LMFDB - Embedded newform 4022.2.a.e.1.17

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:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.923967 q^{3} +1.00000 q^{4} -1.00517 q^{5} +0.923967 q^{6} -1.65407 q^{7} -1.00000 q^{8} -2.14628 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.923967 q^{3} +1.00000 q^{4} -1.00517 q^{5} +0.923967 q^{6} -1.65407 q^{7} -1.00000 q^{8} -2.14628 q^{9} +1.00517 q^{10} -3.52761 q^{11} -0.923967 q^{12} -2.87212 q^{13} +1.65407 q^{14} +0.928748 q^{15} +1.00000 q^{16} -0.517323 q^{17} +2.14628 q^{18} -2.41623 q^{19} -1.00517 q^{20} +1.52831 q^{21} +3.52761 q^{22} -7.18630 q^{23} +0.923967 q^{24} -3.98962 q^{25} +2.87212 q^{26} +4.75500 q^{27} -1.65407 q^{28} +2.16111 q^{29} -0.928748 q^{30} -6.60016 q^{31} -1.00000 q^{32} +3.25940 q^{33} +0.517323 q^{34} +1.66263 q^{35} -2.14628 q^{36} -9.53137 q^{37} +2.41623 q^{38} +2.65375 q^{39} +1.00517 q^{40} -4.03502 q^{41} -1.52831 q^{42} +9.99403 q^{43} -3.52761 q^{44} +2.15739 q^{45} +7.18630 q^{46} +1.45942 q^{47} -0.923967 q^{48} -4.26404 q^{49} +3.98962 q^{50} +0.477989 q^{51} -2.87212 q^{52} -7.71322 q^{53} -4.75500 q^{54} +3.54586 q^{55} +1.65407 q^{56} +2.23251 q^{57} -2.16111 q^{58} -6.62583 q^{59} +0.928748 q^{60} +5.00701 q^{61} +6.60016 q^{62} +3.55011 q^{63} +1.00000 q^{64} +2.88699 q^{65} -3.25940 q^{66} -8.51763 q^{67} -0.517323 q^{68} +6.63990 q^{69} -1.66263 q^{70} +3.57486 q^{71} +2.14628 q^{72} +0.496885 q^{73} +9.53137 q^{74} +3.68628 q^{75} -2.41623 q^{76} +5.83493 q^{77} -2.65375 q^{78} -3.81649 q^{79} -1.00517 q^{80} +2.04539 q^{81} +4.03502 q^{82} -4.39546 q^{83} +1.52831 q^{84} +0.520000 q^{85} -9.99403 q^{86} -1.99679 q^{87} +3.52761 q^{88} -7.28465 q^{89} -2.15739 q^{90} +4.75071 q^{91} -7.18630 q^{92} +6.09833 q^{93} -1.45942 q^{94} +2.42873 q^{95} +0.923967 q^{96} +13.4040 q^{97} +4.26404 q^{98} +7.57126 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * 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
$3$	−0.923967	−0.533453	−0.266726	−	0.963772i	$-0.585942\pi$
$3$	−0.923967	−0.533453	−0.266726	+	0.963772i	$0.585942\pi$
$4$	1.00000	0.500000
$5$	−1.00517	−0.449528	−0.224764	−	0.974413i	$-0.572161\pi$
$5$	−1.00517	−0.449528	−0.224764	+	0.974413i	$0.572161\pi$
$6$	0.923967	0.377208
$7$	−1.65407	−0.625181	−0.312591	−	0.949888i	$-0.601197\pi$
$7$	−1.65407	−0.625181	−0.312591	+	0.949888i	$0.601197\pi$
$8$	−1.00000	−0.353553
$9$	−2.14628	−0.715428
$10$	1.00517	0.317864
$11$	−3.52761	−1.06361	−0.531807	−	0.846865i	$-0.678487\pi$
$11$	−3.52761	−1.06361	−0.531807	+	0.846865i	$0.678487\pi$
$12$	−0.923967	−0.266726
$13$	−2.87212	−0.796584	−0.398292	−	0.917259i	$-0.630397\pi$
$13$	−2.87212	−0.796584	−0.398292	+	0.917259i	$0.630397\pi$
$14$	1.65407	0.442070
$15$	0.928748	0.239802
$16$	1.00000	0.250000
$17$	−0.517323	−0.125469	−0.0627346	−	0.998030i	$-0.519982\pi$
$17$	−0.517323	−0.125469	−0.0627346	+	0.998030i	$0.519982\pi$
$18$	2.14628	0.505884
$19$	−2.41623	−0.554320	−0.277160	−	0.960824i	$-0.589393\pi$
$19$	−2.41623	−0.554320	−0.277160	+	0.960824i	$0.589393\pi$
$20$	−1.00517	−0.224764
$21$	1.52831	0.333505
$22$	3.52761	0.752089
$23$	−7.18630	−1.49845	−0.749223	−	0.662317i	$-0.769573\pi$
$23$	−7.18630	−1.49845	−0.749223	+	0.662317i	$0.769573\pi$
$24$	0.923967	0.188604
$25$	−3.98962	−0.797925
$26$	2.87212	0.563270
$27$	4.75500	0.915100
$28$	−1.65407	−0.312591
$29$	2.16111	0.401308	0.200654	−	0.979662i	$-0.435693\pi$
$29$	2.16111	0.401308	0.200654	+	0.979662i	$0.435693\pi$
$30$	−0.928748	−0.169565
$31$	−6.60016	−1.18542	−0.592712	−	0.805414i	$-0.701943\pi$
$31$	−6.60016	−1.18542	−0.592712	+	0.805414i	$0.701943\pi$
$32$	−1.00000	−0.176777
$33$	3.25940	0.567388
$34$	0.517323	0.0887202
$35$	1.66263	0.281036
$36$	−2.14628	−0.357714
$37$	−9.53137	−1.56695	−0.783474	−	0.621425i	$-0.786554\pi$
$37$	−9.53137	−1.56695	−0.783474	+	0.621425i	$0.786554\pi$
$38$	2.41623	0.391964
$39$	2.65375	0.424940
$40$	1.00517	0.158932
$41$	−4.03502	−0.630164	−0.315082	−	0.949064i	$-0.602032\pi$
$41$	−4.03502	−0.630164	−0.315082	+	0.949064i	$0.602032\pi$
$42$	−1.52831	−0.235823
$43$	9.99403	1.52407	0.762037	−	0.647533i	$-0.224199\pi$
$43$	9.99403	1.52407	0.762037	+	0.647533i	$0.224199\pi$
$44$	−3.52761	−0.531807
$45$	2.15739	0.321605
$46$	7.18630	1.05956
$47$	1.45942	0.212878	0.106439	−	0.994319i	$-0.466055\pi$
$47$	1.45942	0.212878	0.106439	+	0.994319i	$0.466055\pi$
$48$	−0.923967	−0.133363
$49$	−4.26404	−0.609148
$50$	3.98962	0.564218
$51$	0.477989	0.0669319
$52$	−2.87212	−0.398292
$53$	−7.71322	−1.05949	−0.529746	−	0.848156i	$-0.677713\pi$
$53$	−7.71322	−1.05949	−0.529746	+	0.848156i	$0.677713\pi$
$54$	−4.75500	−0.647073
$55$	3.54586	0.478124
$56$	1.65407	0.221035
$57$	2.23251	0.295704
$58$	−2.16111	−0.283767
$59$	−6.62583	−0.862610	−0.431305	−	0.902206i	$-0.641947\pi$
$59$	−6.62583	−0.862610	−0.431305	+	0.902206i	$0.641947\pi$
$60$	0.928748	0.119901
$61$	5.00701	0.641081	0.320541	−	0.947235i	$-0.396135\pi$
$61$	5.00701	0.641081	0.320541	+	0.947235i	$0.396135\pi$
$62$	6.60016	0.838221
$63$	3.55011	0.447272
$64$	1.00000	0.125000
$65$	2.88699	0.358087
$66$	−3.25940	−0.401204
$67$	−8.51763	−1.04059	−0.520297	−	0.853985i	$-0.674179\pi$
$67$	−8.51763	−1.04059	−0.520297	+	0.853985i	$0.674179\pi$
$68$	−0.517323	−0.0627346
$69$	6.63990	0.799350
$70$	−1.66263	−0.198723
$71$	3.57486	0.424258	0.212129	−	0.977242i	$-0.431960\pi$
$71$	3.57486	0.424258	0.212129	+	0.977242i	$0.431960\pi$
$72$	2.14628	0.252942
$73$	0.496885	0.0581560	0.0290780	−	0.999577i	$-0.490743\pi$
$73$	0.496885	0.0581560	0.0290780	+	0.999577i	$0.490743\pi$
$74$	9.53137	1.10800
$75$	3.68628	0.425655
$76$	−2.41623	−0.277160
$77$	5.83493	0.664952
$78$	−2.65375	−0.300478
$79$	−3.81649	−0.429389	−0.214695	−	0.976681i	$-0.568876\pi$
$79$	−3.81649	−0.429389	−0.214695	+	0.976681i	$0.568876\pi$
$80$	−1.00517	−0.112382
$81$	2.04539	0.227266
$82$	4.03502	0.445593
$83$	−4.39546	−0.482465	−0.241232	−	0.970467i	$-0.577552\pi$
$83$	−4.39546	−0.482465	−0.241232	+	0.970467i	$0.577552\pi$
$84$	1.52831	0.166752
$85$	0.520000	0.0564019
$86$	−9.99403	−1.07768
$87$	−1.99679	−0.214079
$88$	3.52761	0.376044
$89$	−7.28465	−0.772172	−0.386086	−	0.922463i	$-0.626173\pi$
$89$	−7.28465	−0.772172	−0.386086	+	0.922463i	$0.626173\pi$
$90$	−2.15739	−0.227409
$91$	4.75071	0.498009
$92$	−7.18630	−0.749223
$93$	6.09833	0.632368
$94$	−1.45942	−0.150528
$95$	2.42873	0.249182
$96$	0.923967	0.0943020
$97$	13.4040	1.36097	0.680486	−	0.732761i	$-0.261769\pi$
$97$	13.4040	1.36097	0.680486	+	0.732761i	$0.261769\pi$
$98$	4.26404	0.430733
$99$	7.57126	0.760940
$100$	−3.98962	−0.398962
$101$	−9.55036	−0.950296	−0.475148	−	0.879906i	$-0.657605\pi$
$101$	−9.55036	−0.950296	−0.475148	+	0.879906i	$0.657605\pi$
$102$	−0.477989	−0.0473280
$103$	−2.58126	−0.254339	−0.127170	−	0.991881i	$-0.540589\pi$
$103$	−2.58126	−0.254339	−0.127170	+	0.991881i	$0.540589\pi$
$104$	2.87212	0.281635
$105$	−1.53622	−0.149920
$106$	7.71322	0.749174
$107$	−5.71252	−0.552250	−0.276125	−	0.961122i	$-0.589050\pi$
$107$	−5.71252	−0.552250	−0.276125	+	0.961122i	$0.589050\pi$
$108$	4.75500	0.457550
$109$	13.7721	1.31913	0.659564	−	0.751648i	$-0.270741\pi$
$109$	13.7721	1.31913	0.659564	+	0.751648i	$0.270741\pi$
$110$	−3.54586	−0.338085
$111$	8.80667	0.835892
$112$	−1.65407	−0.156295
$113$	14.1521	1.33132	0.665661	−	0.746254i	$-0.268150\pi$
$113$	14.1521	1.33132	0.665661	+	0.746254i	$0.268150\pi$
$114$	−2.23251	−0.209094
$115$	7.22348	0.673593
$116$	2.16111	0.200654
$117$	6.16440	0.569899
$118$	6.62583	0.609957
$119$	0.855691	0.0784410
$120$	−0.928748	−0.0847827
$121$	1.44403	0.131276
$122$	−5.00701	−0.453313
$123$	3.72822	0.336163
$124$	−6.60016	−0.592712
$125$	9.03614	0.808217
$126$	−3.55011	−0.316269
$127$	−4.90932	−0.435632	−0.217816	−	0.975990i	$-0.569893\pi$
$127$	−4.90932	−0.435632	−0.217816	+	0.975990i	$0.569893\pi$
$128$	−1.00000	−0.0883883
$129$	−9.23415	−0.813022
$130$	−2.88699	−0.253205
$131$	−14.4202	−1.25990	−0.629948	−	0.776638i	$-0.716924\pi$
$131$	−14.4202	−1.25990	−0.629948	+	0.776638i	$0.716924\pi$
$132$	3.25940	0.283694
$133$	3.99662	0.346551
$134$	8.51763	0.735811
$135$	−4.77960	−0.411363
$136$	0.517323	0.0443601
$137$	0.127294	0.0108755	0.00543775	−	0.999985i	$-0.498269\pi$
$137$	0.127294	0.0108755	0.00543775	+	0.999985i	$0.498269\pi$
$138$	−6.63990	−0.565226
$139$	−11.8791	−1.00757	−0.503786	−	0.863828i	$-0.668060\pi$
$139$	−11.8791	−1.00757	−0.503786	+	0.863828i	$0.668060\pi$
$140$	1.66263	0.140518
$141$	−1.34846	−0.113560
$142$	−3.57486	−0.299996
$143$	10.1317	0.847258
$144$	−2.14628	−0.178857
$145$	−2.17229	−0.180399
$146$	−0.496885	−0.0411225
$147$	3.93983	0.324952
$148$	−9.53137	−0.783474
$149$	−9.77830	−0.801069	−0.400535	−	0.916282i	$-0.631176\pi$
$149$	−9.77830	−0.801069	−0.400535	+	0.916282i	$0.631176\pi$
$150$	−3.68628	−0.300984
$151$	18.4424	1.50082	0.750412	−	0.660971i	$-0.229855\pi$
$151$	18.4424	1.50082	0.750412	+	0.660971i	$0.229855\pi$
$152$	2.41623	0.195982
$153$	1.11032	0.0897642
$154$	−5.83493	−0.470192
$155$	6.63432	0.532881
$156$	2.65375	0.212470
$157$	13.8974	1.10913	0.554567	−	0.832139i	$-0.312884\pi$
$157$	13.8974	1.10913	0.554567	+	0.832139i	$0.312884\pi$
$158$	3.81649	0.303624
$159$	7.12676	0.565189
$160$	1.00517	0.0794660
$161$	11.8867	0.936801
$162$	−2.04539	−0.160701
$163$	−13.3523	−1.04584	−0.522918	−	0.852383i	$-0.675157\pi$
$163$	−13.3523	−1.04584	−0.522918	+	0.852383i	$0.675157\pi$
$164$	−4.03502	−0.315082
$165$	−3.27626	−0.255057
$166$	4.39546	0.341154
$167$	3.94784	0.305493	0.152746	−	0.988265i	$-0.451188\pi$
$167$	3.94784	0.305493	0.152746	+	0.988265i	$0.451188\pi$
$168$	−1.52831	−0.117912
$169$	−4.75090	−0.365454
$170$	−0.520000	−0.0398822
$171$	5.18591	0.396576
$172$	9.99403	0.762037
$173$	−11.9451	−0.908171	−0.454086	−	0.890958i	$-0.650034\pi$
$173$	−11.9451	−0.908171	−0.454086	+	0.890958i	$0.650034\pi$
$174$	1.99679	0.151376
$175$	6.59913	0.498848
$176$	−3.52761	−0.265904
$177$	6.12205	0.460161
$178$	7.28465	0.546008
$179$	−4.12510	−0.308324	−0.154162	−	0.988046i	$-0.549268\pi$
$179$	−4.12510	−0.308324	−0.154162	+	0.988046i	$0.549268\pi$
$180$	2.15739	0.160802
$181$	−6.00802	−0.446572	−0.223286	−	0.974753i	$-0.571678\pi$
$181$	−6.00802	−0.446572	−0.223286	+	0.974753i	$0.571678\pi$
$182$	−4.75071	−0.352146
$183$	−4.62631	−0.341987
$184$	7.18630	0.529781
$185$	9.58069	0.704386
$186$	−6.09833	−0.447152
$187$	1.82491	0.133451
$188$	1.45942	0.106439
$189$	−7.86512	−0.572103
$190$	−2.42873	−0.176199
$191$	−17.0985	−1.23720	−0.618601	−	0.785705i	$-0.712300\pi$
$191$	−17.0985	−1.23720	−0.618601	+	0.785705i	$0.712300\pi$
$192$	−0.923967	−0.0666816
$193$	24.6338	1.77318	0.886590	−	0.462555i	$-0.153067\pi$
$193$	24.6338	1.77318	0.886590	+	0.462555i	$0.153067\pi$
$194$	−13.4040	−0.962352
$195$	−2.66748	−0.191022
$196$	−4.26404	−0.304574
$197$	−5.91303	−0.421286	−0.210643	−	0.977563i	$-0.567556\pi$
$197$	−5.91303	−0.421286	−0.210643	+	0.977563i	$0.567556\pi$
$198$	−7.57126	−0.538066
$199$	13.0563	0.925533	0.462767	−	0.886480i	$-0.346857\pi$
$199$	13.0563	0.925533	0.462767	+	0.886480i	$0.346857\pi$
$200$	3.98962	0.282109
$201$	7.87001	0.555108
$202$	9.55036	0.671961
$203$	−3.57463	−0.250890
$204$	0.477989	0.0334660
$205$	4.05590	0.283276
$206$	2.58126	0.179845
$207$	15.4238	1.07203
$208$	−2.87212	−0.199146
$209$	8.52350	0.589583
$210$	1.53622	0.106009
$211$	−23.0294	−1.58541	−0.792706	−	0.609604i	$-0.791329\pi$
$211$	−23.0294	−1.58541	−0.792706	+	0.609604i	$0.791329\pi$
$212$	−7.71322	−0.529746
$213$	−3.30305	−0.226321
$214$	5.71252	0.390500
$215$	−10.0457	−0.685114
$216$	−4.75500	−0.323537
$217$	10.9172	0.741105
$218$	−13.7721	−0.932765
$219$	−0.459105	−0.0310235
$220$	3.54586	0.239062
$221$	1.48582	0.0999468
$222$	−8.80667	−0.591065
$223$	−26.6644	−1.78558	−0.892789	−	0.450475i	$-0.851255\pi$
$223$	−26.6644	−1.78558	−0.892789	+	0.450475i	$0.851255\pi$
$224$	1.65407	0.110517
$225$	8.56287	0.570858
$226$	−14.1521	−0.941387
$227$	−29.7998	−1.97788	−0.988941	−	0.148312i	$-0.952616\pi$
$227$	−29.7998	−1.97788	−0.988941	+	0.148312i	$0.952616\pi$
$228$	2.23251	0.147852
$229$	24.7680	1.63672	0.818359	−	0.574707i	$-0.194884\pi$
$229$	24.7680	1.63672	0.818359	+	0.574707i	$0.194884\pi$
$230$	−7.22348	−0.476302
$231$	−5.39128	−0.354720
$232$	−2.16111	−0.141884
$233$	20.9193	1.37047	0.685233	−	0.728324i	$-0.259700\pi$
$233$	20.9193	1.37047	0.685233	+	0.728324i	$0.259700\pi$
$234$	−6.16440	−0.402979
$235$	−1.46697	−0.0956946
$236$	−6.62583	−0.431305
$237$	3.52631	0.229059
$238$	−0.855691	−0.0554662
$239$	0.393501	0.0254535	0.0127267	−	0.999919i	$-0.495949\pi$
$239$	0.393501	0.0254535	0.0127267	+	0.999919i	$0.495949\pi$
$240$	0.928748	0.0599504
$241$	−12.6770	−0.816600	−0.408300	−	0.912848i	$-0.633878\pi$
$241$	−12.6770	−0.816600	−0.408300	+	0.912848i	$0.633878\pi$
$242$	−1.44403	−0.0928259
$243$	−16.1549	−1.03634
$244$	5.00701	0.320541
$245$	4.28610	0.273829
$246$	−3.72822	−0.237703
$247$	6.93970	0.441563
$248$	6.60016	0.419111
$249$	4.06126	0.257372
$250$	−9.03614	−0.571496
$251$	23.0290	1.45358	0.726788	−	0.686861i	$-0.241012\pi$
$251$	23.0290	1.45358	0.726788	+	0.686861i	$0.241012\pi$
$252$	3.55011	0.223636
$253$	25.3505	1.59377
$254$	4.90932	0.308038
$255$	−0.480463	−0.0300877
$256$	1.00000	0.0625000
$257$	−20.6440	−1.28774	−0.643869	−	0.765136i	$-0.722672\pi$
$257$	−20.6440	−1.28774	−0.643869	+	0.765136i	$0.722672\pi$
$258$	9.23415	0.574893
$259$	15.7656	0.979626
$260$	2.88699	0.179043
$261$	−4.63835	−0.287107
$262$	14.4202	0.890880
$263$	2.38483	0.147055	0.0735274	−	0.997293i	$-0.476574\pi$
$263$	2.38483	0.147055	0.0735274	+	0.997293i	$0.476574\pi$
$264$	−3.25940	−0.200602
$265$	7.75313	0.476271
$266$	−3.99662	−0.245048
$267$	6.73078	0.411917
$268$	−8.51763	−0.520297
$269$	−17.8347	−1.08740	−0.543699	−	0.839280i	$-0.682977\pi$
$269$	−17.8347	−1.08740	−0.543699	+	0.839280i	$0.682977\pi$
$270$	4.77960	0.290877
$271$	28.5170	1.73228	0.866142	−	0.499797i	$-0.166592\pi$
$271$	28.5170	1.73228	0.866142	+	0.499797i	$0.166592\pi$
$272$	−0.517323	−0.0313673
$273$	−4.38950	−0.265664
$274$	−0.127294	−0.00769014
$275$	14.0738	0.848684
$276$	6.63990	0.399675
$277$	30.1530	1.81172	0.905859	−	0.423580i	$-0.139227\pi$
$277$	30.1530	1.81172	0.905859	+	0.423580i	$0.139227\pi$
$278$	11.8791	0.712462
$279$	14.1658	0.848086
$280$	−1.66263	−0.0993613
$281$	−18.8290	−1.12324	−0.561621	−	0.827394i	$-0.689822\pi$
$281$	−18.8290	−1.12324	−0.561621	+	0.827394i	$0.689822\pi$
$282$	1.34846	0.0802993
$283$	11.3981	0.677547	0.338774	−	0.940868i	$-0.389988\pi$
$283$	11.3981	0.677547	0.338774	+	0.940868i	$0.389988\pi$
$284$	3.57486	0.212129
$285$	−2.24407	−0.132927
$286$	−10.1317	−0.599102
$287$	6.67422	0.393967
$288$	2.14628	0.126471
$289$	−16.7324	−0.984257
$290$	2.17229	0.127561
$291$	−12.3849	−0.726014
$292$	0.496885	0.0290780
$293$	19.9362	1.16469	0.582343	−	0.812943i	$-0.302136\pi$
$293$	19.9362	1.16469	0.582343	+	0.812943i	$0.302136\pi$
$294$	−3.93983	−0.229776
$295$	6.66012	0.387767
$296$	9.53137	0.554000
$297$	−16.7738	−0.973313
$298$	9.77830	0.566442
$299$	20.6399	1.19364
$300$	3.68628	0.212828
$301$	−16.5309	−0.952823
$302$	−18.4424	−1.06124
$303$	8.82422	0.506938
$304$	−2.41623	−0.138580
$305$	−5.03291	−0.288184
$306$	−1.11032	−0.0634729
$307$	17.7512	1.01312	0.506559	−	0.862205i	$-0.330917\pi$
$307$	17.7512	1.01312	0.506559	+	0.862205i	$0.330917\pi$
$308$	5.83493	0.332476
$309$	2.38500	0.135678
$310$	−6.63432	−0.376804
$311$	−6.38318	−0.361957	−0.180978	−	0.983487i	$-0.557926\pi$
$311$	−6.38318	−0.361957	−0.180978	+	0.983487i	$0.557926\pi$
$312$	−2.65375	−0.150239
$313$	−3.71631	−0.210058	−0.105029	−	0.994469i	$-0.533494\pi$
$313$	−3.71631	−0.210058	−0.105029	+	0.994469i	$0.533494\pi$
$314$	−13.8974	−0.784276
$315$	−3.56848	−0.201061
$316$	−3.81649	−0.214695
$317$	−26.1045	−1.46617	−0.733087	−	0.680135i	$-0.761921\pi$
$317$	−26.1045	−1.46617	−0.733087	+	0.680135i	$0.761921\pi$
$318$	−7.12676	−0.399649
$319$	−7.62354	−0.426837
$320$	−1.00517	−0.0561910
$321$	5.27818	0.294599
$322$	−11.8867	−0.662418
$323$	1.24997	0.0695502
$324$	2.04539	0.113633
$325$	11.4587	0.635614
$326$	13.3523	0.739518
$327$	−12.7250	−0.703693
$328$	4.03502	0.222797
$329$	−2.41399	−0.133087
$330$	3.27626	0.180352
$331$	19.1745	1.05393	0.526964	−	0.849888i	$-0.323330\pi$
$331$	19.1745	1.05393	0.526964	+	0.849888i	$0.323330\pi$
$332$	−4.39546	−0.241232
$333$	20.4570	1.12104
$334$	−3.94784	−0.216016
$335$	8.56171	0.467776
$336$	1.52831	0.0833761
$337$	−5.44754	−0.296746	−0.148373	−	0.988931i	$-0.547404\pi$
$337$	−5.44754	−0.296746	−0.148373	+	0.988931i	$0.547404\pi$
$338$	4.75090	0.258415
$339$	−13.0761	−0.710197
$340$	0.520000	0.0282010
$341$	23.2828	1.26083
$342$	−5.18591	−0.280422
$343$	18.6316	1.00601
$344$	−9.99403	−0.538842
$345$	−6.67426	−0.359330
$346$	11.9451	0.642174
$347$	16.7544	0.899422	0.449711	−	0.893174i	$-0.351527\pi$
$347$	16.7544	0.899422	0.449711	+	0.893174i	$0.351527\pi$
$348$	−1.99679	−0.107039
$349$	−4.84395	−0.259291	−0.129645	−	0.991560i	$-0.541384\pi$
$349$	−4.84395	−0.259291	−0.129645	+	0.991560i	$0.541384\pi$
$350$	−6.59913	−0.352739
$351$	−13.6569	−0.728954
$352$	3.52761	0.188022
$353$	25.1064	1.33628	0.668138	−	0.744037i	$-0.267091\pi$
$353$	25.1064	1.33628	0.668138	+	0.744037i	$0.267091\pi$
$354$	−6.12205	−0.325383
$355$	−3.59336	−0.190716
$356$	−7.28465	−0.386086
$357$	−0.790630	−0.0418446
$358$	4.12510	0.218018
$359$	21.0674	1.11189	0.555946	−	0.831218i	$-0.312356\pi$
$359$	21.0674	1.11189	0.555946	+	0.831218i	$0.312356\pi$
$360$	−2.15739	−0.113704
$361$	−13.1618	−0.692729
$362$	6.00802	0.315774
$363$	−1.33424	−0.0700293
$364$	4.75071	0.249005
$365$	−0.499456	−0.0261427
$366$	4.62631	0.241821
$367$	−26.6459	−1.39091	−0.695453	−	0.718571i	$-0.744796\pi$
$367$	−26.6459	−1.39091	−0.695453	+	0.718571i	$0.744796\pi$
$368$	−7.18630	−0.374612
$369$	8.66029	0.450837
$370$	−9.58069	−0.498076
$371$	12.7582	0.662374
$372$	6.09833	0.316184
$373$	14.4837	0.749940	0.374970	−	0.927037i	$-0.377653\pi$
$373$	14.4837	0.749940	0.374970	+	0.927037i	$0.377653\pi$
$374$	−1.82491	−0.0943640
$375$	−8.34910	−0.431146
$376$	−1.45942	−0.0752638
$377$	−6.20697	−0.319675
$378$	7.86512	0.404538
$379$	33.3133	1.71119	0.855594	−	0.517647i	$-0.173192\pi$
$379$	33.3133	1.71119	0.855594	+	0.517647i	$0.173192\pi$
$380$	2.42873	0.124591
$381$	4.53605	0.232389
$382$	17.0985	0.874834
$383$	13.7882	0.704545	0.352273	−	0.935897i	$-0.385409\pi$
$383$	13.7882	0.704545	0.352273	+	0.935897i	$0.385409\pi$
$384$	0.923967	0.0471510
$385$	−5.86512	−0.298914
$386$	−24.6338	−1.25383
$387$	−21.4500	−1.09037
$388$	13.4040	0.680486
$389$	−16.8829	−0.855998	−0.427999	−	0.903779i	$-0.640781\pi$
$389$	−16.8829	−0.855998	−0.427999	+	0.903779i	$0.640781\pi$
$390$	2.66748	0.135073
$391$	3.71764	0.188009
$392$	4.26404	0.215367
$393$	13.3238	0.672095
$394$	5.91303	0.297894
$395$	3.83624	0.193022
$396$	7.57126	0.380470
$397$	16.6050	0.833380	0.416690	−	0.909049i	$-0.363190\pi$
$397$	16.6050	0.833380	0.416690	+	0.909049i	$0.363190\pi$
$398$	−13.0563	−0.654451
$399$	−3.69274	−0.184868
$400$	−3.98962	−0.199481
$401$	−2.53388	−0.126536	−0.0632681	−	0.997997i	$-0.520152\pi$
$401$	−2.53388	−0.126536	−0.0632681	+	0.997997i	$0.520152\pi$
$402$	−7.87001	−0.392521
$403$	18.9565	0.944290
$404$	−9.55036	−0.475148
$405$	−2.05598	−0.102162
$406$	3.57463	0.177406
$407$	33.6230	1.66663
$408$	−0.477989	−0.0236640
$409$	−1.41907	−0.0701683	−0.0350842	−	0.999384i	$-0.511170\pi$
$409$	−1.41907	−0.0701683	−0.0350842	+	0.999384i	$0.511170\pi$
$410$	−4.05590	−0.200306
$411$	−0.117616	−0.00580156
$412$	−2.58126	−0.127170
$413$	10.9596	0.539287
$414$	−15.4238	−0.758040
$415$	4.41821	0.216881
$416$	2.87212	0.140818
$417$	10.9759	0.537492
$418$	−8.52350	−0.416898
$419$	−22.2772	−1.08831	−0.544156	−	0.838984i	$-0.683150\pi$
$419$	−22.2772	−1.08831	−0.544156	+	0.838984i	$0.683150\pi$
$420$	−1.53622	−0.0749598
$421$	6.78643	0.330750	0.165375	−	0.986231i	$-0.447117\pi$
$421$	6.78643	0.330750	0.165375	+	0.986231i	$0.447117\pi$
$422$	23.0294	1.12106
$423$	−3.13233	−0.152299
$424$	7.71322	0.374587
$425$	2.06392	0.100115
$426$	3.30305	0.160033
$427$	−8.28196	−0.400792
$428$	−5.71252	−0.276125
$429$	−9.36139	−0.451972
$430$	10.0457	0.484449
$431$	−0.593406	−0.0285834	−0.0142917	−	0.999898i	$-0.504549\pi$
$431$	−0.593406	−0.0285834	−0.0142917	+	0.999898i	$0.504549\pi$
$432$	4.75500	0.228775
$433$	−37.3036	−1.79270	−0.896349	−	0.443350i	$-0.853790\pi$
$433$	−37.3036	−1.79270	−0.896349	+	0.443350i	$0.853790\pi$
$434$	−10.9172	−0.524040
$435$	2.00712	0.0962343
$436$	13.7721	0.659564
$437$	17.3637	0.830620
$438$	0.459105	0.0219369
$439$	−13.8386	−0.660482	−0.330241	−	0.943897i	$-0.607130\pi$
$439$	−13.8386	−0.660482	−0.330241	+	0.943897i	$0.607130\pi$
$440$	−3.54586	−0.169042
$441$	9.15184	0.435802
$442$	−1.48582	−0.0706731
$443$	−7.27798	−0.345787	−0.172894	−	0.984940i	$-0.555312\pi$
$443$	−7.27798	−0.345787	−0.172894	+	0.984940i	$0.555312\pi$
$444$	8.80667	0.417946
$445$	7.32235	0.347113
$446$	26.6644	1.26259
$447$	9.03483	0.427333
$448$	−1.65407	−0.0781477
$449$	29.9023	1.41118	0.705588	−	0.708622i	$-0.250683\pi$
$449$	29.9023	1.41118	0.705588	+	0.708622i	$0.250683\pi$
$450$	−8.56287	−0.403658
$451$	14.2340	0.670251
$452$	14.1521	0.665661
$453$	−17.0402	−0.800618
$454$	29.7998	1.39857
$455$	−4.77529	−0.223869
$456$	−2.23251	−0.104547
$457$	35.4223	1.65699	0.828493	−	0.559999i	$-0.189199\pi$
$457$	35.4223	1.65699	0.828493	+	0.559999i	$0.189199\pi$
$458$	−24.7680	−1.15733
$459$	−2.45987	−0.114817
$460$	7.22348	0.336797
$461$	28.6300	1.33343	0.666716	−	0.745312i	$-0.267699\pi$
$461$	28.6300	1.33343	0.666716	+	0.745312i	$0.267699\pi$
$462$	5.39128	0.250825
$463$	−16.2806	−0.756625	−0.378312	−	0.925678i	$-0.623495\pi$
$463$	−16.2806	−0.756625	−0.378312	+	0.925678i	$0.623495\pi$
$464$	2.16111	0.100327
$465$	−6.12989	−0.284267
$466$	−20.9193	−0.969066
$467$	−4.65858	−0.215574	−0.107787	−	0.994174i	$-0.534376\pi$
$467$	−4.65858	−0.215574	−0.107787	+	0.994174i	$0.534376\pi$
$468$	6.16440	0.284949
$469$	14.0888	0.650560
$470$	1.46697	0.0676663
$471$	−12.8407	−0.591670
$472$	6.62583	0.304979
$473$	−35.2550	−1.62103
$474$	−3.52631	−0.161969
$475$	9.63984	0.442306
$476$	0.855691	0.0392205
$477$	16.5548	0.757990
$478$	−0.393501	−0.0179983
$479$	−26.0512	−1.19031	−0.595155	−	0.803611i	$-0.702909\pi$
$479$	−26.0512	−1.19031	−0.595155	+	0.803611i	$0.702909\pi$
$480$	−0.928748	−0.0423914
$481$	27.3753	1.24821
$482$	12.6770	0.577424
$483$	−10.9829	−0.499739
$484$	1.44403	0.0656378
$485$	−13.4734	−0.611794
$486$	16.1549	0.732800
$487$	−17.0772	−0.773843	−0.386922	−	0.922113i	$-0.626462\pi$
$487$	−17.0772	−0.773843	−0.386922	+	0.922113i	$0.626462\pi$
$488$	−5.00701	−0.226657
$489$	12.3371	0.557904
$490$	−4.28610	−0.193626
$491$	−8.32570	−0.375734	−0.187867	−	0.982195i	$-0.560157\pi$
$491$	−8.32570	−0.375734	−0.187867	+	0.982195i	$0.560157\pi$
$492$	3.72822	0.168081
$493$	−1.11799	−0.0503518
$494$	−6.93970	−0.312232
$495$	−7.61043	−0.342064
$496$	−6.60016	−0.296356
$497$	−5.91308	−0.265238
$498$	−4.06126	−0.181990
$499$	−27.4836	−1.23033	−0.615167	−	0.788397i	$-0.710911\pi$
$499$	−27.4836	−1.23033	−0.615167	+	0.788397i	$0.710911\pi$
$500$	9.03614	0.404109
$501$	−3.64767	−0.162966
$502$	−23.0290	−1.02783
$503$	15.1109	0.673760	0.336880	−	0.941548i	$-0.390628\pi$
$503$	15.1109	0.673760	0.336880	+	0.941548i	$0.390628\pi$
$504$	−3.55011	−0.158135
$505$	9.59978	0.427184
$506$	−25.3505	−1.12697
$507$	4.38968	0.194952
$508$	−4.90932	−0.217816
$509$	−12.8831	−0.571033	−0.285516	−	0.958374i	$-0.592165\pi$
$509$	−12.8831	−0.571033	−0.285516	+	0.958374i	$0.592165\pi$
$510$	0.480463	0.0212753
$511$	−0.821884	−0.0363580
$512$	−1.00000	−0.0441942
$513$	−11.4892	−0.507258
$514$	20.6440	0.910568
$515$	2.59462	0.114332
$516$	−9.23415	−0.406511
$517$	−5.14826	−0.226420
$518$	−15.7656	−0.692700
$519$	11.0369	0.484466
$520$	−2.88699	−0.126603
$521$	−35.4869	−1.55471	−0.777354	−	0.629064i	$-0.783439\pi$
$521$	−35.4869	−1.55471	−0.777354	+	0.629064i	$0.783439\pi$
$522$	4.63835	0.203015
$523$	27.9105	1.22044	0.610222	−	0.792231i	$-0.291080\pi$
$523$	27.9105	1.22044	0.610222	+	0.792231i	$0.291080\pi$
$524$	−14.4202	−0.629948
$525$	−6.09738	−0.266112
$526$	−2.38483	−0.103983
$527$	3.41442	0.148734
$528$	3.25940	0.141847
$529$	28.6429	1.24534
$530$	−7.75313	−0.336774
$531$	14.2209	0.617135
$532$	3.99662	0.173275
$533$	11.5891	0.501978
$534$	−6.73078	−0.291269
$535$	5.74208	0.248252
$536$	8.51763	0.367906
$537$	3.81145	0.164476
$538$	17.8347	0.768907
$539$	15.0419	0.647899
$540$	−4.77960	−0.205681
$541$	8.27413	0.355733	0.177866	−	0.984055i	$-0.443081\pi$
$541$	8.27413	0.355733	0.177866	+	0.984055i	$0.443081\pi$
$542$	−28.5170	−1.22491
$543$	5.55121	0.238225
$544$	0.517323	0.0221800
$545$	−13.8434	−0.592985
$546$	4.38950	0.187853
$547$	6.31869	0.270168	0.135084	−	0.990834i	$-0.456870\pi$
$547$	6.31869	0.270168	0.135084	+	0.990834i	$0.456870\pi$
$548$	0.127294	0.00543775
$549$	−10.7465	−0.458648
$550$	−14.0738	−0.600110
$551$	−5.22173	−0.222453
$552$	−6.63990	−0.282613
$553$	6.31276	0.268446
$554$	−30.1530	−1.28108
$555$	−8.85224	−0.375757
$556$	−11.8791	−0.503786
$557$	−28.8492	−1.22238	−0.611191	−	0.791483i	$-0.709309\pi$
$557$	−28.8492	−1.22238	−0.611191	+	0.791483i	$0.709309\pi$
$558$	−14.1658	−0.599687
$559$	−28.7041	−1.21405
$560$	1.66263	0.0702591
$561$	−1.68616	−0.0711897
$562$	18.8290	0.794253
$563$	−25.6287	−1.08012	−0.540061	−	0.841626i	$-0.681599\pi$
$563$	−25.6287	−1.08012	−0.540061	+	0.841626i	$0.681599\pi$
$564$	−1.34846	−0.0567802
$565$	−14.2254	−0.598466
$566$	−11.3981	−0.479098
$567$	−3.38323	−0.142082
$568$	−3.57486	−0.149998
$569$	−11.2477	−0.471528	−0.235764	−	0.971810i	$-0.575759\pi$
$569$	−11.2477	−0.471528	−0.235764	+	0.971810i	$0.575759\pi$
$570$	2.24407	0.0939936
$571$	−20.5814	−0.861304	−0.430652	−	0.902518i	$-0.641716\pi$
$571$	−20.5814	−0.861304	−0.430652	+	0.902518i	$0.641716\pi$
$572$	10.1317	0.423629
$573$	15.7984	0.659989
$574$	−6.67422	−0.278576
$575$	28.6706	1.19565
$576$	−2.14628	−0.0894285
$577$	−7.02224	−0.292340	−0.146170	−	0.989260i	$-0.546695\pi$
$577$	−7.02224	−0.292340	−0.146170	+	0.989260i	$0.546695\pi$
$578$	16.7324	0.695975
$579$	−22.7608	−0.945908
$580$	−2.17229	−0.0901994
$581$	7.27042	0.301628
$582$	12.3849	0.513369
$583$	27.2092	1.12689
$584$	−0.496885	−0.0205612
$585$	−6.19629	−0.256185
$586$	−19.9362	−0.823558
$587$	45.9576	1.89687	0.948437	−	0.316966i	$-0.102664\pi$
$587$	45.9576	1.89687	0.948437	+	0.316966i	$0.102664\pi$
$588$	3.93983	0.162476
$589$	15.9475	0.657105
$590$	−6.66012	−0.274193
$591$	5.46344	0.224736
$592$	−9.53137	−0.391737
$593$	−26.6779	−1.09553	−0.547766	−	0.836632i	$-0.684522\pi$
$593$	−26.6779	−1.09553	−0.547766	+	0.836632i	$0.684522\pi$
$594$	16.7738	0.688236
$595$	−0.860118	−0.0352614
$596$	−9.77830	−0.400535
$597$	−12.0635	−0.493728
$598$	−20.6399	−0.844030
$599$	−32.3022	−1.31983	−0.659916	−	0.751339i	$-0.729408\pi$
$599$	−32.3022	−1.31983	−0.659916	+	0.751339i	$0.729408\pi$
$600$	−3.68628	−0.150492
$601$	−4.21818	−0.172063	−0.0860315	−	0.996292i	$-0.527419\pi$
$601$	−4.21818	−0.172063	−0.0860315	+	0.996292i	$0.527419\pi$
$602$	16.5309	0.673747
$603$	18.2813	0.744471
$604$	18.4424	0.750412
$605$	−1.45150	−0.0590120
$606$	−8.82422	−0.358459
$607$	10.1724	0.412885	0.206443	−	0.978459i	$-0.433811\pi$
$607$	10.1724	0.412885	0.206443	+	0.978459i	$0.433811\pi$
$608$	2.41623	0.0979909
$609$	3.30284	0.133838
$610$	5.03291	0.203777
$611$	−4.19163	−0.169575
$612$	1.11032	0.0448821
$613$	−22.9278	−0.926044	−0.463022	−	0.886347i	$-0.653235\pi$
$613$	−22.9278	−0.926044	−0.463022	+	0.886347i	$0.653235\pi$
$614$	−17.7512	−0.716382
$615$	−3.74751	−0.151114
$616$	−5.83493	−0.235096
$617$	−6.80866	−0.274106	−0.137053	−	0.990564i	$-0.543763\pi$
$617$	−6.80866	−0.274106	−0.137053	+	0.990564i	$0.543763\pi$
$618$	−2.38500	−0.0959388
$619$	−29.3146	−1.17825	−0.589127	−	0.808041i	$-0.700528\pi$
$619$	−29.3146	−1.17825	−0.589127	+	0.808041i	$0.700528\pi$
$620$	6.63432	0.266441
$621$	−34.1708	−1.37123
$622$	6.38318	0.255942
$623$	12.0494	0.482747
$624$	2.65375	0.106235
$625$	10.8652	0.434609
$626$	3.71631	0.148533
$627$	−7.87544	−0.314515
$628$	13.8974	0.554567
$629$	4.93080	0.196604
$630$	3.56848	0.142172
$631$	−45.5444	−1.81310	−0.906548	−	0.422103i	$-0.861292\pi$
$631$	−45.5444	−1.81310	−0.906548	+	0.422103i	$0.861292\pi$
$632$	3.81649	0.151812
$633$	21.2785	0.845743
$634$	26.1045	1.03674
$635$	4.93472	0.195828
$636$	7.12676	0.282594
$637$	12.2469	0.485238
$638$	7.62354	0.301819
$639$	−7.67267	−0.303526
$640$	1.00517	0.0397330
$641$	45.3541	1.79138	0.895690	−	0.444679i	$-0.146682\pi$
$641$	45.3541	1.79138	0.895690	+	0.444679i	$0.146682\pi$
$642$	−5.27818	−0.208313
$643$	43.8128	1.72781	0.863903	−	0.503658i	$-0.168013\pi$
$643$	43.8128	1.72781	0.863903	+	0.503658i	$0.168013\pi$
$644$	11.8867	0.468400
$645$	9.28193	0.365476
$646$	−1.24997	−0.0491794
$647$	−45.0833	−1.77241	−0.886203	−	0.463298i	$-0.846666\pi$
$647$	−45.0833	−1.77241	−0.886203	+	0.463298i	$0.846666\pi$
$648$	−2.04539	−0.0803506
$649$	23.3733	0.917484
$650$	−11.4587	−0.449447
$651$	−10.0871	−0.395344
$652$	−13.3523	−0.522918
$653$	−17.3376	−0.678471	−0.339236	−	0.940701i	$-0.610168\pi$
$653$	−17.3376	−0.678471	−0.339236	+	0.940701i	$0.610168\pi$
$654$	12.7250	0.497586
$655$	14.4948	0.566358
$656$	−4.03502	−0.157541
$657$	−1.06646	−0.0416064
$658$	2.41399	0.0941070
$659$	−14.5739	−0.567720	−0.283860	−	0.958866i	$-0.591615\pi$
$659$	−14.5739	−0.567720	−0.283860	+	0.958866i	$0.591615\pi$
$660$	−3.27626	−0.127528
$661$	−6.45400	−0.251031	−0.125516	−	0.992092i	$-0.540059\pi$
$661$	−6.45400	−0.251031	−0.125516	+	0.992092i	$0.540059\pi$
$662$	−19.1745	−0.745240
$663$	−1.37285	−0.0533169
$664$	4.39546	0.170577
$665$	−4.01730	−0.155784
$666$	−20.4570	−0.792694
$667$	−15.5304	−0.601338
$668$	3.94784	0.152746
$669$	24.6370	0.952521
$670$	−8.56171	−0.330768
$671$	−17.6628	−0.681863
$672$	−1.52831	−0.0589558
$673$	24.0171	0.925790	0.462895	−	0.886413i	$-0.346811\pi$
$673$	24.0171	0.925790	0.462895	+	0.886413i	$0.346811\pi$
$674$	5.44754	0.209831
$675$	−18.9707	−0.730181
$676$	−4.75090	−0.182727
$677$	27.5883	1.06031	0.530153	−	0.847902i	$-0.322135\pi$
$677$	27.5883	1.06031	0.530153	+	0.847902i	$0.322135\pi$
$678$	13.0761	0.502185
$679$	−22.1712	−0.850854
$680$	−0.520000	−0.0199411
$681$	27.5340	1.05511
$682$	−23.2828	−0.891544
$683$	−22.7510	−0.870544	−0.435272	−	0.900299i	$-0.643348\pi$
$683$	−22.7510	−0.870544	−0.435272	+	0.900299i	$0.643348\pi$
$684$	5.18591	0.198288
$685$	−0.127953	−0.00488884
$686$	−18.6316	−0.711356
$687$	−22.8849	−0.873112
$688$	9.99403	0.381019
$689$	22.1533	0.843974
$690$	6.67426	0.254085
$691$	−45.1310	−1.71686	−0.858432	−	0.512927i	$-0.828561\pi$
$691$	−45.1310	−1.71686	−0.858432	+	0.512927i	$0.828561\pi$
$692$	−11.9451	−0.454086
$693$	−12.5234	−0.475725
$694$	−16.7544	−0.635988
$695$	11.9406	0.452932
$696$	1.99679	0.0756882
$697$	2.08741	0.0790662
$698$	4.84395	0.183346
$699$	−19.3287	−0.731079
$700$	6.59913	0.249424
$701$	13.1732	0.497543	0.248772	−	0.968562i	$-0.419973\pi$
$701$	13.1732	0.497543	0.248772	+	0.968562i	$0.419973\pi$
$702$	13.6569	0.515448
$703$	23.0300	0.868591
$704$	−3.52761	−0.132952
$705$	1.35543	0.0510485
$706$	−25.1064	−0.944890
$707$	15.7970	0.594107
$708$	6.12205	0.230081
$709$	29.2089	1.09696	0.548481	−	0.836163i	$-0.315206\pi$
$709$	29.2089	1.09696	0.548481	+	0.836163i	$0.315206\pi$
$710$	3.59336	0.134856
$711$	8.19128	0.307197
$712$	7.28465	0.273004
$713$	47.4307	1.77629
$714$	0.790630	0.0295886
$715$	−10.1842	−0.380866
$716$	−4.12510	−0.154162
$717$	−0.363582	−0.0135782
$718$	−21.0674	−0.786227
$719$	−42.9934	−1.60338	−0.801692	−	0.597738i	$-0.796066\pi$
$719$	−42.9934	−1.60338	−0.801692	+	0.597738i	$0.796066\pi$
$720$	2.15739	0.0804012
$721$	4.26960	0.159008
$722$	13.1618	0.489833
$723$	11.7132	0.435618
$724$	−6.00802	−0.223286
$725$	−8.62201	−0.320213
$726$	1.33424	0.0495182
$727$	−11.0918	−0.411371	−0.205686	−	0.978618i	$-0.565942\pi$
$727$	−11.0918	−0.411371	−0.205686	+	0.978618i	$0.565942\pi$
$728$	−4.75071	−0.176073
$729$	8.79039	0.325570
$730$	0.499456	0.0184857
$731$	−5.17014	−0.191225
$732$	−4.62631	−0.170993
$733$	8.23215	0.304061	0.152031	−	0.988376i	$-0.451419\pi$
$733$	8.23215	0.304061	0.152031	+	0.988376i	$0.451419\pi$
$734$	26.6459	0.983519
$735$	−3.96022	−0.146075
$736$	7.18630	0.264890
$737$	30.0469	1.10679
$738$	−8.66029	−0.318790
$739$	−4.30793	−0.158470	−0.0792350	−	0.996856i	$-0.525248\pi$
$739$	−4.30793	−0.158470	−0.0792350	+	0.996856i	$0.525248\pi$
$740$	9.58069	0.352193
$741$	−6.41206	−0.235553
$742$	−12.7582	−0.468369
$743$	−12.0921	−0.443615	−0.221807	−	0.975090i	$-0.571196\pi$
$743$	−12.0921	−0.443615	−0.221807	+	0.975090i	$0.571196\pi$
$744$	−6.09833	−0.223576
$745$	9.82890	0.360103
$746$	−14.4837	−0.530288
$747$	9.43391	0.345169
$748$	1.82491	0.0667255
$749$	9.44892	0.345256
$750$	8.34910	0.304866
$751$	−32.6562	−1.19164	−0.595820	−	0.803118i	$-0.703173\pi$
$751$	−32.6562	−1.19164	−0.595820	+	0.803118i	$0.703173\pi$
$752$	1.45942	0.0532195
$753$	−21.2780	−0.775414
$754$	6.20697	0.226045
$755$	−18.5379	−0.674662
$756$	−7.86512	−0.286052
$757$	1.36889	0.0497532	0.0248766	−	0.999691i	$-0.492081\pi$
$757$	1.36889	0.0497532	0.0248766	+	0.999691i	$0.492081\pi$
$758$	−33.3133	−1.20999
$759$	−23.4230	−0.850201
$760$	−2.42873	−0.0880993
$761$	46.1242	1.67200	0.836000	−	0.548729i	$-0.184888\pi$
$761$	46.1242	1.67200	0.836000	+	0.548729i	$0.184888\pi$
$762$	−4.53605	−0.164324
$763$	−22.7801	−0.824694
$764$	−17.0985	−0.618601
$765$	−1.11607	−0.0403515
$766$	−13.7882	−0.498189
$767$	19.0302	0.687141
$768$	−0.923967	−0.0333408
$769$	−11.1890	−0.403485	−0.201742	−	0.979439i	$-0.564660\pi$
$769$	−11.1890	−0.403485	−0.201742	+	0.979439i	$0.564660\pi$
$770$	5.86512	0.211364
$771$	19.0744	0.686947
$772$	24.6338	0.886590
$773$	8.18173	0.294277	0.147138	−	0.989116i	$-0.452994\pi$
$773$	8.18173	0.294277	0.147138	+	0.989116i	$0.452994\pi$
$774$	21.4500	0.771005
$775$	26.3322	0.945879
$776$	−13.4040	−0.481176
$777$	−14.5669	−0.522584
$778$	16.8829	0.605282
$779$	9.74951	0.349313
$780$	−2.66748	−0.0955111
$781$	−12.6107	−0.451247
$782$	−3.71764	−0.132942
$783$	10.2761	0.367237
$784$	−4.26404	−0.152287
$785$	−13.9693	−0.498586
$786$	−13.3238	−0.475243
$787$	−26.7323	−0.952903	−0.476451	−	0.879201i	$-0.658077\pi$
$787$	−26.7323	−0.952903	−0.476451	+	0.879201i	$0.658077\pi$
$788$	−5.91303	−0.210643
$789$	−2.20350	−0.0784468
$790$	−3.83624	−0.136487
$791$	−23.4087	−0.832317
$792$	−7.57126	−0.269033
$793$	−14.3807	−0.510675
$794$	−16.6050	−0.589289
$795$	−7.16364	−0.254068
$796$	13.0563	0.462767
$797$	41.7020	1.47716	0.738580	−	0.674166i	$-0.235497\pi$
$797$	41.7020	1.47716	0.738580	+	0.674166i	$0.235497\pi$
$798$	3.69274	0.130722
$799$	−0.754991	−0.0267097
$800$	3.98962	0.141055
$801$	15.6349	0.552433
$802$	2.53388	0.0894746
$803$	−1.75282	−0.0618555
$804$	7.87001	0.277554
$805$	−11.9482	−0.421118
$806$	−18.9565	−0.667714
$807$	16.4786	0.580075
$808$	9.55036	0.335980
$809$	−21.7127	−0.763377	−0.381688	−	0.924291i	$-0.624657\pi$
$809$	−21.7127	−0.763377	−0.381688	+	0.924291i	$0.624657\pi$
$810$	2.05598	0.0722396
$811$	−2.39683	−0.0841640	−0.0420820	−	0.999114i	$-0.513399\pi$
$811$	−2.39683	−0.0841640	−0.0420820	+	0.999114i	$0.513399\pi$
$812$	−3.57463	−0.125445
$813$	−26.3488	−0.924092
$814$	−33.6230	−1.17848
$815$	13.4214	0.470132
$816$	0.477989	0.0167330
$817$	−24.1478	−0.844826
$818$	1.41907	0.0496165
$819$	−10.1964	−0.356290
$820$	4.05590	0.141638
$821$	10.6636	0.372163	0.186081	−	0.982534i	$-0.440421\pi$
$821$	10.6636	0.372163	0.186081	+	0.982534i	$0.440421\pi$
$822$	0.117616	0.00410232
$823$	−54.1818	−1.88866	−0.944329	−	0.329003i	$-0.893287\pi$
$823$	−54.1818	−1.88866	−0.944329	+	0.329003i	$0.893287\pi$
$824$	2.58126	0.0899225
$825$	−13.0038	−0.452733
$826$	−10.9596	−0.381334
$827$	−13.8882	−0.482939	−0.241469	−	0.970408i	$-0.577629\pi$
$827$	−13.8882	−0.482939	−0.241469	+	0.970408i	$0.577629\pi$
$828$	15.4238	0.536016
$829$	−15.8787	−0.551491	−0.275746	−	0.961231i	$-0.588925\pi$
$829$	−15.8787	−0.551491	−0.275746	+	0.961231i	$0.588925\pi$
$830$	−4.41821	−0.153358
$831$	−27.8604	−0.966465
$832$	−2.87212	−0.0995730
$833$	2.20589	0.0764294
$834$	−10.9759	−0.380065
$835$	−3.96827	−0.137327
$836$	8.52350	0.294792
$837$	−31.3838	−1.08478
$838$	22.2772	0.769553
$839$	−29.1979	−1.00802	−0.504012	−	0.863697i	$-0.668143\pi$
$839$	−29.1979	−1.00802	−0.504012	+	0.863697i	$0.668143\pi$
$840$	1.53622	0.0530046
$841$	−24.3296	−0.838952
$842$	−6.78643	−0.233876
$843$	17.3974	0.599197
$844$	−23.0294	−0.792706
$845$	4.77548	0.164282
$846$	3.13233	0.107692
$847$	−2.38854	−0.0820711
$848$	−7.71322	−0.264873
$849$	−10.5315	−0.361439
$850$	−2.06392	−0.0707920
$851$	68.4953	2.34799
$852$	−3.30305	−0.113161
$853$	−5.12092	−0.175337	−0.0876684	−	0.996150i	$-0.527942\pi$
$853$	−5.12092	−0.175337	−0.0876684	+	0.996150i	$0.527942\pi$
$854$	8.28196	0.283403
$855$	−5.21274	−0.178272
$856$	5.71252	0.195250
$857$	−22.9054	−0.782432	−0.391216	−	0.920299i	$-0.627945\pi$
$857$	−22.9054	−0.782432	−0.391216	+	0.920299i	$0.627945\pi$
$858$	9.36139	0.319593
$859$	−24.4421	−0.833954	−0.416977	−	0.908917i	$-0.636910\pi$
$859$	−24.4421	−0.833954	−0.416977	+	0.908917i	$0.636910\pi$
$860$	−10.0457	−0.342557
$861$	−6.16676	−0.210162
$862$	0.593406	0.0202115
$863$	−38.9465	−1.32575	−0.662877	−	0.748728i	$-0.730665\pi$
$863$	−38.9465	−1.32575	−0.662877	+	0.748728i	$0.730665\pi$
$864$	−4.75500	−0.161768
$865$	12.0069	0.408248
$866$	37.3036	1.26763
$867$	15.4602	0.525055
$868$	10.9172	0.370552
$869$	13.4631	0.456704
$870$	−2.00712	−0.0680479
$871$	24.4637	0.828921
$872$	−13.7721	−0.466382
$873$	−28.7688	−0.973677
$874$	−17.3637	−0.587337
$875$	−14.9464	−0.505282
$876$	−0.459105	−0.0155117
$877$	22.1060	0.746466	0.373233	−	0.927738i	$-0.378249\pi$
$877$	22.1060	0.746466	0.373233	+	0.927738i	$0.378249\pi$
$878$	13.8386	0.467031
$879$	−18.4204	−0.621305
$880$	3.54586	0.119531
$881$	−24.7628	−0.834280	−0.417140	−	0.908842i	$-0.636968\pi$
$881$	−24.7628	−0.834280	−0.417140	+	0.908842i	$0.636968\pi$
$882$	−9.15184	−0.308159
$883$	52.5950	1.76996	0.884981	−	0.465628i	$-0.154172\pi$
$883$	52.5950	1.76996	0.884981	+	0.465628i	$0.154172\pi$
$884$	1.48582	0.0499734
$885$	−6.15373	−0.206855
$886$	7.27798	0.244509
$887$	−23.2035	−0.779097	−0.389548	−	0.921006i	$-0.627369\pi$
$887$	−23.2035	−0.779097	−0.389548	+	0.921006i	$0.627369\pi$
$888$	−8.80667	−0.295533
$889$	8.12038	0.272349
$890$	−7.32235	−0.245446
$891$	−7.21535	−0.241723
$892$	−26.6644	−0.892789
$893$	−3.52629	−0.118003
$894$	−9.03483	−0.302170
$895$	4.14644	0.138600
$896$	1.65407	0.0552587
$897$	−19.0706	−0.636750
$898$	−29.9023	−0.997852
$899$	−14.2637	−0.475720
$900$	8.56287	0.285429
$901$	3.99022	0.132934
$902$	−14.2340	−0.473939
$903$	15.2740	0.508286
$904$	−14.1521	−0.470693
$905$	6.03911	0.200747
$906$	17.0402	0.566123
$907$	39.2914	1.30465	0.652324	−	0.757940i	$-0.273794\pi$
$907$	39.2914	1.30465	0.652324	+	0.757940i	$0.273794\pi$
$908$	−29.7998	−0.988941
$909$	20.4978	0.679869
$910$	4.77529	0.158299
$911$	25.7116	0.851865	0.425932	−	0.904755i	$-0.359946\pi$
$911$	25.7116	0.851865	0.425932	+	0.904755i	$0.359946\pi$
$912$	2.23251	0.0739259
$913$	15.5055	0.513156
$914$	−35.4223	−1.17167
$915$	4.65025	0.153732
$916$	24.7680	0.818359
$917$	23.8520	0.787663
$918$	2.45987	0.0811878
$919$	−41.8137	−1.37931	−0.689654	−	0.724139i	$-0.742237\pi$
$919$	−41.8137	−1.37931	−0.689654	+	0.724139i	$0.742237\pi$
$920$	−7.22348	−0.238151
$921$	−16.4016	−0.540450
$922$	−28.6300	−0.942879
$923$	−10.2674	−0.337957
$924$	−5.39128	−0.177360
$925$	38.0266	1.25031
$926$	16.2806	0.535014
$927$	5.54012	0.181961
$928$	−2.16111	−0.0709418
$929$	−42.0525	−1.37970	−0.689849	−	0.723953i	$-0.742323\pi$
$929$	−42.0525	−1.37970	−0.689849	+	0.723953i	$0.742323\pi$
$930$	6.12989	0.201007
$931$	10.3029	0.337663
$932$	20.9193	0.685233
$933$	5.89785	0.193087
$934$	4.65858	0.152433
$935$	−1.83436	−0.0599899
$936$	−6.16440	−0.201490
$937$	−28.6455	−0.935807	−0.467904	−	0.883780i	$-0.654991\pi$
$937$	−28.6455	−0.935807	−0.467904	+	0.883780i	$0.654991\pi$
$938$	−14.0888	−0.460015
$939$	3.43374	0.112056
$940$	−1.46697	−0.0478473
$941$	25.2292	0.822449	0.411225	−	0.911534i	$-0.365101\pi$
$941$	25.2292	0.822449	0.411225	+	0.911534i	$0.365101\pi$
$942$	12.8407	0.418374
$943$	28.9968	0.944267
$944$	−6.62583	−0.215652
$945$	7.90582	0.257176
$946$	35.2550	1.14624
$947$	1.69695	0.0551434	0.0275717	−	0.999620i	$-0.491223\pi$
$947$	1.69695	0.0551434	0.0275717	+	0.999620i	$0.491223\pi$
$948$	3.52631	0.114529
$949$	−1.42712	−0.0463261
$950$	−9.63984	−0.312758
$951$	24.1197	0.782134
$952$	−0.855691	−0.0277331
$953$	−54.8886	−1.77802	−0.889008	−	0.457891i	$-0.848605\pi$
$953$	−54.8886	−1.77802	−0.889008	+	0.457891i	$0.848605\pi$
$954$	−16.5548	−0.535980
$955$	17.1869	0.556156
$956$	0.393501	0.0127267
$957$	7.04390	0.227697
$958$	26.0512	0.841676
$959$	−0.210554	−0.00679915
$960$	0.928748	0.0299752
$961$	12.5621	0.405231
$962$	−27.3753	−0.882615
$963$	12.2607	0.395095
$964$	−12.6770	−0.408300
$965$	−24.7613	−0.797094
$966$	10.9829	0.353369
$967$	−4.01187	−0.129013	−0.0645065	−	0.997917i	$-0.520547\pi$
$967$	−4.01187	−0.129013	−0.0645065	+	0.997917i	$0.520547\pi$
$968$	−1.44403	−0.0464129
$969$	−1.15493	−0.0371017
$970$	13.4734	0.432604
$971$	−31.2094	−1.00156	−0.500779	−	0.865575i	$-0.666953\pi$
$971$	−31.2094	−1.00156	−0.500779	+	0.865575i	$0.666953\pi$
$972$	−16.1549	−0.518168
$973$	19.6489	0.629916
$974$	17.0772	0.547190
$975$	−10.5875	−0.339070
$976$	5.00701	0.160270
$977$	−13.5737	−0.434262	−0.217131	−	0.976143i	$-0.569670\pi$
$977$	−13.5737	−0.434262	−0.217131	+	0.976143i	$0.569670\pi$
$978$	−12.3371	−0.394498
$979$	25.6974	0.821293
$980$	4.28610	0.136915
$981$	−29.5589	−0.943742
$982$	8.32570	0.265684
$983$	−47.5607	−1.51695	−0.758475	−	0.651702i	$-0.774055\pi$
$983$	−47.5607	−1.51695	−0.758475	+	0.651702i	$0.774055\pi$
$984$	−3.72822	−0.118851
$985$	5.94362	0.189380
$986$	1.11799	0.0356041
$987$	2.23044	0.0709958
$988$	6.93970	0.220781
$989$	−71.8200	−2.28374
$990$	7.61043	0.241875
$991$	−58.1652	−1.84768	−0.923839	−	0.382782i	$-0.874966\pi$
$991$	−58.1652	−1.84768	−0.923839	+	0.382782i	$0.874966\pi$
$992$	6.60016	0.209555
$993$	−17.7166	−0.562221
$994$	5.91308	0.187552
$995$	−13.1238	−0.416053
$996$	4.06126	0.128686
$997$	50.9251	1.61281	0.806407	−	0.591361i	$-0.201409\pi$
$997$	50.9251	1.61281	0.806407	+	0.591361i	$0.201409\pi$
$998$	27.4836	0.869977
$999$	−45.3217	−1.43391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.17	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.17	✓	46	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.923967 q^{3} +1.00000 q^{4} -1.00517 q^{5} +0.923967 q^{6} -1.65407 q^{7} -1.00000 q^{8} -2.14628 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.923967 q^{3} +1.00000 q^{4} -1.00517 q^{5} +0.923967 q^{6} -1.65407 q^{7} -1.00000 q^{8} -2.14628 q^{9} +1.00517 q^{10} -3.52761 q^{11} -0.923967 q^{12} -2.87212 q^{13} +1.65407 q^{14} +0.928748 q^{15} +1.00000 q^{16} -0.517323 q^{17} +2.14628 q^{18} -2.41623 q^{19} -1.00517 q^{20} +1.52831 q^{21} +3.52761 q^{22} -7.18630 q^{23} +0.923967 q^{24} -3.98962 q^{25} +2.87212 q^{26} +4.75500 q^{27} -1.65407 q^{28} +2.16111 q^{29} -0.928748 q^{30} -6.60016 q^{31} -1.00000 q^{32} +3.25940 q^{33} +0.517323 q^{34} +1.66263 q^{35} -2.14628 q^{36} -9.53137 q^{37} +2.41623 q^{38} +2.65375 q^{39} +1.00517 q^{40} -4.03502 q^{41} -1.52831 q^{42} +9.99403 q^{43} -3.52761 q^{44} +2.15739 q^{45} +7.18630 q^{46} +1.45942 q^{47} -0.923967 q^{48} -4.26404 q^{49} +3.98962 q^{50} +0.477989 q^{51} -2.87212 q^{52} -7.71322 q^{53} -4.75500 q^{54} +3.54586 q^{55} +1.65407 q^{56} +2.23251 q^{57} -2.16111 q^{58} -6.62583 q^{59} +0.928748 q^{60} +5.00701 q^{61} +6.60016 q^{62} +3.55011 q^{63} +1.00000 q^{64} +2.88699 q^{65} -3.25940 q^{66} -8.51763 q^{67} -0.517323 q^{68} +6.63990 q^{69} -1.66263 q^{70} +3.57486 q^{71} +2.14628 q^{72} +0.496885 q^{73} +9.53137 q^{74} +3.68628 q^{75} -2.41623 q^{76} +5.83493 q^{77} -2.65375 q^{78} -3.81649 q^{79} -1.00517 q^{80} +2.04539 q^{81} +4.03502 q^{82} -4.39546 q^{83} +1.52831 q^{84} +0.520000 q^{85} -9.99403 q^{86} -1.99679 q^{87} +3.52761 q^{88} -7.28465 q^{89} -2.15739 q^{90} +4.75071 q^{91} -7.18630 q^{92} +6.09833 q^{93} -1.45942 q^{94} +2.42873 q^{95} +0.923967 q^{96} +13.4040 q^{97} +4.26404 q^{98} +7.57126 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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