LMFDB - Embedded newform 4022.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.653164 q^{3} +1.00000 q^{4} +1.42104 q^{5} -0.653164 q^{6} -3.96008 q^{7} +1.00000 q^{8} -2.57338 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.653164 q^{3} +1.00000 q^{4} +1.42104 q^{5} -0.653164 q^{6} -3.96008 q^{7} +1.00000 q^{8} -2.57338 q^{9} +1.42104 q^{10} -1.17977 q^{11} -0.653164 q^{12} +6.18656 q^{13} -3.96008 q^{14} -0.928170 q^{15} +1.00000 q^{16} -1.77201 q^{17} -2.57338 q^{18} -3.68348 q^{19} +1.42104 q^{20} +2.58658 q^{21} -1.17977 q^{22} +8.67483 q^{23} -0.653164 q^{24} -2.98065 q^{25} +6.18656 q^{26} +3.64033 q^{27} -3.96008 q^{28} +6.63924 q^{29} -0.928170 q^{30} -10.8585 q^{31} +1.00000 q^{32} +0.770585 q^{33} -1.77201 q^{34} -5.62741 q^{35} -2.57338 q^{36} -0.0645259 q^{37} -3.68348 q^{38} -4.04084 q^{39} +1.42104 q^{40} -9.97130 q^{41} +2.58658 q^{42} +8.15716 q^{43} -1.17977 q^{44} -3.65686 q^{45} +8.67483 q^{46} -10.6115 q^{47} -0.653164 q^{48} +8.68221 q^{49} -2.98065 q^{50} +1.15741 q^{51} +6.18656 q^{52} +1.25365 q^{53} +3.64033 q^{54} -1.67650 q^{55} -3.96008 q^{56} +2.40592 q^{57} +6.63924 q^{58} -9.79816 q^{59} -0.928170 q^{60} -10.2357 q^{61} -10.8585 q^{62} +10.1908 q^{63} +1.00000 q^{64} +8.79133 q^{65} +0.770585 q^{66} +1.43135 q^{67} -1.77201 q^{68} -5.66609 q^{69} -5.62741 q^{70} -5.66937 q^{71} -2.57338 q^{72} -2.26871 q^{73} -0.0645259 q^{74} +1.94686 q^{75} -3.68348 q^{76} +4.67199 q^{77} -4.04084 q^{78} -0.132714 q^{79} +1.42104 q^{80} +5.34240 q^{81} -9.97130 q^{82} -14.1027 q^{83} +2.58658 q^{84} -2.51810 q^{85} +8.15716 q^{86} -4.33651 q^{87} -1.17977 q^{88} +3.73243 q^{89} -3.65686 q^{90} -24.4993 q^{91} +8.67483 q^{92} +7.09236 q^{93} -10.6115 q^{94} -5.23437 q^{95} -0.653164 q^{96} +2.98283 q^{97} +8.68221 q^{98} +3.03600 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.653164	−0.377104	−0.188552	−	0.982063i	$-0.560379\pi$
$3$	−0.653164	−0.377104	−0.188552	+	0.982063i	$0.560379\pi$
$4$	1.00000	0.500000
$5$	1.42104	0.635507	0.317753	−	0.948173i	$-0.397072\pi$
$5$	1.42104	0.635507	0.317753	+	0.948173i	$0.397072\pi$
$6$	−0.653164	−0.266653
$7$	−3.96008	−1.49677	−0.748384	−	0.663266i	$-0.769170\pi$
$7$	−3.96008	−1.49677	−0.748384	+	0.663266i	$0.769170\pi$
$8$	1.00000	0.353553
$9$	−2.57338	−0.857792
$10$	1.42104	0.449371
$11$	−1.17977	−0.355715	−0.177857	−	0.984056i	$-0.556917\pi$
$11$	−1.17977	−0.355715	−0.177857	+	0.984056i	$0.556917\pi$
$12$	−0.653164	−0.188552
$13$	6.18656	1.71584	0.857922	−	0.513780i	$-0.171755\pi$
$13$	6.18656	1.71584	0.857922	+	0.513780i	$0.171755\pi$
$14$	−3.96008	−1.05837
$15$	−0.928170	−0.239652
$16$	1.00000	0.250000
$17$	−1.77201	−0.429776	−0.214888	−	0.976639i	$-0.568939\pi$
$17$	−1.77201	−0.429776	−0.214888	+	0.976639i	$0.568939\pi$
$18$	−2.57338	−0.606551
$19$	−3.68348	−0.845049	−0.422525	−	0.906351i	$-0.638856\pi$
$19$	−3.68348	−0.845049	−0.422525	+	0.906351i	$0.638856\pi$
$20$	1.42104	0.317753
$21$	2.58658	0.564438
$22$	−1.17977	−0.251528
$23$	8.67483	1.80883	0.904413	−	0.426657i	$-0.140309\pi$
$23$	8.67483	1.80883	0.904413	+	0.426657i	$0.140309\pi$
$24$	−0.653164	−0.133327
$25$	−2.98065	−0.596131
$26$	6.18656	1.21328
$27$	3.64033	0.700582
$28$	−3.96008	−0.748384
$29$	6.63924	1.23288	0.616438	−	0.787403i	$-0.288575\pi$
$29$	6.63924	1.23288	0.616438	+	0.787403i	$0.288575\pi$
$30$	−0.928170	−0.169460
$31$	−10.8585	−1.95024	−0.975120	−	0.221678i	$-0.928846\pi$
$31$	−10.8585	−1.95024	−0.975120	+	0.221678i	$0.928846\pi$
$32$	1.00000	0.176777
$33$	0.770585	0.134142
$34$	−1.77201	−0.303898
$35$	−5.62741	−0.951207
$36$	−2.57338	−0.428896
$37$	−0.0645259	−0.0106080	−0.00530400	−	0.999986i	$-0.501688\pi$
$37$	−0.0645259	−0.0106080	−0.00530400	+	0.999986i	$0.501688\pi$
$38$	−3.68348	−0.597540
$39$	−4.04084	−0.647052
$40$	1.42104	0.224686
$41$	−9.97130	−1.55726	−0.778628	−	0.627486i	$-0.784084\pi$
$41$	−9.97130	−1.55726	−0.778628	+	0.627486i	$0.784084\pi$
$42$	2.58658	0.399118
$43$	8.15716	1.24395	0.621977	−	0.783035i	$-0.286330\pi$
$43$	8.15716	1.24395	0.621977	+	0.783035i	$0.286330\pi$
$44$	−1.17977	−0.177857
$45$	−3.65686	−0.545133
$46$	8.67483	1.27903
$47$	−10.6115	−1.54784	−0.773921	−	0.633283i	$-0.781707\pi$
$47$	−10.6115	−1.54784	−0.773921	+	0.633283i	$0.781707\pi$
$48$	−0.653164	−0.0942761
$49$	8.68221	1.24032
$50$	−2.98065	−0.421528
$51$	1.15741	0.162071
$52$	6.18656	0.857922
$53$	1.25365	0.172202	0.0861012	−	0.996286i	$-0.472559\pi$
$53$	1.25365	0.172202	0.0861012	+	0.996286i	$0.472559\pi$
$54$	3.64033	0.495386
$55$	−1.67650	−0.226059
$56$	−3.96008	−0.529187
$57$	2.40592	0.318672
$58$	6.63924	0.871775
$59$	−9.79816	−1.27561	−0.637806	−	0.770197i	$-0.720158\pi$
$59$	−9.79816	−1.27561	−0.637806	+	0.770197i	$0.720158\pi$
$60$	−0.928170	−0.119826
$61$	−10.2357	−1.31055	−0.655275	−	0.755391i	$-0.727447\pi$
$61$	−10.2357	−1.31055	−0.655275	+	0.755391i	$0.727447\pi$
$62$	−10.8585	−1.37903
$63$	10.1908	1.28392
$64$	1.00000	0.125000
$65$	8.79133	1.09043
$66$	0.770585	0.0948525
$67$	1.43135	0.174867	0.0874334	−	0.996170i	$-0.472134\pi$
$67$	1.43135	0.174867	0.0874334	+	0.996170i	$0.472134\pi$
$68$	−1.77201	−0.214888
$69$	−5.66609	−0.682117
$70$	−5.62741	−0.672605
$71$	−5.66937	−0.672830	−0.336415	−	0.941714i	$-0.609214\pi$
$71$	−5.66937	−0.672830	−0.336415	+	0.941714i	$0.609214\pi$
$72$	−2.57338	−0.303275
$73$	−2.26871	−0.265532	−0.132766	−	0.991147i	$-0.542386\pi$
$73$	−2.26871	−0.265532	−0.132766	+	0.991147i	$0.542386\pi$
$74$	−0.0645259	−0.00750098
$75$	1.94686	0.224804
$76$	−3.68348	−0.422525
$77$	4.67199	0.532423
$78$	−4.04084	−0.457535
$79$	−0.132714	−0.0149315	−0.00746577	−	0.999972i	$-0.502376\pi$
$79$	−0.132714	−0.0149315	−0.00746577	+	0.999972i	$0.502376\pi$
$80$	1.42104	0.158877
$81$	5.34240	0.593600
$82$	−9.97130	−1.10115
$83$	−14.1027	−1.54797	−0.773985	−	0.633204i	$-0.781739\pi$
$83$	−14.1027	−1.54797	−0.773985	+	0.633204i	$0.781739\pi$
$84$	2.58658	0.282219
$85$	−2.51810	−0.273126
$86$	8.15716	0.879609
$87$	−4.33651	−0.464923
$88$	−1.17977	−0.125764
$89$	3.73243	0.395636	0.197818	−	0.980239i	$-0.436614\pi$
$89$	3.73243	0.395636	0.197818	+	0.980239i	$0.436614\pi$
$90$	−3.65686	−0.385467
$91$	−24.4993	−2.56822
$92$	8.67483	0.904413
$93$	7.09236	0.735444
$94$	−10.6115	−1.09449
$95$	−5.23437	−0.537035
$96$	−0.653164	−0.0666633
$97$	2.98283	0.302861	0.151430	−	0.988468i	$-0.451612\pi$
$97$	2.98283	0.302861	0.151430	+	0.988468i	$0.451612\pi$
$98$	8.68221	0.877035
$99$	3.03600	0.305130
$100$	−2.98065	−0.298065
$101$	−11.6498	−1.15920	−0.579601	−	0.814901i	$-0.696791\pi$
$101$	−11.6498	−1.15920	−0.579601	+	0.814901i	$0.696791\pi$
$102$	1.15741	0.114601
$103$	−18.5674	−1.82950	−0.914750	−	0.404021i	$-0.867612\pi$
$103$	−18.5674	−1.82950	−0.914750	+	0.404021i	$0.867612\pi$
$104$	6.18656	0.606642
$105$	3.67562	0.358704
$106$	1.25365	0.121765
$107$	−18.8355	−1.82090	−0.910451	−	0.413618i	$-0.864265\pi$
$107$	−18.8355	−1.82090	−0.910451	+	0.413618i	$0.864265\pi$
$108$	3.64033	0.350291
$109$	−13.6390	−1.30638	−0.653191	−	0.757194i	$-0.726570\pi$
$109$	−13.6390	−1.30638	−0.653191	+	0.757194i	$0.726570\pi$
$110$	−1.67650	−0.159848
$111$	0.0421460	0.00400032
$112$	−3.96008	−0.374192
$113$	−6.42704	−0.604605	−0.302303	−	0.953212i	$-0.597755\pi$
$113$	−6.42704	−0.604605	−0.302303	+	0.953212i	$0.597755\pi$
$114$	2.40592	0.225335
$115$	12.3273	1.14952
$116$	6.63924	0.616438
$117$	−15.9204	−1.47184
$118$	−9.79816	−0.901993
$119$	7.01731	0.643275
$120$	−0.928170	−0.0847299
$121$	−9.60814	−0.873467
$122$	−10.2357	−0.926698
$123$	6.51290	0.587248
$124$	−10.8585	−0.975120
$125$	−11.3408	−1.01435
$126$	10.1908	0.907866
$127$	15.3813	1.36487	0.682435	−	0.730946i	$-0.260921\pi$
$127$	15.3813	1.36487	0.682435	+	0.730946i	$0.260921\pi$
$128$	1.00000	0.0883883
$129$	−5.32796	−0.469101
$130$	8.79133	0.771051
$131$	6.11543	0.534308	0.267154	−	0.963654i	$-0.413917\pi$
$131$	6.11543	0.534308	0.267154	+	0.963654i	$0.413917\pi$
$132$	0.770585	0.0670708
$133$	14.5869	1.26484
$134$	1.43135	0.123649
$135$	5.17304	0.445225
$136$	−1.77201	−0.151949
$137$	14.3846	1.22896	0.614480	−	0.788933i	$-0.289366\pi$
$137$	14.3846	1.22896	0.614480	+	0.788933i	$0.289366\pi$
$138$	−5.66609	−0.482329
$139$	1.96430	0.166610	0.0833049	−	0.996524i	$-0.473452\pi$
$139$	1.96430	0.166610	0.0833049	+	0.996524i	$0.473452\pi$
$140$	−5.62741	−0.475603
$141$	6.93103	0.583698
$142$	−5.66937	−0.475763
$143$	−7.29874	−0.610351
$144$	−2.57338	−0.214448
$145$	9.43460	0.783501
$146$	−2.26871	−0.187760
$147$	−5.67090	−0.467728
$148$	−0.0645259	−0.00530400
$149$	−7.39214	−0.605588	−0.302794	−	0.953056i	$-0.597919\pi$
$149$	−7.39214	−0.605588	−0.302794	+	0.953056i	$0.597919\pi$
$150$	1.94686	0.158960
$151$	−3.94606	−0.321126	−0.160563	−	0.987026i	$-0.551331\pi$
$151$	−3.94606	−0.321126	−0.160563	+	0.987026i	$0.551331\pi$
$152$	−3.68348	−0.298770
$153$	4.56006	0.368659
$154$	4.67199	0.376480
$155$	−15.4303	−1.23939
$156$	−4.04084	−0.323526
$157$	0.696718	0.0556041	0.0278021	−	0.999613i	$-0.491149\pi$
$157$	0.696718	0.0556041	0.0278021	+	0.999613i	$0.491149\pi$
$158$	−0.132714	−0.0105582
$159$	−0.818840	−0.0649382
$160$	1.42104	0.112343
$161$	−34.3530	−2.70739
$162$	5.34240	0.419738
$163$	8.59598	0.673289	0.336645	−	0.941632i	$-0.390708\pi$
$163$	8.59598	0.673289	0.336645	+	0.941632i	$0.390708\pi$
$164$	−9.97130	−0.778628
$165$	1.09503	0.0852480
$166$	−14.1027	−1.09458
$167$	−1.06449	−0.0823725	−0.0411862	−	0.999151i	$-0.513114\pi$
$167$	−1.06449	−0.0823725	−0.0411862	+	0.999151i	$0.513114\pi$
$168$	2.58658	0.199559
$169$	25.2736	1.94412
$170$	−2.51810	−0.193129
$171$	9.47899	0.724877
$172$	8.15716	0.621977
$173$	20.5593	1.56310	0.781548	−	0.623845i	$-0.214430\pi$
$173$	20.5593	1.56310	0.781548	+	0.623845i	$0.214430\pi$
$174$	−4.33651	−0.328750
$175$	11.8036	0.892270
$176$	−1.17977	−0.0889287
$177$	6.39980	0.481039
$178$	3.73243	0.279757
$179$	8.48280	0.634034	0.317017	−	0.948420i	$-0.397319\pi$
$179$	8.48280	0.634034	0.317017	+	0.948420i	$0.397319\pi$
$180$	−3.65686	−0.272566
$181$	22.9621	1.70676	0.853380	−	0.521289i	$-0.174549\pi$
$181$	22.9621	1.70676	0.853380	+	0.521289i	$0.174549\pi$
$182$	−24.4993	−1.81601
$183$	6.68560	0.494214
$184$	8.67483	0.639517
$185$	−0.0916937	−0.00674145
$186$	7.09236	0.520037
$187$	2.09057	0.152878
$188$	−10.6115	−0.773921
$189$	−14.4160	−1.04861
$190$	−5.23437	−0.379741
$191$	16.6319	1.20344	0.601722	−	0.798706i	$-0.294482\pi$
$191$	16.6319	1.20344	0.601722	+	0.798706i	$0.294482\pi$
$192$	−0.653164	−0.0471381
$193$	14.8544	1.06924	0.534621	−	0.845092i	$-0.320454\pi$
$193$	14.8544	1.06924	0.534621	+	0.845092i	$0.320454\pi$
$194$	2.98283	0.214155
$195$	−5.74218	−0.411206
$196$	8.68221	0.620158
$197$	14.3137	1.01981	0.509906	−	0.860230i	$-0.329680\pi$
$197$	14.3137	1.01981	0.509906	+	0.860230i	$0.329680\pi$
$198$	3.03600	0.215759
$199$	−1.84976	−0.131126	−0.0655628	−	0.997848i	$-0.520884\pi$
$199$	−1.84976	−0.131126	−0.0655628	+	0.997848i	$0.520884\pi$
$200$	−2.98065	−0.210764
$201$	−0.934904	−0.0659430
$202$	−11.6498	−0.819679
$203$	−26.2919	−1.84533
$204$	1.15741	0.0810353
$205$	−14.1696	−0.989647
$206$	−18.5674	−1.29365
$207$	−22.3236	−1.55160
$208$	6.18656	0.428961
$209$	4.34568	0.300597
$210$	3.67562	0.253642
$211$	−24.7329	−1.70269	−0.851343	−	0.524610i	$-0.824211\pi$
$211$	−24.7329	−1.70269	−0.851343	+	0.524610i	$0.824211\pi$
$212$	1.25365	0.0861012
$213$	3.70303	0.253727
$214$	−18.8355	−1.28757
$215$	11.5916	0.790542
$216$	3.64033	0.247693
$217$	43.0004	2.91906
$218$	−13.6390	−0.923751
$219$	1.48184	0.100133
$220$	−1.67650	−0.113030
$221$	−10.9627	−0.737429
$222$	0.0421460	0.00282865
$223$	2.81841	0.188735	0.0943673	−	0.995537i	$-0.469917\pi$
$223$	2.81841	0.188735	0.0943673	+	0.995537i	$0.469917\pi$
$224$	−3.96008	−0.264594
$225$	7.67035	0.511356
$226$	−6.42704	−0.427520
$227$	−24.2026	−1.60638	−0.803191	−	0.595722i	$-0.796866\pi$
$227$	−24.2026	−1.60638	−0.803191	+	0.595722i	$0.796866\pi$
$228$	2.40592	0.159336
$229$	−8.11135	−0.536013	−0.268006	−	0.963417i	$-0.586365\pi$
$229$	−8.11135	−0.536013	−0.268006	+	0.963417i	$0.586365\pi$
$230$	12.3273	0.812835
$231$	−3.05158	−0.200779
$232$	6.63924	0.435887
$233$	14.1947	0.929925	0.464962	−	0.885330i	$-0.346068\pi$
$233$	14.1947	0.929925	0.464962	+	0.885330i	$0.346068\pi$
$234$	−15.9204	−1.04075
$235$	−15.0793	−0.983664
$236$	−9.79816	−0.637806
$237$	0.0866842	0.00563075
$238$	7.01731	0.454864
$239$	−25.8393	−1.67140	−0.835702	−	0.549183i	$-0.814939\pi$
$239$	−25.8393	−1.67140	−0.835702	+	0.549183i	$0.814939\pi$
$240$	−0.928170	−0.0599131
$241$	0.470592	0.0303135	0.0151568	−	0.999885i	$-0.495175\pi$
$241$	0.470592	0.0303135	0.0151568	+	0.999885i	$0.495175\pi$
$242$	−9.60814	−0.617634
$243$	−14.4104	−0.924431
$244$	−10.2357	−0.655275
$245$	12.3377	0.788229
$246$	6.51290	0.415247
$247$	−22.7881	−1.44997
$248$	−10.8585	−0.689514
$249$	9.21136	0.583746
$250$	−11.3408	−0.717255
$251$	−9.15599	−0.577921	−0.288960	−	0.957341i	$-0.593310\pi$
$251$	−9.15599	−0.577921	−0.288960	+	0.957341i	$0.593310\pi$
$252$	10.1908	0.641958
$253$	−10.2343	−0.643427
$254$	15.3813	0.965109
$255$	1.64473	0.102997
$256$	1.00000	0.0625000
$257$	19.4258	1.21175	0.605873	−	0.795562i	$-0.292824\pi$
$257$	19.4258	1.21175	0.605873	+	0.795562i	$0.292824\pi$
$258$	−5.32796	−0.331704
$259$	0.255527	0.0158777
$260$	8.79133	0.545215
$261$	−17.0853	−1.05755
$262$	6.11543	0.377813
$263$	7.13295	0.439836	0.219918	−	0.975518i	$-0.429421\pi$
$263$	7.13295	0.439836	0.219918	+	0.975518i	$0.429421\pi$
$264$	0.770585	0.0474262
$265$	1.78149	0.109436
$266$	14.5869	0.894379
$267$	−2.43789	−0.149196
$268$	1.43135	0.0874334
$269$	12.9113	0.787216	0.393608	−	0.919278i	$-0.371227\pi$
$269$	12.9113	0.787216	0.393608	+	0.919278i	$0.371227\pi$
$270$	5.17304	0.314821
$271$	−13.6883	−0.831507	−0.415753	−	0.909477i	$-0.636482\pi$
$271$	−13.6883	−0.831507	−0.415753	+	0.909477i	$0.636482\pi$
$272$	−1.77201	−0.107444
$273$	16.0020	0.968487
$274$	14.3846	0.869006
$275$	3.51650	0.212053
$276$	−5.66609	−0.341058
$277$	−13.3456	−0.801856	−0.400928	−	0.916109i	$-0.631312\pi$
$277$	−13.3456	−0.801856	−0.400928	+	0.916109i	$0.631312\pi$
$278$	1.96430	0.117811
$279$	27.9429	1.67290
$280$	−5.62741	−0.336302
$281$	−7.36662	−0.439456	−0.219728	−	0.975561i	$-0.570517\pi$
$281$	−7.36662	−0.439456	−0.219728	+	0.975561i	$0.570517\pi$
$282$	6.93103	0.412737
$283$	23.5668	1.40090	0.700451	−	0.713701i	$-0.252982\pi$
$283$	23.5668	1.40090	0.700451	+	0.713701i	$0.252982\pi$
$284$	−5.66937	−0.336415
$285$	3.41890	0.202518
$286$	−7.29874	−0.431584
$287$	39.4871	2.33085
$288$	−2.57338	−0.151638
$289$	−13.8600	−0.815292
$290$	9.43460	0.554019
$291$	−1.94828	−0.114210
$292$	−2.26871	−0.132766
$293$	11.0611	0.646195	0.323098	−	0.946366i	$-0.395276\pi$
$293$	11.0611	0.646195	0.323098	+	0.946366i	$0.395276\pi$
$294$	−5.67090	−0.330734
$295$	−13.9235	−0.810660
$296$	−0.0645259	−0.00375049
$297$	−4.29476	−0.249207
$298$	−7.39214	−0.428215
$299$	53.6674	3.10366
$300$	1.94686	0.112402
$301$	−32.3030	−1.86191
$302$	−3.94606	−0.227070
$303$	7.60925	0.437140
$304$	−3.68348	−0.211262
$305$	−14.5453	−0.832863
$306$	4.56006	0.260681
$307$	11.3475	0.647638	0.323819	−	0.946119i	$-0.395033\pi$
$307$	11.3475	0.647638	0.323819	+	0.946119i	$0.395033\pi$
$308$	4.67199	0.266211
$309$	12.1276	0.689912
$310$	−15.4303	−0.876382
$311$	−30.4488	−1.72659	−0.863296	−	0.504699i	$-0.831604\pi$
$311$	−30.4488	−1.72659	−0.863296	+	0.504699i	$0.831604\pi$
$312$	−4.04084	−0.228768
$313$	−0.0414177	−0.00234106	−0.00117053	−	0.999999i	$-0.500373\pi$
$313$	−0.0414177	−0.00234106	−0.00117053	+	0.999999i	$0.500373\pi$
$314$	0.696718	0.0393181
$315$	14.4815	0.815938
$316$	−0.132714	−0.00746577
$317$	−9.92508	−0.557448	−0.278724	−	0.960371i	$-0.589912\pi$
$317$	−9.92508	−0.557448	−0.278724	+	0.960371i	$0.589912\pi$
$318$	−0.818840	−0.0459183
$319$	−7.83280	−0.438552
$320$	1.42104	0.0794384
$321$	12.3027	0.686670
$322$	−34.3530	−1.91442
$323$	6.52718	0.363182
$324$	5.34240	0.296800
$325$	−18.4400	−1.02287
$326$	8.59598	0.476087
$327$	8.90852	0.492642
$328$	−9.97130	−0.550573
$329$	42.0222	2.31676
$330$	1.09503	0.0602794
$331$	13.9639	0.767526	0.383763	−	0.923432i	$-0.374628\pi$
$331$	13.9639	0.767526	0.383763	+	0.923432i	$0.374628\pi$
$332$	−14.1027	−0.773985
$333$	0.166049	0.00909945
$334$	−1.06449	−0.0582461
$335$	2.03400	0.111129
$336$	2.58658	0.141109
$337$	13.6787	0.745127	0.372563	−	0.928007i	$-0.378479\pi$
$337$	13.6787	0.745127	0.372563	+	0.928007i	$0.378479\pi$
$338$	25.2736	1.37470
$339$	4.19791	0.227999
$340$	−2.51810	−0.136563
$341$	12.8105	0.693729
$342$	9.47899	0.512565
$343$	−6.66166	−0.359696
$344$	8.15716	0.439804
$345$	−8.05172	−0.433490
$346$	20.5593	1.10528
$347$	3.70909	0.199114	0.0995572	−	0.995032i	$-0.468257\pi$
$347$	3.70909	0.199114	0.0995572	+	0.995032i	$0.468257\pi$
$348$	−4.33651	−0.232461
$349$	14.6908	0.786381	0.393191	−	0.919457i	$-0.371371\pi$
$349$	14.6908	0.786381	0.393191	+	0.919457i	$0.371371\pi$
$350$	11.8036	0.630930
$351$	22.5211	1.20209
$352$	−1.17977	−0.0628821
$353$	−30.4837	−1.62248	−0.811242	−	0.584710i	$-0.801208\pi$
$353$	−30.4837	−1.62248	−0.811242	+	0.584710i	$0.801208\pi$
$354$	6.39980	0.340146
$355$	−8.05638	−0.427588
$356$	3.73243	0.197818
$357$	−4.58345	−0.242582
$358$	8.48280	0.448330
$359$	28.7330	1.51647	0.758235	−	0.651981i	$-0.226062\pi$
$359$	28.7330	1.51647	0.758235	+	0.651981i	$0.226062\pi$
$360$	−3.65686	−0.192734
$361$	−5.43194	−0.285892
$362$	22.9621	1.20686
$363$	6.27569	0.329388
$364$	−24.4993	−1.28411
$365$	−3.22392	−0.168748
$366$	6.68560	0.349462
$367$	−3.67521	−0.191844	−0.0959221	−	0.995389i	$-0.530580\pi$
$367$	−3.67521	−0.191844	−0.0959221	+	0.995389i	$0.530580\pi$
$368$	8.67483	0.452207
$369$	25.6599	1.33580
$370$	−0.0916937	−0.00476693
$371$	−4.96456	−0.257747
$372$	7.09236	0.367722
$373$	0.952980	0.0493434	0.0246717	−	0.999696i	$-0.492146\pi$
$373$	0.952980	0.0493434	0.0246717	+	0.999696i	$0.492146\pi$
$374$	2.09057	0.108101
$375$	7.40740	0.382517
$376$	−10.6115	−0.547244
$377$	41.0741	2.11542
$378$	−14.4160	−0.741478
$379$	18.8475	0.968133	0.484067	−	0.875031i	$-0.339159\pi$
$379$	18.8475	0.968133	0.484067	+	0.875031i	$0.339159\pi$
$380$	−5.23437	−0.268517
$381$	−10.0465	−0.514699
$382$	16.6319	0.850963
$383$	−12.2646	−0.626693	−0.313347	−	0.949639i	$-0.601450\pi$
$383$	−12.2646	−0.626693	−0.313347	+	0.949639i	$0.601450\pi$
$384$	−0.653164	−0.0333316
$385$	6.63907	0.338358
$386$	14.8544	0.756069
$387$	−20.9914	−1.06705
$388$	2.98283	0.151430
$389$	−27.6965	−1.40427	−0.702135	−	0.712044i	$-0.747770\pi$
$389$	−27.6965	−1.40427	−0.702135	+	0.712044i	$0.747770\pi$
$390$	−5.74218	−0.290767
$391$	−15.3719	−0.777391
$392$	8.68221	0.438518
$393$	−3.99438	−0.201490
$394$	14.3137	0.721116
$395$	−0.188592	−0.00948909
$396$	3.03600	0.152565
$397$	−33.7183	−1.69227	−0.846136	−	0.532967i	$-0.821077\pi$
$397$	−33.7183	−1.69227	−0.846136	+	0.532967i	$0.821077\pi$
$398$	−1.84976	−0.0927199
$399$	−9.52762	−0.476978
$400$	−2.98065	−0.149033
$401$	6.36050	0.317628	0.158814	−	0.987308i	$-0.449233\pi$
$401$	6.36050	0.317628	0.158814	+	0.987308i	$0.449233\pi$
$402$	−0.934904	−0.0466288
$403$	−67.1766	−3.34631
$404$	−11.6498	−0.579601
$405$	7.59174	0.377237
$406$	−26.2919	−1.30485
$407$	0.0761259	0.00377342
$408$	1.15741	0.0573006
$409$	10.2500	0.506832	0.253416	−	0.967357i	$-0.418446\pi$
$409$	10.2500	0.506832	0.253416	+	0.967357i	$0.418446\pi$
$410$	−14.1696	−0.699786
$411$	−9.39550	−0.463446
$412$	−18.5674	−0.914750
$413$	38.8014	1.90929
$414$	−22.3236	−1.09715
$415$	−20.0404	−0.983745
$416$	6.18656	0.303321
$417$	−1.28301	−0.0628293
$418$	4.34568	0.212554
$419$	−30.5103	−1.49053	−0.745263	−	0.666770i	$-0.767676\pi$
$419$	−30.5103	−1.49053	−0.745263	+	0.666770i	$0.767676\pi$
$420$	3.67562	0.179352
$421$	−17.6029	−0.857911	−0.428955	−	0.903326i	$-0.641118\pi$
$421$	−17.6029	−0.857911	−0.428955	+	0.903326i	$0.641118\pi$
$422$	−24.7329	−1.20398
$423$	27.3073	1.32773
$424$	1.25365	0.0608827
$425$	5.28176	0.256203
$426$	3.70303	0.179412
$427$	40.5342	1.96159
$428$	−18.8355	−0.910451
$429$	4.76727	0.230166
$430$	11.5916	0.558997
$431$	−9.92522	−0.478081	−0.239041	−	0.971010i	$-0.576833\pi$
$431$	−9.92522	−0.478081	−0.239041	+	0.971010i	$0.576833\pi$
$432$	3.64033	0.175145
$433$	28.0195	1.34653	0.673266	−	0.739400i	$-0.264891\pi$
$433$	28.0195	1.34653	0.673266	+	0.739400i	$0.264891\pi$
$434$	43.0004	2.06408
$435$	−6.16234	−0.295462
$436$	−13.6390	−0.653191
$437$	−31.9536	−1.52855
$438$	1.48184	0.0708050
$439$	−9.66635	−0.461350	−0.230675	−	0.973031i	$-0.574093\pi$
$439$	−9.66635	−0.461350	−0.230675	+	0.973031i	$0.574093\pi$
$440$	−1.67650	−0.0799240
$441$	−22.3426	−1.06393
$442$	−10.9627	−0.521441
$443$	−12.2716	−0.583043	−0.291522	−	0.956564i	$-0.594162\pi$
$443$	−12.2716	−0.583043	−0.291522	+	0.956564i	$0.594162\pi$
$444$	0.0421460	0.00200016
$445$	5.30391	0.251430
$446$	2.81841	0.133456
$447$	4.82828	0.228370
$448$	−3.96008	−0.187096
$449$	6.68146	0.315317	0.157659	−	0.987494i	$-0.449605\pi$
$449$	6.68146	0.315317	0.157659	+	0.987494i	$0.449605\pi$
$450$	7.67035	0.361584
$451$	11.7639	0.553939
$452$	−6.42704	−0.302303
$453$	2.57742	0.121098
$454$	−24.2026	−1.13588
$455$	−34.8144	−1.63212
$456$	2.40592	0.112667
$457$	18.1475	0.848903	0.424452	−	0.905451i	$-0.360467\pi$
$457$	18.1475	0.848903	0.424452	+	0.905451i	$0.360467\pi$
$458$	−8.11135	−0.379018
$459$	−6.45071	−0.301093
$460$	12.3273	0.574761
$461$	31.3255	1.45897	0.729486	−	0.683995i	$-0.239759\pi$
$461$	31.3255	1.45897	0.729486	+	0.683995i	$0.239759\pi$
$462$	−3.05158	−0.141972
$463$	18.4607	0.857944	0.428972	−	0.903318i	$-0.358876\pi$
$463$	18.4607	0.857944	0.428972	+	0.903318i	$0.358876\pi$
$464$	6.63924	0.308219
$465$	10.0785	0.467380
$466$	14.1947	0.657556
$467$	9.64438	0.446289	0.223144	−	0.974785i	$-0.428368\pi$
$467$	9.64438	0.446289	0.223144	+	0.974785i	$0.428368\pi$
$468$	−15.9204	−0.735919
$469$	−5.66824	−0.261735
$470$	−15.0793	−0.695555
$471$	−0.455071	−0.0209686
$472$	−9.79816	−0.450997
$473$	−9.62359	−0.442493
$474$	0.0866842	0.00398154
$475$	10.9792	0.503760
$476$	7.01731	0.321638
$477$	−3.22612	−0.147714
$478$	−25.8393	−1.18186
$479$	−7.40532	−0.338358	−0.169179	−	0.985585i	$-0.554112\pi$
$479$	−7.40532	−0.338358	−0.169179	+	0.985585i	$0.554112\pi$
$480$	−0.928170	−0.0423650
$481$	−0.399193	−0.0182017
$482$	0.470592	0.0214349
$483$	22.4381	1.02097
$484$	−9.60814	−0.436733
$485$	4.23872	0.192470
$486$	−14.4104	−0.653671
$487$	−34.1697	−1.54838	−0.774188	−	0.632956i	$-0.781841\pi$
$487$	−34.1697	−1.54838	−0.774188	+	0.632956i	$0.781841\pi$
$488$	−10.2357	−0.463349
$489$	−5.61459	−0.253900
$490$	12.3377	0.557362
$491$	0.827178	0.0373300	0.0186650	−	0.999826i	$-0.494058\pi$
$491$	0.827178	0.0373300	0.0186650	+	0.999826i	$0.494058\pi$
$492$	6.51290	0.293624
$493$	−11.7648	−0.529861
$494$	−22.7881	−1.02529
$495$	4.31427	0.193912
$496$	−10.8585	−0.487560
$497$	22.4511	1.00707
$498$	9.21136	0.412771
$499$	1.74483	0.0781093	0.0390547	−	0.999237i	$-0.487565\pi$
$499$	1.74483	0.0781093	0.0390547	+	0.999237i	$0.487565\pi$
$500$	−11.3408	−0.507176
$501$	0.695285	0.0310630
$502$	−9.15599	−0.408652
$503$	14.0366	0.625863	0.312932	−	0.949776i	$-0.398689\pi$
$503$	14.0366	0.625863	0.312932	+	0.949776i	$0.398689\pi$
$504$	10.1908	0.453933
$505$	−16.5548	−0.736681
$506$	−10.2343	−0.454971
$507$	−16.5078	−0.733136
$508$	15.3813	0.682435
$509$	−40.3889	−1.79021	−0.895104	−	0.445858i	$-0.852898\pi$
$509$	−40.3889	−1.79021	−0.895104	+	0.445858i	$0.852898\pi$
$510$	1.64473	0.0728298
$511$	8.98426	0.397440
$512$	1.00000	0.0441942
$513$	−13.4091	−0.592026
$514$	19.4258	0.856833
$515$	−26.3849	−1.16266
$516$	−5.32796	−0.234550
$517$	12.5191	0.550590
$518$	0.255527	0.0112272
$519$	−13.4286	−0.589451
$520$	8.79133	0.385525
$521$	25.2072	1.10435	0.552173	−	0.833729i	$-0.313799\pi$
$521$	25.2072	1.10435	0.552173	+	0.833729i	$0.313799\pi$
$522$	−17.0853	−0.747802
$523$	14.9061	0.651798	0.325899	−	0.945405i	$-0.394333\pi$
$523$	14.9061	0.651798	0.325899	+	0.945405i	$0.394333\pi$
$524$	6.11543	0.267154
$525$	−7.70970	−0.336479
$526$	7.13295	0.311011
$527$	19.2414	0.838167
$528$	0.770585	0.0335354
$529$	52.2527	2.27185
$530$	1.78149	0.0773828
$531$	25.2143	1.09421
$532$	14.5869	0.632421
$533$	−61.6881	−2.67201
$534$	−2.43789	−0.105498
$535$	−26.7660	−1.15720
$536$	1.43135	0.0618247
$537$	−5.54066	−0.239097
$538$	12.9113	0.556646
$539$	−10.2430	−0.441199
$540$	5.17304	0.222612
$541$	−22.1317	−0.951515	−0.475758	−	0.879576i	$-0.657826\pi$
$541$	−22.1317	−0.951515	−0.475758	+	0.879576i	$0.657826\pi$
$542$	−13.6883	−0.587964
$543$	−14.9980	−0.643627
$544$	−1.77201	−0.0759744
$545$	−19.3815	−0.830214
$546$	16.0020	0.684824
$547$	0.468275	0.0200220	0.0100110	−	0.999950i	$-0.496813\pi$
$547$	0.468275	0.0200220	0.0100110	+	0.999950i	$0.496813\pi$
$548$	14.3846	0.614480
$549$	26.3404	1.12418
$550$	3.51650	0.149944
$551$	−24.4555	−1.04184
$552$	−5.66609	−0.241165
$553$	0.525559	0.0223490
$554$	−13.3456	−0.566998
$555$	0.0598910	0.00254223
$556$	1.96430	0.0833049
$557$	2.28414	0.0967822	0.0483911	−	0.998828i	$-0.484591\pi$
$557$	2.28414	0.0967822	0.0483911	+	0.998828i	$0.484591\pi$
$558$	27.9429	1.18292
$559$	50.4648	2.13443
$560$	−5.62741	−0.237802
$561$	−1.36549	−0.0576509
$562$	−7.36662	−0.310742
$563$	−24.0655	−1.01424	−0.507120	−	0.861876i	$-0.669290\pi$
$563$	−24.0655	−1.01424	−0.507120	+	0.861876i	$0.669290\pi$
$564$	6.93103	0.291849
$565$	−9.13306	−0.384231
$566$	23.5668	0.990587
$567$	−21.1563	−0.888481
$568$	−5.66937	−0.237881
$569$	27.7178	1.16199	0.580995	−	0.813907i	$-0.302664\pi$
$569$	27.7178	1.16199	0.580995	+	0.813907i	$0.302664\pi$
$570$	3.41890	0.143202
$571$	8.63975	0.361562	0.180781	−	0.983523i	$-0.442137\pi$
$571$	8.63975	0.361562	0.180781	+	0.983523i	$0.442137\pi$
$572$	−7.29874	−0.305176
$573$	−10.8634	−0.453824
$574$	39.4871	1.64816
$575$	−25.8567	−1.07830
$576$	−2.57338	−0.107224
$577$	−16.6285	−0.692252	−0.346126	−	0.938188i	$-0.612503\pi$
$577$	−16.6285	−0.692252	−0.346126	+	0.938188i	$0.612503\pi$
$578$	−13.8600	−0.576499
$579$	−9.70235	−0.403216
$580$	9.43460	0.391751
$581$	55.8477	2.31695
$582$	−1.94828	−0.0807588
$583$	−1.47902	−0.0612549
$584$	−2.26871	−0.0938798
$585$	−22.6234	−0.935363
$586$	11.0611	0.456929
$587$	−8.27040	−0.341356	−0.170678	−	0.985327i	$-0.554596\pi$
$587$	−8.27040	−0.341356	−0.170678	+	0.985327i	$0.554596\pi$
$588$	−5.67090	−0.233864
$589$	39.9970	1.64805
$590$	−13.9235	−0.573223
$591$	−9.34922	−0.384575
$592$	−0.0645259	−0.00265200
$593$	29.6037	1.21568	0.607838	−	0.794061i	$-0.292037\pi$
$593$	29.6037	1.21568	0.607838	+	0.794061i	$0.292037\pi$
$594$	−4.29476	−0.176216
$595$	9.97185	0.408806
$596$	−7.39214	−0.302794
$597$	1.20819	0.0494481
$598$	53.6674	2.19462
$599$	9.44648	0.385973	0.192986	−	0.981201i	$-0.438183\pi$
$599$	9.44648	0.385973	0.192986	+	0.981201i	$0.438183\pi$
$600$	1.94686	0.0794801
$601$	−20.3888	−0.831678	−0.415839	−	0.909438i	$-0.636512\pi$
$601$	−20.3888	−0.831678	−0.415839	+	0.909438i	$0.636512\pi$
$602$	−32.3030	−1.31657
$603$	−3.68339	−0.149999
$604$	−3.94606	−0.160563
$605$	−13.6535	−0.555094
$606$	7.60925	0.309105
$607$	35.6260	1.44601	0.723007	−	0.690841i	$-0.242760\pi$
$607$	35.6260	1.44601	0.723007	+	0.690841i	$0.242760\pi$
$608$	−3.68348	−0.149385
$609$	17.1729	0.695882
$610$	−14.5453	−0.588923
$611$	−65.6485	−2.65585
$612$	4.56006	0.184329
$613$	−2.33703	−0.0943918	−0.0471959	−	0.998886i	$-0.515029\pi$
$613$	−2.33703	−0.0943918	−0.0471959	+	0.998886i	$0.515029\pi$
$614$	11.3475	0.457949
$615$	9.25506	0.373200
$616$	4.67199	0.188240
$617$	23.1413	0.931633	0.465817	−	0.884881i	$-0.345761\pi$
$617$	23.1413	0.931633	0.465817	+	0.884881i	$0.345761\pi$
$618$	12.1276	0.487842
$619$	1.08554	0.0436316	0.0218158	−	0.999762i	$-0.493055\pi$
$619$	1.08554	0.0436316	0.0218158	+	0.999762i	$0.493055\pi$
$620$	−15.4303	−0.619695
$621$	31.5792	1.26723
$622$	−30.4488	−1.22088
$623$	−14.7807	−0.592176
$624$	−4.04084	−0.161763
$625$	−1.21243	−0.0484970
$626$	−0.0414177	−0.00165538
$627$	−2.83844	−0.113356
$628$	0.696718	0.0278021
$629$	0.114341	0.00455906
$630$	14.4815	0.576955
$631$	29.8499	1.18831	0.594154	−	0.804352i	$-0.297487\pi$
$631$	29.8499	1.18831	0.594154	+	0.804352i	$0.297487\pi$
$632$	−0.132714	−0.00527909
$633$	16.1547	0.642090
$634$	−9.92508	−0.394175
$635$	21.8574	0.867384
$636$	−0.818840	−0.0324691
$637$	53.7130	2.12819
$638$	−7.83280	−0.310103
$639$	14.5894	0.577148
$640$	1.42104	0.0561714
$641$	−21.5863	−0.852606	−0.426303	−	0.904580i	$-0.640184\pi$
$641$	−21.5863	−0.852606	−0.426303	+	0.904580i	$0.640184\pi$
$642$	12.3027	0.485549
$643$	27.3704	1.07938	0.539691	−	0.841863i	$-0.318541\pi$
$643$	27.3704	1.07938	0.539691	+	0.841863i	$0.318541\pi$
$644$	−34.3530	−1.35370
$645$	−7.57123	−0.298117
$646$	6.52718	0.256809
$647$	−1.25402	−0.0493005	−0.0246503	−	0.999696i	$-0.507847\pi$
$647$	−1.25402	−0.0493005	−0.0246503	+	0.999696i	$0.507847\pi$
$648$	5.34240	0.209869
$649$	11.5596	0.453754
$650$	−18.4400	−0.723277
$651$	−28.0863	−1.10079
$652$	8.59598	0.336645
$653$	21.3327	0.834815	0.417407	−	0.908719i	$-0.362939\pi$
$653$	21.3327	0.834815	0.417407	+	0.908719i	$0.362939\pi$
$654$	8.90852	0.348351
$655$	8.69026	0.339556
$656$	−9.97130	−0.389314
$657$	5.83824	0.227771
$658$	42.0222	1.63820
$659$	−38.0269	−1.48132	−0.740658	−	0.671882i	$-0.765486\pi$
$659$	−38.0269	−1.48132	−0.740658	+	0.671882i	$0.765486\pi$
$660$	1.09503	0.0426240
$661$	−42.3518	−1.64729	−0.823646	−	0.567104i	$-0.808064\pi$
$661$	−42.3518	−1.64729	−0.823646	+	0.567104i	$0.808064\pi$
$662$	13.9639	0.542723
$663$	7.16042	0.278088
$664$	−14.1027	−0.547290
$665$	20.7285	0.803816
$666$	0.166049	0.00643428
$667$	57.5943	2.23006
$668$	−1.06449	−0.0411862
$669$	−1.84088	−0.0711726
$670$	2.03400	0.0785801
$671$	12.0758	0.466182
$672$	2.58658	0.0997795
$673$	−40.5821	−1.56433	−0.782163	−	0.623074i	$-0.785883\pi$
$673$	−40.5821	−1.56433	−0.782163	+	0.623074i	$0.785883\pi$
$674$	13.6787	0.526884
$675$	−10.8506	−0.417638
$676$	25.2736	0.972060
$677$	−16.6730	−0.640794	−0.320397	−	0.947283i	$-0.603816\pi$
$677$	−16.6730	−0.640794	−0.320397	+	0.947283i	$0.603816\pi$
$678$	4.19791	0.161220
$679$	−11.8123	−0.453313
$680$	−2.51810	−0.0965645
$681$	15.8083	0.605774
$682$	12.8105	0.490541
$683$	32.1451	1.23000	0.614999	−	0.788528i	$-0.289156\pi$
$683$	32.1451	1.23000	0.614999	+	0.788528i	$0.289156\pi$
$684$	9.47899	0.362438
$685$	20.4411	0.781012
$686$	−6.66166	−0.254343
$687$	5.29804	0.202133
$688$	8.15716	0.310989
$689$	7.75580	0.295472
$690$	−8.05172	−0.306524
$691$	9.78845	0.372370	0.186185	−	0.982515i	$-0.440388\pi$
$691$	9.78845	0.372370	0.186185	+	0.982515i	$0.440388\pi$
$692$	20.5593	0.781548
$693$	−12.0228	−0.456708
$694$	3.70909	0.140795
$695$	2.79134	0.105882
$696$	−4.33651	−0.164375
$697$	17.6693	0.669272
$698$	14.6908	0.556055
$699$	−9.27146	−0.350679
$700$	11.8036	0.446135
$701$	−16.3754	−0.618491	−0.309246	−	0.950982i	$-0.600077\pi$
$701$	−16.3754	−0.618491	−0.309246	+	0.950982i	$0.600077\pi$
$702$	22.5211	0.850005
$703$	0.237680	0.00896427
$704$	−1.17977	−0.0444644
$705$	9.84924	0.370944
$706$	−30.4837	−1.14727
$707$	46.1342	1.73506
$708$	6.39980	0.240519
$709$	−8.61266	−0.323455	−0.161728	−	0.986835i	$-0.551707\pi$
$709$	−8.61266	−0.323455	−0.161728	+	0.986835i	$0.551707\pi$
$710$	−8.05638	−0.302350
$711$	0.341524	0.0128082
$712$	3.73243	0.139879
$713$	−94.1954	−3.52765
$714$	−4.58345	−0.171531
$715$	−10.3718	−0.387882
$716$	8.48280	0.317017
$717$	16.8773	0.630294
$718$	28.7330	1.07231
$719$	−37.0701	−1.38248	−0.691240	−	0.722625i	$-0.742935\pi$
$719$	−37.0701	−1.38248	−0.691240	+	0.722625i	$0.742935\pi$
$720$	−3.65686	−0.136283
$721$	73.5283	2.73834
$722$	−5.43194	−0.202156
$723$	−0.307374	−0.0114314
$724$	22.9621	0.853380
$725$	−19.7893	−0.734955
$726$	6.27569	0.232913
$727$	−36.8143	−1.36537	−0.682683	−	0.730715i	$-0.739187\pi$
$727$	−36.8143	−1.36537	−0.682683	+	0.730715i	$0.739187\pi$
$728$	−24.4993	−0.908003
$729$	−6.61481	−0.244993
$730$	−3.22392	−0.119323
$731$	−14.4546	−0.534622
$732$	6.68560	0.247107
$733$	−7.66805	−0.283226	−0.141613	−	0.989922i	$-0.545229\pi$
$733$	−7.66805	−0.283226	−0.141613	+	0.989922i	$0.545229\pi$
$734$	−3.67521	−0.135654
$735$	−8.05856	−0.297245
$736$	8.67483	0.319758
$737$	−1.68866	−0.0622027
$738$	25.6599	0.944555
$739$	−21.5251	−0.791812	−0.395906	−	0.918291i	$-0.629569\pi$
$739$	−21.5251	−0.791812	−0.395906	+	0.918291i	$0.629569\pi$
$740$	−0.0916937	−0.00337073
$741$	14.8844	0.546791
$742$	−4.96456	−0.182255
$743$	30.0047	1.10077	0.550383	−	0.834912i	$-0.314482\pi$
$743$	30.0047	1.10077	0.550383	+	0.834912i	$0.314482\pi$
$744$	7.09236	0.260019
$745$	−10.5045	−0.384855
$746$	0.952980	0.0348911
$747$	36.2915	1.32784
$748$	2.09057	0.0764389
$749$	74.5902	2.72547
$750$	7.40740	0.270480
$751$	30.9082	1.12786	0.563929	−	0.825823i	$-0.309289\pi$
$751$	30.9082	1.12786	0.563929	+	0.825823i	$0.309289\pi$
$752$	−10.6115	−0.386960
$753$	5.98036	0.217937
$754$	41.0741	1.49583
$755$	−5.60750	−0.204078
$756$	−14.4160	−0.524304
$757$	14.5142	0.527526	0.263763	−	0.964587i	$-0.415036\pi$
$757$	14.5142	0.527526	0.263763	+	0.964587i	$0.415036\pi$
$758$	18.8475	0.684574
$759$	6.68469	0.242639
$760$	−5.23437	−0.189870
$761$	0.693739	0.0251480	0.0125740	−	0.999921i	$-0.495997\pi$
$761$	0.693739	0.0251480	0.0125740	+	0.999921i	$0.495997\pi$
$762$	−10.0465	−0.363947
$763$	54.0116	1.95535
$764$	16.6319	0.601722
$765$	6.48001	0.234285
$766$	−12.2646	−0.443139
$767$	−60.6169	−2.18875
$768$	−0.653164	−0.0235690
$769$	−15.5212	−0.559708	−0.279854	−	0.960043i	$-0.590286\pi$
$769$	−15.5212	−0.559708	−0.279854	+	0.960043i	$0.590286\pi$
$770$	6.63907	0.239256
$771$	−12.6882	−0.456955
$772$	14.8544	0.534621
$773$	−7.28049	−0.261861	−0.130931	−	0.991392i	$-0.541796\pi$
$773$	−7.28049	−0.261861	−0.130931	+	0.991392i	$0.541796\pi$
$774$	−20.9914	−0.754522
$775$	32.3654	1.16260
$776$	2.98283	0.107078
$777$	−0.166901	−0.00598755
$778$	−27.6965	−0.992969
$779$	36.7291	1.31596
$780$	−5.74218	−0.205603
$781$	6.68856	0.239336
$782$	−15.3719	−0.549698
$783$	24.1690	0.863730
$784$	8.68221	0.310079
$785$	0.990062	0.0353368
$786$	−3.99438	−0.142475
$787$	42.4941	1.51475	0.757375	−	0.652980i	$-0.226481\pi$
$787$	42.4941	1.51475	0.757375	+	0.652980i	$0.226481\pi$
$788$	14.3137	0.509906
$789$	−4.65898	−0.165864
$790$	−0.188592	−0.00670980
$791$	25.4516	0.904954
$792$	3.03600	0.107880
$793$	−63.3239	−2.24870
$794$	−33.7183	−1.19662
$795$	−1.16360	−0.0412687
$796$	−1.84976	−0.0655628
$797$	9.68183	0.342948	0.171474	−	0.985189i	$-0.445147\pi$
$797$	9.68183	0.342948	0.171474	+	0.985189i	$0.445147\pi$
$798$	−9.52762	−0.337274
$799$	18.8036	0.665225
$800$	−2.98065	−0.105382
$801$	−9.60494	−0.339374
$802$	6.36050	0.224597
$803$	2.67656	0.0944538
$804$	−0.934904	−0.0329715
$805$	−48.8169	−1.72057
$806$	−67.1766	−2.36620
$807$	−8.43320	−0.296863
$808$	−11.6498	−0.409840
$809$	20.4672	0.719587	0.359793	−	0.933032i	$-0.382847\pi$
$809$	20.4672	0.719587	0.359793	+	0.933032i	$0.382847\pi$
$810$	7.59174	0.266747
$811$	−11.5497	−0.405566	−0.202783	−	0.979224i	$-0.564999\pi$
$811$	−11.5497	−0.405566	−0.202783	+	0.979224i	$0.564999\pi$
$812$	−26.2919	−0.922665
$813$	8.94072	0.313565
$814$	0.0761259	0.00266821
$815$	12.2152	0.427880
$816$	1.15741	0.0405176
$817$	−30.0468	−1.05120
$818$	10.2500	0.358384
$819$	63.0458	2.20300
$820$	−14.1696	−0.494823
$821$	7.47700	0.260949	0.130475	−	0.991452i	$-0.458350\pi$
$821$	7.47700	0.260949	0.130475	+	0.991452i	$0.458350\pi$
$822$	−9.39550	−0.327706
$823$	−24.9868	−0.870985	−0.435493	−	0.900192i	$-0.643426\pi$
$823$	−24.9868	−0.870985	−0.435493	+	0.900192i	$0.643426\pi$
$824$	−18.5674	−0.646826
$825$	−2.29685	−0.0799660
$826$	38.8014	1.35007
$827$	18.4188	0.640484	0.320242	−	0.947336i	$-0.396236\pi$
$827$	18.4188	0.640484	0.320242	+	0.947336i	$0.396236\pi$
$828$	−22.3236	−0.775799
$829$	41.4946	1.44117	0.720583	−	0.693369i	$-0.243874\pi$
$829$	41.4946	1.44117	0.720583	+	0.693369i	$0.243874\pi$
$830$	−20.0404	−0.695613
$831$	8.71683	0.302384
$832$	6.18656	0.214480
$833$	−15.3850	−0.533058
$834$	−1.28301	−0.0444270
$835$	−1.51268	−0.0523483
$836$	4.34568	0.150298
$837$	−39.5284	−1.36630
$838$	−30.5103	−1.05396
$839$	9.65314	0.333263	0.166632	−	0.986019i	$-0.446711\pi$
$839$	9.65314	0.333263	0.166632	+	0.986019i	$0.446711\pi$
$840$	3.67562	0.126821
$841$	15.0795	0.519983
$842$	−17.6029	−0.606634
$843$	4.81161	0.165721
$844$	−24.7329	−0.851343
$845$	35.9147	1.23550
$846$	27.3073	0.938844
$847$	38.0490	1.30738
$848$	1.25365	0.0430506
$849$	−15.3930	−0.528286
$850$	5.28176	0.181163
$851$	−0.559751	−0.0191880
$852$	3.70303	0.126864
$853$	49.0619	1.67985	0.839923	−	0.542705i	$-0.182600\pi$
$853$	49.0619	1.67985	0.839923	+	0.542705i	$0.182600\pi$
$854$	40.5342	1.38705
$855$	13.4700	0.460664
$856$	−18.8355	−0.643786
$857$	−11.1363	−0.380407	−0.190204	−	0.981745i	$-0.560915\pi$
$857$	−11.1363	−0.380407	−0.190204	+	0.981745i	$0.560915\pi$
$858$	4.76727	0.162752
$859$	15.2425	0.520066	0.260033	−	0.965600i	$-0.416267\pi$
$859$	15.2425	0.520066	0.260033	+	0.965600i	$0.416267\pi$
$860$	11.5916	0.395271
$861$	−25.7916	−0.878974
$862$	−9.92522	−0.338054
$863$	11.3930	0.387823	0.193912	−	0.981019i	$-0.437882\pi$
$863$	11.3930	0.387823	0.193912	+	0.981019i	$0.437882\pi$
$864$	3.64033	0.123847
$865$	29.2156	0.993359
$866$	28.0195	0.952143
$867$	9.05283	0.307450
$868$	43.0004	1.45953
$869$	0.156573	0.00531137
$870$	−6.16234	−0.208923
$871$	8.85511	0.300044
$872$	−13.6390	−0.461876
$873$	−7.67596	−0.259792
$874$	−31.9536	−1.08085
$875$	44.9104	1.51825
$876$	1.48184	0.0500667
$877$	−41.1625	−1.38996	−0.694979	−	0.719030i	$-0.744586\pi$
$877$	−41.1625	−1.38996	−0.694979	+	0.719030i	$0.744586\pi$
$878$	−9.66635	−0.326223
$879$	−7.22470	−0.243683
$880$	−1.67650	−0.0565148
$881$	−2.35707	−0.0794118	−0.0397059	−	0.999211i	$-0.512642\pi$
$881$	−2.35707	−0.0794118	−0.0397059	+	0.999211i	$0.512642\pi$
$882$	−22.3426	−0.752314
$883$	33.9679	1.14311	0.571555	−	0.820564i	$-0.306340\pi$
$883$	33.9679	1.14311	0.571555	+	0.820564i	$0.306340\pi$
$884$	−10.9627	−0.368714
$885$	9.09435	0.305703
$886$	−12.2716	−0.412274
$887$	−41.2203	−1.38404	−0.692022	−	0.721877i	$-0.743280\pi$
$887$	−41.2203	−1.38404	−0.692022	+	0.721877i	$0.743280\pi$
$888$	0.0421460	0.00141433
$889$	−60.9111	−2.04289
$890$	5.30391	0.177788
$891$	−6.30282	−0.211152
$892$	2.81841	0.0943673
$893$	39.0872	1.30800
$894$	4.82828	0.161482
$895$	12.0544	0.402933
$896$	−3.96008	−0.132297
$897$	−35.0536	−1.17041
$898$	6.68146	0.222963
$899$	−72.0920	−2.40440
$900$	7.67035	0.255678
$901$	−2.22149	−0.0740085
$902$	11.7639	0.391694
$903$	21.0991	0.702135
$904$	−6.42704	−0.213760
$905$	32.6300	1.08466
$906$	2.57742	0.0856292
$907$	−12.1044	−0.401921	−0.200961	−	0.979599i	$-0.564406\pi$
$907$	−12.1044	−0.401921	−0.200961	+	0.979599i	$0.564406\pi$
$908$	−24.2026	−0.803191
$909$	29.9794	0.994354
$910$	−34.8144	−1.15408
$911$	54.8306	1.81662	0.908309	−	0.418300i	$-0.137374\pi$
$911$	54.8306	1.81662	0.908309	+	0.418300i	$0.137374\pi$
$912$	2.40592	0.0796679
$913$	16.6380	0.550636
$914$	18.1475	0.600265
$915$	9.50048	0.314076
$916$	−8.11135	−0.268006
$917$	−24.2176	−0.799735
$918$	−6.45071	−0.212905
$919$	12.0243	0.396647	0.198323	−	0.980137i	$-0.436450\pi$
$919$	12.0243	0.396647	0.198323	+	0.980137i	$0.436450\pi$
$920$	12.3273	0.406417
$921$	−7.41180	−0.244227
$922$	31.3255	1.03165
$923$	−35.0739	−1.15447
$924$	−3.05158	−0.100389
$925$	0.192329	0.00632375
$926$	18.4607	0.606658
$927$	47.7809	1.56933
$928$	6.63924	0.217944
$929$	−1.74709	−0.0573200	−0.0286600	−	0.999589i	$-0.509124\pi$
$929$	−1.74709	−0.0573200	−0.0286600	+	0.999589i	$0.509124\pi$
$930$	10.0785	0.330487
$931$	−31.9808	−1.04813
$932$	14.1947	0.464962
$933$	19.8880	0.651105
$934$	9.64438	0.315574
$935$	2.97078	0.0971549
$936$	−15.9204	−0.520373
$937$	−13.0484	−0.426272	−0.213136	−	0.977023i	$-0.568368\pi$
$937$	−13.0484	−0.426272	−0.213136	+	0.977023i	$0.568368\pi$
$938$	−5.66824	−0.185075
$939$	0.0270525	0.000882826 0
$940$	−15.0793	−0.491832
$941$	35.8492	1.16865	0.584325	−	0.811520i	$-0.301359\pi$
$941$	35.8492	1.16865	0.584325	+	0.811520i	$0.301359\pi$
$942$	−0.455071	−0.0148270
$943$	−86.4993	−2.81681
$944$	−9.79816	−0.318903
$945$	−20.4856	−0.666398
$946$	−9.62359	−0.312890
$947$	−42.8889	−1.39370	−0.696852	−	0.717215i	$-0.745416\pi$
$947$	−42.8889	−1.39370	−0.696852	+	0.717215i	$0.745416\pi$
$948$	0.0866842	0.00281537
$949$	−14.0355	−0.455612
$950$	10.9792	0.356212
$951$	6.48271	0.210216
$952$	7.01731	0.227432
$953$	11.7998	0.382232	0.191116	−	0.981567i	$-0.438789\pi$
$953$	11.7998	0.382232	0.191116	+	0.981567i	$0.438789\pi$
$954$	−3.22612	−0.104449
$955$	23.6346	0.764797
$956$	−25.8393	−0.835702
$957$	5.11610	0.165380
$958$	−7.40532	−0.239255
$959$	−56.9641	−1.83947
$960$	−0.928170	−0.0299566
$961$	86.9065	2.80343
$962$	−0.399193	−0.0128705
$963$	48.4710	1.56195
$964$	0.470592	0.0151568
$965$	21.1086	0.679511
$966$	22.4381	0.721935
$967$	−20.1861	−0.649142	−0.324571	−	0.945861i	$-0.605220\pi$
$967$	−20.1861	−0.649142	−0.324571	+	0.945861i	$0.605220\pi$
$968$	−9.60814	−0.308817
$969$	−4.26332	−0.136958
$970$	4.23872	0.136097
$971$	46.4576	1.49089	0.745447	−	0.666565i	$-0.232236\pi$
$971$	46.4576	1.49089	0.745447	+	0.666565i	$0.232236\pi$
$972$	−14.4104	−0.462215
$973$	−7.77878	−0.249376
$974$	−34.1697	−1.09487
$975$	12.0443	0.385728
$976$	−10.2357	−0.327637
$977$	43.9806	1.40706	0.703532	−	0.710663i	$-0.251605\pi$
$977$	43.9806	1.40706	0.703532	+	0.710663i	$0.251605\pi$
$978$	−5.61459	−0.179535
$979$	−4.40342	−0.140734
$980$	12.3377	0.394114
$981$	35.0983	1.12060
$982$	0.827178	0.0263963
$983$	−3.80735	−0.121436	−0.0607178	−	0.998155i	$-0.519339\pi$
$983$	−3.80735	−0.121436	−0.0607178	+	0.998155i	$0.519339\pi$
$984$	6.51290	0.207624
$985$	20.3403	0.648097
$986$	−11.7648	−0.374668
$987$	−27.4474	−0.873660
$988$	−22.7881	−0.724986
$989$	70.7619	2.25010
$990$	4.31427	0.137116
$991$	−19.9213	−0.632822	−0.316411	−	0.948622i	$-0.602478\pi$
$991$	−19.9213	−0.632822	−0.316411	+	0.948622i	$0.602478\pi$
$992$	−10.8585	−0.344757
$993$	−9.12072	−0.289437
$994$	22.4511	0.712106
$995$	−2.62857	−0.0833313
$996$	9.21136	0.291873
$997$	−36.7223	−1.16301	−0.581504	−	0.813544i	$-0.697535\pi$
$997$	−36.7223	−1.16301	−0.581504	+	0.813544i	$0.697535\pi$
$998$	1.74483	0.0552316
$999$	−0.234895	−0.00743176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.c.1.16	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.c.1.16	✓	31	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.653164 q^{3} +1.00000 q^{4} +1.42104 q^{5} -0.653164 q^{6} -3.96008 q^{7} +1.00000 q^{8} -2.57338 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.653164 q^{3} +1.00000 q^{4} +1.42104 q^{5} -0.653164 q^{6} -3.96008 q^{7} +1.00000 q^{8} -2.57338 q^{9} +1.42104 q^{10} -1.17977 q^{11} -0.653164 q^{12} +6.18656 q^{13} -3.96008 q^{14} -0.928170 q^{15} +1.00000 q^{16} -1.77201 q^{17} -2.57338 q^{18} -3.68348 q^{19} +1.42104 q^{20} +2.58658 q^{21} -1.17977 q^{22} +8.67483 q^{23} -0.653164 q^{24} -2.98065 q^{25} +6.18656 q^{26} +3.64033 q^{27} -3.96008 q^{28} +6.63924 q^{29} -0.928170 q^{30} -10.8585 q^{31} +1.00000 q^{32} +0.770585 q^{33} -1.77201 q^{34} -5.62741 q^{35} -2.57338 q^{36} -0.0645259 q^{37} -3.68348 q^{38} -4.04084 q^{39} +1.42104 q^{40} -9.97130 q^{41} +2.58658 q^{42} +8.15716 q^{43} -1.17977 q^{44} -3.65686 q^{45} +8.67483 q^{46} -10.6115 q^{47} -0.653164 q^{48} +8.68221 q^{49} -2.98065 q^{50} +1.15741 q^{51} +6.18656 q^{52} +1.25365 q^{53} +3.64033 q^{54} -1.67650 q^{55} -3.96008 q^{56} +2.40592 q^{57} +6.63924 q^{58} -9.79816 q^{59} -0.928170 q^{60} -10.2357 q^{61} -10.8585 q^{62} +10.1908 q^{63} +1.00000 q^{64} +8.79133 q^{65} +0.770585 q^{66} +1.43135 q^{67} -1.77201 q^{68} -5.66609 q^{69} -5.62741 q^{70} -5.66937 q^{71} -2.57338 q^{72} -2.26871 q^{73} -0.0645259 q^{74} +1.94686 q^{75} -3.68348 q^{76} +4.67199 q^{77} -4.04084 q^{78} -0.132714 q^{79} +1.42104 q^{80} +5.34240 q^{81} -9.97130 q^{82} -14.1027 q^{83} +2.58658 q^{84} -2.51810 q^{85} +8.15716 q^{86} -4.33651 q^{87} -1.17977 q^{88} +3.73243 q^{89} -3.65686 q^{90} -24.4993 q^{91} +8.67483 q^{92} +7.09236 q^{93} -10.6115 q^{94} -5.23437 q^{95} -0.653164 q^{96} +2.98283 q^{97} +8.68221 q^{98} +3.03600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - q^99

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