LMFDB - Embedded newform 4030.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.4418197.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 7x^{4} - x^{3} + 12x^{2} + 3x - 1 $ x^6 - 7x^4 - x^3 + 12x^2 + 3*x - 1
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			1.3
Root			$1.67370$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.33263 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.33263 q^{6} +1.60759 q^{7} +1.00000 q^{8} -1.22409 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.33263 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.33263 q^{6} +1.60759 q^{7} +1.00000 q^{8} -1.22409 q^{9} -1.00000 q^{10} +3.78207 q^{11} -1.33263 q^{12} +1.00000 q^{13} +1.60759 q^{14} +1.33263 q^{15} +1.00000 q^{16} -7.50664 q^{17} -1.22409 q^{18} +1.98730 q^{19} -1.00000 q^{20} -2.14232 q^{21} +3.78207 q^{22} -7.33848 q^{23} -1.33263 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.62916 q^{27} +1.60759 q^{28} -9.25022 q^{29} +1.33263 q^{30} -1.00000 q^{31} +1.00000 q^{32} -5.04011 q^{33} -7.50664 q^{34} -1.60759 q^{35} -1.22409 q^{36} -2.62790 q^{37} +1.98730 q^{38} -1.33263 q^{39} -1.00000 q^{40} -6.29946 q^{41} -2.14232 q^{42} +12.8464 q^{43} +3.78207 q^{44} +1.22409 q^{45} -7.33848 q^{46} +0.235941 q^{47} -1.33263 q^{48} -4.41566 q^{49} +1.00000 q^{50} +10.0036 q^{51} +1.00000 q^{52} +5.87278 q^{53} +5.62916 q^{54} -3.78207 q^{55} +1.60759 q^{56} -2.64834 q^{57} -9.25022 q^{58} +0.614367 q^{59} +1.33263 q^{60} +6.39470 q^{61} -1.00000 q^{62} -1.96784 q^{63} +1.00000 q^{64} -1.00000 q^{65} -5.04011 q^{66} -0.858063 q^{67} -7.50664 q^{68} +9.77949 q^{69} -1.60759 q^{70} -2.99244 q^{71} -1.22409 q^{72} -0.697694 q^{73} -2.62790 q^{74} -1.33263 q^{75} +1.98730 q^{76} +6.08002 q^{77} -1.33263 q^{78} -9.61181 q^{79} -1.00000 q^{80} -3.82932 q^{81} -6.29946 q^{82} +11.1875 q^{83} -2.14232 q^{84} +7.50664 q^{85} +12.8464 q^{86} +12.3271 q^{87} +3.78207 q^{88} -6.48047 q^{89} +1.22409 q^{90} +1.60759 q^{91} -7.33848 q^{92} +1.33263 q^{93} +0.235941 q^{94} -1.98730 q^{95} -1.33263 q^{96} +0.423705 q^{97} -4.41566 q^{98} -4.62961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9} - 6 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} - 8 q^{17} - q^{18} - 9 q^{19} - 6 q^{20} - 5 q^{21} - 4 q^{22} - 7 q^{23} - 3 q^{24} + 6 q^{25} + 6 q^{26} + 9 q^{27} - 2 q^{28} - 14 q^{29} + 3 q^{30} - 6 q^{31} + 6 q^{32} - 6 q^{33} - 8 q^{34} + 2 q^{35} - q^{36} - 9 q^{38} - 3 q^{39} - 6 q^{40} + 2 q^{41} - 5 q^{42} - 7 q^{43} - 4 q^{44} + q^{45} - 7 q^{46} - 8 q^{47} - 3 q^{48} - 14 q^{49} + 6 q^{50} - 5 q^{51} + 6 q^{52} - 24 q^{53} + 9 q^{54} + 4 q^{55} - 2 q^{56} - 15 q^{57} - 14 q^{58} - 5 q^{59} + 3 q^{60} - 5 q^{61} - 6 q^{62} - 19 q^{63} + 6 q^{64} - 6 q^{65} - 6 q^{66} - 12 q^{67} - 8 q^{68} + 2 q^{70} - 10 q^{71} - q^{72} + 5 q^{73} - 3 q^{75} - 9 q^{76} - q^{77} - 3 q^{78} - 16 q^{79} - 6 q^{80} - 10 q^{81} + 2 q^{82} - 22 q^{83} - 5 q^{84} + 8 q^{85} - 7 q^{86} - 31 q^{87} - 4 q^{88} + 14 q^{89} + q^{90} - 2 q^{91} - 7 q^{92} + 3 q^{93} - 8 q^{94} + 9 q^{95} - 3 q^{96} - 9 q^{97} - 14 q^{98} - 21 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9 - 6 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 - 8 * q^17 - q^18 - 9 * q^19 - 6 * q^20 - 5 * q^21 - 4 * q^22 - 7 * q^23 - 3 * q^24 + 6 * q^25 + 6 * q^26 + 9 * q^27 - 2 * q^28 - 14 * q^29 + 3 * q^30 - 6 * q^31 + 6 * q^32 - 6 * q^33 - 8 * q^34 + 2 * q^35 - q^36 - 9 * q^38 - 3 * q^39 - 6 * q^40 + 2 * q^41 - 5 * q^42 - 7 * q^43 - 4 * q^44 + q^45 - 7 * q^46 - 8 * q^47 - 3 * q^48 - 14 * q^49 + 6 * q^50 - 5 * q^51 + 6 * q^52 - 24 * q^53 + 9 * q^54 + 4 * q^55 - 2 * q^56 - 15 * q^57 - 14 * q^58 - 5 * q^59 + 3 * q^60 - 5 * q^61 - 6 * q^62 - 19 * q^63 + 6 * q^64 - 6 * q^65 - 6 * q^66 - 12 * q^67 - 8 * q^68 + 2 * q^70 - 10 * q^71 - q^72 + 5 * q^73 - 3 * q^75 - 9 * q^76 - q^77 - 3 * q^78 - 16 * q^79 - 6 * q^80 - 10 * q^81 + 2 * q^82 - 22 * q^83 - 5 * q^84 + 8 * q^85 - 7 * q^86 - 31 * q^87 - 4 * q^88 + 14 * q^89 + q^90 - 2 * q^91 - 7 * q^92 + 3 * q^93 - 8 * q^94 + 9 * q^95 - 3 * q^96 - 9 * q^97 - 14 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.33263	−0.769395	−0.384698	−	0.923043i	$-0.625694\pi$
$3$	−1.33263	−0.769395	−0.384698	+	0.923043i	$0.625694\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.33263	−0.544045
$7$	1.60759	0.607611	0.303806	−	0.952734i	$-0.401743\pi$
$7$	1.60759	0.607611	0.303806	+	0.952734i	$0.401743\pi$
$8$	1.00000	0.353553
$9$	−1.22409	−0.408031
$10$	−1.00000	−0.316228
$11$	3.78207	1.14034	0.570169	−	0.821527i	$-0.306878\pi$
$11$	3.78207	1.14034	0.570169	+	0.821527i	$0.306878\pi$
$12$	−1.33263	−0.384698
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.60759	0.429646
$15$	1.33263	0.344084
$16$	1.00000	0.250000
$17$	−7.50664	−1.82063	−0.910313	−	0.413920i	$-0.864159\pi$
$17$	−7.50664	−1.82063	−0.910313	+	0.413920i	$0.864159\pi$
$18$	−1.22409	−0.288521
$19$	1.98730	0.455919	0.227959	−	0.973671i	$-0.426795\pi$
$19$	1.98730	0.455919	0.227959	+	0.973671i	$0.426795\pi$
$20$	−1.00000	−0.223607
$21$	−2.14232	−0.467493
$22$	3.78207	0.806341
$23$	−7.33848	−1.53018	−0.765089	−	0.643924i	$-0.777305\pi$
$23$	−7.33848	−1.53018	−0.765089	+	0.643924i	$0.777305\pi$
$24$	−1.33263	−0.272022
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	5.62916	1.08333
$28$	1.60759	0.303806
$29$	−9.25022	−1.71772	−0.858861	−	0.512208i	$-0.828828\pi$
$29$	−9.25022	−1.71772	−0.858861	+	0.512208i	$0.828828\pi$
$30$	1.33263	0.243304
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−5.04011	−0.877371
$34$	−7.50664	−1.28738
$35$	−1.60759	−0.271732
$36$	−1.22409	−0.204015
$37$	−2.62790	−0.432024	−0.216012	−	0.976391i	$-0.569305\pi$
$37$	−2.62790	−0.432024	−0.216012	+	0.976391i	$0.569305\pi$
$38$	1.98730	0.322383
$39$	−1.33263	−0.213392
$40$	−1.00000	−0.158114
$41$	−6.29946	−0.983811	−0.491905	−	0.870649i	$-0.663699\pi$
$41$	−6.29946	−0.983811	−0.491905	+	0.870649i	$0.663699\pi$
$42$	−2.14232	−0.330568
$43$	12.8464	1.95906	0.979529	−	0.201303i	$-0.0645176\pi$
$43$	12.8464	1.95906	0.979529	+	0.201303i	$0.0645176\pi$
$44$	3.78207	0.570169
$45$	1.22409	0.182477
$46$	−7.33848	−1.08200
$47$	0.235941	0.0344156	0.0172078	−	0.999852i	$-0.494522\pi$
$47$	0.235941	0.0344156	0.0172078	+	0.999852i	$0.494522\pi$
$48$	−1.33263	−0.192349
$49$	−4.41566	−0.630808
$50$	1.00000	0.141421
$51$	10.0036	1.40078
$52$	1.00000	0.138675
$53$	5.87278	0.806689	0.403344	−	0.915048i	$-0.367848\pi$
$53$	5.87278	0.806689	0.403344	+	0.915048i	$0.367848\pi$
$54$	5.62916	0.766032
$55$	−3.78207	−0.509975
$56$	1.60759	0.214823
$57$	−2.64834	−0.350782
$58$	−9.25022	−1.21461
$59$	0.614367	0.0799838	0.0399919	−	0.999200i	$-0.487267\pi$
$59$	0.614367	0.0799838	0.0399919	+	0.999200i	$0.487267\pi$
$60$	1.33263	0.172042
$61$	6.39470	0.818758	0.409379	−	0.912364i	$-0.365745\pi$
$61$	6.39470	0.818758	0.409379	+	0.912364i	$0.365745\pi$
$62$	−1.00000	−0.127000
$63$	−1.96784	−0.247924
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−5.04011	−0.620395
$67$	−0.858063	−0.104829	−0.0524145	−	0.998625i	$-0.516692\pi$
$67$	−0.858063	−0.104829	−0.0524145	+	0.998625i	$0.516692\pi$
$68$	−7.50664	−0.910313
$69$	9.77949	1.17731
$70$	−1.60759	−0.192144
$71$	−2.99244	−0.355137	−0.177569	−	0.984108i	$-0.556823\pi$
$71$	−2.99244	−0.355137	−0.177569	+	0.984108i	$0.556823\pi$
$72$	−1.22409	−0.144261
$73$	−0.697694	−0.0816589	−0.0408295	−	0.999166i	$-0.513000\pi$
$73$	−0.697694	−0.0816589	−0.0408295	+	0.999166i	$0.513000\pi$
$74$	−2.62790	−0.305487
$75$	−1.33263	−0.153879
$76$	1.98730	0.227959
$77$	6.08002	0.692883
$78$	−1.33263	−0.150891
$79$	−9.61181	−1.08141	−0.540707	−	0.841211i	$-0.681843\pi$
$79$	−9.61181	−1.08141	−0.540707	+	0.841211i	$0.681843\pi$
$80$	−1.00000	−0.111803
$81$	−3.82932	−0.425480
$82$	−6.29946	−0.695659
$83$	11.1875	1.22798	0.613992	−	0.789312i	$-0.289563\pi$
$83$	11.1875	1.22798	0.613992	+	0.789312i	$0.289563\pi$
$84$	−2.14232	−0.233747
$85$	7.50664	0.814209
$86$	12.8464	1.38526
$87$	12.3271	1.32161
$88$	3.78207	0.403171
$89$	−6.48047	−0.686928	−0.343464	−	0.939166i	$-0.611600\pi$
$89$	−6.48047	−0.686928	−0.343464	+	0.939166i	$0.611600\pi$
$90$	1.22409	0.129031
$91$	1.60759	0.168521
$92$	−7.33848	−0.765089
$93$	1.33263	0.138187
$94$	0.235941	0.0243355
$95$	−1.98730	−0.203893
$96$	−1.33263	−0.136011
$97$	0.423705	0.0430207	0.0215103	−	0.999769i	$-0.493153\pi$
$97$	0.423705	0.0430207	0.0215103	+	0.999769i	$0.493153\pi$
$98$	−4.41566	−0.446049
$99$	−4.62961	−0.465293
$100$	1.00000	0.100000
$101$	−16.8595	−1.67758	−0.838791	−	0.544454i	$-0.816737\pi$
$101$	−16.8595	−1.67758	−0.838791	+	0.544454i	$0.816737\pi$
$102$	10.0036	0.990502
$103$	−5.77995	−0.569515	−0.284758	−	0.958600i	$-0.591913\pi$
$103$	−5.77995	−0.569515	−0.284758	+	0.958600i	$0.591913\pi$
$104$	1.00000	0.0980581
$105$	2.14232	0.209069
$106$	5.87278	0.570415
$107$	−6.73092	−0.650703	−0.325351	−	0.945593i	$-0.605483\pi$
$107$	−6.73092	−0.650703	−0.325351	+	0.945593i	$0.605483\pi$
$108$	5.62916	0.541666
$109$	−6.70105	−0.641844	−0.320922	−	0.947106i	$-0.603993\pi$
$109$	−6.70105	−0.641844	−0.320922	+	0.947106i	$0.603993\pi$
$110$	−3.78207	−0.360607
$111$	3.50203	0.332398
$112$	1.60759	0.151903
$113$	−20.7037	−1.94764	−0.973820	−	0.227321i	$-0.927003\pi$
$113$	−20.7037	−1.94764	−0.973820	+	0.227321i	$0.927003\pi$
$114$	−2.64834	−0.248040
$115$	7.33848	0.684317
$116$	−9.25022	−0.858861
$117$	−1.22409	−0.113167
$118$	0.614367	0.0565571
$119$	−12.0676	−1.10623
$120$	1.33263	0.121652
$121$	3.30409	0.300372
$122$	6.39470	0.578949
$123$	8.39486	0.756939
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	−1.96784	−0.175309
$127$	−1.59487	−0.141522	−0.0707608	−	0.997493i	$-0.522543\pi$
$127$	−1.59487	−0.141522	−0.0707608	+	0.997493i	$0.522543\pi$
$128$	1.00000	0.0883883
$129$	−17.1195	−1.50729
$130$	−1.00000	−0.0877058
$131$	−4.22674	−0.369292	−0.184646	−	0.982805i	$-0.559114\pi$
$131$	−4.22674	−0.369292	−0.184646	+	0.982805i	$0.559114\pi$
$132$	−5.04011	−0.438686
$133$	3.19477	0.277021
$134$	−0.858063	−0.0741253
$135$	−5.62916	−0.484481
$136$	−7.50664	−0.643689
$137$	−20.2651	−1.73136	−0.865680	−	0.500597i	$-0.833114\pi$
$137$	−20.2651	−1.73136	−0.865680	+	0.500597i	$0.833114\pi$
$138$	9.77949	0.832485
$139$	15.8944	1.34815	0.674073	−	0.738665i	$-0.264543\pi$
$139$	15.8944	1.34815	0.674073	+	0.738665i	$0.264543\pi$
$140$	−1.60759	−0.135866
$141$	−0.314423	−0.0264792
$142$	−2.99244	−0.251120
$143$	3.78207	0.316273
$144$	−1.22409	−0.102008
$145$	9.25022	0.768189
$146$	−0.697694	−0.0577416
$147$	5.88445	0.485341
$148$	−2.62790	−0.216012
$149$	−23.3186	−1.91034	−0.955168	−	0.296065i	$-0.904326\pi$
$149$	−23.3186	−1.91034	−0.955168	+	0.296065i	$0.904326\pi$
$150$	−1.33263	−0.108809
$151$	−8.39218	−0.682946	−0.341473	−	0.939892i	$-0.610926\pi$
$151$	−8.39218	−0.682946	−0.341473	+	0.939892i	$0.610926\pi$
$152$	1.98730	0.161192
$153$	9.18882	0.742872
$154$	6.08002	0.489942
$155$	1.00000	0.0803219
$156$	−1.33263	−0.106696
$157$	−10.2898	−0.821219	−0.410609	−	0.911811i	$-0.634684\pi$
$157$	−10.2898	−0.821219	−0.410609	+	0.911811i	$0.634684\pi$
$158$	−9.61181	−0.764675
$159$	−7.82626	−0.620663
$160$	−1.00000	−0.0790569
$161$	−11.7973	−0.929754
$162$	−3.82932	−0.300860
$163$	−2.40960	−0.188734	−0.0943672	−	0.995537i	$-0.530083\pi$
$163$	−2.40960	−0.188734	−0.0943672	+	0.995537i	$0.530083\pi$
$164$	−6.29946	−0.491905
$165$	5.04011	0.392372
$166$	11.1875	0.868316
$167$	13.6758	1.05827	0.529134	−	0.848539i	$-0.322517\pi$
$167$	13.6758	1.05827	0.529134	+	0.848539i	$0.322517\pi$
$168$	−2.14232	−0.165284
$169$	1.00000	0.0769231
$170$	7.50664	0.575733
$171$	−2.43264	−0.186029
$172$	12.8464	0.979529
$173$	18.3393	1.39431	0.697154	−	0.716922i	$-0.254449\pi$
$173$	18.3393	1.39431	0.697154	+	0.716922i	$0.254449\pi$
$174$	12.3271	0.934518
$175$	1.60759	0.121522
$176$	3.78207	0.285085
$177$	−0.818725	−0.0615392
$178$	−6.48047	−0.485732
$179$	−7.36796	−0.550707	−0.275354	−	0.961343i	$-0.588795\pi$
$179$	−7.36796	−0.550707	−0.275354	+	0.961343i	$0.588795\pi$
$180$	1.22409	0.0912385
$181$	−0.113739	−0.00845414	−0.00422707	−	0.999991i	$-0.501346\pi$
$181$	−0.113739	−0.00845414	−0.00422707	+	0.999991i	$0.501346\pi$
$182$	1.60759	0.119162
$183$	−8.52178	−0.629948
$184$	−7.33848	−0.541000
$185$	2.62790	0.193207
$186$	1.33263	0.0977133
$187$	−28.3907	−2.07613
$188$	0.235941	0.0172078
$189$	9.04937	0.658245
$190$	−1.98730	−0.144174
$191$	−18.3453	−1.32742	−0.663710	−	0.747990i	$-0.731019\pi$
$191$	−18.3453	−1.32742	−0.663710	+	0.747990i	$0.731019\pi$
$192$	−1.33263	−0.0961744
$193$	15.1604	1.09127	0.545635	−	0.838023i	$-0.316289\pi$
$193$	15.1604	1.09127	0.545635	+	0.838023i	$0.316289\pi$
$194$	0.423705	0.0304202
$195$	1.33263	0.0954317
$196$	−4.41566	−0.315404
$197$	−6.46630	−0.460705	−0.230352	−	0.973107i	$-0.573988\pi$
$197$	−6.46630	−0.460705	−0.230352	+	0.973107i	$0.573988\pi$
$198$	−4.62961	−0.329012
$199$	−1.74394	−0.123625	−0.0618123	−	0.998088i	$-0.519688\pi$
$199$	−1.74394	−0.123625	−0.0618123	+	0.998088i	$0.519688\pi$
$200$	1.00000	0.0707107
$201$	1.14348	0.0806550
$202$	−16.8595	−1.18623
$203$	−14.8706	−1.04371
$204$	10.0036	0.700391
$205$	6.29946	0.439973
$206$	−5.77995	−0.402708
$207$	8.98298	0.624360
$208$	1.00000	0.0693375
$209$	7.51613	0.519902
$210$	2.14232	0.147834
$211$	5.59671	0.385293	0.192647	−	0.981268i	$-0.438293\pi$
$211$	5.59671	0.385293	0.192647	+	0.981268i	$0.438293\pi$
$212$	5.87278	0.403344
$213$	3.98782	0.273241
$214$	−6.73092	−0.460116
$215$	−12.8464	−0.876117
$216$	5.62916	0.383016
$217$	−1.60759	−0.109130
$218$	−6.70105	−0.453852
$219$	0.929769	0.0628280
$220$	−3.78207	−0.254987
$221$	−7.50664	−0.504951
$222$	3.50203	0.235041
$223$	−24.7089	−1.65463	−0.827316	−	0.561737i	$-0.810133\pi$
$223$	−24.7089	−1.65463	−0.827316	+	0.561737i	$0.810133\pi$
$224$	1.60759	0.107412
$225$	−1.22409	−0.0816062
$226$	−20.7037	−1.37719
$227$	−8.97325	−0.595576	−0.297788	−	0.954632i	$-0.596249\pi$
$227$	−8.97325	−0.595576	−0.297788	+	0.954632i	$0.596249\pi$
$228$	−2.64834	−0.175391
$229$	−2.94499	−0.194610	−0.0973052	−	0.995255i	$-0.531022\pi$
$229$	−2.94499	−0.194610	−0.0973052	+	0.995255i	$0.531022\pi$
$230$	7.33848	0.483885
$231$	−8.10243	−0.533101
$232$	−9.25022	−0.607307
$233$	15.0687	0.987182	0.493591	−	0.869694i	$-0.335684\pi$
$233$	15.0687	0.987182	0.493591	+	0.869694i	$0.335684\pi$
$234$	−1.22409	−0.0800214
$235$	−0.235941	−0.0153911
$236$	0.614367	0.0399919
$237$	12.8090	0.832034
$238$	−12.0676	−0.782225
$239$	−24.6433	−1.59404	−0.797021	−	0.603951i	$-0.793592\pi$
$239$	−24.6433	−1.59404	−0.797021	+	0.603951i	$0.793592\pi$
$240$	1.33263	0.0860210
$241$	10.4708	0.674486	0.337243	−	0.941418i	$-0.390506\pi$
$241$	10.4708	0.674486	0.337243	+	0.941418i	$0.390506\pi$
$242$	3.30409	0.212395
$243$	−11.7844	−0.755970
$244$	6.39470	0.409379
$245$	4.41566	0.282106
$246$	8.39486	0.535237
$247$	1.98730	0.126449
$248$	−1.00000	−0.0635001
$249$	−14.9088	−0.944805
$250$	−1.00000	−0.0632456
$251$	6.08626	0.384161	0.192081	−	0.981379i	$-0.438476\pi$
$251$	6.08626	0.384161	0.192081	+	0.981379i	$0.438476\pi$
$252$	−1.96784	−0.123962
$253$	−27.7547	−1.74492
$254$	−1.59487	−0.100071
$255$	−10.0036	−0.626449
$256$	1.00000	0.0625000
$257$	−14.5157	−0.905465	−0.452732	−	0.891647i	$-0.649551\pi$
$257$	−14.5157	−0.905465	−0.452732	+	0.891647i	$0.649551\pi$
$258$	−17.1195	−1.06581
$259$	−4.22459	−0.262503
$260$	−1.00000	−0.0620174
$261$	11.3231	0.700884
$262$	−4.22674	−0.261129
$263$	13.6068	0.839028	0.419514	−	0.907749i	$-0.362200\pi$
$263$	13.6068	0.839028	0.419514	+	0.907749i	$0.362200\pi$
$264$	−5.04011	−0.310197
$265$	−5.87278	−0.360762
$266$	3.19477	0.195884
$267$	8.63608	0.528519
$268$	−0.858063	−0.0524145
$269$	16.3470	0.996696	0.498348	−	0.866977i	$-0.333940\pi$
$269$	16.3470	0.996696	0.498348	+	0.866977i	$0.333940\pi$
$270$	−5.62916	−0.342580
$271$	8.70647	0.528880	0.264440	−	0.964402i	$-0.414813\pi$
$271$	8.70647	0.528880	0.264440	+	0.964402i	$0.414813\pi$
$272$	−7.50664	−0.455157
$273$	−2.14232	−0.129659
$274$	−20.2651	−1.22426
$275$	3.78207	0.228068
$276$	9.77949	0.588656
$277$	−23.2021	−1.39408	−0.697040	−	0.717032i	$-0.745500\pi$
$277$	−23.2021	−1.39408	−0.697040	+	0.717032i	$0.745500\pi$
$278$	15.8944	0.953283
$279$	1.22409	0.0732845
$280$	−1.60759	−0.0960718
$281$	32.6834	1.94973	0.974864	−	0.222802i	$-0.0715205\pi$
$281$	32.6834	1.94973	0.974864	+	0.222802i	$0.0715205\pi$
$282$	−0.314423	−0.0187236
$283$	31.2336	1.85664	0.928322	−	0.371777i	$-0.121251\pi$
$283$	31.2336	1.85664	0.928322	+	0.371777i	$0.121251\pi$
$284$	−2.99244	−0.177569
$285$	2.64834	0.156874
$286$	3.78207	0.223639
$287$	−10.1269	−0.597775
$288$	−1.22409	−0.0721304
$289$	39.3496	2.31468
$290$	9.25022	0.543192
$291$	−0.564642	−0.0330999
$292$	−0.697694	−0.0408295
$293$	21.0438	1.22939	0.614696	−	0.788764i	$-0.289279\pi$
$293$	21.0438	1.22939	0.614696	+	0.788764i	$0.289279\pi$
$294$	5.88445	0.343188
$295$	−0.614367	−0.0357698
$296$	−2.62790	−0.152744
$297$	21.2899	1.23537
$298$	−23.3186	−1.35081
$299$	−7.33848	−0.424395
$300$	−1.33263	−0.0769395
$301$	20.6517	1.19035
$302$	−8.39218	−0.482916
$303$	22.4675	1.29072
$304$	1.98730	0.113980
$305$	−6.39470	−0.366160
$306$	9.18882	0.525290
$307$	−33.2724	−1.89896	−0.949478	−	0.313832i	$-0.898387\pi$
$307$	−33.2724	−1.89896	−0.949478	+	0.313832i	$0.898387\pi$
$308$	6.08002	0.346441
$309$	7.70254	0.438182
$310$	1.00000	0.0567962
$311$	25.7628	1.46087	0.730436	−	0.682981i	$-0.239317\pi$
$311$	25.7628	1.46087	0.730436	+	0.682981i	$0.239317\pi$
$312$	−1.33263	−0.0754454
$313$	−17.2712	−0.976226	−0.488113	−	0.872780i	$-0.662315\pi$
$313$	−17.2712	−0.976226	−0.488113	+	0.872780i	$0.662315\pi$
$314$	−10.2898	−0.580689
$315$	1.96784	0.110875
$316$	−9.61181	−0.540707
$317$	−16.1651	−0.907924	−0.453962	−	0.891021i	$-0.649990\pi$
$317$	−16.1651	−0.907924	−0.453962	+	0.891021i	$0.649990\pi$
$318$	−7.82626	−0.438875
$319$	−34.9850	−1.95879
$320$	−1.00000	−0.0559017
$321$	8.96984	0.500648
$322$	−11.7973	−0.657435
$323$	−14.9180	−0.830058
$324$	−3.82932	−0.212740
$325$	1.00000	0.0554700
$326$	−2.40960	−0.133455
$327$	8.93003	0.493832
$328$	−6.29946	−0.347830
$329$	0.379297	0.0209113
$330$	5.04011	0.277449
$331$	2.27168	0.124863	0.0624314	−	0.998049i	$-0.480115\pi$
$331$	2.27168	0.124863	0.0624314	+	0.998049i	$0.480115\pi$
$332$	11.1875	0.613992
$333$	3.21680	0.176279
$334$	13.6758	0.748308
$335$	0.858063	0.0468810
$336$	−2.14232	−0.116873
$337$	26.5368	1.44555	0.722775	−	0.691084i	$-0.242866\pi$
$337$	26.5368	1.44555	0.722775	+	0.691084i	$0.242866\pi$
$338$	1.00000	0.0543928
$339$	27.5904	1.49850
$340$	7.50664	0.407104
$341$	−3.78207	−0.204811
$342$	−2.43264	−0.131542
$343$	−18.3517	−0.990898
$344$	12.8464	0.692632
$345$	−9.77949	−0.526510
$346$	18.3393	0.985924
$347$	35.4079	1.90080	0.950399	−	0.311033i	$-0.100675\pi$
$347$	35.4079	1.90080	0.950399	+	0.311033i	$0.100675\pi$
$348$	12.3271	0.660804
$349$	−33.0019	−1.76655	−0.883275	−	0.468856i	$-0.844666\pi$
$349$	−33.0019	−1.76655	−0.883275	+	0.468856i	$0.844666\pi$
$350$	1.60759	0.0859292
$351$	5.62916	0.300462
$352$	3.78207	0.201585
$353$	3.54019	0.188425	0.0942127	−	0.995552i	$-0.469967\pi$
$353$	3.54019	0.188425	0.0942127	+	0.995552i	$0.469967\pi$
$354$	−0.818725	−0.0435148
$355$	2.99244	0.158822
$356$	−6.48047	−0.343464
$357$	16.0816	0.851131
$358$	−7.36796	−0.389409
$359$	0.305070	0.0161010	0.00805048	−	0.999968i	$-0.497437\pi$
$359$	0.305070	0.0161010	0.00805048	+	0.999968i	$0.497437\pi$
$360$	1.22409	0.0645154
$361$	−15.0506	−0.792138
$362$	−0.113739	−0.00597798
$363$	−4.40313	−0.231105
$364$	1.60759	0.0842605
$365$	0.697694	0.0365190
$366$	−8.52178	−0.445441
$367$	19.0805	0.995992	0.497996	−	0.867179i	$-0.334069\pi$
$367$	19.0805	0.995992	0.497996	+	0.867179i	$0.334069\pi$
$368$	−7.33848	−0.382545
$369$	7.71113	0.401425
$370$	2.62790	0.136618
$371$	9.44102	0.490153
$372$	1.33263	0.0690937
$373$	6.62044	0.342793	0.171397	−	0.985202i	$-0.445172\pi$
$373$	6.62044	0.342793	0.171397	+	0.985202i	$0.445172\pi$
$374$	−28.3907	−1.46805
$375$	1.33263	0.0688168
$376$	0.235941	0.0121678
$377$	−9.25022	−0.476411
$378$	9.04937	0.465450
$379$	−12.8868	−0.661949	−0.330974	−	0.943640i	$-0.607377\pi$
$379$	−12.8868	−0.661949	−0.330974	+	0.943640i	$0.607377\pi$
$380$	−1.98730	−0.101947
$381$	2.12537	0.108886
$382$	−18.3453	−0.938628
$383$	0.170091	0.00869126	0.00434563	−	0.999991i	$-0.498617\pi$
$383$	0.170091	0.00869126	0.00434563	+	0.999991i	$0.498617\pi$
$384$	−1.33263	−0.0680056
$385$	−6.08002	−0.309867
$386$	15.1604	0.771644
$387$	−15.7252	−0.799356
$388$	0.423705	0.0215103
$389$	−25.1888	−1.27712	−0.638560	−	0.769572i	$-0.720470\pi$
$389$	−25.1888	−1.27712	−0.638560	+	0.769572i	$0.720470\pi$
$390$	1.33263	0.0674804
$391$	55.0873	2.78588
$392$	−4.41566	−0.223024
$393$	5.63269	0.284132
$394$	−6.46630	−0.325767
$395$	9.61181	0.483623
$396$	−4.62961	−0.232647
$397$	6.54529	0.328499	0.164249	−	0.986419i	$-0.447480\pi$
$397$	6.54529	0.328499	0.164249	+	0.986419i	$0.447480\pi$
$398$	−1.74394	−0.0874157
$399$	−4.25745	−0.213139
$400$	1.00000	0.0500000
$401$	19.3588	0.966733	0.483366	−	0.875418i	$-0.339414\pi$
$401$	19.3588	0.966733	0.483366	+	0.875418i	$0.339414\pi$
$402$	1.14348	0.0570317
$403$	−1.00000	−0.0498135
$404$	−16.8595	−0.838791
$405$	3.82932	0.190280
$406$	−14.8706	−0.738013
$407$	−9.93892	−0.492654
$408$	10.0036	0.495251
$409$	3.72518	0.184199	0.0920993	−	0.995750i	$-0.470642\pi$
$409$	3.72518	0.184199	0.0920993	+	0.995750i	$0.470642\pi$
$410$	6.29946	0.311108
$411$	27.0059	1.33210
$412$	−5.77995	−0.284758
$413$	0.987650	0.0485991
$414$	8.98298	0.441489
$415$	−11.1875	−0.549171
$416$	1.00000	0.0490290
$417$	−21.1814	−1.03726
$418$	7.51613	0.367626
$419$	9.56328	0.467197	0.233598	−	0.972333i	$-0.424950\pi$
$419$	9.56328	0.467197	0.233598	+	0.972333i	$0.424950\pi$
$420$	2.14232	0.104535
$421$	−15.4149	−0.751275	−0.375638	−	0.926767i	$-0.622576\pi$
$421$	−15.4149	−0.751275	−0.375638	+	0.926767i	$0.622576\pi$
$422$	5.59671	0.272444
$423$	−0.288814	−0.0140426
$424$	5.87278	0.285208
$425$	−7.50664	−0.364125
$426$	3.98782	0.193210
$427$	10.2801	0.497487
$428$	−6.73092	−0.325351
$429$	−5.04011	−0.243339
$430$	−12.8464	−0.619509
$431$	32.3013	1.55590	0.777951	−	0.628325i	$-0.216259\pi$
$431$	32.3013	1.55590	0.777951	+	0.628325i	$0.216259\pi$
$432$	5.62916	0.270833
$433$	30.7989	1.48010	0.740051	−	0.672550i	$-0.234801\pi$
$433$	30.7989	1.48010	0.740051	+	0.672550i	$0.234801\pi$
$434$	−1.60759	−0.0771667
$435$	−12.3271	−0.591041
$436$	−6.70105	−0.320922
$437$	−14.5838	−0.697637
$438$	0.929769	0.0444261
$439$	−24.7611	−1.18178	−0.590891	−	0.806752i	$-0.701223\pi$
$439$	−24.7611	−1.18178	−0.590891	+	0.806752i	$0.701223\pi$
$440$	−3.78207	−0.180303
$441$	5.40518	0.257389
$442$	−7.50664	−0.357054
$443$	−3.21255	−0.152633	−0.0763165	−	0.997084i	$-0.524316\pi$
$443$	−3.21255	−0.152633	−0.0763165	+	0.997084i	$0.524316\pi$
$444$	3.50203	0.166199
$445$	6.48047	0.307204
$446$	−24.7089	−1.17000
$447$	31.0751	1.46980
$448$	1.60759	0.0759514
$449$	−12.2838	−0.579707	−0.289853	−	0.957071i	$-0.593607\pi$
$449$	−12.2838	−0.579707	−0.289853	+	0.957071i	$0.593607\pi$
$450$	−1.22409	−0.0577043
$451$	−23.8250	−1.12188
$452$	−20.7037	−0.973820
$453$	11.1837	0.525455
$454$	−8.97325	−0.421136
$455$	−1.60759	−0.0753649
$456$	−2.64834	−0.124020
$457$	−1.71695	−0.0803154	−0.0401577	−	0.999193i	$-0.512786\pi$
$457$	−1.71695	−0.0803154	−0.0401577	+	0.999193i	$0.512786\pi$
$458$	−2.94499	−0.137610
$459$	−42.2561	−1.97234
$460$	7.33848	0.342158
$461$	21.8774	1.01893	0.509466	−	0.860491i	$-0.329843\pi$
$461$	21.8774	1.01893	0.509466	+	0.860491i	$0.329843\pi$
$462$	−8.10243	−0.376959
$463$	−17.6147	−0.818626	−0.409313	−	0.912394i	$-0.634232\pi$
$463$	−17.6147	−0.818626	−0.409313	+	0.912394i	$0.634232\pi$
$464$	−9.25022	−0.429431
$465$	−1.33263	−0.0617993
$466$	15.0687	0.698043
$467$	9.30031	0.430367	0.215183	−	0.976574i	$-0.430965\pi$
$467$	9.30031	0.430367	0.215183	+	0.976574i	$0.430965\pi$
$468$	−1.22409	−0.0565837
$469$	−1.37941	−0.0636953
$470$	−0.235941	−0.0108832
$471$	13.7126	0.631842
$472$	0.614367	0.0282785
$473$	48.5861	2.23399
$474$	12.8090	0.588337
$475$	1.98730	0.0911838
$476$	−12.0676	−0.553117
$477$	−7.18883	−0.329154
$478$	−24.6433	−1.12716
$479$	−18.3745	−0.839551	−0.419776	−	0.907628i	$-0.637891\pi$
$479$	−18.3745	−0.839551	−0.419776	+	0.907628i	$0.637891\pi$
$480$	1.33263	0.0608260
$481$	−2.62790	−0.119822
$482$	10.4708	0.476933
$483$	15.7214	0.715348
$484$	3.30409	0.150186
$485$	−0.423705	−0.0192394
$486$	−11.7844	−0.534552
$487$	37.3823	1.69395	0.846976	−	0.531630i	$-0.178420\pi$
$487$	37.3823	1.69395	0.846976	+	0.531630i	$0.178420\pi$
$488$	6.39470	0.289475
$489$	3.21111	0.145211
$490$	4.41566	0.199479
$491$	−31.5304	−1.42295	−0.711473	−	0.702714i	$-0.751972\pi$
$491$	−31.5304	−1.42295	−0.711473	+	0.702714i	$0.751972\pi$
$492$	8.39486	0.378470
$493$	69.4380	3.12733
$494$	1.98730	0.0894130
$495$	4.62961	0.208086
$496$	−1.00000	−0.0449013
$497$	−4.81061	−0.215785
$498$	−14.9088	−0.668078
$499$	−40.8881	−1.83040	−0.915202	−	0.402996i	$-0.867969\pi$
$499$	−40.8881	−1.83040	−0.915202	+	0.402996i	$0.867969\pi$
$500$	−1.00000	−0.0447214
$501$	−18.2248	−0.814226
$502$	6.08626	0.271643
$503$	4.14266	0.184712	0.0923560	−	0.995726i	$-0.470560\pi$
$503$	4.14266	0.184712	0.0923560	+	0.995726i	$0.470560\pi$
$504$	−1.96784	−0.0876545
$505$	16.8595	0.750237
$506$	−27.7547	−1.23385
$507$	−1.33263	−0.0591843
$508$	−1.59487	−0.0707608
$509$	29.5183	1.30837	0.654187	−	0.756333i	$-0.273011\pi$
$509$	29.5183	1.30837	0.654187	+	0.756333i	$0.273011\pi$
$510$	−10.0036	−0.442966
$511$	−1.12161	−0.0496169
$512$	1.00000	0.0441942
$513$	11.1869	0.493912
$514$	−14.5157	−0.640260
$515$	5.77995	0.254695
$516$	−17.1195	−0.753645
$517$	0.892348	0.0392454
$518$	−4.22459	−0.185618
$519$	−24.4395	−1.07277
$520$	−1.00000	−0.0438529
$521$	−30.0804	−1.31785	−0.658924	−	0.752210i	$-0.728988\pi$
$521$	−30.0804	−1.31785	−0.658924	+	0.752210i	$0.728988\pi$
$522$	11.3231	0.495600
$523$	−1.39983	−0.0612101	−0.0306051	−	0.999532i	$-0.509743\pi$
$523$	−1.39983	−0.0612101	−0.0306051	+	0.999532i	$0.509743\pi$
$524$	−4.22674	−0.184646
$525$	−2.14232	−0.0934987
$526$	13.6068	0.593283
$527$	7.50664	0.326994
$528$	−5.04011	−0.219343
$529$	30.8533	1.34145
$530$	−5.87278	−0.255097
$531$	−0.752042	−0.0326359
$532$	3.19477	0.138511
$533$	−6.29946	−0.272860
$534$	8.63608	0.373720
$535$	6.73092	0.291003
$536$	−0.858063	−0.0370627
$537$	9.81878	0.423711
$538$	16.3470	0.704771
$539$	−16.7003	−0.719335
$540$	−5.62916	−0.242240
$541$	−10.9426	−0.470460	−0.235230	−	0.971940i	$-0.575584\pi$
$541$	−10.9426	−0.470460	−0.235230	+	0.971940i	$0.575584\pi$
$542$	8.70647	0.373975
$543$	0.151572	0.00650458
$544$	−7.50664	−0.321844
$545$	6.70105	0.287041
$546$	−2.14232	−0.0916830
$547$	31.8026	1.35978	0.679889	−	0.733315i	$-0.262028\pi$
$547$	31.8026	1.35978	0.679889	+	0.733315i	$0.262028\pi$
$548$	−20.2651	−0.865680
$549$	−7.82771	−0.334078
$550$	3.78207	0.161268
$551$	−18.3830	−0.783142
$552$	9.77949	0.416243
$553$	−15.4518	−0.657079
$554$	−23.2021	−0.985763
$555$	−3.50203	−0.148653
$556$	15.8944	0.674073
$557$	0.291682	0.0123590	0.00617948	−	0.999981i	$-0.498033\pi$
$557$	0.291682	0.0123590	0.00617948	+	0.999981i	$0.498033\pi$
$558$	1.22409	0.0518200
$559$	12.8464	0.543345
$560$	−1.60759	−0.0679330
$561$	37.8343	1.59736
$562$	32.6834	1.37867
$563$	23.4509	0.988338	0.494169	−	0.869366i	$-0.335472\pi$
$563$	23.4509	0.988338	0.494169	+	0.869366i	$0.335472\pi$
$564$	−0.314423	−0.0132396
$565$	20.7037	0.871011
$566$	31.2336	1.31285
$567$	−6.15597	−0.258526
$568$	−2.99244	−0.125560
$569$	30.7978	1.29111	0.645556	−	0.763713i	$-0.276626\pi$
$569$	30.7978	1.29111	0.645556	+	0.763713i	$0.276626\pi$
$570$	2.64834	0.110927
$571$	−9.94394	−0.416141	−0.208070	−	0.978114i	$-0.566718\pi$
$571$	−9.94394	−0.416141	−0.208070	+	0.978114i	$0.566718\pi$
$572$	3.78207	0.158136
$573$	24.4475	1.02131
$574$	−10.1269	−0.422690
$575$	−7.33848	−0.306036
$576$	−1.22409	−0.0510039
$577$	−46.0243	−1.91602	−0.958008	−	0.286741i	$-0.907428\pi$
$577$	−46.0243	−1.91602	−0.958008	+	0.286741i	$0.907428\pi$
$578$	39.3496	1.63673
$579$	−20.2032	−0.839617
$580$	9.25022	0.384094
$581$	17.9848	0.746137
$582$	−0.564642	−0.0234052
$583$	22.2113	0.919898
$584$	−0.697694	−0.0288708
$585$	1.22409	0.0506100
$586$	21.0438	0.869311
$587$	25.8593	1.06733	0.533664	−	0.845696i	$-0.320815\pi$
$587$	25.8593	1.06733	0.533664	+	0.845696i	$0.320815\pi$
$588$	5.88445	0.242670
$589$	−1.98730	−0.0818854
$590$	−0.614367	−0.0252931
$591$	8.61719	0.354464
$592$	−2.62790	−0.108006
$593$	23.4695	0.963777	0.481889	−	0.876232i	$-0.339951\pi$
$593$	23.4695	0.963777	0.481889	+	0.876232i	$0.339951\pi$
$594$	21.2899	0.873535
$595$	12.0676	0.494723
$596$	−23.3186	−0.955168
$597$	2.32403	0.0951161
$598$	−7.33848	−0.300093
$599$	12.9391	0.528679	0.264339	−	0.964430i	$-0.414846\pi$
$599$	12.9391	0.528679	0.264339	+	0.964430i	$0.414846\pi$
$600$	−1.33263	−0.0544045
$601$	22.6735	0.924873	0.462436	−	0.886652i	$-0.346975\pi$
$601$	22.6735	0.924873	0.462436	+	0.886652i	$0.346975\pi$
$602$	20.6517	0.841702
$603$	1.05035	0.0427735
$604$	−8.39218	−0.341473
$605$	−3.30409	−0.134330
$606$	22.4675	0.912679
$607$	−30.3552	−1.23208	−0.616039	−	0.787716i	$-0.711264\pi$
$607$	−30.3552	−1.23208	−0.616039	+	0.787716i	$0.711264\pi$
$608$	1.98730	0.0805958
$609$	19.8170	0.803024
$610$	−6.39470	−0.258914
$611$	0.235941	0.00954517
$612$	9.18882	0.371436
$613$	−43.8393	−1.77065	−0.885326	−	0.464971i	$-0.846065\pi$
$613$	−43.8393	−1.77065	−0.885326	+	0.464971i	$0.846065\pi$
$614$	−33.2724	−1.34277
$615$	−8.39486	−0.338514
$616$	6.08002	0.244971
$617$	22.1845	0.893114	0.446557	−	0.894755i	$-0.352650\pi$
$617$	22.1845	0.893114	0.446557	+	0.894755i	$0.352650\pi$
$618$	7.70254	0.309842
$619$	4.05899	0.163145	0.0815723	−	0.996667i	$-0.474006\pi$
$619$	4.05899	0.163145	0.0815723	+	0.996667i	$0.474006\pi$
$620$	1.00000	0.0401610
$621$	−41.3095	−1.65769
$622$	25.7628	1.03299
$623$	−10.4179	−0.417385
$624$	−1.33263	−0.0533480
$625$	1.00000	0.0400000
$626$	−17.2712	−0.690296
$627$	−10.0162	−0.400010
$628$	−10.2898	−0.410609
$629$	19.7267	0.786555
$630$	1.96784	0.0784005
$631$	−10.1079	−0.402389	−0.201195	−	0.979551i	$-0.564482\pi$
$631$	−10.1079	−0.402389	−0.201195	+	0.979551i	$0.564482\pi$
$632$	−9.61181	−0.382337
$633$	−7.45835	−0.296443
$634$	−16.1651	−0.641999
$635$	1.59487	0.0632904
$636$	−7.82626	−0.310331
$637$	−4.41566	−0.174955
$638$	−34.9850	−1.38507
$639$	3.66302	0.144907
$640$	−1.00000	−0.0395285
$641$	−11.3771	−0.449368	−0.224684	−	0.974432i	$-0.572135\pi$
$641$	−11.3771	−0.449368	−0.224684	+	0.974432i	$0.572135\pi$
$642$	8.96984	0.354011
$643$	26.8150	1.05748	0.528740	−	0.848784i	$-0.322665\pi$
$643$	26.8150	1.05748	0.528740	+	0.848784i	$0.322665\pi$
$644$	−11.7973	−0.464877
$645$	17.1195	0.674081
$646$	−14.9180	−0.586940
$647$	−16.3749	−0.643764	−0.321882	−	0.946780i	$-0.604315\pi$
$647$	−16.3749	−0.643764	−0.321882	+	0.946780i	$0.604315\pi$
$648$	−3.82932	−0.150430
$649$	2.32358	0.0912086
$650$	1.00000	0.0392232
$651$	2.14232	0.0839643
$652$	−2.40960	−0.0943672
$653$	19.0335	0.744839	0.372419	−	0.928065i	$-0.378528\pi$
$653$	19.0335	0.744839	0.372419	+	0.928065i	$0.378528\pi$
$654$	8.93003	0.349192
$655$	4.22674	0.165153
$656$	−6.29946	−0.245953
$657$	0.854042	0.0333194
$658$	0.379297	0.0147865
$659$	−41.1746	−1.60394	−0.801968	−	0.597367i	$-0.796214\pi$
$659$	−41.1746	−1.60394	−0.801968	+	0.597367i	$0.796214\pi$
$660$	5.04011	0.196186
$661$	−25.2050	−0.980363	−0.490181	−	0.871620i	$-0.663069\pi$
$661$	−25.2050	−0.980363	−0.490181	+	0.871620i	$0.663069\pi$
$662$	2.27168	0.0882914
$663$	10.0036	0.388507
$664$	11.1875	0.434158
$665$	−3.19477	−0.123888
$666$	3.21680	0.124648
$667$	67.8825	2.62842
$668$	13.6758	0.529134
$669$	32.9279	1.27307
$670$	0.858063	0.0331499
$671$	24.1852	0.933661
$672$	−2.14232	−0.0826419
$673$	−23.6889	−0.913140	−0.456570	−	0.889687i	$-0.650922\pi$
$673$	−23.6889	−0.913140	−0.456570	+	0.889687i	$0.650922\pi$
$674$	26.5368	1.02216
$675$	5.62916	0.216666
$676$	1.00000	0.0384615
$677$	14.2210	0.546556	0.273278	−	0.961935i	$-0.411892\pi$
$677$	14.2210	0.546556	0.273278	+	0.961935i	$0.411892\pi$
$678$	27.5904	1.05960
$679$	0.681143	0.0261399
$680$	7.50664	0.287866
$681$	11.9580	0.458233
$682$	−3.78207	−0.144823
$683$	−32.8833	−1.25824	−0.629122	−	0.777307i	$-0.716585\pi$
$683$	−32.8833	−1.25824	−0.629122	+	0.777307i	$0.716585\pi$
$684$	−2.43264	−0.0930145
$685$	20.2651	0.774288
$686$	−18.3517	−0.700671
$687$	3.92459	0.149732
$688$	12.8464	0.489764
$689$	5.87278	0.223735
$690$	−9.77949	−0.372299
$691$	−45.1640	−1.71812	−0.859059	−	0.511877i	$-0.828950\pi$
$691$	−45.1640	−1.71812	−0.859059	+	0.511877i	$0.828950\pi$
$692$	18.3393	0.697154
$693$	−7.44251	−0.282718
$694$	35.4079	1.34407
$695$	−15.8944	−0.602909
$696$	12.3271	0.467259
$697$	47.2878	1.79115
$698$	−33.0019	−1.24914
$699$	−20.0810	−0.759533
$700$	1.60759	0.0607611
$701$	19.6592	0.742519	0.371260	−	0.928529i	$-0.378926\pi$
$701$	19.6592	0.742519	0.371260	+	0.928529i	$0.378926\pi$
$702$	5.62916	0.212459
$703$	−5.22244	−0.196968
$704$	3.78207	0.142542
$705$	0.314423	0.0118419
$706$	3.54019	0.133237
$707$	−27.1031	−1.01932
$708$	−0.818725	−0.0307696
$709$	20.6006	0.773670	0.386835	−	0.922149i	$-0.373568\pi$
$709$	20.6006	0.773670	0.386835	+	0.922149i	$0.373568\pi$
$710$	2.99244	0.112304
$711$	11.7657	0.441250
$712$	−6.48047	−0.242866
$713$	7.33848	0.274828
$714$	16.0816	0.601840
$715$	−3.78207	−0.141442
$716$	−7.36796	−0.275354
$717$	32.8404	1.22645
$718$	0.305070	0.0113851
$719$	31.8647	1.18835	0.594176	−	0.804335i	$-0.297478\pi$
$719$	31.8647	1.18835	0.594176	+	0.804335i	$0.297478\pi$
$720$	1.22409	0.0456192
$721$	−9.29178	−0.346044
$722$	−15.0506	−0.560126
$723$	−13.9538	−0.518946
$724$	−0.113739	−0.00422707
$725$	−9.25022	−0.343545
$726$	−4.40313	−0.163416
$727$	−2.79504	−0.103662	−0.0518312	−	0.998656i	$-0.516506\pi$
$727$	−2.79504	−0.103662	−0.0518312	+	0.998656i	$0.516506\pi$
$728$	1.60759	0.0595812
$729$	27.1922	1.00712
$730$	0.697694	0.0258228
$731$	−96.4333	−3.56671
$732$	−8.52178	−0.314974
$733$	1.98182	0.0732001	0.0366000	−	0.999330i	$-0.488347\pi$
$733$	1.98182	0.0732001	0.0366000	+	0.999330i	$0.488347\pi$
$734$	19.0805	0.704273
$735$	−5.88445	−0.217051
$736$	−7.33848	−0.270500
$737$	−3.24526	−0.119541
$738$	7.71113	0.283850
$739$	52.6166	1.93553	0.967767	−	0.251848i	$-0.0810382\pi$
$739$	52.6166	1.93553	0.967767	+	0.251848i	$0.0810382\pi$
$740$	2.62790	0.0966036
$741$	−2.64834	−0.0972894
$742$	9.44102	0.346591
$743$	6.82229	0.250286	0.125143	−	0.992139i	$-0.460061\pi$
$743$	6.82229	0.250286	0.125143	+	0.992139i	$0.460061\pi$
$744$	1.33263	0.0488566
$745$	23.3186	0.854328
$746$	6.62044	0.242391
$747$	−13.6945	−0.501055
$748$	−28.3907	−1.03807
$749$	−10.8206	−0.395374
$750$	1.33263	0.0486608
$751$	−30.5036	−1.11309	−0.556546	−	0.830817i	$-0.687874\pi$
$751$	−30.5036	−1.11309	−0.556546	+	0.830817i	$0.687874\pi$
$752$	0.235941	0.00860390
$753$	−8.11074	−0.295572
$754$	−9.25022	−0.336873
$755$	8.39218	0.305423
$756$	9.04937	0.329123
$757$	31.3110	1.13802	0.569009	−	0.822331i	$-0.307327\pi$
$757$	31.3110	1.13802	0.569009	+	0.822331i	$0.307327\pi$
$758$	−12.8868	−0.468068
$759$	36.9868	1.34253
$760$	−1.98730	−0.0720871
$761$	−36.3495	−1.31767	−0.658835	−	0.752287i	$-0.728950\pi$
$761$	−36.3495	−1.31767	−0.658835	+	0.752287i	$0.728950\pi$
$762$	2.12537	0.0769941
$763$	−10.7725	−0.389992
$764$	−18.3453	−0.663710
$765$	−9.18882	−0.332222
$766$	0.170091	0.00614565
$767$	0.614367	0.0221835
$768$	−1.33263	−0.0480872
$769$	−13.5460	−0.488482	−0.244241	−	0.969715i	$-0.578539\pi$
$769$	−13.5460	−0.488482	−0.244241	+	0.969715i	$0.578539\pi$
$770$	−6.08002	−0.219109
$771$	19.3441	0.696660
$772$	15.1604	0.545635
$773$	9.64956	0.347071	0.173535	−	0.984828i	$-0.444481\pi$
$773$	9.64956	0.347071	0.173535	+	0.984828i	$0.444481\pi$
$774$	−15.7252	−0.565230
$775$	−1.00000	−0.0359211
$776$	0.423705	0.0152101
$777$	5.62982	0.201969
$778$	−25.1888	−0.903061
$779$	−12.5189	−0.448538
$780$	1.33263	0.0477159
$781$	−11.3176	−0.404976
$782$	55.0873	1.96992
$783$	−52.0710	−1.86086
$784$	−4.41566	−0.157702
$785$	10.2898	0.367260
$786$	5.63269	0.200912
$787$	−12.7149	−0.453237	−0.226619	−	0.973984i	$-0.572767\pi$
$787$	−12.7149	−0.453237	−0.226619	+	0.973984i	$0.572767\pi$
$788$	−6.46630	−0.230352
$789$	−18.1328	−0.645544
$790$	9.61181	0.341973
$791$	−33.2830	−1.18341
$792$	−4.62961	−0.164506
$793$	6.39470	0.227083
$794$	6.54529	0.232284
$795$	7.82626	0.277569
$796$	−1.74394	−0.0618123
$797$	25.8807	0.916741	0.458371	−	0.888761i	$-0.348433\pi$
$797$	25.8807	0.916741	0.458371	+	0.888761i	$0.348433\pi$
$798$	−4.25745	−0.150712
$799$	−1.77113	−0.0626580
$800$	1.00000	0.0353553
$801$	7.93269	0.280288
$802$	19.3588	0.683583
$803$	−2.63873	−0.0931188
$804$	1.14348	0.0403275
$805$	11.7973	0.415799
$806$	−1.00000	−0.0352235
$807$	−21.7846	−0.766853
$808$	−16.8595	−0.593115
$809$	−19.8834	−0.699062	−0.349531	−	0.936925i	$-0.613659\pi$
$809$	−19.8834	−0.699062	−0.349531	+	0.936925i	$0.613659\pi$
$810$	3.82932	0.134549
$811$	25.7884	0.905553	0.452776	−	0.891624i	$-0.350434\pi$
$811$	25.7884	0.905553	0.452776	+	0.891624i	$0.350434\pi$
$812$	−14.8706	−0.521854
$813$	−11.6025	−0.406918
$814$	−9.93892	−0.348359
$815$	2.40960	0.0844046
$816$	10.0036	0.350195
$817$	25.5297	0.893171
$818$	3.72518	0.130248
$819$	−1.96784	−0.0687618
$820$	6.29946	0.219987
$821$	11.1468	0.389027	0.194513	−	0.980900i	$-0.437687\pi$
$821$	11.1468	0.389027	0.194513	+	0.980900i	$0.437687\pi$
$822$	27.0059	0.941938
$823$	9.39920	0.327635	0.163818	−	0.986491i	$-0.447619\pi$
$823$	9.39920	0.327635	0.163818	+	0.986491i	$0.447619\pi$
$824$	−5.77995	−0.201354
$825$	−5.04011	−0.175474
$826$	0.987650	0.0343647
$827$	−38.8186	−1.34985	−0.674927	−	0.737884i	$-0.735825\pi$
$827$	−38.8186	−1.34985	−0.674927	+	0.737884i	$0.735825\pi$
$828$	8.98298	0.312180
$829$	36.2401	1.25867	0.629336	−	0.777134i	$-0.283327\pi$
$829$	36.2401	1.25867	0.629336	+	0.777134i	$0.283327\pi$
$830$	−11.1875	−0.388323
$831$	30.9199	1.07260
$832$	1.00000	0.0346688
$833$	33.1467	1.14847
$834$	−21.1814	−0.733451
$835$	−13.6758	−0.473271
$836$	7.51613	0.259951
$837$	−5.62916	−0.194572
$838$	9.56328	0.330358
$839$	27.3225	0.943277	0.471638	−	0.881792i	$-0.343663\pi$
$839$	27.3225	0.943277	0.471638	+	0.881792i	$0.343663\pi$
$840$	2.14232	0.0739172
$841$	56.5666	1.95057
$842$	−15.4149	−0.531232
$843$	−43.5549	−1.50011
$844$	5.59671	0.192647
$845$	−1.00000	−0.0344010
$846$	−0.288814	−0.00992964
$847$	5.31162	0.182509
$848$	5.87278	0.201672
$849$	−41.6229	−1.42849
$850$	−7.50664	−0.257475
$851$	19.2848	0.661074
$852$	3.98782	0.136620
$853$	47.3193	1.62018	0.810091	−	0.586304i	$-0.199417\pi$
$853$	47.3193	1.62018	0.810091	+	0.586304i	$0.199417\pi$
$854$	10.2801	0.351776
$855$	2.43264	0.0831947
$856$	−6.73092	−0.230058
$857$	2.99223	0.102213	0.0511064	−	0.998693i	$-0.483725\pi$
$857$	2.99223	0.102213	0.0511064	+	0.998693i	$0.483725\pi$
$858$	−5.04011	−0.172067
$859$	−25.9564	−0.885621	−0.442811	−	0.896615i	$-0.646019\pi$
$859$	−25.9564	−0.885621	−0.442811	+	0.896615i	$0.646019\pi$
$860$	−12.8464	−0.438059
$861$	13.4955	0.459925
$862$	32.3013	1.10019
$863$	23.8018	0.810224	0.405112	−	0.914267i	$-0.367233\pi$
$863$	23.8018	0.810224	0.405112	+	0.914267i	$0.367233\pi$
$864$	5.62916	0.191508
$865$	−18.3393	−0.623553
$866$	30.7989	1.04659
$867$	−52.4385	−1.78090
$868$	−1.60759	−0.0545651
$869$	−36.3526	−1.23318
$870$	−12.3271	−0.417929
$871$	−0.858063	−0.0290743
$872$	−6.70105	−0.226926
$873$	−0.518654	−0.0175538
$874$	−14.5838	−0.493304
$875$	−1.60759	−0.0543464
$876$	0.929769	0.0314140
$877$	49.1750	1.66052	0.830261	−	0.557374i	$-0.188191\pi$
$877$	49.1750	1.66052	0.830261	+	0.557374i	$0.188191\pi$
$878$	−24.7611	−0.835645
$879$	−28.0436	−0.945888
$880$	−3.78207	−0.127494
$881$	−22.7367	−0.766020	−0.383010	−	0.923744i	$-0.625113\pi$
$881$	−22.7367	−0.766020	−0.383010	+	0.923744i	$0.625113\pi$
$882$	5.40518	0.182002
$883$	5.17174	0.174043	0.0870214	−	0.996206i	$-0.472265\pi$
$883$	5.17174	0.174043	0.0870214	+	0.996206i	$0.472265\pi$
$884$	−7.50664	−0.252475
$885$	0.818725	0.0275211
$886$	−3.21255	−0.107928
$887$	43.1654	1.44935	0.724677	−	0.689089i	$-0.241989\pi$
$887$	43.1654	1.44935	0.724677	+	0.689089i	$0.241989\pi$
$888$	3.50203	0.117520
$889$	−2.56389	−0.0859902
$890$	6.48047	0.217226
$891$	−14.4828	−0.485191
$892$	−24.7089	−0.827316
$893$	0.468887	0.0156907
$894$	31.0751	1.03931
$895$	7.36796	0.246284
$896$	1.60759	0.0537058
$897$	9.77949	0.326528
$898$	−12.2838	−0.409914
$899$	9.25022	0.308512
$900$	−1.22409	−0.0408031
$901$	−44.0848	−1.46868
$902$	−23.8250	−0.793287
$903$	−27.5212	−0.915847
$904$	−20.7037	−0.688595
$905$	0.113739	0.00378081
$906$	11.1837	0.371553
$907$	18.9913	0.630597	0.315298	−	0.948993i	$-0.397895\pi$
$907$	18.9913	0.630597	0.315298	+	0.948993i	$0.397895\pi$
$908$	−8.97325	−0.297788
$909$	20.6376	0.684505
$910$	−1.60759	−0.0532910
$911$	17.0116	0.563619	0.281810	−	0.959470i	$-0.409065\pi$
$911$	17.0116	0.563619	0.281810	+	0.959470i	$0.409065\pi$
$912$	−2.64834	−0.0876954
$913$	42.3118	1.40032
$914$	−1.71695	−0.0567916
$915$	8.52178	0.281721
$916$	−2.94499	−0.0973052
$917$	−6.79487	−0.224386
$918$	−42.2561	−1.39466
$919$	1.08728	0.0358661	0.0179330	−	0.999839i	$-0.494291\pi$
$919$	1.08728	0.0358661	0.0179330	+	0.999839i	$0.494291\pi$
$920$	7.33848	0.241942
$921$	44.3399	1.46105
$922$	21.8774	0.720494
$923$	−2.99244	−0.0984973
$924$	−8.10243	−0.266550
$925$	−2.62790	−0.0864049
$926$	−17.6147	−0.578856
$927$	7.07519	0.232380
$928$	−9.25022	−0.303653
$929$	−55.7342	−1.82858	−0.914290	−	0.405060i	$-0.867251\pi$
$929$	−55.7342	−1.82858	−0.914290	+	0.405060i	$0.867251\pi$
$930$	−1.33263	−0.0436987
$931$	−8.77526	−0.287597
$932$	15.0687	0.493591
$933$	−34.3323	−1.12399
$934$	9.30031	0.304315
$935$	28.3907	0.928474
$936$	−1.22409	−0.0400107
$937$	17.4774	0.570963	0.285481	−	0.958384i	$-0.407847\pi$
$937$	17.4774	0.570963	0.285481	+	0.958384i	$0.407847\pi$
$938$	−1.37941	−0.0450394
$939$	23.0162	0.751104
$940$	−0.235941	−0.00769556
$941$	8.01048	0.261134	0.130567	−	0.991439i	$-0.458320\pi$
$941$	8.01048	0.261134	0.130567	+	0.991439i	$0.458320\pi$
$942$	13.7126	0.446780
$943$	46.2285	1.50541
$944$	0.614367	0.0199959
$945$	−9.04937	−0.294376
$946$	48.5861	1.57967
$947$	42.3446	1.37602	0.688008	−	0.725703i	$-0.258486\pi$
$947$	42.3446	1.37602	0.688008	+	0.725703i	$0.258486\pi$
$948$	12.8090	0.416017
$949$	−0.697694	−0.0226481
$950$	1.98730	0.0644767
$951$	21.5422	0.698552
$952$	−12.0676	−0.391113
$953$	−38.7034	−1.25372	−0.626862	−	0.779130i	$-0.715661\pi$
$953$	−38.7034	−1.25372	−0.626862	+	0.779130i	$0.715661\pi$
$954$	−7.18883	−0.232747
$955$	18.3453	0.593640
$956$	−24.6433	−0.797021
$957$	46.6222	1.50708
$958$	−18.3745	−0.593653
$959$	−32.5779	−1.05199
$960$	1.33263	0.0430105
$961$	1.00000	0.0322581
$962$	−2.62790	−0.0847270
$963$	8.23927	0.265507
$964$	10.4708	0.337243
$965$	−15.1604	−0.488030
$966$	15.7214	0.505828
$967$	47.4309	1.52527	0.762637	−	0.646827i	$-0.223904\pi$
$967$	47.4309	1.52527	0.762637	+	0.646827i	$0.223904\pi$
$968$	3.30409	0.106197
$969$	19.8802	0.638643
$970$	−0.423705	−0.0136043
$971$	2.65825	0.0853074	0.0426537	−	0.999090i	$-0.486419\pi$
$971$	2.65825	0.0853074	0.0426537	+	0.999090i	$0.486419\pi$
$972$	−11.7844	−0.377985
$973$	25.5517	0.819149
$974$	37.3823	1.19781
$975$	−1.33263	−0.0426784
$976$	6.39470	0.204689
$977$	−37.4446	−1.19796	−0.598980	−	0.800764i	$-0.704427\pi$
$977$	−37.4446	−1.19796	−0.598980	+	0.800764i	$0.704427\pi$
$978$	3.21111	0.102680
$979$	−24.5096	−0.783331
$980$	4.41566	0.141053
$981$	8.20270	0.261892
$982$	−31.5304	−1.00617
$983$	−30.9157	−0.986058	−0.493029	−	0.870013i	$-0.664110\pi$
$983$	−30.9157	−0.986058	−0.493029	+	0.870013i	$0.664110\pi$
$984$	8.39486	0.267618
$985$	6.46630	0.206033
$986$	69.4380	2.21136
$987$	−0.505463	−0.0160891
$988$	1.98730	0.0632246
$989$	−94.2730	−2.99771
$990$	4.62961	0.147139
$991$	−26.7403	−0.849432	−0.424716	−	0.905327i	$-0.639626\pi$
$991$	−26.7403	−0.849432	−0.424716	+	0.905327i	$0.639626\pi$
$992$	−1.00000	−0.0317500
$993$	−3.02731	−0.0960689
$994$	−4.81061	−0.152583
$995$	1.74394	0.0552866
$996$	−14.9088	−0.472403
$997$	24.0696	0.762293	0.381146	−	0.924515i	$-0.375529\pi$
$997$	24.0696	0.762293	0.381146	+	0.924515i	$0.375529\pi$
$998$	−40.8881	−1.29429
$999$	−14.7929	−0.468026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.f.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.f.1.3	✓	6	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.33263 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.33263 q^{6} +1.60759 q^{7} +1.00000 q^{8} -1.22409 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.33263 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.33263 q^{6} +1.60759 q^{7} +1.00000 q^{8} -1.22409 q^{9} -1.00000 q^{10} +3.78207 q^{11} -1.33263 q^{12} +1.00000 q^{13} +1.60759 q^{14} +1.33263 q^{15} +1.00000 q^{16} -7.50664 q^{17} -1.22409 q^{18} +1.98730 q^{19} -1.00000 q^{20} -2.14232 q^{21} +3.78207 q^{22} -7.33848 q^{23} -1.33263 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.62916 q^{27} +1.60759 q^{28} -9.25022 q^{29} +1.33263 q^{30} -1.00000 q^{31} +1.00000 q^{32} -5.04011 q^{33} -7.50664 q^{34} -1.60759 q^{35} -1.22409 q^{36} -2.62790 q^{37} +1.98730 q^{38} -1.33263 q^{39} -1.00000 q^{40} -6.29946 q^{41} -2.14232 q^{42} +12.8464 q^{43} +3.78207 q^{44} +1.22409 q^{45} -7.33848 q^{46} +0.235941 q^{47} -1.33263 q^{48} -4.41566 q^{49} +1.00000 q^{50} +10.0036 q^{51} +1.00000 q^{52} +5.87278 q^{53} +5.62916 q^{54} -3.78207 q^{55} +1.60759 q^{56} -2.64834 q^{57} -9.25022 q^{58} +0.614367 q^{59} +1.33263 q^{60} +6.39470 q^{61} -1.00000 q^{62} -1.96784 q^{63} +1.00000 q^{64} -1.00000 q^{65} -5.04011 q^{66} -0.858063 q^{67} -7.50664 q^{68} +9.77949 q^{69} -1.60759 q^{70} -2.99244 q^{71} -1.22409 q^{72} -0.697694 q^{73} -2.62790 q^{74} -1.33263 q^{75} +1.98730 q^{76} +6.08002 q^{77} -1.33263 q^{78} -9.61181 q^{79} -1.00000 q^{80} -3.82932 q^{81} -6.29946 q^{82} +11.1875 q^{83} -2.14232 q^{84} +7.50664 q^{85} +12.8464 q^{86} +12.3271 q^{87} +3.78207 q^{88} -6.48047 q^{89} +1.22409 q^{90} +1.60759 q^{91} -7.33848 q^{92} +1.33263 q^{93} +0.235941 q^{94} -1.98730 q^{95} -1.33263 q^{96} +0.423705 q^{97} -4.41566 q^{98} -4.62961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9} - 6 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} - 8 q^{17} - q^{18} - 9 q^{19} - 6 q^{20} - 5 q^{21} - 4 q^{22} - 7 q^{23} - 3 q^{24} + 6 q^{25} + 6 q^{26} + 9 q^{27} - 2 q^{28} - 14 q^{29} + 3 q^{30} - 6 q^{31} + 6 q^{32} - 6 q^{33} - 8 q^{34} + 2 q^{35} - q^{36} - 9 q^{38} - 3 q^{39} - 6 q^{40} + 2 q^{41} - 5 q^{42} - 7 q^{43} - 4 q^{44} + q^{45} - 7 q^{46} - 8 q^{47} - 3 q^{48} - 14 q^{49} + 6 q^{50} - 5 q^{51} + 6 q^{52} - 24 q^{53} + 9 q^{54} + 4 q^{55} - 2 q^{56} - 15 q^{57} - 14 q^{58} - 5 q^{59} + 3 q^{60} - 5 q^{61} - 6 q^{62} - 19 q^{63} + 6 q^{64} - 6 q^{65} - 6 q^{66} - 12 q^{67} - 8 q^{68} + 2 q^{70} - 10 q^{71} - q^{72} + 5 q^{73} - 3 q^{75} - 9 q^{76} - q^{77} - 3 q^{78} - 16 q^{79} - 6 q^{80} - 10 q^{81} + 2 q^{82} - 22 q^{83} - 5 q^{84} + 8 q^{85} - 7 q^{86} - 31 q^{87} - 4 q^{88} + 14 q^{89} + q^{90} - 2 q^{91} - 7 q^{92} + 3 q^{93} - 8 q^{94} + 9 q^{95} - 3 q^{96} - 9 q^{97} - 14 q^{98} - 21 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9 - 6 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 - 8 * q^17 - q^18 - 9 * q^19 - 6 * q^20 - 5 * q^21 - 4 * q^22 - 7 * q^23 - 3 * q^24 + 6 * q^25 + 6 * q^26 + 9 * q^27 - 2 * q^28 - 14 * q^29 + 3 * q^30 - 6 * q^31 + 6 * q^32 - 6 * q^33 - 8 * q^34 + 2 * q^35 - q^36 - 9 * q^38 - 3 * q^39 - 6 * q^40 + 2 * q^41 - 5 * q^42 - 7 * q^43 - 4 * q^44 + q^45 - 7 * q^46 - 8 * q^47 - 3 * q^48 - 14 * q^49 + 6 * q^50 - 5 * q^51 + 6 * q^52 - 24 * q^53 + 9 * q^54 + 4 * q^55 - 2 * q^56 - 15 * q^57 - 14 * q^58 - 5 * q^59 + 3 * q^60 - 5 * q^61 - 6 * q^62 - 19 * q^63 + 6 * q^64 - 6 * q^65 - 6 * q^66 - 12 * q^67 - 8 * q^68 + 2 * q^70 - 10 * q^71 - q^72 + 5 * q^73 - 3 * q^75 - 9 * q^76 - q^77 - 3 * q^78 - 16 * q^79 - 6 * q^80 - 10 * q^81 + 2 * q^82 - 22 * q^83 - 5 * q^84 + 8 * q^85 - 7 * q^86 - 31 * q^87 - 4 * q^88 + 14 * q^89 + q^90 - 2 * q^91 - 7 * q^92 + 3 * q^93 - 8 * q^94 + 9 * q^95 - 3 * q^96 - 9 * q^97 - 14 * q^98 - 21 * q^99

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