LMFDB - Embedded newform 4029.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.922410 q^{2} -1.00000 q^{3} -1.14916 q^{4} -0.0437394 q^{5} +0.922410 q^{6} +4.58186 q^{7} +2.90482 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.922410 q^{2} -1.00000 q^{3} -1.14916 q^{4} -0.0437394 q^{5} +0.922410 q^{6} +4.58186 q^{7} +2.90482 q^{8} +1.00000 q^{9} +0.0403457 q^{10} +2.66890 q^{11} +1.14916 q^{12} -0.617504 q^{13} -4.22636 q^{14} +0.0437394 q^{15} -0.381116 q^{16} +1.00000 q^{17} -0.922410 q^{18} -0.396729 q^{19} +0.0502636 q^{20} -4.58186 q^{21} -2.46182 q^{22} -0.881993 q^{23} -2.90482 q^{24} -4.99809 q^{25} +0.569593 q^{26} -1.00000 q^{27} -5.26529 q^{28} -9.81651 q^{29} -0.0403457 q^{30} -3.37439 q^{31} -5.45809 q^{32} -2.66890 q^{33} -0.922410 q^{34} -0.200408 q^{35} -1.14916 q^{36} -9.42586 q^{37} +0.365947 q^{38} +0.617504 q^{39} -0.127055 q^{40} -2.21028 q^{41} +4.22636 q^{42} +0.193035 q^{43} -3.06699 q^{44} -0.0437394 q^{45} +0.813559 q^{46} +4.26731 q^{47} +0.381116 q^{48} +13.9934 q^{49} +4.61029 q^{50} -1.00000 q^{51} +0.709611 q^{52} -11.3329 q^{53} +0.922410 q^{54} -0.116736 q^{55} +13.3095 q^{56} +0.396729 q^{57} +9.05485 q^{58} +7.57636 q^{59} -0.0502636 q^{60} -15.1343 q^{61} +3.11257 q^{62} +4.58186 q^{63} +5.79683 q^{64} +0.0270093 q^{65} +2.46182 q^{66} +0.595255 q^{67} -1.14916 q^{68} +0.881993 q^{69} +0.184858 q^{70} +0.125443 q^{71} +2.90482 q^{72} +2.94358 q^{73} +8.69451 q^{74} +4.99809 q^{75} +0.455905 q^{76} +12.2285 q^{77} -0.569593 q^{78} +1.00000 q^{79} +0.0166698 q^{80} +1.00000 q^{81} +2.03878 q^{82} +4.50328 q^{83} +5.26529 q^{84} -0.0437394 q^{85} -0.178057 q^{86} +9.81651 q^{87} +7.75267 q^{88} +4.43246 q^{89} +0.0403457 q^{90} -2.82932 q^{91} +1.01355 q^{92} +3.37439 q^{93} -3.93622 q^{94} +0.0173527 q^{95} +5.45809 q^{96} -15.7154 q^{97} -12.9077 q^{98} +2.66890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.922410	−0.652243	−0.326121	−	0.945328i	$-0.605742\pi$
$2$	−0.922410	−0.652243	−0.326121	+	0.945328i	$0.605742\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.14916	−0.574579
$5$	−0.0437394	−0.0195609	−0.00978043	−	0.999952i	$-0.503113\pi$
$5$	−0.0437394	−0.0195609	−0.00978043	+	0.999952i	$0.503113\pi$
$6$	0.922410	0.376572
$7$	4.58186	1.73178	0.865890	−	0.500234i	$-0.166753\pi$
$7$	4.58186	1.73178	0.865890	+	0.500234i	$0.166753\pi$
$8$	2.90482	1.02701
$9$	1.00000	0.333333
$10$	0.0403457	0.0127584
$11$	2.66890	0.804704	0.402352	−	0.915485i	$-0.368193\pi$
$11$	2.66890	0.804704	0.402352	+	0.915485i	$0.368193\pi$
$12$	1.14916	0.331734
$13$	−0.617504	−0.171265	−0.0856325	−	0.996327i	$-0.527291\pi$
$13$	−0.617504	−0.171265	−0.0856325	+	0.996327i	$0.527291\pi$
$14$	−4.22636	−1.12954
$15$	0.0437394	0.0112935
$16$	−0.381116	−0.0952790
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.922410	−0.217414
$19$	−0.396729	−0.0910159	−0.0455079	−	0.998964i	$-0.514491\pi$
$19$	−0.396729	−0.0910159	−0.0455079	+	0.998964i	$0.514491\pi$
$20$	0.0502636	0.0112393
$21$	−4.58186	−0.999844
$22$	−2.46182	−0.524862
$23$	−0.881993	−0.183908	−0.0919541	−	0.995763i	$-0.529311\pi$
$23$	−0.881993	−0.183908	−0.0919541	+	0.995763i	$0.529311\pi$
$24$	−2.90482	−0.592943
$25$	−4.99809	−0.999617
$26$	0.569593	0.111706
$27$	−1.00000	−0.192450
$28$	−5.26529	−0.995046
$29$	−9.81651	−1.82288	−0.911440	−	0.411433i	$-0.865029\pi$
$29$	−9.81651	−1.82288	−0.911440	+	0.411433i	$0.865029\pi$
$30$	−0.0403457	−0.00736609
$31$	−3.37439	−0.606057	−0.303029	−	0.952981i	$-0.597998\pi$
$31$	−3.37439	−0.606057	−0.303029	+	0.952981i	$0.597998\pi$
$32$	−5.45809	−0.964863
$33$	−2.66890	−0.464596
$34$	−0.922410	−0.158192
$35$	−0.200408	−0.0338751
$36$	−1.14916	−0.191526
$37$	−9.42586	−1.54960	−0.774801	−	0.632205i	$-0.782150\pi$
$37$	−9.42586	−1.54960	−0.774801	+	0.632205i	$0.782150\pi$
$38$	0.365947	0.0593644
$39$	0.617504	0.0988798
$40$	−0.127055	−0.0200892
$41$	−2.21028	−0.345187	−0.172594	−	0.984993i	$-0.555215\pi$
$41$	−2.21028	−0.345187	−0.172594	+	0.984993i	$0.555215\pi$
$42$	4.22636	0.652141
$43$	0.193035	0.0294375	0.0147188	−	0.999892i	$-0.495315\pi$
$43$	0.193035	0.0294375	0.0147188	+	0.999892i	$0.495315\pi$
$44$	−3.06699	−0.462366
$45$	−0.0437394	−0.00652029
$46$	0.813559	0.119953
$47$	4.26731	0.622452	0.311226	−	0.950336i	$-0.399260\pi$
$47$	4.26731	0.622452	0.311226	+	0.950336i	$0.399260\pi$
$48$	0.381116	0.0550093
$49$	13.9934	1.99906
$50$	4.61029	0.651993
$51$	−1.00000	−0.140028
$52$	0.709611	0.0984053
$53$	−11.3329	−1.55669	−0.778344	−	0.627838i	$-0.783940\pi$
$53$	−11.3329	−1.55669	−0.778344	+	0.627838i	$0.783940\pi$
$54$	0.922410	0.125524
$55$	−0.116736	−0.0157407
$56$	13.3095	1.77855
$57$	0.396729	0.0525480
$58$	9.05485	1.18896
$59$	7.57636	0.986358	0.493179	−	0.869928i	$-0.335835\pi$
$59$	7.57636	0.986358	0.493179	+	0.869928i	$0.335835\pi$
$60$	−0.0502636	−0.00648900
$61$	−15.1343	−1.93775	−0.968877	−	0.247542i	$-0.920377\pi$
$61$	−15.1343	−1.93775	−0.968877	+	0.247542i	$0.920377\pi$
$62$	3.11257	0.395297
$63$	4.58186	0.577260
$64$	5.79683	0.724604
$65$	0.0270093	0.00335009
$66$	2.46182	0.303029
$67$	0.595255	0.0727220	0.0363610	−	0.999339i	$-0.488423\pi$
$67$	0.595255	0.0727220	0.0363610	+	0.999339i	$0.488423\pi$
$68$	−1.14916	−0.139356
$69$	0.881993	0.106179
$70$	0.184858	0.0220948
$71$	0.125443	0.0148874	0.00744370	−	0.999972i	$-0.497631\pi$
$71$	0.125443	0.0148874	0.00744370	+	0.999972i	$0.497631\pi$
$72$	2.90482	0.342336
$73$	2.94358	0.344519	0.172260	−	0.985052i	$-0.444893\pi$
$73$	2.94358	0.344519	0.172260	+	0.985052i	$0.444893\pi$
$74$	8.69451	1.01072
$75$	4.99809	0.577129
$76$	0.455905	0.0522958
$77$	12.2285	1.39357
$78$	−0.569593	−0.0644937
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	0.0166698	0.00186374
$81$	1.00000	0.111111
$82$	2.03878	0.225146
$83$	4.50328	0.494299	0.247150	−	0.968977i	$-0.420506\pi$
$83$	4.50328	0.494299	0.247150	+	0.968977i	$0.420506\pi$
$84$	5.26529	0.574490
$85$	−0.0437394	−0.00474421
$86$	−0.178057	−0.0192004
$87$	9.81651	1.05244
$88$	7.75267	0.826437
$89$	4.43246	0.469840	0.234920	−	0.972015i	$-0.424517\pi$
$89$	4.43246	0.469840	0.234920	+	0.972015i	$0.424517\pi$
$90$	0.0403457	0.00425281
$91$	−2.82932	−0.296593
$92$	1.01355	0.105670
$93$	3.37439	0.349907
$94$	−3.93622	−0.405990
$95$	0.0173527	0.00178035
$96$	5.45809	0.557064
$97$	−15.7154	−1.59566	−0.797831	−	0.602881i	$-0.794019\pi$
$97$	−15.7154	−1.59566	−0.797831	+	0.602881i	$0.794019\pi$
$98$	−12.9077	−1.30388
$99$	2.66890	0.268235
$100$	5.74360	0.574360
$101$	−15.0751	−1.50003	−0.750015	−	0.661420i	$-0.769954\pi$
$101$	−15.0751	−1.50003	−0.750015	+	0.661420i	$0.769954\pi$
$102$	0.922410	0.0913322
$103$	−1.02863	−0.101354	−0.0506768	−	0.998715i	$-0.516138\pi$
$103$	−1.02863	−0.101354	−0.0506768	+	0.998715i	$0.516138\pi$
$104$	−1.79374	−0.175890
$105$	0.200408	0.0195578
$106$	10.4536	1.01534
$107$	−8.89712	−0.860117	−0.430058	−	0.902801i	$-0.641507\pi$
$107$	−8.89712	−0.860117	−0.430058	+	0.902801i	$0.641507\pi$
$108$	1.14916	0.110578
$109$	−7.54888	−0.723052	−0.361526	−	0.932362i	$-0.617744\pi$
$109$	−7.54888	−0.723052	−0.361526	+	0.932362i	$0.617744\pi$
$110$	0.107679	0.0102668
$111$	9.42586	0.894663
$112$	−1.74622	−0.165002
$113$	10.5360	0.991142	0.495571	−	0.868567i	$-0.334959\pi$
$113$	10.5360	0.991142	0.495571	+	0.868567i	$0.334959\pi$
$114$	−0.365947	−0.0342741
$115$	0.0385779	0.00359740
$116$	11.2807	1.04739
$117$	−0.617504	−0.0570883
$118$	−6.98851	−0.643345
$119$	4.58186	0.420019
$120$	0.127055	0.0115985
$121$	−3.87697	−0.352452
$122$	13.9601	1.26389
$123$	2.21028	0.199294
$124$	3.87770	0.348228
$125$	0.437311	0.0391143
$126$	−4.22636	−0.376514
$127$	−6.39075	−0.567087	−0.283544	−	0.958959i	$-0.591510\pi$
$127$	−6.39075	−0.567087	−0.283544	+	0.958959i	$0.591510\pi$
$128$	5.56912	0.492245
$129$	−0.193035	−0.0169958
$130$	−0.0249137	−0.00218507
$131$	−9.68213	−0.845932	−0.422966	−	0.906146i	$-0.639011\pi$
$131$	−9.68213	−0.845932	−0.422966	+	0.906146i	$0.639011\pi$
$132$	3.06699	0.266947
$133$	−1.81776	−0.157619
$134$	−0.549070	−0.0474324
$135$	0.0437394	0.00376449
$136$	2.90482	0.249086
$137$	−8.09423	−0.691537	−0.345769	−	0.938320i	$-0.612382\pi$
$137$	−8.09423	−0.691537	−0.345769	+	0.938320i	$0.612382\pi$
$138$	−0.813559	−0.0692548
$139$	−19.1465	−1.62398	−0.811991	−	0.583669i	$-0.801616\pi$
$139$	−19.1465	−1.62398	−0.811991	+	0.583669i	$0.801616\pi$
$140$	0.230301	0.0194640
$141$	−4.26731	−0.359373
$142$	−0.115710	−0.00971019
$143$	−1.64806	−0.137817
$144$	−0.381116	−0.0317597
$145$	0.429369	0.0356571
$146$	−2.71518	−0.224710
$147$	−13.9934	−1.15416
$148$	10.8318	0.890369
$149$	8.24401	0.675375	0.337688	−	0.941258i	$-0.390355\pi$
$149$	8.24401	0.675375	0.337688	+	0.941258i	$0.390355\pi$
$150$	−4.61029	−0.376428
$151$	10.2103	0.830902	0.415451	−	0.909616i	$-0.363624\pi$
$151$	10.2103	0.830902	0.415451	+	0.909616i	$0.363624\pi$
$152$	−1.15242	−0.0934740
$153$	1.00000	0.0808452
$154$	−11.2797	−0.908946
$155$	0.147594	0.0118550
$156$	−0.709611	−0.0568143
$157$	−8.71308	−0.695380	−0.347690	−	0.937610i	$-0.613034\pi$
$157$	−8.71308	−0.695380	−0.347690	+	0.937610i	$0.613034\pi$
$158$	−0.922410	−0.0733830
$159$	11.3329	0.898755
$160$	0.238734	0.0188736
$161$	−4.04117	−0.318489
$162$	−0.922410	−0.0724714
$163$	1.37765	0.107906	0.0539531	−	0.998543i	$-0.482818\pi$
$163$	1.37765	0.107906	0.0539531	+	0.998543i	$0.482818\pi$
$164$	2.53996	0.198337
$165$	0.116736	0.00908790
$166$	−4.15387	−0.322403
$167$	−3.39286	−0.262548	−0.131274	−	0.991346i	$-0.541907\pi$
$167$	−3.39286	−0.262548	−0.131274	+	0.991346i	$0.541907\pi$
$168$	−13.3095	−1.02685
$169$	−12.6187	−0.970668
$170$	0.0403457	0.00309437
$171$	−0.396729	−0.0303386
$172$	−0.221827	−0.0169142
$173$	9.13400	0.694445	0.347223	−	0.937783i	$-0.387125\pi$
$173$	9.13400	0.694445	0.347223	+	0.937783i	$0.387125\pi$
$174$	−9.05485	−0.686447
$175$	−22.9005	−1.73112
$176$	−1.01716	−0.0766713
$177$	−7.57636	−0.569474
$178$	−4.08855	−0.306449
$179$	25.3112	1.89185	0.945925	−	0.324384i	$-0.105157\pi$
$179$	25.3112	1.89185	0.945925	+	0.324384i	$0.105157\pi$
$180$	0.0502636	0.00374642
$181$	22.3620	1.66216	0.831078	−	0.556156i	$-0.187724\pi$
$181$	22.3620	1.66216	0.831078	+	0.556156i	$0.187724\pi$
$182$	2.60979	0.193451
$183$	15.1343	1.11876
$184$	−2.56203	−0.188875
$185$	0.412282	0.0303116
$186$	−3.11257	−0.228225
$187$	2.66890	0.195169
$188$	−4.90382	−0.357648
$189$	−4.58186	−0.333281
$190$	−0.0160063	−0.00116122
$191$	14.2804	1.03329	0.516646	−	0.856199i	$-0.327180\pi$
$191$	14.2804	1.03329	0.516646	+	0.856199i	$0.327180\pi$
$192$	−5.79683	−0.418350
$193$	−6.52703	−0.469826	−0.234913	−	0.972016i	$-0.575480\pi$
$193$	−6.52703	−0.469826	−0.234913	+	0.972016i	$0.575480\pi$
$194$	14.4961	1.04076
$195$	−0.0270093	−0.00193418
$196$	−16.0807	−1.14862
$197$	16.1964	1.15395	0.576974	−	0.816762i	$-0.304233\pi$
$197$	16.1964	1.15395	0.576974	+	0.816762i	$0.304233\pi$
$198$	−2.46182	−0.174954
$199$	23.0550	1.63432	0.817162	−	0.576408i	$-0.195546\pi$
$199$	23.0550	1.63432	0.817162	+	0.576408i	$0.195546\pi$
$200$	−14.5185	−1.02661
$201$	−0.595255	−0.0419861
$202$	13.9055	0.978384
$203$	−44.9779	−3.15683
$204$	1.14916	0.0804572
$205$	0.0966762	0.00675216
$206$	0.948815	0.0661071
$207$	−0.881993	−0.0613027
$208$	0.235341	0.0163179
$209$	−1.05883	−0.0732408
$210$	−0.184858	−0.0127564
$211$	−1.68314	−0.115872	−0.0579361	−	0.998320i	$-0.518452\pi$
$211$	−1.68314	−0.115872	−0.0579361	+	0.998320i	$0.518452\pi$
$212$	13.0233	0.894441
$213$	−0.125443	−0.00859524
$214$	8.20679	0.561005
$215$	−0.00844323	−0.000575823 0
$216$	−2.90482	−0.197648
$217$	−15.4610	−1.04956
$218$	6.96317	0.471605
$219$	−2.94358	−0.198908
$220$	0.134148	0.00904428
$221$	−0.617504	−0.0415378
$222$	−8.69451	−0.583537
$223$	−6.56815	−0.439836	−0.219918	−	0.975518i	$-0.570579\pi$
$223$	−6.56815	−0.439836	−0.219918	+	0.975518i	$0.570579\pi$
$224$	−25.0082	−1.67093
$225$	−4.99809	−0.333206
$226$	−9.71850	−0.646465
$227$	−5.17041	−0.343172	−0.171586	−	0.985169i	$-0.554889\pi$
$227$	−5.17041	−0.343172	−0.171586	+	0.985169i	$0.554889\pi$
$228$	−0.455905	−0.0301930
$229$	13.7771	0.910418	0.455209	−	0.890385i	$-0.349565\pi$
$229$	13.7771	0.910418	0.455209	+	0.890385i	$0.349565\pi$
$230$	−0.0355846	−0.00234638
$231$	−12.2285	−0.804578
$232$	−28.5152	−1.87211
$233$	−1.69782	−0.111228	−0.0556141	−	0.998452i	$-0.517712\pi$
$233$	−1.69782	−0.111228	−0.0556141	+	0.998452i	$0.517712\pi$
$234$	0.569593	0.0372354
$235$	−0.186650	−0.0121757
$236$	−8.70644	−0.566741
$237$	−1.00000	−0.0649570
$238$	−4.22636	−0.273954
$239$	−5.38341	−0.348224	−0.174112	−	0.984726i	$-0.555705\pi$
$239$	−5.38341	−0.348224	−0.174112	+	0.984726i	$0.555705\pi$
$240$	−0.0166698	−0.00107603
$241$	−20.4705	−1.31862	−0.659311	−	0.751870i	$-0.729152\pi$
$241$	−20.4705	−1.31862	−0.659311	+	0.751870i	$0.729152\pi$
$242$	3.57616	0.229884
$243$	−1.00000	−0.0641500
$244$	17.3918	1.11339
$245$	−0.612066	−0.0391034
$246$	−2.03878	−0.129988
$247$	0.244982	0.0155878
$248$	−9.80197	−0.622426
$249$	−4.50328	−0.285384
$250$	−0.403380	−0.0255120
$251$	−13.3933	−0.845380	−0.422690	−	0.906274i	$-0.638914\pi$
$251$	−13.3933	−0.845380	−0.422690	+	0.906274i	$0.638914\pi$
$252$	−5.26529	−0.331682
$253$	−2.35395	−0.147992
$254$	5.89489	0.369879
$255$	0.0437394	0.00273907
$256$	−16.7307	−1.04567
$257$	−8.44374	−0.526706	−0.263353	−	0.964700i	$-0.584828\pi$
$257$	−8.44374	−0.526706	−0.263353	+	0.964700i	$0.584828\pi$
$258$	0.178057	0.0110854
$259$	−43.1880	−2.68357
$260$	−0.0310380	−0.00192489
$261$	−9.81651	−0.607627
$262$	8.93090	0.551753
$263$	−3.05237	−0.188217	−0.0941086	−	0.995562i	$-0.530000\pi$
$263$	−3.05237	−0.188217	−0.0941086	+	0.995562i	$0.530000\pi$
$264$	−7.75267	−0.477144
$265$	0.495693	0.0304502
$266$	1.67672	0.102806
$267$	−4.43246	−0.271262
$268$	−0.684043	−0.0417846
$269$	−7.24560	−0.441772	−0.220886	−	0.975300i	$-0.570895\pi$
$269$	−7.24560	−0.441772	−0.220886	+	0.975300i	$0.570895\pi$
$270$	−0.0403457	−0.00245536
$271$	10.6365	0.646119	0.323060	−	0.946379i	$-0.395289\pi$
$271$	10.6365	0.646119	0.323060	+	0.946379i	$0.395289\pi$
$272$	−0.381116	−0.0231085
$273$	2.82932	0.171238
$274$	7.46621	0.451050
$275$	−13.3394	−0.804396
$276$	−1.01355	−0.0610085
$277$	−25.6094	−1.53872	−0.769359	−	0.638817i	$-0.779424\pi$
$277$	−25.6094	−1.53872	−0.769359	+	0.638817i	$0.779424\pi$
$278$	17.6609	1.05923
$279$	−3.37439	−0.202019
$280$	−0.582149	−0.0347900
$281$	−26.7540	−1.59601	−0.798005	−	0.602651i	$-0.794111\pi$
$281$	−26.7540	−1.59601	−0.798005	+	0.602651i	$0.794111\pi$
$282$	3.93622	0.234398
$283$	−7.03565	−0.418226	−0.209113	−	0.977891i	$-0.567058\pi$
$283$	−7.03565	−0.418226	−0.209113	+	0.977891i	$0.567058\pi$
$284$	−0.144154	−0.00855399
$285$	−0.0173527	−0.00102789
$286$	1.52019	0.0898904
$287$	−10.1272	−0.597788
$288$	−5.45809	−0.321621
$289$	1.00000	0.0588235
$290$	−0.396054	−0.0232571
$291$	15.7154	0.921256
$292$	−3.38264	−0.197954
$293$	21.2246	1.23995	0.619976	−	0.784621i	$-0.287142\pi$
$293$	21.2246	1.23995	0.619976	+	0.784621i	$0.287142\pi$
$294$	12.9077	0.752793
$295$	−0.331386	−0.0192940
$296$	−27.3804	−1.59145
$297$	−2.66890	−0.154865
$298$	−7.60436	−0.440509
$299$	0.544634	0.0314970
$300$	−5.74360	−0.331607
$301$	0.884458	0.0509793
$302$	−9.41808	−0.541950
$303$	15.0751	0.866043
$304$	0.151200	0.00867190
$305$	0.661968	0.0379042
$306$	−0.922410	−0.0527307
$307$	−6.20816	−0.354319	−0.177159	−	0.984182i	$-0.556691\pi$
$307$	−6.20816	−0.354319	−0.177159	+	0.984182i	$0.556691\pi$
$308$	−14.0525	−0.800717
$309$	1.02863	0.0585165
$310$	−0.136142	−0.00773234
$311$	26.6313	1.51012	0.755061	−	0.655654i	$-0.227607\pi$
$311$	26.6313	1.51012	0.755061	+	0.655654i	$0.227607\pi$
$312$	1.79374	0.101550
$313$	28.5407	1.61321	0.806607	−	0.591088i	$-0.201302\pi$
$313$	28.5407	1.61321	0.806607	+	0.591088i	$0.201302\pi$
$314$	8.03704	0.453556
$315$	−0.200408	−0.0112917
$316$	−1.14916	−0.0646452
$317$	−7.32922	−0.411650	−0.205825	−	0.978589i	$-0.565988\pi$
$317$	−7.32922	−0.411650	−0.205825	+	0.978589i	$0.565988\pi$
$318$	−10.4536	−0.586206
$319$	−26.1993	−1.46688
$320$	−0.253550	−0.0141739
$321$	8.89712	0.496589
$322$	3.72761	0.207732
$323$	−0.396729	−0.0220746
$324$	−1.14916	−0.0638422
$325$	3.08634	0.171199
$326$	−1.27076	−0.0703810
$327$	7.54888	0.417454
$328$	−6.42045	−0.354510
$329$	19.5522	1.07795
$330$	−0.107679	−0.00592752
$331$	−27.0172	−1.48500	−0.742499	−	0.669847i	$-0.766360\pi$
$331$	−27.0172	−1.48500	−0.742499	+	0.669847i	$0.766360\pi$
$332$	−5.17499	−0.284014
$333$	−9.42586	−0.516534
$334$	3.12961	0.171245
$335$	−0.0260361	−0.00142251
$336$	1.74622	0.0952641
$337$	−21.9964	−1.19822	−0.599111	−	0.800666i	$-0.704479\pi$
$337$	−21.9964	−1.19822	−0.599111	+	0.800666i	$0.704479\pi$
$338$	11.6396	0.633111
$339$	−10.5360	−0.572236
$340$	0.0502636	0.00272592
$341$	−9.00590	−0.487697
$342$	0.365947	0.0197881
$343$	32.0430	1.73016
$344$	0.560730	0.0302326
$345$	−0.0385779	−0.00207696
$346$	−8.42530	−0.452947
$347$	−24.3297	−1.30609	−0.653043	−	0.757321i	$-0.726508\pi$
$347$	−24.3297	−1.30609	−0.653043	+	0.757321i	$0.726508\pi$
$348$	−11.2807	−0.604711
$349$	0.972426	0.0520528	0.0260264	−	0.999661i	$-0.491715\pi$
$349$	0.972426	0.0520528	0.0260264	+	0.999661i	$0.491715\pi$
$350$	21.1237	1.12911
$351$	0.617504	0.0329599
$352$	−14.5671	−0.776429
$353$	16.5117	0.878829	0.439415	−	0.898284i	$-0.355186\pi$
$353$	16.5117	0.878829	0.439415	+	0.898284i	$0.355186\pi$
$354$	6.98851	0.371435
$355$	−0.00548682	−0.000291210 0
$356$	−5.09360	−0.269960
$357$	−4.58186	−0.242498
$358$	−23.3473	−1.23395
$359$	28.4695	1.50256	0.751280	−	0.659983i	$-0.229437\pi$
$359$	28.4695	1.50256	0.751280	+	0.659983i	$0.229437\pi$
$360$	−0.127055	−0.00669639
$361$	−18.8426	−0.991716
$362$	−20.6270	−1.08413
$363$	3.87697	0.203488
$364$	3.25134	0.170416
$365$	−0.128750	−0.00673910
$366$	−13.9601	−0.729705
$367$	6.24098	0.325777	0.162888	−	0.986645i	$-0.447919\pi$
$367$	6.24098	0.325777	0.162888	+	0.986645i	$0.447919\pi$
$368$	0.336141	0.0175226
$369$	−2.21028	−0.115062
$370$	−0.380293	−0.0197705
$371$	−51.9256	−2.69584
$372$	−3.87770	−0.201050
$373$	−29.5539	−1.53025	−0.765123	−	0.643885i	$-0.777322\pi$
$373$	−29.5539	−1.53025	−0.765123	+	0.643885i	$0.777322\pi$
$374$	−2.46182	−0.127298
$375$	−0.437311	−0.0225826
$376$	12.3958	0.639263
$377$	6.06174	0.312195
$378$	4.22636	0.217380
$379$	17.6833	0.908329	0.454165	−	0.890918i	$-0.349938\pi$
$379$	17.6833	0.908329	0.454165	+	0.890918i	$0.349938\pi$
$380$	−0.0199410	−0.00102295
$381$	6.39075	0.327408
$382$	−13.1724	−0.673958
$383$	30.9929	1.58367	0.791833	−	0.610738i	$-0.209127\pi$
$383$	30.9929	1.58367	0.791833	+	0.610738i	$0.209127\pi$
$384$	−5.56912	−0.284198
$385$	−0.534869	−0.0272594
$386$	6.02060	0.306440
$387$	0.193035	0.00981250
$388$	18.0595	0.916835
$389$	−15.0925	−0.765220	−0.382610	−	0.923910i	$-0.624975\pi$
$389$	−15.0925	−0.765220	−0.382610	+	0.923910i	$0.624975\pi$
$390$	0.0249137	0.00126155
$391$	−0.881993	−0.0446043
$392$	40.6484	2.05305
$393$	9.68213	0.488399
$394$	−14.9398	−0.752655
$395$	−0.0437394	−0.00220077
$396$	−3.06699	−0.154122
$397$	−15.6742	−0.786668	−0.393334	−	0.919396i	$-0.628678\pi$
$397$	−15.6742	−0.786668	−0.393334	+	0.919396i	$0.628678\pi$
$398$	−21.2661	−1.06598
$399$	1.81776	0.0910017
$400$	1.90485	0.0952425
$401$	6.40443	0.319822	0.159911	−	0.987131i	$-0.448879\pi$
$401$	6.40443	0.319822	0.159911	+	0.987131i	$0.448879\pi$
$402$	0.549070	0.0273851
$403$	2.08370	0.103796
$404$	17.3237	0.861887
$405$	−0.0437394	−0.00217343
$406$	41.4881	2.05902
$407$	−25.1567	−1.24697
$408$	−2.90482	−0.143810
$409$	−4.56631	−0.225790	−0.112895	−	0.993607i	$-0.536012\pi$
$409$	−4.56631	−0.225790	−0.112895	+	0.993607i	$0.536012\pi$
$410$	−0.0891752	−0.00440405
$411$	8.09423	0.399259
$412$	1.18205	0.0582356
$413$	34.7138	1.70816
$414$	0.813559	0.0399842
$415$	−0.196971	−0.00966892
$416$	3.37039	0.165247
$417$	19.1465	0.937607
$418$	0.976676	0.0477708
$419$	32.3030	1.57811	0.789053	−	0.614325i	$-0.210571\pi$
$419$	32.3030	1.57811	0.789053	+	0.614325i	$0.210571\pi$
$420$	−0.230301	−0.0112375
$421$	25.6784	1.25149	0.625745	−	0.780028i	$-0.284795\pi$
$421$	25.6784	1.25149	0.625745	+	0.780028i	$0.284795\pi$
$422$	1.55255	0.0755768
$423$	4.26731	0.207484
$424$	−32.9199	−1.59873
$425$	−4.99809	−0.242443
$426$	0.115710	0.00560618
$427$	−69.3435	−3.35577
$428$	10.2242	0.494205
$429$	1.64806	0.0795690
$430$	0.00778812	0.000375576 0
$431$	36.3777	1.75225	0.876126	−	0.482082i	$-0.160119\pi$
$431$	36.3777	1.75225	0.876126	+	0.482082i	$0.160119\pi$
$432$	0.381116	0.0183364
$433$	20.8109	1.00011	0.500053	−	0.865995i	$-0.333314\pi$
$433$	20.8109	1.00011	0.500053	+	0.865995i	$0.333314\pi$
$434$	14.2614	0.684567
$435$	−0.429369	−0.0205866
$436$	8.67487	0.415451
$437$	0.349912	0.0167386
$438$	2.71518	0.129737
$439$	−7.90782	−0.377420	−0.188710	−	0.982033i	$-0.560431\pi$
$439$	−7.90782	−0.377420	−0.188710	+	0.982033i	$0.560431\pi$
$440$	−0.339097	−0.0161658
$441$	13.9934	0.666355
$442$	0.569593	0.0270928
$443$	11.2819	0.536018	0.268009	−	0.963416i	$-0.413634\pi$
$443$	11.2819	0.536018	0.268009	+	0.963416i	$0.413634\pi$
$444$	−10.8318	−0.514055
$445$	−0.193873	−0.00919047
$446$	6.05853	0.286880
$447$	−8.24401	−0.389928
$448$	26.5603	1.25485
$449$	32.5930	1.53816	0.769079	−	0.639153i	$-0.220715\pi$
$449$	32.5930	1.53816	0.769079	+	0.639153i	$0.220715\pi$
$450$	4.61029	0.217331
$451$	−5.89901	−0.277773
$452$	−12.1075	−0.569490
$453$	−10.2103	−0.479722
$454$	4.76924	0.223831
$455$	0.123753	0.00580162
$456$	1.15242	0.0539672
$457$	8.07875	0.377908	0.188954	−	0.981986i	$-0.439490\pi$
$457$	8.07875	0.377908	0.188954	+	0.981986i	$0.439490\pi$
$458$	−12.7082	−0.593813
$459$	−1.00000	−0.0466760
$460$	−0.0443321	−0.00206699
$461$	−16.4753	−0.767330	−0.383665	−	0.923472i	$-0.625338\pi$
$461$	−16.4753	−0.767330	−0.383665	+	0.923472i	$0.625338\pi$
$462$	11.2797	0.524780
$463$	−31.0759	−1.44422	−0.722111	−	0.691778i	$-0.756828\pi$
$463$	−31.0759	−1.44422	−0.722111	+	0.691778i	$0.756828\pi$
$464$	3.74123	0.173682
$465$	−0.147594	−0.00684449
$466$	1.56609	0.0725478
$467$	−24.6422	−1.14030	−0.570152	−	0.821539i	$-0.693116\pi$
$467$	−24.6422	−1.14030	−0.570152	+	0.821539i	$0.693116\pi$
$468$	0.709611	0.0328018
$469$	2.72738	0.125939
$470$	0.172168	0.00794151
$471$	8.71308	0.401478
$472$	22.0079	1.01300
$473$	0.515190	0.0236885
$474$	0.922410	0.0423677
$475$	1.98289	0.0909810
$476$	−5.26529	−0.241334
$477$	−11.3329	−0.518896
$478$	4.96571	0.227126
$479$	−13.9572	−0.637719	−0.318860	−	0.947802i	$-0.603300\pi$
$479$	−13.9572	−0.637719	−0.318860	+	0.947802i	$0.603300\pi$
$480$	−0.238734	−0.0108967
$481$	5.82051	0.265392
$482$	18.8822	0.860062
$483$	4.04117	0.183879
$484$	4.45526	0.202512
$485$	0.687385	0.0312125
$486$	0.922410	0.0418414
$487$	17.0135	0.770955	0.385478	−	0.922717i	$-0.374037\pi$
$487$	17.0135	0.770955	0.385478	+	0.922717i	$0.374037\pi$
$488$	−43.9625	−1.99009
$489$	−1.37765	−0.0622996
$490$	0.564576	0.0255049
$491$	−0.369603	−0.0166799	−0.00833997	−	0.999965i	$-0.502655\pi$
$491$	−0.369603	−0.0166799	−0.00833997	+	0.999965i	$0.502655\pi$
$492$	−2.53996	−0.114510
$493$	−9.81651	−0.442113
$494$	−0.225974	−0.0101670
$495$	−0.116736	−0.00524690
$496$	1.28603	0.0577445
$497$	0.574764	0.0257817
$498$	4.15387	0.186140
$499$	8.47638	0.379455	0.189727	−	0.981837i	$-0.439240\pi$
$499$	8.47638	0.379455	0.189727	+	0.981837i	$0.439240\pi$
$500$	−0.502539	−0.0224742
$501$	3.39286	0.151582
$502$	12.3542	0.551393
$503$	−6.24400	−0.278406	−0.139203	−	0.990264i	$-0.544454\pi$
$503$	−6.24400	−0.278406	−0.139203	+	0.990264i	$0.544454\pi$
$504$	13.3095	0.592851
$505$	0.659377	0.0293419
$506$	2.17131	0.0965264
$507$	12.6187	0.560416
$508$	7.34399	0.325837
$509$	−9.56004	−0.423741	−0.211871	−	0.977298i	$-0.567956\pi$
$509$	−9.56004	−0.423741	−0.211871	+	0.977298i	$0.567956\pi$
$510$	−0.0403457	−0.00178654
$511$	13.4871	0.596632
$512$	4.29431	0.189783
$513$	0.396729	0.0175160
$514$	7.78859	0.343540
$515$	0.0449915	0.00198256
$516$	0.221827	0.00976541
$517$	11.3890	0.500889
$518$	39.8370	1.75034
$519$	−9.13400	−0.400938
$520$	0.0784571	0.00344057
$521$	−31.7766	−1.39216	−0.696079	−	0.717965i	$-0.745074\pi$
$521$	−31.7766	−1.39216	−0.696079	+	0.717965i	$0.745074\pi$
$522$	9.05485	0.396320
$523$	11.0961	0.485197	0.242599	−	0.970127i	$-0.422000\pi$
$523$	11.0961	0.485197	0.242599	+	0.970127i	$0.422000\pi$
$524$	11.1263	0.486055
$525$	22.9005	0.999461
$526$	2.81554	0.122763
$527$	−3.37439	−0.146991
$528$	1.01716	0.0442662
$529$	−22.2221	−0.966178
$530$	−0.457233	−0.0198609
$531$	7.57636	0.328786
$532$	2.08889	0.0905649
$533$	1.36486	0.0591184
$534$	4.08855	0.176929
$535$	0.389155	0.0168246
$536$	1.72911	0.0746861
$537$	−25.3112	−1.09226
$538$	6.68341	0.288142
$539$	37.3471	1.60865
$540$	−0.0502636	−0.00216300
$541$	9.07063	0.389977	0.194988	−	0.980806i	$-0.437533\pi$
$541$	9.07063	0.389977	0.194988	+	0.980806i	$0.437533\pi$
$542$	−9.81119	−0.421427
$543$	−22.3620	−0.959646
$544$	−5.45809	−0.234014
$545$	0.330184	0.0141435
$546$	−2.60979	−0.111689
$547$	−12.9065	−0.551841	−0.275921	−	0.961180i	$-0.588983\pi$
$547$	−12.9065	−0.551841	−0.275921	+	0.961180i	$0.588983\pi$
$548$	9.30156	0.397343
$549$	−15.1343	−0.645918
$550$	12.3044	0.524661
$551$	3.89449	0.165911
$552$	2.56203	0.109047
$553$	4.58186	0.194841
$554$	23.6223	1.00362
$555$	−0.412282	−0.0175004
$556$	22.0023	0.933107
$557$	18.0668	0.765514	0.382757	−	0.923849i	$-0.374975\pi$
$557$	18.0668	0.765514	0.382757	+	0.923849i	$0.374975\pi$
$558$	3.11257	0.131766
$559$	−0.119200	−0.00504161
$560$	0.0763787	0.00322759
$561$	−2.66890	−0.112681
$562$	24.6782	1.04099
$563$	−5.10706	−0.215237	−0.107618	−	0.994192i	$-0.534322\pi$
$563$	−5.10706	−0.215237	−0.107618	+	0.994192i	$0.534322\pi$
$564$	4.90382	0.206488
$565$	−0.460838	−0.0193876
$566$	6.48976	0.272785
$567$	4.58186	0.192420
$568$	0.364390	0.0152895
$569$	34.2431	1.43554	0.717772	−	0.696278i	$-0.245162\pi$
$569$	34.2431	1.43554	0.717772	+	0.696278i	$0.245162\pi$
$570$	0.0160063	0.000670431 0
$571$	4.85424	0.203144	0.101572	−	0.994828i	$-0.467613\pi$
$571$	4.85424	0.203144	0.101572	+	0.994828i	$0.467613\pi$
$572$	1.89388	0.0791871
$573$	−14.2804	−0.596572
$574$	9.34141	0.389903
$575$	4.40828	0.183838
$576$	5.79683	0.241535
$577$	−40.6417	−1.69194	−0.845968	−	0.533234i	$-0.820976\pi$
$577$	−40.6417	−1.69194	−0.845968	+	0.533234i	$0.820976\pi$
$578$	−0.922410	−0.0383672
$579$	6.52703	0.271254
$580$	−0.493413	−0.0204878
$581$	20.6334	0.856018
$582$	−14.4961	−0.600882
$583$	−30.2463	−1.25267
$584$	8.55055	0.353824
$585$	0.0270093	0.00111670
$586$	−19.5777	−0.808749
$587$	39.9177	1.64758	0.823789	−	0.566896i	$-0.191856\pi$
$587$	39.9177	1.64758	0.823789	+	0.566896i	$0.191856\pi$
$588$	16.0807	0.663157
$589$	1.33872	0.0551608
$590$	0.305674	0.0125844
$591$	−16.1964	−0.666233
$592$	3.59234	0.147644
$593$	−5.36676	−0.220386	−0.110193	−	0.993910i	$-0.535147\pi$
$593$	−5.36676	−0.220386	−0.110193	+	0.993910i	$0.535147\pi$
$594$	2.46182	0.101010
$595$	−0.200408	−0.00821593
$596$	−9.47367	−0.388057
$597$	−23.0550	−0.943577
$598$	−0.502376	−0.0205437
$599$	−33.5712	−1.37168	−0.685841	−	0.727751i	$-0.740566\pi$
$599$	−33.5712	−1.37168	−0.685841	+	0.727751i	$0.740566\pi$
$600$	14.5185	0.592716
$601$	−22.8059	−0.930272	−0.465136	−	0.885239i	$-0.653995\pi$
$601$	−22.8059	−0.930272	−0.465136	+	0.885239i	$0.653995\pi$
$602$	−0.815833	−0.0332509
$603$	0.595255	0.0242407
$604$	−11.7333	−0.477419
$605$	0.169577	0.00689427
$606$	−13.9055	−0.564870
$607$	−11.6592	−0.473230	−0.236615	−	0.971603i	$-0.576038\pi$
$607$	−11.6592	−0.473230	−0.236615	+	0.971603i	$0.576038\pi$
$608$	2.16538	0.0878178
$609$	44.9779	1.82260
$610$	−0.610606	−0.0247227
$611$	−2.63509	−0.106604
$612$	−1.14916	−0.0464520
$613$	−10.8407	−0.437851	−0.218925	−	0.975742i	$-0.570255\pi$
$613$	−10.8407	−0.437851	−0.218925	+	0.975742i	$0.570255\pi$
$614$	5.72648	0.231102
$615$	−0.0966762	−0.00389836
$616$	35.5216	1.43121
$617$	6.28760	0.253129	0.126565	−	0.991958i	$-0.459605\pi$
$617$	6.28760	0.253129	0.126565	+	0.991958i	$0.459605\pi$
$618$	−0.948815	−0.0381669
$619$	7.98242	0.320841	0.160420	−	0.987049i	$-0.448715\pi$
$619$	7.98242	0.320841	0.160420	+	0.987049i	$0.448715\pi$
$620$	−0.169609	−0.00681165
$621$	0.881993	0.0353931
$622$	−24.5650	−0.984966
$623$	20.3089	0.813659
$624$	−0.235341	−0.00942117
$625$	24.9713	0.998852
$626$	−26.3262	−1.05221
$627$	1.05883	0.0422856
$628$	10.0127	0.399551
$629$	−9.42586	−0.375834
$630$	0.184858	0.00736494
$631$	−24.2886	−0.966914	−0.483457	−	0.875368i	$-0.660619\pi$
$631$	−24.2886	−0.966914	−0.483457	+	0.875368i	$0.660619\pi$
$632$	2.90482	0.115547
$633$	1.68314	0.0668988
$634$	6.76055	0.268496
$635$	0.279528	0.0110927
$636$	−13.0233	−0.516406
$637$	−8.64102	−0.342370
$638$	24.1665	0.956761
$639$	0.125443	0.00496246
$640$	−0.243590	−0.00962875
$641$	−17.9359	−0.708425	−0.354213	−	0.935165i	$-0.615251\pi$
$641$	−17.9359	−0.708425	−0.354213	+	0.935165i	$0.615251\pi$
$642$	−8.20679	−0.323896
$643$	−7.20786	−0.284250	−0.142125	−	0.989849i	$-0.545394\pi$
$643$	−7.20786	−0.284250	−0.142125	+	0.989849i	$0.545394\pi$
$644$	4.64394	0.182997
$645$	0.00844323	0.000332452 0
$646$	0.365947	0.0143980
$647$	27.9826	1.10011	0.550056	−	0.835128i	$-0.314607\pi$
$647$	27.9826	1.10011	0.550056	+	0.835128i	$0.314607\pi$
$648$	2.90482	0.114112
$649$	20.2205	0.793726
$650$	−2.84687	−0.111664
$651$	15.4610	0.605963
$652$	−1.58314	−0.0620006
$653$	−1.76814	−0.0691926	−0.0345963	−	0.999401i	$-0.511015\pi$
$653$	−1.76814	−0.0691926	−0.0345963	+	0.999401i	$0.511015\pi$
$654$	−6.96317	−0.272281
$655$	0.423491	0.0165472
$656$	0.842371	0.0328891
$657$	2.94358	0.114840
$658$	−18.0352	−0.703085
$659$	19.0136	0.740666	0.370333	−	0.928899i	$-0.379244\pi$
$659$	19.0136	0.740666	0.370333	+	0.928899i	$0.379244\pi$
$660$	−0.134148	−0.00522172
$661$	14.2092	0.552673	0.276336	−	0.961061i	$-0.410880\pi$
$661$	14.2092	0.552673	0.276336	+	0.961061i	$0.410880\pi$
$662$	24.9209	0.968579
$663$	0.617504	0.0239819
$664$	13.0812	0.507649
$665$	0.0795076	0.00308317
$666$	8.69451	0.336905
$667$	8.65809	0.335243
$668$	3.89894	0.150855
$669$	6.56815	0.253939
$670$	0.0240160	0.000927819 0
$671$	−40.3921	−1.55932
$672$	25.0082	0.964712
$673$	−26.7487	−1.03109	−0.515544	−	0.856863i	$-0.672410\pi$
$673$	−26.7487	−1.03109	−0.515544	+	0.856863i	$0.672410\pi$
$674$	20.2897	0.781531
$675$	4.99809	0.192376
$676$	14.5009	0.557726
$677$	8.50054	0.326702	0.163351	−	0.986568i	$-0.447770\pi$
$677$	8.50054	0.326702	0.163351	+	0.986568i	$0.447770\pi$
$678$	9.71850	0.373237
$679$	−72.0060	−2.76334
$680$	−0.127055	−0.00487234
$681$	5.17041	0.198130
$682$	8.30713	0.318097
$683$	−16.5151	−0.631934	−0.315967	−	0.948770i	$-0.602329\pi$
$683$	−16.5151	−0.631934	−0.315967	+	0.948770i	$0.602329\pi$
$684$	0.455905	0.0174319
$685$	0.354037	0.0135271
$686$	−29.5568	−1.12848
$687$	−13.7771	−0.525630
$688$	−0.0735686	−0.00280478
$689$	6.99809	0.266606
$690$	0.0355846	0.00135468
$691$	−0.417730	−0.0158912	−0.00794559	−	0.999968i	$-0.502529\pi$
$691$	−0.417730	−0.0158912	−0.00794559	+	0.999968i	$0.502529\pi$
$692$	−10.4964	−0.399014
$693$	12.2285	0.464523
$694$	22.4420	0.851885
$695$	0.837456	0.0317665
$696$	28.5152	1.08086
$697$	−2.21028	−0.0837202
$698$	−0.896976	−0.0339510
$699$	1.69782	0.0642176
$700$	26.3164	0.994665
$701$	−2.68913	−0.101567	−0.0507835	−	0.998710i	$-0.516172\pi$
$701$	−2.68913	−0.101567	−0.0507835	+	0.998710i	$0.516172\pi$
$702$	−0.569593	−0.0214979
$703$	3.73951	0.141038
$704$	15.4712	0.583091
$705$	0.186650	0.00702964
$706$	−15.2306	−0.573210
$707$	−69.0721	−2.59772
$708$	8.70644	0.327208
$709$	27.3171	1.02592	0.512958	−	0.858414i	$-0.328550\pi$
$709$	27.3171	1.02592	0.512958	+	0.858414i	$0.328550\pi$
$710$	0.00506110	0.000189940 0
$711$	1.00000	0.0375029
$712$	12.8755	0.482529
$713$	2.97618	0.111459
$714$	4.22636	0.158167
$715$	0.0720851	0.00269583
$716$	−29.0866	−1.08702
$717$	5.38341	0.201047
$718$	−26.2605	−0.980034
$719$	22.5472	0.840867	0.420434	−	0.907323i	$-0.361878\pi$
$719$	22.5472	0.840867	0.420434	+	0.907323i	$0.361878\pi$
$720$	0.0166698	0.000621246 0
$721$	−4.71302	−0.175522
$722$	17.3806	0.646840
$723$	20.4705	0.761307
$724$	−25.6975	−0.955041
$725$	49.0638	1.82218
$726$	−3.57616	−0.132724
$727$	−1.80461	−0.0669294	−0.0334647	−	0.999440i	$-0.510654\pi$
$727$	−1.80461	−0.0669294	−0.0334647	+	0.999440i	$0.510654\pi$
$728$	−8.21866	−0.304604
$729$	1.00000	0.0370370
$730$	0.118761	0.00439553
$731$	0.193035	0.00713964
$732$	−17.3918	−0.642818
$733$	−33.9868	−1.25533	−0.627666	−	0.778483i	$-0.715989\pi$
$733$	−33.9868	−1.25533	−0.627666	+	0.778483i	$0.715989\pi$
$734$	−5.75675	−0.212485
$735$	0.612066	0.0225764
$736$	4.81399	0.177446
$737$	1.58868	0.0585197
$738$	2.03878	0.0750486
$739$	−17.2967	−0.636270	−0.318135	−	0.948045i	$-0.603056\pi$
$739$	−17.2967	−0.636270	−0.318135	+	0.948045i	$0.603056\pi$
$740$	−0.473777	−0.0174164
$741$	−0.244982	−0.00899963
$742$	47.8967	1.75834
$743$	−1.05831	−0.0388258	−0.0194129	−	0.999812i	$-0.506180\pi$
$743$	−1.05831	−0.0388258	−0.0194129	+	0.999812i	$0.506180\pi$
$744$	9.80197	0.359358
$745$	−0.360588	−0.0132109
$746$	27.2609	0.998091
$747$	4.50328	0.164766
$748$	−3.06699	−0.112140
$749$	−40.7654	−1.48953
$750$	0.403380	0.0147294
$751$	19.1762	0.699751	0.349876	−	0.936796i	$-0.386224\pi$
$751$	19.1762	0.699751	0.349876	+	0.936796i	$0.386224\pi$
$752$	−1.62634	−0.0593066
$753$	13.3933	0.488080
$754$	−5.59141	−0.203627
$755$	−0.446593	−0.0162532
$756$	5.26529	0.191497
$757$	43.4154	1.57796	0.788979	−	0.614420i	$-0.210610\pi$
$757$	43.4154	1.57796	0.788979	+	0.614420i	$0.210610\pi$
$758$	−16.3112	−0.592451
$759$	2.35395	0.0854430
$760$	0.0504064	0.00182843
$761$	−22.9128	−0.830589	−0.415295	−	0.909687i	$-0.636321\pi$
$761$	−22.9128	−0.830589	−0.415295	+	0.909687i	$0.636321\pi$
$762$	−5.89489	−0.213549
$763$	−34.5879	−1.25217
$764$	−16.4104	−0.593709
$765$	−0.0437394	−0.00158140
$766$	−28.5882	−1.03293
$767$	−4.67844	−0.168929
$768$	16.7307	0.603716
$769$	−22.2981	−0.804089	−0.402044	−	0.915620i	$-0.631700\pi$
$769$	−22.2981	−0.804089	−0.402044	+	0.915620i	$0.631700\pi$
$770$	0.493369	0.0177798
$771$	8.44374	0.304094
$772$	7.50059	0.269952
$773$	3.08668	0.111020	0.0555101	−	0.998458i	$-0.482321\pi$
$773$	3.08668	0.111020	0.0555101	+	0.998458i	$0.482321\pi$
$774$	−0.178057	−0.00640013
$775$	16.8655	0.605826
$776$	−45.6505	−1.63876
$777$	43.1880	1.54936
$778$	13.9215	0.499109
$779$	0.876880	0.0314175
$780$	0.0310380	0.00111134
$781$	0.334796	0.0119799
$782$	0.813559	0.0290928
$783$	9.81651	0.350813
$784$	−5.33313	−0.190469
$785$	0.381105	0.0136022
$786$	−8.93090	−0.318555
$787$	40.4449	1.44171	0.720853	−	0.693088i	$-0.243750\pi$
$787$	40.4449	1.44171	0.720853	+	0.693088i	$0.243750\pi$
$788$	−18.6123	−0.663035
$789$	3.05237	0.108667
$790$	0.0403457	0.00143544
$791$	48.2744	1.71644
$792$	7.75267	0.275479
$793$	9.34553	0.331869
$794$	14.4581	0.513098
$795$	−0.495693	−0.0175804
$796$	−26.4938	−0.939049
$797$	39.3022	1.39215	0.696077	−	0.717967i	$-0.254927\pi$
$797$	39.3022	1.39215	0.696077	+	0.717967i	$0.254927\pi$
$798$	−1.67672	−0.0593552
$799$	4.26731	0.150967
$800$	27.2800	0.964494
$801$	4.43246	0.156613
$802$	−5.90751	−0.208601
$803$	7.85611	0.277236
$804$	0.684043	0.0241243
$805$	0.176758	0.00622991
$806$	−1.92202	−0.0677004
$807$	7.24560	0.255057
$808$	−43.7905	−1.54054
$809$	−27.3294	−0.960851	−0.480425	−	0.877036i	$-0.659518\pi$
$809$	−27.3294	−0.960851	−0.480425	+	0.877036i	$0.659518\pi$
$810$	0.0403457	0.00141760
$811$	−7.13799	−0.250649	−0.125324	−	0.992116i	$-0.539997\pi$
$811$	−7.13799	−0.250649	−0.125324	+	0.992116i	$0.539997\pi$
$812$	51.6867	1.81385
$813$	−10.6365	−0.373037
$814$	23.2048	0.813327
$815$	−0.0602578	−0.00211074
$816$	0.381116	0.0133417
$817$	−0.0765824	−0.00267928
$818$	4.21201	0.147270
$819$	−2.82932	−0.0988644
$820$	−0.111096	−0.00387965
$821$	−21.2430	−0.741386	−0.370693	−	0.928756i	$-0.620880\pi$
$821$	−21.2430	−0.741386	−0.370693	+	0.928756i	$0.620880\pi$
$822$	−7.46621	−0.260414
$823$	−34.1603	−1.19075	−0.595376	−	0.803447i	$-0.702997\pi$
$823$	−34.1603	−1.19075	−0.595376	+	0.803447i	$0.702997\pi$
$824$	−2.98797	−0.104091
$825$	13.3394	0.464418
$826$	−32.0204	−1.11413
$827$	−16.1376	−0.561161	−0.280580	−	0.959831i	$-0.590527\pi$
$827$	−16.1376	−0.561161	−0.280580	+	0.959831i	$0.590527\pi$
$828$	1.01355	0.0352233
$829$	6.18596	0.214847	0.107424	−	0.994213i	$-0.465740\pi$
$829$	6.18596	0.214847	0.107424	+	0.994213i	$0.465740\pi$
$830$	0.181688	0.00630649
$831$	25.6094	0.888379
$832$	−3.57957	−0.124099
$833$	13.9934	0.484844
$834$	−17.6609	−0.611547
$835$	0.148402	0.00513566
$836$	1.21676	0.0420827
$837$	3.37439	0.116636
$838$	−29.7967	−1.02931
$839$	−47.4504	−1.63817	−0.819085	−	0.573672i	$-0.805519\pi$
$839$	−47.4504	−1.63817	−0.819085	+	0.573672i	$0.805519\pi$
$840$	0.582149	0.0200860
$841$	67.3639	2.32289
$842$	−23.6861	−0.816275
$843$	26.7540	0.921456
$844$	1.93420	0.0665778
$845$	0.551934	0.0189871
$846$	−3.93622	−0.135330
$847$	−17.7638	−0.610370
$848$	4.31913	0.148320
$849$	7.03565	0.241463
$850$	4.61029	0.158132
$851$	8.31354	0.284984
$852$	0.144154	0.00493865
$853$	35.6279	1.21988	0.609938	−	0.792449i	$-0.291194\pi$
$853$	35.6279	1.21988	0.609938	+	0.792449i	$0.291194\pi$
$854$	63.9631	2.18877
$855$	0.0173527	0.000593450 0
$856$	−25.8445	−0.883347
$857$	2.39717	0.0818859	0.0409429	−	0.999161i	$-0.486964\pi$
$857$	2.39717	0.0818859	0.0409429	+	0.999161i	$0.486964\pi$
$858$	−1.52019	−0.0518983
$859$	−53.6350	−1.83000	−0.915001	−	0.403452i	$-0.867810\pi$
$859$	−53.6350	−1.83000	−0.915001	+	0.403452i	$0.867810\pi$
$860$	0.00970261	0.000330856 0
$861$	10.1272	0.345133
$862$	−33.5552	−1.14289
$863$	33.9880	1.15696	0.578482	−	0.815695i	$-0.303645\pi$
$863$	33.9880	1.15696	0.578482	+	0.815695i	$0.303645\pi$
$864$	5.45809	0.185688
$865$	−0.399516	−0.0135840
$866$	−19.1962	−0.652312
$867$	−1.00000	−0.0339618
$868$	17.7671	0.603055
$869$	2.66890	0.0905362
$870$	0.396054	0.0134275
$871$	−0.367573	−0.0124547
$872$	−21.9281	−0.742580
$873$	−15.7154	−0.531887
$874$	−0.322762	−0.0109176
$875$	2.00370	0.0677373
$876$	3.38264	0.114289
$877$	−29.4577	−0.994716	−0.497358	−	0.867545i	$-0.665696\pi$
$877$	−29.4577	−0.994716	−0.497358	+	0.867545i	$0.665696\pi$
$878$	7.29425	0.246169
$879$	−21.2246	−0.715886
$880$	0.0444900	0.00149976
$881$	−24.9731	−0.841365	−0.420682	−	0.907208i	$-0.638209\pi$
$881$	−24.9731	−0.841365	−0.420682	+	0.907208i	$0.638209\pi$
$882$	−12.9077	−0.434625
$883$	37.3525	1.25701	0.628506	−	0.777805i	$-0.283667\pi$
$883$	37.3525	1.25701	0.628506	+	0.777805i	$0.283667\pi$
$884$	0.709611	0.0238668
$885$	0.331386	0.0111394
$886$	−10.4065	−0.349614
$887$	−4.83794	−0.162442	−0.0812211	−	0.996696i	$-0.525882\pi$
$887$	−4.83794	−0.162442	−0.0812211	+	0.996696i	$0.525882\pi$
$888$	27.3804	0.918826
$889$	−29.2815	−0.982071
$890$	0.178831	0.00599442
$891$	2.66890	0.0894115
$892$	7.54784	0.252721
$893$	−1.69297	−0.0566530
$894$	7.60436	0.254328
$895$	−1.10710	−0.0370062
$896$	25.5169	0.852461
$897$	−0.544634	−0.0181848
$898$	−30.0641	−1.00325
$899$	33.1247	1.10477
$900$	5.74360	0.191453
$901$	−11.3329	−0.377553
$902$	5.44130	0.181176
$903$	−0.884458	−0.0294329
$904$	30.6051	1.01791
$905$	−0.978102	−0.0325132
$906$	9.41808	0.312895
$907$	23.7056	0.787131	0.393566	−	0.919297i	$-0.371241\pi$
$907$	23.7056	0.787131	0.393566	+	0.919297i	$0.371241\pi$
$908$	5.94162	0.197180
$909$	−15.0751	−0.500010
$910$	−0.114151	−0.00378407
$911$	25.5367	0.846069	0.423035	−	0.906114i	$-0.360965\pi$
$911$	25.5367	0.846069	0.423035	+	0.906114i	$0.360965\pi$
$912$	−0.151200	−0.00500672
$913$	12.0188	0.397764
$914$	−7.45192	−0.246488
$915$	−0.661968	−0.0218840
$916$	−15.8321	−0.523107
$917$	−44.3622	−1.46497
$918$	0.922410	0.0304441
$919$	−4.54665	−0.149980	−0.0749900	−	0.997184i	$-0.523892\pi$
$919$	−4.54665	−0.149980	−0.0749900	+	0.997184i	$0.523892\pi$
$920$	0.112062	0.00369456
$921$	6.20816	0.204566
$922$	15.1970	0.500485
$923$	−0.0774618	−0.00254969
$924$	14.0525	0.462294
$925$	47.1113	1.54901
$926$	28.6648	0.941983
$927$	−1.02863	−0.0337845
$928$	53.5794	1.75883
$929$	33.5542	1.10088	0.550439	−	0.834875i	$-0.314460\pi$
$929$	33.5542	1.10088	0.550439	+	0.834875i	$0.314460\pi$
$930$	0.136142	0.00446427
$931$	−5.55161	−0.181947
$932$	1.95107	0.0639094
$933$	−26.6313	−0.871870
$934$	22.7302	0.743755
$935$	−0.116736	−0.00381768
$936$	−1.79374	−0.0586301
$937$	32.8800	1.07414	0.537071	−	0.843537i	$-0.319531\pi$
$937$	32.8800	1.07414	0.537071	+	0.843537i	$0.319531\pi$
$938$	−2.51576	−0.0821425
$939$	−28.5407	−0.931389
$940$	0.214490	0.00699591
$941$	−22.2581	−0.725593	−0.362796	−	0.931868i	$-0.618178\pi$
$941$	−22.2581	−0.725593	−0.362796	+	0.931868i	$0.618178\pi$
$942$	−8.03704	−0.261861
$943$	1.94945	0.0634827
$944$	−2.88747	−0.0939792
$945$	0.200408	0.00651927
$946$	−0.475217	−0.0154506
$947$	42.9213	1.39476	0.697378	−	0.716703i	$-0.254350\pi$
$947$	42.9213	1.39476	0.697378	+	0.716703i	$0.254350\pi$
$948$	1.14916	0.0373229
$949$	−1.81767	−0.0590041
$950$	−1.82903	−0.0593417
$951$	7.32922	0.237666
$952$	13.3095	0.431362
$953$	−29.6373	−0.960046	−0.480023	−	0.877256i	$-0.659372\pi$
$953$	−29.6373	−0.960046	−0.480023	+	0.877256i	$0.659372\pi$
$954$	10.4536	0.338446
$955$	−0.624616	−0.0202121
$956$	6.18639	0.200082
$957$	26.1993	0.846903
$958$	12.8742	0.415948
$959$	−37.0867	−1.19759
$960$	0.253550	0.00818329
$961$	−19.6135	−0.632694
$962$	−5.36890	−0.173100
$963$	−8.89712	−0.286706
$964$	23.5239	0.757654
$965$	0.285489	0.00919020
$966$	−3.72761	−0.119934
$967$	3.72847	0.119900	0.0599498	−	0.998201i	$-0.480906\pi$
$967$	3.72847	0.119900	0.0599498	+	0.998201i	$0.480906\pi$
$968$	−11.2619	−0.361971
$969$	0.396729	0.0127448
$970$	−0.634051	−0.0203581
$971$	−7.15940	−0.229756	−0.114878	−	0.993380i	$-0.536648\pi$
$971$	−7.15940	−0.229756	−0.114878	+	0.993380i	$0.536648\pi$
$972$	1.14916	0.0368593
$973$	−87.7265	−2.81238
$974$	−15.6934	−0.502850
$975$	−3.08634	−0.0988420
$976$	5.76794	0.184627
$977$	11.6669	0.373256	0.186628	−	0.982431i	$-0.440244\pi$
$977$	11.6669	0.373256	0.186628	+	0.982431i	$0.440244\pi$
$978$	1.27076	0.0406345
$979$	11.8298	0.378082
$980$	0.703361	0.0224680
$981$	−7.54888	−0.241017
$982$	0.340926	0.0108794
$983$	−45.7785	−1.46011	−0.730054	−	0.683389i	$-0.760505\pi$
$983$	−45.7785	−1.46011	−0.730054	+	0.683389i	$0.760505\pi$
$984$	6.42045	0.204676
$985$	−0.708423	−0.0225722
$986$	9.05485	0.288365
$987$	−19.5522	−0.622355
$988$	−0.281523	−0.00895644
$989$	−0.170255	−0.00541380
$990$	0.107679	0.00342225
$991$	−41.7822	−1.32726	−0.663628	−	0.748062i	$-0.730984\pi$
$991$	−41.7822	−1.32726	−0.663628	+	0.748062i	$0.730984\pi$
$992$	18.4177	0.584762
$993$	27.0172	0.857364
$994$	−0.530168	−0.0168159
$995$	−1.00841	−0.0319688
$996$	5.17499	0.163976
$997$	−31.4891	−0.997268	−0.498634	−	0.866813i	$-0.666165\pi$
$997$	−31.4891	−0.997268	−0.498634	+	0.866813i	$0.666165\pi$
$998$	−7.81870	−0.247497
$999$	9.42586	0.298221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.f.1.8	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.f.1.8	✓	22	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-0.922410 q^{2} -1.00000 q^{3} -1.14916 q^{4} -0.0437394 q^{5} +0.922410 q^{6} +4.58186 q^{7} +2.90482 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.922410 q^{2} -1.00000 q^{3} -1.14916 q^{4} -0.0437394 q^{5} +0.922410 q^{6} +4.58186 q^{7} +2.90482 q^{8} +1.00000 q^{9} +0.0403457 q^{10} +2.66890 q^{11} +1.14916 q^{12} -0.617504 q^{13} -4.22636 q^{14} +0.0437394 q^{15} -0.381116 q^{16} +1.00000 q^{17} -0.922410 q^{18} -0.396729 q^{19} +0.0502636 q^{20} -4.58186 q^{21} -2.46182 q^{22} -0.881993 q^{23} -2.90482 q^{24} -4.99809 q^{25} +0.569593 q^{26} -1.00000 q^{27} -5.26529 q^{28} -9.81651 q^{29} -0.0403457 q^{30} -3.37439 q^{31} -5.45809 q^{32} -2.66890 q^{33} -0.922410 q^{34} -0.200408 q^{35} -1.14916 q^{36} -9.42586 q^{37} +0.365947 q^{38} +0.617504 q^{39} -0.127055 q^{40} -2.21028 q^{41} +4.22636 q^{42} +0.193035 q^{43} -3.06699 q^{44} -0.0437394 q^{45} +0.813559 q^{46} +4.26731 q^{47} +0.381116 q^{48} +13.9934 q^{49} +4.61029 q^{50} -1.00000 q^{51} +0.709611 q^{52} -11.3329 q^{53} +0.922410 q^{54} -0.116736 q^{55} +13.3095 q^{56} +0.396729 q^{57} +9.05485 q^{58} +7.57636 q^{59} -0.0502636 q^{60} -15.1343 q^{61} +3.11257 q^{62} +4.58186 q^{63} +5.79683 q^{64} +0.0270093 q^{65} +2.46182 q^{66} +0.595255 q^{67} -1.14916 q^{68} +0.881993 q^{69} +0.184858 q^{70} +0.125443 q^{71} +2.90482 q^{72} +2.94358 q^{73} +8.69451 q^{74} +4.99809 q^{75} +0.455905 q^{76} +12.2285 q^{77} -0.569593 q^{78} +1.00000 q^{79} +0.0166698 q^{80} +1.00000 q^{81} +2.03878 q^{82} +4.50328 q^{83} +5.26529 q^{84} -0.0437394 q^{85} -0.178057 q^{86} +9.81651 q^{87} +7.75267 q^{88} +4.43246 q^{89} +0.0403457 q^{90} -2.82932 q^{91} +1.01355 q^{92} +3.37439 q^{93} -3.93622 q^{94} +0.0173527 q^{95} +5.45809 q^{96} -15.7154 q^{97} -12.9077 q^{98} +2.66890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * q^99

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