1.13809	0.0586923
$377$	2.80146	0.144282
$378$	−0.519586	−0.0267246
$379$	28.2742	1.45235	0.726173	−	0.687512i	$-0.241297\pi$
$379$	28.2742	1.45235	0.726173	+	0.687512i	$0.241297\pi$
$380$	−21.3530	−1.09538
$381$	9.01284	0.461742
$382$	0.598433	0.0306185
$383$	−17.3694	−0.887536	−0.443768	−	0.896142i	$-0.646359\pi$
$383$	−17.3694	−0.887536	−0.443768	+	0.896142i	$0.646359\pi$
$384$	−11.2842	−0.575843
$385$	18.1881	0.926954
$386$	1.98390	0.100978
$387$	−4.99809	−0.254067
$388$	−13.2885	−0.674620
$389$	19.1794	0.972433	0.486217	−	0.873838i	$-0.338377\pi$
$389$	19.1794	0.972433	0.486217	+	0.873838i	$0.338377\pi$
$390$	2.36132	0.119570
$391$	−1.41140	−0.0713777
$392$	−14.4304	−0.728845
$393$	9.45932	0.477160
$394$	−6.87714	−0.346465
$395$	8.39160	0.422227
$396$	9.51674	0.478234
$397$	−0.185334	−0.00930165	−0.00465083	−	0.999989i	$-0.501480\pi$
$397$	−0.185334	−0.00930165	−0.00465083	+	0.999989i	$0.501480\pi$
$398$	−6.27153	−0.314364
$399$	2.93959	0.147164
$400$	15.5577	0.777883
$401$	2.64763	0.132217	0.0661083	−	0.997812i	$-0.478942\pi$
$401$	2.64763	0.132217	0.0661083	+	0.997812i	$0.478942\pi$
$402$	−7.70705	−0.384393
$403$	2.92031	0.145471
$404$	−12.7705	−0.635358
$405$	3.72594	0.185143
$406$	1.45560	0.0722402
$407$	11.1221	0.551303
$408$	−0.503253	−0.0249148
$409$	−34.1063	−1.68645	−0.843224	−	0.537563i	$-0.819345\pi$
$409$	−34.1063	−1.68645	−0.843224	+	0.537563i	$0.819345\pi$
$410$	−5.37797	−0.265599
$411$	14.0750	0.694270
$412$	−1.59836	−0.0787455
$413$	−0.167003	−0.00821768
$414$	4.05328	0.199208
$415$	−10.4225	−0.511619
$416$	−5.67093	−0.278040
$417$	−11.6301	−0.569528
$418$	13.5295	0.661748
$419$	−22.0383	−1.07664	−0.538321	−	0.842740i	$-0.680941\pi$
$419$	−22.0383	−1.07664	−0.538321	+	0.842740i	$0.680941\pi$
$420$	−4.88258	−0.238245
$421$	14.0051	0.682569	0.341285	−	0.939960i	$-0.389138\pi$
$421$	14.0051	0.682569	0.341285	+	0.939960i	$0.389138\pi$
$422$	14.2384	0.693112
$423$	0.499059	0.0242651
$424$	−14.4239	−0.700485
$425$	1.96022	0.0950845
$426$	5.30683	0.257117
$427$	−3.79919	−0.183856
$428$	−11.3542	−0.548828
$429$	5.95407	0.287465
$430$	11.8021	0.569147
$431$	−13.2292	−0.637230	−0.318615	−	0.947884i	$-0.603218\pi$
$431$	−13.2292	−0.637230	−0.318615	+	0.947884i	$0.603218\pi$
$432$	−1.75147	−0.0842677
$433$	−41.1608	−1.97806	−0.989030	−	0.147712i	$-0.952809\pi$
$433$	−41.1608	−1.97806	−0.989030	+	0.147712i	$0.952809\pi$
$434$	1.51736	0.0728354
$435$	−10.4381	−0.500467
$436$	−9.09728	−0.435681
$437$	−22.9317	−1.09697
$438$	−7.22850	−0.345391
$439$	20.6023	0.983293	0.491647	−	0.870795i	$-0.336395\pi$
$439$	20.6023	0.983293	0.491647	+	0.870795i	$0.336395\pi$
$440$	−50.5910	−2.41183
$441$	−6.32783	−0.301325
$442$	−0.139856	−0.00665229
$443$	−15.2056	−0.722440	−0.361220	−	0.932481i	$-0.617640\pi$
$443$	−15.2056	−0.722440	−0.361220	+	0.932481i	$0.617640\pi$
$444$	−2.98571	−0.141696
$445$	−10.8083	−0.512365
$446$	−15.6371	−0.740440
$447$	23.6249	1.11742
$448$	−0.0746168	−0.00352531
$449$	8.81199	0.415863	0.207932	−	0.978143i	$-0.433327\pi$
$449$	8.81199	0.415863	0.207932	+	0.978143i	$0.433327\pi$
$450$	−5.62937	−0.265371
$451$	−13.5606	−0.638542
$452$	8.54753	0.402042
$453$	10.5878	0.497456
$454$	3.77033	0.176950
$455$	−3.05474	−0.143209
$456$	−8.17657	−0.382903
$457$	−19.5501	−0.914515	−0.457257	−	0.889334i	$-0.651168\pi$
$457$	−19.5501	−0.914515	−0.457257	+	0.889334i	$0.651168\pi$
$458$	−8.31994	−0.388765
$459$	−0.220680	−0.0103005
$460$	38.0888	1.77590
$461$	−0.913638	−0.0425523	−0.0212762	−	0.999774i	$-0.506773\pi$
$461$	−0.913638	−0.0425523	−0.0212762	+	0.999774i	$0.506773\pi$
$462$	3.09365	0.143930
$463$	7.47687	0.347480	0.173740	−	0.984792i	$-0.444415\pi$
$463$	7.47687	0.347480	0.173740	+	0.984792i	$0.444415\pi$
$464$	4.90668	0.227787
$465$	−10.8809	−0.504590
$466$	0.450221	0.0208561
$467$	−15.0753	−0.697604	−0.348802	−	0.937196i	$-0.613411\pi$
$467$	−15.0753	−0.697604	−0.348802	+	0.937196i	$0.613411\pi$
$468$	−1.59836	−0.0738842
$469$	9.97031	0.460386
$470$	−1.17844	−0.0543572
$471$	−5.30126	−0.244269
$472$	0.464524	0.0213815
$473$	29.7590	1.36832
$474$	1.42734	0.0655599
$475$	31.8485	1.46131
$476$	0.289186	0.0132548
$477$	−6.32497	−0.289601
$478$	15.4131	0.704979
$479$	2.27070	0.103751	0.0518755	−	0.998654i	$-0.483480\pi$
$479$	2.27070	0.103751	0.0518755	+	0.998654i	$0.483480\pi$
$480$	21.1295	0.964426
$481$	−1.86799	−0.0851728
$482$	15.7771	0.718629
$483$	−5.24356	−0.238590
$484$	−39.0814	−1.77643
$485$	30.9768	1.40658
$486$	0.633751	0.0287475
$487$	11.2775	0.511031	0.255515	−	0.966805i	$-0.417755\pi$
$487$	11.2775	0.511031	0.255515	+	0.966805i	$0.417755\pi$
$488$	10.5676	0.478372
$489$	−8.10953	−0.366726
$490$	14.9420	0.675012
$491$	14.8840	0.671706	0.335853	−	0.941914i	$-0.390976\pi$
$491$	14.8840	0.671706	0.335853	+	0.941914i	$0.390976\pi$
$492$	3.64031	0.164118
$493$	0.618226	0.0278435
$494$	−2.27231	−0.102236
$495$	−22.1845	−0.997119
$496$	5.11485	0.229664
$497$	−6.86523	−0.307948
$498$	−1.77278	−0.0794400
$499$	−13.3648	−0.598289	−0.299145	−	0.954208i	$-0.596701\pi$
$499$	−13.3648	−0.598289	−0.299145	+	0.954208i	$0.596701\pi$
$500$	−23.1225	−1.03407
$501$	17.2940	0.772637
$502$	9.34199	0.416953
$503$	0.796636	0.0355202	0.0177601	−	0.999842i	$-0.494346\pi$
$503$	0.796636	0.0355202	0.0177601	+	0.999842i	$0.494346\pi$
$504$	−1.86966	−0.0832812
$505$	29.7694	1.32472
$506$	−24.1335	−1.07286
$507$	−1.00000	−0.0444116
$508$	14.4058	0.639152
$509$	−14.4483	−0.640408	−0.320204	−	0.947349i	$-0.603751\pi$
$509$	−14.4483	−0.640408	−0.320204	+	0.947349i	$0.603751\pi$
$510$	0.521096	0.0230745
$511$	9.35122	0.413674
$512$	−17.9208	−0.791995
$513$	−3.58549	−0.158303
$514$	3.97214	0.175203
$515$	3.72594	0.164184
$516$	−7.98875	−0.351685
$517$	−2.97143	−0.130683
$518$	−0.970580	−0.0426448
$519$	−20.1569	−0.884791
$520$	8.49687	0.372612
$521$	34.0757	1.49288	0.746442	−	0.665450i	$-0.231760\pi$
$521$	34.0757	1.49288	0.746442	+	0.665450i	$0.231760\pi$
$522$	−1.77543	−0.0777083
$523$	−21.0221	−0.919233	−0.459617	−	0.888117i	$-0.652013\pi$
$523$	−21.0221	−0.919233	−0.459617	+	0.888117i	$0.652013\pi$
$524$	15.1194	0.660494
$525$	7.28249	0.317834
$526$	10.9661	0.478143
$527$	0.644456	0.0280729
$528$	10.4284	0.453837
$529$	17.9049	0.778472
$530$	14.9353	0.648747
$531$	0.203697	0.00883971
$532$	4.69852	0.203707
$533$	2.27753	0.0986507
$534$	−1.83841	−0.0795558
$535$	26.4679	1.14431
$536$	−27.7328	−1.19787
$537$	21.7398	0.938140
$538$	11.4437	0.493372
$539$	37.6763	1.62284
$540$	5.95539	0.256279
$541$	−5.19119	−0.223187	−0.111593	−	0.993754i	$-0.535595\pi$
$541$	−5.19119	−0.223187	−0.111593	+	0.993754i	$0.535595\pi$
$542$	0.688519	0.0295744
$543$	16.3644	0.702262
$544$	−1.25146	−0.0536560
$545$	21.2067	0.908395
$546$	−0.519586	−0.0222362
$547$	31.2937	1.33802	0.669010	−	0.743253i	$-0.266718\pi$
$547$	31.2937	1.33802	0.669010	+	0.743253i	$0.266718\pi$
$548$	22.4970	0.961022
$549$	4.63396	0.197772
$550$	33.5177	1.42920
$551$	10.0446	0.427914
$552$	14.5851	0.620785
$553$	−1.84649	−0.0785209
$554$	19.6941	0.836724
$555$	6.96000	0.295436
$556$	−18.5891	−0.788352
$557$	−6.44589	−0.273121	−0.136561	−	0.990632i	$-0.543605\pi$
$557$	−6.44589	−0.273121	−0.136561	+	0.990632i	$0.543605\pi$
$558$	−1.85075	−0.0783486
$559$	−4.99809	−0.211397
$560$	−5.35030	−0.226091
$561$	1.31395	0.0554748
$562$	−14.7701	−0.623039
$563$	−24.7156	−1.04164	−0.520818	−	0.853668i	$-0.674373\pi$
$563$	−24.7156	−1.04164	−0.520818	+	0.853668i	$0.674373\pi$
$564$	0.797676	0.0335882
$565$	−19.9252	−0.838258
$566$	3.76422	0.158222
$567$	−0.819859	−0.0344308
$568$	19.0959	0.801245
$569$	23.9448	1.00382	0.501910	−	0.864920i	$-0.332631\pi$
$569$	23.9448	1.00382	0.501910	+	0.864920i	$0.332631\pi$
$570$	8.46647	0.354622
$571$	27.5246	1.15187	0.575935	−	0.817496i	$-0.304638\pi$
$571$	27.5246	1.15187	0.575935	+	0.817496i	$0.304638\pi$
$572$	9.51674	0.397915
$573$	0.944271	0.0394475
$574$	1.18337	0.0493930
$575$	−56.8105	−2.36916
$576$	0.0910118	0.00379216
$577$	24.1736	1.00636	0.503181	−	0.864181i	$-0.332163\pi$
$577$	24.1736	1.00636	0.503181	+	0.864181i	$0.332163\pi$
$578$	10.7429	0.446846
$579$	3.13041	0.130096
$580$	−16.6838	−0.692756
$581$	2.29337	0.0951450
$582$	5.26889	0.218402
$583$	37.6593	1.55969
$584$	−26.0107	−1.07633
$585$	3.72594	0.154049
$586$	11.7035	0.483467
$587$	10.2550	0.423268	0.211634	−	0.977349i	$-0.432122\pi$
$587$	10.2550	0.423268	0.211634	+	0.977349i	$0.432122\pi$
$588$	−10.1142	−0.417101
$589$	10.4707	0.431440
$590$	−0.480994	−0.0198022
$591$	−10.8515	−0.446370
$592$	−3.27173	−0.134467
$593$	−31.2899	−1.28492	−0.642461	−	0.766319i	$-0.722086\pi$
$593$	−31.2899	−1.28492	−0.642461	+	0.766319i	$0.722086\pi$
$594$	−3.77340	−0.154824
$595$	−0.674121	−0.0276363
$596$	37.7611	1.54675
$597$	−9.89589	−0.405012
$598$	4.05328	0.165751
$599$	−14.0827	−0.575405	−0.287703	−	0.957720i	$-0.592891\pi$
$599$	−14.0827	−0.575405	−0.287703	+	0.957720i	$0.592891\pi$
$600$	−20.2565	−0.826968
$601$	9.60472	0.391785	0.195892	−	0.980625i	$-0.437240\pi$
$601$	9.60472	0.391785	0.195892	+	0.980625i	$0.437240\pi$
$602$	−2.59694	−0.105843
$603$	−12.1610	−0.495235
$604$	16.9230	0.688589
$605$	91.1027	3.70385
$606$	5.06353	0.205692
$607$	33.1480	1.34543	0.672717	−	0.739900i	$-0.265127\pi$
$607$	33.1480	1.34543	0.672717	+	0.739900i	$0.265127\pi$
$608$	−20.3330	−0.824613
$609$	2.29680	0.0930710
$610$	−10.9422	−0.443039
$611$	0.499059	0.0201898
$612$	−0.352726	−0.0142581
$613$	17.9252	0.723991	0.361995	−	0.932180i	$-0.382096\pi$
$613$	17.9252	0.723991	0.361995	+	0.932180i	$0.382096\pi$
$614$	17.9783	0.725545
$615$	−8.48593	−0.342186
$616$	11.1321	0.448524
$617$	29.7138	1.19623	0.598116	−	0.801410i	$-0.295916\pi$
$617$	29.7138	1.19623	0.598116	+	0.801410i	$0.295916\pi$
$618$	0.633751	0.0254932
$619$	11.4742	0.461189	0.230594	−	0.973050i	$-0.425933\pi$
$619$	11.4742	0.461189	0.230594	+	0.973050i	$0.425933\pi$
$620$	−17.3916	−0.698464
$621$	6.39569	0.256650
$622$	11.8320	0.474420
$623$	2.37828	0.0952837
$624$	−1.75147	−0.0701150
$625$	9.48783	0.379513
$626$	−18.3668	−0.734086
$627$	21.3482	0.852566
$628$	−8.47332	−0.338122
$629$	−0.412228	−0.0164366
$630$	1.93595	0.0771300
$631$	3.49547	0.139152	0.0695762	−	0.997577i	$-0.477835\pi$
$631$	3.49547	0.139152	0.0695762	+	0.997577i	$0.477835\pi$
$632$	5.13608	0.204302
$633$	22.4668	0.892975
$634$	−12.5759	−0.499455
$635$	−33.5813	−1.33263
$636$	−10.1096	−0.400871
$637$	−6.32783	−0.250718
$638$	10.5710	0.418511
$639$	8.37368	0.331257
$640$	42.0441	1.66194
$641$	−18.8275	−0.743642	−0.371821	−	0.928304i	$-0.621267\pi$
$641$	−18.8275	−0.743642	−0.371821	+	0.928304i	$0.621267\pi$
$642$	4.50197	0.177679
$643$	−2.64650	−0.104368	−0.0521838	−	0.998637i	$-0.516618\pi$
$643$	−2.64650	−0.104368	−0.0521838	+	0.998637i	$0.516618\pi$
$644$	−8.38110	−0.330261
$645$	18.6226	0.733264
$646$	−0.501453	−0.0197294
$647$	19.1712	0.753700	0.376850	−	0.926274i	$-0.377007\pi$
$647$	19.1712	0.753700	0.376850	+	0.926274i	$0.377007\pi$
$648$	2.28046	0.0895851
$649$	−1.21283	−0.0476076
$650$	−5.62937	−0.220802
$651$	2.39424	0.0938379
$652$	−12.9619	−0.507629
$653$	−15.7391	−0.615918	−0.307959	−	0.951400i	$-0.599646\pi$
$653$	−15.7391	−0.615918	−0.307959	+	0.951400i	$0.599646\pi$
$654$	3.60708	0.141048
$655$	−35.2448	−1.37713
$656$	3.98903	0.155745
$657$	−11.4059	−0.444986
$658$	0.259304	0.0101087
$659$	44.7076	1.74156	0.870781	−	0.491671i	$-0.163614\pi$
$659$	44.7076	1.74156	0.870781	+	0.491671i	$0.163614\pi$
$660$	−35.4588	−1.38023
$661$	22.7625	0.885359	0.442680	−	0.896680i	$-0.354028\pi$
$661$	22.7625	0.885359	0.442680	+	0.896680i	$0.354028\pi$
$662$	2.71386	0.105477
$663$	−0.220680	−0.00857051
$664$	−6.37908	−0.247556
$665$	−10.9527	−0.424729
$666$	1.18384	0.0458728
$667$	−17.9173	−0.693759
$668$	27.6420	1.06950
$669$	−24.6739	−0.953950
$670$	28.7160	1.10940
$671$	−27.5909	−1.06513
$672$	−4.64936	−0.179353
$673$	30.3668	1.17055	0.585277	−	0.810833i	$-0.300986\pi$
$673$	30.3668	1.17055	0.585277	+	0.810833i	$0.300986\pi$
$674$	17.6316	0.679146
$675$	−8.88262	−0.341892
$676$	−1.59836	−0.0614754
$677$	−38.4742	−1.47868	−0.739341	−	0.673331i	$-0.764863\pi$
$677$	−38.4742	−1.47868	−0.739341	+	0.673331i	$0.764863\pi$
$678$	−3.38910	−0.130158
$679$	−6.81615	−0.261580
$680$	1.87509	0.0719065
$681$	5.94923	0.227975
$682$	11.0195	0.421959
$683$	−32.4306	−1.24092	−0.620462	−	0.784237i	$-0.713055\pi$
$683$	−32.4306	−1.24092	−0.620462	+	0.784237i	$0.713055\pi$
$684$	−5.73090	−0.219126
$685$	−52.4427	−2.00373
$686$	−6.92496	−0.264396
$687$	−13.1281	−0.500868
$688$	−8.75402	−0.333744
$689$	−6.32497	−0.240962
$690$	−15.1023	−0.574933
$691$	−31.0329	−1.18055	−0.590274	−	0.807203i	$-0.700980\pi$
$691$	−31.0329	−1.18055	−0.590274	+	0.807203i	$0.700980\pi$
$692$	−32.2180	−1.22475
$693$	4.88149	0.185433
$694$	−7.78537	−0.295529
$695$	43.3330	1.64371
$696$	−6.38863	−0.242160
$697$	0.502605	0.0190375
$698$	−6.16994	−0.233536
$699$	0.710407	0.0268701
$700$	11.6400	0.439952
$701$	−48.6962	−1.83923	−0.919616	−	0.392819i	$-0.871500\pi$
$701$	−48.6962	−1.83923	−0.919616	+	0.392819i	$0.871500\pi$
$702$	0.633751	0.0239194
$703$	−6.69764	−0.252606
$704$	−0.541890	−0.0204233
$705$	−1.85946	−0.0700314
$706$	−7.14966	−0.269081
$707$	−6.55049	−0.246357
$708$	0.325581	0.0122361
$709$	36.1582	1.35795	0.678976	−	0.734161i	$-0.262424\pi$
$709$	36.1582	1.35795	0.678976	+	0.734161i	$0.262424\pi$
$710$	−19.7729	−0.742064
$711$	2.25221	0.0844645
$712$	−6.61526	−0.247917
$713$	−18.6774	−0.699475
$714$	−0.114662	−0.00429113
$715$	−22.1845	−0.829653
$716$	34.7479	1.29859
$717$	24.3204	0.908263
$718$	−2.21696	−0.0827361
$719$	−1.79227	−0.0668402	−0.0334201	−	0.999441i	$-0.510640\pi$
$719$	−1.79227	−0.0668402	−0.0334201	+	0.999441i	$0.510640\pi$
$720$	6.52588	0.243205
$721$	−0.819859	−0.0305331
$722$	3.89395	0.144918
$723$	24.8948	0.925849
$724$	26.1561	0.972085
$725$	24.8843	0.924179
$726$	15.4958	0.575103
$727$	6.15430	0.228250	0.114125	−	0.993466i	$-0.463594\pi$
$727$	6.15430	0.228250	0.114125	+	0.993466i	$0.463594\pi$
$728$	−1.86966	−0.0692941
$729$	1.00000	0.0370370
$730$	26.9329	0.996833
$731$	−1.10298	−0.0407952
$732$	7.40673	0.273761
$733$	40.4549	1.49424	0.747119	−	0.664691i	$-0.231437\pi$
$733$	40.4549	1.49424	0.747119	+	0.664691i	$0.231437\pi$
$734$	11.4777	0.423648
$735$	23.5771	0.869655
$736$	36.2695	1.33691
$737$	72.4075	2.66716
$738$	−1.44339	−0.0531318
$739$	6.14731	0.226132	0.113066	−	0.993587i	$-0.463933\pi$
$739$	6.14731	0.226132	0.113066	+	0.993587i	$0.463933\pi$
$740$	11.1246	0.408948
$741$	−3.58549	−0.131716
$742$	−3.28637	−0.120646
$743$	−20.6340	−0.756987	−0.378494	−	0.925604i	$-0.623558\pi$
$743$	−20.6340	−0.756987	−0.378494	+	0.925604i	$0.623558\pi$
$744$	−6.65967	−0.244155
$745$	−88.0249	−3.22498
$746$	14.9858	0.548668
$747$	−2.79727	−0.102347
$748$	2.10016	0.0767893
$749$	−5.82402	−0.212805
$750$	9.16810	0.334772
$751$	23.5592	0.859689	0.429845	−	0.902903i	$-0.358568\pi$
$751$	23.5592	0.859689	0.429845	+	0.902903i	$0.358568\pi$
$752$	0.874088	0.0318747
$753$	14.7408	0.537184
$754$	−1.77543	−0.0646573
$755$	−39.4493	−1.43571
$756$	−1.31043	−0.0476598
$757$	42.1583	1.53227	0.766135	−	0.642679i	$-0.222177\pi$
$757$	42.1583	1.53227	0.766135	+	0.642679i	$0.222177\pi$
$758$	−17.9188	−0.650840
$759$	−38.0804	−1.38223
$760$	30.4654	1.10510
$761$	13.9312	0.505004	0.252502	−	0.967596i	$-0.418747\pi$
$761$	13.9312	0.505004	0.252502	+	0.967596i	$0.418747\pi$
$762$	−5.71190	−0.206920
$763$	−4.66634	−0.168933
$764$	1.50928	0.0546040
$765$	0.822241	0.0297282
$766$	11.0079	0.397731
$767$	0.203697	0.00735508
$768$	7.33338	0.264621
$769$	17.3109	0.624247	0.312124	−	0.950041i	$-0.398960\pi$
$769$	17.3109	0.624247	0.312124	+	0.950041i	$0.398960\pi$
$770$	−11.5268	−0.415396
$771$	6.26766	0.225724
$772$	5.00353	0.180081
$773$	−9.78116	−0.351804	−0.175902	−	0.984408i	$-0.556284\pi$
$773$	−9.78116	−0.351804	−0.175902	+	0.984408i	$0.556284\pi$
$774$	3.16755	0.113855
$775$	25.9400	0.931794
$776$	18.9594	0.680601
$777$	−1.53148	−0.0549417
$778$	−12.1550	−0.435776
$779$	8.16605	0.292579
$780$	5.95539	0.213237
$781$	−49.8574	−1.78404
$782$	0.894478	0.0319865
$783$	−2.80146	−0.100116
$784$	−11.0830	−0.395822
$785$	19.7522	0.704985
$786$	−5.99485	−0.213829
$787$	28.5965	1.01935	0.509677	−	0.860366i	$-0.329765\pi$
$787$	28.5965	1.01935	0.509677	+	0.860366i	$0.329765\pi$
$788$	−17.3446	−0.617875
$789$	17.3034	0.616018
$790$	−5.31818	−0.189212
$791$	4.38435	0.155890
$792$	−13.5780	−0.482475
$793$	4.63396	0.164557
$794$	0.117456	0.00416835
$795$	23.5665	0.835816
$796$	−15.8172	−0.560626
$797$	−44.0984	−1.56205	−0.781023	−	0.624503i	$-0.785302\pi$
$797$	−44.0984	−1.56205	−0.781023	+	0.624503i	$0.785302\pi$
$798$	−1.86297	−0.0659484
$799$	0.110132	0.00389621
$800$	−50.3727	−1.78094
$801$	−2.90084	−0.102496
$802$	−1.67794	−0.0592501
$803$	67.9115	2.39654
$804$	−19.4377	−0.685514
$805$	19.5372	0.688595
$806$	−1.85075	−0.0651900
$807$	18.0570	0.635638
$808$	18.2204	0.640992
$809$	−27.7080	−0.974162	−0.487081	−	0.873357i	$-0.661938\pi$
$809$	−27.7080	−0.974162	−0.487081	+	0.873357i	$0.661938\pi$
$810$	−2.36132	−0.0829683
$811$	−11.8468	−0.415998	−0.207999	−	0.978129i	$-0.566695\pi$
$811$	−11.8468	−0.415998	−0.207999	+	0.978129i	$0.566695\pi$
$812$	3.67111	0.128831
$813$	1.08642	0.0381024
$814$	−7.04865	−0.247055
$815$	30.2156	1.05841
$816$	−0.386515	−0.0135307
$817$	−17.9206	−0.626962
$818$	21.6149	0.755747
$819$	−0.819859	−0.0286482
$820$	−13.5636	−0.473660
$821$	43.1182	1.50484	0.752418	−	0.658686i	$-0.228888\pi$
$821$	43.1182	1.50484	0.752418	+	0.658686i	$0.228888\pi$
$822$	−8.92007	−0.311123
$823$	30.8506	1.07538	0.537692	−	0.843141i	$-0.319296\pi$
$823$	30.8506	1.07538	0.537692	+	0.843141i	$0.319296\pi$
$824$	2.28046	0.0794437
$825$	52.8877	1.84131
$826$	0.105838	0.00368259
$827$	−14.8782	−0.517366	−0.258683	−	0.965962i	$-0.583289\pi$
$827$	−14.8782	−0.517366	−0.258683	+	0.965962i	$0.583289\pi$
$828$	10.2226	0.355260
$829$	20.1131	0.698558	0.349279	−	0.937019i	$-0.386426\pi$
$829$	20.1131	0.698558	0.349279	+	0.937019i	$0.386426\pi$
$830$	6.60525	0.229272
$831$	31.0755	1.07800
$832$	0.0910118	0.00315527
$833$	−1.39643	−0.0483833
$834$	7.37058	0.255222
$835$	−64.4362	−2.22991
$836$	34.1222	1.18014
$837$	−2.92031	−0.100941
$838$	13.9668	0.482475
$839$	−1.62640	−0.0561495	−0.0280748	−	0.999606i	$-0.508938\pi$
$839$	−1.62640	−0.0561495	−0.0280748	+	0.999606i	$0.508938\pi$
$840$	6.96623	0.240358
$841$	−21.1518	−0.729373
$842$	−8.87578	−0.305880
$843$	−23.3058	−0.802696
$844$	35.9100	1.23607
$845$	3.72594	0.128176
$846$	−0.316279	−0.0108739
$847$	−20.0463	−0.688799
$848$	−11.0780	−0.380420
$849$	5.93959	0.203846
$850$	−1.24229	−0.0426102
$851$	11.9471	0.409540
$852$	13.3841	0.458533
$853$	−52.2433	−1.78878	−0.894388	−	0.447292i	$-0.852388\pi$
$853$	−52.2433	−1.78878	−0.894388	+	0.447292i	$0.852388\pi$
$854$	2.40774	0.0823912
$855$	13.3593	0.456879
$856$	16.1997	0.553695
$857$	32.7750	1.11957	0.559786	−	0.828637i	$-0.310883\pi$
$857$	32.7750	1.11957	0.559786	+	0.828637i	$0.310883\pi$
$858$	−3.77340	−0.128822
$859$	50.3521	1.71799	0.858996	−	0.511982i	$-0.171088\pi$
$859$	50.3521	1.71799	0.858996	+	0.511982i	$0.171088\pi$
$860$	29.7656	1.01500
$861$	1.86725	0.0636358
$862$	8.38405	0.285562
$863$	−44.8327	−1.52612	−0.763061	−	0.646326i	$-0.776305\pi$
$863$	−44.8327	−1.52612	−0.763061	+	0.646326i	$0.776305\pi$
$864$	5.67093	0.192929
$865$	75.1035	2.55360
$866$	26.0857	0.886428
$867$	16.9513	0.575696
$868$	3.82686	0.129892
$869$	−13.4098	−0.454897
$870$	6.61513	0.224274
$871$	−12.1610	−0.412060
$872$	12.9796	0.439544
$873$	8.31381	0.281380
$874$	14.5330	0.491585
$875$	−11.8604	−0.400955
$876$	−18.2307	−0.615959
$877$	−11.4251	−0.385797	−0.192898	−	0.981219i	$-0.561789\pi$
$877$	−11.4251	−0.385797	−0.192898	+	0.981219i	$0.561789\pi$
$878$	−13.0567	−0.440643
$879$	18.4670	0.622877
$880$	−38.8555	−1.30982
$881$	−13.0765	−0.440560	−0.220280	−	0.975437i	$-0.570697\pi$
$881$	−13.0765	−0.440560	−0.220280	+	0.975437i	$0.570697\pi$
$882$	4.01027	0.135033
$883$	−33.9643	−1.14299	−0.571495	−	0.820605i	$-0.693637\pi$
$883$	−33.9643	−1.14299	−0.571495	+	0.820605i	$0.693637\pi$
$884$	−0.352726	−0.0118635
$885$	−0.758964	−0.0255123
$886$	9.63657	0.323747
$887$	6.83117	0.229368	0.114684	−	0.993402i	$-0.463414\pi$
$887$	6.83117	0.229368	0.114684	+	0.993402i	$0.463414\pi$
$888$	4.25988	0.142952
$889$	7.38926	0.247828
$890$	6.84980	0.229606
$891$	−5.95407	−0.199469
$892$	−39.4378	−1.32048
$893$	1.78937	0.0598790
$894$	−14.9723	−0.500748
$895$	−81.0010	−2.70756
$896$	−9.25143	−0.309068
$897$	6.39569	0.213546
$898$	−5.58461	−0.186361
$899$	8.18114	0.272856
$900$	−14.1976	−0.473254
$901$	−1.39580	−0.0465007
$902$	8.59402	0.286150
$903$	−4.09773	−0.136364
$904$	−12.1952	−0.405607
$905$	−60.9726	−2.02680
$906$	−6.71001	−0.222925
$907$	56.3054	1.86959	0.934795	−	0.355188i	$-0.115583\pi$
$907$	56.3054	1.86959	0.934795	+	0.355188i	$0.115583\pi$
$908$	9.50900	0.315567
$909$	7.98978	0.265004
$910$	1.93595	0.0641760
$911$	−41.1005	−1.36172	−0.680860	−	0.732413i	$-0.738394\pi$
$911$	−41.1005	−1.36172	−0.680860	+	0.732413i	$0.738394\pi$
$912$	−6.27988	−0.207948
$913$	16.6552	0.551205
$914$	12.3899	0.409821
$915$	−17.2658	−0.570791
$916$	−20.9834	−0.693311
$917$	7.75530	0.256103
$918$	0.139856	0.00461595
$919$	24.9416	0.822746	0.411373	−	0.911467i	$-0.365049\pi$
$919$	24.9416	0.822746	0.411373	+	0.911467i	$0.365049\pi$
$920$	−54.3434	−1.79165
$921$	28.3681	0.934760
$922$	0.579019	0.0190690
$923$	8.37368	0.275623
$924$	7.80238	0.256680
$925$	−16.5926	−0.545562
$926$	−4.73847	−0.155716
$927$	1.00000	0.0328443
$928$	−15.8869	−0.521512
$929$	−36.7745	−1.20653	−0.603266	−	0.797540i	$-0.706134\pi$
$929$	−36.7745	−1.20653	−0.603266	+	0.797540i	$0.706134\pi$
$930$	6.89579	0.226122
$931$	−22.6884	−0.743581
$932$	1.13549	0.0371941
$933$	18.6698	0.611222
$934$	9.55402	0.312617
$935$	−4.89568	−0.160106
$936$	2.28046	0.0745393
$937$	22.7343	0.742696	0.371348	−	0.928494i	$-0.378896\pi$
$937$	22.7343	0.742696	0.371348	+	0.928494i	$0.378896\pi$
$938$	−6.31869	−0.206313
$939$	−28.9811	−0.945763
$940$	−2.97209	−0.0969389
$941$	−11.5693	−0.377148	−0.188574	−	0.982059i	$-0.560387\pi$
$941$	−11.5693	−0.377148	−0.188574	+	0.982059i	$0.560387\pi$
$942$	3.35968	0.109464
$943$	−14.5664	−0.474346
$944$	0.356770	0.0116119
$945$	3.05474	0.0993708
$946$	−18.8598	−0.613185
$947$	−8.55658	−0.278051	−0.139026	−	0.990289i	$-0.544397\pi$
$947$	−8.55658	−0.278051	−0.139026	+	0.990289i	$0.544397\pi$
$948$	3.59984	0.116917
$949$	−11.4059	−0.370251
$950$	−20.1840	−0.654856
$951$	−19.8437	−0.643475
$952$	−0.412597	−0.0133723
$953$	24.9816	0.809234	0.404617	−	0.914486i	$-0.367405\pi$
$953$	24.9816	0.809234	0.404617	+	0.914486i	$0.367405\pi$
$954$	4.00846	0.129779
$955$	−3.51830	−0.113849
$956$	38.8728	1.25724
$957$	16.6801	0.539190
$958$	−1.43906	−0.0464939
$959$	11.5395	0.372631
$960$	−0.339104	−0.0109445
$961$	−22.4718	−0.724896
$962$	1.18384	0.0381685
$963$	7.10369	0.228913
$964$	39.7909	1.28158
$965$	−11.6637	−0.375469
$966$	3.32311	0.106919
$967$	−16.2059	−0.521146	−0.260573	−	0.965454i	$-0.583911\pi$
$967$	−16.2059	−0.521146	−0.260573	+	0.965454i	$0.583911\pi$
$968$	55.7595	1.79218
$969$	−0.791246	−0.0254185
$970$	−19.6316	−0.630331
$971$	−47.1203	−1.51216	−0.756082	−	0.654477i	$-0.772889\pi$
$971$	−47.1203	−1.51216	−0.756082	+	0.654477i	$0.772889\pi$
$972$	1.59836	0.0512674
$973$	−9.53503	−0.305679
$974$	−7.14711	−0.229008
$975$	−8.88262	−0.284471
$976$	8.11625	0.259795
$977$	−8.25374	−0.264061	−0.132030	−	0.991246i	$-0.542150\pi$
$977$	−8.25374	−0.264061	−0.132030	+	0.991246i	$0.542150\pi$
$978$	5.13943	0.164341
$979$	17.2718	0.552009
$980$	37.6847	1.20379
$981$	5.69163	0.181720
$982$	−9.43275	−0.301011
$983$	42.5226	1.35626	0.678130	−	0.734942i	$-0.262791\pi$
$983$	42.5226	1.35626	0.678130	+	0.734942i	$0.262791\pi$
$984$	−5.19382	−0.165573
$985$	40.4320	1.28827
$986$	−0.391802	−0.0124775
$987$	0.409158	0.0130236
$988$	−5.73090	−0.182324
$989$	31.9662	1.01647
$990$	14.0594	0.446839
$991$	59.1320	1.87839	0.939194	−	0.343386i	$-0.111574\pi$
$991$	59.1320	1.87839	0.939194	+	0.343386i	$0.111574\pi$
$992$	−16.5609	−0.525809
$993$	4.28222	0.135892
$994$	4.35085	0.138000
$995$	36.8715	1.16890
$996$	−4.47105	−0.141671
$997$	−12.1746	−0.385574	−0.192787	−	0.981241i	$-0.561753\pi$
$997$	−12.1746	−0.385574	−0.192787	+	0.981241i	$0.561753\pi$
$998$	8.46994	0.268111
$999$	1.86799	0.0591005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.12	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.12	✓	25	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)

\(f(q)\)	\(=\)	\(q-0.633751 q^{2} -1.00000 q^{3} -1.59836 q^{4} +3.72594 q^{5} +0.633751 q^{6} -0.819859 q^{7} +2.28046 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.633751 q^{2} -1.00000 q^{3} -1.59836 q^{4} +3.72594 q^{5} +0.633751 q^{6} -0.819859 q^{7} +2.28046 q^{8} +1.00000 q^{9} -2.36132 q^{10} -5.95407 q^{11} +1.59836 q^{12} +1.00000 q^{13} +0.519586 q^{14} -3.72594 q^{15} +1.75147 q^{16} +0.220680 q^{17} -0.633751 q^{18} +3.58549 q^{19} -5.95539 q^{20} +0.819859 q^{21} +3.77340 q^{22} -6.39569 q^{23} -2.28046 q^{24} +8.88262 q^{25} -0.633751 q^{26} -1.00000 q^{27} +1.31043 q^{28} +2.80146 q^{29} +2.36132 q^{30} +2.92031 q^{31} -5.67093 q^{32} +5.95407 q^{33} -0.139856 q^{34} -3.05474 q^{35} -1.59836 q^{36} -1.86799 q^{37} -2.27231 q^{38} -1.00000 q^{39} +8.49687 q^{40} +2.27753 q^{41} -0.519586 q^{42} -4.99809 q^{43} +9.51674 q^{44} +3.72594 q^{45} +4.05328 q^{46} +0.499059 q^{47} -1.75147 q^{48} -6.32783 q^{49} -5.62937 q^{50} -0.220680 q^{51} -1.59836 q^{52} -6.32497 q^{53} +0.633751 q^{54} -22.1845 q^{55} -1.86966 q^{56} -3.58549 q^{57} -1.77543 q^{58} +0.203697 q^{59} +5.95539 q^{60} +4.63396 q^{61} -1.85075 q^{62} -0.819859 q^{63} +0.0910118 q^{64} +3.72594 q^{65} -3.77340 q^{66} -12.1610 q^{67} -0.352726 q^{68} +6.39569 q^{69} +1.93595 q^{70} +8.37368 q^{71} +2.28046 q^{72} -11.4059 q^{73} +1.18384 q^{74} -8.88262 q^{75} -5.73090 q^{76} +4.88149 q^{77} +0.633751 q^{78} +2.25221 q^{79} +6.52588 q^{80} +1.00000 q^{81} -1.44339 q^{82} -2.79727 q^{83} -1.31043 q^{84} +0.822241 q^{85} +3.16755 q^{86} -2.80146 q^{87} -13.5780 q^{88} -2.90084 q^{89} -2.36132 q^{90} -0.819859 q^{91} +10.2226 q^{92} -2.92031 q^{93} -0.316279 q^{94} +13.3593 q^{95} +5.67093 q^{96} +8.31381 q^{97} +4.01027 q^{98} -5.95407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

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