LMFDB - Embedded newform 2002.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2002,2,Mod(1,2002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2002, 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("2002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2002 = 2 \cdot 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2002.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:	$15.9860504847$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.469.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 4 $ x^3 - x^2 - 5*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.772866$ of defining polynomial
Character	$\chi$	$=$	2002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.772866 q^{3} +1.00000 q^{4} -1.40268 q^{5} -0.772866 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.40268 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.772866 q^{3} +1.00000 q^{4} -1.40268 q^{5} -0.772866 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.40268 q^{9} +1.40268 q^{10} -1.00000 q^{11} +0.772866 q^{12} -1.00000 q^{13} -1.00000 q^{14} -1.08408 q^{15} +1.00000 q^{16} +0.772866 q^{17} +2.40268 q^{18} +3.40268 q^{19} -1.40268 q^{20} +0.772866 q^{21} +1.00000 q^{22} +2.45427 q^{23} -0.772866 q^{24} -3.03249 q^{25} +1.00000 q^{26} -4.17554 q^{27} +1.00000 q^{28} +6.80536 q^{29} +1.08408 q^{30} -4.35109 q^{31} -1.00000 q^{32} -0.772866 q^{33} -0.772866 q^{34} -1.40268 q^{35} -2.40268 q^{36} -3.40268 q^{38} -0.772866 q^{39} +1.40268 q^{40} +10.3511 q^{41} -0.772866 q^{42} +2.31860 q^{43} -1.00000 q^{44} +3.37019 q^{45} -2.45427 q^{46} +9.54573 q^{47} +0.772866 q^{48} +1.00000 q^{49} +3.03249 q^{50} +0.597321 q^{51} -1.00000 q^{52} +8.03249 q^{53} +4.17554 q^{54} +1.40268 q^{55} -1.00000 q^{56} +2.62981 q^{57} -6.80536 q^{58} +3.54573 q^{59} -1.08408 q^{60} -10.4868 q^{61} +4.35109 q^{62} -2.40268 q^{63} +1.00000 q^{64} +1.40268 q^{65} +0.772866 q^{66} -0.772866 q^{67} +0.772866 q^{68} +1.89682 q^{69} +1.40268 q^{70} +13.7538 q^{71} +2.40268 q^{72} +7.25963 q^{73} -2.34371 q^{75} +3.40268 q^{76} -1.00000 q^{77} +0.772866 q^{78} -9.75377 q^{79} -1.40268 q^{80} +3.98090 q^{81} -10.3511 q^{82} +0.311217 q^{83} +0.772866 q^{84} -1.08408 q^{85} -2.31860 q^{86} +5.25963 q^{87} +1.00000 q^{88} +4.77287 q^{89} -3.37019 q^{90} -1.00000 q^{91} +2.45427 q^{92} -3.36281 q^{93} -9.54573 q^{94} -4.77287 q^{95} -0.772866 q^{96} +5.25963 q^{97} -1.00000 q^{98} +2.40268 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - q^{6} + 3 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 - q^6 + 3 * q^7 - 3 * q^8 + 2 * q^9	$ 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - q^{6} + 3 q^{7} - 3 q^{8} + 2 q^{9} - 5 q^{10} - 3 q^{11} + q^{12} - 3 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} + q^{17} - 2 q^{18} + q^{19} + 5 q^{20} + q^{21} + 3 q^{22} + 10 q^{23} - q^{24} + 8 q^{25} + 3 q^{26} - 2 q^{27} + 3 q^{28} + 2 q^{29} - 2 q^{30} + 8 q^{31} - 3 q^{32} - q^{33} - q^{34} + 5 q^{35} + 2 q^{36} - q^{38} - q^{39} - 5 q^{40} + 10 q^{41} - q^{42} + 3 q^{43} - 3 q^{44} + 18 q^{45} - 10 q^{46} + 26 q^{47} + q^{48} + 3 q^{49} - 8 q^{50} + 11 q^{51} - 3 q^{52} + 7 q^{53} + 2 q^{54} - 5 q^{55} - 3 q^{56} - 2 q^{58} + 8 q^{59} + 2 q^{60} - 17 q^{61} - 8 q^{62} + 2 q^{63} + 3 q^{64} - 5 q^{65} + q^{66} - q^{67} + q^{68} - 18 q^{69} - 5 q^{70} + 11 q^{71} - 2 q^{72} + 6 q^{73} + 14 q^{75} + q^{76} - 3 q^{77} + q^{78} + q^{79} + 5 q^{80} - 17 q^{81} - 10 q^{82} - 3 q^{83} + q^{84} + 2 q^{85} - 3 q^{86} + 3 q^{88} + 13 q^{89} - 18 q^{90} - 3 q^{91} + 10 q^{92} - 18 q^{93} - 26 q^{94} - 13 q^{95} - q^{96} - 3 q^{98} - 2 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 - q^6 + 3 * q^7 - 3 * q^8 + 2 * q^9 - 5 * q^10 - 3 * q^11 + q^12 - 3 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 + q^17 - 2 * q^18 + q^19 + 5 * q^20 + q^21 + 3 * q^22 + 10 * q^23 - q^24 + 8 * q^25 + 3 * q^26 - 2 * q^27 + 3 * q^28 + 2 * q^29 - 2 * q^30 + 8 * q^31 - 3 * q^32 - q^33 - q^34 + 5 * q^35 + 2 * q^36 - q^38 - q^39 - 5 * q^40 + 10 * q^41 - q^42 + 3 * q^43 - 3 * q^44 + 18 * q^45 - 10 * q^46 + 26 * q^47 + q^48 + 3 * q^49 - 8 * q^50 + 11 * q^51 - 3 * q^52 + 7 * q^53 + 2 * q^54 - 5 * q^55 - 3 * q^56 - 2 * q^58 + 8 * q^59 + 2 * q^60 - 17 * q^61 - 8 * q^62 + 2 * q^63 + 3 * q^64 - 5 * q^65 + q^66 - q^67 + q^68 - 18 * q^69 - 5 * q^70 + 11 * q^71 - 2 * q^72 + 6 * q^73 + 14 * q^75 + q^76 - 3 * q^77 + q^78 + q^79 + 5 * q^80 - 17 * q^81 - 10 * q^82 - 3 * q^83 + q^84 + 2 * q^85 - 3 * q^86 + 3 * q^88 + 13 * q^89 - 18 * q^90 - 3 * q^91 + 10 * q^92 - 18 * q^93 - 26 * q^94 - 13 * q^95 - q^96 - 3 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.772866	0.446214	0.223107	−	0.974794i	$-0.428380\pi$
$3$	0.772866	0.446214	0.223107	+	0.974794i	$0.428380\pi$
$4$	1.00000	0.500000
$5$	−1.40268	−0.627297	−0.313649	−	0.949539i	$-0.601551\pi$
$5$	−1.40268	−0.627297	−0.313649	+	0.949539i	$0.601551\pi$
$6$	−0.772866	−0.315521
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.40268	−0.800893
$10$	1.40268	0.443566
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.772866	0.223107
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.00000	−0.267261
$15$	−1.08408	−0.279909
$16$	1.00000	0.250000
$17$	0.772866	0.187447	0.0937237	−	0.995598i	$-0.470123\pi$
$17$	0.772866	0.187447	0.0937237	+	0.995598i	$0.470123\pi$
$18$	2.40268	0.566317
$19$	3.40268	0.780628	0.390314	−	0.920682i	$-0.372366\pi$
$19$	3.40268	0.780628	0.390314	+	0.920682i	$0.372366\pi$
$20$	−1.40268	−0.313649
$21$	0.772866	0.168653
$22$	1.00000	0.213201
$23$	2.45427	0.511750	0.255875	−	0.966710i	$-0.417636\pi$
$23$	2.45427	0.511750	0.255875	+	0.966710i	$0.417636\pi$
$24$	−0.772866	−0.157761
$25$	−3.03249	−0.606498
$26$	1.00000	0.196116
$27$	−4.17554	−0.803584
$28$	1.00000	0.188982
$29$	6.80536	1.26372	0.631862	−	0.775081i	$-0.282291\pi$
$29$	6.80536	1.26372	0.631862	+	0.775081i	$0.282291\pi$
$30$	1.08408	0.197925
$31$	−4.35109	−0.781479	−0.390739	−	0.920501i	$-0.627781\pi$
$31$	−4.35109	−0.781479	−0.390739	+	0.920501i	$0.627781\pi$
$32$	−1.00000	−0.176777
$33$	−0.772866	−0.134539
$34$	−0.772866	−0.132545
$35$	−1.40268	−0.237096
$36$	−2.40268	−0.400446
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	−3.40268	−0.551987
$39$	−0.772866	−0.123758
$40$	1.40268	0.221783
$41$	10.3511	1.61657	0.808284	−	0.588792i	$-0.200396\pi$
$41$	10.3511	1.61657	0.808284	+	0.588792i	$0.200396\pi$
$42$	−0.772866	−0.119256
$43$	2.31860	0.353583	0.176791	−	0.984248i	$-0.443428\pi$
$43$	2.31860	0.353583	0.176791	+	0.984248i	$0.443428\pi$
$44$	−1.00000	−0.150756
$45$	3.37019	0.502398
$46$	−2.45427	−0.361862
$47$	9.54573	1.39239	0.696194	−	0.717854i	$-0.254875\pi$
$47$	9.54573	1.39239	0.696194	+	0.717854i	$0.254875\pi$
$48$	0.772866	0.111554
$49$	1.00000	0.142857
$50$	3.03249	0.428859
$51$	0.597321	0.0836417
$52$	−1.00000	−0.138675
$53$	8.03249	1.10335	0.551674	−	0.834060i	$-0.313989\pi$
$53$	8.03249	1.10335	0.551674	+	0.834060i	$0.313989\pi$
$54$	4.17554	0.568220
$55$	1.40268	0.189137
$56$	−1.00000	−0.133631
$57$	2.62981	0.348327
$58$	−6.80536	−0.893587
$59$	3.54573	0.461615	0.230807	−	0.972999i	$-0.425863\pi$
$59$	3.54573	0.461615	0.230807	+	0.972999i	$0.425863\pi$
$60$	−1.08408	−0.139954
$61$	−10.4868	−1.34269	−0.671346	−	0.741144i	$-0.734284\pi$
$61$	−10.4868	−1.34269	−0.671346	+	0.741144i	$0.734284\pi$
$62$	4.35109	0.552589
$63$	−2.40268	−0.302709
$64$	1.00000	0.125000
$65$	1.40268	0.173981
$66$	0.772866	0.0951332
$67$	−0.772866	−0.0944206	−0.0472103	−	0.998885i	$-0.515033\pi$
$67$	−0.772866	−0.0944206	−0.0472103	+	0.998885i	$0.515033\pi$
$68$	0.772866	0.0937237
$69$	1.89682	0.228350
$70$	1.40268	0.167652
$71$	13.7538	1.63227	0.816136	−	0.577860i	$-0.196112\pi$
$71$	13.7538	1.63227	0.816136	+	0.577860i	$0.196112\pi$
$72$	2.40268	0.283158
$73$	7.25963	0.849675	0.424838	−	0.905270i	$-0.360331\pi$
$73$	7.25963	0.849675	0.424838	+	0.905270i	$0.360331\pi$
$74$	0	0
$75$	−2.34371	−0.270628
$76$	3.40268	0.390314
$77$	−1.00000	−0.113961
$78$	0.772866	0.0875098
$79$	−9.75377	−1.09738	−0.548692	−	0.836024i	$-0.684874\pi$
$79$	−9.75377	−1.09738	−0.548692	+	0.836024i	$0.684874\pi$
$80$	−1.40268	−0.156824
$81$	3.98090	0.442322
$82$	−10.3511	−1.14309
$83$	0.311217	0.0341605	0.0170802	−	0.999854i	$-0.494563\pi$
$83$	0.311217	0.0341605	0.0170802	+	0.999854i	$0.494563\pi$
$84$	0.772866	0.0843265
$85$	−1.08408	−0.117585
$86$	−2.31860	−0.250021
$87$	5.25963	0.563891
$88$	1.00000	0.106600
$89$	4.77287	0.505923	0.252961	−	0.967476i	$-0.418595\pi$
$89$	4.77287	0.505923	0.252961	+	0.967476i	$0.418595\pi$
$90$	−3.37019	−0.355249
$91$	−1.00000	−0.104828
$92$	2.45427	0.255875
$93$	−3.36281	−0.348707
$94$	−9.54573	−0.984567
$95$	−4.77287	−0.489686
$96$	−0.772866	−0.0788803
$97$	5.25963	0.534034	0.267017	−	0.963692i	$-0.413962\pi$
$97$	5.25963	0.534034	0.267017	+	0.963692i	$0.413962\pi$
$98$	−1.00000	−0.101015
$99$	2.40268	0.241478
$100$	−3.03249	−0.303249
$101$	−0.780246	−0.0776373	−0.0388187	−	0.999246i	$-0.512359\pi$
$101$	−0.780246	−0.0776373	−0.0388187	+	0.999246i	$0.512359\pi$
$102$	−0.597321	−0.0591436
$103$	−13.6107	−1.34110	−0.670552	−	0.741863i	$-0.733943\pi$
$103$	−13.6107	−1.34110	−0.670552	+	0.741863i	$0.733943\pi$
$104$	1.00000	0.0980581
$105$	−1.08408	−0.105796
$106$	−8.03249	−0.780185
$107$	−3.86433	−0.373579	−0.186789	−	0.982400i	$-0.559808\pi$
$107$	−3.86433	−0.373579	−0.186789	+	0.982400i	$0.559808\pi$
$108$	−4.17554	−0.401792
$109$	11.9219	1.14191	0.570957	−	0.820980i	$-0.306572\pi$
$109$	11.9219	1.14191	0.570957	+	0.820980i	$0.306572\pi$
$110$	−1.40268	−0.133740
$111$	0	0
$112$	1.00000	0.0944911
$113$	6.59732	0.620624	0.310312	−	0.950635i	$-0.399567\pi$
$113$	6.59732	0.620624	0.310312	+	0.950635i	$0.399567\pi$
$114$	−2.62981	−0.246305
$115$	−3.44255	−0.321020
$116$	6.80536	0.631862
$117$	2.40268	0.222128
$118$	−3.54573	−0.326411
$119$	0.772866	0.0708485
$120$	1.08408	0.0989627
$121$	1.00000	0.0909091
$122$	10.4868	0.949427
$123$	8.00000	0.721336
$124$	−4.35109	−0.390739
$125$	11.2670	1.00775
$126$	2.40268	0.214048
$127$	10.6623	0.946127	0.473063	−	0.881028i	$-0.343148\pi$
$127$	10.6623	0.946127	0.473063	+	0.881028i	$0.343148\pi$
$128$	−1.00000	−0.0883883
$129$	1.79196	0.157774
$130$	−1.40268	−0.123023
$131$	5.71390	0.499225	0.249613	−	0.968346i	$-0.419697\pi$
$131$	5.71390	0.499225	0.249613	+	0.968346i	$0.419697\pi$
$132$	−0.772866	−0.0672693
$133$	3.40268	0.295050
$134$	0.772866	0.0667654
$135$	5.85695	0.504086
$136$	−0.772866	−0.0662727
$137$	2.35109	0.200867	0.100434	−	0.994944i	$-0.467977\pi$
$137$	2.35109	0.200867	0.100434	+	0.994944i	$0.467977\pi$
$138$	−1.89682	−0.161468
$139$	2.35109	0.199417	0.0997084	−	0.995017i	$-0.468209\pi$
$139$	2.35109	0.199417	0.0997084	+	0.995017i	$0.468209\pi$
$140$	−1.40268	−0.118548
$141$	7.37757	0.621303
$142$	−13.7538	−1.15419
$143$	1.00000	0.0836242
$144$	−2.40268	−0.200223
$145$	−9.54573	−0.792730
$146$	−7.25963	−0.600811
$147$	0.772866	0.0637449
$148$	0	0
$149$	−10.3112	−0.844728	−0.422364	−	0.906426i	$-0.638800\pi$
$149$	−10.3112	−0.844728	−0.422364	+	0.906426i	$0.638800\pi$
$150$	2.34371	0.191363
$151$	−10.8703	−0.884616	−0.442308	−	0.896863i	$-0.645840\pi$
$151$	−10.8703	−0.884616	−0.442308	+	0.896863i	$0.645840\pi$
$152$	−3.40268	−0.275994
$153$	−1.85695	−0.150125
$154$	1.00000	0.0805823
$155$	6.10318	0.490219
$156$	−0.772866	−0.0618788
$157$	20.8703	1.66563	0.832817	−	0.553548i	$-0.186726\pi$
$157$	20.8703	1.66563	0.832817	+	0.553548i	$0.186726\pi$
$158$	9.75377	0.775968
$159$	6.20804	0.492329
$160$	1.40268	0.110891
$161$	2.45427	0.193423
$162$	−3.98090	−0.312769
$163$	0.311217	0.0243764	0.0121882	−	0.999926i	$-0.496120\pi$
$163$	0.311217	0.0243764	0.0121882	+	0.999926i	$0.496120\pi$
$164$	10.3511	0.808284
$165$	1.08408	0.0843957
$166$	−0.311217	−0.0241551
$167$	−11.9293	−0.923118	−0.461559	−	0.887110i	$-0.652710\pi$
$167$	−11.9293	−0.923118	−0.461559	+	0.887110i	$0.652710\pi$
$168$	−0.772866	−0.0596279
$169$	1.00000	0.0769231
$170$	1.08408	0.0831453
$171$	−8.17554	−0.625200
$172$	2.31860	0.176791
$173$	−4.78025	−0.363435	−0.181718	−	0.983351i	$-0.558166\pi$
$173$	−4.78025	−0.363435	−0.181718	+	0.983351i	$0.558166\pi$
$174$	−5.25963	−0.398731
$175$	−3.03249	−0.229235
$176$	−1.00000	−0.0753778
$177$	2.74037	0.205979
$178$	−4.77287	−0.357741
$179$	2.45427	0.183441	0.0917203	−	0.995785i	$-0.470763\pi$
$179$	2.45427	0.183441	0.0917203	+	0.995785i	$0.470763\pi$
$180$	3.37019	0.251199
$181$	−4.74037	−0.352349	−0.176175	−	0.984359i	$-0.556372\pi$
$181$	−4.74037	−0.352349	−0.176175	+	0.984359i	$0.556372\pi$
$182$	1.00000	0.0741249
$183$	−8.10486	−0.599128
$184$	−2.45427	−0.180931
$185$	0	0
$186$	3.36281	0.246573
$187$	−0.772866	−0.0565175
$188$	9.54573	0.696194
$189$	−4.17554	−0.303726
$190$	4.77287	0.346260
$191$	17.6107	1.27427	0.637133	−	0.770754i	$-0.280120\pi$
$191$	17.6107	1.27427	0.637133	+	0.770754i	$0.280120\pi$
$192$	0.772866	0.0557768
$193$	1.51324	0.108925	0.0544627	−	0.998516i	$-0.482655\pi$
$193$	1.51324	0.108925	0.0544627	+	0.998516i	$0.482655\pi$
$194$	−5.25963	−0.377619
$195$	1.08408	0.0776327
$196$	1.00000	0.0714286
$197$	−11.1240	−0.792549	−0.396274	−	0.918132i	$-0.629697\pi$
$197$	−11.1240	−0.792549	−0.396274	+	0.918132i	$0.629697\pi$
$198$	−2.40268	−0.170751
$199$	−1.29950	−0.0921190	−0.0460595	−	0.998939i	$-0.514666\pi$
$199$	−1.29950	−0.0921190	−0.0460595	+	0.998939i	$0.514666\pi$
$200$	3.03249	0.214430
$201$	−0.597321	−0.0421318
$202$	0.780246	0.0548979
$203$	6.80536	0.477642
$204$	0.597321	0.0418208
$205$	−14.5193	−1.01407
$206$	13.6107	0.948303
$207$	−5.89682	−0.409857
$208$	−1.00000	−0.0693375
$209$	−3.40268	−0.235368
$210$	1.08408	0.0748088
$211$	10.3836	0.714835	0.357418	−	0.933945i	$-0.383657\pi$
$211$	10.3836	0.714835	0.357418	+	0.933945i	$0.383657\pi$
$212$	8.03249	0.551674
$213$	10.6298	0.728343
$214$	3.86433	0.264160
$215$	−3.25225	−0.221801
$216$	4.17554	0.284110
$217$	−4.35109	−0.295371
$218$	−11.9219	−0.807455
$219$	5.61072	0.379137
$220$	1.40268	0.0945686
$221$	−0.772866	−0.0519886
$222$	0	0
$223$	10.5193	0.704421	0.352211	−	0.935921i	$-0.385430\pi$
$223$	10.5193	0.704421	0.352211	+	0.935921i	$0.385430\pi$
$224$	−1.00000	−0.0668153
$225$	7.28610	0.485740
$226$	−6.59732	−0.438847
$227$	20.7729	1.37874	0.689372	−	0.724408i	$-0.257887\pi$
$227$	20.7729	1.37874	0.689372	+	0.724408i	$0.257887\pi$
$228$	2.62981	0.174164
$229$	28.6241	1.89153	0.945767	−	0.324845i	$-0.105312\pi$
$229$	28.6241	1.89153	0.945767	+	0.324845i	$0.105312\pi$
$230$	3.44255	0.226995
$231$	−0.772866	−0.0508508
$232$	−6.80536	−0.446794
$233$	−20.2479	−1.32648	−0.663242	−	0.748405i	$-0.730820\pi$
$233$	−20.2479	−1.32648	−0.663242	+	0.748405i	$0.730820\pi$
$234$	−2.40268	−0.157068
$235$	−13.3896	−0.873441
$236$	3.54573	0.230807
$237$	−7.53835	−0.489669
$238$	−0.772866	−0.0500974
$239$	−6.51925	−0.421695	−0.210848	−	0.977519i	$-0.567622\pi$
$239$	−6.51925	−0.421695	−0.210848	+	0.977519i	$0.567622\pi$
$240$	−1.08408	−0.0699772
$241$	−7.61072	−0.490249	−0.245125	−	0.969492i	$-0.578829\pi$
$241$	−7.61072	−0.490249	−0.245125	+	0.969492i	$0.578829\pi$
$242$	−1.00000	−0.0642824
$243$	15.6033	1.00095
$244$	−10.4868	−0.671346
$245$	−1.40268	−0.0896139
$246$	−8.00000	−0.510061
$247$	−3.40268	−0.216507
$248$	4.35109	0.276294
$249$	0.240529	0.0152429
$250$	−11.2670	−0.712588
$251$	1.50586	0.0950490	0.0475245	−	0.998870i	$-0.484867\pi$
$251$	1.50586	0.0950490	0.0475245	+	0.998870i	$0.484867\pi$
$252$	−2.40268	−0.151355
$253$	−2.45427	−0.154299
$254$	−10.6623	−0.669013
$255$	−0.837850	−0.0524682
$256$	1.00000	0.0625000
$257$	−12.8703	−0.802830	−0.401415	−	0.915896i	$-0.631481\pi$
$257$	−12.8703	−0.802830	−0.401415	+	0.915896i	$0.631481\pi$
$258$	−1.79196	−0.111563
$259$	0	0
$260$	1.40268	0.0869904
$261$	−16.3511	−1.01211
$262$	−5.71390	−0.353006
$263$	10.9484	0.675108	0.337554	−	0.941306i	$-0.390400\pi$
$263$	10.9484	0.675108	0.337554	+	0.941306i	$0.390400\pi$
$264$	0.772866	0.0475666
$265$	−11.2670	−0.692127
$266$	−3.40268	−0.208632
$267$	3.68878	0.225750
$268$	−0.772866	−0.0472103
$269$	5.36281	0.326976	0.163488	−	0.986545i	$-0.447725\pi$
$269$	5.36281	0.326976	0.163488	+	0.986545i	$0.447725\pi$
$270$	−5.85695	−0.356442
$271$	27.0858	1.64534	0.822671	−	0.568517i	$-0.192483\pi$
$271$	27.0858	1.64534	0.822671	+	0.568517i	$0.192483\pi$
$272$	0.772866	0.0468619
$273$	−0.772866	−0.0467760
$274$	−2.35109	−0.142034
$275$	3.03249	0.182866
$276$	1.89682	0.114175
$277$	6.16816	0.370609	0.185305	−	0.982681i	$-0.440673\pi$
$277$	6.16816	0.370609	0.185305	+	0.982681i	$0.440673\pi$
$278$	−2.35109	−0.141009
$279$	10.4543	0.625881
$280$	1.40268	0.0838261
$281$	15.1240	0.902219	0.451110	−	0.892468i	$-0.351028\pi$
$281$	15.1240	0.902219	0.451110	+	0.892468i	$0.351028\pi$
$282$	−7.37757	−0.439328
$283$	−9.09146	−0.540431	−0.270216	−	0.962800i	$-0.587095\pi$
$283$	−9.09146	−0.540431	−0.270216	+	0.962800i	$0.587095\pi$
$284$	13.7538	0.816136
$285$	−3.68878	−0.218505
$286$	−1.00000	−0.0591312
$287$	10.3511	0.611005
$288$	2.40268	0.141579
$289$	−16.4027	−0.964863
$290$	9.54573	0.560545
$291$	4.06498	0.238294
$292$	7.25963	0.424838
$293$	10.2861	0.600921	0.300460	−	0.953794i	$-0.402860\pi$
$293$	10.2861	0.600921	0.300460	+	0.953794i	$0.402860\pi$
$294$	−0.772866	−0.0450744
$295$	−4.97352	−0.289570
$296$	0	0
$297$	4.17554	0.242290
$298$	10.3112	0.597313
$299$	−2.45427	−0.141934
$300$	−2.34371	−0.135314
$301$	2.31860	0.133642
$302$	10.8703	0.625518
$303$	−0.603025	−0.0346429
$304$	3.40268	0.195157
$305$	14.7096	0.842267
$306$	1.85695	0.106155
$307$	5.47504	0.312477	0.156239	−	0.987719i	$-0.450063\pi$
$307$	5.47504	0.312477	0.156239	+	0.987719i	$0.450063\pi$
$308$	−1.00000	−0.0569803
$309$	−10.5193	−0.598419
$310$	−6.10318	−0.346637
$311$	−0.597321	−0.0338710	−0.0169355	−	0.999857i	$-0.505391\pi$
$311$	−0.597321	−0.0338710	−0.0169355	+	0.999857i	$0.505391\pi$
$312$	0.772866	0.0437549
$313$	11.8821	0.671614	0.335807	−	0.941931i	$-0.390991\pi$
$313$	11.8821	0.671614	0.335807	+	0.941931i	$0.390991\pi$
$314$	−20.8703	−1.17778
$315$	3.37019	0.189889
$316$	−9.75377	−0.548692
$317$	−16.7672	−0.941738	−0.470869	−	0.882203i	$-0.656059\pi$
$317$	−16.7672	−0.941738	−0.470869	+	0.882203i	$0.656059\pi$
$318$	−6.20804	−0.348129
$319$	−6.80536	−0.381027
$320$	−1.40268	−0.0784121
$321$	−2.98661	−0.166696
$322$	−2.45427	−0.136771
$323$	2.62981	0.146327
$324$	3.98090	0.221161
$325$	3.03249	0.168212
$326$	−0.311217	−0.0172367
$327$	9.21405	0.509538
$328$	−10.3511	−0.571543
$329$	9.54573	0.526273
$330$	−1.08408	−0.0596768
$331$	−16.1049	−0.885203	−0.442601	−	0.896718i	$-0.645944\pi$
$331$	−16.1049	−0.885203	−0.442601	+	0.896718i	$0.645944\pi$
$332$	0.311217	0.0170802
$333$	0	0
$334$	11.9293	0.652743
$335$	1.08408	0.0592297
$336$	0.772866	0.0421633
$337$	12.1829	0.663646	0.331823	−	0.943342i	$-0.392336\pi$
$337$	12.1829	0.663646	0.331823	+	0.943342i	$0.392336\pi$
$338$	−1.00000	−0.0543928
$339$	5.09884	0.276931
$340$	−1.08408	−0.0587926
$341$	4.35109	0.235625
$342$	8.17554	0.442083
$343$	1.00000	0.0539949
$344$	−2.31860	−0.125010
$345$	−2.66063	−0.143243
$346$	4.78025	0.256988
$347$	−28.4412	−1.52680	−0.763401	−	0.645924i	$-0.776472\pi$
$347$	−28.4412	−1.52680	−0.763401	+	0.645924i	$0.776472\pi$
$348$	5.25963	0.281946
$349$	1.36281	0.0729494	0.0364747	−	0.999335i	$-0.488387\pi$
$349$	1.36281	0.0729494	0.0364747	+	0.999335i	$0.488387\pi$
$350$	3.03249	0.162094
$351$	4.17554	0.222874
$352$	1.00000	0.0533002
$353$	7.07670	0.376655	0.188327	−	0.982106i	$-0.439693\pi$
$353$	7.07670	0.376655	0.188327	+	0.982106i	$0.439693\pi$
$354$	−2.74037	−0.145649
$355$	−19.2921	−1.02392
$356$	4.77287	0.252961
$357$	0.597321	0.0316136
$358$	−2.45427	−0.129712
$359$	6.18292	0.326322	0.163161	−	0.986599i	$-0.447831\pi$
$359$	6.18292	0.326322	0.163161	+	0.986599i	$0.447831\pi$
$360$	−3.37019	−0.177624
$361$	−7.42178	−0.390620
$362$	4.74037	0.249148
$363$	0.772866	0.0405649
$364$	−1.00000	−0.0524142
$365$	−10.1829	−0.532999
$366$	8.10486	0.423648
$367$	−0.707881	−0.0369511	−0.0184756	−	0.999829i	$-0.505881\pi$
$367$	−0.707881	−0.0369511	−0.0184756	+	0.999829i	$0.505881\pi$
$368$	2.45427	0.127938
$369$	−24.8703	−1.29470
$370$	0	0
$371$	8.03249	0.417026
$372$	−3.36281	−0.174353
$373$	−17.2596	−0.893670	−0.446835	−	0.894616i	$-0.647449\pi$
$373$	−17.2596	−0.893670	−0.446835	+	0.894616i	$0.647449\pi$
$374$	0.772866	0.0399639
$375$	8.70788	0.449673
$376$	−9.54573	−0.492283
$377$	−6.80536	−0.350494
$378$	4.17554	0.214767
$379$	−11.2271	−0.576699	−0.288350	−	0.957525i	$-0.593107\pi$
$379$	−11.2271	−0.576699	−0.288350	+	0.957525i	$0.593107\pi$
$380$	−4.77287	−0.244843
$381$	8.24053	0.422175
$382$	−17.6107	−0.901043
$383$	−0.351089	−0.0179398	−0.00896990	−	0.999960i	$-0.502855\pi$
$383$	−0.351089	−0.0179398	−0.00896990	+	0.999960i	$0.502855\pi$
$384$	−0.772866	−0.0394401
$385$	1.40268	0.0714871
$386$	−1.51324	−0.0770218
$387$	−5.57084	−0.283182
$388$	5.25963	0.267017
$389$	−19.6358	−0.995576	−0.497788	−	0.867299i	$-0.665854\pi$
$389$	−19.6358	−0.995576	−0.497788	+	0.867299i	$0.665854\pi$
$390$	−1.08408	−0.0548946
$391$	1.89682	0.0959263
$392$	−1.00000	−0.0505076
$393$	4.41607	0.222761
$394$	11.1240	0.560417
$395$	13.6814	0.688386
$396$	2.40268	0.120739
$397$	18.9176	0.949447	0.474723	−	0.880135i	$-0.342548\pi$
$397$	18.9176	0.949447	0.474723	+	0.880135i	$0.342548\pi$
$398$	1.29950	0.0651380
$399$	2.62981	0.131655
$400$	−3.03249	−0.151625
$401$	3.81708	0.190616	0.0953078	−	0.995448i	$-0.469616\pi$
$401$	3.81708	0.190616	0.0953078	+	0.995448i	$0.469616\pi$
$402$	0.597321	0.0297917
$403$	4.35109	0.216743
$404$	−0.780246	−0.0388187
$405$	−5.58393	−0.277468
$406$	−6.80536	−0.337744
$407$	0	0
$408$	−0.597321	−0.0295718
$409$	−32.3779	−1.60098	−0.800491	−	0.599344i	$-0.795428\pi$
$409$	−32.3779	−1.60098	−0.800491	+	0.599344i	$0.795428\pi$
$410$	14.5193	0.717055
$411$	1.81708	0.0896297
$412$	−13.6107	−0.670552
$413$	3.54573	0.174474
$414$	5.89682	0.289813
$415$	−0.436537	−0.0214288
$416$	1.00000	0.0490290
$417$	1.81708	0.0889826
$418$	3.40268	0.166430
$419$	−7.29212	−0.356243	−0.178122	−	0.984008i	$-0.557002\pi$
$419$	−7.29212	−0.356243	−0.178122	+	0.984008i	$0.557002\pi$
$420$	−1.08408	−0.0528978
$421$	20.7672	1.01213	0.506065	−	0.862495i	$-0.331100\pi$
$421$	20.7672	1.01213	0.506065	+	0.862495i	$0.331100\pi$
$422$	−10.3836	−0.505465
$423$	−22.9353	−1.11515
$424$	−8.03249	−0.390092
$425$	−2.34371	−0.113687
$426$	−10.6298	−0.515016
$427$	−10.4868	−0.507490
$428$	−3.86433	−0.186789
$429$	0.772866	0.0373143
$430$	3.25225	0.156837
$431$	−31.2214	−1.50388	−0.751942	−	0.659230i	$-0.770883\pi$
$431$	−31.2214	−1.50388	−0.751942	+	0.659230i	$0.770883\pi$
$432$	−4.17554	−0.200896
$433$	−26.0650	−1.25260	−0.626302	−	0.779581i	$-0.715432\pi$
$433$	−26.0650	−1.25260	−0.626302	+	0.779581i	$0.715432\pi$
$434$	4.35109	0.208859
$435$	−7.37757	−0.353727
$436$	11.9219	0.570957
$437$	8.35109	0.399487
$438$	−5.61072	−0.268090
$439$	−3.01172	−0.143741	−0.0718707	−	0.997414i	$-0.522897\pi$
$439$	−3.01172	−0.143741	−0.0718707	+	0.997414i	$0.522897\pi$
$440$	−1.40268	−0.0668701
$441$	−2.40268	−0.114413
$442$	0.772866	0.0367615
$443$	−18.1032	−0.860108	−0.430054	−	0.902803i	$-0.641505\pi$
$443$	−18.1032	−0.860108	−0.430054	+	0.902803i	$0.641505\pi$
$444$	0	0
$445$	−6.69480	−0.317364
$446$	−10.5193	−0.498101
$447$	−7.96918	−0.376929
$448$	1.00000	0.0472456
$449$	−6.06498	−0.286224	−0.143112	−	0.989706i	$-0.545711\pi$
$449$	−6.06498	−0.286224	−0.143112	+	0.989706i	$0.545711\pi$
$450$	−7.28610	−0.343470
$451$	−10.3511	−0.487414
$452$	6.59732	0.310312
$453$	−8.40131	−0.394728
$454$	−20.7729	−0.974919
$455$	1.40268	0.0657586
$456$	−2.62981	−0.123152
$457$	−15.2198	−0.711950	−0.355975	−	0.934495i	$-0.615851\pi$
$457$	−15.2198	−0.711950	−0.355975	+	0.934495i	$0.615851\pi$
$458$	−28.6241	−1.33752
$459$	−3.22713	−0.150630
$460$	−3.44255	−0.160510
$461$	−32.3129	−1.50496	−0.752481	−	0.658614i	$-0.771143\pi$
$461$	−32.3129	−1.50496	−0.752481	+	0.658614i	$0.771143\pi$
$462$	0.772866	0.0359570
$463$	33.7789	1.56984	0.784919	−	0.619599i	$-0.212705\pi$
$463$	33.7789	1.56984	0.784919	+	0.619599i	$0.212705\pi$
$464$	6.80536	0.315931
$465$	4.71694	0.218743
$466$	20.2479	0.937966
$467$	−14.0473	−0.650029	−0.325015	−	0.945709i	$-0.605369\pi$
$467$	−14.0473	−0.650029	−0.325015	+	0.945709i	$0.605369\pi$
$468$	2.40268	0.111064
$469$	−0.772866	−0.0356876
$470$	13.3896	0.617616
$471$	16.1300	0.743230
$472$	−3.54573	−0.163206
$473$	−2.31860	−0.106609
$474$	7.53835	0.346248
$475$	−10.3186	−0.473450
$476$	0.772866	0.0354242
$477$	−19.2995	−0.883663
$478$	6.51925	0.298184
$479$	22.8305	1.04315	0.521575	−	0.853205i	$-0.325345\pi$
$479$	22.8305	1.04315	0.521575	+	0.853205i	$0.325345\pi$
$480$	1.08408	0.0494814
$481$	0	0
$482$	7.61072	0.346659
$483$	1.89682	0.0863083
$484$	1.00000	0.0454545
$485$	−7.37757	−0.334998
$486$	−15.6033	−0.707782
$487$	24.5340	1.11174	0.555871	−	0.831268i	$-0.312385\pi$
$487$	24.5340	1.11174	0.555871	+	0.831268i	$0.312385\pi$
$488$	10.4868	0.474713
$489$	0.240529	0.0108771
$490$	1.40268	0.0633666
$491$	1.27439	0.0575123	0.0287561	−	0.999586i	$-0.490845\pi$
$491$	1.27439	0.0575123	0.0287561	+	0.999586i	$0.490845\pi$
$492$	8.00000	0.360668
$493$	5.25963	0.236882
$494$	3.40268	0.153094
$495$	−3.37019	−0.151479
$496$	−4.35109	−0.195370
$497$	13.7538	0.616941
$498$	−0.240529	−0.0107783
$499$	−3.06635	−0.137269	−0.0686343	−	0.997642i	$-0.521864\pi$
$499$	−3.06635	−0.137269	−0.0686343	+	0.997642i	$0.521864\pi$
$500$	11.2670	0.503876
$501$	−9.21975	−0.411908
$502$	−1.50586	−0.0672098
$503$	9.25963	0.412866	0.206433	−	0.978461i	$-0.433814\pi$
$503$	9.25963	0.412866	0.206433	+	0.978461i	$0.433814\pi$
$504$	2.40268	0.107024
$505$	1.09443	0.0487017
$506$	2.45427	0.109106
$507$	0.772866	0.0343242
$508$	10.6623	0.473063
$509$	−16.3893	−0.726442	−0.363221	−	0.931703i	$-0.618323\pi$
$509$	−16.3893	−0.726442	−0.363221	+	0.931703i	$0.618323\pi$
$510$	0.837850	0.0371006
$511$	7.25963	0.321147
$512$	−1.00000	−0.0441942
$513$	−14.2080	−0.627300
$514$	12.8703	0.567686
$515$	19.0915	0.841270
$516$	1.79196	0.0788868
$517$	−9.54573	−0.419821
$518$	0	0
$519$	−3.69449	−0.162170
$520$	−1.40268	−0.0615115
$521$	−4.45427	−0.195145	−0.0975725	−	0.995228i	$-0.531108\pi$
$521$	−4.45427	−0.195145	−0.0975725	+	0.995228i	$0.531108\pi$
$522$	16.3511	0.715668
$523$	−31.3394	−1.37038	−0.685188	−	0.728367i	$-0.740280\pi$
$523$	−31.3394	−1.37038	−0.685188	+	0.728367i	$0.740280\pi$
$524$	5.71390	0.249613
$525$	−2.34371	−0.102288
$526$	−10.9484	−0.477373
$527$	−3.36281	−0.146486
$528$	−0.772866	−0.0336347
$529$	−16.9766	−0.738111
$530$	11.2670	0.489407
$531$	−8.51925	−0.369704
$532$	3.40268	0.147525
$533$	−10.3511	−0.448355
$534$	−3.68878	−0.159629
$535$	5.42041	0.234345
$536$	0.772866	0.0333827
$537$	1.89682	0.0818538
$538$	−5.36281	−0.231207
$539$	−1.00000	−0.0430730
$540$	5.85695	0.252043
$541$	−4.38928	−0.188710	−0.0943550	−	0.995539i	$-0.530079\pi$
$541$	−4.38928	−0.188710	−0.0943550	+	0.995539i	$0.530079\pi$
$542$	−27.0858	−1.16343
$543$	−3.66367	−0.157223
$544$	−0.772866	−0.0331363
$545$	−16.7226	−0.716319
$546$	0.772866	0.0330756
$547$	−15.2214	−0.650821	−0.325411	−	0.945573i	$-0.605503\pi$
$547$	−15.2214	−0.650821	−0.325411	+	0.945573i	$0.605503\pi$
$548$	2.35109	0.100434
$549$	25.1963	1.07535
$550$	−3.03249	−0.129306
$551$	23.1564	0.986498
$552$	−1.89682	−0.0807340
$553$	−9.75377	−0.414772
$554$	−6.16816	−0.262060
$555$	0	0
$556$	2.35109	0.0997084
$557$	−12.8305	−0.543644	−0.271822	−	0.962347i	$-0.587626\pi$
$557$	−12.8305	−0.543644	−0.271822	+	0.962347i	$0.587626\pi$
$558$	−10.4543	−0.442564
$559$	−2.31860	−0.0980662
$560$	−1.40268	−0.0592740
$561$	−0.597321	−0.0252189
$562$	−15.1240	−0.637966
$563$	3.81708	0.160871	0.0804353	−	0.996760i	$-0.474369\pi$
$563$	3.81708	0.160871	0.0804353	+	0.996760i	$0.474369\pi$
$564$	7.37757	0.310652
$565$	−9.25392	−0.389315
$566$	9.09146	0.382143
$567$	3.98090	0.167182
$568$	−13.7538	−0.577095
$569$	−8.38928	−0.351697	−0.175849	−	0.984417i	$-0.556267\pi$
$569$	−8.38928	−0.351697	−0.175849	+	0.984417i	$0.556267\pi$
$570$	3.68878	0.154506
$571$	−10.2080	−0.427193	−0.213597	−	0.976922i	$-0.568518\pi$
$571$	−10.2080	−0.427193	−0.213597	+	0.976922i	$0.568518\pi$
$572$	1.00000	0.0418121
$573$	13.6107	0.568596
$574$	−10.3511	−0.432046
$575$	−7.44255	−0.310376
$576$	−2.40268	−0.100112
$577$	2.31860	0.0965244	0.0482622	−	0.998835i	$-0.484632\pi$
$577$	2.31860	0.0965244	0.0482622	+	0.998835i	$0.484632\pi$
$578$	16.4027	0.682261
$579$	1.16953	0.0486040
$580$	−9.54573	−0.396365
$581$	0.311217	0.0129114
$582$	−4.06498	−0.168499
$583$	−8.03249	−0.332672
$584$	−7.25963	−0.300405
$585$	−3.37019	−0.139340
$586$	−10.2861	−0.424915
$587$	−30.2747	−1.24957	−0.624785	−	0.780797i	$-0.714813\pi$
$587$	−30.2747	−1.24957	−0.624785	+	0.780797i	$0.714813\pi$
$588$	0.772866	0.0318724
$589$	−14.8054	−0.610044
$590$	4.97352	0.204757
$591$	−8.59732	−0.353647
$592$	0	0
$593$	13.2978	0.546076	0.273038	−	0.962003i	$-0.411972\pi$
$593$	13.2978	0.546076	0.273038	+	0.962003i	$0.411972\pi$
$594$	−4.17554	−0.171325
$595$	−1.08408	−0.0444430
$596$	−10.3112	−0.422364
$597$	−1.00434	−0.0411048
$598$	2.45427	0.100363
$599$	9.33937	0.381596	0.190798	−	0.981629i	$-0.438892\pi$
$599$	9.33937	0.381596	0.190798	+	0.981629i	$0.438892\pi$
$600$	2.34371	0.0956815
$601$	−27.4221	−1.11857	−0.559285	−	0.828975i	$-0.688924\pi$
$601$	−27.4221	−1.11857	−0.559285	+	0.828975i	$0.688924\pi$
$602$	−2.31860	−0.0944989
$603$	1.85695	0.0756208
$604$	−10.8703	−0.442308
$605$	−1.40268	−0.0570270
$606$	0.603025	0.0244962
$607$	1.89682	0.0769895	0.0384948	−	0.999259i	$-0.487744\pi$
$607$	1.89682	0.0769895	0.0384948	+	0.999259i	$0.487744\pi$
$608$	−3.40268	−0.137997
$609$	5.25963	0.213131
$610$	−14.7096	−0.595573
$611$	−9.54573	−0.386179
$612$	−1.85695	−0.0750627
$613$	−36.6492	−1.48025	−0.740124	−	0.672470i	$-0.765233\pi$
$613$	−36.6492	−1.48025	−0.740124	+	0.672470i	$0.765233\pi$
$614$	−5.47504	−0.220955
$615$	−11.2214	−0.452492
$616$	1.00000	0.0402911
$617$	32.3779	1.30348	0.651742	−	0.758441i	$-0.274038\pi$
$617$	32.3779	1.30348	0.651742	+	0.758441i	$0.274038\pi$
$618$	10.5193	0.423146
$619$	−10.0502	−0.403953	−0.201976	−	0.979390i	$-0.564736\pi$
$619$	−10.0502	−0.403953	−0.201976	+	0.979390i	$0.564736\pi$
$620$	6.10318	0.245110
$621$	−10.2479	−0.411234
$622$	0.597321	0.0239504
$623$	4.77287	0.191221
$624$	−0.772866	−0.0309394
$625$	−0.641531	−0.0256612
$626$	−11.8821	−0.474903
$627$	−2.62981	−0.105025
$628$	20.8703	0.832817
$629$	0	0
$630$	−3.37019	−0.134271
$631$	21.4368	0.853387	0.426694	−	0.904396i	$-0.359678\pi$
$631$	21.4368	0.853387	0.426694	+	0.904396i	$0.359678\pi$
$632$	9.75377	0.387984
$633$	8.02511	0.318970
$634$	16.7672	0.665909
$635$	−14.9558	−0.593502
$636$	6.20804	0.246165
$637$	−1.00000	−0.0396214
$638$	6.80536	0.269427
$639$	−33.0459	−1.30728
$640$	1.40268	0.0554457
$641$	−1.24189	−0.0490519	−0.0245259	−	0.999699i	$-0.507808\pi$
$641$	−1.24189	−0.0490519	−0.0245259	+	0.999699i	$0.507808\pi$
$642$	2.98661	0.117872
$643$	40.0120	1.57792	0.788960	−	0.614444i	$-0.210620\pi$
$643$	40.0120	1.57792	0.788960	+	0.614444i	$0.210620\pi$
$644$	2.45427	0.0967117
$645$	−2.51355	−0.0989709
$646$	−2.62981	−0.103469
$647$	40.7022	1.60017	0.800084	−	0.599888i	$-0.204788\pi$
$647$	40.7022	1.60017	0.800084	+	0.599888i	$0.204788\pi$
$648$	−3.98090	−0.156385
$649$	−3.54573	−0.139182
$650$	−3.03249	−0.118944
$651$	−3.36281	−0.131799
$652$	0.311217	0.0121882
$653$	−39.1889	−1.53358	−0.766791	−	0.641897i	$-0.778148\pi$
$653$	−39.1889	−1.53358	−0.766791	+	0.641897i	$0.778148\pi$
$654$	−9.21405	−0.360298
$655$	−8.01476	−0.313163
$656$	10.3511	0.404142
$657$	−17.4426	−0.680499
$658$	−9.54573	−0.372131
$659$	−22.4486	−0.874472	−0.437236	−	0.899347i	$-0.644043\pi$
$659$	−22.4486	−0.874472	−0.437236	+	0.899347i	$0.644043\pi$
$660$	1.08408	0.0421978
$661$	7.08979	0.275761	0.137880	−	0.990449i	$-0.455971\pi$
$661$	7.08979	0.275761	0.137880	+	0.990449i	$0.455971\pi$
$662$	16.1049	0.625933
$663$	−0.597321	−0.0231980
$664$	−0.311217	−0.0120775
$665$	−4.77287	−0.185084
$666$	0	0
$667$	16.7022	0.646711
$668$	−11.9293	−0.461559
$669$	8.12997	0.314323
$670$	−1.08408	−0.0418817
$671$	10.4868	0.404837
$672$	−0.772866	−0.0298139
$673$	−33.4426	−1.28912	−0.644558	−	0.764556i	$-0.722958\pi$
$673$	−33.4426	−1.28912	−0.644558	+	0.764556i	$0.722958\pi$
$674$	−12.1829	−0.469269
$675$	12.6623	0.487372
$676$	1.00000	0.0384615
$677$	13.0060	0.499862	0.249931	−	0.968264i	$-0.419592\pi$
$677$	13.0060	0.499862	0.249931	+	0.968264i	$0.419592\pi$
$678$	−5.09884	−0.195820
$679$	5.25963	0.201846
$680$	1.08408	0.0415727
$681$	16.0546	0.615215
$682$	−4.35109	−0.166612
$683$	48.9028	1.87121	0.935607	−	0.353042i	$-0.114853\pi$
$683$	48.9028	1.87121	0.935607	+	0.353042i	$0.114853\pi$
$684$	−8.17554	−0.312600
$685$	−3.29782	−0.126003
$686$	−1.00000	−0.0381802
$687$	22.1226	0.844029
$688$	2.31860	0.0883957
$689$	−8.03249	−0.306014
$690$	2.66063	0.101288
$691$	2.06498	0.0785557	0.0392779	−	0.999228i	$-0.487494\pi$
$691$	2.06498	0.0785557	0.0392779	+	0.999228i	$0.487494\pi$
$692$	−4.78025	−0.181718
$693$	2.40268	0.0912702
$694$	28.4412	1.07961
$695$	−3.29782	−0.125094
$696$	−5.25963	−0.199366
$697$	8.00000	0.303022
$698$	−1.36281	−0.0515830
$699$	−15.6489	−0.591896
$700$	−3.03249	−0.114617
$701$	−40.4013	−1.52594	−0.762968	−	0.646436i	$-0.776259\pi$
$701$	−40.4013	−1.52594	−0.762968	+	0.646436i	$0.776259\pi$
$702$	−4.17554	−0.157596
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	−10.3484	−0.389742
$706$	−7.07670	−0.266335
$707$	−0.780246	−0.0293442
$708$	2.74037	0.102990
$709$	−48.5460	−1.82318	−0.911592	−	0.411095i	$-0.865146\pi$
$709$	−48.5460	−1.82318	−0.911592	+	0.411095i	$0.865146\pi$
$710$	19.2921	0.724020
$711$	23.4352	0.878888
$712$	−4.77287	−0.178871
$713$	−10.6787	−0.399922
$714$	−0.597321	−0.0223542
$715$	−1.40268	−0.0524572
$716$	2.45427	0.0917203
$717$	−5.03851	−0.188166
$718$	−6.18292	−0.230745
$719$	35.6580	1.32982	0.664909	−	0.746924i	$-0.268470\pi$
$719$	35.6580	1.32982	0.664909	+	0.746924i	$0.268470\pi$
$720$	3.37019	0.125599
$721$	−13.6107	−0.506890
$722$	7.42178	0.276210
$723$	−5.88206	−0.218756
$724$	−4.74037	−0.176175
$725$	−20.6372	−0.766446
$726$	−0.772866	−0.0286837
$727$	4.96317	0.184074	0.0920369	−	0.995756i	$-0.470662\pi$
$727$	4.96317	0.184074	0.0920369	+	0.995756i	$0.470662\pi$
$728$	1.00000	0.0370625
$729$	0.116574	0.00431757
$730$	10.1829	0.376887
$731$	1.79196	0.0662782
$732$	−8.10486	−0.299564
$733$	22.6874	0.837979	0.418989	−	0.907991i	$-0.362384\pi$
$733$	22.6874	0.837979	0.418989	+	0.907991i	$0.362384\pi$
$734$	0.707881	0.0261284
$735$	−1.08408	−0.0399870
$736$	−2.45427	−0.0904656
$737$	0.772866	0.0284689
$738$	24.8703	0.915490
$739$	32.2747	1.18724	0.593622	−	0.804744i	$-0.297697\pi$
$739$	32.2747	1.18724	0.593622	+	0.804744i	$0.297697\pi$
$740$	0	0
$741$	−2.62981	−0.0966086
$742$	−8.03249	−0.294882
$743$	−16.9085	−0.620314	−0.310157	−	0.950685i	$-0.600382\pi$
$743$	−16.9085	−0.620314	−0.310157	+	0.950685i	$0.600382\pi$
$744$	3.36281	0.123286
$745$	14.4633	0.529895
$746$	17.2596	0.631920
$747$	−0.747754	−0.0273589
$748$	−0.772866	−0.0282588
$749$	−3.86433	−0.141199
$750$	−8.70788	−0.317967
$751$	−33.6905	−1.22938	−0.614691	−	0.788768i	$-0.710719\pi$
$751$	−33.6905	−1.22938	−0.614691	+	0.788768i	$0.710719\pi$
$752$	9.54573	0.348097
$753$	1.16383	0.0424122
$754$	6.80536	0.247837
$755$	15.2476	0.554917
$756$	−4.17554	−0.151863
$757$	37.8985	1.37744	0.688722	−	0.725025i	$-0.258172\pi$
$757$	37.8985	1.37744	0.688722	+	0.725025i	$0.258172\pi$
$758$	11.2271	0.407788
$759$	−1.89682	−0.0688502
$760$	4.77287	0.173130
$761$	52.9353	1.91890	0.959452	−	0.281872i	$-0.0909553\pi$
$761$	52.9353	1.91890	0.959452	+	0.281872i	$0.0909553\pi$
$762$	−8.24053	−0.298523
$763$	11.9219	0.431603
$764$	17.6107	0.637133
$765$	2.60470	0.0941732
$766$	0.351089	0.0126854
$767$	−3.54573	−0.128029
$768$	0.772866	0.0278884
$769$	−47.7407	−1.72157	−0.860787	−	0.508966i	$-0.830028\pi$
$769$	−47.7407	−1.72157	−0.860787	+	0.508966i	$0.830028\pi$
$770$	−1.40268	−0.0505490
$771$	−9.94704	−0.358234
$772$	1.51324	0.0544627
$773$	31.0476	1.11670	0.558352	−	0.829604i	$-0.311434\pi$
$773$	31.0476	1.11670	0.558352	+	0.829604i	$0.311434\pi$
$774$	5.57084	0.200240
$775$	13.1946	0.473966
$776$	−5.25963	−0.188810
$777$	0	0
$778$	19.6358	0.703979
$779$	35.2214	1.26194
$780$	1.08408	0.0388164
$781$	−13.7538	−0.492148
$782$	−1.89682	−0.0678301
$783$	−28.4161	−1.01551
$784$	1.00000	0.0357143
$785$	−29.2744	−1.04485
$786$	−4.41607	−0.157516
$787$	19.0208	0.678017	0.339009	−	0.940783i	$-0.389908\pi$
$787$	19.0208	0.678017	0.339009	+	0.940783i	$0.389908\pi$
$788$	−11.1240	−0.396274
$789$	8.46165	0.301243
$790$	−13.6814	−0.486762
$791$	6.59732	0.234574
$792$	−2.40268	−0.0853755
$793$	10.4868	0.372396
$794$	−18.9176	−0.671360
$795$	−8.70788	−0.308837
$796$	−1.29950	−0.0460595
$797$	35.3394	1.25178	0.625892	−	0.779909i	$-0.284735\pi$
$797$	35.3394	1.25178	0.625892	+	0.779909i	$0.284735\pi$
$798$	−2.62981	−0.0930944
$799$	7.37757	0.261000
$800$	3.03249	0.107215
$801$	−11.4677	−0.405190
$802$	−3.81708	−0.134786
$803$	−7.25963	−0.256187
$804$	−0.597321	−0.0210659
$805$	−3.44255	−0.121334
$806$	−4.35109	−0.153261
$807$	4.14473	0.145901
$808$	0.780246	0.0274489
$809$	−50.7819	−1.78540	−0.892699	−	0.450654i	$-0.851191\pi$
$809$	−50.7819	−1.78540	−0.892699	+	0.450654i	$0.851191\pi$
$810$	5.58393	0.196199
$811$	15.4824	0.543661	0.271831	−	0.962345i	$-0.412371\pi$
$811$	15.4824	0.543661	0.271831	+	0.962345i	$0.412371\pi$
$812$	6.80536	0.238821
$813$	20.9336	0.734175
$814$	0	0
$815$	−0.436537	−0.0152912
$816$	0.597321	0.0209104
$817$	7.88944	0.276017
$818$	32.3779	1.13207
$819$	2.40268	0.0839564
$820$	−14.5193	−0.507034
$821$	14.2154	0.496121	0.248061	−	0.968744i	$-0.420207\pi$
$821$	14.2154	0.496121	0.248061	+	0.968744i	$0.420207\pi$
$822$	−1.81708	−0.0633778
$823$	49.0385	1.70937	0.854687	−	0.519143i	$-0.173749\pi$
$823$	49.0385	1.70937	0.854687	+	0.519143i	$0.173749\pi$
$824$	13.6107	0.474152
$825$	2.34371	0.0815975
$826$	−3.54573	−0.123372
$827$	35.1564	1.22251	0.611255	−	0.791434i	$-0.290665\pi$
$827$	35.1564	1.22251	0.611255	+	0.791434i	$0.290665\pi$
$828$	−5.89682	−0.204929
$829$	−17.9852	−0.624653	−0.312327	−	0.949975i	$-0.601108\pi$
$829$	−17.9852	−0.624653	−0.312327	+	0.949975i	$0.601108\pi$
$830$	0.436537	0.0151524
$831$	4.76716	0.165371
$832$	−1.00000	−0.0346688
$833$	0.772866	0.0267782
$834$	−1.81708	−0.0629202
$835$	16.7330	0.579069
$836$	−3.40268	−0.117684
$837$	18.1682	0.627984
$838$	7.29212	0.251902
$839$	−30.0268	−1.03664	−0.518320	−	0.855187i	$-0.673442\pi$
$839$	−30.0268	−1.03664	−0.518320	+	0.855187i	$0.673442\pi$
$840$	1.08408	0.0374044
$841$	17.3129	0.596996
$842$	−20.7672	−0.715684
$843$	11.6888	0.402583
$844$	10.3836	0.357418
$845$	−1.40268	−0.0482536
$846$	22.9353	0.788533
$847$	1.00000	0.0343604
$848$	8.03249	0.275837
$849$	−7.02648	−0.241148
$850$	2.34371	0.0803885
$851$	0	0
$852$	10.6298	0.364171
$853$	−33.5873	−1.15001	−0.575003	−	0.818151i	$-0.694999\pi$
$853$	−33.5873	−1.15001	−0.575003	+	0.818151i	$0.694999\pi$
$854$	10.4868	0.358850
$855$	11.4677	0.392186
$856$	3.86433	0.132080
$857$	43.7538	1.49460	0.747300	−	0.664487i	$-0.231350\pi$
$857$	43.7538	1.49460	0.747300	+	0.664487i	$0.231350\pi$
$858$	−0.772866	−0.0263852
$859$	15.9236	0.543307	0.271653	−	0.962395i	$-0.412430\pi$
$859$	15.9236	0.543307	0.271653	+	0.962395i	$0.412430\pi$
$860$	−3.25225	−0.110901
$861$	8.00000	0.272639
$862$	31.2214	1.06341
$863$	−20.0918	−0.683932	−0.341966	−	0.939712i	$-0.611093\pi$
$863$	−20.0918	−0.683932	−0.341966	+	0.939712i	$0.611093\pi$
$864$	4.17554	0.142055
$865$	6.70515	0.227982
$866$	26.0650	0.885724
$867$	−12.6771	−0.430536
$868$	−4.35109	−0.147686
$869$	9.75377	0.330874
$870$	7.37757	0.250123
$871$	0.772866	0.0261876
$872$	−11.9219	−0.403728
$873$	−12.6372	−0.427704
$874$	−8.35109	−0.282480
$875$	11.2670	0.380894
$876$	5.61072	0.189569
$877$	18.7876	0.634413	0.317207	−	0.948356i	$-0.397255\pi$
$877$	18.7876	0.634413	0.317207	+	0.948356i	$0.397255\pi$
$878$	3.01172	0.101641
$879$	7.94978	0.268139
$880$	1.40268	0.0472843
$881$	27.4044	0.923276	0.461638	−	0.887068i	$-0.347262\pi$
$881$	27.4044	0.923276	0.461638	+	0.887068i	$0.347262\pi$
$882$	2.40268	0.0809024
$883$	−43.2067	−1.45402	−0.727010	−	0.686627i	$-0.759091\pi$
$883$	−43.2067	−1.45402	−0.727010	+	0.686627i	$0.759091\pi$
$884$	−0.772866	−0.0259943
$885$	−3.84386	−0.129210
$886$	18.1032	0.608188
$887$	−4.68742	−0.157388	−0.0786940	−	0.996899i	$-0.525075\pi$
$887$	−4.68742	−0.157388	−0.0786940	+	0.996899i	$0.525075\pi$
$888$	0	0
$889$	10.6623	0.357602
$890$	6.69480	0.224410
$891$	−3.98090	−0.133365
$892$	10.5193	0.352211
$893$	32.4811	1.08694
$894$	7.96918	0.266529
$895$	−3.44255	−0.115072
$896$	−1.00000	−0.0334077
$897$	−1.89682	−0.0633330
$898$	6.06498	0.202391
$899$	−29.6107	−0.987573
$900$	7.28610	0.242870
$901$	6.20804	0.206820
$902$	10.3511	0.344654
$903$	1.79196	0.0596328
$904$	−6.59732	−0.219424
$905$	6.64922	0.221028
$906$	8.40131	0.279115
$907$	4.48106	0.148791	0.0743955	−	0.997229i	$-0.476297\pi$
$907$	4.48106	0.148791	0.0743955	+	0.997229i	$0.476297\pi$
$908$	20.7729	0.689372
$909$	1.87468	0.0621792
$910$	−1.40268	−0.0464984
$911$	31.4426	1.04174	0.520869	−	0.853637i	$-0.325608\pi$
$911$	31.4426	1.04174	0.520869	+	0.853637i	$0.325608\pi$
$912$	2.62981	0.0870818
$913$	−0.311217	−0.0102998
$914$	15.2198	0.503425
$915$	11.3685	0.375831
$916$	28.6241	0.945767
$917$	5.71390	0.188689
$918$	3.22713	0.106511
$919$	29.0355	0.957794	0.478897	−	0.877871i	$-0.341037\pi$
$919$	29.0355	0.957794	0.478897	+	0.877871i	$0.341037\pi$
$920$	3.44255	0.113498
$921$	4.23147	0.139432
$922$	32.3129	1.06417
$923$	−13.7538	−0.452711
$924$	−0.772866	−0.0254254
$925$	0	0
$926$	−33.7789	−1.11004
$927$	32.7022	1.07408
$928$	−6.80536	−0.223397
$929$	−43.7230	−1.43450	−0.717252	−	0.696814i	$-0.754600\pi$
$929$	−43.7230	−1.43450	−0.717252	+	0.696814i	$0.754600\pi$
$930$	−4.71694	−0.154674
$931$	3.40268	0.111518
$932$	−20.2479	−0.663242
$933$	−0.461649	−0.0151137
$934$	14.0473	0.459640
$935$	1.08408	0.0354533
$936$	−2.40268	−0.0785340
$937$	41.4147	1.35296	0.676480	−	0.736461i	$-0.263505\pi$
$937$	41.4147	1.35296	0.676480	+	0.736461i	$0.263505\pi$
$938$	0.772866	0.0252350
$939$	9.18323	0.299684
$940$	−13.3896	−0.436720
$941$	3.97656	0.129632	0.0648161	−	0.997897i	$-0.479354\pi$
$941$	3.97656	0.129632	0.0648161	+	0.997897i	$0.479354\pi$
$942$	−16.1300	−0.525543
$943$	25.4044	0.827280
$944$	3.54573	0.115404
$945$	5.85695	0.190527
$946$	2.31860	0.0753841
$947$	23.0208	0.748075	0.374037	−	0.927414i	$-0.377973\pi$
$947$	23.0208	0.748075	0.374037	+	0.927414i	$0.377973\pi$
$948$	−7.53835	−0.244834
$949$	−7.25963	−0.235657
$950$	10.3186	0.334779
$951$	−12.9588	−0.420217
$952$	−0.772866	−0.0250487
$953$	22.9233	0.742558	0.371279	−	0.928521i	$-0.378919\pi$
$953$	22.9233	0.742558	0.371279	+	0.928521i	$0.378919\pi$
$954$	19.2995	0.624844
$955$	−24.7022	−0.799344
$956$	−6.51925	−0.210848
$957$	−5.25963	−0.170020
$958$	−22.8305	−0.737619
$959$	2.35109	0.0759206
$960$	−1.08408	−0.0349886
$961$	−12.0680	−0.389291
$962$	0	0
$963$	9.28474	0.299197
$964$	−7.61072	−0.245125
$965$	−2.12259	−0.0683285
$966$	−1.89682	−0.0610292
$967$	49.2630	1.58419	0.792095	−	0.610397i	$-0.208990\pi$
$967$	49.2630	1.58419	0.792095	+	0.610397i	$0.208990\pi$
$968$	−1.00000	−0.0321412
$969$	2.03249	0.0652931
$970$	7.37757	0.236879
$971$	−19.0402	−0.611029	−0.305514	−	0.952187i	$-0.598828\pi$
$971$	−19.0402	−0.611029	−0.305514	+	0.952187i	$0.598828\pi$
$972$	15.6033	0.500477
$973$	2.35109	0.0753724
$974$	−24.5340	−0.786120
$975$	2.34371	0.0750587
$976$	−10.4868	−0.335673
$977$	30.1447	0.964415	0.482208	−	0.876057i	$-0.339835\pi$
$977$	30.1447	0.964415	0.482208	+	0.876057i	$0.339835\pi$
$978$	−0.240529	−0.00769126
$979$	−4.77287	−0.152541
$980$	−1.40268	−0.0448069
$981$	−28.6446	−0.914551
$982$	−1.27439	−0.0406673
$983$	1.12966	0.0360305	0.0180152	−	0.999838i	$-0.494265\pi$
$983$	1.12966	0.0360305	0.0180152	+	0.999838i	$0.494265\pi$
$984$	−8.00000	−0.255031
$985$	15.6033	0.497164
$986$	−5.25963	−0.167501
$987$	7.37757	0.234831
$988$	−3.40268	−0.108254
$989$	5.69046	0.180946
$990$	3.37019	0.107112
$991$	39.1564	1.24385	0.621923	−	0.783079i	$-0.286352\pi$
$991$	39.1564	1.24385	0.621923	+	0.783079i	$0.286352\pi$
$992$	4.35109	0.138147
$993$	−12.4469	−0.394990
$994$	−13.7538	−0.436243
$995$	1.82278	0.0577860
$996$	0.240529	0.00762144
$997$	24.1316	0.764257	0.382128	−	0.924109i	$-0.375191\pi$
$997$	24.1316	0.764257	0.382128	+	0.924109i	$0.375191\pi$
$998$	3.06635	0.0970636
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2002.2.a.i.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2002.2.a.i.1.2	✓	3	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:	\( N \)	\(=\)	\( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.772866 q^{3} +1.00000 q^{4} -1.40268 q^{5} -0.772866 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.40268 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.772866 q^{3} +1.00000 q^{4} -1.40268 q^{5} -0.772866 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.40268 q^{9} +1.40268 q^{10} -1.00000 q^{11} +0.772866 q^{12} -1.00000 q^{13} -1.00000 q^{14} -1.08408 q^{15} +1.00000 q^{16} +0.772866 q^{17} +2.40268 q^{18} +3.40268 q^{19} -1.40268 q^{20} +0.772866 q^{21} +1.00000 q^{22} +2.45427 q^{23} -0.772866 q^{24} -3.03249 q^{25} +1.00000 q^{26} -4.17554 q^{27} +1.00000 q^{28} +6.80536 q^{29} +1.08408 q^{30} -4.35109 q^{31} -1.00000 q^{32} -0.772866 q^{33} -0.772866 q^{34} -1.40268 q^{35} -2.40268 q^{36} -3.40268 q^{38} -0.772866 q^{39} +1.40268 q^{40} +10.3511 q^{41} -0.772866 q^{42} +2.31860 q^{43} -1.00000 q^{44} +3.37019 q^{45} -2.45427 q^{46} +9.54573 q^{47} +0.772866 q^{48} +1.00000 q^{49} +3.03249 q^{50} +0.597321 q^{51} -1.00000 q^{52} +8.03249 q^{53} +4.17554 q^{54} +1.40268 q^{55} -1.00000 q^{56} +2.62981 q^{57} -6.80536 q^{58} +3.54573 q^{59} -1.08408 q^{60} -10.4868 q^{61} +4.35109 q^{62} -2.40268 q^{63} +1.00000 q^{64} +1.40268 q^{65} +0.772866 q^{66} -0.772866 q^{67} +0.772866 q^{68} +1.89682 q^{69} +1.40268 q^{70} +13.7538 q^{71} +2.40268 q^{72} +7.25963 q^{73} -2.34371 q^{75} +3.40268 q^{76} -1.00000 q^{77} +0.772866 q^{78} -9.75377 q^{79} -1.40268 q^{80} +3.98090 q^{81} -10.3511 q^{82} +0.311217 q^{83} +0.772866 q^{84} -1.08408 q^{85} -2.31860 q^{86} +5.25963 q^{87} +1.00000 q^{88} +4.77287 q^{89} -3.37019 q^{90} -1.00000 q^{91} +2.45427 q^{92} -3.36281 q^{93} -9.54573 q^{94} -4.77287 q^{95} -0.772866 q^{96} +5.25963 q^{97} -1.00000 q^{98} +2.40268 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - q^{6} + 3 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 - q^6 + 3 * q^7 - 3 * q^8 + 2 * q^9	\( 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} - q^{6} + 3 q^{7} - 3 q^{8} + 2 q^{9} - 5 q^{10} - 3 q^{11} + q^{12} - 3 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} + q^{17} - 2 q^{18} + q^{19} + 5 q^{20} + q^{21} + 3 q^{22} + 10 q^{23} - q^{24} + 8 q^{25} + 3 q^{26} - 2 q^{27} + 3 q^{28} + 2 q^{29} - 2 q^{30} + 8 q^{31} - 3 q^{32} - q^{33} - q^{34} + 5 q^{35} + 2 q^{36} - q^{38} - q^{39} - 5 q^{40} + 10 q^{41} - q^{42} + 3 q^{43} - 3 q^{44} + 18 q^{45} - 10 q^{46} + 26 q^{47} + q^{48} + 3 q^{49} - 8 q^{50} + 11 q^{51} - 3 q^{52} + 7 q^{53} + 2 q^{54} - 5 q^{55} - 3 q^{56} - 2 q^{58} + 8 q^{59} + 2 q^{60} - 17 q^{61} - 8 q^{62} + 2 q^{63} + 3 q^{64} - 5 q^{65} + q^{66} - q^{67} + q^{68} - 18 q^{69} - 5 q^{70} + 11 q^{71} - 2 q^{72} + 6 q^{73} + 14 q^{75} + q^{76} - 3 q^{77} + q^{78} + q^{79} + 5 q^{80} - 17 q^{81} - 10 q^{82} - 3 q^{83} + q^{84} + 2 q^{85} - 3 q^{86} + 3 q^{88} + 13 q^{89} - 18 q^{90} - 3 q^{91} + 10 q^{92} - 18 q^{93} - 26 q^{94} - 13 q^{95} - q^{96} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 - q^6 + 3 * q^7 - 3 * q^8 + 2 * q^9 - 5 * q^10 - 3 * q^11 + q^12 - 3 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 + q^17 - 2 * q^18 + q^19 + 5 * q^20 + q^21 + 3 * q^22 + 10 * q^23 - q^24 + 8 * q^25 + 3 * q^26 - 2 * q^27 + 3 * q^28 + 2 * q^29 - 2 * q^30 + 8 * q^31 - 3 * q^32 - q^33 - q^34 + 5 * q^35 + 2 * q^36 - q^38 - q^39 - 5 * q^40 + 10 * q^41 - q^42 + 3 * q^43 - 3 * q^44 + 18 * q^45 - 10 * q^46 + 26 * q^47 + q^48 + 3 * q^49 - 8 * q^50 + 11 * q^51 - 3 * q^52 + 7 * q^53 + 2 * q^54 - 5 * q^55 - 3 * q^56 - 2 * q^58 + 8 * q^59 + 2 * q^60 - 17 * q^61 - 8 * q^62 + 2 * q^63 + 3 * q^64 - 5 * q^65 + q^66 - q^67 + q^68 - 18 * q^69 - 5 * q^70 + 11 * q^71 - 2 * q^72 + 6 * q^73 + 14 * q^75 + q^76 - 3 * q^77 + q^78 + q^79 + 5 * q^80 - 17 * q^81 - 10 * q^82 - 3 * q^83 + q^84 + 2 * q^85 - 3 * q^86 + 3 * q^88 + 13 * q^89 - 18 * q^90 - 3 * q^91 + 10 * q^92 - 18 * q^93 - 26 * q^94 - 13 * q^95 - q^96 - 3 * q^98 - 2 * q^99

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