LMFDB - Embedded newform 4022.2.a.d.1.13

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:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.40012 q^{3} +1.00000 q^{4} -1.65031 q^{5} +1.40012 q^{6} +2.90659 q^{7} -1.00000 q^{8} -1.03967 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.40012 q^{3} +1.00000 q^{4} -1.65031 q^{5} +1.40012 q^{6} +2.90659 q^{7} -1.00000 q^{8} -1.03967 q^{9} +1.65031 q^{10} -1.47758 q^{11} -1.40012 q^{12} +1.93520 q^{13} -2.90659 q^{14} +2.31062 q^{15} +1.00000 q^{16} +1.62573 q^{17} +1.03967 q^{18} -4.58896 q^{19} -1.65031 q^{20} -4.06956 q^{21} +1.47758 q^{22} +7.27839 q^{23} +1.40012 q^{24} -2.27649 q^{25} -1.93520 q^{26} +5.65601 q^{27} +2.90659 q^{28} -2.46680 q^{29} -2.31062 q^{30} -6.97572 q^{31} -1.00000 q^{32} +2.06878 q^{33} -1.62573 q^{34} -4.79676 q^{35} -1.03967 q^{36} -0.384716 q^{37} +4.58896 q^{38} -2.70951 q^{39} +1.65031 q^{40} +4.62974 q^{41} +4.06956 q^{42} -7.14262 q^{43} -1.47758 q^{44} +1.71578 q^{45} -7.27839 q^{46} +11.8044 q^{47} -1.40012 q^{48} +1.44825 q^{49} +2.27649 q^{50} -2.27621 q^{51} +1.93520 q^{52} +8.66181 q^{53} -5.65601 q^{54} +2.43846 q^{55} -2.90659 q^{56} +6.42507 q^{57} +2.46680 q^{58} -9.12278 q^{59} +2.31062 q^{60} -11.6084 q^{61} +6.97572 q^{62} -3.02191 q^{63} +1.00000 q^{64} -3.19368 q^{65} -2.06878 q^{66} +10.4861 q^{67} +1.62573 q^{68} -10.1906 q^{69} +4.79676 q^{70} -1.89812 q^{71} +1.03967 q^{72} +10.6912 q^{73} +0.384716 q^{74} +3.18734 q^{75} -4.58896 q^{76} -4.29471 q^{77} +2.70951 q^{78} +0.0708345 q^{79} -1.65031 q^{80} -4.80005 q^{81} -4.62974 q^{82} -7.35376 q^{83} -4.06956 q^{84} -2.68296 q^{85} +7.14262 q^{86} +3.45380 q^{87} +1.47758 q^{88} +12.1510 q^{89} -1.71578 q^{90} +5.62484 q^{91} +7.27839 q^{92} +9.76682 q^{93} -11.8044 q^{94} +7.57319 q^{95} +1.40012 q^{96} +2.36355 q^{97} -1.44825 q^{98} +1.53620 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) $ 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * 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
$3$	−1.40012	−0.808357	−0.404179	−	0.914680i	$-0.632443\pi$
$3$	−1.40012	−0.808357	−0.404179	+	0.914680i	$0.632443\pi$
$4$	1.00000	0.500000
$5$	−1.65031	−0.738040	−0.369020	−	0.929421i	$-0.620307\pi$
$5$	−1.65031	−0.738040	−0.369020	+	0.929421i	$0.620307\pi$
$6$	1.40012	0.571595
$7$	2.90659	1.09859	0.549294	−	0.835629i	$-0.314897\pi$
$7$	2.90659	1.09859	0.549294	+	0.835629i	$0.314897\pi$
$8$	−1.00000	−0.353553
$9$	−1.03967	−0.346558
$10$	1.65031	0.521873
$11$	−1.47758	−0.445506	−0.222753	−	0.974875i	$-0.571504\pi$
$11$	−1.47758	−0.445506	−0.222753	+	0.974875i	$0.571504\pi$
$12$	−1.40012	−0.404179
$13$	1.93520	0.536729	0.268364	−	0.963317i	$-0.413517\pi$
$13$	1.93520	0.536729	0.268364	+	0.963317i	$0.413517\pi$
$14$	−2.90659	−0.776818
$15$	2.31062	0.596600
$16$	1.00000	0.250000
$17$	1.62573	0.394298	0.197149	−	0.980374i	$-0.436832\pi$
$17$	1.62573	0.394298	0.197149	+	0.980374i	$0.436832\pi$
$18$	1.03967	0.245054
$19$	−4.58896	−1.05278	−0.526389	−	0.850244i	$-0.676455\pi$
$19$	−4.58896	−1.05278	−0.526389	+	0.850244i	$0.676455\pi$
$20$	−1.65031	−0.369020
$21$	−4.06956	−0.888051
$22$	1.47758	0.315020
$23$	7.27839	1.51765	0.758825	−	0.651295i	$-0.225774\pi$
$23$	7.27839	1.51765	0.758825	+	0.651295i	$0.225774\pi$
$24$	1.40012	0.285798
$25$	−2.27649	−0.455297
$26$	−1.93520	−0.379524
$27$	5.65601	1.08850
$28$	2.90659	0.549294
$29$	−2.46680	−0.458073	−0.229036	−	0.973418i	$-0.573557\pi$
$29$	−2.46680	−0.458073	−0.229036	+	0.973418i	$0.573557\pi$
$30$	−2.31062	−0.421860
$31$	−6.97572	−1.25288	−0.626438	−	0.779471i	$-0.715488\pi$
$31$	−6.97572	−1.25288	−0.626438	+	0.779471i	$0.715488\pi$
$32$	−1.00000	−0.176777
$33$	2.06878	0.360128
$34$	−1.62573	−0.278810
$35$	−4.79676	−0.810801
$36$	−1.03967	−0.173279
$37$	−0.384716	−0.0632468	−0.0316234	−	0.999500i	$-0.510068\pi$
$37$	−0.384716	−0.0632468	−0.0316234	+	0.999500i	$0.510068\pi$
$38$	4.58896	0.744427
$39$	−2.70951	−0.433869
$40$	1.65031	0.260937
$41$	4.62974	0.723045	0.361522	−	0.932363i	$-0.382257\pi$
$41$	4.62974	0.723045	0.361522	+	0.932363i	$0.382257\pi$
$42$	4.06956	0.627947
$43$	−7.14262	−1.08924	−0.544620	−	0.838683i	$-0.683326\pi$
$43$	−7.14262	−1.08924	−0.544620	+	0.838683i	$0.683326\pi$
$44$	−1.47758	−0.222753
$45$	1.71578	0.255774
$46$	−7.27839	−1.07314
$47$	11.8044	1.72185	0.860925	−	0.508732i	$-0.169886\pi$
$47$	11.8044	1.72185	0.860925	+	0.508732i	$0.169886\pi$
$48$	−1.40012	−0.202089
$49$	1.44825	0.206894
$50$	2.27649	0.321944
$51$	−2.27621	−0.318733
$52$	1.93520	0.268364
$53$	8.66181	1.18979	0.594895	−	0.803803i	$-0.297194\pi$
$53$	8.66181	1.18979	0.594895	+	0.803803i	$0.297194\pi$
$54$	−5.65601	−0.769686
$55$	2.43846	0.328801
$56$	−2.90659	−0.388409
$57$	6.42507	0.851021
$58$	2.46680	0.323906
$59$	−9.12278	−1.18769	−0.593843	−	0.804581i	$-0.702390\pi$
$59$	−9.12278	−1.18769	−0.593843	+	0.804581i	$0.702390\pi$
$60$	2.31062	0.298300
$61$	−11.6084	−1.48630	−0.743151	−	0.669123i	$-0.766670\pi$
$61$	−11.6084	−1.48630	−0.743151	+	0.669123i	$0.766670\pi$
$62$	6.97572	0.885917
$63$	−3.02191	−0.380724
$64$	1.00000	0.125000
$65$	−3.19368	−0.396127
$66$	−2.06878	−0.254649
$67$	10.4861	1.28108	0.640541	−	0.767924i	$-0.278710\pi$
$67$	10.4861	1.28108	0.640541	+	0.767924i	$0.278710\pi$
$68$	1.62573	0.197149
$69$	−10.1906	−1.22680
$70$	4.79676	0.573323
$71$	−1.89812	−0.225265	−0.112632	−	0.993637i	$-0.535928\pi$
$71$	−1.89812	−0.225265	−0.112632	+	0.993637i	$0.535928\pi$
$72$	1.03967	0.122527
$73$	10.6912	1.25131	0.625654	−	0.780101i	$-0.284832\pi$
$73$	10.6912	1.25131	0.625654	+	0.780101i	$0.284832\pi$
$74$	0.384716	0.0447223
$75$	3.18734	0.368043
$76$	−4.58896	−0.526389
$77$	−4.29471	−0.489427
$78$	2.70951	0.306791
$79$	0.0708345	0.00796951	0.00398475	−	0.999992i	$-0.498732\pi$
$79$	0.0708345	0.00796951	0.00398475	+	0.999992i	$0.498732\pi$
$80$	−1.65031	−0.184510
$81$	−4.80005	−0.533339
$82$	−4.62974	−0.511270
$83$	−7.35376	−0.807180	−0.403590	−	0.914940i	$-0.632238\pi$
$83$	−7.35376	−0.807180	−0.403590	+	0.914940i	$0.632238\pi$
$84$	−4.06956	−0.444026
$85$	−2.68296	−0.291007
$86$	7.14262	0.770209
$87$	3.45380	0.370286
$88$	1.47758	0.157510
$89$	12.1510	1.28801	0.644003	−	0.765023i	$-0.277273\pi$
$89$	12.1510	1.28801	0.644003	+	0.765023i	$0.277273\pi$
$90$	−1.71578	−0.180859
$91$	5.62484	0.589643
$92$	7.27839	0.758825
$93$	9.76682	1.01277
$94$	−11.8044	−1.21753
$95$	7.57319	0.776993
$96$	1.40012	0.142899
$97$	2.36355	0.239982	0.119991	−	0.992775i	$-0.461713\pi$
$97$	2.36355	0.239982	0.119991	+	0.992775i	$0.461713\pi$
$98$	−1.44825	−0.146296
$99$	1.53620	0.154394
$100$	−2.27649	−0.227649
$101$	−8.01069	−0.797094	−0.398547	−	0.917148i	$-0.630485\pi$
$101$	−8.01069	−0.797094	−0.398547	+	0.917148i	$0.630485\pi$
$102$	2.27621	0.225379
$103$	−8.12874	−0.800949	−0.400475	−	0.916308i	$-0.631155\pi$
$103$	−8.12874	−0.800949	−0.400475	+	0.916308i	$0.631155\pi$
$104$	−1.93520	−0.189762
$105$	6.71603	0.655417
$106$	−8.66181	−0.841309
$107$	−10.0663	−0.973147	−0.486573	−	0.873640i	$-0.661753\pi$
$107$	−10.0663	−0.973147	−0.486573	+	0.873640i	$0.661753\pi$
$108$	5.65601	0.544250
$109$	−0.143903	−0.0137834	−0.00689171	−	0.999976i	$-0.502194\pi$
$109$	−0.143903	−0.0137834	−0.00689171	+	0.999976i	$0.502194\pi$
$110$	−2.43846	−0.232498
$111$	0.538646	0.0511261
$112$	2.90659	0.274647
$113$	−1.58797	−0.149384	−0.0746919	−	0.997207i	$-0.523797\pi$
$113$	−1.58797	−0.149384	−0.0746919	+	0.997207i	$0.523797\pi$
$114$	−6.42507	−0.601763
$115$	−12.0116	−1.12009
$116$	−2.46680	−0.229036
$117$	−2.01198	−0.186008
$118$	9.12278	0.839820
$119$	4.72533	0.433170
$120$	−2.31062	−0.210930
$121$	−8.81677	−0.801524
$122$	11.6084	1.05097
$123$	−6.48218	−0.584478
$124$	−6.97572	−0.626438
$125$	12.0084	1.07407
$126$	3.02191	0.269213
$127$	7.21707	0.640411	0.320206	−	0.947348i	$-0.396248\pi$
$127$	7.21707	0.640411	0.320206	+	0.947348i	$0.396248\pi$
$128$	−1.00000	−0.0883883
$129$	10.0005	0.880495
$130$	3.19368	0.280104
$131$	19.5680	1.70967	0.854833	−	0.518903i	$-0.173659\pi$
$131$	19.5680	1.70967	0.854833	+	0.518903i	$0.173659\pi$
$132$	2.06878	0.180064
$133$	−13.3382	−1.15657
$134$	−10.4861	−0.905862
$135$	−9.33416	−0.803357
$136$	−1.62573	−0.139405
$137$	−7.74120	−0.661376	−0.330688	−	0.943740i	$-0.607281\pi$
$137$	−7.74120	−0.661376	−0.330688	+	0.943740i	$0.607281\pi$
$138$	10.1906	0.867481
$139$	−19.6411	−1.66594	−0.832969	−	0.553319i	$-0.813361\pi$
$139$	−19.6411	−1.66594	−0.832969	+	0.553319i	$0.813361\pi$
$140$	−4.79676	−0.405401
$141$	−16.5275	−1.39187
$142$	1.89812	0.159286
$143$	−2.85941	−0.239116
$144$	−1.03967	−0.0866396
$145$	4.07097	0.338076
$146$	−10.6912	−0.884809
$147$	−2.02772	−0.167244
$148$	−0.384716	−0.0316234
$149$	17.7835	1.45688	0.728440	−	0.685109i	$-0.240246\pi$
$149$	17.7835	1.45688	0.728440	+	0.685109i	$0.240246\pi$
$150$	−3.18734	−0.260246
$151$	10.8627	0.883992	0.441996	−	0.897017i	$-0.354271\pi$
$151$	10.8627	0.883992	0.441996	+	0.897017i	$0.354271\pi$
$152$	4.58896	0.372213
$153$	−1.69023	−0.136647
$154$	4.29471	0.346077
$155$	11.5121	0.924673
$156$	−2.70951	−0.216934
$157$	−6.32757	−0.504995	−0.252498	−	0.967597i	$-0.581252\pi$
$157$	−6.32757	−0.504995	−0.252498	+	0.967597i	$0.581252\pi$
$158$	−0.0708345	−0.00563529
$159$	−12.1275	−0.961776
$160$	1.65031	0.130468
$161$	21.1553	1.66727
$162$	4.80005	0.377128
$163$	4.72853	0.370367	0.185184	−	0.982704i	$-0.440712\pi$
$163$	4.72853	0.370367	0.185184	+	0.982704i	$0.440712\pi$
$164$	4.62974	0.361522
$165$	−3.41412	−0.265789
$166$	7.35376	0.570762
$167$	1.95392	0.151199	0.0755993	−	0.997138i	$-0.475913\pi$
$167$	1.95392	0.151199	0.0755993	+	0.997138i	$0.475913\pi$
$168$	4.06956	0.313973
$169$	−9.25499	−0.711922
$170$	2.68296	0.205773
$171$	4.77102	0.364849
$172$	−7.14262	−0.544620
$173$	7.13429	0.542410	0.271205	−	0.962522i	$-0.412578\pi$
$173$	7.13429	0.542410	0.271205	+	0.962522i	$0.412578\pi$
$174$	−3.45380	−0.261832
$175$	−6.61680	−0.500183
$176$	−1.47758	−0.111377
$177$	12.7730	0.960074
$178$	−12.1510	−0.910757
$179$	−14.6705	−1.09652	−0.548262	−	0.836307i	$-0.684710\pi$
$179$	−14.6705	−1.09652	−0.548262	+	0.836307i	$0.684710\pi$
$180$	1.71578	0.127887
$181$	−15.1348	−1.12496	−0.562482	−	0.826810i	$-0.690153\pi$
$181$	−15.1348	−1.12496	−0.562482	+	0.826810i	$0.690153\pi$
$182$	−5.62484	−0.416941
$183$	16.2531	1.20146
$184$	−7.27839	−0.536570
$185$	0.634899	0.0466787
$186$	−9.76682	−0.716138
$187$	−2.40214	−0.175662
$188$	11.8044	0.860925
$189$	16.4397	1.19581
$190$	−7.57319	−0.549417
$191$	9.90307	0.716561	0.358281	−	0.933614i	$-0.383363\pi$
$191$	9.90307	0.716561	0.358281	+	0.933614i	$0.383363\pi$
$192$	−1.40012	−0.101045
$193$	8.52394	0.613567	0.306783	−	0.951779i	$-0.400747\pi$
$193$	8.52394	0.613567	0.306783	+	0.951779i	$0.400747\pi$
$194$	−2.36355	−0.169693
$195$	4.47152	0.320212
$196$	1.44825	0.103447
$197$	−5.02868	−0.358278	−0.179139	−	0.983824i	$-0.557331\pi$
$197$	−5.02868	−0.358278	−0.179139	+	0.983824i	$0.557331\pi$
$198$	−1.53620	−0.109173
$199$	−4.44613	−0.315178	−0.157589	−	0.987505i	$-0.550372\pi$
$199$	−4.44613	−0.315178	−0.157589	+	0.987505i	$0.550372\pi$
$200$	2.27649	0.160972
$201$	−14.6818	−1.03557
$202$	8.01069	0.563630
$203$	−7.16996	−0.503233
$204$	−2.27621	−0.159367
$205$	−7.64050	−0.533636
$206$	8.12874	0.566357
$207$	−7.56716	−0.525954
$208$	1.93520	0.134182
$209$	6.78053	0.469019
$210$	−6.71603	−0.463450
$211$	−26.5811	−1.82992	−0.914959	−	0.403548i	$-0.867777\pi$
$211$	−26.5811	−1.82992	−0.914959	+	0.403548i	$0.867777\pi$
$212$	8.66181	0.594895
$213$	2.65758	0.182095
$214$	10.0663	0.688119
$215$	11.7875	0.803902
$216$	−5.65601	−0.384843
$217$	−20.2755	−1.37639
$218$	0.143903	0.00974635
$219$	−14.9689	−1.01150
$220$	2.43846	0.164401
$221$	3.14612	0.211631
$222$	−0.538646	−0.0361516
$223$	−10.0803	−0.675028	−0.337514	−	0.941321i	$-0.609586\pi$
$223$	−10.0803	−0.675028	−0.337514	+	0.941321i	$0.609586\pi$
$224$	−2.90659	−0.194205
$225$	2.36680	0.157787
$226$	1.58797	0.105630
$227$	8.71957	0.578738	0.289369	−	0.957218i	$-0.406555\pi$
$227$	8.71957	0.578738	0.289369	+	0.957218i	$0.406555\pi$
$228$	6.42507	0.425511
$229$	−0.865941	−0.0572230	−0.0286115	−	0.999591i	$-0.509109\pi$
$229$	−0.865941	−0.0572230	−0.0286115	+	0.999591i	$0.509109\pi$
$230$	12.0116	0.792020
$231$	6.01309	0.395632
$232$	2.46680	0.161953
$233$	−15.3585	−1.00617	−0.503084	−	0.864238i	$-0.667801\pi$
$233$	−15.3585	−1.00617	−0.503084	+	0.864238i	$0.667801\pi$
$234$	2.01198	0.131527
$235$	−19.4809	−1.27079
$236$	−9.12278	−0.593843
$237$	−0.0991766	−0.00644221
$238$	−4.72533	−0.306298
$239$	5.03414	0.325631	0.162816	−	0.986657i	$-0.447942\pi$
$239$	5.03414	0.325631	0.162816	+	0.986657i	$0.447942\pi$
$240$	2.31062	0.149150
$241$	−22.3399	−1.43904	−0.719520	−	0.694472i	$-0.755638\pi$
$241$	−22.3399	−1.43904	−0.719520	+	0.694472i	$0.755638\pi$
$242$	8.81677	0.566763
$243$	−10.2474	−0.657372
$244$	−11.6084	−0.743151
$245$	−2.39007	−0.152696
$246$	6.48218	0.413289
$247$	−8.88056	−0.565056
$248$	6.97572	0.442959
$249$	10.2961	0.652490
$250$	−12.0084	−0.759480
$251$	−2.27835	−0.143808	−0.0719040	−	0.997412i	$-0.522908\pi$
$251$	−2.27835	−0.143808	−0.0719040	+	0.997412i	$0.522908\pi$
$252$	−3.02191	−0.190362
$253$	−10.7544	−0.676122
$254$	−7.21707	−0.452839
$255$	3.75645	0.235238
$256$	1.00000	0.0625000
$257$	−23.5894	−1.47146	−0.735732	−	0.677272i	$-0.763162\pi$
$257$	−23.5894	−1.47146	−0.735732	+	0.677272i	$0.763162\pi$
$258$	−10.0005	−0.622604
$259$	−1.11821	−0.0694822
$260$	−3.19368	−0.198064
$261$	2.56467	0.158749
$262$	−19.5680	−1.20892
$263$	−13.5376	−0.834762	−0.417381	−	0.908731i	$-0.637052\pi$
$263$	−13.5376	−0.834762	−0.417381	+	0.908731i	$0.637052\pi$
$264$	−2.06878	−0.127325
$265$	−14.2946	−0.878113
$266$	13.3382	0.817818
$267$	−17.0128	−1.04117
$268$	10.4861	0.640541
$269$	−1.51496	−0.0923689	−0.0461844	−	0.998933i	$-0.514706\pi$
$269$	−1.51496	−0.0923689	−0.0461844	+	0.998933i	$0.514706\pi$
$270$	9.33416	0.568059
$271$	8.60064	0.522451	0.261226	−	0.965278i	$-0.415873\pi$
$271$	8.60064	0.522451	0.261226	+	0.965278i	$0.415873\pi$
$272$	1.62573	0.0985744
$273$	−7.87543	−0.476642
$274$	7.74120	0.467663
$275$	3.36368	0.202838
$276$	−10.1906	−0.613402
$277$	24.2507	1.45708	0.728542	−	0.685001i	$-0.240198\pi$
$277$	24.2507	1.45708	0.728542	+	0.685001i	$0.240198\pi$
$278$	19.6411	1.17800
$279$	7.25248	0.434195
$280$	4.79676	0.286661
$281$	−15.1651	−0.904674	−0.452337	−	0.891847i	$-0.649410\pi$
$281$	−15.1651	−0.904674	−0.452337	+	0.891847i	$0.649410\pi$
$282$	16.5275	0.984201
$283$	−14.8211	−0.881025	−0.440513	−	0.897746i	$-0.645203\pi$
$283$	−14.8211	−0.881025	−0.440513	+	0.897746i	$0.645203\pi$
$284$	−1.89812	−0.112632
$285$	−10.6033	−0.628088
$286$	2.85941	0.169080
$287$	13.4568	0.794327
$288$	1.03967	0.0612634
$289$	−14.3570	−0.844529
$290$	−4.07097	−0.239056
$291$	−3.30925	−0.193991
$292$	10.6912	0.625654
$293$	−8.95875	−0.523376	−0.261688	−	0.965153i	$-0.584279\pi$
$293$	−8.95875	−0.523376	−0.261688	+	0.965153i	$0.584279\pi$
$294$	2.02772	0.118259
$295$	15.0554	0.876559
$296$	0.384716	0.0223611
$297$	−8.35719	−0.484934
$298$	−17.7835	−1.03017
$299$	14.0852	0.814566
$300$	3.18734	0.184021
$301$	−20.7607	−1.19662
$302$	−10.8627	−0.625077
$303$	11.2159	0.644337
$304$	−4.58896	−0.263195
$305$	19.1574	1.09695
$306$	1.69023	0.0966241
$307$	−12.2361	−0.698350	−0.349175	−	0.937058i	$-0.613538\pi$
$307$	−12.2361	−0.698350	−0.349175	+	0.937058i	$0.613538\pi$
$308$	−4.29471	−0.244714
$309$	11.3812	0.647453
$310$	−11.5121	−0.653842
$311$	−22.2251	−1.26027	−0.630134	−	0.776487i	$-0.717000\pi$
$311$	−22.2251	−1.26027	−0.630134	+	0.776487i	$0.717000\pi$
$312$	2.70951	0.153396
$313$	−11.3648	−0.642376	−0.321188	−	0.947015i	$-0.604082\pi$
$313$	−11.3648	−0.642376	−0.321188	+	0.947015i	$0.604082\pi$
$314$	6.32757	0.357086
$315$	4.98707	0.280990
$316$	0.0708345	0.00398475
$317$	−19.2327	−1.08022	−0.540108	−	0.841595i	$-0.681617\pi$
$317$	−19.2327	−1.08022	−0.540108	+	0.841595i	$0.681617\pi$
$318$	12.1275	0.680078
$319$	3.64488	0.204074
$320$	−1.65031	−0.0922550
$321$	14.0940	0.786651
$322$	−21.1553	−1.17894
$323$	−7.46040	−0.415108
$324$	−4.80005	−0.266670
$325$	−4.40546	−0.244371
$326$	−4.72853	−0.261889
$327$	0.201481	0.0111419
$328$	−4.62974	−0.255635
$329$	34.3105	1.89160
$330$	3.41412	0.187941
$331$	−14.7493	−0.810697	−0.405348	−	0.914162i	$-0.632850\pi$
$331$	−14.7493	−0.810697	−0.405348	+	0.914162i	$0.632850\pi$
$332$	−7.35376	−0.403590
$333$	0.399979	0.0219187
$334$	−1.95392	−0.106914
$335$	−17.3053	−0.945490
$336$	−4.06956	−0.222013
$337$	−20.3698	−1.10961	−0.554806	−	0.831980i	$-0.687207\pi$
$337$	−20.3698	−1.10961	−0.554806	+	0.831980i	$0.687207\pi$
$338$	9.25499	0.503405
$339$	2.22334	0.120756
$340$	−2.68296	−0.145504
$341$	10.3072	0.558164
$342$	−4.77102	−0.257987
$343$	−16.1366	−0.871297
$344$	7.14262	0.385104
$345$	16.8176	0.905430
$346$	−7.13429	−0.383542
$347$	−5.92891	−0.318281	−0.159140	−	0.987256i	$-0.550872\pi$
$347$	−5.92891	−0.318281	−0.159140	+	0.987256i	$0.550872\pi$
$348$	3.45380	0.185143
$349$	−5.89385	−0.315490	−0.157745	−	0.987480i	$-0.550422\pi$
$349$	−5.89385	−0.315490	−0.157745	+	0.987480i	$0.550422\pi$
$350$	6.61680	0.353683
$351$	10.9455	0.584229
$352$	1.47758	0.0787551
$353$	−31.6290	−1.68344	−0.841721	−	0.539913i	$-0.818457\pi$
$353$	−31.6290	−1.68344	−0.841721	+	0.539913i	$0.818457\pi$
$354$	−12.7730	−0.678875
$355$	3.13248	0.166255
$356$	12.1510	0.644003
$357$	−6.61601	−0.350156
$358$	14.6705	0.775360
$359$	12.1567	0.641605	0.320803	−	0.947146i	$-0.396047\pi$
$359$	12.1567	0.641605	0.320803	+	0.947146i	$0.396047\pi$
$360$	−1.71578	−0.0904297
$361$	2.05851	0.108343
$362$	15.1348	0.795469
$363$	12.3445	0.647918
$364$	5.62484	0.294822
$365$	−17.6437	−0.923516
$366$	−16.2531	−0.849563
$367$	4.28416	0.223631	0.111816	−	0.993729i	$-0.464333\pi$
$367$	4.28416	0.223631	0.111816	+	0.993729i	$0.464333\pi$
$368$	7.27839	0.379412
$369$	−4.81343	−0.250577
$370$	−0.634899	−0.0330068
$371$	25.1763	1.30709
$372$	9.76682	0.506386
$373$	18.3368	0.949444	0.474722	−	0.880136i	$-0.342549\pi$
$373$	18.3368	0.949444	0.474722	+	0.880136i	$0.342549\pi$
$374$	2.40214	0.124212
$375$	−16.8132	−0.868230
$376$	−11.8044	−0.608766
$377$	−4.77375	−0.245861
$378$	−16.4397	−0.845567
$379$	−4.42412	−0.227252	−0.113626	−	0.993524i	$-0.536247\pi$
$379$	−4.42412	−0.227252	−0.113626	+	0.993524i	$0.536247\pi$
$380$	7.57319	0.388496
$381$	−10.1047	−0.517681
$382$	−9.90307	−0.506685
$383$	17.4977	0.894090	0.447045	−	0.894511i	$-0.352476\pi$
$383$	17.4977	0.894090	0.447045	+	0.894511i	$0.352476\pi$
$384$	1.40012	0.0714494
$385$	7.08759	0.361217
$386$	−8.52394	−0.433857
$387$	7.42600	0.377485
$388$	2.36355	0.119991
$389$	−21.4150	−1.08578	−0.542892	−	0.839802i	$-0.682671\pi$
$389$	−21.4150	−1.08578	−0.542892	+	0.839802i	$0.682671\pi$
$390$	−4.47152	−0.226424
$391$	11.8327	0.598405
$392$	−1.44825	−0.0731479
$393$	−27.3975	−1.38202
$394$	5.02868	0.253341
$395$	−0.116899	−0.00588182
$396$	1.53620	0.0771969
$397$	29.7543	1.49332	0.746662	−	0.665204i	$-0.231655\pi$
$397$	29.7543	1.49332	0.746662	+	0.665204i	$0.231655\pi$
$398$	4.44613	0.222864
$399$	18.6750	0.934921
$400$	−2.27649	−0.113824
$401$	−21.7075	−1.08402	−0.542010	−	0.840372i	$-0.682337\pi$
$401$	−21.7075	−1.08402	−0.542010	+	0.840372i	$0.682337\pi$
$402$	14.6818	0.732260
$403$	−13.4994	−0.672455
$404$	−8.01069	−0.398547
$405$	7.92156	0.393626
$406$	7.16996	0.355839
$407$	0.568447	0.0281769
$408$	2.27621	0.112689
$409$	7.31365	0.361637	0.180818	−	0.983517i	$-0.442125\pi$
$409$	7.31365	0.361637	0.180818	+	0.983517i	$0.442125\pi$
$410$	7.64050	0.377337
$411$	10.8386	0.534628
$412$	−8.12874	−0.400475
$413$	−26.5162	−1.30478
$414$	7.56716	0.371906
$415$	12.1360	0.595731
$416$	−1.93520	−0.0948811
$417$	27.4999	1.34667
$418$	−6.78053	−0.331647
$419$	−13.1699	−0.643394	−0.321697	−	0.946843i	$-0.604253\pi$
$419$	−13.1699	−0.643394	−0.321697	+	0.946843i	$0.604253\pi$
$420$	6.71603	0.327709
$421$	−8.80366	−0.429064	−0.214532	−	0.976717i	$-0.568823\pi$
$421$	−8.80366	−0.429064	−0.214532	+	0.976717i	$0.568823\pi$
$422$	26.5811	1.29395
$423$	−12.2727	−0.596721
$424$	−8.66181	−0.420654
$425$	−3.70095	−0.179523
$426$	−2.65758	−0.128760
$427$	−33.7408	−1.63283
$428$	−10.0663	−0.486573
$429$	4.00351	0.193291
$430$	−11.7875	−0.568445
$431$	10.3251	0.497342	0.248671	−	0.968588i	$-0.420006\pi$
$431$	10.3251	0.497342	0.248671	+	0.968588i	$0.420006\pi$
$432$	5.65601	0.272125
$433$	−2.40470	−0.115563	−0.0577813	−	0.998329i	$-0.518403\pi$
$433$	−2.40470	−0.115563	−0.0577813	+	0.998329i	$0.518403\pi$
$434$	20.2755	0.973257
$435$	−5.69984	−0.273286
$436$	−0.143903	−0.00689171
$437$	−33.4002	−1.59775
$438$	14.9689	0.715242
$439$	−4.75041	−0.226725	−0.113362	−	0.993554i	$-0.536162\pi$
$439$	−4.75041	−0.226725	−0.113362	+	0.993554i	$0.536162\pi$
$440$	−2.43846	−0.116249
$441$	−1.50571	−0.0717007
$442$	−3.14612	−0.149646
$443$	−8.62907	−0.409979	−0.204990	−	0.978764i	$-0.565716\pi$
$443$	−8.62907	−0.409979	−0.204990	+	0.978764i	$0.565716\pi$
$444$	0.538646	0.0255630
$445$	−20.0529	−0.950599
$446$	10.0803	0.477317
$447$	−24.8990	−1.17768
$448$	2.90659	0.137323
$449$	−37.8750	−1.78743	−0.893715	−	0.448636i	$-0.851910\pi$
$449$	−37.8750	−1.78743	−0.893715	+	0.448636i	$0.851910\pi$
$450$	−2.36680	−0.111572
$451$	−6.84080	−0.322121
$452$	−1.58797	−0.0746919
$453$	−15.2090	−0.714581
$454$	−8.71957	−0.409230
$455$	−9.28271	−0.435180
$456$	−6.42507	−0.300882
$457$	−18.4506	−0.863084	−0.431542	−	0.902093i	$-0.642030\pi$
$457$	−18.4506	−0.863084	−0.431542	+	0.902093i	$0.642030\pi$
$458$	0.865941	0.0404628
$459$	9.19515	0.429193
$460$	−12.0116	−0.560043
$461$	−22.9386	−1.06836	−0.534179	−	0.845372i	$-0.679379\pi$
$461$	−22.9386	−1.06836	−0.534179	+	0.845372i	$0.679379\pi$
$462$	−6.01309	−0.279754
$463$	11.8503	0.550730	0.275365	−	0.961340i	$-0.411201\pi$
$463$	11.8503	0.550730	0.275365	+	0.961340i	$0.411201\pi$
$464$	−2.46680	−0.114518
$465$	−16.1183	−0.747466
$466$	15.3585	0.711468
$467$	−13.6621	−0.632207	−0.316103	−	0.948725i	$-0.602375\pi$
$467$	−13.6621	−0.632207	−0.316103	+	0.948725i	$0.602375\pi$
$468$	−2.01198	−0.0930039
$469$	30.4788	1.40738
$470$	19.4809	0.898587
$471$	8.85934	0.408217
$472$	9.12278	0.419910
$473$	10.5538	0.485263
$474$	0.0991766	0.00455533
$475$	10.4467	0.479327
$476$	4.72533	0.216585
$477$	−9.00546	−0.412332
$478$	−5.03414	−0.230256
$479$	18.8825	0.862765	0.431382	−	0.902169i	$-0.358026\pi$
$479$	18.8825	0.862765	0.431382	+	0.902169i	$0.358026\pi$
$480$	−2.31062	−0.105465
$481$	−0.744503	−0.0339464
$482$	22.3399	1.01756
$483$	−29.6199	−1.34775
$484$	−8.81677	−0.400762
$485$	−3.90059	−0.177117
$486$	10.2474	0.464832
$487$	−8.95896	−0.405969	−0.202985	−	0.979182i	$-0.565064\pi$
$487$	−8.95896	−0.405969	−0.202985	+	0.979182i	$0.565064\pi$
$488$	11.6084	0.525487
$489$	−6.62049	−0.299389
$490$	2.39007	0.107972
$491$	4.69705	0.211975	0.105988	−	0.994367i	$-0.466200\pi$
$491$	4.69705	0.211975	0.105988	+	0.994367i	$0.466200\pi$
$492$	−6.48218	−0.292239
$493$	−4.01035	−0.180617
$494$	8.88056	0.399555
$495$	−2.53520	−0.113949
$496$	−6.97572	−0.313219
$497$	−5.51704	−0.247473
$498$	−10.2961	−0.461380
$499$	25.0161	1.11987	0.559937	−	0.828535i	$-0.310825\pi$
$499$	25.0161	1.11987	0.559937	+	0.828535i	$0.310825\pi$
$500$	12.0084	0.537034
$501$	−2.73571	−0.122222
$502$	2.27835	0.101688
$503$	−4.80007	−0.214025	−0.107012	−	0.994258i	$-0.534128\pi$
$503$	−4.80007	−0.214025	−0.107012	+	0.994258i	$0.534128\pi$
$504$	3.02191	0.134606
$505$	13.2201	0.588287
$506$	10.7544	0.478090
$507$	12.9581	0.575488
$508$	7.21707	0.320206
$509$	37.1712	1.64759	0.823793	−	0.566891i	$-0.191854\pi$
$509$	37.1712	1.64759	0.823793	+	0.566891i	$0.191854\pi$
$510$	−3.75645	−0.166338
$511$	31.0749	1.37467
$512$	−1.00000	−0.0441942
$513$	−25.9552	−1.14595
$514$	23.5894	1.04048
$515$	13.4149	0.591132
$516$	10.0005	0.440247
$517$	−17.4419	−0.767094
$518$	1.11821	0.0491313
$519$	−9.98883	−0.438461
$520$	3.19368	0.140052
$521$	6.35043	0.278217	0.139109	−	0.990277i	$-0.455576\pi$
$521$	6.35043	0.278217	0.139109	+	0.990277i	$0.455576\pi$
$522$	−2.56467	−0.112252
$523$	9.09306	0.397612	0.198806	−	0.980039i	$-0.436294\pi$
$523$	9.09306	0.397612	0.198806	+	0.980039i	$0.436294\pi$
$524$	19.5680	0.854833
$525$	9.26430	0.404327
$526$	13.5376	0.590266
$527$	−11.3406	−0.494006
$528$	2.06878	0.0900320
$529$	29.9750	1.30326
$530$	14.2946	0.620920
$531$	9.48473	0.411602
$532$	−13.3382	−0.578284
$533$	8.95949	0.388079
$534$	17.0128	0.736217
$535$	16.6125	0.718221
$536$	−10.4861	−0.452931
$537$	20.5404	0.886383
$538$	1.51496	0.0653147
$539$	−2.13991	−0.0921723
$540$	−9.33416	−0.401678
$541$	−25.7443	−1.10683	−0.553417	−	0.832905i	$-0.686676\pi$
$541$	−25.7443	−1.10683	−0.553417	+	0.832905i	$0.686676\pi$
$542$	−8.60064	−0.369429
$543$	21.1905	0.909372
$544$	−1.62573	−0.0697026
$545$	0.237484	0.0101727
$546$	7.87543	0.337037
$547$	28.5635	1.22129	0.610643	−	0.791906i	$-0.290911\pi$
$547$	28.5635	1.22129	0.610643	+	0.791906i	$0.290911\pi$
$548$	−7.74120	−0.330688
$549$	12.0690	0.515090
$550$	−3.36368	−0.143428
$551$	11.3200	0.482249
$552$	10.1906	0.433740
$553$	0.205887	0.00875520
$554$	−24.2507	−1.03031
$555$	−0.888932	−0.0377331
$556$	−19.6411	−0.832969
$557$	−37.9765	−1.60911	−0.804557	−	0.593875i	$-0.797597\pi$
$557$	−37.9765	−1.60911	−0.804557	+	0.593875i	$0.797597\pi$
$558$	−7.25248	−0.307022
$559$	−13.8224	−0.584626
$560$	−4.79676	−0.202700
$561$	3.36328	0.141998
$562$	15.1651	0.639701
$563$	−30.9187	−1.30307	−0.651535	−	0.758619i	$-0.725875\pi$
$563$	−30.9187	−1.30307	−0.651535	+	0.758619i	$0.725875\pi$
$564$	−16.5275	−0.695935
$565$	2.62064	0.110251
$566$	14.8211	0.622979
$567$	−13.9518	−0.585920
$568$	1.89812	0.0796432
$569$	−7.10343	−0.297791	−0.148896	−	0.988853i	$-0.547572\pi$
$569$	−7.10343	−0.297791	−0.148896	+	0.988853i	$0.547572\pi$
$570$	10.6033	0.444125
$571$	15.0307	0.629014	0.314507	−	0.949255i	$-0.398161\pi$
$571$	15.0307	0.629014	0.314507	+	0.949255i	$0.398161\pi$
$572$	−2.85941	−0.119558
$573$	−13.8655	−0.579238
$574$	−13.4568	−0.561674
$575$	−16.5691	−0.690981
$576$	−1.03967	−0.0433198
$577$	−1.45580	−0.0606058	−0.0303029	−	0.999541i	$-0.509647\pi$
$577$	−1.45580	−0.0606058	−0.0303029	+	0.999541i	$0.509647\pi$
$578$	14.3570	0.597172
$579$	−11.9345	−0.495981
$580$	4.07097	0.169038
$581$	−21.3744	−0.886758
$582$	3.30925	0.137173
$583$	−12.7985	−0.530059
$584$	−10.6912	−0.442404
$585$	3.32039	0.137281
$586$	8.95875	0.370082
$587$	9.29236	0.383537	0.191768	−	0.981440i	$-0.438578\pi$
$587$	9.29236	0.383537	0.191768	+	0.981440i	$0.438578\pi$
$588$	−2.02772	−0.0836220
$589$	32.0113	1.31900
$590$	−15.0554	−0.619821
$591$	7.04073	0.289617
$592$	−0.384716	−0.0158117
$593$	6.01596	0.247046	0.123523	−	0.992342i	$-0.460581\pi$
$593$	6.01596	0.247046	0.123523	+	0.992342i	$0.460581\pi$
$594$	8.35719	0.342900
$595$	−7.79825	−0.319697
$596$	17.7835	0.728440
$597$	6.22510	0.254776
$598$	−14.0852	−0.575985
$599$	−29.2689	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$599$	−29.2689	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$600$	−3.18734	−0.130123
$601$	12.9928	0.529986	0.264993	−	0.964250i	$-0.414630\pi$
$601$	12.9928	0.529986	0.264993	+	0.964250i	$0.414630\pi$
$602$	20.7607	0.846141
$603$	−10.9021	−0.443970
$604$	10.8627	0.441996
$605$	14.5504	0.591557
$606$	−11.2159	−0.455615
$607$	20.1275	0.816949	0.408474	−	0.912770i	$-0.366061\pi$
$607$	20.1275	0.816949	0.408474	+	0.912770i	$0.366061\pi$
$608$	4.58896	0.186107
$609$	10.0388	0.406792
$610$	−19.1574	−0.775661
$611$	22.8439	0.924166
$612$	−1.69023	−0.0683235
$613$	27.8629	1.12537	0.562687	−	0.826670i	$-0.309768\pi$
$613$	27.8629	1.12537	0.562687	+	0.826670i	$0.309768\pi$
$614$	12.2361	0.493808
$615$	10.6976	0.431368
$616$	4.29471	0.173039
$617$	5.49399	0.221180	0.110590	−	0.993866i	$-0.464726\pi$
$617$	5.49399	0.221180	0.110590	+	0.993866i	$0.464726\pi$
$618$	−11.3812	−0.457819
$619$	−1.84044	−0.0739735	−0.0369868	−	0.999316i	$-0.511776\pi$
$619$	−1.84044	−0.0739735	−0.0369868	+	0.999316i	$0.511776\pi$
$620$	11.5121	0.462336
$621$	41.1667	1.65196
$622$	22.2251	0.891143
$623$	35.3180	1.41499
$624$	−2.70951	−0.108467
$625$	−8.43519	−0.337408
$626$	11.3648	0.454229
$627$	−9.49353	−0.379135
$628$	−6.32757	−0.252498
$629$	−0.625444	−0.0249381
$630$	−4.98707	−0.198690
$631$	0.733207	0.0291885	0.0145943	−	0.999893i	$-0.495354\pi$
$631$	0.733207	0.0291885	0.0145943	+	0.999893i	$0.495354\pi$
$632$	−0.0708345	−0.00281765
$633$	37.2166	1.47923
$634$	19.2327	0.763829
$635$	−11.9104	−0.472649
$636$	−12.1275	−0.480888
$637$	2.80267	0.111046
$638$	−3.64488	−0.144302
$639$	1.97342	0.0780674
$640$	1.65031	0.0652341
$641$	43.0323	1.69967	0.849836	−	0.527047i	$-0.176701\pi$
$641$	43.0323	1.69967	0.849836	+	0.527047i	$0.176701\pi$
$642$	−14.0940	−0.556246
$643$	−10.3797	−0.409335	−0.204668	−	0.978832i	$-0.565611\pi$
$643$	−10.3797	−0.409335	−0.204668	+	0.978832i	$0.565611\pi$
$644$	21.1553	0.833635
$645$	−16.5039	−0.649840
$646$	7.46040	0.293526
$647$	39.7372	1.56223	0.781115	−	0.624387i	$-0.214651\pi$
$647$	39.7372	1.56223	0.781115	+	0.624387i	$0.214651\pi$
$648$	4.80005	0.188564
$649$	13.4796	0.529121
$650$	4.40546	0.172796
$651$	28.3881	1.11262
$652$	4.72853	0.185184
$653$	−3.15386	−0.123420	−0.0617100	−	0.998094i	$-0.519655\pi$
$653$	−3.15386	−0.123420	−0.0617100	+	0.998094i	$0.519655\pi$
$654$	−0.201481	−0.00787854
$655$	−32.2933	−1.26180
$656$	4.62974	0.180761
$657$	−11.1154	−0.433651
$658$	−34.3105	−1.33756
$659$	−8.11269	−0.316025	−0.158013	−	0.987437i	$-0.550509\pi$
$659$	−8.11269	−0.316025	−0.158013	+	0.987437i	$0.550509\pi$
$660$	−3.41412	−0.132894
$661$	−24.0240	−0.934424	−0.467212	−	0.884145i	$-0.654741\pi$
$661$	−24.0240	−0.934424	−0.467212	+	0.884145i	$0.654741\pi$
$662$	14.7493	0.573249
$663$	−4.40493	−0.171073
$664$	7.35376	0.285381
$665$	22.0121	0.853594
$666$	−0.399979	−0.0154989
$667$	−17.9543	−0.695194
$668$	1.95392	0.0755993
$669$	14.1136	0.545664
$670$	17.3053	0.668562
$671$	17.1523	0.662157
$672$	4.06956	0.156987
$673$	−3.92915	−0.151458	−0.0757288	−	0.997128i	$-0.524128\pi$
$673$	−3.92915	−0.151458	−0.0757288	+	0.997128i	$0.524128\pi$
$674$	20.3698	0.784614
$675$	−12.8758	−0.495591
$676$	−9.25499	−0.355961
$677$	17.1535	0.659262	0.329631	−	0.944110i	$-0.393076\pi$
$677$	17.1535	0.659262	0.329631	+	0.944110i	$0.393076\pi$
$678$	−2.22334	−0.0853870
$679$	6.86987	0.263641
$680$	2.68296	0.102887
$681$	−12.2084	−0.467827
$682$	−10.3072	−0.394682
$683$	39.1194	1.49686	0.748432	−	0.663212i	$-0.230807\pi$
$683$	39.1194	1.49686	0.748432	+	0.663212i	$0.230807\pi$
$684$	4.77102	0.182425
$685$	12.7754	0.488122
$686$	16.1366	0.616100
$687$	1.21242	0.0462566
$688$	−7.14262	−0.272310
$689$	16.7623	0.638595
$690$	−16.8176	−0.640236
$691$	−35.6947	−1.35789	−0.678946	−	0.734188i	$-0.737563\pi$
$691$	−35.6947	−1.35789	−0.678946	+	0.734188i	$0.737563\pi$
$692$	7.13429	0.271205
$693$	4.46510	0.169615
$694$	5.92891	0.225058
$695$	32.4139	1.22953
$696$	−3.45380	−0.130916
$697$	7.52672	0.285095
$698$	5.89385	0.223085
$699$	21.5037	0.813343
$700$	−6.61680	−0.250092
$701$	−9.98116	−0.376983	−0.188492	−	0.982075i	$-0.560360\pi$
$701$	−9.98116	−0.376983	−0.188492	+	0.982075i	$0.560360\pi$
$702$	−10.9455	−0.413113
$703$	1.76544	0.0665849
$704$	−1.47758	−0.0556883
$705$	27.2755	1.02726
$706$	31.6290	1.19037
$707$	−23.2838	−0.875677
$708$	12.7730	0.480037
$709$	−27.9187	−1.04851	−0.524255	−	0.851561i	$-0.675656\pi$
$709$	−27.9187	−1.04851	−0.524255	+	0.851561i	$0.675656\pi$
$710$	−3.13248	−0.117560
$711$	−0.0736449	−0.00276190
$712$	−12.1510	−0.455379
$713$	−50.7720	−1.90143
$714$	6.61601	0.247598
$715$	4.71891	0.176477
$716$	−14.6705	−0.548262
$717$	−7.04838	−0.263226
$718$	−12.1567	−0.453683
$719$	10.2850	0.383566	0.191783	−	0.981437i	$-0.438573\pi$
$719$	10.2850	0.383566	0.191783	+	0.981437i	$0.438573\pi$
$720$	1.71578	0.0639435
$721$	−23.6269	−0.879912
$722$	−2.05851	−0.0766099
$723$	31.2785	1.16326
$724$	−15.1348	−0.562482
$725$	5.61563	0.208559
$726$	−12.3445	−0.458147
$727$	24.1344	0.895096	0.447548	−	0.894260i	$-0.352297\pi$
$727$	24.1344	0.895096	0.447548	+	0.894260i	$0.352297\pi$
$728$	−5.62484	−0.208470
$729$	28.7477	1.06473
$730$	17.6437	0.653024
$731$	−11.6120	−0.429484
$732$	16.2531	0.600732
$733$	22.3073	0.823939	0.411970	−	0.911198i	$-0.364841\pi$
$733$	22.3073	0.823939	0.411970	+	0.911198i	$0.364841\pi$
$734$	−4.28416	−0.158131
$735$	3.34637	0.123433
$736$	−7.27839	−0.268285
$737$	−15.4940	−0.570730
$738$	4.81343	0.177185
$739$	−20.0881	−0.738954	−0.369477	−	0.929240i	$-0.620463\pi$
$739$	−20.0881	−0.738954	−0.369477	+	0.929240i	$0.620463\pi$
$740$	0.634899	0.0233394
$741$	12.4338	0.456768
$742$	−25.1763	−0.924251
$743$	−38.5492	−1.41423	−0.707116	−	0.707097i	$-0.750004\pi$
$743$	−38.5492	−1.41423	−0.707116	+	0.707097i	$0.750004\pi$
$744$	−9.76682	−0.358069
$745$	−29.3482	−1.07524
$746$	−18.3368	−0.671358
$747$	7.64552	0.279735
$748$	−2.40214	−0.0878310
$749$	−29.2586	−1.06909
$750$	16.8132	0.613932
$751$	−2.61394	−0.0953840	−0.0476920	−	0.998862i	$-0.515187\pi$
$751$	−2.61394	−0.0953840	−0.0476920	+	0.998862i	$0.515187\pi$
$752$	11.8044	0.430462
$753$	3.18995	0.116248
$754$	4.77375	0.173850
$755$	−17.9268	−0.652421
$756$	16.4397	0.597906
$757$	49.1286	1.78561	0.892805	−	0.450444i	$-0.148734\pi$
$757$	49.1286	1.78561	0.892805	+	0.450444i	$0.148734\pi$
$758$	4.42412	0.160691
$759$	15.0574	0.546548
$760$	−7.57319	−0.274708
$761$	−25.5828	−0.927375	−0.463688	−	0.885999i	$-0.653474\pi$
$761$	−25.5828	−0.927375	−0.463688	+	0.885999i	$0.653474\pi$
$762$	10.1047	0.366056
$763$	−0.418267	−0.0151423
$764$	9.90307	0.358281
$765$	2.78940	0.100851
$766$	−17.4977	−0.632217
$767$	−17.6544	−0.637465
$768$	−1.40012	−0.0505223
$769$	−37.0420	−1.33577	−0.667885	−	0.744264i	$-0.732800\pi$
$769$	−37.0420	−1.33577	−0.667885	+	0.744264i	$0.732800\pi$
$770$	−7.08759	−0.255419
$771$	33.0279	1.18947
$772$	8.52394	0.306783
$773$	−46.6837	−1.67910	−0.839548	−	0.543286i	$-0.817180\pi$
$773$	−46.6837	−1.67910	−0.839548	+	0.543286i	$0.817180\pi$
$774$	−7.42600	−0.266922
$775$	15.8801	0.570431
$776$	−2.36355	−0.0848466
$777$	1.56562	0.0561664
$778$	21.4150	0.767766
$779$	−21.2457	−0.761206
$780$	4.47152	0.160106
$781$	2.80461	0.100357
$782$	−11.8327	−0.423137
$783$	−13.9522	−0.498612
$784$	1.44825	0.0517234
$785$	10.4424	0.372707
$786$	27.3975	0.977237
$787$	−21.4946	−0.766199	−0.383100	−	0.923707i	$-0.625143\pi$
$787$	−21.4946	−0.766199	−0.383100	+	0.923707i	$0.625143\pi$
$788$	−5.02868	−0.179139
$789$	18.9542	0.674786
$790$	0.116899	0.00415907
$791$	−4.61558	−0.164111
$792$	−1.53620	−0.0545864
$793$	−22.4646	−0.797741
$794$	−29.7543	−1.05594
$795$	20.0142	0.709829
$796$	−4.44613	−0.157589
$797$	16.4977	0.584379	0.292190	−	0.956360i	$-0.405616\pi$
$797$	16.4977	0.584379	0.292190	+	0.956360i	$0.405616\pi$
$798$	−18.6750	−0.661089
$799$	19.1908	0.678921
$800$	2.27649	0.0804859
$801$	−12.6331	−0.446369
$802$	21.7075	0.766518
$803$	−15.7970	−0.557465
$804$	−14.6818	−0.517786
$805$	−34.9127	−1.23051
$806$	13.4994	0.475497
$807$	2.12112	0.0746671
$808$	8.01069	0.281815
$809$	9.89800	0.347995	0.173997	−	0.984746i	$-0.444332\pi$
$809$	9.89800	0.347995	0.173997	+	0.984746i	$0.444332\pi$
$810$	−7.92156	−0.278335
$811$	−35.5614	−1.24873	−0.624365	−	0.781133i	$-0.714642\pi$
$811$	−35.5614	−1.24873	−0.624365	+	0.781133i	$0.714642\pi$
$812$	−7.16996	−0.251616
$813$	−12.0419	−0.422327
$814$	−0.568447	−0.0199240
$815$	−7.80353	−0.273346
$816$	−2.27621	−0.0796833
$817$	32.7772	1.14673
$818$	−7.31365	−0.255716
$819$	−5.84800	−0.204346
$820$	−7.64050	−0.266818
$821$	37.6772	1.31494	0.657472	−	0.753479i	$-0.271626\pi$
$821$	37.6772	1.31494	0.657472	+	0.753479i	$0.271626\pi$
$822$	−10.8386	−0.378039
$823$	4.86689	0.169649	0.0848245	−	0.996396i	$-0.472967\pi$
$823$	4.86689	0.169649	0.0848245	+	0.996396i	$0.472967\pi$
$824$	8.12874	0.283178
$825$	−4.70954	−0.163965
$826$	26.5162	0.922616
$827$	5.70654	0.198436	0.0992179	−	0.995066i	$-0.468366\pi$
$827$	5.70654	0.198436	0.0992179	+	0.995066i	$0.468366\pi$
$828$	−7.56716	−0.262977
$829$	4.51774	0.156908	0.0784539	−	0.996918i	$-0.475002\pi$
$829$	4.51774	0.156908	0.0784539	+	0.996918i	$0.475002\pi$
$830$	−12.1360	−0.421246
$831$	−33.9538	−1.17785
$832$	1.93520	0.0670911
$833$	2.35447	0.0815776
$834$	−27.4999	−0.952242
$835$	−3.22456	−0.111591
$836$	6.78053	0.234510
$837$	−39.4548	−1.36376
$838$	13.1699	0.454948
$839$	8.52761	0.294406	0.147203	−	0.989106i	$-0.452973\pi$
$839$	8.52761	0.294406	0.147203	+	0.989106i	$0.452973\pi$
$840$	−6.71603	−0.231725
$841$	−22.9149	−0.790169
$842$	8.80366	0.303394
$843$	21.2329	0.731300
$844$	−26.5811	−0.914959
$845$	15.2736	0.525427
$846$	12.2727	0.421946
$847$	−25.6267	−0.880544
$848$	8.66181	0.297448
$849$	20.7513	0.712183
$850$	3.70095	0.126942
$851$	−2.80011	−0.0959865
$852$	2.65758	0.0910473
$853$	4.36409	0.149424	0.0747119	−	0.997205i	$-0.476196\pi$
$853$	4.36409	0.149424	0.0747119	+	0.997205i	$0.476196\pi$
$854$	33.7408	1.15459
$855$	−7.87365	−0.269273
$856$	10.0663	0.344059
$857$	53.4010	1.82414	0.912071	−	0.410032i	$-0.134482\pi$
$857$	53.4010	1.82414	0.912071	+	0.410032i	$0.134482\pi$
$858$	−4.00351	−0.136677
$859$	−4.85224	−0.165556	−0.0827782	−	0.996568i	$-0.526379\pi$
$859$	−4.85224	−0.165556	−0.0827782	+	0.996568i	$0.526379\pi$
$860$	11.7875	0.401951
$861$	−18.8410	−0.642100
$862$	−10.3251	−0.351674
$863$	40.8772	1.39147	0.695737	−	0.718296i	$-0.255078\pi$
$863$	40.8772	1.39147	0.695737	+	0.718296i	$0.255078\pi$
$864$	−5.65601	−0.192422
$865$	−11.7738	−0.400320
$866$	2.40470	0.0817150
$867$	20.1015	0.682682
$868$	−20.2755	−0.688197
$869$	−0.104663	−0.00355046
$870$	5.69984	0.193243
$871$	20.2927	0.687594
$872$	0.143903	0.00487318
$873$	−2.45732	−0.0831678
$874$	33.4002	1.12978
$875$	34.9036	1.17996
$876$	−14.9689	−0.505752
$877$	−32.9586	−1.11293	−0.556467	−	0.830870i	$-0.687843\pi$
$877$	−32.9586	−1.11293	−0.556467	+	0.830870i	$0.687843\pi$
$878$	4.75041	0.160318
$879$	12.5433	0.423075
$880$	2.43846	0.0822003
$881$	−15.1301	−0.509746	−0.254873	−	0.966975i	$-0.582034\pi$
$881$	−15.1301	−0.509746	−0.254873	+	0.966975i	$0.582034\pi$
$882$	1.50571	0.0507000
$883$	−39.0156	−1.31298	−0.656490	−	0.754335i	$-0.727960\pi$
$883$	−39.0156	−1.31298	−0.656490	+	0.754335i	$0.727960\pi$
$884$	3.14612	0.105815
$885$	−21.0793	−0.708573
$886$	8.62907	0.289899
$887$	−24.7990	−0.832670	−0.416335	−	0.909211i	$-0.636686\pi$
$887$	−24.7990	−0.832670	−0.416335	+	0.909211i	$0.636686\pi$
$888$	−0.538646	−0.0180758
$889$	20.9770	0.703548
$890$	20.0529	0.672175
$891$	7.09245	0.237606
$892$	−10.0803	−0.337514
$893$	−54.1699	−1.81273
$894$	24.8990	0.832746
$895$	24.2108	0.809279
$896$	−2.90659	−0.0971023
$897$	−19.7209	−0.658460
$898$	37.8750	1.26390
$899$	17.2077	0.573908
$900$	2.36680	0.0788935
$901$	14.0818	0.469131
$902$	6.84080	0.227774
$903$	29.0673	0.967300
$904$	1.58797	0.0528152
$905$	24.9771	0.830268
$906$	15.2090	0.505285
$907$	15.4638	0.513468	0.256734	−	0.966482i	$-0.417354\pi$
$907$	15.4638	0.513468	0.256734	+	0.966482i	$0.417354\pi$
$908$	8.71957	0.289369
$909$	8.32851	0.276239
$910$	9.28271	0.307719
$911$	19.0998	0.632806	0.316403	−	0.948625i	$-0.397525\pi$
$911$	19.0998	0.632806	0.316403	+	0.948625i	$0.397525\pi$
$912$	6.42507	0.212755
$913$	10.8657	0.359604
$914$	18.4506	0.610292
$915$	−26.8226	−0.886728
$916$	−0.865941	−0.0286115
$917$	56.8762	1.87822
$918$	−9.19515	−0.303485
$919$	35.3335	1.16554	0.582772	−	0.812636i	$-0.301968\pi$
$919$	35.3335	1.16554	0.582772	+	0.812636i	$0.301968\pi$
$920$	12.0116	0.396010
$921$	17.1319	0.564516
$922$	22.9386	0.755443
$923$	−3.67324	−0.120906
$924$	6.01309	0.197816
$925$	0.875799	0.0287961
$926$	−11.8503	−0.389425
$927$	8.45125	0.277575
$928$	2.46680	0.0809766
$929$	−44.1815	−1.44955	−0.724774	−	0.688987i	$-0.758056\pi$
$929$	−44.1815	−1.44955	−0.724774	+	0.688987i	$0.758056\pi$
$930$	16.1183	0.528538
$931$	−6.64598	−0.217813
$932$	−15.3585	−0.503084
$933$	31.1177	1.01875
$934$	13.6621	0.447038
$935$	3.96427	0.129646
$936$	2.01198	0.0657637
$937$	−1.89370	−0.0618644	−0.0309322	−	0.999521i	$-0.509848\pi$
$937$	−1.89370	−0.0618644	−0.0309322	+	0.999521i	$0.509848\pi$
$938$	−30.4788	−0.995168
$939$	15.9120	0.519270
$940$	−19.4809	−0.635397
$941$	−2.09446	−0.0682776	−0.0341388	−	0.999417i	$-0.510869\pi$
$941$	−2.09446	−0.0682776	−0.0341388	+	0.999417i	$0.510869\pi$
$942$	−8.85934	−0.288653
$943$	33.6971	1.09733
$944$	−9.12278	−0.296921
$945$	−27.1306	−0.882557
$946$	−10.5538	−0.343133
$947$	60.9845	1.98173	0.990865	−	0.134854i	$-0.0430566\pi$
$947$	60.9845	1.98173	0.990865	+	0.134854i	$0.0430566\pi$
$948$	−0.0991766	−0.00322111
$949$	20.6896	0.671613
$950$	−10.4467	−0.338935
$951$	26.9280	0.873201
$952$	−4.72533	−0.153149
$953$	−25.8728	−0.838103	−0.419051	−	0.907962i	$-0.637637\pi$
$953$	−25.8728	−0.838103	−0.419051	+	0.907962i	$0.637637\pi$
$954$	9.00546	0.291562
$955$	−16.3431	−0.528851
$956$	5.03414	0.162816
$957$	−5.10326	−0.164965
$958$	−18.8825	−0.610067
$959$	−22.5005	−0.726579
$960$	2.31062	0.0745750
$961$	17.6607	0.569699
$962$	0.744503	0.0240037
$963$	10.4657	0.337252
$964$	−22.3399	−0.719520
$965$	−14.0671	−0.452837
$966$	29.6199	0.953003
$967$	46.7466	1.50327	0.751635	−	0.659579i	$-0.229265\pi$
$967$	46.7466	1.50327	0.751635	+	0.659579i	$0.229265\pi$
$968$	8.81677	0.283382
$969$	10.4454	0.335556
$970$	3.90059	0.125240
$971$	16.1187	0.517275	0.258637	−	0.965974i	$-0.416727\pi$
$971$	16.1187	0.517275	0.258637	+	0.965974i	$0.416727\pi$
$972$	−10.2474	−0.328686
$973$	−57.0887	−1.83018
$974$	8.95896	0.287064
$975$	6.16816	0.197539
$976$	−11.6084	−0.371576
$977$	−4.13779	−0.132380	−0.0661898	−	0.997807i	$-0.521084\pi$
$977$	−4.13779	−0.132380	−0.0661898	+	0.997807i	$0.521084\pi$
$978$	6.62049	0.211700
$979$	−17.9541	−0.573814
$980$	−2.39007	−0.0763478
$981$	0.149612	0.00477676
$982$	−4.69705	−0.149889
$983$	42.3130	1.34958	0.674788	−	0.738011i	$-0.264235\pi$
$983$	42.3130	1.34958	0.674788	+	0.738011i	$0.264235\pi$
$984$	6.48218	0.206644
$985$	8.29886	0.264424
$986$	4.01035	0.127715
$987$	−48.0388	−1.52909
$988$	−8.88056	−0.282528
$989$	−51.9868	−1.65308
$990$	2.53520	0.0805740
$991$	55.7726	1.77168	0.885838	−	0.463995i	$-0.153585\pi$
$991$	55.7726	1.77168	0.885838	+	0.463995i	$0.153585\pi$
$992$	6.97572	0.221479
$993$	20.6508	0.655333
$994$	5.51704	0.174990
$995$	7.33748	0.232614
$996$	10.2961	0.326245
$997$	55.2400	1.74947	0.874735	−	0.484602i	$-0.161036\pi$
$997$	55.2400	1.74947	0.874735	+	0.484602i	$0.161036\pi$
$998$	−25.0161	−0.791871
$999$	−2.17596	−0.0688442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.13	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.13	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.40012 q^{3} +1.00000 q^{4} -1.65031 q^{5} +1.40012 q^{6} +2.90659 q^{7} -1.00000 q^{8} -1.03967 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.40012 q^{3} +1.00000 q^{4} -1.65031 q^{5} +1.40012 q^{6} +2.90659 q^{7} -1.00000 q^{8} -1.03967 q^{9} +1.65031 q^{10} -1.47758 q^{11} -1.40012 q^{12} +1.93520 q^{13} -2.90659 q^{14} +2.31062 q^{15} +1.00000 q^{16} +1.62573 q^{17} +1.03967 q^{18} -4.58896 q^{19} -1.65031 q^{20} -4.06956 q^{21} +1.47758 q^{22} +7.27839 q^{23} +1.40012 q^{24} -2.27649 q^{25} -1.93520 q^{26} +5.65601 q^{27} +2.90659 q^{28} -2.46680 q^{29} -2.31062 q^{30} -6.97572 q^{31} -1.00000 q^{32} +2.06878 q^{33} -1.62573 q^{34} -4.79676 q^{35} -1.03967 q^{36} -0.384716 q^{37} +4.58896 q^{38} -2.70951 q^{39} +1.65031 q^{40} +4.62974 q^{41} +4.06956 q^{42} -7.14262 q^{43} -1.47758 q^{44} +1.71578 q^{45} -7.27839 q^{46} +11.8044 q^{47} -1.40012 q^{48} +1.44825 q^{49} +2.27649 q^{50} -2.27621 q^{51} +1.93520 q^{52} +8.66181 q^{53} -5.65601 q^{54} +2.43846 q^{55} -2.90659 q^{56} +6.42507 q^{57} +2.46680 q^{58} -9.12278 q^{59} +2.31062 q^{60} -11.6084 q^{61} +6.97572 q^{62} -3.02191 q^{63} +1.00000 q^{64} -3.19368 q^{65} -2.06878 q^{66} +10.4861 q^{67} +1.62573 q^{68} -10.1906 q^{69} +4.79676 q^{70} -1.89812 q^{71} +1.03967 q^{72} +10.6912 q^{73} +0.384716 q^{74} +3.18734 q^{75} -4.58896 q^{76} -4.29471 q^{77} +2.70951 q^{78} +0.0708345 q^{79} -1.65031 q^{80} -4.80005 q^{81} -4.62974 q^{82} -7.35376 q^{83} -4.06956 q^{84} -2.68296 q^{85} +7.14262 q^{86} +3.45380 q^{87} +1.47758 q^{88} +12.1510 q^{89} -1.71578 q^{90} +5.62484 q^{91} +7.27839 q^{92} +9.76682 q^{93} -11.8044 q^{94} +7.57319 q^{95} +1.40012 q^{96} +2.36355 q^{97} -1.44825 q^{98} +1.53620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

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