LMFDB - Embedded newform 429.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(1,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, 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("429.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 3 $ x^3 - x^2 - 5*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.08613$ of defining polynomial
Character	$\chi$	$=$	429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.08613 q^{2} -1.00000 q^{3} +2.35194 q^{4} +2.43807 q^{5} -2.08613 q^{6} +1.35194 q^{7} +0.734191 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.08613 q^{2} -1.00000 q^{3} +2.35194 q^{4} +2.43807 q^{5} -2.08613 q^{6} +1.35194 q^{7} +0.734191 q^{8} +1.00000 q^{9} +5.08613 q^{10} +1.00000 q^{11} -2.35194 q^{12} -1.00000 q^{13} +2.82032 q^{14} -2.43807 q^{15} -3.17226 q^{16} -3.08613 q^{17} +2.08613 q^{18} +2.64806 q^{19} +5.73419 q^{20} -1.35194 q^{21} +2.08613 q^{22} +1.52420 q^{23} -0.734191 q^{24} +0.944182 q^{25} -2.08613 q^{26} -1.00000 q^{27} +3.17968 q^{28} +7.79001 q^{29} -5.08613 q^{30} +8.43807 q^{31} -8.08613 q^{32} -1.00000 q^{33} -6.43807 q^{34} +3.29612 q^{35} +2.35194 q^{36} -11.0484 q^{37} +5.52420 q^{38} +1.00000 q^{39} +1.79001 q^{40} -8.99258 q^{41} -2.82032 q^{42} -6.38225 q^{43} +2.35194 q^{44} +2.43807 q^{45} +3.17968 q^{46} -6.87614 q^{47} +3.17226 q^{48} -5.17226 q^{49} +1.96969 q^{50} +3.08613 q^{51} -2.35194 q^{52} -8.17226 q^{53} -2.08613 q^{54} +2.43807 q^{55} +0.992582 q^{56} -2.64806 q^{57} +16.2510 q^{58} -0.876139 q^{59} -5.73419 q^{60} -2.17226 q^{61} +17.6029 q^{62} +1.35194 q^{63} -10.5242 q^{64} -2.43807 q^{65} -2.08613 q^{66} +1.38967 q^{67} -7.25839 q^{68} -1.52420 q^{69} +6.87614 q^{70} +0.703878 q^{71} +0.734191 q^{72} +10.2887 q^{73} -23.0484 q^{74} -0.944182 q^{75} +6.22808 q^{76} +1.35194 q^{77} +2.08613 q^{78} +9.08613 q^{79} -7.73419 q^{80} +1.00000 q^{81} -18.7597 q^{82} +4.53162 q^{83} -3.17968 q^{84} -7.52420 q^{85} -13.3142 q^{86} -7.79001 q^{87} +0.734191 q^{88} -11.1419 q^{89} +5.08613 q^{90} -1.35194 q^{91} +3.58482 q^{92} -8.43807 q^{93} -14.3445 q^{94} +6.45616 q^{95} +8.08613 q^{96} +7.04840 q^{97} -10.7900 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 3 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 - 3 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - q^{2} - 3 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9} + 8 q^{10} + 3 q^{11} - 5 q^{12} - 3 q^{13} - 4 q^{14} + 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} + 10 q^{19} + 12 q^{20} - 2 q^{21} - q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} + q^{26} - 3 q^{27} + 22 q^{28} + 12 q^{29} - 8 q^{30} + 16 q^{31} - 17 q^{32} - 3 q^{33} - 10 q^{34} + 14 q^{35} + 5 q^{36} + 3 q^{39} - 6 q^{40} + 4 q^{42} - 16 q^{43} + 5 q^{44} - 2 q^{45} + 22 q^{46} - 2 q^{47} - 5 q^{48} - q^{49} + 7 q^{50} + 2 q^{51} - 5 q^{52} - 10 q^{53} + q^{54} - 2 q^{55} - 24 q^{56} - 10 q^{57} + 16 q^{59} - 12 q^{60} + 8 q^{61} + 2 q^{62} + 2 q^{63} - 15 q^{64} + 2 q^{65} + q^{66} + 28 q^{67} + 12 q^{69} + 2 q^{70} - 2 q^{71} - 3 q^{72} + 8 q^{73} - 36 q^{74} - 9 q^{75} - 2 q^{76} + 2 q^{77} - q^{78} + 20 q^{79} - 18 q^{80} + 3 q^{81} - 46 q^{82} + 24 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 12 q^{87} - 3 q^{88} - 20 q^{89} + 8 q^{90} - 2 q^{91} - 8 q^{92} - 16 q^{93} - 14 q^{94} - 22 q^{95} + 17 q^{96} - 12 q^{97} - 21 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - q^2 - 3 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9 + 8 * q^10 + 3 * q^11 - 5 * q^12 - 3 * q^13 - 4 * q^14 + 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 + 10 * q^19 + 12 * q^20 - 2 * q^21 - q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 + q^26 - 3 * q^27 + 22 * q^28 + 12 * q^29 - 8 * q^30 + 16 * q^31 - 17 * q^32 - 3 * q^33 - 10 * q^34 + 14 * q^35 + 5 * q^36 + 3 * q^39 - 6 * q^40 + 4 * q^42 - 16 * q^43 + 5 * q^44 - 2 * q^45 + 22 * q^46 - 2 * q^47 - 5 * q^48 - q^49 + 7 * q^50 + 2 * q^51 - 5 * q^52 - 10 * q^53 + q^54 - 2 * q^55 - 24 * q^56 - 10 * q^57 + 16 * q^59 - 12 * q^60 + 8 * q^61 + 2 * q^62 + 2 * q^63 - 15 * q^64 + 2 * q^65 + q^66 + 28 * q^67 + 12 * q^69 + 2 * q^70 - 2 * q^71 - 3 * q^72 + 8 * q^73 - 36 * q^74 - 9 * q^75 - 2 * q^76 + 2 * q^77 - q^78 + 20 * q^79 - 18 * q^80 + 3 * q^81 - 46 * q^82 + 24 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 12 * q^87 - 3 * q^88 - 20 * q^89 + 8 * q^90 - 2 * q^91 - 8 * q^92 - 16 * q^93 - 14 * q^94 - 22 * q^95 + 17 * q^96 - 12 * q^97 - 21 * q^98 + 3 * 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 $

$2$	2.08613	1.47512	0.737558	−	0.675283i	$-0.235979\pi$
$2$	2.08613	1.47512	0.737558	+	0.675283i	$0.235979\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.35194	1.17597
$5$	2.43807	1.09034	0.545169	−	0.838326i	$-0.316466\pi$
$5$	2.43807	1.09034	0.545169	+	0.838326i	$0.316466\pi$
$6$	−2.08613	−0.851659
$7$	1.35194	0.510985	0.255492	−	0.966811i	$-0.417762\pi$
$7$	1.35194	0.510985	0.255492	+	0.966811i	$0.417762\pi$
$8$	0.734191	0.259576
$9$	1.00000	0.333333
$10$	5.08613	1.60838
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.35194	−0.678946
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.82032	0.753763
$15$	−2.43807	−0.629507
$16$	−3.17226	−0.793065
$17$	−3.08613	−0.748497	−0.374248	−	0.927329i	$-0.622099\pi$
$17$	−3.08613	−0.748497	−0.374248	+	0.927329i	$0.622099\pi$
$18$	2.08613	0.491706
$19$	2.64806	0.607507	0.303753	−	0.952751i	$-0.401760\pi$
$19$	2.64806	0.607507	0.303753	+	0.952751i	$0.401760\pi$
$20$	5.73419	1.28220
$21$	−1.35194	−0.295017
$22$	2.08613	0.444764
$23$	1.52420	0.317818	0.158909	−	0.987293i	$-0.449202\pi$
$23$	1.52420	0.317818	0.158909	+	0.987293i	$0.449202\pi$
$24$	−0.734191	−0.149866
$25$	0.944182	0.188836
$26$	−2.08613	−0.409124
$27$	−1.00000	−0.192450
$28$	3.17968	0.600903
$29$	7.79001	1.44657	0.723284	−	0.690551i	$-0.242632\pi$
$29$	7.79001	1.44657	0.723284	+	0.690551i	$0.242632\pi$
$30$	−5.08613	−0.928596
$31$	8.43807	1.51552	0.757761	−	0.652532i	$-0.226293\pi$
$31$	8.43807	1.51552	0.757761	+	0.652532i	$0.226293\pi$
$32$	−8.08613	−1.42944
$33$	−1.00000	−0.174078
$34$	−6.43807	−1.10412
$35$	3.29612	0.557146
$36$	2.35194	0.391990
$37$	−11.0484	−1.81635	−0.908173	−	0.418595i	$-0.862523\pi$
$37$	−11.0484	−1.81635	−0.908173	+	0.418595i	$0.862523\pi$
$38$	5.52420	0.896144
$39$	1.00000	0.160128
$40$	1.79001	0.283025
$41$	−8.99258	−1.40441	−0.702203	−	0.711977i	$-0.747800\pi$
$41$	−8.99258	−1.40441	−0.702203	+	0.711977i	$0.747800\pi$
$42$	−2.82032	−0.435185
$43$	−6.38225	−0.973284	−0.486642	−	0.873601i	$-0.661778\pi$
$43$	−6.38225	−0.973284	−0.486642	+	0.873601i	$0.661778\pi$
$44$	2.35194	0.354568
$45$	2.43807	0.363446
$46$	3.17968	0.468818
$47$	−6.87614	−1.00299	−0.501494	−	0.865161i	$-0.667216\pi$
$47$	−6.87614	−1.00299	−0.501494	+	0.865161i	$0.667216\pi$
$48$	3.17226	0.457876
$49$	−5.17226	−0.738894
$50$	1.96969	0.278556
$51$	3.08613	0.432145
$52$	−2.35194	−0.326155
$53$	−8.17226	−1.12255	−0.561273	−	0.827631i	$-0.689688\pi$
$53$	−8.17226	−1.12255	−0.561273	+	0.827631i	$0.689688\pi$
$54$	−2.08613	−0.283886
$55$	2.43807	0.328749
$56$	0.992582	0.132639
$57$	−2.64806	−0.350744
$58$	16.2510	2.13386
$59$	−0.876139	−0.114064	−0.0570318	−	0.998372i	$-0.518164\pi$
$59$	−0.876139	−0.114064	−0.0570318	+	0.998372i	$0.518164\pi$
$60$	−5.73419	−0.740281
$61$	−2.17226	−0.278129	−0.139065	−	0.990283i	$-0.544410\pi$
$61$	−2.17226	−0.278129	−0.139065	+	0.990283i	$0.544410\pi$
$62$	17.6029	2.23557
$63$	1.35194	0.170328
$64$	−10.5242	−1.31552
$65$	−2.43807	−0.302405
$66$	−2.08613	−0.256785
$67$	1.38967	0.169775	0.0848876	−	0.996391i	$-0.472947\pi$
$67$	1.38967	0.169775	0.0848876	+	0.996391i	$0.472947\pi$
$68$	−7.25839	−0.880209
$69$	−1.52420	−0.183492
$70$	6.87614	0.821856
$71$	0.703878	0.0835350	0.0417675	−	0.999127i	$-0.486701\pi$
$71$	0.703878	0.0835350	0.0417675	+	0.999127i	$0.486701\pi$
$72$	0.734191	0.0865252
$73$	10.2887	1.20420	0.602101	−	0.798420i	$-0.294331\pi$
$73$	10.2887	1.20420	0.602101	+	0.798420i	$0.294331\pi$
$74$	−23.0484	−2.67932
$75$	−0.944182	−0.109025
$76$	6.22808	0.714410
$77$	1.35194	0.154068
$78$	2.08613	0.236208
$79$	9.08613	1.02227	0.511135	−	0.859501i	$-0.329225\pi$
$79$	9.08613	1.02227	0.511135	+	0.859501i	$0.329225\pi$
$80$	−7.73419	−0.864709
$81$	1.00000	0.111111
$82$	−18.7597	−2.07166
$83$	4.53162	0.497410	0.248705	−	0.968579i	$-0.419995\pi$
$83$	4.53162	0.497410	0.248705	+	0.968579i	$0.419995\pi$
$84$	−3.17968	−0.346931
$85$	−7.52420	−0.816114
$86$	−13.3142	−1.43571
$87$	−7.79001	−0.835177
$88$	0.734191	0.0782650
$89$	−11.1419	−1.18104	−0.590522	−	0.807022i	$-0.701078\pi$
$89$	−11.1419	−1.18104	−0.590522	+	0.807022i	$0.701078\pi$
$90$	5.08613	0.536125
$91$	−1.35194	−0.141722
$92$	3.58482	0.373744
$93$	−8.43807	−0.874987
$94$	−14.3445	−1.47952
$95$	6.45616	0.662388
$96$	8.08613	0.825287
$97$	7.04840	0.715657	0.357828	−	0.933787i	$-0.383517\pi$
$97$	7.04840	0.715657	0.357828	+	0.933787i	$0.383517\pi$
$98$	−10.7900	−1.08996
$99$	1.00000	0.100504
$100$	2.22066	0.222066
$101$	12.7268	1.26636	0.633181	−	0.774004i	$-0.281749\pi$
$101$	12.7268	1.26636	0.633181	+	0.774004i	$0.281749\pi$
$102$	6.43807	0.637464
$103$	12.3445	1.21634	0.608171	−	0.793806i	$-0.291904\pi$
$103$	12.3445	1.21634	0.608171	+	0.793806i	$0.291904\pi$
$104$	−0.734191	−0.0719934
$105$	−3.29612	−0.321669
$106$	−17.0484	−1.65589
$107$	−8.87614	−0.858089	−0.429044	−	0.903283i	$-0.641150\pi$
$107$	−8.87614	−0.858089	−0.429044	+	0.903283i	$0.641150\pi$
$108$	−2.35194	−0.226315
$109$	2.05582	0.196912	0.0984558	−	0.995141i	$-0.468610\pi$
$109$	2.05582	0.196912	0.0984558	+	0.995141i	$0.468610\pi$
$110$	5.08613	0.484943
$111$	11.0484	1.04867
$112$	−4.28870	−0.405244
$113$	2.87614	0.270564	0.135282	−	0.990807i	$-0.456806\pi$
$113$	2.87614	0.270564	0.135282	+	0.990807i	$0.456806\pi$
$114$	−5.52420	−0.517389
$115$	3.71610	0.346529
$116$	18.3216	1.70112
$117$	−1.00000	−0.0924500
$118$	−1.82774	−0.168257
$119$	−4.17226	−0.382470
$120$	−1.79001	−0.163405
$121$	1.00000	0.0909091
$122$	−4.53162	−0.410273
$123$	8.99258	0.810834
$124$	19.8458	1.78221
$125$	−9.88836	−0.884442
$126$	2.82032	0.251254
$127$	10.5545	0.936562	0.468281	−	0.883580i	$-0.344874\pi$
$127$	10.5545	0.936562	0.468281	+	0.883580i	$0.344874\pi$
$128$	−5.78259	−0.511114
$129$	6.38225	0.561926
$130$	−5.08613	−0.446083
$131$	0.951601	0.0831417	0.0415709	−	0.999136i	$-0.486764\pi$
$131$	0.951601	0.0831417	0.0415709	+	0.999136i	$0.486764\pi$
$132$	−2.35194	−0.204710
$133$	3.58002	0.310427
$134$	2.89903	0.250438
$135$	−2.43807	−0.209836
$136$	−2.26581	−0.194292
$137$	−18.0787	−1.54457	−0.772284	−	0.635277i	$-0.780886\pi$
$137$	−18.0787	−1.54457	−0.772284	+	0.635277i	$0.780886\pi$
$138$	−3.17968	−0.270672
$139$	14.6661	1.24397	0.621983	−	0.783031i	$-0.286327\pi$
$139$	14.6661	1.24397	0.621983	+	0.783031i	$0.286327\pi$
$140$	7.75228	0.655187
$141$	6.87614	0.579075
$142$	1.46838	0.123224
$143$	−1.00000	−0.0836242
$144$	−3.17226	−0.264355
$145$	18.9926	1.57725
$146$	21.4636	1.77634
$147$	5.17226	0.426601
$148$	−25.9852	−2.13597
$149$	−0.648061	−0.0530912	−0.0265456	−	0.999648i	$-0.508451\pi$
$149$	−0.648061	−0.0530912	−0.0265456	+	0.999648i	$0.508451\pi$
$150$	−1.96969	−0.160824
$151$	−4.28870	−0.349010	−0.174505	−	0.984656i	$-0.555832\pi$
$151$	−4.28870	−0.349010	−0.174505	+	0.984656i	$0.555832\pi$
$152$	1.94418	0.157694
$153$	−3.08613	−0.249499
$154$	2.82032	0.227268
$155$	20.5726	1.65243
$156$	2.35194	0.188306
$157$	14.9926	1.19654	0.598269	−	0.801295i	$-0.295855\pi$
$157$	14.9926	1.19654	0.598269	+	0.801295i	$0.295855\pi$
$158$	18.9549	1.50797
$159$	8.17226	0.648102
$160$	−19.7145	−1.55857
$161$	2.06063	0.162400
$162$	2.08613	0.163902
$163$	23.1271	1.81146	0.905728	−	0.423860i	$-0.139325\pi$
$163$	23.1271	1.81146	0.905728	+	0.423860i	$0.139325\pi$
$164$	−21.1500	−1.65154
$165$	−2.43807	−0.189803
$166$	9.45355	0.733737
$167$	0.951601	0.0736371	0.0368185	−	0.999322i	$-0.488278\pi$
$167$	0.951601	0.0736371	0.0368185	+	0.999322i	$0.488278\pi$
$168$	−0.992582	−0.0765793
$169$	1.00000	0.0769231
$170$	−15.6965	−1.20386
$171$	2.64806	0.202502
$172$	−15.0107	−1.14455
$173$	7.08613	0.538749	0.269374	−	0.963036i	$-0.413183\pi$
$173$	7.08613	0.538749	0.269374	+	0.963036i	$0.413183\pi$
$174$	−16.2510	−1.23198
$175$	1.27648	0.0964926
$176$	−3.17226	−0.239118
$177$	0.876139	0.0658546
$178$	−23.2436	−1.74218
$179$	−12.0410	−0.899985	−0.449993	−	0.893032i	$-0.648573\pi$
$179$	−12.0410	−0.899985	−0.449993	+	0.893032i	$0.648573\pi$
$180$	5.73419	0.427401
$181$	20.6332	1.53366	0.766828	−	0.641853i	$-0.221834\pi$
$181$	20.6332	1.53366	0.766828	+	0.641853i	$0.221834\pi$
$182$	−2.82032	−0.209056
$183$	2.17226	0.160578
$184$	1.11905	0.0824977
$185$	−26.9368	−1.98043
$186$	−17.6029	−1.29071
$187$	−3.08613	−0.225680
$188$	−16.1723	−1.17948
$189$	−1.35194	−0.0983391
$190$	13.4684	0.977099
$191$	−12.8761	−0.931685	−0.465842	−	0.884868i	$-0.654249\pi$
$191$	−12.8761	−0.931685	−0.465842	+	0.884868i	$0.654249\pi$
$192$	10.5242	0.759519
$193$	−15.6965	−1.12986	−0.564928	−	0.825140i	$-0.691096\pi$
$193$	−15.6965	−1.12986	−0.564928	+	0.825140i	$0.691096\pi$
$194$	14.7039	1.05568
$195$	2.43807	0.174594
$196$	−12.1648	−0.868917
$197$	−8.22808	−0.586226	−0.293113	−	0.956078i	$-0.594691\pi$
$197$	−8.22808	−0.586226	−0.293113	+	0.956078i	$0.594691\pi$
$198$	2.08613	0.148255
$199$	−2.93676	−0.208182	−0.104091	−	0.994568i	$-0.533193\pi$
$199$	−2.93676	−0.208182	−0.104091	+	0.994568i	$0.533193\pi$
$200$	0.693210	0.0490174
$201$	−1.38967	−0.0980198
$202$	26.5497	1.86803
$203$	10.5316	0.739175
$204$	7.25839	0.508189
$205$	−21.9245	−1.53128
$206$	25.7523	1.79425
$207$	1.52420	0.105939
$208$	3.17226	0.219957
$209$	2.64806	0.183170
$210$	−6.87614	−0.474499
$211$	−7.02551	−0.483656	−0.241828	−	0.970319i	$-0.577747\pi$
$211$	−7.02551	−0.483656	−0.241828	+	0.970319i	$0.577747\pi$
$212$	−19.2207	−1.32008
$213$	−0.703878	−0.0482290
$214$	−18.5168	−1.26578
$215$	−15.5604	−1.06121
$216$	−0.734191	−0.0499554
$217$	11.4078	0.774409
$218$	4.28870	0.290468
$219$	−10.2887	−0.695246
$220$	5.73419	0.386599
$221$	3.08613	0.207596
$222$	23.0484	1.54691
$223$	17.3142	1.15945	0.579723	−	0.814814i	$-0.303161\pi$
$223$	17.3142	1.15945	0.579723	+	0.814814i	$0.303161\pi$
$224$	−10.9320	−0.730422
$225$	0.944182	0.0629455
$226$	6.00000	0.399114
$227$	−17.2765	−1.14668	−0.573340	−	0.819318i	$-0.694353\pi$
$227$	−17.2765	−1.14668	−0.573340	+	0.819318i	$0.694353\pi$
$228$	−6.22808	−0.412465
$229$	−8.87614	−0.586552	−0.293276	−	0.956028i	$-0.594745\pi$
$229$	−8.87614	−0.586552	−0.293276	+	0.956028i	$0.594745\pi$
$230$	7.75228	0.511170
$231$	−1.35194	−0.0889511
$232$	5.71935	0.375494
$233$	7.60291	0.498083	0.249042	−	0.968493i	$-0.419884\pi$
$233$	7.60291	0.498083	0.249042	+	0.968493i	$0.419884\pi$
$234$	−2.08613	−0.136375
$235$	−16.7645	−1.09360
$236$	−2.06063	−0.134135
$237$	−9.08613	−0.590208
$238$	−8.70388	−0.564189
$239$	13.0532	0.844342	0.422171	−	0.906516i	$-0.361268\pi$
$239$	13.0532	0.844342	0.422171	+	0.906516i	$0.361268\pi$
$240$	7.73419	0.499240
$241$	15.1090	0.973258	0.486629	−	0.873609i	$-0.338226\pi$
$241$	15.1090	0.973258	0.486629	+	0.873609i	$0.338226\pi$
$242$	2.08613	0.134102
$243$	−1.00000	−0.0641500
$244$	−5.10902	−0.327072
$245$	−12.6103	−0.805644
$246$	18.7597	1.19607
$247$	−2.64806	−0.168492
$248$	6.19515	0.393393
$249$	−4.53162	−0.287180
$250$	−20.6284	−1.30466
$251$	15.8129	0.998102	0.499051	−	0.866573i	$-0.333682\pi$
$251$	15.8129	0.998102	0.499051	+	0.866573i	$0.333682\pi$
$252$	3.17968	0.200301
$253$	1.52420	0.0958256
$254$	22.0181	1.38154
$255$	7.52420	0.471184
$256$	8.98516	0.561573
$257$	−7.29612	−0.455120	−0.227560	−	0.973764i	$-0.573075\pi$
$257$	−7.29612	−0.455120	−0.227560	+	0.973764i	$0.573075\pi$
$258$	13.3142	0.828906
$259$	−14.9368	−0.928125
$260$	−5.73419	−0.355619
$261$	7.79001	0.482189
$262$	1.98516	0.122644
$263$	−2.77934	−0.171381	−0.0856907	−	0.996322i	$-0.527310\pi$
$263$	−2.77934	−0.171381	−0.0856907	+	0.996322i	$0.527310\pi$
$264$	−0.734191	−0.0451863
$265$	−19.9245	−1.22395
$266$	7.46838	0.457916
$267$	11.1419	0.681876
$268$	3.26842	0.199651
$269$	12.1723	0.742156	0.371078	−	0.928602i	$-0.378988\pi$
$269$	12.1723	0.742156	0.371078	+	0.928602i	$0.378988\pi$
$270$	−5.08613	−0.309532
$271$	−27.5242	−1.67198	−0.835988	−	0.548748i	$-0.815105\pi$
$271$	−27.5242	−1.67198	−0.835988	+	0.548748i	$0.815105\pi$
$272$	9.79001	0.593606
$273$	1.35194	0.0818231
$274$	−37.7145	−2.27842
$275$	0.944182	0.0569363
$276$	−3.58482	−0.215781
$277$	−10.2329	−0.614835	−0.307417	−	0.951575i	$-0.599465\pi$
$277$	−10.2329	−0.614835	−0.307417	+	0.951575i	$0.599465\pi$
$278$	30.5955	1.83500
$279$	8.43807	0.505174
$280$	2.41998	0.144622
$281$	30.1016	1.79571	0.897856	−	0.440290i	$-0.145124\pi$
$281$	30.1016	1.79571	0.897856	+	0.440290i	$0.145124\pi$
$282$	14.3445	0.854204
$283$	12.0377	0.715569	0.357784	−	0.933804i	$-0.383532\pi$
$283$	12.0377	0.715569	0.357784	+	0.933804i	$0.383532\pi$
$284$	1.65548	0.0982346
$285$	−6.45616	−0.382430
$286$	−2.08613	−0.123355
$287$	−12.1574	−0.717630
$288$	−8.08613	−0.476480
$289$	−7.47580	−0.439753
$290$	39.6210	2.32663
$291$	−7.04840	−0.413184
$292$	24.1984	1.41610
$293$	24.6842	1.44207	0.721034	−	0.692900i	$-0.243667\pi$
$293$	24.6842	1.44207	0.721034	+	0.692900i	$0.243667\pi$
$294$	10.7900	0.629286
$295$	−2.13609	−0.124368
$296$	−8.11164	−0.471479
$297$	−1.00000	−0.0580259
$298$	−1.35194	−0.0783157
$299$	−1.52420	−0.0881467
$300$	−2.22066	−0.128210
$301$	−8.62842	−0.497334
$302$	−8.94679	−0.514830
$303$	−12.7268	−0.731134
$304$	−8.40034	−0.481792
$305$	−5.29612	−0.303255
$306$	−6.43807	−0.368040
$307$	28.9777	1.65385	0.826924	−	0.562314i	$-0.190089\pi$
$307$	28.9777	1.65385	0.826924	+	0.562314i	$0.190089\pi$
$308$	3.17968	0.181179
$309$	−12.3445	−0.702255
$310$	42.9171	2.43753
$311$	27.1648	1.54038	0.770188	−	0.637816i	$-0.220162\pi$
$311$	27.1648	1.54038	0.770188	+	0.637816i	$0.220162\pi$
$312$	0.734191	0.0415654
$313$	−2.11644	−0.119628	−0.0598142	−	0.998210i	$-0.519051\pi$
$313$	−2.11644	−0.119628	−0.0598142	+	0.998210i	$0.519051\pi$
$314$	31.2765	1.76503
$315$	3.29612	0.185715
$316$	21.3700	1.20216
$317$	13.5471	0.760881	0.380440	−	0.924805i	$-0.375772\pi$
$317$	13.5471	0.760881	0.380440	+	0.924805i	$0.375772\pi$
$318$	17.0484	0.956027
$319$	7.79001	0.436157
$320$	−25.6587	−1.43437
$321$	8.87614	0.495418
$322$	4.29873	0.239559
$323$	−8.17226	−0.454717
$324$	2.35194	0.130663
$325$	−0.944182	−0.0523738
$326$	48.2462	2.67211
$327$	−2.05582	−0.113687
$328$	−6.60227	−0.364550
$329$	−9.29612	−0.512512
$330$	−5.08613	−0.279982
$331$	−14.3626	−0.789440	−0.394720	−	0.918801i	$-0.629158\pi$
$331$	−14.3626	−0.789440	−0.394720	+	0.918801i	$0.629158\pi$
$332$	10.6581	0.584939
$333$	−11.0484	−0.605449
$334$	1.98516	0.108623
$335$	3.38811	0.185112
$336$	4.28870	0.233968
$337$	−20.4051	−1.11154	−0.555770	−	0.831336i	$-0.687576\pi$
$337$	−20.4051	−1.11154	−0.555770	+	0.831336i	$0.687576\pi$
$338$	2.08613	0.113471
$339$	−2.87614	−0.156210
$340$	−17.6965	−0.959725
$341$	8.43807	0.456947
$342$	5.52420	0.298715
$343$	−16.4562	−0.888549
$344$	−4.68579	−0.252641
$345$	−3.71610	−0.200068
$346$	14.7826	0.794717
$347$	−22.6890	−1.21801	−0.609006	−	0.793166i	$-0.708431\pi$
$347$	−22.6890	−1.21801	−0.609006	+	0.793166i	$0.708431\pi$
$348$	−18.3216	−0.982142
$349$	−13.9245	−0.745363	−0.372682	−	0.927959i	$-0.621562\pi$
$349$	−13.9245	−0.745363	−0.372682	+	0.927959i	$0.621562\pi$
$350$	2.66290	0.142338
$351$	1.00000	0.0533761
$352$	−8.08613	−0.430992
$353$	−26.7826	−1.42549	−0.712747	−	0.701421i	$-0.752549\pi$
$353$	−26.7826	−1.42549	−0.712747	+	0.701421i	$0.752549\pi$
$354$	1.82774	0.0971433
$355$	1.71610	0.0910814
$356$	−26.2052	−1.38887
$357$	4.17226	0.220819
$358$	−25.1191	−1.32758
$359$	17.5094	0.924109	0.462054	−	0.886852i	$-0.347112\pi$
$359$	17.5094	0.924109	0.462054	+	0.886852i	$0.347112\pi$
$360$	1.79001	0.0943417
$361$	−11.9878	−0.630935
$362$	43.0436	2.26232
$363$	−1.00000	−0.0524864
$364$	−3.17968	−0.166660
$365$	25.0846	1.31299
$366$	4.53162	0.236871
$367$	−36.6136	−1.91121	−0.955607	−	0.294645i	$-0.904798\pi$
$367$	−36.6136	−1.91121	−0.955607	+	0.294645i	$0.904798\pi$
$368$	−4.83516	−0.252050
$369$	−8.99258	−0.468135
$370$	−56.1936	−2.92137
$371$	−11.0484	−0.573604
$372$	−19.8458	−1.02896
$373$	20.4051	1.05654	0.528269	−	0.849077i	$-0.322841\pi$
$373$	20.4051	1.05654	0.528269	+	0.849077i	$0.322841\pi$
$374$	−6.43807	−0.332905
$375$	9.88836	0.510633
$376$	−5.04840	−0.260351
$377$	−7.79001	−0.401206
$378$	−2.82032	−0.145062
$379$	9.78520	0.502632	0.251316	−	0.967905i	$-0.419137\pi$
$379$	9.78520	0.502632	0.251316	+	0.967905i	$0.419137\pi$
$380$	15.1845	0.778948
$381$	−10.5545	−0.540724
$382$	−26.8613	−1.37434
$383$	−19.5800	−1.00049	−0.500246	−	0.865883i	$-0.666757\pi$
$383$	−19.5800	−1.00049	−0.500246	+	0.865883i	$0.666757\pi$
$384$	5.78259	0.295092
$385$	3.29612	0.167986
$386$	−32.7449	−1.66667
$387$	−6.38225	−0.324428
$388$	16.5774	0.841590
$389$	−20.6284	−1.04590	−0.522951	−	0.852363i	$-0.675169\pi$
$389$	−20.6284	−1.04590	−0.522951	+	0.852363i	$0.675169\pi$
$390$	5.08613	0.257546
$391$	−4.70388	−0.237885
$392$	−3.79743	−0.191799
$393$	−0.951601	−0.0480019
$394$	−17.1648	−0.864752
$395$	22.1526	1.11462
$396$	2.35194	0.118189
$397$	29.8639	1.49883	0.749413	−	0.662102i	$-0.230336\pi$
$397$	29.8639	1.49883	0.749413	+	0.662102i	$0.230336\pi$
$398$	−6.12647	−0.307092
$399$	−3.58002	−0.179225
$400$	−2.99519	−0.149760
$401$	−39.0155	−1.94834	−0.974170	−	0.225816i	$-0.927495\pi$
$401$	−39.0155	−1.94834	−0.974170	+	0.225816i	$0.927495\pi$
$402$	−2.89903	−0.144591
$403$	−8.43807	−0.420330
$404$	29.9326	1.48920
$405$	2.43807	0.121149
$406$	21.9703	1.09037
$407$	−11.0484	−0.547649
$408$	2.26581	0.112174
$409$	7.69646	0.380565	0.190283	−	0.981729i	$-0.439060\pi$
$409$	7.69646	0.380565	0.190283	+	0.981729i	$0.439060\pi$
$410$	−45.7374	−2.25881
$411$	18.0787	0.891757
$412$	29.0336	1.43038
$413$	−1.18449	−0.0582848
$414$	3.17968	0.156273
$415$	11.0484	0.542345
$416$	8.08613	0.396455
$417$	−14.6661	−0.718204
$418$	5.52420	0.270197
$419$	14.7449	0.720334	0.360167	−	0.932888i	$-0.382720\pi$
$419$	14.7449	0.720334	0.360167	+	0.932888i	$0.382720\pi$
$420$	−7.75228	−0.378272
$421$	14.8007	0.721341	0.360670	−	0.932693i	$-0.382548\pi$
$421$	14.8007	0.721341	0.360670	+	0.932693i	$0.382548\pi$
$422$	−14.6561	−0.713449
$423$	−6.87614	−0.334329
$424$	−6.00000	−0.291386
$425$	−2.91387	−0.141343
$426$	−1.46838	−0.0711433
$427$	−2.93676	−0.142120
$428$	−20.8761	−1.00909
$429$	1.00000	0.0482805
$430$	−32.4610	−1.56541
$431$	31.7374	1.52874	0.764369	−	0.644779i	$-0.223050\pi$
$431$	31.7374	1.52874	0.764369	+	0.644779i	$0.223050\pi$
$432$	3.17226	0.152625
$433$	−33.2813	−1.59940	−0.799698	−	0.600402i	$-0.795007\pi$
$433$	−33.2813	−1.59940	−0.799698	+	0.600402i	$0.795007\pi$
$434$	23.7981	1.14234
$435$	−18.9926	−0.910625
$436$	4.83516	0.231562
$437$	4.03617	0.193076
$438$	−21.4636	−1.02557
$439$	15.3700	0.733571	0.366786	−	0.930305i	$-0.380458\pi$
$439$	15.3700	0.733571	0.366786	+	0.930305i	$0.380458\pi$
$440$	1.79001	0.0853353
$441$	−5.17226	−0.246298
$442$	6.43807	0.306228
$443$	−13.7523	−0.653390	−0.326695	−	0.945130i	$-0.605935\pi$
$443$	−13.7523	−0.653390	−0.326695	+	0.945130i	$0.605935\pi$
$444$	25.9852	1.23320
$445$	−27.1648	−1.28774
$446$	36.1197	1.71032
$447$	0.648061	0.0306522
$448$	−14.2281	−0.672214
$449$	1.26320	0.0596140	0.0298070	−	0.999556i	$-0.490511\pi$
$449$	1.26320	0.0596140	0.0298070	+	0.999556i	$0.490511\pi$
$450$	1.96969	0.0928520
$451$	−8.99258	−0.423444
$452$	6.76450	0.318175
$453$	4.28870	0.201501
$454$	−36.0410	−1.69149
$455$	−3.29612	−0.154525
$456$	−1.94418	−0.0910447
$457$	30.4562	1.42468	0.712339	−	0.701835i	$-0.247636\pi$
$457$	30.4562	1.42468	0.712339	+	0.701835i	$0.247636\pi$
$458$	−18.5168	−0.865232
$459$	3.08613	0.144048
$460$	8.74005	0.407507
$461$	−12.9926	−0.605125	−0.302562	−	0.953130i	$-0.597842\pi$
$461$	−12.9926	−0.605125	−0.302562	+	0.953130i	$0.597842\pi$
$462$	−2.82032	−0.131213
$463$	−18.7071	−0.869394	−0.434697	−	0.900577i	$-0.643145\pi$
$463$	−18.7071	−0.869394	−0.434697	+	0.900577i	$0.643145\pi$
$464$	−24.7119	−1.14722
$465$	−20.5726	−0.954031
$466$	15.8607	0.734731
$467$	−1.63583	−0.0756974	−0.0378487	−	0.999283i	$-0.512050\pi$
$467$	−1.63583	−0.0756974	−0.0378487	+	0.999283i	$0.512050\pi$
$468$	−2.35194	−0.108718
$469$	1.87875	0.0867526
$470$	−34.9729	−1.61318
$471$	−14.9926	−0.690822
$472$	−0.643253	−0.0296081
$473$	−6.38225	−0.293456
$474$	−18.9549	−0.870625
$475$	2.50025	0.114719
$476$	−9.81290	−0.449774
$477$	−8.17226	−0.374182
$478$	27.2307	1.24550
$479$	20.4758	0.935563	0.467782	−	0.883844i	$-0.345053\pi$
$479$	20.4758	0.935563	0.467782	+	0.883844i	$0.345053\pi$
$480$	19.7145	0.899842
$481$	11.0484	0.503764
$482$	31.5194	1.43567
$483$	−2.06063	−0.0937617
$484$	2.35194	0.106906
$485$	17.1845	0.780307
$486$	−2.08613	−0.0946288
$487$	16.7220	0.757745	0.378872	−	0.925449i	$-0.376312\pi$
$487$	16.7220	0.757745	0.378872	+	0.925449i	$0.376312\pi$
$488$	−1.59485	−0.0721956
$489$	−23.1271	−1.04584
$490$	−26.3068	−1.18842
$491$	−23.5194	−1.06142	−0.530708	−	0.847555i	$-0.678074\pi$
$491$	−23.5194	−1.06142	−0.530708	+	0.847555i	$0.678074\pi$
$492$	21.1500	0.953516
$493$	−24.0410	−1.08275
$494$	−5.52420	−0.248545
$495$	2.43807	0.109583
$496$	−26.7678	−1.20191
$497$	0.951601	0.0426851
$498$	−9.45355	−0.423623
$499$	−39.4110	−1.76428	−0.882139	−	0.470988i	$-0.843897\pi$
$499$	−39.4110	−1.76428	−0.882139	+	0.470988i	$0.843897\pi$
$500$	−23.2568	−1.04008
$501$	−0.951601	−0.0425144
$502$	32.9878	1.47232
$503$	−31.3175	−1.39638	−0.698188	−	0.715914i	$-0.746010\pi$
$503$	−31.3175	−1.39638	−0.698188	+	0.715914i	$0.746010\pi$
$504$	0.992582	0.0442131
$505$	31.0288	1.38076
$506$	3.17968	0.141354
$507$	−1.00000	−0.0444116
$508$	24.8236	1.10137
$509$	−15.6736	−0.694719	−0.347359	−	0.937732i	$-0.612922\pi$
$509$	−15.6736	−0.694719	−0.347359	+	0.937732i	$0.612922\pi$
$510$	15.6965	0.695051
$511$	13.9097	0.615329
$512$	30.3094	1.33950
$513$	−2.64806	−0.116915
$514$	−15.2207	−0.671355
$515$	30.0968	1.32622
$516$	15.0107	0.660808
$517$	−6.87614	−0.302412
$518$	−31.1600	−1.36909
$519$	−7.08613	−0.311047
$520$	−1.79001	−0.0784971
$521$	−7.52901	−0.329852	−0.164926	−	0.986306i	$-0.552738\pi$
$521$	−7.52901	−0.329852	−0.164926	+	0.986306i	$0.552738\pi$
$522$	16.2510	0.711286
$523$	33.1681	1.45034	0.725170	−	0.688570i	$-0.241761\pi$
$523$	33.1681	1.45034	0.725170	+	0.688570i	$0.241761\pi$
$524$	2.23811	0.0977722
$525$	−1.27648	−0.0557100
$526$	−5.79807	−0.252808
$527$	−26.0410	−1.13436
$528$	3.17226	0.138055
$529$	−20.6768	−0.898992
$530$	−41.5652	−1.80548
$531$	−0.876139	−0.0380212
$532$	8.41998	0.365053
$533$	8.99258	0.389512
$534$	23.2436	1.00585
$535$	−21.6406	−0.935607
$536$	1.02028	0.0440695
$537$	12.0410	0.519607
$538$	25.3929	1.09477
$539$	−5.17226	−0.222785
$540$	−5.73419	−0.246760
$541$	29.2813	1.25890	0.629450	−	0.777041i	$-0.283280\pi$
$541$	29.2813	1.25890	0.629450	+	0.777041i	$0.283280\pi$
$542$	−57.4191	−2.46636
$543$	−20.6332	−0.885456
$544$	24.9549	1.06993
$545$	5.01223	0.214700
$546$	2.82032	0.120699
$547$	−13.1371	−0.561704	−0.280852	−	0.959751i	$-0.590617\pi$
$547$	−13.1371	−0.561704	−0.280852	+	0.959751i	$0.590617\pi$
$548$	−42.5200	−1.81637
$549$	−2.17226	−0.0927098
$550$	1.96969	0.0839878
$551$	20.6284	0.878800
$552$	−1.11905	−0.0476301
$553$	12.2839	0.522364
$554$	−21.3471	−0.906953
$555$	26.9368	1.14340
$556$	34.4939	1.46287
$557$	−13.2159	−0.559974	−0.279987	−	0.960004i	$-0.590330\pi$
$557$	−13.2159	−0.559974	−0.279987	+	0.960004i	$0.590330\pi$
$558$	17.6029	0.745191
$559$	6.38225	0.269940
$560$	−10.4562	−0.441853
$561$	3.08613	0.130297
$562$	62.7959	2.64888
$563$	7.76711	0.327345	0.163672	−	0.986515i	$-0.447666\pi$
$563$	7.76711	0.327345	0.163672	+	0.986515i	$0.447666\pi$
$564$	16.1723	0.680975
$565$	7.01223	0.295007
$566$	25.1123	1.05555
$567$	1.35194	0.0567761
$568$	0.516781	0.0216837
$569$	39.7752	1.66746	0.833731	−	0.552171i	$-0.186200\pi$
$569$	39.7752	1.66746	0.833731	+	0.552171i	$0.186200\pi$
$570$	−13.4684	−0.564128
$571$	−2.91387	−0.121942	−0.0609708	−	0.998140i	$-0.519420\pi$
$571$	−2.91387	−0.121942	−0.0609708	+	0.998140i	$0.519420\pi$
$572$	−2.35194	−0.0983395
$573$	12.8761	0.537908
$574$	−25.3620	−1.05859
$575$	1.43912	0.0600156
$576$	−10.5242	−0.438508
$577$	37.7374	1.57103	0.785515	−	0.618842i	$-0.212398\pi$
$577$	37.7374	1.57103	0.785515	+	0.618842i	$0.212398\pi$
$578$	−15.5955	−0.648687
$579$	15.6965	0.652323
$580$	44.6694	1.85480
$581$	6.12647	0.254169
$582$	−14.7039	−0.609495
$583$	−8.17226	−0.338460
$584$	7.55387	0.312581
$585$	−2.43807	−0.100802
$586$	51.4945	2.12722
$587$	14.2839	0.589559	0.294780	−	0.955565i	$-0.404754\pi$
$587$	14.2839	0.589559	0.294780	+	0.955565i	$0.404754\pi$
$588$	12.1648	0.501670
$589$	22.3445	0.920690
$590$	−4.45616	−0.183457
$591$	8.22808	0.338458
$592$	35.0484	1.44048
$593$	1.52420	0.0625914	0.0312957	−	0.999510i	$-0.490037\pi$
$593$	1.52420	0.0625914	0.0312957	+	0.999510i	$0.490037\pi$
$594$	−2.08613	−0.0855950
$595$	−10.1723	−0.417022
$596$	−1.52420	−0.0624336
$597$	2.93676	0.120194
$598$	−3.17968	−0.130027
$599$	−28.8761	−1.17985	−0.589924	−	0.807459i	$-0.700842\pi$
$599$	−28.8761	−1.17985	−0.589924	+	0.807459i	$0.700842\pi$
$600$	−0.693210	−0.0283002
$601$	28.8155	1.17541	0.587705	−	0.809076i	$-0.300032\pi$
$601$	28.8155	1.17541	0.587705	+	0.809076i	$0.300032\pi$
$602$	−18.0000	−0.733625
$603$	1.38967	0.0565917
$604$	−10.0868	−0.410425
$605$	2.43807	0.0991216
$606$	−26.5497	−1.07851
$607$	−41.4158	−1.68102	−0.840508	−	0.541799i	$-0.817743\pi$
$607$	−41.4158	−1.68102	−0.840508	+	0.541799i	$0.817743\pi$
$608$	−21.4126	−0.868394
$609$	−10.5316	−0.426763
$610$	−11.0484	−0.447337
$611$	6.87614	0.278179
$612$	−7.25839	−0.293403
$613$	40.7300	1.64507	0.822535	−	0.568714i	$-0.192559\pi$
$613$	40.7300	1.64507	0.822535	+	0.568714i	$0.192559\pi$
$614$	60.4513	2.43962
$615$	21.9245	0.884083
$616$	0.992582	0.0399923
$617$	−40.4594	−1.62883	−0.814417	−	0.580280i	$-0.802943\pi$
$617$	−40.4594	−1.62883	−0.814417	+	0.580280i	$0.802943\pi$
$618$	−25.7523	−1.03591
$619$	−14.8942	−0.598649	−0.299325	−	0.954151i	$-0.596761\pi$
$619$	−14.8942	−0.598649	−0.299325	+	0.954151i	$0.596761\pi$
$620$	48.3855	1.94321
$621$	−1.52420	−0.0611640
$622$	56.6694	2.27224
$623$	−15.0632	−0.603496
$624$	−3.17226	−0.126992
$625$	−28.8294	−1.15318
$626$	−4.41518	−0.176466
$627$	−2.64806	−0.105753
$628$	35.2616	1.40709
$629$	34.0968	1.35953
$630$	6.87614	0.273952
$631$	−19.0813	−0.759615	−0.379808	−	0.925065i	$-0.624010\pi$
$631$	−19.0813	−0.759615	−0.379808	+	0.925065i	$0.624010\pi$
$632$	6.67095	0.265356
$633$	7.02551	0.279239
$634$	28.2610	1.12239
$635$	25.7326	1.02117
$636$	19.2207	0.762149
$637$	5.17226	0.204932
$638$	16.2510	0.643382
$639$	0.703878	0.0278450
$640$	−14.0984	−0.557286
$641$	−31.8639	−1.25855	−0.629274	−	0.777183i	$-0.716648\pi$
$641$	−31.8639	−1.25855	−0.629274	+	0.777183i	$0.716648\pi$
$642$	18.5168	0.730799
$643$	−3.14195	−0.123906	−0.0619532	−	0.998079i	$-0.519733\pi$
$643$	−3.14195	−0.123906	−0.0619532	+	0.998079i	$0.519733\pi$
$644$	4.84647	0.190977
$645$	15.5604	0.612689
$646$	−17.0484	−0.670760
$647$	33.2207	1.30604	0.653019	−	0.757341i	$-0.273502\pi$
$647$	33.2207	1.30604	0.653019	+	0.757341i	$0.273502\pi$
$648$	0.734191	0.0288417
$649$	−0.876139	−0.0343915
$650$	−1.96969	−0.0772575
$651$	−11.4078	−0.447105
$652$	54.3936	2.13022
$653$	−15.8639	−0.620803	−0.310401	−	0.950606i	$-0.600463\pi$
$653$	−15.8639	−0.620803	−0.310401	+	0.950606i	$0.600463\pi$
$654$	−4.28870	−0.167702
$655$	2.32007	0.0906526
$656$	28.5268	1.11378
$657$	10.2887	0.401401
$658$	−19.3929	−0.756015
$659$	43.3323	1.68799	0.843993	−	0.536354i	$-0.180199\pi$
$659$	43.3323	1.68799	0.843993	+	0.536354i	$0.180199\pi$
$660$	−5.73419	−0.223203
$661$	−8.51678	−0.331264	−0.165632	−	0.986188i	$-0.552966\pi$
$661$	−8.51678	−0.331264	−0.165632	+	0.986188i	$0.552966\pi$
$662$	−29.9623	−1.16452
$663$	−3.08613	−0.119855
$664$	3.32707	0.129115
$665$	8.72833	0.338470
$666$	−23.0484	−0.893107
$667$	11.8735	0.459745
$668$	2.23811	0.0865950
$669$	−17.3142	−0.669406
$670$	7.06804	0.273062
$671$	−2.17226	−0.0838592
$672$	10.9320	0.421709
$673$	−41.0336	−1.58173	−0.790864	−	0.611992i	$-0.790368\pi$
$673$	−41.0336	−1.58173	−0.790864	+	0.611992i	$0.790368\pi$
$674$	−42.5678	−1.63965
$675$	−0.944182	−0.0363416
$676$	2.35194	0.0904592
$677$	−40.4791	−1.55574	−0.777868	−	0.628428i	$-0.783699\pi$
$677$	−40.4791	−1.55574	−0.777868	+	0.628428i	$0.783699\pi$
$678$	−6.00000	−0.230429
$679$	9.52901	0.365690
$680$	−5.52420	−0.211843
$681$	17.2765	0.662036
$682$	17.6029	0.674050
$683$	41.2717	1.57922	0.789608	−	0.613611i	$-0.210284\pi$
$683$	41.2717	1.57922	0.789608	+	0.613611i	$0.210284\pi$
$684$	6.22808	0.238137
$685$	−44.0772	−1.68410
$686$	−34.3297	−1.31071
$687$	8.87614	0.338646
$688$	20.2462	0.771878
$689$	8.17226	0.311338
$690$	−7.75228	−0.295124
$691$	42.5200	1.61754	0.808769	−	0.588126i	$-0.200134\pi$
$691$	42.5200	1.61754	0.808769	+	0.588126i	$0.200134\pi$
$692$	16.6661	0.633552
$693$	1.35194	0.0513559
$694$	−47.3323	−1.79671
$695$	35.7571	1.35634
$696$	−5.71935	−0.216792
$697$	27.7523	1.05119
$698$	−29.0484	−1.09950
$699$	−7.60291	−0.287569
$700$	3.00220	0.113472
$701$	−17.1468	−0.647624	−0.323812	−	0.946121i	$-0.604965\pi$
$701$	−17.1468	−0.647624	−0.323812	+	0.946121i	$0.604965\pi$
$702$	2.08613	0.0787359
$703$	−29.2568	−1.10344
$704$	−10.5242	−0.396646
$705$	16.7645	0.631388
$706$	−55.8720	−2.10277
$707$	17.2058	0.647092
$708$	2.06063	0.0774430
$709$	1.10902	0.0416503	0.0208251	−	0.999783i	$-0.493371\pi$
$709$	1.10902	0.0416503	0.0208251	+	0.999783i	$0.493371\pi$
$710$	3.58002	0.134356
$711$	9.08613	0.340757
$712$	−8.18032	−0.306570
$713$	12.8613	0.481660
$714$	8.70388	0.325734
$715$	−2.43807	−0.0911786
$716$	−28.3197	−1.05836
$717$	−13.0532	−0.487481
$718$	36.5268	1.36317
$719$	22.0968	0.824072	0.412036	−	0.911168i	$-0.364818\pi$
$719$	22.0968	0.824072	0.412036	+	0.911168i	$0.364818\pi$
$720$	−7.73419	−0.288236
$721$	16.6890	0.621532
$722$	−25.0081	−0.930704
$723$	−15.1090	−0.561911
$724$	48.5281	1.80353
$725$	7.35519	0.273165
$726$	−2.08613	−0.0774236
$727$	7.92454	0.293905	0.146952	−	0.989144i	$-0.453054\pi$
$727$	7.92454	0.293905	0.146952	+	0.989144i	$0.453054\pi$
$728$	−0.992582	−0.0367875
$729$	1.00000	0.0370370
$730$	52.3297	1.93681
$731$	19.6965	0.728500
$732$	5.10902	0.188835
$733$	−12.4971	−0.461592	−0.230796	−	0.973002i	$-0.574133\pi$
$733$	−12.4971	−0.461592	−0.230796	+	0.973002i	$0.574133\pi$
$734$	−76.3807	−2.81926
$735$	12.6103	0.465139
$736$	−12.3249	−0.454301
$737$	1.38967	0.0511892
$738$	−18.7597	−0.690554
$739$	−16.2887	−0.599190	−0.299595	−	0.954067i	$-0.596851\pi$
$739$	−16.2887	−0.599190	−0.299595	+	0.954067i	$0.596851\pi$
$740$	−63.3536	−2.32893
$741$	2.64806	0.0972789
$742$	−23.0484	−0.846133
$743$	43.2058	1.58507	0.792534	−	0.609828i	$-0.208761\pi$
$743$	43.2058	1.58507	0.792534	+	0.609828i	$0.208761\pi$
$744$	−6.19515	−0.227125
$745$	−1.58002	−0.0578874
$746$	42.5678	1.55852
$747$	4.53162	0.165803
$748$	−7.25839	−0.265393
$749$	−12.0000	−0.438470
$750$	20.6284	0.753243
$751$	−18.7401	−0.683834	−0.341917	−	0.939730i	$-0.611076\pi$
$751$	−18.7401	−0.683834	−0.341917	+	0.939730i	$0.611076\pi$
$752$	21.8129	0.795435
$753$	−15.8129	−0.576254
$754$	−16.2510	−0.591826
$755$	−10.4562	−0.380538
$756$	−3.17968	−0.115644
$757$	15.1138	0.549322	0.274661	−	0.961541i	$-0.411434\pi$
$757$	15.1138	0.549322	0.274661	+	0.961541i	$0.411434\pi$
$758$	20.4132	0.741441
$759$	−1.52420	−0.0553249
$760$	4.74005	0.171940
$761$	−29.1500	−1.05669	−0.528343	−	0.849031i	$-0.677187\pi$
$761$	−29.1500	−1.05669	−0.528343	+	0.849031i	$0.677187\pi$
$762$	−22.0181	−0.797631
$763$	2.77934	0.100619
$764$	−30.2839	−1.09563
$765$	−7.52420	−0.272038
$766$	−40.8465	−1.47584
$767$	0.876139	0.0316355
$768$	−8.98516	−0.324224
$769$	−16.7858	−0.605313	−0.302656	−	0.953100i	$-0.597873\pi$
$769$	−16.7858	−0.605313	−0.302656	+	0.953100i	$0.597873\pi$
$770$	6.87614	0.247799
$771$	7.29612	0.262763
$772$	−36.9171	−1.32868
$773$	33.0516	1.18879	0.594393	−	0.804175i	$-0.297393\pi$
$773$	33.0516	1.18879	0.594393	+	0.804175i	$0.297393\pi$
$774$	−13.3142	−0.478569
$775$	7.96708	0.286186
$776$	5.17487	0.185767
$777$	14.9368	0.535853
$778$	−43.0336	−1.54283
$779$	−23.8129	−0.853186
$780$	5.73419	0.205317
$781$	0.703878	0.0251867
$782$	−9.81290	−0.350909
$783$	−7.79001	−0.278392
$784$	16.4078	0.585991
$785$	36.5530	1.30463
$786$	−1.98516	−0.0708084
$787$	−30.3855	−1.08313	−0.541563	−	0.840660i	$-0.682167\pi$
$787$	−30.3855	−1.08313	−0.541563	+	0.840660i	$0.682167\pi$
$788$	−19.3519	−0.689384
$789$	2.77934	0.0989471
$790$	46.2132	1.64419
$791$	3.88836	0.138254
$792$	0.734191	0.0260883
$793$	2.17226	0.0771392
$794$	62.3000	2.21094
$795$	19.9245	0.706651
$796$	−6.90709	−0.244815
$797$	−49.8491	−1.76574	−0.882872	−	0.469613i	$-0.844393\pi$
$797$	−49.8491	−1.76574	−0.882872	+	0.469613i	$0.844393\pi$
$798$	−7.46838	−0.264378
$799$	21.2207	0.750733
$800$	−7.63478	−0.269930
$801$	−11.1419	−0.393681
$802$	−81.3914	−2.87403
$803$	10.2887	0.363080
$804$	−3.26842	−0.115268
$805$	5.02395	0.177071
$806$	−17.6029	−0.620036
$807$	−12.1723	−0.428484
$808$	9.34388	0.328717
$809$	−20.7629	−0.729986	−0.364993	−	0.931010i	$-0.618929\pi$
$809$	−20.7629	−0.729986	−0.364993	+	0.931010i	$0.618929\pi$
$810$	5.08613	0.178708
$811$	4.66290	0.163736	0.0818682	−	0.996643i	$-0.473911\pi$
$811$	4.66290	0.163736	0.0818682	+	0.996643i	$0.473911\pi$
$812$	24.7697	0.869247
$813$	27.5242	0.965316
$814$	−23.0484	−0.807846
$815$	56.3855	1.97510
$816$	−9.79001	−0.342719
$817$	−16.9006	−0.591277
$818$	16.0558	0.561378
$819$	−1.35194	−0.0472406
$820$	−51.5652	−1.80073
$821$	1.41256	0.0492988	0.0246494	−	0.999696i	$-0.492153\pi$
$821$	1.41256	0.0492988	0.0246494	+	0.999696i	$0.492153\pi$
$822$	37.7145	1.31545
$823$	−36.7645	−1.28153	−0.640765	−	0.767737i	$-0.721383\pi$
$823$	−36.7645	−1.28153	−0.640765	+	0.767737i	$0.721383\pi$
$824$	9.06324	0.315733
$825$	−0.944182	−0.0328722
$826$	−2.47099	−0.0859768
$827$	54.0772	1.88045	0.940223	−	0.340558i	$-0.110616\pi$
$827$	54.0772	1.88045	0.940223	+	0.340558i	$0.110616\pi$
$828$	3.58482	0.124581
$829$	−19.7523	−0.686025	−0.343012	−	0.939331i	$-0.611447\pi$
$829$	−19.7523	−0.686025	−0.343012	+	0.939331i	$0.611447\pi$
$830$	23.0484	0.800022
$831$	10.2329	0.354975
$832$	10.5242	0.364861
$833$	15.9623	0.553060
$834$	−30.5955	−1.05944
$835$	2.32007	0.0802893
$836$	6.22808	0.215403
$837$	−8.43807	−0.291662
$838$	30.7597	1.06258
$839$	−33.4897	−1.15619	−0.578097	−	0.815968i	$-0.696204\pi$
$839$	−33.4897	−1.15619	−0.578097	+	0.815968i	$0.696204\pi$
$840$	−2.41998	−0.0834973
$841$	31.6842	1.09256
$842$	30.8761	1.06406
$843$	−30.1016	−1.03675
$844$	−16.5236	−0.568764
$845$	2.43807	0.0838721
$846$	−14.3445	−0.493175
$847$	1.35194	0.0464532
$848$	25.9245	0.890252
$849$	−12.0377	−0.413134
$850$	−6.07871	−0.208498
$851$	−16.8400	−0.577267
$852$	−1.65548	−0.0567158
$853$	−38.8007	−1.32851	−0.664255	−	0.747506i	$-0.731251\pi$
$853$	−38.8007	−1.32851	−0.664255	+	0.747506i	$0.731251\pi$
$854$	−6.12647	−0.209644
$855$	6.45616	0.220796
$856$	−6.51678	−0.222739
$857$	−31.7145	−1.08335	−0.541674	−	0.840589i	$-0.682209\pi$
$857$	−31.7145	−1.08335	−0.541674	+	0.840589i	$0.682209\pi$
$858$	2.08613	0.0712193
$859$	28.9878	0.989050	0.494525	−	0.869163i	$-0.335342\pi$
$859$	28.9878	0.989050	0.494525	+	0.869163i	$0.335342\pi$
$860$	−36.5971	−1.24795
$861$	12.1574	0.414324
$862$	66.2084	2.25507
$863$	−17.1090	−0.582398	−0.291199	−	0.956663i	$-0.594054\pi$
$863$	−17.1090	−0.582398	−0.291199	+	0.956663i	$0.594054\pi$
$864$	8.08613	0.275096
$865$	17.2765	0.587418
$866$	−69.4291	−2.35930
$867$	7.47580	0.253891
$868$	26.8304	0.910681
$869$	9.08613	0.308226
$870$	−39.6210	−1.34328
$871$	−1.38967	−0.0470872
$872$	1.50936	0.0511135
$873$	7.04840	0.238552
$874$	8.41998	0.284810
$875$	−13.3685	−0.451937
$876$	−24.1984	−0.817588
$877$	33.5800	1.13392	0.566958	−	0.823746i	$-0.308120\pi$
$877$	33.5800	1.13392	0.566958	+	0.823746i	$0.308120\pi$
$878$	32.0639	1.08210
$879$	−24.6842	−0.832579
$880$	−7.73419	−0.260720
$881$	−20.4710	−0.689685	−0.344843	−	0.938661i	$-0.612068\pi$
$881$	−20.4710	−0.689685	−0.344843	+	0.938661i	$0.612068\pi$
$882$	−10.7900	−0.363318
$883$	−14.2477	−0.479474	−0.239737	−	0.970838i	$-0.577061\pi$
$883$	−14.2477	−0.479474	−0.239737	+	0.970838i	$0.577061\pi$
$884$	7.25839	0.244126
$885$	2.13609	0.0718038
$886$	−28.6890	−0.963827
$887$	−53.4291	−1.79397	−0.896987	−	0.442058i	$-0.854249\pi$
$887$	−53.4291	−1.79397	−0.896987	+	0.442058i	$0.854249\pi$
$888$	8.11164	0.272209
$889$	14.2691	0.478569
$890$	−56.6694	−1.89956
$891$	1.00000	0.0335013
$892$	40.7220	1.36347
$893$	−18.2084	−0.609322
$894$	1.35194	0.0452156
$895$	−29.3567	−0.981288
$896$	−7.81771	−0.261171
$897$	1.52420	0.0508915
$898$	2.63520	0.0879376
$899$	65.7326	2.19231
$900$	2.22066	0.0740220
$901$	25.2207	0.840222
$902$	−18.7597	−0.624630
$903$	8.62842	0.287136
$904$	2.11164	0.0702319
$905$	50.3052	1.67220
$906$	8.94679	0.297237
$907$	45.3323	1.50523	0.752617	−	0.658458i	$-0.228791\pi$
$907$	45.3323	1.50523	0.752617	+	0.658458i	$0.228791\pi$
$908$	−40.6332	−1.34846
$909$	12.7268	0.422120
$910$	−6.87614	−0.227942
$911$	−22.2839	−0.738298	−0.369149	−	0.929370i	$-0.620351\pi$
$911$	−22.2839	−0.738298	−0.369149	+	0.929370i	$0.620351\pi$
$912$	8.40034	0.278163
$913$	4.53162	0.149975
$914$	63.5355	2.10157
$915$	5.29612	0.175084
$916$	−20.8761	−0.689767
$917$	1.28651	0.0424842
$918$	6.43807	0.212488
$919$	−8.26100	−0.272505	−0.136253	−	0.990674i	$-0.543506\pi$
$919$	−8.26100	−0.272505	−0.136253	+	0.990674i	$0.543506\pi$
$920$	2.72833	0.0899504
$921$	−28.9777	−0.954849
$922$	−27.1042	−0.892630
$923$	−0.703878	−0.0231684
$924$	−3.17968	−0.104604
$925$	−10.4317	−0.342992
$926$	−39.0255	−1.28246
$927$	12.3445	0.405447
$928$	−62.9910	−2.06778
$929$	35.4110	1.16180	0.580899	−	0.813976i	$-0.302701\pi$
$929$	35.4110	1.16180	0.580899	+	0.813976i	$0.302701\pi$
$930$	−42.9171	−1.40731
$931$	−13.6965	−0.448883
$932$	17.8816	0.585731
$933$	−27.1648	−0.889337
$934$	−3.41256	−0.111663
$935$	−7.52420	−0.246068
$936$	−0.734191	−0.0239978
$937$	32.0820	1.04807	0.524036	−	0.851696i	$-0.324426\pi$
$937$	32.0820	1.04807	0.524036	+	0.851696i	$0.324426\pi$
$938$	3.91932	0.127970
$939$	2.11644	0.0690675
$940$	−39.4291	−1.28604
$941$	16.8809	0.550303	0.275152	−	0.961401i	$-0.411272\pi$
$941$	16.8809	0.550303	0.275152	+	0.961401i	$0.411272\pi$
$942$	−31.2765	−1.01904
$943$	−13.7065	−0.446345
$944$	2.77934	0.0904598
$945$	−3.29612	−0.107223
$946$	−13.3142	−0.432882
$947$	−30.7645	−0.999712	−0.499856	−	0.866109i	$-0.666614\pi$
$947$	−30.7645	−0.999712	−0.499856	+	0.866109i	$0.666614\pi$
$948$	−21.3700	−0.694066
$949$	−10.2887	−0.333985
$950$	5.21585	0.169225
$951$	−13.5471	−0.439295
$952$	−3.06324	−0.0992800
$953$	52.5907	1.70358	0.851790	−	0.523884i	$-0.175517\pi$
$953$	52.5907	1.70358	0.851790	+	0.523884i	$0.175517\pi$
$954$	−17.0484	−0.551962
$955$	−31.3929	−1.01585
$956$	30.7003	0.992920
$957$	−7.79001	−0.251815
$958$	42.7152	1.38007
$959$	−24.4413	−0.789251
$960$	25.6587	0.828132
$961$	40.2010	1.29681
$962$	23.0484	0.743110
$963$	−8.87614	−0.286030
$964$	35.5355	1.14452
$965$	−38.2691	−1.23192
$966$	−4.29873	−0.138309
$967$	−5.04359	−0.162191	−0.0810955	−	0.996706i	$-0.525842\pi$
$967$	−5.04359	−0.162191	−0.0810955	+	0.996706i	$0.525842\pi$
$968$	0.734191	0.0235978
$969$	8.17226	0.262531
$970$	35.8491	1.15104
$971$	35.0436	1.12460	0.562301	−	0.826933i	$-0.309916\pi$
$971$	35.0436	1.12460	0.562301	+	0.826933i	$0.309916\pi$
$972$	−2.35194	−0.0754385
$973$	19.8277	0.635648
$974$	34.8842	1.11776
$975$	0.944182	0.0302380
$976$	6.89098	0.220575
$977$	−0.362607	−0.0116008	−0.00580042	−	0.999983i	$-0.501846\pi$
$977$	−0.362607	−0.0116008	−0.00580042	+	0.999983i	$0.501846\pi$
$978$	−48.2462	−1.54274
$979$	−11.1419	−0.356098
$980$	−29.6587	−0.947413
$981$	2.05582	0.0656372
$982$	−49.0645	−1.56571
$983$	−42.7039	−1.36204	−0.681021	−	0.732264i	$-0.738464\pi$
$983$	−42.7039	−1.36204	−0.681021	+	0.732264i	$0.738464\pi$
$984$	6.60227	0.210473
$985$	−20.0606	−0.639185
$986$	−50.1526	−1.59718
$987$	9.29612	0.295899
$988$	−6.22808	−0.198142
$989$	−9.72783	−0.309327
$990$	5.08613	0.161648
$991$	33.5652	1.06623	0.533117	−	0.846042i	$-0.321021\pi$
$991$	33.5652	1.06623	0.533117	+	0.846042i	$0.321021\pi$
$992$	−68.2313	−2.16635
$993$	14.3626	0.455784
$994$	1.98516	0.0629656
$995$	−7.16003	−0.226988
$996$	−10.6581	−0.337715
$997$	−48.6284	−1.54008	−0.770039	−	0.637997i	$-0.779763\pi$
$997$	−48.6284	−1.54008	−0.770039	+	0.637997i	$0.779763\pi$
$998$	−82.2165	−2.60252
$999$	11.0484	0.349556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.a.e.1.3	✓	3
3.2	odd	2		1287.2.a.j.1.1		3
4.3	odd	2		6864.2.a.bu.1.3		3
11.10	odd	2		4719.2.a.u.1.1		3
13.12	even	2		5577.2.a.l.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.a.e.1.3	✓	3	1.1	even	1	trivial
1287.2.a.j.1.1		3	3.2	odd	2
4719.2.a.u.1.1		3	11.10	odd	2
5577.2.a.l.1.1		3	13.12	even	2
6864.2.a.bu.1.3		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.a (trivial)

\(f(q)\)	\(=\)	\(q+2.08613 q^{2} -1.00000 q^{3} +2.35194 q^{4} +2.43807 q^{5} -2.08613 q^{6} +1.35194 q^{7} +0.734191 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.08613 q^{2} -1.00000 q^{3} +2.35194 q^{4} +2.43807 q^{5} -2.08613 q^{6} +1.35194 q^{7} +0.734191 q^{8} +1.00000 q^{9} +5.08613 q^{10} +1.00000 q^{11} -2.35194 q^{12} -1.00000 q^{13} +2.82032 q^{14} -2.43807 q^{15} -3.17226 q^{16} -3.08613 q^{17} +2.08613 q^{18} +2.64806 q^{19} +5.73419 q^{20} -1.35194 q^{21} +2.08613 q^{22} +1.52420 q^{23} -0.734191 q^{24} +0.944182 q^{25} -2.08613 q^{26} -1.00000 q^{27} +3.17968 q^{28} +7.79001 q^{29} -5.08613 q^{30} +8.43807 q^{31} -8.08613 q^{32} -1.00000 q^{33} -6.43807 q^{34} +3.29612 q^{35} +2.35194 q^{36} -11.0484 q^{37} +5.52420 q^{38} +1.00000 q^{39} +1.79001 q^{40} -8.99258 q^{41} -2.82032 q^{42} -6.38225 q^{43} +2.35194 q^{44} +2.43807 q^{45} +3.17968 q^{46} -6.87614 q^{47} +3.17226 q^{48} -5.17226 q^{49} +1.96969 q^{50} +3.08613 q^{51} -2.35194 q^{52} -8.17226 q^{53} -2.08613 q^{54} +2.43807 q^{55} +0.992582 q^{56} -2.64806 q^{57} +16.2510 q^{58} -0.876139 q^{59} -5.73419 q^{60} -2.17226 q^{61} +17.6029 q^{62} +1.35194 q^{63} -10.5242 q^{64} -2.43807 q^{65} -2.08613 q^{66} +1.38967 q^{67} -7.25839 q^{68} -1.52420 q^{69} +6.87614 q^{70} +0.703878 q^{71} +0.734191 q^{72} +10.2887 q^{73} -23.0484 q^{74} -0.944182 q^{75} +6.22808 q^{76} +1.35194 q^{77} +2.08613 q^{78} +9.08613 q^{79} -7.73419 q^{80} +1.00000 q^{81} -18.7597 q^{82} +4.53162 q^{83} -3.17968 q^{84} -7.52420 q^{85} -13.3142 q^{86} -7.79001 q^{87} +0.734191 q^{88} -11.1419 q^{89} +5.08613 q^{90} -1.35194 q^{91} +3.58482 q^{92} -8.43807 q^{93} -14.3445 q^{94} +6.45616 q^{95} +8.08613 q^{96} +7.04840 q^{97} -10.7900 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 3 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 - 3 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - q^{2} - 3 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9} + 8 q^{10} + 3 q^{11} - 5 q^{12} - 3 q^{13} - 4 q^{14} + 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} + 10 q^{19} + 12 q^{20} - 2 q^{21} - q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} + q^{26} - 3 q^{27} + 22 q^{28} + 12 q^{29} - 8 q^{30} + 16 q^{31} - 17 q^{32} - 3 q^{33} - 10 q^{34} + 14 q^{35} + 5 q^{36} + 3 q^{39} - 6 q^{40} + 4 q^{42} - 16 q^{43} + 5 q^{44} - 2 q^{45} + 22 q^{46} - 2 q^{47} - 5 q^{48} - q^{49} + 7 q^{50} + 2 q^{51} - 5 q^{52} - 10 q^{53} + q^{54} - 2 q^{55} - 24 q^{56} - 10 q^{57} + 16 q^{59} - 12 q^{60} + 8 q^{61} + 2 q^{62} + 2 q^{63} - 15 q^{64} + 2 q^{65} + q^{66} + 28 q^{67} + 12 q^{69} + 2 q^{70} - 2 q^{71} - 3 q^{72} + 8 q^{73} - 36 q^{74} - 9 q^{75} - 2 q^{76} + 2 q^{77} - q^{78} + 20 q^{79} - 18 q^{80} + 3 q^{81} - 46 q^{82} + 24 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 12 q^{87} - 3 q^{88} - 20 q^{89} + 8 q^{90} - 2 q^{91} - 8 q^{92} - 16 q^{93} - 14 q^{94} - 22 q^{95} + 17 q^{96} - 12 q^{97} - 21 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - q^2 - 3 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9 + 8 * q^10 + 3 * q^11 - 5 * q^12 - 3 * q^13 - 4 * q^14 + 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 + 10 * q^19 + 12 * q^20 - 2 * q^21 - q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 + q^26 - 3 * q^27 + 22 * q^28 + 12 * q^29 - 8 * q^30 + 16 * q^31 - 17 * q^32 - 3 * q^33 - 10 * q^34 + 14 * q^35 + 5 * q^36 + 3 * q^39 - 6 * q^40 + 4 * q^42 - 16 * q^43 + 5 * q^44 - 2 * q^45 + 22 * q^46 - 2 * q^47 - 5 * q^48 - q^49 + 7 * q^50 + 2 * q^51 - 5 * q^52 - 10 * q^53 + q^54 - 2 * q^55 - 24 * q^56 - 10 * q^57 + 16 * q^59 - 12 * q^60 + 8 * q^61 + 2 * q^62 + 2 * q^63 - 15 * q^64 + 2 * q^65 + q^66 + 28 * q^67 + 12 * q^69 + 2 * q^70 - 2 * q^71 - 3 * q^72 + 8 * q^73 - 36 * q^74 - 9 * q^75 - 2 * q^76 + 2 * q^77 - q^78 + 20 * q^79 - 18 * q^80 + 3 * q^81 - 46 * q^82 + 24 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 12 * q^87 - 3 * q^88 - 20 * q^89 + 8 * q^90 - 2 * q^91 - 8 * q^92 - 16 * q^93 - 14 * q^94 - 22 * q^95 + 17 * q^96 - 12 * q^97 - 21 * q^98 + 3 * q^99

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