LMFDB - Embedded newform 1870.2.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1870,2,Mod(1,1870)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1870, 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("1870.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1870 = 2 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1870.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:	$14.9320251780$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.940.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 7x - 4 $ x^3 - 7*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			$-0.602705$ of defining polynomial
Character	$\chi$	$=$	1870.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.602705 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.602705 q^{6} +3.03404 q^{7} +1.00000 q^{8} -2.63675 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.602705 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.602705 q^{6} +3.03404 q^{7} +1.00000 q^{8} -2.63675 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.602705 q^{12} +4.43134 q^{13} +3.03404 q^{14} +0.602705 q^{15} +1.00000 q^{16} -1.00000 q^{17} -2.63675 q^{18} -1.63675 q^{19} -1.00000 q^{20} -1.82863 q^{21} -1.00000 q^{22} +5.03404 q^{23} -0.602705 q^{24} +1.00000 q^{25} +4.43134 q^{26} +3.39730 q^{27} +3.03404 q^{28} +8.43134 q^{29} +0.602705 q^{30} -2.43134 q^{31} +1.00000 q^{32} +0.602705 q^{33} -1.00000 q^{34} -3.03404 q^{35} -2.63675 q^{36} -3.20541 q^{37} -1.63675 q^{38} -2.67079 q^{39} -1.00000 q^{40} +3.03404 q^{41} -1.82863 q^{42} +1.20541 q^{43} -1.00000 q^{44} +2.63675 q^{45} +5.03404 q^{46} +11.6367 q^{47} -0.602705 q^{48} +2.20541 q^{49} +1.00000 q^{50} +0.602705 q^{51} +4.43134 q^{52} +0.602705 q^{53} +3.39730 q^{54} +1.00000 q^{55} +3.03404 q^{56} +0.986475 q^{57} +8.43134 q^{58} -5.46538 q^{59} +0.602705 q^{60} +0.774073 q^{61} -2.43134 q^{62} -8.00000 q^{63} +1.00000 q^{64} -4.43134 q^{65} +0.602705 q^{66} +8.30754 q^{67} -1.00000 q^{68} -3.03404 q^{69} -3.03404 q^{70} +0.363253 q^{71} -2.63675 q^{72} +11.0816 q^{73} -3.20541 q^{74} -0.602705 q^{75} -1.63675 q^{76} -3.03404 q^{77} -2.67079 q^{78} -17.2735 q^{79} -1.00000 q^{80} +5.86267 q^{81} +3.03404 q^{82} +4.96596 q^{83} -1.82863 q^{84} +1.00000 q^{85} +1.20541 q^{86} -5.08161 q^{87} -1.00000 q^{88} +5.63675 q^{89} +2.63675 q^{90} +13.4449 q^{91} +5.03404 q^{92} +1.46538 q^{93} +11.6367 q^{94} +1.63675 q^{95} -0.602705 q^{96} -9.56866 q^{97} +2.20541 q^{98} +2.63675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 2 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 2 * q^7 + 3 * q^8 + 5 * q^9	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 2 q^{7} + 3 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} + 4 q^{13} - 2 q^{14} + 3 q^{16} - 3 q^{17} + 5 q^{18} + 8 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} + 4 q^{23} + 3 q^{25} + 4 q^{26} + 12 q^{27} - 2 q^{28} + 16 q^{29} + 2 q^{31} + 3 q^{32} - 3 q^{34} + 2 q^{35} + 5 q^{36} - 6 q^{37} + 8 q^{38} + 16 q^{39} - 3 q^{40} - 2 q^{41} + 2 q^{42} - 3 q^{44} - 5 q^{45} + 4 q^{46} + 22 q^{47} + 3 q^{49} + 3 q^{50} + 4 q^{52} + 12 q^{54} + 3 q^{55} - 2 q^{56} + 12 q^{57} + 16 q^{58} + 4 q^{59} + 8 q^{61} + 2 q^{62} - 24 q^{63} + 3 q^{64} - 4 q^{65} - 12 q^{67} - 3 q^{68} + 2 q^{69} + 2 q^{70} + 14 q^{71} + 5 q^{72} + 2 q^{73} - 6 q^{74} + 8 q^{76} + 2 q^{77} + 16 q^{78} - 26 q^{79} - 3 q^{80} - q^{81} - 2 q^{82} + 26 q^{83} + 2 q^{84} + 3 q^{85} + 16 q^{87} - 3 q^{88} + 4 q^{89} - 5 q^{90} + 22 q^{91} + 4 q^{92} - 16 q^{93} + 22 q^{94} - 8 q^{95} - 38 q^{97} + 3 q^{98} - 5 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 2 * q^7 + 3 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 + 4 * q^13 - 2 * q^14 + 3 * q^16 - 3 * q^17 + 5 * q^18 + 8 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 + 4 * q^23 + 3 * q^25 + 4 * q^26 + 12 * q^27 - 2 * q^28 + 16 * q^29 + 2 * q^31 + 3 * q^32 - 3 * q^34 + 2 * q^35 + 5 * q^36 - 6 * q^37 + 8 * q^38 + 16 * q^39 - 3 * q^40 - 2 * q^41 + 2 * q^42 - 3 * q^44 - 5 * q^45 + 4 * q^46 + 22 * q^47 + 3 * q^49 + 3 * q^50 + 4 * q^52 + 12 * q^54 + 3 * q^55 - 2 * q^56 + 12 * q^57 + 16 * q^58 + 4 * q^59 + 8 * q^61 + 2 * q^62 - 24 * q^63 + 3 * q^64 - 4 * q^65 - 12 * q^67 - 3 * q^68 + 2 * q^69 + 2 * q^70 + 14 * q^71 + 5 * q^72 + 2 * q^73 - 6 * q^74 + 8 * q^76 + 2 * q^77 + 16 * q^78 - 26 * q^79 - 3 * q^80 - q^81 - 2 * q^82 + 26 * q^83 + 2 * q^84 + 3 * q^85 + 16 * q^87 - 3 * q^88 + 4 * q^89 - 5 * q^90 + 22 * q^91 + 4 * q^92 - 16 * q^93 + 22 * q^94 - 8 * q^95 - 38 * q^97 + 3 * q^98 - 5 * 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
$3$	−0.602705	−0.347972	−0.173986	−	0.984748i	$-0.555665\pi$
$3$	−0.602705	−0.347972	−0.173986	+	0.984748i	$0.555665\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.602705	−0.246053
$7$	3.03404	1.14676	0.573380	−	0.819290i	$-0.305632\pi$
$7$	3.03404	1.14676	0.573380	+	0.819290i	$0.305632\pi$
$8$	1.00000	0.353553
$9$	−2.63675	−0.878916
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.602705	−0.173986
$13$	4.43134	1.22903	0.614516	−	0.788904i	$-0.289351\pi$
$13$	4.43134	1.22903	0.614516	+	0.788904i	$0.289351\pi$
$14$	3.03404	0.810882
$15$	0.602705	0.155618
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.63675	−0.621487
$19$	−1.63675	−0.375495	−0.187748	−	0.982217i	$-0.560119\pi$
$19$	−1.63675	−0.375495	−0.187748	+	0.982217i	$0.560119\pi$
$20$	−1.00000	−0.223607
$21$	−1.82863	−0.399040
$22$	−1.00000	−0.213201
$23$	5.03404	1.04967	0.524835	−	0.851204i	$-0.324127\pi$
$23$	5.03404	1.04967	0.524835	+	0.851204i	$0.324127\pi$
$24$	−0.602705	−0.123027
$25$	1.00000	0.200000
$26$	4.43134	0.869057
$27$	3.39730	0.653810
$28$	3.03404	0.573380
$29$	8.43134	1.56566	0.782830	−	0.622236i	$-0.213775\pi$
$29$	8.43134	1.56566	0.782830	+	0.622236i	$0.213775\pi$
$30$	0.602705	0.110038
$31$	−2.43134	−0.436681	−0.218340	−	0.975873i	$-0.570064\pi$
$31$	−2.43134	−0.436681	−0.218340	+	0.975873i	$0.570064\pi$
$32$	1.00000	0.176777
$33$	0.602705	0.104917
$34$	−1.00000	−0.171499
$35$	−3.03404	−0.512847
$36$	−2.63675	−0.439458
$37$	−3.20541	−0.526966	−0.263483	−	0.964664i	$-0.584871\pi$
$37$	−3.20541	−0.526966	−0.263483	+	0.964664i	$0.584871\pi$
$38$	−1.63675	−0.265515
$39$	−2.67079	−0.427668
$40$	−1.00000	−0.158114
$41$	3.03404	0.473838	0.236919	−	0.971529i	$-0.423862\pi$
$41$	3.03404	0.473838	0.236919	+	0.971529i	$0.423862\pi$
$42$	−1.82863	−0.282164
$43$	1.20541	0.183823	0.0919116	−	0.995767i	$-0.470702\pi$
$43$	1.20541	0.183823	0.0919116	+	0.995767i	$0.470702\pi$
$44$	−1.00000	−0.150756
$45$	2.63675	0.393063
$46$	5.03404	0.742229
$47$	11.6367	1.69739	0.848697	−	0.528879i	$-0.177388\pi$
$47$	11.6367	1.69739	0.848697	+	0.528879i	$0.177388\pi$
$48$	−0.602705	−0.0869930
$49$	2.20541	0.315059
$50$	1.00000	0.141421
$51$	0.602705	0.0843956
$52$	4.43134	0.614516
$53$	0.602705	0.0827879	0.0413939	−	0.999143i	$-0.486820\pi$
$53$	0.602705	0.0827879	0.0413939	+	0.999143i	$0.486820\pi$
$54$	3.39730	0.462313
$55$	1.00000	0.134840
$56$	3.03404	0.405441
$57$	0.986475	0.130662
$58$	8.43134	1.10709
$59$	−5.46538	−0.711532	−0.355766	−	0.934575i	$-0.615780\pi$
$59$	−5.46538	−0.711532	−0.355766	+	0.934575i	$0.615780\pi$
$60$	0.602705	0.0778089
$61$	0.774073	0.0991099	0.0495549	−	0.998771i	$-0.484220\pi$
$61$	0.774073	0.0991099	0.0495549	+	0.998771i	$0.484220\pi$
$62$	−2.43134	−0.308780
$63$	−8.00000	−1.00791
$64$	1.00000	0.125000
$65$	−4.43134	−0.549640
$66$	0.602705	0.0741878
$67$	8.30754	1.01493	0.507463	−	0.861673i	$-0.330583\pi$
$67$	8.30754	1.01493	0.507463	+	0.861673i	$0.330583\pi$
$68$	−1.00000	−0.121268
$69$	−3.03404	−0.365256
$70$	−3.03404	−0.362637
$71$	0.363253	0.0431102	0.0215551	−	0.999768i	$-0.493138\pi$
$71$	0.363253	0.0431102	0.0215551	+	0.999768i	$0.493138\pi$
$72$	−2.63675	−0.310744
$73$	11.0816	1.29700	0.648502	−	0.761213i	$-0.275396\pi$
$73$	11.0816	1.29700	0.648502	+	0.761213i	$0.275396\pi$
$74$	−3.20541	−0.372621
$75$	−0.602705	−0.0695944
$76$	−1.63675	−0.187748
$77$	−3.03404	−0.345761
$78$	−2.67079	−0.302407
$79$	−17.2735	−1.94342	−0.971710	−	0.236178i	$-0.924105\pi$
$79$	−17.2735	−1.94342	−0.971710	+	0.236178i	$0.924105\pi$
$80$	−1.00000	−0.111803
$81$	5.86267	0.651408
$82$	3.03404	0.335054
$83$	4.96596	0.545085	0.272542	−	0.962144i	$-0.412136\pi$
$83$	4.96596	0.545085	0.272542	+	0.962144i	$0.412136\pi$
$84$	−1.82863	−0.199520
$85$	1.00000	0.108465
$86$	1.20541	0.129983
$87$	−5.08161	−0.544806
$88$	−1.00000	−0.106600
$89$	5.63675	0.597494	0.298747	−	0.954332i	$-0.403431\pi$
$89$	5.63675	0.597494	0.298747	+	0.954332i	$0.403431\pi$
$90$	2.63675	0.277938
$91$	13.4449	1.40940
$92$	5.03404	0.524835
$93$	1.46538	0.151953
$94$	11.6367	1.20024
$95$	1.63675	0.167927
$96$	−0.602705	−0.0615133
$97$	−9.56866	−0.971551	−0.485775	−	0.874084i	$-0.661463\pi$
$97$	−9.56866	−0.971551	−0.485775	+	0.874084i	$0.661463\pi$
$98$	2.20541	0.222780
$99$	2.63675	0.265003
$100$	1.00000	0.100000
$101$	15.8967	1.58178	0.790891	−	0.611957i	$-0.209617\pi$
$101$	15.8967	1.58178	0.790891	+	0.611957i	$0.209617\pi$
$102$	0.602705	0.0596767
$103$	−0.862674	−0.0850018	−0.0425009	−	0.999096i	$-0.513533\pi$
$103$	−0.862674	−0.0850018	−0.0425009	+	0.999096i	$0.513533\pi$
$104$	4.43134	0.434528
$105$	1.82863	0.178456
$106$	0.602705	0.0585399
$107$	17.3416	1.67647	0.838237	−	0.545306i	$-0.183587\pi$
$107$	17.3416	1.67647	0.838237	+	0.545306i	$0.183587\pi$
$108$	3.39730	0.326905
$109$	−18.4994	−1.77192	−0.885962	−	0.463759i	$-0.846500\pi$
$109$	−18.4994	−1.77192	−0.885962	+	0.463759i	$0.846500\pi$
$110$	1.00000	0.0953463
$111$	1.93192	0.183369
$112$	3.03404	0.286690
$113$	14.9102	1.40264	0.701319	−	0.712848i	$-0.252595\pi$
$113$	14.9102	1.40264	0.701319	+	0.712848i	$0.252595\pi$
$114$	0.986475	0.0923919
$115$	−5.03404	−0.469427
$116$	8.43134	0.782830
$117$	−11.6843	−1.08022
$118$	−5.46538	−0.503129
$119$	−3.03404	−0.278130
$120$	0.602705	0.0550192
$121$	1.00000	0.0909091
$122$	0.774073	0.0700813
$123$	−1.82863	−0.164882
$124$	−2.43134	−0.218340
$125$	−1.00000	−0.0894427
$126$	−8.00000	−0.712697
$127$	−8.73887	−0.775450	−0.387725	−	0.921775i	$-0.626739\pi$
$127$	−8.73887	−0.775450	−0.387725	+	0.921775i	$0.626739\pi$
$128$	1.00000	0.0883883
$129$	−0.726506	−0.0639653
$130$	−4.43134	−0.388654
$131$	6.65027	0.581037	0.290518	−	0.956869i	$-0.406172\pi$
$131$	6.65027	0.581037	0.290518	+	0.956869i	$0.406172\pi$
$132$	0.602705	0.0524587
$133$	−4.96596	−0.430603
$134$	8.30754	0.717662
$135$	−3.39730	−0.292393
$136$	−1.00000	−0.0857493
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	−3.03404	−0.258275
$139$	−3.03404	−0.257344	−0.128672	−	0.991687i	$-0.541071\pi$
$139$	−3.03404	−0.257344	−0.128672	+	0.991687i	$0.541071\pi$
$140$	−3.03404	−0.256423
$141$	−7.01352	−0.590645
$142$	0.363253	0.0304835
$143$	−4.43134	−0.370567
$144$	−2.63675	−0.219729
$145$	−8.43134	−0.700184
$146$	11.0816	0.917120
$147$	−1.32921	−0.109632
$148$	−3.20541	−0.263483
$149$	−2.06808	−0.169424	−0.0847120	−	0.996405i	$-0.526997\pi$
$149$	−2.06808	−0.169424	−0.0847120	+	0.996405i	$0.526997\pi$
$150$	−0.602705	−0.0492107
$151$	−10.9308	−0.889532	−0.444766	−	0.895647i	$-0.646713\pi$
$151$	−10.9308	−0.889532	−0.444766	+	0.895647i	$0.646713\pi$
$152$	−1.63675	−0.132758
$153$	2.63675	0.213168
$154$	−3.03404	−0.244490
$155$	2.43134	0.195290
$156$	−2.67079	−0.213834
$157$	−16.5199	−1.31843	−0.659217	−	0.751953i	$-0.729112\pi$
$157$	−16.5199	−1.31843	−0.659217	+	0.751953i	$0.729112\pi$
$158$	−17.2735	−1.37421
$159$	−0.363253	−0.0288079
$160$	−1.00000	−0.0790569
$161$	15.2735	1.20372
$162$	5.86267	0.460615
$163$	4.47890	0.350815	0.175407	−	0.984496i	$-0.443876\pi$
$163$	4.47890	0.350815	0.175407	+	0.984496i	$0.443876\pi$
$164$	3.03404	0.236919
$165$	−0.602705	−0.0469205
$166$	4.96596	0.385433
$167$	−19.7524	−1.52849	−0.764243	−	0.644928i	$-0.776887\pi$
$167$	−19.7524	−1.52849	−0.764243	+	0.644928i	$0.776887\pi$
$168$	−1.82863	−0.141082
$169$	6.63675	0.510519
$170$	1.00000	0.0766965
$171$	4.31569	0.330029
$172$	1.20541	0.0919116
$173$	−11.1021	−0.844079	−0.422039	−	0.906577i	$-0.638686\pi$
$173$	−11.1021	−0.844079	−0.422039	+	0.906577i	$0.638686\pi$
$174$	−5.08161	−0.385236
$175$	3.03404	0.229352
$176$	−1.00000	−0.0753778
$177$	3.29401	0.247593
$178$	5.63675	0.422492
$179$	6.93076	0.518029	0.259015	−	0.965873i	$-0.416602\pi$
$179$	6.93076	0.518029	0.259015	+	0.965873i	$0.416602\pi$
$180$	2.63675	0.196532
$181$	12.0681	0.897014	0.448507	−	0.893779i	$-0.351956\pi$
$181$	12.0681	0.897014	0.448507	+	0.893779i	$0.351956\pi$
$182$	13.4449	0.996599
$183$	−0.466538	−0.0344875
$184$	5.03404	0.371114
$185$	3.20541	0.235666
$186$	1.46538	0.107447
$187$	1.00000	0.0731272
$188$	11.6367	0.848697
$189$	10.3075	0.749763
$190$	1.63675	0.118742
$191$	9.10213	0.658607	0.329303	−	0.944224i	$-0.393186\pi$
$191$	9.10213	0.658607	0.329303	+	0.944224i	$0.393186\pi$
$192$	−0.602705	−0.0434965
$193$	−19.6843	−1.41691	−0.708454	−	0.705757i	$-0.750607\pi$
$193$	−19.6843	−1.41691	−0.708454	+	0.705757i	$0.750607\pi$
$194$	−9.56866	−0.686990
$195$	2.67079	0.191259
$196$	2.20541	0.157529
$197$	17.7524	1.26481	0.632403	−	0.774640i	$-0.282069\pi$
$197$	17.7524	1.26481	0.632403	+	0.774640i	$0.282069\pi$
$198$	2.63675	0.187385
$199$	2.43134	0.172353	0.0861765	−	0.996280i	$-0.472535\pi$
$199$	2.43134	0.172353	0.0861765	+	0.996280i	$0.472535\pi$
$200$	1.00000	0.0707107
$201$	−5.00699	−0.353166
$202$	15.8967	1.11849
$203$	25.5810	1.79544
$204$	0.602705	0.0421978
$205$	−3.03404	−0.211907
$206$	−0.862674	−0.0601053
$207$	−13.2735	−0.922572
$208$	4.43134	0.307258
$209$	1.63675	0.113216
$210$	1.82863	0.126188
$211$	−6.45185	−0.444164	−0.222082	−	0.975028i	$-0.571285\pi$
$211$	−6.45185	−0.444164	−0.222082	+	0.975028i	$0.571285\pi$
$212$	0.602705	0.0413939
$213$	−0.218935	−0.0150011
$214$	17.3416	1.18545
$215$	−1.20541	−0.0822083
$216$	3.39730	0.231157
$217$	−7.37678	−0.500768
$218$	−18.4994	−1.25294
$219$	−6.67894	−0.451321
$220$	1.00000	0.0674200
$221$	−4.43134	−0.298084
$222$	1.93192	0.129662
$223$	18.5675	1.24337	0.621686	−	0.783267i	$-0.286448\pi$
$223$	18.5675	1.24337	0.621686	+	0.783267i	$0.286448\pi$
$224$	3.03404	0.202720
$225$	−2.63675	−0.175783
$226$	14.9102	0.991814
$227$	−23.7729	−1.57786	−0.788932	−	0.614481i	$-0.789366\pi$
$227$	−23.7729	−1.57786	−0.788932	+	0.614481i	$0.789366\pi$
$228$	0.986475	0.0653309
$229$	−8.41082	−0.555803	−0.277901	−	0.960610i	$-0.589639\pi$
$229$	−8.41082	−0.555803	−0.277901	+	0.960610i	$0.589639\pi$
$230$	−5.03404	−0.331935
$231$	1.82863	0.120315
$232$	8.43134	0.553544
$233$	−22.6978	−1.48698	−0.743492	−	0.668744i	$-0.766832\pi$
$233$	−22.6978	−1.48698	−0.743492	+	0.668744i	$0.766832\pi$
$234$	−11.6843	−0.763827
$235$	−11.6367	−0.759098
$236$	−5.46538	−0.355766
$237$	10.4108	0.676255
$238$	−3.03404	−0.196668
$239$	−3.37678	−0.218426	−0.109213	−	0.994018i	$-0.534833\pi$
$239$	−3.37678	−0.218426	−0.109213	+	0.994018i	$0.534833\pi$
$240$	0.602705	0.0389044
$241$	−5.34158	−0.344081	−0.172041	−	0.985090i	$-0.555036\pi$
$241$	−5.34158	−0.344081	−0.172041	+	0.985090i	$0.555036\pi$
$242$	1.00000	0.0642824
$243$	−13.7253	−0.880481
$244$	0.774073	0.0495549
$245$	−2.20541	−0.140898
$246$	−1.82863	−0.116589
$247$	−7.25298	−0.461496
$248$	−2.43134	−0.154390
$249$	−2.99301	−0.189674
$250$	−1.00000	−0.0632456
$251$	14.5470	0.918198	0.459099	−	0.888385i	$-0.348172\pi$
$251$	14.5470	0.918198	0.459099	+	0.888385i	$0.348172\pi$
$252$	−8.00000	−0.503953
$253$	−5.03404	−0.316487
$254$	−8.73887	−0.548326
$255$	−0.602705	−0.0377428
$256$	1.00000	0.0625000
$257$	−13.8557	−0.864294	−0.432147	−	0.901803i	$-0.642244\pi$
$257$	−13.8557	−0.864294	−0.432147	+	0.901803i	$0.642244\pi$
$258$	−0.726506	−0.0452303
$259$	−9.72535	−0.604304
$260$	−4.43134	−0.274820
$261$	−22.2313	−1.37608
$262$	6.65027	0.410855
$263$	−28.3961	−1.75098	−0.875490	−	0.483236i	$-0.839461\pi$
$263$	−28.3961	−1.75098	−0.875490	+	0.483236i	$0.839461\pi$
$264$	0.602705	0.0370939
$265$	−0.602705	−0.0370239
$266$	−4.96596	−0.304482
$267$	−3.39730	−0.207911
$268$	8.30754	0.507463
$269$	−17.0546	−1.03983	−0.519917	−	0.854217i	$-0.674037\pi$
$269$	−17.0546	−1.03983	−0.519917	+	0.854217i	$0.674037\pi$
$270$	−3.39730	−0.206753
$271$	28.3756	1.72370	0.861848	−	0.507167i	$-0.169307\pi$
$271$	28.3756	1.72370	0.861848	+	0.507167i	$0.169307\pi$
$272$	−1.00000	−0.0606339
$273$	−8.10328	−0.490433
$274$	2.00000	0.120824
$275$	−1.00000	−0.0603023
$276$	−3.03404	−0.182628
$277$	−21.6491	−1.30077	−0.650385	−	0.759605i	$-0.725392\pi$
$277$	−21.6491	−1.30077	−0.650385	+	0.759605i	$0.725392\pi$
$278$	−3.03404	−0.181970
$279$	6.41082	0.383806
$280$	−3.03404	−0.181319
$281$	3.32921	0.198604	0.0993021	−	0.995057i	$-0.468339\pi$
$281$	3.32921	0.198604	0.0993021	+	0.995057i	$0.468339\pi$
$282$	−7.01352	−0.417649
$283$	−29.8000	−1.77142	−0.885712	−	0.464235i	$-0.846329\pi$
$283$	−29.8000	−1.77142	−0.885712	+	0.464235i	$0.846329\pi$
$284$	0.363253	0.0215551
$285$	−0.986475	−0.0584338
$286$	−4.43134	−0.262030
$287$	9.20541	0.543378
$288$	−2.63675	−0.155372
$289$	1.00000	0.0588235
$290$	−8.43134	−0.495105
$291$	5.76708	0.338072
$292$	11.0816	0.648502
$293$	0.774073	0.0452218	0.0226109	−	0.999744i	$-0.492802\pi$
$293$	0.774073	0.0452218	0.0226109	+	0.999744i	$0.492802\pi$
$294$	−1.32921	−0.0775212
$295$	5.46538	0.318207
$296$	−3.20541	−0.186311
$297$	−3.39730	−0.197131
$298$	−2.06808	−0.119801
$299$	22.3075	1.29008
$300$	−0.602705	−0.0347972
$301$	3.65726	0.210801
$302$	−10.9308	−0.628994
$303$	−9.58103	−0.550416
$304$	−1.63675	−0.0938739
$305$	−0.774073	−0.0443233
$306$	2.63675	0.150733
$307$	6.55514	0.374122	0.187061	−	0.982348i	$-0.440104\pi$
$307$	6.55514	0.374122	0.187061	+	0.982348i	$0.440104\pi$
$308$	−3.03404	−0.172881
$309$	0.519938	0.0295782
$310$	2.43134	0.138091
$311$	11.2325	0.636934	0.318467	−	0.947934i	$-0.396832\pi$
$311$	11.2325	0.636934	0.318467	+	0.947934i	$0.396832\pi$
$312$	−2.67079	−0.151204
$313$	−27.6573	−1.56328	−0.781640	−	0.623729i	$-0.785617\pi$
$313$	−27.6573	−1.56328	−0.781640	+	0.623729i	$0.785617\pi$
$314$	−16.5199	−0.932274
$315$	8.00000	0.450749
$316$	−17.2735	−0.971710
$317$	−21.9918	−1.23519	−0.617593	−	0.786498i	$-0.711892\pi$
$317$	−21.9918	−1.23519	−0.617593	+	0.786498i	$0.711892\pi$
$318$	−0.363253	−0.0203702
$319$	−8.43134	−0.472064
$320$	−1.00000	−0.0559017
$321$	−10.4519	−0.583366
$322$	15.2735	0.851159
$323$	1.63675	0.0910710
$324$	5.86267	0.325704
$325$	4.43134	0.245806
$326$	4.47890	0.248064
$327$	11.1497	0.616579
$328$	3.03404	0.167527
$329$	35.3064	1.94650
$330$	−0.602705	−0.0331778
$331$	13.8491	0.761218	0.380609	−	0.924736i	$-0.375714\pi$
$331$	13.8491	0.761218	0.380609	+	0.924736i	$0.375714\pi$
$332$	4.96596	0.272542
$333$	8.45185	0.463159
$334$	−19.7524	−1.08080
$335$	−8.30754	−0.453889
$336$	−1.82863	−0.0997601
$337$	−35.2178	−1.91843	−0.959217	−	0.282670i	$-0.908780\pi$
$337$	−35.2178	−1.91843	−0.959217	+	0.282670i	$0.908780\pi$
$338$	6.63675	0.360991
$339$	−8.98648	−0.488078
$340$	1.00000	0.0542326
$341$	2.43134	0.131664
$342$	4.31569	0.233366
$343$	−14.5470	−0.785463
$344$	1.20541	0.0649913
$345$	3.03404	0.163347
$346$	−11.1021	−0.596854
$347$	20.1567	1.08207	0.541034	−	0.841001i	$-0.318033\pi$
$347$	20.1567	1.08207	0.541034	+	0.841001i	$0.318033\pi$
$348$	−5.08161	−0.272403
$349$	21.7253	1.16293	0.581466	−	0.813571i	$-0.302479\pi$
$349$	21.7253	1.16293	0.581466	+	0.813571i	$0.302479\pi$
$350$	3.03404	0.162176
$351$	15.0546	0.803553
$352$	−1.00000	−0.0533002
$353$	0.274652	0.0146183	0.00730914	−	0.999973i	$-0.497673\pi$
$353$	0.274652	0.0146183	0.00730914	+	0.999973i	$0.497673\pi$
$354$	3.29401	0.175075
$355$	−0.363253	−0.0192795
$356$	5.63675	0.298747
$357$	1.82863	0.0967815
$358$	6.93076	0.366302
$359$	−29.8205	−1.57386	−0.786932	−	0.617039i	$-0.788332\pi$
$359$	−29.8205	−1.57386	−0.786932	+	0.617039i	$0.788332\pi$
$360$	2.63675	0.138969
$361$	−16.3211	−0.859003
$362$	12.0681	0.634284
$363$	−0.602705	−0.0316338
$364$	13.4449	0.704702
$365$	−11.0816	−0.580038
$366$	−0.466538	−0.0243863
$367$	11.4449	0.597417	0.298708	−	0.954344i	$-0.403444\pi$
$367$	11.4449	0.597417	0.298708	+	0.954344i	$0.403444\pi$
$368$	5.03404	0.262418
$369$	−8.00000	−0.416463
$370$	3.20541	0.166641
$371$	1.82863	0.0949378
$372$	1.46538	0.0759763
$373$	11.6843	0.604991	0.302495	−	0.953151i	$-0.402180\pi$
$373$	11.6843	0.604991	0.302495	+	0.953151i	$0.402180\pi$
$374$	1.00000	0.0517088
$375$	0.602705	0.0311235
$376$	11.6367	0.600119
$377$	37.3621	1.92425
$378$	10.3075	0.530162
$379$	14.2043	0.729623	0.364812	−	0.931081i	$-0.381133\pi$
$379$	14.2043	0.729623	0.364812	+	0.931081i	$0.381133\pi$
$380$	1.63675	0.0839633
$381$	5.26696	0.269835
$382$	9.10213	0.465705
$383$	−20.1157	−1.02786	−0.513931	−	0.857832i	$-0.671811\pi$
$383$	−20.1157	−1.02786	−0.513931	+	0.857832i	$0.671811\pi$
$384$	−0.602705	−0.0307567
$385$	3.03404	0.154629
$386$	−19.6843	−1.00191
$387$	−3.17836	−0.161565
$388$	−9.56866	−0.485775
$389$	−17.5129	−0.887942	−0.443971	−	0.896041i	$-0.646431\pi$
$389$	−17.5129	−0.887942	−0.443971	+	0.896041i	$0.646431\pi$
$390$	2.67079	0.135241
$391$	−5.03404	−0.254582
$392$	2.20541	0.111390
$393$	−4.00815	−0.202184
$394$	17.7524	0.894353
$395$	17.2735	0.869124
$396$	2.63675	0.132502
$397$	2.19842	0.110335	0.0551677	−	0.998477i	$-0.482431\pi$
$397$	2.19842	0.110335	0.0551677	+	0.998477i	$0.482431\pi$
$398$	2.43134	0.121872
$399$	2.99301	0.149838
$400$	1.00000	0.0500000
$401$	−10.3756	−0.518134	−0.259067	−	0.965859i	$-0.583415\pi$
$401$	−10.3756	−0.518134	−0.259067	+	0.965859i	$0.583415\pi$
$402$	−5.00699	−0.249726
$403$	−10.7741	−0.536695
$404$	15.8967	0.790891
$405$	−5.86267	−0.291319
$406$	25.5810	1.26957
$407$	3.20541	0.158886
$408$	0.602705	0.0298383
$409$	1.91723	0.0948011	0.0474005	−	0.998876i	$-0.484906\pi$
$409$	1.91723	0.0948011	0.0474005	+	0.998876i	$0.484906\pi$
$410$	−3.03404	−0.149841
$411$	−1.20541	−0.0594585
$412$	−0.862674	−0.0425009
$413$	−16.5822	−0.815956
$414$	−13.2735	−0.652357
$415$	−4.96596	−0.243769
$416$	4.43134	0.217264
$417$	1.82863	0.0895485
$418$	1.63675	0.0800559
$419$	−5.68431	−0.277697	−0.138848	−	0.990314i	$-0.544340\pi$
$419$	−5.68431	−0.277697	−0.138848	+	0.990314i	$0.544340\pi$
$420$	1.82863	0.0892281
$421$	−18.9988	−0.925947	−0.462973	−	0.886372i	$-0.653217\pi$
$421$	−18.9988	−0.925947	−0.462973	+	0.886372i	$0.653217\pi$
$422$	−6.45185	−0.314071
$423$	−30.6832	−1.49187
$424$	0.602705	0.0292699
$425$	−1.00000	−0.0485071
$426$	−0.218935	−0.0106074
$427$	2.34857	0.113655
$428$	17.3416	0.838237
$429$	2.67079	0.128947
$430$	−1.20541	−0.0581300
$431$	27.6843	1.33351	0.666753	−	0.745279i	$-0.267684\pi$
$431$	27.6843	1.33351	0.666753	+	0.745279i	$0.267684\pi$
$432$	3.39730	0.163452
$433$	15.5810	0.748776	0.374388	−	0.927272i	$-0.377853\pi$
$433$	15.5810	0.748776	0.374388	+	0.927272i	$0.377853\pi$
$434$	−7.37678	−0.354097
$435$	5.08161	0.243644
$436$	−18.4994	−0.885962
$437$	−8.23945	−0.394146
$438$	−6.67894	−0.319132
$439$	29.0259	1.38533	0.692665	−	0.721259i	$-0.256436\pi$
$439$	29.0259	1.38533	0.692665	+	0.721259i	$0.256436\pi$
$440$	1.00000	0.0476731
$441$	−5.81511	−0.276910
$442$	−4.43134	−0.210777
$443$	9.37678	0.445504	0.222752	−	0.974875i	$-0.428496\pi$
$443$	9.37678	0.445504	0.222752	+	0.974875i	$0.428496\pi$
$444$	1.93192	0.0916847
$445$	−5.63675	−0.267207
$446$	18.5675	0.879197
$447$	1.24644	0.0589548
$448$	3.03404	0.143345
$449$	−15.1432	−0.714650	−0.357325	−	0.933980i	$-0.616311\pi$
$449$	−15.1432	−0.714650	−0.357325	+	0.933980i	$0.616311\pi$
$450$	−2.63675	−0.124297
$451$	−3.03404	−0.142867
$452$	14.9102	0.701319
$453$	6.58802	0.309532
$454$	−23.7729	−1.11572
$455$	−13.4449	−0.630305
$456$	0.986475	0.0461959
$457$	18.5118	0.865945	0.432972	−	0.901407i	$-0.357465\pi$
$457$	18.5118	0.865945	0.432972	+	0.901407i	$0.357465\pi$
$458$	−8.41082	−0.393012
$459$	−3.39730	−0.158572
$460$	−5.03404	−0.234713
$461$	−0.998841	−0.0465207	−0.0232603	−	0.999729i	$-0.507405\pi$
$461$	−0.998841	−0.0465207	−0.0232603	+	0.999729i	$0.507405\pi$
$462$	1.82863	0.0850757
$463$	35.7729	1.66251	0.831254	−	0.555893i	$-0.187623\pi$
$463$	35.7729	1.66251	0.831254	+	0.555893i	$0.187623\pi$
$464$	8.43134	0.391415
$465$	−1.46538	−0.0679553
$466$	−22.6978	−1.05146
$467$	−0.691306	−0.0319898	−0.0159949	−	0.999872i	$-0.505092\pi$
$467$	−0.691306	−0.0319898	−0.0159949	+	0.999872i	$0.505092\pi$
$468$	−11.6843	−0.540108
$469$	25.2054	1.16388
$470$	−11.6367	−0.536763
$471$	9.95665	0.458778
$472$	−5.46538	−0.251564
$473$	−1.20541	−0.0554248
$474$	10.4108	0.478185
$475$	−1.63675	−0.0750991
$476$	−3.03404	−0.139065
$477$	−1.58918	−0.0727636
$478$	−3.37678	−0.154450
$479$	29.1497	1.33188	0.665942	−	0.746004i	$-0.268030\pi$
$479$	29.1497	1.33188	0.665942	+	0.746004i	$0.268030\pi$
$480$	0.602705	0.0275096
$481$	−14.2043	−0.647658
$482$	−5.34158	−0.243302
$483$	−9.20541	−0.418861
$484$	1.00000	0.0454545
$485$	9.56866	0.434491
$486$	−13.7253	−0.622594
$487$	−10.3427	−0.468674	−0.234337	−	0.972155i	$-0.575292\pi$
$487$	−10.3427	−0.468674	−0.234337	+	0.972155i	$0.575292\pi$
$488$	0.774073	0.0350406
$489$	−2.69946	−0.122074
$490$	−2.20541	−0.0996303
$491$	10.3633	0.467687	0.233844	−	0.972274i	$-0.424870\pi$
$491$	10.3633	0.467687	0.233844	+	0.972274i	$0.424870\pi$
$492$	−1.82863	−0.0824411
$493$	−8.43134	−0.379728
$494$	−7.25298	−0.326327
$495$	−2.63675	−0.118513
$496$	−2.43134	−0.109170
$497$	1.10213	0.0494371
$498$	−2.99301	−0.134120
$499$	−32.8627	−1.47114	−0.735568	−	0.677451i	$-0.763084\pi$
$499$	−32.8627	−1.47114	−0.735568	+	0.677451i	$0.763084\pi$
$500$	−1.00000	−0.0447214
$501$	11.9049	0.531870
$502$	14.5470	0.649264
$503$	−22.6832	−1.01139	−0.505696	−	0.862712i	$-0.668764\pi$
$503$	−22.6832	−1.01139	−0.505696	+	0.862712i	$0.668764\pi$
$504$	−8.00000	−0.356348
$505$	−15.8967	−0.707395
$506$	−5.03404	−0.223790
$507$	−4.00000	−0.177646
$508$	−8.73887	−0.387725
$509$	−39.8534	−1.76647	−0.883235	−	0.468931i	$-0.844639\pi$
$509$	−39.8534	−1.76647	−0.883235	+	0.468931i	$0.844639\pi$
$510$	−0.602705	−0.0266882
$511$	33.6221	1.48735
$512$	1.00000	0.0441942
$513$	−5.56051	−0.245503
$514$	−13.8557	−0.611148
$515$	0.862674	0.0380139
$516$	−0.726506	−0.0319827
$517$	−11.6367	−0.511784
$518$	−9.72535	−0.427307
$519$	6.69131	0.293716
$520$	−4.43134	−0.194327
$521$	−29.6162	−1.29751	−0.648755	−	0.760997i	$-0.724710\pi$
$521$	−29.6162	−1.29751	−0.648755	+	0.760997i	$0.724710\pi$
$522$	−22.2313	−0.973038
$523$	36.5118	1.59655	0.798274	−	0.602294i	$-0.205746\pi$
$523$	36.5118	1.59655	0.798274	+	0.602294i	$0.205746\pi$
$524$	6.65027	0.290518
$525$	−1.82863	−0.0798080
$526$	−28.3961	−1.23813
$527$	2.43134	0.105911
$528$	0.602705	0.0262294
$529$	2.34158	0.101808
$530$	−0.602705	−0.0261798
$531$	14.4108	0.625376
$532$	−4.96596	−0.215302
$533$	13.4449	0.582362
$534$	−3.39730	−0.147015
$535$	−17.3416	−0.749742
$536$	8.30754	0.358831
$537$	−4.17720	−0.180260
$538$	−17.0546	−0.735274
$539$	−2.20541	−0.0949937
$540$	−3.39730	−0.146196
$541$	24.9308	1.07186	0.535928	−	0.844263i	$-0.319962\pi$
$541$	24.9308	1.07186	0.535928	+	0.844263i	$0.319962\pi$
$542$	28.3756	1.21884
$543$	−7.27349	−0.312135
$544$	−1.00000	−0.0428746
$545$	18.4994	0.792428
$546$	−8.10328	−0.346789
$547$	−0.747024	−0.0319404	−0.0159702	−	0.999872i	$-0.505084\pi$
$547$	−0.747024	−0.0319404	−0.0159702	+	0.999872i	$0.505084\pi$
$548$	2.00000	0.0854358
$549$	−2.04103	−0.0871092
$550$	−1.00000	−0.0426401
$551$	−13.8000	−0.587898
$552$	−3.03404	−0.129137
$553$	−52.4085	−2.22864
$554$	−21.6491	−0.919783
$555$	−1.93192	−0.0820053
$556$	−3.03404	−0.128672
$557$	−1.54161	−0.0653203	−0.0326601	−	0.999467i	$-0.510398\pi$
$557$	−1.54161	−0.0653203	−0.0326601	+	0.999467i	$0.510398\pi$
$558$	6.41082	0.271392
$559$	5.34158	0.225925
$560$	−3.03404	−0.128212
$561$	−0.602705	−0.0254462
$562$	3.32921	0.140434
$563$	24.3756	1.02731	0.513655	−	0.857997i	$-0.328291\pi$
$563$	24.3756	1.02731	0.513655	+	0.857997i	$0.328291\pi$
$564$	−7.01352	−0.295323
$565$	−14.9102	−0.627279
$566$	−29.8000	−1.25259
$567$	17.7876	0.747009
$568$	0.363253	0.0152418
$569$	−25.3973	−1.06471	−0.532355	−	0.846521i	$-0.678693\pi$
$569$	−25.3973	−1.06471	−0.532355	+	0.846521i	$0.678693\pi$
$570$	−0.986475	−0.0413189
$571$	19.1373	0.800872	0.400436	−	0.916325i	$-0.368859\pi$
$571$	19.1373	0.800872	0.400436	+	0.916325i	$0.368859\pi$
$572$	−4.43134	−0.185284
$573$	−5.48590	−0.229177
$574$	9.20541	0.384226
$575$	5.03404	0.209934
$576$	−2.63675	−0.109864
$577$	22.5199	0.937517	0.468759	−	0.883326i	$-0.344701\pi$
$577$	22.5199	0.937517	0.468759	+	0.883326i	$0.344701\pi$
$578$	1.00000	0.0415945
$579$	11.8638	0.493044
$580$	−8.43134	−0.350092
$581$	15.0669	0.625081
$582$	5.76708	0.239053
$583$	−0.602705	−0.0249615
$584$	11.0816	0.458560
$585$	11.6843	0.483087
$586$	0.774073	0.0319767
$587$	28.4108	1.17264	0.586320	−	0.810080i	$-0.300576\pi$
$587$	28.4108	1.17264	0.586320	+	0.810080i	$0.300576\pi$
$588$	−1.32921	−0.0548158
$589$	3.97948	0.163972
$590$	5.46538	0.225006
$591$	−10.6995	−0.440117
$592$	−3.20541	−0.131742
$593$	−38.0329	−1.56182	−0.780912	−	0.624641i	$-0.785245\pi$
$593$	−38.0329	−1.56182	−0.780912	+	0.624641i	$0.785245\pi$
$594$	−3.39730	−0.139393
$595$	3.03404	0.124384
$596$	−2.06808	−0.0847120
$597$	−1.46538	−0.0599740
$598$	22.3075	0.912223
$599$	−16.3756	−0.669090	−0.334545	−	0.942380i	$-0.608583\pi$
$599$	−16.3756	−0.669090	−0.334545	+	0.942380i	$0.608583\pi$
$600$	−0.602705	−0.0246053
$601$	−10.3075	−0.420453	−0.210227	−	0.977653i	$-0.567420\pi$
$601$	−10.3075	−0.420453	−0.210227	+	0.977653i	$0.567420\pi$
$602$	3.65726	0.149059
$603$	−21.9049	−0.892035
$604$	−10.9308	−0.444766
$605$	−1.00000	−0.0406558
$606$	−9.58103	−0.389203
$607$	48.0247	1.94926	0.974632	−	0.223814i	$-0.0718508\pi$
$607$	48.0247	1.94926	0.974632	+	0.223814i	$0.0718508\pi$
$608$	−1.63675	−0.0663788
$609$	−15.4178	−0.624761
$610$	−0.774073	−0.0313413
$611$	51.5663	2.08615
$612$	2.63675	0.106584
$613$	−26.5405	−1.07196	−0.535979	−	0.844231i	$-0.680058\pi$
$613$	−26.5405	−1.07196	−0.535979	+	0.844231i	$0.680058\pi$
$614$	6.55514	0.264544
$615$	1.82863	0.0737376
$616$	−3.03404	−0.122245
$617$	27.9795	1.12641	0.563206	−	0.826317i	$-0.309568\pi$
$617$	27.9795	1.12641	0.563206	+	0.826317i	$0.309568\pi$
$618$	0.519938	0.0209150
$619$	−22.8275	−0.917514	−0.458757	−	0.888562i	$-0.651705\pi$
$619$	−22.8275	−0.917514	−0.458757	+	0.888562i	$0.651705\pi$
$620$	2.43134	0.0976448
$621$	17.1021	0.686285
$622$	11.2325	0.450381
$623$	17.1021	0.685182
$624$	−2.67079	−0.106917
$625$	1.00000	0.0400000
$626$	−27.6573	−1.10541
$627$	−0.986475	−0.0393960
$628$	−16.5199	−0.659217
$629$	3.20541	0.127808
$630$	8.00000	0.318728
$631$	−0.478903	−0.0190648	−0.00953242	−	0.999955i	$-0.503034\pi$
$631$	−0.478903	−0.0190648	−0.00953242	+	0.999955i	$0.503034\pi$
$632$	−17.2735	−0.687103
$633$	3.88856	0.154557
$634$	−21.9918	−0.873408
$635$	8.73887	0.346792
$636$	−0.363253	−0.0144039
$637$	9.77291	0.387217
$638$	−8.43134	−0.333800
$639$	−0.957807	−0.0378903
$640$	−1.00000	−0.0395285
$641$	−33.6491	−1.32906	−0.664530	−	0.747262i	$-0.731368\pi$
$641$	−33.6491	−1.32906	−0.664530	+	0.747262i	$0.731368\pi$
$642$	−10.4519	−0.412502
$643$	12.8216	0.505636	0.252818	−	0.967514i	$-0.418643\pi$
$643$	12.8216	0.505636	0.252818	+	0.967514i	$0.418643\pi$
$644$	15.2735	0.601860
$645$	0.726506	0.0286062
$646$	1.63675	0.0643969
$647$	12.4584	0.489790	0.244895	−	0.969550i	$-0.421247\pi$
$647$	12.4584	0.489790	0.244895	+	0.969550i	$0.421247\pi$
$648$	5.86267	0.230308
$649$	5.46538	0.214535
$650$	4.43134	0.173811
$651$	4.44602	0.174253
$652$	4.47890	0.175407
$653$	23.8827	0.934603	0.467302	−	0.884098i	$-0.345226\pi$
$653$	23.8827	0.934603	0.467302	+	0.884098i	$0.345226\pi$
$654$	11.1497	0.435987
$655$	−6.65027	−0.259848
$656$	3.03404	0.118459
$657$	−29.2194	−1.13996
$658$	35.3064	1.37639
$659$	−6.59455	−0.256887	−0.128444	−	0.991717i	$-0.540998\pi$
$659$	−6.59455	−0.256887	−0.128444	+	0.991717i	$0.540998\pi$
$660$	−0.602705	−0.0234603
$661$	19.2383	0.748283	0.374141	−	0.927372i	$-0.377937\pi$
$661$	19.2383	0.748283	0.374141	+	0.927372i	$0.377937\pi$
$662$	13.8491	0.538262
$663$	2.67079	0.103725
$664$	4.96596	0.192717
$665$	4.96596	0.192572
$666$	8.45185	0.327503
$667$	42.4437	1.64343
$668$	−19.7524	−0.764243
$669$	−11.1907	−0.432658
$670$	−8.30754	−0.320948
$671$	−0.774073	−0.0298828
$672$	−1.82863	−0.0705410
$673$	−25.5745	−0.985824	−0.492912	−	0.870079i	$-0.664068\pi$
$673$	−25.5745	−0.985824	−0.492912	+	0.870079i	$0.664068\pi$
$674$	−35.2178	−1.35654
$675$	3.39730	0.130762
$676$	6.63675	0.255259
$677$	0.691306	0.0265690	0.0132845	−	0.999912i	$-0.495771\pi$
$677$	0.691306	0.0265690	0.0132845	+	0.999912i	$0.495771\pi$
$678$	−8.98648	−0.345124
$679$	−29.0317	−1.11414
$680$	1.00000	0.0383482
$681$	14.3281	0.549052
$682$	2.43134	0.0931007
$683$	25.8081	0.987520	0.493760	−	0.869598i	$-0.335622\pi$
$683$	25.8081	0.987520	0.493760	+	0.869598i	$0.335622\pi$
$684$	4.31569	0.165014
$685$	−2.00000	−0.0764161
$686$	−14.5470	−0.555407
$687$	5.06924	0.193404
$688$	1.20541	0.0459558
$689$	2.67079	0.101749
$690$	3.03404	0.115504
$691$	17.4859	0.665195	0.332597	−	0.943069i	$-0.392075\pi$
$691$	17.4859	0.665195	0.332597	+	0.943069i	$0.392075\pi$
$692$	−11.1021	−0.422039
$693$	8.00000	0.303895
$694$	20.1567	0.765137
$695$	3.03404	0.115088
$696$	−5.08161	−0.192618
$697$	−3.03404	−0.114923
$698$	21.7253	0.822317
$699$	13.6801	0.517429
$700$	3.03404	0.114676
$701$	42.5388	1.60667	0.803335	−	0.595528i	$-0.203057\pi$
$701$	42.5388	1.60667	0.803335	+	0.595528i	$0.203057\pi$
$702$	15.0546	0.568198
$703$	5.24644	0.197873
$704$	−1.00000	−0.0376889
$705$	7.01352	0.264145
$706$	0.274652	0.0103367
$707$	48.2313	1.81392
$708$	3.29401	0.123797
$709$	−1.49243	−0.0560493	−0.0280247	−	0.999607i	$-0.508922\pi$
$709$	−1.49243	−0.0560493	−0.0280247	+	0.999607i	$0.508922\pi$
$710$	−0.363253	−0.0136327
$711$	45.5458	1.70810
$712$	5.63675	0.211246
$713$	−12.2395	−0.458371
$714$	1.82863	0.0684348
$715$	4.43134	0.165723
$716$	6.93076	0.259015
$717$	2.03520	0.0760060
$718$	−29.8205	−1.11289
$719$	−20.1157	−0.750187	−0.375094	−	0.926987i	$-0.622389\pi$
$719$	−20.1157	−0.750187	−0.375094	+	0.926987i	$0.622389\pi$
$720$	2.63675	0.0982658
$721$	−2.61739	−0.0974766
$722$	−16.3211	−0.607407
$723$	3.21939	0.119731
$724$	12.0681	0.448507
$725$	8.43134	0.313132
$726$	−0.602705	−0.0223685
$727$	−42.1837	−1.56451	−0.782254	−	0.622960i	$-0.785930\pi$
$727$	−42.1837	−1.56451	−0.782254	+	0.622960i	$0.785930\pi$
$728$	13.4449	0.498300
$729$	−9.31569	−0.345025
$730$	−11.0816	−0.410149
$731$	−1.20541	−0.0445837
$732$	−0.466538	−0.0172437
$733$	37.8886	1.39945	0.699723	−	0.714414i	$-0.253307\pi$
$733$	37.8886	1.39945	0.699723	+	0.714414i	$0.253307\pi$
$734$	11.4449	0.422438
$735$	1.32921	0.0490287
$736$	5.03404	0.185557
$737$	−8.30754	−0.306012
$738$	−8.00000	−0.294484
$739$	43.8410	1.61272	0.806359	−	0.591427i	$-0.201435\pi$
$739$	43.8410	1.61272	0.806359	+	0.591427i	$0.201435\pi$
$740$	3.20541	0.117833
$741$	4.37140	0.160588
$742$	1.82863	0.0671312
$743$	−41.1021	−1.50789	−0.753945	−	0.656937i	$-0.771852\pi$
$743$	−41.1021	−1.50789	−0.753945	+	0.656937i	$0.771852\pi$
$744$	1.46538	0.0537234
$745$	2.06808	0.0757687
$746$	11.6843	0.427793
$747$	−13.0940	−0.479083
$748$	1.00000	0.0365636
$749$	52.6151	1.92251
$750$	0.602705	0.0220077
$751$	19.1578	0.699080	0.349540	−	0.936922i	$-0.386338\pi$
$751$	19.1578	0.699080	0.349540	+	0.936922i	$0.386338\pi$
$752$	11.6367	0.424348
$753$	−8.76754	−0.319507
$754$	37.3621	1.36065
$755$	10.9308	0.397811
$756$	10.3075	0.374881
$757$	−47.1497	−1.71368	−0.856842	−	0.515578i	$-0.827577\pi$
$757$	−47.1497	−1.71368	−0.856842	+	0.515578i	$0.827577\pi$
$758$	14.2043	0.515922
$759$	3.03404	0.110129
$760$	1.63675	0.0593710
$761$	−34.8627	−1.26377	−0.631885	−	0.775062i	$-0.717719\pi$
$761$	−34.8627	−1.26377	−0.631885	+	0.775062i	$0.717719\pi$
$762$	5.26696	0.190802
$763$	−56.1280	−2.03197
$764$	9.10213	0.329303
$765$	−2.63675	−0.0953318
$766$	−20.1157	−0.726808
$767$	−24.2189	−0.874495
$768$	−0.602705	−0.0217482
$769$	6.85031	0.247028	0.123514	−	0.992343i	$-0.460584\pi$
$769$	6.85031	0.247028	0.123514	+	0.992343i	$0.460584\pi$
$770$	3.03404	0.109339
$771$	8.35089	0.300750
$772$	−19.6843	−0.708454
$773$	13.8205	0.497088	0.248544	−	0.968621i	$-0.420048\pi$
$773$	13.8205	0.497088	0.248544	+	0.968621i	$0.420048\pi$
$774$	−3.17836	−0.114244
$775$	−2.43134	−0.0873362
$776$	−9.56866	−0.343495
$777$	5.86151	0.210281
$778$	−17.5129	−0.627870
$779$	−4.96596	−0.177924
$780$	2.67079	0.0956296
$781$	−0.363253	−0.0129982
$782$	−5.03404	−0.180017
$783$	28.6437	1.02364
$784$	2.20541	0.0787646
$785$	16.5199	0.589622
$786$	−4.00815	−0.142966
$787$	25.6638	0.914816	0.457408	−	0.889257i	$-0.348778\pi$
$787$	25.6638	0.914816	0.457408	+	0.889257i	$0.348778\pi$
$788$	17.7524	0.632403
$789$	17.1145	0.609292
$790$	17.2735	0.614563
$791$	45.2383	1.60849
$792$	2.63675	0.0936927
$793$	3.43018	0.121809
$794$	2.19842	0.0780189
$795$	0.363253	0.0128833
$796$	2.43134	0.0861765
$797$	8.72651	0.309109	0.154554	−	0.987984i	$-0.450606\pi$
$797$	8.72651	0.309109	0.154554	+	0.987984i	$0.450606\pi$
$798$	2.99301	0.105951
$799$	−11.6367	−0.411679
$800$	1.00000	0.0353553
$801$	−14.8627	−0.525147
$802$	−10.3756	−0.366376
$803$	−11.0816	−0.391061
$804$	−5.00699	−0.176583
$805$	−15.2735	−0.538320
$806$	−10.7741	−0.379501
$807$	10.2789	0.361833
$808$	15.8967	0.559245
$809$	11.4801	0.403617	0.201809	−	0.979425i	$-0.435318\pi$
$809$	11.4801	0.403617	0.201809	+	0.979425i	$0.435318\pi$
$810$	−5.86267	−0.205993
$811$	−28.2313	−0.991335	−0.495668	−	0.868512i	$-0.665077\pi$
$811$	−28.2313	−0.991335	−0.495668	+	0.868512i	$0.665077\pi$
$812$	25.5810	0.897718
$813$	−17.1021	−0.599798
$814$	3.20541	0.112350
$815$	−4.47890	−0.156889
$816$	0.602705	0.0210989
$817$	−1.97295	−0.0690248
$818$	1.91723	0.0670345
$819$	−35.4507	−1.23875
$820$	−3.03404	−0.105953
$821$	−37.0874	−1.29436	−0.647180	−	0.762337i	$-0.724052\pi$
$821$	−37.0874	−1.29436	−0.647180	+	0.762337i	$0.724052\pi$
$822$	−1.20541	−0.0420435
$823$	−25.7853	−0.898818	−0.449409	−	0.893326i	$-0.648365\pi$
$823$	−25.7853	−0.898818	−0.449409	+	0.893326i	$0.648365\pi$
$824$	−0.862674	−0.0300527
$825$	0.602705	0.0209835
$826$	−16.5822	−0.576968
$827$	−26.2994	−0.914519	−0.457260	−	0.889333i	$-0.651169\pi$
$827$	−26.2994	−0.914519	−0.457260	+	0.889333i	$0.651169\pi$
$828$	−13.2735	−0.461286
$829$	−16.3486	−0.567809	−0.283905	−	0.958853i	$-0.591630\pi$
$829$	−16.3486	−0.567809	−0.283905	+	0.958853i	$0.591630\pi$
$830$	−4.96596	−0.172371
$831$	13.0480	0.452631
$832$	4.43134	0.153629
$833$	−2.20541	−0.0764129
$834$	1.82863	0.0633203
$835$	19.7524	0.683560
$836$	1.63675	0.0566081
$837$	−8.25997	−0.285506
$838$	−5.68431	−0.196361
$839$	6.77407	0.233867	0.116933	−	0.993140i	$-0.462694\pi$
$839$	6.77407	0.233867	0.116933	+	0.993140i	$0.462694\pi$
$840$	1.82863	0.0630938
$841$	42.0874	1.45129
$842$	−18.9988	−0.654743
$843$	−2.00653	−0.0691086
$844$	−6.45185	−0.222082
$845$	−6.63675	−0.228311
$846$	−30.6832	−1.05491
$847$	3.03404	0.104251
$848$	0.602705	0.0206970
$849$	17.9606	0.616406
$850$	−1.00000	−0.0342997
$851$	−16.1362	−0.553141
$852$	−0.218935	−0.00750057
$853$	29.5048	1.01022	0.505112	−	0.863054i	$-0.331451\pi$
$853$	29.5048	1.01022	0.505112	+	0.863054i	$0.331451\pi$
$854$	2.34857	0.0803664
$855$	−4.31569	−0.147593
$856$	17.3416	0.592723
$857$	34.1238	1.16565	0.582823	−	0.812599i	$-0.301948\pi$
$857$	34.1238	1.16565	0.582823	+	0.812599i	$0.301948\pi$
$858$	2.67079	0.0911792
$859$	11.4383	0.390271	0.195135	−	0.980776i	$-0.437485\pi$
$859$	11.4383	0.390271	0.195135	+	0.980776i	$0.437485\pi$
$860$	−1.20541	−0.0411041
$861$	−5.54815	−0.189080
$862$	27.6843	0.942931
$863$	13.3416	0.454153	0.227076	−	0.973877i	$-0.427083\pi$
$863$	13.3416	0.454153	0.227076	+	0.973877i	$0.427083\pi$
$864$	3.39730	0.115578
$865$	11.1021	0.377484
$866$	15.5810	0.529465
$867$	−0.602705	−0.0204689
$868$	−7.37678	−0.250384
$869$	17.2735	0.585963
$870$	5.08161	0.172283
$871$	36.8135	1.24738
$872$	−18.4994	−0.626469
$873$	25.2301	0.853911
$874$	−8.23945	−0.278704
$875$	−3.03404	−0.102569
$876$	−6.67894	−0.225660
$877$	−23.7582	−0.802258	−0.401129	−	0.916021i	$-0.631382\pi$
$877$	−23.7582	−0.802258	−0.401129	+	0.916021i	$0.631382\pi$
$878$	29.0259	0.979576
$879$	−0.466538	−0.0157359
$880$	1.00000	0.0337100
$881$	−15.7876	−0.531898	−0.265949	−	0.963987i	$-0.585685\pi$
$881$	−15.7876	−0.531898	−0.265949	+	0.963987i	$0.585685\pi$
$882$	−5.81511	−0.195805
$883$	38.9578	1.31103	0.655517	−	0.755180i	$-0.272451\pi$
$883$	38.9578	1.31103	0.655517	+	0.755180i	$0.272451\pi$
$884$	−4.43134	−0.149042
$885$	−3.29401	−0.110727
$886$	9.37678	0.315019
$887$	−10.2665	−0.344715	−0.172358	−	0.985034i	$-0.555138\pi$
$887$	−10.2665	−0.344715	−0.172358	+	0.985034i	$0.555138\pi$
$888$	1.93192	0.0648309
$889$	−26.5141	−0.889255
$890$	−5.63675	−0.188944
$891$	−5.86267	−0.196407
$892$	18.5675	0.621686
$893$	−19.0464	−0.637364
$894$	1.24644	0.0416873
$895$	−6.93076	−0.231670
$896$	3.03404	0.101360
$897$	−13.4449	−0.448911
$898$	−15.1432	−0.505334
$899$	−20.4994	−0.683694
$900$	−2.63675	−0.0878916
$901$	−0.602705	−0.0200790
$902$	−3.03404	−0.101023
$903$	−2.20425	−0.0733529
$904$	14.9102	0.495907
$905$	−12.0681	−0.401157
$906$	6.58802	0.218872
$907$	−5.28818	−0.175591	−0.0877955	−	0.996139i	$-0.527982\pi$
$907$	−5.28818	−0.175591	−0.0877955	+	0.996139i	$0.527982\pi$
$908$	−23.7729	−0.788932
$909$	−41.9156	−1.39025
$910$	−13.4449	−0.445693
$911$	−21.3416	−0.707078	−0.353539	−	0.935420i	$-0.615022\pi$
$911$	−21.3416	−0.707078	−0.353539	+	0.935420i	$0.615022\pi$
$912$	0.986475	0.0326655
$913$	−4.96596	−0.164349
$914$	18.5118	0.612315
$915$	0.466538	0.0154233
$916$	−8.41082	−0.277901
$917$	20.1772	0.666310
$918$	−3.39730	−0.112127
$919$	−8.33458	−0.274933	−0.137466	−	0.990506i	$-0.543896\pi$
$919$	−8.33458	−0.274933	−0.137466	+	0.990506i	$0.543896\pi$
$920$	−5.03404	−0.165967
$921$	−3.95081	−0.130184
$922$	−0.998841	−0.0328951
$923$	1.60970	0.0529838
$924$	1.82863	0.0601576
$925$	−3.20541	−0.105393
$926$	35.7729	1.17557
$927$	2.27465	0.0747094
$928$	8.43134	0.276772
$929$	52.4847	1.72197	0.860984	−	0.508632i	$-0.169849\pi$
$929$	52.4847	1.72197	0.860984	+	0.508632i	$0.169849\pi$
$930$	−1.46538	−0.0480517
$931$	−3.60970	−0.118303
$932$	−22.6978	−0.743492
$933$	−6.76986	−0.221635
$934$	−0.691306	−0.0226202
$935$	−1.00000	−0.0327035
$936$	−11.6843	−0.381914
$937$	−2.78061	−0.0908384	−0.0454192	−	0.998968i	$-0.514462\pi$
$937$	−2.78061	−0.0908384	−0.0454192	+	0.998968i	$0.514462\pi$
$938$	25.2054	0.822986
$939$	16.6692	0.543978
$940$	−11.6367	−0.379549
$941$	2.26812	0.0739386	0.0369693	−	0.999316i	$-0.488230\pi$
$941$	2.26812	0.0739386	0.0369693	+	0.999316i	$0.488230\pi$
$942$	9.95665	0.324405
$943$	15.2735	0.497373
$944$	−5.46538	−0.177883
$945$	−10.3075	−0.335304
$946$	−1.20541	−0.0391913
$947$	−34.8480	−1.13241	−0.566204	−	0.824265i	$-0.691588\pi$
$947$	−34.8480	−1.13241	−0.566204	+	0.824265i	$0.691588\pi$
$948$	10.4108	0.338128
$949$	49.1063	1.59406
$950$	−1.63675	−0.0531031
$951$	13.2546	0.429810
$952$	−3.03404	−0.0983339
$953$	2.54115	0.0823160	0.0411580	−	0.999153i	$-0.486895\pi$
$953$	2.54115	0.0823160	0.0411580	+	0.999153i	$0.486895\pi$
$954$	−1.58918	−0.0514516
$955$	−9.10213	−0.294538
$956$	−3.37678	−0.109213
$957$	5.08161	0.164265
$958$	29.1497	0.941784
$959$	6.06808	0.195949
$960$	0.602705	0.0194522
$961$	−25.0886	−0.809310
$962$	−14.2043	−0.457963
$963$	−45.7253	−1.47348
$964$	−5.34158	−0.172041
$965$	19.6843	0.633660
$966$	−9.20541	−0.296179
$967$	−16.9578	−0.545326	−0.272663	−	0.962110i	$-0.587904\pi$
$967$	−16.9578	−0.545326	−0.272663	+	0.962110i	$0.587904\pi$
$968$	1.00000	0.0321412
$969$	−0.986475	−0.0316902
$970$	9.56866	0.307231
$971$	−13.8081	−0.443123	−0.221562	−	0.975146i	$-0.571115\pi$
$971$	−13.8081	−0.443123	−0.221562	+	0.975146i	$0.571115\pi$
$972$	−13.7253	−0.440241
$973$	−9.20541	−0.295112
$974$	−10.3427	−0.331403
$975$	−2.67079	−0.0855337
$976$	0.774073	0.0247775
$977$	−21.1292	−0.675982	−0.337991	−	0.941149i	$-0.609747\pi$
$977$	−21.1292	−0.675982	−0.337991	+	0.941149i	$0.609747\pi$
$978$	−2.69946	−0.0863191
$979$	−5.63675	−0.180151
$980$	−2.20541	−0.0704492
$981$	48.7783	1.55737
$982$	10.3633	0.330705
$983$	24.0599	0.767393	0.383696	−	0.923459i	$-0.374651\pi$
$983$	24.0599	0.767393	0.383696	+	0.923459i	$0.374651\pi$
$984$	−1.82863	−0.0582947
$985$	−17.7524	−0.565638
$986$	−8.43134	−0.268508
$987$	−21.2793	−0.677328
$988$	−7.25298	−0.230748
$989$	6.06808	0.192954
$990$	−2.63675	−0.0838013
$991$	−26.5265	−0.842641	−0.421321	−	0.906912i	$-0.638433\pi$
$991$	−26.5265	−0.842641	−0.421321	+	0.906912i	$0.638433\pi$
$992$	−2.43134	−0.0771950
$993$	−8.34695	−0.264882
$994$	1.10213	0.0349573
$995$	−2.43134	−0.0770786
$996$	−2.99301	−0.0948371
$997$	0.0680837	0.00215623	0.00107812	−	0.999999i	$-0.499657\pi$
$997$	0.0680837	0.00215623	0.00107812	+	0.999999i	$0.499657\pi$
$998$	−32.8627	−1.04025
$999$	−10.8897	−0.344536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1870.2.a.r.1.2	✓	3
5.4	even	2		9350.2.a.by.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1870.2.a.r.1.2	✓	3	1.1	even	1	trivial
9350.2.a.by.1.2		3	5.4	even	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:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1870.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.602705 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.602705 q^{6} +3.03404 q^{7} +1.00000 q^{8} -2.63675 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.602705 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.602705 q^{6} +3.03404 q^{7} +1.00000 q^{8} -2.63675 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.602705 q^{12} +4.43134 q^{13} +3.03404 q^{14} +0.602705 q^{15} +1.00000 q^{16} -1.00000 q^{17} -2.63675 q^{18} -1.63675 q^{19} -1.00000 q^{20} -1.82863 q^{21} -1.00000 q^{22} +5.03404 q^{23} -0.602705 q^{24} +1.00000 q^{25} +4.43134 q^{26} +3.39730 q^{27} +3.03404 q^{28} +8.43134 q^{29} +0.602705 q^{30} -2.43134 q^{31} +1.00000 q^{32} +0.602705 q^{33} -1.00000 q^{34} -3.03404 q^{35} -2.63675 q^{36} -3.20541 q^{37} -1.63675 q^{38} -2.67079 q^{39} -1.00000 q^{40} +3.03404 q^{41} -1.82863 q^{42} +1.20541 q^{43} -1.00000 q^{44} +2.63675 q^{45} +5.03404 q^{46} +11.6367 q^{47} -0.602705 q^{48} +2.20541 q^{49} +1.00000 q^{50} +0.602705 q^{51} +4.43134 q^{52} +0.602705 q^{53} +3.39730 q^{54} +1.00000 q^{55} +3.03404 q^{56} +0.986475 q^{57} +8.43134 q^{58} -5.46538 q^{59} +0.602705 q^{60} +0.774073 q^{61} -2.43134 q^{62} -8.00000 q^{63} +1.00000 q^{64} -4.43134 q^{65} +0.602705 q^{66} +8.30754 q^{67} -1.00000 q^{68} -3.03404 q^{69} -3.03404 q^{70} +0.363253 q^{71} -2.63675 q^{72} +11.0816 q^{73} -3.20541 q^{74} -0.602705 q^{75} -1.63675 q^{76} -3.03404 q^{77} -2.67079 q^{78} -17.2735 q^{79} -1.00000 q^{80} +5.86267 q^{81} +3.03404 q^{82} +4.96596 q^{83} -1.82863 q^{84} +1.00000 q^{85} +1.20541 q^{86} -5.08161 q^{87} -1.00000 q^{88} +5.63675 q^{89} +2.63675 q^{90} +13.4449 q^{91} +5.03404 q^{92} +1.46538 q^{93} +11.6367 q^{94} +1.63675 q^{95} -0.602705 q^{96} -9.56866 q^{97} +2.20541 q^{98} +2.63675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 2 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 2 * q^7 + 3 * q^8 + 5 * q^9	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 2 q^{7} + 3 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} + 4 q^{13} - 2 q^{14} + 3 q^{16} - 3 q^{17} + 5 q^{18} + 8 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} + 4 q^{23} + 3 q^{25} + 4 q^{26} + 12 q^{27} - 2 q^{28} + 16 q^{29} + 2 q^{31} + 3 q^{32} - 3 q^{34} + 2 q^{35} + 5 q^{36} - 6 q^{37} + 8 q^{38} + 16 q^{39} - 3 q^{40} - 2 q^{41} + 2 q^{42} - 3 q^{44} - 5 q^{45} + 4 q^{46} + 22 q^{47} + 3 q^{49} + 3 q^{50} + 4 q^{52} + 12 q^{54} + 3 q^{55} - 2 q^{56} + 12 q^{57} + 16 q^{58} + 4 q^{59} + 8 q^{61} + 2 q^{62} - 24 q^{63} + 3 q^{64} - 4 q^{65} - 12 q^{67} - 3 q^{68} + 2 q^{69} + 2 q^{70} + 14 q^{71} + 5 q^{72} + 2 q^{73} - 6 q^{74} + 8 q^{76} + 2 q^{77} + 16 q^{78} - 26 q^{79} - 3 q^{80} - q^{81} - 2 q^{82} + 26 q^{83} + 2 q^{84} + 3 q^{85} + 16 q^{87} - 3 q^{88} + 4 q^{89} - 5 q^{90} + 22 q^{91} + 4 q^{92} - 16 q^{93} + 22 q^{94} - 8 q^{95} - 38 q^{97} + 3 q^{98} - 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 2 * q^7 + 3 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 + 4 * q^13 - 2 * q^14 + 3 * q^16 - 3 * q^17 + 5 * q^18 + 8 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 + 4 * q^23 + 3 * q^25 + 4 * q^26 + 12 * q^27 - 2 * q^28 + 16 * q^29 + 2 * q^31 + 3 * q^32 - 3 * q^34 + 2 * q^35 + 5 * q^36 - 6 * q^37 + 8 * q^38 + 16 * q^39 - 3 * q^40 - 2 * q^41 + 2 * q^42 - 3 * q^44 - 5 * q^45 + 4 * q^46 + 22 * q^47 + 3 * q^49 + 3 * q^50 + 4 * q^52 + 12 * q^54 + 3 * q^55 - 2 * q^56 + 12 * q^57 + 16 * q^58 + 4 * q^59 + 8 * q^61 + 2 * q^62 - 24 * q^63 + 3 * q^64 - 4 * q^65 - 12 * q^67 - 3 * q^68 + 2 * q^69 + 2 * q^70 + 14 * q^71 + 5 * q^72 + 2 * q^73 - 6 * q^74 + 8 * q^76 + 2 * q^77 + 16 * q^78 - 26 * q^79 - 3 * q^80 - q^81 - 2 * q^82 + 26 * q^83 + 2 * q^84 + 3 * q^85 + 16 * q^87 - 3 * q^88 + 4 * q^89 - 5 * q^90 + 22 * q^91 + 4 * q^92 - 16 * q^93 + 22 * q^94 - 8 * q^95 - 38 * q^97 + 3 * q^98 - 5 * q^99

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